LMFDB - Embedded newform 1008.2.cz.g.607.3

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			607.3
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.g.367.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60558 + 0.649697i) q^{3} +(-2.10605 + 1.21593i) q^{5} +(0.347128 + 2.62288i) q^{7} +(2.15579 - 2.08628i) q^{9} +O(q^{10})$	\(q+(-1.60558 + 0.649697i) q^{3} +(-2.10605 + 1.21593i) q^{5} +(0.347128 + 2.62288i) q^{7} +(2.15579 - 2.08628i) q^{9} +(3.88819 + 2.24485i) q^{11} +(0.395715 + 0.228466i) q^{13} +(2.59146 - 3.32057i) q^{15} +(-1.45416 + 0.839559i) q^{17} +(-3.17762 + 5.50381i) q^{19} +(-2.26142 - 3.98572i) q^{21} +(3.03876 - 1.75443i) q^{23} +(0.456976 - 0.791506i) q^{25} +(-2.10584 + 4.75031i) q^{27} +(-1.38240 - 2.39439i) q^{29} +8.92570 q^{31} +(-7.70128 - 1.07814i) q^{33} +(-3.92031 - 5.10184i) q^{35} +(0.463575 - 0.802935i) q^{37} +(-0.783788 - 0.109726i) q^{39} +(-9.08056 - 5.24267i) q^{41} +(-8.87861 + 5.12607i) q^{43} +(-2.00343 + 7.01512i) q^{45} -8.39449 q^{47} +(-6.75900 + 1.82095i) q^{49} +(1.78931 - 2.29274i) q^{51} +(-4.91938 - 8.52062i) q^{53} -10.9183 q^{55} +(1.52613 - 10.9013i) q^{57} -6.45074 q^{59} +5.31355i q^{61} +(6.22041 + 4.93016i) q^{63} -1.11120 q^{65} +13.6441i q^{67} +(-3.73913 + 4.79115i) q^{69} -1.59679i q^{71} +(9.31911 - 5.38039i) q^{73} +(-0.219473 + 1.56772i) q^{75} +(-4.53827 + 10.9775i) q^{77} -10.3204i q^{79} +(0.294837 - 8.99517i) q^{81} +(-0.657501 - 1.13882i) q^{83} +(2.04169 - 3.53632i) q^{85} +(3.77519 + 2.94625i) q^{87} +(13.5161 + 7.80355i) q^{89} +(-0.461876 + 1.11722i) q^{91} +(-14.3309 + 5.79900i) q^{93} -15.4551i q^{95} +(-5.69780 + 3.28963i) q^{97} +(13.0655 - 3.27246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.60558	+	0.649697i	−0.926983	+	0.375103i
$3$	−1.60558	+	0.649697i	−0.926983	+	0.375103i
$4$		0			0
$5$	−2.10605	+	1.21593i	−0.941856	+	0.543781i	−0.890542	−	0.454902i	$-0.849674\pi$
$5$	−2.10605	+	1.21593i	−0.941856	+	0.543781i	−0.0513144	+	0.998683i	$0.516341\pi$
$6$		0			0
$7$	0.347128	+	2.62288i	0.131202	+	0.991356i
$7$	0.347128	+	2.62288i	0.131202	+	0.991356i
$8$		0			0
$9$	2.15579	−	2.08628i	0.718596	−	0.695428i
$10$		0			0
$11$	3.88819	+	2.24485i	1.17233	+	0.676847i	0.954229	−	0.299078i	$-0.0966792\pi$
$11$	3.88819	+	2.24485i	1.17233	+	0.676847i	0.218105	+	0.975925i	$0.430013\pi$
$12$		0			0
$13$	0.395715	+	0.228466i	0.109752	+	0.0633652i	0.553871	−	0.832602i	$-0.313150\pi$
$13$	0.395715	+	0.228466i	0.109752	+	0.0633652i	−0.444119	+	0.895968i	$0.646483\pi$
$14$		0			0
$15$	2.59146	−	3.32057i	0.669111	−	0.857369i
$16$		0			0
$17$	−1.45416	+	0.839559i	−0.352685	+	0.203623i	−0.665867	−	0.746070i	$-0.731938\pi$
$17$	−1.45416	+	0.839559i	−0.352685	+	0.203623i	0.313182	+	0.949693i	$0.398605\pi$
$18$		0			0
$19$	−3.17762	+	5.50381i	−0.728997	+	1.26266i	0.228310	+	0.973588i	$0.426680\pi$
$19$	−3.17762	+	5.50381i	−0.728997	+	1.26266i	−0.957307	+	0.289072i	$0.906653\pi$
$20$		0			0
$21$	−2.26142	−	3.98572i	−0.493482	−	0.869756i
$22$		0			0
$23$	3.03876	−	1.75443i	0.633625	−	0.365823i	−0.148530	−	0.988908i	$-0.547454\pi$
$23$	3.03876	−	1.75443i	0.633625	−	0.365823i	0.782154	+	0.623085i	$0.214121\pi$
$24$		0			0
$25$	0.456976	−	0.791506i	0.0913952	−	0.158301i
$26$		0			0
$27$	−2.10584	+	4.75031i	−0.405269	+	0.914197i
$28$		0			0
$29$	−1.38240	−	2.39439i	−0.256706	−	0.444627i	0.708652	−	0.705558i	$-0.249304\pi$
$29$	−1.38240	−	2.39439i	−0.256706	−	0.444627i	−0.965357	+	0.260931i	$0.915970\pi$
$30$		0			0
$31$	8.92570			1.60310			0.801551	−	0.597926i	$-0.204008\pi$
$31$	8.92570			1.60310			0.801551	+	0.597926i	$0.204008\pi$
$32$		0			0
$33$	−7.70128	−	1.07814i	−1.34062	−	0.187680i
$34$		0			0
$35$	−3.92031	−	5.10184i	−0.662654	−	0.862369i
$36$		0			0
$37$	0.463575	−	0.802935i	0.0762113	−	0.132002i	−0.825401	−	0.564547i	$-0.809051\pi$
$37$	0.463575	−	0.802935i	0.0762113	−	0.132002i	0.901612	+	0.432545i	$0.142384\pi$
$38$		0			0
$39$	−0.783788	−	0.109726i	−0.125506	−	0.0175703i
$40$		0			0
$41$	−9.08056	−	5.24267i	−1.41815	−	0.818767i	−0.422010	−	0.906591i	$-0.638675\pi$
$41$	−9.08056	−	5.24267i	−1.41815	−	0.818767i	−0.996136	+	0.0878245i	$0.972009\pi$
$42$		0			0
$43$	−8.87861	+	5.12607i	−1.35398	+	0.781718i	−0.988804	−	0.149222i	$-0.952323\pi$
$43$	−8.87861	+	5.12607i	−1.35398	+	0.781718i	−0.365172	+	0.930940i	$0.618990\pi$
$44$		0			0
$45$	−2.00343	+	7.01512i	−0.298653	+	1.04575i
$46$		0			0
$47$	−8.39449			−1.22446			−0.612231	−	0.790679i	$-0.709728\pi$
$47$	−8.39449			−1.22446			−0.612231	+	0.790679i	$0.709728\pi$
$48$		0			0
$49$	−6.75900	+	1.82095i	−0.965572	+	0.260136i
$50$		0			0
$51$	1.78931	−	2.29274i	0.250554	−	0.321048i
$52$		0			0
$53$	−4.91938	−	8.52062i	−0.675729	−	1.17040i	−0.976255	−	0.216623i	$-0.930496\pi$
$53$	−4.91938	−	8.52062i	−0.675729	−	1.17040i	0.300526	−	0.953773i	$-0.402838\pi$
$54$		0			0
$55$	−10.9183			−1.47223
$56$		0			0
$57$	1.52613	−	10.9013i	0.202141	−	1.44391i
$58$		0			0
$59$	−6.45074			−0.839815			−0.419907	−	0.907567i	$-0.637937\pi$
$59$	−6.45074			−0.839815			−0.419907	+	0.907567i	$0.637937\pi$
$60$		0			0
$61$			5.31355i			0.680331i	0.940366	+	0.340165i	$0.110483\pi$
$61$			5.31355i			0.680331i	−0.940366	+	0.340165i	$0.889517\pi$
$62$		0			0
$63$	6.22041	+	4.93016i	0.783698	+	0.621142i
$64$		0			0
$65$	−1.11120			−0.137827
$66$		0			0
$67$			13.6441i			1.66689i	0.552601	+	0.833446i	$0.313635\pi$
$67$			13.6441i			1.66689i	−0.552601	+	0.833446i	$0.686365\pi$
$68$		0			0
$69$	−3.73913	+	4.79115i	−0.450138	+	0.576786i
$70$		0			0
$71$		−	1.59679i		−	0.189504i	−0.995501	−	0.0947519i	$-0.969794\pi$
$71$		−	1.59679i		−	0.189504i	0.995501	−	0.0947519i	$-0.0302058\pi$
$72$		0			0
$73$	9.31911	−	5.38039i	1.09072	−	0.629727i	0.156951	−	0.987606i	$-0.449834\pi$
$73$	9.31911	−	5.38039i	1.09072	−	0.629727i	0.933768	+	0.357880i	$0.116500\pi$
$74$		0			0
$75$	−0.219473	+	1.56772i	−0.0253426	+	0.181025i
$76$		0			0
$77$	−4.53827	+	10.9775i	−0.517184	+	1.25100i
$78$		0			0
$79$		−	10.3204i		−	1.16114i	−0.814210	−	0.580570i	$-0.802830\pi$
$79$		−	10.3204i		−	1.16114i	0.814210	−	0.580570i	$-0.197170\pi$
$80$		0			0
$81$	0.294837	−	8.99517i	0.0327597	−	0.999463i
$82$		0			0
$83$	−0.657501	−	1.13882i	−0.0721701	−	0.125002i	0.827682	−	0.561197i	$-0.189659\pi$
$83$	−0.657501	−	1.13882i	−0.0721701	−	0.125002i	−0.899852	+	0.436195i	$0.856326\pi$
$84$		0			0
$85$	2.04169	−	3.53632i	0.221453	−	0.383567i
$86$		0			0
$87$	3.77519	+	2.94625i	0.404743	+	0.315871i
$88$		0			0
$89$	13.5161	+	7.80355i	1.43271	+	0.827175i	0.997327	−	0.0730708i	$-0.0232799\pi$
$89$	13.5161	+	7.80355i	1.43271	+	0.827175i	0.435382	+	0.900246i	$0.356613\pi$
$90$		0			0
$91$	−0.461876	+	1.11722i	−0.0484178	+	0.117117i
$92$		0			0
$93$	−14.3309	+	5.79900i	−1.48605	+	0.601328i
$94$		0			0
$95$		−	15.4551i		−	1.58566i
$96$		0			0
$97$	−5.69780	+	3.28963i	−0.578524	+	0.334011i	−0.760547	−	0.649283i	$-0.775069\pi$
$97$	−5.69780	+	3.28963i	−0.578524	+	0.334011i	0.182022	+	0.983294i	$0.441736\pi$
$98$		0			0
$99$	13.0655	−	3.27246i	1.31313	−	0.328894i
$100$		0			0
$101$	1.78496	+	1.03055i	0.177610	+	0.102543i	0.586169	−	0.810188i	$-0.300635\pi$
$101$	1.78496	+	1.03055i	0.177610	+	0.102543i	−0.408559	+	0.912732i	$0.633969\pi$
$102$		0			0
$103$	−2.93209	−	5.07852i	−0.288907	−	0.500402i	0.684642	−	0.728879i	$-0.259959\pi$
$103$	−2.93209	−	5.07852i	−0.288907	−	0.500402i	−0.973549	+	0.228478i	$0.926625\pi$
$104$		0			0
$105$	9.60904	+	5.64441i	0.937746	+	0.550838i
$106$		0			0
$107$	0.597825	+	0.345154i	0.0577939	+	0.0333673i	0.528619	−	0.848860i	$-0.322710\pi$
$107$	0.597825	+	0.345154i	0.0577939	+	0.0333673i	−0.470825	+	0.882227i	$0.656044\pi$
$108$		0			0
$109$	2.72140	+	4.71360i	0.260663	+	0.451481i	0.966418	−	0.256975i	$-0.0827256\pi$
$109$	2.72140	+	4.71360i	0.260663	+	0.451481i	−0.705756	+	0.708455i	$0.749392\pi$
$110$		0			0
$111$	−0.222643	+	1.59036i	−0.0211323	+	0.150950i
$112$		0			0
$113$	−8.84129	+	15.3136i	−0.831718	+	1.44058i	0.0649566	+	0.997888i	$0.479309\pi$
$113$	−8.84129	+	15.3136i	−0.831718	+	1.44058i	−0.896675	+	0.442690i	$0.854024\pi$
$114$		0			0
$115$	−4.26652	+	7.38984i	−0.397855	+	0.689106i
$116$		0			0
$117$	1.32972	−	0.333050i	0.122933	−	0.0307905i
$118$		0			0
$119$	−2.70684	−	3.52265i	−0.248136	−	0.322921i
$120$		0			0
$121$	4.57868	+	7.93051i	0.416244	+	0.720955i
$122$		0			0
$123$	17.9857	+	2.51791i	1.62172	+	0.227033i
$124$		0			0
$125$		−	9.93670i		−	0.888766i
$126$		0			0
$127$			6.67671i			0.592462i	0.955116	+	0.296231i	$0.0957298\pi$
$127$			6.67671i			0.592462i	−0.955116	+	0.296231i	$0.904270\pi$
$128$		0			0
$129$	10.9249	−	13.9987i	0.961888	−	1.23252i
$130$		0			0
$131$	−8.48439	−	14.6954i	−0.741284	−	1.28394i	−0.951911	−	0.306376i	$-0.900884\pi$
$131$	−8.48439	−	14.6954i	−0.741284	−	1.28394i	0.210626	−	0.977567i	$-0.432450\pi$
$132$		0			0
$133$	−15.5389	−	6.42400i	−1.34739	−	0.557032i
$134$		0			0
$135$	−1.34103	−	12.5650i	−0.115418	−	1.08142i
$136$		0			0
$137$	2.25408	−	3.90418i	0.192579	−	0.333557i	−0.753525	−	0.657419i	$-0.771648\pi$
$137$	2.25408	−	3.90418i	0.192579	−	0.333557i	0.946104	+	0.323862i	$0.104981\pi$
$138$		0			0
$139$	−1.31628	+	2.27987i	−0.111646	+	0.193376i	−0.916434	−	0.400186i	$-0.868945\pi$
$139$	−1.31628	+	2.27987i	−0.111646	+	0.193376i	0.804788	+	0.593562i	$0.202279\pi$
$140$		0			0
$141$	13.4780	−	5.45387i	1.13506	−	0.459299i
$142$		0			0
$143$	1.02574	+	1.77664i	0.0857771	+	0.148570i
$144$		0			0
$145$	5.82283	+	3.36181i	0.483559	+	0.279183i
$146$		0			0
$147$	9.66907	−	7.31499i	0.797491	−	0.603330i
$148$		0			0
$149$	3.50091	+	6.06375i	0.286806	+	0.496762i	0.973045	−	0.230613i	$-0.0740732\pi$
$149$	3.50091	+	6.06375i	0.286806	+	0.496762i	−0.686240	+	0.727375i	$0.740740\pi$
$150$		0			0
$151$	4.00644	+	2.31312i	0.326039	+	0.188239i	0.654081	−	0.756424i	$-0.273055\pi$
$151$	4.00644	+	2.31312i	0.326039	+	0.188239i	−0.328042	+	0.944663i	$0.606389\pi$
$152$		0			0
$153$	−1.38330	+	4.84370i	−0.111833	+	0.391590i
$154$		0			0
$155$	−18.7980	+	10.8530i	−1.50989	+	0.871737i
$156$		0			0
$157$			5.18700i			0.413968i	0.978344	+	0.206984i	$0.0663648\pi$
$157$			5.18700i			0.413968i	−0.978344	+	0.206984i	$0.933635\pi$
$158$		0			0
$159$	13.4343	+	10.4844i	1.06541	+	0.831470i
$160$		0			0
$161$	5.65649	+	7.36129i	0.445794	+	0.580151i
$162$		0			0
$163$	−2.20250	−	1.27161i	−0.172513	−	0.0996005i	0.411257	−	0.911519i	$-0.365090\pi$
$163$	−2.20250	−	1.27161i	−0.172513	−	0.0996005i	−0.583770	+	0.811919i	$0.698423\pi$
$164$		0			0
$165$	17.5303	−	7.09360i	1.36473	−	0.552236i
$166$		0			0
$167$	−4.67825	+	8.10297i	−0.362014	+	0.627027i	−0.988292	−	0.152573i	$-0.951244\pi$
$167$	−4.67825	+	8.10297i	−0.362014	+	0.627027i	0.626278	+	0.779600i	$0.284577\pi$
$168$		0			0
$169$	−6.39561	−	11.0775i	−0.491970	−	0.852117i
$170$		0			0
$171$	4.63222	+	18.4945i	0.354235	+	1.41431i
$172$		0			0
$173$		−	8.17956i		−	0.621880i	−0.950429	−	0.310940i	$-0.899356\pi$
$173$		−	8.17956i		−	0.621880i	0.950429	−	0.310940i	$-0.100644\pi$
$174$		0			0
$175$	2.23465	+	0.923840i	0.168924	+	0.0698357i
$176$		0			0
$177$	10.3572	−	4.19103i	0.778494	−	0.315017i
$178$		0			0
$179$	18.7277	−	10.8124i	1.39977	−	0.808159i	0.405404	−	0.914137i	$-0.367131\pi$
$179$	18.7277	−	10.8124i	1.39977	−	0.808159i	0.994368	+	0.105978i	$0.0337974\pi$
$180$		0			0
$181$		−	6.15376i		−	0.457405i	−0.973496	−	0.228703i	$-0.926552\pi$
$181$		−	6.15376i		−	0.457405i	0.973496	−	0.228703i	$-0.0734484\pi$
$182$		0			0
$183$	−3.45220	−	8.53135i	−0.255194	−	0.630655i
$184$		0			0
$185$			2.25470i			0.165769i
$186$		0			0
$187$	−7.53873			−0.551287
$188$		0			0
$189$	−13.1905	−	3.87440i	−0.959467	−	0.281821i
$190$		0			0
$191$			0.959271i			0.0694104i	0.999398	+	0.0347052i	$0.0110492\pi$
$191$			0.959271i			0.0694104i	−0.999398	+	0.0347052i	$0.988951\pi$
$192$		0			0
$193$	9.73225			0.700542			0.350271	−	0.936648i	$-0.386089\pi$
$193$	9.73225			0.700542			0.350271	+	0.936648i	$0.386089\pi$
$194$		0			0
$195$	1.78412	−	0.721942i	0.127763	−	0.0516993i
$196$		0			0
$197$	6.67981			0.475917			0.237958	−	0.971275i	$-0.423522\pi$
$197$	6.67981			0.475917			0.237958	+	0.971275i	$0.423522\pi$
$198$		0			0
$199$	7.92567	+	13.7277i	0.561836	+	0.973128i	0.997336	+	0.0729396i	$0.0232380\pi$
$199$	7.92567	+	13.7277i	0.561836	+	0.973128i	−0.435501	+	0.900188i	$0.643429\pi$
$200$		0			0
$201$	−8.86453	−	21.9067i	−0.625256	−	1.54518i
$202$		0			0
$203$	5.80033	−	4.45704i	0.407103	−	0.312823i
$204$		0			0
$205$	25.4989			1.78092
$206$		0			0
$207$	2.89068	−	10.1219i	0.200916	−	0.703519i
$208$		0			0
$209$	−24.7104	+	14.2666i	−1.70926	+	0.986839i
$210$		0			0
$211$	−3.79205	−	2.18934i	−0.261056	−	0.150721i	0.363760	−	0.931493i	$-0.381493\pi$
$211$	−3.79205	−	2.18934i	−0.261056	−	0.150721i	−0.624816	+	0.780772i	$0.714826\pi$
$212$		0			0
$213$	1.03743	+	2.56377i	0.0710834	+	0.175667i
$214$		0			0
$215$	12.4659	−	21.5916i	0.850167	−	1.47253i
$216$		0			0
$217$	3.09836	+	23.4110i	0.210330	+	1.58925i
$218$		0			0
$219$	−11.4670	+	14.6933i	−0.774866	+	0.992878i
$220$		0			0
$221$	−0.767244			−0.0516104
$222$		0			0
$223$	−10.1248	−	17.5367i	−0.678010	−	1.17435i	−0.975579	−	0.219647i	$-0.929509\pi$
$223$	−10.1248	−	17.5367i	−0.678010	−	1.17435i	0.297570	−	0.954700i	$-0.403824\pi$
$224$		0			0
$225$	−0.666163	−	2.65970i	−0.0444108	−	0.177313i
$226$		0			0
$227$	−8.60937	+	14.9119i	−0.571424	+	0.989735i	0.424996	+	0.905195i	$0.360275\pi$
$227$	−8.60937	+	14.9119i	−0.571424	+	0.989735i	−0.996420	+	0.0845401i	$0.973058\pi$
$228$		0			0
$229$	16.4919	−	9.52161i	1.08982	−	0.629206i	0.156289	−	0.987711i	$-0.450047\pi$
$229$	16.4919	−	9.52161i	1.08982	−	0.629206i	0.933528	+	0.358506i	$0.116714\pi$
$230$		0			0
$231$	0.154506	−	20.5738i	0.0101657	−	1.35366i
$232$		0			0
$233$	−8.27568	+	14.3339i	−0.542158	+	0.939045i	0.456622	+	0.889661i	$0.349059\pi$
$233$	−8.27568	+	14.3339i	−0.542158	+	0.939045i	−0.998780	+	0.0493838i	$0.984274\pi$
$234$		0			0
$235$	17.6792	−	10.2071i	1.15327	−	0.665839i
$236$		0			0
$237$	6.70516	+	16.5703i	0.435547	+	1.07636i
$238$		0			0
$239$	12.4085	+	7.16408i	0.802642	+	0.463406i	0.844394	−	0.535722i	$-0.179961\pi$
$239$	12.4085	+	7.16408i	0.802642	+	0.463406i	−0.0417519	+	0.999128i	$0.513294\pi$
$240$		0			0
$241$	20.6124	+	11.9006i	1.32776	+	0.766583i	0.984953	−	0.172823i	$-0.0552889\pi$
$241$	20.6124	+	11.9006i	1.32776	+	0.766583i	0.342807	+	0.939406i	$0.388622\pi$
$242$		0			0
$243$	5.37075	+	14.6340i	0.344534	+	0.938774i
$244$		0			0
$245$	12.0207	−	12.0535i	0.767973	−	0.770070i
$246$		0			0
$247$	−2.51487	+	1.45196i	−0.160017	+	0.0923861i
$248$		0			0
$249$	1.79556	+	1.40130i	0.113789	+	0.0888038i
$250$		0			0
$251$	−18.7179			−1.18147			−0.590733	−	0.806867i	$-0.701161\pi$
$251$	−18.7179			−1.18147			−0.590733	+	0.806867i	$0.701161\pi$
$252$		0			0
$253$	15.7537			0.990426
$254$		0			0
$255$	−0.980571	+	7.00433i	−0.0614057	+	0.438628i
$256$		0			0
$257$	−0.774476	+	0.447144i	−0.0483105	+	0.0278921i	−0.523961	−	0.851742i	$-0.675546\pi$
$257$	−0.774476	+	0.447144i	−0.0483105	+	0.0278921i	0.475650	+	0.879635i	$0.342213\pi$
$258$		0			0
$259$	2.26692	+	0.937180i	0.140860	+	0.0582336i
$260$		0			0
$261$	−7.97554	−	2.27771i	−0.493674	−	0.140987i
$262$		0			0
$263$	−6.77645	−	3.91239i	−0.417854	−	0.241248i	0.276305	−	0.961070i	$-0.410890\pi$
$263$	−6.77645	−	3.91239i	−0.417854	−	0.241248i	−0.694159	+	0.719822i	$0.744223\pi$
$264$		0			0
$265$	20.7210	+	11.9633i	1.27288	+	0.734897i
$266$		0			0
$267$	−26.7712	−	3.74784i	−1.63837	−	0.229364i
$268$		0			0
$269$	15.7164	−	9.07386i	0.958245	−	0.553243i	0.0626124	−	0.998038i	$-0.480057\pi$
$269$	15.7164	−	9.07386i	0.958245	−	0.553243i	0.895632	+	0.444795i	$0.146723\pi$
$270$		0			0
$271$	−15.8173	+	27.3965i	−0.960836	+	1.66422i	−0.240425	+	0.970668i	$0.577287\pi$
$271$	−15.8173	+	27.3965i	−0.960836	+	1.66422i	−0.720410	+	0.693548i	$0.756046\pi$
$272$		0			0
$273$	0.0157246	−	2.09387i	0.000951698	−	0.126727i
$274$		0			0
$275$	3.55362	−	2.05168i	0.214291	−	0.123721i
$276$		0			0
$277$	−15.5598	+	26.9504i	−0.934899	+	1.61929i	−0.160084	+	0.987103i	$0.551177\pi$
$277$	−15.5598	+	26.9504i	−0.934899	+	1.61929i	−0.774814	+	0.632189i	$0.782157\pi$
$278$		0			0
$279$	19.2419	−	18.6215i	1.15198	−	1.11484i
$280$		0			0
$281$	−3.95236	−	6.84569i	−0.235778	−	0.408380i	0.723720	−	0.690093i	$-0.242431\pi$
$281$	−3.95236	−	6.84569i	−0.235778	−	0.408380i	−0.959499	+	0.281714i	$0.909097\pi$
$282$		0			0
$283$	9.93156			0.590370			0.295185	−	0.955440i	$-0.404619\pi$
$283$	9.93156			0.590370			0.295185	+	0.955440i	$0.404619\pi$
$284$		0			0
$285$	10.0411	+	24.8144i	0.594785	+	1.46988i
$286$		0			0
$287$	10.5988	−	25.6371i	0.625626	−	1.51331i
$288$		0			0
$289$	−7.09028	+	12.2807i	−0.417075	+	0.722396i
$290$		0			0
$291$	7.01103	−	8.98361i	0.410994	−	0.526629i
$292$		0			0
$293$	10.9727	+	6.33509i	0.641032	+	0.370100i	0.785012	−	0.619481i	$-0.212657\pi$
$293$	10.9727	+	6.33509i	0.641032	+	0.370100i	−0.143980	+	0.989581i	$0.545990\pi$
$294$		0			0
$295$	13.5856	−	7.84365i	0.790985	−	0.456675i
$296$		0			0
$297$	−18.8516	+	13.7428i	−1.09388	+	0.797439i
$298$		0			0
$299$	1.60331			0.0927218
$300$		0			0
$301$	−16.5271	−	21.5081i	−0.952605	−	1.23971i
$302$		0			0
$303$	−3.53545	−	0.494945i	−0.203106	−	0.0284339i
$304$		0			0
$305$	−6.46091	−	11.1906i	−0.369951	−	0.640774i
$306$		0			0
$307$	−0.680046			−0.0388123			−0.0194061	−	0.999812i	$-0.506178\pi$
$307$	−0.680046			−0.0388123			−0.0194061	+	0.999812i	$0.506178\pi$
$308$		0			0
$309$	8.00721	+	6.24902i	0.455514	+	0.355494i
$310$		0			0
$311$	7.40471			0.419883			0.209941	−	0.977714i	$-0.432673\pi$
$311$	7.40471			0.419883			0.209941	+	0.977714i	$0.432673\pi$
$312$		0			0
$313$			0.764315i			0.0432016i	0.999767	+	0.0216008i	$0.00687629\pi$
$313$			0.764315i			0.0432016i	−0.999767	+	0.0216008i	$0.993124\pi$
$314$		0			0
$315$	−19.0953	−	2.81961i	−1.07590	−	0.158867i
$316$		0			0
$317$	−27.5131			−1.54529			−0.772644	−	0.634840i	$-0.781066\pi$
$317$	−27.5131			−1.54529			−0.772644	+	0.634840i	$0.781066\pi$
$318$		0			0
$319$		−	12.4131i		−	0.695002i
$320$		0			0
$321$	−1.18410	−	0.165768i	−0.0660901	−	0.00925229i
$322$		0			0
$323$		−	10.6712i		−	0.593762i
$324$		0			0
$325$	0.361665	−	0.208807i	0.0200616	−	0.0115825i
$326$		0			0
$327$	−7.43184	−	5.79999i	−0.410982	−	0.320740i
$328$		0			0
$329$	−2.91396	−	22.0177i	−0.160652	−	1.21388i
$330$		0			0
$331$		−	8.40291i		−	0.461866i	−0.972970	−	0.230933i	$-0.925822\pi$
$331$		−	8.40291i		−	0.461866i	0.972970	−	0.230933i	$-0.0741778\pi$
$332$		0			0
$333$	−0.675782	−	2.69811i	−0.0370326	−	0.147855i
$334$		0			0
$335$	−16.5903	−	28.7352i	−0.906424	−	1.56997i
$336$		0			0
$337$	−2.06160	+	3.57079i	−0.112302	+	0.194513i	−0.916698	−	0.399580i	$-0.869156\pi$
$337$	−2.06160	+	3.57079i	−0.112302	+	0.194513i	0.804396	+	0.594094i	$0.202489\pi$
$338$		0			0
$339$	4.24624	−	30.3313i	0.230624	−	1.64737i
$340$		0			0
$341$	34.7048	+	20.0368i	1.87937	+	1.08506i
$342$		0			0
$343$	−7.12237	−	17.0960i	−0.384572	−	0.923095i
$344$		0			0
$345$	2.04910	−	14.6369i	0.110320	−	0.788026i
$346$		0			0
$347$			18.8928i			1.01422i	0.861881	+	0.507110i	$0.169286\pi$
$347$			18.8928i			1.01422i	−0.861881	+	0.507110i	$0.830714\pi$
$348$		0			0
$349$	−3.67063	+	2.11924i	−0.196485	+	0.113440i	−0.595015	−	0.803715i	$-0.702854\pi$
$349$	−3.67063	+	2.11924i	−0.196485	+	0.113440i	0.398530	+	0.917155i	$0.369520\pi$
$350$		0			0
$351$	−1.91860	+	1.39866i	−0.102407	+	0.0746548i
$352$		0			0
$353$	−8.57691	−	4.95188i	−0.456503	−	0.263562i	0.254070	−	0.967186i	$-0.418231\pi$
$353$	−8.57691	−	4.95188i	−0.456503	−	0.263562i	−0.710573	+	0.703624i	$0.751564\pi$
$354$		0			0
$355$	1.94158	+	3.36292i	0.103048	+	0.178485i
$356$		0			0
$357$	6.63472	+	3.89728i	0.351146	+	0.206266i
$358$		0			0
$359$	1.14625	+	0.661787i	0.0604967	+	0.0349278i	0.529943	−	0.848033i	$-0.322213\pi$
$359$	1.14625	+	0.661787i	0.0604967	+	0.0349278i	−0.469447	+	0.882961i	$0.655547\pi$
$360$		0			0
$361$	−10.6946	−	18.5236i	−0.562873	−	0.974925i
$362$		0			0
$363$	−12.5039	−	9.75832i	−0.656283	−	0.512179i
$364$		0			0
$365$	−13.0844	+	22.6628i	−0.684867	+	1.18622i
$366$		0			0
$367$	−18.3266	+	31.7426i	−0.956642	+	1.65695i	−0.226077	+	0.974109i	$0.572590\pi$
$367$	−18.3266	+	31.7426i	−0.956642	+	1.65695i	−0.730565	+	0.682843i	$0.760743\pi$
$368$		0			0
$369$	−30.5135	+	7.64256i	−1.58847	+	0.397856i
$370$		0			0
$371$	20.6409	−	15.8607i	1.07162	−	0.823446i
$372$		0			0
$373$	−11.1831	−	19.3698i	−0.579041	−	1.00293i	−0.995590	−	0.0938155i	$-0.970094\pi$
$373$	−11.1831	−	19.3698i	−0.579041	−	1.00293i	0.416548	−	0.909114i	$-0.363240\pi$
$374$		0			0
$375$	6.45585	+	15.9542i	0.333379	+	0.823871i
$376$		0			0
$377$		−	1.26333i		−	0.0650648i
$378$		0			0
$379$			29.0426i			1.49182i	0.666048	+	0.745909i	$0.267985\pi$
$379$			29.0426i			1.49182i	−0.666048	+	0.745909i	$0.732015\pi$
$380$		0			0
$381$	−4.33784	−	10.7200i	−0.222234	−	0.549202i
$382$		0			0
$383$	10.3588	+	17.9419i	0.529309	+	0.916790i	0.999416	+	0.0341804i	$0.0108821\pi$
$383$	10.3588	+	17.9419i	0.529309	+	0.916790i	−0.470107	+	0.882610i	$0.655785\pi$
$384$		0			0
$385$	−3.79005	−	28.6374i	−0.193159	−	1.45950i
$386$		0			0
$387$	−8.44596	+	29.5740i	−0.429332	+	1.50333i
$388$		0			0
$389$	19.0995	−	33.0812i	0.968381	−	1.67728i	0.268137	−	0.963381i	$-0.413592\pi$
$389$	19.0995	−	33.0812i	0.968381	−	1.67728i	0.700244	−	0.713904i	$-0.253075\pi$
$390$		0			0
$391$	−2.94589	+	5.10243i	−0.148980	+	0.258041i
$392$		0			0
$393$	23.1699	+	18.0824i	1.16877	+	0.912135i
$394$		0			0
$395$	12.5489	+	21.7354i	0.631406	+	1.09363i
$396$		0			0
$397$	−22.8326	−	13.1824i	−1.14594	−	0.661606i	−0.198042	−	0.980194i	$-0.563458\pi$
$397$	−22.8326	−	13.1824i	−1.14594	−	0.661606i	−0.947894	+	0.318587i	$0.896792\pi$
$398$		0			0
$399$	29.1226	+	0.218706i	1.45795	+	0.0109490i
$400$		0			0
$401$	14.8837	+	25.7794i	0.743258	+	1.28736i	0.951004	+	0.309178i	$0.100054\pi$
$401$	14.8837	+	25.7794i	0.743258	+	1.28736i	−0.207746	+	0.978183i	$0.566613\pi$
$402$		0			0
$403$	3.53204	+	2.03922i	0.175943	+	0.101581i
$404$		0			0
$405$	10.3166	+	19.3028i	0.512634	+	0.959165i
$406$		0			0
$407$	3.60493	−	2.08131i	0.178690	−	0.103167i
$408$		0			0
$409$		−	11.4389i		−	0.565615i	−0.959177	−	0.282808i	$-0.908734\pi$
$409$		−	11.4389i		−	0.565615i	0.959177	−	0.282808i	$-0.0912658\pi$
$410$		0			0
$411$	−1.08258	+	7.73295i	−0.0533995	+	0.381439i
$412$		0			0
$413$	−2.23923	−	16.9195i	−0.110185	−	0.832555i
$414$		0			0
$415$	2.76946	+	1.59895i	0.135948	+	0.0784894i
$416$		0			0
$417$	0.632175	−	4.51570i	0.0309578	−	0.221135i
$418$		0			0
$419$	−3.62952	+	6.28651i	−0.177314	+	0.307116i	−0.940960	−	0.338519i	$-0.890074\pi$
$419$	−3.62952	+	6.28651i	−0.177314	+	0.307116i	0.763646	+	0.645635i	$0.223407\pi$
$420$		0			0
$421$	3.83542	+	6.64314i	0.186927	+	0.323767i	0.944224	−	0.329304i	$-0.106814\pi$
$421$	3.83542	+	6.64314i	0.186927	+	0.323767i	−0.757297	+	0.653070i	$0.773481\pi$
$422$		0			0
$423$	−18.0967	+	17.5133i	−0.879893	+	0.851525i
$424$		0			0
$425$			1.53463i			0.0744407i
$426$		0			0
$427$	−13.9368	+	1.84448i	−0.674450	+	0.0892608i
$428$		0			0
$429$	−2.80120	−	2.18612i	−0.135243	−	0.105547i
$430$		0			0
$431$	−26.0439	+	15.0364i	−1.25449	+	0.724279i	−0.971998	−	0.234991i	$-0.924494\pi$
$431$	−26.0439	+	15.0364i	−1.25449	+	0.724279i	−0.282491	+	0.959270i	$0.591161\pi$
$432$		0			0
$433$			14.7704i			0.709819i	0.934901	+	0.354909i	$0.115488\pi$
$433$			14.7704i			0.709819i	−0.934901	+	0.354909i	$0.884512\pi$
$434$		0			0
$435$	−11.5332	−	1.61459i	−0.552974	−	0.0774136i
$436$		0			0
$437$			22.2996i			1.06674i
$438$		0			0
$439$	13.5922			0.648719			0.324360	−	0.945934i	$-0.394851\pi$
$439$	13.5922			0.648719			0.324360	+	0.945934i	$0.394851\pi$
$440$		0			0
$441$	−10.7720	+	18.0268i	−0.512950	+	0.858418i
$442$		0			0
$443$			21.0890i			1.00197i	0.865457	+	0.500984i	$0.167028\pi$
$443$			21.0890i			1.00197i	−0.865457	+	0.500984i	$0.832972\pi$
$444$		0			0
$445$	−37.9543			−1.79921
$446$		0			0
$447$	−9.56060	−	7.46132i	−0.452201	−	0.352909i
$448$		0			0
$449$	−18.7307			−0.883959			−0.441979	−	0.897025i	$-0.645724\pi$
$449$	−18.7307			−0.883959			−0.441979	+	0.897025i	$0.645724\pi$
$450$		0			0
$451$	−23.5380	−	40.7690i	−1.10836	−	1.91974i
$452$		0			0
$453$	−7.93549	−	1.11093i	−0.372842	−	0.0521960i
$454$		0			0
$455$	−0.385728	−	2.91454i	−0.0180832	−	0.136636i
$456$		0			0
$457$	29.4099			1.37574			0.687868	−	0.725836i	$-0.258547\pi$
$457$	29.4099			1.37574			0.687868	+	0.725836i	$0.258547\pi$
$458$		0			0
$459$	−0.925939	−	8.67569i	−0.0432191	−	0.404946i
$460$		0			0
$461$	22.2212	−	12.8294i	1.03494	−	0.597525i	0.116547	−	0.993185i	$-0.462817\pi$
$461$	22.2212	−	12.8294i	1.03494	−	0.597525i	0.918397	+	0.395660i	$0.129484\pi$
$462$		0			0
$463$	−3.52873	−	2.03731i	−0.163994	−	0.0946819i	0.415757	−	0.909476i	$-0.363517\pi$
$463$	−3.52873	−	2.03731i	−0.163994	−	0.0946819i	−0.579751	+	0.814794i	$0.696850\pi$
$464$		0			0
$465$	23.1306	−	29.6384i	1.07265	−	1.37445i
$466$		0			0
$467$	−11.0531	+	19.1445i	−0.511475	+	0.885901i	0.488437	+	0.872599i	$0.337567\pi$
$467$	−11.0531	+	19.1445i	−0.511475	+	0.885901i	−0.999912	+	0.0133012i	$0.995766\pi$
$468$		0			0
$469$	−35.7868	+	4.73625i	−1.65248	+	0.218700i
$470$		0			0
$471$	−3.36998	−	8.32816i	−0.155280	−	0.383741i
$472$		0			0
$473$	−46.0290			−2.11641
$474$		0			0
$475$	2.90420	+	5.03022i	0.133254	+	0.230802i
$476$		0			0
$477$	−28.3816	−	8.10541i	−1.29950	−	0.371121i
$478$		0			0
$479$	−12.5218	+	21.6883i	−0.572134	+	0.990965i	0.424213	+	0.905562i	$0.360551\pi$
$479$	−12.5218	+	21.6883i	−0.572134	+	0.990965i	−0.996347	+	0.0854021i	$0.972783\pi$
$480$		0			0
$481$	0.366888	−	0.211823i	0.0167286	−	0.00965828i
$482$		0			0
$483$	−13.8646	−	8.14414i	−0.630859	−	0.370571i
$484$		0			0
$485$	7.99992	−	13.8563i	0.363258	−	0.629181i
$486$		0			0
$487$	36.1701	−	20.8828i	1.63902	−	0.946290i	0.657851	−	0.753148i	$-0.271466\pi$
$487$	36.1701	−	20.8828i	1.63902	−	0.946290i	0.981171	−	0.193142i	$-0.0618678\pi$
$488$		0			0
$489$	4.36246	+	0.610723i	0.197277	+	0.0276178i
$490$		0			0
$491$	23.1251	+	13.3513i	1.04362	+	0.602534i	0.920856	−	0.389902i	$-0.127491\pi$
$491$	23.1251	+	13.3513i	1.04362	+	0.602534i	0.122763	+	0.992436i	$0.460825\pi$
$492$		0			0
$493$	4.02047	+	2.32122i	0.181073	+	0.104542i
$494$		0			0
$495$	−23.5376	+	22.7787i	−1.05794	+	1.02383i
$496$		0			0
$497$	4.18818	−	0.554289i	0.187866	−	0.0248633i
$498$		0			0
$499$	2.19574	−	1.26771i	0.0982950	−	0.0567507i	−0.450047	−	0.893005i	$-0.648593\pi$
$499$	2.19574	−	1.26771i	0.0982950	−	0.0567507i	0.548342	+	0.836254i	$0.315259\pi$
$500$		0			0
$501$	2.24684	−	16.0494i	0.100381	−	0.717036i
$502$		0			0
$503$	17.5814			0.783916			0.391958	−	0.919983i	$-0.371798\pi$
$503$	17.5814			0.783916			0.391958	+	0.919983i	$0.371798\pi$
$504$		0			0
$505$	−5.01230			−0.223045
$506$		0			0
$507$	17.4657	+	13.6307i	0.775679	+	0.605358i
$508$		0			0
$509$	12.4554	−	7.19111i	0.552075	−	0.318740i	−0.197884	−	0.980226i	$-0.563407\pi$
$509$	12.4554	−	7.19111i	0.552075	−	0.318740i	0.749958	+	0.661485i	$0.230073\pi$
$510$		0			0
$511$	17.3470	+	22.5752i	0.767388	+	0.998669i
$512$		0			0
$513$	−19.4532	−	26.6848i	−0.858880	−	1.17816i
$514$		0			0
$515$	12.3503	+	7.13043i	0.544218	+	0.314204i
$516$		0			0
$517$	−32.6394	−	18.8443i	−1.43548	−	0.828773i
$518$		0			0
$519$	5.31424	+	13.1330i	0.233269	+	0.576473i
$520$		0			0
$521$	33.9165	−	19.5817i	1.48591	−	0.857890i	0.486038	−	0.873938i	$-0.338442\pi$
$521$	33.9165	−	19.5817i	1.48591	−	0.857890i	0.999871	+	0.0160476i	$0.00510833\pi$
$522$		0			0
$523$	10.1114	−	17.5134i	0.442139	−	0.765807i	−0.555709	−	0.831377i	$-0.687553\pi$
$523$	10.1114	−	17.5134i	0.442139	−	0.765807i	0.997848	+	0.0655699i	$0.0208865\pi$
$524$		0			0
$525$	−4.18814	−	0.0314523i	−0.182785	−	0.00137269i
$526$		0			0
$527$	−12.9794	+	7.49365i	−0.565391	+	0.326429i
$528$		0			0
$529$	−5.34397	+	9.25603i	−0.232347	+	0.402436i
$530$		0			0
$531$	−13.9064	+	13.4581i	−0.603487	+	0.584031i
$532$		0			0
$533$	−2.39555	−	4.14921i	−0.103763	−	0.179722i
$534$		0			0
$535$	−1.67873			−0.0725780
$536$		0			0
$537$	−23.0440	+	29.5276i	−0.994423	+	1.27421i
$538$		0			0
$539$	−30.3680	−	8.09273i	−1.30804	−	0.348579i
$540$		0			0
$541$	18.0846	−	31.3234i	0.777517	−	1.34670i	−0.155852	−	0.987780i	$-0.549812\pi$
$541$	18.0846	−	31.3234i	0.777517	−	1.34670i	0.933369	−	0.358919i	$-0.116854\pi$
$542$		0			0
$543$	3.99808	+	9.88037i	0.171574	+	0.424007i
$544$		0			0
$545$	−11.4628	−	6.61806i	−0.491013	−	0.283487i
$546$		0			0
$547$	27.2261	−	15.7190i	1.16410	−	0.672096i	0.211820	−	0.977309i	$-0.432061\pi$
$547$	27.2261	−	15.7190i	1.16410	−	0.672096i	0.952284	+	0.305212i	$0.0987275\pi$
$548$		0			0
$549$	11.0856	+	11.4549i	0.473121	+	0.488883i
$550$		0			0
$551$	17.5710			0.748551
$552$		0			0
$553$	27.0693	−	3.58251i	1.15110	−	0.152344i
$554$		0			0
$555$	−1.46487	−	3.62011i	−0.0621804	−	0.153665i
$556$		0			0
$557$	9.22319	+	15.9750i	0.390799	+	0.676884i	0.992555	−	0.121796i	$-0.0388654\pi$
$557$	9.22319	+	15.9750i	0.390799	+	0.676884i	−0.601756	+	0.798680i	$0.705532\pi$
$558$		0			0
$559$	−4.68454			−0.198135
$560$		0			0
$561$	12.1041	−	4.89789i	0.511033	−	0.206789i
$562$		0			0
$563$	26.2712			1.10720			0.553599	−	0.832783i	$-0.313254\pi$
$563$	26.2712			1.10720			0.553599	+	0.832783i	$0.313254\pi$
$564$		0			0
$565$		−	43.0016i		−	1.80909i
$566$		0			0
$567$	23.6956	−	2.34915i	0.995122	−	0.0986551i
$568$		0			0
$569$	−44.2364			−1.85449			−0.927244	−	0.374459i	$-0.877828\pi$
$569$	−44.2364			−1.85449			−0.927244	+	0.374459i	$0.877828\pi$
$570$		0			0
$571$			25.4163i			1.06364i	0.846857	+	0.531820i	$0.178492\pi$
$571$			25.4163i			1.06364i	−0.846857	+	0.531820i	$0.821508\pi$
$572$		0			0
$573$	−0.623236	−	1.54019i	−0.0260361	−	0.0643423i
$574$		0			0
$575$		−	3.20692i		−	0.133738i
$576$		0			0
$577$	−15.0822	+	8.70772i	−0.627881	+	0.362507i	−0.779931	−	0.625866i	$-0.784746\pi$
$577$	−15.0822	+	8.70772i	−0.627881	+	0.362507i	0.152050	+	0.988373i	$0.451413\pi$
$578$		0			0
$579$	−15.6259	+	6.32301i	−0.649391	+	0.262775i
$580$		0			0
$581$	2.75876	−	2.11986i	0.114453	−	0.0879468i
$582$		0			0
$583$		−	44.1730i		−	1.82946i
$584$		0			0
$585$	−2.39551	+	2.31827i	−0.0990420	+	0.0958488i
$586$		0			0
$587$	0.224520	+	0.388879i	0.00926691	+	0.0160508i	0.870622	−	0.491953i	$-0.163717\pi$
$587$	0.224520	+	0.388879i	0.00926691	+	0.0160508i	−0.861355	+	0.508004i	$0.830384\pi$
$588$		0			0
$589$	−28.3625	+	49.1253i	−1.16866	+	2.02417i
$590$		0			0
$591$	−10.7250	+	4.33985i	−0.441167	+	0.178518i
$592$		0			0
$593$	20.4137	+	11.7859i	0.838291	+	0.483987i	0.856683	−	0.515843i	$-0.172521\pi$
$593$	20.4137	+	11.7859i	0.838291	+	0.483987i	−0.0183921	+	0.999831i	$0.505855\pi$
$594$		0			0
$595$	9.98406	+	4.12756i	0.409307	+	0.169214i
$596$		0			0
$597$	−21.6441	−	16.8916i	−0.885835	−	0.691327i
$598$		0			0
$599$			39.6547i			1.62025i	0.586258	+	0.810125i	$0.300601\pi$
$599$			39.6547i			1.62025i	−0.586258	+	0.810125i	$0.699399\pi$
$600$		0			0
$601$	1.68404	−	0.972283i	0.0686936	−	0.0396603i	−0.465260	−	0.885174i	$-0.654039\pi$
$601$	1.68404	−	0.972283i	0.0686936	−	0.0396603i	0.533953	+	0.845514i	$0.320706\pi$
$602$		0			0
$603$	28.4655	+	29.4138i	1.15920	+	1.19782i
$604$		0			0
$605$	−19.2859	−	11.1347i	−0.784083	−	0.452691i
$606$		0			0
$607$	−19.0369	−	32.9728i	−0.772682	−	1.33832i	−0.936088	−	0.351766i	$-0.885581\pi$
$607$	−19.0369	−	32.9728i	−0.772682	−	1.33832i	0.163406	−	0.986559i	$-0.447752\pi$
$608$		0			0
$609$	−6.41718	+	10.9246i	−0.260037	+	0.442687i
$610$		0			0
$611$	−3.32183	−	1.91786i	−0.134387	−	0.0775882i
$612$		0			0
$613$	−8.49783	−	14.7187i	−0.343224	−	0.594482i	0.641805	−	0.766868i	$-0.278186\pi$
$613$	−8.49783	−	14.7187i	−0.343224	−	0.594482i	−0.985029	+	0.172386i	$0.944852\pi$
$614$		0			0
$615$	−40.9405	+	16.5665i	−1.65088	+	0.668028i
$616$		0			0
$617$	9.72221	−	16.8394i	0.391401	−	0.677927i	−0.601233	−	0.799074i	$-0.705324\pi$
$617$	9.72221	−	16.8394i	0.391401	−	0.677927i	0.992635	+	0.121146i	$0.0386571\pi$
$618$		0			0
$619$	5.57182	−	9.65067i	0.223950	−	0.387893i	−0.732054	−	0.681247i	$-0.761438\pi$
$619$	5.57182	−	9.65067i	0.223950	−	0.387893i	0.956004	+	0.293354i	$0.0947714\pi$
$620$		0			0
$621$	1.93493	+	18.1296i	0.0776462	+	0.727515i
$622$		0			0
$623$	−15.7760	+	38.1601i	−0.632050	+	1.52885i
$624$		0			0
$625$	14.3672	+	24.8848i	0.574689	+	0.995391i
$626$		0			0
$627$	30.4057	−	38.9604i	1.21428	−	1.55593i
$628$		0			0
$629$			1.55679i			0.0620735i
$630$		0			0
$631$		−	37.9530i		−	1.51088i	−0.655215	−	0.755442i	$-0.727422\pi$
$631$		−	37.9530i		−	1.51088i	0.655215	−	0.755442i	$-0.272578\pi$
$632$		0			0
$633$	7.51086	+	1.05148i	0.298530	+	0.0417927i
$634$		0			0
$635$	−8.11841	−	14.0615i	−0.322169	−	0.558014i
$636$		0			0
$637$	−3.09067	−	0.823627i	−0.122457	−	0.0326333i
$638$		0			0
$639$	−3.33135	−	3.44233i	−0.131786	−	0.136177i
$640$		0			0
$641$	2.20368	−	3.81689i	0.0870401	−	0.150758i	−0.819219	−	0.573481i	$-0.805593\pi$
$641$	2.20368	−	3.81689i	0.0870401	−	0.150758i	0.906259	+	0.422723i	$0.138926\pi$
$642$		0			0
$643$	15.7031	−	27.1985i	0.619269	−	1.07261i	−0.370350	−	0.928892i	$-0.620762\pi$
$643$	15.7031	−	27.1985i	0.619269	−	1.07261i	0.989619	−	0.143713i	$-0.0459044\pi$
$644$		0			0
$645$	−5.98704	+	42.7661i	−0.235739	+	1.68391i
$646$		0			0
$647$	4.82727	+	8.36107i	0.189779	+	0.328708i	0.945177	−	0.326560i	$-0.105889\pi$
$647$	4.82727	+	8.36107i	0.189779	+	0.328708i	−0.755397	+	0.655267i	$0.772556\pi$
$648$		0			0
$649$	−25.0817	−	14.4809i	−0.984543	−	0.568426i
$650$		0			0
$651$	−20.1848	−	35.5754i	−0.791103	−	1.39431i
$652$		0			0
$653$	−4.42478	−	7.66394i	−0.173155	−	0.299913i	0.766366	−	0.642404i	$-0.222063\pi$
$653$	−4.42478	−	7.66394i	−0.173155	−	0.299913i	−0.939521	+	0.342491i	$0.888729\pi$
$654$		0			0
$655$	35.7372	+	20.6329i	1.39637	+	0.806193i
$656$		0			0
$657$	8.86499	−	31.0413i	0.345856	−	1.21104i
$658$		0			0
$659$	−11.1661	+	6.44675i	−0.434969	+	0.251130i	−0.701461	−	0.712707i	$-0.747469\pi$
$659$	−11.1661	+	6.44675i	−0.434969	+	0.251130i	0.266492	+	0.963837i	$0.414135\pi$
$660$		0			0
$661$			13.9885i			0.544091i	0.962284	+	0.272046i	$0.0877001\pi$
$661$			13.9885i			0.544091i	−0.962284	+	0.272046i	$0.912300\pi$
$662$		0			0
$663$	1.23187	−	0.498477i	0.0478420	−	0.0193592i
$664$		0			0
$665$	40.5368	−	5.36489i	1.57195	−	0.208042i
$666$		0			0
$667$	−8.40157	−	4.85065i	−0.325310	−	0.187818i
$668$		0			0
$669$	27.6498	+	21.5786i	1.06900	+	0.834277i
$670$		0			0
$671$	−11.9281	+	20.6601i	−0.460480	+	0.797574i
$672$		0			0
$673$	20.1596	+	34.9175i	0.777097	+	1.34597i	0.933608	+	0.358295i	$0.116642\pi$
$673$	20.1596	+	34.9175i	0.777097	+	1.34597i	−0.156511	+	0.987676i	$0.550025\pi$
$674$		0			0
$675$	2.79758	+	3.83756i	0.107679	+	0.147708i
$676$		0			0
$677$			20.0178i			0.769347i	0.923053	+	0.384674i	$0.125686\pi$
$677$			20.0178i			0.769347i	−0.923053	+	0.384674i	$0.874314\pi$
$678$		0			0
$679$	−10.6062	−	13.8027i	−0.407027	−	0.529700i
$680$		0			0
$681$	4.13485	−	29.5357i	0.158448	−	1.13181i
$682$		0			0
$683$	−15.6264	+	9.02190i	−0.597927	+	0.345214i	−0.768226	−	0.640179i	$-0.778860\pi$
$683$	−15.6264	+	9.02190i	−0.597927	+	0.345214i	0.170298	+	0.985393i	$0.445527\pi$
$684$		0			0
$685$			10.9632i			0.418883i
$686$		0			0
$687$	−20.2930	+	26.0025i	−0.774225	+	0.992056i
$688$		0			0
$689$		−	4.49565i		−	0.171271i
$690$		0			0
$691$	−32.5408			−1.23791			−0.618956	−	0.785426i	$-0.712444\pi$
$691$	−32.5408			−1.23791			−0.618956	+	0.785426i	$0.712444\pi$
$692$		0			0
$693$	13.1187	+	33.1333i	0.498337	+	1.25863i
$694$		0			0
$695$		−	6.40203i		−	0.242843i
$696$		0			0
$697$	17.6061			0.666879
$698$		0			0
$699$	3.97459	−	28.3909i	0.150333	−	1.07384i
$700$		0			0
$701$	−15.6096			−0.589567			−0.294784	−	0.955564i	$-0.595248\pi$
$701$	−15.6096			−0.589567			−0.294784	+	0.955564i	$0.595248\pi$
$702$		0			0
$703$	2.94613	+	5.10285i	0.111116	+	0.192458i
$704$		0			0
$705$	−21.7539	+	27.8745i	−0.819301	+	1.04982i
$706$		0			0
$707$	−2.08340	+	5.03948i	−0.0783542	+	0.189529i
$708$		0			0
$709$	−40.9710			−1.53870			−0.769349	−	0.638828i	$-0.779419\pi$
$709$	−40.9710			−1.53870			−0.769349	+	0.638828i	$0.779419\pi$
$710$		0			0
$711$	−21.5314	−	22.2487i	−0.807490	−	0.834391i
$712$		0			0
$713$	27.1230	−	15.6595i	1.01577	−	0.586452i
$714$		0			0
$715$	−4.32055	−	2.49447i	−0.161579	−	0.0932878i
$716$		0			0
$717$	−24.5774	−	3.44072i	−0.917861	−	0.128496i
$718$		0			0
$719$	−6.18063	+	10.7052i	−0.230499	+	0.399235i	−0.957955	−	0.286919i	$-0.907369\pi$
$719$	−6.18063	+	10.7052i	−0.230499	+	0.399235i	0.727456	+	0.686154i	$0.240702\pi$
$720$		0			0
$721$	12.3026	−	9.45341i	0.458171	−	0.352063i
$722$		0			0
$723$	−40.8266	−	5.71553i	−1.51836	−	0.212563i
$724$		0			0
$725$	−2.52690			−0.0938467
$726$		0			0
$727$	0.793341	+	1.37411i	0.0294234	+	0.0509628i	0.880362	−	0.474302i	$-0.157300\pi$
$727$	0.793341	+	1.37411i	0.0294234	+	0.0509628i	−0.850939	+	0.525265i	$0.823966\pi$
$728$		0			0
$729$	−18.1309	−	20.0068i	−0.671514	−	0.740992i
$730$		0			0
$731$	8.60728	−	14.9082i	0.318352	−	0.551401i
$732$		0			0
$733$	16.9129	−	9.76469i	0.624694	−	0.360667i	−0.154000	−	0.988071i	$-0.549216\pi$
$733$	16.9129	−	9.76469i	0.624694	−	0.360667i	0.778694	+	0.627404i	$0.215882\pi$
$734$		0			0
$735$	−11.4691	+	27.1627i	−0.423043	+	1.00191i
$736$		0			0
$737$	−30.6289	+	53.0509i	−1.12823	+	1.95415i
$738$		0			0
$739$	10.4675	−	6.04343i	0.385054	−	0.222311i	−0.294961	−	0.955509i	$-0.595307\pi$
$739$	10.4675	−	6.04343i	0.385054	−	0.222311i	0.680015	+	0.733198i	$0.261973\pi$
$740$		0			0
$741$	3.09450	−	3.96515i	0.113679	−	0.145663i
$742$		0			0
$743$	39.1566	+	22.6071i	1.43652	+	0.829373i	0.997606	−	0.0691583i	$-0.0220313\pi$
$743$	39.1566	+	22.6071i	1.43652	+	0.829373i	0.438910	+	0.898531i	$0.355365\pi$
$744$		0			0
$745$	−14.7462	−	8.51373i	−0.540259	−	0.311919i
$746$		0			0
$747$	−3.79334	−	1.08333i	−0.138791	−	0.0396370i
$748$		0			0
$749$	−0.697777	+	1.68783i	−0.0254962	+	0.0616721i
$750$		0			0
$751$	−10.2452	+	5.91510i	−0.373854	+	0.215845i	−0.675141	−	0.737689i	$-0.735917\pi$
$751$	−10.2452	+	5.91510i	−0.373854	+	0.215845i	0.301287	+	0.953534i	$0.402584\pi$
$752$		0			0
$753$	30.0532	−	12.1610i	1.09520	−	0.443171i
$754$		0			0
$755$	−11.2504			−0.409443
$756$		0			0
$757$	−1.13634			−0.0413008			−0.0206504	−	0.999787i	$-0.506574\pi$
$757$	−1.13634			−0.0413008			−0.0206504	+	0.999787i	$0.506574\pi$
$758$		0			0
$759$	−25.2938	+	10.2351i	−0.918108	+	0.371511i
$760$		0			0
$761$	−22.4877	+	12.9833i	−0.815179	+	0.470644i	−0.848751	−	0.528792i	$-0.822645\pi$
$761$	−22.4877	+	12.9833i	−0.815179	+	0.470644i	0.0335719	+	0.999436i	$0.489312\pi$
$762$		0			0
$763$	−11.4185	+	8.77412i	−0.413379	+	0.317645i
$764$		0			0
$765$	−2.97630	−	11.8831i	−0.107608	−	0.429634i
$766$		0			0
$767$	−2.55266	−	1.47378i	−0.0921711	−	0.0532150i
$768$		0			0
$769$	−5.34306	−	3.08482i	−0.192676	−	0.111241i	0.400559	−	0.916271i	$-0.368816\pi$
$769$	−5.34306	−	3.08482i	−0.192676	−	0.111241i	−0.593235	+	0.805030i	$0.702149\pi$
$770$		0			0
$771$	0.952976	−	1.22110i	0.0343206	−	0.0439769i
$772$		0			0
$773$	−22.9774	+	13.2660i	−0.826439	+	0.477145i	−0.852632	−	0.522512i	$-0.824995\pi$
$773$	−22.9774	+	13.2660i	−0.826439	+	0.477145i	0.0261931	+	0.999657i	$0.491662\pi$
$774$		0			0
$775$	4.07883	−	7.06474i	0.146516	−	0.253773i
$776$		0			0
$777$	−4.24862	−	0.0319064i	−0.152418	−	0.00114464i
$778$		0			0
$779$	57.7092	−	33.3184i	2.06765	−	1.19376i
$780$		0			0
$781$	3.58454	−	6.20861i	0.128265	−	0.222162i
$782$		0			0
$783$	14.2852	−	1.52463i	0.510512	−	0.0544859i
$784$		0			0
$785$	−6.30704	−	10.9241i	−0.225108	−	0.389898i
$786$		0			0
$787$	13.7291			0.489391			0.244696	−	0.969600i	$-0.421312\pi$
$787$	13.7291			0.489391			0.244696	+	0.969600i	$0.421312\pi$
$788$		0			0
$789$	13.4220	+	1.87902i	0.477837	+	0.0668947i
$790$		0			0
$791$	−43.2347	−	17.8739i	−1.53725	−	0.635522i
$792$		0			0
$793$	−1.21397	+	2.10266i	−0.0431093	+	0.0746675i
$794$		0			0
$795$	−41.0417	−	5.74563i	−1.45560	−	0.203777i
$796$		0			0
$797$	39.5989	+	22.8624i	1.40267	+	0.809829i	0.994666	−	0.103153i	$-0.0328931\pi$
$797$	39.5989	+	22.8624i	1.40267	+	0.809829i	0.408000	+	0.912982i	$0.366226\pi$
$798$		0			0
$799$	12.2069	−	7.04767i	0.431850	−	0.249329i
$800$		0			0
$801$	45.4184	−	11.3757i	1.60478	−	0.401942i
$802$		0			0
$803$	48.3126			1.70491
$804$		0			0
$805$	−20.8637	−	8.62536i	−0.735348	−	0.304004i
$806$		0			0
$807$	−19.3387	+	24.7797i	−0.680754	+	0.872287i
$808$		0			0
$809$	−11.8728	−	20.5642i	−0.417425	−	0.723001i	0.578255	−	0.815856i	$-0.303734\pi$
$809$	−11.8728	−	20.5642i	−0.417425	−	0.723001i	−0.995680	+	0.0928555i	$0.970401\pi$
$810$		0			0
$811$	48.4581			1.70159			0.850797	−	0.525495i	$-0.176120\pi$
$811$	48.4581			1.70159			0.850797	+	0.525495i	$0.176120\pi$
$812$		0			0
$813$	7.59665	−	54.2637i	0.266426	−	1.90311i
$814$		0			0
$815$	6.18478			0.216643
$816$		0			0
$817$		−	65.1549i		−	2.27948i
$818$		0			0
$819$	1.33513	+	3.37210i	0.0466534	+	0.117831i
$820$		0			0
$821$	37.9070			1.32296			0.661481	−	0.749962i	$-0.269928\pi$
$821$	37.9070			1.32296			0.661481	+	0.749962i	$0.269928\pi$
$822$		0			0
$823$			19.0075i			0.662559i	0.943533	+	0.331280i	$0.107480\pi$
$823$			19.0075i			0.662559i	−0.943533	+	0.331280i	$0.892520\pi$
$824$		0			0
$825$	−4.37265	+	5.60292i	−0.152236	+	0.195069i
$826$		0			0
$827$		−	2.75122i		−	0.0956692i	−0.998855	−	0.0478346i	$-0.984768\pi$
$827$		−	2.75122i		−	0.0956692i	0.998855	−	0.0478346i	$-0.0152320\pi$
$828$		0			0
$829$	27.0931	−	15.6422i	0.940984	−	0.543277i	0.0507153	−	0.998713i	$-0.483850\pi$
$829$	27.0931	−	15.6422i	0.940984	−	0.543277i	0.890269	+	0.455436i	$0.150517\pi$
$830$		0			0
$831$	7.47297	−	53.3802i	0.259234	−	1.85174i
$832$		0			0
$833$	8.29988	−	8.32254i	0.287574	−	0.288359i
$834$		0			0
$835$		−	22.7537i		−	0.787425i
$836$		0			0
$837$	−18.7961	+	42.3998i	−0.649688	+	1.46555i
$838$		0			0
$839$	−1.27568	−	2.20954i	−0.0440413	−	0.0762818i	0.843164	−	0.537656i	$-0.180690\pi$
$839$	−1.27568	−	2.20954i	−0.0440413	−	0.0762818i	−0.887206	+	0.461374i	$0.847357\pi$
$840$		0			0
$841$	10.6779	−	18.4947i	0.368204	−	0.637749i
$842$		0			0
$843$	10.7935	+	8.42348i	0.371747	+	0.290120i
$844$		0			0
$845$	26.9390	+	15.5532i	0.926729	+	0.535047i
$846$		0			0
$847$	−19.2114	+	14.7622i	−0.660111	+	0.507236i
$848$		0			0
$849$	−15.9459	+	6.45250i	−0.547263	+	0.221449i
$850$		0			0
$851$		−	3.25323i		−	0.111519i
$852$		0			0
$853$	−36.1233	+	20.8558i	−1.23684	+	0.714088i	−0.968446	−	0.249222i	$-0.919825\pi$
$853$	−36.1233	+	20.8558i	−1.23684	+	0.714088i	−0.268391	+	0.963310i	$0.586492\pi$
$854$		0			0
$855$	−32.2437	−	33.3179i	−1.10271	−	1.13945i
$856$		0			0
$857$	−33.9310	−	19.5901i	−1.15906	−	0.669183i	−0.207981	−	0.978133i	$-0.566689\pi$
$857$	−33.9310	−	19.5901i	−1.15906	−	0.669183i	−0.951078	+	0.308949i	$0.900023\pi$
$858$		0			0
$859$	−7.69010	−	13.3196i	−0.262383	−	0.454460i	0.704492	−	0.709712i	$-0.251175\pi$
$859$	−7.69010	−	13.3196i	−0.262383	−	0.454460i	−0.966875	+	0.255252i	$0.917842\pi$
$860$		0			0
$861$	−0.360837	+	48.0485i	−0.0122973	+	1.63749i
$862$		0			0
$863$	43.4544	+	25.0884i	1.47921	+	0.854020i	0.999723	−	0.0235310i	$-0.00749084\pi$
$863$	43.4544	+	25.0884i	1.47921	+	0.854020i	0.479483	+	0.877551i	$0.340824\pi$
$864$		0			0
$865$	9.94578	+	17.2266i	0.338167	+	0.585722i
$866$		0			0
$867$	3.40527	−	24.3242i	0.115649	−	0.826095i
$868$		0			0
$869$	23.1678	−	40.1278i	0.785914	−	1.36124i
$870$		0			0
$871$	−3.11722	+	5.39918i	−0.105623	+	0.182944i
$872$		0			0
$873$	−5.42015	+	18.9790i	−0.183444	+	0.642341i
$874$		0			0
$875$	26.0628	−	3.44931i	0.881083	−	0.116608i
$876$		0			0
$877$	18.7034	+	32.3953i	0.631571	+	1.09391i	0.987231	+	0.159297i	$0.0509227\pi$
$877$	18.7034	+	32.3953i	0.631571	+	1.09391i	−0.355660	+	0.934615i	$0.615744\pi$
$878$		0			0
$879$	−21.7335	−	3.04258i	−0.733051	−	0.102624i
$880$		0			0
$881$			2.43451i			0.0820207i	0.999159	+	0.0410104i	$0.0130577\pi$
$881$			2.43451i			0.0820207i	−0.999159	+	0.0410104i	$0.986942\pi$
$882$		0			0
$883$		−	7.56709i		−	0.254653i	−0.991861	−	0.127326i	$-0.959360\pi$
$883$		−	7.56709i		−	0.254653i	0.991861	−	0.127326i	$-0.0406396\pi$
$884$		0			0
$885$	−16.7168	+	21.4202i	−0.561929	+	0.720031i
$886$		0			0
$887$	−2.64424	−	4.57995i	−0.0887848	−	0.153780i	0.818213	−	0.574915i	$-0.194965\pi$
$887$	−2.64424	−	4.57995i	−0.0887848	−	0.153780i	−0.906998	+	0.421136i	$0.861632\pi$
$888$		0			0
$889$	−17.5122	+	2.31767i	−0.587341	+	0.0777322i
$890$		0			0
$891$	21.3392	−	34.3131i	0.714889	−	1.14953i
$892$		0			0
$893$	26.6745	−	46.2016i	0.892629	−	1.54608i
$894$		0			0
$895$	−26.2943	+	45.5431i	−0.878923	+	1.52234i
$896$		0			0
$897$	−2.57425	+	1.04167i	−0.0859516	+	0.0347802i
$898$		0			0
$899$	−12.3389	−	21.3716i	−0.411526	−	0.712783i
$900$		0			0
$901$	14.3071	+	8.26022i	0.476640	+	0.275188i
$902$		0			0
$903$	40.5094	+	23.7955i	1.34807	+	0.791864i
$904$		0			0
$905$	7.48255	+	12.9602i	0.248728	+	0.430810i
$906$		0			0
$907$	−19.4236	−	11.2142i	−0.644949	−	0.372361i	0.141570	−	0.989928i	$-0.454785\pi$
$907$	−19.4236	−	11.2142i	−0.644949	−	0.372361i	−0.786518	+	0.617567i	$0.788118\pi$
$908$		0			0
$909$	5.99802	−	1.50230i	0.198942	−	0.0498280i
$910$		0			0
$911$	−22.0594	+	12.7360i	−0.730861	+	0.421963i	−0.818737	−	0.574168i	$-0.805325\pi$
$911$	−22.0594	+	12.7360i	−0.730861	+	0.421963i	0.0878758	+	0.996131i	$0.471992\pi$
$912$		0			0
$913$		−	5.90396i		−	0.195392i
$914$		0			0
$915$	17.6440	+	13.7698i	0.583294	+	0.455217i
$916$		0			0
$917$	35.5991	−	27.3547i	1.17559	−	0.903332i
$918$		0			0
$919$	20.8803	+	12.0553i	0.688779	+	0.397666i	0.803154	−	0.595771i	$-0.203153\pi$
$919$	20.8803	+	12.0553i	0.688779	+	0.397666i	−0.114376	+	0.993438i	$0.536487\pi$
$920$		0			0
$921$	1.09187	−	0.441824i	0.0359783	−	0.0145586i
$922$		0			0
$923$	0.364812	−	0.631873i	0.0120079	−	0.0207984i
$924$		0			0
$925$	−0.423685	−	0.733844i	−0.0139307	−	0.0241287i
$926$		0			0
$927$	−16.9162	−	4.83105i	−0.555601	−	0.158673i
$928$		0			0
$929$			7.13159i			0.233980i	0.993133	+	0.116990i	$0.0373245\pi$
$929$			7.13159i			0.233980i	−0.993133	+	0.116990i	$0.962675\pi$
$930$		0			0
$931$	11.4554	−	42.9866i	0.375436	−	1.40883i
$932$		0			0
$933$	−11.8889	+	4.81082i	−0.389224	+	0.157499i
$934$		0			0
$935$	15.8770	−	9.16658i	0.519233	−	0.299779i
$936$		0			0
$937$		−	0.272222i		−	0.00889310i	−0.999990	−	0.00444655i	$-0.998585\pi$
$937$		−	0.272222i		−	0.00889310i	0.999990	−	0.00444655i	$-0.00141539\pi$
$938$		0			0
$939$	−0.496573	−	1.22717i	−0.0162051	−	0.0400472i
$940$		0			0
$941$			38.9456i			1.26959i	0.772680	+	0.634795i	$0.218916\pi$
$941$			38.9456i			1.26959i	−0.772680	+	0.634795i	$0.781084\pi$
$942$		0			0
$943$	−36.7915			−1.19810
$944$		0			0
$945$	32.4909	−	7.87902i	1.05693	−	0.256305i
$946$		0			0
$947$		−	23.6886i		−	0.769775i	−0.922964	−	0.384887i	$-0.874240\pi$
$947$		−	23.6886i		−	0.769775i	0.922964	−	0.384887i	$-0.125760\pi$
$948$		0			0
$949$	4.91695			0.159611
$950$		0			0
$951$	44.1745	−	17.8752i	1.43246	−	0.579642i
$952$		0			0
$953$	43.1882			1.39900			0.699501	−	0.714631i	$-0.253406\pi$
$953$	43.1882			1.39900			0.699501	+	0.714631i	$0.253406\pi$
$954$		0			0
$955$	−1.16641	−	2.02028i	−0.0377441	−	0.0653746i
$956$		0			0
$957$	8.06477	+	19.9303i	0.260697	+	0.644255i
$958$		0			0
$959$	11.0227	+	4.55693i	0.355940	+	0.147151i
$960$		0			0
$961$	48.6681			1.56994
$962$		0			0
$963$	2.00887	−	0.503153i	0.0647350	−	0.0162139i
$964$		0			0
$965$	−20.4966	+	11.8337i	−0.659810	+	0.380942i
$966$		0			0
$967$	11.0764	+	6.39497i	0.356193	+	0.205648i	0.667410	−	0.744691i	$-0.267403\pi$
$967$	11.0764	+	6.39497i	0.356193	+	0.205648i	−0.311216	+	0.950339i	$0.600736\pi$
$968$		0			0
$969$	6.93306	+	17.1335i	0.222722	+	0.550408i
$970$		0			0
$971$	2.52582	−	4.37484i	0.0810573	−	0.140395i	−0.822647	−	0.568552i	$-0.807504\pi$
$971$	2.52582	−	4.37484i	0.0810573	−	0.140395i	0.903704	+	0.428157i	$0.140837\pi$
$972$		0			0
$973$	−6.43674	−	2.66104i	−0.206352	−	0.0853092i
$974$		0			0
$975$	−0.445021	+	0.570230i	−0.0142521	+	0.0182620i
$976$		0			0
$977$	11.4724			0.367034			0.183517	−	0.983016i	$-0.441252\pi$
$977$	11.4724			0.367034			0.183517	+	0.983016i	$0.441252\pi$
$978$		0			0
$979$	35.0356	+	60.6834i	1.11974	+	1.93945i
$980$		0			0
$981$	15.7007	+	4.48391i	0.501284	+	0.143160i
$982$		0			0
$983$	21.2544	−	36.8137i	0.677910	−	1.17417i	−0.297699	−	0.954660i	$-0.596219\pi$
$983$	21.2544	−	36.8137i	0.677910	−	1.17417i	0.975609	−	0.219515i	$-0.0704474\pi$
$984$		0			0
$985$	−14.0680	+	8.12219i	−0.448245	+	0.258794i
$986$		0			0
$987$	18.9835	+	33.4581i	0.604250	+	1.06498i
$988$		0			0
$989$	−17.9866	+	31.1538i	−0.571941	+	0.990632i
$990$		0			0
$991$	8.80965	−	5.08625i	0.279848	−	0.161570i	−0.353507	−	0.935432i	$-0.615011\pi$
$991$	8.80965	−	5.08625i	0.279848	−	0.161570i	0.633355	+	0.773862i	$0.281678\pi$
$992$		0			0
$993$	5.45935	+	13.4916i	0.173247	+	0.428142i
$994$		0			0
$995$	−33.3838	−	19.2741i	−1.05834	−	0.611031i
$996$		0			0
$997$	−1.21975	−	0.704225i	−0.0386300	−	0.0223030i	0.480561	−	0.876961i	$-0.340433\pi$
$997$	−1.21975	−	0.704225i	−0.0386300	−	0.0223030i	−0.519191	+	0.854658i	$0.673767\pi$
$998$		0			0
$999$	2.83798	+	3.89298i	0.0897896	+	0.123168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.607.3	yes	24
3.2	odd	2		3024.2.cz.h.1279.10		24
4.3	odd	2		1008.2.cz.h.607.10	yes	24
7.3	odd	6		1008.2.bf.g.31.3	✓	24
9.2	odd	6		3024.2.bf.g.2287.10		24
9.7	even	3		1008.2.bf.h.943.10	yes	24
12.11	even	2		3024.2.cz.g.1279.10		24
21.17	even	6		3024.2.bf.h.1711.3		24
28.3	even	6		1008.2.bf.h.31.10	yes	24
36.7	odd	6		1008.2.bf.g.943.3	yes	24
36.11	even	6		3024.2.bf.h.2287.10		24
63.38	even	6		3024.2.cz.g.2719.10		24
63.52	odd	6		1008.2.cz.h.367.10	yes	24
84.59	odd	6		3024.2.bf.g.1711.3		24
252.115	even	6	inner	1008.2.cz.g.367.3	yes	24
252.227	odd	6		3024.2.cz.h.2719.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.3	✓	24	7.3	odd	6
1008.2.bf.g.943.3	yes	24	36.7	odd	6
1008.2.bf.h.31.10	yes	24	28.3	even	6
1008.2.bf.h.943.10	yes	24	9.7	even	3
1008.2.cz.g.367.3	yes	24	252.115	even	6	inner
1008.2.cz.g.607.3	yes	24	1.1	even	1	trivial
1008.2.cz.h.367.10	yes	24	63.52	odd	6
1008.2.cz.h.607.10	yes	24	4.3	odd	2
3024.2.bf.g.1711.3		24	84.59	odd	6
3024.2.bf.g.2287.10		24	9.2	odd	6
3024.2.bf.h.1711.3		24	21.17	even	6
3024.2.bf.h.2287.10		24	36.11	even	6
3024.2.cz.g.1279.10		24	12.11	even	2
3024.2.cz.g.2719.10		24	63.38	even	6
3024.2.cz.h.1279.10		24	3.2	odd	2
3024.2.cz.h.2719.10		24	252.227	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.60558 + 0.649697i) q^{3} +(-2.10605 + 1.21593i) q^{5} +(0.347128 + 2.62288i) q^{7} +(2.15579 - 2.08628i) q^{9} +O(q^{10})\)	\(q+(-1.60558 + 0.649697i) q^{3} +(-2.10605 + 1.21593i) q^{5} +(0.347128 + 2.62288i) q^{7} +(2.15579 - 2.08628i) q^{9} +(3.88819 + 2.24485i) q^{11} +(0.395715 + 0.228466i) q^{13} +(2.59146 - 3.32057i) q^{15} +(-1.45416 + 0.839559i) q^{17} +(-3.17762 + 5.50381i) q^{19} +(-2.26142 - 3.98572i) q^{21} +(3.03876 - 1.75443i) q^{23} +(0.456976 - 0.791506i) q^{25} +(-2.10584 + 4.75031i) q^{27} +(-1.38240 - 2.39439i) q^{29} +8.92570 q^{31} +(-7.70128 - 1.07814i) q^{33} +(-3.92031 - 5.10184i) q^{35} +(0.463575 - 0.802935i) q^{37} +(-0.783788 - 0.109726i) q^{39} +(-9.08056 - 5.24267i) q^{41} +(-8.87861 + 5.12607i) q^{43} +(-2.00343 + 7.01512i) q^{45} -8.39449 q^{47} +(-6.75900 + 1.82095i) q^{49} +(1.78931 - 2.29274i) q^{51} +(-4.91938 - 8.52062i) q^{53} -10.9183 q^{55} +(1.52613 - 10.9013i) q^{57} -6.45074 q^{59} +5.31355i q^{61} +(6.22041 + 4.93016i) q^{63} -1.11120 q^{65} +13.6441i q^{67} +(-3.73913 + 4.79115i) q^{69} -1.59679i q^{71} +(9.31911 - 5.38039i) q^{73} +(-0.219473 + 1.56772i) q^{75} +(-4.53827 + 10.9775i) q^{77} -10.3204i q^{79} +(0.294837 - 8.99517i) q^{81} +(-0.657501 - 1.13882i) q^{83} +(2.04169 - 3.53632i) q^{85} +(3.77519 + 2.94625i) q^{87} +(13.5161 + 7.80355i) q^{89} +(-0.461876 + 1.11722i) q^{91} +(-14.3309 + 5.79900i) q^{93} -15.4551i q^{95} +(-5.69780 + 3.28963i) q^{97} +(13.0655 - 3.27246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) \) 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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