LMFDB - Embedded newform 572.2.n.b.53.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			53.7
Character	$\chi$	$=$	572.53
Dual form			572.2.n.b.313.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.49464 - 1.81246i) q^{3} +(-1.12366 - 3.45827i) q^{5} +(1.36148 + 0.989171i) q^{7} +(2.01117 - 6.18974i) q^{9} +O(q^{10})$	\(q+(2.49464 - 1.81246i) q^{3} +(-1.12366 - 3.45827i) q^{5} +(1.36148 + 0.989171i) q^{7} +(2.01117 - 6.18974i) q^{9} +(-3.12093 - 1.12240i) q^{11} +(-0.309017 + 0.951057i) q^{13} +(-9.07111 - 6.59055i) q^{15} +(1.71117 + 5.26645i) q^{17} +(-3.91126 + 2.84170i) q^{19} +5.18924 q^{21} +7.77054 q^{23} +(-6.65192 + 4.83290i) q^{25} +(-3.34292 - 10.2885i) q^{27} +(2.51811 + 1.82951i) q^{29} +(0.814984 - 2.50826i) q^{31} +(-9.81992 + 2.85659i) q^{33} +(1.89098 - 5.81984i) q^{35} +(2.27624 + 1.65379i) q^{37} +(0.952869 + 2.93263i) q^{39} +(7.59753 - 5.51993i) q^{41} -5.33087 q^{43} -23.6656 q^{45} +(0.386287 - 0.280654i) q^{47} +(-1.28796 - 3.96393i) q^{49} +(13.8140 + 10.0365i) q^{51} +(1.90247 - 5.85519i) q^{53} +(-0.374700 + 12.0542i) q^{55} +(-4.60673 + 14.1781i) q^{57} +(8.62751 + 6.26825i) q^{59} +(2.18378 + 6.72099i) q^{61} +(8.86087 - 6.43780i) q^{63} +3.63624 q^{65} -4.78992 q^{67} +(19.3847 - 14.0838i) q^{69} +(-0.714076 - 2.19770i) q^{71} +(-9.82103 - 7.13540i) q^{73} +(-7.83470 + 24.1127i) q^{75} +(-3.13883 - 4.61526i) q^{77} +(0.715420 - 2.20183i) q^{79} +(-11.1910 - 8.13072i) q^{81} +(-2.94498 - 9.06372i) q^{83} +(16.2900 - 11.8354i) q^{85} +9.59771 q^{87} +2.83177 q^{89} +(-1.36148 + 0.989171i) q^{91} +(-2.51304 - 7.73435i) q^{93} +(14.2223 + 10.3331i) q^{95} +(-2.79511 + 8.60248i) q^{97} +(-13.2241 + 17.0604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.49464	−	1.81246i	1.44028	−	1.04643i	0.452300	−	0.891866i	$-0.350604\pi$
$3$	2.49464	−	1.81246i	1.44028	−	1.04643i	0.987983	−	0.154561i	$-0.0493963\pi$
$4$		0			0
$5$	−1.12366	−	3.45827i	−0.502516	−	1.54658i	−0.804907	−	0.593400i	$-0.797785\pi$
$5$	−1.12366	−	3.45827i	−0.502516	−	1.54658i	0.302392	−	0.953184i	$-0.402215\pi$
$6$		0			0
$7$	1.36148	+	0.989171i	0.514590	+	0.373872i	0.814562	−	0.580076i	$-0.196977\pi$
$7$	1.36148	+	0.989171i	0.514590	+	0.373872i	−0.299972	+	0.953948i	$0.596977\pi$
$8$		0			0
$9$	2.01117	−	6.18974i	0.670389	−	2.06325i
$10$		0			0
$11$	−3.12093	−	1.12240i	−0.940996	−	0.338417i
$11$	−3.12093	−	1.12240i	−0.940996	−	0.338417i
$12$		0			0
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$		0			0
$15$	−9.07111	−	6.59055i	−2.34215	−	1.70167i
$16$		0			0
$17$	1.71117	+	5.26645i	0.415021	+	1.27730i	0.912232	+	0.409673i	$0.134357\pi$
$17$	1.71117	+	5.26645i	0.415021	+	1.27730i	−0.497212	+	0.867629i	$0.665643\pi$
$18$		0			0
$19$	−3.91126	+	2.84170i	−0.897306	+	0.651931i	−0.937773	−	0.347250i	$-0.887115\pi$
$19$	−3.91126	+	2.84170i	−0.897306	+	0.651931i	0.0404669	+	0.999181i	$0.487115\pi$
$20$		0			0
$21$	5.18924			1.13238
$22$		0			0
$23$	7.77054			1.62027			0.810135	−	0.586243i	$-0.199394\pi$
$23$	7.77054			1.62027			0.810135	+	0.586243i	$0.199394\pi$
$24$		0			0
$25$	−6.65192	+	4.83290i	−1.33038	+	0.966580i
$26$		0			0
$27$	−3.34292	−	10.2885i	−0.643346	−	1.98002i
$28$		0			0
$29$	2.51811	+	1.82951i	0.467601	+	0.339732i	0.796506	−	0.604631i	$-0.206679\pi$
$29$	2.51811	+	1.82951i	0.467601	+	0.339732i	−0.328905	+	0.944363i	$0.606679\pi$
$30$		0			0
$31$	0.814984	−	2.50826i	0.146375	−	0.450497i	−0.850810	−	0.525474i	$-0.823888\pi$
$31$	0.814984	−	2.50826i	0.146375	−	0.450497i	0.997185	+	0.0749764i	$0.0238881\pi$
$32$		0			0
$33$	−9.81992	+	2.85659i	−1.70943	+	0.497268i
$34$		0			0
$35$	1.89098	−	5.81984i	0.319634	−	0.983733i
$36$		0			0
$37$	2.27624	+	1.65379i	0.374212	+	0.271881i	0.758955	−	0.651143i	$-0.225710\pi$
$37$	2.27624	+	1.65379i	0.374212	+	0.271881i	−0.384743	+	0.923024i	$0.625710\pi$
$38$		0			0
$39$	0.952869	+	2.93263i	0.152581	+	0.469596i
$40$		0			0
$41$	7.59753	−	5.51993i	1.18654	−	0.862068i	0.193642	−	0.981072i	$-0.437970\pi$
$41$	7.59753	−	5.51993i	1.18654	−	0.862068i	0.992894	+	0.119004i	$0.0379701\pi$
$42$		0			0
$43$	−5.33087			−0.812950			−0.406475	−	0.913662i	$-0.633242\pi$
$43$	−5.33087			−0.812950			−0.406475	+	0.913662i	$0.633242\pi$
$44$		0			0
$45$	−23.6656			−3.52786
$46$		0			0
$47$	0.386287	−	0.280654i	0.0563457	−	0.0409376i	−0.559256	−	0.828995i	$-0.688913\pi$
$47$	0.386287	−	0.280654i	0.0563457	−	0.0409376i	0.615602	+	0.788058i	$0.288913\pi$
$48$		0			0
$49$	−1.28796	−	3.96393i	−0.183994	−	0.566275i
$50$		0			0
$51$	13.8140	+	10.0365i	1.93435	+	1.40539i
$52$		0			0
$53$	1.90247	−	5.85519i	0.261324	−	0.804273i	−0.731194	−	0.682170i	$-0.761036\pi$
$53$	1.90247	−	5.85519i	0.261324	−	0.804273i	0.992518	−	0.122102i	$-0.0389636\pi$
$54$		0			0
$55$	−0.374700	+	12.0542i	−0.0505246	+	1.62539i
$56$		0			0
$57$	−4.60673	+	14.1781i	−0.610176	+	1.87793i
$58$		0			0
$59$	8.62751	+	6.26825i	1.12321	+	0.816057i	0.984692	−	0.174304i	$-0.0557675\pi$
$59$	8.62751	+	6.26825i	1.12321	+	0.816057i	0.138514	+	0.990361i	$0.455768\pi$
$60$		0			0
$61$	2.18378	+	6.72099i	0.279604	+	0.860534i	0.987964	+	0.154683i	$0.0494355\pi$
$61$	2.18378	+	6.72099i	0.279604	+	0.860534i	−0.708360	+	0.705852i	$0.750565\pi$
$62$		0			0
$63$	8.86087	−	6.43780i	1.11636	−	0.811086i
$64$		0			0
$65$	3.63624			0.451020
$66$		0			0
$67$	−4.78992			−0.585182			−0.292591	−	0.956238i	$-0.594517\pi$
$67$	−4.78992			−0.585182			−0.292591	+	0.956238i	$0.594517\pi$
$68$		0			0
$69$	19.3847	−	14.0838i	2.33365	−	1.69549i
$70$		0			0
$71$	−0.714076	−	2.19770i	−0.0847452	−	0.260819i	0.899701	−	0.436508i	$-0.143785\pi$
$71$	−0.714076	−	2.19770i	−0.0847452	−	0.260819i	−0.984446	+	0.175689i	$0.943785\pi$
$72$		0			0
$73$	−9.82103	−	7.13540i	−1.14946	−	0.835135i	−0.161055	−	0.986945i	$-0.551490\pi$
$73$	−9.82103	−	7.13540i	−1.14946	−	0.835135i	−0.988410	+	0.151810i	$0.951490\pi$
$74$		0			0
$75$	−7.83470	+	24.1127i	−0.904673	+	2.78430i
$76$		0			0
$77$	−3.13883	−	4.61526i	−0.357703	−	0.525958i
$78$		0			0
$79$	0.715420	−	2.20183i	0.0804910	−	0.247726i	−0.902711	−	0.430248i	$-0.858426\pi$
$79$	0.715420	−	2.20183i	0.0804910	−	0.247726i	0.983202	+	0.182522i	$0.0584261\pi$
$80$		0			0
$81$	−11.1910	−	8.13072i	−1.24344	−	0.903413i
$82$		0			0
$83$	−2.94498	−	9.06372i	−0.323254	−	0.994872i	−0.972223	−	0.234057i	$-0.924800\pi$
$83$	−2.94498	−	9.06372i	−0.323254	−	0.994872i	0.648969	−	0.760815i	$-0.275200\pi$
$84$		0			0
$85$	16.2900	−	11.8354i	1.76690	−	1.28373i
$86$		0			0
$87$	9.59771			1.02898
$88$		0			0
$89$	2.83177			0.300167			0.150083	−	0.988673i	$-0.452046\pi$
$89$	2.83177			0.300167			0.150083	+	0.988673i	$0.452046\pi$
$90$		0			0
$91$	−1.36148	+	0.989171i	−0.142722	+	0.103693i
$92$		0			0
$93$	−2.51304	−	7.73435i	−0.260590	−	0.802015i
$94$		0			0
$95$	14.2223	+	10.3331i	1.45918	+	1.06015i
$96$		0			0
$97$	−2.79511	+	8.60248i	−0.283801	+	0.873449i	0.702955	+	0.711235i	$0.251864\pi$
$97$	−2.79511	+	8.60248i	−0.283801	+	0.873449i	−0.986756	+	0.162214i	$0.948136\pi$
$98$		0			0
$99$	−13.2241	+	17.0604i	−1.32907	+	1.71464i
$100$		0			0
$101$	5.78006	−	17.7892i	0.575138	−	1.77009i	−0.0605725	−	0.998164i	$-0.519293\pi$
$101$	5.78006	−	17.7892i	0.575138	−	1.77009i	0.635710	−	0.771928i	$-0.280707\pi$
$102$		0			0
$103$	11.7797	+	8.55847i	1.16069	+	0.843291i	0.989865	−	0.142010i	$-0.0453565\pi$
$103$	11.7797	+	8.55847i	1.16069	+	0.843291i	0.170826	+	0.985301i	$0.445356\pi$
$104$		0			0
$105$	−5.83094	−	17.9458i	−0.569041	−	1.75133i
$106$		0			0
$107$	−15.3067	+	11.1210i	−1.47975	+	1.07510i	−0.502118	+	0.864799i	$0.667446\pi$
$107$	−15.3067	+	11.1210i	−1.47975	+	1.07510i	−0.977636	+	0.210305i	$0.932554\pi$
$108$		0			0
$109$	2.41947			0.231743			0.115871	−	0.993264i	$-0.463034\pi$
$109$	2.41947			0.231743			0.115871	+	0.993264i	$0.463034\pi$
$110$		0			0
$111$	8.67585			0.823475
$112$		0			0
$113$	−7.22938	+	5.25245i	−0.680083	+	0.494109i	−0.873385	−	0.487030i	$-0.838080\pi$
$113$	−7.22938	+	5.25245i	−0.680083	+	0.494109i	0.193302	+	0.981139i	$0.438080\pi$
$114$		0			0
$115$	−8.73144	−	26.8726i	−0.814211	−	2.50588i
$116$		0			0
$117$	5.26530	+	3.82547i	0.486778	+	0.353665i
$118$		0			0
$119$	−2.87970	+	8.86280i	−0.263981	+	0.812451i
$120$		0			0
$121$	8.48043	+	7.00588i	0.770948	+	0.636898i
$122$		0			0
$123$	8.94846	−	27.5405i	0.806855	−	2.48325i
$124$		0			0
$125$	9.47905	+	6.88694i	0.847832	+	0.615986i
$126$		0			0
$127$	4.74393	+	14.6003i	0.420956	+	1.29557i	0.906814	+	0.421532i	$0.138507\pi$
$127$	4.74393	+	14.6003i	0.420956	+	1.29557i	−0.485858	+	0.874038i	$0.661493\pi$
$128$		0			0
$129$	−13.2986	+	9.66201i	−1.17088	+	0.850692i
$130$		0			0
$131$	−12.8487			−1.12260			−0.561298	−	0.827613i	$-0.689698\pi$
$131$	−12.8487			−1.12260			−0.561298	+	0.827613i	$0.689698\pi$
$132$		0			0
$133$	−8.13603			−0.705483
$134$		0			0
$135$	−31.8240	+	23.1215i	−2.73897	+	1.98998i
$136$		0			0
$137$	6.95347	+	21.4006i	0.594075	+	1.82838i	0.559276	+	0.828982i	$0.311079\pi$
$137$	6.95347	+	21.4006i	0.594075	+	1.82838i	0.0347996	+	0.999394i	$0.488921\pi$
$138$		0			0
$139$	8.91528	+	6.47733i	0.756184	+	0.549400i	0.897738	−	0.440531i	$-0.145210\pi$
$139$	8.91528	+	6.47733i	0.756184	+	0.549400i	−0.141553	+	0.989931i	$0.545210\pi$
$140$		0			0
$141$	0.454973	−	1.40026i	0.0383156	−	0.117923i
$142$		0			0
$143$	2.03189	−	2.62134i	0.169915	−	0.219208i
$144$		0			0
$145$	3.49745	−	10.7640i	0.290447	−	0.893905i
$146$		0			0
$147$	−10.3975	−	7.55421i	−0.857569	−	0.623060i
$148$		0			0
$149$	−1.40882	−	4.33589i	−0.115415	−	0.355210i	0.876619	−	0.481186i	$-0.159794\pi$
$149$	−1.40882	−	4.33589i	−0.115415	−	0.355210i	−0.992033	+	0.125976i	$0.959794\pi$
$150$		0			0
$151$	−4.23669	+	3.07813i	−0.344777	+	0.250495i	−0.746674	−	0.665190i	$-0.768351\pi$
$151$	−4.23669	+	3.07813i	−0.344777	+	0.250495i	0.401898	+	0.915685i	$0.368351\pi$
$152$		0			0
$153$	36.0394			2.91361
$154$		0			0
$155$	−9.59001			−0.770288
$156$		0			0
$157$	−6.73710	+	4.89479i	−0.537679	+	0.390647i	−0.823222	−	0.567719i	$-0.807826\pi$
$157$	−6.73710	+	4.89479i	−0.537679	+	0.390647i	0.285543	+	0.958366i	$0.407826\pi$
$158$		0			0
$159$	−5.86635	−	18.0548i	−0.465232	−	1.43184i
$160$		0			0
$161$	10.5794	+	7.68640i	0.833775	+	0.605773i
$162$		0			0
$163$	−5.35980	+	16.4958i	−0.419812	+	1.29205i	0.488063	+	0.872808i	$0.337703\pi$
$163$	−5.35980	+	16.4958i	−0.419812	+	1.29205i	−0.907875	+	0.419240i	$0.862297\pi$
$164$		0			0
$165$	20.9131	+	30.7501i	1.62808	+	2.39389i
$166$		0			0
$167$	−5.00635	+	15.4080i	−0.387403	+	1.19230i	0.547319	+	0.836924i	$0.315648\pi$
$167$	−5.00635	+	15.4080i	−0.387403	+	1.19230i	−0.934722	+	0.355380i	$0.884352\pi$
$168$		0			0
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$		0			0
$171$	9.72317	+	29.9248i	0.743549	+	2.28841i
$172$		0			0
$173$	−0.941562	+	0.684085i	−0.0715856	+	0.0520100i	−0.623003	−	0.782220i	$-0.714087\pi$
$173$	−0.941562	+	0.684085i	−0.0715856	+	0.0520100i	0.551417	+	0.834230i	$0.314087\pi$
$174$		0			0
$175$	−13.8370			−1.04598
$176$		0			0
$177$	32.8835			2.47168
$178$		0			0
$179$	−4.33043	+	3.14624i	−0.323671	+	0.235161i	−0.737740	−	0.675084i	$-0.764107\pi$
$179$	−4.33043	+	3.14624i	−0.323671	+	0.235161i	0.414069	+	0.910245i	$0.364107\pi$
$180$		0			0
$181$	−1.02830	−	3.16478i	−0.0764328	−	0.235236i	0.905539	−	0.424263i	$-0.139467\pi$
$181$	−1.02830	−	3.16478i	−0.0764328	−	0.235236i	−0.981972	+	0.189027i	$0.939467\pi$
$182$		0			0
$183$	17.6293	+	12.8084i	1.30320	+	0.946827i
$184$		0			0
$185$	3.16152	−	9.73015i	0.232439	−	0.715375i
$186$		0			0
$187$	0.570616	−	18.3569i	0.0417276	−	1.34239i
$188$		0			0
$189$	5.62574	−	17.3142i	0.409212	−	1.25943i
$190$		0			0
$191$	19.0484	+	13.8395i	1.37829	+	1.00139i	0.997037	+	0.0769211i	$0.0245090\pi$
$191$	19.0484	+	13.8395i	1.37829	+	1.00139i	0.381258	+	0.924469i	$0.375491\pi$
$192$		0			0
$193$	−1.96661	−	6.05259i	−0.141559	−	0.435675i	0.854993	−	0.518639i	$-0.173561\pi$
$193$	−1.96661	−	6.05259i	−0.141559	−	0.435675i	−0.996553	+	0.0829643i	$0.973561\pi$
$194$		0			0
$195$	9.07111	−	6.59055i	0.649596	−	0.471959i
$196$		0			0
$197$	−13.0004			−0.926241			−0.463121	−	0.886295i	$-0.653270\pi$
$197$	−13.0004			−0.926241			−0.463121	+	0.886295i	$0.653270\pi$
$198$		0			0
$199$	−2.62574			−0.186134			−0.0930668	−	0.995660i	$-0.529667\pi$
$199$	−2.62574			−0.186134			−0.0930668	+	0.995660i	$0.529667\pi$
$200$		0			0
$201$	−11.9491	+	8.68156i	−0.842828	+	0.612350i
$202$		0			0
$203$	1.61865	+	4.98168i	0.113607	+	0.349645i
$204$		0			0
$205$	−27.6264	−	20.0718i	−1.92951	−	1.40187i
$206$		0			0
$207$	15.6279	−	48.0976i	1.08621	−	3.34301i
$208$		0			0
$209$	15.3963	−	4.47874i	1.06499	−	0.309801i
$210$		0			0
$211$	−1.79530	+	5.52537i	−0.123594	+	0.380382i	−0.993642	−	0.112584i	$-0.964087\pi$
$211$	−1.79530	+	5.52537i	−0.123594	+	0.380382i	0.870049	+	0.492966i	$0.164087\pi$
$212$		0			0
$213$	−5.76461	−	4.18824i	−0.394985	−	0.286973i
$214$		0			0
$215$	5.99008	+	18.4356i	0.408520	+	1.25729i
$216$		0			0
$217$	3.59068	−	2.60878i	0.243751	−	0.177096i
$218$		0			0
$219$	−37.4326			−2.52946
$220$		0			0
$221$	−5.53747			−0.372491
$222$		0			0
$223$	−15.8511	+	11.5165i	−1.06147	+	0.771200i	−0.974359	−	0.224999i	$-0.927762\pi$
$223$	−15.8511	+	11.5165i	−1.06147	+	0.771200i	−0.0871072	+	0.996199i	$0.527762\pi$
$224$		0			0
$225$	16.5363	+	50.8934i	1.10242	+	3.39289i
$226$		0			0
$227$	0.951201	+	0.691088i	0.0631334	+	0.0458691i	0.618904	−	0.785466i	$-0.287577\pi$
$227$	0.951201	+	0.691088i	0.0631334	+	0.0458691i	−0.555771	+	0.831335i	$0.687577\pi$
$228$		0			0
$229$	0.588044	−	1.80981i	0.0388591	−	0.119596i	−0.929745	−	0.368204i	$-0.879973\pi$
$229$	0.588044	−	1.80981i	0.0388591	−	0.119596i	0.968604	+	0.248608i	$0.0799730\pi$
$230$		0			0
$231$	−16.1953	−	5.82441i	−1.06557	−	0.383218i
$232$		0			0
$233$	5.39063	−	16.5906i	0.353152	−	1.08689i	−0.603922	−	0.797044i	$-0.706396\pi$
$233$	5.39063	−	16.5906i	0.353152	−	1.08689i	0.957073	−	0.289846i	$-0.0936040\pi$
$234$		0			0
$235$	−1.40463	−	1.02052i	−0.0916280	−	0.0665717i
$236$		0			0
$237$	−2.20603	−	6.78947i	−0.143297	−	0.441023i
$238$		0			0
$239$	−9.50113	+	6.90297i	−0.614577	+	0.446516i	−0.851023	−	0.525128i	$-0.824017\pi$
$239$	−9.50113	+	6.90297i	−0.614577	+	0.446516i	0.236446	+	0.971645i	$0.424017\pi$
$240$		0			0
$241$	−29.0710			−1.87263			−0.936313	−	0.351167i	$-0.885785\pi$
$241$	−29.0710			−1.87263			−0.936313	+	0.351167i	$0.885785\pi$
$242$		0			0
$243$	−10.2003			−0.654351
$244$		0			0
$245$	−12.2611	+	8.90820i	−0.783332	+	0.569124i
$246$		0			0
$247$	−1.49397	−	4.59797i	−0.0950590	−	0.292562i
$248$		0			0
$249$	−23.7743	−	17.2731i	−1.50664	−	1.09464i
$250$		0			0
$251$	−0.801729	+	2.46747i	−0.0506047	+	0.155745i	−0.973165	−	0.230107i	$-0.926092\pi$
$251$	−0.801729	+	2.46747i	−0.0506047	+	0.155745i	0.922561	+	0.385852i	$0.126092\pi$
$252$		0			0
$253$	−24.2513	−	8.72167i	−1.52467	−	0.548326i
$254$		0			0
$255$	19.1866	−	59.0502i	1.20151	−	3.69786i
$256$		0			0
$257$	−15.2330	−	11.0674i	−0.950211	−	0.690369i	0.000645936	−	1.00000i	$-0.499794\pi$
$257$	−15.2330	−	11.0674i	−0.950211	−	0.690369i	−0.950857	+	0.309631i	$0.899794\pi$
$258$		0			0
$259$	1.46317	+	4.50319i	0.0909173	+	0.279815i
$260$		0			0
$261$	16.3885	−	11.9070i	1.01442	−	0.737023i
$262$		0			0
$263$	−5.68095			−0.350303			−0.175151	−	0.984542i	$-0.556041\pi$
$263$	−5.68095			−0.350303			−0.175151	+	0.984542i	$0.556041\pi$
$264$		0			0
$265$	−22.3865			−1.37519
$266$		0			0
$267$	7.06425	−	5.13248i	0.432325	−	0.314103i
$268$		0			0
$269$	−7.82039	−	24.0687i	−0.476818	−	1.46749i	−0.843491	−	0.537144i	$-0.819503\pi$
$269$	−7.82039	−	24.0687i	−0.476818	−	1.46749i	0.366673	−	0.930350i	$-0.380497\pi$
$270$		0			0
$271$	18.9723	+	13.7842i	1.15248	+	0.837328i	0.988809	−	0.149187i	$-0.0476656\pi$
$271$	18.9723	+	13.7842i	1.15248	+	0.837328i	0.163674	+	0.986515i	$0.447666\pi$
$272$		0			0
$273$	−1.60356	+	4.93526i	−0.0970520	+	0.298695i
$274$		0			0
$275$	26.1846	−	7.61703i	1.57899	−	0.459324i
$276$		0			0
$277$	3.67280	−	11.3037i	0.220677	−	0.679175i	−0.778024	−	0.628234i	$-0.783778\pi$
$277$	3.67280	−	11.3037i	0.220677	−	0.679175i	0.998702	−	0.0509410i	$-0.0162220\pi$
$278$		0			0
$279$	−13.8864	−	10.0891i	−0.831358	−	0.604017i
$280$		0			0
$281$	−3.97380	−	12.2301i	−0.237057	−	0.729586i	−0.996842	−	0.0794117i	$-0.974696\pi$
$281$	−3.97380	−	12.2301i	−0.237057	−	0.729586i	0.759785	−	0.650174i	$-0.225304\pi$
$282$		0			0
$283$	8.16527	−	5.93242i	0.485375	−	0.352646i	−0.318028	−	0.948081i	$-0.603021\pi$
$283$	8.16527	−	5.93242i	0.485375	−	0.352646i	0.803403	+	0.595436i	$0.203021\pi$
$284$		0			0
$285$	54.2079			3.21100
$286$		0			0
$287$	15.8040			0.932882
$288$		0			0
$289$	−11.0541	+	8.03128i	−0.650241	+	0.472428i
$290$		0			0
$291$	8.61887	+	26.5262i	0.505247	+	1.55499i
$292$		0			0
$293$	16.7904	+	12.1990i	0.980908	+	0.712672i	0.957911	−	0.287064i	$-0.0926792\pi$
$293$	16.7904	+	12.1990i	0.980908	+	0.712672i	0.0229970	+	0.999736i	$0.492679\pi$
$294$		0			0
$295$	11.9829	−	36.8796i	0.697672	−	2.14721i
$296$		0			0
$297$	−1.11475	+	35.8617i	−0.0646842	+	2.08091i
$298$		0			0
$299$	−2.40123	+	7.39022i	−0.138867	+	0.427388i
$300$		0			0
$301$	−7.25786	−	5.27314i	−0.418336	−	0.303939i
$302$		0			0
$303$	−17.8231	−	54.8539i	−1.02391	−	3.15127i
$304$		0			0
$305$	20.7891	−	15.1042i	1.19038	−	0.864864i
$306$		0			0
$307$	28.8921			1.64896			0.824479	−	0.565892i	$-0.191468\pi$
$307$	28.8921			1.64896			0.824479	+	0.565892i	$0.191468\pi$
$308$		0			0
$309$	44.8981			2.55417
$310$		0			0
$311$	0.701372	−	0.509576i	0.0397711	−	0.0288954i	−0.567722	−	0.823220i	$-0.692175\pi$
$311$	0.701372	−	0.509576i	0.0397711	−	0.0288954i	0.607493	+	0.794325i	$0.292175\pi$
$312$		0			0
$313$	−2.24194	−	6.89997i	−0.126722	−	0.390010i	0.867489	−	0.497456i	$-0.165732\pi$
$313$	−2.24194	−	6.89997i	−0.126722	−	0.390010i	−0.994211	+	0.107447i	$0.965732\pi$
$314$		0			0
$315$	−32.2202	−	23.4094i	−1.81540	−	1.31897i
$316$		0			0
$317$	7.50722	−	23.1048i	0.421647	−	1.29770i	−0.484521	−	0.874780i	$-0.661006\pi$
$317$	7.50722	−	23.1048i	0.421647	−	1.29770i	0.906168	−	0.422918i	$-0.138994\pi$
$318$		0			0
$319$	−5.80540	−	8.53611i	−0.325040	−	0.477931i
$320$		0			0
$321$	−18.0284	+	55.4857i	−1.00625	+	3.09691i
$322$		0			0
$323$	−21.6585	−	15.7358i	−1.20511	−	0.875566i
$324$		0			0
$325$	−2.54081	−	7.81980i	−0.140939	−	0.433764i
$326$		0			0
$327$	6.03570	−	4.38520i	0.333775	−	0.242502i
$328$		0			0
$329$	0.803536			0.0443004
$330$		0			0
$331$	−2.84595			−0.156428			−0.0782138	−	0.996937i	$-0.524922\pi$
$331$	−2.84595			−0.156428			−0.0782138	+	0.996937i	$0.524922\pi$
$332$		0			0
$333$	14.8144	−	10.7633i	0.811825	−	0.589825i
$334$		0			0
$335$	5.38224	+	16.5648i	0.294063	+	0.905033i
$336$		0			0
$337$	13.7427	+	9.98465i	0.748612	+	0.543898i	0.895396	−	0.445270i	$-0.146892\pi$
$337$	13.7427	+	9.98465i	0.748612	+	0.543898i	−0.146784	+	0.989169i	$0.546892\pi$
$338$		0			0
$339$	−8.51484	+	26.2060i	−0.462463	+	1.42331i
$340$		0			0
$341$	−5.35879	+	6.91338i	−0.290195	+	0.374380i
$342$		0			0
$343$	5.80774	−	17.8744i	0.313589	−	0.965127i
$344$		0			0
$345$	−70.4875	−	51.2121i	−3.79492	−	2.75717i
$346$		0			0
$347$	−10.6537	−	32.7889i	−0.571923	−	1.76020i	−0.646425	−	0.762978i	$-0.723737\pi$
$347$	−10.6537	−	32.7889i	−0.571923	−	1.76020i	0.0745014	−	0.997221i	$-0.476263\pi$
$348$		0			0
$349$	−11.6101	+	8.43521i	−0.621473	+	0.451526i	−0.853436	−	0.521198i	$-0.825485\pi$
$349$	−11.6101	+	8.43521i	−0.621473	+	0.451526i	0.231963	+	0.972725i	$0.425485\pi$
$350$		0			0
$351$	10.8179			0.577419
$352$		0			0
$353$	36.3996			1.93736			0.968678	−	0.248320i	$-0.0798785\pi$
$353$	36.3996			1.93736			0.968678	+	0.248320i	$0.0798785\pi$
$354$		0			0
$355$	−6.79785	+	4.93893i	−0.360792	+	0.262131i
$356$		0			0
$357$	8.87969	+	27.3289i	0.469963	+	1.44640i
$358$		0			0
$359$	−21.3952	−	15.5445i	−1.12920	−	0.820409i	−0.143619	−	0.989633i	$-0.545874\pi$
$359$	−21.3952	−	15.5445i	−1.12920	−	0.820409i	−0.985578	+	0.169224i	$0.945874\pi$
$360$		0			0
$361$	1.35141	−	4.15921i	0.0711267	−	0.218906i
$362$		0			0
$363$	33.8536	+	2.10668i	1.77685	+	0.110572i
$364$		0			0
$365$	−13.6406	+	41.9815i	−0.713982	+	2.19741i
$366$		0			0
$367$	9.05468	+	6.57861i	0.472651	+	0.343401i	0.798473	−	0.602030i	$-0.205641\pi$
$367$	9.05468	+	6.57861i	0.472651	+	0.343401i	−0.325823	+	0.945431i	$0.605641\pi$
$368$		0			0
$369$	−18.8870	−	58.1282i	−0.983218	−	3.02603i
$370$		0			0
$371$	8.38196	−	6.08985i	0.435169	−	0.316169i
$372$		0			0
$373$	9.28566			0.480793			0.240397	−	0.970675i	$-0.422723\pi$
$373$	9.28566			0.480793			0.240397	+	0.970675i	$0.422723\pi$
$374$		0			0
$375$	36.1292			1.86570
$376$		0			0
$377$	−2.51811	+	1.82951i	−0.129689	+	0.0942247i
$378$		0			0
$379$	−2.26012	−	6.95592i	−0.116094	−	0.357302i	0.876079	−	0.482167i	$-0.160150\pi$
$379$	−2.26012	−	6.95592i	−0.116094	−	0.357302i	−0.992174	+	0.124865i	$0.960150\pi$
$380$		0			0
$381$	38.2970	+	27.8244i	1.96201	+	1.42549i
$382$		0			0
$383$	−3.47582	+	10.6975i	−0.177606	+	0.546616i	−0.999743	−	0.0226743i	$-0.992782\pi$
$383$	−3.47582	+	10.6975i	−0.177606	+	0.546616i	0.822137	+	0.569290i	$0.192782\pi$
$384$		0			0
$385$	−12.4338	+	16.0409i	−0.633686	+	0.817520i
$386$		0			0
$387$	−10.7213	+	32.9967i	−0.544992	+	1.67731i
$388$		0			0
$389$	−27.9649	−	20.3177i	−1.41787	−	1.03015i	−0.992118	−	0.125308i	$-0.960008\pi$
$389$	−27.9649	−	20.3177i	−1.41787	−	1.03015i	−0.425757	−	0.904838i	$-0.639992\pi$
$390$		0			0
$391$	13.2967	+	40.9232i	0.672445	+	2.06957i
$392$		0			0
$393$	−32.0529	+	23.2878i	−1.61686	+	1.17472i
$394$		0			0
$395$	−8.41842			−0.423577
$396$		0			0
$397$	−11.3080			−0.567531			−0.283766	−	0.958894i	$-0.591584\pi$
$397$	−11.3080			−0.567531			−0.283766	+	0.958894i	$0.591584\pi$
$398$		0			0
$399$	−20.2965	+	14.7463i	−1.01610	+	0.738236i
$400$		0			0
$401$	8.38426	+	25.8041i	0.418690	+	1.28860i	0.908908	+	0.416996i	$0.136917\pi$
$401$	8.38426	+	25.8041i	0.418690	+	1.28860i	−0.490218	+	0.871600i	$0.663083\pi$
$402$		0			0
$403$	2.13366	+	1.55019i	0.106285	+	0.0772205i
$404$		0			0
$405$	−15.5434	+	47.8375i	−0.772355	+	2.37707i
$406$		0			0
$407$	−5.24779	−	7.71622i	−0.260123	−	0.382479i
$408$		0			0
$409$	−2.63655	+	8.11446i	−0.130369	+	0.401234i	−0.994841	−	0.101447i	$-0.967653\pi$
$409$	−2.63655	+	8.11446i	−0.130369	+	0.401234i	0.864472	+	0.502681i	$0.167653\pi$
$410$		0			0
$411$	56.1343	+	40.7839i	2.76890	+	2.01172i
$412$		0			0
$413$	5.54578	+	17.0682i	0.272890	+	0.839869i
$414$		0			0
$415$	−28.0356	+	20.3691i	−1.37621	+	0.999878i
$416$		0			0
$417$	33.9804			1.66403
$418$		0			0
$419$	−0.0481108			−0.00235037			−0.00117518	−	0.999999i	$-0.500374\pi$
$419$	−0.0481108			−0.00235037			−0.00117518	+	0.999999i	$0.500374\pi$
$420$		0			0
$421$	0.0114964	−	0.00835264i	0.000560302	−	0.000407083i	−0.587505	−	0.809220i	$-0.699890\pi$
$421$	0.0114964	−	0.00835264i	0.000560302	−	0.000407083i	0.588065	+	0.808813i	$0.299890\pi$
$422$		0			0
$423$	−0.960286	−	2.95546i	−0.0466907	−	0.143699i
$424$		0			0
$425$	−36.8348	−	26.7621i	−1.78675	−	1.29815i
$426$		0			0
$427$	−3.67504	+	11.3106i	−0.177848	+	0.547359i
$428$		0			0
$429$	0.317748	−	10.2220i	0.0153410	−	0.493525i
$430$		0			0
$431$	7.53060	−	23.1768i	0.362736	−	1.11639i	−0.588650	−	0.808388i	$-0.700340\pi$
$431$	7.53060	−	23.1768i	0.362736	−	1.11639i	0.951386	−	0.308000i	$-0.0996596\pi$
$432$		0			0
$433$	−23.8867	−	17.3547i	−1.14792	−	0.834014i	−0.159719	−	0.987163i	$-0.551059\pi$
$433$	−23.8867	−	17.3547i	−1.14792	−	0.834014i	−0.988203	+	0.153149i	$0.951059\pi$
$434$		0			0
$435$	−10.7846	−	33.1914i	−0.517080	−	1.59141i
$436$		0			0
$437$	−30.3926	+	22.0815i	−1.45388	+	1.05630i
$438$		0			0
$439$	−19.7193			−0.941153			−0.470577	−	0.882359i	$-0.655954\pi$
$439$	−19.7193			−0.941153			−0.470577	+	0.882359i	$0.655954\pi$
$440$		0			0
$441$	−27.1260			−1.29171
$442$		0			0
$443$	9.94357	−	7.22443i	0.472433	−	0.343243i	−0.325955	−	0.945385i	$-0.605686\pi$
$443$	9.94357	−	7.22443i	0.472433	−	0.343243i	0.798389	+	0.602142i	$0.205686\pi$
$444$		0			0
$445$	−3.18194	−	9.79301i	−0.150839	−	0.464233i
$446$		0			0
$447$	−11.3731	−	8.26307i	−0.537931	−	0.390830i
$448$		0			0
$449$	3.96200	−	12.1938i	0.186978	−	0.575460i	−0.812999	−	0.582266i	$-0.802166\pi$
$449$	3.96200	−	12.1938i	0.186978	−	0.575460i	0.999977	+	0.00680596i	$0.00216642\pi$
$450$		0			0
$451$	−29.9070	+	8.69985i	−1.40826	+	0.409660i
$452$		0			0
$453$	−4.99001	+	15.3577i	−0.234451	+	0.721567i
$454$		0			0
$455$	4.95066	+	3.59686i	0.232090	+	0.168623i
$456$		0			0
$457$	−6.32157	−	19.4558i	−0.295711	−	0.910104i	−0.982982	−	0.183703i	$-0.941192\pi$
$457$	−6.32157	−	19.4558i	−0.295711	−	0.910104i	0.687271	−	0.726401i	$-0.258808\pi$
$458$		0			0
$459$	48.4634	−	35.2107i	2.26208	−	1.64349i
$460$		0			0
$461$	18.3640			0.855296			0.427648	−	0.903945i	$-0.359342\pi$
$461$	18.3640			0.855296			0.427648	+	0.903945i	$0.359342\pi$
$462$		0			0
$463$	4.39316			0.204167			0.102084	−	0.994776i	$-0.467449\pi$
$463$	4.39316			0.204167			0.102084	+	0.994776i	$0.467449\pi$
$464$		0			0
$465$	−23.9236	+	17.3815i	−1.10943	+	0.806050i
$466$		0			0
$467$	6.30495	+	19.4046i	0.291758	+	0.897940i	0.984291	+	0.176553i	$0.0564948\pi$
$467$	6.30495	+	19.4046i	0.291758	+	0.897940i	−0.692533	+	0.721386i	$0.743505\pi$
$468$		0			0
$469$	−6.52137	−	4.73805i	−0.301129	−	0.218783i
$470$		0			0
$471$	−7.93503	+	24.4215i	−0.365627	+	1.12528i
$472$		0			0
$473$	16.6373	+	5.98337i	0.764983	+	0.275116i
$474$		0			0
$475$	12.2838	−	37.8055i	0.563617	−	1.73464i
$476$		0			0
$477$	−32.4159	−	23.5515i	−1.48422	−	1.07835i
$478$		0			0
$479$	−2.83854	−	8.73612i	−0.129696	−	0.399163i	0.865031	−	0.501718i	$-0.167298\pi$
$479$	−2.83854	−	8.73612i	−0.129696	−	0.399163i	−0.994727	+	0.102554i	$0.967298\pi$
$480$		0			0
$481$	−2.27624	+	1.65379i	−0.103788	+	0.0754062i
$482$		0			0
$483$	40.3232			1.83477
$484$		0			0
$485$	32.8904			1.49348
$486$		0			0
$487$	8.29154	−	6.02415i	0.375725	−	0.272980i	−0.383856	−	0.923393i	$-0.625404\pi$
$487$	8.29154	−	6.02415i	0.375725	−	0.272980i	0.759581	+	0.650413i	$0.225404\pi$
$488$		0			0
$489$	16.5272	+	50.8655i	0.747386	+	2.30022i
$490$		0			0
$491$	−26.1137	−	18.9727i	−1.17850	−	0.856228i	−0.186495	−	0.982456i	$-0.559713\pi$
$491$	−26.1137	−	18.9727i	−1.17850	−	0.856228i	−0.992001	+	0.126228i	$0.959713\pi$
$492$		0			0
$493$	−5.32612	+	16.3921i	−0.239876	+	0.738263i
$494$		0			0
$495$	73.8588	+	26.5623i	3.31971	+	1.19389i
$496$		0			0
$497$	1.20170	−	3.69846i	0.0539037	−	0.165899i
$498$		0			0
$499$	−11.1736	−	8.11813i	−0.500201	−	0.363417i	0.308893	−	0.951097i	$-0.400042\pi$
$499$	−11.1736	−	8.11813i	−0.500201	−	0.363417i	−0.809094	+	0.587680i	$0.800042\pi$
$500$		0			0
$501$	15.4373	+	47.5112i	0.689689	+	2.12264i
$502$		0			0
$503$	−14.3563	+	10.4305i	−0.640117	+	0.465072i	−0.859890	−	0.510479i	$-0.829468\pi$
$503$	−14.3563	+	10.4305i	−0.640117	+	0.465072i	0.219774	+	0.975551i	$0.429468\pi$
$504$		0			0
$505$	−68.0146			−3.02661
$506$		0			0
$507$	−3.08355			−0.136945
$508$		0			0
$509$	−4.90360	+	3.56267i	−0.217348	+	0.157913i	−0.691132	−	0.722728i	$-0.742888\pi$
$509$	−4.90360	+	3.56267i	−0.217348	+	0.157913i	0.473784	+	0.880641i	$0.342888\pi$
$510$		0			0
$511$	−6.31298	−	19.4294i	−0.279270	−	0.859504i
$512$		0			0
$513$	42.3118	+	30.7413i	1.86811	+	1.35726i
$514$		0			0
$515$	16.3611	−	50.3542i	0.720956	−	2.21887i
$516$		0			0
$517$	−1.52058	+	0.442333i	−0.0668751	+	0.0194538i
$518$		0			0
$519$	−1.10898	+	3.41310i	−0.0486789	+	0.149818i
$520$		0			0
$521$	5.24867	+	3.81338i	0.229949	+	0.167067i	0.696794	−	0.717272i	$-0.254609\pi$
$521$	5.24867	+	3.81338i	0.229949	+	0.167067i	−0.466845	+	0.884339i	$0.654609\pi$
$522$		0			0
$523$	7.66437	+	23.5885i	0.335139	+	1.03145i	0.966653	+	0.256088i	$0.0824338\pi$
$523$	7.66437	+	23.5885i	0.335139	+	1.03145i	−0.631514	+	0.775364i	$0.717566\pi$
$524$		0			0
$525$	−34.5184	+	25.0791i	−1.50651	+	1.09454i
$526$		0			0
$527$	14.6042			0.636170
$528$		0			0
$529$	37.3813			1.62527
$530$		0			0
$531$	56.1502	−	40.7955i	2.43671	−	1.77037i
$532$		0			0
$533$	2.90200	+	8.93144i	0.125700	+	0.386863i
$534$		0			0
$535$	55.6588	+	40.4385i	2.40634	+	1.74831i
$536$		0			0
$537$	−5.10042	+	15.6975i	−0.220100	+	0.677397i
$538$		0			0
$539$	−0.429488	+	13.8167i	−0.0184994	+	0.595130i
$540$		0			0
$541$	−0.132998	+	0.409327i	−0.00571804	+	0.0175983i	−0.953875	−	0.300205i	$-0.902945\pi$
$541$	−0.132998	+	0.409327i	−0.00571804	+	0.0175983i	0.948157	+	0.317803i	$0.102945\pi$
$542$		0			0
$543$	−8.30128	−	6.03124i	−0.356242	−	0.258825i
$544$		0			0
$545$	−2.71865	−	8.36716i	−0.116454	−	0.358410i
$546$		0			0
$547$	−10.7318	+	7.79712i	−0.458859	+	0.333381i	−0.793084	−	0.609113i	$-0.791526\pi$
$547$	−10.7318	+	7.79712i	−0.458859	+	0.333381i	0.334224	+	0.942494i	$0.391526\pi$
$548$		0			0
$549$	45.9931			1.96294
$550$		0			0
$551$	−15.0479			−0.641063
$552$		0			0
$553$	3.15202	−	2.29008i	0.134038	−	0.0973839i
$554$		0			0
$555$	−9.74869	−	30.0034i	−0.413809	−	1.27357i
$556$		0			0
$557$	12.1586	+	8.83376i	0.515178	+	0.374299i	0.814784	−	0.579764i	$-0.196855\pi$
$557$	12.1586	+	8.83376i	0.515178	+	0.374299i	−0.299606	+	0.954063i	$0.596855\pi$
$558$		0			0
$559$	1.64733	−	5.06996i	0.0696746	−	0.214436i
$560$		0			0
$561$	−31.8477	−	46.8280i	−1.34461	−	1.97708i
$562$		0			0
$563$	−6.23897	+	19.2016i	−0.262941	+	0.809250i	0.729219	+	0.684280i	$0.239884\pi$
$563$	−6.23897	+	19.2016i	−0.262941	+	0.809250i	−0.992160	+	0.124970i	$0.960116\pi$
$564$		0			0
$565$	26.2877	+	19.0992i	1.10593	+	0.803508i
$566$		0			0
$567$	−7.19358	−	22.1396i	−0.302102	−	0.929775i
$568$		0			0
$569$	−7.53415	+	5.47388i	−0.315848	+	0.229477i	−0.734402	−	0.678715i	$-0.762537\pi$
$569$	−7.53415	+	5.47388i	−0.315848	+	0.229477i	0.418554	+	0.908192i	$0.362537\pi$
$570$		0			0
$571$	1.88892			0.0790490			0.0395245	−	0.999219i	$-0.487416\pi$
$571$	1.88892			0.0790490			0.0395245	+	0.999219i	$0.487416\pi$
$572$		0			0
$573$	72.6026			3.03302
$574$		0			0
$575$	−51.6890	+	37.5542i	−2.15558	+	1.56612i
$576$		0			0
$577$	−3.38158	−	10.4074i	−0.140777	−	0.433267i	0.855667	−	0.517527i	$-0.173147\pi$
$577$	−3.38158	−	10.4074i	−0.140777	−	0.433267i	−0.996444	+	0.0842601i	$0.973147\pi$
$578$		0			0
$579$	−15.8761	−	11.5347i	−0.659788	−	0.479364i
$580$		0			0
$581$	4.95604	−	15.2531i	0.205611	−	0.632807i
$582$		0			0
$583$	−12.5093	+	16.1383i	−0.518084	+	0.668381i
$584$		0			0
$585$	7.31308	−	22.5073i	0.302359	−	0.930564i
$586$		0			0
$587$	6.61171	+	4.80369i	0.272894	+	0.198269i	0.715812	−	0.698293i	$-0.246057\pi$
$587$	6.61171	+	4.80369i	0.272894	+	0.198269i	−0.442918	+	0.896562i	$0.646057\pi$
$588$		0			0
$589$	3.94011	+	12.1264i	0.162349	+	0.499660i
$590$		0			0
$591$	−32.4314	+	23.5628i	−1.33405	+	0.969244i
$592$		0			0
$593$	−8.71667			−0.357951			−0.178975	−	0.983854i	$-0.557278\pi$
$593$	−8.71667			−0.357951			−0.178975	+	0.983854i	$0.557278\pi$
$594$		0			0
$595$	33.8857			1.38918
$596$		0			0
$597$	−6.55028	+	4.75906i	−0.268085	+	0.194775i
$598$		0			0
$599$	−11.6146	−	35.7459i	−0.474558	−	1.46054i	−0.846553	−	0.532304i	$-0.821326\pi$
$599$	−11.6146	−	35.7459i	−0.474558	−	1.46054i	0.371995	−	0.928235i	$-0.378674\pi$
$600$		0			0
$601$	−24.6853	−	17.9349i	−1.00694	−	0.731581i	−0.0433711	−	0.999059i	$-0.513810\pi$
$601$	−24.6853	−	17.9349i	−1.00694	−	0.731581i	−0.963564	+	0.267478i	$0.913810\pi$
$602$		0			0
$603$	−9.63333	+	29.6483i	−0.392300	+	1.20737i
$604$		0			0
$605$	14.6991	−	37.1998i	0.597603	−	1.51239i
$606$		0			0
$607$	−3.20549	+	9.86548i	−0.130107	+	0.400427i	−0.994797	−	0.101878i	$-0.967515\pi$
$607$	−3.20549	+	9.86548i	−0.130107	+	0.400427i	0.864690	+	0.502306i	$0.167515\pi$
$608$		0			0
$609$	13.0671	+	9.49378i	0.529504	+	0.384707i
$610$		0			0
$611$	0.147548	+	0.454108i	0.00596917	+	0.0183712i
$612$		0			0
$613$	20.8131	−	15.1216i	0.840634	−	0.610757i	−0.0819135	−	0.996639i	$-0.526103\pi$
$613$	20.8131	−	15.1216i	0.840634	−	0.610757i	0.922548	+	0.385883i	$0.126103\pi$
$614$		0			0
$615$	−105.297			−4.24600
$616$		0			0
$617$	5.21698			0.210028			0.105014	−	0.994471i	$-0.466511\pi$
$617$	5.21698			0.210028			0.105014	+	0.994471i	$0.466511\pi$
$618$		0			0
$619$	10.6948	−	7.77026i	0.429862	−	0.312313i	−0.351732	−	0.936101i	$-0.614407\pi$
$619$	10.6948	−	7.77026i	0.429862	−	0.312313i	0.781594	+	0.623788i	$0.214407\pi$
$620$		0			0
$621$	−25.9763	−	79.9469i	−1.04239	−	3.20816i
$622$		0			0
$623$	3.85539	+	2.80110i	0.154463	+	0.112224i
$624$		0			0
$625$	0.461610	−	1.42069i	0.0184644	−	0.0568276i
$626$		0			0
$627$	30.2908	−	39.0781i	1.20970	−	1.56063i
$628$		0			0
$629$	−4.81454	+	14.8176i	−0.191968	+	0.590818i
$630$		0			0
$631$	−15.6256	−	11.3527i	−0.622046	−	0.451943i	0.231589	−	0.972814i	$-0.425607\pi$
$631$	−15.6256	−	11.3527i	−0.622046	−	0.451943i	−0.853636	+	0.520870i	$0.825607\pi$
$632$		0			0
$633$	5.53590	+	17.0378i	0.220032	+	0.677190i
$634$		0			0
$635$	45.1613	−	32.8116i	1.79217	−	1.30209i
$636$		0			0
$637$	4.16792			0.165139
$638$		0			0
$639$	−15.0393			−0.594945
$640$		0			0
$641$	22.4304	−	16.2966i	0.885947	−	0.643678i	−0.0488713	−	0.998805i	$-0.515562\pi$
$641$	22.4304	−	16.2966i	0.885947	−	0.643678i	0.934818	+	0.355127i	$0.115562\pi$
$642$		0			0
$643$	5.09772	+	15.6892i	0.201034	+	0.618720i	0.999853	+	0.0171483i	$0.00545874\pi$
$643$	5.09772	+	15.6892i	0.201034	+	0.618720i	−0.798819	+	0.601572i	$0.794541\pi$
$644$		0			0
$645$	48.3569	+	35.1333i	1.90405	+	1.38337i
$646$		0			0
$647$	−0.226228	+	0.696260i	−0.00889396	+	0.0273728i	−0.955405	−	0.295299i	$-0.904581\pi$
$647$	−0.226228	+	0.696260i	−0.00889396	+	0.0273728i	0.946511	+	0.322671i	$0.104581\pi$
$648$		0			0
$649$	−19.8904	−	29.2463i	−0.780765	−	1.14802i
$650$		0			0
$651$	4.22915	−	13.0160i	0.165753	−	0.510136i
$652$		0			0
$653$	−24.5251	−	17.8185i	−0.959741	−	0.697293i	−0.00665050	−	0.999978i	$-0.502117\pi$
$653$	−24.5251	−	17.8185i	−0.959741	−	0.697293i	−0.953091	+	0.302685i	$0.902117\pi$
$654$		0			0
$655$	14.4376	+	44.4343i	0.564123	+	1.73619i
$656$		0			0
$657$	−63.9180	+	46.4391i	−2.49368	+	1.81176i
$658$		0			0
$659$	−1.78687			−0.0696065			−0.0348032	−	0.999394i	$-0.511080\pi$
$659$	−1.78687			−0.0696065			−0.0348032	+	0.999394i	$0.511080\pi$
$660$		0			0
$661$	−3.92820			−0.152789			−0.0763946	−	0.997078i	$-0.524341\pi$
$661$	−3.92820			−0.152789			−0.0763946	+	0.997078i	$0.524341\pi$
$662$		0			0
$663$	−13.8140	+	10.0365i	−0.536492	+	0.389784i
$664$		0			0
$665$	9.14212	+	28.1366i	0.354516	+	1.09109i
$666$		0			0
$667$	19.5671	+	14.2163i	0.757640	+	0.550457i
$668$		0			0
$669$	−18.6696	+	57.4590i	−0.721807	+	2.22149i
$670$		0			0
$671$	0.728214	−	23.4268i	0.0281124	−	0.904382i
$672$		0			0
$673$	−7.06588	+	21.7465i	−0.272369	+	0.838267i	0.717534	+	0.696524i	$0.245271\pi$
$673$	−7.06588	+	21.7465i	−0.272369	+	0.838267i	−0.989903	+	0.141744i	$0.954729\pi$
$674$		0			0
$675$	71.9600	+	52.2820i	2.76974	+	2.01233i
$676$		0			0
$677$	6.33737	+	19.5044i	0.243565	+	0.749615i	0.995869	+	0.0907997i	$0.0289423\pi$
$677$	6.33737	+	19.5044i	0.243565	+	0.749615i	−0.752304	+	0.658816i	$0.771058\pi$
$678$		0			0
$679$	−12.3148	+	8.94723i	−0.472599	+	0.343363i
$680$		0			0
$681$	3.62548			0.138929
$682$		0			0
$683$	−17.0893			−0.653904			−0.326952	−	0.945041i	$-0.606022\pi$
$683$	−17.0893			−0.653904			−0.326952	+	0.945041i	$0.606022\pi$
$684$		0			0
$685$	66.1956	−	48.0939i	2.52920	−	1.83757i
$686$		0			0
$687$	−1.81326	−	5.58065i	−0.0691803	−	0.212915i
$688$		0			0
$689$	4.98072	+	3.61871i	0.189750	+	0.137862i
$690$		0			0
$691$	−3.14617	+	9.68290i	−0.119686	+	0.368355i	−0.992895	−	0.118990i	$-0.962034\pi$
$691$	−3.14617	+	9.68290i	−0.119686	+	0.368355i	0.873210	+	0.487345i	$0.162034\pi$
$692$		0			0
$693$	−34.8800	+	10.1465i	−1.32498	+	0.385433i
$694$		0			0
$695$	12.3826	−	38.1097i	0.469699	−	1.44558i
$696$		0			0
$697$	42.0711	+	30.5665i	1.59356	+	1.15779i
$698$		0			0
$699$	−16.6223	−	51.1581i	−0.628712	−	1.93498i
$700$		0			0
$701$	18.0929	−	13.1453i	0.683361	−	0.496491i	−0.191110	−	0.981569i	$-0.561209\pi$
$701$	18.0929	−	13.1453i	0.683361	−	0.496491i	0.874471	+	0.485078i	$0.161209\pi$
$702$		0			0
$703$	−13.6026			−0.513030
$704$		0			0
$705$	−5.35372			−0.201633
$706$		0			0
$707$	25.4660	−	18.5021i	0.957747	−	0.695844i
$708$		0			0
$709$	−4.76033	−	14.6508i	−0.178778	−	0.550222i	0.821008	−	0.570917i	$-0.193412\pi$
$709$	−4.76033	−	14.6508i	−0.178778	−	0.550222i	−0.999786	+	0.0206947i	$0.993412\pi$
$710$		0			0
$711$	−12.1899	−	8.85652i	−0.457159	−	0.332145i
$712$		0			0
$713$	6.33287	−	19.4906i	0.237168	−	0.729927i
$714$		0			0
$715$	−11.3484	−	4.08132i	−0.424408	−	0.152633i
$716$		0			0
$717$	−11.1905	+	34.4409i	−0.417918	+	1.28622i
$718$		0			0
$719$	−3.30316	−	2.39988i	−0.123187	−	0.0895005i	0.524486	−	0.851419i	$-0.324258\pi$
$719$	−3.30316	−	2.39988i	−0.123187	−	0.0895005i	−0.647673	+	0.761919i	$0.724258\pi$
$720$		0			0
$721$	7.57204	+	23.3043i	0.281997	+	0.867899i
$722$		0			0
$723$	−72.5217	+	52.6901i	−2.69711	+	1.95957i
$724$		0			0
$725$	−25.5921			−0.950466
$726$		0			0
$727$	9.87480			0.366236			0.183118	−	0.983091i	$-0.441381\pi$
$727$	9.87480			0.366236			0.183118	+	0.983091i	$0.441381\pi$
$728$		0			0
$729$	8.12675	−	5.90443i	0.300991	−	0.218682i
$730$		0			0
$731$	−9.12204	−	28.0748i	−0.337391	−	1.03838i
$732$		0			0
$733$	14.8028	+	10.7548i	0.546752	+	0.397239i	0.826587	−	0.562810i	$-0.190280\pi$
$733$	14.8028	+	10.7548i	0.546752	+	0.397239i	−0.279834	+	0.960048i	$0.590280\pi$
$734$		0			0
$735$	−14.4412	+	44.4456i	−0.532673	+	1.63940i
$736$		0			0
$737$	14.9490	+	5.37621i	0.550654	+	0.198035i
$738$		0			0
$739$	−9.70591	+	29.8717i	−0.357037	+	1.09885i	0.597781	+	0.801659i	$0.296049\pi$
$739$	−9.70591	+	29.8717i	−0.357037	+	1.09885i	−0.954819	+	0.297189i	$0.903951\pi$
$740$		0			0
$741$	−12.0606	−	8.76252i	−0.443056	−	0.321899i
$742$		0			0
$743$	2.37406	+	7.30659i	0.0870957	+	0.268053i	0.985113	−	0.171907i	$-0.0549928\pi$
$743$	2.37406	+	7.30659i	0.0870957	+	0.268053i	−0.898018	+	0.439960i	$0.854993\pi$
$744$		0			0
$745$	−13.4116	+	9.74413i	−0.491365	+	0.356997i
$746$		0			0
$747$	−62.0249			−2.26937
$748$		0			0
$749$	−31.8403			−1.16342
$750$		0			0
$751$	−3.64994	+	2.65183i	−0.133188	+	0.0967668i	−0.652385	−	0.757888i	$-0.726231\pi$
$751$	−3.64994	+	2.65183i	−0.133188	+	0.0967668i	0.519197	+	0.854655i	$0.326231\pi$
$752$		0			0
$753$	2.47217	+	7.60856i	0.0900909	+	0.277271i
$754$		0			0
$755$	15.4056	+	11.1928i	0.560667	+	0.407348i
$756$		0			0
$757$	16.7050	−	51.4128i	0.607155	−	1.86863i	0.125917	−	0.992041i	$-0.459813\pi$
$757$	16.7050	−	51.4128i	0.607155	−	1.86863i	0.481238	−	0.876590i	$-0.340187\pi$
$758$		0			0
$759$	−76.3061	+	22.1972i	−2.76974	+	0.805708i
$760$		0			0
$761$	−7.09354	+	21.8317i	−0.257140	+	0.791397i	0.736260	+	0.676699i	$0.236590\pi$
$761$	−7.09354	+	21.8317i	−0.257140	+	0.791397i	−0.993400	+	0.114698i	$0.963410\pi$
$762$		0			0
$763$	3.29405	+	2.39327i	0.119253	+	0.0866420i
$764$		0			0
$765$	−40.4960	−	124.634i	−1.46414	−	4.50615i
$766$		0			0
$767$	−8.62751	+	6.26825i	−0.311521	+	0.226333i
$768$		0			0
$769$	31.4168			1.13292			0.566459	−	0.824090i	$-0.308313\pi$
$769$	31.4168			1.13292			0.566459	+	0.824090i	$0.308313\pi$
$770$		0			0
$771$	−58.0604			−2.09099
$772$		0			0
$773$	−29.0641	+	21.1163i	−1.04536	+	0.759500i	−0.971325	−	0.237755i	$-0.923588\pi$
$773$	−29.0641	+	21.1163i	−1.04536	+	0.759500i	−0.0740373	+	0.997255i	$0.523588\pi$
$774$		0			0
$775$	6.70098	+	20.6235i	0.240706	+	0.740818i
$776$		0			0
$777$	11.8120	+	8.58190i	0.423752	+	0.307874i
$778$		0			0
$779$	−14.0300	+	43.1798i	−0.502676	+	1.54708i
$780$		0			0
$781$	−0.238119	+	7.66035i	−0.00852056	+	0.274109i
$782$		0			0
$783$	10.4050	−	32.0234i	0.371845	−	1.14442i
$784$		0			0
$785$	24.4977	+	17.7986i	0.874360	+	0.635260i
$786$		0			0
$787$	−9.33562	−	28.7321i	−0.332779	−	1.02419i	−0.967806	−	0.251698i	$-0.919011\pi$
$787$	−9.33562	−	28.7321i	−0.332779	−	1.02419i	0.635027	−	0.772490i	$-0.280989\pi$
$788$		0			0
$789$	−14.1720	+	10.2965i	−0.504535	+	0.366566i
$790$		0			0
$791$	−15.0382			−0.534697
$792$		0			0
$793$	−7.06686			−0.250952
$794$		0			0
$795$	−55.8464	+	40.5748i	−1.98067	+	1.43904i
$796$		0			0
$797$	16.2931	+	50.1449i	0.577130	+	1.77622i	0.628810	+	0.777559i	$0.283542\pi$
$797$	16.2931	+	50.1449i	0.577130	+	1.77622i	−0.0516804	+	0.998664i	$0.516458\pi$
$798$		0			0
$799$	2.13905	+	1.55411i	0.0756743	+	0.0549806i
$800$		0			0
$801$	5.69516	−	17.5279i	0.201229	−	0.619318i
$802$		0			0
$803$	22.6420	+	33.2922i	0.799018	+	1.17486i
$804$		0			0
$805$	14.6940	−	45.2233i	0.517894	−	1.59391i
$806$		0			0
$807$	−63.1327	−	45.8686i	−2.22238	−	1.61465i
$808$		0			0
$809$	6.60253	+	20.3205i	0.232133	+	0.714431i	0.997489	+	0.0708239i	$0.0225628\pi$
$809$	6.60253	+	20.3205i	0.232133	+	0.714431i	−0.765356	+	0.643607i	$0.777437\pi$
$810$		0			0
$811$	22.7123	−	16.5014i	0.797536	−	0.579444i	−0.112654	−	0.993634i	$-0.535935\pi$
$811$	22.7123	−	16.5014i	0.797536	−	0.579444i	0.910190	+	0.414190i	$0.135935\pi$
$812$		0			0
$813$	72.3123			2.53610
$814$		0			0
$815$	63.0694			2.20922
$816$		0			0
$817$	20.8504	−	15.1487i	0.729464	−	0.529987i
$818$		0			0
$819$	3.38455	+	10.4166i	0.118266	+	0.363985i
$820$		0			0
$821$	8.41043	+	6.11053i	0.293526	+	0.213259i	0.724796	−	0.688964i	$-0.241934\pi$
$821$	8.41043	+	6.11053i	0.293526	+	0.213259i	−0.431270	+	0.902223i	$0.641934\pi$
$822$		0			0
$823$	14.3002	−	44.0116i	0.498475	−	1.53415i	−0.312995	−	0.949755i	$-0.601332\pi$
$823$	14.3002	−	44.0116i	0.498475	−	1.53415i	0.811470	−	0.584394i	$-0.198668\pi$
$824$		0			0
$825$	51.5157	−	66.4605i	1.79355	−	2.31386i
$826$		0			0
$827$	4.48534	−	13.8045i	0.155971	−	0.480028i	−0.842287	−	0.539029i	$-0.818791\pi$
$827$	4.48534	−	13.8045i	0.155971	−	0.480028i	0.998258	+	0.0590006i	$0.0187914\pi$
$828$		0			0
$829$	−10.6063	−	7.70596i	−0.368373	−	0.267639i	0.388163	−	0.921591i	$-0.373110\pi$
$829$	−10.6063	−	7.70596i	−0.368373	−	0.267639i	−0.756536	+	0.653952i	$0.773110\pi$
$830$		0			0
$831$	−11.3253	−	34.8556i	−0.392869	−	1.20913i
$832$		0			0
$833$	18.6719	−	13.5659i	0.646943	−	0.470032i
$834$		0			0
$835$	58.9103			2.03867
$836$		0			0
$837$	−28.5306			−0.986162
$838$		0			0
$839$	−18.6667	+	13.5622i	−0.644447	+	0.468218i	−0.861375	−	0.507969i	$-0.830396\pi$
$839$	−18.6667	+	13.5622i	−0.644447	+	0.468218i	0.216928	+	0.976188i	$0.430396\pi$
$840$		0			0
$841$	−5.96774	−	18.3668i	−0.205784	−	0.633339i
$842$		0			0
$843$	−32.0798	−	23.3074i	−1.10489	−	0.802748i
$844$		0			0
$845$	−1.12366	+	3.45827i	−0.0386550	+	0.118968i
$846$		0			0
$847$	4.61590	+	17.9269i	0.158604	+	0.615977i
$848$		0			0
$849$	9.61715	−	29.5985i	0.330060	−	1.01582i
$850$		0			0
$851$	17.6876	+	12.8508i	0.606325	+	0.440521i
$852$		0			0
$853$	−1.94580	−	5.98854i	−0.0666228	−	0.205044i	0.912203	−	0.409738i	$-0.134380\pi$
$853$	−1.94580	−	5.98854i	−0.0666228	−	0.205044i	−0.978826	+	0.204694i	$0.934380\pi$
$854$		0			0
$855$	92.5625	−	67.2506i	3.16557	−	2.29992i
$856$		0			0
$857$	−3.16195			−0.108010			−0.0540051	−	0.998541i	$-0.517199\pi$
$857$	−3.16195			−0.108010			−0.0540051	+	0.998541i	$0.517199\pi$
$858$		0			0
$859$	−12.6058			−0.430105			−0.215053	−	0.976602i	$-0.568992\pi$
$859$	−12.6058			−0.430105			−0.215053	+	0.976602i	$0.568992\pi$
$860$		0			0
$861$	39.4254	−	28.6442i	1.34361	−	0.976193i
$862$		0			0
$863$	7.62069	+	23.4541i	0.259411	+	0.798386i	0.992928	+	0.118715i	$0.0378775\pi$
$863$	7.62069	+	23.4541i	0.259411	+	0.798386i	−0.733517	+	0.679671i	$0.762123\pi$
$864$		0			0
$865$	3.42374	+	2.48750i	0.116411	+	0.0845774i
$866$		0			0
$867$	−13.0196	+	40.0703i	−0.442170	+	1.36086i
$868$		0			0
$869$	−4.70412	+	6.06879i	−0.159576	+	0.205870i
$870$		0			0
$871$	1.48017	−	4.55549i	0.0501535	−	0.154357i
$872$		0			0
$873$	47.6256	+	34.6020i	1.61188	+	1.17110i
$874$		0			0
$875$	6.09316	+	18.7528i	0.205986	+	0.633961i
$876$		0			0
$877$	−11.5958	+	8.42483i	−0.391562	+	0.284486i	−0.766095	−	0.642727i	$-0.777803\pi$
$877$	−11.5958	+	8.42483i	−0.391562	+	0.284486i	0.374533	+	0.927213i	$0.377803\pi$
$878$		0			0
$879$	63.9964			2.15854
$880$		0			0
$881$	−43.8113			−1.47604			−0.738020	−	0.674779i	$-0.764239\pi$
$881$	−43.8113			−1.47604			−0.738020	+	0.674779i	$0.764239\pi$
$882$		0			0
$883$	−34.1028	+	24.7771i	−1.14765	+	0.833817i	−0.988167	−	0.153383i	$-0.950983\pi$
$883$	−34.1028	+	24.7771i	−1.14765	+	0.833817i	−0.159484	+	0.987200i	$0.550983\pi$
$884$		0			0
$885$	−36.9499	−	113.720i	−1.24206	−	3.82266i
$886$		0			0
$887$	−37.8435	−	27.4949i	−1.27066	−	0.923188i	−0.271431	−	0.962458i	$-0.587497\pi$
$887$	−37.8435	−	27.4949i	−1.27066	−	0.923188i	−0.999229	+	0.0392697i	$0.987497\pi$
$888$		0			0
$889$	−7.98347	+	24.5706i	−0.267757	+	0.824071i
$890$		0			0
$891$	25.8003	+	37.9362i	0.864344	+	1.27091i
$892$		0			0
$893$	−0.713336	+	2.19542i	−0.0238709	+	0.0734670i
$894$		0			0
$895$	15.7465	+	11.4405i	0.526346	+	0.382413i
$896$		0			0
$897$	7.40431	+	22.7881i	0.247223	+	0.760873i
$898$		0			0
$899$	6.64112	−	4.82505i	0.221494	−	0.160925i
$900$		0			0
$901$	34.0915			1.13575
$902$		0			0
$903$	−27.6631			−0.920572
$904$		0			0
$905$	−9.78919	+	7.11226i	−0.325404	+	0.236420i
$906$		0			0
$907$	−12.3000	−	37.8554i	−0.408414	−	1.25697i	−0.918011	−	0.396556i	$-0.870205\pi$
$907$	−12.3000	−	37.8554i	−0.408414	−	1.25697i	0.509597	−	0.860413i	$-0.329795\pi$
$908$		0			0
$909$	−98.4858	−	71.5541i	−3.26657	−	2.37330i
$910$		0			0
$911$	5.51607	−	16.9767i	0.182755	−	0.562463i	−0.817147	−	0.576429i	$-0.804446\pi$
$911$	5.51607	−	16.9767i	0.182755	−	0.562463i	0.999902	+	0.0139659i	$0.00444563\pi$
$912$		0			0
$913$	−0.982047	+	31.5927i	−0.0325010	+	1.04557i
$914$		0			0
$915$	24.4857	−	75.3592i	0.809471	−	2.49130i
$916$		0			0
$917$	−17.4932	−	12.7096i	−0.577677	−	0.419707i
$918$		0			0
$919$	−3.04847	−	9.38221i	−0.100560	−	0.309491i	0.888103	−	0.459644i	$-0.152023\pi$
$919$	−3.04847	−	9.38221i	−0.100560	−	0.309491i	−0.988663	+	0.150154i	$0.952023\pi$
$920$		0			0
$921$	72.0755	−	52.3659i	2.37497	−	1.72551i
$922$		0			0
$923$	2.31080			0.0760608
$924$		0			0
$925$	−23.1340			−0.760640
$926$		0			0
$927$	76.6657	−	55.7009i	2.51803	−	1.82946i
$928$		0			0
$929$	4.02076	+	12.3746i	0.131917	+	0.405998i	0.995098	−	0.0988965i	$-0.0315313\pi$
$929$	4.02076	+	12.3746i	0.131917	+	0.405998i	−0.863181	+	0.504895i	$0.831531\pi$
$930$		0			0
$931$	16.3018	+	11.8440i	0.534271	+	0.388171i
$932$		0			0
$933$	0.826083	−	2.54242i	0.0270447	−	0.0832352i
$934$		0			0
$935$	−64.1241	+	18.6535i	−2.09708	+	0.610035i
$936$		0			0
$937$	−6.56793	+	20.2140i	−0.214565	+	0.660363i	0.784619	+	0.619978i	$0.212858\pi$
$937$	−6.56793	+	20.2140i	−0.214565	+	0.660363i	−0.999184	+	0.0403851i	$0.987142\pi$
$938$		0			0
$939$	−18.0988	−	13.1495i	−0.590632	−	0.429119i
$940$		0			0
$941$	2.06886	+	6.36731i	0.0674430	+	0.207568i	0.979098	−	0.203387i	$-0.0651951\pi$
$941$	2.06886	+	6.36731i	0.0674430	+	0.207568i	−0.911655	+	0.410956i	$0.865195\pi$
$942$		0			0
$943$	59.0369	−	42.8929i	1.92251	−	1.39678i
$944$		0			0
$945$	−66.1987			−2.15344
$946$		0			0
$947$	21.8181			0.708993			0.354496	−	0.935057i	$-0.384652\pi$
$947$	21.8181			0.708993			0.354496	+	0.935057i	$0.384652\pi$
$948$		0			0
$949$	9.82103	−	7.13540i	0.318804	−	0.231625i
$950$		0			0
$951$	−23.1489	−	71.2449i	−0.750654	−	2.31028i
$952$		0			0
$953$	−35.2680	−	25.6237i	−1.14244	−	0.830033i	−0.154985	−	0.987917i	$-0.549533\pi$
$953$	−35.2680	−	25.6237i	−1.14244	−	0.830033i	−0.987458	+	0.157883i	$0.949533\pi$
$954$		0			0
$955$	26.4567	−	81.4254i	0.856119	−	2.63486i
$956$		0			0
$957$	−29.9538	−	10.7725i	−0.968269	−	0.348225i
$958$		0			0
$959$	−11.7019	+	36.0146i	−0.377873	+	1.16297i
$960$		0			0
$961$	19.4523	+	14.1330i	0.627495	+	0.455902i
$962$		0			0
$963$	38.0515	+	117.111i	1.22619	+	3.77383i
$964$		0			0
$965$	−18.7217	+	13.6021i	−0.602672	+	0.437867i
$966$		0			0
$967$	51.4180			1.65349			0.826746	−	0.562575i	$-0.190189\pi$
$967$	51.4180			1.65349			0.826746	+	0.562575i	$0.190189\pi$
$968$		0			0
$969$	−82.5510			−2.65192
$970$		0			0
$971$	−5.21157	+	3.78643i	−0.167247	+	0.121512i	−0.668260	−	0.743927i	$-0.732961\pi$
$971$	−5.21157	+	3.78643i	−0.167247	+	0.121512i	0.501013	+	0.865440i	$0.332961\pi$
$972$		0			0
$973$	5.73076	+	17.6375i	0.183720	+	0.565432i
$974$		0			0
$975$	−20.5115	−	14.9025i	−0.656894	−	0.477261i
$976$		0			0
$977$	6.09562	−	18.7604i	0.195016	−	0.600198i	−0.804960	−	0.593329i	$-0.797813\pi$
$977$	6.09562	−	18.7604i	0.195016	−	0.600198i	0.999976	−	0.00686916i	$-0.00218654\pi$
$978$		0			0
$979$	−8.83776	−	3.17838i	−0.282456	−	0.101581i
$980$		0			0
$981$	4.86595	−	14.9759i	0.155358	−	0.478142i
$982$		0			0
$983$	−39.8287	−	28.9373i	−1.27034	−	0.922955i	−0.271123	−	0.962545i	$-0.587395\pi$
$983$	−39.8287	−	28.9373i	−1.27034	−	0.922955i	−0.999216	+	0.0395892i	$0.987395\pi$
$984$		0			0
$985$	14.6080	+	44.9589i	0.465451	+	1.43251i
$986$		0			0
$987$	2.00454	−	1.45638i	0.0638051	−	0.0463571i
$988$		0			0
$989$	−41.4237			−1.31720
$990$		0			0
$991$	−53.4779			−1.69878			−0.849391	−	0.527763i	$-0.823031\pi$
$991$	−53.4779			−1.69878			−0.849391	+	0.527763i	$0.823031\pi$
$992$		0			0
$993$	−7.09963	+	5.15818i	−0.225300	+	0.163690i
$994$		0			0
$995$	2.95043	+	9.08050i	0.0935351	+	0.287871i
$996$		0			0
$997$	11.6278	+	8.44810i	0.368257	+	0.267554i	0.756488	−	0.654008i	$-0.226914\pi$
$997$	11.6278	+	8.44810i	0.368257	+	0.267554i	−0.388231	+	0.921562i	$0.626914\pi$
$998$		0			0
$999$	9.40562	−	28.9475i	0.297581	−	0.915860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.53.7	✓	28
11.4	even	5		6292.2.a.z.1.2		14
11.5	even	5	inner	572.2.n.b.313.7	yes	28
11.7	odd	10		6292.2.a.y.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.53.7	✓	28	1.1	even	1	trivial
572.2.n.b.313.7	yes	28	11.5	even	5	inner
6292.2.a.y.1.2		14	11.7	odd	10
6292.2.a.z.1.2		14	11.4	even	5

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.49464 - 1.81246i) q^{3} +(-1.12366 - 3.45827i) q^{5} +(1.36148 + 0.989171i) q^{7} +(2.01117 - 6.18974i) q^{9} +O(q^{10})\)	\(q+(2.49464 - 1.81246i) q^{3} +(-1.12366 - 3.45827i) q^{5} +(1.36148 + 0.989171i) q^{7} +(2.01117 - 6.18974i) q^{9} +(-3.12093 - 1.12240i) q^{11} +(-0.309017 + 0.951057i) q^{13} +(-9.07111 - 6.59055i) q^{15} +(1.71117 + 5.26645i) q^{17} +(-3.91126 + 2.84170i) q^{19} +5.18924 q^{21} +7.77054 q^{23} +(-6.65192 + 4.83290i) q^{25} +(-3.34292 - 10.2885i) q^{27} +(2.51811 + 1.82951i) q^{29} +(0.814984 - 2.50826i) q^{31} +(-9.81992 + 2.85659i) q^{33} +(1.89098 - 5.81984i) q^{35} +(2.27624 + 1.65379i) q^{37} +(0.952869 + 2.93263i) q^{39} +(7.59753 - 5.51993i) q^{41} -5.33087 q^{43} -23.6656 q^{45} +(0.386287 - 0.280654i) q^{47} +(-1.28796 - 3.96393i) q^{49} +(13.8140 + 10.0365i) q^{51} +(1.90247 - 5.85519i) q^{53} +(-0.374700 + 12.0542i) q^{55} +(-4.60673 + 14.1781i) q^{57} +(8.62751 + 6.26825i) q^{59} +(2.18378 + 6.72099i) q^{61} +(8.86087 - 6.43780i) q^{63} +3.63624 q^{65} -4.78992 q^{67} +(19.3847 - 14.0838i) q^{69} +(-0.714076 - 2.19770i) q^{71} +(-9.82103 - 7.13540i) q^{73} +(-7.83470 + 24.1127i) q^{75} +(-3.13883 - 4.61526i) q^{77} +(0.715420 - 2.20183i) q^{79} +(-11.1910 - 8.13072i) q^{81} +(-2.94498 - 9.06372i) q^{83} +(16.2900 - 11.8354i) q^{85} +9.59771 q^{87} +2.83177 q^{89} +(-1.36148 + 0.989171i) q^{91} +(-2.51304 - 7.73435i) q^{93} +(14.2223 + 10.3331i) q^{95} +(-2.79511 + 8.60248i) q^{97} +(-13.2241 + 17.0604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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