LMFDB - Embedded newform 624.2.cn.f.353.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.5
Character	$\chi$	$=$	624.353
Dual form			624.2.cn.f.449.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.852797 + 1.50756i) q^{3} +(0.477579 + 0.477579i) q^{5} +(-0.988569 + 0.264886i) q^{7} +(-1.54548 - 2.57128i) q^{9} +O(q^{10})$	\(q+(-0.852797 + 1.50756i) q^{3} +(0.477579 + 0.477579i) q^{5} +(-0.988569 + 0.264886i) q^{7} +(-1.54548 - 2.57128i) q^{9} +(-5.10637 - 1.36825i) q^{11} +(-1.49059 - 3.28301i) q^{13} +(-1.12726 + 0.312701i) q^{15} +(-1.22274 + 2.11784i) q^{17} +(1.14039 + 4.25599i) q^{19} +(0.443716 - 1.71622i) q^{21} +(-2.40904 - 4.17258i) q^{23} -4.54384i q^{25} +(5.19434 - 0.137115i) q^{27} +(-3.23138 + 1.86564i) q^{29} +(2.91416 - 2.91416i) q^{31} +(6.41741 - 6.53132i) q^{33} +(-0.598623 - 0.345615i) q^{35} +(-0.898805 + 3.35438i) q^{37} +(6.22050 + 0.552587i) q^{39} +(1.25078 - 4.66796i) q^{41} +(-10.9673 - 6.33197i) q^{43} +(0.489904 - 1.96608i) q^{45} +(0.646174 - 0.646174i) q^{47} +(-5.15507 + 2.97628i) q^{49} +(-2.15003 - 3.64943i) q^{51} +6.56807i q^{53} +(-1.78525 - 3.09214i) q^{55} +(-7.38868 - 1.91029i) q^{57} +(-2.21886 - 8.28091i) q^{59} +(-3.99581 + 6.92094i) q^{61} +(2.20891 + 2.13252i) q^{63} +(0.856021 - 2.27977i) q^{65} +(-3.54515 - 0.949919i) q^{67} +(8.34484 - 0.0734109i) q^{69} +(5.34544 - 1.43231i) q^{71} +(-0.225083 - 0.225083i) q^{73} +(6.85011 + 3.87497i) q^{75} +5.41043 q^{77} +2.70428 q^{79} +(-4.22301 + 7.94772i) q^{81} +(7.41135 + 7.41135i) q^{83} +(-1.59539 + 0.427483i) q^{85} +(-0.0568517 - 6.46251i) q^{87} +(-10.0378 - 2.68962i) q^{89} +(2.34317 + 2.85064i) q^{91} +(1.90809 + 6.87846i) q^{93} +(-1.48794 + 2.57719i) q^{95} +(-2.57029 - 9.59245i) q^{97} +(4.37361 + 15.2445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^7	$ 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.852797	+	1.50756i	−0.492362	+	0.870390i
$3$	−0.852797	+	1.50756i	−0.492362	+	0.870390i
$4$		0			0
$5$	0.477579	+	0.477579i	0.213580	+	0.213580i	0.805786	−	0.592207i	$-0.201743\pi$
$5$	0.477579	+	0.477579i	0.213580	+	0.213580i	−0.592207	+	0.805786i	$0.701743\pi$
$6$		0			0
$7$	−0.988569	+	0.264886i	−0.373644	+	0.100118i	−0.440754	−	0.897628i	$-0.645289\pi$
$7$	−0.988569	+	0.264886i	−0.373644	+	0.100118i	0.0671099	+	0.997746i	$0.478622\pi$
$8$		0			0
$9$	−1.54548	−	2.57128i	−0.515159	−	0.857095i
$10$		0			0
$11$	−5.10637	−	1.36825i	−1.53963	−	0.412542i	−0.613482	−	0.789709i	$-0.710232\pi$
$11$	−5.10637	−	1.36825i	−1.53963	−	0.412542i	−0.926145	+	0.377167i	$0.876898\pi$
$12$		0			0
$13$	−1.49059	−	3.28301i	−0.413415	−	0.910543i
$13$	−1.49059	−	3.28301i	−0.413415	−	0.910543i
$14$		0			0
$15$	−1.12726	+	0.312701i	−0.291056	+	0.0807391i
$16$		0			0
$17$	−1.22274	+	2.11784i	−0.296557	+	0.513652i	−0.975346	−	0.220682i	$-0.929172\pi$
$17$	−1.22274	+	2.11784i	−0.296557	+	0.513652i	0.678789	+	0.734333i	$0.262505\pi$
$18$		0			0
$19$	1.14039	+	4.25599i	0.261623	+	0.976391i	0.964285	+	0.264867i	$0.0853280\pi$
$19$	1.14039	+	4.25599i	0.261623	+	0.976391i	−0.702662	+	0.711524i	$0.748005\pi$
$20$		0			0
$21$	0.443716	−	1.71622i	0.0968268	−	0.374510i
$22$		0			0
$23$	−2.40904	−	4.17258i	−0.502320	−	0.870044i	−0.999996	−	0.00268084i	$-0.999147\pi$
$23$	−2.40904	−	4.17258i	−0.502320	−	0.870044i	0.497677	−	0.867363i	$-0.334187\pi$
$24$		0			0
$25$		−	4.54384i		−	0.908767i
$26$		0			0
$27$	5.19434	−	0.137115i	0.999652	−	0.0263877i
$28$		0			0
$29$	−3.23138	+	1.86564i	−0.600052	+	0.346440i	−0.769062	−	0.639174i	$-0.779276\pi$
$29$	−3.23138	+	1.86564i	−0.600052	+	0.346440i	0.169010	+	0.985614i	$0.445943\pi$
$30$		0			0
$31$	2.91416	−	2.91416i	0.523398	−	0.523398i	−0.395198	−	0.918596i	$-0.629324\pi$
$31$	2.91416	−	2.91416i	0.523398	−	0.523398i	0.918596	+	0.395198i	$0.129324\pi$
$32$		0			0
$33$	6.41741	−	6.53132i	1.11713	−	1.13696i
$34$		0			0
$35$	−0.598623	−	0.345615i	−0.101186	−	0.0584197i
$36$		0			0
$37$	−0.898805	+	3.35438i	−0.147763	+	0.551457i	0.851854	+	0.523779i	$0.175478\pi$
$37$	−0.898805	+	3.35438i	−0.147763	+	0.551457i	−0.999617	+	0.0276786i	$0.991188\pi$
$38$		0			0
$39$	6.22050	+	0.552587i	0.996078	+	0.0884847i
$40$		0			0
$41$	1.25078	−	4.66796i	0.195338	−	0.729013i	−0.796841	−	0.604189i	$-0.793497\pi$
$41$	1.25078	−	4.66796i	0.195338	−	0.729013i	0.992179	−	0.124823i	$-0.0398363\pi$
$42$		0			0
$43$	−10.9673	−	6.33197i	−1.67250	−	0.965616i	−0.966235	−	0.257664i	$-0.917047\pi$
$43$	−10.9673	−	6.33197i	−1.67250	−	0.965616i	−0.706261	−	0.707952i	$-0.749619\pi$
$44$		0			0
$45$	0.489904	−	1.96608i	0.0730306	−	0.293085i
$46$		0			0
$47$	0.646174	−	0.646174i	0.0942541	−	0.0942541i	−0.658408	−	0.752662i	$-0.728770\pi$
$47$	0.646174	−	0.646174i	0.0942541	−	0.0942541i	0.752662	+	0.658408i	$0.228770\pi$
$48$		0			0
$49$	−5.15507	+	2.97628i	−0.736439	+	0.425183i
$50$		0			0
$51$	−2.15003	−	3.64943i	−0.301064	−	0.511023i
$52$		0			0
$53$			6.56807i			0.902194i	0.892475	+	0.451097i	$0.148967\pi$
$53$			6.56807i			0.902194i	−0.892475	+	0.451097i	$0.851033\pi$
$54$		0			0
$55$	−1.78525	−	3.09214i	−0.240722	−	0.416944i
$56$		0			0
$57$	−7.38868	−	1.91029i	−0.978655	−	0.253024i
$58$		0			0
$59$	−2.21886	−	8.28091i	−0.288872	−	1.07808i	−0.945964	−	0.324273i	$-0.894880\pi$
$59$	−2.21886	−	8.28091i	−0.288872	−	1.07808i	0.657092	−	0.753810i	$-0.271786\pi$
$60$		0			0
$61$	−3.99581	+	6.92094i	−0.511611	+	0.886136i	0.488299	+	0.872676i	$0.337618\pi$
$61$	−3.99581	+	6.92094i	−0.511611	+	0.886136i	−0.999909	+	0.0134590i	$0.995716\pi$
$62$		0			0
$63$	2.20891	+	2.13252i	0.278296	+	0.268672i
$64$		0			0
$65$	0.856021	−	2.27977i	0.106176	−	0.282770i
$66$		0			0
$67$	−3.54515	−	0.949919i	−0.433109	−	0.116051i	0.0356764	−	0.999363i	$-0.488641\pi$
$67$	−3.54515	−	0.949919i	−0.433109	−	0.116051i	−0.468785	+	0.883312i	$0.655308\pi$
$68$		0			0
$69$	8.34484	−	0.0734109i	1.00460	−	0.00883764i
$70$		0			0
$71$	5.34544	−	1.43231i	0.634387	−	0.169984i	0.0727276	−	0.997352i	$-0.476830\pi$
$71$	5.34544	−	1.43231i	0.634387	−	0.169984i	0.561660	+	0.827368i	$0.310163\pi$
$72$		0			0
$73$	−0.225083	−	0.225083i	−0.0263440	−	0.0263440i	0.693812	−	0.720156i	$-0.255930\pi$
$73$	−0.225083	−	0.225083i	−0.0263440	−	0.0263440i	−0.720156	+	0.693812i	$0.755930\pi$
$74$		0			0
$75$	6.85011	+	3.87497i	0.790982	+	0.447443i
$76$		0			0
$77$	5.41043			0.616575
$78$		0			0
$79$	2.70428			0.304256			0.152128	−	0.988361i	$-0.451387\pi$
$79$	2.70428			0.304256			0.152128	+	0.988361i	$0.451387\pi$
$80$		0			0
$81$	−4.22301	+	7.94772i	−0.469223	+	0.883080i
$82$		0			0
$83$	7.41135	+	7.41135i	0.813502	+	0.813502i	0.985157	−	0.171655i	$-0.0549115\pi$
$83$	7.41135	+	7.41135i	0.813502	+	0.813502i	−0.171655	+	0.985157i	$0.554911\pi$
$84$		0			0
$85$	−1.59539	+	0.427483i	−0.173044	+	0.0463670i
$86$		0			0
$87$	−0.0568517	−	6.46251i	−0.00609514	−	0.692853i
$88$		0			0
$89$	−10.0378	−	2.68962i	−1.06401	−	0.285099i	−0.315978	−	0.948767i	$-0.602332\pi$
$89$	−10.0378	−	2.68962i	−1.06401	−	0.285099i	−0.748028	+	0.663667i	$0.768999\pi$
$90$		0			0
$91$	2.34317	+	2.85064i	0.245631	+	0.298829i
$92$		0			0
$93$	1.90809	+	6.87846i	0.197859	+	0.713263i
$94$		0			0
$95$	−1.48794	+	2.57719i	−0.152660	+	0.264415i
$96$		0			0
$97$	−2.57029	−	9.59245i	−0.260973	−	0.973966i	−0.964669	−	0.263465i	$-0.915135\pi$
$97$	−2.57029	−	9.59245i	−0.260973	−	0.973966i	0.703696	−	0.710502i	$-0.251532\pi$
$98$		0			0
$99$	4.37361	+	15.2445i	0.439565	+	1.53213i
$100$		0			0
$101$	8.34245	+	14.4495i	0.830105	+	1.43778i	0.897954	+	0.440088i	$0.145053\pi$
$101$	8.34245	+	14.4495i	0.830105	+	1.43778i	−0.0678495	+	0.997696i	$0.521614\pi$
$102$		0			0
$103$			4.13601i			0.407533i	0.979020	+	0.203766i	$0.0653183\pi$
$103$			4.13601i			0.407533i	−0.979020	+	0.203766i	$0.934682\pi$
$104$		0			0
$105$	1.03154	−	0.607721i	0.100668	−	0.0593075i
$106$		0			0
$107$	3.57621	−	2.06472i	0.345725	−	0.199604i	−0.317076	−	0.948400i	$-0.602701\pi$
$107$	3.57621	−	2.06472i	0.345725	−	0.199604i	0.662801	+	0.748796i	$0.269368\pi$
$108$		0			0
$109$	−11.2846	+	11.2846i	−1.08086	+	1.08086i	−0.0844356	+	0.996429i	$0.526909\pi$
$109$	−11.2846	+	11.2846i	−1.08086	+	1.08086i	−0.996429	+	0.0844356i	$0.973091\pi$
$110$		0			0
$111$	−4.29044	−	4.21561i	−0.407230	−	0.400128i
$112$		0			0
$113$	−2.46074	−	1.42071i	−0.231487	−	0.133649i	0.379771	−	0.925081i	$-0.376003\pi$
$113$	−2.46074	−	1.42071i	−0.231487	−	0.133649i	−0.611258	+	0.791431i	$0.709336\pi$
$114$		0			0
$115$	0.842229	−	3.14324i	0.0785383	−	0.293109i
$116$		0			0
$117$	−6.13788	+	8.90654i	−0.567447	+	0.823410i
$118$		0			0
$119$	0.647772	−	2.41752i	0.0593811	−	0.221613i
$120$		0			0
$121$	14.6766	+	8.47354i	1.33424	+	0.770322i
$122$		0			0
$123$	5.97057	+	5.86644i	0.538348	+	0.528959i
$124$		0			0
$125$	4.55793	−	4.55793i	0.407674	−	0.407674i
$126$		0			0
$127$	−17.1930	+	9.92638i	−1.52563	+	0.880823i	−0.526093	+	0.850427i	$0.676344\pi$
$127$	−17.1930	+	9.92638i	−1.52563	+	0.880823i	−0.999538	+	0.0303965i	$0.990323\pi$
$128$		0			0
$129$	18.8987	−	11.1340i	1.66394	−	0.980291i
$130$		0			0
$131$			5.89464i			0.515017i	0.966276	+	0.257509i	$0.0829016\pi$
$131$			5.89464i			0.515017i	−0.966276	+	0.257509i	$0.917098\pi$
$132$		0			0
$133$	−2.25471	−	3.90527i	−0.195508	−	0.338629i
$134$		0			0
$135$	2.54619	+	2.41522i	0.219141	+	0.207869i
$136$		0			0
$137$	−2.47941	−	9.25328i	−0.211830	−	0.790561i	−0.987258	−	0.159125i	$-0.949133\pi$
$137$	−2.47941	−	9.25328i	−0.211830	−	0.790561i	0.775428	−	0.631436i	$-0.217534\pi$
$138$		0			0
$139$	−1.60178	+	2.77436i	−0.135861	+	0.235318i	−0.925926	−	0.377705i	$-0.876713\pi$
$139$	−1.60178	+	2.77436i	−0.135861	+	0.235318i	0.790065	+	0.613023i	$0.210047\pi$
$140$		0			0
$141$	0.423091	+	1.52520i	0.0356307	+	0.128445i
$142$		0			0
$143$	3.11953	+	18.8037i	0.260868	+	1.57245i
$144$		0			0
$145$	−2.43422	−	0.652249i	−0.202151	−	0.0541663i
$146$		0			0
$147$	−0.0906965	−	10.3097i	−0.00748052	−	0.850334i
$148$		0			0
$149$	19.0182	−	5.09591i	1.55803	−	0.417474i	0.625993	−	0.779829i	$-0.284694\pi$
$149$	19.0182	−	5.09591i	1.55803	−	0.417474i	0.932040	+	0.362355i	$0.118027\pi$
$150$		0			0
$151$	13.0832	+	13.0832i	1.06470	+	1.06470i	0.997757	+	0.0669402i	$0.0213237\pi$
$151$	13.0832	+	13.0832i	1.06470	+	1.06470i	0.0669402	+	0.997757i	$0.478676\pi$
$152$		0			0
$153$	7.33528	−	0.129069i	0.593022	−	0.0104346i
$154$		0			0
$155$	2.78348			0.223574
$156$		0			0
$157$	−0.0824533			−0.00658049			−0.00329025	−	0.999995i	$-0.501047\pi$
$157$	−0.0824533			−0.00658049			−0.00329025	+	0.999995i	$0.501047\pi$
$158$		0			0
$159$	−9.90176	−	5.60123i	−0.785261	−	0.444206i
$160$		0			0
$161$	3.48676	+	3.48676i	0.274795	+	0.274795i
$162$		0			0
$163$	−22.9940	+	6.16123i	−1.80103	+	0.482585i	−0.994139	−	0.108112i	$-0.965520\pi$
$163$	−22.9940	+	6.16123i	−1.80103	+	0.482585i	−0.806893	+	0.590697i	$0.798853\pi$
$164$		0			0
$165$	6.18403	−	0.0544019i	0.481426	−	0.00423519i
$166$		0			0
$167$	−21.8268	−	5.84848i	−1.68901	−	0.452569i	−0.718876	−	0.695138i	$-0.755343\pi$
$167$	−21.8268	−	5.84848i	−1.68901	−	0.452569i	−0.970134	+	0.242569i	$0.922010\pi$
$168$		0			0
$169$	−8.55629	+	9.78723i	−0.658176	+	0.752864i
$170$		0			0
$171$	9.18092	−	9.50979i	0.702082	−	0.727232i
$172$		0			0
$173$	−10.6401	+	18.4292i	−0.808954	+	1.40115i	0.104635	+	0.994511i	$0.466633\pi$
$173$	−10.6401	+	18.4292i	−0.808954	+	1.40115i	−0.913589	+	0.406639i	$0.866701\pi$
$174$		0			0
$175$	1.20360	+	4.49190i	0.0909836	+	0.339555i
$176$		0			0
$177$	14.3762	+	3.71686i	1.08058	+	0.279377i
$178$		0			0
$179$	5.21779	+	9.03748i	0.389996	+	0.675493i	0.992449	−	0.122662i	$-0.0391431\pi$
$179$	5.21779	+	9.03748i	0.389996	+	0.675493i	−0.602453	+	0.798155i	$0.705810\pi$
$180$		0			0
$181$		−	15.3678i		−	1.14228i	−0.820852	−	0.571141i	$-0.806501\pi$
$181$		−	15.3678i		−	1.14228i	0.820852	−	0.571141i	$-0.193499\pi$
$182$		0			0
$183$	−7.02612	−	11.9261i	−0.519386	−	0.881601i
$184$		0			0
$185$	−2.03123	+	1.17273i	−0.149339	+	0.0862210i
$186$		0			0
$187$	9.14146	−	9.14146i	0.668490	−	0.668490i
$188$		0			0
$189$	−5.09865	+	1.51146i	−0.370872	+	0.109942i
$190$		0			0
$191$	17.1586	+	9.90652i	1.24155	+	0.716810i	0.969410	−	0.245447i	$-0.0789347\pi$
$191$	17.1586	+	9.90652i	1.24155	+	0.716810i	0.272142	+	0.962257i	$0.412268\pi$
$192$		0			0
$193$	5.30664	−	19.8047i	0.381980	−	1.42557i	−0.460892	−	0.887456i	$-0.652470\pi$
$193$	5.30664	−	19.8047i	0.381980	−	1.42557i	0.842872	−	0.538114i	$-0.180863\pi$
$194$		0			0
$195$	2.70687	+	3.23468i	0.193843	+	0.231640i
$196$		0			0
$197$	4.65798	−	17.3838i	0.331868	−	1.23855i	−0.575358	−	0.817902i	$-0.695137\pi$
$197$	4.65798	−	17.3838i	0.331868	−	1.23855i	0.907225	−	0.420645i	$-0.138196\pi$
$198$		0			0
$199$	15.7149	+	9.07301i	1.11400	+	0.643169i	0.939863	−	0.341553i	$-0.110953\pi$
$199$	15.7149	+	9.07301i	1.11400	+	0.643169i	0.174138	+	0.984721i	$0.444286\pi$
$200$		0			0
$201$	4.45535	−	4.53443i	0.314256	−	0.319834i
$202$		0			0
$203$	2.70026	−	2.70026i	0.189521	−	0.189521i
$204$		0			0
$205$	2.82666	−	1.63197i	0.197423	−	0.113982i
$206$		0			0
$207$	−7.00578	+	12.6430i	−0.486935	+	0.878746i
$208$		0			0
$209$		−	23.2930i		−	1.61121i
$210$		0			0
$211$	−10.5719	−	18.3111i	−0.727801	−	1.26059i	−0.957811	−	0.287400i	$-0.907209\pi$
$211$	−10.5719	−	18.3111i	−0.727801	−	1.26059i	0.230009	−	0.973188i	$-0.426124\pi$
$212$		0			0
$213$	−2.39929	+	9.28005i	−0.164396	+	0.635858i
$214$		0			0
$215$	−2.21373	−	8.26175i	−0.150975	−	0.563447i
$216$		0			0
$217$	−2.10893	+	3.65277i	−0.143163	+	0.247966i
$218$		0			0
$219$	0.531276	−	0.147376i	0.0359003	−	0.00995876i
$220$		0			0
$221$	8.77548	+	0.857423i	0.590303	+	0.0576765i
$222$		0			0
$223$	−0.931275	−	0.249534i	−0.0623628	−	0.0167101i	0.227503	−	0.973777i	$-0.426944\pi$
$223$	−0.931275	−	0.249534i	−0.0623628	−	0.0167101i	−0.289866	+	0.957067i	$0.593611\pi$
$224$		0			0
$225$	−11.6835	+	7.02239i	−0.778900	+	0.468159i
$226$		0			0
$227$	9.18679	−	2.46159i	0.609749	−	0.163382i	0.0592855	−	0.998241i	$-0.481118\pi$
$227$	9.18679	−	2.46159i	0.609749	−	0.163382i	0.550463	+	0.834859i	$0.314451\pi$
$228$		0			0
$229$	−11.7646	−	11.7646i	−0.777428	−	0.777428i	0.201965	−	0.979393i	$-0.435267\pi$
$229$	−11.7646	−	11.7646i	−0.777428	−	0.777428i	−0.979393	+	0.201965i	$0.935267\pi$
$230$		0			0
$231$	−4.61399	+	8.15654i	−0.303578	+	0.536661i
$232$		0			0
$233$	−18.2304			−1.19431			−0.597156	−	0.802125i	$-0.703703\pi$
$233$	−18.2304			−1.19431			−0.597156	+	0.802125i	$0.703703\pi$
$234$		0			0
$235$	0.617197			0.0402615
$236$		0			0
$237$	−2.30621	+	4.07687i	−0.149804	+	0.264821i
$238$		0			0
$239$	−1.82483	−	1.82483i	−0.118039	−	0.118039i	0.645620	−	0.763659i	$-0.276599\pi$
$239$	−1.82483	−	1.82483i	−0.118039	−	0.118039i	−0.763659	+	0.645620i	$0.776599\pi$
$240$		0			0
$241$	3.81149	−	1.02128i	0.245519	−	0.0657867i	−0.133961	−	0.990987i	$-0.542770\pi$
$241$	3.81149	−	1.02128i	0.245519	−	0.0657867i	0.379480	+	0.925200i	$0.376103\pi$
$242$		0			0
$243$	−8.38029	−	13.1442i	−0.537596	−	0.843203i
$244$		0			0
$245$	−3.88336	−	1.04054i	−0.248099	−	0.0664779i
$246$		0			0
$247$	12.2726	−	10.0878i	0.780887	−	0.641874i
$248$		0			0
$249$	−17.4934	+	4.85269i	−1.10860	+	0.307526i
$250$		0			0
$251$	9.23209	−	15.9904i	0.582724	−	1.00931i	−0.412431	−	0.910989i	$-0.635320\pi$
$251$	9.23209	−	15.9904i	0.582724	−	1.00931i	0.995155	−	0.0983191i	$-0.0313466\pi$
$252$		0			0
$253$	6.59233	+	24.6029i	0.414456	+	1.54677i
$254$		0			0
$255$	0.716085	−	2.76970i	0.0448430	−	0.173445i
$256$		0			0
$257$	7.69399	+	13.3264i	0.479938	+	0.831276i	0.999735	−	0.0230131i	$-0.00732594\pi$
$257$	7.69399	+	13.3264i	0.479938	+	0.831276i	−0.519798	+	0.854290i	$0.673993\pi$
$258$		0			0
$259$		−	3.55412i		−	0.220842i
$260$		0			0
$261$	9.79110	+	5.42550i	0.606054	+	0.335830i
$262$		0			0
$263$	−5.28088	+	3.04892i	−0.325633	+	0.188004i	−0.653901	−	0.756580i	$-0.726869\pi$
$263$	−5.28088	+	3.04892i	−0.325633	+	0.188004i	0.328268	+	0.944585i	$0.393535\pi$
$264$		0			0
$265$	−3.13677	+	3.13677i	−0.192690	+	0.192690i
$266$		0			0
$267$	12.6150	−	12.8389i	0.772024	−	0.785728i
$268$		0			0
$269$	−25.7884	−	14.8889i	−1.57234	−	0.907793i	−0.995881	−	0.0906696i	$-0.971099\pi$
$269$	−25.7884	−	14.8889i	−1.57234	−	0.907793i	−0.576463	−	0.817123i	$-0.695567\pi$
$270$		0			0
$271$	3.63143	−	13.5527i	0.220593	−	0.823266i	−0.763529	−	0.645774i	$-0.776535\pi$
$271$	3.63143	−	13.5527i	0.220593	−	0.823266i	0.984122	−	0.177492i	$-0.0567984\pi$
$272$		0			0
$273$	−6.29577	+	1.10146i	−0.381037	+	0.0666631i
$274$		0			0
$275$	−6.21709	+	23.2025i	−0.374905	+	1.39916i
$276$		0			0
$277$	14.7600	+	8.52167i	0.886840	+	0.512017i	0.872908	−	0.487886i	$-0.162232\pi$
$277$	14.7600	+	8.52167i	0.886840	+	0.512017i	0.0139325	+	0.999903i	$0.495565\pi$
$278$		0			0
$279$	−11.9969	−	2.98937i	−0.718235	−	0.178969i
$280$		0			0
$281$	4.61708	−	4.61708i	0.275432	−	0.275432i	−0.555851	−	0.831282i	$-0.687607\pi$
$281$	4.61708	−	4.61708i	0.275432	−	0.275432i	0.831282	+	0.555851i	$0.187607\pi$
$282$		0			0
$283$	−10.4471	+	6.03162i	−0.621014	+	0.358542i	−0.777264	−	0.629175i	$-0.783393\pi$
$283$	−10.4471	+	6.03162i	−0.621014	+	0.358542i	0.156250	+	0.987718i	$0.450059\pi$
$284$		0			0
$285$	−2.61636	−	4.44099i	−0.154980	−	0.263061i
$286$		0			0
$287$			4.94591i			0.291948i
$288$		0			0
$289$	5.50984	+	9.54332i	0.324108	+	0.561372i
$290$		0			0
$291$	16.6531	+	4.30554i	0.976224	+	0.252396i
$292$		0			0
$293$	2.06466	+	7.70541i	0.120619	+	0.450155i	0.999646	−	0.0266171i	$-0.00847349\pi$
$293$	2.06466	+	7.70541i	0.120619	+	0.450155i	−0.879027	+	0.476772i	$0.841807\pi$
$294$		0			0
$295$	2.89510	−	5.01447i	0.168560	−	0.291954i
$296$		0			0
$297$	−26.7118	−	6.40698i	−1.54998	−	0.371771i
$298$		0			0
$299$	−10.1077	+	14.1285i	−0.584545	+	0.817073i
$300$		0			0
$301$	12.5192	+	3.35450i	0.721593	+	0.193350i
$302$		0			0
$303$	−28.8980	+	0.254220i	−1.66015	+	0.0146046i
$304$		0			0
$305$	−5.21360	+	1.39698i	−0.298530	+	0.0799909i
$306$		0			0
$307$	2.20646	+	2.20646i	0.125929	+	0.125929i	0.767262	−	0.641333i	$-0.221618\pi$
$307$	2.20646	+	2.20646i	0.125929	+	0.125929i	−0.641333	+	0.767262i	$0.721618\pi$
$308$		0			0
$309$	−6.23528	−	3.52717i	−0.354713	−	0.200654i
$310$		0			0
$311$	−1.32763			−0.0752831			−0.0376416	−	0.999291i	$-0.511985\pi$
$311$	−1.32763			−0.0752831			−0.0376416	+	0.999291i	$0.511985\pi$
$312$		0			0
$313$	16.9933			0.960519			0.480260	−	0.877126i	$-0.340542\pi$
$313$	16.9933			0.960519			0.480260	+	0.877126i	$0.340542\pi$
$314$		0			0
$315$	0.0364824	+	2.07337i	0.00205555	+	0.116821i
$316$		0			0
$317$	−18.5898	−	18.5898i	−1.04410	−	1.04410i	−0.998981	−	0.0451236i	$-0.985632\pi$
$317$	−18.5898	−	18.5898i	−1.04410	−	1.04410i	−0.0451236	−	0.998981i	$-0.514368\pi$
$318$		0			0
$319$	19.0533	−	5.10530i	1.06678	−	0.285842i
$320$		0			0
$321$	0.0629185	+	7.15213i	0.00351177	+	0.399193i
$322$		0			0
$323$	−10.4079	−	2.78879i	−0.579111	−	0.155172i
$324$		0			0
$325$	−14.9175	+	6.77299i	−0.827472	+	0.375698i
$326$		0			0
$327$	−7.38872	−	26.6356i	−0.408597	−	1.47295i
$328$		0			0
$329$	−0.467625	+	0.809950i	−0.0257810	+	0.0446540i
$330$		0			0
$331$	−2.77794	−	10.3674i	−0.152690	−	0.569845i	−0.999292	−	0.0376195i	$-0.988023\pi$
$331$	−2.77794	−	10.3674i	−0.152690	−	0.569845i	0.846603	−	0.532226i	$-0.178644\pi$
$332$		0			0
$333$	10.0142	−	2.87304i	0.548772	−	0.157441i
$334$		0			0
$335$	−1.23943	−	2.14675i	−0.0677170	−	0.117289i
$336$		0			0
$337$		−	2.17912i		−	0.118704i	−0.998237	−	0.0593522i	$-0.981097\pi$
$337$		−	2.17912i		−	0.118704i	0.998237	−	0.0593522i	$-0.0189035\pi$
$338$		0			0
$339$	4.24032	−	2.49814i	0.230303	−	0.135680i
$340$		0			0
$341$	−18.8681	+	10.8935i	−1.02176	+	0.589915i
$342$		0			0
$343$	9.37355	−	9.37355i	0.506124	−	0.506124i
$344$		0			0
$345$	4.02038	+	3.95026i	0.216450	+	0.212675i
$346$		0			0
$347$	−24.6713	−	14.2440i	−1.32443	−	0.764657i	−0.339994	−	0.940428i	$-0.610425\pi$
$347$	−24.6713	−	14.2440i	−1.32443	−	0.764657i	−0.984431	+	0.175770i	$0.943758\pi$
$348$		0			0
$349$	8.27424	−	30.8799i	0.442910	−	1.65296i	−0.278486	−	0.960440i	$-0.589833\pi$
$349$	8.27424	−	30.8799i	0.442910	−	1.65296i	0.721396	−	0.692522i	$-0.243501\pi$
$350$		0			0
$351$	−8.19278	−	16.8487i	−0.437298	−	0.899317i
$352$		0			0
$353$	−1.25756	+	4.69329i	−0.0669333	+	0.249799i	−0.991283	−	0.131747i	$-0.957941\pi$
$353$	−1.25756	+	4.69329i	−0.0669333	+	0.249799i	0.924350	+	0.381545i	$0.124608\pi$
$354$		0			0
$355$	3.23691	+	1.86883i	0.171797	+	0.0991872i
$356$		0			0
$357$	3.09213	+	3.03820i	0.163653	+	0.160799i
$358$		0			0
$359$	23.0189	−	23.0189i	1.21489	−	1.21489i	0.245491	−	0.969399i	$-0.421051\pi$
$359$	23.0189	−	23.0189i	1.21489	−	1.21489i	0.969399	−	0.245491i	$-0.0789492\pi$
$360$		0			0
$361$	−0.358474	+	0.206965i	−0.0188671	+	0.0108929i
$362$		0			0
$363$	−25.2905	+	14.8997i	−1.32741	+	0.782029i
$364$		0			0
$365$		−	0.214990i		−	0.0112531i
$366$		0			0
$367$	3.89669	+	6.74926i	0.203405	+	0.352308i	0.949623	−	0.313393i	$-0.101466\pi$
$367$	3.89669	+	6.74926i	0.203405	+	0.352308i	−0.746218	+	0.665702i	$0.768132\pi$
$368$		0			0
$369$	−13.9357	+	3.99812i	−0.725463	+	0.208134i
$370$		0			0
$371$	−1.73979	−	6.49299i	−0.0903255	−	0.337099i
$372$		0			0
$373$	−2.55768	+	4.43003i	−0.132432	+	0.229378i	−0.924613	−	0.380907i	$-0.875612\pi$
$373$	−2.55768	+	4.43003i	−0.132432	+	0.229378i	0.792182	+	0.610285i	$0.208945\pi$
$374$		0			0
$375$	2.98437	+	10.7583i	0.154112	+	0.555559i
$376$		0			0
$377$	10.9416	+	7.82774i	0.563519	+	0.403149i
$378$		0			0
$379$	20.9755	+	5.62036i	1.07744	+	0.288699i	0.753546	−	0.657395i	$-0.228342\pi$
$379$	20.9755	+	5.62036i	1.07744	+	0.288699i	0.323892	+	0.946094i	$0.395008\pi$
$380$		0			0
$381$	−0.302487	−	34.3846i	−0.0154969	−	1.76158i
$382$		0			0
$383$	−17.1403	+	4.59273i	−0.875828	+	0.234677i	−0.668606	−	0.743617i	$-0.733109\pi$
$383$	−17.1403	+	4.59273i	−0.875828	+	0.234677i	−0.207222	+	0.978294i	$0.566442\pi$
$384$		0			0
$385$	2.58390	+	2.58390i	0.131688	+	0.131688i
$386$		0			0
$387$	0.668388	+	37.9859i	0.0339761	+	1.93093i
$388$		0			0
$389$	−22.4460			−1.13806			−0.569028	−	0.822318i	$-0.692680\pi$
$389$	−22.4460			−1.13806			−0.569028	+	0.822318i	$0.692680\pi$
$390$		0			0
$391$	11.7825			0.595866
$392$		0			0
$393$	−8.88653	−	5.02693i	−0.448266	−	0.253575i
$394$		0			0
$395$	1.29151	+	1.29151i	0.0649828	+	0.0649828i
$396$		0			0
$397$	7.62283	−	2.04253i	0.382579	−	0.102512i	−0.0624036	−	0.998051i	$-0.519877\pi$
$397$	7.62283	−	2.04253i	0.382579	−	0.102512i	0.444982	+	0.895539i	$0.353210\pi$
$398$		0			0
$399$	7.81023	−	0.0687078i	0.391001	−	0.00343969i
$400$		0			0
$401$	11.4464	+	3.06705i	0.571605	+	0.153161i	0.533033	−	0.846095i	$-0.321052\pi$
$401$	11.4464	+	3.06705i	0.571605	+	0.153161i	0.0385726	+	0.999256i	$0.487719\pi$
$402$		0			0
$403$	−13.9110	−	5.22340i	−0.692957	−	0.260196i
$404$		0			0
$405$	−5.81248	+	1.77884i	−0.288824	+	0.0883913i
$406$		0			0
$407$	9.17925	−	15.8989i	0.454999	−	0.788081i
$408$		0			0
$409$	−2.09514	−	7.81915i	−0.103598	−	0.386632i	0.894585	−	0.446899i	$-0.147472\pi$
$409$	−2.09514	−	7.81915i	−0.103598	−	0.386632i	−0.998182	+	0.0602665i	$0.980805\pi$
$410$		0			0
$411$	16.0643	+	4.15331i	0.792394	+	0.204868i
$412$		0			0
$413$	4.38700	+	7.59851i	0.215870	+	0.373898i
$414$		0			0
$415$			7.07901i			0.347495i
$416$		0			0
$417$	−2.81653	−	4.78074i	−0.137926	−	0.234114i
$418$		0			0
$419$	−19.6793	+	11.3619i	−0.961398	+	0.555064i	−0.896603	−	0.442835i	$-0.853973\pi$
$419$	−19.6793	+	11.3619i	−0.961398	+	0.555064i	−0.0647951	+	0.997899i	$0.520639\pi$
$420$		0			0
$421$	24.6721	−	24.6721i	1.20244	−	1.20244i	0.229023	−	0.973421i	$-0.426447\pi$
$421$	24.6721	−	24.6721i	1.20244	−	1.20244i	0.973421	−	0.229023i	$-0.0735532\pi$
$422$		0			0
$423$	−2.66014	−	0.662851i	−0.129341	−	0.0322289i
$424$		0			0
$425$	9.62312	+	5.55591i	0.466790	+	0.269501i
$426$		0			0
$427$	2.11687	−	7.90026i	0.102442	−	0.382320i
$428$		0			0
$429$	−31.0081	−	11.3329i	−1.49708	−	0.547157i
$430$		0			0
$431$	0.538030	−	2.00795i	0.0259160	−	0.0967198i	−0.951756	−	0.306854i	$-0.900724\pi$
$431$	0.538030	−	2.00795i	0.0259160	−	0.0967198i	0.977672	+	0.210135i	$0.0673902\pi$
$432$		0			0
$433$	−12.6016	−	7.27553i	−0.605593	−	0.349639i	0.165645	−	0.986185i	$-0.447029\pi$
$433$	−12.6016	−	7.27553i	−0.605593	−	0.349639i	−0.771239	+	0.636546i	$0.780363\pi$
$434$		0			0
$435$	3.05920	−	3.11351i	0.146678	−	0.149281i
$436$		0			0
$437$	15.0112	−	15.0112i	0.718084	−	0.718084i
$438$		0			0
$439$	3.37300	−	1.94740i	0.160984	−	0.0929444i	−0.417343	−	0.908749i	$-0.637039\pi$
$439$	3.37300	−	1.94740i	0.160984	−	0.0929444i	0.578328	+	0.815804i	$0.303705\pi$
$440$		0			0
$441$	15.6199	+	8.65539i	0.743805	+	0.412161i
$442$		0			0
$443$		−	36.8108i		−	1.74894i	−0.485084	−	0.874468i	$-0.661211\pi$
$443$		−	36.8108i		−	1.74894i	0.485084	−	0.874468i	$-0.338789\pi$
$444$		0			0
$445$	−3.50934	−	6.07835i	−0.166358	−	0.288141i
$446$		0			0
$447$	−8.53627	+	33.0169i	−0.403752	+	1.56164i
$448$		0			0
$449$	0.879334	+	3.28172i	0.0414983	+	0.154874i	0.983566	−	0.180549i	$-0.0577874\pi$
$449$	0.879334	+	3.28172i	0.0414983	+	0.154874i	−0.942068	+	0.335423i	$0.891121\pi$
$450$		0			0
$451$	−12.7738	+	22.1249i	−0.601496	+	1.04182i
$452$		0			0
$453$	−30.8811	+	8.56641i	−1.45092	+	0.402485i
$454$		0			0
$455$	−0.242357	+	2.48046i	−0.0113619	+	0.116286i
$456$		0			0
$457$	1.41752	+	0.379824i	0.0663090	+	0.0177674i	0.291821	−	0.956473i	$-0.405739\pi$
$457$	1.41752	+	0.379824i	0.0663090	+	0.0177674i	−0.225512	+	0.974240i	$0.572406\pi$
$458$		0			0
$459$	−6.06092	+	11.1684i	−0.282899	+	0.521298i
$460$		0			0
$461$	22.1924	−	5.94644i	1.03360	−	0.276953i	0.298144	−	0.954521i	$-0.403633\pi$
$461$	22.1924	−	5.94644i	1.03360	−	0.276953i	0.735460	+	0.677568i	$0.236966\pi$
$462$		0			0
$463$	−5.38119	−	5.38119i	−0.250085	−	0.250085i	0.570920	−	0.821006i	$-0.306587\pi$
$463$	−5.38119	−	5.38119i	−0.250085	−	0.250085i	−0.821006	+	0.570920i	$0.806587\pi$
$464$		0			0
$465$	−2.37374	+	4.19626i	−0.110080	+	0.194597i
$466$		0			0
$467$	2.33847			0.108211			0.0541057	−	0.998535i	$-0.482769\pi$
$467$	2.33847			0.108211			0.0541057	+	0.998535i	$0.482769\pi$
$468$		0			0
$469$	3.75624			0.173447
$470$		0			0
$471$	0.0703159	−	0.124303i	0.00323999	−	0.00572760i
$472$		0			0
$473$	47.3393	+	47.3393i	2.17666	+	2.17666i
$474$		0			0
$475$	19.3385	−	5.18174i	0.887312	−	0.237755i
$476$		0			0
$477$	16.8884	−	10.1508i	0.773266	−	0.464773i
$478$		0			0
$479$	1.53047	+	0.410089i	0.0699292	+	0.0187375i	0.293614	−	0.955924i	$-0.405142\pi$
$479$	1.53047	+	0.410089i	0.0699292	+	0.0187375i	−0.223685	+	0.974662i	$0.571809\pi$
$480$		0			0
$481$	12.3522	−	2.04922i	0.563213	−	0.0934366i
$482$		0			0
$483$	−8.23001	+	2.28301i	−0.374478	+	0.103880i
$484$		0			0
$485$	3.35363	−	5.80866i	0.152281	−	0.263758i
$486$		0			0
$487$	8.73299	+	32.5920i	0.395730	+	1.47688i	0.820534	+	0.571598i	$0.193676\pi$
$487$	8.73299	+	32.5920i	0.395730	+	1.47688i	−0.424804	+	0.905285i	$0.639657\pi$
$488$		0			0
$489$	10.3208	−	39.9192i	0.466723	−	1.80521i
$490$		0			0
$491$	−3.16125	−	5.47545i	−0.142665	−	0.247104i	0.785834	−	0.618437i	$-0.212234\pi$
$491$	−3.16125	−	5.47545i	−0.142665	−	0.247104i	−0.928499	+	0.371334i	$0.878901\pi$
$492$		0			0
$493$		−	9.12472i		−	0.410957i
$494$		0			0
$495$	−5.19171	+	9.36920i	−0.233350	+	0.421114i
$496$		0			0
$497$	−4.90494	+	2.83187i	−0.220017	+	0.127027i
$498$		0			0
$499$	−10.0492	+	10.0492i	−0.449864	+	0.449864i	−0.895309	−	0.445445i	$-0.853045\pi$
$499$	−10.0492	+	10.0492i	−0.449864	+	0.449864i	0.445445	+	0.895309i	$0.353045\pi$
$500$		0			0
$501$	27.4308	−	27.9177i	1.22552	−	1.24727i
$502$		0			0
$503$	22.7387	+	13.1282i	1.01387	+	0.585358i	0.912322	−	0.409473i	$-0.134287\pi$
$503$	22.7387	+	13.1282i	1.01387	+	0.585358i	0.101547	+	0.994831i	$0.467621\pi$
$504$		0			0
$505$	−2.91662	+	10.8850i	−0.129788	+	0.484375i
$506$		0			0
$507$	−7.45806	−	21.2456i	−0.331224	−	0.943552i
$508$		0			0
$509$	0.773870	−	2.88812i	0.0343012	−	0.128014i	−0.946652	−	0.322257i	$-0.895558\pi$
$509$	0.773870	−	2.88812i	0.0343012	−	0.128014i	0.980953	+	0.194243i	$0.0622251\pi$
$510$		0			0
$511$	0.282132	+	0.162889i	0.0124808	+	0.00720577i
$512$		0			0
$513$	6.50713	+	21.9507i	0.287297	+	0.969147i
$514$		0			0
$515$	−1.97527	+	1.97527i	−0.0870407	+	0.0870407i
$516$		0			0
$517$	−4.18372	+	2.41547i	−0.184000	+	0.106232i
$518$		0			0
$519$	−18.7093	−	31.7570i	−0.821248	−	1.39398i
$520$		0			0
$521$		−	27.3243i		−	1.19710i	−0.801086	−	0.598549i	$-0.795744\pi$
$521$		−	27.3243i		−	1.19710i	0.801086	−	0.598549i	$-0.204256\pi$
$522$		0			0
$523$	−12.3901	−	21.4602i	−0.541780	−	0.938391i	−0.998802	−	0.0489353i	$-0.984417\pi$
$523$	−12.3901	−	21.4602i	−0.541780	−	0.938391i	0.457022	−	0.889456i	$-0.348916\pi$
$524$		0			0
$525$	−7.79823	−	2.01617i	−0.340343	−	0.0879931i
$526$		0			0
$527$	2.60848	+	9.73497i	0.113627	+	0.424062i
$528$		0			0
$529$	−0.106962	+	0.185264i	−0.00465052	+	0.00805495i
$530$		0			0
$531$	−17.8634	+	18.5033i	−0.775205	+	0.802974i
$532$		0			0
$533$	−17.1893	+	2.85170i	−0.744553	+	0.123521i
$534$		0			0
$535$	2.69399	+	0.721852i	0.116471	+	0.0312084i
$536$		0			0
$537$	−18.0743	+	0.159002i	−0.779962	+	0.00686145i
$538$		0			0
$539$	30.3960	−	8.14458i	1.30925	−	0.350812i
$540$		0			0
$541$	24.7719	+	24.7719i	1.06503	+	1.06503i	0.997733	+	0.0672936i	$0.0214364\pi$
$541$	24.7719	+	24.7719i	1.06503	+	1.06503i	0.0672936	+	0.997733i	$0.478564\pi$
$542$		0			0
$543$	23.1679	+	13.1056i	0.994231	+	0.562417i
$544$		0			0
$545$	−10.7785			−0.461701
$546$		0			0
$547$	−1.08492			−0.0463880			−0.0231940	−	0.999731i	$-0.507384\pi$
$547$	−1.08492			−0.0463880			−0.0231940	+	0.999731i	$0.507384\pi$
$548$		0			0
$549$	23.9711	−	0.421788i	1.02306	−	0.0180015i
$550$		0			0
$551$	−11.6252	−	11.6252i	−0.495248	−	0.495248i
$552$		0			0
$553$	−2.67337	+	0.716328i	−0.113683	+	0.0304614i
$554$		0			0
$555$	−0.0357368	−	4.06231i	−0.00151694	−	0.172435i
$556$		0			0
$557$	41.5314	+	11.1283i	1.75974	+	0.471521i	0.986661	−	0.162787i	$-0.0520484\pi$
$557$	41.5314	+	11.1283i	1.75974	+	0.471521i	0.773080	+	0.634308i	$0.218715\pi$
$558$		0			0
$559$	−4.44019	+	45.4440i	−0.187800	+	1.92208i
$560$		0			0
$561$	5.98550	+	21.5771i	0.252708	+	0.910986i
$562$		0			0
$563$	6.04323	−	10.4672i	0.254692	−	0.441139i	−0.710120	−	0.704081i	$-0.751359\pi$
$563$	6.04323	−	10.4672i	0.254692	−	0.441139i	0.964812	+	0.262941i	$0.0846926\pi$
$564$		0			0
$565$	−0.496697	−	1.85370i	−0.0208962	−	0.0779857i
$566$		0			0
$567$	2.06950	−	8.97548i	0.0869106	−	0.376935i
$568$		0			0
$569$	20.9215	+	36.2370i	0.877073	+	1.51914i	0.854538	+	0.519389i	$0.173841\pi$
$569$	20.9215	+	36.2370i	0.877073	+	1.51914i	0.0225354	+	0.999746i	$0.492826\pi$
$570$		0			0
$571$			12.0755i			0.505343i	0.967552	+	0.252671i	$0.0813092\pi$
$571$			12.0755i			0.505343i	−0.967552	+	0.252671i	$0.918691\pi$
$572$		0			0
$573$	−29.5675	+	17.4194i	−1.23520	+	0.727704i
$574$		0			0
$575$	−18.9595	+	10.9463i	−0.790667	+	0.456492i
$576$		0			0
$577$	−17.6869	+	17.6869i	−0.736314	+	0.736314i	−0.971863	−	0.235548i	$-0.924311\pi$
$577$	−17.6869	+	17.6869i	−0.736314	+	0.736314i	0.235548	+	0.971863i	$0.424311\pi$
$578$		0			0
$579$	25.3312	+	24.8894i	1.05273	+	1.03437i
$580$		0			0
$581$	−9.28980	−	5.36347i	−0.385406	−	0.222514i
$582$		0			0
$583$	8.98674	−	33.5390i	0.372193	−	1.38904i
$584$		0			0
$585$	−7.18489	+	1.32225i	−0.297059	+	0.0546683i
$586$		0			0
$587$	−9.99047	+	37.2849i	−0.412351	+	1.53891i	0.377732	+	0.925915i	$0.376704\pi$
$587$	−9.99047	+	37.2849i	−0.412351	+	1.53891i	−0.790083	+	0.612999i	$0.789963\pi$
$588$		0			0
$589$	15.7259	+	9.07936i	0.647975	+	0.374108i
$590$		0			0
$591$	22.2349	+	21.8471i	0.914620	+	0.898668i
$592$		0			0
$593$	−18.9343	+	18.9343i	−0.777538	+	0.777538i	−0.979412	−	0.201874i	$-0.935297\pi$
$593$	−18.9343	+	18.9343i	−0.777538	+	0.777538i	0.201874	+	0.979412i	$0.435297\pi$
$594$		0			0
$595$	1.46392	−	0.845192i	0.0600147	−	0.0346495i
$596$		0			0
$597$	−27.0797	+	15.9537i	−1.10830	+	0.652944i
$598$		0			0
$599$		−	7.02037i		−	0.286845i	−0.989662	−	0.143422i	$-0.954189\pi$
$599$		−	7.02037i		−	0.286845i	0.989662	−	0.143422i	$-0.0458107\pi$
$600$		0			0
$601$	−16.1442	−	27.9626i	−0.658536	−	1.14062i	−0.980995	−	0.194034i	$-0.937843\pi$
$601$	−16.1442	−	27.9626i	−0.658536	−	1.14062i	0.322459	−	0.946583i	$-0.395491\pi$
$602$		0			0
$603$	3.03643	+	10.5837i	0.123653	+	0.431000i
$604$		0			0
$605$	2.96245	+	11.0560i	0.120441	+	0.449491i
$606$		0			0
$607$	8.03959	−	13.9250i	0.326317	−	0.565197i	−0.655461	−	0.755229i	$-0.727526\pi$
$607$	8.03959	−	13.9250i	0.326317	−	0.565197i	0.981778	+	0.190032i	$0.0608590\pi$
$608$		0			0
$609$	1.76803	+	6.37357i	0.0716442	+	0.258270i
$610$		0			0
$611$	−3.08457	−	1.15821i	−0.124788	−	0.0468564i
$612$		0			0
$613$	−5.01679	−	1.34425i	−0.202626	−	0.0542936i	0.156078	−	0.987745i	$-0.450115\pi$
$613$	−5.01679	−	1.34425i	−0.202626	−	0.0542936i	−0.358705	+	0.933451i	$0.616781\pi$
$614$		0			0
$615$	0.0497312	+	5.65310i	0.00200536	+	0.227955i
$616$		0			0
$617$	−21.5594	+	5.77683i	−0.867950	+	0.232567i	−0.665201	−	0.746664i	$-0.731654\pi$
$617$	−21.5594	+	5.77683i	−0.867950	+	0.232567i	−0.202749	+	0.979231i	$0.564988\pi$
$618$		0			0
$619$	−7.41621	−	7.41621i	−0.298083	−	0.298083i	0.542180	−	0.840262i	$-0.317599\pi$
$619$	−7.41621	−	7.41621i	−0.298083	−	0.298083i	−0.840262	+	0.542180i	$0.817599\pi$
$620$		0			0
$621$	−13.0855	−	21.3435i	−0.525103	−	0.856486i
$622$		0			0
$623$	10.6355			0.426103
$624$		0			0
$625$	−18.3656			−0.734626
$626$		0			0
$627$	35.1156	+	19.8642i	1.40238	+	0.793299i
$628$		0			0
$629$	−6.00505	−	6.00505i	−0.239437	−	0.239437i
$630$		0			0
$631$	−21.0236	+	5.63326i	−0.836937	+	0.224257i	−0.651738	−	0.758444i	$-0.725960\pi$
$631$	−21.0236	+	5.63326i	−0.836937	+	0.224257i	−0.185199	+	0.982701i	$0.559293\pi$
$632$		0			0
$633$	36.6208	−	0.322159i	1.45555	−	0.0128047i
$634$		0			0
$635$	−12.9516	−	3.47038i	−0.513970	−	0.137718i
$636$		0			0
$637$	17.4553	+	12.4877i	0.691603	+	0.494782i
$638$		0			0
$639$	−11.9441	−	11.5311i	−0.472502	−	0.456162i
$640$		0			0
$641$	−1.60308	+	2.77662i	−0.0633179	+	0.109670i	−0.895947	−	0.444162i	$-0.853502\pi$
$641$	−1.60308	+	2.77662i	−0.0633179	+	0.109670i	0.832629	+	0.553832i	$0.186835\pi$
$642$		0			0
$643$	−4.14972	−	15.4870i	−0.163649	−	0.610746i	−0.998209	−	0.0598284i	$-0.980945\pi$
$643$	−4.14972	−	15.4870i	−0.163649	−	0.610746i	0.834560	−	0.550917i	$-0.185722\pi$
$644$		0			0
$645$	14.3429	+	3.70826i	0.564753	+	0.146013i
$646$		0			0
$647$	−3.12295	−	5.40911i	−0.122776	−	0.212654i	0.798085	−	0.602544i	$-0.205846\pi$
$647$	−3.12295	−	5.40911i	−0.122776	−	0.212654i	−0.920861	+	0.389890i	$0.872513\pi$
$648$		0			0
$649$			45.3213i			1.77902i
$650$		0			0
$651$	−3.70828	−	6.29440i	−0.145339	−	0.246697i
$652$		0			0
$653$	−4.17845	+	2.41243i	−0.163515	+	0.0944057i	−0.579525	−	0.814955i	$-0.696762\pi$
$653$	−4.17845	+	2.41243i	−0.163515	+	0.0944057i	0.416009	+	0.909360i	$0.363428\pi$
$654$		0			0
$655$	−2.81515	+	2.81515i	−0.109997	+	0.109997i
$656$		0			0
$657$	−0.230892	+	0.926613i	−0.00900796	+	0.0361506i
$658$		0			0
$659$	32.5080	+	18.7685i	1.26633	+	0.731118i	0.974292	−	0.225288i	$-0.0723324\pi$
$659$	32.5080	+	18.7685i	1.26633	+	0.731118i	0.292041	+	0.956406i	$0.405666\pi$
$660$		0			0
$661$	−3.47617	+	12.9732i	−0.135207	+	0.504600i	0.864790	+	0.502134i	$0.167452\pi$
$661$	−3.47617	+	12.9732i	−0.135207	+	0.504600i	−0.999997	+	0.00246616i	$0.999215\pi$
$662$		0			0
$663$	−8.77632	+	12.4984i	−0.340844	+	0.485396i
$664$		0			0
$665$	0.788272	−	2.94187i	0.0305679	−	0.114081i
$666$		0			0
$667$	15.5690	+	8.98879i	0.602836	+	0.348047i
$668$		0			0
$669$	1.17038	−	1.19115i	0.0452494	−	0.0460526i
$670$		0			0
$671$	29.8736	−	29.8736i	1.15326	−	1.15326i
$672$		0			0
$673$	−33.3998	+	19.2834i	−1.28747	+	0.743320i	−0.978202	−	0.207656i	$-0.933417\pi$
$673$	−33.3998	+	19.2834i	−1.28747	+	0.743320i	−0.309266	+	0.950976i	$0.600083\pi$
$674$		0			0
$675$	−0.623027	−	23.6023i	−0.0239803	−	0.908451i
$676$		0			0
$677$		−	20.6740i		−	0.794568i	−0.917696	−	0.397284i	$-0.869953\pi$
$677$		−	20.6740i		−	0.794568i	0.917696	−	0.397284i	$-0.130047\pi$
$678$		0			0
$679$	5.08182	+	8.80197i	0.195022	+	0.337788i
$680$		0			0
$681$	−4.12346	+	15.9489i	−0.158012	+	0.611162i
$682$		0			0
$683$	5.94896	+	22.2018i	0.227631	+	0.849529i	0.981333	+	0.192314i	$0.0615992\pi$
$683$	5.94896	+	22.2018i	0.227631	+	0.849529i	−0.753703	+	0.657215i	$0.771734\pi$
$684$		0			0
$685$	3.23505	−	5.60328i	0.123605	−	0.214090i
$686$		0			0
$687$	27.7687	−	7.70304i	1.05944	−	0.293889i
$688$		0			0
$689$	21.5630	−	9.79029i	0.821486	−	0.372980i
$690$		0			0
$691$	13.1628	+	3.52697i	0.500738	+	0.134172i	0.500342	−	0.865828i	$-0.333208\pi$
$691$	13.1628	+	3.52697i	0.500738	+	0.134172i	0.000395273		1.00000i	$0.499874\pi$
$692$		0			0
$693$	−8.36168	−	13.9117i	−0.317634	−	0.528463i
$694$		0			0
$695$	−2.08995	+	0.560001i	−0.0792763	+	0.0212420i
$696$		0			0
$697$	8.35662	+	8.35662i	0.316530	+	0.316530i
$698$		0			0
$699$	15.5468	−	27.4834i	0.588035	−	1.03952i
$700$		0			0
$701$	−46.1778			−1.74411			−0.872055	−	0.489408i	$-0.837213\pi$
$701$	−46.1778			−1.74411			−0.872055	+	0.489408i	$0.837213\pi$
$702$		0			0
$703$	−15.3012			−0.577096
$704$		0			0
$705$	−0.526344	+	0.930462i	−0.0198233	+	0.0350432i
$706$		0			0
$707$	−12.0746	−	12.0746i	−0.454111	−	0.454111i
$708$		0			0
$709$	−33.9442	+	9.09532i	−1.27480	+	0.341582i	−0.831868	−	0.554973i	$-0.812728\pi$
$709$	−33.9442	+	9.09532i	−1.27480	+	0.341582i	−0.442932	+	0.896555i	$0.646062\pi$
$710$		0			0
$711$	−4.17941	−	6.95349i	−0.156740	−	0.260776i
$712$		0			0
$713$	−19.1799	−	5.13924i	−0.718293	−	0.192466i
$714$		0			0
$715$	−7.49044	+	10.4701i	−0.280127	+	0.391559i
$716$		0			0
$717$	4.30726	−	1.19483i	0.160857	−	0.0446219i
$718$		0			0
$719$	−17.7746	+	30.7866i	−0.662882	+	1.14815i	0.316973	+	0.948435i	$0.397334\pi$
$719$	−17.7746	+	30.7866i	−0.662882	+	1.14815i	−0.979855	+	0.199711i	$0.936000\pi$
$720$		0			0
$721$	−1.09557	−	4.08873i	−0.0408012	−	0.152272i
$722$		0			0
$723$	−1.71077	+	6.61699i	−0.0636244	+	0.246089i
$724$		0			0
$725$	8.47715	+	14.6829i	0.314833	+	0.545308i
$726$		0			0
$727$		−	27.8304i		−	1.03217i	−0.856537	−	0.516086i	$-0.827389\pi$
$727$		−	27.8304i		−	1.03217i	0.856537	−	0.516086i	$-0.172611\pi$
$728$		0			0
$729$	26.9624	−	1.42444i	0.998607	−	0.0527571i
$730$		0			0
$731$	26.8202	−	15.4846i	0.991980	−	0.572720i
$732$		0			0
$733$	37.4547	−	37.4547i	1.38342	−	1.38342i	0.544961	−	0.838462i	$-0.316545\pi$
$733$	37.4547	−	37.4547i	1.38342	−	1.38342i	0.838462	−	0.544961i	$-0.183455\pi$
$734$		0			0
$735$	4.88040	−	4.96703i	0.180016	−	0.183212i
$736$		0			0
$737$	16.8031	+	9.70127i	0.618950	+	0.357351i
$738$		0			0
$739$	5.33765	−	19.9204i	0.196349	−	0.732783i	−0.795565	−	0.605868i	$-0.792826\pi$
$739$	5.33765	−	19.9204i	0.196349	−	0.732783i	0.991914	−	0.126915i	$-0.0405074\pi$
$740$		0			0
$741$	4.74199	+	27.1046i	0.174201	+	0.995711i
$742$		0			0
$743$	−2.94715	+	10.9989i	−0.108120	+	0.403510i	−0.998680	−	0.0513550i	$-0.983646\pi$
$743$	−2.94715	+	10.9989i	−0.108120	+	0.403510i	0.890560	+	0.454865i	$0.150313\pi$
$744$		0			0
$745$	11.5164	+	6.64899i	0.421928	+	0.243600i
$746$		0			0
$747$	7.60263	−	30.5108i	0.278166	−	1.11633i
$748$		0			0
$749$	−2.98841	+	2.98841i	−0.109194	+	0.109194i
$750$		0			0
$751$	16.1054	−	9.29844i	0.587693	−	0.339305i	−0.176492	−	0.984302i	$-0.556475\pi$
$751$	16.1054	−	9.29844i	0.587693	−	0.339305i	0.764185	+	0.644997i	$0.223142\pi$
$752$		0			0
$753$	16.2335	+	27.5545i	0.591580	+	1.00414i
$754$		0			0
$755$			12.4965i			0.454795i
$756$		0			0
$757$	−12.1506	−	21.0455i	−0.441622	−	0.764911i	0.556188	−	0.831056i	$-0.312263\pi$
$757$	−12.1506	−	21.0455i	−0.441622	−	0.764911i	−0.997810	+	0.0661450i	$0.978930\pi$
$758$		0			0
$759$	−42.7123	−	11.0429i	−1.55036	−	0.400833i
$760$		0			0
$761$	−7.86168	−	29.3402i	−0.284986	−	1.06358i	−0.948850	−	0.315728i	$-0.897751\pi$
$761$	−7.86168	−	29.3402i	−0.284986	−	1.06358i	0.663864	−	0.747853i	$-0.268915\pi$
$762$		0			0
$763$	8.16644	−	14.1447i	0.295645	−	0.512072i
$764$		0			0
$765$	3.56481	+	3.44153i	0.128886	+	0.124429i
$766$		0			0
$767$	−23.8789	+	19.6280i	−0.862217	+	0.708726i
$768$		0			0
$769$	16.7832	+	4.49705i	0.605218	+	0.162168i	0.548399	−	0.836217i	$-0.315237\pi$
$769$	16.7832	+	4.49705i	0.605218	+	0.162168i	0.0568192	+	0.998384i	$0.481904\pi$
$770$		0			0
$771$	−26.6517	+	0.234459i	−0.959838	+	0.00844385i
$772$		0			0
$773$	−2.97458	+	0.797037i	−0.106988	+	0.0286674i	−0.311916	−	0.950110i	$-0.600971\pi$
$773$	−2.97458	+	0.797037i	−0.106988	+	0.0286674i	0.204928	+	0.978777i	$0.434304\pi$
$774$		0			0
$775$	−13.2415	−	13.2415i	−0.475647	−	0.475647i
$776$		0			0
$777$	5.35805	+	3.03094i	0.192219	+	0.108734i
$778$		0			0
$779$	21.2931			0.762906
$780$		0			0
$781$	−29.2555			−1.04685
$782$		0			0
$783$	−16.5291	+	10.1338i	−0.590701	+	0.362153i
$784$		0			0
$785$	−0.0393779	−	0.0393779i	−0.00140546	−	0.00140546i
$786$		0			0
$787$	−23.4451	+	6.28211i	−0.835729	+	0.223933i	−0.651211	−	0.758896i	$-0.725739\pi$
$787$	−23.4451	+	6.28211i	−0.835729	+	0.223933i	−0.184518	+	0.982829i	$0.559072\pi$
$788$		0			0
$789$	−0.0929099	−	10.5614i	−0.00330768	−	0.375994i
$790$		0			0
$791$	2.80894	+	0.752654i	0.0998745	+	0.0267613i
$792$		0			0
$793$	28.6776	+	2.80199i	1.01837	+	0.0995017i
$794$		0			0
$795$	−2.05384	−	7.40389i	−0.0728423	−	0.262589i
$796$		0			0
$797$	25.3924	−	43.9809i	0.899445	−	1.55788i	0.0712405	−	0.997459i	$-0.477304\pi$
$797$	25.3924	−	43.9809i	0.899445	−	1.55788i	0.828205	−	0.560426i	$-0.189362\pi$
$798$		0			0
$799$	0.578393	+	2.15859i	0.0204621	+	0.0763655i
$800$		0			0
$801$	8.59740	+	29.9668i	0.303774	+	1.05883i
$802$		0			0
$803$	0.841387	+	1.45733i	0.0296919	+	0.0514279i
$804$		0			0
$805$			3.33041i			0.117381i
$806$		0			0
$807$	44.4382	−	26.1803i	1.56430	−	0.921590i
$808$		0			0
$809$	5.09894	−	2.94388i	0.179269	−	0.103501i	−0.407680	−	0.913125i	$-0.633662\pi$
$809$	5.09894	−	2.94388i	0.179269	−	0.103501i	0.586949	+	0.809624i	$0.300329\pi$
$810$		0			0
$811$	−25.2883	+	25.2883i	−0.887992	+	0.887992i	−0.994330	−	0.106338i	$-0.966087\pi$
$811$	−25.2883	+	25.2883i	−0.887992	+	0.887992i	0.106338	+	0.994330i	$0.466087\pi$
$812$		0			0
$813$	17.3346	+	17.0323i	0.607951	+	0.597347i
$814$		0			0
$815$	−13.9239	−	8.03899i	−0.487734	−	0.281593i
$816$		0			0
$817$	14.4418	−	53.8975i	0.505255	−	1.88564i
$818$		0			0
$819$	3.70850	−	10.4306i	0.129585	−	0.364474i
$820$		0			0
$821$	8.10075	−	30.2324i	0.282718	−	1.05512i	−0.667772	−	0.744366i	$-0.732752\pi$
$821$	8.10075	−	30.2324i	0.282718	−	1.05512i	0.950491	−	0.310753i	$-0.100581\pi$
$822$		0			0
$823$	28.4828	+	16.4446i	0.992849	+	0.573222i	0.906125	−	0.423011i	$-0.139027\pi$
$823$	28.4828	+	16.4446i	0.992849	+	0.573222i	0.0867245	+	0.996232i	$0.472360\pi$
$824$		0			0
$825$	−29.6773	−	29.1597i	−1.03323	−	1.01521i
$826$		0			0
$827$	20.2620	−	20.2620i	0.704578	−	0.704578i	−0.260812	−	0.965390i	$-0.583990\pi$
$827$	20.2620	−	20.2620i	0.704578	−	0.704578i	0.965390	+	0.260812i	$0.0839901\pi$
$828$		0			0
$829$	−43.5233	+	25.1282i	−1.51163	+	0.872739i	−0.511720	+	0.859152i	$0.670992\pi$
$829$	−43.5233	+	25.1282i	−1.51163	+	0.872739i	−0.999908	+	0.0135865i	$0.995675\pi$
$830$		0			0
$831$	−25.4342	+	14.9843i	−0.882302	+	0.519799i
$832$		0			0
$833$		−	14.5568i		−	0.504364i
$834$		0			0
$835$	−7.63091	−	13.2171i	−0.264079	−	0.457398i
$836$		0			0
$837$	14.7376	−	15.5367i	0.509405	−	0.537027i
$838$		0			0
$839$	−5.03499	−	18.7909i	−0.173827	−	0.648732i	−0.996748	−	0.0805766i	$-0.974324\pi$
$839$	−5.03499	−	18.7909i	−0.173827	−	0.648732i	0.822921	−	0.568156i	$-0.192343\pi$
$840$		0			0
$841$	−7.53880	+	13.0576i	−0.259959	+	0.450261i
$842$		0			0
$843$	3.02309	+	10.8979i	0.104121	+	0.375345i
$844$		0			0
$845$	−8.76047	+	0.587870i	−0.301369	+	0.0202234i
$846$		0			0
$847$	−16.7534	−	4.48905i	−0.575652	−	0.154246i
$848$		0			0
$849$	−0.183802	−	20.8933i	−0.00630807	−	0.717057i
$850$		0			0
$851$	16.1617	−	4.33052i	0.554016	−	0.148448i
$852$		0			0
$853$	−15.9691	−	15.9691i	−0.546772	−	0.546772i	0.378733	−	0.925506i	$-0.376360\pi$
$853$	−15.9691	−	15.9691i	−0.546772	−	0.546772i	−0.925506	+	0.378733i	$0.876360\pi$
$854$		0			0
$855$	8.92628	−	0.157064i	0.305272	−	0.00537148i
$856$		0			0
$857$	22.6370			0.773264			0.386632	−	0.922234i	$-0.373638\pi$
$857$	22.6370			0.773264			0.386632	+	0.922234i	$0.373638\pi$
$858$		0			0
$859$	−21.6017			−0.737039			−0.368520	−	0.929620i	$-0.620135\pi$
$859$	−21.6017			−0.737039			−0.368520	+	0.929620i	$0.620135\pi$
$860$		0			0
$861$	−7.45626	−	4.21786i	−0.254109	−	0.143744i
$862$		0			0
$863$	3.21017	+	3.21017i	0.109275	+	0.109275i	0.759630	−	0.650355i	$-0.225380\pi$
$863$	3.21017	+	3.21017i	0.109275	+	0.109275i	−0.650355	+	0.759630i	$0.725380\pi$
$864$		0			0
$865$	−13.8829	+	3.71991i	−0.472033	+	0.126481i
$866$		0			0
$867$	−19.0859	+	0.167902i	−0.648191	+	0.00570224i
$868$		0			0
$869$	−13.8091	−	3.70013i	−0.468441	−	0.125518i
$870$		0			0
$871$	2.16576	+	13.0547i	0.0733841	+	0.442341i
$872$		0			0
$873$	−20.6926	+	21.4338i	−0.700339	+	0.725426i
$874$		0			0
$875$	−3.29850	+	5.71316i	−0.111510	+	0.193140i
$876$		0			0
$877$	2.65569	+	9.91118i	0.0896763	+	0.334677i	0.996159	−	0.0875672i	$-0.0279093\pi$
$877$	2.65569	+	9.91118i	0.0896763	+	0.334677i	−0.906482	+	0.422244i	$0.861243\pi$
$878$		0			0
$879$	−13.3771	−	3.45855i	−0.451198	−	0.116654i
$880$		0			0
$881$	−15.1846	−	26.3004i	−0.511581	−	0.886084i	−0.999910	−	0.0134244i	$-0.995727\pi$
$881$	−15.1846	−	26.3004i	−0.511581	−	0.886084i	0.488329	−	0.872660i	$-0.337607\pi$
$882$		0			0
$883$		−	20.6477i		−	0.694850i	−0.937708	−	0.347425i	$-0.887056\pi$
$883$		−	20.6477i		−	0.694850i	0.937708	−	0.347425i	$-0.112944\pi$
$884$		0			0
$885$	5.09068	+	8.64087i	0.171121	+	0.290460i
$886$		0			0
$887$	−17.5213	+	10.1159i	−0.588307	+	0.339659i	−0.764428	−	0.644709i	$-0.776978\pi$
$887$	−17.5213	+	10.1159i	−0.588307	+	0.339659i	0.176121	+	0.984369i	$0.443645\pi$
$888$		0			0
$889$	14.3671	−	14.3671i	0.481857	−	0.481857i
$890$		0			0
$891$	32.4387	−	34.8058i	1.08674	−	1.16604i
$892$		0			0
$893$	3.48700	+	2.01322i	0.116688	+	0.0673698i
$894$		0			0
$895$	−1.82420	+	6.80801i	−0.0609763	+	0.227567i
$896$		0			0
$897$	−12.6797	−	27.2868i	−0.423364	−	0.911078i
$898$		0			0
$899$	−3.97999	+	14.8535i	−0.132740	+	0.495392i
$900$		0			0
$901$	−13.9101	−	8.03101i	−0.463413	−	0.267552i
$902$		0			0
$903$	−15.7334	+	16.0127i	−0.523575	+	0.532869i
$904$		0			0
$905$	7.33935	−	7.33935i	0.243968	−	0.243968i
$906$		0			0
$907$	−3.56986	+	2.06106i	−0.118535	+	0.0684363i	−0.558095	−	0.829777i	$-0.688468\pi$
$907$	−3.56986	+	2.06106i	−0.118535	+	0.0684363i	0.439560	+	0.898213i	$0.355134\pi$
$908$		0			0
$909$	24.2608	−	43.7822i	0.804682	−	1.45217i
$910$		0			0
$911$			1.58678i			0.0525723i	0.999654	+	0.0262862i	$0.00836811\pi$
$911$			1.58678i			0.0525723i	−0.999654	+	0.0262862i	$0.991632\pi$
$912$		0			0
$913$	−27.7045	−	47.9857i	−0.916886	−	1.58809i
$914$		0			0
$915$	2.34011	−	9.05116i	0.0773617	−	0.299222i
$916$		0			0
$917$	−1.56141	−	5.82726i	−0.0515623	−	0.192433i
$918$		0			0
$919$	−25.9415	+	44.9319i	−0.855730	+	1.48217i	0.0202360	+	0.999795i	$0.493558\pi$
$919$	−25.9415	+	44.9319i	−0.855730	+	1.48217i	−0.875966	+	0.482373i	$0.839775\pi$
$920$		0			0
$921$	−5.20802	+	1.44471i	−0.171610	+	0.0476047i
$922$		0			0
$923$	−12.6701	−	15.4142i	−0.417043	−	0.507363i
$924$		0			0
$925$	15.2418	+	4.08402i	0.501147	+	0.134282i
$926$		0			0
$927$	10.6349	−	6.39210i	0.349294	−	0.209944i
$928$		0			0
$929$	−40.1312	+	10.7531i	−1.31666	+	0.352798i	−0.847726	−	0.530435i	$-0.822029\pi$
$929$	−40.1312	+	10.7531i	−1.31666	+	0.352798i	−0.468935	+	0.883233i	$0.655362\pi$
$930$		0			0
$931$	−18.5458	−	18.5458i	−0.607815	−	0.607815i
$932$		0			0
$933$	1.13220	−	2.00149i	0.0370666	−	0.0655257i
$934$		0			0
$935$	8.73153			0.285552
$936$		0			0
$937$	6.31749			0.206383			0.103192	−	0.994661i	$-0.467094\pi$
$937$	6.31749			0.206383			0.103192	+	0.994661i	$0.467094\pi$
$938$		0			0
$939$	−14.4918	+	25.6184i	−0.472923	+	0.836027i
$940$		0			0
$941$	−0.719674	−	0.719674i	−0.0234607	−	0.0234607i	0.695279	−	0.718740i	$-0.255281\pi$
$941$	−0.719674	−	0.719674i	−0.0234607	−	0.0234607i	−0.718740	+	0.695279i	$0.755281\pi$
$942$		0			0
$943$	−22.4906	+	6.02634i	−0.732395	+	0.196245i
$944$		0			0
$945$	−3.15684	−	1.71316i	−0.102692	−	0.0557292i
$946$		0			0
$947$	−19.9692	−	5.35072i	−0.648910	−	0.173875i	−0.0806743	−	0.996741i	$-0.525707\pi$
$947$	−19.9692	−	5.35072i	−0.648910	−	0.173875i	−0.568236	+	0.822865i	$0.692374\pi$
$948$		0			0
$949$	−0.403443	+	1.07446i	−0.0130963	+	0.0348783i
$950$		0			0
$951$	43.8785	−	12.1719i	1.42286	−	0.394701i
$952$		0			0
$953$	−5.35990	+	9.28362i	−0.173624	+	0.300726i	−0.939684	−	0.342043i	$-0.888881\pi$
$953$	−5.35990	+	9.28362i	−0.173624	+	0.300726i	0.766060	+	0.642769i	$0.222214\pi$
$954$		0			0
$955$	3.46343	+	12.9257i	0.112074	+	0.418266i
$956$		0			0
$957$	−8.55200	+	33.0777i	−0.276447	+	1.06925i
$958$		0			0
$959$	4.90213	+	8.49074i	0.158298	+	0.274180i
$960$		0			0
$961$			14.0154i			0.452108i
$962$		0			0
$963$	−10.8359	−	6.00446i	−0.349183	−	0.193491i
$964$		0			0
$965$	11.9926	−	6.92394i	0.386056	−	0.222889i
$966$		0			0
$967$	12.0599	−	12.0599i	0.387819	−	0.387819i	−0.486090	−	0.873909i	$-0.661577\pi$
$967$	12.0599	−	12.0599i	0.387819	−	0.387819i	0.873909	+	0.486090i	$0.161577\pi$
$968$		0			0
$969$	13.0801	−	13.3123i	0.420193	−	0.427651i
$970$		0			0
$971$	−39.6963	−	22.9187i	−1.27392	−	0.735496i	−0.298194	−	0.954505i	$-0.596384\pi$
$971$	−39.6963	−	22.9187i	−1.27392	−	0.735496i	−0.975723	+	0.219010i	$0.929717\pi$
$972$		0			0
$973$	0.848578	−	3.16694i	0.0272042	−	0.101527i
$974$		0			0
$975$	2.51086	−	28.2650i	0.0804120	−	0.905203i
$976$		0			0
$977$	−1.29921	+	4.84871i	−0.0415653	+	0.155124i	−0.983589	−	0.180421i	$-0.942254\pi$
$977$	−1.29921	+	4.84871i	−0.0415653	+	0.155124i	0.942024	+	0.335545i	$0.108921\pi$
$978$		0			0
$979$	47.5767	+	27.4684i	1.52056	+	0.877894i
$980$		0			0
$981$	46.4558	+	11.5758i	1.48322	+	0.369587i
$982$		0			0
$983$	−31.3213	+	31.3213i	−0.998994	+	0.998994i	−0.999999	−	0.00100577i	$-0.999680\pi$
$983$	−31.3213	+	31.3213i	−0.998994	+	0.998994i	0.00100577	+	0.999999i	$0.499680\pi$
$984$		0			0
$985$	10.5267	−	6.07759i	0.335408	−	0.193648i
$986$		0			0
$987$	−0.822259	−	1.39570i	−0.0261728	−	0.0444255i
$988$		0			0
$989$			61.0159i			1.94019i
$990$		0			0
$991$	12.8503	+	22.2574i	0.408203	+	0.707028i	0.994688	−	0.102932i	$-0.0328223\pi$
$991$	12.8503	+	22.2574i	0.408203	+	0.707028i	−0.586486	+	0.809960i	$0.699489\pi$
$992$		0			0
$993$	17.9985	+	4.65339i	0.571166	+	0.147671i
$994$		0			0
$995$	3.17203	+	11.8382i	0.100560	+	0.375296i
$996$		0			0
$997$	17.9997	−	31.1764i	0.570057	−	0.987368i	−0.426502	−	0.904486i	$-0.640254\pi$
$997$	17.9997	−	31.1764i	0.570057	−	0.987368i	0.996559	−	0.0828814i	$-0.0264123\pi$
$998$		0			0
$999$	−4.20876	+	17.5471i	−0.133159	+	0.555165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.f.353.5		56
3.2	odd	2	inner	624.2.cn.f.353.14		56
4.3	odd	2		312.2.bp.a.41.10	yes	56
12.11	even	2		312.2.bp.a.41.1	✓	56
13.7	odd	12	inner	624.2.cn.f.449.14		56
39.20	even	12	inner	624.2.cn.f.449.5		56
52.7	even	12		312.2.bp.a.137.1	yes	56
156.59	odd	12		312.2.bp.a.137.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.41.1	✓	56	12.11	even	2
312.2.bp.a.41.10	yes	56	4.3	odd	2
312.2.bp.a.137.1	yes	56	52.7	even	12
312.2.bp.a.137.10	yes	56	156.59	odd	12
624.2.cn.f.353.5		56	1.1	even	1	trivial
624.2.cn.f.353.14		56	3.2	odd	2	inner
624.2.cn.f.449.5		56	39.20	even	12	inner
624.2.cn.f.449.14		56	13.7	odd	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.852797 + 1.50756i) q^{3} +(0.477579 + 0.477579i) q^{5} +(-0.988569 + 0.264886i) q^{7} +(-1.54548 - 2.57128i) q^{9} +O(q^{10})\)	\(q+(-0.852797 + 1.50756i) q^{3} +(0.477579 + 0.477579i) q^{5} +(-0.988569 + 0.264886i) q^{7} +(-1.54548 - 2.57128i) q^{9} +(-5.10637 - 1.36825i) q^{11} +(-1.49059 - 3.28301i) q^{13} +(-1.12726 + 0.312701i) q^{15} +(-1.22274 + 2.11784i) q^{17} +(1.14039 + 4.25599i) q^{19} +(0.443716 - 1.71622i) q^{21} +(-2.40904 - 4.17258i) q^{23} -4.54384i q^{25} +(5.19434 - 0.137115i) q^{27} +(-3.23138 + 1.86564i) q^{29} +(2.91416 - 2.91416i) q^{31} +(6.41741 - 6.53132i) q^{33} +(-0.598623 - 0.345615i) q^{35} +(-0.898805 + 3.35438i) q^{37} +(6.22050 + 0.552587i) q^{39} +(1.25078 - 4.66796i) q^{41} +(-10.9673 - 6.33197i) q^{43} +(0.489904 - 1.96608i) q^{45} +(0.646174 - 0.646174i) q^{47} +(-5.15507 + 2.97628i) q^{49} +(-2.15003 - 3.64943i) q^{51} +6.56807i q^{53} +(-1.78525 - 3.09214i) q^{55} +(-7.38868 - 1.91029i) q^{57} +(-2.21886 - 8.28091i) q^{59} +(-3.99581 + 6.92094i) q^{61} +(2.20891 + 2.13252i) q^{63} +(0.856021 - 2.27977i) q^{65} +(-3.54515 - 0.949919i) q^{67} +(8.34484 - 0.0734109i) q^{69} +(5.34544 - 1.43231i) q^{71} +(-0.225083 - 0.225083i) q^{73} +(6.85011 + 3.87497i) q^{75} +5.41043 q^{77} +2.70428 q^{79} +(-4.22301 + 7.94772i) q^{81} +(7.41135 + 7.41135i) q^{83} +(-1.59539 + 0.427483i) q^{85} +(-0.0568517 - 6.46251i) q^{87} +(-10.0378 - 2.68962i) q^{89} +(2.34317 + 2.85064i) q^{91} +(1.90809 + 6.87846i) q^{93} +(-1.48794 + 2.57719i) q^{95} +(-2.57029 - 9.59245i) q^{97} +(4.37361 + 15.2445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^7	\( 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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