LMFDB - Embedded newform 264.2.q.b.97.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(25,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-1,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			97.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	264.97
Dual form			264.2.q.b.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{3} +(0.809017 + 2.48990i) q^{5} +(-0.190983 - 0.138757i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-2.54508 + 2.12663i) q^{11} +(-0.690983 + 2.12663i) q^{13} +(-2.11803 - 1.53884i) q^{15} +(1.50000 + 4.61653i) q^{17} +(-2.11803 + 1.53884i) q^{19} +0.236068 q^{21} +1.76393 q^{23} +(-1.50000 + 1.08981i) q^{25} +(0.309017 + 0.951057i) q^{27} +(6.85410 + 4.97980i) q^{29} +(1.97214 - 6.06961i) q^{31} +(0.809017 - 3.21644i) q^{33} +(0.190983 - 0.587785i) q^{35} +(-6.66312 - 4.84104i) q^{37} +(-0.690983 - 2.12663i) q^{39} +(4.04508 - 2.93893i) q^{41} +2.52786 q^{43} +2.61803 q^{45} +(-5.54508 + 4.02874i) q^{47} +(-2.14590 - 6.60440i) q^{49} +(-3.92705 - 2.85317i) q^{51} +(3.26393 - 10.0453i) q^{53} +(-7.35410 - 4.61653i) q^{55} +(0.809017 - 2.48990i) q^{57} +(4.50000 + 3.26944i) q^{59} +(-0.0450850 - 0.138757i) q^{61} +(-0.190983 + 0.138757i) q^{63} -5.85410 q^{65} +15.5623 q^{67} +(-1.42705 + 1.03681i) q^{69} +(-2.33688 - 7.19218i) q^{71} +(7.85410 + 5.70634i) q^{73} +(0.572949 - 1.76336i) q^{75} +(0.781153 - 0.0530006i) q^{77} +(3.01722 - 9.28605i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.92705 + 15.1639i) q^{83} +(-10.2812 + 7.46969i) q^{85} -8.47214 q^{87} -5.47214 q^{89} +(0.427051 - 0.310271i) q^{91} +(1.97214 + 6.06961i) q^{93} +(-5.54508 - 4.02874i) q^{95} +(-0.0450850 + 0.138757i) q^{97} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + q^{5} - 3 q^{7} - q^{9} + q^{11} - 5 q^{13} - 4 q^{15} + 6 q^{17} - 4 q^{19} - 8 q^{21} + 16 q^{23} - 6 q^{25} - q^{27} + 14 q^{29} - 10 q^{31} + q^{33} + 3 q^{35} - 11 q^{37} - 5 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q - q^3 + q^5 - 3 * q^7 - q^9 + q^11 - 5 * q^13 - 4 * q^15 + 6 * q^17 - 4 * q^19 - 8 * q^21 + 16 * q^23 - 6 * q^25 - q^27 + 14 * q^29 - 10 * q^31 + q^33 + 3 * q^35 - 11 * q^37 - 5 * q^39 + 5 * q^41 + 28 * q^43 + 6 * q^45 - 11 * q^47 - 22 * q^49 - 9 * q^51 + 22 * q^53 - 16 * q^55 + q^57 + 18 * q^59 + 11 * q^61 - 3 * q^63 - 10 * q^65 + 22 * q^67 + q^69 - 25 * q^71 + 18 * q^73 + 9 * q^75 - 17 * q^77 - 17 * q^79 - q^81 + 13 * q^83 - 21 * q^85 - 16 * q^87 - 4 * q^89 - 5 * q^91 - 10 * q^93 - 11 * q^95 + 11 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$		0			0
$5$	0.809017	+	2.48990i	0.361803	+	1.11352i	0.951959	+	0.306227i	$0.0990665\pi$
$5$	0.809017	+	2.48990i	0.361803	+	1.11352i	−0.590155	+	0.807290i	$0.700933\pi$
$6$		0			0
$7$	−0.190983	−	0.138757i	−0.0721848	−	0.0524453i	0.551108	−	0.834434i	$-0.314205\pi$
$7$	−0.190983	−	0.138757i	−0.0721848	−	0.0524453i	−0.623292	+	0.781989i	$0.714205\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$12$		0			0
$13$	−0.690983	+	2.12663i	−0.191644	+	0.589820i	0.808355	+	0.588695i	$0.200358\pi$
$13$	−0.690983	+	2.12663i	−0.191644	+	0.589820i	−0.999999	+	0.00112510i	$0.999642\pi$
$14$		0			0
$15$	−2.11803	−	1.53884i	−0.546874	−	0.397327i
$16$		0			0
$17$	1.50000	+	4.61653i	0.363803	+	1.11967i	0.950727	+	0.310029i	$0.100339\pi$
$17$	1.50000	+	4.61653i	0.363803	+	1.11967i	−0.586924	+	0.809642i	$0.699661\pi$
$18$		0			0
$19$	−2.11803	+	1.53884i	−0.485910	+	0.353035i	−0.803609	−	0.595157i	$-0.797090\pi$
$19$	−2.11803	+	1.53884i	−0.485910	+	0.353035i	0.317699	+	0.948192i	$0.397090\pi$
$20$		0			0
$21$	0.236068			0.0515143
$22$		0			0
$23$	1.76393			0.367805			0.183903	−	0.982944i	$-0.441127\pi$
$23$	1.76393			0.367805			0.183903	+	0.982944i	$0.441127\pi$
$24$		0			0
$25$	−1.50000	+	1.08981i	−0.300000	+	0.217963i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	6.85410	+	4.97980i	1.27277	+	0.924725i	0.999309	−	0.0371569i	$-0.0118301\pi$
$29$	6.85410	+	4.97980i	1.27277	+	0.924725i	0.273465	+	0.961882i	$0.411830\pi$
$30$		0			0
$31$	1.97214	−	6.06961i	0.354206	−	1.09013i	−0.602262	−	0.798298i	$-0.705734\pi$
$31$	1.97214	−	6.06961i	0.354206	−	1.09013i	0.956468	−	0.291836i	$-0.0942661\pi$
$32$		0			0
$33$	0.809017	−	3.21644i	0.140832	−	0.559910i
$34$		0			0
$35$	0.190983	−	0.587785i	0.0322820	−	0.0993538i
$36$		0			0
$37$	−6.66312	−	4.84104i	−1.09541	−	0.795862i	−0.115105	−	0.993353i	$-0.536721\pi$
$37$	−6.66312	−	4.84104i	−1.09541	−	0.795862i	−0.980305	+	0.197491i	$0.936721\pi$
$38$		0			0
$39$	−0.690983	−	2.12663i	−0.110646	−	0.340533i
$40$		0			0
$41$	4.04508	−	2.93893i	0.631736	−	0.458983i	−0.225265	−	0.974298i	$-0.572325\pi$
$41$	4.04508	−	2.93893i	0.631736	−	0.458983i	0.857001	+	0.515314i	$0.172325\pi$
$42$		0			0
$43$	2.52786			0.385496			0.192748	−	0.981248i	$-0.438260\pi$
$43$	2.52786			0.385496			0.192748	+	0.981248i	$0.438260\pi$
$44$		0			0
$45$	2.61803			0.390273
$46$		0			0
$47$	−5.54508	+	4.02874i	−0.808834	+	0.587652i	−0.913492	−	0.406856i	$-0.866625\pi$
$47$	−5.54508	+	4.02874i	−0.808834	+	0.587652i	0.104658	+	0.994508i	$0.466625\pi$
$48$		0			0
$49$	−2.14590	−	6.60440i	−0.306557	−	0.943485i
$50$		0			0
$51$	−3.92705	−	2.85317i	−0.549897	−	0.399524i
$52$		0			0
$53$	3.26393	−	10.0453i	0.448336	−	1.37983i	−0.430448	−	0.902615i	$-0.641645\pi$
$53$	3.26393	−	10.0453i	0.448336	−	1.37983i	0.878784	−	0.477220i	$-0.158355\pi$
$54$		0			0
$55$	−7.35410	−	4.61653i	−0.991627	−	0.622492i
$56$		0			0
$57$	0.809017	−	2.48990i	0.107157	−	0.329795i
$58$		0			0
$59$	4.50000	+	3.26944i	0.585850	+	0.425645i	0.840828	−	0.541302i	$-0.182068\pi$
$59$	4.50000	+	3.26944i	0.585850	+	0.425645i	−0.254978	+	0.966947i	$0.582068\pi$
$60$		0			0
$61$	−0.0450850	−	0.138757i	−0.00577254	−	0.0177660i	0.948129	−	0.317887i	$-0.102973\pi$
$61$	−0.0450850	−	0.138757i	−0.00577254	−	0.0177660i	−0.953901	+	0.300120i	$0.902973\pi$
$62$		0			0
$63$	−0.190983	+	0.138757i	−0.0240616	+	0.0174818i
$64$		0			0
$65$	−5.85410			−0.726112
$66$		0			0
$67$	15.5623			1.90124			0.950619	−	0.310360i	$-0.100450\pi$
$67$	15.5623			1.90124			0.950619	+	0.310360i	$0.100450\pi$
$68$		0			0
$69$	−1.42705	+	1.03681i	−0.171797	+	0.124818i
$70$		0			0
$71$	−2.33688	−	7.19218i	−0.277337	−	0.853555i	−0.988592	−	0.150621i	$-0.951873\pi$
$71$	−2.33688	−	7.19218i	−0.277337	−	0.853555i	0.711255	−	0.702934i	$-0.248127\pi$
$72$		0			0
$73$	7.85410	+	5.70634i	0.919253	+	0.667876i	0.943338	−	0.331833i	$-0.107667\pi$
$73$	7.85410	+	5.70634i	0.919253	+	0.667876i	−0.0240849	+	0.999710i	$0.507667\pi$
$74$		0			0
$75$	0.572949	−	1.76336i	0.0661585	−	0.203615i
$76$		0			0
$77$	0.781153	−	0.0530006i	0.0890206	−	0.00603997i
$78$		0			0
$79$	3.01722	−	9.28605i	0.339464	−	1.04476i	−0.625017	−	0.780611i	$-0.714908\pi$
$79$	3.01722	−	9.28605i	0.339464	−	1.04476i	0.964481	−	0.264152i	$-0.0850919\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	4.92705	+	15.1639i	0.540814	+	1.66445i	0.730740	+	0.682656i	$0.239175\pi$
$83$	4.92705	+	15.1639i	0.540814	+	1.66445i	−0.189926	+	0.981798i	$0.560825\pi$
$84$		0			0
$85$	−10.2812	+	7.46969i	−1.11515	+	0.810202i
$86$		0			0
$87$	−8.47214			−0.908308
$88$		0			0
$89$	−5.47214			−0.580045			−0.290023	−	0.957020i	$-0.593663\pi$
$89$	−5.47214			−0.580045			−0.290023	+	0.957020i	$0.593663\pi$
$90$		0			0
$91$	0.427051	−	0.310271i	0.0447671	−	0.0325252i
$92$		0			0
$93$	1.97214	+	6.06961i	0.204501	+	0.629389i
$94$		0			0
$95$	−5.54508	−	4.02874i	−0.568914	−	0.413340i
$96$		0			0
$97$	−0.0450850	+	0.138757i	−0.00457769	+	0.0140887i	−0.953319	−	0.301964i	$-0.902358\pi$
$97$	−0.0450850	+	0.138757i	−0.00457769	+	0.0140887i	0.948742	+	0.316053i	$0.102358\pi$
$98$		0			0
$99$	1.23607	+	3.07768i	0.124230	+	0.309319i
$100$		0			0
$101$	2.92705	−	9.00854i	0.291252	−	0.896383i	−0.693202	−	0.720743i	$-0.743801\pi$
$101$	2.92705	−	9.00854i	0.291252	−	0.896383i	0.984455	−	0.175640i	$-0.0561993\pi$
$102$		0			0
$103$	10.0902	+	7.33094i	0.994214	+	0.722339i	0.960840	−	0.277104i	$-0.0893747\pi$
$103$	10.0902	+	7.33094i	0.994214	+	0.722339i	0.0333741	+	0.999443i	$0.489375\pi$
$104$		0			0
$105$	0.190983	+	0.587785i	0.0186380	+	0.0573620i
$106$		0			0
$107$	4.80902	−	3.49396i	0.464905	−	0.337773i	−0.330547	−	0.943789i	$-0.607233\pi$
$107$	4.80902	−	3.49396i	0.464905	−	0.337773i	0.795452	+	0.606016i	$0.207233\pi$
$108$		0			0
$109$	−17.8885			−1.71341			−0.856706	−	0.515805i	$-0.827493\pi$
$109$	−17.8885			−1.71341			−0.856706	+	0.515805i	$0.827493\pi$
$110$		0			0
$111$	8.23607			0.781733
$112$		0			0
$113$	−11.1353	+	8.09024i	−1.04752	+	0.761065i	−0.971739	−	0.236059i	$-0.924144\pi$
$113$	−11.1353	+	8.09024i	−1.04752	+	0.761065i	−0.0757780	+	0.997125i	$0.524144\pi$
$114$		0			0
$115$	1.42705	+	4.39201i	0.133073	+	0.409557i
$116$		0			0
$117$	1.80902	+	1.31433i	0.167244	+	0.121510i
$118$		0			0
$119$	0.354102	−	1.08981i	0.0324605	−	0.0999031i
$120$		0			0
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$		0			0
$123$	−1.54508	+	4.75528i	−0.139316	+	0.428769i
$124$		0			0
$125$	6.66312	+	4.84104i	0.595967	+	0.432996i
$126$		0			0
$127$	1.61803	+	4.97980i	0.143577	+	0.441885i	0.996825	−	0.0796199i	$-0.0253706\pi$
$127$	1.61803	+	4.97980i	0.143577	+	0.441885i	−0.853248	+	0.521505i	$0.825371\pi$
$128$		0			0
$129$	−2.04508	+	1.48584i	−0.180060	+	0.130821i
$130$		0			0
$131$	−13.3262			−1.16432			−0.582159	−	0.813075i	$-0.697792\pi$
$131$	−13.3262			−1.16432			−0.582159	+	0.813075i	$0.697792\pi$
$132$		0			0
$133$	0.618034			0.0535903
$134$		0			0
$135$	−2.11803	+	1.53884i	−0.182291	+	0.132442i
$136$		0			0
$137$	−1.07295	−	3.30220i	−0.0916682	−	0.282126i	0.894703	−	0.446662i	$-0.147387\pi$
$137$	−1.07295	−	3.30220i	−0.0916682	−	0.282126i	−0.986371	+	0.164536i	$0.947387\pi$
$138$		0			0
$139$	13.2533	+	9.62908i	1.12413	+	0.816728i	0.984830	−	0.173523i	$-0.0555150\pi$
$139$	13.2533	+	9.62908i	1.12413	+	0.816728i	0.139299	+	0.990250i	$0.455515\pi$
$140$		0			0
$141$	2.11803	−	6.51864i	0.178371	−	0.548968i
$142$		0			0
$143$	−2.76393	−	6.88191i	−0.231132	−	0.575494i
$144$		0			0
$145$	−6.85410	+	21.0948i	−0.569202	+	1.75182i
$146$		0			0
$147$	5.61803	+	4.08174i	0.463368	+	0.336656i
$148$		0			0
$149$	−0.454915	−	1.40008i	−0.0372681	−	0.114699i	0.930692	−	0.365804i	$-0.119206\pi$
$149$	−0.454915	−	1.40008i	−0.0372681	−	0.114699i	−0.967960	+	0.251105i	$0.919206\pi$
$150$		0			0
$151$	−10.8541	+	7.88597i	−0.883294	+	0.641751i	−0.934121	−	0.356957i	$-0.883814\pi$
$151$	−10.8541	+	7.88597i	−0.883294	+	0.641751i	0.0508267	+	0.998707i	$0.483814\pi$
$152$		0			0
$153$	4.85410			0.392431
$154$		0			0
$155$	16.7082			1.34204
$156$		0			0
$157$	5.00000	−	3.63271i	0.399043	−	0.289922i	−0.370108	−	0.928989i	$-0.620679\pi$
$157$	5.00000	−	3.63271i	0.399043	−	0.289922i	0.769151	+	0.639067i	$0.220679\pi$
$158$		0			0
$159$	3.26393	+	10.0453i	0.258847	+	0.796648i
$160$		0			0
$161$	−0.336881	−	0.244758i	−0.0265499	−	0.0192897i
$162$		0			0
$163$	−5.44427	+	16.7557i	−0.426428	+	1.31241i	0.475192	+	0.879882i	$0.342379\pi$
$163$	−5.44427	+	16.7557i	−0.426428	+	1.31241i	−0.901620	+	0.432529i	$0.857621\pi$
$164$		0			0
$165$	8.66312	−	0.587785i	0.674423	−	0.0457590i
$166$		0			0
$167$	2.37132	−	7.29818i	0.183498	−	0.564750i	−0.816421	−	0.577457i	$-0.804045\pi$
$167$	2.37132	−	7.29818i	0.183498	−	0.564750i	0.999919	+	0.0127072i	$0.00404494\pi$
$168$		0			0
$169$	6.47214	+	4.70228i	0.497857	+	0.361714i
$170$		0			0
$171$	0.809017	+	2.48990i	0.0618671	+	0.190407i
$172$		0			0
$173$	−9.73607	+	7.07367i	−0.740220	+	0.537801i	−0.892780	−	0.450493i	$-0.851248\pi$
$173$	−9.73607	+	7.07367i	−0.740220	+	0.537801i	0.152560	+	0.988294i	$0.451248\pi$
$174$		0			0
$175$	0.437694			0.0330866
$176$		0			0
$177$	−5.56231			−0.418089
$178$		0			0
$179$	−3.57295	+	2.59590i	−0.267055	+	0.194027i	−0.713251	−	0.700908i	$-0.752778\pi$
$179$	−3.57295	+	2.59590i	−0.267055	+	0.194027i	0.446197	+	0.894935i	$0.352778\pi$
$180$		0			0
$181$	−6.45492	−	19.8662i	−0.479790	−	1.47664i	−0.839387	−	0.543534i	$-0.817086\pi$
$181$	−6.45492	−	19.8662i	−0.479790	−	1.47664i	0.359597	−	0.933108i	$-0.382914\pi$
$182$		0			0
$183$	0.118034	+	0.0857567i	0.00872532	+	0.00633932i
$184$		0			0
$185$	6.66312	−	20.5070i	0.489882	−	1.50770i
$186$		0			0
$187$	−13.6353	−	8.55951i	−0.997109	−	0.625933i
$188$		0			0
$189$	0.0729490	−	0.224514i	0.00530626	−	0.0163310i
$190$		0			0
$191$	−8.28115	−	6.01661i	−0.599203	−	0.435347i	0.246393	−	0.969170i	$-0.420755\pi$
$191$	−8.28115	−	6.01661i	−0.599203	−	0.435347i	−0.845596	+	0.533823i	$0.820755\pi$
$192$		0			0
$193$	4.73607	+	14.5761i	0.340910	+	1.04921i	0.963737	+	0.266853i	$0.0859838\pi$
$193$	4.73607	+	14.5761i	0.340910	+	1.04921i	−0.622828	+	0.782359i	$0.714016\pi$
$194$		0			0
$195$	4.73607	−	3.44095i	0.339157	−	0.246412i
$196$		0			0
$197$	−14.8541			−1.05831			−0.529155	−	0.848525i	$-0.677491\pi$
$197$	−14.8541			−1.05831			−0.529155	+	0.848525i	$0.677491\pi$
$198$		0			0
$199$	0.527864			0.0374193			0.0187096	−	0.999825i	$-0.494044\pi$
$199$	0.527864			0.0374193			0.0187096	+	0.999825i	$0.494044\pi$
$200$		0			0
$201$	−12.5902	+	9.14729i	−0.888042	+	0.645200i
$202$		0			0
$203$	−0.618034	−	1.90211i	−0.0433775	−	0.133502i
$204$		0			0
$205$	10.5902	+	7.69421i	0.739650	+	0.537387i
$206$		0			0
$207$	0.545085	−	1.67760i	0.0378860	−	0.116601i
$208$		0			0
$209$	2.11803	−	8.42075i	0.146507	−	0.582476i
$210$		0			0
$211$	1.73607	−	5.34307i	0.119516	−	0.367832i	−0.873346	−	0.487100i	$-0.838055\pi$
$211$	1.73607	−	5.34307i	0.119516	−	0.367832i	0.992862	+	0.119268i	$0.0380548\pi$
$212$		0			0
$213$	6.11803	+	4.44501i	0.419201	+	0.304567i
$214$		0			0
$215$	2.04508	+	6.29412i	0.139474	+	0.429256i
$216$		0			0
$217$	−1.21885	+	0.885544i	−0.0827407	+	0.0601147i
$218$		0			0
$219$	−9.70820			−0.656020
$220$		0			0
$221$	−10.8541			−0.730126
$222$		0			0
$223$	17.3713	−	12.6210i	1.16327	−	0.845165i	0.173082	−	0.984907i	$-0.444627\pi$
$223$	17.3713	−	12.6210i	1.16327	−	0.845165i	0.990188	+	0.139742i	$0.0446275\pi$
$224$		0			0
$225$	0.572949	+	1.76336i	0.0381966	+	0.117557i
$226$		0			0
$227$	−23.1353	−	16.8087i	−1.53554	−	1.11564i	−0.953056	−	0.302794i	$-0.902081\pi$
$227$	−23.1353	−	16.8087i	−1.53554	−	1.11564i	−0.582485	−	0.812842i	$-0.697919\pi$
$228$		0			0
$229$	7.38197	−	22.7194i	0.487814	−	1.50134i	−0.340049	−	0.940408i	$-0.610444\pi$
$229$	7.38197	−	22.7194i	0.487814	−	1.50134i	0.827863	−	0.560930i	$-0.189556\pi$
$230$		0			0
$231$	−0.600813	+	0.502029i	−0.0395306	+	0.0330311i
$232$		0			0
$233$	−2.75329	+	8.47375i	−0.180374	+	0.555134i	−0.999838	−	0.0179966i	$-0.994271\pi$
$233$	−2.75329	+	8.47375i	−0.180374	+	0.555134i	0.819464	+	0.573131i	$0.194271\pi$
$234$		0			0
$235$	−14.5172	−	10.5474i	−0.946999	−	0.688035i
$236$		0			0
$237$	3.01722	+	9.28605i	0.195990	+	0.603194i
$238$		0			0
$239$	12.1631	−	8.83702i	0.786767	−	0.571620i	−0.120235	−	0.992745i	$-0.538365\pi$
$239$	12.1631	−	8.83702i	0.786767	−	0.571620i	0.907002	+	0.421126i	$0.138365\pi$
$240$		0			0
$241$	28.0689			1.80808			0.904038	−	0.427452i	$-0.140589\pi$
$241$	28.0689			1.80808			0.904038	+	0.427452i	$0.140589\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	14.7082	−	10.6861i	0.939673	−	0.682712i
$246$		0			0
$247$	−1.80902	−	5.56758i	−0.115105	−	0.354257i
$248$		0			0
$249$	−12.8992	−	9.37181i	−0.817453	−	0.593914i
$250$		0			0
$251$	2.73607	−	8.42075i	0.172699	−	0.531513i	−0.826822	−	0.562464i	$-0.809854\pi$
$251$	2.73607	−	8.42075i	0.172699	−	0.531513i	0.999521	+	0.0309508i	$0.00985352\pi$
$252$		0			0
$253$	−4.48936	+	3.75123i	−0.282243	+	0.235838i
$254$		0			0
$255$	3.92705	−	12.0862i	0.245921	−	0.756868i
$256$		0			0
$257$	5.50000	+	3.99598i	0.343081	+	0.249263i	0.745960	−	0.665990i	$-0.231991\pi$
$257$	5.50000	+	3.99598i	0.343081	+	0.249263i	−0.402880	+	0.915253i	$0.631991\pi$
$258$		0			0
$259$	0.600813	+	1.84911i	0.0373327	+	0.114898i
$260$		0			0
$261$	6.85410	−	4.97980i	0.424258	−	0.308242i
$262$		0			0
$263$	4.14590			0.255647			0.127824	−	0.991797i	$-0.459201\pi$
$263$	4.14590			0.255647			0.127824	+	0.991797i	$0.459201\pi$
$264$		0			0
$265$	27.6525			1.69868
$266$		0			0
$267$	4.42705	−	3.21644i	0.270931	−	0.196843i
$268$		0			0
$269$	7.85410	+	24.1724i	0.478873	+	1.47382i	0.840662	+	0.541560i	$0.182166\pi$
$269$	7.85410	+	24.1724i	0.478873	+	1.47382i	−0.361789	+	0.932260i	$0.617834\pi$
$270$		0			0
$271$	−12.4443	−	9.04129i	−0.755936	−	0.549219i	0.141725	−	0.989906i	$-0.454735\pi$
$271$	−12.4443	−	9.04129i	−0.755936	−	0.549219i	−0.897661	+	0.440687i	$0.854735\pi$
$272$		0			0
$273$	−0.163119	+	0.502029i	−0.00987241	+	0.0303841i
$274$		0			0
$275$	1.50000	−	5.96361i	0.0904534	−	0.359619i
$276$		0			0
$277$	−2.73607	+	8.42075i	−0.164394	+	0.505954i	−0.998991	−	0.0449075i	$-0.985701\pi$
$277$	−2.73607	+	8.42075i	−0.164394	+	0.505954i	0.834597	+	0.550861i	$0.185701\pi$
$278$		0			0
$279$	−5.16312	−	3.75123i	−0.309108	−	0.224580i
$280$		0			0
$281$	−9.76393	−	30.0503i	−0.582467	−	1.79265i	−0.609211	−	0.793008i	$-0.708514\pi$
$281$	−9.76393	−	30.0503i	−0.582467	−	1.79265i	0.0267440	−	0.999642i	$-0.491486\pi$
$282$		0			0
$283$	1.85410	−	1.34708i	0.110215	−	0.0800758i	−0.531313	−	0.847176i	$-0.678301\pi$
$283$	1.85410	−	1.34708i	0.110215	−	0.0800758i	0.641528	+	0.767100i	$0.278301\pi$
$284$		0			0
$285$	6.85410			0.406002
$286$		0			0
$287$	−1.18034			−0.0696733
$288$		0			0
$289$	−5.30902	+	3.85723i	−0.312295	+	0.226896i
$290$		0			0
$291$	−0.0450850	−	0.138757i	−0.00264293	−	0.00813410i
$292$		0			0
$293$	14.0451	+	10.2044i	0.820523	+	0.596145i	0.916862	−	0.399204i	$-0.130713\pi$
$293$	14.0451	+	10.2044i	0.820523	+	0.596145i	−0.0963395	+	0.995349i	$0.530713\pi$
$294$		0			0
$295$	−4.50000	+	13.8496i	−0.262000	+	0.806353i
$296$		0			0
$297$	−2.80902	−	1.76336i	−0.162996	−	0.102320i
$298$		0			0
$299$	−1.21885	+	3.75123i	−0.0704877	+	0.216939i
$300$		0			0
$301$	−0.482779	−	0.350760i	−0.0278269	−	0.0202174i
$302$		0			0
$303$	2.92705	+	9.00854i	0.168155	+	0.517527i
$304$		0			0
$305$	0.309017	−	0.224514i	0.0176943	−	0.0128556i
$306$		0			0
$307$	−13.7984			−0.787515			−0.393757	−	0.919214i	$-0.628825\pi$
$307$	−13.7984			−0.787515			−0.393757	+	0.919214i	$0.628825\pi$
$308$		0			0
$309$	−12.4721			−0.709515
$310$		0			0
$311$	−7.89919	+	5.73910i	−0.447922	+	0.325434i	−0.788775	−	0.614682i	$-0.789284\pi$
$311$	−7.89919	+	5.73910i	−0.447922	+	0.325434i	0.340853	+	0.940117i	$0.389284\pi$
$312$		0			0
$313$	−8.30902	−	25.5725i	−0.469653	−	1.44544i	−0.853035	−	0.521854i	$-0.825240\pi$
$313$	−8.30902	−	25.5725i	−0.469653	−	1.44544i	0.383381	−	0.923590i	$-0.374760\pi$
$314$		0			0
$315$	−0.500000	−	0.363271i	−0.0281718	−	0.0204680i
$316$		0			0
$317$	4.92705	−	15.1639i	0.276731	−	0.851690i	−0.712026	−	0.702154i	$-0.752222\pi$
$317$	4.92705	−	15.1639i	0.276731	−	0.851690i	0.988756	−	0.149536i	$-0.0477780\pi$
$318$		0			0
$319$	−28.0344	+	1.90211i	−1.56963	+	0.106498i
$320$		0			0
$321$	−1.83688	+	5.65334i	−0.102525	+	0.315539i
$322$		0			0
$323$	−10.2812	−	7.46969i	−0.572059	−	0.415625i
$324$		0			0
$325$	−1.28115	−	3.94298i	−0.0710656	−	0.218717i
$326$		0			0
$327$	14.4721	−	10.5146i	0.800311	−	0.581460i
$328$		0			0
$329$	1.61803			0.0892051
$330$		0			0
$331$	−27.0000			−1.48405			−0.742027	−	0.670370i	$-0.766135\pi$
$331$	−27.0000			−1.48405			−0.742027	+	0.670370i	$0.766135\pi$
$332$		0			0
$333$	−6.66312	+	4.84104i	−0.365137	+	0.265287i
$334$		0			0
$335$	12.5902	+	38.7486i	0.687874	+	2.11706i
$336$		0			0
$337$	19.1803	+	13.9353i	1.04482	+	0.759106i	0.971221	−	0.238182i	$-0.0765515\pi$
$337$	19.1803	+	13.9353i	1.04482	+	0.759106i	0.0735991	+	0.997288i	$0.476551\pi$
$338$		0			0
$339$	4.25329	−	13.0903i	0.231007	−	0.710966i
$340$		0			0
$341$	7.88854	+	19.6417i	0.427189	+	1.06366i
$342$		0			0
$343$	−1.01722	+	3.13068i	−0.0549248	+	0.169041i
$344$		0			0
$345$	−3.73607	−	2.71441i	−0.201143	−	0.146139i
$346$		0			0
$347$	4.94427	+	15.2169i	0.265422	+	0.816886i	0.991596	+	0.129375i	$0.0412970\pi$
$347$	4.94427	+	15.2169i	0.265422	+	0.816886i	−0.726173	+	0.687512i	$0.758703\pi$
$348$		0			0
$349$	−6.28115	+	4.56352i	−0.336222	+	0.244280i	−0.743066	−	0.669218i	$-0.766629\pi$
$349$	−6.28115	+	4.56352i	−0.336222	+	0.244280i	0.406844	+	0.913498i	$0.366629\pi$
$350$		0			0
$351$	−2.23607			−0.119352
$352$		0			0
$353$	5.52786			0.294219			0.147109	−	0.989120i	$-0.453003\pi$
$353$	5.52786			0.294219			0.147109	+	0.989120i	$0.453003\pi$
$354$		0			0
$355$	16.0172	−	11.6372i	0.850106	−	0.617638i
$356$		0			0
$357$	0.354102	+	1.08981i	0.0187411	+	0.0576791i
$358$		0			0
$359$	4.61803	+	3.35520i	0.243731	+	0.177081i	0.702944	−	0.711246i	$-0.251869\pi$
$359$	4.61803	+	3.35520i	0.243731	+	0.177081i	−0.459213	+	0.888326i	$0.651869\pi$
$360$		0			0
$361$	−3.75329	+	11.5514i	−0.197542	+	0.607970i
$362$		0			0
$363$	4.78115	+	9.90659i	0.250945	+	0.519961i
$364$		0			0
$365$	−7.85410	+	24.1724i	−0.411102	+	1.26524i
$366$		0			0
$367$	4.59017	+	3.33495i	0.239605	+	0.174083i	0.701107	−	0.713056i	$-0.252689\pi$
$367$	4.59017	+	3.33495i	0.239605	+	0.174083i	−0.461502	+	0.887139i	$0.652689\pi$
$368$		0			0
$369$	−1.54508	−	4.75528i	−0.0804339	−	0.247550i
$370$		0			0
$371$	−2.01722	+	1.46560i	−0.104729	+	0.0760900i
$372$		0			0
$373$	15.9443			0.825563			0.412782	−	0.910830i	$-0.364557\pi$
$373$	15.9443			0.825563			0.412782	+	0.910830i	$0.364557\pi$
$374$		0			0
$375$	−8.23607			−0.425309
$376$		0			0
$377$	−15.3262	+	11.1352i	−0.789341	+	0.573490i
$378$		0			0
$379$	−5.30902	−	16.3395i	−0.272706	−	0.839302i	−0.989817	−	0.142344i	$-0.954536\pi$
$379$	−5.30902	−	16.3395i	−0.272706	−	0.839302i	0.717111	−	0.696959i	$-0.245464\pi$
$380$		0			0
$381$	−4.23607	−	3.07768i	−0.217020	−	0.157675i
$382$		0			0
$383$	−10.1074	+	31.1074i	−0.516464	+	1.58951i	0.264140	+	0.964484i	$0.414912\pi$
$383$	−10.1074	+	31.1074i	−0.516464	+	1.58951i	−0.780603	+	0.625027i	$0.785088\pi$
$384$		0			0
$385$	0.763932	+	1.90211i	0.0389336	+	0.0969407i
$386$		0			0
$387$	0.781153	−	2.40414i	0.0397082	−	0.122209i
$388$		0			0
$389$	−8.25329	−	5.99637i	−0.418458	−	0.304028i	0.358559	−	0.933507i	$-0.383268\pi$
$389$	−8.25329	−	5.99637i	−0.418458	−	0.304028i	−0.777017	+	0.629479i	$0.783268\pi$
$390$		0			0
$391$	2.64590	+	8.14324i	0.133809	+	0.411821i
$392$		0			0
$393$	10.7812	−	7.83297i	0.543837	−	0.395121i
$394$		0			0
$395$	25.5623			1.28618
$396$		0			0
$397$	−34.7082			−1.74195			−0.870977	−	0.491323i	$-0.836513\pi$
$397$	−34.7082			−1.74195			−0.870977	+	0.491323i	$0.836513\pi$
$398$		0			0
$399$	−0.500000	+	0.363271i	−0.0250313	+	0.0181863i
$400$		0			0
$401$	6.93769	+	21.3520i	0.346452	+	1.06627i	0.960802	+	0.277236i	$0.0894183\pi$
$401$	6.93769	+	21.3520i	0.346452	+	1.06627i	−0.614350	+	0.789034i	$0.710582\pi$
$402$		0			0
$403$	11.5451	+	8.38800i	0.575102	+	0.417836i
$404$		0			0
$405$	0.809017	−	2.48990i	0.0402004	−	0.123724i
$406$		0			0
$407$	27.2533	−	1.84911i	1.35090	−	0.0916571i
$408$		0			0
$409$	−0.583592	+	1.79611i	−0.0288568	+	0.0888120i	−0.964448	−	0.264274i	$-0.914868\pi$
$409$	−0.583592	+	1.79611i	−0.0288568	+	0.0888120i	0.935591	+	0.353086i	$0.114868\pi$
$410$		0			0
$411$	2.80902	+	2.04087i	0.138559	+	0.100669i
$412$		0			0
$413$	−0.405765	−	1.24882i	−0.0199664	−	0.0614502i
$414$		0			0
$415$	−33.7705	+	24.5357i	−1.65773	+	1.20441i
$416$		0			0
$417$	−16.3820			−0.802228
$418$		0			0
$419$	35.4508			1.73189			0.865944	−	0.500142i	$-0.166719\pi$
$419$	35.4508			1.73189			0.865944	+	0.500142i	$0.166719\pi$
$420$		0			0
$421$	15.9721	−	11.6044i	0.778434	−	0.565566i	−0.126074	−	0.992021i	$-0.540238\pi$
$421$	15.9721	−	11.6044i	0.778434	−	0.565566i	0.904509	+	0.426455i	$0.140238\pi$
$422$		0			0
$423$	2.11803	+	6.51864i	0.102982	+	0.316947i
$424$		0			0
$425$	−7.28115	−	5.29007i	−0.353188	−	0.256606i
$426$		0			0
$427$	−0.0106431	+	0.0327561i	−0.000515057	+	0.00158518i
$428$		0			0
$429$	6.28115	+	3.94298i	0.303257	+	0.190369i
$430$		0			0
$431$	3.70163	−	11.3924i	0.178301	−	0.548754i	−0.821468	−	0.570255i	$-0.806844\pi$
$431$	3.70163	−	11.3924i	0.178301	−	0.548754i	0.999769	+	0.0215007i	$0.00684442\pi$
$432$		0			0
$433$	10.5623	+	7.67396i	0.507592	+	0.368787i	0.811909	−	0.583784i	$-0.198428\pi$
$433$	10.5623	+	7.67396i	0.507592	+	0.368787i	−0.304317	+	0.952571i	$0.598428\pi$
$434$		0			0
$435$	−6.85410	−	21.0948i	−0.328629	−	1.01142i
$436$		0			0
$437$	−3.73607	+	2.71441i	−0.178720	+	0.129848i
$438$		0			0
$439$	20.5279			0.979741			0.489871	−	0.871795i	$-0.337044\pi$
$439$	20.5279			0.979741			0.489871	+	0.871795i	$0.337044\pi$
$440$		0			0
$441$	−6.94427			−0.330680
$442$		0			0
$443$	−6.32624	+	4.59628i	−0.300569	+	0.218376i	−0.727839	−	0.685748i	$-0.759475\pi$
$443$	−6.32624	+	4.59628i	−0.300569	+	0.218376i	0.427270	+	0.904124i	$0.359475\pi$
$444$		0			0
$445$	−4.42705	−	13.6251i	−0.209862	−	0.645890i
$446$		0			0
$447$	1.19098	+	0.865300i	0.0563316	+	0.0409273i
$448$		0			0
$449$	−8.43769	+	25.9686i	−0.398199	+	1.22553i	0.528242	+	0.849094i	$0.322851\pi$
$449$	−8.43769	+	25.9686i	−0.398199	+	1.22553i	−0.926442	+	0.376438i	$0.877149\pi$
$450$		0			0
$451$	−4.04508	+	16.0822i	−0.190476	+	0.757281i
$452$		0			0
$453$	4.14590	−	12.7598i	0.194791	−	0.599506i
$454$		0			0
$455$	1.11803	+	0.812299i	0.0524142	+	0.0380812i
$456$		0			0
$457$	−12.5902	−	38.7486i	−0.588943	−	1.81258i	−0.582822	−	0.812600i	$-0.698052\pi$
$457$	−12.5902	−	38.7486i	−0.588943	−	1.81258i	−0.00612133	−	0.999981i	$-0.501948\pi$
$458$		0			0
$459$	−3.92705	+	2.85317i	−0.183299	+	0.133175i
$460$		0			0
$461$	−10.9098			−0.508121			−0.254061	−	0.967188i	$-0.581766\pi$
$461$	−10.9098			−0.508121			−0.254061	+	0.967188i	$0.581766\pi$
$462$		0			0
$463$	24.4508			1.13633			0.568164	−	0.822916i	$-0.307654\pi$
$463$	24.4508			1.13633			0.568164	+	0.822916i	$0.307654\pi$
$464$		0			0
$465$	−13.5172	+	9.82084i	−0.626846	+	0.455430i
$466$		0			0
$467$	−6.30902	−	19.4172i	−0.291946	−	0.898519i	−0.984230	−	0.176893i	$-0.943395\pi$
$467$	−6.30902	−	19.4172i	−0.291946	−	0.898519i	0.692284	−	0.721626i	$-0.256605\pi$
$468$		0			0
$469$	−2.97214	−	2.15938i	−0.137240	−	0.0997111i
$470$		0			0
$471$	−1.90983	+	5.87785i	−0.0880003	+	0.270837i
$472$		0			0
$473$	−6.43363	+	5.37582i	−0.295819	+	0.247181i
$474$		0			0
$475$	1.50000	−	4.61653i	0.0688247	−	0.211821i
$476$		0			0
$477$	−8.54508	−	6.20837i	−0.391253	−	0.284262i
$478$		0			0
$479$	2.53444	+	7.80021i	0.115802	+	0.356401i	0.992113	−	0.125344i	$-0.0400034\pi$
$479$	2.53444	+	7.80021i	0.115802	+	0.356401i	−0.876312	+	0.481744i	$0.840003\pi$
$480$		0			0
$481$	14.8992	−	10.8249i	0.679344	−	0.493573i
$482$		0			0
$483$	0.416408			0.0189472
$484$		0			0
$485$	−0.381966			−0.0173442
$486$		0			0
$487$	6.51722	−	4.73504i	0.295323	−	0.214565i	−0.430250	−	0.902710i	$-0.641575\pi$
$487$	6.51722	−	4.73504i	0.295323	−	0.214565i	0.725573	+	0.688145i	$0.241575\pi$
$488$		0			0
$489$	−5.44427	−	16.7557i	−0.246198	−	0.757721i
$490$		0			0
$491$	−30.8156	−	22.3888i	−1.39069	−	1.01039i	−0.995789	−	0.0916696i	$-0.970780\pi$
$491$	−30.8156	−	22.3888i	−1.39069	−	1.01039i	−0.394899	−	0.918725i	$-0.629220\pi$
$492$		0			0
$493$	−12.7082	+	39.1118i	−0.572349	+	1.76151i
$494$		0			0
$495$	−6.66312	+	5.56758i	−0.299485	+	0.250244i
$496$		0			0
$497$	−0.551663	+	1.69784i	−0.0247455	+	0.0761587i
$498$		0			0
$499$	−10.5902	−	7.69421i	−0.474081	−	0.344440i	0.324949	−	0.945732i	$-0.394653\pi$
$499$	−10.5902	−	7.69421i	−0.474081	−	0.344440i	−0.799030	+	0.601292i	$0.794653\pi$
$500$		0			0
$501$	2.37132	+	7.29818i	0.105943	+	0.326059i
$502$		0			0
$503$	1.00000	−	0.726543i	0.0445878	−	0.0323949i	−0.565268	−	0.824907i	$-0.691227\pi$
$503$	1.00000	−	0.726543i	0.0445878	−	0.0323949i	0.609856	+	0.792512i	$0.291227\pi$
$504$		0			0
$505$	24.7984			1.10351
$506$		0			0
$507$	−8.00000			−0.355292
$508$		0			0
$509$	7.39919	−	5.37582i	0.327963	−	0.238279i	−0.411603	−	0.911363i	$-0.635031\pi$
$509$	7.39919	−	5.37582i	0.327963	−	0.238279i	0.739566	+	0.673084i	$0.235031\pi$
$510$		0			0
$511$	−0.708204	−	2.17963i	−0.0313291	−	0.0964210i
$512$		0			0
$513$	−2.11803	−	1.53884i	−0.0935135	−	0.0679415i
$514$		0			0
$515$	−10.0902	+	31.0543i	−0.444626	+	1.36842i
$516$		0			0
$517$	5.54508	−	22.0458i	0.243873	−	0.969574i
$518$		0			0
$519$	3.71885	−	11.4454i	0.163239	−	0.502399i
$520$		0			0
$521$	12.9443	+	9.40456i	0.567099	+	0.412021i	0.834050	−	0.551689i	$-0.186016\pi$
$521$	12.9443	+	9.40456i	0.567099	+	0.412021i	−0.266951	+	0.963710i	$0.586016\pi$
$522$		0			0
$523$	−8.20820	−	25.2623i	−0.358920	−	1.10464i	−0.953702	−	0.300754i	$-0.902762\pi$
$523$	−8.20820	−	25.2623i	−0.358920	−	1.10464i	0.594782	−	0.803887i	$-0.297238\pi$
$524$		0			0
$525$	−0.354102	+	0.257270i	−0.0154543	+	0.0112282i
$526$		0			0
$527$	30.9787			1.34945
$528$		0			0
$529$	−19.8885			−0.864719
$530$		0			0
$531$	4.50000	−	3.26944i	0.195283	−	0.141882i
$532$		0			0
$533$	3.45492	+	10.6331i	0.149649	+	0.460572i
$534$		0			0
$535$	12.5902	+	9.14729i	0.544321	+	0.395472i
$536$		0			0
$537$	1.36475	−	4.20025i	0.0588931	−	0.181254i
$538$		0			0
$539$	19.5066	+	12.2452i	0.840208	+	0.527439i
$540$		0			0
$541$	6.80902	−	20.9560i	0.292743	−	0.900969i	−0.691228	−	0.722637i	$-0.742930\pi$
$541$	6.80902	−	20.9560i	0.292743	−	0.900969i	0.983970	−	0.178332i	$-0.0570701\pi$
$542$		0			0
$543$	16.8992	+	12.2780i	0.725214	+	0.526898i
$544$		0			0
$545$	−14.4721	−	44.5407i	−0.619918	−	1.90791i
$546$		0			0
$547$	18.4894	−	13.4333i	0.790548	−	0.574367i	−0.117578	−	0.993064i	$-0.537513\pi$
$547$	18.4894	−	13.4333i	0.790548	−	0.574367i	0.908126	+	0.418697i	$0.137513\pi$
$548$		0			0
$549$	−0.145898			−0.00622678
$550$		0			0
$551$	−22.1803			−0.944914
$552$		0			0
$553$	−1.86475	+	1.35482i	−0.0792970	+	0.0576127i
$554$		0			0
$555$	6.66312	+	20.5070i	0.282834	+	0.870472i
$556$		0			0
$557$	−1.35410	−	0.983813i	−0.0573751	−	0.0416855i	0.558728	−	0.829351i	$-0.311290\pi$
$557$	−1.35410	−	0.983813i	−0.0573751	−	0.0416855i	−0.616103	+	0.787665i	$0.711290\pi$
$558$		0			0
$559$	−1.74671	+	5.37582i	−0.0738780	+	0.227373i
$560$		0			0
$561$	16.0623	−	1.08981i	0.678151	−	0.0460120i
$562$		0			0
$563$	7.96149	−	24.5030i	0.335537	−	1.03268i	−0.630920	−	0.775848i	$-0.717322\pi$
$563$	7.96149	−	24.5030i	0.335537	−	1.03268i	0.966457	−	0.256829i	$-0.0826776\pi$
$564$		0			0
$565$	−29.1525	−	21.1805i	−1.22645	−	0.891071i
$566$		0			0
$567$	0.0729490	+	0.224514i	0.00306357	+	0.00942870i
$568$		0			0
$569$	16.4164	−	11.9272i	0.688212	−	0.500015i	−0.187860	−	0.982196i	$-0.560155\pi$
$569$	16.4164	−	11.9272i	0.688212	−	0.500015i	0.876072	+	0.482181i	$0.160155\pi$
$570$		0			0
$571$	−29.8541			−1.24936			−0.624678	−	0.780883i	$-0.714770\pi$
$571$	−29.8541			−1.24936			−0.624678	+	0.780883i	$0.714770\pi$
$572$		0			0
$573$	10.2361			0.427618
$574$		0			0
$575$	−2.64590	+	1.92236i	−0.110342	+	0.0801678i
$576$		0			0
$577$	−1.79837	−	5.53483i	−0.0748673	−	0.230418i	0.906619	−	0.421950i	$-0.138654\pi$
$577$	−1.79837	−	5.53483i	−0.0748673	−	0.230418i	−0.981486	+	0.191532i	$0.938654\pi$
$578$		0			0
$579$	−12.3992	−	9.00854i	−0.515293	−	0.374382i
$580$		0			0
$581$	1.16312	−	3.57971i	0.0482543	−	0.148511i
$582$		0			0
$583$	13.0557	+	32.5074i	0.540713	+	1.34632i
$584$		0			0
$585$	−1.80902	+	5.56758i	−0.0747936	+	0.230191i
$586$		0			0
$587$	−0.572949	−	0.416272i	−0.0236481	−	0.0171814i	0.575898	−	0.817521i	$-0.304652\pi$
$587$	−0.572949	−	0.416272i	−0.0236481	−	0.0171814i	−0.599547	+	0.800340i	$0.704652\pi$
$588$		0			0
$589$	5.16312	+	15.8904i	0.212743	+	0.654754i
$590$		0			0
$591$	12.0172	−	8.73102i	0.494322	−	0.359146i
$592$		0			0
$593$	−18.4377			−0.757145			−0.378573	−	0.925572i	$-0.623585\pi$
$593$	−18.4377			−0.757145			−0.378573	+	0.925572i	$0.623585\pi$
$594$		0			0
$595$	3.00000			0.122988
$596$		0			0
$597$	−0.427051	+	0.310271i	−0.0174780	+	0.0126985i
$598$		0			0
$599$	−8.56231	−	26.3521i	−0.349846	−	1.07672i	−0.958938	−	0.283616i	$-0.908466\pi$
$599$	−8.56231	−	26.3521i	−0.349846	−	1.07672i	0.609091	−	0.793100i	$-0.291534\pi$
$600$		0			0
$601$	−3.19098	−	2.31838i	−0.130163	−	0.0945689i	0.520799	−	0.853679i	$-0.325634\pi$
$601$	−3.19098	−	2.31838i	−0.130163	−	0.0945689i	−0.650962	+	0.759111i	$0.725634\pi$
$602$		0			0
$603$	4.80902	−	14.8006i	0.195838	−	0.602728i
$604$		0			0
$605$	28.5344	−	3.88998i	1.16009	−	0.158150i
$606$		0			0
$607$	3.20820	−	9.87384i	0.130217	−	0.400767i	−0.864598	−	0.502463i	$-0.832427\pi$
$607$	3.20820	−	9.87384i	0.130217	−	0.400767i	0.994815	+	0.101697i	$0.0324271\pi$
$608$		0			0
$609$	1.61803	+	1.17557i	0.0655660	+	0.0476365i
$610$		0			0
$611$	−4.73607	−	14.5761i	−0.191601	−	0.589687i
$612$		0			0
$613$	−22.7984	+	16.5640i	−0.920818	+	0.669013i	−0.943727	−	0.330724i	$-0.892707\pi$
$613$	−22.7984	+	16.5640i	−0.920818	+	0.669013i	0.0229097	+	0.999738i	$0.492707\pi$
$614$		0			0
$615$	−13.0902			−0.527847
$616$		0			0
$617$	−21.4721			−0.864436			−0.432218	−	0.901769i	$-0.642269\pi$
$617$	−21.4721			−0.864436			−0.432218	+	0.901769i	$0.642269\pi$
$618$		0			0
$619$	20.6074	−	14.9721i	0.828281	−	0.601781i	−0.0907915	−	0.995870i	$-0.528940\pi$
$619$	20.6074	−	14.9721i	0.828281	−	0.601781i	0.919072	+	0.394089i	$0.128940\pi$
$620$		0			0
$621$	0.545085	+	1.67760i	0.0218735	+	0.0673197i
$622$		0			0
$623$	1.04508	+	0.759299i	0.0418704	+	0.0304207i
$624$		0			0
$625$	−9.52786	+	29.3238i	−0.381115	+	1.17295i
$626$		0			0
$627$	3.23607	+	8.05748i	0.129236	+	0.321785i
$628$		0			0
$629$	12.3541	−	38.0220i	0.492590	−	1.51604i
$630$		0			0
$631$	9.30902	+	6.76340i	0.370586	+	0.269247i	0.757454	−	0.652889i	$-0.226443\pi$
$631$	9.30902	+	6.76340i	0.370586	+	0.269247i	−0.386868	+	0.922135i	$0.626443\pi$
$632$		0			0
$633$	1.73607	+	5.34307i	0.0690025	+	0.212368i
$634$		0			0
$635$	−11.0902	+	8.05748i	−0.440100	+	0.319751i
$636$		0			0
$637$	15.5279			0.615236
$638$		0			0
$639$	−7.56231			−0.299160
$640$		0			0
$641$	5.50000	−	3.99598i	0.217237	−	0.157832i	−0.473845	−	0.880608i	$-0.657134\pi$
$641$	5.50000	−	3.99598i	0.217237	−	0.157832i	0.691082	+	0.722776i	$0.257134\pi$
$642$		0			0
$643$	−8.06231	−	24.8132i	−0.317946	−	0.978538i	−0.974525	−	0.224280i	$-0.927997\pi$
$643$	−8.06231	−	24.8132i	−0.317946	−	0.978538i	0.656578	−	0.754258i	$-0.272003\pi$
$644$		0			0
$645$	−5.35410	−	3.88998i	−0.210818	−	0.153168i
$646$		0			0
$647$	10.3197	−	31.7606i	0.405708	−	1.24864i	−0.514595	−	0.857433i	$-0.672058\pi$
$647$	10.3197	−	31.7606i	0.405708	−	1.24864i	0.920303	−	0.391207i	$-0.127942\pi$
$648$		0			0
$649$	−18.4058	+	1.24882i	−0.722489	+	0.0490203i
$650$		0			0
$651$	0.465558	−	1.43284i	0.0182467	−	0.0561575i
$652$		0			0
$653$	−20.0172	−	14.5434i	−0.783334	−	0.569126i	0.122643	−	0.992451i	$-0.460863\pi$
$653$	−20.0172	−	14.5434i	−0.783334	−	0.569126i	−0.905978	+	0.423325i	$0.860863\pi$
$654$		0			0
$655$	−10.7812	−	33.1810i	−0.421255	−	1.29649i
$656$		0			0
$657$	7.85410	−	5.70634i	0.306418	−	0.222625i
$658$		0			0
$659$	21.1246			0.822898			0.411449	−	0.911433i	$-0.365023\pi$
$659$	21.1246			0.822898			0.411449	+	0.911433i	$0.365023\pi$
$660$		0			0
$661$	−14.8541			−0.577758			−0.288879	−	0.957366i	$-0.593282\pi$
$661$	−14.8541			−0.577758			−0.288879	+	0.957366i	$0.593282\pi$
$662$		0			0
$663$	8.78115	−	6.37988i	0.341032	−	0.247774i
$664$		0			0
$665$	0.500000	+	1.53884i	0.0193892	+	0.0596737i
$666$		0			0
$667$	12.0902	+	8.78402i	0.468133	+	0.340119i
$668$		0			0
$669$	−6.63525	+	20.4212i	−0.256534	+	0.789530i
$670$		0			0
$671$	0.409830	+	0.257270i	0.0158213	+	0.00993180i
$672$		0			0
$673$	−5.39919	+	16.6170i	−0.208123	+	0.640538i	0.791447	+	0.611237i	$0.209328\pi$
$673$	−5.39919	+	16.6170i	−0.208123	+	0.640538i	−0.999571	+	0.0293004i	$0.990672\pi$
$674$		0			0
$675$	−1.50000	−	1.08981i	−0.0577350	−	0.0419470i
$676$		0			0
$677$	−4.76393	−	14.6619i	−0.183093	−	0.563502i	0.816818	−	0.576896i	$-0.195736\pi$
$677$	−4.76393	−	14.6619i	−0.183093	−	0.563502i	−0.999910	+	0.0133945i	$0.995736\pi$
$678$		0			0
$679$	0.0278640	−	0.0202444i	0.00106932	−	0.000776909i
$680$		0			0
$681$	28.5967			1.09583
$682$		0			0
$683$	−50.4853			−1.93177			−0.965883	−	0.258979i	$-0.916614\pi$
$683$	−50.4853			−1.93177			−0.965883	+	0.258979i	$0.916614\pi$
$684$		0			0
$685$	7.35410	−	5.34307i	0.280986	−	0.204148i
$686$		0			0
$687$	7.38197	+	22.7194i	0.281640	+	0.866797i
$688$		0			0
$689$	19.1074	+	13.8823i	0.727934	+	0.528875i
$690$		0			0
$691$	−11.0000	+	33.8545i	−0.418460	+	1.28789i	0.490660	+	0.871351i	$0.336756\pi$
$691$	−11.0000	+	33.8545i	−0.418460	+	1.28789i	−0.909120	+	0.416535i	$0.863244\pi$
$692$		0			0
$693$	0.190983	−	0.759299i	0.00725484	−	0.0288434i
$694$		0			0
$695$	−13.2533	+	40.7894i	−0.502726	+	1.54723i
$696$		0			0
$697$	19.6353	+	14.2658i	0.743738	+	0.540358i
$698$		0			0
$699$	−2.75329	−	8.47375i	−0.104139	−	0.320507i
$700$		0			0
$701$	25.8262	−	18.7639i	0.975444	−	0.708701i	0.0187579	−	0.999824i	$-0.494029\pi$
$701$	25.8262	−	18.7639i	0.975444	−	0.708701i	0.956686	+	0.291123i	$0.0940288\pi$
$702$		0			0
$703$	21.5623			0.813238
$704$		0			0
$705$	17.9443			0.675820
$706$		0			0
$707$	−1.80902	+	1.31433i	−0.0680351	+	0.0494304i
$708$		0			0
$709$	1.64590	+	5.06555i	0.0618130	+	0.190241i	0.977194	−	0.212347i	$-0.0681108\pi$
$709$	1.64590	+	5.06555i	0.0618130	+	0.190241i	−0.915381	+	0.402588i	$0.868111\pi$
$710$		0			0
$711$	−7.89919	−	5.73910i	−0.296243	−	0.215233i
$712$		0			0
$713$	3.47871	−	10.7064i	0.130279	−	0.400957i
$714$		0			0
$715$	14.8992	−	12.4495i	0.557198	−	0.465585i
$716$		0			0
$717$	−4.64590	+	14.2986i	−0.173504	+	0.533991i
$718$		0			0
$719$	7.13525	+	5.18407i	0.266100	+	0.193333i	0.712832	−	0.701335i	$-0.247412\pi$
$719$	7.13525	+	5.18407i	0.266100	+	0.193333i	−0.446732	+	0.894668i	$0.647412\pi$
$720$		0			0
$721$	−0.909830	−	2.80017i	−0.0338838	−	0.104284i
$722$		0			0
$723$	−22.7082	+	16.4985i	−0.844527	+	0.613585i
$724$		0			0
$725$	−15.7082			−0.583388
$726$		0			0
$727$	10.7426			0.398423			0.199211	−	0.979957i	$-0.436162\pi$
$727$	10.7426			0.398423			0.199211	+	0.979957i	$0.436162\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	3.79180	+	11.6699i	0.140245	+	0.431629i
$732$		0			0
$733$	17.8541	+	12.9718i	0.659456	+	0.479123i	0.866479	−	0.499213i	$-0.166377\pi$
$733$	17.8541	+	12.9718i	0.659456	+	0.479123i	−0.207023	+	0.978336i	$0.566377\pi$
$734$		0			0
$735$	−5.61803	+	17.2905i	−0.207224	+	0.637771i
$736$		0			0
$737$	−39.6074	+	33.0952i	−1.45896	+	1.21908i
$738$		0			0
$739$	−15.1631	+	46.6673i	−0.557784	+	1.71668i	0.130690	+	0.991423i	$0.458281\pi$
$739$	−15.1631	+	46.6673i	−0.557784	+	1.71668i	−0.688475	+	0.725260i	$0.741719\pi$
$740$		0			0
$741$	4.73607	+	3.44095i	0.173984	+	0.126407i
$742$		0			0
$743$	−3.07295	−	9.45756i	−0.112736	−	0.346964i	0.878732	−	0.477315i	$-0.158390\pi$
$743$	−3.07295	−	9.45756i	−0.112736	−	0.346964i	−0.991468	+	0.130350i	$0.958390\pi$
$744$		0			0
$745$	3.11803	−	2.26538i	0.114236	−	0.0829973i
$746$		0			0
$747$	15.9443			0.583370
$748$		0			0
$749$	−1.40325			−0.0512737
$750$		0			0
$751$	5.73607	−	4.16750i	0.209312	−	0.152074i	−0.478190	−	0.878256i	$-0.658707\pi$
$751$	5.73607	−	4.16750i	0.209312	−	0.152074i	0.687502	+	0.726182i	$0.258707\pi$
$752$		0			0
$753$	2.73607	+	8.42075i	0.0997079	+	0.306869i
$754$		0			0
$755$	−28.4164	−	20.6457i	−1.03418	−	0.751375i
$756$		0			0
$757$	−5.39919	+	16.6170i	−0.196237	+	0.603955i	0.803723	+	0.595003i	$0.202849\pi$
$757$	−5.39919	+	16.6170i	−0.196237	+	0.603955i	−0.999960	+	0.00895128i	$0.997151\pi$
$758$		0			0
$759$	1.42705	−	5.67358i	0.0517987	−	0.205938i
$760$		0			0
$761$	−2.45492	+	7.55545i	−0.0889906	+	0.273885i	−0.985641	−	0.168854i	$-0.945993\pi$
$761$	−2.45492	+	7.55545i	−0.0889906	+	0.273885i	0.896650	+	0.442739i	$0.145993\pi$
$762$		0			0
$763$	3.41641	+	2.48217i	0.123682	+	0.0898604i
$764$		0			0
$765$	3.92705	+	12.0862i	0.141983	+	0.436978i
$766$		0			0
$767$	−10.0623	+	7.31069i	−0.363329	+	0.263974i
$768$		0			0
$769$	6.43769			0.232149			0.116075	−	0.993240i	$-0.462969\pi$
$769$	6.43769			0.232149			0.116075	+	0.993240i	$0.462969\pi$
$770$		0			0
$771$	−6.79837			−0.244837
$772$		0			0
$773$	37.0795	−	26.9399i	1.33366	−	0.968959i	0.334006	−	0.942571i	$-0.391599\pi$
$773$	37.0795	−	26.9399i	1.33366	−	0.968959i	0.999652	−	0.0263883i	$-0.00840062\pi$
$774$		0			0
$775$	3.65654	+	11.2537i	0.131347	+	0.404244i
$776$		0			0
$777$	−1.57295	−	1.14281i	−0.0564292	−	0.0409982i
$778$		0			0
$779$	−4.04508	+	12.4495i	−0.144930	+	0.446049i
$780$		0			0
$781$	21.2426	+	13.3350i	0.760122	+	0.477165i
$782$		0			0
$783$	−2.61803	+	8.05748i	−0.0935609	+	0.287951i
$784$		0			0
$785$	13.0902	+	9.51057i	0.467208	+	0.339447i
$786$		0			0
$787$	9.58359	+	29.4953i	0.341618	+	1.05139i	0.963369	+	0.268178i	$0.0864215\pi$
$787$	9.58359	+	29.4953i	0.341618	+	1.05139i	−0.621751	+	0.783215i	$0.713579\pi$
$788$		0			0
$789$	−3.35410	+	2.43690i	−0.119409	+	0.0867559i
$790$		0			0
$791$	3.24922			0.115529
$792$		0			0
$793$	0.326238			0.0115850
$794$		0			0
$795$	−22.3713	+	16.2537i	−0.793429	+	0.576460i
$796$		0			0
$797$	2.38197	+	7.33094i	0.0843736	+	0.259675i	0.984339	−	0.176286i	$-0.0564084\pi$
$797$	2.38197	+	7.33094i	0.0843736	+	0.259675i	−0.899965	+	0.435961i	$0.856408\pi$
$798$		0			0
$799$	−26.9164	−	19.5559i	−0.952234	−	0.691839i
$800$		0			0
$801$	−1.69098	+	5.20431i	−0.0597479	+	0.183885i
$802$		0			0
$803$	−32.1246	+	2.17963i	−1.13365	+	0.0769174i
$804$		0			0
$805$	0.336881	−	1.03681i	0.0118735	−	0.0365429i
$806$		0			0
$807$	−20.5623	−	14.9394i	−0.723827	−	0.525891i
$808$		0			0
$809$	7.19098	+	22.1316i	0.252821	+	0.778105i	0.994251	+	0.107074i	$0.0341481\pi$
$809$	7.19098	+	22.1316i	0.252821	+	0.778105i	−0.741430	+	0.671031i	$0.765852\pi$
$810$		0			0
$811$	12.3992	−	9.00854i	0.435394	−	0.316333i	−0.348408	−	0.937343i	$-0.613278\pi$
$811$	12.3992	−	9.00854i	0.435394	−	0.316333i	0.783802	+	0.621011i	$0.213278\pi$
$812$		0			0
$813$	15.3820			0.539469
$814$		0			0
$815$	−46.1246			−1.61567
$816$		0			0
$817$	−5.35410	+	3.88998i	−0.187316	+	0.136093i
$818$		0			0
$819$	−0.163119	−	0.502029i	−0.00569984	−	0.0175423i
$820$		0			0
$821$	−25.0795	−	18.2213i	−0.875282	−	0.635929i	0.0567174	−	0.998390i	$-0.481937\pi$
$821$	−25.0795	−	18.2213i	−0.875282	−	0.635929i	−0.931999	+	0.362461i	$0.881937\pi$
$822$		0			0
$823$	7.89261	−	24.2910i	0.275119	−	0.846729i	−0.714069	−	0.700076i	$-0.753150\pi$
$823$	7.89261	−	24.2910i	0.275119	−	0.846729i	0.989188	−	0.146654i	$-0.0468504\pi$
$824$		0			0
$825$	2.29180	+	5.70634i	0.0797901	+	0.198669i
$826$		0			0
$827$	3.18034	−	9.78808i	0.110591	−	0.340365i	−0.880411	−	0.474212i	$-0.842733\pi$
$827$	3.18034	−	9.78808i	0.110591	−	0.340365i	0.991002	+	0.133847i	$0.0427331\pi$
$828$		0			0
$829$	−22.0172	−	15.9964i	−0.764690	−	0.555580i	0.135655	−	0.990756i	$-0.456686\pi$
$829$	−22.0172	−	15.9964i	−0.764690	−	0.555580i	−0.900345	+	0.435176i	$0.856686\pi$
$830$		0			0
$831$	−2.73607	−	8.42075i	−0.0949131	−	0.292113i
$832$		0			0
$833$	27.2705	−	19.8132i	0.944867	−	0.686486i
$834$		0			0
$835$	20.0902			0.695249
$836$		0			0
$837$	6.38197			0.220593
$838$		0			0
$839$	−27.9336	+	20.2950i	−0.964376	+	0.700660i	−0.954163	−	0.299288i	$-0.903251\pi$
$839$	−27.9336	+	20.2950i	−0.964376	+	0.700660i	−0.0102130	+	0.999948i	$0.503251\pi$
$840$		0			0
$841$	13.2188	+	40.6834i	0.455822	+	1.40288i
$842$		0			0
$843$	25.5623	+	18.5721i	0.880413	+	0.639657i
$844$		0			0
$845$	−6.47214	+	19.9192i	−0.222648	+	0.685241i
$846$		0			0
$847$	−1.87539	+	1.79611i	−0.0644391	+	0.0617151i
$848$		0			0
$849$	−0.708204	+	2.17963i	−0.0243055	+	0.0748046i
$850$		0			0
$851$	−11.7533	−	8.53926i	−0.402898	−	0.292722i
$852$		0			0
$853$	11.5795	+	35.6381i	0.396475	+	1.22023i	0.927807	+	0.373062i	$0.121692\pi$
$853$	11.5795	+	35.6381i	0.396475	+	1.22023i	−0.531331	+	0.847164i	$0.678308\pi$
$854$		0			0
$855$	−5.54508	+	4.02874i	−0.189638	+	0.137780i
$856$		0			0
$857$	−12.8885			−0.440264			−0.220132	−	0.975470i	$-0.570649\pi$
$857$	−12.8885			−0.440264			−0.220132	+	0.975470i	$0.570649\pi$
$858$		0			0
$859$	−11.6525			−0.397577			−0.198789	−	0.980042i	$-0.563701\pi$
$859$	−11.6525			−0.397577			−0.198789	+	0.980042i	$0.563701\pi$
$860$		0			0
$861$	0.954915	−	0.693786i	0.0325434	−	0.0236442i
$862$		0			0
$863$	−14.6180	−	44.9897i	−0.497604	−	1.53147i	−0.812859	−	0.582460i	$-0.802090\pi$
$863$	−14.6180	−	44.9897i	−0.497604	−	1.53147i	0.315256	−	0.949007i	$-0.397910\pi$
$864$		0			0
$865$	−25.4894	−	18.5191i	−0.866664	−	0.629668i
$866$		0			0
$867$	2.02786	−	6.24112i	0.0688699	−	0.211960i
$868$		0			0
$869$	12.0689	+	30.0503i	0.409409	+	1.01939i
$870$		0			0
$871$	−10.7533	+	33.0952i	−0.364361	+	1.12139i
$872$		0			0
$873$	0.118034	+	0.0857567i	0.00399485	+	0.00290242i
$874$		0			0
$875$	−0.600813	−	1.84911i	−0.0203112	−	0.0625114i
$876$		0			0
$877$	−33.8435	+	24.5887i	−1.14281	+	0.830302i	−0.987509	−	0.157565i	$-0.949636\pi$
$877$	−33.8435	+	24.5887i	−1.14281	+	0.830302i	−0.155304	+	0.987867i	$0.549636\pi$
$878$		0			0
$879$	−17.3607			−0.585561
$880$		0			0
$881$	1.14590			0.0386063			0.0193031	−	0.999814i	$-0.493855\pi$
$881$	1.14590			0.0386063			0.0193031	+	0.999814i	$0.493855\pi$
$882$		0			0
$883$	30.5623	−	22.2048i	1.02850	−	0.747252i	0.0604949	−	0.998169i	$-0.480732\pi$
$883$	30.5623	−	22.2048i	1.02850	−	0.747252i	0.968009	+	0.250917i	$0.0807321\pi$
$884$		0			0
$885$	−4.50000	−	13.8496i	−0.151266	−	0.465548i
$886$		0			0
$887$	4.19098	+	3.04493i	0.140719	+	0.102239i	0.655918	−	0.754832i	$-0.272282\pi$
$887$	4.19098	+	3.04493i	0.140719	+	0.102239i	−0.515198	+	0.857071i	$0.672282\pi$
$888$		0			0
$889$	0.381966	−	1.17557i	0.0128107	−	0.0394274i
$890$		0			0
$891$	3.30902	−	0.224514i	0.110856	−	0.00752150i
$892$		0			0
$893$	5.54508	−	17.0660i	0.185559	−	0.571092i
$894$		0			0
$895$	−9.35410	−	6.79615i	−0.312673	−	0.227170i
$896$		0			0
$897$	−1.21885	−	3.75123i	−0.0406961	−	0.125250i
$898$		0			0
$899$	43.7426	−	31.7809i	1.45890	−	1.05995i
$900$		0			0
$901$	51.2705			1.70807
$902$		0			0
$903$	0.596748			0.0198585
$904$		0			0
$905$	44.2426	−	32.1442i	1.47068	−	1.06851i
$906$		0			0
$907$	7.89919	+	24.3112i	0.262288	+	0.807240i	0.992306	+	0.123812i	$0.0395119\pi$
$907$	7.89919	+	24.3112i	0.262288	+	0.807240i	−0.730018	+	0.683428i	$0.760488\pi$
$908$		0			0
$909$	−7.66312	−	5.56758i	−0.254170	−	0.184665i
$910$		0			0
$911$	0.218847	−	0.673542i	0.00725073	−	0.0223154i	−0.947366	−	0.320153i	$-0.896266\pi$
$911$	0.218847	−	0.673542i	0.00725073	−	0.0223154i	0.954616	+	0.297838i	$0.0962655\pi$
$912$		0			0
$913$	−44.7877	−	28.1154i	−1.48226	−	0.930485i
$914$		0			0
$915$	−0.118034	+	0.363271i	−0.00390208	+	0.0120094i
$916$		0			0
$917$	2.54508	+	1.84911i	0.0840461	+	0.0610631i
$918$		0			0
$919$	−10.1631	−	31.2789i	−0.335250	−	1.03179i	−0.966599	−	0.256295i	$-0.917498\pi$
$919$	−10.1631	−	31.2789i	−0.335250	−	1.03179i	0.631348	−	0.775499i	$-0.282502\pi$
$920$		0			0
$921$	11.1631	−	8.11048i	0.367837	−	0.267249i
$922$		0			0
$923$	16.9098			0.556594
$924$		0			0
$925$	15.2705			0.502091
$926$		0			0
$927$	10.0902	−	7.33094i	0.331405	−	0.240780i
$928$		0			0
$929$	6.16312	+	18.9681i	0.202205	+	0.622324i	0.999817	+	0.0191522i	$0.00609672\pi$
$929$	6.16312	+	18.9681i	0.202205	+	0.622324i	−0.797611	+	0.603172i	$0.793903\pi$
$930$		0			0
$931$	14.7082	+	10.6861i	0.482042	+	0.350224i
$932$		0			0
$933$	3.01722	−	9.28605i	0.0987794	−	0.304012i
$934$		0			0
$935$	10.2812	−	40.8752i	0.336230	−	1.33676i
$936$		0			0
$937$	2.69098	−	8.28199i	0.0879106	−	0.270561i	−0.897431	−	0.441155i	$-0.854569\pi$
$937$	2.69098	−	8.28199i	0.0879106	−	0.270561i	0.985341	+	0.170594i	$0.0545688\pi$
$938$		0			0
$939$	21.7533	+	15.8047i	0.709892	+	0.515767i
$940$		0			0
$941$	13.9721	+	43.0018i	0.455479	+	1.40182i	0.870572	+	0.492040i	$0.163749\pi$
$941$	13.9721	+	43.0018i	0.455479	+	1.40182i	−0.415094	+	0.909779i	$0.636251\pi$
$942$		0			0
$943$	7.13525	−	5.18407i	0.232356	−	0.168816i
$944$		0			0
$945$	0.618034			0.0201046
$946$		0			0
$947$	41.2705			1.34111			0.670556	−	0.741859i	$-0.266056\pi$
$947$	41.2705			1.34111			0.670556	+	0.741859i	$0.266056\pi$
$948$		0			0
$949$	−17.5623	+	12.7598i	−0.570097	+	0.414199i
$950$		0			0
$951$	4.92705	+	15.1639i	0.159771	+	0.491723i
$952$		0			0
$953$	−10.2361	−	7.43694i	−0.331579	−	0.240906i	0.409521	−	0.912300i	$-0.365696\pi$
$953$	−10.2361	−	7.43694i	−0.331579	−	0.240906i	−0.741100	+	0.671394i	$0.765696\pi$
$954$		0			0
$955$	8.28115	−	25.4868i	0.267972	−	0.824732i
$956$		0			0
$957$	21.5623	−	18.0171i	0.697010	−	0.582409i
$958$		0			0
$959$	−0.253289	+	0.779543i	−0.00817913	+	0.0251728i
$960$		0			0
$961$	−7.87132	−	5.71885i	−0.253914	−	0.184479i
$962$		0			0
$963$	−1.83688	−	5.65334i	−0.0591927	−	0.182176i
$964$		0			0
$965$	−32.4615	+	23.5847i	−1.04497	+	0.759217i
$966$		0			0
$967$	−24.6180			−0.791663			−0.395831	−	0.918323i	$-0.629544\pi$
$967$	−24.6180			−0.791663			−0.395831	+	0.918323i	$0.629544\pi$
$968$		0			0
$969$	12.7082			0.408246
$970$		0			0
$971$	−22.0902	+	16.0494i	−0.708907	+	0.515051i	−0.882821	−	0.469710i	$-0.844359\pi$
$971$	−22.0902	+	16.0494i	−0.708907	+	0.515051i	0.173914	+	0.984761i	$0.444359\pi$
$972$		0			0
$973$	−1.19505	−	3.67798i	−0.0383115	−	0.117911i
$974$		0			0
$975$	3.35410	+	2.43690i	0.107417	+	0.0780432i
$976$		0			0
$977$	6.30902	−	19.4172i	0.201843	−	0.621210i	−0.797985	−	0.602677i	$-0.794101\pi$
$977$	6.30902	−	19.4172i	0.201843	−	0.621210i	0.999828	−	0.0185325i	$-0.00589942\pi$
$978$		0			0
$979$	13.9271	−	11.6372i	0.445110	−	0.371926i
$980$		0			0
$981$	−5.52786	+	17.0130i	−0.176491	+	0.543184i
$982$		0			0
$983$	−27.3262	−	19.8537i	−0.871572	−	0.633234i	0.0594366	−	0.998232i	$-0.481070\pi$
$983$	−27.3262	−	19.8537i	−0.871572	−	0.633234i	−0.931008	+	0.364998i	$0.881070\pi$
$984$		0			0
$985$	−12.0172	−	36.9852i	−0.382900	−	1.17845i
$986$		0			0
$987$	−1.30902	+	0.951057i	−0.0416665	+	0.0302725i
$988$		0			0
$989$	4.45898			0.141787
$990$		0			0
$991$	−14.3262			−0.455088			−0.227544	−	0.973768i	$-0.573070\pi$
$991$	−14.3262			−0.455088			−0.227544	+	0.973768i	$0.573070\pi$
$992$		0			0
$993$	21.8435	−	15.8702i	0.693181	−	0.503626i
$994$		0			0
$995$	0.427051	+	1.31433i	0.0135384	+	0.0416670i
$996$		0			0
$997$	−41.0967	−	29.8585i	−1.30155	−	0.945629i	−0.301578	−	0.953442i	$-0.597513\pi$
$997$	−41.0967	−	29.8585i	−1.30155	−	0.945629i	−0.999969	+	0.00781235i	$0.997513\pi$
$998$		0			0
$999$	2.54508	−	7.83297i	0.0805229	−	0.247824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.q.b.97.1	yes	4
3.2	odd	2		792.2.r.d.361.1		4
4.3	odd	2		528.2.y.h.97.1		4
11.4	even	5		2904.2.a.z.1.2		2
11.5	even	5	inner	264.2.q.b.49.1	✓	4
11.7	odd	10		2904.2.a.ba.1.2		2
33.5	odd	10		792.2.r.d.577.1		4
33.26	odd	10		8712.2.a.ba.1.1		2
33.29	even	10		8712.2.a.bc.1.1		2
44.7	even	10		5808.2.a.bv.1.2		2
44.15	odd	10		5808.2.a.bw.1.2		2
44.27	odd	10		528.2.y.h.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.q.b.49.1	✓	4	11.5	even	5	inner
264.2.q.b.97.1	yes	4	1.1	even	1	trivial
528.2.y.h.49.1		4	44.27	odd	10
528.2.y.h.97.1		4	4.3	odd	2
792.2.r.d.361.1		4	3.2	odd	2
792.2.r.d.577.1		4	33.5	odd	10
2904.2.a.z.1.2		2	11.4	even	5
2904.2.a.ba.1.2		2	11.7	odd	10
5808.2.a.bv.1.2		2	44.7	even	10
5808.2.a.bw.1.2		2	44.15	odd	10
8712.2.a.ba.1.1		2	33.26	odd	10
8712.2.a.bc.1.1		2	33.29	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(0.809017 + 2.48990i) q^{5} +(-0.190983 - 0.138757i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-2.54508 + 2.12663i) q^{11} +(-0.690983 + 2.12663i) q^{13} +(-2.11803 - 1.53884i) q^{15} +(1.50000 + 4.61653i) q^{17} +(-2.11803 + 1.53884i) q^{19} +0.236068 q^{21} +1.76393 q^{23} +(-1.50000 + 1.08981i) q^{25} +(0.309017 + 0.951057i) q^{27} +(6.85410 + 4.97980i) q^{29} +(1.97214 - 6.06961i) q^{31} +(0.809017 - 3.21644i) q^{33} +(0.190983 - 0.587785i) q^{35} +(-6.66312 - 4.84104i) q^{37} +(-0.690983 - 2.12663i) q^{39} +(4.04508 - 2.93893i) q^{41} +2.52786 q^{43} +2.61803 q^{45} +(-5.54508 + 4.02874i) q^{47} +(-2.14590 - 6.60440i) q^{49} +(-3.92705 - 2.85317i) q^{51} +(3.26393 - 10.0453i) q^{53} +(-7.35410 - 4.61653i) q^{55} +(0.809017 - 2.48990i) q^{57} +(4.50000 + 3.26944i) q^{59} +(-0.0450850 - 0.138757i) q^{61} +(-0.190983 + 0.138757i) q^{63} -5.85410 q^{65} +15.5623 q^{67} +(-1.42705 + 1.03681i) q^{69} +(-2.33688 - 7.19218i) q^{71} +(7.85410 + 5.70634i) q^{73} +(0.572949 - 1.76336i) q^{75} +(0.781153 - 0.0530006i) q^{77} +(3.01722 - 9.28605i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.92705 + 15.1639i) q^{83} +(-10.2812 + 7.46969i) q^{85} -8.47214 q^{87} -5.47214 q^{89} +(0.427051 - 0.310271i) q^{91} +(1.97214 + 6.06961i) q^{93} +(-5.54508 - 4.02874i) q^{95} +(-0.0450850 + 0.138757i) q^{97} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + q^{5} - 3 q^{7} - q^{9} + q^{11} - 5 q^{13} - 4 q^{15} + 6 q^{17} - 4 q^{19} - 8 q^{21} + 16 q^{23} - 6 q^{25} - q^{27} + 14 q^{29} - 10 q^{31} + q^{33} + 3 q^{35} - 11 q^{37} - 5 q^{39}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q - q^3 + q^5 - 3 * q^7 - q^9 + q^11 - 5 * q^13 - 4 * q^15 + 6 * q^17 - 4 * q^19 - 8 * q^21 + 16 * q^23 - 6 * q^25 - q^27 + 14 * q^29 - 10 * q^31 + q^33 + 3 * q^35 - 11 * q^37 - 5 * q^39 + 5 * q^41 + 28 * q^43 + 6 * q^45 - 11 * q^47 - 22 * q^49 - 9 * q^51 + 22 * q^53 - 16 * q^55 + q^57 + 18 * q^59 + 11 * q^61 - 3 * q^63 - 10 * q^65 + 22 * q^67 + q^69 - 25 * q^71 + 18 * q^73 + 9 * q^75 - 17 * q^77 - 17 * q^79 - q^81 + 13 * q^83 - 21 * q^85 - 16 * q^87 - 4 * q^89 - 5 * q^91 - 10 * q^93 - 11 * q^95 + 11 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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