LMFDB - Embedded newform 216.3.h.f.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(53,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("216.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.h (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.242095489024.11
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 32x^{2} + 256 $ x^8 - 2x^6 + 2x^4 - 32*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.8
Root			$1.90839 + 0.598380i$ of defining polynomial
Character	$\chi$	$=$	216.53
Dual form			216.3.h.f.53.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.90839 + 0.598380i) q^{2} +(3.28388 + 2.28388i) q^{4} +2.62001 q^{5} +0.432236 q^{7} +(4.90029 + 6.32354i) q^{8} +O(q^{10})$	\(q+(1.90839 + 0.598380i) q^{2} +(3.28388 + 2.28388i) q^{4} +2.62001 q^{5} +0.432236 q^{7} +(4.90029 + 6.32354i) q^{8} +(5.00000 + 1.56776i) q^{10} +5.01353 q^{11} -1.56776i q^{13} +(0.824873 + 0.258641i) q^{14} +(5.56776 + 15.0000i) q^{16} +19.8276i q^{17} -24.1355i q^{19} +(8.60382 + 5.98380i) q^{20} +(9.56776 + 3.00000i) q^{22} -3.07300i q^{23} -18.1355 q^{25} +(0.938119 - 2.99190i) q^{26} +(1.41941 + 0.987175i) q^{28} +34.4153 q^{29} -43.4066 q^{31} +(1.64975 + 31.9574i) q^{32} +(-11.8645 + 37.8388i) q^{34} +1.13246 q^{35} -52.9744i q^{37} +(14.4422 - 46.0599i) q^{38} +(12.8388 + 16.5678i) q^{40} +56.7343i q^{41} -27.6776i q^{43} +(16.4639 + 11.4503i) q^{44} +(1.83882 - 5.86447i) q^{46} -83.7425i q^{47} -48.8132 q^{49} +(-34.6096 - 10.8519i) q^{50} +(3.58059 - 5.14835i) q^{52} -41.4672 q^{53} +13.1355 q^{55} +(2.11808 + 2.73326i) q^{56} +(65.6776 + 20.5934i) q^{58} -74.2970 q^{59} -28.7033i q^{61} +(-82.8366 - 25.9736i) q^{62} +(-15.9744 + 61.9744i) q^{64} -4.10756i q^{65} +33.8132i q^{67} +(-45.2840 + 65.1117i) q^{68} +(2.16118 + 0.677644i) q^{70} -104.605i q^{71} +53.2711 q^{73} +(31.6988 - 101.096i) q^{74} +(55.1227 - 79.2582i) q^{76} +2.16703 q^{77} +51.8388 q^{79} +(14.5876 + 39.3002i) q^{80} +(-33.9487 + 108.271i) q^{82} -76.3355 q^{83} +51.9487i q^{85} +(16.5618 - 52.8197i) q^{86} +(24.5678 + 31.7033i) q^{88} +131.937i q^{89} -0.677644i q^{91} +(7.01837 - 10.0914i) q^{92} +(50.1099 - 159.813i) q^{94} -63.2354i q^{95} +68.9487 q^{97} +(-93.1544 - 29.2088i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 48 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 48 * q^7	$ 8 q + 4 q^{4} + 48 q^{7} + 40 q^{10} + 32 q^{22} - 56 q^{25} - 100 q^{28} - 80 q^{31} - 184 q^{34} - 120 q^{40} - 208 q^{46} + 144 q^{49} + 140 q^{52} + 16 q^{55} + 80 q^{58} + 184 q^{64} + 240 q^{70} + 248 q^{73} + 196 q^{76} + 192 q^{79} + 352 q^{82} + 152 q^{88} - 72 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 48 * q^7 + 40 * q^10 + 32 * q^22 - 56 * q^25 - 100 * q^28 - 80 * q^31 - 184 * q^34 - 120 * q^40 - 208 * q^46 + 144 * q^49 + 140 * q^52 + 16 * q^55 + 80 * q^58 + 184 * q^64 + 240 * q^70 + 248 * q^73 + 196 * q^76 + 192 * q^79 + 352 * q^82 + 152 * q^88 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.90839	+	0.598380i	0.954194	+	0.299190i
$2$	1.90839	+	0.598380i	0.954194	+	0.299190i
$3$		0			0
$3$		0			0
$4$	3.28388	+	2.28388i	0.820971	+	0.570971i
$5$	2.62001			0.524003			0.262001	−	0.965068i	$-0.415618\pi$
$5$	2.62001			0.524003			0.262001	+	0.965068i	$0.415618\pi$
$6$		0			0
$7$	0.432236			0.0617479			0.0308740	−	0.999523i	$-0.490171\pi$
$7$	0.432236			0.0617479			0.0308740	+	0.999523i	$0.490171\pi$
$8$	4.90029	+	6.32354i	0.612536	+	0.790443i
$9$		0			0
$10$	5.00000	+	1.56776i	0.500000	+	0.156776i
$11$	5.01353			0.455776			0.227888	−	0.973687i	$-0.426818\pi$
$11$	5.01353			0.455776			0.227888	+	0.973687i	$0.426818\pi$
$12$		0			0
$13$		−	1.56776i		−	0.120597i	−0.998180	−	0.0602986i	$-0.980795\pi$
$13$		−	1.56776i		−	0.120597i	0.998180	−	0.0602986i	$-0.0192053\pi$
$14$	0.824873	+	0.258641i	0.0589195	+	0.0184744i
$15$		0			0
$16$	5.56776	+	15.0000i	0.347985	+	0.937500i
$17$			19.8276i			1.16633i	0.812353	+	0.583166i	$0.198186\pi$
$17$			19.8276i			1.16633i	−0.812353	+	0.583166i	$0.801814\pi$
$18$		0			0
$19$		−	24.1355i		−	1.27029i	−0.772393	−	0.635145i	$-0.780940\pi$
$19$		−	24.1355i		−	1.27029i	0.772393	−	0.635145i	$-0.219060\pi$
$20$	8.60382	+	5.98380i	0.430191	+	0.299190i
$21$		0			0
$22$	9.56776	+	3.00000i	0.434898	+	0.136364i
$23$		−	3.07300i		−	0.133609i	−0.997766	−	0.0668043i	$-0.978720\pi$
$23$		−	3.07300i		−	0.133609i	0.997766	−	0.0668043i	$-0.0212803\pi$
$24$		0			0
$25$	−18.1355			−0.725421
$26$	0.938119	−	2.99190i	0.0360815	−	0.115073i
$27$		0			0
$28$	1.41941	+	0.987175i	0.0506932	+	0.0352563i
$29$	34.4153			1.18673			0.593367	−	0.804932i	$-0.297798\pi$
$29$	34.4153			1.18673			0.593367	+	0.804932i	$0.297798\pi$
$30$		0			0
$31$	−43.4066			−1.40021			−0.700106	−	0.714039i	$-0.746864\pi$
$31$	−43.4066			−1.40021			−0.700106	+	0.714039i	$0.746864\pi$
$32$	1.64975	+	31.9574i	0.0515546	+	0.998670i
$33$		0			0
$34$	−11.8645	+	37.8388i	−0.348955	+	1.11291i
$35$	1.13246			0.0323561
$36$		0			0
$37$		−	52.9744i		−	1.43174i	−0.698234	−	0.715870i	$-0.746030\pi$
$37$		−	52.9744i		−	1.43174i	0.698234	−	0.715870i	$-0.253970\pi$
$38$	14.4422	−	46.0599i	0.380059	−	1.21210i
$39$		0			0
$40$	12.8388	+	16.5678i	0.320971	+	0.414194i
$41$			56.7343i			1.38376i	0.722011	+	0.691882i	$0.243218\pi$
$41$			56.7343i			1.38376i	−0.722011	+	0.691882i	$0.756782\pi$
$42$		0			0
$43$		−	27.6776i		−	0.643666i	−0.946796	−	0.321833i	$-0.895701\pi$
$43$		−	27.6776i		−	0.643666i	0.946796	−	0.321833i	$-0.104299\pi$
$44$	16.4639	+	11.4503i	0.374179	+	0.260235i
$45$		0			0
$46$	1.83882	−	5.86447i	0.0399744	−	0.127489i
$47$		−	83.7425i		−	1.78176i	−0.454243	−	0.890878i	$-0.650090\pi$
$47$		−	83.7425i		−	1.78176i	0.454243	−	0.890878i	$-0.349910\pi$
$48$		0			0
$49$	−48.8132			−0.996187
$50$	−34.6096	−	10.8519i	−0.692192	−	0.217039i
$51$		0			0
$52$	3.58059	−	5.14835i	0.0688575	−	0.0990068i
$53$	−41.4672			−0.782401			−0.391200	−	0.920306i	$-0.627940\pi$
$53$	−41.4672			−0.782401			−0.391200	+	0.920306i	$0.627940\pi$
$54$		0			0
$55$	13.1355			0.238828
$56$	2.11808	+	2.73326i	0.0378228	+	0.0488082i
$57$		0			0
$58$	65.6776	+	20.5934i	1.13237	+	0.355059i
$59$	−74.2970			−1.25927			−0.629636	−	0.776890i	$-0.716796\pi$
$59$	−74.2970			−1.25927			−0.629636	+	0.776890i	$0.716796\pi$
$60$		0			0
$61$		−	28.7033i		−	0.470546i	−0.971929	−	0.235273i	$-0.924402\pi$
$61$		−	28.7033i		−	0.470546i	0.971929	−	0.235273i	$-0.0755984\pi$
$62$	−82.8366	−	25.9736i	−1.33607	−	0.418930i
$63$		0			0
$64$	−15.9744	+	61.9744i	−0.249599	+	0.968349i
$65$		−	4.10756i		−	0.0631933i
$66$		0			0
$67$			33.8132i			0.504674i	0.967639	+	0.252337i	$0.0811992\pi$
$67$			33.8132i			0.504674i	−0.967639	+	0.252337i	$0.918801\pi$
$68$	−45.2840	+	65.1117i	−0.665941	+	0.957524i
$69$		0			0
$70$	2.16118	+	0.677644i	0.0308740	+	0.00968062i
$71$		−	104.605i		−	1.47331i	−0.676271	−	0.736653i	$-0.736405\pi$
$71$		−	104.605i		−	1.47331i	0.676271	−	0.736653i	$-0.263595\pi$
$72$		0			0
$73$	53.2711			0.729741			0.364870	−	0.931058i	$-0.381113\pi$
$73$	53.2711			0.729741			0.364870	+	0.931058i	$0.381113\pi$
$74$	31.6988	−	101.096i	0.428362	−	1.36616i
$75$		0			0
$76$	55.1227	−	79.2582i	0.725299	−	1.04287i
$77$	2.16703			0.0281432
$78$		0			0
$79$	51.8388			0.656188			0.328094	−	0.944645i	$-0.393594\pi$
$79$	51.8388			0.656188			0.328094	+	0.944645i	$0.393594\pi$
$80$	14.5876	+	39.3002i	0.182345	+	0.491253i
$81$		0			0
$82$	−33.9487	+	108.271i	−0.414009	+	1.32038i
$83$	−76.3355			−0.919705			−0.459852	−	0.887995i	$-0.652098\pi$
$83$	−76.3355			−0.919705			−0.459852	+	0.887995i	$0.652098\pi$
$84$		0			0
$85$			51.9487i			0.611161i
$86$	16.5618	−	52.8197i	0.192579	−	0.614182i
$87$		0			0
$88$	24.5678	+	31.7033i	0.279179	+	0.360265i
$89$			131.937i			1.48244i	0.671261	+	0.741221i	$0.265753\pi$
$89$			131.937i			1.48244i	−0.671261	+	0.741221i	$0.734247\pi$
$90$		0			0
$91$		−	0.677644i		−	0.00744663i
$92$	7.01837	−	10.0914i	0.0762866	−	0.109689i
$93$		0			0
$94$	50.1099	−	159.813i	0.533084	−	1.70014i
$95$		−	63.2354i		−	0.665636i
$96$		0			0
$97$	68.9487			0.710811			0.355406	−	0.934712i	$-0.384343\pi$
$97$	68.9487			0.710811			0.355406	+	0.934712i	$0.384343\pi$
$98$	−93.1544	−	29.2088i	−0.950555	−	0.298049i
$99$		0			0
$100$	−59.5549	−	41.4194i	−0.595549	−	0.414194i
$101$	115.085			1.13945			0.569727	−	0.821834i	$-0.307049\pi$
$101$	115.085			1.13945			0.569727	+	0.821834i	$0.307049\pi$
$102$		0			0
$103$	−75.2454			−0.730538			−0.365269	−	0.930902i	$-0.619023\pi$
$103$	−75.2454			−0.730538			−0.365269	+	0.930902i	$0.619023\pi$
$104$	9.91382	−	7.68250i	0.0953252	−	0.0738702i
$105$		0			0
$106$	−79.1355	−	24.8132i	−0.746562	−	0.234087i
$107$	112.336			1.04987			0.524935	−	0.851142i	$-0.324089\pi$
$107$	112.336			1.04987			0.524935	+	0.851142i	$0.324089\pi$
$108$		0			0
$109$			110.864i			1.01711i	0.861031	+	0.508553i	$0.169819\pi$
$109$			110.864i			1.01711i	−0.861031	+	0.508553i	$0.830181\pi$
$110$	25.0677	+	7.86004i	0.227888	+	0.0714549i
$111$		0			0
$112$	2.40659	+	6.48353i	0.0214874	+	0.0578887i
$113$			43.7629i			0.387282i	0.981072	+	0.193641i	$0.0620297\pi$
$113$			43.7629i			0.387282i	−0.981072	+	0.193641i	$0.937970\pi$
$114$		0			0
$115$		−	8.05130i		−	0.0700113i
$116$	113.016	+	78.6004i	0.974273	+	0.677590i
$117$		0			0
$118$	−141.788	−	44.4579i	−1.20159	−	0.376762i
$119$			8.57022i			0.0720186i
$120$		0			0
$121$	−95.8645			−0.792268
$122$	17.1755	−	54.7770i	0.140783	−	0.448992i
$123$		0			0
$124$	−142.542	−	99.1355i	−1.14953	−	0.799480i
$125$	−113.016			−0.904125
$126$		0			0
$127$	111.355			0.876813			0.438407	−	0.898777i	$-0.355543\pi$
$127$	111.355			0.876813			0.438407	+	0.898777i	$0.355543\pi$
$128$	−67.5695	+	108.712i	−0.527886	+	0.849315i
$129$		0			0
$130$	2.45789	−	7.83882i	0.0189068	−	0.0602986i
$131$	−13.4552			−0.102711			−0.0513556	−	0.998680i	$-0.516354\pi$
$131$	−13.4552			−0.102711			−0.0513556	+	0.998680i	$0.516354\pi$
$132$		0			0
$133$		−	10.4322i		−	0.0784379i
$134$	−20.2331	+	64.5286i	−0.150994	+	0.481557i
$135$		0			0
$136$	−125.381	+	97.1612i	−0.921919	+	0.714420i
$137$			79.2799i			0.578685i	0.957226	+	0.289343i	$0.0934367\pi$
$137$			79.2799i			0.578685i	−0.957226	+	0.289343i	$0.906563\pi$
$138$		0			0
$139$			145.491i			1.04670i	0.852119	+	0.523348i	$0.175317\pi$
$139$			145.491i			1.04670i	−0.852119	+	0.523348i	$0.824683\pi$
$140$	3.71888	+	2.58641i	0.0265634	+	0.0184744i
$141$		0			0
$142$	62.5934	−	199.626i	0.440799	−	1.40582i
$143$		−	7.86004i		−	0.0549653i
$144$		0			0
$145$	90.1685			0.621851
$146$	101.662	+	31.8763i	0.696314	+	0.218331i
$147$		0			0
$148$	120.987	−	173.962i	0.817481	−	1.17542i
$149$	184.821			1.24041			0.620206	−	0.784439i	$-0.287049\pi$
$149$	184.821			1.24041			0.620206	+	0.784439i	$0.287049\pi$
$150$		0			0
$151$	25.7875			0.170778			0.0853891	−	0.996348i	$-0.472787\pi$
$151$	25.7875			0.170778			0.0853891	+	0.996348i	$0.472787\pi$
$152$	152.622	−	118.271i	1.00409	−	0.778099i
$153$		0			0
$154$	4.13553	+	1.29671i	0.0268541	+	0.00842017i
$155$	−113.726			−0.733715
$156$		0			0
$157$			221.575i			1.41131i	0.708558	+	0.705653i	$0.249346\pi$
$157$			221.575i			1.41131i	−0.708558	+	0.705653i	$0.750654\pi$
$158$	98.9285	+	31.0193i	0.626130	+	0.196325i
$159$		0			0
$160$	4.32236	+	83.7289i	0.0270147	+	0.523306i
$161$		−	1.32826i		−	0.00825006i
$162$		0			0
$163$			42.1355i			0.258500i	0.991612	+	0.129250i	$0.0412570\pi$
$163$			42.1355i			0.258500i	−0.991612	+	0.129250i	$0.958743\pi$
$164$	−129.575	+	186.309i	−0.790089	+	1.13603i
$165$		0			0
$166$	−145.678	−	45.6776i	−0.877576	−	0.275167i
$167$			47.5153i			0.284523i	0.989829	+	0.142261i	$0.0454374\pi$
$167$			47.5153i			0.284523i	−0.989829	+	0.142261i	$0.954563\pi$
$168$		0			0
$169$	166.542			0.985456
$170$	−31.0851	+	99.1382i	−0.182853	+	0.583166i
$171$		0			0
$172$	63.2125	−	90.8901i	0.367514	−	0.528431i
$173$	115.734			0.668980			0.334490	−	0.942399i	$-0.391436\pi$
$173$	115.734			0.668980			0.334490	+	0.942399i	$0.391436\pi$
$174$		0			0
$175$	−7.83882			−0.0447933
$176$	27.9142	+	75.2030i	0.158603	+	0.427290i
$177$		0			0
$178$	−78.9487	+	251.788i	−0.443532	+	1.41454i
$179$	334.517			1.86881			0.934405	−	0.356211i	$-0.115932\pi$
$179$	334.517			1.86881			0.934405	+	0.356211i	$0.115932\pi$
$180$		0			0
$181$		−	190.432i		−	1.05211i	−0.850450	−	0.526056i	$-0.823670\pi$
$181$		−	190.432i		−	1.05211i	0.850450	−	0.526056i	$-0.176330\pi$
$182$	0.405489	−	1.29321i	0.00222796	−	0.00710553i
$183$		0			0
$184$	19.4322	−	15.0586i	0.105610	−	0.0818401i
$185$		−	138.794i		−	0.750235i
$186$		0			0
$187$			99.4066i			0.531586i
$188$	191.258	−	275.001i	1.01733	−	1.46277i
$189$		0			0
$190$	37.8388	−	120.678i	0.199152	−	0.635145i
$191$			270.376i			1.41558i	0.706423	+	0.707790i	$0.250308\pi$
$191$			270.376i			1.41558i	−0.706423	+	0.707790i	$0.749692\pi$
$192$		0			0
$193$	−23.7619			−0.123119			−0.0615593	−	0.998103i	$-0.519607\pi$
$193$	−23.7619			−0.123119			−0.0615593	+	0.998103i	$0.519607\pi$
$194$	131.581	+	41.2575i	0.678252	+	0.212668i
$195$		0			0
$196$	−160.297	−	111.484i	−0.817840	−	0.568794i
$197$	−324.845			−1.64896			−0.824480	−	0.565891i	$-0.808532\pi$
$197$	−324.845			−1.64896			−0.824480	+	0.565891i	$0.808532\pi$
$198$		0			0
$199$	196.652			0.988201			0.494100	−	0.869405i	$-0.335497\pi$
$199$	196.652			0.988201			0.494100	+	0.869405i	$0.335497\pi$
$200$	−88.8693	−	114.681i	−0.444347	−	0.573404i
$201$		0			0
$202$	219.626	+	68.8645i	1.08726	+	0.340913i
$203$	14.8755			0.0732783
$204$		0			0
$205$			148.645i			0.725096i
$206$	−143.597	−	45.0254i	−0.697075	−	0.218570i
$207$		0			0
$208$	23.5165	−	8.72894i	0.113060	−	0.0419661i
$209$		−	121.004i		−	0.578968i
$210$		0			0
$211$			29.3224i			0.138969i	0.997583	+	0.0694843i	$0.0221354\pi$
$211$			29.3224i			0.138969i	−0.997583	+	0.0694843i	$0.977865\pi$
$212$	−136.174	−	94.7063i	−0.642328	−	0.446728i
$213$		0			0
$214$	214.381	+	67.2198i	1.00178	+	0.314111i
$215$		−	72.5158i		−	0.337283i
$216$		0			0
$217$	−18.7619			−0.0864602
$218$	−66.3391	+	211.572i	−0.304308	+	0.970515i
$219$		0			0
$220$	43.1355	+	30.0000i	0.196071	+	0.136364i
$221$	31.0851			0.140656
$222$		0			0
$223$	−67.4066			−0.302272			−0.151136	−	0.988513i	$-0.548293\pi$
$223$	−67.4066			−0.302272			−0.151136	+	0.988513i	$0.548293\pi$
$224$	0.713079	+	13.8131i	0.00318339	+	0.0616658i
$225$		0			0
$226$	−26.1868	+	83.5165i	−0.115871	+	0.369542i
$227$	−360.007			−1.58593			−0.792967	−	0.609264i	$-0.791465\pi$
$227$	−360.007			−1.58593			−0.792967	+	0.609264i	$0.791465\pi$
$228$		0			0
$229$		−	216.542i		−	0.945599i	−0.881170	−	0.472799i	$-0.843244\pi$
$229$		−	216.542i		−	0.945599i	0.881170	−	0.472799i	$-0.156756\pi$
$230$	4.81774	−	15.3650i	0.0209467	−	0.0668043i
$231$		0			0
$232$	168.645	+	217.626i	0.726917	+	0.938045i
$233$		−	148.986i		−	0.639424i	−0.947515	−	0.319712i	$-0.896414\pi$
$233$		−	148.986i		−	0.639424i	0.947515	−	0.319712i	$-0.103586\pi$
$234$		0			0
$235$		−	219.407i		−	0.933645i
$236$	−243.983	−	169.686i	−1.03383	−	0.719007i
$237$		0			0
$238$	−5.12825	+	16.3553i	−0.0215473	+	0.0687197i
$239$			117.607i			0.492079i	0.969260	+	0.246040i	$0.0791293\pi$
$239$			117.607i			0.492079i	−0.969260	+	0.246040i	$0.920871\pi$
$240$		0			0
$241$	−203.220			−0.843236			−0.421618	−	0.906774i	$-0.638538\pi$
$241$	−203.220			−0.843236			−0.421618	+	0.906774i	$0.638538\pi$
$242$	−182.947	−	57.3634i	−0.755977	−	0.237039i
$243$		0			0
$244$	65.5549	−	94.2582i	0.268668	−	0.386304i
$245$	−127.891			−0.522005
$246$		0			0
$247$	−37.8388			−0.153194
$248$	−212.705	−	274.483i	−0.857681	−	1.10679i
$249$		0			0
$250$	−215.678	−	67.6263i	−0.862711	−	0.270505i
$251$	184.821			0.736340			0.368170	−	0.929759i	$-0.379984\pi$
$251$	184.821			0.736340			0.368170	+	0.929759i	$0.379984\pi$
$252$		0			0
$253$		−	15.4066i		−	0.0608956i
$254$	212.509	+	66.6328i	0.836650	+	0.262334i
$255$		0			0
$256$	−194.000	+	167.033i	−0.757812	+	0.652472i
$257$		−	462.861i		−	1.80102i	−0.434839	−	0.900508i	$-0.643195\pi$
$257$		−	462.861i		−	1.80102i	0.434839	−	0.900508i	$-0.356805\pi$
$258$		0			0
$259$		−	22.8974i		−	0.0884070i
$260$	9.38119	−	13.4888i	0.0360815	−	0.0518798i
$261$		0			0
$262$	−25.6776	−	8.05130i	−0.0980063	−	0.0307301i
$263$			315.822i			1.20084i	0.799683	+	0.600422i	$0.205001\pi$
$263$			315.822i			1.20084i	−0.799683	+	0.600422i	$0.794999\pi$
$264$		0			0
$265$	−108.645			−0.409980
$266$	6.24244	−	19.9087i	0.0234678	−	0.0748449i
$267$		0			0
$268$	−77.2253	+	111.038i	−0.288154	+	0.414323i
$269$	−279.693			−1.03975			−0.519875	−	0.854242i	$-0.674021\pi$
$269$	−279.693			−1.03975			−0.519875	+	0.854242i	$0.674021\pi$
$270$		0			0
$271$	−467.685			−1.72577			−0.862887	−	0.505396i	$-0.831346\pi$
$271$	−467.685			−1.72577			−0.862887	+	0.505396i	$0.831346\pi$
$272$	−297.415	+	110.396i	−1.09344	+	0.405866i
$273$		0			0
$274$	−47.4395	+	151.297i	−0.173137	+	0.552178i
$275$	−90.9231			−0.330629
$276$		0			0
$277$		−	399.949i		−	1.44386i	−0.691967	−	0.721929i	$-0.743256\pi$
$277$		−	399.949i		−	1.44386i	0.691967	−	0.721929i	$-0.256744\pi$
$278$	−87.0588	+	277.653i	−0.313161	+	0.998751i
$279$		0			0
$280$	5.54940	+	7.16118i	0.0198193	+	0.0255756i
$281$		−	255.011i		−	0.907512i	−0.891126	−	0.453756i	$-0.850084\pi$
$281$		−	255.011i		−	0.907512i	0.891126	−	0.453756i	$-0.149916\pi$
$282$		0			0
$283$		−	286.491i		−	1.01234i	−0.862435	−	0.506168i	$-0.831062\pi$
$283$		−	286.491i		−	1.01234i	0.862435	−	0.506168i	$-0.168938\pi$
$284$	238.905	−	343.510i	0.841215	−	1.20954i
$285$		0			0
$286$	4.70329	−	15.0000i	0.0164451	−	0.0524476i
$287$			24.5226i			0.0854446i
$288$		0			0
$289$	−104.136			−0.360331
$290$	172.076	+	53.9550i	0.593367	+	0.186052i
$291$		0			0
$292$	174.936	+	121.665i	0.599095	+	0.416660i
$293$	−41.1735			−0.140524			−0.0702620	−	0.997529i	$-0.522384\pi$
$293$	−41.1735			−0.140524			−0.0702620	+	0.997529i	$0.522384\pi$
$294$		0			0
$295$	−194.659			−0.659862
$296$	334.985	−	259.590i	1.13171	−	0.876992i
$297$		0			0
$298$	352.711	+	110.593i	1.18359	+	0.371119i
$299$	−4.81774			−0.0161128
$300$		0			0
$301$		−	11.9633i		−	0.0397451i
$302$	49.2126	+	15.4307i	0.162956	+	0.0510952i
$303$		0			0
$304$	362.033	−	134.381i	1.19090	−	0.442043i
$305$		−	75.2030i		−	0.246567i
$306$		0			0
$307$		−	119.033i		−	0.387729i	−0.981028	−	0.193865i	$-0.937898\pi$
$307$		−	119.033i		−	0.387729i	0.981028	−	0.193865i	$-0.0621023\pi$
$308$	7.11627	+	4.94924i	0.0231048	+	0.0160690i
$309$		0			0
$310$	−217.033	−	68.0513i	−0.700106	−	0.219520i
$311$			54.3715i			0.174828i	0.996172	+	0.0874140i	$0.0278603\pi$
$311$			54.3715i			0.174828i	−0.996172	+	0.0874140i	$0.972140\pi$
$312$		0			0
$313$	−192.033			−0.613524			−0.306762	−	0.951786i	$-0.599246\pi$
$313$	−192.033			−0.613524			−0.306762	+	0.951786i	$0.599246\pi$
$314$	−132.586	+	422.851i	−0.422249	+	1.34666i
$315$		0			0
$316$	170.233	+	118.394i	0.538711	+	0.374664i
$317$	176.606			0.557117			0.278559	−	0.960419i	$-0.410143\pi$
$317$	176.606			0.557117			0.278559	+	0.960419i	$0.410143\pi$
$318$		0			0
$319$	172.542			0.540884
$320$	−41.8530	+	162.374i	−0.130791	+	0.507418i
$321$		0			0
$322$	0.794804	−	2.53483i	0.00246834	−	0.00787215i
$323$	478.551			1.48158
$324$		0			0
$325$			28.4322i			0.0874838i
$326$	−25.2131	+	80.4109i	−0.0773407	+	0.246659i
$327$		0			0
$328$	−358.762	+	278.015i	−1.09379	+	0.847605i
$329$		−	36.1965i		−	0.110020i
$330$		0			0
$331$		−	305.864i		−	0.924062i	−0.886864	−	0.462031i	$-0.847121\pi$
$331$		−	305.864i		−	0.924062i	0.886864	−	0.462031i	$-0.152879\pi$
$332$	−250.677	−	174.341i	−0.755050	−	0.525124i
$333$		0			0
$334$	−28.4322	+	90.6776i	−0.0851265	+	0.271490i
$335$			88.5910i			0.264451i
$336$		0			0
$337$	319.322			0.947544			0.473772	−	0.880648i	$-0.342892\pi$
$337$	319.322			0.947544			0.473772	+	0.880648i	$0.342892\pi$
$338$	317.827	+	99.6555i	0.940316	+	0.294839i
$339$		0			0
$340$	−118.645	+	170.593i	−0.348955	+	0.501745i
$341$	−217.620			−0.638183
$342$		0			0
$343$	−42.2783			−0.123260
$344$	175.021	−	135.628i	0.508781	−	0.394269i
$345$		0			0
$346$	220.864	+	69.2527i	0.638337	+	0.200152i
$347$	−144.003			−0.414994			−0.207497	−	0.978236i	$-0.566532\pi$
$347$	−144.003			−0.414994			−0.207497	+	0.978236i	$0.566532\pi$
$348$		0			0
$349$			486.718i			1.39461i	0.716776	+	0.697304i	$0.245617\pi$
$349$			486.718i			1.39461i	−0.716776	+	0.697304i	$0.754383\pi$
$350$	−14.9595	−	4.69060i	−0.0427414	−	0.0134017i
$351$		0			0
$352$	8.27106	+	160.220i	0.0234973	+	0.455170i
$353$		−	31.4402i		−	0.0890656i	−0.999008	−	0.0445328i	$-0.985820\pi$
$353$		−	31.4402i		−	0.0890656i	0.999008	−	0.0445328i	$-0.0141799\pi$
$354$		0			0
$355$		−	274.066i		−	0.772017i
$356$	−301.329	+	433.267i	−0.846431	+	1.21704i
$357$		0			0
$358$	638.388	+	200.168i	1.78321	+	0.559130i
$359$			459.788i			1.28075i	0.768063	+	0.640374i	$0.221221\pi$
$359$			459.788i			1.28075i	−0.768063	+	0.640374i	$0.778779\pi$
$360$		0			0
$361$	−221.524			−0.613639
$362$	113.951	−	363.418i	0.314781	−	1.00392i
$363$		0			0
$364$	1.54766	−	2.22530i	0.00425181	−	0.00611347i
$365$	139.571			0.382386
$366$		0			0
$367$	312.161			0.850575			0.425288	−	0.905058i	$-0.360173\pi$
$367$	312.161			0.850575			0.425288	+	0.905058i	$0.360173\pi$
$368$	46.0950	−	17.1097i	0.125258	−	0.0464938i
$369$		0			0
$370$	83.0513	−	264.872i	0.224463	−	0.715870i
$371$	−17.9236			−0.0483116
$372$		0			0
$373$		−	636.872i		−	1.70743i	−0.520740	−	0.853715i	$-0.674344\pi$
$373$		−	636.872i		−	1.70743i	0.520740	−	0.853715i	$-0.325656\pi$
$374$	−59.4829	+	189.706i	−0.159045	+	0.507236i
$375$		0			0
$376$	529.549	−	410.363i	1.40838	−	1.09139i
$377$		−	53.9550i		−	0.143117i
$378$		0			0
$379$			711.776i			1.87804i	0.343865	+	0.939019i	$0.388264\pi$
$379$			711.776i			1.87804i	−0.343865	+	0.939019i	$0.611736\pi$
$380$	144.422	−	207.658i	0.380059	−	0.546467i
$381$		0			0
$382$	−161.788	+	515.982i	−0.423528	+	1.35074i
$383$			505.173i			1.31899i	0.751709	+	0.659495i	$0.229230\pi$
$383$			505.173i			1.31899i	−0.751709	+	0.659495i	$0.770770\pi$
$384$		0			0
$385$	5.67764			0.0147471
$386$	−45.3469	−	14.2186i	−0.117479	−	0.0368358i
$387$		0			0
$388$	226.419	+	157.471i	0.583555	+	0.405852i
$389$	503.067			1.29323			0.646616	−	0.762815i	$-0.276183\pi$
$389$	503.067			1.29323			0.646616	+	0.762815i	$0.276183\pi$
$390$		0			0
$391$	60.9303			0.155832
$392$	−239.199	−	308.672i	−0.610201	−	0.787429i
$393$		0			0
$394$	−619.930	−	194.381i	−1.57343	−	0.493353i
$395$	135.818			0.343844
$396$		0			0
$397$			398.864i			1.00470i	0.864665	+	0.502348i	$0.167530\pi$
$397$			398.864i			1.00470i	−0.864665	+	0.502348i	$0.832470\pi$
$398$	375.288	+	117.673i	0.942935	+	0.295660i
$399$		0			0
$400$	−100.974	−	272.033i	−0.252436	−	0.680082i
$401$			601.624i			1.50031i	0.661262	+	0.750155i	$0.270021\pi$
$401$			601.624i			1.50031i	−0.661262	+	0.750155i	$0.729979\pi$
$402$		0			0
$403$			68.0513i			0.168862i
$404$	377.925	+	262.840i	0.935458	+	0.650594i
$405$		0			0
$406$	28.3882	+	8.90121i	0.0699217	+	0.0219242i
$407$		−	265.589i		−	0.652552i
$408$		0			0
$409$	736.267			1.80016			0.900082	−	0.435720i	$-0.143506\pi$
$409$	736.267			1.80016			0.900082	+	0.435720i	$0.143506\pi$
$410$	−88.9461	+	283.672i	−0.216942	+	0.691882i
$411$		0			0
$412$	−247.097	−	171.852i	−0.599750	−	0.417116i
$413$	−32.1138			−0.0777575
$414$		0			0
$415$	−200.000			−0.481928
$416$	50.1017	−	2.58641i	0.120437	−	0.00621734i
$417$		0			0
$418$	72.4066	−	230.923i	0.173221	−	0.552447i
$419$	312.620			0.746111			0.373055	−	0.927809i	$-0.378310\pi$
$419$	312.620			0.746111			0.373055	+	0.927809i	$0.378310\pi$
$420$		0			0
$421$		−	465.619i		−	1.10598i	−0.833187	−	0.552992i	$-0.813486\pi$
$421$		−	465.619i		−	1.10598i	0.833187	−	0.552992i	$-0.186514\pi$
$422$	−17.5459	+	55.9584i	−0.0415780	+	0.132603i
$423$		0			0
$424$	−203.201	−	262.220i	−0.479249	−	0.618443i
$425$		−	359.585i		−	0.846082i
$426$		0			0
$427$		−	12.4066i		−	0.0290552i
$428$	368.899	+	256.563i	0.861913	+	0.599445i
$429$		0			0
$430$	43.3920	−	138.388i	0.100912	−	0.321833i
$431$		−	497.313i		−	1.15386i	−0.816794	−	0.576929i	$-0.804251\pi$
$431$		−	497.313i		−	1.15386i	0.816794	−	0.576929i	$-0.195749\pi$
$432$		0			0
$433$	−376.659			−0.869883			−0.434941	−	0.900459i	$-0.643231\pi$
$433$	−376.659			−0.869883			−0.434941	+	0.900459i	$0.643231\pi$
$434$	−35.8049	−	11.2267i	−0.0824998	−	0.0258681i
$435$		0			0
$436$	−253.201	+	364.066i	−0.580737	+	0.835013i
$437$	−74.1685			−0.169722
$438$		0			0
$439$	−183.070			−0.417015			−0.208508	−	0.978021i	$-0.566861\pi$
$439$	−183.070			−0.417015			−0.208508	+	0.978021i	$0.566861\pi$
$440$	64.3679	+	83.0631i	0.146291	+	0.188780i
$441$		0			0
$442$	59.3224	+	18.6007i	0.134213	+	0.0420830i
$443$	514.356			1.16107			0.580537	−	0.814234i	$-0.302843\pi$
$443$	514.356			1.16107			0.580537	+	0.814234i	$0.302843\pi$
$444$		0			0
$445$			345.678i			0.776804i
$446$	−128.638	−	40.3348i	−0.288426	−	0.0904367i
$447$		0			0
$448$	−6.90468	+	26.7875i	−0.0154122	+	0.0597936i
$449$			533.216i			1.18756i	0.804626	+	0.593782i	$0.202366\pi$
$449$			533.216i			1.18756i	−0.804626	+	0.593782i	$0.797634\pi$
$450$		0			0
$451$			284.440i			0.630686i
$452$	−99.9492	+	143.712i	−0.221127	+	0.317947i
$453$		0			0
$454$	−687.033	−	215.421i	−1.51329	−	0.474496i
$455$		−	1.77544i		−	0.00390206i
$456$		0			0
$457$	−327.033			−0.715608			−0.357804	−	0.933797i	$-0.616474\pi$
$457$	−327.033			−0.715608			−0.357804	+	0.933797i	$0.616474\pi$
$458$	129.575	−	413.246i	0.282914	−	0.902284i
$459$		0			0
$460$	18.3882	−	26.4395i	0.0399744	−	0.0574772i
$461$	−82.1264			−0.178148			−0.0890742	−	0.996025i	$-0.528391\pi$
$461$	−82.1264			−0.178148			−0.0890742	+	0.996025i	$0.528391\pi$
$462$		0			0
$463$	586.344			1.26640			0.633201	−	0.773987i	$-0.281741\pi$
$463$	586.344			1.26640			0.633201	+	0.773987i	$0.281741\pi$
$464$	191.616	+	516.229i	0.412966	+	1.11256i
$465$		0			0
$466$	89.1501	−	284.322i	0.191309	−	0.610134i
$467$	−735.435			−1.57481			−0.787403	−	0.616438i	$-0.788575\pi$
$467$	−735.435			−1.57481			−0.787403	+	0.616438i	$0.788575\pi$
$468$		0			0
$469$			14.6153i			0.0311626i
$470$	131.289	−	418.713i	0.279337	−	0.890878i
$471$		0			0
$472$	−364.077	−	469.820i	−0.771349	−	0.995382i
$473$		−	138.763i		−	0.293367i
$474$		0			0
$475$			437.711i			0.921496i
$476$	−19.5734	+	28.1436i	−0.0411205	+	0.0591252i
$477$		0			0
$478$	−70.3737	+	224.440i	−0.147225	+	0.469539i
$479$		−	381.482i		−	0.796413i	−0.917296	−	0.398206i	$-0.869633\pi$
$479$		−	381.482i		−	0.796413i	0.917296	−	0.398206i	$-0.130367\pi$
$480$		0			0
$481$	−83.0513			−0.172664
$482$	−387.822	−	121.603i	−0.804610	−	0.252288i
$483$		0			0
$484$	−314.808	−	218.943i	−0.650429	−	0.452362i
$485$	180.647			0.372467
$486$		0			0
$487$	−3.51647			−0.00722067			−0.00361033	−	0.999993i	$-0.501149\pi$
$487$	−3.51647			−0.00722067			−0.00361033	+	0.999993i	$0.501149\pi$
$488$	181.506	−	140.654i	0.371939	−	0.288226i
$489$		0			0
$490$	−244.066	−	76.5276i	−0.498094	−	0.156179i
$491$	−682.129			−1.38926			−0.694632	−	0.719365i	$-0.744433\pi$
$491$	−682.129			−1.38926			−0.694632	+	0.719365i	$0.744433\pi$
$492$		0			0
$493$			682.374i			1.38413i
$494$	−72.2111	−	22.6420i	−0.146176	−	0.0458340i
$495$		0			0
$496$	−241.678	−	651.099i	−0.487253	−	1.31270i
$497$		−	45.2139i		−	0.0909736i
$498$		0			0
$499$			189.253i			0.379264i	0.981855	+	0.189632i	$0.0607295\pi$
$499$			189.253i			0.379264i	−0.981855	+	0.189632i	$0.939271\pi$
$500$	−371.130	−	258.114i	−0.742260	−	0.516229i
$501$		0			0
$502$	352.711	+	110.593i	0.702611	+	0.220306i
$503$			1.06526i			0.00211782i	0.999999	+	0.00105891i	$0.000337061\pi$
$503$			1.06526i			0.00211782i	−0.999999	+	0.00105891i	$0.999663\pi$
$504$		0			0
$505$	301.524			0.597077
$506$	9.21900	−	29.4017i	0.0182194	−	0.0581062i
$507$		0			0
$508$	365.678	+	254.322i	0.719838	+	0.500635i
$509$	−312.492			−0.613933			−0.306966	−	0.951720i	$-0.599314\pi$
$509$	−312.492			−0.613933			−0.306966	+	0.951720i	$0.599314\pi$
$510$		0			0
$511$	23.0256			0.0450600
$512$	−470.176	+	202.678i	−0.918313	+	0.395855i
$513$		0			0
$514$	276.967	−	883.319i	0.538846	−	1.71852i
$515$	−197.144			−0.382804
$516$		0			0
$517$		−	419.846i		−	0.812081i
$518$	13.7014	−	43.6971i	0.0264505	−	0.0843573i
$519$		0			0
$520$	25.9744	−	20.1282i	0.0499507	−	0.0387082i
$521$			317.799i			0.609979i	0.952356	+	0.304989i	$0.0986529\pi$
$521$			317.799i			0.609979i	−0.952356	+	0.304989i	$0.901347\pi$
$522$		0			0
$523$		−	488.846i		−	0.934696i	−0.884073	−	0.467348i	$-0.845209\pi$
$523$		−	488.846i		−	0.934696i	0.884073	−	0.467348i	$-0.154791\pi$
$524$	−44.1851	−	30.7300i	−0.0843228	−	0.0586450i
$525$		0			0
$526$	−188.982	+	602.711i	−0.359281	+	1.14584i
$527$		−	860.650i		−	1.63311i
$528$		0			0
$529$	519.557			0.982149
$530$	−207.336	−	65.0108i	−0.391200	−	0.122662i
$531$		0			0
$532$	23.8260	−	34.2582i	0.0447857	−	0.0643952i
$533$	88.9461			0.166878
$534$		0			0
$535$	294.322			0.550135
$536$	−213.819	+	165.694i	−0.398916	+	0.309131i
$537$		0			0
$538$	−533.762	−	167.363i	−0.992122	−	0.311083i
$539$	−244.727			−0.454038
$540$		0			0
$541$			726.718i			1.34329i	0.740875	+	0.671643i	$0.234411\pi$
$541$			726.718i			1.34329i	−0.740875	+	0.671643i	$0.765589\pi$
$542$	−892.524	−	279.853i	−1.64672	−	0.516335i
$543$		0			0
$544$	−633.641	+	32.7106i	−1.16478	+	0.0601297i
$545$			290.466i			0.532966i
$546$		0			0
$547$			434.963i			0.795180i	0.917563	+	0.397590i	$0.130153\pi$
$547$			434.963i			0.795180i	−0.917563	+	0.397590i	$0.869847\pi$
$548$	−181.066	+	260.346i	−0.330412	+	0.475084i
$549$		0			0
$550$	−173.516	−	54.4066i	−0.315484	−	0.0989211i
$551$		−	830.631i		−	1.50750i
$552$		0			0
$553$	22.4066			0.0405182
$554$	239.321	−	763.257i	0.431988	−	1.37772i
$555$		0			0
$556$	−332.284	+	477.775i	−0.597633	+	0.859307i
$557$	−153.160			−0.274974			−0.137487	−	0.990504i	$-0.543903\pi$
$557$	−153.160			−0.274974			−0.137487	+	0.990504i	$0.543903\pi$
$558$		0			0
$559$	−43.3920			−0.0776244
$560$	6.30529	+	16.9869i	0.0112594	+	0.0303338i
$561$		0			0
$562$	152.593	−	486.659i	0.271519	−	0.865942i
$563$	135.531			0.240729			0.120365	−	0.992730i	$-0.461594\pi$
$563$	135.531			0.240729			0.120365	+	0.992730i	$0.461594\pi$
$564$		0			0
$565$			114.659i			0.202937i
$566$	171.430	−	546.735i	0.302881	−	0.965964i
$567$		0			0
$568$	661.472	−	512.593i	1.16456	−	0.902453i
$569$			774.637i			1.36140i	0.732562	+	0.680700i	$0.238324\pi$
$569$			774.637i			1.36140i	−0.732562	+	0.680700i	$0.761676\pi$
$570$		0			0
$571$		−	42.6409i		−	0.0746776i	−0.999303	−	0.0373388i	$-0.988112\pi$
$571$		−	42.6409i		−	0.0746776i	0.999303	−	0.0373388i	$-0.0118881\pi$
$572$	17.9514	−	25.8114i	0.0313836	−	0.0451249i
$573$		0			0
$574$	−14.6738	+	46.7986i	−0.0255642	+	0.0815307i
$575$			55.7305i			0.0969225i
$576$		0			0
$577$	352.150			0.610312			0.305156	−	0.952302i	$-0.401291\pi$
$577$	352.150			0.610312			0.305156	+	0.952302i	$0.401291\pi$
$578$	−198.731	−	62.3126i	−0.343825	−	0.107807i
$579$		0			0
$580$	296.103	+	205.934i	0.510522	+	0.355059i
$581$	−32.9949			−0.0567899
$582$		0			0
$583$	−207.897			−0.356599
$584$	261.044	+	336.862i	0.446992	+	0.576818i
$585$		0			0
$586$	−78.5750	−	24.6374i	−0.134087	−	0.0420434i
$587$	−137.949			−0.235007			−0.117503	−	0.993072i	$-0.537489\pi$
$587$	−137.949			−0.235007			−0.117503	+	0.993072i	$0.537489\pi$
$588$		0			0
$589$			1047.64i			1.77868i
$590$	−371.485	−	116.480i	−0.629636	−	0.197424i
$591$		0			0
$592$	794.615	−	294.949i	1.34226	−	0.498224i
$593$		−	338.460i		−	0.570758i	−0.958415	−	0.285379i	$-0.907880\pi$
$593$		−	338.460i		−	0.570758i	0.958415	−	0.285379i	$-0.0921195\pi$
$594$		0			0
$595$			22.4541i			0.0377379i
$596$	606.931	+	422.110i	1.01834	+	0.708238i
$597$		0			0
$598$	−9.19411	−	2.88284i	−0.0153748	−	0.00482080i
$599$		−	338.337i		−	0.564836i	−0.959291	−	0.282418i	$-0.908863\pi$
$599$		−	338.337i		−	0.564836i	0.959291	−	0.282418i	$-0.0911365\pi$
$600$		0			0
$601$	286.593			0.476861			0.238430	−	0.971160i	$-0.423367\pi$
$601$	286.593			0.476861			0.238430	+	0.971160i	$0.423367\pi$
$602$	7.15858	−	22.8305i	0.0118913	−	0.0379245i
$603$		0			0
$604$	84.6832	+	58.8957i	0.140204	+	0.0975094i
$605$	−251.166			−0.415151
$606$		0			0
$607$	−93.6336			−0.154256			−0.0771282	−	0.997021i	$-0.524575\pi$
$607$	−93.6336			−0.154256			−0.0771282	+	0.997021i	$0.524575\pi$
$608$	771.310	−	39.8175i	1.26860	−	0.0654893i
$609$		0			0
$610$	45.0000	−	143.516i	0.0737705	−	0.235273i
$611$	−131.289			−0.214875
$612$		0			0
$613$		−	1158.72i		−	1.89024i	−0.326722	−	0.945121i	$-0.605944\pi$
$613$		−	1158.72i		−	1.89024i	0.326722	−	0.945121i	$-0.394056\pi$
$614$	71.2270	−	227.161i	0.116005	−	0.369969i
$615$		0			0
$616$	10.6191	+	13.7033i	0.0172387	+	0.0222456i
$617$			477.841i			0.774458i	0.921984	+	0.387229i	$0.126568\pi$
$617$			477.841i			0.774458i	−0.921984	+	0.387229i	$0.873432\pi$
$618$		0			0
$619$			133.879i			0.216283i	0.994136	+	0.108141i	$0.0344899\pi$
$619$			133.879i			0.216283i	−0.994136	+	0.108141i	$0.965510\pi$
$620$	−373.462	−	259.736i	−0.602359	−	0.418930i
$621$		0			0
$622$	−32.5348	+	103.762i	−0.0523068	+	0.166820i
$623$			57.0280i			0.0915378i
$624$		0			0
$625$	157.286			0.251657
$626$	−366.473	−	114.909i	−0.585420	−	0.183560i
$627$		0			0
$628$	−506.051	+	727.626i	−0.805814	+	1.15864i
$629$	1050.36			1.66988
$630$		0			0
$631$	997.245			1.58042			0.790210	−	0.612836i	$-0.209971\pi$
$631$	997.245			1.58042			0.790210	+	0.612836i	$0.209971\pi$
$632$	254.025	+	327.805i	0.401939	+	0.518679i
$633$		0			0
$634$	337.033	+	105.678i	0.531598	+	0.166684i
$635$	291.752			0.459453
$636$		0			0
$637$			76.5276i			0.120137i
$638$	329.277	+	103.246i	0.516108	+	0.161827i
$639$		0			0
$640$	−177.033	+	284.828i	−0.276614	+	0.445043i
$641$			773.896i			1.20733i	0.797239	+	0.603663i	$0.206293\pi$
$641$			773.896i			1.20733i	−0.797239	+	0.603663i	$0.793707\pi$
$642$		0			0
$643$			21.9487i			0.0341348i	0.999854	+	0.0170674i	$0.00543299\pi$
$643$			21.9487i			0.0341348i	−0.999854	+	0.0170674i	$0.994567\pi$
$644$	3.03359	−	4.36185i	0.00471054	−	0.00677306i
$645$		0			0
$646$	913.260	+	286.355i	1.41372	+	0.443274i
$647$		−	689.150i		−	1.06515i	−0.846384	−	0.532573i	$-0.821225\pi$
$647$		−	689.150i		−	1.06515i	0.846384	−	0.532573i	$-0.178775\pi$
$648$		0			0
$649$	−372.491			−0.573946
$650$	−17.0133	+	54.2597i	−0.0261743	+	0.0834765i
$651$		0			0
$652$	−96.2326	+	138.368i	−0.147596	+	0.212221i
$653$	586.749			0.898543			0.449272	−	0.893395i	$-0.351684\pi$
$653$	586.749			0.898543			0.449272	+	0.893395i	$0.351684\pi$
$654$		0			0
$655$	−35.2527			−0.0538209
$656$	−851.015	+	315.883i	−1.29728	+	0.481530i
$657$		0			0
$658$	21.6593	−	69.0769i	0.0329168	−	0.104980i
$659$	166.971			0.253370			0.126685	−	0.991943i	$-0.459566\pi$
$659$	166.971			0.253370			0.126685	+	0.991943i	$0.459566\pi$
$660$		0			0
$661$		−	269.941i		−	0.408383i	−0.978931	−	0.204192i	$-0.934543\pi$
$661$		−	269.941i		−	0.408383i	0.978931	−	0.204192i	$-0.0654566\pi$
$662$	183.023	−	583.708i	0.276470	−	0.881734i
$663$		0			0
$664$	−374.066	−	482.711i	−0.563352	−	0.726974i
$665$		−	27.3326i		−	0.0411017i
$666$		0			0
$667$		−	105.758i		−	0.158558i
$668$	−108.519	+	156.035i	−0.162454	+	0.233585i
$669$		0			0
$670$	−53.0111	+	169.066i	−0.0791210	+	0.252337i
$671$		−	143.905i		−	0.214463i
$672$		0			0
$673$	−450.538			−0.669448			−0.334724	−	0.942316i	$-0.608643\pi$
$673$	−450.538			−0.669448			−0.334724	+	0.942316i	$0.608643\pi$
$674$	609.391	+	191.076i	0.904140	+	0.283496i
$675$		0			0
$676$	546.905	+	380.363i	0.809031	+	0.562667i
$677$	−1205.42			−1.78052			−0.890262	−	0.455448i	$-0.849479\pi$
$677$	−1205.42			−1.78052			−0.890262	+	0.455448i	$0.849479\pi$
$678$		0			0
$679$	29.8021			0.0438911
$680$	−328.500	+	254.564i	−0.483088	+	0.374358i
$681$		0			0
$682$	−415.304	−	130.220i	−0.608950	−	0.190938i
$683$	−913.761			−1.33786			−0.668932	−	0.743324i	$-0.733248\pi$
$683$	−913.761			−1.33786			−0.668932	+	0.743324i	$0.733248\pi$
$684$		0			0
$685$			207.714i			0.303233i
$686$	−80.6834	−	25.2985i	−0.117614	−	0.0368783i
$687$		0			0
$688$	415.165	−	154.103i	0.603437	−	0.223986i
$689$			65.0108i			0.0943554i
$690$		0			0
$691$		−	1072.45i		−	1.55203i	−0.630713	−	0.776016i	$-0.717238\pi$
$691$		−	1072.45i		−	1.55203i	0.630713	−	0.776016i	$-0.282762\pi$
$692$	380.055	+	264.322i	0.549213	+	0.381968i
$693$		0			0
$694$	−274.813	−	86.1685i	−0.395984	−	0.124162i
$695$			381.188i			0.548472i
$696$		0			0
$697$	−1124.91			−1.61393
$698$	−291.242	+	928.846i	−0.417253	+	1.33072i
$699$		0			0
$700$	−25.7418	−	17.9029i	−0.0367740	−	0.0255756i
$701$	1357.63			1.93671			0.968355	−	0.249578i	$-0.0802919\pi$
$701$	1357.63			1.93671			0.968355	+	0.249578i	$0.0802919\pi$
$702$		0			0
$703$	−1278.56			−1.81873
$704$	−80.0880	+	310.711i	−0.113761	+	0.441350i
$705$		0			0
$706$	18.8132	−	60.0000i	0.0266476	−	0.0849858i
$707$	49.7438			0.0703589
$708$		0			0
$709$		−	587.092i		−	0.828056i	−0.910264	−	0.414028i	$-0.864122\pi$
$709$		−	587.092i		−	0.828056i	0.910264	−	0.414028i	$-0.135878\pi$
$710$	163.996	−	523.024i	0.230980	−	0.736653i
$711$		0			0
$712$	−834.311	+	646.531i	−1.17179	+	0.908049i
$713$			133.388i			0.187080i
$714$		0			0
$715$		−	20.5934i		−	0.0288020i
$716$	1098.51	+	763.998i	1.53424	+	1.06704i
$717$		0			0
$718$	−275.128	+	877.454i	−0.383187	+	1.22208i
$719$			106.086i			0.147547i	0.997275	+	0.0737736i	$0.0235042\pi$
$719$			106.086i			0.147547i	−0.997275	+	0.0737736i	$0.976496\pi$
$720$		0			0
$721$	−32.5237			−0.0451092
$722$	−422.753	−	132.555i	−0.585531	−	0.183595i
$723$		0			0
$724$	434.925	−	625.357i	0.600725	−	0.863753i
$725$	−624.139			−0.860881
$726$		0			0
$727$	−943.949			−1.29842			−0.649208	−	0.760611i	$-0.724900\pi$
$727$	−943.949			−1.29842			−0.649208	+	0.760611i	$0.724900\pi$
$728$	4.28511	−	3.32065i	0.00588614	−	0.00456133i
$729$		0			0
$730$	266.355	+	83.5165i	0.364870	+	0.114406i
$731$	548.783			0.750728
$732$		0			0
$733$		−	634.996i		−	0.866298i	−0.901322	−	0.433149i	$-0.857402\pi$
$733$		−	634.996i		−	0.866298i	0.901322	−	0.433149i	$-0.142598\pi$
$734$	595.724	+	186.791i	0.811614	+	0.254484i
$735$		0			0
$736$	98.2052	−	5.06967i	0.133431	−	0.00688813i
$737$			169.524i			0.230018i
$738$		0			0
$739$			10.2565i			0.0138789i	0.999976	+	0.00693944i	$0.00220891\pi$
$739$			10.2565i			0.0138789i	−0.999976	+	0.00693944i	$0.997791\pi$
$740$	316.988	−	455.782i	0.428362	−	0.615921i
$741$		0			0
$742$	−34.2052	−	10.7251i	−0.0460986	−	0.0144544i
$743$		−	46.8052i		−	0.0629948i	−0.999504	−	0.0314974i	$-0.989972\pi$
$743$		−	46.8052i		−	0.0629948i	0.999504	−	0.0314974i	$-0.0100276\pi$
$744$		0			0
$745$	484.234			0.649979
$746$	381.091	−	1215.40i	0.510846	−	1.62922i
$747$		0			0
$748$	−227.033	+	326.440i	−0.303520	+	0.436416i
$749$	48.5557			0.0648274
$750$		0			0
$751$	−904.681			−1.20464			−0.602318	−	0.798257i	$-0.705756\pi$
$751$	−904.681			−1.20464			−0.602318	+	0.798257i	$0.705756\pi$
$752$	1256.14	−	466.259i	1.67040	−	0.620025i
$753$		0			0
$754$	32.2856	−	102.967i	0.0428191	−	0.136561i
$755$	67.5637			0.0894883
$756$		0			0
$757$		−	862.549i		−	1.13943i	−0.821842	−	0.569716i	$-0.807053\pi$
$757$		−	862.549i		−	1.13943i	0.821842	−	0.569716i	$-0.192947\pi$
$758$	−425.913	+	1358.34i	−0.561890	+	1.79201i
$759$		0			0
$760$	399.872	−	309.872i	0.526147	−	0.407726i
$761$			248.063i			0.325969i	0.986629	+	0.162985i	$0.0521121\pi$
$761$			248.063i			0.325969i	−0.986629	+	0.162985i	$0.947888\pi$
$762$		0			0
$763$			47.9196i			0.0628042i
$764$	−617.506	+	887.882i	−0.808254	+	1.16215i
$765$		0			0
$766$	−302.286	+	964.066i	−0.394629	+	1.25857i
$767$			116.480i			0.151865i
$768$		0			0
$769$	−488.897			−0.635757			−0.317879	−	0.948131i	$-0.602970\pi$
$769$	−488.897			−0.635757			−0.317879	+	0.948131i	$0.602970\pi$
$770$	10.8351	+	3.39739i	0.0140716	+	0.00441219i
$771$		0			0
$772$	−78.0312	−	54.2693i	−0.101077	−	0.0702970i
$773$	333.807			0.431833			0.215917	−	0.976412i	$-0.430726\pi$
$773$	333.807			0.431833			0.215917	+	0.976412i	$0.430726\pi$
$774$		0			0
$775$	787.201			1.01574
$776$	337.869	+	436.000i	0.435398	+	0.561856i
$777$		0			0
$778$	960.047	+	301.026i	1.23399	+	0.386922i
$779$	1369.31			1.75778
$780$		0			0
$781$		−	524.440i		−	0.671497i
$782$	116.279	+	36.4595i	0.148694	+	0.0466234i
$783$		0			0
$784$	−271.780	−	732.198i	−0.346658	−	0.933925i
$785$			580.530i			0.739528i
$786$		0			0
$787$		−	549.967i		−	0.698815i	−0.936971	−	0.349407i	$-0.886383\pi$
$787$		−	549.967i		−	0.698815i	0.936971	−	0.349407i	$-0.113617\pi$
$788$	−1066.75	−	741.908i	−1.35375	−	0.941508i
$789$		0			0
$790$	259.194	+	81.2711i	0.328094	+	0.102875i
$791$			18.9159i			0.0239139i
$792$		0			0
$793$	−45.0000			−0.0567465
$794$	−238.673	+	761.188i	−0.300595	+	0.958675i
$795$		0			0
$796$	645.782	+	449.130i	0.811284	+	0.564234i
$797$	204.092			0.256076			0.128038	−	0.991769i	$-0.459132\pi$
$797$	204.092			0.256076			0.128038	+	0.991769i	$0.459132\pi$
$798$		0			0
$799$	1660.42			2.07812
$800$	−29.9190	−	579.565i	−0.0373988	−	0.724456i
$801$		0			0
$802$	−360.000	+	1148.13i	−0.448878	+	1.43159i
$803$	267.076			0.332598
$804$		0			0
$805$		−	3.48006i		−	0.00432305i
$806$	−40.7206	+	129.868i	−0.0505218	+	0.161127i
$807$		0			0
$808$	563.949	+	727.744i	0.697956	+	0.900673i
$809$		−	463.633i		−	0.573094i	−0.958066	−	0.286547i	$-0.907493\pi$
$809$		−	463.633i		−	0.573094i	0.958066	−	0.286547i	$-0.0925074\pi$
$810$		0			0
$811$		−	490.491i		−	0.604798i	−0.953182	−	0.302399i	$-0.902213\pi$
$811$		−	490.491i		−	0.604798i	0.953182	−	0.302399i	$-0.0977874\pi$
$812$	48.8494	+	33.9739i	0.0601594	+	0.0418398i
$813$		0			0
$814$	158.923	−	506.846i	0.195237	−	0.622661i
$815$			110.396i			0.135455i
$816$		0			0
$817$	−668.015			−0.817643
$818$	1405.08	+	440.568i	1.71771	+	0.538591i
$819$		0			0
$820$	−339.487	+	488.132i	−0.414009	+	0.595283i
$821$	−41.0508			−0.0500009			−0.0250005	−	0.999687i	$-0.507959\pi$
$821$	−41.0508			−0.0500009			−0.0250005	+	0.999687i	$0.507959\pi$
$822$		0			0
$823$	−1549.78			−1.88309			−0.941543	−	0.336893i	$-0.890624\pi$
$823$	−1549.78			−1.88309			−0.941543	+	0.336893i	$0.890624\pi$
$824$	−368.724	−	475.817i	−0.447481	−	0.577448i
$825$		0			0
$826$	−61.2856	−	19.2163i	−0.0741957	−	0.0232643i
$827$	−606.895			−0.733851			−0.366926	−	0.930250i	$-0.619590\pi$
$827$	−606.895			−0.733851			−0.366926	+	0.930250i	$0.619590\pi$
$828$		0			0
$829$			1167.35i			1.40814i	0.710131	+	0.704070i	$0.248636\pi$
$829$			1167.35i			1.40814i	−0.710131	+	0.704070i	$0.751364\pi$
$830$	−381.677	−	119.676i	−0.459852	−	0.144188i
$831$		0			0
$832$	97.1612	+	25.0440i	0.116780	+	0.0301010i
$833$		−	967.850i		−	1.16189i
$834$		0			0
$835$			124.491i			0.149091i
$836$	276.360	−	397.364i	0.330574	−	0.475316i
$837$		0			0
$838$	596.601	+	187.066i	0.711934	+	0.223229i
$839$			848.946i			1.01185i	0.862576	+	0.505927i	$0.168850\pi$
$839$			848.946i			1.01185i	−0.862576	+	0.505927i	$0.831150\pi$
$840$		0			0
$841$	343.410			0.408336
$842$	278.617	−	888.581i	0.330899	−	1.05532i
$843$		0			0
$844$	−66.9688	+	96.2912i	−0.0793469	+	0.114089i
$845$	436.343			0.516382
$846$		0			0
$847$	−41.4360			−0.0489209
$848$	−230.880	−	622.008i	−0.272264	−	0.733501i
$849$		0			0
$850$	215.168	−	686.227i	0.253139	−	0.807326i
$851$	−162.790			−0.191293
$852$		0			0
$853$		−	1126.24i		−	1.32033i	−0.751121	−	0.660165i	$-0.770486\pi$
$853$		−	1126.24i		−	1.32033i	0.751121	−	0.660165i	$-0.229514\pi$
$854$	7.42386	−	23.6766i	0.00869304	−	0.0277243i
$855$		0			0
$856$	550.480	+	710.363i	0.643084	+	0.829863i
$857$			83.2647i			0.0971583i	0.998819	+	0.0485792i	$0.0154693\pi$
$857$			83.2647i			0.0971583i	−0.998819	+	0.0485792i	$0.984531\pi$
$858$		0			0
$859$			1113.74i			1.29655i	0.761405	+	0.648277i	$0.224510\pi$
$859$			1113.74i			1.29655i	−0.761405	+	0.648277i	$0.775490\pi$
$860$	165.618	−	238.133i	0.192579	−	0.276899i
$861$		0			0
$862$	297.582	−	949.066i	0.345223	−	1.10100i
$863$			1498.33i			1.73619i	0.496399	+	0.868094i	$0.334655\pi$
$863$			1498.33i			1.73619i	−0.496399	+	0.868094i	$0.665345\pi$
$864$		0			0
$865$	303.224			0.350547
$866$	−718.812	−	225.385i	−0.830037	−	0.260260i
$867$		0			0
$868$	−61.6118	−	42.8499i	−0.0709813	−	0.0493663i
$869$	259.896			0.299074
$870$		0			0
$871$	53.0111			0.0608623
$872$	−701.056	+	543.268i	−0.803963	+	0.623014i
$873$		0			0
$874$	−141.542	−	44.3809i	−0.161947	−	0.0507791i
$875$	−48.8494			−0.0558279
$876$		0			0
$877$			799.414i			0.911532i	0.890100	+	0.455766i	$0.150635\pi$
$877$			799.414i			0.911532i	−0.890100	+	0.455766i	$0.849365\pi$
$878$	−349.368	−	109.545i	−0.397913	−	0.124767i
$879$		0			0
$880$	73.1355	+	197.033i	0.0831086	+	0.223901i
$881$		−	803.298i		−	0.911802i	−0.890030	−	0.455901i	$-0.849317\pi$
$881$		−	803.298i		−	0.911802i	0.890030	−	0.455901i	$-0.150683\pi$
$882$		0			0
$883$		−	622.590i		−	0.705084i	−0.935796	−	0.352542i	$-0.885317\pi$
$883$		−	622.590i		−	0.705084i	0.935796	−	0.352542i	$-0.114683\pi$
$884$	102.080	+	70.9947i	0.115475	+	0.0803107i
$885$		0			0
$886$	981.590	+	307.780i	1.10789	+	0.347382i
$887$		−	442.477i		−	0.498847i	−0.968395	−	0.249423i	$-0.919759\pi$
$887$		−	442.477i		−	0.498847i	0.968395	−	0.249423i	$-0.0802411\pi$
$888$		0			0
$889$	48.1317			0.0541414
$890$	−206.847	+	659.687i	−0.232412	+	0.741221i
$891$		0			0
$892$	−221.355	−	153.949i	−0.248156	−	0.172588i
$893$	−2021.17			−2.26335
$894$		0			0
$895$	876.440			0.979262
$896$	−29.2059	+	46.9893i	−0.0325959	+	0.0524435i
$897$		0			0
$898$	−319.066	+	1017.58i	−0.355307	+	1.13317i
$899$	−1493.85			−1.66168
$900$		0			0
$901$		−	822.198i		−	0.912539i
$902$	−170.203	+	542.821i	−0.188695	+	0.601797i
$903$		0			0
$904$	−276.736	+	214.451i	−0.306124	+	0.237224i
$905$		−	498.935i		−	0.551309i
$906$		0			0
$907$		−	1608.33i		−	1.77324i	−0.462494	−	0.886622i	$-0.653045\pi$
$907$		−	1608.33i		−	1.77324i	0.462494	−	0.886622i	$-0.346955\pi$
$908$	−1182.22	−	822.214i	−1.30201	−	0.905522i
$909$		0			0
$910$	1.06239	−	3.38822i	0.00116746	−	0.00372332i
$911$		−	909.231i		−	0.998058i	−0.866585	−	0.499029i	$-0.833690\pi$
$911$		−	909.231i		−	0.998058i	0.866585	−	0.499029i	$-0.166310\pi$
$912$		0			0
$913$	−382.711			−0.419179
$914$	−624.105	−	195.690i	−0.682829	−	0.214103i
$915$		0			0
$916$	494.557	−	711.099i	0.539909	−	0.776309i
$917$	−5.81580			−0.00634220
$918$		0			0
$919$	715.612			0.778685			0.389343	−	0.921093i	$-0.372702\pi$
$919$	715.612			0.778685			0.389343	+	0.921093i	$0.372702\pi$
$920$	50.9127	−	39.4537i	0.0553399	−	0.0428844i
$921$		0			0
$922$	−156.729	−	49.1428i	−0.169988	−	0.0533002i
$923$	−163.996			−0.177677
$924$		0			0
$925$			960.718i			1.03861i
$926$	1118.97	+	350.857i	1.20839	+	0.378895i
$927$		0			0
$928$	56.7764	+	1099.82i	0.0611815	+	1.18516i
$929$		−	1051.36i		−	1.13171i	−0.824504	−	0.565856i	$-0.808546\pi$
$929$		−	1051.36i		−	1.13171i	0.824504	−	0.565856i	$-0.191454\pi$
$930$		0			0
$931$			1178.13i			1.26545i
$932$	340.266	−	489.251i	0.365092	−	0.524948i
$933$		0			0
$934$	−1403.49	−	440.070i	−1.50267	−	0.471167i
$935$			260.447i			0.278553i
$936$		0			0
$937$	948.670			1.01245			0.506227	−	0.862400i	$-0.331040\pi$
$937$	948.670			1.01245			0.506227	+	0.862400i	$0.331040\pi$
$938$	−8.74548	+	27.8916i	−0.00932354	+	0.0297351i
$939$		0			0
$940$	501.099	−	720.505i	0.533084	−	0.766495i
$941$	−1463.14			−1.55488			−0.777441	−	0.628956i	$-0.783483\pi$
$941$	−1463.14			−1.55488			−0.777441	+	0.628956i	$0.783483\pi$
$942$		0			0
$943$	174.345			0.184883
$944$	−413.668	−	1114.46i	−0.438208	−	1.18057i
$945$		0			0
$946$	83.0329	−	264.813i	0.0877727	−	0.279929i
$947$	1413.98			1.49312			0.746559	−	0.665320i	$-0.231705\pi$
$947$	1413.98			1.49312			0.746559	+	0.665320i	$0.231705\pi$
$948$		0			0
$949$		−	83.5165i		−	0.0880047i
$950$	−261.917	+	835.321i	−0.275702	+	0.879285i
$951$		0			0
$952$	−54.1941	+	41.9965i	−0.0569266	+	0.0441140i
$953$		−	851.291i		−	0.893275i	−0.894715	−	0.446638i	$-0.852621\pi$
$953$		−	851.291i		−	0.893275i	0.894715	−	0.446638i	$-0.147379\pi$
$954$		0			0
$955$			708.388i			0.741768i
$956$	−268.600	+	386.207i	−0.280963	+	0.403982i
$957$		0			0
$958$	228.271	−	728.015i	0.238279	−	0.759932i
$959$			34.2676i			0.0357326i
$960$		0			0
$961$	923.132			0.960595
$962$	−158.494	−	49.6963i	−0.164755	−	0.0516593i
$963$		0			0
$964$	−667.350	−	464.130i	−0.692272	−	0.481463i
$965$	−62.2564			−0.0645144
$966$		0			0
$967$	−1553.14			−1.60615			−0.803073	−	0.595881i	$-0.796803\pi$
$967$	−1553.14			−1.60615			−0.803073	+	0.595881i	$0.796803\pi$
$968$	−469.764	−	606.203i	−0.485293	−	0.626243i
$969$		0			0
$970$	344.744	+	108.095i	0.355406	+	0.111438i
$971$	−211.578			−0.217897			−0.108949	−	0.994047i	$-0.534748\pi$
$971$	−211.578			−0.217897			−0.108949	+	0.994047i	$0.534748\pi$
$972$		0			0
$973$			62.8863i			0.0646314i
$974$	−6.71078	−	2.10418i	−0.00688991	−	0.00216035i
$975$		0			0
$976$	430.549	−	159.813i	0.441137	−	0.163743i
$977$		−	892.213i		−	0.913217i	−0.889668	−	0.456609i	$-0.849064\pi$
$977$		−	892.213i		−	0.913217i	0.889668	−	0.456609i	$-0.150936\pi$
$978$		0			0
$979$			661.472i			0.675661i
$980$	−419.980	−	292.088i	−0.428551	−	0.298049i
$981$		0			0
$982$	−1301.77	−	408.172i	−1.32563	−	0.415654i
$983$			497.190i			0.505789i	0.967494	+	0.252894i	$0.0813825\pi$
$983$			497.190i			0.505789i	−0.967494	+	0.252894i	$0.918617\pi$
$984$		0			0
$985$	−851.099			−0.864060
$986$	−408.319	+	1302.23i	−0.414117	+	1.32072i
$987$		0			0
$988$	−124.258	−	86.4194i	−0.125767	−	0.0874690i
$989$	−85.0534			−0.0859994
$990$		0			0
$991$	−772.484			−0.779499			−0.389750	−	0.920921i	$-0.627438\pi$
$991$	−772.484			−0.779499			−0.389750	+	0.920921i	$0.627438\pi$
$992$	−71.6098	−	1387.16i	−0.0721873	−	1.39835i
$993$		0			0
$994$	27.0551	−	86.2856i	0.0272184	−	0.0868065i
$995$	515.231			0.517820
$996$		0			0
$997$			811.670i			0.814112i	0.913403	+	0.407056i	$0.133445\pi$
$997$			811.670i			0.814112i	−0.913403	+	0.407056i	$0.866555\pi$
$998$	−113.245	+	361.167i	−0.113472	+	0.361891i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.h.f.53.8	yes	8
3.2	odd	2	inner	216.3.h.f.53.1	✓	8
4.3	odd	2		864.3.h.e.593.5		8
8.3	odd	2		864.3.h.e.593.4		8
8.5	even	2	inner	216.3.h.f.53.2	yes	8
12.11	even	2		864.3.h.e.593.3		8
24.5	odd	2	inner	216.3.h.f.53.7	yes	8
24.11	even	2		864.3.h.e.593.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.h.f.53.1	✓	8	3.2	odd	2	inner
216.3.h.f.53.2	yes	8	8.5	even	2	inner
216.3.h.f.53.7	yes	8	24.5	odd	2	inner
216.3.h.f.53.8	yes	8	1.1	even	1	trivial
864.3.h.e.593.3		8	12.11	even	2
864.3.h.e.593.4		8	8.3	odd	2
864.3.h.e.593.5		8	4.3	odd	2
864.3.h.e.593.6		8	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.90839 + 0.598380i) q^{2} +(3.28388 + 2.28388i) q^{4} +2.62001 q^{5} +0.432236 q^{7} +(4.90029 + 6.32354i) q^{8} +O(q^{10})\)	\(q+(1.90839 + 0.598380i) q^{2} +(3.28388 + 2.28388i) q^{4} +2.62001 q^{5} +0.432236 q^{7} +(4.90029 + 6.32354i) q^{8} +(5.00000 + 1.56776i) q^{10} +5.01353 q^{11} -1.56776i q^{13} +(0.824873 + 0.258641i) q^{14} +(5.56776 + 15.0000i) q^{16} +19.8276i q^{17} -24.1355i q^{19} +(8.60382 + 5.98380i) q^{20} +(9.56776 + 3.00000i) q^{22} -3.07300i q^{23} -18.1355 q^{25} +(0.938119 - 2.99190i) q^{26} +(1.41941 + 0.987175i) q^{28} +34.4153 q^{29} -43.4066 q^{31} +(1.64975 + 31.9574i) q^{32} +(-11.8645 + 37.8388i) q^{34} +1.13246 q^{35} -52.9744i q^{37} +(14.4422 - 46.0599i) q^{38} +(12.8388 + 16.5678i) q^{40} +56.7343i q^{41} -27.6776i q^{43} +(16.4639 + 11.4503i) q^{44} +(1.83882 - 5.86447i) q^{46} -83.7425i q^{47} -48.8132 q^{49} +(-34.6096 - 10.8519i) q^{50} +(3.58059 - 5.14835i) q^{52} -41.4672 q^{53} +13.1355 q^{55} +(2.11808 + 2.73326i) q^{56} +(65.6776 + 20.5934i) q^{58} -74.2970 q^{59} -28.7033i q^{61} +(-82.8366 - 25.9736i) q^{62} +(-15.9744 + 61.9744i) q^{64} -4.10756i q^{65} +33.8132i q^{67} +(-45.2840 + 65.1117i) q^{68} +(2.16118 + 0.677644i) q^{70} -104.605i q^{71} +53.2711 q^{73} +(31.6988 - 101.096i) q^{74} +(55.1227 - 79.2582i) q^{76} +2.16703 q^{77} +51.8388 q^{79} +(14.5876 + 39.3002i) q^{80} +(-33.9487 + 108.271i) q^{82} -76.3355 q^{83} +51.9487i q^{85} +(16.5618 - 52.8197i) q^{86} +(24.5678 + 31.7033i) q^{88} +131.937i q^{89} -0.677644i q^{91} +(7.01837 - 10.0914i) q^{92} +(50.1099 - 159.813i) q^{94} -63.2354i q^{95} +68.9487 q^{97} +(-93.1544 - 29.2088i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 48 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 48 * q^7	\( 8 q + 4 q^{4} + 48 q^{7} + 40 q^{10} + 32 q^{22} - 56 q^{25} - 100 q^{28} - 80 q^{31} - 184 q^{34} - 120 q^{40} - 208 q^{46} + 144 q^{49} + 140 q^{52} + 16 q^{55} + 80 q^{58} + 184 q^{64} + 240 q^{70} + 248 q^{73} + 196 q^{76} + 192 q^{79} + 352 q^{82} + 152 q^{88} - 72 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 48 * q^7 + 40 * q^10 + 32 * q^22 - 56 * q^25 - 100 * q^28 - 80 * q^31 - 184 * q^34 - 120 * q^40 - 208 * q^46 + 144 * q^49 + 140 * q^52 + 16 * q^55 + 80 * q^58 + 184 * q^64 + 240 * q^70 + 248 * q^73 + 196 * q^76 + 192 * q^79 + 352 * q^82 + 152 * q^88 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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