LMFDB - Embedded newform 572.2.bg.a.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

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

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

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, degree $8$, 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:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	572.81
Dual form			572.2.bg.a.113.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50220 + 0.531859i) q^{3} +(-0.767747 + 0.557801i) q^{5} +(3.31034 + 0.703635i) q^{7} +(3.23748 - 1.44142i) q^{9} +O(q^{10})$	\(q+(-2.50220 + 0.531859i) q^{3} +(-0.767747 + 0.557801i) q^{5} +(3.31034 + 0.703635i) q^{7} +(3.23748 - 1.44142i) q^{9} +(-0.475835 - 3.28231i) q^{11} +(-1.84521 + 3.09761i) q^{13} +(1.62438 - 1.80406i) q^{15} +(-0.0804194 - 0.765140i) q^{17} +(3.36456 + 3.73672i) q^{19} -8.65736 q^{21} +(-0.332587 - 0.576058i) q^{23} +(-1.26679 + 3.89878i) q^{25} +(-1.12556 + 0.817764i) q^{27} +(-5.91963 + 6.57441i) q^{29} +(-0.203031 - 0.147511i) q^{31} +(2.93636 + 7.95992i) q^{33} +(-2.93399 + 1.30630i) q^{35} +(-6.52508 + 7.24683i) q^{37} +(2.96960 - 8.73223i) q^{39} +(-0.948769 + 0.201667i) q^{41} +(-6.14356 + 10.6410i) q^{43} +(-1.68154 + 2.91252i) q^{45} +(-1.07529 + 3.30941i) q^{47} +(4.06844 + 1.81139i) q^{49} +(0.608171 + 1.87176i) q^{51} +(4.23439 + 3.07646i) q^{53} +(2.19620 + 2.25456i) q^{55} +(-10.4062 - 7.56055i) q^{57} +(9.20729 + 1.95707i) q^{59} +(-0.532499 - 5.06639i) q^{61} +(11.7314 - 2.49359i) q^{63} +(-0.311193 - 3.40744i) q^{65} +(-1.06740 - 1.84879i) q^{67} +(1.13858 + 1.26452i) q^{69} +(-1.51632 - 14.4269i) q^{71} +(0.210989 + 0.649357i) q^{73} +(1.09616 - 10.4293i) q^{75} +(0.734374 - 11.2004i) q^{77} +(-2.89285 - 2.10178i) q^{79} +(-4.73250 + 5.25597i) q^{81} +(6.94061 - 5.04265i) q^{83} +(0.488537 + 0.542575i) q^{85} +(11.3154 - 19.5989i) q^{87} +(7.82210 + 13.5483i) q^{89} +(-8.28787 + 8.95579i) q^{91} +(0.586479 + 0.261117i) q^{93} +(-4.66748 - 0.992103i) q^{95} +(4.25937 - 1.89639i) q^{97} +(-6.27170 - 9.94056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.50220	+	0.531859i	−1.44464	+	0.307069i	−0.862517	−	0.506029i	$-0.831113\pi$
$3$	−2.50220	+	0.531859i	−1.44464	+	0.307069i	−0.582128	+	0.813097i	$0.697780\pi$
$4$		0			0
$5$	−0.767747	+	0.557801i	−0.343347	+	0.249456i	−0.746073	−	0.665865i	$-0.768063\pi$
$5$	−0.767747	+	0.557801i	−0.343347	+	0.249456i	0.402726	+	0.915321i	$0.368063\pi$
$6$		0			0
$7$	3.31034	+	0.703635i	1.25119	+	0.265949i	0.785424	−	0.618958i	$-0.212445\pi$
$7$	3.31034	+	0.703635i	1.25119	+	0.265949i	0.465768	+	0.884907i	$0.345778\pi$
$8$		0			0
$9$	3.23748	−	1.44142i	1.07916	−	0.480473i
$10$		0			0
$11$	−0.475835	−	3.28231i	−0.143470	−	0.989655i
$11$	−0.475835	−	3.28231i	−0.143470	−	0.989655i
$12$		0			0
$13$	−1.84521	+	3.09761i	−0.511770	+	0.859122i
$13$	−1.84521	+	3.09761i	−0.511770	+	0.859122i
$14$		0			0
$15$	1.62438	−	1.80406i	0.419414	−	0.465806i
$16$		0			0
$17$	−0.0804194	−	0.765140i	−0.0195046	−	0.185574i	0.980432	−	0.196859i	$-0.0630742\pi$
$17$	−0.0804194	−	0.765140i	−0.0195046	−	0.185574i	−0.999936	+	0.0112857i	$0.996408\pi$
$18$		0			0
$19$	3.36456	+	3.73672i	0.771883	+	0.857263i	0.993016	−	0.117980i	$-0.0376420\pi$
$19$	3.36456	+	3.73672i	0.771883	+	0.857263i	−0.221132	+	0.975244i	$0.570975\pi$
$20$		0			0
$21$	−8.65736			−1.88919
$22$		0			0
$23$	−0.332587	−	0.576058i	−0.0693493	−	0.120116i	0.829266	−	0.558854i	$-0.188759\pi$
$23$	−0.332587	−	0.576058i	−0.0693493	−	0.120116i	−0.898615	+	0.438738i	$0.855426\pi$
$24$		0			0
$25$	−1.26679	+	3.89878i	−0.253358	+	0.779757i
$26$		0			0
$27$	−1.12556	+	0.817764i	−0.216613	+	0.157379i
$28$		0			0
$29$	−5.91963	+	6.57441i	−1.09925	+	1.22084i	−0.125769	+	0.992060i	$0.540140\pi$
$29$	−5.91963	+	6.57441i	−1.09925	+	1.22084i	−0.973479	+	0.228778i	$0.926527\pi$
$30$		0			0
$31$	−0.203031	−	0.147511i	−0.0364655	−	0.0264937i	0.569403	−	0.822058i	$-0.307174\pi$
$31$	−0.203031	−	0.147511i	−0.0364655	−	0.0264937i	−0.605869	+	0.795565i	$0.707174\pi$
$32$		0			0
$33$	2.93636	+	7.95992i	0.511154	+	1.38564i
$34$		0			0
$35$	−2.93399	+	1.30630i	−0.495935	+	0.220805i
$36$		0			0
$37$	−6.52508	+	7.24683i	−1.07272	+	1.19137i	−0.0920354	+	0.995756i	$0.529337\pi$
$37$	−6.52508	+	7.24683i	−1.07272	+	1.19137i	−0.980681	+	0.195616i	$0.937329\pi$
$38$		0			0
$39$	2.96960	−	8.73223i	0.475516	−	1.39828i
$40$		0			0
$41$	−0.948769	+	0.201667i	−0.148173	+	0.0314951i	−0.281401	−	0.959590i	$-0.590799\pi$
$41$	−0.948769	+	0.201667i	−0.148173	+	0.0314951i	0.133228	+	0.991085i	$0.457466\pi$
$42$		0			0
$43$	−6.14356	+	10.6410i	−0.936883	+	1.62273i	−0.165643	+	0.986186i	$0.552970\pi$
$43$	−6.14356	+	10.6410i	−0.936883	+	1.62273i	−0.771240	+	0.636544i	$0.780363\pi$
$44$		0			0
$45$	−1.68154	+	2.91252i	−0.250669	+	0.434172i
$46$		0			0
$47$	−1.07529	+	3.30941i	−0.156847	+	0.482727i	−0.998343	−	0.0575368i	$-0.981675\pi$
$47$	−1.07529	+	3.30941i	−0.156847	+	0.482727i	0.841496	+	0.540263i	$0.181675\pi$
$48$		0			0
$49$	4.06844	+	1.81139i	0.581206	+	0.258770i
$50$		0			0
$51$	0.608171	+	1.87176i	0.0851610	+	0.262099i
$52$		0			0
$53$	4.23439	+	3.07646i	0.581638	+	0.422585i	0.839314	−	0.543647i	$-0.182957\pi$
$53$	4.23439	+	3.07646i	0.581638	+	0.422585i	−0.257676	+	0.966231i	$0.582957\pi$
$54$		0			0
$55$	2.19620	+	2.25456i	0.296135	+	0.304005i
$56$		0			0
$57$	−10.4062	−	7.56055i	−1.37834	−	1.00142i
$58$		0			0
$59$	9.20729	+	1.95707i	1.19869	+	0.254789i	0.763654	−	0.645625i	$-0.223403\pi$
$59$	9.20729	+	1.95707i	1.19869	+	0.254789i	0.435033	+	0.900414i	$0.356737\pi$
$60$		0			0
$61$	−0.532499	−	5.06639i	−0.0681796	−	0.648685i	−0.974236	−	0.225529i	$-0.927589\pi$
$61$	−0.532499	−	5.06639i	−0.0681796	−	0.648685i	0.906057	−	0.423156i	$-0.139078\pi$
$62$		0			0
$63$	11.7314	−	2.49359i	1.47802	−	0.314163i
$64$		0			0
$65$	−0.311193	−	3.40744i	−0.0385987	−	0.422641i
$66$		0			0
$67$	−1.06740	−	1.84879i	−0.130404	−	0.225866i	0.793429	−	0.608663i	$-0.208294\pi$
$67$	−1.06740	−	1.84879i	−0.130404	−	0.225866i	−0.923832	+	0.382798i	$0.874961\pi$
$68$		0			0
$69$	1.13858	+	1.26452i	0.137069	+	0.152231i
$70$		0			0
$71$	−1.51632	−	14.4269i	−0.179955	−	1.71215i	−0.596145	−	0.802876i	$-0.703302\pi$
$71$	−1.51632	−	14.4269i	−0.179955	−	1.71215i	0.416191	−	0.909277i	$-0.363365\pi$
$72$		0			0
$73$	0.210989	+	0.649357i	0.0246944	+	0.0760015i	0.962644	−	0.270769i	$-0.0872781\pi$
$73$	0.210989	+	0.649357i	0.0246944	+	0.0760015i	−0.937950	+	0.346771i	$0.887278\pi$
$74$		0			0
$75$	1.09616	−	10.4293i	0.126574	−	1.20427i
$76$		0			0
$77$	0.734374	−	11.2004i	0.0836897	−	1.27640i
$78$		0			0
$79$	−2.89285	−	2.10178i	−0.325471	−	0.236469i	0.413035	−	0.910715i	$-0.364469\pi$
$79$	−2.89285	−	2.10178i	−0.325471	−	0.236469i	−0.738507	+	0.674246i	$0.764469\pi$
$80$		0			0
$81$	−4.73250	+	5.25597i	−0.525833	+	0.583997i
$82$		0			0
$83$	6.94061	−	5.04265i	0.761830	−	0.553502i	−0.137641	−	0.990482i	$-0.543952\pi$
$83$	6.94061	−	5.04265i	0.761830	−	0.553502i	0.899471	+	0.436980i	$0.143952\pi$
$84$		0			0
$85$	0.488537	+	0.542575i	0.0529893	+	0.0588506i
$86$		0			0
$87$	11.3154	−	19.5989i	1.21314	−	2.10122i
$88$		0			0
$89$	7.82210	+	13.5483i	0.829141	+	1.43611i	0.898713	+	0.438537i	$0.144503\pi$
$89$	7.82210	+	13.5483i	0.829141	+	1.43611i	−0.0695724	+	0.997577i	$0.522163\pi$
$90$		0			0
$91$	−8.28787	+	8.95579i	−0.868805	+	0.938822i
$92$		0			0
$93$	0.586479	+	0.261117i	0.0608151	+	0.0270766i
$94$		0			0
$95$	−4.66748	−	0.992103i	−0.478873	−	0.101788i
$96$		0			0
$97$	4.25937	−	1.89639i	0.432473	−	0.192550i	−0.178942	−	0.983860i	$-0.557267\pi$
$97$	4.25937	−	1.89639i	0.432473	−	0.192550i	0.611415	+	0.791310i	$0.290601\pi$
$98$		0			0
$99$	−6.27170	−	9.94056i	−0.630330	−	0.999064i
$100$		0			0
$101$	0.480297	−	4.56972i	0.0477913	−	0.454704i	−0.944291	−	0.329113i	$-0.893250\pi$
$101$	0.480297	−	4.56972i	0.0477913	−	0.454704i	0.992082	−	0.125592i	$-0.0400829\pi$
$102$		0			0
$103$	1.62077	+	4.98821i	0.159699	+	0.491503i	0.998607	−	0.0527706i	$-0.0168052\pi$
$103$	1.62077	+	4.98821i	0.159699	+	0.491503i	−0.838908	+	0.544274i	$0.816805\pi$
$104$		0			0
$105$	6.64666	−	4.82908i	0.648648	−	0.471270i
$106$		0			0
$107$	−10.5883	+	2.25062i	−1.02361	+	0.217576i	−0.688986	−	0.724775i	$-0.741944\pi$
$107$	−10.5883	+	2.25062i	−1.02361	+	0.217576i	−0.334628	+	0.942350i	$0.608611\pi$
$108$		0			0
$109$	−9.03708			−0.865595			−0.432798	−	0.901491i	$-0.642474\pi$
$109$	−9.03708			−0.865595			−0.432798	+	0.901491i	$0.642474\pi$
$110$		0			0
$111$	12.4727	−	21.6034i	1.18386	−	2.05051i
$112$		0			0
$113$	10.2389	+	11.3714i	0.963194	+	1.06973i	0.997524	+	0.0703244i	$0.0224034\pi$
$113$	10.2389	+	11.3714i	0.963194	+	1.06973i	−0.0343305	+	0.999411i	$0.510930\pi$
$114$		0			0
$115$	0.576669	+	0.256749i	0.0537746	+	0.0239420i
$116$		0			0
$117$	−1.50889	+	12.6882i	−0.139497	+	1.17302i
$118$		0			0
$119$	0.272163	−	2.58946i	0.0249492	−	0.237375i
$120$		0			0
$121$	−10.5472	+	3.12368i	−0.958833	+	0.283971i
$122$		0			0
$123$	2.26675	−	1.00922i	0.204386	−	0.0909985i
$124$		0			0
$125$	−2.66843	−	8.21260i	−0.238672	−	0.734557i
$126$		0			0
$127$	18.9053	+	8.41718i	1.67757	+	0.746904i	0.999934	+	0.0115111i	$0.00366419\pi$
$127$	18.9053	+	8.41718i	1.67757	+	0.746904i	0.677641	+	0.735393i	$0.263002\pi$
$128$		0			0
$129$	9.71291	−	29.8933i	0.855174	−	2.63195i
$130$		0			0
$131$	2.91428			0.254622			0.127311	−	0.991863i	$-0.459365\pi$
$131$	2.91428			0.254622			0.127311	+	0.991863i	$0.459365\pi$
$132$		0			0
$133$	8.50856	+	14.7373i	0.737786	+	1.27788i
$134$		0			0
$135$	0.407993	−	1.25567i	0.0351144	−	0.108071i
$136$		0			0
$137$	−1.14066	−	10.8526i	−0.0974527	−	0.927201i	−0.928583	−	0.371124i	$-0.878973\pi$
$137$	−1.14066	−	10.8526i	−0.0974527	−	0.927201i	0.831131	−	0.556077i	$-0.187694\pi$
$138$		0			0
$139$	−6.70540	−	1.42528i	−0.568745	−	0.120890i	−0.0854410	−	0.996343i	$-0.527230\pi$
$139$	−6.70540	−	1.42528i	−0.568745	−	0.120890i	−0.483304	+	0.875453i	$0.660563\pi$
$140$		0			0
$141$	0.930455	−	8.85269i	0.0783585	−	0.745531i
$142$		0			0
$143$	11.0453	+	4.58262i	0.923658	+	0.383218i
$144$		0			0
$145$	0.877563	−	8.34946i	0.0728777	−	0.693385i
$146$		0			0
$147$	−11.1434	−	2.36861i	−0.919096	−	0.195360i
$148$		0			0
$149$	1.37371	+	13.0700i	0.112539	+	1.07074i	0.894395	+	0.447277i	$0.147606\pi$
$149$	1.37371	+	13.0700i	0.112539	+	1.07074i	−0.781857	+	0.623458i	$0.785727\pi$
$150$		0			0
$151$	2.39568	−	7.37315i	0.194958	−	0.600018i	−0.805019	−	0.593249i	$-0.797845\pi$
$151$	2.39568	−	7.37315i	0.194958	−	0.600018i	0.999977	−	0.00676966i	$-0.00215487\pi$
$152$		0			0
$153$	−1.36324	−	2.36121i	−0.110212	−	0.190892i
$154$		0			0
$155$	0.238158			0.0191293
$156$		0			0
$157$	−3.62175	+	11.1466i	−0.289047	+	0.889595i	0.696109	+	0.717936i	$0.254913\pi$
$157$	−3.62175	+	11.1466i	−0.289047	+	0.889595i	−0.985156	+	0.171659i	$0.945087\pi$
$158$		0			0
$159$	−12.2315	−	5.44582i	−0.970022	−	0.431882i
$160$		0			0
$161$	−0.695643	−	2.14097i	−0.0548244	−	0.168732i
$162$		0			0
$163$	3.08407	−	1.37312i	0.241563	−	0.107551i	−0.282385	−	0.959301i	$-0.591125\pi$
$163$	3.08407	−	1.37312i	0.241563	−	0.107551i	0.523948	+	0.851750i	$0.324459\pi$
$164$		0			0
$165$	−6.69443	−	4.47330i	−0.521161	−	0.348246i
$166$		0			0
$167$	−2.40793	+	22.9099i	−0.186331	+	1.77282i	0.357776	+	0.933807i	$0.383535\pi$
$167$	−2.40793	+	22.9099i	−0.186331	+	1.77282i	−0.544107	+	0.839016i	$0.683132\pi$
$168$		0			0
$169$	−6.19038	−	11.4315i	−0.476183	−	0.879346i
$170$		0			0
$171$	16.2789	+	7.24783i	1.24488	+	0.554256i
$172$		0			0
$173$	−4.22388	−	4.69109i	−0.321136	−	0.356657i	0.560864	−	0.827908i	$-0.310469\pi$
$173$	−4.22388	−	4.69109i	−0.321136	−	0.356657i	−0.881999	+	0.471251i	$0.843803\pi$
$174$		0			0
$175$	−6.93683	+	12.0149i	−0.524375	+	0.908245i
$176$		0			0
$177$	−24.0794			−1.80992
$178$		0			0
$179$	−11.3729	+	2.41739i	−0.850054	+	0.180684i	−0.612285	−	0.790637i	$-0.709749\pi$
$179$	−11.3729	+	2.41739i	−0.850054	+	0.180684i	−0.237769	+	0.971322i	$0.576416\pi$
$180$		0			0
$181$	19.6883	−	14.3044i	1.46342	−	1.06324i	0.480963	−	0.876741i	$-0.340287\pi$
$181$	19.6883	−	14.3044i	1.46342	−	1.06324i	0.982456	−	0.186495i	$-0.0597128\pi$
$182$		0			0
$183$	4.02702	+	12.3939i	0.297686	+	0.916184i
$184$		0			0
$185$	0.967319	−	9.20342i	0.0711187	−	0.676649i
$186$		0			0
$187$	−2.47316	+	0.628042i	−0.180855	+	0.0459270i
$188$		0			0
$189$	−4.30138	+	1.91510i	−0.312880	+	0.139303i
$190$		0			0
$191$	−15.3311	−	3.25872i	−1.10932	−	0.235793i	−0.383406	−	0.923580i	$-0.625249\pi$
$191$	−15.3311	−	3.25872i	−1.10932	−	0.235793i	−0.725912	+	0.687787i	$0.758582\pi$
$192$		0			0
$193$	21.8620	+	9.73360i	1.57366	+	0.700640i	0.993497	−	0.113858i	$-0.0363209\pi$
$193$	21.8620	+	9.73360i	1.57366	+	0.700640i	0.580166	+	0.814498i	$0.302988\pi$
$194$		0			0
$195$	2.59094	+	8.36058i	0.185541	+	0.598714i
$196$		0			0
$197$	−8.08369	−	14.0014i	−0.575939	−	0.997556i	−0.995939	−	0.0900319i	$-0.971303\pi$
$197$	−8.08369	−	14.0014i	−0.575939	−	0.997556i	0.420000	−	0.907524i	$-0.362030\pi$
$198$		0			0
$199$	−2.95904	+	5.12520i	−0.209761	+	0.363316i	−0.951639	−	0.307218i	$-0.900602\pi$
$199$	−2.95904	+	5.12520i	−0.209761	+	0.363316i	0.741878	+	0.670534i	$0.233935\pi$
$200$		0			0
$201$	3.65414	+	4.05833i	0.257743	+	0.286253i
$202$		0			0
$203$	−24.2220	+	17.5983i	−1.70005	+	1.23516i
$204$		0			0
$205$	0.615924	−	0.684053i	0.0430180	−	0.0477764i
$206$		0			0
$207$	−1.90709	−	1.38558i	−0.132552	−	0.0963045i
$208$		0			0
$209$	10.6641	−	12.8216i	0.737653	−	0.886889i
$210$		0			0
$211$	1.14570	−	10.9007i	0.0788736	−	0.750432i	−0.881588	−	0.472020i	$-0.843525\pi$
$211$	1.14570	−	10.9007i	0.0788736	−	0.750432i	0.960462	−	0.278412i	$-0.0898082\pi$
$212$		0			0
$213$	11.4672	+	35.2924i	0.785719	+	2.41820i
$214$		0			0
$215$	−1.21883	−	11.5964i	−0.0831238	−	0.790870i
$216$		0			0
$217$	−0.568309	−	0.631171i	−0.0385793	−	0.0428467i
$218$		0			0
$219$	−0.873302	−	1.51260i	−0.0590123	−	0.102212i
$220$		0			0
$221$	2.51850	+	1.16274i	0.169412	+	0.0782142i
$222$		0			0
$223$	12.4981	−	2.65655i	0.836934	−	0.177896i	0.230543	−	0.973062i	$-0.425950\pi$
$223$	12.4981	−	2.65655i	0.836934	−	0.177896i	0.606391	+	0.795166i	$0.292616\pi$
$224$		0			0
$225$	1.51857	+	14.4482i	0.101238	+	0.963215i
$226$		0			0
$227$	14.9734	+	3.18270i	0.993822	+	0.211243i	0.675996	−	0.736906i	$-0.263714\pi$
$227$	14.9734	+	3.18270i	0.993822	+	0.211243i	0.317826	+	0.948149i	$0.397047\pi$
$228$		0			0
$229$	−11.9927	−	8.71321i	−0.792500	−	0.575785i	0.116204	−	0.993225i	$-0.462927\pi$
$229$	−11.9927	−	8.71321i	−0.792500	−	0.575785i	−0.908704	+	0.417440i	$0.862927\pi$
$230$		0			0
$231$	4.11947	+	28.4162i	0.271042	+	1.86965i
$232$		0			0
$233$	3.56634	+	2.59110i	0.233639	+	0.169748i	0.698445	−	0.715664i	$-0.253876\pi$
$233$	3.56634	+	2.59110i	0.233639	+	0.169748i	−0.464806	+	0.885413i	$0.653876\pi$
$234$		0			0
$235$	−1.02044	−	3.14058i	−0.0665660	−	0.204869i
$236$		0			0
$237$	8.35634	+	3.72048i	0.542802	+	0.241671i
$238$		0			0
$239$	−2.64346	+	8.13573i	−0.170991	+	0.526256i	−0.999428	−	0.0338263i	$-0.989231\pi$
$239$	−2.64346	+	8.13573i	−0.170991	+	0.526256i	0.828437	+	0.560083i	$0.189231\pi$
$240$		0			0
$241$	−4.96340	+	8.59686i	−0.319721	+	0.553772i	−0.980430	−	0.196870i	$-0.936922\pi$
$241$	−4.96340	+	8.59686i	−0.319721	+	0.553772i	0.660709	+	0.750642i	$0.270256\pi$
$242$		0			0
$243$	11.1331	−	19.2831i	0.714189	−	1.23701i
$244$		0			0
$245$	−4.13393	+	0.878693i	−0.264107	+	0.0561376i
$246$		0			0
$247$	−17.7832	+	3.52705i	−1.13152	+	0.224421i
$248$		0			0
$249$	−14.6848	+	16.3091i	−0.930611	+	1.03355i
$250$		0			0
$251$	5.43097	−	2.41802i	0.342800	−	0.152624i	−0.228114	−	0.973634i	$-0.573256\pi$
$251$	5.43097	−	2.41802i	0.342800	−	0.152624i	0.570913	+	0.821010i	$0.306589\pi$
$252$		0			0
$253$	−1.73255	+	1.36576i	−0.108924	+	0.0858649i
$254$		0			0
$255$	−1.51099	−	1.09780i	−0.0946219	−	0.0687468i
$256$		0			0
$257$	7.76630	−	8.62535i	0.484449	−	0.538035i	−0.450519	−	0.892767i	$-0.648761\pi$
$257$	7.76630	−	8.62535i	0.484449	−	0.538035i	0.934968	+	0.354732i	$0.115428\pi$
$258$		0			0
$259$	−26.6994	+	19.3982i	−1.65902	+	1.20535i
$260$		0			0
$261$	−9.68820	+	29.8172i	−0.599685	+	1.84564i
$262$		0			0
$263$	−8.98073	−	15.5551i	−0.553776	−	0.959168i	−0.997998	−	0.0632509i	$-0.979853\pi$
$263$	−8.98073	−	15.5551i	−0.553776	−	0.959168i	0.444222	−	0.895917i	$-0.353480\pi$
$264$		0			0
$265$	−4.96699			−0.305120
$266$		0			0
$267$	−26.7782	−	29.7402i	−1.63880	−	1.82007i
$268$		0			0
$269$	−2.32165	−	22.0890i	−0.141553	−	1.34679i	−0.802633	−	0.596473i	$-0.796568\pi$
$269$	−2.32165	−	22.0890i	−0.141553	−	1.34679i	0.661080	−	0.750316i	$-0.270099\pi$
$270$		0			0
$271$	−0.693147	+	0.769818i	−0.0421057	+	0.0467631i	−0.763830	−	0.645418i	$-0.776683\pi$
$271$	−0.693147	+	0.769818i	−0.0421057	+	0.0467631i	0.721724	+	0.692181i	$0.243350\pi$
$272$		0			0
$273$	15.9747	−	26.8171i	0.966832	−	1.62305i
$274$		0			0
$275$	13.3998	+	2.30283i	0.808039	+	0.138866i
$276$		0			0
$277$	22.3627	−	9.95653i	1.34365	−	0.598230i	0.396205	−	0.918162i	$-0.370327\pi$
$277$	22.3627	−	9.95653i	1.34365	−	0.598230i	0.947440	+	0.319932i	$0.103660\pi$
$278$		0			0
$279$	−0.869936	−	0.184911i	−0.0520817	−	0.0110703i
$280$		0			0
$281$	−4.72823	+	3.43526i	−0.282062	+	0.204930i	−0.719817	−	0.694164i	$-0.755774\pi$
$281$	−4.72823	+	3.43526i	−0.282062	+	0.204930i	0.437754	+	0.899095i	$0.355774\pi$
$282$		0			0
$283$	18.1192	−	3.85135i	1.07707	−	0.228939i	0.364973	−	0.931018i	$-0.381078\pi$
$283$	18.1192	−	3.85135i	1.07707	−	0.228939i	0.712099	+	0.702079i	$0.247745\pi$
$284$		0			0
$285$	12.2066			0.723057
$286$		0			0
$287$	−3.28265			−0.193769
$288$		0			0
$289$	16.0495	−	3.41143i	0.944090	−	0.200673i
$290$		0			0
$291$	−9.64917	+	7.01053i	−0.565644	+	0.410965i
$292$		0			0
$293$	9.01857	+	1.91696i	0.526871	+	0.111990i	0.463665	−	0.886011i	$-0.346534\pi$
$293$	9.01857	+	1.91696i	0.526871	+	0.111990i	0.0632058	+	0.998001i	$0.479868\pi$
$294$		0			0
$295$	−8.16053	+	3.63330i	−0.475124	+	0.211539i
$296$		0			0
$297$	3.21974	+	3.30531i	0.186828	+	0.191793i
$298$		0			0
$299$	2.39810	+	0.0327242i	0.138686	+	0.00189249i
$300$		0			0
$301$	−27.8246	+	30.9024i	−1.60378	+	1.78118i
$302$		0			0
$303$	1.22865	+	11.6898i	0.0705839	+	0.671561i
$304$		0			0
$305$	3.23486	+	3.59268i	0.185228	+	0.205716i
$306$		0			0
$307$	13.0822			0.746639			0.373319	−	0.927703i	$-0.378220\pi$
$307$	13.0822			0.746639			0.373319	+	0.927703i	$0.378220\pi$
$308$		0			0
$309$	−6.70851	−	11.6195i	−0.381634	−	0.661009i
$310$		0			0
$311$	1.56021	−	4.80184i	0.0884715	−	0.272287i	−0.897026	−	0.441978i	$-0.854277\pi$
$311$	1.56021	−	4.80184i	0.0884715	−	0.272287i	0.985497	+	0.169691i	$0.0542769\pi$
$312$		0			0
$313$	−17.7026	+	12.8617i	−1.00061	+	0.726984i	−0.962218	−	0.272279i	$-0.912223\pi$
$313$	−17.7026	+	12.8617i	−1.00061	+	0.726984i	−0.0383895	+	0.999263i	$0.512223\pi$
$314$		0			0
$315$	−7.61583	+	8.45823i	−0.429103	+	0.476567i
$316$		0			0
$317$	−5.12230	−	3.72157i	−0.287697	−	0.209024i	0.434571	−	0.900638i	$-0.356900\pi$
$317$	−5.12230	−	3.72157i	−0.287697	−	0.209024i	−0.722268	+	0.691614i	$0.756900\pi$
$318$		0			0
$319$	24.3960	+	16.3017i	1.36592	+	0.912722i
$320$		0			0
$321$	25.2971	−	11.2630i	1.41195	−	0.628639i
$322$		0			0
$323$	2.58854	−	2.87486i	0.144030	−	0.159962i
$324$		0			0
$325$	−9.73941	−	11.1181i	−0.540245	−	0.616722i
$326$		0			0
$327$	22.6126	−	4.80645i	1.25048	−	0.265797i
$328$		0			0
$329$	−5.88820	+	10.1987i	−0.324627	+	0.562270i
$330$		0			0
$331$	6.63503	−	11.4922i	0.364694	−	0.631669i	−0.624033	−	0.781398i	$-0.714507\pi$
$331$	6.63503	−	11.4922i	0.364694	−	0.631669i	0.988727	+	0.149729i	$0.0478401\pi$
$332$		0			0
$333$	−10.6791	+	32.8669i	−0.585211	+	1.80109i
$334$		0			0
$335$	1.85075	+	0.824007i	0.101117	+	0.0450203i
$336$		0			0
$337$	7.66115	+	23.5786i	0.417329	+	1.28441i	0.910151	+	0.414277i	$0.135966\pi$
$337$	7.66115	+	23.5786i	0.417329	+	1.28441i	−0.492821	+	0.870131i	$0.664034\pi$
$338$		0			0
$339$	−31.6677	−	23.0079i	−1.71995	−	1.24962i
$340$		0			0
$341$	−0.387568	+	0.736603i	−0.0209880	+	0.0398893i
$342$		0			0
$343$	−6.97230	−	5.06567i	−0.376469	−	0.273521i
$344$		0			0
$345$	−1.57949	−	0.335732i	−0.0850370	−	0.0180752i
$346$		0			0
$347$	−1.15279	−	10.9681i	−0.0618852	−	0.588799i	−0.980891	−	0.194556i	$-0.937674\pi$
$347$	−1.15279	−	10.9681i	−0.0618852	−	0.588799i	0.919006	−	0.394243i	$-0.128993\pi$
$348$		0			0
$349$	8.37079	−	1.77927i	0.448078	−	0.0952420i	0.0216545	−	0.999766i	$-0.493107\pi$
$349$	8.37079	−	1.77927i	0.448078	−	0.0952420i	0.426424	+	0.904524i	$0.359773\pi$
$350$		0			0
$351$	−0.456224	−	4.99548i	−0.0243515	−	0.266639i
$352$		0			0
$353$	−9.93709	−	17.2115i	−0.528898	−	0.916078i	−0.999432	−	0.0336965i	$-0.989272\pi$
$353$	−9.93709	−	17.2115i	−0.528898	−	0.916078i	0.470534	−	0.882382i	$-0.344061\pi$
$354$		0			0
$355$	9.21147	+	10.2304i	0.488894	+	0.542972i
$356$		0			0
$357$	0.696220	+	6.62409i	0.0368479	+	0.350584i
$358$		0			0
$359$	−0.725970	−	2.23431i	−0.0383153	−	0.117922i	0.930069	−	0.367384i	$-0.119746\pi$
$359$	−0.725970	−	2.23431i	−0.0383153	−	0.117922i	−0.968385	+	0.249461i	$0.919746\pi$
$360$		0			0
$361$	−0.656793	+	6.24897i	−0.0345680	+	0.328893i
$362$		0			0
$363$	24.7297	−	13.4257i	1.29797	−	0.704664i
$364$		0			0
$365$	−0.524198	−	0.380852i	−0.0274378	−	0.0199347i
$366$		0			0
$367$	8.50074	−	9.44103i	0.443735	−	0.492818i	−0.479236	−	0.877686i	$-0.659086\pi$
$367$	8.50074	−	9.44103i	0.443735	−	0.492818i	0.922972	+	0.384868i	$0.125753\pi$
$368$		0			0
$369$	−2.78094	+	2.02047i	−0.144770	+	0.105181i
$370$		0			0
$371$	11.8526	+	13.1636i	0.615354	+	0.683420i
$372$		0			0
$373$	−1.22244	+	2.11733i	−0.0632955	+	0.109631i	−0.895937	−	0.444182i	$-0.853494\pi$
$373$	−1.22244	+	2.11733i	−0.0632955	+	0.109631i	0.832641	+	0.553813i	$0.186828\pi$
$374$		0			0
$375$	11.0449	+	19.1303i	0.570356	+	0.987885i
$376$		0			0
$377$	−9.44199	−	30.4679i	−0.486287	−	1.56918i
$378$		0			0
$379$	5.09369	+	2.26786i	0.261645	+	0.116492i	0.533367	−	0.845884i	$-0.320926\pi$
$379$	5.09369	+	2.26786i	0.261645	+	0.116492i	−0.271722	+	0.962376i	$0.587593\pi$
$380$		0			0
$381$	−51.7816	−	11.0065i	−2.65285	−	0.563881i
$382$		0			0
$383$	−28.8347	+	12.8380i	−1.47338	+	0.655992i	−0.977218	−	0.212237i	$-0.931925\pi$
$383$	−28.8347	+	12.8380i	−1.47338	+	0.655992i	−0.496164	+	0.868229i	$0.665259\pi$
$384$		0			0
$385$	5.68377	+	9.00870i	0.289672	+	0.459126i
$386$		0			0
$387$	−4.55157	+	43.3053i	−0.231370	+	2.20133i
$388$		0			0
$389$	−4.13950	−	12.7401i	−0.209881	−	0.645947i	−0.999478	−	0.0323210i	$-0.989710\pi$
$389$	−4.13950	−	12.7401i	−0.209881	−	0.645947i	0.789597	−	0.613626i	$-0.210290\pi$
$390$		0			0
$391$	−0.414018	+	0.300802i	−0.0209378	+	0.0152122i
$392$		0			0
$393$	−7.29212	+	1.54999i	−0.367839	+	0.0781865i
$394$		0			0
$395$	3.39335			0.170738
$396$		0			0
$397$	−18.4235	+	31.9104i	−0.924648	+	1.60154i	−0.132523	+	0.991180i	$0.542308\pi$
$397$	−18.4235	+	31.9104i	−0.924648	+	1.60154i	−0.792126	+	0.610358i	$0.791026\pi$
$398$		0			0
$399$	−29.1282	−	32.3502i	−1.45824	−	1.61953i
$400$		0			0
$401$	−26.5292	−	11.8116i	−1.32480	−	0.589841i	−0.382302	−	0.924038i	$-0.624868\pi$
$401$	−26.5292	−	11.8116i	−1.32480	−	0.589841i	−0.942503	+	0.334196i	$0.891535\pi$
$402$		0			0
$403$	0.831567	−	0.356723i	0.0414233	−	0.0177696i
$404$		0			0
$405$	0.701576	−	6.67505i	0.0348616	−	0.331686i
$406$		0			0
$407$	26.8912	+	17.9691i	1.33295	+	0.890693i
$408$		0			0
$409$	−23.4477	+	10.4396i	−1.15942	+	0.516205i	−0.894061	−	0.447946i	$-0.852156\pi$
$409$	−23.4477	+	10.4396i	−1.15942	+	0.516205i	−0.265355	+	0.964151i	$0.585489\pi$
$410$		0			0
$411$	8.62620	+	26.5487i	0.425499	+	1.30955i
$412$		0			0
$413$	29.1022	+	12.9571i	1.43203	+	0.637579i
$414$		0			0
$415$	−2.51584	+	7.74295i	−0.123498	+	0.380086i
$416$		0			0
$417$	17.5363			0.858755
$418$		0			0
$419$	2.45401	+	4.25048i	0.119886	+	0.207649i	0.919723	−	0.392569i	$-0.128414\pi$
$419$	2.45401	+	4.25048i	0.119886	+	0.207649i	−0.799836	+	0.600219i	$0.795080\pi$
$420$		0			0
$421$	−2.54185	+	7.82300i	−0.123882	+	0.381270i	−0.993696	−	0.112111i	$-0.964239\pi$
$421$	−2.54185	+	7.82300i	−0.123882	+	0.381270i	0.869814	+	0.493380i	$0.164239\pi$
$422$		0			0
$423$	1.28901	+	12.2641i	0.0626737	+	0.596301i
$424$		0			0
$425$	3.08499	+	0.655734i	0.149644	+	0.0318078i
$426$		0			0
$427$	1.80214	−	17.1462i	0.0872115	−	0.829762i
$428$		0			0
$429$	−30.0749	−	5.59205i	−1.45203	−	0.269987i
$430$		0			0
$431$	−3.33028	+	31.6855i	−0.160414	+	1.52624i	0.557542	+	0.830149i	$0.311745\pi$
$431$	−3.33028	+	31.6855i	−0.160414	+	1.52624i	−0.717956	+	0.696088i	$0.754922\pi$
$432$		0			0
$433$	34.4369	+	7.31979i	1.65493	+	0.351766i	0.938336	−	0.345724i	$-0.112367\pi$
$433$	34.4369	+	7.31979i	1.65493	+	0.351766i	0.716594	+	0.697490i	$0.245700\pi$
$434$		0			0
$435$	2.24489	+	21.3587i	0.107634	+	1.02407i
$436$		0			0
$437$	1.03356	−	3.18097i	0.0494419	−	0.152166i
$438$		0			0
$439$	−1.93170	−	3.34580i	−0.0921949	−	0.159686i	0.816240	−	0.577714i	$-0.196055\pi$
$439$	−1.93170	−	3.34580i	−0.0921949	−	0.159686i	−0.908434	+	0.418027i	$0.862722\pi$
$440$		0			0
$441$	15.7825			0.751547
$442$		0			0
$443$	11.2771	−	34.7074i	0.535792	−	1.64900i	−0.206139	−	0.978523i	$-0.566090\pi$
$443$	11.2771	−	34.7074i	0.535792	−	1.64900i	0.741931	−	0.670476i	$-0.233910\pi$
$444$		0			0
$445$	−13.5626	−	6.03847i	−0.642930	−	0.286251i
$446$		0			0
$447$	−10.3887	−	31.9731i	−0.491368	−	1.51228i
$448$		0			0
$449$	0.802564	−	0.357324i	0.0378753	−	0.0168632i	−0.387712	−	0.921781i	$-0.626734\pi$
$449$	0.802564	−	0.357324i	0.0378753	−	0.0168632i	0.425587	+	0.904918i	$0.360068\pi$
$450$		0			0
$451$	1.11339	+	3.01820i	0.0524276	+	0.142121i
$452$		0			0
$453$	−2.07300	+	19.7232i	−0.0973978	+	0.926678i
$454$		0			0
$455$	1.36744	−	11.4988i	0.0641066	−	0.539070i
$456$		0			0
$457$	10.9045	+	4.85501i	0.510093	+	0.227108i	0.645610	−	0.763667i	$-0.276603\pi$
$457$	10.9045	+	4.85501i	0.510093	+	0.227108i	−0.135518	+	0.990775i	$0.543270\pi$
$458$		0			0
$459$	0.716221	+	0.795444i	0.0334303	+	0.0371281i
$460$		0			0
$461$	5.72956	−	9.92389i	0.266852	−	0.462201i	−0.701195	−	0.712969i	$-0.747350\pi$
$461$	5.72956	−	9.92389i	0.266852	−	0.462201i	0.968047	+	0.250768i	$0.0806831\pi$
$462$		0			0
$463$	−26.7437			−1.24288			−0.621442	−	0.783460i	$-0.713453\pi$
$463$	−26.7437			−1.24288			−0.621442	+	0.783460i	$0.713453\pi$
$464$		0			0
$465$	−0.595919	+	0.126667i	−0.0276351	+	0.00587402i
$466$		0			0
$467$	−15.5805	+	11.3199i	−0.720978	+	0.523821i	−0.886697	−	0.462352i	$-0.847006\pi$
$467$	−15.5805	+	11.3199i	−0.720978	+	0.523821i	0.165718	+	0.986173i	$0.447006\pi$
$468$		0			0
$469$	−2.23258	−	6.87119i	−0.103091	−	0.317282i
$470$		0			0
$471$	3.13392	−	29.8172i	0.144403	−	1.37391i
$472$		0			0
$473$	37.8503	+	15.1017i	1.74036	+	0.694379i
$474$		0			0
$475$	−18.8309	+	8.38405i	−0.864020	+	0.384686i
$476$		0			0
$477$	18.1432	+	3.85646i	0.830721	+	0.176575i
$478$		0			0
$479$	−7.88545e−5	0	3.51083e-5i	−3.60296e−6	0	1.60414e-6i	0.406735	−	0.913546i	$-0.366667\pi$
$479$	−7.88545e−5	0	3.51083e-5i	−3.60296e−6	0	1.60414e-6i	−0.406738	+	0.913545i	$0.633334\pi$
$480$		0			0
$481$	−10.4077	−	33.5841i	−0.474550	−	1.53130i
$482$		0			0
$483$	2.87933	+	4.98714i	0.131014	+	0.226923i
$484$		0			0
$485$	−2.21231	+	3.83183i	−0.100456	+	0.173994i
$486$		0			0
$487$	−18.5602	−	20.6132i	−0.841044	−	0.934074i	0.157527	−	0.987515i	$-0.449648\pi$
$487$	−18.5602	−	20.6132i	−0.841044	−	0.934074i	−0.998571	+	0.0534410i	$0.982981\pi$
$488$		0			0
$489$	−6.98665	+	5.07610i	−0.315947	+	0.229549i
$490$		0			0
$491$	17.1512	−	19.0483i	0.774023	−	0.859639i	−0.219223	−	0.975675i	$-0.570352\pi$
$491$	17.1512	−	19.0483i	0.774023	−	0.859639i	0.993245	+	0.116036i	$0.0370187\pi$
$492$		0			0
$493$	5.50640	+	4.00063i	0.247996	+	0.180179i
$494$		0			0
$495$	10.3599	+	4.13347i	0.465644	+	0.185786i
$496$		0			0
$497$	5.13169	−	48.8248i	0.230188	−	2.19009i
$498$		0			0
$499$	4.68009	+	14.4038i	0.209509	+	0.644804i	0.999498	+	0.0316822i	$0.0100864\pi$
$499$	4.68009	+	14.4038i	0.209509	+	0.644804i	−0.789989	+	0.613122i	$0.789914\pi$
$500$		0			0
$501$	−6.15972	−	58.6058i	−0.275196	−	2.61832i
$502$		0			0
$503$	−8.39187	−	9.32012i	−0.374175	−	0.415563i	0.526419	−	0.850226i	$-0.323534\pi$
$503$	−8.39187	−	9.32012i	−0.374175	−	0.415563i	−0.900594	+	0.434662i	$0.856868\pi$
$504$		0			0
$505$	2.18025	+	3.77630i	0.0970197	+	0.168043i
$506$		0			0
$507$	21.5695	+	25.3115i	0.957935	+	1.12412i
$508$		0			0
$509$	8.82334	−	1.87546i	0.391088	−	0.0831282i	−0.00817093	−	0.999967i	$-0.502601\pi$
$509$	8.82334	−	1.87546i	0.391088	−	0.0831282i	0.399259	+	0.916838i	$0.369268\pi$
$510$		0			0
$511$	0.241535	+	2.29805i	0.0106849	+	0.101660i
$512$		0			0
$513$	−6.84276	−	1.45447i	−0.302115	−	0.0642166i
$514$		0			0
$515$	−4.02677	−	2.92562i	−0.177441	−	0.128918i
$516$		0			0
$517$	11.3742	+	1.95471i	0.500235	+	0.0859682i
$518$		0			0
$519$	13.0640	+	9.49154i	0.573445	+	0.416632i
$520$		0			0
$521$	−10.7021	−	32.9378i	−0.468870	−	1.44303i	−0.854050	−	0.520191i	$-0.825861\pi$
$521$	−10.7021	−	32.9378i	−0.468870	−	1.44303i	0.385180	−	0.922841i	$-0.374139\pi$
$522$		0			0
$523$	−14.0040	−	6.23500i	−0.612354	−	0.272638i	0.0770356	−	0.997028i	$-0.475454\pi$
$523$	−14.0040	−	6.23500i	−0.612354	−	0.272638i	−0.689390	+	0.724391i	$0.742121\pi$
$524$		0			0
$525$	10.9671	−	33.7532i	0.478642	−	1.47311i
$526$		0			0
$527$	−0.0965388	+	0.167210i	−0.00420529	+	0.00728378i
$528$		0			0
$529$	11.2788	−	19.5354i	0.490381	−	0.849365i
$530$		0			0
$531$	32.6294	−	6.93560i	1.41600	−	0.300979i
$532$		0			0
$533$	1.12600	−	3.31104i	0.0487723	−	0.143417i
$534$		0			0
$535$	6.87377	−	7.63409i	0.297179	−	0.330051i
$536$		0			0
$537$	27.1716	−	12.0976i	1.17254	−	0.522050i
$538$		0			0
$539$	4.00963	−	14.2158i	0.172707	−	0.612319i
$540$		0			0
$541$	29.7520	+	21.6161i	1.27914	+	0.929349i	0.999527	−	0.0307640i	$-0.00979403\pi$
$541$	29.7520	+	21.6161i	1.27914	+	0.929349i	0.279612	+	0.960113i	$0.409794\pi$
$542$		0			0
$543$	−41.6561	+	46.2638i	−1.78763	+	1.98537i
$544$		0			0
$545$	6.93819	−	5.04089i	0.297199	−	0.215928i
$546$		0			0
$547$	5.77245	−	17.7658i	0.246812	−	0.759609i	−0.748521	−	0.663111i	$-0.769236\pi$
$547$	5.77245	−	17.7658i	0.246812	−	0.759609i	0.995333	−	0.0964984i	$-0.0307643\pi$
$548$		0			0
$549$	−9.02676	−	15.6348i	−0.385253	−	0.667277i
$550$		0			0
$551$	−44.4837			−1.89507
$552$		0			0
$553$	−8.09744	−	8.99312i	−0.344338	−	0.382426i
$554$		0			0
$555$	2.47450	+	23.5433i	0.105037	+	0.999356i
$556$		0			0
$557$	−11.3485	+	12.6038i	−0.480851	+	0.534039i	−0.933942	−	0.357425i	$-0.883655\pi$
$557$	−11.3485	+	12.6038i	−0.480851	+	0.534039i	0.453091	+	0.891464i	$0.350321\pi$
$558$		0			0
$559$	−21.6253	−	38.6652i	−0.914655	−	1.63536i
$560$		0			0
$561$	5.85431	−	2.88686i	0.247169	−	0.121883i
$562$		0			0
$563$	38.8758	−	17.3086i	1.63842	−	0.729472i	0.639204	−	0.769037i	$-0.279264\pi$
$563$	38.8758	−	17.3086i	1.63842	−	0.729472i	0.999217	+	0.0395648i	$0.0125971\pi$
$564$		0			0
$565$	−14.2039	−	3.01913i	−0.597561	−	0.127016i
$566$		0			0
$567$	−19.3645	+	14.0691i	−0.813232	+	0.590847i
$568$		0			0
$569$	−4.05126	+	0.861121i	−0.169837	+	0.0361001i	−0.292045	−	0.956404i	$-0.594336\pi$
$569$	−4.05126	+	0.861121i	−0.169837	+	0.0361001i	0.122208	+	0.992505i	$0.461003\pi$
$570$		0			0
$571$	44.8939			1.87875			0.939376	−	0.342889i	$-0.111406\pi$
$571$	44.8939			1.87875			0.939376	+	0.342889i	$0.111406\pi$
$572$		0			0
$573$	40.0946			1.67497
$574$		0			0
$575$	2.66724	−	0.566940i	0.111232	−	0.0236430i
$576$		0			0
$577$	21.1621	−	15.3752i	0.880991	−	0.640078i	−0.0525221	−	0.998620i	$-0.516726\pi$
$577$	21.1621	−	15.3752i	0.880991	−	0.640078i	0.933514	+	0.358542i	$0.116726\pi$
$578$		0			0
$579$	−59.8800	−	12.7279i	−2.48853	−	0.528953i
$580$		0			0
$581$	26.5240	−	11.8092i	1.10040	−	0.489929i
$582$		0			0
$583$	8.08304	−	15.3625i	0.334765	−	0.636249i
$584$		0			0
$585$	−5.91904	−	10.5830i	−0.244722	−	0.437552i
$586$		0			0
$587$	−15.0752	+	16.7427i	−0.622218	+	0.691043i	−0.969045	−	0.246886i	$-0.920593\pi$
$587$	−15.0752	+	16.7427i	−0.622218	+	0.691043i	0.346826	+	0.937929i	$0.387259\pi$
$588$		0			0
$589$	−0.131904	−	1.25498i	−0.00543500	−	0.0517106i
$590$		0			0
$591$	27.6737	+	30.7348i	1.13835	+	1.26426i
$592$		0			0
$593$	20.8660			0.856866			0.428433	−	0.903574i	$-0.359066\pi$
$593$	20.8660			0.856866			0.428433	+	0.903574i	$0.359066\pi$
$594$		0			0
$595$	1.23545	+	2.13986i	0.0506485	+	0.0877258i
$596$		0			0
$597$	4.67821	−	14.3981i	0.191467	−	0.589273i
$598$		0			0
$599$	24.1884	−	17.5739i	0.988310	−	0.718049i	0.0287599	−	0.999586i	$-0.490844\pi$
$599$	24.1884	−	17.5739i	0.988310	−	0.718049i	0.959550	+	0.281537i	$0.0908442\pi$
$600$		0			0
$601$	15.2462	−	16.9326i	0.621905	−	0.690695i	−0.347074	−	0.937838i	$-0.612825\pi$
$601$	15.2462	−	16.9326i	0.621905	−	0.690695i	0.968979	+	0.247142i	$0.0794915\pi$
$602$		0			0
$603$	−6.12057	−	4.44686i	−0.249249	−	0.181090i
$604$		0			0
$605$	6.35516	−	8.28141i	0.258374	−	0.336687i
$606$		0			0
$607$	12.4511	−	5.54358i	0.505374	−	0.225007i	−0.138181	−	0.990407i	$-0.544126\pi$
$607$	12.4511	−	5.54358i	0.505374	−	0.225007i	0.643555	+	0.765400i	$0.277459\pi$
$608$		0			0
$609$	51.2484	−	56.9171i	2.07669	−	2.30640i
$610$		0			0
$611$	−8.26711	−	9.43739i	−0.334451	−	0.381796i
$612$		0			0
$613$	−25.7306	+	5.46921i	−1.03925	+	0.220899i	−0.695773	−	0.718262i	$-0.744938\pi$
$613$	−25.7306	+	5.46921i	−1.03925	+	0.220899i	−0.343477	+	0.939161i	$0.611605\pi$
$614$		0			0
$615$	−1.17735	+	2.03922i	−0.0474751	+	0.0822293i
$616$		0			0
$617$	−7.48390	+	12.9625i	−0.301291	+	0.521851i	−0.976429	−	0.215841i	$-0.930751\pi$
$617$	−7.48390	+	12.9625i	−0.301291	+	0.521851i	0.675138	+	0.737692i	$0.264084\pi$
$618$		0			0
$619$	10.1383	−	31.2026i	0.407494	−	1.25414i	−0.511300	−	0.859402i	$-0.670836\pi$
$619$	10.1383	−	31.2026i	0.407494	−	1.25414i	0.918794	−	0.394737i	$-0.129164\pi$
$620$		0			0
$621$	0.845426	+	0.376408i	0.0339258	+	0.0151047i
$622$		0			0
$623$	16.3608	+	50.3533i	0.655481	+	2.01736i
$624$		0			0
$625$	−9.95284	−	7.23116i	−0.398114	−	0.289246i
$626$		0			0
$627$	−19.8645	+	37.7540i	−0.793310	+	1.50775i
$628$		0			0
$629$	6.06958	+	4.40981i	0.242010	+	0.175831i
$630$		0			0
$631$	6.89922	+	1.46647i	0.274653	+	0.0583794i	0.343179	−	0.939270i	$-0.388496\pi$
$631$	6.89922	+	1.46647i	0.274653	+	0.0583794i	−0.0685257	+	0.997649i	$0.521830\pi$
$632$		0			0
$633$	2.93083	+	27.8849i	0.116490	+	1.10833i
$634$		0			0
$635$	−19.2096	+	4.08313i	−0.762310	+	0.162034i
$636$		0			0
$637$	−13.1181	+	9.26005i	−0.519759	+	0.366897i
$638$		0			0
$639$	−25.7043	−	44.5211i	−1.01684	−	1.76123i
$640$		0			0
$641$	31.7340	+	35.2442i	1.25342	+	1.39206i	0.887103	+	0.461572i	$0.152714\pi$
$641$	31.7340	+	35.2442i	1.25342	+	1.39206i	0.366316	+	0.930491i	$0.380619\pi$
$642$		0			0
$643$	−4.00981	−	38.1508i	−0.158132	−	1.50452i	−0.729587	−	0.683888i	$-0.760288\pi$
$643$	−4.00981	−	38.1508i	−0.158132	−	1.50452i	0.571455	−	0.820633i	$-0.306379\pi$
$644$		0			0
$645$	9.21743	+	28.3683i	0.362936	+	1.11700i
$646$		0			0
$647$	−4.51484	+	42.9558i	−0.177497	+	1.68877i	0.436694	+	0.899610i	$0.356149\pi$
$647$	−4.51484	+	42.9558i	−0.177497	+	1.68877i	−0.614191	+	0.789157i	$0.710518\pi$
$648$		0			0
$649$	2.04257	−	31.1525i	0.0801779	−	1.22284i
$650$		0			0
$651$	1.75772	+	1.27706i	0.0688903	+	0.0500517i
$652$		0			0
$653$	−24.8718	+	27.6229i	−0.973309	+	1.08097i	0.0233851	+	0.999727i	$0.492556\pi$
$653$	−24.8718	+	27.6229i	−0.973309	+	1.08097i	−0.996694	+	0.0812429i	$0.974111\pi$
$654$		0			0
$655$	−2.23743	+	1.62559i	−0.0874237	+	0.0635171i
$656$		0			0
$657$	1.61907	+	1.79816i	0.0631659	+	0.0701529i
$658$		0			0
$659$	−1.20576	+	2.08843i	−0.0469697	+	0.0813539i	−0.888554	−	0.458771i	$-0.848290\pi$
$659$	−1.20576	+	2.08843i	−0.0469697	+	0.0813539i	0.841585	+	0.540125i	$0.181623\pi$
$660$		0			0
$661$	15.5226	+	26.8859i	0.603759	+	1.04574i	0.992246	+	0.124287i	$0.0396643\pi$
$661$	15.5226	+	26.8859i	0.603759	+	1.04574i	−0.388488	+	0.921454i	$0.627002\pi$
$662$		0			0
$663$	−6.92018	−	1.56992i	−0.268758	−	0.0609705i
$664$		0			0
$665$	−14.7529	−	6.56840i	−0.572092	−	0.254712i
$666$		0			0
$667$	5.75604	+	1.22348i	0.222875	+	0.0473735i
$668$		0			0
$669$	−29.8598	+	13.2944i	−1.15445	+	0.513993i
$670$		0			0
$671$	−16.3761	+	4.15860i	−0.632193	+	0.160541i
$672$		0			0
$673$	0.328337	−	3.12392i	0.0126565	−	0.120418i	−0.986369	−	0.164546i	$-0.947384\pi$
$673$	0.328337	−	3.12392i	0.0126565	−	0.120418i	0.999026	+	0.0441276i	$0.0140508\pi$
$674$		0			0
$675$	−1.76244	−	5.42424i	−0.0678364	−	0.208779i
$676$		0			0
$677$	−29.7472	+	21.6126i	−1.14328	+	0.830641i	−0.987573	−	0.157163i	$-0.949765\pi$
$677$	−29.7472	+	21.6126i	−1.14328	+	0.830641i	−0.155706	+	0.987803i	$0.549765\pi$
$678$		0			0
$679$	15.4343	−	3.28067i	0.592315	−	0.125901i
$680$		0			0
$681$	−39.1592			−1.50059
$682$		0			0
$683$	−15.4054	+	26.6829i	−0.589470	+	1.02099i	0.404831	+	0.914391i	$0.367330\pi$
$683$	−15.4054	+	26.6829i	−0.589470	+	1.02099i	−0.994302	+	0.106601i	$0.966003\pi$
$684$		0			0
$685$	6.92933	+	7.69580i	0.264756	+	0.294041i
$686$		0			0
$687$	34.6423	+	15.4237i	1.32169	+	0.588453i
$688$		0			0
$689$	−17.3430	+	7.43975i	−0.660717	+	0.283432i
$690$		0			0
$691$	−4.17391	+	39.7121i	−0.158783	+	1.51072i	0.567529	+	0.823353i	$0.307899\pi$
$691$	−4.17391	+	39.7121i	−0.158783	+	1.51072i	−0.726312	+	0.687365i	$0.758767\pi$
$692$		0			0
$693$	−13.7669	−	37.3196i	−0.522963	−	1.41766i
$694$		0			0
$695$	5.94307	−	2.64602i	0.225433	−	0.100369i
$696$		0			0
$697$	0.230603	+	0.709723i	0.00873471	+	0.0268827i
$698$		0			0
$699$	−10.3018	−	4.58665i	−0.389649	−	0.173483i
$700$		0			0
$701$	0.722949	−	2.22501i	0.0273054	−	0.0840374i	−0.936475	−	0.350734i	$-0.885932\pi$
$701$	0.722949	−	2.22501i	0.0273054	−	0.0840374i	0.963781	+	0.266697i	$0.0859322\pi$
$702$		0			0
$703$	−49.0334			−1.84933
$704$		0			0
$705$	4.22368	+	7.31563i	0.159073	+	0.275523i
$706$		0			0
$707$	4.80536	−	14.7894i	0.180724	−	0.556212i
$708$		0			0
$709$	1.82254	+	17.3403i	0.0684471	+	0.651230i	0.973930	+	0.226848i	$0.0728421\pi$
$709$	1.82254	+	17.3403i	0.0684471	+	0.651230i	−0.905483	+	0.424382i	$0.860491\pi$
$710$		0			0
$711$	−12.3951	−	2.63466i	−0.464853	−	0.0988075i
$712$		0			0
$713$	−0.0174492	+	0.166018i	−0.000653478	+	0.00621743i
$714$		0			0
$715$	−11.0362	+	2.64281i	−0.412731	+	0.0988355i
$716$		0			0
$717$	2.28740	−	21.7631i	0.0854245	−	0.812760i
$718$		0			0
$719$	−39.6745	−	8.43308i	−1.47961	−	0.314501i	−0.603792	−	0.797142i	$-0.706344\pi$
$719$	−39.6745	−	8.43308i	−1.47961	−	0.314501i	−0.875818	+	0.482641i	$0.839678\pi$
$720$		0			0
$721$	1.85542	+	17.6531i	0.0690994	+	0.657437i
$722$		0			0
$723$	7.84709	−	24.1509i	0.291836	−	0.898180i
$724$		0			0
$725$	−18.1333	−	31.4078i	−0.673453	−	1.16645i
$726$		0			0
$727$	26.5517			0.984747			0.492373	−	0.870384i	$-0.336129\pi$
$727$	26.5517			0.984747			0.492373	+	0.870384i	$0.336129\pi$
$728$		0			0
$729$	−11.0447	+	33.9920i	−0.409062	+	1.25896i
$730$		0			0
$731$	8.63587	+	3.84494i	0.319409	+	0.142210i
$732$		0			0
$733$	5.94334	+	18.2917i	0.219522	+	0.675620i	0.998802	+	0.0489434i	$0.0155854\pi$
$733$	5.94334	+	18.2917i	0.219522	+	0.675620i	−0.779279	+	0.626677i	$0.784415\pi$
$734$		0			0
$735$	9.87656	−	4.39733i	0.364302	−	0.162198i
$736$		0			0
$737$	−5.56040	+	4.38326i	−0.204820	+	0.161459i
$738$		0			0
$739$	2.13664	−	20.3288i	0.0785977	−	0.747807i	−0.882260	−	0.470763i	$-0.843979\pi$
$739$	2.13664	−	20.3288i	0.0785977	−	0.747807i	0.960857	−	0.277044i	$-0.0893547\pi$
$740$		0			0
$741$	42.6213	−	18.2835i	1.56573	−	0.671663i
$742$		0			0
$743$	23.4136	+	10.4244i	0.858962	+	0.382434i	0.788467	−	0.615078i	$-0.210875\pi$
$743$	23.4136	+	10.4244i	0.858962	+	0.382434i	0.0704953	+	0.997512i	$0.477542\pi$
$744$		0			0
$745$	−8.34511	−	9.26819i	−0.305741	−	0.339560i
$746$		0			0
$747$	15.2015	−	26.3298i	0.556195	−	0.963357i
$748$		0			0
$749$	−36.6346			−1.33860
$750$		0			0
$751$	−2.47260	+	0.525567i	−0.0902263	+	0.0191782i	−0.252804	−	0.967518i	$-0.581353\pi$
$751$	−2.47260	+	0.525567i	−0.0902263	+	0.0191782i	0.162577	+	0.986696i	$0.448019\pi$
$752$		0			0
$753$	−12.3033	+	8.93888i	−0.448357	+	0.325751i
$754$		0			0
$755$	2.27347	+	6.99702i	0.0827401	+	0.254648i
$756$		0			0
$757$	1.29790	−	12.3486i	0.0471728	−	0.448819i	−0.945286	−	0.326242i	$-0.894217\pi$
$757$	1.29790	−	12.3486i	0.0471728	−	0.448819i	0.992459	−	0.122577i	$-0.0391159\pi$
$758$		0			0
$759$	3.60878	−	4.33888i	0.130990	−	0.157491i
$760$		0			0
$761$	−26.3727	+	11.7419i	−0.956011	+	0.425644i	−0.824620	−	0.565687i	$-0.808611\pi$
$761$	−26.3727	+	11.7419i	−0.956011	+	0.425644i	−0.131391	+	0.991331i	$0.541944\pi$
$762$		0			0
$763$	−29.9158	−	6.35881i	−1.08303	−	0.230204i
$764$		0			0
$765$	2.36371	+	1.05239i	0.0854601	+	0.0380493i
$766$		0			0
$767$	−23.0517	+	24.9094i	−0.832347	+	0.899426i
$768$		0			0
$769$	12.8462	+	22.2503i	0.463246	+	0.802365i	0.999120	−	0.0419325i	$-0.0133514\pi$
$769$	12.8462	+	22.2503i	0.463246	+	0.802365i	−0.535875	+	0.844297i	$0.680018\pi$
$770$		0			0
$771$	−14.8454	+	25.7129i	−0.534642	+	0.926028i
$772$		0			0
$773$	16.2134	+	18.0068i	0.583155	+	0.647659i	0.960456	−	0.278432i	$-0.0898146\pi$
$773$	16.2134	+	18.0068i	0.583155	+	0.647659i	−0.377301	+	0.926091i	$0.623148\pi$
$774$		0			0
$775$	0.832311	−	0.604710i	0.0298975	−	0.0217218i
$776$		0			0
$777$	56.4900	−	62.7385i	2.02657	−	2.25073i
$778$		0			0
$779$	−3.94577	−	2.86677i	−0.141372	−	0.102713i
$780$		0			0
$781$	−46.6320	+	11.8419i	−1.66862	+	0.423735i
$782$		0			0
$783$	1.28655	−	12.2407i	0.0459777	−	0.437448i
$784$		0			0
$785$	−3.43699	−	10.5780i	−0.122672	−	0.377544i
$786$		0			0
$787$	−1.30781	−	12.4429i	−0.0466182	−	0.443543i	−0.992789	−	0.119875i	$-0.961751\pi$
$787$	−1.30781	−	12.4429i	−0.0466182	−	0.443543i	0.946171	−	0.323668i	$-0.104916\pi$
$788$		0			0
$789$	30.7447	+	34.1454i	1.09454	+	1.21561i
$790$		0			0
$791$	25.8929	+	44.8478i	0.920645	+	1.59460i
$792$		0			0
$793$	16.6763	+	7.69910i	0.592192	+	0.273403i
$794$		0			0
$795$	12.4284	−	2.64174i	0.440790	−	0.0936927i
$796$		0			0
$797$	0.837644	+	7.96965i	0.0296709	+	0.282299i	0.999290	+	0.0376794i	$0.0119966\pi$
$797$	0.837644	+	7.96965i	0.0296709	+	0.282299i	−0.969619	+	0.244620i	$0.921337\pi$
$798$		0			0
$799$	2.61863	+	0.556607i	0.0926405	+	0.0196914i
$800$		0			0
$801$	44.8527	+	32.5874i	1.58479	+	1.15142i
$802$		0			0
$803$	2.03100	−	1.00152i	0.0716723	−	0.0353428i
$804$		0			0
$805$	1.72831	+	1.25569i	0.0609150	+	0.0442573i
$806$		0			0
$807$	17.5574	+	54.0362i	0.618051	+	1.90217i
$808$		0			0
$809$	36.4978	+	16.2499i	1.28319	+	0.571315i	0.931139	−	0.364664i	$-0.118816\pi$
$809$	36.4978	+	16.2499i	1.28319	+	0.571315i	0.352055	+	0.935979i	$0.385483\pi$
$810$		0			0
$811$	−9.13239	+	28.1066i	−0.320682	+	0.986957i	0.652671	+	0.757642i	$0.273649\pi$
$811$	−9.13239	+	28.1066i	−0.320682	+	0.986957i	−0.973352	+	0.229315i	$0.926351\pi$
$812$		0			0
$813$	1.32496	−	2.29489i	0.0464683	−	0.0804854i
$814$		0			0
$815$	−1.60186	+	2.77450i	−0.0561107	+	0.0971866i
$816$		0			0
$817$	−60.4327	+	12.8454i	−2.11427	+	0.449402i
$818$		0			0
$819$	−13.9228	+	40.9405i	−0.486502	+	1.43058i
$820$		0			0
$821$	18.1246	−	20.1294i	0.632554	−	0.702523i	−0.338612	−	0.940926i	$-0.609957\pi$
$821$	18.1246	−	20.1294i	0.632554	−	0.702523i	0.971166	+	0.238404i	$0.0766241\pi$
$822$		0			0
$823$	−2.12243	+	0.944965i	−0.0739831	+	0.0329394i	−0.443395	−	0.896327i	$-0.646226\pi$
$823$	−2.12243	+	0.944965i	−0.0739831	+	0.0329394i	0.369411	+	0.929266i	$0.379559\pi$
$824$		0			0
$825$	−34.7538	+	1.36467i	−1.20997	+	0.0475117i
$826$		0			0
$827$	21.6635	+	15.7394i	0.753312	+	0.547313i	0.896852	−	0.442331i	$-0.145848\pi$
$827$	21.6635	+	15.7394i	0.753312	+	0.547313i	−0.143540	+	0.989645i	$0.545848\pi$
$828$		0			0
$829$	−33.6161	+	37.3345i	−1.16754	+	1.29668i	−0.220562	+	0.975373i	$0.570789\pi$
$829$	−33.6161	+	37.3345i	−1.16754	+	1.29668i	−0.946975	+	0.321308i	$0.895877\pi$
$830$		0			0
$831$	−50.6605	+	36.8070i	−1.75739	+	1.27682i
$832$		0			0
$833$	1.05878	−	3.25860i	0.0366846	−	0.112904i
$834$		0			0
$835$	−10.9305	−	18.9322i	−0.378265	−	0.655175i
$836$		0			0
$837$	0.349152			0.0120685
$838$		0			0
$839$	2.90911	+	3.23089i	0.100434	+	0.111543i	0.791266	−	0.611472i	$-0.209422\pi$
$839$	2.90911	+	3.23089i	0.100434	+	0.111543i	−0.690832	+	0.723015i	$0.742756\pi$
$840$		0			0
$841$	−5.14959	−	48.9950i	−0.177572	−	1.68948i
$842$		0			0
$843$	10.0039	−	11.1104i	0.344552	−	0.382664i
$844$		0			0
$845$	11.1291	+	5.32350i	0.382854	+	0.183134i
$846$		0			0
$847$	−37.1126	+	2.91909i	−1.27521	+	0.100301i
$848$		0			0
$849$	−43.2893	+	19.2737i	−1.48569	+	0.661470i
$850$		0			0
$851$	6.34475	+	1.34862i	0.217495	+	0.0462301i
$852$		0			0
$853$	35.3080	−	25.6528i	1.20892	−	0.878334i	0.213790	−	0.976880i	$-0.431419\pi$
$853$	35.3080	−	25.6528i	1.20892	−	0.878334i	0.995133	+	0.0985459i	$0.0314191\pi$
$854$		0			0
$855$	−16.5409	+	3.51588i	−0.565688	+	0.120241i
$856$		0			0
$857$	−15.4863			−0.529000			−0.264500	−	0.964386i	$-0.585207\pi$
$857$	−15.4863			−0.529000			−0.264500	+	0.964386i	$0.585207\pi$
$858$		0			0
$859$	30.6229			1.04484			0.522420	−	0.852689i	$-0.325030\pi$
$859$	30.6229			1.04484			0.522420	+	0.852689i	$0.325030\pi$
$860$		0			0
$861$	8.21384	−	1.74591i	0.279927	−	0.0595003i
$862$		0			0
$863$	−24.8164	+	18.0302i	−0.844761	+	0.613755i	−0.923696	−	0.383125i	$-0.874848\pi$
$863$	−24.8164	+	18.0302i	−0.844761	+	0.613755i	0.0789357	+	0.996880i	$0.474848\pi$
$864$		0			0
$865$	5.85956	+	1.24549i	0.199231	+	0.0423479i
$866$		0			0
$867$	−38.3447	+	17.0722i	−1.30225	+	0.579801i
$868$		0			0
$869$	−5.52218	+	10.4953i	−0.187327	+	0.356030i
$870$		0			0
$871$	7.69641	+	0.105024i	0.260783	+	0.00355862i
$872$		0			0
$873$	11.0561	−	12.2791i	0.374193	−	0.415584i
$874$		0			0
$875$	−3.05476	−	29.0641i	−0.103270	−	0.982546i
$876$		0			0
$877$	11.5373	+	12.8134i	0.389586	+	0.432679i	0.905751	−	0.423810i	$-0.139308\pi$
$877$	11.5373	+	12.8134i	0.389586	+	0.432679i	−0.516165	+	0.856489i	$0.672641\pi$
$878$		0			0
$879$	−23.5858			−0.795529
$880$		0			0
$881$	−9.20918	−	15.9508i	−0.310265	−	0.537395i	0.668155	−	0.744023i	$-0.267085\pi$
$881$	−9.20918	−	15.9508i	−0.310265	−	0.537395i	−0.978420	+	0.206628i	$0.933751\pi$
$882$		0			0
$883$	−11.3529	+	34.9408i	−0.382057	+	1.17585i	0.556536	+	0.830824i	$0.312130\pi$
$883$	−11.3529	+	34.9408i	−0.382057	+	1.17585i	−0.938593	+	0.345027i	$0.887870\pi$
$884$		0			0
$885$	18.4868	−	13.4315i	0.621429	−	0.451494i
$886$		0			0
$887$	−4.69651	+	5.21600i	−0.157693	+	0.175136i	−0.816814	−	0.576901i	$-0.804262\pi$
$887$	−4.69651	+	5.21600i	−0.157693	+	0.175136i	0.659121	+	0.752037i	$0.270929\pi$
$888$		0			0
$889$	56.6604	+	41.1662i	1.90033	+	1.38067i
$890$		0			0
$891$	19.5036	+	13.0326i	0.653396	+	0.436608i
$892$		0			0
$893$	−15.9842	+	7.11664i	−0.534892	+	0.238149i
$894$		0			0
$895$	7.38312	−	8.19978i	0.246790	−	0.274088i
$896$		0			0
$897$	−6.01792	+	1.19357i	−0.200932	+	0.0398520i
$898$		0			0
$899$	2.17167	−	0.461602i	0.0724292	−	0.0153953i
$900$		0			0
$901$	2.01340	−	3.48730i	0.0670759	−	0.116179i
$902$		0			0
$903$	53.1870	−	92.1226i	1.76995	−	3.06565i
$904$		0			0
$905$	−7.13663	+	21.9643i	−0.237230	+	0.730117i
$906$		0			0
$907$	−6.07754	−	2.70589i	−0.201801	−	0.0898477i	0.303347	−	0.952880i	$-0.401896\pi$
$907$	−6.07754	−	2.70589i	−0.201801	−	0.0898477i	−0.505149	+	0.863032i	$0.668562\pi$
$908$		0			0
$909$	−5.03193	−	15.4867i	−0.166899	−	0.513662i
$910$		0			0
$911$	−8.67032	−	6.29936i	−0.287261	−	0.208707i	0.434817	−	0.900519i	$-0.356813\pi$
$911$	−8.67032	−	6.29936i	−0.287261	−	0.208707i	−0.722078	+	0.691812i	$0.756813\pi$
$912$		0			0
$913$	−19.8541	−	20.3818i	−0.657076	−	0.674538i
$914$		0			0
$915$	−10.0051	−	7.26910i	−0.330757	−	0.240309i
$916$		0			0
$917$	9.64728	+	2.05059i	0.318581	+	0.0677165i
$918$		0			0
$919$	−2.00834	−	19.1081i	−0.0662492	−	0.630319i	−0.976389	−	0.216018i	$-0.930693\pi$
$919$	−2.00834	−	19.1081i	−0.0662492	−	0.630319i	0.910140	−	0.414301i	$-0.135974\pi$
$920$		0			0
$921$	−32.7342	+	6.95786i	−1.07863	+	0.229269i
$922$		0			0
$923$	47.4867	+	21.9237i	1.56305	+	0.721626i
$924$		0			0
$925$	−19.9879	−	34.6201i	−0.657199	−	1.13830i
$926$		0			0
$927$	12.4373	+	13.8130i	0.408495	+	0.453680i
$928$		0			0
$929$	1.81671	+	17.2849i	0.0596045	+	0.567099i	0.983046	+	0.183359i	$0.0586972\pi$
$929$	1.81671	+	17.2849i	0.0596045	+	0.567099i	−0.923441	+	0.383739i	$0.874636\pi$
$930$		0			0
$931$	6.91987	+	21.2972i	0.226790	+	0.697986i
$932$		0			0
$933$	−1.35006	+	12.8450i	−0.0441990	+	0.420525i
$934$		0			0
$935$	1.54844	−	1.86171i	0.0506394	−	0.0608844i
$936$		0			0
$937$	−1.04172	−	0.756857i	−0.0340316	−	0.0247254i	0.570639	−	0.821201i	$-0.306695\pi$
$937$	−1.04172	−	0.756857i	−0.0340316	−	0.0247254i	−0.604671	+	0.796475i	$0.706695\pi$
$938$		0			0
$939$	37.4547	−	41.5977i	1.22229	−	1.35749i
$940$		0			0
$941$	23.1079	−	16.7889i	0.753295	−	0.547301i	−0.143551	−	0.989643i	$-0.545852\pi$
$941$	23.1079	−	16.7889i	0.753295	−	0.547301i	0.896846	+	0.442342i	$0.145852\pi$
$942$		0			0
$943$	0.431721	+	0.479474i	0.0140588	+	0.0156138i
$944$		0			0
$945$	2.23413	−	3.86963i	0.0726762	−	0.125879i
$946$		0			0
$947$	−11.2683	−	19.5172i	−0.366170	−	0.634225i	0.622793	−	0.782386i	$-0.285998\pi$
$947$	−11.2683	−	19.5172i	−0.366170	−	0.634225i	−0.988963	+	0.148162i	$0.952664\pi$
$948$		0			0
$949$	−2.40077	−	0.544641i	−0.0779324	−	0.0176798i
$950$		0			0
$951$	14.7964	+	6.58777i	0.479805	+	0.213623i
$952$		0			0
$953$	−12.6522	−	2.68930i	−0.409843	−	0.0871149i	−0.00162387	−	0.999999i	$-0.500517\pi$
$953$	−12.6522	−	2.68930i	−0.409843	−	0.0871149i	−0.408220	+	0.912884i	$0.633850\pi$
$954$		0			0
$955$	13.5881	−	6.04981i	0.439701	−	0.195767i
$956$		0			0
$957$	−69.7140	−	27.8149i	−2.25353	−	0.899129i
$958$		0			0
$959$	3.86032	−	36.7284i	0.124656	−	1.18602i
$960$		0			0
$961$	−9.56006	−	29.4229i	−0.308389	−	0.949124i
$962$		0			0
$963$	−31.0355	+	22.5486i	−1.00010	+	0.726619i
$964$		0			0
$965$	−22.2139	+	4.72171i	−0.715091	+	0.151997i
$966$		0			0
$967$	−6.46393			−0.207866			−0.103933	−	0.994584i	$-0.533143\pi$
$967$	−6.46393			−0.207866			−0.103933	+	0.994584i	$0.533143\pi$
$968$		0			0
$969$	−4.94802	+	8.57022i	−0.158953	+	0.275315i
$970$		0			0
$971$	35.6455	+	39.5884i	1.14392	+	1.27045i	0.957645	+	0.287953i	$0.0929747\pi$
$971$	35.6455	+	39.5884i	1.14392	+	1.27045i	0.186275	+	0.982498i	$0.440359\pi$
$972$		0			0
$973$	−21.1943	−	9.43631i	−0.679458	−	0.302514i
$974$		0			0
$975$	30.2832	+	22.6397i	0.969838	+	0.725051i
$976$		0			0
$977$	−3.54916	+	33.7680i	−0.113548	+	1.08034i	0.778267	+	0.627934i	$0.216099\pi$
$977$	−3.54916	+	33.7680i	−0.113548	+	1.08034i	−0.891814	+	0.452401i	$0.850567\pi$
$978$		0			0
$979$	40.7476	−	32.1213i	1.30230	−	1.02660i
$980$		0			0
$981$	−29.2574	+	13.0262i	−0.934117	+	0.415896i
$982$		0			0
$983$	−8.78483	−	27.0369i	−0.280192	−	0.862344i	−0.987799	−	0.155737i	$-0.950225\pi$
$983$	−8.78483	−	27.0369i	−0.280192	−	0.862344i	0.707606	−	0.706607i	$-0.249775\pi$
$984$		0			0
$985$	14.0162	+	6.24042i	0.446593	+	0.198836i
$986$		0			0
$987$	9.30919	−	28.6507i	0.296315	−	0.911963i
$988$		0			0
$989$	8.17307			0.259889
$990$		0			0
$991$	−12.0671	−	20.9008i	−0.383323	−	0.663935i	0.608212	−	0.793774i	$-0.291887\pi$
$991$	−12.0671	−	20.9008i	−0.383323	−	0.663935i	−0.991535	+	0.129840i	$0.958554\pi$
$992$		0			0
$993$	−10.4899	+	32.2847i	−0.332888	+	1.02452i
$994$		0			0
$995$	−0.587050	−	5.58541i	−0.0186108	−	0.177069i
$996$		0			0
$997$	43.4282	+	9.23096i	1.37539	+	0.292347i	0.835546	−	0.549420i	$-0.185151\pi$
$997$	43.4282	+	9.23096i	1.37539	+	0.292347i	0.539840	+	0.841768i	$0.318485\pi$
$998$		0			0
$999$	1.41814	−	13.4927i	0.0448679	−	0.426890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.81.3	✓	112
11.3	even	5	inner	572.2.bg.a.289.12	yes	112
13.9	even	3	inner	572.2.bg.a.477.12	yes	112
143.113	even	15	inner	572.2.bg.a.113.3	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.81.3	✓	112	1.1	even	1	trivial
572.2.bg.a.113.3	yes	112	143.113	even	15	inner
572.2.bg.a.289.12	yes	112	11.3	even	5	inner
572.2.bg.a.477.12	yes	112	13.9	even	3	inner

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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.50220 + 0.531859i) q^{3} +(-0.767747 + 0.557801i) q^{5} +(3.31034 + 0.703635i) q^{7} +(3.23748 - 1.44142i) q^{9} +O(q^{10})\)	\(q+(-2.50220 + 0.531859i) q^{3} +(-0.767747 + 0.557801i) q^{5} +(3.31034 + 0.703635i) q^{7} +(3.23748 - 1.44142i) q^{9} +(-0.475835 - 3.28231i) q^{11} +(-1.84521 + 3.09761i) q^{13} +(1.62438 - 1.80406i) q^{15} +(-0.0804194 - 0.765140i) q^{17} +(3.36456 + 3.73672i) q^{19} -8.65736 q^{21} +(-0.332587 - 0.576058i) q^{23} +(-1.26679 + 3.89878i) q^{25} +(-1.12556 + 0.817764i) q^{27} +(-5.91963 + 6.57441i) q^{29} +(-0.203031 - 0.147511i) q^{31} +(2.93636 + 7.95992i) q^{33} +(-2.93399 + 1.30630i) q^{35} +(-6.52508 + 7.24683i) q^{37} +(2.96960 - 8.73223i) q^{39} +(-0.948769 + 0.201667i) q^{41} +(-6.14356 + 10.6410i) q^{43} +(-1.68154 + 2.91252i) q^{45} +(-1.07529 + 3.30941i) q^{47} +(4.06844 + 1.81139i) q^{49} +(0.608171 + 1.87176i) q^{51} +(4.23439 + 3.07646i) q^{53} +(2.19620 + 2.25456i) q^{55} +(-10.4062 - 7.56055i) q^{57} +(9.20729 + 1.95707i) q^{59} +(-0.532499 - 5.06639i) q^{61} +(11.7314 - 2.49359i) q^{63} +(-0.311193 - 3.40744i) q^{65} +(-1.06740 - 1.84879i) q^{67} +(1.13858 + 1.26452i) q^{69} +(-1.51632 - 14.4269i) q^{71} +(0.210989 + 0.649357i) q^{73} +(1.09616 - 10.4293i) q^{75} +(0.734374 - 11.2004i) q^{77} +(-2.89285 - 2.10178i) q^{79} +(-4.73250 + 5.25597i) q^{81} +(6.94061 - 5.04265i) q^{83} +(0.488537 + 0.542575i) q^{85} +(11.3154 - 19.5989i) q^{87} +(7.82210 + 13.5483i) q^{89} +(-8.28787 + 8.95579i) q^{91} +(0.586479 + 0.261117i) q^{93} +(-4.66748 - 0.992103i) q^{95} +(4.25937 - 1.89639i) q^{97} +(-6.27170 - 9.94056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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