LMFDB - Embedded newform 504.2.q.c.121.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (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			121.9
Character	$\chi$	$=$	504.121
Dual form			504.2.q.c.25.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04182 + 1.38370i) q^{3} +(1.33425 + 2.31099i) q^{5} +(2.54743 + 0.714566i) q^{7} +(-0.829236 + 2.88312i) q^{9} +O(q^{10})$	\(q+(1.04182 + 1.38370i) q^{3} +(1.33425 + 2.31099i) q^{5} +(2.54743 + 0.714566i) q^{7} +(-0.829236 + 2.88312i) q^{9} +(1.99189 - 3.45005i) q^{11} +(1.00103 - 1.73384i) q^{13} +(-1.80767 + 4.25383i) q^{15} +(-3.57175 - 6.18646i) q^{17} +(-4.01956 + 6.96208i) q^{19} +(1.66521 + 4.26932i) q^{21} +(0.443909 + 0.768873i) q^{23} +(-1.06046 + 1.83677i) q^{25} +(-4.85327 + 1.85627i) q^{27} +(-1.35035 - 2.33887i) q^{29} -1.22989 q^{31} +(6.84901 - 0.838152i) q^{33} +(1.74756 + 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(3.44200 - 0.421217i) q^{39} +(-1.43477 + 2.48509i) q^{41} +(3.40053 + 5.88989i) q^{43} +(-7.76928 + 1.93045i) q^{45} -12.1369 q^{47} +(5.97879 + 3.64061i) q^{49} +(4.83907 - 11.3874i) q^{51} +(-2.38665 - 4.13380i) q^{53} +10.6307 q^{55} +(-13.8211 + 1.69136i) q^{57} +9.58058 q^{59} -9.49962 q^{61} +(-4.17260 + 6.75199i) q^{63} +5.34252 q^{65} +10.9889 q^{67} +(-0.601415 + 1.41526i) q^{69} -4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(-3.64635 + 0.446224i) q^{75} +(7.53949 - 7.36543i) q^{77} -1.02997 q^{79} +(-7.62474 - 4.78157i) q^{81} +(-5.26656 - 9.12195i) q^{83} +(9.53125 - 16.5086i) q^{85} +(1.82947 - 4.30514i) q^{87} +(1.72788 - 2.99278i) q^{89} +(3.78900 - 3.70153i) q^{91} +(-1.28132 - 1.70179i) q^{93} -21.4524 q^{95} +(-1.12061 - 1.94096i) q^{97} +(8.29516 + 8.60376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.04182	+	1.38370i	0.601493	+	0.798878i
$3$	1.04182	+	1.38370i	0.601493	+	0.798878i
$4$		0			0
$5$	1.33425	+	2.31099i	0.596696	+	1.03351i	0.993305	+	0.115520i	$0.0368535\pi$
$5$	1.33425	+	2.31099i	0.596696	+	1.03351i	−0.396609	+	0.917988i	$0.629813\pi$
$6$		0			0
$7$	2.54743	+	0.714566i	0.962838	+	0.270081i
$7$	2.54743	+	0.714566i	0.962838	+	0.270081i
$8$		0			0
$9$	−0.829236	+	2.88312i	−0.276412	+	0.961039i
$10$		0			0
$11$	1.99189	−	3.45005i	0.600577	−	1.04023i	−0.392157	−	0.919898i	$-0.628271\pi$
$11$	1.99189	−	3.45005i	0.600577	−	1.04023i	0.992734	−	0.120332i	$-0.0383958\pi$
$12$		0			0
$13$	1.00103	−	1.73384i	0.277636	−	0.480880i	−0.693161	−	0.720783i	$-0.743782\pi$
$13$	1.00103	−	1.73384i	0.277636	−	0.480880i	0.970797	+	0.239903i	$0.0771156\pi$
$14$		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
$21$	1.66521	+	4.26932i	0.363379	+	0.931641i
$22$		0			0
$23$	0.443909	+	0.768873i	0.0925614	+	0.160321i	0.908588	−	0.417693i	$-0.137161\pi$
$23$	0.443909	+	0.768873i	0.0925614	+	0.160321i	−0.816027	+	0.578014i	$0.803828\pi$
$24$		0			0
$25$	−1.06046	+	1.83677i	−0.212092	+	0.367355i
$26$		0			0
$27$	−4.85327	+	1.85627i	−0.934013	+	0.357239i
$28$		0			0
$29$	−1.35035	−	2.33887i	−0.250753	−	0.434317i	0.712980	−	0.701184i	$-0.247345\pi$
$29$	−1.35035	−	2.33887i	−0.250753	−	0.434317i	−0.963733	+	0.266867i	$0.914012\pi$
$30$		0			0
$31$	−1.22989			−0.220894			−0.110447	−	0.993882i	$-0.535228\pi$
$31$	−1.22989			−0.220894			−0.110447	+	0.993882i	$0.535228\pi$
$32$		0			0
$33$	6.84901	−	0.838152i	1.19226	−	0.145903i
$34$		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
$39$	3.44200	−	0.421217i	0.551161	−	0.0674486i
$40$		0			0
$41$	−1.43477	+	2.48509i	−0.224073	+	0.388105i	−0.956041	−	0.293234i	$-0.905269\pi$
$41$	−1.43477	+	2.48509i	−0.224073	+	0.388105i	0.731968	+	0.681339i	$0.238602\pi$
$42$		0			0
$43$	3.40053	+	5.88989i	0.518576	+	0.898200i	0.999767	+	0.0215840i	$0.00687093\pi$
$43$	3.40053	+	5.88989i	0.518576	+	0.898200i	−0.481191	+	0.876616i	$0.659796\pi$
$44$		0			0
$45$	−7.76928	+	1.93045i	−1.15818	+	0.287774i
$46$		0			0
$47$	−12.1369			−1.77035			−0.885175	−	0.465258i	$-0.845961\pi$
$47$	−12.1369			−1.77035			−0.885175	+	0.465258i	$0.845961\pi$
$48$		0			0
$49$	5.97879	+	3.64061i	0.854113	+	0.520088i
$50$		0			0
$51$	4.83907	−	11.3874i	0.677606	−	1.59455i
$52$		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
$59$	9.58058			1.24729			0.623643	−	0.781710i	$-0.285652\pi$
$59$	9.58058			1.24729			0.623643	+	0.781710i	$0.285652\pi$
$60$		0			0
$61$	−9.49962			−1.21630			−0.608151	−	0.793821i	$-0.708089\pi$
$61$	−9.49962			−1.21630			−0.608151	+	0.793821i	$0.708089\pi$
$62$		0			0
$63$	−4.17260	+	6.75199i	−0.525698	+	0.850671i
$64$		0			0
$65$	5.34252			0.662658
$66$		0			0
$67$	10.9889			1.34251			0.671255	−	0.741227i	$-0.265756\pi$
$67$	10.9889			1.34251			0.671255	+	0.741227i	$0.265756\pi$
$68$		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
$75$	−3.64635	+	0.446224i	−0.421044	+	0.0515255i
$76$		0			0
$77$	7.53949	−	7.36543i	0.859204	−	0.839368i
$78$		0			0
$79$	−1.02997			−0.115881			−0.0579406	−	0.998320i	$-0.518453\pi$
$79$	−1.02997			−0.115881			−0.0579406	+	0.998320i	$0.518453\pi$
$80$		0			0
$81$	−7.62474	−	4.78157i	−0.847193	−	0.531285i
$82$		0			0
$83$	−5.26656	−	9.12195i	−0.578080	−	1.00126i	−0.995699	−	0.0926419i	$-0.970469\pi$
$83$	−5.26656	−	9.12195i	−0.578080	−	1.00126i	0.417620	−	0.908622i	$-0.362865\pi$
$84$		0			0
$85$	9.53125	−	16.5086i	1.03381	−	1.79061i
$86$		0			0
$87$	1.82947	−	4.30514i	0.196140	−	0.461560i
$88$		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
$93$	−1.28132	−	1.70179i	−0.132866	−	0.176467i
$94$		0			0
$95$	−21.4524			−2.20097
$96$		0			0
$97$	−1.12061	−	1.94096i	−0.113781	−	0.197075i	0.803511	−	0.595290i	$-0.202963\pi$
$97$	−1.12061	−	1.94096i	−0.113781	−	0.197075i	−0.917292	+	0.398216i	$0.869630\pi$
$98$		0			0
$99$	8.29516	+	8.60376i	0.833695	+	0.864710i
$100$		0			0
$101$	2.28415	−	3.95626i	0.227281	−	0.393663i	−0.729720	−	0.683746i	$-0.760350\pi$
$101$	2.28415	−	3.95626i	0.227281	−	0.393663i	0.957001	+	0.290083i	$0.0936830\pi$
$102$		0			0
$103$	6.37509	+	11.0420i	0.628156	+	1.08800i	0.987922	+	0.154955i	$0.0495233\pi$
$103$	6.37509	+	11.0420i	0.628156	+	1.08800i	−0.359766	+	0.933043i	$0.617143\pi$
$104$		0			0
$105$	−7.64456	+	9.54464i	−0.746032	+	0.931462i
$106$		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	−0.888723	−	0.458444i	$-0.848407\pi$
$113$	−0.503200	+	0.871568i	−0.0473371	+	0.0819903i	0.841386	+	0.540435i	$0.181740\pi$
$114$		0			0
$115$	−1.18457	+	2.05174i	−0.110462	+	0.191326i
$116$		0			0
$117$	4.16877	+	4.32385i	0.385403	+	0.399740i
$118$		0			0
$119$	−4.67815	−	18.3118i	−0.428846	−	1.67864i
$120$		0			0
$121$	−2.43524	−	4.21796i	−0.221386	−	0.383451i
$122$		0			0
$123$	−4.93337	+	0.603724i	−0.444827	+	0.0544360i
$124$		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
$129$	−4.60709	+	10.8415i	−0.405632	+	0.954540i
$130$		0			0
$131$	0.164862	+	0.285550i	0.0144041	+	0.0249486i	0.873138	−	0.487474i	$-0.162082\pi$
$131$	0.164862	+	0.285550i	0.0144041	+	0.0249486i	−0.858734	+	0.512422i	$0.828748\pi$
$132$		0			0
$133$	−15.2144	+	14.8632i	−1.31926	+	1.28880i
$134$		0			0
$135$	−10.7653	−	8.73915i	−0.926531	−	0.752147i
$136$		0			0
$137$	−4.47095	+	7.74391i	−0.381979	+	0.661607i	−0.991345	−	0.131282i	$-0.958091\pi$
$137$	−4.47095	+	7.74391i	−0.381979	+	0.661607i	0.609366	+	0.792889i	$0.291424\pi$
$138$		0			0
$139$	3.92869	−	6.80470i	0.333227	−	0.577167i	−0.649915	−	0.760007i	$-0.725196\pi$
$139$	3.92869	−	6.80470i	0.333227	−	0.577167i	0.983143	+	0.182840i	$0.0585290\pi$
$140$		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
$147$	1.19129	+	12.0657i	0.0982563	+	0.995161i
$148$		0			0
$149$	−8.16075	−	14.1348i	−0.668554	−	1.15797i	−0.978308	−	0.207153i	$-0.933580\pi$
$149$	−8.16075	−	14.1348i	−0.668554	−	1.15797i	0.309754	−	0.950817i	$-0.399753\pi$
$150$		0			0
$151$	2.31677	−	4.01276i	0.188536	−	0.326554i	−0.756226	−	0.654310i	$-0.772959\pi$
$151$	2.31677	−	4.01276i	0.188536	−	0.326554i	0.944762	+	0.327756i	$0.106292\pi$
$152$		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
$157$	−8.51852			−0.679852			−0.339926	−	0.940452i	$-0.610402\pi$
$157$	−8.51852			−0.679852			−0.339926	+	0.940452i	$0.610402\pi$
$158$		0			0
$159$	3.23348	−	7.60907i	0.256431	−	0.603438i
$160$		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
$165$	11.0753	+	14.7097i	0.862209	+	1.14515i
$166$		0			0
$167$	−0.0713948	+	0.123659i	−0.00552470	+	0.00956906i	−0.868775	−	0.495208i	$-0.835092\pi$
$167$	−0.0713948	+	0.123659i	−0.00552470	+	0.00956906i	0.863250	+	0.504777i	$0.168425\pi$
$168$		0			0
$169$	4.49587	+	7.78708i	0.345836	+	0.599006i
$170$		0			0
$171$	−16.7393	−	17.3621i	−1.28009	−	1.32771i
$172$		0			0
$173$	17.9967			1.36826			0.684131	−	0.729359i	$-0.260182\pi$
$173$	17.9967			1.36826			0.684131	+	0.729359i	$0.260182\pi$
$174$		0			0
$175$	−4.01395	+	3.92128i	−0.303426	+	0.296421i
$176$		0			0
$177$	9.98121	+	13.2566i	0.750234	+	0.996429i
$178$		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
$185$	28.1009			2.06602
$186$		0			0
$187$	−28.4582			−2.08107
$188$		0			0
$189$	−13.6898	+	1.26073i	−0.995786	+	0.0917044i
$190$		0			0
$191$	18.8091			1.36098			0.680491	−	0.732757i	$-0.261767\pi$
$191$	18.8091			1.36098			0.680491	+	0.732757i	$0.261767\pi$
$192$		0			0
$193$	6.48714			0.466954			0.233477	−	0.972362i	$-0.424990\pi$
$193$	6.48714			0.466954			0.233477	+	0.972362i	$0.424990\pi$
$194$		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
$201$	11.4484	+	15.2053i	0.807510	+	1.07250i
$202$		0			0
$203$	−1.76863	−	6.92301i	−0.124134	−	0.485900i
$204$		0			0
$205$	−7.65736			−0.534813
$206$		0			0
$207$	−2.58486	+	0.642265i	−0.179660	+	0.0446405i
$208$		0			0
$209$	16.0130	+	27.7354i	1.10764	+	1.91850i
$210$		0			0
$211$	−11.9133	+	20.6344i	−0.820145	+	1.42053i	0.0854297	+	0.996344i	$0.472774\pi$
$211$	−11.9133	+	20.6344i	−0.820145	+	1.42053i	−0.905574	+	0.424188i	$0.860560\pi$
$212$		0			0
$213$	−4.82244	−	6.40497i	−0.330428	−	0.438861i
$214$		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
$219$	−2.72324	+	6.40836i	−0.184019	+	0.433037i
$220$		0			0
$221$	−14.3018			−0.962041
$222$		0			0
$223$	6.53734	+	11.3230i	0.437773	+	0.758245i	0.997517	−	0.0704203i	$-0.0224341\pi$
$223$	6.53734	+	11.3230i	0.437773	+	0.758245i	−0.559745	+	0.828665i	$0.689101\pi$
$224$		0			0
$225$	−4.41626	−	4.58056i	−0.294418	−	0.305371i
$226$		0			0
$227$	−11.5845	+	20.0649i	−0.768890	+	1.33176i	0.169275	+	0.985569i	$0.445858\pi$
$227$	−11.5845	+	20.0649i	−0.768890	+	1.33176i	−0.938165	+	0.346188i	$0.887476\pi$
$228$		0			0
$229$	10.7794	+	18.6705i	0.712323	+	1.23378i	0.963983	+	0.265964i	$0.0856904\pi$
$229$	10.7794	+	18.6705i	0.712323	+	1.23378i	−0.251660	+	0.967816i	$0.580976\pi$
$230$		0			0
$231$	18.0463	+	2.75894i	1.18736	+	0.181525i
$232$		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	−0.858953	−	0.512054i	$-0.828885\pi$
$239$	0.216059	−	0.374225i	0.0139757	−	0.0242066i	0.872929	+	0.487848i	$0.162218\pi$
$240$		0			0
$241$	−1.52837	+	2.64721i	−0.0984509	+	0.170522i	−0.911044	−	0.412310i	$-0.864722\pi$
$241$	−1.52837	+	2.64721i	−0.0984509	+	0.170522i	0.812593	+	0.582832i	$0.198055\pi$
$242$		0			0
$243$	−1.32733	−	15.5318i	−0.0851486	−	0.996368i
$244$		0			0
$245$	−0.436221	+	18.6744i	−0.0278691	+	1.19307i
$246$		0			0
$247$	8.04741	+	13.9385i	0.512045	+	0.886887i
$248$		0			0
$249$	7.13522	−	16.7907i	0.452176	−	1.06407i
$250$		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
$255$	32.7727	−	4.01058i	2.05231	−	0.251152i
$256$		0			0
$257$	15.9726	+	27.6654i	0.996346	+	1.72572i	0.572142	+	0.820155i	$0.306113\pi$
$257$	15.9726	+	27.6654i	0.996346	+	1.72572i	0.424204	+	0.905567i	$0.360554\pi$
$258$		0			0
$259$	19.9296	−	19.4695i	1.23836	−	1.20977i
$260$		0			0
$261$	7.86299	−	1.95373i	0.486707	−	0.120933i
$262$		0			0
$263$	−3.35495	+	5.81094i	−0.206875	+	0.358318i	−0.950728	−	0.310025i	$-0.899663\pi$
$263$	−3.35495	+	5.81094i	−0.206875	+	0.358318i	0.743854	+	0.668343i	$0.232996\pi$
$264$		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
$273$	9.06924	+	1.38652i	0.548895	+	0.0839159i
$274$		0			0
$275$	4.22465	+	7.31730i	0.254756	+	0.441250i
$276$		0			0
$277$	10.6433	−	18.4347i	0.639492	−	1.10763i	−0.346052	−	0.938215i	$-0.612478\pi$
$277$	10.6433	−	18.4347i	0.639492	−	1.10763i	0.985544	−	0.169418i	$-0.0541886\pi$
$278$		0			0
$279$	1.01987	−	3.54591i	0.0610578	−	0.212288i
$280$		0			0
$281$	−6.26945	−	10.8590i	−0.374004	−	0.647794i	0.616174	−	0.787610i	$-0.288682\pi$
$281$	−6.26945	−	10.8590i	−0.374004	−	0.647794i	−0.990177	+	0.139817i	$0.955349\pi$
$282$		0			0
$283$	24.9497			1.48311			0.741554	−	0.670893i	$-0.234089\pi$
$283$	24.9497			1.48311			0.741554	+	0.670893i	$0.234089\pi$
$284$		0			0
$285$	−22.3495	−	29.6837i	−1.32387	−	1.75831i
$286$		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
$291$	1.51823	−	3.57271i	0.0890000	−	0.209436i
$292$		0			0
$293$	7.42625	−	12.8626i	0.433846	−	0.751443i	−0.563355	−	0.826215i	$-0.690490\pi$
$293$	7.42625	−	12.8626i	0.433846	−	0.751443i	0.997201	+	0.0747718i	$0.0238228\pi$
$294$		0			0
$295$	12.7829	+	22.1407i	0.744250	+	1.28908i
$296$		0			0
$297$	−3.26295	+	20.4415i	−0.189336	+	1.18614i
$298$		0			0
$299$	1.77747			0.102794
$300$		0			0
$301$	4.45389	+	17.4340i	0.256718	+	1.00488i
$302$		0			0
$303$	7.85393	−	0.961129i	0.451197	−	0.0552154i
$304$		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
$311$	−17.5672			−0.996143			−0.498072	−	0.867136i	$-0.665958\pi$
$311$	−17.5672			−0.996143			−0.498072	+	0.867136i	$0.665958\pi$
$312$		0			0
$313$	−11.9764			−0.676946			−0.338473	−	0.940976i	$-0.609910\pi$
$313$	−11.9764			−0.676946			−0.338473	+	0.940976i	$0.609910\pi$
$314$		0			0
$315$	−21.1711	−	0.633982i	−1.19286	−	0.0357208i
$316$		0			0
$317$	−1.73327			−0.0973499			−0.0486750	−	0.998815i	$-0.515500\pi$
$317$	−1.73327			−0.0973499			−0.0486750	+	0.998815i	$0.515500\pi$
$318$		0			0
$319$	−10.7590			−0.602386
$320$		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
$327$	8.56231	−	20.1490i	0.473497	−	1.11424i
$328$		0			0
$329$	−30.9179	−	8.67263i	−1.70456	−	0.478137i
$330$		0			0
$331$	−0.726254			−0.0399185			−0.0199593	−	0.999801i	$-0.506354\pi$
$331$	−0.726254			−0.0399185			−0.0199593	+	0.999801i	$0.506354\pi$
$332$		0			0
$333$	21.9271	+	22.7428i	1.20160	+	1.24630i
$334$		0			0
$335$	14.6620	+	25.3953i	0.801070	+	1.38749i
$336$		0			0
$337$	−6.84810	+	11.8613i	−0.373040	+	0.646124i	−0.990032	−	0.140846i	$-0.955018\pi$
$337$	−6.84810	+	11.8613i	−0.373040	+	0.646124i	0.616992	+	0.786970i	$0.288351\pi$
$338$		0			0
$339$	−1.73023	+	0.211738i	−0.0939732	+	0.0115000i
$340$		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
$345$	−4.07310	+	0.498448i	−0.219288	+	0.0268355i
$346$		0			0
$347$	−4.21417			−0.226229			−0.113114	−	0.993582i	$-0.536083\pi$
$347$	−4.21417			−0.226229			−0.113114	+	0.993582i	$0.536083\pi$
$348$		0			0
$349$	−10.8070	−	18.7183i	−0.578486	−	1.00197i	−0.995653	−	0.0931372i	$-0.970310\pi$
$349$	−10.8070	−	18.7183i	−0.578486	−	1.00197i	0.417167	−	0.908830i	$-0.363023\pi$
$350$		0			0
$351$	−1.63981	+	10.2730i	−0.0875267	+	0.548331i
$352$		0			0
$353$	−2.42558	+	4.20122i	−0.129100	+	0.223609i	−0.923328	−	0.384012i	$-0.874542\pi$
$353$	−2.42558	+	4.20122i	−0.129100	+	0.223609i	0.794228	+	0.607620i	$0.207876\pi$
$354$		0			0
$355$	−6.17609	−	10.6973i	−0.327793	−	0.567754i
$356$		0			0
$357$	20.4642	−	25.5507i	1.08308	−	1.35229i
$358$		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
$367$	−10.8445	+	18.7832i	−0.566078	+	0.980476i	0.430871	+	0.902414i	$0.358207\pi$
$367$	−10.8445	+	18.7832i	−0.566078	+	0.980476i	−0.996949	+	0.0780619i	$0.975127\pi$
$368$		0			0
$369$	−5.97504	−	6.19732i	−0.311048	−	0.322620i
$370$		0			0
$371$	−3.12595	−	12.2360i	−0.162291	−	0.635261i
$372$		0			0
$373$	−12.3552	−	21.3999i	−0.639729	−	1.10804i	−0.985492	−	0.169721i	$-0.945713\pi$
$373$	−12.3552	−	21.3999i	−0.639729	−	1.10804i	0.345764	−	0.938322i	$-0.387620\pi$
$374$		0			0
$375$	8.00410	+	10.6307i	0.413330	+	0.548967i
$376$		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
$381$	1.44188	+	1.91504i	0.0738695	+	0.0981104i
$382$		0			0
$383$	10.3113	+	17.8598i	0.526884	+	0.912591i	0.999509	+	0.0313269i	$0.00997329\pi$
$383$	10.3113	+	17.8598i	0.526884	+	0.912591i	−0.472625	+	0.881264i	$0.656693\pi$
$384$		0			0
$385$	27.0810	+	7.59637i	1.38018	+	0.387147i
$386$		0			0
$387$	−19.8011	+	4.92002i	−1.00655	+	0.250099i
$388$		0			0
$389$	−8.70035	+	15.0694i	−0.441125	+	0.764051i	−0.997773	−	0.0666973i	$-0.978754\pi$
$389$	−8.70035	+	15.0694i	−0.441125	+	0.764051i	0.556648	+	0.830748i	$0.312087\pi$
$390$		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
$399$	−36.4167	−	5.56744i	−1.82312	−	0.278721i
$400$		0			0
$401$	−3.85264	−	6.67297i	−0.192392	−	0.333232i	0.753651	−	0.657275i	$-0.228291\pi$
$401$	−3.85264	−	6.67297i	−0.192392	−	0.333232i	−0.946042	+	0.324043i	$0.894958\pi$
$402$		0			0
$403$	−1.23116	+	2.13242i	−0.0613282	+	0.106224i
$404$		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
$409$	−15.7351			−0.778050			−0.389025	−	0.921227i	$-0.627188\pi$
$409$	−15.7351			−0.778050			−0.389025	+	0.921227i	$0.627188\pi$
$410$		0			0
$411$	−15.3731	+	1.88130i	−0.758301	+	0.0927975i
$412$		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
$417$	13.5086	−	1.65313i	0.661520	−	0.0809539i
$418$		0			0
$419$	−17.3452	+	30.0428i	−0.847369	+	1.46769i	0.0361784	+	0.999345i	$0.488482\pi$
$419$	−17.3452	+	30.0428i	−0.847369	+	1.46769i	−0.883548	+	0.468341i	$0.844852\pi$
$420$		0			0
$421$	−0.607053	−	1.05145i	−0.0295860	−	0.0512444i	0.850853	−	0.525403i	$-0.176086\pi$
$421$	−0.607053	−	1.05145i	−0.0295860	−	0.0512444i	−0.880439	+	0.474159i	$0.842752\pi$
$422$		0			0
$423$	10.0644	−	34.9921i	0.489346	−	1.70138i
$424$		0			0
$425$	15.1508			0.734924
$426$		0			0
$427$	−24.1996	−	6.78811i	−1.17110	−	0.328500i
$428$		0			0
$429$	5.40286	−	12.7141i	0.260853	−	0.613842i
$430$		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
$437$	−7.13727			−0.341422
$438$		0			0
$439$	−33.0789			−1.57877			−0.789385	−	0.613898i	$-0.789600\pi$
$439$	−33.0789			−1.57877			−0.789385	+	0.613898i	$0.789600\pi$
$440$		0			0
$441$	−15.4541	+	14.2186i	−0.735912	+	0.677077i
$442$		0			0
$443$	2.73364			0.129879			0.0649397	−	0.997889i	$-0.479315\pi$
$443$	2.73364			0.129879			0.0649397	+	0.997889i	$0.479315\pi$
$444$		0			0
$445$	9.22172			0.437152
$446$		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
$453$	7.96609	−	0.974855i	0.374280	−	0.0458027i
$454$		0			0
$455$	13.6097	+	3.81759i	0.638032	+	0.178971i
$456$		0			0
$457$	3.36324			0.157326			0.0786628	−	0.996901i	$-0.474935\pi$
$457$	3.36324			0.157326			0.0786628	+	0.996901i	$0.474935\pi$
$458$		0			0
$459$	28.8184	+	23.3944i	1.34513	+	1.09196i
$460$		0			0
$461$	−10.0040	−	17.3275i	−0.465934	−	0.807021i	0.533309	−	0.845920i	$-0.320948\pi$
$461$	−10.0040	−	17.3275i	−0.465934	−	0.807021i	−0.999243	+	0.0388994i	$0.987615\pi$
$462$		0			0
$463$	7.29434	−	12.6342i	0.338997	−	0.587160i	−0.645247	−	0.763974i	$-0.723246\pi$
$463$	7.29434	−	12.6342i	0.338997	−	0.587160i	0.984244	+	0.176814i	$0.0565791\pi$
$464$		0			0
$465$	2.22323	−	5.23173i	0.103100	−	0.242616i
$466$		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
$471$	−8.87474	−	11.7871i	−0.408926	−	0.543119i
$472$		0			0
$473$	27.0939			1.24578
$474$		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
$479$	5.66216	−	9.80714i	0.258710	−	0.448100i	−0.707186	−	0.707027i	$-0.750036\pi$
$479$	5.66216	−	9.80714i	0.258710	−	0.448100i	0.965897	+	0.258928i	$0.0833691\pi$
$480$		0			0
$481$	−10.5414	−	18.2583i	−0.480648	−	0.832506i
$482$		0			0
$483$	−2.54336	+	3.17552i	−0.115727	+	0.144491i
$484$		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	−0.459180	−	0.888343i	$-0.651857\pi$
$491$	11.9598	−	20.7150i	0.539738	−	0.934853i	0.998918	−	0.0465101i	$-0.0148100\pi$
$492$		0			0
$493$	−9.64621	+	16.7077i	−0.434443	+	0.752478i
$494$		0			0
$495$	−8.81538	+	30.6497i	−0.396222	+	1.37760i
$496$		0			0
$497$	−11.7917	−	3.30764i	−0.528932	−	0.148368i
$498$		0			0
$499$	0.225984	+	0.391416i	0.0101164	+	0.0175222i	0.871039	−	0.491213i	$-0.163446\pi$
$499$	0.225984	+	0.391416i	0.0101164	+	0.0175222i	−0.860923	+	0.508736i	$0.830113\pi$
$500$		0			0
$501$	−0.245488	+	0.0300417i	−0.0109676	+	0.00134216i
$502$		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
$507$	−6.09108	+	14.3336i	−0.270514	+	0.636579i
$508$		0			0
$509$	0.246585	+	0.427099i	0.0109297	+	0.0189308i	0.871439	−	0.490505i	$-0.163188\pi$
$509$	0.246585	+	0.427099i	0.0109297	+	0.0189308i	−0.860509	+	0.509436i	$0.829854\pi$
$510$		0			0
$511$	2.63268	+	10.3052i	0.116463	+	0.455874i
$512$		0			0
$513$	6.58452	−	41.2503i	0.290714	−	1.82124i
$514$		0			0
$515$	−17.0120	+	29.4656i	−0.749636	+	1.29841i
$516$		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
$525$	−9.60767	−	1.46883i	−0.419313	−	0.0641052i
$526$		0			0
$527$	4.39285	+	7.60865i	0.191356	+	0.331438i
$528$		0			0
$529$	11.1059	−	19.2360i	0.482865	−	0.836346i
$530$		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
$535$	−3.52115			−0.152233
$536$		0			0
$537$	1.38750	−	3.26510i	0.0598752	−	0.140899i
$538$		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
$543$	1.88741	+	2.50677i	0.0809963	+	0.107576i
$544$		0			0
$545$	16.8647	−	29.2105i	0.722404	−	1.25124i
$546$		0			0
$547$	−15.2496	−	26.4132i	−0.652028	−	1.12935i	−0.982630	−	0.185575i	$-0.940585\pi$
$547$	−15.2496	−	26.4132i	−0.652028	−	1.12935i	0.330602	−	0.943770i	$-0.392748\pi$
$548$		0			0
$549$	7.87743	−	27.3885i	0.336200	−	1.16891i
$550$		0			0
$551$	21.7112			0.924927
$552$		0			0
$553$	−2.62379	−	0.735985i	−0.111575	−	0.0312973i
$554$		0			0
$555$	29.2760	+	38.8831i	1.24270	+	1.65050i
$556$		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
$563$	2.62822			0.110766			0.0553831	−	0.998465i	$-0.482362\pi$
$563$	2.62822			0.110766			0.0553831	+	0.998465i	$0.482362\pi$
$564$		0			0
$565$	−2.68559			−0.112983
$566$		0			0
$567$	−16.0067	−	17.6291i	−0.672219	−	0.740352i
$568$		0			0
$569$	−32.1162			−1.34638			−0.673191	−	0.739469i	$-0.735077\pi$
$569$	−32.1162			−1.34638			−0.673191	+	0.739469i	$0.735077\pi$
$570$		0			0
$571$	41.1815			1.72339			0.861696	−	0.507425i	$-0.169403\pi$
$571$	41.1815			1.72339			0.861696	+	0.507425i	$0.169403\pi$
$572$		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
$579$	6.75841	+	8.97623i	0.280870	+	0.373040i
$580$		0			0
$581$	−6.89795	−	27.0008i	−0.286175	−	1.12018i
$582$		0			0
$583$	−19.0158			−0.787553
$584$		0			0
$585$	−4.43021	+	15.4031i	−0.183167	+	0.636840i
$586$		0			0
$587$	−3.98618	−	6.90426i	−0.164527	−	0.284969i	0.771960	−	0.635671i	$-0.219277\pi$
$587$	−3.98618	−	6.90426i	−0.164527	−	0.284969i	−0.936487	+	0.350702i	$0.885943\pi$
$588$		0			0
$589$	4.94360	−	8.56257i	0.203698	−	0.352815i
$590$		0			0
$591$	−11.2887	−	14.9932i	−0.464357	−	0.616739i
$592$		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
$597$	12.7877	−	30.0923i	0.523368	−	1.23160i
$598$		0			0
$599$	−37.3771			−1.52719			−0.763594	−	0.645696i	$-0.776567\pi$
$599$	−37.3771			−1.52719			−0.763594	+	0.645696i	$0.776567\pi$
$600$		0			0
$601$	6.81596	+	11.8056i	0.278029	+	0.481560i	0.970895	−	0.239506i	$-0.0769856\pi$
$601$	6.81596	+	11.8056i	0.278029	+	0.481560i	−0.692866	+	0.721066i	$0.743652\pi$
$602$		0			0
$603$	−9.11240	+	31.6823i	−0.371086	+	1.29020i
$604$		0			0
$605$	6.49846	−	11.2557i	0.264200	−	0.457607i
$606$		0			0
$607$	−1.37114	−	2.37489i	−0.0556529	−	0.0963937i	0.836857	−	0.547422i	$-0.184391\pi$
$607$	−1.37114	−	2.37489i	−0.0556529	−	0.0963937i	−0.892510	+	0.451028i	$0.851057\pi$
$608$		0			0
$609$	7.73676	−	9.65976i	0.313509	−	0.391433i
$610$		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	−0.490467	−	0.871460i	$-0.663174\pi$
$617$	12.6551	−	21.9192i	0.509473	−	0.882433i	0.999940	−	0.0109734i	$-0.00349302\pi$
$618$		0			0
$619$	13.5808	−	23.5226i	0.545859	−	0.945455i	−0.452694	−	0.891666i	$-0.649537\pi$
$619$	13.5808	−	23.5226i	0.545859	−	0.945455i	0.998552	−	0.0537888i	$-0.0171298\pi$
$620$		0			0
$621$	−3.58165	−	2.90754i	−0.143727	−	0.116675i
$622$		0			0
$623$	6.54019	−	6.38920i	0.262027	−	0.255978i
$624$		0			0
$625$	15.5532	+	26.9388i	0.622126	+	1.07755i
$626$		0			0
$627$	−21.6947	+	51.0524i	−0.866404	+	2.03883i
$628$		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
$633$	−40.9633	+	5.01290i	−1.62814	+	0.199245i
$634$		0			0
$635$	1.84661	+	3.19842i	0.0732804	+	0.126925i
$636$		0			0
$637$	12.2972	−	6.72188i	0.487233	−	0.266331i
$638$		0			0
$639$	3.83843	−	13.3456i	0.151846	−	0.527944i
$640$		0			0
$641$	−21.0987	+	36.5441i	−0.833350	+	1.44340i	0.0620175	+	0.998075i	$0.480247\pi$
$641$	−21.0987	+	36.5441i	−0.833350	+	1.44340i	−0.895367	+	0.445329i	$0.853087\pi$
$642$		0			0
$643$	10.1099	−	17.5109i	0.398696	−	0.690562i	−0.594869	−	0.803823i	$-0.702796\pi$
$643$	10.1099	−	17.5109i	0.398696	−	0.690562i	0.993565	+	0.113260i	$0.0361294\pi$
$644$		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
$651$	−2.04802	−	5.25078i	−0.0802682	−	0.205794i
$652$		0			0
$653$	17.0535	+	29.5375i	0.667354	+	1.15589i	0.978641	+	0.205575i	$0.0659063\pi$
$653$	17.0535	+	29.5375i	0.667354	+	1.15589i	−0.311288	+	0.950316i	$0.600760\pi$
$654$		0			0
$655$	−0.439936	+	0.761991i	−0.0171897	+	0.0297734i
$656$		0			0
$657$	−11.7044	+	2.90821i	−0.456630	+	0.113460i
$658$		0			0
$659$	−0.994211	−	1.72202i	−0.0387290	−	0.0670805i	0.846011	−	0.533165i	$-0.178998\pi$
$659$	−0.994211	−	1.72202i	−0.0387290	−	0.0670805i	−0.884740	+	0.466085i	$0.845664\pi$
$660$		0			0
$661$	−8.48409			−0.329993			−0.164997	−	0.986294i	$-0.552761\pi$
$661$	−8.48409			−0.329993			−0.164997	+	0.986294i	$0.552761\pi$
$662$		0			0
$663$	−14.8998	−	19.7893i	−0.578661	−	0.768553i
$664$		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
$669$	−8.85690	+	20.8422i	−0.342428	+	0.805806i
$670$		0			0
$671$	−18.9222	+	32.7742i	−0.730483	+	1.26523i
$672$		0			0
$673$	22.4056	+	38.8077i	0.863674	+	1.49593i	0.868358	+	0.495938i	$0.165176\pi$
$673$	22.4056	+	38.8077i	0.863674	+	1.49593i	−0.00468438	+	0.999989i	$0.501491\pi$
$674$		0			0
$675$	1.73717	−	10.8829i	0.0668635	−	0.418882i
$676$		0			0
$677$	8.05367			0.309528			0.154764	−	0.987951i	$-0.450538\pi$
$677$	8.05367			0.309528			0.154764	+	0.987951i	$0.450538\pi$
$678$		0			0
$679$	−1.46774	−	5.74521i	−0.0563267	−	0.220481i
$680$		0			0
$681$	−39.8327	+	4.87455i	−1.52639	+	0.186793i
$682$		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
$689$	−9.55646			−0.364072
$690$		0			0
$691$	11.3269			0.430895			0.215448	−	0.976515i	$-0.430879\pi$
$691$	11.3269			0.430895			0.215448	+	0.976515i	$0.430879\pi$
$692$		0			0
$693$	14.9834	+	27.8449i	0.569172	+	1.05774i
$694$		0			0
$695$	20.9675			0.795342
$696$		0			0
$697$	20.4985			0.776437
$698$		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
$705$	21.9395	−	51.6284i	0.826290	−	1.94444i
$706$		0			0
$707$	8.64572	−	8.44612i	0.325156	−	0.317649i
$708$		0			0
$709$	45.2147			1.69807			0.849037	−	0.528333i	$-0.177183\pi$
$709$	45.2147			1.69807			0.849037	+	0.528333i	$0.177183\pi$
$710$		0			0
$711$	0.854092	−	2.96954i	0.0320309	−	0.111366i
$712$		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
$717$	0.742908	−	0.0909139i	0.0277444	−	0.00339524i
$718$		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
$723$	−5.25522	+	0.643111i	−0.195444	+	0.0239175i
$724$		0			0
$725$	5.72797			0.212731
$726$		0			0
$727$	1.04956	+	1.81789i	0.0389259	+	0.0674217i	0.884832	−	0.465910i	$-0.154273\pi$
$727$	1.04956	+	1.81789i	0.0389259	+	0.0674217i	−0.845906	+	0.533332i	$0.820940\pi$
$728$		0			0
$729$	20.1085	−	18.0180i	0.744760	−	0.667332i
$730$		0			0
$731$	24.2917	−	42.0745i	0.898461	−	1.55618i
$732$		0			0
$733$	15.6453	+	27.0985i	0.577872	+	1.00090i	0.995723	+	0.0923886i	$0.0294502\pi$
$733$	15.6453	+	27.0985i	0.577872	+	1.00090i	−0.417851	+	0.908516i	$0.637216\pi$
$734$		0			0
$735$	−26.2942	+	18.8518i	−0.969878	+	0.695357i
$736$		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	−0.722208	−	0.691676i	$-0.756873\pi$
$743$	6.48482	−	11.2320i	0.237905	−	0.412064i	0.960113	+	0.279612i	$0.0902060\pi$
$744$		0			0
$745$	21.7770	−	37.7189i	0.797848	−	1.38191i
$746$		0			0
$747$	30.6669	−	7.61986i	1.12204	−	0.278796i
$748$		0			0
$749$	−2.49726	+	2.43960i	−0.0912478	+	0.0891412i
$750$		0			0
$751$	−16.3649	−	28.3448i	−0.597164	−	1.03432i	−0.993238	−	0.116099i	$-0.962961\pi$
$751$	−16.3649	−	28.3448i	−0.597164	−	1.03432i	0.396074	−	0.918219i	$-0.370372\pi$
$752$		0			0
$753$	12.4045	+	16.4752i	0.452047	+	0.600389i
$754$		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
$759$	3.68477	+	4.89396i	0.133749	+	0.177639i
$760$		0			0
$761$	19.1468	+	33.1632i	0.694070	+	1.20217i	0.970493	+	0.241129i	$0.0775177\pi$
$761$	19.1468	+	33.1632i	0.694070	+	1.20217i	−0.276423	+	0.961036i	$0.589149\pi$
$762$		0			0
$763$	−8.27758	−	32.4011i	−0.299668	−	1.17300i
$764$		0			0
$765$	39.6926	+	41.1692i	1.43509	+	1.48848i
$766$		0			0
$767$	9.59047	−	16.6112i	0.346292	−	0.599795i
$768$		0			0
$769$	11.0674	−	19.1693i	0.399100	−	0.691262i	−0.594515	−	0.804085i	$-0.702656\pi$
$769$	11.0674	−	19.1693i	0.399100	−	0.691262i	0.993615	+	0.112823i	$0.0359892\pi$
$770$		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
$777$	47.7028	+	7.29288i	1.71133	+	0.261631i
$778$		0			0
$779$	−11.5342	−	19.9779i	−0.413257	−	0.715783i
$780$		0			0
$781$	−9.22021	+	15.9699i	−0.329925	+	0.571447i
$782$		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
$787$	−32.3046			−1.15153			−0.575767	−	0.817614i	$-0.695296\pi$
$787$	−32.3046			−1.15153			−0.575767	+	0.817614i	$0.695296\pi$
$788$		0			0
$789$	−11.5358	+	1.41170i	−0.410686	+	0.0502579i
$790$		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
$795$	21.8988	−	2.67988i	0.776670	−	0.0950454i
$796$		0			0
$797$	−11.6877	+	20.2438i	−0.414001	+	0.717071i	−0.995323	−	0.0966026i	$-0.969202\pi$
$797$	−11.6877	+	20.2438i	−0.414001	+	0.717071i	0.581322	+	0.813674i	$0.302536\pi$
$798$		0			0
$799$	43.3501	+	75.0845i	1.53361	+	2.65630i
$800$		0			0
$801$	7.19571	+	7.46340i	0.254248	+	0.263706i
$802$		0			0
$803$	16.0151			0.565161
$804$		0			0
$805$	−4.48372	+	4.38021i	−0.158030	+	0.154382i
$806$		0			0
$807$	−7.67518	+	18.0614i	−0.270179	+	0.635790i
$808$		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
$815$	6.53004			0.228737
$816$		0			0
$817$	−54.6745			−1.91282
$818$		0			0
$819$	7.52996	+	13.9936i	0.263118	+	0.488975i
$820$		0			0
$821$	−26.7575			−0.933843			−0.466921	−	0.884299i	$-0.654637\pi$
$821$	−26.7575			−0.933843			−0.466921	+	0.884299i	$0.654637\pi$
$822$		0			0
$823$	−40.4898			−1.41139			−0.705693	−	0.708517i	$-0.749364\pi$
$823$	−40.4898			−1.41139			−0.705693	+	0.708517i	$0.749364\pi$
$824$		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
$831$	36.5964	−	4.47850i	1.26951	−	0.155357i
$832$		0			0
$833$	1.16775	−	49.9909i	0.0404601	−	1.73208i
$834$		0			0
$835$	−0.381035			−0.0131863
$836$		0			0
$837$	5.96898	−	2.28300i	0.206318	−	0.0789120i
$838$		0			0
$839$	−16.6312	−	28.8061i	−0.574174	−	0.994499i	−0.996131	−	0.0878827i	$-0.971990\pi$
$839$	−16.6312	−	28.8061i	−0.574174	−	0.994499i	0.421957	−	0.906616i	$-0.361343\pi$
$840$		0			0
$841$	10.8531	−	18.7982i	0.374246	−	0.648213i
$842$		0			0
$843$	8.49395	−	19.9881i	0.292547	−	0.688427i
$844$		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
$849$	25.9930	+	34.5229i	0.892079	+	1.18482i
$850$		0			0
$851$	9.34922			0.320487
$852$		0			0
$853$	−4.38730	−	7.59902i	−0.150218	−	0.260186i	0.781089	−	0.624419i	$-0.214664\pi$
$853$	−4.38730	−	7.59902i	−0.150218	−	0.260186i	−0.931308	+	0.364234i	$0.881331\pi$
$854$		0			0
$855$	17.7891	−	61.8499i	0.608375	−	2.11522i
$856$		0			0
$857$	0.677198	−	1.17294i	0.0231327	−	0.0400669i	−0.854227	−	0.519900i	$-0.825969\pi$
$857$	0.677198	−	1.17294i	0.0231327	−	0.0400669i	0.877360	+	0.479833i	$0.159303\pi$
$858$		0			0
$859$	9.01934	+	15.6220i	0.307736	+	0.533014i	0.977867	−	0.209229i	$-0.0670953\pi$
$859$	9.01934	+	15.6220i	0.307736	+	0.533014i	−0.670131	+	0.742243i	$0.733762\pi$
$860$		0			0
$861$	−12.9988	−	1.98728i	−0.442998	−	0.0677262i
$862$		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
$871$	11.0003	−	19.0530i	0.372729	−	0.645586i
$872$		0			0
$873$	6.52527	−	1.62135i	0.220847	−	0.0548743i
$874$		0			0
$875$	19.5715	+	5.48989i	0.661636	+	0.185592i
$876$		0			0
$877$	8.79034	+	15.2253i	0.296829	+	0.514122i	0.975409	−	0.220404i	$-0.0707376\pi$
$877$	8.79034	+	15.2253i	0.296829	+	0.514122i	−0.678580	+	0.734527i	$0.737404\pi$
$878$		0			0
$879$	25.5348	−	3.12483i	0.861267	−	0.105398i
$880$		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
$885$	−17.3185	+	40.7542i	−0.582156	+	1.36994i
$886$		0			0
$887$	1.46786	+	2.54240i	0.0492858	+	0.0853655i	0.889616	−	0.456710i	$-0.150972\pi$
$887$	1.46786	+	2.54240i	0.0492858	+	0.0853655i	−0.840330	+	0.542075i	$0.817639\pi$
$888$		0			0
$889$	3.52564	+	0.988961i	0.118246	+	0.0331687i
$890$		0			0
$891$	−31.6843	+	16.7814i	−1.06146	+	0.562198i
$892$		0			0
$893$	48.7850	−	84.4981i	1.63253	−	2.82762i
$894$		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
$903$	−19.4832	+	24.3258i	−0.648361	+	0.809513i
$904$		0			0
$905$	2.41720	+	4.18671i	0.0803503	+	0.139171i
$906$		0			0
$907$	17.1395	−	29.6865i	0.569108	−	0.985723i	−0.427547	−	0.903993i	$-0.640622\pi$
$907$	17.1395	−	29.6865i	0.569108	−	0.985723i	0.996655	−	0.0817300i	$-0.0260445\pi$
$908$		0			0
$909$	9.51227	+	9.86614i	0.315502	+	0.327239i
$910$		0			0
$911$	−4.98338	−	8.63146i	−0.165107	−	0.285973i	0.771586	−	0.636124i	$-0.219464\pi$
$911$	−4.98338	−	8.63146i	−0.165107	−	0.285973i	−0.936693	+	0.350151i	$0.886130\pi$
$912$		0			0
$913$	−41.9616			−1.38873
$914$		0			0
$915$	17.1722	−	40.4098i	0.567695	−	1.33591i
$916$		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
$921$	−22.8205	−	30.3093i	−0.751962	−	0.998724i
$922$		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
$927$	−37.1218	+	9.22372i	−1.21924	+	0.302947i
$928$		0			0
$929$	−18.3059			−0.600597			−0.300298	−	0.953845i	$-0.597086\pi$
$929$	−18.3059			−0.600597			−0.300298	+	0.953845i	$0.597086\pi$
$930$		0			0
$931$	−49.3783	+	26.9911i	−1.61831	+	0.884599i
$932$		0			0
$933$	−18.3018	−	24.3077i	−0.599173	−	0.795797i
$934$		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
$941$	36.4501			1.18824			0.594120	−	0.804376i	$-0.297500\pi$
$941$	36.4501			1.18824			0.594120	+	0.804376i	$0.297500\pi$
$942$		0			0
$943$	−2.54762			−0.0829620
$944$		0			0
$945$	−21.1792	−	29.9549i	−0.688959	−	0.974433i
$946$		0			0
$947$	47.4404			1.54161			0.770803	−	0.637074i	$-0.219855\pi$
$947$	47.4404			1.54161			0.770803	+	0.637074i	$0.219855\pi$
$948$		0			0
$949$	8.04846			0.261264
$950$		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
$957$	−11.2089	−	14.8871i	−0.362331	−	0.481233i
$958$		0			0
$959$	−16.9230	+	16.5323i	−0.546471	+	0.533855i
$960$		0			0
$961$	−29.4874			−0.951206
$962$		0			0
$963$	−2.74755	−	2.84977i	−0.0885387	−	0.0918325i
$964$		0			0
$965$	8.65548	+	14.9917i	0.278630	+	0.482601i
$966$		0			0
$967$	7.60180	−	13.1667i	0.244457	−	0.423413i	−0.717522	−	0.696536i	$-0.754724\pi$
$967$	7.60180	−	13.1667i	0.244457	−	0.423413i	0.961979	+	0.273124i	$0.0880568\pi$
$968$		0			0
$969$	59.8289	+	79.4623i	1.92198	+	2.55270i
$970$		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
$975$	−2.87643	+	6.76886i	−0.0921195	+	0.216777i
$976$		0			0
$977$	−43.0405			−1.37699			−0.688494	−	0.725242i	$-0.741728\pi$
$977$	−43.0405			−1.37699			−0.688494	+	0.725242i	$0.741728\pi$
$978$		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
$983$	−21.5191	+	37.2722i	−0.686353	+	1.18880i	0.286657	+	0.958033i	$0.407456\pi$
$983$	−21.5191	+	37.2722i	−0.686353	+	1.18880i	−0.973010	+	0.230765i	$0.925877\pi$
$984$		0			0
$985$	−14.4575	−	25.0411i	−0.460653	−	0.797875i
$986$		0			0
$987$	−20.2105	−	51.8163i	−0.643308	−	1.64933i
$988$		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
$997$	14.1670	−	24.5380i	0.448675	−	0.777128i	−0.549625	−	0.835411i	$-0.685229\pi$
$997$	14.1670	−	24.5380i	0.448675	−	0.777128i	0.998300	+	0.0582836i	$0.0185628\pi$
$998$		0			0
$999$	−8.62517	+	54.0343i	−0.272888	+	1.70957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.c.121.9	yes	22
3.2	odd	2		1512.2.q.d.793.3		22
4.3	odd	2		1008.2.q.l.625.3		22
7.4	even	3		504.2.t.c.193.8	yes	22
9.2	odd	6		1512.2.t.c.289.9		22
9.7	even	3		504.2.t.c.457.8	yes	22
12.11	even	2		3024.2.q.l.2305.3		22
21.11	odd	6		1512.2.t.c.361.9		22
28.11	odd	6		1008.2.t.l.193.4		22
36.7	odd	6		1008.2.t.l.961.4		22
36.11	even	6		3024.2.t.k.289.9		22
63.11	odd	6		1512.2.q.d.1369.3		22
63.25	even	3	inner	504.2.q.c.25.9	✓	22
84.11	even	6		3024.2.t.k.1873.9		22
252.11	even	6		3024.2.q.l.2881.3		22
252.151	odd	6		1008.2.q.l.529.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.9	✓	22	63.25	even	3	inner
504.2.q.c.121.9	yes	22	1.1	even	1	trivial
504.2.t.c.193.8	yes	22	7.4	even	3
504.2.t.c.457.8	yes	22	9.7	even	3
1008.2.q.l.529.3		22	252.151	odd	6
1008.2.q.l.625.3		22	4.3	odd	2
1008.2.t.l.193.4		22	28.11	odd	6
1008.2.t.l.961.4		22	36.7	odd	6
1512.2.q.d.793.3		22	3.2	odd	2
1512.2.q.d.1369.3		22	63.11	odd	6
1512.2.t.c.289.9		22	9.2	odd	6
1512.2.t.c.361.9		22	21.11	odd	6
3024.2.q.l.2305.3		22	12.11	even	2
3024.2.q.l.2881.3		22	252.11	even	6
3024.2.t.k.289.9		22	36.11	even	6
3024.2.t.k.1873.9		22	84.11	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.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04182 + 1.38370i) q^{3} +(1.33425 + 2.31099i) q^{5} +(2.54743 + 0.714566i) q^{7} +(-0.829236 + 2.88312i) q^{9} +O(q^{10})\)	\(q+(1.04182 + 1.38370i) q^{3} +(1.33425 + 2.31099i) q^{5} +(2.54743 + 0.714566i) q^{7} +(-0.829236 + 2.88312i) q^{9} +(1.99189 - 3.45005i) q^{11} +(1.00103 - 1.73384i) q^{13} +(-1.80767 + 4.25383i) q^{15} +(-3.57175 - 6.18646i) q^{17} +(-4.01956 + 6.96208i) q^{19} +(1.66521 + 4.26932i) q^{21} +(0.443909 + 0.768873i) q^{23} +(-1.06046 + 1.83677i) q^{25} +(-4.85327 + 1.85627i) q^{27} +(-1.35035 - 2.33887i) q^{29} -1.22989 q^{31} +(6.84901 - 0.838152i) q^{33} +(1.74756 + 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(3.44200 - 0.421217i) q^{39} +(-1.43477 + 2.48509i) q^{41} +(3.40053 + 5.88989i) q^{43} +(-7.76928 + 1.93045i) q^{45} -12.1369 q^{47} +(5.97879 + 3.64061i) q^{49} +(4.83907 - 11.3874i) q^{51} +(-2.38665 - 4.13380i) q^{53} +10.6307 q^{55} +(-13.8211 + 1.69136i) q^{57} +9.58058 q^{59} -9.49962 q^{61} +(-4.17260 + 6.75199i) q^{63} +5.34252 q^{65} +10.9889 q^{67} +(-0.601415 + 1.41526i) q^{69} -4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(-3.64635 + 0.446224i) q^{75} +(7.53949 - 7.36543i) q^{77} -1.02997 q^{79} +(-7.62474 - 4.78157i) q^{81} +(-5.26656 - 9.12195i) q^{83} +(9.53125 - 16.5086i) q^{85} +(1.82947 - 4.30514i) q^{87} +(1.72788 - 2.99278i) q^{89} +(3.78900 - 3.70153i) q^{91} +(-1.28132 - 1.70179i) q^{93} -21.4524 q^{95} +(-1.12061 - 1.94096i) q^{97} +(8.29516 + 8.60376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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