LMFDB - Embedded newform 1300.2.bs.d.357.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(193,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 7]))

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

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

chi := DirichletCharacter("1300.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bs (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:	$10.3805522628$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.5
Root			$-0.125665i$ of defining polynomial
Character	$\chi$	$=$	1300.357
Dual form			1300.2.bs.d.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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	$0.196570\pi$
$3$	0.690650	+	2.57754i	0.398747	+	1.48814i	−0.416557	+	0.909110i	$0.636763\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.87342	+	1.08162i	−0.708085	+	0.408813i	−0.810351	−	0.585944i	$-0.800724\pi$
$7$	−1.87342	+	1.08162i	−0.708085	+	0.408813i	0.102267	+	0.994757i	$0.467390\pi$
$8$		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
$15$		0			0
$16$		0			0
$17$	−1.07583	−	0.288267i	−0.260927	−	0.0699151i	0.125984	−	0.992032i	$-0.459791\pi$
$17$	−1.07583	−	0.288267i	−0.260927	−	0.0699151i	−0.386911	+	0.922117i	$0.626458\pi$
$18$		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	−0.183095	−	0.983095i	$-0.558612\pi$
$23$	0.718837	−	0.192612i	0.149888	−	0.0401624i	0.332983	+	0.942933i	$0.391945\pi$
$24$		0			0
$25$		0			0
$26$		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
$35$		0			0
$36$		0			0
$37$	−5.91709	−	3.41623i	−0.972764	−	0.561625i	−0.0726861	−	0.997355i	$-0.523157\pi$
$37$	−5.91709	−	3.41623i	−0.972764	−	0.561625i	−0.900078	+	0.435729i	$0.856490\pi$
$38$		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	$0.174520\pi$
$43$	−0.959150	+	3.57960i	−0.146269	+	0.545883i	−0.999696	+	0.0246704i	$0.992146\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	2.04263i		−	0.297948i	−0.988841	−	0.148974i	$-0.952403\pi$
$47$		−	2.04263i		−	0.297948i	0.988841	−	0.148974i	$-0.0475971\pi$
$48$		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	$0.547591\pi$
$53$	−8.28330	+	8.28330i	−1.13780	+	1.13780i	−0.988844	+	0.148955i	$0.952409\pi$
$54$		0			0
$55$		0			0
$56$		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
$65$		0			0
$66$		0			0
$67$	−5.51132	+	9.54588i	−0.673315	+	1.16622i	0.303644	+	0.952786i	$0.401797\pi$
$67$	−5.51132	+	9.54588i	−0.673315	+	1.16622i	−0.976958	+	0.213429i	$0.931537\pi$
$68$		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	$-0.716421\pi$
$73$	−10.7436			−1.25744			−0.628720	+	0.777632i	$0.716421\pi$
$74$		0			0
$75$		0			0
$76$		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	$0.00827240\pi$
$83$			0.473480i			0.0519712i	−0.999662	+	0.0259856i	$0.991728\pi$
$84$		0			0
$85$		0			0
$86$		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
$95$		0			0
$96$		0			0
$97$	−6.34981	−	10.9982i	−0.644725	−	1.11670i	−0.984365	−	0.176141i	$-0.943638\pi$
$97$	−6.34981	−	10.9982i	−0.644725	−	1.11670i	0.339640	−	0.940556i	$-0.389695\pi$
$98$		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	0.909562	−	0.415567i	$-0.136417\pi$
$103$	5.01350	+	5.01350i	0.493995	+	0.493995i	−0.415567	+	0.909562i	$0.636417\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.3783	−	2.78085i	1.00331	−	0.268835i	0.280476	−	0.959861i	$-0.409508\pi$
$107$	10.3783	−	2.78085i	1.00331	−	0.268835i	0.722830	+	0.691026i	$0.242841\pi$
$108$		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	−0.0682952	−	0.997665i	$-0.521756\pi$
$113$	−6.65737	−	1.78384i	−0.626273	−	0.167809i	−0.557978	+	0.829856i	$0.688423\pi$
$114$		0			0
$115$		0			0
$116$		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			0
$126$		0			0
$127$	−3.58896	−	13.3942i	−0.318469	−	1.18854i	−0.920717	−	0.390232i	$-0.872395\pi$
$127$	−3.58896	−	13.3942i	−0.318469	−	1.18854i	0.602248	−	0.798309i	$-0.294272\pi$
$128$		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
$135$		0			0
$136$		0			0
$137$	−9.74706	+	5.62747i	−0.832748	+	0.480787i	−0.854793	−	0.518970i	$-0.826316\pi$
$137$	−9.74706	+	5.62747i	−0.832748	+	0.480787i	0.0220448	+	0.999757i	$0.492982\pi$
$138$		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			0
$146$		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
$155$		0			0
$156$		0			0
$157$	−6.09083	−	6.09083i	−0.486101	−	0.486101i	0.420972	−	0.907073i	$-0.361689\pi$
$157$	−6.09083	−	6.09083i	−0.486101	−	0.486101i	−0.907073	+	0.420972i	$0.861689\pi$
$158$		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	0.559615	−	0.828752i	$-0.310949\pi$
$163$	−5.59090	−	9.68372i	−0.437913	−	0.758488i	−0.997528	+	0.0702649i	$0.977616\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.72554	+	3.88299i	0.520438	+	0.300475i	0.737114	−	0.675769i	$-0.236188\pi$
$167$	6.72554	+	3.88299i	0.520438	+	0.300475i	−0.216676	+	0.976244i	$0.569521\pi$
$168$		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	$-0.724241\pi$
$173$	3.86973	−	14.4420i	0.294210	−	1.09801i	0.941843	−	0.336054i	$-0.109092\pi$
$174$		0			0
$175$		0			0
$176$		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
$185$		0			0
$186$		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	−0.987615	−	0.156899i	$-0.949850\pi$
$193$	−4.97251	+	8.61264i	−0.357929	+	0.619952i	0.629686	+	0.776850i	$0.283184\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.68592	−	4.65216i	0.191364	−	0.331453i	−0.754338	−	0.656486i	$-0.772042\pi$
$197$	2.68592	−	4.65216i	0.191364	−	0.331453i	0.945703	+	0.325033i	$0.105376\pi$
$198$		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
$205$		0			0
$206$		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
$215$		0			0
$216$		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	0.437056	−	0.899434i	$-0.356021\pi$
$223$	−1.84198	−	1.06347i	−0.123348	−	0.0712151i	−0.560405	+	0.828219i	$0.689354\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.2288	−	19.4489i	−0.745282	−	1.29087i	−0.950063	−	0.312058i	$-0.898982\pi$
$227$	−11.2288	−	19.4489i	−0.745282	−	1.29087i	0.204781	−	0.978808i	$-0.434352\pi$
$228$		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	0.451716	−	0.892162i	$-0.350812\pi$
$233$	−6.72311	−	6.72311i	−0.440446	−	0.440446i	−0.892162	+	0.451716i	$0.850812\pi$
$234$		0			0
$235$		0			0
$236$		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
$245$		0			0
$246$		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
$255$		0			0
$256$		0			0
$257$	4.98961	+	18.6215i	0.311243	+	1.16158i	0.927436	+	0.373981i	$0.122007\pi$
$257$	4.98961	+	18.6215i	0.311243	+	1.16158i	−0.616193	+	0.787595i	$0.711326\pi$
$258$		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	$0.153536\pi$
$263$	5.68609	+	21.2208i	0.350619	+	1.30853i	−0.535289	+	0.844669i	$0.679797\pi$
$264$		0			0
$265$		0			0
$266$		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
$275$		0			0
$276$		0			0
$277$	13.6128	+	3.64753i	0.817912	+	0.219159i	0.643434	−	0.765502i	$-0.277509\pi$
$277$	13.6128	+	3.64753i	0.817912	+	0.219159i	0.174479	+	0.984661i	$0.444176\pi$
$278$		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	−0.000267339	−	1.00000i	$-0.500085\pi$
$283$	8.40291	−	2.25155i	0.499501	−	0.133841i	0.499768	+	0.866159i	$0.333418\pi$
$284$		0			0
$285$		0			0
$286$		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	0.986226	−	0.165404i	$-0.0528928\pi$
$293$	5.98879	+	10.3729i	0.349869	+	0.605991i	−0.636357	+	0.771395i	$0.719559\pi$
$294$		0			0
$295$		0			0
$296$		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
$305$		0			0
$306$		0			0
$307$		−	20.0009i		−	1.14151i	−0.821120	−	0.570755i	$-0.806650\pi$
$307$		−	20.0009i		−	1.14151i	0.821120	−	0.570755i	$-0.193350\pi$
$308$		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	$-0.779959\pi$
$313$	−2.35138	+	2.35138i	−0.132908	+	0.132908i	0.637523	+	0.770431i	$0.279959\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.2905			0.858799			0.429399	−	0.903115i	$-0.358725\pi$
$317$	15.2905			0.858799			0.429399	+	0.903115i	$0.358725\pi$
$318$		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
$325$		0			0
$326$		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
$335$		0			0
$336$		0			0
$337$	−15.9698	+	15.9698i	−0.869930	+	0.869930i	−0.992464	−	0.122534i	$-0.960898\pi$
$337$	−15.9698	+	15.9698i	−0.869930	+	0.869930i	0.122534	+	0.992464i	$0.460898\pi$
$338$		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
$345$		0			0
$346$		0			0
$347$	−2.63370	+	9.82910i	−0.141384	+	0.527654i	0.858505	+	0.512805i	$0.171393\pi$
$347$	−2.63370	+	9.82910i	−0.141384	+	0.527654i	−0.999890	+	0.0148492i	$0.995273\pi$
$348$		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	0.999856	−	0.0169962i	$-0.00541032\pi$
$353$	27.9018	+	16.1091i	1.48506	+	0.857402i	0.485209	+	0.874398i	$0.338744\pi$
$354$		0			0
$355$		0			0
$356$		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			0
$366$		0			0
$367$	20.3821	−	5.46138i	1.06394	−	0.285082i	0.315938	−	0.948780i	$-0.397681\pi$
$367$	20.3821	−	5.46138i	1.06394	−	0.285082i	0.748001	+	0.663698i	$0.231014\pi$
$368$		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	0.827129	−	0.562012i	$-0.189972\pi$
$373$	24.3817	+	6.53307i	1.26244	+	0.338269i	0.435309	+	0.900281i	$0.356639\pi$
$374$		0			0
$375$		0			0
$376$		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	$0.710002\pi$
$383$	−31.3842	+	18.1197i	−1.60366	+	0.925873i	−0.990747	+	0.135722i	$0.956664\pi$
$384$		0			0
$385$		0			0
$386$		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
$395$		0			0
$396$		0			0
$397$	18.5248	−	10.6953i	0.929732	−	0.536781i	0.0430054	−	0.999075i	$-0.486307\pi$
$397$	18.5248	−	10.6953i	0.929732	−	0.536781i	0.886727	+	0.462294i	$0.152973\pi$
$398$		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
$405$		0			0
$406$		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
$415$		0			0
$416$		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
$425$		0			0
$426$		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	$0.171709\pi$
$433$	−2.95228	+	11.0180i	−0.141877	+	0.529493i	−0.999875	+	0.0158391i	$0.994958\pi$
$434$		0			0
$435$		0			0
$436$		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	−0.813063	−	0.582175i	$-0.802202\pi$
$443$	−4.85964	+	4.85964i	−0.230888	+	0.230888i	0.582175	+	0.813063i	$0.302202\pi$
$444$		0			0
$445$		0			0
$446$		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
$455$		0			0
$456$		0			0
$457$	−12.2322	+	21.1868i	−0.572198	+	0.991076i	0.424142	+	0.905596i	$0.360576\pi$
$457$	−12.2322	+	21.1868i	−0.572198	+	0.991076i	−0.996340	+	0.0854803i	$0.972758\pi$
$458$		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	$-0.447355\pi$
$463$	7.08508			0.329272			0.164636	+	0.986354i	$0.447355\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.40762	−	4.40762i	0.203960	−	0.203960i	−0.597734	−	0.801694i	$-0.703932\pi$
$467$	4.40762	−	4.40762i	0.203960	−	0.203960i	0.801694	+	0.597734i	$0.203932\pi$
$468$		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
$475$		0			0
$476$		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
$485$		0			0
$486$		0			0
$487$	5.99150	+	10.3776i	0.271501	+	0.470253i	0.969246	−	0.246093i	$-0.0791467\pi$
$487$	5.99150	+	10.3776i	0.271501	+	0.470253i	−0.697746	+	0.716346i	$0.745813\pi$
$488$		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
$495$		0			0
$496$		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	0.269366	−	0.963038i	$-0.413186\pi$
$503$	0.473787	+	0.126951i	0.0211251	+	0.00566046i	−0.248241	+	0.968698i	$0.579852\pi$
$504$		0			0
$505$		0			0
$506$		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
$515$		0			0
$516$		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	$-0.929961\pi$
$523$	−5.48576	−	20.4731i	−0.239875	−	0.895227i	0.736015	−	0.676965i	$-0.236705\pi$
$524$		0			0
$525$		0			0
$526$		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
$535$		0			0
$536$		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
$545$		0			0
$546$		0			0
$547$	7.28589	+	7.28589i	0.311522	+	0.311522i	0.845499	−	0.533977i	$-0.179303\pi$
$547$	7.28589	+	7.28589i	0.311522	+	0.311522i	−0.533977	+	0.845499i	$0.679303\pi$
$548$		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
$555$		0			0
$556$		0			0
$557$	−20.5259	−	11.8506i	−0.869710	−	0.502127i	−0.00245824	−	0.999997i	$-0.500782\pi$
$557$	−20.5259	−	11.8506i	−0.869710	−	0.502127i	−0.867252	+	0.497870i	$0.834116\pi$
$558$		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	$0.230276\pi$
$563$	−5.47068	+	20.4169i	−0.230562	+	0.860468i	−0.980100	+	0.198507i	$0.936391\pi$
$564$		0			0
$565$		0			0
$566$		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
$575$		0			0
$576$		0			0
$577$	−45.6328			−1.89972			−0.949858	−	0.312681i	$-0.898773\pi$
$577$	−45.6328			−1.89972			−0.949858	+	0.312681i	$0.898773\pi$
$578$		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
$585$		0			0
$586$		0			0
$587$	−1.44141	+	2.49660i	−0.0594935	+	0.103046i	−0.894238	−	0.447592i	$-0.852282\pi$
$587$	−1.44141	+	2.49660i	−0.0594935	+	0.103046i	0.834745	+	0.550637i	$0.185615\pi$
$588$		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	$-0.386409\pi$
$593$	17.0136			0.698663			0.349332	+	0.936999i	$0.386409\pi$
$594$		0			0
$595$		0			0
$596$		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
$605$		0			0
$606$		0			0
$607$	0.254323	−	0.949146i	0.0103227	−	0.0385247i	−0.960572	−	0.278030i	$-0.910319\pi$
$607$	0.254323	−	0.949146i	0.0103227	−	0.0385247i	0.970895	+	0.239505i	$0.0769852\pi$
$608$		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	0.643471	−	0.765470i	$-0.277494\pi$
$613$	7.48436	+	4.32110i	0.302291	+	0.174528i	−0.341181	+	0.939998i	$0.610827\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.38476	−	7.59463i	−0.176524	−	0.305748i	0.764164	−	0.645022i	$-0.223152\pi$
$617$	−4.38476	−	7.59463i	−0.176524	−	0.305748i	−0.940688	+	0.339274i	$0.889819\pi$
$618$		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
$625$		0			0
$626$		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
$635$		0			0
$636$		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	−0.931991	−	0.362481i	$-0.881930\pi$
$643$	−27.4892	+	15.8709i	−1.08407	+	0.625887i	−0.152078	+	0.988369i	$0.548596\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.01862	+	3.80155i	0.0400462	+	0.149454i	0.983054	−	0.183316i	$-0.0586832\pi$
$647$	1.01862	+	3.80155i	0.0400462	+	0.149454i	−0.943008	+	0.332771i	$0.892017\pi$
$648$		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	$-0.883287\pi$
$653$	−7.77659	−	29.0226i	−0.304321	−	1.13574i	0.629207	−	0.777238i	$-0.283380\pi$
$654$		0			0
$655$		0			0
$656$		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
$665$		0			0
$666$		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	0.721406	−	0.692513i	$-0.243496\pi$
$673$	43.9051	−	11.7643i	1.69242	−	0.453482i	0.971012	+	0.239031i	$0.0768296\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.14523	+	7.14523i	0.274614	+	0.274614i	0.830954	−	0.556341i	$-0.187795\pi$
$677$	7.14523	+	7.14523i	0.274614	+	0.274614i	−0.556341	+	0.830954i	$0.687795\pi$
$678$		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	0.941213	−	0.337813i	$-0.109687\pi$
$683$	4.65327	+	8.05969i	0.178052	+	0.308396i	−0.763161	+	0.646208i	$0.776354\pi$
$684$		0			0
$685$		0			0
$686$		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
$695$		0			0
$696$		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
$705$		0			0
$706$		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
$715$		0			0
$716$		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			0
$726$		0			0
$727$	−18.2655	+	18.2655i	−0.677429	+	0.677429i	−0.959418	−	0.281989i	$-0.909006\pi$
$727$	−18.2655	+	18.2655i	−0.677429	+	0.677429i	0.281989	+	0.959418i	$0.409006\pi$
$728$		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	$-0.808003\pi$
$733$		−	30.7161i		−	1.13452i	0.823537	−	0.567262i	$-0.191997\pi$
$734$		0			0
$735$		0			0
$736$		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	0.368030	−	0.929814i	$-0.380032\pi$
$743$	−6.90167	−	3.98468i	−0.253198	−	0.146184i	−0.621228	+	0.783630i	$0.713366\pi$
$744$		0			0
$745$		0			0
$746$		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
$755$		0			0
$756$		0			0
$757$	37.8020	−	10.1290i	1.37394	−	0.368145i	0.505021	−	0.863107i	$-0.331485\pi$
$757$	37.8020	−	10.1290i	1.37394	−	0.368145i	0.868915	+	0.494962i	$0.164818\pi$
$758$		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
$765$		0			0
$766$		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	−0.0312766	−	0.999511i	$-0.509957\pi$
$773$	22.7618	−	13.1416i	0.818687	−	0.472669i	0.849963	+	0.526842i	$0.176624\pi$
$774$		0			0
$775$		0			0
$776$		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
$785$		0			0
$786$		0			0
$787$	17.8020	−	10.2780i	0.634573	−	0.366371i	−0.147948	−	0.988995i	$-0.547267\pi$
$787$	17.8020	−	10.2780i	0.634573	−	0.366371i	0.782521	+	0.622624i	$0.213933\pi$
$788$		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
$795$		0			0
$796$		0			0
$797$	−24.6043	−	6.59270i	−0.871529	−	0.233526i	−0.204780	−	0.978808i	$-0.565648\pi$
$797$	−24.6043	−	6.59270i	−0.871529	−	0.233526i	−0.666749	+	0.745282i	$0.732315\pi$
$798$		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
$805$		0			0
$806$		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
$815$		0			0
$816$		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	−0.990221	−	0.139506i	$-0.955448\pi$
$823$	−1.80480	+	6.73560i	−0.0629114	+	0.234788i	0.927310	+	0.374295i	$0.122115\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			34.2158i			1.18980i	0.803800	+	0.594900i	$0.202808\pi$
$827$			34.2158i			1.18980i	−0.803800	+	0.594900i	$0.797192\pi$
$828$		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
$835$		0			0
$836$		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
$845$		0			0
$846$		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	$-0.498212\pi$
$853$	0.328048			0.0112321			0.00561607	+	0.999984i	$0.498212\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.20279	−	7.20279i	0.246043	−	0.246043i	−0.573302	−	0.819344i	$-0.694338\pi$
$857$	7.20279	−	7.20279i	0.246043	−	0.246043i	0.819344	+	0.573302i	$0.194338\pi$
$858$		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	$0.0917954\pi$
$863$			16.7097i			0.568806i	−0.958705	+	0.284403i	$0.908205\pi$
$864$		0			0
$865$		0			0
$866$		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
$875$		0			0
$876$		0			0
$877$	−12.5974	−	21.8193i	−0.425383	−	0.736784i	0.571074	−	0.820899i	$-0.306527\pi$
$877$	−12.5974	−	21.8193i	−0.425383	−	0.736784i	−0.996456	+	0.0841148i	$0.973194\pi$
$878$		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	0.789394	−	0.613887i	$-0.210395\pi$
$883$	5.21525	+	5.21525i	0.175507	+	0.175507i	−0.613887	+	0.789394i	$0.710395\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.8074	−	7.45098i	0.933682	−	0.250179i	0.240258	−	0.970709i	$-0.422768\pi$
$887$	27.8074	−	7.45098i	0.933682	−	0.250179i	0.693424	+	0.720530i	$0.256101\pi$
$888$		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
$895$		0			0
$896$		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
$905$		0			0
$906$		0			0
$907$	−9.40058	−	35.0834i	−0.312141	−	1.16493i	−0.926622	−	0.375994i	$-0.877301\pi$
$907$	−9.40058	−	35.0834i	−0.312141	−	1.16493i	0.614481	−	0.788932i	$-0.289365\pi$
$908$		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
$915$		0			0
$916$		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
$925$		0			0
$926$		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			0
$936$		0			0
$937$	−8.40073	−	8.40073i	−0.274440	−	0.274440i	0.556445	−	0.830885i	$-0.312165\pi$
$937$	−8.40073	−	8.40073i	−0.274440	−	0.274440i	−0.830885	+	0.556445i	$0.812165\pi$
$938$		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
$945$		0			0
$946$		0			0
$947$	−14.3428	−	8.28083i	−0.466079	−	0.269091i	0.248518	−	0.968627i	$-0.420057\pi$
$947$	−14.3428	−	8.28083i	−0.466079	−	0.269091i	−0.714597	+	0.699536i	$0.753390\pi$
$948$		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	$-0.783647\pi$
$953$	6.48521	−	24.2031i	0.210077	−	0.784016i	0.987842	−	0.155462i	$-0.0496865\pi$
$954$		0			0
$955$		0			0
$956$		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
$965$		0			0
$966$		0			0
$967$	31.4641			1.01182			0.505908	−	0.862587i	$-0.331157\pi$
$967$	31.4641			1.01182			0.505908	+	0.862587i	$0.331157\pi$
$968$		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
$975$		0			0
$976$		0			0
$977$	−9.07986	+	15.7268i	−0.290490	+	0.503144i	−0.973926	−	0.226867i	$-0.927152\pi$
$977$	−9.07986	+	15.7268i	−0.290490	+	0.503144i	0.683435	+	0.730011i	$0.260485\pi$
$978$		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	$-0.263646\pi$
$983$	42.3986			1.35230			0.676152	+	0.736762i	$0.263646\pi$
$984$		0			0
$985$		0			0
$986$		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
$995$		0			0
$996$		0			0
$997$	3.27444	−	12.2204i	0.103703	−	0.387023i	−0.894492	−	0.447084i	$-0.852463\pi$
$997$	3.27444	−	12.2204i	0.103703	−	0.387023i	0.998195	+	0.0600602i	$0.0191293\pi$
$998$		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	1300.2.bs.d.357.5		20
5.2	odd	4		260.2.bf.c.253.5	yes	20
5.3	odd	4		1300.2.bn.d.1293.1		20
5.4	even	2		260.2.bk.c.97.1	yes	20
13.11	odd	12		1300.2.bn.d.557.1		20
65.24	odd	12		260.2.bf.c.37.5	✓	20
65.37	even	12		260.2.bk.c.193.1	yes	20
65.63	even	12	inner	1300.2.bs.d.193.5		20

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

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.bs (of order \(12\), degree \(4\), minimal)

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

Introduction

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