LMFDB - Embedded newform 1008.2.q.l.625.2

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			625.2
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.l.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64138 - 0.553060i) q^{3} +(-0.263002 - 0.455533i) q^{5} +(0.333150 - 2.62469i) q^{7} +(2.38825 + 1.81556i) q^{9} +O(q^{10})$	\(q+(-1.64138 - 0.553060i) q^{3} +(-0.263002 - 0.455533i) q^{5} +(0.333150 - 2.62469i) q^{7} +(2.38825 + 1.81556i) q^{9} +(2.30526 - 3.99283i) q^{11} +(0.244554 - 0.423580i) q^{13} +(0.179749 + 0.893158i) q^{15} +(2.75579 + 4.77318i) q^{17} +(-1.83782 + 3.18319i) q^{19} +(-1.99844 + 4.12386i) q^{21} +(-0.0269769 - 0.0467253i) q^{23} +(2.36166 - 4.09051i) q^{25} +(-2.91591 - 4.30087i) q^{27} +(-3.28471 - 5.68929i) q^{29} -6.07640 q^{31} +(-5.99208 + 5.27879i) q^{33} +(-1.28325 + 0.538539i) q^{35} +(0.223731 - 0.387513i) q^{37} +(-0.635671 + 0.560002i) q^{39} +(2.52284 - 4.36968i) q^{41} +(-2.84893 - 4.93449i) q^{43} +(0.198934 - 1.56542i) q^{45} +9.19621 q^{47} +(-6.77802 - 1.74883i) q^{49} +(-1.88345 - 9.35871i) q^{51} +(-4.37138 - 7.57145i) q^{53} -2.42515 q^{55} +(4.77705 - 4.20840i) q^{57} +6.63076 q^{59} -0.465625 q^{61} +(5.56094 - 5.66357i) q^{63} -0.257273 q^{65} -5.19358 q^{67} +(0.0184374 + 0.0916137i) q^{69} -1.76328 q^{71} +(-5.23776 - 9.07207i) q^{73} +(-6.13868 + 5.40794i) q^{75} +(-9.71195 - 7.38081i) q^{77} -16.3702 q^{79} +(2.40747 + 8.67203i) q^{81} +(-4.49251 - 7.78126i) q^{83} +(1.44956 - 2.51071i) q^{85} +(2.24494 + 11.1549i) q^{87} +(-7.05145 + 12.2135i) q^{89} +(-1.03029 - 0.782994i) q^{91} +(9.97367 + 3.36061i) q^{93} +1.93340 q^{95} +(5.22413 + 9.04847i) q^{97} +(12.7548 - 5.35052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

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

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
$3$	−1.64138	−	0.553060i	−0.947651	−	0.319309i
$3$	−1.64138	−	0.553060i	−0.947651	−	0.319309i
$4$		0			0
$5$	−0.263002	−	0.455533i	−0.117618	−	0.203721i	0.801205	−	0.598390i	$-0.204193\pi$
$5$	−0.263002	−	0.455533i	−0.117618	−	0.203721i	−0.918823	+	0.394669i	$0.870859\pi$
$6$		0			0
$7$	0.333150	−	2.62469i	0.125919	−	0.992041i
$7$	0.333150	−	2.62469i	0.125919	−	0.992041i
$8$		0			0
$9$	2.38825	+	1.81556i	0.796083	+	0.605187i
$10$		0			0
$11$	2.30526	−	3.99283i	0.695062	−	1.20388i	−0.275098	−	0.961416i	$-0.588710\pi$
$11$	2.30526	−	3.99283i	0.695062	−	1.20388i	0.970160	−	0.242466i	$-0.0779564\pi$
$12$		0			0
$13$	0.244554	−	0.423580i	0.0678270	−	0.117480i	−0.830118	−	0.557588i	$-0.811727\pi$
$13$	0.244554	−	0.423580i	0.0678270	−	0.117480i	0.897945	+	0.440109i	$0.145060\pi$
$14$		0			0
$15$	0.179749	+	0.893158i	0.0464110	+	0.230613i
$16$		0			0
$17$	2.75579	+	4.77318i	0.668378	+	1.15767i	0.978357	+	0.206922i	$0.0663446\pi$
$17$	2.75579	+	4.77318i	0.668378	+	1.15767i	−0.309979	+	0.950743i	$0.600322\pi$
$18$		0			0
$19$	−1.83782	+	3.18319i	−0.421624	+	0.730274i	−0.996099	−	0.0882484i	$-0.971873\pi$
$19$	−1.83782	+	3.18319i	−0.421624	+	0.730274i	0.574475	+	0.818522i	$0.305206\pi$
$20$		0			0
$21$	−1.99844	+	4.12386i	−0.436095	+	0.899901i
$22$		0			0
$23$	−0.0269769	−	0.0467253i	−0.00562506	−	0.00974289i	0.863199	−	0.504864i	$-0.168457\pi$
$23$	−0.0269769	−	0.0467253i	−0.00562506	−	0.00974289i	−0.868824	+	0.495121i	$0.835124\pi$
$24$		0			0
$25$	2.36166	−	4.09051i	0.472332	−	0.818103i
$26$		0			0
$27$	−2.91591	−	4.30087i	−0.561167	−	0.827703i
$28$		0			0
$29$	−3.28471	−	5.68929i	−0.609956	−	1.05647i	−0.991247	−	0.132019i	$-0.957854\pi$
$29$	−3.28471	−	5.68929i	−0.609956	−	1.05647i	0.381292	−	0.924455i	$-0.375479\pi$
$30$		0			0
$31$	−6.07640			−1.09135			−0.545676	−	0.837996i	$-0.683727\pi$
$31$	−6.07640			−1.09135			−0.545676	+	0.837996i	$0.683727\pi$
$32$		0			0
$33$	−5.99208	+	5.27879i	−1.04309	+	0.918920i
$34$		0			0
$35$	−1.28325	+	0.538539i	−0.216909	+	0.0910297i
$36$		0			0
$37$	0.223731	−	0.387513i	0.0367811	−	0.0637068i	−0.847049	−	0.531515i	$-0.821623\pi$
$37$	0.223731	−	0.387513i	0.0367811	−	0.0637068i	0.883830	+	0.467808i	$0.154956\pi$
$38$		0			0
$39$	−0.635671	+	0.560002i	−0.101789	+	0.0896721i
$40$		0			0
$41$	2.52284	−	4.36968i	0.394001	−	0.682430i	−0.598972	−	0.800770i	$-0.704424\pi$
$41$	2.52284	−	4.36968i	0.394001	−	0.682430i	0.992973	+	0.118340i	$0.0377574\pi$
$42$		0			0
$43$	−2.84893	−	4.93449i	−0.434458	−	0.752503i	0.562794	−	0.826598i	$-0.309727\pi$
$43$	−2.84893	−	4.93449i	−0.434458	−	0.752503i	−0.997251	+	0.0740947i	$0.976393\pi$
$44$		0			0
$45$	0.198934	−	1.56542i	0.0296553	−	0.233360i
$46$		0			0
$47$	9.19621			1.34140			0.670702	−	0.741726i	$-0.265993\pi$
$47$	9.19621			1.34140			0.670702	+	0.741726i	$0.265993\pi$
$48$		0			0
$49$	−6.77802	−	1.74883i	−0.968289	−	0.249833i
$50$		0			0
$51$	−1.88345	−	9.35871i	−0.263736	−	1.31048i
$52$		0			0
$53$	−4.37138	−	7.57145i	−0.600455	−	1.04002i	−0.992752	−	0.120180i	$-0.961653\pi$
$53$	−4.37138	−	7.57145i	−0.600455	−	1.04002i	0.392297	−	0.919839i	$-0.371680\pi$
$54$		0			0
$55$	−2.42515			−0.327008
$56$		0			0
$57$	4.77705	−	4.20840i	0.632735	−	0.557416i
$58$		0			0
$59$	6.63076			0.863252			0.431626	−	0.902053i	$-0.357940\pi$
$59$	6.63076			0.863252			0.431626	+	0.902053i	$0.357940\pi$
$60$		0			0
$61$	−0.465625			−0.0596171			−0.0298086	−	0.999556i	$-0.509490\pi$
$61$	−0.465625			−0.0596171			−0.0298086	+	0.999556i	$0.509490\pi$
$62$		0			0
$63$	5.56094	−	5.66357i	0.700612	−	0.713542i
$64$		0			0
$65$	−0.257273			−0.0319108
$66$		0			0
$67$	−5.19358			−0.634496			−0.317248	−	0.948343i	$-0.602759\pi$
$67$	−5.19358			−0.634496			−0.317248	+	0.948343i	$0.602759\pi$
$68$		0			0
$69$	0.0184374	+	0.0916137i	0.00221960	+	0.0110290i
$70$		0			0
$71$	−1.76328			−0.209263			−0.104632	−	0.994511i	$-0.533366\pi$
$71$	−1.76328			−0.209263			−0.104632	+	0.994511i	$0.533366\pi$
$72$		0			0
$73$	−5.23776	−	9.07207i	−0.613034	−	1.06181i	−0.990726	−	0.135875i	$-0.956616\pi$
$73$	−5.23776	−	9.07207i	−0.613034	−	1.06181i	0.377692	−	0.925931i	$-0.376718\pi$
$74$		0			0
$75$	−6.13868	+	5.40794i	−0.708834	+	0.624456i
$76$		0			0
$77$	−9.71195	−	7.38081i	−1.10678	−	0.841121i
$78$		0			0
$79$	−16.3702			−1.84179			−0.920895	−	0.389812i	$-0.872540\pi$
$79$	−16.3702			−1.84179			−0.920895	+	0.389812i	$0.872540\pi$
$80$		0			0
$81$	2.40747	+	8.67203i	0.267497	+	0.963559i
$82$		0			0
$83$	−4.49251	−	7.78126i	−0.493117	−	0.854104i	0.506851	−	0.862034i	$-0.330809\pi$
$83$	−4.49251	−	7.78126i	−0.493117	−	0.854104i	−0.999969	+	0.00792925i	$0.997476\pi$
$84$		0			0
$85$	1.44956	−	2.51071i	0.157227	−	0.272325i
$86$		0			0
$87$	2.24494	+	11.1549i	0.240683	+	1.19593i
$88$		0			0
$89$	−7.05145	+	12.2135i	−0.747452	+	1.29463i	0.201588	+	0.979470i	$0.435390\pi$
$89$	−7.05145	+	12.2135i	−0.747452	+	1.29463i	−0.949040	+	0.315155i	$0.897944\pi$
$90$		0			0
$91$	−1.03029	−	0.782994i	−0.108004	−	0.0820801i
$92$		0			0
$93$	9.97367	+	3.36061i	1.03422	+	0.348479i
$94$		0			0
$95$	1.93340			0.198363
$96$		0			0
$97$	5.22413	+	9.04847i	0.530430	+	0.918732i	0.999370	+	0.0355020i	$0.0113030\pi$
$97$	5.22413	+	9.04847i	0.530430	+	0.918732i	−0.468939	+	0.883230i	$0.655364\pi$
$98$		0			0
$99$	12.7548	−	5.35052i	1.28190	−	0.537748i
$100$		0			0
$101$	4.98254	−	8.63001i	0.495781	−	0.858718i	−0.504207	−	0.863583i	$-0.668215\pi$
$101$	4.98254	−	8.63001i	0.495781	−	0.858718i	0.999988	+	0.00486475i	$0.00154850\pi$
$102$		0			0
$103$	5.82553	+	10.0901i	0.574006	+	0.994208i	0.996149	+	0.0876783i	$0.0279448\pi$
$103$	5.82553	+	10.0901i	0.574006	+	0.994208i	−0.422143	+	0.906529i	$0.638722\pi$
$104$		0			0
$105$	2.40415	−	0.174231i	0.234621	−	0.0170032i
$106$		0			0
$107$	−2.45556	+	4.25316i	−0.237388	+	0.411168i	−0.959964	−	0.280123i	$-0.909625\pi$
$107$	−2.45556	+	4.25316i	−0.237388	+	0.411168i	0.722576	+	0.691292i	$0.242958\pi$
$108$		0			0
$109$	−9.76353	−	16.9109i	−0.935177	−	1.61977i	−0.774319	−	0.632796i	$-0.781907\pi$
$109$	−9.76353	−	16.9109i	−0.935177	−	1.61977i	−0.160858	−	0.986978i	$-0.551426\pi$
$110$		0			0
$111$	−0.581545	+	0.512319i	−0.0551978	+	0.0486272i
$112$		0			0
$113$	5.48658	−	9.50304i	0.516134	−	0.893971i	−0.483690	−	0.875239i	$-0.660704\pi$
$113$	5.48658	−	9.50304i	0.516134	−	0.893971i	0.999825	−	0.0187317i	$-0.00596282\pi$
$114$		0			0
$115$	−0.0141899	+	0.0245777i	−0.00132322	+	0.00229188i
$116$		0			0
$117$	1.35309	−	0.567611i	0.125093	−	0.0524757i
$118$		0			0
$119$	13.4462	−	5.64293i	1.23261	−	0.517287i
$120$		0			0
$121$	−5.12844	−	8.88272i	−0.466222	−	0.807520i
$122$		0			0
$123$	−6.55763	+	5.77702i	−0.591281	+	0.520897i
$124$		0			0
$125$	−5.11451			−0.457456
$126$		0			0
$127$	16.6107			1.47396			0.736979	−	0.675915i	$-0.236252\pi$
$127$	16.6107			1.47396			0.736979	+	0.675915i	$0.236252\pi$
$128$		0			0
$129$	1.94710	+	9.67500i	0.171433	+	0.851836i
$130$		0			0
$131$	2.90848	+	5.03763i	0.254115	+	0.440140i	0.964655	−	0.263517i	$-0.0848825\pi$
$131$	2.90848	+	5.03763i	0.254115	+	0.440140i	−0.710540	+	0.703657i	$0.751549\pi$
$132$		0			0
$133$	7.74263	+	5.88418i	0.671371	+	0.510223i
$134$		0			0
$135$	−1.19230	+	2.45943i	−0.102617	+	0.211674i
$136$		0			0
$137$	4.61313	−	7.99017i	0.394126	−	0.682647i	−0.598863	−	0.800852i	$-0.704381\pi$
$137$	4.61313	−	7.99017i	0.394126	−	0.682647i	0.992989	+	0.118205i	$0.0377139\pi$
$138$		0			0
$139$	−6.88477	+	11.9248i	−0.583959	+	1.01145i	0.411046	+	0.911615i	$0.365164\pi$
$139$	−6.88477	+	11.9248i	−0.583959	+	1.01145i	−0.995004	+	0.0998314i	$0.968170\pi$
$140$		0			0
$141$	−15.0945	−	5.08606i	−1.27118	−	0.428323i
$142$		0			0
$143$	−1.12752	−	1.95292i	−0.0942880	−	0.163312i
$144$		0			0
$145$	−1.72777	+	2.99259i	−0.143484	+	0.248521i
$146$		0			0
$147$	10.1581	+	6.61915i	0.837826	+	0.545938i
$148$		0			0
$149$	4.15043	+	7.18875i	0.340016	+	0.588926i	0.984435	−	0.175747i	$-0.0562340\pi$
$149$	4.15043	+	7.18875i	0.340016	+	0.588926i	−0.644419	+	0.764673i	$0.722901\pi$
$150$		0			0
$151$	−7.24894	+	12.5555i	−0.589911	+	1.02176i	0.404333	+	0.914612i	$0.367504\pi$
$151$	−7.24894	+	12.5555i	−0.589911	+	1.02176i	−0.994244	+	0.107143i	$0.965830\pi$
$152$		0			0
$153$	−2.08447	+	16.4028i	−0.168520	+	1.32609i
$154$		0			0
$155$	1.59811	+	2.76800i	0.128363	+	0.222331i
$156$		0			0
$157$	−12.4887			−0.996705			−0.498352	−	0.866975i	$-0.666061\pi$
$157$	−12.4887			−0.996705			−0.498352	+	0.866975i	$0.666061\pi$
$158$		0			0
$159$	2.98762	+	14.8452i	0.236934	+	1.17730i
$160$		0			0
$161$	−0.131627	+	0.0552394i	−0.0103736	+	0.00435348i
$162$		0			0
$163$	2.48448	−	4.30325i	0.194600	−	0.337057i	−0.752169	−	0.658970i	$-0.770993\pi$
$163$	2.48448	−	4.30325i	0.194600	−	0.337057i	0.946769	+	0.321913i	$0.104326\pi$
$164$		0			0
$165$	3.98060	+	1.34126i	0.309889	+	0.104417i
$166$		0			0
$167$	10.0088	−	17.3357i	0.774504	−	1.34148i	−0.160569	−	0.987025i	$-0.551333\pi$
$167$	10.0088	−	17.3357i	0.774504	−	1.34148i	0.935073	−	0.354456i	$-0.115334\pi$
$168$		0			0
$169$	6.38039	+	11.0512i	0.490799	+	0.850089i
$170$		0			0
$171$	−10.1684	+	4.26558i	−0.777600	+	0.326197i
$172$		0			0
$173$	9.05485			0.688427			0.344214	−	0.938891i	$-0.388146\pi$
$173$	9.05485			0.688427			0.344214	+	0.938891i	$0.388146\pi$
$174$		0			0
$175$	−9.94956	−	7.56138i	−0.752116	−	0.571587i
$176$		0			0
$177$	−10.8836	−	3.66721i	−0.818061	−	0.275644i
$178$		0			0
$179$	7.69175	+	13.3225i	0.574908	+	0.995770i	0.996052	+	0.0887763i	$0.0282956\pi$
$179$	7.69175	+	13.3225i	0.574908	+	0.995770i	−0.421143	+	0.906994i	$0.638371\pi$
$180$		0			0
$181$	−9.54973			−0.709826			−0.354913	−	0.934899i	$-0.615489\pi$
$181$	−9.54973			−0.709826			−0.354913	+	0.934899i	$0.615489\pi$
$182$		0			0
$183$	0.764266	+	0.257518i	0.0564962	+	0.0190363i
$184$		0			0
$185$	−0.235367			−0.0173045
$186$		0			0
$187$	25.4113			1.85826
$188$		0			0
$189$	−12.2599	+	6.22053i	−0.891776	+	0.452477i
$190$		0			0
$191$	11.0433			0.799063			0.399531	−	0.916720i	$-0.369173\pi$
$191$	11.0433			0.799063			0.399531	+	0.916720i	$0.369173\pi$
$192$		0			0
$193$	26.6991			1.92185			0.960923	−	0.276817i	$-0.0892796\pi$
$193$	26.6991			1.92185			0.960923	+	0.276817i	$0.0892796\pi$
$194$		0			0
$195$	0.422282	+	0.142287i	0.0302403	+	0.0101894i
$196$		0			0
$197$	12.8386			0.914715			0.457357	−	0.889283i	$-0.348796\pi$
$197$	12.8386			0.914715			0.457357	+	0.889283i	$0.348796\pi$
$198$		0			0
$199$	−10.1408	−	17.5644i	−0.718864	−	1.24511i	−0.961450	−	0.274979i	$-0.911329\pi$
$199$	−10.1408	−	17.5644i	−0.718864	−	1.24511i	0.242586	−	0.970130i	$-0.422004\pi$
$200$		0			0
$201$	8.52463	+	2.87236i	0.601281	+	0.202601i
$202$		0			0
$203$	−16.0269	+	6.72597i	−1.12487	+	0.472071i
$204$		0			0
$205$	−2.65405			−0.185367
$206$		0			0
$207$	0.0204052	−	0.160570i	0.00141826	−	0.0111604i
$208$		0			0
$209$	8.47329	+	14.6762i	0.586109	+	1.01517i
$210$		0			0
$211$	−4.77903	+	8.27752i	−0.329002	+	0.569848i	−0.982314	−	0.187241i	$-0.940046\pi$
$211$	−4.77903	+	8.27752i	−0.329002	+	0.569848i	0.653312	+	0.757088i	$0.273379\pi$
$212$		0			0
$213$	2.89422	+	0.975202i	0.198308	+	0.0668197i
$214$		0			0
$215$	−1.49855	+	2.59556i	−0.102200	+	0.177016i
$216$		0			0
$217$	−2.02435	+	15.9487i	−0.137422	+	1.08267i
$218$		0			0
$219$	3.57975	+	17.7875i	0.241897	+	1.20197i
$220$		0			0
$221$	2.69576			0.181337
$222$		0			0
$223$	−11.9155	−	20.6383i	−0.797921	−	1.38204i	−0.920968	−	0.389639i	$-0.872600\pi$
$223$	−11.9155	−	20.6383i	−0.797921	−	1.38204i	0.123046	−	0.992401i	$-0.460734\pi$
$224$		0			0
$225$	13.0668	−	5.48143i	0.871121	−	0.365429i
$226$		0			0
$227$	−1.33567	+	2.31345i	−0.0886514	+	0.153549i	−0.906941	−	0.421257i	$-0.861589\pi$
$227$	−1.33567	+	2.31345i	−0.0886514	+	0.153549i	0.818290	+	0.574806i	$0.194922\pi$
$228$		0			0
$229$	−3.16258	−	5.47775i	−0.208989	−	0.361980i	0.742407	−	0.669949i	$-0.233684\pi$
$229$	−3.16258	−	5.47775i	−0.208989	−	0.361980i	−0.951396	+	0.307969i	$0.900351\pi$
$230$		0			0
$231$	11.8590	+	17.4860i	0.780262	+	1.15049i
$232$		0			0
$233$	4.63381	−	8.02600i	0.303571	−	0.525801i	−0.673371	−	0.739305i	$-0.735154\pi$
$233$	4.63381	−	8.02600i	0.303571	−	0.525801i	0.976942	+	0.213504i	$0.0684877\pi$
$234$		0			0
$235$	−2.41862	−	4.18918i	−0.157774	−	0.273272i
$236$		0			0
$237$	26.8697	+	9.05369i	1.74537	+	0.588100i
$238$		0			0
$239$	−1.69219	+	2.93096i	−0.109459	+	0.189588i	−0.915551	−	0.402202i	$-0.868245\pi$
$239$	−1.69219	+	2.93096i	−0.109459	+	0.189588i	0.806092	+	0.591790i	$0.201578\pi$
$240$		0			0
$241$	−6.57982	+	11.3966i	−0.423844	+	0.734119i	−0.996312	−	0.0858082i	$-0.972653\pi$
$241$	−6.57982	+	11.3966i	−0.423844	+	0.734119i	0.572468	+	0.819927i	$0.305986\pi$
$242$		0			0
$243$	0.844585	−	15.5656i	0.0541801	−	0.998531i
$244$		0			0
$245$	0.985984	+	3.54756i	0.0629922	+	0.226645i
$246$		0			0
$247$	0.898890	+	1.55692i	0.0571950	+	0.0990647i
$248$		0			0
$249$	3.07041	+	15.2566i	0.194579	+	0.966849i
$250$		0			0
$251$	2.30235			0.145323			0.0726614	−	0.997357i	$-0.476851\pi$
$251$	2.30235			0.145323			0.0726614	+	0.997357i	$0.476851\pi$
$252$		0			0
$253$	−0.248755			−0.0156391
$254$		0			0
$255$	−3.76785	+	3.31933i	−0.235952	+	0.207865i
$256$		0			0
$257$	14.5661	+	25.2293i	0.908610	+	1.57376i	0.815997	+	0.578056i	$0.196189\pi$
$257$	14.5661	+	25.2293i	0.908610	+	1.57376i	0.0926132	+	0.995702i	$0.470478\pi$
$258$		0			0
$259$	−0.942567	−	0.716324i	−0.0585683	−	0.0445102i
$260$		0			0
$261$	2.48454	−	19.5510i	0.153789	−	1.21018i
$262$		0			0
$263$	−1.35919	+	2.35418i	−0.0838110	+	0.145165i	−0.904884	−	0.425658i	$-0.860043\pi$
$263$	−1.35919	+	2.35418i	−0.0838110	+	0.145165i	0.821073	+	0.570823i	$0.193376\pi$
$264$		0			0
$265$	−2.29936	+	3.98261i	−0.141249	+	0.244650i
$266$		0			0
$267$	18.3289	−	16.1471i	1.12171	−	0.988184i
$268$		0			0
$269$	2.80840	+	4.86428i	0.171231	+	0.296581i	0.938850	−	0.344325i	$-0.111892\pi$
$269$	2.80840	+	4.86428i	0.171231	+	0.296581i	−0.767620	+	0.640906i	$0.778559\pi$
$270$		0			0
$271$	7.25164	−	12.5602i	0.440506	−	0.762978i	−0.557221	−	0.830364i	$-0.688133\pi$
$271$	7.25164	−	12.5602i	0.440506	−	0.762978i	0.997727	+	0.0673860i	$0.0214659\pi$
$272$		0			0
$273$	1.25806	+	1.85500i	0.0761412	+	0.112270i
$274$		0			0
$275$	−10.8885	−	18.8594i	−0.656600	−	1.13726i
$276$		0			0
$277$	0.873953	−	1.51373i	0.0525108	−	0.0909513i	−0.838575	−	0.544786i	$-0.816611\pi$
$277$	0.873953	−	1.51373i	0.0525108	−	0.0909513i	0.891086	+	0.453835i	$0.149944\pi$
$278$		0			0
$279$	−14.5119	−	11.0321i	−0.868808	−	0.660473i
$280$		0			0
$281$	5.35657	+	9.27786i	0.319546	+	0.553471i	0.980393	−	0.197050i	$-0.0631361\pi$
$281$	5.35657	+	9.27786i	0.319546	+	0.553471i	−0.660847	+	0.750521i	$0.729803\pi$
$282$		0			0
$283$	12.5967			0.748793			0.374397	−	0.927269i	$-0.377850\pi$
$283$	12.5967			0.748793			0.374397	+	0.927269i	$0.377850\pi$
$284$		0			0
$285$	−3.17344	−	1.06929i	−0.187978	−	0.0633390i
$286$		0			0
$287$	−10.6286	−	8.07743i	−0.627386	−	0.476796i
$288$		0			0
$289$	−6.68881	+	11.5854i	−0.393459	+	0.681491i
$290$		0			0
$291$	−3.57044	−	17.7412i	−0.209303	−	1.04001i
$292$		0			0
$293$	−1.57575	+	2.72928i	−0.0920562	+	0.159446i	−0.908376	−	0.418154i	$-0.862677\pi$
$293$	−1.57575	+	2.72928i	−0.0920562	+	0.159446i	0.816320	+	0.577600i	$0.196011\pi$
$294$		0			0
$295$	−1.74391	−	3.02053i	−0.101534	−	0.175862i
$296$		0			0
$297$	−23.8946	+	1.72809i	−1.38650	+	0.100274i
$298$		0			0
$299$	−0.0263892			−0.00152613
$300$		0			0
$301$	−13.9006	+	5.83364i	−0.801220	+	0.336245i
$302$		0			0
$303$	−12.9511	+	11.4095i	−0.744024	+	0.655457i
$304$		0			0
$305$	0.122460	+	0.212107i	0.00701206	+	0.0121452i
$306$		0			0
$307$	20.3884			1.16363			0.581813	−	0.813322i	$-0.302343\pi$
$307$	20.3884			1.16363			0.581813	+	0.813322i	$0.302343\pi$
$308$		0			0
$309$	−3.98146	−	19.7836i	−0.226497	−	1.12545i
$310$		0			0
$311$	−22.7014			−1.28728			−0.643640	−	0.765328i	$-0.722577\pi$
$311$	−22.7014			−1.28728			−0.643640	+	0.765328i	$0.722577\pi$
$312$		0			0
$313$	−16.7078			−0.944380			−0.472190	−	0.881497i	$-0.656536\pi$
$313$	−16.7078			−0.944380			−0.472190	+	0.881497i	$0.656536\pi$
$314$		0			0
$315$	−4.04248	−	1.04366i	−0.227768	−	0.0588036i
$316$		0			0
$317$	10.3280			0.580080			0.290040	−	0.957015i	$-0.406331\pi$
$317$	10.3280			0.580080			0.290040	+	0.957015i	$0.406331\pi$
$318$		0			0
$319$	−30.2884			−1.69583
$320$		0			0
$321$	6.38276	−	5.62297i	0.356251	−	0.313844i
$322$		0			0
$323$	−20.2586			−1.12722
$324$		0			0
$325$	−1.15511	−	2.00070i	−0.0640738	−	0.110979i
$326$		0			0
$327$	6.67289	+	33.1571i	0.369012	+	1.83359i
$328$		0			0
$329$	3.06371	−	24.1372i	0.168908	−	1.33073i
$330$		0			0
$331$	22.6315			1.24394			0.621970	−	0.783041i	$-0.286332\pi$
$331$	22.6315			1.24394			0.621970	+	0.783041i	$0.286332\pi$
$332$		0			0
$333$	1.23788	−	0.519281i	0.0678354	−	0.0284564i
$334$		0			0
$335$	1.36592	+	2.36585i	0.0746283	+	0.129260i
$336$		0			0
$337$	6.78253	−	11.7477i	0.369468	−	0.639938i	−0.620014	−	0.784590i	$-0.712873\pi$
$337$	6.78253	−	11.7477i	0.369468	−	0.639938i	0.989482	+	0.144653i	$0.0462066\pi$
$338$		0			0
$339$	−14.2613	+	12.5637i	−0.774568	+	0.682366i
$340$		0			0
$341$	−14.0077	+	24.2620i	−0.758558	+	1.31386i
$342$		0			0
$343$	−6.84824	+	17.2076i	−0.369770	+	0.929123i
$344$		0			0
$345$	0.0368840	−	0.0324934i	0.00198577	−	0.00174939i
$346$		0			0
$347$	33.0262			1.77294			0.886470	−	0.462786i	$-0.153150\pi$
$347$	33.0262			1.77294			0.886470	+	0.462786i	$0.153150\pi$
$348$		0			0
$349$	−10.1773	−	17.6276i	−0.544778	−	0.943584i	−0.998621	−	0.0525019i	$-0.983280\pi$
$349$	−10.1773	−	17.6276i	−0.544778	−	0.943584i	0.453842	−	0.891082i	$-0.350053\pi$
$350$		0			0
$351$	−2.53486	+	0.183325i	−0.135301	+	0.00978514i
$352$		0			0
$353$	2.75381	−	4.76975i	0.146571	−	0.253868i	−0.783387	−	0.621534i	$-0.786510\pi$
$353$	2.75381	−	4.76975i	0.146571	−	0.253868i	0.929958	+	0.367666i	$0.119843\pi$
$354$		0			0
$355$	0.463748	+	0.803234i	0.0246132	+	0.0426312i
$356$		0			0
$357$	−25.1912	+	1.82563i	−1.33326	+	0.0966224i
$358$		0			0
$359$	10.4656	−	18.1270i	0.552354	−	0.956704i	−0.445751	−	0.895157i	$-0.647063\pi$
$359$	10.4656	−	18.1270i	0.552354	−	0.956704i	0.998104	−	0.0615472i	$-0.0196035\pi$
$360$		0			0
$361$	2.74486	+	4.75424i	0.144467	+	0.250223i
$362$		0			0
$363$	3.50504	+	17.4163i	0.183967	+	0.914116i
$364$		0			0
$365$	−2.75509	+	4.77195i	−0.144208	+	0.249775i
$366$		0			0
$367$	2.14319	−	3.71211i	0.111873	−	0.193770i	−0.804652	−	0.593746i	$-0.797648\pi$
$367$	2.14319	−	3.71211i	0.111873	−	0.193770i	0.916526	+	0.399976i	$0.130982\pi$
$368$		0			0
$369$	13.9586	−	5.85552i	0.726655	−	0.304826i
$370$		0			0
$371$	−21.3290	+	8.95110i	−1.10735	+	0.464718i
$372$		0			0
$373$	5.64461	+	9.77675i	0.292267	+	0.506221i	0.974345	−	0.225058i	$-0.0722571\pi$
$373$	5.64461	+	9.77675i	0.292267	+	0.506221i	−0.682079	+	0.731279i	$0.738924\pi$
$374$		0			0
$375$	8.39485	+	2.82863i	0.433508	+	0.146070i
$376$		0			0
$377$	−3.21316			−0.165486
$378$		0			0
$379$	20.5828			1.05727			0.528634	−	0.848850i	$-0.322705\pi$
$379$	20.5828			1.05727			0.528634	+	0.848850i	$0.322705\pi$
$380$		0			0
$381$	−27.2644	−	9.18670i	−1.39680	−	0.470649i
$382$		0			0
$383$	−10.8108	−	18.7248i	−0.552405	−	0.956793i	−0.998100	−	0.0616083i	$-0.980377\pi$
$383$	−10.8108	−	18.7248i	−0.552405	−	0.956793i	0.445696	−	0.895184i	$-0.352956\pi$
$384$		0			0
$385$	−0.807939	+	6.36528i	−0.0411764	+	0.324405i
$386$		0			0
$387$	2.15492	−	16.9572i	0.109541	−	0.861983i
$388$		0			0
$389$	7.34241	−	12.7174i	0.372275	−	0.644799i	−0.617640	−	0.786461i	$-0.711911\pi$
$389$	7.34241	−	12.7174i	0.372275	−	0.644799i	0.989915	+	0.141662i	$0.0452446\pi$
$390$		0			0
$391$	0.148685	−	0.257531i	0.00751934	−	0.0130239i
$392$		0			0
$393$	−1.98780	−	9.87723i	−0.100271	−	0.498240i
$394$		0			0
$395$	4.30539	+	7.45716i	0.216628	+	0.375210i
$396$		0			0
$397$	−3.13424	+	5.42866i	−0.157303	+	0.272457i	−0.933895	−	0.357547i	$-0.883613\pi$
$397$	−3.13424	+	5.42866i	−0.157303	+	0.272457i	0.776592	+	0.630003i	$0.216947\pi$
$398$		0			0
$399$	−9.45428	−	13.9403i	−0.473306	−	0.697888i
$400$		0			0
$401$	−14.6951	−	25.4526i	−0.733836	−	1.27104i	−0.955232	−	0.295857i	$-0.904395\pi$
$401$	−14.6951	−	25.4526i	−0.733836	−	1.27104i	0.221396	−	0.975184i	$-0.428939\pi$
$402$		0			0
$403$	−1.48601	+	2.57384i	−0.0740232	+	0.128212i
$404$		0			0
$405$	3.31723	−	3.37744i	0.164834	−	0.167827i
$406$		0			0
$407$	−1.03152	−	1.78664i	−0.0511303	−	0.0885603i
$408$		0			0
$409$	−1.63285			−0.0807392			−0.0403696	−	0.999185i	$-0.512854\pi$
$409$	−1.63285			−0.0807392			−0.0403696	+	0.999185i	$0.512854\pi$
$410$		0			0
$411$	−11.9909	+	10.5636i	−0.591469	+	0.521062i
$412$		0			0
$413$	2.20904	−	17.4037i	0.108700	−	0.856381i
$414$		0			0
$415$	−2.36308	+	4.09298i	−0.115999	+	0.200916i
$416$		0			0
$417$	17.8956	−	15.7654i	0.876353	−	0.772034i
$418$		0			0
$419$	9.01823	−	15.6200i	0.440569	−	0.763088i	−0.557162	−	0.830404i	$-0.688110\pi$
$419$	9.01823	−	15.6200i	0.440569	−	0.763088i	0.997732	+	0.0673151i	$0.0214433\pi$
$420$		0			0
$421$	16.8278	+	29.1465i	0.820135	+	1.42052i	0.905581	+	0.424172i	$0.139435\pi$
$421$	16.8278	+	29.1465i	0.820135	+	1.42052i	−0.0854466	+	0.996343i	$0.527232\pi$
$422$		0			0
$423$	21.9628	+	16.6963i	1.06787	+	0.811801i
$424$		0			0
$425$	26.0330			1.26279
$426$		0			0
$427$	−0.155123	+	1.22212i	−0.00750691	+	0.0591426i
$428$		0			0
$429$	0.770605	+	3.82907i	0.0372051	+	0.184869i
$430$		0			0
$431$	11.1545	+	19.3202i	0.537295	+	0.930622i	0.999048	+	0.0436135i	$0.0138870\pi$
$431$	11.1545	+	19.3202i	0.537295	+	0.930622i	−0.461754	+	0.887008i	$0.652780\pi$
$432$		0			0
$433$	7.32414			0.351976			0.175988	−	0.984392i	$-0.443688\pi$
$433$	7.32414			0.351976			0.175988	+	0.984392i	$0.443688\pi$
$434$		0			0
$435$	4.49101	−	3.95641i	0.215327	−	0.189695i
$436$		0			0
$437$	0.198314			0.00948664
$438$		0			0
$439$	24.6728			1.17757			0.588785	−	0.808289i	$-0.299606\pi$
$439$	24.6728			1.17757			0.588785	+	0.808289i	$0.299606\pi$
$440$		0			0
$441$	−13.0125	−	16.4826i	−0.619643	−	0.784884i
$442$		0			0
$443$	−30.5363			−1.45082			−0.725412	−	0.688315i	$-0.758351\pi$
$443$	−30.5363			−1.45082			−0.725412	+	0.688315i	$0.758351\pi$
$444$		0			0
$445$	7.41819			0.351656
$446$		0			0
$447$	−2.83661	−	14.0949i	−0.134167	−	0.666666i
$448$		0			0
$449$	−41.4782			−1.95748			−0.978738	−	0.205116i	$-0.934243\pi$
$449$	−41.4782			−1.95748			−0.978738	+	0.205116i	$0.934243\pi$
$450$		0			0
$451$	−11.6316	−	20.1465i	−0.547710	−	0.948662i
$452$		0			0
$453$	18.8422	−	16.5993i	0.885285	−	0.779903i
$454$		0			0
$455$	−0.0857103	+	0.675262i	−0.00401816	+	0.0316568i
$456$		0			0
$457$	−11.6289			−0.543978			−0.271989	−	0.962300i	$-0.587681\pi$
$457$	−11.6289			−0.543978			−0.271989	+	0.962300i	$0.587681\pi$
$458$		0			0
$459$	12.4932	−	25.7705i	0.583131	−	1.20286i
$460$		0			0
$461$	−5.60886	−	9.71483i	−0.261231	−	0.452465i	0.705339	−	0.708871i	$-0.250795\pi$
$461$	−5.60886	−	9.71483i	−0.261231	−	0.452465i	−0.966569	+	0.256406i	$0.917462\pi$
$462$		0			0
$463$	19.9362	−	34.5305i	0.926514	−	1.60477i	0.137405	−	0.990515i	$-0.456124\pi$
$463$	19.9362	−	34.5305i	0.926514	−	1.60477i	0.789108	−	0.614254i	$-0.210543\pi$
$464$		0			0
$465$	−1.09223	−	5.42718i	−0.0506508	−	0.251680i
$466$		0			0
$467$	−11.7818	+	20.4067i	−0.545198	+	0.944311i	0.453397	+	0.891309i	$0.350212\pi$
$467$	−11.7818	+	20.4067i	−0.545198	+	0.944311i	−0.998594	+	0.0530016i	$0.983121\pi$
$468$		0			0
$469$	−1.73024	+	13.6315i	−0.0798950	+	0.629446i
$470$		0			0
$471$	20.4986	+	6.90699i	0.944528	+	0.318257i
$472$		0			0
$473$	−26.2701			−1.20790
$474$		0			0
$475$	8.68059	+	15.0352i	0.398293	+	0.689864i
$476$		0			0
$477$	3.30650	−	26.0190i	0.151394	−	1.19133i
$478$		0			0
$479$	7.11485	−	12.3233i	0.325086	−	0.563065i	−0.656444	−	0.754375i	$-0.727940\pi$
$479$	7.11485	−	12.3233i	0.325086	−	0.563065i	0.981530	+	0.191310i	$0.0612735\pi$
$480$		0			0
$481$	−0.109428	−	0.189536i	−0.00498951	−	0.00864208i
$482$		0			0
$483$	0.246600	−	0.0178713i	0.0112207	−	0.000813173i
$484$		0			0
$485$	2.74792	−	4.75953i	0.124776	−	0.216119i
$486$		0			0
$487$	13.9818	+	24.2171i	0.633574	+	1.09738i	0.986815	+	0.161850i	$0.0517460\pi$
$487$	13.9818	+	24.2171i	0.633574	+	1.09738i	−0.353242	+	0.935532i	$0.614921\pi$
$488$		0			0
$489$	−6.45794	+	5.68920i	−0.292038	+	0.257275i
$490$		0			0
$491$	−17.2543	+	29.8853i	−0.778676	+	1.34871i	0.154030	+	0.988066i	$0.450775\pi$
$491$	−17.2543	+	29.8853i	−0.778676	+	1.34871i	−0.932705	+	0.360639i	$0.882558\pi$
$492$		0			0
$493$	18.1040	−	31.3570i	0.815362	−	1.41225i
$494$		0			0
$495$	−5.79187	−	4.40302i	−0.260325	−	0.197901i
$496$		0			0
$497$	−0.587437	+	4.62808i	−0.0263502	+	0.207598i
$498$		0			0
$499$	13.1436	+	22.7654i	0.588390	+	1.01912i	0.994443	+	0.105272i	$0.0335712\pi$
$499$	13.1436	+	22.7654i	0.588390	+	1.01912i	−0.406054	+	0.913849i	$0.633095\pi$
$500$		0			0
$501$	−26.0159	+	22.9191i	−1.16231	+	1.02395i
$502$		0			0
$503$	−6.09068			−0.271570			−0.135785	−	0.990738i	$-0.543356\pi$
$503$	−6.09068			−0.271570			−0.135785	+	0.990738i	$0.543356\pi$
$504$		0			0
$505$	−5.24167			−0.233251
$506$		0			0
$507$	−4.36068	−	21.6679i	−0.193665	−	0.962304i
$508$		0			0
$509$	4.08615	+	7.07742i	0.181116	+	0.313701i	0.942261	−	0.334880i	$-0.108696\pi$
$509$	4.08615	+	7.07742i	0.181116	+	0.313701i	−0.761145	+	0.648582i	$0.775363\pi$
$510$		0			0
$511$	−25.5564	+	10.7252i	−1.13055	+	0.474453i
$512$		0			0
$513$	19.0494	−	1.37768i	0.841051	−	0.0608260i
$514$		0			0
$515$	3.06425	−	5.30744i	0.135027	−	0.233874i
$516$		0			0
$517$	21.1996	−	36.7189i	0.932360	−	1.61489i
$518$		0			0
$519$	−14.8624	−	5.00788i	−0.652389	−	0.219821i
$520$		0			0
$521$	13.0485	+	22.6007i	0.571666	+	0.990155i	0.996395	+	0.0848346i	$0.0270362\pi$
$521$	13.0485	+	22.6007i	0.571666	+	0.990155i	−0.424729	+	0.905321i	$0.639630\pi$
$522$		0			0
$523$	−13.6655	+	23.6694i	−0.597553	+	1.03499i	0.395628	+	0.918411i	$0.370527\pi$
$523$	−13.6655	+	23.6694i	−0.597553	+	1.03499i	−0.993181	+	0.116581i	$0.962807\pi$
$524$		0			0
$525$	12.1491	+	17.9138i	0.530230	+	0.781822i
$526$		0			0
$527$	−16.7453	−	29.0037i	−0.729437	−	1.26342i
$528$		0			0
$529$	11.4985	−	19.9161i	0.499937	−	0.865916i
$530$		0			0
$531$	15.8359	+	12.0386i	0.687220	+	0.522429i
$532$		0			0
$533$	−1.23394	−	2.13725i	−0.0534478	−	0.0925744i
$534$		0			0
$535$	2.58327			0.111685
$536$		0			0
$537$	−5.25693	−	26.1213i	−0.226853	−	1.12722i
$538$		0			0
$539$	−22.6079	+	23.0320i	−0.973790	+	0.992057i
$540$		0			0
$541$	−5.79086	+	10.0301i	−0.248969	+	0.431226i	−0.963240	−	0.268643i	$-0.913425\pi$
$541$	−5.79086	+	10.0301i	−0.248969	+	0.431226i	0.714271	+	0.699869i	$0.246758\pi$
$542$		0			0
$543$	15.6747	+	5.28157i	0.672667	+	0.226654i
$544$		0			0
$545$	−5.13566	+	8.89522i	−0.219987	+	0.381029i
$546$		0			0
$547$	−20.3651	−	35.2734i	−0.870750	−	1.50818i	−0.861222	−	0.508228i	$-0.830301\pi$
$547$	−20.3651	−	35.2734i	−0.870750	−	1.50818i	−0.00952755	−	0.999955i	$-0.503033\pi$
$548$		0			0
$549$	−1.11203	−	0.845370i	−0.0474602	−	0.0360795i
$550$		0			0
$551$	24.1468			1.02869
$552$		0			0
$553$	−5.45372	+	42.9667i	−0.231916	+	1.82713i
$554$		0			0
$555$	0.386326	+	0.130172i	0.0163986	+	0.00552549i
$556$		0			0
$557$	10.0085	+	17.3353i	0.424075	+	0.734520i	0.996334	−	0.0855533i	$-0.0272658\pi$
$557$	10.0085	+	17.3353i	0.424075	+	0.734520i	−0.572258	+	0.820074i	$0.693932\pi$
$558$		0			0
$559$	−2.78687			−0.117872
$560$		0			0
$561$	−41.7095	−	14.0540i	−1.76098	−	0.593359i
$562$		0			0
$563$	−24.9328			−1.05079			−0.525396	−	0.850858i	$-0.676083\pi$
$563$	−24.9328			−1.05079			−0.525396	+	0.850858i	$0.676083\pi$
$564$		0			0
$565$	−5.77193			−0.242827
$566$		0			0
$567$	23.5635	−	3.42978i	0.989572	−	0.144037i
$568$		0			0
$569$	−9.80025			−0.410848			−0.205424	−	0.978673i	$-0.565857\pi$
$569$	−9.80025			−0.410848			−0.205424	+	0.978673i	$0.565857\pi$
$570$		0			0
$571$	40.7895			1.70699			0.853494	−	0.521103i	$-0.174479\pi$
$571$	40.7895			1.70699			0.853494	+	0.521103i	$0.174479\pi$
$572$		0			0
$573$	−18.1262	−	6.10759i	−0.757232	−	0.255148i
$574$		0			0
$575$	−0.254841			−0.0106276
$576$		0			0
$577$	−10.2505	−	17.7544i	−0.426734	−	0.739125i	0.569846	−	0.821751i	$-0.307003\pi$
$577$	−10.2505	−	17.7544i	−0.426734	−	0.739125i	−0.996581	+	0.0826259i	$0.973669\pi$
$578$		0			0
$579$	−43.8234	−	14.7662i	−1.82124	−	0.613663i
$580$		0			0
$581$	−21.9201	+	9.19914i	−0.909399	+	0.381645i
$582$		0			0
$583$	−40.3086			−1.66941
$584$		0			0
$585$	−0.614432	−	0.467095i	−0.0254036	−	0.0193120i
$586$		0			0
$587$	19.2916	+	33.4141i	0.796251	+	1.37915i	0.922042	+	0.387090i	$0.126520\pi$
$587$	19.2916	+	33.4141i	0.796251	+	1.37915i	−0.125791	+	0.992057i	$0.540147\pi$
$588$		0			0
$589$	11.1673	−	19.3423i	0.460141	−	0.796987i
$590$		0			0
$591$	−21.0731	−	7.10053i	−0.866830	−	0.292077i
$592$		0			0
$593$	−1.26539	+	2.19172i	−0.0519634	+	0.0900032i	−0.890837	−	0.454323i	$-0.849881\pi$
$593$	−1.26539	+	2.19172i	−0.0519634	+	0.0900032i	0.838874	+	0.544326i	$0.183215\pi$
$594$		0			0
$595$	−6.10693	−	4.64109i	−0.250360	−	0.190266i
$596$		0			0
$597$	6.93076	+	34.4384i	0.283657	+	1.40947i
$598$		0			0
$599$	16.0218			0.654634			0.327317	−	0.944915i	$-0.393855\pi$
$599$	16.0218			0.654634			0.327317	+	0.944915i	$0.393855\pi$
$600$		0			0
$601$	−22.1601	−	38.3824i	−0.903929	−	1.56565i	−0.822349	−	0.568983i	$-0.807337\pi$
$601$	−22.1601	−	38.3824i	−0.903929	−	1.56565i	−0.0815796	−	0.996667i	$-0.525996\pi$
$602$		0			0
$603$	−12.4036	−	9.42926i	−0.505112	−	0.383989i
$604$		0			0
$605$	−2.69758	+	4.67235i	−0.109672	+	0.189958i
$606$		0			0
$607$	−4.79607	−	8.30704i	−0.194666	−	0.337172i	0.752125	−	0.659021i	$-0.229029\pi$
$607$	−4.79607	−	8.30704i	−0.194666	−	0.337172i	−0.946791	+	0.321849i	$0.895696\pi$
$608$		0			0
$609$	30.0261	−	2.17602i	1.21672	−	0.0881767i
$610$		0			0
$611$	2.24897	−	3.89533i	0.0909835	−	0.157588i
$612$		0			0
$613$	11.2371	+	19.4632i	0.453861	+	0.786110i	0.998622	−	0.0524815i	$-0.0167131\pi$
$613$	11.2371	+	19.4632i	0.453861	+	0.786110i	−0.544761	+	0.838591i	$0.683380\pi$
$614$		0			0
$615$	4.35630	+	1.46785i	0.175663	+	0.0591893i
$616$		0			0
$617$	11.7056	−	20.2746i	0.471248	−	0.816226i	−0.528211	−	0.849113i	$-0.677137\pi$
$617$	11.7056	−	20.2746i	0.471248	−	0.816226i	0.999459	+	0.0328875i	$0.0104703\pi$
$618$		0			0
$619$	7.98843	−	13.8364i	0.321082	−	0.556131i	−0.659629	−	0.751591i	$-0.729287\pi$
$619$	7.98843	−	13.8364i	0.321082	−	0.556131i	0.980712	+	0.195460i	$0.0626201\pi$
$620$		0			0
$621$	−0.122297	+	0.252271i	−0.00490762	+	0.0101233i
$622$		0			0
$623$	29.7074	+	22.5768i	1.19020	+	0.904521i
$624$		0			0
$625$	−10.4632	−	18.1227i	−0.418527	−	0.724910i
$626$		0			0
$627$	−5.79107	−	28.7754i	−0.231273	−	1.14918i
$628$		0			0
$629$	2.46622			0.0983348
$630$		0			0
$631$	0.882517			0.0351324			0.0175662	−	0.999846i	$-0.494408\pi$
$631$	0.882517			0.0351324			0.0175662	+	0.999846i	$0.494408\pi$
$632$		0			0
$633$	12.4222	−	10.9435i	0.493736	−	0.434963i
$634$		0			0
$635$	−4.36864	−	7.56671i	−0.173364	−	0.300276i
$636$		0			0
$637$	−2.39836	+	2.44335i	−0.0950265	+	0.0968090i
$638$		0			0
$639$	−4.21116	−	3.20135i	−0.166591	−	0.126644i
$640$		0			0
$641$	−20.2141	+	35.0118i	−0.798408	+	1.38288i	0.122244	+	0.992500i	$0.460991\pi$
$641$	−20.2141	+	35.0118i	−0.798408	+	1.38288i	−0.920652	+	0.390384i	$0.872342\pi$
$642$		0			0
$643$	−2.99047	+	5.17964i	−0.117932	+	0.204265i	−0.918948	−	0.394378i	$-0.870960\pi$
$643$	−2.99047	+	5.17964i	−0.117932	+	0.204265i	0.801016	+	0.598643i	$0.204293\pi$
$644$		0			0
$645$	3.89519	−	3.43152i	0.153373	−	0.135116i
$646$		0			0
$647$	16.4743	+	28.5343i	0.647672	+	1.12180i	0.983677	+	0.179941i	$0.0575906\pi$
$647$	16.4743	+	28.5343i	0.647672	+	1.12180i	−0.336005	+	0.941860i	$0.609076\pi$
$648$		0			0
$649$	15.2856	−	26.4755i	0.600014	−	1.03925i
$650$		0			0
$651$	12.1433	−	25.0582i	0.475933	−	0.982109i
$652$		0			0
$653$	−13.0166	−	22.5455i	−0.509380	−	0.882272i	−0.999941	−	0.0108653i	$-0.996541\pi$
$653$	−13.0166	−	22.5455i	−0.509380	−	0.882272i	0.490561	−	0.871407i	$-0.336792\pi$
$654$		0			0
$655$	1.52987	−	2.64982i	0.0597771	−	0.103537i
$656$		0			0
$657$	3.96183	−	31.1759i	0.154566	−	1.21629i
$658$		0			0
$659$	−4.91651	−	8.51565i	−0.191520	−	0.331722i	0.754234	−	0.656606i	$-0.228008\pi$
$659$	−4.91651	−	8.51565i	−0.191520	−	0.331722i	−0.945754	+	0.324883i	$0.894675\pi$
$660$		0			0
$661$	−5.51520			−0.214516			−0.107258	−	0.994231i	$-0.534207\pi$
$661$	−5.51520			−0.214516			−0.107258	+	0.994231i	$0.534207\pi$
$662$		0			0
$663$	−4.42477	−	1.49092i	−0.171844	−	0.0579024i
$664$		0			0
$665$	0.644111	−	5.07458i	0.0249776	−	0.196784i
$666$		0			0
$667$	−0.177222	+	0.306958i	−0.00686208	+	0.0118855i
$668$		0			0
$669$	8.14366	+	40.4652i	0.314852	+	1.56447i
$670$		0			0
$671$	−1.07339	+	1.85916i	−0.0414376	+	0.0717720i
$672$		0			0
$673$	19.6176	+	33.9788i	0.756205	+	1.30978i	0.944773	+	0.327725i	$0.106282\pi$
$673$	19.6176	+	33.9788i	0.756205	+	1.30978i	−0.188569	+	0.982060i	$0.560385\pi$
$674$		0			0
$675$	−24.4792	+	1.77037i	−0.942203	+	0.0681415i
$676$		0			0
$677$	−37.1632			−1.42830			−0.714149	−	0.699994i	$-0.753186\pi$
$677$	−37.1632			−1.42830			−0.714149	+	0.699994i	$0.753186\pi$
$678$		0			0
$679$	25.4899	−	10.6973i	0.978211	−	0.410523i
$680$		0			0
$681$	3.47181	−	3.05854i	0.133040	−	0.117203i
$682$		0			0
$683$	5.10586	+	8.84360i	0.195370	+	0.338391i	0.947022	−	0.321169i	$-0.104076\pi$
$683$	5.10586	+	8.84360i	0.195370	+	0.338391i	−0.751652	+	0.659560i	$0.770743\pi$
$684$		0			0
$685$	−4.85305			−0.185426
$686$		0			0
$687$	2.16147	+	10.7402i	0.0824651	+	0.409763i
$688$		0			0
$689$	−4.27615			−0.162908
$690$		0			0
$691$	35.0761			1.33436			0.667179	−	0.744897i	$-0.267501\pi$
$691$	35.0761			1.33436			0.667179	+	0.744897i	$0.267501\pi$
$692$		0			0
$693$	−9.79424	−	35.2598i	−0.372052	−	1.33941i
$694$		0			0
$695$	7.24284			0.274737
$696$		0			0
$697$	27.8097			1.05337
$698$		0			0
$699$	−12.0447	+	10.6109i	−0.455572	+	0.401342i
$700$		0			0
$701$	17.2500			0.651522			0.325761	−	0.945452i	$-0.394379\pi$
$701$	17.2500			0.651522			0.325761	+	0.945452i	$0.394379\pi$
$702$		0			0
$703$	0.822352	+	1.42436i	0.0310156	+	0.0537206i
$704$		0			0
$705$	1.65301	+	8.21367i	0.0622560	+	0.309345i
$706$		0			0
$707$	−20.9912	−	15.9527i	−0.789455	−	0.599964i
$708$		0			0
$709$	−14.5147			−0.545110			−0.272555	−	0.962140i	$-0.587869\pi$
$709$	−14.5147			−0.545110			−0.272555	+	0.962140i	$0.587869\pi$
$710$		0			0
$711$	−39.0961	−	29.7211i	−1.46622	−	1.11463i
$712$		0			0
$713$	0.163922	+	0.283921i	0.00613893	+	0.0106329i
$714$		0			0
$715$	−0.593081	+	1.02725i	−0.0221800	+	0.0384168i
$716$		0			0
$717$	4.39852	−	3.87493i	0.164266	−	0.144712i
$718$		0			0
$719$	22.4295	−	38.8491i	0.836480	−	1.44883i	−0.0563403	−	0.998412i	$-0.517943\pi$
$719$	22.4295	−	38.8491i	0.836480	−	1.44883i	0.892820	−	0.450414i	$-0.148723\pi$
$720$		0			0
$721$	28.4242	−	11.9287i	1.05857	−	0.444248i
$722$		0			0
$723$	17.1030	−	15.0671i	0.636067	−	0.560351i
$724$		0			0
$725$	−31.0295			−1.15241
$726$		0			0
$727$	2.22039	+	3.84582i	0.0823496	+	0.142634i	0.904259	−	0.426985i	$-0.140424\pi$
$727$	2.22039	+	3.84582i	0.0823496	+	0.142634i	−0.821909	+	0.569619i	$0.807091\pi$
$728$		0			0
$729$	−9.99497	+	25.0819i	−0.370184	+	0.928958i
$730$		0			0
$731$	15.7021	−	27.1969i	0.580764	−	1.00591i
$732$		0			0
$733$	19.1360	+	33.1445i	0.706803	+	1.22422i	0.966037	+	0.258405i	$0.0831968\pi$
$733$	19.1360	+	33.1445i	0.706803	+	1.22422i	−0.259233	+	0.965815i	$0.583470\pi$
$734$		0			0
$735$	0.343640	−	6.36820i	0.0126753	−	0.234895i
$736$		0			0
$737$	−11.9725	+	20.7370i	−0.441014	+	0.763859i
$738$		0			0
$739$	2.59381	+	4.49261i	0.0954148	+	0.165263i	0.909782	−	0.415087i	$-0.136249\pi$
$739$	2.59381	+	4.49261i	0.0954148	+	0.165263i	−0.814367	+	0.580350i	$0.802916\pi$
$740$		0			0
$741$	−0.614347	−	3.05264i	−0.0225686	−	0.112142i
$742$		0			0
$743$	−16.3351	+	28.2932i	−0.599276	+	1.03798i	0.393653	+	0.919259i	$0.371211\pi$
$743$	−16.3351	+	28.2932i	−0.599276	+	1.03798i	−0.992928	+	0.118716i	$0.962122\pi$
$744$		0			0
$745$	2.18314	−	3.78132i	0.0799842	−	0.138537i
$746$		0			0
$747$	3.39812	−	26.7400i	0.124331	−	0.978366i
$748$		0			0
$749$	10.3452	+	7.86203i	0.378004	+	0.287272i
$750$		0			0
$751$	−8.06106	−	13.9622i	−0.294152	−	0.509487i	0.680635	−	0.732623i	$-0.261704\pi$
$751$	−8.06106	−	13.9622i	−0.294152	−	0.509487i	−0.974787	+	0.223136i	$0.928371\pi$
$752$		0			0
$753$	−3.77902	−	1.27334i	−0.137715	−	0.0464030i
$754$		0			0
$755$	7.62595			0.277537
$756$		0			0
$757$	45.6421			1.65889			0.829444	−	0.558589i	$-0.188657\pi$
$757$	45.6421			1.65889			0.829444	+	0.558589i	$0.188657\pi$
$758$		0			0
$759$	0.408301	+	0.137576i	0.0148204	+	0.00499370i
$760$		0			0
$761$	−6.11500	−	10.5915i	−0.221669	−	0.383942i	0.733646	−	0.679532i	$-0.237817\pi$
$761$	−6.11500	−	10.5915i	−0.221669	−	0.383942i	−0.955315	+	0.295590i	$0.904484\pi$
$762$		0			0
$763$	−47.6387	+	19.9924i	−1.72464	+	0.723773i
$764$		0			0
$765$	8.02026	−	3.36444i	0.289973	−	0.121642i
$766$		0			0
$767$	1.62158	−	2.80866i	0.0585518	−	0.101415i
$768$		0			0
$769$	3.17344	−	5.49656i	0.114437	−	0.198211i	−0.803117	−	0.595821i	$-0.796827\pi$
$769$	3.17344	−	5.49656i	0.114437	−	0.198211i	0.917555	+	0.397610i	$0.130160\pi$
$770$		0			0
$771$	−9.95523	−	49.4667i	−0.358529	−	1.78150i
$772$		0			0
$773$	24.4515	+	42.3512i	0.879459	+	1.52327i	0.851936	+	0.523646i	$0.175428\pi$
$773$	24.4515	+	42.3512i	0.879459	+	1.52327i	0.0275225	+	0.999621i	$0.491238\pi$
$774$		0			0
$775$	−14.3504	+	24.8556i	−0.515481	+	0.892839i
$776$		0			0
$777$	1.15094	+	1.69706i	0.0412897	+	0.0608815i
$778$		0			0
$779$	9.27302	+	16.0613i	0.332240	+	0.575457i
$780$		0			0
$781$	−4.06483	+	7.04049i	−0.145451	+	0.251928i
$782$		0			0
$783$	−14.8910	+	30.7165i	−0.532160	+	1.09772i
$784$		0			0
$785$	3.28455	+	5.68900i	0.117231	+	0.203049i
$786$		0			0
$787$	23.1498			0.825201			0.412600	−	0.910912i	$-0.364621\pi$
$787$	23.1498			0.825201			0.412600	+	0.910912i	$0.364621\pi$
$788$		0			0
$789$	3.53294	−	3.11239i	0.125776	−	0.110804i
$790$		0			0
$791$	−23.1147	−	17.5665i	−0.821864	−	0.624594i
$792$		0			0
$793$	−0.113870	+	0.197229i	−0.00404365	+	0.00700381i
$794$		0			0
$795$	5.97675	−	5.26529i	0.211974	−	0.186741i
$796$		0			0
$797$	24.2284	−	41.9648i	0.858214	−	1.48647i	−0.0154170	−	0.999881i	$-0.504908\pi$
$797$	24.2284	−	41.9648i	0.858214	−	1.48647i	0.873631	−	0.486589i	$-0.161759\pi$
$798$		0			0
$799$	25.3429	+	43.8951i	0.896566	+	1.55290i
$800$		0			0
$801$	−39.0149	+	16.3665i	−1.37853	+	0.578281i
$802$		0			0
$803$	−48.2976			−1.70439
$804$		0			0
$805$	0.0597815	+	0.0454323i	0.00210702	+	0.00160128i
$806$		0			0
$807$	−1.91940	−	9.53734i	−0.0675661	−	0.335730i
$808$		0			0
$809$	−10.2647	−	17.7791i	−0.360889	−	0.625078i	0.627218	−	0.778844i	$-0.284193\pi$
$809$	−10.2647	−	17.7791i	−0.360889	−	0.625078i	−0.988107	+	0.153765i	$0.950860\pi$
$810$		0			0
$811$	−27.7882			−0.975776			−0.487888	−	0.872906i	$-0.662233\pi$
$811$	−27.7882			−0.975776			−0.487888	+	0.872906i	$0.662233\pi$
$812$		0			0
$813$	−18.8492	+	16.6055i	−0.661071	+	0.582379i
$814$		0			0
$815$	−2.61370			−0.0915539
$816$		0			0
$817$	20.9432			0.732711
$818$		0			0
$819$	−1.03902	−	3.74055i	−0.0363064	−	0.130705i
$820$		0			0
$821$	−16.5586			−0.577901			−0.288950	−	0.957344i	$-0.593306\pi$
$821$	−16.5586			−0.577901			−0.288950	+	0.957344i	$0.593306\pi$
$822$		0			0
$823$	−25.4704			−0.887843			−0.443922	−	0.896066i	$-0.646413\pi$
$823$	−25.4704			−0.887843			−0.443922	+	0.896066i	$0.646413\pi$
$824$		0			0
$825$	7.44174	+	36.9774i	0.259088	+	1.28739i
$826$		0			0
$827$	−36.0798			−1.25462			−0.627309	−	0.778771i	$-0.715844\pi$
$827$	−36.0798			−1.25462			−0.627309	+	0.778771i	$0.715844\pi$
$828$		0			0
$829$	22.3539	+	38.7180i	0.776381	+	1.34473i	0.934015	+	0.357234i	$0.116280\pi$
$829$	22.3539	+	38.7180i	0.776381	+	1.34473i	−0.157633	+	0.987498i	$0.550386\pi$
$830$		0			0
$831$	−2.27167	+	2.00126i	−0.0788035	+	0.0694229i
$832$		0			0
$833$	−10.3314	−	37.1721i	−0.357960	−	1.28794i
$834$		0			0
$835$	−10.5293			−0.364383
$836$		0			0
$837$	17.7182	+	26.1338i	0.612431	+	0.903316i
$838$		0			0
$839$	7.86805	+	13.6279i	0.271635	+	0.470486i	0.969281	−	0.245957i	$-0.0791022\pi$
$839$	7.86805	+	13.6279i	0.271635	+	0.470486i	−0.697645	+	0.716443i	$0.745769\pi$
$840$		0			0
$841$	−7.07866	+	12.2606i	−0.244092	+	0.422779i
$842$		0			0
$843$	−3.66095	−	18.1910i	−0.126090	−	0.626531i
$844$		0			0
$845$	3.35611	−	5.81296i	0.115454	−	0.199972i
$846$		0			0
$847$	−25.0230	+	10.5013i	−0.859799	+	0.360829i
$848$		0			0
$849$	−20.6759	−	6.96670i	−0.709594	−	0.239097i
$850$		0			0
$851$	−0.0241422			−0.000827584
$852$		0			0
$853$	14.2010	+	24.5968i	0.486231	+	0.842177i	0.999875	−	0.0158264i	$-0.00503792\pi$
$853$	14.2010	+	24.5968i	0.486231	+	0.842177i	−0.513643	+	0.858004i	$0.671705\pi$
$854$		0			0
$855$	4.61744	+	3.51021i	0.157913	+	0.120046i
$856$		0			0
$857$	4.48867	−	7.77461i	0.153330	−	0.265575i	−0.779120	−	0.626875i	$-0.784334\pi$
$857$	4.48867	−	7.77461i	0.153330	−	0.265575i	0.932450	+	0.361300i	$0.117667\pi$
$858$		0			0
$859$	−0.471450	−	0.816575i	−0.0160857	−	0.0278612i	0.857871	−	0.513866i	$-0.171787\pi$
$859$	−0.471450	−	0.816575i	−0.0160857	−	0.0278612i	−0.873956	+	0.486005i	$0.838454\pi$
$860$		0			0
$861$	12.9782	+	19.1364i	0.442297	+	0.652166i
$862$		0			0
$863$	13.0488	−	22.6011i	0.444185	−	0.769351i	−0.553810	−	0.832643i	$-0.686827\pi$
$863$	13.0488	−	22.6011i	0.444185	−	0.769351i	0.997995	+	0.0632920i	$0.0201600\pi$
$864$		0			0
$865$	−2.38145	−	4.12478i	−0.0809716	−	0.140247i
$866$		0			0
$867$	17.3863	−	15.3166i	0.590468	−	0.520180i
$868$		0			0
$869$	−37.7375	+	65.3633i	−1.28016	+	2.21730i
$870$		0			0
$871$	−1.27011	+	2.19989i	−0.0430360	+	0.0745405i
$872$		0			0
$873$	−3.95152	+	31.0947i	−0.133739	+	1.05240i
$874$		0			0
$875$	−1.70390	+	13.4240i	−0.0576022	+	0.453814i
$876$		0			0
$877$	13.1794	+	22.8275i	0.445038	+	0.770829i	0.998055	−	0.0623413i	$-0.0198567\pi$
$877$	13.1794	+	22.8275i	0.445038	+	0.770829i	−0.553017	+	0.833170i	$0.686523\pi$
$878$		0			0
$879$	4.09586	−	3.60829i	0.138150	−	0.121705i
$880$		0			0
$881$	−45.6077			−1.53656			−0.768281	−	0.640113i	$-0.778888\pi$
$881$	−45.6077			−1.53656			−0.768281	+	0.640113i	$0.778888\pi$
$882$		0			0
$883$	26.1575			0.880271			0.440136	−	0.897931i	$-0.354930\pi$
$883$	26.1575			0.880271			0.440136	+	0.897931i	$0.354930\pi$
$884$		0			0
$885$	1.19187	+	5.92232i	0.0400644	+	0.199077i
$886$		0			0
$887$	18.5963	+	32.2097i	0.624401	+	1.08149i	0.988656	+	0.150196i	$0.0479904\pi$
$887$	18.5963	+	32.2097i	0.624401	+	1.08149i	−0.364255	+	0.931299i	$0.618676\pi$
$888$		0			0
$889$	5.53384	−	43.5979i	0.185599	−	1.46223i
$890$		0			0
$891$	40.1758	+	10.3787i	1.34594	+	0.347699i
$892$		0			0
$893$	−16.9009	+	29.2733i	−0.565568	+	0.979593i
$894$		0			0
$895$	4.04589	−	7.00769i	0.135239	−	0.234241i
$896$		0			0
$897$	0.0433146	+	0.0145948i	0.00144623	+	0.000487306i
$898$		0			0
$899$	19.9592	+	34.5704i	0.665677	+	1.15299i
$900$		0			0
$901$	24.0932	−	41.7307i	0.802662	−	1.39025i
$902$		0			0
$903$	26.0426	−	1.88733i	0.866643	−	0.0628063i
$904$		0			0
$905$	2.51160	+	4.35022i	0.0834884	+	0.144606i
$906$		0			0
$907$	12.9231	−	22.3834i	0.429103	−	0.743229i	−0.567691	−	0.823242i	$-0.692163\pi$
$907$	12.9231	−	22.3834i	0.429103	−	0.743229i	0.996794	+	0.0800134i	$0.0254963\pi$
$908$		0			0
$909$	27.5679	−	11.5645i	0.914368	−	0.383570i
$910$		0			0
$911$	2.41211	+	4.17790i	0.0799169	+	0.138420i	0.903214	−	0.429191i	$-0.141201\pi$
$911$	2.41211	+	4.17790i	0.0799169	+	0.138420i	−0.823297	+	0.567611i	$0.807868\pi$
$912$		0			0
$913$	−41.4256			−1.37099
$914$		0			0
$915$	−0.0836956	−	0.415877i	−0.00276689	−	0.0137485i
$916$		0			0
$917$	14.1912	−	5.95558i	0.468635	−	0.196670i
$918$		0			0
$919$	−9.58183	+	16.5962i	−0.316075	+	0.547459i	−0.979666	−	0.200638i	$-0.935699\pi$
$919$	−9.58183	+	16.5962i	−0.316075	+	0.547459i	0.663590	+	0.748096i	$0.269032\pi$
$920$		0			0
$921$	−33.4651	−	11.2760i	−1.10271	−	0.371557i
$922$		0			0
$923$	−0.431218	+	0.746891i	−0.0141937	+	0.0245842i
$924$		0			0
$925$	−1.05675	−	1.83035i	−0.0347458	−	0.0601815i
$926$		0			0
$927$	−4.40641	+	34.6743i	−0.144725	+	1.13885i
$928$		0			0
$929$	54.0914			1.77468			0.887340	−	0.461115i	$-0.152550\pi$
$929$	54.0914			1.77468			0.887340	+	0.461115i	$0.152550\pi$
$930$		0			0
$931$	18.0236	−	18.3617i	0.590700	−	0.601781i
$932$		0			0
$933$	37.2617	+	12.5553i	1.21989	+	0.411041i
$934$		0			0
$935$	−6.68322	−	11.5757i	−0.218565	−	0.378565i
$936$		0			0
$937$	−16.6345			−0.543426			−0.271713	−	0.962378i	$-0.587590\pi$
$937$	−16.6345			−0.543426			−0.271713	+	0.962378i	$0.587590\pi$
$938$		0			0
$939$	27.4238	+	9.24041i	0.894942	+	0.301549i
$940$		0			0
$941$	−2.89912			−0.0945085			−0.0472543	−	0.998883i	$-0.515047\pi$
$941$	−2.89912			−0.0945085			−0.0472543	+	0.998883i	$0.515047\pi$
$942$		0			0
$943$	−0.272233			−0.00886512
$944$		0			0
$945$	6.05804	+	3.94878i	0.197068	+	0.128454i
$946$		0			0
$947$	57.7311			1.87601			0.938004	−	0.346625i	$-0.112672\pi$
$947$	57.7311			1.87601			0.938004	+	0.346625i	$0.112672\pi$
$948$		0			0
$949$	−5.12366			−0.166321
$950$		0			0
$951$	−16.9522	−	5.71202i	−0.549713	−	0.185225i
$952$		0			0
$953$	20.4070			0.661046			0.330523	−	0.943798i	$-0.392775\pi$
$953$	20.4070			0.661046			0.330523	+	0.943798i	$0.392775\pi$
$954$		0			0
$955$	−2.90440	−	5.03057i	−0.0939843	−	0.162786i
$956$		0			0
$957$	49.7148	+	16.7513i	1.60705	+	0.541494i
$958$		0			0
$959$	−19.4349	−	14.7700i	−0.627585	−	0.476947i
$960$		0			0
$961$	5.92259			0.191051
$962$		0			0
$963$	−13.5864	+	5.69937i	−0.437814	+	0.183660i
$964$		0			0
$965$	−7.02193	−	12.1623i	−0.226044	−	0.391519i
$966$		0			0
$967$	−4.26365	+	7.38486i	−0.137110	+	0.237481i	−0.926401	−	0.376537i	$-0.877115\pi$
$967$	−4.26365	+	7.38486i	−0.137110	+	0.237481i	0.789292	+	0.614019i	$0.210448\pi$
$968$		0			0
$969$	33.2520	+	11.2042i	1.06821	+	0.359931i
$970$		0			0
$971$	−9.42651	+	16.3272i	−0.302511	+	0.523965i	−0.976704	−	0.214590i	$-0.931158\pi$
$971$	−9.42651	+	16.3272i	−0.302511	+	0.523965i	0.674193	+	0.738555i	$0.264492\pi$
$972$		0			0
$973$	29.0052	+	22.0431i	0.929864	+	0.706671i
$974$		0			0
$975$	0.789458	+	3.92275i	0.0252829	+	0.125629i
$976$		0			0
$977$	0.611299			0.0195572			0.00977859	−	0.999952i	$-0.496887\pi$
$977$	0.611299			0.0195572			0.00977859	+	0.999952i	$0.496887\pi$
$978$		0			0
$979$	32.5108	+	56.3104i	1.03905	+	1.79969i
$980$		0			0
$981$	7.38510	−	58.1138i	0.235788	−	1.85543i
$982$		0			0
$983$	−3.62584	+	6.28013i	−0.115646	+	0.200305i	−0.918038	−	0.396493i	$-0.870227\pi$
$983$	−3.62584	+	6.28013i	−0.115646	+	0.200305i	0.802392	+	0.596798i	$0.203561\pi$
$984$		0			0
$985$	−3.37659	−	5.84842i	−0.107587	−	0.186346i
$986$		0			0
$987$	−18.3780	+	37.9239i	−0.584980	+	1.20713i
$988$		0			0
$989$	−0.153710	+	0.266234i	−0.00488770	+	0.00846575i
$990$		0			0
$991$	2.49266	+	4.31741i	0.0791819	+	0.137147i	0.902897	−	0.429857i	$-0.141436\pi$
$991$	2.49266	+	4.31741i	0.0791819	+	0.137147i	−0.823715	+	0.567004i	$0.808103\pi$
$992$		0			0
$993$	−37.1469	−	12.5166i	−1.17882	−	0.397202i
$994$		0			0
$995$	−5.33412	+	9.23896i	−0.169103	+	0.292895i
$996$		0			0
$997$	1.59172	−	2.75694i	0.0504104	−	0.0873133i	−0.839719	−	0.543021i	$-0.817280\pi$
$997$	1.59172	−	2.75694i	0.0504104	−	0.0873133i	0.890130	+	0.455708i	$0.150614\pi$
$998$		0			0
$999$	−2.31902	+	0.167715i	−0.0733706	+	0.00530627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.l.625.2		22
3.2	odd	2		3024.2.q.l.2305.7		22
4.3	odd	2		504.2.q.c.121.10	yes	22
7.4	even	3		1008.2.t.l.193.6		22
9.2	odd	6		3024.2.t.k.289.5		22
9.7	even	3		1008.2.t.l.961.6		22
12.11	even	2		1512.2.q.d.793.7		22
21.11	odd	6		3024.2.t.k.1873.5		22
28.11	odd	6		504.2.t.c.193.6	yes	22
36.7	odd	6		504.2.t.c.457.6	yes	22
36.11	even	6		1512.2.t.c.289.5		22
63.11	odd	6		3024.2.q.l.2881.7		22
63.25	even	3	inner	1008.2.q.l.529.2		22
84.11	even	6		1512.2.t.c.361.5		22
252.11	even	6		1512.2.q.d.1369.7		22
252.151	odd	6		504.2.q.c.25.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.10	✓	22	252.151	odd	6
504.2.q.c.121.10	yes	22	4.3	odd	2
504.2.t.c.193.6	yes	22	28.11	odd	6
504.2.t.c.457.6	yes	22	36.7	odd	6
1008.2.q.l.529.2		22	63.25	even	3	inner
1008.2.q.l.625.2		22	1.1	even	1	trivial
1008.2.t.l.193.6		22	7.4	even	3
1008.2.t.l.961.6		22	9.7	even	3
1512.2.q.d.793.7		22	12.11	even	2
1512.2.q.d.1369.7		22	252.11	even	6
1512.2.t.c.289.5		22	36.11	even	6
1512.2.t.c.361.5		22	84.11	even	6
3024.2.q.l.2305.7		22	3.2	odd	2
3024.2.q.l.2881.7		22	63.11	odd	6
3024.2.t.k.289.5		22	9.2	odd	6
3024.2.t.k.1873.5		22	21.11	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)

\(f(q)\)	\(=\)	\(q+(-1.64138 - 0.553060i) q^{3} +(-0.263002 - 0.455533i) q^{5} +(0.333150 - 2.62469i) q^{7} +(2.38825 + 1.81556i) q^{9} +O(q^{10})\)	\(q+(-1.64138 - 0.553060i) q^{3} +(-0.263002 - 0.455533i) q^{5} +(0.333150 - 2.62469i) q^{7} +(2.38825 + 1.81556i) q^{9} +(2.30526 - 3.99283i) q^{11} +(0.244554 - 0.423580i) q^{13} +(0.179749 + 0.893158i) q^{15} +(2.75579 + 4.77318i) q^{17} +(-1.83782 + 3.18319i) q^{19} +(-1.99844 + 4.12386i) q^{21} +(-0.0269769 - 0.0467253i) q^{23} +(2.36166 - 4.09051i) q^{25} +(-2.91591 - 4.30087i) q^{27} +(-3.28471 - 5.68929i) q^{29} -6.07640 q^{31} +(-5.99208 + 5.27879i) q^{33} +(-1.28325 + 0.538539i) q^{35} +(0.223731 - 0.387513i) q^{37} +(-0.635671 + 0.560002i) q^{39} +(2.52284 - 4.36968i) q^{41} +(-2.84893 - 4.93449i) q^{43} +(0.198934 - 1.56542i) q^{45} +9.19621 q^{47} +(-6.77802 - 1.74883i) q^{49} +(-1.88345 - 9.35871i) q^{51} +(-4.37138 - 7.57145i) q^{53} -2.42515 q^{55} +(4.77705 - 4.20840i) q^{57} +6.63076 q^{59} -0.465625 q^{61} +(5.56094 - 5.66357i) q^{63} -0.257273 q^{65} -5.19358 q^{67} +(0.0184374 + 0.0916137i) q^{69} -1.76328 q^{71} +(-5.23776 - 9.07207i) q^{73} +(-6.13868 + 5.40794i) q^{75} +(-9.71195 - 7.38081i) q^{77} -16.3702 q^{79} +(2.40747 + 8.67203i) q^{81} +(-4.49251 - 7.78126i) q^{83} +(1.44956 - 2.51071i) q^{85} +(2.24494 + 11.1549i) q^{87} +(-7.05145 + 12.2135i) q^{89} +(-1.03029 - 0.782994i) q^{91} +(9.97367 + 3.36061i) q^{93} +1.93340 q^{95} +(5.22413 + 9.04847i) q^{97} +(12.7548 - 5.35052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) \) 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

L-functions

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