LMFDB - Embedded newform 120.4.w.c.53.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, 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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.42
Character	$\chi$	$=$	120.53
Dual form			120.4.w.c.77.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26466 + 2.52995i) q^{2} +(-1.98471 + 4.80218i) q^{3} +(-4.80127 + 6.39905i) q^{4} +(-9.85625 + 5.27772i) q^{5} +(-14.6592 + 1.05193i) q^{6} +(6.52335 - 6.52335i) q^{7} +(-22.2612 - 4.05433i) q^{8} +(-19.1219 - 19.0618i) q^{9} +(-25.8172 - 18.2613i) q^{10} +43.0815 q^{11} +(-21.2003 - 35.7568i) q^{12} +(-10.8773 + 10.8773i) q^{13} +(24.7535 + 8.25390i) q^{14} +(-5.78279 - 57.8062i) q^{15} +(-17.8957 - 61.4471i) q^{16} +(45.8326 + 45.8326i) q^{17} +(24.0427 - 72.4841i) q^{18} -137.797 q^{19} +(13.5501 - 88.4104i) q^{20} +(18.3794 + 44.2732i) q^{21} +(54.4835 + 108.994i) q^{22} +(-113.373 + 113.373i) q^{23} +(63.6516 - 98.8558i) q^{24} +(69.2914 - 104.037i) q^{25} +(-41.2751 - 13.7629i) q^{26} +(129.490 - 53.9946i) q^{27} +(10.4229 + 73.0635i) q^{28} +66.9364i q^{29} +(138.933 - 87.7354i) q^{30} -295.930 q^{31} +(132.826 - 122.985i) q^{32} +(-85.5042 + 206.885i) q^{33} +(-57.9913 + 173.917i) q^{34} +(-29.8674 + 98.7241i) q^{35} +(213.787 - 30.8409i) q^{36} +(-47.8404 - 47.8404i) q^{37} +(-174.266 - 348.619i) q^{38} +(-30.6465 - 73.8231i) q^{39} +(240.810 - 77.5280i) q^{40} +264.624i q^{41} +(-88.7652 + 102.489i) q^{42} +(120.034 - 120.034i) q^{43} +(-206.846 + 275.681i) q^{44} +(289.073 + 86.9583i) q^{45} +(-430.206 - 143.449i) q^{46} +(-28.5512 - 28.5512i) q^{47} +(330.598 + 36.0162i) q^{48} +257.892i q^{49} +(350.838 + 43.7320i) q^{50} +(-311.060 + 129.132i) q^{51} +(-17.3796 - 121.829i) q^{52} +(289.090 + 289.090i) q^{53} +(300.364 + 259.317i) q^{54} +(-424.623 + 227.372i) q^{55} +(-171.666 + 118.770i) q^{56} +(273.486 - 661.726i) q^{57} +(-169.345 + 84.6518i) q^{58} +454.100i q^{59} +(397.670 + 240.539i) q^{60} -93.3056i q^{61} +(-374.252 - 748.688i) q^{62} +(-249.086 + 0.391712i) q^{63} +(479.125 + 180.509i) q^{64} +(49.8021 - 164.617i) q^{65} +(-631.543 + 45.3186i) q^{66} +(381.933 + 381.933i) q^{67} +(-513.339 + 73.2304i) q^{68} +(-319.425 - 769.449i) q^{69} +(-287.539 + 49.2897i) q^{70} -522.462i q^{71} +(348.394 + 501.866i) q^{72} +(617.372 + 617.372i) q^{73} +(60.5319 - 181.536i) q^{74} +(362.082 + 539.233i) q^{75} +(661.600 - 881.770i) q^{76} +(281.036 - 281.036i) q^{77} +(148.011 - 170.895i) q^{78} +374.376i q^{79} +(500.685 + 511.190i) q^{80} +(2.29285 + 728.996i) q^{81} +(-669.485 + 334.660i) q^{82} +(-40.8261 - 40.8261i) q^{83} +(-371.551 - 94.9571i) q^{84} +(-693.628 - 209.846i) q^{85} +(455.482 + 151.877i) q^{86} +(-321.441 - 132.849i) q^{87} +(-959.048 - 174.667i) q^{88} +702.897 q^{89} +(145.579 + 841.312i) q^{90} +141.913i q^{91} +(-181.145 - 1269.81i) q^{92} +(587.335 - 1421.11i) q^{93} +(36.1255 - 108.341i) q^{94} +(1358.16 - 727.254i) q^{95} +(326.975 + 881.943i) q^{96} +(788.538 - 788.538i) q^{97} +(-652.453 + 326.146i) q^{98} +(-823.800 - 821.213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) $ 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Character values

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

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.26466	+	2.52995i	0.447125	+	0.894471i
$2$	1.26466	+	2.52995i	0.447125	+	0.894471i
$3$	−1.98471	+	4.80218i	−0.381957	+	0.924180i
$3$	−1.98471	+	4.80218i	−0.381957	+	0.924180i
$4$	−4.80127	+	6.39905i	−0.600158	+	0.799881i
$5$	−9.85625	+	5.27772i	−0.881570	+	0.472053i
$5$	−9.85625	+	5.27772i	−0.881570	+	0.472053i
$6$	−14.6592	+	1.05193i	−0.997435	+	0.0715746i
$7$	6.52335	−	6.52335i	0.352228	−	0.352228i	−0.508710	−	0.860938i	$-0.669878\pi$
$7$	6.52335	−	6.52335i	0.352228	−	0.352228i	0.860938	+	0.508710i	$0.169878\pi$
$8$	−22.2612	−	4.05433i	−0.983817	−	0.179178i
$9$	−19.1219	−	19.0618i	−0.708218	−	0.705994i
$10$	−25.8172	−	18.2613i	−0.816410	−	0.577472i
$11$	43.0815			1.18087			0.590435	−	0.807085i	$-0.298956\pi$
$11$	43.0815			1.18087			0.590435	+	0.807085i	$0.298956\pi$
$12$	−21.2003	−	35.7568i	−0.510000	−	0.860175i
$13$	−10.8773	+	10.8773i	−0.232063	+	0.232063i	−0.813553	−	0.581490i	$-0.802470\pi$
$13$	−10.8773	+	10.8773i	−0.232063	+	0.232063i	0.581490	+	0.813553i	$0.302470\pi$
$14$	24.7535	+	8.25390i	0.472547	+	0.157568i
$15$	−5.78279	−	57.8062i	−0.0995407	−	0.995033i
$16$	−17.8957	−	61.4471i	−0.279620	−	0.960111i
$17$	45.8326	+	45.8326i	0.653884	+	0.653884i	0.953926	−	0.300042i	$-0.0970007\pi$
$17$	45.8326	+	45.8326i	0.653884	+	0.653884i	−0.300042	+	0.953926i	$0.597001\pi$
$18$	24.0427	−	72.4841i	0.314829	−	0.949148i
$19$	−137.797			−1.66383			−0.831916	−	0.554902i	$-0.812756\pi$
$19$	−137.797			−1.66383			−0.831916	+	0.554902i	$0.812756\pi$
$20$	13.5501	−	88.4104i	0.151495	−	0.988458i
$21$	18.3794	+	44.2732i	0.190986	+	0.460058i
$22$	54.4835	+	108.994i	0.527997	+	1.05625i
$23$	−113.373	+	113.373i	−1.02782	+	1.02782i	−0.0282196	+	0.999602i	$0.508984\pi$
$23$	−113.373	+	113.373i	−1.02782	+	1.02782i	−0.999602	+	0.0282196i	$0.991016\pi$
$24$	63.6516	−	98.8558i	0.541368	−	0.840786i
$25$	69.2914	−	104.037i	0.554331	−	0.832296i
$26$	−41.2751	−	13.7629i	−0.311335	−	0.103813i
$27$	129.490	−	53.9946i	0.922974	−	0.384862i
$28$	10.4229	+	73.0635i	0.0703479	+	0.493133i
$29$			66.9364i			0.428613i	0.976766	+	0.214306i	$0.0687491\pi$
$29$			66.9364i			0.428613i	−0.976766	+	0.214306i	$0.931251\pi$
$30$	138.933	−	87.7354i	0.845522	−	0.533941i
$31$	−295.930			−1.71454			−0.857269	−	0.514869i	$-0.827841\pi$
$31$	−295.930			−1.71454			−0.857269	+	0.514869i	$0.827841\pi$
$32$	132.826	−	122.985i	0.733767	−	0.679401i
$33$	−85.5042	+	206.885i	−0.451042	+	1.09134i
$34$	−57.9913	+	173.917i	−0.292513	+	0.877248i
$35$	−29.8674	+	98.7241i	−0.144243	+	0.476784i
$36$	213.787	−	30.8409i	0.989754	−	0.142782i
$37$	−47.8404	−	47.8404i	−0.212565	−	0.212565i	0.592791	−	0.805356i	$-0.298026\pi$
$37$	−47.8404	−	47.8404i	−0.212565	−	0.212565i	−0.805356	+	0.592791i	$0.798026\pi$
$38$	−174.266	−	348.619i	−0.743941	−	1.48825i
$39$	−30.6465	−	73.8231i	−0.125830	−	0.303106i
$40$	240.810	−	77.5280i	0.951885	−	0.306456i
$41$			264.624i			1.00798i	0.863708	+	0.503992i	$0.168136\pi$
$41$			264.624i			1.00798i	−0.863708	+	0.503992i	$0.831864\pi$
$42$	−88.7652	+	102.489i	−0.326114	+	0.376535i
$43$	120.034	−	120.034i	0.425698	−	0.425698i	−0.461462	−	0.887160i	$-0.652675\pi$
$43$	120.034	−	120.034i	0.425698	−	0.425698i	0.887160	+	0.461462i	$0.152675\pi$
$44$	−206.846	+	275.681i	−0.708709	+	0.944556i
$45$	289.073	+	86.9583i	0.957610	+	0.288066i
$46$	−430.206	−	143.449i	−1.37892	−	0.459792i
$47$	−28.5512	−	28.5512i	−0.0886090	−	0.0886090i	0.661413	−	0.750022i	$-0.269957\pi$
$47$	−28.5512	−	28.5512i	−0.0886090	−	0.0886090i	−0.750022	+	0.661413i	$0.769957\pi$
$48$	330.598	+	36.0162i	0.994118	+	0.108302i
$49$			257.892i			0.751871i
$50$	350.838	+	43.7320i	0.992321	+	0.123693i
$51$	−311.060	+	129.132i	−0.854062	+	0.354551i
$52$	−17.3796	−	121.829i	−0.0463483	−	0.324898i
$53$	289.090	+	289.090i	0.749237	+	0.749237i	0.974336	−	0.225099i	$-0.0722707\pi$
$53$	289.090	+	289.090i	0.749237	+	0.749237i	−0.225099	+	0.974336i	$0.572271\pi$
$54$	300.364	+	259.317i	0.756933	+	0.653493i
$55$	−424.623	+	227.372i	−1.04102	+	0.557434i
$56$	−171.666	+	118.770i	−0.409639	+	0.283416i
$57$	273.486	−	661.726i	0.635512	−	1.53768i
$58$	−169.345	+	84.6518i	−0.383382	+	0.191644i
$59$			454.100i			1.00201i	0.865444	+	0.501006i	$0.167037\pi$
$59$			454.100i			1.00201i	−0.865444	+	0.501006i	$0.832963\pi$
$60$	397.670	+	240.539i	0.855649	+	0.517557i
$61$		−	93.3056i		−	0.195845i	−0.995194	−	0.0979226i	$-0.968780\pi$
$61$		−	93.3056i		−	0.195845i	0.995194	−	0.0979226i	$-0.0312198\pi$
$62$	−374.252	−	748.688i	−0.766613	−	1.53361i
$63$	−249.086	+	0.391712i	−0.498124	+	0.000783351i
$64$	479.125	+	180.509i	0.935791	+	0.352556i
$65$	49.8021	−	164.617i	0.0950337	−	0.314126i
$66$	−631.543	+	45.3186i	−1.17784	+	0.0845203i
$67$	381.933	+	381.933i	0.696427	+	0.696427i	0.963638	−	0.267211i	$-0.0861021\pi$
$67$	381.933	+	381.933i	0.696427	+	0.696427i	−0.267211	+	0.963638i	$0.586102\pi$
$68$	−513.339	+	73.2304i	−0.915463	+	0.130595i
$69$	−319.425	−	769.449i	−0.557309	−	1.34248i
$70$	−287.539	+	49.2897i	−0.490964	+	0.0841606i
$71$		−	522.462i		−	0.873307i	−0.899630	−	0.436654i	$-0.856163\pi$
$71$		−	522.462i		−	0.873307i	0.899630	−	0.436654i	$-0.143837\pi$
$72$	348.394	+	501.866i	0.570258	+	0.821465i
$73$	617.372	+	617.372i	0.989834	+	0.989834i	0.999949	−	0.0101146i	$-0.00321964\pi$
$73$	617.372	+	617.372i	0.989834	+	0.989834i	−0.0101146	+	0.999949i	$0.503220\pi$
$74$	60.5319	−	181.536i	0.0950904	−	0.285177i
$75$	362.082	+	539.233i	0.557461	+	0.830203i
$76$	661.600	−	881.770i	0.998562	−	1.33087i
$77$	281.036	−	281.036i	0.415935	−	0.415935i
$78$	148.011	−	170.895i	0.214858	−	0.248078i
$79$			374.376i			0.533172i	0.963811	+	0.266586i	$0.0858956\pi$
$79$			374.376i			0.533172i	−0.963811	+	0.266586i	$0.914104\pi$
$80$	500.685	+	511.190i	0.699728	+	0.714409i
$81$	2.29285	+	728.996i	0.00314519	+	0.999995i
$82$	−669.485	+	334.660i	−0.901613	+	0.450695i
$83$	−40.8261	−	40.8261i	−0.0539909	−	0.0539909i	0.679596	−	0.733587i	$-0.262155\pi$
$83$	−40.8261	−	40.8261i	−0.0539909	−	0.0539909i	−0.733587	+	0.679596i	$0.762155\pi$
$84$	−371.551	−	94.9571i	−0.482613	−	0.123341i
$85$	−693.628	−	209.846i	−0.885113	−	0.267776i
$86$	455.482	+	151.877i	0.571115	+	0.190434i
$87$	−321.441	−	132.849i	−0.396115	−	0.163712i
$88$	−959.048	−	174.667i	−1.16176	−	0.211586i
$89$	702.897			0.837157			0.418578	−	0.908181i	$-0.362529\pi$
$89$	702.897			0.837157			0.418578	+	0.908181i	$0.362529\pi$
$90$	145.579	+	841.312i	0.170505	+	0.985357i
$91$			141.913i			0.163478i
$92$	−181.145	−	1269.81i	−0.205279	−	1.43899i
$93$	587.335	−	1421.11i	0.654880	−	1.58454i
$94$	36.1255	−	108.341i	0.0396389	−	0.118878i
$95$	1358.16	−	727.254i	1.46678	−	0.785417i
$96$	326.975	+	881.943i	0.347622	+	0.937635i
$97$	788.538	−	788.538i	0.825401	−	0.825401i	−0.161475	−	0.986877i	$-0.551625\pi$
$97$	788.538	−	788.538i	0.825401	−	0.825401i	0.986877	+	0.161475i	$0.0516252\pi$
$98$	−652.453	+	326.146i	−0.672528	+	0.336181i
$99$	−823.800	−	821.213i	−0.836314	−	0.833687i
$100$	333.052	+	942.909i	0.333052	+	0.942909i
$101$	−960.039			−0.945816			−0.472908	−	0.881112i	$-0.656796\pi$
$101$	−960.039			−0.945816			−0.472908	+	0.881112i	$0.656796\pi$
$102$	−720.083	−	623.658i	−0.699008	−	0.605405i
$103$	−1272.34	−	1272.34i	−1.21716	−	1.21716i	−0.968621	−	0.248541i	$-0.920049\pi$
$103$	−1272.34	−	1272.34i	−1.21716	−	1.21716i	−0.248541	−	0.968621i	$-0.579951\pi$
$104$	286.242	−	198.042i	0.269888	−	0.186727i
$105$	−414.813	−	339.367i	−0.385539	−	0.315417i
$106$	−365.781	+	1096.98i	−0.335168	+	1.00517i
$107$	−307.963	+	307.963i	−0.278242	+	0.278242i	−0.832407	−	0.554165i	$-0.813038\pi$
$107$	−307.963	+	307.963i	−0.278242	+	0.278242i	0.554165	+	0.832407i	$0.313038\pi$
$108$	−276.201	+	1087.85i	−0.246087	+	0.969248i
$109$	−337.093			−0.296217			−0.148108	−	0.988971i	$-0.547318\pi$
$109$	−337.093			−0.296217			−0.148108	+	0.988971i	$0.547318\pi$
$110$	−1112.24	−	786.724i	−0.964075	−	0.681920i
$111$	324.688	−	134.789i	0.277639	−	0.115258i
$112$	−517.580	−	284.101i	−0.436667	−	0.239688i
$113$	439.568	−	439.568i	0.365939	−	0.365939i	−0.500055	−	0.865994i	$-0.666687\pi$
$113$	439.568	−	439.568i	0.365939	−	0.365939i	0.865994	+	0.500055i	$0.166687\pi$
$114$	2020.00	−	144.952i	1.65956	−	0.119088i
$115$	519.082	−	1715.78i	0.420910	−	1.39128i
$116$	−428.329	−	321.379i	−0.342839	−	0.257236i
$117$	415.336	−	0.653158i	0.328187	−	0.000516106i
$118$	−1148.85	+	574.282i	−0.896272	+	0.448025i
$119$	597.963			0.460632
$120$	−105.633	+	1310.28i	−0.0803580	+	0.996766i
$121$	525.020			0.394455
$122$	236.058	−	118.000i	0.175178	−	0.0875673i
$123$	−1270.77	−	525.201i	−0.931559	−	0.385006i
$124$	1420.84	−	1893.67i	1.02899	−	1.37143i
$125$	−133.875	+	1391.12i	−0.0957933	+	0.995401i
$126$	−316.000	−	629.678i	−0.223425	−	0.445208i
$127$	−368.158	+	368.158i	−0.257234	+	0.257234i	−0.823928	−	0.566694i	$-0.808222\pi$
$127$	−368.158	+	368.158i	−0.257234	+	0.257234i	0.566694	+	0.823928i	$0.308222\pi$
$128$	149.253	+	1440.44i	0.103064	+	0.994675i
$129$	338.193	+	814.657i	0.230823	+	0.556020i
$130$	479.455	−	82.1877i	0.323469	−	0.0554487i
$131$	−1531.14			−1.02119			−0.510596	−	0.859820i	$-0.670575\pi$
$131$	−1531.14			−1.02119			−0.510596	+	0.859820i	$0.670575\pi$
$132$	−913.341	−	1540.46i	−0.602244	−	1.01575i
$133$	−898.897	+	898.897i	−0.586047	+	0.586047i
$134$	−483.255	+	1449.29i	−0.311544	+	0.934324i
$135$	−991.315	+	1215.59i	−0.631991	+	0.774976i
$136$	−834.469	−	1206.11i	−0.526141	−	0.760463i
$137$	−220.532	−	220.532i	−0.137528	−	0.137528i	0.634991	−	0.772519i	$-0.281004\pi$
$137$	−220.532	−	220.532i	−0.137528	−	0.137528i	−0.772519	+	0.634991i	$0.781004\pi$
$138$	1542.70	−	1781.22i	0.951619	−	1.09875i
$139$	−602.034			−0.367366			−0.183683	−	0.982986i	$-0.558802\pi$
$139$	−602.034			−0.367366			−0.183683	+	0.982986i	$0.558802\pi$
$140$	−488.339	−	665.124i	−0.294801	−	0.401523i
$141$	193.774	−	80.4423i	0.115735	−	0.0480459i
$142$	1321.80	−	660.737i	0.781149	−	0.390478i
$143$	−468.611	+	468.611i	−0.274037	+	0.274037i
$144$	−829.096	+	1516.11i	−0.479801	+	0.877378i
$145$	−353.271	−	659.742i	−0.202328	−	0.377852i
$146$	−781.152	+	2342.68i	−0.442799	+	1.32796i
$147$	−1238.44	−	511.840i	−0.694865	−	0.287182i
$148$	535.828	−	76.4386i	0.297600	−	0.0424541i
$149$			44.4832i			0.0244578i	0.999925	+	0.0122289i	$0.00389267\pi$
$149$			44.4832i			0.0244578i	−0.999925	+	0.0122289i	$0.996107\pi$
$150$	−906.320	+	1597.99i	−0.493338	+	0.869838i
$151$	3558.18			1.91762			0.958809	−	0.284052i	$-0.0916788\pi$
$151$	3558.18			1.91762			0.958809	+	0.284052i	$0.0916788\pi$
$152$	3067.53	+	558.674i	1.63691	+	0.298121i
$153$	−2.75214	−	1750.06i	−0.00145423	−	0.924730i
$154$	1066.42	+	355.591i	0.558017	+	0.186067i
$155$	2916.76	−	1561.84i	1.51149	−	0.809354i
$156$	619.540	+	158.336i	0.317967	+	0.0812627i
$157$	2373.96	+	2373.96i	1.20677	+	1.20677i	0.972068	+	0.234700i	$0.0754109\pi$
$157$	2373.96	+	2373.96i	1.20677	+	1.20677i	0.234700	+	0.972068i	$0.424589\pi$
$158$	−947.151	+	473.458i	−0.476907	+	0.238394i
$159$	−1962.02	+	814.503i	−0.978606	+	0.406253i
$160$	−660.087	+	1913.19i	−0.326153	+	0.945317i
$161$			1479.14i			0.724054i
$162$	−1841.42	+	927.734i	−0.893061	+	0.449936i
$163$	1871.68	−	1871.68i	0.899392	−	0.899392i	−0.0959898	−	0.995382i	$-0.530602\pi$
$163$	1871.68	−	1871.68i	0.899392	−	0.899392i	0.995382	+	0.0959898i	$0.0306016\pi$
$164$	−1693.34	−	1270.53i	−0.806267	−	0.604950i
$165$	−249.132	−	2490.38i	−0.117545	−	1.17501i
$166$	51.6567	−	154.919i	0.0241526	−	0.0724340i
$167$	574.966	+	574.966i	0.266420	+	0.266420i	0.827656	−	0.561236i	$-0.189674\pi$
$167$	574.966	+	574.966i	0.266420	+	0.266420i	−0.561236	+	0.827656i	$0.689674\pi$
$168$	−229.649	−	1060.09i	−0.105463	−	0.486833i
$169$			1960.37i			0.892293i
$170$	−346.305	−	2020.23i	−0.156238	−	0.911437i
$171$	2634.94	+	2626.66i	1.17836	+	1.17465i
$172$	191.788	+	1344.42i	0.0850216	+	0.595994i
$173$	1303.92	+	1303.92i	0.573037	+	0.573037i	0.932976	−	0.359939i	$-0.117203\pi$
$173$	1303.92	+	1303.92i	0.573037	+	0.573037i	−0.359939	+	0.932976i	$0.617203\pi$
$174$	−70.4122	−	981.237i	−0.0306778	−	0.427514i
$175$	−226.658	−	1130.68i	−0.0979070	−	0.488408i
$176$	−770.973	−	2647.24i	−0.330195	−	1.13377i
$177$	−2180.67	−	901.254i	−0.926040	−	0.382726i
$178$	888.926	+	1778.29i	0.374314	+	0.748813i
$179$			2138.51i			0.892960i	0.894794	+	0.446480i	$0.147323\pi$
$179$			2138.51i			0.892960i	−0.894794	+	0.446480i	$0.852677\pi$
$180$	−1944.37	+	1432.28i	−0.805137	+	0.593089i
$181$			3370.59i			1.38416i	0.721819	+	0.692082i	$0.243306\pi$
$181$			3370.59i			1.38416i	−0.721819	+	0.692082i	$0.756694\pi$
$182$	−359.032	+	179.472i	−0.146227	+	0.0730952i
$183$	448.070	+	185.184i	0.180996	+	0.0748044i
$184$	2983.47	−	2064.17i	1.19535	−	0.827025i
$185$	724.016	+	219.039i	0.287733	+	0.0870490i
$186$	4338.12	−	311.297i	1.71014	−	0.122717i
$187$	1974.54	+	1974.54i	0.772152	+	0.772152i
$188$	319.783	−	45.6186i	0.124056	−	0.0176972i
$189$	492.481	−	1196.93i	0.189538	−	0.460656i
$190$	3557.53	+	2516.35i	1.35837	+	0.960816i
$191$			846.152i			0.320552i	0.987072	+	0.160276i	$0.0512384\pi$
$191$			846.152i			0.320552i	−0.987072	+	0.160276i	$0.948762\pi$
$192$	−1817.76	+	1942.59i	−0.683257	+	0.730178i
$193$	−1793.13	−	1793.13i	−0.668769	−	0.668769i	0.288662	−	0.957431i	$-0.406790\pi$
$193$	−1793.13	−	1793.13i	−0.668769	−	0.668769i	−0.957431	+	0.288662i	$0.906790\pi$
$194$	2992.19	+	997.727i	1.10736	+	0.369240i
$195$	691.677	+	565.875i	0.254010	+	0.207811i
$196$	−1650.26	−	1238.21i	−0.601408	−	0.451242i
$197$	130.728	−	130.728i	0.0472793	−	0.0472793i	−0.683072	−	0.730351i	$-0.739356\pi$
$197$	130.728	−	130.728i	0.0472793	−	0.0472793i	0.730351	+	0.683072i	$0.239356\pi$
$198$	1035.80	−	3122.73i	0.371773	−	1.12082i
$199$		−	753.523i		−	0.268421i	−0.990953	−	0.134211i	$-0.957150\pi$
$199$		−	753.523i		−	0.268421i	0.990953	−	0.134211i	$-0.0428499\pi$
$200$	−1964.31	+	2035.06i	−0.694489	+	0.719503i
$201$	−2592.14	+	1076.09i	−0.909629	+	0.377619i
$202$	−1214.12	−	2428.85i	−0.422898	−	0.846006i
$203$	436.649	+	436.649i	0.150969	+	0.150969i
$204$	667.161	−	2610.49i	0.228974	−	0.895935i
$205$	−1396.61	−	2608.20i	−0.475822	−	0.888608i
$206$	1609.88	−	4828.04i	0.544493	−	1.63294i
$207$	4329.00	−	6.80779i	1.45356	−	0.00228586i
$208$	863.036	+	473.722i	0.287696	+	0.157917i
$209$	−5936.51			−1.96477
$210$	333.982	−	1478.64i	0.109748	−	0.485885i
$211$		−	3224.14i		−	1.05194i	−0.850504	−	0.525969i	$-0.823703\pi$
$211$		−	3224.14i		−	1.05194i	0.850504	−	0.525969i	$-0.176297\pi$
$212$	−3237.90	+	461.902i	−1.04896	+	0.149640i
$213$	2508.96	+	1036.93i	0.807093	+	0.333566i
$214$	−1168.60	−	389.661i	−0.373288	−	0.124470i
$215$	−549.580	+	1816.59i	−0.174330	+	0.576235i
$216$	−3101.51	+	676.993i	−0.976996	+	0.213257i
$217$	−1930.46	+	1930.46i	−0.603908	+	0.603908i
$218$	−426.308	−	852.827i	−0.132446	−	0.264957i
$219$	−4190.03	+	1739.43i	−1.29286	+	0.536711i
$220$	583.760	−	3808.86i	0.178896	−	1.16724i
$221$	−997.070			−0.303485
$222$	751.629	+	650.980i	0.227234	+	0.196806i
$223$	926.648	+	926.648i	0.278264	+	0.278264i	0.832416	−	0.554152i	$-0.186957\pi$
$223$	926.648	+	926.648i	0.278264	+	0.278264i	−0.554152	+	0.832416i	$0.686957\pi$
$224$	64.1974	−	1668.74i	0.0191490	−	0.497757i
$225$	−3308.12	+	668.563i	−0.980183	+	0.198093i
$226$	1667.99	+	556.180i	0.490943	+	0.163702i
$227$	−2589.65	+	2589.65i	−0.757185	+	0.757185i	−0.975809	−	0.218624i	$-0.929843\pi$
$227$	−2589.65	+	2589.65i	−0.757185	+	0.757185i	0.218624	+	0.975809i	$0.429843\pi$
$228$	2921.34	+	4927.18i	0.848553	+	1.43119i
$229$	−3678.75			−1.06157			−0.530784	−	0.847507i	$-0.678102\pi$
$229$	−3678.75			−1.06157			−0.530784	+	0.847507i	$0.678102\pi$
$230$	4997.30	−	856.633i	1.43266	−	0.245586i
$231$	791.811	+	1907.36i	0.225530	+	0.543268i
$232$	271.382	−	1490.09i	0.0767979	−	0.421676i
$233$	2931.96	−	2931.96i	0.824375	−	0.824375i	−0.162357	−	0.986732i	$-0.551910\pi$
$233$	2931.96	−	2931.96i	0.824375	−	0.824375i	0.986732	+	0.162357i	$0.0519097\pi$
$234$	526.912	+	1049.95i	0.147202	+	0.293323i
$235$	432.093	+	130.723i	0.119943	+	0.0362868i
$236$	−2905.81	−	2180.25i	−0.801491	−	0.601366i
$237$	−1797.82	−	743.026i	−0.492747	−	0.203649i
$238$	756.221	+	1512.82i	0.205960	+	0.412022i
$239$	−3110.82			−0.841935			−0.420967	−	0.907076i	$-0.638309\pi$
$239$	−3110.82			−0.841935			−0.420967	+	0.907076i	$0.638309\pi$
$240$	−3448.54	+	1389.82i	−0.927509	+	0.373801i
$241$	−443.083			−0.118429			−0.0592147	−	0.998245i	$-0.518860\pi$
$241$	−443.083			−0.118429			−0.0592147	+	0.998245i	$0.518860\pi$
$242$	663.972	+	1328.27i	0.176371	+	0.352829i
$243$	−3505.32	−	1435.83i	−0.925377	−	0.379048i
$244$	597.067	+	447.985i	0.156653	+	0.117538i
$245$	−1361.08	−	2541.85i	−0.354923	−	0.662827i
$246$	−278.365	−	3879.19i	−0.0721460	−	1.00540i
$247$	1498.86	−	1498.86i	0.386114	−	0.386114i
$248$	6587.78	+	1199.80i	1.68679	+	0.307207i
$249$	277.082	−	115.026i	0.0705195	−	0.0292751i
$250$	−3688.76	+	1420.59i	−0.933190	+	0.359384i
$251$	1835.38			0.461547			0.230774	−	0.973007i	$-0.425874\pi$
$251$	1835.38			0.461547			0.230774	+	0.973007i	$0.425874\pi$
$252$	1193.42	−	1595.79i	0.298327	−	0.398910i
$253$	−4884.28	+	4884.28i	−1.21372	+	1.21372i
$254$	−1397.02	−	465.826i	−0.345105	−	0.115073i
$255$	2384.37	−	2914.45i	0.585548	−	0.715724i
$256$	−3455.49	+	2199.27i	−0.843626	+	0.536932i
$257$	2854.46	+	2854.46i	0.692827	+	0.692827i	0.962853	−	0.270026i	$-0.0870322\pi$
$257$	2854.46	+	2854.46i	0.692827	+	0.692827i	−0.270026	+	0.962853i	$0.587032\pi$
$258$	−1633.34	+	1885.87i	−0.394137	+	0.455075i
$259$	−624.159			−0.149743
$260$	814.278	+	1109.06i	0.194228	+	0.264541i
$261$	1275.93	−	1279.95i	0.302598	−	0.303551i
$262$	−1936.37	−	3873.70i	−0.456601	−	0.913428i
$263$	−3421.87	+	3421.87i	−0.802286	+	0.802286i	−0.983453	−	0.181166i	$-0.942013\pi$
$263$	−3421.87	+	3421.87i	−0.802286	+	0.802286i	0.181166	+	0.983453i	$0.442013\pi$
$264$	2742.21	−	4258.86i	0.639286	−	0.992859i
$265$	−4375.08	−	1323.61i	−1.01418	−	0.306825i
$266$	−3410.96	−	1137.36i	−0.786239	−	0.262166i
$267$	−1395.04	+	3375.44i	−0.319758	+	0.773684i
$268$	−4277.78	+	610.246i	−0.975025	+	0.139092i
$269$		−	7558.09i		−	1.71310i	−0.516061	−	0.856552i	$-0.672602\pi$
$269$		−	7558.09i		−	1.71310i	0.516061	−	0.856552i	$-0.327398\pi$
$270$	−4329.07	−	970.660i	−0.975773	−	0.218787i
$271$	−69.2196			−0.0155158			−0.00775792	−	0.999970i	$-0.502469\pi$
$271$	−69.2196			−0.0155158			−0.00775792	+	0.999970i	$0.502469\pi$
$272$	1996.07	−	3636.48i	0.444962	−	0.810640i
$273$	−681.491	−	281.655i	−0.151083	−	0.0624416i
$274$	279.037	−	836.834i	0.0615227	−	0.184507i
$275$	2985.18	−	4482.08i	0.654593	−	0.982834i
$276$	6457.39	+	1650.31i	1.40829	+	0.359917i
$277$	1359.39	+	1359.39i	0.294866	+	0.294866i	0.838999	−	0.544133i	$-0.183141\pi$
$277$	1359.39	+	1359.39i	0.294866	+	0.294866i	−0.544133	+	0.838999i	$0.683141\pi$
$278$	−761.368	−	1523.11i	−0.164258	−	0.328598i
$279$	5658.75	+	5640.98i	1.21427	+	1.21045i
$280$	1065.14	−	2076.63i	0.227338	−	0.443222i
$281$		−	9086.75i		−	1.92907i	−0.263947	−	0.964537i	$-0.585024\pi$
$281$		−	9086.75i		−	1.92907i	0.263947	−	0.964537i	$-0.414976\pi$
$282$	448.573	+	388.505i	0.0947239	+	0.0820396i
$283$	4875.00	−	4875.00i	1.02399	−	1.02399i	0.0242839	−	0.999705i	$-0.492269\pi$
$283$	4875.00	−	4875.00i	1.02399	−	1.02399i	0.999705	−	0.0242839i	$-0.00773055\pi$
$284$	3343.26	+	2508.48i	0.698542	+	0.524123i
$285$	796.851	+	7965.52i	0.165619	+	1.65557i
$286$	−1778.20	−	592.928i	−0.367647	−	0.122589i
$287$	1726.23	+	1726.23i	0.355040	+	0.355040i
$288$	−4884.20	−	180.206i	−0.999320	−	0.0368706i
$289$		−	711.755i		−	0.144872i
$290$	1222.34	−	1728.11i	0.247512	−	0.349924i
$291$	2221.69	+	5351.72i	0.447552	+	1.07809i
$292$	−6914.76	+	986.425i	−1.38581	+	0.197692i
$293$	6520.48	+	6520.48i	1.30010	+	1.30010i	0.928319	+	0.371786i	$0.121254\pi$
$293$	6520.48	+	6520.48i	1.30010	+	1.30010i	0.371786	+	0.928319i	$0.378746\pi$
$294$	−271.283	−	3780.50i	−0.0538149	−	0.749943i
$295$	−2396.61	−	4475.72i	−0.473003	−	0.883344i
$296$	871.026	+	1258.95i	0.171038	+	0.247212i
$297$	5578.62	−	2326.17i	1.08991	−	0.454472i
$298$	−112.540	+	56.2562i	−0.0218768	+	0.0109357i
$299$		−	2466.38i		−	0.477039i
$300$	−5189.03	−	272.022i	−0.998629	−	0.0523507i
$301$		−	1566.05i		−	0.299885i
$302$	4499.89	+	9002.00i	0.857415	+	1.71525i
$303$	1905.39	−	4610.28i	0.361261	−	0.874104i
$304$	2465.97	+	8467.22i	0.465240	+	1.59746i
$305$	492.440	+	919.643i	0.0924494	+	0.172651i
$306$	4424.07	−	2220.19i	0.826495	−	0.414771i
$307$	−5010.33	−	5010.33i	−0.931449	−	0.931449i	0.0663475	−	0.997797i	$-0.478865\pi$
$307$	−5010.33	−	5010.33i	−0.931449	−	0.931449i	−0.997797	+	0.0663475i	$0.978865\pi$
$308$	449.034	+	3147.69i	0.0830717	+	0.582326i
$309$	8635.25	−	3584.79i	1.58978	−	0.659974i
$310$	7640.08	+	5404.07i	1.39977	+	0.990098i
$311$		−	8412.46i		−	1.53385i	−0.641738	−	0.766924i	$-0.721786\pi$
$311$		−	8412.46i		−	1.53385i	0.641738	−	0.766924i	$-0.278214\pi$
$312$	382.927	+	1767.64i	0.0694839	+	0.320747i
$313$	5830.72	+	5830.72i	1.05295	+	1.05295i	0.998518	+	0.0544276i	$0.0173334\pi$
$313$	5830.72	+	5830.72i	1.05295	+	1.05295i	0.0544276	+	0.998518i	$0.482667\pi$
$314$	−3003.74	+	9008.25i	−0.539843	+	1.61900i
$315$	2452.98	−	1318.46i	0.438762	−	0.235832i
$316$	−2395.65	−	1797.48i	−0.426474	−	0.319987i
$317$	3153.06	−	3153.06i	0.558655	−	0.558655i	−0.370269	−	0.928924i	$-0.620735\pi$
$317$	3153.06	−	3153.06i	0.558655	−	0.558655i	0.928924	+	0.370269i	$0.120735\pi$
$318$	−4541.94	−	3933.74i	−0.800941	−	0.693689i
$319$			2883.72i			0.506136i
$320$	−5675.05	+	749.547i	−0.991390	+	0.130940i
$321$	−867.677	−	2090.11i	−0.150869	−	0.363422i
$322$	−3742.15	+	1870.61i	−0.647646	+	0.323743i
$323$	−6315.59	−	6315.59i	−1.08795	−	1.08795i
$324$	−4675.89	−	3485.43i	−0.801765	−	0.597640i
$325$	377.939	+	1885.35i	0.0645055	+	0.321785i
$326$	7102.28	+	2368.21i	1.20662	+	0.402340i
$327$	669.030	−	1618.78i	0.113142	−	0.273758i
$328$	1072.87	−	5890.86i	0.180608	−	0.991672i
$329$	−372.499			−0.0624211
$330$	5985.47	−	3779.78i	0.998452	−	0.630515i
$331$			227.197i			0.0377277i	0.999822	+	0.0188638i	$0.00600490\pi$
$331$			227.197i			0.0377277i	−0.999822	+	0.0188638i	$0.993995\pi$
$332$	457.265	−	65.2311i	0.0755894	−	0.0107832i
$333$	2.87271	+	1826.73i	0.000472743	+	0.300612i
$334$	−727.497	+	2181.77i	−0.119182	+	0.357429i
$335$	−5780.17	−	1748.69i	−0.942700	−	0.285198i
$336$	2391.55	−	1921.66i	0.388303	−	0.312009i
$337$	−1857.83	+	1857.83i	−0.300304	+	0.300304i	−0.841133	−	0.540829i	$-0.818111\pi$
$337$	−1857.83	+	1857.83i	−0.300304	+	0.300304i	0.540829	+	0.841133i	$0.318111\pi$
$338$	−4959.63	+	2479.20i	−0.798131	+	0.398967i
$339$	1238.47	+	2983.30i	0.198421	+	0.477967i
$340$	4673.11	−	3431.04i	0.745397	−	0.547277i
$341$	−12749.1			−2.02465
$342$	−3313.02	+	9988.09i	−0.523823	+	1.57922i
$343$	3919.83	+	3919.83i	0.617057	+	0.617057i
$344$	−3158.76	+	2185.45i	−0.495084	+	0.342533i
$345$	7209.27	+	5898.05i	1.12503	+	0.920407i
$346$	−1649.84	+	4947.87i	−0.256346	+	0.768784i
$347$	−289.575	+	289.575i	−0.0447988	+	0.0447988i	−0.729151	−	0.684352i	$-0.760085\pi$
$347$	−289.575	+	289.575i	−0.0447988	+	0.0447988i	0.684352	+	0.729151i	$0.260085\pi$
$348$	2393.43	−	1419.07i	0.368682	−	0.218592i
$349$	−3255.30			−0.499289			−0.249645	−	0.968338i	$-0.580314\pi$
$349$	−3255.30			−0.499289			−0.249645	+	0.968338i	$0.580314\pi$
$350$	2573.92	−	2003.36i	0.393091	−	0.305955i
$351$	−821.183	+	1995.82i	−0.124876	+	0.303501i
$352$	5722.35	−	5298.38i	0.866484	−	0.802285i
$353$	−6649.04	+	6649.04i	−1.00253	+	1.00253i	−0.00253159	+	0.999997i	$0.500806\pi$
$353$	−6649.04	+	6649.04i	−1.00253	+	1.00253i	−0.999997	+	0.00253159i	$0.999194\pi$
$354$	−477.680	−	6656.76i	−0.0717186	−	0.999443i
$355$	2757.41	+	5149.52i	0.412248	+	0.769882i
$356$	−3374.80	+	4497.87i	−0.502427	+	0.669626i
$357$	−1186.78	+	2871.53i	−0.175942	+	0.425707i
$358$	−5410.32	+	2704.49i	−0.798727	+	0.399265i
$359$	7773.15			1.14276			0.571380	−	0.820685i	$-0.306408\pi$
$359$	7773.15			1.14276			0.571380	+	0.820685i	$0.306408\pi$
$360$	−6082.57	−	3107.80i	−0.890498	−	0.454987i
$361$	12129.0			1.76833
$362$	−8527.40	+	4262.65i	−1.23810	+	0.618894i
$363$	−1042.01	+	2521.24i	−0.150665	+	0.364548i
$364$	−908.108	−	681.362i	−0.130763	−	0.0981128i
$365$	−9343.29	−	2826.66i	−1.33986	−	0.405353i
$366$	98.1506	+	1367.79i	0.0140175	+	0.195343i
$367$	−8931.94	+	8931.94i	−1.27042	+	1.27042i	−0.324550	+	0.945868i	$0.605213\pi$
$367$	−8931.94	+	8931.94i	−1.27042	+	1.27042i	−0.945868	+	0.324550i	$0.894787\pi$
$368$	8995.32	+	4937.55i	1.27422	+	0.699423i
$369$	5044.22	−	5060.11i	0.711631	−	0.713872i
$370$	361.477	+	2108.73i	0.0507900	+	0.296291i
$371$	3771.67			0.527804
$372$	6273.81	+	10581.5i	0.874414	+	1.47480i
$373$	8144.70	−	8144.70i	1.13061	−	1.13061i	0.140531	−	0.990076i	$-0.455119\pi$
$373$	8144.70	−	8144.70i	1.13061	−	1.13061i	0.990076	−	0.140531i	$-0.0448809\pi$
$374$	−2498.36	+	7492.59i	−0.345420	+	1.03592i
$375$	−6414.69	−	3403.85i	−0.883341	−	0.468731i
$376$	519.829	+	751.341i	0.0712982	+	0.103052i
$377$	−728.088	−	728.088i	−0.0994653	−	0.0994653i
$378$	3651.00	−	267.762i	0.496791	−	0.0364344i
$379$	−765.902			−0.103804			−0.0519020	−	0.998652i	$-0.516528\pi$
$379$	−765.902			−0.103804			−0.0519020	+	0.998652i	$0.516528\pi$
$380$	−1867.17	+	12182.7i	−0.252062	+	1.64463i
$381$	−1037.28	−	2498.65i	−0.139478	−	0.335983i
$382$	−2140.72	+	1070.09i	−0.286724	+	0.143327i
$383$	3839.15	−	3839.15i	0.512197	−	0.512197i	−0.403002	−	0.915199i	$-0.632033\pi$
$383$	3839.15	−	3839.15i	0.512197	−	0.512197i	0.915199	+	0.403002i	$0.132033\pi$
$384$	−7213.49	−	2142.12i	−0.958625	−	0.284673i
$385$	−1286.73	+	4253.19i	−0.170332	+	0.563020i
$386$	2268.83	−	6804.23i	0.299172	−	0.897218i
$387$	−4583.34	+	7.20777i	−0.602027	+	0.000946748i
$388$	1259.91	+	8831.88i	0.164851	+	1.15559i
$389$			3050.60i			0.397613i	0.980039	+	0.198807i	$0.0637066\pi$
$389$			3050.60i			0.397613i	−0.980039	+	0.198807i	$0.936293\pi$
$390$	−556.897	+	2465.55i	−0.0723066	+	0.320123i
$391$	−10392.3			−1.34415
$392$	1045.58	−	5740.99i	0.134719	−	0.739704i
$393$	3038.86	−	7352.81i	0.390052	−	0.943766i
$394$	496.063	+	165.409i	0.0634297	+	0.0211502i
$395$	−1975.85	−	3689.94i	−0.251686	−	0.470028i
$396$	9210.27	−	1328.67i	1.16877	−	0.168607i
$397$	1654.18	+	1654.18i	0.209120	+	0.209120i	0.803894	−	0.594773i	$-0.202758\pi$
$397$	1654.18	+	1654.18i	0.209120	+	0.209120i	−0.594773	+	0.803894i	$0.702758\pi$
$398$	1906.37	−	952.951i	0.240095	−	0.120018i
$399$	−2532.62	−	6100.72i	−0.317768	−	0.765458i
$400$	−7632.79	−	2395.94i	−0.954099	−	0.299493i
$401$			13528.0i			1.68468i	0.538947	+	0.842340i	$0.318822\pi$
$401$			13528.0i			1.68468i	−0.538947	+	0.842340i	$0.681178\pi$
$402$	−6000.62	−	5197.09i	−0.744487	−	0.644794i
$403$	3218.93	−	3218.93i	0.397881	−	0.397881i
$404$	4609.40	−	6143.34i	0.567640	−	0.756540i
$405$	−3870.04	−	7173.07i	−0.474824	−	0.880081i
$406$	−552.486	+	1656.91i	−0.0675356	+	0.202540i
$407$	−2061.04	−	2061.04i	−0.251012	−	0.251012i
$408$	7448.13	−	1613.50i	0.903768	−	0.195784i
$409$		−	10602.7i		−	1.28183i	−0.767610	−	0.640917i	$-0.778554\pi$
$409$		−	10602.7i		−	1.28183i	0.767610	−	0.640917i	$-0.221446\pi$
$410$	4832.37	−	6831.84i	0.582083	−	0.822929i
$411$	1496.73	−	621.345i	0.179631	−	0.0745710i
$412$	14250.6	−	2032.93i	1.70408	−	0.243095i
$413$	2962.25	+	2962.25i	0.352936	+	0.352936i
$414$	5491.94	+	10943.5i	0.651966	+	1.29914i
$415$	617.860	+	186.923i	0.0730833	+	0.0221102i
$416$	−107.045	+	2782.53i	−0.0126162	+	0.327944i
$417$	1194.86	−	2891.08i	0.140318	−	0.339512i
$418$	−7507.67	−	15019.1i	−0.878497	−	1.75743i
$419$			9773.94i			1.13959i	0.821787	+	0.569795i	$0.192977\pi$
$419$			9773.94i			1.13959i	−0.821787	+	0.569795i	$0.807023\pi$
$420$	4163.25	−	1025.02i	0.483681	−	0.119085i
$421$		−	6580.18i		−	0.761754i	−0.924626	−	0.380877i	$-0.875622\pi$
$421$		−	6580.18i		−	0.761754i	0.924626	−	0.380877i	$-0.124378\pi$
$422$	8156.90	−	4077.44i	0.940928	−	0.470348i
$423$	1.71444	+	1090.19i	0.000197065	+	0.125312i
$424$	−5263.43	−	7607.56i	−0.602865	−	0.871358i
$425$	7944.08	−	1592.48i	0.906693	−	0.181757i
$426$	549.592	+	7658.90i	0.0625066	+	0.871068i
$427$	−608.665	−	608.665i	−0.0689821	−	0.0689821i
$428$	−492.057	−	3449.28i	−0.0555712	−	0.389549i
$429$	−1320.30	−	3180.41i	−0.148589	−	0.357929i
$430$	−5290.91	+	906.963i	−0.593373	+	0.101715i
$431$			4851.99i			0.542255i	0.962543	+	0.271128i	$0.0873966\pi$
$431$			4851.99i			0.542255i	−0.962543	+	0.271128i	$0.912603\pi$
$432$	−5635.12	−	6990.50i	−0.627592	−	0.778543i
$433$	1620.78	+	1620.78i	0.179883	+	0.179883i	0.791305	−	0.611422i	$-0.209402\pi$
$433$	1620.78	+	1620.78i	0.179883	+	0.179883i	−0.611422	+	0.791305i	$0.709402\pi$
$434$	−7325.33	−	2442.58i	−0.810200	−	0.270156i
$435$	3869.34	−	387.079i	0.426484	−	0.0426644i
$436$	1618.47	−	2157.07i	0.177777	−	0.236938i
$437$	15622.4	−	15622.4i	1.71012	−	1.71012i
$438$	−9699.63	−	8400.77i	−1.05814	−	0.916449i
$439$		−	9133.46i		−	0.992976i	−0.868044	−	0.496488i	$-0.834623\pi$
$439$		−	9133.46i		−	0.992976i	0.868044	−	0.496488i	$-0.165377\pi$
$440$	10374.5	−	3340.03i	1.12405	−	0.361885i
$441$	4915.89	−	4931.38i	0.530817	−	0.532489i
$442$	−1260.95	−	2522.53i	−0.135696	−	0.271459i
$443$	−7659.97	−	7659.97i	−0.821526	−	0.821526i	0.164801	−	0.986327i	$-0.447302\pi$
$443$	−7659.97	−	7659.97i	−0.821526	−	0.821526i	−0.986327	+	0.164801i	$0.947302\pi$
$444$	−696.389	+	2724.85i	−0.0744351	+	0.291252i
$445$	−6927.93	+	3709.69i	−0.738012	+	0.395183i
$446$	−1172.48	+	3516.26i	−0.124481	+	0.373318i
$447$	−213.617	−	88.2862i	−0.0226034	−	0.00934182i
$448$	4303.02	−	1947.98i	0.453791	−	0.205431i
$449$	−17016.0			−1.78849			−0.894247	−	0.447573i	$-0.852288\pi$
$449$	−17016.0			−1.78849			−0.894247	+	0.447573i	$0.852288\pi$
$450$	−5875.08	−	7523.86i	−0.615453	−	0.788174i
$451$			11400.4i			1.19030i
$452$	702.334	+	4923.30i	0.0730864	+	0.512329i
$453$	−7061.93	+	17087.0i	−0.732447	+	1.77222i
$454$	−9826.69	−	3276.65i	−1.01584	−	0.338724i
$455$	−748.976	−	1398.73i	−0.0771704	−	0.144117i
$456$	−8771.00	+	13622.0i	−0.900745	+	1.39893i
$457$	448.866	−	448.866i	0.0459454	−	0.0459454i	−0.683761	−	0.729706i	$-0.739657\pi$
$457$	448.866	−	448.866i	0.0459454	−	0.0459454i	0.729706	+	0.683761i	$0.239657\pi$
$458$	−4652.38	−	9307.06i	−0.474653	−	0.949542i
$459$	8409.55	+	3460.13i	0.855173	+	0.351863i
$460$	8487.13	+	11559.6i	0.860249	+	1.17167i
$461$	13371.1			1.35087			0.675437	−	0.737418i	$-0.263955\pi$
$461$	13371.1			1.35087			0.675437	+	0.737418i	$0.263955\pi$
$462$	−3824.14	+	4415.40i	−0.385098	+	0.444639i
$463$	−6014.92	−	6014.92i	−0.603752	−	0.603752i	0.337554	−	0.941306i	$-0.390400\pi$
$463$	−6014.92	−	6014.92i	−0.603752	−	0.603752i	−0.941306	+	0.337554i	$0.890400\pi$
$464$	4113.05	−	1197.87i	0.411516	−	0.119849i
$465$	1711.30	+	17106.6i	0.170666	+	1.70602i
$466$	11125.7	+	3709.78i	1.10598	+	0.368781i
$467$	−582.941	+	582.941i	−0.0577629	+	0.0577629i	−0.735398	−	0.677635i	$-0.763005\pi$
$467$	−582.941	+	582.941i	−0.0577629	+	0.0577629i	0.677635	+	0.735398i	$0.263005\pi$
$468$	−1989.96	+	2660.89i	−0.196551	+	0.262820i
$469$	4982.97			0.490601
$470$	215.730	+	1258.49i	0.0211721	+	0.123511i
$471$	−16111.8	+	6688.57i	−1.57620	+	0.654338i
$472$	1841.07	−	10108.8i	0.179538	−	0.985797i
$473$	5171.25	−	5171.25i	0.502694	−	0.502694i
$474$	−393.816	−	5488.07i	−0.0381615	−	0.531804i
$475$	−9548.14	+	14336.0i	−0.922313	+	1.38480i
$476$	−2870.98	+	3826.40i	−0.276452	+	0.368451i
$477$	−17.3592	−	11038.5i	−0.00166629	−	1.05958i
$478$	−3934.14	−	7870.22i	−0.376450	−	0.753087i
$479$	11383.1			1.08581			0.542907	−	0.839793i	$-0.317324\pi$
$479$	11383.1			1.08581			0.542907	+	0.839793i	$0.317324\pi$
$480$	−7877.39	−	6966.97i	−0.749067	−	0.662494i
$481$	1040.75			0.0986572
$482$	−560.350	−	1120.98i	−0.0529528	−	0.105932i
$483$	−7103.11	−	2935.66i	−0.669156	−	0.276557i
$484$	−2520.76	+	3359.63i	−0.236736	+	0.315517i
$485$	−3610.35	+	11933.7i	−0.338015	+	1.11728i
$486$	−800.462	−	10684.1i	−0.0747113	−	0.997205i
$487$	1985.60	−	1985.60i	0.184756	−	0.184756i	−0.608669	−	0.793425i	$-0.708296\pi$
$487$	1985.60	−	1985.60i	0.184756	−	0.184756i	0.793425	+	0.608669i	$0.208296\pi$
$488$	−378.291	+	2077.10i	−0.0350911	+	0.192676i
$489$	5273.40	+	12702.9i	0.487672	+	1.17473i
$490$	4709.44	−	6658.04i	0.434185	−	0.613836i
$491$	−5413.85			−0.497604			−0.248802	−	0.968554i	$-0.580037\pi$
$491$	−5413.85			−0.497604			−0.248802	+	0.968554i	$0.580037\pi$
$492$	9462.11	−	5610.11i	0.867042	−	0.514072i
$493$	−3067.86	+	3067.86i	−0.280263	+	0.280263i
$494$	5687.59	+	1896.49i	0.518009	+	0.172727i
$495$	12453.7	+	3746.30i	1.13081	+	0.340169i
$496$	5295.87	+	18184.1i	0.479419	+	1.64615i
$497$	−3408.20	−	3408.20i	−0.307603	−	0.307603i
$498$	641.425	+	555.533i	0.0577168	+	0.0499880i
$499$	−4438.73			−0.398206			−0.199103	−	0.979979i	$-0.563803\pi$
$499$	−4438.73			−0.398206			−0.199103	+	0.979979i	$0.563803\pi$
$500$	−8259.05	−	7535.79i	−0.738712	−	0.674022i
$501$	−3902.23	+	1619.95i	−0.347981	+	0.144459i
$502$	2321.14	+	4643.42i	0.206369	+	0.412841i
$503$	−12298.8	+	12298.8i	−1.09021	+	1.09021i	−0.0947047	+	0.995505i	$0.530191\pi$
$503$	−12298.8	+	12298.8i	−1.09021	+	1.09021i	−0.995505	+	0.0947047i	$0.969809\pi$
$504$	5546.54	+	1001.15i	0.490204	+	0.0884821i
$505$	9462.38	−	5066.81i	0.833803	−	0.446476i
$506$	−18533.9	−	6180.02i	−1.62833	−	0.542955i
$507$	−9414.04	−	3890.76i	−0.824640	−	0.340818i
$508$	−588.236	−	4123.49i	−0.0513755	−	0.360138i
$509$			5599.07i			0.487573i	0.969829	+	0.243786i	$0.0783895\pi$
$509$			5599.07i			0.487573i	−0.969829	+	0.243786i	$0.921610\pi$
$510$	10388.8	+	2346.54i	0.902008	+	0.203738i
$511$	8054.66			0.697294
$512$	−9934.07	−	5960.88i	−0.857476	−	0.514523i
$513$	−17843.3	+	7440.29i	−1.53567	+	0.640345i
$514$	−3611.72	+	10831.6i	−0.309934	+	0.929495i
$515$	19255.6	+	5825.47i	1.64758	+	0.498448i
$516$	−6836.78	−	1747.27i	−0.583280	−	0.149069i
$517$	−1230.03	−	1230.03i	−0.104636	−	0.104636i
$518$	−789.350	−	1579.09i	−0.0669537	−	0.133941i
$519$	−8849.57	+	3673.77i	−0.748465	+	0.310714i
$520$	−1776.07	+	3462.66i	−0.149780	+	0.292015i
$521$			3195.21i			0.268685i	0.990935	+	0.134342i	$0.0428922\pi$
$521$			3195.21i			0.268685i	−0.990935	+	0.134342i	$0.957108\pi$
$522$	4851.82	+	1609.33i	0.406817	+	0.134940i
$523$	−1681.49	+	1681.49i	−0.140586	+	0.140586i	−0.773897	−	0.633311i	$-0.781695\pi$
$523$	−1681.49	+	1681.49i	−0.140586	+	0.140586i	0.633311	+	0.773897i	$0.281695\pi$
$524$	7351.41	−	9797.84i	0.612877	−	0.816833i
$525$	5879.59	+	1155.62i	0.488774	+	0.0960673i
$526$	−12984.6	−	4329.64i	−1.07634	−	0.358900i
$527$	−13563.2	−	13563.2i	−1.12111	−	1.12111i
$528$	14242.7	+	1551.63i	1.17392	+	0.127891i
$529$		−	13539.8i		−	1.11283i
$530$	−2184.33	−	12742.6i	−0.179021	−	1.04435i
$531$	8655.97	−	8683.24i	0.707415	−	0.709643i
$532$	−1436.24	−	10067.9i	−0.117047	−	0.820489i
$533$	−2878.40	−	2878.40i	−0.233916	−	0.233916i
$534$	−10303.9	+	739.396i	−0.835010	+	0.0599191i
$535$	1410.02	−	4660.70i	0.113945	−	0.376634i
$536$	−6953.82	−	10050.8i	−0.560372	−	0.809940i
$537$	−10269.5	−	4244.32i	−0.825256	−	0.341072i
$538$	19121.6	−	9558.42i	1.53232	−	0.765972i
$539$			11110.4i			0.887863i
$540$	−3019.08	−	12179.9i	−0.240594	−	0.970626i
$541$		−	18122.0i		−	1.44016i	−0.693893	−	0.720078i	$-0.744106\pi$
$541$		−	18122.0i		−	1.44016i	0.693893	−	0.720078i	$-0.255894\pi$
$542$	−87.5393	−	175.122i	−0.00693752	−	0.0138785i
$543$	−16186.2	−	6689.62i	−1.27922	−	0.528691i
$544$	11724.5	+	451.046i	0.924048	+	0.0355486i
$545$	3322.47	−	1779.08i	0.261136	−	0.139830i
$546$	−149.282	−	2080.34i	−0.0117009	−	0.163059i
$547$	12469.5	+	12469.5i	0.974691	+	0.974691i	0.999688	−	0.0249966i	$-0.00795750\pi$
$547$	12469.5	+	12469.5i	0.974691	+	0.974691i	−0.0249966	+	0.999688i	$0.507958\pi$
$548$	2470.03	−	352.363i	0.192545	−	0.0274675i
$549$	−1778.58	+	1784.18i	−0.138265	+	0.138701i
$550$	15114.7	+	1884.04i	1.17180	+	0.146065i
$551$		−	9223.63i		−	0.713139i
$552$	3991.20	+	18423.9i	0.307748	+	1.42061i
$553$	2442.18	+	2442.18i	0.187798	+	0.187798i
$554$	−1720.02	+	5158.36i	−0.131907	+	0.395592i
$555$	−2488.82	+	3042.13i	−0.190351	+	0.232669i
$556$	2890.53	−	3852.44i	0.220478	−	0.293849i
$557$	−12191.9	+	12191.9i	−0.927446	+	0.927446i	−0.997540	−	0.0700940i	$-0.977670\pi$
$557$	−12191.9	+	12191.9i	−0.927446	+	0.927446i	0.0700940	+	0.997540i	$0.477670\pi$
$558$	−7114.98	+	21450.3i	−0.539787	+	1.62735i
$559$			2611.29i			0.197578i
$560$	6600.81	+	68.5288i	0.498098	+	0.00517119i
$561$	−13401.0	+	5563.21i	−1.00854	+	0.418679i
$562$	22989.0	−	11491.7i	1.72550	−	0.862537i
$563$	6998.97	+	6998.97i	0.523928	+	0.523928i	0.918755	−	0.394827i	$-0.129196\pi$
$563$	6998.97	+	6998.97i	0.523928	+	0.523928i	−0.394827	+	0.918755i	$0.629196\pi$
$564$	−415.606	+	1626.19i	−0.0310286	+	0.121410i
$565$	−2012.58	+	6652.41i	−0.149858	+	0.495344i
$566$	18498.7	+	6168.28i	1.37378	+	0.458078i
$567$	4770.45	+	4740.54i	0.353334	+	0.351118i
$568$	−2118.23	+	11630.6i	−0.156477	+	0.859174i
$569$	20168.0			1.48592			0.742960	−	0.669336i	$-0.233421\pi$
$569$	20168.0			1.48592			0.742960	+	0.669336i	$0.233421\pi$
$570$	−19144.6	+	12089.7i	−1.40681	+	0.888387i
$571$		−	22973.0i		−	1.68369i	−0.539717	−	0.841846i	$-0.681469\pi$
$571$		−	22973.0i		−	1.68369i	0.539717	−	0.841846i	$-0.318531\pi$
$572$	−748.739	−	5248.59i	−0.0547314	−	0.383662i
$573$	−4063.37	−	1679.36i	−0.296248	−	0.122437i
$574$	−2184.18	+	6550.38i	−0.158826	+	0.476320i
$575$	3939.22	+	19650.8i	0.285699	+	1.42521i
$576$	−5720.94	−	12584.7i	−0.413841	−	0.910349i
$577$	−6387.37	+	6387.37i	−0.460849	+	0.460849i	−0.898934	−	0.438085i	$-0.855657\pi$
$577$	−6387.37	+	6387.37i	−0.460849	+	0.460849i	0.438085	+	0.898934i	$0.355657\pi$
$578$	1800.70	−	900.128i	0.129584	−	0.0647758i
$579$	12169.8	−	5052.10i	0.873504	−	0.362622i
$580$	5917.87	+	906.996i	0.423666	+	0.0649327i
$581$	−532.645			−0.0380342
$582$	−10729.9	+	12388.9i	−0.764207	+	0.882362i
$583$	12454.4	+	12454.4i	0.884751	+	0.884751i
$584$	−11240.4	−	16246.5i	−0.796459	−	1.15117i
$585$	−4090.21	+	2198.46i	−0.289076	+	0.155377i
$586$	−8250.28	+	24742.7i	−0.581597	+	1.74422i
$587$	−3250.85	+	3250.85i	−0.228580	+	0.228580i	−0.812099	−	0.583519i	$-0.801675\pi$
$587$	−3250.85	+	3250.85i	−0.228580	+	0.228580i	0.583519	+	0.812099i	$0.301675\pi$
$588$	9221.39	−	5467.38i	0.646741	−	0.383454i
$589$	40778.3			2.85270
$590$	8292.44	−	11723.6i	0.578634	−	0.818053i
$591$	368.324	+	887.239i	0.0256359	+	0.0617532i
$592$	−2083.52	+	3795.79i	−0.144649	+	0.263524i
$593$	−327.431	+	327.431i	−0.0226745	+	0.0226745i	−0.718353	−	0.695679i	$-0.755104\pi$
$593$	−327.431	+	327.431i	−0.0226745	+	0.0226745i	0.695679	+	0.718353i	$0.255104\pi$
$594$	12940.1	+	11171.8i	0.893839	+	0.771690i
$595$	−5893.68	+	3155.88i	−0.406079	+	0.217443i
$596$	−284.651	−	213.576i	−0.0195633	−	0.0146785i
$597$	3618.56	+	1495.52i	0.248070	+	0.102525i
$598$	6239.82	−	3119.14i	0.426698	−	0.213296i
$599$	3840.04			0.261936			0.130968	−	0.991387i	$-0.458191\pi$
$599$	3840.04			0.261936			0.130968	+	0.991387i	$0.458191\pi$
$600$	−5874.16	−	13472.0i	−0.399686	−	0.916652i
$601$	−21691.0			−1.47220			−0.736102	−	0.676870i	$-0.763336\pi$
$601$	−21691.0			−1.47220			−0.736102	+	0.676870i	$0.763336\pi$
$602$	3962.02	−	1980.52i	0.268239	−	0.134086i
$603$	−22.9342	−	14583.6i	−0.00154885	−	0.984895i
$604$	−17083.8	+	22768.9i	−1.15087	+	1.53387i
$605$	−5174.73	+	2770.91i	−0.347740	+	0.186204i
$606$	14073.4	−	1009.89i	0.943390	−	0.0676964i
$607$	−9396.58	+	9396.58i	−0.628328	+	0.628328i	−0.947647	−	0.319319i	$-0.896546\pi$
$607$	−9396.58	+	9396.58i	−0.628328	+	0.628328i	0.319319	+	0.947647i	$0.396546\pi$
$608$	−18303.0	+	16946.9i	−1.22086	+	1.13041i
$609$	−2963.49	+	1230.25i	−0.197187	+	0.0818591i
$610$	−1703.88	+	2408.88i	−0.113095	+	0.159890i
$611$	621.121			0.0411258
$612$	11211.9	+	8384.88i	0.740547	+	0.553821i
$613$	−554.488	+	554.488i	−0.0365343	+	0.0365343i	−0.725138	−	0.688604i	$-0.758224\pi$
$613$	−554.488	+	554.488i	−0.0365343	+	0.0365343i	0.688604	+	0.725138i	$0.258224\pi$
$614$	6339.51	−	19012.3i	0.416680	−	1.24963i
$615$	15296.9	−	1530.27i	1.00298	−	0.100335i
$616$	−7395.62	+	5116.79i	−0.483730	+	0.334678i
$617$	−2210.84	−	2210.84i	−0.144255	−	0.144255i	0.631291	−	0.775546i	$-0.282525\pi$
$617$	−2210.84	−	2210.84i	−0.144255	−	0.144255i	−0.775546	+	0.631291i	$0.782525\pi$
$618$	19990.0	+	17313.2i	1.30116	+	1.12692i
$619$	−3681.65			−0.239060			−0.119530	−	0.992831i	$-0.538139\pi$
$619$	−3681.65			−0.239060			−0.119530	+	0.992831i	$0.538139\pi$
$620$	−4009.89	+	26163.3i	−0.259744	+	1.69475i
$621$	−8559.10	+	20802.2i	−0.553084	+	1.34422i
$622$	21283.1	−	10638.9i	1.37198	−	0.685822i
$623$	4585.24	−	4585.24i	0.294870	−	0.294870i
$624$	−3987.77	+	3204.25i	−0.255831	+	0.205565i
$625$	−6022.41	−	14417.7i	−0.385434	−	0.922735i
$626$	−7377.54	+	22125.3i	−0.471031	+	1.41263i
$627$	11782.2	−	28508.2i	0.750457	−	1.81580i
$628$	−26589.1	+	3793.07i	−1.68952	+	0.241019i
$629$		−	4385.30i		−	0.277986i
$630$	6437.84	+	4538.51i	0.407126	+	0.287014i
$631$	17310.9			1.09213			0.546065	−	0.837743i	$-0.316125\pi$
$631$	17310.9			1.09213			0.546065	+	0.837743i	$0.316125\pi$
$632$	1517.84	−	8334.07i	0.0955325	−	0.524543i
$633$	15482.9	+	6398.97i	0.972180	+	0.401795i
$634$	11964.6	+	3989.53i	0.749490	+	0.249912i
$635$	1685.62	−	5571.69i	0.105342	−	0.348198i
$636$	4208.14	−	16465.7i	0.262364	−	1.02658i
$637$	−2805.17	−	2805.17i	−0.174482	−	0.174482i
$638$	−7295.67	+	3646.93i	−0.452724	+	0.226306i
$639$	−9959.08	+	9990.46i	−0.616550	+	0.618492i
$640$	−9073.32	−	13409.7i	−0.560398	−	0.828224i
$641$			10668.6i			0.657387i	0.944437	+	0.328694i	$0.106608\pi$
$641$			10668.6i			0.657387i	−0.944437	+	0.328694i	$0.893392\pi$
$642$	4190.54	−	4838.45i	0.257613	−	0.297443i
$643$	−13262.1	+	13262.1i	−0.813383	+	0.813383i	−0.985139	−	0.171756i	$-0.945056\pi$
$643$	−13262.1	+	13262.1i	−0.813383	+	0.813383i	0.171756	+	0.985139i	$0.445056\pi$
$644$	−9465.10	−	7101.76i	−0.579157	−	0.434547i
$645$	−7632.84	−	6244.58i	−0.465958	−	0.381209i
$646$	7991.03	−	23965.2i	0.486692	−	1.45959i
$647$	11506.4	+	11506.4i	0.699172	+	0.699172i	0.964232	−	0.265060i	$-0.0853917\pi$
$647$	11506.4	+	11506.4i	0.699172	+	0.699172i	−0.265060	+	0.964232i	$0.585392\pi$
$648$	2904.55	−	16237.7i	0.176083	−	0.984375i
$649$			19563.3i			1.18325i
$650$	−4291.86	+	3340.49i	−0.258986	+	0.201577i
$651$	−5439.01	−	13101.8i	−0.327453	−	0.788786i
$652$	2990.53	+	20963.4i	0.179629	+	1.25919i
$653$	3244.79	+	3244.79i	0.194454	+	0.194454i	0.797618	−	0.603163i	$-0.206093\pi$
$653$	3244.79	+	3244.79i	0.194454	+	0.194454i	−0.603163	+	0.797618i	$0.706093\pi$
$654$	4941.52	−	354.597i	0.295457	−	0.0212016i
$655$	15091.3	−	8080.92i	0.900253	−	0.482058i
$656$	16260.4	−	4735.62i	0.967776	−	0.281852i
$657$	−37.0718	−	23573.5i	−0.00220138	−	1.39984i
$658$	−471.085	−	942.403i	−0.0279100	−	0.0558339i
$659$		−	789.834i		−	0.0466883i	−0.999727	−	0.0233441i	$-0.992569\pi$
$659$		−	789.834i		−	0.0466883i	0.999727	−	0.0233441i	$-0.00743135\pi$
$660$	17132.2	+	10362.8i	1.01041	+	0.611168i
$661$		−	901.500i		−	0.0530474i	−0.999648	−	0.0265237i	$-0.991556\pi$
$661$		−	901.500i		−	0.0530474i	0.999648	−	0.0265237i	$-0.00844374\pi$
$662$	−574.796	+	287.327i	−0.0337463	+	0.0168690i
$663$	1978.89	−	4788.11i	0.115918	−	0.280475i
$664$	743.316	+	1074.36i	0.0434432	+	0.0627911i
$665$	4115.63	−	13603.9i	0.239996	−	0.793287i
$666$	−4617.89	+	2317.46i	−0.268678	+	0.134834i
$667$	−7588.77	−	7588.77i	−0.440537	−	0.440537i
$668$	−6439.80	+	918.670i	−0.372999	+	0.0532102i
$669$	−6289.05	+	2610.81i	−0.363451	+	0.150881i
$670$	−2885.84	−	16835.0i	−0.166403	−	0.970737i
$671$		−	4019.75i		−	0.231268i
$672$	7886.19	+	3620.25i	0.452703	+	0.207819i
$673$	−4080.64	−	4080.64i	−0.233726	−	0.233726i	0.580520	−	0.814246i	$-0.302849\pi$
$673$	−4080.64	−	4080.64i	−0.233726	−	0.233726i	−0.814246	+	0.580520i	$0.802849\pi$
$674$	−7049.72	−	2350.68i	−0.402886	−	0.134340i
$675$	3355.08	−	17213.1i	0.191314	−	0.981529i
$676$	−12544.5	−	9412.25i	−0.713729	−	0.535517i
$677$	−4629.27	+	4629.27i	−0.262802	+	0.262802i	−0.826192	−	0.563389i	$-0.809497\pi$
$677$	−4629.27	+	4629.27i	−0.262802	+	0.262802i	0.563389	+	0.826192i	$0.309497\pi$
$678$	−5981.35	+	6906.13i	−0.338809	+	0.391192i
$679$		−	10287.8i		−	0.581458i
$680$	14590.2	+	7483.62i	0.822809	+	0.422035i
$681$	−7296.26	−	17575.6i	−0.410563	−	0.988987i
$682$	−16123.3	−	32254.7i	−0.905270	−	1.81099i
$683$	−8897.62	−	8897.62i	−0.498474	−	0.498474i	0.412489	−	0.910963i	$-0.364660\pi$
$683$	−8897.62	−	8897.62i	−0.498474	−	0.498474i	−0.910963	+	0.412489i	$0.864660\pi$
$684$	−29459.2	+	4249.78i	−1.64678	+	0.237565i
$685$	3337.53	+	1009.72i	0.186161	+	0.0563200i
$686$	−4959.70	+	14874.2i	−0.276038	+	0.827842i
$687$	7301.25	−	17666.0i	0.405473	−	0.981080i
$688$	−9523.83	−	5227.65i	−0.527751	−	0.289684i
$689$	−6289.04			−0.347741
$690$	−5804.47	+	25698.1i	−0.320250	+	1.41784i
$691$			6906.27i			0.380213i	0.981764	+	0.190106i	$0.0608833\pi$
$691$			6906.27i			0.380213i	−0.981764	+	0.190106i	$0.939117\pi$
$692$	−14604.3	+	2083.38i	−0.802274	+	0.114448i
$693$	−10731.0	+	16.8756i	−0.588220	+	0.000925036i
$694$	−1098.82	−	366.395i	−0.0601019	−	0.0200406i
$695$	5933.80	−	3177.36i	0.323859	−	0.173416i
$696$	6617.05	+	4260.61i	0.360372	+	0.232037i
$697$	−12128.4	+	12128.4i	−0.659105	+	0.659105i
$698$	−4116.84	−	8235.73i	−0.223245	−	0.446600i
$699$	8260.73	+	19898.9i	0.446995	+	1.07675i
$700$	8323.53	+	3978.31i	0.449428	+	0.214808i
$701$	−1071.73			−0.0577442			−0.0288721	−	0.999583i	$-0.509192\pi$
$701$	−1071.73			−0.0577442			−0.0288721	+	0.999583i	$0.509192\pi$
$702$	−6087.83	+	446.478i	−0.327308	+	0.0240046i
$703$	6592.27	+	6592.27i	0.353673	+	0.353673i
$704$	20641.4	+	7776.59i	1.10505	+	0.416323i
$705$	−1485.33	+	1815.54i	−0.0793487	+	0.0969891i
$706$	−25230.5	−	8412.94i	−1.34499	−	0.448478i
$707$	−6262.67	+	6262.67i	−0.333143	+	0.333143i
$708$	16237.1	−	9627.04i	0.861906	−	0.511026i
$709$	−22295.8			−1.18101			−0.590505	−	0.807034i	$-0.701072\pi$
$709$	−22295.8			−1.18101			−0.590505	+	0.807034i	$0.701072\pi$
$710$	−9540.82	+	13488.5i	−0.504311	+	0.712977i
$711$	7136.29	−	7158.77i	0.376416	−	0.377602i
$712$	−15647.4	−	2849.78i	−0.823609	−	0.150000i
$713$	33550.5	−	33550.5i	1.76224	−	1.76224i
$714$	−8765.69	+	629.014i	−0.459451	+	0.0329695i
$715$	2145.55	−	7091.95i	0.112223	−	0.370942i
$716$	−13684.4	−	10267.6i	−0.714262	−	0.535917i
$717$	6174.07	−	14938.7i	0.321583	−	0.778099i
$718$	9830.39	+	19665.7i	0.510957	+	1.02217i
$719$	12020.6			0.623495			0.311748	−	0.950165i	$-0.399086\pi$
$719$	12020.6			0.623495			0.311748	+	0.950165i	$0.399086\pi$
$720$	170.183	−	19318.9i	0.00880879	−	0.999961i
$721$	−16599.9			−0.857436
$722$	15339.1	+	30685.7i	0.790667	+	1.58172i
$723$	879.390	−	2127.77i	0.0452350	−	0.109450i
$724$	−21568.5	−	16183.1i	−1.10717	−	0.830718i
$725$	6963.86	+	4638.11i	0.356733	+	0.237593i
$726$	−7696.39	+	552.282i	−0.393443	+	0.0282330i
$727$	−4199.81	+	4199.81i	−0.214254	+	0.214254i	−0.806072	−	0.591818i	$-0.798410\pi$
$727$	−4199.81	+	4199.81i	−0.214254	+	0.214254i	0.591818	+	0.806072i	$0.298410\pi$
$728$	575.362	−	3159.16i	0.0292916	−	0.160833i
$729$	13852.2	−	13983.5i	0.703763	−	0.710435i
$730$	−4664.79	−	27212.8i	−0.236509	−	1.37971i
$731$	11002.9			0.556714
$732$	−3336.31	+	1978.10i	−0.168461	+	0.0998810i
$733$	9456.19	−	9456.19i	0.476497	−	0.476497i	−0.427513	−	0.904009i	$-0.640610\pi$
$733$	9456.19	−	9456.19i	0.476497	−	0.476497i	0.904009	+	0.427513i	$0.140610\pi$
$734$	−33893.2	−	11301.5i	−1.70439	−	0.568317i
$735$	14907.8	−	1491.34i	0.748137	−	0.0748418i
$736$	−1115.72	+	29002.0i	−0.0558778	+	1.45248i
$737$	16454.3	+	16454.3i	0.822390	+	0.822390i
$738$	19181.0	+	6362.29i	0.956726	+	0.317343i
$739$	−6060.69			−0.301686			−0.150843	−	0.988558i	$-0.548199\pi$
$739$	−6060.69			−0.301686			−0.150843	+	0.988558i	$0.548199\pi$
$740$	−4877.83	+	3581.35i	−0.242315	+	0.177909i
$741$	4223.00	+	10172.6i	0.209360	+	0.504318i
$742$	4769.88	+	9542.12i	0.235994	+	0.472105i
$743$	−2337.14	+	2337.14i	−0.115399	+	0.115399i	−0.762448	−	0.647049i	$-0.776003\pi$
$743$	−2337.14	+	2337.14i	−0.115399	+	0.115399i	0.647049	+	0.762448i	$0.276003\pi$
$744$	−18836.5	+	29254.4i	−0.928196	+	1.44156i
$745$	−234.770	−	438.438i	−0.0115454	−	0.0215612i
$746$	30905.9	+	10305.4i	1.51682	+	0.505773i
$747$	2.45151	+	1558.89i	0.000120075	+	0.0763545i
$748$	−22115.4	+	3154.88i	−1.08104	+	0.154216i
$749$			4017.89i			0.196009i
$750$	499.158	−	20533.5i	0.0243022	−	0.999705i
$751$	27419.2			1.33228			0.666138	−	0.745828i	$-0.267946\pi$
$751$	27419.2			1.33228			0.666138	+	0.745828i	$0.267946\pi$
$752$	−1243.45	+	2265.33i	−0.0602976	+	0.109851i
$753$	−3642.70	+	8813.84i	−0.176291	+	0.426553i
$754$	921.240	−	2762.81i	0.0444954	−	0.133442i
$755$	−35070.3	+	18779.1i	−1.69051	+	0.905218i
$756$	5294.69	+	8898.20i	0.254717	+	0.428074i
$757$	8471.81	+	8471.81i	0.406754	+	0.406754i	0.880605	−	0.473851i	$-0.157136\pi$
$757$	8471.81	+	8471.81i	0.406754	+	0.406754i	−0.473851	+	0.880605i	$0.657136\pi$
$758$	−968.606	−	1937.69i	−0.0464134	−	0.0928498i
$759$	−13761.3	−	33149.1i	−0.658109	−	1.58529i
$760$	−33182.9	+	10683.1i	−1.58378	+	0.509892i
$761$		−	8462.16i		−	0.403092i	−0.979479	−	0.201546i	$-0.935403\pi$
$761$		−	8462.16i		−	0.403092i	0.979479	−	0.201546i	$-0.0645965\pi$
$762$	5009.64	−	5784.19i	0.238163	−	0.274986i
$763$	−2198.97	+	2198.97i	−0.104336	+	0.104336i
$764$	−5414.57	−	4062.60i	−0.256403	−	0.192382i
$765$	9263.43	+	17234.5i	0.437804	+	0.814528i
$766$	14568.1	+	4857.63i	0.687162	+	0.229130i
$767$	−4939.38	−	4939.38i	−0.232530	−	0.232530i
$768$	−3703.17	−	20958.8i	−0.173993	−	0.984747i
$769$		−	12702.5i		−	0.595664i	−0.954618	−	0.297832i	$-0.903737\pi$
$769$		−	12702.5i		−	0.595664i	0.954618	−	0.297832i	$-0.0962635\pi$
$770$	−12387.6	+	2123.47i	−0.579765	+	0.0993828i
$771$	−19372.9	+	8042.38i	−0.904927	+	0.375667i
$772$	20083.6	−	2865.03i	0.936303	−	0.133568i
$773$	−20651.8	−	20651.8i	−0.960921	−	0.960921i	0.0383433	−	0.999265i	$-0.487792\pi$
$773$	−20651.8	−	20651.8i	−0.960921	−	0.960921i	−0.999265	+	0.0383433i	$0.987792\pi$
$774$	−5814.61	−	11586.5i	−0.270028	−	0.538073i
$775$	−20505.4	+	30787.7i	−0.950422	+	1.42700i
$776$	−20750.8	+	14356.8i	−0.959937	+	0.664150i
$777$	1238.77	−	2997.33i	0.0571953	−	0.138389i
$778$	−7717.86	+	3857.97i	−0.355654	+	0.177783i
$779$		−	36464.4i		−	1.67712i
$780$	−6941.99	+	1709.16i	−0.318671	+	0.0784587i
$781$		−	22508.5i		−	1.03126i
$782$	−13142.8	−	26292.1i	−0.601004	−	1.20231i
$783$	3614.20	+	8667.57i	0.164957	+	0.395599i
$784$	15846.7	−	4615.15i	0.721880	−	0.210238i
$785$	−35927.4	−	10869.3i	−1.63351	−	0.494191i
$786$	22445.3	−	1610.65i	1.01857	−	0.0730914i
$787$	−687.995	−	687.995i	−0.0311618	−	0.0311618i	0.691354	−	0.722516i	$-0.257014\pi$
$787$	−687.995	−	687.995i	−0.0311618	−	0.0311618i	−0.722516	+	0.691354i	$0.757014\pi$
$788$	208.876	+	1464.20i	0.00944275	+	0.0661929i
$789$	−9641.02	−	23223.8i	−0.435018	−	1.04790i
$790$	6836.58	−	9665.32i	0.307892	−	0.435287i
$791$		−	5734.91i		−	0.257788i
$792$	15009.3	+	21621.2i	0.673401	+	0.970044i
$793$	1014.91	+	1014.91i	0.0454485	+	0.0454485i
$794$	−2093.01	+	6276.95i	−0.0935492	+	0.280555i
$795$	15039.4	−	18382.9i	0.670936	−	0.820095i
$796$	4821.83	+	3617.87i	0.214705	+	0.161095i
$797$	832.735	−	832.735i	0.0370100	−	0.0370100i	−0.688360	−	0.725370i	$-0.741669\pi$
$797$	832.735	−	832.735i	0.0370100	−	0.0370100i	0.725370	+	0.688360i	$0.241669\pi$
$798$	12231.6	−	14122.7i	0.542598	−	0.626490i
$799$		−	2617.15i		−	0.115880i
$800$	−3591.28	−	22340.6i	−0.158714	−	0.987325i
$801$	−13440.7	−	13398.5i	−0.592889	−	0.591028i
$802$	−34225.2	+	17108.3i	−1.50690	+	0.753263i
$803$	26597.3	+	26597.3i	1.16887	+	1.16887i
$804$	5559.61	−	21753.8i	0.243871	−	0.954226i
$805$	−7806.49	−	14578.8i	−0.341792	−	0.638304i
$806$	12214.6	+	4072.87i	0.533796	+	0.177991i
$807$	36295.3	+	15000.6i	1.58322	+	0.654332i
$808$	21371.6	+	3892.31i	0.930510	+	0.169469i
$809$	−16567.1			−0.719985			−0.359992	−	0.932955i	$-0.617221\pi$
$809$	−16567.1			−0.719985			−0.359992	+	0.932955i	$0.617221\pi$
$810$	13253.2	−	18862.5i	0.574902	−	0.818223i
$811$			14675.6i			0.635427i	0.948187	+	0.317713i	$0.102915\pi$
$811$			14675.6i			0.635427i	−0.948187	+	0.317713i	$0.897085\pi$
$812$	−4890.61	+	697.670i	−0.211363	+	0.0301520i
$813$	137.381	−	332.405i	0.00592638	−	0.0143394i
$814$	2607.81	−	7820.84i	0.112289	−	0.336757i
$815$	−8569.53	+	28325.9i	−0.368316	+	1.21744i
$816$	13501.4	+	16802.8i	0.579221	+	0.720855i
$817$	−16540.3	+	16540.3i	−0.708290	+	0.708290i
$818$	26824.3	−	13408.8i	1.14656	−	0.573140i
$819$	2705.12	−	2713.64i	0.115415	−	0.115778i
$820$	23395.5	+	3585.69i	0.996350	+	0.152705i
$821$	31226.7			1.32743			0.663714	−	0.747987i	$-0.268979\pi$
$821$	31226.7			1.32743			0.663714	+	0.747987i	$0.268979\pi$
$822$	3464.82	+	3000.85i	0.147019	+	0.127332i
$823$	5296.64	+	5296.64i	0.224337	+	0.224337i	0.810322	−	0.585985i	$-0.199292\pi$
$823$	5296.64	+	5296.64i	0.224337	+	0.224337i	−0.585985	+	0.810322i	$0.699292\pi$
$824$	23165.4	+	33482.4i	0.979376	+	1.41555i
$825$	15599.0	+	23231.0i	0.658289	+	0.980362i
$826$	−3748.10	+	11240.6i	−0.157885	+	0.473498i
$827$	−2269.74	+	2269.74i	−0.0954372	+	0.0954372i	−0.753213	−	0.657776i	$-0.771497\pi$
$827$	−2269.74	+	2269.74i	−0.0954372	+	0.0954372i	0.657776	+	0.753213i	$0.271497\pi$
$828$	−20741.1	+	27734.2i	−0.870536	+	1.16404i
$829$	−5569.55			−0.233340			−0.116670	−	0.993171i	$-0.537222\pi$
$829$	−5569.55			−0.233340			−0.116670	+	0.993171i	$0.537222\pi$
$830$	308.477	+	1799.55i	0.0129005	+	0.0752569i
$831$	−9226.04	+	3830.05i	−0.385136	+	0.159883i
$832$	−7175.04	+	3248.14i	−0.298978	+	0.135347i
$833$	−11819.8	+	11819.8i	−0.491637	+	0.491637i
$834$	8825.36	−	633.296i	0.366424	−	0.0262940i
$835$	−8701.52	−	2632.50i	−0.360633	−	0.109104i
$836$	28502.8	−	37988.0i	1.17917	−	1.57158i
$837$	−38319.9	+	15978.6i	−1.58247	+	0.659860i
$838$	−24727.6	+	12360.7i	−1.01933	+	0.509539i
$839$	22042.5			0.907023			0.453512	−	0.891250i	$-0.350171\pi$
$839$	22042.5			0.907023			0.453512	+	0.891250i	$0.350171\pi$
$840$	7858.35	+	9236.51i	0.322784	+	0.379393i
$841$	19908.5			0.816291
$842$	16647.5	−	8321.70i	0.681367	−	0.340599i
$843$	43636.2	+	18034.5i	1.78281	+	0.736823i
$844$	20631.4	+	15480.0i	0.841425	+	0.631329i
$845$	−10346.3	−	19321.9i	−0.421210	−	0.786619i
$846$	−2755.96	+	1383.06i	−0.112000	+	0.0562063i
$847$	3424.89	−	3424.89i	0.138938	−	0.138938i
$848$	12590.3	−	22937.2i	0.509849	−	0.928851i
$849$	13735.2	+	33086.1i	0.555231	+	1.33747i
$850$	14075.5	+	18084.2i	0.567982	+	0.729743i
$851$	10847.6			0.436958
$852$	−18681.6	+	11076.3i	−0.751197	+	0.445387i
$853$	18865.6	−	18865.6i	0.757264	−	0.757264i	−0.218560	−	0.975824i	$-0.570136\pi$
$853$	18865.6	−	18865.6i	0.757264	−	0.757264i	0.975824	+	0.218560i	$0.0701359\pi$
$854$	770.135	−	2309.64i	0.0308589	−	0.0925461i
$855$	−39833.4	−	11982.6i	−1.59330	−	0.479294i
$856$	8104.21	−	5607.04i	0.323594	−	0.223884i
$857$	10529.8	+	10529.8i	0.419709	+	0.419709i	0.885104	−	0.465394i	$-0.154087\pi$
$857$	10529.8	+	10529.8i	0.419709	+	0.419709i	−0.465394	+	0.885104i	$0.654087\pi$
$858$	6376.54	−	7362.43i	0.253720	−	0.292948i
$859$	−6435.67			−0.255625			−0.127813	−	0.991798i	$-0.540796\pi$
$859$	−6435.67			−0.255625			−0.127813	+	0.991798i	$0.540796\pi$
$860$	−8985.77	−	12238.7i	−0.356293	−	0.485276i
$861$	−11715.8	+	4863.62i	−0.463731	+	0.192511i
$862$	−12275.3	+	6136.12i	−0.485032	+	0.242456i
$863$	−815.098	+	815.098i	−0.0321509	+	0.0321509i	−0.722999	−	0.690849i	$-0.757237\pi$
$863$	−815.098	+	815.098i	−0.0321509	+	0.0321509i	0.690849	+	0.722999i	$0.257237\pi$
$864$	10559.1	−	23097.2i	0.415772	−	0.909469i
$865$	−19733.5	−	5970.05i	−0.775676	−	0.234668i
$866$	−2050.75	+	6150.21i	−0.0804702	+	0.241331i
$867$	3417.97	+	1412.62i	0.133888	+	0.0553347i
$868$	−3084.45	−	21621.7i	−0.120614	−	0.845495i
$869$			16128.7i			0.629607i
$870$	5872.69	+	9299.70i	0.228854	+	0.362402i
$871$	−8308.81			−0.323230
$872$	7504.10	+	1366.68i	0.291423	+	0.0530754i
$873$	−30109.3	+	47.3499i	−1.16729	+	0.00183568i
$874$	59281.1	+	19766.9i	2.29429	+	0.765017i
$875$	8201.41	+	9948.04i	0.316867	+	0.384349i
$876$	8986.77	−	35163.7i	0.346615	−	1.35625i
$877$	7455.64	+	7455.64i	0.287069	+	0.287069i	0.835920	−	0.548851i	$-0.184935\pi$
$877$	7455.64	+	7455.64i	0.287069	+	0.287069i	−0.548851	+	0.835920i	$0.684935\pi$
$878$	23107.2	−	11550.7i	0.888188	−	0.443984i
$879$	−44253.8	+	18371.3i	−1.69811	+	0.704947i
$880$	21570.3	+	22022.8i	0.826288	+	0.843625i
$881$			45602.6i			1.74391i	0.489582	+	0.871957i	$0.337150\pi$
$881$			45602.6i			1.74391i	−0.489582	+	0.871957i	$0.662850\pi$
$882$	18693.1	+	6200.43i	0.713637	+	0.236711i
$883$	−8463.53	+	8463.53i	−0.322560	+	0.322560i	−0.849748	−	0.527188i	$-0.823246\pi$
$883$	−8463.53	+	8463.53i	−0.322560	+	0.322560i	0.527188	+	0.849748i	$0.323246\pi$
$884$	4787.20	−	6380.30i	0.182139	−	0.242752i
$885$	26249.8	−	2625.96i	0.997036	−	0.0997411i
$886$	9692.06	−	29066.6i	0.367507	−	1.10216i
$887$	−6290.14	−	6290.14i	−0.238109	−	0.238109i	0.577958	−	0.816067i	$-0.303850\pi$
$887$	−6290.14	−	6290.14i	−0.238109	−	0.238109i	−0.816067	+	0.577958i	$0.803850\pi$
$888$	−7774.43	+	1684.18i	−0.293798	+	0.0636458i
$889$			4803.25i			0.181210i
$890$	−18146.8	−	12835.8i	−0.683463	−	0.483435i
$891$	98.7793	+	31406.3i	0.00371407	+	1.18086i
$892$	−10378.7	+	1480.58i	−0.389581	+	0.0555757i
$893$	3934.27	+	3934.27i	0.147430	+	0.147430i
$894$	−46.7931	−	652.091i	−0.00175055	−	0.0243951i
$895$	−11286.5	−	21077.7i	−0.421525	−	0.787207i
$896$	10370.1	+	8422.88i	0.386654	+	0.314050i
$897$	11844.0	+	4895.05i	0.440870	+	0.182208i
$898$	−21519.4	−	43049.6i	−0.799681	−	1.59976i
$899$		−	19808.5i		−	0.734873i
$900$	11605.0	−	24378.8i	0.429815	−	0.902917i
$901$			26499.4i			0.979827i
$902$	−28842.5	+	14417.7i	−1.06469	+	0.532212i
$903$	7520.44	+	3108.14i	0.277148	+	0.114543i
$904$	−11567.5	+	8003.18i	−0.425585	+	0.294449i
$905$	−17789.0	−	33221.3i	−0.653399	−	1.22024i
$906$	−52160.2	+	3742.94i	−1.91270	+	0.137253i
$907$	22928.1	+	22928.1i	0.839378	+	0.839378i	0.988777	−	0.149399i	$-0.0477338\pi$
$907$	22928.1	+	22928.1i	0.839378	+	0.839378i	−0.149399	+	0.988777i	$0.547734\pi$
$908$	−4137.69	−	29004.9i	−0.151227	−	1.06009i
$909$	18357.7	+	18300.1i	0.669844	+	0.667740i
$910$	2591.51	−	3663.79i	0.0944041	−	0.133465i
$911$		−	29189.9i		−	1.06159i	−0.847501	−	0.530793i	$-0.821894\pi$
$911$		−	29189.9i		−	1.06159i	0.847501	−	0.530793i	$-0.178106\pi$
$912$	−45555.4	−	4962.92i	−1.65404	−	0.180196i
$913$	−1758.85	−	1758.85i	−0.0637562	−	0.0637562i
$914$	1703.27	+	567.944i	0.0616402	+	0.0205535i
$915$	−5393.64	+	539.567i	−0.194872	+	0.0194946i
$916$	17662.7	−	23540.5i	0.637109	−	0.849128i
$917$	−9988.15	+	9988.15i	−0.359692	+	0.359692i
$918$	1881.28	+	25651.6i	0.0676377	+	0.922255i
$919$		−	6319.38i		−	0.226830i	−0.993548	−	0.113415i	$-0.963821\pi$
$919$		−	6319.38i		−	0.226830i	0.993548	−	0.113415i	$-0.0361790\pi$
$920$	−18511.7	+	36090.9i	−0.663385	+	1.29335i
$921$	34004.6	−	14116.5i	1.21660	−	0.505053i
$922$	16909.9	+	33828.1i	0.604009	+	1.20832i
$923$	5682.98	+	5682.98i	0.202663	+	0.202663i
$924$	−16007.0	−	4090.90i	−0.569904	−	0.145650i
$925$	−8292.11	+	1662.25i	−0.294749	+	0.0590858i
$926$	7610.60	−	22824.3i	0.270086	−	0.809992i
$927$	76.4013	+	48582.8i	0.00270696	+	1.72133i
$928$	8232.16	+	8890.89i	0.291200	+	0.314502i
$929$	−22408.2			−0.791378			−0.395689	−	0.918384i	$-0.629494\pi$
$929$	−22408.2			−0.791378			−0.395689	+	0.918384i	$0.629494\pi$
$930$	−41114.6	+	25963.6i	−1.44968	+	0.915462i
$931$		−	35536.7i		−	1.25099i
$932$	4684.64	+	32838.9i	0.164646	+	1.15416i
$933$	40398.1	+	16696.3i	1.41755	+	0.585864i
$934$	−2212.03	−	737.588i	−0.0774946	−	0.0258400i
$935$	−29882.6	−	9040.49i	−1.04520	−	0.316209i
$936$	−9248.54	−	1669.37i	−0.322968	−	0.0582960i
$937$	32399.3	−	32399.3i	1.12960	−	1.12960i	0.139363	−	0.990241i	$-0.455494\pi$
$937$	32399.3	−	32399.3i	1.12960	−	1.12960i	0.990241	−	0.139363i	$-0.0445056\pi$
$938$	6301.76	+	12606.6i	0.219360	+	0.438829i
$939$	−39572.4	+	16427.9i	−1.37529	+	0.570931i
$940$	−2911.10	+	2137.35i	−0.101010	+	0.0741624i
$941$	15138.1			0.524428			0.262214	−	0.965010i	$-0.415547\pi$
$941$	15138.1			0.524428			0.262214	+	0.965010i	$0.415547\pi$
$942$	−37297.7	−	32303.2i	−1.29005	−	1.11730i
$943$	−30001.2	−	30001.2i	−1.03603	−	1.03603i
$944$	27903.1	−	8126.41i	0.962043	−	0.280182i
$945$	1463.05	+	14396.4i	0.0503631	+	0.495573i
$946$	19622.9	+	6543.11i	0.674413	+	0.224878i
$947$	5723.64	−	5723.64i	0.196403	−	0.196403i	−0.602053	−	0.798456i	$-0.705650\pi$
$947$	5723.64	−	5723.64i	0.196403	−	0.196403i	0.798456	+	0.602053i	$0.205650\pi$
$948$	13386.5	−	7936.87i	0.458621	−	0.271917i
$949$	−13430.7			−0.459408
$950$	−48344.5	−	6026.14i	−1.65105	−	0.205804i
$951$	8883.67	+	21399.5i	0.302916	+	0.729680i
$952$	−13311.4	−	2424.34i	−0.453177	−	0.0825350i
$953$	−13959.6	+	13959.6i	−0.474497	+	0.474497i	−0.903367	−	0.428869i	$-0.858912\pi$
$953$	−13959.6	+	13959.6i	−0.474497	+	0.474497i	0.428869	+	0.903367i	$0.358912\pi$
$954$	27904.9	−	14003.9i	0.947018	−	0.475255i
$955$	−4465.75	−	8339.89i	−0.151318	−	0.282589i
$956$	14935.9	−	19906.3i	0.505294	−	0.673448i
$957$	−13848.2	−	5723.34i	−0.467761	−	0.193322i
$958$	14395.7	+	28798.5i	0.485495	+	0.971230i
$959$	−2877.22			−0.0968824
$960$	7663.85	−	28740.2i	0.257656	−	0.966237i
$961$	57783.8			1.93964
$962$	1316.20	+	2633.04i	0.0441121	+	0.0882461i
$963$	11759.2	−	18.4924i	0.393493	−	0.000618807i
$964$	2127.36	−	2835.31i	0.0710764	−	0.0947295i
$965$	27137.2	+	8209.91i	0.905262	+	0.273872i
$966$	−1555.95	−	21683.1i	−0.0518239	−	0.722197i
$967$	−10085.1	+	10085.1i	−0.335382	+	0.335382i	−0.854626	−	0.519244i	$-0.826214\pi$
$967$	−10085.1	+	10085.1i	−0.335382	+	0.335382i	0.519244	+	0.854626i	$0.326214\pi$
$968$	−11687.6	−	2128.60i	−0.388072	−	0.0706776i
$969$	42863.2	−	17794.0i	1.42101	−	0.589913i
$970$	−34757.5	+	5958.11i	−1.15051	+	0.197220i
$971$	−28852.3			−0.953567			−0.476784	−	0.879021i	$-0.658198\pi$
$971$	−28852.3			−0.953567			−0.476784	+	0.879021i	$0.658198\pi$
$972$	26018.0	−	15536.9i	0.858566	−	0.512703i
$973$	−3927.28	+	3927.28i	−0.129396	+	0.129396i
$974$	7534.57	+	2512.35i	0.247868	+	0.0826499i
$975$	−9803.87	−	1926.93i	−0.322026	−	0.0632934i
$976$	−5733.36	+	1669.76i	−0.188033	+	0.0547622i
$977$	13243.9	+	13243.9i	0.433683	+	0.433683i	0.889879	−	0.456196i	$-0.150788\pi$
$977$	13243.9	+	13243.9i	0.433683	+	0.433683i	−0.456196	+	0.889879i	$0.650788\pi$
$978$	−25468.5	+	29406.2i	−0.832712	+	0.961459i
$979$	30281.9			0.988574
$980$	22800.3	+	3494.47i	0.743193	+	0.113905i
$981$	6445.85	+	6425.60i	0.209786	+	0.209127i
$982$	−6846.68	−	13696.8i	−0.222491	−	0.445093i
$983$	−8645.36	+	8645.36i	−0.280513	+	0.280513i	−0.833313	−	0.552801i	$-0.813559\pi$
$983$	−8645.36	+	8645.36i	−0.280513	+	0.280513i	0.552801	+	0.833313i	$0.313559\pi$
$984$	26159.6	+	16843.8i	0.847499	+	0.545690i
$985$	−598.545	+	1978.44i	−0.0193616	+	0.0639983i
$986$	−11641.3	−	3881.73i	−0.376000	−	0.125375i
$987$	739.301	−	1788.81i	0.0238422	−	0.0576883i
$988$	2394.85	+	16787.7i	0.0771158	+	0.540575i
$989$			27217.2i			0.875083i
$990$	6271.78	+	36245.0i	0.201344	+	1.16358i
$991$	−33546.1			−1.07531			−0.537653	−	0.843166i	$-0.680689\pi$
$991$	−33546.1			−1.07531			−0.537653	+	0.843166i	$0.680689\pi$
$992$	−39307.2	+	36394.9i	−1.25807	+	1.16486i
$993$	−1091.04	−	450.919i	−0.0348672	−	0.0144103i
$994$	4312.35	−	12932.8i	0.137605	−	0.412679i
$995$	3976.88	+	7426.92i	0.126709	+	0.236632i
$996$	−594.284	+	2325.33i	−0.0189062	+	0.0739769i
$997$	2395.65	+	2395.65i	0.0760993	+	0.0760993i	0.744132	−	0.668033i	$-0.232863\pi$
$997$	2395.65	+	2395.65i	0.0760993	+	0.0760993i	−0.668033	+	0.744132i	$0.732863\pi$
$998$	−5613.49	−	11229.8i	−0.178048	−	0.356184i
$999$	−8777.97	−	3611.72i	−0.278001	−	0.114384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.w.c.53.42	yes	128
3.2	odd	2	inner	120.4.w.c.53.23	yes	128
5.2	odd	4	inner	120.4.w.c.77.10	yes	128
8.5	even	2	inner	120.4.w.c.53.55	yes	128
15.2	even	4	inner	120.4.w.c.77.55	yes	128
24.5	odd	2	inner	120.4.w.c.53.10	✓	128
40.37	odd	4	inner	120.4.w.c.77.23	yes	128
120.77	even	4	inner	120.4.w.c.77.42	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.w.c.53.10	✓	128	24.5	odd	2	inner
120.4.w.c.53.23	yes	128	3.2	odd	2	inner
120.4.w.c.53.42	yes	128	1.1	even	1	trivial
120.4.w.c.53.55	yes	128	8.5	even	2	inner
120.4.w.c.77.10	yes	128	5.2	odd	4	inner
120.4.w.c.77.23	yes	128	40.37	odd	4	inner
120.4.w.c.77.42	yes	128	120.77	even	4	inner
120.4.w.c.77.55	yes	128	15.2	even	4	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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26466 + 2.52995i) q^{2} +(-1.98471 + 4.80218i) q^{3} +(-4.80127 + 6.39905i) q^{4} +(-9.85625 + 5.27772i) q^{5} +(-14.6592 + 1.05193i) q^{6} +(6.52335 - 6.52335i) q^{7} +(-22.2612 - 4.05433i) q^{8} +(-19.1219 - 19.0618i) q^{9} +(-25.8172 - 18.2613i) q^{10} +43.0815 q^{11} +(-21.2003 - 35.7568i) q^{12} +(-10.8773 + 10.8773i) q^{13} +(24.7535 + 8.25390i) q^{14} +(-5.78279 - 57.8062i) q^{15} +(-17.8957 - 61.4471i) q^{16} +(45.8326 + 45.8326i) q^{17} +(24.0427 - 72.4841i) q^{18} -137.797 q^{19} +(13.5501 - 88.4104i) q^{20} +(18.3794 + 44.2732i) q^{21} +(54.4835 + 108.994i) q^{22} +(-113.373 + 113.373i) q^{23} +(63.6516 - 98.8558i) q^{24} +(69.2914 - 104.037i) q^{25} +(-41.2751 - 13.7629i) q^{26} +(129.490 - 53.9946i) q^{27} +(10.4229 + 73.0635i) q^{28} +66.9364i q^{29} +(138.933 - 87.7354i) q^{30} -295.930 q^{31} +(132.826 - 122.985i) q^{32} +(-85.5042 + 206.885i) q^{33} +(-57.9913 + 173.917i) q^{34} +(-29.8674 + 98.7241i) q^{35} +(213.787 - 30.8409i) q^{36} +(-47.8404 - 47.8404i) q^{37} +(-174.266 - 348.619i) q^{38} +(-30.6465 - 73.8231i) q^{39} +(240.810 - 77.5280i) q^{40} +264.624i q^{41} +(-88.7652 + 102.489i) q^{42} +(120.034 - 120.034i) q^{43} +(-206.846 + 275.681i) q^{44} +(289.073 + 86.9583i) q^{45} +(-430.206 - 143.449i) q^{46} +(-28.5512 - 28.5512i) q^{47} +(330.598 + 36.0162i) q^{48} +257.892i q^{49} +(350.838 + 43.7320i) q^{50} +(-311.060 + 129.132i) q^{51} +(-17.3796 - 121.829i) q^{52} +(289.090 + 289.090i) q^{53} +(300.364 + 259.317i) q^{54} +(-424.623 + 227.372i) q^{55} +(-171.666 + 118.770i) q^{56} +(273.486 - 661.726i) q^{57} +(-169.345 + 84.6518i) q^{58} +454.100i q^{59} +(397.670 + 240.539i) q^{60} -93.3056i q^{61} +(-374.252 - 748.688i) q^{62} +(-249.086 + 0.391712i) q^{63} +(479.125 + 180.509i) q^{64} +(49.8021 - 164.617i) q^{65} +(-631.543 + 45.3186i) q^{66} +(381.933 + 381.933i) q^{67} +(-513.339 + 73.2304i) q^{68} +(-319.425 - 769.449i) q^{69} +(-287.539 + 49.2897i) q^{70} -522.462i q^{71} +(348.394 + 501.866i) q^{72} +(617.372 + 617.372i) q^{73} +(60.5319 - 181.536i) q^{74} +(362.082 + 539.233i) q^{75} +(661.600 - 881.770i) q^{76} +(281.036 - 281.036i) q^{77} +(148.011 - 170.895i) q^{78} +374.376i q^{79} +(500.685 + 511.190i) q^{80} +(2.29285 + 728.996i) q^{81} +(-669.485 + 334.660i) q^{82} +(-40.8261 - 40.8261i) q^{83} +(-371.551 - 94.9571i) q^{84} +(-693.628 - 209.846i) q^{85} +(455.482 + 151.877i) q^{86} +(-321.441 - 132.849i) q^{87} +(-959.048 - 174.667i) q^{88} +702.897 q^{89} +(145.579 + 841.312i) q^{90} +141.913i q^{91} +(-181.145 - 1269.81i) q^{92} +(587.335 - 1421.11i) q^{93} +(36.1255 - 108.341i) q^{94} +(1358.16 - 727.254i) q^{95} +(326.975 + 881.943i) q^{96} +(788.538 - 788.538i) q^{97} +(-652.453 + 326.146i) q^{98} +(-823.800 - 821.213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{6} - 144 q^{7} - 156 q^{10} - 56 q^{12} + 212 q^{15} + 636 q^{16} + 220 q^{18} - 188 q^{22} - 8 q^{25} + 908 q^{28} + 328 q^{30} - 544 q^{31} - 1624 q^{33} - 1268 q^{36} - 136 q^{40} + 328 q^{42}+ \cdots - 3792 q^{97}+O(q^{100}) \) 128 * q - 4 * q^6 - 144 * q^7 - 156 * q^10 - 56 * q^12 + 212 * q^15 + 636 * q^16 + 220 * q^18 - 188 * q^22 - 8 * q^25 + 908 * q^28 + 328 * q^30 - 544 * q^31 - 1624 * q^33 - 1268 * q^36 - 136 * q^40 + 328 * q^42 + 568 * q^46 - 148 * q^48 + 616 * q^52 + 728 * q^55 - 112 * q^57 + 2196 * q^58 - 424 * q^60 - 2304 * q^63 + 304 * q^66 - 4740 * q^70 + 224 * q^72 + 1280 * q^73 - 1624 * q^76 - 1448 * q^78 + 7056 * q^81 - 1472 * q^82 - 5720 * q^87 + 1516 * q^88 - 996 * q^90 + 2732 * q^96 - 3792 * q^97

Introduction

L-functions

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