LMFDB - Embedded newform 693.2.m.k.631.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.5
Character	$\chi$	$=$	693.631
Dual form			693.2.m.k.190.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.614338 + 0.446343i) q^{2} +(-0.439845 - 1.35370i) q^{4} +(-2.31804 + 1.68415i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.803314 - 2.47235i) q^{8} +O(q^{10})$	\(q+(0.614338 + 0.446343i) q^{2} +(-0.439845 - 1.35370i) q^{4} +(-2.31804 + 1.68415i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.803314 - 2.47235i) q^{8} -2.17577 q^{10} +(-3.15889 - 1.01064i) q^{11} +(5.63576 + 4.09462i) q^{13} +(-0.234656 + 0.722197i) q^{14} +(-0.706036 + 0.512965i) q^{16} +(-5.38702 + 3.91390i) q^{17} +(-1.77718 + 5.46959i) q^{19} +(3.29942 + 2.39717i) q^{20} +(-1.48953 - 2.03082i) q^{22} -0.724581 q^{23} +(0.991838 - 3.05256i) q^{25} +(1.63466 + 5.03096i) q^{26} +(1.15153 - 0.836634i) q^{28} +(2.33846 + 7.19703i) q^{29} +(-2.28117 - 1.65737i) q^{31} -5.86186 q^{32} -5.05639 q^{34} +(-2.31804 - 1.68415i) q^{35} +(-0.532161 - 1.63782i) q^{37} +(-3.53310 + 2.56694i) q^{38} +(2.30170 + 7.08389i) q^{40} +(0.346364 - 1.06600i) q^{41} -11.7092 q^{43} +(0.0213116 + 4.72073i) q^{44} +(-0.445138 - 0.323411i) q^{46} +(1.60366 - 4.93556i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(1.97181 - 1.43261i) q^{50} +(3.06404 - 9.43015i) q^{52} +(5.06259 + 3.67819i) q^{53} +(9.02450 - 2.97735i) q^{55} +2.59958 q^{56} +(-1.77574 + 5.46516i) q^{58} +(1.23059 + 3.78737i) q^{59} +(4.83043 - 3.50951i) q^{61} +(-0.661656 - 2.03637i) q^{62} +(-2.18909 - 1.59047i) q^{64} -19.9599 q^{65} +10.3611 q^{67} +(7.66771 + 5.57092i) q^{68} +(-0.672349 - 2.06928i) q^{70} +(0.805120 - 0.584954i) q^{71} +(1.09294 + 3.36374i) q^{73} +(0.404104 - 1.24370i) q^{74} +8.18588 q^{76} +(-0.0149727 - 3.31659i) q^{77} +(0.541875 + 0.393695i) q^{79} +(0.772706 - 2.37814i) q^{80} +(0.688585 - 0.500286i) q^{82} +(-10.8603 + 7.89044i) q^{83} +(5.89571 - 18.1451i) q^{85} +(-7.19343 - 5.22633i) q^{86} +(-5.03624 + 6.99801i) q^{88} +16.6006 q^{89} +(-2.15267 + 6.62524i) q^{91} +(0.318703 + 0.980868i) q^{92} +(3.18814 - 2.31632i) q^{94} +(-5.09205 - 15.6717i) q^{95} +(-8.18083 - 5.94372i) q^{97} -0.759363 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) $ 32 * q - 10 * q^4 - 8 * q^7	$ 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) $ 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.614338	+	0.446343i	0.434402	+	0.315612i	0.783407	−	0.621509i	$-0.213480\pi$
$2$	0.614338	+	0.446343i	0.434402	+	0.315612i	−0.349004	+	0.937121i	$0.613480\pi$
$3$		0			0
$3$		0			0
$4$	−0.439845	−	1.35370i	−0.219922	−	0.676851i
$5$	−2.31804	+	1.68415i	−1.03666	+	0.753175i	−0.969630	−	0.244576i	$-0.921351\pi$
$5$	−2.31804	+	1.68415i	−1.03666	+	0.753175i	−0.0670269	+	0.997751i	$0.521351\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.803314	−	2.47235i	0.284014	−	0.874107i
$9$		0			0
$10$	−2.17577			−0.688038
$11$	−3.15889	−	1.01064i	−0.952442	−	0.304720i
$11$	−3.15889	−	1.01064i	−0.952442	−	0.304720i
$12$		0			0
$13$	5.63576	+	4.09462i	1.56308	+	1.13564i	0.933427	+	0.358767i	$0.116803\pi$
$13$	5.63576	+	4.09462i	1.56308	+	1.13564i	0.629652	+	0.776877i	$0.283197\pi$
$14$	−0.234656	+	0.722197i	−0.0627145	+	0.193015i
$15$		0			0
$16$	−0.706036	+	0.512965i	−0.176509	+	0.128241i
$17$	−5.38702	+	3.91390i	−1.30654	+	0.949260i	−0.999997	−	0.00259534i	$-0.999174\pi$
$17$	−5.38702	+	3.91390i	−1.30654	+	0.949260i	−0.306548	+	0.951855i	$0.599174\pi$
$18$		0			0
$19$	−1.77718	+	5.46959i	−0.407712	+	1.25481i	0.510897	+	0.859642i	$0.329313\pi$
$19$	−1.77718	+	5.46959i	−0.407712	+	1.25481i	−0.918609	+	0.395167i	$0.870687\pi$
$20$	3.29942	+	2.39717i	0.737772	+	0.536023i
$21$		0			0
$22$	−1.48953	−	2.03082i	−0.317570	−	0.432973i
$23$	−0.724581			−0.151086			−0.0755428	−	0.997143i	$-0.524069\pi$
$23$	−0.724581			−0.151086			−0.0755428	+	0.997143i	$0.524069\pi$
$24$		0			0
$25$	0.991838	−	3.05256i	0.198368	−	0.610513i
$26$	1.63466	+	5.03096i	0.320583	+	0.986653i
$27$		0			0
$28$	1.15153	−	0.836634i	0.217618	−	0.158109i
$29$	2.33846	+	7.19703i	0.434240	+	1.33645i	0.893863	+	0.448340i	$0.147985\pi$
$29$	2.33846	+	7.19703i	0.434240	+	1.33645i	−0.459623	+	0.888114i	$0.652015\pi$
$30$		0			0
$31$	−2.28117	−	1.65737i	−0.409710	−	0.297672i	0.363774	−	0.931487i	$-0.381488\pi$
$31$	−2.28117	−	1.65737i	−0.409710	−	0.297672i	−0.773484	+	0.633815i	$0.781488\pi$
$32$	−5.86186			−1.03624
$33$		0			0
$34$	−5.05639			−0.867164
$35$	−2.31804	−	1.68415i	−0.391820	−	0.284674i
$36$		0			0
$37$	−0.532161	−	1.63782i	−0.0874868	−	0.269257i	0.897736	−	0.440534i	$-0.145211\pi$
$37$	−0.532161	−	1.63782i	−0.0874868	−	0.269257i	−0.985223	+	0.171277i	$0.945211\pi$
$38$	−3.53310	+	2.56694i	−0.573144	+	0.416413i
$39$		0			0
$40$	2.30170	+	7.08389i	0.363930	+	1.12006i
$41$	0.346364	−	1.06600i	0.0540929	−	0.166481i	−0.920360	−	0.391072i	$-0.872104\pi$
$41$	0.346364	−	1.06600i	0.0540929	−	0.166481i	0.974453	+	0.224591i	$0.0721045\pi$
$42$		0			0
$43$	−11.7092			−1.78564			−0.892821	−	0.450411i	$-0.851277\pi$
$43$	−11.7092			−1.78564			−0.892821	+	0.450411i	$0.851277\pi$
$44$	0.0213116	+	4.72073i	0.00321285	+	0.711676i
$45$		0			0
$46$	−0.445138	−	0.323411i	−0.0656320	−	0.0476844i
$47$	1.60366	−	4.93556i	0.233918	−	0.719926i	−0.763345	−	0.645991i	$-0.776444\pi$
$47$	1.60366	−	4.93556i	0.233918	−	0.719926i	0.997263	−	0.0739350i	$-0.0235557\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	1.97181	−	1.43261i	0.278856	−	0.202601i
$51$		0			0
$52$	3.06404	−	9.43015i	0.424906	−	1.30773i
$53$	5.06259	+	3.67819i	0.695401	+	0.505238i	0.878431	−	0.477869i	$-0.158591\pi$
$53$	5.06259	+	3.67819i	0.695401	+	0.505238i	−0.183030	+	0.983107i	$0.558591\pi$
$54$		0			0
$55$	9.02450	−	2.97735i	1.21686	−	0.401465i
$56$	2.59958			0.347383
$57$		0			0
$58$	−1.77574	+	5.46516i	−0.233166	+	0.717611i
$59$	1.23059	+	3.78737i	0.160209	+	0.493074i	0.998651	−	0.0519172i	$-0.0165332\pi$
$59$	1.23059	+	3.78737i	0.160209	+	0.493074i	−0.838442	+	0.544991i	$0.816533\pi$
$60$		0			0
$61$	4.83043	−	3.50951i	0.618473	−	0.449347i	−0.233915	−	0.972257i	$-0.575154\pi$
$61$	4.83043	−	3.50951i	0.618473	−	0.449347i	0.852388	+	0.522910i	$0.175154\pi$
$62$	−0.661656	−	2.03637i	−0.0840303	−	0.258619i
$63$		0			0
$64$	−2.18909	−	1.59047i	−0.273636	−	0.198808i
$65$	−19.9599			−2.47572
$66$		0			0
$67$	10.3611			1.26581			0.632906	−	0.774229i	$-0.281862\pi$
$67$	10.3611			1.26581			0.632906	+	0.774229i	$0.281862\pi$
$68$	7.66771	+	5.57092i	0.929846	+	0.675573i
$69$		0			0
$70$	−0.672349	−	2.06928i	−0.0803610	−	0.247326i
$71$	0.805120	−	0.584954i	0.0955502	−	0.0694213i	−0.538984	−	0.842316i	$-0.681192\pi$
$71$	0.805120	−	0.584954i	0.0955502	−	0.0694213i	0.634535	+	0.772894i	$0.281192\pi$
$72$		0			0
$73$	1.09294	+	3.36374i	0.127919	+	0.393696i	0.994422	−	0.105478i	$-0.0336372\pi$
$73$	1.09294	+	3.36374i	0.127919	+	0.393696i	−0.866502	+	0.499173i	$0.833637\pi$
$74$	0.404104	−	1.24370i	0.0469761	−	0.144578i
$75$		0			0
$76$	8.18588			0.938984
$77$	−0.0149727	−	3.31659i	−0.00170629	−	0.377961i
$78$		0			0
$79$	0.541875	+	0.393695i	0.0609657	+	0.0442942i	0.617851	−	0.786295i	$-0.288004\pi$
$79$	0.541875	+	0.393695i	0.0609657	+	0.0442942i	−0.556885	+	0.830590i	$0.688004\pi$
$80$	0.772706	−	2.37814i	0.0863912	−	0.265885i
$81$		0			0
$82$	0.688585	−	0.500286i	0.0760415	−	0.0552474i
$83$	−10.8603	+	7.89044i	−1.19207	+	0.866089i	−0.993481	−	0.113994i	$-0.963635\pi$
$83$	−10.8603	+	7.89044i	−1.19207	+	0.866089i	−0.198587	+	0.980083i	$0.563635\pi$
$84$		0			0
$85$	5.89571	−	18.1451i	0.639479	−	1.96811i
$86$	−7.19343	−	5.22633i	−0.775688	−	0.563570i
$87$		0			0
$88$	−5.03624	+	6.99801i	−0.536865	+	0.745991i
$89$	16.6006			1.75966			0.879828	−	0.475292i	$-0.157657\pi$
$89$	16.6006			1.75966			0.879828	+	0.475292i	$0.157657\pi$
$90$		0			0
$91$	−2.15267	+	6.62524i	−0.225661	+	0.694514i
$92$	0.318703	+	0.980868i	0.0332271	+	0.102263i
$93$		0			0
$94$	3.18814	−	2.31632i	0.328832	−	0.238910i
$95$	−5.09205	−	15.6717i	−0.522434	−	1.60789i
$96$		0			0
$97$	−8.18083	−	5.94372i	−0.830638	−	0.603493i	0.0891021	−	0.996022i	$-0.471600\pi$
$97$	−8.18083	−	5.94372i	−0.830638	−	0.603493i	−0.919740	+	0.392529i	$0.871600\pi$
$98$	−0.759363			−0.0767073
$99$		0			0
$100$	−4.56852			−0.456852
$101$	−5.19674	−	3.77565i	−0.517095	−	0.375692i	0.298413	−	0.954437i	$-0.403543\pi$
$101$	−5.19674	−	3.77565i	−0.517095	−	0.375692i	−0.815508	+	0.578745i	$0.803543\pi$
$102$		0			0
$103$	−2.76813	−	8.51944i	−0.272752	−	0.839446i	−0.989805	−	0.142427i	$-0.954509\pi$
$103$	−2.76813	−	8.51944i	−0.272752	−	0.839446i	0.717053	−	0.697019i	$-0.245491\pi$
$104$	14.6506	−	10.6443i	1.43661	−	1.04376i
$105$		0			0
$106$	1.46841	+	4.51930i	0.142625	+	0.438953i
$107$	1.39951	−	4.30724i	0.135296	−	0.416397i	−0.860340	−	0.509720i	$-0.829749\pi$
$107$	1.39951	−	4.30724i	0.135296	−	0.416397i	0.995636	+	0.0933231i	$0.0297489\pi$
$108$		0			0
$109$	−1.02744			−0.0984106			−0.0492053	−	0.998789i	$-0.515669\pi$
$109$	−1.02744			−0.0984106			−0.0492053	+	0.998789i	$0.515669\pi$
$110$	6.87301	+	2.19892i	0.655316	+	0.209659i
$111$		0			0
$112$	−0.706036	−	0.512965i	−0.0667142	−	0.0484707i
$113$	4.09077	−	12.5901i	0.384827	−	1.18438i	−0.551778	−	0.833991i	$-0.686050\pi$
$113$	4.09077	−	12.5901i	0.384827	−	1.18438i	0.936605	−	0.350386i	$-0.113950\pi$
$114$		0			0
$115$	1.67961	−	1.22030i	0.156624	−	0.113794i
$116$	8.71408	−	6.33115i	0.809082	−	0.587832i
$117$		0			0
$118$	−0.934466	+	2.87599i	−0.0860245	+	0.264756i
$119$	−5.38702	−	3.91390i	−0.493827	−	0.358787i
$120$		0			0
$121$	8.95720	+	6.38503i	0.814291	+	0.580457i
$122$	4.53396			0.410486
$123$		0			0
$124$	−1.24022	+	3.81701i	−0.111375	+	0.342778i
$125$	−1.58519	−	4.87871i	−0.141784	−	0.436365i
$126$		0			0
$127$	−13.1816	+	9.57702i	−1.16968	+	0.849823i	−0.990971	−	0.134078i	$-0.957193\pi$
$127$	−13.1816	+	9.57702i	−1.16968	+	0.849823i	−0.178711	+	0.983902i	$0.557193\pi$
$128$	2.98788	+	9.19576i	0.264094	+	0.812798i
$129$		0			0
$130$	−12.2621	−	8.90894i	−1.07546	−	0.781365i
$131$	6.19831			0.541549			0.270774	−	0.962643i	$-0.412720\pi$
$131$	6.19831			0.541549			0.270774	+	0.962643i	$0.412720\pi$
$132$		0			0
$133$	−5.75106			−0.498680
$134$	6.36522	+	4.62460i	0.549871	+	0.399505i
$135$		0			0
$136$	5.34905	+	16.4627i	0.458677	+	1.41166i
$137$	−12.9520	+	9.41016i	−1.10656	+	0.803964i	−0.982119	−	0.188262i	$-0.939714\pi$
$137$	−12.9520	+	9.41016i	−1.10656	+	0.803964i	−0.124443	+	0.992227i	$0.539714\pi$
$138$		0			0
$139$	1.42581	+	4.38819i	0.120935	+	0.372201i	0.993139	−	0.116943i	$-0.0373094\pi$
$139$	1.42581	+	4.38819i	0.120935	+	0.372201i	−0.872203	+	0.489144i	$0.837309\pi$
$140$	−1.26026	+	3.87870i	−0.106512	+	0.327810i
$141$		0			0
$142$	0.755706			0.0634174
$143$	−13.6646	−	18.6302i	−1.14269	−	1.55794i
$144$		0			0
$145$	−17.5415	−	12.7447i	−1.45674	−	1.05839i
$146$	−0.829942	+	2.55430i	−0.0686865	+	0.211395i
$147$		0			0
$148$	−1.98306	+	1.44078i	−0.163006	+	0.118431i
$149$	5.83982	−	4.24287i	0.478416	−	0.347590i	−0.322296	−	0.946639i	$-0.604455\pi$
$149$	5.83982	−	4.24287i	0.478416	−	0.347590i	0.800712	+	0.599049i	$0.204455\pi$
$150$		0			0
$151$	0.193552	−	0.595693i	0.0157511	−	0.0484768i	−0.942872	−	0.333155i	$-0.891887\pi$
$151$	0.193552	−	0.595693i	0.0157511	−	0.0484768i	0.958623	+	0.284678i	$0.0918867\pi$
$152$	12.0951	+	8.78759i	0.981041	+	0.712768i
$153$		0			0
$154$	1.47114	−	2.04419i	0.118548	−	0.164726i
$155$	8.07909			0.648928
$156$		0			0
$157$	−1.89969	+	5.84664i	−0.151612	+	0.466613i	−0.997802	−	0.0662683i	$-0.978891\pi$
$157$	−1.89969	+	5.84664i	−0.151612	+	0.466613i	0.846190	+	0.532881i	$0.178891\pi$
$158$	0.157171	+	0.483724i	0.0125039	+	0.0384830i
$159$		0			0
$160$	13.5880	−	9.87226i	1.07423	−	0.780471i
$161$	−0.223908	−	0.689118i	−0.0176464	−	0.0543101i
$162$		0			0
$163$	−17.5084	−	12.7206i	−1.37136	−	0.996352i	−0.997629	−	0.0688158i	$-0.978078\pi$
$163$	−17.5084	−	12.7206i	−1.37136	−	0.996352i	−0.373732	−	0.927537i	$-0.621922\pi$
$164$	−1.59539			−0.124579
$165$		0			0
$166$	−10.1937			−0.791186
$167$	19.4121	+	14.1037i	1.50216	+	1.09138i	0.969513	+	0.245042i	$0.0788017\pi$
$167$	19.4121	+	14.1037i	1.50216	+	1.09138i	0.532644	+	0.846339i	$0.321198\pi$
$168$		0			0
$169$	10.9787	+	33.7889i	0.844514	+	2.59915i
$170$	11.7209	−	8.51573i	0.898951	−	0.653126i
$171$		0			0
$172$	5.15025	+	15.8508i	0.392703	+	1.20861i
$173$	−3.34074	+	10.2817i	−0.253992	+	0.781707i	0.740035	+	0.672569i	$0.234809\pi$
$173$	−3.34074	+	10.2817i	−0.253992	+	0.781707i	−0.994027	+	0.109138i	$0.965191\pi$
$174$		0			0
$175$	3.20966			0.242627
$176$	2.74872	−	0.906852i	0.207192	−	0.0683565i
$177$		0			0
$178$	10.1984	+	7.40954i	0.764399	+	0.555368i
$179$	1.83197	−	5.63824i	0.136928	−	0.421422i	−0.858957	−	0.512048i	$-0.828887\pi$
$179$	1.83197	−	5.63824i	0.136928	−	0.421422i	0.995885	+	0.0906265i	$0.0288869\pi$
$180$		0			0
$181$	3.92063	−	2.84851i	0.291418	−	0.211728i	−0.432464	−	0.901651i	$-0.642356\pi$
$181$	3.92063	−	2.84851i	0.291418	−	0.211728i	0.723882	+	0.689923i	$0.242356\pi$
$182$	−4.27959	+	3.10931i	−0.317224	+	0.230477i
$183$		0			0
$184$	−0.582066	+	1.79142i	−0.0429105	+	0.132065i
$185$	3.99191	+	2.90029i	0.293491	+	0.213234i
$186$		0			0
$187$	20.9726	−	6.91923i	1.53367	−	0.505984i
$188$	−7.38665			−0.538727
$189$		0			0
$190$	3.86672	−	11.9005i	0.280521	−	0.863356i
$191$	−4.84920	−	14.9243i	−0.350876	−	1.07988i	−0.958362	−	0.285555i	$-0.907822\pi$
$191$	−4.84920	−	14.9243i	−0.350876	−	1.07988i	0.607487	−	0.794330i	$-0.292178\pi$
$192$		0			0
$193$	18.4090	−	13.3749i	1.32511	−	0.962749i	0.325257	−	0.945626i	$-0.394549\pi$
$193$	18.4090	−	13.3749i	1.32511	−	0.962749i	0.999853	−	0.0171238i	$-0.00545094\pi$
$194$	−2.37286	−	7.30291i	−0.170361	−	0.524318i
$195$		0			0
$196$	1.15153	+	0.836634i	0.0822520	+	0.0597596i
$197$	15.3025			1.09026			0.545129	−	0.838352i	$-0.316481\pi$
$197$	15.3025			1.09026			0.545129	+	0.838352i	$0.316481\pi$
$198$		0			0
$199$	−0.547814			−0.0388335			−0.0194168	−	0.999811i	$-0.506181\pi$
$199$	−0.547814			−0.0388335			−0.0194168	+	0.999811i	$0.506181\pi$
$200$	−6.75024	−	4.90434i	−0.477314	−	0.346789i
$201$		0			0
$202$	−1.50732	−	4.63905i	−0.106055	−	0.326403i
$203$	−6.12216	+	4.44801i	−0.429691	+	0.312189i
$204$		0			0
$205$	0.992419	+	3.05435i	0.0693135	+	0.213325i
$206$	2.10202	−	6.46935i	0.146455	−	0.450741i
$207$		0			0
$208$	−6.07945			−0.421534
$209$	11.1417	−	15.4817i	0.770688	−	1.07089i
$210$		0			0
$211$	11.2232	+	8.15412i	0.772636	+	0.561353i	0.902760	−	0.430145i	$-0.141538\pi$
$211$	11.2232	+	8.15412i	0.772636	+	0.561353i	−0.130124	+	0.991498i	$0.541538\pi$
$212$	2.75242	−	8.47108i	0.189037	−	0.581796i
$213$		0			0
$214$	2.78228	−	2.02144i	0.190193	−	0.138183i
$215$	27.1424	−	19.7201i	1.85110	−	1.34490i
$216$		0			0
$217$	0.871329	−	2.68168i	0.0591497	−	0.182044i
$218$	−0.631193	−	0.458589i	−0.0427498	−	0.0310595i
$219$		0			0
$220$	−7.99982	−	10.9069i	−0.539348	−	0.735345i
$221$	−46.3859			−3.12025
$222$		0			0
$223$	−2.34908	+	7.22973i	−0.157306	+	0.484138i	−0.998387	−	0.0567705i	$-0.981920\pi$
$223$	−2.34908	+	7.22973i	−0.157306	+	0.484138i	0.841081	+	0.540909i	$0.181920\pi$
$224$	−1.81142	−	5.57496i	−0.121030	−	0.372493i
$225$		0			0
$226$	8.13261	−	5.90869i	0.540973	−	0.393040i
$227$	−0.0912083	−	0.280710i	−0.00605371	−	0.0186314i	0.947984	−	0.318318i	$-0.103118\pi$
$227$	−0.0912083	−	0.280710i	−0.00605371	−	0.0186314i	−0.954038	+	0.299686i	$0.903118\pi$
$228$		0			0
$229$	−5.75269	−	4.17958i	−0.380149	−	0.276194i	0.381258	−	0.924469i	$-0.375491\pi$
$229$	−5.75269	−	4.17958i	−0.380149	−	0.276194i	−0.761407	+	0.648275i	$0.775491\pi$
$230$	1.57652			0.103953
$231$		0			0
$232$	19.6721			1.29153
$233$	−8.29543	−	6.02698i	−0.543452	−	0.394841i	0.281914	−	0.959440i	$-0.409031\pi$
$233$	−8.29543	−	6.02698i	−0.543452	−	0.394841i	−0.825365	+	0.564599i	$0.809031\pi$
$234$		0			0
$235$	4.59489	+	14.1416i	0.299738	+	0.922498i
$236$	4.58570	−	3.33171i	0.298504	−	0.216876i
$237$		0			0
$238$	−1.56251	−	4.80891i	−0.101283	−	0.311716i
$239$	−6.11983	+	18.8349i	−0.395859	+	1.21833i	0.532432	+	0.846473i	$0.321278\pi$
$239$	−6.11983	+	18.8349i	−0.395859	+	1.21833i	−0.928291	+	0.371856i	$0.878722\pi$
$240$		0			0
$241$	−20.0305			−1.29028			−0.645138	−	0.764066i	$-0.723200\pi$
$241$	−20.0305			−1.29028			−0.645138	+	0.764066i	$0.723200\pi$
$242$	2.65284	+	7.92054i	0.170531	+	0.509152i
$243$		0			0
$244$	−6.87548	−	4.99533i	−0.440157	−	0.319793i
$245$	0.885411	−	2.72501i	0.0565668	−	0.174095i
$246$		0			0
$247$	−32.4116	+	23.5484i	−2.06230	+	1.49835i
$248$	−5.93008	+	4.30846i	−0.376561	+	0.273587i
$249$		0			0
$250$	1.20374	−	3.70472i	0.0761309	−	0.234307i
$251$	2.17876	+	1.58296i	0.137522	+	0.0999155i	0.654419	−	0.756132i	$-0.272913\pi$
$251$	2.17876	+	1.58296i	0.137522	+	0.0999155i	−0.516897	+	0.856047i	$0.672913\pi$
$252$		0			0
$253$	2.28887	+	0.732293i	0.143900	+	0.0460389i
$254$	−12.3726			−0.776327
$255$		0			0
$256$	−3.94121	+	12.1298i	−0.246325	+	0.758111i
$257$	7.83640	+	24.1179i	0.488821	+	1.50444i	0.826370	+	0.563128i	$0.190402\pi$
$257$	7.83640	+	24.1179i	0.488821	+	1.50444i	−0.337549	+	0.941308i	$0.609598\pi$
$258$		0			0
$259$	1.39322	−	1.01223i	0.0865702	−	0.0628970i
$260$	8.77924	+	27.0197i	0.544465	+	1.67569i
$261$		0			0
$262$	3.80786	+	2.76657i	0.235250	+	0.170919i
$263$	−9.04980			−0.558034			−0.279017	−	0.960286i	$-0.590009\pi$
$263$	−9.04980			−0.558034			−0.279017	+	0.960286i	$0.590009\pi$
$264$		0			0
$265$	−17.9299			−1.10142
$266$	−3.53310	−	2.56694i	−0.216628	−	0.157389i
$267$		0			0
$268$	−4.55728	−	14.0259i	−0.278380	−	0.856766i
$269$	−2.21095	+	1.60635i	−0.134804	+	0.0979410i	−0.653144	−	0.757234i	$-0.726550\pi$
$269$	−2.21095	+	1.60635i	−0.134804	+	0.0979410i	0.518340	+	0.855175i	$0.326550\pi$
$270$		0			0
$271$	5.54748	+	17.0734i	0.336986	+	1.03714i	0.965736	+	0.259528i	$0.0835669\pi$
$271$	5.54748	+	17.0734i	0.336986	+	1.03714i	−0.628750	+	0.777608i	$0.716433\pi$
$272$	1.79574	−	5.52671i	0.108883	−	0.335106i
$273$		0			0
$274$	−12.1570			−0.734434
$275$	−6.21816	+	8.64033i	−0.374969	+	0.521031i
$276$		0			0
$277$	9.02080	+	6.55399i	0.542007	+	0.393791i	0.824830	−	0.565381i	$-0.191271\pi$
$277$	9.02080	+	6.55399i	0.542007	+	0.393791i	−0.282823	+	0.959172i	$0.591271\pi$
$278$	−1.08271	+	3.33223i	−0.0649364	+	0.199854i
$279$		0			0
$280$	−6.02592	+	4.37809i	−0.360118	+	0.261641i
$281$	−3.20564	+	2.32904i	−0.191233	+	0.138939i	−0.679282	−	0.733877i	$-0.737709\pi$
$281$	−3.20564	+	2.32904i	−0.191233	+	0.138939i	0.488049	+	0.872816i	$0.337709\pi$
$282$		0			0
$283$	1.77657	−	5.46773i	0.105606	−	0.325023i	−0.884266	−	0.466984i	$-0.845341\pi$
$283$	1.77657	−	5.46773i	0.105606	−	0.325023i	0.989872	+	0.141961i	$0.0453407\pi$
$284$	−1.14598	−	0.832605i	−0.0680015	−	0.0494060i
$285$		0			0
$286$	−0.0792034	−	17.5443i	−0.00468340	−	1.03742i
$287$	1.12086			0.0661621
$288$		0			0
$289$	8.44809	−	26.0005i	0.496946	−	1.52944i
$290$	−5.08793	−	15.6590i	−0.298774	−	0.919531i
$291$		0			0
$292$	4.07277	−	2.95904i	0.238341	−	0.173165i
$293$	7.18272	+	22.1061i	0.419619	+	1.29145i	0.908053	+	0.418854i	$0.137568\pi$
$293$	7.18272	+	22.1061i	0.419619	+	1.29145i	−0.488434	+	0.872601i	$0.662432\pi$
$294$		0			0
$295$	−9.23106	−	6.70676i	−0.537453	−	0.390482i
$296$	−4.47676			−0.260206
$297$		0			0
$298$	5.48140			0.317529
$299$	−4.08357	−	2.96689i	−0.236159	−	0.171579i
$300$		0			0
$301$	−3.61835	−	11.1362i	−0.208558	−	0.641877i
$302$	0.384790	−	0.279566i	0.0221422	−	0.0160872i
$303$		0			0
$304$	−1.55096	−	4.77336i	−0.0889535	−	0.273771i
$305$	−5.28656	+	16.2704i	−0.302707	+	0.931638i
$306$		0			0
$307$	3.87940			0.221409			0.110705	−	0.993853i	$-0.464689\pi$
$307$	3.87940			0.221409			0.110705	+	0.993853i	$0.464689\pi$
$308$	−4.48309	+	1.47905i	−0.255448	+	0.0842769i
$309$		0			0
$310$	4.96329	+	3.60604i	0.281896	+	0.204809i
$311$	1.15776	−	3.56321i	0.0656504	−	0.202051i	−0.912850	−	0.408294i	$-0.866124\pi$
$311$	1.15776	−	3.56321i	0.0656504	−	0.202051i	0.978501	+	0.206243i	$0.0661238\pi$
$312$		0			0
$313$	−14.6142	+	10.6178i	−0.826044	+	0.600156i	−0.918437	−	0.395567i	$-0.870548\pi$
$313$	−14.6142	+	10.6178i	−0.826044	+	0.600156i	0.0923934	+	0.995723i	$0.470548\pi$
$314$	−3.77666	+	2.74390i	−0.213129	+	0.154847i
$315$		0			0
$316$	0.294606	−	0.906703i	0.0165729	−	0.0510060i
$317$	−5.99841	−	4.35810i	−0.336904	−	0.244775i	0.406450	−	0.913673i	$-0.366766\pi$
$317$	−5.99841	−	4.35810i	−0.336904	−	0.244775i	−0.743354	+	0.668898i	$0.766766\pi$
$318$		0			0
$319$	−0.113304	−	25.0980i	−0.00634382	−	1.40522i
$320$	7.75298			0.433405
$321$		0			0
$322$	0.170027	−	0.523291i	0.00947526	−	0.0291619i
$323$	−11.8337	−	36.4205i	−0.658446	−	2.02649i
$324$		0			0
$325$	18.0889	−	13.1423i	1.00339	−	0.729005i
$326$	−5.07832	−	15.6295i	−0.281262	−	0.865636i
$327$		0			0
$328$	−2.35728	−	1.71266i	−0.130159	−	0.0945660i
$329$	5.18956			0.286110
$330$		0			0
$331$	14.5172			0.797937			0.398968	−	0.916965i	$-0.369368\pi$
$331$	14.5172			0.797937			0.398968	+	0.916965i	$0.369368\pi$
$332$	15.4581	+	11.2310i	0.848376	+	0.616381i
$333$		0			0
$334$	5.63051	+	17.3289i	0.308088	+	0.948197i
$335$	−24.0174	+	17.4497i	−1.31221	+	0.953378i
$336$		0			0
$337$	3.26146	+	10.0378i	0.177663	+	0.546791i	0.999745	−	0.0225781i	$-0.00718744\pi$
$337$	3.26146	+	10.0378i	0.177663	+	0.546791i	−0.822082	+	0.569369i	$0.807187\pi$
$338$	−8.33681	+	25.6581i	−0.453463	+	1.39561i
$339$		0			0
$340$	−27.1563			−1.47276
$341$	5.53096	+	7.54089i	0.299518	+	0.408362i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−9.40620	+	28.9493i	−0.507148	+	1.56084i
$345$		0			0
$346$	−6.64153	+	4.82535i	−0.357051	+	0.259413i
$347$	18.2109	−	13.2310i	0.977615	−	0.710279i	0.0204406	−	0.999791i	$-0.493493\pi$
$347$	18.2109	−	13.2310i	0.977615	−	0.710279i	0.957174	+	0.289512i	$0.0934931\pi$
$348$		0			0
$349$	−6.40301	+	19.7064i	−0.342745	+	1.05486i	0.620034	+	0.784575i	$0.287119\pi$
$349$	−6.40301	+	19.7064i	−0.342745	+	1.05486i	−0.962780	+	0.270287i	$0.912881\pi$
$350$	1.97181	+	1.43261i	0.105398	+	0.0765760i
$351$		0			0
$352$	18.5170	+	5.92425i	0.986959	+	0.315764i
$353$	6.01460			0.320125			0.160062	−	0.987107i	$-0.448830\pi$
$353$	6.01460			0.320125			0.160062	+	0.987107i	$0.448830\pi$
$354$		0			0
$355$	−0.881146	+	2.71189i	−0.0467664	+	0.143932i
$356$	−7.30167	−	22.4722i	−0.386988	−	1.19103i
$357$		0			0
$358$	3.64204	−	2.64609i	0.192488	−	0.139850i
$359$	−5.70755	−	17.5660i	−0.301233	−	0.927100i	−0.981056	−	0.193724i	$-0.937944\pi$
$359$	−5.70755	−	17.5660i	−0.301233	−	0.927100i	0.679823	−	0.733376i	$-0.262056\pi$
$360$		0			0
$361$	−11.3867	−	8.27292i	−0.599300	−	0.435417i
$362$	3.68000			0.193417
$363$		0			0
$364$	9.91544			0.519710
$365$	−8.19852	−	5.95658i	−0.429130	−	0.311781i
$366$		0			0
$367$	−1.24531	−	3.83267i	−0.0650046	−	0.200063i	0.913279	−	0.407335i	$-0.133542\pi$
$367$	−1.24531	−	3.83267i	−0.0650046	−	0.200063i	−0.978284	+	0.207271i	$0.933542\pi$
$368$	0.511581	−	0.371685i	0.0266680	−	0.0193754i
$369$		0			0
$370$	1.15786	+	3.56352i	0.0601942	+	0.185259i
$371$	−1.93374	+	5.95144i	−0.100395	+	0.308983i
$372$		0			0
$373$	5.06561			0.262287			0.131144	−	0.991363i	$-0.458135\pi$
$373$	5.06561			0.262287			0.131144	+	0.991363i	$0.458135\pi$
$374$	15.9726	+	5.11021i	0.825923	+	0.264242i
$375$		0			0
$376$	−10.9142	−	7.92962i	−0.562856	−	0.408939i
$377$	−16.2901	+	50.1358i	−0.838984	+	2.58213i
$378$		0			0
$379$	−1.77707	+	1.29111i	−0.0912817	+	0.0663201i	−0.632490	−	0.774569i	$-0.717967\pi$
$379$	−1.77707	+	1.29111i	−0.0912817	+	0.0663201i	0.541208	+	0.840889i	$0.317967\pi$
$380$	−18.9752	+	13.7863i	−0.973405	+	0.707220i
$381$		0			0
$382$	3.68230	−	11.3330i	0.188403	−	0.579845i
$383$	19.8093	+	14.3923i	1.01221	+	0.735413i	0.964671	−	0.263457i	$-0.0848627\pi$
$383$	19.8093	+	14.3923i	1.01221	+	0.735413i	0.0475374	+	0.998869i	$0.484863\pi$
$384$		0			0
$385$	5.62035	+	7.66276i	0.286440	+	0.390530i
$386$	17.2792			0.879487
$387$		0			0
$388$	−4.44774	+	13.6887i	−0.225800	+	0.694940i
$389$	10.6057	+	32.6410i	0.537730	+	1.65496i	0.737675	+	0.675156i	$0.235924\pi$
$389$	10.6057	+	32.6410i	0.537730	+	1.65496i	−0.199944	+	0.979807i	$0.564076\pi$
$390$		0			0
$391$	3.90333	−	2.83594i	0.197400	−	0.143420i
$392$	0.803314	+	2.47235i	0.0405735	+	0.124872i
$393$		0			0
$394$	9.40090	+	6.83016i	0.473611	+	0.344098i
$395$	−1.91913			−0.0965618
$396$		0			0
$397$	8.46742			0.424968			0.212484	−	0.977165i	$-0.431845\pi$
$397$	8.46742			0.424968			0.212484	+	0.977165i	$0.431845\pi$
$398$	−0.336543	−	0.244513i	−0.0168694	−	0.0122563i
$399$		0			0
$400$	0.865586	+	2.66400i	0.0432793	+	0.133200i
$401$	−23.3870	+	16.9917i	−1.16789	+	0.848523i	−0.990755	−	0.135663i	$-0.956684\pi$
$401$	−23.3870	+	16.9917i	−1.16789	+	0.848523i	−0.177137	+	0.984186i	$0.556684\pi$
$402$		0			0
$403$	−6.06984	−	18.6811i	−0.302360	−	0.930570i
$404$	−2.82535	+	8.69554i	−0.140567	+	0.432619i
$405$		0			0
$406$	−5.74641			−0.285189
$407$	0.0257846	+	5.71153i	0.00127809	+	0.283110i
$408$		0			0
$409$	1.29084	+	0.937848i	0.0638278	+	0.0463736i	0.619242	−	0.785200i	$-0.287440\pi$
$409$	1.29084	+	0.937848i	0.0638278	+	0.0463736i	−0.555414	+	0.831574i	$0.687440\pi$
$410$	−0.753606	+	2.31936i	−0.0372180	+	0.114545i
$411$		0			0
$412$	−10.3152	+	7.49446i	−0.508196	+	0.369226i
$413$	−3.22173	+	2.34072i	−0.158531	+	0.115179i
$414$		0			0
$415$	11.8858	−	36.5807i	0.583450	−	1.79567i
$416$	−33.0361	−	24.0021i	−1.61973	−	1.17680i
$417$		0			0
$418$	13.7549	−	4.53800i	0.672776	−	0.221961i
$419$	−0.224640			−0.0109744			−0.00548719	−	0.999985i	$-0.501747\pi$
$419$	−0.224640			−0.0109744			−0.00548719	+	0.999985i	$0.501747\pi$
$420$		0			0
$421$	3.56288	−	10.9654i	0.173644	−	0.534422i	−0.825925	−	0.563780i	$-0.809346\pi$
$421$	3.56288	−	10.9654i	0.173644	−	0.534422i	0.999569	+	0.0293585i	$0.00934643\pi$
$422$	3.25530	+	10.0188i	0.158465	+	0.487706i
$423$		0			0
$424$	13.1606	−	9.56175i	0.639136	−	0.464359i
$425$	6.60438	+	20.3262i	0.320359	+	0.985964i
$426$		0			0
$427$	4.83043	+	3.50951i	0.233761	+	0.169837i
$428$	−6.44630			−0.311593
$429$		0			0
$430$	25.4766			1.22859
$431$	−22.5643	−	16.3940i	−1.08689	−	0.789669i	−0.108016	−	0.994149i	$-0.534450\pi$
$431$	−22.5643	−	16.3940i	−1.08689	−	0.789669i	−0.978871	+	0.204480i	$0.934450\pi$
$432$		0			0
$433$	8.02421	+	24.6960i	0.385619	+	1.18681i	0.936030	+	0.351919i	$0.114471\pi$
$433$	8.02421	+	24.6960i	0.385619	+	1.18681i	−0.550412	+	0.834893i	$0.685529\pi$
$434$	1.73224	−	1.25854i	0.0831500	−	0.0604120i
$435$		0			0
$436$	0.451912	+	1.39084i	0.0216427	+	0.0666093i
$437$	1.28771	−	3.96316i	0.0615995	−	0.189584i
$438$		0			0
$439$	23.5551			1.12422			0.562112	−	0.827061i	$-0.309989\pi$
$439$	23.5551			1.12422			0.562112	+	0.827061i	$0.309989\pi$
$440$	−0.111523	−	24.7034i	−0.00531666	−	1.17769i
$441$		0			0
$442$	−28.4966	−	20.7040i	−1.35545	−	0.984789i
$443$	7.67635	−	23.6254i	0.364714	−	1.12248i	−0.585445	−	0.810712i	$-0.699080\pi$
$443$	7.67635	−	23.6254i	0.364714	−	1.12248i	0.950160	−	0.311764i	$-0.100920\pi$
$444$		0			0
$445$	−38.4807	+	27.9579i	−1.82416	+	1.32533i
$446$	−4.67007	+	3.39300i	−0.221134	+	0.160663i
$447$		0			0
$448$	0.836158	−	2.57343i	0.0395048	−	0.121583i
$449$	14.8961	+	10.8227i	0.702993	+	0.510754i	0.880906	−	0.473292i	$-0.156935\pi$
$449$	14.8961	+	10.8227i	0.702993	+	0.510754i	−0.177913	+	0.984046i	$0.556935\pi$
$450$		0			0
$451$	−2.17147	+	3.01732i	−0.102251	+	0.142080i
$452$	−18.8426			−0.886279
$453$		0			0
$454$	0.0692602	−	0.213161i	0.00325054	−	0.0100041i
$455$	−6.16794	−	18.9830i	−0.289157	−	0.889935i
$456$		0			0
$457$	−3.73256	+	2.71186i	−0.174602	+	0.126856i	−0.671654	−	0.740865i	$-0.734416\pi$
$457$	−3.73256	+	2.71186i	−0.174602	+	0.126856i	0.497052	+	0.867721i	$0.334416\pi$
$458$	−1.66857	−	5.13534i	−0.0779673	−	0.239959i
$459$		0			0
$460$	−2.39070	−	1.73694i	−0.111467	−	0.0809853i
$461$	33.5148			1.56094			0.780470	−	0.625193i	$-0.214980\pi$
$461$	33.5148			1.56094			0.780470	+	0.625193i	$0.214980\pi$
$462$		0			0
$463$	−16.5338			−0.768392			−0.384196	−	0.923252i	$-0.625521\pi$
$463$	−16.5338			−0.768392			−0.384196	+	0.923252i	$0.625521\pi$
$464$	−5.34286	−	3.88182i	−0.248036	−	0.180209i
$465$		0			0
$466$	−2.40610	−	7.40521i	−0.111460	−	0.343040i
$467$	15.7310	−	11.4292i	0.727944	−	0.528882i	−0.160969	−	0.986960i	$-0.551462\pi$
$467$	15.7310	−	11.4292i	0.727944	−	0.528882i	0.888912	+	0.458077i	$0.151462\pi$
$468$		0			0
$469$	3.20176	+	9.85400i	0.147844	+	0.455016i
$470$	−3.48919	+	10.7386i	−0.160944	+	0.495336i
$471$		0			0
$472$	10.3522			0.476501
$473$	36.9882	+	11.8339i	1.70072	+	0.544122i
$474$		0			0
$475$	14.9336	+	10.8499i	0.685200	+	0.497827i
$476$	−2.92880	+	9.01393i	−0.134242	+	0.413153i
$477$		0			0
$478$	−12.1665	+	8.83945i	−0.556481	+	0.404307i
$479$	−31.7747	+	23.0857i	−1.45182	+	1.05481i	−0.466423	+	0.884562i	$0.654457\pi$
$479$	−31.7747	+	23.0857i	−1.45182	+	1.05481i	−0.985401	+	0.170250i	$0.945543\pi$
$480$		0			0
$481$	3.70713	−	11.4094i	0.169031	−	0.520223i
$482$	−12.3055	−	8.94045i	−0.560499	−	0.407227i
$483$		0			0
$484$	4.70365	−	14.9338i	0.213802	−	0.678809i
$485$	28.9736			1.31562
$486$		0			0
$487$	−5.28443	+	16.2638i	−0.239461	+	0.736984i	0.757038	+	0.653371i	$0.226646\pi$
$487$	−5.28443	+	16.2638i	−0.239461	+	0.736984i	−0.996498	+	0.0836126i	$0.973354\pi$
$488$	−4.79638	−	14.7617i	−0.217122	−	0.668233i
$489$		0			0
$490$	1.76023	−	1.27888i	0.0795191	−	0.0577740i
$491$	−10.7494	−	33.0833i	−0.485115	−	1.49303i	−0.831815	−	0.555053i	$-0.812698\pi$
$491$	−10.7494	−	33.0833i	−0.485115	−	1.49303i	0.346700	−	0.937976i	$-0.387302\pi$
$492$		0			0
$493$	−40.7657	−	29.6180i	−1.83600	−	1.33393i
$494$	−30.4224			−1.36877
$495$		0			0
$496$	2.46076			0.110491
$497$	0.805120	+	0.584954i	0.0361146	+	0.0262388i
$498$		0			0
$499$	4.83850	+	14.8914i	0.216601	+	0.666629i	0.999036	+	0.0438968i	$0.0139773\pi$
$499$	4.83850	+	14.8914i	0.216601	+	0.666629i	−0.782435	+	0.622732i	$0.786023\pi$
$500$	−5.90709	+	4.29175i	−0.264173	+	0.191933i
$501$		0			0
$502$	0.631951	+	1.94494i	0.0282053	+	0.0868071i
$503$	6.76687	−	20.8263i	0.301720	−	0.928598i	−0.679161	−	0.733989i	$-0.737656\pi$
$503$	6.76687	−	20.8263i	0.301720	−	0.928598i	0.980881	−	0.194609i	$-0.0623438\pi$
$504$		0			0
$505$	18.4050			0.819012
$506$	1.07929	+	1.47150i	0.0479802	+	0.0654160i
$507$		0			0
$508$	18.7623	+	13.6316i	0.832443	+	0.604805i
$509$	8.29518	−	25.5299i	0.367677	−	1.13159i	−0.580610	−	0.814182i	$-0.697186\pi$
$509$	8.29518	−	25.5299i	0.367677	−	1.13159i	0.948287	−	0.317413i	$-0.102814\pi$
$510$		0			0
$511$	−2.86136	+	2.07890i	−0.126579	+	0.0919653i
$512$	7.80948	−	5.67392i	0.345134	−	0.250754i
$513$		0			0
$514$	−5.95067	+	18.3143i	−0.262473	+	0.807809i
$515$	20.7647	+	15.0864i	0.915000	+	0.664787i
$516$		0			0
$517$	−10.0539	+	13.9702i	−0.442170	+	0.614408i
$518$	1.30771			0.0574574
$519$		0			0
$520$	−16.0340	+	49.3477i	−0.703139	+	2.16404i
$521$	4.93408	+	15.1855i	0.216166	+	0.665291i	0.999069	+	0.0431466i	$0.0137383\pi$
$521$	4.93408	+	15.1855i	0.216166	+	0.665291i	−0.782903	+	0.622144i	$0.786262\pi$
$522$		0			0
$523$	−10.7132	+	7.78356i	−0.468453	+	0.340351i	−0.796838	−	0.604193i	$-0.793496\pi$
$523$	−10.7132	+	7.78356i	−0.468453	+	0.340351i	0.328385	+	0.944544i	$0.393496\pi$
$524$	−2.72629	−	8.39067i	−0.119099	−	0.366548i
$525$		0			0
$526$	−5.55963	−	4.03931i	−0.242411	−	0.176122i
$527$	18.7755			0.817873
$528$		0			0
$529$	−22.4750			−0.977173
$530$	−11.0150	−	8.00288i	−0.478462	−	0.347623i
$531$		0			0
$532$	2.52957	+	7.78523i	0.109671	+	0.337533i
$533$	6.31688	−	4.58948i	0.273615	−	0.198793i
$534$		0			0
$535$	4.00994	+	12.3413i	0.173365	+	0.533562i
$536$	8.32323	−	25.6163i	0.359509	−	1.10645i
$537$		0			0
$538$	−2.07526			−0.0894706
$539$	3.14964	−	1.03912i	0.135665	−	0.0447582i
$540$		0			0
$541$	20.7068	+	15.0444i	0.890256	+	0.646809i	0.935945	−	0.352147i	$-0.114548\pi$
$541$	20.7068	+	15.0444i	0.890256	+	0.646809i	−0.0456887	+	0.998956i	$0.514548\pi$
$542$	−4.21256	+	12.9649i	−0.180945	+	0.556891i
$543$		0			0
$544$	31.5780	−	22.9427i	1.35389	−	0.983662i
$545$	2.38163	−	1.73036i	0.102018	−	0.0741204i
$546$		0			0
$547$	9.31845	−	28.6792i	0.398428	−	1.22624i	−0.527831	−	0.849349i	$-0.676995\pi$
$547$	9.31845	−	28.6792i	0.398428	−	1.22624i	0.926259	−	0.376887i	$-0.123005\pi$
$548$	18.4354	+	13.3941i	0.787522	+	0.572168i
$549$		0			0
$550$	−7.67660	+	2.53265i	−0.327331	+	0.107993i
$551$	−43.5206			−1.85404
$552$		0			0
$553$	−0.206978	+	0.637012i	−0.00880159	+	0.0270885i
$554$	2.61649	+	8.05273i	0.111164	+	0.342128i
$555$		0			0
$556$	5.31316	−	3.86024i	0.225328	−	0.163711i
$557$	−0.226688	−	0.697675i	−0.00960509	−	0.0295614i	0.946139	−	0.323760i	$-0.104947\pi$
$557$	−0.226688	−	0.697675i	−0.00960509	−	0.0295614i	−0.955744	+	0.294199i	$0.904947\pi$
$558$		0			0
$559$	−65.9905	−	47.9449i	−2.79110	−	2.02785i
$560$	2.50053			0.105667
$561$		0			0
$562$	−3.00890			−0.126923
$563$	16.9114	+	12.2868i	0.712730	+	0.517828i	0.884053	−	0.467387i	$-0.154804\pi$
$563$	16.9114	+	12.2868i	0.712730	+	0.517828i	−0.171324	+	0.985215i	$0.554804\pi$
$564$		0			0
$565$	11.7211	+	36.0738i	0.493109	+	1.51763i
$566$	3.53190	−	2.56607i	0.148457	−	0.107860i
$567$		0			0
$568$	−0.799445	−	2.46044i	−0.0335440	−	0.103238i
$569$	8.73053	−	26.8698i	0.366003	−	1.12644i	−0.583348	−	0.812222i	$-0.698258\pi$
$569$	8.73053	−	26.8698i	0.366003	−	1.12644i	0.949351	−	0.314218i	$-0.101742\pi$
$570$		0			0
$571$	38.7512			1.62169			0.810843	−	0.585264i	$-0.199009\pi$
$571$	38.7512			1.62169			0.810843	+	0.585264i	$0.199009\pi$
$572$	−19.2095	+	26.6922i	−0.803189	+	1.11606i
$573$		0			0
$574$	0.688585	+	0.500286i	0.0287410	+	0.0208815i
$575$	−0.718667	+	2.21183i	−0.0299705	+	0.0922397i
$576$		0			0
$577$	−10.2889	+	7.47535i	−0.428334	+	0.311203i	−0.780982	−	0.624553i	$-0.785281\pi$
$577$	−10.2889	+	7.47535i	−0.428334	+	0.311203i	0.352648	+	0.935756i	$0.385281\pi$
$578$	16.7951	−	12.2024i	0.698585	−	0.507552i
$579$		0			0
$580$	−9.53693	+	29.3517i	−0.396000	+	1.21876i
$581$	−10.8603	−	7.89044i	−0.450560	−	0.327351i
$582$		0			0
$583$	−12.2748	−	16.7355i	−0.508372	−	0.693113i
$584$	9.19430			0.380463
$585$		0			0
$586$	−5.45430	+	16.7866i	−0.225315	+	0.693448i
$587$	2.40107	+	7.38974i	0.0991029	+	0.305007i	0.988301	−	0.152515i	$-0.0487371\pi$
$587$	2.40107	+	7.38974i	0.0991029	+	0.305007i	−0.889198	+	0.457522i	$0.848737\pi$
$588$		0			0
$589$	13.1192	−	9.53162i	0.540565	−	0.392744i
$590$	−2.67748	−	8.24043i	−0.110230	−	0.339253i
$591$		0			0
$592$	1.21587	+	0.883383i	0.0499720	+	0.0363068i
$593$	−25.2949			−1.03874			−0.519368	−	0.854551i	$-0.673832\pi$
$593$	−25.2949			−1.03874			−0.519368	+	0.854551i	$0.673832\pi$
$594$		0			0
$595$	19.0789			0.782159
$596$	−8.31220	−	6.03917i	−0.340481	−	0.247374i
$597$		0			0
$598$	−1.18444	−	3.64534i	−0.0484355	−	0.149069i
$599$	9.64302	−	7.00606i	0.394003	−	0.286260i	−0.373091	−	0.927795i	$-0.621702\pi$
$599$	9.64302	−	7.00606i	0.394003	−	0.286260i	0.767094	+	0.641535i	$0.221702\pi$
$600$		0			0
$601$	6.49264	+	19.9823i	0.264840	+	0.815095i	0.991730	+	0.128341i	$0.0409650\pi$
$601$	6.49264	+	19.9823i	0.264840	+	0.815095i	−0.726890	+	0.686754i	$0.759035\pi$
$602$	2.74765	−	8.45638i	0.111986	−	0.344657i
$603$		0			0
$604$	−0.891525			−0.0362756
$605$	−31.5165	+	0.284566i	−1.28133	+	0.0115693i
$606$		0			0
$607$	−20.8578	−	15.1541i	−0.846593	−	0.615086i	0.0776118	−	0.996984i	$-0.475271\pi$
$607$	−20.8578	−	15.1541i	−0.846593	−	0.615086i	−0.924204	+	0.381898i	$0.875271\pi$
$608$	10.4176	−	32.0620i	0.422488	−	1.30028i
$609$		0			0
$610$	−10.5099	+	7.63588i	−0.425533	+	0.309168i
$611$	29.2471	−	21.2493i	1.18321	−	0.859654i
$612$		0			0
$613$	−9.86298	+	30.3551i	−0.398362	+	1.22603i	0.527950	+	0.849275i	$0.322961\pi$
$613$	−9.86298	+	30.3551i	−0.398362	+	1.22603i	−0.926312	+	0.376757i	$0.877039\pi$
$614$	2.38326	+	1.73154i	0.0961807	+	0.0698794i
$615$		0			0
$616$	−8.21179	−	2.62725i	−0.330863	−	0.105855i
$617$	13.9772			0.562701			0.281350	−	0.959605i	$-0.409218\pi$
$617$	13.9772			0.562701			0.281350	+	0.959605i	$0.409218\pi$
$618$		0			0
$619$	6.94500	−	21.3745i	0.279143	−	0.859114i	−0.708950	−	0.705259i	$-0.750831\pi$
$619$	6.94500	−	21.3745i	0.279143	−	0.859114i	0.988093	−	0.153856i	$-0.0491691\pi$
$620$	−3.55354	−	10.9367i	−0.142714	−	0.439228i
$621$		0			0
$622$	2.30167	−	1.67226i	0.0922884	−	0.0670515i
$623$	5.12986	+	15.7881i	0.205523	+	0.632536i
$624$		0			0
$625$	24.8744	+	18.0723i	0.994974	+	0.722891i
$626$	−13.7173			−0.548252
$627$		0			0
$628$	8.75018			0.349170
$629$	9.27704	+	6.74016i	0.369900	+	0.268748i
$630$		0			0
$631$	−12.6815	−	39.0297i	−0.504843	−	1.55375i	−0.801034	−	0.598619i	$-0.795716\pi$
$631$	−12.6815	−	39.0297i	−0.504843	−	1.55375i	0.296190	−	0.955129i	$-0.404284\pi$
$632$	1.40865	−	1.02344i	0.0560330	−	0.0407103i
$633$		0			0
$634$	−1.73984	−	5.35469i	−0.0690980	−	0.212662i
$635$	14.4264	−	44.3998i	0.572493	−	1.76195i
$636$		0			0
$637$	−6.96619			−0.276010
$638$	11.1327	−	15.4692i	0.440747	−	0.612432i
$639$		0			0
$640$	−22.4131	−	16.2840i	−0.885954	−	0.643683i
$641$	4.27426	−	13.1548i	0.168823	−	0.519584i	−0.830475	−	0.557057i	$-0.811931\pi$
$641$	4.27426	−	13.1548i	0.168823	−	0.519584i	0.999298	+	0.0374724i	$0.0119306\pi$
$642$		0			0
$643$	27.1122	−	19.6982i	1.06920	−	0.776820i	0.0934326	−	0.995626i	$-0.470216\pi$
$643$	27.1122	−	19.6982i	1.06920	−	0.776820i	0.975768	+	0.218806i	$0.0702160\pi$
$644$	−0.834376	+	0.606210i	−0.0328790	+	0.0238880i
$645$		0			0
$646$	8.98610	−	27.6564i	0.353553	−	1.08813i
$647$	6.94635	+	5.04682i	0.273089	+	0.198411i	0.715897	−	0.698205i	$-0.246018\pi$
$647$	6.94635	+	5.04682i	0.273089	+	0.198411i	−0.442808	+	0.896616i	$0.646018\pi$
$648$		0			0
$649$	−0.0596253	−	13.2076i	−0.00234050	−	0.518443i
$650$	16.9787			0.665957
$651$		0			0
$652$	−9.51892	+	29.2962i	−0.372789	+	1.14733i
$653$	14.6622	+	45.1255i	0.573775	+	1.76590i	0.640312	+	0.768115i	$0.278805\pi$
$653$	14.6622	+	45.1255i	0.573775	+	1.76590i	−0.0665369	+	0.997784i	$0.521195\pi$
$654$		0			0
$655$	−14.3679	+	10.4389i	−0.561400	+	0.407881i
$656$	0.302275	+	0.930306i	0.0118018	+	0.0363224i
$657$		0			0
$658$	3.18814	+	2.31632i	0.124287	+	0.0902996i
$659$	47.4501			1.84839			0.924197	−	0.381916i	$-0.124736\pi$
$659$	47.4501			1.84839			0.924197	+	0.381916i	$0.124736\pi$
$660$		0			0
$661$	−24.3627			−0.947599			−0.473800	−	0.880633i	$-0.657118\pi$
$661$	−24.3627			−0.947599			−0.473800	+	0.880633i	$0.657118\pi$
$662$	8.91846	+	6.47964i	0.346626	+	0.251838i
$663$		0			0
$664$	10.7837	+	33.1888i	0.418489	+	1.28798i
$665$	13.3312	−	9.68566i	0.516961	−	0.375594i
$666$		0			0
$667$	−1.69440	−	5.21483i	−0.0656075	−	0.201919i
$668$	10.5540	−	32.4817i	0.408345	−	1.25676i
$669$		0			0
$670$	−22.5433			−0.870926
$671$	−18.8057	+	6.20433i	−0.725985	+	0.239516i
$672$		0			0
$673$	−25.8454	−	18.7778i	−0.996268	−	0.723831i	−0.0349835	−	0.999388i	$-0.511138\pi$
$673$	−25.8454	−	18.7778i	−0.996268	−	0.723831i	−0.961285	+	0.275557i	$0.911138\pi$
$674$	−2.47664	+	7.62230i	−0.0953965	+	0.293600i
$675$		0			0
$676$	40.9112	−	29.7237i	1.57351	−	1.14322i
$677$	−0.820859	+	0.596389i	−0.0315482	+	0.0229211i	−0.603448	−	0.797403i	$-0.706207\pi$
$677$	−0.820859	+	0.596389i	−0.0315482	+	0.0229211i	0.571899	+	0.820324i	$0.306207\pi$
$678$		0			0
$679$	3.12480	−	9.61714i	0.119919	−	0.369072i
$680$	−40.1249	−	29.1525i	−1.53872	−	1.11795i
$681$		0			0
$682$	0.0320589	+	7.10136i	0.00122760	+	0.271925i
$683$	−0.904878			−0.0346242			−0.0173121	−	0.999850i	$-0.505511\pi$
$683$	−0.904878			−0.0346242			−0.0173121	+	0.999850i	$0.505511\pi$
$684$		0			0
$685$	14.1750	−	43.6262i	0.541599	−	1.66687i
$686$	−0.234656	−	0.722197i	−0.00895921	−	0.0275736i
$687$		0			0
$688$	8.26715	−	6.00644i	0.315182	−	0.228993i
$689$	13.4708	+	41.4588i	0.513196	+	1.57945i
$690$		0			0
$691$	17.3563	+	12.6101i	0.660263	+	0.479709i	0.866752	−	0.498740i	$-0.166204\pi$
$691$	17.3563	+	12.6101i	0.660263	+	0.479709i	−0.206489	+	0.978449i	$0.566204\pi$
$692$	15.3878			0.584958
$693$		0			0
$694$	17.0932			0.648851
$695$	−10.6954	−	7.77069i	−0.405701	−	0.294759i
$696$		0			0
$697$	2.30634	+	7.09819i	0.0873589	+	0.268863i
$698$	−12.7294	+	9.24848i	−0.481816	+	0.350060i
$699$		0			0
$700$	−1.41175	−	4.34492i	−0.0533591	−	0.164223i
$701$	5.89450	−	18.1414i	0.222632	−	0.685192i	−0.775891	−	0.630867i	$-0.782699\pi$
$701$	5.89450	−	18.1414i	0.222632	−	0.685192i	0.998523	−	0.0543248i	$-0.0173006\pi$
$702$		0			0
$703$	9.90396			0.373535
$704$	5.30771	+	7.23651i	0.200042	+	0.272736i
$705$		0			0
$706$	3.69500	+	2.68457i	0.139063	+	0.101035i
$707$	1.98498	−	6.10914i	0.0746528	−	0.229758i
$708$		0			0
$709$	7.86023	−	5.71079i	0.295197	−	0.214473i	−0.430322	−	0.902676i	$-0.641600\pi$
$709$	7.86023	−	5.71079i	0.295197	−	0.214473i	0.725519	+	0.688202i	$0.241600\pi$
$710$	−1.75175	+	1.27272i	−0.0657421	+	0.0477644i
$711$		0			0
$712$	13.3355	−	41.0424i	0.499768	−	1.53813i
$713$	1.65289	+	1.20090i	0.0619013	+	0.0449739i
$714$		0			0
$715$	63.0511	+	20.1723i	2.35798	+	0.754401i
$716$	−8.43828			−0.315353
$717$		0			0
$718$	4.33410	−	13.3390i	0.161747	−	0.497807i
$719$	3.77630	+	11.6223i	0.140832	+	0.433437i	0.996452	−	0.0841686i	$-0.0268234\pi$
$719$	3.77630	+	11.6223i	0.140832	+	0.433437i	−0.855619	+	0.517606i	$0.826823\pi$
$720$		0			0
$721$	7.24707	−	5.26530i	0.269895	−	0.196090i
$722$	−3.30272	−	10.1647i	−0.122915	−	0.378292i
$723$		0			0
$724$	−5.58050	−	4.05447i	−0.207398	−	0.150683i
$725$	24.2888			0.902062
$726$		0			0
$727$	0.0225849			0.000837628			0.000418814	−	1.00000i	$-0.499867\pi$
$727$	0.0225849			0.000837628			0.000418814		1.00000i	$0.499867\pi$
$728$	14.6506	+	10.6443i	0.542988	+	0.394504i
$729$		0			0
$730$	−2.37799	−	7.31870i	−0.0880134	−	0.270877i
$731$	63.0779	−	45.8288i	2.33302	−	1.69504i
$732$		0			0
$733$	1.63230	+	5.02369i	0.0602902	+	0.185554i	0.976666	−	0.214766i	$-0.0688989\pi$
$733$	1.63230	+	5.02369i	0.0602902	+	0.185554i	−0.916375	+	0.400320i	$0.868899\pi$
$734$	0.945642	−	2.91039i	0.0349043	−	0.107424i
$735$		0			0
$736$	4.24740			0.156561
$737$	−32.7296	−	10.4714i	−1.20561	−	0.385718i
$738$		0			0
$739$	29.1919	+	21.2091i	1.07384	+	0.780191i	0.976599	−	0.215070i	$-0.0689979\pi$
$739$	29.1919	+	21.2091i	1.07384	+	0.780191i	0.0972419	+	0.995261i	$0.468998\pi$
$740$	2.17031	−	6.67954i	0.0797823	−	0.245545i
$741$		0			0
$742$	−3.84435	+	2.79308i	−0.141130	+	0.102537i
$743$	−27.6724	+	20.1052i	−1.01520	+	0.737587i	−0.965294	−	0.261167i	$-0.915893\pi$
$743$	−27.6724	+	20.1052i	−1.01520	+	0.737587i	−0.0499072	+	0.998754i	$0.515893\pi$
$744$		0			0
$745$	−6.39126	+	19.6703i	−0.234158	+	0.720663i
$746$	3.11200	+	2.26100i	0.113938	+	0.0827810i
$747$		0			0
$748$	−18.5913	−	25.3472i	−0.679764	−	0.926787i
$749$	4.52891			0.165483
$750$		0			0
$751$	2.26664	−	6.97600i	0.0827108	−	0.254558i	−0.901146	−	0.433516i	$-0.857273\pi$
$751$	2.26664	−	6.97600i	0.0827108	−	0.254558i	0.983857	+	0.178958i	$0.0572727\pi$
$752$	1.39953	+	4.30731i	0.0510356	+	0.157071i
$753$		0			0
$754$	−32.3854	+	23.5294i	−1.17941	+	0.856889i
$755$	0.554576	+	1.70681i	0.0201831	+	0.0621172i
$756$		0			0
$757$	28.2299	+	20.5102i	1.02603	+	0.745457i	0.967511	−	0.252829i	$-0.0813609\pi$
$757$	28.2299	+	20.5102i	1.02603	+	0.745457i	0.0585230	+	0.998286i	$0.481361\pi$
$758$	−1.66800			−0.0605844
$759$		0			0
$760$	−42.8365			−1.55384
$761$	1.85160	+	1.34527i	0.0671205	+	0.0487659i	0.620840	−	0.783938i	$-0.286792\pi$
$761$	1.85160	+	1.34527i	0.0671205	+	0.0487659i	−0.553719	+	0.832704i	$0.686792\pi$
$762$		0			0
$763$	−0.317495	−	0.977150i	−0.0114941	−	0.0353752i
$764$	−18.0702	+	13.1287i	−0.653756	+	0.474981i
$765$		0			0
$766$	5.74571	+	17.6835i	0.207601	+	0.638930i
$767$	−8.57253	+	26.3835i	−0.309536	+	0.952654i
$768$		0			0
$769$	−9.59977			−0.346176			−0.173088	−	0.984906i	$-0.555375\pi$
$769$	−9.59977			−0.346176			−0.173088	+	0.984906i	$0.555375\pi$
$770$	0.0325770	+	7.21612i	0.00117399	+	0.260051i
$771$		0			0
$772$	−26.2028	−	19.0375i	−0.943060	−	0.685173i
$773$	−4.25705	+	13.1019i	−0.153116	+	0.471241i	−0.997965	−	0.0637628i	$-0.979690\pi$
$773$	−4.25705	+	13.1019i	−0.153116	+	0.471241i	0.844850	+	0.535004i	$0.179690\pi$
$774$		0			0
$775$	−7.32177	+	5.31958i	−0.263006	+	0.191085i
$776$	−21.2667	+	15.4512i	−0.763431	+	0.554665i
$777$		0			0
$778$	−8.05358	+	24.7864i	−0.288735	+	0.888634i
$779$	5.21502	+	3.78893i	0.186847	+	0.135753i
$780$		0			0
$781$	−3.13447	+	1.03412i	−0.112160	+	0.0370036i
$782$	3.66377			0.131016
$783$		0			0
$784$	0.269682	−	0.829996i	0.00963150	−	0.0296427i
$785$	−5.44308	−	16.7521i	−0.194272	−	0.597908i
$786$		0			0
$787$	1.81440	−	1.31824i	0.0646763	−	0.0469901i	−0.554977	−	0.831865i	$-0.687273\pi$
$787$	1.81440	−	1.31824i	0.0646763	−	0.0469901i	0.619654	+	0.784875i	$0.287273\pi$
$788$	−6.73072	−	20.7150i	−0.239772	−	0.737942i
$789$		0			0
$790$	−1.17899	−	0.856589i	−0.0419467	−	0.0304761i
$791$	13.2380			0.470689
$792$		0			0
$793$	41.5933			1.47702
$794$	5.20186	+	3.77937i	0.184607	+	0.134125i
$795$		0			0
$796$	0.240953	+	0.741578i	0.00854036	+	0.0262845i
$797$	−14.7167	+	10.6923i	−0.521293	+	0.378741i	−0.817091	−	0.576509i	$-0.804414\pi$
$797$	−14.7167	+	10.6923i	−0.521293	+	0.378741i	0.295798	+	0.955251i	$0.404414\pi$
$798$		0			0
$799$	10.6783	+	32.8646i	0.377773	+	1.16266i
$800$	−5.81402	+	17.8937i	−0.205557	+	0.632638i
$801$		0			0
$802$	−21.9516			−0.775139
$803$	−0.0529560	−	11.7303i	−0.00186878	−	0.413952i
$804$		0			0
$805$	1.67961	+	1.22030i	0.0591983	+	0.0430101i
$806$	4.60922	−	14.1857i	0.162353	−	0.499670i
$807$		0			0
$808$	−13.5093	+	9.81511i	−0.475257	+	0.345294i
$809$	25.2420	−	18.3394i	0.887463	−	0.644780i	−0.0477521	−	0.998859i	$-0.515206\pi$
$809$	25.2420	−	18.3394i	0.887463	−	0.644780i	0.935215	+	0.354079i	$0.115206\pi$
$810$		0			0
$811$	−7.78729	+	23.9668i	−0.273449	+	0.841589i	0.716177	+	0.697919i	$0.245890\pi$
$811$	−7.78729	+	23.9668i	−0.273449	+	0.841589i	−0.989626	+	0.143670i	$0.954110\pi$
$812$	8.71408	+	6.33115i	0.305804	+	0.222180i
$813$		0			0
$814$	−2.53346	+	3.52032i	−0.0887977	+	0.123387i
$815$	62.0084			2.17206
$816$		0			0
$817$	20.8094	−	64.0447i	0.728028	−	2.24064i
$818$	0.374409	+	1.15231i	0.0130909	+	0.0402896i
$819$		0			0
$820$	3.69817	−	2.68688i	0.129146	−	0.0938299i
$821$	−3.67308	−	11.3046i	−0.128191	−	0.394532i	0.866278	−	0.499563i	$-0.166506\pi$
$821$	−3.67308	−	11.3046i	−0.128191	−	0.394532i	−0.994469	+	0.105030i	$0.966506\pi$
$822$		0			0
$823$	−6.17171	−	4.48401i	−0.215132	−	0.156303i	0.475000	−	0.879986i	$-0.342448\pi$
$823$	−6.17171	−	4.48401i	−0.215132	−	0.156303i	−0.690133	+	0.723683i	$0.742448\pi$
$824$	−23.2867			−0.811231
$825$		0			0
$826$	−3.02399			−0.105218
$827$	9.22846	+	6.70487i	0.320905	+	0.233151i	0.736562	−	0.676370i	$-0.236448\pi$
$827$	9.22846	+	6.70487i	0.320905	+	0.233151i	−0.415657	+	0.909522i	$0.636448\pi$
$828$		0			0
$829$	−13.7968	−	42.4622i	−0.479183	−	1.47477i	−0.840233	−	0.542226i	$-0.817582\pi$
$829$	−13.7968	−	42.4622i	−0.479183	−	1.47477i	0.361050	−	0.932546i	$-0.382418\pi$
$830$	23.6294	−	17.1678i	0.820188	−	0.595902i
$831$		0			0
$832$	−5.82484	−	17.9270i	−0.201940	−	0.621507i
$833$	2.05766	−	6.33282i	0.0712936	−	0.219419i
$834$		0			0
$835$	−68.7509			−2.37922
$836$	−25.8583	−	8.27300i	−0.894328	−	0.286128i
$837$		0			0
$838$	−0.138005	−	0.100266i	−0.00476730	−	0.00346364i
$839$	3.11638	−	9.59122i	0.107589	−	0.331126i	−0.882740	−	0.469861i	$-0.844304\pi$
$839$	3.11638	−	9.59122i	0.107589	−	0.331126i	0.990329	+	0.138736i	$0.0443039\pi$
$840$		0			0
$841$	−22.8673	+	16.6141i	−0.788529	+	0.572900i
$842$	7.08315	−	5.14621i	0.244101	−	0.177350i
$843$		0			0
$844$	6.10180	−	18.7794i	0.210033	−	0.646414i
$845$	−82.3546	−	59.8341i	−2.83308	−	2.05836i
$846$		0			0
$847$	−3.30459	+	10.4919i	−0.113547	+	0.360505i
$848$	−5.46116			−0.187537
$849$		0			0
$850$	−5.01512	+	15.4350i	−0.172017	+	0.529415i
$851$	0.385594	+	1.18674i	0.0132180	+	0.0406808i
$852$		0			0
$853$	15.3816	−	11.1754i	0.526654	−	0.382637i	−0.292450	−	0.956281i	$-0.594471\pi$
$853$	15.3816	−	11.1754i	0.526654	−	0.382637i	0.819105	+	0.573644i	$0.194471\pi$
$854$	1.40107	+	4.31205i	0.0479437	+	0.147555i
$855$		0			0
$856$	−9.52476	−	6.92014i	−0.325550	−	0.236526i
$857$	−29.8781			−1.02062			−0.510308	−	0.859992i	$-0.670469\pi$
$857$	−29.8781			−1.02062			−0.510308	+	0.859992i	$0.670469\pi$
$858$		0			0
$859$	−16.6976			−0.569714			−0.284857	−	0.958570i	$-0.591946\pi$
$859$	−16.6976			−0.569714			−0.284857	+	0.958570i	$0.591946\pi$
$860$	−38.6337	−	28.0690i	−1.31740	−	0.957145i
$861$		0			0
$862$	−6.54481	−	20.1429i	−0.222917	−	0.686068i
$863$	−13.5768	+	9.86413i	−0.462160	+	0.335779i	−0.794378	−	0.607424i	$-0.792203\pi$
$863$	−13.5768	+	9.86413i	−0.462160	+	0.335779i	0.332218	+	0.943203i	$0.392203\pi$
$864$		0			0
$865$	−9.57206	−	29.4598i	−0.325460	−	1.00166i
$866$	−6.09329	+	18.7532i	−0.207058	+	0.637260i
$867$		0			0
$868$	−4.01344			−0.136225
$869$	−1.31384	−	1.79128i	−0.0445690	−	0.0607651i
$870$		0			0
$871$	58.3928	+	42.4248i	1.97856	+	1.43751i
$872$	−0.825354	+	2.54018i	−0.0279500	+	0.0860213i
$873$		0			0
$874$	2.56002	−	1.85996i	0.0865938	−	0.0629141i
$875$	4.15008	−	3.01521i	0.140298	−	0.101933i
$876$		0			0
$877$	1.71138	−	5.26709i	0.0577893	−	0.177857i	−0.917995	−	0.396592i	$-0.870193\pi$
$877$	1.71138	−	5.26709i	0.0577893	−	0.177857i	0.975784	+	0.218735i	$0.0701929\pi$
$878$	14.4708	+	10.5136i	0.488365	+	0.354818i
$879$		0			0
$880$	−4.84435	+	6.73137i	−0.163303	+	0.226915i
$881$	−6.77615			−0.228294			−0.114147	−	0.993464i	$-0.536414\pi$
$881$	−6.77615			−0.228294			−0.114147	+	0.993464i	$0.536414\pi$
$882$		0			0
$883$	−7.40416	+	22.7877i	−0.249170	+	0.766866i	0.745753	+	0.666223i	$0.232090\pi$
$883$	−7.40416	+	22.7877i	−0.249170	+	0.766866i	−0.994923	+	0.100643i	$0.967910\pi$
$884$	20.4026	+	62.7927i	0.686213	+	2.11195i
$885$		0			0
$886$	15.2609	−	11.0877i	0.512699	−	0.372498i
$887$	−8.55610	−	26.3330i	−0.287286	−	0.884175i	−0.985704	−	0.168485i	$-0.946113\pi$
$887$	−8.55610	−	26.3330i	−0.287286	−	0.884175i	0.698418	−	0.715690i	$-0.253887\pi$
$888$		0			0
$889$	−13.1816	−	9.57702i	−0.442098	−	0.321203i
$890$	−36.1189			−1.21071
$891$		0			0
$892$	10.8201			0.362285
$893$	24.1455	+	17.5427i	0.807999	+	0.587045i
$894$		0			0
$895$	5.24906	+	16.1550i	0.175457	+	0.540001i
$896$	−7.82238	+	5.68329i	−0.261327	+	0.189865i
$897$		0			0
$898$	4.32064	+	13.2976i	0.144182	+	0.443746i
$899$	6.59370	−	20.2933i	0.219912	−	0.676820i
$900$		0			0
$901$	−41.6684			−1.38817
$902$	−2.68078	+	0.884436i	−0.0892601	+	0.0294485i
$903$		0			0
$904$	−27.8409	−	20.2276i	−0.925975	−	0.672760i
$905$	−4.29085	+	13.2059i	−0.142633	+	0.438978i
$906$		0			0
$907$	−12.1001	+	8.79121i	−0.401776	+	0.291907i	−0.770264	−	0.637725i	$-0.779876\pi$
$907$	−12.1001	+	8.79121i	−0.401776	+	0.291907i	0.368488	+	0.929633i	$0.379876\pi$
$908$	−0.339881	+	0.246938i	−0.0112793	+	0.00819492i
$909$		0			0
$910$	4.68371	−	14.4150i	0.155263	−	0.477851i
$911$	−20.3804	−	14.8073i	−0.675234	−	0.490586i	0.196539	−	0.980496i	$-0.437030\pi$
$911$	−20.3804	−	14.8073i	−0.675234	−	0.490586i	−0.871773	+	0.489910i	$0.837030\pi$
$912$		0			0
$913$	42.2808	−	13.9492i	1.39929	−	0.461651i
$914$	−3.50347			−0.115884
$915$		0			0
$916$	−3.12761	+	9.62580i	−0.103339	+	0.318045i
$917$	1.91538	+	5.89494i	0.0632515	+	0.194668i
$918$		0			0
$919$	−21.6652	+	15.7407i	−0.714668	+	0.519237i	−0.884676	−	0.466206i	$-0.845621\pi$
$919$	−21.6652	+	15.7407i	−0.714668	+	0.519237i	0.170008	+	0.985443i	$0.445621\pi$
$920$	−1.66777	−	5.13286i	−0.0549846	−	0.169225i
$921$		0			0
$922$	20.5894	+	14.9591i	0.678076	+	0.492651i
$923$	6.93263			0.228190
$924$		0			0
$925$	−5.52738			−0.181739
$926$	−10.1574	−	7.37975i	−0.333791	−	0.242514i
$927$		0			0
$928$	−13.7077	−	42.1880i	−0.449978	−	1.38489i
$929$	4.57116	−	3.32114i	0.149975	−	0.108963i	−0.510267	−	0.860016i	$-0.670454\pi$
$929$	4.57116	−	3.32114i	0.149975	−	0.108963i	0.660242	+	0.751053i	$0.270454\pi$
$930$		0			0
$931$	−1.77718	−	5.46959i	−0.0582446	−	0.179258i
$932$	−4.51004	+	13.8805i	−0.147731	+	0.454670i
$933$		0			0
$934$	14.7655			0.483142
$935$	−36.9621	+	51.3600i	−1.20879	+	1.67965i
$936$		0			0
$937$	36.6328	+	26.6153i	1.19674	+	0.869484i	0.993960	−	0.109740i	$-0.0350018\pi$
$937$	36.6328	+	26.6153i	1.19674	+	0.869484i	0.202782	+	0.979224i	$0.435002\pi$
$938$	−2.43130	+	7.48277i	−0.0793847	+	0.244321i
$939$		0			0
$940$	17.1225	−	12.4402i	0.558475	−	0.405756i
$941$	−26.4448	+	19.2133i	−0.862076	+	0.626335i	−0.928449	−	0.371460i	$-0.878857\pi$
$941$	−26.4448	+	19.2133i	−0.862076	+	0.626335i	0.0663733	+	0.997795i	$0.478857\pi$
$942$		0			0
$943$	−0.250969	+	0.772402i	−0.00817267	+	0.0251529i
$944$	−2.81163	−	2.04277i	−0.0915108	−	0.0664865i
$945$		0			0
$946$	17.4413	+	23.7794i	0.567066	+	0.773135i
$947$	39.8004			1.29334			0.646669	−	0.762771i	$-0.276162\pi$
$947$	39.8004			1.29334			0.646669	+	0.762771i	$0.276162\pi$
$948$		0			0
$949$	−7.61365	+	23.4324i	−0.247150	+	0.760648i
$950$	4.33150	+	13.3310i	0.140533	+	0.432515i
$951$		0			0
$952$	−14.0040	+	10.1745i	−0.453872	+	0.329757i
$953$	3.86809	+	11.9048i	0.125300	+	0.385633i	0.993956	−	0.109783i	$-0.0350156\pi$
$953$	3.86809	+	11.9048i	0.125300	+	0.385633i	−0.868656	+	0.495416i	$0.835016\pi$
$954$		0			0
$955$	36.3754	+	26.4283i	1.17708	+	0.855199i
$956$	28.1886			0.911686
$957$		0			0
$958$	−29.8245			−0.963587
$959$	−12.9520	−	9.41016i	−0.418241	−	0.303870i
$960$		0			0
$961$	−7.12266	−	21.9213i	−0.229763	−	0.707138i
$962$	7.36993	−	5.35457i	0.237616	−	0.172638i
$963$		0			0
$964$	8.81030	+	27.1153i	0.283761	+	0.873325i
$965$	−20.1474	+	62.0072i	−0.648566	+	1.99608i
$966$		0			0
$967$	12.7139			0.408850			0.204425	−	0.978882i	$-0.434468\pi$
$967$	12.7139			0.408850			0.204425	+	0.978882i	$0.434468\pi$
$968$	22.9814	−	17.0161i	0.738652	−	0.546919i
$969$		0			0
$970$	17.7996	+	12.9321i	0.571510	+	0.415226i
$971$	−6.98768	+	21.5059i	−0.224245	+	0.690156i	0.774122	+	0.633037i	$0.218192\pi$
$971$	−6.98768	+	21.5059i	−0.224245	+	0.690156i	−0.998367	+	0.0571199i	$0.981808\pi$
$972$		0			0
$973$	−3.73281	+	2.71205i	−0.119669	+	0.0869443i
$974$	−10.5057	+	7.63281i	−0.336623	+	0.244571i
$975$		0			0
$976$	−1.61020	+	4.95569i	−0.0515413	+	0.158628i
$977$	14.5376	+	10.5622i	0.465098	+	0.337913i	0.795528	−	0.605917i	$-0.207194\pi$
$977$	14.5376	+	10.5622i	0.465098	+	0.337913i	−0.330430	+	0.943831i	$0.607194\pi$
$978$		0			0
$979$	−52.4394	−	16.7772i	−1.67597	−	0.536203i
$980$	−4.07830			−0.130277
$981$		0			0
$982$	8.16272	−	25.1223i	0.260483	−	0.801683i
$983$	14.8966	+	45.8471i	0.475129	+	1.46230i	0.845784	+	0.533526i	$0.179133\pi$
$983$	14.8966	+	45.8471i	0.475129	+	1.46230i	−0.370655	+	0.928771i	$0.620867\pi$
$984$		0			0
$985$	−35.4717	+	25.7717i	−1.13022	+	0.821155i
$986$	−11.8241	−	36.3910i	−0.376558	−	1.15892i
$987$		0			0
$988$	46.1337	+	33.5181i	1.46771	+	1.06635i
$989$	8.48430			0.269785
$990$		0			0
$991$	−6.62493			−0.210448			−0.105224	−	0.994449i	$-0.533556\pi$
$991$	−6.62493			−0.210448			−0.105224	+	0.994449i	$0.533556\pi$
$992$	13.3719	+	9.71526i	0.424558	+	0.308460i
$993$		0			0
$994$	0.233526	+	0.718719i	0.00740699	+	0.0227964i
$995$	1.26985	−	0.922602i	0.0402571	−	0.0292485i
$996$		0			0
$997$	−8.69144	−	26.7495i	−0.275261	−	0.847165i	−0.989150	−	0.146907i	$-0.953068\pi$
$997$	−8.69144	−	26.7495i	−0.275261	−	0.847165i	0.713890	−	0.700258i	$-0.246932\pi$
$998$	−3.67418	+	11.3080i	−0.116304	+	0.357947i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.k.631.5	yes	32
3.2	odd	2	inner	693.2.m.k.631.4	yes	32
11.3	even	5	inner	693.2.m.k.190.5	yes	32
11.5	even	5		7623.2.a.dc.1.7		16
11.6	odd	10		7623.2.a.db.1.10		16
33.5	odd	10		7623.2.a.dc.1.10		16
33.14	odd	10	inner	693.2.m.k.190.4	✓	32
33.17	even	10		7623.2.a.db.1.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.190.4	✓	32	33.14	odd	10	inner
693.2.m.k.190.5	yes	32	11.3	even	5	inner
693.2.m.k.631.4	yes	32	3.2	odd	2	inner
693.2.m.k.631.5	yes	32	1.1	even	1	trivial
7623.2.a.db.1.7		16	33.17	even	10
7623.2.a.db.1.10		16	11.6	odd	10
7623.2.a.dc.1.7		16	11.5	even	5
7623.2.a.dc.1.10		16	33.5	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.614338 + 0.446343i) q^{2} +(-0.439845 - 1.35370i) q^{4} +(-2.31804 + 1.68415i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.803314 - 2.47235i) q^{8} +O(q^{10})\)	\(q+(0.614338 + 0.446343i) q^{2} +(-0.439845 - 1.35370i) q^{4} +(-2.31804 + 1.68415i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.803314 - 2.47235i) q^{8} -2.17577 q^{10} +(-3.15889 - 1.01064i) q^{11} +(5.63576 + 4.09462i) q^{13} +(-0.234656 + 0.722197i) q^{14} +(-0.706036 + 0.512965i) q^{16} +(-5.38702 + 3.91390i) q^{17} +(-1.77718 + 5.46959i) q^{19} +(3.29942 + 2.39717i) q^{20} +(-1.48953 - 2.03082i) q^{22} -0.724581 q^{23} +(0.991838 - 3.05256i) q^{25} +(1.63466 + 5.03096i) q^{26} +(1.15153 - 0.836634i) q^{28} +(2.33846 + 7.19703i) q^{29} +(-2.28117 - 1.65737i) q^{31} -5.86186 q^{32} -5.05639 q^{34} +(-2.31804 - 1.68415i) q^{35} +(-0.532161 - 1.63782i) q^{37} +(-3.53310 + 2.56694i) q^{38} +(2.30170 + 7.08389i) q^{40} +(0.346364 - 1.06600i) q^{41} -11.7092 q^{43} +(0.0213116 + 4.72073i) q^{44} +(-0.445138 - 0.323411i) q^{46} +(1.60366 - 4.93556i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(1.97181 - 1.43261i) q^{50} +(3.06404 - 9.43015i) q^{52} +(5.06259 + 3.67819i) q^{53} +(9.02450 - 2.97735i) q^{55} +2.59958 q^{56} +(-1.77574 + 5.46516i) q^{58} +(1.23059 + 3.78737i) q^{59} +(4.83043 - 3.50951i) q^{61} +(-0.661656 - 2.03637i) q^{62} +(-2.18909 - 1.59047i) q^{64} -19.9599 q^{65} +10.3611 q^{67} +(7.66771 + 5.57092i) q^{68} +(-0.672349 - 2.06928i) q^{70} +(0.805120 - 0.584954i) q^{71} +(1.09294 + 3.36374i) q^{73} +(0.404104 - 1.24370i) q^{74} +8.18588 q^{76} +(-0.0149727 - 3.31659i) q^{77} +(0.541875 + 0.393695i) q^{79} +(0.772706 - 2.37814i) q^{80} +(0.688585 - 0.500286i) q^{82} +(-10.8603 + 7.89044i) q^{83} +(5.89571 - 18.1451i) q^{85} +(-7.19343 - 5.22633i) q^{86} +(-5.03624 + 6.99801i) q^{88} +16.6006 q^{89} +(-2.15267 + 6.62524i) q^{91} +(0.318703 + 0.980868i) q^{92} +(3.18814 - 2.31632i) q^{94} +(-5.09205 - 15.6717i) q^{95} +(-8.18083 - 5.94372i) q^{97} -0.759363 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) 32 * q - 10 * q^4 - 8 * q^7	\( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

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