LMFDB - Embedded newform 80.3.k.a.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(19,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("80.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.k (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:	$2.17984211488$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	80.19
Dual form			80.3.k.a.59.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456673 + 1.94716i) q^{2} +(3.41958 + 3.41958i) q^{3} +(-3.58290 + 1.77844i) q^{4} +(4.54060 - 2.09356i) q^{5} +(-5.09686 + 8.22013i) q^{6} -7.35293i q^{7} +(-5.09912 - 6.16433i) q^{8} +14.3871i q^{9} +O(q^{10})$	\(q+(0.456673 + 1.94716i) q^{2} +(3.41958 + 3.41958i) q^{3} +(-3.58290 + 1.77844i) q^{4} +(4.54060 - 2.09356i) q^{5} +(-5.09686 + 8.22013i) q^{6} -7.35293i q^{7} +(-5.09912 - 6.16433i) q^{8} +14.3871i q^{9} +(6.15007 + 7.88522i) q^{10} +(-13.7976 - 13.7976i) q^{11} +(-18.3335 - 6.17052i) q^{12} +(-0.172924 + 0.172924i) q^{13} +(14.3174 - 3.35789i) q^{14} +(22.6860 + 8.36787i) q^{15} +(9.67434 - 12.7439i) q^{16} +13.5885i q^{17} +(-28.0141 + 6.57021i) q^{18} +(-10.7415 + 10.7415i) q^{19} +(-12.5452 + 15.5762i) q^{20} +(25.1440 - 25.1440i) q^{21} +(20.5652 - 33.1672i) q^{22} +20.0028i q^{23} +(3.64258 - 38.5163i) q^{24} +(16.2340 - 19.0120i) q^{25} +(-0.415682 - 0.257742i) q^{26} +(-18.4217 + 18.4217i) q^{27} +(13.0767 + 26.3448i) q^{28} +(8.70697 + 8.70697i) q^{29} +(-5.93350 + 47.9948i) q^{30} -20.8930i q^{31} +(29.2325 + 13.0177i) q^{32} -94.3641i q^{33} +(-26.4591 + 6.20552i) q^{34} +(-15.3938 - 33.3867i) q^{35} +(-25.5866 - 51.5476i) q^{36} +(7.82521 + 7.82521i) q^{37} +(-25.8207 - 16.0101i) q^{38} -1.18266 q^{39} +(-36.0584 - 17.3145i) q^{40} +16.6751i q^{41} +(60.4420 + 37.4769i) q^{42} +(-45.9385 + 45.9385i) q^{43} +(73.9736 + 24.8973i) q^{44} +(30.1202 + 65.3261i) q^{45} +(-38.9488 + 9.13476i) q^{46} -15.2450 q^{47} +(76.6611 - 10.4967i) q^{48} -5.06563 q^{49} +(44.4331 + 22.9281i) q^{50} +(-46.4672 + 46.4672i) q^{51} +(0.312035 - 0.927104i) q^{52} +(31.3522 + 31.3522i) q^{53} +(-44.2828 - 27.4574i) q^{54} +(-91.5354 - 33.7633i) q^{55} +(-45.3259 + 37.4935i) q^{56} -73.4627 q^{57} +(-12.9777 + 20.9302i) q^{58} +(36.3791 + 36.3791i) q^{59} +(-96.1635 + 10.3644i) q^{60} +(-49.0967 - 49.0967i) q^{61} +(40.6821 - 9.54127i) q^{62} +105.788 q^{63} +(-11.9980 + 62.8653i) q^{64} +(-0.423152 + 1.14721i) q^{65} +(183.742 - 43.0936i) q^{66} +(-40.5551 - 40.5551i) q^{67} +(-24.1663 - 48.6864i) q^{68} +(-68.4014 + 68.4014i) q^{69} +(57.9795 - 45.2210i) q^{70} +69.2289 q^{71} +(88.6870 - 73.3616i) q^{72} -15.8463 q^{73} +(-11.6634 + 18.8105i) q^{74} +(120.527 - 9.49940i) q^{75} +(19.3826 - 57.5886i) q^{76} +(-101.453 + 101.453i) q^{77} +(-0.540088 - 2.30283i) q^{78} -134.066i q^{79} +(17.2472 - 78.1187i) q^{80} +3.49487 q^{81} +(-32.4692 + 7.61507i) q^{82} +(1.71167 + 1.71167i) q^{83} +(-45.3714 + 134.805i) q^{84} +(28.4484 + 61.7001i) q^{85} +(-110.429 - 68.4710i) q^{86} +59.5485i q^{87} +(-14.6974 + 155.409i) q^{88} -53.2048i q^{89} +(-113.446 + 88.4817i) q^{90} +(1.27150 + 1.27150i) q^{91} +(-35.5738 - 71.6682i) q^{92} +(71.4454 - 71.4454i) q^{93} +(-6.96199 - 29.6846i) q^{94} +(-26.2848 + 71.2605i) q^{95} +(55.4478 + 144.478i) q^{96} -68.6846i q^{97} +(-2.31334 - 9.86362i) q^{98} +(198.508 - 198.508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6} - 20 q^{10} - 4 q^{11} + 4 q^{14} - 32 q^{16} - 36 q^{19} + 40 q^{20} + 32 q^{21} + 16 q^{24} - 56 q^{26} - 4 q^{29} - 160 q^{30} - 192 q^{34} + 212 q^{36} - 8 q^{39} - 184 q^{40} + 224 q^{44} + 30 q^{45} + 124 q^{46} - 148 q^{49} + 100 q^{50} + 128 q^{51} + 24 q^{54} - 260 q^{55} + 360 q^{56} - 68 q^{59} - 80 q^{60} + 28 q^{61} - 16 q^{64} - 20 q^{65} + 448 q^{66} + 128 q^{69} + 396 q^{70} - 264 q^{71} + 480 q^{74} + 60 q^{75} - 464 q^{76} + 504 q^{80} - 116 q^{81} - 496 q^{84} + 48 q^{85} - 852 q^{86} + 144 q^{90} + 384 q^{91} - 340 q^{94} - 1128 q^{96} + 484 q^{99}+O(q^{100}) $ 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 - 20 * q^10 - 4 * q^11 + 4 * q^14 - 32 * q^16 - 36 * q^19 + 40 * q^20 + 32 * q^21 + 16 * q^24 - 56 * q^26 - 4 * q^29 - 160 * q^30 - 192 * q^34 + 212 * q^36 - 8 * q^39 - 184 * q^40 + 224 * q^44 + 30 * q^45 + 124 * q^46 - 148 * q^49 + 100 * q^50 + 128 * q^51 + 24 * q^54 - 260 * q^55 + 360 * q^56 - 68 * q^59 - 80 * q^60 + 28 * q^61 - 16 * q^64 - 20 * q^65 + 448 * q^66 + 128 * q^69 + 396 * q^70 - 264 * q^71 + 480 * q^74 + 60 * q^75 - 464 * q^76 + 504 * q^80 - 116 * q^81 - 496 * q^84 + 48 * q^85 - 852 * q^86 + 144 * q^90 + 384 * q^91 - 340 * q^94 - 1128 * q^96 + 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.456673	+	1.94716i	0.228337	+	0.973582i
$2$	0.456673	+	1.94716i	0.228337	+	0.973582i
$3$	3.41958	+	3.41958i	1.13986	+	1.13986i	0.988475	+	0.151387i	$0.0483740\pi$
$3$	3.41958	+	3.41958i	1.13986	+	1.13986i	0.151387	+	0.988475i	$0.451626\pi$
$4$	−3.58290	+	1.77844i	−0.895725	+	0.444609i
$5$	4.54060	−	2.09356i	0.908119	−	0.418711i
$5$	4.54060	−	2.09356i	0.908119	−	0.418711i
$6$	−5.09686	+	8.22013i	−0.849477	+	1.37002i
$7$		−	7.35293i		−	1.05042i	−0.850973	−	0.525210i	$-0.823987\pi$
$7$		−	7.35293i		−	1.05042i	0.850973	−	0.525210i	$-0.176013\pi$
$8$	−5.09912	−	6.16433i	−0.637390	−	0.770541i
$9$			14.3871i			1.59857i
$10$	6.15007	+	7.88522i	0.615007	+	0.788522i
$11$	−13.7976	−	13.7976i	−1.25433	−	1.25433i	−0.953761	−	0.300566i	$-0.902824\pi$
$11$	−13.7976	−	13.7976i	−1.25433	−	1.25433i	−0.300566	−	0.953761i	$-0.597176\pi$
$12$	−18.3335	−	6.17052i	−1.52779	−	0.514210i
$13$	−0.172924	+	0.172924i	−0.0133019	+	0.0133019i	−0.713726	−	0.700425i	$-0.752994\pi$
$13$	−0.172924	+	0.172924i	−0.0133019	+	0.0133019i	0.700425	+	0.713726i	$0.252994\pi$
$14$	14.3174	−	3.35789i	1.02267	−	0.239849i
$15$	22.6860	+	8.36787i	1.51240	+	0.557858i
$16$	9.67434	−	12.7439i	0.604646	−	0.796494i
$17$			13.5885i			0.799326i	0.916662	+	0.399663i	$0.130873\pi$
$17$			13.5885i			0.799326i	−0.916662	+	0.399663i	$0.869127\pi$
$18$	−28.0141	+	6.57021i	−1.55634	+	0.365012i
$19$	−10.7415	+	10.7415i	−0.565340	+	0.565340i	−0.930819	−	0.365479i	$-0.880905\pi$
$19$	−10.7415	+	10.7415i	−0.565340	+	0.565340i	0.365479	+	0.930819i	$0.380905\pi$
$20$	−12.5452	+	15.5762i	−0.627262	+	0.778808i
$21$	25.1440	−	25.1440i	1.19733	−	1.19733i
$22$	20.5652	−	33.1672i	0.934782	−	1.50760i
$23$			20.0028i			0.869689i	0.900506	+	0.434844i	$0.143197\pi$
$23$			20.0028i			0.869689i	−0.900506	+	0.434844i	$0.856803\pi$
$24$	3.64258	−	38.5163i	0.151774	−	1.60485i
$25$	16.2340	−	19.0120i	0.649362	−	0.760480i
$26$	−0.415682	−	0.257742i	−0.0159878	−	0.00991315i
$27$	−18.4217	+	18.4217i	−0.682286	+	0.682286i
$28$	13.0767	+	26.3448i	0.467026	+	0.940886i
$29$	8.70697	+	8.70697i	0.300241	+	0.300241i	0.841108	−	0.540867i	$-0.181904\pi$
$29$	8.70697	+	8.70697i	0.300241	+	0.300241i	−0.540867	+	0.841108i	$0.681904\pi$
$30$	−5.93350	+	47.9948i	−0.197783	+	1.59983i
$31$		−	20.8930i		−	0.673968i	−0.941510	−	0.336984i	$-0.890593\pi$
$31$		−	20.8930i		−	0.673968i	0.941510	−	0.336984i	$-0.109407\pi$
$32$	29.2325	+	13.0177i	0.913516	+	0.406804i
$33$		−	94.3641i		−	2.85952i
$34$	−26.4591	+	6.20552i	−0.778210	+	0.182515i
$35$	−15.3938	−	33.3867i	−0.439822	−	0.953906i
$36$	−25.5866	−	51.5476i	−0.710738	−	1.43188i
$37$	7.82521	+	7.82521i	0.211492	+	0.211492i	0.804901	−	0.593409i	$-0.202218\pi$
$37$	7.82521	+	7.82521i	0.211492	+	0.211492i	−0.593409	+	0.804901i	$0.702218\pi$
$38$	−25.8207	−	16.0101i	−0.679493	−	0.421317i
$39$	−1.18266			−0.0303245
$40$	−36.0584	−	17.3145i	−0.901461	−	0.432861i
$41$			16.6751i			0.406710i	0.979105	+	0.203355i	$0.0651846\pi$
$41$			16.6751i			0.406710i	−0.979105	+	0.203355i	$0.934815\pi$
$42$	60.4420	+	37.4769i	1.43910	+	0.892307i
$43$	−45.9385	+	45.9385i	−1.06834	+	1.06834i	−0.0708509	+	0.997487i	$0.522571\pi$
$43$	−45.9385	+	45.9385i	−1.06834	+	1.06834i	−0.997487	+	0.0708509i	$0.977429\pi$
$44$	73.9736	+	24.8973i	1.68122	+	0.565847i
$45$	30.1202	+	65.3261i	0.669339	+	1.45169i
$46$	−38.9488	+	9.13476i	−0.846714	+	0.198582i
$47$	−15.2450			−0.324362			−0.162181	−	0.986761i	$-0.551853\pi$
$47$	−15.2450			−0.324362			−0.162181	+	0.986761i	$0.551853\pi$
$48$	76.6611	−	10.4967i	1.59711	−	0.218681i
$49$	−5.06563			−0.103380
$50$	44.4331	+	22.9281i	0.888662	+	0.458562i
$51$	−46.4672	+	46.4672i	−0.911121	+	0.911121i
$52$	0.312035	−	0.927104i	0.00600068	−	0.0178289i
$53$	31.3522	+	31.3522i	0.591552	+	0.591552i	0.938050	−	0.346499i	$-0.112629\pi$
$53$	31.3522	+	31.3522i	0.591552	+	0.591552i	−0.346499	+	0.938050i	$0.612629\pi$
$54$	−44.2828	−	27.4574i	−0.820052	−	0.508470i
$55$	−91.5354	−	33.7633i	−1.66428	−	0.613878i
$56$	−45.3259	+	37.4935i	−0.809391	+	0.669527i
$57$	−73.4627			−1.28882
$58$	−12.9777	+	20.9302i	−0.223753	+	0.360865i
$59$	36.3791	+	36.3791i	0.616595	+	0.616595i	0.944656	−	0.328062i	$-0.106395\pi$
$59$	36.3791	+	36.3791i	0.616595	+	0.616595i	−0.328062	+	0.944656i	$0.606395\pi$
$60$	−96.1635	+	10.3644i	−1.60273	+	0.172741i
$61$	−49.0967	−	49.0967i	−0.804864	−	0.804864i	0.178988	−	0.983851i	$-0.442718\pi$
$61$	−49.0967	−	49.0967i	−0.804864	−	0.804864i	−0.983851	+	0.178988i	$0.942718\pi$
$62$	40.6821	−	9.54127i	0.656163	−	0.153892i
$63$	105.788			1.67917
$64$	−11.9980	+	62.8653i	−0.187468	+	0.982271i
$65$	−0.423152	+	1.14721i	−0.00651004	+	0.0176493i
$66$	183.742	−	43.0936i	2.78398	−	0.652933i
$67$	−40.5551	−	40.5551i	−0.605299	−	0.605299i	0.336415	−	0.941714i	$-0.390786\pi$
$67$	−40.5551	−	40.5551i	−0.605299	−	0.605299i	−0.941714	+	0.336415i	$0.890786\pi$
$68$	−24.1663	−	48.6864i	−0.355387	−	0.715976i
$69$	−68.4014	+	68.4014i	−0.991325	+	0.991325i
$70$	57.9795	−	45.2210i	0.828278	−	0.646015i
$71$	69.2289			0.975055			0.487528	−	0.873108i	$-0.337899\pi$
$71$	69.2289			0.975055			0.487528	+	0.873108i	$0.337899\pi$
$72$	88.6870	−	73.3616i	1.23176	−	1.01891i
$73$	−15.8463			−0.217073			−0.108536	−	0.994092i	$-0.534616\pi$
$73$	−15.8463			−0.217073			−0.108536	+	0.994092i	$0.534616\pi$
$74$	−11.6634	+	18.8105i	−0.157614	+	0.254196i
$75$	120.527	−	9.49940i	1.60702	−	0.126659i
$76$	19.3826	−	57.5886i	0.255034	−	0.757745i
$77$	−101.453	+	101.453i	−1.31757	+	1.31757i
$78$	−0.540088	−	2.30283i	−0.00692420	−	0.0295234i
$79$		−	134.066i		−	1.69703i	−0.529169	−	0.848516i	$-0.677496\pi$
$79$		−	134.066i		−	1.69703i	0.529169	−	0.848516i	$-0.322504\pi$
$80$	17.2472	−	78.1187i	0.215590	−	0.976484i
$81$	3.49487			0.0431465
$82$	−32.4692	+	7.61507i	−0.395966	+	0.0928668i
$83$	1.71167	+	1.71167i	0.0206226	+	0.0206226i	0.717343	−	0.696720i	$-0.245358\pi$
$83$	1.71167	+	1.71167i	0.0206226	+	0.0206226i	−0.696720	+	0.717343i	$0.745358\pi$
$84$	−45.3714	+	134.805i	−0.540136	+	1.60482i
$85$	28.4484	+	61.7001i	0.334687	+	0.725884i
$86$	−110.429	−	68.4710i	−1.28406	−	0.796174i
$87$			59.5485i			0.684465i
$88$	−14.6974	+	155.409i	−0.167015	+	1.76601i
$89$		−	53.2048i		−	0.597806i	−0.954283	−	0.298903i	$-0.903379\pi$
$89$		−	53.2048i		−	0.597806i	0.954283	−	0.298903i	$-0.0966207\pi$
$90$	−113.446	+	88.4817i	−1.26051	+	0.983130i
$91$	1.27150	+	1.27150i	0.0139725	+	0.0139725i
$92$	−35.5738	−	71.6682i	−0.386671	−	0.779002i
$93$	71.4454	−	71.4454i	0.768230	−	0.768230i
$94$	−6.96199	−	29.6846i	−0.0740637	−	0.315793i
$95$	−26.2848	+	71.2605i	−0.276682	+	0.750111i
$96$	55.4478	+	144.478i	0.577581	+	1.50498i
$97$		−	68.6846i		−	0.708089i	−0.935229	−	0.354045i	$-0.884806\pi$
$97$		−	68.6846i		−	0.708089i	0.935229	−	0.354045i	$-0.115194\pi$
$98$	−2.31334	−	9.86362i	−0.0236055	−	0.100649i
$99$	198.508	−	198.508i	2.00513	−	2.00513i
$100$	−24.3534	+	96.9892i	−0.243534	+	0.969892i
$101$	56.3580	−	56.3580i	0.558000	−	0.558000i	−0.370737	−	0.928738i	$-0.620895\pi$
$101$	56.3580	−	56.3580i	0.558000	−	0.558000i	0.928738	+	0.370737i	$0.120895\pi$
$102$	−111.700	−	69.2589i	−1.09509	−	0.679009i
$103$		−	132.524i		−	1.28664i	−0.765599	−	0.643318i	$-0.777557\pi$
$103$		−	132.524i		−	1.28664i	0.765599	−	0.643318i	$-0.222443\pi$
$104$	1.94772	+	0.184201i	0.0187281	+	0.00177116i
$105$	61.5284	−	166.809i	0.585984	−	1.58866i
$106$	−46.7303	+	75.3657i	−0.440851	+	0.710997i
$107$	−27.2465	+	27.2465i	−0.254640	+	0.254640i	−0.822870	−	0.568230i	$-0.807629\pi$
$107$	−27.2465	+	27.2465i	−0.254640	+	0.254640i	0.568230	+	0.822870i	$0.307629\pi$
$108$	33.2413	−	98.7650i	0.307790	−	0.914490i
$109$	−5.51578	−	5.51578i	−0.0506034	−	0.0506034i	0.681352	−	0.731956i	$-0.261392\pi$
$109$	−5.51578	−	5.51578i	−0.0506034	−	0.0506034i	−0.731956	+	0.681352i	$0.761392\pi$
$110$	23.9409	−	193.653i	0.217645	−	1.76048i
$111$			53.5179i			0.482143i
$112$	−93.7051	−	71.1347i	−0.836653	−	0.635132i
$113$			104.004i			0.920390i	0.887818	+	0.460195i	$0.152221\pi$
$113$			104.004i			0.920390i	−0.887818	+	0.460195i	$0.847779\pi$
$114$	−33.5484	−	143.044i	−0.294285	−	1.25477i
$115$	41.8771	+	90.8249i	0.364148	+	0.789781i
$116$	−46.6810	−	15.7114i	−0.402422	−	0.135443i
$117$	−2.48788	−	2.48788i	−0.0212639	−	0.0212639i
$118$	−54.2227	+	87.4494i	−0.459515	+	0.741097i
$119$	99.9157			0.839628
$120$	−64.0966	−	182.513i	−0.534138	−	1.52094i
$121$			259.748i			2.14667i
$122$	73.1782	−	118.020i	0.599821	−	0.967381i
$123$	−57.0220	+	57.0220i	−0.463593	+	0.463593i
$124$	37.1569	+	74.8575i	0.299652	+	0.603690i
$125$	33.9096	−	120.313i	0.271277	−	0.962501i
$126$	48.3103	+	205.986i	0.383415	+	1.63481i
$127$	20.2694			0.159601			0.0798007	−	0.996811i	$-0.474572\pi$
$127$	20.2694			0.159601			0.0798007	+	0.996811i	$0.474572\pi$
$128$	−127.888	+	5.34691i	−0.999127	+	0.0417727i
$129$	−314.181			−2.43551
$130$	−2.42704	−	0.300050i	−0.0186695	−	0.00230808i
$131$	−161.802	+	161.802i	−1.23513	+	1.23513i	−0.273166	+	0.961967i	$0.588071\pi$
$131$	−161.802	+	161.802i	−1.23513	+	1.23513i	−0.961967	+	0.273166i	$0.911929\pi$
$132$	167.820	+	338.097i	1.27137	+	2.56134i
$133$	78.9813	+	78.9813i	0.593844	+	0.593844i
$134$	60.4470	−	97.4878i	0.451097	−	0.727521i
$135$	−45.0787	+	122.212i	−0.333916	+	0.905277i
$136$	83.7643	−	69.2896i	0.615914	−	0.509483i
$137$	232.781			1.69913			0.849567	−	0.527480i	$-0.176863\pi$
$137$	232.781			1.69913			0.849567	+	0.527480i	$0.176863\pi$
$138$	−164.426	−	101.952i	−1.19149	−	0.738781i
$139$	−15.4818	−	15.4818i	−0.111380	−	0.111380i	0.649220	−	0.760600i	$-0.275095\pi$
$139$	−15.4818	−	15.4818i	−0.111380	−	0.111380i	−0.760600	+	0.649220i	$0.775095\pi$
$140$	114.530	+	92.2444i	0.818075	+	0.658888i
$141$	−52.1316	−	52.1316i	−0.369728	−	0.369728i
$142$	31.6150	+	134.800i	0.222641	+	0.949297i
$143$	4.77188			0.0333698
$144$	183.348	+	139.186i	1.27325	+	0.966568i
$145$	57.7634	+	21.3063i	0.398368	+	0.146940i
$146$	−7.23658	−	30.8554i	−0.0495656	−	0.211338i
$147$	−17.3224	−	17.3224i	−0.117839	−	0.117839i
$148$	−41.9536	−	14.1203i	−0.283470	−	0.0954075i
$149$	−42.5783	+	42.5783i	−0.285760	+	0.285760i	−0.835401	−	0.549641i	$-0.814765\pi$
$149$	−42.5783	+	42.5783i	−0.285760	+	0.285760i	0.549641	+	0.835401i	$0.314765\pi$
$150$	73.5383	+	230.347i	0.490255	+	1.53565i
$151$	252.529			1.67238			0.836189	−	0.548441i	$-0.184779\pi$
$151$	252.529			1.67238			0.836189	+	0.548441i	$0.184779\pi$
$152$	120.986	+	11.4419i	0.795960	+	0.0752759i
$153$	−195.500			−1.27778
$154$	−243.876	−	151.215i	−1.58361	−	0.981913i
$155$	−43.7407	−	94.8667i	−0.282198	−	0.612043i
$156$	4.23734	−	2.10328i	0.0271625	−	0.0134826i
$157$	59.0447	−	59.0447i	0.376081	−	0.376081i	−0.493605	−	0.869686i	$-0.664321\pi$
$157$	59.0447	−	59.0447i	0.376081	−	0.376081i	0.869686	+	0.493605i	$0.164321\pi$
$158$	261.048	−	61.2241i	1.65220	−	0.387495i
$159$			214.423i			1.34857i
$160$	159.986	−	2.09162i	0.999915	−	0.0130727i
$161$	147.080			0.913538
$162$	1.59601	+	6.80508i	0.00985193	+	0.0420067i
$163$	−21.3758	−	21.3758i	−0.131140	−	0.131140i	0.638490	−	0.769630i	$-0.279559\pi$
$163$	−21.3758	−	21.3758i	−0.131140	−	0.131140i	−0.769630	+	0.638490i	$0.779559\pi$
$164$	−29.6556	−	59.7452i	−0.180827	−	0.364300i
$165$	−197.557	−	428.470i	−1.19731	−	2.59678i
$166$	−2.55123	+	4.11458i	−0.0153689	+	0.0247866i
$167$			91.5857i			0.548417i	0.961670	+	0.274209i	$0.0884159\pi$
$167$			91.5857i			0.548417i	−0.961670	+	0.274209i	$0.911584\pi$
$168$	−283.208	−	26.7837i	−1.68576	−	0.159426i
$169$			168.940i			0.999646i
$170$	−107.149	+	83.5705i	−0.630286	+	0.491591i
$171$	−154.539	−	154.539i	−0.903735	−	0.903735i
$172$	82.8944	−	246.292i	0.481944	−	1.43193i
$173$	−197.133	+	197.133i	−1.13950	+	1.13950i	−0.150959	+	0.988540i	$0.548236\pi$
$173$	−197.133	+	197.133i	−1.13950	+	1.13950i	−0.988540	+	0.150959i	$0.951764\pi$
$174$	−115.951	+	27.1942i	−0.666383	+	0.156288i
$175$	−139.794	−	119.368i	−0.798822	−	0.682102i
$176$	−309.318	+	42.3527i	−1.75749	+	0.240641i
$177$			248.803i			1.40567i
$178$	103.598	−	24.2972i	0.582014	−	0.136501i
$179$	−20.2343	+	20.2343i	−0.113041	+	0.113041i	−0.761365	−	0.648324i	$-0.775470\pi$
$179$	−20.2343	+	20.2343i	−0.113041	+	0.113041i	0.648324	+	0.761365i	$0.275470\pi$
$180$	−224.096	−	180.490i	−1.24498	−	1.00272i
$181$	68.7502	−	68.7502i	0.379835	−	0.379835i	−0.491207	−	0.871043i	$-0.663444\pi$
$181$	68.7502	−	68.7502i	0.379835	−	0.379835i	0.871043	+	0.491207i	$0.163444\pi$
$182$	−1.89516	+	3.05648i	−0.0104130	+	0.0167938i
$183$		−	335.781i		−	1.83487i
$184$	123.304	−	101.997i	0.670131	−	0.554331i
$185$	51.9136	+	19.1486i	0.280614	+	0.103506i
$186$	171.743	+	106.489i	0.923350	+	0.572520i
$187$	187.489	−	187.489i	1.00262	−	1.00262i
$188$	54.6214	−	27.1123i	0.290539	−	0.144214i
$189$	135.454	+	135.454i	0.716686	+	0.716686i
$190$	−150.760	−	18.6381i	−0.793471	−	0.0980952i
$191$			49.8857i			0.261182i	0.991436	+	0.130591i	$0.0416874\pi$
$191$			49.8857i			0.261182i	−0.991436	+	0.130591i	$0.958313\pi$
$192$	−256.001	+	173.945i	−1.33334	+	0.905965i
$193$		−	99.2548i		−	0.514273i	−0.966375	−	0.257137i	$-0.917221\pi$
$193$		−	99.2548i		−	0.514273i	0.966375	−	0.257137i	$-0.0827791\pi$
$194$	133.740	−	31.3664i	0.689383	−	0.161683i
$195$	−5.36997	+	2.47596i	−0.0275383	+	0.0126972i
$196$	18.1496	−	9.00890i	0.0926002	−	0.0459638i
$197$	−264.258	−	264.258i	−1.34141	−	1.34141i	−0.894654	−	0.446759i	$-0.852578\pi$
$197$	−264.258	−	264.258i	−1.34141	−	1.34141i	−0.446759	−	0.894654i	$-0.647422\pi$
$198$	477.180	+	295.874i	2.41000	+	1.49431i
$199$	−126.972			−0.638050			−0.319025	−	0.947746i	$-0.603355\pi$
$199$	−126.972			−0.638050			−0.319025	+	0.947746i	$0.603355\pi$
$200$	−199.976	−	3.12764i	−0.999878	−	0.0156382i
$201$		−	277.363i		−	1.37991i
$202$	135.476	+	84.0012i	0.670671	+	0.415847i
$203$	64.0218	−	64.0218i	0.315378	−	0.315378i
$204$	83.8484	−	249.126i	0.411021	−	1.22121i
$205$	34.9103	+	75.7150i	0.170294	+	0.369341i
$206$	258.045	−	60.5199i	1.25265	−	0.293786i
$207$	−287.783			−1.39026
$208$	0.530803	+	3.87666i	0.00255194	+	0.0186378i
$209$	296.413			1.41824
$210$	352.903	+	43.6287i	1.68049	+	0.207755i
$211$	107.013	−	107.013i	0.507170	−	0.507170i	−0.406487	−	0.913657i	$-0.633246\pi$
$211$	107.013	−	107.013i	0.507170	−	0.507170i	0.913657	+	0.406487i	$0.133246\pi$
$212$	−168.090	−	56.5740i	−0.792877	−	0.266859i
$213$	236.734	+	236.734i	1.11143	+	1.11143i
$214$	−65.4962	−	40.6107i	−0.306057	−	0.189770i
$215$	−112.413	+	304.763i	−0.522853	+	1.41750i
$216$	207.492	+	19.6230i	0.960611	+	0.0908473i
$217$	−153.625			−0.707949
$218$	8.22122	−	13.2590i	0.0377120	−	0.0608212i
$219$	−54.1878	−	54.1878i	−0.247433	−	0.247433i
$220$	388.008	−	41.8193i	1.76367	−	0.190088i
$221$	−2.34979	−	2.34979i	−0.0106325	−	0.0106325i
$222$	−104.208	+	24.4402i	−0.469406	+	0.110091i
$223$	−177.302			−0.795076			−0.397538	−	0.917586i	$-0.630135\pi$
$223$	−177.302			−0.795076			−0.397538	+	0.917586i	$0.630135\pi$
$224$	95.7185	−	214.945i	0.427315	−	0.959574i
$225$	273.528	+	233.561i	1.21568	+	1.03805i
$226$	−202.513	+	47.4959i	−0.896076	+	0.210159i
$227$	229.481	+	229.481i	1.01093	+	1.01093i	0.999940	+	0.0109885i	$0.00349781\pi$
$227$	229.481	+	229.481i	1.01093	+	1.01093i	0.0109885	+	0.999940i	$0.496502\pi$
$228$	263.209	−	130.649i	1.15443	−	0.573020i
$229$	−295.113	+	295.113i	−1.28870	+	1.28870i	−0.353126	+	0.935576i	$0.614881\pi$
$229$	−295.113	+	295.113i	−1.28870	+	1.28870i	−0.935576	+	0.353126i	$0.885119\pi$
$230$	−157.727	+	123.019i	−0.685769	+	0.534864i
$231$	−693.853			−3.00369
$232$	9.27477	−	98.0706i	0.0399774	−	0.422718i
$233$	−194.762			−0.835887			−0.417943	−	0.908473i	$-0.637249\pi$
$233$	−194.762			−0.835887			−0.417943	+	0.908473i	$0.637249\pi$
$234$	3.70816	−	5.98046i	0.0158469	−	0.0255575i
$235$	−69.2215	+	31.9163i	−0.294560	+	0.135814i
$236$	−195.040	−	65.6448i	−0.826443	−	0.278156i
$237$	458.449	−	458.449i	1.93438	−	1.93438i
$238$	45.6288	+	194.552i	0.191718	+	0.817446i
$239$		−	252.140i		−	1.05498i	−0.849562	−	0.527489i	$-0.823134\pi$
$239$		−	252.140i		−	1.05498i	0.849562	−	0.527489i	$-0.176866\pi$
$240$	326.112	−	208.155i	1.35880	−	0.867314i
$241$	67.3325			0.279388			0.139694	−	0.990195i	$-0.455388\pi$
$241$	67.3325			0.279388			0.139694	+	0.990195i	$0.455388\pi$
$242$	−505.771	+	118.620i	−2.08996	+	0.490164i
$243$	177.746	+	177.746i	0.731467	+	0.731467i
$244$	263.224	+	88.5932i	1.07879	+	0.363087i
$245$	−23.0010	+	10.6052i	−0.0938816	+	0.0432865i
$246$	−137.072	−	84.9907i	−0.557201	−	0.345491i
$247$		−	3.71492i		−	0.0150401i
$248$	−128.791	+	106.536i	−0.519320	+	0.429580i
$249$			11.7064i			0.0470137i
$250$	249.754	+	11.0840i	0.999017	+	0.0443361i
$251$	300.166	+	300.166i	1.19588	+	1.19588i	0.975388	+	0.220494i	$0.0707669\pi$
$251$	300.166	+	300.166i	1.19588	+	1.19588i	0.220494	+	0.975388i	$0.429233\pi$
$252$	−379.026	+	188.136i	−1.50407	+	0.746573i
$253$	275.991	−	275.991i	1.09087	−	1.09087i
$254$	9.25648	+	39.4678i	0.0364428	+	0.155385i
$255$	−113.707	+	308.270i	−0.445910	+	1.20890i
$256$	−68.8144	−	246.578i	−0.268806	−	0.963194i
$257$		−	43.0554i		−	0.167531i	−0.996486	−	0.0837653i	$-0.973305\pi$
$257$		−	43.0554i		−	0.167531i	0.996486	−	0.0837653i	$-0.0266946\pi$
$258$	−143.478	−	611.763i	−0.556117	−	2.37117i
$259$	57.5382	−	57.5382i	0.222155	−	0.222155i
$260$	−0.524117	−	4.86287i	−0.00201584	−	0.0187033i
$261$	−125.268	+	125.268i	−0.479955	+	0.479955i
$262$	−388.947	−	241.165i	−1.48453	−	0.920477i
$263$			207.527i			0.789076i	0.918880	+	0.394538i	$0.129095\pi$
$263$			207.527i			0.789076i	−0.918880	+	0.394538i	$0.870905\pi$
$264$	−581.692	+	481.174i	−2.20338	+	1.82263i
$265$	207.996	+	76.7202i	0.784889	+	0.289510i
$266$	−117.721	+	189.858i	−0.442560	+	0.713753i
$267$	181.938	−	181.938i	0.681416	−	0.681416i
$268$	217.429	+	73.1801i	0.811303	+	0.273060i
$269$	−206.984	−	206.984i	−0.769457	−	0.769457i	0.208554	−	0.978011i	$-0.433124\pi$
$269$	−206.984	−	206.984i	−0.769457	−	0.769457i	−0.978011	+	0.208554i	$0.933124\pi$
$270$	−258.554	−	31.9645i	−0.957607	−	0.118387i
$271$		−	46.6309i		−	0.172070i	−0.996292	−	0.0860348i	$-0.972580\pi$
$271$		−	46.6309i		−	0.172070i	0.996292	−	0.0860348i	$-0.0274196\pi$
$272$	173.171	+	131.460i	0.636659	+	0.483309i
$273$			8.69600i			0.0318535i
$274$	106.305	+	453.264i	0.387975	+	1.65425i
$275$	−486.311	+	38.3289i	−1.76840	+	0.139378i
$276$	123.428	−	366.723i	0.447203	−	1.32871i
$277$	−17.2344	−	17.2344i	−0.0622180	−	0.0622180i	0.675313	−	0.737531i	$-0.264009\pi$
$277$	−17.2344	−	17.2344i	−0.0622180	−	0.0622180i	−0.737531	+	0.675313i	$0.764009\pi$
$278$	23.0756	−	37.2158i	0.0830056	−	0.133870i
$279$	300.590			1.07738
$280$	−127.312	+	265.135i	−0.454686	+	0.946911i
$281$		−	500.431i		−	1.78089i	−0.455089	−	0.890446i	$-0.650392\pi$
$281$		−	500.431i		−	1.78089i	0.455089	−	0.890446i	$-0.349608\pi$
$282$	77.7018	−	125.316i	0.275538	−	0.444383i
$283$	−265.793	+	265.793i	−0.939200	+	0.939200i	−0.998255	−	0.0590552i	$-0.981191\pi$
$283$	−265.793	+	265.793i	−0.939200	+	0.939200i	0.0590552	+	0.998255i	$0.481191\pi$
$284$	−248.040	+	123.119i	−0.873381	+	0.433518i
$285$	−333.565	+	153.798i	−1.17040	+	0.539643i
$286$	2.17919	+	9.29163i	0.00761954	+	0.0324882i
$287$	122.611			0.427216
$288$	−187.288	+	420.571i	−0.650304	+	1.46032i
$289$	104.351			0.361078
$290$	−15.1079	+	122.205i	−0.0520963	+	0.421396i
$291$	234.873	−	234.873i	0.807124	−	0.807124i
$292$	56.7757	−	28.1816i	0.194437	−	0.0965125i
$293$	81.7222	+	81.7222i	0.278915	+	0.278915i	0.832676	−	0.553761i	$-0.186808\pi$
$293$	81.7222	+	81.7222i	0.278915	+	0.278915i	−0.553761	+	0.832676i	$0.686808\pi$
$294$	25.8188	−	41.6401i	0.0878191	−	0.141633i
$295$	241.344	+	89.0211i	0.818117	+	0.301767i
$296$	8.33550	−	88.1388i	0.0281605	−	0.297766i
$297$	508.351			1.71162
$298$	−102.351	−	63.4625i	−0.343460	−	0.212962i
$299$	−3.45897	−	3.45897i	−0.0115685	−	0.0115685i
$300$	−414.941	+	248.385i	−1.38314	+	0.827948i
$301$	337.783	+	337.783i	1.12220	+	1.12220i
$302$	115.323	+	491.716i	0.381865	+	1.62820i
$303$	385.442			1.27209
$304$	32.9717	+	240.805i	0.108460	+	0.792121i
$305$	−325.715	−	120.142i	−1.06792	−	0.393907i
$306$	−89.2796	−	380.671i	−0.291763	−	1.24402i
$307$	132.851	+	132.851i	0.432739	+	0.432739i	0.889559	−	0.456820i	$-0.151012\pi$
$307$	132.851	+	132.851i	0.432739	+	0.432739i	−0.456820	+	0.889559i	$0.651012\pi$
$308$	183.068	−	543.923i	0.594377	−	1.76598i
$309$	453.175	−	453.175i	1.46659	−	1.46659i
$310$	164.746	−	128.493i	0.531438	−	0.414495i
$311$	87.7229			0.282067			0.141034	−	0.990005i	$-0.454957\pi$
$311$	87.7229			0.282067			0.141034	+	0.990005i	$0.454957\pi$
$312$	6.03051	+	7.29029i	0.0193286	+	0.0233663i
$313$	34.8150			0.111230			0.0556149	−	0.998452i	$-0.482288\pi$
$313$	34.8150			0.111230			0.0556149	+	0.998452i	$0.482288\pi$
$314$	141.934	+	88.0057i	0.452019	+	0.280273i
$315$	480.339	−	221.472i	1.52488	−	0.703086i
$316$	238.427	+	480.343i	0.754516	+	1.52007i
$317$	−367.714	+	367.714i	−1.15998	+	1.15998i	−0.175501	+	0.984479i	$0.556155\pi$
$317$	−367.714	+	367.714i	−1.15998	+	1.15998i	−0.984479	+	0.175501i	$0.943845\pi$
$318$	−417.517	+	97.9214i	−1.31295	+	0.307929i
$319$		−	240.271i		−	0.753200i
$320$	77.1342	+	310.565i	0.241044	+	0.970514i
$321$	−186.344			−0.580510
$322$	67.1673	+	286.388i	0.208594	+	0.889404i
$323$	−145.961	−	145.961i	−0.451891	−	0.451891i
$324$	−12.5218	+	6.21540i	−0.0386474	+	0.0191833i
$325$	0.480373	+	6.09489i	0.00147807	+	0.0187535i
$326$	31.8605	−	51.3841i	0.0977316	−	0.157620i
$327$		−	37.7233i		−	0.115362i
$328$	102.791	−	85.0284i	0.313387	−	0.259233i
$329$			112.096i			0.340716i
$330$	744.082	−	580.346i	2.25479	−	1.75862i
$331$	−359.811	−	359.811i	−1.08704	−	1.08704i	−0.995832	−	0.0912091i	$-0.970927\pi$
$331$	−359.811	−	359.811i	−1.08704	−	1.08704i	−0.0912091	−	0.995832i	$-0.529073\pi$
$332$	−9.17685	−	3.08865i	−0.0276411	−	0.00930317i
$333$	−112.582	+	112.582i	−0.338085	+	0.338085i
$334$	−178.332	+	41.8247i	−0.533930	+	0.125224i
$335$	−269.048	−	99.2399i	−0.803130	−	0.296239i
$336$	−77.1813	−	563.684i	−0.229706	−	1.67763i
$337$			71.8926i			0.213331i	0.994295	+	0.106666i	$0.0340174\pi$
$337$			71.8926i			0.213331i	−0.994295	+	0.106666i	$0.965983\pi$
$338$	−328.954	+	77.1504i	−0.973238	+	0.228256i
$339$	−355.651	+	355.651i	−1.04912	+	1.04912i
$340$	−211.657	−	170.472i	−0.622522	−	0.501387i
$341$	−288.273	+	288.273i	−0.845376	+	0.845376i
$342$	230.339	−	371.486i	0.673505	−	1.08622i
$343$		−	323.046i		−	0.941827i
$344$	517.426	+	48.9342i	1.50415	+	0.142251i
$345$	−167.381	+	453.786i	−0.485163	+	1.31532i
$346$	−473.876	−	293.825i	−1.36959	−	0.849207i
$347$	262.837	−	262.837i	0.757456	−	0.757456i	−0.218403	−	0.975859i	$-0.570085\pi$
$347$	262.837	−	262.837i	0.757456	−	0.757456i	0.975859	+	0.218403i	$0.0700846\pi$
$348$	−105.903	−	213.356i	−0.304319	−	0.613093i
$349$	−281.607	−	281.607i	−0.806897	−	0.806897i	0.177266	−	0.984163i	$-0.443275\pi$
$349$	−281.607	−	281.607i	−0.806897	−	0.806897i	−0.984163	+	0.177266i	$0.943275\pi$
$350$	168.589	−	326.714i	0.481682	−	0.933468i
$351$		−	6.37112i		−	0.0181513i
$352$	−223.725	−	582.952i	−0.635582	−	1.65611i
$353$		−	480.829i		−	1.36212i	−0.732227	−	0.681061i	$-0.761519\pi$
$353$		−	480.829i		−	1.36212i	0.732227	−	0.681061i	$-0.238481\pi$
$354$	−484.460	+	113.622i	−1.36853	+	0.320965i
$355$	314.341	−	144.935i	0.885467	−	0.408267i
$356$	94.6212	+	190.627i	0.265790	+	0.535470i
$357$	341.670	+	341.670i	0.957059	+	0.957059i
$358$	−48.6399	−	30.1590i	−0.135866	−	0.0842431i
$359$	264.410			0.736518			0.368259	−	0.929723i	$-0.379954\pi$
$359$	264.410			0.736518			0.368259	+	0.929723i	$0.379954\pi$
$360$	249.105	−	518.777i	0.691959	−	1.44105i
$361$			130.242i			0.360781i
$362$	165.264	+	102.472i	0.456531	+	0.283071i
$363$	−888.229	+	888.229i	−2.44691	+	2.44691i
$364$	−6.81693	−	2.29438i	−0.0187278	−	0.00630323i
$365$	−71.9517	+	33.1751i	−0.197128	+	0.0908908i
$366$	653.820	−	153.342i	1.78639	−	0.418967i
$367$	363.729			0.991088			0.495544	−	0.868583i	$-0.334969\pi$
$367$	363.729			0.991088			0.495544	+	0.868583i	$0.334969\pi$
$368$	254.914	+	193.514i	0.692702	+	0.525854i
$369$	−239.907			−0.650154
$370$	−13.5779	+	109.829i	−0.0366971	+	0.296835i
$371$	230.531	−	230.531i	0.621377	−	0.621377i
$372$	−128.921	+	383.043i	−0.346561	+	1.02968i
$373$	−292.903	−	292.903i	−0.785263	−	0.785263i	0.195451	−	0.980714i	$-0.437383\pi$
$373$	−292.903	−	292.903i	−0.785263	−	0.785263i	−0.980714	+	0.195451i	$0.937383\pi$
$374$	450.694	+	279.451i	1.20506	+	0.747196i
$375$	527.376	−	295.463i	1.40634	−	0.787900i
$376$	77.7362	+	93.9753i	0.206745	+	0.249934i
$377$	−3.01129			−0.00798751
$378$	−201.892	+	325.609i	−0.534107	+	0.861398i
$379$	92.6285	+	92.6285i	0.244402	+	0.244402i	0.818669	−	0.574266i	$-0.194713\pi$
$379$	92.6285	+	92.6285i	0.244402	+	0.244402i	−0.574266	+	0.818669i	$0.694713\pi$
$380$	−32.5564	−	302.065i	−0.0856747	−	0.794908i
$381$	69.3129	+	69.3129i	0.181924	+	0.181924i
$382$	−97.1357	+	22.7815i	−0.254282	+	0.0596374i
$383$	580.159			1.51478			0.757388	−	0.652966i	$-0.226475\pi$
$383$	580.159			1.51478			0.757388	+	0.652966i	$0.226475\pi$
$384$	−455.609	−	419.041i	−1.18648	−	1.09125i
$385$	−248.259	+	673.054i	−0.644829	+	1.74819i
$386$	193.265	−	45.3270i	0.500688	−	0.117427i
$387$	−660.923	−	660.923i	−1.70781	−	1.70781i
$388$	122.151	+	246.090i	0.314823	+	0.634253i
$389$	270.466	−	270.466i	0.695285	−	0.695285i	−0.268105	−	0.963390i	$-0.586397\pi$
$389$	270.466	−	270.466i	0.695285	−	0.695285i	0.963390	+	0.268105i	$0.0863973\pi$
$390$	−7.27342	−	9.32551i	−0.0186498	−	0.0239116i
$391$	−271.810			−0.695165
$392$	25.8303	+	31.2262i	0.0658935	+	0.0796587i
$393$	−1106.59			−2.81576
$394$	393.875	−	635.234i	0.999683	−	1.61227i
$395$	−280.674	−	608.738i	−0.710566	−	1.54111i
$396$	−358.200	+	1064.27i	−0.904546	+	2.68754i
$397$	−228.232	+	228.232i	−0.574892	+	0.574892i	−0.933492	−	0.358599i	$-0.883254\pi$
$397$	−228.232	+	228.232i	−0.574892	+	0.574892i	0.358599	+	0.933492i	$0.383254\pi$
$398$	−57.9847	−	247.235i	−0.145690	−	0.621195i
$399$			540.166i			1.35380i
$400$	−85.2334	−	390.814i	−0.213084	−	0.977034i
$401$	−646.544			−1.61233			−0.806165	−	0.591691i	$-0.798461\pi$
$401$	−646.544			−1.61233			−0.806165	+	0.591691i	$0.798461\pi$
$402$	540.071	−	126.664i	1.34346	−	0.315085i
$403$	3.61290	+	3.61290i	0.00896502	+	0.00896502i
$404$	−101.696	+	302.154i	−0.251723	+	0.747907i
$405$	15.8688	−	7.31670i	0.0391822	−	0.0180659i
$406$	153.898	+	95.4240i	0.379059	+	0.235034i
$407$		−	215.938i		−	0.530561i
$408$	523.381	+	49.4974i	1.28280	+	0.121317i
$409$			53.0666i			0.129747i	0.997893	+	0.0648736i	$0.0206644\pi$
$409$			53.0666i			0.129747i	−0.997893	+	0.0648736i	$0.979336\pi$
$410$	−131.487	+	102.553i	−0.320700	+	0.250129i
$411$	796.016	+	796.016i	1.93678	+	1.93678i
$412$	235.685	+	474.818i	0.572050	+	1.15247i
$413$	267.493	−	267.493i	0.647683	−	0.647683i
$414$	−131.423	−	560.361i	−0.317447	−	1.35353i
$415$	11.3555	+	4.18853i	0.0273627	+	0.0100929i
$416$	−7.30608	+	2.80393i	−0.0175627	+	0.00674021i
$417$		−	105.883i		−	0.253916i
$418$	135.364	+	577.165i	0.323837	+	1.38078i
$419$	−122.873	+	122.873i	−0.293254	+	0.293254i	−0.838364	−	0.545111i	$-0.816488\pi$
$419$	−122.873	+	122.873i	−0.293254	+	0.293254i	0.545111	+	0.838364i	$0.316488\pi$
$420$	76.2091	+	707.084i	0.181450	+	1.68353i
$421$	137.974	−	137.974i	0.327729	−	0.327729i	−0.523994	−	0.851722i	$-0.675558\pi$
$421$	137.974	−	137.974i	0.327729	−	0.327729i	0.851722	+	0.523994i	$0.175558\pi$
$422$	257.241	+	159.502i	0.609577	+	0.377966i
$423$		−	219.332i		−	0.518515i
$424$	33.3968	−	353.134i	0.0787660	−	0.832864i
$425$	258.345	+	220.597i	0.607871	+	0.519052i
$426$	−352.850	+	569.071i	−0.828287	+	1.33585i
$427$	−361.005	+	361.005i	−0.845444	+	0.845444i
$428$	49.1654	−	146.078i	0.114872	−	0.341303i
$429$	16.3178	+	16.3178i	0.0380369	+	0.0380369i
$430$	−644.760	−	79.7104i	−1.49944	−	0.185373i
$431$			194.587i			0.451477i	0.974188	+	0.225739i	$0.0724796\pi$
$431$			194.587i			0.451477i	−0.974188	+	0.225739i	$0.927520\pi$
$432$	56.5468	+	412.982i	0.130895	+	0.955978i
$433$		−	497.381i		−	1.14869i	−0.818615	−	0.574343i	$-0.805257\pi$
$433$		−	497.381i		−	1.14869i	0.818615	−	0.574343i	$-0.194743\pi$
$434$	−70.1563	−	299.133i	−0.161651	−	0.689246i
$435$	124.668	+	270.386i	0.286593	+	0.621576i
$436$	29.5719	+	9.95302i	0.0678255	+	0.0228280i
$437$	−214.860	−	214.860i	−0.491670	−	0.491670i
$438$	80.7665	−	130.259i	0.184398	−	0.297394i
$439$	−109.485			−0.249395			−0.124698	−	0.992195i	$-0.539796\pi$
$439$	−109.485			−0.249395			−0.124698	+	0.992195i	$0.539796\pi$
$440$	258.622	+	736.418i	0.587777	+	1.67368i
$441$		−	72.8798i		−	0.165260i
$442$	3.50234	−	5.64851i	0.00792384	−	0.0127794i
$443$	88.4685	−	88.4685i	0.199703	−	0.199703i	−0.600170	−	0.799873i	$-0.704900\pi$
$443$	88.4685	−	88.4685i	0.199703	−	0.199703i	0.799873	+	0.600170i	$0.204900\pi$
$444$	−95.1782	−	191.749i	−0.214365	−	0.431868i
$445$	−111.387	−	241.581i	−0.250308	−	0.542879i
$446$	−80.9691	−	345.236i	−0.181545	−	0.774072i
$447$	−291.200			−0.651454
$448$	462.245	+	88.2202i	1.03180	+	0.196920i
$449$	264.577			0.589258			0.294629	−	0.955612i	$-0.404804\pi$
$449$	264.577			0.589258			0.294629	+	0.955612i	$0.404804\pi$
$450$	−329.869	+	639.265i	−0.733043	+	1.42059i
$451$	230.077	−	230.077i	0.510147	−	0.510147i
$452$	−184.965	−	372.636i	−0.409214	−	0.824416i
$453$	863.545	+	863.545i	1.90628	+	1.90628i
$454$	−342.039	+	551.634i	−0.753390	+	1.21505i
$455$	8.43532	+	3.11141i	0.0185392	+	0.00683827i
$456$	374.595	+	452.848i	0.821480	+	0.993089i
$457$	−236.612			−0.517750			−0.258875	−	0.965911i	$-0.583352\pi$
$457$	−236.612			−0.517750			−0.258875	+	0.965911i	$0.583352\pi$
$458$	−709.403	−	439.863i	−1.54892	−	0.960400i
$459$	−250.324	−	250.324i	−0.545369	−	0.545369i
$460$	−311.567	−	250.941i	−0.677321	−	0.545523i
$461$	−43.5825	−	43.5825i	−0.0945391	−	0.0945391i	0.658255	−	0.752795i	$-0.271295\pi$
$461$	−43.5825	−	43.5825i	−0.0945391	−	0.0945391i	−0.752795	+	0.658255i	$0.771295\pi$
$462$	−316.864	−	1351.05i	−0.685853	−	2.92434i
$463$	−341.664			−0.737934			−0.368967	−	0.929442i	$-0.620289\pi$
$463$	−341.664			−0.737934			−0.368967	+	0.929442i	$0.620289\pi$
$464$	195.195	−	26.7267i	0.420679	−	0.0576006i
$465$	174.830	−	473.980i	0.375978	−	1.01931i
$466$	−88.9424	−	379.233i	−0.190864	−	0.813805i
$467$	−331.496	−	331.496i	−0.709842	−	0.709842i	0.256660	−	0.966502i	$-0.417378\pi$
$467$	−331.496	−	331.496i	−0.709842	−	0.709842i	−0.966502	+	0.256660i	$0.917378\pi$
$468$	13.3384	+	4.48929i	0.0285008	+	0.00959250i
$469$	−298.199	+	298.199i	−0.635818	+	0.635818i
$470$	−93.7579	−	120.210i	−0.199485	−	0.255767i
$471$	403.817			0.857361
$472$	38.7514	−	409.754i	0.0821005	−	0.868123i
$473$	1267.68			2.68009
$474$	1102.04	+	683.314i	2.32497	+	1.44159i
$475$	29.8392	+	378.594i	0.0628193	+	0.797040i
$476$	−357.988	+	177.694i	−0.752075	+	0.373306i
$477$	−451.069	+	451.069i	−0.945636	+	0.945636i
$478$	490.957	−	115.145i	1.02711	−	0.240890i
$479$			86.2950i			0.180157i	0.995935	+	0.0900783i	$0.0287117\pi$
$479$			86.2950i			0.180157i	−0.995935	+	0.0900783i	$0.971288\pi$
$480$	554.239	+	539.934i	1.15467	+	1.12486i
$481$	−2.70633			−0.00562647
$482$	30.7489	+	131.107i	0.0637945	+	0.272007i
$483$	502.951	+	502.951i	1.04131	+	1.04131i
$484$	−461.944	−	930.649i	−0.954430	−	1.92283i
$485$	−143.795	−	311.869i	−0.296485	−	0.643030i
$486$	−264.929	+	427.273i	−0.545122	+	0.879164i
$487$			674.294i			1.38459i	0.721616	+	0.692294i	$0.243400\pi$
$487$			674.294i			1.38459i	−0.721616	+	0.692294i	$0.756600\pi$
$488$	−52.2983	+	552.998i	−0.107169	+	1.13319i
$489$		−	146.193i		−	0.298963i
$490$	−31.1540	−	39.9436i	−0.0635795	−	0.0815176i
$491$	65.7623	+	65.7623i	0.133935	+	0.133935i	0.770896	−	0.636961i	$-0.219809\pi$
$491$	65.7623	+	65.7623i	0.133935	+	0.133935i	−0.636961	+	0.770896i	$0.719809\pi$
$492$	102.894	−	305.714i	0.209134	−	0.621369i
$493$	−118.315	+	118.315i	−0.239990	+	0.239990i
$494$	7.23355	−	1.69650i	0.0146428	−	0.00343422i
$495$	485.757	−	1316.93i	0.981327	−	2.66047i
$496$	−266.259	−	202.126i	−0.536812	−	0.407512i
$497$		−	509.036i		−	1.02422i
$498$	−22.7943	+	5.34601i	−0.0457717	+	0.0107350i
$499$	−410.769	+	410.769i	−0.823184	+	0.823184i	−0.986563	−	0.163379i	$-0.947761\pi$
$499$	−410.769	+	410.769i	−0.823184	+	0.823184i	0.163379	+	0.986563i	$0.447761\pi$
$500$	92.4736	+	491.374i	0.184947	+	0.982748i
$501$	−313.185	+	313.185i	−0.625120	+	0.625120i
$502$	−447.395	+	721.551i	−0.891226	+	1.43735i
$503$			381.080i			0.757614i	0.925476	+	0.378807i	$0.123666\pi$
$503$			381.080i			0.757614i	−0.925476	+	0.378807i	$0.876334\pi$
$504$	−539.423	−	652.109i	−1.07028	−	1.29387i
$505$	137.910	−	373.888i	0.273090	−	0.740372i
$506$	663.438	+	411.363i	1.31114	+	0.812970i
$507$	−577.705	+	577.705i	−1.13946	+	1.13946i
$508$	−72.6232	+	36.0478i	−0.142959	+	0.0709602i
$509$	659.492	+	659.492i	1.29566	+	1.29566i	0.931230	+	0.364431i	$0.118737\pi$
$509$	659.492	+	659.492i	1.29566	+	1.29566i	0.364431	+	0.931230i	$0.381263\pi$
$510$	−652.180	−	80.6277i	−1.27878	−	0.158093i
$511$			116.517i			0.228017i
$512$	448.702	−	246.598i	0.876370	−	0.481638i
$513$		−	395.752i		−	0.771447i
$514$	83.8359	−	19.6622i	0.163105	−	0.0382534i
$515$	−277.445	−	601.736i	−0.538729	−	1.16842i
$516$	1125.68	−	558.751i	2.18155	−	1.08285i
$517$	210.345	+	210.345i	0.406856	+	0.406856i
$518$	138.313	+	85.7602i	0.267013	+	0.165560i
$519$	−1348.23			−2.59774
$520$	9.22946	−	3.24128i	0.0177490	−	0.00623324i
$521$		−	62.6462i		−	0.120242i	−0.998191	−	0.0601211i	$-0.980851\pi$
$521$		−	62.6462i		−	0.120242i	0.998191	−	0.0601211i	$-0.0191487\pi$
$522$	−301.125	−	186.711i	−0.576867	−	0.357685i
$523$	519.335	−	519.335i	0.992992	−	0.992992i	−0.00698315	−	0.999976i	$-0.502223\pi$
$523$	519.335	−	519.335i	0.992992	−	0.992992i	0.999976	+	0.00698315i	$0.00222282\pi$
$524$	291.967	−	867.477i	0.557188	−	1.65549i
$525$	−69.8485	−	886.226i	−0.133045	−	1.68805i
$526$	−404.089	+	94.7720i	−0.768230	+	0.180175i
$527$	283.906			0.538720
$528$	−1202.57	−	912.910i	−2.27759	−	1.72900i
$529$	128.886			0.243641
$530$	−54.4009	+	440.038i	−0.102643	+	0.830260i
$531$	−523.390	+	523.390i	−0.985669	+	0.985669i
$532$	−423.445	−	142.519i	−0.795949	−	0.267893i
$533$	−2.88353	−	2.88353i	−0.00541000	−	0.00541000i
$534$	437.350	+	271.177i	0.819007	+	0.507823i
$535$	−66.6734	+	180.758i	−0.124623	+	0.337865i
$536$	−43.1997	+	456.790i	−0.0805965	+	0.852220i
$537$	−138.386			−0.257702
$538$	308.508	−	497.556i	0.573434	−	0.924824i
$539$	69.8936	+	69.8936i	0.129673	+	0.129673i
$540$	−55.8345	−	518.044i	−0.103397	−	0.959342i
$541$	297.277	+	297.277i	0.549495	+	0.549495i	0.926295	−	0.376800i	$-0.122976\pi$
$541$	297.277	+	297.277i	0.549495	+	0.549495i	−0.376800	+	0.926295i	$0.622976\pi$
$542$	90.7980	−	21.2951i	0.167524	−	0.0392898i
$543$	470.194			0.865920
$544$	−176.892	+	397.227i	−0.325169	+	0.730197i
$545$	−36.5925	−	13.4973i	−0.0671422	−	0.0247657i
$546$	−16.9325	+	3.97123i	−0.0310120	+	0.00727331i
$547$	402.706	+	402.706i	0.736209	+	0.736209i	0.971842	−	0.235633i	$-0.0757164\pi$
$547$	402.706	+	402.706i	0.736209	+	0.736209i	−0.235633	+	0.971842i	$0.575716\pi$
$548$	−834.033	+	413.987i	−1.52196	+	0.755450i
$549$	706.360	−	706.360i	1.28663	−	1.28663i
$550$	−296.718	−	929.423i	−0.539487	−	1.68986i
$551$	−187.051			−0.339476
$552$	770.436	+	72.8620i	1.39572	+	0.131996i
$553$	−985.775			−1.78260
$554$	25.6877	−	41.4287i	0.0463677	−	0.0747810i
$555$	112.043	+	243.003i	0.201879	+	0.437844i
$556$	83.0034	+	27.9364i	0.149287	+	0.0502454i
$557$	401.151	−	401.151i	0.720199	−	0.720199i	−0.248446	−	0.968646i	$-0.579920\pi$
$557$	401.151	−	401.151i	0.720199	−	0.720199i	0.968646	+	0.248446i	$0.0799200\pi$
$558$	137.271	+	585.299i	0.246006	+	1.04892i
$559$		−	15.8878i		−	0.0284218i
$560$	−574.402	−	126.817i	−1.02572	−	0.226460i
$561$	1282.27			2.28569
$562$	974.421	−	228.533i	1.73385	−	0.406643i
$563$	−390.009	−	390.009i	−0.692734	−	0.692734i	0.270098	−	0.962833i	$-0.412944\pi$
$563$	−390.009	−	390.009i	−0.692734	−	0.692734i	−0.962833	+	0.270098i	$0.912944\pi$
$564$	279.495	+	94.0697i	0.495559	+	0.166790i
$565$	217.738	+	472.241i	0.385378	+	0.835824i
$566$	−638.924	−	396.163i	−1.12884	−	0.699934i
$567$		−	25.6975i		−	0.0453219i
$568$	−353.007	−	426.750i	−0.621490	−	0.751320i
$569$		−	863.946i		−	1.51836i	−0.650881	−	0.759179i	$-0.725600\pi$
$569$		−	863.946i		−	1.51836i	0.650881	−	0.759179i	$-0.274400\pi$
$570$	−451.800	−	579.269i	−0.792632	−	1.01626i
$571$	−465.765	−	465.765i	−0.815700	−	0.815700i	0.169781	−	0.985482i	$-0.445694\pi$
$571$	−465.765	−	465.765i	−0.815700	−	0.815700i	−0.985482	+	0.169781i	$0.945694\pi$
$572$	−17.0972	+	8.48647i	−0.0298901	+	0.0148365i
$573$	−170.588	+	170.588i	−0.297711	+	0.297711i
$574$	55.9931	+	238.744i	0.0975490	+	0.415930i
$575$	380.294	+	324.727i	0.661381	+	0.564743i
$576$	−904.451	−	172.616i	−1.57023	−	0.299681i
$577$			724.607i			1.25582i	0.778287	+	0.627909i	$0.216089\pi$
$577$			724.607i			1.25582i	−0.778287	+	0.627909i	$0.783911\pi$
$578$	47.6545	+	203.189i	0.0824472	+	0.351539i
$579$	339.410	−	339.410i	0.586201	−	0.586201i
$580$	−244.852	+	26.3900i	−0.422159	+	0.0455001i
$581$	12.5858	−	12.5858i	0.0216623	−	0.0216623i
$582$	564.597	+	350.076i	0.970097	+	0.601505i
$583$		−	865.172i		−	1.48400i
$584$	80.8022	+	97.6819i	0.138360	+	0.167264i
$585$	−16.5050	−	6.08795i	−0.0282136	−	0.0104067i
$586$	−121.806	+	196.447i	−0.207860	+	0.335234i
$587$	286.090	−	286.090i	0.487376	−	0.487376i	−0.420101	−	0.907477i	$-0.638005\pi$
$587$	286.090	−	286.090i	0.487376	−	0.487376i	0.907477	+	0.420101i	$0.138005\pi$
$588$	92.8709	+	31.2576i	0.157944	+	0.0531591i
$589$	224.421	+	224.421i	0.381021	+	0.381021i
$590$	−63.1233	+	510.591i	−0.106989	+	0.865408i
$591$		−	1807.31i		−	3.05805i
$592$	175.427	−	24.0200i	0.296330	−	0.0405744i
$593$			726.715i			1.22549i	0.790281	+	0.612744i	$0.209934\pi$
$593$			726.715i			1.22549i	−0.790281	+	0.612744i	$0.790066\pi$
$594$	232.150	+	989.843i	0.390825	+	1.66640i
$595$	453.677	−	209.179i	0.762482	−	0.351561i
$596$	76.8309	−	228.276i	0.128911	−	0.383014i
$597$	−434.192	−	434.192i	−0.727289	−	0.727289i
$598$	5.15557	−	8.31481i	0.00862136	−	0.0139044i
$599$	−136.294			−0.227536			−0.113768	−	0.993507i	$-0.536292\pi$
$599$	−136.294			−0.227536			−0.113768	+	0.993507i	$0.536292\pi$
$600$	−673.138	−	694.529i	−1.12190	−	1.15755i
$601$			640.499i			1.06572i	0.846203	+	0.532861i	$0.178883\pi$
$601$			640.499i			1.06572i	−0.846203	+	0.532861i	$0.821117\pi$
$602$	−503.463	+	811.975i	−0.836317	+	1.34880i
$603$	583.470	−	583.470i	0.967613	−	0.967613i
$604$	−904.786	+	449.107i	−1.49799	+	0.743554i
$605$	543.796	+	1179.41i	0.898836	+	1.94944i
$606$	176.021	+	750.519i	0.290464	+	1.23848i
$607$	−51.8360			−0.0853971			−0.0426985	−	0.999088i	$-0.513595\pi$
$607$	−51.8360			−0.0853971			−0.0426985	+	0.999088i	$0.513595\pi$
$608$	−453.829	+	174.170i	−0.746430	+	0.286465i
$609$	437.856			0.718975
$610$	85.1903	−	689.086i	0.139656	−	1.12965i
$611$	2.63623	−	2.63623i	0.00431462	−	0.00431462i
$612$	700.457	−	347.684i	1.14454	−	0.568111i
$613$	555.773	+	555.773i	0.906644	+	0.906644i	0.996000	−	0.0893558i	$-0.0284808\pi$
$613$	555.773	+	555.773i	0.906644	+	0.906644i	−0.0893558	+	0.996000i	$0.528481\pi$
$614$	−198.013	+	319.352i	−0.322497	+	0.520117i
$615$	−139.535	+	378.292i	−0.226886	+	0.615110i
$616$	1142.71	+	108.069i	1.85505	+	0.175436i
$617$	−521.252			−0.844817			−0.422409	−	0.906405i	$-0.638815\pi$
$617$	−521.252			−0.844817			−0.422409	+	0.906405i	$0.638815\pi$
$618$	1089.36	+	675.454i	1.76272	+	1.09297i
$619$	485.733	+	485.733i	0.784706	+	0.784706i	0.980621	−	0.195915i	$-0.0627677\pi$
$619$	485.733	+	485.733i	0.784706	+	0.784706i	−0.195915	+	0.980621i	$0.562768\pi$
$620$	325.433	+	262.108i	0.524892	+	0.422755i
$621$	−368.487	−	368.487i	−0.593376	−	0.593376i
$622$	40.0607	+	170.811i	0.0644062	+	0.274616i
$623$	−391.211			−0.627947
$624$	−11.4414	+	15.0717i	−0.0183356	+	0.0241533i
$625$	−97.9114	−	617.283i	−0.156658	−	0.987653i
$626$	15.8991	+	67.7904i	0.0253978	+	0.108291i
$627$	1013.61	+	1013.61i	1.61660	+	1.61660i
$628$	−106.544	+	316.559i	−0.169656	+	0.504074i
$629$	−106.333	+	106.333i	−0.169051	+	0.169051i
$630$	650.600	+	834.158i	1.03270	+	1.32406i
$631$	−98.9094			−0.156750			−0.0783751	−	0.996924i	$-0.524973\pi$
$631$	−98.9094			−0.156750			−0.0783751	+	0.996924i	$0.524973\pi$
$632$	−826.425	+	683.616i	−1.30763	+	1.08167i
$633$	731.878			1.15621
$634$	−883.924	−	548.074i	−1.39420	−	0.864471i
$635$	92.0351	−	42.4351i	0.144937	−	0.0668269i
$636$	−381.338	−	768.257i	−0.599588	−	1.20795i
$637$	0.875970	−	0.875970i	0.00137515	−	0.00137515i
$638$	467.847	−	109.725i	0.733302	−	0.171983i
$639$			996.005i			1.55869i
$640$	−569.495	+	292.019i	−0.889836	+	0.456280i
$641$	−483.949			−0.754991			−0.377496	−	0.926011i	$-0.623215\pi$
$641$	−483.949			−0.754991			−0.377496	+	0.926011i	$0.623215\pi$
$642$	−85.0981	−	362.842i	−0.132552	−	0.565174i
$643$	−684.371	−	684.371i	−1.06434	−	1.06434i	−0.997783	−	0.0665572i	$-0.978798\pi$
$643$	−684.371	−	684.371i	−1.06434	−	1.06434i	−0.0665572	−	0.997783i	$-0.521202\pi$
$644$	−526.971	+	261.572i	−0.818279	+	0.406167i
$645$	−1426.57	+	657.756i	−2.21174	+	1.01978i
$646$	217.553	−	350.866i	0.336770	−	0.543137i
$647$			352.664i			0.545076i	0.962145	+	0.272538i	$0.0878631\pi$
$647$			352.664i			0.545076i	−0.962145	+	0.272538i	$0.912137\pi$
$648$	−17.8208	−	21.5435i	−0.0275012	−	0.0332462i
$649$		−	1003.89i		−	1.54682i
$650$	−11.6484	+	3.71874i	−0.0179206	+	0.00572113i
$651$	−525.333	−	525.333i	−0.806964	−	0.806964i
$652$	114.603	+	38.5719i	0.175772	+	0.0591594i
$653$	−563.720	+	563.720i	−0.863277	+	0.863277i	−0.991717	−	0.128440i	$-0.959003\pi$
$653$	−563.720	+	563.720i	−0.863277	+	0.863277i	0.128440	+	0.991717i	$0.459003\pi$
$654$	73.4535	−	17.2272i	0.112314	−	0.0263413i
$655$	−395.937	+	1073.42i	−0.604484	+	1.63881i
$656$	212.506	+	161.321i	0.323942	+	0.245916i
$657$		−	227.983i		−	0.347006i
$658$	−218.269	+	51.1910i	−0.331715	+	0.0777979i
$659$	−341.565	+	341.565i	−0.518308	+	0.518308i	−0.917059	−	0.398751i	$-0.869444\pi$
$659$	−341.565	+	341.565i	−0.518308	+	0.518308i	0.398751	+	0.917059i	$0.369444\pi$
$660$	1469.83	+	1183.82i	2.22702	+	1.79367i
$661$	578.357	−	578.357i	0.874973	−	0.874973i	−0.118036	−	0.993009i	$-0.537660\pi$
$661$	578.357	−	578.357i	0.874973	−	0.874973i	0.993009	+	0.118036i	$0.0376598\pi$
$662$	536.294	−	864.926i	0.810113	−	1.30653i
$663$		−	16.0706i		−	0.0242392i
$664$	1.82329	−	19.2793i	0.00274592	−	0.0290352i
$665$	523.974	+	193.270i	0.787931	+	0.290632i
$666$	−270.629	−	167.803i	−0.406350	−	0.251956i
$667$	−174.164	+	174.164i	−0.261116	+	0.261116i
$668$	−162.879	−	328.142i	−0.243831	−	0.491231i
$669$	−606.299	−	606.299i	−0.906277	−	0.906277i
$670$	70.3692	−	569.202i	0.105029	−	0.849555i
$671$			1354.83i			2.01913i
$672$	1062.34	−	407.704i	1.58086	−	0.606702i
$673$			399.687i			0.593888i	0.954895	+	0.296944i	$0.0959675\pi$
$673$			399.687i			0.593888i	−0.954895	+	0.296944i	$0.904032\pi$
$674$	−139.987	+	32.8314i	−0.207695	+	0.0487113i
$675$	51.1744	+	649.292i	0.0758140	+	0.961915i
$676$	−300.449	−	605.296i	−0.444451	−	0.895408i
$677$	−556.517	−	556.517i	−0.822034	−	0.822034i	0.164366	−	0.986399i	$-0.447442\pi$
$677$	−556.517	−	556.517i	−0.822034	−	0.822034i	−0.986399	+	0.164366i	$0.947442\pi$
$678$	−854.927	−	530.095i	−1.26095	−	0.781850i
$679$	−505.034			−0.743790
$680$	235.278	−	489.982i	0.345997	−	0.720561i
$681$			1569.46i			2.30464i
$682$	−692.962	−	429.669i	−1.01607	−	0.630013i
$683$	−344.386	+	344.386i	−0.504226	+	0.504226i	−0.912748	−	0.408523i	$-0.866044\pi$
$683$	−344.386	+	344.386i	−0.504226	+	0.504226i	0.408523	+	0.912748i	$0.366044\pi$
$684$	828.534	+	278.860i	1.21131	+	0.407689i
$685$	1056.97	−	487.341i	1.54302	−	0.711447i
$686$	629.025	−	147.527i	0.916946	−	0.215053i
$687$	−2018.33			−2.93788
$688$	141.012	+	1029.86i	0.204959	+	1.49689i
$689$	−10.8431			−0.0157375
$690$	−960.034	−	118.687i	−1.39135	−	0.172010i
$691$	−372.188	+	372.188i	−0.538623	+	0.538623i	−0.923124	−	0.384502i	$-0.874373\pi$
$691$	−372.188	+	372.188i	−0.538623	+	0.538623i	0.384502	+	0.923124i	$0.374373\pi$
$692$	355.720	−	1056.90i	0.514046	−	1.52731i
$693$	−1459.61	−	1459.61i	−2.10623	−	2.10623i
$694$	631.818	+	391.757i	0.910401	+	0.564491i
$695$	−102.709	−	37.8847i	−0.147783	−	0.0545104i
$696$	367.077	−	303.645i	0.527409	−	0.436271i
$697$	−226.591			−0.325094
$698$	419.733	−	676.938i	0.601337	−	0.969825i
$699$	−666.004	−	666.004i	−0.952795	−	0.952795i
$700$	713.155	+	179.069i	1.01879	+	0.255812i
$701$	−771.687	−	771.687i	−1.10084	−	1.10084i	−0.994310	−	0.106527i	$-0.966027\pi$
$701$	−771.687	−	771.687i	−1.10084	−	1.10084i	−0.106527	−	0.994310i	$-0.533973\pi$
$702$	12.4056	−	2.90952i	0.0176718	−	0.00414461i
$703$	−168.108			−0.239130
$704$	1032.93	−	701.848i	1.46724	−	0.996943i
$705$	−345.849	−	127.568i	−0.490566	−	0.180948i
$706$	936.253	−	219.582i	1.32614	−	0.311022i
$707$	−414.397	−	414.397i	−0.586134	−	0.586134i
$708$	−442.480	−	891.435i	−0.624971	−	1.25909i
$709$	587.231	−	587.231i	0.828253	−	0.828253i	−0.159022	−	0.987275i	$-0.550834\pi$
$709$	587.231	−	587.231i	0.828253	−	0.828253i	0.987275	+	0.159022i	$0.0508342\pi$
$710$	425.762	+	545.885i	0.599665	+	0.768853i
$711$	1928.82			2.71282
$712$	−327.972	+	271.297i	−0.460634	+	0.381036i
$713$	417.920			0.586142
$714$	−509.256	+	821.319i	−0.713244	+	1.15031i
$715$	21.6672	−	9.99019i	0.0303037	−	0.0139723i
$716$	36.5121	−	108.483i	0.0509945	−	0.151512i
$717$	862.213	−	862.213i	1.20253	−	1.20253i
$718$	120.749	+	514.850i	0.168174	+	0.717061i
$719$		−	645.101i		−	0.897220i	−0.893728	−	0.448610i	$-0.851919\pi$
$719$		−	645.101i		−	0.897220i	0.893728	−	0.448610i	$-0.148081\pi$
$720$	1123.90	+	248.137i	1.56098	+	0.344635i
$721$	−974.437			−1.35151
$722$	−253.602	+	59.4780i	−0.351250	+	0.0823794i
$723$	230.249	+	230.249i	0.318464	+	0.318464i
$724$	−124.057	+	368.593i	−0.171350	+	0.509106i
$725$	306.886	−	24.1875i	0.423292	−	0.0333620i
$726$	−2135.16	−	1323.90i	−2.94099	−	1.82355i
$727$		−	497.513i		−	0.684336i	−0.939639	−	0.342168i	$-0.888839\pi$
$727$		−	497.513i		−	0.684336i	0.939639	−	0.342168i	$-0.111161\pi$
$728$	1.35442	−	14.3215i	0.00186046	−	0.0196724i
$729$			1184.18i			1.62439i
$730$	−97.4559	−	124.952i	−0.133501	−	0.171167i
$731$	−624.238	−	624.238i	−0.853950	−	0.853950i
$732$	597.164	+	1203.07i	0.815798	+	1.64354i
$733$	666.877	−	666.877i	0.909791	−	0.909791i	−0.0864639	−	0.996255i	$-0.527557\pi$
$733$	666.877	−	666.877i	0.909791	−	0.909791i	0.996255	+	0.0864639i	$0.0275567\pi$
$734$	166.105	+	708.240i	0.226302	+	0.964905i
$735$	−114.919	−	42.3885i	−0.156353	−	0.0576715i
$736$	−260.392	+	584.733i	−0.353793	+	0.794474i
$737$			1119.12i			1.51849i
$738$	−109.559	−	467.138i	−0.148454	−	0.632978i
$739$	601.668	−	601.668i	0.814165	−	0.814165i	−0.171091	−	0.985255i	$-0.554729\pi$
$739$	601.668	−	601.668i	0.814165	−	0.814165i	0.985255	+	0.171091i	$0.0547291\pi$
$740$	−220.056	+	23.7175i	−0.297373	+	0.0320507i
$741$	12.7035	−	12.7035i	0.0171437	−	0.0171437i
$742$	554.159	+	343.604i	0.746845	+	0.463079i
$743$			792.904i			1.06717i	0.845748	+	0.533583i	$0.179155\pi$
$743$			792.904i			1.06717i	−0.845748	+	0.533583i	$0.820845\pi$
$744$	−804.722	−	76.1045i	−1.08162	−	0.102291i
$745$	−104.191	+	282.471i	−0.139853	+	0.379155i
$746$	436.569	−	704.091i	0.585214	−	0.943822i
$747$	−24.6260	+	24.6260i	−0.0329666	+	0.0329666i
$748$	−338.318	+	1005.19i	−0.452296	+	1.34384i
$749$	200.342	+	200.342i	0.267479	+	0.267479i
$750$	816.153	+	891.958i	1.08820	+	1.18928i
$751$			456.092i			0.607312i	0.952782	+	0.303656i	$0.0982074\pi$
$751$			456.092i			0.607312i	−0.952782	+	0.303656i	$0.901793\pi$
$752$	−147.485	+	194.281i	−0.196124	+	0.258353i
$753$			2052.89i			2.72628i
$754$	−1.37518	−	5.86348i	−0.00182384	−	0.00777650i
$755$	1146.63	−	528.684i	1.51872	−	0.700243i
$756$	−726.212	−	244.421i	−0.960598	−	0.323308i
$757$	512.280	+	512.280i	0.676724	+	0.676724i	0.959258	−	0.282533i	$-0.0911747\pi$
$757$	512.280	+	512.280i	0.676724	+	0.676724i	−0.282533	+	0.959258i	$0.591175\pi$
$758$	−138.062	+	222.664i	−0.182140	+	0.293752i
$759$	1887.55			2.48689
$760$	573.303	−	201.338i	0.754346	−	0.264918i
$761$		−	682.433i		−	0.896758i	−0.893844	−	0.448379i	$-0.852002\pi$
$761$		−	682.433i		−	0.896758i	0.893844	−	0.448379i	$-0.147998\pi$
$762$	−103.310	+	166.617i	−0.135578	+	0.218657i
$763$	−40.5571	+	40.5571i	−0.0531548	+	0.0531548i
$764$	−88.7185	−	178.736i	−0.116124	−	0.233947i
$765$	−887.687	+	409.290i	−1.16038	+	0.535020i
$766$	264.943	+	1129.66i	0.345879	+	1.47476i
$767$	−12.5816			−0.0164037
$768$	607.877	−	1078.51i	0.791506	−	1.40431i
$769$	628.900			0.817815			0.408908	−	0.912576i	$-0.365910\pi$
$769$	628.900			0.817815			0.408908	+	0.912576i	$0.365910\pi$
$770$	−1423.92	−	176.036i	−1.84925	−	0.228618i
$771$	147.232	−	147.232i	0.190962	−	0.190962i
$772$	176.518	+	355.620i	0.228651	+	0.460648i
$773$	−379.170	−	379.170i	−0.490517	−	0.490517i	0.417952	−	0.908469i	$-0.362748\pi$
$773$	−379.170	−	379.170i	−0.490517	−	0.490517i	−0.908469	+	0.417952i	$0.862748\pi$
$774$	985.100	−	1588.75i	1.27274	−	2.05265i
$775$	−397.218	−	339.178i	−0.512539	−	0.437649i
$776$	−423.395	+	350.231i	−0.545612	+	0.451329i
$777$	393.514			0.506453
$778$	650.156	+	403.127i	0.835677	+	0.518158i
$779$	−179.115	−	179.115i	−0.229930	−	0.229930i
$780$	14.8367	−	18.4213i	0.0190215	−	0.0236170i
$781$	−955.193	−	955.193i	−1.22304	−	1.22304i
$782$	−124.128	−	529.258i	−0.158732	−	0.676801i
$783$	−320.795			−0.409700
$784$	−49.0066	+	64.5559i	−0.0625084	+	0.0823418i
$785$	144.485	−	391.712i	0.184057	−	0.498996i
$786$	−505.352	−	2154.72i	−0.642941	−	2.74137i
$787$	−439.685	−	439.685i	−0.558685	−	0.558685i	0.370248	−	0.928933i	$-0.379273\pi$
$787$	−439.685	−	439.685i	−0.558685	−	0.558685i	−0.928933	+	0.370248i	$0.879273\pi$
$788$	1416.78	+	476.845i	1.79794	+	0.605133i
$789$	−709.656	+	709.656i	−0.899437	+	0.899437i
$790$	1057.14	−	824.512i	1.33815	−	1.04369i
$791$	764.735			0.966795
$792$	−2235.88	−	211.453i	−2.82308	−	0.266986i
$793$	16.9800			0.0214124
$794$	−548.633	−	340.178i	−0.690974	−	0.428436i
$795$	448.907	+	973.610i	0.564663	+	1.22467i
$796$	454.928	−	225.812i	0.571518	−	0.283683i
$797$	−214.817	+	214.817i	−0.269532	+	0.269532i	−0.828912	−	0.559380i	$-0.811039\pi$
$797$	−214.817	+	214.817i	−0.269532	+	0.269532i	0.559380	+	0.828912i	$0.311039\pi$
$798$	−1051.79	+	246.679i	−1.31804	+	0.309122i
$799$		−	207.158i		−	0.259271i
$800$	722.055	−	344.438i	0.902568	−	0.430547i
$801$	765.463			0.955634
$802$	−295.259	−	1258.93i	−0.368154	−	1.56974i
$803$	218.641	+	218.641i	0.272280	+	0.272280i
$804$	493.272	+	993.763i	0.613522	+	1.23602i
$805$	667.829	−	307.919i	0.829601	−	0.382509i
$806$	−5.38500	+	8.68484i	−0.00668115	+	0.0107752i
$807$		−	1415.60i		−	1.75415i
$808$	−634.786	−	60.0332i	−0.785626	−	0.0742985i
$809$			447.353i			0.552971i	0.961018	+	0.276485i	$0.0891697\pi$
$809$			447.353i			0.552971i	−0.961018	+	0.276485i	$0.910830\pi$
$810$	21.4937	+	27.5578i	0.0265354	+	0.0340220i
$811$	429.030	+	429.030i	0.529013	+	0.529013i	0.920278	−	0.391265i	$-0.127962\pi$
$811$	429.030	+	429.030i	0.529013	+	0.529013i	−0.391265	+	0.920278i	$0.627962\pi$
$812$	−115.525	+	343.242i	−0.142272	+	0.422712i
$813$	159.458	−	159.458i	0.196136	−	0.196136i
$814$	420.467	−	98.6132i	0.516544	−	0.121146i
$815$	−141.811	−	52.3076i	−0.174001	−	0.0641811i
$816$	142.634	+	1041.71i	0.174797	+	1.27661i
$817$		−	986.894i		−	1.20795i
$818$	−103.329	+	24.2341i	−0.126320	+	0.0296260i
$819$	−18.2932	+	18.2932i	−0.0223360	+	0.0223360i
$820$	−259.734	−	209.193i	−0.316749	−	0.255114i
$821$	450.943	−	450.943i	0.549260	−	0.549260i	−0.376967	−	0.926227i	$-0.623033\pi$
$821$	450.943	−	450.943i	0.549260	−	0.549260i	0.926227	+	0.376967i	$0.123033\pi$
$822$	−1186.45	+	1913.49i	−1.44338	+	2.32785i
$823$		−	294.392i		−	0.357705i	−0.983876	−	0.178853i	$-0.942761\pi$
$823$		−	294.392i		−	0.357705i	0.983876	−	0.178853i	$-0.0572386\pi$
$824$	−816.919	+	675.753i	−0.991406	+	0.820089i
$825$	−1794.05	−	1531.91i	−2.17461	−	1.85686i
$826$	643.010	+	398.696i	0.778462	+	0.482683i
$827$	1015.70	−	1015.70i	1.22818	−	1.22818i	0.263523	−	0.964653i	$-0.415116\pi$
$827$	1015.70	−	1015.70i	1.22818	−	1.22818i	0.964653	−	0.263523i	$-0.0848845\pi$
$828$	1031.10	−	511.804i	1.24529	−	0.618121i
$829$	−402.136	−	402.136i	−0.485085	−	0.485085i	0.421666	−	0.906751i	$-0.361445\pi$
$829$	−402.136	−	402.136i	−0.485085	−	0.485085i	−0.906751	+	0.421666i	$0.861445\pi$
$830$	−2.97001	+	24.0238i	−0.00357833	+	0.0289444i
$831$		−	117.869i		−	0.141840i
$832$	−8.79620	−	12.9457i	−0.0105724	−	0.0155597i
$833$		−	68.8346i		−	0.0826345i
$834$	206.172	−	48.3539i	0.247208	−	0.0579783i
$835$	191.740	+	415.854i	0.229629	+	0.498029i
$836$	−1062.02	+	527.151i	−1.27036	+	0.630564i
$837$	384.885	+	384.885i	0.459839	+	0.459839i
$838$	−295.367	−	183.142i	−0.352467	−	0.218546i
$839$	−826.671			−0.985305			−0.492652	−	0.870226i	$-0.663973\pi$
$839$	−826.671			−0.985305			−0.492652	+	0.870226i	$0.663973\pi$
$840$	−1342.01	+	471.298i	−1.59763	+	0.561069i
$841$		−	689.377i		−	0.819711i
$842$	331.667	+	205.649i	0.393903	+	0.244238i
$843$	1711.27	−	1711.27i	2.02997	−	2.02997i
$844$	−193.101	+	573.731i	−0.228792	+	0.679776i
$845$	353.686	+	767.089i	0.418563	+	0.907798i
$846$	427.075	−	100.163i	0.504817	−	0.118396i
$847$	1909.91			2.25491
$848$	702.862	−	96.2380i	0.828847	−	0.113488i
$849$	−1817.81			−2.14111
$850$	−311.560	+	603.782i	−0.366541	+	0.710331i
$851$	−156.526	+	156.526i	−0.183932	+	0.183932i
$852$	−1269.21	−	427.178i	−1.48968	−	0.501383i
$853$	−1061.55	−	1061.55i	−1.24449	−	1.24449i	−0.958117	−	0.286376i	$-0.907550\pi$
$853$	−1061.55	−	1061.55i	−1.24449	−	1.24449i	−0.286376	−	0.958117i	$-0.592450\pi$
$854$	−867.797	−	538.074i	−1.01616	−	0.630064i
$855$	−1025.23	−	378.163i	−1.19910	−	0.442296i
$856$	306.890	+	29.0233i	0.358516	+	0.0339057i
$857$	397.961			0.464365			0.232182	−	0.972672i	$-0.425413\pi$
$857$	397.961			0.464365			0.232182	+	0.972672i	$0.425413\pi$
$858$	−24.3216	+	39.2254i	−0.0283468	+	0.0457173i
$859$	1012.11	+	1012.11i	1.17825	+	1.17825i	0.980190	+	0.198057i	$0.0634632\pi$
$859$	1012.11	+	1012.11i	1.17825	+	1.17825i	0.198057	+	0.980190i	$0.436537\pi$
$860$	−139.235	−	1291.86i	−0.161902	−	1.50216i
$861$	419.279	+	419.279i	0.486967	+	0.486967i
$862$	−378.892	+	88.8625i	−0.439550	+	0.103089i
$863$	−1099.26			−1.27377			−0.636883	−	0.770960i	$-0.719777\pi$
$863$	−1099.26			−1.27377			−0.636883	+	0.770960i	$0.719777\pi$
$864$	−778.321	+	298.704i	−0.900835	+	0.345722i
$865$	−482.393	+	1307.81i	−0.557680	+	1.51192i
$866$	968.483	−	227.141i	1.11834	−	0.262287i
$867$	356.838	+	356.838i	0.411578	+	0.411578i
$868$	550.422	−	273.212i	0.634127	−	0.314760i
$869$	−1849.78	+	1849.78i	−2.12863	+	2.12863i
$870$	−469.553	+	366.227i	−0.539716	+	0.420951i
$871$	14.0259			0.0161032
$872$	−5.87547	+	62.1267i	−0.00673792	+	0.0712462i
$873$	988.174			1.13193
$874$	320.247	−	516.488i	0.366415	−	0.590948i
$875$	−884.651	−	249.335i	−1.01103	−	0.284954i
$876$	290.519	+	97.7799i	0.331643	+	0.111621i
$877$	−1115.85	+	1115.85i	−1.27235	+	1.27235i	−0.327496	+	0.944852i	$0.606205\pi$
$877$	−1115.85	+	1115.85i	−1.27235	+	1.27235i	−0.944852	+	0.327496i	$0.893795\pi$
$878$	−49.9987	−	213.184i	−0.0569461	−	0.242807i
$879$			558.912i			0.635850i
$880$	−1315.82	+	839.881i	−1.49525	+	0.954411i
$881$	−380.477			−0.431870			−0.215935	−	0.976408i	$-0.569280\pi$
$881$	−380.477			−0.431870			−0.215935	+	0.976408i	$0.569280\pi$
$882$	141.909	−	33.2823i	0.160895	−	0.0377350i
$883$	856.732	+	856.732i	0.970251	+	0.970251i	0.999570	−	0.0293188i	$-0.00933381\pi$
$883$	856.732	+	856.732i	0.970251	+	0.970251i	−0.0293188	+	0.999570i	$0.509334\pi$
$884$	12.5980	+	4.24011i	0.0142511	+	0.00479650i
$885$	520.882	+	1129.71i	0.588568	+	1.27651i
$886$	212.664	+	131.862i	0.240027	+	0.148828i
$887$			1518.45i			1.71190i	0.517059	+	0.855950i	$0.327027\pi$
$887$			1518.45i			1.71190i	−0.517059	+	0.855950i	$0.672973\pi$
$888$	329.902	−	272.894i	0.371511	−	0.307313i
$889$		−	149.039i		−	0.167648i
$890$	419.531	−	327.213i	0.471383	−	0.367655i
$891$	−48.2208	−	48.2208i	−0.0541199	−	0.0541199i
$892$	635.255	−	315.320i	0.712170	−	0.353498i
$893$	163.754	−	163.754i	0.183375	−	0.183375i
$894$	−132.983	−	567.014i	−0.148751	−	0.634244i
$895$	−49.5141	+	134.237i	−0.0553231	+	0.149986i
$896$	39.3155	+	940.354i	0.0438789	+	1.04950i
$897$		−	23.6565i		−	0.0263729i
$898$	120.825	+	515.175i	0.134549	+	0.573692i
$899$	181.915	−	181.915i	0.202352	−	0.202352i
$900$	−1395.40	−	350.375i	−1.55044	−	0.389305i
$901$	−426.031	+	426.031i	−0.472843	+	0.472843i
$902$	553.067	+	342.927i	0.613156	+	0.380185i
$903$			2310.15i			2.55831i
$904$	641.116	−	530.329i	0.709199	−	0.586648i
$905$	168.235	−	456.099i	0.185895	−	0.503977i
$906$	−1287.11	+	2075.82i	−1.42065	+	2.29119i
$907$	−33.4987	+	33.4987i	−0.0369335	+	0.0369335i	−0.725332	−	0.688399i	$-0.758314\pi$
$907$	−33.4987	+	33.4987i	−0.0369335	+	0.0369335i	0.688399	+	0.725332i	$0.258314\pi$
$908$	−1230.32	−	414.090i	−1.35498	−	0.456046i
$909$	810.830	+	810.830i	0.892002	+	0.892002i
$910$	−2.20625	+	17.8459i	−0.00242445	+	0.0196108i
$911$		−	1161.25i		−	1.27470i	−0.770574	−	0.637350i	$-0.780030\pi$
$911$		−	1161.25i		−	1.27470i	0.770574	−	0.637350i	$-0.219970\pi$
$912$	−710.703	+	936.202i	−0.779279	+	1.02654i
$913$		−	47.2340i		−	0.0517349i
$914$	−108.054	−	460.722i	−0.118221	−	0.504072i
$915$	−702.975	−	1524.64i	−0.768279	−	1.66628i
$916$	532.520	−	1582.20i	0.581354	−	1.72729i
$917$	1189.72	+	1189.72i	1.29741	+	1.29741i
$918$	373.106	−	601.739i	0.406434	−	0.655489i
$919$	412.372			0.448718			0.224359	−	0.974507i	$-0.427971\pi$
$919$	412.372			0.448718			0.224359	+	0.974507i	$0.427971\pi$
$920$	346.338	−	721.271i	0.376455	−	0.783990i
$921$			908.590i			0.986526i
$922$	64.9594	−	104.765i	0.0704549	−	0.113628i
$923$	−11.9714	+	11.9714i	−0.0129700	+	0.0129700i
$924$	2486.01	−	1233.97i	2.69048	−	1.33547i
$925$	275.808	−	21.7380i	0.298170	−	0.0235005i
$926$	−156.029	−	665.275i	−0.168497	−	0.718440i
$927$	1906.63			2.05678
$928$	141.182	+	367.872i	0.152135	+	0.396413i
$929$	1118.33			1.20380			0.601900	−	0.798572i	$-0.294411\pi$
$929$	1118.33			1.20380			0.601900	+	0.798572i	$0.294411\pi$
$930$	1002.76	+	123.969i	1.07823	+	0.133300i
$931$	54.4123	−	54.4123i	0.0584450	−	0.0584450i
$932$	697.811	−	346.371i	0.748725	−	0.371643i
$933$	299.976	+	299.976i	0.321517	+	0.321517i
$934$	494.092	−	796.863i	0.529007	−	0.853173i
$935$	458.794	−	1243.83i	0.490689	−	1.33030i
$936$	−2.65012	+	28.0221i	−0.00283132	+	0.0299382i
$937$	1515.26			1.61714			0.808569	−	0.588402i	$-0.200243\pi$
$937$	1515.26			1.61714			0.808569	+	0.588402i	$0.200243\pi$
$938$	−716.821	−	444.463i	−0.764202	−	0.473841i
$939$	119.053	+	119.053i	0.126787	+	0.126787i
$940$	191.253	−	237.459i	0.203460	−	0.252616i
$941$	302.710	+	302.710i	0.321690	+	0.321690i	0.849415	−	0.527725i	$-0.176955\pi$
$941$	302.710	+	302.710i	0.321690	+	0.321690i	−0.527725	+	0.849415i	$0.676955\pi$
$942$	184.412	+	786.298i	0.195767	+	0.834711i
$943$	−333.550			−0.353711
$944$	815.555	−	111.668i	0.863936	−	0.118293i
$945$	898.620	+	331.461i	0.950921	+	0.350752i
$946$	578.917	+	2468.39i	0.611963	+	2.60929i
$947$	−328.255	−	328.255i	−0.346627	−	0.346627i	0.512225	−	0.858851i	$-0.328821\pi$
$947$	−328.255	−	328.255i	−0.346627	−	0.346627i	−0.858851	+	0.512225i	$0.828821\pi$
$948$	−827.254	+	2457.90i	−0.872631	+	2.59272i
$949$	2.74021	−	2.74021i	0.00288747	−	0.00288747i
$950$	−723.558	+	230.995i	−0.761640	+	0.243153i
$951$	−2514.86			−2.64443
$952$	−509.482	−	615.913i	−0.535170	−	0.646968i
$953$	274.672			0.288218			0.144109	−	0.989562i	$-0.453968\pi$
$953$	274.672			0.288218			0.144109	+	0.989562i	$0.453968\pi$
$954$	−1084.30	−	672.314i	−1.13658	−	0.704731i
$955$	104.439	+	226.511i	0.109360	+	0.237184i
$956$	448.414	+	903.391i	0.469052	+	0.944970i
$957$	821.626	−	821.626i	0.858543	−	0.858543i
$958$	−168.031	+	39.4086i	−0.175397	+	0.0411363i
$959$		−	1711.63i		−	1.78480i
$960$	−798.235	+	1325.77i	−0.831495	+	1.38101i
$961$	524.482			0.545767
$962$	−1.23591	−	5.26968i	−0.00128473	−	0.00547784i
$963$	−391.999	−	391.999i	−0.407060	−	0.407060i
$964$	−241.246	+	119.747i	−0.250255	+	0.124218i
$965$	−207.795	−	450.676i	−0.215332	−	0.467022i
$966$	−749.644	+	1209.01i	−0.776029	+	1.25157i
$967$		−	474.871i		−	0.491076i	−0.969387	−	0.245538i	$-0.921035\pi$
$967$		−	474.871i		−	0.491076i	0.969387	−	0.245538i	$-0.0789647\pi$
$968$	1601.17	−	1324.48i	1.65410	−	1.36827i
$969$		−	998.251i		−	1.03019i
$970$	541.594	−	422.415i	0.558344	−	0.435480i
$971$	565.643	+	565.643i	0.582536	+	0.582536i	0.935600	−	0.353063i	$-0.114860\pi$
$971$	565.643	+	565.643i	0.582536	+	0.582536i	−0.353063	+	0.935600i	$0.614860\pi$
$972$	−952.958	−	320.737i	−0.980409	−	0.329976i
$973$	−113.837	+	113.837i	−0.116996	+	0.116996i
$974$	−1312.96	+	307.932i	−1.34801	+	0.316152i
$975$	−19.1993	+	22.4847i	−0.0196916	+	0.0230612i
$976$	−1100.66	+	150.706i	−1.12773	+	0.154412i
$977$		−	318.232i		−	0.325723i	−0.986649	−	0.162862i	$-0.947928\pi$
$977$		−	318.232i		−	0.325723i	0.986649	−	0.162862i	$-0.0520724\pi$
$978$	284.662	−	66.7624i	0.291065	−	0.0682642i
$979$	−734.098	+	734.098i	−0.749845	+	0.749845i
$980$	63.5496	−	78.9031i	0.0648465	−	0.0805133i
$981$	79.3561	−	79.3561i	0.0808931	−	0.0808931i
$982$	−98.0181	+	158.082i	−0.0998148	+	0.160980i
$983$			1277.48i			1.29957i	0.760116	+	0.649787i	$0.225142\pi$
$983$			1277.48i			1.29957i	−0.760116	+	0.649787i	$0.774858\pi$
$984$	642.264	+	60.7404i	0.652707	+	0.0617281i
$985$	−1753.13	−	646.651i	−1.77983	−	0.656499i
$986$	−284.410	−	176.348i	−0.288449	−	0.178852i
$987$	−383.320	+	383.320i	−0.388369	+	0.388369i
$988$	6.60674	+	13.3102i	0.00668698	+	0.0134718i
$989$	−918.901	−	918.901i	−0.929122	−	0.929122i
$990$	2786.11	+	344.441i	2.81426	+	0.347920i
$991$			172.244i			0.173809i	0.996217	+	0.0869043i	$0.0276974\pi$
$991$			172.244i			0.173809i	−0.996217	+	0.0869043i	$0.972303\pi$
$992$	271.979	−	610.755i	0.274173	−	0.615680i
$993$		−	2460.81i		−	2.47815i
$994$	991.176	−	232.463i	0.997159	−	0.233866i
$995$	−576.529	+	265.823i	−0.579426	+	0.267159i
$996$	−20.8191	−	41.9429i	−0.0209027	−	0.0421114i
$997$	−1299.92	−	1299.92i	−1.30383	−	1.30383i	−0.925789	−	0.378041i	$-0.876598\pi$
$997$	−1299.92	−	1299.92i	−1.30383	−	1.30383i	−0.378041	−	0.925789i	$-0.623402\pi$
$998$	−987.421	−	612.247i	−0.989400	−	0.613474i
$999$	−288.307			−0.288596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.k.a.19.12	yes	44
4.3	odd	2		320.3.k.a.239.2		44
5.2	odd	4		400.3.r.g.51.1		44
5.3	odd	4		400.3.r.g.51.22		44
5.4	even	2	inner	80.3.k.a.19.11	✓	44
8.3	odd	2		640.3.k.a.479.21		44
8.5	even	2		640.3.k.b.479.2		44
16.3	odd	4		640.3.k.b.159.21		44
16.5	even	4		320.3.k.a.79.21		44
16.11	odd	4	inner	80.3.k.a.59.11	yes	44
16.13	even	4		640.3.k.a.159.2		44
20.19	odd	2		320.3.k.a.239.21		44
40.19	odd	2		640.3.k.a.479.2		44
40.29	even	2		640.3.k.b.479.21		44
80.19	odd	4		640.3.k.b.159.2		44
80.27	even	4		400.3.r.g.251.1		44
80.29	even	4		640.3.k.a.159.21		44
80.43	even	4		400.3.r.g.251.22		44
80.59	odd	4	inner	80.3.k.a.59.12	yes	44
80.69	even	4		320.3.k.a.79.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.k.a.19.11	✓	44	5.4	even	2	inner
80.3.k.a.19.12	yes	44	1.1	even	1	trivial
80.3.k.a.59.11	yes	44	16.11	odd	4	inner
80.3.k.a.59.12	yes	44	80.59	odd	4	inner
320.3.k.a.79.2		44	80.69	even	4
320.3.k.a.79.21		44	16.5	even	4
320.3.k.a.239.2		44	4.3	odd	2
320.3.k.a.239.21		44	20.19	odd	2
400.3.r.g.51.1		44	5.2	odd	4
400.3.r.g.51.22		44	5.3	odd	4
400.3.r.g.251.1		44	80.27	even	4
400.3.r.g.251.22		44	80.43	even	4
640.3.k.a.159.2		44	16.13	even	4
640.3.k.a.159.21		44	80.29	even	4
640.3.k.a.479.2		44	40.19	odd	2
640.3.k.a.479.21		44	8.3	odd	2
640.3.k.b.159.2		44	80.19	odd	4
640.3.k.b.159.21		44	16.3	odd	4
640.3.k.b.479.2		44	8.5	even	2
640.3.k.b.479.21		44	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.456673 + 1.94716i) q^{2} +(3.41958 + 3.41958i) q^{3} +(-3.58290 + 1.77844i) q^{4} +(4.54060 - 2.09356i) q^{5} +(-5.09686 + 8.22013i) q^{6} -7.35293i q^{7} +(-5.09912 - 6.16433i) q^{8} +14.3871i q^{9} +O(q^{10})\)	\(q+(0.456673 + 1.94716i) q^{2} +(3.41958 + 3.41958i) q^{3} +(-3.58290 + 1.77844i) q^{4} +(4.54060 - 2.09356i) q^{5} +(-5.09686 + 8.22013i) q^{6} -7.35293i q^{7} +(-5.09912 - 6.16433i) q^{8} +14.3871i q^{9} +(6.15007 + 7.88522i) q^{10} +(-13.7976 - 13.7976i) q^{11} +(-18.3335 - 6.17052i) q^{12} +(-0.172924 + 0.172924i) q^{13} +(14.3174 - 3.35789i) q^{14} +(22.6860 + 8.36787i) q^{15} +(9.67434 - 12.7439i) q^{16} +13.5885i q^{17} +(-28.0141 + 6.57021i) q^{18} +(-10.7415 + 10.7415i) q^{19} +(-12.5452 + 15.5762i) q^{20} +(25.1440 - 25.1440i) q^{21} +(20.5652 - 33.1672i) q^{22} +20.0028i q^{23} +(3.64258 - 38.5163i) q^{24} +(16.2340 - 19.0120i) q^{25} +(-0.415682 - 0.257742i) q^{26} +(-18.4217 + 18.4217i) q^{27} +(13.0767 + 26.3448i) q^{28} +(8.70697 + 8.70697i) q^{29} +(-5.93350 + 47.9948i) q^{30} -20.8930i q^{31} +(29.2325 + 13.0177i) q^{32} -94.3641i q^{33} +(-26.4591 + 6.20552i) q^{34} +(-15.3938 - 33.3867i) q^{35} +(-25.5866 - 51.5476i) q^{36} +(7.82521 + 7.82521i) q^{37} +(-25.8207 - 16.0101i) q^{38} -1.18266 q^{39} +(-36.0584 - 17.3145i) q^{40} +16.6751i q^{41} +(60.4420 + 37.4769i) q^{42} +(-45.9385 + 45.9385i) q^{43} +(73.9736 + 24.8973i) q^{44} +(30.1202 + 65.3261i) q^{45} +(-38.9488 + 9.13476i) q^{46} -15.2450 q^{47} +(76.6611 - 10.4967i) q^{48} -5.06563 q^{49} +(44.4331 + 22.9281i) q^{50} +(-46.4672 + 46.4672i) q^{51} +(0.312035 - 0.927104i) q^{52} +(31.3522 + 31.3522i) q^{53} +(-44.2828 - 27.4574i) q^{54} +(-91.5354 - 33.7633i) q^{55} +(-45.3259 + 37.4935i) q^{56} -73.4627 q^{57} +(-12.9777 + 20.9302i) q^{58} +(36.3791 + 36.3791i) q^{59} +(-96.1635 + 10.3644i) q^{60} +(-49.0967 - 49.0967i) q^{61} +(40.6821 - 9.54127i) q^{62} +105.788 q^{63} +(-11.9980 + 62.8653i) q^{64} +(-0.423152 + 1.14721i) q^{65} +(183.742 - 43.0936i) q^{66} +(-40.5551 - 40.5551i) q^{67} +(-24.1663 - 48.6864i) q^{68} +(-68.4014 + 68.4014i) q^{69} +(57.9795 - 45.2210i) q^{70} +69.2289 q^{71} +(88.6870 - 73.3616i) q^{72} -15.8463 q^{73} +(-11.6634 + 18.8105i) q^{74} +(120.527 - 9.49940i) q^{75} +(19.3826 - 57.5886i) q^{76} +(-101.453 + 101.453i) q^{77} +(-0.540088 - 2.30283i) q^{78} -134.066i q^{79} +(17.2472 - 78.1187i) q^{80} +3.49487 q^{81} +(-32.4692 + 7.61507i) q^{82} +(1.71167 + 1.71167i) q^{83} +(-45.3714 + 134.805i) q^{84} +(28.4484 + 61.7001i) q^{85} +(-110.429 - 68.4710i) q^{86} +59.5485i q^{87} +(-14.6974 + 155.409i) q^{88} -53.2048i q^{89} +(-113.446 + 88.4817i) q^{90} +(1.27150 + 1.27150i) q^{91} +(-35.5738 - 71.6682i) q^{92} +(71.4454 - 71.4454i) q^{93} +(-6.96199 - 29.6846i) q^{94} +(-26.2848 + 71.2605i) q^{95} +(55.4478 + 144.478i) q^{96} -68.6846i q^{97} +(-2.31334 - 9.86362i) q^{98} +(198.508 - 198.508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 44 q - 4 q^{4} - 2 q^{5} - 4 q^{6} - 20 q^{10} - 4 q^{11} + 4 q^{14} - 32 q^{16} - 36 q^{19} + 40 q^{20} + 32 q^{21} + 16 q^{24} - 56 q^{26} - 4 q^{29} - 160 q^{30} - 192 q^{34} + 212 q^{36} - 8 q^{39} - 184 q^{40} + 224 q^{44} + 30 q^{45} + 124 q^{46} - 148 q^{49} + 100 q^{50} + 128 q^{51} + 24 q^{54} - 260 q^{55} + 360 q^{56} - 68 q^{59} - 80 q^{60} + 28 q^{61} - 16 q^{64} - 20 q^{65} + 448 q^{66} + 128 q^{69} + 396 q^{70} - 264 q^{71} + 480 q^{74} + 60 q^{75} - 464 q^{76} + 504 q^{80} - 116 q^{81} - 496 q^{84} + 48 q^{85} - 852 q^{86} + 144 q^{90} + 384 q^{91} - 340 q^{94} - 1128 q^{96} + 484 q^{99}+O(q^{100}) \) 44 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 - 20 * q^10 - 4 * q^11 + 4 * q^14 - 32 * q^16 - 36 * q^19 + 40 * q^20 + 32 * q^21 + 16 * q^24 - 56 * q^26 - 4 * q^29 - 160 * q^30 - 192 * q^34 + 212 * q^36 - 8 * q^39 - 184 * q^40 + 224 * q^44 + 30 * q^45 + 124 * q^46 - 148 * q^49 + 100 * q^50 + 128 * q^51 + 24 * q^54 - 260 * q^55 + 360 * q^56 - 68 * q^59 - 80 * q^60 + 28 * q^61 - 16 * q^64 - 20 * q^65 + 448 * q^66 + 128 * q^69 + 396 * q^70 - 264 * q^71 + 480 * q^74 + 60 * q^75 - 464 * q^76 + 504 * q^80 - 116 * q^81 - 496 * q^84 + 48 * q^85 - 852 * q^86 + 144 * q^90 + 384 * q^91 - 340 * q^94 - 1128 * q^96 + 484 * q^99

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