LMFDB - Embedded newform 756.2.ck.a.605.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			605.2
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69135 - 0.373296i) q^{3} +(-0.203680 - 1.15512i) q^{5} +(2.02312 - 1.70498i) q^{7} +(2.72130 + 1.26275i) q^{9} +O(q^{10})$	\(q+(-1.69135 - 0.373296i) q^{3} +(-0.203680 - 1.15512i) q^{5} +(2.02312 - 1.70498i) q^{7} +(2.72130 + 1.26275i) q^{9} +(3.15137 + 0.555671i) q^{11} +(-1.12364 - 1.33911i) q^{13} +(-0.0867108 + 2.02975i) q^{15} -3.16451 q^{17} +6.65556i q^{19} +(-4.05827 + 2.12849i) q^{21} +(-3.65594 - 4.35698i) q^{23} +(3.40564 - 1.23955i) q^{25} +(-4.13128 - 3.15159i) q^{27} +(3.84940 - 4.58754i) q^{29} +(1.52309 - 4.18464i) q^{31} +(-5.12262 - 2.11622i) q^{33} +(-2.38154 - 1.98969i) q^{35} +(4.75241 - 8.23142i) q^{37} +(1.40059 + 2.68434i) q^{39} +(7.74888 - 6.50209i) q^{41} +(3.80179 - 1.38374i) q^{43} +(0.904355 - 3.40063i) q^{45} +(-7.95967 + 2.89708i) q^{47} +(1.18606 - 6.89879i) q^{49} +(5.35228 + 1.18130i) q^{51} +(-11.7526 - 6.78537i) q^{53} -3.75340i q^{55} +(2.48449 - 11.2568i) q^{57} +(-8.39859 + 7.04726i) q^{59} +(-0.888063 - 2.43993i) q^{61} +(7.65849 - 2.08508i) q^{63} +(-1.31797 + 1.57070i) q^{65} +(2.66559 + 15.1173i) q^{67} +(4.55701 + 8.73390i) q^{69} +(2.08522 - 1.20391i) q^{71} +(1.01078 - 0.583575i) q^{73} +(-6.22283 + 0.825197i) q^{75} +(7.32301 - 4.24883i) q^{77} +(1.74259 - 9.88269i) q^{79} +(5.81095 + 6.87262i) q^{81} +(-5.29556 - 4.44350i) q^{83} +(0.644546 + 3.65540i) q^{85} +(-8.22318 + 6.32215i) q^{87} +11.4908 q^{89} +(-4.55643 - 0.793385i) q^{91} +(-4.13817 + 6.50912i) q^{93} +(7.68800 - 1.35560i) q^{95} +(-0.0688894 - 0.189272i) q^{97} +(7.87414 + 5.49152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−1.69135	−	0.373296i	−0.976499	−	0.215523i
$3$	−1.69135	−	0.373296i	−0.976499	−	0.215523i
$4$		0			0
$5$	−0.203680	−	1.15512i	−0.0910883	−	0.516587i	−0.995876	−	0.0907245i	$-0.971082\pi$
$5$	−0.203680	−	1.15512i	−0.0910883	−	0.516587i	0.904788	−	0.425863i	$-0.140029\pi$
$6$		0			0
$7$	2.02312	−	1.70498i	0.764669	−	0.644423i
$7$	2.02312	−	1.70498i	0.764669	−	0.644423i
$8$		0			0
$9$	2.72130	+	1.26275i	0.907100	+	0.420915i
$10$		0			0
$11$	3.15137	+	0.555671i	0.950172	+	0.167541i	0.627192	−	0.778865i	$-0.284204\pi$
$11$	3.15137	+	0.555671i	0.950172	+	0.167541i	0.322980	+	0.946406i	$0.395315\pi$
$12$		0			0
$13$	−1.12364	−	1.33911i	−0.311643	−	0.371401i	0.587374	−	0.809316i	$-0.300162\pi$
$13$	−1.12364	−	1.33911i	−0.311643	−	0.371401i	−0.899017	+	0.437914i	$0.855717\pi$
$14$		0			0
$15$	−0.0867108	+	2.02975i	−0.0223886	+	0.524078i
$16$		0			0
$17$	−3.16451			−0.767506			−0.383753	−	0.923436i	$-0.625369\pi$
$17$	−3.16451			−0.767506			−0.383753	+	0.923436i	$0.625369\pi$
$18$		0			0
$19$			6.65556i			1.52689i	0.645873	+	0.763445i	$0.276494\pi$
$19$			6.65556i			1.52689i	−0.645873	+	0.763445i	$0.723506\pi$
$20$		0			0
$21$	−4.05827	+	2.12849i	−0.885586	+	0.464475i
$22$		0			0
$23$	−3.65594	−	4.35698i	−0.762315	−	0.908492i	0.235677	−	0.971832i	$-0.424269\pi$
$23$	−3.65594	−	4.35698i	−0.762315	−	0.908492i	−0.997992	+	0.0633394i	$0.979825\pi$
$24$		0			0
$25$	3.40564	−	1.23955i	0.681127	−	0.247910i
$26$		0			0
$27$	−4.13128	−	3.15159i	−0.795065	−	0.606524i
$28$		0			0
$29$	3.84940	−	4.58754i	0.714816	−	0.851885i	−0.279300	−	0.960204i	$-0.590102\pi$
$29$	3.84940	−	4.58754i	0.714816	−	0.851885i	0.994116	+	0.108319i	$0.0345467\pi$
$30$		0			0
$31$	1.52309	−	4.18464i	0.273554	−	0.751584i	−0.724502	−	0.689272i	$-0.757930\pi$
$31$	1.52309	−	4.18464i	0.273554	−	0.751584i	0.998057	−	0.0623119i	$-0.0198474\pi$
$32$		0			0
$33$	−5.12262	−	2.11622i	−0.891733	−	0.368387i
$34$		0			0
$35$	−2.38154	−	1.98969i	−0.402553	−	0.336319i
$36$		0			0
$37$	4.75241	−	8.23142i	0.781292	−	1.35324i	−0.149898	−	0.988702i	$-0.547894\pi$
$37$	4.75241	−	8.23142i	0.781292	−	1.35324i	0.931189	−	0.364535i	$-0.118772\pi$
$38$		0			0
$39$	1.40059	+	2.68434i	0.224273	+	0.429839i
$40$		0			0
$41$	7.74888	−	6.50209i	1.21017	−	1.01546i	0.210893	−	0.977509i	$-0.432363\pi$
$41$	7.74888	−	6.50209i	1.21017	−	1.01546i	0.999280	−	0.0379460i	$-0.0120815\pi$
$42$		0			0
$43$	3.80179	−	1.38374i	0.579768	−	0.211018i	−0.0354555	−	0.999371i	$-0.511288\pi$
$43$	3.80179	−	1.38374i	0.579768	−	0.211018i	0.615223	+	0.788353i	$0.289066\pi$
$44$		0			0
$45$	0.904355	−	3.40063i	0.134813	−	0.506937i
$46$		0			0
$47$	−7.95967	+	2.89708i	−1.16104	+	0.422583i	−0.849468	−	0.527641i	$-0.823077\pi$
$47$	−7.95967	+	2.89708i	−1.16104	+	0.422583i	−0.311569	+	0.950224i	$0.600855\pi$
$48$		0			0
$49$	1.18606	−	6.89879i	0.169438	−	0.985541i
$50$		0			0
$51$	5.35228	+	1.18130i	0.749469	+	0.165415i
$52$		0			0
$53$	−11.7526	−	6.78537i	−1.61434	−	0.932042i	−0.988347	−	0.152215i	$-0.951359\pi$
$53$	−11.7526	−	6.78537i	−1.61434	−	0.932042i	−0.625996	−	0.779826i	$-0.715307\pi$
$54$		0			0
$55$		−	3.75340i		−	0.506108i
$56$		0			0
$57$	2.48449	−	11.2568i	0.329079	−	1.49101i
$58$		0			0
$59$	−8.39859	+	7.04726i	−1.09340	+	0.917475i	−0.996964	−	0.0778642i	$-0.975190\pi$
$59$	−8.39859	+	7.04726i	−1.09340	+	0.917475i	−0.0964398	+	0.995339i	$0.530746\pi$
$60$		0			0
$61$	−0.888063	−	2.43993i	−0.113705	−	0.312402i	0.869767	−	0.493463i	$-0.164269\pi$
$61$	−0.888063	−	2.43993i	−0.113705	−	0.312402i	−0.983472	+	0.181061i	$0.942047\pi$
$62$		0			0
$63$	7.65849	−	2.08508i	0.964879	−	0.262695i
$64$		0			0
$65$	−1.31797	+	1.57070i	−0.163474	+	0.194821i
$66$		0			0
$67$	2.66559	+	15.1173i	0.325654	+	1.84688i	0.505039	+	0.863096i	$0.331478\pi$
$67$	2.66559	+	15.1173i	0.325654	+	1.84688i	−0.179385	+	0.983779i	$0.557411\pi$
$68$		0			0
$69$	4.55701	+	8.73390i	0.548600	+	1.05144i
$70$		0			0
$71$	2.08522	−	1.20391i	0.247471	−	0.142877i	−0.371135	−	0.928579i	$-0.621031\pi$
$71$	2.08522	−	1.20391i	0.247471	−	0.142877i	0.618606	+	0.785702i	$0.287698\pi$
$72$		0			0
$73$	1.01078	−	0.583575i	0.118303	−	0.0683023i	−0.439681	−	0.898154i	$-0.644908\pi$
$73$	1.01078	−	0.583575i	0.118303	−	0.0683023i	0.557984	+	0.829852i	$0.311575\pi$
$74$		0			0
$75$	−6.22283	+	0.825197i	−0.718550	+	0.0952856i
$76$		0			0
$77$	7.32301	−	4.24883i	0.834535	−	0.484200i
$78$		0			0
$79$	1.74259	−	9.88269i	0.196056	−	1.11189i	−0.714851	−	0.699277i	$-0.753505\pi$
$79$	1.74259	−	9.88269i	0.196056	−	1.11189i	0.910907	−	0.412612i	$-0.135384\pi$
$80$		0			0
$81$	5.81095	+	6.87262i	0.645661	+	0.763624i
$82$		0			0
$83$	−5.29556	−	4.44350i	−0.581263	−	0.487738i	0.304098	−	0.952641i	$-0.401645\pi$
$83$	−5.29556	−	4.44350i	−0.581263	−	0.487738i	−0.885362	+	0.464903i	$0.846089\pi$
$84$		0			0
$85$	0.644546	+	3.65540i	0.0699108	+	0.396484i
$86$		0			0
$87$	−8.22318	+	6.32215i	−0.881618	+	0.677806i
$88$		0			0
$89$	11.4908			1.21802			0.609011	−	0.793161i	$-0.291566\pi$
$89$	11.4908			1.21802			0.609011	+	0.793161i	$0.291566\pi$
$90$		0			0
$91$	−4.55643	−	0.793385i	−0.477643	−	0.0831693i
$92$		0			0
$93$	−4.13817	+	6.50912i	−0.429109	+	0.674964i
$94$		0			0
$95$	7.68800	−	1.35560i	0.788772	−	0.139082i
$96$		0			0
$97$	−0.0688894	−	0.189272i	−0.00699466	−	0.0192177i	0.936146	−	0.351611i	$-0.114366\pi$
$97$	−0.0688894	−	0.189272i	−0.00699466	−	0.0192177i	−0.943141	+	0.332393i	$0.892144\pi$
$98$		0			0
$99$	7.87414	+	5.49152i	0.791381	+	0.551918i
$100$		0			0
$101$	−4.44873	−	3.73293i	−0.442666	−	0.371441i	0.394040	−	0.919093i	$-0.371077\pi$
$101$	−4.44873	−	3.73293i	−0.442666	−	0.371441i	−0.836706	+	0.547653i	$0.815522\pi$
$102$		0			0
$103$	5.21603	−	0.919726i	0.513950	−	0.0906233i	0.0893431	−	0.996001i	$-0.471523\pi$
$103$	5.21603	−	0.919726i	0.513950	−	0.0906233i	0.424607	+	0.905378i	$0.360412\pi$
$104$		0			0
$105$	3.28526	+	4.25427i	0.320608	+	0.415174i
$106$		0			0
$107$	−8.16755	+	4.71554i	−0.789587	+	0.455868i	−0.839817	−	0.542870i	$-0.817338\pi$
$107$	−8.16755	+	4.71554i	−0.789587	+	0.455868i	0.0502303	+	0.998738i	$0.484004\pi$
$108$		0			0
$109$	−8.19677	+	14.1972i	−0.785108	+	1.35985i	0.143826	+	0.989603i	$0.454059\pi$
$109$	−8.19677	+	14.1972i	−0.785108	+	1.35985i	−0.928934	+	0.370244i	$0.879274\pi$
$110$		0			0
$111$	−11.1107	+	12.1481i	−1.05458	+	1.15305i
$112$		0			0
$113$	2.80986	−	7.72002i	0.264329	−	0.726238i	−0.734534	−	0.678572i	$-0.762599\pi$
$113$	2.80986	−	7.72002i	0.264329	−	0.726238i	0.998863	−	0.0476665i	$-0.0151785\pi$
$114$		0			0
$115$	−4.28821	+	5.11049i	−0.399877	+	0.476555i
$116$		0			0
$117$	−1.36682	−	5.06299i	−0.126363	−	0.468073i
$118$		0			0
$119$	−6.40220	+	5.39544i	−0.586888	+	0.494599i
$120$		0			0
$121$	−0.714285	−	0.259978i	−0.0649350	−	0.0236344i
$122$		0			0
$123$	−15.5332	+	8.10465i	−1.40059	+	0.730771i
$124$		0			0
$125$	−5.05785	−	8.76046i	−0.452388	−	0.783559i
$126$		0			0
$127$	2.19382	−	3.79980i	0.194670	−	0.337178i	−0.752123	−	0.659023i	$-0.770970\pi$
$127$	2.19382	−	3.79980i	0.194670	−	0.337178i	0.946792	+	0.321846i	$0.104303\pi$
$128$		0			0
$129$	−6.94668	+	0.921186i	−0.611621	+	0.0811059i
$130$		0			0
$131$	7.95915	−	6.67852i	0.695395	−	0.583505i	−0.225065	−	0.974344i	$-0.572259\pi$
$131$	7.95915	−	6.67852i	0.695395	−	0.583505i	0.920459	+	0.390839i	$0.127815\pi$
$132$		0			0
$133$	11.3476	+	13.4650i	0.983963	+	1.16757i
$134$		0			0
$135$	−2.79902	+	5.41406i	−0.240901	+	0.465968i
$136$		0			0
$137$	2.88034	+	7.91366i	0.246084	+	0.676109i	0.999821	+	0.0189333i	$0.00602702\pi$
$137$	2.88034	+	7.91366i	0.246084	+	0.676109i	−0.753737	+	0.657176i	$0.771751\pi$
$138$		0			0
$139$	17.3552	−	3.06020i	1.47205	−	0.259563i	0.620655	−	0.784083i	$-0.286867\pi$
$139$	17.3552	−	3.06020i	1.47205	−	0.259563i	0.851398	+	0.524521i	$0.175755\pi$
$140$		0			0
$141$	14.5440	−	1.92865i	1.22483	−	0.162422i
$142$		0			0
$143$	−2.79691	−	4.84439i	−0.233889	−	0.405108i
$144$		0			0
$145$	−6.08323	−	3.51215i	−0.505184	−	0.291668i
$146$		0			0
$147$	−4.58133	+	11.2255i	−0.377862	+	0.925862i
$148$		0			0
$149$	−6.37048	+	17.5027i	−0.521890	+	1.43388i	0.346524	+	0.938041i	$0.387362\pi$
$149$	−6.37048	+	17.5027i	−0.521890	+	1.43388i	−0.868414	+	0.495840i	$0.834860\pi$
$150$		0			0
$151$	1.11679	−	6.33365i	0.0908834	−	0.515425i	−0.905048	−	0.425310i	$-0.860165\pi$
$151$	1.11679	−	6.33365i	0.0908834	−	0.515425i	0.995931	−	0.0901156i	$-0.0287236\pi$
$152$		0			0
$153$	−8.61158	−	3.99597i	−0.696205	−	0.323055i
$154$		0			0
$155$	−5.14400	−	0.907027i	−0.413176	−	0.0728541i
$156$		0			0
$157$	2.53024	+	3.01542i	0.201935	+	0.240657i	0.857503	−	0.514480i	$-0.172015\pi$
$157$	2.53024	+	3.01542i	0.201935	+	0.240657i	−0.655567	+	0.755137i	$0.727570\pi$
$158$		0			0
$159$	17.3448	+	15.8636i	1.37553	+	1.25807i
$160$		0			0
$161$	−14.8250	−	2.58139i	−1.16837	−	0.203442i
$162$		0			0
$163$	12.2039	+	21.1378i	0.955882	+	1.65564i	0.732336	+	0.680944i	$0.238430\pi$
$163$	12.2039	+	21.1378i	0.955882	+	1.65564i	0.223547	+	0.974693i	$0.428237\pi$
$164$		0			0
$165$	−1.40113	+	6.34829i	−0.109078	+	0.494214i
$166$		0			0
$167$	3.10807	+	1.13125i	0.240510	+	0.0875384i	0.459463	−	0.888197i	$-0.348042\pi$
$167$	3.10807	+	1.13125i	0.240510	+	0.0875384i	−0.218953	+	0.975735i	$0.570264\pi$
$168$		0			0
$169$	1.72680	−	9.79314i	0.132830	−	0.753319i
$170$		0			0
$171$	−8.40428	+	18.1118i	−0.642691	+	1.38504i
$172$		0			0
$173$	5.12258	+	4.29835i	0.389462	+	0.326798i	0.816404	−	0.577482i	$-0.195964\pi$
$173$	5.12258	+	4.29835i	0.389462	+	0.326798i	−0.426941	+	0.904279i	$0.640409\pi$
$174$		0			0
$175$	4.77661	−	8.31432i	0.361078	−	0.628503i
$176$		0			0
$177$	16.8356	−	8.78418i	1.26544	−	0.660260i
$178$		0			0
$179$			6.24539i			0.466803i	0.972380	+	0.233401i	$0.0749856\pi$
$179$			6.24539i			0.466803i	−0.972380	+	0.233401i	$0.925014\pi$
$180$		0			0
$181$	0.630501	+	0.364020i	0.0468648	+	0.0270574i	0.523249	−	0.852180i	$-0.324720\pi$
$181$	0.630501	+	0.364020i	0.0468648	+	0.0270574i	−0.476385	+	0.879237i	$0.658053\pi$
$182$		0			0
$183$	0.591204	+	4.45828i	0.0437031	+	0.329566i
$184$		0			0
$185$	−10.4763	−	3.81305i	−0.770231	−	0.280341i
$186$		0			0
$187$	−9.97253	−	1.75843i	−0.729263	−	0.128589i
$188$		0			0
$189$	−13.7315	+	0.667708i	−0.998820	+	0.0485686i
$190$		0			0
$191$	−2.44587	−	0.431272i	−0.176977	−	0.0312058i	0.0844574	−	0.996427i	$-0.473084\pi$
$191$	−2.44587	−	0.431272i	−0.176977	−	0.0312058i	−0.261434	+	0.965221i	$0.584195\pi$
$192$		0			0
$193$	16.7694	+	6.10356i	1.20709	+	0.439344i	0.865693	−	0.500576i	$-0.166878\pi$
$193$	16.7694	+	6.10356i	1.20709	+	0.439344i	0.341395	+	0.939920i	$0.389101\pi$
$194$		0			0
$195$	2.81548	−	2.16460i	0.201621	−	0.155010i
$196$		0			0
$197$	−4.49176	−	2.59332i	−0.320025	−	0.184766i	0.331379	−	0.943498i	$-0.392486\pi$
$197$	−4.49176	−	2.59332i	−0.320025	−	0.184766i	−0.651404	+	0.758731i	$0.725820\pi$
$198$		0			0
$199$			21.3548i			1.51380i	0.653531	+	0.756900i	$0.273287\pi$
$199$			21.3548i			1.51380i	−0.653531	+	0.756900i	$0.726713\pi$
$200$		0			0
$201$	1.13480	−	26.5637i	0.0800427	−	1.87366i
$202$		0			0
$203$	−0.0338585	−	15.8443i	−0.00237640	−	1.11205i
$204$		0			0
$205$	−9.08901	−	7.62658i	−0.634804	−	0.532664i
$206$		0			0
$207$	−4.44715	−	16.4732i	−0.309098	−	1.14496i
$208$		0			0
$209$	−3.69830	+	20.9741i	−0.255817	+	1.45081i
$210$		0			0
$211$	15.7930	+	5.74820i	1.08724	+	0.395722i	0.822597	−	0.568625i	$-0.192524\pi$
$211$	15.7930	+	5.74820i	1.08724	+	0.395722i	0.264641	+	0.964347i	$0.414747\pi$
$212$		0			0
$213$	−3.97625	+	1.25781i	−0.272448	+	0.0861839i
$214$		0			0
$215$	−2.37274	−	4.10970i	−0.161819	−	0.280279i
$216$		0			0
$217$	−4.05336	−	11.0629i	−0.275160	−	0.750998i
$218$		0			0
$219$	−1.92743	+	0.609706i	−0.130243	+	0.0412001i
$220$		0			0
$221$	3.55578	+	4.23762i	0.239188	+	0.285053i
$222$		0			0
$223$	0.0697119	+	0.0122921i	0.00466825	+	0.000823139i	0.175982	−	0.984393i	$-0.443690\pi$
$223$	0.0697119	+	0.0122921i	0.00466825	+	0.000823139i	−0.171314	+	0.985217i	$0.554801\pi$
$224$		0			0
$225$	10.8330	+	0.927264i	0.722200	+	0.0618176i
$226$		0			0
$227$	1.52723	−	8.66137i	0.101366	−	0.574876i	−0.891244	−	0.453525i	$-0.850166\pi$
$227$	1.52723	−	8.66137i	0.101366	−	0.574876i	0.992610	−	0.121351i	$-0.0387226\pi$
$228$		0			0
$229$	−7.04568	+	19.3578i	−0.465591	+	1.27920i	0.455632	+	0.890168i	$0.349413\pi$
$229$	−7.04568	+	19.3578i	−0.465591	+	1.27920i	−0.921224	+	0.389034i	$0.872809\pi$
$230$		0			0
$231$	−13.9718	+	4.45260i	−0.919278	+	0.292959i
$232$		0			0
$233$	9.43506	+	5.44734i	0.618111	+	0.356867i	0.776133	−	0.630569i	$-0.217178\pi$
$233$	9.43506	+	5.44734i	0.618111	+	0.356867i	−0.158022	+	0.987436i	$0.550512\pi$
$234$		0			0
$235$	4.96771	+	8.60433i	0.324058	+	0.561284i
$236$		0			0
$237$	−6.63648	+	16.0645i	−0.431086	+	1.04350i
$238$		0			0
$239$	4.63739	−	0.817697i	0.299968	−	0.0528924i	−0.0216386	−	0.999766i	$-0.506888\pi$
$239$	4.63739	−	0.817697i	0.299968	−	0.0528924i	0.321606	+	0.946873i	$0.395777\pi$
$240$		0			0
$241$	−6.76085	−	18.5753i	−0.435505	−	1.19654i	−0.942387	−	0.334524i	$-0.891424\pi$
$241$	−6.76085	−	18.5753i	−0.435505	−	1.19654i	0.506882	−	0.862015i	$-0.330798\pi$
$242$		0			0
$243$	−7.26280	−	13.7932i	−0.465909	−	0.884833i
$244$		0			0
$245$	−8.21053	+	0.0350911i	−0.524552	+	0.00224189i
$246$		0			0
$247$	8.91250	−	7.47848i	0.567089	−	0.475844i
$248$		0			0
$249$	7.29788	+	9.49231i	0.462484	+	0.601551i
$250$		0			0
$251$	4.08899	−	7.08234i	0.258095	−	0.447033i	−0.707637	−	0.706576i	$-0.750239\pi$
$251$	4.08899	−	7.08234i	0.258095	−	0.447033i	0.965731	+	0.259543i	$0.0835720\pi$
$252$		0			0
$253$	−9.10015	−	15.7619i	−0.572121	−	0.990943i
$254$		0			0
$255$	0.274397	−	6.42315i	0.0171834	−	0.402234i
$256$		0			0
$257$	18.2251	+	6.63338i	1.13685	+	0.413779i	0.840774	−	0.541387i	$-0.182100\pi$
$257$	18.2251	+	6.63338i	1.13685	+	0.413779i	0.296074	+	0.955165i	$0.404323\pi$
$258$		0			0
$259$	−4.41971	−	24.7560i	−0.274628	−	1.53826i
$260$		0			0
$261$	16.2683	−	7.62326i	1.00698	−	0.471868i
$262$		0			0
$263$	−6.79618	+	8.09938i	−0.419071	+	0.499429i	−0.933736	−	0.357962i	$-0.883472\pi$
$263$	−6.79618	+	8.09938i	−0.419071	+	0.499429i	0.514665	+	0.857391i	$0.327916\pi$
$264$		0			0
$265$	−5.44418	+	14.9577i	−0.334433	+	0.918847i
$266$		0			0
$267$	−19.4349	−	4.28947i	−1.18940	−	0.262511i
$268$		0			0
$269$	1.21301	−	2.10099i	0.0739585	−	0.128100i	−0.826674	−	0.562681i	$-0.809770\pi$
$269$	1.21301	−	2.10099i	0.0739585	−	0.128100i	0.900633	+	0.434581i	$0.143103\pi$
$270$		0			0
$271$	−13.7260	+	7.92468i	−0.833792	+	0.481390i	−0.855149	−	0.518382i	$-0.826535\pi$
$271$	−13.7260	+	7.92468i	−0.833792	+	0.481390i	0.0213570	+	0.999772i	$0.493201\pi$
$272$		0			0
$273$	7.41032	+	3.04278i	0.448493	+	0.184158i
$274$		0			0
$275$	11.4212	−	2.01386i	0.688724	−	0.121441i
$276$		0			0
$277$	−5.08767	−	4.26906i	−0.305688	−	0.256503i	0.477019	−	0.878893i	$-0.341717\pi$
$277$	−5.08767	−	4.26906i	−0.305688	−	0.256503i	−0.782707	+	0.622390i	$0.786162\pi$
$278$		0			0
$279$	9.42891	−	9.46440i	0.564494	−	0.566619i
$280$		0			0
$281$	5.25557	+	14.4396i	0.313521	+	0.861392i	0.991939	+	0.126716i	$0.0404436\pi$
$281$	5.25557	+	14.4396i	0.313521	+	0.861392i	−0.678418	+	0.734676i	$0.737334\pi$
$282$		0			0
$283$	−2.48443	+	0.438073i	−0.147684	+	0.0260407i	−0.247001	−	0.969015i	$-0.579445\pi$
$283$	−2.48443	+	0.438073i	−0.147684	+	0.0260407i	0.0993172	+	0.995056i	$0.468334\pi$
$284$		0			0
$285$	−13.5091	−	0.577109i	−0.800210	−	0.0341850i
$286$		0			0
$287$	4.59101	−	26.3662i	0.270999	−	1.55635i
$288$		0			0
$289$	−6.98588			−0.410934
$290$		0			0
$291$	0.0458612	+	0.345840i	0.00268843	+	0.0202735i
$292$		0			0
$293$	0.425049	+	2.41057i	0.0248316	+	0.140827i	0.994703	−	0.102790i	$-0.0327770\pi$
$293$	0.425049	+	2.41057i	0.0248316	+	0.140827i	−0.969871	+	0.243617i	$0.921666\pi$
$294$		0			0
$295$	9.85108	+	8.26604i	0.573552	+	0.481267i
$296$		0			0
$297$	−11.2679	−	12.2274i	−0.653832	−	0.709508i
$298$		0			0
$299$	−1.72648	+	9.79138i	−0.0998451	+	0.566250i
$300$		0			0
$301$	5.33224	−	9.28146i	0.307345	−	0.534975i
$302$		0			0
$303$	6.13086	+	7.97437i	0.352209	+	0.458116i
$304$		0			0
$305$	−2.63755	+	1.52279i	−0.151025	+	0.0871946i
$306$		0			0
$307$	−16.1947	+	9.34999i	−0.924278	+	0.533632i	−0.884997	−	0.465596i	$-0.845840\pi$
$307$	−16.1947	+	9.34999i	−0.924278	+	0.533632i	−0.0392804	+	0.999228i	$0.512507\pi$
$308$		0			0
$309$	−9.16544	−	0.391548i	−0.521403	−	0.0222744i
$310$		0			0
$311$	−0.0875069	−	0.496276i	−0.00496206	−	0.0281413i	0.982226	−	0.187701i	$-0.0601036\pi$
$311$	−0.0875069	−	0.496276i	−0.00496206	−	0.0281413i	−0.987188	+	0.159560i	$0.948993\pi$
$312$		0			0
$313$	12.0362	−	14.3442i	0.680327	−	0.810782i	−0.309823	−	0.950794i	$-0.600270\pi$
$313$	12.0362	−	14.3442i	0.680327	−	0.810782i	0.990150	+	0.140012i	$0.0447142\pi$
$314$		0			0
$315$	−3.96840	−	8.42182i	−0.223594	−	0.474516i
$316$		0			0
$317$	8.95841	+	24.6130i	0.503155	+	1.38241i	0.888178	+	0.459499i	$0.151971\pi$
$317$	8.95841	+	24.6130i	0.503155	+	1.38241i	−0.385023	+	0.922907i	$0.625807\pi$
$318$		0			0
$319$	14.6800	−	12.3180i	0.821925	−	0.689677i
$320$		0			0
$321$	15.5744	−	4.92669i	0.869280	−	0.274981i
$322$		0			0
$323$		−	21.0616i		−	1.17190i
$324$		0			0
$325$	−5.48661	−	3.16770i	−0.304342	−	0.175712i
$326$		0			0
$327$	19.1633	−	20.9526i	1.05973	−	1.15868i
$328$		0			0
$329$	−11.1639	+	19.4323i	−0.615487	+	1.07133i
$330$		0			0
$331$	−14.3667	+	5.22905i	−0.789666	+	0.287415i	−0.705197	−	0.709011i	$-0.749141\pi$
$331$	−14.3667	+	5.22905i	−0.789666	+	0.287415i	−0.0844686	+	0.996426i	$0.526919\pi$
$332$		0			0
$333$	23.3269	−	16.3991i	1.27831	−	0.898664i
$334$		0			0
$335$	16.9195	−	6.15818i	0.924409	−	0.336457i
$336$		0			0
$337$	−10.5844	+	8.88138i	−0.576570	+	0.483800i	−0.883819	−	0.467830i	$-0.845036\pi$
$337$	−10.5844	+	8.88138i	−0.576570	+	0.483800i	0.307249	+	0.951629i	$0.400592\pi$
$338$		0			0
$339$	−7.63429	+	12.0083i	−0.414638	+	0.652202i
$340$		0			0
$341$	7.12508	−	12.3410i	0.385845	−	0.668303i
$342$		0			0
$343$	−9.36276	−	15.9793i	−0.505542	−	0.862802i
$344$		0			0
$345$	9.16057	−	7.04283i	0.493188	−	0.379173i
$346$		0			0
$347$	−5.65264	+	15.5305i	−0.303450	+	0.833721i	0.690445	+	0.723385i	$0.257415\pi$
$347$	−5.65264	+	15.5305i	−0.303450	+	0.833721i	−0.993894	+	0.110336i	$0.964807\pi$
$348$		0			0
$349$	−4.58698	+	5.46655i	−0.245535	+	0.292618i	−0.874710	−	0.484646i	$-0.838948\pi$
$349$	−4.58698	+	5.46655i	−0.245535	+	0.292618i	0.629175	+	0.777264i	$0.283393\pi$
$350$		0			0
$351$	0.421774	+	9.07349i	0.0225126	+	0.484307i
$352$		0			0
$353$	13.7755	−	5.01387i	0.733195	−	0.266861i	0.0516785	−	0.998664i	$-0.483543\pi$
$353$	13.7755	−	5.01387i	0.733195	−	0.266861i	0.681517	+	0.731803i	$0.261321\pi$
$354$		0			0
$355$	−1.81538	−	2.16348i	−0.0963502	−	0.114826i
$356$		0			0
$357$	12.8424	−	6.73563i	0.679693	−	0.356488i
$358$		0			0
$359$			4.76141i			0.251298i	0.992075	+	0.125649i	$0.0401013\pi$
$359$			4.76141i			0.251298i	−0.992075	+	0.125649i	$0.959899\pi$
$360$		0			0
$361$	−25.2964			−1.33139
$362$		0			0
$363$	1.11105	+	0.706353i	0.0583152	+	0.0370739i
$364$		0			0
$365$	−0.879977	−	1.04872i	−0.0460601	−	0.0548923i
$366$		0			0
$367$	5.90362	+	1.04097i	0.308166	+	0.0543380i	0.325593	−	0.945510i	$-0.394436\pi$
$367$	5.90362	+	1.04097i	0.308166	+	0.0543380i	−0.0174264	+	0.999848i	$0.505547\pi$
$368$		0			0
$369$	29.2975	−	7.90926i	1.52517	−	0.411740i
$370$		0			0
$371$	−35.3459	+	6.31035i	−1.83507	+	0.327617i
$372$		0			0
$373$	−5.93592	−	33.6643i	−0.307350	−	1.74307i	−0.612230	−	0.790680i	$-0.709727\pi$
$373$	−5.93592	−	33.6643i	−0.307350	−	1.74307i	0.304879	−	0.952391i	$-0.401384\pi$
$374$		0			0
$375$	5.28433	+	16.7050i	0.272882	+	0.862644i
$376$		0			0
$377$	−10.4686			−0.539159
$378$		0			0
$379$	−8.62058			−0.442810			−0.221405	−	0.975182i	$-0.571064\pi$
$379$	−8.62058			−0.442810			−0.221405	+	0.975182i	$0.571064\pi$
$380$		0			0
$381$	−5.12895	+	5.60783i	−0.262764	+	0.287298i
$382$		0			0
$383$	2.43473	+	13.8080i	0.124409	+	0.705558i	0.981657	+	0.190655i	$0.0610611\pi$
$383$	2.43473	+	13.8080i	0.124409	+	0.705558i	−0.857248	+	0.514903i	$0.827828\pi$
$384$		0			0
$385$	−6.39948	−	7.59359i	−0.326148	−	0.387005i
$386$		0			0
$387$	12.0931	+	1.03513i	0.614728	+	0.0526184i
$388$		0			0
$389$	32.0313	+	5.64799i	1.62405	+	0.286364i	0.910274	−	0.414007i	$-0.135871\pi$
$389$	32.0313	+	5.64799i	1.62405	+	0.286364i	0.713779	+	0.700371i	$0.246982\pi$
$390$		0			0
$391$	11.5692	+	13.7877i	0.585082	+	0.697274i
$392$		0			0
$393$	−15.9547	+	8.32457i	−0.804811	+	0.419919i
$394$		0			0
$395$	−11.7707			−0.592246
$396$		0			0
$397$			1.96860i			0.0988013i	0.998779	+	0.0494007i	$0.0157311\pi$
$397$			1.96860i			0.0988013i	−0.998779	+	0.0494007i	$0.984269\pi$
$398$		0			0
$399$	−14.1663	−	27.0100i	−0.709202	−	1.35219i
$400$		0			0
$401$	−15.9098	−	18.9605i	−0.794495	−	0.946842i	0.204995	−	0.978763i	$-0.434282\pi$
$401$	−15.9098	−	18.9605i	−0.794495	−	0.946842i	−0.999490	+	0.0319205i	$0.989838\pi$
$402$		0			0
$403$	−7.31509	+	2.66247i	−0.364390	+	0.132627i
$404$		0			0
$405$	6.75516	−	8.11218i	0.335666	−	0.403097i
$406$		0			0
$407$	19.5505	−	23.2994i	0.969085	−	1.15491i
$408$		0			0
$409$	−10.8941	+	29.9314i	−0.538680	+	1.48001i	0.309809	+	0.950799i	$0.399735\pi$
$409$	−10.8941	+	29.9314i	−0.538680	+	1.48001i	−0.848489	+	0.529213i	$0.822487\pi$
$410$		0			0
$411$	−1.91751	−	14.4599i	−0.0945836	−	0.713257i
$412$		0			0
$413$	−4.97594	+	28.5769i	−0.244850	+	1.40618i
$414$		0			0
$415$	−4.05420	+	7.02208i	−0.199013	+	0.344700i
$416$		0			0
$417$	−30.4961	−	1.30279i	−1.49340	−	0.0637981i
$418$		0			0
$419$	28.8373	−	24.1974i	1.40879	−	1.18212i	0.451763	−	0.892138i	$-0.350795\pi$
$419$	28.8373	−	24.1974i	1.40879	−	1.18212i	0.957032	−	0.289981i	$-0.0936491\pi$
$420$		0			0
$421$	3.47410	−	1.26447i	0.169317	−	0.0616264i	−0.255971	−	0.966685i	$-0.582395\pi$
$421$	3.47410	−	1.26447i	0.169317	−	0.0616264i	0.425288	+	0.905058i	$0.360173\pi$
$422$		0			0
$423$	−25.3189	−	2.16720i	−1.23105	−	0.105373i
$424$		0			0
$425$	−10.7772	+	3.92257i	−0.522770	+	0.190273i
$426$		0			0
$427$	−5.95671	−	3.42216i	−0.288265	−	0.165610i
$428$		0			0
$429$	2.92215	+	9.23761i	0.141083	+	0.445996i
$430$		0			0
$431$	4.28781	+	2.47557i	0.206536	+	0.119244i	0.599701	−	0.800224i	$-0.295286\pi$
$431$	4.28781	+	2.47557i	0.206536	+	0.119244i	−0.393164	+	0.919468i	$0.628620\pi$
$432$		0			0
$433$			6.70918i			0.322423i	0.986920	+	0.161211i	$0.0515401\pi$
$433$			6.70918i			0.322423i	−0.986920	+	0.161211i	$0.948460\pi$
$434$		0			0
$435$	8.97776	+	8.21111i	0.430451	+	0.393692i
$436$		0			0
$437$	28.9981	−	24.3323i	1.38717	−	1.16397i
$438$		0			0
$439$	−0.129633	−	0.356163i	−0.00618704	−	0.0169988i	0.936561	−	0.350506i	$-0.113990\pi$
$439$	−0.129633	−	0.356163i	−0.00618704	−	0.0169988i	−0.942748	+	0.333507i	$0.891768\pi$
$440$		0			0
$441$	11.9390	−	17.2760i	0.568526	−	0.822665i
$442$		0			0
$443$	−10.8964	+	12.9858i	−0.517705	+	0.616976i	−0.960036	−	0.279875i	$-0.909707\pi$
$443$	−10.8964	+	12.9858i	−0.517705	+	0.616976i	0.442332	+	0.896851i	$0.354151\pi$
$444$		0			0
$445$	−2.34044	−	13.2733i	−0.110948	−	0.629215i
$446$		0			0
$447$	17.3084	−	27.2251i	0.818659	−	1.28770i
$448$		0			0
$449$	−15.9872	+	9.23020i	−0.754481	+	0.435600i	−0.827311	−	0.561744i	$-0.810130\pi$
$449$	−15.9872	+	9.23020i	−0.754481	+	0.435600i	0.0728294	+	0.997344i	$0.476797\pi$
$450$		0			0
$451$	28.0326	−	16.1846i	1.32000	−	0.762104i
$452$		0			0
$453$	−4.25321	+	10.2955i	−0.199833	+	0.483725i
$454$		0			0
$455$	0.0115926	+	5.42483i	0.000543469	+	0.254320i
$456$		0			0
$457$	−0.345758	+	1.96089i	−0.0161739	+	0.0917266i	−0.991826	−	0.127596i	$-0.959274\pi$
$457$	−0.345758	+	1.96089i	−0.0161739	+	0.0917266i	0.975652	+	0.219323i	$0.0703849\pi$
$458$		0			0
$459$	13.0735	+	9.97324i	0.610218	+	0.465511i
$460$		0			0
$461$	23.4896	+	19.7101i	1.09402	+	0.917992i	0.997009	−	0.0772911i	$-0.0246271\pi$
$461$	23.4896	+	19.7101i	1.09402	+	0.917992i	0.0970119	+	0.995283i	$0.469072\pi$
$462$		0			0
$463$	1.76880	+	10.0313i	0.0822029	+	0.466196i	0.997925	+	0.0643841i	$0.0205083\pi$
$463$	1.76880	+	10.0313i	0.0822029	+	0.466196i	−0.915722	+	0.401812i	$0.868381\pi$
$464$		0			0
$465$	8.36170	+	3.45433i	0.387764	+	0.160191i
$466$		0			0
$467$	−12.6759			−0.586569			−0.293285	−	0.956025i	$-0.594748\pi$
$467$	−12.6759			−0.586569			−0.293285	+	0.956025i	$0.594748\pi$
$468$		0			0
$469$	31.1676	+	26.0394i	1.43919	+	1.20239i
$470$		0			0
$471$	−3.15387	−	6.04465i	−0.145322	−	0.278523i
$472$		0			0
$473$	12.7497	−	2.24812i	0.586233	−	0.103369i
$474$		0			0
$475$	8.24990	+	22.6664i	0.378531	+	1.04001i
$476$		0			0
$477$	−23.4142	−	33.3056i	−1.07206	−	1.52496i
$478$		0			0
$479$	−26.8830	−	22.5575i	−1.22831	−	1.03068i	−0.998347	−	0.0574804i	$-0.981693\pi$
$479$	−26.8830	−	22.5575i	−1.22831	−	1.03068i	−0.229968	−	0.973198i	$-0.573862\pi$
$480$		0			0
$481$	−16.3628	+	2.88520i	−0.746078	+	0.131554i
$482$		0			0
$483$	24.1105	+	9.90013i	1.09707	+	0.450472i
$484$		0			0
$485$	−0.204601	+	0.118127i	−0.00929046	+	0.00536385i
$486$		0			0
$487$	−2.49812	+	4.32688i	−0.113201	+	0.196070i	−0.917059	−	0.398751i	$-0.869444\pi$
$487$	−2.49812	+	4.32688i	−0.113201	+	0.196070i	0.803858	+	0.594821i	$0.202777\pi$
$488$		0			0
$489$	−12.7504	−	40.3069i	−0.576591	−	1.82274i
$490$		0			0
$491$	4.65547	−	12.7908i	0.210098	−	0.577241i	−0.789222	−	0.614108i	$-0.789516\pi$
$491$	4.65547	−	12.7908i	0.210098	−	0.577241i	0.999320	+	0.0368676i	$0.0117380\pi$
$492$		0			0
$493$	−12.1815	+	14.5173i	−0.548626	+	0.653827i
$494$		0			0
$495$	4.73958	−	10.2141i	0.213029	−	0.459091i
$496$		0			0
$497$	2.16603	−	5.99092i	0.0971598	−	0.268730i
$498$		0			0
$499$	15.5283	+	5.65183i	0.695141	+	0.253011i	0.665335	−	0.746545i	$-0.268289\pi$
$499$	15.5283	+	5.65183i	0.695141	+	0.253011i	0.0298062	+	0.999556i	$0.490511\pi$
$500$		0			0
$501$	−4.83453	−	3.07356i	−0.215991	−	0.137316i
$502$		0			0
$503$	4.71614	+	8.16859i	0.210282	+	0.364219i	0.951803	−	0.306711i	$-0.0992284\pi$
$503$	4.71614	+	8.16859i	0.210282	+	0.364219i	−0.741521	+	0.670930i	$0.765895\pi$
$504$		0			0
$505$	−3.40588	+	5.89916i	−0.151560	+	0.262509i
$506$		0			0
$507$	−6.57635	+	15.9190i	−0.292066	+	0.706987i
$508$		0			0
$509$	25.2080	−	21.1520i	1.11733	−	0.937547i	0.118859	−	0.992911i	$-0.462076\pi$
$509$	25.2080	−	21.1520i	1.11733	−	0.937547i	0.998466	+	0.0553640i	$0.0176319\pi$
$510$		0			0
$511$	1.04995	−	2.90401i	0.0464471	−	0.128466i
$512$		0			0
$513$	20.9756	−	27.4960i	0.926095	−	1.21398i
$514$		0			0
$515$	−2.12480	−	5.83783i	−0.0936297	−	0.257246i
$516$		0			0
$517$	−26.6936	+	4.70681i	−1.17399	+	0.207005i
$518$		0			0
$519$	−7.05949	−	9.18224i	−0.309877	−	0.403056i
$520$		0			0
$521$	2.24316	+	3.88526i	0.0982745	+	0.170216i	0.910971	−	0.412471i	$-0.135334\pi$
$521$	2.24316	+	3.88526i	0.0982745	+	0.170216i	−0.812696	+	0.582688i	$0.802001\pi$
$522$		0			0
$523$	−29.1689	−	16.8407i	−1.27547	−	0.736391i	−0.299455	−	0.954110i	$-0.596805\pi$
$523$	−29.1689	−	16.8407i	−1.27547	−	0.736391i	−0.976011	+	0.217719i	$0.930138\pi$
$524$		0			0
$525$	−11.1826	+	12.2793i	−0.488049	+	0.535912i
$526$		0			0
$527$	−4.81982	+	13.2423i	−0.209955	+	0.576846i
$528$		0			0
$529$	−1.62346	+	9.20707i	−0.0705850	+	0.400307i
$530$		0			0
$531$	−31.7540	+	8.57241i	−1.37801	+	0.372011i
$532$		0			0
$533$	−17.4140	−	3.07055i	−0.754283	−	0.133000i
$534$		0			0
$535$	7.11059	+	8.47407i	0.307418	+	0.366366i
$536$		0			0
$537$	2.33138	−	10.5631i	0.100607	−	0.455832i
$538$		0			0
$539$	7.57117	−	21.0815i	0.326114	−	0.908046i
$540$		0			0
$541$	−13.5046	−	23.3907i	−0.580610	−	1.00565i	−0.995407	−	0.0957324i	$-0.969481\pi$
$541$	−13.5046	−	23.3907i	−0.580610	−	1.00565i	0.414797	−	0.909914i	$-0.363853\pi$
$542$		0			0
$543$	−0.930509	−	0.851048i	−0.0399319	−	0.0365220i
$544$		0			0
$545$	18.0691	+	6.57660i	0.773994	+	0.281711i
$546$		0			0
$547$	7.54588	−	42.7948i	0.322638	−	1.82977i	−0.203137	−	0.979150i	$-0.565114\pi$
$547$	7.54588	−	42.7948i	0.322638	−	1.82977i	0.525775	−	0.850623i	$-0.323775\pi$
$548$		0			0
$549$	0.664329	−	7.76119i	0.0283529	−	0.331240i
$550$		0			0
$551$	30.5326	+	25.6199i	1.30073	+	1.09145i
$552$		0			0
$553$	−13.3244	−	22.9650i	−0.566609	−	0.976571i
$554$		0			0
$555$	16.2956	+	10.3599i	0.691710	+	0.439755i
$556$		0			0
$557$		−	13.7719i		−	0.583536i	−0.956489	−	0.291768i	$-0.905756\pi$
$557$		−	13.7719i		−	0.583536i	0.956489	−	0.291768i	$-0.0942436\pi$
$558$		0			0
$559$	−6.12483	−	3.53617i	−0.259053	−	0.149564i
$560$		0			0
$561$	16.2106	+	6.69681i	0.684411	+	0.282740i
$562$		0			0
$563$	17.8735	+	6.50544i	0.753280	+	0.274172i	0.689985	−	0.723823i	$-0.257617\pi$
$563$	17.8735	+	6.50544i	0.753280	+	0.274172i	0.0632947	+	0.997995i	$0.479839\pi$
$564$		0			0
$565$	−9.48989	−	1.67332i	−0.399243	−	0.0703972i
$566$		0			0
$567$	23.4740	+	3.99659i	0.985814	+	0.167841i
$568$		0			0
$569$	15.2893	+	2.69591i	0.640959	+	0.113018i	0.484676	−	0.874694i	$-0.338938\pi$
$569$	15.2893	+	2.69591i	0.640959	+	0.113018i	0.156283	+	0.987712i	$0.450049\pi$
$570$		0			0
$571$	−18.8715	−	6.86868i	−0.789749	−	0.287445i	−0.0845175	−	0.996422i	$-0.526935\pi$
$571$	−18.8715	−	6.86868i	−0.789749	−	0.287445i	−0.705232	+	0.708977i	$0.749157\pi$
$572$		0			0
$573$	3.97581	+	1.64246i	0.166092	+	0.0686149i
$574$		0			0
$575$	−17.8515	−	10.3066i	−0.744458	−	0.429813i
$576$		0			0
$577$		−	18.1983i		−	0.757606i	−0.925477	−	0.378803i	$-0.876336\pi$
$577$		−	18.1983i		−	0.757606i	0.925477	−	0.378803i	$-0.123664\pi$
$578$		0			0
$579$	−26.0844	−	16.5832i	−1.08403	−	0.689174i
$580$		0			0
$581$	−18.2897	+	0.0390841i	−0.758784	+	0.00162148i
$582$		0			0
$583$	−33.2663	−	27.9137i	−1.37775	−	1.15607i
$584$		0			0
$585$	−5.56998	+	2.61007i	−0.230291	+	0.107913i
$586$		0			0
$587$	−7.53824	+	42.7515i	−0.311136	+	1.76454i	0.281974	+	0.959422i	$0.409011\pi$
$587$	−7.53824	+	42.7515i	−0.311136	+	1.76454i	−0.593111	+	0.805121i	$0.702100\pi$
$588$		0			0
$589$	27.8511	+	10.1370i	1.14759	+	0.417687i
$590$		0			0
$591$	6.62905	+	6.06296i	0.272683	+	0.249397i
$592$		0			0
$593$	19.1883	+	33.2351i	0.787970	+	1.36480i	0.927209	+	0.374544i	$0.122201\pi$
$593$	19.1883	+	33.2351i	0.787970	+	1.36480i	−0.139239	+	0.990259i	$0.544466\pi$
$594$		0			0
$595$	7.53640	+	6.29639i	0.308962	+	0.258127i
$596$		0			0
$597$	7.97165	−	36.1183i	0.326258	−	1.47822i
$598$		0			0
$599$	6.15487	+	7.33509i	0.251481	+	0.299704i	0.876985	−	0.480517i	$-0.159551\pi$
$599$	6.15487	+	7.33509i	0.251481	+	0.299704i	−0.625504	+	0.780221i	$0.715107\pi$
$600$		0			0
$601$	−22.7261	−	4.00723i	−0.927018	−	0.163458i	−0.310297	−	0.950640i	$-0.600428\pi$
$601$	−22.7261	−	4.00723i	−0.927018	−	0.163458i	−0.616721	+	0.787181i	$0.711540\pi$
$602$		0			0
$603$	−11.8355	+	44.5047i	−0.481977	+	1.81237i
$604$		0			0
$605$	−0.154822	+	0.878040i	−0.00629442	+	0.0356974i
$606$		0			0
$607$	2.50667	−	6.88703i	0.101743	−	0.279536i	−0.878369	−	0.477984i	$-0.841368\pi$
$607$	2.50667	−	6.88703i	0.101743	−	0.279536i	0.980111	+	0.198448i	$0.0635900\pi$
$608$		0			0
$609$	−5.85736	+	26.8109i	−0.237352	+	1.08643i
$610$		0			0
$611$	12.8233	+	7.40355i	0.518776	+	0.299516i
$612$		0			0
$613$	9.67118	+	16.7510i	0.390615	+	0.676566i	0.992531	−	0.121994i	$-0.0389289\pi$
$613$	9.67118	+	16.7510i	0.390615	+	0.676566i	−0.601916	+	0.798560i	$0.705596\pi$
$614$		0			0
$615$	12.5257	+	16.2921i	0.505084	+	0.656960i
$616$		0			0
$617$	−18.4581	+	3.25466i	−0.743094	+	0.131028i	−0.532362	−	0.846517i	$-0.678696\pi$
$617$	−18.4581	+	3.25466i	−0.743094	+	0.131028i	−0.210731	+	0.977544i	$0.567585\pi$
$618$		0			0
$619$	12.5229	+	34.4065i	0.503339	+	1.38291i	0.887995	+	0.459853i	$0.152098\pi$
$619$	12.5229	+	34.4065i	0.503339	+	1.38291i	−0.384655	+	0.923060i	$0.625680\pi$
$620$		0			0
$621$	1.37230	+	29.5219i	0.0550686	+	1.18467i
$622$		0			0
$623$	23.2473	−	19.5916i	0.931385	−	0.784922i
$624$		0			0
$625$	4.79227	−	4.02119i	0.191691	−	0.160848i
$626$		0			0
$627$	14.0846	−	34.0939i	0.562487	−	1.36158i
$628$		0			0
$629$	−15.0391	+	26.0484i	−0.599646	+	1.03862i
$630$		0			0
$631$	11.0792	+	19.1897i	0.441056	+	0.763931i	0.997768	−	0.0667740i	$-0.0212707\pi$
$631$	11.0792	+	19.1897i	0.441056	+	0.763931i	−0.556712	+	0.830706i	$0.687937\pi$
$632$		0			0
$633$	−24.5657	−	15.6177i	−0.976399	−	0.620746i
$634$		0			0
$635$	−4.83608	−	1.76019i	−0.191914	−	0.0698509i
$636$		0			0
$637$	−10.5709	+	6.16351i	−0.418835	+	0.244207i
$638$		0			0
$639$	7.19475	−	0.643079i	0.284620	−	0.0254398i
$640$		0			0
$641$	−30.2591	+	36.0614i	−1.19516	+	1.42434i	−0.315381	+	0.948965i	$0.602132\pi$
$641$	−30.2591	+	36.0614i	−1.19516	+	1.42434i	−0.879783	+	0.475376i	$0.842312\pi$
$642$		0			0
$643$	−2.45049	+	6.73265i	−0.0966377	+	0.265510i	−0.978587	−	0.205835i	$-0.934009\pi$
$643$	−2.45049	+	6.73265i	−0.0966377	+	0.265510i	0.881949	+	0.471345i	$0.156231\pi$
$644$		0			0
$645$	2.47898	+	7.83666i	0.0976098	+	0.308568i
$646$		0			0
$647$	9.26911	−	16.0546i	0.364406	−	0.631170i	−0.624274	−	0.781205i	$-0.714605\pi$
$647$	9.26911	−	16.0546i	0.364406	−	0.631170i	0.988681	+	0.150035i	$0.0479386\pi$
$648$		0			0
$649$	−30.3830	+	17.5416i	−1.19264	+	0.688569i
$650$		0			0
$651$	2.72589	+	20.2243i	0.106836	+	0.792652i
$652$		0			0
$653$	−43.2991	+	7.63480i	−1.69442	+	0.298773i	−0.935741	−	0.352687i	$-0.885268\pi$
$653$	−43.2991	+	7.63480i	−1.69442	+	0.298773i	−0.758683	+	0.651460i	$0.774157\pi$
$654$		0			0
$655$	−9.33564	−	7.83353i	−0.364774	−	0.306081i
$656$		0			0
$657$	3.48755	−	0.311723i	0.136062	−	0.0121615i
$658$		0			0
$659$	12.0098	+	32.9965i	0.467834	+	1.28536i	0.919470	+	0.393160i	$0.128618\pi$
$659$	12.0098	+	32.9965i	0.467834	+	1.28536i	−0.451636	+	0.892202i	$0.649160\pi$
$660$		0			0
$661$	2.60599	−	0.459507i	0.101361	−	0.0178728i	−0.122737	−	0.992439i	$-0.539167\pi$
$661$	2.60599	−	0.459507i	0.101361	−	0.0178728i	0.224099	+	0.974566i	$0.428056\pi$
$662$		0			0
$663$	−4.43217	−	8.49463i	−0.172131	−	0.329904i
$664$		0			0
$665$	13.2425	−	15.8505i	0.513522	−	0.614654i
$666$		0			0
$667$	−34.0610			−1.31885
$668$		0			0
$669$	−0.113318	−	0.0468133i	−0.00438114	−	0.00180991i
$670$		0			0
$671$	−1.44281	−	8.18259i	−0.0556991	−	0.315886i
$672$		0			0
$673$	8.03878	+	6.74534i	0.309872	+	0.260014i	0.784439	−	0.620206i	$-0.212951\pi$
$673$	8.03878	+	6.74534i	0.309872	+	0.260014i	−0.474567	+	0.880219i	$0.657395\pi$
$674$		0			0
$675$	−17.9762	−	5.61224i	−0.691904	−	0.216015i
$676$		0			0
$677$	7.64065	−	43.3323i	0.293654	−	1.66539i	−0.378969	−	0.925409i	$-0.623721\pi$
$677$	7.64065	−	43.3323i	0.293654	−	1.66539i	0.672623	−	0.739985i	$-0.265168\pi$
$678$		0			0
$679$	−0.462077	−	0.265465i	−0.0177329	−	0.0101876i
$680$		0			0
$681$	−5.81634	+	14.0793i	−0.222883	+	0.539519i
$682$		0			0
$683$	14.2133	−	8.20603i	0.543855	−	0.313995i	−0.202785	−	0.979223i	$-0.564999\pi$
$683$	14.2133	−	8.20603i	0.543855	−	0.313995i	0.746640	+	0.665228i	$0.231666\pi$
$684$		0			0
$685$	8.55459	−	4.93900i	0.326854	−	0.188709i
$686$		0			0
$687$	19.1429	−	30.1107i	0.730346	−	1.14879i
$688$		0			0
$689$	4.11941	+	23.3623i	0.156937	+	0.890033i
$690$		0			0
$691$	0.431926	−	0.514749i	0.0164312	−	0.0195820i	−0.757766	−	0.652526i	$-0.773709\pi$
$691$	0.431926	−	0.514749i	0.0164312	−	0.0195820i	0.774197	+	0.632944i	$0.218154\pi$
$692$		0			0
$693$	25.2933	−	2.31525i	0.960813	−	0.0879492i
$694$		0			0
$695$	−7.06982	−	19.4242i	−0.268174	−	0.736801i
$696$		0			0
$697$	−24.5214	+	20.5759i	−0.928815	+	0.779368i
$698$		0			0
$699$	−13.9245	−	12.7354i	−0.526672	−	0.481697i
$700$		0			0
$701$			51.7991i			1.95643i	0.207606	+	0.978213i	$0.433433\pi$
$701$			51.7991i			1.95643i	−0.207606	+	0.978213i	$0.566567\pi$
$702$		0			0
$703$	54.7847	+	31.6300i	2.06624	+	1.19295i
$704$		0			0
$705$	−5.19015	−	16.4073i	−0.195472	−	0.617935i
$706$		0			0
$707$	−15.3649	+	0.0328341i	−0.577858	+	0.00123485i
$708$		0			0
$709$	−16.4657	+	5.99302i	−0.618382	+	0.225073i	−0.632167	−	0.774832i	$-0.717834\pi$
$709$	−16.4657	+	5.99302i	−0.618382	+	0.225073i	0.0137846	+	0.999905i	$0.495612\pi$
$710$		0			0
$711$	17.2214	−	24.6933i	0.645854	−	0.926072i
$712$		0			0
$713$	−23.8007	+	8.66274i	−0.891343	+	0.324422i
$714$		0			0
$715$	−5.02620	+	4.21748i	−0.187969	+	0.157725i
$716$		0			0
$717$	−8.14867	−	0.348111i	−0.304318	−	0.0130005i
$718$		0			0
$719$	−8.95164	+	15.5047i	−0.333840	+	0.578228i	−0.983261	−	0.182201i	$-0.941678\pi$
$719$	−8.95164	+	15.5047i	−0.333840	+	0.578228i	0.649421	+	0.760429i	$0.275011\pi$
$720$		0			0
$721$	8.98455	−	10.7540i	0.334602	−	0.400498i
$722$		0			0
$723$	4.50086	+	33.9410i	0.167389	+	1.26228i
$724$		0			0
$725$	7.42318	−	20.3950i	0.275690	−	0.757452i
$726$		0			0
$727$	20.1921	−	24.0641i	0.748885	−	0.892487i	−0.248206	−	0.968707i	$-0.579841\pi$
$727$	20.1921	−	24.0641i	0.748885	−	0.892487i	0.997091	+	0.0762207i	$0.0242854\pi$
$728$		0			0
$729$	7.13497	+	26.0402i	0.264258	+	0.964452i
$730$		0			0
$731$	−12.0308	+	4.37885i	−0.444975	+	0.161958i
$732$		0			0
$733$	27.6262	+	32.9236i	1.02040	+	1.21606i	0.976163	+	0.217041i	$0.0696404\pi$
$733$	27.6262	+	32.9236i	1.02040	+	1.21606i	0.0442345	+	0.999021i	$0.485915\pi$
$734$		0			0
$735$	13.8999	+	3.00561i	0.512707	+	0.110864i
$736$		0			0
$737$			49.1214i			1.80941i
$738$		0			0
$739$	−18.4984			−0.680476			−0.340238	−	0.940339i	$-0.610508\pi$
$739$	−18.4984			−0.680476			−0.340238	+	0.940339i	$0.610508\pi$
$740$		0			0
$741$	−17.8658	+	9.32169i	−0.656317	+	0.342441i
$742$		0			0
$743$	2.62524	+	3.12864i	0.0963108	+	0.114779i	0.812047	−	0.583592i	$-0.198353\pi$
$743$	2.62524	+	3.12864i	0.0963108	+	0.114779i	−0.715736	+	0.698371i	$0.753909\pi$
$744$		0			0
$745$	21.5154	+	3.79374i	0.788262	+	0.138992i
$746$		0			0
$747$	−8.79980	−	18.7790i	−0.321968	−	0.687089i
$748$		0			0
$749$	−8.48405	+	23.4657i	−0.310001	+	0.857416i
$750$		0			0
$751$	−2.26625	−	12.8525i	−0.0826965	−	0.468995i	−0.997830	−	0.0658441i	$-0.979026\pi$
$751$	−2.26625	−	12.8525i	−0.0826965	−	0.468995i	0.915133	−	0.403151i	$-0.132085\pi$
$752$		0			0
$753$	−9.55970	+	10.4523i	−0.348375	+	0.380902i
$754$		0			0
$755$	−7.54362			−0.274540
$756$		0			0
$757$	−13.3825			−0.486396			−0.243198	−	0.969977i	$-0.578196\pi$
$757$	−13.3825			−0.486396			−0.243198	+	0.969977i	$0.578196\pi$
$758$		0			0
$759$	9.50763	+	30.0559i	0.345105	+	1.09096i
$760$		0			0
$761$	8.32479	+	47.2122i	0.301773	+	1.71144i	0.638317	+	0.769774i	$0.279631\pi$
$761$	8.32479	+	47.2122i	0.301773	+	1.71144i	−0.336544	+	0.941668i	$0.609258\pi$
$762$		0			0
$763$	7.62294	+	42.6981i	0.275969	+	1.54577i
$764$		0			0
$765$	−2.86184	+	10.7613i	−0.103470	+	0.389077i
$766$		0			0
$767$	18.8741	+	3.32800i	0.681503	+	0.120167i
$768$		0			0
$769$	−3.11190	−	3.70862i	−0.112218	−	0.133736i	0.707011	−	0.707202i	$-0.250043\pi$
$769$	−3.11190	−	3.70862i	−0.112218	−	0.133736i	−0.819229	+	0.573466i	$0.805599\pi$
$770$		0			0
$771$	−28.3486	−	18.0227i	−1.02095	−	0.649071i
$772$		0			0
$773$	5.99893			0.215766			0.107883	−	0.994164i	$-0.465593\pi$
$773$	5.99893			0.215766			0.107883	+	0.994164i	$0.465593\pi$
$774$		0			0
$775$		−	16.1393i		−	0.579741i
$776$		0			0
$777$	−1.76604	+	43.5208i	−0.0633565	+	1.56130i
$778$		0			0
$779$	43.2750	+	51.5731i	1.55049	+	1.84780i
$780$		0			0
$781$	7.24028	−	2.63525i	0.259078	−	0.0942965i
$782$		0			0
$783$	−30.3610	+	6.82068i	−1.08501	+	0.243751i
$784$		0			0
$785$	2.96783	−	3.53692i	0.105926	−	0.126238i
$786$		0			0
$787$	6.70963	−	18.4346i	0.239172	−	0.657121i	−0.760795	−	0.648993i	$-0.775191\pi$
$787$	6.70963	−	18.4346i	0.239172	−	0.657121i	0.999967	−	0.00812804i	$-0.00258726\pi$
$788$		0			0
$789$	14.5182	−	11.1619i	0.516860	−	0.397373i
$790$		0			0
$791$	−7.47781	−	20.4093i	−0.265880	−	0.725672i
$792$		0			0
$793$	−2.26946	+	3.93083i	−0.0805911	+	0.139588i
$794$		0			0
$795$	14.7917	−	23.2664i	0.524606	−	0.825175i
$796$		0			0
$797$	31.8094	−	26.6913i	1.12675	−	0.945453i	0.127822	−	0.991797i	$-0.459201\pi$
$797$	31.8094	−	26.6913i	1.12675	−	0.945453i	0.998926	+	0.0463437i	$0.0147569\pi$
$798$		0			0
$799$	25.1884	−	9.16784i	0.891103	−	0.324335i
$800$		0			0
$801$	31.2699	+	14.5100i	1.10487	+	0.512684i
$802$		0			0
$803$	3.50962	−	1.27740i	0.123852	−	0.0450783i
$804$		0			0
$805$	0.0377182	+	17.6505i	0.00132939	+	0.622097i
$806$		0			0
$807$	−2.83591	+	3.10070i	−0.0998288	+	0.109150i
$808$		0			0
$809$	13.2864	+	7.67091i	0.467125	+	0.269695i	0.715035	−	0.699088i	$-0.246411\pi$
$809$	13.2864	+	7.67091i	0.467125	+	0.269695i	−0.247910	+	0.968783i	$0.579744\pi$
$810$		0			0
$811$		−	16.9980i		−	0.596882i	−0.954428	−	0.298441i	$-0.903533\pi$
$811$		−	16.9980i		−	0.596882i	0.954428	−	0.298441i	$-0.0964666\pi$
$812$		0			0
$813$	26.1736	−	8.27953i	0.917948	−	0.290376i
$814$		0			0
$815$	21.9311	−	18.4023i	0.768211	−	0.644606i
$816$		0			0
$817$	9.20955	+	25.3030i	0.322201	+	0.885241i
$818$		0			0
$819$	−11.3976	−	7.91264i	−0.398263	−	0.276490i
$820$		0			0
$821$	23.3379	−	27.8131i	0.814499	−	0.970683i	−0.185429	−	0.982658i	$-0.559367\pi$
$821$	23.3379	−	27.8131i	0.814499	−	0.970683i	0.999928	+	0.0119751i	$0.00381189\pi$
$822$		0			0
$823$	−0.181904	−	1.03163i	−0.00634079	−	0.0359604i	0.981473	−	0.191599i	$-0.0613674\pi$
$823$	−0.181904	−	1.03163i	−0.00634079	−	0.0359604i	−0.987814	+	0.155639i	$0.950256\pi$
$824$		0			0
$825$	−20.0689	−	0.857346i	−0.698711	−	0.0298489i
$826$		0			0
$827$	5.66180	−	3.26884i	0.196880	−	0.113669i	−0.398319	−	0.917247i	$-0.630406\pi$
$827$	5.66180	−	3.26884i	0.196880	−	0.113669i	0.595199	+	0.803578i	$0.297073\pi$
$828$		0			0
$829$	−26.6598	+	15.3920i	−0.925933	+	0.534588i	−0.885523	−	0.464595i	$-0.846200\pi$
$829$	−26.6598	+	15.3920i	−0.925933	+	0.534588i	−0.0404103	+	0.999183i	$0.512866\pi$
$830$		0			0
$831$	7.01138	+	9.11967i	0.243222	+	0.316358i
$832$		0			0
$833$	−3.75331	+	21.8313i	−0.130044	+	0.756409i
$834$		0			0
$835$	0.673678	−	3.82062i	0.0233136	−	0.132218i
$836$		0			0
$837$	−19.4806	+	12.4878i	−0.673347	+	0.431641i
$838$		0			0
$839$	−42.4205	−	35.5951i	−1.46452	−	1.22888i	−0.921047	−	0.389451i	$-0.872665\pi$
$839$	−42.4205	−	35.5951i	−1.46452	−	1.22888i	−0.543472	−	0.839427i	$-0.682891\pi$
$840$		0			0
$841$	−1.19183	−	6.75918i	−0.0410975	−	0.233075i
$842$		0			0
$843$	−3.49875	−	26.3842i	−0.120503	−	0.908719i
$844$		0			0
$845$	−11.6640			−0.401254
$846$		0			0
$847$	−1.88835	+	0.691875i	−0.0648843	+	0.0237731i
$848$		0			0
$849$	4.36557	+	0.186497i	0.149826	+	0.00640056i
$850$		0			0
$851$	−53.2386	+	9.38740i	−1.82500	+	0.321796i
$852$		0			0
$853$	14.1563	+	38.8942i	0.484704	+	1.33171i	0.905418	+	0.424520i	$0.139557\pi$
$853$	14.1563	+	38.8942i	0.484704	+	1.33171i	−0.420714	+	0.907193i	$0.638221\pi$
$854$		0			0
$855$	22.6331	+	6.01898i	0.774036	+	0.205845i
$856$		0			0
$857$	3.28562	+	2.75696i	0.112235	+	0.0941760i	0.697178	−	0.716898i	$-0.254439\pi$
$857$	3.28562	+	2.75696i	0.112235	+	0.0941760i	−0.584943	+	0.811074i	$0.698883\pi$
$858$		0			0
$859$	−32.4780	+	5.72675i	−1.10814	+	0.195394i	−0.697626	−	0.716462i	$-0.745760\pi$
$859$	−32.4780	+	5.72675i	−1.10814	+	0.195394i	−0.410510	+	0.911856i	$0.634649\pi$
$860$		0			0
$861$	−17.6074	+	42.8806i	−0.600058	+	1.46137i
$862$		0			0
$863$	−0.465639	+	0.268837i	−0.0158505	+	0.00915131i	−0.507904	−	0.861413i	$-0.669580\pi$
$863$	−0.465639	+	0.268837i	−0.0158505	+	0.00915131i	0.492054	+	0.870565i	$0.336246\pi$
$864$		0			0
$865$	3.92177	−	6.79270i	0.133344	−	0.230959i
$866$		0			0
$867$	11.8155	+	2.60780i	0.401277	+	0.0885656i
$868$		0			0
$869$	10.9830	−	30.1757i	0.372574	−	1.02364i
$870$		0			0
$871$	17.2485	−	20.5560i	0.584444	−	0.696514i
$872$		0			0
$873$	0.0515337	−	0.602056i	0.00174415	−	0.0203765i
$874$		0			0
$875$	−25.1691	−	9.09994i	−0.850871	−	0.307634i
$876$		0			0
$877$	−28.3985	−	10.3362i	−0.958948	−	0.349028i	−0.185327	−	0.982677i	$-0.559334\pi$
$877$	−28.3985	−	10.3362i	−0.958948	−	0.349028i	−0.773621	+	0.633649i	$0.781557\pi$
$878$		0			0
$879$	0.180953	−	4.23578i	0.00610338	−	0.142869i
$880$		0			0
$881$	−21.8626	−	37.8672i	−0.736571	−	1.27578i	−0.954031	−	0.299709i	$-0.903110\pi$
$881$	−21.8626	−	37.8672i	−0.736571	−	1.27578i	0.217459	−	0.976069i	$-0.430223\pi$
$882$		0			0
$883$	−10.7189	+	18.5657i	−0.360719	+	0.624784i	−0.988079	−	0.153945i	$-0.950802\pi$
$883$	−10.7189	+	18.5657i	−0.360719	+	0.624784i	0.627360	+	0.778729i	$0.284135\pi$
$884$		0			0
$885$	−13.5759	−	17.6581i	−0.456349	−	0.593570i
$886$		0			0
$887$	−28.1960	+	23.6593i	−0.946730	+	0.794401i	−0.978744	−	0.205086i	$-0.934252\pi$
$887$	−28.1960	+	23.6593i	−0.946730	+	0.794401i	0.0320135	+	0.999487i	$0.489808\pi$
$888$		0			0
$889$	−2.04023	−	11.4279i	−0.0684273	−	0.383279i
$890$		0			0
$891$	14.4935	+	24.8871i	0.485551	+	0.833749i
$892$		0			0
$893$	−19.2817	−	52.9760i	−0.645237	−	1.77277i
$894$		0			0
$895$	7.21421	−	1.27206i	0.241144	−	0.0425203i
$896$		0			0
$897$	6.57516	−	15.9161i	0.219538	−	0.531423i
$898$		0			0
$899$	−13.3343	−	23.0956i	−0.444722	−	0.770281i
$900$		0			0
$901$	37.1912	+	21.4724i	1.23902	+	0.715348i
$902$		0			0
$903$	−12.4834	+	13.7077i	−0.415422	+	0.456162i
$904$		0			0
$905$	0.292068	−	0.802451i	0.00970868	−	0.0266744i
$906$		0			0
$907$	9.50956	−	53.9314i	0.315760	−	1.79076i	−0.252167	−	0.967684i	$-0.581143\pi$
$907$	9.50956	−	53.9314i	0.315760	−	1.79076i	0.567926	−	0.823079i	$-0.307746\pi$
$908$		0			0
$909$	−7.39260	−	15.7760i	−0.245197	−	0.523258i
$910$		0			0
$911$	12.9660	+	2.28626i	0.429583	+	0.0757471i	0.384259	−	0.923225i	$-0.374457\pi$
$911$	12.9660	+	2.28626i	0.429583	+	0.0757471i	0.0453238	+	0.998972i	$0.485568\pi$
$912$		0			0
$913$	−14.2191	−	16.9457i	−0.470584	−	0.560820i
$914$		0			0
$915$	5.02945	−	1.59098i	0.166269	−	0.0525960i
$916$		0			0
$917$	4.71559	−	27.0817i	0.155722	−	0.894317i
$918$		0			0
$919$	2.86759	+	4.96681i	0.0945931	+	0.163840i	0.909439	−	0.415838i	$-0.136512\pi$
$919$	2.86759	+	4.96681i	0.0945931	+	0.163840i	−0.814846	+	0.579678i	$0.803178\pi$
$920$		0			0
$921$	30.8811	−	9.76866i	1.01757	−	0.321888i
$922$		0			0
$923$	−3.95521	−	1.43958i	−0.130187	−	0.0473843i
$924$		0			0
$925$	5.98173	−	33.9241i	0.196678	−	1.11542i
$926$		0			0
$927$	15.3558	+	4.08366i	0.504349	+	0.134125i
$928$		0			0
$929$	40.4029	+	33.9020i	1.32557	+	1.11229i	0.985090	+	0.172039i	$0.0550356\pi$
$929$	40.4029	+	33.9020i	1.32557	+	1.11229i	0.340485	+	0.940250i	$0.389409\pi$
$930$		0			0
$931$	45.9153	+	7.89391i	1.50481	+	0.258713i
$932$		0			0
$933$	−0.0372536	+	0.872041i	−0.00121963	+	0.0285493i
$934$		0			0
$935$			11.8777i			0.388441i
$936$		0			0
$937$	−4.51411	−	2.60622i	−0.147470	−	0.0851416i	0.424450	−	0.905452i	$-0.360468\pi$
$937$	−4.51411	−	2.60622i	−0.147470	−	0.0851416i	−0.571919	+	0.820310i	$0.693801\pi$
$938$		0			0
$939$	−25.7120	+	19.7679i	−0.839080	+	0.645102i
$940$		0			0
$941$	−55.4525	−	20.1831i	−1.80770	−	0.657949i	−0.997410	−	0.0719205i	$-0.977087\pi$
$941$	−55.4525	−	20.1831i	−1.80770	−	0.657949i	−0.810290	−	0.586029i	$-0.800691\pi$
$942$		0			0
$943$	−56.6589	−	9.99049i	−1.84507	−	0.325335i
$944$		0			0
$945$	3.56811	+	15.7256i	0.116071	+	0.511554i
$946$		0			0
$947$	−42.0366	−	7.41218i	−1.36601	−	0.240864i	−0.557903	−	0.829906i	$-0.688394\pi$
$947$	−42.0366	−	7.41218i	−1.36601	−	0.240864i	−0.808102	+	0.589043i	$0.799505\pi$
$948$		0			0
$949$	−1.91723	−	0.697813i	−0.0622358	−	0.0226520i
$950$		0			0
$951$	−5.96382	−	44.9733i	−0.193390	−	1.45836i
$952$		0			0
$953$	4.12069	+	2.37908i	0.133482	+	0.0770660i	0.565254	−	0.824917i	$-0.308778\pi$
$953$	4.12069	+	2.37908i	0.133482	+	0.0770660i	−0.431772	+	0.901983i	$0.642111\pi$
$954$		0			0
$955$			2.91312i			0.0942664i
$956$		0			0
$957$	−29.4273	+	15.3540i	−0.951249	+	0.496325i
$958$		0			0
$959$	19.3199	+	11.0994i	0.623873	+	0.358418i
$960$		0			0
$961$	8.55593	+	7.17928i	0.275998	+	0.231590i
$962$		0			0
$963$	−28.1809	+	2.51885i	−0.908116	+	0.0811690i
$964$		0			0
$965$	3.63479	−	20.6139i	0.117008	−	0.663585i
$966$		0			0
$967$	−4.84439	−	1.76321i	−0.155785	−	0.0567011i	0.262951	−	0.964809i	$-0.415304\pi$
$967$	−4.84439	−	1.76321i	−0.155785	−	0.0567011i	−0.418736	+	0.908108i	$0.637527\pi$
$968$		0			0
$969$	−7.86220	+	35.6224i	−0.252570	+	1.14436i
$970$		0			0
$971$	−1.16700	−	2.02131i	−0.0374509	−	0.0648669i	0.846692	−	0.532083i	$-0.178590\pi$
$971$	−1.16700	−	2.02131i	−0.0374509	−	0.0648669i	−0.884143	+	0.467216i	$0.845257\pi$
$972$		0			0
$973$	29.8942	−	35.7816i	0.958365	−	1.14710i
$974$		0			0
$975$	8.09727	+	7.40580i	0.259320	+	0.237175i
$976$		0			0
$977$	−15.2186	−	18.1369i	−0.486887	−	0.580249i	0.465536	−	0.885029i	$-0.345862\pi$
$977$	−15.2186	−	18.1369i	−0.486887	−	0.580249i	−0.952423	+	0.304780i	$0.901417\pi$
$978$		0			0
$979$	36.2117	+	6.38510i	1.15733	+	0.204069i
$980$		0			0
$981$	−40.2333	+	28.2845i	−1.28455	+	0.903053i
$982$		0			0
$983$	3.23861	−	18.3671i	0.103296	−	0.585819i	−0.888592	−	0.458699i	$-0.848316\pi$
$983$	3.23861	−	18.3671i	0.103296	−	0.585819i	0.991887	−	0.127120i	$-0.0405733\pi$
$984$		0			0
$985$	−2.08073	+	5.71675i	−0.0662975	+	0.182151i
$986$		0			0
$987$	26.1360	−	28.6992i	0.831919	−	0.913506i
$988$		0			0
$989$	−19.9280	−	11.5054i	−0.633674	−	0.365852i
$990$		0			0
$991$	20.8439	+	36.1027i	0.662129	+	1.14684i	0.980055	+	0.198725i	$0.0636802\pi$
$991$	20.8439	+	36.1027i	0.662129	+	1.14684i	−0.317926	+	0.948115i	$0.602986\pi$
$992$		0			0
$993$	26.2511	−	3.48110i	0.833052	−	0.110469i
$994$		0			0
$995$	24.6674	−	4.34953i	0.782010	−	0.137889i
$996$		0			0
$997$	2.76914	+	7.60816i	0.0876996	+	0.240953i	0.975787	−	0.218721i	$-0.0701885\pi$
$997$	2.76914	+	7.60816i	0.0876996	+	0.240953i	−0.888088	+	0.459674i	$0.847966\pi$
$998$		0			0
$999$	−45.5756	+	19.0287i	−1.44195	+	0.602040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.2	yes	144
7.5	odd	6		756.2.ca.a.173.7	✓	144
27.5	odd	18		756.2.ca.a.437.7	yes	144
189.5	even	18	inner	756.2.ck.a.5.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.7	✓	144	7.5	odd	6
756.2.ca.a.437.7	yes	144	27.5	odd	18
756.2.ck.a.5.2	yes	144	189.5	even	18	inner
756.2.ck.a.605.2	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69135 - 0.373296i) q^{3} +(-0.203680 - 1.15512i) q^{5} +(2.02312 - 1.70498i) q^{7} +(2.72130 + 1.26275i) q^{9} +O(q^{10})\)	\(q+(-1.69135 - 0.373296i) q^{3} +(-0.203680 - 1.15512i) q^{5} +(2.02312 - 1.70498i) q^{7} +(2.72130 + 1.26275i) q^{9} +(3.15137 + 0.555671i) q^{11} +(-1.12364 - 1.33911i) q^{13} +(-0.0867108 + 2.02975i) q^{15} -3.16451 q^{17} +6.65556i q^{19} +(-4.05827 + 2.12849i) q^{21} +(-3.65594 - 4.35698i) q^{23} +(3.40564 - 1.23955i) q^{25} +(-4.13128 - 3.15159i) q^{27} +(3.84940 - 4.58754i) q^{29} +(1.52309 - 4.18464i) q^{31} +(-5.12262 - 2.11622i) q^{33} +(-2.38154 - 1.98969i) q^{35} +(4.75241 - 8.23142i) q^{37} +(1.40059 + 2.68434i) q^{39} +(7.74888 - 6.50209i) q^{41} +(3.80179 - 1.38374i) q^{43} +(0.904355 - 3.40063i) q^{45} +(-7.95967 + 2.89708i) q^{47} +(1.18606 - 6.89879i) q^{49} +(5.35228 + 1.18130i) q^{51} +(-11.7526 - 6.78537i) q^{53} -3.75340i q^{55} +(2.48449 - 11.2568i) q^{57} +(-8.39859 + 7.04726i) q^{59} +(-0.888063 - 2.43993i) q^{61} +(7.65849 - 2.08508i) q^{63} +(-1.31797 + 1.57070i) q^{65} +(2.66559 + 15.1173i) q^{67} +(4.55701 + 8.73390i) q^{69} +(2.08522 - 1.20391i) q^{71} +(1.01078 - 0.583575i) q^{73} +(-6.22283 + 0.825197i) q^{75} +(7.32301 - 4.24883i) q^{77} +(1.74259 - 9.88269i) q^{79} +(5.81095 + 6.87262i) q^{81} +(-5.29556 - 4.44350i) q^{83} +(0.644546 + 3.65540i) q^{85} +(-8.22318 + 6.32215i) q^{87} +11.4908 q^{89} +(-4.55643 - 0.793385i) q^{91} +(-4.13817 + 6.50912i) q^{93} +(7.68800 - 1.35560i) q^{95} +(-0.0688894 - 0.189272i) q^{97} +(7.87414 + 5.49152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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