LMFDB - Embedded newform 1764.2.j.i.1177.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(589,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("1764.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.j (of order $3$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1177.7
Character	$\chi$	$=$	1764.1177
Dual form			1764.2.j.i.589.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.241270 + 1.71516i) q^{3} +(0.0111913 + 0.0193839i) q^{5} +(-2.88358 + 0.827636i) q^{9} +O(q^{10})$	\(q+(0.241270 + 1.71516i) q^{3} +(0.0111913 + 0.0193839i) q^{5} +(-2.88358 + 0.827636i) q^{9} +(0.280281 - 0.485460i) q^{11} +(-2.06442 - 3.57567i) q^{13} +(-0.0305465 + 0.0238717i) q^{15} -2.58304 q^{17} -3.39339 q^{19} +(-2.24626 - 3.89064i) q^{23} +(2.49975 - 4.32969i) q^{25} +(-2.11525 - 4.74613i) q^{27} +(2.57275 - 4.45613i) q^{29} +(0.407568 + 0.705929i) q^{31} +(0.900268 + 0.363600i) q^{33} +0.471092 q^{37} +(5.63478 - 4.40351i) q^{39} +(-3.02774 - 5.24420i) q^{41} +(0.811935 - 1.40631i) q^{43} +(-0.0483138 - 0.0466327i) q^{45} +(-6.05540 + 10.4883i) q^{47} +(-0.623211 - 4.43034i) q^{51} -2.91845 q^{53} +0.0125468 q^{55} +(-0.818723 - 5.82022i) q^{57} +(4.47941 + 7.75856i) q^{59} +(1.05692 - 1.83064i) q^{61} +(0.0462070 - 0.0800329i) q^{65} +(-7.54544 - 13.0691i) q^{67} +(6.13113 - 4.79140i) q^{69} +2.16045 q^{71} -7.10410 q^{73} +(8.02925 + 3.24286i) q^{75} +(-1.15891 + 2.00729i) q^{79} +(7.63004 - 4.77310i) q^{81} +(3.83160 - 6.63653i) q^{83} +(-0.0289077 - 0.0500695i) q^{85} +(8.26373 + 3.33756i) q^{87} +1.00473 q^{89} +(-1.11245 + 0.869366i) q^{93} +(-0.0379765 - 0.0657772i) q^{95} +(7.32986 - 12.6957i) q^{97} +(-0.406427 + 1.63183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9}+O(q^{10}) $ 24 * q + 8 * q^9	$ 24 q + 8 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} + 24 q^{37} - 40 q^{51} + 32 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} + 16 q^{81} + 12 q^{85} + 48 q^{93} + 32 q^{95} - 4 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.241270	+	1.71516i	0.139297	+	0.990251i
$3$	0.241270	+	1.71516i	0.139297	+	0.990251i
$4$		0			0
$5$	0.0111913	+	0.0193839i	0.00500491	+	0.00866875i	0.868517	−	0.495659i	$-0.165074\pi$
$5$	0.0111913	+	0.0193839i	0.00500491	+	0.00866875i	−0.863512	+	0.504328i	$0.831740\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.88358	+	0.827636i	−0.961193	+	0.275879i
$10$		0			0
$11$	0.280281	−	0.485460i	0.0845078	−	0.146372i	−0.820674	−	0.571397i	$-0.806402\pi$
$11$	0.280281	−	0.485460i	0.0845078	−	0.146372i	0.905181	+	0.425025i	$0.139735\pi$
$12$		0			0
$13$	−2.06442	−	3.57567i	−0.572566	−	0.991713i	−0.996301	−	0.0859272i	$-0.972615\pi$
$13$	−2.06442	−	3.57567i	−0.572566	−	0.991713i	0.423736	−	0.905786i	$-0.360719\pi$
$14$		0			0
$15$	−0.0305465	+	0.0238717i	−0.00788707	+	0.00616365i
$16$		0			0
$17$	−2.58304			−0.626480			−0.313240	−	0.949674i	$-0.601414\pi$
$17$	−2.58304			−0.626480			−0.313240	+	0.949674i	$0.601414\pi$
$18$		0			0
$19$	−3.39339			−0.778497			−0.389248	−	0.921133i	$-0.627265\pi$
$19$	−3.39339			−0.778497			−0.389248	+	0.921133i	$0.627265\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.24626	−	3.89064i	−0.468378	−	0.811255i	0.530969	−	0.847391i	$-0.321828\pi$
$23$	−2.24626	−	3.89064i	−0.468378	−	0.811255i	−0.999347	+	0.0361367i	$0.988495\pi$
$24$		0			0
$25$	2.49975	−	4.32969i	0.499950	−	0.865939i
$26$		0			0
$27$	−2.11525	−	4.74613i	−0.407080	−	0.913392i
$28$		0			0
$29$	2.57275	−	4.45613i	0.477748	−	0.827483i	−0.521927	−	0.852990i	$-0.674787\pi$
$29$	2.57275	−	4.45613i	0.477748	−	0.827483i	0.999675	+	0.0255069i	$0.00811996\pi$
$30$		0			0
$31$	0.407568	+	0.705929i	0.0732014	+	0.126789i	0.900303	−	0.435264i	$-0.143345\pi$
$31$	0.407568	+	0.705929i	0.0732014	+	0.126789i	−0.827101	+	0.562053i	$0.810012\pi$
$32$		0			0
$33$	0.900268	+	0.363600i	0.156717	+	0.0632947i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.471092			0.0774471			0.0387236	−	0.999250i	$-0.487671\pi$
$37$	0.471092			0.0774471			0.0387236	+	0.999250i	$0.487671\pi$
$38$		0			0
$39$	5.63478	−	4.40351i	0.902288	−	0.705127i
$40$		0			0
$41$	−3.02774	−	5.24420i	−0.472854	−	0.819007i	0.526663	−	0.850074i	$-0.323443\pi$
$41$	−3.02774	−	5.24420i	−0.472854	−	0.819007i	−0.999517	+	0.0310669i	$0.990110\pi$
$42$		0			0
$43$	0.811935	−	1.40631i	0.123819	−	0.214461i	−0.797452	−	0.603383i	$-0.793819\pi$
$43$	0.811935	−	1.40631i	0.123819	−	0.214461i	0.921271	+	0.388922i	$0.127152\pi$
$44$		0			0
$45$	−0.0483138	−	0.0466327i	−0.00720220	−	0.00695160i
$46$		0			0
$47$	−6.05540	+	10.4883i	−0.883271	+	1.52987i	−0.0355879	+	0.999367i	$0.511330\pi$
$47$	−6.05540	+	10.4883i	−0.883271	+	1.52987i	−0.847683	+	0.530503i	$0.822003\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.623211	−	4.43034i	−0.0872670	−	0.620372i
$52$		0			0
$53$	−2.91845			−0.400880			−0.200440	−	0.979706i	$-0.564237\pi$
$53$	−2.91845			−0.400880			−0.200440	+	0.979706i	$0.564237\pi$
$54$		0			0
$55$	0.0125468			0.00169182
$56$		0			0
$57$	−0.818723	−	5.82022i	−0.108443	−	0.770907i
$58$		0			0
$59$	4.47941	+	7.75856i	0.583169	+	1.01008i	0.995101	+	0.0988641i	$0.0315209\pi$
$59$	4.47941	+	7.75856i	0.583169	+	1.01008i	−0.411932	+	0.911215i	$0.635146\pi$
$60$		0			0
$61$	1.05692	−	1.83064i	0.135325	−	0.234390i	−0.790397	−	0.612596i	$-0.790125\pi$
$61$	1.05692	−	1.83064i	0.135325	−	0.234390i	0.925722	+	0.378206i	$0.123459\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0462070	−	0.0800329i	0.00573128	−	0.00992686i
$66$		0			0
$67$	−7.54544	−	13.0691i	−0.921822	−	1.59664i	−0.796594	−	0.604514i	$-0.793367\pi$
$67$	−7.54544	−	13.0691i	−0.921822	−	1.59664i	−0.125227	−	0.992128i	$-0.539966\pi$
$68$		0			0
$69$	6.13113	−	4.79140i	0.738102	−	0.576817i
$70$		0			0
$71$	2.16045			0.256398			0.128199	−	0.991748i	$-0.459080\pi$
$71$	2.16045			0.256398			0.128199	+	0.991748i	$0.459080\pi$
$72$		0			0
$73$	−7.10410			−0.831472			−0.415736	−	0.909485i	$-0.636476\pi$
$73$	−7.10410			−0.831472			−0.415736	+	0.909485i	$0.636476\pi$
$74$		0			0
$75$	8.02925	+	3.24286i	0.927138	+	0.374453i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.15891	+	2.00729i	−0.130387	+	0.225837i	−0.923826	−	0.382813i	$-0.874955\pi$
$79$	−1.15891	+	2.00729i	−0.130387	+	0.225837i	0.793439	+	0.608650i	$0.208289\pi$
$80$		0			0
$81$	7.63004	−	4.77310i	0.847782	−	0.530345i
$82$		0			0
$83$	3.83160	−	6.63653i	0.420573	−	0.728454i	−0.575423	−	0.817856i	$-0.695162\pi$
$83$	3.83160	−	6.63653i	0.420573	−	0.728454i	0.995996	+	0.0894025i	$0.0284958\pi$
$84$		0			0
$85$	−0.0289077	−	0.0500695i	−0.00313548	−	0.00543080i
$86$		0			0
$87$	8.26373	+	3.33756i	0.885965	+	0.357824i
$88$		0			0
$89$	1.00473			0.106501			0.0532506	−	0.998581i	$-0.483042\pi$
$89$	1.00473			0.106501			0.0532506	+	0.998581i	$0.483042\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.11245	+	0.869366i	−0.115356	+	0.0901490i
$94$		0			0
$95$	−0.0379765	−	0.0657772i	−0.00389630	−	0.00674860i
$96$		0			0
$97$	7.32986	−	12.6957i	0.744235	−	1.28905i	−0.206316	−	0.978485i	$-0.566148\pi$
$97$	7.32986	−	12.6957i	0.744235	−	1.28905i	0.950551	−	0.310567i	$-0.100519\pi$
$98$		0			0
$99$	−0.406427	+	1.63183i	−0.0408474	+	0.164005i
$100$		0			0
$101$	−7.57250	+	13.1160i	−0.753492	+	1.30509i	0.192629	+	0.981272i	$0.438299\pi$
$101$	−7.57250	+	13.1160i	−0.753492	+	1.30509i	−0.946121	+	0.323814i	$0.895035\pi$
$102$		0			0
$103$	−4.45031	−	7.70817i	−0.438502	−	0.759508i	0.559072	−	0.829119i	$-0.311158\pi$
$103$	−4.45031	−	7.70817i	−0.438502	−	0.759508i	−0.997574	+	0.0696109i	$0.977824\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	17.7169			1.71276			0.856380	−	0.516346i	$-0.172708\pi$
$107$	17.7169			1.71276			0.856380	+	0.516346i	$0.172708\pi$
$108$		0			0
$109$	−11.9487			−1.14447			−0.572237	−	0.820088i	$-0.693924\pi$
$109$	−11.9487			−1.14447			−0.572237	+	0.820088i	$0.693924\pi$
$110$		0			0
$111$	0.113660	+	0.808001i	0.0107882	+	0.0766920i
$112$		0			0
$113$	−7.50835	−	13.0048i	−0.706326	−	1.22339i	−0.966211	−	0.257753i	$-0.917018\pi$
$113$	−7.50835	−	13.0048i	−0.706326	−	1.22339i	0.259884	−	0.965640i	$-0.416316\pi$
$114$		0			0
$115$	0.0502773	−	0.0870828i	0.00468838	−	0.00812051i
$116$		0			0
$117$	8.91226	+	8.60215i	0.823938	+	0.795269i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.34289	+	9.25415i	0.485717	+	0.841286i
$122$		0			0
$123$	8.26417	−	6.45835i	0.745155	−	0.582329i
$124$		0			0
$125$	0.223815			0.0200186
$126$		0			0
$127$	4.17511			0.370481			0.185240	−	0.982693i	$-0.440694\pi$
$127$	4.17511			0.370481			0.185240	+	0.982693i	$0.440694\pi$
$128$		0			0
$129$	2.60795	+	1.05330i	0.229617	+	0.0927379i
$130$		0			0
$131$	3.03947	+	5.26451i	0.265560	+	0.459963i	0.967710	−	0.252066i	$-0.0811100\pi$
$131$	3.03947	+	5.26451i	0.265560	+	0.459963i	−0.702150	+	0.712029i	$0.747777\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.0683261	−	0.0941173i	0.00588057	−	0.00810032i
$136$		0			0
$137$	−8.04927	+	13.9418i	−0.687696	+	1.19112i	0.284886	+	0.958562i	$0.408044\pi$
$137$	−8.04927	+	13.9418i	−0.687696	+	1.19112i	−0.972581	+	0.232563i	$0.925289\pi$
$138$		0			0
$139$	−1.83849	−	3.18435i	−0.155938	−	0.270093i	0.777462	−	0.628930i	$-0.216507\pi$
$139$	−1.83849	−	3.18435i	−0.155938	−	0.270093i	−0.933400	+	0.358837i	$0.883173\pi$
$140$		0			0
$141$	−19.4501	−	7.85550i	−1.63799	−	0.661553i
$142$		0			0
$143$	−2.31446			−0.193545
$144$		0			0
$145$	0.115170			0.00956433
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.57786	−	7.92909i	−0.375033	−	0.649576i	0.615299	−	0.788294i	$-0.289035\pi$
$149$	−4.57786	−	7.92909i	−0.375033	−	0.649576i	−0.990332	+	0.138718i	$0.955702\pi$
$150$		0			0
$151$	9.28603	−	16.0839i	0.755687	−	1.30889i	−0.189346	−	0.981910i	$-0.560637\pi$
$151$	9.28603	−	16.0839i	0.755687	−	1.30889i	0.945032	−	0.326977i	$-0.106030\pi$
$152$		0			0
$153$	7.44841	−	2.13782i	0.602168	−	0.172832i
$154$		0			0
$155$	−0.00912245	+	0.0158005i	−0.000732732	+	0.00126913i
$156$		0			0
$157$	−5.83095	−	10.0995i	−0.465361	−	0.806028i	0.533857	−	0.845575i	$-0.320742\pi$
$157$	−5.83095	−	10.0995i	−0.465361	−	0.806028i	−0.999218	+	0.0395465i	$0.987409\pi$
$158$		0			0
$159$	−0.704134	−	5.00562i	−0.0558415	−	0.396971i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	13.0614			1.02305			0.511523	−	0.859270i	$-0.329082\pi$
$163$	13.0614			1.02305			0.511523	+	0.859270i	$0.329082\pi$
$164$		0			0
$165$	0.00302718	+	0.0215199i	0.000235665	+	0.00167532i
$166$		0			0
$167$	6.86282	+	11.8867i	0.531061	+	0.919824i	0.999343	+	0.0362450i	$0.0115397\pi$
$167$	6.86282	+	11.8867i	0.531061	+	0.919824i	−0.468282	+	0.883579i	$0.655127\pi$
$168$		0			0
$169$	−2.02362	+	3.50502i	−0.155663	+	0.269617i
$170$		0			0
$171$	9.78510	−	2.80849i	0.748285	−	0.214771i
$172$		0			0
$173$	−12.4629	+	21.5863i	−0.947534	+	1.64118i	−0.196936	+	0.980416i	$0.563099\pi$
$173$	−12.4629	+	21.5863i	−0.947534	+	1.64118i	−0.750597	+	0.660760i	$0.770234\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.2265	+	9.55483i	−0.918997	+	0.718185i
$178$		0			0
$179$	−9.16404			−0.684952			−0.342476	−	0.939527i	$-0.611266\pi$
$179$	−9.16404			−0.684952			−0.342476	+	0.939527i	$0.611266\pi$
$180$		0			0
$181$	0.882658			0.0656075			0.0328037	−	0.999462i	$-0.489556\pi$
$181$	0.882658			0.0656075			0.0328037	+	0.999462i	$0.489556\pi$
$182$		0			0
$183$	3.39486	+	1.37112i	0.250955	+	0.101356i
$184$		0			0
$185$	0.00527214	+	0.00913162i	0.000387616	+	0.000671370i
$186$		0			0
$187$	−0.723977	+	1.25397i	−0.0529425	+	0.0916991i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.30753	−	14.3891i	0.601111	−	1.04116i	−0.391542	−	0.920160i	$-0.628058\pi$
$191$	8.30753	−	14.3891i	0.601111	−	1.04116i	0.992653	−	0.120995i	$-0.0386086\pi$
$192$		0			0
$193$	−9.29344	−	16.0967i	−0.668957	−	1.15867i	−0.978196	−	0.207683i	$-0.933408\pi$
$193$	−9.29344	−	16.0967i	−0.668957	−	1.15867i	0.309240	−	0.950984i	$-0.399925\pi$
$194$		0			0
$195$	0.148418	+	0.0599431i	0.0106284	+	0.00429262i
$196$		0			0
$197$	23.4037			1.66744			0.833722	−	0.552184i	$-0.186205\pi$
$197$	23.4037			1.66744			0.833722	+	0.552184i	$0.186205\pi$
$198$		0			0
$199$	8.06852			0.571962			0.285981	−	0.958235i	$-0.407681\pi$
$199$	8.06852			0.571962			0.285981	+	0.958235i	$0.407681\pi$
$200$		0			0
$201$	20.5951	−	16.0948i	1.45267	−	1.13524i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.0677688	−	0.117379i	0.00473318	−	0.00819811i
$206$		0			0
$207$	9.69730	+	9.35988i	0.674009	+	0.650556i
$208$		0			0
$209$	−0.951102	+	1.64736i	−0.0657891	+	0.113950i
$210$		0			0
$211$	6.94647	+	12.0316i	0.478215	+	0.828292i	0.999688	−	0.0249755i	$-0.00795078\pi$
$211$	6.94647	+	12.0316i	0.478215	+	0.828292i	−0.521473	+	0.853268i	$0.674617\pi$
$212$		0			0
$213$	0.521252	+	3.70553i	0.0357156	+	0.253899i
$214$		0			0
$215$	0.0363465			0.00247881
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.71401	−	12.1847i	−0.115822	−	0.823366i
$220$		0			0
$221$	5.33248	+	9.23612i	0.358701	+	0.621289i
$222$		0			0
$223$	−8.28588	+	14.3516i	−0.554863	+	0.961052i	0.443051	+	0.896497i	$0.353896\pi$
$223$	−8.28588	+	14.3516i	−0.554863	+	0.961052i	−0.997914	+	0.0645551i	$0.979437\pi$
$224$		0			0
$225$	−3.62481	+	14.5539i	−0.241654	+	0.970259i
$226$		0			0
$227$	3.06311	−	5.30547i	0.203306	−	0.352136i	−0.746286	−	0.665626i	$-0.768165\pi$
$227$	3.06311	−	5.30547i	0.203306	−	0.352136i	0.949592	+	0.313490i	$0.101498\pi$
$228$		0			0
$229$	−14.4155	−	24.9683i	−0.952600	−	1.64995i	−0.739767	−	0.672863i	$-0.765064\pi$
$229$	−14.4155	−	24.9683i	−0.952600	−	1.64995i	−0.212833	−	0.977089i	$-0.568269\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.8999			−1.10715			−0.553575	−	0.832799i	$-0.686737\pi$
$233$	−16.8999			−1.10715			−0.553575	+	0.832799i	$0.686737\pi$
$234$		0			0
$235$	−0.271071			−0.0176828
$236$		0			0
$237$	−3.72244	−	1.50342i	−0.241798	−	0.0976575i
$238$		0			0
$239$	−7.63989	−	13.2327i	−0.494184	−	0.855951i	0.505794	−	0.862654i	$-0.331200\pi$
$239$	−7.63989	−	13.2327i	−0.494184	−	0.855951i	−0.999978	+	0.00670310i	$0.997866\pi$
$240$		0			0
$241$	2.09714	−	3.63236i	0.135089	−	0.233981i	−0.790543	−	0.612407i	$-0.790201\pi$
$241$	2.09714	−	3.63236i	0.135089	−	0.233981i	0.925631	+	0.378426i	$0.123535\pi$
$242$		0			0
$243$	10.0276	+	11.9352i	0.643268	+	0.765641i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.00537	+	12.1336i	0.445741	+	0.772046i
$248$		0			0
$249$	12.3072	+	4.97063i	0.779936	+	0.315001i
$250$		0			0
$251$	−19.7104			−1.24411			−0.622056	−	0.782973i	$-0.713702\pi$
$251$	−19.7104			−1.24411			−0.622056	+	0.782973i	$0.713702\pi$
$252$		0			0
$253$	−2.51834			−0.158326
$254$		0			0
$255$	0.0789029	−	0.0616617i	0.00494109	−	0.00386140i
$256$		0			0
$257$	−2.47060	−	4.27921i	−0.154112	−	0.266930i	0.778623	−	0.627492i	$-0.215918\pi$
$257$	−2.47060	−	4.27921i	−0.154112	−	0.266930i	−0.932735	+	0.360562i	$0.882585\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.73067	+	14.9789i	−0.230923	+	0.927171i
$262$		0			0
$263$	−13.5987	+	23.5537i	−0.838533	+	1.45238i	0.0525879	+	0.998616i	$0.483253\pi$
$263$	−13.5987	+	23.5537i	−0.838533	+	1.45238i	−0.891121	+	0.453766i	$0.850080\pi$
$264$		0			0
$265$	−0.0326613	−	0.0565710i	−0.00200637	−	0.00347513i
$266$		0			0
$267$	0.242411	+	1.72328i	0.0148353	+	0.105463i
$268$		0			0
$269$	−21.1769			−1.29118			−0.645588	−	0.763686i	$-0.723388\pi$
$269$	−21.1769			−1.29118			−0.645588	+	0.763686i	$0.723388\pi$
$270$		0			0
$271$	−23.5397			−1.42994			−0.714968	−	0.699157i	$-0.753559\pi$
$271$	−23.5397			−1.42994			−0.714968	+	0.699157i	$0.753559\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.40126	−	2.42706i	−0.0844994	−	0.146357i
$276$		0			0
$277$	−10.1560	+	17.5907i	−0.610216	+	1.05693i	0.380988	+	0.924580i	$0.375584\pi$
$277$	−10.1560	+	17.5907i	−0.610216	+	1.05693i	−0.991204	+	0.132345i	$0.957749\pi$
$278$		0			0
$279$	−1.75951	−	1.69828i	−0.105339	−	0.101674i
$280$		0			0
$281$	−9.63184	+	16.6828i	−0.574587	+	0.995215i	0.421499	+	0.906829i	$0.361504\pi$
$281$	−9.63184	+	16.6828i	−0.574587	+	0.995215i	−0.996086	+	0.0883856i	$0.971829\pi$
$282$		0			0
$283$	−8.99799	−	15.5850i	−0.534875	−	0.926430i	−0.999169	−	0.0407496i	$-0.987025\pi$
$283$	−8.99799	−	15.5850i	−0.534875	−	0.926430i	0.464295	−	0.885681i	$-0.346308\pi$
$284$		0			0
$285$	0.103656	−	0.0810060i	0.00614006	−	0.00479838i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−10.3279			−0.607523
$290$		0			0
$291$	23.5437	+	9.50883i	1.38016	+	0.557417i
$292$		0			0
$293$	5.27396	+	9.13477i	0.308108	+	0.533659i	0.977949	−	0.208846i	$-0.0669708\pi$
$293$	5.27396	+	9.13477i	0.308108	+	0.533659i	−0.669840	+	0.742505i	$0.733637\pi$
$294$		0			0
$295$	−0.100261	+	0.173657i	−0.00583742	+	0.0101107i
$296$		0			0
$297$	−2.89692	−	0.303376i	−0.168096	−	0.0176037i
$298$		0			0
$299$	−9.27444	+	16.0638i	−0.536355	+	0.928993i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−24.3230	−	9.82359i	−1.39732	−	0.564351i
$304$		0			0
$305$	0.0473134			0.00270916
$306$		0			0
$307$	−16.2337			−0.926506			−0.463253	−	0.886226i	$-0.653318\pi$
$307$	−16.2337			−0.926506			−0.463253	+	0.886226i	$0.653318\pi$
$308$		0			0
$309$	12.1470	−	9.49277i	0.691021	−	0.540025i
$310$		0			0
$311$	7.85512	+	13.6055i	0.445423	+	0.771495i	0.998082	−	0.0619125i	$-0.0197200\pi$
$311$	7.85512	+	13.6055i	0.445423	+	0.771495i	−0.552659	+	0.833408i	$0.686387\pi$
$312$		0			0
$313$	16.5194	−	28.6124i	0.933729	−	1.61727i	0.156846	−	0.987623i	$-0.449868\pi$
$313$	16.5194	−	28.6124i	0.933729	−	1.61727i	0.776884	−	0.629644i	$-0.216799\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.13063	+	7.15446i	−0.231999	+	0.401834i	−0.958396	−	0.285441i	$-0.907860\pi$
$317$	−4.13063	+	7.15446i	−0.231999	+	0.401834i	0.726397	+	0.687275i	$0.241193\pi$
$318$		0			0
$319$	−1.44218	−	2.49794i	−0.0807468	−	0.139858i
$320$		0			0
$321$	4.27456	+	30.3874i	0.238583	+	1.69606i
$322$		0			0
$323$	8.76527			0.487713
$324$		0			0
$325$	−20.6421			−1.14502
$326$		0			0
$327$	−2.88286	−	20.4939i	−0.159422	−	1.13332i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−9.13837	+	15.8281i	−0.502290	+	0.869992i	0.497706	+	0.867346i	$0.334176\pi$
$331$	−9.13837	+	15.8281i	−0.502290	+	0.869992i	−0.999996	+	0.00264661i	$0.999158\pi$
$332$		0			0
$333$	−1.35843	+	0.389893i	−0.0744416	+	0.0213660i
$334$		0			0
$335$	0.168887	−	0.292520i	0.00922727	−	0.0159821i
$336$		0			0
$337$	10.6530	+	18.4516i	0.580307	+	1.00512i	0.995443	+	0.0953621i	$0.0304009\pi$
$337$	10.6530	+	18.4516i	0.580307	+	1.00512i	−0.415135	+	0.909760i	$0.636266\pi$
$338$		0			0
$339$	20.4939	−	16.0157i	1.11308	−	0.869855i
$340$		0			0
$341$	0.456934			0.0247444
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.161492	+	0.0652233i	0.00869442	+	0.00351150i
$346$		0			0
$347$	10.9378	+	18.9448i	0.587170	+	1.01701i	0.994601	+	0.103773i	$0.0330915\pi$
$347$	10.9378	+	18.9448i	0.587170	+	1.01701i	−0.407431	+	0.913236i	$0.633575\pi$
$348$		0			0
$349$	−2.46155	+	4.26354i	−0.131764	+	0.228222i	−0.924357	−	0.381530i	$-0.875397\pi$
$349$	−2.46155	+	4.26354i	−0.131764	+	0.228222i	0.792593	+	0.609751i	$0.208731\pi$
$350$		0			0
$351$	−12.6038	+	17.3614i	−0.672743	+	0.926684i
$352$		0			0
$353$	2.30915	−	3.99956i	0.122903	−	0.212875i	−0.798008	−	0.602647i	$-0.794113\pi$
$353$	2.30915	−	3.99956i	0.122903	−	0.212875i	0.920911	+	0.389772i	$0.127446\pi$
$354$		0			0
$355$	0.0241783	+	0.0418780i	0.00128325	+	0.00222265i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	27.3390			1.44290			0.721449	−	0.692468i	$-0.243476\pi$
$359$	27.3390			1.44290			0.721449	+	0.692468i	$0.243476\pi$
$360$		0			0
$361$	−7.48491			−0.393943
$362$		0			0
$363$	−14.5833	+	11.3967i	−0.765425	+	0.598170i
$364$		0			0
$365$	−0.0795042	−	0.137705i	−0.00416144	−	0.00720783i
$366$		0			0
$367$	12.0924	−	20.9446i	0.631217	−	1.09330i	−0.356086	−	0.934453i	$-0.615889\pi$
$367$	12.0924	−	20.9446i	0.631217	−	1.09330i	0.987303	−	0.158847i	$-0.0507776\pi$
$368$		0			0
$369$	13.0710	+	12.6162i	0.680450	+	0.656773i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.11620	−	12.3256i	−0.368463	−	0.638196i	0.620863	−	0.783919i	$-0.286782\pi$
$373$	−7.11620	−	12.3256i	−0.368463	−	0.638196i	−0.989325	+	0.145723i	$0.953449\pi$
$374$		0			0
$375$	0.0539999	+	0.383880i	0.00278854	+	0.0198235i
$376$		0			0
$377$	−21.2449			−1.09417
$378$		0			0
$379$	14.5071			0.745178			0.372589	−	0.927996i	$-0.378470\pi$
$379$	14.5071			0.745178			0.372589	+	0.927996i	$0.378470\pi$
$380$		0			0
$381$	1.00733	+	7.16100i	0.0516070	+	0.366869i
$382$		0			0
$383$	−12.4659	−	21.5916i	−0.636979	−	1.10328i	−0.986092	−	0.166199i	$-0.946851\pi$
$383$	−12.4659	−	21.5916i	−0.636979	−	1.10328i	0.349113	−	0.937080i	$-0.386483\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.17736	+	4.72720i	−0.0598487	+	0.240297i
$388$		0			0
$389$	−15.5536	+	26.9396i	−0.788599	+	1.36589i	0.138226	+	0.990401i	$0.455860\pi$
$389$	−15.5536	+	26.9396i	−0.788599	+	1.36589i	−0.926825	+	0.375493i	$0.877473\pi$
$390$		0			0
$391$	5.80219	+	10.0497i	0.293430	+	0.508235i
$392$		0			0
$393$	−8.29617	+	6.48336i	−0.418487	+	0.327042i
$394$		0			0
$395$	−0.0518788			−0.00261030
$396$		0			0
$397$	3.04486			0.152817			0.0764086	−	0.997077i	$-0.475655\pi$
$397$	3.04486			0.152817			0.0764086	+	0.997077i	$0.475655\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.73300	−	9.92985i	−0.286292	−	0.495873i	0.686629	−	0.727008i	$-0.259090\pi$
$401$	−5.73300	−	9.92985i	−0.286292	−	0.495873i	−0.972922	+	0.231135i	$0.925756\pi$
$402$		0			0
$403$	1.68278	−	2.91466i	0.0838252	−	0.145190i
$404$		0			0
$405$	0.177912	+	0.0944828i	0.00884050	+	0.00469489i
$406$		0			0
$407$	0.132038	−	0.228697i	0.00654489	−	0.0113361i
$408$		0			0
$409$	−2.56246	−	4.43832i	−0.126706	−	0.219461i	0.795693	−	0.605700i	$-0.207107\pi$
$409$	−2.56246	−	4.43832i	−0.126706	−	0.219461i	−0.922398	+	0.386240i	$0.873774\pi$
$410$		0			0
$411$	−25.8544	−	10.4421i	−1.27531	−	0.515071i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.171523			0.00841971
$416$		0			0
$417$	5.01811	−	3.92159i	0.245738	−	0.192041i
$418$		0			0
$419$	17.2951	+	29.9560i	0.844921	+	1.46345i	0.885690	+	0.464278i	$0.153686\pi$
$419$	17.2951	+	29.9560i	0.844921	+	1.46345i	−0.0407685	+	0.999169i	$0.512981\pi$
$420$		0			0
$421$	−16.3403	+	28.3023i	−0.796379	+	1.37937i	0.125581	+	0.992083i	$0.459920\pi$
$421$	−16.3403	+	28.3023i	−0.796379	+	1.37937i	−0.921960	+	0.387285i	$0.873413\pi$
$422$		0			0
$423$	8.78076	−	35.2554i	0.426935	−	1.71417i
$424$		0			0
$425$	−6.45696	+	11.1838i	−0.313209	+	0.542493i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.558411	−	3.96969i	−0.0269603	−	0.191658i
$430$		0			0
$431$	0.145103			0.00698937			0.00349468	−	0.999994i	$-0.498888\pi$
$431$	0.145103			0.00698937			0.00349468	+	0.999994i	$0.498888\pi$
$432$		0			0
$433$	19.1583			0.920690			0.460345	−	0.887740i	$-0.347726\pi$
$433$	19.1583			0.920690			0.460345	+	0.887740i	$0.347726\pi$
$434$		0			0
$435$	0.0277870	+	0.197535i	0.00133229	+	0.00947109i
$436$		0			0
$437$	7.62244	+	13.2025i	0.364631	+	0.631559i
$438$		0			0
$439$	−3.79250	+	6.56881i	−0.181006	+	0.313512i	−0.942223	−	0.334985i	$-0.891269\pi$
$439$	−3.79250	+	6.56881i	−0.181006	+	0.313512i	0.761217	+	0.648497i	$0.224602\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.63242	−	2.82743i	0.0775586	−	0.134335i	−0.824637	−	0.565662i	$-0.808621\pi$
$443$	1.63242	−	2.82743i	0.0775586	−	0.134335i	0.902196	+	0.431326i	$0.141954\pi$
$444$		0			0
$445$	0.0112443	+	0.0194756i	0.000533029	+	0.000923233i
$446$		0			0
$447$	12.4952	−	9.76483i	0.591002	−	0.461861i
$448$		0			0
$449$	19.8316			0.935909			0.467955	−	0.883752i	$-0.344991\pi$
$449$	19.8316			0.935909			0.467955	+	0.883752i	$0.344991\pi$
$450$		0			0
$451$	−3.39447			−0.159839
$452$		0			0
$453$	29.8269	+	12.0465i	1.40139	+	0.565995i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.23051	−	3.86336i	0.104339	−	0.180720i	−0.809129	−	0.587631i	$-0.800061\pi$
$457$	2.23051	−	3.86336i	0.104339	−	0.180720i	0.913468	+	0.406911i	$0.133394\pi$
$458$		0			0
$459$	5.46379	+	12.2595i	0.255028	+	0.572222i
$460$		0			0
$461$	−7.88515	+	13.6575i	−0.367248	+	0.636092i	−0.989134	−	0.147015i	$-0.953033\pi$
$461$	−7.88515	+	13.6575i	−0.367248	+	0.636092i	0.621886	+	0.783108i	$0.286367\pi$
$462$		0			0
$463$	−8.34621	−	14.4561i	−0.387881	−	0.671830i	0.604283	−	0.796770i	$-0.293460\pi$
$463$	−8.34621	−	14.4561i	−0.387881	−	0.671830i	−0.992164	+	0.124940i	$0.960126\pi$
$464$		0			0
$465$	−0.0293015	−	0.0118343i	−0.00135882	−	0.000548802i
$466$		0			0
$467$	29.3947			1.36022			0.680112	−	0.733108i	$-0.261931\pi$
$467$	29.3947			1.36022			0.680112	+	0.733108i	$0.261931\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	15.9155	−	12.4377i	0.733346	−	0.573101i
$472$		0			0
$473$	−0.455139	−	0.788324i	−0.0209273	−	0.0362472i
$474$		0			0
$475$	−8.48262	+	14.6923i	−0.389209	+	0.674131i
$476$		0			0
$477$	8.41557	−	2.41541i	0.385322	−	0.110594i
$478$		0			0
$479$	9.16675	−	15.8773i	0.418839	−	0.725451i	−0.576984	−	0.816756i	$-0.695770\pi$
$479$	9.16675	−	15.8773i	0.418839	−	0.725451i	0.995823	+	0.0913046i	$0.0291037\pi$
$480$		0			0
$481$	−0.972530	−	1.68447i	−0.0443436	−	0.0768053i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.328123			0.0148993
$486$		0			0
$487$	−12.4953			−0.566217			−0.283108	−	0.959088i	$-0.591366\pi$
$487$	−12.4953			−0.566217			−0.283108	+	0.959088i	$0.591366\pi$
$488$		0			0
$489$	3.15132	+	22.4024i	0.142508	+	1.01307i
$490$		0			0
$491$	−1.75354	−	3.03721i	−0.0791359	−	0.137067i	0.823741	−	0.566966i	$-0.191883\pi$
$491$	−1.75354	−	3.03721i	−0.0791359	−	0.137067i	−0.902877	+	0.429898i	$0.858549\pi$
$492$		0			0
$493$	−6.64553	+	11.5104i	−0.299299	+	0.518402i
$494$		0			0
$495$	−0.0361798	+	0.0103842i	−0.00162616	+	0.000466735i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	16.1819	+	28.0279i	0.724402	+	1.25470i	0.959220	+	0.282662i	$0.0912175\pi$
$499$	16.1819	+	28.0279i	0.724402	+	1.25470i	−0.234817	+	0.972040i	$0.575449\pi$
$500$		0			0
$501$	−18.7319	+	14.6388i	−0.836881	+	0.654012i
$502$		0			0
$503$	15.3277			0.683430			0.341715	−	0.939804i	$-0.388992\pi$
$503$	15.3277			0.683430			0.341715	+	0.939804i	$0.388992\pi$
$504$		0			0
$505$	−0.338985			−0.0150846
$506$		0			0
$507$	−6.49992	−	2.62519i	−0.288672	−	0.116589i
$508$		0			0
$509$	−8.47237	−	14.6746i	−0.375531	−	0.650439i	0.614875	−	0.788625i	$-0.289206\pi$
$509$	−8.47237	−	14.6746i	−0.375531	−	0.650439i	−0.990406	+	0.138185i	$0.955873\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	7.17787	+	16.1055i	0.316911	+	0.711073i
$514$		0			0
$515$	0.0996097	−	0.172529i	0.00438933	−	0.00760254i
$516$		0			0
$517$	3.39442	+	5.87931i	0.149287	+	0.258572i
$518$		0			0
$519$	−40.0310	−	16.1677i	−1.75716	−	0.709684i
$520$		0			0
$521$	−18.7395			−0.820994			−0.410497	−	0.911862i	$-0.634645\pi$
$521$	−18.7395			−0.820994			−0.410497	+	0.911862i	$0.634645\pi$
$522$		0			0
$523$	8.96764			0.392127			0.196064	−	0.980591i	$-0.437184\pi$
$523$	8.96764			0.392127			0.196064	+	0.980591i	$0.437184\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.05277	−	1.82344i	−0.0458592	−	0.0794305i
$528$		0			0
$529$	1.40861	−	2.43978i	0.0612439	−	0.106078i
$530$		0			0
$531$	−19.3380	−	18.6651i	−0.839197	−	0.809996i
$532$		0			0
$533$	−12.5010	+	21.6524i	−0.541480	+	0.937871i
$534$		0			0
$535$	0.198276	+	0.343423i	0.00857220	+	0.0148475i
$536$		0			0
$537$	−2.21101	−	15.7178i	−0.0954120	−	0.678274i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	35.1518			1.51129			0.755646	−	0.654980i	$-0.227323\pi$
$541$	35.1518			1.51129			0.755646	+	0.654980i	$0.227323\pi$
$542$		0			0
$543$	0.212959	+	1.51390i	0.00913894	+	0.0649678i
$544$		0			0
$545$	−0.133721	−	0.231612i	−0.00572799	−	0.00992117i
$546$		0			0
$547$	7.75354	−	13.4295i	0.331517	−	0.574205i	−0.651292	−	0.758827i	$-0.725773\pi$
$547$	7.75354	−	13.4295i	0.331517	−	0.574205i	0.982810	+	0.184622i	$0.0591061\pi$
$548$		0			0
$549$	−1.53261	+	6.15355i	−0.0654103	+	0.262627i
$550$		0			0
$551$	−8.73034	+	15.1214i	−0.371925	+	0.644193i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.0143902	+	0.0112458i	−0.000610831	+	0.000477357i
$556$		0			0
$557$	2.96505			0.125633			0.0628166	−	0.998025i	$-0.479992\pi$
$557$	2.96505			0.125633			0.0628166	+	0.998025i	$0.479992\pi$
$558$		0			0
$559$	−6.70468			−0.283578
$560$		0			0
$561$	−2.32543	−	0.939196i	−0.0981798	−	0.0396529i
$562$		0			0
$563$	−12.1857	−	21.1062i	−0.513564	−	0.889520i	−0.999876	−	0.0157343i	$-0.994991\pi$
$563$	−12.1857	−	21.1062i	−0.513564	−	0.889520i	0.486312	−	0.873785i	$-0.338342\pi$
$564$		0			0
$565$	0.168057	−	0.291083i	0.00707020	−	0.0122459i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.4801	+	38.9366i	−0.942414	+	1.63231i	−0.181567	+	0.983379i	$0.558117\pi$
$569$	−22.4801	+	38.9366i	−0.942414	+	1.63231i	−0.760848	+	0.648931i	$0.775217\pi$
$570$		0			0
$571$	7.83880	+	13.5772i	0.328043	+	0.568188i	0.982124	−	0.188237i	$-0.0602774\pi$
$571$	7.83880	+	13.5772i	0.328043	+	0.568188i	−0.654080	+	0.756425i	$0.726944\pi$
$572$		0			0
$573$	26.6840	+	10.7771i	1.11474	+	0.450221i
$574$		0			0
$575$	−22.4604			−0.936662
$576$		0			0
$577$	27.4971			1.14472			0.572360	−	0.820003i	$-0.306028\pi$
$577$	27.4971			1.14472			0.572360	+	0.820003i	$0.306028\pi$
$578$		0			0
$579$	25.3663	−	19.8234i	1.05419	−	0.823834i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.817985	+	1.41679i	−0.0338775	+	0.0586775i
$584$		0			0
$585$	−0.0670035	+	0.269024i	−0.00277025	+	0.0111228i
$586$		0			0
$587$	13.3162	−	23.0644i	0.549619	−	0.951968i	−0.448681	−	0.893692i	$-0.648106\pi$
$587$	13.3162	−	23.0644i	0.549619	−	0.951968i	0.998300	−	0.0582763i	$-0.0185604\pi$
$588$		0			0
$589$	−1.38304	−	2.39549i	−0.0569871	−	0.0987045i
$590$		0			0
$591$	5.64661	+	40.1412i	0.232271	+	1.65119i
$592$		0			0
$593$	17.7599			0.729311			0.364656	−	0.931142i	$-0.381187\pi$
$593$	17.7599			0.729311			0.364656	+	0.931142i	$0.381187\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.94669	+	13.8388i	0.0796728	+	0.566386i
$598$		0			0
$599$	−8.29043	−	14.3594i	−0.338738	−	0.586711i	0.645458	−	0.763796i	$-0.276667\pi$
$599$	−8.29043	−	14.3594i	−0.338738	−	0.586711i	−0.984196	+	0.177085i	$0.943333\pi$
$600$		0			0
$601$	12.3406	−	21.3746i	0.503384	−	0.871886i	−0.496608	−	0.867975i	$-0.665422\pi$
$601$	12.3406	−	21.3746i	0.503384	−	0.871886i	0.999992	−	0.00391177i	$-0.00124516\pi$
$602$		0			0
$603$	32.5743	+	31.4408i	1.32653	+	1.28037i
$604$		0			0
$605$	−0.119588	+	0.207132i	−0.00486194	+	0.00842112i
$606$		0			0
$607$	−6.19000	−	10.7214i	−0.251244	−	0.435168i	0.712624	−	0.701546i	$-0.247506\pi$
$607$	−6.19000	−	10.7214i	−0.251244	−	0.435168i	−0.963869	+	0.266378i	$0.914173\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	50.0034			2.02292
$612$		0			0
$613$	−5.49601			−0.221982			−0.110991	−	0.993821i	$-0.535402\pi$
$613$	−5.49601			−0.221982			−0.110991	+	0.993821i	$0.535402\pi$
$614$		0			0
$615$	0.217675	+	0.0879146i	0.00877750	+	0.00354506i
$616$		0			0
$617$	−11.4573	−	19.8446i	−0.461254	−	0.798916i	0.537770	−	0.843092i	$-0.319267\pi$
$617$	−11.4573	−	19.8446i	−0.461254	−	0.798916i	−0.999024	+	0.0441763i	$0.985934\pi$
$618$		0			0
$619$	3.49256	−	6.04930i	0.140378	−	0.243142i	−0.787261	−	0.616620i	$-0.788502\pi$
$619$	3.49256	−	6.04930i	0.140378	−	0.243142i	0.927639	+	0.373478i	$0.121835\pi$
$620$		0			0
$621$	−13.7141	+	18.8907i	−0.550326	+	0.758059i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.4962	−	21.6441i	−0.499850	−	0.865765i
$626$		0			0
$627$	−3.05496	−	1.23384i	−0.122003	−	0.0492747i
$628$		0			0
$629$	−1.21685			−0.0485191
$630$		0			0
$631$	−14.7028			−0.585310			−0.292655	−	0.956218i	$-0.594539\pi$
$631$	−14.7028			−0.585310			−0.292655	+	0.956218i	$0.594539\pi$
$632$		0			0
$633$	−18.9603	+	14.8172i	−0.753603	+	0.588931i
$634$		0			0
$635$	0.0467249	+	0.0809300i	0.00185422	+	0.00321161i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−6.22983	+	1.78807i	−0.246448	+	0.0707348i
$640$		0			0
$641$	10.8057	−	18.7161i	0.426801	−	0.739241i	−0.569786	−	0.821793i	$-0.692974\pi$
$641$	10.8057	−	18.7161i	0.426801	−	0.739241i	0.996587	+	0.0825523i	$0.0263072\pi$
$642$		0			0
$643$	6.78105	+	11.7451i	0.267418	+	0.463182i	0.968194	−	0.250199i	$-0.0804961\pi$
$643$	6.78105	+	11.7451i	0.267418	+	0.463182i	−0.700776	+	0.713381i	$0.747163\pi$
$644$		0			0
$645$	0.00876931	+	0.0623401i	0.000345291	+	0.00245464i
$646$		0			0
$647$	20.4148			0.802590			0.401295	−	0.915949i	$-0.368560\pi$
$647$	20.4148			0.802590			0.401295	+	0.915949i	$0.368560\pi$
$648$		0			0
$649$	5.02197			0.197129
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24.3462	−	42.1689i	−0.952741	−	1.65020i	−0.739454	−	0.673207i	$-0.764916\pi$
$653$	−24.3462	−	42.1689i	−0.952741	−	1.65020i	−0.213287	−	0.976990i	$-0.568417\pi$
$654$		0			0
$655$	−0.0680313	+	0.117834i	−0.00265820	+	0.00460414i
$656$		0			0
$657$	20.4852	−	5.87961i	0.799205	−	0.229385i
$658$		0			0
$659$	−7.65029	+	13.2507i	−0.298013	+	0.516174i	−0.975681	−	0.219194i	$-0.929657\pi$
$659$	−7.65029	+	13.2507i	−0.298013	+	0.516174i	0.677668	+	0.735368i	$0.262991\pi$
$660$		0			0
$661$	8.77495	+	15.1987i	0.341306	+	0.591159i	0.984676	−	0.174397i	$-0.0557974\pi$
$661$	8.77495	+	15.1987i	0.341306	+	0.591159i	−0.643370	+	0.765556i	$0.722464\pi$
$662$		0			0
$663$	−14.5549	+	11.3745i	−0.565265	+	0.441748i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−23.1163			−0.895066
$668$		0			0
$669$	−26.6144	−	10.7490i	−1.02897	−	0.415582i
$670$		0			0
$671$	−0.592470	−	1.02619i	−0.0228721	−	0.0396156i
$672$		0			0
$673$	3.79336	−	6.57029i	0.146223	−	0.253266i	−0.783605	−	0.621259i	$-0.786622\pi$
$673$	3.79336	−	6.57029i	0.146223	−	0.253266i	0.929829	+	0.367993i	$0.119955\pi$
$674$		0			0
$675$	−25.8369	−	2.70573i	−0.994462	−	0.104144i
$676$		0			0
$677$	−5.76627	+	9.98748i	−0.221616	+	0.383850i	−0.955299	−	0.295642i	$-0.904466\pi$
$677$	−5.76627	+	9.98748i	−0.221616	+	0.383850i	0.733683	+	0.679492i	$0.237800\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	9.83878	+	3.97369i	0.377023	+	0.152272i
$682$		0			0
$683$	−14.9587			−0.572380			−0.286190	−	0.958173i	$-0.592389\pi$
$683$	−14.9587			−0.572380			−0.286190	+	0.958173i	$0.592389\pi$
$684$		0			0
$685$	−0.360328			−0.0137674
$686$		0			0
$687$	39.3467	−	30.7490i	1.50117	−	1.17315i
$688$		0			0
$689$	6.02489	+	10.4354i	0.229530	+	0.397558i
$690$		0			0
$691$	−9.94803	+	17.2305i	−0.378441	+	0.655479i	−0.990836	−	0.135073i	$-0.956873\pi$
$691$	−9.94803	+	17.2305i	−0.378441	+	0.655479i	0.612395	+	0.790552i	$0.290206\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.0411501	−	0.0712741i	0.00156091	−	0.00270358i
$696$		0			0
$697$	7.82079	+	13.5460i	0.296234	+	0.513092i
$698$		0			0
$699$	−4.07744	−	28.9861i	−0.154223	−	1.09636i
$700$		0			0
$701$	34.9655			1.32063			0.660315	−	0.750989i	$-0.270423\pi$
$701$	34.9655			1.32063			0.660315	+	0.750989i	$0.270423\pi$
$702$		0			0
$703$	−1.59860			−0.0602923
$704$		0			0
$705$	−0.0654014	−	0.464932i	−0.00246316	−	0.0175104i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	9.65227	−	16.7182i	0.362499	−	0.627866i	−0.625873	−	0.779925i	$-0.715257\pi$
$709$	9.65227	−	16.7182i	0.362499	−	0.627866i	0.988371	+	0.152059i	$0.0485904\pi$
$710$		0			0
$711$	1.68050	−	6.74732i	0.0630236	−	0.253044i
$712$		0			0
$713$	1.83101	−	3.17140i	0.0685719	−	0.118770i
$714$		0			0
$715$	−0.0259019	−	0.0448634i	−0.000968676	−	0.00167780i
$716$		0			0
$717$	20.8530	−	16.2963i	0.778768	−	0.608597i
$718$		0			0
$719$	35.4569			1.32232			0.661159	−	0.750246i	$-0.270065\pi$
$719$	35.4569			1.32232			0.661159	+	0.750246i	$0.270065\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	6.73607	+	2.72056i	0.250517	+	0.101179i
$724$		0			0
$725$	−12.8625	−	22.2784i	−0.477700	−	0.827400i
$726$		0			0
$727$	−2.27159	+	3.93452i	−0.0842487	+	0.145923i	−0.905071	−	0.425261i	$-0.860182\pi$
$727$	−2.27159	+	3.93452i	−0.0842487	+	0.145923i	0.820822	+	0.571184i	$0.193516\pi$
$728$		0			0
$729$	−18.0514	+	20.0785i	−0.668571	+	0.743648i
$730$		0			0
$731$	−2.09726	+	3.63257i	−0.0775701	+	0.134355i
$732$		0			0
$733$	16.6444	+	28.8290i	0.614777	+	1.06482i	0.990424	+	0.138062i	$0.0440872\pi$
$733$	16.6444	+	28.8290i	0.614777	+	1.06482i	−0.375647	+	0.926763i	$0.622579\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.45936			−0.311605
$738$		0			0
$739$	41.3199			1.51998			0.759988	−	0.649937i	$-0.225205\pi$
$739$	41.3199			1.51998			0.759988	+	0.649937i	$0.225205\pi$
$740$		0			0
$741$	−19.1210	+	14.9428i	−0.702428	+	0.548939i
$742$		0			0
$743$	−13.7638	−	23.8396i	−0.504946	−	0.874592i	−0.999984	−	0.00572027i	$-0.998179\pi$
$743$	−13.7638	−	23.8396i	−0.504946	−	0.874592i	0.495038	−	0.868871i	$-0.335154\pi$
$744$		0			0
$745$	0.102465	−	0.177474i	0.00375401	−	0.00650214i
$746$		0			0
$747$	−5.55609	+	22.3081i	−0.203287	+	0.816211i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−6.58398	−	11.4038i	−0.240253	−	0.416130i	0.720533	−	0.693420i	$-0.243897\pi$
$751$	−6.58398	−	11.4038i	−0.240253	−	0.416130i	−0.960786	+	0.277290i	$0.910564\pi$
$752$		0			0
$753$	−4.75554	−	33.8067i	−0.173302	−	1.23198i
$754$		0			0
$755$	0.415692			0.0151286
$756$		0			0
$757$	−13.7925			−0.501297			−0.250648	−	0.968078i	$-0.580644\pi$
$757$	−13.7925			−0.501297			−0.250648	+	0.968078i	$0.580644\pi$
$758$		0			0
$759$	−0.607599	−	4.31936i	−0.0220545	−	0.156783i
$760$		0			0
$761$	−15.6055	−	27.0294i	−0.565697	−	0.979816i	−0.996984	−	0.0776016i	$-0.975274\pi$
$761$	−15.6055	−	27.0294i	−0.565697	−	0.979816i	0.431287	−	0.902215i	$-0.358060\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.124797	+	0.120454i	0.00451204	+	0.00435504i
$766$		0			0
$767$	18.4947	−	32.0338i	0.667806	−	1.15667i
$768$		0			0
$769$	−19.1337	−	33.1405i	−0.689977	−	1.19508i	−0.971845	−	0.235622i	$-0.924287\pi$
$769$	−19.1337	−	33.1405i	−0.689977	−	1.19508i	0.281867	−	0.959453i	$-0.409046\pi$
$770$		0			0
$771$	6.74346	−	5.26993i	0.242860	−	0.189792i
$772$		0			0
$773$	−7.46790			−0.268602			−0.134301	−	0.990941i	$-0.542879\pi$
$773$	−7.46790			−0.268602			−0.134301	+	0.990941i	$0.542879\pi$
$774$		0			0
$775$	4.07527			0.146388
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.2743	+	17.7956i	0.368115	+	0.637594i
$780$		0			0
$781$	0.605533	−	1.04881i	0.0216677	−	0.0375295i
$782$		0			0
$783$	−26.5914	−	2.78475i	−0.950299	−	0.0995189i
$784$		0			0
$785$	0.130512	−	0.226053i	0.00465817	−	0.00806819i
$786$		0			0
$787$	10.3451	+	17.9182i	0.368761	+	0.638713i	0.989372	−	0.145405i	$-0.0464486\pi$
$787$	10.3451	+	17.9182i	0.368761	+	0.638713i	−0.620611	+	0.784119i	$0.713115\pi$
$788$		0			0
$789$	−43.6794	−	17.6412i	−1.55503	−	0.628045i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−8.72771			−0.309930
$794$		0			0
$795$	0.0891483	−	0.0696683i	0.00316176	−	0.00247088i
$796$		0			0
$797$	−15.8354	−	27.4276i	−0.560917	−	0.971537i	−0.997417	−	0.0718325i	$-0.977115\pi$
$797$	−15.8354	−	27.4276i	−0.560917	−	0.971537i	0.436500	−	0.899704i	$-0.356218\pi$
$798$		0			0
$799$	15.6414	−	27.0916i	0.553352	−	0.958433i
$800$		0			0
$801$	−2.89722	+	0.831551i	−0.102368	+	0.0293814i
$802$		0			0
$803$	−1.99114	+	3.44876i	−0.0702659	+	0.121704i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.10934	−	36.3218i	−0.179857	−	1.27859i
$808$		0			0
$809$	48.0861			1.69062			0.845308	−	0.534279i	$-0.179417\pi$
$809$	48.0861			1.69062			0.845308	+	0.534279i	$0.179417\pi$
$810$		0			0
$811$	−17.6685			−0.620427			−0.310213	−	0.950667i	$-0.600400\pi$
$811$	−17.6685			−0.620427			−0.310213	+	0.950667i	$0.600400\pi$
$812$		0			0
$813$	−5.67943	−	40.3745i	−0.199186	−	1.41600i
$814$		0			0
$815$	0.146174	+	0.253181i	0.00512025	+	0.00886853i
$816$		0			0
$817$	−2.75521	+	4.77216i	−0.0963926	+	0.166957i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−14.4990	+	25.1129i	−0.506017	+	0.876448i	0.493958	+	0.869486i	$0.335550\pi$
$821$	−14.4990	+	25.1129i	−0.506017	+	0.876448i	−0.999976	+	0.00696234i	$0.997784\pi$
$822$		0			0
$823$	−6.88723	−	11.9290i	−0.240074	−	0.415820i	0.720661	−	0.693287i	$-0.243838\pi$
$823$	−6.88723	−	11.9290i	−0.240074	−	0.415820i	−0.960735	+	0.277467i	$0.910505\pi$
$824$		0			0
$825$	3.82472	−	2.98897i	0.133160	−	0.104063i
$826$		0			0
$827$	21.4150			0.744673			0.372337	−	0.928098i	$-0.378557\pi$
$827$	21.4150			0.744673			0.372337	+	0.928098i	$0.378557\pi$
$828$		0			0
$829$	−18.8154			−0.653487			−0.326744	−	0.945113i	$-0.605951\pi$
$829$	−18.8154			−0.653487			−0.326744	+	0.945113i	$0.605951\pi$
$830$		0			0
$831$	−32.6214	−	13.1751i	−1.13162	−	0.457040i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.153608	+	0.266057i	−0.00531582	+	0.00920727i
$836$		0			0
$837$	2.48832	−	3.42759i	0.0860088	−	0.118475i
$838$		0			0
$839$	21.4124	−	37.0874i	0.739239	−	1.28040i	−0.213600	−	0.976921i	$-0.568519\pi$
$839$	21.4124	−	37.0874i	0.739239	−	1.28040i	0.952839	−	0.303477i	$-0.0981477\pi$
$840$		0			0
$841$	1.26191	+	2.18569i	0.0435142	+	0.0753688i
$842$		0			0
$843$	−30.9377	−	12.4951i	−1.06555	−	0.430355i
$844$		0			0
$845$	−0.0905880			−0.00311632
$846$		0			0
$847$		0			0
$848$		0			0
$849$	24.5598	−	19.1932i	0.842892	−	0.658709i
$850$		0			0
$851$	−1.05820	−	1.83285i	−0.0362745	−	0.0628293i
$852$		0			0
$853$	13.3281	−	23.0849i	0.456345	−	0.790412i	−0.542420	−	0.840108i	$-0.682492\pi$
$853$	13.3281	−	23.0849i	0.456345	−	0.790412i	0.998764	+	0.0496954i	$0.0158251\pi$
$854$		0			0
$855$	0.163948	+	0.158243i	0.00560689	+	0.00541180i
$856$		0			0
$857$	15.5907	−	27.0040i	0.532570	−	0.922438i	−0.466707	−	0.884412i	$-0.654560\pi$
$857$	15.5907	−	27.0040i	0.532570	−	0.922438i	0.999277	−	0.0380257i	$-0.0121069\pi$
$858$		0			0
$859$	26.9668	+	46.7078i	0.920094	+	1.59365i	0.799267	+	0.600976i	$0.205221\pi$
$859$	26.9668	+	46.7078i	0.920094	+	1.59365i	0.120827	+	0.992674i	$0.461445\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−33.7510			−1.14890			−0.574448	−	0.818541i	$-0.694783\pi$
$863$	−33.7510			−1.14890			−0.574448	+	0.818541i	$0.694783\pi$
$864$		0			0
$865$	−0.557903			−0.0189693
$866$		0			0
$867$	−2.49181	−	17.7140i	−0.0846263	−	0.601600i
$868$		0			0
$869$	0.649639	+	1.12521i	0.0220375	+	0.0381700i
$870$		0			0
$871$	−31.1538	+	53.9600i	−1.05561	+	1.82837i
$872$		0			0
$873$	−10.6288	+	42.6755i	−0.359731	+	1.44435i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.60808	−	2.78527i	−0.0543009	−	0.0940519i	0.837597	−	0.546288i	$-0.183960\pi$
$877$	−1.60808	−	2.78527i	−0.0543009	−	0.0940519i	−0.891898	+	0.452236i	$0.850626\pi$
$878$		0			0
$879$	−14.3952	+	11.2497i	−0.485538	+	0.379442i
$880$		0			0
$881$	−35.9141			−1.20998			−0.604989	−	0.796234i	$-0.706822\pi$
$881$	−35.9141			−1.20998			−0.604989	+	0.796234i	$0.706822\pi$
$882$		0			0
$883$	4.58572			0.154322			0.0771609	−	0.997019i	$-0.475414\pi$
$883$	4.58572			0.154322			0.0771609	+	0.997019i	$0.475414\pi$
$884$		0			0
$885$	−0.322040	−	0.130066i	−0.0108253	−	0.00437211i
$886$		0			0
$887$	−27.5154	−	47.6581i	−0.923877	−	1.60020i	−0.793357	−	0.608757i	$-0.791668\pi$
$887$	−27.5154	−	47.6581i	−0.923877	−	1.60020i	−0.130521	−	0.991446i	$-0.541665\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.178600	−	5.04189i	−0.00598331	−	0.168910i
$892$		0			0
$893$	20.5483	−	35.5907i	0.687624	−	1.19100i
$894$		0			0
$895$	−0.102558	−	0.177635i	−0.00342812	−	0.00593768i
$896$		0			0
$897$	−29.7897	−	12.0315i	−0.994649	−	0.401719i
$898$		0			0
$899$	4.19428			0.139887
$900$		0			0
$901$	7.53848			0.251143
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.00987810	+	0.0171094i	0.000328359	+	0.000568735i
$906$		0			0
$907$	6.38823	−	11.0647i	0.212118	−	0.367399i	−0.740259	−	0.672321i	$-0.765297\pi$
$907$	6.38823	−	11.0647i	0.212118	−	0.367399i	0.952377	+	0.304923i	$0.0986307\pi$
$908$		0			0
$909$	10.9807	−	44.0881i	0.364205	−	1.46231i
$910$		0			0
$911$	−15.9053	+	27.5489i	−0.526968	+	0.912735i	0.472539	+	0.881310i	$0.343338\pi$
$911$	−15.9053	+	27.5489i	−0.526968	+	0.912735i	−0.999506	+	0.0314246i	$0.989996\pi$
$912$		0			0
$913$	−2.14785	−	3.72018i	−0.0710834	−	0.123120i
$914$		0			0
$915$	0.0114153	+	0.0811503i	0.000377378	+	0.00268275i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−58.5448			−1.93121			−0.965607	−	0.260006i	$-0.916275\pi$
$919$	−58.5448			−1.93121			−0.965607	+	0.260006i	$0.916275\pi$
$920$		0			0
$921$	−3.91671	−	27.8435i	−0.129060	−	0.917474i
$922$		0			0
$923$	−4.46007	−	7.72506i	−0.146805	−	0.254274i
$924$		0			0
$925$	1.17761	−	2.03969i	0.0387197	−	0.0670644i
$926$		0			0
$927$	19.2124	+	18.5439i	0.631017	+	0.609060i
$928$		0			0
$929$	6.36634	−	11.0268i	0.208873	−	0.361779i	−0.742487	−	0.669861i	$-0.766354\pi$
$929$	6.36634	−	11.0268i	0.208873	−	0.361779i	0.951360	+	0.308082i	$0.0996872\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−21.4404	+	16.7554i	−0.701927	+	0.548548i
$934$		0			0
$935$	−0.0324090			−0.00105989
$936$		0			0
$937$	28.2201			0.921911			0.460956	−	0.887423i	$-0.347507\pi$
$937$	28.2201			0.921911			0.460956	+	0.887423i	$0.347507\pi$
$938$		0			0
$939$	53.0605	+	21.4301i	1.73157	+	0.699345i
$940$		0			0
$941$	24.3023	+	42.0928i	0.792232	+	1.37219i	0.924582	+	0.380983i	$0.124414\pi$
$941$	24.3023	+	42.0928i	0.792232	+	1.37219i	−0.132350	+	0.991203i	$0.542252\pi$
$942$		0			0
$943$	−13.6022	+	23.5597i	−0.442949	+	0.767210i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.10659	+	10.5769i	−0.198437	+	0.343704i	−0.948022	−	0.318205i	$-0.896920\pi$
$947$	−6.10659	+	10.5769i	−0.198437	+	0.343704i	0.749585	+	0.661909i	$0.230253\pi$
$948$		0			0
$949$	14.6658	+	25.4019i	0.476072	+	0.824582i
$950$		0			0
$951$	−13.2677	−	5.35855i	−0.430234	−	0.173763i
$952$		0			0
$953$	22.7206			0.735993			0.367996	−	0.929827i	$-0.380044\pi$
$953$	22.7206			0.735993			0.367996	+	0.929827i	$0.380044\pi$
$954$		0			0
$955$	0.371889			0.0120340
$956$		0			0
$957$	3.93642	−	3.07626i	0.127246	−	0.0994414i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.1678	−	26.2714i	0.489283	−	0.847463i
$962$		0			0
$963$	−51.0881	+	14.6632i	−1.64629	+	0.472514i
$964$		0			0
$965$	0.208012	−	0.360287i	0.00669613	−	0.0115980i
$966$		0			0
$967$	−26.9926	−	46.7526i	−0.868024	−	1.50346i	−0.864013	−	0.503469i	$-0.832057\pi$
$967$	−26.9926	−	46.7526i	−0.868024	−	1.50346i	−0.00401026	−	0.999992i	$-0.501277\pi$
$968$		0			0
$969$	2.11480	+	15.0339i	0.0679371	+	0.482958i
$970$		0			0
$971$	40.6374			1.30412			0.652059	−	0.758169i	$-0.273906\pi$
$971$	40.6374			1.30412			0.652059	+	0.758169i	$0.273906\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−4.98032	−	35.4046i	−0.159498	−	1.13385i
$976$		0			0
$977$	−10.0220	−	17.3586i	−0.320632	−	0.555351i	0.659987	−	0.751277i	$-0.270562\pi$
$977$	−10.0220	−	17.3586i	−0.320632	−	0.555351i	−0.980619	+	0.195927i	$0.937229\pi$
$978$		0			0
$979$	0.281607	−	0.487757i	0.00900018	−	0.0155888i
$980$		0			0
$981$	34.4549	−	9.88914i	1.10006	−	0.315736i
$982$		0			0
$983$	−4.83700	+	8.37793i	−0.154276	+	0.267214i	−0.932795	−	0.360407i	$-0.882638\pi$
$983$	−4.83700	+	8.37793i	−0.154276	+	0.267214i	0.778519	+	0.627621i	$0.215971\pi$
$984$		0			0
$985$	0.261918	+	0.453655i	0.00834540	+	0.0144547i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.29527			−0.231976
$990$		0			0
$991$	12.9376			0.410975			0.205488	−	0.978660i	$-0.434122\pi$
$991$	12.9376			0.410975			0.205488	+	0.978660i	$0.434122\pi$
$992$		0			0
$993$	−29.3526	−	11.8550i	−0.931478	−	0.376206i
$994$		0			0
$995$	0.0902974	+	0.156400i	0.00286262	+	0.00495820i
$996$		0			0
$997$	0.856372	−	1.48328i	0.0271216	−	0.0469759i	−0.852146	−	0.523304i	$-0.824699\pi$
$997$	0.856372	−	1.48328i	0.0271216	−	0.0469759i	0.879268	+	0.476328i	$0.158033\pi$
$998$		0			0
$999$	−0.996479	−	2.23586i	−0.0315272	−	0.0707396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.j.i.1177.7	yes	24
3.2	odd	2		5292.2.j.i.3529.6		24
7.2	even	3		1764.2.i.j.1537.2		24
7.3	odd	6		1764.2.l.j.961.3		24
7.4	even	3		1764.2.l.j.961.10		24
7.5	odd	6		1764.2.i.j.1537.11		24
7.6	odd	2	inner	1764.2.j.i.1177.6	yes	24
9.4	even	3	inner	1764.2.j.i.589.7	yes	24
9.5	odd	6		5292.2.j.i.1765.6		24
21.2	odd	6		5292.2.i.j.2125.6		24
21.5	even	6		5292.2.i.j.2125.7		24
21.11	odd	6		5292.2.l.j.3313.7		24
21.17	even	6		5292.2.l.j.3313.6		24
21.20	even	2		5292.2.j.i.3529.7		24
63.4	even	3		1764.2.i.j.373.2		24
63.5	even	6		5292.2.l.j.361.6		24
63.13	odd	6	inner	1764.2.j.i.589.6	✓	24
63.23	odd	6		5292.2.l.j.361.7		24
63.31	odd	6		1764.2.i.j.373.11		24
63.32	odd	6		5292.2.i.j.1549.6		24
63.40	odd	6		1764.2.l.j.949.3		24
63.41	even	6		5292.2.j.i.1765.7		24
63.58	even	3		1764.2.l.j.949.10		24
63.59	even	6		5292.2.i.j.1549.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.j.373.2		24	63.4	even	3
1764.2.i.j.373.11		24	63.31	odd	6
1764.2.i.j.1537.2		24	7.2	even	3
1764.2.i.j.1537.11		24	7.5	odd	6
1764.2.j.i.589.6	✓	24	63.13	odd	6	inner
1764.2.j.i.589.7	yes	24	9.4	even	3	inner
1764.2.j.i.1177.6	yes	24	7.6	odd	2	inner
1764.2.j.i.1177.7	yes	24	1.1	even	1	trivial
1764.2.l.j.949.3		24	63.40	odd	6
1764.2.l.j.949.10		24	63.58	even	3
1764.2.l.j.961.3		24	7.3	odd	6
1764.2.l.j.961.10		24	7.4	even	3
5292.2.i.j.1549.6		24	63.32	odd	6
5292.2.i.j.1549.7		24	63.59	even	6
5292.2.i.j.2125.6		24	21.2	odd	6
5292.2.i.j.2125.7		24	21.5	even	6
5292.2.j.i.1765.6		24	9.5	odd	6
5292.2.j.i.1765.7		24	63.41	even	6
5292.2.j.i.3529.6		24	3.2	odd	2
5292.2.j.i.3529.7		24	21.20	even	2
5292.2.l.j.361.6		24	63.5	even	6
5292.2.l.j.361.7		24	63.23	odd	6
5292.2.l.j.3313.6		24	21.17	even	6
5292.2.l.j.3313.7		24	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.241270 + 1.71516i) q^{3} +(0.0111913 + 0.0193839i) q^{5} +(-2.88358 + 0.827636i) q^{9} +O(q^{10})\)	\(q+(0.241270 + 1.71516i) q^{3} +(0.0111913 + 0.0193839i) q^{5} +(-2.88358 + 0.827636i) q^{9} +(0.280281 - 0.485460i) q^{11} +(-2.06442 - 3.57567i) q^{13} +(-0.0305465 + 0.0238717i) q^{15} -2.58304 q^{17} -3.39339 q^{19} +(-2.24626 - 3.89064i) q^{23} +(2.49975 - 4.32969i) q^{25} +(-2.11525 - 4.74613i) q^{27} +(2.57275 - 4.45613i) q^{29} +(0.407568 + 0.705929i) q^{31} +(0.900268 + 0.363600i) q^{33} +0.471092 q^{37} +(5.63478 - 4.40351i) q^{39} +(-3.02774 - 5.24420i) q^{41} +(0.811935 - 1.40631i) q^{43} +(-0.0483138 - 0.0466327i) q^{45} +(-6.05540 + 10.4883i) q^{47} +(-0.623211 - 4.43034i) q^{51} -2.91845 q^{53} +0.0125468 q^{55} +(-0.818723 - 5.82022i) q^{57} +(4.47941 + 7.75856i) q^{59} +(1.05692 - 1.83064i) q^{61} +(0.0462070 - 0.0800329i) q^{65} +(-7.54544 - 13.0691i) q^{67} +(6.13113 - 4.79140i) q^{69} +2.16045 q^{71} -7.10410 q^{73} +(8.02925 + 3.24286i) q^{75} +(-1.15891 + 2.00729i) q^{79} +(7.63004 - 4.77310i) q^{81} +(3.83160 - 6.63653i) q^{83} +(-0.0289077 - 0.0500695i) q^{85} +(8.26373 + 3.33756i) q^{87} +1.00473 q^{89} +(-1.11245 + 0.869366i) q^{93} +(-0.0379765 - 0.0657772i) q^{95} +(7.32986 - 12.6957i) q^{97} +(-0.406427 + 1.63183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9}+O(q^{10}) \) 24 * q + 8 * q^9	\( 24 q + 8 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} + 24 q^{37} - 40 q^{51} + 32 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} + 16 q^{81} + 12 q^{85} + 48 q^{93} + 32 q^{95} - 4 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more