LMFDB - Embedded newform 1008.2.t.g.961.3

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)

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")

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);

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			961.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1008.961
Dual form			1008.2.t.g.193.3

$q$-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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

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

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	0.615862	−	0.787854i	$-0.288808\pi$
$13$	−1.34981	−	2.33795i	−0.374371	−	0.648430i	−0.990233	+	0.139425i	$0.955475\pi$
$14$		0			0
$15$	1.29418	+	6.27589i	0.334156	+	1.62043i
$16$		0			0
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	0.921268	+	0.388927i	$0.127154\pi$
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	−0.123813	+	0.992306i	$0.539512\pi$
$18$		0			0
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	−0.810541	−	0.585682i	$-0.800827\pi$
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	0.912486	+	0.409108i	$0.134160\pi$
$20$		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	−0.725622	−	0.688094i	$-0.758448\pi$
$29$	1.25526	−	2.17417i	0.233096	−	0.403734i	0.958718	+	0.284360i	$0.0917810\pi$
$30$		0			0
$31$	3.40545	−	5.89841i	0.611636	−	1.05938i	−0.379329	−	0.925262i	$-0.623845\pi$
$31$	3.40545	−	5.89841i	0.611636	−	1.05938i	0.990965	−	0.134123i	$-0.0428217\pi$
$32$		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	−0.957306	−	0.289075i	$-0.906652\pi$
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	0.729000	+	0.684514i	$0.239986\pi$
$38$		0			0
$39$	3.49381	−	3.10761i	0.559457	−	0.497617i
$40$		0			0
$41$	−2.05563	−	3.56046i	−0.321036	−	0.556050i	0.659666	−	0.751559i	$-0.270698\pi$
$41$	−2.05563	−	3.56046i	−0.321036	−	0.556050i	−0.980702	+	0.195508i	$0.937364\pi$
$42$		0			0
$43$	−0.00618986	+	0.0107211i	−0.000943944	+	0.00163496i	−0.866497	−	0.499182i	$-0.833634\pi$
$43$	−0.00618986	+	0.0107211i	−0.000943944	+	0.00163496i	0.865553	+	0.500817i	$0.166967\pi$
$44$		0			0
$45$	−10.1934	+	4.39079i	−1.51955	+	0.654541i
$46$		0			0
$47$	−3.49381	−	6.05146i	−0.509625	−	0.882696i	−0.999938	−	0.0111494i	$-0.996451\pi$
$47$	−3.49381	−	6.05146i	−0.509625	−	0.882696i	0.490313	−	0.871546i	$-0.336882\pi$
$48$		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	0.734478	−	0.678632i	$-0.237427\pi$
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	−0.954952	+	0.296760i	$0.904094\pi$
$54$		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	−0.548584	−	0.836096i	$-0.684833\pi$
$59$	3.45489	−	5.98404i	0.449788	−	0.779056i	0.998372	+	0.0570397i	$0.0181661\pi$
$60$		0			0
$61$	2.86652	+	4.96497i	0.367021	+	0.635699i	0.989098	−	0.147257i	$-0.0470444\pi$
$61$	2.86652	+	4.96497i	0.367021	+	0.635699i	−0.622077	+	0.782956i	$0.713711\pi$
$62$		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	0.417542	+	0.908658i	$0.362892\pi$
$67$	−4.73236	+	8.19669i	−0.578150	+	1.00138i	−0.995692	+	0.0927271i	$0.970442\pi$
$68$		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	−0.966301	−	0.257414i	$-0.917130\pi$
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	0.260223	−	0.965548i	$-0.416204\pi$
$74$		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	0.984475	+	0.175522i	$0.0561614\pi$
$79$	5.72617	+	9.91802i	0.644244	+	1.11586i	−0.340231	+	0.940342i	$0.610505\pi$
$80$		0			0
$81$	6.18292	−	6.53999i	0.686991	−	0.726666i
$82$		0			0
$83$	−2.23855	+	3.87728i	−0.245713	+	0.425587i	−0.962332	−	0.271878i	$-0.912355\pi$
$83$	−2.23855	+	3.87728i	−0.245713	+	0.425587i	0.716619	+	0.697465i	$0.245689\pi$
$84$		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	−0.999429	−	0.0337963i	$-0.989240\pi$
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	0.528983	+	0.848633i	$0.322574\pi$
$90$		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	0.309252	+	0.950980i	$0.399921\pi$
$97$	−6.58836	+	11.4114i	−0.668947	+	1.15865i	−0.978199	+	0.207670i	$0.933412\pi$
$98$		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	−0.479370	−	0.877613i	$-0.659135\pi$
$107$	5.38255	−	9.32284i	0.520350	−	0.901273i	0.999720	−	0.0236602i	$-0.00753198\pi$
$108$		0			0
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	0.861462	−	0.507823i	$-0.169550\pi$
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	−0.870518	+	0.492136i	$0.836216\pi$
$110$		0			0
$111$	−4.56615	−	1.51436i	−0.433400	−	0.143737i
$112$		0			0
$113$	−6.78180	−	11.7464i	−0.637978	−	1.10501i	−0.985876	−	0.167478i	$-0.946438\pi$
$113$	−6.78180	−	11.7464i	−0.637978	−	1.10501i	0.347897	−	0.937533i	$-0.386896\pi$
$114$		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	0.996259	+	0.0864229i	$0.0275436\pi$
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	−0.423285	+	0.905997i	$0.639123\pi$
$140$		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	−0.693001	−	0.720936i	$-0.743712\pi$
$157$	3.48143	−	6.03001i	0.277848	−	0.481248i	0.970850	+	0.239689i	$0.0770454\pi$
$158$		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	−0.979693	−	0.200502i	$-0.935743\pi$
$163$	−4.03706	+	6.99240i	−0.316207	+	0.547687i	0.663486	+	0.748189i	$0.269076\pi$
$164$		0			0
$165$	1.91164	+	9.27012i	0.148821	+	0.721678i
$166$		0			0
$167$	−9.74288	−	16.8752i	−0.753927	−	1.30584i	−0.945906	−	0.324440i	$-0.894824\pi$
$167$	−9.74288	−	16.8752i	−0.753927	−	1.30584i	0.191979	−	0.981399i	$-0.438509\pi$
$168$		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	−0.874080	−	0.485782i	$-0.838535\pi$
$173$	−11.2818	−	19.5407i	−0.857740	−	1.48565i	0.0163405	−	0.999866i	$-0.494798\pi$
$174$		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	0.859721	−	0.510764i	$-0.170637\pi$
$179$	−0.166896	−	0.289073i	−0.0124744	−	0.0216063i	−0.872195	+	0.489158i	$0.837304\pi$
$180$		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	−0.994167	−	0.107854i	$-0.965602\pi$
$191$	−8.16071	−	14.1348i	−0.590488	−	1.02276i	0.403679	−	0.914901i	$-0.367731\pi$
$192$		0			0
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	−0.484400	−	0.874846i	$-0.660962\pi$
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	0.999839	−	0.0179200i	$-0.00570443\pi$
$194$		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	0.953769	−	0.300541i	$-0.0971673\pi$
$199$	3.05563	+	5.29251i	0.216608	+	0.375176i	−0.737161	+	0.675717i	$0.763834\pi$
$200$		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	0.599012	−	0.800740i	$-0.295560\pi$
$211$	−5.72253	−	9.91171i	−0.393955	−	0.682350i	−0.992967	+	0.118390i	$0.962227\pi$
$212$		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	−0.719407	−	0.694589i	$-0.755586\pi$
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	0.961235	+	0.275730i	$0.0889196\pi$
$224$		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	−0.500725	−	0.865606i	$-0.666933\pi$
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	1.00000		0.000837426i	$0.000266561\pi$
$234$		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	−0.990749	−	0.135710i	$-0.956669\pi$
$239$	−9.47524	−	16.4116i	−0.612902	−	1.06158i	0.377846	−	0.925868i	$-0.376665\pi$
$240$		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	0.997187	+	0.0749550i	$0.0238813\pi$
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	−0.433681	+	0.901067i	$0.642785\pi$
$270$		0			0
$271$	3.67742	−	6.36947i	0.223387	−	0.386918i	−0.732447	−	0.680824i	$-0.761622\pi$
$271$	3.67742	−	6.36947i	0.223387	−	0.386918i	0.955834	+	0.293906i	$0.0949552\pi$
$272$		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	−0.629470	−	0.777025i	$-0.716728\pi$
$281$	6.00433	−	10.3998i	0.358188	−	0.620400i	0.987658	+	0.156624i	$0.0500612\pi$
$282$		0			0
$283$	4.92147	−	8.52423i	0.292551	−	0.506713i	−0.681861	−	0.731481i	$-0.738829\pi$
$283$	4.92147	−	8.52423i	0.292551	−	0.506713i	0.974412	+	0.224768i	$0.0721626\pi$
$284$		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	0.988406	+	0.151832i	$0.0485173\pi$
$293$	10.7101	+	18.5505i	0.625694	+	1.08373i	−0.362713	+	0.931901i	$0.618149\pi$
$294$		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	−0.982964	−	0.183797i	$-0.941161\pi$
$311$	−5.86033	+	10.1504i	−0.332309	+	0.575576i	0.650655	+	0.759373i	$0.274494\pi$
$312$		0			0
$313$	13.3869	+	23.1868i	0.756671	+	1.31059i	0.944539	+	0.328398i	$0.106509\pi$
$313$	13.3869	+	23.1868i	0.756671	+	1.31059i	−0.187868	+	0.982194i	$0.560158\pi$
$314$		0			0
$315$	−24.1687	−	16.6785i	−1.36175	−	0.939726i
$316$		0			0
$317$	−0.951246	−	1.64761i	−0.0534273	−	0.0925388i	0.838075	−	0.545555i	$-0.183681\pi$
$317$	−0.951246	−	1.64761i	−0.0534273	−	0.0925388i	−0.891502	+	0.453016i	$0.850348\pi$
$318$		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	0.932330	−	0.361608i	$-0.117772\pi$
$331$	2.78366	+	4.82144i	0.153004	+	0.265010i	−0.779327	+	0.626618i	$0.784439\pi$
$332$		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	−0.799585	−	0.600553i	$-0.794947\pi$
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.120302	−	0.992737i	$-0.538386\pi$
$338$		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	0.0923418	+	0.995727i	$0.470565\pi$
$347$	−15.2033	+	26.3328i	−0.816154	+	1.41362i	−0.908496	+	0.417893i	$0.862769\pi$
$348$		0			0
$349$	−6.29782	+	10.9082i	−0.337115	+	0.583900i	−0.983889	−	0.178782i	$-0.942784\pi$
$349$	−6.29782	+	10.9082i	−0.337115	+	0.583900i	0.646774	+	0.762682i	$0.276118\pi$
$350$		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	−0.760575	−	0.649250i	$-0.775083\pi$
$359$	3.44801	−	5.97213i	0.181979	−	0.315197i	0.942554	+	0.334053i	$0.108416\pi$
$360$		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	0.483481	+	0.875355i	$0.339372\pi$
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	−0.999820	+	0.0189712i	$0.993961\pi$
$398$		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	−0.990888	−	0.134691i	$-0.956996\pi$
$409$	−7.66071	+	13.2687i	−0.378798	+	0.656097i	0.612090	+	0.790788i	$0.290329\pi$
$410$		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	0.952064	−	0.305900i	$-0.0989573\pi$
$419$	4.32141	+	7.48491i	0.211115	+	0.365662i	−0.740949	+	0.671561i	$0.765624\pi$
$420$		0			0
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.0834618	−	0.996511i	$-0.473402\pi$
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.821273	−	0.570536i	$-0.193264\pi$
$422$		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	0.956882	−	0.290478i	$-0.0938142\pi$
$431$	4.71015	+	8.15822i	0.226880	+	0.392967i	−0.730002	+	0.683445i	$0.760481\pi$
$432$		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	0.722231	−	0.691652i	$-0.243117\pi$
$439$	−4.98398	−	8.63250i	−0.237872	−	0.412007i	−0.960104	+	0.279645i	$0.909783\pi$
$440$		0			0
$441$	0.924016	−	20.9797i	0.0440007	−	0.999031i
$442$		0			0
$443$	−7.84981	−	13.5963i	−0.372956	−	0.645979i	0.617063	−	0.786914i	$-0.288322\pi$
$443$	−7.84981	−	13.5963i	−0.372956	−	0.645979i	−0.990019	+	0.140935i	$0.954989\pi$
$444$		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	−0.940239	−	0.340516i	$-0.889398\pi$
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	0.175224	−	0.984529i	$-0.443935\pi$
$458$		0			0
$459$	14.4647	−	30.9572i	0.675155	−	1.44496i
$460$		0			0
$461$	−2.07165	+	3.58821i	−0.0964865	+	0.167120i	−0.910228	−	0.414107i	$-0.864094\pi$
$461$	−2.07165	+	3.58821i	−0.0964865	+	0.167120i	0.813742	+	0.581227i	$0.197427\pi$
$462$		0			0
$463$	8.34176	+	14.4484i	0.387675	+	0.671472i	0.992136	−	0.125162i	$-0.0399451\pi$
$463$	8.34176	+	14.4484i	0.387675	+	0.671472i	−0.604462	+	0.796634i	$0.706612\pi$
$464$		0			0
$465$	41.4250	+	13.7386i	1.92104	+	0.637113i
$466$		0			0
$467$	−14.9585	+	25.9089i	−0.692198	+	1.19892i	0.278918	+	0.960315i	$0.410024\pi$
$467$	−14.9585	+	25.9089i	−0.692198	+	1.19892i	−0.971116	+	0.238608i	$0.923309\pi$
$468$		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	0.986345	+	0.164691i	$0.0526628\pi$
$487$	14.0309	+	24.3022i	0.635800	+	1.10124i	−0.350546	+	0.936546i	$0.614004\pi$
$488$		0			0
$489$	−13.2738	−	4.40226i	−0.600263	−	0.199077i
$490$		0			0
$491$	−17.0734	−	29.5721i	−0.770513	−	1.33457i	−0.937282	−	0.348572i	$-0.886667\pi$
$491$	−17.0734	−	29.5721i	−0.770513	−	1.33457i	0.166769	−	0.985996i	$-0.446667\pi$
$492$		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	−0.805130	−	0.593099i	$-0.797904\pi$
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.111073	−	0.993812i	$-0.535429\pi$
$522$		0			0
$523$	−7.88323	+	13.6542i	−0.344710	+	0.597055i	−0.985301	−	0.170827i	$-0.945356\pi$
$523$	−7.88323	+	13.6542i	−0.344710	+	0.597055i	0.640591	+	0.767882i	$0.278689\pi$
$524$		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	−0.0887957	+	0.996050i	$0.528302\pi$
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.818207	+	0.574924i	$0.805031\pi$
$542$		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	−0.00696400	+	0.999976i	$0.502217\pi$
$547$	−20.3356	+	35.2222i	−0.869486	+	1.50599i	−0.862522	+	0.506019i	$0.831117\pi$
$548$		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	0.972214	−	0.234093i	$-0.0752119\pi$
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	−0.688837	+	0.724916i	$0.741879\pi$
$558$		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	0.281355	+	0.959604i	$0.409216\pi$
$563$	−16.3807	+	28.3722i	−0.690364	+	1.19574i	−0.971719	+	0.236141i	$0.924117\pi$
$564$		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	0.986361	−	0.164596i	$-0.0526321\pi$
$569$	8.36398	+	14.4868i	0.350636	+	0.607320i	−0.635725	+	0.771916i	$0.719299\pi$
$570$		0			0
$571$	−13.7367	+	23.7926i	−0.574863	+	0.995691i	0.421194	+	0.906971i	$0.361611\pi$
$571$	−13.7367	+	23.7926i	−0.574863	+	0.995691i	−0.996057	+	0.0887207i	$0.971722\pi$
$572$		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	0.894015	−	0.448037i	$-0.147877\pi$
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	−0.835019	+	0.550221i	$0.814543\pi$
$578$		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	−0.813494	−	0.581573i	$-0.802437\pi$
$587$	2.34795	−	4.06678i	0.0969105	−	0.167854i	0.910404	+	0.413720i	$0.135771\pi$
$588$		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	−0.852671	−	0.522449i	$-0.825019\pi$
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	0.878789	+	0.477210i	$0.158352\pi$
$594$		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	0.0631320	−	0.998005i	$-0.479891\pi$
$599$	21.9258	−	37.9766i	0.895864	−	1.55168i	0.832732	−	0.553676i	$-0.186776\pi$
$600$		0			0
$601$	−6.71634	+	11.6330i	−0.273965	+	0.474522i	−0.969874	−	0.243609i	$-0.921669\pi$
$601$	−6.71634	+	11.6330i	−0.273965	+	0.474522i	0.695908	+	0.718131i	$0.255002\pi$
$602$		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	0.551695	−	0.834046i	$-0.313981\pi$
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	−0.998152	+	0.0607587i	$0.980648\pi$
$614$		0			0
$615$	19.6847	−	17.5088i	0.793764	−	0.706023i
$616$		0			0
$617$	6.00433	+	10.3998i	0.241725	+	0.418680i	0.961206	−	0.275832i	$-0.0889534\pi$
$617$	6.00433	+	10.3998i	0.241725	+	0.418680i	−0.719481	+	0.694513i	$0.755620\pi$
$618$		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	0.722258	−	0.691623i	$-0.243104\pi$
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	−0.960093	+	0.279682i	$0.909771\pi$
$644$		0			0
$645$	−0.0752956	−	0.0249718i	−0.00296476	−	0.000983262i
$646$		0			0
$647$	−18.8825	−	32.7055i	−0.742349	−	1.28579i	−0.951423	−	0.307887i	$-0.900378\pi$
$647$	−18.8825	−	32.7055i	−0.742349	−	1.28579i	0.209073	−	0.977900i	$-0.432955\pi$
$648$		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	0.413455	+	0.910524i	$0.364322\pi$
$659$	−14.9356	+	25.8693i	−0.581810	+	1.00772i	−0.995265	+	0.0971993i	$0.969012\pi$
$660$		0			0
$661$	−2.80401	+	4.85669i	−0.109063	+	0.188904i	−0.915391	−	0.402566i	$-0.868119\pi$
$661$	−2.80401	+	4.85669i	−0.109063	+	0.188904i	0.806328	+	0.591469i	$0.201452\pi$
$662$		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	−0.942575	−	0.333994i	$-0.891603\pi$
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	0.760535	+	0.649297i	$0.224937\pi$
$674$		0			0
$675$	−25.8628	−	36.9967i	−0.995460	−	1.42401i
$676$		0			0
$677$	−5.53087	−	9.57975i	−0.212569	−	0.368180i	0.739949	−	0.672663i	$-0.234850\pi$
$677$	−5.53087	−	9.57975i	−0.212569	−	0.368180i	−0.952518	+	0.304483i	$0.901516\pi$
$678$		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	0.938108	−	0.346343i	$-0.112577\pi$
$683$	4.41961	+	7.65499i	0.169112	+	0.292910i	−0.768996	+	0.639253i	$0.779243\pi$
$684$		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	0.999643	−	0.0267023i	$-0.00850061\pi$
$691$	12.5309	+	21.7041i	0.476697	+	0.825663i	−0.522947	+	0.852365i	$0.675167\pi$
$692$		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	0.996606	−	0.0823158i	$-0.0262316\pi$
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	−0.569591	+	0.821928i	$0.692898\pi$
$710$		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	−0.956639	−	0.291275i	$-0.905920\pi$
$719$	−6.06182	+	10.4994i	−0.226068	+	0.391561i	0.730571	+	0.682836i	$0.239254\pi$
$720$		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	0.0189562	+	0.999820i	$0.493966\pi$
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	−0.875348	+	0.483494i	$0.839368\pi$
$728$		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	−0.877694	−	0.479221i	$-0.840919\pi$
$739$	−23.2119	−	40.2042i	−0.853865	−	1.47894i	0.0238296	−	0.999716i	$-0.492414\pi$
$740$		0			0
$741$	−0.839294	−	4.07000i	−0.0308322	−	0.149515i
$742$		0			0
$743$	−0.598884	−	1.03730i	−0.0219709	−	0.0380548i	0.854831	−	0.518907i	$-0.173661\pi$
$743$	−0.598884	−	1.03730i	−0.0219709	−	0.0380548i	−0.876802	+	0.480852i	$0.840327\pi$
$744$		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	0.514506	−	0.857486i	$-0.327975\pi$
$769$	−13.4592	−	23.3121i	−0.485352	−	0.840654i	−0.999858	+	0.0168324i	$0.994642\pi$
$770$		0			0
$771$	−2.87154	−	13.9250i	−0.103416	−	0.501497i
$772$		0			0
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.823245	+	0.567687i	$0.192162\pi$
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.0800089	+	0.996794i	$0.474505\pi$
$774$		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	−0.880430	−	0.474176i	$-0.842746\pi$
$787$	−0.829462	+	1.43667i	−0.0295671	+	0.0512118i	0.850863	+	0.525387i	$0.176080\pi$
$788$		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	−0.998642	−	0.0520981i	$-0.983409\pi$
$797$	−15.3702	−	26.6219i	−0.544439	−	0.942996i	0.454203	−	0.890898i	$-0.349924\pi$
$798$		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	0.839553	−	0.543278i	$-0.182817\pi$
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	−0.890269	+	0.455435i	$0.849484\pi$
$810$		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	0.788107	−	0.615538i	$-0.211061\pi$
$821$	−3.98329	−	6.89926i	−0.139018	−	0.240786i	−0.927125	+	0.374752i	$0.877728\pi$
$822$		0			0
$823$	20.2731	−	35.1140i	0.706675	−	1.22400i	−0.259409	−	0.965768i	$-0.583528\pi$
$823$	20.2731	−	35.1140i	0.706675	−	1.22400i	0.966084	−	0.258229i	$-0.0831388\pi$
$824$		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	0.716603	−	0.697481i	$-0.245696\pi$
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	−0.962338	+	0.271856i	$0.912363\pi$
$830$		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	−0.885932	−	0.463815i	$-0.846480\pi$
$839$	−1.19599	+	2.07151i	−0.0412900	+	0.0715164i	0.844642	+	0.535332i	$0.179813\pi$
$840$		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	−0.972744	−	0.231883i	$-0.925511\pi$
$853$	−8.33998	+	14.4453i	−0.285556	+	0.494597i	0.687188	+	0.726479i	$0.258845\pi$
$854$		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	−0.912074	−	0.410026i	$-0.865520\pi$
$863$	−2.96541	+	5.13624i	−0.100944	+	0.174840i	0.811130	+	0.584866i	$0.198853\pi$
$864$		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	−0.571980	−	0.820267i	$-0.693825\pi$
$911$	12.8090	−	22.1859i	0.424382	−	0.735052i	0.996363	+	0.0852158i	$0.0271580\pi$
$912$		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	−0.984615	−	0.174740i	$-0.944091\pi$
$919$	−10.3367	+	17.9038i	−0.340978	+	0.590591i	0.643637	+	0.765331i	$0.277425\pi$
$920$		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	0.895073	−	0.445920i	$-0.147123\pi$
$929$	1.87017	+	3.23922i	0.0613582	+	0.106275i	−0.833715	+	0.552196i	$0.813790\pi$
$930$		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	−0.912983	−	0.407998i	$-0.866227\pi$
$941$	−3.16435	+	5.48081i	−0.103155	+	0.178669i	0.809828	+	0.586667i	$0.199560\pi$
$942$		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	0.999955	+	0.00951587i	$0.00302904\pi$
$947$	15.6396	+	27.0886i	0.508218	+	0.880260i	−0.491736	+	0.870744i	$0.663638\pi$
$948$		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	0.961890	−	0.273436i	$-0.0881602\pi$
$967$	7.59201	+	13.1497i	0.244142	+	0.422867i	−0.717748	+	0.696303i	$0.754827\pi$
$968$		0			0
$969$	2.04442	+	9.91405i	0.0656763	+	0.318485i
$970$		0			0
$971$	−1.62364	+	2.81223i	−0.0521052	+	0.0902489i	−0.890902	−	0.454196i	$-0.849926\pi$
$971$	−1.62364	+	2.81223i	−0.0521052	+	0.0902489i	0.838796	+	0.544445i	$0.183260\pi$
$972$		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	−0.963151	−	0.268962i	$-0.913319\pi$
$977$	−7.77197	+	13.4614i	−0.248647	+	0.430670i	0.714503	+	0.699632i	$0.246653\pi$
$978$		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	0.914026	−	0.405656i	$-0.132957\pi$
$991$	3.32760	+	5.76358i	0.105705	+	0.183086i	−0.808321	+	0.588742i	$0.799623\pi$
$992$		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.961.3		6
3.2	odd	2		3024.2.t.g.289.1		6
4.3	odd	2		126.2.h.c.79.1	yes	6
7.4	even	3		1008.2.q.h.529.3		6
9.4	even	3		1008.2.q.h.625.3		6
9.5	odd	6		3024.2.q.h.2305.3		6
12.11	even	2		378.2.h.d.289.1		6
21.11	odd	6		3024.2.q.h.2881.3		6
28.3	even	6		882.2.e.p.655.3		6
28.11	odd	6		126.2.e.d.25.1	✓	6
28.19	even	6		882.2.f.m.295.1		6
28.23	odd	6		882.2.f.l.295.3		6
28.27	even	2		882.2.h.o.79.3		6
36.7	odd	6		1134.2.g.k.163.1		6
36.11	even	6		1134.2.g.n.163.3		6
36.23	even	6		378.2.e.c.37.3		6
36.31	odd	6		126.2.e.d.121.1	yes	6
63.4	even	3	inner	1008.2.t.g.193.3		6
63.32	odd	6		3024.2.t.g.1873.1		6
84.11	even	6		378.2.e.c.235.3		6
84.23	even	6		2646.2.f.o.883.3		6
84.47	odd	6		2646.2.f.n.883.1		6
84.59	odd	6		2646.2.e.o.2125.1		6
84.83	odd	2		2646.2.h.p.667.3		6
252.11	even	6		1134.2.g.n.487.3		6
252.23	even	6		2646.2.f.o.1765.3		6
252.31	even	6		882.2.h.o.67.3		6
252.47	odd	6		7938.2.a.bx.1.3		3
252.59	odd	6		2646.2.h.p.361.3		6
252.67	odd	6		126.2.h.c.67.1	yes	6
252.79	odd	6		7938.2.a.cb.1.3		3
252.95	even	6		378.2.h.d.361.1		6
252.103	even	6		882.2.f.m.589.1		6
252.131	odd	6		2646.2.f.n.1765.1		6
252.139	even	6		882.2.e.p.373.3		6
252.151	odd	6		1134.2.g.k.487.1		6
252.167	odd	6		2646.2.e.o.1549.1		6
252.187	even	6		7938.2.a.by.1.1		3
252.191	even	6		7938.2.a.bu.1.1		3
252.247	odd	6		882.2.f.l.589.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	28.11	odd	6
126.2.e.d.121.1	yes	6	36.31	odd	6
126.2.h.c.67.1	yes	6	252.67	odd	6
126.2.h.c.79.1	yes	6	4.3	odd	2
378.2.e.c.37.3		6	36.23	even	6
378.2.e.c.235.3		6	84.11	even	6
378.2.h.d.289.1		6	12.11	even	2
378.2.h.d.361.1		6	252.95	even	6
882.2.e.p.373.3		6	252.139	even	6
882.2.e.p.655.3		6	28.3	even	6
882.2.f.l.295.3		6	28.23	odd	6
882.2.f.l.589.3		6	252.247	odd	6
882.2.f.m.295.1		6	28.19	even	6
882.2.f.m.589.1		6	252.103	even	6
882.2.h.o.67.3		6	252.31	even	6
882.2.h.o.79.3		6	28.27	even	2
1008.2.q.h.529.3		6	7.4	even	3
1008.2.q.h.625.3		6	9.4	even	3
1008.2.t.g.193.3		6	63.4	even	3	inner
1008.2.t.g.961.3		6	1.1	even	1	trivial
1134.2.g.k.163.1		6	36.7	odd	6
1134.2.g.k.487.1		6	252.151	odd	6
1134.2.g.n.163.3		6	36.11	even	6
1134.2.g.n.487.3		6	252.11	even	6
2646.2.e.o.1549.1		6	252.167	odd	6
2646.2.e.o.2125.1		6	84.59	odd	6
2646.2.f.n.883.1		6	84.47	odd	6
2646.2.f.n.1765.1		6	252.131	odd	6
2646.2.f.o.883.3		6	84.23	even	6
2646.2.f.o.1765.3		6	252.23	even	6
2646.2.h.p.361.3		6	252.59	odd	6
2646.2.h.p.667.3		6	84.83	odd	2
3024.2.q.h.2305.3		6	9.5	odd	6
3024.2.q.h.2881.3		6	21.11	odd	6
3024.2.t.g.289.1		6	3.2	odd	2
3024.2.t.g.1873.1		6	63.32	odd	6
7938.2.a.bu.1.1		3	252.191	even	6
7938.2.a.bx.1.3		3	252.47	odd	6
7938.2.a.by.1.1		3	252.187	even	6
7938.2.a.cb.1.3		3	252.79	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

Introduction

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