LMFDB - Embedded newform 260.2.bk.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(33,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bk (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.33
Dual form			260.2.bk.a.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.133975i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.133975i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-2.36603 + 1.36603i) q^{9} +(-1.13397 - 4.23205i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(1.13397 + 0.232051i) q^{15} +(-0.232051 + 0.866025i) q^{17} +(-2.86603 - 0.767949i) q^{19} +(0.901924 - 0.901924i) q^{21} +(-0.0358984 - 0.133975i) q^{23} +(3.00000 + 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(-1.50000 - 0.866025i) q^{29} +(-5.19615 - 5.19615i) q^{31} +(1.13397 + 1.96410i) q^{33} +(5.50000 - 0.330127i) q^{35} +(1.33013 + 0.767949i) q^{37} +(0.598076 - 1.76795i) q^{39} +(9.33013 - 2.50000i) q^{41} +(-5.96410 - 1.59808i) q^{43} +(6.09808 - 0.366025i) q^{45} +10.9282i q^{47} +(-0.464102 + 0.803848i) q^{49} -0.464102i q^{51} +(2.46410 + 2.46410i) q^{53} +(-1.96410 + 9.59808i) q^{55} +1.53590 q^{57} +(2.33013 - 8.69615i) q^{59} +(4.50000 + 7.79423i) q^{61} +(3.36603 - 5.83013i) q^{63} +(7.00000 - 4.00000i) q^{65} +(6.13397 - 10.6244i) q^{67} +(0.0358984 + 0.0621778i) q^{69} +(0.598076 - 2.23205i) q^{71} -14.9282 q^{73} +(-2.03590 - 1.59808i) q^{75} +(7.63397 + 7.63397i) q^{77} -0.535898i q^{79} +(3.33013 - 5.76795i) q^{81} +2.92820i q^{83} +(1.33013 - 1.50000i) q^{85} +(0.866025 + 0.232051i) q^{87} +(-14.7942 + 3.96410i) q^{89} +(0.571797 - 8.86603i) q^{91} +(3.29423 + 1.90192i) q^{93} +(4.96410 + 4.40192i) q^{95} +(3.86603 + 6.69615i) q^{97} +(8.46410 + 8.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9	$ 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9} - 8 q^{11} - 8 q^{13} + 8 q^{15} + 6 q^{17} - 8 q^{19} + 14 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} - 6 q^{29} + 8 q^{33} + 22 q^{35} - 12 q^{37} - 8 q^{39} + 20 q^{41} - 10 q^{43} + 14 q^{45} + 12 q^{49} - 4 q^{53} + 6 q^{55} + 20 q^{57} - 8 q^{59} + 18 q^{61} + 10 q^{63} + 28 q^{65} + 28 q^{67} + 14 q^{69} - 8 q^{71} - 32 q^{73} - 22 q^{75} + 34 q^{77} - 4 q^{81} - 12 q^{85} - 28 q^{89} + 30 q^{91} - 18 q^{93} + 6 q^{95} + 12 q^{97} + 20 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9 - 8 * q^11 - 8 * q^13 + 8 * q^15 + 6 * q^17 - 8 * q^19 + 14 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 - 6 * q^29 + 8 * q^33 + 22 * q^35 - 12 * q^37 - 8 * q^39 + 20 * q^41 - 10 * q^43 + 14 * q^45 + 12 * q^49 - 4 * q^53 + 6 * q^55 + 20 * q^57 - 8 * q^59 + 18 * q^61 + 10 * q^63 + 28 * q^65 + 28 * q^67 + 14 * q^69 - 8 * q^71 - 32 * q^73 - 22 * q^75 + 34 * q^77 - 4 * q^81 - 12 * q^85 - 28 * q^89 + 30 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.133975i	−0.288675	+	0.0773503i	−0.400251	−	0.916406i	$-0.631077\pi$
$3$	−0.500000	+	0.133975i	−0.288675	+	0.0773503i	0.111576	+	0.993756i	$0.464410\pi$
$4$		0			0
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	−2.13397	+	1.23205i	−0.806567	+	0.465671i	−0.845762	−	0.533560i	$-0.820854\pi$
$7$	−2.13397	+	1.23205i	−0.806567	+	0.465671i	0.0391956	+	0.999232i	$0.487520\pi$
$8$		0			0
$9$	−2.36603	+	1.36603i	−0.788675	+	0.455342i
$10$		0			0
$11$	−1.13397	−	4.23205i	−0.341906	−	1.27601i	−0.896185	−	0.443680i	$-0.853673\pi$
$11$	−1.13397	−	4.23205i	−0.341906	−	1.27601i	0.554279	−	0.832331i	$-0.312994\pi$
$12$		0			0
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$		0			0
$15$	1.13397	+	0.232051i	0.292791	+	0.0599153i
$16$		0			0
$17$	−0.232051	+	0.866025i	−0.0562806	+	0.210042i	−0.988340	−	0.152264i	$-0.951344\pi$
$17$	−0.232051	+	0.866025i	−0.0562806	+	0.210042i	0.932059	+	0.362306i	$0.118010\pi$
$18$		0			0
$19$	−2.86603	−	0.767949i	−0.657511	−	0.176180i	−0.0853887	−	0.996348i	$-0.527213\pi$
$19$	−2.86603	−	0.767949i	−0.657511	−	0.176180i	−0.572123	+	0.820168i	$0.693880\pi$
$20$		0			0
$21$	0.901924	−	0.901924i	0.196816	−	0.196816i
$22$		0			0
$23$	−0.0358984	−	0.133975i	−0.00748533	−	0.0279356i	0.962082	−	0.272760i	$-0.0879364\pi$
$23$	−0.0358984	−	0.133975i	−0.00748533	−	0.0279356i	−0.969567	+	0.244824i	$0.921270\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$	2.09808	−	2.09808i	0.403775	−	0.403775i
$28$		0			0
$29$	−1.50000	−	0.866025i	−0.278543	−	0.160817i	0.354221	−	0.935162i	$-0.384746\pi$
$29$	−1.50000	−	0.866025i	−0.278543	−	0.160817i	−0.632764	+	0.774345i	$0.718080\pi$
$30$		0			0
$31$	−5.19615	−	5.19615i	−0.933257	−	0.933257i	0.0646514	−	0.997908i	$-0.479406\pi$
$31$	−5.19615	−	5.19615i	−0.933257	−	0.933257i	−0.997908	+	0.0646514i	$0.979406\pi$
$32$		0			0
$33$	1.13397	+	1.96410i	0.197400	+	0.341906i
$34$		0			0
$35$	5.50000	−	0.330127i	0.929670	−	0.0558017i
$36$		0			0
$37$	1.33013	+	0.767949i	0.218672	+	0.126250i	0.605335	−	0.795971i	$-0.293039\pi$
$37$	1.33013	+	0.767949i	0.218672	+	0.126250i	−0.386663	+	0.922221i	$0.626372\pi$
$38$		0			0
$39$	0.598076	−	1.76795i	0.0957688	−	0.283098i
$40$		0			0
$41$	9.33013	−	2.50000i	1.45712	−	0.390434i	0.558627	−	0.829419i	$-0.311329\pi$
$41$	9.33013	−	2.50000i	1.45712	−	0.390434i	0.898494	+	0.438985i	$0.144662\pi$
$42$		0			0
$43$	−5.96410	−	1.59808i	−0.909517	−	0.243704i	−0.226418	−	0.974030i	$-0.572702\pi$
$43$	−5.96410	−	1.59808i	−0.909517	−	0.243704i	−0.683099	+	0.730326i	$0.739368\pi$
$44$		0			0
$45$	6.09808	−	0.366025i	0.909048	−	0.0545638i
$46$		0			0
$47$			10.9282i			1.59404i	0.603951	+	0.797021i	$0.293592\pi$
$47$			10.9282i			1.59404i	−0.603951	+	0.797021i	$0.706408\pi$
$48$		0			0
$49$	−0.464102	+	0.803848i	−0.0663002	+	0.114835i
$50$		0			0
$51$		−	0.464102i		−	0.0649872i
$52$		0			0
$53$	2.46410	+	2.46410i	0.338470	+	0.338470i	0.855791	−	0.517321i	$-0.173071\pi$
$53$	2.46410	+	2.46410i	0.338470	+	0.338470i	−0.517321	+	0.855791i	$0.673071\pi$
$54$		0			0
$55$	−1.96410	+	9.59808i	−0.264839	+	1.29420i
$56$		0			0
$57$	1.53590			0.203435
$58$		0			0
$59$	2.33013	−	8.69615i	0.303357	−	1.13214i	−0.630994	−	0.775788i	$-0.717353\pi$
$59$	2.33013	−	8.69615i	0.303357	−	1.13214i	0.934351	−	0.356355i	$-0.115981\pi$
$60$		0			0
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	0.995914	+	0.0903080i	$0.0287851\pi$
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	−0.419748	+	0.907641i	$0.637882\pi$
$62$		0			0
$63$	3.36603	−	5.83013i	0.424079	−	0.734527i
$64$		0			0
$65$	7.00000	−	4.00000i	0.868243	−	0.496139i
$66$		0			0
$67$	6.13397	−	10.6244i	0.749384	−	1.29797i	−0.198734	−	0.980053i	$-0.563683\pi$
$67$	6.13397	−	10.6244i	0.749384	−	1.29797i	0.948118	−	0.317918i	$-0.102984\pi$
$68$		0			0
$69$	0.0358984	+	0.0621778i	0.00432166	+	0.00748533i
$70$		0			0
$71$	0.598076	−	2.23205i	0.0709786	−	0.264896i	−0.921313	−	0.388822i	$-0.872882\pi$
$71$	0.598076	−	2.23205i	0.0709786	−	0.264896i	0.992291	+	0.123927i	$0.0395487\pi$
$72$		0			0
$73$	−14.9282			−1.74721			−0.873607	−	0.486632i	$-0.838225\pi$
$73$	−14.9282			−1.74721			−0.873607	+	0.486632i	$0.838225\pi$
$74$		0			0
$75$	−2.03590	−	1.59808i	−0.235085	−	0.184530i
$76$		0			0
$77$	7.63397	+	7.63397i	0.869972	+	0.869972i
$78$		0			0
$79$		−	0.535898i		−	0.0602933i	−0.999545	−	0.0301466i	$-0.990403\pi$
$79$		−	0.535898i		−	0.0602933i	0.999545	−	0.0301466i	$-0.00959743\pi$
$80$		0			0
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$		0			0
$83$			2.92820i			0.321412i	0.987002	+	0.160706i	$0.0513771\pi$
$83$			2.92820i			0.321412i	−0.987002	+	0.160706i	$0.948623\pi$
$84$		0			0
$85$	1.33013	−	1.50000i	0.144273	−	0.162698i
$86$		0			0
$87$	0.866025	+	0.232051i	0.0928477	+	0.0248785i
$88$		0			0
$89$	−14.7942	+	3.96410i	−1.56819	+	0.420194i	−0.935243	−	0.354005i	$-0.884819\pi$
$89$	−14.7942	+	3.96410i	−1.56819	+	0.420194i	−0.632942	+	0.774199i	$0.718153\pi$
$90$		0			0
$91$	0.571797	−	8.86603i	0.0599406	−	0.929412i
$92$		0			0
$93$	3.29423	+	1.90192i	0.341596	+	0.197220i
$94$		0			0
$95$	4.96410	+	4.40192i	0.509306	+	0.451628i
$96$		0			0
$97$	3.86603	+	6.69615i	0.392535	+	0.679891i	0.992783	−	0.119923i	$-0.0382647\pi$
$97$	3.86603	+	6.69615i	0.392535	+	0.679891i	−0.600248	+	0.799814i	$0.704931\pi$
$98$		0			0
$99$	8.46410	+	8.46410i	0.850674	+	0.850674i
$100$		0			0
$101$	−14.8923	−	8.59808i	−1.48184	−	0.855541i	−0.482052	−	0.876143i	$-0.660108\pi$
$101$	−14.8923	−	8.59808i	−1.48184	−	0.855541i	−0.999788	+	0.0206021i	$0.993442\pi$
$102$		0			0
$103$	−11.1962	+	11.1962i	−1.10319	+	1.10319i	−0.109166	+	0.994024i	$0.534818\pi$
$103$	−11.1962	+	11.1962i	−1.10319	+	1.10319i	−0.994024	+	0.109166i	$0.965182\pi$
$104$		0			0
$105$	−2.70577	+	0.901924i	−0.264056	+	0.0880187i
$106$		0			0
$107$	−1.96410	−	7.33013i	−0.189877	−	0.708630i	−0.993534	−	0.113537i	$-0.963782\pi$
$107$	−1.96410	−	7.33013i	−0.189877	−	0.708630i	0.803657	−	0.595093i	$-0.202885\pi$
$108$		0			0
$109$	−3.53590	+	3.53590i	−0.338678	+	0.338678i	−0.855869	−	0.517192i	$-0.826977\pi$
$109$	−3.53590	+	3.53590i	−0.338678	+	0.338678i	0.517192	+	0.855869i	$0.326977\pi$
$110$		0			0
$111$	−0.767949	−	0.205771i	−0.0728905	−	0.0195310i
$112$		0			0
$113$	0.767949	−	2.86603i	0.0722426	−	0.269613i	−0.920351	−	0.391093i	$-0.872097\pi$
$113$	0.767949	−	2.86603i	0.0722426	−	0.269613i	0.992594	+	0.121480i	$0.0387639\pi$
$114$		0			0
$115$	−0.0621778	+	0.303848i	−0.00579811	+	0.0283339i
$116$		0			0
$117$	0.633975	−	9.83013i	0.0586110	−	0.908796i
$118$		0			0
$119$	−0.571797	−	2.13397i	−0.0524165	−	0.195621i
$120$		0			0
$121$	−7.09808	+	4.09808i	−0.645280	+	0.372552i
$122$		0			0
$123$	−4.33013	+	2.50000i	−0.390434	+	0.225417i
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	−19.8923	+	5.33013i	−1.76516	+	0.472972i	−0.987752	−	0.156029i	$-0.950131\pi$
$127$	−19.8923	+	5.33013i	−1.76516	+	0.472972i	−0.777404	+	0.629001i	$0.783464\pi$
$128$		0			0
$129$	3.19615			0.281406
$130$		0			0
$131$	5.85641			0.511677			0.255838	−	0.966720i	$-0.417649\pi$
$131$	5.85641			0.511677			0.255838	+	0.966720i	$0.417649\pi$
$132$		0			0
$133$	7.06218	−	1.89230i	0.612368	−	0.164084i
$134$		0			0
$135$	−6.29423	+	2.09808i	−0.541721	+	0.180574i
$136$		0			0
$137$	−12.4019	+	7.16025i	−1.05957	+	0.611742i	−0.925313	−	0.379205i	$-0.876198\pi$
$137$	−12.4019	+	7.16025i	−1.05957	+	0.611742i	−0.134255	+	0.990947i	$0.542864\pi$
$138$		0			0
$139$	−4.50000	+	2.59808i	−0.381685	+	0.220366i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−4.50000	+	2.59808i	−0.381685	+	0.220366i	0.296866	+	0.954919i	$0.404058\pi$
$140$		0			0
$141$	−1.46410	−	5.46410i	−0.123300	−	0.460160i
$142$		0			0
$143$	14.9641	+	5.06218i	1.25136	+	0.423321i
$144$		0			0
$145$	2.13397	+	3.23205i	0.177217	+	0.268407i
$146$		0			0
$147$	0.124356	−	0.464102i	0.0102567	−	0.0382785i
$148$		0			0
$149$	−3.33013	−	0.892305i	−0.272815	−	0.0731005i	0.119818	−	0.992796i	$-0.461769\pi$
$149$	−3.33013	−	0.892305i	−0.272815	−	0.0731005i	−0.392633	+	0.919695i	$0.628436\pi$
$150$		0			0
$151$	−0.267949	+	0.267949i	−0.0218054	+	0.0218054i	−0.717925	−	0.696120i	$-0.754908\pi$
$151$	−0.267949	+	0.267949i	−0.0218054	+	0.0218054i	0.696120	+	0.717925i	$0.254908\pi$
$152$		0			0
$153$	−0.633975	−	2.36603i	−0.0512538	−	0.191282i
$154$		0			0
$155$	5.19615	+	15.5885i	0.417365	+	1.25210i
$156$		0			0
$157$	6.46410	−	6.46410i	0.515891	−	0.515891i	−0.400434	−	0.916326i	$-0.631141\pi$
$157$	6.46410	−	6.46410i	0.515891	−	0.515891i	0.916326	+	0.400434i	$0.131141\pi$
$158$		0			0
$159$	−1.56218	−	0.901924i	−0.123889	−	0.0715272i
$160$		0			0
$161$	0.241670	+	0.241670i	0.0190462	+	0.0190462i
$162$		0			0
$163$	−1.59808	−	2.76795i	−0.125171	−	0.216803i	0.796629	−	0.604469i	$-0.206615\pi$
$163$	−1.59808	−	2.76795i	−0.125171	−	0.216803i	−0.921800	+	0.387666i	$0.873281\pi$
$164$		0			0
$165$	−0.303848	−	5.06218i	−0.0236545	−	0.394090i
$166$		0			0
$167$	−15.9904	−	9.23205i	−1.23737	−	0.714398i	−0.268816	−	0.963191i	$-0.586632\pi$
$167$	−15.9904	−	9.23205i	−1.23737	−	0.714398i	−0.968556	+	0.248794i	$0.919966\pi$
$168$		0			0
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$		0			0
$171$	7.83013	−	2.09808i	0.598785	−	0.160444i
$172$		0			0
$173$	−2.76795	−	0.741670i	−0.210443	−	0.0563881i	0.152057	−	0.988372i	$-0.451410\pi$
$173$	−2.76795	−	0.741670i	−0.210443	−	0.0563881i	−0.362500	+	0.931984i	$0.618077\pi$
$174$		0			0
$175$	−11.3301	−	4.83975i	−0.856477	−	0.365850i
$176$		0			0
$177$			4.66025i			0.350286i
$178$		0			0
$179$	6.96410	−	12.0622i	0.520521	−	0.901570i	−0.479194	−	0.877709i	$-0.659071\pi$
$179$	6.96410	−	12.0622i	0.520521	−	0.901570i	0.999715	−	0.0238604i	$-0.00759573\pi$
$180$		0			0
$181$			22.9282i			1.70424i	0.523347	+	0.852120i	$0.324683\pi$
$181$			22.9282i			1.70424i	−0.523347	+	0.852120i	$0.675317\pi$
$182$		0			0
$183$	−3.29423	−	3.29423i	−0.243516	−	0.243516i
$184$		0			0
$185$	−1.89230	−	2.86603i	−0.139125	−	0.210714i
$186$		0			0
$187$	3.92820			0.287259
$188$		0			0
$189$	−1.89230	+	7.06218i	−0.137645	+	0.513698i
$190$		0			0
$191$	7.50000	+	12.9904i	0.542681	+	0.939951i	0.998749	+	0.0500060i	$0.0159241\pi$
$191$	7.50000	+	12.9904i	0.542681	+	0.939951i	−0.456068	+	0.889945i	$0.650743\pi$
$192$		0			0
$193$	12.7942	−	22.1603i	0.920949	−	1.59513i	0.122998	−	0.992407i	$-0.460749\pi$
$193$	12.7942	−	22.1603i	0.920949	−	1.59513i	0.797950	−	0.602723i	$-0.205918\pi$
$194$		0			0
$195$	−2.96410	+	2.93782i	−0.212264	+	0.210382i
$196$		0			0
$197$	2.13397	−	3.69615i	0.152039	−	0.263340i	−0.779938	−	0.625857i	$-0.784749\pi$
$197$	2.13397	−	3.69615i	0.152039	−	0.263340i	0.931977	+	0.362517i	$0.118083\pi$
$198$		0			0
$199$	9.42820	+	16.3301i	0.668348	+	1.15761i	0.978366	+	0.206881i	$0.0663314\pi$
$199$	9.42820	+	16.3301i	0.668348	+	1.15761i	−0.310018	+	0.950731i	$0.600335\pi$
$200$		0			0
$201$	−1.64359	+	6.13397i	−0.115930	+	0.432657i
$202$		0			0
$203$	4.26795			0.299551
$204$		0			0
$205$	−21.1603	−	4.33013i	−1.47790	−	0.302429i
$206$		0			0
$207$	0.267949	+	0.267949i	0.0186238	+	0.0186238i
$208$		0			0
$209$			13.0000i			0.899229i
$210$		0			0
$211$	−2.96410	+	5.13397i	−0.204057	+	0.353437i	−0.949832	−	0.312761i	$-0.898746\pi$
$211$	−2.96410	+	5.13397i	−0.204057	+	0.353437i	0.745775	+	0.666198i	$0.232080\pi$
$212$		0			0
$213$			1.19615i			0.0819590i
$214$		0			0
$215$	10.3301	+	9.16025i	0.704509	+	0.624724i
$216$		0			0
$217$	17.4904	+	4.68653i	1.18732	+	0.318143i
$218$		0			0
$219$	7.46410	−	2.00000i	0.504377	−	0.135147i
$220$		0			0
$221$	−2.13397	−	2.42820i	−0.143547	−	0.163339i
$222$		0			0
$223$	−1.33013	−	0.767949i	−0.0890719	−	0.0514257i	0.454802	−	0.890592i	$-0.349710\pi$
$223$	−1.33013	−	0.767949i	−0.0890719	−	0.0514257i	−0.543874	+	0.839167i	$0.683043\pi$
$224$		0			0
$225$	−12.5622	−	5.36603i	−0.837479	−	0.357735i
$226$		0			0
$227$	1.59808	+	2.76795i	0.106068	+	0.183715i	0.914174	−	0.405322i	$-0.132841\pi$
$227$	1.59808	+	2.76795i	0.106068	+	0.183715i	−0.808106	+	0.589037i	$0.799507\pi$
$228$		0			0
$229$	0.0717968	+	0.0717968i	0.00474446	+	0.00474446i	0.709475	−	0.704731i	$-0.248932\pi$
$229$	0.0717968	+	0.0717968i	0.00474446	+	0.00474446i	−0.704731	+	0.709475i	$0.748932\pi$
$230$		0			0
$231$	−4.83975	−	2.79423i	−0.318432	−	0.183847i
$232$		0			0
$233$	12.8564	−	12.8564i	0.842251	−	0.842251i	−0.146900	−	0.989151i	$-0.546930\pi$
$233$	12.8564	−	12.8564i	0.842251	−	0.842251i	0.989151	+	0.146900i	$0.0469296\pi$
$234$		0			0
$235$	10.9282	−	21.8564i	0.712877	−	1.42575i
$236$		0			0
$237$	0.0717968	+	0.267949i	0.00466370	+	0.0174052i
$238$		0			0
$239$	16.6603	−	16.6603i	1.07766	−	1.07766i	0.0809436	−	0.996719i	$-0.474207\pi$
$239$	16.6603	−	16.6603i	1.07766	−	1.07766i	0.996719	−	0.0809436i	$-0.0257934\pi$
$240$		0			0
$241$	11.3301	+	3.03590i	0.729838	+	0.195559i	0.604557	−	0.796562i	$-0.293350\pi$
$241$	11.3301	+	3.03590i	0.729838	+	0.195559i	0.125281	+	0.992121i	$0.460017\pi$
$242$		0			0
$243$	−3.19615	+	11.9282i	−0.205033	+	0.765195i
$244$		0			0
$245$	1.73205	−	1.14359i	0.110657	−	0.0730615i
$246$		0			0
$247$	8.03590	−	7.06218i	0.511312	−	0.449356i
$248$		0			0
$249$	−0.392305	−	1.46410i	−0.0248613	−	0.0927837i
$250$		0			0
$251$	−15.3564	+	8.86603i	−0.969288	+	0.559619i	−0.899019	−	0.437910i	$-0.855719\pi$
$251$	−15.3564	+	8.86603i	−0.969288	+	0.559619i	−0.0702687	+	0.997528i	$0.522386\pi$
$252$		0			0
$253$	−0.526279	+	0.303848i	−0.0330869	+	0.0191027i
$254$		0			0
$255$	−0.464102	+	0.928203i	−0.0290632	+	0.0581263i
$256$		0			0
$257$	21.6244	−	5.79423i	1.34889	−	0.361434i	0.489165	−	0.872191i	$-0.337302\pi$
$257$	21.6244	−	5.79423i	1.34889	−	0.361434i	0.859725	+	0.510757i	$0.170635\pi$
$258$		0			0
$259$	−3.78461			−0.235164
$260$		0			0
$261$	4.73205			0.292907
$262$		0			0
$263$	13.8923	−	3.72243i	0.856636	−	0.229535i	0.196336	−	0.980537i	$-0.437096\pi$
$263$	13.8923	−	3.72243i	0.856636	−	0.229535i	0.660300	+	0.751002i	$0.270429\pi$
$264$		0			0
$265$	−2.46410	−	7.39230i	−0.151369	−	0.454106i
$266$		0			0
$267$	6.86603	−	3.96410i	0.420194	−	0.242599i
$268$		0			0
$269$	15.8205	−	9.13397i	0.964593	−	0.556908i	0.0670097	−	0.997752i	$-0.478654\pi$
$269$	15.8205	−	9.13397i	0.964593	−	0.556908i	0.897584	+	0.440844i	$0.145321\pi$
$270$		0			0
$271$	4.33013	+	16.1603i	0.263036	+	0.981666i	0.963441	+	0.267920i	$0.0863362\pi$
$271$	4.33013	+	16.1603i	0.263036	+	0.981666i	−0.700405	+	0.713746i	$0.746997\pi$
$272$		0			0
$273$	0.901924	+	4.50962i	0.0545869	+	0.272935i
$274$		0			0
$275$	13.5263	−	17.2321i	0.815665	−	1.03913i
$276$		0			0
$277$	−2.76795	+	10.3301i	−0.166310	+	0.620677i	0.831560	+	0.555436i	$0.187448\pi$
$277$	−2.76795	+	10.3301i	−0.166310	+	0.620677i	−0.997869	+	0.0652416i	$0.979218\pi$
$278$		0			0
$279$	19.3923	+	5.19615i	1.16099	+	0.311086i
$280$		0			0
$281$	−16.4641	+	16.4641i	−0.982166	+	0.982166i	−0.999844	−	0.0176778i	$-0.994373\pi$
$281$	−16.4641	+	16.4641i	−0.982166	+	0.982166i	0.0176778	+	0.999844i	$0.494373\pi$
$282$		0			0
$283$	7.96410	+	29.7224i	0.473417	+	1.76682i	0.627354	+	0.778735i	$0.284138\pi$
$283$	7.96410	+	29.7224i	0.473417	+	1.76682i	−0.153937	+	0.988081i	$0.549195\pi$
$284$		0			0
$285$	−3.07180	−	1.53590i	−0.181958	−	0.0909788i
$286$		0			0
$287$	−16.8301	+	16.8301i	−0.993451	+	0.993451i
$288$		0			0
$289$	14.0263	+	8.09808i	0.825075	+	0.476357i
$290$		0			0
$291$	−2.83013	−	2.83013i	−0.165905	−	0.165905i
$292$		0			0
$293$	−10.2583	−	17.7679i	−0.599298	−	1.03801i	−0.992925	−	0.118744i	$-0.962113\pi$
$293$	−10.2583	−	17.7679i	−0.599298	−	1.03801i	0.393627	−	0.919270i	$-0.371220\pi$
$294$		0			0
$295$	−13.3564	+	15.0622i	−0.777640	+	0.876954i
$296$		0			0
$297$	−11.2583	−	6.50000i	−0.653275	−	0.377168i
$298$		0			0
$299$	0.473721	+	0.160254i	0.0273960	+	0.00926773i
$300$		0			0
$301$	14.6962	−	3.93782i	0.847072	−	0.226972i
$302$		0			0
$303$	8.59808	+	2.30385i	0.493947	+	0.132353i
$304$		0			0
$305$	−1.20577	−	20.0885i	−0.0690423	−	1.15026i
$306$		0			0
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	4.09808	−	7.09808i	0.233131	−	0.403795i
$310$		0			0
$311$		−	3.46410i		−	0.196431i	−0.995165	−	0.0982156i	$-0.968687\pi$
$311$		−	3.46410i		−	0.196431i	0.995165	−	0.0982156i	$-0.0313135\pi$
$312$		0			0
$313$	−5.53590	−	5.53590i	−0.312907	−	0.312907i	0.533127	−	0.846035i	$-0.321017\pi$
$313$	−5.53590	−	5.53590i	−0.312907	−	0.312907i	−0.846035	+	0.533127i	$0.821017\pi$
$314$		0			0
$315$	−12.5622	+	8.29423i	−0.707799	+	0.467327i
$316$		0			0
$317$	−18.9282			−1.06311			−0.531557	−	0.847023i	$-0.678393\pi$
$317$	−18.9282			−1.06311			−0.531557	+	0.847023i	$0.678393\pi$
$318$		0			0
$319$	−1.96410	+	7.33013i	−0.109969	+	0.410408i
$320$		0			0
$321$	1.96410	+	3.40192i	0.109625	+	0.189877i
$322$		0			0
$323$	1.33013	−	2.30385i	0.0740102	−	0.128190i
$324$		0			0
$325$	−18.0000	+	1.00000i	−0.998460	+	0.0554700i
$326$		0			0
$327$	1.29423	−	2.24167i	0.0715710	−	0.123965i
$328$		0			0
$329$	−13.4641	−	23.3205i	−0.742300	−	1.28570i
$330$		0			0
$331$	4.45448	−	16.6244i	0.244841	−	0.913757i	−0.728623	−	0.684915i	$-0.759839\pi$
$331$	4.45448	−	16.6244i	0.244841	−	0.913757i	0.973464	−	0.228842i	$-0.0734940\pi$
$332$		0			0
$333$	−4.19615			−0.229948
$334$		0			0
$335$	−22.8923	+	15.1147i	−1.25074	+	0.825806i
$336$		0			0
$337$	−15.9282	−	15.9282i	−0.867665	−	0.867665i	0.124549	−	0.992213i	$-0.460252\pi$
$337$	−15.9282	−	15.9282i	−0.867665	−	0.867665i	−0.992213	+	0.124549i	$0.960252\pi$
$338$		0			0
$339$			1.53590i			0.0834185i
$340$		0			0
$341$	−16.0981	+	27.8827i	−0.871760	+	1.50993i
$342$		0			0
$343$		−	19.5359i		−	1.05484i
$344$		0			0
$345$	−0.00961894	−	0.160254i	−0.000517866	−	0.00862779i
$346$		0			0
$347$	−10.4282	−	2.79423i	−0.559815	−	0.150002i	−0.0321938	−	0.999482i	$-0.510249\pi$
$347$	−10.4282	−	2.79423i	−0.559815	−	0.150002i	−0.527621	+	0.849480i	$0.676916\pi$
$348$		0			0
$349$	−7.86603	+	2.10770i	−0.421059	+	0.112822i	−0.463126	−	0.886292i	$-0.653272\pi$
$349$	−7.86603	+	2.10770i	−0.421059	+	0.112822i	0.0420673	+	0.999115i	$0.486606\pi$
$350$		0			0
$351$	2.09808	+	10.4904i	0.111987	+	0.559935i
$352$		0			0
$353$	9.06218	+	5.23205i	0.482331	+	0.278474i	0.721387	−	0.692532i	$-0.243505\pi$
$353$	9.06218	+	5.23205i	0.482331	+	0.278474i	−0.239056	+	0.971006i	$0.576838\pi$
$354$		0			0
$355$	−3.42820	+	3.86603i	−0.181950	+	0.205187i
$356$		0			0
$357$	0.571797	+	0.990381i	0.0302627	+	0.0524165i
$358$		0			0
$359$	13.1962	+	13.1962i	0.696466	+	0.696466i	0.963647	−	0.267180i	$-0.0860919\pi$
$359$	13.1962	+	13.1962i	0.696466	+	0.696466i	−0.267180	+	0.963647i	$0.586092\pi$
$360$		0			0
$361$	−8.83013	−	5.09808i	−0.464744	−	0.268320i
$362$		0			0
$363$	3.00000	−	3.00000i	0.157459	−	0.157459i
$364$		0			0
$365$	29.8564	+	14.9282i	1.56276	+	0.781378i
$366$		0			0
$367$	−3.96410	−	14.7942i	−0.206924	−	0.772252i	−0.988854	−	0.148886i	$-0.952431\pi$
$367$	−3.96410	−	14.7942i	−0.206924	−	0.772252i	0.781930	−	0.623366i	$-0.214235\pi$
$368$		0			0
$369$	−18.6603	+	18.6603i	−0.971414	+	0.971414i
$370$		0			0
$371$	−8.29423	−	2.22243i	−0.430615	−	0.115383i
$372$		0			0
$373$	5.30385	−	19.7942i	0.274623	−	1.02491i	−0.681471	−	0.731845i	$-0.738659\pi$
$373$	5.30385	−	19.7942i	0.274623	−	1.02491i	0.956094	−	0.293061i	$-0.0946739\pi$
$374$		0			0
$375$	2.47372	+	5.23205i	0.127742	+	0.270182i
$376$		0			0
$377$	5.59808	−	2.76795i	0.288316	−	0.142557i
$378$		0			0
$379$	2.59808	+	9.69615i	0.133454	+	0.498058i	0.999999	−	0.00104063i	$-0.000331242\pi$
$379$	2.59808	+	9.69615i	0.133454	+	0.498058i	−0.866545	+	0.499099i	$0.833665\pi$
$380$		0			0
$381$	9.23205	−	5.33013i	0.472972	−	0.273071i
$382$		0			0
$383$	−22.1147	+	12.7679i	−1.13001	+	0.652412i	−0.943937	−	0.330124i	$-0.892909\pi$
$383$	−22.1147	+	12.7679i	−1.13001	+	0.652412i	−0.186073	+	0.982536i	$0.559576\pi$
$384$		0			0
$385$	−7.63397	−	22.9019i	−0.389063	−	1.16719i
$386$		0			0
$387$	16.2942	−	4.36603i	0.828282	−	0.221938i
$388$		0			0
$389$	−15.0718			−0.764170			−0.382085	−	0.924127i	$-0.624794\pi$
$389$	−15.0718			−0.764170			−0.382085	+	0.924127i	$0.624794\pi$
$390$		0			0
$391$	0.124356			0.00628894
$392$		0			0
$393$	−2.92820	+	0.784610i	−0.147708	+	0.0395783i
$394$		0			0
$395$	−0.535898	+	1.07180i	−0.0269640	+	0.0539279i
$396$		0			0
$397$	−9.86603	+	5.69615i	−0.495162	+	0.285882i	−0.726713	−	0.686941i	$-0.758953\pi$
$397$	−9.86603	+	5.69615i	−0.495162	+	0.285882i	0.231552	+	0.972823i	$0.425620\pi$
$398$		0			0
$399$	−3.27757	+	1.89230i	−0.164084	+	0.0947337i
$400$		0			0
$401$	2.66987	+	9.96410i	0.133327	+	0.497583i	0.999999	−	0.00129478i	$-0.000412141\pi$
$401$	2.66987	+	9.96410i	0.133327	+	0.497583i	−0.866672	+	0.498878i	$0.833745\pi$
$402$		0			0
$403$	25.9808	−	5.19615i	1.29419	−	0.258839i
$404$		0			0
$405$	−12.4282	+	8.20577i	−0.617562	+	0.407748i
$406$		0			0
$407$	1.74167	−	6.50000i	0.0863314	−	0.322193i
$408$		0			0
$409$	18.5263	+	4.96410i	0.916066	+	0.245459i	0.685903	−	0.727693i	$-0.259407\pi$
$409$	18.5263	+	4.96410i	0.916066	+	0.245459i	0.230163	+	0.973152i	$0.426074\pi$
$410$		0			0
$411$	5.24167	−	5.24167i	0.258553	−	0.258553i
$412$		0			0
$413$	5.74167	+	21.4282i	0.282529	+	1.05441i
$414$		0			0
$415$	2.92820	−	5.85641i	0.143740	−	0.287480i
$416$		0			0
$417$	1.90192	−	1.90192i	0.0931376	−	0.0931376i
$418$		0			0
$419$	−31.5000	−	18.1865i	−1.53888	−	0.888470i	−0.998905	−	0.0467865i	$-0.985102\pi$
$419$	−31.5000	−	18.1865i	−1.53888	−	0.888470i	−0.539971	−	0.841684i	$-0.681565\pi$
$420$		0			0
$421$	6.85641	+	6.85641i	0.334161	+	0.334161i	0.854164	−	0.520003i	$-0.174069\pi$
$421$	6.85641	+	6.85641i	0.334161	+	0.334161i	−0.520003	+	0.854164i	$0.674069\pi$
$422$		0			0
$423$	−14.9282	−	25.8564i	−0.725834	−	1.25718i
$424$		0			0
$425$	−4.16025	+	1.66987i	−0.201802	+	0.0810007i
$426$		0			0
$427$	−19.2058	−	11.0885i	−0.929432	−	0.536608i
$428$		0			0
$429$	−8.16025	−	0.526279i	−0.393981	−	0.0254090i
$430$		0			0
$431$	−23.2583	+	6.23205i	−1.12031	+	0.300187i	−0.771011	−	0.636822i	$-0.780249\pi$
$431$	−23.2583	+	6.23205i	−1.12031	+	0.300187i	−0.349304	+	0.937010i	$0.613582\pi$
$432$		0			0
$433$	32.5526	+	8.72243i	1.56438	+	0.419173i	0.934046	−	0.357154i	$-0.116253\pi$
$433$	32.5526	+	8.72243i	1.56438	+	0.419173i	0.630330	+	0.776327i	$0.282919\pi$
$434$		0			0
$435$	−1.50000	−	1.33013i	−0.0719195	−	0.0637747i
$436$		0			0
$437$			0.411543i			0.0196868i
$438$		0			0
$439$	0.0358984	−	0.0621778i	0.00171334	−	0.00296759i	−0.865167	−	0.501483i	$-0.832788\pi$
$439$	0.0358984	−	0.0621778i	0.00171334	−	0.00296759i	0.866881	+	0.498515i	$0.166121\pi$
$440$		0			0
$441$		−	2.53590i		−	0.120757i
$442$		0			0
$443$	−15.5885	−	15.5885i	−0.740630	−	0.740630i	0.232069	−	0.972699i	$-0.425450\pi$
$443$	−15.5885	−	15.5885i	−0.740630	−	0.740630i	−0.972699	+	0.232069i	$0.925450\pi$
$444$		0			0
$445$	33.5526	+	6.86603i	1.59054	+	0.325481i
$446$		0			0
$447$	1.78461			0.0844091
$448$		0			0
$449$	−5.20577	+	19.4282i	−0.245676	+	0.916874i	0.727367	+	0.686249i	$0.240744\pi$
$449$	−5.20577	+	19.4282i	−0.245676	+	0.916874i	−0.973043	+	0.230625i	$0.925923\pi$
$450$		0			0
$451$	−21.1603	−	36.6506i	−0.996397	−	1.72581i
$452$		0			0
$453$	0.0980762	−	0.169873i	0.00460802	−	0.00798133i
$454$		0			0
$455$	−10.0096	+	17.1603i	−0.469258	+	0.804485i
$456$		0			0
$457$	−6.79423	+	11.7679i	−0.317821	+	0.550481i	−0.980033	−	0.198835i	$-0.936284\pi$
$457$	−6.79423	+	11.7679i	−0.317821	+	0.550481i	0.662212	+	0.749316i	$0.269618\pi$
$458$		0			0
$459$	1.33013	+	2.30385i	0.0620850	+	0.107534i
$460$		0			0
$461$	0.813467	−	3.03590i	0.0378869	−	0.141396i	−0.944392	−	0.328823i	$-0.893348\pi$
$461$	0.813467	−	3.03590i	0.0378869	−	0.141396i	0.982279	+	0.187427i	$0.0600148\pi$
$462$		0			0
$463$	−21.6077			−1.00419			−0.502097	−	0.864811i	$-0.667438\pi$
$463$	−21.6077			−1.00419			−0.502097	+	0.864811i	$0.667438\pi$
$464$		0			0
$465$	−4.68653	−	7.09808i	−0.217333	−	0.329165i
$466$		0			0
$467$	16.6603	+	16.6603i	0.770945	+	0.770945i	0.978272	−	0.207327i	$-0.0664764\pi$
$467$	16.6603	+	16.6603i	0.770945	+	0.770945i	−0.207327	+	0.978272i	$0.566476\pi$
$468$		0			0
$469$			30.2295i			1.39587i
$470$		0			0
$471$	−2.36603	+	4.09808i	−0.109021	+	0.188829i
$472$		0			0
$473$			27.0526i			1.24388i
$474$		0			0
$475$	−5.52628	−	13.7679i	−0.253563	−	0.631717i
$476$		0			0
$477$	−9.19615	−	2.46410i	−0.421063	−	0.112823i
$478$		0			0
$479$	−3.13397	+	0.839746i	−0.143195	+	0.0383690i	−0.329705	−	0.944084i	$-0.606949\pi$
$479$	−3.13397	+	0.839746i	−0.143195	+	0.0383690i	0.186510	+	0.982453i	$0.440282\pi$
$480$		0			0
$481$	−4.96410	+	2.45448i	−0.226344	+	0.111915i
$482$		0			0
$483$	−0.153212	−	0.0884573i	−0.00697141	−	0.00402495i
$484$		0			0
$485$	−1.03590	−	17.2583i	−0.0470377	−	0.783660i
$486$		0			0
$487$	−0.794229	−	1.37564i	−0.0359899	−	0.0623364i	0.847469	−	0.530844i	$-0.178125\pi$
$487$	−0.794229	−	1.37564i	−0.0359899	−	0.0623364i	−0.883459	+	0.468508i	$0.844792\pi$
$488$		0			0
$489$	1.16987	+	1.16987i	0.0529035	+	0.0529035i
$490$		0			0
$491$	5.89230	+	3.40192i	0.265916	+	0.153527i	0.627030	−	0.778995i	$-0.284270\pi$
$491$	5.89230	+	3.40192i	0.265916	+	0.153527i	−0.361114	+	0.932522i	$0.617604\pi$
$492$		0			0
$493$	1.09808	−	1.09808i	0.0494549	−	0.0494549i
$494$		0			0
$495$	−8.46410	−	25.3923i	−0.380433	−	1.14130i
$496$		0			0
$497$	1.47372	+	5.50000i	0.0661054	+	0.246709i
$498$		0			0
$499$	20.2679	−	20.2679i	0.907318	−	0.907318i	−0.0887371	−	0.996055i	$-0.528283\pi$
$499$	20.2679	−	20.2679i	0.907318	−	0.907318i	0.996055	+	0.0887371i	$0.0282831\pi$
$500$		0			0
$501$	9.23205	+	2.47372i	0.412458	+	0.110518i
$502$		0			0
$503$	−3.35641	+	12.5263i	−0.149655	+	0.558519i	0.849849	+	0.527026i	$0.176693\pi$
$503$	−3.35641	+	12.5263i	−0.149655	+	0.558519i	−0.999504	+	0.0314933i	$0.989974\pi$
$504$		0			0
$505$	21.1865	+	32.0885i	0.942788	+	1.42792i
$506$		0			0
$507$	4.10770	+	5.33013i	0.182429	+	0.236719i
$508$		0			0
$509$	−7.45448	−	27.8205i	−0.330414	−	1.23312i	−0.908756	−	0.417328i	$-0.862967\pi$
$509$	−7.45448	−	27.8205i	−0.330414	−	1.23312i	0.578342	−	0.815795i	$-0.303700\pi$
$510$		0			0
$511$	31.8564	−	18.3923i	1.40924	−	0.813628i
$512$		0			0
$513$	−7.62436	+	4.40192i	−0.336624	+	0.194350i
$514$		0			0
$515$	33.5885	−	11.1962i	1.48008	−	0.493361i
$516$		0			0
$517$	46.2487	−	12.3923i	2.03402	−	0.545013i
$518$		0			0
$519$	1.48334			0.0651114
$520$		0			0
$521$	−7.85641			−0.344195			−0.172098	−	0.985080i	$-0.555054\pi$
$521$	−7.85641			−0.344195			−0.172098	+	0.985080i	$0.555054\pi$
$522$		0			0
$523$	10.9641	−	2.93782i	0.479427	−	0.128462i	−0.0110090	−	0.999939i	$-0.503504\pi$
$523$	10.9641	−	2.93782i	0.479427	−	0.128462i	0.490436	+	0.871477i	$0.336838\pi$
$524$		0			0
$525$	6.31347	+	0.901924i	0.275542	+	0.0393632i
$526$		0			0
$527$	5.70577	−	3.29423i	0.248547	−	0.143499i
$528$		0			0
$529$	19.9019	−	11.4904i	0.865301	−	0.499582i
$530$		0			0
$531$	6.36603	+	23.7583i	0.276262	+	1.03102i
$532$		0			0
$533$	−11.1603	+	32.9904i	−0.483404	+	1.42897i
$534$		0			0
$535$	−3.40192	+	16.6244i	−0.147078	+	0.718734i
$536$		0			0
$537$	−1.86603	+	6.96410i	−0.0805249	+	0.300523i
$538$		0			0
$539$	3.92820	+	1.05256i	0.169200	+	0.0453369i
$540$		0			0
$541$	21.7846	−	21.7846i	0.936594	−	0.936594i	−0.0615128	−	0.998106i	$-0.519592\pi$
$541$	21.7846	−	21.7846i	0.936594	−	0.936594i	0.998106	+	0.0615128i	$0.0195925\pi$
$542$		0			0
$543$	−3.07180	−	11.4641i	−0.131823	−	0.491972i
$544$		0			0
$545$	10.6077	−	3.53590i	0.454384	−	0.151461i
$546$		0			0
$547$	−0.124356	+	0.124356i	−0.00531706	+	0.00531706i	−0.709760	−	0.704443i	$-0.751197\pi$
$547$	−0.124356	+	0.124356i	−0.00531706	+	0.00531706i	0.704443	+	0.709760i	$0.251197\pi$
$548$		0			0
$549$	−21.2942	−	12.2942i	−0.908816	−	0.524705i
$550$		0			0
$551$	3.63397	+	3.63397i	0.154813	+	0.154813i
$552$		0			0
$553$	0.660254	+	1.14359i	0.0280769	+	0.0486305i
$554$		0			0
$555$	1.33013	+	1.17949i	0.0564607	+	0.0500666i
$556$		0			0
$557$	13.3301	+	7.69615i	0.564816	+	0.326096i	0.755076	−	0.655637i	$-0.227600\pi$
$557$	13.3301	+	7.69615i	0.564816	+	0.326096i	−0.190260	+	0.981734i	$0.560933\pi$
$558$		0			0
$559$	16.7224	−	14.6962i	0.707284	−	0.621581i
$560$		0			0
$561$	−1.96410	+	0.526279i	−0.0829244	+	0.0222195i
$562$		0			0
$563$	−24.8923	−	6.66987i	−1.04909	−	0.281102i	−0.307212	−	0.951641i	$-0.599396\pi$
$563$	−24.8923	−	6.66987i	−1.04909	−	0.281102i	−0.741874	+	0.670540i	$0.766063\pi$
$564$		0			0
$565$	−4.40192	+	4.96410i	−0.185190	+	0.208841i
$566$		0			0
$567$			16.4115i			0.689220i
$568$		0			0
$569$	18.8205	−	32.5981i	0.788997	−	1.36658i	−0.137585	−	0.990490i	$-0.543934\pi$
$569$	18.8205	−	32.5981i	0.788997	−	1.36658i	0.926582	−	0.376093i	$-0.122733\pi$
$570$		0			0
$571$		−	21.6077i		−	0.904254i	−0.891954	−	0.452127i	$-0.850665\pi$
$571$		−	21.6077i		−	0.904254i	0.891954	−	0.452127i	$-0.149335\pi$
$572$		0			0
$573$	−5.49038	−	5.49038i	−0.229364	−	0.229364i
$574$		0			0
$575$	0.428203	−	0.545517i	0.0178573	−	0.0227496i
$576$		0			0
$577$	20.7846			0.865275			0.432637	−	0.901568i	$-0.357583\pi$
$577$	20.7846			0.865275			0.432637	+	0.901568i	$0.357583\pi$
$578$		0			0
$579$	−3.42820	+	12.7942i	−0.142471	+	0.531710i
$580$		0			0
$581$	−3.60770	−	6.24871i	−0.149672	−	0.259240i
$582$		0			0
$583$	7.63397	−	13.2224i	0.316167	−	0.547617i
$584$		0			0
$585$	−11.0981	+	19.0263i	−0.458849	+	0.786640i
$586$		0			0
$587$	−23.7224	+	41.0885i	−0.979130	+	1.69590i	−0.313556	+	0.949570i	$0.601520\pi$
$587$	−23.7224	+	41.0885i	−0.979130	+	1.69590i	−0.665573	+	0.746333i	$0.731813\pi$
$588$		0			0
$589$	10.9019	+	18.8827i	0.449206	+	0.778048i
$590$		0			0
$591$	−0.571797	+	2.13397i	−0.0235206	+	0.0877800i
$592$		0			0
$593$	−30.9282			−1.27007			−0.635035	−	0.772484i	$-0.719014\pi$
$593$	−30.9282			−1.27007			−0.635035	+	0.772484i	$0.719014\pi$
$594$		0			0
$595$	−0.990381	+	4.83975i	−0.0406017	+	0.198410i
$596$		0			0
$597$	−6.90192	−	6.90192i	−0.282477	−	0.282477i
$598$		0			0
$599$		−	36.2487i		−	1.48108i	−0.672011	−	0.740541i	$-0.734569\pi$
$599$		−	36.2487i		−	1.48108i	0.672011	−	0.740541i	$-0.265431\pi$
$600$		0			0
$601$	7.42820	−	12.8660i	0.303003	−	0.524816i	−0.673812	−	0.738903i	$-0.735344\pi$
$601$	7.42820	−	12.8660i	0.303003	−	0.524816i	0.976815	+	0.214087i	$0.0686775\pi$
$602$		0			0
$603$			33.5167i			1.36490i
$604$		0			0
$605$	18.2942	−	1.09808i	0.743766	−	0.0446431i
$606$		0			0
$607$	3.03590	+	0.813467i	0.123223	+	0.0330176i	0.319904	−	0.947450i	$-0.396349\pi$
$607$	3.03590	+	0.813467i	0.123223	+	0.0330176i	−0.196680	+	0.980468i	$0.563016\pi$
$608$		0			0
$609$	−2.13397	+	0.571797i	−0.0864730	+	0.0231704i
$610$		0			0
$611$	−32.7846	−	21.8564i	−1.32632	−	0.884216i
$612$		0			0
$613$	−21.1865	−	12.2321i	−0.855716	−	0.494048i	0.00685934	−	0.999976i	$-0.497817\pi$
$613$	−21.1865	−	12.2321i	−0.855716	−	0.494048i	−0.862575	+	0.505929i	$0.831150\pi$
$614$		0			0
$615$	11.1603	−	0.669873i	0.450025	−	0.0270119i
$616$		0			0
$617$	8.79423	+	15.2321i	0.354042	+	0.613219i	0.986954	−	0.161005i	$-0.0514735\pi$
$617$	8.79423	+	15.2321i	0.354042	+	0.613219i	−0.632911	+	0.774224i	$0.718140\pi$
$618$		0			0
$619$	14.6603	+	14.6603i	0.589245	+	0.589245i	0.937427	−	0.348182i	$-0.113201\pi$
$619$	14.6603	+	14.6603i	0.589245	+	0.589245i	−0.348182	+	0.937427i	$0.613201\pi$
$620$		0			0
$621$	−0.356406	−	0.205771i	−0.0143021	−	0.00825732i
$622$		0			0
$623$	26.6865	−	26.6865i	1.06917	−	1.06917i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	−1.74167	−	6.50000i	−0.0695556	−	0.259585i
$628$		0			0
$629$	−0.973721	+	0.973721i	−0.0388248	+	0.0388248i
$630$		0			0
$631$	41.6506	+	11.1603i	1.65809	+	0.444283i	0.961860	−	0.273541i	$-0.0881948\pi$
$631$	41.6506	+	11.1603i	1.65809	+	0.444283i	0.696225	+	0.717823i	$0.254862\pi$
$632$		0			0
$633$	0.794229	−	2.96410i	0.0315678	−	0.117812i
$634$		0			0
$635$	45.1147	+	9.23205i	1.79032	+	0.366363i
$636$		0			0
$637$	−1.48334	−	3.00000i	−0.0587721	−	0.118864i
$638$		0			0
$639$	1.63397	+	6.09808i	0.0646390	+	0.241236i
$640$		0			0
$641$	5.64359	−	3.25833i	0.222909	−	0.128696i	−0.384388	−	0.923172i	$-0.625587\pi$
$641$	5.64359	−	3.25833i	0.222909	−	0.128696i	0.607296	+	0.794475i	$0.292254\pi$
$642$		0			0
$643$	−31.3301	+	18.0885i	−1.23554	+	0.713339i	−0.968179	−	0.250258i	$-0.919485\pi$
$643$	−31.3301	+	18.0885i	−1.23554	+	0.713339i	−0.267360	+	0.963597i	$0.586151\pi$
$644$		0			0
$645$	−6.39230	−	3.19615i	−0.251697	−	0.125848i
$646$		0			0
$647$	2.50000	−	0.669873i	0.0982851	−	0.0263354i	−0.209341	−	0.977843i	$-0.567132\pi$
$647$	2.50000	−	0.669873i	0.0982851	−	0.0263354i	0.307626	+	0.951507i	$0.400465\pi$
$648$		0			0
$649$	−39.4449			−1.54835
$650$		0			0
$651$	−9.37307			−0.367359
$652$		0			0
$653$	47.9449	−	12.8468i	1.87623	−	0.502734i	0.876453	−	0.481487i	$-0.159903\pi$
$653$	47.9449	−	12.8468i	1.87623	−	0.502734i	0.999774	−	0.0212467i	$-0.00676353\pi$
$654$		0			0
$655$	−11.7128	−	5.85641i	−0.457657	−	0.228829i
$656$		0			0
$657$	35.3205	−	20.3923i	1.37798	−	0.795580i
$658$		0			0
$659$	−35.4282	+	20.4545i	−1.38009	+	0.796794i	−0.992169	−	0.124901i	$-0.960139\pi$
$659$	−35.4282	+	20.4545i	−1.38009	+	0.796794i	−0.387918	+	0.921694i	$0.626805\pi$
$660$		0			0
$661$	−0.794229	−	2.96410i	−0.0308919	−	0.115290i	0.948758	−	0.316003i	$-0.102341\pi$
$661$	−0.794229	−	2.96410i	−0.0308919	−	0.115290i	−0.979650	+	0.200713i	$0.935674\pi$
$662$		0			0
$663$	1.39230	+	0.928203i	0.0540726	+	0.0360484i
$664$		0			0
$665$	−16.0167	−	3.27757i	−0.621099	−	0.127099i
$666$		0			0
$667$	−0.0621778	+	0.232051i	−0.00240754	+	0.00898504i
$668$		0			0
$669$	0.767949	+	0.205771i	0.0296906	+	0.00795558i
$670$		0			0
$671$	27.8827	−	27.8827i	1.07640	−	1.07640i
$672$		0			0
$673$	9.62436	+	35.9186i	0.370992	+	1.38456i	0.859114	+	0.511784i	$0.171015\pi$
$673$	9.62436	+	35.9186i	0.370992	+	1.38456i	−0.488122	+	0.872775i	$0.662318\pi$
$674$		0			0
$675$	14.6865	+	2.09808i	0.565285	+	0.0807550i
$676$		0			0
$677$	−28.1769	+	28.1769i	−1.08293	+	1.08293i	−0.0866916	+	0.996235i	$0.527629\pi$
$677$	−28.1769	+	28.1769i	−1.08293	+	1.08293i	−0.996235	+	0.0866916i	$0.972371\pi$
$678$		0			0
$679$	−16.5000	−	9.52628i	−0.633212	−	0.365585i
$680$		0			0
$681$	−1.16987	−	1.16987i	−0.0448296	−	0.0448296i
$682$		0			0
$683$	7.33013	+	12.6962i	0.280480	+	0.485805i	0.971503	−	0.237028i	$-0.0761732\pi$
$683$	7.33013	+	12.6962i	0.280480	+	0.485805i	−0.691023	+	0.722832i	$0.742840\pi$
$684$		0			0
$685$	31.9641	−	1.91858i	1.22129	−	0.0733053i
$686$		0			0
$687$	−0.0455173	−	0.0262794i	−0.00173659	−	0.00100262i
$688$		0			0
$689$	−12.3205	+	2.46410i	−0.469374	+	0.0938748i
$690$		0			0
$691$	−37.6506	+	10.0885i	−1.43230	+	0.383783i	−0.889829	−	0.456293i	$-0.849177\pi$
$691$	−37.6506	+	10.0885i	−1.43230	+	0.383783i	−0.542468	+	0.840076i	$0.682510\pi$
$692$		0			0
$693$	−28.4904	−	7.63397i	−1.08226	−	0.289991i
$694$		0			0
$695$	11.5981	−	0.696152i	0.439940	−	0.0264066i
$696$		0			0
$697$			8.66025i			0.328031i
$698$		0			0
$699$	−4.70577	+	8.15064i	−0.177989	+	0.308285i
$700$		0			0
$701$		−	21.0718i		−	0.795871i	−0.917413	−	0.397935i	$-0.869727\pi$
$701$		−	21.0718i		−	0.795871i	0.917413	−	0.397935i	$-0.130273\pi$
$702$		0			0
$703$	−3.22243	−	3.22243i	−0.121536	−	0.121536i
$704$		0			0
$705$	−2.53590	+	12.3923i	−0.0955075	+	0.466721i
$706$		0			0
$707$	42.3731			1.59360
$708$		0			0
$709$	−4.27757	+	15.9641i	−0.160647	+	0.599544i	0.837908	+	0.545812i	$0.183779\pi$
$709$	−4.27757	+	15.9641i	−0.160647	+	0.599544i	−0.998555	+	0.0537328i	$0.982888\pi$
$710$		0			0
$711$	0.732051	+	1.26795i	0.0274541	+	0.0475518i
$712$		0			0
$713$	−0.509619	+	0.882686i	−0.0190854	+	0.0330568i
$714$		0			0
$715$	−24.8660	−	25.0885i	−0.929937	−	0.938255i
$716$		0			0
$717$	−6.09808	+	10.5622i	−0.227737	+	0.394452i
$718$		0			0
$719$	−20.9641	−	36.3109i	−0.781829	−	1.35417i	−0.930875	−	0.365337i	$-0.880954\pi$
$719$	−20.9641	−	36.3109i	−0.781829	−	1.35417i	0.149046	−	0.988830i	$-0.452380\pi$
$720$		0			0
$721$	10.0981	−	37.6865i	0.376072	−	1.40352i
$722$		0			0
$723$	−6.07180			−0.225813
$724$		0			0
$725$	−1.03590	−	8.59808i	−0.0384723	−	0.319325i
$726$		0			0
$727$	−33.5885	−	33.5885i	−1.24573	−	1.24573i	−0.957589	−	0.288138i	$-0.906964\pi$
$727$	−33.5885	−	33.5885i	−1.24573	−	1.24573i	−0.288138	−	0.957589i	$-0.593036\pi$
$728$		0			0
$729$			13.5885i			0.503276i
$730$		0			0
$731$	2.76795	−	4.79423i	0.102376	−	0.177321i
$732$		0			0
$733$			26.7846i			0.989312i	0.869089	+	0.494656i	$0.164706\pi$
$733$			26.7846i			0.989312i	−0.869089	+	0.494656i	$0.835294\pi$
$734$		0			0
$735$	−0.712813	+	0.803848i	−0.0262925	+	0.0296504i
$736$		0			0
$737$	−51.9186	−	13.9115i	−1.91245	−	0.512438i
$738$		0			0
$739$	−37.9186	+	10.1603i	−1.39486	+	0.373751i	−0.876495	−	0.481410i	$-0.840125\pi$
$739$	−37.9186	+	10.1603i	−1.39486	+	0.373751i	−0.518362	+	0.855161i	$0.673458\pi$
$740$		0			0
$741$	−3.07180	+	4.60770i	−0.112845	+	0.169268i
$742$		0			0
$743$	−19.3301	−	11.1603i	−0.709154	−	0.409430i	0.101594	−	0.994826i	$-0.467606\pi$
$743$	−19.3301	−	11.1603i	−0.709154	−	0.409430i	−0.810748	+	0.585396i	$0.800939\pi$
$744$		0			0
$745$	5.76795	+	5.11474i	0.211321	+	0.187389i
$746$		0			0
$747$	−4.00000	−	6.92820i	−0.146352	−	0.253490i
$748$		0			0
$749$	13.2224	+	13.2224i	0.483137	+	0.483137i
$750$		0			0
$751$	17.6436	+	10.1865i	0.643824	+	0.371712i	0.786086	−	0.618117i	$-0.212104\pi$
$751$	17.6436	+	10.1865i	0.643824	+	0.371712i	−0.142262	+	0.989829i	$0.545438\pi$
$752$		0			0
$753$	6.49038	−	6.49038i	0.236523	−	0.236523i
$754$		0			0
$755$	0.803848	−	0.267949i	0.0292550	−	0.00975167i
$756$		0			0
$757$	−4.83975	−	18.0622i	−0.175904	−	0.656481i	−0.996396	−	0.0848236i	$-0.972967\pi$
$757$	−4.83975	−	18.0622i	−0.175904	−	0.656481i	0.820492	−	0.571657i	$-0.193699\pi$
$758$		0			0
$759$	0.222432	−	0.222432i	0.00807377	−	0.00807377i
$760$		0			0
$761$	−0.669873	−	0.179492i	−0.0242829	−	0.00650658i	0.246657	−	0.969103i	$-0.420668\pi$
$761$	−0.669873	−	0.179492i	−0.0242829	−	0.00650658i	−0.270940	+	0.962596i	$0.587335\pi$
$762$		0			0
$763$	3.18911	−	11.9019i	0.115454	−	0.430879i
$764$		0			0
$765$	−1.09808	+	5.36603i	−0.0397010	+	0.194009i
$766$		0			0
$767$	21.4282	+	24.3827i	0.773728	+	0.880408i
$768$		0			0
$769$	5.47372	+	20.4282i	0.197387	+	0.736660i	0.991636	+	0.129067i	$0.0411982\pi$
$769$	5.47372	+	20.4282i	0.197387	+	0.736660i	−0.794248	+	0.607593i	$0.792135\pi$
$770$		0			0
$771$	−10.0359	+	5.79423i	−0.361434	+	0.208674i
$772$		0			0
$773$	17.0429	−	9.83975i	0.612992	−	0.353911i	−0.161144	−	0.986931i	$-0.551518\pi$
$773$	17.0429	−	9.83975i	0.612992	−	0.353911i	0.774136	+	0.633020i	$0.218185\pi$
$774$		0			0
$775$	5.19615	−	36.3731i	0.186651	−	1.30656i
$776$		0			0
$777$	1.89230	−	0.507042i	0.0678861	−	0.0181900i
$778$		0			0
$779$	−28.6603			−1.02686
$780$		0			0
$781$	−10.1244			−0.362278
$782$		0			0
$783$	−4.96410	+	1.33013i	−0.177403	+	0.0475349i
$784$		0			0
$785$	−19.3923	+	6.46410i	−0.692141	+	0.230714i
$786$		0			0
$787$	−37.4545	+	21.6244i	−1.33511	+	0.770825i	−0.986078	−	0.166286i	$-0.946822\pi$
$787$	−37.4545	+	21.6244i	−1.33511	+	0.770825i	−0.349031	+	0.937111i	$0.613489\pi$
$788$		0			0
$789$	−6.44744	+	3.72243i	−0.229535	+	0.132522i
$790$		0			0
$791$	1.89230	+	7.06218i	0.0672826	+	0.251102i
$792$		0			0
$793$	−32.3827	−	2.08846i	−1.14994	−	0.0741633i
$794$		0			0
$795$	2.22243	+	3.36603i	0.0788215	+	0.119381i
$796$		0			0
$797$	5.62436	−	20.9904i	0.199225	−	0.743517i	−0.791908	−	0.610641i	$-0.790912\pi$
$797$	5.62436	−	20.9904i	0.199225	−	0.743517i	0.991133	−	0.132877i	$-0.0424214\pi$
$798$		0			0
$799$	−9.46410	−	2.53590i	−0.334816	−	0.0897136i
$800$		0			0
$801$	29.5885	−	29.5885i	1.04546	−	1.04546i
$802$		0			0
$803$	16.9282	+	63.1769i	0.597383	+	2.22946i
$804$		0			0
$805$	−0.241670	−	0.725009i	−0.00851774	−	0.0255532i
$806$		0			0
$807$	−6.68653	+	6.68653i	−0.235377	+	0.235377i
$808$		0			0
$809$	−10.2846	−	5.93782i	−0.361588	−	0.208763i	0.308189	−	0.951325i	$-0.400277\pi$
$809$	−10.2846	−	5.93782i	−0.361588	−	0.208763i	−0.669777	+	0.742562i	$0.733610\pi$
$810$		0			0
$811$	−23.0526	−	23.0526i	−0.809485	−	0.809485i	0.175071	−	0.984556i	$-0.443985\pi$
$811$	−23.0526	−	23.0526i	−0.809485	−	0.809485i	−0.984556	+	0.175071i	$0.943985\pi$
$812$		0			0
$813$	−4.33013	−	7.50000i	−0.151864	−	0.263036i
$814$		0			0
$815$	0.428203	+	7.13397i	0.0149993	+	0.249892i
$816$		0			0
$817$	15.8660	+	9.16025i	0.555082	+	0.320477i
$818$		0			0
$819$	10.7583	+	21.7583i	0.375926	+	0.760298i
$820$		0			0
$821$	−27.4545	+	7.35641i	−0.958168	+	0.256740i	−0.703825	−	0.710374i	$-0.748526\pi$
$821$	−27.4545	+	7.35641i	−0.958168	+	0.256740i	−0.254343	+	0.967114i	$0.581859\pi$
$822$		0			0
$823$	23.8923	+	6.40192i	0.832833	+	0.223157i	0.649949	−	0.759977i	$-0.274790\pi$
$823$	23.8923	+	6.40192i	0.832833	+	0.223157i	0.182884	+	0.983135i	$0.441457\pi$
$824$		0			0
$825$	−4.45448	+	10.4282i	−0.155085	+	0.363063i
$826$		0			0
$827$			25.8564i			0.899115i	0.893251	+	0.449558i	$0.148418\pi$
$827$			25.8564i			0.899115i	−0.893251	+	0.449558i	$0.851582\pi$
$828$		0			0
$829$	4.42820	−	7.66987i	0.153798	−	0.266386i	−0.778823	−	0.627244i	$-0.784183\pi$
$829$	4.42820	−	7.66987i	0.153798	−	0.266386i	0.932621	+	0.360858i	$0.117516\pi$
$830$		0			0
$831$		−	5.53590i		−	0.192038i
$832$		0			0
$833$	−0.588457	−	0.588457i	−0.0203888	−	0.0203888i
$834$		0			0
$835$	22.7487	+	34.4545i	0.787252	+	1.19235i
$836$		0			0
$837$	−21.8038			−0.753651
$838$		0			0
$839$	7.79423	−	29.0885i	0.269087	−	1.00425i	−0.690615	−	0.723223i	$-0.742660\pi$
$839$	7.79423	−	29.0885i	0.269087	−	1.00425i	0.959701	−	0.281022i	$-0.0906734\pi$
$840$		0			0
$841$	−13.0000	−	22.5167i	−0.448276	−	0.776437i
$842$		0			0
$843$	6.02628	−	10.4378i	0.207556	−	0.359498i
$844$		0			0
$845$	−2.00000	+	29.0000i	−0.0688021	+	0.997630i
$846$		0			0
$847$	10.0981	−	17.4904i	0.346974	−	0.600977i
$848$		0			0
$849$	−7.96410	−	13.7942i	−0.273327	−	0.473417i
$850$		0			0
$851$	0.0551363	−	0.205771i	0.00189005	−	0.00705375i
$852$		0			0
$853$	−53.8564			−1.84401			−0.922004	−	0.387180i	$-0.873449\pi$
$853$	−53.8564			−1.84401			−0.922004	+	0.387180i	$0.873449\pi$
$854$		0			0
$855$	−17.7583	−	3.63397i	−0.607322	−	0.124279i
$856$		0			0
$857$	−19.2487	−	19.2487i	−0.657523	−	0.657523i	0.297270	−	0.954793i	$-0.403924\pi$
$857$	−19.2487	−	19.2487i	−0.657523	−	0.657523i	−0.954793	+	0.297270i	$0.903924\pi$
$858$		0			0
$859$			2.39230i			0.0816244i	0.999167	+	0.0408122i	$0.0129945\pi$
$859$			2.39230i			0.0816244i	−0.999167	+	0.0408122i	$0.987005\pi$
$860$		0			0
$861$	6.16025	−	10.6699i	0.209941	−	0.363628i
$862$		0			0
$863$		−	2.14359i		−	0.0729688i	−0.999334	−	0.0364844i	$-0.988384\pi$
$863$		−	2.14359i		−	0.0729688i	0.999334	−	0.0364844i	$-0.0116159\pi$
$864$		0			0
$865$	4.79423	+	4.25129i	0.163009	+	0.144548i
$866$		0			0
$867$	−8.09808	−	2.16987i	−0.275025	−	0.0736927i
$868$		0			0
$869$	−2.26795	+	0.607695i	−0.0769349	+	0.0206146i
$870$		0			0
$871$	19.6051	+	39.6506i	0.664294	+	1.34351i
$872$		0			0
$873$	−18.2942	−	10.5622i	−0.619166	−	0.357476i
$874$		0			0
$875$	17.8205	+	21.0096i	0.602443	+	0.710255i
$876$		0			0
$877$	18.7942	+	32.5526i	0.634636	+	1.09922i	0.986592	+	0.163205i	$0.0521833\pi$
$877$	18.7942	+	32.5526i	0.634636	+	1.09922i	−0.351956	+	0.936017i	$0.614483\pi$
$878$		0			0
$879$	7.50962	+	7.50962i	0.253293	+	0.253293i
$880$		0			0
$881$	4.96410	+	2.86603i	0.167245	+	0.0965588i	0.581286	−	0.813699i	$-0.302550\pi$
$881$	4.96410	+	2.86603i	0.167245	+	0.0965588i	−0.414041	+	0.910258i	$0.635883\pi$
$882$		0			0
$883$	0.803848	−	0.803848i	0.0270516	−	0.0270516i	−0.693452	−	0.720503i	$-0.743911\pi$
$883$	0.803848	−	0.803848i	0.0270516	−	0.0270516i	0.720503	+	0.693452i	$0.243911\pi$
$884$		0			0
$885$	4.66025	−	9.32051i	0.156653	−	0.313305i
$886$		0			0
$887$	0.0358984	+	0.133975i	0.00120535	+	0.00449843i	0.966526	−	0.256569i	$-0.0825921\pi$
$887$	0.0358984	+	0.133975i	0.00120535	+	0.00449843i	−0.965321	+	0.261068i	$0.915925\pi$
$888$		0			0
$889$	35.8827	−	35.8827i	1.20347	−	1.20347i
$890$		0			0
$891$	−28.1865	−	7.55256i	−0.944284	−	0.253020i
$892$		0			0
$893$	8.39230	−	31.3205i	0.280838	−	1.04810i
$894$		0			0
$895$	−25.9904	+	17.1603i	−0.868763	+	0.573604i
$896$		0			0
$897$	−0.258330	−	0.0166605i	−0.00862540	−	0.000556278i
$898$		0			0
$899$	3.29423	+	12.2942i	0.109869	+	0.410035i
$900$		0			0
$901$	−2.70577	+	1.56218i	−0.0901423	+	0.0520437i
$902$		0			0
$903$	−6.82051	+	3.93782i	−0.226972	+	0.131043i
$904$		0			0
$905$	22.9282	−	45.8564i	0.762159	−	1.52432i
$906$		0			0
$907$	42.3564	−	11.3494i	1.40642	−	0.376849i	0.525775	−	0.850624i	$-0.323775\pi$
$907$	42.3564	−	11.3494i	1.40642	−	0.376849i	0.880646	+	0.473774i	$0.157109\pi$
$908$		0			0
$909$	46.9808			1.55825
$910$		0			0
$911$	25.5692			0.847146			0.423573	−	0.905862i	$-0.360776\pi$
$911$	25.5692			0.847146			0.423573	+	0.905862i	$0.360776\pi$
$912$		0			0
$913$	12.3923	−	3.32051i	0.410125	−	0.109893i
$914$		0			0
$915$	3.29423	+	9.88269i	0.108904	+	0.326712i
$916$		0			0
$917$	−12.4974	+	7.21539i	−0.412701	+	0.238273i
$918$		0			0
$919$	−33.1410	+	19.1340i	−1.09322	+	0.631172i	−0.934432	−	0.356141i	$-0.884092\pi$
$919$	−33.1410	+	19.1340i	−1.09322	+	0.631172i	−0.158789	+	0.987313i	$0.550759\pi$
$920$		0			0
$921$	0.535898	+	2.00000i	0.0176585	+	0.0659022i
$922$		0			0
$923$	5.50000	+	6.25833i	0.181035	+	0.205995i
$924$		0			0
$925$	0.918584	+	7.62436i	0.0302029	+	0.250687i
$926$		0			0
$927$	11.1962	−	41.7846i	0.367730	−	1.37239i
$928$		0			0
$929$	21.9904	+	5.89230i	0.721481	+	0.193320i	0.600832	−	0.799375i	$-0.294836\pi$
$929$	21.9904	+	5.89230i	0.721481	+	0.193320i	0.120649	+	0.992695i	$0.461503\pi$
$930$		0			0
$931$	1.94744	−	1.94744i	0.0638248	−	0.0638248i
$932$		0			0
$933$	0.464102	+	1.73205i	0.0151940	+	0.0567048i
$934$		0			0
$935$	−7.85641	−	3.92820i	−0.256932	−	0.128466i
$936$		0			0
$937$	2.85641	−	2.85641i	0.0933147	−	0.0933147i	−0.658908	−	0.752223i	$-0.728982\pi$
$937$	2.85641	−	2.85641i	0.0933147	−	0.0933147i	0.752223	+	0.658908i	$0.228982\pi$
$938$		0			0
$939$	3.50962	+	2.02628i	0.114532	+	0.0661251i
$940$		0			0
$941$	6.85641	+	6.85641i	0.223512	+	0.223512i	0.809976	−	0.586463i	$-0.199480\pi$
$941$	6.85641	+	6.85641i	0.223512	+	0.223512i	−0.586463	+	0.809976i	$0.699480\pi$
$942$		0			0
$943$	−0.669873	−	1.16025i	−0.0218141	−	0.0377831i
$944$		0			0
$945$	10.8468	−	12.2321i	0.352846	−	0.397909i
$946$		0			0
$947$	4.54552	+	2.62436i	0.147709	+	0.0852801i	0.572033	−	0.820230i	$-0.306155\pi$
$947$	4.54552	+	2.62436i	0.147709	+	0.0852801i	−0.424324	+	0.905511i	$0.639488\pi$
$948$		0			0
$949$	29.8564	−	44.7846i	0.969180	−	1.45377i
$950$		0			0
$951$	9.46410	−	2.53590i	0.306895	−	0.0822321i
$952$		0			0
$953$	−12.6244	−	3.38269i	−0.408943	−	0.109576i	0.0484822	−	0.998824i	$-0.484562\pi$
$953$	−12.6244	−	3.38269i	−0.408943	−	0.109576i	−0.457425	+	0.889248i	$0.651228\pi$
$954$		0			0
$955$	−2.00962	−	33.4808i	−0.0650297	−	1.08341i
$956$		0			0
$957$		−	3.92820i		−	0.126981i
$958$		0			0
$959$	17.6436	−	30.5596i	0.569741	−	0.986821i
$960$		0			0
$961$			23.0000i			0.741935i
$962$		0			0
$963$	14.6603	+	14.6603i	0.472420	+	0.472420i
$964$		0			0
$965$	−47.7487	+	31.5263i	−1.53709	+	1.01487i
$966$		0			0
$967$	58.3923			1.87777			0.938885	−	0.344231i	$-0.111860\pi$
$967$	58.3923			1.87777			0.938885	+	0.344231i	$0.111860\pi$
$968$		0			0
$969$	−0.356406	+	1.33013i	−0.0114494	+	0.0427298i
$970$		0			0
$971$	17.8923	+	30.9904i	0.574191	+	0.994529i	0.996129	+	0.0879038i	$0.0280168\pi$
$971$	17.8923	+	30.9904i	0.574191	+	0.994529i	−0.421938	+	0.906625i	$0.638650\pi$
$972$		0			0
$973$	6.40192	−	11.0885i	0.205236	−	0.355480i
$974$		0			0
$975$	8.86603	−	2.91154i	0.283940	−	0.0932440i
$976$		0			0
$977$	−8.79423	+	15.2321i	−0.281352	+	0.487316i	−0.971718	−	0.236144i	$-0.924116\pi$
$977$	−8.79423	+	15.2321i	−0.281352	+	0.487316i	0.690366	+	0.723461i	$0.257450\pi$
$978$		0			0
$979$	33.5526	+	58.1147i	1.07234	+	1.85736i
$980$		0			0
$981$	3.53590	−	13.1962i	0.112893	−	0.421321i
$982$		0			0
$983$	1.60770			0.0512775			0.0256388	−	0.999671i	$-0.491838\pi$
$983$	1.60770			0.0512775			0.0256388	+	0.999671i	$0.491838\pi$
$984$		0			0
$985$	−7.96410	+	5.25833i	−0.253757	+	0.167544i
$986$		0			0
$987$	9.85641	+	9.85641i	0.313733	+	0.313733i
$988$		0			0
$989$			0.856406i			0.0272321i
$990$		0			0
$991$	−20.8205	+	36.0622i	−0.661385	+	1.14555i	0.318867	+	0.947800i	$0.396698\pi$
$991$	−20.8205	+	36.0622i	−0.661385	+	1.14555i	−0.980252	+	0.197753i	$0.936636\pi$
$992$		0			0
$993$			8.90897i			0.282717i
$994$		0			0
$995$	−2.52628	−	42.0885i	−0.0800884	−	1.33429i
$996$		0			0
$997$	8.23205	+	2.20577i	0.260712	+	0.0698575i	0.386807	−	0.922161i	$-0.373578\pi$
$997$	8.23205	+	2.20577i	0.260712	+	0.0698575i	−0.126095	+	0.992018i	$0.540245\pi$
$998$		0			0
$999$	4.40192	−	1.17949i	0.139271	−	0.0373175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bk.a.33.1	yes	4
5.2	odd	4		260.2.bf.b.137.1	yes	4
5.3	odd	4		1300.2.bn.a.657.1		4
5.4	even	2		1300.2.bs.b.293.1		4
13.2	odd	12		260.2.bf.b.93.1	✓	4
65.2	even	12	inner	260.2.bk.a.197.1	yes	4
65.28	even	12		1300.2.bs.b.457.1		4
65.54	odd	12		1300.2.bn.a.93.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.b.93.1	✓	4	13.2	odd	12
260.2.bf.b.137.1	yes	4	5.2	odd	4
260.2.bk.a.33.1	yes	4	1.1	even	1	trivial
260.2.bk.a.197.1	yes	4	65.2	even	12	inner
1300.2.bn.a.93.1		4	65.54	odd	12
1300.2.bn.a.657.1		4	5.3	odd	4
1300.2.bs.b.293.1		4	5.4	even	2
1300.2.bs.b.457.1		4	65.28	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bk (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.133975i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-2.36603 + 1.36603i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.133975i) q^{3} +(-2.00000 - 1.00000i) q^{5} +(-2.13397 + 1.23205i) q^{7} +(-2.36603 + 1.36603i) q^{9} +(-1.13397 - 4.23205i) q^{11} +(-2.00000 + 3.00000i) q^{13} +(1.13397 + 0.232051i) q^{15} +(-0.232051 + 0.866025i) q^{17} +(-2.86603 - 0.767949i) q^{19} +(0.901924 - 0.901924i) q^{21} +(-0.0358984 - 0.133975i) q^{23} +(3.00000 + 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(-1.50000 - 0.866025i) q^{29} +(-5.19615 - 5.19615i) q^{31} +(1.13397 + 1.96410i) q^{33} +(5.50000 - 0.330127i) q^{35} +(1.33013 + 0.767949i) q^{37} +(0.598076 - 1.76795i) q^{39} +(9.33013 - 2.50000i) q^{41} +(-5.96410 - 1.59808i) q^{43} +(6.09808 - 0.366025i) q^{45} +10.9282i q^{47} +(-0.464102 + 0.803848i) q^{49} -0.464102i q^{51} +(2.46410 + 2.46410i) q^{53} +(-1.96410 + 9.59808i) q^{55} +1.53590 q^{57} +(2.33013 - 8.69615i) q^{59} +(4.50000 + 7.79423i) q^{61} +(3.36603 - 5.83013i) q^{63} +(7.00000 - 4.00000i) q^{65} +(6.13397 - 10.6244i) q^{67} +(0.0358984 + 0.0621778i) q^{69} +(0.598076 - 2.23205i) q^{71} -14.9282 q^{73} +(-2.03590 - 1.59808i) q^{75} +(7.63397 + 7.63397i) q^{77} -0.535898i q^{79} +(3.33013 - 5.76795i) q^{81} +2.92820i q^{83} +(1.33013 - 1.50000i) q^{85} +(0.866025 + 0.232051i) q^{87} +(-14.7942 + 3.96410i) q^{89} +(0.571797 - 8.86603i) q^{91} +(3.29423 + 1.90192i) q^{93} +(4.96410 + 4.40192i) q^{95} +(3.86603 + 6.69615i) q^{97} +(8.46410 + 8.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9	\( 4 q - 2 q^{3} - 8 q^{5} - 12 q^{7} - 6 q^{9} - 8 q^{11} - 8 q^{13} + 8 q^{15} + 6 q^{17} - 8 q^{19} + 14 q^{21} - 14 q^{23} + 12 q^{25} - 2 q^{27} - 6 q^{29} + 8 q^{33} + 22 q^{35} - 12 q^{37} - 8 q^{39} + 20 q^{41} - 10 q^{43} + 14 q^{45} + 12 q^{49} - 4 q^{53} + 6 q^{55} + 20 q^{57} - 8 q^{59} + 18 q^{61} + 10 q^{63} + 28 q^{65} + 28 q^{67} + 14 q^{69} - 8 q^{71} - 32 q^{73} - 22 q^{75} + 34 q^{77} - 4 q^{81} - 12 q^{85} - 28 q^{89} + 30 q^{91} - 18 q^{93} + 6 q^{95} + 12 q^{97} + 20 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 8 * q^5 - 12 * q^7 - 6 * q^9 - 8 * q^11 - 8 * q^13 + 8 * q^15 + 6 * q^17 - 8 * q^19 + 14 * q^21 - 14 * q^23 + 12 * q^25 - 2 * q^27 - 6 * q^29 + 8 * q^33 + 22 * q^35 - 12 * q^37 - 8 * q^39 + 20 * q^41 - 10 * q^43 + 14 * q^45 + 12 * q^49 - 4 * q^53 + 6 * q^55 + 20 * q^57 - 8 * q^59 + 18 * q^61 + 10 * q^63 + 28 * q^65 + 28 * q^67 + 14 * q^69 - 8 * q^71 - 32 * q^73 - 22 * q^75 + 34 * q^77 - 4 * q^81 - 12 * q^85 - 28 * q^89 + 30 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more