LMFDB - Embedded newform 684.2.r.b.559.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(487,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.487"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 2 x^{17} + x^{16} + 3 x^{14} - 12 x^{13} + 28 x^{12} - 24 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 2x^17 + x^16 + 3x^14 - 12x^13 + 28x^12 - 24x^11 + 40x^10 - 48x^9 + 112x^8 - 96x^7 + 48x^6 + 64x^4 - 256x^3 + 768x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.7
Root			$0.818463 - 1.15331i$ of defining polynomial
Character	$\chi$	$=$	684.559
Dual form			684.2.r.b.487.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.589563 + 1.28546i) q^{2} +(-1.30483 + 1.51572i) q^{4} +(2.18826 - 3.79018i) q^{5} +0.239504i q^{7} +(-2.71769 - 0.783701i) q^{8} +(6.16226 + 0.578382i) q^{10} -4.67278i q^{11} +(-2.48235 + 1.43318i) q^{13} +(-0.307873 + 0.141202i) q^{14} +(-0.594827 - 3.95553i) q^{16} +(1.08855 - 1.88543i) q^{17} +(4.03471 - 1.64957i) q^{19} +(2.88955 + 8.26235i) q^{20} +(6.00668 - 2.75489i) q^{22} +(-0.110122 + 0.0635792i) q^{23} +(-7.07699 - 12.2577i) q^{25} +(-3.30580 - 2.34601i) q^{26} +(-0.363021 - 0.312512i) q^{28} +(1.35698 - 0.783454i) q^{29} +5.03817 q^{31} +(4.73399 - 3.09666i) q^{32} +(3.06542 + 0.287717i) q^{34} +(0.907762 + 0.524097i) q^{35} +11.2173i q^{37} +(4.49918 + 4.21395i) q^{38} +(-8.91738 + 8.58558i) q^{40} +(0.433736 + 0.250418i) q^{41} +(-5.18284 - 2.99231i) q^{43} +(7.08263 + 6.09719i) q^{44} +(-0.146653 - 0.104074i) q^{46} +(1.85862 - 1.07308i) q^{47} +6.94264 q^{49} +(11.5845 - 16.3239i) q^{50} +(1.06674 - 5.63261i) q^{52} +(-0.825696 + 0.476716i) q^{53} +(-17.7107 - 10.2253i) q^{55} +(0.187699 - 0.650895i) q^{56} +(1.80713 + 1.28245i) q^{58} +(-5.47728 + 9.48693i) q^{59} +(2.77228 + 4.80174i) q^{61} +(2.97031 + 6.47638i) q^{62} +(6.77163 + 4.25970i) q^{64} +12.5447i q^{65} +(4.16350 + 7.21139i) q^{67} +(1.43741 + 4.11011i) q^{68} +(-0.138525 + 1.47588i) q^{70} +(3.74409 - 6.48496i) q^{71} +(-3.16780 + 5.48679i) q^{73} +(-14.4195 + 6.61331i) q^{74} +(-2.76433 + 8.26792i) q^{76} +1.11915 q^{77} +(4.85783 - 8.41402i) q^{79} +(-16.2938 - 6.40123i) q^{80} +(-0.0661882 + 0.705189i) q^{82} +12.7727i q^{83} +(-4.76408 - 8.25163i) q^{85} +(0.790901 - 8.42651i) q^{86} +(-3.66206 + 12.6991i) q^{88} +(-4.53985 + 2.62108i) q^{89} +(-0.343252 - 0.594531i) q^{91} +(0.0473228 - 0.249875i) q^{92} +(2.47518 + 1.75655i) q^{94} +(2.57683 - 18.9020i) q^{95} +(-7.33528 - 4.23502i) q^{97} +(4.09312 + 8.92451i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + q^{4} - 4 q^{8} + 6 q^{10} + 6 q^{13} - 9 q^{14} - 11 q^{16} + 12 q^{19} + 14 q^{20} + 8 q^{22} - 10 q^{25} + 7 q^{28} + 12 q^{31} + 29 q^{32} - 6 q^{34} - 25 q^{38} - 46 q^{40} - 12 q^{41}+ \cdots - 12 q^{97}+O(q^{100}) $ 20 * q - q^2 + q^4 - 4 * q^8 + 6 * q^10 + 6 * q^13 - 9 * q^14 - 11 * q^16 + 12 * q^19 + 14 * q^20 + 8 * q^22 - 10 * q^25 + 7 * q^28 + 12 * q^31 + 29 * q^32 - 6 * q^34 - 25 * q^38 - 46 * q^40 - 12 * q^41 - 18 * q^43 + 12 * q^44 - 32 * q^46 + 36 * q^47 - 24 * q^49 + 34 * q^50 + 3 * q^52 + 12 * q^53 - 38 * q^56 + 16 * q^58 + 10 * q^61 + 55 * q^62 - 14 * q^64 + 14 * q^67 - 40 * q^68 + 26 * q^70 - 8 * q^71 - 6 * q^73 - 45 * q^74 - 69 * q^76 + 32 * q^77 - 6 * q^79 - 22 * q^80 + 24 * q^82 + 8 * q^85 - 7 * q^86 + 44 * q^88 + 24 * q^89 + 26 * q^91 + 18 * q^92 - 52 * q^94 - 4 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.589563	+	1.28546i	0.416884	+	0.908960i
$2$	0.589563	+	1.28546i	0.416884	+	0.908960i
$3$		0			0
$3$		0			0
$4$	−1.30483	+	1.51572i	−0.652416	+	0.757861i
$5$	2.18826	−	3.79018i	0.978621	−	1.69502i	0.311194	−	0.950347i	$-0.399271\pi$
$5$	2.18826	−	3.79018i	0.978621	−	1.69502i	0.667427	−	0.744675i	$-0.267395\pi$
$6$		0			0
$7$			0.239504i			0.0905238i	0.998975	+	0.0452619i	$0.0144122\pi$
$7$			0.239504i			0.0905238i	−0.998975	+	0.0452619i	$0.985588\pi$
$8$	−2.71769	−	0.783701i	−0.960847	−	0.277080i
$9$		0			0
$10$	6.16226	+	0.578382i	1.94868	+	0.182900i
$11$		−	4.67278i		−	1.40890i	−0.709756	−	0.704448i	$-0.751195\pi$
$11$		−	4.67278i		−	1.40890i	0.709756	−	0.704448i	$-0.248805\pi$
$12$		0			0
$13$	−2.48235	+	1.43318i	−0.688479	+	0.397493i	−0.803042	−	0.595923i	$-0.796787\pi$
$13$	−2.48235	+	1.43318i	−0.688479	+	0.397493i	0.114563	+	0.993416i	$0.463453\pi$
$14$	−0.307873	+	0.141202i	−0.0822825	+	0.0377379i
$15$		0			0
$16$	−0.594827	−	3.95553i	−0.148707	−	0.988881i
$17$	1.08855	−	1.88543i	0.264013	−	0.457284i	−0.703292	−	0.710901i	$-0.748287\pi$
$17$	1.08855	−	1.88543i	0.264013	−	0.457284i	0.967305	+	0.253618i	$0.0816205\pi$
$18$		0			0
$19$	4.03471	−	1.64957i	0.925627	−	0.378438i
$19$	4.03471	−	1.64957i	0.925627	−	0.378438i
$20$	2.88955	+	8.26235i	0.646123	+	1.84752i
$21$		0			0
$22$	6.00668	−	2.75489i	1.28063	−	0.587345i
$23$	−0.110122	+	0.0635792i	−0.0229621	+	0.0132572i	−0.511437	−	0.859321i	$-0.670887\pi$
$23$	−0.110122	+	0.0635792i	−0.0229621	+	0.0132572i	0.488475	+	0.872578i	$0.337553\pi$
$24$		0			0
$25$	−7.07699	−	12.2577i	−1.41540	−	2.45154i
$26$	−3.30580	−	2.34601i	−0.648321	−	0.460091i
$27$		0			0
$28$	−0.363021	−	0.312512i	−0.0686045	−	0.0590592i
$29$	1.35698	−	0.783454i	0.251985	−	0.145484i	−0.368688	−	0.929553i	$-0.620193\pi$
$29$	1.35698	−	0.783454i	0.251985	−	0.145484i	0.620673	+	0.784070i	$0.286860\pi$
$30$		0			0
$31$	5.03817			0.904881			0.452441	−	0.891795i	$-0.350553\pi$
$31$	5.03817			0.904881			0.452441	+	0.891795i	$0.350553\pi$
$32$	4.73399	−	3.09666i	0.836860	−	0.547417i
$33$		0			0
$34$	3.06542	+	0.287717i	0.525715	+	0.0493430i
$35$	0.907762	+	0.524097i	0.153440	+	0.0885885i
$36$		0			0
$37$			11.2173i			1.84412i	0.387051	+	0.922058i	$0.373494\pi$
$37$			11.2173i			1.84412i	−0.387051	+	0.922058i	$0.626506\pi$
$38$	4.49918	+	4.21395i	0.729864	+	0.683593i
$39$		0			0
$40$	−8.91738	+	8.58558i	−1.40996	+	1.35750i
$41$	0.433736	+	0.250418i	0.0677382	+	0.0391087i	0.533487	−	0.845809i	$-0.320881\pi$
$41$	0.433736	+	0.250418i	0.0677382	+	0.0391087i	−0.465748	+	0.884917i	$0.654215\pi$
$42$		0			0
$43$	−5.18284	−	2.99231i	−0.790376	−	0.456324i	0.0497191	−	0.998763i	$-0.484167\pi$
$43$	−5.18284	−	2.99231i	−0.790376	−	0.456324i	−0.840095	+	0.542440i	$0.817501\pi$
$44$	7.08263	+	6.09719i	1.06775	+	0.919186i
$45$		0			0
$46$	−0.146653	−	0.104074i	−0.0216228	−	0.0153449i
$47$	1.85862	−	1.07308i	0.271108	−	0.156524i	−0.358283	−	0.933613i	$-0.616638\pi$
$47$	1.85862	−	1.07308i	0.271108	−	0.156524i	0.629391	+	0.777089i	$0.283304\pi$
$48$		0			0
$49$	6.94264			0.991805
$50$	11.5845	−	16.3239i	1.63830	−	2.30855i
$51$		0			0
$52$	1.06674	−	5.63261i	0.147930	−	0.781102i
$53$	−0.825696	+	0.476716i	−0.113418	+	0.0654820i	−0.555636	−	0.831426i	$-0.687525\pi$
$53$	−0.825696	+	0.476716i	−0.113418	+	0.0654820i	0.442218	+	0.896908i	$0.354192\pi$
$54$		0			0
$55$	−17.7107	−	10.2253i	−2.38811	−	1.37877i
$56$	0.187699	−	0.650895i	0.0250823	−	0.0869795i
$57$		0			0
$58$	1.80713	+	1.28245i	0.237287	+	0.168395i
$59$	−5.47728	+	9.48693i	−0.713081	+	1.23509i	0.250614	+	0.968087i	$0.419368\pi$
$59$	−5.47728	+	9.48693i	−0.713081	+	1.23509i	−0.963695	+	0.267006i	$0.913966\pi$
$60$		0			0
$61$	2.77228	+	4.80174i	0.354955	+	0.614799i	0.987110	−	0.160042i	$-0.0511630\pi$
$61$	2.77228	+	4.80174i	0.354955	+	0.614799i	−0.632156	+	0.774841i	$0.717830\pi$
$62$	2.97031	+	6.47638i	0.377230	+	0.822501i
$63$		0			0
$64$	6.77163	+	4.25970i	0.846453	+	0.532463i
$65$			12.5447i			1.55598i
$66$		0			0
$67$	4.16350	+	7.21139i	0.508652	+	0.881012i	0.999950	+	0.0100198i	$0.00318946\pi$
$67$	4.16350	+	7.21139i	0.508652	+	0.881012i	−0.491297	+	0.870992i	$0.663477\pi$
$68$	1.43741	+	4.11011i	0.174311	+	0.498424i
$69$		0			0
$70$	−0.138525	+	1.47588i	−0.0165568	+	0.176402i
$71$	3.74409	−	6.48496i	0.444342	−	0.769623i	−0.553664	−	0.832740i	$-0.686771\pi$
$71$	3.74409	−	6.48496i	0.444342	−	0.769623i	0.998006	+	0.0631171i	$0.0201042\pi$
$72$		0			0
$73$	−3.16780	+	5.48679i	−0.370763	+	0.642180i	−0.989683	−	0.143274i	$-0.954237\pi$
$73$	−3.16780	+	5.48679i	−0.370763	+	0.642180i	0.618920	+	0.785454i	$0.287570\pi$
$74$	−14.4195	+	6.61331i	−1.67623	+	0.768782i
$75$		0			0
$76$	−2.76433	+	8.26792i	−0.317090	+	0.948395i
$77$	1.11915			0.127539
$78$		0			0
$79$	4.85783	−	8.41402i	0.546549	−	0.946651i	−0.451959	−	0.892039i	$-0.649275\pi$
$79$	4.85783	−	8.41402i	0.546549	−	0.946651i	0.998508	−	0.0546119i	$-0.0173922\pi$
$80$	−16.2938	−	6.40123i	−1.82170	−	0.715679i
$81$		0			0
$82$	−0.0661882	+	0.705189i	−0.00730926	+	0.0778751i
$83$			12.7727i			1.40198i	0.713170	+	0.700991i	$0.247259\pi$
$83$			12.7727i			1.40198i	−0.713170	+	0.700991i	$0.752741\pi$
$84$		0			0
$85$	−4.76408	−	8.25163i	−0.516737	−	0.895015i
$86$	0.790901	−	8.42651i	0.0852851	−	0.908654i
$87$		0			0
$88$	−3.66206	+	12.6991i	−0.390377	+	1.35373i
$89$	−4.53985	+	2.62108i	−0.481223	+	0.277834i	−0.720926	−	0.693012i	$-0.756283\pi$
$89$	−4.53985	+	2.62108i	−0.481223	+	0.277834i	0.239703	+	0.970846i	$0.422950\pi$
$90$		0			0
$91$	−0.343252	−	0.594531i	−0.0359826	−	0.0623237i
$92$	0.0473228	−	0.249875i	0.00493374	−	0.0260513i
$93$		0			0
$94$	2.47518	+	1.75655i	0.255295	+	0.181174i
$95$	2.57683	−	18.9020i	0.264377	−	1.93930i
$96$		0			0
$97$	−7.33528	−	4.23502i	−0.744784	−	0.430001i	0.0790219	−	0.996873i	$-0.474820\pi$
$97$	−7.33528	−	4.23502i	−0.744784	−	0.430001i	−0.823806	+	0.566871i	$0.808154\pi$
$98$	4.09312	+	8.92451i	0.413468	+	0.901511i
$99$		0			0
$100$	27.8136	+	5.26750i	2.78136	+	0.526750i
$101$	−0.920375	−	1.59414i	−0.0915808	−	0.158623i	0.816596	−	0.577210i	$-0.195859\pi$
$101$	−0.920375	−	1.59414i	−0.0915808	−	0.158623i	−0.908176	+	0.418588i	$0.862525\pi$
$102$		0			0
$103$	6.25383			0.616209			0.308104	−	0.951353i	$-0.400305\pi$
$103$	6.25383			0.616209			0.308104	+	0.951353i	$0.400305\pi$
$104$	7.86942	−	1.94952i	0.771660	−	0.191167i
$105$		0			0
$106$	−1.09960	−	0.780348i	−0.106803	−	0.0757941i
$107$	−10.5621			−1.02108			−0.510538	−	0.859855i	$-0.670554\pi$
$107$	−10.5621			−1.02108			−0.510538	+	0.859855i	$0.670554\pi$
$108$		0			0
$109$	7.09063	+	4.09378i	0.679159	+	0.392113i	0.799538	−	0.600615i	$-0.205078\pi$
$109$	7.09063	+	4.09378i	0.679159	+	0.392113i	−0.120379	+	0.992728i	$0.538411\pi$
$110$	2.70265	−	28.7949i	0.257688	−	2.74548i
$111$		0			0
$112$	0.947362	−	0.142463i	0.0895173	−	0.0134615i
$113$		−	3.64620i		−	0.343006i	−0.985184	−	0.171503i	$-0.945138\pi$
$113$		−	3.64620i		−	0.343006i	0.985184	−	0.171503i	$-0.0548623\pi$
$114$		0			0
$115$			0.556512i			0.0518950i
$116$	−0.583135	+	3.07908i	−0.0541427	+	0.285886i
$117$		0			0
$118$	−15.4243	−	1.44771i	−1.41992	−	0.133272i
$119$	0.451567	+	0.260712i	0.0413951	+	0.0238995i
$120$		0			0
$121$	−10.8348			−0.984985
$122$	−4.53802	+	6.39459i	−0.410853	+	0.578939i
$123$		0			0
$124$	−6.57396	+	7.63646i	−0.590359	+	0.685774i
$125$	−40.0627			−3.58331
$126$		0			0
$127$	−7.95258	−	13.7743i	−0.705677	−	1.22227i	−0.966447	−	0.256867i	$-0.917310\pi$
$127$	−7.95258	−	13.7743i	−0.705677	−	1.22227i	0.260770	−	0.965401i	$-0.416024\pi$
$128$	−1.48339	+	11.2160i	−0.131115	+	0.991367i
$129$		0			0
$130$	−16.1258	+	7.39590i	−1.41432	+	0.648663i
$131$	−3.69633	−	2.13407i	−0.322949	−	0.186455i	0.329757	−	0.944066i	$-0.393033\pi$
$131$	−3.69633	−	2.13407i	−0.322949	−	0.186455i	−0.652706	+	0.757611i	$0.726367\pi$
$132$		0			0
$133$	0.395078	+	0.966328i	0.0342576	+	0.0837913i
$134$	−6.81534	+	9.60359i	−0.588755	+	0.829624i
$135$		0			0
$136$	−4.43596	+	4.27090i	−0.380380	+	0.366227i
$137$	−3.13941	−	5.43762i	−0.268218	−	0.464567i	0.700184	−	0.713963i	$-0.253101\pi$
$137$	−3.13941	−	5.43762i	−0.268218	−	0.464567i	−0.968402	+	0.249395i	$0.919768\pi$
$138$		0			0
$139$	10.9010	−	6.29369i	0.924611	−	0.533824i	0.0395075	−	0.999219i	$-0.487421\pi$
$139$	10.9010	−	6.29369i	0.924611	−	0.533824i	0.885103	+	0.465395i	$0.154088\pi$
$140$	−1.97886	+	0.692057i	−0.167244	+	0.0584895i
$141$		0			0
$142$	10.5436	+	0.989605i	0.884795	+	0.0830458i
$143$	6.69694	+	11.5994i	0.560026	+	0.969994i
$144$		0			0
$145$		−	6.85761i		−	0.569494i
$146$	−8.92069	−	0.837285i	−0.738281	−	0.0692942i
$147$		0			0
$148$	−17.0023	−	14.6367i	−1.39758	−	1.20313i
$149$	−0.500289	+	0.866526i	−0.0409853	+	0.0709886i	−0.885790	−	0.464086i	$-0.846383\pi$
$149$	−0.500289	+	0.866526i	−0.0409853	+	0.0709886i	0.844805	+	0.535074i	$0.179716\pi$
$150$		0			0
$151$	10.0189			0.815323			0.407661	−	0.913133i	$-0.366344\pi$
$151$	10.0189			0.815323			0.407661	+	0.913133i	$0.366344\pi$
$152$	−12.2579	+	1.32101i	−0.994243	+	0.107148i
$153$		0			0
$154$	0.659807	+	1.43862i	0.0531687	+	0.115927i
$155$	11.0248	−	19.0956i	0.885536	−	1.53379i
$156$		0			0
$157$	6.73633	−	11.6677i	0.537618	−	0.931181i	−0.461414	−	0.887185i	$-0.652658\pi$
$157$	6.73633	−	11.6677i	0.537618	−	0.931181i	0.999032	−	0.0439960i	$-0.0140089\pi$
$158$	13.6799	+	1.28398i	1.08831	+	0.102148i
$159$		0			0
$160$	−1.37767	−	24.7190i	−0.108915	−	1.95421i
$161$	−0.0152274	−	0.0263747i	−0.00120009	−	0.00207862i
$162$		0			0
$163$			20.0318i			1.56901i	0.620123	+	0.784505i	$0.287083\pi$
$163$			20.0318i			1.56901i	−0.620123	+	0.784505i	$0.712917\pi$
$164$	−0.945517	+	0.330671i	−0.0738325	+	0.0258210i
$165$		0			0
$166$	−16.4188	+	7.53028i	−1.27434	+	0.584463i
$167$	1.87933	+	3.25510i	0.145427	+	0.251887i	0.929532	−	0.368741i	$-0.120211\pi$
$167$	1.87933	+	3.25510i	0.145427	+	0.251887i	−0.784105	+	0.620628i	$0.786878\pi$
$168$		0			0
$169$	−2.39197	+	4.14302i	−0.183998	+	0.318694i
$170$	7.79845	−	10.9889i	0.598113	−	0.842811i
$171$		0			0
$172$	11.2983	−	3.95128i	0.861484	−	0.301282i
$173$	−6.73650	−	3.88932i	−0.512167	−	0.295700i	0.221557	−	0.975147i	$-0.428886\pi$
$173$	−6.73650	−	3.88932i	−0.512167	−	0.295700i	−0.733724	+	0.679448i	$0.762219\pi$
$174$		0			0
$175$	2.93576	−	1.69496i	0.221923	−	0.128127i
$176$	−18.4833	+	2.77949i	−1.39323	+	0.209512i
$177$		0			0
$178$	−6.04584	−	4.29052i	−0.453155	−	0.321588i
$179$	12.2389			0.914778			0.457389	−	0.889267i	$-0.348785\pi$
$179$	12.2389			0.914778			0.457389	+	0.889267i	$0.348785\pi$
$180$		0			0
$181$	−4.52118	+	2.61031i	−0.336057	+	0.194023i	−0.658527	−	0.752557i	$-0.728820\pi$
$181$	−4.52118	+	2.61031i	−0.336057	+	0.194023i	0.322470	+	0.946580i	$0.395487\pi$
$182$	0.561878	−	0.791751i	0.0416492	−	0.0586885i
$183$		0			0
$184$	0.349105	−	0.0864852i	0.0257364	−	0.00637577i
$185$	42.5157	+	24.5465i	3.12582	+	1.80469i
$186$		0			0
$187$	−8.81019	−	5.08657i	−0.644265	−	0.371966i
$188$	−0.798705	+	4.21734i	−0.0582516	+	0.307581i
$189$		0			0
$190$	25.8170	−	7.83149i	1.87296	−	0.568156i
$191$		−	14.9269i		−	1.08008i	−0.841641	−	0.540038i	$-0.818410\pi$
$191$		−	14.9269i		−	1.08008i	0.841641	−	0.540038i	$-0.181590\pi$
$192$		0			0
$193$	13.2285	+	7.63746i	0.952206	+	0.549757i	0.893766	−	0.448534i	$-0.148054\pi$
$193$	13.2285	+	7.63746i	0.952206	+	0.549757i	0.0584407	+	0.998291i	$0.481387\pi$
$194$	1.11936	−	11.9260i	0.0803656	−	0.856240i
$195$		0			0
$196$	−9.05898	+	10.5231i	−0.647070	+	0.751651i
$197$	21.2411			1.51336			0.756682	−	0.653783i	$-0.226819\pi$
$197$	21.2411			1.51336			0.756682	+	0.653783i	$0.226819\pi$
$198$		0			0
$199$	−16.3956	+	9.46600i	−1.16225	+	0.671027i	−0.951843	−	0.306586i	$-0.900813\pi$
$199$	−16.3956	+	9.46600i	−1.16225	+	0.671027i	−0.210410	+	0.977613i	$0.567480\pi$
$200$	9.62666	+	38.8588i	0.680708	+	2.74773i
$201$		0			0
$202$	1.50659	−	2.12295i	0.106003	−	0.149370i
$203$	0.187640	+	0.325002i	0.0131697	+	0.0228107i
$204$		0			0
$205$	1.89826	−	1.09596i	0.132580	−	0.0765452i
$206$	3.68703	+	8.03907i	0.256887	+	0.560109i
$207$		0			0
$208$	7.14556	+	8.96648i	0.495455	+	0.621714i
$209$	−7.70808	−	18.8533i	−0.533179	−	1.30411i
$210$		0			0
$211$	−13.2887	+	23.0167i	−0.914832	+	1.58454i	−0.107685	+	0.994185i	$0.534344\pi$
$211$	−13.2887	+	23.0167i	−0.914832	+	1.58454i	−0.807147	+	0.590350i	$0.798990\pi$
$212$	0.354826	−	1.87356i	0.0243695	−	0.128677i
$213$		0			0
$214$	−6.22702	−	13.5772i	−0.425670	−	0.928118i
$215$	−22.6828	+	13.0959i	−1.54696	+	0.893136i
$216$		0			0
$217$			1.20666i			0.0819133i
$218$	−1.08203	+	11.5283i	−0.0732844	+	0.780794i
$219$		0			0
$220$	38.6081	−	13.5022i	2.60296	−	0.910319i
$221$			6.24038i			0.419774i
$222$		0			0
$223$	4.99275	−	8.64770i	0.334339	−	0.579093i	−0.649018	−	0.760773i	$-0.724820\pi$
$223$	4.99275	−	8.64770i	0.334339	−	0.579093i	0.983358	+	0.181680i	$0.0581535\pi$
$224$	0.741661	+	1.13381i	0.0495543	+	0.0757558i
$225$		0			0
$226$	4.68706	−	2.14967i	0.311779	−	0.142994i
$227$	−8.45242			−0.561007			−0.280503	−	0.959853i	$-0.590501\pi$
$227$	−8.45242			−0.561007			−0.280503	+	0.959853i	$0.590501\pi$
$228$		0			0
$229$	13.7714			0.910043			0.455021	−	0.890481i	$-0.349632\pi$
$229$	13.7714			0.910043			0.455021	+	0.890481i	$0.349632\pi$
$230$	−0.715375	+	0.328099i	−0.0471705	+	0.0216342i
$231$		0			0
$232$	−4.30184	+	1.06571i	−0.282430	+	0.0699675i
$233$	−0.711952	+	1.23314i	−0.0466415	+	0.0807854i	−0.888404	−	0.459063i	$-0.848185\pi$
$233$	−0.711952	+	1.23314i	−0.0466415	+	0.0807854i	0.841762	+	0.539849i	$0.181519\pi$
$234$		0			0
$235$		−	9.39270i		−	0.612712i
$236$	−7.23262	−	20.6809i	−0.470803	−	1.34621i
$237$		0			0
$238$	−0.0689091	+	0.734179i	−0.00446672	+	0.0475898i
$239$			19.9629i			1.29129i	0.763637	+	0.645646i	$0.223412\pi$
$239$			19.9629i			1.29129i	−0.763637	+	0.645646i	$0.776588\pi$
$240$		0			0
$241$	−7.75801	+	4.47909i	−0.499738	+	0.288524i	−0.728605	−	0.684934i	$-0.759831\pi$
$241$	−7.75801	+	4.47909i	−0.499738	+	0.288524i	0.228868	+	0.973458i	$0.426498\pi$
$242$	−6.38782	−	13.9278i	−0.410624	−	0.895312i
$243$		0			0
$244$	−10.8955	−	2.06345i	−0.697510	−	0.132099i
$245$	15.1923	−	26.3139i	0.970602	−	1.68113i
$246$		0			0
$247$	−7.65141	+	9.87729i	−0.486848	+	0.628477i
$248$	−13.6921	−	3.94841i	−0.869452	−	0.250725i
$249$		0			0
$250$	−23.6194	−	51.4991i	−1.49382	−	3.25709i
$251$	14.1105	−	8.14673i	0.890650	−	0.514217i	0.0164947	−	0.999864i	$-0.494749\pi$
$251$	14.1105	−	8.14673i	0.890650	−	0.514217i	0.874155	+	0.485647i	$0.161416\pi$
$252$		0			0
$253$	0.297091	+	0.514577i	0.0186780	+	0.0323512i
$254$	13.0178	−	18.3435i	0.816808	−	1.15098i
$255$		0			0
$256$	−15.2924	+	4.70571i	−0.955773	+	0.294107i
$257$	−13.8688	+	8.00714i	−0.865110	+	0.499472i	−0.865720	−	0.500528i	$-0.833139\pi$
$257$	−13.8688	+	8.00714i	−0.865110	+	0.499472i	0.000609991		1.00000i	$0.499806\pi$
$258$		0			0
$259$	−2.68659			−0.166936
$260$	−19.0143	−	16.3688i	−1.17922	−	1.01515i
$261$		0			0
$262$	0.564059	−	6.00966i	0.0348477	−	0.371278i
$263$	9.02588	+	5.21109i	0.556559	+	0.321330i	0.751763	−	0.659433i	$-0.229204\pi$
$263$	9.02588	+	5.21109i	0.556559	+	0.321330i	−0.195204	+	0.980763i	$0.562537\pi$
$264$		0			0
$265$			4.17272i			0.256328i
$266$	−1.00926	+	1.07757i	−0.0618814	+	0.0660700i
$267$		0			0
$268$	−16.3631	−	3.09895i	−0.999537	−	0.189298i
$269$	4.84447	+	2.79696i	0.295373	+	0.170534i	0.640362	−	0.768073i	$-0.278784\pi$
$269$	4.84447	+	2.79696i	0.295373	+	0.170534i	−0.344990	+	0.938607i	$0.612118\pi$
$270$		0			0
$271$	19.1570	+	11.0603i	1.16370	+	0.671865i	0.952189	−	0.305510i	$-0.0988270\pi$
$271$	19.1570	+	11.0603i	1.16370	+	0.671865i	0.211515	+	0.977375i	$0.432160\pi$
$272$	−8.10536	−	3.18429i	−0.491460	−	0.193076i
$273$		0			0
$274$	5.13898	−	7.24142i	0.310457	−	0.437470i
$275$	−57.2775	+	33.0692i	−3.45397	+	1.99415i
$276$		0			0
$277$	−17.6484			−1.06039			−0.530193	−	0.847877i	$-0.677881\pi$
$277$	−17.6484			−1.06039			−0.530193	+	0.847877i	$0.677881\pi$
$278$	14.5171	+	10.3023i	0.870680	+	0.617891i
$279$		0			0
$280$	−2.05628	−	2.13574i	−0.122886	−	0.127635i
$281$	−20.0321	+	11.5656i	−1.19502	+	0.689943i	−0.959440	−	0.281913i	$-0.909031\pi$
$281$	−20.0321	+	11.5656i	−1.19502	+	0.689943i	−0.235576	+	0.971856i	$0.575698\pi$
$282$		0			0
$283$	4.47260	+	2.58226i	0.265868	+	0.153499i	0.627009	−	0.779012i	$-0.284279\pi$
$283$	4.47260	+	2.58226i	0.265868	+	0.153499i	−0.361140	+	0.932512i	$0.617612\pi$
$284$	4.94398	+	14.1368i	0.293371	+	0.838864i
$285$		0			0
$286$	−10.9624	+	15.4473i	−0.648220	+	0.913416i
$287$	−0.0599759	+	0.103881i	−0.00354027	+	0.00613192i
$288$		0			0
$289$	6.13010	+	10.6177i	0.360594	+	0.624568i
$290$	8.81521	−	4.04299i	0.517647	−	0.237413i
$291$		0			0
$292$	−4.18300	−	11.9608i	−0.244792	−	0.699956i
$293$			4.82921i			0.282125i	0.990001	+	0.141063i	$0.0450519\pi$
$293$			4.82921i			0.282125i	−0.990001	+	0.141063i	$0.954948\pi$
$294$		0			0
$295$	23.9715	+	41.5198i	1.39567	+	2.41738i
$296$	8.79102	−	30.4852i	0.510968	−	1.77191i
$297$		0			0
$298$	−1.40884	−	0.132232i	−0.0816118	−	0.00765999i
$299$	0.182241	−	0.315651i	0.0105393	−	0.0182546i
$300$		0			0
$301$	0.716670	−	1.24131i	0.0413082	−	0.0715478i
$302$	5.90674	+	12.8789i	0.339895	+	0.741095i
$303$		0			0
$304$	−8.92488	−	14.9782i	−0.511877	−	0.859059i
$305$	24.2659			1.38946
$306$		0			0
$307$	−9.58882	+	16.6083i	−0.547263	+	0.947888i	0.451198	+	0.892424i	$0.350997\pi$
$307$	−9.58882	+	16.6083i	−0.547263	+	0.947888i	−0.998461	+	0.0554634i	$0.982336\pi$
$308$	−1.46030	+	1.69631i	−0.0832082	+	0.0966565i
$309$		0			0
$310$	31.0465	+	2.91398i	1.76332	+	0.165503i
$311$		−	8.28172i		−	0.469613i	−0.972042	−	0.234807i	$-0.924554\pi$
$311$		−	8.28172i		−	0.469613i	0.972042	−	0.234807i	$-0.0754457\pi$
$312$		0			0
$313$	−10.3863	−	17.9895i	−0.587067	−	1.01683i	−0.994614	−	0.103645i	$-0.966949\pi$
$313$	−10.3863	−	17.9895i	−0.587067	−	1.01683i	0.407548	−	0.913184i	$-0.366384\pi$
$314$	18.9698	+	1.78049i	1.07053	+	0.100479i
$315$		0			0
$316$	6.41465	+	18.3420i	0.360852	+	1.03182i
$317$	12.2188	−	7.05454i	0.686277	−	0.396222i	−0.115939	−	0.993256i	$-0.536988\pi$
$317$	12.2188	−	7.05454i	0.686277	−	0.396222i	0.802216	+	0.597034i	$0.203654\pi$
$318$		0			0
$319$	−3.66090	−	6.34087i	−0.204971	−	0.355021i
$320$	30.9632	−	16.3444i	1.73089	−	0.913677i
$321$		0			0
$322$	0.0249262	−	0.0351238i	0.00138908	−	0.00195737i
$323$	1.28185	−	9.40281i	0.0713239	−	0.523187i
$324$		0			0
$325$	35.1351	+	20.2852i	1.94894	+	1.12522i
$326$	−25.7501	+	11.8100i	−1.42617	+	0.654094i
$327$		0			0
$328$	−0.982506	−	1.02048i	−0.0542498	−	0.0563464i
$329$	0.257006	+	0.445147i	0.0141692	+	0.0245417i
$330$		0			0
$331$	13.6376			0.749592			0.374796	−	0.927107i	$-0.377713\pi$
$331$	13.6376			0.749592			0.374796	+	0.927107i	$0.377713\pi$
$332$	−19.3598	−	16.6662i	−1.06251	−	0.914675i
$333$		0			0
$334$	−3.07632	+	4.33489i	−0.168329	+	0.237195i
$335$	36.4433			1.99111
$336$		0			0
$337$	−5.27825	−	3.04740i	−0.287525	−	0.166002i	0.349300	−	0.937011i	$-0.386419\pi$
$337$	−5.27825	−	3.04740i	−0.287525	−	0.166002i	−0.636825	+	0.771008i	$0.719753\pi$
$338$	−6.73592	−	0.632225i	−0.366386	−	0.0343885i
$339$		0			0
$340$	18.7235	+	3.54597i	1.01542	+	0.192307i
$341$		−	23.5422i		−	1.27488i
$342$		0			0
$343$			3.33931i			0.180306i
$344$	11.7402	+	12.1940i	0.632992	+	0.657454i
$345$		0			0
$346$	1.02799	−	10.9525i	0.0552651	−	0.588812i
$347$	−6.24383	−	3.60488i	−0.335186	−	0.193520i	0.322955	−	0.946414i	$-0.395324\pi$
$347$	−6.24383	−	3.60488i	−0.335186	−	0.193520i	−0.658141	+	0.752894i	$0.728657\pi$
$348$		0			0
$349$	0.239146			0.0128012			0.00640060	−	0.999980i	$-0.497963\pi$
$349$	0.239146			0.0128012			0.00640060	+	0.999980i	$0.497963\pi$
$350$	3.90963	+	2.77453i	0.208979	+	0.148305i
$351$		0			0
$352$	−14.4700	−	22.1209i	−0.771253	−	1.17905i
$353$	27.7812			1.47864			0.739322	−	0.673352i	$-0.235146\pi$
$353$	27.7812			1.47864			0.739322	+	0.673352i	$0.235146\pi$
$354$		0			0
$355$	−16.3861	−	28.3816i	−0.869685	−	1.50634i
$356$	1.95091	−	10.3012i	0.103398	−	0.545964i
$357$		0			0
$358$	7.21559	+	15.7326i	0.381356	+	0.831496i
$359$	18.0826	+	10.4400i	0.954362	+	0.551001i	0.894433	−	0.447201i	$-0.147579\pi$
$359$	18.0826	+	10.4400i	0.954362	+	0.551001i	0.0599291	+	0.998203i	$0.480913\pi$
$360$		0			0
$361$	13.5578	−	13.3111i	0.713570	−	0.700584i
$362$	−6.02097	−	4.27288i	−0.316455	−	0.224577i
$363$		0			0
$364$	1.34903	+	0.255487i	0.0707084	+	0.0133912i
$365$	13.8640	+	24.0131i	0.725673	+	1.25690i
$366$		0			0
$367$	0.657637	−	0.379687i	0.0343284	−	0.0198195i	−0.482738	−	0.875765i	$-0.660358\pi$
$367$	0.657637	−	0.379687i	0.0343284	−	0.0198195i	0.517066	+	0.855946i	$0.327024\pi$
$368$	0.316993	+	0.397773i	0.0165244	+	0.0207354i
$369$		0			0
$370$	−6.48790	+	69.1240i	−0.337290	+	3.59359i
$371$	−0.114175	−	0.197757i	−0.00592768	−	0.0102670i
$372$		0			0
$373$			24.1303i			1.24942i	0.780857	+	0.624709i	$0.214782\pi$
$373$			24.1303i			1.24942i	−0.780857	+	0.624709i	$0.785218\pi$
$374$	1.34444	−	14.3240i	0.0695191	−	0.740678i
$375$		0			0
$376$	−5.89213	+	1.45968i	−0.303863	+	0.0752773i
$377$	−2.24566	+	3.88960i	−0.115658	+	0.200325i
$378$		0			0
$379$	0.598000			0.0307172			0.0153586	−	0.999882i	$-0.495111\pi$
$379$	0.598000			0.0307172			0.0153586	+	0.999882i	$0.495111\pi$
$380$	25.2878	+	28.5697i	1.29724	+	1.46559i
$381$		0			0
$382$	19.1880	−	8.80037i	0.981746	−	0.450266i
$383$	6.48012	−	11.2239i	0.331119	−	0.573515i	−0.651613	−	0.758552i	$-0.725907\pi$
$383$	6.48012	−	11.2239i	0.331119	−	0.573515i	0.982732	+	0.185037i	$0.0592406\pi$
$384$		0			0
$385$	2.44899	−	4.24177i	0.124812	−	0.216181i
$386$	−2.01867	+	21.5075i	−0.102747	+	1.09470i
$387$		0			0
$388$	15.9904	−	5.59225i	0.811791	−	0.283903i
$389$	−8.14560	−	14.1086i	−0.412998	−	0.715334i	0.582218	−	0.813033i	$-0.302185\pi$
$389$	−8.14560	−	14.1086i	−0.412998	−	0.715334i	−0.995216	+	0.0976991i	$0.968852\pi$
$390$		0			0
$391$			0.276837i			0.0140003i
$392$	−18.8679	−	5.44095i	−0.952973	−	0.274809i
$393$		0			0
$394$	12.5229	+	27.3046i	0.630897	+	1.37559i
$395$	−21.2604	−	36.8242i	−1.06973	−	1.85282i
$396$		0			0
$397$	8.40683	−	14.5611i	0.421927	−	0.730799i	−0.574201	−	0.818714i	$-0.694687\pi$
$397$	8.40683	−	14.5611i	0.421927	−	0.730799i	0.996128	+	0.0879156i	$0.0280206\pi$
$398$	−21.8344	−	15.4951i	−1.09446	−	0.776701i
$399$		0			0
$400$	−44.2761	+	35.2844i	−2.21380	+	1.76422i
$401$	−9.52128	−	5.49711i	−0.475470	−	0.274513i	0.243057	−	0.970012i	$-0.421850\pi$
$401$	−9.52128	−	5.49711i	−0.475470	−	0.274513i	−0.718527	+	0.695499i	$0.755183\pi$
$402$		0			0
$403$	−12.5065	+	7.22061i	−0.622992	+	0.359684i
$404$	3.61720	+	0.685048i	0.179963	+	0.0340824i
$405$		0			0
$406$	−0.307152	+	0.432813i	−0.0152437	+	0.0214802i
$407$	52.4160			2.59817
$408$		0			0
$409$	22.5210	−	13.0025i	1.11359	−	0.642932i	0.173834	−	0.984775i	$-0.444384\pi$
$409$	22.5210	−	13.0025i	1.11359	−	0.642932i	0.939757	+	0.341843i	$0.111051\pi$
$410$	2.52796	+	1.79400i	0.124847	+	0.0885996i
$411$		0			0
$412$	−8.16020	+	9.47907i	−0.402024	+	0.467001i
$413$	−2.27215	−	1.31183i	−0.111805	−	0.0645509i
$414$		0			0
$415$	48.4107	+	27.9499i	2.37639	+	1.37201i
$416$	−7.31333	+	14.4717i	−0.358566	+	0.709531i
$417$		0			0
$418$	19.6908	−	21.0237i	0.963111	−	1.02830i
$419$			33.6123i			1.64207i	0.570879	+	0.821034i	$0.306603\pi$
$419$			33.6123i			1.64207i	−0.570879	+	0.821034i	$0.693397\pi$
$420$		0			0
$421$	−19.3211	−	11.1551i	−0.941655	−	0.543665i	−0.0511764	−	0.998690i	$-0.516297\pi$
$421$	−19.3211	−	11.1551i	−0.941655	−	0.543665i	−0.890479	+	0.455025i	$0.849630\pi$
$422$	−37.4217	−	3.51235i	−1.82166	−	0.170979i
$423$		0			0
$424$	2.61758	−	0.648465i	0.127121	−	0.0314923i
$425$	−30.8147			−1.49473
$426$		0			0
$427$	−1.15003	+	0.663972i	−0.0556540	+	0.0321318i
$428$	13.7818	−	16.0092i	0.666167	−	0.773834i
$429$		0			0
$430$	−30.2073	−	21.4371i	−1.45673	−	1.03379i
$431$	15.0017	+	25.9837i	0.722605	+	1.25159i	0.959952	+	0.280164i	$0.0903890\pi$
$431$	15.0017	+	25.9837i	0.722605	+	1.25159i	−0.237347	+	0.971425i	$0.576278\pi$
$432$		0			0
$433$	24.7775	−	14.3053i	1.19073	−	0.687470i	0.232260	−	0.972654i	$-0.425388\pi$
$433$	24.7775	−	14.3053i	1.19073	−	0.687470i	0.958473	+	0.285184i	$0.0920546\pi$
$434$	−1.55112	+	0.711401i	−0.0744559	+	0.0341483i
$435$		0			0
$436$	−15.4571	+	5.40574i	−0.740262	+	0.258888i
$437$	−0.339434	+	0.438178i	−0.0162373	+	0.0209609i
$438$		0			0
$439$	8.02837	−	13.9055i	0.383173	−	0.663675i	−0.608341	−	0.793676i	$-0.708165\pi$
$439$	8.02837	−	13.9055i	0.383173	−	0.663675i	0.991514	+	0.130001i	$0.0414980\pi$
$440$	40.1185	+	41.6689i	1.91257	+	1.98649i
$441$		0			0
$442$	−8.02178	+	3.67910i	−0.381557	+	0.174997i
$443$	−22.0523	+	12.7319i	−1.04774	+	0.604911i	−0.922015	−	0.387154i	$-0.873458\pi$
$443$	−22.0523	+	12.7319i	−1.04774	+	0.604911i	−0.125722	+	0.992066i	$0.540125\pi$
$444$		0			0
$445$			22.9425i			1.08758i
$446$	14.0598	+	1.31964i	0.665753	+	0.0624867i
$447$		0			0
$448$	−1.02021	+	1.62183i	−0.0482006	+	0.0766242i
$449$		−	13.9298i		−	0.657388i	−0.944436	−	0.328694i	$-0.893391\pi$
$449$		−	13.9298i		−	0.657388i	0.944436	−	0.328694i	$-0.106609\pi$
$450$		0			0
$451$	1.17015	−	2.02675i	0.0551000	−	0.0954361i
$452$	5.52663	+	4.75768i	0.259951	+	0.223783i
$453$		0			0
$454$	−4.98323	−	10.8653i	−0.233875	−	0.509933i
$455$	−3.00451			−0.140853
$456$		0			0
$457$	29.1395			1.36309			0.681545	−	0.731777i	$-0.261309\pi$
$457$	29.1395			1.36309			0.681545	+	0.731777i	$0.261309\pi$
$458$	8.11913	+	17.7027i	0.379382	+	0.827192i
$459$		0			0
$460$	−0.843517	−	0.726154i	−0.0393292	−	0.0338571i
$461$	10.3043	−	17.8475i	0.479917	−	0.831241i	−0.519817	−	0.854277i	$-0.674000\pi$
$461$	10.3043	−	17.8475i	0.479917	−	0.831241i	0.999735	+	0.0230363i	$0.00733333\pi$
$462$		0			0
$463$		−	31.0667i		−	1.44379i	−0.692002	−	0.721896i	$-0.743271\pi$
$463$		−	31.0667i		−	1.44379i	0.692002	−	0.721896i	$-0.256729\pi$
$464$	−3.90614	−	4.90155i	−0.181338	−	0.227549i
$465$		0			0
$466$	−2.00489	−	0.188177i	−0.0928748	−	0.00871711i
$467$			2.26975i			0.105032i	0.998620	+	0.0525158i	$0.0167240\pi$
$467$			2.26975i			0.105032i	−0.998620	+	0.0525158i	$0.983276\pi$
$468$		0			0
$469$	−1.72715	+	0.997173i	−0.0797525	+	0.0460452i
$470$	12.0740	−	5.53758i	0.556931	−	0.255430i
$471$		0			0
$472$	22.3204	−	21.4899i	1.02738	−	0.989155i
$473$	−13.9824	+	24.2182i	−0.642912	+	1.11356i
$474$		0			0
$475$	−48.7736	−	37.7823i	−2.23789	−	1.73357i
$476$	−0.984386	+	0.344264i	−0.0451193	+	0.0157793i
$477$		0			0
$478$	−25.6616	+	11.7694i	−1.17373	+	0.538319i
$479$	−29.8172	+	17.2150i	−1.36238	+	0.786572i	−0.989941	−	0.141483i	$-0.954813\pi$
$479$	−29.8172	+	17.2150i	−1.36238	+	0.786572i	−0.372442	+	0.928055i	$0.621480\pi$
$480$		0			0
$481$	−16.0765	−	27.8453i	−0.733024	−	1.26963i
$482$	−10.3315	−	7.33194i	−0.470589	−	0.333961i
$483$		0			0
$484$	14.1376	−	16.4226i	0.642620	−	0.746482i
$485$	−32.1030	+	18.5347i	−1.45772	+	0.841617i
$486$		0			0
$487$	−7.86738			−0.356505			−0.178253	−	0.983985i	$-0.557044\pi$
$487$	−7.86738			−0.356505			−0.178253	+	0.983985i	$0.557044\pi$
$488$	−3.77107	−	15.2222i	−0.170708	−	0.689079i
$489$		0			0
$490$	42.7823	+	4.01550i	1.93271	+	0.181402i
$491$	21.6785	+	12.5161i	0.978337	+	0.564843i	0.901768	−	0.432221i	$-0.142270\pi$
$491$	21.6785	+	12.5161i	0.978337	+	0.564843i	0.0765694	+	0.997064i	$0.475603\pi$
$492$		0			0
$493$		−	3.41132i		−	0.153638i
$494$	−17.2079	−	4.01233i	−0.774219	−	0.180523i
$495$		0			0
$496$	−2.99684	−	19.9286i	−0.134562	−	0.894820i
$497$	1.55317	+	0.896723i	0.0696692	+	0.0402235i
$498$		0			0
$499$	−24.2549	−	14.0036i	−1.08580	−	0.626887i	−0.153345	−	0.988173i	$-0.549005\pi$
$499$	−24.2549	−	14.0036i	−1.08580	−	0.626887i	−0.932455	+	0.361286i	$0.882338\pi$
$500$	52.2750	−	60.7238i	2.33781	−	2.71565i
$501$		0			0
$502$	18.7914	+	13.3356i	0.838700	+	0.595196i
$503$	−3.15704	+	1.82272i	−0.140766	+	0.0812711i	−0.568729	−	0.822525i	$-0.692565\pi$
$503$	−3.15704	+	1.82272i	−0.140766	+	0.0812711i	0.427963	+	0.903796i	$0.359231\pi$
$504$		0			0
$505$	−8.05610			−0.358492
$506$	−0.486316	+	0.685275i	−0.0216194	+	0.0304642i
$507$		0			0
$508$	31.2547	+	5.91921i	1.38670	+	0.262622i
$509$	−4.76629	+	2.75182i	−0.211262	+	0.121972i	−0.601898	−	0.798573i	$-0.705589\pi$
$509$	−4.76629	+	2.75182i	−0.211262	+	0.121972i	0.390636	+	0.920545i	$0.372255\pi$
$510$		0			0
$511$	−1.31411	−	0.758699i	−0.0581326	−	0.0335629i
$512$	−15.0648	−	16.8835i	−0.665777	−	0.746151i
$513$		0			0
$514$	−18.4694	−	13.1071i	−0.814650	−	0.578129i
$515$	13.6850	−	23.7032i	0.603035	−	1.04449i
$516$		0			0
$517$	−5.01425	−	8.68493i	−0.220526	−	0.381963i
$518$	−1.58391	−	3.45351i	−0.0695931	−	0.151739i
$519$		0			0
$520$	9.83131	−	34.0926i	0.431131	−	1.49506i
$521$		−	27.5982i		−	1.20910i	−0.796567	−	0.604550i	$-0.793353\pi$
$521$		−	27.5982i		−	1.20910i	0.796567	−	0.604550i	$-0.206647\pi$
$522$		0			0
$523$	−7.33484	−	12.7043i	−0.320730	−	0.555521i	0.659909	−	0.751346i	$-0.270595\pi$
$523$	−7.33484	−	12.7043i	−0.320730	−	0.555521i	−0.980639	+	0.195825i	$0.937262\pi$
$524$	8.05775	−	2.81799i	0.352004	−	0.123105i
$525$		0			0
$526$	−1.37735	+	14.6747i	−0.0600553	+	0.639847i
$527$	5.48431	−	9.49911i	0.238900	−	0.413788i
$528$		0			0
$529$	−11.4919	+	19.9046i	−0.499648	+	0.865417i
$530$	−5.36388	+	2.46008i	−0.232992	+	0.106859i
$531$		0			0
$532$	−1.98020	−	0.662067i	−0.0858524	−	0.0287042i
$533$	−1.43558			−0.0621818
$534$		0			0
$535$	−23.1127	+	40.0323i	−0.999247	+	1.73075i
$536$	−5.66351	−	22.8612i	−0.244626	−	0.987455i
$537$		0			0
$538$	−0.739267	+	7.87637i	−0.0318720	+	0.339575i
$539$		−	32.4414i		−	1.39735i
$540$		0			0
$541$	−14.2204	−	24.6304i	−0.611381	−	1.05894i	−0.991008	−	0.133804i	$-0.957281\pi$
$541$	−14.2204	−	24.6304i	−0.611381	−	1.05894i	0.379627	−	0.925140i	$-0.376052\pi$
$542$	−2.92336	+	31.1463i	−0.125569	+	1.33785i
$543$		0			0
$544$	−0.685325	−	12.2965i	−0.0293831	−	0.527208i
$545$	31.0323	−	17.9165i	1.32928	−	0.767460i
$546$		0			0
$547$	12.7597	+	22.1004i	0.545564	+	0.944944i	0.998571	+	0.0534373i	$0.0170177\pi$
$547$	12.7597	+	22.1004i	0.545564	+	0.944944i	−0.453008	+	0.891507i	$0.649649\pi$
$548$	12.3383	+	2.33671i	0.527067	+	0.0998191i
$549$		0			0
$550$	−76.2779	−	54.1318i	−3.25250	−	2.30819i
$551$	4.18267	−	5.39945i	0.178188	−	0.230024i
$552$		0			0
$553$	2.01519	+	1.16347i	0.0856945	+	0.0494757i
$554$	−10.4048	−	22.6863i	−0.442058	−	0.963849i
$555$		0			0
$556$	−4.68448	+	24.7351i	−0.198666	+	1.04900i
$557$	11.6534	+	20.1843i	0.493770	+	0.855235i	0.999974	−	0.00717894i	$-0.00228515\pi$
$557$	11.6534	+	20.1843i	0.493770	+	0.855235i	−0.506204	+	0.862414i	$0.668952\pi$
$558$		0			0
$559$	17.1541			0.725542
$560$	1.53312	−	3.90242i	0.0647860	−	0.164907i
$561$		0			0
$562$	−26.6773	−	18.9319i	−1.12531	−	0.798596i
$563$	−34.9445			−1.47274			−0.736368	−	0.676581i	$-0.763461\pi$
$563$	−34.9445			−1.47274			−0.736368	+	0.676581i	$0.763461\pi$
$564$		0			0
$565$	−13.8198	−	7.97885i	−0.581403	−	0.335673i
$566$	−0.682519	+	7.27177i	−0.0286884	+	0.305655i
$567$		0			0
$568$	−15.2575	+	14.6898i	−0.640192	+	0.616372i
$569$			19.6125i			0.822200i	0.911590	+	0.411100i	$0.134855\pi$
$569$			19.6125i			0.822200i	−0.911590	+	0.411100i	$0.865145\pi$
$570$		0			0
$571$		−	19.0983i		−	0.799240i	−0.916681	−	0.399620i	$-0.869142\pi$
$571$		−	19.0983i		−	0.799240i	0.916681	−	0.399620i	$-0.130858\pi$
$572$	−26.3199	−	4.98462i	−1.10049	−	0.208418i
$573$		0			0
$574$	−0.168895	−	0.0158523i	−0.00704955	−	0.000661662i
$575$	1.55867	+	0.899898i	0.0650010	+	0.0375284i
$576$		0			0
$577$	−33.8434			−1.40892			−0.704460	−	0.709744i	$-0.748811\pi$
$577$	−33.8434			−1.40892			−0.704460	+	0.709744i	$0.748811\pi$
$578$	−10.0345	+	14.1398i	−0.417381	+	0.588138i
$579$		0			0
$580$	10.3942	+	8.94803i	0.431597	+	0.371547i
$581$	−3.05910			−0.126913
$582$		0			0
$583$	2.22759	+	3.85829i	0.0922572	+	0.159794i
$584$	12.9091	−	12.4288i	0.534182	−	0.514306i
$585$		0			0
$586$	−6.20777	+	2.84712i	−0.256441	+	0.117614i
$587$	0.0311422	+	0.0179800i	0.00128538	+	0.000742113i	0.500643	−	0.865654i	$-0.333097\pi$
$587$	0.0311422	+	0.0179800i	0.00128538	+	0.000742113i	−0.499357	+	0.866396i	$0.666430\pi$
$588$		0			0
$589$	20.3276	−	8.31082i	0.837582	−	0.342441i
$590$	−39.2395	+	55.2930i	−1.61546	+	2.27638i
$591$		0			0
$592$	44.3704	−	6.67237i	1.82361	−	0.274233i
$593$	7.10342	+	12.3035i	0.291703	+	0.505244i	0.974212	−	0.225633i	$-0.0724449\pi$
$593$	7.10342	+	12.3035i	0.291703	+	0.505244i	−0.682510	+	0.730876i	$0.739112\pi$
$594$		0			0
$595$	1.97629	−	1.14101i	0.0810202	−	0.0467770i
$596$	−0.660619	−	1.88897i	−0.0270600	−	0.0773752i
$597$		0			0
$598$	0.513200	+	0.0481683i	0.0209863	+	0.00196975i
$599$	−9.32795	−	16.1565i	−0.381130	−	0.660136i	0.610094	−	0.792329i	$-0.291132\pi$
$599$	−9.32795	−	16.1565i	−0.381130	−	0.660136i	−0.991224	+	0.132193i	$0.957798\pi$
$600$		0			0
$601$		−	18.5537i		−	0.756820i	−0.925638	−	0.378410i	$-0.876471\pi$
$601$		−	18.5537i		−	0.756820i	0.925638	−	0.378410i	$-0.123529\pi$
$602$	2.01818	+	0.189424i	0.0822548	+	0.00772033i
$603$		0			0
$604$	−13.0729	+	15.1858i	−0.531929	+	0.617901i
$605$	−23.7095	+	41.0660i	−0.963927	+	1.66957i
$606$		0			0
$607$	−15.3817			−0.624322			−0.312161	−	0.950029i	$-0.601053\pi$
$607$	−15.3817			−0.624322			−0.312161	+	0.950029i	$0.601053\pi$
$608$	13.9921	−	20.3032i	0.567457	−	0.823403i
$609$		0			0
$610$	14.3063	+	31.1930i	0.579245	+	1.26297i
$611$	−3.07583	+	5.32750i	−0.124435	+	0.215527i
$612$		0			0
$613$	5.04739	−	8.74233i	0.203862	−	0.353099i	−0.745908	−	0.666050i	$-0.767984\pi$
$613$	5.04739	−	8.74233i	0.203862	−	0.353099i	0.949770	+	0.312950i	$0.101317\pi$
$614$	−27.0026	−	2.53443i	−1.08974	−	0.102281i
$615$		0			0
$616$	−3.04149	−	0.877076i	−0.122545	−	0.0353384i
$617$	−16.9940	−	29.4344i	−0.684151	−	1.18499i	−0.973703	−	0.227823i	$-0.926839\pi$
$617$	−16.9940	−	29.4344i	−0.684151	−	1.18499i	0.289551	−	0.957163i	$-0.406494\pi$
$618$		0			0
$619$		−	12.8492i		−	0.516453i	−0.966084	−	0.258226i	$-0.916862\pi$
$619$		−	12.8492i		−	0.516453i	0.966084	−	0.258226i	$-0.0831381\pi$
$620$	14.5580	+	41.6271i	0.584664	+	1.67178i
$621$		0			0
$622$	10.6459	−	4.88259i	0.426860	−	0.195774i
$623$	−0.627759	−	1.08731i	−0.0251506	−	0.0435622i
$624$		0			0
$625$	−52.2827	+	90.5562i	−2.09131	+	3.62225i
$626$	17.0015	−	23.9571i	0.679519	−	0.957520i
$627$		0			0
$628$	8.89516	+	25.4347i	0.354955	+	1.01496i
$629$	21.1495	+	12.2107i	0.843284	+	0.486871i
$630$		0			0
$631$	41.6289	−	24.0344i	1.65722	−	0.956796i	0.683230	−	0.730203i	$-0.260574\pi$
$631$	41.6289	−	24.0344i	1.65722	−	0.956796i	0.973989	−	0.226594i	$-0.0727589\pi$
$632$	−19.7961	+	19.0596i	−0.787448	+	0.758149i
$633$		0			0
$634$	16.2721	+	11.5478i	0.646248	+	0.458620i
$635$	−69.6093			−2.76236
$636$		0			0
$637$	−17.2340	+	9.95007i	−0.682837	+	0.394236i
$638$	5.99262	−	8.44430i	0.237250	−	0.334313i
$639$		0			0
$640$	39.2648	+	30.1660i	1.55208	+	1.19242i
$641$	−31.1211	−	17.9677i	−1.22921	−	0.709683i	−0.262343	−	0.964975i	$-0.584495\pi$
$641$	−31.1211	−	17.9677i	−1.22921	−	0.709683i	−0.966864	+	0.255291i	$0.917829\pi$
$642$		0			0
$643$	1.91374	+	1.10490i	0.0754705	+	0.0435729i	0.537260	−	0.843416i	$-0.319459\pi$
$643$	1.91374	+	1.10490i	0.0754705	+	0.0435729i	−0.461790	+	0.886989i	$0.652793\pi$
$644$	0.0598459	+	0.0113340i	0.00235826	+	0.000446621i
$645$		0			0
$646$	12.8427	−	3.89578i	0.505289	−	0.153277i
$647$			16.5467i			0.650518i	0.945625	+	0.325259i	$0.105452\pi$
$647$			16.5467i			0.650518i	−0.945625	+	0.325259i	$0.894548\pi$
$648$		0			0
$649$	44.3303	+	25.5941i	1.74012	+	1.00466i
$650$	−5.36161	+	57.1243i	−0.210300	+	2.24060i
$651$		0			0
$652$	−30.3626	−	26.1381i	−1.18909	−	1.02365i
$653$	14.2851			0.559019			0.279509	−	0.960143i	$-0.409828\pi$
$653$	14.2851			0.559019			0.279509	+	0.960143i	$0.409828\pi$
$654$		0			0
$655$	−16.1771	+	9.33983i	−0.632090	+	0.364938i
$656$	0.732536	−	1.86461i	0.0286007	−	0.0728008i
$657$		0			0
$658$	−0.420699	+	0.592813i	−0.0164006	+	0.0231103i
$659$	−5.21869	−	9.03904i	−0.203291	−	0.352111i	0.746296	−	0.665615i	$-0.231831\pi$
$659$	−5.21869	−	9.03904i	−0.203291	−	0.352111i	−0.949587	+	0.313504i	$0.898497\pi$
$660$		0			0
$661$	−7.22027	+	4.16862i	−0.280836	+	0.162141i	−0.633802	−	0.773496i	$-0.718506\pi$
$661$	−7.22027	+	4.16862i	−0.280836	+	0.162141i	0.352966	+	0.935636i	$0.385173\pi$
$662$	8.04024	+	17.5307i	0.312493	+	0.681349i
$663$		0			0
$664$	10.0099	−	34.7121i	0.388461	−	1.34709i
$665$	4.52710	+	0.617160i	0.175553	+	0.0239325i
$666$		0			0
$667$	−0.0996226	+	0.172551i	−0.00385740	+	0.00668122i
$668$	−7.38603	−	1.39881i	−0.285774	−	0.0541216i
$669$		0			0
$670$	21.4856	+	46.8466i	0.830062	+	1.80984i
$671$	22.4374	−	12.9543i	0.866188	−	0.500094i
$672$		0			0
$673$			31.6397i			1.21962i	0.792547	+	0.609811i	$0.208755\pi$
$673$			31.6397i			1.21962i	−0.792547	+	0.609811i	$0.791245\pi$
$674$	0.805461	−	8.58163i	0.0310252	−	0.330552i
$675$		0			0
$676$	−3.15854	−	9.03151i	−0.121482	−	0.347366i
$677$			44.1257i			1.69589i	0.530087	+	0.847943i	$0.322159\pi$
$677$			44.1257i			1.69589i	−0.530087	+	0.847943i	$0.677841\pi$
$678$		0			0
$679$	1.01430	−	1.75682i	0.0389254	−	0.0674207i
$680$	6.48047	+	26.1590i	0.248515	+	1.00315i
$681$		0			0
$682$	30.2627	−	13.8796i	1.15882	−	0.531478i
$683$	3.14107			0.120190			0.0600949	−	0.998193i	$-0.480860\pi$
$683$	3.14107			0.120190			0.0600949	+	0.998193i	$0.480860\pi$
$684$		0			0
$685$	−27.4794			−1.04994
$686$	−4.29256	+	1.96873i	−0.163891	+	0.0751666i
$687$		0			0
$688$	−8.75328	+	22.2808i	−0.333716	+	0.849446i
$689$	1.36644	−	2.36675i	0.0520573	−	0.0901659i
$690$		0			0
$691$		−	36.3881i		−	1.38427i	−0.721769	−	0.692134i	$-0.756671\pi$
$691$		−	36.3881i		−	1.38427i	0.721769	−	0.692134i	$-0.243329\pi$
$692$	14.6851	−	5.13576i	0.558245	−	0.195232i
$693$		0			0
$694$	0.952809	−	10.1515i	0.0361681	−	0.385346i
$695$		−	55.0890i		−	2.08965i
$696$		0			0
$697$	0.944290	−	0.545186i	0.0357675	−	0.0206504i
$698$	0.140992	+	0.307414i	0.00533661	+	0.0116358i
$699$		0			0
$700$	−1.26158	+	6.66145i	−0.0476834	+	0.251779i
$701$	−0.756319	+	1.30998i	−0.0285658	+	0.0494773i	−0.879955	−	0.475057i	$-0.842427\pi$
$701$	−0.756319	+	1.30998i	−0.0285658	+	0.0494773i	0.851389	+	0.524535i	$0.175761\pi$
$702$		0			0
$703$	18.5038	+	45.2587i	0.697884	+	1.70696i
$704$	19.9046	−	31.6423i	0.750184	−	1.19256i
$705$		0			0
$706$	16.3788	+	35.7117i	0.616422	+	1.34403i
$707$	0.381801	−	0.220433i	0.0143591	−	0.00829024i
$708$		0			0
$709$	7.54529	+	13.0688i	0.283369	+	0.490810i	0.972212	−	0.234100i	$-0.0752145\pi$
$709$	7.54529	+	13.0688i	0.283369	+	0.490810i	−0.688843	+	0.724910i	$0.741881\pi$
$710$	26.8229	−	37.7965i	1.00664	−	1.41848i
$711$		0			0
$712$	14.3920	−	3.56540i	0.539364	−	0.133619i
$713$	−0.554815	+	0.320322i	−0.0207780	+	0.0119962i
$714$		0			0
$715$	58.6187			2.19221
$716$	−15.9697	+	18.5508i	−0.596816	+	0.693274i
$717$		0			0
$718$	−2.75940	+	29.3995i	−0.102980	+	1.09718i
$719$	−8.23299	−	4.75332i	−0.307039	−	0.177269i	0.338562	−	0.940944i	$-0.390060\pi$
$719$	−8.23299	−	4.75332i	−0.307039	−	0.177269i	−0.645601	+	0.763675i	$0.723393\pi$
$720$		0			0
$721$			1.49782i			0.0557816i
$722$	25.1041	+	9.58035i	0.934279	+	0.356544i
$723$		0			0
$724$	1.94288	−	10.2589i	0.0722068	−	0.381268i
$725$	−19.2067	−	11.0890i	−0.713319	−	0.411835i
$726$		0			0
$727$	−6.51295	−	3.76026i	−0.241552	−	0.139460i	0.374338	−	0.927292i	$-0.377870\pi$
$727$	−6.51295	−	3.76026i	−0.241552	−	0.139460i	−0.615890	+	0.787832i	$0.711203\pi$
$728$	0.466918	+	1.88475i	0.0173051	+	0.0698536i
$729$		0			0
$730$	−22.6943	+	31.9788i	−0.839953	+	1.18359i
$731$	−11.2836	+	6.51459i	−0.417339	+	0.240951i
$732$		0			0
$733$	−34.5713			−1.27692			−0.638460	−	0.769655i	$-0.720428\pi$
$733$	−34.5713			−1.27692			−0.638460	+	0.769655i	$0.720428\pi$
$734$	0.875791	+	0.621519i	0.0323261	+	0.0229407i
$735$		0			0
$736$	−0.324436	+	0.641995i	−0.0119589	+	0.0236642i
$737$	33.6972	−	19.4551i	1.24125	−	0.716638i
$738$		0			0
$739$	18.0526	+	10.4227i	0.664075	+	0.383404i	0.793828	−	0.608143i	$-0.208085\pi$
$739$	18.0526	+	10.4227i	0.664075	+	0.383404i	−0.129753	+	0.991546i	$0.541418\pi$
$740$	−92.6814	+	32.4130i	−3.40704	+	1.19153i
$741$		0			0
$742$	0.186896	−	0.263358i	0.00686117	−	0.00966818i
$743$	−14.7223	+	25.4997i	−0.540107	+	0.935494i	0.458790	+	0.888545i	$0.348283\pi$
$743$	−14.7223	+	25.4997i	−0.540107	+	0.935494i	−0.998897	+	0.0469488i	$0.985050\pi$
$744$		0			0
$745$	2.18953	+	3.79237i	0.0802181	+	0.138942i
$746$	−31.0186	+	14.2263i	−1.13567	+	0.520862i
$747$		0			0
$748$	19.2056	−	6.71669i	0.702228	−	0.245586i
$749$		−	2.52966i		−	0.0924318i
$750$		0			0
$751$	−0.0915128	−	0.158505i	−0.00333935	−	0.00578392i	0.864351	−	0.502889i	$-0.167730\pi$
$751$	−0.0915128	−	0.158505i	−0.00333935	−	0.00578392i	−0.867690	+	0.497105i	$0.834396\pi$
$752$	−5.35014	−	6.71354i	−0.195100	−	0.244818i
$753$		0			0
$754$	−6.32390	−	0.593554i	−0.230303	−	0.0216160i
$755$	21.9239	−	37.9733i	0.797892	−	1.38199i
$756$		0			0
$757$	−0.412765	+	0.714929i	−0.0150022	+	0.0259845i	−0.873429	−	0.486951i	$-0.838109\pi$
$757$	−0.412765	+	0.714929i	−0.0150022	+	0.0259845i	0.858427	+	0.512936i	$0.171442\pi$
$758$	0.352558	+	0.768707i	0.0128055	+	0.0279207i
$759$		0			0
$760$	−21.8165	+	49.3502i	−0.791369	+	1.79012i
$761$	−38.9955			−1.41358			−0.706792	−	0.707421i	$-0.749858\pi$
$761$	−38.9955			−1.41358			−0.706792	+	0.707421i	$0.749858\pi$
$762$		0			0
$763$	−0.980474	+	1.69823i	−0.0354956	+	0.0614801i
$764$	22.6251	+	19.4772i	0.818548	+	0.704659i
$765$		0			0
$766$	18.2484	+	1.71277i	0.659340	+	0.0618848i
$767$		−	31.3998i		−	1.13378i
$768$		0			0
$769$	−10.5294	−	18.2374i	−0.379699	−	0.657657i	0.611320	−	0.791384i	$-0.290639\pi$
$769$	−10.5294	−	18.2374i	−0.379699	−	0.657657i	−0.991018	+	0.133727i	$0.957306\pi$
$770$	6.89647	+	0.647294i	0.248532	+	0.0233269i
$771$		0			0
$772$	−28.8372	+	10.0851i	−1.03787	+	0.362970i
$773$	15.5604	−	8.98380i	0.559669	−	0.323125i	−0.193344	−	0.981131i	$-0.561933\pi$
$773$	15.5604	−	8.98380i	0.559669	−	0.323125i	0.753012	+	0.658006i	$0.228600\pi$
$774$		0			0
$775$	−35.6551	−	61.7564i	−1.28077	−	2.21835i
$776$	16.6160	+	17.2581i	0.596479	+	0.619530i
$777$		0			0
$778$	13.3337	−	18.7888i	0.478037	−	0.673610i
$779$	2.16308	+	0.294884i	0.0775005	+	0.0105653i
$780$		0			0
$781$	−30.3028	−	17.4953i	−1.08432	−	0.626031i
$782$	−0.355864	+	0.163213i	−0.0127257	+	0.00583648i
$783$		0			0
$784$	−4.12967	−	27.4618i	−0.147488	−	0.980778i
$785$	−29.4817	−	51.0638i	−1.05225	−	1.82255i
$786$		0			0
$787$	−11.7070			−0.417309			−0.208655	−	0.977989i	$-0.566908\pi$
$787$	−11.7070			−0.417309			−0.208655	+	0.977989i	$0.566908\pi$
$788$	−27.7160	+	32.1956i	−0.987343	+	1.14692i
$789$		0			0
$790$	34.8018	−	49.0397i	1.23819	−	1.74475i
$791$	0.873279			0.0310502
$792$		0			0
$793$	−13.7635	−	7.94638i	−0.488757	−	0.282184i
$794$	23.6741	+	2.22202i	0.840161	+	0.0788565i
$795$		0			0
$796$	7.04567	−	37.2027i	0.249727	−	1.31862i
$797$			48.7535i			1.72694i	0.504403	+	0.863469i	$0.331713\pi$
$797$			48.7535i			1.72694i	−0.504403	+	0.863469i	$0.668287\pi$
$798$		0			0
$799$		−	4.67241i		−	0.165298i
$800$	−71.4604	−	36.1129i	−2.52651	−	1.27678i
$801$		0			0
$802$	1.45295	−	15.4801i	0.0513054	−	0.546623i
$803$	25.6386	+	14.8024i	0.904765	+	0.522366i
$804$		0			0
$805$	−0.133287			−0.00469773
$806$	−16.6552	−	11.8196i	−0.586654	−	0.416328i
$807$		0			0
$808$	1.25196	+	5.05366i	0.0440440	+	0.177787i
$809$	−9.79587			−0.344404			−0.172202	−	0.985062i	$-0.555088\pi$
$809$	−9.79587			−0.344404			−0.172202	+	0.985062i	$0.555088\pi$
$810$		0			0
$811$	−7.80774	−	13.5234i	−0.274167	−	0.474871i	0.695758	−	0.718277i	$-0.255069\pi$
$811$	−7.80774	−	13.5234i	−0.274167	−	0.474871i	−0.969925	+	0.243405i	$0.921735\pi$
$812$	−0.737451	−	0.139663i	−0.0258795	−	0.00490120i
$813$		0			0
$814$	30.9025	+	67.3789i	1.08313	+	2.36163i
$815$	75.9241	+	43.8348i	2.65950	+	1.53547i
$816$		0			0
$817$	−25.8473	−	3.52366i	−0.904283	−	0.123277i
$818$	29.9918	+	21.2841i	1.04864	+	0.744182i
$819$		0			0
$820$	−0.815738	+	4.30728i	−0.0284868	+	0.150417i
$821$	−19.8442	−	34.3712i	−0.692569	−	1.19956i	−0.970993	−	0.239106i	$-0.923146\pi$
$821$	−19.8442	−	34.3712i	−0.692569	−	1.19956i	0.278425	−	0.960458i	$-0.410188\pi$
$822$		0			0
$823$	0.409585	−	0.236474i	0.0142772	−	0.00824297i	−0.492844	−	0.870117i	$-0.664043\pi$
$823$	0.409585	−	0.236474i	0.0142772	−	0.00824297i	0.507122	+	0.861874i	$0.330709\pi$
$824$	−16.9960	−	4.90113i	−0.592082	−	0.170739i
$825$		0			0
$826$	0.346731	−	3.69417i	0.0120643	−	0.128537i
$827$	4.32281	+	7.48733i	0.150319	+	0.260360i	0.931345	−	0.364139i	$-0.118637\pi$
$827$	4.32281	+	7.48733i	0.150319	+	0.260360i	−0.781026	+	0.624499i	$0.785303\pi$
$828$		0			0
$829$		−	34.5533i		−	1.20009i	−0.799968	−	0.600043i	$-0.795150\pi$
$829$		−	34.5533i		−	1.20009i	0.799968	−	0.600043i	$-0.204850\pi$
$830$	−7.38748	+	78.7084i	−0.256423	+	2.73201i
$831$		0			0
$832$	−22.9145	−	0.869076i	−0.794416	−	0.0301298i
$833$	7.55743	−	13.0899i	0.261849	−	0.453537i
$834$		0			0
$835$	16.4499			0.569272
$836$	38.6341	+	12.9171i	1.33619	+	0.446747i
$837$		0			0
$838$	−43.2074	+	19.8166i	−1.49257	+	0.684552i
$839$	12.6767	−	21.9567i	0.437648	−	0.758028i	−0.559860	−	0.828587i	$-0.689145\pi$
$839$	12.6767	−	21.9567i	0.437648	−	0.758028i	0.997508	+	0.0705590i	$0.0224783\pi$
$840$		0			0
$841$	−13.2724	+	22.9885i	−0.457669	+	0.792706i
$842$	2.94841	−	31.4132i	0.101609	−	1.08257i
$843$		0			0
$844$	−17.5474	−	50.1749i	−0.604007	−	1.72709i
$845$	10.4685	+	18.1320i	0.360129	+	0.623761i
$846$		0			0
$847$		−	2.59498i		−	0.0891646i
$848$	2.37681	+	2.98250i	0.0816199	+	0.102419i
$849$		0			0
$850$	−18.1672	−	39.6112i	−0.623130	−	1.35865i
$851$	−0.713188	−	1.23528i	−0.0244478	−	0.0423448i
$852$		0			0
$853$	−3.19049	+	5.52610i	−0.109240	+	0.189210i	−0.915463	−	0.402403i	$-0.868175\pi$
$853$	−3.19049	+	5.52610i	−0.109240	+	0.189210i	0.806222	+	0.591613i	$0.201509\pi$
$854$	−1.53153	−	1.08687i	−0.0524078	−	0.0371920i
$855$		0			0
$856$	28.7045	+	8.27753i	0.981099	+	0.282920i
$857$	19.9983	+	11.5460i	0.683127	+	0.394404i	0.801032	−	0.598621i	$-0.204284\pi$
$857$	19.9983	+	11.5460i	0.683127	+	0.394404i	−0.117905	+	0.993025i	$0.537618\pi$
$858$		0			0
$859$	−40.6638	+	23.4773i	−1.38743	+	0.801034i	−0.993025	−	0.117902i	$-0.962383\pi$
$859$	−40.6638	+	23.4773i	−1.38743	+	0.801034i	−0.394406	+	0.918936i	$0.629050\pi$
$860$	9.74748	−	51.4689i	0.332386	−	1.75507i
$861$		0			0
$862$	−24.5566	+	34.6031i	−0.836402	+	1.17859i
$863$	16.9298			0.576296			0.288148	−	0.957586i	$-0.406960\pi$
$863$	16.9298			0.576296			0.288148	+	0.957586i	$0.406960\pi$
$864$		0			0
$865$	−29.4825	+	17.0217i	−1.00243	+	0.578756i
$866$	32.9969	+	23.4167i	1.12128	+	0.795733i
$867$		0			0
$868$	−1.82896	−	1.57449i	−0.0620789	−	0.0534416i
$869$	−39.3168	−	22.6996i	−1.33373	−	0.770030i
$870$		0			0
$871$	−20.6705	−	11.9341i	−0.700393	−	0.404372i
$872$	−16.0618	−	16.6825i	−0.543922	−	0.564942i
$873$		0			0
$874$	−0.763380	−	0.177996i	−0.0258217	−	0.00602080i
$875$		−	9.59515i		−	0.324375i
$876$		0			0
$877$	−27.1037	−	15.6483i	−0.915227	−	0.528407i	−0.0331180	−	0.999451i	$-0.510544\pi$
$877$	−27.1037	−	15.6483i	−0.915227	−	0.528407i	−0.882109	+	0.471045i	$0.843877\pi$
$878$	22.6083	+	2.12199i	0.762993	+	0.0716136i
$879$		0			0
$880$	−29.9115	+	76.1373i	−1.00832	+	2.56659i
$881$	−15.7315			−0.530007			−0.265004	−	0.964247i	$-0.585373\pi$
$881$	−15.7315			−0.530007			−0.265004	+	0.964247i	$0.585373\pi$
$882$		0			0
$883$	−21.5867	+	12.4631i	−0.726452	+	0.419417i	−0.817123	−	0.576464i	$-0.804432\pi$
$883$	−21.5867	+	12.4631i	−0.726452	+	0.419417i	0.0906710	+	0.995881i	$0.471099\pi$
$884$	−9.45869	−	8.14265i	−0.318130	−	0.273867i
$885$		0			0
$886$	−29.3676	−	20.8412i	−0.986624	−	0.700173i
$887$	−21.7463	−	37.6658i	−0.730171	−	1.26469i	−0.956810	−	0.290714i	$-0.906107\pi$
$887$	−21.7463	−	37.6658i	−0.730171	−	1.26469i	0.226639	−	0.973979i	$-0.427226\pi$
$888$		0			0
$889$	3.29899	−	1.90467i	0.110644	−	0.0638806i
$890$	−29.4917	+	13.5260i	−0.988565	+	0.453394i
$891$		0			0
$892$	6.59281	+	18.8514i	0.220744	+	0.631192i
$893$	5.72890	−	7.39549i	0.191710	−	0.247481i
$894$		0			0
$895$	26.7819	−	46.3876i	0.895221	−	1.55057i
$896$	−2.68628	−	0.355278i	−0.0897423	−	0.0118690i
$897$		0			0
$898$	17.9063	−	8.21249i	0.597540	−	0.274054i
$899$	6.83670	−	3.94717i	0.228017	−	0.131645i
$900$		0			0
$901$			2.07572i			0.0691523i
$902$	3.29519	+	0.309283i	0.109718	+	0.0102980i
$903$		0			0
$904$	−2.85753	+	9.90924i	−0.0950401	+	0.329576i
$905$			22.8481i			0.759498i
$906$		0			0
$907$	−0.723484	+	1.25311i	−0.0240229	+	0.0416089i	−0.877787	−	0.479051i	$-0.840981\pi$
$907$	−0.723484	+	1.25311i	−0.0240229	+	0.0416089i	0.853764	+	0.520660i	$0.174314\pi$
$908$	11.0290	−	12.8115i	0.366010	−	0.425165i
$909$		0			0
$910$	−1.77134	−	3.86218i	−0.0587195	−	0.128030i
$911$	−16.4377			−0.544607			−0.272303	−	0.962211i	$-0.587785\pi$
$911$	−16.4377			−0.544607			−0.272303	+	0.962211i	$0.587785\pi$
$912$		0			0
$913$	59.6838			1.97524
$914$	17.1796	+	37.4578i	0.568250	+	1.23899i
$915$		0			0
$916$	−17.9694	+	20.8737i	−0.593726	+	0.689686i
$917$	0.511118	−	0.885283i	0.0168786	−	0.0292346i
$918$		0			0
$919$			14.6577i			0.483513i	0.970337	+	0.241756i	$0.0777234\pi$
$919$			14.6577i			0.483513i	−0.970337	+	0.241756i	$0.922277\pi$
$920$	0.436139	−	1.51242i	0.0143791	−	0.0498631i
$921$		0			0
$922$	29.0173	+	2.72353i	0.955634	+	0.0896947i
$923$			21.4639i			0.706492i
$924$		0			0
$925$	137.499	−	79.3849i	4.52093	−	2.61016i
$926$	39.9351	−	18.3158i	1.31235	−	0.601893i
$927$		0			0
$928$	3.99786	−	7.91097i	0.131236	−	0.259690i
$929$	−14.1568	+	24.5202i	−0.464468	+	0.804483i	−0.999177	−	0.0405536i	$-0.987088\pi$
$929$	−14.1568	+	24.5202i	−0.464468	+	0.804483i	0.534709	+	0.845036i	$0.320421\pi$
$930$		0			0
$931$	28.0116	−	11.4524i	0.918042	−	0.375337i
$932$	−0.940115	−	2.68816i	−0.0307945	−	0.0880535i
$933$		0			0
$934$	−2.91769	+	1.33816i	−0.0954696	+	0.0437860i
$935$	−38.5580	+	22.2615i	−1.26098	+	0.728028i
$936$		0			0
$937$	8.76699	+	15.1849i	0.286405	+	0.496068i	0.972949	−	0.231020i	$-0.0742064\pi$
$937$	8.76699	+	15.1849i	0.286405	+	0.496068i	−0.686544	+	0.727088i	$0.740873\pi$
$938$	−2.30009	−	1.63230i	−0.0751007	−	0.0532964i
$939$		0			0
$940$	14.2367	+	12.2559i	0.464351	+	0.399743i
$941$	30.8958	−	17.8377i	1.00717	−	0.581491i	0.0968101	−	0.995303i	$-0.469136\pi$
$941$	30.8958	−	17.8377i	1.00717	−	0.581491i	0.910363	+	0.413811i	$0.135803\pi$
$942$		0			0
$943$	−0.0636854			−0.00207388
$944$	40.7838	+	16.0224i	1.32740	+	0.521486i
$945$		0			0
$946$	−39.3752	−	3.69571i	−1.28020	−	0.120158i
$947$	26.9058	+	15.5341i	0.874320	+	0.504789i	0.868781	−	0.495196i	$-0.164904\pi$
$947$	26.9058	+	15.5341i	0.874320	+	0.504789i	0.00553875	+	0.999985i	$0.498237\pi$
$948$		0			0
$949$		−	18.1602i		−	0.589503i
$950$	19.8127	−	84.9717i	0.642809	−	2.75685i
$951$		0			0
$952$	−1.02290	−	1.06243i	−0.0331523	−	0.0344335i
$953$	−4.89263	−	2.82476i	−0.158488	−	0.0915030i	0.418658	−	0.908144i	$-0.362500\pi$
$953$	−4.89263	−	2.82476i	−0.158488	−	0.0915030i	−0.577146	+	0.816641i	$0.695834\pi$
$954$		0			0
$955$	−56.5759	−	32.6641i	−1.83075	−	1.05699i
$956$	−30.2582	−	26.0482i	−0.978621	−	0.842460i
$957$		0			0
$958$	−39.7083	−	28.1796i	−1.28292	−	0.910442i
$959$	1.30233	−	0.751900i	0.0420544	−	0.0242801i
$960$		0			0
$961$	−5.61689			−0.181190
$962$	26.3160	−	37.0822i	0.848461	−	1.19558i
$963$		0			0
$964$	3.33385	−	17.6035i	0.107376	−	0.566969i
$965$	57.8948	−	33.4256i	1.86370	−	1.07601i
$966$		0			0
$967$	12.1691	+	7.02582i	0.391331	+	0.225935i	0.682737	−	0.730665i	$-0.260790\pi$
$967$	12.1691	+	7.02582i	0.391331	+	0.225935i	−0.291406	+	0.956600i	$0.594123\pi$
$968$	29.4457	+	8.49127i	0.946420	+	0.272920i
$969$		0			0
$970$	−42.7524	−	30.3399i	−1.37270	−	0.974156i
$971$	8.53968	−	14.7912i	0.274051	−	0.474671i	−0.695844	−	0.718193i	$-0.744970\pi$
$971$	8.53968	−	14.7912i	0.274051	−	0.474671i	0.969895	+	0.243522i	$0.0783029\pi$
$972$		0			0
$973$	1.50736	+	2.61083i	0.0483238	+	0.0836993i
$974$	−4.63831	−	10.1132i	−0.148621	−	0.324049i
$975$		0			0
$976$	17.3444	−	13.8220i	0.555179	−	0.442433i
$977$			7.32115i			0.234224i	0.993119	+	0.117112i	$0.0373637\pi$
$977$			7.32115i			0.234224i	−0.993119	+	0.117112i	$0.962636\pi$
$978$		0			0
$979$	12.2477	+	21.2137i	0.391440	+	0.677993i
$980$	20.0611	+	57.3625i	0.640828	+	1.83238i
$981$		0			0
$982$	−3.30814	+	35.2459i	−0.105567	+	1.12474i
$983$	−2.33635	+	4.04667i	−0.0745179	+	0.129069i	−0.900877	−	0.434075i	$-0.857075\pi$
$983$	−2.33635	+	4.04667i	−0.0745179	+	0.129069i	0.826359	+	0.563144i	$0.190408\pi$
$984$		0			0
$985$	46.4811	−	80.5076i	1.48101	−	2.56518i
$986$	4.38513	−	2.01119i	0.139651	−	0.0640493i
$987$		0			0
$988$	−4.98742	−	24.4856i	−0.158671	−	0.778991i
$989$	0.760995			0.0241982
$990$		0			0
$991$	24.8465	−	43.0353i	0.789274	−	1.36706i	−0.137138	−	0.990552i	$-0.543790\pi$
$991$	24.8465	−	43.0353i	0.789274	−	1.36706i	0.926412	−	0.376511i	$-0.122876\pi$
$992$	23.8507	−	15.6015i	0.757259	−	0.495347i
$993$		0			0
$994$	−0.237014	+	2.52522i	−0.00751762	+	0.0800951i
$995$			82.8564i			2.62673i
$996$		0			0
$997$	24.1946	+	41.9062i	0.766250	+	1.32718i	0.939583	+	0.342321i	$0.111213\pi$
$997$	24.1946	+	41.9062i	0.766250	+	1.32718i	−0.173333	+	0.984863i	$0.555454\pi$
$998$	3.70130	−	39.4348i	0.117163	−	1.24829i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.r.b.559.7		20
3.2	odd	2		228.2.k.b.103.4	yes	20
4.3	odd	2		684.2.r.c.559.10		20
12.11	even	2		228.2.k.a.103.1	yes	20
19.12	odd	6		684.2.r.c.487.10		20
57.50	even	6		228.2.k.a.31.1	✓	20
76.31	even	6	inner	684.2.r.b.487.7		20
228.107	odd	6		228.2.k.b.31.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.k.a.31.1	✓	20	57.50	even	6
228.2.k.a.103.1	yes	20	12.11	even	2
228.2.k.b.31.4	yes	20	228.107	odd	6
228.2.k.b.103.4	yes	20	3.2	odd	2
684.2.r.b.487.7		20	76.31	even	6	inner
684.2.r.b.559.7		20	1.1	even	1	trivial
684.2.r.c.487.10		20	19.12	odd	6
684.2.r.c.559.10		20	4.3	odd	2

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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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.589563 + 1.28546i) q^{2} +(-1.30483 + 1.51572i) q^{4} +(2.18826 - 3.79018i) q^{5} +0.239504i q^{7} +(-2.71769 - 0.783701i) q^{8} +(6.16226 + 0.578382i) q^{10} -4.67278i q^{11} +(-2.48235 + 1.43318i) q^{13} +(-0.307873 + 0.141202i) q^{14} +(-0.594827 - 3.95553i) q^{16} +(1.08855 - 1.88543i) q^{17} +(4.03471 - 1.64957i) q^{19} +(2.88955 + 8.26235i) q^{20} +(6.00668 - 2.75489i) q^{22} +(-0.110122 + 0.0635792i) q^{23} +(-7.07699 - 12.2577i) q^{25} +(-3.30580 - 2.34601i) q^{26} +(-0.363021 - 0.312512i) q^{28} +(1.35698 - 0.783454i) q^{29} +5.03817 q^{31} +(4.73399 - 3.09666i) q^{32} +(3.06542 + 0.287717i) q^{34} +(0.907762 + 0.524097i) q^{35} +11.2173i q^{37} +(4.49918 + 4.21395i) q^{38} +(-8.91738 + 8.58558i) q^{40} +(0.433736 + 0.250418i) q^{41} +(-5.18284 - 2.99231i) q^{43} +(7.08263 + 6.09719i) q^{44} +(-0.146653 - 0.104074i) q^{46} +(1.85862 - 1.07308i) q^{47} +6.94264 q^{49} +(11.5845 - 16.3239i) q^{50} +(1.06674 - 5.63261i) q^{52} +(-0.825696 + 0.476716i) q^{53} +(-17.7107 - 10.2253i) q^{55} +(0.187699 - 0.650895i) q^{56} +(1.80713 + 1.28245i) q^{58} +(-5.47728 + 9.48693i) q^{59} +(2.77228 + 4.80174i) q^{61} +(2.97031 + 6.47638i) q^{62} +(6.77163 + 4.25970i) q^{64} +12.5447i q^{65} +(4.16350 + 7.21139i) q^{67} +(1.43741 + 4.11011i) q^{68} +(-0.138525 + 1.47588i) q^{70} +(3.74409 - 6.48496i) q^{71} +(-3.16780 + 5.48679i) q^{73} +(-14.4195 + 6.61331i) q^{74} +(-2.76433 + 8.26792i) q^{76} +1.11915 q^{77} +(4.85783 - 8.41402i) q^{79} +(-16.2938 - 6.40123i) q^{80} +(-0.0661882 + 0.705189i) q^{82} +12.7727i q^{83} +(-4.76408 - 8.25163i) q^{85} +(0.790901 - 8.42651i) q^{86} +(-3.66206 + 12.6991i) q^{88} +(-4.53985 + 2.62108i) q^{89} +(-0.343252 - 0.594531i) q^{91} +(0.0473228 - 0.249875i) q^{92} +(2.47518 + 1.75655i) q^{94} +(2.57683 - 18.9020i) q^{95} +(-7.33528 - 4.23502i) q^{97} +(4.09312 + 8.92451i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} - 4 q^{8} + 6 q^{10} + 6 q^{13} - 9 q^{14} - 11 q^{16} + 12 q^{19} + 14 q^{20} + 8 q^{22} - 10 q^{25} + 7 q^{28} + 12 q^{31} + 29 q^{32} - 6 q^{34} - 25 q^{38} - 46 q^{40} - 12 q^{41}+ \cdots - 12 q^{97}+O(q^{100}) \) 20 * q - q^2 + q^4 - 4 * q^8 + 6 * q^10 + 6 * q^13 - 9 * q^14 - 11 * q^16 + 12 * q^19 + 14 * q^20 + 8 * q^22 - 10 * q^25 + 7 * q^28 + 12 * q^31 + 29 * q^32 - 6 * q^34 - 25 * q^38 - 46 * q^40 - 12 * q^41 - 18 * q^43 + 12 * q^44 - 32 * q^46 + 36 * q^47 - 24 * q^49 + 34 * q^50 + 3 * q^52 + 12 * q^53 - 38 * q^56 + 16 * q^58 + 10 * q^61 + 55 * q^62 - 14 * q^64 + 14 * q^67 - 40 * q^68 + 26 * q^70 - 8 * q^71 - 6 * q^73 - 45 * q^74 - 69 * q^76 + 32 * q^77 - 6 * q^79 - 22 * q^80 + 24 * q^82 + 8 * q^85 - 7 * q^86 + 44 * q^88 + 24 * q^89 + 26 * q^91 + 18 * q^92 - 52 * q^94 - 4 * q^95 - 12 * q^97

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