LMFDB - Embedded newform 1216.2.i.o.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, degree $2$, not 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.41342275584.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} + 2x^{5} + 81x^{4} - 8x^{3} + 208x^{2} + 128x + 256 $ x^8 - 2x^7 + 13x^6 + 2x^5 + 81x^4 - 8x^3 + 208x^2 + 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 608)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.1
Root			$-0.564469 + 0.977689i$ of defining polynomial
Character	$\chi$	$=$	1216.577
Dual form			1216.2.i.o.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 - 2.09077i) q^{3} +(-1.06447 - 1.84371i) q^{5} +1.59656 q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-1.20711 - 2.09077i) q^{3} +(-1.06447 - 1.84371i) q^{5} +1.59656 q^{7} +(-1.41421 + 2.44949i) q^{9} -1.12894 q^{11} +(3.27696 - 5.67587i) q^{13} +(-2.56986 + 4.45112i) q^{15} +(-2.14802 - 3.72049i) q^{17} +(-2.69341 + 3.42718i) q^{19} +(-1.92722 - 3.33804i) q^{21} +(2.85513 - 4.94523i) q^{23} +(0.233811 - 0.404972i) q^{25} -0.414214 q^{27} +(0.882123 - 1.52788i) q^{29} -5.25341 q^{31} +(1.36275 + 2.36035i) q^{33} +(-1.69949 - 2.94360i) q^{35} +1.23187 q^{37} -15.8226 q^{39} +(4.04315 + 7.00294i) q^{41} +(2.35736 + 4.08307i) q^{43} +6.02155 q^{45} +(-0.973296 + 1.68580i) q^{47} -4.45100 q^{49} +(-5.18579 + 8.98205i) q^{51} +(4.56224 - 7.90203i) q^{53} +(1.20172 + 2.08144i) q^{55} +(10.4167 + 1.49433i) q^{57} +(-1.33605 - 2.31410i) q^{59} +(-5.89290 + 10.2068i) q^{61} +(-2.25788 + 3.91076i) q^{63} -13.9529 q^{65} +(-5.87920 + 10.1831i) q^{67} -13.7858 q^{69} +(-2.71817 - 4.70800i) q^{71} +(0.967622 + 1.67597i) q^{73} -1.12894 q^{75} -1.80242 q^{77} +(7.49707 + 12.9853i) q^{79} +(4.74264 + 8.21449i) q^{81} +4.06418 q^{83} +(-4.57301 + 7.92069i) q^{85} -4.25927 q^{87} +(0.680403 - 1.17849i) q^{89} +(5.23187 - 9.06186i) q^{91} +(6.34143 + 10.9837i) q^{93} +(9.18579 + 1.31775i) q^{95} +(-9.00052 - 15.5894i) q^{97} +(1.59656 - 2.76532i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7	$ 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7} + 4 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{17} - 2 q^{19} + 8 q^{21} + 2 q^{23} - 2 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - 6 q^{33} - 4 q^{35} + 8 q^{37} - 12 q^{39} + 8 q^{41} + 18 q^{43} - 16 q^{45} - 6 q^{47} + 32 q^{49} - 18 q^{51} + 10 q^{53} + 20 q^{55} + 10 q^{57} + 8 q^{59} - 18 q^{61} + 8 q^{63} - 36 q^{65} - 4 q^{67} - 52 q^{69} - 6 q^{71} + 4 q^{75} - 16 q^{77} + 14 q^{79} + 4 q^{81} + 4 q^{83} + 22 q^{85} - 60 q^{87} - 2 q^{89} + 40 q^{91} + 16 q^{93} + 50 q^{95} - 12 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7 + 4 * q^11 - 2 * q^13 + 2 * q^15 - 2 * q^17 - 2 * q^19 + 8 * q^21 + 2 * q^23 - 2 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - 6 * q^33 - 4 * q^35 + 8 * q^37 - 12 * q^39 + 8 * q^41 + 18 * q^43 - 16 * q^45 - 6 * q^47 + 32 * q^49 - 18 * q^51 + 10 * q^53 + 20 * q^55 + 10 * q^57 + 8 * q^59 - 18 * q^61 + 8 * q^63 - 36 * q^65 - 4 * q^67 - 52 * q^69 - 6 * q^71 + 4 * q^75 - 16 * q^77 + 14 * q^79 + 4 * q^81 + 4 * q^83 + 22 * q^85 - 60 * q^87 - 2 * q^89 + 40 * q^91 + 16 * q^93 + 50 * q^95 - 12 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	−0.969528	−	0.244981i	$-0.921218\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	0.272605	−	0.962126i	$-0.412115\pi$
$4$		0			0
$5$	−1.06447	−	1.84371i	−0.476045	−	0.824534i	0.523578	−	0.851978i	$-0.324597\pi$
$5$	−1.06447	−	1.84371i	−0.476045	−	0.824534i	−0.999623	+	0.0274433i	$0.991263\pi$
$6$		0			0
$7$	1.59656			0.603443			0.301721	−	0.953396i	$-0.402439\pi$
$7$	1.59656			0.603443			0.301721	+	0.953396i	$0.402439\pi$
$8$		0			0
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$		0			0
$11$	−1.12894			−0.340388			−0.170194	−	0.985411i	$-0.554439\pi$
$11$	−1.12894			−0.340388			−0.170194	+	0.985411i	$0.554439\pi$
$12$		0			0
$13$	3.27696	−	5.67587i	0.908866	−	1.57420i	0.0932238	−	0.995645i	$-0.470283\pi$
$13$	3.27696	−	5.67587i	0.908866	−	1.57420i	0.815642	−	0.578557i	$-0.196384\pi$
$14$		0			0
$15$	−2.56986	+	4.45112i	−0.663534	+	1.14927i
$16$		0			0
$17$	−2.14802	−	3.72049i	−0.520972	−	0.902351i	−0.999703	−	0.0243886i	$-0.992236\pi$
$17$	−2.14802	−	3.72049i	−0.520972	−	0.902351i	0.478730	−	0.877962i	$-0.341097\pi$
$18$		0			0
$19$	−2.69341	+	3.42718i	−0.617910	+	0.786249i
$19$	−2.69341	+	3.42718i	−0.617910	+	0.786249i
$20$		0			0
$21$	−1.92722	−	3.33804i	−0.420554	−	0.728420i
$22$		0			0
$23$	2.85513	−	4.94523i	0.595336	−	1.03115i	−0.398163	−	0.917315i	$-0.630352\pi$
$23$	2.85513	−	4.94523i	0.595336	−	1.03115i	0.993499	−	0.113838i	$-0.0363144\pi$
$24$		0			0
$25$	0.233811	−	0.404972i	0.0467622	−	0.0809944i
$26$		0			0
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	0.882123	−	1.52788i	0.163806	−	0.283720i	−0.772425	−	0.635107i	$-0.780956\pi$
$29$	0.882123	−	1.52788i	0.163806	−	0.283720i	0.936231	+	0.351386i	$0.114290\pi$
$30$		0			0
$31$	−5.25341			−0.943541			−0.471771	−	0.881721i	$-0.656385\pi$
$31$	−5.25341			−0.943541			−0.471771	+	0.881721i	$0.656385\pi$
$32$		0			0
$33$	1.36275	+	2.36035i	0.237224	+	0.410884i
$34$		0			0
$35$	−1.69949	−	2.94360i	−0.287266	−	0.497559i
$36$		0			0
$37$	1.23187			0.202518			0.101259	−	0.994860i	$-0.467713\pi$
$37$	1.23187			0.202518			0.101259	+	0.994860i	$0.467713\pi$
$38$		0			0
$39$	−15.8226			−2.53364
$40$		0			0
$41$	4.04315	+	7.00294i	0.631434	+	1.09368i	0.987259	+	0.159123i	$0.0508668\pi$
$41$	4.04315	+	7.00294i	0.631434	+	1.09368i	−0.355824	+	0.934553i	$0.615800\pi$
$42$		0			0
$43$	2.35736	+	4.08307i	0.359494	+	0.622663i	0.987876	−	0.155242i	$-0.0496158\pi$
$43$	2.35736	+	4.08307i	0.359494	+	0.622663i	−0.628382	+	0.777905i	$0.716283\pi$
$44$		0			0
$45$	6.02155			0.897639
$46$		0			0
$47$	−0.973296	+	1.68580i	−0.141970	+	0.245899i	−0.928238	−	0.371986i	$-0.878677\pi$
$47$	−0.973296	+	1.68580i	−0.141970	+	0.245899i	0.786269	+	0.617885i	$0.212010\pi$
$48$		0			0
$49$	−4.45100			−0.635857
$50$		0			0
$51$	−5.18579	+	8.98205i	−0.726156	+	1.25774i
$52$		0			0
$53$	4.56224	−	7.90203i	0.626672	−	1.08543i	−0.361544	−	0.932355i	$-0.617750\pi$
$53$	4.56224	−	7.90203i	0.626672	−	1.08543i	0.988215	−	0.153072i	$-0.0489166\pi$
$54$		0			0
$55$	1.20172	+	2.08144i	0.162040	+	0.280661i
$56$		0			0
$57$	10.4167	+	1.49433i	1.37972	+	0.197928i
$58$		0			0
$59$	−1.33605	−	2.31410i	−0.173938	−	0.301270i	0.765855	−	0.643013i	$-0.222316\pi$
$59$	−1.33605	−	2.31410i	−0.173938	−	0.301270i	−0.939793	+	0.341743i	$0.888983\pi$
$60$		0			0
$61$	−5.89290	+	10.2068i	−0.754508	+	1.30685i	0.191110	+	0.981569i	$0.438791\pi$
$61$	−5.89290	+	10.2068i	−0.754508	+	1.30685i	−0.945619	+	0.325278i	$0.894542\pi$
$62$		0			0
$63$	−2.25788	+	3.91076i	−0.284466	+	0.492709i
$64$		0			0
$65$	−13.9529			−1.73064
$66$		0			0
$67$	−5.87920	+	10.1831i	−0.718258	+	1.24406i	0.243431	+	0.969918i	$0.421727\pi$
$67$	−5.87920	+	10.1831i	−0.718258	+	1.24406i	−0.961689	+	0.274142i	$0.911606\pi$
$68$		0			0
$69$	−13.7858			−1.65961
$70$		0			0
$71$	−2.71817	−	4.70800i	−0.322587	−	0.558737i	0.658434	−	0.752639i	$-0.271219\pi$
$71$	−2.71817	−	4.70800i	−0.322587	−	0.558737i	−0.981021	+	0.193901i	$0.937886\pi$
$72$		0			0
$73$	0.967622	+	1.67597i	0.113252	+	0.196157i	0.917079	−	0.398704i	$-0.130540\pi$
$73$	0.967622	+	1.67597i	0.113252	+	0.196157i	−0.803828	+	0.594862i	$0.797207\pi$
$74$		0			0
$75$	−1.12894			−0.130359
$76$		0			0
$77$	−1.80242			−0.205405
$78$		0			0
$79$	7.49707	+	12.9853i	0.843487	+	1.46096i	0.886929	+	0.461906i	$0.152834\pi$
$79$	7.49707	+	12.9853i	0.843487	+	1.46096i	−0.0434422	+	0.999056i	$0.513832\pi$
$80$		0			0
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$		0			0
$83$	4.06418			0.446102			0.223051	−	0.974807i	$-0.428398\pi$
$83$	4.06418			0.446102			0.223051	+	0.974807i	$0.428398\pi$
$84$		0			0
$85$	−4.57301	+	7.92069i	−0.496013	+	0.859119i
$86$		0			0
$87$	−4.25927			−0.456641
$88$		0			0
$89$	0.680403	−	1.17849i	0.0721226	−	0.124920i	−0.827709	−	0.561158i	$-0.810356\pi$
$89$	0.680403	−	1.17849i	0.0721226	−	0.124920i	0.899831	+	0.436238i	$0.143689\pi$
$90$		0			0
$91$	5.23187	−	9.06186i	0.548449	−	0.949941i
$92$		0			0
$93$	6.34143	+	10.9837i	0.657576	+	1.13895i
$94$		0			0
$95$	9.18579	+	1.31775i	0.942442	+	0.135198i
$96$		0			0
$97$	−9.00052	−	15.5894i	−0.913864	−	1.58286i	−0.808556	−	0.588419i	$-0.799750\pi$
$97$	−9.00052	−	15.5894i	−0.913864	−	1.58286i	−0.105308	−	0.994440i	$-0.533583\pi$
$98$		0			0
$99$	1.59656	−	2.76532i	0.160460	−	0.277925i
$100$		0			0
$101$	0.220806	−	0.382447i	0.0219710	−	0.0380549i	−0.854831	−	0.518907i	$-0.826339\pi$
$101$	0.220806	−	0.382447i	0.0219710	−	0.0380549i	0.876802	+	0.480852i	$0.159673\pi$
$102$		0			0
$103$	3.39898			0.334911			0.167456	−	0.985880i	$-0.446445\pi$
$103$	3.39898			0.334911			0.167456	+	0.985880i	$0.446445\pi$
$104$		0			0
$105$	−4.10293	+	7.10648i	−0.400405	+	0.693522i
$106$		0			0
$107$	−19.7089			−1.90533			−0.952664	−	0.304024i	$-0.901670\pi$
$107$	−19.7089			−1.90533			−0.952664	+	0.304024i	$0.901670\pi$
$108$		0			0
$109$	7.63777	+	13.2290i	0.731566	+	1.26711i	0.956214	+	0.292669i	$0.0945433\pi$
$109$	7.63777	+	13.2290i	0.731566	+	1.26711i	−0.224648	+	0.974440i	$0.572123\pi$
$110$		0			0
$111$	−1.48700	−	2.57555i	−0.141139	−	0.244461i
$112$		0			0
$113$	12.1460			1.14260			0.571301	−	0.820741i	$-0.306439\pi$
$113$	12.1460			1.14260			0.571301	+	0.820741i	$0.306439\pi$
$114$		0			0
$115$	−12.1568			−1.13363
$116$		0			0
$117$	9.26865	+	16.0538i	0.856887	+	1.48417i
$118$		0			0
$119$	−3.42945	−	5.93998i	−0.314377	−	0.544517i
$120$		0			0
$121$	−9.72550			−0.884136
$122$		0			0
$123$	9.76103	−	16.9066i	0.880123	−	1.52442i
$124$		0			0
$125$	−11.6402			−1.04113
$126$		0			0
$127$	4.82498	−	8.35712i	0.428148	−	0.741574i	−0.568561	−	0.822641i	$-0.692499\pi$
$127$	4.82498	−	8.35712i	0.428148	−	0.741574i	0.996709	+	0.0810672i	$0.0258328\pi$
$128$		0			0
$129$	5.69118	−	9.85741i	0.501080	−	0.867896i
$130$		0			0
$131$	−6.80367	−	11.7843i	−0.594439	−	1.02960i	−0.993626	−	0.112729i	$-0.964041\pi$
$131$	−6.80367	−	11.7843i	−0.594439	−	1.02960i	0.399187	−	0.916870i	$-0.369293\pi$
$132$		0			0
$133$	−4.30019	+	5.47170i	−0.372873	+	0.474456i
$134$		0			0
$135$	0.440918	+	0.763692i	0.0379481	+	0.0657281i
$136$		0			0
$137$	4.14608	−	7.18122i	0.354224	−	0.613533i	−0.632761	−	0.774347i	$-0.718079\pi$
$137$	4.14608	−	7.18122i	0.354224	−	0.613533i	0.986985	+	0.160814i	$0.0514118\pi$
$138$		0			0
$139$	0.464983	−	0.805375i	0.0394394	−	0.0683110i	−0.845632	−	0.533766i	$-0.820776\pi$
$139$	0.464983	−	0.805375i	0.0394394	−	0.0683110i	0.885071	+	0.465455i	$0.154109\pi$
$140$		0			0
$141$	4.69949			0.395768
$142$		0			0
$143$	−3.69949	+	6.40770i	−0.309367	+	0.535839i
$144$		0			0
$145$	−3.75597			−0.311916
$146$		0			0
$147$	5.37283	+	9.30601i	0.443143	+	0.767547i
$148$		0			0
$149$	−7.90367	−	13.6896i	−0.647494	−	1.12149i	−0.983719	−	0.179711i	$-0.942484\pi$
$149$	−7.90367	−	13.6896i	−0.647494	−	1.12149i	0.336226	−	0.941781i	$-0.390850\pi$
$150$		0			0
$151$	−2.53180			−0.206035			−0.103018	−	0.994680i	$-0.532850\pi$
$151$	−2.53180			−0.206035			−0.103018	+	0.994680i	$0.532850\pi$
$152$		0			0
$153$	12.1511			0.982355
$154$		0			0
$155$	5.59210	+	9.68580i	0.449168	+	0.777982i
$156$		0			0
$157$	−2.47593	−	4.28844i	−0.197601	−	0.342255i	0.750149	−	0.661269i	$-0.229982\pi$
$157$	−2.47593	−	4.28844i	−0.197601	−	0.342255i	−0.947750	+	0.319014i	$0.896648\pi$
$158$		0			0
$159$	−22.0284			−1.74697
$160$		0			0
$161$	4.55839	−	7.89536i	0.359251	−	0.622241i
$162$		0			0
$163$	6.66520			0.522059			0.261030	−	0.965331i	$-0.415938\pi$
$163$	6.66520			0.522059			0.261030	+	0.965331i	$0.415938\pi$
$164$		0			0
$165$	2.90121	−	5.02504i	0.225859	−	0.391199i
$166$		0			0
$167$	8.97158	−	15.5392i	0.694242	−	1.20246i	−0.276194	−	0.961102i	$-0.589073\pi$
$167$	8.97158	−	15.5392i	0.694242	−	1.20246i	0.970436	−	0.241360i	$-0.0775935\pi$
$168$		0			0
$169$	−14.9770	−	25.9409i	−1.15207	−	1.99545i
$170$		0			0
$171$	−4.58579	−	11.4442i	−0.350684	−	0.875163i
$172$		0			0
$173$	6.56224	+	11.3661i	0.498918	+	0.864151i	0.999999	−	0.00124927i	$-0.000397655\pi$
$173$	6.56224	+	11.3661i	0.498918	+	0.864151i	−0.501082	+	0.865400i	$0.667064\pi$
$174$		0			0
$175$	0.373293	−	0.646562i	0.0282183	−	0.0488755i
$176$		0			0
$177$	−3.22550	+	5.58673i	−0.242443	+	0.419924i
$178$		0			0
$179$	22.7005			1.69672			0.848358	−	0.529422i	$-0.177591\pi$
$179$	22.7005			1.69672			0.848358	+	0.529422i	$0.177591\pi$
$180$		0			0
$181$	10.9144	−	18.9044i	0.811264	−	1.40515i	−0.100715	−	0.994915i	$-0.532113\pi$
$181$	10.9144	−	18.9044i	0.811264	−	1.40515i	0.911980	−	0.410235i	$-0.134553\pi$
$182$		0			0
$183$	28.4534			2.10334
$184$		0			0
$185$	−1.31128	−	2.27121i	−0.0964076	−	0.166983i
$186$		0			0
$187$	2.42499	+	4.20020i	0.177333	+	0.307149i
$188$		0			0
$189$	−0.661317			−0.0481037
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	5.13725	+	8.89798i	0.369787	+	0.640491i	0.989532	−	0.144313i	$-0.0460972\pi$
$193$	5.13725	+	8.89798i	0.369787	+	0.640491i	−0.619745	+	0.784803i	$0.712764\pi$
$194$		0			0
$195$	16.8426	+	29.1723i	1.20613	+	2.08907i
$196$		0			0
$197$	−12.4250			−0.885244			−0.442622	−	0.896708i	$-0.645952\pi$
$197$	−12.4250			−0.885244			−0.442622	+	0.896708i	$0.645952\pi$
$198$		0			0
$199$	5.01422	−	8.68488i	0.355448	−	0.615655i	−0.631746	−	0.775175i	$-0.717662\pi$
$199$	5.01422	−	8.68488i	0.355448	−	0.615655i	0.987195	+	0.159521i	$0.0509948\pi$
$200$		0			0
$201$	28.3873			2.00228
$202$		0			0
$203$	1.40836	−	2.43935i	0.0988476	−	0.171209i
$204$		0			0
$205$	8.60762	−	14.9088i	0.601182	−	1.04128i
$206$		0			0
$207$	8.07553	+	13.9872i	0.561288	+	0.972180i
$208$		0			0
$209$	3.04069	−	3.86907i	0.210329	−	0.267629i
$210$		0			0
$211$	12.6108	+	21.8425i	0.868162	+	1.50370i	0.863873	+	0.503709i	$0.168032\pi$
$211$	12.6108	+	21.8425i	0.868162	+	1.50370i	0.00428844	+	0.999991i	$0.498635\pi$
$212$		0			0
$213$	−6.56224	+	11.3661i	−0.449637	+	0.778794i
$214$		0			0
$215$	5.01868	−	8.69261i	0.342271	−	0.592831i
$216$		0			0
$217$	−8.38739			−0.569373
$218$		0			0
$219$	2.33605	−	4.04615i	0.157855	−	0.273413i
$220$		0			0
$221$	−28.1560			−1.89398
$222$		0			0
$223$	−0.155642	−	0.269580i	−0.0104226	−	0.0180524i	0.860767	−	0.508999i	$-0.169984\pi$
$223$	−0.155642	−	0.269580i	−0.0104226	−	0.0180524i	−0.871190	+	0.490947i	$0.836651\pi$
$224$		0			0
$225$	0.661317	+	1.14543i	0.0440878	+	0.0763623i
$226$		0			0
$227$	−14.1073			−0.936333			−0.468166	−	0.883640i	$-0.655085\pi$
$227$	−14.1073			−0.936333			−0.468166	+	0.883640i	$0.655085\pi$
$228$		0			0
$229$	12.1511			0.802965			0.401482	−	0.915867i	$-0.368495\pi$
$229$	12.1511			0.802965			0.401482	+	0.915867i	$0.368495\pi$
$230$		0			0
$231$	2.17571	+	3.76844i	0.143151	+	0.247945i
$232$		0			0
$233$	−0.424470	−	0.735203i	−0.0278079	−	0.0481648i	0.851787	−	0.523889i	$-0.175519\pi$
$233$	−0.424470	−	0.735203i	−0.0278079	−	0.0481648i	−0.879594	+	0.475724i	$0.842186\pi$
$234$		0			0
$235$	4.14417			0.270336
$236$		0			0
$237$	18.0995	−	31.3493i	1.17569	−	2.03636i
$238$		0			0
$239$	−18.9352			−1.22482			−0.612410	−	0.790541i	$-0.709800\pi$
$239$	−18.9352			−1.22482			−0.612410	+	0.790541i	$0.709800\pi$
$240$		0			0
$241$	2.81128	−	4.86929i	0.181091	−	0.313658i	−0.761161	−	0.648562i	$-0.775371\pi$
$241$	2.81128	−	4.86929i	0.181091	−	0.313658i	0.942252	+	0.334904i	$0.108704\pi$
$242$		0			0
$243$	10.8284	−	18.7554i	0.694644	−	1.20316i
$244$		0			0
$245$	4.73795	+	8.20637i	0.302696	+	0.524286i
$246$		0			0
$247$	10.6260	+	26.5182i	0.676117	+	1.68731i
$248$		0			0
$249$	−4.90590	−	8.49727i	−0.310899	−	0.538493i
$250$		0			0
$251$	11.3537	−	19.6652i	0.716640	−	1.24126i	−0.245684	−	0.969350i	$-0.579013\pi$
$251$	11.3537	−	19.6652i	0.716640	−	1.24126i	0.962324	−	0.271906i	$-0.0876540\pi$
$252$		0			0
$253$	−3.22327	+	5.58286i	−0.202645	+	0.350992i
$254$		0			0
$255$	22.0805			1.38273
$256$		0			0
$257$	−6.79605	+	11.7711i	−0.423926	+	0.734261i	−0.996319	−	0.0857179i	$-0.972682\pi$
$257$	−6.79605	+	11.7711i	−0.423926	+	0.734261i	0.572394	+	0.819979i	$0.306015\pi$
$258$		0			0
$259$	1.96675			0.122208
$260$		0			0
$261$	2.49502	+	4.32150i	0.154438	+	0.267494i
$262$		0			0
$263$	−13.1993	−	22.8619i	−0.813904	−	1.40972i	−0.910112	−	0.414363i	$-0.864005\pi$
$263$	−13.1993	−	22.8619i	−0.813904	−	1.40972i	0.0962075	−	0.995361i	$-0.469329\pi$
$264$		0			0
$265$	−19.4254			−1.19330
$266$		0			0
$267$	−3.28528			−0.201056
$268$		0			0
$269$	−6.29851	−	10.9093i	−0.384027	−	0.665154i	0.607607	−	0.794238i	$-0.292130\pi$
$269$	−6.29851	−	10.9093i	−0.384027	−	0.665154i	−0.991634	+	0.129084i	$0.958796\pi$
$270$		0			0
$271$	3.65616	+	6.33265i	0.222096	+	0.384681i	0.955444	−	0.295172i	$-0.0953769\pi$
$271$	3.65616	+	6.33265i	0.222096	+	0.384681i	−0.733348	+	0.679853i	$0.762044\pi$
$272$		0			0
$273$	−25.2617			−1.52891
$274$		0			0
$275$	−0.263958	+	0.457189i	−0.0159173	+	0.0275695i
$276$		0			0
$277$	22.3917			1.34539			0.672695	−	0.739920i	$-0.265137\pi$
$277$	22.3917			1.34539			0.672695	+	0.739920i	$0.265137\pi$
$278$		0			0
$279$	7.42945	−	12.8682i	0.444790	−	0.770398i
$280$		0			0
$281$	−15.7971	+	27.3614i	−0.942375	+	1.63224i	−0.181451	+	0.983400i	$0.558079\pi$
$281$	−15.7971	+	27.3614i	−0.942375	+	1.63224i	−0.760924	+	0.648841i	$0.775254\pi$
$282$		0			0
$283$	−11.8297	−	20.4896i	−0.703201	−	1.21798i	−0.967337	−	0.253495i	$-0.918420\pi$
$283$	−11.8297	−	20.4896i	−0.703201	−	1.21798i	0.264136	−	0.964486i	$-0.414913\pi$
$284$		0			0
$285$	−8.33312	−	20.7960i	−0.493611	−	1.23185i
$286$		0			0
$287$	6.45513	+	11.1806i	0.381035	+	0.659971i
$288$		0			0
$289$	−0.728017	+	1.26096i	−0.0428245	+	0.0741743i
$290$		0			0
$291$	−21.7292	+	37.6360i	−1.27379	+	2.20626i
$292$		0			0
$293$	−0.176035			−0.0102841			−0.00514205	−	0.999987i	$-0.501637\pi$
$293$	−0.176035			−0.0102841			−0.00514205	+	0.999987i	$0.501637\pi$
$294$		0			0
$295$	−2.84436	+	4.92657i	−0.165605	+	0.286836i
$296$		0			0
$297$	0.467622			0.0271342
$298$		0			0
$299$	−18.7123	−	32.4107i	−1.08216	−	1.87436i
$300$		0			0
$301$	3.76367	+	6.51887i	0.216934	+	0.375741i
$302$		0			0
$303$	−1.06615			−0.0612485
$304$		0			0
$305$	25.0912			1.43672
$306$		0			0
$307$	−13.5673	−	23.4993i	−0.774329	−	1.34118i	−0.935171	−	0.354197i	$-0.884754\pi$
$307$	−13.5673	−	23.4993i	−0.774329	−	1.34118i	0.160842	−	0.986980i	$-0.448579\pi$
$308$		0			0
$309$	−4.10293	−	7.10648i	−0.233407	−	0.404274i
$310$		0			0
$311$	17.0829			0.968681			0.484341	−	0.874880i	$-0.339060\pi$
$311$	17.0829			0.968681			0.484341	+	0.874880i	$0.339060\pi$
$312$		0			0
$313$	4.61370	−	7.99117i	0.260782	−	0.451687i	−0.705668	−	0.708543i	$-0.749353\pi$
$313$	4.61370	−	7.99117i	0.260782	−	0.451687i	0.966450	+	0.256855i	$0.0826863\pi$
$314$		0			0
$315$	9.61376			0.541674
$316$		0			0
$317$	2.34172	−	4.05598i	0.131524	−	0.227806i	−0.792740	−	0.609560i	$-0.791346\pi$
$317$	2.34172	−	4.05598i	0.131524	−	0.227806i	0.924264	+	0.381753i	$0.124680\pi$
$318$		0			0
$319$	−0.995862	+	1.72488i	−0.0557576	+	0.0965750i
$320$		0			0
$321$	23.7907	+	41.2067i	1.32787	+	2.29994i
$322$		0			0
$323$	18.5363	+	2.65912i	1.03139	+	0.147958i
$324$		0			0
$325$	−1.53238	−	2.65416i	−0.0850011	−	0.147226i
$326$		0			0
$327$	18.4392	−	31.9376i	1.01969	−	1.76616i
$328$		0			0
$329$	−1.55393	+	2.69148i	−0.0856707	+	0.148386i
$330$		0			0
$331$	30.2279			1.66147			0.830737	−	0.556665i	$-0.187919\pi$
$331$	30.2279			1.66147			0.830737	+	0.556665i	$0.187919\pi$
$332$		0			0
$333$	−1.74212	+	3.01745i	−0.0954678	+	0.165355i
$334$		0			0
$335$	25.0329			1.36769
$336$		0			0
$337$	3.98286	+	6.89851i	0.216960	+	0.375786i	0.953877	−	0.300197i	$-0.0970525\pi$
$337$	3.98286	+	6.89851i	0.216960	+	0.375786i	−0.736917	+	0.675983i	$0.763719\pi$
$338$		0			0
$339$	−14.6615	−	25.3945i	−0.796306	−	1.37924i
$340$		0			0
$341$	5.93078			0.321170
$342$		0			0
$343$	−18.2822			−0.987146
$344$		0			0
$345$	14.6746	+	25.4171i	0.790051	+	1.36841i
$346$		0			0
$347$	11.0889	+	19.2066i	0.595286	+	1.03106i	0.993507	+	0.113775i	$0.0362944\pi$
$347$	11.0889	+	19.2066i	0.595286	+	1.03106i	−0.398221	+	0.917290i	$0.630372\pi$
$348$		0			0
$349$	−22.7509			−1.21783			−0.608915	−	0.793236i	$-0.708395\pi$
$349$	−22.7509			−1.21783			−0.608915	+	0.793236i	$0.708395\pi$
$350$		0			0
$351$	−1.35736	+	2.35102i	−0.0724506	+	0.125488i
$352$		0			0
$353$	5.63919			0.300144			0.150072	−	0.988675i	$-0.452049\pi$
$353$	5.63919			0.300144			0.150072	+	0.988675i	$0.452049\pi$
$354$		0			0
$355$	−5.78681	+	10.0231i	−0.307132	+	0.531968i
$356$		0			0
$357$	−8.27942	+	14.3404i	−0.438194	+	0.758974i
$358$		0			0
$359$	−1.90326	−	3.29655i	−0.100450	−	0.173985i	0.811420	−	0.584464i	$-0.198695\pi$
$359$	−1.90326	−	3.29655i	−0.100450	−	0.173985i	−0.911870	+	0.410478i	$0.865362\pi$
$360$		0			0
$361$	−4.49111	−	18.4616i	−0.236374	−	0.971662i
$362$		0			0
$363$	11.7397	+	20.3338i	0.616175	+	1.06725i
$364$		0			0
$365$	2.06001	−	3.56804i	0.107826	−	0.186760i
$366$		0			0
$367$	2.49879	−	4.32803i	0.130436	−	0.225921i	−0.793409	−	0.608689i	$-0.791696\pi$
$367$	2.49879	−	4.32803i	0.130436	−	0.225921i	0.923845	+	0.382768i	$0.125029\pi$
$368$		0			0
$369$	−22.8715			−1.19064
$370$		0			0
$371$	7.28389	−	12.6161i	0.378161	−	0.654993i
$372$		0			0
$373$	6.76470			0.350263			0.175132	−	0.984545i	$-0.443965\pi$
$373$	6.76470			0.350263			0.175132	+	0.984545i	$0.443965\pi$
$374$		0			0
$375$	14.0510	+	24.3370i	0.725590	+	1.25676i
$376$		0			0
$377$	−5.78137	−	10.0136i	−0.297756	−	0.515728i
$378$		0			0
$379$	27.1509			1.39465			0.697325	−	0.716755i	$-0.254373\pi$
$379$	27.1509			1.39465			0.697325	+	0.716755i	$0.254373\pi$
$380$		0			0
$381$	−23.2971			−1.19355
$382$		0			0
$383$	−3.04883	−	5.28072i	−0.155788	−	0.269832i	0.777558	−	0.628811i	$-0.216458\pi$
$383$	−3.04883	−	5.28072i	−0.155788	−	0.269832i	−0.933346	+	0.358979i	$0.883125\pi$
$384$		0			0
$385$	1.91862	+	3.32314i	0.0977818	+	0.169363i
$386$		0			0
$387$	−13.3353			−0.677869
$388$		0			0
$389$	8.45931	−	14.6520i	0.428904	−	0.742884i	−0.567872	−	0.823117i	$-0.692233\pi$
$389$	8.45931	−	14.6520i	0.428904	−	0.742884i	0.996776	+	0.0802333i	$0.0255665\pi$
$390$		0			0
$391$	−24.5316			−1.24061
$392$		0			0
$393$	−16.4255	+	28.4498i	−0.828557	+	1.43510i
$394$		0			0
$395$	15.9608	−	27.6449i	0.803075	−	1.39097i
$396$		0			0
$397$	11.4086	+	19.7604i	0.572584	+	0.991744i	0.996300	+	0.0859489i	$0.0273922\pi$
$397$	11.4086	+	19.7604i	0.572584	+	0.991744i	−0.423716	+	0.905795i	$0.639274\pi$
$398$		0			0
$399$	16.6308	+	2.38578i	0.832584	+	0.119438i
$400$		0			0
$401$	18.1128	+	31.3723i	0.904512	+	1.56666i	0.821571	+	0.570106i	$0.193098\pi$
$401$	18.1128	+	31.3723i	0.904512	+	1.56666i	0.0829401	+	0.996555i	$0.473569\pi$
$402$		0			0
$403$	−17.2152	+	29.8177i	−0.857552	+	1.48532i
$404$		0			0
$405$	10.0968	−	17.4882i	0.501714	−	0.868993i
$406$		0			0
$407$	−1.39070			−0.0689345
$408$		0			0
$409$	−9.46125	+	16.3874i	−0.467829	+	0.810303i	−0.999324	−	0.0367579i	$-0.988297\pi$
$409$	−9.46125	+	16.3874i	−0.467829	+	0.810303i	0.531495	+	0.847061i	$0.321630\pi$
$410$		0			0
$411$	−20.0190			−0.987467
$412$		0			0
$413$	−2.13308	−	3.69460i	−0.104962	−	0.181799i
$414$		0			0
$415$	−4.32620	−	7.49319i	−0.212365	−	0.367826i
$416$		0			0
$417$	−2.24514			−0.109945
$418$		0			0
$419$	28.0862			1.37210			0.686050	−	0.727554i	$-0.259343\pi$
$419$	28.0862			1.37210			0.686050	+	0.727554i	$0.259343\pi$
$420$		0			0
$421$	13.6610	+	23.6616i	0.665798	+	1.15320i	0.979068	+	0.203532i	$0.0652420\pi$
$421$	13.6610	+	23.6616i	0.665798	+	1.15320i	−0.313271	+	0.949664i	$0.601425\pi$
$422$		0			0
$423$	−2.75290	−	4.76816i	−0.133850	−	0.231836i
$424$		0			0
$425$	−2.00893			−0.0974472
$426$		0			0
$427$	−9.40836	+	16.2958i	−0.455303	+	0.788607i
$428$		0			0
$429$	17.8627			0.862420
$430$		0			0
$431$	15.6534	−	27.1125i	0.753998	−	1.30596i	−0.191873	−	0.981420i	$-0.561456\pi$
$431$	15.6534	−	27.1125i	0.753998	−	1.30596i	0.945871	−	0.324543i	$-0.105211\pi$
$432$		0			0
$433$	11.8201	−	20.4730i	0.568038	−	0.983871i	−0.428721	−	0.903437i	$-0.641036\pi$
$433$	11.8201	−	20.4730i	0.568038	−	0.983871i	0.996760	−	0.0804347i	$-0.0256309\pi$
$434$		0			0
$435$	4.53386	+	7.85287i	0.217382	+	0.376516i
$436$		0			0
$437$	9.25816	+	23.1046i	0.442878	+	1.10524i
$438$		0			0
$439$	−8.59725	−	14.8909i	−0.410325	−	0.710703i	0.584601	−	0.811321i	$-0.301251\pi$
$439$	−8.59725	−	14.8909i	−0.410325	−	0.710703i	−0.994925	+	0.100618i	$0.967918\pi$
$440$		0			0
$441$	6.29466	−	10.9027i	0.299746	−	0.519175i
$442$		0			0
$443$	1.46052	−	2.52970i	0.0693914	−	0.120190i	−0.829242	−	0.558890i	$-0.811228\pi$
$443$	1.46052	−	2.52970i	0.0693914	−	0.120190i	0.898634	+	0.438700i	$0.144561\pi$
$444$		0			0
$445$	−2.89707			−0.137334
$446$		0			0
$447$	−19.0811	+	33.0495i	−0.902507	+	1.56319i
$448$		0			0
$449$	−17.5108			−0.826387			−0.413194	−	0.910643i	$-0.635587\pi$
$449$	−17.5108			−0.826387			−0.413194	+	0.910643i	$0.635587\pi$
$450$		0			0
$451$	−4.56447	−	7.90589i	−0.214932	−	0.372274i
$452$		0			0
$453$	3.05616	+	5.29342i	0.143591	+	0.248706i
$454$		0			0
$455$	−22.2766			−1.04435
$456$		0			0
$457$	−9.52460			−0.445542			−0.222771	−	0.974871i	$-0.571510\pi$
$457$	−9.52460			−0.445542			−0.222771	+	0.974871i	$0.571510\pi$
$458$		0			0
$459$	0.889741	+	1.54108i	0.0415295	+	0.0719313i
$460$		0			0
$461$	−16.8956	−	29.2641i	−0.786909	−	1.36297i	−0.927852	−	0.372948i	$-0.878347\pi$
$461$	−16.8956	−	29.2641i	−0.786909	−	1.36297i	0.140944	−	0.990018i	$-0.454986\pi$
$462$		0			0
$463$	−29.0226			−1.34879			−0.674397	−	0.738369i	$-0.735596\pi$
$463$	−29.0226			−1.34879			−0.674397	+	0.738369i	$0.735596\pi$
$464$		0			0
$465$	13.5005	−	23.3836i	0.626072	−	1.08439i
$466$		0			0
$467$	17.8583			0.826385			0.413192	−	0.910644i	$-0.364414\pi$
$467$	17.8583			0.826385			0.413192	+	0.910644i	$0.364414\pi$
$468$		0			0
$469$	−9.38649	+	16.2579i	−0.433428	+	0.750719i
$470$		0			0
$471$	−5.97743	+	10.3532i	−0.275426	+	0.477051i
$472$		0			0
$473$	−2.66132	−	4.60954i	−0.122367	−	0.211947i
$474$		0			0
$475$	0.758164	+	1.89207i	0.0347870	+	0.0868140i
$476$		0			0
$477$	12.9040	+	22.3503i	0.590832	+	1.02335i
$478$		0			0
$479$	0.121608	−	0.210631i	0.00555641	−	0.00962399i	−0.863234	−	0.504804i	$-0.831565\pi$
$479$	0.121608	−	0.210631i	0.00555641	−	0.00962399i	0.868790	+	0.495180i	$0.164898\pi$
$480$		0			0
$481$	4.03678	−	6.99191i	0.184061	−	0.318804i
$482$		0			0
$483$	−22.0098			−1.00148
$484$		0			0
$485$	−19.1615	+	33.1888i	−0.870081	+	1.50702i
$486$		0			0
$487$	−36.6545			−1.66097			−0.830486	−	0.557039i	$-0.811937\pi$
$487$	−36.6545			−1.66097			−0.830486	+	0.557039i	$0.811937\pi$
$488$		0			0
$489$	−8.04561	−	13.9354i	−0.363835	−	0.630181i
$490$		0			0
$491$	−13.0465	−	22.5973i	−0.588782	−	1.01980i	−0.994392	−	0.105754i	$-0.966274\pi$
$491$	−13.0465	−	22.5973i	−0.588782	−	1.01980i	0.405610	−	0.914046i	$-0.367059\pi$
$492$		0			0
$493$	−7.57929			−0.341354
$494$		0			0
$495$	−6.79796			−0.305545
$496$		0			0
$497$	−4.33972	−	7.51661i	−0.194663	−	0.337166i
$498$		0			0
$499$	−0.486530	−	0.842695i	−0.0217801	−	0.0377242i	0.854930	−	0.518744i	$-0.173600\pi$
$499$	−0.486530	−	0.842695i	−0.0217801	−	0.0377242i	−0.876710	+	0.481019i	$0.840267\pi$
$500$		0			0
$501$	−43.3186			−1.93533
$502$		0			0
$503$	9.77432	−	16.9296i	0.435816	−	0.754855i	−0.561546	−	0.827445i	$-0.689793\pi$
$503$	9.77432	−	16.9296i	0.435816	−	0.754855i	0.997362	+	0.0725906i	$0.0231267\pi$
$504$		0			0
$505$	−0.940165			−0.0418368
$506$		0			0
$507$	−36.1576	+	62.6268i	−1.60582	+	2.78135i
$508$		0			0
$509$	−2.76224	+	4.78435i	−0.122434	+	0.212062i	−0.920727	−	0.390207i	$-0.872403\pi$
$509$	−2.76224	+	4.78435i	−0.122434	+	0.212062i	0.798293	+	0.602270i	$0.205737\pi$
$510$		0			0
$511$	1.54487	+	2.67579i	0.0683408	+	0.118370i
$512$		0			0
$513$	1.11565	−	1.41958i	0.0492570	−	0.0626762i
$514$		0			0
$515$	−3.61811	−	6.26674i	−0.159433	−	0.276146i
$516$		0			0
$517$	1.09879	−	1.90316i	0.0483248	−	0.0837010i
$518$		0			0
$519$	15.8426	−	27.4403i	0.695415	−	1.20449i
$520$		0			0
$521$	22.4177			0.982136			0.491068	−	0.871121i	$-0.336607\pi$
$521$	22.4177			0.982136			0.491068	+	0.871121i	$0.336607\pi$
$522$		0			0
$523$	−11.5034	+	19.9244i	−0.503008	+	0.871235i	0.496986	+	0.867759i	$0.334440\pi$
$523$	−11.5034	+	19.9244i	−0.503008	+	0.871235i	−0.999994	+	0.00347673i	$0.998893\pi$
$524$		0			0
$525$	−1.80242			−0.0786640
$526$		0			0
$527$	11.2845	+	19.5453i	0.491559	+	0.851405i
$528$		0			0
$529$	−4.80355	−	8.31999i	−0.208850	−	0.361739i
$530$		0			0
$531$	7.55781			0.327981
$532$		0			0
$533$	52.9970			2.29556
$534$		0			0
$535$	20.9795	+	36.3375i	0.907022	+	1.57101i
$536$		0			0
$537$	−27.4020	−	47.4616i	−1.18248	−	2.04812i
$538$		0			0
$539$	5.02490			0.216438
$540$		0			0
$541$	−0.0495580	+	0.0858369i	−0.00213066	+	0.00369042i	−0.867089	−	0.498154i	$-0.834012\pi$
$541$	−0.0495580	+	0.0858369i	−0.00213066	+	0.00369042i	0.864958	+	0.501844i	$0.167345\pi$
$542$		0			0
$543$	−52.6996			−2.26156
$544$		0			0
$545$	16.2603	−	28.1637i	0.696516	−	1.20640i
$546$		0			0
$547$	11.7710	−	20.3880i	0.503292	−	0.871727i	−0.496701	−	0.867922i	$-0.665455\pi$
$547$	11.7710	−	20.3880i	0.503292	−	0.871727i	0.999993	−	0.00380504i	$-0.00121118\pi$
$548$		0			0
$549$	−16.6676	−	28.8692i	−0.711357	−	1.23211i
$550$		0			0
$551$	2.86041	+	7.13840i	0.121857	+	0.304106i
$552$		0			0
$553$	11.9695	+	20.7318i	0.508996	+	0.881607i
$554$		0			0
$555$	−3.16572	+	5.48319i	−0.134377	+	0.232748i
$556$		0			0
$557$	4.54458	−	7.87144i	0.192560	−	0.333524i	−0.753538	−	0.657404i	$-0.771654\pi$
$557$	4.54458	−	7.87144i	0.192560	−	0.333524i	0.946098	+	0.323881i	$0.104988\pi$
$558$		0			0
$559$	30.9000			1.30693
$560$		0			0
$561$	5.85444	−	10.1402i	0.247175	−	0.428119i
$562$		0			0
$563$	−30.1682			−1.27144			−0.635719	−	0.771920i	$-0.719296\pi$
$563$	−30.1682			−1.27144			−0.635719	+	0.771920i	$0.719296\pi$
$564$		0			0
$565$	−12.9291	−	22.3938i	−0.543930	−	0.942114i
$566$		0			0
$567$	7.57191	+	13.1149i	0.317990	+	0.550775i
$568$		0			0
$569$	−3.75590			−0.157455			−0.0787277	−	0.996896i	$-0.525086\pi$
$569$	−3.75590			−0.157455			−0.0787277	+	0.996896i	$0.525086\pi$
$570$		0			0
$571$	−39.5858			−1.65661			−0.828307	−	0.560274i	$-0.810696\pi$
$571$	−39.5858			−1.65661			−0.828307	+	0.560274i	$0.810696\pi$
$572$		0			0
$573$	9.65685	+	16.7262i	0.403421	+	0.698745i
$574$		0			0
$575$	−1.33512	−	2.31250i	−0.0556784	−	0.0964378i
$576$		0			0
$577$	−15.4854			−0.644664			−0.322332	−	0.946627i	$-0.604467\pi$
$577$	−15.4854			−0.644664			−0.322332	+	0.946627i	$0.604467\pi$
$578$		0			0
$579$	12.4024	−	21.4816i	0.515427	−	0.892746i
$580$		0			0
$581$	6.48871			0.269197
$582$		0			0
$583$	−5.15049	+	8.92090i	−0.213311	+	0.369466i
$584$		0			0
$585$	19.7324	−	34.1775i	0.815834	−	1.41307i
$586$		0			0
$587$	6.10441	+	10.5731i	0.251956	+	0.436400i	0.964064	−	0.265669i	$-0.0855929\pi$
$587$	6.10441	+	10.5731i	0.251956	+	0.436400i	−0.712108	+	0.702070i	$0.752260\pi$
$588$		0			0
$589$	14.1496	−	18.0044i	0.583023	−	0.741858i
$590$		0			0
$591$	14.9983	+	25.9778i	0.616947	+	1.06858i
$592$		0			0
$593$	−14.0813	+	24.3896i	−0.578251	+	1.00156i	0.417429	+	0.908709i	$0.362931\pi$
$593$	−14.0813	+	24.3896i	−0.578251	+	1.00156i	−0.995680	+	0.0928502i	$0.970402\pi$
$594$		0			0
$595$	−7.30109	+	12.6459i	−0.299315	+	0.518429i
$596$		0			0
$597$	−24.2108			−0.990881
$598$		0			0
$599$	−8.63461	+	14.9556i	−0.352801	+	0.611069i	−0.986739	−	0.162315i	$-0.948104\pi$
$599$	−8.63461	+	14.9556i	−0.352801	+	0.611069i	0.633938	+	0.773384i	$0.281437\pi$
$600$		0			0
$601$	5.73546			0.233954			0.116977	−	0.993135i	$-0.462680\pi$
$601$	5.73546			0.233954			0.116977	+	0.993135i	$0.462680\pi$
$602$		0			0
$603$	−16.6289	−	28.8021i	−0.677180	−	1.17291i
$604$		0			0
$605$	10.3525	+	17.9310i	0.420889	+	0.729001i
$606$		0			0
$607$	1.00331			0.0407232			0.0203616	−	0.999793i	$-0.493518\pi$
$607$	1.00331			0.0407232			0.0203616	+	0.999793i	$0.493518\pi$
$608$		0			0
$609$	−6.80017			−0.275557
$610$		0			0
$611$	6.37891	+	11.0486i	0.258063	+	0.446978i
$612$		0			0
$613$	7.17015	+	12.4191i	0.289599	+	0.501601i	0.973714	−	0.227773i	$-0.0731446\pi$
$613$	7.17015	+	12.4191i	0.289599	+	0.501601i	−0.684115	+	0.729374i	$0.739811\pi$
$614$		0			0
$615$	−41.5613			−1.67591
$616$		0			0
$617$	4.10345	−	7.10738i	0.165199	−	0.286132i	−0.771527	−	0.636196i	$-0.780507\pi$
$617$	4.10345	−	7.10738i	0.165199	−	0.286132i	0.936726	+	0.350064i	$0.113840\pi$
$618$		0			0
$619$	11.1500			0.448157			0.224079	−	0.974571i	$-0.428063\pi$
$619$	11.1500			0.448157			0.224079	+	0.974571i	$0.428063\pi$
$620$		0			0
$621$	−1.18263	+	2.04838i	−0.0474575	+	0.0821987i
$622$		0			0
$623$	1.08630	−	1.88153i	0.0435218	−	0.0753820i
$624$		0			0
$625$	11.2216	+	19.4364i	0.448864	+	0.777456i
$626$		0			0
$627$	−11.7598	−	1.68700i	−0.469641	−	0.0673723i
$628$		0			0
$629$	−2.64608	−	4.58315i	−0.105506	−	0.182742i
$630$		0			0
$631$	8.19828	−	14.1998i	0.326368	−	0.565286i	−0.655420	−	0.755265i	$-0.727508\pi$
$631$	8.19828	−	14.1998i	0.326368	−	0.565286i	0.981788	+	0.189978i	$0.0608417\pi$
$632$		0			0
$633$	30.4451	−	52.7325i	1.21008	−	2.09593i
$634$		0			0
$635$	−20.5442			−0.815271
$636$		0			0
$637$	−14.5857	+	25.2633i	−0.577908	+	1.00097i
$638$		0			0
$639$	15.3763			0.608276
$640$		0			0
$641$	−1.52155	−	2.63540i	−0.0600975	−	0.104092i	0.834411	−	0.551142i	$-0.185808\pi$
$641$	−1.52155	−	2.63540i	−0.0600975	−	0.104092i	−0.894509	+	0.447050i	$0.852474\pi$
$642$		0			0
$643$	−12.4611	−	21.5833i	−0.491418	−	0.851160i	0.508534	−	0.861042i	$-0.330188\pi$
$643$	−12.4611	−	21.5833i	−0.491418	−	0.851160i	−0.999951	+	0.00988183i	$0.996854\pi$
$644$		0			0
$645$	−24.2323			−0.954147
$646$		0			0
$647$	−7.65801			−0.301067			−0.150534	−	0.988605i	$-0.548099\pi$
$647$	−7.65801			−0.301067			−0.150534	+	0.988605i	$0.548099\pi$
$648$		0			0
$649$	1.50831	+	2.61247i	0.0592064	+	0.102549i
$650$		0			0
$651$	10.1245	+	17.5361i	0.396809	+	0.687294i
$652$		0			0
$653$	25.8941			1.01331			0.506657	−	0.862148i	$-0.330881\pi$
$653$	25.8941			1.01331			0.506657	+	0.862148i	$0.330881\pi$
$654$		0			0
$655$	−14.4846	+	25.0880i	−0.565960	+	0.980271i
$656$		0			0
$657$	−5.47369			−0.213549
$658$		0			0
$659$	−9.78624	+	16.9503i	−0.381218	+	0.660288i	−0.991237	−	0.132098i	$-0.957828\pi$
$659$	−9.78624	+	16.9503i	−0.381218	+	0.660288i	0.610019	+	0.792387i	$0.291162\pi$
$660$		0			0
$661$	13.2163	−	22.8914i	0.514056	−	0.890371i	−0.485811	−	0.874064i	$-0.661476\pi$
$661$	13.2163	−	22.8914i	0.514056	−	0.890371i	0.999867	−	0.0163075i	$-0.00519106\pi$
$662$		0			0
$663$	33.9873	+	58.8677i	1.31996	+	2.28623i
$664$		0			0
$665$	14.6657	+	2.10386i	0.568710	+	0.0815844i
$666$		0			0
$667$	−5.03715	−	8.72460i	−0.195039	−	0.337818i
$668$		0			0
$669$	−0.375754	+	0.650825i	−0.0145275	+	0.0251623i
$670$		0			0
$671$	6.65272	−	11.5228i	0.256825	−	0.444834i
$672$		0			0
$673$	30.3668			1.17055			0.585276	−	0.810834i	$-0.300986\pi$
$673$	30.3668			1.17055			0.585276	+	0.810834i	$0.300986\pi$
$674$		0			0
$675$	−0.0968476	+	0.167745i	−0.00372767	+	0.00645651i
$676$		0			0
$677$	5.38843			0.207094			0.103547	−	0.994625i	$-0.466981\pi$
$677$	5.38843			0.207094			0.103547	+	0.994625i	$0.466981\pi$
$678$		0			0
$679$	−14.3699	−	24.8893i	−0.551465	−	0.955165i
$680$		0			0
$681$	17.0290	+	29.4951i	0.652552	+	1.13025i
$682$		0			0
$683$	0.762636			0.0291814			0.0145907	−	0.999894i	$-0.495355\pi$
$683$	0.762636			0.0291814			0.0145907	+	0.999894i	$0.495355\pi$
$684$		0			0
$685$	−17.6535			−0.674506
$686$		0			0
$687$	−14.6676	−	25.4051i	−0.559605	−	0.969264i
$688$		0			0
$689$	−29.9006	−	51.7893i	−1.13912	−	1.97302i
$690$		0			0
$691$	−9.65685			−0.367364			−0.183682	−	0.982986i	$-0.558802\pi$
$691$	−9.65685			−0.367364			−0.183682	+	0.982986i	$0.558802\pi$
$692$		0			0
$693$	2.54900	−	4.41500i	0.0968286	−	0.167712i
$694$		0			0
$695$	−1.97984			−0.0750997
$696$		0			0
$697$	17.3696	−	30.0850i	0.657920	−	1.13955i
$698$		0			0
$699$	−1.02476	+	1.77494i	−0.0387600	+	0.0671343i
$700$		0			0
$701$	−7.64191	−	13.2362i	−0.288631	−	0.499923i	0.684852	−	0.728682i	$-0.259867\pi$
$701$	−7.64191	−	13.2362i	−0.288631	−	0.499923i	−0.973483	+	0.228759i	$0.926533\pi$
$702$		0			0
$703$	−3.31792	+	4.22183i	−0.125138	+	0.159229i
$704$		0			0
$705$	−5.00246	−	8.66452i	−0.188404	−	0.326325i
$706$		0			0
$707$	0.352530	−	0.610600i	0.0132583	−	0.0229640i
$708$		0			0
$709$	3.02241	−	5.23497i	0.113509	−	0.196603i	−0.803674	−	0.595070i	$-0.797124\pi$
$709$	3.02241	−	5.23497i	0.113509	−	0.196603i	0.917183	+	0.398467i	$0.130458\pi$
$710$		0			0
$711$	−42.4099			−1.59049
$712$		0			0
$713$	−14.9992	+	25.9794i	−0.561724	+	0.972934i
$714$		0			0
$715$	15.7520			0.589090
$716$		0			0
$717$	22.8569	+	39.5892i	0.853605	+	1.47849i
$718$		0			0
$719$	−17.8947	−	30.9945i	−0.667358	−	1.15590i	−0.978640	−	0.205581i	$-0.934092\pi$
$719$	−17.8947	−	30.9945i	−0.667358	−	1.15590i	0.311282	−	0.950318i	$-0.399242\pi$
$720$		0			0
$721$	5.42667			0.202100
$722$		0			0
$723$	−13.5741			−0.504826
$724$		0			0
$725$	−0.412500	−	0.714470i	−0.0153199	−	0.0265348i
$726$		0			0
$727$	−2.07736	−	3.59810i	−0.0770451	−	0.133446i	0.824929	−	0.565237i	$-0.191215\pi$
$727$	−2.07736	−	3.59810i	−0.0770451	−	0.133446i	−0.901974	+	0.431791i	$0.857882\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	10.1273	−	17.5411i	0.374573	−	0.648780i
$732$		0			0
$733$	−10.2024			−0.376835			−0.188418	−	0.982089i	$-0.560336\pi$
$733$	−10.2024			−0.376835			−0.188418	+	0.982089i	$0.560336\pi$
$734$		0			0
$735$	11.4384	−	19.8119i	0.421912	−	0.730774i
$736$		0			0
$737$	6.63725	−	11.4961i	0.244486	−	0.423463i
$738$		0			0
$739$	−19.6542	−	34.0421i	−0.722992	−	1.25226i	−0.959795	−	0.280701i	$-0.909433\pi$
$739$	−19.6542	−	34.0421i	−0.722992	−	1.25226i	0.236803	−	0.971558i	$-0.423900\pi$
$740$		0			0
$741$	42.6166	−	54.2268i	1.56556	−	1.99207i
$742$		0			0
$743$	−24.7748	−	42.9112i	−0.908899	−	1.57426i	−0.815597	−	0.578621i	$-0.803591\pi$
$743$	−24.7748	−	42.9112i	−0.908899	−	1.57426i	−0.0933020	−	0.995638i	$-0.529742\pi$
$744$		0			0
$745$	−16.8264	+	29.1442i	−0.616473	+	1.06776i
$746$		0			0
$747$	−5.74762	+	9.95517i	−0.210294	+	0.364241i
$748$		0			0
$749$	−31.4664			−1.14976
$750$		0			0
$751$	3.28872	−	5.69623i	0.120007	−	0.207858i	−0.799763	−	0.600316i	$-0.795042\pi$
$751$	3.28872	−	5.69623i	0.120007	−	0.207858i	0.919770	+	0.392457i	$0.128375\pi$
$752$		0			0
$753$	−54.8205			−1.99777
$754$		0			0
$755$	2.69503	+	4.66792i	0.0980820	+	0.169883i
$756$		0			0
$757$	2.76810	+	4.79448i	0.100608	+	0.174258i	0.911935	−	0.410334i	$-0.134588\pi$
$757$	2.76810	+	4.79448i	0.100608	+	0.174258i	−0.811327	+	0.584592i	$0.801254\pi$
$758$		0			0
$759$	15.5633			0.564912
$760$		0			0
$761$	−38.1371			−1.38247			−0.691234	−	0.722631i	$-0.742933\pi$
$761$	−38.1371			−1.38247			−0.691234	+	0.722631i	$0.742933\pi$
$762$		0			0
$763$	12.1942	+	21.1209i	0.441458	+	0.764628i
$764$		0			0
$765$	−12.9344	−	22.4031i	−0.467645	−	0.809985i
$766$		0			0
$767$	−17.5127			−0.632346
$768$		0			0
$769$	0.324873	−	0.562697i	0.0117152	−	0.0202914i	−0.860108	−	0.510111i	$-0.829604\pi$
$769$	0.324873	−	0.562697i	0.0117152	−	0.0202914i	0.871824	+	0.489820i	$0.162938\pi$
$770$		0			0
$771$	32.8142			1.18178
$772$		0			0
$773$	−8.44740	+	14.6313i	−0.303832	+	0.526252i	−0.977001	−	0.213237i	$-0.931599\pi$
$773$	−8.44740	+	14.6313i	−0.303832	+	0.526252i	0.673169	+	0.739489i	$0.264933\pi$
$774$		0			0
$775$	−1.22830	+	2.12749i	−0.0441220	+	0.0764216i
$776$		0			0
$777$	−2.37408	−	4.11202i	−0.0851695	−	0.147518i
$778$		0			0
$779$	−34.8902	−	5.00518i	−1.25007	−	0.179329i
$780$		0			0
$781$	3.06864	+	5.31505i	0.109805	+	0.190187i
$782$		0			0
$783$	−0.365387	+	0.632869i	−0.0130579	+	0.0226169i
$784$		0			0
$785$	−5.27111	+	9.12983i	−0.188134	+	0.325858i
$786$		0			0
$787$	19.3868			0.691065			0.345533	−	0.938407i	$-0.387698\pi$
$787$	19.3868			0.691065			0.345533	+	0.938407i	$0.387698\pi$
$788$		0			0
$789$	−31.8660	+	55.1935i	−1.13446	+	1.96494i
$790$		0			0
$791$	19.3919			0.689495
$792$		0			0
$793$	38.6216	+	66.8946i	1.37149	+	2.37550i
$794$		0			0
$795$	23.4486	+	40.6141i	0.831636	+	1.44044i
$796$		0			0
$797$	44.3750			1.57184			0.785922	−	0.618325i	$-0.212189\pi$
$797$	44.3750			1.57184			0.785922	+	0.618325i	$0.212189\pi$
$798$		0			0
$799$	8.36265			0.295849
$800$		0			0
$801$	1.92447	+	3.33328i	0.0679978	+	0.117776i
$802$		0			0
$803$	−1.09239	−	1.89207i	−0.0385494	−	0.0667696i
$804$		0			0
$805$	−19.4091			−0.684079
$806$		0			0
$807$	−15.2059	+	26.3375i	−0.535275	+	0.927123i
$808$		0			0
$809$	17.0138			0.598175			0.299088	−	0.954226i	$-0.403318\pi$
$809$	17.0138			0.598175			0.299088	+	0.954226i	$0.403318\pi$
$810$		0			0
$811$	−11.7397	+	20.3338i	−0.412237	+	0.714016i	−0.995134	−	0.0985305i	$-0.968586\pi$
$811$	−11.7397	+	20.3338i	−0.412237	+	0.714016i	0.582897	+	0.812546i	$0.301919\pi$
$812$		0			0
$813$	8.82675	−	15.2884i	0.309568	−	0.536187i
$814$		0			0
$815$	−7.09490	−	12.2887i	−0.248524	−	0.430456i
$816$		0			0
$817$	−20.3428	−	2.91827i	−0.711703	−	0.102097i
$818$		0			0
$819$	14.7980	+	25.6308i	0.517082	+	0.895613i
$820$		0			0
$821$	11.7074	−	20.2779i	0.408593	−	0.707703i	−0.586140	−	0.810210i	$-0.699353\pi$
$821$	11.7074	−	20.2779i	0.408593	−	0.707703i	0.994732	+	0.102507i	$0.0326863\pi$
$822$		0			0
$823$	5.46418	−	9.46423i	0.190469	−	0.329902i	−0.754937	−	0.655798i	$-0.772332\pi$
$823$	5.46418	−	9.46423i	0.190469	−	0.329902i	0.945406	+	0.325895i	$0.105666\pi$
$824$		0			0
$825$	1.27450			0.0443725
$826$		0			0
$827$	18.2502	−	31.6103i	0.634622	−	1.09920i	−0.351974	−	0.936010i	$-0.614489\pi$
$827$	18.2502	−	31.6103i	0.634622	−	1.09920i	0.986595	−	0.163187i	$-0.0521774\pi$
$828$		0			0
$829$	39.9489			1.38748			0.693741	−	0.720224i	$-0.255961\pi$
$829$	39.9489			1.38748			0.693741	+	0.720224i	$0.255961\pi$
$830$		0			0
$831$	−27.0292	−	46.8160i	−0.937633	−	1.62403i
$832$		0			0
$833$	9.56085	+	16.5599i	0.331264	+	0.573766i
$834$		0			0
$835$	−38.1999			−1.32196
$836$		0			0
$837$	2.17604			0.0752148
$838$		0			0
$839$	9.30752	+	16.1211i	0.321331	+	0.556562i	0.980763	−	0.195202i	$-0.0625364\pi$
$839$	9.30752	+	16.1211i	0.321331	+	0.556562i	−0.659432	+	0.751764i	$0.729203\pi$
$840$		0			0
$841$	12.9437	+	22.4192i	0.446335	+	0.773075i
$842$		0			0
$843$	76.2751			2.62705
$844$		0			0
$845$	−31.8850	+	55.2265i	−1.09688	+	1.89985i
$846$		0			0
$847$	−15.5273			−0.533526
$848$		0			0
$849$	−28.5594	+	49.4663i	−0.980155	+	1.69768i
$850$		0			0
$851$	3.51714	−	6.09187i	0.120566	−	0.208827i
$852$		0			0
$853$	−6.10458	−	10.5734i	−0.209017	−	0.362028i	0.742388	−	0.669970i	$-0.233693\pi$
$853$	−6.10458	−	10.5734i	−0.209017	−	0.362028i	−0.951405	+	0.307942i	$0.900360\pi$
$854$		0			0
$855$	−16.2185	+	20.6369i	−0.554660	+	0.705768i
$856$		0			0
$857$	22.4186	+	38.8302i	0.765805	+	1.32641i	0.939820	+	0.341671i	$0.110993\pi$
$857$	22.4186	+	38.8302i	0.765805	+	1.32641i	−0.174014	+	0.984743i	$0.555674\pi$
$858$		0			0
$859$	−2.52285	+	4.36971i	−0.0860787	+	0.149093i	−0.905850	−	0.423598i	$-0.860767\pi$
$859$	−2.52285	+	4.36971i	−0.0860787	+	0.149093i	0.819772	+	0.572690i	$0.194100\pi$
$860$		0			0
$861$	15.5841	−	26.9924i	0.531104	−	0.919899i
$862$		0			0
$863$	8.85825			0.301538			0.150769	−	0.988569i	$-0.451825\pi$
$863$	8.85825			0.301538			0.150769	+	0.988569i	$0.451825\pi$
$864$		0			0
$865$	13.9706	−	24.1978i	0.475015	−	0.822750i
$866$		0			0
$867$	3.51518			0.119382
$868$		0			0
$869$	−8.46373	−	14.6596i	−0.287113	−	0.497293i
$870$		0			0
$871$	38.5318	+	66.7391i	1.30560	+	2.26137i
$872$		0			0
$873$	50.9146			1.72320
$874$		0			0
$875$	−18.5843			−0.628265
$876$		0			0
$877$	6.71386	+	11.6287i	0.226711	+	0.392675i	0.956831	−	0.290644i	$-0.0938694\pi$
$877$	6.71386	+	11.6287i	0.226711	+	0.392675i	−0.730120	+	0.683319i	$0.760536\pi$
$878$		0			0
$879$	0.212494	+	0.368050i	0.00716723	+	0.0124140i
$880$		0			0
$881$	45.2128			1.52326			0.761630	−	0.648012i	$-0.224400\pi$
$881$	45.2128			1.52326			0.761630	+	0.648012i	$0.224400\pi$
$882$		0			0
$883$	−13.8908	+	24.0595i	−0.467462	+	0.809668i	−0.999309	−	0.0371725i	$-0.988165\pi$
$883$	−13.8908	+	24.0595i	−0.467462	+	0.809668i	0.531847	+	0.846841i	$0.321498\pi$
$884$		0			0
$885$	13.7338			0.461656
$886$		0			0
$887$	−24.1931	+	41.9037i	−0.812326	+	1.40699i	0.0989062	+	0.995097i	$0.468466\pi$
$887$	−24.1931	+	41.9037i	−0.812326	+	1.40699i	−0.911232	+	0.411893i	$0.864868\pi$
$888$		0			0
$889$	7.70338	−	13.3426i	0.258363	−	0.447498i
$890$		0			0
$891$	−5.35415	−	9.27366i	−0.179371	−	0.310679i
$892$		0			0
$893$	−3.15605	−	7.87620i	−0.105613	−	0.263567i
$894$		0			0
$895$	−24.1640	−	41.8533i	−0.807714	−	1.39900i
$896$		0			0
$897$	−45.1755	+	78.2463i	−1.50837	+	2.61257i
$898$		0			0
$899$	−4.63416	+	8.02659i	−0.154558	+	0.267702i
$900$		0			0
$901$	−39.1992			−1.30591
$902$		0			0
$903$	9.08630	−	15.7379i	0.302373	−	0.523726i
$904$		0			0
$905$	−46.4724			−1.54479
$906$		0			0
$907$	17.0303	+	29.4973i	0.565480	+	0.979441i	0.997005	+	0.0773396i	$0.0246426\pi$
$907$	17.0303	+	29.4973i	0.565480	+	0.979441i	−0.431524	+	0.902101i	$0.642024\pi$
$908$		0			0
$909$	0.624534	+	1.08172i	0.0207145	+	0.0358785i
$910$		0			0
$911$	4.88594			0.161879			0.0809393	−	0.996719i	$-0.474208\pi$
$911$	4.88594			0.161879			0.0809393	+	0.996719i	$0.474208\pi$
$912$		0			0
$913$	−4.58821			−0.151848
$914$		0			0
$915$	−30.2878	−	52.4600i	−1.00128	−	1.73427i
$916$		0			0
$917$	−10.8625	−	18.8143i	−0.358710	−	0.621304i
$918$		0			0
$919$	55.0148			1.81477			0.907386	−	0.420299i	$-0.138075\pi$
$919$	55.0148			1.81477			0.907386	+	0.420299i	$0.138075\pi$
$920$		0			0
$921$	−32.7544	+	56.7324i	−1.07930	+	1.86940i
$922$		0			0
$923$	−35.6293			−1.17275
$924$		0			0
$925$	0.288024	−	0.498872i	0.00947017	−	0.0164028i
$926$		0			0
$927$	−4.80688	+	8.32576i	−0.157879	+	0.273454i
$928$		0			0
$929$	1.20395	+	2.08530i	0.0395004	+	0.0684166i	0.885100	−	0.465401i	$-0.154090\pi$
$929$	1.20395	+	2.08530i	0.0395004	+	0.0684166i	−0.845599	+	0.533818i	$0.820757\pi$
$930$		0			0
$931$	11.9883	−	15.2544i	0.392902	−	0.499942i
$932$		0			0
$933$	−20.6209	−	35.7164i	−0.675096	−	1.16930i
$934$		0			0
$935$	5.16265	−	8.94197i	0.168837	−	0.292434i
$936$		0			0
$937$	−4.08821	+	7.08099i	−0.133556	+	0.231326i	−0.925045	−	0.379858i	$-0.875973\pi$
$937$	−4.08821	+	7.08099i	−0.133556	+	0.231326i	0.791489	+	0.611184i	$0.209306\pi$
$938$		0			0
$939$	−22.2769			−0.726980
$940$		0			0
$941$	−18.6309	+	32.2696i	−0.607349	+	1.05196i	0.384326	+	0.923197i	$0.374434\pi$
$941$	−18.6309	+	32.2696i	−0.607349	+	1.05196i	−0.991675	+	0.128763i	$0.958899\pi$
$942$		0			0
$943$	46.1749			1.50366
$944$		0			0
$945$	0.703951	+	1.21928i	0.0228995	+	0.0396632i
$946$		0			0
$947$	20.5903	+	35.6634i	0.669094	+	1.15890i	0.978158	+	0.207863i	$0.0666509\pi$
$947$	20.5903	+	35.6634i	0.669094	+	1.15890i	−0.309064	+	0.951041i	$0.600016\pi$
$948$		0			0
$949$	12.6834			0.411722
$950$		0			0
$951$	−11.3068			−0.366649
$952$		0			0
$953$	2.81267	+	4.87169i	0.0911114	+	0.157810i	0.907979	−	0.419016i	$-0.137625\pi$
$953$	2.81267	+	4.87169i	0.0911114	+	0.157810i	−0.816868	+	0.576825i	$0.804291\pi$
$954$		0			0
$955$	8.51575	+	14.7497i	0.275563	+	0.477290i
$956$		0			0
$957$	4.80845			0.155435
$958$		0			0
$959$	6.61947	−	11.4653i	0.213754	−	0.370232i
$960$		0			0
$961$	−3.40164			−0.109730
$962$		0			0
$963$	27.8726	−	48.2767i	0.898181	−	1.55569i
$964$		0			0
$965$	10.9369	−	18.9432i	0.352071	−	0.609805i
$966$		0			0
$967$	16.6260	+	28.7971i	0.534657	+	0.926052i	0.999180	+	0.0404914i	$0.0128923\pi$
$967$	16.6260	+	28.7971i	0.534657	+	0.926052i	−0.464523	+	0.885561i	$0.653774\pi$
$968$		0			0
$969$	−16.8157	−	41.9650i	−0.540197	−	1.34811i
$970$		0			0
$971$	−19.9160	−	34.4955i	−0.639134	−	1.10701i	−0.985623	−	0.168959i	$-0.945959\pi$
$971$	−19.9160	−	34.4955i	−0.639134	−	1.10701i	0.346489	−	0.938054i	$-0.387374\pi$
$972$		0			0
$973$	0.742374	−	1.28583i	0.0237994	−	0.0412218i
$974$		0			0
$975$	−3.69949	+	6.40770i	−0.118478	+	0.205211i
$976$		0			0
$977$	7.54500			0.241386			0.120693	−	0.992690i	$-0.461488\pi$
$977$	7.54500			0.241386			0.120693	+	0.992690i	$0.461488\pi$
$978$		0			0
$979$	−0.768133	+	1.33044i	−0.0245496	+	0.0425212i
$980$		0			0
$981$	−43.2057			−1.37945
$982$		0			0
$983$	13.3598	+	23.1398i	0.426111	+	0.738046i	0.996523	−	0.0833125i	$-0.0265500\pi$
$983$	13.3598	+	23.1398i	0.426111	+	0.738046i	−0.570412	+	0.821358i	$0.693217\pi$
$984$		0			0
$985$	13.2260	+	22.9081i	0.421416	+	0.729914i
$986$		0			0
$987$	7.50302			0.238824
$988$		0			0
$989$	26.9223			0.856080
$990$		0			0
$991$	0.753916	+	1.30582i	0.0239489	+	0.0414808i	0.877751	−	0.479116i	$-0.159043\pi$
$991$	0.753916	+	1.30582i	0.0239489	+	0.0414808i	−0.853803	+	0.520597i	$0.825709\pi$
$992$		0			0
$993$	−36.4883	−	63.1995i	−1.15792	−	2.00558i
$994$		0			0
$995$	−21.3499			−0.676838
$996$		0			0
$997$	2.01634	−	3.49240i	0.0638580	−	0.110605i	−0.832329	−	0.554282i	$-0.812993\pi$
$997$	2.01634	−	3.49240i	0.0638580	−	0.110605i	0.896187	+	0.443677i	$0.146326\pi$
$998$		0			0
$999$	−0.510256			−0.0161438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.o.577.1		8
4.3	odd	2		1216.2.i.q.577.3		8
8.3	odd	2		608.2.i.c.577.2	yes	8
8.5	even	2		608.2.i.e.577.4	yes	8
19.11	even	3	inner	1216.2.i.o.961.1		8
76.11	odd	6		1216.2.i.q.961.3		8
152.11	odd	6		608.2.i.c.353.2	✓	8
152.125	even	6		608.2.i.e.353.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.i.c.353.2	✓	8	152.11	odd	6
608.2.i.c.577.2	yes	8	8.3	odd	2
608.2.i.e.353.4	yes	8	152.125	even	6
608.2.i.e.577.4	yes	8	8.5	even	2
1216.2.i.o.577.1		8	1.1	even	1	trivial
1216.2.i.o.961.1		8	19.11	even	3	inner
1216.2.i.q.577.3		8	4.3	odd	2
1216.2.i.q.961.3		8	76.11	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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 - 2.09077i) q^{3} +(-1.06447 - 1.84371i) q^{5} +1.59656 q^{7} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-1.20711 - 2.09077i) q^{3} +(-1.06447 - 1.84371i) q^{5} +1.59656 q^{7} +(-1.41421 + 2.44949i) q^{9} -1.12894 q^{11} +(3.27696 - 5.67587i) q^{13} +(-2.56986 + 4.45112i) q^{15} +(-2.14802 - 3.72049i) q^{17} +(-2.69341 + 3.42718i) q^{19} +(-1.92722 - 3.33804i) q^{21} +(2.85513 - 4.94523i) q^{23} +(0.233811 - 0.404972i) q^{25} -0.414214 q^{27} +(0.882123 - 1.52788i) q^{29} -5.25341 q^{31} +(1.36275 + 2.36035i) q^{33} +(-1.69949 - 2.94360i) q^{35} +1.23187 q^{37} -15.8226 q^{39} +(4.04315 + 7.00294i) q^{41} +(2.35736 + 4.08307i) q^{43} +6.02155 q^{45} +(-0.973296 + 1.68580i) q^{47} -4.45100 q^{49} +(-5.18579 + 8.98205i) q^{51} +(4.56224 - 7.90203i) q^{53} +(1.20172 + 2.08144i) q^{55} +(10.4167 + 1.49433i) q^{57} +(-1.33605 - 2.31410i) q^{59} +(-5.89290 + 10.2068i) q^{61} +(-2.25788 + 3.91076i) q^{63} -13.9529 q^{65} +(-5.87920 + 10.1831i) q^{67} -13.7858 q^{69} +(-2.71817 - 4.70800i) q^{71} +(0.967622 + 1.67597i) q^{73} -1.12894 q^{75} -1.80242 q^{77} +(7.49707 + 12.9853i) q^{79} +(4.74264 + 8.21449i) q^{81} +4.06418 q^{83} +(-4.57301 + 7.92069i) q^{85} -4.25927 q^{87} +(0.680403 - 1.17849i) q^{89} +(5.23187 - 9.06186i) q^{91} +(6.34143 + 10.9837i) q^{93} +(9.18579 + 1.31775i) q^{95} +(-9.00052 - 15.5894i) q^{97} +(1.59656 - 2.76532i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7	\( 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7} + 4 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{17} - 2 q^{19} + 8 q^{21} + 2 q^{23} - 2 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - 6 q^{33} - 4 q^{35} + 8 q^{37} - 12 q^{39} + 8 q^{41} + 18 q^{43} - 16 q^{45} - 6 q^{47} + 32 q^{49} - 18 q^{51} + 10 q^{53} + 20 q^{55} + 10 q^{57} + 8 q^{59} - 18 q^{61} + 8 q^{63} - 36 q^{65} - 4 q^{67} - 52 q^{69} - 6 q^{71} + 4 q^{75} - 16 q^{77} + 14 q^{79} + 4 q^{81} + 4 q^{83} + 22 q^{85} - 60 q^{87} - 2 q^{89} + 40 q^{91} + 16 q^{93} + 50 q^{95} - 12 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7 + 4 * q^11 - 2 * q^13 + 2 * q^15 - 2 * q^17 - 2 * q^19 + 8 * q^21 + 2 * q^23 - 2 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - 6 * q^33 - 4 * q^35 + 8 * q^37 - 12 * q^39 + 8 * q^41 + 18 * q^43 - 16 * q^45 - 6 * q^47 + 32 * q^49 - 18 * q^51 + 10 * q^53 + 20 * q^55 + 10 * q^57 + 8 * q^59 - 18 * q^61 + 8 * q^63 - 36 * q^65 - 4 * q^67 - 52 * q^69 - 6 * q^71 + 4 * q^75 - 16 * q^77 + 14 * q^79 + 4 * q^81 + 4 * q^83 + 22 * q^85 - 60 * q^87 - 2 * q^89 + 40 * q^91 + 16 * q^93 + 50 * q^95 - 12 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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