LMFDB - Embedded newform 660.2.y.b.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [660,2,Mod(181,660)] 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("660.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(660, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	660.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,2] 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:	$5.27012653340$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$1.43801 - 1.04478i$ of defining polynomial
Character	$\chi$	$=$	660.361
Dual form			660.2.y.b.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(-1.12900 - 0.820265i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-0.660531 + 3.25018i) q^{11} +(-0.591770 + 1.82128i) q^{13} +(0.809017 + 0.587785i) q^{15} +(1.46847 + 4.51948i) q^{17} +(0.439763 - 0.319507i) q^{19} +1.39552 q^{21} -1.43100 q^{23} +(-0.809017 + 0.587785i) q^{25} +(0.309017 + 0.951057i) q^{27} +(7.72730 + 5.61421i) q^{29} +(-2.92597 + 9.00521i) q^{31} +(-1.37603 - 3.01770i) q^{33} +(-0.431239 + 1.32722i) q^{35} +(0.517740 + 0.376160i) q^{37} +(-0.591770 - 1.82128i) q^{39} +(3.32959 - 2.41909i) q^{41} -7.84844 q^{43} -1.00000 q^{45} +(-9.43603 + 6.85567i) q^{47} +(-1.56132 - 4.80524i) q^{49} +(-3.84450 - 2.79319i) q^{51} +(-3.55538 + 10.9423i) q^{53} +(3.29522 - 0.376160i) q^{55} +(-0.167975 + 0.516973i) q^{57} +(6.48027 + 4.70819i) q^{59} +(-1.85302 - 5.70301i) q^{61} +(-1.12900 + 0.820265i) q^{63} +1.91501 q^{65} +9.66707 q^{67} +(1.15770 - 0.841120i) q^{69} +(0.332025 + 1.02187i) q^{71} +(-8.28929 - 6.02252i) q^{73} +(0.309017 - 0.951057i) q^{75} +(3.41175 - 3.12764i) q^{77} +(-2.33688 + 7.19218i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.06349 - 3.27309i) q^{83} +(3.84450 - 2.79319i) q^{85} -9.55147 q^{87} +11.0079 q^{89} +(2.16204 - 1.57081i) q^{91} +(-2.92597 - 9.00521i) q^{93} +(-0.439763 - 0.319507i) q^{95} +(4.07271 - 12.5345i) q^{97} +(2.88699 + 1.63256i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9} - 5 q^{11} - 8 q^{13} + 2 q^{15} + 6 q^{17} + 6 q^{19} - 8 q^{21} + 30 q^{23} - 2 q^{25} - 2 q^{27} - 9 q^{31} + 10 q^{33} - 7 q^{35} - 7 q^{37} - 8 q^{39} + 25 q^{41}+ \cdots + 5 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 2 * q^5 - 3 * q^7 - 2 * q^9 - 5 * q^11 - 8 * q^13 + 2 * q^15 + 6 * q^17 + 6 * q^19 - 8 * q^21 + 30 * q^23 - 2 * q^25 - 2 * q^27 - 9 * q^31 + 10 * q^33 - 7 * q^35 - 7 * q^37 - 8 * q^39 + 25 * q^41 - 8 * q^43 - 8 * q^45 - 7 * q^47 - 11 * q^49 - 4 * q^51 + 3 * q^53 + 5 * q^55 + q^57 + 5 * q^59 + 13 * q^61 - 3 * q^63 - 2 * q^65 + 18 * q^67 - 5 * q^69 + 5 * q^71 - 15 * q^73 - 2 * q^75 + 29 * q^77 - 50 * q^79 - 2 * q^81 + 13 * q^83 + 4 * q^85 - 30 * q^87 + 32 * q^89 - 15 * q^91 - 9 * q^93 - 6 * q^95 + q^97 + 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/660\mathbb{Z}\right)^\times$.

$n$	$221$	$331$	$397$	$541$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$		0			0
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	−1.12900	−	0.820265i	−0.426721	−	0.310031i	0.353615	−	0.935391i	$-0.384952\pi$
$7$	−1.12900	−	0.820265i	−0.426721	−	0.310031i	−0.780336	+	0.625360i	$0.784952\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−0.660531	+	3.25018i	−0.199158	+	0.979967i
$11$	−0.660531	+	3.25018i	−0.199158	+	0.979967i
$12$		0			0
$13$	−0.591770	+	1.82128i	−0.164127	+	0.505132i	−0.998971	−	0.0453552i	$-0.985558\pi$
$13$	−0.591770	+	1.82128i	−0.164127	+	0.505132i	0.834844	+	0.550487i	$0.185558\pi$
$14$		0			0
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$		0			0
$17$	1.46847	+	4.51948i	0.356156	+	1.09613i	0.955336	+	0.295521i	$0.0954931\pi$
$17$	1.46847	+	4.51948i	0.356156	+	1.09613i	−0.599181	+	0.800614i	$0.704507\pi$
$18$		0			0
$19$	0.439763	−	0.319507i	0.100889	−	0.0732999i	−0.536197	−	0.844093i	$-0.680140\pi$
$19$	0.439763	−	0.319507i	0.100889	−	0.0732999i	0.637086	+	0.770793i	$0.280140\pi$
$20$		0			0
$21$	1.39552			0.304527
$22$		0			0
$23$	−1.43100			−0.298384			−0.149192	−	0.988808i	$-0.547667\pi$
$23$	−1.43100			−0.298384			−0.149192	+	0.988808i	$0.547667\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	7.72730	+	5.61421i	1.43492	+	1.04253i	0.989073	+	0.147426i	$0.0470989\pi$
$29$	7.72730	+	5.61421i	1.43492	+	1.04253i	0.445851	+	0.895107i	$0.352901\pi$
$30$		0			0
$31$	−2.92597	+	9.00521i	−0.525520	+	1.61738i	0.237766	+	0.971323i	$0.423585\pi$
$31$	−2.92597	+	9.00521i	−0.525520	+	1.61738i	−0.763286	+	0.646061i	$0.776415\pi$
$32$		0			0
$33$	−1.37603	−	3.01770i	−0.239536	−	0.525315i
$34$		0			0
$35$	−0.431239	+	1.32722i	−0.0728927	+	0.224341i
$36$		0			0
$37$	0.517740	+	0.376160i	0.0851159	+	0.0618404i	0.629529	−	0.776977i	$-0.283248\pi$
$37$	0.517740	+	0.376160i	0.0851159	+	0.0618404i	−0.544413	+	0.838817i	$0.683248\pi$
$38$		0			0
$39$	−0.591770	−	1.82128i	−0.0947590	−	0.291638i
$40$		0			0
$41$	3.32959	−	2.41909i	0.519994	−	0.377798i	−0.296608	−	0.954999i	$-0.595855\pi$
$41$	3.32959	−	2.41909i	0.519994	−	0.377798i	0.816602	+	0.577202i	$0.195855\pi$
$42$		0			0
$43$	−7.84844			−1.19688			−0.598438	−	0.801169i	$-0.704212\pi$
$43$	−7.84844			−1.19688			−0.598438	+	0.801169i	$0.704212\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−9.43603	+	6.85567i	−1.37639	+	1.00000i	−0.379178	+	0.925324i	$0.623793\pi$
$47$	−9.43603	+	6.85567i	−1.37639	+	1.00000i	−0.997208	+	0.0746793i	$0.976207\pi$
$48$		0			0
$49$	−1.56132	−	4.80524i	−0.223045	−	0.686463i
$50$		0			0
$51$	−3.84450	−	2.79319i	−0.538337	−	0.391125i
$52$		0			0
$53$	−3.55538	+	10.9423i	−0.488369	+	1.50305i	0.338672	+	0.940904i	$0.390022\pi$
$53$	−3.55538	+	10.9423i	−0.488369	+	1.50305i	−0.827041	+	0.562141i	$0.809978\pi$
$54$		0			0
$55$	3.29522	−	0.376160i	0.444328	−	0.0507214i
$56$		0			0
$57$	−0.167975	+	0.516973i	−0.0222488	+	0.0684747i
$58$		0			0
$59$	6.48027	+	4.70819i	0.843659	+	0.612954i	0.923390	−	0.383862i	$-0.125406\pi$
$59$	6.48027	+	4.70819i	0.843659	+	0.612954i	−0.0797310	+	0.996816i	$0.525406\pi$
$60$		0			0
$61$	−1.85302	−	5.70301i	−0.237255	−	0.730196i	−0.996814	−	0.0797579i	$-0.974585\pi$
$61$	−1.85302	−	5.70301i	−0.237255	−	0.730196i	0.759559	−	0.650438i	$-0.225415\pi$
$62$		0			0
$63$	−1.12900	+	0.820265i	−0.142240	+	0.103344i
$64$		0			0
$65$	1.91501			0.237527
$66$		0			0
$67$	9.66707			1.18102			0.590510	−	0.807030i	$-0.298927\pi$
$67$	9.66707			1.18102			0.590510	+	0.807030i	$0.298927\pi$
$68$		0			0
$69$	1.15770	−	0.841120i	0.139371	−	0.101259i
$70$		0			0
$71$	0.332025	+	1.02187i	0.0394042	+	0.121274i	0.968824	−	0.247752i	$-0.0796917\pi$
$71$	0.332025	+	1.02187i	0.0394042	+	0.121274i	−0.929419	+	0.369025i	$0.879692\pi$
$72$		0			0
$73$	−8.28929	−	6.02252i	−0.970188	−	0.704883i	−0.0146934	−	0.999892i	$-0.504677\pi$
$73$	−8.28929	−	6.02252i	−0.970188	−	0.704883i	−0.955494	+	0.295009i	$0.904677\pi$
$74$		0			0
$75$	0.309017	−	0.951057i	0.0356822	−	0.109819i
$76$		0			0
$77$	3.41175	−	3.12764i	0.388805	−	0.356428i
$78$		0			0
$79$	−2.33688	+	7.19218i	−0.262920	+	0.809184i	0.729246	+	0.684252i	$0.239871\pi$
$79$	−2.33688	+	7.19218i	−0.262920	+	0.809184i	−0.992165	+	0.124932i	$0.960129\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−1.06349	−	3.27309i	−0.116734	−	0.359269i	0.875571	−	0.483089i	$-0.160485\pi$
$83$	−1.06349	−	3.27309i	−0.116734	−	0.359269i	−0.992305	+	0.123820i	$0.960485\pi$
$84$		0			0
$85$	3.84450	−	2.79319i	0.416994	−	0.302964i
$86$		0			0
$87$	−9.55147			−1.02403
$88$		0			0
$89$	11.0079			1.16683			0.583417	−	0.812173i	$-0.301715\pi$
$89$	11.0079			1.16683			0.583417	+	0.812173i	$0.301715\pi$
$90$		0			0
$91$	2.16204	−	1.57081i	0.226643	−	0.164666i
$92$		0			0
$93$	−2.92597	−	9.00521i	−0.303409	−	0.933797i
$94$		0			0
$95$	−0.439763	−	0.319507i	−0.0451187	−	0.0327807i
$96$		0			0
$97$	4.07271	−	12.5345i	0.413521	−	1.27269i	−0.500046	−	0.865999i	$-0.666684\pi$
$97$	4.07271	−	12.5345i	0.413521	−	1.27269i	0.913567	−	0.406688i	$-0.133316\pi$
$98$		0			0
$99$	2.88699	+	1.63256i	0.290154	+	0.164079i
$100$		0			0
$101$	−2.78793	+	8.58036i	−0.277409	+	0.853778i	0.711163	+	0.703028i	$0.248169\pi$
$101$	−2.78793	+	8.58036i	−0.277409	+	0.853778i	−0.988572	+	0.150750i	$0.951831\pi$
$102$		0			0
$103$	−3.24923	−	2.36070i	−0.320156	−	0.232607i	0.416086	−	0.909325i	$-0.363402\pi$
$103$	−3.24923	−	2.36070i	−0.320156	−	0.232607i	−0.736242	+	0.676718i	$0.763402\pi$
$104$		0			0
$105$	−0.431239	−	1.32722i	−0.0420846	−	0.129523i
$106$		0			0
$107$	7.65041	−	5.55835i	0.739593	−	0.537346i	−0.152991	−	0.988228i	$-0.548890\pi$
$107$	7.65041	−	5.55835i	0.739593	−	0.537346i	0.892584	+	0.450882i	$0.148890\pi$
$108$		0			0
$109$	18.8247			1.80308			0.901540	−	0.432697i	$-0.142438\pi$
$109$	18.8247			1.80308			0.901540	+	0.432697i	$0.142438\pi$
$110$		0			0
$111$	−0.639962			−0.0607425
$112$		0			0
$113$	−4.88630	+	3.55011i	−0.459665	+	0.333966i	−0.793400	−	0.608701i	$-0.791691\pi$
$113$	−4.88630	+	3.55011i	−0.459665	+	0.333966i	0.333735	+	0.942667i	$0.391691\pi$
$114$		0			0
$115$	0.442203	+	1.36096i	0.0412356	+	0.126910i
$116$		0			0
$117$	1.54927	+	1.12561i	0.143230	+	0.104063i
$118$		0			0
$119$	2.04927	−	6.30701i	0.187857	−	0.578163i
$120$		0			0
$121$	−10.1274	−	4.29369i	−0.920673	−	0.390336i
$122$		0			0
$123$	−1.27179	+	3.91416i	−0.114673	+	0.352928i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	−4.09436	−	12.6011i	−0.363316	−	1.11817i	−0.951029	−	0.309101i	$-0.899972\pi$
$127$	−4.09436	−	12.6011i	−0.363316	−	1.11817i	0.587714	−	0.809069i	$-0.300028\pi$
$128$		0			0
$129$	6.34953	−	4.61320i	0.559045	−	0.406170i
$130$		0			0
$131$	−0.385462			−0.0336780			−0.0168390	−	0.999858i	$-0.505360\pi$
$131$	−0.385462			−0.0336780			−0.0168390	+	0.999858i	$0.505360\pi$
$132$		0			0
$133$	−0.758572			−0.0657765
$134$		0			0
$135$	0.809017	−	0.587785i	0.0696291	−	0.0505885i
$136$		0			0
$137$	0.751220	+	2.31202i	0.0641810	+	0.197529i	0.978005	−	0.208582i	$-0.0668847\pi$
$137$	0.751220	+	2.31202i	0.0641810	+	0.197529i	−0.913824	+	0.406111i	$0.866885\pi$
$138$		0			0
$139$	−10.4161	−	7.56773i	−0.883481	−	0.641886i	0.0506891	−	0.998714i	$-0.483858\pi$
$139$	−10.4161	−	7.56773i	−0.883481	−	0.641886i	−0.934170	+	0.356828i	$0.883858\pi$
$140$		0			0
$141$	3.60424	−	11.0927i	0.303532	−	0.934175i
$142$		0			0
$143$	−5.52861	−	3.12637i	−0.462326	−	0.261440i
$144$		0			0
$145$	2.95157	−	9.08399i	0.245114	−	0.754384i
$146$		0			0
$147$	4.08758	+	2.96980i	0.337138	+	0.244945i
$148$		0			0
$149$	−5.22929	−	16.0941i	−0.428400	−	1.31848i	−0.899701	−	0.436508i	$-0.856215\pi$
$149$	−5.22929	−	16.0941i	−0.428400	−	1.31848i	0.471300	−	0.881973i	$-0.343785\pi$
$150$		0			0
$151$	1.35015	−	0.980945i	0.109874	−	0.0798281i	−0.531491	−	0.847064i	$-0.678368\pi$
$151$	1.35015	−	0.980945i	0.109874	−	0.0798281i	0.641365	+	0.767235i	$0.278368\pi$
$152$		0			0
$153$	4.75206			0.384181
$154$		0			0
$155$	9.46864			0.760539
$156$		0			0
$157$	5.62526	−	4.08699i	0.448945	−	0.326177i	−0.340234	−	0.940341i	$-0.610506\pi$
$157$	5.62526	−	4.08699i	0.448945	−	0.326177i	0.789179	+	0.614163i	$0.210506\pi$
$158$		0			0
$159$	−3.55538	−	10.9423i	−0.281960	−	0.867784i
$160$		0			0
$161$	1.61559	+	1.17380i	0.127327	+	0.0925082i
$162$		0			0
$163$	−3.62548	+	11.1581i	−0.283969	+	0.873968i	0.702736	+	0.711450i	$0.251961\pi$
$163$	−3.62548	+	11.1581i	−0.283969	+	0.873968i	−0.986706	+	0.162517i	$0.948039\pi$
$164$		0			0
$165$	−2.44479	+	2.24120i	−0.190327	+	0.174478i
$166$		0			0
$167$	−5.52466	+	17.0032i	−0.427511	+	1.31574i	0.473058	+	0.881032i	$0.343150\pi$
$167$	−5.52466	+	17.0032i	−0.427511	+	1.31574i	−0.900569	+	0.434713i	$0.856850\pi$
$168$		0			0
$169$	7.55035	+	5.48565i	0.580796	+	0.421973i
$170$		0			0
$171$	−0.167975	−	0.516973i	−0.0128453	−	0.0395339i
$172$		0			0
$173$	7.81443	−	5.67752i	0.594120	−	0.431654i	−0.249667	−	0.968332i	$-0.580321\pi$
$173$	7.81443	−	5.67752i	0.594120	−	0.431654i	0.843787	+	0.536678i	$0.180321\pi$
$174$		0			0
$175$	1.39552			0.105491
$176$		0			0
$177$	−8.01006			−0.602073
$178$		0			0
$179$	9.58168	−	6.96150i	0.716169	−	0.520327i	−0.168989	−	0.985618i	$-0.554050\pi$
$179$	9.58168	−	6.96150i	0.716169	−	0.520327i	0.885158	+	0.465291i	$0.154050\pi$
$180$		0			0
$181$	−0.932079	−	2.86864i	−0.0692809	−	0.213225i	0.910422	−	0.413682i	$-0.135757\pi$
$181$	−0.932079	−	2.86864i	−0.0692809	−	0.213225i	−0.979703	+	0.200457i	$0.935757\pi$
$182$		0			0
$183$	4.85127	+	3.52466i	0.358616	+	0.260550i
$184$		0			0
$185$	0.197759	−	0.608640i	0.0145395	−	0.0447481i
$186$		0			0
$187$	−15.6591	+	1.78754i	−1.14511	+	0.130718i
$188$		0			0
$189$	0.431239	−	1.32722i	0.0313680	−	0.0965408i
$190$		0			0
$191$	−0.491235	−	0.356903i	−0.0355445	−	0.0258246i	0.569871	−	0.821734i	$-0.306993\pi$
$191$	−0.491235	−	0.356903i	−0.0355445	−	0.0258246i	−0.605416	+	0.795909i	$0.706993\pi$
$192$		0			0
$193$	−0.614365	−	1.89082i	−0.0442230	−	0.136104i	0.926507	−	0.376277i	$-0.122796\pi$
$193$	−0.614365	−	1.89082i	−0.0442230	−	0.136104i	−0.970730	+	0.240173i	$0.922796\pi$
$194$		0			0
$195$	−1.54927	+	1.12561i	−0.110946	+	0.0806068i
$196$		0			0
$197$	−10.1402			−0.722462			−0.361231	−	0.932476i	$-0.617643\pi$
$197$	−10.1402			−0.722462			−0.361231	+	0.932476i	$0.617643\pi$
$198$		0			0
$199$	11.4830			0.814006			0.407003	−	0.913427i	$-0.366574\pi$
$199$	11.4830			0.814006			0.407003	+	0.913427i	$0.366574\pi$
$200$		0			0
$201$	−7.82082	+	5.68216i	−0.551638	+	0.400789i
$202$		0			0
$203$	−4.11897	−	12.6769i	−0.289095	−	0.889742i
$204$		0			0
$205$	−3.32959	−	2.41909i	−0.232548	−	0.168956i
$206$		0			0
$207$	−0.442203	+	1.36096i	−0.0307352	+	0.0945933i
$208$		0			0
$209$	0.747978	+	1.64036i	0.0517388	+	0.113466i
$210$		0			0
$211$	0.125891	−	0.387451i	0.00866666	−	0.0266732i	−0.946630	−	0.322323i	$-0.895536\pi$
$211$	0.125891	−	0.387451i	0.00866666	−	0.0266732i	0.955296	+	0.295650i	$0.0955362\pi$
$212$		0			0
$213$	−0.869254	−	0.631550i	−0.0595603	−	0.0432731i
$214$		0			0
$215$	2.42530	+	7.46431i	0.165404	+	0.509062i
$216$		0			0
$217$	10.6901	−	7.76679i	0.725690	−	0.527244i
$218$		0			0
$219$	10.2461			0.692369
$220$		0			0
$221$	−9.10023			−0.612147
$222$		0			0
$223$	−23.7856	+	17.2812i	−1.59280	+	1.15724i	−0.692993	+	0.720944i	$0.743708\pi$
$223$	−23.7856	+	17.2812i	−1.59280	+	1.15724i	−0.899806	+	0.436291i	$0.856292\pi$
$224$		0			0
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$		0			0
$227$	−2.26613	−	1.64644i	−0.150408	−	0.109278i	0.510036	−	0.860153i	$-0.329632\pi$
$227$	−2.26613	−	1.64644i	−0.150408	−	0.109278i	−0.660444	+	0.750875i	$0.729632\pi$
$228$		0			0
$229$	−4.71861	+	14.5224i	−0.311814	+	0.959666i	0.665232	+	0.746637i	$0.268333\pi$
$229$	−4.71861	+	14.5224i	−0.311814	+	0.959666i	−0.977046	+	0.213029i	$0.931667\pi$
$230$		0			0
$231$	−0.921783	+	4.53569i	−0.0606488	+	0.298427i
$232$		0			0
$233$	−2.20294	+	6.77994i	−0.144319	+	0.444169i	−0.996923	−	0.0783895i	$-0.975022\pi$
$233$	−2.20294	+	6.77994i	−0.144319	+	0.444169i	0.852604	+	0.522558i	$0.175022\pi$
$234$		0			0
$235$	9.43603	+	6.85567i	0.615538	+	0.447215i
$236$		0			0
$237$	−2.33688	−	7.19218i	−0.151797	−	0.467182i
$238$		0			0
$239$	9.24899	−	6.71979i	0.598267	−	0.434667i	−0.246996	−	0.969016i	$-0.579443\pi$
$239$	9.24899	−	6.71979i	0.598267	−	0.434667i	0.845263	+	0.534350i	$0.179443\pi$
$240$		0			0
$241$	−28.8264			−1.85687			−0.928435	−	0.371494i	$-0.878846\pi$
$241$	−28.8264			−1.85687			−0.928435	+	0.371494i	$0.878846\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−4.08758	+	2.96980i	−0.261146	+	0.189734i
$246$		0			0
$247$	0.321672	+	0.990006i	0.0204675	+	0.0629926i
$248$		0			0
$249$	2.78426	+	2.02288i	0.176445	+	0.128195i
$250$		0			0
$251$	0.591102	−	1.81922i	0.0373100	−	0.114828i	−0.930667	−	0.365868i	$-0.880772\pi$
$251$	0.591102	−	1.81922i	0.0373100	−	0.114828i	0.967977	+	0.251039i	$0.0807723\pi$
$252$		0			0
$253$	0.945218	−	4.65101i	0.0594254	−	0.292406i
$254$		0			0
$255$	−1.46847	+	4.51948i	−0.0919590	+	0.283021i
$256$		0			0
$257$	6.68938	+	4.86012i	0.417272	+	0.303166i	0.776539	−	0.630069i	$-0.216973\pi$
$257$	6.68938	+	4.86012i	0.417272	+	0.303166i	−0.359267	+	0.933235i	$0.616973\pi$
$258$		0			0
$259$	−0.275976	−	0.849368i	−0.0171483	−	0.0527772i
$260$		0			0
$261$	7.72730	−	5.61421i	0.478308	−	0.347511i
$262$		0			0
$263$	−0.344325			−0.0212320			−0.0106160	−	0.999944i	$-0.503379\pi$
$263$	−0.344325			−0.0212320			−0.0106160	+	0.999944i	$0.503379\pi$
$264$		0			0
$265$	11.5055			0.706774
$266$		0			0
$267$	−8.90557	+	6.47028i	−0.545012	+	0.395975i
$268$		0			0
$269$	4.26218	+	13.1177i	0.259870	+	0.799797i	0.992831	+	0.119527i	$0.0381377\pi$
$269$	4.26218	+	13.1177i	0.259870	+	0.799797i	−0.732961	+	0.680271i	$0.761862\pi$
$270$		0			0
$271$	−0.297213	−	0.215938i	−0.0180544	−	0.0131173i	0.578721	−	0.815525i	$-0.303552\pi$
$271$	−0.297213	−	0.215938i	−0.0180544	−	0.0131173i	−0.596776	+	0.802408i	$0.703552\pi$
$272$		0			0
$273$	−0.825825	+	2.54163i	−0.0499812	+	0.153826i
$274$		0			0
$275$	−1.37603	−	3.01770i	−0.0829777	−	0.181974i
$276$		0			0
$277$	2.19584	−	6.75810i	0.131935	−	0.406055i	−0.863166	−	0.504921i	$-0.831522\pi$
$277$	2.19584	−	6.75810i	0.131935	−	0.406055i	0.995101	+	0.0988663i	$0.0315216\pi$
$278$		0			0
$279$	7.66029	+	5.56553i	0.458610	+	0.333199i
$280$		0			0
$281$	−4.75271	−	14.6273i	−0.283523	−	0.872594i	−0.986837	−	0.161715i	$-0.948297\pi$
$281$	−4.75271	−	14.6273i	−0.283523	−	0.872594i	0.703314	−	0.710879i	$-0.251703\pi$
$282$		0			0
$283$	13.6235	−	9.89802i	0.809830	−	0.588376i	−0.103951	−	0.994582i	$-0.533149\pi$
$283$	13.6235	−	9.89802i	0.809830	−	0.588376i	0.913781	+	0.406206i	$0.133149\pi$
$284$		0			0
$285$	0.543577			0.0321987
$286$		0			0
$287$	−5.74339			−0.339021
$288$		0			0
$289$	−4.51599	+	3.28106i	−0.265647	+	0.193004i
$290$		0			0
$291$	4.07271	+	12.5345i	0.238746	+	0.734786i
$292$		0			0
$293$	18.2697	+	13.2737i	1.06733	+	0.775457i	0.975430	−	0.220311i	$-0.0707073\pi$
$293$	18.2697	+	13.2737i	1.06733	+	0.775457i	0.0918959	+	0.995769i	$0.470707\pi$
$294$		0			0
$295$	2.47524	−	7.61802i	0.144114	−	0.443538i
$296$		0			0
$297$	−3.29522	+	0.376160i	−0.191208	+	0.0218270i
$298$		0			0
$299$	0.846821	−	2.60625i	0.0489729	−	0.150723i
$300$		0			0
$301$	8.86088	+	6.43780i	0.510733	+	0.371069i
$302$		0			0
$303$	−2.78793	−	8.58036i	−0.160162	−	0.492929i
$304$		0			0
$305$	−4.85127	+	3.52466i	−0.277783	+	0.201821i
$306$		0			0
$307$	20.5602			1.17343			0.586717	−	0.809792i	$-0.300420\pi$
$307$	20.5602			1.17343			0.586717	+	0.809792i	$0.300420\pi$
$308$		0			0
$309$	4.01627			0.228478
$310$		0			0
$311$	−2.91393	+	2.11709i	−0.165234	+	0.120049i	−0.667329	−	0.744763i	$-0.732563\pi$
$311$	−2.91393	+	2.11709i	−0.165234	+	0.120049i	0.502096	+	0.864812i	$0.332563\pi$
$312$		0			0
$313$	6.04375	+	18.6007i	0.341613	+	1.05138i	0.963372	+	0.268168i	$0.0864182\pi$
$313$	6.04375	+	18.6007i	0.341613	+	1.05138i	−0.621759	+	0.783208i	$0.713582\pi$
$314$		0			0
$315$	1.12900	+	0.820265i	0.0636118	+	0.0462167i
$316$		0			0
$317$	−4.19627	+	12.9148i	−0.235686	+	0.725366i	0.761344	+	0.648348i	$0.224540\pi$
$317$	−4.19627	+	12.9148i	−0.235686	+	0.725366i	−0.997030	+	0.0770180i	$0.975460\pi$
$318$		0			0
$319$	−23.3514	+	21.4068i	−1.30742	+	1.19855i
$320$		0			0
$321$	−2.92220	+	8.99359i	−0.163101	+	0.501973i
$322$		0			0
$323$	2.08978	+	1.51831i	0.116279	+	0.0844813i
$324$		0			0
$325$	−0.591770	−	1.82128i	−0.0328255	−	0.101026i
$326$		0			0
$327$	−15.2295	+	11.0649i	−0.842193	+	0.611889i
$328$		0			0
$329$	16.2767			0.897365
$330$		0			0
$331$	28.4887			1.56588			0.782940	−	0.622097i	$-0.213719\pi$
$331$	28.4887			1.56588			0.782940	+	0.622097i	$0.213719\pi$
$332$		0			0
$333$	0.517740	−	0.376160i	0.0283720	−	0.0206135i
$334$		0			0
$335$	−2.98729	−	9.19393i	−0.163213	−	0.502318i
$336$		0			0
$337$	9.80070	+	7.12063i	0.533878	+	0.387885i	0.821806	−	0.569767i	$-0.192966\pi$
$337$	9.80070	+	7.12063i	0.533878	+	0.387885i	−0.287928	+	0.957652i	$0.592966\pi$
$338$		0			0
$339$	1.86640	−	5.74419i	0.101369	−	0.311982i
$340$		0			0
$341$	−27.3359	−	15.4582i	−1.48032	−	0.837106i
$342$		0			0
$343$	−5.19752	+	15.9963i	−0.280640	+	0.863720i
$344$		0			0
$345$	−1.15770	−	0.841120i	−0.0623286	−	0.0452844i
$346$		0			0
$347$	−6.08950	−	18.7416i	−0.326902	−	1.00610i	−0.970575	−	0.240799i	$-0.922590\pi$
$347$	−6.08950	−	18.7416i	−0.326902	−	1.00610i	0.643673	−	0.765300i	$-0.277410\pi$
$348$		0			0
$349$	−11.7532	+	8.53918i	−0.629133	+	0.457092i	−0.856100	−	0.516810i	$-0.827119\pi$
$349$	−11.7532	+	8.53918i	−0.629133	+	0.457092i	0.226967	+	0.973903i	$0.427119\pi$
$350$		0			0
$351$	−1.91501			−0.102215
$352$		0			0
$353$	−28.0107			−1.49086			−0.745429	−	0.666584i	$-0.767756\pi$
$353$	−28.0107			−1.49086			−0.745429	+	0.666584i	$0.767756\pi$
$354$		0			0
$355$	0.869254	−	0.631550i	0.0461352	−	0.0335192i
$356$		0			0
$357$	2.04927	+	6.30701i	0.108459	+	0.333803i
$358$		0			0
$359$	−24.4377	−	17.7550i	−1.28977	−	0.937075i	−0.289972	−	0.957035i	$-0.593646\pi$
$359$	−24.4377	−	17.7550i	−1.28977	−	0.937075i	−0.999801	+	0.0199603i	$0.993646\pi$
$360$		0			0
$361$	−5.78002	+	17.7891i	−0.304211	+	0.936266i
$362$		0			0
$363$	10.7170	−	2.47906i	0.562497	−	0.130117i
$364$		0			0
$365$	−3.16623	+	9.74464i	−0.165728	+	0.510058i
$366$		0			0
$367$	−0.800944	−	0.581920i	−0.0418089	−	0.0303760i	0.566685	−	0.823935i	$-0.308226\pi$
$367$	−0.800944	−	0.581920i	−0.0418089	−	0.0303760i	−0.608493	+	0.793559i	$0.708226\pi$
$368$		0			0
$369$	−1.27179	−	3.91416i	−0.0662067	−	0.203763i
$370$		0			0
$371$	12.9896	−	9.43752i	0.674388	−	0.489972i
$372$		0			0
$373$	11.5466			0.597860			0.298930	−	0.954275i	$-0.403370\pi$
$373$	11.5466			0.597860			0.298930	+	0.954275i	$0.403370\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−14.7978	+	10.7513i	−0.762127	+	0.553718i
$378$		0			0
$379$	5.72849	+	17.6305i	0.294253	+	0.905617i	0.983471	+	0.181063i	$0.0579540\pi$
$379$	5.72849	+	17.6305i	0.294253	+	0.905617i	−0.689219	+	0.724553i	$0.742046\pi$
$380$		0			0
$381$	10.7192	+	7.78793i	0.549160	+	0.398988i
$382$		0			0
$383$	1.34559	−	4.14131i	0.0687566	−	0.211611i	−0.910774	−	0.412904i	$-0.864514\pi$
$383$	1.34559	−	4.14131i	0.0687566	−	0.211611i	0.979531	+	0.201293i	$0.0645144\pi$
$384$		0			0
$385$	−4.02885	−	2.27827i	−0.205329	−	0.116112i
$386$		0			0
$387$	−2.42530	+	7.46431i	−0.123285	+	0.379432i
$388$		0			0
$389$	20.7009	+	15.0401i	1.04958	+	0.762563i	0.972132	−	0.234434i	$-0.0753236\pi$
$389$	20.7009	+	15.0401i	1.04958	+	0.762563i	0.0774456	+	0.996997i	$0.475324\pi$
$390$		0			0
$391$	−2.10137	−	6.46737i	−0.106271	−	0.327069i
$392$		0			0
$393$	0.311846	−	0.226569i	0.0157305	−	0.0114289i
$394$		0			0
$395$	7.56231			0.380501
$396$		0			0
$397$	22.4876			1.12862			0.564311	−	0.825562i	$-0.309142\pi$
$397$	22.4876			1.12862			0.564311	+	0.825562i	$0.309142\pi$
$398$		0			0
$399$	0.613698	−	0.445877i	0.0307233	−	0.0223218i
$400$		0			0
$401$	4.43365	+	13.6454i	0.221406	+	0.681418i	0.998637	+	0.0522020i	$0.0166240\pi$
$401$	4.43365	+	13.6454i	0.221406	+	0.681418i	−0.777230	+	0.629216i	$0.783376\pi$
$402$		0			0
$403$	−14.6695	−	10.6580i	−0.730740	−	0.530914i
$404$		0			0
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$		0			0
$407$	−1.56457	+	1.43429i	−0.0775530	+	0.0710949i
$408$		0			0
$409$	−1.82268	+	5.60962i	−0.0901255	+	0.277378i	−0.985953	−	0.167025i	$-0.946584\pi$
$409$	−1.82268	+	5.60962i	−0.0901255	+	0.277378i	0.895827	+	0.444403i	$0.146584\pi$
$410$		0			0
$411$	−1.96672	−	1.42891i	−0.0970111	−	0.0704827i
$412$		0			0
$413$	−3.45425	−	10.6311i	−0.169972	−	0.523121i
$414$		0			0
$415$	−2.78426	+	2.02288i	−0.136674	+	0.0992994i
$416$		0			0
$417$	12.8750			0.630491
$418$		0			0
$419$	−12.4887			−0.610113			−0.305057	−	0.952334i	$-0.598675\pi$
$419$	−12.4887			−0.610113			−0.305057	+	0.952334i	$0.598675\pi$
$420$		0			0
$421$	−7.06988	+	5.13657i	−0.344565	+	0.250341i	−0.746585	−	0.665290i	$-0.768308\pi$
$421$	−7.06988	+	5.13657i	−0.344565	+	0.250341i	0.402020	+	0.915631i	$0.368308\pi$
$422$		0			0
$423$	3.60424	+	11.0927i	0.175244	+	0.539346i
$424$		0			0
$425$	−3.84450	−	2.79319i	−0.186486	−	0.135490i
$426$		0			0
$427$	−2.58593	+	7.95866i	−0.125142	+	0.385147i
$428$		0			0
$429$	6.31038	−	0.720349i	0.304668	−	0.0347788i
$430$		0			0
$431$	1.25893	−	3.87458i	0.0606404	−	0.186632i	−0.916147	−	0.400842i	$-0.868718\pi$
$431$	1.25893	−	3.87458i	0.0606404	−	0.186632i	0.976788	+	0.214210i	$0.0687177\pi$
$432$		0			0
$433$	−4.05979	−	2.94961i	−0.195101	−	0.141749i	0.485946	−	0.873989i	$-0.338475\pi$
$433$	−4.05979	−	2.94961i	−0.195101	−	0.141749i	−0.681047	+	0.732240i	$0.738475\pi$
$434$		0			0
$435$	2.95157	+	9.08399i	0.141517	+	0.435544i
$436$		0			0
$437$	−0.629300	+	0.457214i	−0.0301035	+	0.0218715i
$438$		0			0
$439$	−36.6472			−1.74908			−0.874539	−	0.484956i	$-0.838836\pi$
$439$	−36.6472			−1.74908			−0.874539	+	0.484956i	$0.838836\pi$
$440$		0			0
$441$	−5.05253			−0.240597
$442$		0			0
$443$	−4.92876	+	3.58095i	−0.234172	+	0.170136i	−0.698683	−	0.715431i	$-0.746230\pi$
$443$	−4.92876	+	3.58095i	−0.234172	+	0.170136i	0.464511	+	0.885568i	$0.346230\pi$
$444$		0			0
$445$	−3.40163	−	10.4691i	−0.161253	−	0.496284i
$446$		0			0
$447$	13.6905	+	9.94670i	0.647537	+	0.470463i
$448$		0			0
$449$	8.10724	−	24.9515i	0.382604	−	1.17754i	−0.555599	−	0.831451i	$-0.687511\pi$
$449$	8.10724	−	24.9515i	0.382604	−	1.17754i	0.938203	−	0.346085i	$-0.112489\pi$
$450$		0			0
$451$	5.66318	+	12.4196i	0.266669	+	0.584818i
$452$		0			0
$453$	−0.515713	+	1.58720i	−0.0242303	+	0.0745732i
$454$		0			0
$455$	−2.16204	−	1.57081i	−0.101358	−	0.0736408i
$456$		0			0
$457$	4.66530	+	14.3583i	0.218234	+	0.671654i	0.998908	+	0.0467164i	$0.0148757\pi$
$457$	4.66530	+	14.3583i	0.218234	+	0.671654i	−0.780674	+	0.624938i	$0.785124\pi$
$458$		0			0
$459$	−3.84450	+	2.79319i	−0.179446	+	0.130375i
$460$		0			0
$461$	−7.31588			−0.340735			−0.170367	−	0.985381i	$-0.554495\pi$
$461$	−7.31588			−0.340735			−0.170367	+	0.985381i	$0.554495\pi$
$462$		0			0
$463$	21.4870			0.998587			0.499293	−	0.866433i	$-0.333593\pi$
$463$	21.4870			0.998587			0.499293	+	0.866433i	$0.333593\pi$
$464$		0			0
$465$	−7.66029	+	5.56553i	−0.355237	+	0.258095i
$466$		0			0
$467$	−8.91829	−	27.4477i	−0.412689	−	1.27013i	−0.914302	−	0.405034i	$-0.867260\pi$
$467$	−8.91829	−	27.4477i	−0.412689	−	1.27013i	0.501613	−	0.865092i	$-0.332740\pi$
$468$		0			0
$469$	−10.9141	−	7.92956i	−0.503966	−	0.366153i
$470$		0			0
$471$	−2.14866	+	6.61289i	−0.0990050	+	0.304706i
$472$		0			0
$473$	5.18414	−	25.5089i	0.238367	−	1.17290i
$474$		0			0
$475$	−0.167975	+	0.516973i	−0.00770720	+	0.0237203i
$476$		0			0
$477$	9.30811	+	6.76274i	0.426189	+	0.309644i
$478$		0			0
$479$	−10.5727	−	32.5395i	−0.483080	−	1.48677i	−0.834742	−	0.550641i	$-0.814383\pi$
$479$	−10.5727	−	32.5395i	−0.483080	−	1.48677i	0.351662	−	0.936127i	$-0.385617\pi$
$480$		0			0
$481$	−0.991476	+	0.720349i	−0.0452074	+	0.0328451i
$482$		0			0
$483$	−1.99698			−0.0908659
$484$		0			0
$485$	−13.1796			−0.598453
$486$		0			0
$487$	26.9647	−	19.5910i	1.22189	−	0.887752i	0.225630	−	0.974213i	$-0.427556\pi$
$487$	26.9647	−	19.5910i	1.22189	−	0.887752i	0.996255	+	0.0864612i	$0.0275559\pi$
$488$		0			0
$489$	−3.62548	−	11.1581i	−0.163950	−	0.504586i
$490$		0			0
$491$	31.5917	+	22.9527i	1.42571	+	1.03584i	0.990795	+	0.135370i	$0.0432223\pi$
$491$	31.5917	+	22.9527i	1.42571	+	1.03584i	0.434917	+	0.900471i	$0.356778\pi$
$492$		0			0
$493$	−14.0260	+	43.1677i	−0.631700	+	1.94417i
$494$		0			0
$495$	0.660531	−	3.25018i	0.0296886	−	0.146085i
$496$		0			0
$497$	0.463348	−	1.42604i	0.0207840	−	0.0639665i
$498$		0			0
$499$	16.7584	+	12.1757i	0.750208	+	0.545058i	0.895891	−	0.444273i	$-0.146538\pi$
$499$	16.7584	+	12.1757i	0.750208	+	0.545058i	−0.145683	+	0.989331i	$0.546538\pi$
$500$		0			0
$501$	−5.52466	−	17.0032i	−0.246824	−	0.759646i
$502$		0			0
$503$	27.2658	−	19.8098i	1.21572	−	0.883273i	0.219984	−	0.975504i	$-0.429400\pi$
$503$	27.2658	−	19.8098i	1.21572	−	0.883273i	0.995738	+	0.0922304i	$0.0293996\pi$
$504$		0			0
$505$	9.02193			0.401471
$506$		0			0
$507$	−9.33275			−0.414482
$508$		0			0
$509$	−32.4760	+	23.5952i	−1.43947	+	1.04584i	−0.451322	+	0.892361i	$0.649047\pi$
$509$	−32.4760	+	23.5952i	−1.43947	+	1.04584i	−0.988152	+	0.153478i	$0.950953\pi$
$510$		0			0
$511$	4.41853	+	13.5988i	0.195464	+	0.601577i
$512$		0			0
$513$	0.439763	+	0.319507i	0.0194160	+	0.0141066i
$514$		0			0
$515$	−1.24110	+	3.81970i	−0.0546892	+	0.168316i
$516$		0			0
$517$	−16.0494	−	35.1972i	−0.705853	−	1.54797i
$518$		0			0
$519$	−2.98485	+	9.18642i	−0.131020	+	0.403239i
$520$		0			0
$521$	3.15742	+	2.29400i	0.138329	+	0.100502i	0.654798	−	0.755804i	$-0.272754\pi$
$521$	3.15742	+	2.29400i	0.138329	+	0.100502i	−0.516469	+	0.856306i	$0.672754\pi$
$522$		0			0
$523$	7.63051	+	23.4843i	0.333659	+	1.02690i	0.967379	+	0.253334i	$0.0815270\pi$
$523$	7.63051	+	23.4843i	0.333659	+	1.02690i	−0.633720	+	0.773562i	$0.718473\pi$
$524$		0			0
$525$	−1.12900	+	0.820265i	−0.0492735	+	0.0357993i
$526$		0			0
$527$	−44.9955			−1.96004
$528$		0			0
$529$	−20.9522			−0.910967
$530$		0			0
$531$	6.48027	−	4.70819i	0.281220	−	0.204318i
$532$		0			0
$533$	2.43548	+	7.49565i	0.105492	+	0.324673i
$534$		0			0
$535$	−7.65041	−	5.55835i	−0.330756	−	0.240308i
$536$		0			0
$537$	−3.65988	+	11.2639i	−0.157935	+	0.486075i
$538$		0			0
$539$	16.6492	−	1.90056i	0.717133	−	0.0818629i
$540$		0			0
$541$	12.6897	−	39.0548i	0.545571	−	1.67910i	−0.174057	−	0.984736i	$-0.555688\pi$
$541$	12.6897	−	39.0548i	0.545571	−	1.67910i	0.719628	−	0.694360i	$-0.244312\pi$
$542$		0			0
$543$	2.44021	+	1.77292i	0.104720	+	0.0760833i
$544$		0			0
$545$	−5.81715	−	17.9034i	−0.249179	−	0.766895i
$546$		0			0
$547$	24.3370	−	17.6819i	1.04058	−	0.756023i	0.0701781	−	0.997534i	$-0.477643\pi$
$547$	24.3370	−	17.6819i	1.04058	−	0.756023i	0.970398	+	0.241512i	$0.0776432\pi$
$548$		0			0
$549$	−5.99650			−0.255925
$550$		0			0
$551$	5.19196			0.221185
$552$		0			0
$553$	8.53783	−	6.20310i	0.363065	−	0.263782i
$554$		0			0
$555$	0.197759	+	0.608640i	0.00839441	+	0.0258353i
$556$		0			0
$557$	9.82015	+	7.13476i	0.416093	+	0.302309i	0.776064	−	0.630654i	$-0.217213\pi$
$557$	9.82015	+	7.13476i	0.416093	+	0.302309i	−0.359971	+	0.932964i	$0.617213\pi$
$558$		0			0
$559$	4.64447	−	14.2942i	0.196440	−	0.604581i
$560$		0			0
$561$	11.6178	−	10.6503i	0.490504	−	0.449658i
$562$		0			0
$563$	6.29173	−	19.3639i	0.265165	−	0.816093i	−0.726491	−	0.687176i	$-0.758850\pi$
$563$	6.29173	−	19.3639i	0.265165	−	0.816093i	0.991655	−	0.128917i	$-0.0411500\pi$
$564$		0			0
$565$	4.88630	+	3.55011i	0.205568	+	0.149354i
$566$		0			0
$567$	0.431239	+	1.32722i	0.0181103	+	0.0557379i
$568$		0			0
$569$	−25.9035	+	18.8200i	−1.08593	+	0.788976i	−0.978708	−	0.205259i	$-0.934196\pi$
$569$	−25.9035	+	18.8200i	−1.08593	+	0.788976i	−0.107224	+	0.994235i	$0.534196\pi$
$570$		0			0
$571$	27.1436			1.13593			0.567963	−	0.823054i	$-0.307732\pi$
$571$	27.1436			1.13593			0.567963	+	0.823054i	$0.307732\pi$
$572$		0			0
$573$	0.607200			0.0253662
$574$		0			0
$575$	1.15770	−	0.841120i	0.0482795	−	0.0350771i
$576$		0			0
$577$	4.45657	+	13.7159i	0.185529	+	0.571001i	0.999957	−	0.00926412i	$-0.00294890\pi$
$577$	4.45657	+	13.7159i	0.185529	+	0.571001i	−0.814428	+	0.580265i	$0.802949\pi$
$578$		0			0
$579$	1.60843	+	1.16859i	0.0668440	+	0.0485650i
$580$		0			0
$581$	−1.48412	+	4.56766i	−0.0615718	+	0.189499i
$582$		0			0
$583$	−33.2162	−	18.7834i	−1.37567	−	0.777929i
$584$		0			0
$585$	0.591770	−	1.82128i	0.0244667	−	0.0753006i
$586$		0			0
$587$	1.35151	+	0.981932i	0.0557829	+	0.0405287i	0.615327	−	0.788272i	$-0.289024\pi$
$587$	1.35151	+	0.981932i	0.0557829	+	0.0405287i	−0.559544	+	0.828800i	$0.689024\pi$
$588$		0			0
$589$	1.59049	+	4.89503i	0.0655350	+	0.201696i
$590$		0			0
$591$	8.20363	−	5.96028i	0.337452	−	0.245173i
$592$		0			0
$593$	27.8693			1.14446			0.572228	−	0.820094i	$-0.306079\pi$
$593$	27.8693			1.14446			0.572228	+	0.820094i	$0.306079\pi$
$594$		0			0
$595$	−6.63159			−0.271869
$596$		0			0
$597$	−9.28992	+	6.74952i	−0.380211	+	0.276239i
$598$		0			0
$599$	−8.27079	−	25.4549i	−0.337935	−	1.04006i	−0.965258	−	0.261298i	$-0.915849\pi$
$599$	−8.27079	−	25.4549i	−0.337935	−	1.04006i	0.627323	−	0.778759i	$-0.284151\pi$
$600$		0			0
$601$	−21.5788	−	15.6779i	−0.880217	−	0.639515i	0.0530918	−	0.998590i	$-0.483092\pi$
$601$	−21.5788	−	15.6779i	−0.880217	−	0.639515i	−0.933309	+	0.359074i	$0.883092\pi$
$602$		0			0
$603$	2.98729	−	9.19393i	0.121652	−	0.374406i
$604$		0			0
$605$	−0.954007	+	10.9586i	−0.0387859	+	0.445529i
$606$		0			0
$607$	10.0670	−	30.9831i	0.408608	−	1.25757i	−0.509237	−	0.860627i	$-0.670072\pi$
$607$	10.0670	−	30.9831i	0.408608	−	1.25757i	0.917845	−	0.396940i	$-0.129928\pi$
$608$		0			0
$609$	10.7836	+	7.83474i	0.436973	+	0.317480i
$610$		0			0
$611$	−6.90215	−	21.2426i	−0.279231	−	0.859384i
$612$		0			0
$613$	24.6158	−	17.8844i	0.994223	−	0.722345i	0.0333812	−	0.999443i	$-0.489372\pi$
$613$	24.6158	−	17.8844i	0.994223	−	0.722345i	0.960842	+	0.277097i	$0.0893725\pi$
$614$		0			0
$615$	4.11559			0.165957
$616$		0			0
$617$	21.7638			0.876177			0.438089	−	0.898932i	$-0.355656\pi$
$617$	21.7638			0.876177			0.438089	+	0.898932i	$0.355656\pi$
$618$		0			0
$619$	−27.5685	+	20.0297i	−1.10807	+	0.805061i	−0.982359	−	0.187006i	$-0.940122\pi$
$619$	−27.5685	+	20.0297i	−1.10807	+	0.805061i	−0.125712	+	0.992067i	$0.540122\pi$
$620$		0			0
$621$	−0.442203	−	1.36096i	−0.0177450	−	0.0546135i
$622$		0			0
$623$	−12.4279	−	9.02939i	−0.497913	−	0.361755i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	−1.56930	−	0.887425i	−0.0626720	−	0.0354403i
$628$		0			0
$629$	−0.939763	+	2.89229i	−0.0374708	+	0.115323i
$630$		0			0
$631$	26.1837	+	19.0236i	1.04236	+	0.757317i	0.970744	−	0.240115i	$-0.0771853\pi$
$631$	26.1837	+	19.0236i	1.04236	+	0.757317i	0.0716131	+	0.997432i	$0.477185\pi$
$632$		0			0
$633$	0.125891	+	0.387451i	0.00500370	+	0.0153998i
$634$		0			0
$635$	−10.7192	+	7.78793i	−0.425377	+	0.309055i
$636$		0			0
$637$	9.67563			0.383362
$638$		0			0
$639$	1.07446			0.0425049
$640$		0			0
$641$	27.7945	−	20.1939i	1.09782	−	0.797611i	0.117115	−	0.993118i	$-0.462635\pi$
$641$	27.7945	−	20.1939i	1.09782	−	0.797611i	0.980702	+	0.195507i	$0.0626352\pi$
$642$		0			0
$643$	−9.82594	−	30.2411i	−0.387497	−	1.19259i	−0.934652	−	0.355563i	$-0.884289\pi$
$643$	−9.82594	−	30.2411i	−0.387497	−	1.19259i	0.547155	−	0.837031i	$-0.315711\pi$
$644$		0			0
$645$	−6.34953	−	4.61320i	−0.250012	−	0.181645i
$646$		0			0
$647$	9.70223	−	29.8604i	0.381434	−	1.17393i	−0.557601	−	0.830109i	$-0.688278\pi$
$647$	9.70223	−	29.8604i	0.381434	−	1.17393i	0.939034	−	0.343823i	$-0.111722\pi$
$648$		0			0
$649$	−19.5829	+	17.9522i	−0.768697	+	0.704684i
$650$		0			0
$651$	−4.08325	+	12.5669i	−0.160035	+	0.492537i
$652$		0			0
$653$	−19.4155	−	14.1062i	−0.759786	−	0.552017i	0.139059	−	0.990284i	$-0.455592\pi$
$653$	−19.4155	−	14.1062i	−0.759786	−	0.552017i	−0.898845	+	0.438268i	$0.855592\pi$
$654$		0			0
$655$	0.119114	+	0.366597i	0.00465419	+	0.0143241i
$656$		0			0
$657$	−8.28929	+	6.02252i	−0.323396	+	0.234961i
$658$		0			0
$659$	44.0862			1.71735			0.858677	−	0.512517i	$-0.171287\pi$
$659$	44.0862			1.71735			0.858677	+	0.512517i	$0.171287\pi$
$660$		0			0
$661$	−36.0143			−1.40079			−0.700396	−	0.713754i	$-0.746993\pi$
$661$	−36.0143			−1.40079			−0.700396	+	0.713754i	$0.746993\pi$
$662$		0			0
$663$	7.36224	−	5.34898i	0.285926	−	0.207737i
$664$		0			0
$665$	0.234412	+	0.721445i	0.00909009	+	0.0279764i
$666$		0			0
$667$	−11.0578	−	8.03393i	−0.428158	−	0.311075i
$668$		0			0
$669$	9.08527	−	27.9616i	0.351257	−	1.08106i
$670$		0			0
$671$	19.7598	−	2.25565i	0.762820	−	0.0870782i
$672$		0			0
$673$	13.6013	−	41.8605i	0.524292	−	1.61360i	−0.241420	−	0.970421i	$-0.577613\pi$
$673$	13.6013	−	41.8605i	0.524292	−	1.61360i	0.765712	−	0.643184i	$-0.222387\pi$
$674$		0			0
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$		0			0
$677$	−2.15811	−	6.64197i	−0.0829427	−	0.255272i	0.900982	−	0.433857i	$-0.142848\pi$
$677$	−2.15811	−	6.64197i	−0.0829427	−	0.255272i	−0.983924	+	0.178586i	$0.942848\pi$
$678$		0			0
$679$	−14.8797	+	10.8107i	−0.571030	+	0.414878i
$680$		0			0
$681$	2.80109			0.107338
$682$		0			0
$683$	37.2317			1.42463			0.712315	−	0.701859i	$-0.247647\pi$
$683$	37.2317			1.42463			0.712315	+	0.701859i	$0.247647\pi$
$684$		0			0
$685$	1.96672	−	1.42891i	0.0751445	−	0.0545957i
$686$		0			0
$687$	−4.71861	−	14.5224i	−0.180026	−	0.554063i
$688$		0			0
$689$	−17.8251	−	12.9507i	−0.679082	−	0.493382i
$690$		0			0
$691$	−2.88019	+	8.86433i	−0.109568	+	0.337215i	−0.990775	−	0.135515i	$-0.956731\pi$
$691$	−2.88019	+	8.86433i	−0.109568	+	0.337215i	0.881208	+	0.472729i	$0.156731\pi$
$692$		0			0
$693$	−1.92027	−	4.21126i	−0.0729452	−	0.159973i
$694$		0			0
$695$	−3.97859	+	12.2448i	−0.150917	+	0.464473i
$696$		0			0
$697$	15.8224	+	11.4956i	0.599316	+	0.435428i
$698$		0			0
$699$	−2.20294	−	6.77994i	−0.0833227	−	0.256441i
$700$		0			0
$701$	−6.38173	+	4.63660i	−0.241034	+	0.175122i	−0.701744	−	0.712429i	$-0.747595\pi$
$701$	−6.38173	+	4.63660i	−0.241034	+	0.175122i	0.460710	+	0.887551i	$0.347595\pi$
$702$		0			0
$703$	0.347869			0.0131201
$704$		0			0
$705$	−11.6636			−0.439275
$706$		0			0
$707$	10.1857	−	7.40037i	0.383074	−	0.278320i
$708$		0			0
$709$	−5.14449	−	15.8331i	−0.193205	−	0.594624i	−0.999993	−	0.00378295i	$-0.998796\pi$
$709$	−5.14449	−	15.8331i	−0.193205	−	0.594624i	0.806788	−	0.590842i	$-0.201204\pi$
$710$		0			0
$711$	6.11803	+	4.44501i	0.229444	+	0.166701i
$712$		0			0
$713$	4.18706	−	12.8864i	0.156807	−	0.482601i
$714$		0			0
$715$	−1.26492	+	6.22412i	−0.0473053	+	0.232769i
$716$		0			0
$717$	−3.53280	+	10.8728i	−0.131935	+	0.406054i
$718$		0			0
$719$	−7.34648	−	5.33753i	−0.273977	−	0.199056i	0.442309	−	0.896863i	$-0.354160\pi$
$719$	−7.34648	−	5.33753i	−0.273977	−	0.199056i	−0.716286	+	0.697807i	$0.754160\pi$
$720$		0			0
$721$	1.73197	+	5.33046i	0.0645020	+	0.198517i
$722$		0			0
$723$	23.3210	−	16.9437i	0.867318	−	0.630144i
$724$		0			0
$725$	−9.55147			−0.354733
$726$		0			0
$727$	−2.09806			−0.0778129			−0.0389065	−	0.999243i	$-0.512387\pi$
$727$	−2.09806			−0.0778129			−0.0389065	+	0.999243i	$0.512387\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−11.5252	−	35.4709i	−0.426274	−	1.31194i
$732$		0			0
$733$	25.3733	+	18.4348i	0.937186	+	0.680905i	0.947742	−	0.319039i	$-0.103360\pi$
$733$	25.3733	+	18.4348i	0.937186	+	0.680905i	−0.0105558	+	0.999944i	$0.503360\pi$
$734$		0			0
$735$	1.56132	−	4.80524i	0.0575901	−	0.177244i
$736$		0			0
$737$	−6.38539	+	31.4197i	−0.235209	+	1.15736i
$738$		0			0
$739$	−0.703653	+	2.16562i	−0.0258843	+	0.0796637i	−0.963164	−	0.268914i	$-0.913335\pi$
$739$	−0.703653	+	2.16562i	−0.0258843	+	0.0796637i	0.937280	+	0.348578i	$0.113335\pi$
$740$		0			0
$741$	−0.842149	−	0.611857i	−0.0309371	−	0.0224771i
$742$		0			0
$743$	11.8208	+	36.3808i	0.433664	+	1.33468i	0.894449	+	0.447170i	$0.147568\pi$
$743$	11.8208	+	36.3808i	0.433664	+	1.33468i	−0.460785	+	0.887512i	$0.652432\pi$
$744$		0			0
$745$	−13.6905	+	9.94670i	−0.501580	+	0.364419i
$746$		0			0
$747$	−3.44154			−0.125919
$748$		0			0
$749$	−13.1966			−0.482194
$750$		0			0
$751$	5.49732	−	3.99404i	0.200600	−	0.145744i	−0.482950	−	0.875648i	$-0.660435\pi$
$751$	5.49732	−	3.99404i	0.200600	−	0.145744i	0.683551	+	0.729903i	$0.260435\pi$
$752$		0			0
$753$	0.591102	+	1.81922i	0.0215409	+	0.0662962i
$754$		0			0
$755$	−1.35015	−	0.980945i	−0.0491372	−	0.0357002i
$756$		0			0
$757$	−1.64882	+	5.07454i	−0.0599273	+	0.184437i	−0.976539	−	0.215342i	$-0.930913\pi$
$757$	−1.64882	+	5.07454i	−0.0599273	+	0.184437i	0.916611	+	0.399780i	$0.130913\pi$
$758$		0			0
$759$	1.96910	+	4.31833i	0.0714737	+	0.156745i
$760$		0			0
$761$	−0.522421	+	1.60785i	−0.0189378	+	0.0582844i	−0.960079	−	0.279730i	$-0.909755\pi$
$761$	−0.522421	+	1.60785i	−0.0189378	+	0.0582844i	0.941141	+	0.338014i	$0.109755\pi$
$762$		0			0
$763$	−21.2530	−	15.4412i	−0.769412	−	0.559011i
$764$		0			0
$765$	−1.46847	−	4.51948i	−0.0530925	−	0.163402i
$766$		0			0
$767$	−12.4098	+	9.01622i	−0.448091	+	0.325557i
$768$		0			0
$769$	2.91325			0.105054			0.0525272	−	0.998619i	$-0.483272\pi$
$769$	2.91325			0.105054			0.0525272	+	0.998619i	$0.483272\pi$
$770$		0			0
$771$	−8.26853			−0.297784
$772$		0			0
$773$	−40.2154	+	29.2182i	−1.44645	+	1.05091i	−0.459802	+	0.888021i	$0.652080\pi$
$773$	−40.2154	+	29.2182i	−1.44645	+	1.05091i	−0.986645	+	0.162884i	$0.947920\pi$
$774$		0			0
$775$	−2.92597	−	9.00521i	−0.105104	−	0.323477i
$776$		0			0
$777$	0.722516	+	0.524938i	0.0259201	+	0.0188321i
$778$		0			0
$779$	0.691315	−	2.12765i	0.0247689	−	0.0762310i
$780$		0			0
$781$	−3.54058	+	0.404168i	−0.126692	+	0.0144623i
$782$		0			0
$783$	−2.95157	+	9.08399i	−0.105480	+	0.324635i
$784$		0			0
$785$	−5.62526	−	4.08699i	−0.200774	−	0.145871i
$786$		0			0
$787$	−4.96321	−	15.2752i	−0.176919	−	0.544501i	0.822797	−	0.568336i	$-0.192413\pi$
$787$	−4.96321	−	15.2752i	−0.176919	−	0.544501i	−0.999716	+	0.0238344i	$0.992413\pi$
$788$		0			0
$789$	0.278565	−	0.202389i	0.00991717	−	0.00720524i
$790$		0			0
$791$	8.42865			0.299688
$792$		0			0
$793$	11.4833			0.407785
$794$		0			0
$795$	−9.30811	+	6.76274i	−0.330125	+	0.239850i
$796$		0			0
$797$	17.0949	+	52.6127i	0.605532	+	1.86364i	0.493091	+	0.869978i	$0.335867\pi$
$797$	17.0949	+	52.6127i	0.605532	+	1.86364i	0.112441	+	0.993658i	$0.464133\pi$
$798$		0			0
$799$	−44.8406	−	32.5786i	−1.58635	−	1.15255i
$800$		0			0
$801$	3.40163	−	10.4691i	0.120191	−	0.369909i
$802$		0			0
$803$	25.0496	−	22.9637i	0.883982	−	0.810370i
$804$		0			0
$805$	0.617102	−	1.89925i	0.0217500	−	0.0669396i
$806$		0			0
$807$	−11.1585	−	8.10716i	−0.392799	−	0.285385i
$808$		0			0
$809$	3.37192	+	10.3777i	0.118550	+	0.364861i	0.992671	−	0.120848i	$-0.0385614\pi$
$809$	3.37192	+	10.3777i	0.118550	+	0.364861i	−0.874121	+	0.485709i	$0.838561\pi$
$810$		0			0
$811$	44.8730	−	32.6022i	1.57571	−	1.14482i	0.654287	−	0.756247i	$-0.272969\pi$
$811$	44.8730	−	32.6022i	1.57571	−	1.14482i	0.921419	−	0.388570i	$-0.127031\pi$
$812$		0			0
$813$	0.367375			0.0128844
$814$		0			0
$815$	11.7323			0.410964
$816$		0			0
$817$	−3.45146	+	2.50763i	−0.120751	+	0.0877309i
$818$		0			0
$819$	−0.825825	−	2.54163i	−0.0288567	−	0.0888117i
$820$		0			0
$821$	15.9477	+	11.5867i	0.556580	+	0.404379i	0.830206	−	0.557457i	$-0.188223\pi$
$821$	15.9477	+	11.5867i	0.556580	+	0.404379i	−0.273626	+	0.961836i	$0.588223\pi$
$822$		0			0
$823$	−13.4107	+	41.2738i	−0.467467	+	1.43871i	0.388387	+	0.921496i	$0.373032\pi$
$823$	−13.4107	+	41.2738i	−0.467467	+	1.43871i	−0.855854	+	0.517218i	$0.826968\pi$
$824$		0			0
$825$	2.88699	+	1.63256i	0.100512	+	0.0568386i
$826$		0			0
$827$	−11.6513	+	35.8591i	−0.405156	+	1.24694i	0.515608	+	0.856825i	$0.327566\pi$
$827$	−11.6513	+	35.8591i	−0.405156	+	1.24694i	−0.920765	+	0.390119i	$0.872434\pi$
$828$		0			0
$829$	−7.69227	−	5.58876i	−0.267164	−	0.194106i	0.446136	−	0.894965i	$-0.352800\pi$
$829$	−7.69227	−	5.58876i	−0.267164	−	0.194106i	−0.713299	+	0.700860i	$0.752800\pi$
$830$		0			0
$831$	2.19584	+	6.75810i	0.0761728	+	0.234436i
$832$		0			0
$833$	19.4244	−	14.1127i	0.673017	−	0.488975i
$834$		0			0
$835$	17.8782			0.618700
$836$		0			0
$837$	−9.46864			−0.327284
$838$		0			0
$839$	−16.6202	+	12.0753i	−0.573792	+	0.416884i	−0.836481	−	0.547996i	$-0.815391\pi$
$839$	−16.6202	+	12.0753i	−0.573792	+	0.416884i	0.262689	+	0.964881i	$0.415391\pi$
$840$		0			0
$841$	19.2303	+	59.1848i	0.663114	+	2.04086i
$842$		0			0
$843$	12.4428	+	9.04020i	0.428552	+	0.311361i
$844$		0			0
$845$	2.88398	−	8.87597i	0.0992119	−	0.305343i
$846$		0			0
$847$	7.91185	+	13.1547i	0.271854	+	0.452002i
$848$		0			0
$849$	−5.20370	+	16.0153i	−0.178590	+	0.549645i
$850$		0			0
$851$	−0.740885	−	0.538285i	−0.0253972	−	0.0184522i
$852$		0			0
$853$	8.56308	+	26.3545i	0.293194	+	0.902359i	0.983822	+	0.179149i	$0.0573343\pi$
$853$	8.56308	+	26.3545i	0.293194	+	0.902359i	−0.690628	+	0.723210i	$0.742666\pi$
$854$		0			0
$855$	−0.439763	+	0.319507i	−0.0150396	+	0.0109269i
$856$		0			0
$857$	19.4762			0.665296			0.332648	−	0.943051i	$-0.392058\pi$
$857$	19.4762			0.665296			0.332648	+	0.943051i	$0.392058\pi$
$858$		0			0
$859$	51.3540			1.75218			0.876088	−	0.482152i	$-0.160145\pi$
$859$	51.3540			1.75218			0.876088	+	0.482152i	$0.160145\pi$
$860$		0			0
$861$	4.64650	−	3.37588i	0.158352	−	0.115050i
$862$		0			0
$863$	10.9398	+	33.6693i	0.372395	+	1.14612i	0.945219	+	0.326437i	$0.105848\pi$
$863$	10.9398	+	33.6693i	0.372395	+	1.14612i	−0.572824	+	0.819679i	$0.694152\pi$
$864$		0			0
$865$	−7.81443	−	5.67752i	−0.265699	−	0.193041i
$866$		0			0
$867$	1.72496	−	5.30887i	0.0585826	−	0.180299i
$868$		0			0
$869$	−21.8323	−	12.3460i	−0.740611	−	0.418808i
$870$		0			0
$871$	−5.72068	+	17.6064i	−0.193838	+	0.596571i
$872$		0			0
$873$	−10.6625	−	7.74675i	−0.360871	−	0.262188i
$874$		0			0
$875$	−0.431239	−	1.32722i	−0.0145785	−	0.0448681i
$876$		0			0
$877$	0.753208	−	0.547238i	0.0254340	−	0.0184789i	−0.574996	−	0.818156i	$-0.694996\pi$
$877$	0.753208	−	0.547238i	0.0254340	−	0.0184789i	0.600430	+	0.799678i	$0.294996\pi$
$878$		0			0
$879$	−22.5826			−0.761691
$880$		0			0
$881$	−11.0121			−0.371008			−0.185504	−	0.982643i	$-0.559392\pi$
$881$	−11.0121			−0.371008			−0.185504	+	0.982643i	$0.559392\pi$
$882$		0			0
$883$	43.4193	−	31.5459i	1.46117	−	1.06161i	0.478120	−	0.878295i	$-0.341318\pi$
$883$	43.4193	−	31.5459i	1.46117	−	1.06161i	0.983055	−	0.183311i	$-0.0586815\pi$
$884$		0			0
$885$	2.47524	+	7.61802i	0.0832044	+	0.256077i
$886$		0			0
$887$	13.2997	+	9.66278i	0.446559	+	0.324444i	0.788236	−	0.615373i	$-0.210995\pi$
$887$	13.2997	+	9.66278i	0.446559	+	0.324444i	−0.341677	+	0.939818i	$0.610995\pi$
$888$		0			0
$889$	−5.71375	+	17.5851i	−0.191633	+	0.589786i
$890$		0			0
$891$	2.44479	−	2.24120i	0.0819036	−	0.0750832i
$892$		0			0
$893$	−1.95918	+	6.02975i	−0.0655616	+	0.201778i
$894$		0			0
$895$	−9.58168	−	6.96150i	−0.320280	−	0.232697i
$896$		0			0
$897$	0.846821	+	2.60625i	0.0282745	+	0.0870201i
$898$		0			0
$899$	−73.1670	+	53.1590i	−2.44026	+	1.77295i
$900$		0			0
$901$	−54.6746			−1.82148
$902$		0			0
$903$	−10.9526			−0.364481
$904$		0			0
$905$	−2.44021	+	1.77292i	−0.0811155	+	0.0589338i
$906$		0			0
$907$	−5.30635	−	16.3313i	−0.176194	−	0.542270i	0.823492	−	0.567328i	$-0.192023\pi$
$907$	−5.30635	−	16.3313i	−0.176194	−	0.542270i	−0.999686	+	0.0250580i	$0.992023\pi$
$908$		0			0
$909$	7.29889	+	5.30296i	0.242089	+	0.175888i
$910$		0			0
$911$	−5.72588	+	17.6224i	−0.189707	+	0.583857i	−0.999998	−	0.00217056i	$-0.999309\pi$
$911$	−5.72588	+	17.6224i	−0.189707	+	0.583857i	0.810291	+	0.586028i	$0.199309\pi$
$912$		0			0
$913$	11.3406	−	1.29457i	0.375320	−	0.0428440i
$914$		0			0
$915$	1.85302	−	5.70301i	0.0612590	−	0.188536i
$916$		0			0
$917$	0.435186	+	0.316181i	0.0143711	+	0.0104412i
$918$		0			0
$919$	5.43115	+	16.7154i	0.179157	+	0.551389i	0.999799	−	0.0200542i	$-0.00638389\pi$
$919$	5.43115	+	16.7154i	0.179157	+	0.551389i	−0.820642	+	0.571443i	$0.806384\pi$
$920$		0			0
$921$	−16.6336	+	12.0850i	−0.548095	+	0.398214i
$922$		0			0
$923$	−2.05759			−0.0677265
$924$		0			0
$925$	−0.639962			−0.0210418
$926$		0			0
$927$	−3.24923	+	2.36070i	−0.106719	+	0.0775357i
$928$		0			0
$929$	0.892461	+	2.74671i	0.0292807	+	0.0901167i	0.964629	−	0.263612i	$-0.0849137\pi$
$929$	0.892461	+	2.74671i	0.0292807	+	0.0901167i	−0.935348	+	0.353728i	$0.884914\pi$
$930$		0			0
$931$	−2.22192	−	1.61432i	−0.0728204	−	0.0529071i
$932$		0			0
$933$	1.11302	−	3.42553i	0.0364387	−	0.112147i
$934$		0			0
$935$	6.53898	+	14.3403i	0.213847	+	0.468978i
$936$		0			0
$937$	16.3594	−	50.3492i	0.534439	−	1.64484i	−0.210418	−	0.977612i	$-0.567482\pi$
$937$	16.3594	−	50.3492i	0.534439	−	1.64484i	0.744857	−	0.667224i	$-0.232518\pi$
$938$		0			0
$939$	−15.8227	−	11.4959i	−0.516356	−	0.375154i
$940$		0			0
$941$	4.72833	+	14.5523i	0.154139	+	0.474391i	0.998073	−	0.0620564i	$-0.0197659\pi$
$941$	4.72833	+	14.5523i	0.154139	+	0.474391i	−0.843934	+	0.536448i	$0.819766\pi$
$942$		0			0
$943$	−4.76463	+	3.46171i	−0.155158	+	0.112729i
$944$		0			0
$945$	−1.39552			−0.0453962
$946$		0			0
$947$	−16.7641			−0.544759			−0.272379	−	0.962190i	$-0.587811\pi$
$947$	−16.7641			−0.544759			−0.272379	+	0.962190i	$0.587811\pi$
$948$		0			0
$949$	15.8740	−	11.5332i	0.515293	−	0.374382i
$950$		0			0
$951$	−4.19627	−	12.9148i	−0.136073	−	0.418790i
$952$		0			0
$953$	46.7909	+	33.9956i	1.51571	+	1.10123i	0.963565	+	0.267476i	$0.0861896\pi$
$953$	46.7909	+	33.9956i	1.51571	+	1.10123i	0.552143	+	0.833750i	$0.313810\pi$
$954$		0			0
$955$	−0.187635	+	0.577482i	−0.00607173	+	0.0186869i
$956$		0			0
$957$	6.30904	−	31.0440i	0.203942	−	1.00351i
$958$		0			0
$959$	1.04834	−	3.22646i	0.0338527	−	0.104188i
$960$		0			0
$961$	−47.4530	−	34.4766i	−1.53074	−	1.11215i
$962$		0			0
$963$	−2.92220	−	8.99359i	−0.0941664	−	0.289814i
$964$		0			0
$965$	−1.60843	+	1.16859i	−0.0517772	+	0.0376183i
$966$		0			0
$967$	−9.60043			−0.308729			−0.154364	−	0.988014i	$-0.549333\pi$
$967$	−9.60043			−0.308729			−0.154364	+	0.988014i	$0.549333\pi$
$968$		0			0
$969$	−2.58311			−0.0829815
$970$		0			0
$971$	−15.9408	+	11.5817i	−0.511564	+	0.371673i	−0.813416	−	0.581682i	$-0.802395\pi$
$971$	−15.9408	+	11.5817i	−0.511564	+	0.371673i	0.301853	+	0.953355i	$0.402395\pi$
$972$		0			0
$973$	5.55220	+	17.0879i	0.177995	+	0.547813i
$974$		0			0
$975$	1.54927	+	1.12561i	0.0496164	+	0.0360485i
$976$		0			0
$977$	−6.80611	+	20.9470i	−0.217747	+	0.670155i	0.781201	+	0.624280i	$0.214608\pi$
$977$	−6.80611	+	20.9470i	−0.217747	+	0.670155i	−0.998947	+	0.0458750i	$0.985392\pi$
$978$		0			0
$979$	−7.27105	+	35.7777i	−0.232384	+	1.14346i
$980$		0			0
$981$	5.81715	−	17.9034i	0.185727	−	0.571610i
$982$		0			0
$983$	13.4794	+	9.79336i	0.429926	+	0.312360i	0.781619	−	0.623756i	$-0.214394\pi$
$983$	13.4794	+	9.79336i	0.429926	+	0.312360i	−0.351693	+	0.936115i	$0.614394\pi$
$984$		0			0
$985$	3.13351	+	9.64394i	0.0998418	+	0.307282i
$986$		0			0
$987$	−13.1681	+	9.56722i	−0.419147	+	0.304528i
$988$		0			0
$989$	11.2311			0.357129
$990$		0			0
$991$	44.6873			1.41954			0.709770	−	0.704433i	$-0.248799\pi$
$991$	44.6873			1.41954			0.709770	+	0.704433i	$0.248799\pi$
$992$		0			0
$993$	−23.0478	+	16.7452i	−0.731401	+	0.531394i
$994$		0			0
$995$	−3.54843	−	10.9210i	−0.112493	−	0.346217i
$996$		0			0
$997$	−47.6954	−	34.6527i	−1.51053	−	1.09746i	−0.965942	−	0.258759i	$-0.916686\pi$
$997$	−47.6954	−	34.6527i	−1.51053	−	1.09746i	−0.544587	−	0.838704i	$-0.683314\pi$
$998$		0			0
$999$	−0.197759	+	0.608640i	−0.00625682	+	0.0192565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	660.2.y.b.361.1	yes	8
3.2	odd	2		1980.2.z.b.361.1		8
11.4	even	5		7260.2.a.be.1.4		4
11.5	even	5	inner	660.2.y.b.181.1	✓	8
11.7	odd	10		7260.2.a.bg.1.1		4
33.5	odd	10		1980.2.z.b.181.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.2.y.b.181.1	✓	8	11.5	even	5	inner
660.2.y.b.361.1	yes	8	1.1	even	1	trivial
1980.2.z.b.181.1		8	33.5	odd	10
1980.2.z.b.361.1		8	3.2	odd	2
7260.2.a.be.1.4		4	11.4	even	5
7260.2.a.bg.1.1		4	11.7	odd	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:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(-1.12900 - 0.820265i) q^{7} +(0.309017 - 0.951057i) q^{9} +(-0.660531 + 3.25018i) q^{11} +(-0.591770 + 1.82128i) q^{13} +(0.809017 + 0.587785i) q^{15} +(1.46847 + 4.51948i) q^{17} +(0.439763 - 0.319507i) q^{19} +1.39552 q^{21} -1.43100 q^{23} +(-0.809017 + 0.587785i) q^{25} +(0.309017 + 0.951057i) q^{27} +(7.72730 + 5.61421i) q^{29} +(-2.92597 + 9.00521i) q^{31} +(-1.37603 - 3.01770i) q^{33} +(-0.431239 + 1.32722i) q^{35} +(0.517740 + 0.376160i) q^{37} +(-0.591770 - 1.82128i) q^{39} +(3.32959 - 2.41909i) q^{41} -7.84844 q^{43} -1.00000 q^{45} +(-9.43603 + 6.85567i) q^{47} +(-1.56132 - 4.80524i) q^{49} +(-3.84450 - 2.79319i) q^{51} +(-3.55538 + 10.9423i) q^{53} +(3.29522 - 0.376160i) q^{55} +(-0.167975 + 0.516973i) q^{57} +(6.48027 + 4.70819i) q^{59} +(-1.85302 - 5.70301i) q^{61} +(-1.12900 + 0.820265i) q^{63} +1.91501 q^{65} +9.66707 q^{67} +(1.15770 - 0.841120i) q^{69} +(0.332025 + 1.02187i) q^{71} +(-8.28929 - 6.02252i) q^{73} +(0.309017 - 0.951057i) q^{75} +(3.41175 - 3.12764i) q^{77} +(-2.33688 + 7.19218i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-1.06349 - 3.27309i) q^{83} +(3.84450 - 2.79319i) q^{85} -9.55147 q^{87} +11.0079 q^{89} +(2.16204 - 1.57081i) q^{91} +(-2.92597 - 9.00521i) q^{93} +(-0.439763 - 0.319507i) q^{95} +(4.07271 - 12.5345i) q^{97} +(2.88699 + 1.63256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9} - 5 q^{11} - 8 q^{13} + 2 q^{15} + 6 q^{17} + 6 q^{19} - 8 q^{21} + 30 q^{23} - 2 q^{25} - 2 q^{27} - 9 q^{31} + 10 q^{33} - 7 q^{35} - 7 q^{37} - 8 q^{39} + 25 q^{41}+ \cdots + 5 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 2 * q^5 - 3 * q^7 - 2 * q^9 - 5 * q^11 - 8 * q^13 + 2 * q^15 + 6 * q^17 + 6 * q^19 - 8 * q^21 + 30 * q^23 - 2 * q^25 - 2 * q^27 - 9 * q^31 + 10 * q^33 - 7 * q^35 - 7 * q^37 - 8 * q^39 + 25 * q^41 - 8 * q^43 - 8 * q^45 - 7 * q^47 - 11 * q^49 - 4 * q^51 + 3 * q^53 + 5 * q^55 + q^57 + 5 * q^59 + 13 * q^61 - 3 * q^63 - 2 * q^65 + 18 * q^67 - 5 * q^69 + 5 * q^71 - 15 * q^73 - 2 * q^75 + 29 * q^77 - 50 * q^79 - 2 * q^81 + 13 * q^83 + 4 * q^85 - 30 * q^87 + 32 * q^89 - 15 * q^91 - 9 * q^93 - 6 * q^95 + q^97 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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