LMFDB - Embedded newform 450.3.n.a.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,3,Mod(71,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("450.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.2616118962$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.1
Character	$\chi$	$=$	450.161
Dual form			450.3.n.a.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.831254 - 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} +(-4.91641 - 0.910429i) q^{5} -1.49980 q^{7} +(2.68999 - 0.874032i) q^{8} +O(q^{10})$	\(q+(-0.831254 - 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} +(-4.91641 - 0.910429i) q^{5} -1.49980 q^{7} +(2.68999 - 0.874032i) q^{8} +(3.04515 + 6.38178i) q^{10} +(-5.85772 - 8.06245i) q^{11} +(3.00062 + 2.18008i) q^{13} +(1.24672 + 1.71596i) q^{14} +(-3.23607 - 2.35114i) q^{16} +(-2.47472 + 0.804085i) q^{17} +(5.78349 + 17.7997i) q^{19} +(4.77025 - 8.78890i) q^{20} +(-4.35519 + 13.4039i) q^{22} +(1.70590 + 2.34798i) q^{23} +(23.3422 + 8.95209i) q^{25} -5.24527i q^{26} +(0.926929 - 2.85280i) q^{28} +(21.2454 + 6.90306i) q^{29} +(11.5942 + 35.6834i) q^{31} +5.65685i q^{32} +(2.97709 + 2.16298i) q^{34} +(7.37365 + 1.36546i) q^{35} +(26.3519 + 19.1458i) q^{37} +(15.5575 - 21.4131i) q^{38} +(-14.0209 + 1.84805i) q^{40} +(-12.9274 + 17.7931i) q^{41} +30.8625 q^{43} +(18.9560 - 6.15917i) q^{44} +(1.26833 - 3.90353i) q^{46} +(37.3634 + 12.1401i) q^{47} -46.7506 q^{49} +(-9.16104 - 34.1478i) q^{50} +(-6.00124 + 4.36015i) q^{52} +(37.8510 + 12.2985i) q^{53} +(21.4587 + 44.9714i) q^{55} +(-4.03446 + 1.31088i) q^{56} +(-9.76239 - 30.0456i) q^{58} +(7.44680 - 10.2496i) q^{59} +(-29.4291 + 21.3815i) q^{61} +(31.1884 - 42.9272i) q^{62} +(6.47214 - 4.70228i) q^{64} +(-12.7675 - 13.4500i) q^{65} +(22.6871 + 69.8236i) q^{67} -5.20415i q^{68} +(-4.56712 - 9.57141i) q^{70} +(-61.7104 - 20.0509i) q^{71} +(91.8321 - 66.7199i) q^{73} -46.0648i q^{74} -37.4315 q^{76} +(8.78542 + 12.0921i) q^{77} +(14.2736 - 43.9295i) q^{79} +(13.7693 + 14.5054i) q^{80} +31.1035 q^{82} +(13.5557 - 4.40452i) q^{83} +(12.8988 - 1.70016i) q^{85} +(-25.6546 - 35.3105i) q^{86} +(-22.8041 - 16.5681i) q^{88} +(84.3402 + 116.084i) q^{89} +(-4.50034 - 3.26969i) q^{91} +(-5.52042 + 1.79369i) q^{92} +(-17.1687 - 52.8398i) q^{94} +(-12.2286 - 92.7764i) q^{95} +(4.99340 - 15.3681i) q^{97} +(38.8616 + 53.4884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 8 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 + 8 * q^7	$ 32 q + 16 q^{4} + 8 q^{7} - 20 q^{10} - 16 q^{13} - 32 q^{16} - 12 q^{19} - 32 q^{22} - 20 q^{25} + 24 q^{28} - 12 q^{31} + 116 q^{34} + 88 q^{37} - 40 q^{43} + 168 q^{46} - 416 q^{49} + 32 q^{52} + 320 q^{55} + 192 q^{58} - 280 q^{61} + 64 q^{64} - 96 q^{67} + 160 q^{70} - 248 q^{73} - 16 q^{76} + 328 q^{79} - 688 q^{82} - 380 q^{85} - 56 q^{88} + 256 q^{91} + 160 q^{94} - 852 q^{97}+O(q^{100}) $ 32 * q + 16 * q^4 + 8 * q^7 - 20 * q^10 - 16 * q^13 - 32 * q^16 - 12 * q^19 - 32 * q^22 - 20 * q^25 + 24 * q^28 - 12 * q^31 + 116 * q^34 + 88 * q^37 - 40 * q^43 + 168 * q^46 - 416 * q^49 + 32 * q^52 + 320 * q^55 + 192 * q^58 - 280 * q^61 + 64 * q^64 - 96 * q^67 + 160 * q^70 - 248 * q^73 - 16 * q^76 + 328 * q^79 - 688 * q^82 - 380 * q^85 - 56 * q^88 + 256 * q^91 + 160 * q^94 - 852 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.831254	−	1.14412i	−0.415627	−	0.572061i
$2$	−0.831254	−	1.14412i	−0.415627	−	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.618034	+	1.90211i	−0.154508	+	0.475528i
$5$	−4.91641	−	0.910429i	−0.983283	−	0.182086i
$5$	−4.91641	−	0.910429i	−0.983283	−	0.182086i
$6$		0			0
$7$	−1.49980			−0.214258			−0.107129	−	0.994245i	$-0.534166\pi$
$7$	−1.49980			−0.214258			−0.107129	+	0.994245i	$0.534166\pi$
$8$	2.68999	−	0.874032i	0.336249	−	0.109254i
$9$		0			0
$10$	3.04515	+	6.38178i	0.304515	+	0.638178i
$11$	−5.85772	−	8.06245i	−0.532520	−	0.732950i	0.454992	−	0.890495i	$-0.349642\pi$
$11$	−5.85772	−	8.06245i	−0.532520	−	0.732950i	−0.987512	+	0.157545i	$0.949642\pi$
$12$		0			0
$13$	3.00062	+	2.18008i	0.230817	+	0.167698i	0.697182	−	0.716894i	$-0.254437\pi$
$13$	3.00062	+	2.18008i	0.230817	+	0.167698i	−0.466365	+	0.884592i	$0.654437\pi$
$14$	1.24672	+	1.71596i	0.0890512	+	0.122569i
$15$		0			0
$16$	−3.23607	−	2.35114i	−0.202254	−	0.146946i
$17$	−2.47472	+	0.804085i	−0.145572	+	0.0472991i	−0.380897	−	0.924618i	$-0.624385\pi$
$17$	−2.47472	+	0.804085i	−0.145572	+	0.0472991i	0.235325	+	0.971917i	$0.424385\pi$
$18$		0			0
$19$	5.78349	+	17.7997i	0.304394	+	0.936829i	0.979903	+	0.199477i	$0.0639242\pi$
$19$	5.78349	+	17.7997i	0.304394	+	0.936829i	−0.675508	+	0.737352i	$0.736076\pi$
$20$	4.77025	−	8.78890i	0.238512	−	0.439445i
$21$		0			0
$22$	−4.35519	+	13.4039i	−0.197963	+	0.609268i
$23$	1.70590	+	2.34798i	0.0741698	+	0.102086i	0.844490	−	0.535571i	$-0.179904\pi$
$23$	1.70590	+	2.34798i	0.0741698	+	0.102086i	−0.770320	+	0.637657i	$0.779904\pi$
$24$		0			0
$25$	23.3422	+	8.95209i	0.933690	+	0.358084i
$26$		−	5.24527i		−	0.201741i
$27$		0			0
$28$	0.926929	−	2.85280i	0.0331046	−	0.101886i
$29$	21.2454	+	6.90306i	0.732601	+	0.238036i	0.651478	−	0.758668i	$-0.274149\pi$
$29$	21.2454	+	6.90306i	0.732601	+	0.238036i	0.0811229	+	0.996704i	$0.474149\pi$
$30$		0			0
$31$	11.5942	+	35.6834i	0.374008	+	1.15108i	0.944146	+	0.329528i	$0.106890\pi$
$31$	11.5942	+	35.6834i	0.374008	+	1.15108i	−0.570138	+	0.821549i	$0.693110\pi$
$32$			5.65685i			0.176777i
$33$		0			0
$34$	2.97709	+	2.16298i	0.0875615	+	0.0636172i
$35$	7.37365	+	1.36546i	0.210676	+	0.0390133i
$36$		0			0
$37$	26.3519	+	19.1458i	0.712214	+	0.517454i	0.883887	−	0.467700i	$-0.154917\pi$
$37$	26.3519	+	19.1458i	0.712214	+	0.517454i	−0.171673	+	0.985154i	$0.554917\pi$
$38$	15.5575	−	21.4131i	0.409409	−	0.563503i
$39$		0			0
$40$	−14.0209	+	1.84805i	−0.350522	+	0.0462014i
$41$	−12.9274	+	17.7931i	−0.315304	+	0.433978i	−0.937026	−	0.349259i	$-0.886433\pi$
$41$	−12.9274	+	17.7931i	−0.315304	+	0.433978i	0.621722	+	0.783238i	$0.286433\pi$
$42$		0			0
$43$	30.8625			0.717732			0.358866	−	0.933389i	$-0.383163\pi$
$43$	30.8625			0.717732			0.358866	+	0.933389i	$0.383163\pi$
$44$	18.9560	−	6.15917i	0.430817	−	0.139981i
$45$		0			0
$46$	1.26833	−	3.90353i	0.0275725	−	0.0848593i
$47$	37.3634	+	12.1401i	0.794966	+	0.258300i	0.678217	−	0.734861i	$-0.262753\pi$
$47$	37.3634	+	12.1401i	0.794966	+	0.258300i	0.116749	+	0.993161i	$0.462753\pi$
$48$		0			0
$49$	−46.7506			−0.954094
$50$	−9.16104	−	34.1478i	−0.183221	−	0.682957i
$51$		0			0
$52$	−6.00124	+	4.36015i	−0.115408	+	0.0838491i
$53$	37.8510	+	12.2985i	0.714170	+	0.232048i	0.643494	−	0.765451i	$-0.277484\pi$
$53$	37.8510	+	12.2985i	0.714170	+	0.232048i	0.0706762	+	0.997499i	$0.477484\pi$
$54$		0			0
$55$	21.4587	+	44.9714i	0.390157	+	0.817662i
$56$	−4.03446	+	1.31088i	−0.0720440	+	0.0234085i
$57$		0			0
$58$	−9.76239	−	30.0456i	−0.168317	−	0.518027i
$59$	7.44680	−	10.2496i	0.126217	−	0.173723i	−0.741232	−	0.671249i	$-0.765758\pi$
$59$	7.44680	−	10.2496i	0.126217	−	0.173723i	0.867449	+	0.497526i	$0.165758\pi$
$60$		0			0
$61$	−29.4291	+	21.3815i	−0.482444	+	0.350516i	−0.802271	−	0.596960i	$-0.796375\pi$
$61$	−29.4291	+	21.3815i	−0.482444	+	0.350516i	0.319827	+	0.947476i	$0.396375\pi$
$62$	31.1884	−	42.9272i	0.503039	−	0.692374i
$63$		0			0
$64$	6.47214	−	4.70228i	0.101127	−	0.0734732i
$65$	−12.7675	−	13.4500i	−0.196423	−	0.206923i
$66$		0			0
$67$	22.6871	+	69.8236i	0.338613	+	1.04214i	0.964915	+	0.262563i	$0.0845676\pi$
$67$	22.6871	+	69.8236i	0.338613	+	1.04214i	−0.626302	+	0.779580i	$0.715432\pi$
$68$		−	5.20415i		−	0.0765316i
$69$		0			0
$70$	−4.56712	−	9.57141i	−0.0652446	−	0.136734i
$71$	−61.7104	−	20.0509i	−0.869161	−	0.282407i	−0.159711	−	0.987164i	$-0.551056\pi$
$71$	−61.7104	−	20.0509i	−0.869161	−	0.282407i	−0.709450	+	0.704756i	$0.751056\pi$
$72$		0			0
$73$	91.8321	−	66.7199i	1.25797	−	0.913972i	0.259318	−	0.965792i	$-0.416502\pi$
$73$	91.8321	−	66.7199i	1.25797	−	0.913972i	0.998656	+	0.0518206i	$0.0165024\pi$
$74$		−	46.0648i		−	0.622498i
$75$		0			0
$76$	−37.4315			−0.492520
$77$	8.78542	+	12.0921i	0.114096	+	0.157040i
$78$		0			0
$79$	14.2736	−	43.9295i	0.180678	−	0.556070i	−0.819169	−	0.573552i	$-0.805565\pi$
$79$	14.2736	−	43.9295i	0.180678	−	0.556070i	0.999847	+	0.0174823i	$0.00556508\pi$
$80$	13.7693	+	14.5054i	0.172116	+	0.181317i
$81$		0			0
$82$	31.1035			0.379311
$83$	13.5557	−	4.40452i	0.163322	−	0.0530664i	−0.226215	−	0.974077i	$-0.572635\pi$
$83$	13.5557	−	4.40452i	0.163322	−	0.0530664i	0.389537	+	0.921011i	$0.372635\pi$
$84$		0			0
$85$	12.8988	−	1.70016i	0.151751	−	0.0200019i
$86$	−25.6546	−	35.3105i	−0.298309	−	0.410587i
$87$		0			0
$88$	−22.8041	−	16.5681i	−0.259137	−	0.188274i
$89$	84.3402	+	116.084i	0.947643	+	1.30432i	0.952566	+	0.304331i	$0.0984328\pi$
$89$	84.3402	+	116.084i	0.947643	+	1.30432i	−0.00492338	+	0.999988i	$0.501567\pi$
$90$		0			0
$91$	−4.50034	−	3.26969i	−0.0494543	−	0.0359306i
$92$	−5.52042	+	1.79369i	−0.0600046	+	0.0194967i
$93$		0			0
$94$	−17.1687	−	52.8398i	−0.182646	−	0.562126i
$95$	−12.2286	−	92.7764i	−0.128722	−	0.976593i
$96$		0			0
$97$	4.99340	−	15.3681i	0.0514783	−	0.158434i	−0.922012	−	0.387160i	$-0.873456\pi$
$97$	4.99340	−	15.3681i	0.0514783	−	0.158434i	0.973491	+	0.228726i	$0.0734560\pi$
$98$	38.8616	+	53.4884i	0.396547	+	0.545800i
$99$		0			0
$100$	−31.4542	+	38.8669i	−0.314542	+	0.388669i
$101$			108.325i			1.07252i	0.844052	+	0.536261i	$0.180164\pi$
$101$			108.325i			1.07252i	−0.844052	+	0.536261i	$0.819836\pi$
$102$		0			0
$103$	29.7696	−	91.6214i	0.289025	−	0.889528i	−0.696138	−	0.717908i	$-0.745100\pi$
$103$	29.7696	−	91.6214i	0.289025	−	0.889528i	0.985163	−	0.171620i	$-0.0549002\pi$
$104$	9.97710	+	3.24176i	0.0959337	+	0.0311707i
$105$		0			0
$106$	−17.3928	−	53.5294i	−0.164083	−	0.504994i
$107$			112.804i			1.05424i	0.849790	+	0.527122i	$0.176729\pi$
$107$			112.804i			1.05424i	−0.849790	+	0.527122i	$0.823271\pi$
$108$		0			0
$109$	−65.4515	−	47.5533i	−0.600473	−	0.436269i	0.245574	−	0.969378i	$-0.421024\pi$
$109$	−65.4515	−	47.5533i	−0.600473	−	0.436269i	−0.846047	+	0.533109i	$0.821024\pi$
$110$	33.6152	−	61.9340i	0.305593	−	0.563036i
$111$		0			0
$112$	4.85347	+	3.52625i	0.0433345	+	0.0314844i
$113$	−35.6957	+	49.1309i	−0.315891	+	0.434786i	−0.937207	−	0.348773i	$-0.886598\pi$
$113$	−35.6957	+	49.1309i	−0.315891	+	0.434786i	0.621316	+	0.783560i	$0.286598\pi$
$114$		0			0
$115$	−6.24927	−	13.0967i	−0.0543415	−	0.113885i
$116$	−26.2608	+	36.1449i	−0.226386	+	0.311594i
$117$		0			0
$118$	−17.9170			−0.151839
$119$	3.71159	−	1.20597i	0.0311898	−	0.0101342i
$120$		0			0
$121$	6.70073	−	20.6227i	0.0553779	−	0.170436i
$122$	48.9261	+	15.8971i	0.401034	+	0.130304i
$123$		0			0
$124$	−75.0395			−0.605157
$125$	−106.610	−	65.2636i	−0.852879	−	0.522109i
$126$		0			0
$127$	55.7272	−	40.4882i	0.438797	−	0.318805i	−0.346360	−	0.938102i	$-0.612582\pi$
$127$	55.7272	−	40.4882i	0.438797	−	0.318805i	0.785157	+	0.619297i	$0.212582\pi$
$128$	−10.7600	−	3.49613i	−0.0840623	−	0.0273135i
$129$		0			0
$130$	−4.77545	+	25.7879i	−0.0367342	+	0.198369i
$131$	−225.427	+	73.2456i	−1.72081	+	0.559126i	−0.992073	−	0.125663i	$-0.959894\pi$
$131$	−225.427	+	73.2456i	−1.72081	+	0.559126i	−0.728741	+	0.684789i	$0.759894\pi$
$132$		0			0
$133$	−8.67409	−	26.6961i	−0.0652188	−	0.200723i
$134$	61.0280	−	83.9979i	0.455433	−	0.626850i
$135$		0			0
$136$	−5.95418	+	4.32597i	−0.0437808	+	0.0318086i
$137$	−127.125	+	174.972i	−0.927917	+	1.27717i	0.0327502	+	0.999464i	$0.489573\pi$
$137$	−127.125	+	174.972i	−0.927917	+	1.27717i	−0.960667	+	0.277704i	$0.910427\pi$
$138$		0			0
$139$	−158.563	+	115.203i	−1.14074	+	0.828799i	−0.987223	−	0.159346i	$-0.949061\pi$
$139$	−158.563	+	115.203i	−1.14074	+	0.828799i	−0.153521	+	0.988145i	$0.549061\pi$
$140$	−7.15444	+	13.1816i	−0.0511031	+	0.0941544i
$141$		0			0
$142$	28.3563	+	87.2717i	0.199692	+	0.614590i
$143$		−	36.9626i		−	0.258480i
$144$		0			0
$145$	−98.1665	−	53.2807i	−0.677010	−	0.367453i
$146$	−152.672	−	49.6060i	−1.04570	−	0.339767i
$147$		0			0
$148$	−52.7038	+	38.2916i	−0.356107	+	0.258727i
$149$		−	115.112i		−	0.772564i	−0.922381	−	0.386282i	$-0.873759\pi$
$149$		−	115.112i		−	0.772564i	0.922381	−	0.386282i	$-0.126241\pi$
$150$		0			0
$151$	−3.96618			−0.0262661			−0.0131331	−	0.999914i	$-0.504181\pi$
$151$	−3.96618			−0.0262661			−0.0131331	+	0.999914i	$0.504181\pi$
$152$	31.1151	+	42.8263i	0.204705	+	0.281752i
$153$		0			0
$154$	6.53193	−	20.1032i	0.0424151	−	0.130540i
$155$	−24.5149	−	185.990i	−0.158161	−	1.19994i
$156$		0			0
$157$	14.8685			0.0947036			0.0473518	−	0.998878i	$-0.484922\pi$
$157$	14.8685			0.0947036			0.0473518	+	0.998878i	$0.484922\pi$
$158$	−62.1257	+	20.1859i	−0.393201	+	0.127759i
$159$		0			0
$160$	5.15016	−	27.8114i	0.0321885	−	0.173821i
$161$	−2.55852	−	3.52150i	−0.0158914	−	0.0218727i
$162$		0			0
$163$	−80.5807	−	58.5453i	−0.494360	−	0.359174i	0.312499	−	0.949918i	$-0.398834\pi$
$163$	−80.5807	−	58.5453i	−0.494360	−	0.359174i	−0.806859	+	0.590745i	$0.798834\pi$
$164$	−25.8549	−	35.5862i	−0.157652	−	0.216989i
$165$		0			0
$166$	−16.3075	−	11.8481i	−0.0982382	−	0.0713742i
$167$	−305.972	+	99.4164i	−1.83217	+	0.595308i	−0.833055	+	0.553189i	$0.813411\pi$
$167$	−305.972	+	99.4164i	−1.83217	+	0.595308i	−0.999113	+	0.0421181i	$0.986589\pi$
$168$		0			0
$169$	−47.9729	−	147.645i	−0.283863	−	0.873641i
$170$	−12.6674	−	13.3446i	−0.0745139	−	0.0784974i
$171$		0			0
$172$	−19.0741	+	58.7039i	−0.110896	+	0.341302i
$173$	112.697	+	155.114i	0.651429	+	0.896615i	0.999160	−	0.0409793i	$-0.0130478\pi$
$173$	112.697	+	155.114i	0.651429	+	0.896615i	−0.347731	+	0.937594i	$0.613048\pi$
$174$		0			0
$175$	−35.0088	−	13.4264i	−0.200050	−	0.0767221i
$176$			39.8630i			0.226494i
$177$		0			0
$178$	62.7066	−	192.991i	0.352284	−	1.08422i
$179$	80.0601	+	26.0131i	0.447263	+	0.145325i	0.523984	−	0.851728i	$-0.324445\pi$
$179$	80.0601	+	26.0131i	0.447263	+	0.145325i	−0.0767211	+	0.997053i	$0.524445\pi$
$180$		0			0
$181$	39.1454	+	120.477i	0.216273	+	0.665620i	0.999061	+	0.0433313i	$0.0137971\pi$
$181$	39.1454	+	120.477i	0.216273	+	0.665620i	−0.782788	+	0.622289i	$0.786203\pi$
$182$			7.86688i			0.0432246i
$183$		0			0
$184$	6.64108	+	4.82503i	0.0360928	+	0.0262230i
$185$	−112.126	−	118.120i	−0.606087	−	0.638487i
$186$		0			0
$187$	20.9791	+	15.2422i	0.112188	+	0.0815091i
$188$	−46.1837	+	63.5664i	−0.245658	+	0.338119i
$189$		0			0
$190$	−95.9825	+	91.1117i	−0.505171	+	0.479536i
$191$	44.6300	−	61.4280i	0.233665	−	0.321612i	−0.676042	−	0.736863i	$-0.736306\pi$
$191$	44.6300	−	61.4280i	0.233665	−	0.321612i	0.909707	+	0.415251i	$0.136306\pi$
$192$		0			0
$193$	270.488			1.40149			0.700747	−	0.713410i	$-0.252850\pi$
$193$	270.488			1.40149			0.700747	+	0.713410i	$0.252850\pi$
$194$	−21.7338	+	7.06173i	−0.112030	+	0.0364007i
$195$		0			0
$196$	28.8935	−	88.9249i	0.147416	−	0.453699i
$197$	167.594	+	54.4547i	0.850733	+	0.276420i	0.701753	−	0.712420i	$-0.252401\pi$
$197$	167.594	+	54.4547i	0.850733	+	0.276420i	0.148980	+	0.988840i	$0.452401\pi$
$198$		0			0
$199$	−231.292			−1.16227			−0.581135	−	0.813807i	$-0.697391\pi$
$199$	−231.292			−1.16227			−0.581135	+	0.813807i	$0.697391\pi$
$200$	70.6149	+	3.67920i	0.353074	+	0.0183960i
$201$		0			0
$202$	123.937	−	90.0453i	0.613548	−	0.445769i
$203$	−31.8640	−	10.3532i	−0.156965	−	0.0510011i
$204$		0			0
$205$	79.7560	−	75.7087i	0.389054	−	0.369311i
$206$	−129.572	+	42.1006i	−0.628991	+	0.204372i
$207$		0			0
$208$	−4.58454	−	14.1098i	−0.0220410	−	0.0678354i
$209$	109.632	−	150.895i	0.524553	−	0.721985i
$210$		0			0
$211$	−260.986	+	189.618i	−1.23690	+	0.898662i	−0.997388	−	0.0722314i	$-0.976988\pi$
$211$	−260.986	+	189.618i	−1.23690	+	0.898662i	−0.239514	+	0.970893i	$0.576988\pi$
$212$	−46.7864	+	64.3960i	−0.220691	+	0.303755i
$213$		0			0
$214$	129.062	−	93.7689i	0.603092	−	0.438172i
$215$	−151.733	−	28.0981i	−0.705734	−	0.130689i
$216$		0			0
$217$	−17.3891	−	53.5181i	−0.0801340	−	0.246627i
$218$			114.413i			0.524832i
$219$		0			0
$220$	−98.8028	+	13.0230i	−0.449104	+	0.0591952i
$221$	−9.17866	−	2.98233i	−0.0415324	−	0.0134947i
$222$		0			0
$223$	143.425	−	104.204i	0.643159	−	0.467283i	−0.217775	−	0.975999i	$-0.569880\pi$
$223$	143.425	−	104.204i	0.643159	−	0.467283i	0.860934	+	0.508716i	$0.169880\pi$
$224$		−	8.48417i		−	0.0378758i
$225$		0			0
$226$	85.8839			0.380017
$227$	145.899	+	200.812i	0.642725	+	0.884635i	0.998757	−	0.0498386i	$-0.0158707\pi$
$227$	145.899	+	200.812i	0.642725	+	0.884635i	−0.356032	+	0.934474i	$0.615871\pi$
$228$		0			0
$229$	30.6448	−	94.3151i	0.133820	−	0.411856i	−0.861584	−	0.507614i	$-0.830527\pi$
$229$	30.6448	−	94.3151i	0.133820	−	0.411856i	0.995405	+	0.0957580i	$0.0305275\pi$
$230$	−9.78954	+	18.0366i	−0.0425632	+	0.0784201i
$231$		0			0
$232$	63.1835			0.272343
$233$	334.764	−	108.771i	1.43676	−	0.466830i	0.515871	−	0.856666i	$-0.327468\pi$
$233$	334.764	−	108.771i	1.43676	−	0.466830i	0.920884	+	0.389836i	$0.127468\pi$
$234$		0			0
$235$	−172.641	−	93.7025i	−0.734644	−	0.398734i
$236$	14.8936	+	20.4993i	0.0631085	+	0.0868613i
$237$		0			0
$238$	−4.46505	−	3.24405i	−0.0187607	−	0.0136305i
$239$	−38.0408	−	52.3587i	−0.159167	−	0.219074i	0.721984	−	0.691910i	$-0.243230\pi$
$239$	−38.0408	−	52.3587i	−0.159167	−	0.219074i	−0.881151	+	0.472836i	$0.843230\pi$
$240$		0			0
$241$	296.093	+	215.124i	1.22860	+	0.892631i	0.996785	−	0.0801287i	$-0.0255331\pi$
$241$	296.093	+	215.124i	1.22860	+	0.892631i	0.231816	+	0.972760i	$0.425533\pi$
$242$	−29.1649	+	9.47626i	−0.120516	+	0.0391581i
$243$		0			0
$244$	−22.4818	−	69.1920i	−0.0921387	−	0.283574i
$245$	229.845	+	42.5631i	0.938144	+	0.173727i
$246$		0			0
$247$	−21.4508	+	66.0187i	−0.0868452	+	0.267282i
$248$	62.3769	+	85.8544i	0.251520	+	0.346187i
$249$		0			0
$250$	13.9503	+	176.225i	0.0558011	+	0.704902i
$251$		−	75.9333i		−	0.302523i	−0.988494	−	0.151262i	$-0.951666\pi$
$251$		−	75.9333i		−	0.302523i	0.988494	−	0.151262i	$-0.0483336\pi$
$252$		0			0
$253$	8.93775	−	27.5076i	0.0353271	−	0.108726i
$254$	−92.6470	−	30.1028i	−0.364752	−	0.118515i
$255$		0			0
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$		−	6.24916i		−	0.0243158i	−0.999926	−	0.0121579i	$-0.996130\pi$
$257$		−	6.24916i		−	0.0243158i	0.999926	−	0.0121579i	$-0.00387008\pi$
$258$		0			0
$259$	−39.5227	−	28.7149i	−0.152597	−	0.110868i
$260$	33.4742	−	15.9726i	0.128747	−	0.0614332i
$261$		0			0
$262$	271.189	+	197.030i	1.03507	+	0.752023i
$263$	162.842	−	224.133i	0.619172	−	0.852217i	−0.378121	−	0.925756i	$-0.623430\pi$
$263$	162.842	−	224.133i	0.619172	−	0.852217i	0.997292	+	0.0735397i	$0.0234296\pi$
$264$		0			0
$265$	−174.894	−	94.9253i	−0.659978	−	0.358209i
$266$	−23.3333	+	32.1155i	−0.0877190	+	0.120735i
$267$		0			0
$268$	−146.834			−0.547887
$269$	435.813	−	141.604i	1.62012	−	0.526410i	0.648153	−	0.761510i	$-0.275542\pi$
$269$	435.813	−	141.604i	1.62012	−	0.526410i	0.971971	+	0.235100i	$0.0755419\pi$
$270$		0			0
$271$	−31.5532	+	97.1108i	−0.116433	+	0.358342i	−0.992243	−	0.124313i	$-0.960327\pi$
$271$	−31.5532	+	97.1108i	−0.116433	+	0.358342i	0.875811	+	0.482655i	$0.160327\pi$
$272$	9.89888	+	3.21634i	0.0363929	+	0.0118248i
$273$		0			0
$274$	305.862			1.11629
$275$	−64.5564	−	240.635i	−0.234751	−	0.875035i
$276$		0			0
$277$	345.707	−	251.171i	1.24804	−	0.906753i	0.249932	−	0.968263i	$-0.419592\pi$
$277$	345.707	−	251.171i	1.24804	−	0.906753i	0.998106	+	0.0615099i	$0.0195916\pi$
$278$	263.613	+	85.6530i	0.948248	+	0.308104i
$279$		0			0
$280$	21.0285	−	2.77172i	0.0751019	−	0.00989899i
$281$	80.8710	−	26.2766i	0.287797	−	0.0935110i	−0.161561	−	0.986863i	$-0.551653\pi$
$281$	80.8710	−	26.2766i	0.287797	−	0.0935110i	0.449358	+	0.893352i	$0.351653\pi$
$282$		0			0
$283$	99.0692	+	304.904i	0.350068	+	1.07740i	0.958814	+	0.284033i	$0.0916727\pi$
$283$	99.0692	+	304.904i	0.350068	+	1.07740i	−0.608746	+	0.793365i	$0.708327\pi$
$284$	76.2783	−	104.988i	0.268585	−	0.369676i
$285$		0			0
$286$	−42.2898	+	30.7253i	−0.147866	+	0.107431i
$287$	19.3886	−	26.6862i	0.0675562	−	0.0929831i
$288$		0			0
$289$	−228.328	+	165.890i	−0.790063	+	0.574014i
$290$	20.6416	+	156.604i	0.0711780	+	0.540015i
$291$		0			0
$292$	70.1535	+	215.910i	0.240252	+	0.739419i
$293$			122.381i			0.417684i	0.977949	+	0.208842i	$0.0669695\pi$
$293$			122.381i			0.417684i	−0.977949	+	0.208842i	$0.933031\pi$
$294$		0			0
$295$	−45.9431	+	43.6117i	−0.155739	+	0.147836i
$296$	87.6205	+	28.4696i	0.296015	+	0.0961812i
$297$		0			0
$298$	−131.702	+	95.6873i	−0.441954	+	0.321098i
$299$			10.7644i			0.0360013i
$300$		0			0
$301$	−46.2877			−0.153780
$302$	3.29691	+	4.53780i	0.0109169	+	0.0150258i
$303$		0			0
$304$	23.1340	−	71.1990i	0.0760985	−	0.234207i
$305$	164.152	−	78.3272i	0.538203	−	0.256810i
$306$		0			0
$307$	−400.558			−1.30475			−0.652375	−	0.757896i	$-0.726227\pi$
$307$	−400.558			−1.30475			−0.652375	+	0.757896i	$0.726227\pi$
$308$	−28.4302	+	9.23754i	−0.0923059	+	0.0299920i
$309$		0			0
$310$	−192.417	+	182.653i	−0.620701	+	0.589203i
$311$	−118.019	−	162.440i	−0.379483	−	0.522314i	0.575964	−	0.817475i	$-0.304627\pi$
$311$	−118.019	−	162.440i	−0.379483	−	0.522314i	−0.955448	+	0.295161i	$0.904627\pi$
$312$		0			0
$313$	14.8924	+	10.8200i	0.0475796	+	0.0345686i	0.611321	−	0.791383i	$-0.290638\pi$
$313$	14.8924	+	10.8200i	0.0475796	+	0.0345686i	−0.563741	+	0.825951i	$0.690638\pi$
$314$	−12.3595	−	17.0114i	−0.0393614	−	0.0541763i
$315$		0			0
$316$	74.7373	+	54.2998i	0.236511	+	0.171835i
$317$	−232.050	+	75.3976i	−0.732019	+	0.237847i	−0.651226	−	0.758884i	$-0.725745\pi$
$317$	−232.050	+	75.3976i	−0.732019	+	0.237847i	−0.0807925	+	0.996731i	$0.525745\pi$
$318$		0			0
$319$	−68.7941	−	211.726i	−0.215655	−	0.663719i
$320$	−36.1008	+	17.2259i	−0.112815	+	0.0538311i
$321$		0			0
$322$	−1.90225	+	5.85453i	−0.00590761	+	0.0181818i
$323$	−28.6250	−	39.3990i	−0.0886223	−	0.121978i
$324$		0			0
$325$	50.5249	+	77.7497i	0.155461	+	0.239230i
$326$			140.860i			0.432086i
$327$		0			0
$328$	−19.2230	+	59.1624i	−0.0586068	+	0.180373i
$329$	−56.0378	−	18.2078i	−0.170328	−	0.0553428i
$330$		0			0
$331$	199.650	+	614.459i	0.603172	+	1.85637i	0.508901	+	0.860825i	$0.330052\pi$
$331$	199.650	+	614.459i	0.603172	+	1.85637i	0.0942704	+	0.995547i	$0.469948\pi$
$332$			28.5066i			0.0858633i
$333$		0			0
$334$	368.085	+	267.429i	1.10205	+	0.800687i
$335$	−47.9695	−	363.937i	−0.143193	−	1.08638i
$336$		0			0
$337$	49.8138	+	36.1919i	0.147816	+	0.107394i	0.659235	−	0.751937i	$-0.270880\pi$
$337$	49.8138	+	36.1919i	0.147816	+	0.107394i	−0.511420	+	0.859331i	$0.670880\pi$
$338$	−129.047	+	177.618i	−0.381795	+	0.525496i
$339$		0			0
$340$	−4.73801	+	25.5857i	−0.0139353	+	0.0752522i
$341$	219.780	−	302.501i	0.644516	−	0.887100i
$342$		0			0
$343$	143.607			0.418679
$344$	83.0199	−	26.9748i	0.241337	−	0.0784151i
$345$		0			0
$346$	83.7899	−	257.879i	0.242167	−	0.745315i
$347$	−251.842	−	81.8284i	−0.725769	−	0.235817i	−0.0772465	−	0.997012i	$-0.524613\pi$
$347$	−251.842	−	81.8284i	−0.725769	−	0.235817i	−0.648523	+	0.761195i	$0.724613\pi$
$348$		0			0
$349$	239.867			0.687298			0.343649	−	0.939098i	$-0.388337\pi$
$349$	239.867			0.687298			0.343649	+	0.939098i	$0.388337\pi$
$350$	13.7398	+	51.2151i	0.0392564	+	0.146329i
$351$		0			0
$352$	45.6081	−	33.1362i	0.129569	−	0.0941371i
$353$	387.790	+	126.001i	1.09855	+	0.356942i	0.801546	−	0.597933i	$-0.204011\pi$
$353$	387.790	+	126.001i	1.09855	+	0.356942i	0.297009	+	0.954875i	$0.404011\pi$
$354$		0			0
$355$	285.139	+	154.762i	0.803208	+	0.435948i
$356$	−272.931	+	88.6806i	−0.766659	+	0.249103i
$357$		0			0
$358$	−36.7881	−	113.222i	−0.102760	−	0.316263i
$359$	292.726	−	402.903i	0.815394	−	1.12229i	−0.175075	−	0.984555i	$-0.556017\pi$
$359$	292.726	−	402.903i	0.815394	−	1.12229i	0.990469	−	0.137738i	$-0.0439833\pi$
$360$		0			0
$361$	8.67292	−	6.30124i	0.0240247	−	0.0174550i
$362$	105.301	−	144.934i	0.290887	−	0.400371i
$363$		0			0
$364$	9.00067	−	6.53937i	0.0247271	−	0.0179653i
$365$	−512.228	+	244.416i	−1.40337	+	0.669633i
$366$		0			0
$367$	−114.138	−	351.281i	−0.311003	−	0.957168i	−0.977369	−	0.211543i	$-0.932151\pi$
$367$	−114.138	−	351.281i	−0.311003	−	0.957168i	0.666366	−	0.745625i	$-0.267849\pi$
$368$		−	11.6090i		−	0.0315463i
$369$		0			0
$370$	−41.9387	+	226.474i	−0.113348	+	0.612091i
$371$	−56.7690	−	18.4454i	−0.153016	−	0.0497180i
$372$		0			0
$373$	−208.831	+	151.725i	−0.559869	+	0.406769i	−0.831411	−	0.555658i	$-0.812466\pi$
$373$	−208.831	+	151.725i	−0.559869	+	0.406769i	0.271542	+	0.962427i	$0.412466\pi$
$374$		−	36.6728i		−	0.0980556i
$375$		0			0
$376$	111.118			0.295527
$377$	48.7002	+	67.0301i	0.129178	+	0.177799i
$378$		0			0
$379$	51.7857	−	159.380i	0.136638	−	0.420528i	−0.859203	−	0.511634i	$-0.829040\pi$
$379$	51.7857	−	159.380i	0.136638	−	0.420528i	0.995841	+	0.0911065i	$0.0290404\pi$
$380$	184.029	+	34.0787i	0.484286	+	0.0896809i
$381$		0			0
$382$	−107.380			−0.281100
$383$	278.048	−	90.3432i	0.725973	−	0.235883i	0.0773622	−	0.997003i	$-0.475350\pi$
$383$	278.048	−	90.3432i	0.725973	−	0.235883i	0.648611	+	0.761120i	$0.275350\pi$
$384$		0			0
$385$	−32.1838	−	67.4482i	−0.0835942	−	0.175190i
$386$	−224.844	−	309.472i	−0.582498	−	0.801740i
$387$		0			0
$388$	26.1458	+	18.9960i	0.0673860	+	0.0489588i
$389$	163.081	+	224.462i	0.419232	+	0.577024i	0.965440	−	0.260626i	$-0.0839290\pi$
$389$	163.081	+	224.462i	0.419232	+	0.577024i	−0.546208	+	0.837650i	$0.683929\pi$
$390$		0			0
$391$	−6.10961	−	4.43889i	−0.0156256	−	0.0113527i
$392$	−125.759	+	40.8615i	−0.320813	+	0.104239i
$393$		0			0
$394$	−77.0106	−	237.014i	−0.195458	−	0.601559i
$395$	−110.169	+	202.981i	−0.278910	+	0.513875i
$396$		0			0
$397$	130.110	−	400.439i	0.327734	−	1.00866i	−0.642457	−	0.766321i	$-0.722085\pi$
$397$	130.110	−	400.439i	0.327734	−	1.00866i	0.970191	−	0.242340i	$-0.0779149\pi$
$398$	192.262	+	264.626i	0.483071	+	0.664890i
$399$		0			0
$400$	−54.4894	−	83.8505i	−0.136224	−	0.209626i
$401$			203.057i			0.506377i	0.967417	+	0.253188i	$0.0814792\pi$
$401$			203.057i			0.506377i	−0.967417	+	0.253188i	$0.918521\pi$
$402$		0			0
$403$	−43.0027	+	132.349i	−0.106706	+	0.328408i
$404$	−206.046	−	66.9483i	−0.510014	−	0.165714i
$405$		0			0
$406$	14.6417	+	45.0624i	0.0360632	+	0.110991i
$407$		−	324.612i		−	0.797572i
$408$		0			0
$409$	457.097	+	332.100i	1.11760	+	0.811981i	0.983843	−	0.179033i	$-0.0572970\pi$
$409$	457.097	+	332.100i	1.11760	+	0.811981i	0.133753	+	0.991015i	$0.457297\pi$
$410$	−152.918	−	28.3175i	−0.372970	−	0.0690671i
$411$		0			0
$412$	155.876	+	113.250i	0.378339	+	0.274879i
$413$	−11.1687	+	15.3724i	−0.0270429	+	0.0372214i
$414$		0			0
$415$	−70.6554	+	9.31291i	−0.170254	+	0.0224408i
$416$	−12.3324	+	16.9741i	−0.0296451	+	0.0408030i
$417$		0			0
$418$	−263.774			−0.631038
$419$	−630.921	+	204.999i	−1.50578	+	0.489257i	−0.941697	−	0.336462i	$-0.890770\pi$
$419$	−630.921	+	204.999i	−1.50578	+	0.489257i	−0.564081	+	0.825719i	$0.690770\pi$
$420$		0			0
$421$	−127.993	+	393.922i	−0.304021	+	0.935681i	0.676019	+	0.736884i	$0.263704\pi$
$421$	−127.993	+	393.922i	−0.304021	+	0.935681i	−0.980041	+	0.198797i	$0.936296\pi$
$422$	433.892	+	140.980i	1.02818	+	0.334076i
$423$		0			0
$424$	112.568			0.265491
$425$	−64.9637	−	3.38476i	−0.152856	−	0.00796414i
$426$		0			0
$427$	44.1379	−	32.0680i	0.103367	−	0.0751008i
$428$	−214.566	−	69.7168i	−0.501323	−	0.162890i
$429$		0			0
$430$	93.9807	+	196.958i	0.218560	+	0.458041i
$431$	229.668	−	74.6237i	0.532873	−	0.173141i	−0.0302067	−	0.999544i	$-0.509617\pi$
$431$	229.668	−	74.6237i	0.532873	−	0.173141i	0.563079	+	0.826403i	$0.309617\pi$
$432$		0			0
$433$	−75.2612	−	231.630i	−0.173813	−	0.534942i	0.825764	−	0.564016i	$-0.190744\pi$
$433$	−75.2612	−	231.630i	−0.173813	−	0.534942i	−0.999577	+	0.0290734i	$0.990744\pi$
$434$	−46.7765	+	64.3824i	−0.107780	+	0.148346i
$435$		0			0
$436$	130.903	−	95.1066i	0.300236	−	0.218134i
$437$	−31.9273	+	43.9442i	−0.0730602	+	0.100559i
$438$		0			0
$439$	−447.625	+	325.219i	−1.01965	+	0.740817i	−0.966211	−	0.257754i	$-0.917018\pi$
$439$	−447.625	+	325.219i	−1.01965	+	0.740817i	−0.0534370	+	0.998571i	$0.517018\pi$
$440$	97.0301	+	102.217i	0.220523	+	0.232312i
$441$		0			0
$442$	4.21765	+	12.9806i	0.00954218	+	0.0293678i
$443$		−	59.2555i		−	0.133760i	−0.997761	−	0.0668798i	$-0.978696\pi$
$443$		−	59.2555i		−	0.133760i	0.997761	−	0.0668798i	$-0.0213044\pi$
$444$		0			0
$445$	−308.965	−	647.504i	−0.694303	−	1.45507i
$446$	−238.444	−	77.4753i	−0.534629	−	0.173711i
$447$		0			0
$448$	−9.70693	+	7.05250i	−0.0216673	+	0.0157422i
$449$			521.198i			1.16080i	0.814333	+	0.580399i	$0.197103\pi$
$449$			521.198i			1.16080i	−0.814333	+	0.580399i	$0.802897\pi$
$450$		0			0
$451$	219.181			0.485990
$452$	−71.3913	−	98.2617i	−0.157945	−	0.217393i
$453$		0			0
$454$	108.475	−	333.852i	0.238932	−	0.735356i
$455$	19.1487	+	20.1724i	0.0420851	+	0.0443349i
$456$		0			0
$457$	−808.871			−1.76996			−0.884979	−	0.465631i	$-0.845827\pi$
$457$	−808.871			−1.76996			−0.884979	+	0.465631i	$0.845827\pi$
$458$	−133.382	+	43.3383i	−0.291226	+	0.0946252i
$459$		0			0
$460$	28.7737	−	3.79259i	0.0625516	−	0.00824476i
$461$	3.79295	+	5.22055i	0.00822767	+	0.0113244i	0.813111	−	0.582109i	$-0.197772\pi$
$461$	3.79295	+	5.22055i	0.00822767	+	0.0113244i	−0.804883	+	0.593433i	$0.797772\pi$
$462$		0			0
$463$	350.274	+	254.489i	0.756532	+	0.549652i	0.897845	−	0.440313i	$-0.145132\pi$
$463$	350.274	+	254.489i	0.756532	+	0.549652i	−0.141313	+	0.989965i	$0.545132\pi$
$464$	−52.5216	−	72.2897i	−0.113193	−	0.155797i
$465$		0			0
$466$	−402.722	−	292.594i	−0.864210	−	0.627885i
$467$	−641.853	+	208.551i	−1.37442	+	0.446575i	−0.900830	−	0.434172i	$-0.857041\pi$
$467$	−641.853	+	208.551i	−1.37442	+	0.446575i	−0.473587	+	0.880747i	$0.657041\pi$
$468$		0			0
$469$	−34.0261	−	104.722i	−0.0725504	−	0.223287i
$470$	36.3015	+	275.413i	0.0772373	+	0.585986i
$471$		0			0
$472$	11.0733	−	34.0802i	0.0234604	−	0.0722038i
$473$	−180.784	−	248.827i	−0.382206	−	0.526062i
$474$		0			0
$475$	−24.3453	+	467.260i	−0.0512534	+	0.983706i
$476$			7.80520i			0.0163975i
$477$		0			0
$478$	−28.2832	+	87.0468i	−0.0591699	+	0.182106i
$479$	−63.2191	−	20.5411i	−0.131981	−	0.0428834i	0.242281	−	0.970206i	$-0.422104\pi$
$479$	−63.2191	−	20.5411i	−0.131981	−	0.0428834i	−0.374263	+	0.927323i	$0.622104\pi$
$480$		0			0
$481$	37.3327	+	114.898i	0.0776149	+	0.238874i
$482$		−	517.589i		−	1.07384i
$483$		0			0
$484$	35.0855	+	25.4911i	0.0724906	+	0.0526675i
$485$	−38.5412	+	71.0098i	−0.0794663	+	0.146412i
$486$		0			0
$487$	−111.939	−	81.3287i	−0.229855	−	0.166999i	0.466897	−	0.884312i	$-0.345372\pi$
$487$	−111.939	−	81.3287i	−0.229855	−	0.166999i	−0.696752	+	0.717313i	$0.745372\pi$
$488$	−60.4760	+	83.2381i	−0.123926	+	0.170570i
$489$		0			0
$490$	−142.362	−	298.352i	−0.290535	−	0.608881i
$491$	116.995	−	161.030i	0.238280	−	0.327964i	−0.673084	−	0.739566i	$-0.735031\pi$
$491$	116.995	−	161.030i	0.238280	−	0.327964i	0.911364	+	0.411602i	$0.135031\pi$
$492$		0			0
$493$	−58.1271			−0.117905
$494$	93.3645	−	30.3360i	0.188997	−	0.0614089i
$495$		0			0
$496$	46.3770	−	142.734i	0.0935019	−	0.287769i
$497$	92.5535	+	30.0725i	0.186224	+	0.0605080i
$498$		0			0
$499$	−221.452			−0.443791			−0.221896	−	0.975070i	$-0.571224\pi$
$499$	−221.452			−0.443791			−0.221896	+	0.975070i	$0.571224\pi$
$500$	190.027	−	162.449i	0.380055	−	0.324898i
$501$		0			0
$502$	−86.8771	+	63.1199i	−0.173062	+	0.125737i
$503$	−754.331	−	245.097i	−1.49966	−	0.487271i	−0.559744	−	0.828665i	$-0.689101\pi$
$503$	−754.331	−	245.097i	−1.49966	−	0.487271i	−0.939920	+	0.341395i	$0.889101\pi$
$504$		0			0
$505$	98.6219	−	532.569i	0.195291	−	1.05459i
$506$	−38.9016	+	12.6399i	−0.0768805	+	0.0249800i
$507$		0			0
$508$	42.5718	+	131.023i	0.0838028	+	0.257919i
$509$	15.2916	−	21.0471i	0.0300424	−	0.0413498i	−0.793732	−	0.608268i	$-0.791865\pi$
$509$	15.2916	−	21.0471i	0.0300424	−	0.0413498i	0.823774	+	0.566918i	$0.191865\pi$
$510$		0			0
$511$	−137.730	+	100.067i	−0.269530	+	0.195825i
$512$	13.3001	−	18.3060i	0.0259767	−	0.0357538i
$513$		0			0
$514$	−7.14981	+	5.19464i	−0.0139101	+	0.0101063i
$515$	−229.774	+	423.346i	−0.446164	+	0.822030i
$516$		0			0
$517$	−120.985	−	372.354i	−0.234014	−	0.720221i
$518$			69.0882i			0.133375i
$519$		0			0
$520$	−46.1002	−	25.0213i	−0.0886542	−	0.0481178i
$521$	896.186	+	291.188i	1.72013	+	0.558903i	0.991966	−	0.126504i	$-0.0403756\pi$
$521$	896.186	+	291.188i	1.72013	+	0.558903i	0.728160	+	0.685407i	$0.240376\pi$
$522$		0			0
$523$	147.579	−	107.223i	0.282178	−	0.205015i	−0.437689	−	0.899127i	$-0.644203\pi$
$523$	147.579	−	107.223i	0.282178	−	0.205015i	0.719867	+	0.694112i	$0.244203\pi$
$524$		−	474.055i		−	0.904685i
$525$		0			0
$526$	−391.799			−0.744865
$527$	−57.3850	−	78.9836i	−0.108890	−	0.149874i
$528$		0			0
$529$	160.867	−	495.098i	0.304097	−	0.935913i
$530$	36.7753	+	279.007i	0.0693873	+	0.526429i
$531$		0			0
$532$	56.1399			0.105526
$533$	−77.5807	+	25.2075i	−0.145555	+	0.0472936i
$534$		0			0
$535$	102.700	−	554.592i	0.191963	−	1.03662i
$536$	122.056	+	167.996i	0.227717	+	0.313425i
$537$		0			0
$538$	−524.284	−	380.915i	−0.974506	−	0.708020i
$539$	273.852	+	376.924i	0.508074	+	0.699303i
$540$		0			0
$541$	−113.385	−	82.3793i	−0.209585	−	0.152272i	0.478041	−	0.878338i	$-0.341347\pi$
$541$	−113.385	−	82.3793i	−0.209585	−	0.152272i	−0.687626	+	0.726065i	$0.741347\pi$
$542$	137.335	−	44.6230i	0.253386	−	0.0823302i
$543$		0			0
$544$	−4.54859	−	13.9991i	−0.00836138	−	0.0257337i
$545$	278.493	+	293.381i	0.510996	+	0.538313i
$546$		0			0
$547$	−204.716	+	630.050i	−0.374251	+	1.15183i	0.569731	+	0.821831i	$0.307047\pi$
$547$	−204.716	+	630.050i	−0.374251	+	1.15183i	−0.943982	+	0.329996i	$0.892953\pi$
$548$	−254.249	−	349.944i	−0.463958	−	0.638584i
$549$		0			0
$550$	−221.653	+	273.889i	−0.403005	+	0.497980i
$551$			418.087i			0.758778i
$552$		0			0
$553$	−21.4075	+	65.8856i	−0.0387116	+	0.119142i
$554$	−574.740	−	186.744i	−1.03744	−	0.337084i
$555$		0			0
$556$	−121.132	−	372.805i	−0.217863	−	0.670513i
$557$			350.065i			0.628483i	0.949343	+	0.314242i	$0.101750\pi$
$557$			350.065i			0.628483i	−0.949343	+	0.314242i	$0.898250\pi$
$558$		0			0
$559$	92.6065	+	67.2826i	0.165665	+	0.120362i
$560$	−20.6512	−	21.7552i	−0.0368772	−	0.0388486i
$561$		0			0
$562$	−97.2880	−	70.6838i	−0.173110	−	0.125772i
$563$	100.931	−	138.919i	0.179273	−	0.246748i	−0.709918	−	0.704284i	$-0.751268\pi$
$563$	100.931	−	138.919i	0.179273	−	0.246748i	0.889191	+	0.457536i	$0.151268\pi$
$564$		0			0
$565$	220.225	−	209.049i	0.389778	−	0.369999i
$566$	266.496	−	366.800i	0.470840	−	0.648056i
$567$		0			0
$568$	−183.526			−0.323109
$569$	−1048.59	+	340.707i	−1.84286	+	0.598783i	−0.844906	+	0.534915i	$0.820344\pi$
$569$	−1048.59	+	340.707i	−1.84286	+	0.598783i	−0.997958	+	0.0638680i	$0.979656\pi$
$570$		0			0
$571$	296.136	−	911.412i	0.518626	−	1.59617i	−0.257959	−	0.966156i	$-0.583050\pi$
$571$	296.136	−	911.412i	0.518626	−	1.59617i	0.776585	−	0.630012i	$-0.216950\pi$
$572$	70.3071	+	22.8442i	0.122914	+	0.0399373i
$573$		0			0
$574$	−46.6491			−0.0812702
$575$	18.8003	+	70.0784i	0.0326962	+	0.121876i
$576$		0			0
$577$	807.392	−	586.605i	1.39929	−	1.01665i	0.404521	−	0.914529i	$-0.367438\pi$
$577$	807.392	−	586.605i	1.39929	−	1.01665i	0.994772	−	0.102117i	$-0.0325618\pi$
$578$	379.597	+	123.339i	0.656743	+	0.213389i
$579$		0			0
$580$	162.016	−	153.795i	0.279338	−	0.265163i
$581$	−20.3309	+	6.60591i	−0.0349929	+	0.0113699i
$582$		0			0
$583$	−122.564	−	377.213i	−0.210230	−	0.647021i
$584$	188.712	−	259.740i	0.323138	−	0.444761i
$585$		0			0
$586$	140.019	−	101.730i	0.238941	−	0.173601i
$587$	386.514	−	531.991i	0.658457	−	0.906288i	−0.340972	−	0.940073i	$-0.610756\pi$
$587$	386.514	−	531.991i	0.658457	−	0.906288i	0.999429	+	0.0337852i	$0.0107562\pi$
$588$		0			0
$589$	−568.100	+	412.749i	−0.964517	+	0.700762i
$590$	88.0875	+	16.3122i	0.149301	+	0.0276478i
$591$		0			0
$592$	−40.2621	−	123.914i	−0.0680104	−	0.209314i
$593$			8.75123i			0.0147576i	0.999973	+	0.00737878i	$0.00234876\pi$
$593$			8.75123i			0.0147576i	−0.999973	+	0.00737878i	$0.997651\pi$
$594$		0			0
$595$	−19.3457	+	2.54990i	−0.0325137	+	0.00428555i
$596$	218.956	+	71.1431i	0.367376	+	0.119368i
$597$		0			0
$598$	12.3158	−	8.94794i	0.0205949	−	0.0149631i
$599$			610.559i			1.01930i	0.860383	+	0.509649i	$0.170225\pi$
$599$			610.559i			1.01930i	−0.860383	+	0.509649i	$0.829775\pi$
$600$		0			0
$601$	263.034			0.437661			0.218830	−	0.975763i	$-0.429776\pi$
$601$	263.034			0.437661			0.218830	+	0.975763i	$0.429776\pi$
$602$	38.4768	+	52.9588i	0.0639149	+	0.0879714i
$603$		0			0
$604$	2.45124	−	7.54413i	0.00405834	−	0.0124903i
$605$	−51.7190	+	95.2892i	−0.0854860	+	0.157503i
$606$		0			0
$607$	−418.607			−0.689633			−0.344817	−	0.938670i	$-0.612059\pi$
$607$	−418.607			−0.689633			−0.344817	+	0.938670i	$0.612059\pi$
$608$	−100.691	+	32.7163i	−0.165609	+	0.0538098i
$609$		0			0
$610$	−226.068	−	122.700i	−0.370603	−	0.201148i
$611$	85.6470	+	117.883i	0.140175	+	0.192934i
$612$		0			0
$613$	86.3846	+	62.7621i	0.140921	+	0.102385i	0.656012	−	0.754750i	$-0.272242\pi$
$613$	86.3846	+	62.7621i	0.140921	+	0.102385i	−0.515091	+	0.857135i	$0.672242\pi$
$614$	332.966	+	458.288i	0.542289	+	0.746397i
$615$		0			0
$616$	34.2016	+	24.8489i	0.0555221	+	0.0403392i
$617$	−704.533	+	228.917i	−1.14187	+	0.371016i	−0.818075	−	0.575112i	$-0.804958\pi$
$617$	−704.533	+	228.917i	−1.14187	+	0.371016i	−0.323794	+	0.946128i	$0.604958\pi$
$618$		0			0
$619$	57.0793	+	175.672i	0.0922122	+	0.283800i	0.986517	−	0.163658i	$-0.0523294\pi$
$619$	57.0793	+	175.672i	0.0922122	+	0.283800i	−0.894305	+	0.447458i	$0.852329\pi$
$620$	368.925	+	68.3181i	0.595041	+	0.110191i
$621$		0			0
$622$	−87.7469	+	270.057i	−0.141072	+	0.434175i
$623$	−126.494	−	174.104i	−0.203040	−	0.279460i
$624$		0			0
$625$	464.720	+	417.924i	0.743552	+	0.668678i
$626$		−	26.0329i		−	0.0415861i
$627$		0			0
$628$	−9.18922	+	28.2815i	−0.0146325	+	0.0450342i
$629$	−80.6084	−	26.1913i	−0.128153	−	0.0416395i
$630$		0			0
$631$	−326.930	−	1006.19i	−0.518114	−	1.59459i	−0.777544	−	0.628829i	$-0.783535\pi$
$631$	−326.930	−	1006.19i	−0.518114	−	1.59459i	0.259430	−	0.965762i	$-0.416465\pi$
$632$		−	130.646i		−	0.206718i
$633$		0			0
$634$	279.157	+	202.819i	0.440310	+	0.319904i
$635$	−310.840	+	148.321i	−0.489511	+	0.233577i
$636$		0			0
$637$	−140.281	−	101.920i	−0.220221	−	0.160000i
$638$	−185.056	+	254.707i	−0.290056	+	0.399228i
$639$		0			0
$640$	49.7175	+	26.9846i	0.0776836	+	0.0421634i
$641$	65.0684	−	89.5590i	0.101511	−	0.139718i	−0.755240	−	0.655449i	$-0.772480\pi$
$641$	65.0684	−	89.5590i	0.101511	−	0.139718i	0.856751	+	0.515731i	$0.172480\pi$
$642$		0			0
$643$	808.338			1.25714			0.628568	−	0.777755i	$-0.283642\pi$
$643$	808.338			1.25714			0.628568	+	0.777755i	$0.283642\pi$
$644$	8.27955	−	2.69019i	0.0128564	−	0.00417731i
$645$		0			0
$646$	−21.2826	+	65.5011i	−0.0329452	+	0.101395i
$647$	1155.38	+	375.406i	1.78575	+	0.580226i	0.999299	−	0.0374249i	$-0.0119155\pi$
$647$	1155.38	+	375.406i	1.78575	+	0.580226i	0.786452	+	0.617651i	$0.211915\pi$
$648$		0			0
$649$	−126.258			−0.194543
$650$	46.9562	−	122.436i	0.0722402	−	0.188364i
$651$		0			0
$652$	161.161	−	117.091i	0.247180	−	0.179587i
$653$	−482.410	−	156.744i	−0.738759	−	0.240037i	−0.0846216	−	0.996413i	$-0.526968\pi$
$653$	−482.410	−	156.744i	−0.738759	−	0.240037i	−0.654137	+	0.756376i	$0.726968\pi$
$654$		0			0
$655$	1174.98	−	154.871i	1.79386	−	0.236444i
$656$	83.6682	−	27.1854i	0.127543	−	0.0414412i
$657$		0			0
$658$	25.7497	+	79.2494i	0.0391332	+	0.120440i
$659$	−125.068	+	172.142i	−0.189785	+	0.261216i	−0.893297	−	0.449467i	$-0.851614\pi$
$659$	−125.068	+	172.142i	−0.189785	+	0.261216i	0.703512	+	0.710683i	$0.251614\pi$
$660$		0			0
$661$	−199.837	+	145.190i	−0.302325	+	0.219652i	−0.728596	−	0.684943i	$-0.759827\pi$
$661$	−199.837	+	145.190i	−0.302325	+	0.219652i	0.426271	+	0.904595i	$0.359827\pi$
$662$	537.057	−	739.195i	0.811264	−	1.11661i
$663$		0			0
$664$	32.6151	−	23.6962i	0.0491191	−	0.0356871i
$665$	18.3405	+	139.146i	0.0275797	+	0.209243i
$666$		0			0
$667$	20.0344	+	61.6597i	0.0300367	+	0.0924433i
$668$		−	643.436i		−	0.963228i
$669$		0			0
$670$	−376.513	+	357.407i	−0.561960	+	0.533443i
$671$	344.775	+	112.024i	0.513822	+	0.166951i
$672$		0			0
$673$	−705.555	+	512.615i	−1.04837	+	0.761687i	−0.971902	−	0.235385i	$-0.924365\pi$
$673$	−705.555	+	512.615i	−1.04837	+	0.761687i	−0.0764702	+	0.997072i	$0.524365\pi$
$674$		−	87.0778i		−	0.129196i
$675$		0			0
$676$	310.487			0.459300
$677$	−475.512	−	654.486i	−0.702381	−	0.966744i	−0.999928	−	0.0120367i	$-0.996168\pi$
$677$	−475.512	−	654.486i	−0.702381	−	0.966744i	0.297547	−	0.954707i	$-0.403832\pi$
$678$		0			0
$679$	−7.48911	+	23.0491i	−0.0110296	+	0.0339457i
$680$	33.2117	−	15.8474i	0.0488408	−	0.0233050i
$681$		0			0
$682$	−528.792			−0.775354
$683$	−925.965	+	300.864i	−1.35573	+	0.440504i	−0.894616	−	0.446836i	$-0.852551\pi$
$683$	−925.965	+	300.864i	−1.35573	+	0.440504i	−0.461116	+	0.887340i	$0.652551\pi$
$684$		0			0
$685$	784.296	−	744.497i	1.14496	−	1.08686i
$686$	−119.374	−	164.304i	−0.174014	−	0.239510i
$687$		0			0
$688$	−99.8731	−	72.5621i	−0.145164	−	0.105468i
$689$	86.7646	+	119.421i	0.125928	+	0.173326i
$690$		0			0
$691$	−330.881	−	240.399i	−0.478844	−	0.347900i	0.322034	−	0.946728i	$-0.395633\pi$
$691$	−330.881	−	240.399i	−0.478844	−	0.347900i	−0.800878	+	0.598828i	$0.795633\pi$
$692$	−364.696	+	118.497i	−0.527017	+	0.171238i
$693$		0			0
$694$	115.723	+	356.158i	0.166748	+	0.513196i
$695$	884.448	−	422.025i	1.27259	−	0.607231i
$696$		0			0
$697$	17.6846	−	54.4277i	0.0253725	−	0.0780885i
$698$	−199.391	−	274.437i	−0.285660	−	0.393177i
$699$		0			0
$700$	47.1751	−	58.2927i	0.0673930	−	0.0832753i
$701$		−	96.9819i		−	0.138348i	−0.997605	−	0.0691740i	$-0.977964\pi$
$701$		−	96.9819i		−	0.138348i	0.997605	−	0.0691740i	$-0.0220364\pi$
$702$		0			0
$703$	−188.384	+	579.787i	−0.267972	+	0.824732i
$704$	−75.8239	−	24.6367i	−0.107704	−	0.0349953i
$705$		0			0
$706$	−178.192	−	548.418i	−0.252396	−	0.776796i
$707$		−	162.466i		−	0.229796i
$708$		0			0
$709$	1103.46	+	801.708i	1.55636	+	1.13076i	0.938919	+	0.344139i	$0.111829\pi$
$709$	1103.46	+	801.708i	1.55636	+	1.13076i	0.617437	+	0.786620i	$0.288171\pi$
$710$	−59.9566	−	454.880i	−0.0844459	−	0.640676i
$711$		0			0
$712$	328.336	+	238.550i	0.461146	+	0.335042i
$713$	−64.0051	+	88.0955i	−0.0897687	+	0.123556i
$714$		0			0
$715$	−33.6518	+	181.724i	−0.0470655	+	0.254159i
$716$	−98.9597	+	136.206i	−0.138212	+	0.190232i
$717$		0			0
$718$	−704.301			−0.980921
$719$	−547.401	+	177.861i	−0.761336	+	0.247373i	−0.663852	−	0.747864i	$-0.731080\pi$
$719$	−547.401	+	177.861i	−0.761336	+	0.247373i	−0.0974841	+	0.995237i	$0.531080\pi$
$720$		0			0
$721$	−44.6485	+	137.414i	−0.0619259	+	0.190588i
$722$	−14.4188	−	4.68495i	−0.0199706	−	0.00648885i
$723$		0			0
$724$	−253.355			−0.349937
$725$	434.119	+	351.324i	0.598785	+	0.484584i
$726$		0			0
$727$	−823.675	+	598.435i	−1.13298	+	0.823156i	−0.986125	−	0.166002i	$-0.946914\pi$
$727$	−823.675	+	598.435i	−1.13298	+	0.823156i	−0.146852	+	0.989158i	$0.546914\pi$
$728$	−14.9637	−	4.86200i	−0.0205545	−	0.00667857i
$729$		0			0
$730$	705.434	+	382.880i	0.966348	+	0.524493i
$731$	−76.3760	+	24.8161i	−0.104482	+	0.0339481i
$732$		0			0
$733$	314.799	+	968.851i	0.429466	+	1.32176i	0.898652	+	0.438662i	$0.144547\pi$
$733$	314.799	+	968.851i	0.429466	+	1.32176i	−0.469186	+	0.883099i	$0.655453\pi$
$734$	−307.031	+	422.591i	−0.418298	+	0.575738i
$735$		0			0
$736$	−13.2822	+	9.65005i	−0.0180464	+	0.0131115i
$737$	430.055	−	591.920i	0.583521	−	0.803148i
$738$		0			0
$739$	−974.108	+	707.731i	−1.31814	+	0.957688i	−0.318191	+	0.948027i	$0.603075\pi$
$739$	−974.108	+	707.731i	−1.31814	+	0.957688i	−0.999953	+	0.00966089i	$0.996925\pi$
$740$	293.975	−	140.274i	0.397264	−	0.189560i
$741$		0			0
$742$	26.0857	+	80.2836i	0.0351559	+	0.108199i
$743$		−	81.3081i		−	0.109432i	−0.998502	−	0.0547161i	$-0.982575\pi$
$743$		−	81.3081i		−	0.109432i	0.998502	−	0.0547161i	$-0.0174254\pi$
$744$		0			0
$745$	−104.801	+	565.938i	−0.140673	+	0.759648i
$746$	347.183	+	112.807i	0.465393	+	0.151215i
$747$		0			0
$748$	−41.9582	+	30.4844i	−0.0560939	+	0.0407546i
$749$		−	169.184i		−	0.225880i
$750$		0			0
$751$	58.6390			0.0780813			0.0390406	−	0.999238i	$-0.487570\pi$
$751$	58.6390			0.0780813			0.0390406	+	0.999238i	$0.487570\pi$
$752$	−92.3674	−	127.133i	−0.122829	−	0.169060i
$753$		0			0
$754$	36.2084	−	111.438i	0.0480218	−	0.147796i
$755$	19.4994	+	3.61093i	0.0258270	+	0.00478269i
$756$		0			0
$757$	−797.925			−1.05406			−0.527031	−	0.849846i	$-0.676695\pi$
$757$	−797.925			−1.05406			−0.527031	+	0.849846i	$0.676695\pi$
$758$	−225.397	+	73.2360i	−0.297358	+	0.0966174i
$759$		0			0
$760$	−113.984	−	238.880i	−0.149979	−	0.314315i
$761$	−22.0551	−	30.3563i	−0.0289818	−	0.0398900i	0.794280	−	0.607552i	$-0.207848\pi$
$761$	−22.0551	−	30.3563i	−0.0289818	−	0.0398900i	−0.823262	+	0.567662i	$0.807848\pi$
$762$		0			0
$763$	98.1644	+	71.3206i	0.128656	+	0.0934739i
$764$	89.2601	+	122.856i	0.116833	+	0.160806i
$765$		0			0
$766$	−334.492	−	243.023i	−0.436674	−	0.317262i
$767$	44.6900	−	14.5207i	0.0582660	−	0.0189318i
$768$		0			0
$769$	153.310	+	471.839i	0.199363	+	0.613575i	0.999898	+	0.0142893i	$0.00454858\pi$
$769$	153.310	+	471.839i	0.199363	+	0.613575i	−0.800535	+	0.599286i	$0.795451\pi$
$770$	−50.4162	+	92.8888i	−0.0654756	+	0.120635i
$771$		0			0
$772$	−167.171	+	514.499i	−0.216543	+	0.666450i
$773$	−378.855	−	521.449i	−0.490110	−	0.674578i	0.490298	−	0.871555i	$-0.336888\pi$
$773$	−378.855	−	521.449i	−0.490110	−	0.674578i	−0.980408	+	0.196976i	$0.936888\pi$
$774$		0			0
$775$	−48.8055	+	936.723i	−0.0629748	+	1.20868i
$776$		−	45.7045i		−	0.0588975i
$777$		0			0
$778$	121.250	−	373.170i	0.155849	−	0.479653i
$779$	−391.479	−	127.199i	−0.502540	−	0.163285i
$780$		0			0
$781$	199.822	+	614.990i	0.255855	+	0.787439i
$782$			10.6800i			0.0136573i
$783$		0			0
$784$	151.288	+	109.917i	0.192969	+	0.140201i
$785$	−73.0995	−	13.5367i	−0.0931204	−	0.0172442i
$786$		0			0
$787$	992.457	+	721.062i	1.26106	+	0.916216i	0.998809	−	0.0487826i	$-0.0155341\pi$
$787$	992.457	+	721.062i	1.26106	+	0.916216i	0.262254	+	0.964999i	$0.415534\pi$
$788$	−207.158	+	285.129i	−0.262891	+	0.361838i
$789$		0			0
$790$	323.813	−	42.6810i	0.409890	−	0.0540266i
$791$	53.5365	−	73.6866i	0.0676820	−	0.0931563i
$792$		0			0
$793$	−134.919			−0.170137
$794$	−566.306	+	184.004i	−0.713231	+	0.231743i
$795$		0			0
$796$	142.946	−	439.943i	0.179581	−	0.552692i
$797$	564.257	+	183.338i	0.707976	+	0.230035i	0.640802	−	0.767706i	$-0.278602\pi$
$797$	564.257	+	183.338i	0.707976	+	0.230035i	0.0671737	+	0.997741i	$0.478602\pi$
$798$		0			0
$799$	−102.226			−0.127942
$800$	−50.6407	+	132.044i	−0.0633008	+	0.165055i
$801$		0			0
$802$	232.322	−	168.792i	0.289679	−	0.210464i
$803$	−1075.85	−	349.566i	−1.33979	−	0.435325i
$804$		0			0
$805$	9.37267	+	19.6425i	0.0116431	+	0.0244006i
$806$	187.169	−	60.8150i	0.232220	−	0.0754528i
$807$		0			0
$808$	94.6792	+	291.393i	0.117177	+	0.360634i
$809$	527.214	−	725.648i	0.651686	−	0.896969i	−0.347485	−	0.937686i	$-0.612964\pi$
$809$	527.214	−	725.648i	0.651686	−	0.896969i	0.999171	+	0.0407167i	$0.0129641\pi$
$810$		0			0
$811$	650.550	−	472.652i	0.802157	−	0.582801i	−0.109389	−	0.993999i	$-0.534889\pi$
$811$	650.550	−	472.652i	0.802157	−	0.582801i	0.911546	+	0.411198i	$0.134889\pi$
$812$	39.3860	−	54.2102i	0.0485049	−	0.0667613i
$813$		0			0
$814$	−371.396	+	269.835i	−0.456260	+	0.331492i
$815$	342.867	+	361.196i	0.420695	+	0.443185i
$816$		0			0
$817$	178.493	+	549.344i	0.218473	+	0.672392i
$818$		−	799.035i		−	0.976815i
$819$		0			0
$820$	94.7146	+	198.496i	0.115506	+	0.242068i
$821$	1174.33	+	381.564i	1.43037	+	0.464755i	0.918881	−	0.394535i	$-0.129094\pi$
$821$	1174.33	+	381.564i	1.43037	+	0.464755i	0.511489	+	0.859290i	$0.329094\pi$
$822$		0			0
$823$	414.345	−	301.039i	0.503457	−	0.365783i	−0.306879	−	0.951749i	$-0.599285\pi$
$823$	414.345	−	301.039i	0.503457	−	0.365783i	0.810336	+	0.585966i	$0.199285\pi$
$824$		−	272.481i		−	0.330680i
$825$		0			0
$826$	26.8720			0.0325327
$827$	194.021	+	267.046i	0.234608	+	0.322910i	0.910046	−	0.414506i	$-0.136046\pi$
$827$	194.021	+	267.046i	0.234608	+	0.322910i	−0.675439	+	0.737416i	$0.736046\pi$
$828$		0			0
$829$	−57.6889	+	177.548i	−0.0695885	+	0.214171i	−0.979803	−	0.199966i	$-0.935917\pi$
$829$	−57.6889	+	177.548i	−0.0695885	+	0.214171i	0.910214	+	0.414138i	$0.135917\pi$
$830$	69.3877	+	73.0971i	0.0835997	+	0.0880688i
$831$		0			0
$832$	29.6717			0.0356632
$833$	115.695	−	37.5914i	0.138889	−	0.0451278i
$834$		0			0
$835$	1594.80	−	210.206i	1.90994	−	0.251744i
$836$	219.263	+	301.790i	0.262277	+	0.360993i
$837$		0			0
$838$	758.999	+	551.445i	0.905727	+	0.658049i
$839$	788.764	+	1085.64i	0.940124	+	1.29397i	0.955777	+	0.294093i	$0.0950174\pi$
$839$	788.764	+	1085.64i	0.940124	+	1.29397i	−0.0156525	+	0.999877i	$0.504983\pi$
$840$		0			0
$841$	−276.668	−	201.011i	−0.328975	−	0.239014i
$842$	557.090	−	181.009i	0.661627	−	0.214976i
$843$		0			0
$844$	−199.376	−	613.615i	−0.236227	−	0.727032i
$845$	101.434	+	769.562i	0.120040	+	0.910724i
$846$		0			0
$847$	−10.0498	+	30.9300i	−0.0118651	+	0.0365171i
$848$	−93.5728	−	128.792i	−0.110345	−	0.151877i
$849$		0			0
$850$	50.1288	+	77.1401i	0.0589750	+	0.0907530i
$851$			94.5345i			0.111086i
$852$		0			0
$853$	−115.338	+	354.975i	−0.135215	+	0.416149i	−0.995623	−	0.0934560i	$-0.970209\pi$
$853$	−115.338	+	354.975i	−0.135215	+	0.416149i	0.860408	+	0.509605i	$0.170209\pi$
$854$	−73.3795	−	23.8425i	−0.0859245	−	0.0279186i
$855$		0			0
$856$	98.5944	+	303.442i	0.115180	+	0.354489i
$857$		−	1517.12i		−	1.77027i	−0.465335	−	0.885135i	$-0.654066\pi$
$857$		−	1517.12i		−	1.77027i	0.465335	−	0.885135i	$-0.345934\pi$
$858$		0			0
$859$	842.615	+	612.196i	0.980926	+	0.712684i	0.957915	−	0.287051i	$-0.0926748\pi$
$859$	842.615	+	612.196i	0.980926	+	0.712684i	0.0230106	+	0.999735i	$0.492675\pi$
$860$	147.222	−	271.247i	0.171188	−	0.315404i
$861$		0			0
$862$	−276.291	−	200.737i	−0.320523	−	0.232874i
$863$	740.943	−	1019.82i	0.858567	−	1.18172i	−0.123343	−	0.992364i	$-0.539361\pi$
$863$	740.943	−	1019.82i	0.858567	−	1.18172i	0.981909	−	0.189352i	$-0.0606386\pi$
$864$		0			0
$865$	−412.845	−	865.209i	−0.477278	−	1.00024i
$866$	−202.452	+	278.651i	−0.233778	+	0.321768i
$867$		0			0
$868$	112.544			0.129660
$869$	−437.790	+	142.247i	−0.503786	+	0.163690i
$870$		0			0
$871$	−84.1456	+	258.973i	−0.0966080	+	0.297329i
$872$	−217.627	−	70.7114i	−0.249573	−	0.0810910i
$873$		0			0
$874$	76.8172			0.0878915
$875$	159.894	+	97.8826i	0.182736	+	0.111866i
$876$		0			0
$877$	467.897	−	339.947i	0.533520	−	0.387625i	−0.288153	−	0.957584i	$-0.593041\pi$
$877$	467.897	−	339.947i	0.533520	−	0.387625i	0.821673	+	0.569960i	$0.193041\pi$
$878$	744.181	+	241.799i	0.847586	+	0.275397i
$879$		0			0
$880$	36.2924	−	195.983i	0.0412414	−	0.222708i
$881$	132.261	−	42.9742i	0.150126	−	0.0487789i	−0.232990	−	0.972479i	$-0.574851\pi$
$881$	132.261	−	42.9742i	0.150126	−	0.0487789i	0.383116	+	0.923700i	$0.374851\pi$
$882$		0			0
$883$	−190.533	−	586.400i	−0.215779	−	0.664100i	−0.999097	−	0.0424792i	$-0.986474\pi$
$883$	−190.533	−	586.400i	−0.215779	−	0.664100i	0.783318	−	0.621621i	$-0.213526\pi$
$884$	11.3454	−	15.6157i	0.0128342	−	0.0176648i
$885$		0			0
$886$	−67.7955	+	49.2563i	−0.0765187	+	0.0555941i
$887$	532.775	−	733.302i	0.600648	−	0.826722i	−0.395119	−	0.918630i	$-0.629297\pi$
$887$	532.775	−	733.302i	0.600648	−	0.826722i	0.995767	+	0.0919083i	$0.0292967\pi$
$888$		0			0
$889$	−83.5799	+	60.7244i	−0.0940156	+	0.0683064i
$890$	−483.996	+	891.734i	−0.543816	+	1.00195i
$891$		0			0
$892$	109.567	+	337.211i	0.122833	+	0.378040i
$893$			735.271i			0.823372i
$894$		0			0
$895$	−369.925	−	200.780i	−0.413324	−	0.224335i
$896$	16.1378	+	5.24350i	0.0180110	+	0.00585213i
$897$		0			0
$898$	596.314	−	433.248i	0.664047	−	0.482459i
$899$			838.145i			0.932308i
$900$		0			0
$901$	−103.560			−0.114939
$902$	−182.195	−	250.770i	−0.201990	−	0.278016i
$903$		0			0
$904$	−53.0792	+	163.361i	−0.0587159	+	0.180709i
$905$	−82.7692	−	627.955i	−0.0914576	−	0.693873i
$906$		0			0
$907$	−873.716			−0.963304			−0.481652	−	0.876363i	$-0.659963\pi$
$907$	−873.716			−0.963304			−0.481652	+	0.876363i	$0.659963\pi$
$908$	−472.138	+	153.407i	−0.519975	+	0.168950i
$909$		0			0
$910$	7.16223	−	38.6768i	0.00787059	−	0.0425020i
$911$	162.716	+	223.959i	0.178612	+	0.245839i	0.888931	−	0.458042i	$-0.151449\pi$
$911$	162.716	+	223.959i	0.178612	+	0.245839i	−0.710318	+	0.703881i	$0.751449\pi$
$912$		0			0
$913$	−114.917	−	83.4918i	−0.125867	−	0.0914478i
$914$	672.377	+	925.448i	0.735642	+	1.01252i
$915$		0			0
$916$	160.458	+	116.580i	0.175173	+	0.127271i
$917$	338.096	−	109.854i	0.368698	−	0.119797i
$918$		0			0
$919$	−371.584	−	1143.62i	−0.404336	−	1.24442i	−0.921449	−	0.388500i	$-0.872993\pi$
$919$	−371.584	−	1143.62i	−0.404336	−	1.24442i	0.517113	−	0.855917i	$-0.327007\pi$
$920$	−28.2574	−	29.7681i	−0.0307146	−	0.0323566i
$921$		0			0
$922$	2.82005	−	8.67921i	0.00305862	−	0.00941346i
$923$	−141.457	−	194.699i	−0.153258	−	0.210941i
$924$		0			0
$925$	443.718	+	682.810i	0.479695	+	0.738173i
$926$		−	612.302i		−	0.661233i
$927$		0			0
$928$	−39.0496	+	120.182i	−0.0420793	+	0.129507i
$929$	−542.164	−	176.160i	−0.583600	−	0.189623i	0.00231270	−	0.999997i	$-0.499264\pi$
$929$	−542.164	−	176.160i	−0.583600	−	0.189623i	−0.585913	+	0.810374i	$0.699264\pi$
$930$		0			0
$931$	−270.381	−	832.149i	−0.290420	−	0.893822i
$932$			703.983i			0.755347i
$933$		0			0
$934$	772.150	+	561.000i	0.826713	+	0.600642i
$935$	−89.2650	−	94.0370i	−0.0954706	−	0.100574i
$936$		0			0
$937$	−65.8306	−	47.8288i	−0.0702568	−	0.0510446i	0.552102	−	0.833776i	$-0.313826\pi$
$937$	−65.8306	−	47.8288i	−0.0702568	−	0.0510446i	−0.622359	+	0.782732i	$0.713826\pi$
$938$	−91.5301	+	125.980i	−0.0975800	+	0.134307i
$939$		0			0
$940$	284.931	−	270.472i	0.303118	−	0.287736i
$941$	464.420	−	639.220i	0.493539	−	0.679298i	−0.487497	−	0.873125i	$-0.662090\pi$
$941$	464.420	−	639.220i	0.493539	−	0.679298i	0.981036	+	0.193827i	$0.0620899\pi$
$942$		0			0
$943$	−63.8308			−0.0676891
$944$	−48.1967	+	15.6601i	−0.0510558	+	0.0165890i
$945$		0			0
$946$	−134.412	+	413.677i	−0.142085	+	0.437291i
$947$	601.850	+	195.553i	0.635534	+	0.206497i	0.609025	−	0.793151i	$-0.291561\pi$
$947$	601.850	+	195.553i	0.635534	+	0.206497i	0.0265089	+	0.999649i	$0.491561\pi$
$948$		0			0
$949$	421.008			0.443633
$950$	554.840	−	360.558i	0.584042	−	0.379535i
$951$		0			0
$952$	8.93010	−	6.48810i	0.00938036	−	0.00681523i
$953$	−960.909	−	312.218i	−1.00830	−	0.327616i	−0.242122	−	0.970246i	$-0.577843\pi$
$953$	−960.909	−	312.218i	−1.00830	−	0.327616i	−0.766177	+	0.642630i	$0.777843\pi$
$954$		0			0
$955$	−275.345	+	261.373i	−0.288320	+	0.273689i
$956$	123.103	−	39.9985i	0.128769	−	0.0418394i
$957$		0			0
$958$	29.0495	+	89.4053i	0.0303231	+	0.0933250i
$959$	190.662	−	262.424i	0.198813	−	0.273643i
$960$		0			0
$961$	−361.413	+	262.582i	−0.376081	+	0.273239i
$962$	100.425	−	138.223i	0.104392	−	0.143683i
$963$		0			0
$964$	−592.186	+	430.248i	−0.614300	+	0.446315i
$965$	−1329.83	−	246.260i	−1.37806	−	0.255192i
$966$		0			0
$967$	−321.337	−	988.974i	−0.332303	−	1.02272i	−0.968035	−	0.250814i	$-0.919302\pi$
$967$	−321.337	−	988.974i	−0.332303	−	1.02272i	0.635732	−	0.771910i	$-0.280698\pi$
$968$		−	61.3316i		−	0.0633591i
$969$		0			0
$970$	113.281	−	14.9313i	0.116785	−	0.0153931i
$971$	−1054.06	−	342.485i	−1.08554	−	0.352714i	−0.289019	−	0.957323i	$-0.593329\pi$
$971$	−1054.06	−	342.485i	−1.08554	−	0.352714i	−0.796522	+	0.604610i	$0.793329\pi$
$972$		0			0
$973$	237.814	−	172.782i	0.244413	−	0.177577i
$974$			195.677i			0.200901i
$975$		0			0
$976$	145.505			0.149083
$977$	−631.704	−	869.466i	−0.646575	−	0.889934i	0.352370	−	0.935861i	$-0.385376\pi$
$977$	−631.704	−	869.466i	−0.646575	−	0.889934i	−0.998945	+	0.0459265i	$0.985376\pi$
$978$		0			0
$979$	441.884	−	1359.98i	0.451362	−	1.38915i
$980$	−223.012	+	410.886i	−0.227563	+	0.419272i
$981$		0			0
$982$	−281.492			−0.286651
$983$	991.000	−	321.995i	1.00814	−	0.327564i	0.242025	−	0.970270i	$-0.422188\pi$
$983$	991.000	−	321.995i	1.00814	−	0.327564i	0.766113	+	0.642706i	$0.222188\pi$
$984$		0			0
$985$	−774.386	−	420.305i	−0.786179	−	0.426705i
$986$	48.3184	+	66.5045i	0.0490044	+	0.0674488i
$987$		0			0
$988$	−112.318	−	81.6036i	−0.113682	−	0.0825947i
$989$	52.6485	+	72.4644i	0.0532340	+	0.0732704i
$990$		0			0
$991$	−1465.79	−	1064.96i	−1.47910	−	1.07463i	−0.977846	−	0.209326i	$-0.932873\pi$
$991$	−1465.79	−	1064.96i	−1.47910	−	1.07463i	−0.501252	−	0.865302i	$-0.667127\pi$
$992$	−201.856	+	65.5869i	−0.203484	+	0.0661159i
$993$		0			0
$994$	−42.5289	−	130.890i	−0.0427856	−	0.131680i
$995$	1137.13	+	210.575i	1.14284	+	0.211633i
$996$		0			0
$997$	−366.037	+	1126.55i	−0.367138	+	1.12994i	0.581493	+	0.813552i	$0.302469\pi$
$997$	−366.037	+	1126.55i	−0.367138	+	1.12994i	−0.948631	+	0.316384i	$0.897531\pi$
$998$	184.083	+	253.368i	0.184452	+	0.253876i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.n.a.161.1	✓	32
3.2	odd	2	inner	450.3.n.a.161.8	yes	32
25.16	even	5	inner	450.3.n.a.341.8	yes	32
75.41	odd	10	inner	450.3.n.a.341.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.3.n.a.161.1	✓	32	1.1	even	1	trivial
450.3.n.a.161.8	yes	32	3.2	odd	2	inner
450.3.n.a.341.1	yes	32	75.41	odd	10	inner
450.3.n.a.341.8	yes	32	25.16	even	5	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831254 - 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} +(-4.91641 - 0.910429i) q^{5} -1.49980 q^{7} +(2.68999 - 0.874032i) q^{8} +O(q^{10})\)	\(q+(-0.831254 - 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} +(-4.91641 - 0.910429i) q^{5} -1.49980 q^{7} +(2.68999 - 0.874032i) q^{8} +(3.04515 + 6.38178i) q^{10} +(-5.85772 - 8.06245i) q^{11} +(3.00062 + 2.18008i) q^{13} +(1.24672 + 1.71596i) q^{14} +(-3.23607 - 2.35114i) q^{16} +(-2.47472 + 0.804085i) q^{17} +(5.78349 + 17.7997i) q^{19} +(4.77025 - 8.78890i) q^{20} +(-4.35519 + 13.4039i) q^{22} +(1.70590 + 2.34798i) q^{23} +(23.3422 + 8.95209i) q^{25} -5.24527i q^{26} +(0.926929 - 2.85280i) q^{28} +(21.2454 + 6.90306i) q^{29} +(11.5942 + 35.6834i) q^{31} +5.65685i q^{32} +(2.97709 + 2.16298i) q^{34} +(7.37365 + 1.36546i) q^{35} +(26.3519 + 19.1458i) q^{37} +(15.5575 - 21.4131i) q^{38} +(-14.0209 + 1.84805i) q^{40} +(-12.9274 + 17.7931i) q^{41} +30.8625 q^{43} +(18.9560 - 6.15917i) q^{44} +(1.26833 - 3.90353i) q^{46} +(37.3634 + 12.1401i) q^{47} -46.7506 q^{49} +(-9.16104 - 34.1478i) q^{50} +(-6.00124 + 4.36015i) q^{52} +(37.8510 + 12.2985i) q^{53} +(21.4587 + 44.9714i) q^{55} +(-4.03446 + 1.31088i) q^{56} +(-9.76239 - 30.0456i) q^{58} +(7.44680 - 10.2496i) q^{59} +(-29.4291 + 21.3815i) q^{61} +(31.1884 - 42.9272i) q^{62} +(6.47214 - 4.70228i) q^{64} +(-12.7675 - 13.4500i) q^{65} +(22.6871 + 69.8236i) q^{67} -5.20415i q^{68} +(-4.56712 - 9.57141i) q^{70} +(-61.7104 - 20.0509i) q^{71} +(91.8321 - 66.7199i) q^{73} -46.0648i q^{74} -37.4315 q^{76} +(8.78542 + 12.0921i) q^{77} +(14.2736 - 43.9295i) q^{79} +(13.7693 + 14.5054i) q^{80} +31.1035 q^{82} +(13.5557 - 4.40452i) q^{83} +(12.8988 - 1.70016i) q^{85} +(-25.6546 - 35.3105i) q^{86} +(-22.8041 - 16.5681i) q^{88} +(84.3402 + 116.084i) q^{89} +(-4.50034 - 3.26969i) q^{91} +(-5.52042 + 1.79369i) q^{92} +(-17.1687 - 52.8398i) q^{94} +(-12.2286 - 92.7764i) q^{95} +(4.99340 - 15.3681i) q^{97} +(38.8616 + 53.4884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 8 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 + 8 * q^7	\( 32 q + 16 q^{4} + 8 q^{7} - 20 q^{10} - 16 q^{13} - 32 q^{16} - 12 q^{19} - 32 q^{22} - 20 q^{25} + 24 q^{28} - 12 q^{31} + 116 q^{34} + 88 q^{37} - 40 q^{43} + 168 q^{46} - 416 q^{49} + 32 q^{52} + 320 q^{55} + 192 q^{58} - 280 q^{61} + 64 q^{64} - 96 q^{67} + 160 q^{70} - 248 q^{73} - 16 q^{76} + 328 q^{79} - 688 q^{82} - 380 q^{85} - 56 q^{88} + 256 q^{91} + 160 q^{94} - 852 q^{97}+O(q^{100}) \) 32 * q + 16 * q^4 + 8 * q^7 - 20 * q^10 - 16 * q^13 - 32 * q^16 - 12 * q^19 - 32 * q^22 - 20 * q^25 + 24 * q^28 - 12 * q^31 + 116 * q^34 + 88 * q^37 - 40 * q^43 + 168 * q^46 - 416 * q^49 + 32 * q^52 + 320 * q^55 + 192 * q^58 - 280 * q^61 + 64 * q^64 - 96 * q^67 + 160 * q^70 - 248 * q^73 - 16 * q^76 + 328 * q^79 - 688 * q^82 - 380 * q^85 - 56 * q^88 + 256 * q^91 + 160 * q^94 - 852 * q^97

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