LMFDB - Embedded newform 52.3.g.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,3,Mod(5,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("52.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	52.g (of order $4$, 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:	$1.41689737467$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.20819026944.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 42x^{4} + 441x^{2} + 36 $ x^6 + 42x^4 + 441x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.1
Root			$4.43242i$ of defining polynomial
Character	$\chi$	$=$	52.5
Dual form			52.3.g.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.43242 q^{3} +(-6.03938 + 6.03938i) q^{5} +(0.393041 + 0.393041i) q^{7} +10.6463 q^{9} +O(q^{10})$	\(q-4.43242 q^{3} +(-6.03938 + 6.03938i) q^{5} +(0.393041 + 0.393041i) q^{7} +10.6463 q^{9} +(-11.8648 - 11.8648i) q^{11} +(8.90422 + 9.47180i) q^{13} +(26.7691 - 26.7691i) q^{15} +10.0833i q^{17} +(-8.56758 + 8.56758i) q^{19} +(-1.74212 - 1.74212i) q^{21} +30.0788i q^{23} -47.9482i q^{25} -7.29726 q^{27} -26.6733 q^{29} +(-3.00458 + 3.00458i) q^{31} +(52.5899 + 52.5899i) q^{33} -4.74744 q^{35} +(-14.0394 - 14.0394i) q^{37} +(-39.4672 - 41.9830i) q^{39} +(-22.4548 + 22.4548i) q^{41} +49.8826i q^{43} +(-64.2973 + 64.2973i) q^{45} +(-24.8300 - 24.8300i) q^{47} -48.6910i q^{49} -44.6936i q^{51} +65.8084 q^{53} +143.312 q^{55} +(37.9751 - 37.9751i) q^{57} +(7.62399 + 7.62399i) q^{59} +89.6169 q^{61} +(4.18444 + 4.18444i) q^{63} +(-110.980 - 3.42784i) q^{65} +(-12.3806 + 12.3806i) q^{67} -133.322i q^{69} +(-7.79853 + 7.79853i) q^{71} +(-36.2093 - 36.2093i) q^{73} +212.526i q^{75} -9.32673i q^{77} -7.20475 q^{79} -63.4725 q^{81} +(-53.9095 + 53.9095i) q^{83} +(-60.8971 - 60.8971i) q^{85} +118.227 q^{87} +(70.0269 + 70.0269i) q^{89} +(-0.223083 + 7.22252i) q^{91} +(13.3176 - 13.3176i) q^{93} -103.486i q^{95} +(-124.696 + 124.696i) q^{97} +(-126.317 - 126.317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} + 6 q^{7} + 30 q^{9}+O(q^{10}) $ 6 * q - 6 * q^5 + 6 * q^7 + 30 * q^9	$ 6 q - 6 q^{5} + 6 q^{7} + 30 q^{9} - 18 q^{11} - 30 q^{13} + 24 q^{15} - 78 q^{19} - 60 q^{21} + 36 q^{27} + 60 q^{29} - 6 q^{31} + 168 q^{33} + 240 q^{35} - 54 q^{37} - 192 q^{39} + 66 q^{41} - 306 q^{45} - 114 q^{47} + 228 q^{53} + 132 q^{55} - 84 q^{57} + 186 q^{59} + 204 q^{61} - 282 q^{63} - 342 q^{65} + 78 q^{67} - 210 q^{71} - 222 q^{73} - 60 q^{79} - 18 q^{81} + 78 q^{83} + 192 q^{85} + 552 q^{87} + 234 q^{89} + 30 q^{91} + 324 q^{93} - 354 q^{97} - 18 q^{99}+O(q^{100}) $ 6 * q - 6 * q^5 + 6 * q^7 + 30 * q^9 - 18 * q^11 - 30 * q^13 + 24 * q^15 - 78 * q^19 - 60 * q^21 + 36 * q^27 + 60 * q^29 - 6 * q^31 + 168 * q^33 + 240 * q^35 - 54 * q^37 - 192 * q^39 + 66 * q^41 - 306 * q^45 - 114 * q^47 + 228 * q^53 + 132 * q^55 - 84 * q^57 + 186 * q^59 + 204 * q^61 - 282 * q^63 - 342 * q^65 + 78 * q^67 - 210 * q^71 - 222 * q^73 - 60 * q^79 - 18 * q^81 + 78 * q^83 + 192 * q^85 + 552 * q^87 + 234 * q^89 + 30 * q^91 + 324 * q^93 - 354 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.43242			−1.47747			−0.738736	−	0.673994i	$-0.764577\pi$
$3$	−4.43242			−1.47747			−0.738736	+	0.673994i	$0.764577\pi$
$4$		0			0
$5$	−6.03938	+	6.03938i	−1.20788	+	1.20788i	−0.236162	+	0.971714i	$0.575890\pi$
$5$	−6.03938	+	6.03938i	−1.20788	+	1.20788i	−0.971714	+	0.236162i	$0.924110\pi$
$6$		0			0
$7$	0.393041	+	0.393041i	0.0561487	+	0.0561487i	0.734624	−	0.678475i	$-0.237359\pi$
$7$	0.393041	+	0.393041i	0.0561487	+	0.0561487i	−0.678475	+	0.734624i	$0.737359\pi$
$8$		0			0
$9$	10.6463			1.18293
$10$		0			0
$11$	−11.8648	−	11.8648i	−1.07862	−	1.07862i	−0.996633	−	0.0819883i	$-0.973873\pi$
$11$	−11.8648	−	11.8648i	−1.07862	−	1.07862i	−0.0819883	−	0.996633i	$-0.526127\pi$
$12$		0			0
$13$	8.90422	+	9.47180i	0.684940	+	0.728600i
$13$	8.90422	+	9.47180i	0.684940	+	0.728600i
$14$		0			0
$15$	26.7691	−	26.7691i	1.78460	−	1.78460i
$16$		0			0
$17$			10.0833i			0.593138i	0.955011	+	0.296569i	$0.0958424\pi$
$17$			10.0833i			0.593138i	−0.955011	+	0.296569i	$0.904158\pi$
$18$		0			0
$19$	−8.56758	+	8.56758i	−0.450925	+	0.450925i	−0.895662	−	0.444736i	$-0.853297\pi$
$19$	−8.56758	+	8.56758i	−0.450925	+	0.450925i	0.444736	+	0.895662i	$0.353297\pi$
$20$		0			0
$21$	−1.74212	−	1.74212i	−0.0829582	−	0.0829582i
$22$		0			0
$23$			30.0788i			1.30777i	0.756593	+	0.653886i	$0.226862\pi$
$23$			30.0788i			1.30777i	−0.756593	+	0.653886i	$0.773138\pi$
$24$		0			0
$25$		−	47.9482i		−	1.91793i
$26$		0			0
$27$	−7.29726			−0.270269
$28$		0			0
$29$	−26.6733			−0.919768			−0.459884	−	0.887979i	$-0.652109\pi$
$29$	−26.6733			−0.919768			−0.459884	+	0.887979i	$0.652109\pi$
$30$		0			0
$31$	−3.00458	+	3.00458i	−0.0969220	+	0.0969220i	−0.753905	−	0.656983i	$-0.771832\pi$
$31$	−3.00458	+	3.00458i	−0.0969220	+	0.0969220i	0.656983	+	0.753905i	$0.271832\pi$
$32$		0			0
$33$	52.5899	+	52.5899i	1.59363	+	1.59363i
$34$		0			0
$35$	−4.74744			−0.135641
$36$		0			0
$37$	−14.0394	−	14.0394i	−0.379443	−	0.379443i	0.491458	−	0.870901i	$-0.336464\pi$
$37$	−14.0394	−	14.0394i	−0.379443	−	0.379443i	−0.870901	+	0.491458i	$0.836464\pi$
$38$		0			0
$39$	−39.4672	−	41.9830i	−1.01198	−	1.07649i
$40$		0			0
$41$	−22.4548	+	22.4548i	−0.547677	+	0.547677i	−0.925768	−	0.378091i	$-0.876581\pi$
$41$	−22.4548	+	22.4548i	−0.547677	+	0.547677i	0.378091	+	0.925768i	$0.376581\pi$
$42$		0			0
$43$			49.8826i			1.16006i	0.814595	+	0.580030i	$0.196959\pi$
$43$			49.8826i			1.16006i	−0.814595	+	0.580030i	$0.803041\pi$
$44$		0			0
$45$	−64.2973	+	64.2973i	−1.42883	+	1.42883i
$46$		0			0
$47$	−24.8300	−	24.8300i	−0.528299	−	0.528299i	0.391766	−	0.920065i	$-0.371864\pi$
$47$	−24.8300	−	24.8300i	−0.528299	−	0.528299i	−0.920065	+	0.391766i	$0.871864\pi$
$48$		0			0
$49$		−	48.6910i		−	0.993695i
$50$		0			0
$51$		−	44.6936i		−	0.876345i
$52$		0			0
$53$	65.8084			1.24167			0.620834	−	0.783942i	$-0.286794\pi$
$53$	65.8084			1.24167			0.620834	+	0.783942i	$0.286794\pi$
$54$		0			0
$55$	143.312			2.60568
$56$		0			0
$57$	37.9751	−	37.9751i	0.666230	−	0.666230i
$58$		0			0
$59$	7.62399	+	7.62399i	0.129220	+	0.129220i	0.768759	−	0.639539i	$-0.220875\pi$
$59$	7.62399	+	7.62399i	0.129220	+	0.129220i	−0.639539	+	0.768759i	$0.720875\pi$
$60$		0			0
$61$	89.6169			1.46913			0.734564	−	0.678539i	$-0.237387\pi$
$61$	89.6169			1.46913			0.734564	+	0.678539i	$0.237387\pi$
$62$		0			0
$63$	4.18444	+	4.18444i	0.0664198	+	0.0664198i
$64$		0			0
$65$	−110.980	−	3.42784i	−1.70738	−	0.0527360i
$66$		0			0
$67$	−12.3806	+	12.3806i	−0.184785	+	0.184785i	−0.793437	−	0.608652i	$-0.791711\pi$
$67$	−12.3806	+	12.3806i	−0.184785	+	0.184785i	0.608652	+	0.793437i	$0.291711\pi$
$68$		0			0
$69$		−	133.322i		−	1.93220i
$70$		0			0
$71$	−7.79853	+	7.79853i	−0.109838	+	0.109838i	−0.759890	−	0.650052i	$-0.774747\pi$
$71$	−7.79853	+	7.79853i	−0.109838	+	0.109838i	0.650052	+	0.759890i	$0.274747\pi$
$72$		0			0
$73$	−36.2093	−	36.2093i	−0.496018	−	0.496018i	0.414178	−	0.910196i	$-0.364069\pi$
$73$	−36.2093	−	36.2093i	−0.496018	−	0.496018i	−0.910196	+	0.414178i	$0.864069\pi$
$74$		0			0
$75$			212.526i			2.83369i
$76$		0			0
$77$		−	9.32673i		−	0.121126i
$78$		0			0
$79$	−7.20475			−0.0911994			−0.0455997	−	0.998960i	$-0.514520\pi$
$79$	−7.20475			−0.0911994			−0.0455997	+	0.998960i	$0.514520\pi$
$80$		0			0
$81$	−63.4725			−0.783612
$82$		0			0
$83$	−53.9095	+	53.9095i	−0.649513	+	0.649513i	−0.952875	−	0.303363i	$-0.901891\pi$
$83$	−53.9095	+	53.9095i	−0.649513	+	0.649513i	0.303363	+	0.952875i	$0.401891\pi$
$84$		0			0
$85$	−60.8971	−	60.8971i	−0.716436	−	0.716436i
$86$		0			0
$87$	118.227			1.35893
$88$		0			0
$89$	70.0269	+	70.0269i	0.786819	+	0.786819i	0.980971	−	0.194152i	$-0.0621955\pi$
$89$	70.0269	+	70.0269i	0.786819	+	0.786819i	−0.194152	+	0.980971i	$0.562195\pi$
$90$		0			0
$91$	−0.223083	+	7.22252i	−0.00245146	+	0.0793684i
$92$		0			0
$93$	13.3176	−	13.3176i	0.143200	−	0.143200i
$94$		0			0
$95$		−	103.486i		−	1.08932i
$96$		0			0
$97$	−124.696	+	124.696i	−1.28552	+	1.28552i	−0.348043	+	0.937478i	$0.613154\pi$
$97$	−124.696	+	124.696i	−1.28552	+	1.28552i	−0.937478	+	0.348043i	$0.886846\pi$
$98$		0			0
$99$	−126.317	−	126.317i	−1.27593	−	1.27593i
$100$		0			0
$101$		−	52.1758i		−	0.516592i	−0.966066	−	0.258296i	$-0.916839\pi$
$101$		−	52.1758i		−	0.516592i	0.966066	−	0.258296i	$-0.0831611\pi$
$102$		0			0
$103$			129.461i			1.25690i	0.777849	+	0.628451i	$0.216311\pi$
$103$			129.461i			1.25690i	−0.777849	+	0.628451i	$0.783689\pi$
$104$		0			0
$105$	21.0427			0.200406
$106$		0			0
$107$	28.4462			0.265852			0.132926	−	0.991126i	$-0.457563\pi$
$107$	28.4462			0.265852			0.132926	+	0.991126i	$0.457563\pi$
$108$		0			0
$109$	−33.1837	+	33.1837i	−0.304438	+	0.304438i	−0.842747	−	0.538310i	$-0.819063\pi$
$109$	−33.1837	+	33.1837i	−0.304438	+	0.304438i	0.538310	+	0.842747i	$0.319063\pi$
$110$		0			0
$111$	62.2284	+	62.2284i	0.560616	+	0.560616i
$112$		0			0
$113$	61.0854			0.540579			0.270289	−	0.962779i	$-0.412881\pi$
$113$	61.0854			0.540579			0.270289	+	0.962779i	$0.412881\pi$
$114$		0			0
$115$	−181.657	−	181.657i	−1.57963	−	1.57963i
$116$		0			0
$117$	94.7973	+	100.840i	0.810233	+	0.861880i
$118$		0			0
$119$	−3.96316	+	3.96316i	−0.0333039	+	0.0333039i
$120$		0			0
$121$			160.549i			1.32685i
$122$		0			0
$123$	99.5289	−	99.5289i	0.809178	−	0.809178i
$124$		0			0
$125$	138.593	+	138.593i	1.10874	+	1.10874i
$126$		0			0
$127$		−	170.483i		−	1.34239i	−0.741282	−	0.671194i	$-0.765782\pi$
$127$		−	170.483i		−	1.34239i	0.741282	−	0.671194i	$-0.234218\pi$
$128$		0			0
$129$		−	221.101i		−	1.71396i
$130$		0			0
$131$	14.6255			0.111645			0.0558224	−	0.998441i	$-0.482222\pi$
$131$	14.6255			0.111645			0.0558224	+	0.998441i	$0.482222\pi$
$132$		0			0
$133$	−6.73482			−0.0506377
$134$		0			0
$135$	44.0709	−	44.0709i	0.326451	−	0.326451i
$136$		0			0
$137$	−0.0904616	−	0.0904616i	−0.000660304	−	0.000660304i	0.706777	−	0.707437i	$-0.250149\pi$
$137$	−0.0904616	−	0.0904616i	−0.000660304	−	0.000660304i	−0.707437	+	0.706777i	$0.750149\pi$
$138$		0			0
$139$	−138.968			−0.999770			−0.499885	−	0.866092i	$-0.666624\pi$
$139$	−138.968			−0.999770			−0.499885	+	0.866092i	$0.666624\pi$
$140$		0			0
$141$	110.057	+	110.057i	0.780547	+	0.780547i
$142$		0			0
$143$	6.73426	−	218.028i	0.0470927	−	1.52467i
$144$		0			0
$145$	161.090	−	161.090i	1.11097	−	1.11097i
$146$		0			0
$147$			215.819i			1.46816i
$148$		0			0
$149$	144.587	−	144.587i	0.970385	−	0.970385i	−0.0291887	−	0.999574i	$-0.509292\pi$
$149$	144.587	−	144.587i	0.970385	−	0.970385i	0.999574	+	0.0291887i	$0.00929239\pi$
$150$		0			0
$151$	193.041	+	193.041i	1.27842	+	1.27842i	0.941552	+	0.336868i	$0.109368\pi$
$151$	193.041	+	193.041i	1.27842	+	1.27842i	0.336868	+	0.941552i	$0.390632\pi$
$152$		0			0
$153$			107.351i			0.701638i
$154$		0			0
$155$		−	36.2916i		−	0.234139i
$156$		0			0
$157$	−49.0487			−0.312412			−0.156206	−	0.987724i	$-0.549926\pi$
$157$	−49.0487			−0.312412			−0.156206	+	0.987724i	$0.549926\pi$
$158$		0			0
$159$	−291.691			−1.83453
$160$		0			0
$161$	−11.8222	+	11.8222i	−0.0734297	+	0.0734297i
$162$		0			0
$163$	84.5828	+	84.5828i	0.518913	+	0.518913i	0.917242	−	0.398329i	$-0.130410\pi$
$163$	84.5828	+	84.5828i	0.518913	+	0.518913i	−0.398329	+	0.917242i	$0.630410\pi$
$164$		0			0
$165$	−635.221			−3.84982
$166$		0			0
$167$	−25.6174	−	25.6174i	−0.153398	−	0.153398i	0.626236	−	0.779634i	$-0.284595\pi$
$167$	−25.6174	−	25.6174i	−0.153398	−	0.153398i	−0.779634	+	0.626236i	$0.784595\pi$
$168$		0			0
$169$	−10.4299	+	168.678i	−0.0617153	+	0.998094i
$170$		0			0
$171$	−91.2134	+	91.2134i	−0.533411	+	0.533411i
$172$		0			0
$173$			82.1184i			0.474673i	0.971428	+	0.237336i	$0.0762743\pi$
$173$			82.1184i			0.474673i	−0.971428	+	0.237336i	$0.923726\pi$
$174$		0			0
$175$	18.8456	−	18.8456i	0.107689	−	0.107689i
$176$		0			0
$177$	−33.7927	−	33.7927i	−0.190919	−	0.190919i
$178$		0			0
$179$		−	125.292i		−	0.699956i	−0.936758	−	0.349978i	$-0.886189\pi$
$179$		−	125.292i		−	0.699956i	0.936758	−	0.349978i	$-0.113811\pi$
$180$		0			0
$181$			104.543i			0.577587i	0.957391	+	0.288794i	$0.0932541\pi$
$181$			104.543i			0.577587i	−0.957391	+	0.288794i	$0.906746\pi$
$182$		0			0
$183$	−397.219			−2.17060
$184$		0			0
$185$	169.578			0.916639
$186$		0			0
$187$	119.637	−	119.637i	0.639771	−	0.639771i
$188$		0			0
$189$	−2.86812	−	2.86812i	−0.0151752	−	0.0151752i
$190$		0			0
$191$	215.628			1.12894			0.564470	−	0.825454i	$-0.309081\pi$
$191$	215.628			1.12894			0.564470	+	0.825454i	$0.309081\pi$
$192$		0			0
$193$	−55.7810	−	55.7810i	−0.289021	−	0.289021i	0.547672	−	0.836693i	$-0.315514\pi$
$193$	−55.7810	−	55.7810i	−0.289021	−	0.289021i	−0.836693	+	0.547672i	$0.815514\pi$
$194$		0			0
$195$	491.908	+	15.1936i	2.52261	+	0.0779159i
$196$		0			0
$197$	−49.3844	+	49.3844i	−0.250682	+	0.250682i	−0.821250	−	0.570568i	$-0.806723\pi$
$197$	−49.3844	+	49.3844i	−0.250682	+	0.250682i	0.570568	+	0.821250i	$0.306723\pi$
$198$		0			0
$199$			69.7637i			0.350572i	0.984518	+	0.175286i	$0.0560849\pi$
$199$			69.7637i			0.350572i	−0.984518	+	0.175286i	$0.943915\pi$
$200$		0			0
$201$	54.8760	−	54.8760i	0.273015	−	0.273015i
$202$		0			0
$203$	−10.4837	−	10.4837i	−0.0516438	−	0.0516438i
$204$		0			0
$205$		−	271.226i		−	1.32305i
$206$		0			0
$207$			320.229i			1.54700i
$208$		0			0
$209$	203.306			0.972756
$210$		0			0
$211$	−197.446			−0.935761			−0.467881	−	0.883792i	$-0.654982\pi$
$211$	−197.446			−0.935761			−0.467881	+	0.883792i	$0.654982\pi$
$212$		0			0
$213$	34.5663	−	34.5663i	0.162283	−	0.162283i
$214$		0			0
$215$	−301.260	−	301.260i	−1.40121	−	1.40121i
$216$		0			0
$217$	−2.36185			−0.0108841
$218$		0			0
$219$	160.495	+	160.495i	0.732854	+	0.732854i
$220$		0			0
$221$	−95.5073	+	89.7842i	−0.432160	+	0.406263i
$222$		0			0
$223$	−163.226	+	163.226i	−0.731957	+	0.731957i	−0.971007	−	0.239050i	$-0.923164\pi$
$223$	−163.226	+	163.226i	−0.731957	+	0.731957i	0.239050	+	0.971007i	$0.423164\pi$
$224$		0			0
$225$		−	510.472i		−	2.26877i
$226$		0			0
$227$	152.446	−	152.446i	0.671567	−	0.671567i	−0.286511	−	0.958077i	$-0.592495\pi$
$227$	152.446	−	152.446i	0.671567	−	0.671567i	0.958077	+	0.286511i	$0.0924953\pi$
$228$		0			0
$229$	−32.6090	−	32.6090i	−0.142397	−	0.142397i	0.632314	−	0.774712i	$-0.282105\pi$
$229$	−32.6090	−	32.6090i	−0.142397	−	0.142397i	−0.774712	+	0.632314i	$0.782105\pi$
$230$		0			0
$231$			41.3400i			0.178961i
$232$		0			0
$233$			381.064i			1.63547i	0.575597	+	0.817734i	$0.304770\pi$
$233$			381.064i			1.63547i	−0.575597	+	0.817734i	$0.695230\pi$
$234$		0			0
$235$	299.916			1.27624
$236$		0			0
$237$	31.9345			0.134745
$238$		0			0
$239$	−142.133	+	142.133i	−0.594700	+	0.594700i	−0.938897	−	0.344197i	$-0.888151\pi$
$239$	−142.133	+	142.133i	−0.594700	+	0.594700i	0.344197	+	0.938897i	$0.388151\pi$
$240$		0			0
$241$	−189.679	−	189.679i	−0.787051	−	0.787051i	0.193959	−	0.981010i	$-0.437867\pi$
$241$	−189.679	−	189.679i	−0.787051	−	0.787051i	−0.981010	+	0.193959i	$0.937867\pi$
$242$		0			0
$243$	347.012			1.42803
$244$		0			0
$245$	294.064	+	294.064i	1.20026	+	1.20026i
$246$		0			0
$247$	−157.438	−	4.86280i	−0.637401	−	0.0196874i
$248$		0			0
$249$	238.950	−	238.950i	0.959637	−	0.959637i
$250$		0			0
$251$		−	352.293i		−	1.40356i	−0.712395	−	0.701778i	$-0.752390\pi$
$251$		−	352.293i		−	1.40356i	0.712395	−	0.701778i	$-0.247610\pi$
$252$		0			0
$253$	356.880	−	356.880i	1.41059	−	1.41059i
$254$		0			0
$255$	269.921	+	269.921i	1.05852	+	1.05852i
$256$		0			0
$257$		−	10.5071i		−	0.0408836i	−0.999791	−	0.0204418i	$-0.993493\pi$
$257$		−	10.5071i		−	0.0408836i	0.999791	−	0.0204418i	$-0.00650729\pi$
$258$		0			0
$259$		−	11.0361i		−	0.0426104i
$260$		0			0
$261$	−283.973			−1.08802
$262$		0			0
$263$	267.748			1.01805			0.509027	−	0.860751i	$-0.330005\pi$
$263$	267.748			1.01805			0.509027	+	0.860751i	$0.330005\pi$
$264$		0			0
$265$	−397.442	+	397.442i	−1.49978	+	1.49978i
$266$		0			0
$267$	−310.389	−	310.389i	−1.16250	−	1.16250i
$268$		0			0
$269$	−297.780			−1.10699			−0.553494	−	0.832853i	$-0.686706\pi$
$269$	−297.780			−1.10699			−0.553494	+	0.832853i	$0.686706\pi$
$270$		0			0
$271$	−118.767	−	118.767i	−0.438255	−	0.438255i	0.453170	−	0.891424i	$-0.350293\pi$
$271$	−118.767	−	118.767i	−0.438255	−	0.438255i	−0.891424	+	0.453170i	$0.850293\pi$
$272$		0			0
$273$	0.988795	−	32.0132i	0.00362196	−	0.117265i
$274$		0			0
$275$	−568.897	+	568.897i	−2.06872	+	2.06872i
$276$		0			0
$277$			91.5366i			0.330457i	0.986255	+	0.165229i	$0.0528362\pi$
$277$			91.5366i			0.330457i	−0.986255	+	0.165229i	$0.947164\pi$
$278$		0			0
$279$	−31.9878	+	31.9878i	−0.114652	+	0.114652i
$280$		0			0
$281$	−297.778	−	297.778i	−1.05971	−	1.05971i	−0.998100	−	0.0616074i	$-0.980377\pi$
$281$	−297.778	−	297.778i	−1.05971	−	1.05971i	−0.0616074	−	0.998100i	$-0.519623\pi$
$282$		0			0
$283$			374.832i			1.32450i	0.749285	+	0.662248i	$0.230397\pi$
$283$			374.832i			1.32450i	−0.749285	+	0.662248i	$0.769603\pi$
$284$		0			0
$285$			458.692i			1.60945i
$286$		0			0
$287$	−17.6513			−0.0615027
$288$		0			0
$289$	187.326			0.648188
$290$		0			0
$291$	552.703	−	552.703i	1.89932	−	1.89932i
$292$		0			0
$293$	−162.854	−	162.854i	−0.555817	−	0.555817i	0.372297	−	0.928114i	$-0.378570\pi$
$293$	−162.854	−	162.854i	−0.555817	−	0.555817i	−0.928114	+	0.372297i	$0.878570\pi$
$294$		0			0
$295$	−92.0883			−0.312164
$296$		0			0
$297$	86.5808	+	86.5808i	0.291518	+	0.291518i
$298$		0			0
$299$	−284.900	+	267.828i	−0.952842	+	0.895745i
$300$		0			0
$301$	−19.6059	+	19.6059i	−0.0651359	+	0.0651359i
$302$		0			0
$303$			231.265i			0.763251i
$304$		0			0
$305$	−541.230	+	541.230i	−1.77453	+	1.77453i
$306$		0			0
$307$	96.9116	+	96.9116i	0.315673	+	0.315673i	0.847102	−	0.531430i	$-0.178345\pi$
$307$	96.9116	+	96.9116i	0.315673	+	0.315673i	−0.531430	+	0.847102i	$0.678345\pi$
$308$		0			0
$309$		−	573.825i		−	1.85704i
$310$		0			0
$311$			12.0062i			0.0386052i	0.999814	+	0.0193026i	$0.00614458\pi$
$311$			12.0062i			0.0386052i	−0.999814	+	0.0193026i	$0.993855\pi$
$312$		0			0
$313$	68.4167			0.218584			0.109292	−	0.994010i	$-0.465142\pi$
$313$	68.4167			0.218584			0.109292	+	0.994010i	$0.465142\pi$
$314$		0			0
$315$	−50.5429			−0.160454
$316$		0			0
$317$	244.393	−	244.393i	0.770957	−	0.770957i	−0.207317	−	0.978274i	$-0.566473\pi$
$317$	244.393	−	244.393i	0.770957	−	0.770957i	0.978274	+	0.207317i	$0.0664732\pi$
$318$		0			0
$319$	316.474	+	316.474i	0.992082	+	0.992082i
$320$		0			0
$321$	−126.085			−0.392789
$322$		0			0
$323$	−86.3898	−	86.3898i	−0.267461	−	0.267461i
$324$		0			0
$325$	454.155	−	426.941i	1.39740	−	1.31366i
$326$		0			0
$327$	147.084	−	147.084i	0.449798	−	0.449798i
$328$		0			0
$329$		−	19.5184i		−	0.0593266i
$330$		0			0
$331$	275.224	−	275.224i	0.831491	−	0.831491i	−0.156230	−	0.987721i	$-0.549934\pi$
$331$	275.224	−	275.224i	0.831491	−	0.831491i	0.987721	+	0.156230i	$0.0499340\pi$
$332$		0			0
$333$	−149.468	−	149.468i	−0.448853	−	0.448853i
$334$		0			0
$335$		−	149.542i		−	0.446395i
$336$		0			0
$337$		−	647.689i		−	1.92193i	−0.276678	−	0.960963i	$-0.589233\pi$
$337$		−	647.689i		−	1.92193i	0.276678	−	0.960963i	$-0.410767\pi$
$338$		0			0
$339$	−270.756			−0.798690
$340$		0			0
$341$	71.2978			0.209084
$342$		0			0
$343$	38.3966	−	38.3966i	0.111943	−	0.111943i
$344$		0			0
$345$	805.180	+	805.180i	2.33385	+	2.33385i
$346$		0			0
$347$	−71.7372			−0.206736			−0.103368	−	0.994643i	$-0.532962\pi$
$347$	−71.7372			−0.206736			−0.103368	+	0.994643i	$0.532962\pi$
$348$		0			0
$349$	442.834	+	442.834i	1.26887	+	1.26887i	0.946675	+	0.322190i	$0.104419\pi$
$349$	442.834	+	442.834i	1.26887	+	1.26887i	0.322190	+	0.946675i	$0.395581\pi$
$350$		0			0
$351$	−64.9763	−	69.1181i	−0.185118	−	0.196918i
$352$		0			0
$353$	−177.592	+	177.592i	−0.503093	+	0.503093i	−0.912398	−	0.409305i	$-0.865771\pi$
$353$	−177.592	+	177.592i	−0.503093	+	0.503093i	0.409305	+	0.912398i	$0.365771\pi$
$354$		0			0
$355$		−	94.1965i		−	0.265342i
$356$		0			0
$357$	17.5664	−	17.5664i	0.0492056	−	0.0492056i
$358$		0			0
$359$	201.035	+	201.035i	0.559986	+	0.559986i	0.929303	−	0.369317i	$-0.120408\pi$
$359$	201.035	+	201.035i	0.559986	+	0.559986i	−0.369317	+	0.929303i	$0.620408\pi$
$360$		0			0
$361$			214.193i			0.593333i
$362$		0			0
$363$		−	711.619i		−	1.96038i
$364$		0			0
$365$	437.364			1.19826
$366$		0			0
$367$	−625.023			−1.70306			−0.851530	−	0.524306i	$-0.824325\pi$
$367$	−625.023			−1.70306			−0.851530	+	0.524306i	$0.824325\pi$
$368$		0			0
$369$	−239.061	+	239.061i	−0.647862	+	0.647862i
$370$		0			0
$371$	25.8654	+	25.8654i	0.0697181	+	0.0697181i
$372$		0			0
$373$	−37.9411			−0.101719			−0.0508593	−	0.998706i	$-0.516196\pi$
$373$	−37.9411			−0.101719			−0.0508593	+	0.998706i	$0.516196\pi$
$374$		0			0
$375$	−614.301	−	614.301i	−1.63814	−	1.63814i
$376$		0			0
$377$	−237.505	−	252.644i	−0.629986	−	0.670143i
$378$		0			0
$379$	508.424	−	508.424i	1.34149	−	1.34149i	0.446910	−	0.894579i	$-0.352524\pi$
$379$	508.424	−	508.424i	1.34149	−	1.34149i	0.894579	−	0.446910i	$-0.147476\pi$
$380$		0			0
$381$			755.653i			1.98334i
$382$		0			0
$383$	37.6964	−	37.6964i	0.0984239	−	0.0984239i	−0.656180	−	0.754604i	$-0.727829\pi$
$383$	37.6964	−	37.6964i	0.0984239	−	0.0984239i	0.754604	+	0.656180i	$0.227829\pi$
$384$		0			0
$385$	56.3277	+	56.3277i	0.146306	+	0.146306i
$386$		0			0
$387$			531.067i			1.37227i
$388$		0			0
$389$			339.848i			0.873646i	0.899547	+	0.436823i	$0.143896\pi$
$389$			339.848i			0.873646i	−0.899547	+	0.436823i	$0.856104\pi$
$390$		0			0
$391$	−303.294			−0.775689
$392$		0			0
$393$	−64.8262			−0.164952
$394$		0			0
$395$	43.5122	−	43.5122i	0.110158	−	0.110158i
$396$		0			0
$397$	−51.8720	−	51.8720i	−0.130660	−	0.130660i	0.638752	−	0.769412i	$-0.279451\pi$
$397$	−51.8720	−	51.8720i	−0.130660	−	0.130660i	−0.769412	+	0.638752i	$0.779451\pi$
$398$		0			0
$399$	29.8515			0.0748159
$400$		0			0
$401$	−416.732	−	416.732i	−1.03923	−	1.03923i	−0.999198	−	0.0400326i	$-0.987254\pi$
$401$	−416.732	−	416.732i	−1.03923	−	1.03923i	−0.0400326	−	0.999198i	$-0.512746\pi$
$402$		0			0
$403$	−55.2122	−	1.70534i	−0.137003	−	0.00423162i
$404$		0			0
$405$	383.335	−	383.335i	0.946505	−	0.946505i
$406$		0			0
$407$			333.150i			0.818550i
$408$		0			0
$409$	−342.563	+	342.563i	−0.837563	+	0.837563i	−0.988538	−	0.150975i	$-0.951759\pi$
$409$	−342.563	+	342.563i	−0.837563	+	0.837563i	0.150975	+	0.988538i	$0.451759\pi$
$410$		0			0
$411$	0.400964	+	0.400964i	0.000975581	+	0.000975581i
$412$		0			0
$413$			5.99308i			0.0145111i
$414$		0			0
$415$		−	651.160i		−	1.56906i
$416$		0			0
$417$	615.964			1.47713
$418$		0			0
$419$	766.950			1.83043			0.915214	−	0.402967i	$-0.132021\pi$
$419$	766.950			1.83043			0.915214	+	0.402967i	$0.132021\pi$
$420$		0			0
$421$	−513.458	+	513.458i	−1.21962	+	1.21962i	−0.251850	+	0.967766i	$0.581039\pi$
$421$	−513.458	+	513.458i	−1.21962	+	1.21962i	−0.967766	+	0.251850i	$0.918961\pi$
$422$		0			0
$423$	−264.349	−	264.349i	−0.624939	−	0.624939i
$424$		0			0
$425$	483.478			1.13759
$426$		0			0
$427$	35.2231	+	35.2231i	0.0824897	+	0.0824897i
$428$		0			0
$429$	−29.8491	+	966.393i	−0.0695782	+	2.25266i
$430$		0			0
$431$	218.539	−	218.539i	0.507052	−	0.507052i	−0.406569	−	0.913620i	$-0.633275\pi$
$431$	218.539	−	218.539i	0.507052	−	0.507052i	0.913620	+	0.406569i	$0.133275\pi$
$432$		0			0
$433$			136.399i			0.315010i	0.987518	+	0.157505i	$0.0503451\pi$
$433$			136.399i			0.315010i	−0.987518	+	0.157505i	$0.949655\pi$
$434$		0			0
$435$	−714.018	+	714.018i	−1.64142	+	1.64142i
$436$		0			0
$437$	−257.702	−	257.702i	−0.589708	−	0.589708i
$438$		0			0
$439$			61.3626i			0.139778i	0.997555	+	0.0698891i	$0.0222645\pi$
$439$			61.3626i			0.139778i	−0.997555	+	0.0698891i	$0.977735\pi$
$440$		0			0
$441$		−	518.381i		−	1.17547i
$442$		0			0
$443$	−810.003			−1.82845			−0.914224	−	0.405209i	$-0.867199\pi$
$443$	−810.003			−1.82845			−0.914224	+	0.405209i	$0.867199\pi$
$444$		0			0
$445$	−845.838			−1.90076
$446$		0			0
$447$	−640.872	+	640.872i	−1.43372	+	1.43372i
$448$		0			0
$449$	158.025	+	158.025i	0.351949	+	0.351949i	0.860834	−	0.508886i	$-0.169942\pi$
$449$	158.025	+	158.025i	0.351949	+	0.351949i	−0.508886	+	0.860834i	$0.669942\pi$
$450$		0			0
$451$	532.844			1.18147
$452$		0			0
$453$	−855.640	−	855.640i	−1.88883	−	1.88883i
$454$		0			0
$455$	−42.2723	−	44.9668i	−0.0929061	−	0.0988282i
$456$		0			0
$457$	322.166	−	322.166i	0.704959	−	0.704959i	−0.260512	−	0.965471i	$-0.583891\pi$
$457$	322.166	−	322.166i	0.704959	−	0.704959i	0.965471	+	0.260512i	$0.0838913\pi$
$458$		0			0
$459$		−	73.5807i		−	0.160307i
$460$		0			0
$461$	13.8270	−	13.8270i	0.0299935	−	0.0299935i	−0.691951	−	0.721944i	$-0.743249\pi$
$461$	13.8270	−	13.8270i	0.0299935	−	0.0299935i	0.721944	+	0.691951i	$0.243249\pi$
$462$		0			0
$463$	53.7709	+	53.7709i	0.116136	+	0.116136i	0.762786	−	0.646651i	$-0.223831\pi$
$463$	53.7709	+	53.7709i	0.116136	+	0.116136i	−0.646651	+	0.762786i	$0.723831\pi$
$464$		0			0
$465$			160.860i			0.345935i
$466$		0			0
$467$			694.236i			1.48659i	0.668966	+	0.743293i	$0.266737\pi$
$467$			694.236i			1.48659i	−0.668966	+	0.743293i	$0.733263\pi$
$468$		0			0
$469$	−9.73216			−0.0207509
$470$		0			0
$471$	217.404			0.461581
$472$		0			0
$473$	591.849	−	591.849i	1.25127	−	1.25127i
$474$		0			0
$475$	410.800	+	410.800i	0.864842	+	0.864842i
$476$		0			0
$477$	700.619			1.46880
$478$		0			0
$479$	552.049	+	552.049i	1.15250	+	1.15250i	0.986049	+	0.166453i	$0.0532313\pi$
$479$	552.049	+	552.049i	1.15250	+	1.15250i	0.166453	+	0.986049i	$0.446769\pi$
$480$		0			0
$481$	7.96849	−	257.988i	0.0165665	−	0.536357i
$482$		0			0
$483$	52.4008	−	52.4008i	0.108490	−	0.108490i
$484$		0			0
$485$		−	1506.17i		−	3.10550i
$486$		0			0
$487$	108.399	−	108.399i	0.222585	−	0.222585i	−0.587001	−	0.809586i	$-0.699692\pi$
$487$	108.399	−	108.399i	0.222585	−	0.222585i	0.809586	+	0.587001i	$0.199692\pi$
$488$		0			0
$489$	−374.906	−	374.906i	−0.766680	−	0.766680i
$490$		0			0
$491$			549.283i			1.11870i	0.828931	+	0.559351i	$0.188950\pi$
$491$			549.283i			1.11870i	−0.828931	+	0.559351i	$0.811050\pi$
$492$		0			0
$493$		−	268.956i		−	0.545549i
$494$		0			0
$495$	1525.75			3.08233
$496$		0			0
$497$	−6.13028			−0.0123346
$498$		0			0
$499$	22.8430	−	22.8430i	0.0457775	−	0.0457775i	−0.683847	−	0.729625i	$-0.739695\pi$
$499$	22.8430	−	22.8430i	0.0457775	−	0.0457775i	0.729625	+	0.683847i	$0.239695\pi$
$500$		0			0
$501$	113.547	+	113.547i	0.226641	+	0.226641i
$502$		0			0
$503$	865.245			1.72017			0.860084	−	0.510152i	$-0.170411\pi$
$503$	865.245			1.72017			0.860084	+	0.510152i	$0.170411\pi$
$504$		0			0
$505$	315.110	+	315.110i	0.623979	+	0.623979i
$506$		0			0
$507$	46.2296	−	747.651i	0.0911826	−	1.47466i
$508$		0			0
$509$	−367.011	+	367.011i	−0.721044	+	0.721044i	−0.968818	−	0.247774i	$-0.920301\pi$
$509$	−367.011	+	367.011i	−0.721044	+	0.721044i	0.247774	+	0.968818i	$0.420301\pi$
$510$		0			0
$511$		−	28.4635i		−	0.0557015i
$512$		0			0
$513$	62.5198	−	62.5198i	0.121871	−	0.121871i
$514$		0			0
$515$	−781.863	−	781.863i	−1.51818	−	1.51818i
$516$		0			0
$517$			589.209i			1.13967i
$518$		0			0
$519$		−	363.983i		−	0.701316i
$520$		0			0
$521$	−244.720			−0.469713			−0.234856	−	0.972030i	$-0.575462\pi$
$521$	−244.720			−0.469713			−0.234856	+	0.972030i	$0.575462\pi$
$522$		0			0
$523$	−455.570			−0.871071			−0.435535	−	0.900172i	$-0.643441\pi$
$523$	−455.570			−0.871071			−0.435535	+	0.900172i	$0.643441\pi$
$524$		0			0
$525$	−83.5315	+	83.5315i	−0.159108	+	0.159108i
$526$		0			0
$527$	−30.2962	−	30.2962i	−0.0574881	−	0.0574881i
$528$		0			0
$529$	−375.732			−0.710268
$530$		0			0
$531$	81.1675	+	81.1675i	0.152858	+	0.152858i
$532$		0			0
$533$	−412.629	−	12.7449i	−0.774163	−	0.0239116i
$534$		0			0
$535$	−171.797	+	171.797i	−0.321116	+	0.321116i
$536$		0			0
$537$			555.347i			1.03417i
$538$		0			0
$539$	−577.711	+	577.711i	−1.07182	+	1.07182i
$540$		0			0
$541$	283.267	+	283.267i	0.523598	+	0.523598i	0.918656	−	0.395058i	$-0.129276\pi$
$541$	283.267	+	283.267i	0.523598	+	0.523598i	−0.395058	+	0.918656i	$0.629276\pi$
$542$		0			0
$543$		−	463.379i		−	0.853369i
$544$		0			0
$545$		−	400.818i		−	0.735446i
$546$		0			0
$547$	−234.065			−0.427908			−0.213954	−	0.976844i	$-0.568634\pi$
$547$	−234.065			−0.427908			−0.213954	+	0.976844i	$0.568634\pi$
$548$		0			0
$549$	954.091			1.73787
$550$		0			0
$551$	228.525	−	228.525i	0.414747	−	0.414747i
$552$		0			0
$553$	−2.83176	−	2.83176i	−0.00512073	−	0.00512073i
$554$		0			0
$555$	−751.642			−1.35431
$556$		0			0
$557$	534.694	+	534.694i	0.959954	+	0.959954i	0.999228	−	0.0392744i	$-0.0125046\pi$
$557$	534.694	+	534.694i	0.959954	+	0.959954i	−0.0392744	+	0.999228i	$0.512505\pi$
$558$		0			0
$559$	−472.478	+	444.165i	−0.845220	+	0.794572i
$560$		0			0
$561$	−530.282	+	530.282i	−0.945244	+	0.945244i
$562$		0			0
$563$		−	387.128i		−	0.687616i	−0.939040	−	0.343808i	$-0.888283\pi$
$563$		−	387.128i		−	0.687616i	0.939040	−	0.343808i	$-0.111717\pi$
$564$		0			0
$565$	−368.918	+	368.918i	−0.652952	+	0.652952i
$566$		0			0
$567$	−24.9473	−	24.9473i	−0.0439988	−	0.0439988i
$568$		0			0
$569$		−	384.213i		−	0.675243i	−0.941282	−	0.337622i	$-0.890378\pi$
$569$		−	384.213i		−	0.675243i	0.941282	−	0.337622i	$-0.109622\pi$
$570$		0			0
$571$			1016.14i			1.77958i	0.456373	+	0.889789i	$0.349148\pi$
$571$			1016.14i			1.77958i	−0.456373	+	0.889789i	$0.650852\pi$
$572$		0			0
$573$	−955.751			−1.66798
$574$		0			0
$575$	1442.22			2.50821
$576$		0			0
$577$	717.901	−	717.901i	1.24420	−	1.24420i	0.285953	−	0.958244i	$-0.407690\pi$
$577$	717.901	−	717.901i	1.24420	−	1.24420i	0.958244	−	0.285953i	$-0.0923101\pi$
$578$		0			0
$579$	247.245	+	247.245i	0.427020	+	0.427020i
$580$		0			0
$581$	−42.3773			−0.0729385
$582$		0			0
$583$	−780.806	−	780.806i	−1.33929	−	1.33929i
$584$		0			0
$585$	−1181.53	−	36.4939i	−2.01970	−	0.0623827i
$586$		0			0
$587$	−348.797	+	348.797i	−0.594203	+	0.594203i	−0.938764	−	0.344561i	$-0.888028\pi$
$587$	−348.797	+	348.797i	−0.594203	+	0.594203i	0.344561	+	0.938764i	$0.388028\pi$
$588$		0			0
$589$		−	51.4840i		−	0.0874092i
$590$		0			0
$591$	218.893	−	218.893i	0.370376	−	0.370376i
$592$		0			0
$593$	633.494	+	633.494i	1.06829	+	1.06829i	0.997491	+	0.0707962i	$0.0225540\pi$
$593$	633.494	+	633.494i	1.06829	+	1.06829i	0.0707962	+	0.997491i	$0.477446\pi$
$594$		0			0
$595$		−	47.8701i		−	0.0804539i
$596$		0			0
$597$		−	309.222i		−	0.517960i
$598$		0			0
$599$	1122.70			1.87429			0.937146	−	0.348938i	$-0.113458\pi$
$599$	1122.70			1.87429			0.937146	+	0.348938i	$0.113458\pi$
$600$		0			0
$601$	659.039			1.09657			0.548286	−	0.836291i	$-0.315281\pi$
$601$	659.039			1.09657			0.548286	+	0.836291i	$0.315281\pi$
$602$		0			0
$603$	−131.808	+	131.808i	−0.218587	+	0.218587i
$604$		0			0
$605$	−969.615	−	969.615i	−1.60267	−	1.60267i
$606$		0			0
$607$	−904.658			−1.49038			−0.745188	−	0.666854i	$-0.767640\pi$
$607$	−904.658			−1.49038			−0.745188	+	0.666854i	$0.767640\pi$
$608$		0			0
$609$	46.4681	+	46.4681i	0.0763023	+	0.0763023i
$610$		0			0
$611$	14.0931	−	456.277i	0.0230656	−	0.746771i
$612$		0			0
$613$	−348.891	+	348.891i	−0.569153	+	0.569153i	−0.931891	−	0.362738i	$-0.881842\pi$
$613$	−348.891	+	348.891i	−0.569153	+	0.569153i	0.362738	+	0.931891i	$0.381842\pi$
$614$		0			0
$615$			1202.19i			1.95477i
$616$		0			0
$617$	−74.5346	+	74.5346i	−0.120802	+	0.120802i	−0.764923	−	0.644122i	$-0.777223\pi$
$617$	−74.5346	+	74.5346i	−0.120802	+	0.120802i	0.644122	+	0.764923i	$0.277223\pi$
$618$		0			0
$619$	−624.958	−	624.958i	−1.00963	−	1.00963i	−0.999953	−	0.00967178i	$-0.996921\pi$
$619$	−624.958	−	624.958i	−1.00963	−	1.00963i	−0.00967178	−	0.999953i	$-0.503079\pi$
$620$		0			0
$621$		−	219.492i		−	0.353450i
$622$		0			0
$623$			55.0469i			0.0883578i
$624$		0			0
$625$	−475.323			−0.760517
$626$		0			0
$627$	−901.137			−1.43722
$628$		0			0
$629$	141.564	−	141.564i	0.225062	−	0.225062i
$630$		0			0
$631$	420.333	+	420.333i	0.666139	+	0.666139i	0.956820	−	0.290681i	$-0.0938819\pi$
$631$	420.333	+	420.333i	0.666139	+	0.666139i	−0.290681	+	0.956820i	$0.593882\pi$
$632$		0			0
$633$	875.162			1.38256
$634$		0			0
$635$	1029.61	+	1029.61i	1.62144	+	1.62144i
$636$		0			0
$637$	461.192	−	433.556i	0.724006	−	0.680621i
$638$		0			0
$639$	−83.0258	+	83.0258i	−0.129931	+	0.129931i
$640$		0			0
$641$		−	270.092i		−	0.421361i	−0.977555	−	0.210680i	$-0.932432\pi$
$641$		−	270.092i		−	0.421361i	0.977555	−	0.210680i	$-0.0675679\pi$
$642$		0			0
$643$	296.047	−	296.047i	0.460416	−	0.460416i	−0.438376	−	0.898792i	$-0.644446\pi$
$643$	296.047	−	296.047i	0.460416	−	0.460416i	0.898792	+	0.438376i	$0.144446\pi$
$644$		0			0
$645$	1335.31	+	1335.31i	2.07025	+	2.07025i
$646$		0			0
$647$		−	161.632i		−	0.249818i	−0.992168	−	0.124909i	$-0.960136\pi$
$647$		−	161.632i		−	0.249818i	0.992168	−	0.124909i	$-0.0398639\pi$
$648$		0			0
$649$		−	180.915i		−	0.278759i
$650$		0			0
$651$	10.4687			0.0160809
$652$		0			0
$653$	−412.304			−0.631399			−0.315700	−	0.948859i	$-0.602239\pi$
$653$	−412.304			−0.631399			−0.315700	+	0.948859i	$0.602239\pi$
$654$		0			0
$655$	−88.3287	+	88.3287i	−0.134853	+	0.134853i
$656$		0			0
$657$	−385.497	−	385.497i	−0.586753	−	0.586753i
$658$		0			0
$659$	−576.662			−0.875056			−0.437528	−	0.899205i	$-0.644146\pi$
$659$	−576.662			−0.875056			−0.437528	+	0.899205i	$0.644146\pi$
$660$		0			0
$661$	−264.568	−	264.568i	−0.400254	−	0.400254i	0.478069	−	0.878322i	$-0.341337\pi$
$661$	−264.568	−	264.568i	−0.400254	−	0.400254i	−0.878322	+	0.478069i	$0.841337\pi$
$662$		0			0
$663$	423.329	−	397.961i	0.638505	−	0.600243i
$664$		0			0
$665$	40.6741	−	40.6741i	0.0611641	−	0.0611641i
$666$		0			0
$667$		−	802.299i		−	1.20285i
$668$		0			0
$669$	723.488	−	723.488i	1.08145	−	1.08145i
$670$		0			0
$671$	−1063.29	−	1063.29i	−1.58463	−	1.58463i
$672$		0			0
$673$			547.327i			0.813265i	0.913592	+	0.406632i	$0.133297\pi$
$673$			547.327i			0.813265i	−0.913592	+	0.406632i	$0.866703\pi$
$674$		0			0
$675$			349.890i			0.518356i
$676$		0			0
$677$	658.800			0.973117			0.486558	−	0.873648i	$-0.338252\pi$
$677$	658.800			0.973117			0.486558	+	0.873648i	$0.338252\pi$
$678$		0			0
$679$	−98.0209			−0.144361
$680$		0			0
$681$	−675.703	+	675.703i	−0.992221	+	0.992221i
$682$		0			0
$683$	718.145	+	718.145i	1.05146	+	1.05146i	0.998602	+	0.0528548i	$0.0168321\pi$
$683$	718.145	+	718.145i	1.05146	+	1.05146i	0.0528548	+	0.998602i	$0.483168\pi$
$684$		0			0
$685$	1.09266			0.00159513
$686$		0			0
$687$	144.537	+	144.537i	0.210388	+	0.210388i
$688$		0			0
$689$	585.972	+	623.324i	0.850468	+	0.904679i
$690$		0			0
$691$	782.796	−	782.796i	1.13284	−	1.13284i	0.143142	−	0.989702i	$-0.454279\pi$
$691$	782.796	−	782.796i	1.13284	−	1.13284i	0.989702	−	0.143142i	$-0.0457207\pi$
$692$		0			0
$693$		−	99.2955i		−	0.143284i
$694$		0			0
$695$	839.280	−	839.280i	1.20760	−	1.20760i
$696$		0			0
$697$	−226.419	−	226.419i	−0.324848	−	0.324848i
$698$		0			0
$699$		−	1689.04i		−	2.41636i
$700$		0			0
$701$			135.826i			0.193760i	0.995296	+	0.0968798i	$0.0308863\pi$
$701$			135.826i			0.193760i	−0.995296	+	0.0968798i	$0.969114\pi$
$702$		0			0
$703$	240.567			0.342201
$704$		0			0
$705$	−1329.35			−1.88561
$706$		0			0
$707$	20.5072	−	20.5072i	0.0290060	−	0.0290060i
$708$		0			0
$709$	463.251	+	463.251i	0.653387	+	0.653387i	0.953807	−	0.300420i	$-0.0971269\pi$
$709$	463.251	+	463.251i	0.653387	+	0.653387i	−0.300420	+	0.953807i	$0.597127\pi$
$710$		0			0
$711$	−76.7042			−0.107882
$712$		0			0
$713$	−90.3741	−	90.3741i	−0.126752	−	0.126752i
$714$		0			0
$715$	1276.09	+	1357.43i	1.78473	+	1.89850i
$716$		0			0
$717$	629.995	−	629.995i	0.878654	−	0.878654i
$718$		0			0
$719$		−	1017.87i		−	1.41568i	−0.706374	−	0.707839i	$-0.749670\pi$
$719$		−	1017.87i		−	1.41568i	0.706374	−	0.707839i	$-0.250330\pi$
$720$		0			0
$721$	−50.8834	+	50.8834i	−0.0705734	+	0.0705734i
$722$		0			0
$723$	840.738	+	840.738i	1.16285	+	1.16285i
$724$		0			0
$725$			1278.93i			1.76405i
$726$		0			0
$727$			505.072i			0.694734i	0.937729	+	0.347367i	$0.112924\pi$
$727$			505.072i			0.694734i	−0.937729	+	0.347367i	$0.887076\pi$
$728$		0			0
$729$	−966.851			−1.32627
$730$		0			0
$731$	−502.983			−0.688076
$732$		0			0
$733$	894.499	−	894.499i	1.22033	−	1.22033i	0.252811	−	0.967516i	$-0.418645\pi$
$733$	894.499	−	894.499i	1.22033	−	1.22033i	0.967516	−	0.252811i	$-0.0813550\pi$
$734$		0			0
$735$	−1303.41	−	1303.41i	−1.77335	−	1.77335i
$736$		0			0
$737$	293.788			0.398626
$738$		0			0
$739$	−439.748	−	439.748i	−0.595059	−	0.595059i	0.343935	−	0.938993i	$-0.388240\pi$
$739$	−439.748	−	439.748i	−0.595059	−	0.595059i	−0.938993	+	0.343935i	$0.888240\pi$
$740$		0			0
$741$	697.831	+	21.5540i	0.941742	+	0.0290877i
$742$		0			0
$743$	−812.067	+	812.067i	−1.09296	+	1.09296i	−0.0977456	+	0.995211i	$0.531163\pi$
$743$	−812.067	+	812.067i	−1.09296	+	1.09296i	−0.995211	+	0.0977456i	$0.968837\pi$
$744$		0			0
$745$			1746.44i			2.34421i
$746$		0			0
$747$	−573.939	+	573.939i	−0.768325	+	0.768325i
$748$		0			0
$749$	11.1805	+	11.1805i	0.0149272	+	0.0149272i
$750$		0			0
$751$		−	684.964i		−	0.912070i	−0.889962	−	0.456035i	$-0.849269\pi$
$751$		−	684.964i		−	0.912070i	0.889962	−	0.456035i	$-0.150731\pi$
$752$		0			0
$753$			1561.51i			2.07372i
$754$		0			0
$755$	−2331.70			−3.08834
$756$		0			0
$757$	−215.537			−0.284726			−0.142363	−	0.989815i	$-0.545470\pi$
$757$	−215.537			−0.284726			−0.142363	+	0.989815i	$0.545470\pi$
$758$		0			0
$759$	−1581.84	+	1581.84i	−2.08411	+	2.08411i
$760$		0			0
$761$	−871.356	−	871.356i	−1.14501	−	1.14501i	−0.987520	−	0.157494i	$-0.949659\pi$
$761$	−871.356	−	871.356i	−1.14501	−	1.14501i	−0.157494	−	0.987520i	$-0.550341\pi$
$762$		0			0
$763$	−26.0851			−0.0341875
$764$		0			0
$765$	−648.331	−	648.331i	−0.847491	−	0.847491i
$766$		0			0
$767$	−4.32723	+	140.098i	−0.00564176	+	0.182658i
$768$		0			0
$769$	562.757	−	562.757i	0.731804	−	0.731804i	−0.239173	−	0.970977i	$-0.576876\pi$
$769$	562.757	−	562.757i	0.731804	−	0.731804i	0.970977	+	0.239173i	$0.0768763\pi$
$770$		0			0
$771$			46.5718i			0.0604045i
$772$		0			0
$773$	−97.0992	+	97.0992i	−0.125613	+	0.125613i	−0.767119	−	0.641505i	$-0.778310\pi$
$773$	−97.0992	+	97.0992i	−0.125613	+	0.125613i	0.641505	+	0.767119i	$0.278310\pi$
$774$		0			0
$775$	144.064	+	144.064i	0.185889	+	0.185889i
$776$		0			0
$777$			48.9166i			0.0629557i
$778$		0			0
$779$		−	384.766i		−	0.493923i
$780$		0			0
$781$	185.057			0.236948
$782$		0			0
$783$	194.642			0.248585
$784$		0			0
$785$	296.224	−	296.224i	0.377355	−	0.377355i
$786$		0			0
$787$	−650.868	−	650.868i	−0.827025	−	0.827025i	0.160080	−	0.987104i	$-0.448825\pi$
$787$	−650.868	−	650.868i	−0.827025	−	0.827025i	−0.987104	+	0.160080i	$0.948825\pi$
$788$		0			0
$789$	−1186.77			−1.50415
$790$		0			0
$791$	24.0090	+	24.0090i	0.0303528	+	0.0303528i
$792$		0			0
$793$	797.968	+	848.833i	1.00626	+	1.07041i
$794$		0			0
$795$	1761.63	−	1761.63i	2.21589	−	2.21589i
$796$		0			0
$797$			901.322i			1.13089i	0.824785	+	0.565447i	$0.191296\pi$
$797$			901.322i			1.13089i	−0.824785	+	0.565447i	$0.808704\pi$
$798$		0			0
$799$	250.370	−	250.370i	0.313354	−	0.313354i
$800$		0			0
$801$	745.530	+	745.530i	0.930749	+	0.930749i
$802$		0			0
$803$			859.236i			1.07003i
$804$		0			0
$805$		−	142.797i		−	0.177388i
$806$		0			0
$807$	1319.88			1.63554
$808$		0			0
$809$	−1041.59			−1.28750			−0.643749	−	0.765237i	$-0.722622\pi$
$809$	−1041.59			−1.28750			−0.643749	+	0.765237i	$0.722622\pi$
$810$		0			0
$811$	50.7958	−	50.7958i	0.0626335	−	0.0626335i	−0.675096	−	0.737730i	$-0.735898\pi$
$811$	50.7958	−	50.7958i	0.0626335	−	0.0626335i	0.737730	+	0.675096i	$0.235898\pi$
$812$		0			0
$813$	526.425	+	526.425i	0.647509	+	0.647509i
$814$		0			0
$815$	−1021.66			−1.25356
$816$		0			0
$817$	−427.373	−	427.373i	−0.523101	−	0.523101i
$818$		0			0
$819$	−2.37501	+	76.8934i	−0.00289989	+	0.0938869i
$820$		0			0
$821$	−959.345	+	959.345i	−1.16851	+	1.16851i	−0.185949	+	0.982559i	$0.559536\pi$
$821$	−959.345	+	959.345i	−1.16851	+	1.16851i	−0.982559	+	0.185949i	$0.940464\pi$
$822$		0			0
$823$			520.691i			0.632674i	0.948647	+	0.316337i	$0.102453\pi$
$823$			520.691i			0.632674i	−0.948647	+	0.316337i	$0.897547\pi$
$824$		0			0
$825$	2521.59	−	2521.59i	3.05647	−	3.05647i
$826$		0			0
$827$	603.369	+	603.369i	0.729588	+	0.729588i	0.970538	−	0.240950i	$-0.0774589\pi$
$827$	603.369	+	603.369i	0.729588	+	0.729588i	−0.240950	+	0.970538i	$0.577459\pi$
$828$		0			0
$829$		−	889.955i		−	1.07353i	−0.843732	−	0.536764i	$-0.819646\pi$
$829$		−	889.955i		−	1.07353i	0.843732	−	0.536764i	$-0.180354\pi$
$830$		0			0
$831$		−	405.729i		−	0.488241i
$832$		0			0
$833$	490.968			0.589398
$834$		0			0
$835$	309.427			0.370571
$836$		0			0
$837$	21.9252	−	21.9252i	0.0261950	−	0.0261950i
$838$		0			0
$839$	585.049	+	585.049i	0.697318	+	0.697318i	0.963831	−	0.266514i	$-0.0858717\pi$
$839$	585.049	+	585.049i	0.697318	+	0.697318i	−0.266514	+	0.963831i	$0.585872\pi$
$840$		0			0
$841$	−129.537			−0.154027
$842$		0			0
$843$	1319.88	+	1319.88i	1.56569	+	1.56569i
$844$		0			0
$845$	−955.719	−	1081.70i	−1.13103	−	1.28012i
$846$		0			0
$847$	−63.1022	+	63.1022i	−0.0745008	+	0.0745008i
$848$		0			0
$849$		−	1661.41i		−	1.95691i
$850$		0			0
$851$	422.287	−	422.287i	0.496224	−	0.496224i
$852$		0			0
$853$	−294.894	−	294.894i	−0.345714	−	0.345714i	0.512797	−	0.858510i	$-0.328610\pi$
$853$	−294.894	−	294.894i	−0.345714	−	0.345714i	−0.858510	+	0.512797i	$0.828610\pi$
$854$		0			0
$855$		−	1101.74i		−	1.28859i
$856$		0			0
$857$			909.483i			1.06124i	0.847610	+	0.530620i	$0.178041\pi$
$857$			909.483i			1.06124i	−0.847610	+	0.530620i	$0.821959\pi$
$858$		0			0
$859$	−826.078			−0.961674			−0.480837	−	0.876810i	$-0.659667\pi$
$859$	−826.078			−0.961674			−0.480837	+	0.876810i	$0.659667\pi$
$860$		0			0
$861$	78.2379			0.0908686
$862$		0			0
$863$	−658.414	+	658.414i	−0.762936	+	0.762936i	−0.976852	−	0.213916i	$-0.931378\pi$
$863$	−658.414	+	658.414i	−0.762936	+	0.762936i	0.213916	+	0.976852i	$0.431378\pi$
$864$		0			0
$865$	−495.944	−	495.944i	−0.573346	−	0.573346i
$866$		0			0
$867$	−830.309			−0.957680
$868$		0			0
$869$	85.4832	+	85.4832i	0.0983697	+	0.0983697i
$870$		0			0
$871$	−227.506	−	7.02699i	−0.261201	−	0.00806773i
$872$		0			0
$873$	−1327.55	+	1327.55i	−1.52068	+	1.52068i
$874$		0			0
$875$			108.945i			0.124509i
$876$		0			0
$877$	−768.569	+	768.569i	−0.876361	+	0.876361i	−0.993156	−	0.116795i	$-0.962738\pi$
$877$	−768.569	+	768.569i	−0.876361	+	0.876361i	0.116795	+	0.993156i	$0.462738\pi$
$878$		0			0
$879$	721.839	+	721.839i	0.821205	+	0.821205i
$880$		0			0
$881$		−	608.060i		−	0.690193i	−0.938567	−	0.345096i	$-0.887846\pi$
$881$		−	608.060i		−	0.690193i	0.938567	−	0.345096i	$-0.112154\pi$
$882$		0			0
$883$		−	624.258i		−	0.706974i	−0.935440	−	0.353487i	$-0.884996\pi$
$883$		−	624.258i		−	0.706974i	0.935440	−	0.353487i	$-0.115004\pi$
$884$		0			0
$885$	408.174			0.461213
$886$		0			0
$887$	76.0762			0.0857679			0.0428840	−	0.999080i	$-0.486345\pi$
$887$	76.0762			0.0857679			0.0428840	+	0.999080i	$0.486345\pi$
$888$		0			0
$889$	67.0068	−	67.0068i	0.0753733	−	0.0753733i
$890$		0			0
$891$	753.091	+	753.091i	0.845220	+	0.845220i
$892$		0			0
$893$	425.467			0.476447
$894$		0			0
$895$	756.687	+	756.687i	0.845460	+	0.845460i
$896$		0			0
$897$	1262.80	−	1187.12i	1.40780	−	1.32344i
$898$		0			0
$899$	80.1420	−	80.1420i	0.0891457	−	0.0891457i
$900$		0			0
$901$			663.569i			0.736480i
$902$		0			0
$903$	86.9016	−	86.9016i	0.0962365	−	0.0962365i
$904$		0			0
$905$	−631.376	−	631.376i	−0.697653	−	0.697653i
$906$		0			0
$907$		−	595.072i		−	0.656088i	−0.944662	−	0.328044i	$-0.893611\pi$
$907$		−	595.072i		−	0.656088i	0.944662	−	0.328044i	$-0.106389\pi$
$908$		0			0
$909$		−	555.482i		−	0.611091i
$910$		0			0
$911$	604.391			0.663437			0.331718	−	0.943378i	$-0.392372\pi$
$911$	604.391			0.663437			0.331718	+	0.943378i	$0.392372\pi$
$912$		0			0
$913$	1279.26			1.40116
$914$		0			0
$915$	2398.96	−	2398.96i	2.62181	−	2.62181i
$916$		0			0
$917$	5.74841	+	5.74841i	0.00626871	+	0.00626871i
$918$		0			0
$919$	−87.7344			−0.0954672			−0.0477336	−	0.998860i	$-0.515200\pi$
$919$	−87.7344			−0.0954672			−0.0477336	+	0.998860i	$0.515200\pi$
$920$		0			0
$921$	−429.553	−	429.553i	−0.466398	−	0.466398i
$922$		0			0
$923$	−143.306	−	4.42630i	−0.155261	−	0.00479555i
$924$		0			0
$925$	−673.163	+	673.163i	−0.727743	+	0.727743i
$926$		0			0
$927$			1378.28i			1.48682i
$928$		0			0
$929$	−72.6596	+	72.6596i	−0.0782127	+	0.0782127i	−0.745131	−	0.666918i	$-0.767613\pi$
$929$	−72.6596	+	72.6596i	−0.0782127	+	0.0782127i	0.666918	+	0.745131i	$0.267613\pi$
$930$		0			0
$931$	417.164	+	417.164i	0.448082	+	0.448082i
$932$		0			0
$933$		−	53.2165i		−	0.0570381i
$934$		0			0
$935$			1445.07i			1.54553i
$936$		0			0
$937$	−1009.60			−1.07748			−0.538738	−	0.842473i	$-0.681099\pi$
$937$	−1009.60			−1.07748			−0.538738	+	0.842473i	$0.681099\pi$
$938$		0			0
$939$	−303.251			−0.322951
$940$		0			0
$941$	362.860	−	362.860i	0.385611	−	0.385611i	−0.487508	−	0.873119i	$-0.662094\pi$
$941$	362.860	−	362.860i	0.385611	−	0.385611i	0.873119	+	0.487508i	$0.162094\pi$
$942$		0			0
$943$	−675.412	−	675.412i	−0.716237	−	0.716237i
$944$		0			0
$945$	34.6433			0.0366596
$946$		0			0
$947$	359.812	+	359.812i	0.379949	+	0.379949i	0.871084	−	0.491134i	$-0.163418\pi$
$947$	359.812	+	359.812i	0.379949	+	0.379949i	−0.491134	+	0.871084i	$0.663418\pi$
$948$		0			0
$949$	20.5517	−	665.383i	0.0216562	−	0.701141i
$950$		0			0
$951$	−1083.25	+	1083.25i	−1.13907	+	1.13907i
$952$		0			0
$953$		−	1294.05i		−	1.35787i	−0.734198	−	0.678935i	$-0.762442\pi$
$953$		−	1294.05i		−	1.35787i	0.734198	−	0.678935i	$-0.237558\pi$
$954$		0			0
$955$	−1302.26	+	1302.26i	−1.36362	+	1.36362i
$956$		0			0
$957$	−1402.75	−	1402.75i	−1.46577	−	1.46577i
$958$		0			0
$959$		−	0.0711102i		−	7.41504e-5i
$960$		0			0
$961$			942.945i			0.981212i
$962$		0			0
$963$	302.847			0.314483
$964$		0			0
$965$	673.765			0.698202
$966$		0			0
$967$	842.215	−	842.215i	0.870957	−	0.870957i	−0.121620	−	0.992577i	$-0.538809\pi$
$967$	842.215	−	842.215i	0.870957	−	0.870957i	0.992577	+	0.121620i	$0.0388090\pi$
$968$		0			0
$969$	382.916	+	382.916i	0.395166	+	0.395166i
$970$		0			0
$971$	−1113.43			−1.14669			−0.573343	−	0.819316i	$-0.694354\pi$
$971$	−1113.43			−1.14669			−0.573343	+	0.819316i	$0.694354\pi$
$972$		0			0
$973$	−54.6201	−	54.6201i	−0.0561358	−	0.0561358i
$974$		0			0
$975$	−2013.01	+	1892.38i	−2.06462	+	1.94090i
$976$		0			0
$977$	−328.248	+	328.248i	−0.335975	+	0.335975i	−0.854850	−	0.518875i	$-0.826351\pi$
$977$	−328.248	+	328.248i	−0.335975	+	0.335975i	0.518875	+	0.854850i	$0.326351\pi$
$978$		0			0
$979$		−	1661.72i		−	1.69736i
$980$		0			0
$981$	−353.285	+	353.285i	−0.360127	+	0.360127i
$982$		0			0
$983$	196.292	+	196.292i	0.199687	+	0.199687i	0.799866	−	0.600179i	$-0.204904\pi$
$983$	196.292	+	196.292i	0.199687	+	0.199687i	−0.600179	+	0.799866i	$0.704904\pi$
$984$		0			0
$985$		−	596.503i		−	0.605586i
$986$		0			0
$987$			86.5139i			0.0876534i
$988$		0			0
$989$	−1500.41			−1.51709
$990$		0			0
$991$	784.869			0.791997			0.395998	−	0.918251i	$-0.370399\pi$
$991$	784.869			0.791997			0.395998	+	0.918251i	$0.370399\pi$
$992$		0			0
$993$	−1219.91	+	1219.91i	−1.22851	+	1.22851i
$994$		0			0
$995$	−421.330	−	421.330i	−0.423447	−	0.423447i
$996$		0			0
$997$	909.188			0.911924			0.455962	−	0.889999i	$-0.349295\pi$
$997$	909.188			0.911924			0.455962	+	0.889999i	$0.349295\pi$
$998$		0			0
$999$	102.449	+	102.449i	0.102551	+	0.102551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.3.g.a.5.1	✓	6
3.2	odd	2		468.3.m.c.109.3		6
4.3	odd	2		208.3.t.d.161.3		6
5.2	odd	4		1300.3.k.a.1149.3		6
5.3	odd	4		1300.3.k.b.1149.1		6
5.4	even	2		1300.3.t.a.1201.3		6
13.5	odd	4		676.3.g.b.437.1		6
13.8	odd	4	inner	52.3.g.a.21.1	yes	6
13.12	even	2		676.3.g.b.577.1		6
39.8	even	4		468.3.m.c.73.3		6
52.47	even	4		208.3.t.d.177.3		6
65.8	even	4		1300.3.k.a.749.1		6
65.34	odd	4		1300.3.t.a.801.3		6
65.47	even	4		1300.3.k.b.749.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.3.g.a.5.1	✓	6	1.1	even	1	trivial
52.3.g.a.21.1	yes	6	13.8	odd	4	inner
208.3.t.d.161.3		6	4.3	odd	2
208.3.t.d.177.3		6	52.47	even	4
468.3.m.c.73.3		6	39.8	even	4
468.3.m.c.109.3		6	3.2	odd	2
676.3.g.b.437.1		6	13.5	odd	4
676.3.g.b.577.1		6	13.12	even	2
1300.3.k.a.749.1		6	65.8	even	4
1300.3.k.a.1149.3		6	5.2	odd	4
1300.3.k.b.749.3		6	65.47	even	4
1300.3.k.b.1149.1		6	5.3	odd	4
1300.3.t.a.801.3		6	65.34	odd	4
1300.3.t.a.1201.3		6	5.4	even	2

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	52.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-4.43242 q^{3} +(-6.03938 + 6.03938i) q^{5} +(0.393041 + 0.393041i) q^{7} +10.6463 q^{9} +O(q^{10})\)	\(q-4.43242 q^{3} +(-6.03938 + 6.03938i) q^{5} +(0.393041 + 0.393041i) q^{7} +10.6463 q^{9} +(-11.8648 - 11.8648i) q^{11} +(8.90422 + 9.47180i) q^{13} +(26.7691 - 26.7691i) q^{15} +10.0833i q^{17} +(-8.56758 + 8.56758i) q^{19} +(-1.74212 - 1.74212i) q^{21} +30.0788i q^{23} -47.9482i q^{25} -7.29726 q^{27} -26.6733 q^{29} +(-3.00458 + 3.00458i) q^{31} +(52.5899 + 52.5899i) q^{33} -4.74744 q^{35} +(-14.0394 - 14.0394i) q^{37} +(-39.4672 - 41.9830i) q^{39} +(-22.4548 + 22.4548i) q^{41} +49.8826i q^{43} +(-64.2973 + 64.2973i) q^{45} +(-24.8300 - 24.8300i) q^{47} -48.6910i q^{49} -44.6936i q^{51} +65.8084 q^{53} +143.312 q^{55} +(37.9751 - 37.9751i) q^{57} +(7.62399 + 7.62399i) q^{59} +89.6169 q^{61} +(4.18444 + 4.18444i) q^{63} +(-110.980 - 3.42784i) q^{65} +(-12.3806 + 12.3806i) q^{67} -133.322i q^{69} +(-7.79853 + 7.79853i) q^{71} +(-36.2093 - 36.2093i) q^{73} +212.526i q^{75} -9.32673i q^{77} -7.20475 q^{79} -63.4725 q^{81} +(-53.9095 + 53.9095i) q^{83} +(-60.8971 - 60.8971i) q^{85} +118.227 q^{87} +(70.0269 + 70.0269i) q^{89} +(-0.223083 + 7.22252i) q^{91} +(13.3176 - 13.3176i) q^{93} -103.486i q^{95} +(-124.696 + 124.696i) q^{97} +(-126.317 - 126.317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} + 6 q^{7} + 30 q^{9}+O(q^{10}) \) 6 * q - 6 * q^5 + 6 * q^7 + 30 * q^9	\( 6 q - 6 q^{5} + 6 q^{7} + 30 q^{9} - 18 q^{11} - 30 q^{13} + 24 q^{15} - 78 q^{19} - 60 q^{21} + 36 q^{27} + 60 q^{29} - 6 q^{31} + 168 q^{33} + 240 q^{35} - 54 q^{37} - 192 q^{39} + 66 q^{41} - 306 q^{45} - 114 q^{47} + 228 q^{53} + 132 q^{55} - 84 q^{57} + 186 q^{59} + 204 q^{61} - 282 q^{63} - 342 q^{65} + 78 q^{67} - 210 q^{71} - 222 q^{73} - 60 q^{79} - 18 q^{81} + 78 q^{83} + 192 q^{85} + 552 q^{87} + 234 q^{89} + 30 q^{91} + 324 q^{93} - 354 q^{97} - 18 q^{99}+O(q^{100}) \) 6 * q - 6 * q^5 + 6 * q^7 + 30 * q^9 - 18 * q^11 - 30 * q^13 + 24 * q^15 - 78 * q^19 - 60 * q^21 + 36 * q^27 + 60 * q^29 - 6 * q^31 + 168 * q^33 + 240 * q^35 - 54 * q^37 - 192 * q^39 + 66 * q^41 - 306 * q^45 - 114 * q^47 + 228 * q^53 + 132 * q^55 - 84 * q^57 + 186 * q^59 + 204 * q^61 - 282 * q^63 - 342 * q^65 + 78 * q^67 - 210 * q^71 - 222 * q^73 - 60 * q^79 - 18 * q^81 + 78 * q^83 + 192 * q^85 + 552 * q^87 + 234 * q^89 + 30 * q^91 + 324 * q^93 - 354 * q^97 - 18 * q^99

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