LMFDB - Embedded newform 416.2.w.d.257.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(225,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("416.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.w (of order $6$, degree $2$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.18092737797525504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 12x^{10} + 108x^{8} - 430x^{6} + 1284x^{4} - 36x^{2} + 1 $ x^12 - 12x^10 + 108x^8 - 430x^6 + 1284x^4 - 36*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.5
Root			$-2.19011 - 1.26446i$ of defining polynomial
Character	$\chi$	$=$	416.257
Dual form			416.2.w.d.225.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13286 + 1.96217i) q^{3} -3.99777i q^{5} +(0.981633 + 0.566746i) q^{7} +(-1.06675 + 1.84766i) q^{9} +O(q^{10})$	\(q+(1.13286 + 1.96217i) q^{3} -3.99777i q^{5} +(0.981633 + 0.566746i) q^{7} +(-1.06675 + 1.84766i) q^{9} +(0.981633 - 0.566746i) q^{11} +(3.59566 - 0.266835i) q^{13} +(7.84432 - 4.52892i) q^{15} +(-0.500000 + 0.866025i) q^{17} +(3.39858 + 1.96217i) q^{19} +2.56818i q^{21} +(-4.59696 - 7.96217i) q^{23} -10.9822 q^{25} +1.96327 q^{27} +(2.02892 + 3.51419i) q^{29} +9.05784i q^{31} +(2.22411 + 1.28409i) q^{33} +(2.26572 - 3.92434i) q^{35} +(2.16241 - 1.24847i) q^{37} +(4.59696 + 6.75302i) q^{39} +(-2.42434 + 1.39970i) q^{41} +(-3.24735 + 5.62458i) q^{43} +(7.38652 + 4.26461i) q^{45} +6.79085i q^{47} +(-2.85760 - 4.94950i) q^{49} -2.26572 q^{51} -8.92434 q^{53} +(-2.26572 - 3.92434i) q^{55} +8.89147i q^{57} +(-7.77880 - 4.49109i) q^{59} +(3.89543 - 6.74708i) q^{61} +(-2.09431 + 1.20915i) q^{63} +(-1.06675 - 14.3746i) q^{65} +(8.36352 - 4.82868i) q^{67} +(10.4154 - 18.0401i) q^{69} +(-6.86268 - 3.96217i) q^{71} +9.29410i q^{73} +(-12.4413 - 21.5489i) q^{75} +1.28480 q^{77} -12.9894 q^{79} +(5.42434 + 9.39524i) q^{81} +5.73302i q^{83} +(3.46217 + 1.99889i) q^{85} +(-4.59696 + 7.96217i) q^{87} +(12.1485 - 7.01391i) q^{89} +(3.68085 + 1.77589i) q^{91} +(-17.7730 + 10.2613i) q^{93} +(7.84432 - 13.5868i) q^{95} +(-7.70024 - 4.44573i) q^{97} +2.41830i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^9	$ 12 q - 12 q^{9} + 12 q^{13} - 6 q^{17} - 12 q^{25} - 6 q^{29} - 30 q^{33} - 6 q^{37} + 30 q^{41} + 24 q^{49} - 48 q^{53} + 18 q^{61} - 12 q^{65} + 6 q^{69} + 132 q^{77} + 6 q^{81} + 12 q^{85} + 30 q^{89} - 36 q^{93} - 90 q^{97}+O(q^{100}) $ 12 * q - 12 * q^9 + 12 * q^13 - 6 * q^17 - 12 * q^25 - 6 * q^29 - 30 * q^33 - 6 * q^37 + 30 * q^41 + 24 * q^49 - 48 * q^53 + 18 * q^61 - 12 * q^65 + 6 * q^69 + 132 * q^77 + 6 * q^81 + 12 * q^85 + 30 * q^89 - 36 * q^93 - 90 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.13286	+	1.96217i	0.654057	+	1.13286i	0.982129	+	0.188208i	$0.0602678\pi$
$3$	1.13286	+	1.96217i	0.654057	+	1.13286i	−0.328072	+	0.944653i	$0.606399\pi$
$4$		0			0
$5$		−	3.99777i		−	1.78786i	−0.448209	−	0.893929i	$-0.647938\pi$
$5$		−	3.99777i		−	1.78786i	0.448209	−	0.893929i	$-0.352062\pi$
$6$		0			0
$7$	0.981633	+	0.566746i	0.371022	+	0.214210i	0.673905	−	0.738818i	$-0.264616\pi$
$7$	0.981633	+	0.566746i	0.371022	+	0.214210i	−0.302883	+	0.953028i	$0.597949\pi$
$8$		0			0
$9$	−1.06675	+	1.84766i	−0.355582	+	0.615886i
$10$		0			0
$11$	0.981633	−	0.566746i	0.295973	−	0.170880i	−0.344659	−	0.938728i	$-0.612006\pi$
$11$	0.981633	−	0.566746i	0.295973	−	0.170880i	0.640633	+	0.767848i	$0.278672\pi$
$12$		0			0
$13$	3.59566	−	0.266835i	0.997258	−	0.0740067i
$13$	3.59566	−	0.266835i	0.997258	−	0.0740067i
$14$		0			0
$15$	7.84432	−	4.52892i	2.02539	−	1.16936i
$16$		0			0
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$		0			0
$19$	3.39858	+	1.96217i	0.779688	+	0.450153i	0.836320	−	0.548242i	$-0.184703\pi$
$19$	3.39858	+	1.96217i	0.779688	+	0.450153i	−0.0566316	+	0.998395i	$0.518036\pi$
$20$		0			0
$21$			2.56818i			0.560422i
$22$		0			0
$23$	−4.59696	−	7.96217i	−0.958533	−	1.66023i	−0.726068	−	0.687623i	$-0.758654\pi$
$23$	−4.59696	−	7.96217i	−0.958533	−	1.66023i	−0.232465	−	0.972605i	$-0.574679\pi$
$24$		0			0
$25$	−10.9822			−2.19644
$26$		0			0
$27$	1.96327			0.377831
$28$		0			0
$29$	2.02892	+	3.51419i	0.376761	+	0.652569i	0.990589	−	0.136871i	$-0.0437046\pi$
$29$	2.02892	+	3.51419i	0.376761	+	0.652569i	−0.613828	+	0.789440i	$0.710371\pi$
$30$		0			0
$31$			9.05784i			1.62684i	0.581680	+	0.813418i	$0.302396\pi$
$31$			9.05784i			1.62684i	−0.581680	+	0.813418i	$0.697604\pi$
$32$		0			0
$33$	2.22411	+	1.28409i	0.387167	+	0.223531i
$34$		0			0
$35$	2.26572	−	3.92434i	0.382977	−	0.663335i
$36$		0			0
$37$	2.16241	−	1.24847i	0.355498	−	0.205247i	−0.311606	−	0.950211i	$-0.600867\pi$
$37$	2.16241	−	1.24847i	0.355498	−	0.205247i	0.667104	+	0.744964i	$0.267534\pi$
$38$		0			0
$39$	4.59696	+	6.75302i	0.736103	+	1.08135i
$40$		0			0
$41$	−2.42434	+	1.39970i	−0.378619	+	0.218596i	−0.677217	−	0.735783i	$-0.736814\pi$
$41$	−2.42434	+	1.39970i	−0.378619	+	0.218596i	0.298598	+	0.954379i	$0.403481\pi$
$42$		0			0
$43$	−3.24735	+	5.62458i	−0.495217	+	0.857741i	−0.999985	−	0.00551436i	$-0.998245\pi$
$43$	−3.24735	+	5.62458i	−0.495217	+	0.857741i	0.504768	+	0.863255i	$0.331578\pi$
$44$		0			0
$45$	7.38652	+	4.26461i	1.10112	+	0.635730i
$46$		0			0
$47$			6.79085i			0.990548i	0.868737	+	0.495274i	$0.164932\pi$
$47$			6.79085i			0.990548i	−0.868737	+	0.495274i	$0.835068\pi$
$48$		0			0
$49$	−2.85760	−	4.94950i	−0.408228	−	0.707072i
$50$		0			0
$51$	−2.26572			−0.317264
$52$		0			0
$53$	−8.92434			−1.22585			−0.612926	−	0.790140i	$-0.710008\pi$
$53$	−8.92434			−1.22585			−0.612926	+	0.790140i	$0.710008\pi$
$54$		0			0
$55$	−2.26572	−	3.92434i	−0.305510	−	0.529158i
$56$		0			0
$57$			8.89147i			1.17770i
$58$		0			0
$59$	−7.77880	−	4.49109i	−1.01271	−	0.584690i	−0.100728	−	0.994914i	$-0.532117\pi$
$59$	−7.77880	−	4.49109i	−1.01271	−	0.584690i	−0.911985	+	0.410224i	$0.865451\pi$
$60$		0			0
$61$	3.89543	−	6.74708i	0.498758	−	0.863875i	−0.501241	−	0.865308i	$-0.667123\pi$
$61$	3.89543	−	6.74708i	0.498758	−	0.863875i	0.999999	+	0.00143332i	$0.000456240\pi$
$62$		0			0
$63$	−2.09431	+	1.20915i	−0.263858	+	0.152338i
$64$		0			0
$65$	−1.06675	−	14.3746i	−0.132314	−	1.78296i
$66$		0			0
$67$	8.36352	−	4.82868i	1.02177	−	0.589917i	0.107151	−	0.994243i	$-0.465827\pi$
$67$	8.36352	−	4.82868i	1.02177	−	0.589917i	0.914615	+	0.404326i	$0.132494\pi$
$68$		0			0
$69$	10.4154	−	18.0401i	1.25387	−	2.17177i
$70$		0			0
$71$	−6.86268	−	3.96217i	−0.814451	−	0.470223i	0.0340484	−	0.999420i	$-0.489160\pi$
$71$	−6.86268	−	3.96217i	−0.814451	−	0.470223i	−0.848499	+	0.529197i	$0.822493\pi$
$72$		0			0
$73$			9.29410i			1.08779i	0.839153	+	0.543896i	$0.183051\pi$
$73$			9.29410i			1.08779i	−0.839153	+	0.543896i	$0.816949\pi$
$74$		0			0
$75$	−12.4413	−	21.5489i	−1.43660	−	2.48826i
$76$		0			0
$77$	1.28480			0.146417
$78$		0			0
$79$	−12.9894			−1.46142			−0.730712	−	0.682686i	$-0.760812\pi$
$79$	−12.9894			−1.46142			−0.730712	+	0.682686i	$0.760812\pi$
$80$		0			0
$81$	5.42434	+	9.39524i	0.602705	+	1.04392i
$82$		0			0
$83$			5.73302i			0.629280i	0.949211	+	0.314640i	$0.101884\pi$
$83$			5.73302i			0.629280i	−0.949211	+	0.314640i	$0.898116\pi$
$84$		0			0
$85$	3.46217	+	1.99889i	0.375525	+	0.216810i
$86$		0			0
$87$	−4.59696	+	7.96217i	−0.492846	+	0.853634i
$88$		0			0
$89$	12.1485	−	7.01391i	1.28773	−	0.743473i	0.309484	−	0.950905i	$-0.399844\pi$
$89$	12.1485	−	7.01391i	1.28773	−	0.743473i	0.978250	+	0.207432i	$0.0665105\pi$
$90$		0			0
$91$	3.68085	+	1.77589i	0.385858	+	0.186164i
$92$		0			0
$93$	−17.7730	+	10.2613i	−1.84298	+	1.06404i
$94$		0			0
$95$	7.84432	−	13.5868i	0.804810	−	1.39397i
$96$		0			0
$97$	−7.70024	−	4.44573i	−0.781841	−	0.451396i	0.0552415	−	0.998473i	$-0.482407\pi$
$97$	−7.70024	−	4.44573i	−0.781841	−	0.451396i	−0.837082	+	0.547077i	$0.815740\pi$
$98$		0			0
$99$			2.41830i			0.243048i
$100$		0			0
$101$	−4.02892	−	6.97829i	−0.400892	−	0.694366i	0.592942	−	0.805246i	$-0.297967\pi$
$101$	−4.02892	−	6.97829i	−0.400892	−	0.694366i	−0.993834	+	0.110880i	$0.964633\pi$
$102$		0			0
$103$	−6.36367			−0.627031			−0.313515	−	0.949583i	$-0.601507\pi$
$103$	−6.36367			−0.627031			−0.313515	+	0.949583i	$0.601507\pi$
$104$		0			0
$105$	10.2670			1.00196
$106$		0			0
$107$	5.66430	+	9.81086i	0.547589	+	0.948452i	0.998439	+	0.0558520i	$0.0177875\pi$
$107$	5.66430	+	9.81086i	0.547589	+	0.948452i	−0.450850	+	0.892600i	$0.648879\pi$
$108$		0			0
$109$		−	11.4596i		−	1.09763i	−0.835942	−	0.548817i	$-0.815078\pi$
$109$		−	11.4596i		−	1.09763i	0.835942	−	0.548817i	$-0.184922\pi$
$110$		0			0
$111$	4.89942	+	2.82868i	0.465032	+	0.268486i
$112$		0			0
$113$	−2.23302	+	3.86770i	−0.210064	+	0.363842i	−0.951734	−	0.306923i	$-0.900701\pi$
$113$	−2.23302	+	3.86770i	−0.210064	+	0.363842i	0.741670	+	0.670765i	$0.234034\pi$
$114$		0			0
$115$	−31.8309	+	18.3776i	−2.96825	+	1.71372i
$116$		0			0
$117$	−3.34264	+	6.92820i	−0.309027	+	0.640513i
$118$		0			0
$119$	−0.981633	+	0.566746i	−0.0899861	+	0.0519535i
$120$		0			0
$121$	−4.85760	+	8.41361i	−0.441600	+	0.764873i
$122$		0			0
$123$	−5.49289	−	3.17132i	−0.495277	−	0.285948i
$124$		0			0
$125$			23.9154i			2.13906i
$126$		0			0
$127$	1.89775	+	3.28699i	0.168398	+	0.291673i	0.937857	−	0.347023i	$-0.112807\pi$
$127$	1.89775	+	3.28699i	0.168398	+	0.291673i	−0.769459	+	0.638696i	$0.779474\pi$
$128$		0			0
$129$	−14.7152			−1.29560
$130$		0			0
$131$	4.83390			0.422340			0.211170	−	0.977449i	$-0.432273\pi$
$131$	4.83390			0.422340			0.211170	+	0.977449i	$0.432273\pi$
$132$		0			0
$133$	2.22411	+	3.85226i	0.192854	+	0.334034i
$134$		0			0
$135$		−	7.84869i		−	0.675508i
$136$		0			0
$137$	3.74916	+	2.16458i	0.320313	+	0.184933i	0.651532	−	0.758621i	$-0.274127\pi$
$137$	3.74916	+	2.16458i	0.320313	+	0.184933i	−0.331219	+	0.943554i	$0.607460\pi$
$138$		0			0
$139$	−7.90984	+	13.7002i	−0.670904	+	1.16204i	0.306745	+	0.951792i	$0.400760\pi$
$139$	−7.90984	+	13.7002i	−0.670904	+	1.16204i	−0.977648	+	0.210247i	$0.932573\pi$
$140$		0			0
$141$	−13.3248	+	7.69309i	−1.12215	+	0.647875i
$142$		0			0
$143$	3.37839	−	2.29976i	0.282515	−	0.192316i
$144$		0			0
$145$	14.0489	−	8.11115i	1.16670	−	0.673594i
$146$		0			0
$147$	6.47452	−	11.2142i	0.534009	−	0.924931i
$148$		0			0
$149$	4.23807	+	2.44685i	0.347196	+	0.200454i	0.663450	−	0.748221i	$-0.269092\pi$
$149$	4.23807	+	2.44685i	0.347196	+	0.200454i	−0.316254	+	0.948675i	$0.602425\pi$
$150$		0			0
$151$			9.05784i			0.737116i	0.929605	+	0.368558i	$0.120148\pi$
$151$			9.05784i			0.737116i	−0.929605	+	0.368558i	$0.879852\pi$
$152$		0			0
$153$	−1.06675	−	1.84766i	−0.0862413	−	0.149374i
$154$		0			0
$155$	36.2112			2.90855
$156$		0			0
$157$	−9.19133			−0.733548			−0.366774	−	0.930310i	$-0.619538\pi$
$157$	−9.19133			−0.733548			−0.366774	+	0.930310i	$0.619538\pi$
$158$		0			0
$159$	−10.1100	−	17.5111i	−0.801778	−	1.38872i
$160$		0			0
$161$		−	10.4212i		−	0.821309i
$162$		0			0
$163$	5.94657	+	3.43325i	0.465771	+	0.268913i	0.714468	−	0.699668i	$-0.246669\pi$
$163$	5.94657	+	3.43325i	0.465771	+	0.268913i	−0.248697	+	0.968581i	$0.580002\pi$
$164$		0			0
$165$	5.13349	−	8.89147i	0.399642	−	0.692200i
$166$		0			0
$167$	9.61102	−	5.54893i	0.743723	−	0.429389i	−0.0796983	−	0.996819i	$-0.525396\pi$
$167$	9.61102	−	5.54893i	0.743723	−	0.429389i	0.823421	+	0.567430i	$0.192062\pi$
$168$		0			0
$169$	12.8576	−	1.91890i	0.989046	−	0.147608i
$170$		0			0
$171$	−7.25085	+	4.18628i	−0.554486	+	0.320133i
$172$		0			0
$173$	−9.75807	+	16.9015i	−0.741893	+	1.28500i	0.209740	+	0.977757i	$0.432738\pi$
$173$	−9.75807	+	16.9015i	−0.741893	+	1.28500i	−0.951633	+	0.307238i	$0.900595\pi$
$174$		0			0
$175$	−10.7805	−	6.22411i	−0.814927	−	0.470498i
$176$		0			0
$177$		−	20.3511i		−	1.52968i
$178$		0			0
$179$	−3.68085	−	6.37542i	−0.275120	−	0.476521i	0.695046	−	0.718966i	$-0.255384\pi$
$179$	−3.68085	−	6.37542i	−0.275120	−	0.476521i	−0.970165	+	0.242444i	$0.922051\pi$
$180$		0			0
$181$	−5.19133			−0.385868			−0.192934	−	0.981212i	$-0.561800\pi$
$181$	−5.19133			−0.385868			−0.192934	+	0.981212i	$0.561800\pi$
$182$		0			0
$183$	17.6519			1.30487
$184$		0			0
$185$	−4.99109	−	8.64482i	−0.366952	−	0.635580i
$186$		0			0
$187$			1.13349i			0.0828891i
$188$		0			0
$189$	1.92721	+	1.11267i	0.140184	+	0.0809350i
$190$		0			0
$191$	−2.63370	+	4.56170i	−0.190568	+	0.330073i	−0.945438	−	0.325801i	$-0.894366\pi$
$191$	−2.63370	+	4.56170i	−0.190568	+	0.330073i	0.754871	+	0.655873i	$0.227700\pi$
$192$		0			0
$193$	4.90048	−	2.82929i	0.352744	−	0.203657i	−0.313149	−	0.949704i	$-0.601384\pi$
$193$	4.90048	−	2.82929i	0.352744	−	0.203657i	0.665893	+	0.746047i	$0.268051\pi$
$194$		0			0
$195$	26.9970	−	18.3776i	1.93330	−	1.31605i
$196$		0			0
$197$	12.1485	−	7.01391i	0.865541	−	0.499720i	−0.000322751	−	1.00000i	$-0.500103\pi$
$197$	12.1485	−	7.01391i	0.865541	−	0.499720i	0.865864	+	0.500279i	$0.166769\pi$
$198$		0			0
$199$	2.63370	−	4.56170i	0.186698	−	0.323370i	−0.757450	−	0.652894i	$-0.773555\pi$
$199$	2.63370	−	4.56170i	0.186698	−	0.323370i	0.944147	+	0.329524i	$0.106888\pi$
$200$		0			0
$201$	18.9494	+	10.9404i	1.33659	+	0.771679i
$202$		0			0
$203$			4.59952i			0.322823i
$204$		0			0
$205$	5.59566	+	9.69197i	0.390818	+	0.676917i
$206$		0			0
$207$	19.6152			1.36335
$208$		0			0
$209$	4.44821			0.307689
$210$		0			0
$211$	−6.09780	−	10.5617i	−0.419790	−	0.727097i	0.576128	−	0.817359i	$-0.304563\pi$
$211$	−6.09780	−	10.5617i	−0.419790	−	0.727097i	−0.995918	+	0.0902621i	$0.971230\pi$
$212$		0			0
$213$		−	17.9544i		−	1.23021i
$214$		0			0
$215$	22.4858	+	12.9822i	1.53352	+	0.885377i
$216$		0			0
$217$	−5.13349	+	8.89147i	−0.348484	+	0.603592i
$218$		0			0
$219$	−18.2366	+	10.5289i	−1.23232	+	0.711478i
$220$		0			0
$221$	−1.56675	+	3.24735i	−0.105391	+	0.218441i
$222$		0			0
$223$	−8.69491	+	5.02001i	−0.582254	+	0.336165i	−0.762029	−	0.647543i	$-0.775797\pi$
$223$	−8.69491	+	5.02001i	−0.582254	+	0.336165i	0.179775	+	0.983708i	$0.442463\pi$
$224$		0			0
$225$	11.7152	−	20.2913i	0.781013	−	1.35275i
$226$		0			0
$227$	−6.53129	−	3.77084i	−0.433497	−	0.250280i	0.267338	−	0.963603i	$-0.413856\pi$
$227$	−6.53129	−	3.77084i	−0.433497	−	0.250280i	−0.700835	+	0.713323i	$0.747189\pi$
$228$		0			0
$229$		−	6.66612i		−	0.440510i	−0.975442	−	0.220255i	$-0.929311\pi$
$229$		−	6.66612i		−	0.440510i	0.975442	−	0.220255i	$-0.0706889\pi$
$230$		0			0
$231$	1.45550	+	2.52101i	0.0957651	+	0.165870i
$232$		0			0
$233$	2.38266			0.156093			0.0780465	−	0.996950i	$-0.475132\pi$
$233$	2.38266			0.156093			0.0780465	+	0.996950i	$0.475132\pi$
$234$		0			0
$235$	27.1483			1.77096
$236$		0			0
$237$	−14.7152	−	25.4875i	−0.955855	−	1.65559i
$238$		0			0
$239$			21.4304i			1.38622i	0.720833	+	0.693108i	$0.243759\pi$
$239$			21.4304i			1.38622i	−0.720833	+	0.693108i	$0.756241\pi$
$240$		0			0
$241$	−0.175180	−	0.101140i	−0.0112844	−	0.00651502i	0.494347	−	0.869265i	$-0.335407\pi$
$241$	−0.175180	−	0.101140i	−0.0112844	−	0.00651502i	−0.505632	+	0.862750i	$0.668740\pi$
$242$		0			0
$243$	−9.34515	+	16.1863i	−0.599492	+	1.03835i
$244$		0			0
$245$	−19.7870	+	11.4240i	−1.26414	+	0.729854i
$246$		0			0
$247$	12.7437	+	6.14845i	0.810864	+	0.391217i
$248$		0			0
$249$	−11.2492	+	6.49471i	−0.712887	+	0.411585i
$250$		0			0
$251$	10.6292	−	18.4104i	0.670912	−	1.16205i	−0.306734	−	0.951795i	$-0.599236\pi$
$251$	10.6292	−	18.4104i	0.670912	−	1.16205i	0.977646	−	0.210258i	$-0.0674304\pi$
$252$		0			0
$253$	−9.02506	−	5.21062i	−0.567401	−	0.327589i
$254$		0			0
$255$			9.05784i			0.567224i
$256$		0			0
$257$	8.15736	+	14.1290i	0.508842	+	0.881340i	0.999948	+	0.0102403i	$0.00325965\pi$
$257$	8.15736	+	14.1290i	0.508842	+	0.881340i	−0.491105	+	0.871100i	$0.663407\pi$
$258$		0			0
$259$	2.83026			0.175864
$260$		0			0
$261$	−8.65736			−0.535877
$262$		0			0
$263$	−3.54981	−	6.14845i	−0.218891	−	0.379130i	0.735578	−	0.677440i	$-0.236910\pi$
$263$	−3.54981	−	6.14845i	−0.218891	−	0.379130i	−0.954469	+	0.298310i	$0.903577\pi$
$264$		0			0
$265$			35.6775i			2.19165i
$266$		0			0
$267$	27.5250	+	15.8916i	1.68450	+	0.972548i
$268$		0			0
$269$	3.64240	−	6.30883i	0.222081	−	0.384656i	−0.733359	−	0.679842i	$-0.762048\pi$
$269$	3.64240	−	6.30883i	0.222081	−	0.384656i	0.955440	+	0.295186i	$0.0953817\pi$
$270$		0			0
$271$	−6.07761	+	3.50891i	−0.369189	+	0.213151i	−0.673104	−	0.739548i	$-0.735039\pi$
$271$	−6.07761	+	3.50891i	−0.369189	+	0.213151i	0.303915	+	0.952699i	$0.401706\pi$
$272$		0			0
$273$	0.685280	+	9.23430i	0.0414750	+	0.558885i
$274$		0			0
$275$	−10.7805	+	6.22411i	−0.650087	+	0.375328i
$276$		0			0
$277$	−6.55279	+	11.3498i	−0.393719	+	0.681941i	−0.992937	−	0.118645i	$-0.962145\pi$
$277$	−6.55279	+	11.3498i	−0.393719	+	0.681941i	0.599218	+	0.800586i	$0.295478\pi$
$278$		0			0
$279$	−16.7358	−	9.66241i	−1.00195	−	0.578473i
$280$		0			0
$281$		−	24.6803i		−	1.47230i	−0.676817	−	0.736151i	$-0.736641\pi$
$281$		−	24.6803i		−	1.47230i	0.676817	−	0.736151i	$-0.263359\pi$
$282$		0			0
$283$	3.24735	+	5.62458i	0.193035	+	0.334347i	0.946255	−	0.323423i	$-0.104834\pi$
$283$	3.24735	+	5.62458i	0.193035	+	0.334347i	−0.753219	+	0.657769i	$0.771500\pi$
$284$		0			0
$285$	35.5461			2.10557
$286$		0			0
$287$	−3.17309			−0.187301
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$		0			0
$291$		−	20.1456i		−	1.18096i
$292$		0			0
$293$	17.6863	+	10.2112i	1.03324	+	0.596543i	0.917912	−	0.396784i	$-0.129874\pi$
$293$	17.6863	+	10.2112i	1.03324	+	0.596543i	0.115331	+	0.993327i	$0.463207\pi$
$294$		0			0
$295$	−17.9544	+	31.0979i	−1.04534	+	1.81059i
$296$		0			0
$297$	1.92721	−	1.11267i	0.111828	−	0.0645638i
$298$		0			0
$299$	−18.6537	−	27.4027i	−1.07877	−	1.58474i
$300$		0			0
$301$	−6.37542	+	3.68085i	−0.367473	+	0.212161i
$302$		0			0
$303$	9.12840	−	15.8109i	0.524413	−	0.908310i
$304$		0			0
$305$	−26.9733	−	15.5730i	−1.54448	−	0.891709i
$306$		0			0
$307$		−	13.0578i		−	0.745250i	−0.927982	−	0.372625i	$-0.878458\pi$
$307$		−	13.0578i		−	0.745250i	0.927982	−	0.372625i	$-0.121542\pi$
$308$		0			0
$309$	−7.20915	−	12.4866i	−0.410114	−	0.710338i
$310$		0			0
$311$	3.30413			0.187360			0.0936799	−	0.995602i	$-0.470137\pi$
$311$	3.30413			0.187360			0.0936799	+	0.995602i	$0.470137\pi$
$312$		0			0
$313$	5.31472			0.300406			0.150203	−	0.988655i	$-0.452007\pi$
$313$	5.31472			0.300406			0.150203	+	0.988655i	$0.452007\pi$
$314$		0			0
$315$	4.83390	+	8.37256i	0.272359	+	0.471740i
$316$		0			0
$317$			28.1848i			1.58301i	0.611160	+	0.791507i	$0.290703\pi$
$317$			28.1848i			1.58301i	−0.611160	+	0.791507i	$0.709297\pi$
$318$		0			0
$319$	3.98330	+	2.29976i	0.223022	+	0.128762i
$320$		0			0
$321$	−12.8337	+	22.2287i	−0.716309	+	1.24068i
$322$		0			0
$323$	−3.39858	+	1.96217i	−0.189102	+	0.109178i
$324$		0			0
$325$	−39.4882	+	2.93043i	−2.19041	+	0.162551i
$326$		0			0
$327$	22.4858	−	12.9822i	1.24347	−	0.717916i
$328$		0			0
$329$	−3.84869	+	6.66612i	−0.212185	+	0.367515i
$330$		0			0
$331$	−16.6703	−	9.62458i	−0.916281	−	0.529015i	−0.0338340	−	0.999427i	$-0.510772\pi$
$331$	−16.6703	−	9.62458i	−0.916281	−	0.529015i	−0.882447	+	0.470413i	$0.844105\pi$
$332$		0			0
$333$			5.32719i			0.291928i
$334$		0			0
$335$	−19.3040	−	33.4354i	−1.05469	−	1.82677i
$336$		0			0
$337$	31.4126			1.71115			0.855576	−	0.517677i	$-0.173203\pi$
$337$	31.4126			1.71115			0.855576	+	0.517677i	$0.173203\pi$
$338$		0			0
$339$	−10.1188			−0.549577
$340$		0			0
$341$	5.13349	+	8.89147i	0.277994	+	0.481500i
$342$		0			0
$343$		−	14.4126i		−	0.778206i
$344$		0			0
$345$	−72.1200	−	41.6385i	−3.88281	−	2.24174i
$346$		0			0
$347$	7.93002	−	13.7352i	0.425706	−	0.737344i	−0.570780	−	0.821103i	$-0.693359\pi$
$347$	7.93002	−	13.7352i	0.425706	−	0.737344i	0.996486	+	0.0837586i	$0.0266925\pi$
$348$		0			0
$349$	30.1986	−	17.4351i	1.61649	−	0.933282i	0.628674	−	0.777669i	$-0.283598\pi$
$349$	30.1986	−	17.4351i	1.61649	−	0.933282i	0.987818	−	0.155613i	$-0.0497354\pi$
$350$		0			0
$351$	7.05924	−	0.523868i	0.376795	−	0.0279620i
$352$		0			0
$353$	4.27303	−	2.46704i	0.227431	−	0.131307i	−0.381956	−	0.924181i	$-0.624749\pi$
$353$	4.27303	−	2.46704i	0.227431	−	0.131307i	0.609386	+	0.792874i	$0.291416\pi$
$354$		0			0
$355$	−15.8399	+	27.4354i	−0.840692	+	1.45612i
$356$		0			0
$357$	−2.22411	−	1.28409i	−0.117712	−	0.0679612i
$358$		0			0
$359$			8.15131i			0.430210i	0.976591	+	0.215105i	$0.0690093\pi$
$359$			8.15131i			0.430210i	−0.976591	+	0.215105i	$0.930991\pi$
$360$		0			0
$361$	−1.79976	−	3.11728i	−0.0947243	−	0.164067i
$362$		0			0
$363$	−22.0119			−1.15533
$364$		0			0
$365$	37.1557			1.94482
$366$		0			0
$367$	−0.0655200	−	0.113484i	−0.00342012	−	0.00592382i	0.864310	−	0.502959i	$-0.167755\pi$
$367$	−0.0655200	−	0.113484i	−0.00342012	−	0.00592382i	−0.867730	+	0.497035i	$0.834422\pi$
$368$		0			0
$369$		−	5.97248i		−	0.310915i
$370$		0			0
$371$	−8.76043	−	5.05784i	−0.454819	−	0.262590i
$372$		0			0
$373$	3.83759	−	6.64690i	0.198703	−	0.344163i	−0.749405	−	0.662112i	$-0.769660\pi$
$373$	3.83759	−	6.64690i	0.198703	−	0.344163i	0.948108	+	0.317948i	$0.102994\pi$
$374$		0			0
$375$	−46.9261	+	27.0928i	−2.42325	+	1.39907i
$376$		0			0
$377$	8.23302	+	12.0945i	0.424022	+	0.622896i
$378$		0			0
$379$	8.49456	−	4.90434i	0.436336	−	0.251919i	−0.265706	−	0.964054i	$-0.585605\pi$
$379$	8.49456	−	4.90434i	0.436336	−	0.251919i	0.702042	+	0.712135i	$0.252272\pi$
$380$		0			0
$381$	−4.29976	+	7.44741i	−0.220283	+	0.381542i
$382$		0			0
$383$	−27.3940	−	15.8159i	−1.39977	−	0.808155i	−0.405398	−	0.914140i	$-0.632867\pi$
$383$	−27.3940	−	15.8159i	−1.39977	−	0.808155i	−0.994368	+	0.105985i	$0.966200\pi$
$384$		0			0
$385$		−	5.13635i		−	0.261773i
$386$		0			0
$387$	−6.92820	−	12.0000i	−0.352180	−	0.609994i
$388$		0			0
$389$	12.7730			0.647618			0.323809	−	0.946122i	$-0.395036\pi$
$389$	12.7730			0.647618			0.323809	+	0.946122i	$0.395036\pi$
$390$		0			0
$391$	9.19392			0.464957
$392$		0			0
$393$	5.47613	+	9.48494i	0.276234	+	0.478452i
$394$		0			0
$395$			51.9287i			2.61282i
$396$		0			0
$397$	20.7480	+	11.9788i	1.04131	+	0.601201i	0.920204	−	0.391438i	$-0.128022\pi$
$397$	20.7480	+	11.9788i	1.04131	+	0.601201i	0.121107	+	0.992640i	$0.461356\pi$
$398$		0			0
$399$	−5.03920	+	8.72816i	−0.252276	+	0.436954i
$400$		0			0
$401$	−2.82482	+	1.63091i	−0.141065	+	0.0814438i	−0.568871	−	0.822427i	$-0.692620\pi$
$401$	−2.82482	+	1.63091i	−0.141065	+	0.0814438i	0.427807	+	0.903870i	$0.359286\pi$
$402$		0			0
$403$	2.41695	+	32.5689i	0.120397	+	1.62237i
$404$		0			0
$405$	37.5600	−	21.6853i	1.86637	−	1.07755i
$406$		0			0
$407$	1.41513	−	2.45107i	0.0701453	−	0.121495i
$408$		0			0
$409$	−11.5979	−	6.69602i	−0.573477	−	0.331097i	0.185060	−	0.982727i	$-0.440752\pi$
$409$	−11.5979	−	6.69602i	−0.573477	−	0.331097i	−0.758537	+	0.651630i	$0.774085\pi$
$410$		0			0
$411$			9.80867i			0.483826i
$412$		0			0
$413$	−5.09061	−	8.81720i	−0.250493	−	0.433866i
$414$		0			0
$415$	22.9193			1.12506
$416$		0			0
$417$	−35.8430			−1.75524
$418$		0			0
$419$	−2.66263	−	4.61181i	−0.130078	−	0.225302i	0.793628	−	0.608403i	$-0.208189\pi$
$419$	−2.66263	−	4.61181i	−0.130078	−	0.225302i	−0.923706	+	0.383101i	$0.874856\pi$
$420$		0			0
$421$			5.52754i			0.269396i	0.990887	+	0.134698i	$0.0430064\pi$
$421$			5.52754i			0.269396i	−0.990887	+	0.134698i	$0.956994\pi$
$422$		0			0
$423$	−12.5472	−	7.24411i	−0.610064	−	0.352221i
$424$		0			0
$425$	5.49109	−	9.51085i	0.266357	−	0.461344i
$426$		0			0
$427$	7.64776	−	4.41543i	0.370101	−	0.213678i
$428$		0			0
$429$	8.33978	+	4.02368i	0.402648	+	0.194265i
$430$		0			0
$431$	−23.4674	+	13.5489i	−1.13039	+	0.652629i	−0.944032	−	0.329854i	$-0.893001\pi$
$431$	−23.4674	+	13.5489i	−1.13039	+	0.652629i	−0.186354	+	0.982483i	$0.559667\pi$
$432$		0			0
$433$	6.57566	−	11.3894i	0.316006	−	0.547338i	−0.663645	−	0.748048i	$-0.730991\pi$
$433$	6.57566	−	11.3894i	0.316006	−	0.547338i	0.979651	+	0.200710i	$0.0643247\pi$
$434$		0			0
$435$	31.8309	+	18.3776i	1.52618	+	0.881139i
$436$		0			0
$437$		−	36.0801i		−	1.72595i
$438$		0			0
$439$	−10.0445	−	17.3976i	−0.479399	−	0.830343i	0.520322	−	0.853970i	$-0.325812\pi$
$439$	−10.0445	−	17.3976i	−0.479399	−	0.830343i	−0.999721	+	0.0236272i	$0.992479\pi$
$440$		0			0
$441$	12.1933			0.580635
$442$		0			0
$443$	−40.4401			−1.92137			−0.960685	−	0.277642i	$-0.910447\pi$
$443$	−40.4401			−1.92137			−0.960685	+	0.277642i	$0.910447\pi$
$444$		0			0
$445$	−28.0400	−	48.5667i	−1.32922	−	2.30228i
$446$		0			0
$447$			11.0878i			0.524433i
$448$		0			0
$449$	−18.9494	−	10.9404i	−0.894278	−	0.516311i	−0.0189383	−	0.999821i	$-0.506029\pi$
$449$	−18.9494	−	10.9404i	−0.894278	−	0.516311i	−0.875339	+	0.483509i	$0.839362\pi$
$450$		0			0
$451$	−1.58654	+	2.74797i	−0.0747074	+	0.129397i
$452$		0			0
$453$	−17.7730	+	10.2613i	−0.835050	+	0.482116i
$454$		0			0
$455$	7.09962	−	14.7152i	0.332835	−	0.689859i
$456$		0			0
$457$	7.50000	−	4.33013i	0.350835	−	0.202555i	−0.314218	−	0.949351i	$-0.601742\pi$
$457$	7.50000	−	4.33013i	0.350835	−	0.202555i	0.665053	+	0.746796i	$0.268409\pi$
$458$		0			0
$459$	−0.981633	+	1.70024i	−0.0458187	+	0.0793603i
$460$		0			0
$461$	−6.21015	−	3.58543i	−0.289235	−	0.166990i	0.348362	−	0.937360i	$-0.386738\pi$
$461$	−6.21015	−	3.58543i	−0.289235	−	0.166990i	−0.637597	+	0.770370i	$0.720071\pi$
$462$		0			0
$463$		−	5.73302i		−	0.266436i	−0.991087	−	0.133218i	$-0.957469\pi$
$463$		−	5.73302i		−	0.266436i	0.991087	−	0.133218i	$-0.0425310\pi$
$464$		0			0
$465$	41.0222	+	71.0525i	1.90236	+	3.29498i
$466$		0			0
$467$	−5.13635			−0.237682			−0.118841	−	0.992913i	$-0.537918\pi$
$467$	−5.13635			−0.237682			−0.118841	+	0.992913i	$0.537918\pi$
$468$		0			0
$469$	10.9465			0.505464
$470$		0			0
$471$	−10.4125	−	18.0350i	−0.479782	−	0.831007i
$472$		0			0
$473$			7.36170i			0.338491i
$474$		0			0
$475$	−37.3238	−	21.5489i	−1.71253	−	0.988733i
$476$		0			0
$477$	9.52001	−	16.4891i	0.435891	−	0.754986i
$478$		0			0
$479$	23.4587	−	13.5439i	1.07185	−	0.618835i	0.143167	−	0.989699i	$-0.454271\pi$
$479$	23.4587	−	13.5439i	1.07185	−	0.618835i	0.928688	+	0.370863i	$0.120938\pi$
$480$		0			0
$481$	7.44216	−	5.06608i	0.339333	−	0.230993i
$482$		0			0
$483$	20.4483	−	11.8058i	0.930428	−	0.537183i
$484$		0			0
$485$	−17.7730	+	30.7838i	−0.807032	+	1.39782i
$486$		0			0
$487$	30.1336	+	17.3976i	1.36548	+	0.788361i	0.990347	−	0.138609i	$-0.0442632\pi$
$487$	30.1336	+	17.3976i	1.36548	+	0.788361i	0.375134	+	0.926970i	$0.377597\pi$
$488$		0			0
$489$			15.5576i			0.703539i
$490$		0			0
$491$	−10.4780	−	18.1485i	−0.472866	−	0.819028i	0.526652	−	0.850081i	$-0.323447\pi$
$491$	−10.4780	−	18.1485i	−0.472866	−	0.819028i	−0.999518	+	0.0310531i	$0.990114\pi$
$492$		0			0
$493$	−4.05784			−0.182756
$494$		0			0
$495$	9.66780			0.434535
$496$		0			0
$497$	−4.49109	−	7.77880i	−0.201453	−	0.348927i
$498$		0			0
$499$		−	25.2892i		−	1.13210i	−0.824371	−	0.566050i	$-0.808471\pi$
$499$		−	25.2892i		−	1.13210i	0.824371	−	0.566050i	$-0.191529\pi$
$500$		0			0
$501$	21.7759	+	12.5723i	0.972875	+	0.561690i
$502$		0			0
$503$	14.4045	−	24.9494i	0.642267	−	1.11244i	−0.342659	−	0.939460i	$-0.611327\pi$
$503$	14.4045	−	24.9494i	0.642267	−	1.11244i	0.984926	−	0.172979i	$-0.0553392\pi$
$504$		0			0
$505$	−27.8976	+	16.1067i	−1.24143	+	0.716739i
$506$		0			0
$507$	18.3311	+	23.0550i	0.814112	+	1.02391i
$508$		0			0
$509$	−8.91325	+	5.14607i	−0.395073	+	0.228095i	−0.684356	−	0.729148i	$-0.739916\pi$
$509$	−8.91325	+	5.14607i	−0.395073	+	0.228095i	0.289283	+	0.957244i	$0.406583\pi$
$510$		0			0
$511$	−5.26739	+	9.12339i	−0.233016	+	0.403595i
$512$		0			0
$513$	6.67232	+	3.85226i	0.294590	+	0.170082i
$514$		0			0
$515$			25.4405i			1.12104i
$516$		0			0
$517$	3.84869	+	6.66612i	0.169265	+	0.293176i
$518$		0			0
$519$	−44.2181			−1.94096
$520$		0			0
$521$	12.7831			0.560039			0.280020	−	0.959994i	$-0.409659\pi$
$521$	12.7831			0.560039			0.280020	+	0.959994i	$0.409659\pi$
$522$		0			0
$523$	−10.4780	−	18.1485i	−0.458171	−	0.793576i	0.540693	−	0.841220i	$-0.318162\pi$
$523$	−10.4780	−	18.1485i	−0.458171	−	0.793576i	−0.998864	+	0.0476437i	$0.984829\pi$
$524$		0			0
$525$		−	28.2042i		−	1.23093i
$526$		0			0
$527$	−7.84432	−	4.52892i	−0.341704	−	0.197283i
$528$		0			0
$529$	−30.7641	+	53.2850i	−1.33757	+	2.31674i
$530$		0			0
$531$	16.5960	−	9.58170i	0.720205	−	0.415811i
$532$		0			0
$533$	−8.34364	+	5.67974i	−0.361403	+	0.246017i
$534$		0			0
$535$	39.2216	−	22.6446i	1.69570	−	0.979011i
$536$		0			0
$537$	8.33978	−	14.4449i	0.359888	−	0.623344i
$538$		0			0
$539$	−5.61022	−	3.23906i	−0.241649	−	0.139516i
$540$		0			0
$541$		−	24.9827i		−	1.07409i	−0.843553	−	0.537046i	$-0.819540\pi$
$541$		−	24.9827i		−	1.07409i	0.843553	−	0.537046i	$-0.180460\pi$
$542$		0			0
$543$	−5.88105	−	10.1863i	−0.252380	−	0.437135i
$544$		0			0
$545$	−45.8130			−1.96242
$546$		0			0
$547$	21.1449			0.904092			0.452046	−	0.891995i	$-0.350694\pi$
$547$	21.1449			0.904092			0.452046	+	0.891995i	$0.350694\pi$
$548$		0			0
$549$	8.31086	+	14.3948i	0.354699	+	0.614356i
$550$		0			0
$551$			15.9243i			0.678400i
$552$		0			0
$553$	−12.7508	−	7.36170i	−0.542221	−	0.313051i
$554$		0			0
$555$	11.3084	−	19.5868i	0.480016	−	0.831411i
$556$		0			0
$557$	−20.1624	+	11.6408i	−0.854309	+	0.493235i	−0.862102	−	0.506734i	$-0.830853\pi$
$557$	−20.1624	+	11.6408i	−0.854309	+	0.493235i	0.00779359	+	0.999970i	$0.497519\pi$
$558$		0			0
$559$	−10.1756	+	21.0906i	−0.430380	+	0.892038i
$560$		0			0
$561$	−2.22411	+	1.28409i	−0.0939018	+	0.0542142i
$562$		0			0
$563$	14.4045	−	24.9494i	0.607079	−	1.05149i	−0.384640	−	0.923067i	$-0.625674\pi$
$563$	14.4045	−	24.9494i	0.607079	−	1.05149i	0.991719	−	0.128425i	$-0.0409922\pi$
$564$		0			0
$565$	15.4622	+	8.92709i	0.650498	+	0.375565i
$566$		0			0
$567$			12.2969i			0.516421i
$568$		0			0
$569$	−8.54893	−	14.8072i	−0.358390	−	0.620749i	0.629302	−	0.777161i	$-0.283341\pi$
$569$	−8.54893	−	14.8072i	−0.358390	−	0.620749i	−0.987692	+	0.156412i	$0.950007\pi$
$570$		0			0
$571$	22.3144			0.933828			0.466914	−	0.884303i	$-0.345366\pi$
$571$	22.3144			0.933828			0.466914	+	0.884303i	$0.345366\pi$
$572$		0			0
$573$	−11.9344			−0.498569
$574$		0			0
$575$	50.4847	+	87.4420i	2.10536	+	3.64658i
$576$		0			0
$577$			2.36590i			0.0984935i	0.998787	+	0.0492468i	$0.0156821\pi$
$577$			2.36590i			0.0984935i	−0.998787	+	0.0492468i	$0.984318\pi$
$578$		0			0
$579$	11.1031	+	6.41038i	0.461430	+	0.266406i
$580$		0			0
$581$	−3.24916	+	5.62772i	−0.134798	+	0.233477i
$582$		0			0
$583$	−8.76043	+	5.05784i	−0.362820	+	0.209474i
$584$		0			0
$585$	27.6974	+	13.3631i	1.14515	+	0.552497i
$586$		0			0
$587$	23.4674	−	13.5489i	0.968604	−	0.559224i	0.0697939	−	0.997561i	$-0.477766\pi$
$587$	23.4674	−	13.5489i	0.968604	−	0.559224i	0.898810	+	0.438337i	$0.144432\pi$
$588$		0			0
$589$	−17.7730	+	30.7838i	−0.732325	+	1.26842i
$590$		0			0
$591$	27.5250	+	15.8916i	1.13223	+	0.653692i
$592$		0			0
$593$		−	23.2930i		−	0.956528i	−0.878216	−	0.478264i	$-0.841266\pi$
$593$		−	23.2930i		−	0.956528i	0.878216	−	0.478264i	$-0.158734\pi$
$594$		0			0
$595$	2.26572	+	3.92434i	0.0928855	+	0.160882i
$596$		0			0
$597$	11.9344			0.488444
$598$		0			0
$599$	−38.6079			−1.57748			−0.788738	−	0.614729i	$-0.789265\pi$
$599$	−38.6079			−1.57748			−0.788738	+	0.614729i	$0.789265\pi$
$600$		0			0
$601$	−17.9405	−	31.0738i	−0.731808	−	1.26753i	−0.956110	−	0.293009i	$-0.905343\pi$
$601$	−17.9405	−	31.0738i	−0.731808	−	1.26753i	0.224302	−	0.974520i	$-0.427990\pi$
$602$		0			0
$603$			20.6039i			0.839056i
$604$		0			0
$605$	33.6357	+	19.4196i	1.36748	+	0.789518i
$606$		0			0
$607$	15.3207	−	26.5362i	0.621846	−	1.07707i	−0.367295	−	0.930104i	$-0.619716\pi$
$607$	15.3207	−	26.5362i	0.621846	−	1.07707i	0.989142	−	0.146965i	$-0.0469505\pi$
$608$		0			0
$609$	−9.02506	+	5.21062i	−0.365714	+	0.211145i
$610$		0			0
$611$	1.81204	+	24.4176i	0.0733072	+	0.987831i
$612$		0			0
$613$	12.8376	−	7.41179i	0.518505	−	0.299359i	−0.217818	−	0.975990i	$-0.569894\pi$
$613$	12.8376	−	7.41179i	0.518505	−	0.299359i	0.736323	+	0.676630i	$0.236560\pi$
$614$		0			0
$615$	−12.6782	+	21.9593i	−0.511235	+	0.885485i
$616$		0			0
$617$	31.4465	+	18.1557i	1.26599	+	0.730920i	0.974227	−	0.225571i	$-0.0724247\pi$
$617$	31.4465	+	18.1557i	1.26599	+	0.730920i	0.291763	+	0.956491i	$0.405758\pi$
$618$		0			0
$619$		−	6.03564i		−	0.242593i	−0.992616	−	0.121296i	$-0.961295\pi$
$619$		−	6.03564i		−	0.242593i	0.992616	−	0.121296i	$-0.0387052\pi$
$620$		0			0
$621$	−9.02506	−	15.6319i	−0.362163	−	0.627285i
$622$		0			0
$623$	15.9004			0.637037
$624$		0			0
$625$	40.6974			1.62790
$626$		0			0
$627$	5.03920	+	8.72816i	0.201246	+	0.348569i
$628$		0			0
$629$			2.49694i			0.0995594i
$630$		0			0
$631$	−4.24538	−	2.45107i	−0.169006	−	0.0975757i	0.413111	−	0.910681i	$-0.364442\pi$
$631$	−4.24538	−	2.45107i	−0.169006	−	0.0975757i	−0.582117	+	0.813105i	$0.697775\pi$
$632$		0			0
$633$	13.8159	−	23.9299i	0.549133	−	0.951126i
$634$		0			0
$635$	13.1406	−	7.58675i	0.521471	−	0.301071i
$636$		0			0
$637$	−11.5957	−	17.0342i	−0.459437	−	0.674922i
$638$		0			0
$639$	14.6415	−	8.45326i	0.579208	−	0.334406i
$640$		0			0
$641$	18.5578	−	32.1431i	0.732990	−	1.26958i	−0.222609	−	0.974908i	$-0.571457\pi$
$641$	18.5578	−	32.1431i	0.732990	−	1.26958i	0.955599	−	0.294669i	$-0.0952094\pi$
$642$		0			0
$643$	−18.7646	−	10.8337i	−0.740002	−	0.427241i	0.0820678	−	0.996627i	$-0.473848\pi$
$643$	−18.7646	−	10.8337i	−0.740002	−	0.427241i	−0.822070	+	0.569386i	$0.807181\pi$
$644$		0			0
$645$			58.8280i			2.31635i
$646$		0			0
$647$	12.7525	+	22.0879i	0.501352	+	0.868367i	0.999999	+	0.00156154i	$0.000497053\pi$
$647$	12.7525	+	22.0879i	0.501352	+	0.868367i	−0.498647	+	0.866805i	$0.666170\pi$
$648$		0			0
$649$	−10.1812			−0.399648
$650$		0			0
$651$	−23.2621			−0.911714
$652$		0			0
$653$	−2.09061	−	3.62105i	−0.0818121	−	0.141703i	0.822216	−	0.569175i	$-0.192737\pi$
$653$	−2.09061	−	3.62105i	−0.0818121	−	0.141703i	−0.904028	+	0.427473i	$0.859404\pi$
$654$		0			0
$655$		−	19.3248i		−	0.755083i
$656$		0			0
$657$	−17.1723	−	9.91444i	−0.669956	−	0.386799i
$658$		0			0
$659$	−15.9343	+	27.5990i	−0.620713	+	1.07511i	0.368641	+	0.929572i	$0.379823\pi$
$659$	−15.9343	+	27.5990i	−0.620713	+	1.07511i	−0.989353	+	0.145534i	$0.953510\pi$
$660$		0			0
$661$	28.5350	−	16.4747i	1.10988	−	0.640790i	0.171083	−	0.985257i	$-0.445273\pi$
$661$	28.5350	−	16.4747i	1.10988	−	0.640790i	0.938799	+	0.344466i	$0.111940\pi$
$662$		0			0
$663$	−8.14677	+	0.604574i	−0.316394	+	0.0234797i
$664$		0			0
$665$	15.4005	−	8.89147i	0.597205	−	0.344796i
$666$		0			0
$667$	18.6537	−	32.3092i	0.722275	−	1.25102i
$668$		0			0
$669$	−19.7002	−	11.3739i	−0.761655	−	0.439742i
$670$		0			0
$671$		−	8.83087i		−	0.340912i
$672$		0			0
$673$	−17.3309	−	30.0179i	−0.668056	−	1.15711i	−0.978447	−	0.206498i	$-0.933793\pi$
$673$	−17.3309	−	30.0179i	−0.668056	−	1.15711i	0.310391	−	0.950609i	$-0.399540\pi$
$674$		0			0
$675$	−21.5609			−0.829881
$676$		0			0
$677$	−30.6140			−1.17659			−0.588296	−	0.808646i	$-0.700201\pi$
$677$	−30.6140			−1.17659			−0.588296	+	0.808646i	$0.700201\pi$
$678$		0			0
$679$	−5.03920	−	8.72816i	−0.193387	−	0.334956i
$680$		0			0
$681$		−	17.0874i		−	0.654789i
$682$		0			0
$683$	26.0154	+	15.0200i	0.995452	+	0.574725i	0.906900	−	0.421347i	$-0.138442\pi$
$683$	26.0154	+	15.0200i	0.995452	+	0.574725i	0.0885527	+	0.996071i	$0.471776\pi$
$684$		0			0
$685$	8.65350	−	14.9883i	0.330633	−	0.572674i
$686$		0			0
$687$	13.0801	−	7.55179i	0.499036	−	0.288119i
$688$		0			0
$689$	−32.0889	+	2.38133i	−1.22249	+	0.0907214i
$690$		0			0
$691$	32.0968	−	18.5311i	1.22102	−	0.704956i	0.255885	−	0.966707i	$-0.417633\pi$
$691$	32.0968	−	18.5311i	1.22102	−	0.704956i	0.965136	+	0.261751i	$0.0842998\pi$
$692$		0			0
$693$	−1.37056	+	2.37388i	−0.0520632	+	0.0901762i
$694$		0			0
$695$	54.7704	+	31.6217i	2.07756	+	1.19948i
$696$		0			0
$697$		−	2.79939i		−	0.106035i
$698$		0			0
$699$	2.69922	+	4.67518i	0.102094	+	0.176832i
$700$		0			0
$701$	8.03564			0.303502			0.151751	−	0.988419i	$-0.451509\pi$
$701$	8.03564			0.303502			0.151751	+	0.988419i	$0.451509\pi$
$702$		0			0
$703$	9.79884			0.369570
$704$		0			0
$705$	30.7552	+	53.2696i	1.15831	+	2.00625i
$706$		0			0
$707$		−	9.13349i		−	0.343500i
$708$		0			0
$709$	8.96336	+	5.17500i	0.336626	+	0.194351i	0.658779	−	0.752336i	$-0.271073\pi$
$709$	8.96336	+	5.17500i	0.336626	+	0.194351i	−0.322153	+	0.946688i	$0.604407\pi$
$710$		0			0
$711$	13.8564	−	24.0000i	0.519656	−	0.900070i
$712$		0			0
$713$	72.1200	−	41.6385i	2.70092	−	1.55938i
$714$		0			0
$715$	−9.19392	−	13.5060i	−0.343833	−	0.505098i
$716$		0			0
$717$	−42.0501	+	24.2776i	−1.57039	+	0.906665i
$718$		0			0
$719$	−5.51307	+	9.54893i	−0.205603	+	0.356115i	−0.950325	−	0.311260i	$-0.899249\pi$
$719$	−5.51307	+	9.54893i	−0.205603	+	0.356115i	0.744722	+	0.667375i	$0.232582\pi$
$720$		0			0
$721$	−6.24678	−	3.60658i	−0.232642	−	0.134316i
$722$		0			0
$723$		−	0.458312i		−	0.0170448i
$724$		0			0
$725$	−22.2819	−	38.5935i	−0.827531	−	1.43332i
$726$		0			0
$727$	8.45797			0.313689			0.156844	−	0.987623i	$-0.449868\pi$
$727$	8.45797			0.313689			0.156844	+	0.987623i	$0.449868\pi$
$728$		0			0
$729$	−9.80095			−0.362998
$730$		0			0
$731$	−3.24735	−	5.62458i	−0.120108	−	0.208033i
$732$		0			0
$733$		−	23.9154i		−	0.883335i	−0.897179	−	0.441668i	$-0.854387\pi$
$733$		−	23.9154i		−	0.883335i	0.897179	−	0.441668i	$-0.145613\pi$
$734$		0			0
$735$	−44.8318	−	25.8837i	−1.65365	−	0.954733i
$736$		0			0
$737$	5.47327	−	9.47998i	0.201610	−	0.349200i
$738$		0			0
$739$	6.87143	−	3.96722i	0.252770	−	0.145937i	−0.368262	−	0.929722i	$-0.620047\pi$
$739$	6.87143	−	3.96722i	0.252770	−	0.145937i	0.621032	+	0.783785i	$0.286714\pi$
$740$		0			0
$741$	2.37256	+	31.9707i	0.0871580	+	1.17447i
$742$		0			0
$743$	−30.3956	+	17.5489i	−1.11511	+	0.643808i	−0.940147	−	0.340768i	$-0.889313\pi$
$743$	−30.3956	+	17.5489i	−1.11511	+	0.643808i	−0.174960	+	0.984576i	$0.555980\pi$
$744$		0			0
$745$	9.78194	−	16.9428i	0.358383	−	0.620737i
$746$		0			0
$747$	−10.5927	−	6.11567i	−0.387565	−	0.223761i
$748$		0			0
$749$			12.8409i			0.469196i
$750$		0			0
$751$	6.07761	+	10.5267i	0.221775	+	0.384126i	0.955347	−	0.295486i	$-0.0954816\pi$
$751$	6.07761	+	10.5267i	0.221775	+	0.384126i	−0.733572	+	0.679612i	$0.762148\pi$
$752$		0			0
$753$	48.1658			1.75526
$754$		0			0
$755$	36.2112			1.31786
$756$		0			0
$757$	15.7581	+	27.2938i	0.572737	+	0.992009i	0.996283	+	0.0861351i	$0.0274517\pi$
$757$	15.7581	+	27.2938i	0.572737	+	0.992009i	−0.423547	+	0.905874i	$0.639215\pi$
$758$		0			0
$759$		−	23.6116i		−	0.857048i
$760$		0			0
$761$	−0.602386	−	0.347788i	−0.0218365	−	0.0126073i	0.489042	−	0.872260i	$-0.337346\pi$
$761$	−0.602386	−	0.347788i	−0.0218365	−	0.0126073i	−0.510879	+	0.859653i	$0.670680\pi$
$762$		0			0
$763$	6.49471	−	11.2492i	0.235124	−	0.407247i
$764$		0			0
$765$	−7.38652	+	4.26461i	−0.267060	+	0.154187i
$766$		0			0
$767$	−29.1683	−	14.0728i	−1.05321	−	0.508139i
$768$		0			0
$769$	−38.7981	+	22.4001i	−1.39909	+	0.807768i	−0.994298	−	0.106639i	$-0.965991\pi$
$769$	−38.7981	+	22.4001i	−1.39909	+	0.807768i	−0.404797	+	0.914407i	$0.632658\pi$
$770$		0			0
$771$	−18.4823	+	32.0123i	−0.665624	+	1.15289i
$772$		0			0
$773$	−8.27422	−	4.77712i	−0.297603	−	0.171821i	0.343763	−	0.939057i	$-0.388298\pi$
$773$	−8.27422	−	4.77712i	−0.297603	−	0.171821i	−0.641366	+	0.767235i	$0.721632\pi$
$774$		0			0
$775$		−	99.4748i		−	3.57324i
$776$		0			0
$777$	3.20629	+	5.55345i	0.115025	+	0.199229i
$778$		0			0
$779$	−10.9858			−0.393606
$780$		0			0
$781$	−8.98218			−0.321408
$782$		0			0
$783$	3.98330	+	6.89929i	0.142352	+	0.246560i
$784$		0			0
$785$			36.7448i			1.31148i
$786$		0			0
$787$	11.1206	+	6.42048i	0.396407	+	0.228866i	0.684932	−	0.728607i	$-0.259832\pi$
$787$	11.1206	+	6.42048i	0.396407	+	0.228866i	−0.288526	+	0.957472i	$0.593165\pi$
$788$		0			0
$789$	8.04288	−	13.9307i	0.286334	−	0.495945i
$790$		0			0
$791$	−4.38400	+	2.53111i	−0.155877	+	0.0899958i
$792$		0			0
$793$	12.2063	−	25.2997i	0.433458	−	0.898417i
$794$		0			0
$795$	−70.0054	+	40.4176i	−2.48283	+	1.43347i
$796$		0			0
$797$	14.8916	−	25.7929i	0.527486	−	0.913633i	−0.472000	−	0.881598i	$-0.656468\pi$
$797$	14.8916	−	25.7929i	0.527486	−	0.913633i	0.999487	−	0.0320348i	$-0.0101987\pi$
$798$		0			0
$799$	−5.88105	−	3.39543i	−0.208057	−	0.120122i
$800$		0			0
$801$			29.9282i			1.05746i
$802$		0			0
$803$	5.26739	+	9.12339i	0.185882	+	0.321958i
$804$		0			0
$805$	−41.6617			−1.46838
$806$		0			0
$807$	16.5053			0.581015
$808$		0			0
$809$	13.1974	+	22.8585i	0.463995	+	0.803663i	0.999156	−	0.0410874i	$-0.0130822\pi$
$809$	13.1974	+	22.8585i	0.463995	+	0.803663i	−0.535161	+	0.844750i	$0.679749\pi$
$810$		0			0
$811$			29.9543i			1.05184i	0.850535	+	0.525918i	$0.176278\pi$
$811$			29.9543i			1.05184i	−0.850535	+	0.525918i	$0.823722\pi$
$812$		0			0
$813$	−13.7702	−	7.95021i	−0.482941	−	0.278826i
$814$		0			0
$815$	13.7254	−	23.7730i	0.480779	−	0.832733i
$816$		0			0
$817$	−22.0728	+	12.7437i	−0.772229	+	0.445847i
$818$		0			0
$819$	−7.20778	+	4.90652i	−0.251860	+	0.171448i
$820$		0			0
$821$	−26.0473	+	15.0384i	−0.909055	+	0.524843i	−0.880127	−	0.474738i	$-0.842543\pi$
$821$	−26.0473	+	15.0384i	−0.909055	+	0.524843i	−0.0289283	+	0.999581i	$0.509209\pi$
$822$		0			0
$823$	−26.1666	+	45.3220i	−0.912112	+	1.57982i	−0.101036	+	0.994883i	$0.532216\pi$
$823$	−26.1666	+	45.3220i	−0.912112	+	1.57982i	−0.811076	+	0.584941i	$0.801117\pi$
$824$		0			0
$825$	−24.4255	−	14.1021i	−0.850388	−	0.490972i
$826$		0			0
$827$			42.7297i			1.48586i	0.669371	+	0.742928i	$0.266564\pi$
$827$			42.7297i			1.48586i	−0.669371	+	0.742928i	$0.733436\pi$
$828$		0			0
$829$	5.77975	+	10.0108i	0.200739	+	0.347690i	0.948767	−	0.315977i	$-0.102332\pi$
$829$	5.77975	+	10.0108i	0.200739	+	0.347690i	−0.748028	+	0.663668i	$0.768999\pi$
$830$		0			0
$831$	−29.6936			−1.03006
$832$		0			0
$833$	5.71520			0.198020
$834$		0			0
$835$	−22.1833	−	38.4227i	−0.767686	−	1.32967i
$836$		0			0
$837$			17.7829i			0.614668i
$838$		0			0
$839$	−24.1215	−	13.9265i	−0.832765	−	0.480797i	0.0220332	−	0.999757i	$-0.492986\pi$
$839$	−24.1215	−	13.9265i	−0.832765	−	0.480797i	−0.854799	+	0.518960i	$0.826319\pi$
$840$		0			0
$841$	6.26698	−	10.8547i	0.216103	−	0.374301i
$842$		0			0
$843$	48.4269	−	27.9593i	1.66791	−	0.962970i
$844$		0			0
$845$	−7.67132	−	51.4017i	−0.263901	−	1.76827i
$846$		0			0
$847$	−9.53676	+	5.50605i	−0.327687	+	0.189190i
$848$		0			0
$849$	−7.35760	+	12.7437i	−0.252512	+	0.437364i
$850$		0			0
$851$	−19.8810	−	11.4783i	−0.681513	−	0.393472i
$852$		0			0
$853$			31.0439i			1.06292i	0.847082	+	0.531462i	$0.178357\pi$
$853$			31.0439i			1.06292i	−0.847082	+	0.531462i	$0.821643\pi$
$854$		0			0
$855$	16.7358	+	28.9872i	0.572352	+	0.991342i
$856$		0			0
$857$	−44.9943			−1.53698			−0.768488	−	0.639865i	$-0.778990\pi$
$857$	−44.9943			−1.53698			−0.768488	+	0.639865i	$0.778990\pi$
$858$		0			0
$859$	−27.1483			−0.926287			−0.463144	−	0.886283i	$-0.653279\pi$
$859$	−27.1483			−0.926287			−0.463144	+	0.886283i	$0.653279\pi$
$860$		0			0
$861$	−3.59467	−	6.22614i	−0.122506	−	0.212186i
$862$		0			0
$863$			13.4506i			0.457863i	0.973442	+	0.228932i	$0.0735233\pi$
$863$			13.4506i			0.457863i	−0.973442	+	0.228932i	$0.926477\pi$
$864$		0			0
$865$	67.5683	+	39.0106i	2.29739	+	1.32640i
$866$		0			0
$867$	−18.1258	+	31.3948i	−0.615583	+	1.06622i
$868$		0			0
$869$	−12.7508	+	7.36170i	−0.432542	+	0.249729i
$870$		0			0
$871$	28.7839	−	19.5940i	0.975307	−	0.663917i
$872$		0			0
$873$	16.4284	−	9.48494i	0.556017	−	0.321017i
$874$		0			0
$875$	−13.5540	+	23.4761i	−0.458207	+	0.793638i
$876$		0			0
$877$	42.0333	+	24.2679i	1.41936	+	0.819470i	0.996243	−	0.0866035i	$-0.0276013\pi$
$877$	42.0333	+	24.2679i	1.41936	+	0.819470i	0.423121	+	0.906073i	$0.360935\pi$
$878$		0			0
$879$			46.2714i			1.56069i
$880$		0			0
$881$	10.5757	+	18.3176i	0.356303	+	0.617135i	0.987340	−	0.158618i	$-0.0507038\pi$
$881$	10.5757	+	18.3176i	0.356303	+	0.617135i	−0.631037	+	0.775753i	$0.717370\pi$
$882$		0			0
$883$	−26.0192			−0.875616			−0.437808	−	0.899068i	$-0.644245\pi$
$883$	−26.0192			−0.875616			−0.437808	+	0.899068i	$0.644245\pi$
$884$		0			0
$885$	−81.3591			−2.73486
$886$		0			0
$887$	−7.34530	−	12.7224i	−0.246631	−	0.427178i	0.715958	−	0.698143i	$-0.245990\pi$
$887$	−7.34530	−	12.7224i	−0.246631	−	0.427178i	−0.962589	+	0.270966i	$0.912657\pi$
$888$		0			0
$889$			4.30216i			0.144290i
$890$		0			0
$891$	10.6494	+	6.14845i	0.356769	+	0.205981i
$892$		0			0
$893$	−13.3248	+	23.0793i	−0.445898	+	0.772318i
$894$		0			0
$895$	−25.4875	+	14.7152i	−0.851952	+	0.491875i
$896$		0			0
$897$	32.6367	−	67.6452i	1.08971	−	2.25861i
$898$		0			0
$899$	−31.8309	+	18.3776i	−1.06162	+	0.612927i
$900$		0			0
$901$	4.46217	−	7.72871i	0.148657	−	0.257481i
$902$		0			0
$903$	−14.4449	−	8.33978i	−0.480697	−	0.277530i
$904$		0			0
$905$			20.7537i			0.689878i
$906$		0			0
$907$	24.9393	+	43.1962i	0.828097	+	1.43431i	0.899529	+	0.436860i	$0.143910\pi$
$907$	24.9393	+	43.1962i	0.828097	+	1.43431i	−0.0714325	+	0.997445i	$0.522757\pi$
$908$		0			0
$909$	17.1913			0.570200
$910$		0			0
$911$	4.18861			0.138775			0.0693874	−	0.997590i	$-0.477896\pi$
$911$	4.18861			0.138775			0.0693874	+	0.997590i	$0.477896\pi$
$912$		0			0
$913$	3.24916	+	5.62772i	0.107532	+	0.186250i
$914$		0			0
$915$		−	70.5683i		−	2.33291i
$916$		0			0
$917$	4.74511	+	2.73959i	0.156697	+	0.0904693i
$918$		0			0
$919$	−8.95699	+	15.5140i	−0.295464	+	0.511758i	−0.975093	−	0.221798i	$-0.928808\pi$
$919$	−8.95699	+	15.5140i	−0.295464	+	0.511758i	0.679629	+	0.733556i	$0.262141\pi$
$920$		0			0
$921$	25.6217	−	14.7927i	0.844264	−	0.487436i
$922$		0			0
$923$	−25.7331	−	12.4154i	−0.847017	−	0.408659i
$924$		0			0
$925$	−23.7480	+	13.7109i	−0.780829	+	0.450812i
$926$		0			0
$927$	6.78842	−	11.7579i	0.222961	−	0.386180i
$928$		0			0
$929$	4.90048	+	2.82929i	0.160779	+	0.0928260i	0.578231	−	0.815873i	$-0.303743\pi$
$929$	4.90048	+	2.82929i	0.160779	+	0.0928260i	−0.417451	+	0.908699i	$0.637077\pi$
$930$		0			0
$931$		−	22.4284i		−	0.735061i
$932$		0			0
$933$	3.74312	+	6.48327i	0.122544	+	0.212253i
$934$		0			0
$935$	4.53144			0.148194
$936$		0			0
$937$	−21.2969			−0.695739			−0.347870	−	0.937543i	$-0.613095\pi$
$937$	−21.2969			−0.695739			−0.347870	+	0.937543i	$0.613095\pi$
$938$		0			0
$939$	6.02084	+	10.4284i	0.196483	+	0.340318i
$940$		0			0
$941$		−	24.1291i		−	0.786587i	−0.919413	−	0.393293i	$-0.871336\pi$
$941$		−	24.1291i		−	0.786587i	0.919413	−	0.393293i	$-0.128664\pi$
$942$		0			0
$943$	22.2892	+	12.8687i	0.725837	+	0.419062i
$944$		0			0
$945$	4.44821	−	7.70453i	0.144700	−	0.250628i
$946$		0			0
$947$	20.2567	−	11.6952i	0.658253	−	0.380043i	−0.133358	−	0.991068i	$-0.542576\pi$
$947$	20.2567	−	11.6952i	0.658253	−	0.380043i	0.791611	+	0.611025i	$0.209243\pi$
$948$		0			0
$949$	2.47999	+	33.4185i	0.0805039	+	1.08481i
$950$		0			0
$951$	−55.3033	+	31.9294i	−1.79333	+	1.03538i
$952$		0			0
$953$	−21.3398	+	36.9616i	−0.691263	+	1.19730i	0.280161	+	0.959953i	$0.409612\pi$
$953$	−21.3398	+	36.9616i	−0.691263	+	1.19730i	−0.971424	+	0.237350i	$0.923721\pi$
$954$		0			0
$955$	18.2366	+	10.5289i	0.590123	+	0.340708i
$956$		0			0
$957$			10.4212i			0.336871i
$958$		0			0
$959$	2.45353	+	4.24965i	0.0792288	+	0.137228i
$960$		0			0
$961$	−51.0444			−1.64659
$962$		0			0
$963$	−24.1695			−0.778851
$964$		0			0
$965$	−11.3109	−	19.5910i	−0.364109	−	0.630656i
$966$		0			0
$967$		−	12.5239i		−	0.402740i	−0.979515	−	0.201370i	$-0.935461\pi$
$967$		−	12.5239i		−	0.402740i	0.979515	−	0.201370i	$-0.0645394\pi$
$968$		0			0
$969$	−7.70024	−	4.44573i	−0.247367	−	0.142818i
$970$		0			0
$971$	1.86881	−	3.23688i	0.0599730	−	0.103876i	−0.834480	−	0.551038i	$-0.814232\pi$
$971$	1.86881	−	3.23688i	0.0599730	−	0.103876i	0.894453	+	0.447162i	$0.147565\pi$
$972$		0			0
$973$	−15.5291	+	8.96574i	−0.497840	+	0.287428i
$974$		0			0
$975$	−50.4847	−	74.1629i	−1.61680	−	2.37511i
$976$		0			0
$977$	11.7212	−	6.76726i	0.374996	−	0.216504i	−0.300643	−	0.953737i	$-0.597201\pi$
$977$	11.7212	−	6.76726i	0.374996	−	0.216504i	0.675639	+	0.737233i	$0.263868\pi$
$978$		0			0
$979$	7.95021	−	13.7702i	0.254090	−	0.440097i
$980$		0			0
$981$	21.1735	+	12.2245i	0.676018	+	0.390299i
$982$		0			0
$983$		−	13.5918i		−	0.433511i	−0.976226	−	0.216756i	$-0.930453\pi$
$983$		−	13.5918i		−	0.433511i	0.976226	−	0.216756i	$-0.0695475\pi$
$984$		0			0
$985$	−28.0400	−	48.5667i	−0.893429	−	1.54746i
$986$		0			0
$987$	−17.4401			−0.555125
$988$		0			0
$989$	59.7119			1.89873
$990$		0			0
$991$	−27.6473	−	47.8865i	−0.878245	−	1.52117i	−0.853265	−	0.521477i	$-0.825381\pi$
$991$	−27.6473	−	47.8865i	−0.878245	−	1.52117i	−0.0249801	−	0.999688i	$-0.507952\pi$
$992$		0			0
$993$		−	43.6132i		−	1.38402i
$994$		0			0
$995$	−18.2366	−	10.5289i	−0.578140	−	0.333789i
$996$		0			0
$997$	21.7441	−	37.6619i	0.688643	−	1.19276i	−0.283634	−	0.958933i	$-0.591540\pi$
$997$	21.7441	−	37.6619i	0.688643	−	1.19276i	0.972277	−	0.233832i	$-0.0751266\pi$
$998$		0			0
$999$	4.24538	−	2.45107i	0.134318	−	0.0775486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.w.d.257.5	yes	12
4.3	odd	2	inner	416.2.w.d.257.2	yes	12
8.3	odd	2		832.2.w.j.257.5		12
8.5	even	2		832.2.w.j.257.2		12
13.2	odd	12		5408.2.a.bn.1.2		6
13.4	even	6	inner	416.2.w.d.225.5	yes	12
13.11	odd	12		5408.2.a.bm.1.2		6
52.11	even	12		5408.2.a.bn.1.5		6
52.15	even	12		5408.2.a.bm.1.5		6
52.43	odd	6	inner	416.2.w.d.225.2	✓	12
104.43	odd	6		832.2.w.j.641.5		12
104.69	even	6		832.2.w.j.641.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.w.d.225.2	✓	12	52.43	odd	6	inner
416.2.w.d.225.5	yes	12	13.4	even	6	inner
416.2.w.d.257.2	yes	12	4.3	odd	2	inner
416.2.w.d.257.5	yes	12	1.1	even	1	trivial
832.2.w.j.257.2		12	8.5	even	2
832.2.w.j.257.5		12	8.3	odd	2
832.2.w.j.641.2		12	104.69	even	6
832.2.w.j.641.5		12	104.43	odd	6
5408.2.a.bm.1.2		6	13.11	odd	12
5408.2.a.bm.1.5		6	52.15	even	12
5408.2.a.bn.1.2		6	13.2	odd	12
5408.2.a.bn.1.5		6	52.11	even	12

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13286 + 1.96217i) q^{3} -3.99777i q^{5} +(0.981633 + 0.566746i) q^{7} +(-1.06675 + 1.84766i) q^{9} +O(q^{10})\)	\(q+(1.13286 + 1.96217i) q^{3} -3.99777i q^{5} +(0.981633 + 0.566746i) q^{7} +(-1.06675 + 1.84766i) q^{9} +(0.981633 - 0.566746i) q^{11} +(3.59566 - 0.266835i) q^{13} +(7.84432 - 4.52892i) q^{15} +(-0.500000 + 0.866025i) q^{17} +(3.39858 + 1.96217i) q^{19} +2.56818i q^{21} +(-4.59696 - 7.96217i) q^{23} -10.9822 q^{25} +1.96327 q^{27} +(2.02892 + 3.51419i) q^{29} +9.05784i q^{31} +(2.22411 + 1.28409i) q^{33} +(2.26572 - 3.92434i) q^{35} +(2.16241 - 1.24847i) q^{37} +(4.59696 + 6.75302i) q^{39} +(-2.42434 + 1.39970i) q^{41} +(-3.24735 + 5.62458i) q^{43} +(7.38652 + 4.26461i) q^{45} +6.79085i q^{47} +(-2.85760 - 4.94950i) q^{49} -2.26572 q^{51} -8.92434 q^{53} +(-2.26572 - 3.92434i) q^{55} +8.89147i q^{57} +(-7.77880 - 4.49109i) q^{59} +(3.89543 - 6.74708i) q^{61} +(-2.09431 + 1.20915i) q^{63} +(-1.06675 - 14.3746i) q^{65} +(8.36352 - 4.82868i) q^{67} +(10.4154 - 18.0401i) q^{69} +(-6.86268 - 3.96217i) q^{71} +9.29410i q^{73} +(-12.4413 - 21.5489i) q^{75} +1.28480 q^{77} -12.9894 q^{79} +(5.42434 + 9.39524i) q^{81} +5.73302i q^{83} +(3.46217 + 1.99889i) q^{85} +(-4.59696 + 7.96217i) q^{87} +(12.1485 - 7.01391i) q^{89} +(3.68085 + 1.77589i) q^{91} +(-17.7730 + 10.2613i) q^{93} +(7.84432 - 13.5868i) q^{95} +(-7.70024 - 4.44573i) q^{97} +2.41830i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^9	\( 12 q - 12 q^{9} + 12 q^{13} - 6 q^{17} - 12 q^{25} - 6 q^{29} - 30 q^{33} - 6 q^{37} + 30 q^{41} + 24 q^{49} - 48 q^{53} + 18 q^{61} - 12 q^{65} + 6 q^{69} + 132 q^{77} + 6 q^{81} + 12 q^{85} + 30 q^{89} - 36 q^{93} - 90 q^{97}+O(q^{100}) \) 12 * q - 12 * q^9 + 12 * q^13 - 6 * q^17 - 12 * q^25 - 6 * q^29 - 30 * q^33 - 6 * q^37 + 30 * q^41 + 24 * q^49 - 48 * q^53 + 18 * q^61 - 12 * q^65 + 6 * q^69 + 132 * q^77 + 6 * q^81 + 12 * q^85 + 30 * q^89 - 36 * q^93 - 90 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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