LMFDB - Embedded newform 1008.2.cj.c.767.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(527,1008)]

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([3, 0, 5, 2]))

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

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

chi := DirichletCharacter("1008.527");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			767.7
Character	$\chi$	$=$	1008.767
Dual form			1008.2.cj.c.527.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.743588 + 1.56431i) q^{3} +(-0.126591 - 0.0730873i) q^{5} +(-0.562042 - 2.58536i) q^{7} +(-1.89415 - 2.32641i) q^{9} +O(q^{10})$	\(q+(-0.743588 + 1.56431i) q^{3} +(-0.126591 - 0.0730873i) q^{5} +(-0.562042 - 2.58536i) q^{7} +(-1.89415 - 2.32641i) q^{9} +(2.18696 + 3.78792i) q^{11} +(0.804550 + 1.39352i) q^{13} +(0.208463 - 0.143681i) q^{15} +(-4.71916 - 2.72461i) q^{17} +(-4.28579 + 2.47440i) q^{19} +(4.46225 + 1.04324i) q^{21} +(-4.26992 + 7.39571i) q^{23} +(-2.48932 - 4.31162i) q^{25} +(5.04770 - 1.23316i) q^{27} +(-0.394626 - 0.227837i) q^{29} +6.13326i q^{31} +(-7.55170 + 0.604433i) q^{33} +(-0.117808 + 0.368362i) q^{35} +(-0.739819 - 1.28140i) q^{37} +(-2.77816 + 0.222362i) q^{39} +(1.15040 - 0.664185i) q^{41} +(-7.33030 - 4.23215i) q^{43} +(0.0697515 + 0.432941i) q^{45} -6.21361 q^{47} +(-6.36822 + 2.90616i) q^{49} +(7.77125 - 5.35626i) q^{51} +(3.76314 + 2.17265i) q^{53} -0.639355i q^{55} +(-0.683877 - 8.54426i) q^{57} -7.02273 q^{59} -11.7369 q^{61} +(-4.95003 + 6.20461i) q^{63} -0.235210i q^{65} -9.33942i q^{67} +(-8.39415 - 12.1789i) q^{69} +15.0642 q^{71} +(3.45880 - 5.99082i) q^{73} +(8.59576 - 0.687999i) q^{75} +(8.56400 - 7.78306i) q^{77} +0.640995i q^{79} +(-1.82437 + 8.81315i) q^{81} +(1.54280 - 2.67220i) q^{83} +(0.398268 + 0.689821i) q^{85} +(0.649848 - 0.447901i) q^{87} +(-2.58407 + 1.49191i) q^{89} +(3.15057 - 2.86327i) q^{91} +(-9.59434 - 4.56062i) q^{93} +0.723390 q^{95} +(-5.24637 + 9.08698i) q^{97} +(4.66983 - 12.2627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{5} - 7 q^{7} + 8 q^{9}+O(q^{10}) $ 30 * q + 3 * q^5 - 7 * q^7 + 8 * q^9	$ 30 q + 3 q^{5} - 7 q^{7} + 8 q^{9} - 3 q^{11} - 12 q^{17} - 9 q^{19} + 2 q^{21} + 12 q^{23} + 18 q^{25} + 27 q^{27} + 27 q^{29} + 13 q^{33} - 6 q^{35} + 6 q^{37} + 12 q^{39} + 9 q^{41} - 21 q^{43} + 13 q^{45} - 3 q^{49} + 12 q^{51} + 3 q^{53} + 20 q^{57} - 6 q^{59} + 6 q^{61} + 51 q^{63} + 10 q^{69} + 18 q^{71} + 21 q^{73} - 3 q^{75} + 72 q^{77} - 20 q^{81} - 15 q^{83} - 3 q^{85} - 57 q^{87} - 6 q^{89} + 26 q^{91} + 9 q^{93} + 54 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) $ 30 * q + 3 * q^5 - 7 * q^7 + 8 * q^9 - 3 * q^11 - 12 * q^17 - 9 * q^19 + 2 * q^21 + 12 * q^23 + 18 * q^25 + 27 * q^27 + 27 * q^29 + 13 * q^33 - 6 * q^35 + 6 * q^37 + 12 * q^39 + 9 * q^41 - 21 * q^43 + 13 * q^45 - 3 * q^49 + 12 * q^51 + 3 * q^53 + 20 * q^57 - 6 * q^59 + 6 * q^61 + 51 * q^63 + 10 * q^69 + 18 * q^71 + 21 * q^73 - 3 * q^75 + 72 * q^77 - 20 * q^81 - 15 * q^83 - 3 * q^85 - 57 * q^87 - 6 * q^89 + 26 * q^91 + 9 * q^93 + 54 * q^95 - 6 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.743588	+	1.56431i	−0.429311	+	0.903157i
$3$	−0.743588	+	1.56431i	−0.429311	+	0.903157i
$4$		0			0
$5$	−0.126591	−	0.0730873i	−0.0566132	−	0.0326856i	0.471426	−	0.881905i	$-0.343739\pi$
$5$	−0.126591	−	0.0730873i	−0.0566132	−	0.0326856i	−0.528039	+	0.849220i	$0.677073\pi$
$6$		0			0
$7$	−0.562042	−	2.58536i	−0.212432	−	0.977176i
$7$	−0.562042	−	2.58536i	−0.212432	−	0.977176i
$8$		0			0
$9$	−1.89415	−	2.32641i	−0.631384	−	0.775470i
$10$		0			0
$11$	2.18696	+	3.78792i	0.659393	+	1.14210i	0.980773	+	0.195152i	$0.0625199\pi$
$11$	2.18696	+	3.78792i	0.659393	+	1.14210i	−0.321380	+	0.946950i	$0.604147\pi$
$12$		0			0
$13$	0.804550	+	1.39352i	0.223142	+	0.386494i	0.955760	−	0.294146i	$-0.0950353\pi$
$13$	0.804550	+	1.39352i	0.223142	+	0.386494i	−0.732618	+	0.680640i	$0.761702\pi$
$14$		0			0
$15$	0.208463	−	0.143681i	0.0538249	−	0.0370983i
$16$		0			0
$17$	−4.71916	−	2.72461i	−1.14456	−	0.660814i	−0.197007	−	0.980402i	$-0.563122\pi$
$17$	−4.71916	−	2.72461i	−1.14456	−	0.660814i	−0.947557	+	0.319588i	$0.896456\pi$
$18$		0			0
$19$	−4.28579	+	2.47440i	−0.983228	+	0.567667i	−0.903243	−	0.429129i	$-0.858821\pi$
$19$	−4.28579	+	2.47440i	−0.983228	+	0.567667i	−0.0799849	+	0.996796i	$0.525487\pi$
$20$		0			0
$21$	4.46225	+	1.04324i	0.973742	+	0.227653i
$22$		0			0
$23$	−4.26992	+	7.39571i	−0.890339	+	1.54211i	−0.0508697	+	0.998705i	$0.516199\pi$
$23$	−4.26992	+	7.39571i	−0.890339	+	1.54211i	−0.839469	+	0.543407i	$0.817134\pi$
$24$		0			0
$25$	−2.48932	−	4.31162i	−0.497863	−	0.862325i
$26$		0			0
$27$	5.04770	−	1.23316i	0.971431	−	0.237321i
$28$		0			0
$29$	−0.394626	−	0.227837i	−0.0732801	−	0.0423083i	0.462912	−	0.886404i	$-0.346805\pi$
$29$	−0.394626	−	0.227837i	−0.0732801	−	0.0423083i	−0.536192	+	0.844096i	$0.680138\pi$
$30$		0			0
$31$			6.13326i			1.10157i	0.834649	+	0.550783i	$0.185671\pi$
$31$			6.13326i			1.10157i	−0.834649	+	0.550783i	$0.814329\pi$
$32$		0			0
$33$	−7.55170	+	0.604433i	−1.31458	+	0.105218i
$34$		0			0
$35$	−0.117808	+	0.368362i	−0.0199132	+	0.0622645i
$36$		0			0
$37$	−0.739819	−	1.28140i	−0.121625	−	0.210662i	0.798783	−	0.601619i	$-0.205477\pi$
$37$	−0.739819	−	1.28140i	−0.121625	−	0.210662i	−0.920409	+	0.390957i	$0.872144\pi$
$38$		0			0
$39$	−2.77816	+	0.222362i	−0.444862	+	0.0356064i
$40$		0			0
$41$	1.15040	−	0.664185i	0.179663	−	0.103728i	−0.407472	−	0.913218i	$-0.633589\pi$
$41$	1.15040	−	0.664185i	0.179663	−	0.103728i	0.587134	+	0.809490i	$0.300256\pi$
$42$		0			0
$43$	−7.33030	−	4.23215i	−1.11786	−	0.645397i	−0.177006	−	0.984210i	$-0.556641\pi$
$43$	−7.33030	−	4.23215i	−1.11786	−	0.645397i	−0.940854	+	0.338813i	$0.889975\pi$
$44$		0			0
$45$	0.0697515	+	0.432941i	0.0103979	+	0.0645390i
$46$		0			0
$47$	−6.21361			−0.906348			−0.453174	−	0.891422i	$-0.649708\pi$
$47$	−6.21361			−0.906348			−0.453174	+	0.891422i	$0.649708\pi$
$48$		0			0
$49$	−6.36822	+	2.90616i	−0.909746	+	0.415166i
$50$		0			0
$51$	7.77125	−	5.35626i	1.08819	−	0.750026i
$52$		0			0
$53$	3.76314	+	2.17265i	0.516907	+	0.298436i	0.735668	−	0.677342i	$-0.236868\pi$
$53$	3.76314	+	2.17265i	0.516907	+	0.298436i	−0.218761	+	0.975778i	$0.570202\pi$
$54$		0			0
$55$		−	0.639355i		−	0.0862107i
$56$		0			0
$57$	−0.683877	−	8.54426i	−0.0905818	−	1.13171i
$58$		0			0
$59$	−7.02273			−0.914282			−0.457141	−	0.889394i	$-0.651126\pi$
$59$	−7.02273			−0.914282			−0.457141	+	0.889394i	$0.651126\pi$
$60$		0			0
$61$	−11.7369			−1.50276			−0.751378	−	0.659872i	$-0.770611\pi$
$61$	−11.7369			−1.50276			−0.751378	+	0.659872i	$0.770611\pi$
$62$		0			0
$63$	−4.95003	+	6.20461i	−0.623645	+	0.781708i
$64$		0			0
$65$		−	0.235210i		−	0.0291742i
$66$		0			0
$67$		−	9.33942i		−	1.14099i	−0.821301	−	0.570496i	$-0.806751\pi$
$67$		−	9.33942i		−	1.14099i	0.821301	−	0.570496i	$-0.193249\pi$
$68$		0			0
$69$	−8.39415	−	12.1789i	−1.01054	−	1.46616i
$70$		0			0
$71$	15.0642			1.78779			0.893895	−	0.448276i	$-0.147962\pi$
$71$	15.0642			1.78779			0.893895	+	0.448276i	$0.147962\pi$
$72$		0			0
$73$	3.45880	−	5.99082i	0.404822	−	0.701172i	−0.589479	−	0.807784i	$-0.700667\pi$
$73$	3.45880	−	5.99082i	0.404822	−	0.701172i	0.994301	+	0.106612i	$0.0340002\pi$
$74$		0			0
$75$	8.59576	−	0.687999i	0.992552	−	0.0794433i
$76$		0			0
$77$	8.56400	−	7.78306i	0.975959	−	0.886961i
$78$		0			0
$79$			0.640995i			0.0721176i	0.999350	+	0.0360588i	$0.0114804\pi$
$79$			0.640995i			0.0721176i	−0.999350	+	0.0360588i	$0.988520\pi$
$80$		0			0
$81$	−1.82437	+	8.81315i	−0.202708	+	0.979239i
$82$		0			0
$83$	1.54280	−	2.67220i	0.169344	−	0.293312i	−0.768845	−	0.639435i	$-0.779168\pi$
$83$	1.54280	−	2.67220i	0.169344	−	0.293312i	0.938189	+	0.346122i	$0.112502\pi$
$84$		0			0
$85$	0.398268	+	0.689821i	0.0431983	+	0.0748216i
$86$		0			0
$87$	0.649848	−	0.447901i	0.0696710	−	0.0480200i
$88$		0			0
$89$	−2.58407	+	1.49191i	−0.273911	+	0.158142i	−0.630663	−	0.776056i	$-0.717217\pi$
$89$	−2.58407	+	1.49191i	−0.273911	+	0.158142i	0.356753	+	0.934199i	$0.383884\pi$
$90$		0			0
$91$	3.15057	−	2.86327i	0.330270	−	0.300153i
$92$		0			0
$93$	−9.59434	−	4.56062i	−0.994886	−	0.472914i
$94$		0			0
$95$	0.723390			0.0742182
$96$		0			0
$97$	−5.24637	+	9.08698i	−0.532688	+	0.922643i	0.466583	+	0.884477i	$0.345485\pi$
$97$	−5.24637	+	9.08698i	−0.532688	+	0.922643i	−0.999271	+	0.0381656i	$0.987849\pi$
$98$		0			0
$99$	4.66983	−	12.2627i	0.469336	−	1.23244i
$100$		0			0
$101$	3.54304	−	2.04557i	0.352545	−	0.203542i	−0.313260	−	0.949667i	$-0.601421\pi$
$101$	3.54304	−	2.04557i	0.352545	−	0.203542i	0.665806	+	0.746125i	$0.268088\pi$
$102$		0			0
$103$	−17.0491	−	9.84329i	−1.67990	−	0.969888i	−0.961723	−	0.274024i	$-0.911645\pi$
$103$	−17.0491	−	9.84329i	−1.67990	−	0.969888i	−0.718173	−	0.695865i	$-0.755021\pi$
$104$		0			0
$105$	−0.488633	−	0.458198i	−0.0476856	−	0.0447155i
$106$		0			0
$107$	3.94062	+	6.82536i	0.380954	+	0.659832i	0.991199	−	0.132381i	$-0.0422622\pi$
$107$	3.94062	+	6.82536i	0.380954	+	0.659832i	−0.610245	+	0.792213i	$0.708929\pi$
$108$		0			0
$109$	−6.91888	+	11.9839i	−0.662709	+	1.14785i	0.317192	+	0.948361i	$0.397260\pi$
$109$	−6.91888	+	11.9839i	−0.662709	+	1.14785i	−0.979901	+	0.199484i	$0.936073\pi$
$110$		0			0
$111$	2.55464	−	0.204472i	0.242476	−	0.0194076i
$112$		0			0
$113$	7.30059	−	4.21500i	0.686782	−	0.396514i	−0.115623	−	0.993293i	$-0.536887\pi$
$113$	7.30059	−	4.21500i	0.686782	−	0.396514i	0.802405	+	0.596779i	$0.203553\pi$
$114$		0			0
$115$	1.08106	−	0.624153i	0.100810	−	0.0582026i
$116$		0			0
$117$	1.71796	−	4.51126i	0.158826	−	0.417066i
$118$		0			0
$119$	−4.39174	+	13.7321i	−0.402590	+	1.25882i
$120$		0			0
$121$	−4.06558	+	7.04179i	−0.369598	+	0.640162i
$122$		0			0
$123$	0.183568	+	2.29347i	0.0165517	+	0.206795i
$124$		0			0
$125$			1.45862i			0.130463i
$126$		0			0
$127$			9.10068i			0.807555i	0.914857	+	0.403777i	$0.132303\pi$
$127$			9.10068i			0.807555i	−0.914857	+	0.403777i	$0.867697\pi$
$128$		0			0
$129$	12.0711	−	8.31991i	1.06280	−	0.732527i
$130$		0			0
$131$	−6.50183	+	11.2615i	−0.568067	+	0.983921i	0.428690	+	0.903452i	$0.358975\pi$
$131$	−6.50183	+	11.2615i	−0.568067	+	0.983921i	−0.996757	+	0.0804694i	$0.974358\pi$
$132$		0			0
$133$	8.80603	+	9.68962i	0.763579	+	0.840196i
$134$		0			0
$135$	−0.729122	−	0.212817i	−0.0627528	−	0.0183163i
$136$		0			0
$137$	−15.3690	+	8.87329i	−1.31306	+	0.758096i	−0.982602	−	0.185724i	$-0.940537\pi$
$137$	−15.3690	+	8.87329i	−1.31306	+	0.758096i	−0.330459	+	0.943820i	$0.607204\pi$
$138$		0			0
$139$	−16.6885	+	9.63509i	−1.41550	+	0.817238i	−0.995899	−	0.0904719i	$-0.971162\pi$
$139$	−16.6885	+	9.63509i	−1.41550	+	0.817238i	−0.419599	+	0.907710i	$0.637829\pi$
$140$		0			0
$141$	4.62037	−	9.72003i	0.389105	−	0.818574i
$142$		0			0
$143$	−3.51904	+	6.09515i	−0.294277	+	0.509702i
$144$		0			0
$145$	0.0333040	+	0.0576842i	0.00276575	+	0.00479041i
$146$		0			0
$147$	0.189181	−	12.1229i	0.0156034	−	0.999878i
$148$		0			0
$149$	15.6504	+	9.03576i	1.28213	+	0.740238i	0.977237	−	0.212149i	$-0.0680461\pi$
$149$	15.6504	+	9.03576i	1.28213	+	0.740238i	0.304893	+	0.952387i	$0.401379\pi$
$150$		0			0
$151$	4.30087	−	2.48311i	0.349999	−	0.202072i	−0.314686	−	0.949196i	$-0.601899\pi$
$151$	4.30087	−	2.48311i	0.349999	−	0.202072i	0.664685	+	0.747124i	$0.268566\pi$
$152$		0			0
$153$	2.60025	+	16.1395i	0.210218	+	1.30480i
$154$		0			0
$155$	0.448263	−	0.776414i	0.0360054	−	0.0623631i
$156$		0			0
$157$	12.4557			0.994077			0.497038	−	0.867729i	$-0.334421\pi$
$157$	12.4557			0.994077			0.497038	+	0.867729i	$0.334421\pi$
$158$		0			0
$159$	−6.19693	+	4.27117i	−0.491449	+	0.338726i
$160$		0			0
$161$	21.5205	+	6.88259i	1.69605	+	0.542424i
$162$		0			0
$163$	13.7047	−	7.91240i	1.07343	−	0.619747i	0.144315	−	0.989532i	$-0.453902\pi$
$163$	13.7047	−	7.91240i	1.07343	−	0.619747i	0.929117	+	0.369785i	$0.120569\pi$
$164$		0			0
$165$	1.00015	+	0.475417i	0.0778618	+	0.0370112i
$166$		0			0
$167$	6.67704	+	11.5650i	0.516685	+	0.894924i	0.999812	+	0.0193741i	$0.00616736\pi$
$167$	6.67704	+	11.5650i	0.516685	+	0.894924i	−0.483128	+	0.875550i	$0.660499\pi$
$168$		0			0
$169$	5.20540	−	9.01601i	0.400415	−	0.693539i
$170$		0			0
$171$	13.8744	+	5.28361i	1.06100	+	0.404048i
$172$		0			0
$173$			7.84806i			0.596677i	0.954460	+	0.298339i	$0.0964324\pi$
$173$			7.84806i			0.596677i	−0.954460	+	0.298339i	$0.903568\pi$
$174$		0			0
$175$	−9.74802	+	8.85910i	−0.736881	+	0.669685i
$176$		0			0
$177$	5.22202	−	10.9858i	0.392511	−	0.825740i
$178$		0			0
$179$	8.04574	−	13.9356i	0.601367	−	1.04160i	−0.391247	−	0.920286i	$-0.627956\pi$
$179$	8.04574	−	13.9356i	0.601367	−	1.04160i	0.992614	−	0.121313i	$-0.0387104\pi$
$180$		0			0
$181$	8.76175			0.651256			0.325628	−	0.945498i	$-0.394424\pi$
$181$	8.76175			0.651256			0.325628	+	0.945498i	$0.394424\pi$
$182$		0			0
$183$	8.72742	−	18.3602i	0.645150	−	1.35722i
$184$		0			0
$185$			0.216285i			0.0159016i
$186$		0			0
$187$		−	23.8344i		−	1.74294i
$188$		0			0
$189$	−6.02518	−	12.3571i	−0.438267	−	0.898845i
$190$		0			0
$191$	−15.5202			−1.12300			−0.561502	−	0.827475i	$-0.689776\pi$
$191$	−15.5202			−1.12300			−0.561502	+	0.827475i	$0.689776\pi$
$192$		0			0
$193$	9.87213			0.710612			0.355306	−	0.934750i	$-0.384377\pi$
$193$	9.87213			0.710612			0.355306	+	0.934750i	$0.384377\pi$
$194$		0			0
$195$	0.367942	+	0.174899i	0.0263488	+	0.0125248i
$196$		0			0
$197$			11.8541i			0.844570i	0.906463	+	0.422285i	$0.138772\pi$
$197$			11.8541i			0.844570i	−0.906463	+	0.422285i	$0.861228\pi$
$198$		0			0
$199$	−9.99510	−	5.77067i	−0.708534	−	0.409072i	0.101984	−	0.994786i	$-0.467481\pi$
$199$	−9.99510	−	5.77067i	−0.708534	−	0.409072i	−0.810518	+	0.585714i	$0.800814\pi$
$200$		0			0
$201$	14.6098	+	6.94468i	1.03049	+	0.489840i
$202$		0			0
$203$	−0.367246	+	1.14830i	−0.0257756	+	0.0805952i
$204$		0			0
$205$	−0.194174			−0.0135617
$206$		0			0
$207$	25.2933	−	4.07503i	1.75801	−	0.283234i
$208$		0			0
$209$	−18.7457	−	10.8228i	−1.29667	−	0.748631i
$210$		0			0
$211$	12.7677	−	7.37141i	0.878962	−	0.507469i	0.00864606	−	0.999963i	$-0.497248\pi$
$211$	12.7677	−	7.37141i	0.878962	−	0.507469i	0.870316	+	0.492494i	$0.163915\pi$
$212$		0			0
$213$	−11.2016	+	23.5651i	−0.767518	+	1.61465i
$214$		0			0
$215$	0.618633	+	1.07150i	0.0421904	+	0.0730759i
$216$		0			0
$217$	15.8567	−	3.44714i	1.07642	−	0.234007i
$218$		0			0
$219$	6.79959	+	9.86535i	0.459474	+	0.666638i
$220$		0			0
$221$		−	8.76833i		−	0.589822i
$222$		0			0
$223$	−1.17836	−	0.680324i	−0.0789085	−	0.0455579i	0.460027	−	0.887905i	$-0.347840\pi$
$223$	−1.17836	−	0.680324i	−0.0789085	−	0.0455579i	−0.538935	+	0.842347i	$0.681173\pi$
$224$		0			0
$225$	−5.31546	+	13.9580i	−0.354364	+	0.930536i
$226$		0			0
$227$	13.3915	+	23.1947i	0.888823	+	1.53949i	0.841269	+	0.540617i	$0.181809\pi$
$227$	13.3915	+	23.1947i	0.888823	+	1.53949i	0.0475542	+	0.998869i	$0.484857\pi$
$228$		0			0
$229$	−6.26919	+	10.8585i	−0.414279	+	0.717553i	−0.995353	−	0.0962983i	$-0.969300\pi$
$229$	−6.26919	+	10.8585i	−0.414279	+	0.717553i	0.581073	+	0.813851i	$0.302633\pi$
$230$		0			0
$231$	5.80705	+	19.1842i	0.382076	+	1.26223i
$232$		0			0
$233$	14.9625	−	8.63859i	0.980224	−	0.565933i	0.0778864	−	0.996962i	$-0.475183\pi$
$233$	14.9625	−	8.63859i	0.980224	−	0.565933i	0.902338	+	0.431029i	$0.141850\pi$
$234$		0			0
$235$	0.786586	+	0.454136i	0.0513112	+	0.0296245i
$236$		0			0
$237$	−1.00272	−	0.476637i	−0.0651335	−	0.0309609i
$238$		0			0
$239$	−0.689496	−	1.19424i	−0.0445998	−	0.0772491i	0.842864	−	0.538127i	$-0.180868\pi$
$239$	−0.689496	−	1.19424i	−0.0445998	−	0.0772491i	−0.887464	+	0.460878i	$0.847535\pi$
$240$		0			0
$241$	−1.97545	−	3.42158i	−0.127250	−	0.220403i	0.795360	−	0.606137i	$-0.207282\pi$
$241$	−1.97545	−	3.42158i	−0.127250	−	0.220403i	−0.922610	+	0.385734i	$0.873948\pi$
$242$		0			0
$243$	−12.4300	−	9.40724i	−0.797382	−	0.603475i
$244$		0			0
$245$	1.01856	+	0.0975419i	0.0650735	+	0.00623172i
$246$		0			0
$247$	−6.89627	−	3.98156i	−0.438799	−	0.253341i
$248$		0			0
$249$	3.03296	+	4.40043i	0.192206	+	0.278866i
$250$		0			0
$251$	3.47465			0.219318			0.109659	−	0.993969i	$-0.465024\pi$
$251$	3.47465			0.219318			0.109659	+	0.993969i	$0.465024\pi$
$252$		0			0
$253$	−37.3525			−2.34833
$254$		0			0
$255$	−1.37524	+	0.110074i	−0.0861211	+	0.00689308i
$256$		0			0
$257$	−2.01194	−	1.16159i	−0.125501	−	0.0724583i	0.435935	−	0.899978i	$-0.356418\pi$
$257$	−2.01194	−	1.16159i	−0.125501	−	0.0724583i	−0.561436	+	0.827520i	$0.689751\pi$
$258$		0			0
$259$	−2.89709	+	2.63290i	−0.180016	+	0.163601i
$260$		0			0
$261$	0.217438	+	1.34962i	0.0134591	+	0.0835393i
$262$		0			0
$263$	−7.70694	−	13.3488i	−0.475230	−	0.823123i	0.524367	−	0.851492i	$-0.324302\pi$
$263$	−7.70694	−	13.3488i	−0.475230	−	0.823123i	−0.999598	+	0.0283695i	$0.990968\pi$
$264$		0			0
$265$	−0.317586	−	0.550075i	−0.0195092	−	0.0337909i
$266$		0			0
$267$	−0.412336	−	5.15166i	−0.0252345	−	0.315277i
$268$		0			0
$269$	16.2047	+	9.35577i	0.988016	+	0.570431i	0.904681	−	0.426090i	$-0.140109\pi$
$269$	16.2047	+	9.35577i	0.988016	+	0.570431i	0.0833354	+	0.996522i	$0.473443\pi$
$270$		0			0
$271$	−10.4279	+	6.02052i	−0.633447	+	0.365721i	−0.782086	−	0.623171i	$-0.785844\pi$
$271$	−10.4279	+	6.02052i	−0.633447	+	0.365721i	0.148639	+	0.988892i	$0.452511\pi$
$272$		0			0
$273$	2.13633	+	7.05758i	0.129296	+	0.427144i
$274$		0			0
$275$	10.8881	−	18.8587i	0.656575	−	1.13722i
$276$		0			0
$277$	2.61966	+	4.53738i	0.157400	+	0.272625i	0.933930	−	0.357455i	$-0.116355\pi$
$277$	2.61966	+	4.53738i	0.157400	+	0.272625i	−0.776530	+	0.630080i	$0.783022\pi$
$278$		0			0
$279$	14.2685	−	11.6173i	0.854231	−	0.695511i
$280$		0			0
$281$	−2.89961	−	1.67409i	−0.172976	−	0.0998678i	0.411012	−	0.911630i	$-0.365175\pi$
$281$	−2.89961	−	1.67409i	−0.172976	−	0.0998678i	−0.583988	+	0.811762i	$0.698509\pi$
$282$		0			0
$283$		−	2.70826i		−	0.160989i	−0.996755	−	0.0804945i	$-0.974350\pi$
$283$		−	2.70826i		−	0.160989i	0.996755	−	0.0804945i	$-0.0256500\pi$
$284$		0			0
$285$	−0.537904	+	1.13161i	−0.0318627	+	0.0670307i
$286$		0			0
$287$	−2.36373	−	2.60091i	−0.139527	−	0.153527i
$288$		0			0
$289$	6.34696	+	10.9933i	0.373351	+	0.646663i
$290$		0			0
$291$	−10.3137	−	14.9639i	−0.604602	−	0.877202i
$292$		0			0
$293$	24.4902	−	14.1394i	1.43073	−	0.826035i	0.433558	−	0.901126i	$-0.357258\pi$
$293$	24.4902	−	14.1394i	1.43073	−	0.826035i	0.997177	+	0.0750909i	$0.0239247\pi$
$294$		0			0
$295$	0.889014	+	0.513272i	0.0517604	+	0.0298839i
$296$		0			0
$297$	15.7102	+	16.4235i	0.911600	+	0.952986i
$298$		0			0
$299$	−13.7414			−0.794689
$300$		0			0
$301$	−6.82172	+	21.3301i	−0.393197	+	1.22945i
$302$		0			0
$303$	0.565357	+	7.06348i	0.0324789	+	0.405787i
$304$		0			0
$305$	1.48578	+	0.857818i	0.0850758	+	0.0491185i
$306$		0			0
$307$		−	15.2762i		−	0.871858i	−0.899981	−	0.435929i	$-0.856420\pi$
$307$		−	15.2762i		−	0.871858i	0.899981	−	0.435929i	$-0.143580\pi$
$308$		0			0
$309$	28.0755	−	19.3507i	1.59716	−	1.10083i
$310$		0			0
$311$	−7.59714			−0.430794			−0.215397	−	0.976527i	$-0.569105\pi$
$311$	−7.59714			−0.430794			−0.215397	+	0.976527i	$0.569105\pi$
$312$		0			0
$313$	15.8753			0.897326			0.448663	−	0.893701i	$-0.351900\pi$
$313$	15.8753			0.897326			0.448663	+	0.893701i	$0.351900\pi$
$314$		0			0
$315$	1.08011	−	0.423664i	0.0608571	−	0.0238707i
$316$		0			0
$317$		−	20.8686i		−	1.17210i	−0.810275	−	0.586050i	$-0.800682\pi$
$317$		−	20.8686i		−	1.17210i	0.810275	−	0.586050i	$-0.199318\pi$
$318$		0			0
$319$		−	1.99308i		−	0.111591i
$320$		0			0
$321$	−13.6072	+	1.08911i	−0.759480	+	0.0607883i
$322$		0			0
$323$	26.9671			1.50049
$324$		0			0
$325$	4.00556	−	6.93784i	0.222189	−	0.384842i
$326$		0			0
$327$	−13.6017	−	19.7344i	−0.752176	−	1.09131i
$328$		0			0
$329$	3.49231	+	16.0644i	0.192537	+	0.885661i
$330$		0			0
$331$			0.264856i			0.0145578i	0.999974	+	0.00727890i	$0.00231697\pi$
$331$			0.264856i			0.0145578i	−0.999974	+	0.00727890i	$0.997683\pi$
$332$		0			0
$333$	−1.57974	+	4.14830i	−0.0865693	+	0.227325i
$334$		0			0
$335$	−0.682593	+	1.18229i	−0.0372940	+	0.0645951i
$336$		0			0
$337$	−17.5570	−	30.4097i	−0.956393	−	1.65652i	−0.731147	−	0.682220i	$-0.761015\pi$
$337$	−17.5570	−	30.4097i	−0.956393	−	1.65652i	−0.225247	−	0.974302i	$-0.572319\pi$
$338$		0			0
$339$	1.16494	+	14.5546i	0.0632711	+	0.790500i
$340$		0			0
$341$	−23.2323	+	13.4132i	−1.25810	+	0.726364i
$342$		0			0
$343$	11.0927	+	14.8308i	0.598949	+	0.800787i
$344$		0			0
$345$	0.172504	+	2.15524i	0.00928730	+	0.116034i
$346$		0			0
$347$	−10.4792			−0.562553			−0.281276	−	0.959627i	$-0.590758\pi$
$347$	−10.4792			−0.562553			−0.281276	+	0.959627i	$0.590758\pi$
$348$		0			0
$349$	0.826518	−	1.43157i	0.0442425	−	0.0766303i	−0.843056	−	0.537826i	$-0.819246\pi$
$349$	0.826518	−	1.43157i	0.0442425	−	0.0766303i	0.887299	+	0.461195i	$0.152579\pi$
$350$		0			0
$351$	5.77956	+	6.04195i	0.308490	+	0.322496i
$352$		0			0
$353$	−25.3427	+	14.6316i	−1.34886	+	0.778763i	−0.988088	−	0.153892i	$-0.950819\pi$
$353$	−25.3427	+	14.6316i	−1.34886	+	0.778763i	−0.360769	+	0.932655i	$0.617486\pi$
$354$		0			0
$355$	−1.90699	−	1.10100i	−0.101212	−	0.0584350i
$356$		0			0
$357$	−18.2156	−	17.0811i	−0.964074	−	0.904026i
$358$		0			0
$359$	2.14163	+	3.70941i	0.113031	+	0.195775i	0.916991	−	0.398908i	$-0.130611\pi$
$359$	2.14163	+	3.70941i	0.113031	+	0.195775i	−0.803960	+	0.594683i	$0.797277\pi$
$360$		0			0
$361$	2.74534	−	4.75507i	0.144492	−	0.250267i
$362$		0			0
$363$	−7.99244	−	11.5960i	−0.419495	−	0.608633i
$364$		0			0
$365$	−0.875705	+	0.505588i	−0.0458365	+	0.0264637i
$366$		0			0
$367$	−0.801583	+	0.462794i	−0.0418423	+	0.0241577i	−0.520775	−	0.853694i	$-0.674357\pi$
$367$	−0.801583	+	0.462794i	−0.0418423	+	0.0241577i	0.478933	+	0.877851i	$0.341024\pi$
$368$		0			0
$369$	−3.72420	−	1.41824i	−0.193874	−	0.0738306i
$370$		0			0
$371$	3.50205	−	10.9502i	0.181817	−	0.568507i
$372$		0			0
$373$	4.17963	−	7.23934i	0.216413	−	0.374839i	−0.737296	−	0.675570i	$-0.763897\pi$
$373$	4.17963	−	7.23934i	0.216413	−	0.374839i	0.953709	+	0.300732i	$0.0972308\pi$
$374$		0			0
$375$	−2.28174	−	1.08461i	−0.117829	−	0.0560093i
$376$		0			0
$377$		−	0.733226i		−	0.0377631i
$378$		0			0
$379$			10.9470i			0.562311i	0.959662	+	0.281155i	$0.0907177\pi$
$379$			10.9470i			0.562311i	−0.959662	+	0.281155i	$0.909282\pi$
$380$		0			0
$381$	−14.2363	−	6.76716i	−0.729348	−	0.346692i
$382$		0			0
$383$	6.42795	−	11.1335i	0.328453	−	0.568897i	−0.653752	−	0.756709i	$-0.726806\pi$
$383$	6.42795	−	11.1335i	0.328453	−	0.568897i	0.982205	+	0.187811i	$0.0601394\pi$
$384$		0			0
$385$	−1.65297	+	0.359344i	−0.0842430	+	0.0183139i
$386$		0			0
$387$	4.03899	+	25.0696i	0.205313	+	1.27436i
$388$		0			0
$389$	−5.13728	+	2.96601i	−0.260471	+	0.150383i	−0.624549	−	0.780985i	$-0.714717\pi$
$389$	−5.13728	+	2.96601i	−0.260471	+	0.150383i	0.364079	+	0.931368i	$0.381384\pi$
$390$		0			0
$391$	40.3008	−	23.2677i	2.03810	−	1.17670i
$392$		0			0
$393$	−12.7818	−	18.5448i	−0.644758	−	0.935462i
$394$		0			0
$395$	0.0468486	−	0.0811442i	0.00235721	−	0.00408281i
$396$		0			0
$397$	−3.85939	−	6.68466i	−0.193697	−	0.335494i	0.752775	−	0.658277i	$-0.228715\pi$
$397$	−3.85939	−	6.68466i	−0.193697	−	0.335494i	−0.946473	+	0.322784i	$0.895381\pi$
$398$		0			0
$399$	−21.7057	+	6.57030i	−1.08664	+	0.328926i
$400$		0			0
$401$	−15.6902	−	9.05876i	−0.783533	−	0.452373i	0.0541479	−	0.998533i	$-0.482756\pi$
$401$	−15.6902	−	9.05876i	−0.783533	−	0.452373i	−0.837681	+	0.546160i	$0.816089\pi$
$402$		0			0
$403$	−8.54683	+	4.93451i	−0.425748	+	0.245806i
$404$		0			0
$405$	0.875078	−	0.982327i	0.0434830	−	0.0488122i
$406$		0			0
$407$	3.23591	−	5.60476i	0.160398	−	0.277817i
$408$		0			0
$409$	22.6048			1.11774			0.558868	−	0.829257i	$-0.311236\pi$
$409$	22.6048			1.11774			0.558868	+	0.829257i	$0.311236\pi$
$410$		0			0
$411$	−2.45241	−	30.6400i	−0.120968	−	1.51136i
$412$		0			0
$413$	3.94707	+	18.1563i	0.194222	+	0.893414i
$414$		0			0
$415$	−0.390608	+	0.225518i	−0.0191742	+	0.0110702i
$416$		0			0
$417$	−2.66295	−	33.2705i	−0.130405	−	1.62927i
$418$		0			0
$419$	−6.20744	−	10.7516i	−0.303253	−	0.525250i	0.673618	−	0.739080i	$-0.264739\pi$
$419$	−6.20744	−	10.7516i	−0.303253	−	0.525250i	−0.976871	+	0.213830i	$0.931406\pi$
$420$		0			0
$421$	−14.5609	+	25.2203i	−0.709657	+	1.22916i	0.255327	+	0.966855i	$0.417817\pi$
$421$	−14.5609	+	25.2203i	−0.709657	+	1.22916i	−0.964984	+	0.262308i	$0.915516\pi$
$422$		0			0
$423$	11.7695	+	14.4554i	0.572254	+	0.702846i
$424$		0			0
$425$			27.1296i			1.31598i
$426$		0			0
$427$	6.59663	+	30.3442i	0.319233	+	1.46846i
$428$		0			0
$429$	−6.91801	−	10.0372i	−0.334005	−	0.484599i
$430$		0			0
$431$	−16.5088	+	28.5940i	−0.795200	+	1.37733i	0.127512	+	0.991837i	$0.459301\pi$
$431$	−16.5088	+	28.5940i	−0.795200	+	1.37733i	−0.922712	+	0.385490i	$0.874033\pi$
$432$		0			0
$433$	19.1386			0.919743			0.459871	−	0.887986i	$-0.347896\pi$
$433$	19.1386			0.919743			0.459871	+	0.887986i	$0.347896\pi$
$434$		0			0
$435$	−0.115001	+	0.00920458i	−0.00551386	+	0.000441326i
$436$		0			0
$437$		−	42.2620i		−	2.02166i
$438$		0			0
$439$			11.2734i			0.538051i	0.963133	+	0.269026i	$0.0867017\pi$
$439$			11.2734i			0.538051i	−0.963133	+	0.269026i	$0.913298\pi$
$440$		0			0
$441$	18.8233	+	9.31037i	0.896348	+	0.443351i
$442$		0			0
$443$	13.5495			0.643758			0.321879	−	0.946781i	$-0.395686\pi$
$443$	13.5495			0.643758			0.321879	+	0.946781i	$0.395686\pi$
$444$		0			0
$445$	0.436159			0.0206759
$446$		0			0
$447$	−25.7722	+	17.7632i	−1.21898	+	0.840172i
$448$		0			0
$449$			28.8966i			1.36371i	0.731485	+	0.681857i	$0.238827\pi$
$449$			28.8966i			1.36371i	−0.731485	+	0.681857i	$0.761173\pi$
$450$		0			0
$451$	5.03176	+	2.90509i	0.236936	+	0.136795i
$452$		0			0
$453$	0.686282	+	8.57431i	0.0322444	+	0.402856i
$454$		0			0
$455$	−0.608103	+	0.132198i	−0.0285083	+	0.00619752i
$456$		0			0
$457$	−8.12636			−0.380135			−0.190067	−	0.981771i	$-0.560871\pi$
$457$	−8.12636			−0.380135			−0.190067	+	0.981771i	$0.560871\pi$
$458$		0			0
$459$	−27.1808	−	7.93355i	−1.26869	−	0.370306i
$460$		0			0
$461$	2.17450	+	1.25545i	0.101276	+	0.0584720i	0.549783	−	0.835308i	$-0.314711\pi$
$461$	2.17450	+	1.25545i	0.101276	+	0.0584720i	−0.448506	+	0.893780i	$0.648044\pi$
$462$		0			0
$463$	−11.3199	+	6.53552i	−0.526078	+	0.303732i	−0.739418	−	0.673247i	$-0.764899\pi$
$463$	−11.3199	+	6.53552i	−0.526078	+	0.303732i	0.213340	+	0.976978i	$0.431566\pi$
$464$		0			0
$465$	0.881232	+	1.27856i	0.0408662	+	0.0592916i
$466$		0			0
$467$	−13.1187	−	22.7223i	−0.607063	−	1.05146i	−0.991722	−	0.128405i	$-0.959014\pi$
$467$	−13.1187	−	22.7223i	−0.607063	−	1.05146i	0.384659	−	0.923059i	$-0.374319\pi$
$468$		0			0
$469$	−24.1458	+	5.24914i	−1.11495	+	0.242383i
$470$		0			0
$471$	−9.26195	+	19.4847i	−0.426768	+	0.897807i
$472$		0			0
$473$		−	37.0222i		−	1.70228i
$474$		0			0
$475$	21.3374	+	12.3191i	0.979026	+	0.565241i
$476$		0			0
$477$	−2.07349	−	12.8699i	−0.0949385	−	0.589274i
$478$		0			0
$479$	12.8923	+	22.3301i	0.589064	+	1.02029i	0.994355	+	0.106102i	$0.0338369\pi$
$479$	12.8923	+	22.3301i	0.589064	+	1.02029i	−0.405291	+	0.914188i	$0.632830\pi$
$480$		0			0
$481$	1.19044	−	2.06191i	0.0542795	−	0.0940149i
$482$		0			0
$483$	−26.7689	+	28.5470i	−1.21803	+	1.29893i
$484$		0			0
$485$	1.32829	−	0.766886i	0.0603143	−	0.0348225i
$486$		0			0
$487$	−4.16732	−	2.40600i	−0.188839	−	0.109026i	0.402600	−	0.915376i	$-0.368107\pi$
$487$	−4.16732	−	2.40600i	−0.188839	−	0.109026i	−0.591439	+	0.806350i	$0.701440\pi$
$488$		0			0
$489$	2.18683	+	27.3220i	0.0988920	+	1.23554i
$490$		0			0
$491$	−5.24017	−	9.07624i	−0.236485	−	0.409605i	0.723218	−	0.690620i	$-0.242662\pi$
$491$	−5.24017	−	9.07624i	−0.236485	−	0.409605i	−0.959703	+	0.281015i	$0.909329\pi$
$492$		0			0
$493$	1.24153	+	2.15040i	0.0559158	+	0.0968491i
$494$		0			0
$495$	−1.48740	+	1.21104i	−0.0668538	+	0.0544321i
$496$		0			0
$497$	−8.46670	−	38.9464i	−0.379783	−	1.74699i
$498$		0			0
$499$	21.7419	+	12.5527i	0.973302	+	0.561936i	0.900241	−	0.435391i	$-0.143390\pi$
$499$	21.7419	+	12.5527i	0.973302	+	0.561936i	0.0730608	+	0.997327i	$0.476723\pi$
$500$		0			0
$501$	−23.0562	+	1.84540i	−1.03008	+	0.0824466i
$502$		0			0
$503$	−11.7233			−0.522716			−0.261358	−	0.965242i	$-0.584170\pi$
$503$	−11.7233			−0.522716			−0.261358	+	0.965242i	$0.584170\pi$
$504$		0			0
$505$	−0.598022			−0.0266116
$506$		0			0
$507$	10.2332	+	14.8471i	0.454472	+	0.659382i
$508$		0			0
$509$	5.80033	+	3.34882i	0.257095	+	0.148434i	0.623009	−	0.782215i	$-0.285910\pi$
$509$	5.80033	+	3.34882i	0.257095	+	0.148434i	−0.365914	+	0.930649i	$0.619243\pi$
$510$		0			0
$511$	−17.4324	−	5.57517i	−0.771165	−	0.246631i
$512$		0			0
$513$	−18.5821	+	17.7751i	−0.820419	+	0.784790i
$514$		0			0
$515$	1.43884	+	2.49214i	0.0634028	+	0.109817i
$516$		0			0
$517$	−13.5889	−	23.5367i	−0.597639	−	1.03514i
$518$		0			0
$519$	−12.2768	−	5.83573i	−0.538893	−	0.256160i
$520$		0			0
$521$	−34.0702	−	19.6704i	−1.49264	−	0.861777i	−0.492677	−	0.870212i	$-0.663981\pi$
$521$	−34.0702	−	19.6704i	−1.49264	−	0.861777i	−0.999964	+	0.00843580i	$0.997315\pi$
$522$		0			0
$523$	−23.3882	+	13.5032i	−1.02269	+	0.590452i	−0.914883	−	0.403720i	$-0.867717\pi$
$523$	−23.3882	+	13.5032i	−1.02269	+	0.590452i	−0.107810	+	0.994172i	$0.534384\pi$
$524$		0			0
$525$	−6.60990	−	21.8365i	−0.288480	−	0.953022i
$526$		0			0
$527$	16.7107	−	28.9438i	0.727930	−	1.26081i
$528$		0			0
$529$	−24.9644	−	43.2395i	−1.08541	−	1.87998i
$530$		0			0
$531$	13.3021	+	16.3378i	0.577263	+	0.708998i
$532$		0			0
$533$	1.85111	+	1.06874i	0.0801806	+	0.0462923i
$534$		0			0
$535$		−	1.15204i		−	0.0498069i
$536$		0			0
$537$	15.8170	+	22.9484i	0.682553	+	0.990298i
$538$		0			0
$539$	−24.9354	−	17.7667i	−1.07404	−	0.765264i
$540$		0			0
$541$	21.6648	+	37.5245i	0.931443	+	1.61331i	0.780858	+	0.624709i	$0.214782\pi$
$541$	21.6648	+	37.5245i	0.931443	+	1.61331i	0.150585	+	0.988597i	$0.451884\pi$
$542$		0			0
$543$	−6.51514	+	13.7061i	−0.279591	+	0.588186i
$544$		0			0
$545$	1.75173	−	1.01136i	0.0750361	−	0.0433221i
$546$		0			0
$547$	30.7085	+	17.7296i	1.31300	+	0.758062i	0.982592	−	0.185775i	$-0.0594796\pi$
$547$	30.7085	+	17.7296i	1.31300	+	0.758062i	0.330410	+	0.943837i	$0.392813\pi$
$548$		0			0
$549$	22.2315	+	27.3048i	0.948817	+	1.16534i
$550$		0			0
$551$	2.25504			0.0960681
$552$		0			0
$553$	1.65721	−	0.360266i	0.0704716	−	0.0153201i
$554$		0			0
$555$	−0.338338	−	0.160827i	−0.0143617	−	0.00682674i
$556$		0			0
$557$	13.5351	+	7.81446i	0.573498	+	0.331109i	0.758545	−	0.651620i	$-0.225910\pi$
$557$	13.5351	+	7.81446i	0.573498	+	0.331109i	−0.185047	+	0.982730i	$0.559244\pi$
$558$		0			0
$559$		−	13.6199i		−	0.576061i
$560$		0			0
$561$	37.2845	+	17.7230i	1.57415	+	0.748265i
$562$		0			0
$563$	−33.5379			−1.41346			−0.706728	−	0.707485i	$-0.749830\pi$
$563$	−33.5379			−1.41346			−0.706728	+	0.707485i	$0.749830\pi$
$564$		0			0
$565$	−1.23225			−0.0518412
$566$		0			0
$567$	23.8106	−	0.236697i	0.999951	−	0.00994033i
$568$		0			0
$569$		−	13.5405i		−	0.567647i	−0.958877	−	0.283823i	$-0.908397\pi$
$569$		−	13.5405i		−	0.567647i	0.958877	−	0.283823i	$-0.0916030\pi$
$570$		0			0
$571$		−	1.16974i		−	0.0489523i	−0.999700	−	0.0244761i	$-0.992208\pi$
$571$		−	1.16974i		−	0.0489523i	0.999700	−	0.0244761i	$-0.00779178\pi$
$572$		0			0
$573$	11.5407	−	24.2785i	0.482118	−	1.01425i
$574$		0			0
$575$	42.5167			1.77307
$576$		0			0
$577$	14.2810	−	24.7354i	0.594525	−	1.02975i	−0.399089	−	0.916912i	$-0.630673\pi$
$577$	14.2810	−	24.7354i	0.594525	−	1.02975i	0.993614	−	0.112835i	$-0.0359933\pi$
$578$		0			0
$579$	−7.34080	+	15.4431i	−0.305073	+	0.641794i
$580$		0			0
$581$	−7.77573	−	2.48680i	−0.322592	−	0.103170i
$582$		0			0
$583$			19.0060i			0.787147i
$584$		0			0
$585$	−0.547194	+	0.445523i	−0.0226237	+	0.0184201i
$586$		0			0
$587$	−18.8936	+	32.7248i	−0.779824	+	1.35070i	0.152218	+	0.988347i	$0.451358\pi$
$587$	−18.8936	+	32.7248i	−0.779824	+	1.35070i	−0.932043	+	0.362348i	$0.881975\pi$
$588$		0			0
$589$	−15.1761	−	26.2859i	−0.625322	−	1.08309i
$590$		0			0
$591$	−18.5435	−	8.81458i	−0.762779	−	0.362583i
$592$		0			0
$593$	−12.2747	+	7.08678i	−0.504060	+	0.291019i	−0.730388	−	0.683032i	$-0.760661\pi$
$593$	−12.2747	+	7.08678i	−0.504060	+	0.291019i	0.226329	+	0.974051i	$0.427328\pi$
$594$		0			0
$595$	1.55959	−	1.41738i	0.0639372	−	0.0581068i
$596$		0			0
$597$	16.4594	−	11.3445i	0.673637	−	0.464298i
$598$		0			0
$599$	−3.12448			−0.127663			−0.0638315	−	0.997961i	$-0.520332\pi$
$599$	−3.12448			−0.127663			−0.0638315	+	0.997961i	$0.520332\pi$
$600$		0			0
$601$	11.8507	−	20.5261i	0.483402	−	0.837276i	−0.516417	−	0.856337i	$-0.672734\pi$
$601$	11.8507	−	20.5261i	0.483402	−	0.837276i	0.999818	+	0.0190613i	$0.00606778\pi$
$602$		0			0
$603$	−21.7273	+	17.6903i	−0.884805	+	0.720404i
$604$		0			0
$605$	1.02933	−	0.594284i	0.0418482	−	0.0241611i
$606$		0			0
$607$	22.7909	+	13.1583i	0.925053	+	0.534080i	0.885244	−	0.465128i	$-0.153992\pi$
$607$	22.7909	+	13.1583i	0.925053	+	0.534080i	0.0398095	+	0.999207i	$0.487325\pi$
$608$		0			0
$609$	−1.52323	−	1.42835i	−0.0617243	−	0.0578798i
$610$		0			0
$611$	−4.99916	−	8.65880i	−0.202244	−	0.350298i
$612$		0			0
$613$	17.8753	−	30.9609i	0.721976	−	1.25050i	−0.238230	−	0.971209i	$-0.576567\pi$
$613$	17.8753	−	30.9609i	0.721976	−	1.25050i	0.960207	−	0.279291i	$-0.0900994\pi$
$614$		0			0
$615$	0.144385	−	0.303749i	0.00582218	−	0.0122483i
$616$		0			0
$617$	−39.3761	+	22.7338i	−1.58522	+	0.915229i	−0.591144	+	0.806566i	$0.701324\pi$
$617$	−39.3761	+	22.7338i	−1.58522	+	0.915229i	−0.994079	+	0.108663i	$0.965343\pi$
$618$		0			0
$619$	−30.6287	+	17.6835i	−1.23107	+	0.710759i	−0.967253	−	0.253813i	$-0.918315\pi$
$619$	−30.6287	+	17.6835i	−1.23107	+	0.710759i	−0.263818	+	0.964572i	$0.584982\pi$
$620$		0			0
$621$	−12.4332	+	42.5968i	−0.498927	+	1.70935i
$622$		0			0
$623$	5.30949	+	5.84224i	0.212720	+	0.234064i
$624$		0			0
$625$	−12.3400	+	21.3735i	−0.493599	+	0.854939i
$626$		0			0
$627$	30.8694	−	21.2764i	1.23280	−	0.849698i
$628$		0			0
$629$			8.06286i			0.321487i
$630$		0			0
$631$		−	24.0061i		−	0.955666i	−0.878451	−	0.477833i	$-0.841422\pi$
$631$		−	24.0061i		−	0.955666i	0.878451	−	0.477833i	$-0.158578\pi$
$632$		0			0
$633$	2.03732	+	25.4539i	0.0809760	+	1.01170i
$634$		0			0
$635$	0.665144	−	1.15206i	0.0263954	−	0.0457182i
$636$		0			0
$637$	−9.17336	−	6.53610i	−0.363462	−	0.258970i
$638$		0			0
$639$	−28.5339	−	35.0455i	−1.12878	−	1.38638i
$640$		0			0
$641$	−21.1585	+	12.2159i	−0.835710	+	0.482497i	−0.855804	−	0.517301i	$-0.826937\pi$
$641$	−21.1585	+	12.2159i	−0.835710	+	0.482497i	0.0200938	+	0.999798i	$0.493604\pi$
$642$		0			0
$643$	−3.61446	+	2.08681i	−0.142540	+	0.0822958i	−0.569574	−	0.821940i	$-0.692892\pi$
$643$	−3.61446	+	2.08681i	−0.142540	+	0.0822958i	0.427034	+	0.904236i	$0.359559\pi$
$644$		0			0
$645$	−2.13618	+	0.170978i	−0.0841118	+	0.00673226i
$646$		0			0
$647$	8.96257	−	15.5236i	0.352355	−	0.610297i	−0.634307	−	0.773082i	$-0.718714\pi$
$647$	8.96257	−	15.5236i	0.352355	−	0.610297i	0.986662	+	0.162785i	$0.0520476\pi$
$648$		0			0
$649$	−15.3584	−	26.6016i	−0.602871	−	1.04420i
$650$		0			0
$651$	−6.39844	+	27.3681i	−0.250775	+	1.07264i
$652$		0			0
$653$	−8.63577	−	4.98586i	−0.337944	−	0.195112i	0.321419	−	0.946937i	$-0.395840\pi$
$653$	−8.63577	−	4.98586i	−0.337944	−	0.195112i	−0.659362	+	0.751825i	$0.729174\pi$
$654$		0			0
$655$	1.64614	−	0.950401i	0.0643202	−	0.0371353i
$656$		0			0
$657$	−20.4886	+	3.30094i	−0.799336	+	0.128782i
$658$		0			0
$659$	13.4365	−	23.2727i	0.523412	−	0.906577i	−0.476217	−	0.879328i	$-0.657992\pi$
$659$	13.4365	−	23.2727i	0.523412	−	0.906577i	0.999629	−	0.0272484i	$-0.00867452\pi$
$660$		0			0
$661$	20.4690			0.796152			0.398076	−	0.917352i	$-0.369678\pi$
$661$	20.4690			0.796152			0.398076	+	0.917352i	$0.369678\pi$
$662$		0			0
$663$	13.7164	+	6.52003i	0.532702	+	0.253217i
$664$		0			0
$665$	−0.406575	−	1.87023i	−0.0157663	−	0.0725242i
$666$		0			0
$667$	3.37004	−	1.94569i	0.130488	−	0.0753375i
$668$		0			0
$669$	1.94045	−	1.33744i	0.0750222	−	0.0517083i
$670$		0			0
$671$	−25.6681	−	44.4585i	−0.990907	−	1.71630i
$672$		0			0
$673$	17.6903	−	30.6405i	0.681911	−	1.18110i	−0.292486	−	0.956270i	$-0.594482\pi$
$673$	17.6903	−	30.6405i	0.681911	−	1.18110i	0.974397	−	0.224835i	$-0.0721842\pi$
$674$		0			0
$675$	−17.8822	−	18.6941i	−0.688288	−	0.719535i
$676$		0			0
$677$		−	16.4045i		−	0.630477i	−0.949012	−	0.315238i	$-0.897915\pi$
$677$		−	16.4045i		−	0.630477i	0.949012	−	0.315238i	$-0.102085\pi$
$678$		0			0
$679$	26.4418	+	8.45652i	1.01474	+	0.324531i
$680$		0			0
$681$	−46.2415	+	3.70114i	−1.77198	+	0.141828i
$682$		0			0
$683$	13.4445	−	23.2865i	0.514439	−	0.891035i	−0.485421	−	0.874281i	$-0.661333\pi$
$683$	13.4445	−	23.2865i	0.514439	−	0.891035i	0.999860	−	0.0167539i	$-0.00533318\pi$
$684$		0			0
$685$	2.59410			0.0991154
$686$		0			0
$687$	−12.3245	−	17.8813i	−0.470208	−	0.682213i
$688$		0			0
$689$			6.99203i			0.266375i
$690$		0			0
$691$			11.8176i			0.449563i	0.974409	+	0.224782i	$0.0721669\pi$
$691$			11.8176i			0.449563i	−0.974409	+	0.224782i	$0.927833\pi$
$692$		0			0
$693$	−34.3281	−	5.18108i	−1.30402	−	0.196813i
$694$		0			0
$695$	2.81681			0.106848
$696$		0			0
$697$	−7.23857			−0.274180
$698$		0			0
$699$	2.38754	+	29.8296i	0.0903050	+	1.12826i
$700$		0			0
$701$			46.6469i			1.76183i	0.473274	+	0.880915i	$0.343072\pi$
$701$			46.6469i			1.76183i	−0.473274	+	0.880915i	$0.656928\pi$
$702$		0			0
$703$	6.34142	+	3.66122i	0.239171	+	0.138086i
$704$		0			0
$705$	−1.29531	+	0.892777i	−0.0487841	+	0.0336239i
$706$		0			0
$707$	−7.27989	−	8.01034i	−0.273788	−	0.301260i
$708$		0			0
$709$	29.4129			1.10463			0.552313	−	0.833637i	$-0.313745\pi$
$709$	29.4129			1.10463			0.552313	+	0.833637i	$0.313745\pi$
$710$		0			0
$711$	1.49122	−	1.21414i	0.0559251	−	0.0455339i
$712$		0			0
$713$	−45.3598	−	26.1885i	−1.69874	−	0.980767i
$714$		0			0
$715$	0.890956	−	0.514394i	0.0333199	−	0.0192372i
$716$		0			0
$717$	2.38087	−	0.190563i	0.0889153	−	0.00711672i
$718$		0			0
$719$	1.20141	+	2.08089i	0.0448049	+	0.0776043i	0.887558	−	0.460696i	$-0.152400\pi$
$719$	1.20141	+	2.08089i	0.0448049	+	0.0776043i	−0.842753	+	0.538300i	$0.819067\pi$
$720$		0			0
$721$	−15.8662	+	49.6104i	−0.590888	+	1.84759i
$722$		0			0
$723$	6.82134	−	0.545976i	0.253688	−	0.0203051i
$724$		0			0
$725$			2.26864i			0.0842550i
$726$		0			0
$727$	−9.56368	−	5.52160i	−0.354697	−	0.204785i	0.312055	−	0.950064i	$-0.398983\pi$
$727$	−9.56368	−	5.52160i	−0.354697	−	0.204785i	−0.666752	+	0.745279i	$0.732316\pi$
$728$		0			0
$729$	23.9586	−	12.4492i	0.887357	−	0.461082i
$730$		0			0
$731$	23.0619	+	39.9444i	0.852975	+	1.47740i
$732$		0			0
$733$	12.6022	−	21.8277i	0.465474	−	0.806225i	−0.533749	−	0.845643i	$-0.679217\pi$
$733$	12.6022	−	21.8277i	0.465474	−	0.806225i	0.999223	+	0.0394184i	$0.0125505\pi$
$734$		0			0
$735$	−0.909977	+	1.52082i	−0.0335650	+	0.0560963i
$736$		0			0
$737$	35.3770	−	20.4249i	1.30313	−	0.752362i
$738$		0			0
$739$	−18.2167	−	10.5174i	−0.670111	−	0.386889i	0.126007	−	0.992029i	$-0.459784\pi$
$739$	−18.2167	−	10.5174i	−0.670111	−	0.386889i	−0.796119	+	0.605140i	$0.793117\pi$
$740$		0			0
$741$	11.3564	−	7.82729i	0.417188	−	0.287543i
$742$		0			0
$743$	−5.28467	−	9.15331i	−0.193876	−	0.335802i	0.752656	−	0.658414i	$-0.228772\pi$
$743$	−5.28467	−	9.15331i	−0.193876	−	0.335802i	−0.946531	+	0.322612i	$0.895439\pi$
$744$		0			0
$745$	−1.32080	−	2.28769i	−0.0483903	−	0.0838144i
$746$		0			0
$747$	−9.13893	+	1.47238i	−0.334376	+	0.0538716i
$748$		0			0
$749$	15.4312	−	14.0241i	0.563845	−	0.512429i
$750$		0			0
$751$	23.9955	+	13.8538i	0.875607	+	0.505532i	0.869207	−	0.494448i	$-0.164630\pi$
$751$	23.9955	+	13.8538i	0.875607	+	0.505532i	0.00639961	+	0.999980i	$0.497963\pi$
$752$		0			0
$753$	−2.58371	+	5.43545i	−0.0941557	+	0.198079i
$754$		0			0
$755$	−0.725934			−0.0264194
$756$		0			0
$757$	−31.5160			−1.14547			−0.572734	−	0.819742i	$-0.694117\pi$
$757$	−31.5160			−1.14547			−0.572734	+	0.819742i	$0.694117\pi$
$758$		0			0
$759$	27.7749	−	58.4310i	1.00816	−	2.12091i
$760$		0			0
$761$	−2.60582	−	1.50447i	−0.0944610	−	0.0545371i	0.452025	−	0.892005i	$-0.350702\pi$
$761$	−2.60582	−	1.50447i	−0.0944610	−	0.0545371i	−0.546486	+	0.837468i	$0.684035\pi$
$762$		0			0
$763$	34.8713	+	11.1524i	1.26243	+	0.403744i
$764$		0			0
$765$	0.850425	−	2.23316i	0.0307472	−	0.0807401i
$766$		0			0
$767$	−5.65014	−	9.78633i	−0.204015	−	0.353364i
$768$		0			0
$769$	18.4251	+	31.9132i	0.664426	+	1.15082i	0.979441	+	0.201733i	$0.0646572\pi$
$769$	18.4251	+	31.9132i	0.664426	+	1.15082i	−0.315015	+	0.949087i	$0.602009\pi$
$770$		0			0
$771$	3.31315	−	2.28356i	0.119320	−	0.0822403i
$772$		0			0
$773$	−32.5149	−	18.7725i	−1.16948	−	0.675200i	−0.215924	−	0.976410i	$-0.569276\pi$
$773$	−32.5149	−	18.7725i	−1.16948	−	0.675200i	−0.953558	+	0.301210i	$0.902610\pi$
$774$		0			0
$775$	26.4443	−	15.2676i	0.949907	−	0.548429i
$776$		0			0
$777$	−1.96445	−	6.48975i	−0.0704741	−	0.232818i
$778$		0			0
$779$	−3.28692	+	5.69311i	−0.117766	+	0.203977i
$780$		0			0
$781$	32.9448	+	57.0620i	1.17886	+	2.04184i
$782$		0			0
$783$	−2.27291	−	0.663419i	−0.0812273	−	0.0237087i
$784$		0			0
$785$	−1.57678	−	0.910357i	−0.0562778	−	0.0324920i
$786$		0			0
$787$		−	39.3905i		−	1.40412i	−0.712118	−	0.702060i	$-0.752264\pi$
$787$		−	39.3905i		−	1.40412i	0.712118	−	0.702060i	$-0.247736\pi$
$788$		0			0
$789$	26.6125	−	2.13005i	0.947430	−	0.0758317i
$790$		0			0
$791$	−15.0005	−	16.5057i	−0.533358	−	0.586875i
$792$		0			0
$793$	−9.44293	−	16.3556i	−0.335328	−	0.580805i
$794$		0			0
$795$	1.09664	−	0.0877747i	0.0388939	−	0.00311305i
$796$		0			0
$797$	22.1551	−	12.7912i	0.784773	−	0.453089i	−0.0533461	−	0.998576i	$-0.516989\pi$
$797$	22.1551	−	12.7912i	0.784773	−	0.453089i	0.838119	+	0.545487i	$0.183655\pi$
$798$		0			0
$799$	29.3230	+	16.9296i	1.03737	+	0.598928i
$800$		0			0
$801$	8.36542	+	3.18569i	0.295578	+	0.112561i
$802$		0			0
$803$	30.2570			1.06775
$804$		0			0
$805$	−2.22127	−	2.44415i	−0.0782894	−	0.0861449i
$806$		0			0
$807$	−26.6850	+	18.3923i	−0.939355	+	0.647441i
$808$		0			0
$809$	−39.8718	−	23.0200i	−1.40182	−	0.809341i	−0.407240	−	0.913321i	$-0.633509\pi$
$809$	−39.8718	−	23.0200i	−1.40182	−	0.809341i	−0.994579	+	0.103981i	$0.966842\pi$
$810$		0			0
$811$		−	2.17040i		−	0.0762131i	−0.999274	−	0.0381065i	$-0.987867\pi$
$811$		−	2.17040i		−	0.0762131i	0.999274	−	0.0381065i	$-0.0121326\pi$
$812$		0			0
$813$	−1.66396	−	20.7892i	−0.0583575	−	0.729110i
$814$		0			0
$815$	−2.31318			−0.0810272
$816$		0			0
$817$	41.8882			1.46548
$818$		0			0
$819$	−12.6288	−	1.90605i	−0.441286	−	0.0666026i
$820$		0			0
$821$			44.3710i			1.54856i	0.632844	+	0.774279i	$0.281887\pi$
$821$			44.3710i			1.54856i	−0.632844	+	0.774279i	$0.718113\pi$
$822$		0			0
$823$		−	15.5524i		−	0.542123i	−0.962562	−	0.271062i	$-0.912625\pi$
$823$		−	15.5524i		−	0.542123i	0.962562	−	0.271062i	$-0.0873747\pi$
$824$		0			0
$825$	21.4047	+	31.0554i	0.745214	+	1.08121i
$826$		0			0
$827$	−19.0429			−0.662187			−0.331094	−	0.943598i	$-0.607418\pi$
$827$	−19.0429			−0.662187			−0.331094	+	0.943598i	$0.607418\pi$
$828$		0			0
$829$	−3.57307	+	6.18873i	−0.124098	+	0.214944i	−0.921380	−	0.388663i	$-0.872937\pi$
$829$	−3.57307	+	6.18873i	−0.124098	+	0.214944i	0.797282	+	0.603607i	$0.206270\pi$
$830$		0			0
$831$	−9.04583	+	0.724023i	−0.313796	+	0.0251161i
$832$		0			0
$833$	37.9708	+	3.63625i	1.31561	+	0.125988i
$834$		0			0
$835$		−	1.95203i		−	0.0675526i
$836$		0			0
$837$	7.56327	+	30.9589i	0.261425	+	1.07010i
$838$		0			0
$839$	27.0822	−	46.9078i	0.934982	−	1.61944i	0.160315	−	0.987066i	$-0.448749\pi$
$839$	27.0822	−	46.9078i	0.934982	−	1.61944i	0.774667	−	0.632370i	$-0.217918\pi$
$840$		0			0
$841$	−14.3962	−	24.9349i	−0.496420	−	0.859825i
$842$		0			0
$843$	4.77492	−	3.29106i	0.164457	−	0.113350i
$844$		0			0
$845$	−1.31791	+	0.760897i	−0.0453375	+	0.0261756i
$846$		0			0
$847$	20.4906	+	6.55322i	0.704065	+	0.225171i
$848$		0			0
$849$	4.23656	+	2.01383i	0.145398	+	0.0691144i
$850$		0			0
$851$	12.6359			0.433152
$852$		0			0
$853$	−11.3115	+	19.5920i	−0.387298	+	0.670819i	−0.992085	−	0.125568i	$-0.959925\pi$
$853$	−11.3115	+	19.5920i	−0.387298	+	0.670819i	0.604787	+	0.796387i	$0.293258\pi$
$854$		0			0
$855$	−1.37021	−	1.68290i	−0.0468602	−	0.0575540i
$856$		0			0
$857$	−3.63517	+	2.09876i	−0.124175	+	0.0716924i	−0.560801	−	0.827951i	$-0.689507\pi$
$857$	−3.63517	+	2.09876i	−0.124175	+	0.0716924i	0.436626	+	0.899643i	$0.356173\pi$
$858$		0			0
$859$	−38.1314	−	22.0152i	−1.30103	−	0.751147i	−0.320446	−	0.947267i	$-0.603833\pi$
$859$	−38.1314	−	22.0152i	−1.30103	−	0.751147i	−0.980580	+	0.196120i	$0.937166\pi$
$860$		0			0
$861$	5.82628	−	1.76361i	0.198559	−	0.0601038i
$862$		0			0
$863$	−12.9076	−	22.3566i	−0.439380	−	0.761028i	0.558262	−	0.829665i	$-0.311468\pi$
$863$	−12.9076	−	22.3566i	−0.439380	−	0.761028i	−0.997642	+	0.0686366i	$0.978135\pi$
$864$		0			0
$865$	0.573594	−	0.993493i	0.0195028	−	0.0337798i
$866$		0			0
$867$	−21.9164	+	1.75418i	−0.744321	+	0.0595750i
$868$		0			0
$869$	−2.42804	+	1.40183i	−0.0823657	+	0.0475538i
$870$		0			0
$871$	13.0147	−	7.51403i	0.440986	−	0.254603i
$872$		0			0
$873$	31.0775	−	5.00692i	1.05181	−	0.169459i
$874$		0			0
$875$	3.77107	−	0.819806i	0.127485	−	0.0277145i
$876$		0			0
$877$	−8.31521	+	14.4024i	−0.280785	+	0.486334i	−0.971578	−	0.236719i	$-0.923928\pi$
$877$	−8.31521	+	14.4024i	−0.280785	+	0.486334i	0.690793	+	0.723052i	$0.257261\pi$
$878$		0			0
$879$	3.90787	+	48.8243i	0.131809	+	1.64680i
$880$		0			0
$881$			56.0413i			1.88808i	0.329831	+	0.944040i	$0.393008\pi$
$881$			56.0413i			1.88808i	−0.329831	+	0.944040i	$0.606992\pi$
$882$		0			0
$883$			38.2465i			1.28710i	0.765406	+	0.643548i	$0.222538\pi$
$883$			38.2465i			1.28710i	−0.765406	+	0.643548i	$0.777462\pi$
$884$		0			0
$885$	−1.46398	+	1.00903i	−0.0492111	+	0.0339183i
$886$		0			0
$887$	29.1295	−	50.4537i	0.978072	−	1.69407i	0.308671	−	0.951169i	$-0.400116\pi$
$887$	29.1295	−	50.4537i	0.978072	−	1.69407i	0.669401	−	0.742901i	$-0.266551\pi$
$888$		0			0
$889$	23.5286	−	5.11496i	0.789123	−	0.171550i
$890$		0			0
$891$	−37.3734	+	12.3634i	−1.25206	+	0.414190i
$892$		0			0
$893$	26.6302	−	15.3750i	0.891147	−	0.514504i
$894$		0			0
$895$	−2.03704	+	1.17608i	−0.0680906	+	0.0393121i
$896$		0			0
$897$	10.2180	−	21.4959i	0.341168	−	0.717728i
$898$		0			0
$899$	1.39738	−	2.42034i	0.0466054	−	0.0807228i
$900$		0			0
$901$	−11.8392	−	20.5062i	−0.394422	−	0.683159i
$902$		0			0
$903$	−28.2945	−	26.5321i	−0.941581	−	0.882935i
$904$		0			0
$905$	−1.10916	−	0.640373i	−0.0368697	−	0.0212867i
$906$		0			0
$907$	−14.7276	+	8.50300i	−0.489023	+	0.282337i	−0.724169	−	0.689623i	$-0.757776\pi$
$907$	−14.7276	+	8.50300i	−0.489023	+	0.282337i	0.235146	+	0.971960i	$0.424443\pi$
$908$		0			0
$909$	−11.4699	−	4.36793i	−0.380432	−	0.144875i
$910$		0			0
$911$	−16.2113	+	28.0787i	−0.537103	+	0.930290i	0.461955	+	0.886903i	$0.347148\pi$
$911$	−16.2113	+	28.0787i	−0.537103	+	0.930290i	−0.999058	+	0.0433865i	$0.986185\pi$
$912$		0			0
$913$	13.4961			0.446657
$914$		0			0
$915$	−2.44671	+	1.68637i	−0.0808857	+	0.0557497i
$916$		0			0
$917$	32.7694	+	10.4802i	1.08214	+	0.346085i
$918$		0			0
$919$	27.5766	−	15.9213i	0.909667	−	0.525196i	0.0293428	−	0.999569i	$-0.490659\pi$
$919$	27.5766	−	15.9213i	0.909667	−	0.525196i	0.880324	+	0.474373i	$0.157325\pi$
$920$		0			0
$921$	23.8968	+	11.3592i	0.787425	+	0.374298i
$922$		0			0
$923$	12.1199	+	20.9923i	0.398931	+	0.690969i
$924$		0			0
$925$	−3.68329	+	6.37964i	−0.121106	+	0.209761i
$926$		0			0
$927$	9.39403	+	58.3079i	0.308540	+	1.91508i
$928$		0			0
$929$		−	17.2768i		−	0.566834i	−0.958997	−	0.283417i	$-0.908532\pi$
$929$		−	17.2768i		−	0.566834i	0.958997	−	0.283417i	$-0.0914681\pi$
$930$		0			0
$931$	20.1018	−	28.2128i	0.658811	−	0.924636i
$932$		0			0
$933$	5.64914	−	11.8843i	0.184945	−	0.389075i
$934$		0			0
$935$	−1.74199	+	3.01722i	−0.0569692	+	0.0986736i
$936$		0			0
$937$	4.75647			0.155387			0.0776935	−	0.996977i	$-0.475244\pi$
$937$	4.75647			0.155387			0.0776935	+	0.996977i	$0.475244\pi$
$938$		0			0
$939$	−11.8047	+	24.8340i	−0.385232	+	0.810426i
$940$		0			0
$941$			37.0718i			1.20851i	0.796792	+	0.604253i	$0.206528\pi$
$941$			37.0718i			1.20851i	−0.796792	+	0.604253i	$0.793472\pi$
$942$		0			0
$943$			11.3440i			0.369413i
$944$		0			0
$945$	−0.140412	+	2.00466i	−0.00456760	+	0.0652115i
$946$		0			0
$947$	−57.2728			−1.86112			−0.930559	−	0.366143i	$-0.880678\pi$
$947$	−57.2728			−1.86112			−0.930559	+	0.366143i	$0.880678\pi$
$948$		0			0
$949$	11.1311			0.361331
$950$		0			0
$951$	32.6451	+	15.5177i	1.05859	+	0.503195i
$952$		0			0
$953$			36.6932i			1.18861i	0.804240	+	0.594305i	$0.202573\pi$
$953$			36.6932i			1.18861i	−0.804240	+	0.594305i	$0.797427\pi$
$954$		0			0
$955$	1.96472	+	1.13433i	0.0635768	+	0.0367061i
$956$		0			0
$957$	3.11780	+	1.48203i	0.100784	+	0.0479073i
$958$		0			0
$959$	31.5787	+	34.7473i	1.01973	+	1.12205i
$960$		0			0
$961$	−6.61684			−0.213446
$962$		0			0
$963$	8.41444	−	22.0958i	0.271152	−	0.712026i
$964$		0			0
$965$	−1.24972	−	0.721527i	−0.0402300	−	0.0232268i
$966$		0			0
$967$	−45.3226	+	26.1670i	−1.45748	+	0.841475i	−0.998887	−	0.0471723i	$-0.984979\pi$
$967$	−45.3226	+	26.1670i	−1.45748	+	0.841475i	−0.458591	+	0.888647i	$0.651646\pi$
$968$		0			0
$969$	−20.0524	+	42.1850i	−0.644177	+	1.35518i
$970$		0			0
$971$	28.4609	+	49.2957i	0.913352	+	1.58197i	0.809296	+	0.587401i	$0.199849\pi$
$971$	28.4609	+	49.2957i	0.913352	+	1.58197i	0.104057	+	0.994571i	$0.466818\pi$
$972$		0			0
$973$	34.2898	+	37.7305i	1.09928	+	1.20958i
$974$		0			0
$975$	7.87446	+	11.4248i	0.252185	+	0.365888i
$976$		0			0
$977$			34.4113i			1.10092i	0.834863	+	0.550458i	$0.185547\pi$
$977$			34.4113i			1.10092i	−0.834863	+	0.550458i	$0.814453\pi$
$978$		0			0
$979$	−11.3025	−	6.52550i	−0.361229	−	0.208556i
$980$		0			0
$981$	40.9848	−	6.60310i	1.30854	−	0.210821i
$982$		0			0
$983$	−12.6685	−	21.9424i	−0.404061	−	0.699854i	0.590151	−	0.807293i	$-0.299068\pi$
$983$	−12.6685	−	21.9424i	−0.404061	−	0.699854i	−0.994212	+	0.107439i	$0.965735\pi$
$984$		0			0
$985$	0.866385	−	1.50062i	0.0276053	−	0.0478138i
$986$		0			0
$987$	−27.7267	−	6.48227i	−0.882549	−	0.206333i
$988$		0			0
$989$	62.5995	−	36.1419i	1.99055	−	1.14924i
$990$		0			0
$991$	−5.91348	−	3.41415i	−0.187848	−	0.108454i	0.403127	−	0.915144i	$-0.367923\pi$
$991$	−5.91348	−	3.41415i	−0.187848	−	0.108454i	−0.590975	+	0.806690i	$0.701257\pi$
$992$		0			0
$993$	−0.414318	−	0.196944i	−0.0131480	−	0.00624982i
$994$		0			0
$995$	0.843525	+	1.46103i	0.0267416	+	0.0463177i
$996$		0			0
$997$	6.11461	+	10.5908i	0.193652	+	0.335415i	0.946458	−	0.322828i	$-0.104634\pi$
$997$	6.11461	+	10.5908i	0.193652	+	0.335415i	−0.752806	+	0.658242i	$0.771300\pi$
$998$		0			0
$999$	−5.31456	−	5.55584i	−0.168145	−	0.175779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cj.c.767.7	yes	30
3.2	odd	2		3024.2.cj.c.1439.9		30
4.3	odd	2		1008.2.cj.d.767.9	yes	30
7.2	even	3		1008.2.bh.c.191.5	yes	30
9.4	even	3		3024.2.bh.d.2447.9		30
9.5	odd	6		1008.2.bh.d.95.11	yes	30
12.11	even	2		3024.2.cj.d.1439.9		30
21.2	odd	6		3024.2.bh.c.1871.7		30
28.23	odd	6		1008.2.bh.d.191.11	yes	30
36.23	even	6		1008.2.bh.c.95.5	✓	30
36.31	odd	6		3024.2.bh.c.2447.9		30
63.23	odd	6		1008.2.cj.d.527.9	yes	30
63.58	even	3		3024.2.cj.d.2879.9		30
84.23	even	6		3024.2.bh.d.1871.7		30
252.23	even	6	inner	1008.2.cj.c.527.7	yes	30
252.247	odd	6		3024.2.cj.c.2879.9		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.c.95.5	✓	30	36.23	even	6
1008.2.bh.c.191.5	yes	30	7.2	even	3
1008.2.bh.d.95.11	yes	30	9.5	odd	6
1008.2.bh.d.191.11	yes	30	28.23	odd	6
1008.2.cj.c.527.7	yes	30	252.23	even	6	inner
1008.2.cj.c.767.7	yes	30	1.1	even	1	trivial
1008.2.cj.d.527.9	yes	30	63.23	odd	6
1008.2.cj.d.767.9	yes	30	4.3	odd	2
3024.2.bh.c.1871.7		30	21.2	odd	6
3024.2.bh.c.2447.9		30	36.31	odd	6
3024.2.bh.d.1871.7		30	84.23	even	6
3024.2.bh.d.2447.9		30	9.4	even	3
3024.2.cj.c.1439.9		30	3.2	odd	2
3024.2.cj.c.2879.9		30	252.247	odd	6
3024.2.cj.d.1439.9		30	12.11	even	2
3024.2.cj.d.2879.9		30	63.58	even	3

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.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.743588 + 1.56431i) q^{3} +(-0.126591 - 0.0730873i) q^{5} +(-0.562042 - 2.58536i) q^{7} +(-1.89415 - 2.32641i) q^{9} +O(q^{10})\)	\(q+(-0.743588 + 1.56431i) q^{3} +(-0.126591 - 0.0730873i) q^{5} +(-0.562042 - 2.58536i) q^{7} +(-1.89415 - 2.32641i) q^{9} +(2.18696 + 3.78792i) q^{11} +(0.804550 + 1.39352i) q^{13} +(0.208463 - 0.143681i) q^{15} +(-4.71916 - 2.72461i) q^{17} +(-4.28579 + 2.47440i) q^{19} +(4.46225 + 1.04324i) q^{21} +(-4.26992 + 7.39571i) q^{23} +(-2.48932 - 4.31162i) q^{25} +(5.04770 - 1.23316i) q^{27} +(-0.394626 - 0.227837i) q^{29} +6.13326i q^{31} +(-7.55170 + 0.604433i) q^{33} +(-0.117808 + 0.368362i) q^{35} +(-0.739819 - 1.28140i) q^{37} +(-2.77816 + 0.222362i) q^{39} +(1.15040 - 0.664185i) q^{41} +(-7.33030 - 4.23215i) q^{43} +(0.0697515 + 0.432941i) q^{45} -6.21361 q^{47} +(-6.36822 + 2.90616i) q^{49} +(7.77125 - 5.35626i) q^{51} +(3.76314 + 2.17265i) q^{53} -0.639355i q^{55} +(-0.683877 - 8.54426i) q^{57} -7.02273 q^{59} -11.7369 q^{61} +(-4.95003 + 6.20461i) q^{63} -0.235210i q^{65} -9.33942i q^{67} +(-8.39415 - 12.1789i) q^{69} +15.0642 q^{71} +(3.45880 - 5.99082i) q^{73} +(8.59576 - 0.687999i) q^{75} +(8.56400 - 7.78306i) q^{77} +0.640995i q^{79} +(-1.82437 + 8.81315i) q^{81} +(1.54280 - 2.67220i) q^{83} +(0.398268 + 0.689821i) q^{85} +(0.649848 - 0.447901i) q^{87} +(-2.58407 + 1.49191i) q^{89} +(3.15057 - 2.86327i) q^{91} +(-9.59434 - 4.56062i) q^{93} +0.723390 q^{95} +(-5.24637 + 9.08698i) q^{97} +(4.66983 - 12.2627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{5} - 7 q^{7} + 8 q^{9}+O(q^{10}) \) 30 * q + 3 * q^5 - 7 * q^7 + 8 * q^9	\( 30 q + 3 q^{5} - 7 q^{7} + 8 q^{9} - 3 q^{11} - 12 q^{17} - 9 q^{19} + 2 q^{21} + 12 q^{23} + 18 q^{25} + 27 q^{27} + 27 q^{29} + 13 q^{33} - 6 q^{35} + 6 q^{37} + 12 q^{39} + 9 q^{41} - 21 q^{43} + 13 q^{45} - 3 q^{49} + 12 q^{51} + 3 q^{53} + 20 q^{57} - 6 q^{59} + 6 q^{61} + 51 q^{63} + 10 q^{69} + 18 q^{71} + 21 q^{73} - 3 q^{75} + 72 q^{77} - 20 q^{81} - 15 q^{83} - 3 q^{85} - 57 q^{87} - 6 q^{89} + 26 q^{91} + 9 q^{93} + 54 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) \) 30 * q + 3 * q^5 - 7 * q^7 + 8 * q^9 - 3 * q^11 - 12 * q^17 - 9 * q^19 + 2 * q^21 + 12 * q^23 + 18 * q^25 + 27 * q^27 + 27 * q^29 + 13 * q^33 - 6 * q^35 + 6 * q^37 + 12 * q^39 + 9 * q^41 - 21 * q^43 + 13 * q^45 - 3 * q^49 + 12 * q^51 + 3 * q^53 + 20 * q^57 - 6 * q^59 + 6 * q^61 + 51 * q^63 + 10 * q^69 + 18 * q^71 + 21 * q^73 - 3 * q^75 + 72 * q^77 - 20 * q^81 - 15 * q^83 - 3 * q^85 - 57 * q^87 - 6 * q^89 + 26 * q^91 + 9 * q^93 + 54 * q^95 - 6 * q^97 - 48 * q^99

Introduction

L-functions

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