LMFDB - Embedded newform 260.2.bk.c.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.1
Root			$0.125665i$ of defining polynomial
Character	$\chi$	$=$	260.97
Dual form			260.2.bk.c.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690650 - 2.57754i) q^{3} +(-0.0143596 - 2.23602i) q^{5} +(1.87342 - 1.08162i) q^{7} +(-3.56864 + 2.06036i) q^{9} +O(q^{10})$	\(q+(-0.690650 - 2.57754i) q^{3} +(-0.0143596 - 2.23602i) q^{5} +(1.87342 - 1.08162i) q^{7} +(-3.56864 + 2.06036i) q^{9} +(-5.13447 + 1.37578i) q^{11} +(2.35570 + 2.72959i) q^{13} +(-5.75352 + 1.58132i) q^{15} +(1.07583 + 0.288267i) q^{17} +(1.69845 - 6.33871i) q^{19} +(-4.08179 - 4.08179i) q^{21} +(-0.718837 + 0.192612i) q^{23} +(-4.99959 + 0.0642168i) q^{25} +(2.11466 + 2.11466i) q^{27} +(-0.0866681 - 0.0500378i) q^{29} +(3.90035 - 3.90035i) q^{31} +(7.09224 + 12.2841i) q^{33} +(-2.44542 - 4.17347i) q^{35} +(5.91709 + 3.41623i) q^{37} +(5.40866 - 7.95711i) q^{39} +(1.36667 + 5.10047i) q^{41} +(0.959150 - 3.57960i) q^{43} +(4.65825 + 7.94997i) q^{45} +2.04263i q^{47} +(-1.16021 + 2.00954i) q^{49} -2.97208i q^{51} +(8.28330 - 8.28330i) q^{53} +(3.15000 + 11.4610i) q^{55} -17.5113 q^{57} +(12.1618 + 3.25875i) q^{59} +(-4.66503 - 8.08007i) q^{61} +(-4.45703 + 7.71981i) q^{63} +(6.06959 - 5.30660i) q^{65} +(5.51132 - 9.54588i) q^{67} +(0.992930 + 1.71981i) q^{69} +(-9.19754 - 2.46447i) q^{71} +10.7436 q^{73} +(3.61849 + 12.8423i) q^{75} +(-8.13093 + 8.13093i) q^{77} +15.3154i q^{79} +(-2.19093 + 3.79481i) q^{81} -0.473480i q^{83} +(0.629124 - 2.40971i) q^{85} +(-0.0691173 + 0.257949i) q^{87} +(-0.560208 - 2.09072i) q^{89} +(7.36558 + 2.56569i) q^{91} +(-12.7471 - 7.35953i) q^{93} +(-14.1979 - 3.70675i) q^{95} +(6.34981 + 10.9982i) q^{97} +(15.4885 - 15.4885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.690650	−	2.57754i	−0.398747	−	1.48814i	−0.815303	−	0.579034i	$-0.803430\pi$
$3$	−0.690650	−	2.57754i	−0.398747	−	1.48814i	0.416557	−	0.909110i	$-0.363237\pi$
$4$		0			0
$5$	−0.0143596	−	2.23602i	−0.00642181	−	0.999979i
$5$	−0.0143596	−	2.23602i	−0.00642181	−	0.999979i
$6$		0			0
$7$	1.87342	−	1.08162i	0.708085	−	0.408813i	−0.102267	−	0.994757i	$-0.532610\pi$
$7$	1.87342	−	1.08162i	0.708085	−	0.408813i	0.810351	+	0.585944i	$0.199276\pi$
$8$		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
$13$	2.35570	+	2.72959i	0.653355	+	0.757052i
$13$	2.35570	+	2.72959i	0.653355	+	0.757052i
$14$		0			0
$15$	−5.75352	+	1.58132i	−1.48555	+	0.408295i
$16$		0			0
$17$	1.07583	+	0.288267i	0.260927	+	0.0699151i	0.386911	−	0.922117i	$-0.373542\pi$
$17$	1.07583	+	0.288267i	0.260927	+	0.0699151i	−0.125984	+	0.992032i	$0.540209\pi$
$18$		0			0
$19$	1.69845	−	6.33871i	0.389652	−	1.45420i	−0.441050	−	0.897482i	$-0.645394\pi$
$19$	1.69845	−	6.33871i	0.389652	−	1.45420i	0.830702	−	0.556717i	$-0.187939\pi$
$20$		0			0
$21$	−4.08179	−	4.08179i	−0.890719	−	0.890719i
$22$		0			0
$23$	−0.718837	+	0.192612i	−0.149888	+	0.0401624i	−0.332983	−	0.942933i	$-0.608055\pi$
$23$	−0.718837	+	0.192612i	−0.149888	+	0.0401624i	0.183095	+	0.983095i	$0.441388\pi$
$24$		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	0.491931	−	0.870634i	$-0.336291\pi$
$29$	−0.0866681	−	0.0500378i	−0.0160939	−	0.00929179i	−0.508025	+	0.861342i	$0.669624\pi$
$30$		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
$33$	7.09224	+	12.2841i	1.23460	+	2.13839i
$34$		0			0
$35$	−2.44542	−	4.17347i	−0.413352	−	0.705445i
$36$		0			0
$37$	5.91709	+	3.41623i	0.972764	+	0.561625i	0.900078	−	0.435729i	$-0.143510\pi$
$37$	5.91709	+	3.41623i	0.972764	+	0.561625i	0.0726861	+	0.997355i	$0.476843\pi$
$38$		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
$43$	0.959150	−	3.57960i	0.146269	−	0.545883i	−0.853427	−	0.521213i	$-0.825480\pi$
$43$	0.959150	−	3.57960i	0.146269	−	0.545883i	0.999696	−	0.0246704i	$-0.00785364\pi$
$44$		0			0
$45$	4.65825	+	7.94997i	0.694410	+	1.18511i
$46$		0			0
$47$			2.04263i			0.297948i	0.988841	+	0.148974i	$0.0475971\pi$
$47$			2.04263i			0.297948i	−0.988841	+	0.148974i	$0.952403\pi$
$48$		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	0.148955	−	0.988844i	$-0.452409\pi$
$53$	8.28330	−	8.28330i	1.13780	−	1.13780i	0.988844	−	0.148955i	$-0.0475908\pi$
$54$		0			0
$55$	3.15000	+	11.4610i	0.424745	+	1.54540i
$56$		0			0
$57$	−17.5113			−2.31943
$58$		0			0
$59$	12.1618	+	3.25875i	1.58333	+	0.424253i	0.939956	−	0.341296i	$-0.110866\pi$
$59$	12.1618	+	3.25875i	1.58333	+	0.424253i	0.643378	+	0.765549i	$0.277533\pi$
$60$		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
$63$	−4.45703	+	7.71981i	−0.561533	+	0.972604i
$64$		0			0
$65$	6.06959	−	5.30660i	0.752841	−	0.658203i
$66$		0			0
$67$	5.51132	−	9.54588i	0.673315	−	1.16622i	−0.303644	−	0.952786i	$-0.598203\pi$
$67$	5.51132	−	9.54588i	0.673315	−	1.16622i	0.976958	−	0.213429i	$-0.0684633\pi$
$68$		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
$73$	10.7436			1.25744			0.628720	−	0.777632i	$-0.283579\pi$
$73$	10.7436			1.25744			0.628720	+	0.777632i	$0.283579\pi$
$74$		0			0
$75$	3.61849	+	12.8423i	0.417827	+	1.48290i
$76$		0			0
$77$	−8.13093	+	8.13093i	−0.926606	+	0.926606i
$78$		0			0
$79$			15.3154i			1.72312i	0.507655	+	0.861560i	$0.330512\pi$
$79$			15.3154i			1.72312i	−0.507655	+	0.861560i	$0.669488\pi$
$80$		0			0
$81$	−2.19093	+	3.79481i	−0.243437	+	0.421645i
$82$		0			0
$83$		−	0.473480i		−	0.0519712i	−0.999662	−	0.0259856i	$-0.991728\pi$
$83$		−	0.473480i		−	0.0519712i	0.999662	−	0.0259856i	$-0.00827240\pi$
$84$		0			0
$85$	0.629124	−	2.40971i	0.0682380	−	0.261370i
$86$		0			0
$87$	−0.0691173	+	0.257949i	−0.00741015	+	0.0276551i
$88$		0			0
$89$	−0.560208	−	2.09072i	−0.0593819	−	0.221616i	0.929858	−	0.367918i	$-0.119929\pi$
$89$	−0.560208	−	2.09072i	−0.0593819	−	0.221616i	−0.989240	+	0.146302i	$0.953263\pi$
$90$		0			0
$91$	7.36558	+	2.56569i	0.772123	+	0.268957i
$92$		0			0
$93$	−12.7471	−	7.35953i	−1.32181	−	0.763147i
$94$		0			0
$95$	−14.1979	−	3.70675i	−1.45667	−	0.380305i
$96$		0			0
$97$	6.34981	+	10.9982i	0.644725	+	1.11670i	0.984365	+	0.176141i	$0.0563616\pi$
$97$	6.34981	+	10.9982i	0.644725	+	1.11670i	−0.339640	+	0.940556i	$0.610305\pi$
$98$		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	$-0.363583\pi$
$103$	−5.01350	−	5.01350i	−0.493995	−	0.493995i	−0.909562	+	0.415567i	$0.863583\pi$
$104$		0			0
$105$	−9.06835	+	9.18558i	−0.884980	+	0.896421i
$106$		0			0
$107$	−10.3783	+	2.78085i	−1.00331	+	0.268835i	−0.722830	−	0.691026i	$-0.757159\pi$
$107$	−10.3783	+	2.78085i	−1.00331	+	0.268835i	−0.280476	+	0.959861i	$0.590492\pi$
$108$		0			0
$109$	−2.36072	−	2.36072i	−0.226116	−	0.226116i	0.584952	−	0.811068i	$-0.301113\pi$
$109$	−2.36072	−	2.36072i	−0.226116	−	0.226116i	−0.811068	+	0.584952i	$0.801113\pi$
$110$		0			0
$111$	4.71884	−	17.6110i	0.447893	−	1.67156i
$112$		0			0
$113$	6.65737	+	1.78384i	0.626273	+	0.167809i	0.557978	−	0.829856i	$-0.311577\pi$
$113$	6.65737	+	1.78384i	0.626273	+	0.167809i	0.0682952	+	0.997665i	$0.478244\pi$
$114$		0			0
$115$	0.441007	+	1.60457i	0.0411241	+	0.149627i
$116$		0			0
$117$	−14.0306	−	4.88734i	−1.29713	−	0.451834i
$118$		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
$123$	12.2028	−	7.04528i	1.10029	−	0.635251i
$124$		0			0
$125$	0.215382	+	11.1783i	0.0192644	+	0.999814i
$126$		0			0
$127$	3.58896	+	13.3942i	0.318469	+	1.18854i	0.920717	+	0.390232i	$0.127605\pi$
$127$	3.58896	+	13.3942i	0.318469	+	1.18854i	−0.602248	+	0.798309i	$0.705728\pi$
$128$		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
$133$	−3.67415	−	13.7121i	−0.318589	−	1.18899i
$134$		0			0
$135$	4.69806	−	4.75879i	0.404345	−	0.409572i
$136$		0			0
$137$	9.74706	−	5.62747i	0.832748	−	0.480787i	−0.0220448	−	0.999757i	$-0.507018\pi$
$137$	9.74706	−	5.62747i	0.832748	−	0.480787i	0.854793	+	0.518970i	$0.173684\pi$
$138$		0			0
$139$	−7.54341	+	4.35519i	−0.639823	+	0.369402i	−0.784546	−	0.620070i	$-0.787104\pi$
$139$	−7.54341	+	4.35519i	−0.639823	+	0.369402i	0.144723	+	0.989472i	$0.453771\pi$
$140$		0			0
$141$	5.26497	−	1.41074i	0.443390	−	0.118806i
$142$		0			0
$143$	−15.8506	−	10.7741i	−1.32549	−	0.900973i
$144$		0			0
$145$	−0.110641	+	0.194510i	−0.00918825	+	0.0161532i
$146$		0			0
$147$	5.98097	+	1.60260i	0.493302	+	0.132180i
$148$		0			0
$149$	1.07157	−	3.99916i	0.0877865	−	0.327624i	−0.908041	−	0.418882i	$-0.862422\pi$
$149$	1.07157	−	3.99916i	0.0877865	−	0.327624i	0.995827	+	0.0912581i	$0.0290888\pi$
$150$		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
$153$	−4.43318	+	1.18787i	−0.358401	+	0.0960333i
$154$		0			0
$155$	−8.77727	−	8.66525i	−0.705007	−	0.696010i
$156$		0			0
$157$	6.09083	+	6.09083i	0.486101	+	0.486101i	0.907073	−	0.420972i	$-0.138311\pi$
$157$	6.09083	+	6.09083i	0.486101	+	0.486101i	−0.420972	+	0.907073i	$0.638311\pi$
$158$		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
$163$	5.59090	+	9.68372i	0.437913	+	0.758488i	0.997528	−	0.0702649i	$-0.0223844\pi$
$163$	5.59090	+	9.68372i	0.437913	+	0.758488i	−0.559615	+	0.828752i	$0.689051\pi$
$164$		0			0
$165$	27.3657	−	16.0348i	2.13042	−	1.24831i
$166$		0			0
$167$	−6.72554	−	3.88299i	−0.520438	−	0.300475i	0.216676	−	0.976244i	$-0.430479\pi$
$167$	−6.72554	−	3.88299i	−0.520438	−	0.300475i	−0.737114	+	0.675769i	$0.763812\pi$
$168$		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
$173$	−3.86973	+	14.4420i	−0.294210	+	1.09801i	0.647633	+	0.761952i	$0.275759\pi$
$173$	−3.86973	+	14.4420i	−0.294210	+	1.09801i	−0.941843	+	0.336054i	$0.890908\pi$
$174$		0			0
$175$	−9.29685	+	5.52794i	−0.702776	+	0.417873i
$176$		0			0
$177$		−	33.5982i		−	2.52540i
$178$		0			0
$179$	−0.627120	+	1.08620i	−0.0468731	+	0.0811867i	−0.888510	−	0.458857i	$-0.848259\pi$
$179$	−0.627120	+	1.08620i	−0.0468731	+	0.0811867i	0.841637	+	0.540044i	$0.181592\pi$
$180$		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
$185$	7.55381	−	13.2798i	0.555367	−	0.976350i
$186$		0			0
$187$	−5.92040			−0.432942
$188$		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
$193$	4.97251	−	8.61264i	0.357929	−	0.619952i	−0.629686	−	0.776850i	$-0.716816\pi$
$193$	4.97251	−	8.61264i	0.357929	−	0.619952i	0.987615	+	0.156899i	$0.0501496\pi$
$194$		0			0
$195$	−17.8699	−	11.9796i	−1.27969	−	0.857878i
$196$		0			0
$197$	−2.68592	+	4.65216i	−0.191364	+	0.331453i	−0.945703	−	0.325033i	$-0.894624\pi$
$197$	−2.68592	+	4.65216i	−0.191364	+	0.331453i	0.754338	+	0.656486i	$0.227958\pi$
$198$		0			0
$199$	3.24212	+	5.61552i	0.229828	+	0.398073i	0.957757	−	0.287579i	$-0.0928504\pi$
$199$	3.24212	+	5.61552i	0.229828	+	0.398073i	−0.727929	+	0.685652i	$0.759517\pi$
$200$		0			0
$201$	−28.4113	−	7.61278i	−2.00398	−	0.536964i
$202$		0			0
$203$	−0.216487			−0.0151944
$204$		0			0
$205$	11.3851	−	3.12914i	0.795172	−	0.218548i
$206$		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
$213$			25.4091i			1.74100i
$214$		0			0
$215$	−8.01783	−	2.09328i	−0.546812	−	0.142760i
$216$		0			0
$217$	3.08829	−	11.5257i	0.209647	−	0.782412i
$218$		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
$223$	1.84198	+	1.06347i	0.123348	+	0.0712151i	0.560405	−	0.828219i	$-0.310646\pi$
$223$	1.84198	+	1.06347i	0.123348	+	0.0712151i	−0.437056	+	0.899434i	$0.643979\pi$
$224$		0			0
$225$	17.7094	−	10.5301i	1.18063	−	0.702006i
$226$		0			0
$227$	11.2288	+	19.4489i	0.745282	+	1.29087i	0.950063	+	0.312058i	$0.101018\pi$
$227$	11.2288	+	19.4489i	0.745282	+	1.29087i	−0.204781	+	0.978808i	$0.565648\pi$
$228$		0			0
$229$	0.742654	−	0.742654i	0.0490760	−	0.0490760i	−0.682143	−	0.731219i	$-0.738952\pi$
$229$	0.742654	−	0.742654i	0.0490760	−	0.0490760i	0.731219	+	0.682143i	$0.238952\pi$
$230$		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	$-0.149188\pi$
$233$	6.72311	+	6.72311i	0.440446	+	0.440446i	−0.451716	+	0.892162i	$0.649188\pi$
$234$		0			0
$235$	4.56737	−	0.0293314i	0.297942	−	0.00191337i
$236$		0			0
$237$	39.4761	−	10.5776i	2.56425	−	0.687089i
$238$		0			0
$239$	1.41635	+	1.41635i	0.0916161	+	0.0916161i	0.751430	−	0.659813i	$-0.229365\pi$
$239$	1.41635	+	1.41635i	0.0916161	+	0.0916161i	−0.659813	+	0.751430i	$0.729365\pi$
$240$		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
$243$	19.9605	+	5.34840i	1.28047	+	0.343100i
$244$		0			0
$245$	4.51004	+	2.56540i	0.288136	+	0.163897i
$246$		0			0
$247$	21.3031	−	10.2960i	1.35549	−	0.655122i
$248$		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
$253$	3.42586	−	1.97792i	0.215382	−	0.124351i
$254$		0			0
$255$	−6.64564	+	0.0426779i	−0.416166	+	0.00267260i
$256$		0			0
$257$	−4.98961	−	18.6215i	−0.311243	−	1.16158i	−0.927436	−	0.373981i	$-0.877993\pi$
$257$	−4.98961	−	18.6215i	−0.311243	−	1.16158i	0.616193	−	0.787595i	$-0.288674\pi$
$258$		0			0
$259$	14.7802			0.918399
$260$		0			0
$261$	0.412383			0.0255259
$262$		0			0
$263$	−5.68609	−	21.2208i	−0.350619	−	1.30853i	−0.885908	−	0.463860i	$-0.846464\pi$
$263$	−5.68609	−	21.2208i	−0.350619	−	1.30853i	0.535289	−	0.844669i	$-0.320203\pi$
$264$		0			0
$265$	−18.6406	−	18.4027i	−1.14508	−	1.13047i
$266$		0			0
$267$	−5.00202	+	2.88792i	−0.306118	+	0.176738i
$268$		0			0
$269$	9.22286	−	5.32482i	0.562328	−	0.324660i	−0.191751	−	0.981444i	$-0.561417\pi$
$269$	9.22286	−	5.32482i	0.562328	−	0.324660i	0.754079	+	0.656783i	$0.228083\pi$
$270$		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
$273$	1.52612	−	20.7571i	0.0923649	−	1.25628i
$274$		0			0
$275$	25.5819	−	7.20803i	1.54265	−	0.434661i
$276$		0			0
$277$	−13.6128	−	3.64753i	−0.817912	−	0.219159i	−0.174479	−	0.984661i	$-0.555824\pi$
$277$	−13.6128	−	3.64753i	−0.817912	−	0.219159i	−0.643434	+	0.765502i	$0.722491\pi$
$278$		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
$283$	−8.40291	+	2.25155i	−0.499501	+	0.133841i	−0.499768	−	0.866159i	$-0.666582\pi$
$283$	−8.40291	+	2.25155i	−0.499501	+	0.133841i	0.000267339		1.00000i	$0.499915\pi$
$284$		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
$293$	−5.98879	−	10.3729i	−0.349869	−	0.605991i	0.636357	−	0.771395i	$-0.280441\pi$
$293$	−5.98879	−	10.3729i	−0.349869	−	0.605991i	−0.986226	+	0.165404i	$0.947107\pi$
$294$		0			0
$295$	7.11199	−	27.2409i	0.414076	−	1.58603i
$296$		0			0
$297$	−13.7670	−	7.94836i	−0.798840	−	0.461211i
$298$		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
$303$	−12.2740	+	45.8071i	−0.705121	+	2.63155i
$304$		0			0
$305$	−18.0002	+	10.5471i	−1.03069	+	0.603928i
$306$		0			0
$307$			20.0009i			1.14151i	0.821120	+	0.570755i	$0.193350\pi$
$307$			20.0009i			1.14151i	−0.821120	+	0.570755i	$0.806650\pi$
$308$		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	−0.637523	−	0.770431i	$-0.720041\pi$
$313$	2.35138	−	2.35138i	0.132908	−	0.132908i	0.770431	+	0.637523i	$0.220041\pi$
$314$		0			0
$315$	17.3257	+	9.85517i	0.976190	+	0.555276i
$316$		0			0
$317$	−15.2905			−0.858799			−0.429399	−	0.903115i	$-0.641275\pi$
$317$	−15.2905			−0.858799			−0.429399	+	0.903115i	$0.641275\pi$
$318$		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
$323$	3.65449	−	6.32975i	0.203341	−	0.352197i
$324$		0			0
$325$	−11.9528	−	13.4955i	−0.663024	−	0.748598i
$326$		0			0
$327$	−4.45443	+	7.71529i	−0.246330	+	0.426657i
$328$		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
$333$	−28.1546			−1.54286
$334$		0			0
$335$	−21.4239	−	12.1864i	−1.17051	−	0.665811i
$336$		0			0
$337$	15.9698	−	15.9698i	0.869930	−	0.869930i	−0.122534	−	0.992464i	$-0.539102\pi$
$337$	15.9698	−	15.9698i	0.869930	−	0.869930i	0.992464	+	0.122534i	$0.0391022\pi$
$338$		0			0
$339$		−	18.3917i		−	0.998898i
$340$		0			0
$341$	−14.6602	+	25.3922i	−0.793894	+	1.37507i
$342$		0			0
$343$			20.1622i			1.08866i
$344$		0			0
$345$	3.83126	−	2.24491i	0.206268	−	0.120862i
$346$		0			0
$347$	2.63370	−	9.82910i	0.141384	−	0.527654i	−0.858505	−	0.512805i	$-0.828607\pi$
$347$	2.63370	−	9.82910i	0.141384	−	0.527654i	0.999890	−	0.0148492i	$-0.00472683\pi$
$348$		0			0
$349$	−0.766967	−	2.86236i	−0.0410548	−	0.153219i	0.942356	−	0.334613i	$-0.108606\pi$
$349$	−0.766967	−	2.86236i	−0.0410548	−	0.153219i	−0.983410	+	0.181394i	$0.941939\pi$
$350$		0			0
$351$	−0.790640	+	10.7537i	−0.0422012	+	0.573989i
$352$		0			0
$353$	−27.9018	−	16.1091i	−1.48506	−	0.857402i	−0.485209	−	0.874398i	$-0.661256\pi$
$353$	−27.9018	−	16.1091i	−1.48506	−	0.857402i	−0.999856	+	0.0169962i	$0.994590\pi$
$354$		0			0
$355$	−5.37854	+	20.6013i	−0.285463	+	1.09340i
$356$		0			0
$357$	−3.21466	−	5.56795i	−0.170138	−	0.294687i
$358$		0			0
$359$	1.11254	−	1.11254i	0.0587178	−	0.0587178i	−0.677138	−	0.735856i	$-0.736780\pi$
$359$	1.11254	−	1.11254i	0.0587178	−	0.0587178i	0.735856	+	0.677138i	$0.236780\pi$
$360$		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
$367$	−20.3821	+	5.46138i	−1.06394	+	0.285082i	−0.748001	−	0.663698i	$-0.768986\pi$
$367$	−20.3821	+	5.46138i	−1.06394	+	0.285082i	−0.315938	+	0.948780i	$0.602319\pi$
$368$		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
$373$	−24.3817	−	6.53307i	−1.26244	−	0.338269i	−0.435309	−	0.900281i	$-0.643361\pi$
$373$	−24.3817	−	6.53307i	−1.26244	−	0.338269i	−0.827129	+	0.562012i	$0.810028\pi$
$374$		0			0
$375$	28.6637	−	8.27542i	1.48019	−	0.427341i
$376$		0			0
$377$	−0.0675816	−	0.354443i	−0.00348063	−	0.0182547i
$378$		0			0
$379$	−25.4336	+	6.81491i	−1.30644	+	0.350058i	−0.843880	−	0.536532i	$-0.819734\pi$
$379$	−25.4336	+	6.81491i	−1.30644	+	0.350058i	−0.462556	+	0.886590i	$0.653067\pi$
$380$		0			0
$381$	32.0453	−	18.5014i	1.64173	−	0.947854i
$382$		0			0
$383$	31.3842	−	18.1197i	1.60366	−	0.925873i	0.612913	−	0.790151i	$-0.289998\pi$
$383$	31.3842	−	18.1197i	1.60366	−	0.925873i	0.990747	−	0.135722i	$-0.0433356\pi$
$384$		0			0
$385$	18.2977	+	18.0642i	0.932537	+	0.920636i
$386$		0			0
$387$	3.95238	+	14.7505i	0.200911	+	0.749810i
$388$		0			0
$389$	16.9315			0.858462			0.429231	−	0.903195i	$-0.358785\pi$
$389$	16.9315			0.858462			0.429231	+	0.903195i	$0.358785\pi$
$390$		0			0
$391$	−0.828869			−0.0419177
$392$		0			0
$393$	−3.45356	−	12.8889i	−0.174209	−	0.650158i
$394$		0			0
$395$	34.2456	−	0.219924i	1.72309	−	0.0110656i
$396$		0			0
$397$	−18.5248	+	10.6953i	−0.929732	+	0.536781i	−0.886727	−	0.462294i	$-0.847027\pi$
$397$	−18.5248	+	10.6953i	−0.929732	+	0.536781i	−0.0430054	+	0.999075i	$0.513693\pi$
$398$		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
$403$	19.8344	+	1.45828i	0.988022	+	0.0726421i
$404$		0			0
$405$	8.51674	+	4.84448i	0.423200	+	0.240724i
$406$		0			0
$407$	−35.0811	−	9.39995i	−1.73891	−	0.465938i
$408$		0			0
$409$	1.43399	−	5.35172i	0.0709062	−	0.264625i	−0.921368	−	0.388692i	$-0.872927\pi$
$409$	1.43399	−	5.35172i	0.0709062	−	0.264625i	0.992274	+	0.124067i	$0.0395937\pi$
$410$		0			0
$411$	−21.2368	−	21.2368i	−1.04754	−	1.04754i
$412$		0			0
$413$	26.3089	−	7.04944i	1.29457	−	0.346880i
$414$		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	0.740752	−	0.671779i	$-0.234469\pi$
$419$	10.8355	+	6.25590i	0.529351	+	0.305621i	−0.211401	+	0.977399i	$0.567803\pi$
$420$		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
$423$	−4.20855	−	7.28942i	−0.204627	−	0.354424i
$424$		0			0
$425$	−5.39721	−	1.37213i	−0.261803	−	0.0665582i
$426$		0			0
$427$	−17.4791	−	10.0916i	−0.845873	−	0.488365i
$428$		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
$433$	2.95228	−	11.0180i	0.141877	−	0.529493i	−0.857997	−	0.513654i	$-0.828291\pi$
$433$	2.95228	−	11.0180i	0.141877	−	0.529493i	0.999875	−	0.0158391i	$-0.00504196\pi$
$434$		0			0
$435$	0.577772	+	0.150844i	0.0277021	+	0.00723240i
$436$		0			0
$437$			4.88364i			0.233616i
$438$		0			0
$439$	17.3246	−	30.0071i	0.826858	−	1.43216i	−0.0736324	−	0.997285i	$-0.523459\pi$
$439$	17.3246	−	30.0071i	0.826858	−	1.43216i	0.900491	−	0.434875i	$-0.143208\pi$
$440$		0			0
$441$		−	9.56177i		−	0.455322i
$442$		0			0
$443$	4.85964	−	4.85964i	0.230888	−	0.230888i	−0.582175	−	0.813063i	$-0.697798\pi$
$443$	4.85964	−	4.85964i	0.230888	−	0.230888i	0.813063	+	0.582175i	$0.197798\pi$
$444$		0			0
$445$	−4.66686	+	1.28266i	−0.221230	+	0.0608038i
$446$		0			0
$447$	−11.0481			−0.522556
$448$		0			0
$449$	28.2416	+	7.56732i	1.33280	+	0.357124i	0.853760	−	0.520667i	$-0.174317\pi$
$449$	28.2416	+	7.56732i	1.33280	+	0.357124i	0.479044	+	0.877791i	$0.340983\pi$
$450$		0			0
$451$	−14.0342	−	24.3080i	−0.660845	−	1.14462i
$452$		0			0
$453$	−7.57248	+	13.1159i	−0.355786	+	0.616240i
$454$		0			0
$455$	5.63116	−	16.5065i	0.263993	−	0.773834i
$456$		0			0
$457$	12.2322	−	21.1868i	0.572198	−	0.991076i	−0.424142	−	0.905596i	$-0.639424\pi$
$457$	12.2322	−	21.1868i	0.572198	−	0.991076i	0.996340	−	0.0854803i	$-0.0272425\pi$
$458$		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
$463$	−7.08508			−0.329272			−0.164636	−	0.986354i	$-0.552645\pi$
$463$	−7.08508			−0.329272			−0.164636	+	0.986354i	$0.552645\pi$
$464$		0			0
$465$	−16.2730	+	28.6084i	−0.754643	+	1.32668i
$466$		0			0
$467$	−4.40762	+	4.40762i	−0.203960	+	0.203960i	−0.801694	−	0.597734i	$-0.796068\pi$
$467$	−4.40762	+	4.40762i	−0.203960	+	0.203960i	0.597734	+	0.801694i	$0.296068\pi$
$468$		0			0
$469$		−	23.8445i		−	1.10104i
$470$		0			0
$471$	11.4927	−	19.9060i	0.529557	−	0.917219i
$472$		0			0
$473$			19.6989i			0.905757i
$474$		0			0
$475$	−8.08451	+	31.8000i	−0.370943	+	1.45908i
$476$		0			0
$477$	−12.4936	+	46.6267i	−0.572042	+	2.13489i
$478$		0			0
$479$	8.30384	+	30.9903i	0.379412	+	1.41598i	0.846790	+	0.531927i	$0.178532\pi$
$479$	8.30384	+	30.9903i	0.379412	+	1.41598i	−0.467378	+	0.884058i	$0.654801\pi$
$480$		0			0
$481$	4.61400	+	24.1989i	0.210380	+	1.10337i
$482$		0			0
$483$	3.72034	+	2.14794i	0.169281	+	0.0977347i
$484$		0			0
$485$	24.5010	−	14.3562i	1.11253	−	0.651883i
$486$		0			0
$487$	−5.99150	−	10.3776i	−0.271501	−	0.470253i	0.697746	−	0.716346i	$-0.254187\pi$
$487$	−5.99150	−	10.3776i	−0.271501	−	0.470253i	−0.969246	+	0.246093i	$0.920853\pi$
$488$		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
$497$	−19.8964	+	5.33123i	−0.892477	+	0.239138i
$498$		0			0
$499$	−23.7196	−	23.7196i	−1.06183	−	1.06183i	−0.997958	−	0.0638768i	$-0.979654\pi$
$499$	−23.7196	−	23.7196i	−1.06183	−	1.06183i	−0.0638768	−	0.997958i	$-0.520346\pi$
$500$		0			0
$501$	−5.36358	+	20.0171i	−0.239627	+	0.894300i
$502$		0			0
$503$	−0.473787	−	0.126951i	−0.0211251	−	0.00566046i	0.248241	−	0.968698i	$-0.420148\pi$
$503$	−0.473787	−	0.126951i	−0.0211251	−	0.00566046i	−0.269366	+	0.963038i	$0.586814\pi$
$504$		0			0
$505$	−19.6479	+	34.5415i	−0.874319	+	1.53708i
$506$		0			0
$507$	34.4609	−	3.98119i	1.53046	−	0.176811i
$508$		0			0
$509$	14.5334	−	3.89421i	0.644181	−	0.172608i	0.0780847	−	0.996947i	$-0.475120\pi$
$509$	14.5334	−	3.89421i	0.644181	−	0.172608i	0.566097	+	0.824339i	$0.308453\pi$
$510$		0			0
$511$	20.1272	−	11.6204i	0.890373	−	0.514057i
$512$		0			0
$513$	16.9959	−	9.81257i	0.750386	−	0.433236i
$514$		0			0
$515$	−11.1383	+	11.2823i	−0.490813	+	0.497157i
$516$		0			0
$517$	−2.81020	−	10.4878i	−0.123593	−	0.461254i
$518$		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
$523$	5.48576	+	20.4731i	0.239875	+	0.895227i	0.975890	+	0.218262i	$0.0700387\pi$
$523$	5.48576	+	20.4731i	0.239875	+	0.895227i	−0.736015	+	0.676965i	$0.763295\pi$
$524$		0			0
$525$	20.6694	+	20.1451i	0.902085	+	0.879206i
$526$		0			0
$527$	5.32045	−	3.07176i	0.231762	−	0.133808i
$528$		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
$533$	−10.7027	+	15.7456i	−0.463586	+	0.682019i
$534$		0			0
$535$	6.36707	+	23.1661i	0.275273	+	1.00156i
$536$		0			0
$537$	3.23285	+	0.866241i	0.139508	+	0.0373810i
$538$		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
$543$	18.6419	−	4.99507i	0.799999	−	0.214359i
$544$		0			0
$545$	−5.24473	+	5.31253i	−0.224660	+	0.227564i
$546$		0			0
$547$	−7.28589	−	7.28589i	−0.311522	−	0.311522i	0.533977	−	0.845499i	$-0.320697\pi$
$547$	−7.28589	−	7.28589i	−0.311522	−	0.311522i	−0.845499	+	0.533977i	$0.820697\pi$
$548$		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
$553$	16.5654	+	28.6922i	0.704434	+	1.22012i
$554$		0			0
$555$	−39.4463	−	10.2986i	−1.67440	−	0.437149i
$556$		0			0
$557$	20.5259	+	11.8506i	0.869710	+	0.502127i	0.867252	−	0.497870i	$-0.165884\pi$
$557$	20.5259	+	11.8506i	0.869710	+	0.502127i	0.00245824	+	0.999997i	$0.499218\pi$
$558$		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
$563$	5.47068	−	20.4169i	0.230562	−	0.860468i	−0.749538	−	0.661962i	$-0.769724\pi$
$563$	5.47068	−	20.4169i	0.230562	−	0.860468i	0.980100	−	0.198507i	$-0.0636091\pi$
$564$		0			0
$565$	3.89310	−	14.9117i	0.163784	−	0.627338i
$566$		0			0
$567$			9.47901i			0.398081i
$568$		0			0
$569$	5.92902	−	10.2694i	0.248557	−	0.430514i	−0.714568	−	0.699566i	$-0.753377\pi$
$569$	5.92902	−	10.2694i	0.248557	−	0.430514i	0.963126	+	0.269052i	$0.0867102\pi$
$570$		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
$575$	3.58152	−	1.00914i	0.149360	−	0.0420841i
$576$		0			0
$577$	45.6328			1.89972			0.949858	−	0.312681i	$-0.101227\pi$
$577$	45.6328			1.89972			0.949858	+	0.312681i	$0.101227\pi$
$578$		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
$583$	−31.1344	+	53.9263i	−1.28945	+	2.23340i
$584$		0			0
$585$	−10.7267	+	31.4429i	−0.443495	+	1.30000i
$586$		0			0
$587$	1.44141	−	2.49660i	0.0594935	−	0.103046i	−0.834745	−	0.550637i	$-0.814385\pi$
$587$	1.44141	−	2.49660i	0.0594935	−	0.103046i	0.894238	+	0.447592i	$0.147718\pi$
$588$		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
$593$	−17.0136			−0.698663			−0.349332	−	0.936999i	$-0.613591\pi$
$593$	−17.0136			−0.698663			−0.349332	+	0.936999i	$0.613591\pi$
$594$		0			0
$595$	−1.42778	−	5.19487i	−0.0585332	−	0.212969i
$596$		0			0
$597$	12.2351	−	12.2351i	0.500747	−	0.500747i
$598$		0			0
$599$			15.8501i			0.647618i	0.946123	+	0.323809i	$0.104963\pi$
$599$			15.8501i			0.647618i	−0.946123	+	0.323809i	$0.895037\pi$
$600$		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
$603$			45.4211i			1.84969i
$604$		0			0
$605$	−19.5065	−	33.2906i	−0.793050	−	1.35346i
$606$		0			0
$607$	−0.254323	+	0.949146i	−0.0103227	+	0.0385247i	−0.970895	−	0.239505i	$-0.923015\pi$
$607$	−0.254323	+	0.949146i	−0.0103227	+	0.0385247i	0.960572	+	0.278030i	$0.0896814\pi$
$608$		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
$613$	−7.48436	−	4.32110i	−0.302291	−	0.174528i	0.341181	−	0.939998i	$-0.389173\pi$
$613$	−7.48436	−	4.32110i	−0.302291	−	0.174528i	−0.643471	+	0.765470i	$0.722506\pi$
$614$		0			0
$615$	−15.9286	−	27.1845i	−0.642304	−	1.09619i
$616$		0			0
$617$	4.38476	+	7.59463i	0.176524	+	0.305748i	0.940688	−	0.339274i	$-0.110181\pi$
$617$	4.38476	+	7.59463i	0.176524	+	0.305748i	−0.764164	+	0.645022i	$0.776848\pi$
$618$		0			0
$619$	8.20840	−	8.20840i	0.329924	−	0.329924i	−0.522634	−	0.852557i	$-0.675050\pi$
$619$	8.20840	−	8.20840i	0.329924	−	0.329924i	0.852557	+	0.522634i	$0.175050\pi$
$620$		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
$627$	89.9113	−	24.0917i	3.59071	−	0.962128i
$628$		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
$633$	70.5173	+	18.8950i	2.80281	+	0.751011i
$634$		0			0
$635$	29.8981	−	8.21733i	1.18647	−	0.326095i
$636$		0			0
$637$	−8.21833	+	1.56699i	−0.325622	+	0.0620864i
$638$		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
$643$	27.4892	−	15.8709i	1.08407	−	0.625887i	0.152078	−	0.988369i	$-0.451404\pi$
$643$	27.4892	−	15.8709i	1.08407	−	0.625887i	0.931991	+	0.362481i	$0.118070\pi$
$644$		0			0
$645$	0.142002	+	22.1120i	0.00559133	+	0.870659i
$646$		0			0
$647$	−1.01862	−	3.80155i	−0.0400462	−	0.149454i	0.943008	−	0.332771i	$-0.107983\pi$
$647$	−1.01862	−	3.80155i	−0.0400462	−	0.149454i	−0.983054	+	0.183316i	$0.941317\pi$
$648$		0			0
$649$	−66.9278			−2.62714
$650$		0			0
$651$	−31.8408			−1.24794
$652$		0			0
$653$	7.77659	+	29.0226i	0.304321	+	1.13574i	0.933528	+	0.358505i	$0.116713\pi$
$653$	7.77659	+	29.0226i	0.304321	+	1.13574i	−0.629207	+	0.777238i	$0.716620\pi$
$654$		0			0
$655$	−0.0718046	−	11.1811i	−0.00280564	−	0.436883i
$656$		0			0
$657$	−38.3399	+	22.1356i	−1.49578	+	0.863591i
$658$		0			0
$659$	−17.0616	+	9.85051i	−0.664625	+	0.383721i	−0.794037	−	0.607870i	$-0.792024\pi$
$659$	−17.0616	+	9.85051i	−0.664625	+	0.383721i	0.129412	+	0.991591i	$0.458691\pi$
$660$		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
$663$	8.11256	−	7.00135i	0.315066	−	0.271910i
$664$		0			0
$665$	−30.6078	+	8.41238i	−1.18692	+	0.326218i
$666$		0			0
$667$	0.0719382	+	0.0192758i	0.00278546	+	0.000746361i
$668$		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
$673$	−43.9051	+	11.7643i	−1.69242	+	0.453482i	−0.971012	−	0.239031i	$-0.923170\pi$
$673$	−43.9051	+	11.7643i	−1.69242	+	0.453482i	−0.721406	+	0.692513i	$0.756504\pi$
$674$		0			0
$675$	−10.7082	−	10.4366i	−0.412160	−	0.401706i
$676$		0			0
$677$	−7.14523	−	7.14523i	−0.274614	−	0.274614i	0.556341	−	0.830954i	$-0.312205\pi$
$677$	−7.14523	−	7.14523i	−0.274614	−	0.274614i	−0.830954	+	0.556341i	$0.812205\pi$
$678$		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
$683$	−4.65327	−	8.05969i	−0.178052	−	0.308396i	0.763161	−	0.646208i	$-0.223646\pi$
$683$	−4.65327	−	8.05969i	−0.178052	−	0.308396i	−0.941213	+	0.337813i	$0.890313\pi$
$684$		0			0
$685$	−12.7231	−	21.7138i	−0.486125	−	0.829643i
$686$		0			0
$687$	−2.42714	−	1.40131i	−0.0926010	−	0.0534632i
$688$		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
$693$	12.2638	−	45.7690i	0.465862	−	1.73862i
$694$		0			0
$695$	9.84661	+	16.8047i	0.373503	+	0.637438i
$696$		0			0
$697$			5.88119i			0.222766i
$698$		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
$705$	−3.23006	−	11.7523i	−0.121651	−	0.442618i
$706$		0			0
$707$	−38.4442			−1.44584
$708$		0			0
$709$	−47.9316	−	12.8432i	−1.80011	−	0.482337i	−0.806112	−	0.591762i	$-0.798432\pi$
$709$	−47.9316	−	12.8432i	−1.80011	−	0.482337i	−0.993995	+	0.109425i	$0.965099\pi$
$710$		0			0
$711$	−31.5552	−	54.6553i	−1.18341	−	2.04973i
$712$		0			0
$713$	−2.05246	+	3.55497i	−0.0768653	+	0.133135i
$714$		0			0
$715$	−23.8634	+	35.5970i	−0.892442	+	1.33125i
$716$		0			0
$717$	2.67250	−	4.62890i	0.0998063	−	0.172870i
$718$		0			0
$719$	−3.49009	−	6.04502i	−0.130159	−	0.225441i	0.793579	−	0.608467i	$-0.208215\pi$
$719$	−3.49009	−	6.04502i	−0.130159	−	0.225441i	−0.923738	+	0.383026i	$0.874882\pi$
$720$		0			0
$721$	−14.8151	−	3.96969i	−0.551742	−	0.147839i
$722$		0			0
$723$	−0.393233			−0.0146245
$724$		0			0
$725$	0.436518	+	0.244603i	0.0162119	+	0.00908433i
$726$		0			0
$727$	18.2655	−	18.2655i	0.677429	−	0.677429i	−0.281989	−	0.959418i	$-0.590994\pi$
$727$	18.2655	−	18.2655i	0.677429	−	0.677429i	0.959418	+	0.281989i	$0.0909941\pi$
$728$		0			0
$729$		−	41.9972i		−	1.55545i
$730$		0			0
$731$	2.06376	−	3.57454i	0.0763310	−	0.132209i
$732$		0			0
$733$			30.7161i			1.13452i	0.823537	+	0.567262i	$0.191997\pi$
$733$			30.7161i			1.13452i	−0.823537	+	0.567262i	$0.808003\pi$
$734$		0			0
$735$	3.49755	−	13.3966i	0.129009	−	0.494141i
$736$		0			0
$737$	−15.1647	+	56.5954i	−0.558598	+	2.08472i
$738$		0			0
$739$	7.17064	+	26.7612i	0.263776	+	0.984427i	0.962995	+	0.269519i	$0.0868647\pi$
$739$	7.17064	+	26.7612i	0.263776	+	0.984427i	−0.699219	+	0.714908i	$0.746469\pi$
$740$		0			0
$741$	−41.2515	−	47.7987i	−1.51541	−	1.75593i
$742$		0			0
$743$	6.90167	+	3.98468i	0.253198	+	0.146184i	0.621228	−	0.783630i	$-0.286634\pi$
$743$	6.90167	+	3.98468i	0.253198	+	0.146184i	−0.368030	+	0.929814i	$0.619968\pi$
$744$		0			0
$745$	−8.95759	−	2.33863i	−0.328181	−	0.0856807i
$746$		0			0
$747$	0.975537	+	1.68968i	0.0356930	+	0.0618222i
$748$		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
$757$	−37.8020	+	10.1290i	−1.37394	+	0.368145i	−0.868915	−	0.494962i	$-0.835182\pi$
$757$	−37.8020	+	10.1290i	−1.37394	+	0.368145i	−0.505021	+	0.863107i	$0.668515\pi$
$758$		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
$763$	−6.97602	−	1.86922i	−0.252549	−	0.0676702i
$764$		0			0
$765$	2.71975	+	9.89563i	0.0983329	+	0.357777i
$766$		0			0
$767$	19.7546	+	40.8734i	0.713297	+	1.47585i
$768$		0			0
$769$	32.5217	−	8.71417i	1.17276	−	0.314241i	0.380711	−	0.924694i	$-0.375679\pi$
$769$	32.5217	−	8.71417i	1.17276	−	0.314241i	0.792052	+	0.610453i	$0.209013\pi$
$770$		0			0
$771$	−44.5516	+	25.7219i	−1.60449	+	0.926350i
$772$		0			0
$773$	−22.7618	+	13.1416i	−0.818687	+	0.472669i	−0.849963	−	0.526842i	$-0.823376\pi$
$773$	−22.7618	+	13.1416i	−0.818687	+	0.472669i	0.0312766	+	0.999511i	$0.490043\pi$
$774$		0			0
$775$	−19.2497	+	19.7506i	−0.691468	+	0.709462i
$776$		0			0
$777$	−10.2080	−	38.0966i	−0.366209	−	1.36671i
$778$		0			0
$779$	34.6516			1.24152
$780$		0			0
$781$	50.6150			1.81115
$782$		0			0
$783$	−0.0774606	−	0.289087i	−0.00276821	−	0.0103311i
$784$		0			0
$785$	13.5318	−	13.7067i	0.482969	−	0.489213i
$786$		0			0
$787$	−17.8020	+	10.2780i	−0.634573	+	0.366371i	−0.782521	−	0.622624i	$-0.786067\pi$
$787$	−17.8020	+	10.2780i	−0.634573	+	0.366371i	0.147948	+	0.988995i	$0.452733\pi$
$788$		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
$793$	11.0658	−	31.7679i	0.392960	−	1.12811i
$794$		0			0
$795$	−34.5596	+	60.7567i	−1.22570	+	2.15482i
$796$		0			0
$797$	24.6043	+	6.59270i	0.871529	+	0.233526i	0.666749	−	0.745282i	$-0.267685\pi$
$797$	24.6043	+	6.59270i	0.871529	+	0.233526i	0.204780	+	0.978808i	$0.434352\pi$
$798$		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
$803$	−55.1625	+	14.7807i	−1.94664	+	0.521601i
$804$		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	0.731482	−	0.681861i	$-0.238829\pi$
$809$	14.4124	+	8.32102i	0.506714	+	0.292551i	−0.224768	+	0.974412i	$0.572162\pi$
$810$		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
$813$	−5.12576	−	8.87807i	−0.179768	−	0.311368i
$814$		0			0
$815$	21.5727	−	12.6404i	0.755660	−	0.442775i
$816$		0			0
$817$	−21.0610	−	12.1595i	−0.736830	−	0.425409i
$818$		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
$823$	1.80480	−	6.73560i	0.0629114	−	0.234788i	−0.927310	−	0.374295i	$-0.877885\pi$
$823$	1.80480	−	6.73560i	0.0629114	−	0.234788i	0.990221	+	0.139506i	$0.0445515\pi$
$824$		0			0
$825$	−36.2471	−	60.9601i	−1.26196	−	2.12236i
$826$		0			0
$827$		−	34.2158i		−	1.18980i	−0.803800	−	0.594900i	$-0.797192\pi$
$827$		−	34.2158i		−	1.18980i	0.803800	−	0.594900i	$-0.202808\pi$
$828$		0			0
$829$	13.9995	−	24.2478i	0.486222	−	0.842161i	−0.513653	−	0.857998i	$-0.671708\pi$
$829$	13.9995	−	24.2478i	0.486222	−	0.842161i	0.999875	+	0.0158373i	$0.00504139\pi$
$830$		0			0
$831$			37.6066i			1.30456i
$832$		0			0
$833$	−1.82747	+	1.82747i	−0.0633181	+	0.0633181i
$834$		0			0
$835$	−8.58588	+	15.0942i	−0.297127	+	0.522357i
$836$		0			0
$837$	16.4958			0.570179
$838$		0			0
$839$	−44.5978	−	11.9500i	−1.53969	−	0.412558i	−0.613523	−	0.789677i	$-0.710248\pi$
$839$	−44.5978	−	11.9500i	−1.53969	−	0.412558i	−0.926165	+	0.377119i	$0.876915\pi$
$840$		0			0
$841$	−14.4950	−	25.1061i	−0.499827	−	0.865726i
$842$		0			0
$843$	23.9235	−	41.4368i	0.823970	−	1.42716i
$844$		0			0
$845$	28.7830	+	4.06671i	0.990166	+	0.139899i
$846$		0			0
$847$	18.6639	−	32.3268i	0.641298	−	1.11076i
$848$		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
$853$	−0.328048			−0.0112321			−0.00561607	−	0.999984i	$-0.501788\pi$
$853$	−0.328048			−0.0112321			−0.00561607	+	0.999984i	$0.501788\pi$
$854$		0			0
$855$	58.3044	−	16.0246i	1.99397	−	0.548030i
$856$		0			0
$857$	−7.20279	+	7.20279i	−0.246043	+	0.246043i	−0.819344	−	0.573302i	$-0.805662\pi$
$857$	−7.20279	+	7.20279i	−0.246043	+	0.246043i	0.573302	+	0.819344i	$0.305662\pi$
$858$		0			0
$859$			19.2793i			0.657800i	0.944365	+	0.328900i	$0.106678\pi$
$859$			19.2793i			0.657800i	−0.944365	+	0.328900i	$0.893322\pi$
$860$		0			0
$861$	15.2406	−	26.3975i	0.519398	−	0.899623i
$862$		0			0
$863$		−	16.7097i		−	0.568806i	−0.958705	−	0.284403i	$-0.908205\pi$
$863$		−	16.7097i		−	0.568806i	0.958705	−	0.284403i	$-0.0917954\pi$
$864$		0			0
$865$	32.3482	+	8.44541i	1.09987	+	0.287153i
$866$		0			0
$867$	−10.8843	+	40.6207i	−0.369650	+	1.37955i
$868$		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
$873$	−45.3204	−	26.1657i	−1.53386	−	0.885576i
$874$		0			0
$875$	12.4941	+	20.7086i	0.422378	+	0.700078i
$876$		0			0
$877$	12.5974	+	21.8193i	0.425383	+	0.736784i	0.996456	−	0.0841148i	$-0.0268062\pi$
$877$	12.5974	+	21.8193i	0.425383	+	0.736784i	−0.571074	+	0.820899i	$0.693473\pi$
$878$		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	$-0.289605\pi$
$883$	−5.21525	−	5.21525i	−0.175507	−	0.175507i	−0.789394	+	0.613887i	$0.789605\pi$
$884$		0			0
$885$	−75.1264	+	0.482457i	−2.52535	+	0.0162176i
$886$		0			0
$887$	−27.8074	+	7.45098i	−0.933682	+	0.250179i	−0.693424	−	0.720530i	$-0.743899\pi$
$887$	−27.8074	+	7.45098i	−0.933682	+	0.250179i	−0.240258	+	0.970709i	$0.577232\pi$
$888$		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
$893$	12.9476	+	3.46931i	0.433276	+	0.116096i
$894$		0			0
$895$	2.43778	+	1.38666i	0.0814860	+	0.0463508i
$896$		0			0
$897$	−2.35531	+	6.76164i	−0.0786416	+	0.225765i
$898$		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
$903$	−18.5262	+	10.6961i	−0.616513	+	0.355944i
$904$		0			0
$905$	16.1719	−	0.103855i	0.537570	−	0.00345225i
$906$		0			0
$907$	9.40058	+	35.0834i	0.312141	+	1.16493i	0.926622	+	0.375994i	$0.122699\pi$
$907$	9.40058	+	35.0834i	0.312141	+	1.16493i	−0.614481	+	0.788932i	$0.710635\pi$
$908$		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
$913$	0.651403	+	2.43107i	0.0215583	+	0.0804566i
$914$		0			0
$915$	39.6175	+	39.1119i	1.30972	+	1.29300i
$916$		0			0
$917$	9.36793	−	5.40858i	0.309356	−	0.178607i
$918$		0			0
$919$	33.0949	−	19.1073i	1.09170	−	0.630293i	0.157671	−	0.987492i	$-0.449601\pi$
$919$	33.0949	−	19.1073i	1.09170	−	0.630293i	0.934028	+	0.357199i	$0.116268\pi$
$920$		0			0
$921$	51.5531	−	13.8136i	1.69873	−	0.455174i
$922$		0			0
$923$	−14.9397	−	30.9111i	−0.491745	−	1.01745i
$924$		0			0
$925$	−29.8024	−	16.6998i	−0.979897	−	0.549086i
$926$		0			0
$927$	28.2210	+	7.56180i	0.926899	+	0.248362i
$928$		0			0
$929$	−0.860601	+	3.21181i	−0.0282354	+	0.105376i	−0.978605	−	0.205746i	$-0.934038\pi$
$929$	−0.860601	+	3.21181i	−0.0282354	+	0.105376i	0.950370	+	0.311122i	$0.100705\pi$
$930$		0			0
$931$	10.7673	+	10.7673i	0.352885	+	0.352885i
$932$		0			0
$933$	38.1788	−	10.2300i	1.24992	−	0.334914i
$934$		0			0
$935$	0.0850146	+	13.2381i	0.00278027	+	0.432933i
$936$		0			0
$937$	8.40073	+	8.40073i	0.274440	+	0.274440i	0.830885	−	0.556445i	$-0.187835\pi$
$937$	8.40073	+	8.40073i	0.274440	+	0.274440i	−0.556445	+	0.830885i	$0.687835\pi$
$938$		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
$943$	−1.96482	−	3.40317i	−0.0639834	−	0.110823i
$944$		0			0
$945$	3.65423	−	13.9967i	0.118872	−	0.455313i
$946$		0			0
$947$	14.3428	+	8.28083i	0.466079	+	0.269091i	0.714597	−	0.699536i	$-0.246610\pi$
$947$	14.3428	+	8.28083i	0.466079	+	0.269091i	−0.248518	+	0.968627i	$0.579943\pi$
$948$		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
$953$	−6.48521	+	24.2031i	−0.210077	+	0.784016i	0.777765	+	0.628555i	$0.216353\pi$
$953$	−6.48521	+	24.2031i	−0.210077	+	0.784016i	−0.987842	+	0.155462i	$0.950313\pi$
$954$		0			0
$955$	40.6024	−	23.7907i	1.31386	−	0.769850i
$956$		0			0
$957$		−	1.41952i		−	0.0458866i
$958$		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
$965$	−19.3295	−	10.9950i	−0.622237	−	0.353941i
$966$		0			0
$967$	−31.4641			−1.01182			−0.505908	−	0.862587i	$-0.668843\pi$
$967$	−31.4641			−1.01182			−0.505908	+	0.862587i	$0.668843\pi$
$968$		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
$973$	−9.42129	+	16.3182i	−0.302033	+	0.523136i
$974$		0			0
$975$	−26.5301	+	40.1296i	−0.849643	+	1.28518i
$976$		0			0
$977$	9.07986	−	15.7268i	0.290490	−	0.503144i	−0.683435	−	0.730011i	$-0.739515\pi$
$977$	9.07986	−	15.7268i	0.290490	−	0.503144i	0.973926	+	0.226867i	$0.0728483\pi$
$978$		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
$983$	−42.3986			−1.35230			−0.676152	−	0.736762i	$-0.736354\pi$
$983$	−42.3986			−1.35230			−0.676152	+	0.736762i	$0.736354\pi$
$984$		0			0
$985$	10.4409	+	5.93898i	0.332675	+	0.189232i
$986$		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
$993$		−	2.48848i		−	0.0789697i
$994$		0			0
$995$	12.5099	−	7.33009i	0.396589	−	0.232379i
$996$		0			0
$997$	−3.27444	+	12.2204i	−0.103703	+	0.387023i	−0.998195	−	0.0600602i	$-0.980871\pi$
$997$	−3.27444	+	12.2204i	−0.103703	+	0.387023i	0.894492	+	0.447084i	$0.147537\pi$
$998$		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.bk.c.97.1	yes	20
5.2	odd	4		1300.2.bn.d.1293.1		20
5.3	odd	4		260.2.bf.c.253.5	yes	20
5.4	even	2		1300.2.bs.d.357.5		20
13.11	odd	12		260.2.bf.c.37.5	✓	20
65.24	odd	12		1300.2.bn.d.557.1		20
65.37	even	12		1300.2.bs.d.193.5		20
65.63	even	12	inner	260.2.bk.c.193.1	yes	20

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.690650 - 2.57754i) q^{3} +(-0.0143596 - 2.23602i) q^{5} +(1.87342 - 1.08162i) q^{7} +(-3.56864 + 2.06036i) q^{9} +O(q^{10})\)	\(q+(-0.690650 - 2.57754i) q^{3} +(-0.0143596 - 2.23602i) q^{5} +(1.87342 - 1.08162i) q^{7} +(-3.56864 + 2.06036i) q^{9} +(-5.13447 + 1.37578i) q^{11} +(2.35570 + 2.72959i) q^{13} +(-5.75352 + 1.58132i) q^{15} +(1.07583 + 0.288267i) q^{17} +(1.69845 - 6.33871i) q^{19} +(-4.08179 - 4.08179i) q^{21} +(-0.718837 + 0.192612i) q^{23} +(-4.99959 + 0.0642168i) q^{25} +(2.11466 + 2.11466i) q^{27} +(-0.0866681 - 0.0500378i) q^{29} +(3.90035 - 3.90035i) q^{31} +(7.09224 + 12.2841i) q^{33} +(-2.44542 - 4.17347i) q^{35} +(5.91709 + 3.41623i) q^{37} +(5.40866 - 7.95711i) q^{39} +(1.36667 + 5.10047i) q^{41} +(0.959150 - 3.57960i) q^{43} +(4.65825 + 7.94997i) q^{45} +2.04263i q^{47} +(-1.16021 + 2.00954i) q^{49} -2.97208i q^{51} +(8.28330 - 8.28330i) q^{53} +(3.15000 + 11.4610i) q^{55} -17.5113 q^{57} +(12.1618 + 3.25875i) q^{59} +(-4.66503 - 8.08007i) q^{61} +(-4.45703 + 7.71981i) q^{63} +(6.06959 - 5.30660i) q^{65} +(5.51132 - 9.54588i) q^{67} +(0.992930 + 1.71981i) q^{69} +(-9.19754 - 2.46447i) q^{71} +10.7436 q^{73} +(3.61849 + 12.8423i) q^{75} +(-8.13093 + 8.13093i) q^{77} +15.3154i q^{79} +(-2.19093 + 3.79481i) q^{81} -0.473480i q^{83} +(0.629124 - 2.40971i) q^{85} +(-0.0691173 + 0.257949i) q^{87} +(-0.560208 - 2.09072i) q^{89} +(7.36558 + 2.56569i) q^{91} +(-12.7471 - 7.35953i) q^{93} +(-14.1979 - 3.70675i) q^{95} +(6.34981 + 10.9982i) q^{97} +(15.4885 - 15.4885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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