LMFDB - Embedded newform 693.2.m.j.190.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [693,2,Mod(64,693)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121$ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$2^{4}$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.1
Root			$-2.14548 - 1.55878i$ of defining polynomial
Character	$\chi$	$=$	693.190
Dual form			693.2.m.j.631.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14548 + 1.55878i) q^{2} +(1.55524 - 4.78653i) q^{4} +(1.38593 + 1.00694i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(2.48543 + 7.64935i) q^{8} -4.54308 q^{10} +(-2.49598 - 2.18405i) q^{11} +(-1.22292 + 0.888505i) q^{13} +(-0.819499 - 2.52216i) q^{14} +(-9.11274 - 6.62079i) q^{16} +(-1.93668 - 1.40708i) q^{17} +(1.95646 + 6.02136i) q^{19} +(6.97521 - 5.06779i) q^{20} +(8.75952 + 0.795152i) q^{22} +5.05885 q^{23} +(-0.638201 - 1.96418i) q^{25} +(1.23877 - 3.81253i) q^{26} +(4.07167 + 2.95824i) q^{28} +(-2.57892 + 7.93708i) q^{29} +(-4.88551 + 3.54953i) q^{31} +13.7855 q^{32} +6.34841 q^{34} +(-1.38593 + 1.00694i) q^{35} +(-2.30953 + 7.10802i) q^{37} +(-13.5835 - 9.86900i) q^{38} +(-4.25780 + 13.1042i) q^{40} +(1.55577 + 4.78817i) q^{41} +2.02506 q^{43} +(-14.3359 + 8.55037i) q^{44} +(-10.8536 + 7.88563i) q^{46} +(1.70895 + 5.25959i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(4.43097 + 3.21929i) q^{50} +(2.35092 + 7.23540i) q^{52} +(5.04607 - 3.66618i) q^{53} +(-1.26005 - 5.54025i) q^{55} -8.04301 q^{56} +(-6.83916 - 21.0488i) q^{58} +(-3.45303 + 10.6273i) q^{59} +(-11.1722 - 8.11711i) q^{61} +(4.94881 - 15.2309i) q^{62} +(-11.3510 + 8.24697i) q^{64} -2.58956 q^{65} +13.6173 q^{67} +(-9.74702 + 7.08162i) q^{68} +(1.40389 - 4.32073i) q^{70} +(-11.5956 - 8.42466i) q^{71} +(-0.441988 + 1.36030i) q^{73} +(-6.12478 - 18.8501i) q^{74} +31.8642 q^{76} +(2.84846 - 1.69891i) q^{77} +(-5.43444 + 3.94835i) q^{79} +(-5.96291 - 18.3520i) q^{80} +(-10.8016 - 7.84779i) q^{82} +(4.74874 + 3.45016i) q^{83} +(-1.26726 - 3.90023i) q^{85} +(-4.34471 + 3.15662i) q^{86} +(10.5030 - 24.5209i) q^{88} -16.4241 q^{89} +(-0.467115 - 1.43763i) q^{91} +(7.86773 - 24.2144i) q^{92} +(-11.8650 - 8.62046i) q^{94} +(-3.35163 + 10.3152i) q^{95} +(-9.74994 + 7.08375i) q^{97} +2.65195 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32}+ \cdots - 27 q^{97}+O(q^{100})$ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

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

)

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

$2$	−2.14548	+	1.55878i	−1.51708	+	1.10222i	−0.554170	+	0.832404i	$0.686964\pi$
$2$	−2.14548	+	1.55878i	−1.51708	+	1.10222i	−0.962911	+	0.269820i	$0.913036\pi$
$3$		0			0
$3$		0			0
$4$	1.55524	−	4.78653i	0.777620	−	2.39327i
$5$	1.38593	+	1.00694i	0.619808	+	0.450317i	0.852855	−	0.522149i	$-0.174869\pi$
$5$	1.38593	+	1.00694i	0.619808	+	0.450317i	−0.233046	+	0.972466i	$0.574869\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	2.48543	+	7.64935i	0.878731	+	2.70446i
$9$		0			0
$10$	−4.54308			−1.43665
$11$	−2.49598	−	2.18405i	−0.752566	−	0.658517i
$11$	−2.49598	−	2.18405i	−0.752566	−	0.658517i
$12$		0			0
$13$	−1.22292	+	0.888505i	−0.339178	+	0.246427i	−0.744315	−	0.667829i	$-0.767224\pi$
$13$	−1.22292	+	0.888505i	−0.339178	+	0.246427i	0.405137	+	0.914256i	$0.367224\pi$
$14$	−0.819499	−	2.52216i	−0.219020	−	0.674075i
$15$		0			0
$16$	−9.11274	−	6.62079i	−2.27818	−	1.65520i
$17$	−1.93668	−	1.40708i	−0.469713	−	0.341266i	0.327617	−	0.944811i	$-0.393755\pi$
$17$	−1.93668	−	1.40708i	−0.469713	−	0.341266i	−0.797329	+	0.603544i	$0.793755\pi$
$18$		0			0
$19$	1.95646	+	6.02136i	0.448842	+	1.38140i	0.878214	+	0.478267i	$0.158735\pi$
$19$	1.95646	+	6.02136i	0.448842	+	1.38140i	−0.429372	+	0.903128i	$0.641265\pi$
$20$	6.97521	−	5.06779i	1.55970	−	1.13319i
$21$		0			0
$22$	8.75952	+	0.795152i	1.86754	+	0.169527i
$23$	5.05885			1.05484			0.527422	−	0.849604i	$-0.323159\pi$
$23$	5.05885			1.05484			0.527422	+	0.849604i	$0.323159\pi$
$24$		0			0
$25$	−0.638201	−	1.96418i	−0.127640	−	0.392836i
$26$	1.23877	−	3.81253i	0.242942	−	0.747699i
$27$		0			0
$28$	4.07167	+	2.95824i	0.769473	+	0.559055i
$29$	−2.57892	+	7.93708i	−0.478893	+	1.47388i	0.361743	+	0.932278i	$0.382182\pi$
$29$	−2.57892	+	7.93708i	−0.478893	+	1.47388i	−0.840635	+	0.541602i	$0.817818\pi$
$30$		0			0
$31$	−4.88551	+	3.54953i	−0.877463	+	0.637514i	−0.932579	−	0.360966i	$-0.882447\pi$
$31$	−4.88551	+	3.54953i	−0.877463	+	0.637514i	0.0551159	+	0.998480i	$0.482447\pi$
$32$	13.7855			2.43696
$33$		0			0
$34$	6.34841			1.08874
$35$	−1.38593	+	1.00694i	−0.234265	+	0.170204i
$36$		0			0
$37$	−2.30953	+	7.10802i	−0.379685	+	1.16855i	0.560578	+	0.828102i	$0.310579\pi$
$37$	−2.30953	+	7.10802i	−0.379685	+	1.16855i	−0.940263	+	0.340449i	$0.889421\pi$
$38$	−13.5835	−	9.86900i	−2.20354	−	1.60096i
$39$		0			0
$40$	−4.25780	+	13.1042i	−0.673218	+	2.07195i
$41$	1.55577	+	4.78817i	0.242970	+	0.747786i	0.995964	+	0.0897576i	$0.0286092\pi$
$41$	1.55577	+	4.78817i	0.242970	+	0.747786i	−0.752993	+	0.658028i	$0.771391\pi$
$42$		0			0
$43$	2.02506			0.308818			0.154409	−	0.988007i	$-0.450653\pi$
$43$	2.02506			0.308818			0.154409	+	0.988007i	$0.450653\pi$
$44$	−14.3359	+	8.55037i	−2.16122	+	1.28902i
$45$		0			0
$46$	−10.8536	+	7.88563i	−1.60028	+	1.16267i
$47$	1.70895	+	5.25959i	0.249275	+	0.767190i	0.994904	+	0.100829i	$0.0321494\pi$
$47$	1.70895	+	5.25959i	0.249275	+	0.767190i	−0.745629	+	0.666362i	$0.767851\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	4.43097	+	3.21929i	0.626634	+	0.455276i
$51$		0			0
$52$	2.35092	+	7.23540i	0.326014	+	1.00337i
$53$	5.04607	−	3.66618i	0.693131	−	0.503589i	−0.184557	−	0.982822i	$-0.559085\pi$
$53$	5.04607	−	3.66618i	0.693131	−	0.503589i	0.877688	+	0.479233i	$0.159085\pi$
$54$		0			0
$55$	−1.26005	−	5.54025i	−0.169905	−	0.747047i
$56$	−8.04301			−1.07479
$57$		0			0
$58$	−6.83916	−	21.0488i	−0.898026	−	2.76384i
$59$	−3.45303	+	10.6273i	−0.449546	+	1.38356i	0.427874	+	0.903838i	$0.359263\pi$
$59$	−3.45303	+	10.6273i	−0.449546	+	1.38356i	−0.877420	+	0.479723i	$0.840737\pi$
$60$		0			0
$61$	−11.1722	−	8.11711i	−1.43046	−	1.03929i	−0.989931	−	0.141550i	$-0.954791\pi$
$61$	−11.1722	−	8.11711i	−1.43046	−	1.03929i	−0.440527	−	0.897739i	$-0.645209\pi$
$62$	4.94881	−	15.2309i	0.628499	−	1.93432i
$63$		0			0
$64$	−11.3510	+	8.24697i	−1.41887	+	1.03087i
$65$	−2.58956			−0.321195
$66$		0			0
$67$	13.6173			1.66362			0.831811	−	0.555059i	$-0.187304\pi$
$67$	13.6173			1.66362			0.831811	+	0.555059i	$0.187304\pi$
$68$	−9.74702	+	7.08162i	−1.18200	+	0.858773i
$69$		0			0
$70$	1.40389	−	4.32073i	0.167797	−	0.516426i
$71$	−11.5956	−	8.42466i	−1.37614	−	0.999823i	−0.997229	−	0.0743897i	$-0.976299\pi$
$71$	−11.5956	−	8.42466i	−1.37614	−	0.999823i	−0.378910	−	0.925434i	$-0.623701\pi$
$72$		0			0
$73$	−0.441988	+	1.36030i	−0.0517308	+	0.159211i	−0.973584	−	0.228327i	$-0.926674\pi$
$73$	−0.441988	+	1.36030i	−0.0517308	+	0.159211i	0.921854	+	0.387538i	$0.126674\pi$
$74$	−6.12478	−	18.8501i	−0.711991	−	2.19128i
$75$		0			0
$76$	31.8642			3.65508
$77$	2.84846	−	1.69891i	0.324612	−	0.193609i
$78$		0			0
$79$	−5.43444	+	3.94835i	−0.611423	+	0.444225i	−0.849915	−	0.526920i	$-0.823347\pi$
$79$	−5.43444	+	3.94835i	−0.611423	+	0.444225i	0.238492	+	0.971144i	$0.423347\pi$
$80$	−5.96291	−	18.3520i	−0.666674	−	2.05181i
$81$		0			0
$82$	−10.8016	−	7.84779i	−1.19283	−	0.866644i
$83$	4.74874	+	3.45016i	0.521242	+	0.378705i	0.817072	−	0.576536i	$-0.195596\pi$
$83$	4.74874	+	3.45016i	0.521242	+	0.378705i	−0.295829	+	0.955241i	$0.595596\pi$
$84$		0			0
$85$	−1.26726	−	3.90023i	−0.137454	−	0.423039i
$86$	−4.34471	+	3.15662i	−0.468502	+	0.340387i
$87$		0			0
$88$	10.5030	−	24.5209i	1.11963	−	2.61394i
$89$	−16.4241			−1.74095			−0.870473	−	0.492215i	$-0.836187\pi$
$89$	−16.4241			−1.74095			−0.870473	+	0.492215i	$0.836187\pi$
$90$		0			0
$91$	−0.467115	−	1.43763i	−0.0489669	−	0.150705i
$92$	7.86773	−	24.2144i	0.820267	−	2.52452i
$93$		0			0
$94$	−11.8650	−	8.62046i	−1.22379	−	0.889133i
$95$	−3.35163	+	10.3152i	−0.343869	+	1.05832i
$96$		0			0
$97$	−9.74994	+	7.08375i	−0.989957	+	0.719246i	−0.959912	−	0.280303i	$-0.909565\pi$
$97$	−9.74994	+	7.08375i	−0.989957	+	0.719246i	−0.0300450	+	0.999549i	$0.509565\pi$
$98$	2.65195			0.267888
$99$		0			0
$100$	−10.3942			−1.03942
$101$	−4.32699	+	3.14374i	−0.430551	+	0.312814i	−0.781869	−	0.623442i	$-0.785734\pi$
$101$	−4.32699	+	3.14374i	−0.430551	+	0.312814i	0.351318	+	0.936256i	$0.385734\pi$
$102$		0			0
$103$	2.89788	−	8.91875i	0.285536	−	0.878791i	−0.700701	−	0.713455i	$-0.747129\pi$
$103$	2.89788	−	8.91875i	0.285536	−	0.878791i	0.986237	−	0.165336i	$-0.0528707\pi$
$104$	−9.83597	−	7.14625i	−0.964496	−	0.700748i
$105$		0			0
$106$	−5.11145	+	15.7314i	−0.496468	+	1.52797i
$107$	3.76107	+	11.5754i	0.363596	+	1.11903i	0.950856	+	0.309635i	$0.100207\pi$
$107$	3.76107	+	11.5754i	0.363596	+	1.11903i	−0.587259	+	0.809399i	$0.699793\pi$
$108$		0			0
$109$	−6.31429			−0.604799			−0.302399	−	0.953181i	$-0.597788\pi$
$109$	−6.31429			−0.604799			−0.302399	+	0.953181i	$0.597788\pi$
$110$	11.3394	+	9.92233i	1.08117	+	0.946057i
$111$		0			0
$112$	9.11274	−	6.62079i	0.861073	−	0.625606i
$113$	−1.04067	−	3.20285i	−0.0978978	−	0.301298i	0.890100	−	0.455765i	$-0.150634\pi$
$113$	−1.04067	−	3.20285i	−0.0978978	−	0.301298i	−0.987998	+	0.154466i	$0.950634\pi$
$114$		0			0
$115$	7.01123	+	5.09396i	0.653801	+	0.475014i
$116$	33.9803	+	24.6881i	3.15499	+	2.29224i
$117$		0			0
$118$	−9.15728	−	28.1832i	−0.842996	−	2.59447i
$119$	1.93668	−	1.40708i	0.177535	−	0.128987i
$120$		0			0
$121$	1.45982	+	10.9027i	0.132711	+	0.991155i
$122$	36.6225			3.31565
$123$		0			0
$124$	9.39181	+	28.9050i	0.843410	+	2.59575i
$125$	3.74020	−	11.5112i	0.334534	−	1.02959i
$126$		0			0
$127$	0.901033	+	0.654639i	0.0799537	+	0.0580898i	0.627044	−	0.778984i	$-0.284265\pi$
$127$	0.901033	+	0.654639i	0.0799537	+	0.0580898i	−0.547090	+	0.837074i	$0.684265\pi$
$128$	2.97814	−	9.16578i	0.263233	−	0.810149i
$129$		0			0
$130$	5.55584	−	4.03655i	0.487279	−	0.354029i
$131$	14.3843			1.25676			0.628379	−	0.777907i	$-0.283719\pi$
$131$	14.3843			1.25676			0.628379	+	0.777907i	$0.283719\pi$
$132$		0			0
$133$	−6.33123			−0.548988
$134$	−29.2157	+	21.2264i	−2.52385	+	1.83368i
$135$		0			0
$136$	5.94977	−	18.3115i	0.510188	−	1.57020i
$137$	2.20692	+	1.60342i	0.188550	+	0.136990i	0.678056	−	0.735010i	$-0.262823\pi$
$137$	2.20692	+	1.60342i	0.188550	+	0.136990i	−0.489506	+	0.872000i	$0.662823\pi$
$138$		0			0
$139$	0.109127	−	0.335860i	0.00925607	−	0.0284872i	−0.946322	−	0.323226i	$-0.895233\pi$
$139$	0.109127	−	0.335860i	0.00925607	−	0.0284872i	0.955578	+	0.294739i	$0.0952326\pi$
$140$	2.66429	+	8.19985i	0.225174	+	0.693014i
$141$		0			0
$142$	38.0102			3.18974
$143$	4.99293	+	0.453237i	0.417530	+	0.0379016i
$144$		0			0
$145$	−11.5664	+	8.40346i	−0.960535	+	0.697869i
$146$	−1.17213	−	3.60745i	−0.0970064	−	0.298555i
$147$		0			0
$148$	30.4309	+	22.1093i	2.50140	+	1.81738i
$149$	−0.413730	−	0.300593i	−0.0338941	−	0.0246255i	0.570709	−	0.821152i	$-0.306668\pi$
$149$	−0.413730	−	0.300593i	−0.0338941	−	0.0246255i	−0.604603	+	0.796527i	$0.706668\pi$
$150$		0			0
$151$	0.302146	+	0.929908i	0.0245883	+	0.0756749i	0.962598	−	0.270935i	$-0.0873328\pi$
$151$	0.302146	+	0.929908i	0.0245883	+	0.0756749i	−0.938009	+	0.346610i	$0.887333\pi$
$152$	−41.1969	+	29.9313i	−3.34151	+	2.42775i
$153$		0			0
$154$	−3.46308	+	8.08508i	−0.279063	+	0.651515i
$155$	−10.3452			−0.830942
$156$		0			0
$157$	−1.01655	−	3.12862i	−0.0811296	−	0.249691i	0.902262	−	0.431189i	$-0.141906\pi$
$157$	−1.01655	−	3.12862i	−0.0811296	−	0.249691i	−0.983391	+	0.181497i	$0.941906\pi$
$158$	5.50485	−	16.9422i	0.437943	−	1.34785i
$159$		0			0
$160$	19.1058	+	13.8812i	1.51044	+	1.09740i
$161$	−1.56327	+	4.81125i	−0.123203	+	0.379180i
$162$		0			0
$163$	−2.81720	+	2.04682i	−0.220660	+	0.160319i	−0.692624	−	0.721299i	$-0.743545\pi$
$163$	−2.81720	+	2.04682i	−0.220660	+	0.160319i	0.471964	+	0.881618i	$0.343545\pi$
$164$	25.3383			1.97859
$165$		0			0
$166$	−15.5664			−1.20818
$167$	−3.70106	+	2.68898i	−0.286397	+	0.208080i	−0.721703	−	0.692203i	$-0.756640\pi$
$167$	−3.70106	+	2.68898i	−0.286397	+	0.208080i	0.435306	+	0.900283i	$0.356640\pi$
$168$		0			0
$169$	−3.31112	+	10.1906i	−0.254702	+	0.783892i
$170$	8.79848	+	6.39247i	0.674812	+	0.490280i
$171$		0			0
$172$	3.14945	−	9.69301i	0.240143	−	0.739085i
$173$	−1.76904	−	5.44456i	−0.134498	−	0.413942i	0.861014	−	0.508582i	$-0.169830\pi$
$173$	−1.76904	−	5.44456i	−0.134498	−	0.413942i	−0.995512	+	0.0946399i	$0.969830\pi$
$174$		0			0
$175$	2.06526			0.156119
$176$	8.28505	+	36.4281i	0.624509	+	2.74587i
$177$		0			0
$178$	35.2374	−	25.6015i	2.64116	−	1.91891i
$179$	−0.913765	−	2.81228i	−0.0682980	−	0.210200i	0.911082	−	0.412224i	$-0.135248\pi$
$179$	−0.913765	−	2.81228i	−0.0682980	−	0.210200i	−0.979380	+	0.202024i	$0.935248\pi$
$180$		0			0
$181$	7.60479	+	5.52520i	0.565260	+	0.410685i	0.833380	−	0.552700i	$-0.186403\pi$
$181$	7.60479	+	5.52520i	0.565260	+	0.410685i	−0.268121	+	0.963385i	$0.586403\pi$
$182$	3.24313	+	2.35627i	0.240397	+	0.174659i
$183$		0			0
$184$	12.5734	+	38.6969i	0.926923	+	2.85278i
$185$	−10.3582	+	7.52567i	−0.761550	+	0.553299i
$186$		0			0
$187$	1.76077	+	7.74184i	0.128760	+	0.566139i
$188$	27.8330			2.02993
$189$		0			0
$190$	−8.88836	−	27.3555i	−0.644829	−	1.98458i
$191$	2.84577	−	8.75838i	0.205913	−	0.633734i	−0.793762	−	0.608229i	$-0.791880\pi$
$191$	2.84577	−	8.75838i	0.205913	−	0.633734i	0.999675	−	0.0255056i	$-0.00811957\pi$
$192$		0			0
$193$	1.20723	+	0.877101i	0.0868980	+	0.0631351i	0.630386	−	0.776282i	$-0.282897\pi$
$193$	1.20723	+	0.877101i	0.0868980	+	0.0631351i	−0.543488	+	0.839417i	$0.682897\pi$
$194$	9.87627	−	30.3960i	0.709075	−	2.18231i
$195$		0			0
$196$	−4.07167	+	2.95824i	−0.290834	+	0.211303i
$197$	−3.37718			−0.240614			−0.120307	−	0.992737i	$-0.538388\pi$
$197$	−3.37718			−0.240614			−0.120307	+	0.992737i	$0.538388\pi$
$198$		0			0
$199$	27.8114			1.97150			0.985750	−	0.168215i	$-0.0538002\pi$
$199$	27.8114			1.97150			0.985750	+	0.168215i	$0.0538002\pi$
$200$	13.4385	−	9.76365i	0.950246	−	0.690394i
$201$		0			0
$202$	4.38305	−	13.4896i	0.308390	−	0.949127i
$203$	−6.75169	−	4.90539i	−0.473876	−	0.344291i
$204$		0			0
$205$	−2.66520	+	8.20264i	−0.186146	+	0.572897i
$206$	7.68504	+	23.6521i	0.535442	+	1.64792i
$207$		0			0
$208$	17.0268			1.18059
$209$	8.26769	−	19.3022i	0.571888	−	1.33516i
$210$		0			0
$211$	19.4219	−	14.1109i	1.33706	−	0.971432i	0.337516	−	0.941320i	$-0.390413\pi$
$211$	19.4219	−	14.1109i	1.33706	−	0.971432i	0.999547	−	0.0301125i	$-0.00958657\pi$
$212$	−9.70047	−	29.8550i	−0.666231	−	2.05045i
$213$		0			0
$214$	−26.1127	−	18.9720i	−1.78503	−	1.29690i
$215$	2.80659	+	2.03911i	0.191408	+	0.139066i
$216$		0			0
$217$	−1.86610	−	5.74326i	−0.126679	−	0.389878i
$218$	13.5471	−	9.84258i	0.917529	−	0.666624i
$219$		0			0
$220$	−28.4783	−	2.58514i	−1.92001	−	0.174290i
$221$	3.61860			0.243413
$222$		0			0
$223$	7.05109	+	21.7010i	0.472176	+	1.45321i	0.849729	+	0.527220i	$0.176766\pi$
$223$	7.05109	+	21.7010i	0.472176	+	1.45321i	−0.377553	+	0.925988i	$0.623234\pi$
$224$	−4.25995	+	13.1108i	−0.284630	+	0.876002i
$225$		0			0
$226$	7.22526	+	5.24946i	0.480617	+	0.349189i
$227$	−4.45128	+	13.6996i	−0.295442	+	0.909277i	0.687630	+	0.726061i	$0.258651\pi$
$227$	−4.45128	+	13.6996i	−0.295442	+	0.909277i	−0.983073	+	0.183217i	$0.941349\pi$
$228$		0			0
$229$	3.06915	−	2.22986i	0.202815	−	0.147354i	−0.481742	−	0.876313i	$-0.659996\pi$
$229$	3.06915	−	2.22986i	0.202815	−	0.147354i	0.684557	+	0.728959i	$0.259996\pi$
$230$	−22.9828			−1.51544
$231$		0			0
$232$	−67.1233			−4.40686
$233$	22.2354	−	16.1549i	1.45669	−	1.05834i	0.472476	−	0.881343i	$-0.343360\pi$
$233$	22.2354	−	16.1549i	1.45669	−	1.05834i	0.984211	−	0.177001i	$-0.0566397\pi$
$234$		0			0
$235$	−2.92761	+	9.01025i	−0.190976	+	0.587764i
$236$	45.4978	+	33.0561i	2.96166	+	2.15177i
$237$		0			0
$238$	−1.96177	+	6.03770i	−0.127163	+	0.391366i
$239$	−3.47135	−	10.6837i	−0.224543	−	0.691072i	−0.998338	−	0.0576354i	$-0.981644\pi$
$239$	−3.47135	−	10.6837i	−0.224543	−	0.691072i	0.773795	−	0.633436i	$-0.218356\pi$
$240$		0			0
$241$	14.7496			0.950105			0.475052	−	0.879958i	$-0.342429\pi$
$241$	14.7496			0.950105			0.475052	+	0.879958i	$0.342429\pi$
$242$	−20.1269	−	21.1159i	−1.29381	−	1.35738i
$243$		0			0
$244$	−56.2283	+	40.8523i	−3.59965	+	2.61530i
$245$	−0.529379	−	1.62926i	−0.0338208	−	0.104090i
$246$		0			0
$247$	−7.74261	−	5.62533i	−0.492650	−	0.357931i
$248$	−39.2942	−	28.5489i	−2.49518	−	1.81286i
$249$		0			0
$250$	9.91885	+	30.5271i	0.627323	+	1.93070i
$251$	6.16417	−	4.47853i	0.389079	−	0.282682i	−0.375999	−	0.926620i	$-0.622700\pi$
$251$	6.16417	−	4.47853i	0.389079	−	0.282682i	0.765078	+	0.643938i	$0.222700\pi$
$252$		0			0
$253$	−12.6268	−	11.0488i	−0.793839	−	0.694632i
$254$	−2.95358			−0.185324
$255$		0			0
$256$	−0.773480	−	2.38053i	−0.0483425	−	0.148783i
$257$	0.0894241	−	0.275219i	0.00557812	−	0.0171677i	−0.948229	−	0.317588i	$-0.897127\pi$
$257$	0.0894241	−	0.275219i	0.00557812	−	0.0171677i	0.953807	+	0.300421i	$0.0971270\pi$
$258$		0			0
$259$	−6.04644	−	4.39299i	−0.375707	−	0.272967i
$260$	−4.02738	+	12.3950i	−0.249768	+	0.768706i
$261$		0			0
$262$	−30.8611	+	22.4219i	−1.90660	+	1.38523i
$263$	−12.3251			−0.759998			−0.379999	−	0.924987i	$-0.624076\pi$
$263$	−12.3251			−0.759998			−0.379999	+	0.924987i	$0.624076\pi$
$264$		0			0
$265$	10.6851			0.656383
$266$	13.5835	−	9.86900i	0.832858	−	0.605107i
$267$		0			0
$268$	21.1782	−	65.1798i	1.29367	−	3.98149i
$269$	10.2349	+	7.43611i	0.624034	+	0.453388i	0.854328	−	0.519734i	$-0.173969\pi$
$269$	10.2349	+	7.43611i	0.624034	+	0.453388i	−0.230294	+	0.973121i	$0.573969\pi$
$270$		0			0
$271$	3.32200	−	10.2241i	0.201797	−	0.621068i	−0.798033	−	0.602614i	$-0.794126\pi$
$271$	3.32200	−	10.2241i	0.201797	−	0.621068i	0.999830	−	0.0184533i	$-0.00587420\pi$
$272$	8.33245	+	25.6447i	0.505229	+	1.55494i
$273$		0			0
$274$	−7.23428			−0.437039
$275$	−2.69694	+	6.29642i	−0.162632	+	0.379688i
$276$		0			0
$277$	4.92607	−	3.57900i	0.295979	−	0.215041i	−0.429878	−	0.902887i	$-0.641443\pi$
$277$	4.92607	−	3.57900i	0.295979	−	0.215041i	0.725857	+	0.687846i	$0.241443\pi$
$278$	0.289401	+	0.890685i	0.0173571	+	0.0534197i
$279$		0			0
$280$	−11.1471	−	8.09882i	−0.666165	−	0.483997i
$281$	−6.96666	−	5.06158i	−0.415596	−	0.301948i	0.360267	−	0.932849i	$-0.382686\pi$
$281$	−6.96666	−	5.06158i	−0.415596	−	0.301948i	−0.775864	+	0.630901i	$0.782686\pi$
$282$		0			0
$283$	0.987485	+	3.03917i	0.0586999	+	0.180660i	0.976107	−	0.217290i	$-0.0697218\pi$
$283$	0.987485	+	3.03917i	0.0586999	+	0.180660i	−0.917407	+	0.397950i	$0.869722\pi$
$284$	−58.3588	+	42.4001i	−3.46296	+	2.51599i
$285$		0			0
$286$	−11.4187	+	6.81047i	−0.675202	+	0.402711i
$287$	−5.03457			−0.297182
$288$		0			0
$289$	−3.48244	−	10.7179i	−0.204850	−	0.630462i
$290$	11.7162	−	36.0588i	0.688000	−	2.11745i
$291$		0			0
$292$	5.82373	+	4.23119i	0.340808	+	0.247611i
$293$	2.64263	−	8.13317i	0.154384	−	0.475145i	−0.843714	−	0.536793i	$-0.819636\pi$
$293$	2.64263	−	8.13317i	0.154384	−	0.475145i	0.998098	+	0.0616479i	$0.0196356\pi$
$294$		0			0
$295$	−15.4868	+	11.2518i	−0.901673	+	0.655104i
$296$	−60.1119			−3.49393
$297$		0			0
$298$	1.35621			0.0785629
$299$	−6.18658	+	4.49481i	−0.357779	+	0.259942i
$300$		0			0
$301$	−0.625777	+	1.92594i	−0.0360692	+	0.111010i
$302$	−2.09777	−	1.52412i	−0.120713	−	0.0877031i
$303$		0			0
$304$	22.0375	−	67.8244i	1.26394	−	3.89000i
$305$	−7.31054	−	22.4995i	−0.418600	−	1.28832i
$306$		0			0
$307$	−3.49789			−0.199635			−0.0998176	−	0.995006i	$-0.531826\pi$
$307$	−3.49789			−0.199635			−0.0998176	+	0.995006i	$0.531826\pi$
$308$	−3.70185	−	16.2765i	−0.210932	−	0.927437i
$309$		0			0
$310$	22.1953	−	16.1258i	1.26061	−	0.915884i
$311$	1.14039	+	3.50976i	0.0646656	+	0.199020i	0.978169	−	0.207811i	$-0.0666338\pi$
$311$	1.14039	+	3.50976i	0.0646656	+	0.199020i	−0.913503	+	0.406831i	$0.866634\pi$
$312$		0			0
$313$	21.2482	+	15.4377i	1.20102	+	0.872590i	0.994384	−	0.105828i	$-0.0337494\pi$
$313$	21.2482	+	15.4377i	1.20102	+	0.872590i	0.206633	+	0.978419i	$0.433749\pi$
$314$	7.05782	+	5.12780i	0.398296	+	0.289379i
$315$		0			0
$316$	10.4471	+	32.1528i	0.587694	+	1.80874i
$317$	10.5821	−	7.68834i	0.594350	−	0.431820i	−0.249519	−	0.968370i	$-0.580273\pi$
$317$	10.5821	−	7.68834i	0.594350	−	0.431820i	0.843869	+	0.536550i	$0.180273\pi$
$318$		0			0
$319$	23.7719	−	14.1783i	1.33097	−	0.793833i
$320$	−24.0359			−1.34365
$321$		0			0
$322$	−4.14572	−	12.7592i	−0.231032	−	0.711044i
$323$	4.68349	−	14.4143i	0.260597	−	0.802034i
$324$		0			0
$325$	2.52565	+	1.83500i	0.140098	+	0.101787i
$326$	2.85370	−	8.78278i	0.158052	−	0.486433i
$327$		0			0
$328$	−32.7596	+	23.8013i	−1.80885	+	1.31420i
$329$	−5.53026			−0.304893
$330$		0			0
$331$	7.93676			0.436244			0.218122	−	0.975922i	$-0.430007\pi$
$331$	7.93676			0.436244			0.218122	+	0.975922i	$0.430007\pi$
$332$	23.8998	−	17.3642i	1.31167	−	0.952984i
$333$		0			0
$334$	3.74902	−	11.5383i	0.205137	−	0.631347i
$335$	18.8727	+	13.7118i	1.03113	+	0.749157i
$336$		0			0
$337$	3.09034	−	9.51109i	0.168342	−	0.518102i	−0.830925	−	0.556384i	$-0.812188\pi$
$337$	3.09034	−	9.51109i	0.168342	−	0.518102i	0.999267	+	0.0382818i	$0.0121884\pi$
$338$	−8.78095	−	27.0250i	−0.477621	−	1.46997i
$339$		0			0
$340$	−20.6395			−1.11933
$341$	19.9465	+	1.81066i	1.08016	+	0.0980526i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	5.03313	+	15.4904i	0.271368	+	0.835185i
$345$		0			0
$346$	12.2823	+	8.92361i	0.660301	+	0.479736i
$347$	−4.37559	−	3.17905i	−0.234894	−	0.170661i	0.464111	−	0.885777i	$-0.346374\pi$
$347$	−4.37559	−	3.17905i	−0.234894	−	0.170661i	−0.699006	+	0.715116i	$0.746374\pi$
$348$		0			0
$349$	−8.81659	−	27.1347i	−0.471941	−	1.45249i	−0.850039	−	0.526720i	$-0.823422\pi$
$349$	−8.81659	−	27.1347i	−0.471941	−	1.45249i	0.378098	−	0.925766i	$-0.376578\pi$
$350$	−4.43097	+	3.21929i	−0.236845	+	0.172078i
$351$		0			0
$352$	−34.4083	−	30.1083i	−1.83397	−	1.60478i
$353$	19.2226			1.02312			0.511559	−	0.859248i	$-0.329068\pi$
$353$	19.2226			1.02312			0.511559	+	0.859248i	$0.329068\pi$
$354$		0			0
$355$	−7.58754	−	23.3520i	−0.402705	−	1.23940i
$356$	−25.5433	+	78.6143i	−1.35379	+	4.16655i
$357$		0			0
$358$	6.34419	+	4.60932i	0.335301	+	0.243610i
$359$	−6.90739	+	21.2588i	−0.364558	+	1.12199i	0.585699	+	0.810529i	$0.300820\pi$
$359$	−6.90739	+	21.2588i	−0.364558	+	1.12199i	−0.950257	+	0.311466i	$0.899180\pi$
$360$		0			0
$361$	−17.0577	+	12.3932i	−0.897776	+	0.652272i
$362$	−24.9285			−1.31021
$363$		0			0
$364$	−7.60775			−0.398754
$365$	−1.98231	+	1.44023i	−0.103759	+	0.0753851i
$366$		0			0
$367$	−7.24485	+	22.2974i	−0.378178	+	1.16391i	0.563131	+	0.826368i	$0.309597\pi$
$367$	−7.24485	+	22.2974i	−0.378178	+	1.16391i	−0.941309	+	0.337545i	$0.890403\pi$
$368$	−46.1000	−	33.4936i	−2.40313	−	1.74597i
$369$		0			0
$370$	10.4924	−	32.2923i	0.545474	−	1.67880i
$371$	1.92743	+	5.93201i	0.100067	+	0.307975i
$372$		0			0
$373$	−33.4536			−1.73216			−0.866082	−	0.499903i	$-0.833369\pi$
$373$	−33.4536			−1.73216			−0.866082	+	0.499903i	$0.833369\pi$
$374$	−15.8455	−	13.8653i	−0.819352	−	0.716956i
$375$		0			0
$376$	−35.9850	+	26.1447i	−1.85579	+	1.34831i
$377$	−3.89833	−	11.9978i	−0.200774	−	0.617919i
$378$		0			0
$379$	14.8694	+	10.8032i	0.763788	+	0.554925i	0.900070	−	0.435745i	$-0.143515\pi$
$379$	14.8694	+	10.8032i	0.763788	+	0.554925i	−0.136282	+	0.990670i	$0.543515\pi$
$380$	44.1617	+	32.0853i	2.26545	+	1.64594i
$381$		0			0
$382$	7.54685	+	23.2268i	0.386131	+	1.18839i
$383$	17.2647	−	12.5435i	0.882185	−	0.640945i	−0.0516438	−	0.998666i	$-0.516446\pi$
$383$	17.2647	−	12.5435i	0.882185	−	0.640945i	0.933829	+	0.357721i	$0.116446\pi$
$384$		0			0
$385$	5.65847	+	0.513652i	0.288382	+	0.0261781i
$386$	−3.95728			−0.201420
$387$		0			0
$388$	18.7431	+	57.6854i	0.951537	+	2.92853i
$389$	−4.79639	+	14.7618i	−0.243187	+	0.748452i	0.752743	+	0.658315i	$0.228730\pi$
$389$	−4.79639	+	14.7618i	−0.243187	+	0.748452i	−0.995929	+	0.0901368i	$0.971270\pi$
$390$		0			0
$391$	−9.79735	−	7.11819i	−0.495474	−	0.359983i
$392$	2.48543	−	7.64935i	0.125533	−	0.386351i
$393$		0			0
$394$	7.24567	−	5.26429i	0.365031	−	0.265211i
$395$	−11.5075			−0.579007
$396$		0			0
$397$	21.4777			1.07794			0.538968	−	0.842326i	$-0.318815\pi$
$397$	21.4777			1.07794			0.538968	+	0.842326i	$0.318815\pi$
$398$	−59.6688	+	43.3519i	−2.99093	+	2.17303i
$399$		0			0
$400$	−7.18867	+	22.1245i	−0.359434	+	1.10622i
$401$	7.18493	+	5.22015i	0.358798	+	0.260682i	0.752551	−	0.658534i	$-0.228823\pi$
$401$	7.18493	+	5.22015i	0.358798	+	0.260682i	−0.393753	+	0.919216i	$0.628823\pi$
$402$		0			0
$403$	2.82082	−	8.68160i	0.140515	−	0.432461i
$404$	8.31812	+	25.6005i	0.413842	+	1.27367i
$405$		0			0
$406$	22.1320			1.09839
$407$	21.2888	−	12.6973i	1.05525	−	0.629382i
$408$		0			0
$409$	−4.41542	+	3.20799i	−0.218329	+	0.158625i	−0.691574	−	0.722306i	$-0.743082\pi$
$409$	−4.41542	+	3.20799i	−0.218329	+	0.158625i	0.473245	+	0.880931i	$0.343082\pi$
$410$	−7.06799	−	21.7530i	−0.349063	−	1.07431i
$411$		0			0
$412$	−38.1830	−	27.7416i	−1.88114	−	1.36673i
$413$	−9.04015	−	6.56805i	−0.444837	−	0.323193i
$414$		0			0
$415$	3.10733	+	9.56339i	0.152533	+	0.469448i
$416$	−16.8586	+	12.2485i	−0.826561	+	0.600531i
$417$		0			0
$418$	12.3497	+	54.2999i	0.604046	+	2.65590i
$419$	−19.9805			−0.976114			−0.488057	−	0.872812i	$-0.662294\pi$
$419$	−19.9805			−0.976114			−0.488057	+	0.872812i	$0.662294\pi$
$420$		0			0
$421$	−8.74895	−	26.9265i	−0.426398	−	1.31232i	−0.901649	−	0.432468i	$-0.857643\pi$
$421$	−8.74895	−	26.9265i	−0.426398	−	1.31232i	0.475252	−	0.879850i	$-0.342357\pi$
$422$	−19.6736	+	60.5491i	−0.957695	+	2.94748i
$423$		0			0
$424$	40.5856	+	29.4871i	1.97101	+	1.43202i
$425$	−1.52777	+	4.70198i	−0.0741075	+	0.228079i
$426$		0			0
$427$	11.1722	−	8.11711i	0.540663	−	0.392814i
$428$	61.2553			2.96089
$429$		0			0
$430$	−9.20000			−0.443664
$431$	25.6982	−	18.6708i	1.23784	−	0.899342i	0.240386	−	0.970677i	$-0.422726\pi$
$431$	25.6982	−	18.6708i	1.23784	−	0.899342i	0.997452	+	0.0713351i	$0.0227260\pi$
$432$		0			0
$433$	−4.06856	+	12.5217i	−0.195523	+	0.601757i	0.804447	+	0.594024i	$0.202462\pi$
$433$	−4.06856	+	12.5217i	−0.195523	+	0.601757i	−0.999970	+	0.00773305i	$0.997538\pi$
$434$	12.9561	+	9.41319i	0.621915	+	0.451848i
$435$		0			0
$436$	−9.82023	+	30.2235i	−0.470304	+	1.44745i
$437$	9.89744	+	30.4612i	0.473459	+	1.45716i
$438$		0			0
$439$	−9.81161			−0.468283			−0.234141	−	0.972203i	$-0.575228\pi$
$439$	−9.81161			−0.468283			−0.234141	+	0.972203i	$0.575228\pi$
$440$	39.2476	−	23.4085i	1.87106	−	1.11595i
$441$		0			0
$442$	−7.76362	+	5.64060i	−0.369278	+	0.268296i
$443$	−0.767950	−	2.36351i	−0.0364864	−	0.112294i	0.931155	−	0.364625i	$-0.118803\pi$
$443$	−0.767950	−	2.36351i	−0.0364864	−	0.112294i	−0.967641	+	0.252331i	$0.918803\pi$
$444$		0			0
$445$	−22.7627	−	16.5380i	−1.07905	−	0.783978i
$446$	−48.9551	−	35.5679i	−2.31809	−	1.68419i
$447$		0			0
$448$	−4.33569	−	13.3439i	−0.204842	−	0.630439i
$449$	−12.6285	+	9.17515i	−0.595976	+	0.433002i	−0.844448	−	0.535637i	$-0.820072\pi$
$449$	−12.6285	+	9.17515i	−0.595976	+	0.433002i	0.248472	+	0.968639i	$0.420072\pi$
$450$		0			0
$451$	6.57444	−	15.3490i	0.309578	−	0.722758i
$452$	−16.9490			−0.797215
$453$		0			0
$454$	−11.8046	−	36.3308i	−0.554017	−	1.70509i
$455$	0.800218	−	2.46282i	0.0375148	−	0.115459i
$456$		0			0
$457$	−11.0554	−	8.03223i	−0.517150	−	0.375732i	0.298379	−	0.954447i	$-0.403554\pi$
$457$	−11.0554	−	8.03223i	−0.517150	−	0.375732i	−0.815529	+	0.578716i	$0.803554\pi$
$458$	−3.10891	+	9.56824i	−0.145270	+	0.447095i
$459$		0			0
$460$	35.2865	−	25.6372i	1.64524	−	1.19534i
$461$	−18.6545			−0.868825			−0.434412	−	0.900714i	$-0.643044\pi$
$461$	−18.6545			−0.868825			−0.434412	+	0.900714i	$0.643044\pi$
$462$		0			0
$463$	−18.5697			−0.863006			−0.431503	−	0.902111i	$-0.642017\pi$
$463$	−18.5697			−0.863006			−0.431503	+	0.902111i	$0.642017\pi$
$464$	76.0508	−	55.2541i	3.53057	−	2.56511i
$465$		0			0
$466$	−22.5234	+	69.3200i	−1.04338	+	3.21119i
$467$	28.2815	+	20.5477i	1.30871	+	0.950835i	1.00000		0.000321071i	$-0.000102200\pi$
$467$	28.2815	+	20.5477i	1.30871	+	0.950835i	0.308712	+	0.951156i	$0.400102\pi$
$468$		0			0
$469$	−4.20799	+	12.9509i	−0.194307	+	0.598015i
$470$	−7.76388	−	23.8948i	−0.358121	−	1.10218i
$471$		0			0
$472$	−89.8745			−4.13681
$473$	−5.05450	−	4.42283i	−0.232406	−	0.203362i
$474$		0			0
$475$	10.5784	−	7.68568i	0.485372	−	0.352643i
$476$	−3.72303	−	11.4583i	−0.170645	−	0.525191i
$477$		0			0
$478$	24.1012	+	17.5106i	1.10236	+	0.800915i
$479$	32.8011	+	23.8314i	1.49872	+	1.08888i	0.970888	+	0.239532i	$0.0769942\pi$
$479$	32.8011	+	23.8314i	1.49872	+	1.08888i	0.527830	+	0.849350i	$0.323006\pi$
$480$		0			0
$481$	−3.49113	−	10.7446i	−0.159182	−	0.489911i
$482$	−31.6449	+	22.9914i	−1.44139	+	1.04723i
$483$		0			0
$484$	54.4565	+	9.96881i	2.47530	+	0.453128i
$485$	−20.6457			−0.937472
$486$		0			0
$487$	4.18930	+	12.8933i	0.189835	+	0.584253i	0.999998	−	0.00195204i	$-0.000621354\pi$
$487$	4.18930	+	12.8933i	0.189835	+	0.584253i	−0.810163	+	0.586205i	$0.800621\pi$
$488$	34.3229	−	105.635i	1.55372	−	4.78187i
$489$		0			0
$490$	3.67543	+	2.67036i	0.166039	+	0.120634i
$491$	7.24935	−	22.3112i	0.327158	−	1.00689i	−0.643298	−	0.765616i	$-0.722435\pi$
$491$	7.24935	−	22.3112i	0.327158	−	1.00689i	0.970457	−	0.241275i	$-0.0775655\pi$
$492$		0			0
$493$	16.1626	−	11.7428i	0.727927	−	0.528870i
$494$	25.3802			1.14191
$495$		0			0
$496$	68.0211			3.05424
$497$	11.5956	−	8.42466i	0.520132	−	0.377898i
$498$		0			0
$499$	5.34216	−	16.4415i	0.239148	−	0.736021i	−0.757396	−	0.652956i	$-0.773529\pi$
$499$	5.34216	−	16.4415i	0.239148	−	0.736021i	0.996544	−	0.0830658i	$-0.0264712\pi$
$500$	−49.2817	−	35.8052i	−2.20394	−	1.60126i
$501$		0			0
$502$	−6.24403	+	19.2172i	−0.278685	+	0.857704i
$503$	−1.00304	−	3.08705i	−0.0447235	−	0.137645i	0.926201	−	0.377029i	$-0.123054\pi$
$503$	−1.00304	−	3.08705i	−0.0447235	−	0.137645i	−0.970925	+	0.239384i	$0.923054\pi$
$504$		0			0
$505$	−9.16247			−0.407724
$506$	44.3131	+	4.02255i	1.96996	+	0.178824i
$507$		0			0
$508$	4.53477	−	3.29470i	0.201198	−	0.146179i
$509$	4.82082	+	14.8370i	0.213679	+	0.657636i	0.999245	+	0.0388581i	$0.0123720\pi$
$509$	4.82082	+	14.8370i	0.213679	+	0.657636i	−0.785566	+	0.618778i	$0.787628\pi$
$510$		0			0
$511$	−1.15714	−	0.840712i	−0.0511889	−	0.0371909i
$512$	20.9640	+	15.2312i	0.926485	+	0.673131i
$513$		0			0
$514$	0.237148	+	0.729868i	0.0104602	+	0.0321931i
$515$	12.9969	−	9.44281i	0.572712	−	0.416100i
$516$		0			0
$517$	7.22174	−	16.8603i	0.317612	−	0.741513i
$518$	19.8202			0.870850
$519$		0			0
$520$	−6.43616	−	19.8085i	−0.282244	−	0.868658i
$521$	1.34232	−	4.13123i	0.0588080	−	0.180993i	−0.917337	−	0.398111i	$-0.869666\pi$
$521$	1.34232	−	4.13123i	0.0588080	−	0.180993i	0.976145	+	0.217119i	$0.0696658\pi$
$522$		0			0
$523$	−10.0849	−	7.32713i	−0.440983	−	0.320393i	0.345042	−	0.938587i	$-0.387865\pi$
$523$	−10.0849	−	7.32713i	−0.440983	−	0.320393i	−0.786026	+	0.618194i	$0.787865\pi$
$524$	22.3710	−	68.8507i	0.977280	−	3.00776i
$525$		0			0
$526$	26.4432	−	19.2121i	1.15298	−	0.837687i
$527$	14.4561			0.629718
$528$		0			0
$529$	2.59198			0.112695
$530$	−22.9247	+	16.6558i	−0.995785	+	0.723480i
$531$		0			0
$532$	−9.84659	+	30.3047i	−0.426904	+	1.31387i
$533$	−6.15689	−	4.47324i	−0.266685	−	0.193758i
$534$		0			0
$535$	−6.44311	+	19.8299i	−0.278560	+	0.857320i
$536$	33.8449	+	104.164i	1.46188	+	4.49919i
$537$		0			0
$538$	−33.5500			−1.44644
$539$	0.735535	+	3.23404i	0.0316818	+	0.139300i
$540$		0			0
$541$	10.1738	−	7.39173i	0.437408	−	0.317795i	−0.347196	−	0.937792i	$-0.612866\pi$
$541$	10.1738	−	7.39173i	0.437408	−	0.317795i	0.784604	+	0.619997i	$0.212866\pi$
$542$	8.80979	+	27.1137i	0.378413	+	1.16463i
$543$		0			0
$544$	−26.6980	−	19.3973i	−1.14467	−	0.831651i
$545$	−8.75118	−	6.35810i	−0.374859	−	0.272351i
$546$		0			0
$547$	−0.0775023	−	0.238528i	−0.00331376	−	0.0101987i	0.949386	−	0.314112i	$-0.101707\pi$
$547$	−0.0775023	−	0.238528i	−0.00331376	−	0.0101987i	−0.952700	+	0.303913i	$0.901707\pi$
$548$	11.1071	−	8.06981i	0.474473	−	0.344725i
$549$		0			0
$550$	−4.02851	−	17.7127i	−0.171776	−	0.755274i
$551$	−52.8376			−2.25096
$552$		0			0
$553$	−2.07577	−	6.38857i	−0.0882708	−	0.271670i
$554$	−4.98989	+	15.3573i	−0.212000	+	0.652470i
$555$		0			0
$556$	−1.43788	−	1.04468i	−0.0609799	−	0.0443045i
$557$	−8.75028	+	26.9306i	−0.370761	+	1.14109i	0.575533	+	0.817779i	$0.304795\pi$
$557$	−8.75028	+	26.9306i	−0.370761	+	1.14109i	−0.946294	+	0.323307i	$0.895205\pi$
$558$		0			0
$559$	−2.47649	+	1.79927i	−0.104744	+	0.0761012i
$560$	19.2964			0.815421
$561$		0			0
$562$	22.8367			0.963308
$563$	13.1091	−	9.52433i	0.552483	−	0.401403i	−0.276217	−	0.961095i	$-0.589081\pi$
$563$	13.1091	−	9.52433i	0.552483	−	0.401403i	0.828700	+	0.559693i	$0.189081\pi$
$564$		0			0
$565$	1.78278	−	5.48682i	0.0750019	−	0.230832i
$566$	−6.85602	−	4.98119i	−0.288180	−	0.209375i
$567$		0			0
$568$	35.6233	−	109.637i	1.49472	−	4.60028i
$569$	1.97953	+	6.09236i	0.0829862	+	0.255405i	0.983937	−	0.178516i	$-0.0571296\pi$
$569$	1.97953	+	6.09236i	0.0829862	+	0.255405i	−0.900951	+	0.433921i	$0.857130\pi$
$570$		0			0
$571$	25.9443			1.08574			0.542868	−	0.839818i	$-0.317338\pi$
$571$	25.9443			1.08574			0.542868	+	0.839818i	$0.317338\pi$
$572$	9.93463	−	23.1939i	0.415388	−	0.969787i
$573$		0			0
$574$	10.8016	−	7.84779i	0.450848	−	0.327561i
$575$	−3.22856	−	9.93650i	−0.134640	−	0.414381i
$576$		0			0
$577$	−7.25058	−	5.26785i	−0.301845	−	0.219304i	0.426544	−	0.904467i	$-0.359731\pi$
$577$	−7.25058	−	5.26785i	−0.301845	−	0.219304i	−0.728390	+	0.685163i	$0.759731\pi$
$578$	24.1783	+	17.5665i	1.00568	+	0.730672i
$579$		0			0
$580$	22.2350	+	68.4322i	0.923257	+	2.84149i
$581$	−4.74874	+	3.45016i	−0.197011	+	0.143137i
$582$		0			0
$583$	−20.6020	−	1.87016i	−0.853248	−	0.0774542i
$584$	−11.5039			−0.476037
$585$		0			0
$586$	7.00813	+	21.5688i	0.289503	+	0.890999i
$587$	−1.53315	+	4.71854i	−0.0632798	+	0.194755i	−0.977698	−	0.210015i	$-0.932649\pi$
$587$	−1.53315	+	4.71854i	−0.0632798	+	0.194755i	0.914418	+	0.404771i	$0.132649\pi$
$588$		0			0
$589$	−30.9313	−	22.4729i	−1.27450	−	0.925980i
$590$	15.6874	−	48.2809i	0.645840	−	1.98769i
$591$		0			0
$592$	68.1069	−	49.4825i	2.79918	−	2.03372i
$593$	−30.7179			−1.26143			−0.630716	−	0.776013i	$-0.717239\pi$
$593$	−30.7179			−1.26143			−0.630716	+	0.776013i	$0.717239\pi$
$594$		0			0
$595$	4.10094			0.168122
$596$	−2.08225	+	1.51284i	−0.0852921	+	0.0619684i
$597$		0			0
$598$	6.26674	−	19.2870i	0.256266	−	0.788705i
$599$	−26.4690	−	19.2309i	−1.08149	−	0.785752i	−0.103552	−	0.994624i	$-0.533021\pi$
$599$	−26.4690	−	19.2309i	−1.08149	−	0.785752i	−0.977943	+	0.208872i	$0.933021\pi$
$600$		0			0
$601$	−12.5977	+	38.7716i	−0.513869	+	1.58153i	0.271460	+	0.962450i	$0.412493\pi$
$601$	−12.5977	+	38.7716i	−0.513869	+	1.58153i	−0.785330	+	0.619078i	$0.787507\pi$
$602$	−1.65953	−	5.10752i	−0.0676375	−	0.208167i
$603$		0			0
$604$	4.92095			0.200230
$605$	−8.95514	+	16.5804i	−0.364078	+	0.674088i
$606$		0			0
$607$	20.6513	−	15.0041i	0.838212	−	0.608997i	−0.0836587	−	0.996494i	$-0.526661\pi$
$607$	20.6513	−	15.0041i	0.838212	−	0.608997i	0.921871	+	0.387498i	$0.126661\pi$
$608$	26.9708	+	83.0075i	1.09381	+	3.36640i
$609$		0			0
$610$	50.7564	+	36.8767i	2.05507	+	1.49309i
$611$	−6.76308	−	4.91367i	−0.273605	−	0.198786i
$612$		0			0
$613$	−11.4336	−	35.1891i	−0.461800	−	1.42127i	−0.862963	−	0.505267i	$-0.831394\pi$
$613$	−11.4336	−	35.1891i	−0.461800	−	1.42127i	0.401163	−	0.916007i	$-0.368606\pi$
$614$	7.50464	−	5.45244i	0.302863	−	0.220043i
$615$		0			0
$616$	20.0752	+	17.5664i	0.808852	+	0.707769i
$617$	43.0676			1.73384			0.866918	−	0.498452i	$-0.166098\pi$
$617$	43.0676			1.73384			0.866918	+	0.498452i	$0.166098\pi$
$618$		0			0
$619$	4.49645	+	13.8387i	0.180728	+	0.556223i	0.999849	−	0.0173982i	$-0.00553830\pi$
$619$	4.49645	+	13.8387i	0.180728	+	0.556223i	−0.819121	+	0.573621i	$0.805538\pi$
$620$	−16.0892	+	49.5174i	−0.646157	+	1.98867i
$621$		0			0
$622$	−7.91762	−	5.75249i	−0.317468	−	0.230654i
$623$	5.07531	−	15.6202i	0.203338	−	0.625810i
$624$		0			0
$625$	8.42056	−	6.11789i	0.336822	−	0.244716i
$626$	−69.6514			−2.78383
$627$		0			0
$628$	−16.5562			−0.660666
$629$	14.4743	−	10.5162i	0.577130	−	0.419309i
$630$		0			0
$631$	2.11020	−	6.49452i	0.0840057	−	0.258543i	−0.900227	−	0.435421i	$-0.856600\pi$
$631$	2.11020	−	6.49452i	0.0840057	−	0.258543i	0.984233	+	0.176878i	$0.0565997\pi$
$632$	−43.7093	−	31.7566i	−1.73866	−	1.26321i
$633$		0			0
$634$	−10.7192	+	32.9903i	−0.425714	+	1.31021i
$635$	0.589590	+	1.81457i	0.0233972	+	0.0720090i
$636$		0			0
$637$	1.51161			0.0598924
$638$	−28.9012	+	67.4744i	−1.14421	+	2.67134i
$639$		0			0
$640$	13.3569	−	9.70436i	0.527978	−	0.383598i
$641$	3.52797	+	10.8580i	0.139346	+	0.428864i	0.996241	−	0.0866281i	$-0.0276092\pi$
$641$	3.52797	+	10.8580i	0.139346	+	0.428864i	−0.856894	+	0.515492i	$0.827609\pi$
$642$		0			0
$643$	29.3099	+	21.2949i	1.15587	+	0.839790i	0.989250	−	0.146231i	$-0.0467143\pi$
$643$	29.3099	+	21.2949i	1.15587	+	0.839790i	0.166621	+	0.986021i	$0.446714\pi$
$644$	20.5980	+	14.9653i	0.811674	+	0.589716i
$645$		0			0
$646$	12.4204	+	38.2261i	0.488675	+	1.50399i
$647$	−19.5403	+	14.1968i	−0.768208	+	0.558136i	−0.901417	−	0.432952i	$-0.857472\pi$
$647$	−19.5403	+	14.1968i	−0.768208	+	0.558136i	0.133209	+	0.991088i	$0.457472\pi$
$648$		0			0
$649$	31.8294	−	18.9840i	1.24941	−	0.745187i
$650$	−8.27908			−0.324732
$651$		0			0
$652$	5.41573	+	16.6679i	0.212096	+	0.652766i
$653$	5.66913	−	17.4478i	0.221850	−	0.682784i	−0.776746	−	0.629814i	$-0.783131\pi$
$653$	5.66913	−	17.4478i	0.221850	−	0.682784i	0.998596	−	0.0529703i	$-0.0168689\pi$
$654$		0			0
$655$	19.9356	+	14.4841i	0.778949	+	0.565940i
$656$	17.5241	−	53.9337i	0.684202	−	2.10576i
$657$		0			0
$658$	11.8650	−	8.62046i	0.462548	−	0.336061i
$659$	9.32284			0.363166			0.181583	−	0.983376i	$-0.441878\pi$
$659$	9.32284			0.363166			0.181583	+	0.983376i	$0.441878\pi$
$660$		0			0
$661$	−9.30120			−0.361775			−0.180887	−	0.983504i	$-0.557897\pi$
$661$	−9.30120			−0.361775			−0.180887	+	0.983504i	$0.557897\pi$
$662$	−17.0281	+	12.3717i	−0.661817	+	0.480838i
$663$		0			0
$664$	−14.5889	+	44.8999i	−0.566158	+	1.74246i
$665$	−8.77467	−	6.37517i	−0.340267	−	0.247218i
$666$		0			0
$667$	−13.0463	+	40.1525i	−0.505157	+	1.55471i
$668$	7.11486	+	21.8973i	0.275282	+	0.847231i
$669$		0			0
$670$	−61.8647			−2.39004
$671$	10.1575	+	44.6609i	0.392125	+	1.72411i
$672$		0			0
$673$	−29.0694	+	21.1202i	−1.12054	+	0.814123i	−0.984292	−	0.176551i	$-0.943506\pi$
$673$	−29.0694	+	21.1202i	−1.12054	+	0.814123i	−0.136253	+	0.990674i	$0.543506\pi$
$674$	8.19544	+	25.2230i	0.315677	+	0.971553i
$675$		0			0
$676$	43.6280	+	31.6976i	1.67800	+	1.21914i
$677$	−38.4071	−	27.9044i	−1.47610	−	1.07245i	−0.978786	−	0.204884i	$-0.934318\pi$
$677$	−38.4071	−	27.9044i	−1.47610	−	1.07245i	−0.497318	−	0.867568i	$-0.665682\pi$
$678$		0			0
$679$	−3.72415	−	11.4617i	−0.142920	−	0.439861i
$680$	26.6846	−	19.3875i	1.02331	−	0.743475i
$681$		0			0
$682$	−45.6171	+	27.2075i	−1.74677	+	1.04183i
$683$	30.1415			1.15333			0.576667	−	0.816980i	$-0.304353\pi$
$683$	30.1415			1.15333			0.576667	+	0.816980i	$0.304353\pi$
$684$		0			0
$685$	1.44410	+	4.44448i	0.0551761	+	0.169815i
$686$	−0.819499	+	2.52216i	−0.0312886	+	0.0962964i
$687$		0			0
$688$	−18.4538	−	13.4075i	−0.703545	−	0.511156i
$689$	−2.91353	+	8.96691i	−0.110996	+	0.341612i
$690$		0			0
$691$	−37.0354	+	26.9078i	−1.40889	+	1.02362i	−0.415409	+	0.909635i	$0.636362\pi$
$691$	−37.0354	+	26.9078i	−1.40889	+	1.02362i	−0.993482	+	0.113985i	$0.963638\pi$
$692$	−28.8118			−1.09526
$693$		0			0
$694$	14.3432			0.544459
$695$	0.489434	−	0.355594i	0.0185653	−	0.0134885i
$696$		0			0
$697$	3.72430	−	11.4622i	0.141068	−	0.434162i
$698$	61.2127	+	44.4737i	2.31694	+	1.68335i
$699$		0			0
$700$	3.21198	−	9.88545i	0.121401	−	0.373635i
$701$	−3.83930	−	11.8162i	−0.145008	−	0.446290i	0.852004	−	0.523536i	$-0.175387\pi$
$701$	−3.83930	−	11.8162i	−0.145008	−	0.446290i	−0.997012	+	0.0772457i	$0.975387\pi$
$702$		0			0
$703$	−47.3184			−1.78465
$704$	46.3437	+	4.20688i	1.74664	+	0.158553i
$705$		0			0
$706$	−41.2417	+	29.9639i	−1.55215	+	1.12771i
$707$	−1.65276	−	5.08668i	−0.0621585	−	0.191304i
$708$		0			0
$709$	3.65899	+	2.65841i	0.137416	+	0.0998388i	0.654370	−	0.756175i	$-0.272934\pi$
$709$	3.65899	+	2.65841i	0.137416	+	0.0998388i	−0.516953	+	0.856013i	$0.672934\pi$
$710$	52.6796	+	38.2739i	1.97703	+	1.43640i
$711$		0			0
$712$	−40.8208	−	125.633i	−1.52982	−	4.70831i
$713$	−24.7151	+	17.9565i	−0.925586	+	0.672478i
$714$		0			0
$715$	6.46349	+	5.65573i	0.241721	+	0.211512i
$716$	−14.8822			−0.556174
$717$		0			0
$718$	−18.3181	−	56.3773i	−0.683625	−	2.10398i
$719$	2.57112	−	7.91310i	0.0958867	−	0.295109i	−0.891597	−	0.452830i	$-0.850415\pi$
$719$	2.57112	−	7.91310i	0.0958867	−	0.295109i	0.987484	+	0.157721i	$0.0504146\pi$
$720$		0			0
$721$	7.58674	+	5.51209i	0.282545	+	0.205281i
$722$	17.2787	−	53.1785i	0.643048	−	1.97910i
$723$		0			0
$724$	38.2738	−	27.8076i	1.42244	−	1.03346i
$725$	17.2357			0.640119
$726$		0			0
$727$	39.9612			1.48208			0.741040	−	0.671461i	$-0.234333\pi$
$727$	39.9612			1.48208			0.741040	+	0.671461i	$0.234333\pi$
$728$	9.83597	−	7.14625i	0.364545	−	0.264858i
$729$		0			0
$730$	2.00799	−	6.17996i	0.0743190	−	0.228731i
$731$	−3.92188	−	2.84941i	−0.145056	−	0.105389i
$732$		0			0
$733$	−4.10613	+	12.6374i	−0.151663	+	0.466772i	−0.997808	−	0.0661822i	$-0.978918\pi$
$733$	−4.10613	+	12.6374i	−0.151663	+	0.466772i	0.846144	+	0.532954i	$0.178918\pi$
$734$	−19.2130	−	59.1316i	−0.709165	−	2.18259i
$735$		0			0
$736$	69.7388			2.57061
$737$	−33.9886	−	29.7410i	−1.25199	−	1.09552i
$738$		0			0
$739$	5.29565	−	3.84752i	0.194804	−	0.141533i	−0.486108	−	0.873899i	$-0.661584\pi$
$739$	5.29565	−	3.84752i	0.194804	−	0.141533i	0.680912	+	0.732366i	$0.261584\pi$
$740$	19.9124	+	61.2841i	0.731995	+	2.25285i
$741$		0			0
$742$	−13.3819	−	9.72255i	−0.491266	−	0.356926i
$743$	−26.9014	−	19.5450i	−0.986915	−	0.717036i	−0.0276716	−	0.999617i	$-0.508809\pi$
$743$	−26.9014	−	19.5450i	−0.986915	−	0.717036i	−0.959243	+	0.282581i	$0.908809\pi$
$744$		0			0
$745$	−0.270724	−	0.833203i	−0.00991856	−	0.0305262i
$746$	71.7740	−	52.1468i	2.62783	−	1.90923i
$747$		0			0
$748$	39.7950	+	3.61242i	1.45505	+	0.132083i
$749$	−12.1711			−0.444721
$750$		0			0
$751$	−0.237730	−	0.731659i	−0.00867490	−	0.0266986i	0.946625	−	0.322336i	$-0.104468\pi$
$751$	−0.237730	−	0.731659i	−0.00867490	−	0.0266986i	−0.955300	+	0.295637i	$0.904468\pi$
$752$	19.2495	−	59.2439i	0.701957	−	2.16040i
$753$		0			0
$754$	27.0657	+	19.6644i	0.985675	+	0.716135i
$755$	−0.517608	+	1.59303i	−0.0188377	+	0.0579764i
$756$		0			0
$757$	1.85608	−	1.34852i	0.0674602	−	0.0490127i	−0.553544	−	0.832820i	$-0.686725\pi$
$757$	1.85608	−	1.34852i	0.0674602	−	0.0490127i	0.621004	+	0.783807i	$0.286725\pi$
$758$	−48.7417			−1.77038
$759$		0			0
$760$	−87.2351			−3.16435
$761$	−3.23539	+	2.35065i	−0.117283	+	0.0852109i	−0.644880	−	0.764283i	$-0.723093\pi$
$761$	−3.23539	+	2.35065i	−0.117283	+	0.0852109i	0.527598	+	0.849494i	$0.323093\pi$
$762$		0			0
$763$	1.95122	−	6.00524i	0.0706390	−	0.217404i
$764$	−37.4964	−	27.2428i	−1.35657	−	0.985608i
$765$		0			0
$766$	−17.4884	+	53.8237i	−0.631881	+	1.94473i
$767$	−5.21965	−	16.0644i	−0.188471	−	0.580053i
$768$		0			0
$769$	48.3136			1.74223			0.871116	−	0.491077i	$-0.163396\pi$
$769$	48.3136			1.74223			0.871116	+	0.491077i	$0.163396\pi$
$770$	−12.9408	+	7.71828i	−0.466353	+	0.278147i
$771$		0			0
$772$	6.07580	−	4.41433i	0.218673	−	0.158875i
$773$	4.15257	+	12.7803i	0.149358	+	0.459675i	0.997546	−	0.0700199i	$-0.0223063\pi$
$773$	4.15257	+	12.7803i	0.149358	+	0.459675i	−0.848188	+	0.529695i	$0.822306\pi$
$774$		0			0
$775$	10.0899	+	7.33071i	0.362438	+	0.263327i
$776$	−78.4188	−	56.9746i	−2.81507	−	2.04527i
$777$		0			0
$778$	−12.7198	−	39.1475i	−0.456027	−	1.40351i
$779$	−25.7875	+	18.7357i	−0.923932	+	0.671276i
$780$		0			0
$781$	10.5423	+	46.3531i	0.377235	+	1.65864i
$782$	32.1157			1.14845
$783$		0			0
$784$	3.48076	+	10.7127i	0.124313	+	0.382595i
$785$	1.74146	−	5.35967i	0.0621554	−	0.191295i
$786$		0			0
$787$	5.95242	+	4.32469i	0.212181	+	0.154158i	0.688800	−	0.724952i	$-0.258138\pi$
$787$	5.95242	+	4.32469i	0.212181	+	0.154158i	−0.476619	+	0.879110i	$0.658138\pi$
$788$	−5.25233	+	16.1650i	−0.187106	+	0.575855i
$789$		0			0
$790$	24.6891	−	17.9377i	0.878400	−	0.638195i
$791$	3.36767			0.119741
$792$		0			0
$793$	20.8749			0.741288
$794$	−46.0799	+	33.4790i	−1.63531	+	1.18813i
$795$		0			0
$796$	43.2534	−	133.120i	1.53308	−	4.71833i
$797$	−3.90464	−	2.83689i	−0.138309	−	0.100488i	0.516479	−	0.856300i	$-0.327242\pi$
$797$	−3.90464	−	2.83689i	−0.138309	−	0.100488i	−0.654789	+	0.755812i	$0.727242\pi$
$798$		0			0
$799$	4.09098	−	12.5907i	0.144728	−	0.445428i
$800$	−8.79792	−	27.0772i	−0.311053	−	0.957324i
$801$		0			0
$802$	−23.5522			−0.831655
$803$	4.07416	−	2.42996i	0.143774	−	0.0857513i
$804$		0			0
$805$	−7.01123	+	5.09396i	−0.247113	+	0.179538i
$806$	7.48069	+	23.0232i	0.263496	+	0.810957i
$807$		0			0
$808$	−34.8020	−	25.2851i	−1.22433	−	0.889527i
$809$	−42.2996	−	30.7325i	−1.48718	−	1.08050i	−0.975155	−	0.221524i	$-0.928897\pi$
$809$	−42.2996	−	30.7325i	−1.48718	−	1.08050i	−0.512021	−	0.858973i	$-0.671103\pi$
$810$		0			0
$811$	−10.9156	−	33.5947i	−0.383298	−	1.17967i	−0.937708	−	0.347426i	$-0.887056\pi$
$811$	−10.9156	−	33.5947i	−0.383298	−	1.17967i	0.554410	−	0.832244i	$-0.312944\pi$
$812$	−33.9803	+	24.6881i	−1.19247	+	0.866384i
$813$		0			0
$814$	−25.8824	+	60.4264i	−0.907176	+	2.11794i
$815$	−5.96547			−0.208961
$816$		0			0
$817$	3.96194	+	12.1936i	0.138611	+	0.426600i
$818$	4.47263	−	13.7653i	0.156382	−	0.481294i
$819$		0			0
$820$	35.1172	+	25.5141i	1.22635	+	0.890993i
$821$	−9.40526	+	28.9464i	−0.328246	+	1.01024i	0.641708	+	0.766949i	$0.278226\pi$
$821$	−9.40526	+	28.9464i	−0.328246	+	1.01024i	−0.969954	+	0.243288i	$0.921774\pi$
$822$		0			0
$823$	−37.1206	+	26.9697i	−1.29394	+	0.940104i	−0.999877	−	0.0156819i	$-0.995008\pi$
$823$	−37.1206	+	26.9697i	−1.29394	+	0.940104i	−0.294065	+	0.955786i	$0.595008\pi$
$824$	75.4251			2.62756
$825$		0			0
$826$	29.6336			1.03108
$827$	9.89408	−	7.18847i	0.344051	−	0.249968i	−0.402318	−	0.915500i	$-0.631795\pi$
$827$	9.89408	−	7.18847i	0.344051	−	0.249968i	0.746369	+	0.665532i	$0.231795\pi$
$828$		0			0
$829$	6.10050	−	18.7754i	0.211879	−	0.652097i	−0.787481	−	0.616339i	$-0.788615\pi$
$829$	6.10050	−	18.7754i	0.211879	−	0.652097i	0.999360	−	0.0357585i	$-0.0113847\pi$
$830$	−21.5739	−	15.6744i	−0.748842	−	0.544066i
$831$		0			0
$832$	6.55389	−	20.1708i	0.227215	−	0.699297i
$833$	0.739744	+	2.27670i	0.0256306	+	0.0788829i
$834$		0			0
$835$	−7.83707			−0.271213
$836$	−79.5324	−	69.5931i	−2.75069	−	2.40693i
$837$		0			0
$838$	42.8678	−	31.1453i	1.48084	−	1.07590i
$839$	−3.08217	−	9.48594i	−0.106408	−	0.327491i	0.883650	−	0.468148i	$-0.155079\pi$
$839$	−3.08217	−	9.48594i	−0.106408	−	0.327491i	−0.990058	+	0.140657i	$0.955079\pi$
$840$		0			0
$841$	−32.8850	−	23.8924i	−1.13397	−	0.823875i
$842$	60.7431	+	44.1325i	2.09335	+	1.52091i
$843$		0			0
$844$	−37.3364	−	114.910i	−1.28517	−	3.95535i
$845$	−14.8503	+	10.7894i	−0.510866	+	0.371166i
$846$		0			0
$847$	−10.8202	−	1.98074i	−0.371786	−	0.0680592i
$848$	−70.2565			−2.41262
$849$		0			0
$850$	−4.05156	−	12.4694i	−0.138968	−	0.427698i
$851$	−11.6836	+	35.9584i	−0.400508	+	1.23264i
$852$		0			0
$853$	0.565471	+	0.410839i	0.0193614	+	0.0140669i	0.597424	−	0.801926i	$-0.296191\pi$
$853$	0.565471	+	0.410839i	0.0193614	+	0.0140669i	−0.578062	+	0.815993i	$0.696191\pi$
$854$	−11.3170	+	34.8301i	−0.387259	+	1.19186i
$855$		0			0
$856$	−79.1963	+	57.5395i	−2.70687	+	1.96666i
$857$	40.0835			1.36922			0.684612	−	0.728907i	$-0.259972\pi$
$857$	40.0835			1.36922			0.684612	+	0.728907i	$0.259972\pi$
$858$		0			0
$859$	−28.0045			−0.955503			−0.477751	−	0.878495i	$-0.658548\pi$
$859$	−28.0045			−0.955503			−0.477751	+	0.878495i	$0.658548\pi$
$860$	14.1252	−	10.2626i	0.481665	−	0.349950i
$861$		0			0
$862$	−26.0311	+	80.1156i	−0.886624	+	2.72875i
$863$	−21.0736	−	15.3109i	−0.717354	−	0.521188i	0.168184	−	0.985756i	$-0.446210\pi$
$863$	−21.0736	−	15.3109i	−0.717354	−	0.521188i	−0.885538	+	0.464567i	$0.846210\pi$
$864$		0			0
$865$	3.03056	−	9.32711i	0.103042	−	0.317131i
$866$	−10.7896	−	33.2071i	−0.366647	−	1.12842i
$867$		0			0
$868$	−30.3925			−1.03159
$869$	22.1877	+	2.01410i	0.752665	+	0.0683237i
$870$		0			0
$871$	−16.6529	+	12.0991i	−0.564263	+	0.409961i
$872$	−15.6937	−	48.3002i	−0.531455	−	1.63565i
$873$		0			0
$874$	−68.7170	−	49.9258i	−2.32439	−	1.68877i
$875$	9.79198	+	7.11429i	0.331029	+	0.240507i
$876$		0			0
$877$	−13.1771	−	40.5550i	−0.444960	−	1.36945i	−0.882527	−	0.470261i	$-0.844160\pi$
$877$	−13.1771	−	40.5550i	−0.444960	−	1.36945i	0.437567	−	0.899186i	$-0.355840\pi$
$878$	21.0506	−	15.2941i	0.710422	−	0.516152i
$879$		0			0
$880$	−25.1983	+	58.8294i	−0.849436	+	1.98314i
$881$	5.07985			0.171144			0.0855722	−	0.996332i	$-0.472728\pi$
$881$	5.07985			0.171144			0.0855722	+	0.996332i	$0.472728\pi$
$882$		0			0
$883$	15.1568	+	46.6478i	0.510066	+	1.56982i	0.792083	+	0.610414i	$0.208997\pi$
$883$	15.1568	+	46.6478i	0.510066	+	1.56982i	−0.282016	+	0.959410i	$0.591003\pi$
$884$	5.62779	−	17.3205i	0.189283	−	0.582553i
$885$		0			0
$886$	5.33180	+	3.87378i	0.179125	+	0.130142i
$887$	−16.6644	+	51.2876i	−0.559534	+	1.72207i	0.124123	+	0.992267i	$0.460388\pi$
$887$	−16.6644	+	51.2876i	−0.559534	+	1.72207i	−0.683657	+	0.729803i	$0.739612\pi$
$888$		0			0
$889$	−0.901033	+	0.654639i	−0.0302197	+	0.0219559i
$890$	74.6159			2.50113
$891$		0			0
$892$	114.839			3.84509
$893$	−28.3264	+	20.5804i	−0.947908	+	0.688695i
$894$		0			0
$895$	1.56538	−	4.81774i	0.0523248	−	0.161039i
$896$	7.79688	+	5.66477i	0.260476	+	0.189247i
$897$		0			0
$898$	12.7921	−	39.3701i	0.426879	−	1.31380i
$899$	−15.5736	−	47.9306i	−0.519409	−	1.59858i
$900$		0			0
$901$	−14.9312			−0.497430
$902$	9.82047	+	43.1791i	0.326986	+	1.43771i
$903$		0			0
$904$	21.9132	−	15.9209i	0.728822	−	0.529520i
$905$	4.97619	+	15.3151i	0.165414	+	0.509092i
$906$		0			0
$907$	−20.8424	−	15.1429i	−0.692061	−	0.502812i	0.185276	−	0.982687i	$-0.440682\pi$
$907$	−20.8424	−	15.1429i	−0.692061	−	0.502812i	−0.877337	+	0.479875i	$0.840682\pi$
$908$	58.6510	+	42.6125i	1.94640	+	1.41414i
$909$		0			0
$910$	2.12214	+	6.53128i	0.0703483	+	0.216510i
$911$	−23.6129	+	17.1558i	−0.782331	+	0.568397i	−0.905678	−	0.423967i	$-0.860637\pi$
$911$	−23.6129	+	17.1558i	−0.782331	+	0.568397i	0.123346	+	0.992364i	$0.460637\pi$
$912$		0			0
$913$	−4.31742	−	18.9830i	−0.142886	−	0.628247i
$914$	36.2396			1.19870
$915$		0			0
$916$	−5.90007	−	18.1585i	−0.194944	−	0.599975i
$917$	−4.44498	+	13.6802i	−0.146786	+	0.451761i
$918$		0			0
$919$	32.7816	+	23.8172i	1.08136	+	0.785657i	0.977920	−	0.208978i	$-0.0670138\pi$
$919$	32.7816	+	23.8172i	1.08136	+	0.785657i	0.103444	+	0.994635i	$0.467014\pi$
$920$	−21.5396	+	66.2920i	−0.710139	+	2.18558i
$921$		0			0
$922$	40.0227	−	29.0782i	1.31808	−	0.957639i
$923$	21.6658			0.713139
$924$		0			0
$925$	15.4354			0.507512
$926$	39.8408	−	28.9460i	1.30925	−	0.951226i
$927$		0			0
$928$	−35.5516	+	109.417i	−1.16704	+	3.59178i
$929$	4.15304	+	3.01736i	0.136257	+	0.0989963i	0.653826	−	0.756645i	$-0.273163\pi$
$929$	4.15304	+	3.01736i	0.136257	+	0.0989963i	−0.517569	+	0.855641i	$0.673163\pi$
$930$		0			0
$931$	1.95646	−	6.02136i	0.0641204	−	0.197342i
$932$	−42.7448	−	131.555i	−1.40015	−	4.30923i
$933$		0			0
$934$	−92.7066			−3.03345
$935$	−5.35525	+	12.5027i	−0.175135	+	0.408881i
$936$		0			0
$937$	20.4911	−	14.8877i	0.669416	−	0.486359i	−0.200414	−	0.979711i	$-0.564229\pi$
$937$	20.4911	−	14.8877i	0.669416	−	0.486359i	0.869830	+	0.493352i	$0.164229\pi$
$938$	−11.1594	−	34.3451i	−0.364367	−	1.12141i
$939$		0			0
$940$	38.5747	+	28.0262i	1.25817	+	0.914114i
$941$	17.2117	+	12.5051i	0.561086	+	0.407653i	0.831856	−	0.554991i	$-0.187278\pi$
$941$	17.2117	+	12.5051i	0.561086	+	0.407653i	−0.270770	+	0.962644i	$0.587278\pi$
$942$		0			0
$943$	7.87041	+	24.2226i	0.256296	+	0.788797i
$944$	101.828	−	73.9823i	3.31422	−	2.40792i
$945$		0			0
$946$	17.7385	+	1.61023i	0.576729	+	0.0523530i
$947$	30.1418			0.979476			0.489738	−	0.871870i	$-0.337092\pi$
$947$	30.1418			0.979476			0.489738	+	0.871870i	$0.337092\pi$
$948$		0			0
$949$	−0.668116	−	2.05625i	−0.0216880	−	0.0667487i
$950$	−10.7155	+	32.9789i	−0.347656	+	1.06998i
$951$		0			0
$952$	15.5767	+	11.3171i	0.504844	+	0.366790i
$953$	−2.75961	+	8.49320i	−0.0893925	+	0.275122i	−0.985752	−	0.168207i	$-0.946202\pi$
$953$	−2.75961	+	8.49320i	−0.0893925	+	0.275122i	0.896359	+	0.443328i	$0.146202\pi$
$954$		0			0
$955$	12.7632	−	9.27301i	0.413008	−	0.300068i
$956$	−56.5367			−1.82853
$957$		0			0
$958$	−107.522			−3.47387
$959$	−2.20692	+	1.60342i	−0.0712653	+	0.0517772i
$960$		0			0
$961$	1.68951	−	5.19976i	0.0545002	−	0.167734i
$962$	24.2386	+	17.6103i	0.781482	+	0.567780i
$963$		0			0
$964$	22.9391	−	70.5994i	0.738820	−	2.27385i
$965$	0.789947	+	2.43121i	0.0254293	+	0.0782633i
$966$		0			0
$967$	−38.3461			−1.23313			−0.616564	−	0.787305i	$-0.711476\pi$
$967$	−38.3461			−1.23313			−0.616564	+	0.787305i	$0.711476\pi$
$968$	−79.7703	+	38.2646i	−2.56392	+	1.22987i
$969$		0			0
$970$	44.2948	−	32.1821i	1.42222	−	1.03330i
$971$	−9.62612	−	29.6262i	−0.308917	−	0.950749i	−0.978186	−	0.207729i	$-0.933393\pi$
$971$	−9.62612	−	29.6262i	−0.308917	−	0.950749i	0.669269	−	0.743020i	$-0.266607\pi$
$972$		0			0
$973$	0.285699	+	0.207573i	0.00915910	+	0.00665448i
$974$	−29.0859	−	21.1322i	−0.931973	−	0.677118i
$975$		0			0
$976$	48.0680	+	147.938i	1.53862	+	4.73538i
$977$	24.0815	−	17.4962i	0.770435	−	0.559754i	−0.131658	−	0.991295i	$-0.542030\pi$
$977$	24.0815	−	17.4962i	0.770435	−	0.559754i	0.902093	+	0.431542i	$0.142030\pi$
$978$		0			0
$979$	40.9941	+	35.8710i	1.31018	+	1.14644i
$980$	−8.62183			−0.275414
$981$		0			0
$982$	19.2249	+	59.1683i	0.613492	+	1.88814i
$983$	12.3319	−	37.9537i	0.393326	−	1.21053i	−0.536931	−	0.843626i	$-0.680417\pi$
$983$	12.3319	−	37.9537i	0.393326	−	1.21053i	0.930257	−	0.366908i	$-0.119583\pi$
$984$		0			0
$985$	−4.68055	−	3.40062i	−0.149135	−	0.108353i
$986$	−16.3720	+	50.3879i	−0.521391	+	1.60468i
$987$		0			0
$988$	−38.9675	+	28.3115i	−1.23972	+	0.900709i
$989$	10.2445			0.325755
$990$		0			0
$991$	−10.7771			−0.342345			−0.171173	−	0.985241i	$-0.554756\pi$
$991$	−10.7771			−0.342345			−0.171173	+	0.985241i	$0.554756\pi$
$992$	−67.3492	+	48.9320i	−2.13834	+	1.55359i
$993$		0			0
$994$	−11.7458	+	36.1498i	−0.372554	+	1.14660i
$995$	38.5448	+	28.0044i	1.22195	+	0.887800i
$996$		0			0
$997$	0.352040	−	1.08347i	0.0111492	−	0.0343137i	−0.945327	−	0.326124i	$-0.894257\pi$
$997$	0.352040	−	1.08347i	0.0111492	−	0.0343137i	0.956476	+	0.291810i	$0.0942574\pi$
$998$	14.1672	+	43.6020i	0.448454	+	1.38020i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.j.190.1		20
3.2	odd	2		231.2.j.g.190.5	yes	20
11.2	odd	10		7623.2.a.cy.1.1		10
11.4	even	5	inner	693.2.m.j.631.1		20
11.9	even	5		7623.2.a.cx.1.10		10
33.2	even	10		2541.2.a.br.1.10		10
33.20	odd	10		2541.2.a.bq.1.1		10
33.26	odd	10		231.2.j.g.169.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.5	✓	20	33.26	odd	10
231.2.j.g.190.5	yes	20	3.2	odd	2
693.2.m.j.190.1		20	1.1	even	1	trivial
693.2.m.j.631.1		20	11.4	even	5	inner
2541.2.a.bq.1.1		10	33.20	odd	10
2541.2.a.br.1.10		10	33.2	even	10
7623.2.a.cx.1.10		10	11.9	even	5
7623.2.a.cy.1.1		10	11.2	odd	10

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	693.2.m.j.190.1

Level	$693$
Weight	$2$
Character	693.190
Analytic conductor	$5.534$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$