LMFDB - Embedded newform 84.5.m.a.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,5,Mod(61,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("84.61");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	84.m (of order $6$, 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:	$8.68307689904$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.2
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	84.73
Dual form			84.5.m.a.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.50000 + 2.59808i) q^{3} +(26.7371 - 15.4367i) q^{5} +(-17.5000 - 45.7684i) q^{7} +(13.5000 + 23.3827i) q^{9} +(40.3866 - 69.9517i) q^{11} +28.7961i q^{13} +160.423 q^{15} +(161.474 + 93.2272i) q^{17} +(482.804 - 278.747i) q^{19} +(40.1599 - 251.424i) q^{21} +(-54.5980 - 94.5665i) q^{23} +(164.083 - 284.199i) q^{25} +140.296i q^{27} -833.310 q^{29} +(965.768 + 557.587i) q^{31} +(363.480 - 209.855i) q^{33} +(-1174.41 - 953.575i) q^{35} +(351.732 + 609.218i) q^{37} +(-74.8144 + 129.582i) q^{39} -81.9587i q^{41} -602.062 q^{43} +(721.902 + 416.791i) q^{45} +(-2922.62 + 1687.38i) q^{47} +(-1788.50 + 1601.90i) q^{49} +(484.423 + 839.045i) q^{51} +(-2618.31 + 4535.04i) q^{53} -2493.74i q^{55} +2896.83 q^{57} +(-5342.12 - 3084.28i) q^{59} +(-3596.39 + 2076.38i) q^{61} +(833.939 - 1027.07i) q^{63} +(444.516 + 769.924i) q^{65} +(3901.99 - 6758.45i) q^{67} -567.399i q^{69} +4230.76 q^{71} +(8418.76 + 4860.57i) q^{73} +(1476.74 - 852.598i) q^{75} +(-3908.35 - 624.278i) q^{77} +(1125.02 + 1948.60i) q^{79} +(-364.500 + 631.333i) q^{81} -6950.76i q^{83} +5756.48 q^{85} +(-3749.89 - 2165.00i) q^{87} +(-7375.76 + 4258.40i) q^{89} +(1317.95 - 503.931i) q^{91} +(2897.30 + 5018.28i) q^{93} +(8605.87 - 14905.8i) q^{95} -2356.24i q^{97} +2180.88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} + 39 q^{5} - 70 q^{7} + 54 q^{9} + 3 q^{11} + 234 q^{15} + 510 q^{17} + 459 q^{19} - 315 q^{21} + 144 q^{23} - 227 q^{25} - 570 q^{29} + 2640 q^{31} + 27 q^{33} - 2478 q^{35} + 433 q^{37}+ \cdots + 162 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 + 39 * q^5 - 70 * q^7 + 54 * q^9 + 3 * q^11 + 234 * q^15 + 510 * q^17 + 459 * q^19 - 315 * q^21 + 144 * q^23 - 227 * q^25 - 570 * q^29 + 2640 * q^31 + 27 * q^33 - 2478 * q^35 + 433 * q^37 - 639 * q^39 - 98 * q^43 + 1053 * q^45 - 1770 * q^47 - 7154 * q^49 + 1530 * q^51 - 213 * q^53 + 2754 * q^57 - 4857 * q^59 - 12936 * q^61 - 945 * q^63 + 102 * q^65 + 7205 * q^67 + 19188 * q^71 + 14355 * q^73 - 2043 * q^75 - 12621 * q^77 + 13424 * q^79 - 1458 * q^81 + 9708 * q^85 - 2565 * q^87 - 36162 * q^89 - 5985 * q^91 + 7920 * q^93 + 19656 * q^95 + 162 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	4.50000	+	2.59808i	0.500000	+	0.288675i
$3$	4.50000	+	2.59808i	0.500000	+	0.288675i
$4$		0			0
$5$	26.7371	−	15.4367i	1.06949	−	0.617468i	0.141444	−	0.989946i	$-0.454825\pi$
$5$	26.7371	−	15.4367i	1.06949	−	0.617468i	0.928041	+	0.372479i	$0.121492\pi$
$6$		0			0
$7$	−17.5000	−	45.7684i	−0.357143	−	0.934050i
$7$	−17.5000	−	45.7684i	−0.357143	−	0.934050i
$8$		0			0
$9$	13.5000	+	23.3827i	0.166667	+	0.288675i
$10$		0			0
$11$	40.3866	−	69.9517i	0.333774	−	0.578113i	−0.649475	−	0.760383i	$-0.725011\pi$
$11$	40.3866	−	69.9517i	0.333774	−	0.578113i	0.983249	+	0.182270i	$0.0583445\pi$
$12$		0			0
$13$			28.7961i			0.170391i	0.996364	+	0.0851954i	$0.0271515\pi$
$13$			28.7961i			0.170391i	−0.996364	+	0.0851954i	$0.972849\pi$
$14$		0			0
$15$	160.423			0.712990
$16$		0			0
$17$	161.474	+	93.2272i	0.558734	+	0.322585i	0.752637	−	0.658435i	$-0.228781\pi$
$17$	161.474	+	93.2272i	0.558734	+	0.322585i	−0.193903	+	0.981021i	$0.562115\pi$
$18$		0			0
$19$	482.804	−	278.747i	1.33741	−	0.772153i	0.350986	−	0.936381i	$-0.385846\pi$
$19$	482.804	−	278.747i	1.33741	−	0.772153i	0.986422	+	0.164228i	$0.0525132\pi$
$20$		0			0
$21$	40.1599	−	251.424i	0.0910655	−	0.570123i
$22$		0			0
$23$	−54.5980	−	94.5665i	−0.103210	−	0.178765i	0.809796	−	0.586712i	$-0.199578\pi$
$23$	−54.5980	−	94.5665i	−0.103210	−	0.178765i	−0.913005	+	0.407947i	$0.866245\pi$
$24$		0			0
$25$	164.083	−	284.199i	0.262532	−	0.454719i
$26$		0			0
$27$			140.296i			0.192450i
$28$		0			0
$29$	−833.310			−0.990856			−0.495428	−	0.868649i	$-0.664989\pi$
$29$	−833.310			−0.990856			−0.495428	+	0.868649i	$0.664989\pi$
$30$		0			0
$31$	965.768	+	557.587i	1.00496	+	0.580215i	0.909713	−	0.415238i	$-0.136302\pi$
$31$	965.768	+	557.587i	1.00496	+	0.580215i	0.0952492	+	0.995453i	$0.469635\pi$
$32$		0			0
$33$	363.480	−	209.855i	0.333774	−	0.192704i
$34$		0			0
$35$	−1174.41	−	953.575i	−0.958704	−	0.778428i
$36$		0			0
$37$	351.732	+	609.218i	0.256926	+	0.445009i	0.965417	−	0.260711i	$-0.0839569\pi$
$37$	351.732	+	609.218i	0.256926	+	0.445009i	−0.708491	+	0.705720i	$0.750624\pi$
$38$		0			0
$39$	−74.8144	+	129.582i	−0.0491876	+	0.0851954i
$40$		0			0
$41$		−	81.9587i		−	0.0487559i	−0.999703	−	0.0243780i	$-0.992239\pi$
$41$		−	81.9587i		−	0.0487559i	0.999703	−	0.0243780i	$-0.00776051\pi$
$42$		0			0
$43$	−602.062			−0.325615			−0.162808	−	0.986658i	$-0.552055\pi$
$43$	−602.062			−0.325615			−0.162808	+	0.986658i	$0.552055\pi$
$44$		0			0
$45$	721.902	+	416.791i	0.356495	+	0.205823i
$46$		0			0
$47$	−2922.62	+	1687.38i	−1.32305	+	0.763864i	−0.984214	−	0.176981i	$-0.943367\pi$
$47$	−2922.62	+	1687.38i	−1.32305	+	0.763864i	−0.338837	+	0.940845i	$0.610034\pi$
$48$		0			0
$49$	−1788.50	+	1601.90i	−0.744898	+	0.667178i
$50$		0			0
$51$	484.423	+	839.045i	0.186245	+	0.322585i
$52$		0			0
$53$	−2618.31	+	4535.04i	−0.932113	+	1.61447i	−0.152411	+	0.988317i	$0.548704\pi$
$53$	−2618.31	+	4535.04i	−0.932113	+	1.61447i	−0.779702	+	0.626150i	$0.784630\pi$
$54$		0			0
$55$		−	2493.74i		−	0.824378i
$56$		0			0
$57$	2896.83			0.891606
$58$		0			0
$59$	−5342.12	−	3084.28i	−1.53465	−	0.886031i	−0.999138	−	0.0415046i	$-0.986785\pi$
$59$	−5342.12	−	3084.28i	−1.53465	−	0.886031i	−0.535513	−	0.844527i	$-0.679882\pi$
$60$		0			0
$61$	−3596.39	+	2076.38i	−0.966512	+	0.558016i	−0.898171	−	0.439646i	$-0.855104\pi$
$61$	−3596.39	+	2076.38i	−0.966512	+	0.558016i	−0.0683411	+	0.997662i	$0.521771\pi$
$62$		0			0
$63$	833.939	−	1027.07i	0.210113	−	0.258773i
$64$		0			0
$65$	444.516	+	769.924i	0.105211	+	0.182231i
$66$		0			0
$67$	3901.99	−	6758.45i	0.869234	−	1.50556i	0.00645326	−	0.999979i	$-0.497946\pi$
$67$	3901.99	−	6758.45i	0.869234	−	1.50556i	0.862781	−	0.505578i	$-0.168721\pi$
$68$		0			0
$69$		−	567.399i		−	0.119176i
$70$		0			0
$71$	4230.76			0.839270			0.419635	−	0.907693i	$-0.362158\pi$
$71$	4230.76			0.839270			0.419635	+	0.907693i	$0.362158\pi$
$72$		0			0
$73$	8418.76	+	4860.57i	1.57980	+	0.912098i	0.994886	+	0.101003i	$0.0322052\pi$
$73$	8418.76	+	4860.57i	1.57980	+	0.912098i	0.584914	+	0.811095i	$0.301128\pi$
$74$		0			0
$75$	1476.74	−	852.598i	0.262532	−	0.151573i
$76$		0			0
$77$	−3908.35	−	624.278i	−0.659191	−	0.105292i
$78$		0			0
$79$	1125.02	+	1948.60i	0.180263	+	0.312225i	0.941970	−	0.335696i	$-0.108972\pi$
$79$	1125.02	+	1948.60i	0.180263	+	0.312225i	−0.761707	+	0.647922i	$0.775638\pi$
$80$		0			0
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	6950.76i		−	1.00896i	−0.863422	−	0.504482i	$-0.831683\pi$
$83$		−	6950.76i		−	1.00896i	0.863422	−	0.504482i	$-0.168317\pi$
$84$		0			0
$85$	5756.48			0.796744
$86$		0			0
$87$	−3749.89	−	2165.00i	−0.495428	−	0.286035i
$88$		0			0
$89$	−7375.76	+	4258.40i	−0.931165	+	0.537609i	−0.887180	−	0.461424i	$-0.847339\pi$
$89$	−7375.76	+	4258.40i	−0.931165	+	0.537609i	−0.0439855	+	0.999032i	$0.514006\pi$
$90$		0			0
$91$	1317.95	−	503.931i	0.159154	−	0.0608539i
$92$		0			0
$93$	2897.30	+	5018.28i	0.334987	+	0.580215i
$94$		0			0
$95$	8605.87	−	14905.8i	0.953559	−	1.65161i
$96$		0			0
$97$		−	2356.24i		−	0.250424i	−0.992130	−	0.125212i	$-0.960039\pi$
$97$		−	2356.24i		−	0.250424i	0.992130	−	0.125212i	$-0.0399611\pi$
$98$		0			0
$99$	2180.88			0.222516
$100$		0			0
$101$	3848.54	+	2221.96i	0.377271	+	0.217817i	0.676630	−	0.736323i	$-0.263440\pi$
$101$	3848.54	+	2221.96i	0.377271	+	0.217817i	−0.299359	+	0.954140i	$0.596773\pi$
$102$		0			0
$103$	−7634.42	+	4407.74i	−0.719618	+	0.415471i	−0.814612	−	0.580006i	$-0.803050\pi$
$103$	−7634.42	+	4407.74i	−0.719618	+	0.415471i	0.0949943	+	0.995478i	$0.469717\pi$
$104$		0			0
$105$	−2807.40	−	7342.30i	−0.254639	−	0.665968i
$106$		0			0
$107$	9370.54	+	16230.3i	0.818459	+	1.41761i	0.906817	+	0.421524i	$0.138505\pi$
$107$	9370.54	+	16230.3i	0.818459	+	1.41761i	−0.0883577	+	0.996089i	$0.528162\pi$
$108$		0			0
$109$	7926.20	−	13728.6i	0.667132	−	1.15551i	−0.311570	−	0.950223i	$-0.600855\pi$
$109$	7926.20	−	13728.6i	0.667132	−	1.15551i	0.978703	−	0.205284i	$-0.0658117\pi$
$110$		0			0
$111$			3655.31i			0.296673i
$112$		0			0
$113$	8142.87			0.637706			0.318853	−	0.947804i	$-0.396702\pi$
$113$	8142.87			0.637706			0.318853	+	0.947804i	$0.396702\pi$
$114$		0			0
$115$	−2919.59	−	1685.62i	−0.220763	−	0.127457i
$116$		0			0
$117$	−673.329	+	388.747i	−0.0491876	+	0.0283985i
$118$		0			0
$119$	1441.06	−	9021.90i	0.101763	−	0.637095i
$120$		0			0
$121$	4058.34	+	7029.25i	0.277190	+	0.480107i
$122$		0			0
$123$	212.935	−	368.814i	0.0140746	−	0.0243780i
$124$		0			0
$125$			9164.29i			0.586514i
$126$		0			0
$127$	−28274.4			−1.75301			−0.876507	−	0.481388i	$-0.840133\pi$
$127$	−28274.4			−1.75301			−0.876507	+	0.481388i	$0.840133\pi$
$128$		0			0
$129$	−2709.28	−	1564.20i	−0.162808	−	0.0939970i
$130$		0			0
$131$	−5308.55	+	3064.89i	−0.309338	+	0.178596i	−0.646630	−	0.762804i	$-0.723822\pi$
$131$	−5308.55	+	3064.89i	−0.309338	+	0.178596i	0.337292	+	0.941400i	$0.390489\pi$
$132$		0			0
$133$	−21206.9	−	17219.1i	−1.19888	−	0.973437i
$134$		0			0
$135$	2165.71	+	3751.12i	0.118832	+	0.205823i
$136$		0			0
$137$	722.018	−	1250.57i	0.0384686	−	0.0666297i	−0.846150	−	0.532945i	$-0.821085\pi$
$137$	722.018	−	1250.57i	0.0384686	−	0.0666297i	0.884619	+	0.466315i	$0.154419\pi$
$138$		0			0
$139$			23411.3i			1.21170i	0.795578	+	0.605851i	$0.207167\pi$
$139$			23411.3i			1.21170i	−0.795578	+	0.605851i	$0.792833\pi$
$140$		0			0
$141$	−17535.7			−0.882034
$142$		0			0
$143$	2014.33	+	1162.98i	0.0985052	+	0.0568720i
$144$		0			0
$145$	−22280.3	+	12863.5i	−1.05971	+	0.611821i
$146$		0			0
$147$	−12210.1	+	2561.87i	−0.565047	+	0.118556i
$148$		0			0
$149$	7864.49	+	13621.7i	0.354240	+	0.613562i	0.986988	−	0.160796i	$-0.0514062\pi$
$149$	7864.49	+	13621.7i	0.354240	+	0.613562i	−0.632747	+	0.774358i	$0.718073\pi$
$150$		0			0
$151$	−54.8582	+	95.0172i	−0.00240596	+	0.00416724i	−0.867226	−	0.497915i	$-0.834099\pi$
$151$	−54.8582	+	95.0172i	−0.00240596	+	0.00416724i	0.864820	+	0.502082i	$0.167433\pi$
$152$		0			0
$153$			5034.27i			0.215057i
$154$		0			0
$155$	34429.2			1.43306
$156$		0			0
$157$	−6418.59	−	3705.77i	−0.260399	−	0.150342i	0.364117	−	0.931353i	$-0.381371\pi$
$157$	−6418.59	−	3705.77i	−0.260399	−	0.150342i	−0.624517	+	0.781011i	$0.714704\pi$
$158$		0			0
$159$	−23564.8	+	13605.1i	−0.932113	+	0.538156i
$160$		0			0
$161$	−3372.70	+	4153.78i	−0.130114	+	0.160248i
$162$		0			0
$163$	18175.0	+	31480.0i	0.684068	+	1.18484i	0.973729	+	0.227711i	$0.0731241\pi$
$163$	18175.0	+	31480.0i	0.684068	+	1.18484i	−0.289661	+	0.957129i	$0.593543\pi$
$164$		0			0
$165$	6478.93	−	11221.8i	0.237977	−	0.412189i
$166$		0			0
$167$		−	41582.3i		−	1.49099i	−0.666510	−	0.745496i	$-0.732212\pi$
$167$		−	41582.3i		−	1.49099i	0.666510	−	0.745496i	$-0.267788\pi$
$168$		0			0
$169$	27731.8			0.970967
$170$		0			0
$171$	13035.7	+	7526.18i	0.445803	+	0.257384i
$172$		0			0
$173$	−26202.2	+	15127.9i	−0.875480	+	0.505459i	−0.869165	−	0.494521i	$-0.835343\pi$
$173$	−26202.2	+	15127.9i	−0.875480	+	0.505459i	−0.00631464	+	0.999980i	$0.502010\pi$
$174$		0			0
$175$	−15878.8	−	2536.32i	−0.518492	−	0.0828185i
$176$		0			0
$177$	−16026.4	−	27758.5i	−0.511551	−	0.886031i
$178$		0			0
$179$	12830.4	−	22222.8i	0.400435	−	0.693575i	−0.593343	−	0.804950i	$-0.702192\pi$
$179$	12830.4	−	22222.8i	0.400435	−	0.693575i	0.993778	+	0.111375i	$0.0355255\pi$
$180$		0			0
$181$		−	35378.2i		−	1.07989i	−0.841701	−	0.539943i	$-0.818446\pi$
$181$		−	35378.2i		−	1.07989i	0.841701	−	0.539943i	$-0.181554\pi$
$182$		0			0
$183$	−21578.4			−0.644341
$184$		0			0
$185$	18808.6	+	10859.2i	0.549558	+	0.317287i
$186$		0			0
$187$	13042.8	−	7530.27i	0.372982	−	0.215341i
$188$		0			0
$189$	6421.13	−	2455.18i	0.179758	−	0.0687322i
$190$		0			0
$191$	2521.50	+	4367.36i	0.0691181	+	0.119716i	0.898513	−	0.438946i	$-0.144648\pi$
$191$	2521.50	+	4367.36i	0.0691181	+	0.119716i	−0.829395	+	0.558662i	$0.811315\pi$
$192$		0			0
$193$	455.204	−	788.436i	0.0122206	−	0.0211666i	−0.859850	−	0.510546i	$-0.829443\pi$
$193$	455.204	−	788.436i	0.0122206	−	0.0211666i	0.872071	+	0.489379i	$0.162777\pi$
$194$		0			0
$195$			4619.54i			0.121487i
$196$		0			0
$197$	51842.5			1.33584			0.667918	−	0.744235i	$-0.267186\pi$
$197$	51842.5			1.33584			0.667918	+	0.744235i	$0.267186\pi$
$198$		0			0
$199$	−14759.6	−	8521.47i	−0.372708	−	0.215183i	0.301933	−	0.953329i	$-0.402368\pi$
$199$	−14759.6	−	8521.47i	−0.372708	−	0.215183i	−0.674641	+	0.738146i	$0.735702\pi$
$200$		0			0
$201$	35117.9	−	20275.3i	0.869234	−	0.501852i
$202$		0			0
$203$	14582.9	+	38139.3i	0.353877	+	0.925509i
$204$		0			0
$205$	−1265.17	−	2191.34i	−0.0301052	−	0.0521437i
$206$		0			0
$207$	1474.15	−	2553.30i	0.0344033	−	0.0595882i
$208$		0			0
$209$		−	45030.7i		−	1.03090i
$210$		0			0
$211$	36047.9			0.809684			0.404842	−	0.914387i	$-0.367327\pi$
$211$	36047.9			0.809684			0.404842	+	0.914387i	$0.367327\pi$
$212$		0			0
$213$	19038.4	+	10991.8i	0.419635	+	0.242277i
$214$		0			0
$215$	−16097.4	+	9293.85i	−0.348241	+	0.201057i
$216$		0			0
$217$	8618.92	−	53959.5i	0.183035	−	1.14590i
$218$		0			0
$219$	25256.3	+	43745.1i	0.526600	+	0.912098i
$220$		0			0
$221$	−2684.58	+	4649.82i	−0.0549656	+	0.0952033i
$222$		0			0
$223$		−	8665.34i		−	0.174251i	−0.996197	−	0.0871256i	$-0.972232\pi$
$223$		−	8665.34i		−	0.174251i	0.996197	−	0.0871256i	$-0.0277682\pi$
$224$		0			0
$225$	8860.46			0.175022
$226$		0			0
$227$	18607.3	+	10742.9i	0.361103	+	0.208483i	0.669565	−	0.742754i	$-0.266481\pi$
$227$	18607.3	+	10742.9i	0.361103	+	0.208483i	−0.308461	+	0.951237i	$0.599814\pi$
$228$		0			0
$229$	33210.6	−	19174.1i	0.633294	−	0.365632i	−0.148733	−	0.988877i	$-0.547519\pi$
$229$	33210.6	−	19174.1i	0.633294	−	0.365632i	0.782027	+	0.623245i	$0.214186\pi$
$230$		0			0
$231$	−15965.6	−	12963.4i	−0.299200	−	0.242938i
$232$		0			0
$233$	−38291.4	−	66322.6i	−0.705325	−	1.22166i	−0.966574	−	0.256387i	$-0.917468\pi$
$233$	−38291.4	−	66322.6i	−0.705325	−	1.22166i	0.261250	−	0.965271i	$-0.415865\pi$
$234$		0			0
$235$	−52095.0	+	90231.2i	−0.943323	+	1.63388i
$236$		0			0
$237$			11691.6i			0.208150i
$238$		0			0
$239$	−27955.3			−0.489404			−0.244702	−	0.969598i	$-0.578690\pi$
$239$	−27955.3			−0.489404			−0.244702	+	0.969598i	$0.578690\pi$
$240$		0			0
$241$	−18586.6	−	10731.0i	−0.320011	−	0.184759i	0.331386	−	0.943495i	$-0.392484\pi$
$241$	−18586.6	−	10731.0i	−0.320011	−	0.184759i	−0.651398	+	0.758737i	$0.725817\pi$
$242$		0			0
$243$	−3280.50	+	1894.00i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−23091.4	+	70438.6i	−0.384696	+	1.17349i
$246$		0			0
$247$	8026.82	+	13902.9i	0.131568	+	0.227882i
$248$		0			0
$249$	18058.6	−	31278.4i	0.291263	−	0.504482i
$250$		0			0
$251$		−	75356.9i		−	1.19612i	−0.801450	−	0.598061i	$-0.795938\pi$
$251$		−	75356.9i		−	1.19612i	0.801450	−	0.598061i	$-0.204062\pi$
$252$		0			0
$253$	−8820.12			−0.137795
$254$		0			0
$255$	25904.1	+	14955.8i	0.398372	+	0.230000i
$256$		0			0
$257$	−80929.3	+	46724.5i	−1.22529	+	0.707422i	−0.966041	−	0.258388i	$-0.916809\pi$
$257$	−80929.3	+	46724.5i	−1.22529	+	0.707422i	−0.259250	+	0.965810i	$0.583475\pi$
$258$		0			0
$259$	21727.6	−	26759.5i	0.323902	−	0.398914i
$260$		0			0
$261$	−11249.7	−	19485.0i	−0.165143	−	0.286035i
$262$		0			0
$263$	−38300.6	+	66338.6i	−0.553725	+	0.959080i	0.444276	+	0.895890i	$0.353461\pi$
$263$	−38300.6	+	66338.6i	−0.553725	+	0.959080i	−0.998001	+	0.0631906i	$0.979872\pi$
$264$		0			0
$265$			161672.i			2.30220i
$266$		0			0
$267$	−44254.6			−0.620777
$268$		0			0
$269$	−112153.	−	64751.7i	−1.54991	−	0.894843i	−0.998147	−	0.0608439i	$-0.980621\pi$
$269$	−112153.	−	64751.7i	−1.54991	−	0.894843i	−0.551766	−	0.833999i	$-0.686046\pi$
$270$		0			0
$271$	86449.8	−	49911.8i	1.17713	−	0.679618i	0.221783	−	0.975096i	$-0.428812\pi$
$271$	86449.8	−	49911.8i	1.17713	−	0.679618i	0.955349	+	0.295479i	$0.0954791\pi$
$272$		0			0
$273$	7240.03	+	1156.45i	0.0971438	+	0.0155167i
$274$		0			0
$275$	−13253.5	−	22955.7i	−0.175253	−	0.303547i
$276$		0			0
$277$	51676.3	−	89505.9i	0.673491	−	1.16652i	−0.303417	−	0.952858i	$-0.598127\pi$
$277$	51676.3	−	89505.9i	0.673491	−	1.16652i	0.976908	−	0.213662i	$-0.0685393\pi$
$278$		0			0
$279$			30109.7i			0.386810i
$280$		0			0
$281$	−73016.5			−0.924716			−0.462358	−	0.886693i	$-0.652997\pi$
$281$	−73016.5			−0.924716			−0.462358	+	0.886693i	$0.652997\pi$
$282$		0			0
$283$	100470.	+	58006.5i	1.25448	+	0.724275i	0.971996	−	0.234997i	$-0.0755079\pi$
$283$	100470.	+	58006.5i	1.25448	+	0.724275i	0.282485	+	0.959272i	$0.408841\pi$
$284$		0			0
$285$	77452.8	−	44717.4i	0.953559	−	0.550537i
$286$		0			0
$287$	−3751.12	+	1434.28i	−0.0455405	+	0.0174128i
$288$		0			0
$289$	−24377.9	−	42223.7i	−0.291877	−	0.505546i
$290$		0			0
$291$	6121.69	−	10603.1i	0.0722912	−	0.125212i
$292$		0			0
$293$			133255.i			1.55221i	0.630607	+	0.776103i	$0.282806\pi$
$293$			133255.i			1.55221i	−0.630607	+	0.776103i	$0.717194\pi$
$294$		0			0
$295$	−190444.			−2.18838
$296$		0			0
$297$	9813.95	+	5666.09i	0.111258	+	0.0642348i
$298$		0			0
$299$	2723.14	−	1572.21i	0.0304599	−	0.0175860i
$300$		0			0
$301$	10536.1	+	27555.5i	0.116291	+	0.304141i
$302$		0			0
$303$	11545.6	+	19997.6i	0.125757	+	0.217817i
$304$		0			0
$305$	−64104.8	+	111033.i	−0.689114	+	1.19358i
$306$		0			0
$307$			35822.8i			0.380087i	0.981776	+	0.190044i	$0.0608629\pi$
$307$			35822.8i			0.380087i	−0.981776	+	0.190044i	$0.939137\pi$
$308$		0			0
$309$	−45806.5			−0.479745
$310$		0			0
$311$	−120008.	−	69286.5i	−1.24076	−	0.716354i	−0.271512	−	0.962435i	$-0.587524\pi$
$311$	−120008.	−	69286.5i	−1.24076	−	0.716354i	−0.969249	+	0.246081i	$0.920857\pi$
$312$		0			0
$313$	19645.7	−	11342.4i	0.200530	−	0.115776i	−0.396373	−	0.918090i	$-0.629731\pi$
$313$	19645.7	−	11342.4i	0.200530	−	0.115776i	0.596903	+	0.802314i	$0.296398\pi$
$314$		0			0
$315$	6442.56	−	40334.2i	0.0649288	−	0.406492i
$316$		0			0
$317$	−12162.7	−	21066.4i	−0.121035	−	0.209638i	0.799141	−	0.601143i	$-0.205288\pi$
$317$	−12162.7	−	21066.4i	−0.121035	−	0.209638i	−0.920176	+	0.391505i	$0.871955\pi$
$318$		0			0
$319$	−33654.6	+	58291.4i	−0.330722	+	0.572827i
$320$		0			0
$321$			97381.5i			0.945075i
$322$		0			0
$323$	103947.			0.996342
$324$		0			0
$325$	8183.83	+	4724.93i	0.0774800	+	0.0447331i
$326$		0			0
$327$	71335.8	−	41185.7i	0.667132	−	0.385169i
$328$		0			0
$329$	128374.	+	104235.i	1.18601	+	0.962987i
$330$		0			0
$331$	−86681.1	−	150136.i	−0.791168	−	1.37034i	−0.925244	−	0.379372i	$-0.876140\pi$
$331$	−86681.1	−	150136.i	−0.791168	−	1.37034i	0.134077	−	0.990971i	$-0.457193\pi$
$332$		0			0
$333$	−9496.77	+	16448.9i	−0.0856421	+	0.148336i
$334$		0			0
$335$		−	240935.i		−	2.14690i
$336$		0			0
$337$	17517.9			0.154249			0.0771245	−	0.997021i	$-0.475426\pi$
$337$	17517.9			0.154249			0.0771245	+	0.997021i	$0.475426\pi$
$338$		0			0
$339$	36642.9	+	21155.8i	0.318853	+	0.184090i
$340$		0			0
$341$	78008.3	−	45038.1i	0.670860	−	0.387321i
$342$		0			0
$343$	104615.	+	53823.7i	0.889213	+	0.457494i
$344$		0			0
$345$	−8758.76	−	15170.6i	−0.0735876	−	0.127457i
$346$		0			0
$347$	7496.34	−	12984.0i	0.0622573	−	0.107833i	−0.833217	−	0.552947i	$-0.813503\pi$
$347$	7496.34	−	12984.0i	0.0622573	−	0.107833i	0.895474	+	0.445114i	$0.146837\pi$
$348$		0			0
$349$		−	17312.7i		−	0.142139i	−0.997471	−	0.0710694i	$-0.977359\pi$
$349$		−	17312.7i		−	0.142139i	0.997471	−	0.0710694i	$-0.0226412\pi$
$350$		0			0
$351$	−4039.98			−0.0327917
$352$		0			0
$353$	−29232.8	−	16877.6i	−0.234596	−	0.135444i	0.378094	−	0.925767i	$-0.376580\pi$
$353$	−29232.8	−	16877.6i	−0.234596	−	0.135444i	−0.612691	+	0.790323i	$0.709913\pi$
$354$		0			0
$355$	113118.	−	65309.0i	0.897587	−	0.518222i
$356$		0			0
$357$	29924.4	−	36854.6i	0.234795	−	0.289171i
$358$		0			0
$359$	−51246.0	−	88760.6i	−0.397622	−	0.688702i	0.595810	−	0.803126i	$-0.296831\pi$
$359$	−51246.0	−	88760.6i	−0.397622	−	0.688702i	−0.993432	+	0.114424i	$0.963498\pi$
$360$		0			0
$361$	90239.6	−	156300.i	0.692441	−	1.19934i
$362$		0			0
$363$			42175.5i			0.320072i
$364$		0			0
$365$	300124.			2.25276
$366$		0			0
$367$	−65619.3	−	37885.3i	−0.487191	−	0.281280i	0.236217	−	0.971700i	$-0.424092\pi$
$367$	−65619.3	−	37885.3i	−0.487191	−	0.281280i	−0.723409	+	0.690420i	$0.757426\pi$
$368$		0			0
$369$	1916.41	−	1106.44i	0.0140746	−	0.00812599i
$370$		0			0
$371$	253382.	+	40472.6i	1.84089	+	0.294045i
$372$		0			0
$373$	84927.1	+	147098.i	0.610420	+	1.05728i	0.991170	+	0.132600i	$0.0423327\pi$
$373$	84927.1	+	147098.i	0.610420	+	1.05728i	−0.380749	+	0.924678i	$0.624334\pi$
$374$		0			0
$375$	−23809.5	+	41239.3i	−0.169312	+	0.293257i
$376$		0			0
$377$		−	23996.0i		−	0.168833i
$378$		0			0
$379$	−125458.			−0.873417			−0.436708	−	0.899603i	$-0.643856\pi$
$379$	−125458.			−0.873417			−0.436708	+	0.899603i	$0.643856\pi$
$380$		0			0
$381$	−127235.	−	73459.0i	−0.876507	−	0.506052i
$382$		0			0
$383$	−75623.7	+	43661.4i	−0.515538	+	0.297646i	−0.735107	−	0.677951i	$-0.762868\pi$
$383$	−75623.7	+	43661.4i	−0.515538	+	0.297646i	0.219569	+	0.975597i	$0.429535\pi$
$384$		0			0
$385$	−114135.	+	43640.5i	−0.770010	+	0.294421i
$386$		0			0
$387$	−8127.84	−	14077.8i	−0.0542692	−	0.0939970i
$388$		0			0
$389$	−85004.5	+	147232.i	−0.561749	+	0.972978i	0.435595	+	0.900143i	$0.356538\pi$
$389$	−85004.5	+	147232.i	−0.561749	+	0.972978i	−0.997344	+	0.0728354i	$0.976795\pi$
$390$		0			0
$391$		−	20360.1i		−	0.133176i
$392$		0			0
$393$	−31851.3			−0.206225
$394$		0			0
$395$	60159.8	+	34733.3i	0.385578	+	0.222614i
$396$		0			0
$397$	62056.9	−	35828.6i	0.393739	−	0.227326i	−0.290040	−	0.957015i	$-0.593669\pi$
$397$	62056.9	−	35828.6i	0.393739	−	0.227326i	0.683779	+	0.729689i	$0.260335\pi$
$398$		0			0
$399$	−50694.5	−	132583.i	−0.318431	−	0.832804i
$400$		0			0
$401$	−115108.	−	199374.i	−0.715844	−	1.23988i	−0.962633	−	0.270809i	$-0.912709\pi$
$401$	−115108.	−	199374.i	−0.715844	−	1.23988i	0.246789	−	0.969069i	$-0.420625\pi$
$402$		0			0
$403$	−16056.3	+	27810.3i	−0.0988633	+	0.171236i
$404$		0			0
$405$			22506.7i			0.137215i
$406$		0			0
$407$	56821.1			0.343021
$408$		0			0
$409$	138232.	+	79808.1i	0.826344	+	0.477090i	0.852599	−	0.522565i	$-0.175025\pi$
$409$	138232.	+	79808.1i	0.826344	+	0.477090i	−0.0262553	+	0.999655i	$0.508358\pi$
$410$		0			0
$411$	6498.16	−	3751.72i	0.0384686	−	0.0222099i
$412$		0			0
$413$	−47675.3	+	298475.i	−0.279508	+	1.74988i
$414$		0			0
$415$	−107297.	−	185843.i	−0.623003	−	1.07907i
$416$		0			0
$417$	−60824.3	+	105351.i	−0.349788	+	0.605851i
$418$		0			0
$419$		−	142239.i		−	0.810195i	−0.914274	−	0.405097i	$-0.867238\pi$
$419$		−	142239.i		−	0.810195i	0.914274	−	0.405097i	$-0.132762\pi$
$420$		0			0
$421$	−204443.			−1.15347			−0.576736	−	0.816931i	$-0.695674\pi$
$421$	−204443.			−1.15347			−0.576736	+	0.816931i	$0.695674\pi$
$422$		0			0
$423$	−78910.8	−	45559.1i	−0.441017	−	0.254621i
$424$		0			0
$425$	52990.2	−	30593.9i	0.293372	−	0.169378i
$426$		0			0
$427$	157969.	+	128265.i	0.866398	+	0.703479i
$428$		0			0
$429$	6043.00	+	10466.8i	0.0328351	+	0.0568720i
$430$		0			0
$431$	13493.7	−	23371.7i	0.0726399	−	0.125816i	−0.827418	−	0.561587i	$-0.810191\pi$
$431$	13493.7	−	23371.7i	0.0726399	−	0.125816i	0.900058	+	0.435771i	$0.143524\pi$
$432$		0			0
$433$			274334.i			1.46320i	0.681733	+	0.731601i	$0.261227\pi$
$433$			274334.i			1.46320i	−0.681733	+	0.731601i	$0.738773\pi$
$434$		0			0
$435$	−133682.			−0.706470
$436$		0			0
$437$	−52720.3	−	30438.1i	−0.276067	−	0.159388i
$438$		0			0
$439$	132.549	−	76.5273i	0.000687778	−	0.000397089i	−0.499656	−	0.866224i	$-0.666540\pi$
$439$	132.549	−	76.5273i	0.000687778	−	0.000397089i	0.500344	+	0.865827i	$0.333207\pi$
$440$		0			0
$441$	−61601.4	−	20194.3i	−0.316747	−	0.103837i
$442$		0			0
$443$	140880.	+	244011.i	0.717863	+	1.24337i	0.961845	+	0.273595i	$0.0882127\pi$
$443$	140880.	+	244011.i	0.717863	+	1.24337i	−0.243982	+	0.969780i	$0.578454\pi$
$444$		0			0
$445$	−131471.	+	227715.i	−0.663912	+	1.14993i
$446$		0			0
$447$			81730.2i			0.409041i
$448$		0			0
$449$	381037.			1.89005			0.945026	−	0.326994i	$-0.106036\pi$
$449$	381037.			1.89005			0.945026	+	0.326994i	$0.106036\pi$
$450$		0			0
$451$	−5733.15	−	3310.04i	−0.0281864	−	0.0162734i
$452$		0			0
$453$	−493.724	+	285.052i	−0.00240596	+	0.00138908i
$454$		0			0
$455$	27459.2	−	33818.5i	0.132637	−	0.163354i
$456$		0			0
$457$	−142055.	−	246046.i	−0.680179	−	1.17810i	−0.974926	−	0.222529i	$-0.928569\pi$
$457$	−142055.	−	246046.i	−0.680179	−	1.17810i	0.294747	−	0.955575i	$-0.404764\pi$
$458$		0			0
$459$	−13079.4	+	22654.2i	−0.0620816	+	0.107528i
$460$		0			0
$461$		−	259491.i		−	1.22101i	−0.792011	−	0.610507i	$-0.790966\pi$
$461$		−	259491.i		−	1.22101i	0.792011	−	0.610507i	$-0.209034\pi$
$462$		0			0
$463$	−337437.			−1.57410			−0.787048	−	0.616892i	$-0.788392\pi$
$463$	−337437.			−1.57410			−0.787048	+	0.616892i	$0.788392\pi$
$464$		0			0
$465$	154931.	+	89449.6i	0.716528	+	0.413688i
$466$		0			0
$467$	−193149.	+	111514.i	−0.885641	+	0.511325i	−0.872514	−	0.488589i	$-0.837512\pi$
$467$	−193149.	+	111514.i	−0.885641	+	0.511325i	−0.0131267	+	0.999914i	$0.504178\pi$
$468$		0			0
$469$	−377608.	−	60315.2i	−1.71671	−	0.274209i
$470$		0			0
$471$	−19255.8	−	33351.9i	−0.0867998	−	0.150342i
$472$		0			0
$473$	−24315.3	+	42115.3i	−0.108682	+	0.188242i
$474$		0			0
$475$		−	182950.i		−	0.810860i
$476$		0			0
$477$	−141389.			−0.621409
$478$		0			0
$479$	30605.3	+	17670.0i	0.133391	+	0.0770130i	0.565210	−	0.824947i	$-0.308795\pi$
$479$	30605.3	+	17670.0i	0.133391	+	0.0770130i	−0.431820	+	0.901960i	$0.642128\pi$
$480$		0			0
$481$	−17543.1	+	10128.5i	−0.0758256	+	0.0437779i
$482$		0			0
$483$	−25969.0	+	9929.49i	−0.111317	+	0.0425630i
$484$		0			0
$485$	−36372.6	−	62999.1i	−0.154629	−	0.267825i
$486$		0			0
$487$	15664.8	−	27132.2i	0.0660491	−	0.114400i	−0.831110	−	0.556108i	$-0.812294\pi$
$487$	15664.8	−	27132.2i	0.0660491	−	0.114400i	0.897159	+	0.441708i	$0.145627\pi$
$488$		0			0
$489$			188880.i			0.789893i
$490$		0			0
$491$	−24200.2			−0.100382			−0.0501911	−	0.998740i	$-0.515983\pi$
$491$	−24200.2			−0.100382			−0.0501911	+	0.998740i	$0.515983\pi$
$492$		0			0
$493$	−134558.	−	77687.1i	−0.553625	−	0.319636i
$494$		0			0
$495$	58310.4	−	33665.5i	0.237977	−	0.137396i
$496$		0			0
$497$	−74038.3	−	193635.i	−0.299739	−	0.783920i
$498$		0			0
$499$	225811.	+	391117.i	0.906869	+	1.57074i	0.818388	+	0.574666i	$0.194868\pi$
$499$	225811.	+	391117.i	0.906869	+	1.57074i	0.0884813	+	0.996078i	$0.471799\pi$
$500$		0			0
$501$	108034.	−	187120.i	0.430413	−	0.745496i
$502$		0			0
$503$			339101.i			1.34027i	0.742239	+	0.670135i	$0.233764\pi$
$503$			339101.i			1.34027i	−0.742239	+	0.670135i	$0.766236\pi$
$504$		0			0
$505$	137199.			0.537981
$506$		0			0
$507$	124793.	+	72049.3i	0.485483	+	0.280294i
$508$		0			0
$509$	287788.	−	166155.i	1.11080	−	0.641323i	0.171766	−	0.985138i	$-0.445053\pi$
$509$	287788.	−	166155.i	1.11080	−	0.641323i	0.939037	+	0.343815i	$0.111719\pi$
$510$		0			0
$511$	75132.5	−	470373.i	0.287731	−	1.80136i
$512$		0			0
$513$	39107.2	+	67735.6i	0.148601	+	0.257384i
$514$		0			0
$515$	−136082.	+	235700.i	−0.513080	+	0.888681i
$516$		0			0
$517$			272590.i			1.01983i
$518$		0			0
$519$	−157213.			−0.583653
$520$		0			0
$521$	−6031.52	−	3482.30i	−0.0222204	−	0.0128289i	0.488849	−	0.872369i	$-0.337417\pi$
$521$	−6031.52	−	3482.30i	−0.0222204	−	0.0128289i	−0.511069	+	0.859540i	$0.670750\pi$
$522$		0			0
$523$	−29677.5	+	17134.3i	−0.108499	+	0.0626417i	−0.553267	−	0.833004i	$-0.686619\pi$
$523$	−29677.5	+	17134.3i	−0.108499	+	0.0626417i	0.444769	+	0.895645i	$0.353286\pi$
$524$		0			0
$525$	−64865.1	−	52667.8i	−0.235338	−	0.191085i
$526$		0			0
$527$	103964.	+	180072.i	0.374338	+	0.648372i
$528$		0			0
$529$	133959.	−	232023.i	0.478695	−	0.829125i
$530$		0			0
$531$		−	166551.i		−	0.590688i
$532$		0			0
$533$	2360.09			0.00830756
$534$		0			0
$535$	501083.	+	289300.i	1.75066	+	1.01074i
$536$		0			0
$537$	115473.	−	66668.5i	0.400435	−	0.231192i
$538$		0			0
$539$	39823.8	+	189804.i	0.137077	+	0.653322i
$540$		0			0
$541$	−17123.6	−	29659.0i	−0.0585061	−	0.101336i	0.835289	−	0.549811i	$-0.185300\pi$
$541$	−17123.6	−	29659.0i	−0.0585061	−	0.101336i	−0.893795	+	0.448476i	$0.851967\pi$
$542$		0			0
$543$	91915.2	−	159202.i	0.311736	−	0.539943i
$544$		0			0
$545$		−	489417.i		−	1.64773i
$546$		0			0
$547$	199345.			0.666242			0.333121	−	0.942884i	$-0.391898\pi$
$547$	199345.			0.666242			0.333121	+	0.942884i	$0.391898\pi$
$548$		0			0
$549$	−97102.6	−	56062.2i	−0.322171	−	0.186005i
$550$		0			0
$551$	−402326.	+	232283.i	−1.32518	+	0.765092i
$552$		0			0
$553$	69496.4	−	85591.1i	0.227254	−	0.279884i
$554$		0			0
$555$	56425.8	+	97732.4i	0.183186	+	0.317287i
$556$		0			0
$557$	238517.	−	413123.i	0.768792	−	1.33159i	−0.169426	−	0.985543i	$-0.554191\pi$
$557$	238517.	−	413123.i	0.768792	−	1.33159i	0.938218	−	0.346044i	$-0.112475\pi$
$558$		0			0
$559$		−	17337.0i		−	0.0554819i
$560$		0			0
$561$	78256.8			0.248655
$562$		0			0
$563$	−172367.	−	99516.1i	−0.543798	−	0.313962i	0.202819	−	0.979216i	$-0.434990\pi$
$563$	−172367.	−	99516.1i	−0.543798	−	0.313962i	−0.746617	+	0.665255i	$0.768323\pi$
$564$		0			0
$565$	217717.	−	125699.i	0.682017	−	0.393763i
$566$		0			0
$567$	35273.9	+	5634.28i	0.109720	+	0.0175256i
$568$		0			0
$569$	−107710.	−	186559.i	−0.332683	−	0.576224i	0.650354	−	0.759631i	$-0.274621\pi$
$569$	−107710.	−	186559.i	−0.332683	−	0.576224i	−0.983037	+	0.183407i	$0.941287\pi$
$570$		0			0
$571$	40895.7	−	70833.4i	0.125431	−	0.217253i	−0.796470	−	0.604678i	$-0.793302\pi$
$571$	40895.7	−	70833.4i	0.125431	−	0.217253i	0.921901	+	0.387425i	$0.126635\pi$
$572$		0			0
$573$			26204.2i			0.0798107i
$574$		0			0
$575$	−35834.3			−0.108384
$576$		0			0
$577$	−120612.	−	69635.5i	−0.362276	−	0.209160i	0.307803	−	0.951450i	$-0.400406\pi$
$577$	−120612.	−	69635.5i	−0.362276	−	0.209160i	−0.670079	+	0.742290i	$0.733740\pi$
$578$		0			0
$579$	4096.83	−	2365.31i	0.0122206	−	0.00705554i
$580$		0			0
$581$	−318125.	+	121638.i	−0.942423	+	0.360345i
$582$		0			0
$583$	211489.	+	366310.i	0.622230	+	1.07773i
$584$		0			0
$585$	−12001.9	+	20787.9i	−0.0350703	+	0.0607435i
$586$		0			0
$587$		−	442737.i		−	1.28490i	−0.766327	−	0.642451i	$-0.777918\pi$
$587$		−	442737.i		−	1.28490i	0.766327	−	0.642451i	$-0.222082\pi$
$588$		0			0
$589$	621703.			1.79206
$590$		0			0
$591$	233291.	+	134691.i	0.667918	+	0.385623i
$592$		0			0
$593$	−433993.	+	250566.i	−1.23417	+	0.712546i	−0.967896	−	0.251353i	$-0.919125\pi$
$593$	−433993.	+	250566.i	−1.23417	+	0.712546i	−0.266270	+	0.963898i	$0.585791\pi$
$594$		0			0
$595$	−100738.	−	263465.i	−0.284552	−	0.744199i
$596$		0			0
$597$	−44278.9	−	76693.2i	−0.124236	−	0.215183i
$598$		0			0
$599$	78875.6	−	136616.i	0.219831	−	0.380758i	−0.734925	−	0.678148i	$-0.762783\pi$
$599$	78875.6	−	136616.i	0.219831	−	0.380758i	0.954756	+	0.297390i	$0.0961161\pi$
$600$		0			0
$601$		−	129315.i		−	0.358013i	−0.983848	−	0.179006i	$-0.942712\pi$
$601$		−	129315.i		−	0.358013i	0.983848	−	0.179006i	$-0.0572883\pi$
$602$		0			0
$603$	210708.			0.579489
$604$		0			0
$605$	217017.	+	125295.i	0.592901	+	0.342312i
$606$		0			0
$607$	−167505.	+	96709.3i	−0.454623	+	0.262477i	−0.709781	−	0.704423i	$-0.751206\pi$
$607$	−167505.	+	96709.3i	−0.454623	+	0.262477i	0.255158	+	0.966899i	$0.417873\pi$
$608$		0			0
$609$	−33465.6	+	209514.i	−0.0902328	+	0.564910i
$610$		0			0
$611$	−48589.8	−	84160.0i	−0.130155	−	0.225436i
$612$		0			0
$613$	26167.3	−	45323.2i	0.0696368	−	0.120614i	−0.829105	−	0.559093i	$-0.811149\pi$
$613$	26167.3	−	45323.2i	0.0696368	−	0.120614i	0.898741	+	0.438479i	$0.144483\pi$
$614$		0			0
$615$		−	13148.0i		−	0.0347625i
$616$		0			0
$617$	151761.			0.398648			0.199324	−	0.979934i	$-0.436125\pi$
$617$	151761.			0.398648			0.199324	+	0.979934i	$0.436125\pi$
$618$		0			0
$619$	−545231.	−	314789.i	−1.42298	−	0.821559i	−0.426430	−	0.904521i	$-0.640229\pi$
$619$	−545231.	−	314789.i	−1.42298	−	0.821559i	−0.996553	+	0.0829613i	$0.973562\pi$
$620$		0			0
$621$	13267.3	−	7659.89i	0.0344033	−	0.0198627i
$622$		0			0
$623$	323976.	+	263055.i	0.834712	+	0.677752i
$624$		0			0
$625$	244018.	+	422651.i	0.624686	+	1.08199i
$626$		0			0
$627$	116993.	−	202638.i	0.297595	−	0.515449i
$628$		0			0
$629$			131164.i			0.331523i
$630$		0			0
$631$	204849.			0.514489			0.257244	−	0.966346i	$-0.417185\pi$
$631$	204849.			0.514489			0.257244	+	0.966346i	$0.417185\pi$
$632$		0			0
$633$	162216.	+	93655.3i	0.404842	+	0.233736i
$634$		0			0
$635$	−755976.	+	436463.i	−1.87482	+	1.08243i
$636$		0			0
$637$	−46128.3	−	51501.8i	−0.113681	−	0.126924i
$638$		0			0
$639$	57115.3	+	98926.6i	0.139878	+	0.242277i
$640$		0			0
$641$	231581.	−	401110.i	0.563621	−	0.976219i	−0.433556	−	0.901127i	$-0.642741\pi$
$641$	231581.	−	401110.i	0.563621	−	0.976219i	0.997177	−	0.0750928i	$-0.0239253\pi$
$642$		0			0
$643$			59250.0i			0.143307i	0.997430	+	0.0716534i	$0.0228275\pi$
$643$			59250.0i			0.143307i	−0.997430	+	0.0716534i	$0.977172\pi$
$644$		0			0
$645$	−96584.5			−0.232160
$646$		0			0
$647$	−234043.	−	135125.i	−0.559096	−	0.322794i	0.193686	−	0.981063i	$-0.437956\pi$
$647$	−234043.	−	135125.i	−0.559096	−	0.322794i	−0.752783	+	0.658269i	$0.771289\pi$
$648$		0			0
$649$	−431501.	+	249127.i	−1.02445	+	0.591468i
$650$		0			0
$651$	178976.	−	220425.i	0.422311	−	0.520114i
$652$		0			0
$653$	171942.	+	297813.i	0.403233	+	0.698420i	0.994114	−	0.108338i	$-0.0345530\pi$
$653$	171942.	+	297813.i	0.403233	+	0.698420i	−0.590881	+	0.806759i	$0.701220\pi$
$654$		0			0
$655$	−94623.6	+	163893.i	−0.220555	+	0.382013i
$656$		0			0
$657$			262471.i			0.608065i
$658$		0			0
$659$	−726498.			−1.67288			−0.836438	−	0.548061i	$-0.815366\pi$
$659$	−726498.			−1.67288			−0.836438	+	0.548061i	$0.815366\pi$
$660$		0			0
$661$	−432110.	−	249479.i	−0.988989	−	0.570993i	−0.0840168	−	0.996464i	$-0.526775\pi$
$661$	−432110.	−	249479.i	−0.988989	−	0.570993i	−0.904972	+	0.425471i	$0.860108\pi$
$662$		0			0
$663$	−24161.2	+	13949.5i	−0.0549656	+	0.0317344i
$664$		0			0
$665$	−832818.	−	133026.i	−1.88324	−	0.300810i
$666$		0			0
$667$	45497.1	+	78803.2i	0.102266	+	0.177130i
$668$		0			0
$669$	22513.2	−	38994.0i	0.0503020	−	0.0871256i
$670$		0			0
$671$			335432.i			0.745005i
$672$		0			0
$673$	−74418.2			−0.164304			−0.0821522	−	0.996620i	$-0.526179\pi$
$673$	−74418.2			−0.164304			−0.0821522	+	0.996620i	$0.526179\pi$
$674$		0			0
$675$	39872.1	+	23020.2i	0.0875108	+	0.0505244i
$676$		0			0
$677$	−545262.	+	314807.i	−1.18967	+	0.686858i	−0.958232	−	0.285991i	$-0.907677\pi$
$677$	−545262.	+	314807.i	−1.18967	+	0.686858i	−0.231441	+	0.972849i	$0.574344\pi$
$678$		0			0
$679$	−107841.	+	41234.2i	−0.233909	+	0.0894372i
$680$		0			0
$681$	55821.9	+	96686.3i	0.120368	+	0.208483i
$682$		0			0
$683$	−119621.	+	207189.i	−0.256428	+	0.444146i	−0.965282	−	0.261209i	$-0.915879\pi$
$683$	−119621.	+	207189.i	−0.256428	+	0.444146i	0.708854	+	0.705355i	$0.249212\pi$
$684$		0			0
$685$		−	44582.3i		−	0.0950126i
$686$		0			0
$687$	199263.			0.422196
$688$		0			0
$689$	−130591.	−	75396.9i	−0.275091	−	0.158824i
$690$		0			0
$691$	−248878.	+	143690.i	−0.521232	+	0.300934i	−0.737439	−	0.675414i	$-0.763965\pi$
$691$	−248878.	+	143690.i	−0.521232	+	0.300934i	0.216206	+	0.976348i	$0.430632\pi$
$692$		0			0
$693$	−38165.4	−	99815.4i	−0.0794700	−	0.207841i
$694$		0			0
$695$	361393.	+	625951.i	0.748187	+	1.29590i
$696$		0			0
$697$	7640.78	−	13234.2i	0.0157280	−	0.0272416i
$698$		0			0
$699$		−	397936.i		−	0.814439i
$700$		0			0
$701$	576577.			1.17333			0.586667	−	0.809828i	$-0.300440\pi$
$701$	576577.			1.17333			0.586667	+	0.809828i	$0.300440\pi$
$702$		0			0
$703$	339636.	+	196089.i	0.687231	+	0.396773i
$704$		0			0
$705$	−468855.	+	270693.i	−0.943323	+	0.544628i
$706$		0			0
$707$	34346.0	−	215026.i	0.0687127	−	0.430182i
$708$		0			0
$709$	−135055.	−	233923.i	−0.268670	−	0.465350i	0.699849	−	0.714291i	$-0.253251\pi$
$709$	−135055.	−	233923.i	−0.268670	−	0.465350i	−0.968519	+	0.248941i	$0.919917\pi$
$710$		0			0
$711$	−30375.6	+	52612.2i	−0.0600878	+	0.104075i
$712$		0			0
$713$		−	121772.i		−	0.239536i
$714$		0			0
$715$	71810.0			0.140466
$716$		0			0
$717$	−125799.	−	72629.9i	−0.244702	−	0.141279i
$718$		0			0
$719$	623402.	−	359922.i	1.20590	−	0.696226i	0.244038	−	0.969766i	$-0.421528\pi$
$719$	623402.	−	359922.i	1.20590	−	0.696226i	0.961861	+	0.273540i	$0.0881946\pi$
$720$		0			0
$721$	335338.	+	272280.i	0.645077	+	0.523776i
$722$		0			0
$723$	−55759.7	−	96578.7i	−0.106670	−	0.184759i
$724$		0			0
$725$	−136732.	+	236826.i	−0.260132	+	0.450561i
$726$		0			0
$727$		−	537629.i		−	1.01722i	−0.860998	−	0.508608i	$-0.830160\pi$
$727$		−	537629.i		−	1.01722i	0.860998	−	0.508608i	$-0.169840\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$		0			0
$731$	−97217.6	−	56128.6i	−0.181932	−	0.105039i
$732$		0			0
$733$	166185.	−	95946.8i	0.309302	−	0.178576i	−0.337312	−	0.941393i	$-0.609518\pi$
$733$	166185.	−	95946.8i	0.309302	−	0.178576i	0.646614	+	0.762817i	$0.276184\pi$
$734$		0			0
$735$	−286916.	+	256980.i	−0.531105	+	0.475692i
$736$		0			0
$737$	−315177.	−	545902.i	−0.580255	−	1.00503i
$738$		0			0
$739$	240143.	−	415941.i	0.439726	−	0.761627i	−0.557942	−	0.829880i	$-0.688409\pi$
$739$	240143.	−	415941.i	0.439726	−	0.761627i	0.997668	+	0.0682524i	$0.0217423\pi$
$740$		0			0
$741$			83417.2i			0.151921i
$742$		0			0
$743$	73908.4			0.133880			0.0669401	−	0.997757i	$-0.478676\pi$
$743$	73908.4			0.133880			0.0669401	+	0.997757i	$0.478676\pi$
$744$		0			0
$745$	420548.	+	242803.i	0.757709	+	0.437464i
$746$		0			0
$747$	162527.	−	93835.2i	0.291263	−	0.168161i
$748$		0			0
$749$	578849.	−	712904.i	1.03181	−	1.27077i
$750$		0			0
$751$	359828.	+	623241.i	0.637992	+	1.10503i	0.985873	+	0.167496i	$0.0535681\pi$
$751$	359828.	+	623241.i	0.637992	+	1.10503i	−0.347881	+	0.937539i	$0.613099\pi$
$752$		0			0
$753$	195783.	−	339106.i	0.345291	−	0.598061i
$754$		0			0
$755$			3387.32i			0.00594240i
$756$		0			0
$757$	−313914.			−0.547795			−0.273898	−	0.961759i	$-0.588313\pi$
$757$	−313914.			−0.547795			−0.273898	+	0.961759i	$0.588313\pi$
$758$		0			0
$759$	−39690.5	−	22915.3i	−0.0688975	−	0.0397780i
$760$		0			0
$761$	618023.	−	356816.i	1.06718	−	0.616134i	0.139767	−	0.990184i	$-0.455365\pi$
$761$	618023.	−	356816.i	1.06718	−	0.616134i	0.927408	+	0.374051i	$0.122031\pi$
$762$		0			0
$763$	−767044.	−	122520.i	−1.31756	−	0.210454i
$764$		0			0
$765$	77712.4	+	134602.i	0.132791	+	0.230000i
$766$		0			0
$767$	88815.0	−	153832.i	0.150972	−	0.261491i
$768$		0			0
$769$			814619.i			1.37753i	0.724984	+	0.688766i	$0.241847\pi$
$769$			814619.i			1.37753i	−0.724984	+	0.688766i	$0.758153\pi$
$770$		0			0
$771$	−485576.			−0.816861
$772$		0			0
$773$	377176.	+	217763.i	0.631226	+	0.364439i	0.781227	−	0.624247i	$-0.214594\pi$
$773$	377176.	+	217763.i	0.631226	+	0.364439i	−0.150001	+	0.988686i	$0.547928\pi$
$774$		0			0
$775$	316932.	−	182981.i	0.527670	−	0.304650i
$776$		0			0
$777$	167298.	−	63967.9i	0.277107	−	0.105955i
$778$		0			0
$779$	−22845.8	−	39570.0i	−0.0376470	−	0.0652066i
$780$		0			0
$781$	170866.	−	295949.i	0.280126	−	0.485193i
$782$		0			0
$783$		−	116910.i		−	0.190690i
$784$		0			0
$785$	−228819.			−0.371324
$786$		0			0
$787$	424554.	+	245116.i	0.685462	+	0.395752i	0.801910	−	0.597445i	$-0.203817\pi$
$787$	424554.	+	245116.i	0.685462	+	0.395752i	−0.116448	+	0.993197i	$0.537151\pi$
$788$		0			0
$789$	−344706.	+	199016.i	−0.553725	+	0.319693i
$790$		0			0
$791$	−142500.	−	372686.i	−0.227752	−	0.595649i
$792$		0			0
$793$	−59791.5	−	103562.i	−0.0950809	−	0.164685i
$794$		0			0
$795$	−420036.	+	727524.i	−0.664588	+	1.15110i
$796$		0			0
$797$			1.03685e6i			1.63230i	0.577837	+	0.816152i	$0.303897\pi$
$797$			1.03685e6i			1.63230i	−0.577837	+	0.816152i	$0.696103\pi$
$798$		0			0
$799$	−629237.			−0.985646
$800$		0			0
$801$	−199146.	−	114977.i	−0.310388	−	0.179203i
$802$		0			0
$803$	680010.	−	392604.i	1.05459	−	0.608869i
$804$		0			0
$805$	−26055.6	+	163123.i	−0.0402078	+	0.251724i
$806$		0			0
$807$	−336460.	−	582766.i	−0.516638	−	0.894843i
$808$		0			0
$809$	463952.	−	803588.i	0.708885	−	1.22782i	−0.256386	−	0.966574i	$-0.582532\pi$
$809$	463952.	−	803588.i	0.708885	−	1.22782i	0.965271	−	0.261250i	$-0.0841348\pi$
$810$		0			0
$811$		−	868999.i		−	1.32123i	−0.750726	−	0.660614i	$-0.770296\pi$
$811$		−	868999.i		−	1.32123i	0.750726	−	0.660614i	$-0.229704\pi$
$812$		0			0
$813$	518699.			0.784755
$814$		0			0
$815$	971894.	+	561123.i	1.46320	+	0.844779i
$816$		0			0
$817$	−290678.	+	167823.i	−0.435480	+	0.251425i
$818$		0			0
$819$	29575.6	+	24014.2i	0.0440926	+	0.0358014i
$820$		0			0
$821$	635551.	+	1.10081e6i	0.942896	+	1.63314i	0.759910	+	0.650028i	$0.225243\pi$
$821$	635551.	+	1.10081e6i	0.942896	+	1.63314i	0.182986	+	0.983116i	$0.441424\pi$
$822$		0			0
$823$	178833.	−	309748.i	0.264027	−	0.457308i	−0.703281	−	0.710912i	$-0.748282\pi$
$823$	178833.	−	309748.i	0.264027	−	0.457308i	0.967308	+	0.253603i	$0.0816158\pi$
$824$		0			0
$825$		−	137734.i		−	0.202364i
$826$		0			0
$827$	409303.			0.598458			0.299229	−	0.954181i	$-0.403271\pi$
$827$	409303.			0.598458			0.299229	+	0.954181i	$0.403271\pi$
$828$		0			0
$829$	−153277.	−	88494.3i	−0.223032	−	0.128767i	0.384322	−	0.923199i	$-0.374435\pi$
$829$	−153277.	−	88494.3i	−0.223032	−	0.128767i	−0.607353	+	0.794432i	$0.707769\pi$
$830$		0			0
$831$	465087.	−	268518.i	0.673491	−	0.388840i
$832$		0			0
$833$	−438137.	+	91928.0i	−0.631422	+	0.132482i
$834$		0			0
$835$	−641893.	−	1.11179e6i	−0.920640	−	1.59459i
$836$		0			0
$837$	−78227.2	+	135494.i	−0.111662	+	0.193405i
$838$		0			0
$839$		−	336396.i		−	0.477889i	−0.971033	−	0.238945i	$-0.923199\pi$
$839$		−	336396.i		−	0.477889i	0.971033	−	0.238945i	$-0.0768014\pi$
$840$		0			0
$841$	−12875.7			−0.0182045
$842$		0			0
$843$	−328574.	−	189703.i	−0.462358	−	0.266943i
$844$		0			0
$845$	741468.	−	428087.i	1.03843	−	0.599541i
$846$		0			0
$847$	250697.	−	308756.i	0.349448	−	0.430376i
$848$		0			0
$849$	301410.	+	522058.i	0.418160	+	0.724275i
$850$		0			0
$851$	38407.8	−	66524.2i	0.0530347	−	0.0918587i
$852$		0			0
$853$			117802.i			0.161903i	0.996718	+	0.0809513i	$0.0257958\pi$
$853$			117802.i			0.161903i	−0.996718	+	0.0809513i	$0.974204\pi$
$854$		0			0
$855$	464717.			0.635706
$856$		0			0
$857$	383927.	+	221660.i	0.522742	+	0.301805i	0.738056	−	0.674740i	$-0.235744\pi$
$857$	383927.	+	221660.i	0.522742	+	0.301805i	−0.215314	+	0.976545i	$0.569077\pi$
$858$		0			0
$859$	−346427.	+	200010.i	−0.469489	+	0.271060i	−0.716026	−	0.698074i	$-0.754041\pi$
$859$	−346427.	+	200010.i	−0.469489	+	0.271060i	0.246537	+	0.969133i	$0.420707\pi$
$860$		0			0
$861$	−20606.4	−	3291.45i	−0.0277969	−	0.00443998i
$862$		0			0
$863$	−85231.5	−	147625.i	−0.114440	−	0.198216i	0.803116	−	0.595823i	$-0.203174\pi$
$863$	−85231.5	−	147625.i	−0.114440	−	0.198216i	−0.917556	+	0.397607i	$0.869841\pi$
$864$		0			0
$865$	−467048.	+	808952.i	−0.624209	+	1.08116i
$866$		0			0
$867$		−	253342.i		−	0.337031i
$868$		0			0
$869$	181744.			0.240669
$870$		0			0
$871$	194617.	+	112362.i	0.256533	+	0.148110i
$872$		0			0
$873$	55095.2	−	31809.3i	0.0722912	−	0.0417374i
$874$		0			0
$875$	419435.	−	160375.i	0.547834	−	0.209469i
$876$		0			0
$877$	−722377.	−	1.25119e6i	−0.939215	−	1.62677i	−0.766940	−	0.641719i	$-0.778221\pi$
$877$	−722377.	−	1.25119e6i	−0.939215	−	1.62677i	−0.172275	−	0.985049i	$-0.555112\pi$
$878$		0			0
$879$	−346207.	+	599649.i	−0.448083	+	0.776103i
$880$		0			0
$881$			562100.i			0.724206i	0.932138	+	0.362103i	$0.117941\pi$
$881$			562100.i			0.724206i	−0.932138	+	0.362103i	$0.882059\pi$
$882$		0			0
$883$	374231.			0.479975			0.239987	−	0.970776i	$-0.422857\pi$
$883$	374231.			0.479975			0.239987	+	0.970776i	$0.422857\pi$
$884$		0			0
$885$	−856998.	−	494788.i	−1.09419	−	0.631732i
$886$		0			0
$887$	716350.	−	413585.i	0.910495	−	0.525675i	0.0299049	−	0.999553i	$-0.490480\pi$
$887$	716350.	−	413585.i	0.910495	−	0.525675i	0.880591	+	0.473878i	$0.157146\pi$
$888$		0			0
$889$	494802.	+	1.29407e6i	0.626077	+	1.63740i
$890$		0			0
$891$	29441.9	+	50994.8i	0.0370860	+	0.0642348i
$892$		0			0
$893$	−940703.	+	1.62935e6i	−1.17964	+	2.04320i
$894$		0			0
$895$		−	792233.i		−	0.989024i
$896$		0			0
$897$	16338.9			0.0203066
$898$		0			0
$899$	−804784.	−	464642.i	−0.995772	−	0.574909i
$900$		0			0
$901$	−845578.	+	488195.i	−1.04161	+	0.601372i
$902$		0			0
$903$	−24178.8	+	151373.i	−0.0296523	+	0.185641i
$904$		0			0
$905$	−546122.	−	945911.i	−0.666795	−	1.15492i
$906$		0			0
$907$	−315810.	+	547000.i	−0.383895	+	0.664925i	−0.991615	−	0.129226i	$-0.958751\pi$
$907$	−315810.	+	547000.i	−0.383895	+	0.664925i	0.607721	+	0.794151i	$0.292084\pi$
$908$		0			0
$909$			119986.i			0.145212i
$910$		0			0
$911$	−1.36370e6			−1.64317			−0.821583	−	0.570089i	$-0.806909\pi$
$911$	−1.36370e6			−1.64317			−0.821583	+	0.570089i	$0.806909\pi$
$912$		0			0
$913$	−486217.	−	280718.i	−0.583296	−	0.336766i
$914$		0			0
$915$	−576943.	+	333098.i	−0.689114	+	0.397860i
$916$		0			0
$917$	233175.	+	189329.i	0.277296	+	0.225153i
$918$		0			0
$919$	287855.	+	498579.i	0.340834	+	0.590341i	0.984588	−	0.174891i	$-0.0559574\pi$
$919$	287855.	+	498579.i	0.340834	+	0.590341i	−0.643754	+	0.765232i	$0.722624\pi$
$920$		0			0
$921$	−93070.5	+	161203.i	−0.109722	+	0.190044i
$922$		0			0
$923$			121829.i			0.143004i
$924$		0			0
$925$	230853.			0.269806
$926$		0			0
$927$	−206129.	−	119009.i	−0.239873	−	0.138490i
$928$		0			0
$929$	455506.	−	262987.i	0.527792	−	0.304721i	−0.212325	−	0.977199i	$-0.568103\pi$
$929$	455506.	−	262987.i	0.527792	−	0.304721i	0.740117	+	0.672478i	$0.234770\pi$
$930$		0			0
$931$	−416972.	+	1.27194e6i	−0.481069	+	1.46747i
$932$		0			0
$933$	−360023.	−	623578.i	−0.413587	−	0.716354i
$934$		0			0
$935$	232485.	−	402675.i	0.265932	−	0.460608i
$936$		0			0
$937$			16374.0i			0.0186499i	0.999957	+	0.00932495i	$0.00296827\pi$
$937$			16374.0i			0.0186499i	−0.999957	+	0.00932495i	$0.997032\pi$
$938$		0			0
$939$	117874.			0.133686
$940$		0			0
$941$	504236.	+	291121.i	0.569448	+	0.328771i	0.756929	−	0.653497i	$-0.226699\pi$
$941$	504236.	+	291121.i	0.569448	+	0.328771i	−0.187481	+	0.982268i	$0.560032\pi$
$942$		0			0
$943$	−7750.55	+	4474.78i	−0.00871584	+	0.00503209i
$944$		0			0
$945$	133783.	−	164766.i	0.149809	−	0.184503i
$946$		0			0
$947$	−91148.9	−	157874.i	−0.101637	−	0.176040i	0.810722	−	0.585431i	$-0.199075\pi$
$947$	−91148.9	−	157874.i	−0.101637	−	0.176040i	−0.912359	+	0.409391i	$0.865741\pi$
$948$		0			0
$949$	−139965.	+	242427.i	−0.155413	+	0.269184i
$950$		0			0
$951$		−	126398.i		−	0.139759i
$952$		0			0
$953$	−1.16269e6			−1.28020			−0.640099	−	0.768293i	$-0.721107\pi$
$953$	−1.16269e6			−1.28020			−0.640099	+	0.768293i	$0.721107\pi$
$954$		0			0
$955$	134835.	+	77847.1i	0.147842	+	0.0853563i
$956$		0			0
$957$	−302891.	+	174874.i	−0.330722	+	0.190942i
$958$		0			0
$959$	−69872.0	−	11160.6i	−0.0759742	−	0.0121353i
$960$		0			0
$961$	160045.	+	277206.i	0.173299	+	0.300162i
$962$		0			0
$963$	−253005.	+	438217.i	−0.272820	+	0.472538i
$964$		0			0
$965$		−	28107.4i		−	0.0301832i
$966$		0			0
$967$	81805.3			0.0874840			0.0437420	−	0.999043i	$-0.486072\pi$
$967$	81805.3			0.0874840			0.0437420	+	0.999043i	$0.486072\pi$
$968$		0			0
$969$	467763.	+	270063.i	0.498171	+	0.287619i
$970$		0			0
$971$	−31947.3	+	18444.8i	−0.0338841	+	0.0195630i	−0.516846	−	0.856078i	$-0.672894\pi$
$971$	−31947.3	+	18444.8i	−0.0338841	+	0.0195630i	0.482962	+	0.875641i	$0.339561\pi$
$972$		0			0
$973$	1.07150e6	−	409698.i	1.13179	−	0.432751i
$974$		0			0
$975$	24551.5	+	42524.4i	0.0258267	+	0.0447331i
$976$		0			0
$977$	−498061.	+	862667.i	−0.521787	+	0.903762i	0.477892	+	0.878419i	$0.341401\pi$
$977$	−498061.	+	862667.i	−0.521787	+	0.903762i	−0.999679	+	0.0253433i	$0.991932\pi$
$978$		0			0
$979$			687929.i			0.717759i
$980$		0			0
$981$	428015.			0.444755
$982$		0			0
$983$	−1.06858e6	−	616944.i	−1.10586	−	0.638467i	−0.168104	−	0.985769i	$-0.553764\pi$
$983$	−1.06858e6	−	616944.i	−1.10586	−	0.638467i	−0.937753	+	0.347302i	$0.887098\pi$
$984$		0			0
$985$	1.38612e6	−	800276.i	1.42866	−	0.824835i
$986$		0			0
$987$	306875.	+	802583.i	0.315012	+	0.823864i
$988$		0			0
$989$	32871.4	+	56934.9i	0.0336067	+	0.0582085i
$990$		0			0
$991$	−537650.	+	931237.i	−0.547460	+	0.948228i	0.450988	+	0.892530i	$0.351072\pi$
$991$	−537650.	+	931237.i	−0.547460	+	0.948228i	−0.998448	+	0.0556982i	$0.982262\pi$
$992$		0			0
$993$		−	900817.i		−	0.913562i
$994$		0			0
$995$	−526173.			−0.531475
$996$		0			0
$997$	−70027.3	−	40430.3i	−0.0704493	−	0.0406739i	0.464362	−	0.885646i	$-0.346284\pi$
$997$	−70027.3	−	40430.3i	−0.0704493	−	0.0406739i	−0.534811	+	0.844972i	$0.679617\pi$
$998$		0			0
$999$	−85470.9	+	49346.7i	−0.0856421	+	0.0494455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.5.m.a.73.2	yes	4
3.2	odd	2		252.5.z.b.73.1		4
4.3	odd	2		336.5.bh.c.241.2		4
7.2	even	3		588.5.m.a.313.1		4
7.3	odd	6		588.5.d.a.97.3		4
7.4	even	3		588.5.d.a.97.2		4
7.5	odd	6	inner	84.5.m.a.61.2	✓	4
7.6	odd	2		588.5.m.a.325.1		4
21.5	even	6		252.5.z.b.145.1		4
28.19	even	6		336.5.bh.c.145.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.5.m.a.61.2	✓	4	7.5	odd	6	inner
84.5.m.a.73.2	yes	4	1.1	even	1	trivial
252.5.z.b.73.1		4	3.2	odd	2
252.5.z.b.145.1		4	21.5	even	6
336.5.bh.c.145.2		4	28.19	even	6
336.5.bh.c.241.2		4	4.3	odd	2
588.5.d.a.97.2		4	7.4	even	3
588.5.d.a.97.3		4	7.3	odd	6
588.5.m.a.313.1		4	7.2	even	3
588.5.m.a.325.1		4	7.6	odd	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	84.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.50000 + 2.59808i) q^{3} +(26.7371 - 15.4367i) q^{5} +(-17.5000 - 45.7684i) q^{7} +(13.5000 + 23.3827i) q^{9} +(40.3866 - 69.9517i) q^{11} +28.7961i q^{13} +160.423 q^{15} +(161.474 + 93.2272i) q^{17} +(482.804 - 278.747i) q^{19} +(40.1599 - 251.424i) q^{21} +(-54.5980 - 94.5665i) q^{23} +(164.083 - 284.199i) q^{25} +140.296i q^{27} -833.310 q^{29} +(965.768 + 557.587i) q^{31} +(363.480 - 209.855i) q^{33} +(-1174.41 - 953.575i) q^{35} +(351.732 + 609.218i) q^{37} +(-74.8144 + 129.582i) q^{39} -81.9587i q^{41} -602.062 q^{43} +(721.902 + 416.791i) q^{45} +(-2922.62 + 1687.38i) q^{47} +(-1788.50 + 1601.90i) q^{49} +(484.423 + 839.045i) q^{51} +(-2618.31 + 4535.04i) q^{53} -2493.74i q^{55} +2896.83 q^{57} +(-5342.12 - 3084.28i) q^{59} +(-3596.39 + 2076.38i) q^{61} +(833.939 - 1027.07i) q^{63} +(444.516 + 769.924i) q^{65} +(3901.99 - 6758.45i) q^{67} -567.399i q^{69} +4230.76 q^{71} +(8418.76 + 4860.57i) q^{73} +(1476.74 - 852.598i) q^{75} +(-3908.35 - 624.278i) q^{77} +(1125.02 + 1948.60i) q^{79} +(-364.500 + 631.333i) q^{81} -6950.76i q^{83} +5756.48 q^{85} +(-3749.89 - 2165.00i) q^{87} +(-7375.76 + 4258.40i) q^{89} +(1317.95 - 503.931i) q^{91} +(2897.30 + 5018.28i) q^{93} +(8605.87 - 14905.8i) q^{95} -2356.24i q^{97} +2180.88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} + 39 q^{5} - 70 q^{7} + 54 q^{9} + 3 q^{11} + 234 q^{15} + 510 q^{17} + 459 q^{19} - 315 q^{21} + 144 q^{23} - 227 q^{25} - 570 q^{29} + 2640 q^{31} + 27 q^{33} - 2478 q^{35} + 433 q^{37}+ \cdots + 162 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 + 39 * q^5 - 70 * q^7 + 54 * q^9 + 3 * q^11 + 234 * q^15 + 510 * q^17 + 459 * q^19 - 315 * q^21 + 144 * q^23 - 227 * q^25 - 570 * q^29 + 2640 * q^31 + 27 * q^33 - 2478 * q^35 + 433 * q^37 - 639 * q^39 - 98 * q^43 + 1053 * q^45 - 1770 * q^47 - 7154 * q^49 + 1530 * q^51 - 213 * q^53 + 2754 * q^57 - 4857 * q^59 - 12936 * q^61 - 945 * q^63 + 102 * q^65 + 7205 * q^67 + 19188 * q^71 + 14355 * q^73 - 2043 * q^75 - 12621 * q^77 + 13424 * q^79 - 1458 * q^81 + 9708 * q^85 - 2565 * q^87 - 36162 * q^89 - 5985 * q^91 + 7920 * q^93 + 19656 * q^95 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more