LMFDB - Embedded newform 84.5.m.a.73.1

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			73.1
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	84.73
Dual form			84.5.m.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.50000 + 2.59808i) q^{3} +(-7.23713 + 4.17836i) q^{5} +(-17.5000 + 45.7684i) q^{7} +(13.5000 + 23.3827i) q^{9} +(-38.8866 + 67.3536i) q^{11} +94.1795i q^{13} -43.4228 q^{15} +(93.5257 + 53.9971i) q^{17} +(-253.304 + 146.245i) q^{19} +(-197.660 + 160.492i) q^{21} +(126.598 + 219.274i) q^{23} +(-277.583 + 480.787i) q^{25} +140.296i q^{27} +548.310 q^{29} +(354.232 + 204.516i) q^{31} +(-349.980 + 202.061i) q^{33} +(-64.5872 - 404.353i) q^{35} +(-135.232 - 234.229i) q^{37} +(-244.686 + 423.808i) q^{39} -3063.45i q^{41} +553.062 q^{43} +(-195.402 - 112.816i) q^{45} +(2037.62 - 1176.42i) q^{47} +(-1788.50 - 1601.90i) q^{49} +(280.577 + 485.974i) q^{51} +(2511.81 - 4350.58i) q^{53} -649.929i q^{55} -1519.83 q^{57} +(2913.62 + 1682.18i) q^{59} +(-2871.61 + 1657.92i) q^{61} +(-1306.44 + 208.677i) q^{63} +(-393.516 - 681.589i) q^{65} +(-299.491 + 518.734i) q^{67} +1315.65i q^{69} +5363.24 q^{71} +(-1241.26 - 716.640i) q^{73} +(-2498.24 + 1442.36i) q^{75} +(-2402.15 - 2958.47i) q^{77} +(5586.98 + 9676.93i) q^{79} +(-364.500 + 631.333i) q^{81} +1326.79i q^{83} -902.477 q^{85} +(2467.39 + 1424.55i) q^{87} +(-10705.2 + 6180.67i) q^{89} +(-4310.45 - 1648.14i) q^{91} +(1062.70 + 1840.64i) q^{93} +(1222.13 - 2116.79i) q^{95} +5319.78i q^{97} -2099.88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−7.23713	+	4.17836i	−0.289485	+	0.167134i	−0.637710	−	0.770277i	$-0.720118\pi$
$5$	−7.23713	+	4.17836i	−0.289485	+	0.167134i	0.348225	+	0.937411i	$0.386785\pi$
$6$		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
$11$	−38.8866	+	67.3536i	−0.321377	+	0.556641i	−0.980772	−	0.195155i	$-0.937479\pi$
$11$	−38.8866	+	67.3536i	−0.321377	+	0.556641i	0.659395	+	0.751796i	$0.270812\pi$
$12$		0			0
$13$			94.1795i			0.557275i	0.960396	+	0.278638i	$0.0898829\pi$
$13$			94.1795i			0.557275i	−0.960396	+	0.278638i	$0.910117\pi$
$14$		0			0
$15$	−43.4228			−0.192990
$16$		0			0
$17$	93.5257	+	53.9971i	0.323618	+	0.186841i	0.653004	−	0.757354i	$-0.273508\pi$
$17$	93.5257	+	53.9971i	0.323618	+	0.186841i	−0.329386	+	0.944195i	$0.606842\pi$
$18$		0			0
$19$	−253.304	+	146.245i	−0.701674	+	0.405112i	−0.807971	−	0.589223i	$-0.799434\pi$
$19$	−253.304	+	146.245i	−0.701674	+	0.405112i	0.106296	+	0.994334i	$0.466101\pi$
$20$		0			0
$21$	−197.660	+	160.492i	−0.448208	+	0.363927i
$22$		0			0
$23$	126.598	+	219.274i	0.239316	+	0.414507i	0.960518	−	0.278217i	$-0.0897436\pi$
$23$	126.598	+	219.274i	0.239316	+	0.414507i	−0.721202	+	0.692724i	$0.756410\pi$
$24$		0			0
$25$	−277.583	+	480.787i	−0.444132	+	0.769260i
$26$		0			0
$27$			140.296i			0.192450i
$28$		0			0
$29$	548.310			0.651974			0.325987	−	0.945374i	$-0.394303\pi$
$29$	548.310			0.651974			0.325987	+	0.945374i	$0.394303\pi$
$30$		0			0
$31$	354.232	+	204.516i	0.368607	+	0.212816i	0.672850	−	0.739779i	$-0.265070\pi$
$31$	354.232	+	204.516i	0.368607	+	0.212816i	−0.304242	+	0.952595i	$0.598403\pi$
$32$		0			0
$33$	−349.980	+	202.061i	−0.321377	+	0.185547i
$34$		0			0
$35$	−64.5872	−	404.353i	−0.0527242	−	0.330084i
$36$		0			0
$37$	−135.232	−	234.229i	−0.0987817	−	0.171095i	0.812399	−	0.583102i	$-0.198161\pi$
$37$	−135.232	−	234.229i	−0.0987817	−	0.171095i	−0.911181	+	0.412007i	$0.864828\pi$
$38$		0			0
$39$	−244.686	+	423.808i	−0.160872	+	0.278638i
$40$		0			0
$41$		−	3063.45i		−	1.82239i	−0.411970	−	0.911197i	$-0.635159\pi$
$41$		−	3063.45i		−	1.82239i	0.411970	−	0.911197i	$-0.364841\pi$
$42$		0			0
$43$	553.062			0.299114			0.149557	−	0.988753i	$-0.452215\pi$
$43$	553.062			0.299114			0.149557	+	0.988753i	$0.452215\pi$
$44$		0			0
$45$	−195.402	−	112.816i	−0.0964950	−	0.0557114i
$46$		0			0
$47$	2037.62	−	1176.42i	0.922418	−	0.532558i	0.0380121	−	0.999277i	$-0.487897\pi$
$47$	2037.62	−	1176.42i	0.922418	−	0.532558i	0.884406	+	0.466719i	$0.154564\pi$
$48$		0			0
$49$	−1788.50	−	1601.90i	−0.744898	−	0.667178i
$50$		0			0
$51$	280.577	+	485.974i	0.107873	+	0.186841i
$52$		0			0
$53$	2511.81	−	4350.58i	0.894199	−	1.54880i	0.0594072	−	0.998234i	$-0.481079\pi$
$53$	2511.81	−	4350.58i	0.894199	−	1.54880i	0.834792	−	0.550565i	$-0.185588\pi$
$54$		0			0
$55$		−	649.929i		−	0.214853i
$56$		0			0
$57$	−1519.83			−0.467783
$58$		0			0
$59$	2913.62	+	1682.18i	0.837007	+	0.483246i	0.856246	−	0.516569i	$-0.172791\pi$
$59$	2913.62	+	1682.18i	0.837007	+	0.483246i	−0.0192386	+	0.999815i	$0.506124\pi$
$60$		0			0
$61$	−2871.61	+	1657.92i	−0.771730	+	0.445559i	−0.833491	−	0.552532i	$-0.813662\pi$
$61$	−2871.61	+	1657.92i	−0.771730	+	0.445559i	0.0617613	+	0.998091i	$0.480328\pi$
$62$		0			0
$63$	−1306.44	+	208.677i	−0.329161	+	0.0525767i
$64$		0			0
$65$	−393.516	−	681.589i	−0.0931398	−	0.161323i
$66$		0			0
$67$	−299.491	+	518.734i	−0.0667167	+	0.115557i	−0.897454	−	0.441108i	$-0.854586\pi$
$67$	−299.491	+	518.734i	−0.0667167	+	0.115557i	0.830737	+	0.556664i	$0.187919\pi$
$68$		0			0
$69$			1315.65i			0.276338i
$70$		0			0
$71$	5363.24			1.06392			0.531962	−	0.846768i	$-0.321455\pi$
$71$	5363.24			1.06392			0.531962	+	0.846768i	$0.321455\pi$
$72$		0			0
$73$	−1241.26	−	716.640i	−0.232925	−	0.134479i	0.378996	−	0.925398i	$-0.376269\pi$
$73$	−1241.26	−	716.640i	−0.232925	−	0.134479i	−0.611921	+	0.790919i	$0.709603\pi$
$74$		0			0
$75$	−2498.24	+	1442.36i	−0.444132	+	0.256420i
$76$		0			0
$77$	−2402.15	−	2958.47i	−0.405153	−	0.498983i
$78$		0			0
$79$	5586.98	+	9676.93i	0.895205	+	1.55054i	0.833550	+	0.552443i	$0.186304\pi$
$79$	5586.98	+	9676.93i	0.895205	+	1.55054i	0.0616549	+	0.998098i	$0.480362\pi$
$80$		0			0
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			1326.79i			0.192595i	0.995353	+	0.0962977i	$0.0307001\pi$
$83$			1326.79i			0.192595i	−0.995353	+	0.0962977i	$0.969300\pi$
$84$		0			0
$85$	−902.477			−0.124910
$86$		0			0
$87$	2467.39	+	1424.55i	0.325987	+	0.188209i
$88$		0			0
$89$	−10705.2	+	6180.67i	−1.35150	+	0.780289i	−0.988460	−	0.151484i	$-0.951595\pi$
$89$	−10705.2	+	6180.67i	−1.35150	+	0.780289i	−0.363041	+	0.931773i	$0.618262\pi$
$90$		0			0
$91$	−4310.45	−	1648.14i	−0.520523	−	0.199027i
$92$		0			0
$93$	1062.70	+	1840.64i	0.122869	+	0.212816i
$94$		0			0
$95$	1222.13	−	2116.79i	0.135416	−	0.234548i
$96$		0			0
$97$			5319.78i			0.565393i	0.959209	+	0.282696i	$0.0912289\pi$
$97$			5319.78i			0.565393i	−0.959209	+	0.282696i	$0.908771\pi$
$98$		0			0
$99$	−2099.88			−0.214251
$100$		0			0
$101$	−3965.54	−	2289.51i	−0.388740	−	0.224439i	0.292874	−	0.956151i	$-0.405388\pi$
$101$	−3965.54	−	2289.51i	−0.388740	−	0.224439i	−0.681614	+	0.731712i	$0.738722\pi$
$102$		0			0
$103$	−6332.08	+	3655.83i	−0.596859	+	0.344597i	−0.767805	−	0.640684i	$-0.778651\pi$
$103$	−6332.08	+	3655.83i	−0.596859	+	0.344597i	0.170946	+	0.985280i	$0.445318\pi$
$104$		0			0
$105$	759.898	−	1987.39i	0.0689250	−	0.180262i
$106$		0			0
$107$	9698.96	+	16799.1i	0.847145	+	1.46730i	0.883746	+	0.467968i	$0.155014\pi$
$107$	9698.96	+	16799.1i	0.847145	+	1.46730i	−0.0366010	+	0.999330i	$0.511653\pi$
$108$		0			0
$109$	6465.30	−	11198.2i	0.544172	−	0.942533i	−0.454487	−	0.890753i	$-0.650177\pi$
$109$	6465.30	−	11198.2i	0.544172	−	0.942533i	0.998659	−	0.0517795i	$-0.0164893\pi$
$110$		0			0
$111$		−	1405.37i		−	0.114063i
$112$		0			0
$113$	5153.13			0.403566			0.201783	−	0.979430i	$-0.435326\pi$
$113$	5153.13			0.403566			0.201783	+	0.979430i	$0.435326\pi$
$114$		0			0
$115$	−1832.41	−	1057.94i	−0.138557	−	0.0799957i
$116$		0			0
$117$	−2202.17	+	1271.42i	−0.160872	+	0.0928792i
$118$		0			0
$119$	−4108.06	+	3335.58i	−0.290097	+	0.235547i
$120$		0			0
$121$	4296.16	+	7441.17i	0.293434	+	0.508242i
$122$		0			0
$123$	7959.07	−	13785.5i	0.526080	−	0.911197i
$124$		0			0
$125$		−	9862.31i		−	0.631188i
$126$		0			0
$127$	10320.4			0.639865			0.319932	−	0.947440i	$-0.396340\pi$
$127$	10320.4			0.639865			0.319932	+	0.947440i	$0.396340\pi$
$128$		0			0
$129$	2488.78	+	1436.90i	0.149557	+	0.0863469i
$130$		0			0
$131$	−27221.9	+	15716.6i	−1.58627	+	0.915832i	−0.592354	+	0.805678i	$0.701801\pi$
$131$	−27221.9	+	15716.6i	−1.58627	+	0.915832i	−0.993915	+	0.110154i	$0.964866\pi$
$132$		0			0
$133$	−2260.60	−	14152.6i	−0.127797	−	0.800082i
$134$		0			0
$135$	−586.207	−	1015.34i	−0.0321650	−	0.0557114i
$136$		0			0
$137$	6927.98	−	11999.6i	0.369118	−	0.639332i	−0.620310	−	0.784357i	$-0.712993\pi$
$137$	6927.98	−	11999.6i	0.369118	−	0.639332i	0.989428	+	0.145025i	$0.0463264\pi$
$138$		0			0
$139$		−	24750.2i		−	1.28100i	−0.767959	−	0.640499i	$-0.778727\pi$
$139$		−	24750.2i		−	1.28100i	0.767959	−	0.640499i	$-0.221273\pi$
$140$		0			0
$141$	12225.7			0.614945
$142$		0			0
$143$	−6343.33	−	3662.33i	−0.310203	−	0.179096i
$144$		0			0
$145$	−3968.19	+	2291.03i	−0.188737	+	0.108967i
$146$		0			0
$147$	−3886.40	−	11855.2i	−0.179851	−	0.548623i
$148$		0			0
$149$	−85.4878	−	148.069i	−0.00385063	−	0.00666949i	0.864094	−	0.503331i	$-0.167892\pi$
$149$	−85.4878	−	148.069i	−0.00385063	−	0.00666949i	−0.867944	+	0.496662i	$0.834559\pi$
$150$		0			0
$151$	18574.4	−	32171.7i	0.814629	−	1.41098i	−0.0949648	−	0.995481i	$-0.530274\pi$
$151$	18574.4	−	32171.7i	0.814629	−	1.41098i	0.909594	−	0.415498i	$-0.136393\pi$
$152$		0			0
$153$			2915.84i			0.124561i
$154$		0			0
$155$	−3418.16			−0.142275
$156$		0			0
$157$	13150.6	+	7592.49i	0.533514	+	0.308024i	0.742446	−	0.669906i	$-0.233665\pi$
$157$	13150.6	+	7592.49i	0.533514	+	0.308024i	−0.208932	+	0.977930i	$0.566999\pi$
$158$		0			0
$159$	22606.3	−	13051.7i	0.894199	−	0.516266i
$160$		0			0
$161$	−12251.3	+	1956.90i	−0.472640	+	0.0754946i
$162$		0			0
$163$	1890.00	+	3273.58i	0.0711357	+	0.123211i	0.899399	−	0.437128i	$-0.144004\pi$
$163$	1890.00	+	3273.58i	0.0711357	+	0.123211i	−0.828264	+	0.560339i	$0.810671\pi$
$164$		0			0
$165$	1688.57	−	2924.68i	0.0620226	−	0.107426i
$166$		0			0
$167$		−	10590.5i		−	0.379739i	−0.981809	−	0.189869i	$-0.939194\pi$
$167$		−	10590.5i		−	0.379739i	0.981809	−	0.189869i	$-0.0608064\pi$
$168$		0			0
$169$	19691.2			0.689444
$170$		0			0
$171$	−6839.22	−	3948.63i	−0.233891	−	0.135037i
$172$		0			0
$173$	−34763.8	+	20070.9i	−1.16154	+	0.670616i	−0.951673	−	0.307114i	$-0.900637\pi$
$173$	−34763.8	+	20070.9i	−1.16154	+	0.670616i	−0.209868	+	0.977730i	$0.567303\pi$
$174$		0			0
$175$	−17147.2	−	21118.3i	−0.559908	−	0.689577i
$176$		0			0
$177$	8740.87	+	15139.6i	0.279002	+	0.483246i
$178$		0			0
$179$	−18788.4	+	32542.4i	−0.586385	+	1.01565i	0.408317	+	0.912840i	$0.366116\pi$
$179$	−18788.4	+	32542.4i	−0.586385	+	1.01565i	−0.994701	+	0.102808i	$0.967217\pi$
$180$		0			0
$181$			39852.1i			1.21645i	0.793765	+	0.608224i	$0.208118\pi$
$181$			39852.1i			1.21645i	−0.793765	+	0.608224i	$0.791882\pi$
$182$		0			0
$183$	−17229.6			−0.514487
$184$		0			0
$185$	1957.38	+	1130.10i	0.0571917	+	0.0330196i
$186$		0			0
$187$	−7273.80	+	4199.53i	−0.208007	+	0.120093i
$188$		0			0
$189$	−6421.13	−	2455.18i	−0.179758	−	0.0687322i
$190$		0			0
$191$	22747.5	+	39399.8i	0.623544	+	1.08001i	0.988821	+	0.149111i	$0.0476411\pi$
$191$	22747.5	+	39399.8i	0.623544	+	1.08001i	−0.365277	+	0.930899i	$0.619026\pi$
$192$		0			0
$193$	−6045.20	+	10470.6i	−0.162292	+	0.281097i	−0.935690	−	0.352823i	$-0.885222\pi$
$193$	−6045.20	+	10470.6i	−0.162292	+	0.281097i	0.773399	+	0.633920i	$0.218555\pi$
$194$		0			0
$195$		−	4089.54i		−	0.107549i
$196$		0			0
$197$	43371.5			1.11756			0.558782	−	0.829315i	$-0.311269\pi$
$197$	43371.5			1.11756			0.558782	+	0.829315i	$0.311269\pi$
$198$		0			0
$199$	19667.6	+	11355.1i	0.496645	+	0.286738i	0.727327	−	0.686291i	$-0.240762\pi$
$199$	19667.6	+	11355.1i	0.496645	+	0.286738i	−0.230682	+	0.973029i	$0.574096\pi$
$200$		0			0
$201$	−2695.42	+	1556.20i	−0.0667167	+	0.0385189i
$202$		0			0
$203$	−9595.42	+	25095.3i	−0.232848	+	0.608976i
$204$		0			0
$205$	12800.2	+	22170.5i	0.304585	+	0.527556i
$206$		0			0
$207$	−3418.15	+	5920.40i	−0.0797719	+	0.138169i
$208$		0			0
$209$		−	22748.0i		−	0.520775i
$210$		0			0
$211$	−75885.9			−1.70450			−0.852249	−	0.523137i	$-0.824762\pi$
$211$	−75885.9			−1.70450			−0.852249	+	0.523137i	$0.824762\pi$
$212$		0			0
$213$	24134.6	+	13934.1i	0.531962	+	0.307128i
$214$		0			0
$215$	−4002.58	+	2310.89i	−0.0865891	+	0.0499923i
$216$		0			0
$217$	−15559.4	+	12633.6i	−0.330426	+	0.268292i
$218$		0			0
$219$	−3723.77	−	6449.76i	−0.0776416	−	0.134479i
$220$		0			0
$221$	−5085.42	+	8808.21i	−0.104122	+	0.180345i
$222$		0			0
$223$		−	18276.7i		−	0.367526i	−0.982971	−	0.183763i	$-0.941172\pi$
$223$		−	18276.7i		−	0.367526i	0.982971	−	0.183763i	$-0.0588279\pi$
$224$		0			0
$225$	−14989.5			−0.296088
$226$		0			0
$227$	−10304.8	−	5949.48i	−0.199981	−	0.115459i	0.396666	−	0.917963i	$-0.370167\pi$
$227$	−10304.8	−	5949.48i	−0.199981	−	0.115459i	−0.596646	+	0.802504i	$0.703500\pi$
$228$		0			0
$229$	−254.071	+	146.688i	−0.00484488	+	0.00279720i	−0.502420	−	0.864623i	$-0.667557\pi$
$229$	−254.071	+	146.688i	−0.00484488	+	0.00279720i	0.497576	+	0.867421i	$0.334224\pi$
$230$		0			0
$231$	−3123.37	−	19554.1i	−0.0585327	−	0.366449i
$232$		0			0
$233$	−35754.6	−	61928.8i	−0.658598	−	1.14073i	−0.980979	−	0.194115i	$-0.937816\pi$
$233$	−35754.6	−	61928.8i	−0.658598	−	1.14073i	0.322381	−	0.946610i	$-0.395517\pi$
$234$		0			0
$235$	−9831.01	+	17027.8i	−0.178017	+	0.308335i
$236$		0			0
$237$			58061.6i			1.03369i
$238$		0			0
$239$	62869.3			1.10063			0.550316	−	0.834956i	$-0.314507\pi$
$239$	62869.3			1.10063			0.550316	+	0.834956i	$0.314507\pi$
$240$		0			0
$241$	52680.1	+	30414.9i	0.907011	+	0.523663i	0.879468	−	0.475958i	$-0.157899\pi$
$241$	52680.1	+	30414.9i	0.907011	+	0.523663i	0.0275425	+	0.999621i	$0.491232\pi$
$242$		0			0
$243$	−3280.50	+	1894.00i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	19636.9	+	4120.13i	0.327145	+	0.0686402i
$246$		0			0
$247$	−13773.3	−	23856.1i	−0.225759	−	0.391026i
$248$		0			0
$249$	−3447.10	+	5970.56i	−0.0555975	+	0.0962977i
$250$		0			0
$251$		−	71630.1i		−	1.13697i	−0.822695	−	0.568484i	$-0.807530\pi$
$251$		−	71630.1i		−	1.13697i	0.822695	−	0.568484i	$-0.192470\pi$
$252$		0			0
$253$	−19691.9			−0.307642
$254$		0			0
$255$	−4061.15	−	2344.70i	−0.0624552	−	0.0360585i
$256$		0			0
$257$	50347.3	−	29068.0i	0.762271	−	0.440098i	−0.0678393	−	0.997696i	$-0.521611\pi$
$257$	50347.3	−	29068.0i	0.762271	−	0.440098i	0.830111	+	0.557599i	$0.188277\pi$
$258$		0			0
$259$	13086.9	−	2090.36i	0.195090	−	0.0311617i
$260$		0			0
$261$	7402.18	+	12821.0i	0.108662	+	0.188209i
$262$		0			0
$263$	15899.6	−	27539.0i	0.229866	−	0.398140i	−0.727902	−	0.685681i	$-0.759504\pi$
$263$	15899.6	−	27539.0i	0.229866	−	0.398140i	0.957768	+	0.287541i	$0.0928377\pi$
$264$		0			0
$265$			41980.9i			0.597806i
$266$		0			0
$267$	−64231.4			−0.901001
$268$		0			0
$269$	−47568.2	−	27463.5i	−0.657374	−	0.379535i	0.133902	−	0.990995i	$-0.457249\pi$
$269$	−47568.2	−	27463.5i	−0.657374	−	0.379535i	−0.791276	+	0.611460i	$0.790583\pi$
$270$		0			0
$271$	79439.7	−	45864.6i	1.08168	−	0.624509i	0.150332	−	0.988636i	$-0.451966\pi$
$271$	79439.7	−	45864.6i	1.08168	−	0.624509i	0.931349	+	0.364127i	$0.118633\pi$
$272$		0			0
$273$	−15115.0	−	18615.5i	−0.202807	−	0.249776i
$274$		0			0
$275$	−21588.5	−	37392.4i	−0.285468	−	0.494445i
$276$		0			0
$277$	−3667.78	+	6352.78i	−0.0478018	+	0.0827951i	−0.888936	−	0.458031i	$-0.848555\pi$
$277$	−3667.78	+	6352.78i	−0.0478018	+	0.0827951i	0.841135	+	0.540826i	$0.181888\pi$
$278$		0			0
$279$			11043.9i			0.141877i
$280$		0			0
$281$	133185.			1.68671			0.843356	−	0.537355i	$-0.180576\pi$
$281$	133185.			1.68671			0.843356	+	0.537355i	$0.180576\pi$
$282$		0			0
$283$	−108302.	−	62528.0i	−1.35227	−	0.780731i	−0.363700	−	0.931516i	$-0.618487\pi$
$283$	−108302.	−	62528.0i	−1.35227	−	0.780731i	−0.988567	+	0.150785i	$0.951820\pi$
$284$		0			0
$285$	10999.2	−	6350.38i	0.135416	−	0.0781826i
$286$		0			0
$287$	140209.	+	53610.3i	1.70221	+	0.650855i
$288$		0			0
$289$	−35929.1	−	62231.1i	−0.430181	−	0.745095i
$290$		0			0
$291$	−13821.2	+	23939.0i	−0.163215	+	0.282696i
$292$		0			0
$293$		−	137393.i		−	1.60040i	−0.599730	−	0.800202i	$-0.704725\pi$
$293$		−	137393.i		−	1.60040i	0.599730	−	0.800202i	$-0.295275\pi$
$294$		0			0
$295$	−28115.0			−0.323068
$296$		0			0
$297$	−9449.45	−	5455.64i	−0.107126	−	0.0618491i
$298$		0			0
$299$	−20651.1	+	11922.9i	−0.230995	+	0.133365i
$300$		0			0
$301$	−9678.59	+	25312.8i	−0.106827	+	0.279388i
$302$		0			0
$303$	−11896.6	−	20605.5i	−0.129580	−	0.224439i
$304$		0			0
$305$	13854.8	−	23997.2i	0.148936	−	0.257965i
$306$		0			0
$307$			59400.1i			0.630247i	0.949051	+	0.315123i	$0.102046\pi$
$307$			59400.1i			0.630247i	−0.949051	+	0.315123i	$0.897954\pi$
$308$		0			0
$309$	−37992.5			−0.397906
$310$		0			0
$311$	39127.7	+	22590.4i	0.404542	+	0.233562i	0.688442	−	0.725291i	$-0.258295\pi$
$311$	39127.7	+	22590.4i	0.404542	+	0.233562i	−0.283900	+	0.958854i	$0.591628\pi$
$312$		0			0
$313$	92305.3	−	53292.5i	0.942189	−	0.543973i	0.0515431	−	0.998671i	$-0.483586\pi$
$313$	92305.3	−	53292.5i	0.942189	−	0.543973i	0.890646	+	0.454698i	$0.150253\pi$
$314$		0			0
$315$	8582.94	−	6968.99i	0.0864998	−	0.0702342i
$316$		0			0
$317$	−76611.8	−	132696.i	−0.762390	−	1.32050i	−0.941615	−	0.336691i	$-0.890692\pi$
$317$	−76611.8	−	132696.i	−0.762390	−	1.32050i	0.179225	−	0.983808i	$-0.442641\pi$
$318$		0			0
$319$	−21321.9	+	36930.7i	−0.209529	+	0.362916i
$320$		0			0
$321$			100795.i			0.978198i
$322$		0			0
$323$	−31587.3			−0.302766
$324$		0			0
$325$	−45280.3	−	26142.6i	−0.428689	−	0.247504i
$326$		0			0
$327$	58187.7	−	33594.7i	0.544172	−	0.314178i
$328$		0			0
$329$	18184.6	+	113846.i	0.168001	+	1.05178i
$330$		0			0
$331$	56180.6	+	97307.7i	0.512779	+	0.888160i	0.999890	+	0.0148198i	$0.00471745\pi$
$331$	56180.6	+	97307.7i	0.512779	+	0.888160i	−0.487111	+	0.873340i	$0.661949\pi$
$332$		0			0
$333$	3651.27	−	6324.18i	0.0329272	−	0.0570316i
$334$		0			0
$335$		−	5005.53i		−	0.0446026i
$336$		0			0
$337$	−141074.			−1.24219			−0.621093	−	0.783737i	$-0.713311\pi$
$337$	−141074.			−1.24219			−0.621093	+	0.783737i	$0.713311\pi$
$338$		0			0
$339$	23189.1	+	13388.2i	0.201783	+	0.116499i
$340$		0			0
$341$	−27549.8	+	15905.9i	−0.236924	+	0.136788i
$342$		0			0
$343$	104615.	−	53823.7i	0.889213	−	0.457494i
$344$		0			0
$345$	−5497.24	−	9521.49i	−0.0461856	−	0.0799957i
$346$		0			0
$347$	−100247.	+	173633.i	−0.832557	+	1.44203i	0.0634473	+	0.997985i	$0.479791\pi$
$347$	−100247.	+	173633.i	−0.832557	+	1.44203i	−0.896004	+	0.444046i	$0.853543\pi$
$348$		0			0
$349$			209647.i			1.72122i	0.509263	+	0.860611i	$0.329918\pi$
$349$			209647.i			1.72122i	−0.509263	+	0.860611i	$0.670082\pi$
$350$		0			0
$351$	−13213.0			−0.107248
$352$		0			0
$353$	−138290.	−	79841.9i	−1.10979	−	0.640739i	−0.171017	−	0.985268i	$-0.554705\pi$
$353$	−138290.	−	79841.9i	−1.10979	−	0.640739i	−0.938776	+	0.344529i	$0.888039\pi$
$354$		0			0
$355$	−38814.4	+	22409.5i	−0.307990	+	0.177818i
$356$		0			0
$357$	−27152.4	+	4337.04i	−0.213045	+	0.0340296i
$358$		0			0
$359$	35094.0	+	60784.5i	0.272297	+	0.471633i	0.969450	−	0.245290i	$-0.0788832\pi$
$359$	35094.0	+	60784.5i	0.272297	+	0.471633i	−0.697152	+	0.716923i	$0.745550\pi$
$360$		0			0
$361$	−22385.1	+	38772.1i	−0.171769	+	0.297512i
$362$		0			0
$363$			44647.0i			0.338828i
$364$		0			0
$365$	11977.5			0.0899044
$366$		0			0
$367$	205812.	+	118826.i	1.52806	+	0.882223i	0.999443	+	0.0333603i	$0.0106209\pi$
$367$	205812.	+	118826.i	1.52806	+	0.882223i	0.528613	+	0.848863i	$0.322712\pi$
$368$		0			0
$369$	71631.6	−	41356.5i	0.526080	−	0.303732i
$370$		0			0
$371$	155162.	+	191097.i	1.12730	+	1.38837i
$372$		0			0
$373$	−122554.	−	212269.i	−0.880863	−	1.52570i	−0.850383	−	0.526165i	$-0.823630\pi$
$373$	−122554.	−	212269.i	−0.880863	−	1.52570i	−0.0304807	−	0.999535i	$-0.509704\pi$
$374$		0			0
$375$	25623.0	−	44380.4i	0.182208	−	0.315594i
$376$		0			0
$377$			51639.6i			0.363329i
$378$		0			0
$379$	−95402.6			−0.664174			−0.332087	−	0.943249i	$-0.607753\pi$
$379$	−95402.6			−0.664174			−0.332087	+	0.943249i	$0.607753\pi$
$380$		0			0
$381$	46441.7	+	26813.1i	0.319932	+	0.184713i
$382$		0			0
$383$	−57753.3	+	33343.9i	−0.393712	+	0.227310i	−0.683767	−	0.729700i	$-0.739660\pi$
$383$	−57753.3	+	33343.9i	−0.393712	+	0.227310i	0.290055	+	0.957010i	$0.406326\pi$
$384$		0			0
$385$	29746.2	+	11373.8i	0.200683	+	0.0767331i
$386$		0			0
$387$	7466.34	+	12932.1i	0.0498524	+	0.0863469i
$388$		0			0
$389$	−77439.5	+	134129.i	−0.511757	+	0.886389i	0.488150	+	0.872760i	$0.337672\pi$
$389$	−77439.5	+	134129.i	−0.511757	+	0.886389i	−0.999907	+	0.0136291i	$0.995662\pi$
$390$		0			0
$391$			27343.7i			0.178856i
$392$		0			0
$393$	−163332.			−1.05751
$394$		0			0
$395$	−80867.3	−	46688.8i	−0.518297	−	0.299239i
$396$		0			0
$397$	174546.	−	100774.i	1.10746	−	0.639392i	0.169290	−	0.985566i	$-0.445853\pi$
$397$	174546.	−	100774.i	1.10746	−	0.639392i	0.938170	+	0.346174i	$0.112519\pi$
$398$		0			0
$399$	26597.0	−	69560.1i	0.167065	−	0.436932i
$400$		0			0
$401$	−16945.5	−	29350.5i	−0.105382	−	0.182527i	0.808512	−	0.588479i	$-0.200273\pi$
$401$	−16945.5	−	29350.5i	−0.105382	−	0.182527i	−0.913894	+	0.405952i	$0.866940\pi$
$402$		0			0
$403$	−19261.2	+	33361.4i	−0.118597	+	0.205416i
$404$		0			0
$405$		−	6092.05i		−	0.0371410i
$406$		0			0
$407$	21034.9			0.126985
$408$		0			0
$409$	−201013.	−	116055.i	−1.20165	−	0.693771i	−0.240725	−	0.970593i	$-0.577385\pi$
$409$	−201013.	−	116055.i	−1.20165	−	0.693771i	−0.960921	+	0.276822i	$0.910719\pi$
$410$		0			0
$411$	62351.8	−	35998.9i	0.369118	−	0.213111i
$412$		0			0
$413$	−127979.	+	103914.i	−0.750307	+	0.609218i
$414$		0			0
$415$	−5543.80	−	9602.15i	−0.0321893	−	0.0557535i
$416$		0			0
$417$	64302.8	−	111376.i	0.369792	−	0.640499i
$418$		0			0
$419$		−	162717.i		−	0.926838i	−0.886139	−	0.463419i	$-0.846622\pi$
$419$		−	162717.i		−	0.926838i	0.886139	−	0.463419i	$-0.153378\pi$
$420$		0			0
$421$	244086.			1.37714			0.688570	−	0.725170i	$-0.258239\pi$
$421$	244086.			1.37714			0.688570	+	0.725170i	$0.258239\pi$
$422$		0			0
$423$	55015.8	+	31763.4i	0.307473	+	0.177519i
$424$		0			0
$425$	−51922.2	+	29977.3i	−0.287459	+	0.165964i
$426$		0			0
$427$	−25627.4	−	160443.i	−0.140556	−	0.879962i
$428$		0			0
$429$	−19030.0	−	32960.9i	−0.103401	−	0.179096i
$430$		0			0
$431$	−57761.7	+	100046.i	−0.310946	+	0.538575i	−0.978567	−	0.205926i	$-0.933979\pi$
$431$	−57761.7	+	100046.i	−0.310946	+	0.538575i	0.667621	+	0.744501i	$0.267313\pi$
$432$		0			0
$433$		−	54296.2i		−	0.289597i	−0.989461	−	0.144798i	$-0.953747\pi$
$433$		−	54296.2i		−	0.289597i	0.989461	−	0.144798i	$-0.0462534\pi$
$434$		0			0
$435$	−23809.1			−0.125824
$436$		0			0
$437$	−64135.7	−	37028.7i	−0.335843	−	0.193899i
$438$		0			0
$439$	279367.	−	161293.i	1.44959	−	0.836923i	0.451136	−	0.892455i	$-0.351019\pi$
$439$	279367.	−	161293.i	1.44959	−	0.836923i	0.998457	+	0.0555326i	$0.0176857\pi$
$440$		0			0
$441$	13311.9	−	63445.5i	0.0684482	−	0.326230i
$442$		0			0
$443$	−105739.	−	183146.i	−0.538802	−	0.933232i	−0.998969	−	0.0453997i	$-0.985544\pi$
$443$	−105739.	−	183146.i	−0.538802	−	0.933232i	0.460167	−	0.887832i	$-0.347789\pi$
$444$		0			0
$445$	51650.1	−	89460.6i	0.260826	−	0.451764i
$446$		0			0
$447$		−	888.416i		−	0.00444632i
$448$		0			0
$449$	223169.			1.10699			0.553493	−	0.832854i	$-0.313295\pi$
$449$	223169.			1.10699			0.553493	+	0.832854i	$0.313295\pi$
$450$		0			0
$451$	206334.	+	119127.i	1.01442	+	0.585676i
$452$		0			0
$453$	167169.	−	96515.2i	0.814629	−	0.470326i
$454$		0			0
$455$	38081.8	−	6082.79i	0.183948	−	0.0293819i
$456$		0			0
$457$	93.6414	+	162.192i	0.000448369	+	0.000776598i	0.866250	−	0.499612i	$-0.166524\pi$
$457$	93.6414	+	162.192i	0.000448369	+	0.000776598i	−0.865801	+	0.500388i	$0.833191\pi$
$458$		0			0
$459$	−7575.59	+	13121.3i	−0.0359576	+	0.0622804i
$460$		0			0
$461$			8842.64i			0.0416083i	0.999784	+	0.0208042i	$0.00662265\pi$
$461$			8842.64i			0.0416083i	−0.999784	+	0.0208042i	$0.993377\pi$
$462$		0			0
$463$	−363326.			−1.69486			−0.847431	−	0.530906i	$-0.821852\pi$
$463$	−363326.			−1.69486			−0.847431	+	0.530906i	$0.821852\pi$
$464$		0			0
$465$	−15381.7	−	8880.64i	−0.0711376	−	0.0410713i
$466$		0			0
$467$	−211698.	+	122224.i	−0.970698	+	0.560433i	−0.899449	−	0.437026i	$-0.856032\pi$
$467$	−211698.	+	122224.i	−0.970698	+	0.560433i	−0.0712488	+	0.997459i	$0.522698\pi$
$468$		0			0
$469$	−18500.6	−	22785.1i	−0.0841084	−	0.103587i
$470$		0			0
$471$	39451.8	+	68332.4i	0.177838	+	0.308024i
$472$		0			0
$473$	−21506.7	+	37250.8i	−0.0961285	+	0.166499i
$474$		0			0
$475$		−	162381.i		−	0.719693i
$476$		0			0
$477$	135638.			0.596133
$478$		0			0
$479$	−30752.3	−	17754.8i	−0.134031	−	0.0773829i	0.431485	−	0.902120i	$-0.357990\pi$
$479$	−30752.3	−	17754.8i	−0.134031	−	0.0773829i	−0.565516	+	0.824737i	$0.691323\pi$
$480$		0			0
$481$	22059.6	−	12736.1i	0.0953470	−	0.0550486i
$482$		0			0
$483$	−60215.0	−	23023.8i	−0.258113	−	0.0986921i
$484$		0			0
$485$	−22227.9	−	38499.9i	−0.0944965	−	0.163673i
$486$		0			0
$487$	−27074.8	+	46894.9i	−0.114158	+	0.197728i	−0.917443	−	0.397867i	$-0.869750\pi$
$487$	−27074.8	+	46894.9i	−0.114158	+	0.197728i	0.803285	+	0.595595i	$0.203084\pi$
$488$		0			0
$489$			19641.5i			0.0821404i
$490$		0			0
$491$	92603.2			0.384117			0.192058	−	0.981384i	$-0.438484\pi$
$491$	92603.2			0.384117			0.192058	+	0.981384i	$0.438484\pi$
$492$		0			0
$493$	51281.1	+	29607.1i	0.210991	+	0.121816i
$494$		0			0
$495$	15197.1	−	8774.04i	0.0620226	−	0.0358088i
$496$		0			0
$497$	−93856.7	+	245467.i	−0.379973	+	0.993757i
$498$		0			0
$499$	−3480.87	−	6029.05i	−0.0139794	−	0.0242130i	0.858951	−	0.512058i	$-0.171117\pi$
$499$	−3480.87	−	6029.05i	−0.0139794	−	0.0242130i	−0.872930	+	0.487845i	$0.837783\pi$
$500$		0			0
$501$	27515.0	−	47657.4i	0.109621	−	0.189869i
$502$		0			0
$503$		−	466372.i		−	1.84330i	−0.388021	−	0.921650i	$-0.626841\pi$
$503$		−	466372.i		−	1.84330i	0.388021	−	0.921650i	$-0.373159\pi$
$504$		0			0
$505$	38265.5			0.150046
$506$		0			0
$507$	88610.5	+	51159.3i	0.344722	+	0.199025i
$508$		0			0
$509$	−174228.	+	100590.i	−0.672483	+	0.388259i	−0.797017	−	0.603957i	$-0.793590\pi$
$509$	−174228.	+	100590.i	−0.672483	+	0.388259i	0.124533	+	0.992215i	$0.460257\pi$
$510$		0			0
$511$	54521.5	−	44269.2i	0.208798	−	0.169535i
$512$		0			0
$513$	−20517.7	−	35537.6i	−0.0779638	−	0.135037i
$514$		0			0
$515$	30550.7	−	52915.4i	0.115188	−	0.199511i
$516$		0			0
$517$			182988.i			0.684608i
$518$		0			0
$519$	−208583.			−0.774361
$520$		0			0
$521$	300077.	+	173249.i	1.10549	+	0.638258i	0.937659	−	0.347557i	$-0.112989\pi$
$521$	300077.	+	173249.i	1.10549	+	0.638258i	0.167836	+	0.985815i	$0.446322\pi$
$522$		0			0
$523$	−252492.	+	145776.i	−0.923090	+	0.532946i	−0.884620	−	0.466313i	$-0.845582\pi$
$523$	−252492.	+	145776.i	−0.923090	+	0.532946i	−0.0384707	+	0.999260i	$0.512249\pi$
$524$		0			0
$525$	−22295.4	−	139582.i	−0.0808903	−	0.506420i
$526$		0			0
$527$	22086.5	+	38255.0i	0.0795254	+	0.137742i
$528$		0			0
$529$	107866.	−	186830.i	0.385456	−	0.667629i
$530$		0			0
$531$			90837.7i			0.322164i
$532$		0			0
$533$	288514.			1.01558
$534$		0			0
$535$	−140385.	−	81051.4i	−0.490471	−	0.283174i
$536$		0			0
$537$	−169095.	+	97627.1i	−0.586385	+	0.338549i
$538$		0			0
$539$	177442.	−	58169.6i	0.610772	−	0.200225i
$540$		0			0
$541$	193007.	+	334298.i	0.659445	+	1.14219i	0.980759	+	0.195220i	$0.0625422\pi$
$541$	193007.	+	334298.i	0.659445	+	1.14219i	−0.321314	+	0.946973i	$0.604125\pi$
$542$		0			0
$543$	−103539.	+	179334.i	−0.351158	+	0.608224i
$544$		0			0
$545$			108057.i			0.363799i
$546$		0			0
$547$	122247.			0.408566			0.204283	−	0.978912i	$-0.434514\pi$
$547$	122247.			0.408566			0.204283	+	0.978912i	$0.434514\pi$
$548$		0			0
$549$	−77533.4	−	44763.9i	−0.257243	−	0.148520i
$550$		0			0
$551$	−138889.	+	80187.8i	−0.457473	+	0.264122i
$552$		0			0
$553$	−540670.	+	86361.0i	−1.76800	+	0.282402i
$554$		0			0
$555$	5872.15	+	10170.9i	0.0190639	+	0.0330196i
$556$		0			0
$557$	−53061.4	+	91905.1i	−0.171029	+	0.296230i	−0.938780	−	0.344518i	$-0.888042\pi$
$557$	−53061.4	+	91905.1i	−0.171029	+	0.296230i	0.767751	+	0.640748i	$0.221376\pi$
$558$		0			0
$559$			52087.2i			0.166689i
$560$		0			0
$561$	−43642.8			−0.138671
$562$		0			0
$563$	−254823.	−	147122.i	−0.803935	−	0.464152i	0.0409102	−	0.999163i	$-0.486974\pi$
$563$	−254823.	−	147122.i	−0.803935	−	0.464152i	−0.844845	+	0.535011i	$0.820308\pi$
$564$		0			0
$565$	−37293.9	+	21531.6i	−0.116826	+	0.0674497i
$566$		0			0
$567$	−22516.4	−	27730.9i	−0.0700377	−	0.0862577i
$568$		0			0
$569$	237514.	+	411386.i	0.733609	+	1.27065i	0.955331	+	0.295538i	$0.0954988\pi$
$569$	237514.	+	411386.i	0.733609	+	1.27065i	−0.221722	+	0.975110i	$0.571168\pi$
$570$		0			0
$571$	−92589.2	+	160369.i	−0.283980	+	0.491868i	−0.972361	−	0.233481i	$-0.924988\pi$
$571$	−92589.2	+	160369.i	−0.283980	+	0.491868i	0.688381	+	0.725349i	$0.258322\pi$
$572$		0			0
$573$			236399.i			0.720006i
$574$		0			0
$575$	−140566.			−0.425151
$576$		0			0
$577$	139857.	+	80746.6i	0.420081	+	0.242534i	0.695112	−	0.718901i	$-0.255355\pi$
$577$	139857.	+	80746.6i	0.420081	+	0.242534i	−0.275031	+	0.961435i	$0.588688\pi$
$578$		0			0
$579$	−54406.8	+	31411.8i	−0.162292	+	0.0936992i
$580$		0			0
$581$	−60725.1	−	23218.8i	−0.179894	−	0.0687841i
$582$		0			0
$583$	195351.	+	338358.i	0.574750	+	0.995497i
$584$		0			0
$585$	10624.9	−	18402.9i	0.0310466	−	0.0537743i
$586$		0			0
$587$		−	333168.i		−	0.966911i	−0.875369	−	0.483456i	$-0.839381\pi$
$587$		−	333168.i		−	0.966911i	0.875369	−	0.483456i	$-0.160619\pi$
$588$		0			0
$589$	−119638.			−0.344856
$590$		0			0
$591$	195172.	+	112683.i	0.558782	+	0.322613i
$592$		0			0
$593$	97432.1	−	56252.5i	0.277072	−	0.159968i	−0.355025	−	0.934857i	$-0.615528\pi$
$593$	97432.1	−	56252.5i	0.277072	−	0.159968i	0.632097	+	0.774889i	$0.282194\pi$
$594$		0			0
$595$	15793.3	−	41305.0i	0.0446108	−	0.116672i
$596$		0			0
$597$	59002.9	+	102196.i	0.165548	+	0.286738i
$598$		0			0
$599$	202632.	−	350970.i	0.564749	−	0.978174i	−0.432324	−	0.901718i	$-0.642306\pi$
$599$	202632.	−	350970.i	0.564749	−	0.978174i	0.997073	−	0.0764554i	$-0.0243603\pi$
$600$		0			0
$601$			372831.i			1.03220i	0.856529	+	0.516098i	$0.172616\pi$
$601$			372831.i			1.03220i	−0.856529	+	0.516098i	$0.827384\pi$
$602$		0			0
$603$	−16172.5			−0.0444778
$604$		0			0
$605$	−62183.7	−	35901.8i	−0.169889	−	0.0980856i
$606$		0			0
$607$	−472368.	+	272722.i	−1.28204	+	0.740188i	−0.977222	−	0.212221i	$-0.931930\pi$
$607$	−472368.	+	272722.i	−1.28204	+	0.740188i	−0.304822	+	0.952409i	$0.598597\pi$
$608$		0			0
$609$	−108379.	+	87999.1i	−0.292220	+	0.237271i
$610$		0			0
$611$	110795.	+	191902.i	0.296782	+	0.514041i
$612$		0			0
$613$	219300.	−	379838.i	0.583602	−	1.01083i	−0.411446	−	0.911434i	$-0.634976\pi$
$613$	219300.	−	379838.i	0.583602	−	1.01083i	0.995048	−	0.0993946i	$-0.0316906\pi$
$614$		0			0
$615$			133023.i			0.351704i
$616$		0			0
$617$	663957.			1.74409			0.872046	−	0.489423i	$-0.162793\pi$
$617$	663957.			1.74409			0.872046	+	0.489423i	$0.162793\pi$
$618$		0			0
$619$	237343.	+	137030.i	0.619434	+	0.357630i	0.776649	−	0.629934i	$-0.216918\pi$
$619$	237343.	+	137030.i	0.619434	+	0.357630i	−0.157215	+	0.987564i	$0.550251\pi$
$620$		0			0
$621$	−30763.3	+	17761.2i	−0.0797719	+	0.0460563i
$622$		0			0
$623$	−95538.1	−	598124.i	−0.246150	−	1.54104i
$624$		0			0
$625$	−132281.	−	229117.i	−0.338639	−	0.586540i
$626$		0			0
$627$	59100.9	−	102366.i	0.150335	−	0.260387i
$628$		0			0
$629$		−	29208.6i		−	0.0738260i
$630$		0			0
$631$	−217088.			−0.545227			−0.272614	−	0.962124i	$-0.587888\pi$
$631$	−217088.			−0.545227			−0.272614	+	0.962124i	$0.587888\pi$
$632$		0			0
$633$	−341487.	−	197157.i	−0.852249	−	0.492046i
$634$		0			0
$635$	−74689.9	+	43122.2i	−0.185231	+	0.106943i
$636$		0			0
$637$	150866.	−	168440.i	0.371802	−	0.415113i
$638$		0			0
$639$	72403.7	+	125407.i	0.177321	+	0.307128i
$640$		0			0
$641$	261433.	−	452815.i	0.636274	−	1.10206i	−0.349969	−	0.936761i	$-0.613808\pi$
$641$	261433.	−	452815.i	0.636274	−	1.10206i	0.986244	−	0.165298i	$-0.0528587\pi$
$642$		0			0
$643$		−	447328.i		−	1.08194i	−0.841041	−	0.540971i	$-0.818057\pi$
$643$		−	447328.i		−	1.08194i	0.841041	−	0.540971i	$-0.181943\pi$
$644$		0			0
$645$	−24015.5			−0.0577261
$646$		0			0
$647$	−168608.	−	97346.0i	−0.402782	−	0.232546i	0.284901	−	0.958557i	$-0.408039\pi$
$647$	−168608.	−	97346.0i	−0.402782	−	0.232546i	−0.687684	+	0.726010i	$0.741372\pi$
$648$		0			0
$649$	−226602.	+	130829.i	−0.537990	+	0.310609i
$650$		0			0
$651$	−102840.	+	16426.7i	−0.242662	+	0.0387603i
$652$		0			0
$653$	−92320.8	−	159904.i	−0.216508	−	0.375002i	0.737230	−	0.675642i	$-0.236133\pi$
$653$	−92320.8	−	159904.i	−0.216508	−	0.375002i	−0.953738	+	0.300639i	$0.902800\pi$
$654$		0			0
$655$	131339.	−	227486.i	0.306134	−	0.530240i
$656$		0			0
$657$		−	38698.6i		−	0.0896528i
$658$		0			0
$659$	269400.			0.620336			0.310168	−	0.950682i	$-0.399615\pi$
$659$	269400.			0.620336			0.310168	+	0.950682i	$0.399615\pi$
$660$		0			0
$661$	−273711.	−	158027.i	−0.626453	−	0.361683i	0.152924	−	0.988238i	$-0.451131\pi$
$661$	−273711.	−	158027.i	−0.626453	−	0.361683i	−0.779377	+	0.626555i	$0.784464\pi$
$662$		0			0
$663$	−45768.8	+	26424.6i	−0.104122	+	0.0601149i
$664$		0			0
$665$	75495.0	+	92978.9i	0.170716	+	0.210252i
$666$		0			0
$667$	69414.9	+	120230.i	0.156028	+	0.270248i
$668$		0			0
$669$	47484.3	−	82245.2i	0.106096	−	0.183763i
$670$		0			0
$671$		−	257884.i		−	0.572769i
$672$		0			0
$673$	85940.2			0.189743			0.0948716	−	0.995490i	$-0.469756\pi$
$673$	85940.2			0.189743			0.0948716	+	0.995490i	$0.469756\pi$
$674$		0			0
$675$	−67452.6	−	38943.8i	−0.148044	−	0.0854733i
$676$		0			0
$677$	−43495.9	+	25112.3i	−0.0949010	+	0.0547911i	−0.546699	−	0.837329i	$-0.684116\pi$
$677$	−43495.9	+	25112.3i	−0.0949010	+	0.0547911i	0.451798	+	0.892120i	$0.350783\pi$
$678$		0			0
$679$	−243478.	−	93096.1i	−0.528105	−	0.201926i
$680$		0			0
$681$	−30914.4	−	53545.3i	−0.0666602	−	0.115459i
$682$		0			0
$683$	373719.	−	647301.i	0.801132	−	1.38760i	−0.117739	−	0.993045i	$-0.537565\pi$
$683$	373719.	−	647301.i	0.801132	−	1.38760i	0.918871	−	0.394557i	$-0.129102\pi$
$684$		0			0
$685$			115790.i			0.246769i
$686$		0			0
$687$	−1524.42			−0.00322992
$688$		0			0
$689$	409735.	+	236561.i	0.863108	+	0.498315i
$690$		0			0
$691$	151644.	−	87551.7i	0.317592	−	0.183362i	−0.332727	−	0.943023i	$-0.607969\pi$
$691$	151644.	−	87551.7i	0.317592	−	0.183362i	0.650319	+	0.759662i	$0.274635\pi$
$692$		0			0
$693$	36747.9	−	96108.1i	0.0765184	−	0.200121i
$694$		0			0
$695$	103415.	+	179120.i	0.214099	+	0.370830i
$696$		0			0
$697$	165417.	−	286511.i	0.340498	−	0.589761i
$698$		0			0
$699$		−	371573.i		−	0.760483i
$700$		0			0
$701$	−91696.3			−0.186602			−0.0933009	−	0.995638i	$-0.529742\pi$
$701$	−91696.3			−0.186602			−0.0933009	+	0.995638i	$0.529742\pi$
$702$		0			0
$703$	68509.8	+	39554.2i	0.138625	+	0.0800353i
$704$		0			0
$705$	−88479.1	+	51083.4i	−0.178017	+	0.102778i
$706$		0			0
$707$	174184.	−	141430.i	0.348473	−	0.282946i
$708$		0			0
$709$	45597.2	+	78976.7i	0.0907081	+	0.157111i	0.907809	−	0.419383i	$-0.137754\pi$
$709$	45597.2	+	78976.7i	0.0907081	+	0.157111i	−0.817101	+	0.576494i	$0.804420\pi$
$710$		0			0
$711$	−150848.	+	261277.i	−0.298402	+	0.516847i
$712$		0			0
$713$			103565.i			0.203720i
$714$		0			0
$715$	61210.0			0.119732
$716$		0			0
$717$	282912.	+	163339.i	0.550316	+	0.317725i
$718$		0			0
$719$	−143600.	+	82907.7i	−0.277778	+	0.160375i	−0.632417	−	0.774628i	$-0.717937\pi$
$719$	−143600.	+	82907.7i	−0.277778	+	0.160375i	0.354639	+	0.935003i	$0.384604\pi$
$720$		0			0
$721$	−56510.1	−	353786.i	−0.108707	−	0.680566i
$722$		0			0
$723$	158040.	+	273734.i	0.302337	+	0.523663i
$724$		0			0
$725$	−152201.	+	263620.i	−0.289563	+	0.501537i
$726$		0			0
$727$			90288.3i			0.170829i	0.996345	+	0.0854147i	$0.0272215\pi$
$727$			90288.3i			0.170829i	−0.996345	+	0.0854147i	$0.972778\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$		0			0
$731$	51725.6	+	29863.8i	0.0967989	+	0.0558869i
$732$		0			0
$733$	−272185.	+	157146.i	−0.506590	+	0.292480i	−0.731431	−	0.681916i	$-0.761147\pi$
$733$	−272185.	+	157146.i	−0.506590	+	0.292480i	0.224841	+	0.974395i	$0.427814\pi$
$734$		0			0
$735$	77661.6	+	69558.7i	0.143758	+	0.128759i
$736$		0			0
$737$	−23292.4	−	40343.7i	−0.0428825	−	0.0742746i
$738$		0			0
$739$	−56214.0	+	97365.4i	−0.102933	+	0.178285i	−0.912892	−	0.408201i	$-0.866156\pi$
$739$	−56214.0	+	97365.4i	−0.102933	+	0.178285i	0.809959	+	0.586487i	$0.199489\pi$
$740$		0			0
$741$		−	143137.i		−	0.260684i
$742$		0			0
$743$	−805662.			−1.45940			−0.729702	−	0.683765i	$-0.760341\pi$
$743$	−805662.			−1.45940			−0.729702	+	0.683765i	$0.760341\pi$
$744$		0			0
$745$	1237.37	+	714.397i	0.00222940	+	0.00128714i
$746$		0			0
$747$	−31023.9	+	17911.7i	−0.0555975	+	0.0320992i
$748$		0			0
$749$	−938600.	+	149922.i	−1.67308	+	0.267240i
$750$		0			0
$751$	184929.	+	320306.i	0.327887	+	0.567917i	0.982092	−	0.188400i	$-0.0603300\pi$
$751$	184929.	+	320306.i	0.327887	+	0.567917i	−0.654205	+	0.756317i	$0.726997\pi$
$752$		0			0
$753$	186100.	−	322335.i	0.328214	−	0.568484i
$754$		0			0
$755$			310441.i			0.544610i
$756$		0			0
$757$	736616.			1.28543			0.642716	−	0.766104i	$-0.277807\pi$
$757$	736616.			1.28543			0.642716	+	0.766104i	$0.277807\pi$
$758$		0			0
$759$	−88613.5	−	51161.0i	−0.153821	−	0.0888087i
$760$		0			0
$761$	−111743.	+	64515.1i	−0.192954	+	0.111402i	−0.593365	−	0.804934i	$-0.702201\pi$
$761$	−111743.	+	64515.1i	−0.192954	+	0.111402i	0.400411	+	0.916336i	$0.368867\pi$
$762$		0			0
$763$	399383.	+	491876.i	0.686026	+	0.844902i
$764$		0			0
$765$	−12183.4	−	21102.3i	−0.0208184	−	0.0360585i
$766$		0			0
$767$	−158427.	+	274404.i	−0.269301	+	0.466444i
$768$		0			0
$769$		−	485806.i		−	0.821506i	−0.911747	−	0.410753i	$-0.865266\pi$
$769$		−	485806.i		−	0.821506i	0.911747	−	0.410753i	$-0.134734\pi$
$770$		0			0
$771$	302084.			0.508181
$772$		0			0
$773$	−239185.	−	138094.i	−0.400290	−	0.231108i	0.286319	−	0.958134i	$-0.407568\pi$
$773$	−239185.	−	138094.i	−0.400290	−	0.231108i	−0.686609	+	0.727027i	$0.740902\pi$
$774$		0			0
$775$	−196657.	+	113540.i	−0.327421	+	0.189037i
$776$		0			0
$777$	64321.8	+	24594.0i	0.106541	+	0.0407369i
$778$		0			0
$779$	448015.	+	775984.i	0.738274	+	1.27873i
$780$		0			0
$781$	−208558.	+	361233.i	−0.341921	+	0.592224i
$782$		0			0
$783$			76925.7i			0.125472i
$784$		0			0
$785$	−126897.			−0.205926
$786$		0			0
$787$	83633.8	+	48286.0i	0.135031	+	0.0779600i	0.565994	−	0.824410i	$-0.308493\pi$
$787$	83633.8	+	48286.0i	0.135031	+	0.0779600i	−0.430963	+	0.902370i	$0.641826\pi$
$788$		0			0
$789$	143097.	−	82616.9i	0.229866	−	0.132713i
$790$		0			0
$791$	−90179.8	+	235851.i	−0.144131	+	0.376951i
$792$		0			0
$793$	−156142.	−	270447.i	−0.248299	−	0.430066i
$794$		0			0
$795$	−109070.	+	188914.i	−0.172572	+	0.298903i
$796$		0			0
$797$			540869.i			0.851481i	0.904845	+	0.425741i	$0.139986\pi$
$797$			540869.i			0.851481i	−0.904845	+	0.425741i	$0.860014\pi$
$798$		0			0
$799$	254093.			0.398015
$800$		0			0
$801$	−289041.	−	166878.i	−0.450500	−	0.260096i
$802$		0			0
$803$	96536.6	−	55735.4i	0.149713	−	0.0864371i
$804$		0			0
$805$	80487.6	−	65352.6i	0.124205	−	0.100849i
$806$		0			0
$807$	−142705.	−	247172.i	−0.219125	−	0.379535i
$808$		0			0
$809$	−477611.	+	827246.i	−0.729755	+	1.26397i	0.227232	+	0.973841i	$0.427033\pi$
$809$	−477611.	+	827246.i	−0.729755	+	1.26397i	−0.956987	+	0.290132i	$0.906301\pi$
$810$		0			0
$811$		−	352574.i		−	0.536055i	−0.963411	−	0.268027i	$-0.913628\pi$
$811$		−	352574.i		−	0.536055i	0.963411	−	0.268027i	$-0.0863718\pi$
$812$		0			0
$813$	476638.			0.721121
$814$		0			0
$815$	−27356.4	−	15794.2i	−0.0411854	−	0.0237784i
$816$		0			0
$817$	−140093.	+	80882.8i	−0.209881	+	0.121175i
$818$		0			0
$819$	−19653.1	−	123040.i	−0.0292997	−	0.183433i
$820$		0			0
$821$	−393020.	−	680731.i	−0.583080	−	1.00992i	−0.995112	−	0.0987551i	$-0.968514\pi$
$821$	−393020.	−	680731.i	−0.583080	−	1.00992i	0.412031	−	0.911170i	$-0.364819\pi$
$822$		0			0
$823$	−366023.	+	633971.i	−0.540392	+	0.935987i	0.458489	+	0.888700i	$0.348391\pi$
$823$	−366023.	+	633971.i	−0.540392	+	0.935987i	−0.998881	+	0.0472866i	$0.984943\pi$
$824$		0			0
$825$		−	224354.i		−	0.329630i
$826$		0			0
$827$	−279220.			−0.408258			−0.204129	−	0.978944i	$-0.565436\pi$
$827$	−279220.			−0.408258			−0.204129	+	0.978944i	$0.565436\pi$
$828$		0			0
$829$	−176164.	−	101708.i	−0.256335	−	0.147995i	0.366327	−	0.930486i	$-0.380615\pi$
$829$	−176164.	−	101708.i	−0.256335	−	0.147995i	−0.622662	+	0.782491i	$0.713949\pi$
$830$		0			0
$831$	−33010.0	+	19058.3i	−0.0478018	+	0.0275984i
$832$		0			0
$833$	−80773.1	−	246392.i	−0.116406	−	0.355089i
$834$		0			0
$835$	44251.0	+	76645.0i	0.0634674	+	0.109929i
$836$		0			0
$837$	−28692.8	+	49697.3i	−0.0409564	+	0.0709385i
$838$		0			0
$839$			1.36972e6i			1.94584i	0.231134	+	0.972922i	$0.425756\pi$
$839$			1.36972e6i			1.94584i	−0.231134	+	0.972922i	$0.574244\pi$
$840$		0			0
$841$	−406637.			−0.574930
$842$		0			0
$843$	599330.	+	346024.i	0.843356	+	0.486912i
$844$		0			0
$845$	−142508.	+	82276.9i	−0.199584	+	0.115230i
$846$		0			0
$847$	−415753.	+	66408.1i	−0.579521	+	0.0925666i
$848$		0			0
$849$	−324905.	−	562752.i	−0.450755	−	0.780731i
$850$		0			0
$851$	34240.2	−	59305.8i	0.0472800	−	0.0818914i
$852$		0			0
$853$		−	110844.i		−	0.152340i	−0.997095	−	0.0761702i	$-0.975731\pi$
$853$		−	110844.i		−	0.152340i	0.997095	−	0.0761702i	$-0.0242692\pi$
$854$		0			0
$855$	65995.1			0.0902774
$856$		0			0
$857$	917323.	+	529617.i	1.24899	+	0.721107i	0.970909	−	0.239449i	$-0.0769667\pi$
$857$	917323.	+	529617.i	1.24899	+	0.721107i	0.278086	+	0.960556i	$0.410300\pi$
$858$		0			0
$859$	1.00197e6	−	578485.i	1.35790	−	0.783982i	0.368556	−	0.929605i	$-0.379852\pi$
$859$	1.00197e6	−	578485.i	1.35790	−	0.783982i	0.989340	+	0.145624i	$0.0465188\pi$
$860$		0			0
$861$	491657.	+	605520.i	0.663218	+	0.816813i
$862$		0			0
$863$	39295.5	+	68061.8i	0.0527620	+	0.0913864i	0.891200	−	0.453610i	$-0.149864\pi$
$863$	39295.5	+	68061.8i	0.0527620	+	0.0913864i	−0.838438	+	0.544997i	$0.816531\pi$
$864$		0			0
$865$	167726.	−	290511.i	0.224166	−	0.388267i
$866$		0			0
$867$		−	373386.i		−	0.496730i
$868$		0			0
$869$	−869035.			−1.15079
$870$		0			0
$871$	−48854.2	−	28206.0i	−0.0643970	−	0.0371796i
$872$		0			0
$873$	−124391.	+	71817.0i	−0.163215	+	0.0942321i
$874$		0			0
$875$	451382.	+	172590.i	0.589561	+	0.225424i
$876$		0			0
$877$	−32541.5	−	56363.6i	−0.0423096	−	0.0732824i	0.844095	−	0.536193i	$-0.180138\pi$
$877$	−32541.5	−	56363.6i	−0.0423096	−	0.0732824i	−0.886405	+	0.462911i	$0.846805\pi$
$878$		0			0
$879$	356958.	−	618269.i	0.461997	−	0.800202i
$880$		0			0
$881$		−	510450.i		−	0.657661i	−0.944389	−	0.328830i	$-0.893346\pi$
$881$		−	510450.i		−	0.657661i	0.944389	−	0.328830i	$-0.106654\pi$
$882$		0			0
$883$	684144.			0.877458			0.438729	−	0.898620i	$-0.355429\pi$
$883$	684144.			0.877458			0.438729	+	0.898620i	$0.355429\pi$
$884$		0			0
$885$	−126518.	−	73044.9i	−0.161534	−	0.0932617i
$886$		0			0
$887$	251921.	−	145447.i	0.320198	−	0.184866i	−0.331283	−	0.943531i	$-0.607482\pi$
$887$	251921.	−	145447.i	0.320198	−	0.184866i	0.651481	+	0.758665i	$0.274148\pi$
$888$		0			0
$889$	−180607.	+	472348.i	−0.228523	+	0.597665i
$890$		0			0
$891$	−28348.4	−	49100.8i	−0.0357086	−	0.0618491i
$892$		0			0
$893$	−344092.	+	595985.i	−0.431491	+	0.747365i
$894$		0			0
$895$		−	314018.i		−	0.392020i
$896$		0			0
$897$	−123907.			−0.153996
$898$		0			0
$899$	194229.	+	112138.i	0.240322	+	0.138750i
$900$		0			0
$901$	469837.	−	271261.i	0.578759	−	0.334147i
$902$		0			0
$903$	−109318.	+	88761.9i	−0.134066	+	0.108856i
$904$		0			0
$905$	−166516.	−	288414.i	−0.203310	−	0.352144i
$906$		0			0
$907$	19708.0	−	34135.2i	0.0239567	−	0.0414942i	−0.853798	−	0.520604i	$-0.825707\pi$
$907$	19708.0	−	34135.2i	0.0239567	−	0.0414942i	0.877755	+	0.479109i	$0.159040\pi$
$908$		0			0
$909$		−	123633.i		−	0.149626i
$910$		0			0
$911$	−1.07089e6			−1.29035			−0.645173	−	0.764036i	$-0.723215\pi$
$911$	−1.07089e6			−1.29035			−0.645173	+	0.764036i	$0.723215\pi$
$912$		0			0
$913$	−89364.1	−	51594.4i	−0.107207	−	0.0618958i
$914$		0			0
$915$	124693.	−	71991.6i	0.148936	−	0.0859884i
$916$		0			0
$917$	−242940.	−	1.52095e6i	−0.288909	−	1.80874i
$918$		0			0
$919$	−607876.	−	1.05287e6i	−0.719754	−	1.24665i	−0.961097	−	0.276211i	$-0.910921\pi$
$919$	−607876.	−	1.05287e6i	−0.719754	−	1.24665i	0.241343	−	0.970440i	$-0.422412\pi$
$920$		0			0
$921$	−154326.	+	267301.i	−0.181937	+	0.315123i
$922$		0			0
$923$			505107.i			0.592898i
$924$		0			0
$925$	150152.			0.175489
$926$		0			0
$927$	−170966.	−	98707.3i	−0.198953	−	0.114866i
$928$		0			0
$929$	1.29549e6	−	747949.i	1.50107	−	0.866644i	0.501072	−	0.865406i	$-0.332939\pi$
$929$	1.29549e6	−	747949.i	1.50107	−	0.866644i	0.999999	−	0.00123791i	$-0.000394039\pi$
$930$		0			0
$931$	687305.	+	144207.i	0.792958	+	0.166375i
$932$		0			0
$933$	117383.	+	203314.i	0.134847	+	0.233562i
$934$		0			0
$935$	35094.3	−	60785.1i	0.0401433	−	0.0695303i
$936$		0			0
$937$			254082.i			0.289398i	0.989476	+	0.144699i	$0.0462213\pi$
$937$			254082.i			0.289398i	−0.989476	+	0.144699i	$0.953779\pi$
$938$		0			0
$939$	553832.			0.628126
$940$		0			0
$941$	−642429.	−	370907.i	−0.725514	−	0.418876i	0.0912645	−	0.995827i	$-0.470909\pi$
$941$	−642429.	−	370907.i	−0.725514	−	0.418876i	−0.816779	+	0.576951i	$0.804242\pi$
$942$		0			0
$943$	671735.	−	387826.i	0.755395	−	0.436128i
$944$		0			0
$945$	56729.2	−	9061.33i	0.0635248	−	0.0101468i
$946$		0			0
$947$	−477051.	−	826277.i	−0.531943	−	0.921352i	−0.999305	−	0.0372859i	$-0.988129\pi$
$947$	−477051.	−	826277.i	−0.531943	−	0.921352i	0.467362	−	0.884066i	$-0.345205\pi$
$948$		0			0
$949$	67492.8	−	116901.i	0.0749420	−	0.129803i
$950$		0			0
$951$		−	796174.i		−	0.880332i
$952$		0			0
$953$	−792911.			−0.873049			−0.436525	−	0.899692i	$-0.643791\pi$
$953$	−792911.			−0.873049			−0.436525	+	0.899692i	$0.643791\pi$
$954$		0			0
$955$	−329253.	−	190094.i	−0.361013	−	0.208431i
$956$		0			0
$957$	−191897.	+	110792.i	−0.209529	+	0.120972i
$958$		0			0
$959$	427964.	+	527076.i	0.465340	+	0.573108i
$960$		0			0
$961$	−378107.	−	654901.i	−0.409419	−	0.709135i
$962$		0			0
$963$	−261872.	+	453575.i	−0.282382	+	0.489099i
$964$		0			0
$965$		−	101036.i		−	0.108498i
$966$		0			0
$967$	−23877.3			−0.0255348			−0.0127674	−	0.999918i	$-0.504064\pi$
$967$	−23877.3			−0.0255348			−0.0127674	+	0.999918i	$0.504064\pi$
$968$		0			0
$969$	−142143.	−	82066.2i	−0.151383	−	0.0874011i
$970$		0			0
$971$	969512.	−	559748.i	1.02829	−	0.593682i	0.111794	−	0.993731i	$-0.464340\pi$
$971$	969512.	−	559748.i	1.02829	−	0.593682i	0.916494	+	0.400049i	$0.131007\pi$
$972$		0			0
$973$	1.13278e6	+	433128.i	1.19652	+	0.457500i
$974$		0			0
$975$	−135841.	−	235283.i	−0.142896	−	0.247504i
$976$		0			0
$977$	522163.	−	904413.i	0.547037	−	0.947497i	−0.451438	−	0.892302i	$-0.649089\pi$
$977$	522163.	−	904413.i	0.547037	−	0.947497i	0.998476	−	0.0551943i	$-0.0175778\pi$
$978$		0			0
$979$		−	961382.i		−	1.00307i
$980$		0			0
$981$	349126.			0.362781
$982$		0			0
$983$	−187897.	−	108482.i	−0.194452	−	0.112267i	0.399613	−	0.916684i	$-0.369145\pi$
$983$	−187897.	−	108482.i	−0.194452	−	0.112267i	−0.594065	+	0.804417i	$0.702478\pi$
$984$		0			0
$985$	−313885.	+	181222.i	−0.323518	+	0.186783i
$986$		0			0
$987$	−213950.	+	559552.i	−0.219623	+	0.574389i
$988$		0			0
$989$	70016.6	+	121272.i	0.0715828	+	0.123985i
$990$		0			0
$991$	−496994.	+	860819.i	−0.506062	+	0.876525i	0.493913	+	0.869511i	$0.335566\pi$
$991$	−496994.	+	860819.i	−0.506062	+	0.876525i	−0.999975	+	0.00701423i	$0.997767\pi$
$992$		0			0
$993$			583846.i			0.592107i
$994$		0			0
$995$	−189783.			−0.191695
$996$		0			0
$997$	−674463.	−	389402.i	−0.678528	−	0.391748i	0.120772	−	0.992680i	$-0.461463\pi$
$997$	−674463.	−	389402.i	−0.678528	−	0.391748i	−0.799300	+	0.600932i	$0.794796\pi$
$998$		0			0
$999$	32861.4	−	18972.5i	0.0329272	−	0.0190105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.5.m.a.73.1	yes	4
3.2	odd	2		252.5.z.b.73.2		4
4.3	odd	2		336.5.bh.c.241.1		4
7.2	even	3		588.5.m.a.313.2		4
7.3	odd	6		588.5.d.a.97.4		4
7.4	even	3		588.5.d.a.97.1		4
7.5	odd	6	inner	84.5.m.a.61.1	✓	4
7.6	odd	2		588.5.m.a.325.2		4
21.5	even	6		252.5.z.b.145.2		4
28.19	even	6		336.5.bh.c.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.5.m.a.61.1	✓	4	7.5	odd	6	inner
84.5.m.a.73.1	yes	4	1.1	even	1	trivial
252.5.z.b.73.2		4	3.2	odd	2
252.5.z.b.145.2		4	21.5	even	6
336.5.bh.c.145.1		4	28.19	even	6
336.5.bh.c.241.1		4	4.3	odd	2
588.5.d.a.97.1		4	7.4	even	3
588.5.d.a.97.4		4	7.3	odd	6
588.5.m.a.313.2		4	7.2	even	3
588.5.m.a.325.2		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)

\(f(q)\)	\(=\)	\(q+(4.50000 + 2.59808i) q^{3} +(-7.23713 + 4.17836i) q^{5} +(-17.5000 + 45.7684i) q^{7} +(13.5000 + 23.3827i) q^{9} +(-38.8866 + 67.3536i) q^{11} +94.1795i q^{13} -43.4228 q^{15} +(93.5257 + 53.9971i) q^{17} +(-253.304 + 146.245i) q^{19} +(-197.660 + 160.492i) q^{21} +(126.598 + 219.274i) q^{23} +(-277.583 + 480.787i) q^{25} +140.296i q^{27} +548.310 q^{29} +(354.232 + 204.516i) q^{31} +(-349.980 + 202.061i) q^{33} +(-64.5872 - 404.353i) q^{35} +(-135.232 - 234.229i) q^{37} +(-244.686 + 423.808i) q^{39} -3063.45i q^{41} +553.062 q^{43} +(-195.402 - 112.816i) q^{45} +(2037.62 - 1176.42i) q^{47} +(-1788.50 - 1601.90i) q^{49} +(280.577 + 485.974i) q^{51} +(2511.81 - 4350.58i) q^{53} -649.929i q^{55} -1519.83 q^{57} +(2913.62 + 1682.18i) q^{59} +(-2871.61 + 1657.92i) q^{61} +(-1306.44 + 208.677i) q^{63} +(-393.516 - 681.589i) q^{65} +(-299.491 + 518.734i) q^{67} +1315.65i q^{69} +5363.24 q^{71} +(-1241.26 - 716.640i) q^{73} +(-2498.24 + 1442.36i) q^{75} +(-2402.15 - 2958.47i) q^{77} +(5586.98 + 9676.93i) q^{79} +(-364.500 + 631.333i) q^{81} +1326.79i q^{83} -902.477 q^{85} +(2467.39 + 1424.55i) q^{87} +(-10705.2 + 6180.67i) q^{89} +(-4310.45 - 1648.14i) q^{91} +(1062.70 + 1840.64i) q^{93} +(1222.13 - 2116.79i) q^{95} +5319.78i q^{97} -2099.88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} + 39 q^{5} - 70 q^{7} + 54 q^{9} + 3 q^{11} + 234 q^{15} + 510 q^{17} + 459 q^{19} - 315 q^{21} + 144 q^{23} - 227 q^{25} - 570 q^{29} + 2640 q^{31} + 27 q^{33} - 2478 q^{35} + 433 q^{37}+ \cdots + 162 q^{99}+O(q^{100}) \) 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

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