LMFDB - Embedded newform 693.2.m.k.190.4

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			190.4
Character	$\chi$	$=$	693.190
Dual form			693.2.m.k.631.4

$q$-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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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	$-0.786520\pi$
$2$	−0.614338	+	0.446343i	−0.434402	+	0.315612i	0.349004	+	0.937121i	$0.386520\pi$
$3$		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	$-0.0786487\pi$
$5$	2.31804	+	1.68415i	1.03666	+	0.753175i	0.0670269	+	0.997751i	$0.478649\pi$
$6$		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	0.629652	−	0.776877i	$-0.283197\pi$
$13$	5.63576	−	4.09462i	1.56308	−	1.13564i	0.933427	−	0.358767i	$-0.116803\pi$
$14$	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	$-0.000826122\pi$
$17$	5.38702	+	3.91390i	1.30654	+	0.949260i	0.306548	+	0.951855i	$0.400826\pi$
$18$		0			0
$19$	−1.77718	−	5.46959i	−0.407712	−	1.25481i	−0.918609	−	0.395167i	$-0.870687\pi$
$19$	−1.77718	−	5.46959i	−0.407712	−	1.25481i	0.510897	−	0.859642i	$-0.329313\pi$
$20$	−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	$-0.475931\pi$
$23$	0.724581			0.151086			0.0755428	+	0.997143i	$0.475931\pi$
$24$		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	0.459623	+	0.888114i	$0.347985\pi$
$29$	−2.33846	+	7.19703i	−0.434240	+	1.33645i	−0.893863	+	0.448340i	$0.852015\pi$
$30$		0			0
$31$	−2.28117	+	1.65737i	−0.409710	+	0.297672i	−0.773484	−	0.633815i	$-0.781488\pi$
$31$	−2.28117	+	1.65737i	−0.409710	+	0.297672i	0.363774	+	0.931487i	$0.381488\pi$
$32$	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	−0.985223	−	0.171277i	$-0.945211\pi$
$37$	−0.532161	+	1.63782i	−0.0874868	+	0.269257i	0.897736	+	0.440534i	$0.145211\pi$
$38$	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	$-0.127896\pi$
$41$	−0.346364	−	1.06600i	−0.0540929	−	0.166481i	−0.974453	+	0.224591i	$0.927896\pi$
$42$		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	−0.997263	−	0.0739350i	$-0.976444\pi$
$47$	−1.60366	−	4.93556i	−0.233918	−	0.719926i	0.763345	−	0.645991i	$-0.223556\pi$
$48$		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	$-0.841409\pi$
$53$	−5.06259	+	3.67819i	−0.695401	+	0.505238i	0.183030	+	0.983107i	$0.441409\pi$
$54$		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	$-0.983467\pi$
$59$	−1.23059	+	3.78737i	−0.160209	+	0.493074i	0.838442	+	0.544991i	$0.183467\pi$
$60$		0			0
$61$	4.83043	+	3.50951i	0.618473	+	0.449347i	0.852388	−	0.522910i	$-0.175154\pi$
$61$	4.83043	+	3.50951i	0.618473	+	0.449347i	−0.233915	+	0.972257i	$0.575154\pi$
$62$	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	$-0.318808\pi$
$71$	−0.805120	−	0.584954i	−0.0955502	−	0.0694213i	−0.634535	+	0.772894i	$0.718808\pi$
$72$		0			0
$73$	1.09294	−	3.36374i	0.127919	−	0.393696i	−0.866502	−	0.499173i	$-0.833637\pi$
$73$	1.09294	−	3.36374i	0.127919	−	0.393696i	0.994422	+	0.105478i	$0.0336372\pi$
$74$	−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	−0.556885	−	0.830590i	$-0.688004\pi$
$79$	0.541875	−	0.393695i	0.0609657	−	0.0442942i	0.617851	+	0.786295i	$0.288004\pi$
$80$	−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	$-0.0363646\pi$
$83$	10.8603	+	7.89044i	1.19207	+	0.866089i	0.198587	+	0.980083i	$0.436365\pi$
$84$		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	$-0.842343\pi$
$89$	−16.6006			−1.75966			−0.879828	+	0.475292i	$0.842343\pi$
$90$		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	−0.919740	−	0.392529i	$-0.871600\pi$
$97$	−8.18083	+	5.94372i	−0.830638	+	0.603493i	0.0891021	+	0.996022i	$0.471600\pi$
$98$	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	$-0.596457\pi$
$101$	5.19674	−	3.77565i	0.517095	−	0.375692i	0.815508	+	0.578745i	$0.196457\pi$
$102$		0			0
$103$	−2.76813	+	8.51944i	−0.272752	+	0.839446i	0.717053	+	0.697019i	$0.245491\pi$
$103$	−2.76813	+	8.51944i	−0.272752	+	0.839446i	−0.989805	+	0.142427i	$0.954509\pi$
$104$	−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	$-0.170251\pi$
$107$	−1.39951	−	4.30724i	−0.135296	−	0.416397i	−0.995636	+	0.0933231i	$0.970251\pi$
$108$		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	−0.936605	−	0.350386i	$-0.886050\pi$
$113$	−4.09077	−	12.5901i	−0.384827	−	1.18438i	0.551778	−	0.833991i	$-0.313950\pi$
$114$		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	−0.178711	−	0.983902i	$-0.557193\pi$
$127$	−13.1816	−	9.57702i	−1.16968	−	0.849823i	−0.990971	+	0.134078i	$0.957193\pi$
$128$	−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	$-0.587280\pi$
$131$	−6.19831			−0.541549			−0.270774	+	0.962643i	$0.587280\pi$
$132$		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	$-0.0602856\pi$
$137$	12.9520	+	9.41016i	1.10656	+	0.803964i	0.124443	+	0.992227i	$0.460286\pi$
$138$		0			0
$139$	1.42581	−	4.38819i	0.120935	−	0.372201i	−0.872203	−	0.489144i	$-0.837309\pi$
$139$	1.42581	−	4.38819i	0.120935	−	0.372201i	0.993139	+	0.116943i	$0.0373094\pi$
$140$	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	$-0.395545\pi$
$149$	−5.83982	−	4.24287i	−0.478416	−	0.347590i	−0.800712	+	0.599049i	$0.795545\pi$
$150$		0			0
$151$	0.193552	+	0.595693i	0.0157511	+	0.0484768i	0.958623	−	0.284678i	$-0.0918867\pi$
$151$	0.193552	+	0.595693i	0.0157511	+	0.0484768i	−0.942872	+	0.333155i	$0.891887\pi$
$152$	−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	0.846190	−	0.532881i	$-0.178891\pi$
$157$	−1.89969	−	5.84664i	−0.151612	−	0.466613i	−0.997802	+	0.0662683i	$0.978891\pi$
$158$	−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	−0.373732	+	0.927537i	$0.621922\pi$
$163$	−17.5084	+	12.7206i	−1.37136	+	0.996352i	−0.997629	+	0.0688158i	$0.978078\pi$
$164$	1.59539			0.124579
$165$		0			0
$166$	−10.1937			−0.791186
$167$	−19.4121	+	14.1037i	−1.50216	+	1.09138i	−0.532644	+	0.846339i	$0.678802\pi$
$167$	−19.4121	+	14.1037i	−1.50216	+	1.09138i	−0.969513	+	0.245042i	$0.921198\pi$
$168$		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	0.994027	+	0.109138i	$0.0348091\pi$
$173$	3.34074	+	10.2817i	0.253992	+	0.781707i	−0.740035	+	0.672569i	$0.765191\pi$
$174$		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	$-0.171113\pi$
$179$	−1.83197	−	5.63824i	−0.136928	−	0.421422i	−0.995885	+	0.0906265i	$0.971113\pi$
$180$		0			0
$181$	3.92063	+	2.84851i	0.291418	+	0.211728i	0.723882	−	0.689923i	$-0.242356\pi$
$181$	3.92063	+	2.84851i	0.291418	+	0.211728i	−0.432464	+	0.901651i	$0.642356\pi$
$182$	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	−0.607487	−	0.794330i	$-0.707822\pi$
$191$	4.84920	−	14.9243i	0.350876	−	1.07988i	0.958362	−	0.285555i	$-0.0921778\pi$
$192$		0			0
$193$	18.4090	+	13.3749i	1.32511	+	0.962749i	0.999853	+	0.0171238i	$0.00545094\pi$
$193$	18.4090	+	13.3749i	1.32511	+	0.962749i	0.325257	+	0.945626i	$0.394549\pi$
$194$	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	$-0.683519\pi$
$197$	−15.3025			−1.09026			−0.545129	+	0.838352i	$0.683519\pi$
$198$		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	−0.130124	−	0.991498i	$-0.541538\pi$
$211$	11.2232	−	8.15412i	0.772636	−	0.561353i	0.902760	+	0.430145i	$0.141538\pi$
$212$	−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	0.841081	−	0.540909i	$-0.181920\pi$
$223$	−2.34908	−	7.22973i	−0.157306	−	0.484138i	−0.998387	+	0.0567705i	$0.981920\pi$
$224$	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	$-0.896882\pi$
$227$	0.0912083	−	0.280710i	0.00605371	−	0.0186314i	0.954038	+	0.299686i	$0.0968821\pi$
$228$		0			0
$229$	−5.75269	+	4.17958i	−0.380149	+	0.276194i	−0.761407	−	0.648275i	$-0.775491\pi$
$229$	−5.75269	+	4.17958i	−0.380149	+	0.276194i	0.381258	+	0.924469i	$0.375491\pi$
$230$	−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	$-0.590969\pi$
$233$	8.29543	−	6.02698i	0.543452	−	0.394841i	0.825365	+	0.564599i	$0.190969\pi$
$234$		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	0.928291	+	0.371856i	$0.121278\pi$
$239$	6.11983	+	18.8349i	0.395859	+	1.21833i	−0.532432	+	0.846473i	$0.678722\pi$
$240$		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	$-0.727087\pi$
$251$	−2.17876	+	1.58296i	−0.137522	+	0.0999155i	0.516897	+	0.856047i	$0.327087\pi$
$252$		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	0.337549	+	0.941308i	$0.390402\pi$
$257$	−7.83640	+	24.1179i	−0.488821	+	1.50444i	−0.826370	+	0.563128i	$0.809598\pi$
$258$		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	$-0.409991\pi$
$263$	9.04980			0.558034			0.279017	+	0.960286i	$0.409991\pi$
$264$		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	$-0.273450\pi$
$269$	2.21095	+	1.60635i	0.134804	+	0.0979410i	−0.518340	+	0.855175i	$0.673450\pi$
$270$		0			0
$271$	5.54748	−	17.0734i	0.336986	−	1.03714i	−0.628750	−	0.777608i	$-0.716433\pi$
$271$	5.54748	−	17.0734i	0.336986	−	1.03714i	0.965736	−	0.259528i	$-0.0835669\pi$
$272$	−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	−0.282823	−	0.959172i	$-0.591271\pi$
$277$	9.02080	−	6.55399i	0.542007	−	0.393791i	0.824830	+	0.565381i	$0.191271\pi$
$278$	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	$-0.262291\pi$
$281$	3.20564	+	2.32904i	0.191233	+	0.138939i	−0.488049	+	0.872816i	$0.662291\pi$
$282$		0			0
$283$	1.77657	+	5.46773i	0.105606	+	0.325023i	0.989872	−	0.141961i	$-0.0453407\pi$
$283$	1.77657	+	5.46773i	0.105606	+	0.325023i	−0.884266	+	0.466984i	$0.845341\pi$
$284$	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	0.488434	+	0.872601i	$0.337568\pi$
$293$	−7.18272	+	22.1061i	−0.419619	+	1.29145i	−0.908053	+	0.418854i	$0.862432\pi$
$294$		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	$-0.133876\pi$
$311$	−1.15776	−	3.56321i	−0.0656504	−	0.202051i	−0.978501	+	0.206243i	$0.933876\pi$
$312$		0			0
$313$	−14.6142	−	10.6178i	−0.826044	−	0.600156i	0.0923934	−	0.995723i	$-0.470548\pi$
$313$	−14.6142	−	10.6178i	−0.826044	−	0.600156i	−0.918437	+	0.395567i	$0.870548\pi$
$314$	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	$-0.633234\pi$
$317$	5.99841	−	4.35810i	0.336904	−	0.244775i	0.743354	+	0.668898i	$0.233234\pi$
$318$		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	−0.822082	−	0.569369i	$-0.807187\pi$
$337$	3.26146	−	10.0378i	0.177663	−	0.546791i	0.999745	+	0.0225781i	$0.00718744\pi$
$338$	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	$-0.506507\pi$
$347$	−18.2109	−	13.2310i	−0.977615	−	0.710279i	−0.957174	+	0.289512i	$0.906507\pi$
$348$		0			0
$349$	−6.40301	−	19.7064i	−0.342745	−	1.05486i	−0.962780	−	0.270287i	$-0.912881\pi$
$349$	−6.40301	−	19.7064i	−0.342745	−	1.05486i	0.620034	−	0.784575i	$-0.287119\pi$
$350$	−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	$-0.551170\pi$
$353$	−6.01460			−0.320125			−0.160062	+	0.987107i	$0.551170\pi$
$354$		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	−0.679823	−	0.733376i	$-0.737944\pi$
$359$	5.70755	−	17.5660i	0.301233	−	0.927100i	0.981056	−	0.193724i	$-0.0620565\pi$
$360$		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	−0.978284	−	0.207271i	$-0.933542\pi$
$367$	−1.24531	+	3.83267i	−0.0650046	+	0.200063i	0.913279	+	0.407335i	$0.133542\pi$
$368$	−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	0.541208	−	0.840889i	$-0.317967\pi$
$379$	−1.77707	−	1.29111i	−0.0912817	−	0.0663201i	−0.632490	+	0.774569i	$0.717967\pi$
$380$	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	$-0.915137\pi$
$383$	−19.8093	+	14.3923i	−1.01221	+	0.735413i	−0.0475374	+	0.998869i	$0.515137\pi$
$384$		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	0.199944	+	0.979807i	$0.435924\pi$
$389$	−10.6057	+	32.6410i	−0.537730	+	1.65496i	−0.737675	+	0.675156i	$0.764076\pi$
$390$		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	$-0.0433164\pi$
$401$	23.3870	+	16.9917i	1.16789	+	0.848523i	0.177137	+	0.984186i	$0.443316\pi$
$402$		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	−0.555414	−	0.831574i	$-0.687440\pi$
$409$	1.29084	−	0.937848i	0.0638278	−	0.0463736i	0.619242	+	0.785200i	$0.287440\pi$
$410$	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	$-0.498253\pi$
$419$	0.224640			0.0109744			0.00548719	+	0.999985i	$0.498253\pi$
$420$		0			0
$421$	3.56288	+	10.9654i	0.173644	+	0.534422i	0.999569	−	0.0293585i	$-0.00934643\pi$
$421$	3.56288	+	10.9654i	0.173644	+	0.534422i	−0.825925	+	0.563780i	$0.809346\pi$
$422$	−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	$-0.465550\pi$
$431$	22.5643	−	16.3940i	1.08689	−	0.789669i	0.978871	+	0.204480i	$0.0655504\pi$
$432$		0			0
$433$	8.02421	−	24.6960i	0.385619	−	1.18681i	−0.550412	−	0.834893i	$-0.685529\pi$
$433$	8.02421	−	24.6960i	0.385619	−	1.18681i	0.936030	−	0.351919i	$-0.114471\pi$
$434$	−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	−0.950160	−	0.311764i	$-0.899080\pi$
$443$	−7.67635	−	23.6254i	−0.364714	−	1.12248i	0.585445	−	0.810712i	$-0.300920\pi$
$444$		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	$-0.843065\pi$
$449$	−14.8961	+	10.8227i	−0.702993	+	0.510754i	0.177913	+	0.984046i	$0.443065\pi$
$450$		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	0.497052	−	0.867721i	$-0.334416\pi$
$457$	−3.73256	−	2.71186i	−0.174602	−	0.126856i	−0.671654	+	0.740865i	$0.734416\pi$
$458$	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	$-0.785020\pi$
$461$	−33.5148			−1.56094			−0.780470	+	0.625193i	$0.785020\pi$
$462$		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	$-0.448538\pi$
$467$	−15.7310	−	11.4292i	−0.727944	−	0.528882i	−0.888912	+	0.458077i	$0.848538\pi$
$468$		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	0.985401	+	0.170250i	$0.0544575\pi$
$479$	31.7747	+	23.0857i	1.45182	+	1.05481i	0.466423	+	0.884562i	$0.345543\pi$
$480$		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	−0.996498	−	0.0836126i	$-0.973354\pi$
$487$	−5.28443	−	16.2638i	−0.239461	−	0.736984i	0.757038	−	0.653371i	$-0.226646\pi$
$488$	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	−0.346700	−	0.937976i	$-0.612698\pi$
$491$	10.7494	−	33.0833i	0.485115	−	1.49303i	0.831815	−	0.555053i	$-0.187302\pi$
$492$		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	−0.782435	−	0.622732i	$-0.786023\pi$
$499$	4.83850	−	14.8914i	0.216601	−	0.666629i	0.999036	−	0.0438968i	$-0.0139773\pi$
$500$	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	−0.980881	−	0.194609i	$-0.937656\pi$
$503$	−6.76687	−	20.8263i	−0.301720	−	0.928598i	0.679161	−	0.733989i	$-0.262344\pi$
$504$		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	−0.948287	−	0.317413i	$-0.897186\pi$
$509$	−8.29518	−	25.5299i	−0.367677	−	1.13159i	0.580610	−	0.814182i	$-0.302814\pi$
$510$		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	0.782903	+	0.622144i	$0.213738\pi$
$521$	−4.93408	+	15.1855i	−0.216166	+	0.665291i	−0.999069	+	0.0431466i	$0.986262\pi$
$522$		0			0
$523$	−10.7132	−	7.78356i	−0.468453	−	0.340351i	0.328385	−	0.944544i	$-0.393496\pi$
$523$	−10.7132	−	7.78356i	−0.468453	−	0.340351i	−0.796838	+	0.604193i	$0.793496\pi$
$524$	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	−0.0456887	−	0.998956i	$-0.514548\pi$
$541$	20.7068	−	15.0444i	0.890256	−	0.646809i	0.935945	+	0.352147i	$0.114548\pi$
$542$	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	0.926259	+	0.376887i	$0.123005\pi$
$547$	9.31845	+	28.6792i	0.398428	+	1.22624i	−0.527831	+	0.849349i	$0.676995\pi$
$548$	−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	$-0.895053\pi$
$557$	0.226688	−	0.697675i	0.00960509	−	0.0295614i	0.955744	+	0.294199i	$0.0950528\pi$
$558$		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	$-0.845196\pi$
$563$	−16.9114	+	12.2868i	−0.712730	+	0.517828i	0.171324	+	0.985215i	$0.445196\pi$
$564$		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	−0.949351	−	0.314218i	$-0.898258\pi$
$569$	−8.73053	−	26.8698i	−0.366003	−	1.12644i	0.583348	−	0.812222i	$-0.301742\pi$
$570$		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	0.352648	−	0.935756i	$-0.385281\pi$
$577$	−10.2889	−	7.47535i	−0.428334	−	0.311203i	−0.780982	+	0.624553i	$0.785281\pi$
$578$	−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	$-0.951263\pi$
$587$	−2.40107	+	7.38974i	−0.0991029	+	0.305007i	0.889198	+	0.457522i	$0.151263\pi$
$588$		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	$-0.326168\pi$
$593$	25.2949			1.03874			0.519368	+	0.854551i	$0.326168\pi$
$594$		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	$-0.378298\pi$
$599$	−9.64302	−	7.00606i	−0.394003	−	0.286260i	−0.767094	+	0.641535i	$0.778298\pi$
$600$		0			0
$601$	6.49264	−	19.9823i	0.264840	−	0.815095i	−0.726890	−	0.686754i	$-0.759035\pi$
$601$	6.49264	−	19.9823i	0.264840	−	0.815095i	0.991730	−	0.128341i	$-0.0409650\pi$
$602$	−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	−0.924204	−	0.381898i	$-0.875271\pi$
$607$	−20.8578	+	15.1541i	−0.846593	+	0.615086i	0.0776118	+	0.996984i	$0.475271\pi$
$608$	−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	−0.926312	−	0.376757i	$-0.877039\pi$
$613$	−9.86298	−	30.3551i	−0.398362	−	1.22603i	0.527950	−	0.849275i	$-0.322961\pi$
$614$	−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	$-0.590782\pi$
$617$	−13.9772			−0.562701			−0.281350	+	0.959605i	$0.590782\pi$
$618$		0			0
$619$	6.94500	+	21.3745i	0.279143	+	0.859114i	0.988093	+	0.153856i	$0.0491691\pi$
$619$	6.94500	+	21.3745i	0.279143	+	0.859114i	−0.708950	+	0.705259i	$0.750831\pi$
$620$	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	0.296190	+	0.955129i	$0.404284\pi$
$631$	−12.6815	+	39.0297i	−0.504843	+	1.55375i	−0.801034	+	0.598619i	$0.795716\pi$
$632$	−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	$-0.188069\pi$
$641$	−4.27426	−	13.1548i	−0.168823	−	0.519584i	−0.999298	+	0.0374724i	$0.988069\pi$
$642$		0			0
$643$	27.1122	+	19.6982i	1.06920	+	0.776820i	0.975768	−	0.218806i	$-0.0702160\pi$
$643$	27.1122	+	19.6982i	1.06920	+	0.776820i	0.0934326	+	0.995626i	$0.470216\pi$
$644$	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	$-0.753982\pi$
$647$	−6.94635	+	5.04682i	−0.273089	+	0.198411i	0.442808	+	0.896616i	$0.353982\pi$
$648$		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	0.0665369	+	0.997784i	$0.478805\pi$
$653$	−14.6622	+	45.1255i	−0.573775	+	1.76590i	−0.640312	+	0.768115i	$0.721195\pi$
$654$		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	$-0.875264\pi$
$659$	−47.4501			−1.84839			−0.924197	+	0.381916i	$0.875264\pi$
$660$		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	−0.961285	−	0.275557i	$-0.911138\pi$
$673$	−25.8454	+	18.7778i	−0.996268	+	0.723831i	−0.0349835	+	0.999388i	$0.511138\pi$
$674$	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	$-0.293793\pi$
$677$	0.820859	+	0.596389i	0.0315482	+	0.0229211i	−0.571899	+	0.820324i	$0.693793\pi$
$678$		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	$-0.494489\pi$
$683$	0.904878			0.0346242			0.0173121	+	0.999850i	$0.494489\pi$
$684$		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	−0.206489	−	0.978449i	$-0.566204\pi$
$691$	17.3563	−	12.6101i	0.660263	−	0.479709i	0.866752	+	0.498740i	$0.166204\pi$
$692$	−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	−0.998523	−	0.0543248i	$-0.982699\pi$
$701$	−5.89450	−	18.1414i	−0.222632	−	0.685192i	0.775891	−	0.630867i	$-0.217301\pi$
$702$		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	0.725519	−	0.688202i	$-0.241600\pi$
$709$	7.86023	+	5.71079i	0.295197	+	0.214473i	−0.430322	+	0.902676i	$0.641600\pi$
$710$	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	$-0.973177\pi$
$719$	−3.77630	+	11.6223i	−0.140832	+	0.433437i	0.855619	+	0.517606i	$0.173177\pi$
$720$		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	−0.916375	−	0.400320i	$-0.868899\pi$
$733$	1.63230	−	5.02369i	0.0602902	−	0.185554i	0.976666	+	0.214766i	$0.0688989\pi$
$734$	−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	0.0972419	−	0.995261i	$-0.468998\pi$
$739$	29.1919	−	21.2091i	1.07384	−	0.780191i	0.976599	+	0.215070i	$0.0689979\pi$
$740$	−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	$-0.0841074\pi$
$743$	27.6724	+	20.1052i	1.01520	+	0.737587i	0.0499072	+	0.998754i	$0.484107\pi$
$744$		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	0.983857	−	0.178958i	$-0.0572727\pi$
$751$	2.26664	+	6.97600i	0.0827108	+	0.254558i	−0.901146	+	0.433516i	$0.857273\pi$
$752$	−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	0.0585230	−	0.998286i	$-0.481361\pi$
$757$	28.2299	−	20.5102i	1.02603	−	0.745457i	0.967511	+	0.252829i	$0.0813609\pi$
$758$	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	$-0.713208\pi$
$761$	−1.85160	+	1.34527i	−0.0671205	+	0.0487659i	0.553719	+	0.832704i	$0.313208\pi$
$762$		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	$-0.0203101\pi$
$773$	4.25705	+	13.1019i	0.153116	+	0.471241i	−0.844850	+	0.535004i	$0.820310\pi$
$774$		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	0.619654	−	0.784875i	$-0.287273\pi$
$787$	1.81440	+	1.31824i	0.0646763	+	0.0469901i	−0.554977	+	0.831865i	$0.687273\pi$
$788$	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	$-0.195586\pi$
$797$	14.7167	+	10.6923i	0.521293	+	0.378741i	−0.295798	+	0.955251i	$0.595586\pi$
$798$		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	$-0.484794\pi$
$809$	−25.2420	−	18.3394i	−0.887463	−	0.644780i	−0.935215	+	0.354079i	$0.884794\pi$
$810$		0			0
$811$	−7.78729	−	23.9668i	−0.273449	−	0.841589i	−0.989626	−	0.143670i	$-0.954110\pi$
$811$	−7.78729	−	23.9668i	−0.273449	−	0.841589i	0.716177	−	0.697919i	$-0.245890\pi$
$812$	−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	$-0.833494\pi$
$821$	3.67308	−	11.3046i	0.128191	−	0.394532i	0.994469	+	0.105030i	$0.0334940\pi$
$822$		0			0
$823$	−6.17171	+	4.48401i	−0.215132	+	0.156303i	−0.690133	−	0.723683i	$-0.742448\pi$
$823$	−6.17171	+	4.48401i	−0.215132	+	0.156303i	0.475000	+	0.879986i	$0.342448\pi$
$824$	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	$-0.763552\pi$
$827$	−9.22846	+	6.70487i	−0.320905	+	0.233151i	0.415657	+	0.909522i	$0.363552\pi$
$828$		0			0
$829$	−13.7968	+	42.4622i	−0.479183	+	1.47477i	0.361050	+	0.932546i	$0.382418\pi$
$829$	−13.7968	+	42.4622i	−0.479183	+	1.47477i	−0.840233	+	0.542226i	$0.817582\pi$
$830$	−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	$-0.155696\pi$
$839$	−3.11638	−	9.59122i	−0.107589	−	0.331126i	−0.990329	+	0.138736i	$0.955696\pi$
$840$		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	0.819105	−	0.573644i	$-0.194471\pi$
$853$	15.3816	+	11.1754i	0.526654	+	0.382637i	−0.292450	+	0.956281i	$0.594471\pi$
$854$	−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	$-0.329531\pi$
$857$	29.8781			1.02062			0.510308	+	0.859992i	$0.329531\pi$
$858$		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	$-0.207797\pi$
$863$	13.5768	+	9.86413i	0.462160	+	0.335779i	−0.332218	+	0.943203i	$0.607797\pi$
$864$		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	0.975784	−	0.218735i	$-0.0701929\pi$
$877$	1.71138	+	5.26709i	0.0577893	+	0.177857i	−0.917995	+	0.396592i	$0.870193\pi$
$878$	−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	$-0.463586\pi$
$881$	6.77615			0.228294			0.114147	+	0.993464i	$0.463586\pi$
$882$		0			0
$883$	−7.40416	−	22.7877i	−0.249170	−	0.766866i	−0.994923	−	0.100643i	$-0.967910\pi$
$883$	−7.40416	−	22.7877i	−0.249170	−	0.766866i	0.745753	−	0.666223i	$-0.232090\pi$
$884$	−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	−0.698418	−	0.715690i	$-0.746113\pi$
$887$	8.55610	−	26.3330i	0.287286	−	0.884175i	0.985704	−	0.168485i	$-0.0538875\pi$
$888$		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	0.368488	−	0.929633i	$-0.379876\pi$
$907$	−12.1001	−	8.79121i	−0.401776	−	0.291907i	−0.770264	+	0.637725i	$0.779876\pi$
$908$	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	$-0.562970\pi$
$911$	20.3804	−	14.8073i	0.675234	−	0.490586i	0.871773	+	0.489910i	$0.162970\pi$
$912$		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	0.170008	−	0.985443i	$-0.445621\pi$
$919$	−21.6652	−	15.7407i	−0.714668	−	0.519237i	−0.884676	+	0.466206i	$0.845621\pi$
$920$	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	$-0.329546\pi$
$929$	−4.57116	−	3.32114i	−0.149975	−	0.108963i	−0.660242	+	0.751053i	$0.729546\pi$
$930$		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	0.202782	−	0.979224i	$-0.435002\pi$
$937$	36.6328	−	26.6153i	1.19674	−	0.869484i	0.993960	+	0.109740i	$0.0350018\pi$
$938$	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	$-0.121143\pi$
$941$	26.4448	+	19.2133i	0.862076	+	0.626335i	−0.0663733	+	0.997795i	$0.521143\pi$
$942$		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	$-0.723838\pi$
$947$	−39.8004			−1.29334			−0.646669	+	0.762771i	$0.723838\pi$
$948$		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	$-0.964984\pi$
$953$	−3.86809	+	11.9048i	−0.125300	+	0.385633i	0.868656	+	0.495416i	$0.164984\pi$
$954$		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	0.998367	+	0.0571199i	$0.0181917\pi$
$971$	6.98768	+	21.5059i	0.224245	+	0.690156i	−0.774122	+	0.633037i	$0.781808\pi$
$972$		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	$-0.792806\pi$
$977$	−14.5376	+	10.5622i	−0.465098	+	0.337913i	0.330430	+	0.943831i	$0.392806\pi$
$978$		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	0.370655	+	0.928771i	$0.379133\pi$
$983$	−14.8966	+	45.8471i	−0.475129	+	1.46230i	−0.845784	+	0.533526i	$0.820867\pi$
$984$		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	0.713890	+	0.700258i	$0.246932\pi$
$997$	−8.69144	+	26.7495i	−0.275261	+	0.847165i	−0.989150	+	0.146907i	$0.953068\pi$
$998$	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.190.4	✓	32
3.2	odd	2	inner	693.2.m.k.190.5	yes	32
11.2	odd	10		7623.2.a.db.1.7		16
11.4	even	5	inner	693.2.m.k.631.4	yes	32
11.9	even	5		7623.2.a.dc.1.10		16
33.2	even	10		7623.2.a.db.1.10		16
33.20	odd	10		7623.2.a.dc.1.7		16
33.26	odd	10	inner	693.2.m.k.631.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.190.4	✓	32	1.1	even	1	trivial
693.2.m.k.190.5	yes	32	3.2	odd	2	inner
693.2.m.k.631.4	yes	32	11.4	even	5	inner
693.2.m.k.631.5	yes	32	33.26	odd	10	inner
7623.2.a.db.1.7		16	11.2	odd	10
7623.2.a.db.1.10		16	33.2	even	10
7623.2.a.dc.1.7		16	33.20	odd	10
7623.2.a.dc.1.10		16	11.9	even	5

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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