LMFDB - Embedded newform 1300.2.bs.d.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(193,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 7]))

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

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

chi := DirichletCharacter("1300.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bs (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.1
Root			$2.44766i$ of defining polynomial
Character	$\chi$	$=$	1300.193
Dual form			1300.2.bs.d.357.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877081 + 3.27331i) q^{3} +(-2.27273 - 1.31216i) q^{7} +(-7.34722 - 4.24192i) q^{9} +O(q^{10})$	\(q+(-0.877081 + 3.27331i) q^{3} +(-2.27273 - 1.31216i) q^{7} +(-7.34722 - 4.24192i) q^{9} +(1.71196 + 0.458719i) q^{11} +(-1.21746 - 3.39379i) q^{13} +(-0.363048 + 0.0972783i) q^{17} +(-0.462233 - 1.72508i) q^{19} +(6.28849 - 6.28849i) q^{21} +(4.72966 + 1.26731i) q^{23} +(13.1405 - 13.1405i) q^{27} +(6.28709 - 3.62985i) q^{29} +(2.98238 + 2.98238i) q^{31} +(-3.00306 + 5.20145i) q^{33} +(-8.83378 + 5.10019i) q^{37} +(12.1767 - 1.00852i) q^{39} +(1.59861 - 5.96611i) q^{41} +(-0.427024 - 1.59368i) q^{43} -1.19733i q^{47} +(-0.0564545 - 0.0977821i) q^{49} -1.27369i q^{51} +(-5.13227 - 5.13227i) q^{53} +6.05214 q^{57} +(-2.89607 + 0.776000i) q^{59} +(-2.45432 + 4.25101i) q^{61} +(11.1322 + 19.2815i) q^{63} +(-3.98715 - 6.90594i) q^{67} +(-8.29659 + 14.3701i) q^{69} +(4.02481 - 1.07844i) q^{71} +11.2043 q^{73} +(-3.28892 - 3.28892i) q^{77} +2.72484i q^{79} +(18.7620 + 32.4967i) q^{81} -11.2434i q^{83} +(6.36735 + 23.7633i) q^{87} +(1.91334 - 7.14070i) q^{89} +(-1.68623 + 9.31068i) q^{91} +(-12.3780 + 7.14647i) q^{93} +(0.838229 - 1.45185i) q^{97} +(-10.6323 - 10.6323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9	$ 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9} - 8 q^{13} + 20 q^{19} - 12 q^{21} - 6 q^{23} + 20 q^{27} + 24 q^{29} + 8 q^{31} + 10 q^{33} + 4 q^{39} + 6 q^{41} - 38 q^{43} + 14 q^{49} - 30 q^{53} + 76 q^{57} - 24 q^{59} - 32 q^{61} + 24 q^{63} - 22 q^{67} - 16 q^{69} + 44 q^{73} + 12 q^{77} + 2 q^{81} - 38 q^{87} - 30 q^{89} - 72 q^{91} + 48 q^{93} - 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9 - 8 * q^13 + 20 * q^19 - 12 * q^21 - 6 * q^23 + 20 * q^27 + 24 * q^29 + 8 * q^31 + 10 * q^33 + 4 * q^39 + 6 * q^41 - 38 * q^43 + 14 * q^49 - 30 * q^53 + 76 * q^57 - 24 * q^59 - 32 * q^61 + 24 * q^63 - 22 * q^67 - 16 * q^69 + 44 * q^73 + 12 * q^77 + 2 * q^81 - 38 * q^87 - 30 * q^89 - 72 * q^91 + 48 * q^93 - 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.877081	+	3.27331i	−0.506383	+	1.88985i	−0.0528610	+	0.998602i	$0.516834\pi$
$3$	−0.877081	+	3.27331i	−0.506383	+	1.88985i	−0.453522	+	0.891245i	$0.649833\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.27273	−	1.31216i	−0.859013	−	0.495951i	0.00466893	−	0.999989i	$-0.498514\pi$
$7$	−2.27273	−	1.31216i	−0.859013	−	0.495951i	−0.863682	+	0.504038i	$0.831847\pi$
$8$		0			0
$9$	−7.34722	−	4.24192i	−2.44907	−	1.41397i
$10$		0			0
$11$	1.71196	+	0.458719i	0.516176	+	0.138309i	0.507497	−	0.861653i	$-0.330571\pi$
$11$	1.71196	+	0.458719i	0.516176	+	0.138309i	0.00867863	+	0.999962i	$0.497237\pi$
$12$		0			0
$13$	−1.21746	−	3.39379i	−0.337664	−	0.941267i
$13$	−1.21746	−	3.39379i	−0.337664	−	0.941267i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.363048	+	0.0972783i	−0.0880520	+	0.0235935i	−0.302576	−	0.953125i	$-0.597847\pi$
$17$	−0.363048	+	0.0972783i	−0.0880520	+	0.0235935i	0.214524	+	0.976719i	$0.431180\pi$
$18$		0			0
$19$	−0.462233	−	1.72508i	−0.106044	−	0.395760i	0.892418	−	0.451210i	$-0.149007\pi$
$19$	−0.462233	−	1.72508i	−0.106044	−	0.395760i	−0.998461	+	0.0554497i	$0.982341\pi$
$20$		0			0
$21$	6.28849	−	6.28849i	1.37226	−	1.37226i
$22$		0			0
$23$	4.72966	+	1.26731i	0.986203	+	0.264252i	0.715655	−	0.698454i	$-0.246128\pi$
$23$	4.72966	+	1.26731i	0.986203	+	0.264252i	0.270548	+	0.962707i	$0.412795\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	13.1405	−	13.1405i	2.52890	−	2.52890i
$28$		0			0
$29$	6.28709	−	3.62985i	1.16748	−	0.674047i	0.214398	−	0.976746i	$-0.431221\pi$
$29$	6.28709	−	3.62985i	1.16748	−	0.674047i	0.953086	+	0.302699i	$0.0978878\pi$
$30$		0			0
$31$	2.98238	+	2.98238i	0.535651	+	0.535651i	0.922249	−	0.386597i	$-0.126350\pi$
$31$	2.98238	+	2.98238i	0.535651	+	0.535651i	−0.386597	+	0.922249i	$0.626350\pi$
$32$		0			0
$33$	−3.00306	+	5.20145i	−0.522765	+	0.905456i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−8.83378	+	5.10019i	−1.45226	+	0.838465i	−0.998610	−	0.0527119i	$-0.983214\pi$
$37$	−8.83378	+	5.10019i	−1.45226	+	0.838465i	−0.453655	+	0.891177i	$0.649880\pi$
$38$		0			0
$39$	12.1767	−	1.00852i	1.94984	−	0.161492i
$40$		0			0
$41$	1.59861	−	5.96611i	0.249662	−	0.931750i	−0.721321	−	0.692601i	$-0.756465\pi$
$41$	1.59861	−	5.96611i	0.249662	−	0.931750i	0.970983	−	0.239149i	$-0.0768686\pi$
$42$		0			0
$43$	−0.427024	−	1.59368i	−0.0651205	−	0.243033i	0.925691	−	0.378279i	$-0.123484\pi$
$43$	−0.427024	−	1.59368i	−0.0651205	−	0.243033i	−0.990812	+	0.135246i	$0.956817\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	1.19733i		−	0.174649i	−0.996180	−	0.0873244i	$-0.972168\pi$
$47$		−	1.19733i		−	0.174649i	0.996180	−	0.0873244i	$-0.0278317\pi$
$48$		0			0
$49$	−0.0564545	−	0.0977821i	−0.00806493	−	0.0139689i
$50$		0			0
$51$		−	1.27369i		−	0.178352i
$52$		0			0
$53$	−5.13227	−	5.13227i	−0.704971	−	0.704971i	0.260502	−	0.965473i	$-0.416112\pi$
$53$	−5.13227	−	5.13227i	−0.704971	−	0.704971i	−0.965473	+	0.260502i	$0.916112\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	6.05214			0.801625
$58$		0			0
$59$	−2.89607	+	0.776000i	−0.377036	+	0.101027i	−0.442360	−	0.896838i	$-0.645859\pi$
$59$	−2.89607	+	0.776000i	−0.377036	+	0.101027i	0.0653237	+	0.997864i	$0.479192\pi$
$60$		0			0
$61$	−2.45432	+	4.25101i	−0.314244	+	0.544286i	−0.979276	−	0.202528i	$-0.935084\pi$
$61$	−2.45432	+	4.25101i	−0.314244	+	0.544286i	0.665033	+	0.746814i	$0.268418\pi$
$62$		0			0
$63$	11.1322	+	19.2815i	1.40252	+	2.42924i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.98715	−	6.90594i	−0.487107	−	0.843695i	0.512783	−	0.858518i	$-0.328615\pi$
$67$	−3.98715	−	6.90594i	−0.487107	−	0.843695i	−0.999890	+	0.0148238i	$0.995281\pi$
$68$		0			0
$69$	−8.29659	+	14.3701i	−0.998792	+	1.72996i
$70$		0			0
$71$	4.02481	−	1.07844i	0.477657	−	0.127988i	−0.0119546	−	0.999929i	$-0.503805\pi$
$71$	4.02481	−	1.07844i	0.477657	−	0.127988i	0.489611	+	0.871941i	$0.337139\pi$
$72$		0			0
$73$	11.2043			1.31137			0.655683	−	0.755037i	$-0.272381\pi$
$73$	11.2043			1.31137			0.655683	+	0.755037i	$0.272381\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.28892	−	3.28892i	−0.374807	−	0.374807i
$78$		0			0
$79$			2.72484i			0.306569i	0.988182	+	0.153284i	$0.0489851\pi$
$79$			2.72484i			0.306569i	−0.988182	+	0.153284i	$0.951015\pi$
$80$		0			0
$81$	18.7620	+	32.4967i	2.08466	+	3.61074i
$82$		0			0
$83$		−	11.2434i		−	1.23413i	−0.786913	−	0.617064i	$-0.788322\pi$
$83$		−	11.2434i		−	1.23413i	0.786913	−	0.617064i	$-0.211678\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.36735	+	23.7633i	0.682652	+	2.54769i
$88$		0			0
$89$	1.91334	−	7.14070i	0.202814	−	0.756913i	−0.787291	−	0.616582i	$-0.788517\pi$
$89$	1.91334	−	7.14070i	0.202814	−	0.756913i	0.990105	−	0.140330i	$-0.0448165\pi$
$90$		0			0
$91$	−1.68623	+	9.31068i	−0.176765	+	0.976025i
$92$		0			0
$93$	−12.3780	+	7.14647i	−1.28354	+	0.741054i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.838229	−	1.45185i	0.0851092	−	0.147413i	−0.820329	−	0.571893i	$-0.806209\pi$
$97$	0.838229	−	1.45185i	0.0851092	−	0.147413i	0.905438	+	0.424479i	$0.139543\pi$
$98$		0			0
$99$	−10.6323	−	10.6323i	−1.06859	−	1.06859i
$100$		0			0
$101$	−12.2100	+	7.04945i	−1.21494	+	0.701447i	−0.963832	−	0.266512i	$-0.914129\pi$
$101$	−12.2100	+	7.04945i	−1.21494	+	0.701447i	−0.251110	+	0.967959i	$0.580796\pi$
$102$		0			0
$103$	8.21560	−	8.21560i	0.809508	−	0.809508i	−0.175052	−	0.984559i	$-0.556009\pi$
$103$	8.21560	−	8.21560i	0.809508	−	0.809508i	0.984559	+	0.175052i	$0.0560093\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.71070	+	2.33402i	0.842095	+	0.225639i	0.653983	−	0.756509i	$-0.273097\pi$
$107$	8.71070	+	2.33402i	0.842095	+	0.225639i	0.188112	+	0.982148i	$0.439763\pi$
$108$		0			0
$109$	8.48128	−	8.48128i	0.812359	−	0.812359i	−0.172628	−	0.984987i	$-0.555226\pi$
$109$	8.48128	−	8.48128i	0.812359	−	0.812359i	0.984987	+	0.172628i	$0.0552258\pi$
$110$		0			0
$111$	−8.94655	−	33.3890i	−0.849169	−	3.16914i
$112$		0			0
$113$	−2.71713	+	0.728053i	−0.255606	+	0.0684895i	−0.384347	−	0.923189i	$-0.625573\pi$
$113$	−2.71713	+	0.728053i	−0.255606	+	0.0684895i	0.128740	+	0.991678i	$0.458907\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.45118	+	30.0993i	−0.503962	+	2.78268i
$118$		0			0
$119$	0.952755	+	0.255290i	0.0873389	+	0.0234024i
$120$		0			0
$121$	−6.80589	−	3.92938i	−0.618717	−	0.357217i
$122$		0			0
$123$	18.1268	+	10.4655i	1.63444	+	0.943645i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.71429	−	6.39781i	0.152119	−	0.567714i	−0.847216	−	0.531248i	$-0.821723\pi$
$127$	1.71429	−	6.39781i	0.152119	−	0.567714i	0.999335	−	0.0364661i	$-0.0116101\pi$
$128$		0			0
$129$	5.59113			0.492271
$130$		0			0
$131$	2.68334			0.234444			0.117222	−	0.993106i	$-0.462601\pi$
$131$	2.68334			0.234444			0.117222	+	0.993106i	$0.462601\pi$
$132$		0			0
$133$	−1.21305	+	4.52717i	−0.105185	+	0.392555i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.78743	+	1.03197i	0.152710	+	0.0881674i	0.574408	−	0.818569i	$-0.305232\pi$
$137$	1.78743	+	1.03197i	0.152710	+	0.0881674i	−0.421698	+	0.906737i	$0.638566\pi$
$138$		0			0
$139$	12.7676	+	7.37138i	1.08293	+	0.625233i	0.931687	−	0.363263i	$-0.118337\pi$
$139$	12.7676	+	7.37138i	1.08293	+	0.625233i	0.151248	+	0.988496i	$0.451671\pi$
$140$		0			0
$141$	3.91924	+	1.05016i	0.330060	+	0.0884392i
$142$		0			0
$143$	−0.527460	−	6.36850i	−0.0441084	−	0.532561i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.369586	−	0.0990304i	0.0304830	−	0.00816789i
$148$		0			0
$149$	−0.823027	−	3.07158i	−0.0674250	−	0.251633i	0.923984	−	0.382431i	$-0.124913\pi$
$149$	−0.823027	−	3.07158i	−0.0674250	−	0.251633i	−0.991409	+	0.130797i	$0.958246\pi$
$150$		0			0
$151$	7.20288	−	7.20288i	0.586162	−	0.586162i	−0.350428	−	0.936590i	$-0.613964\pi$
$151$	7.20288	−	7.20288i	0.586162	−	0.586162i	0.936590	+	0.350428i	$0.113964\pi$
$152$		0			0
$153$	3.08004	+	0.825293i	0.249006	+	0.0667210i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.0556926	−	0.0556926i	0.00444476	−	0.00444476i	−0.704881	−	0.709326i	$-0.749000\pi$
$157$	0.0556926	−	0.0556926i	0.00444476	−	0.00444476i	0.709326	+	0.704881i	$0.249000\pi$
$158$		0			0
$159$	21.3009	−	12.2981i	1.68927	−	0.975303i
$160$		0			0
$161$	−9.08634	−	9.08634i	−0.716104	−	0.716104i
$162$		0			0
$163$	8.92131	−	15.4522i	0.698771	−	1.21031i	−0.270122	−	0.962826i	$-0.587064\pi$
$163$	8.92131	−	15.4522i	0.698771	−	1.21031i	0.968893	−	0.247481i	$-0.0796027\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.20710	−	1.27427i	0.170791	−	0.0986060i	−0.412168	−	0.911108i	$-0.635228\pi$
$167$	2.20710	−	1.27427i	0.170791	−	0.0986060i	0.582959	+	0.812502i	$0.301895\pi$
$168$		0			0
$169$	−10.0356	+	8.26363i	−0.771966	+	0.635664i
$170$		0			0
$171$	−3.92151	+	14.6353i	−0.299886	+	1.11919i
$172$		0			0
$173$	3.65644	+	13.6460i	0.277994	+	1.03749i	0.953809	+	0.300415i	$0.0971252\pi$
$173$	3.65644	+	13.6460i	0.277994	+	1.03749i	−0.675815	+	0.737071i	$0.736208\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	10.1604i		−	0.763699i
$178$		0			0
$179$	−7.85350	−	13.6027i	−0.586998	−	1.01671i	−0.994623	−	0.103561i	$-0.966976\pi$
$179$	−7.85350	−	13.6027i	−0.586998	−	1.01671i	0.407625	−	0.913149i	$-0.366357\pi$
$180$		0			0
$181$		−	7.87942i		−	0.585673i	−0.956163	−	0.292836i	$-0.905401\pi$
$181$		−	7.87942i		−	0.585673i	0.956163	−	0.292836i	$-0.0945991\pi$
$182$		0			0
$183$	−11.7622	−	11.7622i	−0.869490	−	0.869490i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.666147			−0.0487135
$188$		0			0
$189$	−47.1075	+	12.6224i	−3.42656	+	0.918145i
$190$		0			0
$191$	−9.41812	+	16.3127i	−0.681471	+	1.18034i	0.293061	+	0.956094i	$0.405326\pi$
$191$	−9.41812	+	16.3127i	−0.681471	+	1.18034i	−0.974532	+	0.224249i	$0.928007\pi$
$192$		0			0
$193$	−12.2328	−	21.1878i	−0.880533	−	1.52513i	−0.850749	−	0.525572i	$-0.823851\pi$
$193$	−12.2328	−	21.1878i	−0.880533	−	1.52513i	−0.0297844	−	0.999556i	$-0.509482\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.08076	−	12.2642i	−0.504484	−	0.873791i	−0.999987	−	0.00518489i	$-0.998350\pi$
$197$	−7.08076	−	12.2642i	−0.504484	−	0.873791i	0.495503	−	0.868606i	$-0.334984\pi$
$198$		0			0
$199$	1.57563	−	2.72908i	0.111694	−	0.193459i	−0.804760	−	0.593601i	$-0.797706\pi$
$199$	1.57563	−	2.72908i	0.111694	−	0.193459i	0.916453	+	0.400142i	$0.131039\pi$
$200$		0			0
$201$	26.1023	−	6.99410i	1.84112	−	0.493326i
$202$		0			0
$203$	−19.0518			−1.33718
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−29.3740	−	29.3740i	−2.04164	−	2.04164i
$208$		0			0
$209$		−	3.16530i		−	0.218949i
$210$		0			0
$211$	−0.323466	−	0.560259i	−0.0222683	−	0.0385698i	0.854677	−	0.519161i	$-0.173755\pi$
$211$	−0.323466	−	0.560259i	−0.0222683	−	0.0385698i	−0.876945	+	0.480591i	$0.840422\pi$
$212$		0			0
$213$			14.1203i			0.967509i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.86479	−	10.6915i	−0.194474	−	0.725788i
$218$		0			0
$219$	−9.82709	+	36.6752i	−0.664053	+	2.47828i
$220$		0			0
$221$	0.772139	+	1.11367i	0.0519397	+	0.0749137i
$222$		0			0
$223$	11.0872	−	6.40121i	0.742456	−	0.428657i	−0.0805058	−	0.996754i	$-0.525654\pi$
$223$	11.0872	−	6.40121i	0.742456	−	0.428657i	0.822961	+	0.568097i	$0.192320\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.20690	−	9.01862i	0.345594	−	0.598587i	−0.639867	−	0.768485i	$-0.721011\pi$
$227$	5.20690	−	9.01862i	0.345594	−	0.598587i	0.985462	+	0.169899i	$0.0543441\pi$
$228$		0			0
$229$	4.26361	+	4.26361i	0.281747	+	0.281747i	0.833806	−	0.552058i	$-0.186157\pi$
$229$	4.26361	+	4.26361i	0.281747	+	0.281747i	−0.552058	+	0.833806i	$0.686157\pi$
$230$		0			0
$231$	13.6503	−	7.88100i	0.898124	−	0.518532i
$232$		0			0
$233$	−0.786053	+	0.786053i	−0.0514960	+	0.0514960i	−0.732386	−	0.680890i	$-0.761593\pi$
$233$	−0.786053	+	0.786053i	−0.0514960	+	0.0514960i	0.680890	+	0.732386i	$0.261593\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−8.91926	−	2.38991i	−0.579368	−	0.155241i
$238$		0			0
$239$	−18.7521	+	18.7521i	−1.21297	+	1.21297i	−0.242925	+	0.970045i	$0.578107\pi$
$239$	−18.7521	+	18.7521i	−1.21297	+	1.21297i	−0.970045	+	0.242925i	$0.921893\pi$
$240$		0			0
$241$	−2.89785	−	10.8149i	−0.186667	−	0.696652i	−0.994267	−	0.106921i	$-0.965901\pi$
$241$	−2.89785	−	10.8149i	−0.186667	−	0.696652i	0.807600	−	0.589730i	$-0.200766\pi$
$242$		0			0
$243$	−68.9767	+	18.4823i	−4.42486	+	1.18564i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.29179	+	3.66894i	−0.336709	+	0.233449i
$248$		0			0
$249$	36.8033	+	9.86140i	2.33231	+	0.624941i
$250$		0			0
$251$	−24.6347	−	14.2228i	−1.55493	−	0.897737i	−0.997729	−	0.0673574i	$-0.978543\pi$
$251$	−24.6347	−	14.2228i	−1.55493	−	0.897737i	−0.557198	−	0.830380i	$-0.688123\pi$
$252$		0			0
$253$	7.51566	+	4.33917i	0.472505	+	0.272801i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.88190	−	25.6836i	0.429281	−	1.60210i	−0.325112	−	0.945675i	$-0.605402\pi$
$257$	6.88190	−	25.6836i	0.429281	−	1.60210i	0.754393	−	0.656423i	$-0.227931\pi$
$258$		0			0
$259$	26.7691			1.66335
$260$		0			0
$261$	−61.5902			−3.81234
$262$		0			0
$263$	−2.86411	+	10.6890i	−0.176609	+	0.659112i	0.819663	+	0.572845i	$0.194160\pi$
$263$	−2.86411	+	10.6890i	−0.176609	+	0.659112i	−0.996272	+	0.0862670i	$0.972506\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	21.6956	+	12.5259i	1.32775	+	0.766575i
$268$		0			0
$269$	−3.97689	−	2.29606i	−0.242475	−	0.139993i	0.373839	−	0.927494i	$-0.378041\pi$
$269$	−3.97689	−	2.29606i	−0.242475	−	0.139993i	−0.616314	+	0.787501i	$0.711375\pi$
$270$		0			0
$271$	4.90421	+	1.31408i	0.297909	+	0.0798245i	0.404678	−	0.914459i	$-0.367384\pi$
$271$	4.90421	+	1.31408i	0.297909	+	0.0798245i	−0.106768	+	0.994284i	$0.534050\pi$
$272$		0			0
$273$	−28.9978	−	13.6858i	−1.75503	−	0.828301i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−16.1826	+	4.33613i	−0.972321	+	0.260533i	−0.709807	−	0.704396i	$-0.751218\pi$
$277$	−16.1826	+	4.33613i	−0.972321	+	0.260533i	−0.262513	+	0.964928i	$0.584551\pi$
$278$		0			0
$279$	−9.26118	−	34.5632i	−0.554452	−	2.06924i
$280$		0			0
$281$	18.3528	−	18.3528i	1.09483	−	1.09483i	0.0998291	−	0.995005i	$-0.468170\pi$
$281$	18.3528	−	18.3528i	1.09483	−	1.09483i	0.995005	−	0.0998291i	$-0.0318296\pi$
$282$		0			0
$283$	−5.82286	−	1.56023i	−0.346133	−	0.0927461i	0.0815641	−	0.996668i	$-0.474008\pi$
$283$	−5.82286	−	1.56023i	−0.346133	−	0.0927461i	−0.427697	+	0.903922i	$0.640675\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.4617	+	11.4617i	−0.676565	+	0.676565i
$288$		0			0
$289$	−14.6001	+	8.42937i	−0.858829	+	0.495845i
$290$		0			0
$291$	4.01718	+	4.01718i	0.235491	+	0.235491i
$292$		0			0
$293$	7.86812	−	13.6280i	0.459661	−	0.796156i	−0.539282	−	0.842125i	$-0.681304\pi$
$293$	7.86812	−	13.6280i	0.459661	−	0.796156i	0.998943	+	0.0459695i	$0.0146377\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	28.5239	−	16.4683i	1.65512	−	0.955586i
$298$		0			0
$299$	−1.45722	−	17.5944i	−0.0842733	−	1.01751i
$300$		0			0
$301$	−1.12065	+	4.18232i	−0.0645932	+	0.241065i
$302$		0			0
$303$	−12.3659	−	46.1501i	−0.710401	−	2.65125i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			28.0727i			1.60219i	0.598536	+	0.801096i	$0.295749\pi$
$307$			28.0727i			1.60219i	−0.598536	+	0.801096i	$0.704251\pi$
$308$		0			0
$309$	19.6865	+	34.0980i	1.11992	+	1.93977i
$310$		0			0
$311$			7.33583i			0.415977i	0.978131	+	0.207988i	$0.0666916\pi$
$311$			7.33583i			0.415977i	−0.978131	+	0.207988i	$0.933308\pi$
$312$		0			0
$313$	6.41291	+	6.41291i	0.362479	+	0.362479i	0.864725	−	0.502246i	$-0.167493\pi$
$313$	6.41291	+	6.41291i	0.362479	+	0.362479i	−0.502246	+	0.864725i	$0.667493\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−31.9597			−1.79503			−0.897517	−	0.440980i	$-0.854631\pi$
$317$	−31.9597			−1.79503			−0.897517	+	0.440980i	$0.854631\pi$
$318$		0			0
$319$	12.4283	−	3.33016i	0.695853	−	0.186453i
$320$		0			0
$321$	−15.2800	+	26.4657i	−0.852845	+	1.47717i
$322$		0			0
$323$	0.335625	+	0.581320i	0.0186747	+	0.0323455i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	20.3231	+	35.2006i	1.12387	+	1.94660i
$328$		0			0
$329$	−1.57110	+	2.72122i	−0.0866173	+	0.150026i
$330$		0			0
$331$	4.58649	−	1.22895i	0.252096	−	0.0675489i	−0.130558	−	0.991441i	$-0.541677\pi$
$331$	4.58649	−	1.22895i	0.252096	−	0.0675489i	0.382654	+	0.923892i	$0.375010\pi$
$332$		0			0
$333$	86.5383			4.74227
$334$		0			0
$335$		0			0
$336$		0			0
$337$	23.5944	+	23.5944i	1.28527	+	1.28527i	0.937626	+	0.347645i	$0.113018\pi$
$337$	23.5944	+	23.5944i	1.28527	+	1.28527i	0.347645	+	0.937626i	$0.386982\pi$
$338$		0			0
$339$		−	9.53258i		−	0.517738i
$340$		0			0
$341$	3.73764	+	6.47379i	0.202405	+	0.350575i
$342$		0			0
$343$			18.6666i			1.00790i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.947430	+	3.53586i	0.0508607	+	0.189815i	0.986682	−	0.162659i	$-0.0520071\pi$
$347$	0.947430	+	3.53586i	0.0508607	+	0.189815i	−0.935822	+	0.352474i	$0.885340\pi$
$348$		0			0
$349$	0.937727	−	3.49965i	0.0501954	−	0.187332i	−0.936276	−	0.351265i	$-0.885752\pi$
$349$	0.937727	−	3.49965i	0.0501954	−	0.187332i	0.986471	+	0.163933i	$0.0524182\pi$
$350$		0			0
$351$	−60.5943	−	28.5980i	−3.23428	−	1.52645i
$352$		0			0
$353$	8.13057	−	4.69419i	0.432747	−	0.249846i	−0.267769	−	0.963483i	$-0.586287\pi$
$353$	8.13057	−	4.69419i	0.432747	−	0.249846i	0.700516	+	0.713637i	$0.252953\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.67129	+	2.89475i	−0.0884539	+	0.153207i
$358$		0			0
$359$	−9.90682	−	9.90682i	−0.522862	−	0.522862i	0.395573	−	0.918435i	$-0.370546\pi$
$359$	−9.90682	−	9.90682i	−0.522862	−	0.522862i	−0.918435	+	0.395573i	$0.870546\pi$
$360$		0			0
$361$	13.6922	−	7.90522i	0.720645	−	0.416064i
$362$		0			0
$363$	18.8314	−	18.8314i	0.988393	−	0.988393i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	5.44176	+	1.45811i	0.284057	+	0.0761130i	0.398035	−	0.917370i	$-0.369692\pi$
$367$	5.44176	+	1.45811i	0.284057	+	0.0761130i	−0.113977	+	0.993483i	$0.536359\pi$
$368$		0			0
$369$	−37.0531	+	37.0531i	−1.92891	+	1.92891i
$370$		0			0
$371$	4.92991	+	18.3987i	0.255948	+	0.955211i
$372$		0			0
$373$	−10.2192	+	2.73824i	−0.529132	+	0.141780i	−0.513487	−	0.858097i	$-0.671647\pi$
$373$	−10.2192	+	2.73824i	−0.529132	+	0.141780i	−0.0156446	+	0.999878i	$0.504980\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−19.9733	−	16.9178i	−1.02868	−	0.871312i
$378$		0			0
$379$	25.5928	+	6.85758i	1.31462	+	0.352250i	0.846958	−	0.531660i	$-0.178431\pi$
$379$	25.5928	+	6.85758i	1.31462	+	0.352250i	0.467657	+	0.883910i	$0.345098\pi$
$380$		0			0
$381$	19.4385	+	11.2228i	0.995863	+	0.574962i
$382$		0			0
$383$	−19.8344	−	11.4514i	−1.01349	−	0.585139i	−0.101278	−	0.994858i	$-0.532293\pi$
$383$	−19.8344	−	11.4514i	−1.01349	−	0.585139i	−0.912212	+	0.409720i	$0.865627\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.62280	+	13.5205i	−0.184157	+	0.687285i
$388$		0			0
$389$	−1.00709			−0.0510614			−0.0255307	−	0.999674i	$-0.508128\pi$
$389$	−1.00709			−0.0510614			−0.0255307	+	0.999674i	$0.508128\pi$
$390$		0			0
$391$	−1.84037			−0.0930717
$392$		0			0
$393$	−2.35350	+	8.78339i	−0.118718	+	0.443063i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.488978	+	0.282311i	0.0245411	+	0.0141688i	0.512220	−	0.858854i	$-0.328823\pi$
$397$	0.488978	+	0.282311i	0.0245411	+	0.0141688i	−0.487679	+	0.873023i	$0.662156\pi$
$398$		0			0
$399$	−13.7549	−	7.94139i	−0.688606	−	0.397567i
$400$		0			0
$401$	2.79748	+	0.749581i	0.139699	+	0.0374323i	0.327991	−	0.944681i	$-0.393628\pi$
$401$	2.79748	+	0.749581i	0.139699	+	0.0374323i	−0.188292	+	0.982113i	$0.560295\pi$
$402$		0			0
$403$	6.49061	−	13.7525i	0.323321	−	0.685061i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.4626	+	4.67910i	−0.865591	+	0.231934i
$408$		0			0
$409$	−7.82267	−	29.1946i	−0.386806	−	1.44358i	−0.835300	−	0.549795i	$-0.814706\pi$
$409$	−7.82267	−	29.1946i	−0.386806	−	1.44358i	0.448493	−	0.893786i	$-0.351961\pi$
$410$		0			0
$411$	−4.94569	+	4.94569i	−0.243953	+	0.243953i
$412$		0			0
$413$	7.60024	+	2.03648i	0.373983	+	0.100208i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−35.3271	+	35.3271i	−1.72997	+	1.72997i
$418$		0			0
$419$	5.06888	−	2.92652i	0.247631	−	0.142970i	−0.371048	−	0.928614i	$-0.621002\pi$
$419$	5.06888	−	2.92652i	0.247631	−	0.142970i	0.618679	+	0.785644i	$0.287668\pi$
$420$		0			0
$421$	−10.2231	−	10.2231i	−0.498244	−	0.498244i	0.412647	−	0.910891i	$-0.364604\pi$
$421$	−10.2231	−	10.2231i	−0.498244	−	0.498244i	−0.910891	+	0.412647i	$0.864604\pi$
$422$		0			0
$423$	−5.07899	+	8.79706i	−0.246949	+	0.427728i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	11.1560	−	6.44095i	0.539879	−	0.311699i
$428$		0			0
$429$	21.3087	+	3.85915i	1.02879	+	0.186322i
$430$		0			0
$431$	−9.50264	+	35.4643i	−0.457726	+	1.70826i	0.222221	+	0.974996i	$0.428669\pi$
$431$	−9.50264	+	35.4643i	−0.457726	+	1.70826i	−0.679947	+	0.733261i	$0.737997\pi$
$432$		0			0
$433$	5.99453	+	22.3719i	0.288079	+	1.07513i	0.946560	+	0.322528i	$0.104533\pi$
$433$	5.99453	+	22.3719i	0.288079	+	1.07513i	−0.658481	+	0.752597i	$0.728801\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	8.74483i		−	0.418322i
$438$		0			0
$439$	−1.34925	−	2.33697i	−0.0643962	−	0.111537i	0.832030	−	0.554731i	$-0.187179\pi$
$439$	−1.34925	−	2.33697i	−0.0643962	−	0.111537i	−0.896426	+	0.443193i	$0.853845\pi$
$440$		0			0
$441$			0.957902i			0.0456144i
$442$		0			0
$443$	9.66186	+	9.66186i	0.459049	+	0.459049i	0.898343	−	0.439295i	$-0.144772\pi$
$443$	9.66186	+	9.66186i	0.459049	+	0.459049i	−0.439295	+	0.898343i	$0.644772\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	10.7761			0.509692
$448$		0			0
$449$	−1.88121	+	0.504069i	−0.0887799	+	0.0237885i	−0.302936	−	0.953011i	$-0.597967\pi$
$449$	−1.88121	+	0.504069i	−0.0887799	+	0.0237885i	0.214156	+	0.976800i	$0.431300\pi$
$450$		0			0
$451$	5.47353	−	9.48044i	0.257739	−	0.446416i
$452$		0			0
$453$	17.2598	+	29.8948i	0.810934	+	1.40458i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.52855	+	11.3078i	0.305393	+	0.528956i	0.977349	−	0.211635i	$-0.0678789\pi$
$457$	6.52855	+	11.3078i	0.305393	+	0.528956i	−0.671956	+	0.740591i	$0.734546\pi$
$458$		0			0
$459$	−3.49235	+	6.04893i	−0.163009	+	0.282340i
$460$		0			0
$461$	−1.43252	+	0.383843i	−0.0667191	+	0.0178773i	−0.292024	−	0.956411i	$-0.594329\pi$
$461$	−1.43252	+	0.383843i	−0.0667191	+	0.0178773i	0.225305	+	0.974288i	$0.427662\pi$
$462$		0			0
$463$	−27.4825			−1.27722			−0.638609	−	0.769531i	$-0.720490\pi$
$463$	−27.4825			−1.27722			−0.638609	+	0.769531i	$0.720490\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.0831885	+	0.0831885i	0.00384950	+	0.00384950i	0.709029	−	0.705179i	$-0.249134\pi$
$467$	0.0831885	+	0.0831885i	0.00384950	+	0.00384950i	−0.705179	+	0.709029i	$0.749134\pi$
$468$		0			0
$469$			20.9271i			0.966326i
$470$		0			0
$471$	0.133452	+	0.231146i	0.00614916	+	0.0106507i
$472$		0			0
$473$		−	2.92419i		−	0.134455i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	15.9372	+	59.4786i	0.729716	+	2.72334i
$478$		0			0
$479$	6.12267	−	22.8501i	0.279752	−	1.04405i	−0.672837	−	0.739790i	$-0.734925\pi$
$479$	6.12267	−	22.8501i	0.279752	−	1.04405i	0.952589	−	0.304259i	$-0.0984087\pi$
$480$		0			0
$481$	28.0638	+	23.7707i	1.27960	+	1.08385i
$482$		0			0
$483$	37.7119	−	21.7730i	1.71595	−	0.990704i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	10.7169	−	18.5622i	0.485628	−	0.841133i	−0.514235	−	0.857649i	$-0.671924\pi$
$487$	10.7169	−	18.5622i	0.485628	−	0.841133i	0.999864	+	0.0165161i	$0.00525746\pi$
$488$		0			0
$489$	42.7550	+	42.7550i	1.93345	+	1.93345i
$490$		0			0
$491$	−13.2578	+	7.65438i	−0.598315	+	0.345437i	−0.768378	−	0.639996i	$-0.778936\pi$
$491$	−13.2578	+	7.65438i	−0.598315	+	0.345437i	0.170063	+	0.985433i	$0.445603\pi$
$492$		0			0
$493$	−1.92941	+	1.92941i	−0.0868961	+	0.0868961i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.5624	−	2.83019i	−0.473789	−	0.126951i
$498$		0			0
$499$	−8.64170	+	8.64170i	−0.386856	+	0.386856i	−0.873564	−	0.486709i	$-0.838197\pi$
$499$	−8.64170	+	8.64170i	−0.386856	+	0.386856i	0.486709	+	0.873564i	$0.338197\pi$
$500$		0			0
$501$	2.23528	+	8.34216i	0.0998648	+	0.372700i
$502$		0			0
$503$	21.5394	−	5.77147i	0.960396	−	0.257337i	0.255628	−	0.966775i	$-0.417718\pi$
$503$	21.5394	−	5.77147i	0.960396	−	0.257337i	0.704768	+	0.709438i	$0.251051\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−18.2474	−	40.0974i	−0.810397	−	1.78079i
$508$		0			0
$509$	−24.4129	−	6.54140i	−1.08208	−	0.289943i	−0.326633	−	0.945151i	$-0.605914\pi$
$509$	−24.4129	−	6.54140i	−1.08208	−	0.289943i	−0.755448	+	0.655209i	$0.772581\pi$
$510$		0			0
$511$	−25.4644	−	14.7019i	−1.12648	−	0.650373i
$512$		0			0
$513$	−28.7424	−	16.5945i	−1.26901	−	0.732663i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.549239	−	2.04979i	0.0241555	−	0.0901495i
$518$		0			0
$519$	−47.8746			−2.10146
$520$		0			0
$521$	19.3421			0.847393			0.423697	−	0.905804i	$-0.360732\pi$
$521$	19.3421			0.847393			0.423697	+	0.905804i	$0.360732\pi$
$522$		0			0
$523$	−8.06014	+	30.0808i	−0.352445	+	1.31534i	0.531224	+	0.847231i	$0.321732\pi$
$523$	−8.06014	+	30.0808i	−0.352445	+	1.31534i	−0.883669	+	0.468112i	$0.844934\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.37287	−	0.792625i	−0.0598030	−	0.0345273i
$528$		0			0
$529$	0.845038	+	0.487883i	0.0367408	+	0.0212123i
$530$		0			0
$531$	24.5698	+	6.58346i	1.06624	+	0.285698i
$532$		0			0
$533$	−22.1940	+	1.83818i	−0.961327	+	0.0796202i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	51.4139	−	13.7763i	2.21867	−	0.594492i
$538$		0			0
$539$	−0.0517935	−	0.193296i	−0.00223090	−	0.00832584i
$540$		0			0
$541$	10.9495	−	10.9495i	0.470757	−	0.470757i	−0.431403	−	0.902159i	$-0.641981\pi$
$541$	10.9495	−	10.9495i	0.470757	−	0.470757i	0.902159	+	0.431403i	$0.141981\pi$
$542$		0			0
$543$	25.7918	+	6.91089i	1.10683	+	0.296575i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−25.2846	+	25.2846i	−1.08109	+	1.08109i	−0.0846839	+	0.996408i	$0.526988\pi$
$547$	−25.2846	+	25.2846i	−1.08109	+	1.08109i	−0.996408	+	0.0846839i	$0.973012\pi$
$548$		0			0
$549$	36.0649	−	20.8221i	1.53921	−	0.888664i
$550$		0			0
$551$	−9.16789	−	9.16789i	−0.390565	−	0.390565i
$552$		0			0
$553$	3.57544	−	6.19284i	0.152043	−	0.263347i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.6667	−	8.46780i	0.621447	−	0.358792i	−0.155985	−	0.987759i	$-0.549855\pi$
$557$	14.6667	−	8.46780i	0.621447	−	0.358792i	0.777432	+	0.628967i	$0.216522\pi$
$558$		0			0
$559$	−4.88870	+	3.38947i	−0.206770	+	0.143359i
$560$		0			0
$561$	0.584265	−	2.18051i	0.0246677	−	0.0920610i
$562$		0			0
$563$	−6.67250	−	24.9021i	−0.281212	−	1.04950i	−0.951563	−	0.307454i	$-0.900523\pi$
$563$	−6.67250	−	24.9021i	−0.281212	−	1.04950i	0.670351	−	0.742044i	$-0.266144\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	98.4751i		−	4.13557i
$568$		0			0
$569$	−17.6372	−	30.5485i	−0.739390	−	1.28066i	−0.952770	−	0.303692i	$-0.901781\pi$
$569$	−17.6372	−	30.5485i	−0.739390	−	1.28066i	0.213380	−	0.976969i	$-0.431553\pi$
$570$		0			0
$571$		−	34.8260i		−	1.45742i	−0.684821	−	0.728711i	$-0.740120\pi$
$571$		−	34.8260i		−	1.45742i	0.684821	−	0.728711i	$-0.259880\pi$
$572$		0			0
$573$	−45.1359	−	45.1359i	−1.88558	−	1.88558i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	27.5561			1.14717			0.573587	−	0.819145i	$-0.305552\pi$
$577$	27.5561			1.14717			0.573587	+	0.819145i	$0.305552\pi$
$578$		0			0
$579$	80.0833	−	21.4582i	3.32815	−	0.891774i
$580$		0			0
$581$	−14.7532	+	25.5533i	−0.612067	+	1.06013i
$582$		0			0
$583$	−6.43198	−	11.1405i	−0.266385	−	0.461393i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.693144	+	1.20056i	0.0286091	+	0.0495524i	0.879975	−	0.475019i	$-0.157559\pi$
$587$	0.693144	+	1.20056i	0.0286091	+	0.0495524i	−0.851366	+	0.524572i	$0.824226\pi$
$588$		0			0
$589$	3.76628	−	6.52340i	0.155187	−	0.268792i
$590$		0			0
$591$	46.3551	−	12.4208i	1.90679	−	0.510924i
$592$		0			0
$593$	−11.7399			−0.482102			−0.241051	−	0.970512i	$-0.577492\pi$
$593$	−11.7399			−0.482102			−0.241051	+	0.970512i	$0.577492\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.55116	+	7.55116i	0.309048	+	0.309048i
$598$		0			0
$599$			28.5588i			1.16688i	0.812155	+	0.583441i	$0.198294\pi$
$599$			28.5588i			1.16688i	−0.812155	+	0.583441i	$0.801706\pi$
$600$		0			0
$601$	−16.1665	−	28.0013i	−0.659447	−	1.14220i	−0.980759	−	0.195222i	$-0.937457\pi$
$601$	−16.1665	−	28.0013i	−0.659447	−	1.14220i	0.321312	−	0.946973i	$-0.395876\pi$
$602$		0			0
$603$			67.6526i			2.75503i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	3.24785	+	12.1211i	0.131826	+	0.491982i	0.999991	−	0.00429458i	$-0.00136701\pi$
$607$	3.24785	+	12.1211i	0.131826	+	0.491982i	−0.868165	+	0.496276i	$0.834700\pi$
$608$		0			0
$609$	16.7100	−	62.3626i	0.677124	−	2.52706i
$610$		0			0
$611$	−4.06349	+	1.45771i	−0.164391	+	0.0589726i
$612$		0			0
$613$	−10.8044	+	6.23790i	−0.436384	+	0.251946i	−0.702063	−	0.712115i	$-0.747737\pi$
$613$	−10.8044	+	6.23790i	−0.436384	+	0.251946i	0.265679	+	0.964062i	$0.414404\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.2948	−	31.6876i	0.736523	−	1.27569i	−0.217530	−	0.976054i	$-0.569800\pi$
$617$	18.2948	−	31.6876i	0.736523	−	1.27569i	0.954052	−	0.299641i	$-0.0968668\pi$
$618$		0			0
$619$	1.93560	+	1.93560i	0.0777985	+	0.0777985i	0.744935	−	0.667137i	$-0.232480\pi$
$619$	1.93560	+	1.93560i	0.0777985	+	0.0777985i	−0.667137	+	0.744935i	$0.732480\pi$
$620$		0			0
$621$	78.8034	−	45.4971i	3.16227	−	1.82574i
$622$		0			0
$623$	−13.7183	+	13.7183i	−0.549611	+	0.549611i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	10.3610	+	2.77623i	0.413779	+	0.110872i
$628$		0			0
$629$	2.71095	−	2.71095i	0.108092	−	0.108092i
$630$		0			0
$631$	4.99996	+	18.6601i	0.199045	+	0.742848i	0.991182	+	0.132504i	$0.0423018\pi$
$631$	4.99996	+	18.6601i	0.199045	+	0.742848i	−0.792137	+	0.610343i	$0.791031\pi$
$632$		0			0
$633$	2.11761	−	0.567411i	0.0841674	−	0.0225526i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.263120	+	0.310641i	−0.0104252	+	0.0123080i
$638$		0			0
$639$	−34.1458	−	9.14934i	−1.35079	−	0.361942i
$640$		0			0
$641$	−0.725792	−	0.419036i	−0.0286671	−	0.0165509i	0.485598	−	0.874182i	$-0.338602\pi$
$641$	−0.725792	−	0.419036i	−0.0286671	−	0.0165509i	−0.514265	+	0.857631i	$0.671935\pi$
$642$		0			0
$643$	21.9500	+	12.6729i	0.865625	+	0.499769i	0.865892	−	0.500231i	$-0.166752\pi$
$643$	21.9500	+	12.6729i	0.865625	+	0.499769i	−0.000267216		1.00000i	$0.500085\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.72177	−	17.6219i	0.185632	−	0.692787i	−0.808863	−	0.587998i	$-0.799916\pi$
$647$	4.72177	−	17.6219i	0.185632	−	0.692787i	0.994494	−	0.104790i	$-0.0334169\pi$
$648$		0			0
$649$	−5.31393			−0.208590
$650$		0			0
$651$	37.5093			1.47011
$652$		0			0
$653$	−7.58401	+	28.3039i	−0.296785	+	1.10762i	0.643004	+	0.765863i	$0.277688\pi$
$653$	−7.58401	+	28.3039i	−0.296785	+	1.10762i	−0.939789	+	0.341755i	$0.888979\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−82.3205	−	47.5278i	−3.21163	−	1.85423i
$658$		0			0
$659$	−25.2957	−	14.6045i	−0.985380	−	0.568909i	−0.0814899	−	0.996674i	$-0.525968\pi$
$659$	−25.2957	−	14.6045i	−0.985380	−	0.568909i	−0.903890	+	0.427765i	$0.859301\pi$
$660$		0			0
$661$	9.01504	+	2.41557i	0.350645	+	0.0939549i	0.429842	−	0.902904i	$-0.358569\pi$
$661$	9.01504	+	2.41557i	0.350645	+	0.0939549i	−0.0791977	+	0.996859i	$0.525236\pi$
$662$		0			0
$663$	−4.32263	+	1.55067i	−0.167877	+	0.0602231i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	34.3360	−	9.20029i	1.32949	−	0.356237i
$668$		0			0
$669$	11.2288	+	41.9063i	0.434129	+	1.62019i
$670$		0			0
$671$	−6.15172	+	6.15172i	−0.237485	+	0.237485i
$672$		0			0
$673$	−15.4318	−	4.13494i	−0.594852	−	0.159390i	−0.0511823	−	0.998689i	$-0.516299\pi$
$673$	−15.4318	−	4.13494i	−0.594852	−	0.159390i	−0.543670	+	0.839299i	$0.682966\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.10291	−	5.10291i	0.196121	−	0.196121i	−0.602214	−	0.798335i	$-0.705715\pi$
$677$	5.10291	−	5.10291i	0.196121	−	0.196121i	0.798335	+	0.602214i	$0.205715\pi$
$678$		0			0
$679$	−3.81014	+	2.19979i	−0.146220	+	0.0844200i
$680$		0			0
$681$	24.9539	+	24.9539i	0.956234	+	0.956234i
$682$		0			0
$683$	−13.5781	+	23.5179i	−0.519550	+	0.899888i	0.480191	+	0.877164i	$0.340567\pi$
$683$	−13.5781	+	23.5179i	−0.519550	+	0.899888i	−0.999742	+	0.0227240i	$0.992766\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−17.6956	+	10.2166i	−0.675131	+	0.389787i
$688$		0			0
$689$	−11.1695	+	23.6662i	−0.425523	+	0.901610i
$690$		0			0
$691$	7.84688	−	29.2849i	0.298509	−	1.11405i	−0.639881	−	0.768474i	$-0.721016\pi$
$691$	7.84688	−	29.2849i	0.298509	−	1.11405i	0.938390	−	0.345578i	$-0.112317\pi$
$692$		0			0
$693$	10.2131	+	38.1157i	0.387963	+	1.44790i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			2.32149i			0.0879328i
$698$		0			0
$699$	−1.88356	−	3.26243i	−0.0712429	−	0.123396i
$700$		0			0
$701$			21.4987i			0.811995i	0.913874	+	0.405998i	$0.133076\pi$
$701$			21.4987i			0.811995i	−0.913874	+	0.405998i	$0.866924\pi$
$702$		0			0
$703$	12.8815	+	12.8815i	0.485835	+	0.485835i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	37.0001			1.39153
$708$		0			0
$709$	−34.6698	+	9.28974i	−1.30205	+	0.348883i	−0.842225	−	0.539126i	$-0.818755\pi$
$709$	−34.6698	+	9.28974i	−1.30205	+	0.348883i	−0.459825	+	0.888009i	$0.652088\pi$
$710$		0			0
$711$	11.5586	−	20.0200i	0.433480	−	0.750809i
$712$		0			0
$713$	10.3260	+	17.8852i	0.386714	+	0.669808i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−44.9342	−	77.8284i	−1.67810	−	2.90655i
$718$		0			0
$719$	−12.3572	+	21.4033i	−0.460845	+	0.798207i	−0.999003	−	0.0446370i	$-0.985787\pi$
$719$	−12.3572	+	21.4033i	−0.460845	+	0.798207i	0.538158	+	0.842844i	$0.319120\pi$
$720$		0			0
$721$	−29.4521	+	7.89167i	−1.09685	+	0.293901i
$722$		0			0
$723$	37.9423			1.41109
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−18.6487	−	18.6487i	−0.691643	−	0.691643i	0.270950	−	0.962593i	$-0.412662\pi$
$727$	−18.6487	−	18.6487i	−0.691643	−	0.691643i	−0.962593	+	0.270950i	$0.912662\pi$
$728$		0			0
$729$		−	129.421i		−	4.79336i
$730$		0			0
$731$	0.310060	+	0.537040i	0.0114680	+	0.0198631i
$732$		0			0
$733$			7.50510i			0.277207i	0.990348	+	0.138604i	$0.0442614\pi$
$733$			7.50510i			0.277207i	−0.990348	+	0.138604i	$0.955739\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.65796	−	13.6517i	−0.134743	−	0.502866i
$738$		0			0
$739$	−8.26789	+	30.8562i	−0.304139	+	1.13506i	0.629544	+	0.776965i	$0.283242\pi$
$739$	−8.26789	+	30.8562i	−0.304139	+	1.13506i	−0.933684	+	0.358099i	$0.883425\pi$
$740$		0			0
$741$	−7.36826	−	20.5396i	−0.270680	−	0.754543i
$742$		0			0
$743$	2.89526	−	1.67158i	0.106217	−	0.0613242i	−0.445951	−	0.895058i	$-0.647134\pi$
$743$	2.89526	−	1.67158i	0.106217	−	0.0613242i	0.552167	+	0.833733i	$0.313801\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−47.6937	+	82.6080i	−1.74502	+	3.02247i
$748$		0			0
$749$	−16.7345	−	16.7345i	−0.611464	−	0.611464i
$750$		0			0
$751$	−27.6186	+	15.9456i	−1.00782	+	0.581864i	−0.910552	−	0.413395i	$-0.864343\pi$
$751$	−27.6186	+	15.9456i	−1.00782	+	0.581864i	−0.0972656	+	0.995258i	$0.531010\pi$
$752$		0			0
$753$	68.1624	−	68.1624i	2.48397	−	2.48397i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.14545	−	1.91462i	−0.259706	−	0.0695879i	0.126617	−	0.991952i	$-0.459588\pi$
$757$	−7.14545	−	1.91462i	−0.259706	−	0.0695879i	−0.386322	+	0.922364i	$0.626255\pi$
$758$		0			0
$759$	−20.7953	+	20.7953i	−0.754821	+	0.754821i
$760$		0			0
$761$	−2.23786	−	8.35181i	−0.0811224	−	0.302753i	0.913429	−	0.406997i	$-0.133424\pi$
$761$	−2.23786	−	8.35181i	−0.0811224	−	0.302753i	−0.994552	+	0.104244i	$0.966758\pi$
$762$		0			0
$763$	−30.4045	+	8.14686i	−1.10072	+	0.294936i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.15944	+	8.88389i	0.222405	+	0.320779i
$768$		0			0
$769$	15.8736	+	4.25333i	0.572418	+	0.153379i	0.533405	−	0.845860i	$-0.320912\pi$
$769$	15.8736	+	4.25333i	0.572418	+	0.153379i	0.0390126	+	0.999239i	$0.487579\pi$
$770$		0			0
$771$	78.0344	+	45.0532i	2.81034	+	1.62255i
$772$		0			0
$773$	−35.5561	−	20.5283i	−1.27886	−	0.738352i	−0.302223	−	0.953237i	$-0.597729\pi$
$773$	−35.5561	−	20.5283i	−1.27886	−	0.738352i	−0.976639	+	0.214885i	$0.931062\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−23.4787	+	87.6236i	−0.842293	+	3.14348i
$778$		0			0
$779$	−11.0309			−0.395225
$780$		0			0
$781$	7.38502			0.264257
$782$		0			0
$783$	34.9175	−	130.314i	1.24785	−	4.65704i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	26.3157	+	15.1934i	0.938053	+	0.541585i	0.889350	−	0.457228i	$-0.151158\pi$
$787$	26.3157	+	15.1934i	0.938053	+	0.541585i	0.0487038	+	0.998813i	$0.484491\pi$
$788$		0			0
$789$	−32.4764	−	18.7503i	−1.15619	−	0.667527i
$790$		0			0
$791$	7.13064	+	1.91065i	0.253536	+	0.0679349i
$792$		0			0
$793$	17.4151	+	3.15399i	0.618427	+	0.112001i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	29.0048	−	7.77181i	1.02740	−	0.275292i	0.294518	−	0.955646i	$-0.404841\pi$
$797$	29.0048	−	7.77181i	1.02740	−	0.275292i	0.732883	+	0.680354i	$0.238174\pi$
$798$		0			0
$799$	0.116474	+	0.434689i	0.00412057	+	0.0153782i
$800$		0			0
$801$	−44.3480	+	44.3480i	−1.56696	+	1.56696i
$802$		0			0
$803$	19.1813	+	5.13963i	0.676895	+	0.181373i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	11.0038	−	11.0038i	0.387351	−	0.387351i
$808$		0			0
$809$	−28.0361	+	16.1867i	−0.985698	+	0.569093i	−0.903986	−	0.427563i	$-0.859372\pi$
$809$	−28.0361	+	16.1867i	−0.985698	+	0.569093i	−0.0817125	+	0.996656i	$0.526039\pi$
$810$		0			0
$811$	34.6643	+	34.6643i	1.21723	+	1.21723i	0.968599	+	0.248628i	$0.0799796\pi$
$811$	34.6643	+	34.6643i	1.21723	+	1.21723i	0.248628	+	0.968599i	$0.420020\pi$
$812$		0			0
$813$	−8.60277	+	14.9004i	−0.301712	+	0.522581i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.55183	+	1.47330i	−0.0892772	+	0.0515442i
$818$		0			0
$819$	51.8842	−	61.2548i	1.81298	−	2.14041i
$820$		0			0
$821$	5.18587	−	19.3539i	0.180988	−	0.675457i	−0.814466	−	0.580212i	$-0.802970\pi$
$821$	5.18587	−	19.3539i	0.180988	−	0.675457i	0.995454	−	0.0952454i	$-0.0303636\pi$
$822$		0			0
$823$	12.0671	+	45.0352i	0.420634	+	1.56983i	0.773276	+	0.634069i	$0.218617\pi$
$823$	12.0671	+	45.0352i	0.420634	+	1.56983i	−0.352643	+	0.935758i	$0.614717\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			17.0353i			0.592376i	0.955130	+	0.296188i	$0.0957155\pi$
$827$			17.0353i			0.592376i	−0.955130	+	0.296188i	$0.904285\pi$
$828$		0			0
$829$	12.2763	+	21.2632i	0.426373	+	0.738500i	0.996548	−	0.0830237i	$-0.0264577\pi$
$829$	12.2763	+	21.2632i	0.426373	+	0.738500i	−0.570174	+	0.821524i	$0.693124\pi$
$830$		0			0
$831$		−	56.7740i		−	1.96947i
$832$		0			0
$833$	0.0300078	+	0.0300078i	0.00103971	+	0.00103971i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	78.3801			2.70921
$838$		0			0
$839$	16.2633	−	4.35773i	0.561470	−	0.150446i	0.0330886	−	0.999452i	$-0.489466\pi$
$839$	16.2633	−	4.35773i	0.561470	−	0.150446i	0.528382	+	0.849007i	$0.322799\pi$
$840$		0			0
$841$	11.8517	−	20.5277i	0.408679	−	0.707852i
$842$		0			0
$843$	43.9774	+	76.1711i	1.51466	+	2.62347i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	10.3120	+	17.8609i	0.354324	+	0.613707i
$848$		0			0
$849$	10.2142	−	17.6916i	0.350552	−	0.607174i
$850$		0			0
$851$	−48.2443	+	12.9270i	−1.65379	+	0.443133i
$852$		0			0
$853$	7.14403			0.244607			0.122303	−	0.992493i	$-0.460972\pi$
$853$	7.14403			0.244607			0.122303	+	0.992493i	$0.460972\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.5242	+	14.5242i	0.496138	+	0.496138i	0.910233	−	0.414096i	$-0.135902\pi$
$857$	14.5242	+	14.5242i	0.496138	+	0.496138i	−0.414096	+	0.910233i	$0.635902\pi$
$858$		0			0
$859$		−	23.3877i		−	0.797977i	−0.916956	−	0.398989i	$-0.869361\pi$
$859$		−	23.3877i		−	0.797977i	0.916956	−	0.398989i	$-0.130639\pi$
$860$		0			0
$861$	−27.4650	−	47.5707i	−0.936003	−	1.62121i
$862$		0			0
$863$			37.5180i			1.27713i	0.769569	+	0.638564i	$0.220471\pi$
$863$			37.5180i			1.27713i	−0.769569	+	0.638564i	$0.779529\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−14.7865	−	55.1839i	−0.502175	−	1.87414i
$868$		0			0
$869$	−1.24994	+	4.66483i	−0.0424012	+	0.158243i
$870$		0			0
$871$	−18.5831	+	21.9393i	−0.629663	+	0.743383i
$872$		0			0
$873$	−12.3173	+	7.11139i	−0.416877	+	0.240684i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.7859	+	27.3420i	−0.533052	+	0.923273i	0.466203	+	0.884678i	$0.345622\pi$
$877$	−15.7859	+	27.3420i	−0.533052	+	0.923273i	−0.999255	+	0.0385955i	$0.987712\pi$
$878$		0			0
$879$	37.7077	+	37.7077i	1.27185	+	1.27185i
$880$		0			0
$881$	15.9389	−	9.20231i	0.536994	−	0.310034i	−0.206866	−	0.978369i	$-0.566326\pi$
$881$	15.9389	−	9.20231i	0.536994	−	0.310034i	0.743860	+	0.668336i	$0.232993\pi$
$882$		0			0
$883$	−25.8290	+	25.8290i	−0.869216	+	0.869216i	−0.992386	−	0.123170i	$-0.960694\pi$
$883$	−25.8290	+	25.8290i	−0.869216	+	0.869216i	0.123170	+	0.992386i	$0.460694\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	53.7095	+	14.3914i	1.80339	+	0.483216i	0.994499	−	0.104746i	$-0.0334029\pi$
$887$	53.7095	+	14.3914i	1.80339	+	0.483216i	0.808889	+	0.587962i	$0.200070\pi$
$888$		0			0
$889$	−12.2911	+	12.2911i	−0.412230	+	0.412230i
$890$		0			0
$891$	17.2129	+	64.2396i	0.576655	+	2.15211i
$892$		0			0
$893$	−2.06549	+	0.553447i	−0.0691191	+	0.0185204i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	58.8699	+	10.6617i	1.96561	+	0.355985i
$898$		0			0
$899$	29.5761	+	7.92489i	0.986418	+	0.264310i
$900$		0			0
$901$	2.36252	+	1.36400i	0.0787068	+	0.0454414i
$902$		0			0
$903$	−12.7071	−	7.33647i	−0.422867	−	0.244143i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.71757	−	6.41005i	0.0570309	−	0.212842i	−0.931530	−	0.363665i	$-0.881525\pi$
$907$	1.71757	−	6.41005i	0.0570309	−	0.212842i	0.988561	+	0.150822i	$0.0481921\pi$
$908$		0			0
$909$	119.613			3.96731
$910$		0			0
$911$	37.4367			1.24033			0.620167	−	0.784470i	$-0.287065\pi$
$911$	37.4367			1.24033			0.620167	+	0.784470i	$0.287065\pi$
$912$		0			0
$913$	5.15757	−	19.2483i	0.170691	−	0.637027i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.09851	−	3.52097i	−0.201390	−	0.116273i
$918$		0			0
$919$	27.6405	+	15.9583i	0.911776	+	0.526414i	0.881002	−	0.473112i	$-0.156869\pi$
$919$	27.6405	+	15.9583i	0.911776	+	0.526414i	0.0307739	+	0.999526i	$0.490203\pi$
$920$		0			0
$921$	−91.8906	−	24.6220i	−3.02790	−	0.811323i
$922$		0			0
$923$	−8.56007	−	12.3464i	−0.281758	−	0.406386i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−95.2118	+	25.5119i	−3.12716	+	0.837921i
$928$		0			0
$929$	−8.48551	−	31.6684i	−0.278401	−	1.03900i	−0.953528	−	0.301304i	$-0.902578\pi$
$929$	−8.48551	−	31.6684i	−0.278401	−	1.03900i	0.675128	−	0.737701i	$-0.264089\pi$
$930$		0			0
$931$	−0.142587	+	0.142587i	−0.00467309	+	0.00467309i
$932$		0			0
$933$	−24.0124	−	6.43411i	−0.786132	−	0.210643i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−4.85825	+	4.85825i	−0.158712	+	0.158712i	−0.781996	−	0.623284i	$-0.785798\pi$
$937$	−4.85825	+	4.85825i	−0.158712	+	0.158712i	0.623284	+	0.781996i	$0.285798\pi$
$938$		0			0
$939$	−26.6161	+	15.3668i	−0.868584	+	0.501477i
$940$		0			0
$941$	33.3418	+	33.3418i	1.08691	+	1.08691i	0.995845	+	0.0910661i	$0.0290275\pi$
$941$	33.3418	+	33.3418i	1.08691	+	1.08691i	0.0910661	+	0.995845i	$0.470973\pi$
$942$		0			0
$943$	15.1218	−	26.1917i	0.492434	−	0.852921i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−31.9537	+	18.4485i	−1.03836	+	0.599495i	−0.919367	−	0.393401i	$-0.871298\pi$
$947$	−31.9537	+	18.4485i	−1.03836	+	0.599495i	−0.118988	+	0.992896i	$0.537965\pi$
$948$		0			0
$949$	−13.6409	−	38.0250i	−0.442801	−	1.23434i
$950$		0			0
$951$	28.0312	−	104.614i	0.908975	−	3.39234i
$952$		0			0
$953$	−1.52690	−	5.69846i	−0.0494611	−	0.184591i	0.936776	−	0.349930i	$-0.113795\pi$
$953$	−1.52690	−	5.69846i	−0.0494611	−	0.184591i	−0.986237	+	0.165339i	$0.947128\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			43.6026i			1.40947i
$958$		0			0
$959$	−2.70823	−	4.69080i	−0.0874535	−	0.151474i
$960$		0			0
$961$		−	13.2108i		−	0.426156i
$962$		0			0
$963$	−54.0986	−	54.0986i	−1.74330	−	1.74330i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	5.23575			0.168370			0.0841851	−	0.996450i	$-0.473171\pi$
$967$	5.23575			0.168370			0.0841851	+	0.996450i	$0.473171\pi$
$968$		0			0
$969$	−2.19721	+	0.588741i	−0.0705847	+	0.0189131i
$970$		0			0
$971$	−25.3905	+	43.9776i	−0.814820	+	1.41131i	0.0946379	+	0.995512i	$0.469831\pi$
$971$	−25.3905	+	43.9776i	−0.814820	+	1.41131i	−0.909457	+	0.415797i	$0.863503\pi$
$972$		0			0
$973$	−19.3449	−	33.5064i	−0.620170	−	1.07417i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.82225	+	11.8165i	0.218263	+	0.378043i	0.954277	−	0.298924i	$-0.0966275\pi$
$977$	6.82225	+	11.8165i	0.218263	+	0.378043i	−0.736014	+	0.676966i	$0.763294\pi$
$978$		0			0
$979$	6.55114	−	11.3469i	0.209375	−	0.362649i
$980$		0			0
$981$	−98.2907	+	26.3369i	−3.13818	+	0.840873i
$982$		0			0
$983$	26.5627			0.847217			0.423609	−	0.905845i	$-0.360763\pi$
$983$	26.5627			0.847217			0.423609	+	0.905845i	$0.360763\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−7.52941	−	7.52941i	−0.239664	−	0.239664i
$988$		0			0
$989$		−	8.07871i		−	0.256888i
$990$		0			0
$991$	9.37032	+	16.2299i	0.297658	+	0.515559i	0.975600	−	0.219557i	$-0.0704611\pi$
$991$	9.37032	+	16.2299i	0.297658	+	0.515559i	−0.677942	+	0.735116i	$0.737128\pi$
$992$		0			0
$993$			16.0909i			0.510629i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.37101	−	8.84872i	−0.0750906	−	0.280242i	0.918163	−	0.396202i	$-0.129672\pi$
$997$	−2.37101	−	8.84872i	−0.0750906	−	0.280242i	−0.993254	+	0.115960i	$0.963005\pi$
$998$		0			0
$999$	−49.0614	+	183.100i	−1.55223	+	5.79302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.bs.d.193.1		20
5.2	odd	4		1300.2.bn.d.557.5		20
5.3	odd	4		260.2.bf.c.37.1	✓	20
5.4	even	2		260.2.bk.c.193.5	yes	20
13.6	odd	12		1300.2.bn.d.1293.5		20
65.19	odd	12		260.2.bf.c.253.1	yes	20
65.32	even	12	inner	1300.2.bs.d.357.1		20
65.58	even	12		260.2.bk.c.97.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.37.1	✓	20	5.3	odd	4
260.2.bf.c.253.1	yes	20	65.19	odd	12
260.2.bk.c.97.5	yes	20	65.58	even	12
260.2.bk.c.193.5	yes	20	5.4	even	2
1300.2.bn.d.557.5		20	5.2	odd	4
1300.2.bn.d.1293.5		20	13.6	odd	12
1300.2.bs.d.193.1		20	1.1	even	1	trivial
1300.2.bs.d.357.1		20	65.32	even	12	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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877081 + 3.27331i) q^{3} +(-2.27273 - 1.31216i) q^{7} +(-7.34722 - 4.24192i) q^{9} +O(q^{10})\)	\(q+(-0.877081 + 3.27331i) q^{3} +(-2.27273 - 1.31216i) q^{7} +(-7.34722 - 4.24192i) q^{9} +(1.71196 + 0.458719i) q^{11} +(-1.21746 - 3.39379i) q^{13} +(-0.363048 + 0.0972783i) q^{17} +(-0.462233 - 1.72508i) q^{19} +(6.28849 - 6.28849i) q^{21} +(4.72966 + 1.26731i) q^{23} +(13.1405 - 13.1405i) q^{27} +(6.28709 - 3.62985i) q^{29} +(2.98238 + 2.98238i) q^{31} +(-3.00306 + 5.20145i) q^{33} +(-8.83378 + 5.10019i) q^{37} +(12.1767 - 1.00852i) q^{39} +(1.59861 - 5.96611i) q^{41} +(-0.427024 - 1.59368i) q^{43} -1.19733i q^{47} +(-0.0564545 - 0.0977821i) q^{49} -1.27369i q^{51} +(-5.13227 - 5.13227i) q^{53} +6.05214 q^{57} +(-2.89607 + 0.776000i) q^{59} +(-2.45432 + 4.25101i) q^{61} +(11.1322 + 19.2815i) q^{63} +(-3.98715 - 6.90594i) q^{67} +(-8.29659 + 14.3701i) q^{69} +(4.02481 - 1.07844i) q^{71} +11.2043 q^{73} +(-3.28892 - 3.28892i) q^{77} +2.72484i q^{79} +(18.7620 + 32.4967i) q^{81} -11.2434i q^{83} +(6.36735 + 23.7633i) q^{87} +(1.91334 - 7.14070i) q^{89} +(-1.68623 + 9.31068i) q^{91} +(-12.3780 + 7.14647i) q^{93} +(0.838229 - 1.45185i) q^{97} +(-10.6323 - 10.6323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9	\( 20 q + 2 q^{3} - 6 q^{7} - 12 q^{9} - 8 q^{13} + 20 q^{19} - 12 q^{21} - 6 q^{23} + 20 q^{27} + 24 q^{29} + 8 q^{31} + 10 q^{33} + 4 q^{39} + 6 q^{41} - 38 q^{43} + 14 q^{49} - 30 q^{53} + 76 q^{57} - 24 q^{59} - 32 q^{61} + 24 q^{63} - 22 q^{67} - 16 q^{69} + 44 q^{73} + 12 q^{77} + 2 q^{81} - 38 q^{87} - 30 q^{89} - 72 q^{91} + 48 q^{93} - 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 6 * q^7 - 12 * q^9 - 8 * q^13 + 20 * q^19 - 12 * q^21 - 6 * q^23 + 20 * q^27 + 24 * q^29 + 8 * q^31 + 10 * q^33 + 4 * q^39 + 6 * q^41 - 38 * q^43 + 14 * q^49 - 30 * q^53 + 76 * q^57 - 24 * q^59 - 32 * q^61 + 24 * q^63 - 22 * q^67 - 16 * q^69 + 44 * q^73 + 12 * q^77 + 2 * q^81 - 38 * q^87 - 30 * q^89 - 72 * q^91 + 48 * q^93 - 46 * q^97 + 20 * q^99

Introduction

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