LMFDB - Embedded newform 1008.2.cz.h.607.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.9
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.h.367.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42297 + 0.987503i) q^{3} +(-0.679706 + 0.392428i) q^{5} +(2.49091 - 0.891831i) q^{7} +(1.04968 + 2.81037i) q^{9} +O(q^{10})$	\(q+(1.42297 + 0.987503i) q^{3} +(-0.679706 + 0.392428i) q^{5} +(2.49091 - 0.891831i) q^{7} +(1.04968 + 2.81037i) q^{9} +(1.22712 + 0.708477i) q^{11} +(-1.50450 - 0.868623i) q^{13} +(-1.35472 - 0.112799i) q^{15} +(5.43701 - 3.13906i) q^{17} +(-0.736632 + 1.27588i) q^{19} +(4.42517 + 1.19073i) q^{21} +(4.85720 - 2.80431i) q^{23} +(-2.19200 + 3.79666i) q^{25} +(-1.28159 + 5.03562i) q^{27} +(3.95678 + 6.85335i) q^{29} -8.41859 q^{31} +(1.04653 + 2.21992i) q^{33} +(-1.34311 + 1.58369i) q^{35} +(3.74187 - 6.48111i) q^{37} +(-1.28309 - 2.72172i) q^{39} +(7.19180 + 4.15219i) q^{41} +(-7.85087 + 4.53270i) q^{43} +(-1.81634 - 1.49830i) q^{45} +0.110085 q^{47} +(5.40927 - 4.44294i) q^{49} +(10.8365 + 0.902283i) q^{51} +(-4.28575 - 7.42313i) q^{53} -1.11211 q^{55} +(-2.30814 + 1.08812i) q^{57} +0.0736173 q^{59} +1.23776i q^{61} +(5.12102 + 6.06425i) q^{63} +1.36349 q^{65} +11.8735i q^{67} +(9.68091 + 0.806063i) q^{69} -0.390149i q^{71} +(3.70538 - 2.13930i) q^{73} +(-6.86835 + 3.23791i) q^{75} +(3.68848 + 0.670370i) q^{77} +6.00205i q^{79} +(-6.79636 + 5.89995i) q^{81} +(-7.88696 - 13.6606i) q^{83} +(-2.46371 + 4.26727i) q^{85} +(-1.13733 + 13.6594i) q^{87} +(6.15579 + 3.55405i) q^{89} +(-4.52224 - 0.821903i) q^{91} +(-11.9794 - 8.31338i) q^{93} -1.15630i q^{95} +(5.89647 - 3.40433i) q^{97} +(-0.703006 + 4.19233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9	$ 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9} + 9 q^{11} - 3 q^{13} + 6 q^{15} - 3 q^{17} + 4 q^{19} + 13 q^{21} + 6 q^{23} + 15 q^{25} - 9 q^{27} + 18 q^{29} - 34 q^{31} - 21 q^{33} + 42 q^{35} - 3 q^{37} - 27 q^{39} + 36 q^{41} - 24 q^{43} + 21 q^{45} + 42 q^{47} + 30 q^{49} + 6 q^{51} - 12 q^{53} + 30 q^{55} - 13 q^{57} + 12 q^{59} + 3 q^{63} + 6 q^{69} + 48 q^{73} - 36 q^{75} - 48 q^{77} - 31 q^{81} + 48 q^{83} - 21 q^{85} - 15 q^{87} + 39 q^{89} - 9 q^{91} + 10 q^{93} + 3 q^{97} - 30 q^{99}+O(q^{100}) $ 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9 + 9 * q^11 - 3 * q^13 + 6 * q^15 - 3 * q^17 + 4 * q^19 + 13 * q^21 + 6 * q^23 + 15 * q^25 - 9 * q^27 + 18 * q^29 - 34 * q^31 - 21 * q^33 + 42 * q^35 - 3 * q^37 - 27 * q^39 + 36 * q^41 - 24 * q^43 + 21 * q^45 + 42 * q^47 + 30 * q^49 + 6 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 + 12 * q^59 + 3 * q^63 + 6 * q^69 + 48 * q^73 - 36 * q^75 - 48 * q^77 - 31 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 + 10 * q^93 + 3 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.42297	+	0.987503i	0.821551	+	0.570135i
$3$	1.42297	+	0.987503i	0.821551	+	0.570135i
$4$		0			0
$5$	−0.679706	+	0.392428i	−0.303974	+	0.175499i	−0.644227	−	0.764835i	$-0.722821\pi$
$5$	−0.679706	+	0.392428i	−0.303974	+	0.175499i	0.340253	+	0.940334i	$0.389487\pi$
$6$		0			0
$7$	2.49091	−	0.891831i	0.941476	−	0.337081i
$7$	2.49091	−	0.891831i	0.941476	−	0.337081i
$8$		0			0
$9$	1.04968	+	2.81037i	0.349892	+	0.936790i
$10$		0			0
$11$	1.22712	+	0.708477i	0.369990	+	0.213614i	0.673454	−	0.739229i	$-0.264810\pi$
$11$	1.22712	+	0.708477i	0.369990	+	0.213614i	−0.303464	+	0.952843i	$0.598143\pi$
$12$		0			0
$13$	−1.50450	−	0.868623i	−0.417273	−	0.240913i	0.276637	−	0.960975i	$-0.410780\pi$
$13$	−1.50450	−	0.868623i	−0.417273	−	0.240913i	−0.693910	+	0.720062i	$0.744113\pi$
$14$		0			0
$15$	−1.35472	−	0.112799i	−0.349788	−	0.0291245i
$16$		0			0
$17$	5.43701	−	3.13906i	1.31867	−	0.761334i	0.335154	−	0.942163i	$-0.391212\pi$
$17$	5.43701	−	3.13906i	1.31867	−	0.761334i	0.983514	+	0.180829i	$0.0578782\pi$
$18$		0			0
$19$	−0.736632	+	1.27588i	−0.168995	+	0.292708i	−0.938067	−	0.346455i	$-0.887385\pi$
$19$	−0.736632	+	1.27588i	−0.168995	+	0.292708i	0.769072	+	0.639162i	$0.220719\pi$
$20$		0			0
$21$	4.42517	+	1.19073i	0.965652	+	0.259840i
$22$		0			0
$23$	4.85720	−	2.80431i	1.01280	−	0.584739i	0.100787	−	0.994908i	$-0.467864\pi$
$23$	4.85720	−	2.80431i	1.01280	−	0.584739i	0.912009	+	0.410169i	$0.134530\pi$
$24$		0			0
$25$	−2.19200	+	3.79666i	−0.438400	+	0.759331i
$26$		0			0
$27$	−1.28159	+	5.03562i	−0.246643	+	0.969106i
$28$		0			0
$29$	3.95678	+	6.85335i	0.734756	+	1.27263i	0.954830	+	0.297151i	$0.0960366\pi$
$29$	3.95678	+	6.85335i	0.734756	+	1.27263i	−0.220075	+	0.975483i	$0.570630\pi$
$30$		0			0
$31$	−8.41859			−1.51202			−0.756011	−	0.654559i	$-0.772855\pi$
$31$	−8.41859			−1.51202			−0.756011	+	0.654559i	$0.772855\pi$
$32$		0			0
$33$	1.04653	+	2.21992i	0.182177	+	0.386439i
$34$		0			0
$35$	−1.34311	+	1.58369i	−0.227026	+	0.267692i
$36$		0			0
$37$	3.74187	−	6.48111i	0.615160	−	1.06549i	−0.375196	−	0.926945i	$-0.622425\pi$
$37$	3.74187	−	6.48111i	0.615160	−	1.06549i	0.990356	−	0.138543i	$-0.0442420\pi$
$38$		0			0
$39$	−1.28309	−	2.72172i	−0.205458	−	0.435824i
$40$		0			0
$41$	7.19180	+	4.15219i	1.12317	+	0.648463i	0.942208	−	0.335027i	$-0.108746\pi$
$41$	7.19180	+	4.15219i	1.12317	+	0.648463i	0.180962	+	0.983490i	$0.442079\pi$
$42$		0			0
$43$	−7.85087	+	4.53270i	−1.19725	+	0.691230i	−0.959940	−	0.280205i	$-0.909598\pi$
$43$	−7.85087	+	4.53270i	−1.19725	+	0.691230i	−0.237306	+	0.971435i	$0.576264\pi$
$44$		0			0
$45$	−1.81634	−	1.49830i	−0.270764	−	0.223354i
$46$		0			0
$47$	0.110085			0.0160576			0.00802880	−	0.999968i	$-0.497444\pi$
$47$	0.110085			0.0160576			0.00802880	+	0.999968i	$0.497444\pi$
$48$		0			0
$49$	5.40927	−	4.44294i	0.772753	−	0.634706i
$50$		0			0
$51$	10.8365	+	0.902283i	1.51742	+	0.126345i
$52$		0			0
$53$	−4.28575	−	7.42313i	−0.588693	−	1.01965i	−0.994404	−	0.105644i	$-0.966309\pi$
$53$	−4.28575	−	7.42313i	−0.588693	−	1.01965i	0.405711	−	0.914001i	$-0.367024\pi$
$54$		0			0
$55$	−1.11211			−0.149956
$56$		0			0
$57$	−2.30814	+	1.08812i	−0.305721	+	0.144124i
$58$		0			0
$59$	0.0736173			0.00958415			0.00479208	−	0.999989i	$-0.498475\pi$
$59$	0.0736173			0.00958415			0.00479208	+	0.999989i	$0.498475\pi$
$60$		0			0
$61$			1.23776i			0.158479i	0.996856	+	0.0792394i	$0.0252492\pi$
$61$			1.23776i			0.158479i	−0.996856	+	0.0792394i	$0.974751\pi$
$62$		0			0
$63$	5.12102	+	6.06425i	0.645188	+	0.764023i
$64$		0			0
$65$	1.36349			0.169120
$66$		0			0
$67$			11.8735i			1.45058i	0.688442	+	0.725291i	$0.258295\pi$
$67$			11.8735i			1.45058i	−0.688442	+	0.725291i	$0.741705\pi$
$68$		0			0
$69$	9.68091	+	0.806063i	1.16544	+	0.0970386i
$70$		0			0
$71$		−	0.390149i		−	0.0463021i	−0.999732	−	0.0231511i	$-0.992630\pi$
$71$		−	0.390149i		−	0.0463021i	0.999732	−	0.0231511i	$-0.00736987\pi$
$72$		0			0
$73$	3.70538	−	2.13930i	0.433682	−	0.250386i	−0.267232	−	0.963632i	$-0.586109\pi$
$73$	3.70538	−	2.13930i	0.433682	−	0.250386i	0.700914	+	0.713246i	$0.252776\pi$
$74$		0			0
$75$	−6.86835	+	3.23791i	−0.793089	+	0.373882i
$76$		0			0
$77$	3.68848	+	0.670370i	0.420342	+	0.0763958i
$78$		0			0
$79$			6.00205i			0.675283i	0.941275	+	0.337642i	$0.109629\pi$
$79$			6.00205i			0.675283i	−0.941275	+	0.337642i	$0.890371\pi$
$80$		0			0
$81$	−6.79636	+	5.89995i	−0.755151	+	0.655551i
$82$		0			0
$83$	−7.88696	−	13.6606i	−0.865706	−	1.49945i	−0.866344	−	0.499447i	$-0.833536\pi$
$83$	−7.88696	−	13.6606i	−0.865706	−	1.49945i	0.000637973	−	1.00000i	$-0.499797\pi$
$84$		0			0
$85$	−2.46371	+	4.26727i	−0.267227	+	0.462851i
$86$		0			0
$87$	−1.13733	+	13.6594i	−0.121934	+	1.46444i
$88$		0			0
$89$	6.15579	+	3.55405i	0.652513	+	0.376729i	0.789418	−	0.613856i	$-0.210382\pi$
$89$	6.15579	+	3.55405i	0.652513	+	0.376729i	−0.136905	+	0.990584i	$0.543716\pi$
$90$		0			0
$91$	−4.52224	−	0.821903i	−0.474060	−	0.0861589i
$92$		0			0
$93$	−11.9794	−	8.31338i	−1.24220	−	0.862057i
$94$		0			0
$95$		−	1.15630i		−	0.118634i
$96$		0			0
$97$	5.89647	−	3.40433i	0.598695	−	0.345657i	−0.169833	−	0.985473i	$-0.554323\pi$
$97$	5.89647	−	3.40433i	0.598695	−	0.345657i	0.768528	+	0.639816i	$0.220989\pi$
$98$		0			0
$99$	−0.703006	+	4.19233i	−0.0706548	+	0.421345i
$100$		0			0
$101$	−2.82630	−	1.63176i	−0.281227	−	0.162366i	0.352752	−	0.935717i	$-0.385246\pi$
$101$	−2.82630	−	1.63176i	−0.281227	−	0.162366i	−0.633979	+	0.773350i	$0.718579\pi$
$102$		0			0
$103$	−8.39149	−	14.5345i	−0.826838	−	1.43212i	−0.900507	−	0.434842i	$-0.856804\pi$
$103$	−8.39149	−	14.5345i	−0.826838	−	1.43212i	0.0736690	−	0.997283i	$-0.476529\pi$
$104$		0			0
$105$	−3.47509	+	0.927214i	−0.339134	+	0.0904868i
$106$		0			0
$107$	−8.07017	−	4.65932i	−0.780173	−	0.450433i	0.0563185	−	0.998413i	$-0.482064\pi$
$107$	−8.07017	−	4.65932i	−0.780173	−	0.450433i	−0.836492	+	0.547980i	$0.815397\pi$
$108$		0			0
$109$	1.10094	+	1.90688i	0.105451	+	0.182646i	0.913922	−	0.405889i	$-0.133038\pi$
$109$	1.10094	+	1.90688i	0.105451	+	0.182646i	−0.808471	+	0.588535i	$0.799705\pi$
$110$		0			0
$111$	11.7247	−	5.52731i	1.11286	−	0.524629i
$112$		0			0
$113$	−3.33634	+	5.77872i	−0.313857	+	0.543616i	−0.979194	−	0.202927i	$-0.934955\pi$
$113$	−3.33634	+	5.77872i	−0.313857	+	0.543616i	0.665337	+	0.746543i	$0.268288\pi$
$114$		0			0
$115$	−2.20098	+	3.81221i	−0.205242	+	0.355490i
$116$		0			0
$117$	0.861916	−	5.13997i	0.0796842	−	0.475191i
$118$		0			0
$119$	10.7436	−	12.6680i	0.984864	−	1.16127i
$120$		0			0
$121$	−4.49612	−	7.78751i	−0.408738	−	0.707955i
$122$		0			0
$123$	6.13340	+	13.0104i	0.553030	+	1.17310i
$124$		0			0
$125$		−	7.36510i		−	0.658754i
$126$		0			0
$127$		−	15.5443i		−	1.37934i	−0.724125	−	0.689669i	$-0.757756\pi$
$127$		−	15.5443i		−	1.37934i	0.724125	−	0.689669i	$-0.242244\pi$
$128$		0			0
$129$	−15.6476	−	1.30287i	−1.37769	−	0.114711i
$130$		0			0
$131$	2.63094	+	4.55693i	0.229867	+	0.398140i	0.957768	−	0.287541i	$-0.0928377\pi$
$131$	2.63094	+	4.55693i	0.229867	+	0.398140i	−0.727902	+	0.685681i	$0.759504\pi$
$132$		0			0
$133$	−0.697011	+	3.83506i	−0.0604385	+	0.332542i
$134$		0			0
$135$	−1.10501	−	3.92568i	−0.0951045	−	0.337869i
$136$		0			0
$137$	−6.84273	+	11.8520i	−0.584614	+	1.01258i	0.410309	+	0.911946i	$0.365421\pi$
$137$	−6.84273	+	11.8520i	−0.584614	+	1.01258i	−0.994923	+	0.100635i	$0.967913\pi$
$138$		0			0
$139$	−4.61572	+	7.99465i	−0.391500	+	0.678098i	−0.992648	−	0.121040i	$-0.961377\pi$
$139$	−4.61572	+	7.99465i	−0.391500	+	0.678098i	0.601148	+	0.799138i	$0.294710\pi$
$140$		0			0
$141$	0.156648	+	0.108710i	0.0131921	+	0.00915500i
$142$		0			0
$143$	−1.23080	−	2.13181i	−0.102925	−	0.178271i
$144$		0			0
$145$	−5.37889	−	3.10551i	−0.446693	−	0.257898i
$146$		0			0
$147$	12.0846	−	0.980495i	0.996725	−	0.0808698i
$148$		0			0
$149$	9.44849	+	16.3653i	0.774051	+	1.34070i	0.935326	+	0.353786i	$0.115106\pi$
$149$	9.44849	+	16.3653i	0.774051	+	1.34070i	−0.161276	+	0.986909i	$0.551561\pi$
$150$		0			0
$151$	2.66662	+	1.53957i	0.217006	+	0.125289i	0.604563	−	0.796557i	$-0.293348\pi$
$151$	2.66662	+	1.53957i	0.217006	+	0.125289i	−0.387557	+	0.921846i	$0.626681\pi$
$152$		0			0
$153$	14.5290	+	11.9850i	1.17460	+	0.968931i
$154$		0			0
$155$	5.72216	−	3.30369i	0.459615	−	0.265359i
$156$		0			0
$157$		−	15.2290i		−	1.21541i	−0.794164	−	0.607703i	$-0.792091\pi$
$157$		−	15.2290i		−	1.21541i	0.794164	−	0.607703i	$-0.207909\pi$
$158$		0			0
$159$	1.23188	−	14.7951i	0.0976948	−	1.17333i
$160$		0			0
$161$	9.59789	−	11.3171i	0.756420	−	0.891911i
$162$		0			0
$163$	−4.96129	−	2.86440i	−0.388599	−	0.224357i	0.292954	−	0.956126i	$-0.405362\pi$
$163$	−4.96129	−	2.86440i	−0.388599	−	0.224357i	−0.681553	+	0.731769i	$0.738695\pi$
$164$		0			0
$165$	−1.58249	−	1.09821i	−0.123197	−	0.0854953i
$166$		0			0
$167$	2.28326	−	3.95472i	0.176684	−	0.306025i	−0.764059	−	0.645147i	$-0.776796\pi$
$167$	2.28326	−	3.95472i	0.176684	−	0.306025i	0.940743	+	0.339121i	$0.110130\pi$
$168$		0			0
$169$	−4.99099	−	8.64464i	−0.383922	−	0.664973i
$170$		0			0
$171$	−4.35893	−	0.730944i	−0.333336	−	0.0558967i
$172$		0			0
$173$		−	17.8762i		−	1.35910i	−0.733628	−	0.679551i	$-0.762174\pi$
$173$		−	17.8762i		−	1.35910i	0.733628	−	0.679551i	$-0.237826\pi$
$174$		0			0
$175$	−2.07410	+	11.4120i	−0.156787	+	0.862668i
$176$		0			0
$177$	0.104755	+	0.0726973i	0.00787387	+	0.00546426i
$178$		0			0
$179$	6.15176	−	3.55172i	0.459804	−	0.265468i	−0.252158	−	0.967686i	$-0.581140\pi$
$179$	6.15176	−	3.55172i	0.459804	−	0.265468i	0.711962	+	0.702218i	$0.247807\pi$
$180$		0			0
$181$			6.31771i			0.469591i	0.972045	+	0.234796i	$0.0754421\pi$
$181$			6.31771i			0.469591i	−0.972045	+	0.234796i	$0.924558\pi$
$182$		0			0
$183$	−1.22229	+	1.76129i	−0.0903544	+	0.130198i
$184$		0			0
$185$			5.87367i			0.431841i
$186$		0			0
$187$	8.89580			0.650526
$188$		0			0
$189$	1.29859	+	13.6863i	0.0944586	+	0.995529i
$190$		0			0
$191$		−	21.6174i		−	1.56418i	−0.623165	−	0.782090i	$-0.714153\pi$
$191$		−	21.6174i		−	1.56418i	0.623165	−	0.782090i	$-0.285847\pi$
$192$		0			0
$193$	−5.11201			−0.367970			−0.183985	−	0.982929i	$-0.558900\pi$
$193$	−5.11201			−0.367970			−0.183985	+	0.982929i	$0.558900\pi$
$194$		0			0
$195$	1.94020	+	1.34645i	0.138941	+	0.0964213i
$196$		0			0
$197$	−12.7051			−0.905199			−0.452599	−	0.891714i	$-0.649503\pi$
$197$	−12.7051			−0.905199			−0.452599	+	0.891714i	$0.649503\pi$
$198$		0			0
$199$	−1.35332	−	2.34401i	−0.0959341	−	0.166163i	0.814064	−	0.580775i	$-0.197250\pi$
$199$	−1.35332	−	2.34401i	−0.0959341	−	0.166163i	−0.909998	+	0.414612i	$0.863917\pi$
$200$		0			0
$201$	−11.7251	+	16.8957i	−0.827028	+	1.19173i
$202$		0			0
$203$	15.9680	+	13.5423i	1.12074	+	0.950483i
$204$		0			0
$205$	−6.51774			−0.455219
$206$		0			0
$207$	12.9796	+	10.7069i	0.902147	+	0.744183i
$208$		0			0
$209$	−1.80787	+	1.04377i	−0.125053	+	0.0721993i
$210$		0			0
$211$	−7.54303	−	4.35497i	−0.519284	−	0.299809i	0.217358	−	0.976092i	$-0.430256\pi$
$211$	−7.54303	−	4.35497i	−0.519284	−	0.299809i	−0.736641	+	0.676283i	$0.763589\pi$
$212$		0			0
$213$	0.385273	−	0.555169i	0.0263985	−	0.0380396i
$214$		0			0
$215$	3.55752	−	6.16181i	0.242621	−	0.420232i
$216$		0			0
$217$	−20.9699	+	7.50796i	−1.42353	+	0.509673i
$218$		0			0
$219$	7.38521	+	0.614916i	0.499046	+	0.0415522i
$220$		0			0
$221$	−10.9066			−0.733660
$222$		0			0
$223$	−4.60457	−	7.97535i	−0.308345	−	0.534069i	0.669656	−	0.742672i	$-0.266442\pi$
$223$	−4.60457	−	7.97535i	−0.308345	−	0.534069i	−0.978000	+	0.208603i	$0.933108\pi$
$224$		0			0
$225$	−12.9709	−	2.17507i	−0.864726	−	0.145005i
$226$		0			0
$227$	4.08469	−	7.07489i	0.271110	−	0.469577i	−0.698036	−	0.716063i	$-0.745943\pi$
$227$	4.08469	−	7.07489i	0.271110	−	0.469577i	0.969146	+	0.246486i	$0.0792759\pi$
$228$		0			0
$229$	1.76036	−	1.01634i	0.116328	−	0.0671618i	−0.440707	−	0.897651i	$-0.645272\pi$
$229$	1.76036	−	1.01634i	0.116328	−	0.0671618i	0.557035	+	0.830489i	$0.311939\pi$
$230$		0			0
$231$	4.58660	+	4.59630i	0.301776	+	0.302415i
$232$		0			0
$233$	5.74641	−	9.95307i	0.376460	−	0.652047i	−0.614085	−	0.789240i	$-0.710475\pi$
$233$	5.74641	−	9.95307i	0.376460	−	0.652047i	0.990544	+	0.137193i	$0.0438080\pi$
$234$		0			0
$235$	−0.0748256	+	0.0432006i	−0.00488109	+	0.00281810i
$236$		0			0
$237$	−5.92704	+	8.54072i	−0.385003	+	0.554780i
$238$		0			0
$239$	−15.1651	−	8.75560i	−0.980952	−	0.566353i	−0.0783945	−	0.996922i	$-0.524979\pi$
$239$	−15.1651	−	8.75560i	−0.980952	−	0.566353i	−0.902557	+	0.430570i	$0.858313\pi$
$240$		0			0
$241$	−17.6422	−	10.1858i	−1.13644	−	0.656122i	−0.190891	−	0.981611i	$-0.561138\pi$
$241$	−17.6422	−	10.1858i	−1.13644	−	0.656122i	−0.945546	+	0.325489i	$0.894471\pi$
$242$		0			0
$243$	−15.4972	+	1.68402i	−0.994148	+	0.108030i
$244$		0			0
$245$	−1.93318	+	5.14265i	−0.123506	+	0.328552i
$246$		0			0
$247$	2.21652	−	1.27971i	0.141034	−	0.0814260i
$248$		0			0
$249$	2.26701	−	27.2270i	0.143666	−	1.72544i
$250$		0			0
$251$	7.09897			0.448083			0.224041	−	0.974580i	$-0.428075\pi$
$251$	7.09897			0.448083			0.224041	+	0.974580i	$0.428075\pi$
$252$		0			0
$253$	7.94715			0.499633
$254$		0			0
$255$	−7.71973	+	3.63927i	−0.483428	+	0.227900i
$256$		0			0
$257$	22.4449	−	12.9585i	1.40007	−	0.808332i	0.405672	−	0.914019i	$-0.367037\pi$
$257$	22.4449	−	12.9585i	1.40007	−	0.808332i	0.994399	+	0.105687i	$0.0337042\pi$
$258$		0			0
$259$	3.54061	−	19.4810i	0.220003	−	1.21049i
$260$		0			0
$261$	−15.1071	+	18.3138i	−0.935106	+	1.13360i
$262$		0			0
$263$	−4.18333	−	2.41525i	−0.257955	−	0.148931i	0.365446	−	0.930832i	$-0.380916\pi$
$263$	−4.18333	−	2.41525i	−0.257955	−	0.148931i	−0.623401	+	0.781902i	$0.714250\pi$
$264$		0			0
$265$	5.82610	+	3.36370i	0.357894	+	0.206630i
$266$		0			0
$267$	5.24986	+	11.1362i	0.321286	+	0.681522i
$268$		0			0
$269$	−6.63937	+	3.83324i	−0.404809	+	0.233717i	−0.688557	−	0.725182i	$-0.741756\pi$
$269$	−6.63937	+	3.83324i	−0.404809	+	0.233717i	0.283748	+	0.958899i	$0.408422\pi$
$270$		0			0
$271$	−2.53360	+	4.38832i	−0.153905	+	0.266571i	−0.932660	−	0.360757i	$-0.882518\pi$
$271$	−2.53360	+	4.38832i	−0.153905	+	0.266571i	0.778755	+	0.627328i	$0.215852\pi$
$272$		0			0
$273$	−5.62337	−	5.63527i	−0.340342	−	0.341062i
$274$		0			0
$275$	−5.37968	+	3.10596i	−0.324407	+	0.187297i
$276$		0			0
$277$	−10.9256	+	18.9237i	−0.656455	+	1.13701i	0.325071	+	0.945689i	$0.394612\pi$
$277$	−10.9256	+	18.9237i	−0.656455	+	1.13701i	−0.981527	+	0.191325i	$0.938722\pi$
$278$		0			0
$279$	−8.83678	−	23.6593i	−0.529044	−	1.41645i
$280$		0			0
$281$	1.09695	+	1.89998i	0.0654388	+	0.113343i	0.896889	−	0.442257i	$-0.145822\pi$
$281$	1.09695	+	1.89998i	0.0654388	+	0.113343i	−0.831450	+	0.555600i	$0.812489\pi$
$282$		0			0
$283$	−15.3003			−0.909509			−0.454754	−	0.890617i	$-0.650273\pi$
$283$	−15.3003			−0.909509			−0.454754	+	0.890617i	$0.650273\pi$
$284$		0			0
$285$	1.14185	−	1.64538i	0.0676374	−	0.0974638i
$286$		0			0
$287$	21.6172	+	3.92886i	1.27602	+	0.231913i
$288$		0			0
$289$	11.2074	−	19.4118i	0.659258	−	1.14187i
$290$		0			0
$291$	11.7523	+	0.978531i	0.688930	+	0.0573625i
$292$		0			0
$293$	5.07666	+	2.93101i	0.296581	+	0.171231i	0.640906	−	0.767619i	$-0.278559\pi$
$293$	5.07666	+	2.93101i	0.296581	+	0.171231i	−0.344325	+	0.938851i	$0.611892\pi$
$294$		0			0
$295$	−0.0500381	+	0.0288895i	−0.00291333	+	0.00168201i
$296$		0			0
$297$	−5.14029	+	5.27133i	−0.298270	+	0.305873i
$298$		0			0
$299$	−9.74355			−0.563484
$300$		0			0
$301$	−15.5134	+	18.2922i	−0.894178	+	1.05435i
$302$		0			0
$303$	−2.41036	−	5.11292i	−0.138471	−	0.293730i
$304$		0			0
$305$	−0.485732	−	0.841312i	−0.0278129	−	0.0481734i
$306$		0			0
$307$	−8.38567			−0.478596			−0.239298	−	0.970946i	$-0.576917\pi$
$307$	−8.38567			−0.478596			−0.239298	+	0.970946i	$0.576917\pi$
$308$		0			0
$309$	2.41203	−	28.9687i	0.137215	−	1.64797i
$310$		0			0
$311$	−28.8576			−1.63636			−0.818182	−	0.574960i	$-0.805018\pi$
$311$	−28.8576			−1.63636			−0.818182	+	0.574960i	$0.805018\pi$
$312$		0			0
$313$		−	28.4132i		−	1.60601i	−0.595973	−	0.803005i	$-0.703233\pi$
$313$		−	28.4132i		−	1.60601i	0.595973	−	0.803005i	$-0.296767\pi$
$314$		0			0
$315$	−5.86057	−	2.11227i	−0.330206	−	0.119013i
$316$		0			0
$317$	−8.98308			−0.504540			−0.252270	−	0.967657i	$-0.581177\pi$
$317$	−8.98308			−0.504540			−0.252270	+	0.967657i	$0.581177\pi$
$318$		0			0
$319$			11.2131i			0.627816i
$320$		0			0
$321$	−6.88251	−	14.5994i	−0.384144	−	0.814858i
$322$		0			0
$323$			9.24932i			0.514646i
$324$		0			0
$325$	6.59573	−	3.80804i	0.365865	−	0.211232i
$326$		0			0
$327$	−0.316451	+	3.80062i	−0.0174998	+	0.210175i
$328$		0			0
$329$	0.274213	−	0.0981775i	0.0151178	−	0.00541270i
$330$		0			0
$331$			6.80699i			0.374146i	0.982346	+	0.187073i	$0.0599001\pi$
$331$			6.80699i			0.374146i	−0.982346	+	0.187073i	$0.940100\pi$
$332$		0			0
$333$	22.1421	+	3.71298i	1.21338	+	0.203470i
$334$		0			0
$335$	−4.65951	−	8.07051i	−0.254576	−	0.440939i
$336$		0			0
$337$	8.43310	−	14.6066i	0.459380	−	0.795670i	−0.539548	−	0.841955i	$-0.681405\pi$
$337$	8.43310	−	14.6066i	0.459380	−	0.795670i	0.998928	+	0.0462849i	$0.0147382\pi$
$338$		0			0
$339$	−10.4540	+	4.92828i	−0.567784	+	0.267667i
$340$		0			0
$341$	−10.3306	−	5.96437i	−0.559433	−	0.322989i
$342$		0			0
$343$	9.51166	−	15.8911i	0.513581	−	0.858041i
$344$		0			0
$345$	−6.89649	+	3.25118i	−0.371295	+	0.175037i
$346$		0			0
$347$			33.9020i			1.81995i	0.414659	+	0.909977i	$0.363901\pi$
$347$			33.9020i			1.81995i	−0.414659	+	0.909977i	$0.636099\pi$
$348$		0			0
$349$	8.57679	−	4.95181i	0.459105	−	0.265065i	−0.252563	−	0.967581i	$-0.581273\pi$
$349$	8.57679	−	4.95181i	0.459105	−	0.265065i	0.711668	+	0.702516i	$0.247940\pi$
$350$		0			0
$351$	6.30222	−	6.46287i	0.336388	−	0.344963i
$352$		0			0
$353$	−25.7683	−	14.8774i	−1.37151	−	0.791842i	−0.380392	−	0.924825i	$-0.624211\pi$
$353$	−25.7683	−	14.8774i	−1.37151	−	0.791842i	−0.991118	+	0.132983i	$0.957544\pi$
$354$		0			0
$355$	0.153105	+	0.265186i	0.00812599	+	0.0140746i
$356$		0			0
$357$	27.7975	−	7.41684i	1.47120	−	0.392541i
$358$		0			0
$359$	11.8705	+	6.85344i	0.626502	+	0.361711i	0.779396	−	0.626532i	$-0.215526\pi$
$359$	11.8705	+	6.85344i	0.626502	+	0.361711i	−0.152894	+	0.988243i	$0.548859\pi$
$360$		0			0
$361$	8.41475	+	14.5748i	0.442881	+	0.767093i
$362$		0			0
$363$	1.29235	−	15.5213i	0.0678310	−	0.814658i
$364$		0			0
$365$	−1.67905	+	2.90819i	−0.0878853	+	0.152222i
$366$		0			0
$367$	−16.3229	+	28.2720i	−0.852047	+	1.47579i	0.0273109	+	0.999627i	$0.491306\pi$
$367$	−16.3229	+	28.2720i	−0.852047	+	1.47579i	−0.879358	+	0.476162i	$0.842028\pi$
$368$		0			0
$369$	−4.12013	+	24.5701i	−0.214485	+	1.27907i
$370$		0			0
$371$	−17.2956	−	14.6682i	−0.897943	−	0.761535i
$372$		0			0
$373$	10.1393	+	17.5618i	0.524995	+	0.909317i	0.999576	+	0.0291058i	$0.00926598\pi$
$373$	10.1393	+	17.5618i	0.524995	+	0.909317i	−0.474582	+	0.880211i	$0.657401\pi$
$374$		0			0
$375$	7.27305	−	10.4803i	0.375579	−	0.541200i
$376$		0			0
$377$		−	13.7478i		−	0.708048i
$378$		0			0
$379$			22.3099i			1.14598i	0.819561	+	0.572992i	$0.194217\pi$
$379$			22.3099i			1.14598i	−0.819561	+	0.572992i	$0.805783\pi$
$380$		0			0
$381$	15.3501	−	22.1191i	0.786409	−	1.13320i
$382$		0			0
$383$	10.4652	+	18.1262i	0.534746	+	0.926207i	0.999176	+	0.0405971i	$0.0129260\pi$
$383$	10.4652	+	18.1262i	0.534746	+	0.926207i	−0.464430	+	0.885610i	$0.653741\pi$
$384$		0			0
$385$	−2.77016	+	0.991811i	−0.141180	+	0.0505474i
$386$		0			0
$387$	−20.9794	−	17.3060i	−1.06644	−	0.879712i
$388$		0			0
$389$	−6.14324	+	10.6404i	−0.311475	+	0.539490i	−0.978682	−	0.205382i	$-0.934156\pi$
$389$	−6.14324	+	10.6404i	−0.311475	+	0.539490i	0.667207	+	0.744872i	$0.267490\pi$
$390$		0			0
$391$	17.6058	−	30.4941i	0.890362	−	1.54215i
$392$		0			0
$393$	−0.756231	+	9.08242i	−0.0381468	+	0.458148i
$394$		0			0
$395$	−2.35537	−	4.07963i	−0.118512	−	0.205268i
$396$		0			0
$397$	−21.2792	−	12.2856i	−1.06797	−	0.616594i	−0.140346	−	0.990103i	$-0.544821\pi$
$397$	−21.2792	−	12.2856i	−1.06797	−	0.616594i	−0.927627	+	0.373508i	$0.878155\pi$
$398$		0			0
$399$	−4.77896	+	4.76887i	−0.239247	+	0.238742i
$400$		0			0
$401$	18.3595	+	31.7997i	0.916832	+	1.58800i	0.804197	+	0.594362i	$0.202595\pi$
$401$	18.3595	+	31.7997i	0.916832	+	1.58800i	0.112634	+	0.993637i	$0.464071\pi$
$402$		0			0
$403$	12.6658	+	7.31258i	0.630926	+	0.364266i
$404$		0			0
$405$	2.30422	−	6.67732i	0.114497	−	0.331799i
$406$		0			0
$407$	9.18344	−	5.30206i	0.455206	−	0.262813i
$408$		0			0
$409$		−	8.40233i		−	0.415468i	−0.978185	−	0.207734i	$-0.933391\pi$
$409$		−	8.40233i		−	0.415468i	0.978185	−	0.207734i	$-0.0666089\pi$
$410$		0			0
$411$	−21.4408	+	10.1077i	−1.05760	+	0.498578i
$412$		0			0
$413$	0.183374	−	0.0656542i	0.00902325	−	0.00323063i
$414$		0			0
$415$	10.7216	+	6.19013i	0.526304	+	0.303862i
$416$		0			0
$417$	−14.4628	+	6.81810i	−0.708244	+	0.333884i
$418$		0			0
$419$	14.1563	−	24.5195i	0.691583	−	1.19786i	−0.279736	−	0.960077i	$-0.590247\pi$
$419$	14.1563	−	24.5195i	0.691583	−	1.19786i	0.971319	−	0.237780i	$-0.0764197\pi$
$420$		0			0
$421$	14.2835	+	24.7397i	0.696133	+	1.20574i	0.969797	+	0.243912i	$0.0784309\pi$
$421$	14.2835	+	24.7397i	0.696133	+	1.20574i	−0.273664	+	0.961825i	$0.588236\pi$
$422$		0			0
$423$	0.115554	+	0.309380i	0.00561842	+	0.0150426i
$424$		0			0
$425$			27.5233i			1.33507i
$426$		0			0
$427$	1.10387	+	3.08315i	0.0534201	+	0.149204i
$428$		0			0
$429$	0.353778	−	4.24891i	0.0170805	−	0.205139i
$430$		0			0
$431$	9.31259	−	5.37663i	0.448572	−	0.258983i	−0.258655	−	0.965970i	$-0.583279\pi$
$431$	9.31259	−	5.37663i	0.448572	−	0.258983i	0.707227	+	0.706987i	$0.249946\pi$
$432$		0			0
$433$			2.52301i			0.121248i	0.998161	+	0.0606241i	$0.0193091\pi$
$433$			2.52301i			0.121248i	−0.998161	+	0.0606241i	$0.980691\pi$
$434$		0			0
$435$	−4.58730	−	9.73071i	−0.219944	−	0.466552i
$436$		0			0
$437$			8.26296i			0.395271i
$438$		0			0
$439$	2.12556			0.101447			0.0507237	−	0.998713i	$-0.483847\pi$
$439$	2.12556			0.101447			0.0507237	+	0.998713i	$0.483847\pi$
$440$		0			0
$441$	18.1643	+	10.5384i	0.864967	+	0.501829i
$442$		0			0
$443$			34.4346i			1.63604i	0.575193	+	0.818018i	$0.304927\pi$
$443$			34.4346i			1.63604i	−0.575193	+	0.818018i	$0.695073\pi$
$444$		0			0
$445$	−5.57884			−0.264462
$446$		0			0
$447$	−2.71585	+	32.6177i	−0.128455	+	1.54276i
$448$		0			0
$449$	25.1970			1.18912			0.594560	−	0.804051i	$-0.297326\pi$
$449$	25.1970			1.18912			0.594560	+	0.804051i	$0.297326\pi$
$450$		0			0
$451$	5.88346	+	10.1904i	0.277041	+	0.479849i
$452$		0			0
$453$	2.27418	+	4.82406i	0.106850	+	0.226654i
$454$		0			0
$455$	3.39633	−	1.21600i	0.159222	−	0.0570071i
$456$		0			0
$457$	38.3416			1.79354			0.896771	−	0.442494i	$-0.145906\pi$
$457$	38.3416			1.79354			0.896771	+	0.442494i	$0.145906\pi$
$458$		0			0
$459$	8.83908	+	31.4017i	0.412573	+	1.46571i
$460$		0			0
$461$	−22.0353	+	12.7221i	−1.02629	+	0.592527i	−0.915919	−	0.401364i	$-0.868536\pi$
$461$	−22.0353	+	12.7221i	−1.02629	+	0.592527i	−0.110368	+	0.993891i	$0.535203\pi$
$462$		0			0
$463$	19.6432	+	11.3410i	0.912897	+	0.527061i	0.881362	−	0.472441i	$-0.156627\pi$
$463$	19.6432	+	11.3410i	0.912897	+	0.527061i	0.0315350	+	0.999503i	$0.489960\pi$
$464$		0			0
$465$	11.4049	+	0.949605i	0.528888	+	0.0440369i
$466$		0			0
$467$	−3.19769	+	5.53857i	−0.147972	+	0.256294i	−0.930478	−	0.366349i	$-0.880608\pi$
$467$	−3.19769	+	5.53857i	−0.147972	+	0.256294i	0.782506	+	0.622643i	$0.213941\pi$
$468$		0			0
$469$	10.5892	+	29.5759i	0.488963	+	1.36569i
$470$		0			0
$471$	15.0387	−	21.6704i	0.692946	−	0.998519i
$472$		0			0
$473$	−12.8453			−0.590625
$474$		0			0
$475$	−3.22939	−	5.59347i	−0.148175	−	0.256646i
$476$		0			0
$477$	16.3631	−	19.8364i	0.749215	−	0.908247i
$478$		0			0
$479$	−16.6853	+	28.8999i	−0.762373	+	1.32047i	0.179252	+	0.983803i	$0.442632\pi$
$479$	−16.6853	+	28.8999i	−0.762373	+	1.32047i	−0.941625	+	0.336665i	$0.890701\pi$
$480$		0			0
$481$	−11.2593	+	6.50056i	−0.513380	+	0.296400i
$482$		0			0
$483$	24.8331	−	6.62591i	1.12995	−	0.301489i
$484$		0			0
$485$	−2.67191	+	4.62788i	−0.121325	+	0.210141i
$486$		0			0
$487$	−32.8011	+	18.9377i	−1.48636	+	0.858150i	−0.999879	−	0.0155410i	$-0.995053\pi$
$487$	−32.8011	+	18.9377i	−1.48636	+	0.858150i	−0.486481	+	0.873691i	$0.661720\pi$
$488$		0			0
$489$	−4.23115	−	8.97525i	−0.191339	−	0.405875i
$490$		0			0
$491$	−21.1550	−	12.2138i	−0.954711	−	0.551203i	−0.0601697	−	0.998188i	$-0.519164\pi$
$491$	−21.1550	−	12.2138i	−0.954711	−	0.551203i	−0.894541	+	0.446986i	$0.852498\pi$
$492$		0			0
$493$	43.0261	+	24.8411i	1.93780	+	1.11879i
$494$		0			0
$495$	−1.16735	−	3.12543i	−0.0524685	−	0.140478i
$496$		0			0
$497$	−0.347947	−	0.971826i	−0.0156075	−	0.0435923i
$498$		0			0
$499$	31.4156	−	18.1378i	1.40636	−	0.811961i	0.411322	−	0.911490i	$-0.365067\pi$
$499$	31.4156	−	18.1378i	1.40636	−	0.811961i	0.995035	+	0.0995293i	$0.0317337\pi$
$500$		0			0
$501$	7.15430	−	3.37271i	0.319631	−	0.150682i
$502$		0			0
$503$	−7.84762			−0.349908			−0.174954	−	0.984577i	$-0.555978\pi$
$503$	−7.84762			−0.349908			−0.174954	+	0.984577i	$0.555978\pi$
$504$		0			0
$505$	2.56140			0.113981
$506$		0			0
$507$	1.43460	−	17.2297i	0.0637127	−	0.765196i
$508$		0			0
$509$	33.4820	−	19.3308i	1.48406	−	0.856824i	0.484228	−	0.874942i	$-0.339101\pi$
$509$	33.4820	−	19.3308i	1.48406	−	0.856824i	0.999836	+	0.0181176i	$0.00576731\pi$
$510$		0			0
$511$	7.32188	−	8.63339i	0.323901	−	0.381919i
$512$		0			0
$513$	−5.48081	−	5.34456i	−0.241984	−	0.235968i
$514$		0			0
$515$	11.4075	+	6.58611i	0.502674	+	0.290219i
$516$		0			0
$517$	0.135088	+	0.0779929i	0.00594115	+	0.00343012i
$518$		0			0
$519$	17.6528	−	25.4373i	0.774872	−	1.11657i
$520$		0			0
$521$	21.3950	−	12.3524i	0.937332	−	0.541169i	0.0482092	−	0.998837i	$-0.484649\pi$
$521$	21.3950	−	12.3524i	0.937332	−	0.541169i	0.889123	+	0.457668i	$0.151315\pi$
$522$		0			0
$523$	20.0144	−	34.6660i	0.875168	−	1.51584i	0.0185852	−	0.999827i	$-0.494084\pi$
$523$	20.0144	−	34.6660i	0.875168	−	1.51584i	0.856583	−	0.516009i	$-0.172583\pi$
$524$		0			0
$525$	−14.2208	+	14.1908i	−0.620646	+	0.619336i
$526$		0			0
$527$	−45.7719	+	26.4264i	−1.99386	+	1.15115i
$528$		0			0
$529$	4.22828	−	7.32359i	0.183838	−	0.318417i
$530$		0			0
$531$	0.0772742	+	0.206892i	0.00335342	+	0.00897834i
$532$		0			0
$533$	−7.21337	−	12.4939i	−0.312446	−	0.541172i
$534$		0			0
$535$	7.31379			0.316203
$536$		0			0
$537$	12.2611	+	1.02090i	0.529105	+	0.0440550i
$538$		0			0
$539$	9.78554	−	1.61967i	0.421493	−	0.0697642i
$540$		0			0
$541$	10.0341	−	17.3795i	0.431399	−	0.747205i	−0.565595	−	0.824683i	$-0.691353\pi$
$541$	10.0341	−	17.3795i	0.431399	−	0.747205i	0.996994	+	0.0774780i	$0.0246868\pi$
$542$		0			0
$543$	−6.23875	+	8.98989i	−0.267731	+	0.385793i
$544$		0			0
$545$	−1.49663	−	0.864081i	−0.0641086	−	0.0370131i
$546$		0			0
$547$	6.60776	−	3.81499i	0.282528	−	0.163117i	−0.352040	−	0.935985i	$-0.614512\pi$
$547$	6.60776	−	3.81499i	0.282528	−	0.163117i	0.634567	+	0.772868i	$0.281178\pi$
$548$		0			0
$549$	−3.47856	+	1.29925i	−0.148461	+	0.0554505i
$550$		0			0
$551$	−11.6588			−0.496680
$552$		0			0
$553$	5.35282	+	14.9506i	0.227625	+	0.635763i
$554$		0			0
$555$	−5.80027	+	8.35804i	−0.246208	+	0.354779i
$556$		0			0
$557$	−15.0488	−	26.0653i	−0.637638	−	1.10442i	−0.985950	−	0.167042i	$-0.946578\pi$
$557$	−15.0488	−	26.0653i	−0.637638	−	1.10442i	0.348312	−	0.937379i	$-0.386755\pi$
$558$		0			0
$559$	15.7488			0.666105
$560$		0			0
$561$	12.6584	+	8.78463i	0.534440	+	0.370887i
$562$		0			0
$563$	1.89980			0.0800669			0.0400335	−	0.999198i	$-0.487254\pi$
$563$	1.89980			0.0800669			0.0400335	+	0.999198i	$0.487254\pi$
$564$		0			0
$565$		−	5.23710i		−	0.220327i
$566$		0			0
$567$	−11.6674	+	20.7575i	−0.489983	+	0.871732i
$568$		0			0
$569$	10.9733			0.460024			0.230012	−	0.973188i	$-0.426124\pi$
$569$	10.9733			0.460024			0.230012	+	0.973188i	$0.426124\pi$
$570$		0			0
$571$		−	13.1336i		−	0.549625i	−0.961498	−	0.274813i	$-0.911384\pi$
$571$		−	13.1336i		−	0.549625i	0.961498	−	0.274813i	$-0.0886159\pi$
$572$		0			0
$573$	21.3473	−	30.7609i	0.891794	−	1.28505i
$574$		0			0
$575$			24.5882i			1.02540i
$576$		0			0
$577$	−24.2132	+	13.9795i	−1.00801	+	0.581973i	−0.910608	−	0.413272i	$-0.864386\pi$
$577$	−24.2132	+	13.9795i	−1.00801	+	0.581973i	−0.0973997	+	0.995245i	$0.531053\pi$
$578$		0			0
$579$	−7.27422	−	5.04812i	−0.302306	−	0.209793i
$580$		0			0
$581$	−31.8287	−	26.9935i	−1.32048	−	1.11988i
$582$		0			0
$583$		−	12.1454i		−	0.503011i
$584$		0			0
$585$	1.43122	+	3.83191i	0.0591737	+	0.158430i
$586$		0			0
$587$	7.27205	+	12.5956i	0.300150	+	0.519875i	0.976170	−	0.217009i	$-0.0696300\pi$
$587$	7.27205	+	12.5956i	0.300150	+	0.519875i	−0.676020	+	0.736883i	$0.736297\pi$
$588$		0			0
$589$	6.20140	−	10.7411i	0.255524	−	0.442581i
$590$		0			0
$591$	−18.0789	−	12.5463i	−0.743667	−	0.516086i
$592$		0			0
$593$	37.9941	+	21.9359i	1.56023	+	0.900800i	0.997233	+	0.0743413i	$0.0236854\pi$
$593$	37.9941	+	21.9359i	1.56023	+	0.900800i	0.562998	+	0.826458i	$0.309648\pi$
$594$		0			0
$595$	−2.33120	+	12.8266i	−0.0955698	+	0.525840i
$596$		0			0
$597$	0.388994	−	4.67186i	0.0159205	−	0.191207i
$598$		0			0
$599$		−	12.1395i		−	0.496008i	−0.968759	−	0.248004i	$-0.920225\pi$
$599$		−	12.1395i		−	0.496008i	0.968759	−	0.248004i	$-0.0797745\pi$
$600$		0			0
$601$	−34.5034	+	19.9205i	−1.40742	+	0.812576i	−0.995139	−	0.0984793i	$-0.968602\pi$
$601$	−34.5034	+	19.9205i	−1.40742	+	0.812576i	−0.412284	+	0.911055i	$0.635269\pi$
$602$		0			0
$603$	−33.3690	+	12.4634i	−1.35889	+	0.507547i
$604$		0			0
$605$	6.11208	+	3.52881i	0.248491	+	0.143467i
$606$		0			0
$607$	8.03387	+	13.9151i	0.326085	+	0.564795i	0.981731	−	0.190273i	$-0.0609372\pi$
$607$	8.03387	+	13.9151i	0.326085	+	0.564795i	−0.655647	+	0.755068i	$0.727604\pi$
$608$		0			0
$609$	9.34892	+	35.0387i	0.378838	+	1.41984i
$610$		0			0
$611$	−0.165623	−	0.0956227i	−0.00670040	−	0.00386848i
$612$		0			0
$613$	17.8831	+	30.9744i	0.722290	+	1.25104i	0.960080	+	0.279727i	$0.0902439\pi$
$613$	17.8831	+	30.9744i	0.722290	+	1.25104i	−0.237789	+	0.971317i	$0.576423\pi$
$614$		0			0
$615$	−9.27454	−	6.43629i	−0.373986	−	0.259536i
$616$		0			0
$617$	6.64049	−	11.5017i	0.267336	−	0.463040i	−0.700837	−	0.713322i	$-0.747190\pi$
$617$	6.64049	−	11.5017i	0.267336	−	0.463040i	0.968173	+	0.250282i	$0.0805232\pi$
$618$		0			0
$619$	12.9291	−	22.3939i	0.519666	−	0.900088i	−0.480073	−	0.877229i	$-0.659390\pi$
$619$	12.9291	−	22.3939i	0.519666	−	0.900088i	0.999739	−	0.0228592i	$-0.00727694\pi$
$620$		0			0
$621$	7.89648	+	28.0530i	0.316875	+	1.12573i
$622$		0			0
$623$	18.5031	+	3.36289i	0.741313	+	0.134731i
$624$		0			0
$625$	−8.06973	−	13.9772i	−0.322789	−	0.559087i
$626$		0			0
$627$	−3.60327	−	0.300019i	−0.143901	−	0.0119816i
$628$		0			0
$629$		−	46.9839i		−	1.87337i
$630$		0			0
$631$			35.8684i			1.42790i	0.700198	+	0.713948i	$0.253095\pi$
$631$			35.8684i			1.42790i	−0.700198	+	0.713948i	$0.746905\pi$
$632$		0			0
$633$	−6.43294	−	13.6457i	−0.255687	−	0.542370i
$634$		0			0
$635$	6.10004	+	10.5656i	0.242073	+	0.419282i
$636$		0			0
$637$	−11.9975	+	1.98579i	−0.475358	+	0.0786798i
$638$		0			0
$639$	1.09646	−	0.409530i	0.0433754	−	0.0162007i
$640$		0			0
$641$	−12.0641	+	20.8956i	−0.476502	+	0.825325i	−0.999637	−	0.0269240i	$-0.991429\pi$
$641$	−12.0641	+	20.8956i	−0.476502	+	0.825325i	0.523136	+	0.852249i	$0.324762\pi$
$642$		0			0
$643$	7.71638	−	13.3652i	0.304304	−	0.527070i	−0.672802	−	0.739823i	$-0.734909\pi$
$643$	7.71638	−	13.3652i	0.304304	−	0.527070i	0.977106	+	0.212752i	$0.0682427\pi$
$644$		0			0
$645$	11.1470	−	5.25499i	0.438914	−	0.206915i
$646$		0			0
$647$	20.0842	+	34.7869i	0.789592	+	1.36761i	0.926217	+	0.376991i	$0.123041\pi$
$647$	20.0842	+	34.7869i	0.789592	+	1.36761i	−0.136625	+	0.990623i	$0.543625\pi$
$648$		0			0
$649$	0.0903371	+	0.0521561i	0.00354604	+	0.00204731i
$650$		0			0
$651$	−37.2537	−	10.0243i	−1.46009	−	0.392883i
$652$		0			0
$653$	25.2555	+	43.7438i	0.988324	+	1.71183i	0.626117	+	0.779729i	$0.284643\pi$
$653$	25.2555	+	43.7438i	0.988324	+	1.71183i	0.362206	+	0.932098i	$0.382024\pi$
$654$		0			0
$655$	−3.57653	−	2.06491i	−0.139747	−	0.0806828i
$656$		0			0
$657$	9.90168	+	8.16792i	0.386301	+	0.318661i
$658$		0			0
$659$	−16.7746	+	9.68482i	−0.653446	+	0.377267i	−0.789775	−	0.613397i	$-0.789803\pi$
$659$	−16.7746	+	9.68482i	−0.653446	+	0.377267i	0.136329	+	0.990664i	$0.456469\pi$
$660$		0			0
$661$			25.3992i			0.987915i	0.869486	+	0.493957i	$0.164450\pi$
$661$			25.3992i			0.987915i	−0.869486	+	0.493957i	$0.835550\pi$
$662$		0			0
$663$	−15.5198	−	10.7703i	−0.602739	−	0.418285i
$664$		0			0
$665$	−1.03123	−	2.88024i	−0.0399892	−	0.111691i
$666$		0			0
$667$	38.4378	+	22.1921i	1.48832	+	0.859280i
$668$		0			0
$669$	1.32353	−	15.8957i	0.0511705	−	0.614563i
$670$		0			0
$671$	−0.876924	+	1.51888i	−0.0338533	+	0.0586356i
$672$		0			0
$673$	−9.47290	−	16.4075i	−0.365153	−	0.632464i	0.623647	−	0.781706i	$-0.285650\pi$
$673$	−9.47290	−	16.4075i	−0.365153	−	0.632464i	−0.988801	+	0.149242i	$0.952317\pi$
$674$		0			0
$675$	−16.3093	−	15.9039i	−0.627744	−	0.612140i
$676$		0			0
$677$		−	48.4853i		−	1.86344i	−0.363178	−	0.931720i	$-0.618308\pi$
$677$		−	48.4853i		−	1.86344i	0.363178	−	0.931720i	$-0.381692\pi$
$678$		0			0
$679$	11.6515	−	13.7385i	0.447143	−	0.527236i
$680$		0			0
$681$	12.7989	−	6.03370i	0.490453	−	0.231212i
$682$		0			0
$683$	21.1815	−	12.2292i	0.810489	−	0.467936i	−0.0366369	−	0.999329i	$-0.511664\pi$
$683$	21.1815	−	12.2292i	0.810489	−	0.467936i	0.847126	+	0.531393i	$0.178331\pi$
$684$		0			0
$685$		−	10.7411i		−	0.410398i
$686$		0			0
$687$	3.50857	+	0.292135i	0.133860	+	0.0111456i
$688$		0			0
$689$			14.8908i			0.567294i
$690$		0			0
$691$	−38.3164			−1.45763			−0.728813	−	0.684713i	$-0.759928\pi$
$691$	−38.3164			−1.45763			−0.728813	+	0.684713i	$0.759928\pi$
$692$		0			0
$693$	1.98772	+	11.0697i	0.0755073	+	0.420502i
$694$		0			0
$695$		−	7.24535i		−	0.274832i
$696$		0			0
$697$	52.1359			1.97479
$698$		0			0
$699$	18.0056	−	8.48831i	0.681036	−	0.321057i
$700$		0			0
$701$	−33.3296			−1.25884			−0.629421	−	0.777064i	$-0.716708\pi$
$701$	−33.3296			−1.25884			−0.629421	+	0.777064i	$0.716708\pi$
$702$		0			0
$703$	5.51276	+	9.54839i	0.207918	+	0.360124i
$704$		0			0
$705$	−0.149135	−	0.0124175i	−0.00561676	−	0.000467669i
$706$		0			0
$707$	−8.49531	−	1.54400i	−0.319499	−	0.0580680i
$708$		0			0
$709$	1.43783			0.0539990			0.0269995	−	0.999635i	$-0.491405\pi$
$709$	1.43783			0.0539990			0.0269995	+	0.999635i	$0.491405\pi$
$710$		0			0
$711$	−16.8680	+	6.30021i	−0.632599	+	0.236276i
$712$		0			0
$713$	−40.8908	+	23.6083i	−1.53137	+	0.884138i
$714$		0			0
$715$	1.67316	+	0.966001i	0.0625727	+	0.0361264i
$716$		0			0
$717$	−12.9333	−	27.4346i	−0.483004	−	1.02456i
$718$		0			0
$719$	−12.0257	+	20.8291i	−0.448481	+	0.776793i	−0.998287	−	0.0584998i	$-0.981368\pi$
$719$	−12.0257	+	20.8291i	−0.448481	+	0.776793i	0.549806	+	0.835292i	$0.314702\pi$
$720$		0			0
$721$	−33.8647	−	28.7203i	−1.26119	−	1.06960i
$722$		0			0
$723$	−15.0459	−	31.9158i	−0.559563	−	1.18696i
$724$		0			0
$725$	−34.6931			−1.28847
$726$		0			0
$727$	−7.87496	−	13.6398i	−0.292066	−	0.505873i	0.682232	−	0.731136i	$-0.261009\pi$
$727$	−7.87496	−	13.6398i	−0.292066	−	0.505873i	−0.974298	+	0.225262i	$0.927676\pi$
$728$		0			0
$729$	−23.7150	−	12.9073i	−0.878335	−	0.478046i
$730$		0			0
$731$	−28.4568	+	49.2887i	−1.05251	+	1.82301i
$732$		0			0
$733$	−36.2669	+	20.9387i	−1.33955	+	0.773389i	−0.986740	−	0.162306i	$-0.948107\pi$
$733$	−36.2669	+	20.9387i	−1.33955	+	0.773389i	−0.352809	+	0.935695i	$0.614774\pi$
$734$		0			0
$735$	−7.82923	+	5.40881i	−0.288786	+	0.199507i
$736$		0			0
$737$	−8.41212	+	14.5702i	−0.309864	+	0.536701i
$738$		0			0
$739$	−1.29085	+	0.745272i	−0.0474846	+	0.0274153i	−0.523554	−	0.851992i	$-0.675394\pi$
$739$	−1.29085	+	0.745272i	−0.0474846	+	0.0274153i	0.476070	+	0.879408i	$0.342061\pi$
$740$		0			0
$741$	4.41776	+	0.367837i	0.162290	+	0.0135128i
$742$		0			0
$743$	−6.96436	−	4.02088i	−0.255498	−	0.147512i	0.366781	−	0.930307i	$-0.380460\pi$
$743$	−6.96436	−	4.02088i	−0.255498	−	0.147512i	−0.622279	+	0.782796i	$0.713793\pi$
$744$		0			0
$745$	−12.8444	−	7.41571i	−0.470582	−	0.271691i
$746$		0			0
$747$	30.1126	−	36.5045i	1.10176	−	1.33563i
$748$		0			0
$749$	−24.2574	−	4.40871i	−0.886346	−	0.161091i
$750$		0			0
$751$	−13.4437	+	7.76170i	−0.490566	+	0.283229i	−0.724809	−	0.688949i	$-0.758072\pi$
$751$	−13.4437	+	7.76170i	−0.490566	+	0.283229i	0.234243	+	0.972178i	$0.424739\pi$
$752$		0			0
$753$	10.1016	+	7.01025i	0.368123	+	0.255468i
$754$		0			0
$755$	−2.41669			−0.0879523
$756$		0			0
$757$	19.4868			0.708260			0.354130	−	0.935196i	$-0.384777\pi$
$757$	19.4868			0.708260			0.354130	+	0.935196i	$0.384777\pi$
$758$		0			0
$759$	11.3085	+	7.84783i	0.410474	+	0.284858i
$760$		0			0
$761$	20.0623	−	11.5830i	0.727259	−	0.419883i	−0.0901595	−	0.995927i	$-0.528738\pi$
$761$	20.0623	−	11.5830i	0.727259	−	0.419883i	0.817419	+	0.576044i	$0.195404\pi$
$762$		0			0
$763$	4.44296	+	3.76803i	0.160846	+	0.136412i
$764$		0			0
$765$	−14.5787	−	2.44469i	−0.527095	−	0.0883879i
$766$		0			0
$767$	−0.110757	−	0.0639457i	−0.00399921	−	0.00230894i
$768$		0			0
$769$	28.2140	+	16.2894i	1.01742	+	0.587410i	0.913357	−	0.407160i	$-0.133481\pi$
$769$	28.2140	+	16.2894i	1.01742	+	0.587410i	0.104067	+	0.994570i	$0.466814\pi$
$770$		0			0
$771$	44.7349	+	3.72477i	1.61109	+	0.134144i
$772$		0			0
$773$	6.85868	−	3.95986i	0.246690	−	0.142426i	−0.371558	−	0.928410i	$-0.621176\pi$
$773$	6.85868	−	3.95986i	0.246690	−	0.142426i	0.618248	+	0.785983i	$0.287843\pi$
$774$		0			0
$775$	18.4535	−	31.9625i	0.662871	−	1.14813i
$776$		0			0
$777$	24.2757	−	24.2245i	0.870887	−	0.869048i
$778$		0			0
$779$	−10.5954	+	6.11726i	−0.379620	+	0.219174i
$780$		0			0
$781$	0.276411	−	0.478758i	0.00989077	−	0.0171313i
$782$		0			0
$783$	−39.5819	+	11.1417i	−1.41454	+	0.398170i
$784$		0			0
$785$	5.97629	+	10.3512i	0.213303	+	0.369452i
$786$		0			0
$787$	30.2452			1.07813			0.539063	−	0.842266i	$-0.318779\pi$
$787$	30.2452			1.07813			0.539063	+	0.842266i	$0.318779\pi$
$788$		0			0
$789$	−3.56768	−	7.56787i	−0.127013	−	0.269423i
$790$		0			0
$791$	−3.15689	+	17.3697i	−0.112246	+	0.617596i
$792$		0			0
$793$	1.07515	−	1.86221i	0.0381796	−	0.0661290i
$794$		0			0
$795$	4.96869	+	10.5397i	0.176221	+	0.373805i
$796$		0			0
$797$	26.9751	+	15.5741i	0.955507	+	0.551662i	0.894787	−	0.446493i	$-0.147327\pi$
$797$	26.9751	+	15.5741i	0.955507	+	0.551662i	0.0607197	+	0.998155i	$0.480660\pi$
$798$		0			0
$799$	0.598535	−	0.345564i	0.0211746	−	0.0122252i
$800$		0			0
$801$	−3.52661	+	21.0307i	−0.124607	+	0.743082i
$802$		0			0
$803$	6.06259			0.213944
$804$		0			0
$805$	−2.08260	+	11.4588i	−0.0734019	+	0.403869i
$806$		0			0
$807$	−13.2329	−	1.10182i	−0.465822	−	0.0387858i
$808$		0			0
$809$	−10.0362	−	17.3832i	−0.352853	−	0.611160i	0.633895	−	0.773419i	$-0.281455\pi$
$809$	−10.0362	−	17.3832i	−0.352853	−	0.611160i	−0.986748	+	0.162259i	$0.948122\pi$
$810$		0			0
$811$	−20.4633			−0.718564			−0.359282	−	0.933229i	$-0.616978\pi$
$811$	−20.4633			−0.718564			−0.359282	+	0.933229i	$0.616978\pi$
$812$		0			0
$813$	−7.93870	+	3.74250i	−0.278422	+	0.131255i
$814$		0			0
$815$	4.49629			0.157498
$816$		0			0
$817$		−	13.3557i		−	0.467258i
$818$		0			0
$819$	−2.43703	−	13.5719i	−0.0851568	−	0.474241i
$820$		0			0
$821$	−42.5686			−1.48566			−0.742828	−	0.669483i	$-0.766516\pi$
$821$	−42.5686			−1.48566			−0.742828	+	0.669483i	$0.766516\pi$
$822$		0			0
$823$			12.2908i			0.428432i	0.976786	+	0.214216i	$0.0687196\pi$
$823$			12.2908i			0.428432i	−0.976786	+	0.214216i	$0.931280\pi$
$824$		0			0
$825$	−10.7223	−	0.892770i	−0.373301	−	0.0310822i
$826$		0			0
$827$		−	16.1935i		−	0.563104i	−0.959546	−	0.281552i	$-0.909151\pi$
$827$		−	16.1935i		−	0.563104i	0.959546	−	0.281552i	$-0.0908493\pi$
$828$		0			0
$829$	0.0315654	−	0.0182243i	0.00109631	−	0.000632956i	−0.499452	−	0.866342i	$-0.666465\pi$
$829$	0.0315654	−	0.0182243i	0.00109631	−	0.000632956i	0.500548	+	0.865709i	$0.333132\pi$
$830$		0			0
$831$	−34.2340	+	16.1387i	−1.18756	+	0.559847i
$832$		0			0
$833$	15.4636	−	41.1364i	0.535782	−	1.42529i
$834$		0			0
$835$			3.58406i			0.124032i
$836$		0			0
$837$	10.7892	−	42.3928i	0.372930	−	1.46531i
$838$		0			0
$839$	21.2294	+	36.7705i	0.732921	+	1.26946i	0.955629	+	0.294572i	$0.0951771\pi$
$839$	21.2294	+	36.7705i	0.732921	+	1.26946i	−0.222708	+	0.974885i	$0.571490\pi$
$840$		0			0
$841$	−16.8122	+	29.1196i	−0.579732	+	1.00413i
$842$		0			0
$843$	−0.315306	+	3.78686i	−0.0108597	+	0.130426i
$844$		0			0
$845$	6.78481	+	3.91721i	0.233404	+	0.134756i
$846$		0			0
$847$	−18.1446	−	15.3882i	−0.623455	−	0.528745i
$848$		0			0
$849$	−21.7718	−	15.1091i	−0.747208	−	0.518543i
$850$		0			0
$851$		−	41.9735i		−	1.43883i
$852$		0			0
$853$	−3.60970	+	2.08406i	−0.123594	+	0.0713568i	−0.560522	−	0.828139i	$-0.689400\pi$
$853$	−3.60970	+	2.08406i	−0.123594	+	0.0713568i	0.436929	+	0.899496i	$0.356066\pi$
$854$		0			0
$855$	3.24963	−	1.21374i	0.111135	−	0.0415091i
$856$		0			0
$857$	−9.96984	−	5.75609i	−0.340563	−	0.196624i	0.319958	−	0.947432i	$-0.396331\pi$
$857$	−9.96984	−	5.75609i	−0.340563	−	0.196624i	−0.660521	+	0.750808i	$0.729665\pi$
$858$		0			0
$859$	−2.10057	−	3.63829i	−0.0716704	−	0.124137i	0.827963	−	0.560783i	$-0.189500\pi$
$859$	−2.10057	−	3.63829i	−0.0716704	−	0.124137i	−0.899633	+	0.436646i	$0.856166\pi$
$860$		0			0
$861$	26.8808	+	26.9377i	0.916095	+	0.918033i
$862$		0			0
$863$	−15.9911	−	9.23249i	−0.544345	−	0.314278i	0.202493	−	0.979284i	$-0.435096\pi$
$863$	−15.9911	−	9.23249i	−0.544345	−	0.314278i	−0.746838	+	0.665006i	$0.768429\pi$
$864$		0			0
$865$	7.01513	+	12.1506i	0.238522	+	0.413132i
$866$		0			0
$867$	35.1169	−	16.5550i	1.19263	−	0.562237i
$868$		0			0
$869$	−4.25231	+	7.36522i	−0.144250	+	0.249848i
$870$		0			0
$871$	10.3136	−	17.8637i	0.349464	−	0.605289i
$872$		0			0
$873$	15.7568	+	12.9978i	0.533287	+	0.439909i
$874$		0			0
$875$	−6.56842	−	18.3458i	−0.222053	−	0.620201i
$876$		0			0
$877$	−2.77845	−	4.81242i	−0.0938217	−	0.162504i	0.815295	−	0.579046i	$-0.196575\pi$
$877$	−2.77845	−	4.81242i	−0.0938217	−	0.162504i	−0.909116	+	0.416543i	$0.863242\pi$
$878$		0			0
$879$	4.32954	+	9.18394i	0.146032	+	0.309767i
$880$		0			0
$881$			22.3336i			0.752438i	0.926531	+	0.376219i	$0.122776\pi$
$881$			22.3336i			0.752438i	−0.926531	+	0.376219i	$0.877224\pi$
$882$		0			0
$883$		−	36.9024i		−	1.24186i	−0.783865	−	0.620932i	$-0.786754\pi$
$883$		−	36.9024i		−	1.24186i	0.783865	−	0.620932i	$-0.213246\pi$
$884$		0			0
$885$	−0.0997311	−	0.00830392i	−0.00335242	−	0.000279133i
$886$		0			0
$887$	3.40494	+	5.89752i	0.114327	+	0.198020i	0.917510	−	0.397712i	$-0.130196\pi$
$887$	3.40494	+	5.89752i	0.114327	+	0.198020i	−0.803184	+	0.595731i	$0.796862\pi$
$888$		0			0
$889$	−13.8629	−	38.7196i	−0.464948	−	1.29861i
$890$		0			0
$891$	−12.5199	+	2.42487i	−0.419433	+	0.0812364i
$892$		0			0
$893$	−0.0810923	+	0.140456i	−0.00271365	+	0.00470018i
$894$		0			0
$895$	−2.78759	+	4.82825i	−0.0931789	+	0.161391i
$896$		0			0
$897$	−13.8648	−	9.62178i	−0.462931	−	0.321262i
$898$		0			0
$899$	−33.3105	−	57.6955i	−1.11097	−	1.92425i
$900$		0			0
$901$	−46.6033	−	26.9064i	−1.55258	−	0.896383i
$902$		0			0
$903$	−40.1387	+	10.7097i	−1.33573	+	0.356396i
$904$		0			0
$905$	−2.47925	−	4.29418i	−0.0824130	−	0.142743i
$906$		0			0
$907$	3.60190	+	2.07956i	0.119599	+	0.0690506i	0.558606	−	0.829433i	$-0.311336\pi$
$907$	3.60190	+	2.07956i	0.119599	+	0.0690506i	−0.439007	+	0.898484i	$0.644670\pi$
$908$		0			0
$909$	1.61916	−	9.65576i	0.0537043	−	0.320261i
$910$		0			0
$911$	4.80883	−	2.77638i	0.159324	−	0.0919856i	−0.418218	−	0.908347i	$-0.637345\pi$
$911$	4.80883	−	2.77638i	0.159324	−	0.0919856i	0.577542	+	0.816361i	$0.304012\pi$
$912$		0			0
$913$		−	22.3509i		−	0.739707i
$914$		0			0
$915$	0.139618	−	1.67682i	0.00461561	−	0.0554340i
$916$		0			0
$917$	10.6175	+	9.00454i	0.350619	+	0.297356i
$918$		0			0
$919$	23.2582	+	13.4281i	0.767216	+	0.442952i	0.831880	−	0.554955i	$-0.187264\pi$
$919$	23.2582	+	13.4281i	0.767216	+	0.442952i	−0.0646648	+	0.997907i	$0.520598\pi$
$920$		0			0
$921$	−11.9325	−	8.28088i	−0.393191	−	0.272864i
$922$		0			0
$923$	−0.338892	+	0.586979i	−0.0111548	+	0.0193206i
$924$		0			0
$925$	16.4044	+	28.4132i	0.539372	+	0.934220i
$926$		0			0
$927$	32.0389	−	38.8397i	1.05230	−	1.27566i
$928$		0			0
$929$		−	28.0523i		−	0.920365i	−0.887824	−	0.460183i	$-0.847784\pi$
$929$		−	28.0523i		−	0.920365i	0.887824	−	0.460183i	$-0.152216\pi$
$930$		0			0
$931$	1.68404	+	10.1744i	0.0551921	+	0.333453i
$932$		0			0
$933$	−41.0634	−	28.4969i	−1.34436	−	0.932948i
$934$		0			0
$935$	−6.04653	+	3.49097i	−0.197743	+	0.114167i
$936$		0			0
$937$			15.2285i			0.497493i	0.968569	+	0.248746i	$0.0800186\pi$
$937$			15.2285i			0.497493i	−0.968569	+	0.248746i	$0.919981\pi$
$938$		0			0
$939$	28.0581	−	40.4311i	0.915642	−	1.31942i
$940$		0			0
$941$			3.21460i			0.104793i	0.998626	+	0.0523965i	$0.0166860\pi$
$941$			3.21460i			0.104793i	−0.998626	+	0.0523965i	$0.983314\pi$
$942$		0			0
$943$	46.5760			1.51672
$944$		0			0
$945$	−6.25354	−	8.79303i	−0.203428	−	0.286037i
$946$		0			0
$947$			20.4308i			0.663911i	0.943295	+	0.331956i	$0.107708\pi$
$947$			20.4308i			0.663911i	−0.943295	+	0.331956i	$0.892292\pi$
$948$		0			0
$949$	−7.43299			−0.241285
$950$		0			0
$951$	−12.7826	−	8.87082i	−0.414505	−	0.287656i
$952$		0			0
$953$	−57.3984			−1.85932			−0.929658	−	0.368423i	$-0.879898\pi$
$953$	−57.3984			−1.85932			−0.929658	+	0.368423i	$0.879898\pi$
$954$		0			0
$955$	8.48329	+	14.6935i	0.274513	+	0.475470i
$956$		0			0
$957$	−11.0730	+	15.9560i	−0.357940	+	0.515783i
$958$		0			0
$959$	−6.47469	+	35.6247i	−0.209079	+	1.15038i
$960$		0			0
$961$	39.8726			1.28621
$962$		0			0
$963$	4.62334	−	27.5710i	0.148985	−	0.888461i
$964$		0			0
$965$	3.47466	−	2.00610i	0.111853	−	0.0645785i
$966$		0			0
$967$	31.0281	+	17.9141i	0.997797	+	0.576078i	0.907596	−	0.419845i	$-0.137916\pi$
$967$	31.0281	+	17.9141i	0.997797	+	0.576078i	0.0902010	+	0.995924i	$0.471249\pi$
$968$		0			0
$969$	−9.13373	+	13.1615i	−0.293418	+	0.422808i
$970$		0			0
$971$	27.6346	−	47.8645i	0.886836	−	1.53605i	0.0432421	−	0.999065i	$-0.486231\pi$
$971$	27.6346	−	47.8645i	0.886836	−	1.53605i	0.843594	−	0.536981i	$-0.180435\pi$
$972$		0			0
$973$	−4.36745	+	24.0304i	−0.140014	+	0.770380i
$974$		0			0
$975$	13.1460	+	1.09457i	0.421008	+	0.0350544i
$976$		0			0
$977$	3.30526			0.105745			0.0528723	−	0.998601i	$-0.483162\pi$
$977$	3.30526			0.105745			0.0528723	+	0.998601i	$0.483162\pi$
$978$		0			0
$979$	5.03592	+	8.72248i	0.160949	+	0.278772i
$980$		0			0
$981$	−4.20342	+	5.09566i	−0.134205	+	0.162692i
$982$		0			0
$983$	29.6188	−	51.3012i	0.944692	−	1.63626i	0.188327	−	0.982106i	$-0.439694\pi$
$983$	29.6188	−	51.3012i	0.944692	−	1.63626i	0.756366	−	0.654149i	$-0.226973\pi$
$984$		0			0
$985$	8.63571	−	4.98583i	0.275157	−	0.158862i
$986$		0			0
$987$	0.487147	+	0.131082i	0.0155060	+	0.00417240i
$988$		0			0
$989$	−25.4222	+	44.0325i	−0.808378	+	1.40015i
$990$		0			0
$991$	−15.3830	+	8.88141i	−0.488659	+	0.282127i	−0.724018	−	0.689781i	$-0.757707\pi$
$991$	−15.3830	+	8.88141i	−0.488659	+	0.282127i	0.235359	+	0.971908i	$0.424373\pi$
$992$		0			0
$993$	−6.72192	+	9.68613i	−0.213314	+	0.307380i
$994$		0			0
$995$	1.83972	+	1.06216i	0.0583229	+	0.0336727i
$996$		0			0
$997$	−12.4110	−	7.16551i	−0.393061	−	0.226934i	0.290424	−	0.956898i	$-0.406204\pi$
$997$	−12.4110	−	7.16551i	−0.393061	−	0.226934i	−0.683486	+	0.729964i	$0.739537\pi$
$998$		0			0
$999$	27.8409	+	27.1488i	0.880847	+	0.858951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.h.607.9	yes	24
3.2	odd	2		3024.2.cz.g.1279.7		24
4.3	odd	2		1008.2.cz.g.607.4	yes	24
7.3	odd	6		1008.2.bf.h.31.6	yes	24
9.2	odd	6		3024.2.bf.h.2287.7		24
9.7	even	3		1008.2.bf.g.943.7	yes	24
12.11	even	2		3024.2.cz.h.1279.7		24
21.17	even	6		3024.2.bf.g.1711.6		24
28.3	even	6		1008.2.bf.g.31.7	✓	24
36.7	odd	6		1008.2.bf.h.943.6	yes	24
36.11	even	6		3024.2.bf.g.2287.7		24
63.38	even	6		3024.2.cz.h.2719.7		24
63.52	odd	6		1008.2.cz.g.367.4	yes	24
84.59	odd	6		3024.2.bf.h.1711.6		24
252.115	even	6	inner	1008.2.cz.h.367.9	yes	24
252.227	odd	6		3024.2.cz.g.2719.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.7	✓	24	28.3	even	6
1008.2.bf.g.943.7	yes	24	9.7	even	3
1008.2.bf.h.31.6	yes	24	7.3	odd	6
1008.2.bf.h.943.6	yes	24	36.7	odd	6
1008.2.cz.g.367.4	yes	24	63.52	odd	6
1008.2.cz.g.607.4	yes	24	4.3	odd	2
1008.2.cz.h.367.9	yes	24	252.115	even	6	inner
1008.2.cz.h.607.9	yes	24	1.1	even	1	trivial
3024.2.bf.g.1711.6		24	21.17	even	6
3024.2.bf.g.2287.7		24	36.11	even	6
3024.2.bf.h.1711.6		24	84.59	odd	6
3024.2.bf.h.2287.7		24	9.2	odd	6
3024.2.cz.g.1279.7		24	3.2	odd	2
3024.2.cz.g.2719.7		24	252.227	odd	6
3024.2.cz.h.1279.7		24	12.11	even	2
3024.2.cz.h.2719.7		24	63.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.42297 + 0.987503i) q^{3} +(-0.679706 + 0.392428i) q^{5} +(2.49091 - 0.891831i) q^{7} +(1.04968 + 2.81037i) q^{9} +O(q^{10})\)	\(q+(1.42297 + 0.987503i) q^{3} +(-0.679706 + 0.392428i) q^{5} +(2.49091 - 0.891831i) q^{7} +(1.04968 + 2.81037i) q^{9} +(1.22712 + 0.708477i) q^{11} +(-1.50450 - 0.868623i) q^{13} +(-1.35472 - 0.112799i) q^{15} +(5.43701 - 3.13906i) q^{17} +(-0.736632 + 1.27588i) q^{19} +(4.42517 + 1.19073i) q^{21} +(4.85720 - 2.80431i) q^{23} +(-2.19200 + 3.79666i) q^{25} +(-1.28159 + 5.03562i) q^{27} +(3.95678 + 6.85335i) q^{29} -8.41859 q^{31} +(1.04653 + 2.21992i) q^{33} +(-1.34311 + 1.58369i) q^{35} +(3.74187 - 6.48111i) q^{37} +(-1.28309 - 2.72172i) q^{39} +(7.19180 + 4.15219i) q^{41} +(-7.85087 + 4.53270i) q^{43} +(-1.81634 - 1.49830i) q^{45} +0.110085 q^{47} +(5.40927 - 4.44294i) q^{49} +(10.8365 + 0.902283i) q^{51} +(-4.28575 - 7.42313i) q^{53} -1.11211 q^{55} +(-2.30814 + 1.08812i) q^{57} +0.0736173 q^{59} +1.23776i q^{61} +(5.12102 + 6.06425i) q^{63} +1.36349 q^{65} +11.8735i q^{67} +(9.68091 + 0.806063i) q^{69} -0.390149i q^{71} +(3.70538 - 2.13930i) q^{73} +(-6.86835 + 3.23791i) q^{75} +(3.68848 + 0.670370i) q^{77} +6.00205i q^{79} +(-6.79636 + 5.89995i) q^{81} +(-7.88696 - 13.6606i) q^{83} +(-2.46371 + 4.26727i) q^{85} +(-1.13733 + 13.6594i) q^{87} +(6.15579 + 3.55405i) q^{89} +(-4.52224 - 0.821903i) q^{91} +(-11.9794 - 8.31338i) q^{93} -1.15630i q^{95} +(5.89647 - 3.40433i) q^{97} +(-0.703006 + 4.19233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9	\( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9} + 9 q^{11} - 3 q^{13} + 6 q^{15} - 3 q^{17} + 4 q^{19} + 13 q^{21} + 6 q^{23} + 15 q^{25} - 9 q^{27} + 18 q^{29} - 34 q^{31} - 21 q^{33} + 42 q^{35} - 3 q^{37} - 27 q^{39} + 36 q^{41} - 24 q^{43} + 21 q^{45} + 42 q^{47} + 30 q^{49} + 6 q^{51} - 12 q^{53} + 30 q^{55} - 13 q^{57} + 12 q^{59} + 3 q^{63} + 6 q^{69} + 48 q^{73} - 36 q^{75} - 48 q^{77} - 31 q^{81} + 48 q^{83} - 21 q^{85} - 15 q^{87} + 39 q^{89} - 9 q^{91} + 10 q^{93} + 3 q^{97} - 30 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 3 * q^5 - 4 * q^7 + 17 * q^9 + 9 * q^11 - 3 * q^13 + 6 * q^15 - 3 * q^17 + 4 * q^19 + 13 * q^21 + 6 * q^23 + 15 * q^25 - 9 * q^27 + 18 * q^29 - 34 * q^31 - 21 * q^33 + 42 * q^35 - 3 * q^37 - 27 * q^39 + 36 * q^41 - 24 * q^43 + 21 * q^45 + 42 * q^47 + 30 * q^49 + 6 * q^51 - 12 * q^53 + 30 * q^55 - 13 * q^57 + 12 * q^59 + 3 * q^63 + 6 * q^69 + 48 * q^73 - 36 * q^75 - 48 * q^77 - 31 * q^81 + 48 * q^83 - 21 * q^85 - 15 * q^87 + 39 * q^89 - 9 * q^91 + 10 * q^93 + 3 * q^97 - 30 * q^99

Introduction

L-functions

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