LMFDB - Embedded newform 504.2.t.c.457.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.8
Character	$\chi$	$=$	504.457
Dual form			504.2.t.c.193.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.677409 + 1.59409i) q^{3} -2.66851 q^{5} +(-0.654882 - 2.56342i) q^{7} +(-2.08224 + 2.15970i) q^{9} +O(q^{10})$	\(q+(0.677409 + 1.59409i) q^{3} -2.66851 q^{5} +(-0.654882 - 2.56342i) q^{7} +(-2.08224 + 2.15970i) q^{9} -3.98378 q^{11} +(1.00103 + 1.73384i) q^{13} +(-1.80767 - 4.25383i) q^{15} +(-3.57175 - 6.18646i) q^{17} +(-4.01956 + 6.96208i) q^{19} +(3.64270 - 2.78042i) q^{21} -0.887818 q^{23} +2.12092 q^{25} +(-4.85327 - 1.85627i) q^{27} +(-1.35035 + 2.33887i) q^{29} +(0.614943 - 1.06511i) q^{31} +(-2.69864 - 6.35049i) q^{33} +(1.74756 + 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(-2.08578 + 2.77025i) q^{39} +(-1.43477 - 2.48509i) q^{41} +(3.40053 - 5.88989i) q^{43} +(5.55646 - 5.76317i) q^{45} +(6.06845 + 10.5109i) q^{47} +(-6.14226 + 3.35748i) q^{49} +(7.44223 - 9.88445i) q^{51} +(-2.38665 - 4.13380i) q^{53} +10.6307 q^{55} +(-13.8211 - 1.69136i) q^{57} +(-4.79029 + 8.29703i) q^{59} +(4.74981 + 8.22692i) q^{61} +(6.89983 + 3.92330i) q^{63} +(-2.67126 - 4.62676i) q^{65} +(-5.49446 + 9.51668i) q^{67} +(-0.601415 - 1.41526i) q^{69} -4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(1.43673 + 3.38094i) q^{75} +(2.60890 + 10.2121i) q^{77} +(0.514987 + 0.891984i) q^{79} +(-0.328592 - 8.99400i) q^{81} +(-5.26656 + 9.12195i) q^{83} +(9.53125 + 16.5086i) q^{85} +(-4.64310 - 0.568202i) q^{87} +(1.72788 - 2.99278i) q^{89} +(3.78900 - 3.70153i) q^{91} +(2.11445 + 0.258757i) q^{93} +(10.7262 - 18.5784i) q^{95} +(-1.12061 + 1.94096i) q^{97} +(8.29516 - 8.60376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.677409	+	1.59409i	0.391102	+	0.920347i
$3$	0.677409	+	1.59409i	0.391102	+	0.920347i
$4$		0			0
$5$	−2.66851			−1.19339			−0.596696	−	0.802467i	$-0.703520\pi$
$5$	−2.66851			−1.19339			−0.596696	+	0.802467i	$0.703520\pi$
$6$		0			0
$7$	−0.654882	−	2.56342i	−0.247522	−	0.968882i
$7$	−0.654882	−	2.56342i	−0.247522	−	0.968882i
$8$		0			0
$9$	−2.08224	+	2.15970i	−0.694078	+	0.719899i
$10$		0			0
$11$	−3.98378			−1.20115			−0.600577	−	0.799567i	$-0.705062\pi$
$11$	−3.98378			−1.20115			−0.600577	+	0.799567i	$0.705062\pi$
$12$		0			0
$13$	1.00103	+	1.73384i	0.277636	+	0.480880i	0.970797	−	0.239903i	$-0.0771156\pi$
$13$	1.00103	+	1.73384i	0.277636	+	0.480880i	−0.693161	+	0.720783i	$0.743782\pi$
$14$		0			0
$15$	−1.80767	−	4.25383i	−0.466738	−	1.09834i
$16$		0			0
$17$	−3.57175	−	6.18646i	−0.866278	−	1.50044i	−0.865773	−	0.500437i	$-0.833173\pi$
$17$	−3.57175	−	6.18646i	−0.866278	−	1.50044i	−0.000504947	−	1.00000i	$-0.500161\pi$
$18$		0			0
$19$	−4.01956	+	6.96208i	−0.922150	+	1.59721i	−0.126068	+	0.992022i	$0.540236\pi$
$19$	−4.01956	+	6.96208i	−0.922150	+	1.59721i	−0.796082	+	0.605189i	$0.793097\pi$
$20$		0			0
$21$	3.64270	−	2.78042i	0.794902	−	0.606738i
$22$		0			0
$23$	−0.887818			−0.185123			−0.0925614	−	0.995707i	$-0.529505\pi$
$23$	−0.887818			−0.185123			−0.0925614	+	0.995707i	$0.529505\pi$
$24$		0			0
$25$	2.12092			0.424185
$26$		0			0
$27$	−4.85327	−	1.85627i	−0.934013	−	0.357239i
$28$		0			0
$29$	−1.35035	+	2.33887i	−0.250753	+	0.434317i	−0.963733	−	0.266867i	$-0.914012\pi$
$29$	−1.35035	+	2.33887i	−0.250753	+	0.434317i	0.712980	+	0.701184i	$0.247345\pi$
$30$		0			0
$31$	0.614943	−	1.06511i	0.110447	−	0.191300i	−0.805504	−	0.592591i	$-0.798105\pi$
$31$	0.614943	−	1.06511i	0.110447	−	0.191300i	0.915951	+	0.401291i	$0.131438\pi$
$32$		0			0
$33$	−2.69864	−	6.35049i	−0.469774	−	1.10548i
$34$		0			0
$35$	1.74756	+	6.84051i	0.295391	+	1.15626i
$36$		0			0
$37$	5.26528	−	9.11973i	0.865607	−	1.49928i	−0.000836477	−	1.00000i	$-0.500266\pi$
$37$	5.26528	−	9.11973i	0.865607	−	1.49928i	0.866443	−	0.499275i	$-0.166400\pi$
$38$		0			0
$39$	−2.08578	+	2.77025i	−0.333993	+	0.443595i
$40$		0			0
$41$	−1.43477	−	2.48509i	−0.224073	−	0.388105i	0.731968	−	0.681339i	$-0.238602\pi$
$41$	−1.43477	−	2.48509i	−0.224073	−	0.388105i	−0.956041	+	0.293234i	$0.905269\pi$
$42$		0			0
$43$	3.40053	−	5.88989i	0.518576	−	0.898200i	−0.481191	−	0.876616i	$-0.659796\pi$
$43$	3.40053	−	5.88989i	0.518576	−	0.898200i	0.999767	−	0.0215840i	$-0.00687093\pi$
$44$		0			0
$45$	5.55646	−	5.76317i	0.828308	−	0.859122i
$46$		0			0
$47$	6.06845	+	10.5109i	0.885175	+	1.53317i	0.845513	+	0.533955i	$0.179295\pi$
$47$	6.06845	+	10.5109i	0.885175	+	1.53317i	0.0396620	+	0.999213i	$0.487372\pi$
$48$		0			0
$49$	−6.14226	+	3.35748i	−0.877466	+	0.479639i
$50$		0			0
$51$	7.44223	−	9.88445i	1.04212	−	1.38410i
$52$		0			0
$53$	−2.38665	−	4.13380i	−0.327832	−	0.567821i	0.654250	−	0.756279i	$-0.272985\pi$
$53$	−2.38665	−	4.13380i	−0.327832	−	0.567821i	−0.982081	+	0.188457i	$0.939651\pi$
$54$		0			0
$55$	10.6307			1.43345
$56$		0			0
$57$	−13.8211	−	1.69136i	−1.83064	−	0.224026i
$58$		0			0
$59$	−4.79029	+	8.29703i	−0.623643	+	1.08018i	0.365159	+	0.930945i	$0.381015\pi$
$59$	−4.79029	+	8.29703i	−0.623643	+	1.08018i	−0.988802	+	0.149236i	$0.952319\pi$
$60$		0			0
$61$	4.74981	+	8.22692i	0.608151	+	1.05335i	0.991545	+	0.129764i	$0.0414218\pi$
$61$	4.74981	+	8.22692i	0.608151	+	1.05335i	−0.383394	+	0.923585i	$0.625245\pi$
$62$		0			0
$63$	6.89983	+	3.92330i	0.869297	+	0.494289i
$64$		0			0
$65$	−2.67126	−	4.62676i	−0.331329	−	0.573879i
$66$		0			0
$67$	−5.49446	+	9.51668i	−0.671255	+	1.16265i	0.306294	+	0.951937i	$0.400911\pi$
$67$	−5.49446	+	9.51668i	−0.671255	+	1.16265i	−0.977549	+	0.210710i	$0.932422\pi$
$68$		0			0
$69$	−0.601415	−	1.41526i	−0.0724019	−	0.170377i
$70$		0			0
$71$	−4.62888			−0.549347			−0.274673	−	0.961538i	$-0.588570\pi$
$71$	−4.62888			−0.549347			−0.274673	+	0.961538i	$0.588570\pi$
$72$		0			0
$73$	2.01004	+	3.48149i	0.235257	+	0.407478i	0.959347	−	0.282228i	$-0.0910733\pi$
$73$	2.01004	+	3.48149i	0.235257	+	0.407478i	−0.724090	+	0.689705i	$0.757740\pi$
$74$		0			0
$75$	1.43673	+	3.38094i	0.165900	+	0.390398i
$76$		0			0
$77$	2.60890	+	10.2121i	0.297312	+	1.16378i
$78$		0			0
$79$	0.514987	+	0.891984i	0.0579406	+	0.100356i	0.893541	−	0.448982i	$-0.148213\pi$
$79$	0.514987	+	0.891984i	0.0579406	+	0.100356i	−0.835600	+	0.549338i	$0.814880\pi$
$80$		0			0
$81$	−0.328592	−	8.99400i	−0.0365102	−	0.999333i
$82$		0			0
$83$	−5.26656	+	9.12195i	−0.578080	+	1.00126i	0.417620	+	0.908622i	$0.362865\pi$
$83$	−5.26656	+	9.12195i	−0.578080	+	1.00126i	−0.995699	+	0.0926419i	$0.970469\pi$
$84$		0			0
$85$	9.53125	+	16.5086i	1.03381	+	1.79061i
$86$		0			0
$87$	−4.64310	−	0.568202i	−0.497792	−	0.0609176i
$88$		0			0
$89$	1.72788	−	2.99278i	0.183155	−	0.317234i	−0.759798	−	0.650159i	$-0.774702\pi$
$89$	1.72788	−	2.99278i	0.183155	−	0.317234i	0.942953	+	0.332925i	$0.108036\pi$
$90$		0			0
$91$	3.78900	−	3.70153i	0.397195	−	0.388025i
$92$		0			0
$93$	2.11445	+	0.258757i	0.219258	+	0.0268319i
$94$		0			0
$95$	10.7262	−	18.5784i	1.10049	−	1.90610i
$96$		0			0
$97$	−1.12061	+	1.94096i	−0.113781	+	0.197075i	−0.917292	−	0.398216i	$-0.869630\pi$
$97$	−1.12061	+	1.94096i	−0.113781	+	0.197075i	0.803511	+	0.595290i	$0.202963\pi$
$98$		0			0
$99$	8.29516	−	8.60376i	0.833695	−	0.864710i
$100$		0			0
$101$	−4.56830			−0.454562			−0.227281	−	0.973829i	$-0.572984\pi$
$101$	−4.56830			−0.454562			−0.227281	+	0.973829i	$0.572984\pi$
$102$		0			0
$103$	−12.7502			−1.25631			−0.628156	−	0.778088i	$-0.716190\pi$
$103$	−12.7502			−1.25631			−0.628156	+	0.778088i	$0.716190\pi$
$104$		0			0
$105$	−9.72056	+	7.41958i	−0.948630	+	0.724076i
$106$		0			0
$107$	−0.659761	+	1.14274i	−0.0637815	+	0.110473i	−0.896153	−	0.443746i	$-0.853649\pi$
$107$	−0.659761	+	1.14274i	−0.0637815	+	0.110473i	0.832371	+	0.554218i	$0.186983\pi$
$108$		0			0
$109$	−6.31990	−	10.9464i	−0.605337	−	1.04847i	−0.991998	−	0.126252i	$-0.959705\pi$
$109$	−6.31990	−	10.9464i	−0.605337	−	1.04847i	0.386661	−	0.922222i	$-0.373628\pi$
$110$		0			0
$111$	18.1044	+	2.21554i	1.71839	+	0.210289i
$112$		0			0
$113$	−0.503200	−	0.871568i	−0.0473371	−	0.0819903i	0.841386	−	0.540435i	$-0.181740\pi$
$113$	−0.503200	−	0.871568i	−0.0473371	−	0.0819903i	−0.888723	+	0.458444i	$0.848407\pi$
$114$		0			0
$115$	2.36915			0.220924
$116$		0			0
$117$	−5.82895	−	1.44833i	−0.538887	−	0.133898i
$118$		0			0
$119$	−13.5194	+	13.2073i	−1.23932	+	1.21071i
$120$		0			0
$121$	4.87048			0.442771
$122$		0			0
$123$	2.98953	−	3.97056i	0.269556	−	0.358014i
$124$		0			0
$125$	7.68283			0.687173
$126$		0			0
$127$	1.38400			0.122810			0.0614051	−	0.998113i	$-0.480442\pi$
$127$	1.38400			0.122810			0.0614051	+	0.998113i	$0.480442\pi$
$128$		0			0
$129$	11.6926	+	1.43088i	1.02947	+	0.125982i
$130$		0			0
$131$	−0.329724			−0.0288081			−0.0144041	−	0.999896i	$-0.504585\pi$
$131$	−0.329724			−0.0288081			−0.0144041	+	0.999896i	$0.504585\pi$
$132$		0			0
$133$	20.4791	+	5.74448i	1.77576	+	0.498110i
$134$		0			0
$135$	12.9510	+	4.95347i	1.11464	+	0.426326i
$136$		0			0
$137$	8.94189			0.763958			0.381979	−	0.924171i	$-0.375243\pi$
$137$	8.94189			0.763958			0.381979	+	0.924171i	$0.375243\pi$
$138$		0			0
$139$	3.92869	+	6.80470i	0.333227	+	0.577167i	0.983143	−	0.182840i	$-0.0585290\pi$
$139$	3.92869	+	6.80470i	0.333227	+	0.577167i	−0.649915	+	0.760007i	$0.725196\pi$
$140$		0			0
$141$	−12.6444	+	16.7938i	−1.06485	+	1.41429i
$142$		0			0
$143$	−3.98789	−	6.90723i	−0.333484	−	0.577611i
$144$		0			0
$145$	3.60341	−	6.24128i	0.299247	−	0.518310i
$146$		0			0
$147$	−9.51293	−	7.51692i	−0.784613	−	0.619985i
$148$		0			0
$149$	16.3215			1.33711			0.668554	−	0.743663i	$-0.266913\pi$
$149$	16.3215			1.33711			0.668554	+	0.743663i	$0.266913\pi$
$150$		0			0
$151$	−4.63354			−0.377072			−0.188536	−	0.982066i	$-0.560374\pi$
$151$	−4.63354			−0.377072			−0.188536	+	0.982066i	$0.560374\pi$
$152$		0			0
$153$	20.7981	+	5.16776i	1.68143	+	0.417788i
$154$		0			0
$155$	−1.64098	+	2.84226i	−0.131807	+	0.228296i
$156$		0			0
$157$	4.25926	−	7.37725i	0.339926	−	0.588769i	−0.644493	−	0.764611i	$-0.722931\pi$
$157$	4.25926	−	7.37725i	0.339926	−	0.588769i	0.984418	+	0.175842i	$0.0562647\pi$
$158$		0			0
$159$	4.97291	−	6.60481i	0.394377	−	0.523795i
$160$		0			0
$161$	0.581416	+	2.27585i	0.0458220	+	0.179362i
$162$		0			0
$163$	1.22354	−	2.11923i	0.0958350	−	0.165991i	−0.814122	−	0.580694i	$-0.802781\pi$
$163$	1.22354	−	2.11923i	0.0958350	−	0.165991i	0.909957	+	0.414703i	$0.136115\pi$
$164$		0			0
$165$	7.20135	+	16.9463i	0.560624	+	1.31927i
$166$		0			0
$167$	−0.0713948	−	0.123659i	−0.00552470	−	0.00956906i	0.863250	−	0.504777i	$-0.168425\pi$
$167$	−0.0713948	−	0.123659i	−0.00552470	−	0.00956906i	−0.868775	+	0.495208i	$0.835092\pi$
$168$		0			0
$169$	4.49587	−	7.78708i	0.345836	−	0.599006i
$170$		0			0
$171$	−6.66632	−	23.1777i	−0.509787	−	1.77244i
$172$		0			0
$173$	−8.99834	−	15.5856i	−0.684131	−	1.18495i	−0.973709	−	0.227795i	$-0.926848\pi$
$173$	−8.99834	−	15.5856i	−0.684131	−	1.18495i	0.289578	−	0.957154i	$-0.406485\pi$
$174$		0			0
$175$	−1.38896	−	5.43682i	−0.104995	−	0.410985i
$176$		0			0
$177$	−16.4712	−	2.01567i	−1.23805	−	0.151507i
$178$		0			0
$179$	−1.02413	−	1.77384i	−0.0765468	−	0.132583i	0.825211	−	0.564824i	$-0.191056\pi$
$179$	−1.02413	−	1.77384i	−0.0765468	−	0.132583i	−0.901758	+	0.432242i	$0.857723\pi$
$180$		0			0
$181$	1.81165			0.134659			0.0673294	−	0.997731i	$-0.478552\pi$
$181$	1.81165			0.134659			0.0673294	+	0.997731i	$0.478552\pi$
$182$		0			0
$183$	−9.89687	+	13.1446i	−0.731597	+	0.971677i
$184$		0			0
$185$	−14.0504	+	24.3361i	−1.03301	+	1.78922i
$186$		0			0
$187$	14.2291	+	24.6455i	1.04053	+	1.80226i
$188$		0			0
$189$	−1.58008	+	13.6566i	−0.114934	+	0.993373i
$190$		0			0
$191$	−9.40457	−	16.2892i	−0.680491	−	1.17864i	−0.974831	−	0.222944i	$-0.928433\pi$
$191$	−9.40457	−	16.2892i	−0.680491	−	1.17864i	0.294341	−	0.955701i	$-0.404900\pi$
$192$		0			0
$193$	−3.24357	+	5.61803i	−0.233477	+	0.404394i	−0.958829	−	0.283984i	$-0.908344\pi$
$193$	−3.24357	+	5.61803i	−0.233477	+	0.404394i	0.725352	+	0.688378i	$0.241677\pi$
$194$		0			0
$195$	5.56593	−	7.39243i	0.398584	−	0.529383i
$196$		0			0
$197$	−10.8356			−0.772007			−0.386003	−	0.922497i	$-0.626145\pi$
$197$	−10.8356			−0.772007			−0.386003	+	0.922497i	$0.626145\pi$
$198$		0			0
$199$	−9.43873	−	16.3484i	−0.669094	−	1.15890i	−0.978158	−	0.207863i	$-0.933349\pi$
$199$	−9.43873	−	16.3484i	−0.669094	−	1.15890i	0.309064	−	0.951041i	$-0.399984\pi$
$200$		0			0
$201$	−18.8924	−	2.31197i	−1.33257	−	0.163074i
$202$		0			0
$203$	6.87982	+	1.92982i	0.482869	+	0.135447i
$204$		0			0
$205$	3.82868	+	6.63147i	0.267407	+	0.463162i
$206$		0			0
$207$	1.84865	−	1.91742i	0.128490	−	0.133270i
$208$		0			0
$209$	16.0130	−	27.7354i	1.10764	−	1.91850i
$210$		0			0
$211$	−11.9133	−	20.6344i	−0.820145	−	1.42053i	−0.905574	−	0.424188i	$-0.860560\pi$
$211$	−11.9133	−	20.6344i	−0.820145	−	1.42053i	0.0854297	−	0.996344i	$-0.472774\pi$
$212$		0			0
$213$	−3.13564	−	7.37884i	−0.214851	−	0.505590i
$214$		0			0
$215$	−9.07433	+	15.7172i	−0.618864	+	1.07190i
$216$		0			0
$217$	−3.13305	−	0.878836i	−0.212685	−	0.0596593i
$218$		0			0
$219$	−4.18819	+	5.56258i	−0.283012	+	0.375884i
$220$		0			0
$221$	7.15088	−	12.3857i	0.481020	−	0.833152i
$222$		0			0
$223$	6.53734	−	11.3230i	0.437773	−	0.758245i	−0.559745	−	0.828665i	$-0.689101\pi$
$223$	6.53734	−	11.3230i	0.437773	−	0.758245i	0.997517	+	0.0704203i	$0.0224341\pi$
$224$		0			0
$225$	−4.41626	+	4.58056i	−0.294418	+	0.305371i
$226$		0			0
$227$	23.1690			1.53778			0.768890	−	0.639381i	$-0.220809\pi$
$227$	23.1690			1.53778			0.768890	+	0.639381i	$0.220809\pi$
$228$		0			0
$229$	−21.5588			−1.42465			−0.712323	−	0.701851i	$-0.752357\pi$
$229$	−21.5588			−1.42465			−0.712323	+	0.701851i	$0.752357\pi$
$230$		0			0
$231$	−14.5117	+	11.0766i	−0.954800	+	0.728786i
$232$		0			0
$233$	−8.05558	+	13.9527i	−0.527739	+	0.914070i	0.471738	+	0.881739i	$0.343627\pi$
$233$	−8.05558	+	13.9527i	−0.527739	+	0.914070i	−0.999477	+	0.0323318i	$0.989707\pi$
$234$		0			0
$235$	−16.1937	−	28.0483i	−1.05636	−	1.82967i
$236$		0			0
$237$	−1.07304	+	1.42517i	−0.0697017	+	0.0925749i
$238$		0			0
$239$	0.216059	+	0.374225i	0.0139757	+	0.0242066i	0.872929	−	0.487848i	$-0.162218\pi$
$239$	0.216059	+	0.374225i	0.0139757	+	0.0242066i	−0.858953	+	0.512054i	$0.828885\pi$
$240$		0			0
$241$	3.05674			0.196902			0.0984509	−	0.995142i	$-0.468611\pi$
$241$	3.05674			0.196902			0.0984509	+	0.995142i	$0.468611\pi$
$242$		0			0
$243$	14.1146	−	6.61642i	0.905455	−	0.424443i
$244$		0			0
$245$	16.3907	−	8.95945i	1.04716	−	0.572398i
$246$		0			0
$247$	−16.0948			−1.02409
$248$		0			0
$249$	−18.1088	−	2.21608i	−1.14760	−	0.140438i
$250$		0			0
$251$	11.9066			0.751541			0.375770	−	0.926713i	$-0.377378\pi$
$251$	11.9066			0.751541			0.375770	+	0.926713i	$0.377378\pi$
$252$		0			0
$253$	3.53687			0.222361
$254$		0			0
$255$	−19.8596	+	26.3767i	−1.24366	+	1.65177i
$256$		0			0
$257$	−31.9453			−1.99269			−0.996346	−	0.0854116i	$-0.972779\pi$
$257$	−31.9453			−1.99269			−0.996346	+	0.0854116i	$0.972779\pi$
$258$		0			0
$259$	−26.8259	−	7.52479i	−1.66688	−	0.467567i
$260$		0			0
$261$	−2.23951	−	7.78641i	−0.138622	−	0.481967i
$262$		0			0
$263$	6.70989			0.413750			0.206875	−	0.978367i	$-0.433671\pi$
$263$	6.70989			0.413750			0.206875	+	0.978367i	$0.433671\pi$
$264$		0			0
$265$	6.36879	+	11.0311i	0.391232	+	0.677634i
$266$		0			0
$267$	5.94124	+	0.727062i	0.363598	+	0.0444955i
$268$		0			0
$269$	5.66510	+	9.81225i	0.345408	+	0.598263i	0.985428	−	0.170095i	$-0.0544074\pi$
$269$	5.66510	+	9.81225i	0.345408	+	0.598263i	−0.640020	+	0.768358i	$0.721074\pi$
$270$		0			0
$271$	−5.06846	+	8.77884i	−0.307887	+	0.533276i	−0.977900	−	0.209073i	$-0.932955\pi$
$271$	−5.06846	+	8.77884i	−0.307887	+	0.533276i	0.670013	+	0.742350i	$0.266289\pi$
$272$		0			0
$273$	8.46726	+	3.53256i	0.512462	+	0.213800i
$274$		0			0
$275$	−8.44929			−0.509512
$276$		0			0
$277$	−21.2865			−1.27898			−0.639492	−	0.768798i	$-0.720855\pi$
$277$	−21.2865			−1.27898			−0.639492	+	0.768798i	$0.720855\pi$
$278$		0			0
$279$	1.01987	+	3.54591i	0.0610578	+	0.212288i
$280$		0			0
$281$	−6.26945	+	10.8590i	−0.374004	+	0.647794i	−0.990177	−	0.139817i	$-0.955349\pi$
$281$	−6.26945	+	10.8590i	−0.374004	+	0.647794i	0.616174	+	0.787610i	$0.288682\pi$
$282$		0			0
$283$	−12.4749	+	21.6071i	−0.741554	+	1.28441i	0.210234	+	0.977651i	$0.432577\pi$
$283$	−12.4749	+	21.6071i	−0.741554	+	1.28441i	−0.951788	+	0.306758i	$0.900756\pi$
$284$		0			0
$285$	36.8816	+	4.51340i	2.18468	+	0.267351i
$286$		0			0
$287$	−5.43072	+	5.30535i	−0.320565	+	0.313165i
$288$		0			0
$289$	−17.0149	+	29.4706i	−1.00087	+	1.73357i
$290$		0			0
$291$	−3.85317	−	0.471534i	−0.225877	−	0.0276418i
$292$		0			0
$293$	7.42625	+	12.8626i	0.433846	+	0.751443i	0.997201	−	0.0747718i	$-0.0238228\pi$
$293$	7.42625	+	12.8626i	0.433846	+	0.751443i	−0.563355	+	0.826215i	$0.690490\pi$
$294$		0			0
$295$	12.7829	−	22.1407i	0.744250	−	1.28908i
$296$		0			0
$297$	19.3344	+	7.39496i	1.12189	+	0.429099i
$298$		0			0
$299$	−0.888734	−	1.53933i	−0.0513968	−	0.0890219i
$300$		0			0
$301$	−17.3252	−	4.85981i	−0.998609	−	0.280115i
$302$		0			0
$303$	−3.09460	−	7.28227i	−0.177780	−	0.418355i
$304$		0			0
$305$	−12.6749	−	21.9536i	−0.725763	−	1.25706i
$306$		0			0
$307$	−21.9045			−1.25016			−0.625079	−	0.780561i	$-0.714933\pi$
$307$	−21.9045			−1.25016			−0.625079	+	0.780561i	$0.714933\pi$
$308$		0			0
$309$	−8.63707	−	20.3249i	−0.491346	−	1.15624i
$310$		0			0
$311$	8.78359	−	15.2136i	0.498072	−	0.862686i	−0.501926	−	0.864911i	$-0.667375\pi$
$311$	8.78359	−	15.2136i	0.498072	−	0.862686i	0.999998	+	0.00222515i	$0.000708287\pi$
$312$		0			0
$313$	5.98820	+	10.3719i	0.338473	+	0.586252i	0.984146	−	0.177362i	$-0.0567563\pi$
$313$	5.98820	+	10.3719i	0.338473	+	0.586252i	−0.645673	+	0.763614i	$0.723423\pi$
$314$		0			0
$315$	−18.4123	−	10.4693i	−1.03741	−	0.589881i
$316$		0			0
$317$	0.866633	+	1.50105i	0.0486750	+	0.0843075i	0.889336	−	0.457254i	$-0.151167\pi$
$317$	0.866633	+	1.50105i	0.0486750	+	0.0843075i	−0.840661	+	0.541561i	$0.817833\pi$
$318$		0			0
$319$	5.37948	−	9.31753i	0.301193	−	0.521681i
$320$		0			0
$321$	−2.26855	−	0.277616i	−0.126618	−	0.0154950i
$322$		0			0
$323$	57.4275			3.19535
$324$		0			0
$325$	2.12311	+	3.67734i	0.117769	+	0.203982i
$326$		0			0
$327$	13.1684	−	17.4897i	0.728212	−	0.967180i
$328$		0			0
$329$	22.9697	−	22.4394i	1.26636	−	1.23712i
$330$		0			0
$331$	0.363127	+	0.628954i	0.0199593	+	0.0345705i	0.875833	−	0.482615i	$-0.160313\pi$
$331$	0.363127	+	0.628954i	0.0199593	+	0.0345705i	−0.855873	+	0.517186i	$0.826980\pi$
$332$		0			0
$333$	8.73232	+	30.3609i	0.478528	+	1.66376i
$334$		0			0
$335$	14.6620	−	25.3953i	0.801070	−	1.38749i
$336$		0			0
$337$	−6.84810	−	11.8613i	−0.373040	−	0.646124i	0.616992	−	0.786970i	$-0.288351\pi$
$337$	−6.84810	−	11.8613i	−0.373040	−	0.646124i	−0.990032	+	0.140846i	$0.955018\pi$
$338$		0			0
$339$	1.04848	−	1.39255i	0.0569459	−	0.0756331i
$340$		0			0
$341$	−2.44980	+	4.24317i	−0.132664	+	0.229781i
$342$		0			0
$343$	12.6291	+	13.5465i	0.681906	+	0.731440i
$344$		0			0
$345$	1.60488	+	3.77663i	0.0864039	+	0.203327i
$346$		0			0
$347$	2.10709	−	3.64958i	0.113114	−	0.195920i	−0.803910	−	0.594751i	$-0.797251\pi$
$347$	2.10709	−	3.64958i	0.113114	−	0.195920i	0.917024	+	0.398831i	$0.130584\pi$
$348$		0			0
$349$	−10.8070	+	18.7183i	−0.578486	+	1.00197i	0.417167	+	0.908830i	$0.363023\pi$
$349$	−10.8070	+	18.7183i	−0.578486	+	1.00197i	−0.995653	+	0.0931372i	$0.970310\pi$
$350$		0			0
$351$	−1.63981	−	10.2730i	−0.0875267	−	0.548331i
$352$		0			0
$353$	4.85115			0.258201			0.129100	−	0.991632i	$-0.458791\pi$
$353$	4.85115			0.258201			0.129100	+	0.991632i	$0.458791\pi$
$354$		0			0
$355$	12.3522			0.655586
$356$		0			0
$357$	−30.2118	−	12.6044i	−1.59898	−	0.667097i
$358$		0			0
$359$	2.90433	−	5.03045i	0.153285	−	0.265497i	−0.779148	−	0.626839i	$-0.784348\pi$
$359$	2.90433	−	5.03045i	0.153285	−	0.265497i	0.932433	+	0.361343i	$0.117682\pi$
$360$		0			0
$361$	−22.8137	−	39.5145i	−1.20072	−	2.07971i
$362$		0			0
$363$	3.29931	+	7.76398i	0.173169	+	0.407503i
$364$		0			0
$365$	−5.36381	−	9.29038i	−0.280754	−	0.486281i
$366$		0			0
$367$	21.6890			1.13216			0.566078	−	0.824352i	$-0.308460\pi$
$367$	21.6890			1.13216			0.566078	+	0.824352i	$0.308460\pi$
$368$		0			0
$369$	8.35456	+	2.07588i	0.434921	+	0.108066i
$370$		0			0
$371$	−9.03370	+	8.82515i	−0.469006	+	0.458179i
$372$		0			0
$373$	24.7104			1.27946			0.639729	−	0.768601i	$-0.279047\pi$
$373$	24.7104			1.27946			0.639729	+	0.768601i	$0.279047\pi$
$374$		0			0
$375$	5.20441	+	12.2471i	0.268755	+	0.632438i
$376$		0			0
$377$	−5.40696			−0.278473
$378$		0			0
$379$	−27.9950			−1.43801			−0.719005	−	0.695005i	$-0.755402\pi$
$379$	−27.9950			−1.43801			−0.719005	+	0.695005i	$0.755402\pi$
$380$		0			0
$381$	0.937534	+	2.20622i	0.0480313	+	0.113028i
$382$		0			0
$383$	−20.6227			−1.05377			−0.526884	−	0.849937i	$-0.676640\pi$
$383$	−20.6227			−1.05377			−0.526884	+	0.849937i	$0.676640\pi$
$384$		0			0
$385$	−6.96187	−	27.2511i	−0.354810	−	1.38884i
$386$		0			0
$387$	5.63968	+	19.6083i	0.286681	+	0.996743i
$388$		0			0
$389$	17.4007			0.882250			0.441125	−	0.897446i	$-0.354580\pi$
$389$	17.4007			0.882250			0.441125	+	0.897446i	$0.354580\pi$
$390$		0			0
$391$	3.17107	+	5.49245i	0.160368	+	0.277765i
$392$		0			0
$393$	−0.223358	−	0.525610i	−0.0112669	−	0.0265135i
$394$		0			0
$395$	−1.37425	−	2.38026i	−0.0691458	−	0.119764i
$396$		0			0
$397$	9.74152	−	16.8728i	0.488913	−	0.846822i	−0.511006	−	0.859577i	$-0.670727\pi$
$397$	9.74152	−	16.8728i	0.488913	−	0.846822i	0.999919	+	0.0127553i	$0.00406024\pi$
$398$		0			0
$399$	4.71549	+	36.5368i	0.236070	+	1.82913i
$400$		0			0
$401$	7.70529			0.384784			0.192392	−	0.981318i	$-0.438376\pi$
$401$	7.70529			0.384784			0.192392	+	0.981318i	$0.438376\pi$
$402$		0			0
$403$	2.46231			0.122656
$404$		0			0
$405$	0.876849	+	24.0005i	0.0435710	+	1.19260i
$406$		0			0
$407$	−20.9757	+	36.3310i	−1.03973	+	1.80086i
$408$		0			0
$409$	7.86755	−	13.6270i	0.389025	−	0.673811i	−0.603294	−	0.797519i	$-0.706145\pi$
$409$	7.86755	−	13.6270i	0.389025	−	0.673811i	0.992319	+	0.123708i	$0.0394786\pi$
$410$		0			0
$411$	6.05732	+	14.2542i	0.298785	+	0.703106i
$412$		0			0
$413$	24.4058	+	6.84596i	1.20093	+	0.336868i
$414$		0			0
$415$	14.0538	−	24.3420i	0.689876	−	1.19490i
$416$		0			0
$417$	−8.18596	+	10.8722i	−0.400868	+	0.532416i
$418$		0			0
$419$	−17.3452	−	30.0428i	−0.847369	−	1.46769i	−0.883548	−	0.468341i	$-0.844852\pi$
$419$	−17.3452	−	30.0428i	−0.847369	−	1.46769i	0.0361784	−	0.999345i	$-0.488482\pi$
$420$		0			0
$421$	−0.607053	+	1.05145i	−0.0295860	+	0.0512444i	−0.880439	−	0.474159i	$-0.842752\pi$
$421$	−0.607053	+	1.05145i	−0.0295860	+	0.0512444i	0.850853	+	0.525403i	$0.176086\pi$
$422$		0			0
$423$	−35.3363	−	8.78008i	−1.71811	−	0.426902i
$424$		0			0
$425$	−7.57542	−	13.1210i	−0.367462	−	0.636463i
$426$		0			0
$427$	17.9785	−	17.5634i	0.870040	−	0.849954i
$428$		0			0
$429$	8.30930	−	11.0361i	0.401177	−	0.532826i
$430$		0			0
$431$	1.68495	+	2.91841i	0.0811610	+	0.140575i	0.903749	−	0.428063i	$-0.140804\pi$
$431$	1.68495	+	2.91841i	0.0811610	+	0.140575i	−0.822588	+	0.568638i	$0.807471\pi$
$432$		0			0
$433$	−30.8651			−1.48328			−0.741640	−	0.670798i	$-0.765952\pi$
$433$	−30.8651			−1.48328			−0.741640	+	0.670798i	$0.765952\pi$
$434$		0			0
$435$	12.3901	+	1.51625i	0.594062	+	0.0726986i
$436$		0			0
$437$	3.56864	−	6.18106i	0.170711	−	0.295680i
$438$		0			0
$439$	16.5395	+	28.6472i	0.789385	+	1.36725i	0.926344	+	0.376678i	$0.122934\pi$
$439$	16.5395	+	28.6472i	0.789385	+	1.36725i	−0.136959	+	0.990577i	$0.543733\pi$
$440$		0			0
$441$	5.53849	−	20.2565i	0.263738	−	0.964594i
$442$		0			0
$443$	−1.36682	−	2.36740i	−0.0649397	−	0.112479i	0.831728	−	0.555184i	$-0.187352\pi$
$443$	−1.36682	−	2.36740i	−0.0649397	−	0.112479i	−0.896667	+	0.442705i	$0.854019\pi$
$444$		0			0
$445$	−4.61086	+	7.98625i	−0.218576	+	0.378584i
$446$		0			0
$447$	11.0563	+	26.0179i	0.522946	+	1.23060i
$448$		0			0
$449$	22.7472			1.07351			0.536753	−	0.843740i	$-0.319651\pi$
$449$	22.7472			1.07351			0.536753	+	0.843740i	$0.319651\pi$
$450$		0			0
$451$	5.71579	+	9.90003i	0.269146	+	0.466174i
$452$		0			0
$453$	−3.13880	−	7.38627i	−0.147474	−	0.347037i
$454$		0			0
$455$	−10.1110	+	9.87754i	−0.474010	+	0.463066i
$456$		0			0
$457$	−1.68162	−	2.91265i	−0.0786628	−	0.136248i	0.824010	−	0.566575i	$-0.191732\pi$
$457$	−1.68162	−	2.91265i	−0.0786628	−	0.136248i	−0.902673	+	0.430327i	$0.858398\pi$
$458$		0			0
$459$	5.85097	+	36.6547i	0.273100	+	1.71090i
$460$		0			0
$461$	−10.0040	+	17.3275i	−0.465934	+	0.807021i	−0.999243	−	0.0388994i	$-0.987615\pi$
$461$	−10.0040	+	17.3275i	−0.465934	+	0.807021i	0.533309	+	0.845920i	$0.320948\pi$
$462$		0			0
$463$	7.29434	+	12.6342i	0.338997	+	0.587160i	0.984244	−	0.176814i	$-0.0565791\pi$
$463$	7.29434	+	12.6342i	0.338997	+	0.587160i	−0.645247	+	0.763974i	$0.723246\pi$
$464$		0			0
$465$	−5.64243	−	0.690495i	−0.261661	−	0.0320210i
$466$		0			0
$467$	7.26334	−	12.5805i	0.336107	−	0.582155i	−0.647590	−	0.761989i	$-0.724223\pi$
$467$	7.26334	−	12.5805i	0.336107	−	0.582155i	0.983697	+	0.179834i	$0.0575562\pi$
$468$		0			0
$469$	27.9935	+	7.85231i	1.29262	+	0.362586i
$470$		0			0
$471$	14.6453	+	1.79222i	0.674818	+	0.0825812i
$472$		0			0
$473$	−13.5470	+	23.4640i	−0.622889	+	1.07888i
$474$		0			0
$475$	−8.52518	+	14.7660i	−0.391162	+	0.677513i
$476$		0			0
$477$	13.8973	+	3.45310i	0.636315	+	0.158107i
$478$		0			0
$479$	−11.3243			−0.517421			−0.258710	−	0.965955i	$-0.583298\pi$
$479$	−11.3243			−0.517421			−0.258710	+	0.965955i	$0.583298\pi$
$480$		0			0
$481$	21.0829			0.961296
$482$		0			0
$483$	−3.23405	+	2.46851i	−0.147154	+	0.112321i
$484$		0			0
$485$	2.99036	−	5.17946i	0.135785	−	0.235187i
$486$		0			0
$487$	5.93684	+	10.2829i	0.269024	+	0.465963i	0.968610	−	0.248585i	$-0.0799657\pi$
$487$	5.93684	+	10.2829i	0.269024	+	0.465963i	−0.699586	+	0.714548i	$0.746632\pi$
$488$		0			0
$489$	4.20708	+	0.514844i	0.190251	+	0.0232820i
$490$		0			0
$491$	11.9598	+	20.7150i	0.539738	+	0.934853i	0.998918	+	0.0465101i	$0.0148100\pi$
$491$	11.9598	+	20.7150i	0.539738	+	0.934853i	−0.459180	+	0.888343i	$0.651857\pi$
$492$		0			0
$493$	19.2924			0.868887
$494$		0			0
$495$	−22.1357	+	22.9592i	−0.994925	+	1.03194i
$496$		0			0
$497$	3.03137	+	11.8658i	0.135975	+	0.532252i
$498$		0			0
$499$	−0.451968			−0.0202329			−0.0101164	−	0.999949i	$-0.503220\pi$
$499$	−0.451968			−0.0202329			−0.0101164	+	0.999949i	$0.503220\pi$
$500$		0			0
$501$	0.148761	−	0.197578i	0.00664614	−	0.00882712i
$502$		0			0
$503$	−14.6077			−0.651326			−0.325663	−	0.945486i	$-0.605587\pi$
$503$	−14.6077			−0.651326			−0.325663	+	0.945486i	$0.605587\pi$
$504$		0			0
$505$	12.1905			0.542471
$506$		0			0
$507$	15.4588	+	1.89178i	0.686551	+	0.0840170i
$508$		0			0
$509$	−0.493171			−0.0218594			−0.0109297	−	0.999940i	$-0.503479\pi$
$509$	−0.493171			−0.0218594			−0.0109297	+	0.999940i	$0.503479\pi$
$510$		0			0
$511$	7.60819	−	7.43255i	0.336567	−	0.328797i
$512$		0			0
$513$	32.4315	−	26.3275i	1.43189	−	1.16239i
$514$		0			0
$515$	34.0239			1.49927
$516$		0			0
$517$	−24.1754	−	41.8730i	−1.06323	−	1.84157i
$518$		0			0
$519$	18.7492	−	24.9020i	0.823000	−	1.09307i
$520$		0			0
$521$	−6.06874	−	10.5114i	−0.265876	−	0.460511i	0.701917	−	0.712259i	$-0.252328\pi$
$521$	−6.06874	−	10.5114i	−0.265876	−	0.460511i	−0.967793	+	0.251748i	$0.918995\pi$
$522$		0			0
$523$	1.34058	−	2.32195i	0.0586193	−	0.101532i	−0.835227	−	0.549906i	$-0.814664\pi$
$523$	1.34058	−	2.32195i	0.0586193	−	0.101532i	0.893846	+	0.448374i	$0.147997\pi$
$524$		0			0
$525$	7.72589	−	5.89707i	0.337185	−	0.257369i
$526$		0			0
$527$	−8.78571			−0.382711
$528$		0			0
$529$	−22.2118			−0.965730
$530$		0			0
$531$	−7.94456	−	27.6219i	−0.344764	−	1.19869i
$532$		0			0
$533$	2.87249	−	4.97530i	0.124421	−	0.215504i
$534$		0			0
$535$	1.76058	−	3.04941i	0.0761163	−	0.131837i
$536$		0			0
$537$	2.13390	−	2.83416i	0.0920848	−	0.122303i
$538$		0			0
$539$	24.4694	−	13.3754i	1.05397	−	0.576121i
$540$		0			0
$541$	−13.5072	+	23.3951i	−0.580719	+	1.00583i	0.414676	+	0.909969i	$0.363895\pi$
$541$	−13.5072	+	23.3951i	−0.580719	+	1.00583i	−0.995394	+	0.0958650i	$0.969438\pi$
$542$		0			0
$543$	1.22723	+	2.88793i	0.0526653	+	0.123933i
$544$		0			0
$545$	16.8647	+	29.2105i	0.722404	+	1.25124i
$546$		0			0
$547$	−15.2496	+	26.4132i	−0.652028	+	1.12935i	0.330602	+	0.943770i	$0.392748\pi$
$547$	−15.2496	+	26.4132i	−0.652028	+	1.12935i	−0.982630	+	0.185575i	$0.940585\pi$
$548$		0			0
$549$	−27.6579	−	6.87221i	−1.18041	−	0.293299i
$550$		0			0
$551$	−10.8556	−	18.8024i	−0.462464	−	0.801011i
$552$		0			0
$553$	1.94928	−	1.90427i	0.0828916	−	0.0809779i
$554$		0			0
$555$	−48.3117	−	5.91217i	−2.05072	−	0.250958i
$556$		0			0
$557$	−7.39250	−	12.8042i	−0.313230	−	0.542531i	0.665829	−	0.746104i	$-0.268078\pi$
$557$	−7.39250	−	12.8042i	−0.313230	−	0.542531i	−0.979060	+	0.203573i	$0.934745\pi$
$558$		0			0
$559$	13.6162			0.575902
$560$		0			0
$561$	−29.6482	+	39.3775i	−1.25175	+	1.66252i
$562$		0			0
$563$	−1.31411	+	2.27611i	−0.0553831	+	0.0959264i	−0.892388	−	0.451269i	$-0.850971\pi$
$563$	−1.31411	+	2.27611i	−0.0553831	+	0.0959264i	0.837005	+	0.547196i	$0.184305\pi$
$564$		0			0
$565$	1.34279	+	2.32579i	0.0564917	+	0.0978465i
$566$		0			0
$567$	−22.8402	+	6.73233i	−0.959199	+	0.282731i
$568$		0			0
$569$	16.0581	+	27.8134i	0.673191	+	1.16600i	0.976994	+	0.213266i	$0.0684100\pi$
$569$	16.0581	+	27.8134i	0.673191	+	1.16600i	−0.303804	+	0.952735i	$0.598257\pi$
$570$		0			0
$571$	−20.5907	+	35.6642i	−0.861696	+	1.49250i	0.00859553	+	0.999963i	$0.497264\pi$
$571$	−20.5907	+	35.6642i	−0.861696	+	1.49250i	−0.870291	+	0.492538i	$0.836069\pi$
$572$		0			0
$573$	19.5957	−	26.0262i	0.818621	−	1.08726i
$574$		0			0
$575$	−1.88300			−0.0785263
$576$		0			0
$577$	12.0735	+	20.9119i	0.502625	+	0.870573i	0.999995	+	0.00303429i	$0.000965847\pi$
$577$	12.0735	+	20.9119i	0.502625	+	0.870573i	−0.497370	+	0.867539i	$0.665701\pi$
$578$		0			0
$579$	−11.1529	−	1.36484i	−0.463497	−	0.0567207i
$580$		0			0
$581$	26.8324	+	7.52661i	1.11319	+	0.312257i
$582$		0			0
$583$	9.50789	+	16.4681i	0.393777	+	0.682041i
$584$		0			0
$585$	15.5546	+	3.86488i	0.643103	+	0.159793i
$586$		0			0
$587$	−3.98618	+	6.90426i	−0.164527	+	0.284969i	−0.936487	−	0.350702i	$-0.885943\pi$
$587$	−3.98618	+	6.90426i	−0.164527	+	0.284969i	0.771960	+	0.635671i	$0.219277\pi$
$588$		0			0
$589$	4.94360	+	8.56257i	0.203698	+	0.352815i
$590$		0			0
$591$	−7.34015	−	17.2730i	−0.301933	−	0.710514i
$592$		0			0
$593$	−2.10338	+	3.64316i	−0.0863753	+	0.149606i	−0.905976	−	0.423328i	$-0.860862\pi$
$593$	−2.10338	+	3.64316i	−0.0863753	+	0.149606i	0.819601	+	0.572935i	$0.194195\pi$
$594$		0			0
$595$	36.0767	−	35.2438i	1.47900	−	1.44485i
$596$		0			0
$597$	19.6668	−	26.1207i	0.804910	−	1.06905i
$598$		0			0
$599$	18.6886	−	32.3696i	0.763594	−	1.32258i	−0.177392	−	0.984140i	$-0.556766\pi$
$599$	18.6886	−	32.3696i	0.763594	−	1.32258i	0.940987	−	0.338444i	$-0.109901\pi$
$600$		0			0
$601$	6.81596	−	11.8056i	0.278029	−	0.481560i	−0.692866	−	0.721066i	$-0.743652\pi$
$601$	6.81596	−	11.8056i	0.278029	−	0.481560i	0.970895	+	0.239506i	$0.0769856\pi$
$602$		0			0
$603$	−9.11240	−	31.6823i	−0.371086	−	1.29020i
$604$		0			0
$605$	−12.9969			−0.528400
$606$		0			0
$607$	2.74228			0.111306			0.0556529	−	0.998450i	$-0.482276\pi$
$607$	2.74228			0.111306			0.0556529	+	0.998450i	$0.482276\pi$
$608$		0			0
$609$	1.58414	+	12.2743i	0.0641926	+	0.497381i
$610$		0			0
$611$	−12.1494	+	21.0434i	−0.491513	+	0.851326i
$612$		0			0
$613$	0.798502	+	1.38305i	0.0322512	+	0.0558607i	0.881700	−	0.471810i	$-0.156399\pi$
$613$	0.798502	+	1.38305i	0.0322512	+	0.0558607i	−0.849449	+	0.527670i	$0.823066\pi$
$614$		0			0
$615$	−7.97757	+	10.5955i	−0.321687	+	0.427251i
$616$		0			0
$617$	12.6551	+	21.9192i	0.509473	+	0.882433i	0.999940	+	0.0109734i	$0.00349302\pi$
$617$	12.6551	+	21.9192i	0.509473	+	0.882433i	−0.490467	+	0.871460i	$0.663174\pi$
$618$		0			0
$619$	−27.1616			−1.09172			−0.545859	−	0.837877i	$-0.683796\pi$
$619$	−27.1616			−1.09172			−0.545859	+	0.837877i	$0.683796\pi$
$620$		0			0
$621$	4.30882	+	1.64803i	0.172907	+	0.0661331i
$622$		0			0
$623$	−8.80331	−	2.46937i	−0.352697	−	0.0989333i
$624$		0			0
$625$	−31.1063			−1.24425
$626$		0			0
$627$	55.0600	+	6.73800i	2.19888	+	0.269090i
$628$		0			0
$629$	−75.2252			−2.99942
$630$		0			0
$631$	−29.6597			−1.18073			−0.590366	−	0.807136i	$-0.701017\pi$
$631$	−29.6597			−1.18073			−0.590366	+	0.807136i	$0.701017\pi$
$632$		0			0
$633$	24.8229	−	32.9688i	0.986623	−	1.31039i
$634$		0			0
$635$	−3.69321			−0.146561
$636$		0			0
$637$	−11.9699	−	7.28874i	−0.474265	−	0.288791i
$638$		0			0
$639$	9.63841	−	9.99698i	0.381290	−	0.395474i
$640$		0			0
$641$	42.1975			1.66670			0.833350	−	0.552746i	$-0.186420\pi$
$641$	42.1975			1.66670			0.833350	+	0.552746i	$0.186420\pi$
$642$		0			0
$643$	10.1099	+	17.5109i	0.398696	+	0.690562i	0.993565	−	0.113260i	$-0.0361294\pi$
$643$	10.1099	+	17.5109i	0.398696	+	0.690562i	−0.594869	+	0.803823i	$0.702796\pi$
$644$		0			0
$645$	−31.2016	−	3.81832i	−1.22856	−	0.150346i
$646$		0			0
$647$	−1.08988	−	1.88772i	−0.0428475	−	0.0742141i	0.843806	−	0.536648i	$-0.180310\pi$
$647$	−1.08988	−	1.88772i	−0.0428475	−	0.0742141i	−0.886654	+	0.462434i	$0.846976\pi$
$648$		0			0
$649$	19.0834	−	33.0535i	0.749091	−	1.29746i
$650$		0			0
$651$	−0.721412	−	5.58969i	−0.0282744	−	0.219077i
$652$		0			0
$653$	−34.1069			−1.33471			−0.667354	−	0.744741i	$-0.732573\pi$
$653$	−34.1069			−1.33471			−0.667354	+	0.744741i	$0.732573\pi$
$654$		0			0
$655$	0.879871			0.0343794
$656$		0			0
$657$	−11.7044	−	2.90821i	−0.456630	−	0.113460i
$658$		0			0
$659$	−0.994211	+	1.72202i	−0.0387290	+	0.0670805i	−0.884740	−	0.466085i	$-0.845664\pi$
$659$	−0.994211	+	1.72202i	−0.0387290	+	0.0670805i	0.846011	+	0.533165i	$0.178998\pi$
$660$		0			0
$661$	4.24205	−	7.34744i	0.164997	−	0.285782i	−0.771658	−	0.636038i	$-0.780572\pi$
$661$	4.24205	−	7.34744i	0.164997	−	0.285782i	0.936654	+	0.350256i	$0.113905\pi$
$662$		0			0
$663$	24.5880	+	3.00896i	0.954917	+	0.116859i
$664$		0			0
$665$	−54.6486	−	15.3292i	−2.11918	−	0.594440i
$666$		0			0
$667$	1.19886	−	2.07649i	0.0464201	−	0.0804020i
$668$		0			0
$669$	22.4783	+	2.75080i	0.869063	+	0.106352i
$670$		0			0
$671$	−18.9222	−	32.7742i	−0.730483	−	1.26523i
$672$		0			0
$673$	22.4056	−	38.8077i	0.863674	−	1.49593i	−0.00468438	−	0.999989i	$-0.501491\pi$
$673$	22.4056	−	38.8077i	0.863674	−	1.49593i	0.868358	−	0.495938i	$-0.165176\pi$
$674$		0			0
$675$	−10.2934	−	3.93701i	−0.396194	−	0.151535i
$676$		0			0
$677$	−4.02684	−	6.97469i	−0.154764	−	0.268059i	0.778209	−	0.628005i	$-0.216128\pi$
$677$	−4.02684	−	6.97469i	−0.154764	−	0.268059i	−0.932973	+	0.359946i	$0.882795\pi$
$678$		0			0
$679$	5.70937	+	1.60151i	0.219105	+	0.0614602i
$680$		0			0
$681$	15.6949	+	36.9334i	0.601429	+	1.41529i
$682$		0			0
$683$	20.8446	+	36.1039i	0.797597	+	1.38148i	0.921177	+	0.389144i	$0.127229\pi$
$683$	20.8446	+	36.1039i	0.797597	+	1.38148i	−0.123580	+	0.992335i	$0.539438\pi$
$684$		0			0
$685$	−23.8615			−0.911701
$686$		0			0
$687$	−14.6041	−	34.3667i	−0.557182	−	1.31117i
$688$		0			0
$689$	4.77823	−	8.27614i	0.182036	−	0.315296i
$690$		0			0
$691$	−5.66345	−	9.80938i	−0.215448	−	0.373166i	0.737963	−	0.674841i	$-0.235788\pi$
$691$	−5.66345	−	9.80938i	−0.215448	−	0.373166i	−0.953411	+	0.301674i	$0.902454\pi$
$692$		0			0
$693$	−27.4874	−	15.6296i	−1.04416	−	0.593718i
$694$		0			0
$695$	−10.4837	−	18.1584i	−0.397671	−	0.688786i
$696$		0			0
$697$	−10.2493	+	17.7522i	−0.388218	+	0.672414i
$698$		0			0
$699$	−27.6987	−	3.38965i	−1.04766	−	0.128208i
$700$		0			0
$701$	−22.6560			−0.855705			−0.427853	−	0.903849i	$-0.640730\pi$
$701$	−22.6560			−0.855705			−0.427853	+	0.903849i	$0.640730\pi$
$702$		0			0
$703$	42.3282	+	73.3146i	1.59644	+	2.76511i
$704$		0			0
$705$	33.7417	−	44.8144i	1.27079	−	1.68781i
$706$		0			0
$707$	2.99169	+	11.7105i	0.112514	+	0.440418i
$708$		0			0
$709$	−22.6074	−	39.1571i	−0.849037	−	1.47058i	−0.882069	−	0.471121i	$-0.843850\pi$
$709$	−22.6074	−	39.1571i	−0.849037	−	1.47058i	0.0330317	−	0.999454i	$-0.489484\pi$
$710$		0			0
$711$	−2.99874	−	0.745104i	−0.112462	−	0.0279436i
$712$		0			0
$713$	−0.545958	+	0.945626i	−0.0204463	+	0.0354140i
$714$		0			0
$715$	10.6417	+	18.4320i	0.397977	+	0.689317i
$716$		0			0
$717$	−0.450188	+	0.597921i	−0.0168126	+	0.0223298i
$718$		0			0
$719$	11.3171	−	19.6018i	0.422057	−	0.731024i	−0.574084	−	0.818797i	$-0.694642\pi$
$719$	11.3171	−	19.6018i	0.422057	−	0.731024i	0.996141	+	0.0877727i	$0.0279749\pi$
$720$		0			0
$721$	8.34986	+	32.6841i	0.310965	+	1.21722i
$722$		0			0
$723$	2.07066	+	4.87271i	0.0770087	+	0.181218i
$724$		0			0
$725$	−2.86398	+	4.96056i	−0.106366	+	0.184231i
$726$		0			0
$727$	1.04956	−	1.81789i	0.0389259	−	0.0674217i	−0.845906	−	0.533332i	$-0.820940\pi$
$727$	1.04956	−	1.81789i	0.0389259	−	0.0674217i	0.884832	+	0.465910i	$0.154273\pi$
$728$		0			0
$729$	20.1085	+	18.0180i	0.744760	+	0.667332i
$730$		0			0
$731$	−48.5834			−1.79692
$732$		0			0
$733$	−31.2906			−1.15574			−0.577872	−	0.816127i	$-0.696117\pi$
$733$	−31.2906			−1.15574			−0.577872	+	0.816127i	$0.696117\pi$
$734$		0			0
$735$	25.3853	+	20.0590i	0.936352	+	0.739886i
$736$		0			0
$737$	21.8887	−	37.9123i	0.806280	−	1.39652i
$738$		0			0
$739$	21.1229	+	36.5859i	0.777017	+	1.34583i	0.933654	+	0.358177i	$0.116601\pi$
$739$	21.1229	+	36.5859i	0.777017	+	1.34583i	−0.156637	+	0.987656i	$0.550065\pi$
$740$		0			0
$741$	−10.9028	−	25.6566i	−0.400523	−	0.942518i
$742$		0			0
$743$	6.48482	+	11.2320i	0.237905	+	0.412064i	0.960113	−	0.279612i	$-0.0902060\pi$
$743$	6.48482	+	11.2320i	0.237905	+	0.412064i	−0.722208	+	0.691676i	$0.756873\pi$
$744$		0			0
$745$	−43.5540			−1.59570
$746$		0			0
$747$	−8.73444	−	30.3682i	−0.319576	−	1.11112i
$748$		0			0
$749$	3.36139	+	0.942886i	0.122822	+	0.0344523i
$750$		0			0
$751$	32.7298			1.19433			0.597164	−	0.802119i	$-0.296294\pi$
$751$	32.7298			1.19433			0.597164	+	0.802119i	$0.296294\pi$
$752$		0			0
$753$	8.06566	+	18.9802i	0.293929	+	0.691679i
$754$		0			0
$755$	12.3646			0.449995
$756$		0			0
$757$	31.6305			1.14963			0.574815	−	0.818283i	$-0.305074\pi$
$757$	31.6305			1.14963			0.574815	+	0.818283i	$0.305074\pi$
$758$		0			0
$759$	2.39591	+	5.63808i	0.0869658	+	0.204649i
$760$		0			0
$761$	−38.2936			−1.38814			−0.694070	−	0.719907i	$-0.744184\pi$
$761$	−38.2936			−1.38814			−0.694070	+	0.719907i	$0.744184\pi$
$762$		0			0
$763$	−23.9214	+	23.3692i	−0.866014	+	0.846020i
$764$		0			0
$765$	−55.4999	−	13.7902i	−2.00660	−	0.498585i
$766$		0			0
$767$	−19.1809			−0.692583
$768$		0			0
$769$	11.0674	+	19.1693i	0.399100	+	0.691262i	0.993615	−	0.112823i	$-0.0359892\pi$
$769$	11.0674	+	19.1693i	0.399100	+	0.691262i	−0.594515	+	0.804085i	$0.702656\pi$
$770$		0			0
$771$	−21.6400	−	50.9236i	−0.779346	−	1.83397i
$772$		0			0
$773$	25.8165	+	44.7155i	0.928555	+	1.60830i	0.785742	+	0.618555i	$0.212281\pi$
$773$	25.8165	+	44.7155i	0.928555	+	1.60830i	0.142813	+	0.989750i	$0.454385\pi$
$774$		0			0
$775$	1.30425	−	2.25902i	0.0468500	−	0.0811466i
$776$		0			0
$777$	−6.17689	−	47.8601i	−0.221595	−	1.71697i
$778$		0			0
$779$	23.0685			0.826515
$780$		0			0
$781$	18.4404			0.659850
$782$		0			0
$783$	10.8952	−	8.84456i	0.389362	−	0.316079i
$784$		0			0
$785$	−11.3659	+	19.6862i	−0.405665	+	0.702632i
$786$		0			0
$787$	16.1523	−	27.9766i	0.575767	−	0.997257i	−0.420191	−	0.907436i	$-0.638037\pi$
$787$	16.1523	−	27.9766i	0.575767	−	0.997257i	0.995958	−	0.0898216i	$-0.0286297\pi$
$788$		0			0
$789$	4.54534	+	10.6962i	0.161818	+	0.380793i
$790$		0			0
$791$	−1.90466	+	1.86069i	−0.0677219	+	0.0661585i
$792$		0			0
$793$	−9.50943	+	16.4708i	−0.337690	+	0.584896i
$794$		0			0
$795$	−13.2702	+	17.6250i	−0.470647	+	0.625093i
$796$		0			0
$797$	−11.6877	−	20.2438i	−0.414001	−	0.717071i	0.581322	−	0.813674i	$-0.302536\pi$
$797$	−11.6877	−	20.2438i	−0.414001	−	0.717071i	−0.995323	+	0.0966026i	$0.969202\pi$
$798$		0			0
$799$	43.3501	−	75.0845i	1.53361	−	2.65630i
$800$		0			0
$801$	2.86564	+	9.96337i	0.101252	+	0.352038i
$802$		0			0
$803$	−8.00755	−	13.8695i	−0.282580	−	0.489444i
$804$		0			0
$805$	−1.55151	−	6.07312i	−0.0546836	−	0.214049i
$806$		0			0
$807$	−11.8040	+	15.6776i	−0.415521	+	0.551877i
$808$		0			0
$809$	15.2503	+	26.4143i	0.536171	+	0.928676i	0.999106	+	0.0422832i	$0.0134632\pi$
$809$	15.2503	+	26.4143i	0.536171	+	0.928676i	−0.462935	+	0.886392i	$0.653203\pi$
$810$		0			0
$811$	−51.6454			−1.81352			−0.906758	−	0.421652i	$-0.861450\pi$
$811$	−51.6454			−1.81352			−0.906758	+	0.421652i	$0.861450\pi$
$812$		0			0
$813$	−17.4277	−	2.13272i	−0.611215	−	0.0747978i
$814$		0			0
$815$	−3.26502	+	5.65518i	−0.114369	+	0.198092i
$816$		0			0
$817$	27.3373	+	47.3495i	0.956409	+	1.65655i
$818$		0			0
$819$	0.104588	+	15.8905i	0.00365459	+	0.555261i
$820$		0			0
$821$	13.3787	+	23.1727i	0.466921	+	0.808731i	0.999286	−	0.0377837i	$-0.0120298\pi$
$821$	13.3787	+	23.1727i	0.466921	+	0.808731i	−0.532365	+	0.846515i	$0.678696\pi$
$822$		0			0
$823$	20.2449	−	35.0652i	0.705693	−	1.22230i	−0.260747	−	0.965407i	$-0.583969\pi$
$823$	20.2449	−	35.0652i	0.705693	−	1.22230i	0.966441	−	0.256890i	$-0.0826977\pi$
$824$		0			0
$825$	−5.72362	−	13.4689i	−0.199271	−	0.468928i
$826$		0			0
$827$	−27.9452			−0.971749			−0.485875	−	0.874029i	$-0.661499\pi$
$827$	−27.9452			−0.971749			−0.485875	+	0.874029i	$0.661499\pi$
$828$		0			0
$829$	−20.0226	−	34.6802i	−0.695415	−	1.20449i	−0.970040	−	0.242943i	$-0.921887\pi$
$829$	−20.0226	−	34.6802i	−0.695415	−	1.20449i	0.274625	−	0.961551i	$-0.411446\pi$
$830$		0			0
$831$	−14.4197	−	33.9326i	−0.500213	−	1.17711i
$832$		0			0
$833$	42.7095	+	26.0068i	1.47980	+	0.901081i
$834$		0			0
$835$	0.190518	+	0.329986i	0.00659313	+	0.0114196i
$836$		0			0
$837$	−4.96162	+	4.02778i	−0.171499	+	0.139221i
$838$		0			0
$839$	−16.6312	+	28.8061i	−0.574174	+	0.994499i	0.421957	+	0.906616i	$0.361343\pi$
$839$	−16.6312	+	28.8061i	−0.574174	+	0.994499i	−0.996131	+	0.0878827i	$0.971990\pi$
$840$		0			0
$841$	10.8531	+	18.7982i	0.374246	+	0.648213i
$842$		0			0
$843$	−21.5572	−	2.63807i	−0.742469	−	0.0908601i
$844$		0			0
$845$	−11.9973	+	20.7799i	−0.412718	+	0.714849i
$846$		0			0
$847$	−3.18959	−	12.4851i	−0.109596	−	0.428993i
$848$		0			0
$849$	−42.8942	−	5.24920i	−1.47213	−	0.180152i
$850$		0			0
$851$	−4.67461	+	8.09666i	−0.160244	+	0.277550i
$852$		0			0
$853$	−4.38730	+	7.59902i	−0.150218	+	0.260186i	−0.931308	−	0.364234i	$-0.881331\pi$
$853$	−4.38730	+	7.59902i	−0.150218	+	0.260186i	0.781089	+	0.624419i	$0.214664\pi$
$854$		0			0
$855$	17.7891	+	61.8499i	0.608375	+	2.11522i
$856$		0			0
$857$	−1.35440			−0.0462653			−0.0231327	−	0.999732i	$-0.507364\pi$
$857$	−1.35440			−0.0462653			−0.0231327	+	0.999732i	$0.507364\pi$
$858$		0			0
$859$	−18.0387			−0.615472			−0.307736	−	0.951472i	$-0.599571\pi$
$859$	−18.0387			−0.615472			−0.307736	+	0.951472i	$0.599571\pi$
$860$		0			0
$861$	−12.1360	−	5.06317i	−0.413594	−	0.172552i
$862$		0			0
$863$	−6.37624	+	11.0440i	−0.217050	+	0.375941i	−0.953905	−	0.300110i	$-0.902977\pi$
$863$	−6.37624	+	11.0440i	−0.217050	+	0.375941i	0.736855	+	0.676051i	$0.236310\pi$
$864$		0			0
$865$	24.0121	+	41.5902i	0.816437	+	1.41411i
$866$		0			0
$867$	−58.5048	−	7.15955i	−1.98693	−	0.243151i
$868$		0			0
$869$	−2.05159	−	3.55347i	−0.0695956	−	0.120543i
$870$		0			0
$871$	−22.0005			−0.745459
$872$		0			0
$873$	−1.85851	−	6.46172i	−0.0629009	−	0.218696i
$874$		0			0
$875$	−5.03135	−	19.6943i	−0.170091	−	0.665790i
$876$		0			0
$877$	−17.5807			−0.593657			−0.296829	−	0.954931i	$-0.595929\pi$
$877$	−17.5807			−0.593657			−0.296829	+	0.954931i	$0.595929\pi$
$878$		0			0
$879$	−15.4736	+	20.5514i	−0.521911	+	0.693180i
$880$		0			0
$881$	−25.8682			−0.871523			−0.435762	−	0.900062i	$-0.643521\pi$
$881$	−25.8682			−0.871523			−0.435762	+	0.900062i	$0.643521\pi$
$882$		0			0
$883$	40.5923			1.36604			0.683020	−	0.730400i	$-0.260666\pi$
$883$	40.5923			1.36604			0.683020	+	0.730400i	$0.260666\pi$
$884$		0			0
$885$	43.9534	+	5.37883i	1.47748	+	0.180807i
$886$		0			0
$887$	−2.93571			−0.0985715			−0.0492858	−	0.998785i	$-0.515695\pi$
$887$	−2.93571			−0.0985715			−0.0492858	+	0.998785i	$0.515695\pi$
$888$		0			0
$889$	−0.906357	−	3.54778i	−0.0303982	−	0.118989i
$890$		0			0
$891$	1.30904	+	35.8301i	0.0438544	+	1.20035i
$892$		0			0
$893$	−97.5700			−3.26506
$894$		0			0
$895$	2.73289	+	4.73350i	0.0913504	+	0.158223i
$896$		0			0
$897$	1.85180	−	2.45948i	0.0618297	−	0.0821196i
$898$		0			0
$899$	1.66077	+	2.87654i	0.0553899	+	0.0959381i
$900$		0			0
$901$	−17.0491	+	29.5299i	−0.567987	+	0.983782i
$902$		0			0
$903$	−3.98928	−	30.9100i	−0.132755	−	1.02862i
$904$		0			0
$905$	−4.83439			−0.160701
$906$		0			0
$907$	−34.2790			−1.13822			−0.569108	−	0.822263i	$-0.692711\pi$
$907$	−34.2790			−1.13822			−0.569108	+	0.822263i	$0.692711\pi$
$908$		0			0
$909$	9.51227	−	9.86614i	0.315502	−	0.327239i
$910$		0			0
$911$	−4.98338	+	8.63146i	−0.165107	+	0.285973i	−0.936693	−	0.350151i	$-0.886130\pi$
$911$	−4.98338	+	8.63146i	−0.165107	+	0.285973i	0.771586	+	0.636124i	$0.219464\pi$
$912$		0			0
$913$	20.9808	−	36.3398i	0.694363	−	1.20267i
$914$		0			0
$915$	26.4098	−	35.0765i	0.873083	−	1.15959i
$916$		0			0
$917$	0.215930	+	0.845222i	0.00713065	+	0.0279117i
$918$		0			0
$919$	13.9444	−	24.1524i	0.459983	−	0.796714i	−0.538976	−	0.842321i	$-0.681189\pi$
$919$	13.9444	−	24.1524i	0.459983	−	0.796714i	0.998959	+	0.0456069i	$0.0145222\pi$
$920$		0			0
$921$	−14.8383	−	34.9178i	−0.488940	−	1.15058i
$922$		0			0
$923$	−4.63365	−	8.02573i	−0.152519	−	0.264170i
$924$		0			0
$925$	11.1673	−	19.3423i	0.367177	−	0.635970i
$926$		0			0
$927$	26.5489	−	27.5365i	0.871979	−	0.904418i
$928$		0			0
$929$	9.15294	+	15.8534i	0.300298	+	0.520132i	0.976203	−	0.216857i	$-0.0695804\pi$
$929$	9.15294	+	15.8534i	0.300298	+	0.520132i	−0.675905	+	0.736989i	$0.736247\pi$
$930$		0			0
$931$	1.31415	−	56.2585i	0.0430697	−	1.84380i
$932$		0			0
$933$	30.2019	+	3.69598i	0.988767	+	0.121001i
$934$		0			0
$935$	−37.9704	−	65.7666i	−1.24176	−	2.15080i
$936$		0			0
$937$	46.2063			1.50950			0.754748	−	0.656015i	$-0.227759\pi$
$937$	46.2063			1.50950			0.754748	+	0.656015i	$0.227759\pi$
$938$		0			0
$939$	−12.4772	+	16.5717i	−0.407178	+	0.540797i
$940$		0			0
$941$	−18.2251	+	31.5668i	−0.594120	+	1.02905i	0.399550	+	0.916711i	$0.369166\pi$
$941$	−18.2251	+	31.5668i	−0.594120	+	1.02905i	−0.993670	+	0.112335i	$0.964167\pi$
$942$		0			0
$943$	1.27381	+	2.20630i	0.0414810	+	0.0718472i
$944$		0			0
$945$	4.21645	−	36.4428i	0.137161	−	1.18548i
$946$		0			0
$947$	−23.7202	−	41.0846i	−0.770803	−	1.33507i	−0.937124	−	0.348998i	$-0.886522\pi$
$947$	−23.7202	−	41.0846i	−0.770803	−	1.33507i	0.166321	−	0.986072i	$-0.446811\pi$
$948$		0			0
$949$	−4.02423	+	6.97017i	−0.130632	+	0.226261i
$950$		0			0
$951$	−1.80575	+	2.39832i	−0.0585553	+	0.0777707i
$952$		0			0
$953$	−6.68090			−0.216415			−0.108208	−	0.994128i	$-0.534511\pi$
$953$	−6.68090			−0.216415			−0.108208	+	0.994128i	$0.534511\pi$
$954$		0			0
$955$	25.0961	+	43.4678i	0.812092	+	1.40659i
$956$		0			0
$957$	18.4971	+	2.26359i	0.597925	+	0.0731715i
$958$		0			0
$959$	−5.85588	−	22.9218i	−0.189096	−	0.740185i
$960$		0			0
$961$	14.7437	+	25.5368i	0.475603	+	0.823768i
$962$		0			0
$963$	−1.09419	−	3.80434i	−0.0352599	−	0.122593i
$964$		0			0
$965$	8.65548	−	14.9917i	0.278630	−	0.482601i
$966$		0			0
$967$	7.60180	+	13.1667i	0.244457	+	0.423413i	0.961979	−	0.273124i	$-0.0880568\pi$
$967$	7.60180	+	13.1667i	0.244457	+	0.423413i	−0.717522	+	0.696536i	$0.754724\pi$
$968$		0			0
$969$	38.9019	+	91.5445i	1.24971	+	2.94083i
$970$		0			0
$971$	0.363057	−	0.628834i	0.0116511	−	0.0201802i	−0.860141	−	0.510056i	$-0.829625\pi$
$971$	0.363057	−	0.628834i	0.0116511	−	0.0201802i	0.871792	+	0.489876i	$0.162958\pi$
$972$		0			0
$973$	14.8705	−	14.5272i	0.476726	−	0.465720i
$974$		0			0
$975$	−4.42379	+	5.87549i	−0.141675	+	0.188166i
$976$		0			0
$977$	21.5203	−	37.2742i	0.688494	−	1.19251i	−0.283831	−	0.958874i	$-0.591605\pi$
$977$	21.5203	−	37.2742i	0.688494	−	1.19251i	0.972325	−	0.233633i	$-0.0750613\pi$
$978$		0			0
$979$	−6.88350	+	11.9226i	−0.219997	+	0.381047i
$980$		0			0
$981$	36.8004	+	9.14388i	1.17495	+	0.291942i
$982$		0			0
$983$	43.0382			1.37271			0.686353	−	0.727269i	$-0.259211\pi$
$983$	43.0382			1.37271			0.686353	+	0.727269i	$0.259211\pi$
$984$		0			0
$985$	28.9149			0.921307
$986$		0			0
$987$	51.3302	+	21.4151i	1.63386	+	0.681649i
$988$		0			0
$989$	−3.01905	+	5.22915i	−0.0960002	+	0.166277i
$990$		0			0
$991$	−11.2758	−	19.5302i	−0.358187	−	0.620398i	0.629471	−	0.777024i	$-0.283272\pi$
$991$	−11.2758	−	19.5302i	−0.358187	−	0.620398i	−0.987658	+	0.156626i	$0.949938\pi$
$992$		0			0
$993$	−0.756624	+	1.00492i	−0.0240107	+	0.0318900i
$994$		0			0
$995$	25.1873	+	43.6257i	0.798491	+	1.38303i
$996$		0			0
$997$	−28.3341			−0.897350			−0.448675	−	0.893695i	$-0.648104\pi$
$997$	−28.3341			−0.897350			−0.448675	+	0.893695i	$0.648104\pi$
$998$		0			0
$999$	−42.4825	+	34.4868i	−1.34409	+	1.09111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.457.8	yes	22
3.2	odd	2		1512.2.t.c.289.9		22
4.3	odd	2		1008.2.t.l.961.4		22
7.4	even	3		504.2.q.c.25.9	✓	22
9.4	even	3		504.2.q.c.121.9	yes	22
9.5	odd	6		1512.2.q.d.793.3		22
12.11	even	2		3024.2.t.k.289.9		22
21.11	odd	6		1512.2.q.d.1369.3		22
28.11	odd	6		1008.2.q.l.529.3		22
36.23	even	6		3024.2.q.l.2305.3		22
36.31	odd	6		1008.2.q.l.625.3		22
63.4	even	3	inner	504.2.t.c.193.8	yes	22
63.32	odd	6		1512.2.t.c.361.9		22
84.11	even	6		3024.2.q.l.2881.3		22
252.67	odd	6		1008.2.t.l.193.4		22
252.95	even	6		3024.2.t.k.1873.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.9	✓	22	7.4	even	3
504.2.q.c.121.9	yes	22	9.4	even	3
504.2.t.c.193.8	yes	22	63.4	even	3	inner
504.2.t.c.457.8	yes	22	1.1	even	1	trivial
1008.2.q.l.529.3		22	28.11	odd	6
1008.2.q.l.625.3		22	36.31	odd	6
1008.2.t.l.193.4		22	252.67	odd	6
1008.2.t.l.961.4		22	4.3	odd	2
1512.2.q.d.793.3		22	9.5	odd	6
1512.2.q.d.1369.3		22	21.11	odd	6
1512.2.t.c.289.9		22	3.2	odd	2
1512.2.t.c.361.9		22	63.32	odd	6
3024.2.q.l.2305.3		22	36.23	even	6
3024.2.q.l.2881.3		22	84.11	even	6
3024.2.t.k.289.9		22	12.11	even	2
3024.2.t.k.1873.9		22	252.95	even	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.677409 + 1.59409i) q^{3} -2.66851 q^{5} +(-0.654882 - 2.56342i) q^{7} +(-2.08224 + 2.15970i) q^{9} +O(q^{10})\)	\(q+(0.677409 + 1.59409i) q^{3} -2.66851 q^{5} +(-0.654882 - 2.56342i) q^{7} +(-2.08224 + 2.15970i) q^{9} -3.98378 q^{11} +(1.00103 + 1.73384i) q^{13} +(-1.80767 - 4.25383i) q^{15} +(-3.57175 - 6.18646i) q^{17} +(-4.01956 + 6.96208i) q^{19} +(3.64270 - 2.78042i) q^{21} -0.887818 q^{23} +2.12092 q^{25} +(-4.85327 - 1.85627i) q^{27} +(-1.35035 + 2.33887i) q^{29} +(0.614943 - 1.06511i) q^{31} +(-2.69864 - 6.35049i) q^{33} +(1.74756 + 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(-2.08578 + 2.77025i) q^{39} +(-1.43477 - 2.48509i) q^{41} +(3.40053 - 5.88989i) q^{43} +(5.55646 - 5.76317i) q^{45} +(6.06845 + 10.5109i) q^{47} +(-6.14226 + 3.35748i) q^{49} +(7.44223 - 9.88445i) q^{51} +(-2.38665 - 4.13380i) q^{53} +10.6307 q^{55} +(-13.8211 - 1.69136i) q^{57} +(-4.79029 + 8.29703i) q^{59} +(4.74981 + 8.22692i) q^{61} +(6.89983 + 3.92330i) q^{63} +(-2.67126 - 4.62676i) q^{65} +(-5.49446 + 9.51668i) q^{67} +(-0.601415 - 1.41526i) q^{69} -4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(1.43673 + 3.38094i) q^{75} +(2.60890 + 10.2121i) q^{77} +(0.514987 + 0.891984i) q^{79} +(-0.328592 - 8.99400i) q^{81} +(-5.26656 + 9.12195i) q^{83} +(9.53125 + 16.5086i) q^{85} +(-4.64310 - 0.568202i) q^{87} +(1.72788 - 2.99278i) q^{89} +(3.78900 - 3.70153i) q^{91} +(2.11445 + 0.258757i) q^{93} +(10.7262 - 18.5784i) q^{95} +(-1.12061 + 1.94096i) q^{97} +(8.29516 - 8.60376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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