LMFDB - Embedded newform 1008.2.q.l.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, 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("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Character	$\chi$	$=$	1008.529
Dual form			1008.2.q.l.625.3

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−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	−0.396609	−	0.917988i	$-0.629813\pi$
$5$	1.33425	−	2.31099i	0.596696	−	1.03351i	0.993305	−	0.115520i	$-0.0368535\pi$
$6$		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	−0.992734	−	0.120332i	$-0.961604\pi$
$11$	−1.99189	−	3.45005i	−0.600577	−	1.04023i	0.392157	−	0.919898i	$-0.371729\pi$
$12$		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	−0.000504947		1.00000i	$0.500161\pi$
$17$	−3.57175	+	6.18646i	−0.866278	+	1.50044i	−0.865773	+	0.500437i	$0.833173\pi$
$18$		0			0
$19$	4.01956	+	6.96208i	0.922150	+	1.59721i	0.796082	+	0.605189i	$0.206903\pi$
$19$	4.01956	+	6.96208i	0.922150	+	1.59721i	0.126068	+	0.992022i	$0.459764\pi$
$20$		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	$-0.862839\pi$
$23$	−0.443909	+	0.768873i	−0.0925614	+	0.160321i	0.816027	+	0.578014i	$0.196172\pi$
$24$		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	−0.963733	−	0.266867i	$-0.914012\pi$
$29$	−1.35035	+	2.33887i	−0.250753	+	0.434317i	0.712980	+	0.701184i	$0.247345\pi$
$30$		0			0
$31$	1.22989			0.220894			0.110447	−	0.993882i	$-0.464772\pi$
$31$	1.22989			0.220894			0.110447	+	0.993882i	$0.464772\pi$
$32$		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	0.866443	+	0.499275i	$0.166400\pi$
$37$	5.26528	+	9.11973i	0.865607	+	1.49928i	−0.000836477		1.00000i	$0.500266\pi$
$38$		0			0
$39$	−3.44200	−	0.421217i	−0.551161	−	0.0674486i
$40$		0			0
$41$	−1.43477	−	2.48509i	−0.224073	−	0.388105i	0.731968	−	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	$0.340204\pi$
$43$	−3.40053	+	5.88989i	−0.518576	+	0.898200i	−0.999767	+	0.0215840i	$0.993129\pi$
$44$		0			0
$45$	−7.76928	−	1.93045i	−1.15818	−	0.287774i
$46$		0			0
$47$	12.1369			1.77035			0.885175	−	0.465258i	$-0.154039\pi$
$47$	12.1369			1.77035			0.885175	+	0.465258i	$0.154039\pi$
$48$		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	−0.982081	−	0.188457i	$-0.939651\pi$
$53$	−2.38665	+	4.13380i	−0.327832	+	0.567821i	0.654250	+	0.756279i	$0.272985\pi$
$54$		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	$-0.714348\pi$
$59$	−9.58058			−1.24729			−0.623643	+	0.781710i	$0.714348\pi$
$60$		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	$-0.734244\pi$
$67$	−10.9889			−1.34251			−0.671255	+	0.741227i	$0.734244\pi$
$68$		0			0
$69$	−0.601415	−	1.41526i	−0.0724019	−	0.170377i
$70$		0			0
$71$	4.62888			0.549347			0.274673	−	0.961538i	$-0.411430\pi$
$71$	4.62888			0.549347			0.274673	+	0.961538i	$0.411430\pi$
$72$		0			0
$73$	2.01004	−	3.48149i	0.235257	−	0.407478i	−0.724090	−	0.689705i	$-0.757740\pi$
$73$	2.01004	−	3.48149i	0.235257	−	0.407478i	0.959347	+	0.282228i	$0.0910733\pi$
$74$		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	$-0.481547\pi$
$79$	1.02997			0.115881			0.0579406	+	0.998320i	$0.481547\pi$
$80$		0			0
$81$	−7.62474	+	4.78157i	−0.847193	+	0.531285i
$82$		0			0
$83$	5.26656	−	9.12195i	0.578080	−	1.00126i	−0.417620	−	0.908622i	$-0.637135\pi$
$83$	5.26656	−	9.12195i	0.578080	−	1.00126i	0.995699	−	0.0926419i	$-0.0295312\pi$
$84$		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	0.942953	−	0.332925i	$-0.108036\pi$
$89$	1.72788	+	2.99278i	0.183155	+	0.317234i	−0.759798	+	0.650159i	$0.774702\pi$
$90$		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	−0.917292	−	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
$101$	2.28415	+	3.95626i	0.227281	+	0.393663i	0.957001	−	0.290083i	$-0.0936830\pi$
$101$	2.28415	+	3.95626i	0.227281	+	0.393663i	−0.729720	+	0.683746i	$0.760350\pi$
$102$		0			0
$103$	−6.37509	+	11.0420i	−0.628156	+	1.08800i	0.359766	+	0.933043i	$0.382857\pi$
$103$	−6.37509	+	11.0420i	−0.628156	+	1.08800i	−0.987922	+	0.154955i	$0.950477\pi$
$104$		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	$-0.146351\pi$
$107$	0.659761	+	1.14274i	0.0637815	+	0.110473i	−0.832371	+	0.554218i	$0.813017\pi$
$108$		0			0
$109$	−6.31990	+	10.9464i	−0.605337	+	1.04847i	0.386661	+	0.922222i	$0.373628\pi$
$109$	−6.31990	+	10.9464i	−0.605337	+	1.04847i	−0.991998	+	0.126252i	$0.959705\pi$
$110$		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
$115$	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	$-0.519558\pi$
$127$	−1.38400			−0.122810			−0.0614051	+	0.998113i	$0.519558\pi$
$128$		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	$-0.837918\pi$
$131$	−0.164862	+	0.285550i	−0.0144041	+	0.0249486i	0.858734	+	0.512422i	$0.171252\pi$
$132$		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	0.609366	−	0.792889i	$-0.291424\pi$
$137$	−4.47095	−	7.74391i	−0.381979	−	0.661607i	−0.991345	+	0.131282i	$0.958091\pi$
$138$		0			0
$139$	−3.92869	−	6.80470i	−0.333227	−	0.577167i	0.649915	−	0.760007i	$-0.274804\pi$
$139$	−3.92869	−	6.80470i	−0.333227	−	0.577167i	−0.983143	+	0.182840i	$0.941471\pi$
$140$		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	0.309754	+	0.950817i	$0.399753\pi$
$149$	−8.16075	+	14.1348i	−0.668554	+	1.15797i	−0.978308	+	0.207153i	$0.933580\pi$
$150$		0			0
$151$	−2.31677	−	4.01276i	−0.188536	−	0.326554i	0.756226	−	0.654310i	$-0.227041\pi$
$151$	−2.31677	−	4.01276i	−0.188536	−	0.326554i	−0.944762	+	0.327756i	$0.893708\pi$
$152$		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	$-0.197219\pi$
$163$	−1.22354	−	2.11923i	−0.0958350	−	0.165991i	−0.909957	+	0.414703i	$0.863885\pi$
$164$		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	$-0.164908\pi$
$167$	0.0713948	+	0.123659i	0.00552470	+	0.00956906i	−0.863250	+	0.504777i	$0.831575\pi$
$168$		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	$-0.808944\pi$
$179$	1.02413	−	1.77384i	0.0765468	−	0.132583i	0.901758	+	0.432242i	$0.142277\pi$
$180$		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	$-0.738233\pi$
$191$	−18.8091			−1.36098			−0.680491	+	0.732757i	$0.738233\pi$
$192$		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	−0.309064	−	0.951041i	$-0.600016\pi$
$199$	9.43873	−	16.3484i	0.669094	−	1.15890i	0.978158	−	0.207863i	$-0.0666508\pi$
$200$		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	0.905574	+	0.424188i	$0.139440\pi$
$211$	11.9133	+	20.6344i	0.820145	+	1.42053i	−0.0854297	+	0.996344i	$0.527226\pi$
$212$		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	$-0.977566\pi$
$223$	−6.53734	+	11.3230i	−0.437773	+	0.758245i	0.559745	+	0.828665i	$0.310899\pi$
$224$		0			0
$225$	−4.41626	+	4.58056i	−0.294418	+	0.305371i
$226$		0			0
$227$	11.5845	+	20.0649i	0.768890	+	1.33176i	0.938165	+	0.346188i	$0.112524\pi$
$227$	11.5845	+	20.0649i	0.768890	+	1.33176i	−0.169275	+	0.985569i	$0.554142\pi$
$228$		0			0
$229$	10.7794	−	18.6705i	0.712323	−	1.23378i	−0.251660	−	0.967816i	$-0.580976\pi$
$229$	10.7794	−	18.6705i	0.712323	−	1.23378i	0.963983	−	0.265964i	$-0.0856904\pi$
$230$		0			0
$231$	−18.0463	+	2.75894i	−1.18736	+	0.181525i
$232$		0			0
$233$	−8.05558	−	13.9527i	−0.527739	−	0.914070i	−0.999477	−	0.0323318i	$-0.989707\pi$
$233$	−8.05558	−	13.9527i	−0.527739	−	0.914070i	0.471738	−	0.881739i	$-0.343627\pi$
$234$		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	$-0.171115\pi$
$239$	−0.216059	−	0.374225i	−0.0139757	−	0.0242066i	−0.872929	+	0.487848i	$0.837782\pi$
$240$		0			0
$241$	−1.52837	−	2.64721i	−0.0984509	−	0.170522i	0.812593	−	0.582832i	$-0.198055\pi$
$241$	−1.52837	−	2.64721i	−0.0984509	−	0.170522i	−0.911044	+	0.412310i	$0.864722\pi$
$242$		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	$-0.622622\pi$
$251$	−11.9066			−0.751541			−0.375770	+	0.926713i	$0.622622\pi$
$252$		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	0.424204	−	0.905567i	$-0.360554\pi$
$257$	15.9726	−	27.6654i	0.996346	−	1.72572i	0.572142	−	0.820155i	$-0.306113\pi$
$258$		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	$-0.100337\pi$
$263$	3.35495	+	5.81094i	0.206875	+	0.358318i	−0.743854	+	0.668343i	$0.767004\pi$
$264$		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	−0.640020	−	0.768358i	$-0.721074\pi$
$269$	5.66510	−	9.81225i	0.345408	−	0.598263i	0.985428	+	0.170095i	$0.0544074\pi$
$270$		0			0
$271$	5.06846	+	8.77884i	0.307887	+	0.533276i	0.977900	−	0.209073i	$-0.0670447\pi$
$271$	5.06846	+	8.77884i	0.307887	+	0.533276i	−0.670013	+	0.742350i	$0.733711\pi$
$272$		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	0.985544	+	0.169418i	$0.0541886\pi$
$277$	10.6433	+	18.4347i	0.639492	+	1.10763i	−0.346052	+	0.938215i	$0.612478\pi$
$278$		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
$283$	−24.9497			−1.48311			−0.741554	−	0.670893i	$-0.765911\pi$
$283$	−24.9497			−1.48311			−0.741554	+	0.670893i	$0.765911\pi$
$284$		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	0.997201	−	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
$297$	−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	$-0.285067\pi$
$307$	21.9045			1.25016			0.625079	+	0.780561i	$0.285067\pi$
$308$		0			0
$309$	−8.63707	−	20.3249i	−0.491346	−	1.15624i
$310$		0			0
$311$	17.5672			0.996143			0.498072	−	0.867136i	$-0.334042\pi$
$311$	17.5672			0.996143			0.498072	+	0.867136i	$0.334042\pi$
$312$		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	$-0.493646\pi$
$331$	0.726254			0.0399185			0.0199593	+	0.999801i	$0.493646\pi$
$332$		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	0.616992	−	0.786970i	$-0.288351\pi$
$337$	−6.84810	−	11.8613i	−0.373040	−	0.646124i	−0.990032	+	0.140846i	$0.955018\pi$
$338$		0			0
$339$	1.73023	+	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	$-0.463917\pi$
$347$	4.21417			0.226229			0.113114	+	0.993582i	$0.463917\pi$
$348$		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
$353$	−2.42558	−	4.20122i	−0.129100	−	0.223609i	0.794228	−	0.607620i	$-0.207876\pi$
$353$	−2.42558	−	4.20122i	−0.129100	−	0.223609i	−0.923328	+	0.384012i	$0.874542\pi$
$354$		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	$-0.215652\pi$
$359$	−2.90433	−	5.03045i	−0.153285	−	0.265497i	−0.932433	+	0.361343i	$0.882318\pi$
$360$		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	0.996949	+	0.0780619i	$0.0248732\pi$
$367$	10.8445	+	18.7832i	0.566078	+	0.980476i	−0.430871	+	0.902414i	$0.641793\pi$
$368$		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	0.345764	+	0.938322i	$0.387620\pi$
$373$	−12.3552	+	21.3999i	−0.639729	+	1.10804i	−0.985492	+	0.169721i	$0.945713\pi$
$374$		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	$-0.244598\pi$
$379$	27.9950			1.43801			0.719005	+	0.695005i	$0.244598\pi$
$380$		0			0
$381$	1.44188	−	1.91504i	0.0738695	−	0.0981104i
$382$		0			0
$383$	−10.3113	+	17.8598i	−0.526884	+	0.912591i	0.472625	+	0.881264i	$0.343307\pi$
$383$	−10.3113	+	17.8598i	−0.526884	+	0.912591i	−0.999509	+	0.0313269i	$0.990027\pi$
$384$		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	0.556648	−	0.830748i	$-0.312087\pi$
$389$	−8.70035	−	15.0694i	−0.441125	−	0.764051i	−0.997773	+	0.0666973i	$0.978754\pi$
$390$		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	0.999919	−	0.0127553i	$-0.00406024\pi$
$397$	9.74152	+	16.8728i	0.488913	+	0.846822i	−0.511006	+	0.859577i	$0.670727\pi$
$398$		0			0
$399$	36.4167	−	5.56744i	1.82312	−	0.278721i
$400$		0			0
$401$	−3.85264	+	6.67297i	−0.192392	+	0.333232i	−0.946042	−	0.324043i	$-0.894958\pi$
$401$	−3.85264	+	6.67297i	−0.192392	+	0.333232i	0.753651	+	0.657275i	$0.228291\pi$
$402$		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	0.883548	+	0.468341i	$0.155148\pi$
$419$	17.3452	+	30.0428i	0.847369	+	1.46769i	−0.0361784	+	0.999345i	$0.511518\pi$
$420$		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
$423$	−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	$-0.859196\pi$
$431$	−1.68495	+	2.91841i	−0.0811610	+	0.140575i	0.822588	+	0.568638i	$0.192529\pi$
$432$		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	$-0.210400\pi$
$439$	33.0789			1.57877			0.789385	+	0.613898i	$0.210400\pi$
$440$		0			0
$441$	−15.4541	−	14.2186i	−0.735912	−	0.677077i
$442$		0			0
$443$	−2.73364			−0.129879			−0.0649397	−	0.997889i	$-0.520685\pi$
$443$	−2.73364			−0.129879			−0.0649397	+	0.997889i	$0.520685\pi$
$444$		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	−0.999243	−	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	0.645247	−	0.763974i	$-0.276754\pi$
$463$	−7.29434	−	12.6342i	−0.338997	−	0.587160i	−0.984244	+	0.176814i	$0.943421\pi$
$464$		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	$-0.275777\pi$
$467$	−7.26334	−	12.5805i	−0.336107	−	0.582155i	−0.983697	+	0.179834i	$0.942444\pi$
$468$		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	$-0.249964\pi$
$479$	−5.66216	−	9.80714i	−0.258710	−	0.448100i	−0.965897	+	0.258928i	$0.916631\pi$
$480$		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	$-0.920034\pi$
$487$	−5.93684	+	10.2829i	−0.269024	+	0.465963i	0.699586	+	0.714548i	$0.253368\pi$
$488$		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	$-0.985190\pi$
$491$	−11.9598	−	20.7150i	−0.539738	−	0.934853i	0.459180	−	0.888343i	$-0.348143\pi$
$492$		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	$-0.836554\pi$
$499$	−0.225984	+	0.391416i	−0.0101164	+	0.0175222i	0.860923	+	0.508736i	$0.169887\pi$
$500$		0			0
$501$	−0.245488	−	0.0300417i	−0.0109676	−	0.00134216i
$502$		0			0
$503$	14.6077			0.651326			0.325663	−	0.945486i	$-0.394413\pi$
$503$	14.6077			0.651326			0.325663	+	0.945486i	$0.394413\pi$
$504$		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	−0.860509	−	0.509436i	$-0.829854\pi$
$509$	0.246585	−	0.427099i	0.0109297	−	0.0189308i	0.871439	+	0.490505i	$0.163188\pi$
$510$		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	−0.967793	−	0.251748i	$-0.918995\pi$
$521$	−6.06874	+	10.5114i	−0.265876	+	0.460511i	0.701917	+	0.712259i	$0.252328\pi$
$522$		0			0
$523$	−1.34058	−	2.32195i	−0.0586193	−	0.101532i	0.835227	−	0.549906i	$-0.185336\pi$
$523$	−1.34058	−	2.32195i	−0.0586193	−	0.101532i	−0.893846	+	0.448374i	$0.852003\pi$
$524$		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	−0.995394	−	0.0958650i	$-0.969438\pi$
$541$	−13.5072	−	23.3951i	−0.580719	−	1.00583i	0.414676	−	0.909969i	$-0.363895\pi$
$542$		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	−0.330602	−	0.943770i	$-0.607252\pi$
$547$	15.2496	−	26.4132i	0.652028	−	1.12935i	0.982630	−	0.185575i	$-0.0594149\pi$
$548$		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	−0.979060	−	0.203573i	$-0.934745\pi$
$557$	−7.39250	+	12.8042i	−0.313230	+	0.542531i	0.665829	+	0.746104i	$0.268078\pi$
$558$		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	$-0.517638\pi$
$563$	−2.62822			−0.110766			−0.0553831	+	0.998465i	$0.517638\pi$
$564$		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	$-0.830597\pi$
$571$	−41.1815			−1.72339			−0.861696	+	0.507425i	$0.830597\pi$
$572$		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	−0.497370	−	0.867539i	$-0.665701\pi$
$577$	12.0735	−	20.9119i	0.502625	−	0.870573i	0.999995	−	0.00303429i	$-0.000965847\pi$
$578$		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	$-0.780723\pi$
$587$	3.98618	−	6.90426i	0.164527	−	0.284969i	0.936487	+	0.350702i	$0.114057\pi$
$588$		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	0.819601	−	0.572935i	$-0.194195\pi$
$593$	−2.10338	−	3.64316i	−0.0863753	−	0.149606i	−0.905976	+	0.423328i	$0.860862\pi$
$594$		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	$-0.223433\pi$
$599$	37.3771			1.52719			0.763594	+	0.645696i	$0.223433\pi$
$600$		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
$605$	6.49846	+	11.2557i	0.264200	+	0.457607i
$606$		0			0
$607$	1.37114	−	2.37489i	0.0556529	−	0.0963937i	−0.836857	−	0.547422i	$-0.815609\pi$
$607$	1.37114	−	2.37489i	0.0556529	−	0.0963937i	0.892510	+	0.451028i	$0.148943\pi$
$608$		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	−0.849449	−	0.527670i	$-0.823066\pi$
$613$	0.798502	−	1.38305i	0.0322512	−	0.0558607i	0.881700	+	0.471810i	$0.156399\pi$
$614$		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
$619$	−13.5808	−	23.5226i	−0.545859	−	0.945455i	−0.998552	−	0.0537888i	$-0.982870\pi$
$619$	−13.5808	−	23.5226i	−0.545859	−	0.945455i	0.452694	−	0.891666i	$-0.350463\pi$
$620$		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	$-0.298983\pi$
$631$	29.6597			1.18073			0.590366	+	0.807136i	$0.298983\pi$
$632$		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	−0.895367	−	0.445329i	$-0.853087\pi$
$641$	−21.0987	−	36.5441i	−0.833350	−	1.44340i	0.0620175	−	0.998075i	$-0.480247\pi$
$642$		0			0
$643$	−10.1099	−	17.5109i	−0.398696	−	0.690562i	0.594869	−	0.803823i	$-0.297204\pi$
$643$	−10.1099	−	17.5109i	−0.398696	−	0.690562i	−0.993565	+	0.113260i	$0.963871\pi$
$644$		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	$-0.819690\pi$
$647$	1.08988	−	1.88772i	0.0428475	−	0.0742141i	0.886654	+	0.462434i	$0.153024\pi$
$648$		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	−0.311288	−	0.950316i	$-0.600760\pi$
$653$	17.0535	−	29.5375i	0.667354	−	1.15589i	0.978641	−	0.205575i	$-0.0659063\pi$
$654$		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	$-0.821002\pi$
$659$	0.994211	−	1.72202i	0.0387290	−	0.0670805i	0.884740	+	0.466085i	$0.154336\pi$
$660$		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	−0.00468438	−	0.999989i	$-0.501491\pi$
$673$	22.4056	−	38.8077i	0.863674	−	1.49593i	0.868358	−	0.495938i	$-0.165176\pi$
$674$		0			0
$675$	−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	0.123580	+	0.992335i	$0.460562\pi$
$683$	−20.8446	+	36.1039i	−0.797597	+	1.38148i	−0.921177	+	0.389144i	$0.872771\pi$
$684$		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	$-0.569121\pi$
$691$	−11.3269			−0.430895			−0.215448	+	0.976515i	$0.569121\pi$
$692$		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	$-0.305358\pi$
$719$	−11.3171	−	19.6018i	−0.422057	−	0.731024i	−0.996141	+	0.0877727i	$0.972025\pi$
$720$		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	$-0.845727\pi$
$727$	−1.04956	+	1.81789i	−0.0389259	+	0.0674217i	0.845906	+	0.533332i	$0.179060\pi$
$728$		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	−0.417851	−	0.908516i	$-0.637216\pi$
$733$	15.6453	−	27.0985i	0.577872	−	1.00090i	0.995723	−	0.0923886i	$-0.0294502\pi$
$734$		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	0.156637	+	0.987656i	$0.449935\pi$
$739$	−21.1229	+	36.5859i	−0.777017	+	1.34583i	−0.933654	+	0.358177i	$0.883399\pi$
$740$		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	$-0.243127\pi$
$743$	−6.48482	−	11.2320i	−0.237905	−	0.412064i	−0.960113	+	0.279612i	$0.909794\pi$
$744$		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	−0.396074	−	0.918219i	$-0.629628\pi$
$751$	16.3649	−	28.3448i	0.597164	−	1.03432i	0.993238	−	0.116099i	$-0.0370391\pi$
$752$		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	−0.276423	−	0.961036i	$-0.589149\pi$
$761$	19.1468	−	33.1632i	0.694070	−	1.20217i	0.970493	−	0.241129i	$-0.0775177\pi$
$762$		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	0.993615	−	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	0.142813	−	0.989750i	$-0.454385\pi$
$773$	25.8165	−	44.7155i	0.928555	−	1.60830i	0.785742	−	0.618555i	$-0.212281\pi$
$774$		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	$-0.304704\pi$
$787$	32.3046			1.15153			0.575767	+	0.817614i	$0.304704\pi$
$788$		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	0.581322	−	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
$801$	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	−0.462935	−	0.886392i	$-0.653203\pi$
$809$	15.2503	−	26.4143i	0.536171	−	0.928676i	0.999106	−	0.0422832i	$-0.0134632\pi$
$810$		0			0
$811$	51.6454			1.81352			0.906758	−	0.421652i	$-0.138550\pi$
$811$	51.6454			1.81352			0.906758	+	0.421652i	$0.138550\pi$
$812$		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	$-0.250636\pi$
$823$	40.4898			1.41139			0.705693	+	0.708517i	$0.250636\pi$
$824$		0			0
$825$	−5.72362	−	13.4689i	−0.199271	−	0.468928i
$826$		0			0
$827$	27.9452			0.971749			0.485875	−	0.874029i	$-0.338501\pi$
$827$	27.9452			0.971749			0.485875	+	0.874029i	$0.338501\pi$
$828$		0			0
$829$	−20.0226	+	34.6802i	−0.695415	+	1.20449i	0.274625	+	0.961551i	$0.411446\pi$
$829$	−20.0226	+	34.6802i	−0.695415	+	1.20449i	−0.970040	+	0.242943i	$0.921887\pi$
$830$		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	−0.421957	−	0.906616i	$-0.638657\pi$
$839$	16.6312	−	28.8061i	0.574174	−	0.994499i	0.996131	−	0.0878827i	$-0.0280101\pi$
$840$		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	−0.931308	−	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
$857$	0.677198	+	1.17294i	0.0231327	+	0.0400669i	0.877360	−	0.479833i	$-0.159303\pi$
$857$	0.677198	+	1.17294i	0.0231327	+	0.0400669i	−0.854227	+	0.519900i	$0.825969\pi$
$858$		0			0
$859$	−9.01934	+	15.6220i	−0.307736	+	0.533014i	−0.977867	−	0.209229i	$-0.932905\pi$
$859$	−9.01934	+	15.6220i	−0.307736	+	0.533014i	0.670131	+	0.742243i	$0.266238\pi$
$860$		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	$-0.0970233\pi$
$863$	6.37624	+	11.0440i	0.217050	+	0.375941i	−0.736855	+	0.676051i	$0.763690\pi$
$864$		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	−0.678580	−	0.734527i	$-0.737404\pi$
$877$	8.79034	−	15.2253i	0.296829	−	0.514122i	0.975409	+	0.220404i	$0.0707376\pi$
$878$		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	$-0.739334\pi$
$883$	−40.5923			−1.36604			−0.683020	+	0.730400i	$0.739334\pi$
$884$		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	$-0.849028\pi$
$887$	−1.46786	+	2.54240i	−0.0492858	+	0.0853655i	0.840330	+	0.542075i	$0.182361\pi$
$888$		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	−0.996655	−	0.0817300i	$-0.973955\pi$
$907$	−17.1395	−	29.6865i	−0.569108	−	0.985723i	0.427547	−	0.903993i	$-0.359378\pi$
$908$		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	$-0.780536\pi$
$911$	4.98338	−	8.63146i	0.165107	−	0.285973i	0.936693	+	0.350151i	$0.113870\pi$
$912$		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	$-0.318811\pi$
$919$	−13.9444	−	24.1524i	−0.459983	−	0.796714i	−0.998959	+	0.0456069i	$0.985478\pi$
$920$		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	$-0.780145\pi$
$947$	−47.4404			−1.54161			−0.770803	+	0.637074i	$0.780145\pi$
$948$		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	$-0.245276\pi$
$967$	−7.60180	−	13.1667i	−0.244457	−	0.423413i	−0.961979	+	0.273124i	$0.911943\pi$
$968$		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	$-0.170375\pi$
$971$	−0.363057	−	0.628834i	−0.0116511	−	0.0201802i	−0.871792	+	0.489876i	$0.837042\pi$
$972$		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	0.973010	+	0.230765i	$0.0741228\pi$
$983$	21.5191	+	37.2722i	0.686353	+	1.18880i	−0.286657	+	0.958033i	$0.592544\pi$
$984$		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	$-0.716728\pi$
$991$	11.2758	−	19.5302i	0.358187	−	0.620398i	0.987658	+	0.156626i	$0.0500618\pi$
$992$		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	0.998300	−	0.0582836i	$-0.0185628\pi$
$997$	14.1670	+	24.5380i	0.448675	+	0.777128i	−0.549625	+	0.835411i	$0.685229\pi$
$998$		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	1008.2.q.l.529.3		22
3.2	odd	2		3024.2.q.l.2881.3		22
4.3	odd	2		504.2.q.c.25.9	✓	22
7.2	even	3		1008.2.t.l.961.4		22
9.4	even	3		1008.2.t.l.193.4		22
9.5	odd	6		3024.2.t.k.1873.9		22
12.11	even	2		1512.2.q.d.1369.3		22
21.2	odd	6		3024.2.t.k.289.9		22
28.23	odd	6		504.2.t.c.457.8	yes	22
36.23	even	6		1512.2.t.c.361.9		22
36.31	odd	6		504.2.t.c.193.8	yes	22
63.23	odd	6		3024.2.q.l.2305.3		22
63.58	even	3	inner	1008.2.q.l.625.3		22
84.23	even	6		1512.2.t.c.289.9		22
252.23	even	6		1512.2.q.d.793.3		22
252.247	odd	6		504.2.q.c.121.9	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.9	✓	22	4.3	odd	2
504.2.q.c.121.9	yes	22	252.247	odd	6
504.2.t.c.193.8	yes	22	36.31	odd	6
504.2.t.c.457.8	yes	22	28.23	odd	6
1008.2.q.l.529.3		22	1.1	even	1	trivial
1008.2.q.l.625.3		22	63.58	even	3	inner
1008.2.t.l.193.4		22	9.4	even	3
1008.2.t.l.961.4		22	7.2	even	3
1512.2.q.d.793.3		22	252.23	even	6
1512.2.q.d.1369.3		22	12.11	even	2
1512.2.t.c.289.9		22	84.23	even	6
1512.2.t.c.361.9		22	36.23	even	6
3024.2.q.l.2305.3		22	63.23	odd	6
3024.2.q.l.2881.3		22	3.2	odd	2
3024.2.t.k.289.9		22	21.2	odd	6
3024.2.t.k.1873.9		22	9.5	odd	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not 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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