LMFDB - Embedded newform 1764.2.w.c.1109.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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, 5, 5]))

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

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

chi := DirichletCharacter("1764.509");

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.w (of order $6$, degree $2$, not 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1109.16
Character	$\chi$	$=$	1764.1109
Dual form			1764.2.w.c.509.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.724112 - 1.57342i) q^{3} +(1.31387 - 2.27569i) q^{5} +(-1.95132 - 2.27867i) q^{9} +O(q^{10})$	\(q+(0.724112 - 1.57342i) q^{3} +(1.31387 - 2.27569i) q^{5} +(-1.95132 - 2.27867i) q^{9} +(-5.18523 + 2.99370i) q^{11} +(2.54231 - 1.46780i) q^{13} +(-2.62923 - 3.71513i) q^{15} +(0.0167322 - 0.0289811i) q^{17} +(-7.07369 + 4.08400i) q^{19} +(-7.04605 - 4.06804i) q^{23} +(-0.952507 - 1.64979i) q^{25} +(-4.99829 + 1.42024i) q^{27} +(-0.949006 - 0.547909i) q^{29} -8.10282i q^{31} +(0.955659 + 10.3263i) q^{33} +(-0.105898 - 0.183421i) q^{37} +(-0.468558 - 5.06298i) q^{39} +(2.23087 + 3.86399i) q^{41} +(3.78001 - 6.54717i) q^{43} +(-7.74933 + 1.44673i) q^{45} -7.07610 q^{47} +(-0.0334835 - 0.0473125i) q^{51} +(-1.59204 - 0.919166i) q^{53} +15.7333i q^{55} +(1.30371 + 14.0872i) q^{57} +4.73688 q^{59} -11.9827i q^{61} -7.71401i q^{65} +7.62295 q^{67} +(-11.5029 + 8.14070i) q^{69} -3.52461i q^{71} +(-2.24398 - 1.29556i) q^{73} +(-3.28554 + 0.304063i) q^{75} -7.17904 q^{79} +(-1.38468 + 8.89284i) q^{81} +(0.932743 - 1.61556i) q^{83} +(-0.0439680 - 0.0761548i) q^{85} +(-1.54928 + 1.09644i) q^{87} +(3.56125 + 6.16826i) q^{89} +(-12.7492 - 5.86735i) q^{93} +21.4634i q^{95} +(13.2520 + 7.65104i) q^{97} +(16.9397 + 5.97378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{9}+O(q^{10}) $ 48 * q - 8 * q^9	$ 48 q - 8 q^{9} + 24 q^{11} + 24 q^{15} - 48 q^{23} - 24 q^{25} + 56 q^{39} + 72 q^{51} - 48 q^{53} + 16 q^{57} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 48 q^{93} - 40 q^{99}+O(q^{100}) $ 48 * q - 8 * q^9 + 24 * q^11 + 24 * q^15 - 48 * q^23 - 24 * q^25 + 56 * q^39 + 72 * q^51 - 48 * q^53 + 16 * q^57 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 48 * q^93 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.724112	−	1.57342i	0.418067	−	0.908416i
$3$	0.724112	−	1.57342i	0.418067	−	0.908416i
$4$		0			0
$5$	1.31387	−	2.27569i	0.587580	−	1.01772i	−0.406968	−	0.913442i	$-0.633414\pi$
$5$	1.31387	−	2.27569i	0.587580	−	1.01772i	0.994548	−	0.104277i	$-0.0332527\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.95132	−	2.27867i	−0.650441	−	0.759557i
$10$		0			0
$11$	−5.18523	+	2.99370i	−1.56341	+	0.902633i	−0.566498	+	0.824063i	$0.691702\pi$
$11$	−5.18523	+	2.99370i	−1.56341	+	0.902633i	−0.996909	+	0.0785701i	$0.974965\pi$
$12$		0			0
$13$	2.54231	−	1.46780i	0.705110	−	0.407095i	−0.104138	−	0.994563i	$-0.533208\pi$
$13$	2.54231	−	1.46780i	0.705110	−	0.407095i	0.809248	+	0.587467i	$0.199875\pi$
$14$		0			0
$15$	−2.62923	−	3.71513i	−0.678865	−	0.959242i
$16$		0			0
$17$	0.0167322	−	0.0289811i	0.00405817	−	0.00702895i	−0.863989	−	0.503510i	$-0.832042\pi$
$17$	0.0167322	−	0.0289811i	0.00405817	−	0.00702895i	0.868047	+	0.496481i	$0.165375\pi$
$18$		0			0
$19$	−7.07369	+	4.08400i	−1.62282	+	0.936933i	−0.636653	+	0.771150i	$0.719682\pi$
$19$	−7.07369	+	4.08400i	−1.62282	+	0.936933i	−0.986162	+	0.165783i	$0.946985\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.04605	−	4.06804i	−1.46920	−	0.848244i	−0.469799	−	0.882774i	$-0.655673\pi$
$23$	−7.04605	−	4.06804i	−1.46920	−	0.848244i	−0.999404	+	0.0345292i	$0.989007\pi$
$24$		0			0
$25$	−0.952507	−	1.64979i	−0.190501	−	0.329958i
$26$		0			0
$27$	−4.99829	+	1.42024i	−0.961922	+	0.273326i
$28$		0			0
$29$	−0.949006	−	0.547909i	−0.176226	−	0.101744i	0.409292	−	0.912403i	$-0.365776\pi$
$29$	−0.949006	−	0.547909i	−0.176226	−	0.101744i	−0.585518	+	0.810659i	$0.699109\pi$
$30$		0			0
$31$		−	8.10282i		−	1.45531i	−0.685944	−	0.727654i	$-0.740611\pi$
$31$		−	8.10282i		−	1.45531i	0.685944	−	0.727654i	$-0.259389\pi$
$32$		0			0
$33$	0.955659	+	10.3263i	0.166359	+	1.79758i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.105898	−	0.183421i	−0.0174095	−	0.0301542i	0.857189	−	0.515001i	$-0.172209\pi$
$37$	−0.105898	−	0.183421i	−0.0174095	−	0.0301542i	−0.874599	+	0.484847i	$0.838875\pi$
$38$		0			0
$39$	−0.468558	−	5.06298i	−0.0750293	−	0.810726i
$40$		0			0
$41$	2.23087	+	3.86399i	0.348404	+	0.603453i	0.985966	−	0.166946i	$-0.0533904\pi$
$41$	2.23087	+	3.86399i	0.348404	+	0.603453i	−0.637562	+	0.770399i	$0.720057\pi$
$42$		0			0
$43$	3.78001	−	6.54717i	0.576446	−	0.998434i	−0.419437	−	0.907785i	$-0.637772\pi$
$43$	3.78001	−	6.54717i	0.576446	−	0.998434i	0.995883	−	0.0906496i	$-0.0288943\pi$
$44$		0			0
$45$	−7.74933	+	1.44673i	−1.15520	+	0.215665i
$46$		0			0
$47$	−7.07610			−1.03216			−0.516078	−	0.856542i	$-0.672609\pi$
$47$	−7.07610			−1.03216			−0.516078	+	0.856542i	$0.672609\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.0334835	−	0.0473125i	−0.00468863	−	0.00662507i
$52$		0			0
$53$	−1.59204	−	0.919166i	−0.218684	−	0.126257i	0.386657	−	0.922224i	$-0.373630\pi$
$53$	−1.59204	−	0.919166i	−0.218684	−	0.126257i	−0.605341	+	0.795967i	$0.706963\pi$
$54$		0			0
$55$			15.7333i			2.12148i
$56$		0			0
$57$	1.30371	+	14.0872i	0.172680	+	1.86589i
$58$		0			0
$59$	4.73688			0.616689			0.308344	−	0.951275i	$-0.400225\pi$
$59$	4.73688			0.616689			0.308344	+	0.951275i	$0.400225\pi$
$60$		0			0
$61$		−	11.9827i		−	1.53423i	−0.641509	−	0.767115i	$-0.721691\pi$
$61$		−	11.9827i		−	1.53423i	0.641509	−	0.767115i	$-0.278309\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	7.71401i		−	0.956805i
$66$		0			0
$67$	7.62295			0.931291			0.465646	−	0.884971i	$-0.345822\pi$
$67$	7.62295			0.931291			0.465646	+	0.884971i	$0.345822\pi$
$68$		0			0
$69$	−11.5029	+	8.14070i	−1.38478	+	0.980025i
$70$		0			0
$71$		−	3.52461i		−	0.418294i	−0.977884	−	0.209147i	$-0.932931\pi$
$71$		−	3.52461i		−	0.418294i	0.977884	−	0.209147i	$-0.0670687\pi$
$72$		0			0
$73$	−2.24398	−	1.29556i	−0.262638	−	0.151634i	0.362899	−	0.931828i	$-0.381787\pi$
$73$	−2.24398	−	1.29556i	−0.262638	−	0.151634i	−0.625537	+	0.780194i	$0.715120\pi$
$74$		0			0
$75$	−3.28554	+	0.304063i	−0.379382	+	0.0351102i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.17904			−0.807705			−0.403852	−	0.914824i	$-0.632329\pi$
$79$	−7.17904			−0.807705			−0.403852	+	0.914824i	$0.632329\pi$
$80$		0			0
$81$	−1.38468	+	8.89284i	−0.153854	+	0.988094i
$82$		0			0
$83$	0.932743	−	1.61556i	0.102382	−	0.177331i	−0.810284	−	0.586038i	$-0.800687\pi$
$83$	0.932743	−	1.61556i	0.102382	−	0.177331i	0.912666	+	0.408707i	$0.134020\pi$
$84$		0			0
$85$	−0.0439680	−	0.0761548i	−0.00476900	−	0.00826014i
$86$		0			0
$87$	−1.54928	+	1.09644i	−0.166100	+	0.117551i
$88$		0			0
$89$	3.56125	+	6.16826i	0.377492	+	0.653835i	0.990697	−	0.136089i	$-0.0434534\pi$
$89$	3.56125	+	6.16826i	0.377492	+	0.653835i	−0.613205	+	0.789924i	$0.710120\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−12.7492	−	5.86735i	−1.32203	−	0.608416i
$94$		0			0
$95$			21.4634i			2.20209i
$96$		0			0
$97$	13.2520	+	7.65104i	1.34554	+	0.776845i	0.987613	−	0.156907i	$-0.0501522\pi$
$97$	13.2520	+	7.65104i	1.34554	+	0.776845i	0.357922	+	0.933752i	$0.383486\pi$
$98$		0			0
$99$	16.9397	+	5.97378i	1.70250	+	0.600387i
$100$		0			0
$101$	−3.38758	−	5.86746i	−0.337077	−	0.583834i	0.646805	−	0.762655i	$-0.276105\pi$
$101$	−3.38758	−	5.86746i	−0.337077	−	0.583834i	−0.983881	+	0.178822i	$0.942771\pi$
$102$		0			0
$103$	4.22811	+	2.44110i	0.416608	+	0.240529i	0.693625	−	0.720336i	$-0.256012\pi$
$103$	4.22811	+	2.44110i	0.416608	+	0.240529i	−0.277017	+	0.960865i	$0.589346\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.8238	−	7.40383i	1.23972	−	0.715756i	0.270687	−	0.962667i	$-0.412749\pi$
$107$	12.8238	−	7.40383i	1.23972	−	0.715756i	0.969038	+	0.246912i	$0.0794158\pi$
$108$		0			0
$109$	5.82144	−	10.0830i	0.557593	−	0.965780i	−0.440104	−	0.897947i	$-0.645058\pi$
$109$	5.82144	−	10.0830i	0.557593	−	0.965780i	0.997697	−	0.0678327i	$-0.0216084\pi$
$110$		0			0
$111$	−0.365281	+	0.0338052i	−0.0346709	+	0.00320865i
$112$		0			0
$113$	−1.24947	+	0.721383i	−0.117540	+	0.0678620i	−0.557618	−	0.830098i	$-0.688284\pi$
$113$	−1.24947	+	0.721383i	−0.117540	+	0.0678620i	0.440077	+	0.897960i	$0.354951\pi$
$114$		0			0
$115$	−18.5152	+	10.6897i	−1.72655	+	0.996824i
$116$		0			0
$117$	−8.30551	−	2.92893i	−0.767844	−	0.270780i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	12.4244	−	21.5197i	1.12949	−	1.95634i
$122$		0			0
$123$	7.69509	−	0.712148i	0.693843	−	0.0642122i
$124$		0			0
$125$	8.13282			0.727421
$126$		0			0
$127$	8.25511			0.732523			0.366261	−	0.930512i	$-0.380638\pi$
$127$	8.25511			0.732523			0.366261	+	0.930512i	$0.380638\pi$
$128$		0			0
$129$	−7.56432	−	10.6884i	−0.666001	−	0.941065i
$130$		0			0
$131$	−6.64453	+	11.5087i	−0.580536	+	1.00552i	0.414880	+	0.909876i	$0.363823\pi$
$131$	−6.64453	+	11.5087i	−0.580536	+	1.00552i	−0.995416	+	0.0956411i	$0.969510\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.33507	+	13.2406i	−0.287037	+	1.13957i
$136$		0			0
$137$	−5.79362	+	3.34495i	−0.494982	+	0.285778i	−0.726639	−	0.687020i	$-0.758919\pi$
$137$	−5.79362	+	3.34495i	−0.494982	+	0.285778i	0.231657	+	0.972798i	$0.425585\pi$
$138$		0			0
$139$	−5.65156	+	3.26293i	−0.479359	+	0.276758i	−0.720149	−	0.693819i	$-0.755927\pi$
$139$	−5.65156	+	3.26293i	−0.479359	+	0.276758i	0.240790	+	0.970577i	$0.422593\pi$
$140$		0			0
$141$	−5.12390	+	11.1337i	−0.431510	+	0.937627i
$142$		0			0
$143$	−8.78831	+	15.2218i	−0.734916	+	1.27291i
$144$		0			0
$145$	−2.49374	+	1.43976i	−0.207094	+	0.119566i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.68597	−	2.70544i	−0.383889	−	0.221639i	0.295620	−	0.955306i	$-0.404474\pi$
$149$	−4.68597	−	2.70544i	−0.383889	−	0.221639i	−0.679509	+	0.733667i	$0.737807\pi$
$150$		0			0
$151$	−10.0358	−	17.3825i	−0.816699	−	1.41456i	−0.908101	−	0.418750i	$-0.862468\pi$
$151$	−10.0358	−	17.3825i	−0.816699	−	1.41456i	0.0914023	−	0.995814i	$-0.470865\pi$
$152$		0			0
$153$	−0.0986884	+	0.0184242i	−0.00797848	+	0.00148951i
$154$		0			0
$155$	−18.4395	−	10.6460i	−1.48110	−	0.855111i
$156$		0			0
$157$			1.31400i			0.104869i	0.998624	+	0.0524343i	$0.0166980\pi$
$157$			1.31400i			0.104869i	−0.998624	+	0.0524343i	$0.983302\pi$
$158$		0			0
$159$	−2.59905	+	1.83938i	−0.206118	+	0.145872i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	8.30283	+	14.3809i	0.650328	+	1.12640i	0.983043	+	0.183374i	$0.0587018\pi$
$163$	8.30283	+	14.3809i	0.650328	+	1.12640i	−0.332716	+	0.943027i	$0.607965\pi$
$164$		0			0
$165$	24.7551	+	11.3927i	1.92719	+	0.886919i
$166$		0			0
$167$	−6.18145	−	10.7066i	−0.478335	−	0.828501i	0.521356	−	0.853339i	$-0.325426\pi$
$167$	−6.18145	−	10.7066i	−0.478335	−	0.828501i	−0.999691	+	0.0248384i	$0.992093\pi$
$168$		0			0
$169$	−2.19111	+	3.79511i	−0.168547	+	0.291931i
$170$		0			0
$171$	23.1091	+	8.14942i	1.76720	+	0.623201i
$172$		0			0
$173$	−10.3691			−0.788349			−0.394174	−	0.919036i	$-0.628969\pi$
$173$	−10.3691			−0.788349			−0.394174	+	0.919036i	$0.628969\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.43003	−	7.45311i	0.257817	−	0.560210i
$178$		0			0
$179$	−19.5936	−	11.3124i	−1.46450	−	0.845528i	−0.465284	−	0.885162i	$-0.654048\pi$
$179$	−19.5936	−	11.3124i	−1.46450	−	0.845528i	−0.999214	+	0.0396332i	$0.987381\pi$
$180$		0			0
$181$			6.15765i			0.457695i	0.973462	+	0.228847i	$0.0734956\pi$
$181$			6.15765i			0.457695i	−0.973462	+	0.228847i	$0.926504\pi$
$182$		0			0
$183$	−18.8539	−	8.67684i	−1.39372	−	0.641410i
$184$		0			0
$185$	−0.556545			−0.0409180
$186$		0			0
$187$			0.200365i			0.0146521i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	22.9913i		−	1.66359i	−0.555084	−	0.831794i	$-0.687314\pi$
$191$		−	22.9913i		−	1.66359i	0.555084	−	0.831794i	$-0.312686\pi$
$192$		0			0
$193$	−17.2302			−1.24026			−0.620130	−	0.784499i	$-0.712920\pi$
$193$	−17.2302			−1.24026			−0.620130	+	0.784499i	$0.712920\pi$
$194$		0			0
$195$	−12.1374	−	5.58581i	−0.869177	−	0.400008i
$196$		0			0
$197$			4.31094i			0.307141i	0.988138	+	0.153571i	$0.0490773\pi$
$197$			4.31094i			0.307141i	−0.988138	+	0.153571i	$0.950923\pi$
$198$		0			0
$199$	6.35934	+	3.67156i	0.450801	+	0.260270i	0.708169	−	0.706043i	$-0.249522\pi$
$199$	6.35934	+	3.67156i	0.450801	+	0.260270i	−0.257367	+	0.966314i	$0.582855\pi$
$200$		0			0
$201$	5.51987	−	11.9941i	0.389342	−	0.846000i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	11.7243			0.818861
$206$		0			0
$207$	4.47939	+	23.9937i	0.311339	+	1.66768i
$208$		0			0
$209$	24.4525	−	42.3529i	1.69141	−	2.92961i
$210$		0			0
$211$	−6.79668	−	11.7722i	−0.467903	−	0.810431i	0.531425	−	0.847106i	$-0.321657\pi$
$211$	−6.79668	−	11.7722i	−0.467903	−	0.810431i	−0.999327	+	0.0366744i	$0.988324\pi$
$212$		0			0
$213$	−5.54570	−	2.55221i	−0.379985	−	0.174875i
$214$		0			0
$215$	−9.93288	−	17.2043i	−0.677417	−	1.17332i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.66336	+	2.59260i	−0.247547	+	0.175191i
$220$		0			0
$221$		−	0.0982386i		−	0.00660824i
$222$		0			0
$223$	22.6248	+	13.0624i	1.51507	+	0.874725i	0.999844	+	0.0176705i	$0.00562499\pi$
$223$	22.6248	+	13.0624i	1.51507	+	0.874725i	0.515225	+	0.857055i	$0.327708\pi$
$224$		0			0
$225$	−1.90068	+	5.38972i	−0.126712	+	0.359315i
$226$		0			0
$227$	−1.58102	−	2.73840i	−0.104936	−	0.181754i	0.808776	−	0.588117i	$-0.200130\pi$
$227$	−1.58102	−	2.73840i	−0.104936	−	0.181754i	−0.913712	+	0.406362i	$0.866797\pi$
$228$		0			0
$229$	11.7934	+	6.80892i	0.779330	+	0.449946i	0.836193	−	0.548436i	$-0.184777\pi$
$229$	11.7934	+	6.80892i	0.779330	+	0.449946i	−0.0568630	+	0.998382i	$0.518110\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−23.3765	+	13.4964i	−1.53145	+	0.884182i	−0.532152	+	0.846649i	$0.678617\pi$
$233$	−23.3765	+	13.4964i	−1.53145	+	0.884182i	−0.999295	+	0.0375332i	$0.988050\pi$
$234$		0			0
$235$	−9.29708	+	16.1030i	−0.606475	+	1.05044i
$236$		0			0
$237$	−5.19843	+	11.2957i	−0.337674	+	0.733732i
$238$		0			0
$239$	−7.46107	+	4.30765i	−0.482617	+	0.278639i	−0.721506	−	0.692408i	$-0.756550\pi$
$239$	−7.46107	+	4.30765i	−0.482617	+	0.278639i	0.238890	+	0.971047i	$0.423217\pi$
$240$		0			0
$241$	20.1317	−	11.6230i	1.29680	−	0.748706i	0.316947	−	0.948443i	$-0.397342\pi$
$241$	20.1317	−	11.6230i	1.29680	−	0.748706i	0.979849	+	0.199737i	$0.0640089\pi$
$242$		0			0
$243$	12.9895	+	8.61811i	0.833279	+	0.552852i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−11.9890	+	20.7656i	−0.762842	+	1.32128i
$248$		0			0
$249$	−1.86655	−	2.63745i	−0.118288	−	0.167141i
$250$		0			0
$251$	−9.09095			−0.573816			−0.286908	−	0.957958i	$-0.592627\pi$
$251$	−9.09095			−0.573816			−0.286908	+	0.957958i	$0.592627\pi$
$252$		0			0
$253$	48.7139			3.06261
$254$		0			0
$255$	−0.151661	+	0.0140356i	−0.00949741	+	0.000878945i
$256$		0			0
$257$	7.36958	−	12.7645i	0.459702	−	0.796226i	−0.539243	−	0.842150i	$-0.681290\pi$
$257$	7.36958	−	12.7645i	0.459702	−	0.796226i	0.998945	+	0.0459235i	$0.0146230\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.603312	+	3.23162i	0.0373441	+	0.200032i
$262$		0			0
$263$	24.1622	−	13.9501i	1.48991	−	0.860198i	0.489974	−	0.871737i	$-0.337006\pi$
$263$	24.1622	−	13.9501i	1.48991	−	0.860198i	0.999933	+	0.0115386i	$0.00367293\pi$
$264$		0			0
$265$	−4.18347	+	2.41533i	−0.256989	+	0.148372i
$266$		0			0
$267$	12.2840	−	1.13684i	0.751771	−	0.0695732i
$268$		0			0
$269$	6.57488	−	11.3880i	0.400878	−	0.694341i	−0.592954	−	0.805236i	$-0.702039\pi$
$269$	6.57488	−	11.3880i	0.400878	−	0.694341i	0.993832	+	0.110896i	$0.0353719\pi$
$270$		0			0
$271$	15.4231	−	8.90451i	0.936885	−	0.540911i	0.0479022	−	0.998852i	$-0.484746\pi$
$271$	15.4231	−	8.90451i	0.936885	−	0.540911i	0.888982	+	0.457941i	$0.151413\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.87794	+	5.70303i	0.595662	+	0.343906i
$276$		0			0
$277$	−8.89435	−	15.4055i	−0.534410	−	0.925625i	−0.999192	−	0.0401999i	$-0.987201\pi$
$277$	−8.89435	−	15.4055i	−0.534410	−	0.925625i	0.464782	−	0.885425i	$-0.346133\pi$
$278$		0			0
$279$	−18.4637	+	15.8112i	−1.10539	+	0.946592i
$280$		0			0
$281$	−18.3680	−	10.6048i	−1.09574	−	0.632628i	−0.160644	−	0.987012i	$-0.551357\pi$
$281$	−18.3680	−	10.6048i	−1.09574	−	0.632628i	−0.935100	+	0.354384i	$0.884691\pi$
$282$		0			0
$283$			18.7643i			1.11542i	0.830035	+	0.557711i	$0.188320\pi$
$283$			18.7643i			1.11542i	−0.830035	+	0.557711i	$0.811680\pi$
$284$		0			0
$285$	33.7709	+	15.5419i	2.00042	+	0.920622i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.49944	+	14.7215i	0.499967	+	0.865968i
$290$		0			0
$291$	21.6342	−	15.3108i	1.26822	−	0.897533i
$292$		0			0
$293$	−6.40500	−	11.0938i	−0.374184	−	0.648106i	0.616020	−	0.787730i	$-0.288744\pi$
$293$	−6.40500	−	11.0938i	−0.374184	−	0.648106i	−0.990205	+	0.139624i	$0.955411\pi$
$294$		0			0
$295$	6.22364	−	10.7797i	0.362354	−	0.627616i
$296$		0			0
$297$	21.6655	−	22.3276i	1.25716	−	1.29558i
$298$		0			0
$299$	−23.8843			−1.38127
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−11.6850	+	1.08140i	−0.671284	+	0.0621245i
$304$		0			0
$305$	−27.2689	−	15.7437i	−1.56142	−	0.901484i
$306$		0			0
$307$			3.97281i			0.226740i	0.993553	+	0.113370i	$0.0361646\pi$
$307$			3.97281i			0.226740i	−0.993553	+	0.113370i	$0.963835\pi$
$308$		0			0
$309$	6.90252	−	4.88498i	0.392670	−	0.277897i
$310$		0			0
$311$	−0.586407			−0.0332521			−0.0166260	−	0.999862i	$-0.505292\pi$
$311$	−0.586407			−0.0332521			−0.0166260	+	0.999862i	$0.505292\pi$
$312$		0			0
$313$		−	0.993112i		−	0.0561340i	−0.999606	−	0.0280670i	$-0.991065\pi$
$313$		−	0.993112i		−	0.0561340i	0.999606	−	0.0280670i	$-0.00893518\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			23.7894i			1.33615i	0.744096	+	0.668073i	$0.232881\pi$
$317$			23.7894i			1.33615i	−0.744096	+	0.668073i	$0.767119\pi$
$318$		0			0
$319$	6.56109			0.367350
$320$		0			0
$321$	−2.36348	−	25.5385i	−0.131917	−	1.42542i
$322$		0			0
$323$			0.273338i			0.0152089i
$324$		0			0
$325$	−4.84314	−	2.79619i	−0.268649	−	0.155105i
$326$		0			0
$327$	−11.6495	−	16.4608i	−0.644219	−	0.910287i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	27.0971			1.48939			0.744697	−	0.667403i	$-0.232594\pi$
$331$	27.0971			1.48939			0.744697	+	0.667403i	$0.232594\pi$
$332$		0			0
$333$	−0.211315	+	0.599220i	−0.0115800	+	0.0328371i
$334$		0			0
$335$	10.0156	−	17.3475i	0.547208	−	0.947793i
$336$		0			0
$337$	0.618503	+	1.07128i	0.0336920	+	0.0583562i	0.882380	−	0.470538i	$-0.155940\pi$
$337$	0.618503	+	1.07128i	0.0336920	+	0.0583562i	−0.848688	+	0.528894i	$0.822607\pi$
$338$		0			0
$339$	0.230283	+	2.48831i	0.0125072	+	0.135146i
$340$		0			0
$341$	24.2574	+	42.0150i	1.31361	+	2.27524i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3.41242	+	36.8728i	0.183718	+	1.98516i
$346$		0			0
$347$			13.4486i			0.721958i	0.932574	+	0.360979i	$0.117557\pi$
$347$			13.4486i			0.721958i	−0.932574	+	0.360979i	$0.882443\pi$
$348$		0			0
$349$	−12.4728	−	7.20115i	−0.667652	−	0.385469i	0.127535	−	0.991834i	$-0.459294\pi$
$349$	−12.4728	−	7.20115i	−0.667652	−	0.385469i	−0.795186	+	0.606365i	$0.792627\pi$
$350$		0			0
$351$	−10.6226	+	10.9472i	−0.566991	+	0.584319i
$352$		0			0
$353$	−3.77665	−	6.54134i	−0.201011	−	0.348161i	0.747844	−	0.663875i	$-0.231089\pi$
$353$	−3.77665	−	6.54134i	−0.201011	−	0.348161i	−0.948854	+	0.315714i	$0.897756\pi$
$354$		0			0
$355$	−8.02091	−	4.63087i	−0.425706	−	0.245781i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	20.8285	−	12.0253i	1.09928	−	0.634672i	0.163251	−	0.986585i	$-0.447802\pi$
$359$	20.8285	−	12.0253i	1.09928	−	0.634672i	0.936033	+	0.351913i	$0.114469\pi$
$360$		0			0
$361$	23.8580	−	41.3233i	1.25569	−	2.17491i
$362$		0			0
$363$	−24.8630	−	35.1316i	−1.30497	−	1.84393i
$364$		0			0
$365$	−5.89659	+	3.40440i	−0.308642	+	0.178194i
$366$		0			0
$367$	6.28058	−	3.62610i	0.327844	−	0.189281i	−0.327040	−	0.945011i	$-0.606051\pi$
$367$	6.28058	−	3.62610i	0.327844	−	0.189281i	0.654883	+	0.755730i	$0.272718\pi$
$368$		0			0
$369$	4.45160	−	12.6233i	0.231741	−	0.657143i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−6.15315	+	10.6576i	−0.318598	+	0.551828i	−0.980196	−	0.198031i	$-0.936545\pi$
$373$	−6.15315	+	10.6576i	−0.318598	+	0.551828i	0.661598	+	0.749859i	$0.269879\pi$
$374$		0			0
$375$	5.88907	−	12.7964i	0.304110	−	0.660801i
$376$		0			0
$377$	−3.21689			−0.165678
$378$		0			0
$379$	−20.4289			−1.04936			−0.524680	−	0.851299i	$-0.675815\pi$
$379$	−20.4289			−1.04936			−0.524680	+	0.851299i	$0.675815\pi$
$380$		0			0
$381$	5.97763	−	12.9888i	0.306243	−	0.665436i
$382$		0			0
$383$	17.6460	−	30.5638i	0.901668	−	1.56174i	0.0763399	−	0.997082i	$-0.475677\pi$
$383$	17.6460	−	30.5638i	0.901668	−	1.56174i	0.825328	−	0.564653i	$-0.190990\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−22.2949	+	4.16224i	−1.13331	+	0.211578i
$388$		0			0
$389$	−19.2835	+	11.1334i	−0.977714	+	0.564484i	−0.901579	−	0.432614i	$-0.857591\pi$
$389$	−19.2835	+	11.1334i	−0.977714	+	0.564484i	−0.0761350	+	0.997098i	$0.524258\pi$
$390$		0			0
$391$	−0.235792	+	0.136135i	−0.0119245	+	0.00688463i
$392$		0			0
$393$	13.2966	+	18.7882i	0.670726	+	0.947741i
$394$		0			0
$395$	−9.43232	+	16.3373i	−0.474592	+	0.822017i
$396$		0			0
$397$	16.8558	−	9.73170i	0.845969	−	0.488420i	−0.0133200	−	0.999911i	$-0.504240\pi$
$397$	16.8558	−	9.73170i	0.845969	−	0.488420i	0.859289	+	0.511491i	$0.170907\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.45051	−	4.30155i	−0.372061	−	0.214809i	0.302298	−	0.953214i	$-0.402246\pi$
$401$	−7.45051	−	4.30155i	−0.372061	−	0.214809i	−0.674358	+	0.738404i	$0.735580\pi$
$402$		0			0
$403$	−11.8933	−	20.5999i	−0.592449	−	1.02615i
$404$		0			0
$405$	18.4181	+	14.8351i	0.915200	+	0.737164i
$406$		0			0
$407$	1.09821	+	0.634053i	0.0544364	+	0.0314289i
$408$		0			0
$409$			19.3494i			0.956768i	0.878151	+	0.478384i	$0.158777\pi$
$409$			19.3494i			0.956768i	−0.878151	+	0.478384i	$0.841223\pi$
$410$		0			0
$411$	1.06779	+	11.5379i	0.0526700	+	0.569124i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.45101	−	4.24527i	−0.120315	−	0.208392i
$416$		0			0
$417$	1.04160	+	11.2550i	0.0510076	+	0.551161i
$418$		0			0
$419$	8.81222	+	15.2632i	0.430505	+	0.745657i	0.996917	−	0.0784657i	$-0.0250021\pi$
$419$	8.81222	+	15.2632i	0.430505	+	0.745657i	−0.566412	+	0.824122i	$0.691669\pi$
$420$		0			0
$421$	−5.77040	+	9.99463i	−0.281232	+	0.487109i	−0.971689	−	0.236266i	$-0.924076\pi$
$421$	−5.77040	+	9.99463i	−0.281232	+	0.487109i	0.690456	+	0.723374i	$0.257410\pi$
$422$		0			0
$423$	13.8078	+	16.1241i	0.671356	+	0.783981i
$424$		0			0
$425$	−0.0637503			−0.00309235
$426$		0			0
$427$		0			0
$428$		0			0
$429$	17.5866	+	24.8500i	0.849090	+	1.19977i
$430$		0			0
$431$	9.90849	+	5.72067i	0.477275	+	0.275555i	0.719280	−	0.694720i	$-0.244472\pi$
$431$	9.90849	+	5.72067i	0.477275	+	0.275555i	−0.242005	+	0.970275i	$0.577805\pi$
$432$		0			0
$433$		−	6.25525i		−	0.300608i	−0.988640	−	0.150304i	$-0.951975\pi$
$433$		−	6.25525i		−	0.300608i	0.988640	−	0.150304i	$-0.0480253\pi$
$434$		0			0
$435$	0.459606	+	4.96626i	0.0220364	+	0.238114i
$436$		0			0
$437$	66.4554			3.17899
$438$		0			0
$439$		−	15.3048i		−	0.730457i	−0.930918	−	0.365229i	$-0.880991\pi$
$439$		−	15.3048i		−	0.730457i	0.930918	−	0.365229i	$-0.119009\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			22.4980i			1.06891i	0.845196	+	0.534456i	$0.179483\pi$
$443$			22.4980i			1.06891i	−0.845196	+	0.534456i	$0.820517\pi$
$444$		0			0
$445$	18.7161			0.887227
$446$		0			0
$447$	−7.64997	+	5.41396i	−0.361831	+	0.256072i
$448$		0			0
$449$		−	25.9709i		−	1.22564i	−0.790222	−	0.612821i	$-0.790035\pi$
$449$		−	25.9709i		−	1.22564i	0.790222	−	0.612821i	$-0.209965\pi$
$450$		0			0
$451$	−23.1352	−	13.3571i	−1.08939	−	0.628962i
$452$		0			0
$453$	−34.6170	+	3.20366i	−1.62645	+	0.150521i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.0444037			0.00207712			0.00103856	−	0.999999i	$-0.499669\pi$
$457$	0.0444037			0.00207712			0.00103856	+	0.999999i	$0.499669\pi$
$458$		0			0
$459$	−0.0424725	+	0.168620i	−0.00198244	+	0.00787050i
$460$		0			0
$461$	1.46783	−	2.54236i	0.0683636	−	0.118409i	−0.829817	−	0.558035i	$-0.811556\pi$
$461$	1.46783	−	2.54236i	0.0683636	−	0.118409i	0.898181	+	0.439626i	$0.144889\pi$
$462$		0			0
$463$	−19.2017	−	33.2583i	−0.892378	−	1.54564i	−0.837017	−	0.547177i	$-0.815702\pi$
$463$	−19.2017	−	33.2583i	−0.892378	−	1.54564i	−0.0553609	−	0.998466i	$-0.517631\pi$
$464$		0			0
$465$	−30.1030	+	21.3042i	−1.39599	+	0.987958i
$466$		0			0
$467$	8.63913	+	14.9634i	0.399771	+	0.692424i	0.993697	−	0.112095i	$-0.0357562\pi$
$467$	8.63913	+	14.9634i	0.399771	+	0.692424i	−0.593926	+	0.804520i	$0.702423\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.06748	+	0.951483i	0.0952643	+	0.0438420i
$472$		0			0
$473$			45.2648i			2.08128i
$474$		0			0
$475$	13.4755	+	7.78007i	0.618297	+	0.356974i
$476$		0			0
$477$	1.01211	+	5.42133i	0.0463413	+	0.248226i
$478$		0			0
$479$	18.4571	+	31.9686i	0.843326	+	1.46068i	0.887067	+	0.461640i	$0.152739\pi$
$479$	18.4571	+	31.9686i	0.843326	+	1.46068i	−0.0437419	+	0.999043i	$0.513928\pi$
$480$		0			0
$481$	−0.538451	−	0.310875i	−0.0245513	−	0.0141747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	34.8228	−	20.1049i	1.58122	−	0.912918i
$486$		0			0
$487$	−2.03199	+	3.51951i	−0.0920783	+	0.159484i	−0.908385	−	0.418134i	$-0.862684\pi$
$487$	−2.03199	+	3.51951i	−0.0920783	+	0.159484i	0.816307	+	0.577618i	$0.196018\pi$
$488$		0			0
$489$	28.6395	−	2.65046i	1.29512	−	0.119858i
$490$		0			0
$491$	4.30460	−	2.48526i	0.194264	−	0.112158i	−0.399713	−	0.916640i	$-0.630890\pi$
$491$	4.30460	−	2.48526i	0.194264	−	0.112158i	0.593977	+	0.804482i	$0.297557\pi$
$492$		0			0
$493$	−0.0317580	+	0.0183355i	−0.00143031	+	0.000825789i
$494$		0			0
$495$	35.8510	−	30.7007i	1.61138	−	1.37990i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−4.60335	+	7.97323i	−0.206074	+	0.356931i	−0.950474	−	0.310803i	$-0.899402\pi$
$499$	−4.60335	+	7.97323i	−0.206074	+	0.356931i	0.744400	+	0.667734i	$0.232735\pi$
$500$		0			0
$501$	−21.3221	+	1.97327i	−0.952599	+	0.0881590i
$502$		0			0
$503$	1.16946			0.0521436			0.0260718	−	0.999660i	$-0.491700\pi$
$503$	1.16946			0.0521436			0.0260718	+	0.999660i	$0.491700\pi$
$504$		0			0
$505$	−17.8033			−0.792238
$506$		0			0
$507$	4.38470	+	6.19562i	0.194732	+	0.275157i
$508$		0			0
$509$	4.86206	−	8.42133i	0.215507	−	0.373269i	−0.737922	−	0.674886i	$-0.764193\pi$
$509$	4.86206	−	8.42133i	0.215507	−	0.373269i	0.953429	+	0.301617i	$0.0975263\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	29.5561	−	30.4593i	1.30493	−	1.34481i
$514$		0			0
$515$	11.1104	−	6.41458i	0.489582	−	0.282660i
$516$		0			0
$517$	36.6912	−	21.1837i	1.61368	−	0.931658i
$518$		0			0
$519$	−7.50840	+	16.3150i	−0.329582	+	0.716149i
$520$		0			0
$521$	−6.23317	+	10.7962i	−0.273080	+	0.472989i	−0.969649	−	0.244501i	$-0.921376\pi$
$521$	−6.23317	+	10.7962i	−0.273080	+	0.472989i	0.696569	+	0.717490i	$0.254709\pi$
$522$		0			0
$523$	15.6222	−	9.01951i	0.683113	−	0.394395i	−0.117914	−	0.993024i	$-0.537621\pi$
$523$	15.6222	−	9.01951i	0.683113	−	0.394395i	0.801027	+	0.598628i	$0.204287\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.234828	−	0.135578i	−0.0102293	−	0.00590588i
$528$		0			0
$529$	21.5979	+	37.4086i	0.939037	+	1.62646i
$530$		0			0
$531$	−9.24317	−	10.7938i	−0.401119	−	0.468410i
$532$		0			0
$533$	11.3431	+	6.54897i	0.491326	+	0.283667i
$534$		0			0
$535$		−	38.9107i		−	1.68226i
$536$		0			0
$537$	−31.9872	+	22.6377i	−1.38035	+	0.976887i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.87785	−	3.25253i	−0.0807349	−	0.139837i	0.822831	−	0.568286i	$-0.192393\pi$
$541$	−1.87785	−	3.25253i	−0.0807349	−	0.139837i	−0.903566	+	0.428449i	$0.859060\pi$
$542$		0			0
$543$	9.68859	+	4.45883i	0.415777	+	0.191347i
$544$		0			0
$545$	−15.2972	−	26.4956i	−0.655262	−	1.13495i
$546$		0			0
$547$	5.05062	−	8.74793i	0.215949	−	0.374034i	−0.737617	−	0.675219i	$-0.764049\pi$
$547$	5.05062	−	8.74793i	0.215949	−	0.374034i	0.953566	+	0.301185i	$0.0973822\pi$
$548$		0			0
$549$	−27.3047	+	23.3822i	−1.16534	+	0.997926i
$550$		0			0
$551$	8.95063			0.381310
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.403001	+	0.875681i	−0.0171065	+	0.0371706i
$556$		0			0
$557$	−15.7817	−	9.11158i	−0.668693	−	0.386070i	0.126888	−	0.991917i	$-0.459501\pi$
$557$	−15.7817	−	9.11158i	−0.668693	−	0.386070i	−0.795581	+	0.605847i	$0.792834\pi$
$558$		0			0
$559$		−	22.1933i		−	0.938674i
$560$		0			0
$561$	0.315259	+	0.145087i	0.0133102	+	0.00612557i
$562$		0			0
$563$	−16.6938			−0.703560			−0.351780	−	0.936083i	$-0.614424\pi$
$563$	−16.6938			−0.703560			−0.351780	+	0.936083i	$0.614424\pi$
$564$		0			0
$565$			3.79121i			0.159497i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	25.2546i		−	1.05873i	−0.848394	−	0.529365i	$-0.822430\pi$
$569$		−	25.2546i		−	1.05873i	0.848394	−	0.529365i	$-0.177570\pi$
$570$		0			0
$571$	−5.77962			−0.241869			−0.120935	−	0.992660i	$-0.538589\pi$
$571$	−5.77962			−0.241869			−0.120935	+	0.992660i	$0.538589\pi$
$572$		0			0
$573$	−36.1750	−	16.6483i	−1.51123	−	0.695491i
$574$		0			0
$575$			15.4993i			0.646367i
$576$		0			0
$577$	28.6539	+	16.5433i	1.19288	+	0.688708i	0.958958	−	0.283548i	$-0.0915115\pi$
$577$	28.6539	+	16.5433i	1.19288	+	0.688708i	0.233919	+	0.972256i	$0.424845\pi$
$578$		0			0
$579$	−12.4766	+	27.1105i	−0.518511	+	1.12667i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	11.0068			0.455855
$584$		0			0
$585$	−17.5777	+	15.0525i	−0.726748	+	0.622345i
$586$		0			0
$587$	14.1186	−	24.4541i	0.582737	−	1.00933i	−0.412417	−	0.910995i	$-0.635315\pi$
$587$	14.1186	−	24.4541i	0.582737	−	1.00933i	0.995153	−	0.0983341i	$-0.0313514\pi$
$588$		0			0
$589$	33.0919	+	57.3168i	1.36353	+	2.36170i
$590$		0			0
$591$	6.78293	+	3.12160i	0.279012	+	0.128406i
$592$		0			0
$593$	−9.29769	−	16.1041i	−0.381810	−	0.661315i	0.609511	−	0.792778i	$-0.291366\pi$
$593$	−9.29769	−	16.1041i	−0.381810	−	0.661315i	−0.991321	+	0.131463i	$0.958033\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	10.3818	−	7.34730i	0.424899	−	0.300705i
$598$		0			0
$599$			8.97521i			0.366717i	0.983046	+	0.183358i	$0.0586969\pi$
$599$			8.97521i			0.366717i	−0.983046	+	0.183358i	$0.941303\pi$
$600$		0			0
$601$	4.71245	+	2.72073i	0.192225	+	0.110981i	0.593024	−	0.805185i	$-0.297934\pi$
$601$	4.71245	+	2.72073i	0.192225	+	0.110981i	−0.400799	+	0.916166i	$0.631267\pi$
$602$		0			0
$603$	−14.8748	−	17.3702i	−0.605750	−	0.707369i
$604$		0			0
$605$	−32.6482	−	56.5483i	−1.32734	−	2.29901i
$606$		0			0
$607$	−32.0240	−	18.4890i	−1.29981	−	0.750447i	−0.319441	−	0.947606i	$-0.603495\pi$
$607$	−32.0240	−	18.4890i	−1.29981	−	0.750447i	−0.980372	+	0.197159i	$0.936829\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.9897	+	10.3863i	−0.727783	+	0.420186i
$612$		0			0
$613$	5.93439	−	10.2787i	0.239688	−	0.415151i	−0.720937	−	0.693001i	$-0.756288\pi$
$613$	5.93439	−	10.2787i	0.239688	−	0.415151i	0.960625	+	0.277849i	$0.0896216\pi$
$614$		0			0
$615$	8.48972	−	18.4473i	0.342339	−	0.743867i
$616$		0			0
$617$	16.2845	−	9.40188i	0.655591	−	0.378506i	−0.135004	−	0.990845i	$-0.543105\pi$
$617$	16.2845	−	9.40188i	0.655591	−	0.378506i	0.790595	+	0.612339i	$0.209771\pi$
$618$		0			0
$619$	−10.2892	+	5.94048i	−0.413558	+	0.238768i	−0.692318	−	0.721593i	$-0.743410\pi$
$619$	−10.2892	+	5.94048i	−0.413558	+	0.238768i	0.278759	+	0.960361i	$0.410077\pi$
$620$		0			0
$621$	40.9958	+	10.3261i	1.64510	+	0.414374i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.4480	−	26.7567i	0.617920	−	1.07027i
$626$		0			0
$627$	−48.9328	−	69.1424i	−1.95419	−	2.76128i
$628$		0			0
$629$	−0.00708765			−0.000282603
$630$		0			0
$631$	−28.3350			−1.12800			−0.563998	−	0.825776i	$-0.690738\pi$
$631$	−28.3350			−1.12800			−0.563998	+	0.825776i	$0.690738\pi$
$632$		0			0
$633$	−23.4442	+	2.16966i	−0.931823	+	0.0862363i
$634$		0			0
$635$	10.8461	−	18.7861i	0.430416	−	0.745502i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−8.03142	+	6.87764i	−0.317718	+	0.272075i
$640$		0			0
$641$	24.5634	−	14.1817i	0.970195	−	0.560142i	0.0708994	−	0.997483i	$-0.477413\pi$
$641$	24.5634	−	14.1817i	0.970195	−	0.560142i	0.899296	+	0.437341i	$0.144080\pi$
$642$		0			0
$643$	−16.0912	+	9.29024i	−0.634573	+	0.366371i	−0.782521	−	0.622624i	$-0.786067\pi$
$643$	−16.0912	+	9.29024i	−0.634573	+	0.366371i	0.147948	+	0.988995i	$0.452733\pi$
$644$		0			0
$645$	−34.2621	+	3.17081i	−1.34907	+	0.124851i
$646$		0			0
$647$	−21.4482	+	37.1494i	−0.843216	+	1.46049i	0.0439448	+	0.999034i	$0.486007\pi$
$647$	−21.4482	+	37.1494i	−0.843216	+	1.46049i	−0.887161	+	0.461460i	$0.847326\pi$
$648$		0			0
$649$	−24.5618	+	14.1808i	−0.964135	+	0.556644i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.18721	+	1.84014i	0.124725	+	0.0720101i	0.561065	−	0.827772i	$-0.310392\pi$
$653$	3.18721	+	1.84014i	0.124725	+	0.0720101i	−0.436339	+	0.899782i	$0.643725\pi$
$654$		0			0
$655$	17.4601	+	30.2418i	0.682223	+	1.18164i
$656$		0			0
$657$	1.42657	+	7.64135i	0.0556557	+	0.298117i
$658$		0			0
$659$	−13.7955	−	7.96483i	−0.537396	−	0.310266i	0.206627	−	0.978420i	$-0.433751\pi$
$659$	−13.7955	−	7.96483i	−0.537396	−	0.310266i	−0.744023	+	0.668154i	$0.767085\pi$
$660$		0			0
$661$		−	1.32072i		−	0.0513700i	−0.999670	−	0.0256850i	$-0.991823\pi$
$661$		−	1.32072i		−	0.0513700i	0.999670	−	0.0256850i	$-0.00817669\pi$
$662$		0			0
$663$	−0.154571	−	0.0711358i	−0.00600304	−	0.00276268i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.45783	+	7.72118i	0.172608	+	0.298965i
$668$		0			0
$669$	36.9356	−	26.1397i	1.42801	−	1.01062i
$670$		0			0
$671$	35.8726	+	62.1332i	1.38485	+	2.39863i
$672$		0			0
$673$	21.7987	−	37.7565i	0.840280	−	1.45541i	−0.0493788	−	0.998780i	$-0.515724\pi$
$673$	21.7987	−	37.7565i	0.840280	−	1.45541i	0.889658	−	0.456627i	$-0.150943\pi$
$674$		0			0
$675$	7.10401	+	6.89334i	0.273434	+	0.265325i
$676$		0			0
$677$	−28.9354			−1.11208			−0.556039	−	0.831156i	$-0.687680\pi$
$677$	−28.9354			−1.11208			−0.556039	+	0.831156i	$0.687680\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−5.45350	+	0.504699i	−0.208979	+	0.0193401i
$682$		0			0
$683$	1.90755	+	1.10132i	0.0729903	+	0.0421410i	0.536051	−	0.844186i	$-0.319915\pi$
$683$	1.90755	+	1.10132i	0.0729903	+	0.0421410i	−0.463061	+	0.886327i	$0.653249\pi$
$684$		0			0
$685$			17.5793i			0.671670i
$686$		0			0
$687$	19.2531	−	13.6256i	0.734550	−	0.519848i
$688$		0			0
$689$	−5.39662			−0.205595
$690$		0			0
$691$			29.8948i			1.13725i	0.822597	+	0.568625i	$0.192525\pi$
$691$			29.8948i			1.13725i	−0.822597	+	0.568625i	$0.807475\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			17.1483i			0.650471i
$696$		0			0
$697$	0.149310			0.00565552
$698$		0			0
$699$	4.30839	+	46.5541i	0.162958	+	1.76084i
$700$		0			0
$701$			45.4119i			1.71518i	0.514332	+	0.857591i	$0.328040\pi$
$701$			45.4119i			1.71518i	−0.514332	+	0.857591i	$0.671960\pi$
$702$		0			0
$703$	1.49818	+	0.864975i	0.0565049	+	0.0326231i
$704$		0			0
$705$	18.6047	+	26.2886i	0.700695	+	0.990087i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−15.8518			−0.595328			−0.297664	−	0.954671i	$-0.596207\pi$
$709$	−15.8518			−0.595328			−0.297664	+	0.954671i	$0.596207\pi$
$710$		0			0
$711$	14.0086	+	16.3587i	0.525364	+	0.613498i
$712$		0			0
$713$	−32.9626	+	57.0928i	−1.23446	+	2.13814i
$714$		0			0
$715$	23.0934	+	39.9989i	0.863644	+	1.49588i
$716$		0			0
$717$	1.37510	+	14.8586i	0.0513542	+	0.554906i
$718$		0			0
$719$	3.30154	+	5.71844i	0.123127	+	0.213262i	0.920999	−	0.389565i	$-0.127375\pi$
$719$	3.30154	+	5.71844i	0.123127	+	0.213262i	−0.797872	+	0.602826i	$0.794041\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−3.71035	−	40.0921i	−0.137989	−	1.49104i
$724$		0			0
$725$			2.08755i			0.0775296i
$726$		0			0
$727$	−31.2086	−	18.0183i	−1.15746	−	0.668261i	−0.206767	−	0.978390i	$-0.566294\pi$
$727$	−31.2086	−	18.0183i	−1.15746	−	0.668261i	−0.950694	+	0.310129i	$0.899628\pi$
$728$		0			0
$729$	22.9658	−	14.1976i	0.850586	−	0.525836i
$730$		0			0
$731$	−0.126496	−	0.219098i	−0.00467863	−	0.00810362i
$732$		0			0
$733$	−26.0312	−	15.0291i	−0.961486	−	0.555114i	−0.0648557	−	0.997895i	$-0.520659\pi$
$733$	−26.0312	−	15.0291i	−0.961486	−	0.555114i	−0.896630	+	0.442781i	$0.853992\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−39.5268	+	22.8208i	−1.45599	+	0.840614i
$738$		0			0
$739$	−4.83576	+	8.37577i	−0.177886	+	0.308108i	−0.941156	−	0.337972i	$-0.890259\pi$
$739$	−4.83576	+	8.37577i	−0.177886	+	0.308108i	0.763270	+	0.646079i	$0.223593\pi$
$740$		0			0
$741$	23.9916	+	33.9004i	0.881355	+	1.24536i
$742$		0			0
$743$	11.0205	−	6.36269i	0.404303	−	0.233424i	−0.284036	−	0.958814i	$-0.591674\pi$
$743$	11.0205	−	6.36269i	0.404303	−	0.233424i	0.688339	+	0.725389i	$0.258340\pi$
$744$		0			0
$745$	−12.3135	+	7.10920i	−0.451132	+	0.260461i
$746$		0			0
$747$	−5.50141	+	1.02706i	−0.201286	+	0.0375782i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.6870	+	18.5105i	−0.389975	+	0.675457i	−0.992446	−	0.122684i	$-0.960850\pi$
$751$	−10.6870	+	18.5105i	−0.389975	+	0.675457i	0.602471	+	0.798141i	$0.294183\pi$
$752$		0			0
$753$	−6.58287	+	14.3039i	−0.239893	+	0.521264i
$754$		0			0
$755$	−52.7428			−1.91951
$756$		0			0
$757$	−7.21065			−0.262076			−0.131038	−	0.991377i	$-0.541831\pi$
$757$	−7.21065			−0.262076			−0.131038	+	0.991377i	$0.541831\pi$
$758$		0			0
$759$	35.2743	−	76.6475i	1.28038	−	2.78213i
$760$		0			0
$761$	11.1620	−	19.3332i	0.404623	−	0.700827i	−0.589655	−	0.807655i	$-0.700736\pi$
$761$	11.1620	−	19.3332i	0.404623	−	0.700827i	0.994277	+	0.106829i	$0.0340696\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.0877360	+	0.248791i	−0.00317210	+	0.00899506i
$766$		0			0
$767$	12.0426	−	6.95280i	0.434833	−	0.251051i
$768$		0			0
$769$	13.3202	−	7.69042i	0.480338	−	0.277324i	−0.240219	−	0.970719i	$-0.577219\pi$
$769$	13.3202	−	7.69042i	0.480338	−	0.277324i	0.720558	+	0.693395i	$0.243886\pi$
$770$		0			0
$771$	−14.7475	−	20.8384i	−0.531119	−	0.750476i
$772$		0			0
$773$	6.17527	−	10.6959i	0.222109	−	0.384704i	−0.733339	−	0.679863i	$-0.762039\pi$
$773$	6.17527	−	10.6959i	0.222109	−	0.384704i	0.955448	+	0.295159i	$0.0953726\pi$
$774$		0			0
$775$	−13.3680	+	7.71799i	−0.480191	+	0.277238i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−31.5610	−	18.2218i	−1.13079	−	0.652862i
$780$		0			0
$781$	10.5516	+	18.2759i	0.377566	+	0.653963i
$782$		0			0
$783$	5.52157	+	1.39079i	0.197325	+	0.0497028i
$784$		0			0
$785$	2.99025	+	1.72642i	0.106727	+	0.0616187i
$786$		0			0
$787$		−	14.5290i		−	0.517904i	−0.965890	−	0.258952i	$-0.916623\pi$
$787$		−	14.5290i		−	0.517904i	0.965890	−	0.258952i	$-0.0833771\pi$
$788$		0			0
$789$	−4.45320	−	48.1189i	−0.158538	−	1.71308i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−17.5883	−	30.4638i	−0.624578	−	1.08180i
$794$		0			0
$795$	0.771030	+	8.33134i	0.0273456	+	0.295482i
$796$		0			0
$797$	22.0040	+	38.1120i	0.779420	+	1.35000i	0.932276	+	0.361747i	$0.117819\pi$
$797$	22.0040	+	38.1120i	0.779420	+	1.35000i	−0.152856	+	0.988248i	$0.548847\pi$
$798$		0			0
$799$	−0.118399	+	0.205073i	−0.00418866	+	0.00725497i
$800$		0			0
$801$	7.10630	−	20.1512i	0.251089	−	0.712007i
$802$		0			0
$803$	15.5141			0.547480
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−13.1572	−	18.5913i	−0.463157	−	0.654444i
$808$		0			0
$809$	−41.4554	−	23.9343i	−1.45749	−	0.841484i	−0.458606	−	0.888640i	$-0.651651\pi$
$809$	−41.4554	−	23.9343i	−1.45749	−	0.841484i	−0.998888	+	0.0471551i	$0.984985\pi$
$810$		0			0
$811$			17.4775i			0.613720i	0.951755	+	0.306860i	$0.0992783\pi$
$811$			17.4775i			0.613720i	−0.951755	+	0.306860i	$0.900722\pi$
$812$		0			0
$813$	−2.84253	−	30.7149i	−0.0996919	−	1.07722i
$814$		0			0
$815$	43.6353			1.52848
$816$		0			0
$817$			61.7502i			2.16037i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			7.39671i			0.258147i	0.991635	+	0.129074i	$0.0412003\pi$
$821$			7.39671i			0.258147i	−0.991635	+	0.129074i	$0.958800\pi$
$822$		0			0
$823$	−42.9436			−1.49692			−0.748460	−	0.663179i	$-0.769207\pi$
$823$	−42.9436			−1.49692			−0.748460	+	0.663179i	$0.769207\pi$
$824$		0			0
$825$	16.1260	−	11.4126i	0.561436	−	0.397334i
$826$		0			0
$827$			43.0042i			1.49540i	0.664035	+	0.747701i	$0.268843\pi$
$827$			43.0042i			1.49540i	−0.664035	+	0.747701i	$0.731157\pi$
$828$		0			0
$829$	10.0780	+	5.81851i	0.350022	+	0.202085i	0.664695	−	0.747115i	$-0.268561\pi$
$829$	10.0780	+	5.81851i	0.350022	+	0.202085i	−0.314673	+	0.949200i	$0.601895\pi$
$830$		0			0
$831$	−30.6798	+	2.83929i	−1.06427	+	0.0984939i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−32.4865			−1.12424
$836$		0			0
$837$	11.5080	+	40.5002i	0.397773	+	1.39989i
$838$		0			0
$839$	0.936892	−	1.62274i	0.0323451	−	0.0560234i	−0.849400	−	0.527750i	$-0.823036\pi$
$839$	0.936892	−	1.62274i	0.0323451	−	0.0560234i	0.881745	+	0.471727i	$0.156369\pi$
$840$		0			0
$841$	−13.8996	−	24.0748i	−0.479296	−	0.830166i
$842$		0			0
$843$	−29.9863	+	21.2216i	−1.03278	+	0.730911i
$844$		0			0
$845$	5.75766	+	9.97255i	0.198069	+	0.343066i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	29.5242	+	13.5875i	1.01327	+	0.466321i
$850$		0			0
$851$			1.72319i			0.0590702i
$852$		0			0
$853$	−34.9301	−	20.1669i	−1.19598	−	0.690501i	−0.236325	−	0.971674i	$-0.575943\pi$
$853$	−34.9301	−	20.1669i	−1.19598	−	0.690501i	−0.959657	+	0.281173i	$0.909276\pi$
$854$		0			0
$855$	48.9079	−	41.8819i	1.67262	−	1.43233i
$856$		0			0
$857$	−16.1341	−	27.9450i	−0.551129	−	0.954583i	−0.998193	−	0.0600814i	$-0.980864\pi$
$857$	−16.1341	−	27.9450i	−0.551129	−	0.954583i	0.447065	−	0.894502i	$-0.352469\pi$
$858$		0			0
$859$	33.6905	+	19.4512i	1.14951	+	0.663668i	0.948767	−	0.315977i	$-0.102332\pi$
$859$	33.6905	+	19.4512i	1.14951	+	0.663668i	0.200740	+	0.979645i	$0.435665\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	33.1319	−	19.1287i	1.12782	−	0.651148i	0.184435	−	0.982845i	$-0.440954\pi$
$863$	33.1319	−	19.1287i	1.12782	−	0.651148i	0.943386	+	0.331697i	$0.107621\pi$
$864$		0			0
$865$	−13.6237	+	23.5969i	−0.463218	+	0.802318i
$866$		0			0
$867$	29.3176	−	2.71322i	0.995679	−	0.0921459i
$868$		0			0
$869$	37.2250	−	21.4919i	1.26277	−	0.729061i
$870$		0			0
$871$	19.3799	−	11.1890i	0.656663	−	0.379124i
$872$		0			0
$873$	−8.42470	−	45.1265i	−0.285133	−	1.52730i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.76152	+	8.24719i	−0.160785	+	0.278488i	−0.935150	−	0.354251i	$-0.884736\pi$
$877$	−4.76152	+	8.24719i	−0.160785	+	0.278488i	0.774365	+	0.632739i	$0.218069\pi$
$878$		0			0
$879$	−22.0932	+	2.04463i	−0.745184	+	0.0689636i
$880$		0			0
$881$	−16.5770			−0.558493			−0.279247	−	0.960219i	$-0.590085\pi$
$881$	−16.5770			−0.558493			−0.279247	+	0.960219i	$0.590085\pi$
$882$		0			0
$883$	−34.9830			−1.17727			−0.588636	−	0.808398i	$-0.700335\pi$
$883$	−34.9830			−1.17727			−0.588636	+	0.808398i	$0.700335\pi$
$884$		0			0
$885$	−12.4543	−	17.5981i	−0.418648	−	0.591554i
$886$		0			0
$887$	−17.3795	+	30.1022i	−0.583547	+	1.01073i	0.411508	+	0.911406i	$0.365002\pi$
$887$	−17.3795	+	30.1022i	−0.583547	+	1.01073i	−0.995055	+	0.0993271i	$0.968331\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−19.4426	−	50.2568i	−0.651350	−	1.68367i
$892$		0			0
$893$	50.0542	−	28.8988i	1.67500	−	0.967061i
$894$		0			0
$895$	−51.4870	+	29.7260i	−1.72102	+	0.993632i
$896$		0			0
$897$	−17.2949	+	37.5801i	−0.577461	+	1.25476i
$898$		0			0
$899$	−4.43960	+	7.68962i	−0.148069	+	0.256463i
$900$		0			0
$901$	−0.0532769	+	0.0307594i	−0.00177491	+	0.00102474i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.0129	+	8.09035i	0.465805	+	0.268932i
$906$		0			0
$907$	−15.9116	−	27.5597i	−0.528336	−	0.915105i	−0.999454	−	0.0330347i	$-0.989483\pi$
$907$	−15.9116	−	27.5597i	−0.528336	−	0.915105i	0.471118	−	0.882070i	$-0.343851\pi$
$908$		0			0
$909$	−6.75975	+	19.1685i	−0.224207	+	0.635778i
$910$		0			0
$911$	7.51591	+	4.33931i	0.249013	+	0.143768i	0.619312	−	0.785145i	$-0.287411\pi$
$911$	7.51591	+	4.33931i	0.249013	+	0.143768i	−0.370299	+	0.928913i	$0.620745\pi$
$912$		0			0
$913$			11.1694i			0.369653i
$914$		0			0
$915$	−44.5173	+	31.5054i	−1.47170	+	1.04154i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−10.3922	−	17.9999i	−0.342808	−	0.593760i	0.642145	−	0.766583i	$-0.278045\pi$
$919$	−10.3922	−	17.9999i	−0.342808	−	0.593760i	−0.984953	+	0.172823i	$0.944711\pi$
$920$		0			0
$921$	6.25091	+	2.87676i	0.205975	+	0.0947925i
$922$		0			0
$923$	−5.17343	−	8.96064i	−0.170286	−	0.294943i
$924$		0			0
$925$	−0.201737	+	0.349419i	−0.00663308	+	0.0114888i
$926$		0			0
$927$	−2.68794	−	14.3979i	−0.0882836	−	0.472888i
$928$		0			0
$929$	−41.0722			−1.34753			−0.673767	−	0.738944i	$-0.735325\pi$
$929$	−41.0722			−1.34753			−0.673767	+	0.738944i	$0.735325\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.424625	+	0.922666i	−0.0139016	+	0.0302067i
$934$		0			0
$935$	0.455968	+	0.263254i	0.0149118	+	0.00860931i
$936$		0			0
$937$			8.38277i			0.273853i	0.990581	+	0.136927i	$0.0437225\pi$
$937$			8.38277i			0.273853i	−0.990581	+	0.136927i	$0.956278\pi$
$938$		0			0
$939$	−1.56259	−	0.719125i	−0.0509931	−	0.0234678i
$940$		0			0
$941$	9.99340			0.325775			0.162888	−	0.986645i	$-0.447919\pi$
$941$	9.99340			0.325775			0.162888	+	0.986645i	$0.447919\pi$
$942$		0			0
$943$		−	36.3011i		−	1.18213i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	23.5165i		−	0.764182i	−0.924125	−	0.382091i	$-0.875204\pi$
$947$		−	23.5165i		−	0.764182i	0.924125	−	0.382091i	$-0.124796\pi$
$948$		0			0
$949$	−7.60652			−0.246918
$950$		0			0
$951$	37.4308	+	17.2262i	1.21378	+	0.558598i
$952$		0			0
$953$		−	34.7300i		−	1.12501i	−0.826793	−	0.562507i	$-0.809837\pi$
$953$		−	34.7300i		−	1.12501i	0.826793	−	0.562507i	$-0.190163\pi$
$954$		0			0
$955$	−52.3210	−	30.2075i	−1.69307	−	0.977492i
$956$		0			0
$957$	4.75096	−	10.3234i	0.153577	−	0.333707i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−34.6556			−1.11792
$962$		0			0
$963$	−41.8943	−	14.7740i	−1.35002	−	0.476085i
$964$		0			0
$965$	−22.6383	+	39.2107i	−0.728753	+	1.26224i
$966$		0			0
$967$	8.98645	+	15.5650i	0.288985	+	0.500536i	0.973568	−	0.228399i	$-0.0733489\pi$
$967$	8.98645	+	15.5650i	0.288985	+	0.500536i	−0.684583	+	0.728935i	$0.740016\pi$
$968$		0			0
$969$	0.430076	+	0.197927i	0.0138160	+	0.00635834i
$970$		0			0
$971$	20.9001	+	36.2001i	0.670717	+	1.16172i	0.977701	+	0.210001i	$0.0673468\pi$
$971$	20.9001	+	36.2001i	0.670717	+	1.16172i	−0.306984	+	0.951715i	$0.599320\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7.90656	+	5.59555i	−0.253213	+	0.179201i
$976$		0			0
$977$		−	44.6291i		−	1.42781i	−0.700242	−	0.713905i	$-0.746925\pi$
$977$		−	44.6291i		−	1.42781i	0.700242	−	0.713905i	$-0.253075\pi$
$978$		0			0
$979$	−36.9318	−	21.3226i	−1.18035	−	0.681473i
$980$		0			0
$981$	−34.3354	+	6.41010i	−1.09625	+	0.204659i
$982$		0			0
$983$	−28.5601	−	49.4675i	−0.910925	−	1.57777i	−0.812760	−	0.582599i	$-0.802036\pi$
$983$	−28.5601	−	49.4675i	−0.910925	−	1.57777i	−0.0981655	−	0.995170i	$-0.531297\pi$
$984$		0			0
$985$	9.81035	+	5.66401i	0.312584	+	0.180470i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−53.2683	+	30.7544i	−1.69383	+	0.977935i
$990$		0			0
$991$	−18.6791	+	32.3532i	−0.593362	+	1.02773i	0.400413	+	0.916335i	$0.368867\pi$
$991$	−18.6791	+	32.3532i	−0.593362	+	1.02773i	−0.993776	+	0.111399i	$0.964467\pi$
$992$		0			0
$993$	19.6214	−	42.6353i	0.622665	−	1.35299i
$994$		0			0
$995$	16.7107	−	9.64792i	0.529764	−	0.305859i
$996$		0			0
$997$	−34.0530	+	19.6605i	−1.07847	+	0.622654i	−0.930483	−	0.366335i	$-0.880612\pi$
$997$	−34.0530	+	19.6605i	−1.07847	+	0.622654i	−0.147986	+	0.988990i	$0.547279\pi$
$998$		0			0
$999$	0.789811	+	0.766390i	0.0249885	+	0.0242475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.c.1109.16		48
3.2	odd	2		5292.2.w.c.521.5		48
7.2	even	3		1764.2.bm.c.1685.18		48
7.3	odd	6		1764.2.x.c.1469.23	yes	48
7.4	even	3		1764.2.x.c.1469.2	yes	48
7.5	odd	6		1764.2.bm.c.1685.7		48
7.6	odd	2	inner	1764.2.w.c.1109.9		48
9.4	even	3		5292.2.bm.c.2285.5		48
9.5	odd	6		1764.2.bm.c.1697.7		48
21.2	odd	6		5292.2.bm.c.4625.20		48
21.5	even	6		5292.2.bm.c.4625.5		48
21.11	odd	6		5292.2.x.c.4409.5		48
21.17	even	6		5292.2.x.c.4409.20		48
21.20	even	2		5292.2.w.c.521.20		48
63.4	even	3		5292.2.x.c.881.20		48
63.5	even	6	inner	1764.2.w.c.509.16		48
63.13	odd	6		5292.2.bm.c.2285.20		48
63.23	odd	6	inner	1764.2.w.c.509.9		48
63.31	odd	6		5292.2.x.c.881.5		48
63.32	odd	6		1764.2.x.c.293.23	yes	48
63.40	odd	6		5292.2.w.c.1097.5		48
63.41	even	6		1764.2.bm.c.1697.18		48
63.58	even	3		5292.2.w.c.1097.20		48
63.59	even	6		1764.2.x.c.293.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.w.c.509.9		48	63.23	odd	6	inner
1764.2.w.c.509.16		48	63.5	even	6	inner
1764.2.w.c.1109.9		48	7.6	odd	2	inner
1764.2.w.c.1109.16		48	1.1	even	1	trivial
1764.2.x.c.293.2	✓	48	63.59	even	6
1764.2.x.c.293.23	yes	48	63.32	odd	6
1764.2.x.c.1469.2	yes	48	7.4	even	3
1764.2.x.c.1469.23	yes	48	7.3	odd	6
1764.2.bm.c.1685.7		48	7.5	odd	6
1764.2.bm.c.1685.18		48	7.2	even	3
1764.2.bm.c.1697.7		48	9.5	odd	6
1764.2.bm.c.1697.18		48	63.41	even	6
5292.2.w.c.521.5		48	3.2	odd	2
5292.2.w.c.521.20		48	21.20	even	2
5292.2.w.c.1097.5		48	63.40	odd	6
5292.2.w.c.1097.20		48	63.58	even	3
5292.2.x.c.881.5		48	63.31	odd	6
5292.2.x.c.881.20		48	63.4	even	3
5292.2.x.c.4409.5		48	21.11	odd	6
5292.2.x.c.4409.20		48	21.17	even	6
5292.2.bm.c.2285.5		48	9.4	even	3
5292.2.bm.c.2285.20		48	63.13	odd	6
5292.2.bm.c.4625.5		48	21.5	even	6
5292.2.bm.c.4625.20		48	21.2	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.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.724112 - 1.57342i) q^{3} +(1.31387 - 2.27569i) q^{5} +(-1.95132 - 2.27867i) q^{9} +O(q^{10})\)	\(q+(0.724112 - 1.57342i) q^{3} +(1.31387 - 2.27569i) q^{5} +(-1.95132 - 2.27867i) q^{9} +(-5.18523 + 2.99370i) q^{11} +(2.54231 - 1.46780i) q^{13} +(-2.62923 - 3.71513i) q^{15} +(0.0167322 - 0.0289811i) q^{17} +(-7.07369 + 4.08400i) q^{19} +(-7.04605 - 4.06804i) q^{23} +(-0.952507 - 1.64979i) q^{25} +(-4.99829 + 1.42024i) q^{27} +(-0.949006 - 0.547909i) q^{29} -8.10282i q^{31} +(0.955659 + 10.3263i) q^{33} +(-0.105898 - 0.183421i) q^{37} +(-0.468558 - 5.06298i) q^{39} +(2.23087 + 3.86399i) q^{41} +(3.78001 - 6.54717i) q^{43} +(-7.74933 + 1.44673i) q^{45} -7.07610 q^{47} +(-0.0334835 - 0.0473125i) q^{51} +(-1.59204 - 0.919166i) q^{53} +15.7333i q^{55} +(1.30371 + 14.0872i) q^{57} +4.73688 q^{59} -11.9827i q^{61} -7.71401i q^{65} +7.62295 q^{67} +(-11.5029 + 8.14070i) q^{69} -3.52461i q^{71} +(-2.24398 - 1.29556i) q^{73} +(-3.28554 + 0.304063i) q^{75} -7.17904 q^{79} +(-1.38468 + 8.89284i) q^{81} +(0.932743 - 1.61556i) q^{83} +(-0.0439680 - 0.0761548i) q^{85} +(-1.54928 + 1.09644i) q^{87} +(3.56125 + 6.16826i) q^{89} +(-12.7492 - 5.86735i) q^{93} +21.4634i q^{95} +(13.2520 + 7.65104i) q^{97} +(16.9397 + 5.97378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{9}+O(q^{10}) \) 48 * q - 8 * q^9	\( 48 q - 8 q^{9} + 24 q^{11} + 24 q^{15} - 48 q^{23} - 24 q^{25} + 56 q^{39} + 72 q^{51} - 48 q^{53} + 16 q^{57} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 48 q^{93} - 40 q^{99}+O(q^{100}) \) 48 * q - 8 * q^9 + 24 * q^11 + 24 * q^15 - 48 * q^23 - 24 * q^25 + 56 * q^39 + 72 * q^51 - 48 * q^53 + 16 * q^57 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 48 * q^93 - 40 * q^99

Introduction

L-functions

Modular forms

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