LMFDB - Embedded newform 1008.2.t.g.193.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(193,1008)] 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("1008.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-4,0,10] 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.g.961.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.349814 - 1.69636i) q^{3} +3.69963 q^{5} +(1.40545 - 2.24159i) q^{7} +(-2.75526 - 1.18682i) q^{9} +1.47710 q^{11} +(-1.34981 + 2.33795i) q^{13} +(1.29418 - 6.27589i) q^{15} +(3.28799 - 5.69497i) q^{17} +(0.444368 + 0.769668i) q^{19} +(-3.31089 - 3.16828i) q^{21} -6.28799 q^{23} +8.68725 q^{25} +(-2.97710 + 4.25874i) q^{27} +(1.25526 + 2.17417i) q^{29} +(3.40545 + 5.89841i) q^{31} +(0.516710 - 2.50569i) q^{33} +(5.19963 - 8.29305i) q^{35} +(-1.38874 - 2.40536i) q^{37} +(3.49381 + 3.10761i) q^{39} +(-2.05563 + 3.56046i) q^{41} +(-0.00618986 - 0.0107211i) q^{43} +(-10.1934 - 4.39079i) q^{45} +(-3.49381 + 6.05146i) q^{47} +(-3.04944 - 6.30087i) q^{49} +(-8.51052 - 7.56979i) q^{51} +(-1.60507 + 2.78007i) q^{53} +5.46472 q^{55} +(1.46108 - 0.484566i) q^{57} +(3.45489 + 5.98404i) q^{59} +(2.86652 - 4.96497i) q^{61} +(-6.53273 + 4.50815i) q^{63} +(-4.99381 + 8.64953i) q^{65} +(-4.73236 - 8.19669i) q^{67} +(-2.19963 + 10.6667i) q^{69} +5.46472 q^{71} +(-6.03273 + 10.4490i) q^{73} +(3.03892 - 14.7367i) q^{75} +(2.07598 - 3.31105i) q^{77} +(5.72617 - 9.91802i) q^{79} +(6.18292 + 6.53999i) q^{81} +(-2.23855 - 3.87728i) q^{83} +(12.1643 - 21.0693i) q^{85} +(4.12729 - 1.36881i) q^{87} +(-4.43818 - 7.68715i) q^{89} +(3.34362 + 6.31159i) q^{91} +(11.1971 - 3.71351i) q^{93} +(1.64400 + 2.84748i) q^{95} +(-6.58836 - 11.4114i) q^{97} +(-4.06979 - 1.75305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} + 4 q^{25} - 7 q^{27} - 5 q^{29} + 14 q^{31} - 4 q^{33} + 19 q^{35} - 9 q^{37}+ \cdots + 41 q^{99}+O(q^{100}) $ 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 7 * q^21 - 14 * q^23 + 4 * q^25 - 7 * q^27 - 5 * q^29 + 14 * q^31 - 4 * q^33 + 19 * q^35 - 9 * q^37 + 3 * q^39 - 12 * q^41 - 18 * q^43 - 31 * q^45 - 3 * q^47 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 - 4 * q^59 + 4 * q^61 - 28 * q^63 - 12 * q^65 - 5 * q^67 - q^69 - 14 * q^71 - 25 * q^73 + 25 * q^75 - 35 * q^77 - 7 * q^79 + 32 * q^81 - 8 * q^83 + 14 * q^85 + 20 * q^87 - 9 * q^89 - 4 * q^91 - 3 * q^93 - 2 * q^95 - 28 * q^97 + 41 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.349814	−	1.69636i	0.201965	−	0.979393i
$3$	0.349814	−	1.69636i	0.201965	−	0.979393i
$4$		0			0
$5$	3.69963			1.65452			0.827262	−	0.561816i	$-0.189897\pi$
$5$	3.69963			1.65452			0.827262	+	0.561816i	$0.189897\pi$
$6$		0			0
$7$	1.40545	−	2.24159i	0.531209	−	0.847241i
$7$	1.40545	−	2.24159i	0.531209	−	0.847241i
$8$		0			0
$9$	−2.75526	−	1.18682i	−0.918420	−	0.395607i
$10$		0			0
$11$	1.47710			0.445362			0.222681	−	0.974891i	$-0.428519\pi$
$11$	1.47710			0.445362			0.222681	+	0.974891i	$0.428519\pi$
$12$		0			0
$13$	−1.34981	+	2.33795i	−0.374371	+	0.648430i	−0.990233	−	0.139425i	$-0.955475\pi$
$13$	−1.34981	+	2.33795i	−0.374371	+	0.648430i	0.615862	+	0.787854i	$0.288808\pi$
$14$		0			0
$15$	1.29418	−	6.27589i	0.334156	−	1.62043i
$16$		0			0
$17$	3.28799	−	5.69497i	0.797455	−	1.38123i	−0.123813	−	0.992306i	$-0.539512\pi$
$17$	3.28799	−	5.69497i	0.797455	−	1.38123i	0.921268	−	0.388927i	$-0.127154\pi$
$18$		0			0
$19$	0.444368	+	0.769668i	0.101945	+	0.176574i	0.912486	−	0.409108i	$-0.134160\pi$
$19$	0.444368	+	0.769668i	0.101945	+	0.176574i	−0.810541	+	0.585682i	$0.800827\pi$
$20$		0			0
$21$	−3.31089	−	3.16828i	−0.722496	−	0.691375i
$22$		0			0
$23$	−6.28799			−1.31114			−0.655568	−	0.755136i	$-0.727571\pi$
$23$	−6.28799			−1.31114			−0.655568	+	0.755136i	$0.727571\pi$
$24$		0			0
$25$	8.68725			1.73745
$26$		0			0
$27$	−2.97710	+	4.25874i	−0.572943	+	0.819595i
$28$		0			0
$29$	1.25526	+	2.17417i	0.233096	+	0.403734i	0.958718	−	0.284360i	$-0.0917810\pi$
$29$	1.25526	+	2.17417i	0.233096	+	0.403734i	−0.725622	+	0.688094i	$0.758448\pi$
$30$		0			0
$31$	3.40545	+	5.89841i	0.611636	+	1.05938i	0.990965	+	0.134123i	$0.0428217\pi$
$31$	3.40545	+	5.89841i	0.611636	+	1.05938i	−0.379329	+	0.925262i	$0.623845\pi$
$32$		0			0
$33$	0.516710	−	2.50569i	0.0899477	−	0.436185i
$34$		0			0
$35$	5.19963	−	8.29305i	0.878898	−	1.40178i
$36$		0			0
$37$	−1.38874	−	2.40536i	−0.228307	−	0.395439i	0.729000	−	0.684514i	$-0.239986\pi$
$37$	−1.38874	−	2.40536i	−0.228307	−	0.395439i	−0.957306	+	0.289075i	$0.906652\pi$
$38$		0			0
$39$	3.49381	+	3.10761i	0.559457	+	0.497617i
$40$		0			0
$41$	−2.05563	+	3.56046i	−0.321036	+	0.556050i	−0.980702	−	0.195508i	$-0.937364\pi$
$41$	−2.05563	+	3.56046i	−0.321036	+	0.556050i	0.659666	+	0.751559i	$0.270698\pi$
$42$		0			0
$43$	−0.00618986	−	0.0107211i	−0.000943944	−	0.00163496i	0.865553	−	0.500817i	$-0.166967\pi$
$43$	−0.00618986	−	0.0107211i	−0.000943944	−	0.00163496i	−0.866497	+	0.499182i	$0.833634\pi$
$44$		0			0
$45$	−10.1934	−	4.39079i	−1.51955	−	0.654541i
$46$		0			0
$47$	−3.49381	+	6.05146i	−0.509625	+	0.882696i	0.490313	+	0.871546i	$0.336882\pi$
$47$	−3.49381	+	6.05146i	−0.509625	+	0.882696i	−0.999938	+	0.0111494i	$0.996451\pi$
$48$		0			0
$49$	−3.04944	−	6.30087i	−0.435635	−	0.900124i
$50$		0			0
$51$	−8.51052	−	7.56979i	−1.19171	−	1.05998i
$52$		0			0
$53$	−1.60507	+	2.78007i	−0.220474	+	0.381872i	−0.954952	−	0.296760i	$-0.904094\pi$
$53$	−1.60507	+	2.78007i	−0.220474	+	0.381872i	0.734478	+	0.678632i	$0.237427\pi$
$54$		0			0
$55$	5.46472			0.736863
$56$		0			0
$57$	1.46108	−	0.484566i	0.193525	−	0.0641824i
$58$		0			0
$59$	3.45489	+	5.98404i	0.449788	+	0.779056i	0.998372	−	0.0570397i	$-0.0181661\pi$
$59$	3.45489	+	5.98404i	0.449788	+	0.779056i	−0.548584	+	0.836096i	$0.684833\pi$
$60$		0			0
$61$	2.86652	−	4.96497i	0.367021	−	0.635699i	−0.622077	−	0.782956i	$-0.713711\pi$
$61$	2.86652	−	4.96497i	0.367021	−	0.635699i	0.989098	+	0.147257i	$0.0470444\pi$
$62$		0			0
$63$	−6.53273	+	4.50815i	−0.823047	+	0.567973i
$64$		0			0
$65$	−4.99381	+	8.64953i	−0.619406	+	1.07284i
$66$		0			0
$67$	−4.73236	−	8.19669i	−0.578150	−	1.00138i	−0.995692	−	0.0927271i	$-0.970442\pi$
$67$	−4.73236	−	8.19669i	−0.578150	−	1.00138i	0.417542	−	0.908658i	$-0.362892\pi$
$68$		0			0
$69$	−2.19963	+	10.6667i	−0.264804	+	1.28412i
$70$		0			0
$71$	5.46472			0.648543			0.324271	−	0.945964i	$-0.394881\pi$
$71$	5.46472			0.648543			0.324271	+	0.945964i	$0.394881\pi$
$72$		0			0
$73$	−6.03273	+	10.4490i	−0.706078	+	1.22296i	0.260223	+	0.965548i	$0.416204\pi$
$73$	−6.03273	+	10.4490i	−0.706078	+	1.22296i	−0.966301	+	0.257414i	$0.917130\pi$
$74$		0			0
$75$	3.03892	−	14.7367i	0.350904	−	1.70165i
$76$		0			0
$77$	2.07598	−	3.31105i	0.236580	−	0.377329i
$78$		0			0
$79$	5.72617	−	9.91802i	0.644244	−	1.11586i	−0.340231	−	0.940342i	$-0.610505\pi$
$79$	5.72617	−	9.91802i	0.644244	−	1.11586i	0.984475	−	0.175522i	$-0.0561614\pi$
$80$		0			0
$81$	6.18292	+	6.53999i	0.686991	+	0.726666i
$82$		0			0
$83$	−2.23855	−	3.87728i	−0.245713	−	0.425587i	0.716619	−	0.697465i	$-0.245689\pi$
$83$	−2.23855	−	3.87728i	−0.245713	−	0.425587i	−0.962332	+	0.271878i	$0.912355\pi$
$84$		0			0
$85$	12.1643	−	21.0693i	1.31941	−	2.28528i
$86$		0			0
$87$	4.12729	−	1.36881i	0.442491	−	0.146752i
$88$		0			0
$89$	−4.43818	−	7.68715i	−0.470446	−	0.814836i	0.528983	−	0.848633i	$-0.322574\pi$
$89$	−4.43818	−	7.68715i	−0.470446	−	0.814836i	−0.999429	+	0.0337963i	$0.989240\pi$
$90$		0			0
$91$	3.34362	+	6.31159i	0.350507	+	0.661634i
$92$		0			0
$93$	11.1971	−	3.71351i	1.16108	−	0.385073i
$94$		0			0
$95$	1.64400	+	2.84748i	0.168670	+	0.292146i
$96$		0			0
$97$	−6.58836	−	11.4114i	−0.668947	−	1.15865i	−0.978199	−	0.207670i	$-0.933412\pi$
$97$	−6.58836	−	11.4114i	−0.668947	−	1.15865i	0.309252	−	0.950980i	$-0.399921\pi$
$98$		0			0
$99$	−4.06979	−	1.75305i	−0.409030	−	0.176188i
$100$		0			0
$101$	5.25457			0.522849			0.261425	−	0.965224i	$-0.415808\pi$
$101$	5.25457			0.522849			0.261425	+	0.965224i	$0.415808\pi$
$102$		0			0
$103$	−1.66621			−0.164176			−0.0820882	−	0.996625i	$-0.526159\pi$
$103$	−1.66621			−0.164176			−0.0820882	+	0.996625i	$0.526159\pi$
$104$		0			0
$105$	−12.2491	−	11.7215i	−1.19539	−	1.14390i
$106$		0			0
$107$	5.38255	+	9.32284i	0.520350	+	0.901273i	0.999720	+	0.0236602i	$0.00753198\pi$
$107$	5.38255	+	9.32284i	0.520350	+	0.901273i	−0.479370	+	0.877613i	$0.659135\pi$
$108$		0			0
$109$	−0.0945538	+	0.163772i	−0.00905662	+	0.0156865i	−0.870518	−	0.492136i	$-0.836216\pi$
$109$	−0.0945538	+	0.163772i	−0.00905662	+	0.0156865i	0.861462	+	0.507823i	$0.169550\pi$
$110$		0			0
$111$	−4.56615	+	1.51436i	−0.433400	+	0.143737i
$112$		0			0
$113$	−6.78180	+	11.7464i	−0.637978	+	1.10501i	0.347897	+	0.937533i	$0.386896\pi$
$113$	−6.78180	+	11.7464i	−0.637978	+	1.10501i	−0.985876	+	0.167478i	$0.946438\pi$
$114$		0			0
$115$	−23.2632			−2.16931
$116$		0			0
$117$	6.49381	−	4.83967i	0.600353	−	0.447427i
$118$		0			0
$119$	−8.14468	−	15.3743i	−0.746622	−	1.40936i
$120$		0			0
$121$	−8.81818			−0.801652
$122$		0			0
$123$	5.32072	+	4.73259i	0.479754	+	0.426723i
$124$		0			0
$125$	13.6414			1.22013
$126$		0			0
$127$	2.85669			0.253490			0.126745	−	0.991935i	$-0.459547\pi$
$127$	2.85669			0.253490			0.126745	+	0.991935i	$0.459547\pi$
$128$		0			0
$129$	−0.0203522	+	0.00674980i	−0.00179191	+	0.000594287i
$130$		0			0
$131$	−0.155687			−0.0136024			−0.00680122	−	0.999977i	$-0.502165\pi$
$131$	−0.155687			−0.0136024			−0.00680122	+	0.999977i	$0.502165\pi$
$132$		0			0
$133$	2.34981	+	0.0856364i	0.203755	+	0.00742562i
$134$		0			0
$135$	−11.0142	+	15.7558i	−0.947948	+	1.35604i
$136$		0			0
$137$	−3.41164			−0.291476			−0.145738	−	0.989323i	$-0.546556\pi$
$137$	−3.41164			−0.291476			−0.145738	+	0.989323i	$0.546556\pi$
$138$		0			0
$139$	6.75526	−	11.7005i	0.572974	−	0.992420i	−0.423285	−	0.905997i	$-0.639123\pi$
$139$	6.75526	−	11.7005i	0.572974	−	0.992420i	0.996259	−	0.0864229i	$-0.0275436\pi$
$140$		0			0
$141$	9.04325	+	8.04364i	0.761579	+	0.677396i
$142$		0			0
$143$	−1.99381	+	3.45338i	−0.166731	+	0.288786i
$144$		0			0
$145$	4.64400	+	8.04364i	0.385663	+	0.667988i
$146$		0			0
$147$	−11.7553	+	2.96881i	−0.969558	+	0.244864i
$148$		0			0
$149$	0.333792			0.0273453			0.0136727	−	0.999907i	$-0.495648\pi$
$149$	0.333792			0.0273453			0.0136727	+	0.999907i	$0.495648\pi$
$150$		0			0
$151$	19.9098			1.62023			0.810117	−	0.586268i	$-0.199403\pi$
$151$	19.9098			1.62023			0.810117	+	0.586268i	$0.199403\pi$
$152$		0			0
$153$	−15.8182	+	11.7889i	−1.27882	+	0.953074i
$154$		0			0
$155$	12.5989	+	21.8219i	1.01197	+	1.75278i
$156$		0			0
$157$	3.48143	+	6.03001i	0.277848	+	0.481248i	0.970850	−	0.239689i	$-0.0770454\pi$
$157$	3.48143	+	6.03001i	0.277848	+	0.481248i	−0.693001	+	0.720936i	$0.743712\pi$
$158$		0			0
$159$	4.15452	+	3.69529i	0.329475	+	0.293055i
$160$		0			0
$161$	−8.83743	+	14.0951i	−0.696487	+	1.11085i
$162$		0			0
$163$	−4.03706	−	6.99240i	−0.316207	−	0.547687i	0.663486	−	0.748189i	$-0.269076\pi$
$163$	−4.03706	−	6.99240i	−0.316207	−	0.547687i	−0.979693	+	0.200502i	$0.935743\pi$
$164$		0			0
$165$	1.91164	−	9.27012i	0.148821	−	0.721678i
$166$		0			0
$167$	−9.74288	+	16.8752i	−0.753927	+	1.30584i	0.191979	+	0.981399i	$0.438509\pi$
$167$	−9.74288	+	16.8752i	−0.753927	+	1.30584i	−0.945906	+	0.324440i	$0.894824\pi$
$168$		0			0
$169$	2.85600	+	4.94674i	0.219693	+	0.380519i
$170$		0			0
$171$	−0.310892	−	2.64802i	−0.0237745	−	0.202499i
$172$		0			0
$173$	−11.2818	+	19.5407i	−0.857740	+	1.48565i	0.0163405	+	0.999866i	$0.494798\pi$
$173$	−11.2818	+	19.5407i	−0.857740	+	1.48565i	−0.874080	+	0.485782i	$0.838535\pi$
$174$		0			0
$175$	12.2095	−	19.4732i	0.922948	−	1.47204i
$176$		0			0
$177$	11.3596	−	3.76742i	0.853843	−	0.283177i
$178$		0			0
$179$	−0.166896	+	0.289073i	−0.0124744	+	0.0216063i	−0.872195	−	0.489158i	$-0.837304\pi$
$179$	−0.166896	+	0.289073i	−0.0124744	+	0.0216063i	0.859721	+	0.510764i	$0.170637\pi$
$180$		0			0
$181$	23.2422			1.72758			0.863789	−	0.503853i	$-0.168085\pi$
$181$	23.2422			1.72758			0.863789	+	0.503853i	$0.168085\pi$
$182$		0			0
$183$	−7.41961	−	6.59947i	−0.548473	−	0.487847i
$184$		0			0
$185$	−5.13781	−	8.89894i	−0.377739	−	0.654263i
$186$		0			0
$187$	4.85669	−	8.41204i	0.355157	−	0.615149i
$188$		0			0
$189$	5.36219	+	12.6589i	0.390042	+	0.920797i
$190$		0			0
$191$	−8.16071	+	14.1348i	−0.590488	+	1.02276i	0.403679	+	0.914901i	$0.367731\pi$
$191$	−8.16071	+	14.1348i	−0.590488	+	1.02276i	−0.994167	+	0.107854i	$0.965602\pi$
$192$		0			0
$193$	7.16071	+	12.4027i	0.515439	+	0.892766i	0.999839	+	0.0179200i	$0.00570443\pi$
$193$	7.16071	+	12.4027i	0.515439	+	0.892766i	−0.484400	+	0.874846i	$0.660962\pi$
$194$		0			0
$195$	12.9258	+	11.4970i	0.925636	+	0.823319i
$196$		0			0
$197$	2.42402			0.172704			0.0863520	−	0.996265i	$-0.472479\pi$
$197$	2.42402			0.172704			0.0863520	+	0.996265i	$0.472479\pi$
$198$		0			0
$199$	3.05563	−	5.29251i	0.216608	−	0.375176i	−0.737161	−	0.675717i	$-0.763834\pi$
$199$	3.05563	−	5.29251i	0.216608	−	0.375176i	0.953769	+	0.300541i	$0.0971673\pi$
$200$		0			0
$201$	−15.5600	+	5.16046i	−1.09752	+	0.363991i
$202$		0			0
$203$	6.63781	+	0.241908i	0.465883	+	0.0169786i
$204$		0			0
$205$	−7.60507	+	13.1724i	−0.531161	+	0.919999i
$206$		0			0
$207$	17.3251	+	7.46271i	1.20417	+	0.518694i
$208$		0			0
$209$	0.656376	+	1.13688i	0.0454025	+	0.0786394i
$210$		0			0
$211$	−5.72253	+	9.91171i	−0.393955	+	0.682350i	−0.992967	−	0.118390i	$-0.962227\pi$
$211$	−5.72253	+	9.91171i	−0.393955	+	0.682350i	0.599012	+	0.800740i	$0.295560\pi$
$212$		0			0
$213$	1.91164	−	9.27012i	0.130983	−	0.635178i
$214$		0			0
$215$	−0.0229002	−	0.0396643i	−0.00156178	−	0.00270508i
$216$		0			0
$217$	18.0080	+	0.656281i	1.22246	+	0.0445513i
$218$		0			0
$219$	15.6149	+	13.8889i	1.05516	+	0.938523i
$220$		0			0
$221$	8.87636	+	15.3743i	0.597088	+	1.03419i
$222$		0			0
$223$	3.61126	+	6.25489i	0.241828	+	0.418859i	0.961235	−	0.275730i	$-0.0889196\pi$
$223$	3.61126	+	6.25489i	0.241828	+	0.418859i	−0.719407	+	0.694589i	$0.755586\pi$
$224$		0			0
$225$	−23.9356	−	10.3102i	−1.59571	−	0.687347i
$226$		0			0
$227$	−13.6552			−0.906328			−0.453164	−	0.891427i	$-0.649705\pi$
$227$	−13.6552			−0.906328			−0.453164	+	0.891427i	$0.649705\pi$
$228$		0			0
$229$	17.3745			1.14814			0.574070	−	0.818807i	$-0.305364\pi$
$229$	17.3745			1.14814			0.574070	+	0.818807i	$0.305364\pi$
$230$		0			0
$231$	−4.89052	−	4.67986i	−0.321772	−	0.307912i
$232$		0			0
$233$	7.62110	+	13.2001i	0.499275	+	0.864769i	1.00000		0.000837426i	$-0.000266561\pi$
$233$	7.62110	+	13.2001i	0.499275	+	0.864769i	−0.500725	+	0.865606i	$0.666933\pi$
$234$		0			0
$235$	−12.9258	+	22.3881i	−0.843186	+	1.46044i
$236$		0			0
$237$	−14.8214	−	13.1831i	−0.962754	−	0.856334i
$238$		0			0
$239$	−9.47524	+	16.4116i	−0.612902	+	1.06158i	0.377846	+	0.925868i	$0.376665\pi$
$239$	−9.47524	+	16.4116i	−0.612902	+	1.06158i	−0.990749	+	0.135710i	$0.956669\pi$
$240$		0			0
$241$	−24.5054			−1.57853			−0.789267	−	0.614051i	$-0.789539\pi$
$241$	−24.5054			−1.57853			−0.789267	+	0.614051i	$0.789539\pi$
$242$		0			0
$243$	13.2570	−	8.20066i	0.850440	−	0.526073i
$244$		0			0
$245$	−11.2818	−	23.3109i	−0.720768	−	1.48928i
$246$		0			0
$247$	−2.39926			−0.152661
$248$		0			0
$249$	−7.36033	+	2.44105i	−0.466442	+	0.154696i
$250$		0			0
$251$	12.1236			0.765238			0.382619	−	0.923906i	$-0.375022\pi$
$251$	12.1236			0.765238			0.382619	+	0.923906i	$0.375022\pi$
$252$		0			0
$253$	−9.28799			−0.583931
$254$		0			0
$255$	−31.4858	−	28.0054i	−1.97171	−	1.75377i
$256$		0			0
$257$	−8.20877			−0.512049			−0.256025	−	0.966670i	$-0.582413\pi$
$257$	−8.20877			−0.512049			−0.256025	+	0.966670i	$0.582413\pi$
$258$		0			0
$259$	−7.34362	−	0.267630i	−0.456311	−	0.0166297i
$260$		0			0
$261$	−0.878215	−	7.48018i	−0.0543602	−	0.463012i
$262$		0			0
$263$	5.34617			0.329659			0.164830	−	0.986322i	$-0.447293\pi$
$263$	5.34617			0.329659			0.164830	+	0.986322i	$0.447293\pi$
$264$		0			0
$265$	−5.93818	+	10.2852i	−0.364779	+	0.631816i
$266$		0			0
$267$	−14.5927	+	4.83967i	−0.893058	+	0.296183i
$268$		0			0
$269$	9.24219	−	16.0079i	0.563506	−	0.976022i	−0.433681	−	0.901067i	$-0.642785\pi$
$269$	9.24219	−	16.0079i	0.563506	−	0.976022i	0.997187	−	0.0749550i	$-0.0238813\pi$
$270$		0			0
$271$	3.67742	+	6.36947i	0.223387	+	0.386918i	0.955834	−	0.293906i	$-0.0949552\pi$
$271$	3.67742	+	6.36947i	0.223387	+	0.386918i	−0.732447	+	0.680824i	$0.761622\pi$
$272$		0			0
$273$	11.8764	−	3.46410i	0.718790	−	0.209657i
$274$		0			0
$275$	12.8319			0.773795
$276$		0			0
$277$	−9.09888			−0.546699			−0.273349	−	0.961915i	$-0.588132\pi$
$277$	−9.09888			−0.546699			−0.273349	+	0.961915i	$0.588132\pi$
$278$		0			0
$279$	−2.38255	−	20.2933i	−0.142639	−	1.21493i
$280$		0			0
$281$	6.00433	+	10.3998i	0.358188	+	0.620400i	0.987658	−	0.156624i	$-0.0500612\pi$
$281$	6.00433	+	10.3998i	0.358188	+	0.620400i	−0.629470	+	0.777025i	$0.716728\pi$
$282$		0			0
$283$	4.92147	+	8.52423i	0.292551	+	0.506713i	0.974412	−	0.224768i	$-0.0721626\pi$
$283$	4.92147	+	8.52423i	0.292551	+	0.506713i	−0.681861	+	0.731481i	$0.738829\pi$
$284$		0			0
$285$	5.40545	−	1.79272i	0.320191	−	0.106191i
$286$		0			0
$287$	5.09201	+	9.61192i	0.300572	+	0.567373i
$288$		0			0
$289$	−13.1218	−	22.7276i	−0.771870	−	1.33692i
$290$		0			0
$291$	−21.6625	+	7.18436i	−1.26988	+	0.421155i
$292$		0			0
$293$	10.7101	−	18.5505i	0.625694	−	1.08373i	−0.362713	−	0.931901i	$-0.618149\pi$
$293$	10.7101	−	18.5505i	0.625694	−	1.08373i	0.988406	−	0.151832i	$-0.0485173\pi$
$294$		0			0
$295$	12.7818	+	22.1387i	0.744185	+	1.28897i
$296$		0			0
$297$	−4.39747	+	6.29059i	−0.255167	+	0.365017i
$298$		0			0
$299$	8.48762	−	14.7010i	0.490852	−	0.850180i
$300$		0			0
$301$	−0.0327319	−	0.00119288i	−0.00188664	−	6.87564e-5i
$302$		0			0
$303$	1.83812	−	8.91363i	0.105597	−	0.512075i
$304$		0			0
$305$	10.6051	−	18.3685i	0.607245	−	1.05178i
$306$		0			0
$307$	5.68725			0.324588			0.162294	−	0.986742i	$-0.448111\pi$
$307$	5.68725			0.324588			0.162294	+	0.986742i	$0.448111\pi$
$308$		0			0
$309$	−0.582863	+	2.82648i	−0.0331579	+	0.160793i
$310$		0			0
$311$	−5.86033	−	10.1504i	−0.332309	−	0.575576i	0.650655	−	0.759373i	$-0.274494\pi$
$311$	−5.86033	−	10.1504i	−0.332309	−	0.575576i	−0.982964	+	0.183797i	$0.941161\pi$
$312$		0			0
$313$	13.3869	−	23.1868i	0.756671	−	1.31059i	−0.187868	−	0.982194i	$-0.560158\pi$
$313$	13.3869	−	23.1868i	0.756671	−	1.31059i	0.944539	−	0.328398i	$-0.106509\pi$
$314$		0			0
$315$	−24.1687	+	16.6785i	−1.36175	+	0.939726i
$316$		0			0
$317$	−0.951246	+	1.64761i	−0.0534273	+	0.0925388i	−0.891502	−	0.453016i	$-0.850348\pi$
$317$	−0.951246	+	1.64761i	−0.0534273	+	0.0925388i	0.838075	+	0.545555i	$0.183681\pi$
$318$		0			0
$319$	1.85414	+	3.21147i	0.103812	+	0.179808i
$320$		0			0
$321$	17.6978	−	5.86946i	0.987793	−	0.327601i
$322$		0			0
$323$	5.84431			0.325186
$324$		0			0
$325$	−11.7262	+	20.3103i	−0.650451	+	1.12661i
$326$		0			0
$327$	0.244740	+	0.217687i	0.0135341	+	0.0120381i
$328$		0			0
$329$	8.65452	+	16.3367i	0.477139	+	0.900670i
$330$		0			0
$331$	2.78366	−	4.82144i	0.153004	−	0.265010i	−0.779327	−	0.626618i	$-0.784439\pi$
$331$	2.78366	−	4.82144i	0.153004	−	0.265010i	0.932330	+	0.361608i	$0.117772\pi$
$332$		0			0
$333$	0.971599	+	8.27557i	0.0532433	+	0.453499i
$334$		0			0
$335$	−17.5080	−	30.3247i	−0.956563	−	1.65682i
$336$		0			0
$337$	−16.8869	+	29.2489i	−0.919887	+	1.59329i	−0.120302	+	0.992737i	$0.538386\pi$
$337$	−16.8869	+	29.2489i	−0.919887	+	1.59329i	−0.799585	+	0.600553i	$0.794947\pi$
$338$		0			0
$339$	17.5538	+	15.6134i	0.953390	+	0.848005i
$340$		0			0
$341$	5.03018	+	8.71253i	0.272400	+	0.471810i
$342$		0			0
$343$	−18.4098	−	2.01993i	−0.994035	−	0.109066i
$344$		0			0
$345$	−8.13781	+	39.4628i	−0.438125	+	2.12460i
$346$		0			0
$347$	−15.2033	−	26.3328i	−0.816154	−	1.41362i	−0.908496	−	0.417893i	$-0.862769\pi$
$347$	−15.2033	−	26.3328i	−0.816154	−	1.41362i	0.0923418	−	0.995727i	$-0.470565\pi$
$348$		0			0
$349$	−6.29782	−	10.9082i	−0.337115	−	0.583900i	0.646774	−	0.762682i	$-0.276118\pi$
$349$	−6.29782	−	10.9082i	−0.337115	−	0.583900i	−0.983889	+	0.178782i	$0.942784\pi$
$350$		0			0
$351$	−5.93818	−	12.7088i	−0.316956	−	0.678346i
$352$		0			0
$353$	−7.53156			−0.400865			−0.200432	−	0.979708i	$-0.564235\pi$
$353$	−7.53156			−0.400865			−0.200432	+	0.979708i	$0.564235\pi$
$354$		0			0
$355$	20.2174			1.07303
$356$		0			0
$357$	−28.9294	+	8.43815i	−1.53111	+	0.446594i
$358$		0			0
$359$	3.44801	+	5.97213i	0.181979	+	0.315197i	0.942554	−	0.334053i	$-0.108416\pi$
$359$	3.44801	+	5.97213i	0.181979	+	0.315197i	−0.760575	+	0.649250i	$0.775083\pi$
$360$		0			0
$361$	9.10507	−	15.7705i	0.479214	−	0.830024i
$362$		0			0
$363$	−3.08472	+	14.9588i	−0.161906	+	0.785132i
$364$		0			0
$365$	−22.3189	+	38.6574i	−1.16822	+	2.02342i
$366$		0			0
$367$	−23.1236			−1.20704			−0.603522	−	0.797346i	$-0.706237\pi$
$367$	−23.1236			−1.20704			−0.603522	+	0.797346i	$0.706237\pi$
$368$		0			0
$369$	9.88942	−	7.37033i	0.514823	−	0.383684i
$370$		0			0
$371$	3.97593	+	7.50516i	0.206420	+	0.389648i
$372$		0			0
$373$	29.1643			1.51007			0.755036	−	0.655683i	$-0.227619\pi$
$373$	29.1643			1.51007			0.755036	+	0.655683i	$0.227619\pi$
$374$		0			0
$375$	4.77197	−	23.1408i	0.246423	−	1.19498i
$376$		0			0
$377$	−6.77747			−0.349058
$378$		0			0
$379$	13.5622			0.696645			0.348322	−	0.937375i	$-0.386751\pi$
$379$	13.5622			0.696645			0.348322	+	0.937375i	$0.386751\pi$
$380$		0			0
$381$	0.999311	−	4.84597i	0.0511963	−	0.248267i
$382$		0			0
$383$	2.83565			0.144895			0.0724475	−	0.997372i	$-0.476919\pi$
$383$	2.83565			0.144895			0.0724475	+	0.997372i	$0.476919\pi$
$384$		0			0
$385$	7.68037	−	12.2497i	0.391428	−	0.624300i
$386$		0			0
$387$	0.00433060	+	0.0368858i	0.000220137	+	0.00187501i
$388$		0			0
$389$	−18.6080			−0.943464			−0.471732	−	0.881742i	$-0.656371\pi$
$389$	−18.6080			−0.943464			−0.471732	+	0.881742i	$0.656371\pi$
$390$		0			0
$391$	−20.6749	+	35.8099i	−1.04557	+	1.81099i
$392$		0			0
$393$	−0.0544615	+	0.264101i	−0.00274722	+	0.0133221i
$394$		0			0
$395$	21.1847	−	36.6930i	1.06592	−	1.84622i
$396$		0			0
$397$	−10.2880	−	17.8193i	−0.516340	−	0.894326i	−0.999820	−	0.0189712i	$-0.993961\pi$
$397$	−10.2880	−	17.8193i	−0.516340	−	0.894326i	0.483481	−	0.875355i	$-0.339372\pi$
$398$		0			0
$399$	0.967268	−	3.95617i	0.0484240	−	0.198056i
$400$		0			0
$401$	−6.75409			−0.337283			−0.168642	−	0.985677i	$-0.553938\pi$
$401$	−6.75409			−0.337283			−0.168642	+	0.985677i	$0.553938\pi$
$402$		0			0
$403$	−18.3869			−0.915916
$404$		0			0
$405$	22.8745	+	24.1955i	1.13664	+	1.20229i
$406$		0			0
$407$	−2.05130	−	3.55296i	−0.101679	−	0.176114i
$408$		0			0
$409$	−7.66071	−	13.2687i	−0.378798	−	0.656097i	0.612090	−	0.790788i	$-0.290329\pi$
$409$	−7.66071	−	13.2687i	−0.378798	−	0.656097i	−0.990888	+	0.134691i	$0.956996\pi$
$410$		0			0
$411$	−1.19344	+	5.78736i	−0.0588680	+	0.285469i
$412$		0			0
$413$	18.2694	+	0.665809i	0.898980	+	0.0327623i
$414$		0			0
$415$	−8.28180	−	14.3445i	−0.406538	−	0.704144i
$416$		0			0
$417$	−17.4851	−	15.5523i	−0.856248	−	0.761601i
$418$		0			0
$419$	4.32141	−	7.48491i	0.211115	−	0.365662i	−0.740949	−	0.671561i	$-0.765624\pi$
$419$	4.32141	−	7.48491i	0.211115	−	0.365662i	0.952064	+	0.305900i	$0.0989573\pi$
$420$		0			0
$421$	18.5636	+	32.1531i	0.904735	+	1.56705i	0.821273	+	0.570536i	$0.193264\pi$
$421$	18.5636	+	32.1531i	0.904735	+	1.56705i	0.0834618	+	0.996511i	$0.473402\pi$
$422$		0			0
$423$	16.8083	−	12.5268i	0.817250	−	0.609075i
$424$		0			0
$425$	28.5636	−	49.4736i	1.38554	−	2.39982i
$426$		0			0
$427$	−7.10067	−	13.4036i	−0.343625	−	0.648644i
$428$		0			0
$429$	5.16071	+	4.59026i	0.249161	+	0.221620i
$430$		0			0
$431$	4.71015	−	8.15822i	0.226880	−	0.392967i	−0.730002	−	0.683445i	$-0.760481\pi$
$431$	4.71015	−	8.15822i	0.226880	−	0.392967i	0.956882	+	0.290478i	$0.0938142\pi$
$432$		0			0
$433$	−0.208771			−0.0100329			−0.00501645	−	0.999987i	$-0.501597\pi$
$433$	−0.208771			−0.0100329			−0.00501645	+	0.999987i	$0.501597\pi$
$434$		0			0
$435$	15.2694	−	5.06410i	0.732113	−	0.242805i
$436$		0			0
$437$	−2.79418	−	4.83967i	−0.133664	−	0.231513i
$438$		0			0
$439$	−4.98398	+	8.63250i	−0.237872	+	0.412007i	−0.960104	−	0.279645i	$-0.909783\pi$
$439$	−4.98398	+	8.63250i	−0.237872	+	0.412007i	0.722231	+	0.691652i	$0.243117\pi$
$440$		0			0
$441$	0.924016	+	20.9797i	0.0440007	+	0.999031i
$442$		0			0
$443$	−7.84981	+	13.5963i	−0.372956	+	0.645979i	−0.990019	−	0.140935i	$-0.954989\pi$
$443$	−7.84981	+	13.5963i	−0.372956	+	0.645979i	0.617063	+	0.786914i	$0.288322\pi$
$444$		0			0
$445$	−16.4196	−	28.4396i	−0.778364	−	1.34817i
$446$		0			0
$447$	0.116765	−	0.566231i	0.00552281	−	0.0267818i
$448$		0			0
$449$	33.6253			1.58688			0.793439	−	0.608650i	$-0.208288\pi$
$449$	33.6253			1.58688			0.793439	+	0.608650i	$0.208288\pi$
$450$		0			0
$451$	−3.03637	+	5.25915i	−0.142977	+	0.247644i
$452$		0			0
$453$	6.96472	−	33.7741i	0.327231	−	1.58685i
$454$		0			0
$455$	12.3702	+	23.3505i	0.579922	+	1.09469i
$456$		0			0
$457$	−16.3541	+	28.3262i	−0.765015	+	1.32504i	0.175224	+	0.984529i	$0.443935\pi$
$457$	−16.3541	+	28.3262i	−0.765015	+	1.32504i	−0.940239	+	0.340516i	$0.889398\pi$
$458$		0			0
$459$	14.4647	+	30.9572i	0.675155	+	1.44496i
$460$		0			0
$461$	−2.07165	−	3.58821i	−0.0964865	−	0.167120i	0.813742	−	0.581227i	$-0.197427\pi$
$461$	−2.07165	−	3.58821i	−0.0964865	−	0.167120i	−0.910228	+	0.414107i	$0.864094\pi$
$462$		0			0
$463$	8.34176	−	14.4484i	0.387675	−	0.671472i	−0.604462	−	0.796634i	$-0.706612\pi$
$463$	8.34176	−	14.4484i	0.387675	−	0.671472i	0.992136	+	0.125162i	$0.0399451\pi$
$464$		0			0
$465$	41.4250	−	13.7386i	1.92104	−	0.637113i
$466$		0			0
$467$	−14.9585	−	25.9089i	−0.692198	−	1.19892i	−0.971116	−	0.238608i	$-0.923309\pi$
$467$	−14.9585	−	25.9089i	−0.692198	−	1.19892i	0.278918	−	0.960315i	$-0.410024\pi$
$468$		0			0
$469$	−25.0247	−	0.911998i	−1.15553	−	0.0421121i
$470$		0			0
$471$	11.4469	−	3.79637i	0.527446	−	0.174927i
$472$		0			0
$473$	−0.00914304	−	0.0158362i	−0.000420397	−	0.000728149i
$474$		0			0
$475$	3.86033	+	6.68630i	0.177124	+	0.306788i
$476$		0			0
$477$	7.72184	−	5.75488i	0.353559	−	0.263498i
$478$		0			0
$479$	2.95930			0.135214			0.0676068	−	0.997712i	$-0.478464\pi$
$479$	2.95930			0.135214			0.0676068	+	0.997712i	$0.478464\pi$
$480$		0			0
$481$	7.49814			0.341886
$482$		0			0
$483$	20.8189	+	19.9221i	0.947291	+	0.906488i
$484$		0			0
$485$	−24.3745	−	42.2179i	−1.10679	−	1.91701i
$486$		0			0
$487$	14.0309	−	24.3022i	0.635800	−	1.10124i	−0.350546	−	0.936546i	$-0.614004\pi$
$487$	14.0309	−	24.3022i	0.635800	−	1.10124i	0.986345	−	0.164691i	$-0.0526628\pi$
$488$		0			0
$489$	−13.2738	+	4.40226i	−0.600263	+	0.199077i
$490$		0			0
$491$	−17.0734	+	29.5721i	−0.770513	+	1.33457i	0.166769	+	0.985996i	$0.446667\pi$
$491$	−17.0734	+	29.5721i	−0.770513	+	1.33457i	−0.937282	+	0.348572i	$0.886667\pi$
$492$		0			0
$493$	16.5091			0.743534
$494$		0			0
$495$	−15.0567	−	6.48564i	−0.676750	−	0.291508i
$496$		0			0
$497$	7.68037	−	12.2497i	0.344512	−	0.549472i
$498$		0			0
$499$	2.28071			0.102099			0.0510493	−	0.998696i	$-0.483743\pi$
$499$	2.28071			0.102099			0.0510493	+	0.998696i	$0.483743\pi$
$500$		0			0
$501$	25.2181	+	22.4306i	1.12666	+	1.00212i
$502$		0			0
$503$	−13.9890			−0.623739			−0.311869	−	0.950125i	$-0.600955\pi$
$503$	−13.9890			−0.623739			−0.311869	+	0.950125i	$0.600955\pi$
$504$		0			0
$505$	19.4400			0.865067
$506$		0			0
$507$	9.39052	−	3.11436i	0.417048	−	0.138314i
$508$		0			0
$509$	25.6181			1.13550			0.567750	−	0.823201i	$-0.307814\pi$
$509$	25.6181			1.13550			0.567750	+	0.823201i	$0.307814\pi$
$510$		0			0
$511$	14.9437	+	28.2084i	0.661069	+	1.24787i
$512$		0			0
$513$	−4.60074	−	0.398930i	−0.203128	−	0.0176132i
$514$		0			0
$515$	−6.16435			−0.271634
$516$		0			0
$517$	−5.16071	+	8.93861i	−0.226968	+	0.393119i
$518$		0			0
$519$	29.2014	+	25.9736i	1.28180	+	1.14011i
$520$		0			0
$521$	−20.9127	+	36.2219i	−0.916203	+	1.58691i	−0.111073	+	0.993812i	$0.535429\pi$
$521$	−20.9127	+	36.2219i	−0.916203	+	1.58691i	−0.805130	+	0.593099i	$0.797904\pi$
$522$		0			0
$523$	−7.88323	−	13.6542i	−0.344710	−	0.597055i	0.640591	−	0.767882i	$-0.278689\pi$
$523$	−7.88323	−	13.6542i	−0.344710	−	0.597055i	−0.985301	+	0.170827i	$0.945356\pi$
$524$		0			0
$525$	−28.7625	−	27.5236i	−1.25530	−	1.20123i
$526$		0			0
$527$	44.7883			1.95101
$528$		0			0
$529$	16.5388			0.719080
$530$		0			0
$531$	−2.41714	−	20.5879i	−0.104895	−	0.893440i
$532$		0			0
$533$	−5.54944	−	9.61192i	−0.240373	−	0.416338i
$534$		0			0
$535$	19.9134	+	34.4911i	0.860932	+	1.49118i
$536$		0			0
$537$	0.431988	+	0.384237i	0.0186417	+	0.0165811i
$538$		0			0
$539$	−4.50433	−	9.30701i	−0.194015	−	0.400881i
$540$		0			0
$541$	−21.0963	−	36.5399i	−0.907002	−	1.57097i	−0.818207	−	0.574924i	$-0.805031\pi$
$541$	−21.0963	−	36.5399i	−0.907002	−	1.57097i	−0.0887957	−	0.996050i	$-0.528302\pi$
$542$		0			0
$543$	8.13045	−	39.4271i	0.348911	−	1.69198i
$544$		0			0
$545$	−0.349814	+	0.605896i	−0.0149844	+	0.0259537i
$546$		0			0
$547$	−20.3356	−	35.2222i	−0.869486	−	1.50599i	−0.862522	−	0.506019i	$-0.831117\pi$
$547$	−20.3356	−	35.2222i	−0.869486	−	1.50599i	−0.00696400	−	0.999976i	$-0.502217\pi$
$548$		0			0
$549$	−13.7905	+	10.2777i	−0.588566	+	0.438643i
$550$		0			0
$551$	−1.11559	+	1.93227i	−0.0475259	+	0.0823173i
$552$		0			0
$553$	−14.1843	−	26.7750i	−0.603178	−	1.13859i
$554$		0			0
$555$	−16.8931	+	5.60258i	−0.717071	+	0.237816i
$556$		0			0
$557$	6.68794	−	11.5838i	0.283377	−	0.490823i	−0.688837	−	0.724916i	$-0.741879\pi$
$557$	6.68794	−	11.5838i	0.283377	−	0.490823i	0.972214	+	0.234093i	$0.0752119\pi$
$558$		0			0
$559$	0.0334206			0.00141354
$560$		0			0
$561$	−12.5709	−	11.1813i	−0.530743	−	0.472076i
$562$		0			0
$563$	−16.3807	−	28.3722i	−0.690364	−	1.19574i	−0.971719	−	0.236141i	$-0.924117\pi$
$563$	−16.3807	−	28.3722i	−0.690364	−	1.19574i	0.281355	−	0.959604i	$-0.409216\pi$
$564$		0			0
$565$	−25.0901	+	43.4574i	−1.05555	+	1.82827i
$566$		0			0
$567$	23.3497	−	4.66795i	0.980597	−	0.196035i
$568$		0			0
$569$	8.36398	−	14.4868i	0.350636	−	0.607320i	−0.635725	−	0.771916i	$-0.719299\pi$
$569$	8.36398	−	14.4868i	0.350636	−	0.607320i	0.986361	+	0.164596i	$0.0526321\pi$
$570$		0			0
$571$	−13.7367	−	23.7926i	−0.574863	−	0.995691i	−0.996057	−	0.0887207i	$-0.971722\pi$
$571$	−13.7367	−	23.7926i	−0.574863	−	0.995691i	0.421194	−	0.906971i	$-0.361611\pi$
$572$		0			0
$573$	21.1229	+	18.7880i	0.882421	+	0.784881i
$574$		0			0
$575$	−54.6253			−2.27803
$576$		0			0
$577$	1.41714	−	2.45455i	0.0589962	−	0.102184i	−0.835019	−	0.550221i	$-0.814543\pi$
$577$	1.41714	−	2.45455i	0.0589962	−	0.102184i	0.894015	+	0.448037i	$0.147877\pi$
$578$		0			0
$579$	23.5443	−	7.80848i	0.978470	−	0.324509i
$580$		0			0
$581$	−11.8374	−	0.431403i	−0.491100	−	0.0178976i
$582$		0			0
$583$	−2.37085	+	4.10644i	−0.0981908	+	0.170071i
$584$		0			0
$585$	24.0247	−	17.9050i	0.993298	−	0.740279i
$586$		0			0
$587$	2.34795	+	4.06678i	0.0969105	+	0.167854i	0.910404	−	0.413720i	$-0.135771\pi$
$587$	2.34795	+	4.06678i	0.0969105	+	0.167854i	−0.813494	+	0.581573i	$0.802437\pi$
$588$		0			0
$589$	−3.02654	+	5.24212i	−0.124706	+	0.215998i
$590$		0			0
$591$	0.847955	−	4.11200i	0.0348802	−	0.169145i
$592$		0			0
$593$	0.636024	+	1.10163i	0.0261184	+	0.0452383i	0.878789	−	0.477210i	$-0.158352\pi$
$593$	0.636024	+	1.10163i	0.0261184	+	0.0452383i	−0.852671	+	0.522449i	$0.825019\pi$
$594$		0			0
$595$	−30.1323	−	56.8792i	−1.23530	−	2.33182i
$596$		0			0
$597$	−7.90909	−	7.03484i	−0.323697	−	0.287917i
$598$		0			0
$599$	21.9258	+	37.9766i	0.895864	+	1.55168i	0.832732	+	0.553676i	$0.186776\pi$
$599$	21.9258	+	37.9766i	0.895864	+	1.55168i	0.0631320	+	0.998005i	$0.479891\pi$
$600$		0			0
$601$	−6.71634	−	11.6330i	−0.273965	−	0.474522i	0.695908	−	0.718131i	$-0.255002\pi$
$601$	−6.71634	−	11.6330i	−0.273965	−	0.474522i	−0.969874	+	0.243609i	$0.921669\pi$
$602$		0			0
$603$	3.31089	+	28.2005i	0.134830	+	1.14841i
$604$		0			0
$605$	−32.6240			−1.32635
$606$		0			0
$607$	4.58465			0.186085			0.0930425	−	0.995662i	$-0.470341\pi$
$607$	4.58465			0.186085			0.0930425	+	0.995662i	$0.470341\pi$
$608$		0			0
$609$	2.73236	−	11.1755i	0.110721	−	0.452853i
$610$		0			0
$611$	−9.43199	−	16.3367i	−0.381577	−	0.660911i
$612$		0			0
$613$	−11.0538	+	19.1457i	−0.446458	+	0.773287i	−0.998152	−	0.0607587i	$-0.980648\pi$
$613$	−11.0538	+	19.1457i	−0.446458	+	0.773287i	0.551695	+	0.834046i	$0.313981\pi$
$614$		0			0
$615$	19.6847	+	17.5088i	0.793764	+	0.706023i
$616$		0			0
$617$	6.00433	−	10.3998i	0.241725	−	0.418680i	−0.719481	−	0.694513i	$-0.755620\pi$
$617$	6.00433	−	10.3998i	0.241725	−	0.418680i	0.961206	+	0.275832i	$0.0889534\pi$
$618$		0			0
$619$	17.5636			0.705941			0.352970	−	0.935634i	$-0.385172\pi$
$619$	17.5636			0.705941			0.352970	+	0.935634i	$0.385172\pi$
$620$		0			0
$621$	18.7200	−	26.7789i	0.751207	−	1.07460i
$622$		0			0
$623$	−23.4691	−	0.855304i	−0.940268	−	0.0342670i
$624$		0			0
$625$	7.03204			0.281282
$626$		0			0
$627$	2.15816	−	0.715753i	0.0861885	−	0.0285844i
$628$		0			0
$629$	−18.2646			−0.728258
$630$		0			0
$631$	44.9381			1.78896			0.894479	−	0.447110i	$-0.147547\pi$
$631$	44.9381			1.78896			0.894479	+	0.447110i	$0.147547\pi$
$632$		0			0
$633$	14.8120	+	13.1747i	0.588724	+	0.523648i
$634$		0			0
$635$	10.5687			0.419406
$636$		0			0
$637$	18.8473	+	1.37556i	0.746756	+	0.0545018i
$638$		0			0
$639$	−15.0567	−	6.48564i	−0.595635	−	0.256568i
$640$		0			0
$641$	−28.9839			−1.14480			−0.572398	−	0.819976i	$-0.693987\pi$
$641$	−28.9839			−1.14480			−0.572398	+	0.819976i	$0.693987\pi$
$642$		0			0
$643$	−6.03087	+	10.4458i	−0.237834	+	0.411941i	−0.960093	−	0.279682i	$-0.909771\pi$
$643$	−6.03087	+	10.4458i	−0.237834	+	0.411941i	0.722258	+	0.691623i	$0.243104\pi$
$644$		0			0
$645$	−0.0752956	+	0.0249718i	−0.00296476	+	0.000983262i
$646$		0			0
$647$	−18.8825	+	32.7055i	−0.742349	+	1.28579i	0.209073	+	0.977900i	$0.432955\pi$
$647$	−18.8825	+	32.7055i	−0.742349	+	1.28579i	−0.951423	+	0.307887i	$0.900378\pi$
$648$		0			0
$649$	5.10322	+	8.83903i	0.200319	+	0.346962i
$650$		0			0
$651$	7.41273	−	30.3184i	0.290528	−	1.18827i
$652$		0			0
$653$	37.4079			1.46388			0.731942	−	0.681366i	$-0.238614\pi$
$653$	37.4079			1.46388			0.731942	+	0.681366i	$0.238614\pi$
$654$		0			0
$655$	−0.575984			−0.0225056
$656$		0			0
$657$	29.0228	−	21.6299i	1.13229	−	0.843864i
$658$		0			0
$659$	−14.9356	−	25.8693i	−0.581810	−	1.00772i	−0.995265	−	0.0971993i	$-0.969012\pi$
$659$	−14.9356	−	25.8693i	−0.581810	−	1.00772i	0.413455	−	0.910524i	$-0.364322\pi$
$660$		0			0
$661$	−2.80401	−	4.85669i	−0.109063	−	0.188904i	0.806328	−	0.591469i	$-0.201452\pi$
$661$	−2.80401	−	4.85669i	−0.109063	−	0.188904i	−0.915391	+	0.402566i	$0.868119\pi$
$662$		0			0
$663$	29.1854	−	9.67933i	1.13347	−	0.375914i
$664$		0			0
$665$	8.69344	+	0.316823i	0.337117	+	0.0122859i
$666$		0			0
$667$	−7.89307	−	13.6712i	−0.305621	−	0.529351i
$668$		0			0
$669$	11.8738	−	3.93795i	0.459068	−	0.152250i
$670$		0			0
$671$	4.23414	−	7.33375i	0.163457	−	0.283116i
$672$		0			0
$673$	−4.72253	−	8.17966i	−0.182040	−	0.315303i	0.760535	−	0.649297i	$-0.224937\pi$
$673$	−4.72253	−	8.17966i	−0.182040	−	0.315303i	−0.942575	+	0.333994i	$0.891603\pi$
$674$		0			0
$675$	−25.8628	+	36.9967i	−0.995460	+	1.42401i
$676$		0			0
$677$	−5.53087	+	9.57975i	−0.212569	+	0.368180i	−0.952518	−	0.304483i	$-0.901516\pi$
$677$	−5.53087	+	9.57975i	−0.212569	+	0.368180i	0.739949	+	0.672663i	$0.234850\pi$
$678$		0			0
$679$	−34.8392	−	1.26968i	−1.33701	−	0.0487258i
$680$		0			0
$681$	−4.77678	+	23.1641i	−0.183047	+	0.887651i
$682$		0			0
$683$	4.41961	−	7.65499i	0.169112	−	0.292910i	−0.768996	−	0.639253i	$-0.779243\pi$
$683$	4.41961	−	7.65499i	0.169112	−	0.292910i	0.938108	+	0.346343i	$0.112577\pi$
$684$		0			0
$685$	−12.6218			−0.482254
$686$		0			0
$687$	6.07784	−	29.4734i	0.231884	−	1.12448i
$688$		0			0
$689$	−4.33310	−	7.50516i	−0.165078	−	0.285924i
$690$		0			0
$691$	12.5309	−	21.7041i	0.476697	−	0.825663i	−0.522947	−	0.852365i	$-0.675167\pi$
$691$	12.5309	−	21.7041i	0.476697	−	0.825663i	0.999643	+	0.0267023i	$0.00850061\pi$
$692$		0			0
$693$	−9.64950	+	6.65899i	−0.366554	+	0.252954i
$694$		0			0
$695$	24.9920	−	43.2873i	0.947999	−	1.64198i
$696$		0			0
$697$	13.5178	+	23.4135i	0.512023	+	0.886850i
$698$		0			0
$699$	25.0581	−	8.31052i	0.947785	−	0.314333i
$700$		0			0
$701$	−43.4858			−1.64243			−0.821217	−	0.570616i	$-0.806705\pi$
$701$	−43.4858			−1.64243			−0.821217	+	0.570616i	$0.806705\pi$
$702$		0			0
$703$	1.23422	−	2.13773i	0.0465495	−	0.0806260i
$704$		0			0
$705$	33.4567	+	29.7585i	1.26005	+	1.12077i
$706$		0			0
$707$	7.38502	−	11.7786i	0.277742	−	0.442979i
$708$		0			0
$709$	11.3702	−	19.6937i	0.427016	−	0.739613i	−0.569591	−	0.821928i	$-0.692898\pi$
$709$	11.3702	−	19.6937i	0.427016	−	0.739613i	0.996606	+	0.0823158i	$0.0262316\pi$
$710$		0			0
$711$	−27.5480	+	20.5308i	−1.03313	+	0.769965i
$712$		0			0
$713$	−21.4134	−	37.0891i	−0.801939	−	1.38900i
$714$		0			0
$715$	−7.37636	+	12.7762i	−0.275860	+	0.477804i
$716$		0			0
$717$	24.5254	+	21.8144i	0.915917	+	0.814674i
$718$		0			0
$719$	−6.06182	−	10.4994i	−0.226068	−	0.391561i	0.730571	−	0.682836i	$-0.239254\pi$
$719$	−6.06182	−	10.4994i	−0.226068	−	0.391561i	−0.956639	+	0.291275i	$0.905920\pi$
$720$		0			0
$721$	−2.34176	+	3.73495i	−0.0872119	+	0.139097i
$722$		0			0
$723$	−8.57234	+	41.5700i	−0.318809	+	1.54600i
$724$		0			0
$725$	10.9048	+	18.8876i	0.404993	+	0.701468i
$726$		0			0
$727$	−23.0908	−	39.9945i	−0.856392	−	1.48331i	−0.875348	−	0.483494i	$-0.839368\pi$
$727$	−23.0908	−	39.9945i	−0.856392	−	1.48331i	0.0189562	−	0.999820i	$-0.493966\pi$
$728$		0			0
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$		0			0
$731$	−0.0814088			−0.00301101
$732$		0			0
$733$	−36.0297			−1.33079			−0.665394	−	0.746493i	$-0.731736\pi$
$733$	−36.0297			−1.33079			−0.665394	+	0.746493i	$0.731736\pi$
$734$		0			0
$735$	−43.4901	+	10.9835i	−1.60416	+	0.405133i
$736$		0			0
$737$	−6.99017	−	12.1073i	−0.257486	−	0.445979i
$738$		0			0
$739$	−23.2119	+	40.2042i	−0.853865	+	1.47894i	0.0238296	+	0.999716i	$0.492414\pi$
$739$	−23.2119	+	40.2042i	−0.853865	+	1.47894i	−0.877694	+	0.479221i	$0.840919\pi$
$740$		0			0
$741$	−0.839294	+	4.07000i	−0.0308322	+	0.149515i
$742$		0			0
$743$	−0.598884	+	1.03730i	−0.0219709	+	0.0380548i	−0.876802	−	0.480852i	$-0.840327\pi$
$743$	−0.598884	+	1.03730i	−0.0219709	+	0.0380548i	0.854831	+	0.518907i	$0.173661\pi$
$744$		0			0
$745$	1.23491			0.0452435
$746$		0			0
$747$	1.56615	+	13.3397i	0.0573025	+	0.488073i
$748$		0			0
$749$	28.4629	+	1.03730i	1.04001	+	0.0379021i
$750$		0			0
$751$	−48.1199			−1.75592			−0.877961	−	0.478733i	$-0.841096\pi$
$751$	−48.1199			−1.75592			−0.877961	+	0.478733i	$0.841096\pi$
$752$		0			0
$753$	4.24102	−	20.5660i	0.154551	−	0.749468i
$754$		0			0
$755$	73.6588			2.68072
$756$		0			0
$757$	49.6006			1.80276			0.901382	−	0.433025i	$-0.142554\pi$
$757$	49.6006			1.80276			0.901382	+	0.433025i	$0.142554\pi$
$758$		0			0
$759$	−3.24907	+	15.7558i	−0.117934	+	0.571898i
$760$		0			0
$761$	−37.5402			−1.36083			−0.680416	−	0.732826i	$-0.738201\pi$
$761$	−37.5402			−1.36083			−0.680416	+	0.732826i	$0.738201\pi$
$762$		0			0
$763$	0.234219	+	0.442124i	0.00847931	+	0.0160060i
$764$		0			0
$765$	−58.5214	+	43.6144i	−2.11584	+	1.57688i
$766$		0			0
$767$	−18.6538			−0.673551
$768$		0			0
$769$	−13.4592	+	23.3121i	−0.485352	+	0.840654i	−0.999858	−	0.0168324i	$-0.994642\pi$
$769$	−13.4592	+	23.3121i	−0.485352	+	0.840654i	0.514506	+	0.857486i	$0.327975\pi$
$770$		0			0
$771$	−2.87154	+	13.9250i	−0.103416	+	0.501497i
$772$		0			0
$773$	25.1130	−	43.4971i	0.903254	−	1.56448i	0.0800089	−	0.996794i	$-0.474505\pi$
$773$	25.1130	−	43.4971i	0.903254	−	1.56448i	0.823245	−	0.567687i	$-0.192162\pi$
$774$		0			0
$775$	29.5840	+	51.2409i	1.06269	+	1.84063i
$776$		0			0
$777$	−3.02290	+	12.3638i	−0.108446	+	0.443549i
$778$		0			0
$779$	−3.65383			−0.130912
$780$		0			0
$781$	8.07194			0.288837
$782$		0			0
$783$	−12.9963	−	1.12691i	−0.464449	−	0.0402723i
$784$		0			0
$785$	12.8800	+	22.3088i	0.459707	+	0.796236i
$786$		0			0
$787$	−0.829462	−	1.43667i	−0.0295671	−	0.0512118i	0.850863	−	0.525387i	$-0.176080\pi$
$787$	−0.829462	−	1.43667i	−0.0295671	−	0.0512118i	−0.880430	+	0.474176i	$0.842746\pi$
$788$		0			0
$789$	1.87017	−	9.06902i	0.0665797	−	0.322866i
$790$		0			0
$791$	16.7992	+	31.7110i	0.597311	+	1.12751i
$792$		0			0
$793$	7.73855	+	13.4036i	0.274804	+	0.475974i
$794$		0			0
$795$	15.3702	+	13.6712i	0.545124	+	0.484867i
$796$		0			0
$797$	−15.3702	+	26.6219i	−0.544439	+	0.942996i	0.454203	+	0.890898i	$0.349924\pi$
$797$	−15.3702	+	26.6219i	−0.544439	+	0.942996i	−0.998642	+	0.0520981i	$0.983409\pi$
$798$		0			0
$799$	22.9752	+	39.7943i	0.812806	+	1.40782i
$800$		0			0
$801$	3.10507	+	26.4474i	0.109712	+	0.934473i
$802$		0			0
$803$	−8.91095	+	15.4342i	−0.314461	+	0.544662i
$804$		0			0
$805$	−32.6952	+	52.1466i	−1.15236	+	1.83793i
$806$		0			0
$807$	−23.9222	−	21.2779i	−0.842100	−	0.749016i
$808$		0			0
$809$	−1.44251	+	2.49850i	−0.0507159	+	0.0878425i	−0.890269	−	0.455435i	$-0.849484\pi$
$809$	−1.44251	+	2.49850i	−0.0507159	+	0.0878425i	0.839553	+	0.543278i	$0.182817\pi$
$810$		0			0
$811$	−28.5461			−1.00239			−0.501195	−	0.865334i	$-0.667106\pi$
$811$	−28.5461			−1.00239			−0.501195	+	0.865334i	$0.667106\pi$
$812$		0			0
$813$	12.0913	−	4.01008i	0.424061	−	0.140640i
$814$		0			0
$815$	−14.9356	−	25.8693i	−0.523172	−	0.906161i
$816$		0			0
$817$	0.00550115	−	0.00952827i	0.000192461	−	0.000333352i
$818$		0			0
$819$	−1.72184	−	21.3583i	−0.0601659	−	0.746321i
$820$		0			0
$821$	−3.98329	+	6.89926i	−0.139018	+	0.240786i	−0.927125	−	0.374752i	$-0.877728\pi$
$821$	−3.98329	+	6.89926i	−0.139018	+	0.240786i	0.788107	+	0.615538i	$0.211061\pi$
$822$		0			0
$823$	20.2731	+	35.1140i	0.706675	+	1.22400i	0.966084	+	0.258229i	$0.0831388\pi$
$823$	20.2731	+	35.1140i	0.706675	+	1.22400i	−0.259409	+	0.965768i	$0.583528\pi$
$824$		0			0
$825$	4.48879	−	21.7676i	0.156280	−	0.757849i
$826$		0			0
$827$	−1.22115			−0.0424636			−0.0212318	−	0.999775i	$-0.506759\pi$
$827$	−1.22115			−0.0424636			−0.0212318	+	0.999775i	$0.506759\pi$
$828$		0			0
$829$	−7.07530	+	12.2548i	−0.245735	+	0.425626i	−0.962338	−	0.271856i	$-0.912363\pi$
$829$	−7.07530	+	12.2548i	−0.245735	+	0.425626i	0.716603	+	0.697481i	$0.245696\pi$
$830$		0			0
$831$	−3.18292	+	15.4350i	−0.110414	+	0.535433i
$832$		0			0
$833$	−45.9098	−	3.35071i	−1.59068	−	0.116095i
$834$		0			0
$835$	−36.0450	+	62.4318i	−1.24739	+	2.16054i
$836$		0			0
$837$	−35.2581	−	3.05723i	−1.21870	−	0.105673i
$838$		0			0
$839$	−1.19599	−	2.07151i	−0.0412900	−	0.0715164i	0.844642	−	0.535332i	$-0.179813\pi$
$839$	−1.19599	−	2.07151i	−0.0412900	−	0.0715164i	−0.885932	+	0.463815i	$0.846480\pi$
$840$		0			0
$841$	11.3486	−	19.6564i	0.391333	−	0.677808i
$842$		0			0
$843$	19.7422	−	6.54750i	0.679957	−	0.225508i
$844$		0			0
$845$	10.5662	+	18.3011i	0.363487	+	0.629577i
$846$		0			0
$847$	−12.3935	+	19.7667i	−0.425845	+	0.679193i
$848$		0			0
$849$	16.1817	−	5.36667i	0.555356	−	0.184184i
$850$		0			0
$851$	8.73236	+	15.1249i	0.299341	+	0.518475i
$852$		0			0
$853$	−8.33998	−	14.4453i	−0.285556	−	0.494597i	0.687188	−	0.726479i	$-0.258845\pi$
$853$	−8.33998	−	14.4453i	−0.285556	−	0.494597i	−0.972744	+	0.231883i	$0.925511\pi$
$854$		0			0
$855$	−1.15019	−	9.79669i	−0.0393355	−	0.335040i
$856$		0			0
$857$	−13.8516			−0.473162			−0.236581	−	0.971612i	$-0.576027\pi$
$857$	−13.8516			−0.473162			−0.236581	+	0.971612i	$0.576027\pi$
$858$		0			0
$859$	−48.4944			−1.65461			−0.827304	−	0.561754i	$-0.810127\pi$
$859$	−48.4944			−1.65461			−0.827304	+	0.561754i	$0.810127\pi$
$860$		0			0
$861$	18.0865	−	5.27548i	0.616386	−	0.179788i
$862$		0			0
$863$	−2.96541	−	5.13624i	−0.100944	−	0.174840i	0.811130	−	0.584866i	$-0.198853\pi$
$863$	−2.96541	−	5.13624i	−0.100944	−	0.174840i	−0.912074	+	0.410026i	$0.865520\pi$
$864$		0			0
$865$	−41.7385	+	72.2932i	−1.41915	+	2.45804i
$866$		0			0
$867$	−43.1443	+	14.3088i	−1.46526	+	0.485953i
$868$		0			0
$869$	8.45813	−	14.6499i	0.286922	−	0.496964i
$870$		0			0
$871$	25.5512			0.865770
$872$		0			0
$873$	4.60940	+	39.2605i	0.156005	+	1.32877i
$874$		0			0
$875$	19.1723	−	30.5785i	0.648143	−	1.03374i
$876$		0			0
$877$	3.92944			0.132688			0.0663439	−	0.997797i	$-0.478867\pi$
$877$	3.92944			0.132688			0.0663439	+	0.997797i	$0.478867\pi$
$878$		0			0
$879$	−27.7218	−	24.6575i	−0.935032	−	0.831676i
$880$		0			0
$881$	37.6552			1.26864			0.634318	−	0.773072i	$-0.281281\pi$
$881$	37.6552			1.26864			0.634318	+	0.773072i	$0.281281\pi$
$882$		0			0
$883$	53.2334			1.79145			0.895723	−	0.444613i	$-0.146659\pi$
$883$	53.2334			1.79145			0.895723	+	0.444613i	$0.146659\pi$
$884$		0			0
$885$	42.0265	−	13.9381i	1.41270	−	0.468523i
$886$		0			0
$887$	36.9876			1.24192			0.620961	−	0.783841i	$-0.286742\pi$
$887$	36.9876			1.24192			0.620961	+	0.783841i	$0.286742\pi$
$888$		0			0
$889$	4.01493	−	6.40353i	0.134656	−	0.214768i
$890$		0			0
$891$	9.13279	+	9.66022i	0.305960	+	0.323630i
$892$		0			0
$893$	−6.21015			−0.207815
$894$		0			0
$895$	−0.617454	+	1.06946i	−0.0206392	+	0.0357482i
$896$		0			0
$897$	−21.9691	−	19.5407i	−0.733525	−	0.652443i
$898$		0			0
$899$	−8.54944	+	14.8081i	−0.285140	+	0.493877i
$900$		0			0
$901$	10.5549	+	18.2817i	0.351636	+	0.609052i
$902$		0			0
$903$	−0.0134736	+	0.0551078i	−0.000448374	+	0.00183387i
$904$		0			0
$905$	85.9875			2.85832
$906$		0			0
$907$	39.0159			1.29550			0.647752	−	0.761852i	$-0.275709\pi$
$907$	39.0159			1.29550			0.647752	+	0.761852i	$0.275709\pi$
$908$		0			0
$909$	−14.4777	−	6.23623i	−0.480195	−	0.206843i
$910$		0			0
$911$	12.8090	+	22.1859i	0.424382	+	0.735052i	0.996363	−	0.0852158i	$-0.0271580\pi$
$911$	12.8090	+	22.1859i	0.424382	+	0.735052i	−0.571980	+	0.820267i	$0.693825\pi$
$912$		0			0
$913$	−3.30656	−	5.72713i	−0.109431	−	0.189540i
$914$		0			0
$915$	−27.4498	−	24.4156i	−0.907462	−	0.807154i
$916$		0			0
$917$	−0.218810	+	0.348986i	−0.00722574	+	0.0115245i
$918$		0			0
$919$	−10.3367	−	17.9038i	−0.340978	−	0.590591i	0.643637	−	0.765331i	$-0.277425\pi$
$919$	−10.3367	−	17.9038i	−0.340978	−	0.590591i	−0.984615	+	0.174740i	$0.944091\pi$
$920$		0			0
$921$	1.98948	−	9.64761i	0.0655556	−	0.317900i
$922$		0			0
$923$	−7.37636	+	12.7762i	−0.242796	+	0.420535i
$924$		0			0
$925$	−12.0643	−	20.8960i	−0.396672	−	0.687055i
$926$		0			0
$927$	4.59084	+	1.97749i	0.150783	+	0.0649492i
$928$		0			0
$929$	1.87017	−	3.23922i	0.0613582	−	0.106275i	−0.833715	−	0.552196i	$-0.813790\pi$
$929$	1.87017	−	3.23922i	0.0613582	−	0.106275i	0.895073	+	0.445920i	$0.147123\pi$
$930$		0			0
$931$	3.49450	−	5.14696i	0.114528	−	0.168685i
$932$		0			0
$933$	−19.2687	+	6.39047i	−0.630830	+	0.209215i
$934$		0			0
$935$	17.9680	−	31.1214i	0.587615	−	1.01778i
$936$		0			0
$937$	−27.1345			−0.886445			−0.443223	−	0.896412i	$-0.646165\pi$
$937$	−27.1345			−0.886445			−0.443223	+	0.896412i	$0.646165\pi$
$938$		0			0
$939$	−34.6501	−	30.8200i	−1.13076	−	1.00577i
$940$		0			0
$941$	−3.16435	−	5.48081i	−0.103155	−	0.178669i	0.809828	−	0.586667i	$-0.199560\pi$
$941$	−3.16435	−	5.48081i	−0.103155	−	0.178669i	−0.912983	+	0.407998i	$0.866227\pi$
$942$		0			0
$943$	12.9258	−	22.3881i	0.420922	−	0.729058i
$944$		0			0
$945$	19.8381	+	46.8331i	0.645334	+	1.52348i
$946$		0			0
$947$	15.6396	−	27.0886i	0.508218	−	0.880260i	−0.491736	−	0.870744i	$-0.663638\pi$
$947$	15.6396	−	27.0886i	0.508218	−	0.880260i	0.999955	−	0.00951587i	$-0.00302904\pi$
$948$		0			0
$949$	−16.2861	−	28.2084i	−0.528670	−	0.915684i
$950$		0			0
$951$	2.46217	+	2.19001i	0.0798414	+	0.0710160i
$952$		0			0
$953$	4.28937			0.138946			0.0694732	−	0.997584i	$-0.477868\pi$
$953$	4.28937			0.138946			0.0694732	+	0.997584i	$0.477868\pi$
$954$		0			0
$955$	−30.1916	+	52.2933i	−0.976977	+	1.69217i
$956$		0			0
$957$	6.09641	−	2.02187i	0.197069	−	0.0653579i
$958$		0			0
$959$	−4.79487	+	7.64749i	−0.154834	+	0.246950i
$960$		0			0
$961$	−7.69413	+	13.3266i	−0.248198	+	0.429891i
$962$		0			0
$963$	−3.76578	−	32.0750i	−0.121351	−	1.03360i
$964$		0			0
$965$	26.4920	+	45.8854i	0.852806	+	1.47710i
$966$		0			0
$967$	7.59201	−	13.1497i	0.244142	−	0.422867i	−0.717748	−	0.696303i	$-0.754827\pi$
$967$	7.59201	−	13.1497i	0.244142	−	0.422867i	0.961890	+	0.273436i	$0.0881602\pi$
$968$		0			0
$969$	2.04442	−	9.91405i	0.0656763	−	0.318485i
$970$		0			0
$971$	−1.62364	−	2.81223i	−0.0521052	−	0.0902489i	0.838796	−	0.544445i	$-0.183260\pi$
$971$	−1.62364	−	2.81223i	−0.0521052	−	0.0902489i	−0.890902	+	0.454196i	$0.849926\pi$
$972$		0			0
$973$	−16.7335	−	31.5869i	−0.536450	−	1.01263i
$974$		0			0
$975$	30.3516	+	26.9966i	0.972029	+	0.864584i
$976$		0			0
$977$	−7.77197	−	13.4614i	−0.248647	−	0.430670i	0.714503	−	0.699632i	$-0.246653\pi$
$977$	−7.77197	−	13.4614i	−0.248647	−	0.430670i	−0.963151	+	0.268962i	$0.913319\pi$
$978$		0			0
$979$	−6.55563	−	11.3547i	−0.209519	−	0.362897i
$980$		0			0
$981$	0.454888	−	0.339016i	0.0145235	−	0.0108240i
$982$		0			0
$983$	−12.3832			−0.394961			−0.197481	−	0.980307i	$-0.563276\pi$
$983$	−12.3832			−0.394961			−0.197481	+	0.980307i	$0.563276\pi$
$984$		0			0
$985$	8.96796			0.285743
$986$		0			0
$987$	30.7403	−	8.96636i	0.978476	−	0.285402i
$988$		0			0
$989$	0.0389218	+	0.0674145i	0.00123764	+	0.00214366i
$990$		0			0
$991$	3.32760	−	5.76358i	0.105705	−	0.183086i	−0.808321	−	0.588742i	$-0.799623\pi$
$991$	3.32760	−	5.76358i	0.105705	−	0.183086i	0.914026	+	0.405656i	$0.132957\pi$
$992$		0			0
$993$	−7.20513	−	6.40869i	−0.228648	−	0.203374i
$994$		0			0
$995$	11.3047	−	19.5803i	0.358383	−	0.620738i
$996$		0			0
$997$	4.80208			0.152083			0.0760417	−	0.997105i	$-0.475772\pi$
$997$	4.80208			0.152083			0.0760417	+	0.997105i	$0.475772\pi$
$998$		0			0
$999$	14.3782	+	1.24673i	0.454907	+	0.0394449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.g.193.3		6
3.2	odd	2		3024.2.t.g.1873.1		6
4.3	odd	2		126.2.h.c.67.1	yes	6
7.2	even	3		1008.2.q.h.625.3		6
9.2	odd	6		3024.2.q.h.2881.3		6
9.7	even	3		1008.2.q.h.529.3		6
12.11	even	2		378.2.h.d.361.1		6
21.2	odd	6		3024.2.q.h.2305.3		6
28.3	even	6		882.2.f.m.589.1		6
28.11	odd	6		882.2.f.l.589.3		6
28.19	even	6		882.2.e.p.373.3		6
28.23	odd	6		126.2.e.d.121.1	yes	6
28.27	even	2		882.2.h.o.67.3		6
36.7	odd	6		126.2.e.d.25.1	✓	6
36.11	even	6		378.2.e.c.235.3		6
36.23	even	6		1134.2.g.n.487.3		6
36.31	odd	6		1134.2.g.k.487.1		6
63.2	odd	6		3024.2.t.g.289.1		6
63.16	even	3	inner	1008.2.t.g.961.3		6
84.11	even	6		2646.2.f.o.1765.3		6
84.23	even	6		378.2.e.c.37.3		6
84.47	odd	6		2646.2.e.o.1549.1		6
84.59	odd	6		2646.2.f.n.1765.1		6
84.83	odd	2		2646.2.h.p.361.3		6
252.11	even	6		2646.2.f.o.883.3		6
252.23	even	6		1134.2.g.n.163.3		6
252.31	even	6		7938.2.a.by.1.1		3
252.47	odd	6		2646.2.h.p.667.3		6
252.59	odd	6		7938.2.a.bx.1.3		3
252.67	odd	6		7938.2.a.cb.1.3		3
252.79	odd	6		126.2.h.c.79.1	yes	6
252.83	odd	6		2646.2.e.o.2125.1		6
252.95	even	6		7938.2.a.bu.1.1		3
252.115	even	6		882.2.f.m.295.1		6
252.151	odd	6		882.2.f.l.295.3		6
252.187	even	6		882.2.h.o.79.3		6
252.191	even	6		378.2.h.d.289.1		6
252.223	even	6		882.2.e.p.655.3		6
252.227	odd	6		2646.2.f.n.883.1		6
252.247	odd	6		1134.2.g.k.163.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	36.7	odd	6
126.2.e.d.121.1	yes	6	28.23	odd	6
126.2.h.c.67.1	yes	6	4.3	odd	2
126.2.h.c.79.1	yes	6	252.79	odd	6
378.2.e.c.37.3		6	84.23	even	6
378.2.e.c.235.3		6	36.11	even	6
378.2.h.d.289.1		6	252.191	even	6
378.2.h.d.361.1		6	12.11	even	2
882.2.e.p.373.3		6	28.19	even	6
882.2.e.p.655.3		6	252.223	even	6
882.2.f.l.295.3		6	252.151	odd	6
882.2.f.l.589.3		6	28.11	odd	6
882.2.f.m.295.1		6	252.115	even	6
882.2.f.m.589.1		6	28.3	even	6
882.2.h.o.67.3		6	28.27	even	2
882.2.h.o.79.3		6	252.187	even	6
1008.2.q.h.529.3		6	9.7	even	3
1008.2.q.h.625.3		6	7.2	even	3
1008.2.t.g.193.3		6	1.1	even	1	trivial
1008.2.t.g.961.3		6	63.16	even	3	inner
1134.2.g.k.163.1		6	252.247	odd	6
1134.2.g.k.487.1		6	36.31	odd	6
1134.2.g.n.163.3		6	252.23	even	6
1134.2.g.n.487.3		6	36.23	even	6
2646.2.e.o.1549.1		6	84.47	odd	6
2646.2.e.o.2125.1		6	252.83	odd	6
2646.2.f.n.883.1		6	252.227	odd	6
2646.2.f.n.1765.1		6	84.59	odd	6
2646.2.f.o.883.3		6	252.11	even	6
2646.2.f.o.1765.3		6	84.11	even	6
2646.2.h.p.361.3		6	84.83	odd	2
2646.2.h.p.667.3		6	252.47	odd	6
3024.2.q.h.2305.3		6	21.2	odd	6
3024.2.q.h.2881.3		6	9.2	odd	6
3024.2.t.g.289.1		6	63.2	odd	6
3024.2.t.g.1873.1		6	3.2	odd	2
7938.2.a.bu.1.1		3	252.95	even	6
7938.2.a.bx.1.3		3	252.59	odd	6
7938.2.a.by.1.1		3	252.31	even	6
7938.2.a.cb.1.3		3	252.67	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.349814 - 1.69636i) q^{3} +3.69963 q^{5} +(1.40545 - 2.24159i) q^{7} +(-2.75526 - 1.18682i) q^{9} +1.47710 q^{11} +(-1.34981 + 2.33795i) q^{13} +(1.29418 - 6.27589i) q^{15} +(3.28799 - 5.69497i) q^{17} +(0.444368 + 0.769668i) q^{19} +(-3.31089 - 3.16828i) q^{21} -6.28799 q^{23} +8.68725 q^{25} +(-2.97710 + 4.25874i) q^{27} +(1.25526 + 2.17417i) q^{29} +(3.40545 + 5.89841i) q^{31} +(0.516710 - 2.50569i) q^{33} +(5.19963 - 8.29305i) q^{35} +(-1.38874 - 2.40536i) q^{37} +(3.49381 + 3.10761i) q^{39} +(-2.05563 + 3.56046i) q^{41} +(-0.00618986 - 0.0107211i) q^{43} +(-10.1934 - 4.39079i) q^{45} +(-3.49381 + 6.05146i) q^{47} +(-3.04944 - 6.30087i) q^{49} +(-8.51052 - 7.56979i) q^{51} +(-1.60507 + 2.78007i) q^{53} +5.46472 q^{55} +(1.46108 - 0.484566i) q^{57} +(3.45489 + 5.98404i) q^{59} +(2.86652 - 4.96497i) q^{61} +(-6.53273 + 4.50815i) q^{63} +(-4.99381 + 8.64953i) q^{65} +(-4.73236 - 8.19669i) q^{67} +(-2.19963 + 10.6667i) q^{69} +5.46472 q^{71} +(-6.03273 + 10.4490i) q^{73} +(3.03892 - 14.7367i) q^{75} +(2.07598 - 3.31105i) q^{77} +(5.72617 - 9.91802i) q^{79} +(6.18292 + 6.53999i) q^{81} +(-2.23855 - 3.87728i) q^{83} +(12.1643 - 21.0693i) q^{85} +(4.12729 - 1.36881i) q^{87} +(-4.43818 - 7.68715i) q^{89} +(3.34362 + 6.31159i) q^{91} +(11.1971 - 3.71351i) q^{93} +(1.64400 + 2.84748i) q^{95} +(-6.58836 - 11.4114i) q^{97} +(-4.06979 - 1.75305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} + 4 q^{25} - 7 q^{27} - 5 q^{29} + 14 q^{31} - 4 q^{33} + 19 q^{35} - 9 q^{37}+ \cdots + 41 q^{99}+O(q^{100}) \) 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 7 * q^21 - 14 * q^23 + 4 * q^25 - 7 * q^27 - 5 * q^29 + 14 * q^31 - 4 * q^33 + 19 * q^35 - 9 * q^37 + 3 * q^39 - 12 * q^41 - 18 * q^43 - 31 * q^45 - 3 * q^47 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 - 4 * q^59 + 4 * q^61 - 28 * q^63 - 12 * q^65 - 5 * q^67 - q^69 - 14 * q^71 - 25 * q^73 + 25 * q^75 - 35 * q^77 - 7 * q^79 + 32 * q^81 - 8 * q^83 + 14 * q^85 + 20 * q^87 - 9 * q^89 - 4 * q^91 - 3 * q^93 - 2 * q^95 - 28 * q^97 + 41 * q^99

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