LMFDB - Embedded newform 260.2.bf.b.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(37,260)]

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, 3, 7]))

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bf (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:	$0$
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			93.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.93
Dual form			260.2.bf.b.137.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-1.23205 + 2.13397i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})$	\(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-1.23205 + 2.13397i) q^{7} +(2.36603 + 1.36603i) q^{9} +(-1.13397 + 4.23205i) q^{11} +(3.00000 - 2.00000i) q^{13} +(0.866025 + 0.767949i) q^{15} +(-0.866025 + 0.232051i) q^{17} +(2.86603 - 0.767949i) q^{19} +(0.901924 + 0.901924i) q^{21} +(-0.133975 - 0.0358984i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(1.50000 - 0.866025i) q^{29} +(-5.19615 + 5.19615i) q^{31} +(1.96410 + 1.13397i) q^{33} +(-3.03590 - 4.59808i) q^{35} +(-0.767949 - 1.33013i) q^{37} +(-0.598076 - 1.76795i) q^{39} +(9.33013 + 2.50000i) q^{41} +(-1.59808 - 5.96410i) q^{43} +(-5.09808 + 3.36603i) q^{45} -10.9282 q^{47} +(0.464102 + 0.803848i) q^{49} +0.464102i q^{51} +(2.46410 + 2.46410i) q^{53} +(-7.33013 - 6.50000i) q^{55} -1.53590i q^{57} +(-2.33013 - 8.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(-5.83013 + 3.36603i) q^{63} +(1.00000 + 8.00000i) q^{65} +(10.6244 - 6.13397i) q^{67} +(-0.0358984 + 0.0621778i) q^{69} +(0.598076 + 2.23205i) q^{71} -14.9282i q^{73} +(-2.40192 + 0.964102i) q^{75} +(-7.63397 - 7.63397i) q^{77} -0.535898i q^{79} +(3.33013 + 5.76795i) q^{81} +2.92820 q^{83} +(0.401924 - 1.96410i) q^{85} +(-0.232051 - 0.866025i) q^{87} +(14.7942 + 3.96410i) q^{89} +(0.571797 + 8.86603i) q^{91} +(1.90192 + 3.29423i) q^{93} +(-1.33013 + 6.50000i) q^{95} +(-6.69615 - 3.86603i) q^{97} +(-8.46410 + 8.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 + 6 * q^9	$ 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9} - 8 q^{11} + 12 q^{13} + 8 q^{19} + 14 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} + 6 q^{29} - 6 q^{33} - 26 q^{35} - 10 q^{37} + 8 q^{39} + 20 q^{41} + 4 q^{43} - 10 q^{45} - 16 q^{47} - 12 q^{49} - 4 q^{53} - 12 q^{55} + 8 q^{59} + 18 q^{61} - 6 q^{63} + 4 q^{65} - 6 q^{67} - 14 q^{69} - 8 q^{71} - 20 q^{75} - 34 q^{77} - 4 q^{81} - 16 q^{83} + 12 q^{85} + 6 q^{87} + 28 q^{89} + 30 q^{91} + 18 q^{93} + 12 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 + 6 * q^9 - 8 * q^11 + 12 * q^13 + 8 * q^19 + 14 * q^21 - 4 * q^23 - 12 * q^25 - 2 * q^27 + 6 * q^29 - 6 * q^33 - 26 * q^35 - 10 * q^37 + 8 * q^39 + 20 * q^41 + 4 * q^43 - 10 * q^45 - 16 * q^47 - 12 * q^49 - 4 * q^53 - 12 * q^55 + 8 * q^59 + 18 * q^61 - 6 * q^63 + 4 * q^65 - 6 * q^67 - 14 * q^69 - 8 * q^71 - 20 * q^75 - 34 * q^77 - 4 * q^81 - 16 * q^83 + 12 * q^85 + 6 * q^87 + 28 * q^89 + 30 * q^91 + 18 * q^93 + 12 * q^95 - 6 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.133975	−	0.500000i	0.0773503	−	0.288675i	−0.916406	−	0.400251i	$-0.868923\pi$
$3$	0.133975	−	0.500000i	0.0773503	−	0.288675i	0.993756	+	0.111576i	$0.0355897\pi$
$4$		0			0
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$	−1.23205	+	2.13397i	−0.465671	+	0.806567i	−0.999232	−	0.0391956i	$-0.987520\pi$
$7$	−1.23205	+	2.13397i	−0.465671	+	0.806567i	0.533560	+	0.845762i	$0.320854\pi$
$8$		0			0
$9$	2.36603	+	1.36603i	0.788675	+	0.455342i
$10$		0			0
$11$	−1.13397	+	4.23205i	−0.341906	+	1.27601i	0.554279	+	0.832331i	$0.312994\pi$
$11$	−1.13397	+	4.23205i	−0.341906	+	1.27601i	−0.896185	+	0.443680i	$0.853673\pi$
$12$		0			0
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$14$		0			0
$15$	0.866025	+	0.767949i	0.223607	+	0.198284i
$16$		0			0
$17$	−0.866025	+	0.232051i	−0.210042	+	0.0562806i	−0.362306	−	0.932059i	$-0.618010\pi$
$17$	−0.866025	+	0.232051i	−0.210042	+	0.0562806i	0.152264	+	0.988340i	$0.451344\pi$
$18$		0			0
$19$	2.86603	−	0.767949i	0.657511	−	0.176180i	0.0853887	−	0.996348i	$-0.472787\pi$
$19$	2.86603	−	0.767949i	0.657511	−	0.176180i	0.572123	+	0.820168i	$0.306120\pi$
$20$		0			0
$21$	0.901924	+	0.901924i	0.196816	+	0.196816i
$22$		0			0
$23$	−0.133975	−	0.0358984i	−0.0279356	−	0.00748533i	0.244824	−	0.969567i	$-0.421270\pi$
$23$	−0.133975	−	0.0358984i	−0.0279356	−	0.00748533i	−0.272760	+	0.962082i	$0.587936\pi$
$24$		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	$-0.615254\pi$
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	0.632764	+	0.774345i	$0.281920\pi$
$30$		0			0
$31$	−5.19615	+	5.19615i	−0.933257	+	0.933257i	−0.997908	−	0.0646514i	$-0.979406\pi$
$31$	−5.19615	+	5.19615i	−0.933257	+	0.933257i	0.0646514	+	0.997908i	$0.479406\pi$
$32$		0			0
$33$	1.96410	+	1.13397i	0.341906	+	0.197400i
$34$		0			0
$35$	−3.03590	−	4.59808i	−0.513160	−	0.777217i
$36$		0			0
$37$	−0.767949	−	1.33013i	−0.126250	−	0.218672i	0.795971	−	0.605335i	$-0.206961\pi$
$37$	−0.767949	−	1.33013i	−0.126250	−	0.218672i	−0.922221	+	0.386663i	$0.873628\pi$
$38$		0			0
$39$	−0.598076	−	1.76795i	−0.0957688	−	0.283098i
$40$		0			0
$41$	9.33013	+	2.50000i	1.45712	+	0.390434i	0.898494	−	0.438985i	$-0.144662\pi$
$41$	9.33013	+	2.50000i	1.45712	+	0.390434i	0.558627	+	0.829419i	$0.311329\pi$
$42$		0			0
$43$	−1.59808	−	5.96410i	−0.243704	−	0.909517i	−0.974030	−	0.226418i	$-0.927298\pi$
$43$	−1.59808	−	5.96410i	−0.243704	−	0.909517i	0.730326	−	0.683099i	$-0.239368\pi$
$44$		0			0
$45$	−5.09808	+	3.36603i	−0.759976	+	0.501777i
$46$		0			0
$47$	−10.9282			−1.59404			−0.797021	−	0.603951i	$-0.793592\pi$
$47$	−10.9282			−1.59404			−0.797021	+	0.603951i	$0.793592\pi$
$48$		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
$55$	−7.33013	−	6.50000i	−0.988394	−	0.876460i
$56$		0			0
$57$		−	1.53590i		−	0.203435i
$58$		0			0
$59$	−2.33013	−	8.69615i	−0.303357	−	1.13214i	−0.934351	−	0.356355i	$-0.884019\pi$
$59$	−2.33013	−	8.69615i	−0.303357	−	1.13214i	0.630994	−	0.775788i	$-0.282647\pi$
$60$		0			0
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	−0.419748	−	0.907641i	$-0.637882\pi$
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	0.995914	−	0.0903080i	$-0.0287851\pi$
$62$		0			0
$63$	−5.83013	+	3.36603i	−0.734527	+	0.424079i
$64$		0			0
$65$	1.00000	+	8.00000i	0.124035	+	0.992278i
$66$		0			0
$67$	10.6244	−	6.13397i	1.29797	−	0.749384i	0.317918	−	0.948118i	$-0.397016\pi$
$67$	10.6244	−	6.13397i	1.29797	−	0.749384i	0.980053	+	0.198734i	$0.0636829\pi$
$68$		0			0
$69$	−0.0358984	+	0.0621778i	−0.00432166	+	0.00748533i
$70$		0			0
$71$	0.598076	+	2.23205i	0.0709786	+	0.264896i	0.992291	−	0.123927i	$-0.0395487\pi$
$71$	0.598076	+	2.23205i	0.0709786	+	0.264896i	−0.921313	+	0.388822i	$0.872882\pi$
$72$		0			0
$73$		−	14.9282i		−	1.74721i	−0.486632	−	0.873607i	$-0.661775\pi$
$73$		−	14.9282i		−	1.74721i	0.486632	−	0.873607i	$-0.338225\pi$
$74$		0			0
$75$	−2.40192	+	0.964102i	−0.277350	+	0.111325i
$76$		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
$83$	2.92820			0.321412			0.160706	−	0.987002i	$-0.448623\pi$
$83$	2.92820			0.321412			0.160706	+	0.987002i	$0.448623\pi$
$84$		0			0
$85$	0.401924	−	1.96410i	0.0435948	−	0.213037i
$86$		0			0
$87$	−0.232051	−	0.866025i	−0.0248785	−	0.0928477i
$88$		0			0
$89$	14.7942	+	3.96410i	1.56819	+	0.420194i	0.935243	−	0.354005i	$-0.115181\pi$
$89$	14.7942	+	3.96410i	1.56819	+	0.420194i	0.632942	+	0.774199i	$0.281847\pi$
$90$		0			0
$91$	0.571797	+	8.86603i	0.0599406	+	0.929412i
$92$		0			0
$93$	1.90192	+	3.29423i	0.197220	+	0.341596i
$94$		0			0
$95$	−1.33013	+	6.50000i	−0.136468	+	0.666886i
$96$		0			0
$97$	−6.69615	−	3.86603i	−0.679891	−	0.392535i	0.119923	−	0.992783i	$-0.461735\pi$
$97$	−6.69615	−	3.86603i	−0.679891	−	0.392535i	−0.799814	+	0.600248i	$0.795069\pi$
$98$		0			0
$99$	−8.46410	+	8.46410i	−0.850674	+	0.850674i
$100$		0			0
$101$	−14.8923	+	8.59808i	−1.48184	+	0.855541i	−0.999788	−	0.0206021i	$-0.993442\pi$
$101$	−14.8923	+	8.59808i	−1.48184	+	0.855541i	−0.482052	+	0.876143i	$0.660108\pi$
$102$		0			0
$103$	11.1962	−	11.1962i	1.10319	−	1.10319i	0.109166	−	0.994024i	$-0.465182\pi$
$103$	11.1962	−	11.1962i	1.10319	−	1.10319i	0.994024	−	0.109166i	$-0.0348181\pi$
$104$		0			0
$105$	−2.70577	+	0.901924i	−0.264056	+	0.0880187i
$106$		0			0
$107$	7.33013	+	1.96410i	0.708630	+	0.189877i	0.595093	−	0.803657i	$-0.297115\pi$
$107$	7.33013	+	1.96410i	0.708630	+	0.189877i	0.113537	+	0.993534i	$0.463782\pi$
$108$		0			0
$109$	3.53590	+	3.53590i	0.338678	+	0.338678i	0.855869	−	0.517192i	$-0.173023\pi$
$109$	3.53590	+	3.53590i	0.338678	+	0.338678i	−0.517192	+	0.855869i	$0.673023\pi$
$110$		0			0
$111$	−0.767949	+	0.205771i	−0.0728905	+	0.0195310i
$112$		0			0
$113$	−2.86603	+	0.767949i	−0.269613	+	0.0722426i	−0.391093	−	0.920351i	$-0.627903\pi$
$113$	−2.86603	+	0.767949i	−0.269613	+	0.0722426i	0.121480	+	0.992594i	$0.461236\pi$
$114$		0			0
$115$	0.205771	−	0.232051i	0.0191883	−	0.0216388i
$116$		0			0
$117$	9.83013	−	0.633975i	0.908796	−	0.0586110i
$118$		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
$123$	2.50000	−	4.33013i	0.225417	−	0.390434i
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	−5.33013	+	19.8923i	−0.472972	+	1.76516i	0.156029	+	0.987752i	$0.450131\pi$
$127$	−5.33013	+	19.8923i	−0.472972	+	1.76516i	−0.629001	+	0.777404i	$0.716536\pi$
$128$		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
$133$	−1.89230	+	7.06218i	−0.164084	+	0.612368i
$134$		0			0
$135$	2.09808	+	6.29423i	0.180574	+	0.541721i
$136$		0			0
$137$	−7.16025	+	12.4019i	−0.611742	+	1.05957i	0.379205	+	0.925313i	$0.376198\pi$
$137$	−7.16025	+	12.4019i	−0.611742	+	1.05957i	−0.990947	+	0.134255i	$0.957136\pi$
$138$		0			0
$139$	4.50000	+	2.59808i	0.381685	+	0.220366i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	4.50000	+	2.59808i	0.381685	+	0.220366i	−0.296866	+	0.954919i	$0.595942\pi$
$140$		0			0
$141$	−1.46410	+	5.46410i	−0.123300	+	0.460160i
$142$		0			0
$143$	5.06218	+	14.9641i	0.423321	+	1.25136i
$144$		0			0
$145$	0.232051	+	3.86603i	0.0192708	+	0.321056i
$146$		0			0
$147$	0.464102	−	0.124356i	0.0382785	−	0.0102567i
$148$		0			0
$149$	3.33013	−	0.892305i	0.272815	−	0.0731005i	−0.119818	−	0.992796i	$-0.538231\pi$
$149$	3.33013	−	0.892305i	0.272815	−	0.0731005i	0.392633	+	0.919695i	$0.371564\pi$
$150$		0			0
$151$	−0.267949	−	0.267949i	−0.0218054	−	0.0218054i	0.696120	−	0.717925i	$-0.254908\pi$
$151$	−0.267949	−	0.267949i	−0.0218054	−	0.0218054i	−0.717925	+	0.696120i	$0.754908\pi$
$152$		0			0
$153$	−2.36603	−	0.633975i	−0.191282	−	0.0512538i
$154$		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
$163$	−2.76795	−	1.59808i	−0.216803	−	0.125171i	0.387666	−	0.921800i	$-0.373281\pi$
$163$	−2.76795	−	1.59808i	−0.216803	−	0.125171i	−0.604469	+	0.796629i	$0.706615\pi$
$164$		0			0
$165$	−4.23205	+	2.79423i	−0.329465	+	0.217530i
$166$		0			0
$167$	9.23205	+	15.9904i	0.714398	+	1.23737i	0.963191	+	0.268816i	$0.0866325\pi$
$167$	9.23205	+	15.9904i	0.714398	+	1.23737i	−0.248794	+	0.968556i	$0.580034\pi$
$168$		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
$173$	−0.741670	−	2.76795i	−0.0563881	−	0.210443i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	−0.741670	−	2.76795i	−0.0563881	−	0.210443i	−0.988372	+	0.152057i	$0.951410\pi$
$174$		0			0
$175$	12.2321	−	1.47372i	0.924656	−	0.111403i
$176$		0			0
$177$	−4.66025			−0.350286
$178$		0			0
$179$	−6.96410	−	12.0622i	−0.520521	−	0.901570i	−0.999715	−	0.0238604i	$-0.992404\pi$
$179$	−6.96410	−	12.0622i	−0.520521	−	0.901570i	0.479194	−	0.877709i	$-0.340929\pi$
$180$		0			0
$181$		−	22.9282i		−	1.70424i	−0.523347	−	0.852120i	$-0.675317\pi$
$181$		−	22.9282i		−	1.70424i	0.523347	−	0.852120i	$-0.324683\pi$
$182$		0			0
$183$	−3.29423	−	3.29423i	−0.243516	−	0.243516i
$184$		0			0
$185$	3.42820	−	0.205771i	0.252047	−	0.0151286i
$186$		0			0
$187$		−	3.92820i		−	0.287259i
$188$		0			0
$189$	1.89230	+	7.06218i	0.137645	+	0.513698i
$190$		0			0
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	−0.456068	−	0.889945i	$-0.650743\pi$
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	0.998749	−	0.0500060i	$-0.0159241\pi$
$192$		0			0
$193$	−22.1603	+	12.7942i	−1.59513	+	0.920949i	−0.602723	+	0.797950i	$0.705918\pi$
$193$	−22.1603	+	12.7942i	−1.59513	+	0.920949i	−0.992407	+	0.122998i	$0.960749\pi$
$194$		0			0
$195$	4.13397	+	0.571797i	0.296040	+	0.0409472i
$196$		0			0
$197$	3.69615	−	2.13397i	0.263340	−	0.152039i	−0.362517	−	0.931977i	$-0.618083\pi$
$197$	3.69615	−	2.13397i	0.263340	−	0.152039i	0.625857	+	0.779938i	$0.284749\pi$
$198$		0			0
$199$	−9.42820	+	16.3301i	−0.668348	+	1.15761i	0.310018	+	0.950731i	$0.399665\pi$
$199$	−9.42820	+	16.3301i	−0.668348	+	1.15761i	−0.978366	+	0.206881i	$0.933669\pi$
$200$		0			0
$201$	−1.64359	−	6.13397i	−0.115930	−	0.432657i
$202$		0			0
$203$			4.26795i			0.299551i
$204$		0			0
$205$	−14.3301	+	16.1603i	−1.00086	+	1.12868i
$206$		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	0.745775	−	0.666198i	$-0.232080\pi$
$211$	−2.96410	−	5.13397i	−0.204057	−	0.353437i	−0.949832	+	0.312761i	$0.898746\pi$
$212$		0			0
$213$	1.19615			0.0819590
$214$		0			0
$215$	13.5263	+	2.76795i	0.922485	+	0.188773i
$216$		0			0
$217$	−4.68653	−	17.4904i	−0.318143	−	1.18732i
$218$		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
$223$	−0.767949	−	1.33013i	−0.0514257	−	0.0890719i	0.839167	−	0.543874i	$-0.183043\pi$
$223$	−0.767949	−	1.33013i	−0.0514257	−	0.0890719i	−0.890592	+	0.454802i	$0.849710\pi$
$224$		0			0
$225$	−1.63397	−	13.5622i	−0.108932	−	0.904145i
$226$		0			0
$227$	−2.76795	−	1.59808i	−0.183715	−	0.106068i	0.405322	−	0.914174i	$-0.367159\pi$
$227$	−2.76795	−	1.59808i	−0.183715	−	0.106068i	−0.589037	+	0.808106i	$0.700493\pi$
$228$		0			0
$229$	−0.0717968	+	0.0717968i	−0.00474446	+	0.00474446i	−0.709475	−	0.704731i	$-0.751068\pi$
$229$	−0.0717968	+	0.0717968i	−0.00474446	+	0.00474446i	0.704731	+	0.709475i	$0.251068\pi$
$230$		0			0
$231$	−4.83975	+	2.79423i	−0.318432	+	0.183847i
$232$		0			0
$233$	−12.8564	+	12.8564i	−0.842251	+	0.842251i	−0.989151	−	0.146900i	$-0.953070\pi$
$233$	−12.8564	+	12.8564i	−0.842251	+	0.842251i	0.146900	+	0.989151i	$0.453070\pi$
$234$		0			0
$235$	10.9282	−	21.8564i	0.712877	−	1.42575i
$236$		0			0
$237$	−0.267949	−	0.0717968i	−0.0174052	−	0.00466370i
$238$		0			0
$239$	−16.6603	−	16.6603i	−1.07766	−	1.07766i	−0.996719	−	0.0809436i	$-0.974207\pi$
$239$	−16.6603	−	16.6603i	−1.07766	−	1.07766i	−0.0809436	−	0.996719i	$-0.525793\pi$
$240$		0			0
$241$	11.3301	−	3.03590i	0.729838	−	0.195559i	0.125281	−	0.992121i	$-0.460017\pi$
$241$	11.3301	−	3.03590i	0.729838	−	0.195559i	0.604557	+	0.796562i	$0.293350\pi$
$242$		0			0
$243$	11.9282	−	3.19615i	0.765195	−	0.205033i
$244$		0			0
$245$	−2.07180	+	0.124356i	−0.132362	+	0.00794479i
$246$		0			0
$247$	7.06218	−	8.03590i	0.449356	−	0.511312i
$248$		0			0
$249$	0.392305	−	1.46410i	0.0248613	−	0.0927837i
$250$		0			0
$251$	−15.3564	−	8.86603i	−0.969288	−	0.559619i	−0.0702687	−	0.997528i	$-0.522386\pi$
$251$	−15.3564	−	8.86603i	−0.969288	−	0.559619i	−0.899019	+	0.437910i	$0.855719\pi$
$252$		0			0
$253$	0.303848	−	0.526279i	0.0191027	−	0.0330869i
$254$		0			0
$255$	−0.928203	−	0.464102i	−0.0581263	−	0.0290632i
$256$		0			0
$257$	5.79423	−	21.6244i	0.361434	−	1.34889i	−0.510757	−	0.859725i	$-0.670635\pi$
$257$	5.79423	−	21.6244i	0.361434	−	1.34889i	0.872191	−	0.489165i	$-0.162698\pi$
$258$		0			0
$259$	3.78461			0.235164
$260$		0			0
$261$	4.73205			0.292907
$262$		0			0
$263$	−3.72243	+	13.8923i	−0.229535	+	0.856636i	0.751002	+	0.660300i	$0.229571\pi$
$263$	−3.72243	+	13.8923i	−0.229535	+	0.856636i	−0.980537	+	0.196336i	$0.937096\pi$
$264$		0			0
$265$	−7.39230	+	2.46410i	−0.454106	+	0.151369i
$266$		0			0
$267$	3.96410	−	6.86603i	0.242599	−	0.420194i
$268$		0			0
$269$	−15.8205	−	9.13397i	−0.964593	−	0.556908i	−0.0670097	−	0.997752i	$-0.521346\pi$
$269$	−15.8205	−	9.13397i	−0.964593	−	0.556908i	−0.897584	+	0.440844i	$0.854679\pi$
$270$		0			0
$271$	4.33013	−	16.1603i	0.263036	−	0.981666i	−0.700405	−	0.713746i	$-0.746997\pi$
$271$	4.33013	−	16.1603i	0.263036	−	0.981666i	0.963441	−	0.267920i	$-0.0863362\pi$
$272$		0			0
$273$	4.50962	+	0.901924i	0.272935	+	0.0545869i
$274$		0			0
$275$	20.3301	−	8.16025i	1.22595	−	0.492082i
$276$		0			0
$277$	−10.3301	+	2.76795i	−0.620677	+	0.166310i	−0.555436	−	0.831560i	$-0.687448\pi$
$277$	−10.3301	+	2.76795i	−0.620677	+	0.166310i	−0.0652416	+	0.997869i	$0.520782\pi$
$278$		0			0
$279$	−19.3923	+	5.19615i	−1.16099	+	0.311086i
$280$		0			0
$281$	−16.4641	−	16.4641i	−0.982166	−	0.982166i	0.0176778	−	0.999844i	$-0.494373\pi$
$281$	−16.4641	−	16.4641i	−0.982166	−	0.982166i	−0.999844	+	0.0176778i	$0.994373\pi$
$282$		0			0
$283$	29.7224	+	7.96410i	1.76682	+	0.473417i	0.988081	−	0.153937i	$-0.0491953\pi$
$283$	29.7224	+	7.96410i	1.76682	+	0.473417i	0.778735	+	0.627354i	$0.215862\pi$
$284$		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
$293$	−17.7679	−	10.2583i	−1.03801	−	0.599298i	−0.118744	−	0.992925i	$-0.537887\pi$
$293$	−17.7679	−	10.2583i	−1.03801	−	0.599298i	−0.919270	+	0.393627i	$0.871220\pi$
$294$		0			0
$295$	19.7224	+	4.03590i	1.14828	+	0.234979i
$296$		0			0
$297$	6.50000	+	11.2583i	0.377168	+	0.653275i
$298$		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
$303$	2.30385	+	8.59808i	0.132353	+	0.493947i
$304$		0			0
$305$	11.0885	+	16.7942i	0.634923	+	0.961635i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	−4.09808	−	7.09808i	−0.233131	−	0.403795i
$310$		0			0
$311$			3.46410i			0.196431i	0.995165	+	0.0982156i	$0.0313135\pi$
$311$			3.46410i			0.196431i	−0.995165	+	0.0982156i	$0.968687\pi$
$312$		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
$315$	−0.901924	−	15.0263i	−0.0508176	−	0.846635i
$316$		0			0
$317$			18.9282i			1.06311i	0.847023	+	0.531557i	$0.178393\pi$
$317$			18.9282i			1.06311i	−0.847023	+	0.531557i	$0.821607\pi$
$318$		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
$323$	−2.30385	+	1.33013i	−0.128190	+	0.0740102i
$324$		0			0
$325$	−17.0000	−	6.00000i	−0.942990	−	0.332820i
$326$		0			0
$327$	2.24167	−	1.29423i	0.123965	−	0.0715710i
$328$		0			0
$329$	13.4641	−	23.3205i	0.742300	−	1.28570i
$330$		0			0
$331$	4.45448	+	16.6244i	0.244841	+	0.913757i	0.973464	+	0.228842i	$0.0734940\pi$
$331$	4.45448	+	16.6244i	0.244841	+	0.913757i	−0.728623	+	0.684915i	$0.759839\pi$
$332$		0			0
$333$		−	4.19615i		−	0.229948i
$334$		0			0
$335$	1.64359	+	27.3827i	0.0897991	+	1.49608i
$336$		0			0
$337$	15.9282	+	15.9282i	0.867665	+	0.867665i	0.992213	−	0.124549i	$-0.0397484\pi$
$337$	15.9282	+	15.9282i	0.867665	+	0.867665i	−0.124549	+	0.992213i	$0.539748\pi$
$338$		0			0
$339$			1.53590i			0.0834185i
$340$		0			0
$341$	−16.0981	−	27.8827i	−0.871760	−	1.50993i
$342$		0			0
$343$	−19.5359			−1.05484
$344$		0			0
$345$	−0.0884573	−	0.133975i	−0.00476238	−	0.00721295i
$346$		0			0
$347$	2.79423	+	10.4282i	0.150002	+	0.559815i	0.999482	+	0.0321938i	$0.0102494\pi$
$347$	2.79423	+	10.4282i	0.150002	+	0.559815i	−0.849480	+	0.527621i	$0.823084\pi$
$348$		0			0
$349$	7.86603	+	2.10770i	0.421059	+	0.112822i	0.463126	−	0.886292i	$-0.346728\pi$
$349$	7.86603	+	2.10770i	0.421059	+	0.112822i	−0.0420673	+	0.999115i	$0.513394\pi$
$350$		0			0
$351$	2.09808	−	10.4904i	0.111987	−	0.559935i
$352$		0			0
$353$	5.23205	+	9.06218i	0.278474	+	0.482331i	0.971006	−	0.239056i	$-0.0768381\pi$
$353$	5.23205	+	9.06218i	0.278474	+	0.482331i	−0.692532	+	0.721387i	$0.743505\pi$
$354$		0			0
$355$	−5.06218	−	1.03590i	−0.268673	−	0.0549798i
$356$		0			0
$357$	−0.990381	−	0.571797i	−0.0524165	−	0.0302627i
$358$		0			0
$359$	−13.1962	+	13.1962i	−0.696466	+	0.696466i	−0.963647	−	0.267180i	$-0.913908\pi$
$359$	−13.1962	+	13.1962i	−0.696466	+	0.696466i	0.267180	+	0.963647i	$0.413908\pi$
$360$		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
$367$	14.7942	+	3.96410i	0.772252	+	0.206924i	0.623366	−	0.781930i	$-0.285765\pi$
$367$	14.7942	+	3.96410i	0.772252	+	0.206924i	0.148886	+	0.988854i	$0.452431\pi$
$368$		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
$373$	−19.7942	+	5.30385i	−1.02491	+	0.274623i	−0.731845	−	0.681471i	$-0.761341\pi$
$373$	−19.7942	+	5.30385i	−1.02491	+	0.274623i	−0.293061	+	0.956094i	$0.594674\pi$
$374$		0			0
$375$	0.473721	−	5.76795i	0.0244628	−	0.297856i
$376$		0			0
$377$	2.76795	−	5.59808i	0.142557	−	0.288316i
$378$		0			0
$379$	−2.59808	+	9.69615i	−0.133454	+	0.498058i	−0.999999	−	0.00104063i	$-0.999669\pi$
$379$	−2.59808	+	9.69615i	−0.133454	+	0.498058i	0.866545	+	0.499099i	$0.166335\pi$
$380$		0			0
$381$	9.23205	+	5.33013i	0.472972	+	0.273071i
$382$		0			0
$383$	12.7679	−	22.1147i	0.652412	−	1.13001i	−0.330124	−	0.943937i	$-0.607091\pi$
$383$	12.7679	−	22.1147i	0.652412	−	1.13001i	0.982536	−	0.186073i	$-0.0595760\pi$
$384$		0			0
$385$	22.9019	−	7.63397i	1.16719	−	0.389063i
$386$		0			0
$387$	4.36603	−	16.2942i	0.221938	−	0.828282i
$388$		0			0
$389$	15.0718			0.764170			0.382085	−	0.924127i	$-0.375206\pi$
$389$	15.0718			0.764170			0.382085	+	0.924127i	$0.375206\pi$
$390$		0			0
$391$	0.124356			0.00628894
$392$		0			0
$393$	0.784610	−	2.92820i	0.0395783	−	0.147708i
$394$		0			0
$395$	1.07180	+	0.535898i	0.0539279	+	0.0269640i
$396$		0			0
$397$	−5.69615	+	9.86603i	−0.285882	+	0.495162i	−0.972823	−	0.231552i	$-0.925620\pi$
$397$	−5.69615	+	9.86603i	−0.285882	+	0.495162i	0.686941	+	0.726713i	$0.258953\pi$
$398$		0			0
$399$	3.27757	+	1.89230i	0.164084	+	0.0947337i
$400$		0			0
$401$	2.66987	−	9.96410i	0.133327	−	0.497583i	−0.866672	−	0.498878i	$-0.833745\pi$
$401$	2.66987	−	9.96410i	0.133327	−	0.497583i	0.999999	+	0.00129478i	$0.000412141\pi$
$402$		0			0
$403$	−5.19615	+	25.9808i	−0.258839	+	1.29419i
$404$		0			0
$405$	−14.8660	+	0.892305i	−0.738699	+	0.0443390i
$406$		0			0
$407$	6.50000	−	1.74167i	0.322193	−	0.0863314i
$408$		0			0
$409$	−18.5263	+	4.96410i	−0.916066	+	0.245459i	−0.685903	−	0.727693i	$-0.740593\pi$
$409$	−18.5263	+	4.96410i	−0.916066	+	0.245459i	−0.230163	+	0.973152i	$0.573926\pi$
$410$		0			0
$411$	5.24167	+	5.24167i	0.258553	+	0.258553i
$412$		0			0
$413$	21.4282	+	5.74167i	1.05441	+	0.282529i
$414$		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	0.539971	−	0.841684i	$-0.318435\pi$
$419$	31.5000	−	18.1865i	1.53888	−	0.888470i	0.998905	−	0.0467865i	$-0.0148981\pi$
$420$		0			0
$421$	6.85641	−	6.85641i	0.334161	−	0.334161i	−0.520003	−	0.854164i	$-0.674069\pi$
$421$	6.85641	−	6.85641i	0.334161	−	0.334161i	0.854164	+	0.520003i	$0.174069\pi$
$422$		0			0
$423$	−25.8564	−	14.9282i	−1.25718	−	0.725834i
$424$		0			0
$425$	3.52628	+	2.76795i	0.171050	+	0.134265i
$426$		0			0
$427$	11.0885	+	19.2058i	0.536608	+	0.929432i
$428$		0			0
$429$	8.16025	−	0.526279i	0.393981	−	0.0254090i
$430$		0			0
$431$	−23.2583	−	6.23205i	−1.12031	−	0.300187i	−0.349304	−	0.937010i	$-0.613582\pi$
$431$	−23.2583	−	6.23205i	−1.12031	−	0.300187i	−0.771011	+	0.636822i	$0.780249\pi$
$432$		0			0
$433$	8.72243	+	32.5526i	0.419173	+	1.56438i	0.776327	+	0.630330i	$0.217081\pi$
$433$	8.72243	+	32.5526i	0.419173	+	1.56438i	−0.357154	+	0.934046i	$0.616253\pi$
$434$		0			0
$435$	1.96410	+	0.401924i	0.0941715	+	0.0192708i
$436$		0			0
$437$	−0.411543			−0.0196868
$438$		0			0
$439$	−0.0358984	−	0.0621778i	−0.00171334	−	0.00296759i	0.865167	−	0.501483i	$-0.167212\pi$
$439$	−0.0358984	−	0.0621778i	−0.00171334	−	0.00296759i	−0.866881	+	0.498515i	$0.833879\pi$
$440$		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
$445$	−22.7224	+	25.6244i	−1.07715	+	1.21471i
$446$		0			0
$447$		−	1.78461i		−	0.0844091i
$448$		0			0
$449$	5.20577	+	19.4282i	0.245676	+	0.916874i	0.973043	+	0.230625i	$0.0740771\pi$
$449$	5.20577	+	19.4282i	0.245676	+	0.916874i	−0.727367	+	0.686249i	$0.759256\pi$
$450$		0			0
$451$	−21.1603	+	36.6506i	−0.996397	+	1.72581i
$452$		0			0
$453$	−0.169873	+	0.0980762i	−0.00798133	+	0.00460802i
$454$		0			0
$455$	−18.3038	−	7.72243i	−0.858098	−	0.362033i
$456$		0			0
$457$	−11.7679	+	6.79423i	−0.550481	+	0.317821i	−0.749316	−	0.662212i	$-0.769618\pi$
$457$	−11.7679	+	6.79423i	−0.550481	+	0.317821i	0.198835	+	0.980033i	$0.436284\pi$
$458$		0			0
$459$	−1.33013	+	2.30385i	−0.0620850	+	0.107534i
$460$		0			0
$461$	0.813467	+	3.03590i	0.0378869	+	0.141396i	0.982279	−	0.187427i	$-0.0600148\pi$
$461$	0.813467	+	3.03590i	0.0378869	+	0.141396i	−0.944392	+	0.328823i	$0.893348\pi$
$462$		0			0
$463$		−	21.6077i		−	1.00419i	−0.864811	−	0.502097i	$-0.832562\pi$
$463$		−	21.6077i		−	1.00419i	0.864811	−	0.502097i	$-0.167438\pi$
$464$		0			0
$465$	−8.49038	+	0.509619i	−0.393732	+	0.0236330i
$466$		0			0
$467$	−16.6603	−	16.6603i	−0.770945	−	0.770945i	0.207327	−	0.978272i	$-0.433524\pi$
$467$	−16.6603	−	16.6603i	−0.770945	−	0.770945i	−0.978272	+	0.207327i	$0.933524\pi$
$468$		0			0
$469$			30.2295i			1.39587i
$470$		0			0
$471$	−2.36603	−	4.09808i	−0.109021	−	0.188829i
$472$		0			0
$473$	27.0526			1.24388
$474$		0			0
$475$	−11.6699	−	9.16025i	−0.535450	−	0.420301i
$476$		0			0
$477$	2.46410	+	9.19615i	0.112823	+	0.421063i
$478$		0			0
$479$	3.13397	+	0.839746i	0.143195	+	0.0383690i	0.329705	−	0.944084i	$-0.393051\pi$
$479$	3.13397	+	0.839746i	0.143195	+	0.0383690i	−0.186510	+	0.982453i	$0.559718\pi$
$480$		0			0
$481$	−4.96410	−	2.45448i	−0.226344	−	0.111915i
$482$		0			0
$483$	−0.0884573	−	0.153212i	−0.00402495	−	0.00697141i
$484$		0			0
$485$	14.4282	−	9.52628i	0.655151	−	0.432566i
$486$		0			0
$487$	1.37564	+	0.794229i	0.0623364	+	0.0359899i	0.530844	−	0.847469i	$-0.321875\pi$
$487$	1.37564	+	0.794229i	0.0623364	+	0.0359899i	−0.468508	+	0.883459i	$0.655208\pi$
$488$		0			0
$489$	−1.16987	+	1.16987i	−0.0529035	+	0.0529035i
$490$		0			0
$491$	5.89230	−	3.40192i	0.265916	−	0.153527i	−0.361114	−	0.932522i	$-0.617604\pi$
$491$	5.89230	−	3.40192i	0.265916	−	0.153527i	0.627030	+	0.778995i	$0.284270\pi$
$492$		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
$497$	−5.50000	−	1.47372i	−0.246709	−	0.0661054i
$498$		0			0
$499$	−20.2679	−	20.2679i	−0.907318	−	0.907318i	0.0887371	−	0.996055i	$-0.471717\pi$
$499$	−20.2679	−	20.2679i	−0.907318	−	0.907318i	−0.996055	+	0.0887371i	$0.971717\pi$
$500$		0			0
$501$	9.23205	−	2.47372i	0.412458	−	0.110518i
$502$		0			0
$503$	12.5263	−	3.35641i	0.558519	−	0.149655i	0.0314933	−	0.999504i	$-0.489974\pi$
$503$	12.5263	−	3.35641i	0.558519	−	0.149655i	0.527026	+	0.849849i	$0.323307\pi$
$504$		0			0
$505$	−2.30385	−	38.3827i	−0.102520	−	1.70801i
$506$		0			0
$507$	−5.33013	−	4.10770i	−0.236719	−	0.182429i
$508$		0			0
$509$	7.45448	−	27.8205i	0.330414	−	1.23312i	−0.578342	−	0.815795i	$-0.696300\pi$
$509$	7.45448	−	27.8205i	0.330414	−	1.23312i	0.908756	−	0.417328i	$-0.137033\pi$
$510$		0			0
$511$	31.8564	+	18.3923i	1.40924	+	0.813628i
$512$		0			0
$513$	4.40192	−	7.62436i	0.194350	−	0.336624i
$514$		0			0
$515$	11.1962	+	33.5885i	0.493361	+	1.48008i
$516$		0			0
$517$	12.3923	−	46.2487i	0.545013	−	2.03402i
$518$		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
$523$	−2.93782	+	10.9641i	−0.128462	+	0.479427i	−0.999939	−	0.0110090i	$-0.996496\pi$
$523$	−2.93782	+	10.9641i	−0.128462	+	0.479427i	0.871477	+	0.490436i	$0.163162\pi$
$524$		0			0
$525$	0.901924	−	6.31347i	0.0393632	−	0.275542i
$526$		0			0
$527$	3.29423	−	5.70577i	0.143499	−	0.248547i
$528$		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
$533$	32.9904	−	11.1603i	1.42897	−	0.483404i
$534$		0			0
$535$	−11.2583	+	12.6962i	−0.486740	+	0.548903i
$536$		0			0
$537$	−6.96410	+	1.86603i	−0.300523	+	0.0805249i
$538$		0			0
$539$	−3.92820	+	1.05256i	−0.169200	+	0.0453369i
$540$		0			0
$541$	21.7846	+	21.7846i	0.936594	+	0.936594i	0.998106	−	0.0615128i	$-0.0195925\pi$
$541$	21.7846	+	21.7846i	0.936594	+	0.936594i	−0.0615128	+	0.998106i	$0.519592\pi$
$542$		0			0
$543$	−11.4641	−	3.07180i	−0.491972	−	0.131823i
$544$		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
$553$	1.14359	+	0.660254i	0.0486305	+	0.0280769i
$554$		0			0
$555$	0.356406	−	1.74167i	0.0151286	−	0.0739298i
$556$		0			0
$557$	−7.69615	−	13.3301i	−0.326096	−	0.564816i	0.655637	−	0.755076i	$-0.272400\pi$
$557$	−7.69615	−	13.3301i	−0.326096	−	0.564816i	−0.981734	+	0.190260i	$0.939067\pi$
$558$		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
$563$	−6.66987	−	24.8923i	−0.281102	−	1.04909i	−0.951641	−	0.307212i	$-0.900604\pi$
$563$	−6.66987	−	24.8923i	−0.281102	−	1.04909i	0.670540	−	0.741874i	$-0.266063\pi$
$564$		0			0
$565$	1.33013	−	6.50000i	0.0559589	−	0.273457i
$566$		0			0
$567$	−16.4115			−0.689220
$568$		0			0
$569$	−18.8205	−	32.5981i	−0.788997	−	1.36658i	−0.926582	−	0.376093i	$-0.877267\pi$
$569$	−18.8205	−	32.5981i	−0.788997	−	1.36658i	0.137585	−	0.990490i	$-0.456066\pi$
$570$		0			0
$571$			21.6077i			0.904254i	0.891954	+	0.452127i	$0.149335\pi$
$571$			21.6077i			0.904254i	−0.891954	+	0.452127i	$0.850665\pi$
$572$		0			0
$573$	−5.49038	−	5.49038i	−0.229364	−	0.229364i
$574$		0			0
$575$	0.258330	+	0.643594i	0.0107731	+	0.0268397i
$576$		0			0
$577$		−	20.7846i		−	0.865275i	−0.901568	−	0.432637i	$-0.857583\pi$
$577$		−	20.7846i		−	0.865275i	0.901568	−	0.432637i	$-0.142417\pi$
$578$		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
$583$	−13.2224	+	7.63397i	−0.547617	+	0.316167i
$584$		0			0
$585$	−8.56218	+	20.2942i	−0.354002	+	0.839063i
$586$		0			0
$587$	−41.0885	+	23.7224i	−1.69590	+	0.979130i	−0.746333	+	0.665573i	$0.768187\pi$
$587$	−41.0885	+	23.7224i	−1.69590	+	0.979130i	−0.949570	+	0.313556i	$0.898480\pi$
$588$		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
$593$		−	30.9282i		−	1.27007i	−0.772484	−	0.635035i	$-0.780986\pi$
$593$		−	30.9282i		−	1.27007i	0.772484	−	0.635035i	$-0.219014\pi$
$594$		0			0
$595$	3.69615	+	3.27757i	0.151527	+	0.134367i
$596$		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	0.976815	−	0.214087i	$-0.0686775\pi$
$601$	7.42820	+	12.8660i	0.303003	+	0.524816i	−0.673812	+	0.738903i	$0.735344\pi$
$602$		0			0
$603$	33.5167			1.36490
$604$		0			0
$605$	15.2942	−	10.0981i	0.621799	−	0.410545i
$606$		0			0
$607$	−0.813467	−	3.03590i	−0.0330176	−	0.123223i	0.947450	−	0.319904i	$-0.103651\pi$
$607$	−0.813467	−	3.03590i	−0.0330176	−	0.123223i	−0.980468	+	0.196680i	$0.936984\pi$
$608$		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
$613$	−12.2321	−	21.1865i	−0.494048	−	0.855716i	0.505929	−	0.862575i	$-0.331150\pi$
$613$	−12.2321	−	21.1865i	−0.494048	−	0.855716i	−0.999976	+	0.00685934i	$0.997817\pi$
$614$		0			0
$615$	6.16025	+	9.33013i	0.248405	+	0.376227i
$616$		0			0
$617$	−15.2321	−	8.79423i	−0.613219	−	0.354042i	0.161005	−	0.986954i	$-0.448526\pi$
$617$	−15.2321	−	8.79423i	−0.613219	−	0.354042i	−0.774224	+	0.632911i	$0.781860\pi$
$618$		0			0
$619$	−14.6603	+	14.6603i	−0.589245	+	0.589245i	−0.937427	−	0.348182i	$-0.886799\pi$
$619$	−14.6603	+	14.6603i	−0.589245	+	0.589245i	0.348182	+	0.937427i	$0.386799\pi$
$620$		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
$627$	6.50000	+	1.74167i	0.259585	+	0.0695556i
$628$		0			0
$629$	0.973721	+	0.973721i	0.0388248	+	0.0388248i
$630$		0			0
$631$	41.6506	−	11.1603i	1.65809	−	0.444283i	0.696225	−	0.717823i	$-0.254862\pi$
$631$	41.6506	−	11.1603i	1.65809	−	0.444283i	0.961860	+	0.273541i	$0.0881948\pi$
$632$		0			0
$633$	−2.96410	+	0.794229i	−0.117812	+	0.0315678i
$634$		0			0
$635$	−34.4545	−	30.5526i	−1.36728	−	1.21244i
$636$		0			0
$637$	3.00000	+	1.48334i	0.118864	+	0.0587721i
$638$		0			0
$639$	−1.63397	+	6.09808i	−0.0646390	+	0.241236i
$640$		0			0
$641$	5.64359	+	3.25833i	0.222909	+	0.128696i	0.607296	−	0.794475i	$-0.292254\pi$
$641$	5.64359	+	3.25833i	0.222909	+	0.128696i	−0.384388	+	0.923172i	$0.625587\pi$
$642$		0			0
$643$	18.0885	−	31.3301i	0.713339	−	1.23554i	−0.250258	−	0.968179i	$-0.580515\pi$
$643$	18.0885	−	31.3301i	0.713339	−	1.23554i	0.963597	−	0.267360i	$-0.0861514\pi$
$644$		0			0
$645$	3.19615	−	6.39230i	0.125848	−	0.251697i
$646$		0			0
$647$	0.669873	−	2.50000i	0.0263354	−	0.0982851i	−0.951507	−	0.307626i	$-0.900465\pi$
$647$	0.669873	−	2.50000i	0.0263354	−	0.0982851i	0.977843	+	0.209341i	$0.0671320\pi$
$648$		0			0
$649$	39.4449			1.54835
$650$		0			0
$651$	−9.37307			−0.367359
$652$		0			0
$653$	−12.8468	+	47.9449i	−0.502734	+	1.87623i	−0.0212467	+	0.999774i	$0.506764\pi$
$653$	−12.8468	+	47.9449i	−0.502734	+	1.87623i	−0.481487	+	0.876453i	$0.659903\pi$
$654$		0			0
$655$	−5.85641	+	11.7128i	−0.228829	+	0.457657i
$656$		0			0
$657$	20.3923	−	35.3205i	0.795580	−	1.37798i
$658$		0			0
$659$	35.4282	+	20.4545i	1.38009	+	0.796794i	0.992169	−	0.124901i	$-0.0398612\pi$
$659$	35.4282	+	20.4545i	1.38009	+	0.796794i	0.387918	+	0.921694i	$0.373195\pi$
$660$		0			0
$661$	−0.794229	+	2.96410i	−0.0308919	+	0.115290i	−0.979650	−	0.200713i	$-0.935674\pi$
$661$	−0.794229	+	2.96410i	−0.0308919	+	0.115290i	0.948758	+	0.316003i	$0.102341\pi$
$662$		0			0
$663$	0.928203	+	1.39230i	0.0360484	+	0.0540726i
$664$		0			0
$665$	−12.2321	−	10.8468i	−0.474339	−	0.420620i
$666$		0			0
$667$	−0.232051	+	0.0621778i	−0.00898504	+	0.00240754i
$668$		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
$673$	35.9186	+	9.62436i	1.38456	+	0.370992i	0.872775	−	0.488122i	$-0.162318\pi$
$673$	35.9186	+	9.62436i	1.38456	+	0.370992i	0.511784	+	0.859114i	$0.328985\pi$
$674$		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
$683$	12.6962	+	7.33013i	0.485805	+	0.280480i	0.722832	−	0.691023i	$-0.242840\pi$
$683$	12.6962	+	7.33013i	0.485805	+	0.280480i	−0.237028	+	0.971503i	$0.576173\pi$
$684$		0			0
$685$	−17.6436	−	26.7224i	−0.674127	−	1.02101i
$686$		0			0
$687$	0.0262794	+	0.0455173i	0.00100262	+	0.00173659i
$688$		0			0
$689$	12.3205	+	2.46410i	0.469374	+	0.0938748i
$690$		0			0
$691$	−37.6506	−	10.0885i	−1.43230	−	0.383783i	−0.542468	−	0.840076i	$-0.682510\pi$
$691$	−37.6506	−	10.0885i	−1.43230	−	0.383783i	−0.889829	+	0.456293i	$0.849177\pi$
$692$		0			0
$693$	−7.63397	−	28.4904i	−0.289991	−	1.08226i
$694$		0			0
$695$	−9.69615	+	6.40192i	−0.367796	+	0.242839i
$696$		0			0
$697$	−8.66025			−0.328031
$698$		0			0
$699$	4.70577	+	8.15064i	0.177989	+	0.308285i
$700$		0			0
$701$			21.0718i			0.795871i	0.917413	+	0.397935i	$0.130273\pi$
$701$			21.0718i			0.795871i	−0.917413	+	0.397935i	$0.869727\pi$
$702$		0			0
$703$	−3.22243	−	3.22243i	−0.121536	−	0.121536i
$704$		0			0
$705$	−9.46410	−	8.39230i	−0.356439	−	0.316072i
$706$		0			0
$707$		−	42.3731i		−	1.59360i
$708$		0			0
$709$	4.27757	+	15.9641i	0.160647	+	0.599544i	0.998555	+	0.0537328i	$0.0171119\pi$
$709$	4.27757	+	15.9641i	0.160647	+	0.599544i	−0.837908	+	0.545812i	$0.816221\pi$
$710$		0			0
$711$	0.732051	−	1.26795i	0.0274541	−	0.0475518i
$712$		0			0
$713$	0.882686	−	0.509619i	0.0330568	−	0.0190854i
$714$		0			0
$715$	−34.9904	−	4.83975i	−1.30857	−	0.180996i
$716$		0			0
$717$	−10.5622	+	6.09808i	−0.394452	+	0.227737i
$718$		0			0
$719$	20.9641	−	36.3109i	0.781829	−	1.35417i	−0.149046	−	0.988830i	$-0.547620\pi$
$719$	20.9641	−	36.3109i	0.781829	−	1.35417i	0.930875	−	0.365337i	$-0.119046\pi$
$720$		0			0
$721$	10.0981	+	37.6865i	0.376072	+	1.40352i
$722$		0			0
$723$		−	6.07180i		−	0.225813i
$724$		0			0
$725$	−7.96410	−	3.40192i	−0.295779	−	0.126344i
$726$		0			0
$727$	33.5885	+	33.5885i	1.24573	+	1.24573i	0.957589	+	0.288138i	$0.0930362\pi$
$727$	33.5885	+	33.5885i	1.24573	+	1.24573i	0.288138	+	0.957589i	$0.406964\pi$
$728$		0			0
$729$			13.5885i			0.503276i
$730$		0			0
$731$	2.76795	+	4.79423i	0.102376	+	0.177321i
$732$		0			0
$733$	26.7846			0.989312			0.494656	−	0.869089i	$-0.335294\pi$
$733$	26.7846			0.989312			0.494656	+	0.869089i	$0.335294\pi$
$734$		0			0
$735$	−0.215390	+	1.05256i	−0.00794479	+	0.0388242i
$736$		0			0
$737$	13.9115	+	51.9186i	0.512438	+	1.91245i
$738$		0			0
$739$	37.9186	+	10.1603i	1.39486	+	0.373751i	0.876495	−	0.481410i	$-0.159875\pi$
$739$	37.9186	+	10.1603i	1.39486	+	0.373751i	0.518362	+	0.855161i	$0.326542\pi$
$740$		0			0
$741$	−3.07180	−	4.60770i	−0.112845	−	0.169268i
$742$		0			0
$743$	−11.1603	−	19.3301i	−0.409430	−	0.709154i	0.585396	−	0.810748i	$-0.300939\pi$
$743$	−11.1603	−	19.3301i	−0.409430	−	0.709154i	−0.994826	+	0.101594i	$0.967606\pi$
$744$		0			0
$745$	−1.54552	+	7.55256i	−0.0566234	+	0.276704i
$746$		0			0
$747$	6.92820	+	4.00000i	0.253490	+	0.146352i
$748$		0			0
$749$	−13.2224	+	13.2224i	−0.483137	+	0.483137i
$750$		0			0
$751$	17.6436	−	10.1865i	0.643824	−	0.371712i	−0.142262	−	0.989829i	$-0.545438\pi$
$751$	17.6436	−	10.1865i	0.643824	−	0.371712i	0.786086	+	0.618117i	$0.212104\pi$
$752$		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
$757$	18.0622	+	4.83975i	0.656481	+	0.175904i	0.571657	−	0.820492i	$-0.306301\pi$
$757$	18.0622	+	4.83975i	0.656481	+	0.175904i	0.0848236	+	0.996396i	$0.472967\pi$
$758$		0			0
$759$	−0.222432	−	0.222432i	−0.00807377	−	0.00807377i
$760$		0			0
$761$	−0.669873	+	0.179492i	−0.0242829	+	0.00650658i	−0.270940	−	0.962596i	$-0.587335\pi$
$761$	−0.669873	+	0.179492i	−0.0242829	+	0.00650658i	0.246657	+	0.969103i	$0.420668\pi$
$762$		0			0
$763$	−11.9019	+	3.18911i	−0.430879	+	0.115454i
$764$		0			0
$765$	3.63397	−	4.09808i	0.131387	−	0.148166i
$766$		0			0
$767$	−24.3827	−	21.4282i	−0.880408	−	0.773728i
$768$		0			0
$769$	−5.47372	+	20.4282i	−0.197387	+	0.736660i	0.794248	+	0.607593i	$0.207865\pi$
$769$	−5.47372	+	20.4282i	−0.197387	+	0.736660i	−0.991636	+	0.129067i	$0.958802\pi$
$770$		0			0
$771$	−10.0359	−	5.79423i	−0.361434	−	0.208674i
$772$		0			0
$773$	−9.83975	+	17.0429i	−0.353911	+	0.612992i	−0.986931	−	0.161144i	$-0.948482\pi$
$773$	−9.83975	+	17.0429i	−0.353911	+	0.612992i	0.633020	+	0.774136i	$0.281815\pi$
$774$		0			0
$775$	36.3731	+	5.19615i	1.30656	+	0.186651i
$776$		0			0
$777$	0.507042	−	1.89230i	0.0181900	−	0.0678861i
$778$		0			0
$779$	28.6603			1.02686
$780$		0			0
$781$	−10.1244			−0.362278
$782$		0			0
$783$	1.33013	−	4.96410i	0.0475349	−	0.177403i
$784$		0			0
$785$	6.46410	+	19.3923i	0.230714	+	0.692141i
$786$		0			0
$787$	−21.6244	+	37.4545i	−0.770825	+	1.33511i	0.166286	+	0.986078i	$0.446822\pi$
$787$	−21.6244	+	37.4545i	−0.770825	+	1.33511i	−0.937111	+	0.349031i	$0.886511\pi$
$788$		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
$793$	−2.08846	−	32.3827i	−0.0741633	−	1.14994i
$794$		0			0
$795$	0.241670	+	4.02628i	0.00857114	+	0.142797i
$796$		0			0
$797$	20.9904	−	5.62436i	0.743517	−	0.199225i	0.132877	−	0.991133i	$-0.457579\pi$
$797$	20.9904	−	5.62436i	0.743517	−	0.199225i	0.610641	+	0.791908i	$0.290912\pi$
$798$		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
$803$	63.1769	+	16.9282i	2.22946	+	0.597383i
$804$		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	$-0.599723\pi$
$809$	10.2846	−	5.93782i	0.361588	−	0.208763i	0.669777	+	0.742562i	$0.266390\pi$
$810$		0			0
$811$	−23.0526	+	23.0526i	−0.809485	+	0.809485i	−0.984556	−	0.175071i	$-0.943985\pi$
$811$	−23.0526	+	23.0526i	−0.809485	+	0.809485i	0.175071	+	0.984556i	$0.443985\pi$
$812$		0			0
$813$	−7.50000	−	4.33013i	−0.263036	−	0.151864i
$814$		0			0
$815$	5.96410	−	3.93782i	0.208913	−	0.137936i
$816$		0			0
$817$	−9.16025	−	15.8660i	−0.320477	−	0.555082i
$818$		0			0
$819$	−10.7583	+	21.7583i	−0.375926	+	0.760298i
$820$		0			0
$821$	−27.4545	−	7.35641i	−0.958168	−	0.256740i	−0.254343	−	0.967114i	$-0.581859\pi$
$821$	−27.4545	−	7.35641i	−0.958168	−	0.256740i	−0.703825	+	0.710374i	$0.748526\pi$
$822$		0			0
$823$	6.40192	+	23.8923i	0.223157	+	0.832833i	0.983135	+	0.182884i	$0.0585433\pi$
$823$	6.40192	+	23.8923i	0.223157	+	0.832833i	−0.759977	+	0.649949i	$0.774790\pi$
$824$		0			0
$825$	−1.35641	−	11.2583i	−0.0472240	−	0.391965i
$826$		0			0
$827$	−25.8564			−0.899115			−0.449558	−	0.893251i	$-0.648418\pi$
$827$	−25.8564			−0.899115			−0.449558	+	0.893251i	$0.648418\pi$
$828$		0			0
$829$	−4.42820	−	7.66987i	−0.153798	−	0.266386i	0.778823	−	0.627244i	$-0.215817\pi$
$829$	−4.42820	−	7.66987i	−0.153798	−	0.266386i	−0.932621	+	0.360858i	$0.882484\pi$
$830$		0			0
$831$			5.53590i			0.192038i
$832$		0			0
$833$	−0.588457	−	0.588457i	−0.0203888	−	0.0203888i
$834$		0			0
$835$	−41.2128	+	2.47372i	−1.42623	+	0.0856066i
$836$		0			0
$837$			21.8038i			0.753651i
$838$		0			0
$839$	−7.79423	−	29.0885i	−0.269087	−	1.00425i	−0.959701	−	0.281022i	$-0.909327\pi$
$839$	−7.79423	−	29.0885i	−0.269087	−	1.00425i	0.690615	−	0.723223i	$-0.257340\pi$
$840$		0			0
$841$	−13.0000	+	22.5167i	−0.448276	+	0.776437i
$842$		0			0
$843$	−10.4378	+	6.02628i	−0.359498	+	0.207556i
$844$		0			0
$845$	19.0000	+	22.0000i	0.653620	+	0.756823i
$846$		0			0
$847$	17.4904	−	10.0981i	0.600977	−	0.346974i
$848$		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
$853$		−	53.8564i		−	1.84401i	−0.387180	−	0.922004i	$-0.626551\pi$
$853$		−	53.8564i		−	1.84401i	0.387180	−	0.922004i	$-0.373449\pi$
$854$		0			0
$855$	−12.0263	+	13.5622i	−0.411290	+	0.463817i
$856$		0			0
$857$	19.2487	+	19.2487i	0.657523	+	0.657523i	0.954793	−	0.297270i	$-0.0960761\pi$
$857$	19.2487	+	19.2487i	0.657523	+	0.657523i	−0.297270	+	0.954793i	$0.596076\pi$
$858$		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
$863$	−2.14359			−0.0729688			−0.0364844	−	0.999334i	$-0.511616\pi$
$863$	−2.14359			−0.0729688			−0.0364844	+	0.999334i	$0.511616\pi$
$864$		0			0
$865$	6.27757	+	1.28461i	0.213444	+	0.0436780i
$866$		0			0
$867$	2.16987	+	8.09808i	0.0736927	+	0.275025i
$868$		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
$873$	−10.5622	−	18.2942i	−0.357476	−	0.619166i
$874$		0			0
$875$	−9.28461	+	25.9378i	−0.313877	+	0.876858i
$876$		0			0
$877$	−32.5526	−	18.7942i	−1.09922	−	0.634636i	−0.163205	−	0.986592i	$-0.552183\pi$
$877$	−32.5526	−	18.7942i	−1.09922	−	0.634636i	−0.936017	+	0.351956i	$0.885517\pi$
$878$		0			0
$879$	−7.50962	+	7.50962i	−0.253293	+	0.253293i
$880$		0			0
$881$	4.96410	−	2.86603i	0.167245	−	0.0965588i	−0.414041	−	0.910258i	$-0.635883\pi$
$881$	4.96410	−	2.86603i	0.167245	−	0.0965588i	0.581286	+	0.813699i	$0.302550\pi$
$882$		0			0
$883$	−0.803848	+	0.803848i	−0.0270516	+	0.0270516i	−0.720503	−	0.693452i	$-0.756089\pi$
$883$	−0.803848	+	0.803848i	−0.0270516	+	0.0270516i	0.693452	+	0.720503i	$0.256089\pi$
$884$		0			0
$885$	4.66025	−	9.32051i	0.156653	−	0.313305i
$886$		0			0
$887$	−0.133975	−	0.0358984i	−0.00449843	−	0.00120535i	0.256569	−	0.966526i	$-0.417408\pi$
$887$	−0.133975	−	0.0358984i	−0.00449843	−	0.00120535i	−0.261068	+	0.965321i	$0.584075\pi$
$888$		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
$893$	−31.3205	+	8.39230i	−1.04810	+	0.280838i
$894$		0			0
$895$	31.0885	−	1.86603i	1.03917	−	0.0623744i
$896$		0			0
$897$	0.0166605	+	0.258330i	0.000556278	+	0.00862540i
$898$		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
$903$	3.93782	−	6.82051i	0.131043	−	0.226972i
$904$		0			0
$905$	45.8564	+	22.9282i	1.52432	+	0.762159i
$906$		0			0
$907$	11.3494	−	42.3564i	0.376849	−	1.40642i	−0.473774	−	0.880646i	$-0.657109\pi$
$907$	11.3494	−	42.3564i	0.376849	−	1.40642i	0.850624	−	0.525775i	$-0.176225\pi$
$908$		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
$913$	−3.32051	+	12.3923i	−0.109893	+	0.410125i
$914$		0			0
$915$	9.88269	−	3.29423i	0.326712	−	0.108904i
$916$		0			0
$917$	−7.21539	+	12.4974i	−0.238273	+	0.412701i
$918$		0			0
$919$	33.1410	+	19.1340i	1.09322	+	0.631172i	0.934432	−	0.356141i	$-0.115908\pi$
$919$	33.1410	+	19.1340i	1.09322	+	0.631172i	0.158789	+	0.987313i	$0.449241\pi$
$920$		0			0
$921$	0.535898	−	2.00000i	0.0176585	−	0.0659022i
$922$		0			0
$923$	6.25833	+	5.50000i	0.205995	+	0.181035i
$924$		0			0
$925$	−3.01666	+	7.06218i	−0.0991872	+	0.232203i
$926$		0			0
$927$	41.7846	−	11.1962i	1.37239	−	0.367730i
$928$		0			0
$929$	−21.9904	+	5.89230i	−0.721481	+	0.193320i	−0.600832	−	0.799375i	$-0.705164\pi$
$929$	−21.9904	+	5.89230i	−0.721481	+	0.193320i	−0.120649	+	0.992695i	$0.538497\pi$
$930$		0			0
$931$	1.94744	+	1.94744i	0.0638248	+	0.0638248i
$932$		0			0
$933$	1.73205	+	0.464102i	0.0567048	+	0.0151940i
$934$		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	−0.586463	−	0.809976i	$-0.699480\pi$
$941$	6.85641	−	6.85641i	0.223512	−	0.223512i	0.809976	+	0.586463i	$0.199480\pi$
$942$		0			0
$943$	−1.16025	−	0.669873i	−0.0377831	−	0.0218141i
$944$		0			0
$945$	−16.0167	−	3.27757i	−0.521022	−	0.106619i
$946$		0			0
$947$	−2.62436	−	4.54552i	−0.0852801	−	0.147709i	0.820230	−	0.572033i	$-0.193845\pi$
$947$	−2.62436	−	4.54552i	−0.0852801	−	0.147709i	−0.905511	+	0.424324i	$0.860512\pi$
$948$		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
$953$	−3.38269	−	12.6244i	−0.109576	−	0.408943i	0.889248	−	0.457425i	$-0.151228\pi$
$953$	−3.38269	−	12.6244i	−0.109576	−	0.408943i	−0.998824	+	0.0484822i	$0.984562\pi$
$954$		0			0
$955$	18.4808	+	27.9904i	0.598023	+	0.905747i
$956$		0			0
$957$	3.92820			0.126981
$958$		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
$965$	−3.42820	−	57.1147i	−0.110358	−	1.83859i
$966$		0			0
$967$		−	58.3923i		−	1.87777i	−0.344231	−	0.938885i	$-0.611860\pi$
$967$		−	58.3923i		−	1.87777i	0.344231	−	0.938885i	$-0.388140\pi$
$968$		0			0
$969$	0.356406	+	1.33013i	0.0114494	+	0.0427298i
$970$		0			0
$971$	17.8923	−	30.9904i	0.574191	−	0.994529i	−0.421938	−	0.906625i	$-0.638650\pi$
$971$	17.8923	−	30.9904i	0.574191	−	0.994529i	0.996129	−	0.0879038i	$-0.0280168\pi$
$972$		0			0
$973$	−11.0885	+	6.40192i	−0.355480	+	0.205236i
$974$		0			0
$975$	−5.27757	+	7.69615i	−0.169017	+	0.246474i
$976$		0			0
$977$	−15.2321	+	8.79423i	−0.487316	+	0.281352i	−0.723461	−	0.690366i	$-0.757450\pi$
$977$	−15.2321	+	8.79423i	−0.487316	+	0.281352i	0.236144	+	0.971718i	$0.424116\pi$
$978$		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
$983$			1.60770i			0.0512775i	0.999671	+	0.0256388i	$0.00816196\pi$
$983$			1.60770i			0.0512775i	−0.999671	+	0.0256388i	$0.991838\pi$
$984$		0			0
$985$	0.571797	+	9.52628i	0.0182190	+	0.303533i
$986$		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	−0.980252	−	0.197753i	$-0.936636\pi$
$991$	−20.8205	−	36.0622i	−0.661385	−	1.14555i	0.318867	−	0.947800i	$-0.396698\pi$
$992$		0			0
$993$	8.90897			0.282717
$994$		0			0
$995$	−23.2321	−	35.1865i	−0.736506	−	1.11549i
$996$		0			0
$997$	−2.20577	−	8.23205i	−0.0698575	−	0.260712i	0.922161	−	0.386807i	$-0.126422\pi$
$997$	−2.20577	−	8.23205i	−0.0698575	−	0.260712i	−0.992018	+	0.126095i	$0.959755\pi$
$998$		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.bf.b.93.1	✓	4
5.2	odd	4		260.2.bk.a.197.1	yes	4
5.3	odd	4		1300.2.bs.b.457.1		4
5.4	even	2		1300.2.bn.a.93.1		4
13.7	odd	12		260.2.bk.a.33.1	yes	4
65.7	even	12	inner	260.2.bf.b.137.1	yes	4
65.33	even	12		1300.2.bn.a.657.1		4
65.59	odd	12		1300.2.bs.b.293.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.b.93.1	✓	4	1.1	even	1	trivial
260.2.bf.b.137.1	yes	4	65.7	even	12	inner
260.2.bk.a.33.1	yes	4	13.7	odd	12
260.2.bk.a.197.1	yes	4	5.2	odd	4
1300.2.bn.a.93.1		4	5.4	even	2
1300.2.bn.a.657.1		4	65.33	even	12
1300.2.bs.b.293.1		4	65.59	odd	12
1300.2.bs.b.457.1		4	5.3	odd	4

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.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-1.23205 + 2.13397i) q^{7} +(2.36603 + 1.36603i) q^{9} +O(q^{10})\)	\(q+(0.133975 - 0.500000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-1.23205 + 2.13397i) q^{7} +(2.36603 + 1.36603i) q^{9} +(-1.13397 + 4.23205i) q^{11} +(3.00000 - 2.00000i) q^{13} +(0.866025 + 0.767949i) q^{15} +(-0.866025 + 0.232051i) q^{17} +(2.86603 - 0.767949i) q^{19} +(0.901924 + 0.901924i) q^{21} +(-0.133975 - 0.0358984i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(2.09808 - 2.09808i) q^{27} +(1.50000 - 0.866025i) q^{29} +(-5.19615 + 5.19615i) q^{31} +(1.96410 + 1.13397i) q^{33} +(-3.03590 - 4.59808i) q^{35} +(-0.767949 - 1.33013i) q^{37} +(-0.598076 - 1.76795i) q^{39} +(9.33013 + 2.50000i) q^{41} +(-1.59808 - 5.96410i) q^{43} +(-5.09808 + 3.36603i) q^{45} -10.9282 q^{47} +(0.464102 + 0.803848i) q^{49} +0.464102i q^{51} +(2.46410 + 2.46410i) q^{53} +(-7.33013 - 6.50000i) q^{55} -1.53590i q^{57} +(-2.33013 - 8.69615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(-5.83013 + 3.36603i) q^{63} +(1.00000 + 8.00000i) q^{65} +(10.6244 - 6.13397i) q^{67} +(-0.0358984 + 0.0621778i) q^{69} +(0.598076 + 2.23205i) q^{71} -14.9282i q^{73} +(-2.40192 + 0.964102i) q^{75} +(-7.63397 - 7.63397i) q^{77} -0.535898i q^{79} +(3.33013 + 5.76795i) q^{81} +2.92820 q^{83} +(0.401924 - 1.96410i) q^{85} +(-0.232051 - 0.866025i) q^{87} +(14.7942 + 3.96410i) q^{89} +(0.571797 + 8.86603i) q^{91} +(1.90192 + 3.29423i) q^{93} +(-1.33013 + 6.50000i) q^{95} +(-6.69615 - 3.86603i) q^{97} +(-8.46410 + 8.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 + 6 * q^9	\( 4 q + 4 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{9} - 8 q^{11} + 12 q^{13} + 8 q^{19} + 14 q^{21} - 4 q^{23} - 12 q^{25} - 2 q^{27} + 6 q^{29} - 6 q^{33} - 26 q^{35} - 10 q^{37} + 8 q^{39} + 20 q^{41} + 4 q^{43} - 10 q^{45} - 16 q^{47} - 12 q^{49} - 4 q^{53} - 12 q^{55} + 8 q^{59} + 18 q^{61} - 6 q^{63} + 4 q^{65} - 6 q^{67} - 14 q^{69} - 8 q^{71} - 20 q^{75} - 34 q^{77} - 4 q^{81} - 16 q^{83} + 12 q^{85} + 6 q^{87} + 28 q^{89} + 30 q^{91} + 18 q^{93} + 12 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 + 6 * q^9 - 8 * q^11 + 12 * q^13 + 8 * q^19 + 14 * q^21 - 4 * q^23 - 12 * q^25 - 2 * q^27 + 6 * q^29 - 6 * q^33 - 26 * q^35 - 10 * q^37 + 8 * q^39 + 20 * q^41 + 4 * q^43 - 10 * q^45 - 16 * q^47 - 12 * q^49 - 4 * q^53 - 12 * q^55 + 8 * q^59 + 18 * q^61 - 6 * q^63 + 4 * q^65 - 6 * q^67 - 14 * q^69 - 8 * q^71 - 20 * q^75 - 34 * q^77 - 4 * q^81 - 16 * q^83 + 12 * q^85 + 6 * q^87 + 28 * q^89 + 30 * q^91 + 18 * q^93 + 12 * q^95 - 6 * q^97 - 20 * q^99

Introduction

L-functions

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Database

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