LMFDB - Embedded newform 294.4.d.a.293.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(293,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("294.293");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.d (of order $2$, degree $1$, 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:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{8}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.7
Root			$-0.0204843 + 2.99993i$ of defining polynomial
Character	$\chi$	$=$	294.293
Dual form			294.4.d.a.293.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +(4.51764 + 2.56729i) q^{3} -4.00000 q^{4} -10.5451 q^{5} +(5.13458 - 9.03527i) q^{6} +8.00000i q^{8} +(13.8181 + 23.1962i) q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +(4.51764 + 2.56729i) q^{3} -4.00000 q^{4} -10.5451 q^{5} +(5.13458 - 9.03527i) q^{6} +8.00000i q^{8} +(13.8181 + 23.1962i) q^{9} +21.0903i q^{10} -30.8211i q^{11} +(-18.0705 - 10.2692i) q^{12} +19.8400i q^{13} +(-47.6391 - 27.0724i) q^{15} +16.0000 q^{16} -92.6905 q^{17} +(46.3923 - 27.6361i) q^{18} +137.295i q^{19} +42.1806 q^{20} -61.6421 q^{22} +43.4973i q^{23} +(-20.5383 + 36.1411i) q^{24} -13.7999 q^{25} +39.6801 q^{26} +(2.87369 + 140.267i) q^{27} +134.318i q^{29} +(-54.1449 + 95.2782i) q^{30} +167.389i q^{31} -32.0000i q^{32} +(79.1266 - 139.238i) q^{33} +185.381i q^{34} +(-55.2722 - 92.7846i) q^{36} -383.494 q^{37} +274.590 q^{38} +(-50.9351 + 89.6301i) q^{39} -84.3612i q^{40} +107.887 q^{41} -285.480 q^{43} +123.284i q^{44} +(-145.713 - 244.607i) q^{45} +86.9945 q^{46} -241.813 q^{47} +(72.2822 + 41.0766i) q^{48} +27.5998i q^{50} +(-418.742 - 237.963i) q^{51} -79.3602i q^{52} -499.632i q^{53} +(280.533 - 5.74739i) q^{54} +325.013i q^{55} +(-352.476 + 620.248i) q^{57} +268.637 q^{58} +732.425 q^{59} +(190.556 + 108.290i) q^{60} +306.235i q^{61} +334.778 q^{62} -64.0000 q^{64} -209.216i q^{65} +(-278.477 - 158.253i) q^{66} +560.099 q^{67} +370.762 q^{68} +(-111.670 + 196.505i) q^{69} -74.2161i q^{71} +(-185.569 + 110.544i) q^{72} +163.285i q^{73} +766.987i q^{74} +(-62.3429 - 35.4283i) q^{75} -549.180i q^{76} +(179.260 + 101.870i) q^{78} +874.320 q^{79} -168.722 q^{80} +(-347.123 + 641.051i) q^{81} -215.774i q^{82} +406.600 q^{83} +977.435 q^{85} +570.961i q^{86} +(-344.834 + 606.801i) q^{87} +246.569 q^{88} -1052.18 q^{89} +(-489.214 + 291.427i) q^{90} -173.989i q^{92} +(-429.736 + 756.203i) q^{93} +483.625i q^{94} -1447.79i q^{95} +(82.1533 - 144.564i) q^{96} -243.235i q^{97} +(714.930 - 425.887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 64 q^{4} - 36 q^{9}+O(q^{10}) $ 16 * q - 64 * q^4 - 36 * q^9	$ 16 q - 64 q^{4} - 36 q^{9} + 256 q^{16} + 96 q^{18} + 24 q^{22} + 388 q^{25} - 720 q^{30} + 144 q^{36} + 1924 q^{37} - 1188 q^{39} + 1732 q^{43} - 336 q^{46} - 3276 q^{51} - 2664 q^{57} + 1560 q^{58} - 1024 q^{64} + 1412 q^{67} - 384 q^{72} + 2832 q^{78} + 5312 q^{79} - 252 q^{81} + 5232 q^{85} - 96 q^{88} - 4032 q^{93} - 4284 q^{99}+O(q^{100}) $ 16 * q - 64 * q^4 - 36 * q^9 + 256 * q^16 + 96 * q^18 + 24 * q^22 + 388 * q^25 - 720 * q^30 + 144 * q^36 + 1924 * q^37 - 1188 * q^39 + 1732 * q^43 - 336 * q^46 - 3276 * q^51 - 2664 * q^57 + 1560 * q^58 - 1024 * q^64 + 1412 * q^67 - 384 * q^72 + 2832 * q^78 + 5312 * q^79 - 252 * q^81 + 5232 * q^85 - 96 * q^88 - 4032 * q^93 - 4284 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	4.51764	+	2.56729i	0.869419	+	0.494075i
$3$	4.51764	+	2.56729i	0.869419	+	0.494075i
$4$	−4.00000			−0.500000
$5$	−10.5451			−0.943186			−0.471593	−	0.881816i	$-0.656321\pi$
$5$	−10.5451			−0.943186			−0.471593	+	0.881816i	$0.656321\pi$
$6$	5.13458	−	9.03527i	0.349364	−	0.614772i
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	13.8181	+	23.1962i	0.511780	+	0.859117i
$10$			21.0903i			0.666934i
$11$		−	30.8211i		−	0.844809i	−0.906407	−	0.422405i	$-0.861186\pi$
$11$		−	30.8211i		−	0.844809i	0.906407	−	0.422405i	$-0.138814\pi$
$12$	−18.0705	−	10.2692i	−0.434710	−	0.247038i
$13$			19.8400i			0.423280i	0.977348	+	0.211640i	$0.0678804\pi$
$13$			19.8400i			0.423280i	−0.977348	+	0.211640i	$0.932120\pi$
$14$		0			0
$15$	−47.6391	−	27.0724i	−0.820025	−	0.466005i
$16$	16.0000			0.250000
$17$	−92.6905			−1.32240			−0.661199	−	0.750211i	$-0.729952\pi$
$17$	−92.6905			−1.32240			−0.661199	+	0.750211i	$0.729952\pi$
$18$	46.3923	−	27.6361i	0.607487	−	0.361883i
$19$			137.295i			1.65777i	0.559420	+	0.828884i	$0.311024\pi$
$19$			137.295i			1.65777i	−0.559420	+	0.828884i	$0.688976\pi$
$20$	42.1806			0.471593
$21$		0			0
$22$	−61.6421			−0.597370
$23$			43.4973i			0.394339i	0.980369	+	0.197170i	$0.0631750\pi$
$23$			43.4973i			0.394339i	−0.980369	+	0.197170i	$0.936825\pi$
$24$	−20.5383	+	36.1411i	−0.174682	+	0.307386i
$25$	−13.7999			−0.110399
$26$	39.6801			0.299304
$27$	2.87369	+	140.267i	0.0204831	+	0.999790i
$28$		0			0
$29$			134.318i			0.860079i	0.902810	+	0.430039i	$0.141500\pi$
$29$			134.318i			0.860079i	−0.902810	+	0.430039i	$0.858500\pi$
$30$	−54.1449	+	95.2782i	−0.329515	+	0.579845i
$31$			167.389i			0.969805i	0.874568	+	0.484903i	$0.161145\pi$
$31$			167.389i			0.969805i	−0.874568	+	0.484903i	$0.838855\pi$
$32$		−	32.0000i		−	0.176777i
$33$	79.1266	−	139.238i	0.417399	−	0.734493i
$34$			185.381i			0.935076i
$35$		0			0
$36$	−55.2722	−	92.7846i	−0.255890	−	0.429558i
$37$	−383.494			−1.70394			−0.851972	−	0.523587i	$-0.824594\pi$
$37$	−383.494			−1.70394			−0.851972	+	0.523587i	$0.824594\pi$
$38$	274.590			1.17222
$39$	−50.9351	+	89.6301i	−0.209132	+	0.368008i
$40$		−	84.3612i		−	0.333467i
$41$	107.887			0.410954			0.205477	−	0.978662i	$-0.434125\pi$
$41$	107.887			0.410954			0.205477	+	0.978662i	$0.434125\pi$
$42$		0			0
$43$	−285.480			−1.01245			−0.506225	−	0.862402i	$-0.668959\pi$
$43$	−285.480			−1.01245			−0.506225	+	0.862402i	$0.668959\pi$
$44$			123.284i			0.422405i
$45$	−145.713	−	244.607i	−0.482704	−	0.810307i
$46$	86.9945			0.278840
$47$	−241.813			−0.750468			−0.375234	−	0.926930i	$-0.622438\pi$
$47$	−241.813			−0.750468			−0.375234	+	0.926930i	$0.622438\pi$
$48$	72.2822	+	41.0766i	0.217355	+	0.123519i
$49$		0			0
$50$			27.5998i			0.0780640i
$51$	−418.742	−	237.963i	−1.14972	−	0.653364i
$52$		−	79.3602i		−	0.211640i
$53$		−	499.632i		−	1.29490i	−0.762107	−	0.647451i	$-0.775835\pi$
$53$		−	499.632i		−	1.29490i	0.762107	−	0.647451i	$-0.224165\pi$
$54$	280.533	−	5.74739i	0.706958	−	0.0144837i
$55$			325.013i			0.796813i
$56$		0			0
$57$	−352.476	+	620.248i	−0.819062	+	1.44130i
$58$	268.637			0.608168
$59$	732.425			1.61616			0.808081	−	0.589071i	$-0.200506\pi$
$59$	732.425			1.61616			0.808081	+	0.589071i	$0.200506\pi$
$60$	190.556	+	108.290i	0.410012	+	0.233002i
$61$			306.235i			0.642776i	0.946948	+	0.321388i	$0.104149\pi$
$61$			306.235i			0.642776i	−0.946948	+	0.321388i	$0.895851\pi$
$62$	334.778			0.685756
$63$		0			0
$64$	−64.0000			−0.125000
$65$		−	209.216i		−	0.399232i
$66$	−278.477	−	158.253i	−0.519365	−	0.295146i
$67$	560.099			1.02130			0.510649	−	0.859789i	$-0.329405\pi$
$67$	560.099			1.02130			0.510649	+	0.859789i	$0.329405\pi$
$68$	370.762			0.661199
$69$	−111.670	+	196.505i	−0.194833	+	0.342846i
$70$		0			0
$71$		−	74.2161i		−	0.124054i	−0.998074	−	0.0620270i	$-0.980244\pi$
$71$		−	74.2161i		−	0.124054i	0.998074	−	0.0620270i	$-0.0197565\pi$
$72$	−185.569	+	110.544i	−0.303744	+	0.180941i
$73$			163.285i			0.261796i	0.991396	+	0.130898i	$0.0417860\pi$
$73$			163.285i			0.261796i	−0.991396	+	0.130898i	$0.958214\pi$
$74$			766.987i			1.20487i
$75$	−62.3429	−	35.4283i	−0.0959832	−	0.0545455i
$76$		−	549.180i		−	0.828884i
$77$		0			0
$78$	179.260	+	101.870i	0.260221	+	0.147879i
$79$	874.320			1.24517			0.622586	−	0.782551i	$-0.286082\pi$
$79$	874.320			1.24517			0.622586	+	0.782551i	$0.286082\pi$
$80$	−168.722			−0.235797
$81$	−347.123	+	641.051i	−0.476163	+	0.879357i
$82$		−	215.774i		−	0.290588i
$83$	406.600			0.537712			0.268856	−	0.963180i	$-0.413354\pi$
$83$	406.600			0.537712			0.268856	+	0.963180i	$0.413354\pi$
$84$		0			0
$85$	977.435			1.24727
$86$			570.961i			0.715910i
$87$	−344.834	+	606.801i	−0.424943	+	0.747769i
$88$	246.569			0.298685
$89$	−1052.18			−1.25316			−0.626579	−	0.779358i	$-0.715545\pi$
$89$	−1052.18			−1.25316			−0.626579	+	0.779358i	$0.715545\pi$
$90$	−489.214	+	291.427i	−0.572974	+	0.341323i
$91$		0			0
$92$		−	173.989i		−	0.197170i
$93$	−429.736	+	756.203i	−0.479157	+	0.843167i
$94$			483.625i			0.530661i
$95$		−	1447.79i		−	1.56359i
$96$	82.1533	−	144.564i	0.0873410	−	0.153693i
$97$		−	243.235i		−	0.254606i	−0.991864	−	0.127303i	$-0.959368\pi$
$97$		−	243.235i		−	0.254606i	0.991864	−	0.127303i	$-0.0406320\pi$
$98$		0			0
$99$	714.930	−	425.887i	0.725790	−	0.432356i
$100$	55.1996			0.0551996
$101$	−212.017			−0.208876			−0.104438	−	0.994531i	$-0.533304\pi$
$101$	−212.017			−0.208876			−0.104438	+	0.994531i	$0.533304\pi$
$102$	−475.927	+	837.484i	−0.461998	+	0.812973i
$103$			857.916i			0.820708i	0.911926	+	0.410354i	$0.134595\pi$
$103$			857.916i			0.820708i	−0.911926	+	0.410354i	$0.865405\pi$
$104$	−158.720			−0.149652
$105$		0			0
$106$	−999.264			−0.915633
$107$		−	2148.16i		−	1.94085i	−0.241407	−	0.970424i	$-0.577609\pi$
$107$		−	2148.16i		−	1.94085i	0.241407	−	0.970424i	$-0.422391\pi$
$108$	−11.4948	−	561.067i	−0.0102415	−	0.499895i
$109$	−1243.02			−1.09229			−0.546145	−	0.837690i	$-0.683905\pi$
$109$	−1243.02			−1.09229			−0.546145	+	0.837690i	$0.683905\pi$
$110$	650.025			0.563432
$111$	−1732.48	−	984.539i	−1.48144	−	0.841877i
$112$		0			0
$113$		−	193.701i		−	0.161256i	−0.996744	−	0.0806278i	$-0.974307\pi$
$113$		−	193.701i		−	0.161256i	0.996744	−	0.0806278i	$-0.0256925\pi$
$114$	1240.50	+	704.951i	1.01915	+	0.579164i
$115$		−	458.685i		−	0.371936i
$116$		−	537.273i		−	0.430039i
$117$	−460.213	+	274.151i	−0.363647	+	0.216626i
$118$		−	1464.85i		−	1.14280i
$119$		0			0
$120$	216.580	−	381.113i	0.164758	−	0.289922i
$121$	381.062			0.286297
$122$	612.470			0.454511
$123$	487.394	+	276.977i	0.357291	+	0.203042i
$124$		−	669.556i		−	0.484903i
$125$	1463.67			1.04731
$126$		0			0
$127$	1010.51			0.706052			0.353026	−	0.935614i	$-0.385153\pi$
$127$	1010.51			0.706052			0.353026	+	0.935614i	$0.385153\pi$
$128$			128.000i			0.0883883i
$129$	−1289.70	−	732.910i	−0.880243	−	0.500226i
$130$	−418.432			−0.282300
$131$	358.628			0.239187			0.119593	−	0.992823i	$-0.461841\pi$
$131$	358.628			0.239187			0.119593	+	0.992823i	$0.461841\pi$
$132$	−316.506	+	556.953i	−0.208700	+	0.367247i
$133$		0			0
$134$		−	1120.20i		−	0.722167i
$135$	−30.3035	−	1479.13i	−0.0193193	−	0.942989i
$136$		−	741.524i		−	0.467538i
$137$		−	1378.76i		−	0.859818i	−0.902872	−	0.429909i	$-0.858546\pi$
$137$		−	1378.76i		−	0.859818i	0.902872	−	0.429909i	$-0.141454\pi$
$138$	393.009	+	223.340i	0.242429	+	0.137768i
$139$			474.488i			0.289536i	0.989466	+	0.144768i	$0.0462436\pi$
$139$			474.488i			0.289536i	−0.989466	+	0.144768i	$0.953756\pi$
$140$		0			0
$141$	−1092.42	−	620.803i	−0.652471	−	0.370787i
$142$	−148.432			−0.0877194
$143$	611.491			0.357591
$144$	221.089	+	371.138i	0.127945	+	0.214779i
$145$		−	1416.41i		−	0.811215i
$146$	326.570			0.185117
$147$		0			0
$148$	1533.97			0.851972
$149$			599.434i			0.329581i	0.986329	+	0.164791i	$0.0526948\pi$
$149$			599.434i			0.329581i	−0.986329	+	0.164791i	$0.947305\pi$
$150$	−70.8567	+	124.686i	−0.0385695	+	0.0678704i
$151$	−1995.18			−1.07527			−0.537633	−	0.843179i	$-0.680681\pi$
$151$	−1995.18			−1.07527			−0.537633	+	0.843179i	$0.680681\pi$
$152$	−1098.36			−0.586110
$153$	−1280.80	−	2150.06i	−0.676776	−	1.13609i
$154$		0			0
$155$		−	1765.14i		−	0.914707i
$156$	203.741	−	358.520i	0.104566	−	0.184004i
$157$		−	884.461i		−	0.449603i	−0.974405	−	0.224802i	$-0.927827\pi$
$157$		−	884.461i		−	0.449603i	0.974405	−	0.224802i	$-0.0721734\pi$
$158$		−	1748.64i		−	0.880470i
$159$	1282.70	−	2257.16i	0.639778	−	1.12581i
$160$			337.445i			0.166733i
$161$		0			0
$162$	1282.10	+	694.246i	0.621799	+	0.336698i
$163$	−676.984			−0.325310			−0.162655	−	0.986683i	$-0.552006\pi$
$163$	−676.984			−0.325310			−0.162655	+	0.986683i	$0.552006\pi$
$164$	−431.548			−0.205477
$165$	−834.401	+	1468.29i	−0.393685	+	0.692764i
$166$		−	813.199i		−	0.380220i
$167$	−3718.74			−1.72314			−0.861571	−	0.507637i	$-0.830519\pi$
$167$	−3718.74			−1.72314			−0.861571	+	0.507637i	$0.830519\pi$
$168$		0			0
$169$	1803.37			0.820834
$170$		−	1954.87i		−	0.881951i
$171$	−3184.71	+	1897.15i	−1.42422	+	0.848413i
$172$	1141.92			0.506225
$173$	−2637.94			−1.15930			−0.579650	−	0.814865i	$-0.696811\pi$
$173$	−2637.94			−1.15930			−0.579650	+	0.814865i	$0.696811\pi$
$174$	1213.60	+	689.668i	0.528753	+	0.300480i
$175$		0			0
$176$		−	493.137i		−	0.211202i
$177$	3308.83	+	1880.35i	1.40512	+	0.798506i
$178$			2104.36i			0.886116i
$179$			3304.24i			1.37972i	0.723941	+	0.689862i	$0.242329\pi$
$179$			3304.24i			1.37972i	−0.723941	+	0.689862i	$0.757671\pi$
$180$	582.854	+	978.427i	0.241352	+	0.405154i
$181$		−	417.941i		−	0.171631i	−0.996311	−	0.0858157i	$-0.972650\pi$
$181$		−	417.941i		−	0.171631i	0.996311	−	0.0858157i	$-0.0273496\pi$
$182$		0			0
$183$	−786.193	+	1383.46i	−0.317580	+	0.558842i
$184$	−347.978			−0.139420
$185$	4044.00			1.60714
$186$	1512.41	+	859.472i	0.596209	+	0.338815i
$187$			2856.82i			1.11717i
$188$	967.250			0.375234
$189$		0			0
$190$	−2895.59			−1.10562
$191$			1062.89i			0.402661i	0.979523	+	0.201331i	$0.0645266\pi$
$191$			1062.89i			0.402661i	−0.979523	+	0.201331i	$0.935473\pi$
$192$	−289.129	−	164.307i	−0.108677	−	0.0617594i
$193$	3890.05			1.45084			0.725420	−	0.688306i	$-0.241645\pi$
$193$	3890.05			1.45084			0.725420	+	0.688306i	$0.241645\pi$
$194$	−486.470			−0.180033
$195$	537.118	−	945.162i	0.197250	−	0.347100i
$196$		0			0
$197$			3227.57i			1.16728i	0.812011	+	0.583642i	$0.198373\pi$
$197$			3227.57i			1.16728i	−0.812011	+	0.583642i	$0.801627\pi$
$198$	−851.774	−	1429.86i	−0.305722	−	0.513211i
$199$		−	2769.87i		−	0.986688i	−0.869834	−	0.493344i	$-0.835774\pi$
$199$		−	2769.87i		−	0.986688i	0.869834	−	0.493344i	$-0.164226\pi$
$200$		−	110.399i		−	0.0390320i
$201$	2530.32	+	1437.94i	0.887936	+	0.504598i
$202$			424.034i			0.147698i
$203$		0			0
$204$	1674.97	+	951.854i	0.574859	+	0.326682i
$205$	−1137.68			−0.387606
$206$	1715.83			0.580328
$207$	−1008.97	+	601.047i	−0.338784	+	0.201815i
$208$			317.441i			0.105820i
$209$	4231.58			1.40050
$210$		0			0
$211$	−1978.76			−0.645610			−0.322805	−	0.946465i	$-0.604626\pi$
$211$	−1978.76			−0.645610			−0.322805	+	0.946465i	$0.604626\pi$
$212$			1998.53i			0.647451i
$213$	190.534	−	335.281i	0.0612919	−	0.107855i
$214$	−4296.33			−1.37239
$215$	3010.43			0.954929
$216$	−1122.13	+	22.9895i	−0.353479	+	0.00724185i
$217$		0			0
$218$			2486.04i			0.772366i
$219$	−419.200	+	737.663i	−0.129347	+	0.227610i
$220$		−	1300.05i		−	0.398406i
$221$		−	1838.98i		−	0.559744i
$222$	−1969.08	+	3464.97i	−0.595297	+	1.04754i
$223$			2434.70i			0.731120i	0.930788	+	0.365560i	$0.119122\pi$
$223$			2434.70i			0.731120i	−0.930788	+	0.365560i	$0.880878\pi$
$224$		0			0
$225$	−190.688	−	320.105i	−0.0565001	−	0.0948458i
$226$	−387.402			−0.114025
$227$	−331.723			−0.0969922			−0.0484961	−	0.998823i	$-0.515443\pi$
$227$	−331.723			−0.0969922			−0.0484961	+	0.998823i	$0.515443\pi$
$228$	1409.90	−	2480.99i	0.409531	−	0.720648i
$229$		−	2127.29i		−	0.613866i	−0.951731	−	0.306933i	$-0.900697\pi$
$229$		−	2127.29i		−	0.613866i	0.951731	−	0.306933i	$-0.0993028\pi$
$230$	−917.370			−0.262998
$231$		0			0
$232$	−1074.55			−0.304084
$233$			934.608i			0.262782i	0.991331	+	0.131391i	$0.0419443\pi$
$233$			934.608i			0.262782i	−0.991331	+	0.131391i	$0.958056\pi$
$234$	548.302	+	920.425i	0.153178	+	0.257137i
$235$	2549.95			0.707831
$236$	−2929.70			−0.808081
$237$	3949.86	+	2244.63i	1.08258	+	0.615209i
$238$		0			0
$239$		−	1923.73i		−	0.520651i	−0.965521	−	0.260325i	$-0.916170\pi$
$239$		−	1923.73i		−	0.520651i	0.965521	−	0.260325i	$-0.0838298\pi$
$240$	−762.226	−	433.159i	−0.205006	−	0.116501i
$241$			3286.43i			0.878414i	0.898386	+	0.439207i	$0.144741\pi$
$241$			3286.43i			0.878414i	−0.898386	+	0.439207i	$0.855259\pi$
$242$		−	762.124i		−	0.202443i
$243$	−3213.94	+	2004.87i	−0.848454	+	0.529270i
$244$		−	1224.94i		−	0.321388i
$245$		0			0
$246$	553.954	−	974.788i	0.143572	−	0.252643i
$247$	−2723.94			−0.701700
$248$	−1339.11			−0.342878
$249$	1836.87	+	1043.86i	0.467497	+	0.265670i
$250$		−	2927.33i		−	0.740563i
$251$	4303.94			1.08232			0.541160	−	0.840919i	$-0.317985\pi$
$251$	4303.94			1.08232			0.541160	+	0.840919i	$0.317985\pi$
$252$		0			0
$253$	1340.63			0.333142
$254$		−	2021.03i		−	0.499254i
$255$	4415.70	+	2509.36i	1.08440	+	0.616244i
$256$	256.000			0.0625000
$257$	4691.91			1.13881			0.569403	−	0.822058i	$-0.307174\pi$
$257$	4691.91			1.13881			0.569403	+	0.822058i	$0.307174\pi$
$258$	−1465.82	+	2579.39i	−0.353713	+	0.622426i
$259$		0			0
$260$			836.865i			0.199616i
$261$	−3115.67	+	1856.02i	−0.738908	+	0.440171i
$262$		−	717.256i		−	0.169131i
$263$			1052.99i			0.246883i	0.992352	+	0.123442i	$0.0393932\pi$
$263$			1052.99i			0.246883i	−0.992352	+	0.123442i	$0.960607\pi$
$264$	1113.91	+	633.013i	0.259683	+	0.147573i
$265$			5268.69i			1.22133i
$266$		0			0
$267$	−4753.37	−	2701.25i	−1.08952	−	0.619154i
$268$	−2240.40			−0.510649
$269$	−2654.98			−0.601773			−0.300887	−	0.953660i	$-0.597283\pi$
$269$	−2654.98			−0.601773			−0.300887	+	0.953660i	$0.597283\pi$
$270$	−2958.27	+	60.6070i	−0.666794	+	0.0136608i
$271$		−	2710.60i		−	0.607591i	−0.952737	−	0.303795i	$-0.901746\pi$
$271$		−	2710.60i		−	0.607591i	0.952737	−	0.303795i	$-0.0982539\pi$
$272$	−1483.05			−0.330599
$273$		0			0
$274$	−2757.51			−0.607983
$275$			425.328i			0.0932663i
$276$	446.680	−	786.019i	0.0974166	−	0.171423i
$277$	1920.44			0.416563			0.208281	−	0.978069i	$-0.433213\pi$
$277$	1920.44			0.416563			0.208281	+	0.978069i	$0.433213\pi$
$278$	948.976			0.204733
$279$	−3882.78	+	2312.99i	−0.833176	+	0.496327i
$280$		0			0
$281$			5730.99i			1.21666i	0.793683	+	0.608331i	$0.208161\pi$
$281$			5730.99i			1.21666i	−0.793683	+	0.608331i	$0.791839\pi$
$282$	−1241.61	+	2184.84i	−0.262186	+	0.461367i
$283$		−	1834.53i		−	0.385341i	−0.981264	−	0.192670i	$-0.938285\pi$
$283$		−	1834.53i		−	0.385341i	0.981264	−	0.192670i	$-0.0617148\pi$
$284$			296.864i			0.0620270i
$285$	3716.91	−	6540.61i	0.772528	−	1.35941i
$286$		−	1222.98i		−	0.252855i
$287$		0			0
$288$	742.277	−	442.178i	0.151872	−	0.0904707i
$289$	3678.54			0.748735
$290$	−2832.81			−0.573615
$291$	624.454	−	1098.85i	0.125794	−	0.221359i
$292$		−	653.141i		−	0.130898i
$293$	−1206.83			−0.240627			−0.120314	−	0.992736i	$-0.538390\pi$
$293$	−1206.83			−0.240627			−0.120314	+	0.992736i	$0.538390\pi$
$294$		0			0
$295$	−7723.53			−1.52434
$296$		−	3067.95i		−	0.602435i
$297$	4323.17	−	88.5703i	0.844632	−	0.0173043i
$298$	1198.87			0.233049
$299$	−862.987			−0.166916
$300$	249.372	+	141.713i	0.0479916	+	0.0272728i
$301$		0			0
$302$			3990.35i			0.760328i
$303$	−957.815	−	544.309i	−0.181601	−	0.103200i
$304$			2196.72i			0.414442i
$305$		−	3229.29i		−	0.606258i
$306$	−4300.13	+	2561.61i	−0.803340	+	0.478553i
$307$			5508.71i			1.02410i	0.858955	+	0.512050i	$0.171114\pi$
$307$			5508.71i			1.02410i	−0.858955	+	0.512050i	$0.828886\pi$
$308$		0			0
$309$	−2202.52	+	3875.75i	−0.405491	+	0.713539i
$310$	−3530.28			−0.646796
$311$	−4229.03			−0.771081			−0.385540	−	0.922691i	$-0.625985\pi$
$311$	−4229.03			−0.771081			−0.385540	+	0.922691i	$0.625985\pi$
$312$	−717.041	−	407.481i	−0.130110	−	0.0739393i
$313$			5395.50i			0.974351i	0.873304	+	0.487176i	$0.161973\pi$
$313$			5395.50i			0.974351i	−0.873304	+	0.487176i	$0.838027\pi$
$314$	−1768.92			−0.317917
$315$		0			0
$316$	−3497.28			−0.622586
$317$			7124.01i			1.26222i	0.775693	+	0.631111i	$0.217401\pi$
$317$			7124.01i			1.26222i	−0.775693	+	0.631111i	$0.782599\pi$
$318$	−4514.31	−	2565.40i	−0.796069	−	0.452392i
$319$	4139.83			0.726603
$320$	674.889			0.117898
$321$	5514.96	−	9704.62i	0.958925	−	1.68741i
$322$		0			0
$323$		−	12725.9i		−	2.19223i
$324$	1388.49	−	2564.21i	0.238082	−	0.439679i
$325$		−	273.791i		−	0.0467298i
$326$			1353.97i			0.230029i
$327$	−5615.51	−	3191.19i	−0.949659	−	0.539674i
$328$			863.096i			0.145294i
$329$		0			0
$330$	2936.58	+	1668.80i	0.489858	+	0.278377i
$331$	1772.45			0.294328			0.147164	−	0.989112i	$-0.452985\pi$
$331$	1772.45			0.294328			0.147164	+	0.989112i	$0.452985\pi$
$332$	−1626.40			−0.268856
$333$	−5299.13	−	8895.57i	−0.872044	−	1.46389i
$334$			7437.48i			1.21845i
$335$	−5906.32			−0.963275
$336$		0			0
$337$	7800.94			1.26096			0.630481	−	0.776205i	$-0.282858\pi$
$337$	7800.94			1.26096			0.630481	+	0.776205i	$0.282858\pi$
$338$		−	3606.75i		−	0.580417i
$339$	497.287	−	875.071i	0.0796723	−	0.140199i
$340$	−3909.74			−0.623634
$341$	5159.11			0.819301
$342$	3794.30	+	6369.43i	0.599918	+	1.00707i
$343$		0			0
$344$		−	2283.84i		−	0.357955i
$345$	1177.58	−	2072.17i	0.183764	−	0.323368i
$346$			5275.88i			0.819749i
$347$			7169.97i			1.10923i	0.832106	+	0.554617i	$0.187135\pi$
$347$			7169.97i			1.10923i	−0.832106	+	0.554617i	$0.812865\pi$
$348$	1379.34	−	2427.20i	0.212472	−	0.373885i
$349$		−	5543.44i		−	0.850240i	−0.905137	−	0.425120i	$-0.860232\pi$
$349$		−	5543.44i		−	0.850240i	0.905137	−	0.425120i	$-0.139768\pi$
$350$		0			0
$351$	−2782.90	+	57.0142i	−0.423191	+	0.00867006i
$352$	−986.274			−0.149343
$353$	30.9338			0.00466414			0.00233207	−	0.999997i	$-0.499258\pi$
$353$	30.9338			0.00466414			0.00233207	+	0.999997i	$0.499258\pi$
$354$	3760.69	−	6617.66i	0.564629	−	0.993572i
$355$			782.619i			0.117006i
$356$	4208.72			0.626579
$357$		0			0
$358$	6608.48			0.975612
$359$			6575.26i			0.966655i	0.875440	+	0.483327i	$0.160572\pi$
$359$			6575.26i			0.966655i	−0.875440	+	0.483327i	$0.839428\pi$
$360$	1956.85	−	1165.71i	0.286487	−	0.170662i
$361$	−11990.9			−1.74820
$362$	−835.881			−0.121362
$363$	1721.50	+	978.296i	0.248912	+	0.141452i
$364$		0			0
$365$		−	1721.87i		−	0.246922i
$366$	2766.91	+	1572.39i	0.395161	+	0.224563i
$367$			2419.44i			0.344125i	0.985086	+	0.172062i	$0.0550431\pi$
$367$			2419.44i			0.344125i	−0.985086	+	0.172062i	$0.944957\pi$
$368$			695.956i			0.0985848i
$369$	1490.79	+	2502.56i	0.210318	+	0.353057i
$370$		−	8087.99i		−	1.13642i
$371$		0			0
$372$	1718.94	−	3024.81i	0.239578	−	0.421584i
$373$	9791.32			1.35918			0.679591	−	0.733591i	$-0.262157\pi$
$373$	9791.32			1.35918			0.679591	+	0.733591i	$0.262157\pi$
$374$	5713.64			0.789961
$375$	6612.31	+	3757.65i	0.910555	+	0.517451i
$376$		−	1934.50i		−	0.265330i
$377$	−2664.88			−0.364054
$378$		0			0
$379$	12660.9			1.71595			0.857977	−	0.513689i	$-0.171721\pi$
$379$	12660.9			1.71595			0.857977	+	0.513689i	$0.171721\pi$
$380$			5791.18i			0.781793i
$381$	4565.13	+	2594.28i	0.613855	+	0.348842i
$382$	2125.79			0.284725
$383$	−9098.83			−1.21391			−0.606957	−	0.794735i	$-0.707610\pi$
$383$	−9098.83			−1.21391			−0.606957	+	0.794735i	$0.707610\pi$
$384$	−328.613	+	578.257i	−0.0436705	+	0.0768465i
$385$		0			0
$386$		−	7780.11i		−	1.02590i
$387$	−3944.78	−	6622.04i	−0.518151	−	0.869812i
$388$			972.940i			0.127303i
$389$			9757.22i			1.27175i	0.771792	+	0.635875i	$0.219360\pi$
$389$			9757.22i			1.27175i	−0.771792	+	0.635875i	$0.780640\pi$
$390$	−1890.32	−	1074.24i	−0.245437	−	0.139477i
$391$		−	4031.78i		−	0.521473i
$392$		0			0
$393$	1620.15	+	920.701i	0.207954	+	0.118176i
$394$	6455.14			0.825395
$395$	−9219.83			−1.17443
$396$	−2859.72	+	1703.55i	−0.362895	+	0.216178i
$397$			8162.78i			1.03193i	0.856608	+	0.515967i	$0.172567\pi$
$397$			8162.78i			1.03193i	−0.856608	+	0.515967i	$0.827433\pi$
$398$	−5539.74			−0.697694
$399$		0			0
$400$	−220.798			−0.0275998
$401$		−	10259.8i		−	1.27768i	−0.769341	−	0.638838i	$-0.779415\pi$
$401$		−	10259.8i		−	1.27768i	0.769341	−	0.638838i	$-0.220585\pi$
$402$	2875.87	−	5060.64i	0.356805	−	0.627866i
$403$	−3321.01			−0.410499
$404$	848.068			0.104438
$405$	3660.46	−	6759.98i	0.449111	−	0.829398i
$406$		0			0
$407$			11819.7i			1.43951i
$408$	1903.71	−	3349.94i	0.230999	−	0.406487i
$409$		−	2073.23i		−	0.250647i	−0.992116	−	0.125323i	$-0.960003\pi$
$409$		−	2073.23i		−	0.250647i	0.992116	−	0.125323i	$-0.0399969\pi$
$410$			2275.37i			0.274079i
$411$	3539.67	−	6228.72i	0.424815	−	0.747543i
$412$		−	3431.66i		−	0.410354i
$413$		0			0
$414$	1202.09	+	2017.94i	0.142705	+	0.239556i
$415$	−4287.65			−0.507163
$416$	634.881			0.0748260
$417$	−1218.15	+	2143.56i	−0.143053	+	0.251728i
$418$		−	8463.15i		−	0.990302i
$419$	−11576.2			−1.34973			−0.674863	−	0.737943i	$-0.735797\pi$
$419$	−11576.2			−1.34973			−0.674863	+	0.737943i	$0.735797\pi$
$420$		0			0
$421$	−1493.04			−0.172842			−0.0864208	−	0.996259i	$-0.527543\pi$
$421$	−1493.04			−0.172842			−0.0864208	+	0.996259i	$0.527543\pi$
$422$			3957.53i			0.456515i
$423$	−3341.38	−	5609.12i	−0.384074	−	0.644739i
$424$	3997.06			0.457817
$425$	1279.12			0.145992
$426$	−670.562	−	381.068i	−0.0762649	−	0.0433399i
$427$		0			0
$428$			8592.65i			0.970424i
$429$	2762.49	+	1569.88i	0.310896	+	0.176677i
$430$		−	6020.86i		−	0.675237i
$431$			3873.08i			0.432853i	0.976299	+	0.216427i	$0.0694402\pi$
$431$			3873.08i			0.432853i	−0.976299	+	0.216427i	$0.930560\pi$
$432$	45.9791	+	2244.27i	0.00512076	+	0.249948i
$433$		−	5450.01i		−	0.604875i	−0.953169	−	0.302437i	$-0.902200\pi$
$433$		−	5450.01i		−	0.604875i	0.953169	−	0.302437i	$-0.0978003\pi$
$434$		0			0
$435$	3636.32	−	6398.81i	0.400801	−	0.705286i
$436$	4972.08			0.546145
$437$	−5971.95			−0.653724
$438$	1475.33	+	838.400i	0.160945	+	0.0914619i
$439$			2713.77i			0.295037i	0.989059	+	0.147519i	$0.0471286\pi$
$439$			2713.77i			0.295037i	−0.989059	+	0.147519i	$0.952871\pi$
$440$	−2600.10			−0.281716
$441$		0			0
$442$	−3677.97			−0.395799
$443$		−	11066.3i		−	1.18685i	−0.804890	−	0.593424i	$-0.797776\pi$
$443$		−	11066.3i		−	1.18685i	0.804890	−	0.593424i	$-0.202224\pi$
$444$	6929.94	+	3938.16i	0.740721	+	0.420938i
$445$	11095.4			1.18196
$446$	4869.40			0.516980
$447$	−1538.92	+	2708.03i	−0.162838	+	0.286544i
$448$		0			0
$449$			3599.14i			0.378294i	0.981949	+	0.189147i	$0.0605722\pi$
$449$			3599.14i			0.378294i	−0.981949	+	0.189147i	$0.939428\pi$
$450$	−640.209	+	381.376i	−0.0670661	+	0.0399516i
$451$		−	3325.19i		−	0.347178i
$452$			774.805i			0.0806278i
$453$	−9013.48	−	5122.20i	−0.934857	−	0.531262i
$454$			663.446i			0.0685839i
$455$		0			0
$456$	−4961.99	−	2819.81i	−0.509575	−	0.289582i
$457$	8315.09			0.851123			0.425562	−	0.904929i	$-0.360077\pi$
$457$	8315.09			0.851123			0.425562	+	0.904929i	$0.360077\pi$
$458$	−4254.58			−0.434069
$459$	−266.364	−	13001.4i	−0.0270867	−	1.32212i
$460$			1834.74i			0.185968i
$461$	−5672.08			−0.573048			−0.286524	−	0.958073i	$-0.592500\pi$
$461$	−5672.08			−0.573048			−0.286524	+	0.958073i	$0.592500\pi$
$462$		0			0
$463$	6332.06			0.635585			0.317792	−	0.948160i	$-0.397058\pi$
$463$	6332.06			0.635585			0.317792	+	0.948160i	$0.397058\pi$
$464$			2149.09i			0.215020i
$465$	4531.63	−	7974.27i	0.451934	−	0.795264i
$466$	1869.22			0.185815
$467$	12939.3			1.28214			0.641069	−	0.767484i	$-0.278491\pi$
$467$	12939.3			1.28214			0.641069	+	0.767484i	$0.278491\pi$
$468$	1840.85	−	1096.60i	0.181823	−	0.108313i
$469$		0			0
$470$		−	5099.90i		−	0.500512i
$471$	2270.67	−	3995.67i	0.222138	−	0.390894i
$472$			5859.40i			0.571400i
$473$			8798.81i			0.855327i
$474$	4489.26	−	7899.72i	0.435018	−	0.765498i
$475$		−	1894.66i		−	0.183016i
$476$		0			0
$477$	11589.5	−	6903.94i	1.11247	−	0.662704i
$478$	−3847.45			−0.368156
$479$	2103.98			0.200696			0.100348	−	0.994952i	$-0.468004\pi$
$479$	2103.98			0.200696			0.100348	+	0.994952i	$0.468004\pi$
$480$	−866.318	+	1524.45i	−0.0823788	+	0.144961i
$481$		−	7608.53i		−	0.721245i
$482$	6572.87			0.621132
$483$		0			0
$484$	−1524.25			−0.143149
$485$			2564.95i			0.240141i
$486$	4009.74	+	6427.88i	0.374250	+	0.599947i
$487$	−12592.0			−1.17166			−0.585828	−	0.810436i	$-0.699230\pi$
$487$	−12592.0			−1.17166			−0.585828	+	0.810436i	$0.699230\pi$
$488$	−2449.88			−0.227256
$489$	−3058.37	−	1738.01i	−0.282831	−	0.160727i
$490$		0			0
$491$		−	1372.36i		−	0.126138i	−0.998009	−	0.0630689i	$-0.979911\pi$
$491$		−	1372.36i		−	0.126138i	0.998009	−	0.0630689i	$-0.0200888\pi$
$492$	−1949.58	−	1107.91i	−0.178646	−	0.101521i
$493$		−	12450.0i		−	1.13737i
$494$			5447.87i			0.496177i
$495$	−7539.04	+	4491.04i	−0.684555	+	0.407793i
$496$			2678.23i			0.242451i
$497$		0			0
$498$	2087.72	−	3673.74i	0.187857	−	0.330570i
$499$	−9177.51			−0.823330			−0.411665	−	0.911335i	$-0.635053\pi$
$499$	−9177.51			−0.823330			−0.411665	+	0.911335i	$0.635053\pi$
$500$	−5854.66			−0.523657
$501$	−16799.9	−	9547.08i	−1.49813	−	0.851362i
$502$		−	8607.89i		−	0.765316i
$503$	−1025.01			−0.0908605			−0.0454302	−	0.998968i	$-0.514466\pi$
$503$	−1025.01			−0.0908605			−0.0454302	+	0.998968i	$0.514466\pi$
$504$		0			0
$505$	2235.75			0.197009
$506$		−	2681.26i		−	0.235567i
$507$	8146.98	+	4629.78i	0.713649	+	0.405554i
$508$	−4042.05			−0.353026
$509$	−4617.75			−0.402118			−0.201059	−	0.979579i	$-0.564438\pi$
$509$	−4617.75			−0.402118			−0.201059	+	0.979579i	$0.564438\pi$
$510$	5018.72	−	8831.39i	0.435750	−	0.766785i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$	−19257.9	+	394.543i	−1.65742	+	0.0339562i
$514$		−	9383.82i		−	0.805258i
$515$		−	9046.84i		−	0.774081i
$516$	5158.78	+	2931.64i	0.440122	+	0.250113i
$517$			7452.92i			0.634002i
$518$		0			0
$519$	−11917.3	−	6772.36i	−1.00792	−	0.572781i
$520$	1673.73			0.141150
$521$	12024.8			1.01116			0.505580	−	0.862780i	$-0.331279\pi$
$521$	12024.8			1.01116			0.505580	+	0.862780i	$0.331279\pi$
$522$	3712.04	+	6231.34i	0.311248	+	0.522487i
$523$		−	2361.55i		−	0.197444i	−0.995115	−	0.0987222i	$-0.968524\pi$
$523$		−	2361.55i		−	0.197444i	0.995115	−	0.0987222i	$-0.0314755\pi$
$524$	−1434.51			−0.119593
$525$		0			0
$526$	2105.98			0.174573
$527$		−	15515.4i		−	1.28247i
$528$	1266.03	−	2227.81i	0.104350	−	0.183623i
$529$	10275.0			0.844496
$530$	10537.4			0.863613
$531$	10120.7	+	16989.4i	0.827119	+	1.38847i
$532$		0			0
$533$			2140.48i			0.173949i
$534$	−5402.51	+	9506.74i	−0.437808	+	0.770406i
$535$			22652.7i			1.83058i
$536$			4480.79i			0.361083i
$537$	−8482.95	+	14927.4i	−0.681687	+	1.19956i
$538$			5309.96i			0.425518i
$539$		0			0
$540$	121.214	+	5916.53i	0.00965967	+	0.471494i
$541$	−2958.95			−0.235148			−0.117574	−	0.993064i	$-0.537512\pi$
$541$	−2958.95			−0.235148			−0.117574	+	0.993064i	$0.537512\pi$
$542$	−5421.20			−0.429631
$543$	1072.97	−	1888.10i	0.0847988	−	0.149220i
$544$			2966.10i			0.233769i
$545$	13107.8			1.03023
$546$		0			0
$547$	−8615.33			−0.673427			−0.336714	−	0.941607i	$-0.609315\pi$
$547$	−8615.33			−0.673427			−0.336714	+	0.941607i	$0.609315\pi$
$548$			5515.03i			0.429909i
$549$	−7103.47	+	4231.57i	−0.552220	+	0.328960i
$550$	850.655			0.0659492
$551$	−18441.2			−1.42581
$552$	−1572.04	−	893.360i	−0.121214	−	0.0688839i
$553$		0			0
$554$		−	3840.87i		−	0.294554i
$555$	18269.3	+	10382.1i	1.39728	+	0.794047i
$556$		−	1897.95i		−	0.144768i
$557$		−	23863.0i		−	1.81527i	−0.419760	−	0.907635i	$-0.637886\pi$
$557$		−	23863.0i		−	1.81527i	0.419760	−	0.907635i	$-0.362114\pi$
$558$	4625.98	+	7765.56i	0.350956	+	0.589144i
$559$		−	5663.94i		−	0.428550i
$560$		0			0
$561$	−7334.29	+	12906.1i	−0.551968	+	0.971292i
$562$	11462.0			0.860310
$563$	−11104.2			−0.831236			−0.415618	−	0.909539i	$-0.636435\pi$
$563$	−11104.2			−0.831236			−0.415618	+	0.909539i	$0.636435\pi$
$564$	4369.68	+	2483.21i	0.326236	+	0.185394i
$565$			2042.61i			0.152094i
$566$	−3669.06			−0.272477
$567$		0			0
$568$	593.729			0.0438597
$569$			23261.1i			1.71381i	0.515477	+	0.856903i	$0.327615\pi$
$569$			23261.1i			1.71381i	−0.515477	+	0.856903i	$0.672385\pi$
$570$	−13081.2	−	7433.82i	−0.961249	−	0.546260i
$571$	−3043.09			−0.223029			−0.111514	−	0.993763i	$-0.535570\pi$
$571$	−3043.09			−0.223029			−0.111514	+	0.993763i	$0.535570\pi$
$572$	−2445.97			−0.178795
$573$	−2728.76	+	4801.77i	−0.198945	+	0.350082i
$574$		0			0
$575$		−	600.258i		−	0.0435348i
$576$	−884.355	−	1484.55i	−0.0639725	−	0.107390i
$577$			9896.16i			0.714008i	0.934103	+	0.357004i	$0.116202\pi$
$577$			9896.16i			0.714008i	−0.934103	+	0.357004i	$0.883798\pi$
$578$		−	7357.07i		−	0.529436i
$579$	17573.8	+	9986.90i	1.26139	+	0.716824i
$580$			5665.63i			0.405607i
$581$		0			0
$582$	−2197.69	−	1248.91i	−0.156525	−	0.0889500i
$583$	−15399.2			−1.09394
$584$	−1306.28			−0.0925587
$585$	4853.01	−	2890.96i	0.342987	−	0.204319i
$586$			2413.66i			0.170149i
$587$	−14853.9			−1.04444			−0.522219	−	0.852812i	$-0.674896\pi$
$587$	−14853.9			−1.04444			−0.522219	+	0.852812i	$0.674896\pi$
$588$		0			0
$589$	−22981.7			−1.60771
$590$			15447.1i			1.07787i
$591$	−8286.11	+	14581.0i	−0.576726	+	1.01486i
$592$	−6135.90			−0.425986
$593$	−4144.85			−0.287029			−0.143515	−	0.989648i	$-0.545840\pi$
$593$	−4144.85			−0.287029			−0.143515	+	0.989648i	$0.545840\pi$
$594$	−177.141	−	8646.34i	−0.0122360	−	0.597245i
$595$		0			0
$596$		−	2397.74i		−	0.164791i
$597$	7111.06	−	12513.3i	0.487498	−	0.857846i
$598$			1725.97i			0.118027i
$599$			4978.68i			0.339605i	0.985478	+	0.169802i	$0.0543130\pi$
$599$			4978.68i			0.339605i	−0.985478	+	0.169802i	$0.945687\pi$
$600$	283.427	−	498.743i	0.0192847	−	0.0339352i
$601$			6641.45i			0.450766i	0.974270	+	0.225383i	$0.0723633\pi$
$601$			6641.45i			0.450766i	−0.974270	+	0.225383i	$0.927637\pi$
$602$		0			0
$603$	7739.48	+	12992.1i	0.522680	+	0.877414i
$604$	7980.71			0.537633
$605$	−4018.35			−0.270032
$606$	−1088.62	+	1915.63i	−0.0729737	+	0.128411i
$607$			7688.42i			0.514107i	0.966397	+	0.257054i	$0.0827517\pi$
$607$			7688.42i			0.514107i	−0.966397	+	0.257054i	$0.917248\pi$
$608$	4393.44			0.293055
$609$		0			0
$610$	−6458.58			−0.428689
$611$		−	4797.57i		−	0.317658i
$612$	5123.21	+	8600.26i	0.338388	+	0.568047i
$613$	9416.75			0.620455			0.310227	−	0.950662i	$-0.399595\pi$
$613$	9416.75			0.620455			0.310227	+	0.950662i	$0.399595\pi$
$614$	11017.4			0.724149
$615$	−5139.64	−	2920.76i	−0.336992	−	0.191507i
$616$		0			0
$617$			9209.91i			0.600935i	0.953792	+	0.300468i	$0.0971428\pi$
$617$			9209.91i			0.600935i	−0.953792	+	0.300468i	$0.902857\pi$
$618$	7751.50	+	4405.03i	0.504549	+	0.286726i
$619$		−	10239.1i		−	0.664851i	−0.943130	−	0.332425i	$-0.892133\pi$
$619$		−	10239.1i		−	0.664851i	0.943130	−	0.332425i	$-0.107867\pi$
$620$			7060.57i			0.457354i
$621$	−6101.22	+	124.998i	−0.394257	+	0.00807727i
$622$			8458.05i			0.545236i
$623$		0			0
$624$	−814.962	+	1434.08i	−0.0522830	+	0.0920019i
$625$	−13709.6			−0.877413
$626$	10791.0			0.688970
$627$	19116.7	+	10863.7i	1.21762	+	0.691951i
$628$			3537.85i			0.224802i
$629$	35546.2			2.25329
$630$		0			0
$631$	−25041.7			−1.57987			−0.789934	−	0.613192i	$-0.789885\pi$
$631$	−25041.7			−1.57987			−0.789934	+	0.613192i	$0.789885\pi$
$632$			6994.56i			0.440235i
$633$	−8939.33	−	5080.06i	−0.561306	−	0.318980i
$634$	14248.0			0.892525
$635$	−10656.0			−0.665938
$636$	−5130.80	+	9028.62i	−0.319889	+	0.562906i
$637$		0			0
$638$		−	8279.67i		−	0.513786i
$639$	1721.53	−	1025.52i	0.106577	−	0.0634883i
$640$		−	1349.78i		−	0.0833667i
$641$			629.415i			0.0387837i	0.999812	+	0.0193919i	$0.00617301\pi$
$641$			629.415i			0.0387837i	−0.999812	+	0.0193919i	$0.993827\pi$
$642$	−19409.2	−	11029.9i	−1.19318	−	0.678062i
$643$			11568.9i			0.709538i	0.934954	+	0.354769i	$0.115441\pi$
$643$			11568.9i			0.709538i	−0.934954	+	0.354769i	$0.884559\pi$
$644$		0			0
$645$	13600.0	+	7728.65i	0.830234	+	0.471807i
$646$	−25451.9			−1.55014
$647$	19569.2			1.18909			0.594547	−	0.804061i	$-0.297332\pi$
$647$	19569.2			1.18909			0.594547	+	0.804061i	$0.297332\pi$
$648$	−5128.41	−	2776.98i	−0.310900	−	0.168349i
$649$		−	22574.1i		−	1.36535i
$650$	−547.581			−0.0330429
$651$		0			0
$652$	2707.94			0.162655
$653$			6736.86i			0.403727i	0.979414	+	0.201863i	$0.0646997\pi$
$653$			6736.86i			0.403727i	−0.979414	+	0.201863i	$0.935300\pi$
$654$	−6382.38	+	11231.0i	−0.381607	+	0.671510i
$655$	−3781.78			−0.225598
$656$	1726.19			0.102739
$657$	−3787.59	+	2256.28i	−0.224913	+	0.133982i
$658$		0			0
$659$		−	3912.25i		−	0.231259i	−0.993292	−	0.115629i	$-0.963112\pi$
$659$		−	3912.25i		−	0.231259i	0.993292	−	0.115629i	$-0.0368885\pi$
$660$	3337.61	−	5873.15i	0.196843	−	0.346382i
$661$			27714.9i			1.63084i	0.578870	+	0.815420i	$0.303494\pi$
$661$			27714.9i			1.63084i	−0.578870	+	0.815420i	$0.696506\pi$
$662$		−	3544.90i		−	0.208121i
$663$	4721.20	−	8307.86i	0.276556	−	0.486652i
$664$			3252.80i			0.190110i
$665$		0			0
$666$	−17791.1	+	10598.3i	−1.03512	+	0.616629i
$667$	−5842.48			−0.339163
$668$	14875.0			0.861571
$669$	−6250.58	+	10999.1i	−0.361228	+	0.635650i
$670$			11812.6i			0.681138i
$671$	9438.48			0.543023
$672$		0			0
$673$	27462.5			1.57296			0.786479	−	0.617617i	$-0.211902\pi$
$673$	27462.5			1.57296			0.786479	+	0.617617i	$0.211902\pi$
$674$		−	15601.9i		−	0.891635i
$675$	−39.6567	−	1935.67i	−0.00226131	−	0.110376i
$676$	−7213.49			−0.410417
$677$	9514.36			0.540128			0.270064	−	0.962842i	$-0.412955\pi$
$677$	9514.36			0.540128			0.270064	+	0.962842i	$0.412955\pi$
$678$	−1750.14	−	994.574i	−0.0991354	−	0.0563369i
$679$		0			0
$680$			7819.48i			0.440976i
$681$	−1498.60	−	851.629i	−0.0843269	−	0.0479214i
$682$		−	10318.2i		−	0.579333i
$683$		−	26281.4i		−	1.47237i	−0.676779	−	0.736186i	$-0.736625\pi$
$683$		−	26281.4i		−	1.47237i	0.676779	−	0.736186i	$-0.263375\pi$
$684$	12738.9	−	7588.59i	0.712108	−	0.424206i
$685$			14539.2i			0.810969i
$686$		0			0
$687$	5461.37	−	9610.33i	0.303296	−	0.533707i
$688$	−4567.68			−0.253112
$689$	9912.73			0.548106
$690$	−4144.34	−	2355.15i	−0.228656	−	0.129941i
$691$			7734.58i			0.425814i	0.977073	+	0.212907i	$0.0682931\pi$
$691$			7734.58i			0.425814i	−0.977073	+	0.212907i	$0.931707\pi$
$692$	10551.8			0.579650
$693$		0			0
$694$	14339.9			0.784347
$695$		−	5003.55i		−	0.273087i
$696$	−4854.41	−	2758.67i	−0.264376	−	0.150240i
$697$	−10000.1			−0.543445
$698$	−11086.9			−0.601210
$699$	−2399.41	+	4222.22i	−0.129834	+	0.228468i
$700$		0			0
$701$		−	16405.7i		−	0.883929i	−0.897033	−	0.441964i	$-0.854282\pi$
$701$		−	16405.7i		−	0.883929i	0.897033	−	0.441964i	$-0.145718\pi$
$702$	114.028	+	5565.79i	0.00613066	+	0.299241i
$703$		−	52651.7i		−	2.82475i
$704$			1972.55i			0.105601i
$705$	11519.7	+	6546.45i	0.615402	+	0.349722i
$706$		−	61.8677i		−	0.00329805i
$707$		0			0
$708$	−13235.3	−	7521.39i	−0.702562	−	0.399253i
$709$	−10609.4			−0.561982			−0.280991	−	0.959710i	$-0.590663\pi$
$709$	−10609.4			−0.561982			−0.280991	+	0.959710i	$0.590663\pi$
$710$	1565.24			0.0827357
$711$	12081.4	+	20280.9i	0.637254	+	1.06975i
$712$		−	8417.45i		−	0.443058i
$713$	−7280.97			−0.382432
$714$		0			0
$715$	−6448.26			−0.337275
$716$		−	13217.0i		−	0.689862i
$717$	4938.76	−	8690.69i	0.257240	−	0.452664i
$718$	13150.5			0.683528
$719$	20150.5			1.04518			0.522591	−	0.852584i	$-0.324966\pi$
$719$	20150.5			1.04518			0.522591	+	0.852584i	$0.324966\pi$
$720$	−2331.41	−	3913.71i	−0.120676	−	0.202577i
$721$		0			0
$722$			23981.8i			1.23616i
$723$	−8437.22	+	14846.9i	−0.434002	+	0.763710i
$724$			1671.76i			0.0858157i
$725$		−	1853.58i		−	0.0949520i
$726$	1956.59	−	3443.00i	0.100022	−	0.176008i
$727$		−	26758.5i		−	1.36509i	−0.730846	−	0.682543i	$-0.760874\pi$
$727$		−	26758.5i		−	1.36509i	0.730846	−	0.682543i	$-0.239126\pi$
$728$		0			0
$729$	−19666.5	+	806.167i	−0.999161	+	0.0409575i
$730$	−3443.73			−0.174600
$731$	26461.3			1.33886
$732$	3144.77	−	5533.83i	0.158790	−	0.279421i
$733$		−	8205.75i		−	0.413488i	−0.978395	−	0.206744i	$-0.933713\pi$
$733$		−	8205.75i		−	0.413488i	0.978395	−	0.206744i	$-0.0662866\pi$
$734$	4838.88			0.243333
$735$		0			0
$736$	1391.91			0.0697100
$737$		−	17262.8i		−	0.862802i
$738$	5005.13	−	2981.58i	0.249649	−	0.148717i
$739$	−20649.7			−1.02789			−0.513946	−	0.857823i	$-0.671817\pi$
$739$	−20649.7			−1.02789			−0.513946	+	0.857823i	$0.671817\pi$
$740$	−16176.0			−0.803569
$741$	−12305.8	−	6993.13i	−0.610072	−	0.346693i
$742$		0			0
$743$			8375.29i			0.413539i	0.978390	+	0.206769i	$0.0662950\pi$
$743$			8375.29i			0.413539i	−0.978390	+	0.206769i	$0.933705\pi$
$744$	−6049.62	−	3437.89i	−0.298105	−	0.169407i
$745$		−	6321.12i		−	0.310856i
$746$		−	19582.6i		−	0.961087i
$747$	5618.41	+	9431.55i	0.275190	+	0.461957i
$748$		−	11427.3i		−	0.558587i
$749$		0			0
$750$	7515.30	−	13224.6i	0.365893	−	0.643859i
$751$	26597.7			1.29236			0.646181	−	0.763185i	$-0.276365\pi$
$751$	26597.7			1.29236			0.646181	+	0.763185i	$0.276365\pi$
$752$	−3869.00			−0.187617
$753$	19443.6	+	11049.5i	0.940991	+	0.534748i
$754$			5329.76i			0.257425i
$755$	21039.4			1.01418
$756$		0			0
$757$	−26633.6			−1.27875			−0.639376	−	0.768894i	$-0.720807\pi$
$757$	−26633.6			−1.27875			−0.639376	+	0.768894i	$0.720807\pi$
$758$		−	25321.8i		−	1.21336i
$759$	6056.49	+	3441.79i	0.289640	+	0.164597i
$760$	11582.4			0.552811
$761$	8487.74			0.404311			0.202155	−	0.979353i	$-0.435205\pi$
$761$	8487.74			0.404311			0.202155	+	0.979353i	$0.435205\pi$
$762$	5188.56	−	9130.26i	0.246669	−	0.434061i
$763$		0			0
$764$		−	4251.58i		−	0.201331i
$765$	13506.3	+	22672.7i	0.638326	+	1.07155i
$766$			18197.7i			0.858366i
$767$			14531.3i			0.684089i
$768$	1156.51	+	657.226i	0.0543387	+	0.0308797i
$769$			22673.5i			1.06324i	0.846984	+	0.531618i	$0.178416\pi$
$769$			22673.5i			1.06324i	−0.846984	+	0.531618i	$0.821584\pi$
$770$		0			0
$771$	21196.3	+	12045.5i	0.990100	+	0.562656i
$772$	−15560.2			−0.725420
$773$	−36282.3			−1.68821			−0.844103	−	0.536180i	$-0.819867\pi$
$773$	−36282.3			−1.68821			−0.844103	+	0.536180i	$0.819867\pi$
$774$	−13244.1	+	7889.56i	−0.615050	+	0.366388i
$775$		−	2309.95i		−	0.107066i
$776$	1945.88			0.0900167
$777$		0			0
$778$	19514.4			0.899263
$779$			14812.3i			0.681267i
$780$	−2148.47	+	3780.65i	−0.0986252	+	0.173550i
$781$	−2287.42			−0.104802
$782$	−8063.57			−0.368737
$783$	−18840.4	+	385.990i	−0.859898	+	0.0176170i
$784$		0			0
$785$			9326.77i			0.424060i
$786$	1841.40	−	3240.30i	0.0835632	−	0.147045i
$787$		−	2207.14i		−	0.0999698i	−0.998750	−	0.0499849i	$-0.984083\pi$
$787$		−	2207.14i		−	0.0999698i	0.998750	−	0.0499849i	$-0.0159173\pi$
$788$		−	12910.3i		−	0.583642i
$789$	−2703.33	+	4757.03i	−0.121979	+	0.214645i
$790$			18439.7i			0.830448i
$791$		0			0
$792$	3407.10	+	5719.44i	0.152861	+	0.256605i
$793$	−6075.71			−0.272074
$794$	16325.6			0.729688
$795$	−13526.3	+	23802.0i	−0.603430	+	1.06185i
$796$			11079.5i			0.493344i
$797$	−43496.3			−1.93315			−0.966574	−	0.256388i	$-0.917467\pi$
$797$	−43496.3			−1.93315			−0.966574	+	0.256388i	$0.917467\pi$
$798$		0			0
$799$	22413.7			0.992417
$800$			441.597i			0.0195160i
$801$	−14539.1	−	24406.6i	−0.641340	−	1.07661i
$802$	−20519.5			−0.903453
$803$	5032.62			0.221167
$804$	−10121.3	−	5751.74i	−0.443968	−	0.252299i
$805$		0			0
$806$			6642.01i			0.290267i
$807$	−11994.2	−	6816.10i	−0.523193	−	0.297321i
$808$		−	1696.14i		−	0.0738488i
$809$			26739.1i			1.16205i	0.813887	+	0.581024i	$0.197348\pi$
$809$			26739.1i			1.16205i	−0.813887	+	0.581024i	$0.802652\pi$
$810$	−13520.0	−	7320.92i	−0.586473	−	0.317569i
$811$		−	43614.5i		−	1.88842i	−0.329338	−	0.944212i	$-0.606826\pi$
$811$		−	43614.5i		−	1.88842i	0.329338	−	0.944212i	$-0.393174\pi$
$812$		0			0
$813$	6958.89	−	12245.5i	0.300195	−	0.528251i
$814$	23639.4			1.01789
$815$	7138.90			0.306828
$816$	−6699.87	−	3807.41i	−0.287429	−	0.163341i
$817$		−	39195.0i		−	1.67841i
$818$	−4146.46			−0.177234
$819$		0			0
$820$	4550.74			0.193803
$821$		−	3694.69i		−	0.157059i	−0.996912	−	0.0785297i	$-0.974977\pi$
$821$		−	3694.69i		−	0.157059i	0.996912	−	0.0785297i	$-0.0250225\pi$
$822$	−12457.4	−	7079.33i	−0.528592	−	0.300389i
$823$	17467.4			0.739824			0.369912	−	0.929067i	$-0.379388\pi$
$823$	17467.4			0.739824			0.369912	+	0.929067i	$0.379388\pi$
$824$	−6863.32			−0.290164
$825$	−1091.94	+	1921.48i	−0.0460805	+	0.0810875i
$826$		0			0
$827$		−	37321.1i		−	1.56926i	−0.619962	−	0.784632i	$-0.712852\pi$
$827$		−	37321.1i		−	1.56926i	0.619962	−	0.784632i	$-0.287148\pi$
$828$	4035.88	−	2404.19i	0.169392	−	0.100907i
$829$			45843.2i			1.92063i	0.278924	+	0.960313i	$0.410022\pi$
$829$			45843.2i			1.92063i	−0.278924	+	0.960313i	$0.589978\pi$
$830$			8575.30i			0.358618i
$831$	8675.83	+	4930.32i	0.362168	+	0.205813i
$832$		−	1269.76i		−	0.0529100i
$833$		0			0
$834$	4287.13	+	2436.30i	0.177999	+	0.101154i
$835$	39214.7			1.62524
$836$	−16926.3			−0.700249
$837$	−23479.1	+	481.025i	−0.969602	+	0.0198646i
$838$			23152.4i			0.954401i
$839$	11522.6			0.474141			0.237071	−	0.971492i	$-0.423813\pi$
$839$	11522.6			0.474141			0.237071	+	0.971492i	$0.423813\pi$
$840$		0			0
$841$	6347.59			0.260264
$842$			2986.08i			0.122217i
$843$	−14713.1	+	25890.5i	−0.601122	+	1.05779i
$844$	7915.06			0.322805
$845$	−19016.8			−0.774200
$846$	−11218.2	+	6682.76i	−0.455900	+	0.271581i
$847$		0			0
$848$		−	7994.12i		−	0.323725i
$849$	4709.77	−	8287.74i	0.190387	−	0.335023i
$850$		−	2558.24i		−	0.103232i
$851$		−	16680.9i		−	0.671932i
$852$	−762.136	+	1341.12i	−0.0306460	+	0.0539274i
$853$		−	44074.7i		−	1.76915i	−0.466395	−	0.884577i	$-0.654447\pi$
$853$		−	44074.7i		−	1.76915i	0.466395	−	0.884577i	$-0.345553\pi$
$854$		0			0
$855$	33583.3	−	20005.7i	1.34330	−	0.800211i
$856$	17185.3			0.686193
$857$	16075.2			0.640746			0.320373	−	0.947292i	$-0.396192\pi$
$857$	16075.2			0.640746			0.320373	+	0.947292i	$0.396192\pi$
$858$	3139.75	−	5524.99i	0.124929	−	0.219837i
$859$		−	19245.0i		−	0.764415i	−0.924077	−	0.382207i	$-0.875164\pi$
$859$		−	19245.0i		−	0.764415i	0.924077	−	0.382207i	$-0.124836\pi$
$860$	−12041.7			−0.477464
$861$		0			0
$862$	7746.16			0.306073
$863$			11660.7i			0.459948i	0.973197	+	0.229974i	$0.0738641\pi$
$863$			11660.7i			0.459948i	−0.973197	+	0.229974i	$0.926136\pi$
$864$	4488.53	−	91.9582i	0.176740	−	0.00362093i
$865$	27817.5			1.09344
$866$	−10900.0			−0.427711
$867$	16618.3	+	9443.87i	0.650965	+	0.369931i
$868$		0			0
$869$		−	26947.5i		−	1.05193i
$870$	−12797.6	−	7272.65i	−0.498712	−	0.283409i
$871$			11112.4i			0.432295i
$872$		−	9944.16i		−	0.386183i
$873$	5642.11	−	3361.03i	0.218736	−	0.130302i
$874$			11943.9i			0.462252i
$875$		0			0
$876$	1676.80	−	2950.65i	0.0646733	−	0.113805i
$877$	37827.9			1.45651			0.728254	−	0.685308i	$-0.240332\pi$
$877$	37827.9			1.45651			0.728254	+	0.685308i	$0.240332\pi$
$878$	5427.54			0.208623
$879$	−5452.02	−	3098.28i	−0.209206	−	0.118888i
$880$			5200.20i			0.199203i
$881$	26234.8			1.00326			0.501631	−	0.865082i	$-0.332734\pi$
$881$	26234.8			1.00326			0.501631	+	0.865082i	$0.332734\pi$
$882$		0			0
$883$	−6803.07			−0.259277			−0.129639	−	0.991561i	$-0.541382\pi$
$883$	−6803.07			−0.259277			−0.129639	+	0.991561i	$0.541382\pi$
$884$			7355.94i			0.279872i
$885$	−34892.1	−	19828.5i	−1.32529	−	0.753140i
$886$	−22132.5			−0.839228
$887$	−12230.0			−0.462959			−0.231480	−	0.972840i	$-0.574357\pi$
$887$	−12230.0			−0.462959			−0.231480	+	0.972840i	$0.574357\pi$
$888$	7876.31	−	13859.9i	0.297648	−	0.523769i
$889$		0			0
$890$		−	22190.8i		−	0.835773i
$891$	19757.9	+	10698.7i	0.742889	+	0.402267i
$892$		−	9738.81i		−	0.365560i
$893$		−	33199.6i		−	1.24410i
$894$	5416.05	+	3077.84i	0.202617	+	0.115144i
$895$		−	34843.7i		−	1.30134i
$896$		0			0
$897$	−3898.66	−	2215.54i	−0.145120	−	0.0824690i
$898$	7198.28			0.267494
$899$	−22483.4			−0.834109
$900$	762.751	+	1280.42i	0.0282500	+	0.0474229i
$901$			46311.2i			1.71237i
$902$	−6650.38			−0.245492
$903$		0			0
$904$	1549.61			0.0570125
$905$			4407.25i			0.161880i
$906$	−10244.4	+	18027.0i	−0.375659	+	0.661044i
$907$	−19841.4			−0.726376			−0.363188	−	0.931716i	$-0.618312\pi$
$907$	−19841.4			−0.726376			−0.363188	+	0.931716i	$0.618312\pi$
$908$	1326.89			0.0484961
$909$	−2929.66	−	4917.98i	−0.106898	−	0.179449i
$910$		0			0
$911$			48153.2i			1.75125i	0.482995	+	0.875623i	$0.339549\pi$
$911$			48153.2i			1.75125i	−0.482995	+	0.875623i	$0.660451\pi$
$912$	−5639.61	+	9923.97i	−0.204766	+	0.360324i
$913$		−	12531.8i		−	0.454264i
$914$		−	16630.2i		−	0.601835i
$915$	8290.52	−	14588.8i	0.299537	−	0.527092i
$916$			8509.17i			0.306933i
$917$		0			0
$918$	−26002.8	+	532.728i	−0.934880	+	0.0191532i
$919$	23119.6			0.829863			0.414932	−	0.909853i	$-0.363805\pi$
$919$	23119.6			0.829863			0.414932	+	0.909853i	$0.363805\pi$
$920$	3669.48			0.131499
$921$	−14142.5	+	24886.4i	−0.505983	+	0.890373i
$922$			11344.2i			0.405206i
$923$	1472.45			0.0525095
$924$		0			0
$925$	5292.17			0.188114
$926$		−	12664.1i		−	0.449426i
$927$	−19900.3	+	11854.7i	−0.705084	+	0.420022i
$928$	4298.19			0.152042
$929$	−32002.6			−1.13022			−0.565109	−	0.825016i	$-0.691166\pi$
$929$	−32002.6			−1.13022			−0.565109	+	0.825016i	$0.691166\pi$
$930$	−15948.5	−	9063.26i	−0.562337	−	0.319566i
$931$		0			0
$932$		−	3738.43i		−	0.131391i
$933$	−19105.2	−	10857.1i	−0.670392	−	0.380972i
$934$		−	25878.5i		−	0.906608i
$935$		−	30125.6i		−	1.05370i
$936$	−2193.21	−	3681.70i	−0.0765889	−	0.128569i
$937$		−	22855.6i		−	0.796863i	−0.917198	−	0.398431i	$-0.869555\pi$
$937$		−	22855.6i		−	0.796863i	0.917198	−	0.398431i	$-0.130445\pi$
$938$		0			0
$939$	−13851.8	+	24374.9i	−0.481403	+	0.847120i
$940$	−10199.8			−0.353915
$941$	55407.4			1.91948			0.959739	−	0.280892i	$-0.0906302\pi$
$941$	55407.4			1.91948			0.959739	+	0.280892i	$0.0906302\pi$
$942$	−7991.35	−	4541.34i	−0.276404	−	0.157075i
$943$			4692.79i			0.162055i
$944$	11718.8			0.404041
$945$		0			0
$946$	17597.6			0.604807
$947$		−	6888.63i		−	0.236378i	−0.992991	−	0.118189i	$-0.962291\pi$
$947$		−	6888.63i		−	0.236378i	0.992991	−	0.118189i	$-0.0377089\pi$
$948$	−15799.4	−	8978.53i	−0.541289	−	0.307604i
$949$	−3239.58			−0.110813
$950$	−3789.31			−0.129412
$951$	−18289.4	+	32183.7i	−0.623632	+	1.09740i
$952$		0			0
$953$		−	50638.7i		−	1.72125i	−0.509242	−	0.860623i	$-0.670074\pi$
$953$		−	50638.7i		−	1.72125i	0.509242	−	0.860623i	$-0.329926\pi$
$954$	−13807.9	−	23179.1i	−0.468603	−	0.786636i
$955$		−	11208.4i		−	0.379785i
$956$			7694.90i			0.260325i
$957$	18702.3	+	10628.2i	0.631722	+	0.358996i
$958$		−	4207.97i		−	0.141914i
$959$		0			0
$960$	3048.90	+	1732.64i	0.102503	+	0.0582506i
$961$	1771.89			0.0594775
$962$	−15217.1			−0.509998
$963$	49829.1	−	29683.4i	1.66741	−	0.993287i
$964$		−	13145.7i		−	0.439207i
$965$	−41021.2			−1.36841
$966$		0			0
$967$	−15112.3			−0.502562			−0.251281	−	0.967914i	$-0.580852\pi$
$967$	−15112.3			−0.502562			−0.251281	+	0.967914i	$0.580852\pi$
$968$			3048.49i			0.101221i
$969$	32671.2	−	57491.1i	1.08313	−	1.90597i
$970$	5129.89			0.169805
$971$	28092.3			0.928451			0.464226	−	0.885717i	$-0.346333\pi$
$971$	28092.3			0.928451			0.464226	+	0.885717i	$0.346333\pi$
$972$	12855.8	−	8019.48i	0.424227	−	0.264635i
$973$		0			0
$974$			25183.9i			0.828485i
$975$	702.900	−	1236.89i	0.0230880	−	0.0406278i
$976$			4899.76i			0.160694i
$977$			40148.8i			1.31471i	0.753580	+	0.657356i	$0.228325\pi$
$977$			40148.8i			1.31471i	−0.753580	+	0.657356i	$0.771675\pi$
$978$	−3476.03	+	6116.74i	−0.113651	+	0.199991i
$979$			32429.3i			1.05868i
$980$		0			0
$981$	−17176.1	−	28833.3i	−0.559012	−	0.938405i
$982$	−2744.71			−0.0891928
$983$	14553.1			0.472198			0.236099	−	0.971729i	$-0.424131\pi$
$983$	14553.1			0.472198			0.236099	+	0.971729i	$0.424131\pi$
$984$	−2215.82	+	3899.15i	−0.0717862	+	0.126322i
$985$		−	34035.2i		−	1.10097i
$986$	−24900.1			−0.804239
$987$		0			0
$988$	10895.7			0.350850
$989$		−	12417.6i		−	0.399249i
$990$	8982.08	+	15078.1i	0.288353	+	0.484054i
$991$	−33100.0			−1.06101			−0.530503	−	0.847683i	$-0.677997\pi$
$991$	−33100.0			−1.06101			−0.530503	+	0.847683i	$0.677997\pi$
$992$	5356.45			0.171439
$993$	8007.28	+	4550.39i	0.255894	+	0.145420i
$994$		0			0
$995$			29208.7i			0.930631i
$996$	−7347.47	−	4175.43i	−0.233749	−	0.132835i
$997$			50399.8i			1.60098i	0.599345	+	0.800491i	$0.295428\pi$
$997$			50399.8i			1.60098i	−0.599345	+	0.800491i	$0.704572\pi$
$998$			18355.0i			0.582182i
$999$	−1102.04	−	53791.4i	−0.0349020	−	1.70359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.d.a.293.7		16
3.2	odd	2	inner	294.4.d.a.293.10		16
7.2	even	3		294.4.f.a.227.1		16
7.3	odd	6		294.4.f.a.215.7		16
7.4	even	3		42.4.f.a.5.6	yes	16
7.5	odd	6		42.4.f.a.17.4	yes	16
7.6	odd	2	inner	294.4.d.a.293.2		16
21.2	odd	6		294.4.f.a.227.7		16
21.5	even	6		42.4.f.a.17.6	yes	16
21.11	odd	6		42.4.f.a.5.4	✓	16
21.17	even	6		294.4.f.a.215.1		16
21.20	even	2	inner	294.4.d.a.293.15		16
28.11	odd	6		336.4.bc.e.257.5		16
28.19	even	6		336.4.bc.e.17.2		16
84.11	even	6		336.4.bc.e.257.2		16
84.47	odd	6		336.4.bc.e.17.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.4	✓	16	21.11	odd	6
42.4.f.a.5.6	yes	16	7.4	even	3
42.4.f.a.17.4	yes	16	7.5	odd	6
42.4.f.a.17.6	yes	16	21.5	even	6
294.4.d.a.293.2		16	7.6	odd	2	inner
294.4.d.a.293.7		16	1.1	even	1	trivial
294.4.d.a.293.10		16	3.2	odd	2	inner
294.4.d.a.293.15		16	21.20	even	2	inner
294.4.f.a.215.1		16	21.17	even	6
294.4.f.a.215.7		16	7.3	odd	6
294.4.f.a.227.1		16	7.2	even	3
294.4.f.a.227.7		16	21.2	odd	6
336.4.bc.e.17.2		16	28.19	even	6
336.4.bc.e.17.5		16	84.47	odd	6
336.4.bc.e.257.2		16	84.11	even	6
336.4.bc.e.257.5		16	28.11	odd	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +(4.51764 + 2.56729i) q^{3} -4.00000 q^{4} -10.5451 q^{5} +(5.13458 - 9.03527i) q^{6} +8.00000i q^{8} +(13.8181 + 23.1962i) q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +(4.51764 + 2.56729i) q^{3} -4.00000 q^{4} -10.5451 q^{5} +(5.13458 - 9.03527i) q^{6} +8.00000i q^{8} +(13.8181 + 23.1962i) q^{9} +21.0903i q^{10} -30.8211i q^{11} +(-18.0705 - 10.2692i) q^{12} +19.8400i q^{13} +(-47.6391 - 27.0724i) q^{15} +16.0000 q^{16} -92.6905 q^{17} +(46.3923 - 27.6361i) q^{18} +137.295i q^{19} +42.1806 q^{20} -61.6421 q^{22} +43.4973i q^{23} +(-20.5383 + 36.1411i) q^{24} -13.7999 q^{25} +39.6801 q^{26} +(2.87369 + 140.267i) q^{27} +134.318i q^{29} +(-54.1449 + 95.2782i) q^{30} +167.389i q^{31} -32.0000i q^{32} +(79.1266 - 139.238i) q^{33} +185.381i q^{34} +(-55.2722 - 92.7846i) q^{36} -383.494 q^{37} +274.590 q^{38} +(-50.9351 + 89.6301i) q^{39} -84.3612i q^{40} +107.887 q^{41} -285.480 q^{43} +123.284i q^{44} +(-145.713 - 244.607i) q^{45} +86.9945 q^{46} -241.813 q^{47} +(72.2822 + 41.0766i) q^{48} +27.5998i q^{50} +(-418.742 - 237.963i) q^{51} -79.3602i q^{52} -499.632i q^{53} +(280.533 - 5.74739i) q^{54} +325.013i q^{55} +(-352.476 + 620.248i) q^{57} +268.637 q^{58} +732.425 q^{59} +(190.556 + 108.290i) q^{60} +306.235i q^{61} +334.778 q^{62} -64.0000 q^{64} -209.216i q^{65} +(-278.477 - 158.253i) q^{66} +560.099 q^{67} +370.762 q^{68} +(-111.670 + 196.505i) q^{69} -74.2161i q^{71} +(-185.569 + 110.544i) q^{72} +163.285i q^{73} +766.987i q^{74} +(-62.3429 - 35.4283i) q^{75} -549.180i q^{76} +(179.260 + 101.870i) q^{78} +874.320 q^{79} -168.722 q^{80} +(-347.123 + 641.051i) q^{81} -215.774i q^{82} +406.600 q^{83} +977.435 q^{85} +570.961i q^{86} +(-344.834 + 606.801i) q^{87} +246.569 q^{88} -1052.18 q^{89} +(-489.214 + 291.427i) q^{90} -173.989i q^{92} +(-429.736 + 756.203i) q^{93} +483.625i q^{94} -1447.79i q^{95} +(82.1533 - 144.564i) q^{96} -243.235i q^{97} +(714.930 - 425.887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 64 q^{4} - 36 q^{9}+O(q^{10}) \) 16 * q - 64 * q^4 - 36 * q^9	\( 16 q - 64 q^{4} - 36 q^{9} + 256 q^{16} + 96 q^{18} + 24 q^{22} + 388 q^{25} - 720 q^{30} + 144 q^{36} + 1924 q^{37} - 1188 q^{39} + 1732 q^{43} - 336 q^{46} - 3276 q^{51} - 2664 q^{57} + 1560 q^{58} - 1024 q^{64} + 1412 q^{67} - 384 q^{72} + 2832 q^{78} + 5312 q^{79} - 252 q^{81} + 5232 q^{85} - 96 q^{88} - 4032 q^{93} - 4284 q^{99}+O(q^{100}) \) 16 * q - 64 * q^4 - 36 * q^9 + 256 * q^16 + 96 * q^18 + 24 * q^22 + 388 * q^25 - 720 * q^30 + 144 * q^36 + 1924 * q^37 - 1188 * q^39 + 1732 * q^43 - 336 * q^46 - 3276 * q^51 - 2664 * q^57 + 1560 * q^58 - 1024 * q^64 + 1412 * q^67 - 384 * q^72 + 2832 * q^78 + 5312 * q^79 - 252 * q^81 + 5232 * q^85 - 96 * q^88 - 4032 * q^93 - 4284 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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