LMFDB - Embedded newform 592.2.bq.d.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(65,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("592.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bq (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 30x^{16} + 333x^{14} + 1826x^{12} + 5490x^{10} + 9432x^{8} + 9385x^{6} + 5316x^{4} + 1584x^{2} + 192 $ x^18 + 30x^16 + 333x^14 + 1826x^12 + 5490x^10 + 9432x^8 + 9385x^6 + 5316x^4 + 1584x^2 + 192
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			321.2
Root			$1.23399i$ of defining polynomial
Character	$\chi$	$=$	592.321
Dual form			592.2.bq.d.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.968719 + 0.812851i) q^{3} +(-0.681528 - 1.87248i) q^{5} +(-2.99976 + 1.09182i) q^{7} +(-0.243256 - 1.37957i) q^{9} +O(q^{10})$	\(q+(0.968719 + 0.812851i) q^{3} +(-0.681528 - 1.87248i) q^{5} +(-2.99976 + 1.09182i) q^{7} +(-0.243256 - 1.37957i) q^{9} +(-2.73288 - 4.73349i) q^{11} +(-1.50836 - 0.265964i) q^{13} +(0.861842 - 2.36789i) q^{15} +(-0.794131 + 0.140027i) q^{17} +(1.35888 - 1.61945i) q^{19} +(-3.79342 - 1.38069i) q^{21} +(-3.02834 - 1.74842i) q^{23} +(0.788506 - 0.661636i) q^{25} +(2.78260 - 4.81961i) q^{27} +(-0.122232 + 0.0705708i) q^{29} +3.37454i q^{31} +(1.20023 - 6.80685i) q^{33} +(4.08885 + 4.87290i) q^{35} +(0.539604 + 6.05878i) q^{37} +(-1.24498 - 1.48371i) q^{39} +(0.0732041 - 0.415161i) q^{41} +2.00540i q^{43} +(-2.41745 + 1.39571i) q^{45} +(0.842972 - 1.46007i) q^{47} +(2.44419 - 2.05092i) q^{49} +(-0.883111 - 0.509864i) q^{51} +(-6.86119 - 2.49727i) q^{53} +(-7.00085 + 8.34329i) q^{55} +(2.63275 - 0.464224i) q^{57} +(3.65272 - 10.0358i) q^{59} +(11.3492 + 2.00116i) q^{61} +(2.23597 + 3.87281i) q^{63} +(0.529974 + 3.00563i) q^{65} +(7.25752 - 2.64152i) q^{67} +(-1.51241 - 4.15532i) q^{69} +(-6.78889 - 5.69655i) q^{71} -8.77446 q^{73} +1.30165 q^{75} +(13.3662 + 11.2155i) q^{77} +(-1.54413 - 4.24247i) q^{79} +(2.66406 - 0.969637i) q^{81} +(1.81973 + 10.3202i) q^{83} +(0.803421 + 1.39157i) q^{85} +(-0.175772 - 0.0309934i) q^{87} +(0.914163 - 2.51164i) q^{89} +(4.81510 - 0.849032i) q^{91} +(-2.74300 + 3.26898i) q^{93} +(-3.95851 - 1.44078i) q^{95} +(-13.3681 - 7.71809i) q^{97} +(-5.86542 + 4.92167i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{3} - 3 q^{5} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 18 * q + 9 * q^3 - 3 * q^5 + 3 * q^7 - 3 * q^9	$ 18 q + 9 q^{3} - 3 q^{5} + 3 q^{7} - 3 q^{9} - 9 q^{11} + 9 q^{13} + 15 q^{15} - 15 q^{17} - 6 q^{19} - 12 q^{21} + 9 q^{23} + 21 q^{25} - 21 q^{27} - 18 q^{29} + 6 q^{33} + 12 q^{35} + 6 q^{37} + 6 q^{39} - 24 q^{41} + 36 q^{47} + 21 q^{49} - 81 q^{51} - 39 q^{53} - 12 q^{55} + 15 q^{57} + 6 q^{59} + 42 q^{61} + 27 q^{63} + 18 q^{65} - 36 q^{69} + 9 q^{71} - 54 q^{73} - 18 q^{75} + 33 q^{77} + 6 q^{79} - 45 q^{81} + 24 q^{83} + 6 q^{85} - 21 q^{87} + 18 q^{89} + 3 q^{91} + 66 q^{93} + 15 q^{95} - 9 q^{97} - 60 q^{99}+O(q^{100}) $ 18 * q + 9 * q^3 - 3 * q^5 + 3 * q^7 - 3 * q^9 - 9 * q^11 + 9 * q^13 + 15 * q^15 - 15 * q^17 - 6 * q^19 - 12 * q^21 + 9 * q^23 + 21 * q^25 - 21 * q^27 - 18 * q^29 + 6 * q^33 + 12 * q^35 + 6 * q^37 + 6 * q^39 - 24 * q^41 + 36 * q^47 + 21 * q^49 - 81 * q^51 - 39 * q^53 - 12 * q^55 + 15 * q^57 + 6 * q^59 + 42 * q^61 + 27 * q^63 + 18 * q^65 - 36 * q^69 + 9 * q^71 - 54 * q^73 - 18 * q^75 + 33 * q^77 + 6 * q^79 - 45 * q^81 + 24 * q^83 + 6 * q^85 - 21 * q^87 + 18 * q^89 + 3 * q^91 + 66 * q^93 + 15 * q^95 - 9 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.968719	+	0.812851i	0.559290	+	0.469300i	0.878072	−	0.478528i	$-0.158829\pi$
$3$	0.968719	+	0.812851i	0.559290	+	0.469300i	−0.318782	+	0.947828i	$0.603274\pi$
$4$		0			0
$5$	−0.681528	−	1.87248i	−0.304789	−	0.837400i	−0.993651	−	0.112508i	$-0.964112\pi$
$5$	−0.681528	−	1.87248i	−0.304789	−	0.837400i	0.688862	−	0.724892i	$-0.258111\pi$
$6$		0			0
$7$	−2.99976	+	1.09182i	−1.13380	+	0.412671i	−0.839672	−	0.543094i	$-0.817253\pi$
$7$	−2.99976	+	1.09182i	−1.13380	+	0.412671i	−0.294132	+	0.955765i	$0.595031\pi$
$8$		0			0
$9$	−0.243256	−	1.37957i	−0.0810854	−	0.459858i
$10$		0			0
$11$	−2.73288	−	4.73349i	−0.823995	−	1.42720i	−0.902685	−	0.430303i	$-0.858407\pi$
$11$	−2.73288	−	4.73349i	−0.823995	−	1.42720i	0.0786894	−	0.996899i	$-0.474926\pi$
$12$		0			0
$13$	−1.50836	−	0.265964i	−0.418343	−	0.0737651i	−0.0394852	−	0.999220i	$-0.512572\pi$
$13$	−1.50836	−	0.265964i	−0.418343	−	0.0737651i	−0.378857	+	0.925455i	$0.623683\pi$
$14$		0			0
$15$	0.861842	−	2.36789i	0.222527	−	0.611387i
$16$		0			0
$17$	−0.794131	+	0.140027i	−0.192605	+	0.0339615i	−0.269118	−	0.963107i	$-0.586732\pi$
$17$	−0.794131	+	0.140027i	−0.192605	+	0.0339615i	0.0765134	+	0.997069i	$0.475621\pi$
$18$		0			0
$19$	1.35888	−	1.61945i	0.311749	−	0.371527i	−0.587305	−	0.809365i	$-0.699811\pi$
$19$	1.35888	−	1.61945i	0.311749	−	0.371527i	0.899054	+	0.437838i	$0.144256\pi$
$20$		0			0
$21$	−3.79342	−	1.38069i	−0.827792	−	0.301292i
$22$		0			0
$23$	−3.02834	−	1.74842i	−0.631453	−	0.364570i	0.149861	−	0.988707i	$-0.452117\pi$
$23$	−3.02834	−	1.74842i	−0.631453	−	0.364570i	−0.781315	+	0.624137i	$0.785451\pi$
$24$		0			0
$25$	0.788506	−	0.661636i	0.157701	−	0.132327i
$26$		0			0
$27$	2.78260	−	4.81961i	0.535512	−	0.927534i
$28$		0			0
$29$	−0.122232	+	0.0705708i	−0.0226980	+	0.0131047i	−0.511306	−	0.859399i	$-0.670838\pi$
$29$	−0.122232	+	0.0705708i	−0.0226980	+	0.0131047i	0.488608	+	0.872503i	$0.337505\pi$
$30$		0			0
$31$			3.37454i			0.606085i	0.952977	+	0.303042i	$0.0980024\pi$
$31$			3.37454i			0.606085i	−0.952977	+	0.303042i	$0.901998\pi$
$32$		0			0
$33$	1.20023	−	6.80685i	0.208933	−	1.18492i
$34$		0			0
$35$	4.08885	+	4.87290i	0.691142	+	0.823671i
$36$		0			0
$37$	0.539604	+	6.05878i	0.0887103	+	0.996057i
$37$	0.539604	+	6.05878i	0.0887103	+	0.996057i
$38$		0			0
$39$	−1.24498	−	1.48371i	−0.199357	−	0.237584i
$40$		0			0
$41$	0.0732041	−	0.415161i	0.0114326	−	0.0648373i	−0.978558	−	0.205973i	$-0.933964\pi$
$41$	0.0732041	−	0.415161i	0.0114326	−	0.0648373i	0.989990	+	0.141135i	$0.0450753\pi$
$42$		0			0
$43$			2.00540i			0.305820i	0.988240	+	0.152910i	$0.0488645\pi$
$43$			2.00540i			0.305820i	−0.988240	+	0.152910i	$0.951135\pi$
$44$		0			0
$45$	−2.41745	+	1.39571i	−0.360372	+	0.208061i
$46$		0			0
$47$	0.842972	−	1.46007i	0.122960	−	0.212973i	−0.797974	−	0.602692i	$-0.794095\pi$
$47$	0.842972	−	1.46007i	0.122960	−	0.212973i	0.920934	+	0.389719i	$0.127428\pi$
$48$		0			0
$49$	2.44419	−	2.05092i	0.349171	−	0.292989i
$50$		0			0
$51$	−0.883111	−	0.509864i	−0.123660	−	0.0713953i
$52$		0			0
$53$	−6.86119	−	2.49727i	−0.942457	−	0.343026i	−0.175321	−	0.984511i	$-0.556096\pi$
$53$	−6.86119	−	2.49727i	−0.942457	−	0.343026i	−0.767136	+	0.641485i	$0.778319\pi$
$54$		0			0
$55$	−7.00085	+	8.34329i	−0.943995	+	1.12501i
$56$		0			0
$57$	2.63275	−	0.464224i	0.348716	−	0.0614880i
$58$		0			0
$59$	3.65272	−	10.0358i	0.475544	−	1.30655i	−0.437696	−	0.899123i	$-0.644205\pi$
$59$	3.65272	−	10.0358i	0.475544	−	1.30655i	0.913240	−	0.407422i	$-0.133572\pi$
$60$		0			0
$61$	11.3492	+	2.00116i	1.45311	+	0.256222i	0.843778	−	0.536693i	$-0.180327\pi$
$61$	11.3492	+	2.00116i	1.45311	+	0.256222i	0.609332	+	0.792915i	$0.291438\pi$
$62$		0			0
$63$	2.23597	+	3.87281i	0.281705	+	0.487928i
$64$		0			0
$65$	0.529974	+	3.00563i	0.0657352	+	0.372803i
$66$		0			0
$67$	7.25752	−	2.64152i	0.886648	−	0.322713i	0.141758	−	0.989901i	$-0.454724\pi$
$67$	7.25752	−	2.64152i	0.886648	−	0.322713i	0.744889	+	0.667188i	$0.232502\pi$
$68$		0			0
$69$	−1.51241	−	4.15532i	−0.182073	−	0.500241i
$70$		0			0
$71$	−6.78889	−	5.69655i	−0.805693	−	0.676056i	0.143883	−	0.989595i	$-0.454041\pi$
$71$	−6.78889	−	5.69655i	−0.805693	−	0.676056i	−0.949576	+	0.313538i	$0.898486\pi$
$72$		0			0
$73$	−8.77446			−1.02697			−0.513486	−	0.858098i	$-0.671646\pi$
$73$	−8.77446			−1.02697			−0.513486	+	0.858098i	$0.671646\pi$
$74$		0			0
$75$	1.30165			0.150302
$76$		0			0
$77$	13.3662	+	11.2155i	1.52321	+	1.27813i
$78$		0			0
$79$	−1.54413	−	4.24247i	−0.173729	−	0.477316i	0.822017	−	0.569463i	$-0.192849\pi$
$79$	−1.54413	−	4.24247i	−0.173729	−	0.477316i	−0.995745	+	0.0921478i	$0.970627\pi$
$80$		0			0
$81$	2.66406	−	0.969637i	0.296006	−	0.107737i
$82$		0			0
$83$	1.81973	+	10.3202i	0.199741	+	1.13279i	0.905504	+	0.424338i	$0.139493\pi$
$83$	1.81973	+	10.3202i	0.199741	+	1.13279i	−0.705763	+	0.708448i	$0.749396\pi$
$84$		0			0
$85$	0.803421	+	1.39157i	0.0871432	+	0.150937i
$86$		0			0
$87$	−0.175772	−	0.0309934i	−0.0188448	−	0.00332284i
$88$		0			0
$89$	0.914163	−	2.51164i	0.0969011	−	0.266234i	−0.881766	−	0.471688i	$-0.843645\pi$
$89$	0.914163	−	2.51164i	0.0969011	−	0.266234i	0.978667	+	0.205454i	$0.0658672\pi$
$90$		0			0
$91$	4.81510	−	0.849032i	0.504759	−	0.0890027i
$92$		0			0
$93$	−2.74300	+	3.26898i	−0.284436	+	0.338977i
$94$		0			0
$95$	−3.95851	−	1.44078i	−0.406135	−	0.147821i
$96$		0			0
$97$	−13.3681	−	7.71809i	−1.35733	−	0.783654i	−0.368065	−	0.929800i	$-0.619980\pi$
$97$	−13.3681	−	7.71809i	−1.35733	−	0.783654i	−0.989263	+	0.146146i	$0.953313\pi$
$98$		0			0
$99$	−5.86542	+	4.92167i	−0.589497	+	0.494646i
$100$		0			0
$101$	8.33907	−	14.4437i	0.829769	−	1.43720i	−0.0684504	−	0.997655i	$-0.521805\pi$
$101$	8.33907	−	14.4437i	0.829769	−	1.43720i	0.898219	−	0.439547i	$-0.144861\pi$
$102$		0			0
$103$	−3.81111	+	2.20034i	−0.375520	+	0.216806i	−0.675867	−	0.737024i	$-0.736231\pi$
$103$	−3.81111	+	2.20034i	−0.375520	+	0.216806i	0.300348	+	0.953830i	$0.402897\pi$
$104$		0			0
$105$			8.04410i			0.785024i
$106$		0			0
$107$	−1.47160	+	8.34584i	−0.142265	+	0.806823i	0.827258	+	0.561822i	$0.189899\pi$
$107$	−1.47160	+	8.34584i	−0.142265	+	0.806823i	−0.969523	+	0.245001i	$0.921212\pi$
$108$		0			0
$109$	−6.61006	−	7.87757i	−0.633129	−	0.754534i	0.350139	−	0.936698i	$-0.386134\pi$
$109$	−6.61006	−	7.87757i	−0.633129	−	0.754534i	−0.983268	+	0.182164i	$0.941690\pi$
$110$		0			0
$111$	−4.40216	+	6.30787i	−0.417835	+	0.598717i
$112$		0			0
$113$	7.37783	+	8.79256i	0.694048	+	0.827134i	0.991839	−	0.127497i	$-0.0406943\pi$
$113$	7.37783	+	8.79256i	0.694048	+	0.827134i	−0.297791	+	0.954631i	$0.596250\pi$
$114$		0			0
$115$	−1.20998	+	6.86212i	−0.112831	+	0.639896i
$116$		0			0
$117$			2.14559i			0.198360i
$118$		0			0
$119$	2.22932	−	1.28710i	0.204362	−	0.117988i
$120$		0			0
$121$	−9.43730	+	16.3459i	−0.857937	+	1.48599i
$122$		0			0
$123$	0.408378	−	0.342670i	0.0368222	−	0.0308975i
$124$		0			0
$125$	−10.4047	−	6.00718i	−0.930629	−	0.537299i
$126$		0			0
$127$	−1.92172	−	0.699449i	−0.170525	−	0.0620660i	0.255347	−	0.966850i	$-0.417810\pi$
$127$	−1.92172	−	0.699449i	−0.170525	−	0.0620660i	−0.425872	+	0.904783i	$0.640033\pi$
$128$		0			0
$129$	−1.63009	+	1.94267i	−0.143521	+	0.171042i
$130$		0			0
$131$	19.0577	−	3.36038i	1.66508	−	0.293598i	0.739782	−	0.672846i	$-0.234928\pi$
$131$	19.0577	−	3.36038i	1.66508	−	0.293598i	0.925295	+	0.379248i	$0.123817\pi$
$132$		0			0
$133$	−2.30816	+	6.34163i	−0.200143	+	0.549889i
$134$		0			0
$135$	−10.9211	−	1.92568i	−0.939935	−	0.165736i
$136$		0			0
$137$	8.52635	+	14.7681i	0.728456	+	1.26172i	0.957536	+	0.288314i	$0.0930948\pi$
$137$	8.52635	+	14.7681i	0.728456	+	1.26172i	−0.229080	+	0.973408i	$0.573572\pi$
$138$		0			0
$139$	1.47009	+	8.33729i	0.124691	+	0.707160i	0.981491	+	0.191510i	$0.0613384\pi$
$139$	1.47009	+	8.33729i	0.124691	+	0.707160i	−0.856799	+	0.515650i	$0.827551\pi$
$140$		0			0
$141$	2.00342	−	0.729186i	0.168719	−	0.0614086i
$142$		0			0
$143$	2.86322	+	7.86664i	0.239435	+	0.657841i
$144$		0			0
$145$	0.215448	+	0.180782i	0.0178919	+	0.0150131i
$146$		0			0
$147$	4.03483			0.332787
$148$		0			0
$149$	8.48511			0.695128			0.347564	−	0.937656i	$-0.387009\pi$
$149$	8.48511			0.695128			0.347564	+	0.937656i	$0.387009\pi$
$150$		0			0
$151$	9.09996	+	7.63577i	0.740544	+	0.621391i	0.932984	−	0.359918i	$-0.117195\pi$
$151$	9.09996	+	7.63577i	0.740544	+	0.621391i	−0.192439	+	0.981309i	$0.561640\pi$
$152$		0			0
$153$	0.386355	+	1.06150i	0.0312349	+	0.0858173i
$154$		0			0
$155$	6.31877	−	2.29984i	0.507536	−	0.184728i
$156$		0			0
$157$	3.91222	+	22.1873i	0.312230	+	1.77074i	0.587351	+	0.809332i	$0.300171\pi$
$157$	3.91222	+	22.1873i	0.312230	+	1.77074i	−0.275122	+	0.961409i	$0.588718\pi$
$158$		0			0
$159$	−4.61665	−	7.99628i	−0.366125	−	0.634146i
$160$		0			0
$161$	10.9933	+	1.93841i	0.866392	+	0.152768i
$162$		0			0
$163$	6.68120	−	18.3564i	0.523312	−	1.43779i	−0.343501	−	0.939152i	$-0.611613\pi$
$163$	6.68120	−	18.3564i	0.523312	−	1.43779i	0.866812	−	0.498635i	$-0.166165\pi$
$164$		0			0
$165$	−13.5637	+	2.39165i	−1.05593	+	0.186190i
$166$		0			0
$167$	9.74390	−	11.6123i	0.754006	−	0.898589i	−0.243447	−	0.969914i	$-0.578278\pi$
$167$	9.74390	−	11.6123i	0.754006	−	0.898589i	0.997453	+	0.0713251i	$0.0227228\pi$
$168$		0			0
$169$	−10.0116	−	3.64393i	−0.770123	−	0.280302i
$170$		0			0
$171$	−2.56471	−	1.48074i	−0.196128	−	0.113235i
$172$		0			0
$173$	6.01265	−	5.04521i	0.457133	−	0.383580i	−0.384942	−	0.922941i	$-0.625778\pi$
$173$	6.01265	−	5.04521i	0.457133	−	0.383580i	0.842075	+	0.539361i	$0.181334\pi$
$174$		0			0
$175$	−1.64294	+	2.84566i	−0.124195	+	0.215112i
$176$		0			0
$177$	11.6960	−	6.75271i	0.879128	−	0.507565i
$178$		0			0
$179$			3.28655i			0.245648i	0.992428	+	0.122824i	$0.0391951\pi$
$179$			3.28655i			0.245648i	−0.992428	+	0.122824i	$0.960805\pi$
$180$		0			0
$181$	3.52659	−	20.0003i	0.262129	−	1.48661i	−0.514959	−	0.857215i	$-0.672193\pi$
$181$	3.52659	−	20.0003i	0.262129	−	1.48661i	0.777088	−	0.629392i	$-0.216696\pi$
$182$		0			0
$183$	9.36749	+	11.1637i	0.692465	+	0.825247i
$184$		0			0
$185$	10.9772	−	5.13963i	0.807061	−	0.377873i
$186$		0			0
$187$	2.83308	+	3.37634i	0.207176	+	0.246902i
$188$		0			0
$189$	−3.08498	+	17.4958i	−0.224399	+	1.27263i
$190$		0			0
$191$			8.10362i			0.586357i	0.956058	+	0.293179i	$0.0947131\pi$
$191$			8.10362i			0.586357i	−0.956058	+	0.293179i	$0.905287\pi$
$192$		0			0
$193$	5.43147	−	3.13586i	0.390966	−	0.225724i	−0.291613	−	0.956536i	$-0.594192\pi$
$193$	5.43147	−	3.13586i	0.390966	−	0.225724i	0.682579	+	0.730812i	$0.260859\pi$
$194$		0			0
$195$	−1.92974	+	3.34240i	−0.138191	+	0.239354i
$196$		0			0
$197$	3.58285	−	3.00637i	0.255268	−	0.214195i	−0.506169	−	0.862434i	$-0.668939\pi$
$197$	3.58285	−	3.00637i	0.255268	−	0.214195i	0.761437	+	0.648239i	$0.224494\pi$
$198$		0			0
$199$	−16.7401	−	9.66490i	−1.18667	−	0.685126i	−0.229125	−	0.973397i	$-0.573586\pi$
$199$	−16.7401	−	9.66490i	−1.18667	−	0.685126i	−0.957549	+	0.288271i	$0.906920\pi$
$200$		0			0
$201$	9.17766	+	3.34040i	0.647342	+	0.235613i
$202$		0			0
$203$	0.289617	−	0.345152i	0.0203271	−	0.0242249i
$204$		0			0
$205$	−0.827273	+	0.145871i	−0.0577793	+	0.0101880i
$206$		0			0
$207$	−1.67541	+	4.60314i	−0.116449	+	0.319940i
$208$		0			0
$209$	−11.3793	−	2.00648i	−0.787124	−	0.138791i
$210$		0			0
$211$	5.13734	+	8.89813i	0.353669	+	0.612573i	0.986889	−	0.161399i	$-0.0516006\pi$
$211$	5.13734	+	8.89813i	0.353669	+	0.612573i	−0.633220	+	0.773972i	$0.718267\pi$
$212$		0			0
$213$	−1.94607	−	11.0367i	−0.133343	−	0.756223i
$214$		0			0
$215$	3.75508	−	1.36674i	0.256094	−	0.0932106i
$216$		0			0
$217$	−3.68440	−	10.1228i	−0.250114	−	0.687182i
$218$		0			0
$219$	−8.49998	−	7.13233i	−0.574375	−	0.481958i
$220$		0			0
$221$	1.23507			0.0830801
$222$		0			0
$223$	−14.0167			−0.938628			−0.469314	−	0.883031i	$-0.655499\pi$
$223$	−14.0167			−0.938628			−0.469314	+	0.883031i	$0.655499\pi$
$224$		0			0
$225$	−1.10458	−	0.926857i	−0.0736390	−	0.0617904i
$226$		0			0
$227$	−1.16095	−	3.18969i	−0.0770552	−	0.211707i	0.895184	−	0.445697i	$-0.147044\pi$
$227$	−1.16095	−	3.18969i	−0.0770552	−	0.211707i	−0.972239	+	0.233990i	$0.924822\pi$
$228$		0			0
$229$	2.11117	−	0.768402i	0.139510	−	0.0507774i	−0.271322	−	0.962489i	$-0.587461\pi$
$229$	2.11117	−	0.768402i	0.139510	−	0.0507774i	0.410831	+	0.911711i	$0.365238\pi$
$230$		0			0
$231$	3.83148	+	21.7294i	0.252093	+	1.42969i
$232$		0			0
$233$	−5.01753	−	8.69062i	−0.328709	−	0.569341i	0.653547	−	0.756886i	$-0.273280\pi$
$233$	−5.01753	−	8.69062i	−0.328709	−	0.569341i	−0.982256	+	0.187545i	$0.939947\pi$
$234$		0			0
$235$	−3.30847	−	0.583372i	−0.215821	−	0.0380550i
$236$		0			0
$237$	1.95267	−	5.36491i	0.126839	−	0.348489i
$238$		0			0
$239$	−0.0459930	+	0.00810981i	−0.00297504	+	0.000524580i	−0.175136	−	0.984544i	$-0.556036\pi$
$239$	−0.0459930	+	0.00810981i	−0.00297504	+	0.000524580i	0.172160	+	0.985069i	$0.444925\pi$
$240$		0			0
$241$	0.670857	−	0.799496i	0.0432137	−	0.0515000i	−0.744005	−	0.668174i	$-0.767076\pi$
$241$	0.670857	−	0.799496i	0.0432137	−	0.0515000i	0.787218	+	0.616674i	$0.211520\pi$
$242$		0			0
$243$	−12.3198	−	4.48406i	−0.790318	−	0.287652i
$244$		0			0
$245$	−5.50611	−	3.17895i	−0.351772	−	0.203096i
$246$		0			0
$247$	−2.48039	+	2.08129i	−0.157823	+	0.132430i
$248$		0			0
$249$	−6.62597	+	11.4765i	−0.419904	+	0.727295i
$250$		0			0
$251$	3.41584	−	1.97214i	0.215606	−	0.124480i	−0.388308	−	0.921530i	$-0.626940\pi$
$251$	3.41584	−	1.97214i	0.215606	−	0.124480i	0.603914	+	0.797050i	$0.293607\pi$
$252$		0			0
$253$			19.1129i			1.20162i
$254$		0			0
$255$	−0.352848	+	2.00110i	−0.0220962	+	0.125314i
$256$		0			0
$257$	−10.7236	−	12.7799i	−0.668918	−	0.797186i	0.319718	−	0.947513i	$-0.396412\pi$
$257$	−10.7236	−	12.7799i	−0.668918	−	0.797186i	−0.988636	+	0.150327i	$0.951967\pi$
$258$		0			0
$259$	−8.23381	−	17.5858i	−0.511624	−	1.09273i
$260$		0			0
$261$	0.127092	+	0.151462i	0.00786677	+	0.00937525i
$262$		0			0
$263$	2.41429	−	13.6921i	0.148872	−	0.844292i	−0.815305	−	0.579032i	$-0.803431\pi$
$263$	2.41429	−	13.6921i	0.148872	−	0.844292i	0.964177	−	0.265261i	$-0.0854581\pi$
$264$		0			0
$265$			14.5494i			0.893765i
$266$		0			0
$267$	2.92716	−	1.69000i	0.179139	−	0.103426i
$268$		0			0
$269$	3.35403	−	5.80935i	0.204499	−	0.354202i	−0.745474	−	0.666535i	$-0.767777\pi$
$269$	3.35403	−	5.80935i	0.204499	−	0.354202i	0.949973	+	0.312332i	$0.101110\pi$
$270$		0			0
$271$	−3.46200	+	2.90496i	−0.210302	+	0.176464i	−0.741854	−	0.670561i	$-0.766053\pi$
$271$	−3.46200	+	2.90496i	−0.210302	+	0.176464i	0.531552	+	0.847025i	$0.321609\pi$
$272$		0			0
$273$	5.35461	+	3.09149i	0.324076	+	0.187105i
$274$		0			0
$275$	−5.28674	−	1.92422i	−0.318803	−	0.116035i
$276$		0			0
$277$	5.61647	−	6.69345i	0.337461	−	0.402170i	−0.570451	−	0.821332i	$-0.693231\pi$
$277$	5.61647	−	6.69345i	0.337461	−	0.402170i	0.907912	+	0.419161i	$0.137676\pi$
$278$		0			0
$279$	4.65543	−	0.820877i	0.278713	−	0.0491446i
$280$		0			0
$281$	0.335767	−	0.922512i	0.0200302	−	0.0550324i	−0.929275	−	0.369390i	$-0.879567\pi$
$281$	0.335767	−	0.922512i	0.0200302	−	0.0550324i	0.949305	+	0.314357i	$0.101789\pi$
$282$		0			0
$283$	6.22077	+	1.09689i	0.369786	+	0.0652033i	0.355453	−	0.934694i	$-0.384326\pi$
$283$	6.22077	+	1.09689i	0.369786	+	0.0652033i	0.0143328	+	0.999897i	$0.495438\pi$
$284$		0			0
$285$	−2.66354	−	4.61339i	−0.157775	−	0.273274i
$286$		0			0
$287$	0.233688	+	1.32531i	0.0137942	+	0.0782307i
$288$		0			0
$289$	−15.3637	+	5.59194i	−0.903749	+	0.328938i
$290$		0			0
$291$	−6.67629	−	18.3430i	−0.391371	−	1.07528i
$292$		0			0
$293$	−3.33190	−	2.79580i	−0.194652	−	0.163332i	0.540253	−	0.841503i	$-0.318329\pi$
$293$	−3.33190	−	2.79580i	−0.194652	−	0.163332i	−0.734904	+	0.678171i	$0.762773\pi$
$294$		0			0
$295$	−21.2812			−1.23904
$296$		0			0
$297$	−30.4181			−1.76504
$298$		0			0
$299$	4.10280	+	3.44266i	0.237271	+	0.199094i
$300$		0			0
$301$	−2.18954	−	6.01572i	−0.126203	−	0.346740i
$302$		0			0
$303$	19.8188	−	7.21345i	1.13856	−	0.414402i
$304$		0			0
$305$	−3.98763	−	22.6150i	−0.228331	−	1.29493i
$306$		0			0
$307$	−8.24984	−	14.2892i	−0.470844	−	0.815525i	0.528600	−	0.848871i	$-0.322717\pi$
$307$	−8.24984	−	14.2892i	−0.470844	−	0.815525i	−0.999444	+	0.0333459i	$0.989384\pi$
$308$		0			0
$309$	−5.48044	−	0.966350i	−0.311771	−	0.0549737i
$310$		0			0
$311$	7.85426	−	21.5794i	0.445374	−	1.22366i	−0.490537	−	0.871420i	$-0.663199\pi$
$311$	7.85426	−	21.5794i	0.445374	−	1.22366i	0.935912	−	0.352235i	$-0.114578\pi$
$312$		0			0
$313$	31.3739	−	5.53206i	1.77336	−	0.312691i	0.811115	−	0.584887i	$-0.198861\pi$
$313$	31.3739	−	5.53206i	1.77336	−	0.312691i	0.962242	+	0.272196i	$0.0877499\pi$
$314$		0			0
$315$	5.72789	−	6.82624i	0.322730	−	0.384615i
$316$		0			0
$317$	−8.34465	−	3.03720i	−0.468682	−	0.170586i	0.0968731	−	0.995297i	$-0.469116\pi$
$317$	−8.34465	−	3.03720i	−0.468682	−	0.170586i	−0.565555	+	0.824710i	$0.691338\pi$
$318$		0			0
$319$	0.668093	+	0.385724i	0.0374060	+	0.0215964i
$320$		0			0
$321$	−8.20949	+	6.88858i	−0.458209	+	0.384483i
$322$		0			0
$323$	−0.852363	+	1.47634i	−0.0474267	+	0.0821455i
$324$		0			0
$325$	−1.36532	+	0.788267i	−0.0757343	+	0.0437252i
$326$		0			0
$327$		−	13.0041i		−	0.719131i
$328$		0			0
$329$	−0.934576	+	5.30025i	−0.0515249	+	0.292212i
$330$		0			0
$331$	−9.58689	−	11.4252i	−0.526943	−	0.627986i	0.435265	−	0.900302i	$-0.356655\pi$
$331$	−9.58689	−	11.4252i	−0.526943	−	0.627986i	−0.962208	+	0.272316i	$0.912210\pi$
$332$		0			0
$333$	8.22728	−	2.21826i	0.450852	−	0.121560i
$334$		0			0
$335$	−9.89242	−	11.7893i	−0.540480	−	0.644120i
$336$		0			0
$337$	5.18509	−	29.4061i	0.282450	−	1.60185i	−0.431806	−	0.901966i	$-0.642124\pi$
$337$	5.18509	−	29.4061i	0.282450	−	1.60185i	0.714256	−	0.699885i	$-0.246765\pi$
$338$		0			0
$339$			14.5146i			0.788325i
$340$		0			0
$341$	15.9733	−	9.22222i	0.865005	−	0.499411i
$342$		0			0
$343$	6.08023	−	10.5313i	0.328302	−	0.568635i
$344$		0			0
$345$	−6.75001	+	5.66393i	−0.363408	+	0.304936i
$346$		0			0
$347$	5.67160	+	3.27450i	0.304467	+	0.175784i	0.644448	−	0.764648i	$-0.277087\pi$
$347$	5.67160	+	3.27450i	0.304467	+	0.175784i	−0.339981	+	0.940432i	$0.610421\pi$
$348$		0			0
$349$	−29.2299	−	10.6388i	−1.56464	−	0.569483i	−0.592848	−	0.805314i	$-0.701997\pi$
$349$	−29.2299	−	10.6388i	−1.56464	−	0.569483i	−0.971794	+	0.235831i	$0.924219\pi$
$350$		0			0
$351$	−5.47899	+	6.52961i	−0.292447	+	0.348525i
$352$		0			0
$353$	−18.9726	+	3.34538i	−1.00981	+	0.178056i	−0.653994	−	0.756500i	$-0.726908\pi$
$353$	−18.9726	+	3.34538i	−1.00981	+	0.178056i	−0.355815	+	0.934556i	$0.615797\pi$
$354$		0			0
$355$	−6.03988	+	16.5944i	−0.320564	+	0.880742i
$356$		0			0
$357$	3.20581	+	0.565270i	0.169669	+	0.0299173i
$358$		0			0
$359$	6.15563	+	10.6619i	0.324882	+	0.562712i	0.981488	−	0.191521i	$-0.0613422\pi$
$359$	6.15563	+	10.6619i	0.324882	+	0.562712i	−0.656607	+	0.754233i	$0.728009\pi$
$360$		0			0
$361$	2.52325	+	14.3101i	0.132803	+	0.753161i
$362$		0			0
$363$	−22.4289	+	8.16344i	−1.17721	+	0.428469i
$364$		0			0
$365$	5.98004	+	16.4300i	0.313010	+	0.859987i
$366$		0			0
$367$	20.8149	+	17.4658i	1.08653	+	0.911707i	0.996447	−	0.0842269i	$-0.0268420\pi$
$367$	20.8149	+	17.4658i	1.08653	+	0.911707i	0.0900839	+	0.995934i	$0.471286\pi$
$368$		0			0
$369$	−0.590553			−0.0307430
$370$		0			0
$371$	23.3085			1.21012
$372$		0			0
$373$	6.53564	+	5.48405i	0.338403	+	0.283954i	0.796113	−	0.605148i	$-0.206886\pi$
$373$	6.53564	+	5.48405i	0.338403	+	0.283954i	−0.457711	+	0.889101i	$0.651330\pi$
$374$		0			0
$375$	−5.19632	−	14.2768i	−0.268337	−	0.737250i
$376$		0			0
$377$	0.203139	−	0.0739366i	0.0104622	−	0.00380793i
$378$		0			0
$379$	−0.430632	−	2.44224i	−0.0221201	−	0.125449i	0.971748	−	0.236020i	$-0.0758432\pi$
$379$	−0.430632	−	2.44224i	−0.0221201	−	0.125449i	−0.993868	+	0.110571i	$0.964732\pi$
$380$		0			0
$381$	−1.29306	−	2.23964i	−0.0662453	−	0.114740i
$382$		0			0
$383$	8.54812	+	1.50726i	0.436789	+	0.0770176i	0.387719	−	0.921778i	$-0.373263\pi$
$383$	8.54812	+	1.50726i	0.436789	+	0.0770176i	0.0490699	+	0.998795i	$0.484374\pi$
$384$		0			0
$385$	11.8915	−	32.6716i	0.606047	−	1.66510i
$386$		0			0
$387$	2.76660	−	0.487826i	0.140634	−	0.0247976i
$388$		0			0
$389$	19.5961	−	23.3537i	0.993561	−	1.18408i	0.0106603	−	0.999943i	$-0.496607\pi$
$389$	19.5961	−	23.3537i	0.993561	−	1.18408i	0.982901	−	0.184137i	$-0.0589489\pi$
$390$		0			0
$391$	2.64973	+	0.964422i	0.134002	+	0.0487729i
$392$		0			0
$393$	21.1930	+	12.2358i	1.06905	+	0.617214i
$394$		0			0
$395$	−6.89159	+	5.78273i	−0.346754	+	0.290961i
$396$		0			0
$397$	1.48812	−	2.57749i	0.0746865	−	0.129361i	−0.826263	−	0.563284i	$-0.809538\pi$
$397$	1.48812	−	2.57749i	0.0746865	−	0.129361i	0.900950	+	0.433923i	$0.142871\pi$
$398$		0			0
$399$	−7.39076	+	4.26706i	−0.370001	+	0.213620i
$400$		0			0
$401$		−	14.5237i		−	0.725279i	−0.931930	−	0.362639i	$-0.881876\pi$
$401$		−	14.5237i		−	0.725279i	0.931930	−	0.362639i	$-0.118124\pi$
$402$		0			0
$403$	0.897505	−	5.09000i	0.0447079	−	0.253551i
$404$		0			0
$405$	−3.63126	−	4.32757i	−0.180439	−	0.215039i
$406$		0			0
$407$	27.2045	−	19.1122i	1.34848	−	0.947354i
$408$		0			0
$409$	18.9147	+	22.5417i	0.935272	+	1.11461i	0.993215	+	0.116294i	$0.0371014\pi$
$409$	18.9147	+	22.5417i	0.935272	+	1.11461i	−0.0579428	+	0.998320i	$0.518454\pi$
$410$		0			0
$411$	−3.74462	+	21.2368i	−0.184708	+	1.04753i
$412$		0			0
$413$			34.0931i			1.67761i
$414$		0			0
$415$	18.0842	−	10.4409i	0.887717	−	0.512524i
$416$		0			0
$417$	−5.35287	+	9.27145i	−0.262131	+	0.454025i
$418$		0			0
$419$	−26.4711	+	22.2119i	−1.29320	+	1.08512i	−0.301921	+	0.953333i	$0.597628\pi$
$419$	−26.4711	+	22.2119i	−1.29320	+	1.08512i	−0.991278	+	0.131789i	$0.957928\pi$
$420$		0			0
$421$	−1.37981	−	0.796635i	−0.0672480	−	0.0388256i	0.465999	−	0.884785i	$-0.345695\pi$
$421$	−1.37981	−	0.796635i	−0.0672480	−	0.0388256i	−0.533247	+	0.845960i	$0.679028\pi$
$422$		0			0
$423$	−2.21933	−	0.807772i	−0.107908	−	0.0392752i
$424$		0			0
$425$	−0.533531	+	0.635837i	−0.0258801	+	0.0308426i
$426$		0			0
$427$	−36.2297	+	6.38827i	−1.75328	+	0.309150i
$428$		0			0
$429$	−3.62075	+	9.94793i	−0.174812	+	0.480291i
$430$		0			0
$431$	15.9475	+	2.81198i	0.768165	+	0.135448i	0.543980	−	0.839098i	$-0.316917\pi$
$431$	15.9475	+	2.81198i	0.768165	+	0.135448i	0.224185	+	0.974547i	$0.428028\pi$
$432$		0			0
$433$	10.7421	+	18.6058i	0.516231	+	0.894139i	0.999822	+	0.0188448i	$0.00599884\pi$
$433$	10.7421	+	18.6058i	0.516231	+	0.894139i	−0.483591	+	0.875294i	$0.660668\pi$
$434$		0			0
$435$	0.0617592	+	0.350254i	0.00296113	+	0.0167934i
$436$		0			0
$437$	−6.94663	+	2.52837i	−0.332302	+	0.120948i
$438$		0			0
$439$	0.818338	+	2.24837i	0.0390572	+	0.107309i	0.957688	−	0.287808i	$-0.0929264\pi$
$439$	0.818338	+	2.24837i	0.0390572	+	0.107309i	−0.918631	+	0.395116i	$0.870704\pi$
$440$		0			0
$441$	−3.42397	−	2.87305i	−0.163046	−	0.136812i
$442$		0			0
$443$	−6.54020			−0.310734			−0.155367	−	0.987857i	$-0.549656\pi$
$443$	−6.54020			−0.310734			−0.155367	+	0.987857i	$0.549656\pi$
$444$		0			0
$445$	−5.32604			−0.252478
$446$		0			0
$447$	8.21969	+	6.89714i	0.388778	+	0.326223i
$448$		0			0
$449$	−13.2795	−	36.4852i	−0.626699	−	1.72184i	−0.689964	−	0.723844i	$-0.742373\pi$
$449$	−13.2795	−	36.4852i	−0.626699	−	1.72184i	0.0632647	−	0.997997i	$-0.479849\pi$
$450$		0			0
$451$	−2.16522	+	0.788076i	−0.101956	+	0.0371090i
$452$		0			0
$453$	2.60855	+	14.7938i	0.122560	+	0.695075i
$454$		0			0
$455$	−4.87142	−	8.43755i	−0.228376	−	0.395559i
$456$		0			0
$457$	15.0919	+	2.66111i	0.705969	+	0.124481i	0.515095	−	0.857133i	$-0.327757\pi$
$457$	15.0919	+	2.66111i	0.705969	+	0.124481i	0.190874	+	0.981615i	$0.438868\pi$
$458$		0			0
$459$	−1.53488	+	4.21704i	−0.0716419	+	0.196835i
$460$		0			0
$461$	−15.9863	+	2.81882i	−0.744557	+	0.131285i	−0.533041	−	0.846089i	$-0.678951\pi$
$461$	−15.9863	+	2.81882i	−0.744557	+	0.131285i	−0.211516	+	0.977375i	$0.567840\pi$
$462$		0			0
$463$	5.36317	−	6.39158i	0.249248	−	0.297042i	−0.626885	−	0.779112i	$-0.715670\pi$
$463$	5.36317	−	6.39158i	0.249248	−	0.297042i	0.876133	+	0.482070i	$0.160115\pi$
$464$		0			0
$465$	7.99054	+	2.90832i	0.370552	+	0.134870i
$466$		0			0
$467$	5.78049	+	3.33737i	0.267489	+	0.154435i	0.627746	−	0.778418i	$-0.283978\pi$
$467$	5.78049	+	3.33737i	0.267489	+	0.154435i	−0.360257	+	0.932853i	$0.617311\pi$
$468$		0			0
$469$	−18.8868	+	15.8479i	−0.872110	+	0.731788i
$470$		0			0
$471$	−14.2452	+	24.6733i	−0.656382	+	1.13689i
$472$		0			0
$473$	9.49254	−	5.48052i	0.436467	−	0.251995i
$474$		0			0
$475$		−	2.17603i		−	0.0998431i
$476$		0			0
$477$	−1.77614	+	10.0730i	−0.0813240	+	0.461211i
$478$		0			0
$479$	−22.6567	−	27.0012i	−1.03521	−	1.23372i	−0.971819	−	0.235729i	$-0.924252\pi$
$479$	−22.6567	−	27.0012i	−1.03521	−	1.23372i	−0.0633927	−	0.997989i	$-0.520192\pi$
$480$		0			0
$481$	0.797502	−	9.28231i	0.0363630	−	0.423237i
$482$		0			0
$483$	9.07375	+	10.8137i	0.412870	+	0.492039i
$484$		0			0
$485$	−5.34125	+	30.2917i	−0.242533	+	1.37548i
$486$		0			0
$487$		−	7.27548i		−	0.329683i	−0.986320	−	0.164842i	$-0.947289\pi$
$487$		−	7.27548i		−	0.329683i	0.986320	−	0.164842i	$-0.0527113\pi$
$488$		0			0
$489$	21.3933	−	12.3514i	0.967436	−	0.558550i
$490$		0			0
$491$	−11.2013	+	19.4012i	−0.505506	+	0.875562i	0.494474	+	0.869193i	$0.335361\pi$
$491$	−11.2013	+	19.4012i	−0.505506	+	0.875562i	−0.999980	+	0.00636940i	$0.997973\pi$
$492$		0			0
$493$	0.0871867	−	0.0731583i	0.00392669	−	0.00329488i
$494$		0			0
$495$	13.2132	+	7.62864i	0.593889	+	0.342882i
$496$		0			0
$497$	26.5847	+	9.67604i	1.19249	+	0.434030i
$498$		0			0
$499$	14.4636	−	17.2370i	0.647478	−	0.771634i	−0.338054	−	0.941127i	$-0.609769\pi$
$499$	14.4636	−	17.2370i	0.647478	−	0.771634i	0.985531	+	0.169493i	$0.0542130\pi$
$500$		0			0
$501$	18.8782	−	3.32874i	0.843416	−	0.148717i
$502$		0			0
$503$	−9.70488	+	26.6639i	−0.432719	+	1.18889i	0.511417	+	0.859332i	$0.329121\pi$
$503$	−9.70488	+	26.6639i	−0.432719	+	1.18889i	−0.944137	+	0.329554i	$0.893102\pi$
$504$		0			0
$505$	−32.7289	−	5.77099i	−1.45642	−	0.256806i
$506$		0			0
$507$	−6.73646	−	11.6679i	−0.299177	−	0.518189i
$508$		0			0
$509$	0.834169	+	4.73081i	0.0369739	+	0.209689i	0.997698	−	0.0678167i	$-0.0216033\pi$
$509$	0.834169	+	4.73081i	0.0369739	+	0.209689i	−0.960724	+	0.277506i	$0.910492\pi$
$510$		0			0
$511$	26.3213	−	9.58017i	1.16439	−	0.423802i
$512$		0			0
$513$	−4.02389	−	11.0556i	−0.177659	−	0.488115i
$514$		0			0
$515$	6.71749	+	5.63664i	0.296008	+	0.248380i
$516$		0			0
$517$	−9.21498			−0.405274
$518$		0			0
$519$	9.92557			0.435684
$520$		0			0
$521$	−7.02658	−	5.89600i	−0.307840	−	0.258309i	0.475758	−	0.879576i	$-0.342174\pi$
$521$	−7.02658	−	5.89600i	−0.307840	−	0.258309i	−0.783599	+	0.621267i	$0.786618\pi$
$522$		0			0
$523$	3.70717	+	10.1854i	0.162103	+	0.445375i	0.993977	−	0.109590i	$-0.0349538\pi$
$523$	3.70717	+	10.1854i	0.162103	+	0.445375i	−0.831874	+	0.554965i	$0.812732\pi$
$524$		0			0
$525$	−3.90465	+	1.42118i	−0.170413	+	0.0620252i
$526$		0			0
$527$	−0.472526	−	2.67983i	−0.0205835	−	0.116735i
$528$		0			0
$529$	−5.38609	−	9.32898i	−0.234178	−	0.405608i
$530$		0			0
$531$	−14.7336	−	2.59794i	−0.639385	−	0.112741i
$532$		0			0
$533$	−0.220836	+	0.606741i	−0.00956545	+	0.0262809i
$534$		0			0
$535$	16.6304	−	2.93239i	0.718994	−	0.126778i
$536$		0			0
$537$	−2.67148	+	3.18374i	−0.115283	+	0.137389i
$538$		0			0
$539$	−16.3877	−	5.96464i	−0.705869	−	0.256915i
$540$		0			0
$541$	5.20115	+	3.00288i	0.223615	+	0.129104i	0.607623	−	0.794226i	$-0.292123\pi$
$541$	5.20115	+	3.00288i	0.223615	+	0.129104i	−0.384008	+	0.923330i	$0.625457\pi$
$542$		0			0
$543$	19.6735	−	16.5080i	0.844271	−	0.708427i
$544$		0			0
$545$	−10.2457	+	17.7460i	−0.438876	+	0.760156i
$546$		0			0
$547$	−36.1860	+	20.8920i	−1.54720	+	0.893276i	−0.548846	+	0.835924i	$0.684933\pi$
$547$	−36.1860	+	20.8920i	−1.54720	+	0.893276i	−0.998354	+	0.0573527i	$0.981734\pi$
$548$		0			0
$549$		−	16.1438i		−	0.689000i
$550$		0			0
$551$	−0.0518131	+	0.293846i	−0.00220731	+	0.0125183i
$552$		0			0
$553$	9.26408	+	11.0405i	0.393949	+	0.469490i
$554$		0			0
$555$	14.8116	+	3.94399i	0.628717	+	0.167413i
$556$		0			0
$557$	5.05953	+	6.02971i	0.214379	+	0.255487i	0.862508	−	0.506044i	$-0.168893\pi$
$557$	5.05953	+	6.02971i	0.214379	+	0.255487i	−0.648129	+	0.761531i	$0.724448\pi$
$558$		0			0
$559$	0.533363	−	3.02485i	0.0225589	−	0.127938i
$560$		0			0
$561$			5.57360i			0.235317i
$562$		0			0
$563$	20.1096	−	11.6103i	0.847517	−	0.489314i	−0.0122951	−	0.999924i	$-0.503914\pi$
$563$	20.1096	−	11.6103i	0.847517	−	0.489314i	0.859812	+	0.510610i	$0.170580\pi$
$564$		0			0
$565$	11.4357	−	19.8073i	0.481104	−	0.833297i
$566$		0			0
$567$	−6.93287	+	5.81737i	−0.291153	+	0.244306i
$568$		0			0
$569$	35.3242	+	20.3944i	1.48087	+	0.854978i	0.999765	−	0.0216869i	$-0.00690369\pi$
$569$	35.3242	+	20.3944i	1.48087	+	0.854978i	0.481101	+	0.876665i	$0.340237\pi$
$570$		0			0
$571$	33.6112	+	12.2335i	1.40658	+	0.511954i	0.930125	−	0.367243i	$-0.119698\pi$
$571$	33.6112	+	12.2335i	1.40658	+	0.511954i	0.476458	+	0.879197i	$0.341920\pi$
$572$		0			0
$573$	−6.58704	+	7.85013i	−0.275177	+	0.327944i
$574$		0			0
$575$	−3.54468	+	0.625023i	−0.147823	+	0.0260653i
$576$		0			0
$577$	3.63320	−	9.98213i	0.151252	−	0.415561i	−0.840807	−	0.541335i	$-0.817919\pi$
$577$	3.63320	−	9.98213i	0.151252	−	0.415561i	0.992059	+	0.125774i	$0.0401413\pi$
$578$		0			0
$579$	7.81055	+	1.37721i	0.324596	+	0.0572350i
$580$		0			0
$581$	−16.7266	−	28.9713i	−0.693935	−	1.20193i
$582$		0			0
$583$	6.93003	+	39.3021i	0.287012	+	1.62773i
$584$		0			0
$585$	4.01758	−	1.46228i	0.166106	−	0.0604578i
$586$		0			0
$587$	−3.49256	−	9.59573i	−0.144153	−	0.396058i	0.846513	−	0.532368i	$-0.178698\pi$
$587$	−3.49256	−	9.59573i	−0.144153	−	0.396058i	−0.990666	+	0.136310i	$0.956476\pi$
$588$		0			0
$589$	5.46490	+	4.58559i	0.225177	+	0.188946i
$590$		0			0
$591$	5.91451			0.243290
$592$		0			0
$593$	−9.92034			−0.407380			−0.203690	−	0.979035i	$-0.565293\pi$
$593$	−9.92034			−0.407380			−0.203690	+	0.979035i	$0.565293\pi$
$594$		0			0
$595$	−3.92942	−	3.29718i	−0.161091	−	0.135171i
$596$		0			0
$597$	−8.36031	−	22.9698i	−0.342165	−	0.940090i
$598$		0			0
$599$	16.4377	−	5.98284i	0.671627	−	0.244452i	0.0163788	−	0.999866i	$-0.494786\pi$
$599$	16.4377	−	5.98284i	0.671627	−	0.244452i	0.655248	+	0.755414i	$0.272564\pi$
$600$		0			0
$601$	8.06439	+	45.7354i	0.328953	+	1.86559i	0.480297	+	0.877106i	$0.340529\pi$
$601$	8.06439	+	45.7354i	0.328953	+	1.86559i	−0.151344	+	0.988481i	$0.548360\pi$
$602$		0			0
$603$	−5.40962	−	9.36973i	−0.220297	−	0.381565i
$604$		0			0
$605$	37.0392	+	6.53101i	1.50586	+	0.265523i
$606$		0			0
$607$	−14.1766	+	38.9499i	−0.575411	+	1.58093i	0.220417	+	0.975406i	$0.429258\pi$
$607$	−14.1766	+	38.9499i	−0.575411	+	1.58093i	−0.795828	+	0.605523i	$0.792964\pi$
$608$		0			0
$609$	0.561115	−	0.0989397i	0.0227375	−	0.00400924i
$610$		0			0
$611$	−1.65983	+	1.97811i	−0.0671494	+	0.0800256i
$612$		0			0
$613$	−24.4090	−	8.88414i	−0.985869	−	0.358827i	−0.201750	−	0.979437i	$-0.564663\pi$
$613$	−24.4090	−	8.88414i	−0.985869	−	0.358827i	−0.784119	+	0.620610i	$0.786885\pi$
$614$		0			0
$615$	−0.919966	−	0.531143i	−0.0370966	−	0.0214177i
$616$		0			0
$617$	−13.0464	+	10.9472i	−0.525229	+	0.440720i	−0.866450	−	0.499264i	$-0.833604\pi$
$617$	−13.0464	+	10.9472i	−0.525229	+	0.440720i	0.341221	+	0.939983i	$0.389160\pi$
$618$		0			0
$619$	−2.04260	+	3.53788i	−0.0820989	+	0.142199i	−0.904151	−	0.427212i	$-0.859496\pi$
$619$	−2.04260	+	3.53788i	−0.0820989	+	0.142199i	0.822052	+	0.569412i	$0.192829\pi$
$620$		0			0
$621$	−16.8533	+	9.73028i	−0.676301	+	0.390463i
$622$		0			0
$623$			8.53244i			0.341845i
$624$		0			0
$625$	−3.26352	+	18.5084i	−0.130541	+	0.740335i
$626$		0			0
$627$	−9.39239	−	11.1934i	−0.375096	−	0.447022i
$628$		0			0
$629$	−1.27691	−	4.73591i	−0.0509136	−	0.188833i
$630$		0			0
$631$	23.5841	+	28.1064i	0.938867	+	1.11890i	0.992731	+	0.120350i	$0.0384018\pi$
$631$	23.5841	+	28.1064i	0.938867	+	1.11890i	−0.0538642	+	0.998548i	$0.517154\pi$
$632$		0			0
$633$	−2.25622	+	12.7957i	−0.0896768	+	0.508583i
$634$		0			0
$635$			4.07508i			0.161715i
$636$		0			0
$637$	−4.23219	+	2.44345i	−0.167685	+	0.0968131i
$638$		0			0
$639$	−6.20738	+	10.7515i	−0.245560	+	0.425323i
$640$		0			0
$641$	−24.6811	+	20.7099i	−0.974847	+	0.817993i	−0.983304	−	0.181971i	$-0.941752\pi$
$641$	−24.6811	+	20.7099i	−0.974847	+	0.817993i	0.00845730	+	0.999964i	$0.497308\pi$
$642$		0			0
$643$	−19.5344	−	11.2782i	−0.770363	−	0.444769i	0.0626409	−	0.998036i	$-0.480048\pi$
$643$	−19.5344	−	11.2782i	−0.770363	−	0.444769i	−0.833004	+	0.553267i	$0.813381\pi$
$644$		0			0
$645$	4.74857	+	1.72834i	0.186975	+	0.0680532i
$646$		0			0
$647$	5.02992	−	5.99443i	0.197747	−	0.235665i	−0.658054	−	0.752970i	$-0.728620\pi$
$647$	5.02992	−	5.99443i	0.197747	−	0.235665i	0.855801	+	0.517305i	$0.173065\pi$
$648$		0			0
$649$	−57.4867	+	10.1365i	−2.25655	+	0.397891i
$650$		0			0
$651$	4.65920	−	12.8010i	0.182608	−	0.501712i
$652$		0			0
$653$	33.1336	+	5.84235i	1.29662	+	0.228629i	0.779022	−	0.626996i	$-0.215716\pi$
$653$	33.1336	+	5.84235i	1.29662	+	0.228629i	0.517596	+	0.855625i	$0.326827\pi$
$654$		0			0
$655$	−19.2806	−	33.3950i	−0.753356	−	1.30485i
$656$		0			0
$657$	2.13444	+	12.1050i	0.0832725	+	0.472262i
$658$		0			0
$659$	−25.7385	+	9.36806i	−1.00263	+	0.364928i	−0.790598	−	0.612335i	$-0.790230\pi$
$659$	−25.7385	+	9.36806i	−1.00263	+	0.364928i	−0.212032	+	0.977263i	$0.568008\pi$
$660$		0			0
$661$	12.3983	+	34.0640i	0.482237	+	1.32493i	0.907571	+	0.419898i	$0.137934\pi$
$661$	12.3983	+	34.0640i	0.482237	+	1.32493i	−0.425334	+	0.905036i	$0.639844\pi$
$662$		0			0
$663$	1.19644	+	1.00393i	0.0464659	+	0.0389895i
$664$		0			0
$665$	13.4477			0.521479
$666$		0			0
$667$	0.493548			0.0191103
$668$		0			0
$669$	−13.5782	−	11.3935i	−0.524965	−	0.440498i
$670$		0			0
$671$	−21.5434	−	59.1901i	−0.831675	−	2.28501i
$672$		0			0
$673$	11.4951	−	4.18387i	0.443103	−	0.161276i	−0.110827	−	0.993840i	$-0.535350\pi$
$673$	11.4951	−	4.18387i	0.443103	−	0.161276i	0.553930	+	0.832564i	$0.313128\pi$
$674$		0			0
$675$	−0.994724	−	5.64136i	−0.0382869	−	0.217136i
$676$		0			0
$677$	0.924945	+	1.60205i	0.0355485	+	0.0615719i	0.883252	−	0.468898i	$-0.155349\pi$
$677$	0.924945	+	1.60205i	0.0355485	+	0.0615719i	−0.847704	+	0.530470i	$0.822015\pi$
$678$		0			0
$679$	48.5280	+	8.55680i	1.86234	+	0.328380i
$680$		0			0
$681$	1.46811	−	4.03360i	0.0562581	−	0.154568i
$682$		0			0
$683$	−9.88984	+	1.74385i	−0.378424	+	0.0667264i	−0.359625	−	0.933097i	$-0.617095\pi$
$683$	−9.88984	+	1.74385i	−0.378424	+	0.0667264i	−0.0187992	+	0.999823i	$0.505984\pi$
$684$		0			0
$685$	21.8420	−	26.0303i	0.834541	−	0.994568i
$686$		0			0
$687$	2.66972	+	0.971699i	0.101856	+	0.0370726i
$688$		0			0
$689$	9.68493	+	5.59160i	0.368967	+	0.213023i
$690$		0			0
$691$	−5.08725	+	4.26871i	−0.193528	+	0.162389i	−0.734403	−	0.678714i	$-0.762538\pi$
$691$	−5.08725	+	4.26871i	−0.193528	+	0.162389i	0.540875	+	0.841103i	$0.318093\pi$
$692$		0			0
$693$	12.2213	−	21.1679i	0.464248	−	0.804100i
$694$		0			0
$695$	14.6095	−	8.43482i	0.554171	−	0.319951i
$696$		0			0
$697$			0.339943i			0.0128763i
$698$		0			0
$699$	2.20361	−	12.4973i	0.0833481	−	0.472690i
$700$		0			0
$701$	10.4394	+	12.4412i	0.394290	+	0.469897i	0.926270	−	0.376860i	$-0.122996\pi$
$701$	10.4394	+	12.4412i	0.394290	+	0.469897i	−0.531980	+	0.846757i	$0.678552\pi$
$702$		0			0
$703$	10.5452	+	7.35930i	0.397718	+	0.277561i
$704$		0			0
$705$	−2.73078	−	3.25442i	−0.102847	−	0.122568i
$706$		0			0
$707$	−9.24527	+	52.4325i	−0.347704	+	1.97193i
$708$		0			0
$709$		−	18.3839i		−	0.690421i	−0.938525	−	0.345210i	$-0.887808\pi$
$709$		−	18.3839i		−	0.690421i	0.938525	−	0.345210i	$-0.112192\pi$
$710$		0			0
$711$	−5.47719	+	3.16226i	−0.205411	+	0.118594i
$712$		0			0
$713$	5.90009	−	10.2193i	0.220960	−	0.382714i
$714$		0			0
$715$	12.7788	−	10.7227i	0.477900	−	0.401005i
$716$		0			0
$717$	−0.0511464	−	0.0295294i	−0.00191010	−	0.00110279i
$718$		0			0
$719$	−27.7891	−	10.1144i	−1.03636	−	0.377203i	−0.232859	−	0.972511i	$-0.574808\pi$
$719$	−27.7891	−	10.1144i	−1.03636	−	0.377203i	−0.803498	+	0.595307i	$0.797030\pi$
$720$		0			0
$721$	9.03003	−	10.7616i	0.336296	−	0.400782i
$722$		0			0
$723$	1.29974	−	0.229180i	0.0483379	−	0.00852328i
$724$		0			0
$725$	−0.0496888	+	0.136519i	−0.00184539	+	0.00507018i
$726$		0			0
$727$	−9.40598	−	1.65853i	−0.348848	−	0.0615114i	−0.00352135	−	0.999994i	$-0.501121\pi$
$727$	−9.40598	−	1.65853i	−0.348848	−	0.0615114i	−0.345327	+	0.938482i	$0.612232\pi$
$728$		0			0
$729$	−12.5421	−	21.7236i	−0.464524	−	0.804578i
$730$		0			0
$731$	−0.280809	−	1.59255i	−0.0103861	−	0.0589026i
$732$		0			0
$733$	11.7162	−	4.26436i	0.432749	−	0.157508i	−0.116455	−	0.993196i	$-0.537153\pi$
$733$	11.7162	−	4.26436i	0.432749	−	0.157508i	0.549204	+	0.835688i	$0.314931\pi$
$734$		0			0
$735$	−2.74985	−	7.55516i	−0.101430	−	0.278676i
$736$		0			0
$737$	−32.3376	−	27.1345i	−1.19117	−	0.999511i
$738$		0			0
$739$	−42.1916			−1.55204			−0.776022	−	0.630706i	$-0.782765\pi$
$739$	−42.1916			−1.55204			−0.776022	+	0.630706i	$0.782765\pi$
$740$		0			0
$741$	−4.09458			−0.150418
$742$		0			0
$743$	14.1347	+	11.8604i	0.518551	+	0.435116i	0.864126	−	0.503275i	$-0.167872\pi$
$743$	14.1347	+	11.8604i	0.518551	+	0.435116i	−0.345575	+	0.938391i	$0.612316\pi$
$744$		0			0
$745$	−5.78285	−	15.8882i	−0.211867	−	0.582100i
$746$		0			0
$747$	13.7948	−	5.02090i	0.504725	−	0.183705i
$748$		0			0
$749$	−4.69775	−	26.6423i	−0.171652	−	0.973488i
$750$		0			0
$751$	17.8761	+	30.9623i	0.652307	+	1.12983i	0.982562	+	0.185937i	$0.0595321\pi$
$751$	17.8761	+	30.9623i	0.652307	+	1.12983i	−0.330254	+	0.943892i	$0.607135\pi$
$752$		0			0
$753$	4.91204	+	0.866125i	0.179005	+	0.0315633i
$754$		0			0
$755$	8.09598	−	22.2435i	0.294643	−	0.809525i
$756$		0			0
$757$	36.2457	−	6.39109i	1.31737	−	0.232288i	0.529595	−	0.848250i	$-0.322344\pi$
$757$	36.2457	−	6.39109i	1.31737	−	0.232288i	0.787776	+	0.615962i	$0.211233\pi$
$758$		0			0
$759$	−15.5359	+	18.5150i	−0.563918	+	0.672051i
$760$		0			0
$761$	11.1361	+	4.05322i	0.403684	+	0.146929i	0.535879	−	0.844295i	$-0.319980\pi$
$761$	11.1361	+	4.05322i	0.403684	+	0.146929i	−0.132195	+	0.991224i	$0.542202\pi$
$762$		0			0
$763$	28.4296	+	16.4138i	1.02922	+	0.594220i
$764$		0			0
$765$	1.72433	−	1.44689i	0.0623434	−	0.0523123i
$766$		0			0
$767$	−8.17875	+	14.1660i	−0.295318	+	0.511505i
$768$		0			0
$769$	−35.2131	+	20.3303i	−1.26982	+	0.733129i	−0.974953	−	0.222410i	$-0.928607\pi$
$769$	−35.2131	+	20.3303i	−1.26982	+	0.733129i	−0.294863	+	0.955539i	$0.595274\pi$
$770$		0			0
$771$		−	21.0968i		−	0.759781i
$772$		0			0
$773$	−3.57314	+	20.2643i	−0.128517	+	0.728856i	0.850640	+	0.525749i	$0.176215\pi$
$773$	−3.57314	+	20.2643i	−0.128517	+	0.728856i	−0.979157	+	0.203107i	$0.934896\pi$
$774$		0			0
$775$	2.23271	+	2.66084i	0.0802015	+	0.0955804i
$776$		0			0
$777$	6.31837	−	23.7285i	0.226670	−	0.851256i
$778$		0			0
$779$	−0.572857	−	0.682705i	−0.0205247	−	0.0244604i
$780$		0			0
$781$	−8.41135	+	47.7032i	−0.300982	+	1.70695i
$782$		0			0
$783$			0.785482i			0.0280708i
$784$		0			0
$785$	38.8791	−	22.4469i	1.38766	−	0.801163i
$786$		0			0
$787$	10.1490	−	17.5786i	0.361773	−	0.626609i	−0.626480	−	0.779438i	$-0.715505\pi$
$787$	10.1490	−	17.5786i	0.361773	−	0.626609i	0.988253	+	0.152828i	$0.0488382\pi$
$788$		0			0
$789$	13.4684	−	11.3014i	0.479489	−	0.402339i
$790$		0			0
$791$	−31.7317	−	18.3203i	−1.12825	−	0.651395i
$792$		0			0
$793$	−16.5863	−	6.03693i	−0.588997	−	0.214378i
$794$		0			0
$795$	−11.8265	+	14.0943i	−0.419444	+	0.499874i
$796$		0			0
$797$	0.177449	−	0.0312890i	0.00628557	−	0.00110831i	−0.170505	−	0.985357i	$-0.554540\pi$
$797$	0.177449	−	0.0312890i	0.00628557	−	0.00110831i	0.176790	+	0.984249i	$0.443429\pi$
$798$		0			0
$799$	−0.464982	+	1.27753i	−0.0164499	+	0.0451956i
$800$		0			0
$801$	−3.68737	−	0.650184i	−0.130287	−	0.0229731i
$802$		0			0
$803$	23.9796	+	41.5338i	0.846220	+	1.46570i
$804$		0			0
$805$	−3.86259	−	21.9058i	−0.136138	−	0.772079i
$806$		0			0
$807$	7.97125	−	2.90130i	0.280601	−	0.102130i
$808$		0			0
$809$	−8.22721	−	22.6041i	−0.289253	−	0.794717i	−0.996171	−	0.0874217i	$-0.972137\pi$
$809$	−8.22721	−	22.6041i	−0.289253	−	0.794717i	0.706918	−	0.707296i	$-0.250085\pi$
$810$		0			0
$811$	−31.4326	−	26.3751i	−1.10375	−	0.926154i	−0.106076	−	0.994358i	$-0.533829\pi$
$811$	−31.4326	−	26.3751i	−1.10375	−	0.926154i	−0.997671	+	0.0682040i	$0.978273\pi$
$812$		0			0
$813$	−5.71501			−0.200434
$814$		0			0
$815$	−38.9256			−1.36350
$816$		0			0
$817$	3.24764	+	2.72510i	0.113621	+	0.0953390i
$818$		0			0
$819$	−2.34261	−	6.43625i	−0.0818572	−	0.224901i
$820$		0			0
$821$	9.77043	−	3.55615i	0.340991	−	0.124110i	−0.165848	−	0.986151i	$-0.553036\pi$
$821$	9.77043	−	3.55615i	0.340991	−	0.124110i	0.506839	+	0.862041i	$0.330814\pi$
$822$		0			0
$823$	1.48559	+	8.42523i	0.0517846	+	0.293685i	0.999691	−	0.0248645i	$-0.00791543\pi$
$823$	1.48559	+	8.42523i	0.0517846	+	0.293685i	−0.947906	+	0.318549i	$0.896804\pi$
$824$		0			0
$825$	−3.55726	−	6.16136i	−0.123848	−	0.214511i
$826$		0			0
$827$	28.5159	+	5.02812i	0.991595	+	0.174845i	0.645834	−	0.763478i	$-0.276510\pi$
$827$	28.5159	+	5.02812i	0.991595	+	0.174845i	0.345761	+	0.938323i	$0.387621\pi$
$828$		0			0
$829$	2.47167	−	6.79085i	0.0858446	−	0.235856i	−0.889341	−	0.457244i	$-0.848837\pi$
$829$	2.47167	−	6.79085i	0.0858446	−	0.235856i	0.975186	+	0.221388i	$0.0710588\pi$
$830$		0			0
$831$	10.8816	−	1.91871i	0.377477	−	0.0665594i
$832$		0			0
$833$	−1.65383	+	1.97095i	−0.0573017	+	0.0682895i
$834$		0			0
$835$	−28.3846	−	10.3312i	−0.982291	−	0.357525i
$836$		0			0
$837$	16.2639	+	9.38999i	0.562164	+	0.324566i
$838$		0			0
$839$	−2.80572	+	2.35428i	−0.0968643	+	0.0812788i	−0.689934	−	0.723872i	$-0.742360\pi$
$839$	−2.80572	+	2.35428i	−0.0968643	+	0.0812788i	0.593069	+	0.805151i	$0.297916\pi$
$840$		0			0
$841$	−14.4900	+	25.0975i	−0.499657	+	0.865431i
$842$		0			0
$843$	1.07513	−	0.620726i	0.0370294	−	0.0213789i
$844$		0			0
$845$			21.2300i			0.730335i
$846$		0			0
$847$	10.4628	−	59.3377i	0.359507	−	2.03887i
$848$		0			0
$849$	5.13456	+	6.11914i	0.176218	+	0.210008i
$850$		0			0
$851$	8.95916	−	19.2915i	0.307116	−	0.661305i
$852$		0			0
$853$	−20.4726	−	24.3983i	−0.700968	−	0.835381i	0.291667	−	0.956520i	$-0.405790\pi$
$853$	−20.4726	−	24.3983i	−0.700968	−	0.835381i	−0.992636	+	0.121138i	$0.961345\pi$
$854$		0			0
$855$	−1.02473	+	5.81154i	−0.0350451	+	0.198751i
$856$		0			0
$857$			2.91354i			0.0995246i	0.998761	+	0.0497623i	$0.0158464\pi$
$857$			2.91354i			0.0995246i	−0.998761	+	0.0497623i	$0.984154\pi$
$858$		0			0
$859$	27.9477	−	16.1356i	0.953564	−	0.550541i	0.0593778	−	0.998236i	$-0.481088\pi$
$859$	27.9477	−	16.1356i	0.953564	−	0.550541i	0.894186	+	0.447695i	$0.147755\pi$
$860$		0			0
$861$	−0.850903	+	1.47381i	−0.0289987	+	0.0502272i
$862$		0			0
$863$	13.5923	−	11.4053i	0.462686	−	0.388240i	−0.381432	−	0.924397i	$-0.624569\pi$
$863$	13.5923	−	11.4053i	0.462686	−	0.388240i	0.844118	+	0.536157i	$0.180125\pi$
$864$		0			0
$865$	−13.5449	−	7.82013i	−0.460539	−	0.265893i
$866$		0			0
$867$	−19.4286	−	7.07142i	−0.659828	−	0.240158i
$868$		0			0
$869$	−15.8618	+	18.9033i	−0.538074	+	0.641252i
$870$		0			0
$871$	−11.6495	+	2.05412i	−0.394727	+	0.0696011i
$872$		0			0
$873$	−7.39581	+	20.3198i	−0.250310	+	0.687721i
$874$		0			0
$875$	37.7706	+	6.65997i	1.27688	+	0.225148i
$876$		0			0
$877$	1.59299	+	2.75913i	0.0537913	+	0.0931693i	0.891667	−	0.452691i	$-0.149536\pi$
$877$	1.59299	+	2.75913i	0.0537913	+	0.0931693i	−0.837876	+	0.545861i	$0.816203\pi$
$878$		0			0
$879$	−0.955106	−	5.41668i	−0.0322149	−	0.182700i
$880$		0			0
$881$	5.23136	−	1.90406i	0.176249	−	0.0641493i	−0.252388	−	0.967626i	$-0.581216\pi$
$881$	5.23136	−	1.90406i	0.176249	−	0.0641493i	0.428637	+	0.903477i	$0.358994\pi$
$882$		0			0
$883$	−4.46487	−	12.2671i	−0.150255	−	0.412822i	0.841615	−	0.540078i	$-0.181605\pi$
$883$	−4.46487	−	12.2671i	−0.150255	−	0.412822i	−0.991870	+	0.127256i	$0.959383\pi$
$884$		0			0
$885$	−20.6155	−	17.2985i	−0.692984	−	0.581482i
$886$		0			0
$887$	−4.57250			−0.153529			−0.0767647	−	0.997049i	$-0.524459\pi$
$887$	−4.57250			−0.153529			−0.0767647	+	0.997049i	$0.524459\pi$
$888$		0			0
$889$	6.52838			0.218955
$890$		0			0
$891$	−11.8703	−	9.96038i	−0.397671	−	0.333685i
$892$		0			0
$893$	−1.21901	−	3.34921i	−0.0407927	−	0.112077i
$894$		0			0
$895$	6.15401	−	2.23988i	0.205706	−	0.0748708i
$896$		0			0
$897$	1.17609	+	6.66994i	0.0392685	+	0.222703i
$898$		0			0
$899$	−0.238144	−	0.412477i	−0.00794255	−	0.0137569i
$900$		0			0
$901$	5.79837	+	1.02241i	0.193172	+	0.0340614i
$902$		0			0
$903$	2.76884	−	7.60732i	0.0921411	−	0.253156i
$904$		0			0
$905$	−39.8536	+	7.02727i	−1.32478	+	0.233594i
$906$		0			0
$907$	−8.33097	+	9.92846i	−0.276625	+	0.329669i	−0.886413	−	0.462896i	$-0.846810\pi$
$907$	−8.33097	+	9.92846i	−0.276625	+	0.329669i	0.609787	+	0.792565i	$0.291255\pi$
$908$		0			0
$909$	−21.9547	−	7.99086i	−0.728191	−	0.265040i
$910$		0			0
$911$	5.79091	+	3.34338i	0.191861	+	0.110771i	0.592854	−	0.805310i	$-0.298001\pi$
$911$	5.79091	+	3.34338i	0.191861	+	0.110771i	−0.400992	+	0.916081i	$0.631335\pi$
$912$		0			0
$913$	43.8774	−	36.8175i	1.45213	−	1.21848i
$914$		0			0
$915$	14.5197	−	25.1489i	0.480007	−	0.831396i
$916$		0			0
$917$	−53.4996	+	30.8880i	−1.76671	+	1.02001i
$918$		0			0
$919$		−	1.26433i		−	0.0417065i	−0.999783	−	0.0208533i	$-0.993362\pi$
$919$		−	1.26433i		−	0.0417065i	0.999783	−	0.0208533i	$-0.00663828\pi$
$920$		0			0
$921$	3.62318	−	20.5481i	0.119388	−	0.677082i
$922$		0			0
$923$	8.72498	+	10.3980i	0.287186	+	0.342255i
$924$		0			0
$925$	4.43419	+	4.42037i	0.145795	+	0.145341i
$926$		0			0
$927$	3.96261	+	4.72246i	0.130149	+	0.155106i
$928$		0			0
$929$	−3.85014	+	21.8352i	−0.126319	+	0.716391i	0.854197	+	0.519950i	$0.174049\pi$
$929$	−3.85014	+	21.8352i	−0.126319	+	0.716391i	−0.980516	+	0.196441i	$0.937062\pi$
$930$		0			0
$931$		−	6.74521i		−	0.221065i
$932$		0			0
$933$	25.1494	−	14.5200i	0.823355	−	0.475364i
$934$		0			0
$935$	4.39131	−	7.60598i	0.143611	−	0.248742i
$936$		0			0
$937$	14.4280	−	12.1065i	0.471342	−	0.395503i	−0.375942	−	0.926643i	$-0.622681\pi$
$937$	14.4280	−	12.1065i	0.471342	−	0.395503i	0.847284	+	0.531140i	$0.178236\pi$
$938$		0			0
$939$	34.8892	+	20.1433i	1.13857	+	0.657352i
$940$		0			0
$941$	−16.9915	−	6.18442i	−0.553908	−	0.201606i	0.0498737	−	0.998756i	$-0.484118\pi$
$941$	−16.9915	−	6.18442i	−0.553908	−	0.201606i	−0.603782	+	0.797149i	$0.706340\pi$
$942$		0			0
$943$	−0.947561	+	1.12926i	−0.0308568	+	0.0367737i
$944$		0			0
$945$	34.8631	−	6.14731i	1.13410	−	0.199972i
$946$		0			0
$947$	−0.896201	+	2.46229i	−0.0291226	+	0.0800138i	−0.953402	−	0.301703i	$-0.902445\pi$
$947$	−0.896201	+	2.46229i	−0.0291226	+	0.0800138i	0.924279	+	0.381717i	$0.124667\pi$
$948$		0			0
$949$	13.2350	+	2.33369i	0.429626	+	0.0757547i
$950$		0			0
$951$	−5.61482	−	9.72516i	−0.182073	−	0.315360i
$952$		0			0
$953$	7.73875	+	43.8886i	0.250683	+	1.42169i	0.806916	+	0.590666i	$0.201135\pi$
$953$	7.73875	+	43.8886i	0.250683	+	1.42169i	−0.556234	+	0.831026i	$0.687754\pi$
$954$		0			0
$955$	15.1739	−	5.52285i	0.491016	−	0.178715i
$956$		0			0
$957$	0.333658	+	0.916718i	0.0107856	+	0.0296333i
$958$		0			0
$959$	−41.7012	−	34.9915i	−1.34660	−	1.12993i
$960$		0			0
$961$	19.6125			0.632661
$962$		0			0
$963$	11.8717			0.382560
$964$		0			0
$965$	−9.57355	−	8.03316i	−0.308184	−	0.258597i
$966$		0			0
$967$	−6.97181	−	19.1549i	−0.224198	−	0.615980i	0.775687	−	0.631118i	$-0.217404\pi$
$967$	−6.97181	−	19.1549i	−0.224198	−	0.615980i	−0.999885	+	0.0151377i	$0.995181\pi$
$968$		0			0
$969$	−2.02574	+	0.737310i	−0.0650762	+	0.0236858i
$970$		0			0
$971$	−7.13666	−	40.4740i	−0.229026	−	1.29887i	−0.854837	−	0.518897i	$-0.826343\pi$
$971$	−7.13666	−	40.4740i	−0.229026	−	1.29887i	0.625810	−	0.779975i	$-0.284768\pi$
$972$		0			0
$973$	−13.5128	−	23.4048i	−0.433200	−	0.750324i
$974$		0			0
$975$	−1.96335	−	0.346192i	−0.0628777	−	0.0110870i
$976$		0			0
$977$	−9.00892	+	24.7518i	−0.288221	+	0.791881i	0.708095	+	0.706118i	$0.249555\pi$
$977$	−9.00892	+	24.7518i	−0.288221	+	0.791881i	−0.996316	+	0.0857630i	$0.972667\pi$
$978$		0			0
$979$	−14.3871	+	2.53684i	−0.459815	+	0.0810778i
$980$		0			0
$981$	−9.25975	+	11.0353i	−0.295641	+	0.352331i
$982$		0			0
$983$	−35.2068	−	12.8142i	−1.12292	−	0.408710i	−0.287204	−	0.957869i	$-0.592726\pi$
$983$	−35.2068	−	12.8142i	−1.12292	−	0.408710i	−0.835718	+	0.549159i	$0.814948\pi$
$984$		0			0
$985$	−8.07120	−	4.65991i	−0.257170	−	0.148477i
$986$		0			0
$987$	−5.21365	+	4.37478i	−0.165952	+	0.139251i
$988$		0			0
$989$	3.50627	−	6.07303i	0.111493	−	0.193111i
$990$		0			0
$991$	−49.3800	+	28.5095i	−1.56861	+	0.905635i	−0.572275	+	0.820062i	$0.693939\pi$
$991$	−49.3800	+	28.5095i	−1.56861	+	0.905635i	−0.996332	+	0.0855733i	$0.972728\pi$
$992$		0			0
$993$		−	18.8605i		−	0.598521i
$994$		0			0
$995$	−6.68852	+	37.9325i	−0.212040	+	1.20254i
$996$		0			0
$997$	−7.64536	−	9.11139i	−0.242131	−	0.288560i	0.631269	−	0.775564i	$-0.282534\pi$
$997$	−7.64536	−	9.11139i	−0.242131	−	0.288560i	−0.873400	+	0.487003i	$0.838090\pi$
$998$		0			0
$999$	30.7024	+	14.2585i	0.971382	+	0.451119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bq.d.321.2		18
4.3	odd	2		37.2.h.a.25.1	yes	18
12.11	even	2		333.2.bl.d.136.3		18
20.3	even	4		925.2.ba.a.99.1		36
20.7	even	4		925.2.ba.a.99.6		36
20.19	odd	2		925.2.bb.a.876.3		18
37.3	even	18	inner	592.2.bq.d.225.2		18
148.3	odd	18		37.2.h.a.3.1	✓	18
148.15	even	36		1369.2.a.m.1.17		18
148.59	even	36		1369.2.a.m.1.2		18
148.95	odd	18		1369.2.b.g.1368.17		18
148.127	odd	18		1369.2.b.g.1368.2		18
444.299	even	18		333.2.bl.d.262.3		18
740.3	even	36		925.2.ba.a.299.6		36
740.299	odd	18		925.2.bb.a.151.3		18
740.447	even	36		925.2.ba.a.299.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.h.a.3.1	✓	18	148.3	odd	18
37.2.h.a.25.1	yes	18	4.3	odd	2
333.2.bl.d.136.3		18	12.11	even	2
333.2.bl.d.262.3		18	444.299	even	18
592.2.bq.d.225.2		18	37.3	even	18	inner
592.2.bq.d.321.2		18	1.1	even	1	trivial
925.2.ba.a.99.1		36	20.3	even	4
925.2.ba.a.99.6		36	20.7	even	4
925.2.ba.a.299.1		36	740.447	even	36
925.2.ba.a.299.6		36	740.3	even	36
925.2.bb.a.151.3		18	740.299	odd	18
925.2.bb.a.876.3		18	20.19	odd	2
1369.2.a.m.1.2		18	148.59	even	36
1369.2.a.m.1.17		18	148.15	even	36
1369.2.b.g.1368.2		18	148.127	odd	18
1369.2.b.g.1368.17		18	148.95	odd	18

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bq (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.968719 + 0.812851i) q^{3} +(-0.681528 - 1.87248i) q^{5} +(-2.99976 + 1.09182i) q^{7} +(-0.243256 - 1.37957i) q^{9} +O(q^{10})\)	\(q+(0.968719 + 0.812851i) q^{3} +(-0.681528 - 1.87248i) q^{5} +(-2.99976 + 1.09182i) q^{7} +(-0.243256 - 1.37957i) q^{9} +(-2.73288 - 4.73349i) q^{11} +(-1.50836 - 0.265964i) q^{13} +(0.861842 - 2.36789i) q^{15} +(-0.794131 + 0.140027i) q^{17} +(1.35888 - 1.61945i) q^{19} +(-3.79342 - 1.38069i) q^{21} +(-3.02834 - 1.74842i) q^{23} +(0.788506 - 0.661636i) q^{25} +(2.78260 - 4.81961i) q^{27} +(-0.122232 + 0.0705708i) q^{29} +3.37454i q^{31} +(1.20023 - 6.80685i) q^{33} +(4.08885 + 4.87290i) q^{35} +(0.539604 + 6.05878i) q^{37} +(-1.24498 - 1.48371i) q^{39} +(0.0732041 - 0.415161i) q^{41} +2.00540i q^{43} +(-2.41745 + 1.39571i) q^{45} +(0.842972 - 1.46007i) q^{47} +(2.44419 - 2.05092i) q^{49} +(-0.883111 - 0.509864i) q^{51} +(-6.86119 - 2.49727i) q^{53} +(-7.00085 + 8.34329i) q^{55} +(2.63275 - 0.464224i) q^{57} +(3.65272 - 10.0358i) q^{59} +(11.3492 + 2.00116i) q^{61} +(2.23597 + 3.87281i) q^{63} +(0.529974 + 3.00563i) q^{65} +(7.25752 - 2.64152i) q^{67} +(-1.51241 - 4.15532i) q^{69} +(-6.78889 - 5.69655i) q^{71} -8.77446 q^{73} +1.30165 q^{75} +(13.3662 + 11.2155i) q^{77} +(-1.54413 - 4.24247i) q^{79} +(2.66406 - 0.969637i) q^{81} +(1.81973 + 10.3202i) q^{83} +(0.803421 + 1.39157i) q^{85} +(-0.175772 - 0.0309934i) q^{87} +(0.914163 - 2.51164i) q^{89} +(4.81510 - 0.849032i) q^{91} +(-2.74300 + 3.26898i) q^{93} +(-3.95851 - 1.44078i) q^{95} +(-13.3681 - 7.71809i) q^{97} +(-5.86542 + 4.92167i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{3} - 3 q^{5} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 18 * q + 9 * q^3 - 3 * q^5 + 3 * q^7 - 3 * q^9	\( 18 q + 9 q^{3} - 3 q^{5} + 3 q^{7} - 3 q^{9} - 9 q^{11} + 9 q^{13} + 15 q^{15} - 15 q^{17} - 6 q^{19} - 12 q^{21} + 9 q^{23} + 21 q^{25} - 21 q^{27} - 18 q^{29} + 6 q^{33} + 12 q^{35} + 6 q^{37} + 6 q^{39} - 24 q^{41} + 36 q^{47} + 21 q^{49} - 81 q^{51} - 39 q^{53} - 12 q^{55} + 15 q^{57} + 6 q^{59} + 42 q^{61} + 27 q^{63} + 18 q^{65} - 36 q^{69} + 9 q^{71} - 54 q^{73} - 18 q^{75} + 33 q^{77} + 6 q^{79} - 45 q^{81} + 24 q^{83} + 6 q^{85} - 21 q^{87} + 18 q^{89} + 3 q^{91} + 66 q^{93} + 15 q^{95} - 9 q^{97} - 60 q^{99}+O(q^{100}) \) 18 * q + 9 * q^3 - 3 * q^5 + 3 * q^7 - 3 * q^9 - 9 * q^11 + 9 * q^13 + 15 * q^15 - 15 * q^17 - 6 * q^19 - 12 * q^21 + 9 * q^23 + 21 * q^25 - 21 * q^27 - 18 * q^29 + 6 * q^33 + 12 * q^35 + 6 * q^37 + 6 * q^39 - 24 * q^41 + 36 * q^47 + 21 * q^49 - 81 * q^51 - 39 * q^53 - 12 * q^55 + 15 * q^57 + 6 * q^59 + 42 * q^61 + 27 * q^63 + 18 * q^65 - 36 * q^69 + 9 * q^71 - 54 * q^73 - 18 * q^75 + 33 * q^77 + 6 * q^79 - 45 * q^81 + 24 * q^83 + 6 * q^85 - 21 * q^87 + 18 * q^89 + 3 * q^91 + 66 * q^93 + 15 * q^95 - 9 * q^97 - 60 * q^99

Introduction

L-functions

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