LMFDB - Embedded newform 260.2.bf.c.253.5

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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			253.5
Root			$0.125665i$ of defining polynomial
Character	$\chi$	$=$	260.253
Dual form			260.2.bf.c.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.57754 - 0.690650i) q^{3} +(2.23602 + 0.0143596i) q^{5} +(-1.08162 - 1.87342i) q^{7} +(3.56864 - 2.06036i) q^{9} +O(q^{10})$	\(q+(2.57754 - 0.690650i) q^{3} +(2.23602 + 0.0143596i) q^{5} +(-1.08162 - 1.87342i) q^{7} +(3.56864 - 2.06036i) q^{9} +(-5.13447 + 1.37578i) q^{11} +(-2.72959 + 2.35570i) q^{13} +(5.77335 - 1.50730i) q^{15} +(0.288267 - 1.07583i) q^{17} +(-1.69845 + 6.33871i) q^{19} +(-4.08179 - 4.08179i) q^{21} +(-0.192612 - 0.718837i) q^{23} +(4.99959 + 0.0642168i) q^{25} +(2.11466 - 2.11466i) q^{27} +(0.0866681 + 0.0500378i) q^{29} +(3.90035 - 3.90035i) q^{31} +(-12.2841 + 7.09224i) q^{33} +(-2.39162 - 4.20453i) q^{35} +(3.41623 - 5.91709i) q^{37} +(-5.40866 + 7.95711i) q^{39} +(1.36667 + 5.10047i) q^{41} +(3.57960 + 0.959150i) q^{43} +(8.00915 - 4.55576i) q^{45} +2.04263 q^{47} +(1.16021 - 2.00954i) q^{49} -2.97208i q^{51} +(8.28330 + 8.28330i) q^{53} +(-11.5005 + 3.00254i) q^{55} +17.5113i q^{57} +(-12.1618 - 3.25875i) q^{59} +(-4.66503 - 8.08007i) q^{61} +(-7.71981 - 4.45703i) q^{63} +(-6.13725 + 5.22821i) q^{65} +(-9.54588 - 5.51132i) q^{67} +(-0.992930 - 1.71981i) q^{69} +(-9.19754 - 2.46447i) q^{71} +10.7436i q^{73} +(12.9310 - 3.28744i) q^{75} +(8.13093 + 8.13093i) q^{77} -15.3154i q^{79} +(-2.19093 + 3.79481i) q^{81} +0.473480 q^{83} +(0.660020 - 2.40144i) q^{85} +(0.257949 + 0.0691173i) q^{87} +(0.560208 + 2.09072i) q^{89} +(7.36558 + 2.56569i) q^{91} +(7.35953 - 12.7471i) q^{93} +(-3.88880 + 14.1491i) q^{95} +(10.9982 - 6.34981i) q^{97} +(-15.4885 + 15.4885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	2.57754	−	0.690650i	1.48814	−	0.398747i	0.579034	−	0.815303i	$-0.303430\pi$
$3$	2.57754	−	0.690650i	1.48814	−	0.398747i	0.909110	+	0.416557i	$0.136763\pi$
$4$		0			0
$5$	2.23602	+	0.0143596i	0.999979	+	0.00642181i
$5$	2.23602	+	0.0143596i	0.999979	+	0.00642181i
$6$		0			0
$7$	−1.08162	−	1.87342i	−0.408813	−	0.708085i	0.585944	−	0.810351i	$-0.300724\pi$
$7$	−1.08162	−	1.87342i	−0.408813	−	0.708085i	−0.994757	+	0.102267i	$0.967390\pi$
$8$		0			0
$9$	3.56864	−	2.06036i	1.18955	−	0.686785i
$10$		0			0
$11$	−5.13447	+	1.37578i	−1.54810	+	0.414812i	−0.928873	−	0.370399i	$-0.879221\pi$
$11$	−5.13447	+	1.37578i	−1.54810	+	0.414812i	−0.619228	+	0.785211i	$0.712554\pi$
$12$		0			0
$13$	−2.72959	+	2.35570i	−0.757052	+	0.653355i
$13$	−2.72959	+	2.35570i	−0.757052	+	0.653355i
$14$		0			0
$15$	5.77335	−	1.50730i	1.49067	−	0.389182i
$16$		0			0
$17$	0.288267	−	1.07583i	0.0699151	−	0.260927i	−0.922117	−	0.386911i	$-0.873542\pi$
$17$	0.288267	−	1.07583i	0.0699151	−	0.260927i	0.992032	+	0.125984i	$0.0402088\pi$
$18$		0			0
$19$	−1.69845	+	6.33871i	−0.389652	+	1.45420i	0.441050	+	0.897482i	$0.354606\pi$
$19$	−1.69845	+	6.33871i	−0.389652	+	1.45420i	−0.830702	+	0.556717i	$0.812061\pi$
$20$		0			0
$21$	−4.08179	−	4.08179i	−0.890719	−	0.890719i
$22$		0			0
$23$	−0.192612	−	0.718837i	−0.0401624	−	0.149888i	0.942933	−	0.332983i	$-0.108055\pi$
$23$	−0.192612	−	0.718837i	−0.0401624	−	0.149888i	−0.983095	+	0.183095i	$0.941388\pi$
$24$		0			0
$25$	4.99959	+	0.0642168i	0.999918	+	0.0128434i
$26$		0			0
$27$	2.11466	−	2.11466i	0.406967	−	0.406967i
$28$		0			0
$29$	0.0866681	+	0.0500378i	0.0160939	+	0.00929179i	0.508025	−	0.861342i	$-0.330376\pi$
$29$	0.0866681	+	0.0500378i	0.0160939	+	0.00929179i	−0.491931	+	0.870634i	$0.663709\pi$
$30$		0			0
$31$	3.90035	−	3.90035i	0.700523	−	0.700523i	−0.264000	−	0.964523i	$-0.585042\pi$
$31$	3.90035	−	3.90035i	0.700523	−	0.700523i	0.964523	+	0.264000i	$0.0850418\pi$
$32$		0			0
$33$	−12.2841	+	7.09224i	−2.13839	+	1.23460i
$34$		0			0
$35$	−2.39162	−	4.20453i	−0.404257	−	0.710695i
$36$		0			0
$37$	3.41623	−	5.91709i	0.561625	−	0.972764i	−0.435729	−	0.900078i	$-0.643510\pi$
$37$	3.41623	−	5.91709i	0.561625	−	0.972764i	0.997355	−	0.0726861i	$-0.0231571\pi$
$38$		0			0
$39$	−5.40866	+	7.95711i	−0.866079	+	1.27416i
$40$		0			0
$41$	1.36667	+	5.10047i	0.213437	+	0.796559i	0.986711	+	0.162487i	$0.0519514\pi$
$41$	1.36667	+	5.10047i	0.213437	+	0.796559i	−0.773273	+	0.634073i	$0.781382\pi$
$42$		0			0
$43$	3.57960	+	0.959150i	0.545883	+	0.146269i	0.521213	−	0.853427i	$-0.325480\pi$
$43$	3.57960	+	0.959150i	0.545883	+	0.146269i	0.0246704	+	0.999696i	$0.492146\pi$
$44$		0			0
$45$	8.00915	−	4.55576i	1.19393	−	0.679132i
$46$		0			0
$47$	2.04263			0.297948			0.148974	−	0.988841i	$-0.452403\pi$
$47$	2.04263			0.297948			0.148974	+	0.988841i	$0.452403\pi$
$48$		0			0
$49$	1.16021	−	2.00954i	0.165744	−	0.287077i
$50$		0			0
$51$		−	2.97208i		−	0.416175i
$52$		0			0
$53$	8.28330	+	8.28330i	1.13780	+	1.13780i	0.988844	+	0.148955i	$0.0475908\pi$
$53$	8.28330	+	8.28330i	1.13780	+	1.13780i	0.148955	+	0.988844i	$0.452409\pi$
$54$		0			0
$55$	−11.5005	+	3.00254i	−1.55073	+	0.404862i
$56$		0			0
$57$			17.5113i			2.31943i
$58$		0			0
$59$	−12.1618	−	3.25875i	−1.58333	−	0.424253i	−0.643378	−	0.765549i	$-0.722467\pi$
$59$	−12.1618	−	3.25875i	−1.58333	−	0.424253i	−0.939956	+	0.341296i	$0.889134\pi$
$60$		0			0
$61$	−4.66503	−	8.08007i	−0.597296	−	1.03455i	−0.993218	−	0.116263i	$-0.962908\pi$
$61$	−4.66503	−	8.08007i	−0.597296	−	1.03455i	0.395922	−	0.918284i	$-0.370425\pi$
$62$		0			0
$63$	−7.71981	−	4.45703i	−0.972604	−	0.561533i
$64$		0			0
$65$	−6.13725	+	5.22821i	−0.761232	+	0.648480i
$66$		0			0
$67$	−9.54588	−	5.51132i	−1.16622	−	0.673315i	−0.213429	−	0.976958i	$-0.568463\pi$
$67$	−9.54588	−	5.51132i	−1.16622	−	0.673315i	−0.952786	+	0.303644i	$0.901797\pi$
$68$		0			0
$69$	−0.992930	−	1.71981i	−0.119535	−	0.207040i
$70$		0			0
$71$	−9.19754	−	2.46447i	−1.09155	−	0.292479i	−0.332229	−	0.943199i	$-0.607801\pi$
$71$	−9.19754	−	2.46447i	−1.09155	−	0.292479i	−0.759318	+	0.650720i	$0.774467\pi$
$72$		0			0
$73$			10.7436i			1.25744i	0.777632	+	0.628720i	$0.216421\pi$
$73$			10.7436i			1.25744i	−0.777632	+	0.628720i	$0.783579\pi$
$74$		0			0
$75$	12.9310	−	3.28744i	1.49314	−	0.379601i
$76$		0			0
$77$	8.13093	+	8.13093i	0.926606	+	0.926606i
$78$		0			0
$79$		−	15.3154i		−	1.72312i	−0.507655	−	0.861560i	$-0.669488\pi$
$79$		−	15.3154i		−	1.72312i	0.507655	−	0.861560i	$-0.330512\pi$
$80$		0			0
$81$	−2.19093	+	3.79481i	−0.243437	+	0.421645i
$82$		0			0
$83$	0.473480			0.0519712			0.0259856	−	0.999662i	$-0.491728\pi$
$83$	0.473480			0.0519712			0.0259856	+	0.999662i	$0.491728\pi$
$84$		0			0
$85$	0.660020	−	2.40144i	0.0715893	−	0.260472i
$86$		0			0
$87$	0.257949	+	0.0691173i	0.0276551	+	0.00741015i
$88$		0			0
$89$	0.560208	+	2.09072i	0.0593819	+	0.221616i	0.989240	−	0.146302i	$-0.0467372\pi$
$89$	0.560208	+	2.09072i	0.0593819	+	0.221616i	−0.929858	+	0.367918i	$0.880071\pi$
$90$		0			0
$91$	7.36558	+	2.56569i	0.772123	+	0.268957i
$92$		0			0
$93$	7.35953	−	12.7471i	0.763147	−	1.32181i
$94$		0			0
$95$	−3.88880	+	14.1491i	−0.398982	+	1.45167i
$96$		0			0
$97$	10.9982	−	6.34981i	1.11670	−	0.644725i	0.176141	−	0.984365i	$-0.443638\pi$
$97$	10.9982	−	6.34981i	1.11670	−	0.644725i	0.940556	+	0.339640i	$0.110305\pi$
$98$		0			0
$99$	−15.4885	+	15.4885i	−1.55665	+	1.55665i
$100$		0			0
$101$	−15.3907	−	8.88581i	−1.53143	−	0.884172i	−0.999296	−	0.0375113i	$-0.988057\pi$
$101$	−15.3907	−	8.88581i	−1.53143	−	0.884172i	−0.532134	−	0.846660i	$-0.678610\pi$
$102$		0			0
$103$	5.01350	−	5.01350i	0.493995	−	0.493995i	−0.415567	−	0.909562i	$-0.636417\pi$
$103$	5.01350	−	5.01350i	0.493995	−	0.493995i	0.909562	+	0.415567i	$0.136417\pi$
$104$		0			0
$105$	−9.06835	−	9.18558i	−0.884980	−	0.896421i
$106$		0			0
$107$	2.78085	+	10.3783i	0.268835	+	1.00331i	0.959861	+	0.280476i	$0.0904923\pi$
$107$	2.78085	+	10.3783i	0.268835	+	1.00331i	−0.691026	+	0.722830i	$0.742841\pi$
$108$		0			0
$109$	2.36072	+	2.36072i	0.226116	+	0.226116i	0.811068	−	0.584952i	$-0.198887\pi$
$109$	2.36072	+	2.36072i	0.226116	+	0.226116i	−0.584952	+	0.811068i	$0.698887\pi$
$110$		0			0
$111$	4.71884	−	17.6110i	0.447893	−	1.67156i
$112$		0			0
$113$	−1.78384	+	6.65737i	−0.167809	+	0.626273i	0.829856	+	0.557978i	$0.188423\pi$
$113$	−1.78384	+	6.65737i	−0.167809	+	0.626273i	−0.997665	+	0.0682952i	$0.978244\pi$
$114$		0			0
$115$	−0.420362	−	1.61010i	−0.0391990	−	0.150143i
$116$		0			0
$117$	−4.88734	+	14.0306i	−0.451834	+	1.29713i
$118$		0			0
$119$	−2.32727	+	0.623590i	−0.213340	+	0.0571644i
$120$		0			0
$121$	14.9437	−	8.62776i	1.35852	−	0.784342i
$122$		0			0
$123$	7.04528	+	12.2028i	0.635251	+	1.10029i
$124$		0			0
$125$	11.1783	+	0.215382i	0.999814	+	0.0192644i
$126$		0			0
$127$	13.3942	−	3.58896i	1.18854	−	0.318469i	0.390232	−	0.920717i	$-0.372395\pi$
$127$	13.3942	−	3.58896i	1.18854	−	0.318469i	0.798309	+	0.602248i	$0.205728\pi$
$128$		0			0
$129$	9.88899			0.870677
$130$		0			0
$131$	5.00046			0.436892			0.218446	−	0.975849i	$-0.429901\pi$
$131$	5.00046			0.436892			0.218446	+	0.975849i	$0.429901\pi$
$132$		0			0
$133$	13.7121	−	3.67415i	1.18899	−	0.318589i
$134$		0			0
$135$	4.75879	−	4.69806i	0.409572	−	0.404345i
$136$		0			0
$137$	−5.62747	−	9.74706i	−0.480787	−	0.832748i	0.518970	−	0.854793i	$-0.326316\pi$
$137$	−5.62747	−	9.74706i	−0.480787	−	0.832748i	−0.999757	+	0.0220448i	$0.992982\pi$
$138$		0			0
$139$	7.54341	−	4.35519i	0.639823	−	0.369402i	−0.144723	−	0.989472i	$-0.546229\pi$
$139$	7.54341	−	4.35519i	0.639823	−	0.369402i	0.784546	+	0.620070i	$0.212896\pi$
$140$		0			0
$141$	5.26497	−	1.41074i	0.443390	−	0.118806i
$142$		0			0
$143$	10.7741	−	15.8506i	0.900973	−	1.32549i
$144$		0			0
$145$	0.193073	+	0.113130i	0.0160339	+	0.00939495i
$146$		0			0
$147$	1.60260	−	5.98097i	0.132180	−	0.493302i
$148$		0			0
$149$	−1.07157	+	3.99916i	−0.0877865	+	0.327624i	−0.995827	−	0.0912581i	$-0.970911\pi$
$149$	−1.07157	+	3.99916i	−0.0877865	+	0.327624i	0.908041	+	0.418882i	$0.137578\pi$
$150$		0			0
$151$	−4.01320	−	4.01320i	−0.326590	−	0.326590i	0.524698	−	0.851288i	$-0.324178\pi$
$151$	−4.01320	−	4.01320i	−0.326590	−	0.326590i	−0.851288	+	0.524698i	$0.824178\pi$
$152$		0			0
$153$	−1.18787	−	4.43318i	−0.0960333	−	0.358401i
$154$		0			0
$155$	8.77727	−	8.66525i	0.705007	−	0.696010i
$156$		0			0
$157$	6.09083	−	6.09083i	0.486101	−	0.486101i	−0.420972	−	0.907073i	$-0.638311\pi$
$157$	6.09083	−	6.09083i	0.486101	−	0.486101i	0.907073	+	0.420972i	$0.138311\pi$
$158$		0			0
$159$	27.0714	+	15.6297i	2.14690	+	1.23951i
$160$		0			0
$161$	−1.13835	+	1.13835i	−0.0897145	+	0.0897145i
$162$		0			0
$163$	−9.68372	+	5.59090i	−0.758488	+	0.437913i	−0.828752	−	0.559615i	$-0.810949\pi$
$163$	−9.68372	+	5.59090i	−0.758488	+	0.437913i	0.0702649	+	0.997528i	$0.477616\pi$
$164$		0			0
$165$	−27.5694	+	15.6820i	−2.14627	+	1.22084i
$166$		0			0
$167$	−3.88299	+	6.72554i	−0.300475	+	0.520438i	−0.976244	−	0.216676i	$-0.930479\pi$
$167$	−3.88299	+	6.72554i	−0.300475	+	0.520438i	0.675769	+	0.737114i	$0.263812\pi$
$168$		0			0
$169$	1.90131	−	12.8602i	0.146255	−	0.989247i
$170$		0			0
$171$	6.99883	+	26.1200i	0.535214	+	1.99745i
$172$		0			0
$173$	−14.4420	−	3.86973i	−1.09801	−	0.294210i	−0.336054	−	0.941843i	$-0.609092\pi$
$173$	−14.4420	−	3.86973i	−1.09801	−	0.294210i	−0.761952	+	0.647633i	$0.775759\pi$
$174$		0			0
$175$	−5.28734	−	9.43577i	−0.399685	−	0.713277i
$176$		0			0
$177$	−33.5982			−2.52540
$178$		0			0
$179$	0.627120	−	1.08620i	0.0468731	−	0.0811867i	−0.841637	−	0.540044i	$-0.818408\pi$
$179$	0.627120	−	1.08620i	0.0468731	−	0.0811867i	0.888510	+	0.458857i	$0.151741\pi$
$180$		0			0
$181$			7.23242i			0.537582i	0.963199	+	0.268791i	$0.0866240\pi$
$181$			7.23242i			0.537582i	−0.963199	+	0.268791i	$0.913376\pi$
$182$		0			0
$183$	−17.6048	−	17.6048i	−1.30139	−	1.30139i
$184$		0			0
$185$	7.72374	−	13.1817i	0.567861	−	0.969137i
$186$		0			0
$187$			5.92040i			0.432942i
$188$		0			0
$189$	−6.24889	−	1.67439i	−0.454540	−	0.121794i
$190$		0			0
$191$	10.5227	+	18.2259i	0.761397	+	1.31878i	0.942131	+	0.335246i	$0.108819\pi$
$191$	10.5227	+	18.2259i	0.761397	+	1.31878i	−0.180734	+	0.983532i	$0.557847\pi$
$192$		0			0
$193$	8.61264	+	4.97251i	0.619952	+	0.357929i	0.776850	−	0.629686i	$-0.216816\pi$
$193$	8.61264	+	4.97251i	0.619952	+	0.357929i	−0.156899	+	0.987615i	$0.550150\pi$
$194$		0			0
$195$	−12.2081	+	17.7146i	−0.874243	+	1.26857i
$196$		0			0
$197$	4.65216	+	2.68592i	0.331453	+	0.191364i	0.656486	−	0.754338i	$-0.272042\pi$
$197$	4.65216	+	2.68592i	0.331453	+	0.191364i	−0.325033	+	0.945703i	$0.605376\pi$
$198$		0			0
$199$	−3.24212	−	5.61552i	−0.229828	−	0.398073i	0.727929	−	0.685652i	$-0.240483\pi$
$199$	−3.24212	−	5.61552i	−0.229828	−	0.398073i	−0.957757	+	0.287579i	$0.907150\pi$
$200$		0			0
$201$	−28.4113	−	7.61278i	−2.00398	−	0.536964i
$202$		0			0
$203$		−	0.216487i		−	0.0151944i
$204$		0			0
$205$	2.98266	+	11.4244i	0.208318	+	0.797914i
$206$		0			0
$207$	−2.16842	−	2.16842i	−0.150716	−	0.150716i
$208$		0			0
$209$		−	34.8826i		−	2.41288i
$210$		0			0
$211$	−13.6792	+	23.6930i	−0.941713	+	1.63110i	−0.179512	+	0.983756i	$0.557452\pi$
$211$	−13.6792	+	23.6930i	−0.941713	+	1.63110i	−0.762202	+	0.647340i	$0.775882\pi$
$212$		0			0
$213$	−25.4091			−1.74100
$214$		0			0
$215$	7.99028	+	2.19608i	0.544933	+	0.149772i
$216$		0			0
$217$	−11.5257	−	3.08829i	−0.782412	−	0.209647i
$218$		0			0
$219$	7.42004	+	27.6920i	0.501400	+	1.87125i
$220$		0			0
$221$	1.74748	+	3.61564i	0.117548	+	0.243214i
$222$		0			0
$223$	−1.06347	+	1.84198i	−0.0712151	+	0.123348i	−0.899434	−	0.437056i	$-0.856021\pi$
$223$	−1.06347	+	1.84198i	−0.0712151	+	0.123348i	0.828219	+	0.560405i	$0.189354\pi$
$224$		0			0
$225$	17.9740	−	10.0718i	1.19827	−	0.671451i
$226$		0			0
$227$	19.4489	−	11.2288i	1.29087	−	0.745282i	0.312058	−	0.950063i	$-0.398982\pi$
$227$	19.4489	−	11.2288i	1.29087	−	0.745282i	0.978808	+	0.204781i	$0.0656483\pi$
$228$		0			0
$229$	−0.742654	+	0.742654i	−0.0490760	+	0.0490760i	−0.731219	−	0.682143i	$-0.761048\pi$
$229$	−0.742654	+	0.742654i	−0.0490760	+	0.0490760i	0.682143	+	0.731219i	$0.261048\pi$
$230$		0			0
$231$	26.5734	+	15.3422i	1.74840	+	1.00944i
$232$		0			0
$233$	−6.72311	+	6.72311i	−0.440446	+	0.440446i	−0.892162	−	0.451716i	$-0.850812\pi$
$233$	−6.72311	+	6.72311i	−0.440446	+	0.440446i	0.451716	+	0.892162i	$0.350812\pi$
$234$		0			0
$235$	4.56737	+	0.0293314i	0.297942	+	0.00191337i
$236$		0			0
$237$	−10.5776	−	39.4761i	−0.687089	−	2.56425i
$238$		0			0
$239$	−1.41635	−	1.41635i	−0.0916161	−	0.0916161i	0.659813	−	0.751430i	$-0.270635\pi$
$239$	−1.41635	−	1.41635i	−0.0916161	−	0.0916161i	−0.751430	+	0.659813i	$0.770635\pi$
$240$		0			0
$241$	0.0381404	−	0.142342i	0.00245684	−	0.00916904i	−0.964687	−	0.263401i	$-0.915156\pi$
$241$	0.0381404	−	0.142342i	0.00245684	−	0.00916904i	0.967143	+	0.254232i	$0.0818226\pi$
$242$		0			0
$243$	−5.34840	+	19.9605i	−0.343100	+	1.28047i
$244$		0			0
$245$	2.62311	−	4.47671i	0.167584	−	0.286007i
$246$		0			0
$247$	−10.2960	−	21.3031i	−0.655122	−	1.35549i
$248$		0			0
$249$	1.22041	−	0.327009i	0.0773406	−	0.0207233i
$250$		0			0
$251$	−12.1871	+	7.03620i	−0.769240	+	0.444121i	−0.832604	−	0.553869i	$-0.813151\pi$
$251$	−12.1871	+	7.03620i	−0.769240	+	0.444121i	0.0633631	+	0.997991i	$0.479817\pi$
$252$		0			0
$253$	1.97792	+	3.42586i	0.124351	+	0.215382i
$254$		0			0
$255$	0.0426779	−	6.64564i	0.00267260	−	0.416166i
$256$		0			0
$257$	−18.6215	+	4.98961i	−1.16158	+	0.311243i	−0.787595	−	0.616193i	$-0.788674\pi$
$257$	−18.6215	+	4.98961i	−1.16158	+	0.311243i	−0.373981	+	0.927436i	$0.622007\pi$
$258$		0			0
$259$	−14.7802			−0.918399
$260$		0			0
$261$	0.412383			0.0255259
$262$		0			0
$263$	21.2208	−	5.68609i	1.30853	−	0.350619i	0.463860	−	0.885908i	$-0.346464\pi$
$263$	21.2208	−	5.68609i	1.30853	−	0.350619i	0.844669	+	0.535289i	$0.179797\pi$
$264$		0			0
$265$	18.4027	+	18.6406i	1.13047	+	1.14508i
$266$		0			0
$267$	2.88792	+	5.00202i	0.176738	+	0.306118i
$268$		0			0
$269$	−9.22286	+	5.32482i	−0.562328	+	0.324660i	−0.754079	−	0.656783i	$-0.771917\pi$
$269$	−9.22286	+	5.32482i	−0.562328	+	0.324660i	0.191751	+	0.981444i	$0.438583\pi$
$270$		0			0
$271$	3.71082	−	0.994312i	0.225416	−	0.0604001i	−0.144343	−	0.989528i	$-0.546107\pi$
$271$	3.71082	−	0.994312i	0.225416	−	0.0604001i	0.369759	+	0.929128i	$0.379440\pi$
$272$		0			0
$273$	20.7571	+	1.52612i	1.25628	+	0.0923649i
$274$		0			0
$275$	−25.7586	+	6.54860i	−1.55330	+	0.394895i
$276$		0			0
$277$	−3.64753	+	13.6128i	−0.219159	+	0.817912i	0.765502	+	0.643434i	$0.222491\pi$
$277$	−3.64753	+	13.6128i	−0.219159	+	0.817912i	−0.984661	+	0.174479i	$0.944176\pi$
$278$		0			0
$279$	5.88284	−	21.9550i	0.352196	−	1.31441i
$280$		0			0
$281$	12.6788	+	12.6788i	0.756354	+	0.756354i	0.975657	−	0.219303i	$-0.0703782\pi$
$281$	12.6788	+	12.6788i	0.756354	+	0.756354i	−0.219303	+	0.975657i	$0.570378\pi$
$282$		0			0
$283$	−2.25155	−	8.40291i	−0.133841	−	0.499501i	0.866159	−	0.499768i	$-0.166582\pi$
$283$	−2.25155	−	8.40291i	−0.133841	−	0.499501i	−1.00000		0.000267339i	$0.999915\pi$
$284$		0			0
$285$	−0.251456	+	39.1557i	−0.0148949	+	2.31938i
$286$		0			0
$287$	8.07709	−	8.07709i	0.476776	−	0.476776i
$288$		0			0
$289$	13.6481	+	7.87975i	0.802831	+	0.463515i
$290$		0			0
$291$	23.9628	−	23.9628i	1.40472	−	1.40472i
$292$		0			0
$293$	10.3729	−	5.98879i	0.605991	−	0.349869i	−0.165404	−	0.986226i	$-0.552893\pi$
$293$	10.3729	−	5.98879i	0.605991	−	0.349869i	0.771395	+	0.636357i	$0.219559\pi$
$294$		0			0
$295$	−27.1473	−	7.46127i	−1.58058	−	0.434412i
$296$		0			0
$297$	−7.94836	+	13.7670i	−0.461211	+	0.798840i
$298$		0			0
$299$	2.21912	+	1.50839i	0.128335	+	0.0872327i
$300$		0			0
$301$	−2.07487	−	7.74351i	−0.119593	−	0.446328i
$302$		0			0
$303$	−45.8071	−	12.2740i	−2.63155	−	0.705121i
$304$		0			0
$305$	−10.3151	−	18.1342i	−0.590640	−	1.03836i
$306$		0			0
$307$	20.0009			1.14151			0.570755	−	0.821120i	$-0.306650\pi$
$307$	20.0009			1.14151			0.570755	+	0.821120i	$0.306650\pi$
$308$		0			0
$309$	9.45993	−	16.3851i	0.538157	−	0.932115i
$310$		0			0
$311$			14.8121i			0.839916i	0.907543	+	0.419958i	$0.137955\pi$
$311$			14.8121i			0.839916i	−0.907543	+	0.419958i	$0.862045\pi$
$312$		0			0
$313$	2.35138	+	2.35138i	0.132908	+	0.132908i	0.770431	−	0.637523i	$-0.220041\pi$
$313$	2.35138	+	2.35138i	0.132908	+	0.132908i	−0.637523	+	0.770431i	$0.720041\pi$
$314$		0			0
$315$	−17.1977	−	10.0769i	−0.968978	−	0.567768i
$316$		0			0
$317$			15.2905i			0.858799i	0.903115	+	0.429399i	$0.141275\pi$
$317$			15.2905i			0.858799i	−0.903115	+	0.429399i	$0.858725\pi$
$318$		0			0
$319$	−0.513835	−	0.137682i	−0.0287693	−	0.00770870i
$320$		0			0
$321$	14.3355	+	24.8298i	0.800130	+	1.38587i
$322$		0			0
$323$	6.32975	+	3.65449i	0.352197	+	0.203341i
$324$		0			0
$325$	−13.7981	+	11.6023i	−0.765381	+	0.643578i
$326$		0			0
$327$	7.71529	+	4.45443i	0.426657	+	0.246330i
$328$		0			0
$329$	−2.20935	−	3.82670i	−0.121805	−	0.210973i
$330$		0			0
$331$	0.900776	+	0.241362i	0.0495111	+	0.0132665i	0.283490	−	0.958975i	$-0.408508\pi$
$331$	0.900776	+	0.241362i	0.0495111	+	0.0132665i	−0.233978	+	0.972242i	$0.575175\pi$
$332$		0			0
$333$		−	28.1546i		−	1.54286i
$334$		0			0
$335$	−21.2657	−	12.4605i	−1.16187	−	0.680790i
$336$		0			0
$337$	−15.9698	−	15.9698i	−0.869930	−	0.869930i	0.122534	−	0.992464i	$-0.460898\pi$
$337$	−15.9698	−	15.9698i	−0.869930	−	0.869930i	−0.992464	+	0.122534i	$0.960898\pi$
$338$		0			0
$339$			18.3917i			0.998898i
$340$		0			0
$341$	−14.6602	+	25.3922i	−0.793894	+	1.37507i
$342$		0			0
$343$	−20.1622			−1.08866
$344$		0			0
$345$	−2.19552	−	3.85978i	−0.118203	−	0.207804i
$346$		0			0
$347$	−9.82910	−	2.63370i	−0.527654	−	0.141384i	−0.0148492	−	0.999890i	$-0.504727\pi$
$347$	−9.82910	−	2.63370i	−0.527654	−	0.141384i	−0.512805	+	0.858505i	$0.671393\pi$
$348$		0			0
$349$	0.766967	+	2.86236i	0.0410548	+	0.153219i	0.983410	−	0.181394i	$-0.0580611\pi$
$349$	0.766967	+	2.86236i	0.0410548	+	0.153219i	−0.942356	+	0.334613i	$0.891394\pi$
$350$		0			0
$351$	−0.790640	+	10.7537i	−0.0422012	+	0.573989i
$352$		0			0
$353$	16.1091	−	27.9018i	0.857402	−	1.48506i	−0.0169962	−	0.999856i	$-0.505410\pi$
$353$	16.1091	−	27.9018i	0.857402	−	1.48506i	0.874398	−	0.485209i	$-0.161256\pi$
$354$		0			0
$355$	−20.5305	−	5.64269i	−1.08965	−	0.299483i
$356$		0			0
$357$	−5.56795	+	3.21466i	−0.294687	+	0.170138i
$358$		0			0
$359$	−1.11254	+	1.11254i	−0.0587178	+	0.0587178i	−0.735856	−	0.677138i	$-0.763220\pi$
$359$	−1.11254	+	1.11254i	−0.0587178	+	0.0587178i	0.677138	+	0.735856i	$0.263220\pi$
$360$		0			0
$361$	−20.8400	−	12.0320i	−1.09684	−	0.633262i
$362$		0			0
$363$	32.5593	−	32.5593i	1.70892	−	1.70892i
$364$		0			0
$365$	−0.154273	+	24.0228i	−0.00807504	+	1.25741i
$366$		0			0
$367$	5.46138	+	20.3821i	0.285082	+	1.06394i	0.948780	+	0.315938i	$0.102319\pi$
$367$	5.46138	+	20.3821i	0.285082	+	1.06394i	−0.663698	+	0.748001i	$0.731014\pi$
$368$		0			0
$369$	15.3859	+	15.3859i	0.800959	+	0.800959i
$370$		0			0
$371$	6.55871	−	24.4774i	0.340511	−	1.27080i
$372$		0			0
$373$	6.53307	−	24.3817i	0.338269	−	1.26244i	−0.562012	−	0.827129i	$-0.689972\pi$
$373$	6.53307	−	24.3817i	0.338269	−	1.26244i	0.900281	−	0.435309i	$-0.143361\pi$
$374$		0			0
$375$	28.9612	−	7.16511i	1.49555	−	0.370005i
$376$		0			0
$377$	−0.354443	+	0.0675816i	−0.0182547	+	0.00348063i
$378$		0			0
$379$	25.4336	−	6.81491i	1.30644	−	0.350058i	0.462556	−	0.886590i	$-0.346933\pi$
$379$	25.4336	−	6.81491i	1.30644	−	0.350058i	0.843880	+	0.536532i	$0.180266\pi$
$380$		0			0
$381$	32.0453	−	18.5014i	1.64173	−	0.947854i
$382$		0			0
$383$	18.1197	+	31.3842i	0.925873	+	1.60366i	0.790151	+	0.612913i	$0.210002\pi$
$383$	18.1197	+	31.3842i	0.925873	+	1.60366i	0.135722	+	0.990747i	$0.456664\pi$
$384$		0			0
$385$	18.0642	+	18.2977i	0.920636	+	0.932537i
$386$		0			0
$387$	14.7505	−	3.95238i	0.749810	−	0.200911i
$388$		0			0
$389$	−16.9315			−0.858462			−0.429231	−	0.903195i	$-0.641215\pi$
$389$	−16.9315			−0.858462			−0.429231	+	0.903195i	$0.641215\pi$
$390$		0			0
$391$	−0.828869			−0.0419177
$392$		0			0
$393$	12.8889	−	3.45356i	0.650158	−	0.174209i
$394$		0			0
$395$	0.219924	−	34.2456i	0.0110656	−	1.72309i
$396$		0			0
$397$	10.6953	+	18.5248i	0.536781	+	0.929732i	0.999075	+	0.0430054i	$0.0136933\pi$
$397$	10.6953	+	18.5248i	0.536781	+	0.929732i	−0.462294	+	0.886727i	$0.652973\pi$
$398$		0			0
$399$	32.8060	−	18.9405i	1.64235	−	0.948213i
$400$		0			0
$401$	34.4734	−	9.23713i	1.72152	−	0.461280i	0.743319	−	0.668937i	$-0.233251\pi$
$401$	34.4734	−	9.23713i	1.72152	−	0.461280i	0.978202	+	0.207657i	$0.0665839\pi$
$402$		0			0
$403$	−1.45828	+	19.8344i	−0.0726421	+	0.988022i
$404$		0			0
$405$	−4.95347	+	8.45382i	−0.246140	+	0.420073i
$406$		0			0
$407$	−9.39995	+	35.0811i	−0.465938	+	1.73891i
$408$		0			0
$409$	−1.43399	+	5.35172i	−0.0709062	+	0.264625i	−0.992274	−	0.124067i	$-0.960406\pi$
$409$	−1.43399	+	5.35172i	−0.0709062	+	0.264625i	0.921368	+	0.388692i	$0.127073\pi$
$410$		0			0
$411$	−21.2368	−	21.2368i	−1.04754	−	1.04754i
$412$		0			0
$413$	7.04944	+	26.3089i	0.346880	+	1.29457i
$414$		0			0
$415$	1.05871	+	0.00679899i	0.0519701	+	0.000333749i
$416$		0			0
$417$	16.4355	−	16.4355i	0.804851	−	0.804851i
$418$		0			0
$419$	−10.8355	−	6.25590i	−0.529351	−	0.305621i	0.211401	−	0.977399i	$-0.432197\pi$
$419$	−10.8355	−	6.25590i	−0.529351	−	0.305621i	−0.740752	+	0.671779i	$0.765531\pi$
$420$		0			0
$421$	−0.936634	+	0.936634i	−0.0456488	+	0.0456488i	−0.729563	−	0.683914i	$-0.760276\pi$
$421$	−0.936634	+	0.936634i	−0.0456488	+	0.0456488i	0.683914	+	0.729563i	$0.260276\pi$
$422$		0			0
$423$	7.28942	−	4.20855i	0.354424	−	0.204627i
$424$		0			0
$425$	1.51030	−	5.36019i	0.0732605	−	0.260007i
$426$		0			0
$427$	−10.0916	+	17.4791i	−0.488365	+	0.845873i
$428$		0			0
$429$	16.8234	−	48.2967i	0.812240	−	2.33178i
$430$		0			0
$431$	−3.95753	−	14.7697i	−0.190628	−	0.711432i	−0.993355	−	0.115087i	$-0.963285\pi$
$431$	−3.95753	−	14.7697i	−0.190628	−	0.711432i	0.802728	−	0.596346i	$-0.203381\pi$
$432$		0			0
$433$	11.0180	+	2.95228i	0.529493	+	0.141877i	0.513654	−	0.857997i	$-0.328291\pi$
$433$	11.0180	+	2.95228i	0.529493	+	0.141877i	0.0158391	+	0.999875i	$0.494958\pi$
$434$		0			0
$435$	0.575787	+	0.158252i	0.0276069	+	0.00758759i
$436$		0			0
$437$	4.88364			0.233616
$438$		0			0
$439$	−17.3246	+	30.0071i	−0.826858	+	1.43216i	0.0736324	+	0.997285i	$0.476541\pi$
$439$	−17.3246	+	30.0071i	−0.826858	+	1.43216i	−0.900491	+	0.434875i	$0.856792\pi$
$440$		0			0
$441$		−	9.56177i		−	0.455322i
$442$		0			0
$443$	4.85964	+	4.85964i	0.230888	+	0.230888i	0.813063	−	0.582175i	$-0.197798\pi$
$443$	4.85964	+	4.85964i	0.230888	+	0.230888i	−0.582175	+	0.813063i	$0.697798\pi$
$444$		0			0
$445$	1.22261	+	4.68295i	0.0579575	+	0.221993i
$446$		0			0
$447$			11.0481i			0.522556i
$448$		0			0
$449$	−28.2416	−	7.56732i	−1.33280	−	0.357124i	−0.479044	−	0.877791i	$-0.659017\pi$
$449$	−28.2416	−	7.56732i	−1.33280	−	0.357124i	−0.853760	+	0.520667i	$0.825683\pi$
$450$		0			0
$451$	−14.0342	−	24.3080i	−0.660845	−	1.14462i
$452$		0			0
$453$	−13.1159	−	7.57248i	−0.616240	−	0.355786i
$454$		0			0
$455$	16.4328	+	5.84270i	0.770380	+	0.273910i
$456$		0			0
$457$	−21.1868	−	12.2322i	−0.991076	−	0.572198i	−0.0854803	−	0.996340i	$-0.527242\pi$
$457$	−21.1868	−	12.2322i	−0.991076	−	0.572198i	−0.905596	+	0.424142i	$0.860576\pi$
$458$		0			0
$459$	−1.66542	−	2.88460i	−0.0777354	−	0.134642i
$460$		0			0
$461$	−13.4819	−	3.61245i	−0.627912	−	0.168249i	−0.0691902	−	0.997603i	$-0.522042\pi$
$461$	−13.4819	−	3.61245i	−0.627912	−	0.168249i	−0.558722	+	0.829355i	$0.688708\pi$
$462$		0			0
$463$		−	7.08508i		−	0.329272i	−0.986354	−	0.164636i	$-0.947355\pi$
$463$		−	7.08508i		−	0.329272i	0.986354	−	0.164636i	$-0.0526449\pi$
$464$		0			0
$465$	16.6391	−	28.3971i	0.771620	−	1.31688i
$466$		0			0
$467$	4.40762	+	4.40762i	0.203960	+	0.203960i	0.801694	−	0.597734i	$-0.203932\pi$
$467$	4.40762	+	4.40762i	0.203960	+	0.203960i	−0.597734	+	0.801694i	$0.703932\pi$
$468$		0			0
$469$			23.8445i			1.10104i
$470$		0			0
$471$	11.4927	−	19.9060i	0.529557	−	0.917219i
$472$		0			0
$473$	−19.6989			−0.905757
$474$		0			0
$475$	−8.89861	+	31.5819i	−0.408296	+	1.44908i
$476$		0			0
$477$	46.6267	+	12.4936i	2.13489	+	0.572042i
$478$		0			0
$479$	−8.30384	−	30.9903i	−0.379412	−	1.41598i	−0.846790	−	0.531927i	$-0.821468\pi$
$479$	−8.30384	−	30.9903i	−0.379412	−	1.41598i	0.467378	−	0.884058i	$-0.345199\pi$
$480$		0			0
$481$	4.61400	+	24.1989i	0.210380	+	1.10337i
$482$		0			0
$483$	−2.14794	+	3.72034i	−0.0977347	+	0.169281i
$484$		0			0
$485$	24.6834	−	14.0404i	1.12081	−	0.637541i
$486$		0			0
$487$	−10.3776	+	5.99150i	−0.470253	+	0.271501i	−0.716346	−	0.697746i	$-0.754187\pi$
$487$	−10.3776	+	5.99150i	−0.470253	+	0.271501i	0.246093	+	0.969246i	$0.420853\pi$
$488$		0			0
$489$	−21.0988	+	21.0988i	−0.954122	+	0.954122i
$490$		0			0
$491$	20.9648	+	12.1041i	0.946130	+	0.546248i	0.891877	−	0.452279i	$-0.149389\pi$
$491$	20.9648	+	12.1041i	0.946130	+	0.546248i	0.0542534	+	0.998527i	$0.482722\pi$
$492$		0			0
$493$	0.0788157	−	0.0788157i	0.00354968	−	0.00354968i
$494$		0			0
$495$	−34.8550	+	34.4102i	−1.56662	+	1.54662i
$496$		0			0
$497$	5.33123	+	19.8964i	0.239138	+	0.892477i
$498$		0			0
$499$	23.7196	+	23.7196i	1.06183	+	1.06183i	0.997958	+	0.0638768i	$0.0203465\pi$
$499$	23.7196	+	23.7196i	1.06183	+	1.06183i	0.0638768	+	0.997958i	$0.479654\pi$
$500$		0			0
$501$	−5.36358	+	20.0171i	−0.239627	+	0.894300i
$502$		0			0
$503$	0.126951	−	0.473787i	0.00566046	−	0.0211251i	−0.963038	−	0.269366i	$-0.913186\pi$
$503$	0.126951	−	0.473787i	0.00566046	−	0.0211251i	0.968698	+	0.248241i	$0.0798525\pi$
$504$		0			0
$505$	−34.2863	−	20.0899i	−1.52572	−	0.893988i
$506$		0			0
$507$	−3.98119	−	34.4609i	−0.176811	−	1.53046i
$508$		0			0
$509$	−14.5334	+	3.89421i	−0.644181	+	0.172608i	−0.566097	−	0.824339i	$-0.691547\pi$
$509$	−14.5334	+	3.89421i	−0.644181	+	0.172608i	−0.0780847	+	0.996947i	$0.524880\pi$
$510$		0			0
$511$	20.1272	−	11.6204i	0.890373	−	0.514057i
$512$		0			0
$513$	9.81257	+	16.9959i	0.433236	+	0.750386i
$514$		0			0
$515$	11.2823	−	11.1383i	0.497157	−	0.490813i
$516$		0			0
$517$	−10.4878	+	2.81020i	−0.461254	+	0.123593i
$518$		0			0
$519$	−39.8975			−1.75131
$520$		0			0
$521$	−38.1804			−1.67271			−0.836357	−	0.548185i	$-0.815319\pi$
$521$	−38.1804			−1.67271			−0.836357	+	0.548185i	$0.815319\pi$
$522$		0			0
$523$	−20.4731	+	5.48576i	−0.895227	+	0.239875i	−0.676965	−	0.736015i	$-0.736705\pi$
$523$	−20.4731	+	5.48576i	−0.895227	+	0.239875i	−0.218262	+	0.975890i	$0.570039\pi$
$524$		0			0
$525$	−20.1451	−	20.6694i	−0.879206	−	0.902085i
$526$		0			0
$527$	−3.07176	−	5.32045i	−0.133808	−	0.231762i
$528$		0			0
$529$	19.4390	−	11.2231i	0.845172	−	0.487960i
$530$		0			0
$531$	−50.1153	+	13.4284i	−2.17482	+	0.582741i
$532$		0			0
$533$	−15.7456	−	10.7027i	−0.682019	−	0.463586i
$534$		0			0
$535$	6.06902	+	23.2460i	0.262386	+	1.00501i
$536$		0			0
$537$	0.866241	−	3.23285i	0.0373810	−	0.139508i
$538$		0			0
$539$	−3.19238	+	11.9141i	−0.137505	+	0.513177i
$540$		0			0
$541$	−0.700130	−	0.700130i	−0.0301009	−	0.0301009i	0.691896	−	0.721997i	$-0.256776\pi$
$541$	−0.700130	−	0.700130i	−0.0301009	−	0.0301009i	−0.721997	+	0.691896i	$0.756776\pi$
$542$		0			0
$543$	4.99507	+	18.6419i	0.214359	+	0.799999i
$544$		0			0
$545$	5.24473	+	5.31253i	0.224660	+	0.227564i
$546$		0			0
$547$	−7.28589	+	7.28589i	−0.311522	+	0.311522i	−0.845499	−	0.533977i	$-0.820697\pi$
$547$	−7.28589	+	7.28589i	−0.311522	+	0.311522i	0.533977	+	0.845499i	$0.320697\pi$
$548$		0			0
$549$	−33.2957	−	19.2233i	−1.42102	−	0.820429i
$550$		0			0
$551$	−0.464377	+	0.464377i	−0.0197831	+	0.0197831i
$552$		0			0
$553$	−28.6922	+	16.5654i	−1.22012	+	0.704434i
$554$		0			0
$555$	10.8043	−	39.3107i	0.458618	−	1.66865i
$556$		0			0
$557$	11.8506	−	20.5259i	0.502127	−	0.869710i	−0.497870	−	0.867252i	$-0.665884\pi$
$557$	11.8506	−	20.5259i	0.502127	−	0.869710i	0.999997	−	0.00245824i	$-0.000782482\pi$
$558$		0			0
$559$	−12.0303	+	5.81439i	−0.508828	+	0.245922i
$560$		0			0
$561$	4.08892	+	15.2601i	0.172634	+	0.644280i
$562$		0			0
$563$	20.4169	+	5.47068i	0.860468	+	0.230562i	0.661962	−	0.749538i	$-0.269724\pi$
$563$	20.4169	+	5.47068i	0.860468	+	0.230562i	0.198507	+	0.980100i	$0.436391\pi$
$564$		0			0
$565$	−4.08430	+	14.8604i	−0.171828	+	0.625183i
$566$		0			0
$567$	9.47901			0.398081
$568$		0			0
$569$	−5.92902	+	10.2694i	−0.248557	+	0.430514i	−0.963126	−	0.269052i	$-0.913290\pi$
$569$	−5.92902	+	10.2694i	−0.248557	+	0.430514i	0.714568	+	0.699566i	$0.246623\pi$
$570$		0			0
$571$		−	6.26224i		−	0.262067i	−0.991378	−	0.131033i	$-0.958171\pi$
$571$		−	6.26224i		−	0.262067i	0.991378	−	0.131033i	$-0.0418295\pi$
$572$		0			0
$573$	39.7104	+	39.7104i	1.65893	+	1.65893i
$574$		0			0
$575$	−0.916819	−	3.60626i	−0.0382340	−	0.150391i
$576$		0			0
$577$		−	45.6328i		−	1.89972i	−0.312681	−	0.949858i	$-0.601227\pi$
$577$		−	45.6328i		−	1.89972i	0.312681	−	0.949858i	$-0.398773\pi$
$578$		0			0
$579$	25.6337	+	6.86853i	1.06530	+	0.285446i
$580$		0			0
$581$	−0.512124	−	0.887025i	−0.0212465	−	0.0368000i
$582$		0			0
$583$	−53.9263	−	31.1344i	−2.23340	−	1.28945i
$584$		0			0
$585$	−11.1297	+	31.3025i	−0.460155	+	1.29420i
$586$		0			0
$587$	−2.49660	−	1.44141i	−0.103046	−	0.0594935i	0.447592	−	0.894238i	$-0.352282\pi$
$587$	−2.49660	−	1.44141i	−0.103046	−	0.0594935i	−0.550637	+	0.834745i	$0.685615\pi$
$588$		0			0
$589$	18.0986	+	31.3477i	0.745740	+	1.29166i
$590$		0			0
$591$	13.8462	+	3.71007i	0.569555	+	0.152612i
$592$		0			0
$593$		−	17.0136i		−	0.698663i	−0.936999	−	0.349332i	$-0.886409\pi$
$593$		−	17.0136i		−	0.698663i	0.936999	−	0.349332i	$-0.113591\pi$
$594$		0			0
$595$	−5.21278	+	1.36094i	−0.213703	+	0.0557932i
$596$		0			0
$597$	−12.2351	−	12.2351i	−0.500747	−	0.500747i
$598$		0			0
$599$		−	15.8501i		−	0.647618i	−0.946123	−	0.323809i	$-0.895037\pi$
$599$		−	15.8501i		−	0.647618i	0.946123	−	0.323809i	$-0.104963\pi$
$600$		0			0
$601$	−7.73635	+	13.3998i	−0.315572	+	0.546587i	−0.979559	−	0.201157i	$-0.935530\pi$
$601$	−7.73635	+	13.3998i	−0.315572	+	0.546587i	0.663987	+	0.747744i	$0.268863\pi$
$602$		0			0
$603$	−45.4211			−1.84969
$604$		0			0
$605$	33.5384	−	19.0773i	1.36353	−	0.775602i
$606$		0			0
$607$	0.949146	+	0.254323i	0.0385247	+	0.0103227i	0.278030	−	0.960572i	$-0.410319\pi$
$607$	0.949146	+	0.254323i	0.0385247	+	0.0103227i	−0.239505	+	0.970895i	$0.576985\pi$
$608$		0			0
$609$	−0.149517	−	0.558004i	−0.00605873	−	0.0226115i
$610$		0			0
$611$	−5.57554	+	4.81184i	−0.225562	+	0.194666i
$612$		0			0
$613$	4.32110	−	7.48436i	0.174528	−	0.302291i	−0.765470	−	0.643471i	$-0.777494\pi$
$613$	4.32110	−	7.48436i	0.174528	−	0.302291i	0.939998	+	0.341181i	$0.110827\pi$
$614$		0			0
$615$	15.5782	+	27.3868i	0.628172	+	1.10434i
$616$		0			0
$617$	7.59463	−	4.38476i	0.305748	−	0.176524i	−0.339274	−	0.940688i	$-0.610181\pi$
$617$	7.59463	−	4.38476i	0.305748	−	0.176524i	0.645022	+	0.764164i	$0.276848\pi$
$618$		0			0
$619$	−8.20840	+	8.20840i	−0.329924	+	0.329924i	−0.852557	−	0.522634i	$-0.824950\pi$
$619$	−8.20840	+	8.20840i	−0.329924	+	0.329924i	0.522634	+	0.852557i	$0.324950\pi$
$620$		0			0
$621$	−1.92741	−	1.11279i	−0.0773442	−	0.0446547i
$622$		0			0
$623$	3.31086	−	3.31086i	0.132647	−	0.132647i
$624$		0			0
$625$	24.9918	+	0.642115i	0.999670	+	0.0256846i
$626$		0			0
$627$	−24.0917	−	89.9113i	−0.962128	−	3.59071i
$628$		0			0
$629$	−5.38099	−	5.38099i	−0.214554	−	0.214554i
$630$		0			0
$631$	1.58993	−	5.93370i	0.0632941	−	0.236217i	−0.927031	−	0.374985i	$-0.877648\pi$
$631$	1.58993	−	5.93370i	0.0632941	−	0.236217i	0.990325	+	0.138769i	$0.0443144\pi$
$632$		0			0
$633$	−18.8950	+	70.5173i	−0.751011	+	2.80281i
$634$		0			0
$635$	30.0012	−	7.83266i	1.19056	−	0.310829i
$636$		0			0
$637$	1.56699	+	8.21833i	0.0620864	+	0.325622i
$638$		0			0
$639$	−37.9004	+	10.1554i	−1.49932	+	0.401741i
$640$		0			0
$641$	−24.8739	+	14.3609i	−0.982459	+	0.567223i	−0.903012	−	0.429616i	$-0.858649\pi$
$641$	−24.8739	+	14.3609i	−0.982459	+	0.567223i	−0.0794473	+	0.996839i	$0.525316\pi$
$642$		0			0
$643$	15.8709	+	27.4892i	0.625887	+	1.08407i	0.988369	+	0.152078i	$0.0485963\pi$
$643$	15.8709	+	27.4892i	0.625887	+	1.08407i	−0.362481	+	0.931991i	$0.618070\pi$
$644$		0			0
$645$	22.1120	+	0.142002i	0.870659	+	0.00559133i
$646$		0			0
$647$	−3.80155	+	1.01862i	−0.149454	+	0.0400462i	−0.332771	−	0.943008i	$-0.607983\pi$
$647$	−3.80155	+	1.01862i	−0.149454	+	0.0400462i	0.183316	+	0.983054i	$0.441317\pi$
$648$		0			0
$649$	66.9278			2.62714
$650$		0			0
$651$	−31.8408			−1.24794
$652$		0			0
$653$	−29.0226	+	7.77659i	−1.13574	+	0.304321i	−0.777238	−	0.629207i	$-0.783380\pi$
$653$	−29.0226	+	7.77659i	−1.13574	+	0.304321i	−0.358505	+	0.933528i	$0.616713\pi$
$654$		0			0
$655$	11.1811	+	0.0718046i	0.436883	+	0.00280564i
$656$		0			0
$657$	22.1356	+	38.3399i	0.863591	+	1.49578i
$658$		0			0
$659$	17.0616	−	9.85051i	0.664625	−	0.383721i	−0.129412	−	0.991591i	$-0.541309\pi$
$659$	17.0616	−	9.85051i	0.664625	−	0.383721i	0.794037	+	0.607870i	$0.207976\pi$
$660$		0			0
$661$	−12.2450	+	3.28105i	−0.476277	+	0.127618i	−0.488968	−	0.872301i	$-0.662627\pi$
$661$	−12.2450	+	3.28105i	−0.476277	+	0.127618i	0.0126917	+	0.999919i	$0.495960\pi$
$662$		0			0
$663$	7.00135	+	8.11256i	0.271910	+	0.315066i
$664$		0			0
$665$	30.7133	−	8.01858i	1.19101	−	0.310947i
$666$		0			0
$667$	0.0192758	−	0.0719382i	0.000746361	−	0.00278546i
$668$		0			0
$669$	−1.46897	+	5.48227i	−0.0567936	+	0.211957i
$670$		0			0
$671$	35.0688	+	35.0688i	1.35382	+	1.35382i
$672$		0			0
$673$	−11.7643	−	43.9051i	−0.453482	−	1.69242i	−0.692513	−	0.721406i	$-0.743496\pi$
$673$	−11.7643	−	43.9051i	−0.453482	−	1.69242i	0.239031	−	0.971012i	$-0.423170\pi$
$674$		0			0
$675$	10.7082	−	10.4366i	0.412160	−	0.401706i
$676$		0			0
$677$	−7.14523	+	7.14523i	−0.274614	+	0.274614i	−0.830954	−	0.556341i	$-0.812205\pi$
$677$	−7.14523	+	7.14523i	−0.274614	+	0.274614i	0.556341	+	0.830954i	$0.312205\pi$
$678$		0			0
$679$	−23.7917	−	13.7361i	−0.913040	−	0.527144i
$680$		0			0
$681$	42.3750	−	42.3750i	1.62381	−	1.62381i
$682$		0			0
$683$	8.05969	−	4.65327i	0.308396	−	0.178052i	−0.337813	−	0.941213i	$-0.609687\pi$
$683$	8.05969	−	4.65327i	0.308396	−	0.178052i	0.646208	+	0.763161i	$0.276354\pi$
$684$		0			0
$685$	−12.4432	−	21.8755i	−0.475429	−	0.835818i
$686$		0			0
$687$	−1.40131	+	2.42714i	−0.0534632	+	0.0926010i
$688$		0			0
$689$	−42.1230	−	3.09700i	−1.60476	−	0.117986i
$690$		0			0
$691$	−0.156512	−	0.584112i	−0.00595401	−	0.0222207i	0.962885	−	0.269912i	$-0.0869947\pi$
$691$	−0.156512	−	0.584112i	−0.00595401	−	0.0222207i	−0.968839	+	0.247692i	$0.920328\pi$
$692$		0			0
$693$	45.7690	+	12.2638i	1.73862	+	0.465862i
$694$		0			0
$695$	16.9298	−	9.62997i	0.642182	−	0.365286i
$696$		0			0
$697$	5.88119			0.222766
$698$		0			0
$699$	−12.6858	+	21.9724i	−0.479820	+	0.831072i
$700$		0			0
$701$		−	42.5349i		−	1.60652i	−0.595627	−	0.803261i	$-0.703096\pi$
$701$		−	42.5349i		−	1.60652i	0.595627	−	0.803261i	$-0.296904\pi$
$702$		0			0
$703$	31.7044	+	31.7044i	1.19575	+	1.19575i
$704$		0			0
$705$	11.7928	−	3.07885i	0.444144	−	0.115956i
$706$		0			0
$707$			38.4442i			1.44584i
$708$		0			0
$709$	47.9316	+	12.8432i	1.80011	+	0.482337i	0.993995	−	0.109425i	$-0.0349009\pi$
$709$	47.9316	+	12.8432i	1.80011	+	0.482337i	0.806112	+	0.591762i	$0.201568\pi$
$710$		0			0
$711$	−31.5552	−	54.6553i	−1.18341	−	2.04973i
$712$		0			0
$713$	−3.55497	−	2.05246i	−0.133135	−	0.0768653i
$714$		0			0
$715$	24.3187	−	35.2876i	0.909466	−	1.31968i
$716$		0			0
$717$	−4.62890	−	2.67250i	−0.172870	−	0.0998063i
$718$		0			0
$719$	3.49009	+	6.04502i	0.130159	+	0.225441i	0.923738	−	0.383026i	$-0.125118\pi$
$719$	3.49009	+	6.04502i	0.130159	+	0.225441i	−0.793579	+	0.608467i	$0.791785\pi$
$720$		0			0
$721$	−14.8151	−	3.96969i	−0.551742	−	0.147839i
$722$		0			0
$723$		−	0.393233i		−	0.0146245i
$724$		0			0
$725$	0.430091	+	0.255734i	0.0159732	+	0.00949773i
$726$		0			0
$727$	−18.2655	−	18.2655i	−0.677429	−	0.677429i	0.281989	−	0.959418i	$-0.409006\pi$
$727$	−18.2655	−	18.2655i	−0.677429	−	0.677429i	−0.959418	+	0.281989i	$0.909006\pi$
$728$		0			0
$729$			41.9972i			1.55545i
$730$		0			0
$731$	2.06376	−	3.57454i	0.0763310	−	0.132209i
$732$		0			0
$733$	−30.7161			−1.13452			−0.567262	−	0.823537i	$-0.691997\pi$
$733$	−30.7161			−1.13452			−0.567262	+	0.823537i	$0.691997\pi$
$734$		0			0
$735$	3.66932	−	13.3506i	0.135345	−	0.492443i
$736$		0			0
$737$	56.5954	+	15.1647i	2.08472	+	0.558598i
$738$		0			0
$739$	−7.17064	−	26.7612i	−0.263776	−	0.984427i	−0.962995	−	0.269519i	$-0.913135\pi$
$739$	−7.17064	−	26.7612i	−0.263776	−	0.984427i	0.699219	−	0.714908i	$-0.253531\pi$
$740$		0			0
$741$	−41.2515	−	47.7987i	−1.51541	−	1.75593i
$742$		0			0
$743$	−3.98468	+	6.90167i	−0.146184	+	0.253198i	−0.929814	−	0.368030i	$-0.880032\pi$
$743$	−3.98468	+	6.90167i	−0.146184	+	0.253198i	0.783630	+	0.621228i	$0.213366\pi$
$744$		0			0
$745$	−2.45348	+	8.92681i	−0.0898886	+	0.327053i
$746$		0			0
$747$	1.68968	−	0.975537i	0.0618222	−	0.0356930i
$748$		0			0
$749$	16.4350	−	16.4350i	0.600522	−	0.600522i
$750$		0			0
$751$	−27.1108	−	15.6524i	−0.989287	−	0.571165i	−0.0842259	−	0.996447i	$-0.526842\pi$
$751$	−27.1108	−	15.6524i	−0.989287	−	0.571165i	−0.905061	+	0.425282i	$0.860175\pi$
$752$		0			0
$753$	−26.5531	+	26.5531i	−0.967648	+	0.967648i
$754$		0			0
$755$	−8.91599	−	9.03124i	−0.324486	−	0.328681i
$756$		0			0
$757$	10.1290	+	37.8020i	0.368145	+	1.37394i	0.863107	+	0.505021i	$0.168515\pi$
$757$	10.1290	+	37.8020i	0.368145	+	1.37394i	−0.494962	+	0.868915i	$0.664818\pi$
$758$		0			0
$759$	7.46424	+	7.46424i	0.270935	+	0.270935i
$760$		0			0
$761$	−7.61145	+	28.4063i	−0.275915	+	1.02973i	0.679311	+	0.733850i	$0.262279\pi$
$761$	−7.61145	+	28.4063i	−0.275915	+	1.02973i	−0.955226	+	0.295877i	$0.904388\pi$
$762$		0			0
$763$	1.86922	−	6.97602i	0.0676702	−	0.252549i
$764$		0			0
$765$	−2.59244	−	9.92974i	−0.0937298	−	0.359011i
$766$		0			0
$767$	40.8734	−	19.7546i	1.47585	−	0.713297i
$768$		0			0
$769$	−32.5217	+	8.71417i	−1.17276	+	0.314241i	−0.792052	−	0.610453i	$-0.790987\pi$
$769$	−32.5217	+	8.71417i	−1.17276	+	0.314241i	−0.380711	+	0.924694i	$0.624321\pi$
$770$		0			0
$771$	−44.5516	+	25.7219i	−1.60449	+	0.926350i
$772$		0			0
$773$	−13.1416	−	22.7618i	−0.472669	−	0.818687i	0.526842	−	0.849963i	$-0.323376\pi$
$773$	−13.1416	−	22.7618i	−0.472669	−	0.818687i	−0.999511	+	0.0312766i	$0.990043\pi$
$774$		0			0
$775$	19.7506	−	19.2497i	0.709462	−	0.691468i
$776$		0			0
$777$	−38.0966	+	10.2080i	−1.36671	+	0.366209i
$778$		0			0
$779$	−34.6516			−1.24152
$780$		0			0
$781$	50.6150			1.81115
$782$		0			0
$783$	0.289087	−	0.0774606i	0.0103311	−	0.00276821i
$784$		0			0
$785$	13.7067	−	13.5318i	0.489213	−	0.482969i
$786$		0			0
$787$	10.2780	+	17.8020i	0.366371	+	0.634573i	0.988995	−	0.147948i	$-0.0472668\pi$
$787$	10.2780	+	17.8020i	0.366371	+	0.634573i	−0.622624	+	0.782521i	$0.713933\pi$
$788$		0			0
$789$	50.7703	−	29.3123i	1.80747	−	1.04354i
$790$		0			0
$791$	14.4015	−	3.85886i	0.512057	−	0.137205i
$792$		0			0
$793$	31.7679	+	11.0658i	1.12811	+	0.392960i
$794$		0			0
$795$	60.3078	+	35.3370i	2.13890	+	1.25328i
$796$		0			0
$797$	6.59270	−	24.6043i	0.233526	−	0.871529i	−0.745282	−	0.666749i	$-0.767685\pi$
$797$	6.59270	−	24.6043i	0.233526	−	0.871529i	0.978808	−	0.204780i	$-0.0656480\pi$
$798$		0			0
$799$	0.588824	−	2.19752i	0.0208311	−	0.0777427i
$800$		0			0
$801$	6.30681	+	6.30681i	0.222840	+	0.222840i
$802$		0			0
$803$	−14.7807	−	55.1625i	−0.521601	−	1.94664i
$804$		0			0
$805$	−2.56172	+	2.52903i	−0.0902888	+	0.0891365i
$806$		0			0
$807$	−20.0947	+	20.0947i	−0.707368	+	0.707368i
$808$		0			0
$809$	−14.4124	−	8.32102i	−0.506714	−	0.292551i	0.224768	−	0.974412i	$-0.427838\pi$
$809$	−14.4124	−	8.32102i	−0.506714	−	0.292551i	−0.731482	+	0.681861i	$0.761171\pi$
$810$		0			0
$811$	−12.1054	+	12.1054i	−0.425079	+	0.425079i	−0.886948	−	0.461869i	$-0.847179\pi$
$811$	−12.1054	+	12.1054i	−0.425079	+	0.425079i	0.461869	+	0.886948i	$0.347179\pi$
$812$		0			0
$813$	8.87807	−	5.12576i	0.311368	−	0.179768i
$814$		0			0
$815$	−21.7333	+	12.3623i	−0.761284	+	0.433033i
$816$		0			0
$817$	−12.1595	+	21.0610i	−0.425409	+	0.736830i
$818$		0			0
$819$	31.5714	−	6.01971i	1.10319	−	0.210346i
$820$		0			0
$821$	−8.36891	−	31.2332i	−0.292077	−	1.09005i	−0.943511	−	0.331341i	$-0.892499\pi$
$821$	−8.36891	−	31.2332i	−0.292077	−	1.09005i	0.651434	−	0.758705i	$-0.274168\pi$
$822$		0			0
$823$	6.73560	+	1.80480i	0.234788	+	0.0629114i	0.374295	−	0.927310i	$-0.377885\pi$
$823$	6.73560	+	1.80480i	0.234788	+	0.0629114i	−0.139506	+	0.990221i	$0.544552\pi$
$824$		0			0
$825$	−61.8710	+	34.6694i	−2.15407	+	1.20703i
$826$		0			0
$827$	−34.2158			−1.18980			−0.594900	−	0.803800i	$-0.702808\pi$
$827$	−34.2158			−1.18980			−0.594900	+	0.803800i	$0.702808\pi$
$828$		0			0
$829$	−13.9995	+	24.2478i	−0.486222	+	0.842161i	−0.999875	−	0.0158373i	$-0.994959\pi$
$829$	−13.9995	+	24.2478i	−0.486222	+	0.842161i	0.513653	+	0.857998i	$0.328292\pi$
$830$		0			0
$831$			37.6066i			1.30456i
$832$		0			0
$833$	−1.82747	−	1.82747i	−0.0633181	−	0.0633181i
$834$		0			0
$835$	−8.77903	+	14.9827i	−0.303811	+	0.518498i
$836$		0			0
$837$		−	16.4958i		−	0.570179i
$838$		0			0
$839$	44.5978	+	11.9500i	1.53969	+	0.412558i	0.926165	−	0.377119i	$-0.123085\pi$
$839$	44.5978	+	11.9500i	1.53969	+	0.412558i	0.613523	+	0.789677i	$0.289752\pi$
$840$		0			0
$841$	−14.4950	−	25.1061i	−0.499827	−	0.865726i
$842$		0			0
$843$	41.4368	+	23.9235i	1.42716	+	0.823970i
$844$		0			0
$845$	4.43605	−	28.7284i	0.152605	−	0.988287i
$846$		0			0
$847$	−32.3268	−	18.6639i	−1.11076	−	0.641298i
$848$		0			0
$849$	−11.6069	−	20.1038i	−0.398349	−	0.689961i
$850$		0			0
$851$	−4.91143	−	1.31601i	−0.168362	−	0.0451124i
$852$		0			0
$853$		−	0.328048i		−	0.0112321i	−0.999984	−	0.00561607i	$-0.998212\pi$
$853$		−	0.328048i		−	0.0112321i	0.999984	−	0.00561607i	$-0.00178766\pi$
$854$		0			0
$855$	15.2745	+	58.5054i	0.522376	+	2.00084i
$856$		0			0
$857$	7.20279	+	7.20279i	0.246043	+	0.246043i	0.819344	−	0.573302i	$-0.194338\pi$
$857$	7.20279	+	7.20279i	0.246043	+	0.246043i	−0.573302	+	0.819344i	$0.694338\pi$
$858$		0			0
$859$		−	19.2793i		−	0.657800i	−0.944365	−	0.328900i	$-0.893322\pi$
$859$		−	19.2793i		−	0.657800i	0.944365	−	0.328900i	$-0.106678\pi$
$860$		0			0
$861$	15.2406	−	26.3975i	0.519398	−	0.899623i
$862$		0			0
$863$	16.7097			0.568806			0.284403	−	0.958705i	$-0.408205\pi$
$863$	16.7097			0.568806			0.284403	+	0.958705i	$0.408205\pi$
$864$		0			0
$865$	−32.2371	−	8.86018i	−1.09609	−	0.301255i
$866$		0			0
$867$	40.6207	+	10.8843i	1.37955	+	0.369650i
$868$		0			0
$869$	21.0706	+	78.6366i	0.714772	+	2.66756i
$870$		0			0
$871$	39.0394	−	7.44364i	1.32280	−	0.252218i
$872$		0			0
$873$	26.1657	−	45.3204i	0.885576	−	1.53386i
$874$		0			0
$875$	−11.6871	−	21.1745i	−0.395096	−	0.715829i
$876$		0			0
$877$	21.8193	−	12.5974i	0.736784	−	0.425383i	−0.0841148	−	0.996456i	$-0.526806\pi$
$877$	21.8193	−	12.5974i	0.736784	−	0.425383i	0.820899	+	0.571074i	$0.193473\pi$
$878$		0			0
$879$	22.6004	−	22.6004i	0.762292	−	0.762292i
$880$		0			0
$881$	46.8238	+	27.0337i	1.57753	+	0.910790i	0.995202	+	0.0978396i	$0.0311932\pi$
$881$	46.8238	+	27.0337i	1.57753	+	0.910790i	0.582333	+	0.812951i	$0.302140\pi$
$882$		0			0
$883$	5.21525	−	5.21525i	0.175507	−	0.175507i	−0.613887	−	0.789394i	$-0.710395\pi$
$883$	5.21525	−	5.21525i	0.175507	−	0.175507i	0.789394	+	0.613887i	$0.210395\pi$
$884$		0			0
$885$	−75.1264	−	0.482457i	−2.52535	−	0.0162176i
$886$		0			0
$887$	7.45098	+	27.8074i	0.250179	+	0.933682i	0.970709	+	0.240258i	$0.0772320\pi$
$887$	7.45098	+	27.8074i	0.250179	+	0.933682i	−0.720530	+	0.693424i	$0.756101\pi$
$888$		0			0
$889$	−21.2110	−	21.2110i	−0.711394	−	0.711394i
$890$		0			0
$891$	6.02847	−	22.4986i	0.201961	−	0.753730i
$892$		0			0
$893$	−3.46931	+	12.9476i	−0.116096	+	0.433276i
$894$		0			0
$895$	1.41785	−	2.41977i	0.0473935	−	0.0808840i
$896$		0			0
$897$	6.76164	+	2.35531i	0.225765	+	0.0786416i
$898$		0			0
$899$	0.533201	−	0.142871i	0.0177832	−	0.00476500i
$900$		0			0
$901$	11.2992	−	6.52360i	0.376431	−	0.217333i
$902$		0			0
$903$	−10.6961	−	18.5262i	−0.355944	−	0.616513i
$904$		0			0
$905$	−0.103855	+	16.1719i	−0.00345225	+	0.537570i
$906$		0			0
$907$	35.0834	−	9.40058i	1.16493	−	0.312141i	0.375994	−	0.926622i	$-0.377301\pi$
$907$	35.0834	−	9.40058i	1.16493	−	0.312141i	0.788932	+	0.614481i	$0.210635\pi$
$908$		0			0
$909$	−73.2318			−2.42894
$910$		0			0
$911$	1.89993			0.0629473			0.0314737	−	0.999505i	$-0.489980\pi$
$911$	1.89993			0.0629473			0.0314737	+	0.999505i	$0.489980\pi$
$912$		0			0
$913$	−2.43107	+	0.651403i	−0.0804566	+	0.0215583i
$914$		0			0
$915$	−39.1119	−	39.6175i	−1.29300	−	1.30972i
$916$		0			0
$917$	−5.40858	−	9.36793i	−0.178607	−	0.309356i
$918$		0			0
$919$	−33.0949	+	19.1073i	−1.09170	+	0.630293i	−0.934028	−	0.357199i	$-0.883732\pi$
$919$	−33.0949	+	19.1073i	−1.09170	+	0.630293i	−0.157671	+	0.987492i	$0.550399\pi$
$920$		0			0
$921$	51.5531	−	13.8136i	1.69873	−	0.455174i
$922$		0			0
$923$	30.9111	−	14.9397i	1.01745	−	0.491745i
$924$		0			0
$925$	17.4597	−	29.3636i	0.574073	−	0.965470i
$926$		0			0
$927$	7.56180	−	28.2210i	0.248362	−	0.926899i
$928$		0			0
$929$	0.860601	−	3.21181i	0.0282354	−	0.105376i	−0.950370	−	0.311122i	$-0.899295\pi$
$929$	0.860601	−	3.21181i	0.0282354	−	0.105376i	0.978605	+	0.205746i	$0.0659620\pi$
$930$		0			0
$931$	10.7673	+	10.7673i	0.352885	+	0.352885i
$932$		0			0
$933$	10.2300	+	38.1788i	0.334914	+	1.24992i
$934$		0			0
$935$	−0.0850146	+	13.2381i	−0.00278027	+	0.432933i
$936$		0			0
$937$	8.40073	−	8.40073i	0.274440	−	0.274440i	−0.556445	−	0.830885i	$-0.687835\pi$
$937$	8.40073	−	8.40073i	0.274440	−	0.274440i	0.830885	+	0.556445i	$0.187835\pi$
$938$		0			0
$939$	7.68475	+	4.43679i	0.250782	+	0.144789i
$940$		0			0
$941$	−22.2587	+	22.2587i	−0.725614	+	0.725614i	−0.969743	−	0.244129i	$-0.921498\pi$
$941$	−22.2587	+	22.2587i	−0.725614	+	0.725614i	0.244129	+	0.969743i	$0.421498\pi$
$942$		0			0
$943$	3.40317	−	1.96482i	0.110823	−	0.0639834i
$944$		0			0
$945$	−13.9486	−	3.83370i	−0.453749	−	0.124710i
$946$		0			0
$947$	8.28083	−	14.3428i	0.269091	−	0.466079i	−0.699536	−	0.714597i	$-0.746610\pi$
$947$	8.28083	−	14.3428i	0.269091	−	0.466079i	0.968627	+	0.248518i	$0.0799434\pi$
$948$		0			0
$949$	−25.3087	−	29.3255i	−0.821554	−	0.951947i
$950$		0			0
$951$	10.5604	+	39.4118i	0.342443	+	1.27802i
$952$		0			0
$953$	−24.2031	−	6.48521i	−0.784016	−	0.210077i	−0.155462	−	0.987842i	$-0.549687\pi$
$953$	−24.2031	−	6.48521i	−0.784016	−	0.210077i	−0.628555	+	0.777765i	$0.716353\pi$
$954$		0			0
$955$	23.2673	+	40.9046i	0.752912	+	1.32364i
$956$		0			0
$957$	−1.41952			−0.0458866
$958$		0			0
$959$	−12.1735	+	21.0852i	−0.393104	+	0.680876i
$960$		0			0
$961$			0.574591i			0.0185352i
$962$		0			0
$963$	31.3068	+	31.3068i	1.00885	+	1.00885i
$964$		0			0
$965$	19.1867	+	11.2423i	0.617640	+	0.361903i
$966$		0			0
$967$			31.4641i			1.01182i	0.862587	+	0.505908i	$0.168843\pi$
$967$			31.4641i			1.01182i	−0.862587	+	0.505908i	$0.831157\pi$
$968$		0			0
$969$	18.8392	+	5.04794i	0.605201	+	0.162163i
$970$		0			0
$971$	−0.0733855	−	0.127107i	−0.00235505	−	0.00407907i	0.864845	−	0.502038i	$-0.167416\pi$
$971$	−0.0733855	−	0.127107i	−0.00235505	−	0.00407907i	−0.867201	+	0.497959i	$0.834083\pi$
$972$		0			0
$973$	−16.3182	−	9.42129i	−0.523136	−	0.302033i
$974$		0			0
$975$	−27.5520	+	39.4350i	−0.882372	+	1.26293i
$976$		0			0
$977$	−15.7268	−	9.07986i	−0.503144	−	0.290490i	0.226867	−	0.973926i	$-0.427152\pi$
$977$	−15.7268	−	9.07986i	−0.503144	−	0.290490i	−0.730011	+	0.683435i	$0.760485\pi$
$978$		0			0
$979$	−5.75274	−	9.96403i	−0.183858	−	0.318452i
$980$		0			0
$981$	13.2885	+	3.56064i	0.424269	+	0.113683i
$982$		0			0
$983$		−	42.3986i		−	1.35230i	−0.736762	−	0.676152i	$-0.763646\pi$
$983$		−	42.3986i		−	1.35230i	0.736762	−	0.676152i	$-0.236354\pi$
$984$		0			0
$985$	10.3638	+	6.07259i	0.330217	+	0.193489i
$986$		0			0
$987$	−8.33759	−	8.33759i	−0.265388	−	0.265388i
$988$		0			0
$989$		−	2.75789i		−	0.0876959i
$990$		0			0
$991$	16.8511	−	29.1869i	0.535292	−	0.927152i	−0.463857	−	0.885910i	$-0.653535\pi$
$991$	16.8511	−	29.1869i	0.535292	−	0.927152i	0.999149	−	0.0412426i	$-0.0131317\pi$
$992$		0			0
$993$	2.48848			0.0789697
$994$		0			0
$995$	−7.16882	−	12.6030i	−0.227267	−	0.399541i
$996$		0			0
$997$	12.2204	+	3.27444i	0.387023	+	0.103703i	0.447084	−	0.894492i	$-0.352463\pi$
$997$	12.2204	+	3.27444i	0.387023	+	0.103703i	−0.0600602	+	0.998195i	$0.519129\pi$
$998$		0			0
$999$	−5.28846	−	19.7368i	−0.167320	−	0.624445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bf.c.253.5	yes	20
5.2	odd	4		260.2.bk.c.97.1	yes	20
5.3	odd	4		1300.2.bs.d.357.5		20
5.4	even	2		1300.2.bn.d.1293.1		20
13.11	odd	12		260.2.bk.c.193.1	yes	20
65.24	odd	12		1300.2.bs.d.193.5		20
65.37	even	12	inner	260.2.bf.c.37.5	✓	20
65.63	even	12		1300.2.bn.d.557.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.37.5	✓	20	65.37	even	12	inner
260.2.bf.c.253.5	yes	20	1.1	even	1	trivial
260.2.bk.c.97.1	yes	20	5.2	odd	4
260.2.bk.c.193.1	yes	20	13.11	odd	12
1300.2.bn.d.557.1		20	65.63	even	12
1300.2.bn.d.1293.1		20	5.4	even	2
1300.2.bs.d.193.5		20	65.24	odd	12
1300.2.bs.d.357.5		20	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)

\(f(q)\)	\(=\)	\(q+(2.57754 - 0.690650i) q^{3} +(2.23602 + 0.0143596i) q^{5} +(-1.08162 - 1.87342i) q^{7} +(3.56864 - 2.06036i) q^{9} +O(q^{10})\)	\(q+(2.57754 - 0.690650i) q^{3} +(2.23602 + 0.0143596i) q^{5} +(-1.08162 - 1.87342i) q^{7} +(3.56864 - 2.06036i) q^{9} +(-5.13447 + 1.37578i) q^{11} +(-2.72959 + 2.35570i) q^{13} +(5.77335 - 1.50730i) q^{15} +(0.288267 - 1.07583i) q^{17} +(-1.69845 + 6.33871i) q^{19} +(-4.08179 - 4.08179i) q^{21} +(-0.192612 - 0.718837i) q^{23} +(4.99959 + 0.0642168i) q^{25} +(2.11466 - 2.11466i) q^{27} +(0.0866681 + 0.0500378i) q^{29} +(3.90035 - 3.90035i) q^{31} +(-12.2841 + 7.09224i) q^{33} +(-2.39162 - 4.20453i) q^{35} +(3.41623 - 5.91709i) q^{37} +(-5.40866 + 7.95711i) q^{39} +(1.36667 + 5.10047i) q^{41} +(3.57960 + 0.959150i) q^{43} +(8.00915 - 4.55576i) q^{45} +2.04263 q^{47} +(1.16021 - 2.00954i) q^{49} -2.97208i q^{51} +(8.28330 + 8.28330i) q^{53} +(-11.5005 + 3.00254i) q^{55} +17.5113i q^{57} +(-12.1618 - 3.25875i) q^{59} +(-4.66503 - 8.08007i) q^{61} +(-7.71981 - 4.45703i) q^{63} +(-6.13725 + 5.22821i) q^{65} +(-9.54588 - 5.51132i) q^{67} +(-0.992930 - 1.71981i) q^{69} +(-9.19754 - 2.46447i) q^{71} +10.7436i q^{73} +(12.9310 - 3.28744i) q^{75} +(8.13093 + 8.13093i) q^{77} -15.3154i q^{79} +(-2.19093 + 3.79481i) q^{81} +0.473480 q^{83} +(0.660020 - 2.40144i) q^{85} +(0.257949 + 0.0691173i) q^{87} +(0.560208 + 2.09072i) q^{89} +(7.36558 + 2.56569i) q^{91} +(7.35953 - 12.7471i) q^{93} +(-3.88880 + 14.1491i) q^{95} +(10.9982 - 6.34981i) q^{97} +(-15.4885 + 15.4885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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