LMFDB - Embedded newform 1638.2.m.h.1621.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("1638.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.m (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.1
Root			$-1.38232 + 0.298668i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.h.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-1.75410 - 3.03819i) q^{5} +(-2.63641 - 0.222079i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.75410 - 3.03819i) q^{5} +(-2.63641 - 0.222079i) q^{7} -1.00000 q^{8} +(1.75410 + 3.03819i) q^{10} +(-3.20391 - 5.54934i) q^{11} +(-0.213022 - 3.59925i) q^{13} +(2.63641 + 0.222079i) q^{14} +1.00000 q^{16} -4.67781 q^{17} +(-2.61911 + 4.53642i) q^{19} +(-1.75410 - 3.03819i) q^{20} +(3.20391 + 5.54934i) q^{22} +2.16961 q^{23} +(-3.65372 + 6.32843i) q^{25} +(0.213022 + 3.59925i) q^{26} +(-2.63641 - 0.222079i) q^{28} +(1.23033 - 2.13099i) q^{29} +(4.46035 - 7.72555i) q^{31} -1.00000 q^{32} +4.67781 q^{34} +(3.94981 + 8.39947i) q^{35} +3.89962 q^{37} +(2.61911 - 4.53642i) q^{38} +(1.75410 + 3.03819i) q^{40} +(-5.09300 + 8.82134i) q^{41} +(-1.19338 - 2.06699i) q^{43} +(-3.20391 - 5.54934i) q^{44} -2.16961 q^{46} +(2.44070 + 4.22742i) q^{47} +(6.90136 + 1.17099i) q^{49} +(3.65372 - 6.32843i) q^{50} +(-0.213022 - 3.59925i) q^{52} +(1.05395 - 1.82549i) q^{53} +(-11.2399 + 19.4682i) q^{55} +(2.63641 + 0.222079i) q^{56} +(-1.23033 + 2.13099i) q^{58} +11.7946 q^{59} +(-4.67781 + 8.10220i) q^{61} +(-4.46035 + 7.72555i) q^{62} +1.00000 q^{64} +(-10.5615 + 6.96065i) q^{65} +(-3.64461 - 6.31265i) q^{67} -4.67781 q^{68} +(-3.94981 - 8.39947i) q^{70} +(-2.79339 - 4.83829i) q^{71} +(4.23175 - 7.32961i) q^{73} -3.89962 q^{74} +(-2.61911 + 4.53642i) q^{76} +(7.21444 + 15.3419i) q^{77} +(0.893764 + 1.54804i) q^{79} +(-1.75410 - 3.03819i) q^{80} +(5.09300 - 8.82134i) q^{82} +2.59218 q^{83} +(8.20533 + 14.2121i) q^{85} +(1.19338 + 2.06699i) q^{86} +(3.20391 + 5.54934i) q^{88} -7.00752 q^{89} +(-0.237705 + 9.53643i) q^{91} +2.16961 q^{92} +(-2.44070 - 4.22742i) q^{94} +18.3767 q^{95} +(-4.92513 - 8.53057i) q^{97} +(-6.90136 - 1.17099i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} + 2 q^{10} - 4 q^{11} + 3 q^{13} - 3 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{25} - 3 q^{26} + 3 q^{28} - 2 q^{29} + 14 q^{31} - 8 q^{32} + 4 q^{34} + 22 q^{35} + 12 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} - 8 q^{46} - 7 q^{47} + 5 q^{49} - 2 q^{50} + 3 q^{52} + q^{53} - 25 q^{55} - 3 q^{56} + 2 q^{58} + 32 q^{59} - 4 q^{61} - 14 q^{62} + 8 q^{64} - 10 q^{65} + 19 q^{67} - 4 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} - 12 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} - 2 q^{80} + 12 q^{82} + 64 q^{83} + 15 q^{85} + 4 q^{88} - 22 q^{89} - 38 q^{91} + 8 q^{92} + 7 q^{94} + 56 q^{95} + 11 q^{97} - 5 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 + 2 * q^10 - 4 * q^11 + 3 * q^13 - 3 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + 2 * q^25 - 3 * q^26 + 3 * q^28 - 2 * q^29 + 14 * q^31 - 8 * q^32 + 4 * q^34 + 22 * q^35 + 12 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 8 * q^46 - 7 * q^47 + 5 * q^49 - 2 * q^50 + 3 * q^52 + q^53 - 25 * q^55 - 3 * q^56 + 2 * q^58 + 32 * q^59 - 4 * q^61 - 14 * q^62 + 8 * q^64 - 10 * q^65 + 19 * q^67 - 4 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 - 12 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 - 2 * q^80 + 12 * q^82 + 64 * q^83 + 15 * q^85 + 4 * q^88 - 22 * q^89 - 38 * q^91 + 8 * q^92 + 7 * q^94 + 56 * q^95 + 11 * q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.75410	−	3.03819i	−0.784457	−	1.35872i	−0.929323	−	0.369268i	$-0.879609\pi$
$5$	−1.75410	−	3.03819i	−0.784457	−	1.35872i	0.144866	−	0.989451i	$-0.453725\pi$
$6$		0			0
$7$	−2.63641	−	0.222079i	−0.996471	−	0.0839380i
$7$	−2.63641	−	0.222079i	−0.996471	−	0.0839380i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.75410	+	3.03819i	0.554695	+	0.960759i
$11$	−3.20391	−	5.54934i	−0.966015	−	1.67319i	−0.706862	−	0.707352i	$-0.749890\pi$
$11$	−3.20391	−	5.54934i	−0.966015	−	1.67319i	−0.259154	−	0.965836i	$-0.583444\pi$
$12$		0			0
$13$	−0.213022	−	3.59925i	−0.0590817	−	0.998253i
$13$	−0.213022	−	3.59925i	−0.0590817	−	0.998253i
$14$	2.63641	+	0.222079i	0.704611	+	0.0593532i
$15$		0			0
$16$	1.00000			0.250000
$17$	−4.67781			−1.13453			−0.567267	−	0.823534i	$-0.691999\pi$
$17$	−4.67781			−1.13453			−0.567267	+	0.823534i	$0.691999\pi$
$18$		0			0
$19$	−2.61911	+	4.53642i	−0.600864	+	1.04073i	0.391826	+	0.920039i	$0.371843\pi$
$19$	−2.61911	+	4.53642i	−0.600864	+	1.04073i	−0.992690	+	0.120688i	$0.961490\pi$
$20$	−1.75410	−	3.03819i	−0.392228	−	0.679359i
$21$		0			0
$22$	3.20391	+	5.54934i	0.683076	+	1.18312i
$23$	2.16961			0.452395			0.226197	−	0.974081i	$-0.427371\pi$
$23$	2.16961			0.452395			0.226197	+	0.974081i	$0.427371\pi$
$24$		0			0
$25$	−3.65372	+	6.32843i	−0.730745	+	1.26569i
$26$	0.213022	+	3.59925i	0.0417771	+	0.705872i
$27$		0			0
$28$	−2.63641	−	0.222079i	−0.498235	−	0.0419690i
$29$	1.23033	−	2.13099i	0.228467	−	0.395716i	−0.728887	−	0.684634i	$-0.759962\pi$
$29$	1.23033	−	2.13099i	0.228467	−	0.395716i	0.957354	+	0.288918i	$0.0932955\pi$
$30$		0			0
$31$	4.46035	−	7.72555i	0.801102	−	1.38755i	−0.117790	−	0.993039i	$-0.537581\pi$
$31$	4.46035	−	7.72555i	0.801102	−	1.38755i	0.918892	−	0.394510i	$-0.129086\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	4.67781			0.802237
$35$	3.94981	+	8.39947i	0.667640	+	1.41977i
$36$		0			0
$37$	3.89962			0.641094			0.320547	−	0.947233i	$-0.396133\pi$
$37$	3.89962			0.641094			0.320547	+	0.947233i	$0.396133\pi$
$38$	2.61911	−	4.53642i	0.424875	−	0.735905i
$39$		0			0
$40$	1.75410	+	3.03819i	0.277347	+	0.480380i
$41$	−5.09300	+	8.82134i	−0.795393	+	1.37766i	0.127196	+	0.991878i	$0.459402\pi$
$41$	−5.09300	+	8.82134i	−0.795393	+	1.37766i	−0.922589	+	0.385784i	$0.873931\pi$
$42$		0			0
$43$	−1.19338	−	2.06699i	−0.181988	−	0.315213i	0.760569	−	0.649257i	$-0.224920\pi$
$43$	−1.19338	−	2.06699i	−0.181988	−	0.315213i	−0.942558	+	0.334044i	$0.891587\pi$
$44$	−3.20391	−	5.54934i	−0.483008	−	0.836594i
$45$		0			0
$46$	−2.16961			−0.319891
$47$	2.44070	+	4.22742i	0.356013	+	0.616632i	0.987291	−	0.158924i	$-0.0508026\pi$
$47$	2.44070	+	4.22742i	0.356013	+	0.616632i	−0.631278	+	0.775557i	$0.717469\pi$
$48$		0			0
$49$	6.90136	+	1.17099i	0.985909	+	0.167284i
$50$	3.65372	−	6.32843i	0.516714	−	0.894976i
$51$		0			0
$52$	−0.213022	−	3.59925i	−0.0295409	−	0.499127i
$53$	1.05395	−	1.82549i	0.144771	−	0.250750i	−0.784517	−	0.620108i	$-0.787089\pi$
$53$	1.05395	−	1.82549i	0.144771	−	0.250750i	0.929287	+	0.369358i	$0.120422\pi$
$54$		0			0
$55$	−11.2399	+	19.4682i	−1.51559	+	2.62509i
$56$	2.63641	+	0.222079i	0.352306	+	0.0296766i
$57$		0			0
$58$	−1.23033	+	2.13099i	−0.161550	+	0.279813i
$59$	11.7946			1.53552			0.767761	−	0.640736i	$-0.221371\pi$
$59$	11.7946			1.53552			0.767761	+	0.640736i	$0.221371\pi$
$60$		0			0
$61$	−4.67781	+	8.10220i	−0.598932	+	1.03738i	0.394047	+	0.919090i	$0.371075\pi$
$61$	−4.67781	+	8.10220i	−0.598932	+	1.03738i	−0.992979	+	0.118290i	$0.962259\pi$
$62$	−4.46035	+	7.72555i	−0.566464	+	0.981145i
$63$		0			0
$64$	1.00000			0.125000
$65$	−10.5615	+	6.96065i	−1.31000	+	0.863362i
$66$		0			0
$67$	−3.64461	−	6.31265i	−0.445260	−	0.771213i	0.552810	−	0.833307i	$-0.313555\pi$
$67$	−3.64461	−	6.31265i	−0.445260	−	0.771213i	−0.998070	+	0.0620940i	$0.980222\pi$
$68$	−4.67781			−0.567267
$69$		0			0
$70$	−3.94981	−	8.39947i	−0.472093	−	1.00393i
$71$	−2.79339	−	4.83829i	−0.331514	−	0.574199i	0.651295	−	0.758825i	$-0.274226\pi$
$71$	−2.79339	−	4.83829i	−0.331514	−	0.574199i	−0.982809	+	0.184625i	$0.940893\pi$
$72$		0			0
$73$	4.23175	−	7.32961i	0.495289	−	0.857866i	−0.504696	−	0.863297i	$-0.668395\pi$
$73$	4.23175	−	7.32961i	0.495289	−	0.857866i	0.999985	+	0.00543110i	$0.00172878\pi$
$74$	−3.89962			−0.453322
$75$		0			0
$76$	−2.61911	+	4.53642i	−0.300432	+	0.520364i
$77$	7.21444	+	15.3419i	0.822162	+	1.74837i
$78$		0			0
$79$	0.893764	+	1.54804i	0.100556	+	0.174169i	0.911914	−	0.410381i	$-0.134604\pi$
$79$	0.893764	+	1.54804i	0.100556	+	0.174169i	−0.811358	+	0.584550i	$0.801271\pi$
$80$	−1.75410	−	3.03819i	−0.196114	−	0.339680i
$81$		0			0
$82$	5.09300	−	8.82134i	0.562428	−	0.974154i
$83$	2.59218			0.284529			0.142264	−	0.989829i	$-0.454562\pi$
$83$	2.59218			0.284529			0.142264	+	0.989829i	$0.454562\pi$
$84$		0			0
$85$	8.20533	+	14.2121i	0.889993	+	1.54151i
$86$	1.19338	+	2.06699i	0.128685	+	0.222889i
$87$		0			0
$88$	3.20391	+	5.54934i	0.341538	+	0.591561i
$89$	−7.00752			−0.742795			−0.371398	−	0.928474i	$-0.621121\pi$
$89$	−7.00752			−0.742795			−0.371398	+	0.928474i	$0.621121\pi$
$90$		0			0
$91$	−0.237705	+	9.53643i	−0.0249182	+	0.999689i
$92$	2.16961			0.226197
$93$		0			0
$94$	−2.44070	−	4.22742i	−0.251739	−	0.436025i
$95$	18.3767			1.88541
$96$		0			0
$97$	−4.92513	−	8.53057i	−0.500071	−	0.866149i	−1.00000		8.21569e-5i	$-0.999974\pi$
$97$	−4.92513	−	8.53057i	−0.500071	−	0.866149i	0.499929	−	0.866066i	$-0.333359\pi$
$98$	−6.90136	−	1.17099i	−0.697143	−	0.118287i
$99$		0			0
$100$	−3.65372	+	6.32843i	−0.365372	+	0.632843i
$101$	6.91016	+	11.9687i	0.687586	+	1.19093i	0.972616	+	0.232416i	$0.0746631\pi$
$101$	6.91016	+	11.9687i	0.687586	+	1.19093i	−0.285030	+	0.958519i	$0.592004\pi$
$102$		0			0
$103$	−6.56658	−	11.3737i	−0.647025	−	1.12068i	−0.983830	−	0.179105i	$-0.942680\pi$
$103$	−6.56658	−	11.3737i	−0.647025	−	1.12068i	0.336805	−	0.941574i	$-0.390654\pi$
$104$	0.213022	+	3.59925i	0.0208885	+	0.352936i
$105$		0			0
$106$	−1.05395	+	1.82549i	−0.102368	+	0.177307i
$107$	9.76463			0.943983			0.471991	−	0.881603i	$-0.343535\pi$
$107$	9.76463			0.943983			0.471991	+	0.881603i	$0.343535\pi$
$108$		0			0
$109$	1.14786	−	1.98816i	0.109945	−	0.190431i	−0.805803	−	0.592184i	$-0.798266\pi$
$109$	1.14786	−	1.98816i	0.109945	−	0.190431i	0.915748	+	0.401753i	$0.131599\pi$
$110$	11.2399	−	19.4682i	1.07169	−	1.85622i
$111$		0			0
$112$	−2.63641	−	0.222079i	−0.249118	−	0.0209845i
$113$	−1.96268	−	3.39947i	−0.184634	−	0.319795i	0.758819	−	0.651301i	$-0.225777\pi$
$113$	−1.96268	−	3.39947i	−0.184634	−	0.319795i	−0.943453	+	0.331506i	$0.892443\pi$
$114$		0			0
$115$	−3.80571	−	6.59168i	−0.354884	−	0.614677i
$116$	1.23033	−	2.13099i	0.114233	−	0.197858i
$117$		0			0
$118$	−11.7946			−1.08578
$119$	12.3326	+	1.03884i	1.13053	+	0.0952306i
$120$		0			0
$121$	−15.0301	+	26.0329i	−1.36637	+	2.36662i
$122$	4.67781	−	8.10220i	0.423509	−	0.733539i
$123$		0			0
$124$	4.46035	−	7.72555i	0.400551	−	0.693774i
$125$	8.09497			0.724036
$126$		0			0
$127$	3.51196	−	6.08289i	0.311636	−	0.539769i	−0.667081	−	0.744985i	$-0.732457\pi$
$127$	3.51196	−	6.08289i	0.311636	−	0.539769i	0.978717	+	0.205216i	$0.0657898\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	10.5615	−	6.96065i	0.926309	−	0.610489i
$131$	4.56251	+	7.90250i	0.398628	+	0.690444i	0.993557	−	0.113334i	$-0.0361531\pi$
$131$	4.56251	+	7.90250i	0.398628	+	0.690444i	−0.594929	+	0.803778i	$0.702820\pi$
$132$		0			0
$133$	7.91249	−	11.3782i	0.686100	−	0.986619i
$134$	3.64461	+	6.31265i	0.314846	+	0.545330i
$135$		0			0
$136$	4.67781			0.401119
$137$	−15.0674			−1.28730			−0.643648	−	0.765322i	$-0.722580\pi$
$137$	−15.0674			−1.28730			−0.643648	+	0.765322i	$0.722580\pi$
$138$		0			0
$139$	7.02519	+	12.1680i	0.595869	+	1.03208i	0.993424	+	0.114497i	$0.0365255\pi$
$139$	7.02519	+	12.1680i	0.595869	+	1.03208i	−0.397555	+	0.917578i	$0.630141\pi$
$140$	3.94981	+	8.39947i	0.333820	+	0.709885i
$141$		0			0
$142$	2.79339	+	4.83829i	0.234416	+	0.406020i
$143$	−19.2910	+	12.7138i	−1.61319	+	1.06318i
$144$		0			0
$145$	−8.63248			−0.716889
$146$	−4.23175	+	7.32961i	−0.350222	+	0.606603i
$147$		0			0
$148$	3.89962			0.320547
$149$	0.614668	−	1.06464i	0.0503555	−	0.0872183i	−0.839749	−	0.542975i	$-0.817298\pi$
$149$	0.614668	−	1.06464i	0.0503555	−	0.0872183i	0.890104	+	0.455757i	$0.150631\pi$
$150$		0			0
$151$	8.17245	−	14.1551i	0.665065	−	1.15193i	−0.314203	−	0.949356i	$-0.601737\pi$
$151$	8.17245	−	14.1551i	0.665065	−	1.15193i	0.979268	−	0.202570i	$-0.0649294\pi$
$152$	2.61911	−	4.53642i	0.212438	−	0.367953i
$153$		0			0
$154$	−7.21444	−	15.3419i	−0.581356	−	1.23628i
$155$	−31.2955			−2.51372
$156$		0			0
$157$	−7.98494	+	13.8303i	−0.637267	+	1.10378i	0.348763	+	0.937211i	$0.386602\pi$
$157$	−7.98494	+	13.8303i	−0.637267	+	1.10378i	−0.986030	+	0.166568i	$0.946731\pi$
$158$	−0.893764	−	1.54804i	−0.0711040	−	0.123156i
$159$		0			0
$160$	1.75410	+	3.03819i	0.138674	+	0.240190i
$161$	−5.71999	−	0.481825i	−0.450798	−	0.0379731i
$162$		0			0
$163$	−3.89316	+	6.74316i	−0.304936	+	0.528165i	−0.977247	−	0.212104i	$-0.931968\pi$
$163$	−3.89316	+	6.74316i	−0.304936	+	0.528165i	0.672311	+	0.740269i	$0.265302\pi$
$164$	−5.09300	+	8.82134i	−0.397697	+	0.688831i
$165$		0			0
$166$	−2.59218			−0.201192
$167$	−3.32333	+	5.75618i	−0.257167	+	0.445427i	−0.965482	−	0.260470i	$-0.916122\pi$
$167$	−3.32333	+	5.75618i	−0.257167	+	0.445427i	0.708315	+	0.705897i	$0.249456\pi$
$168$		0			0
$169$	−12.9092	+	1.53344i	−0.993019	+	0.117957i
$170$	−8.20533	−	14.2121i	−0.629320	−	1.09001i
$171$		0			0
$172$	−1.19338	−	2.06699i	−0.0909942	−	0.157607i
$173$	−7.30337	+	12.6498i	−0.555265	+	0.961747i	0.442618	+	0.896710i	$0.354050\pi$
$173$	−7.30337	+	12.6498i	−0.555265	+	0.961747i	−0.997883	+	0.0650369i	$0.979283\pi$
$174$		0			0
$175$	11.0381	−	15.8730i	0.834405	−	1.19988i
$176$	−3.20391	−	5.54934i	−0.241504	−	0.418297i
$177$		0			0
$178$	7.00752			0.525236
$179$	−7.06425	−	12.2356i	−0.528006	−	0.914534i	−0.999467	−	0.0326468i	$-0.989606\pi$
$179$	−7.06425	−	12.2356i	−0.528006	−	0.914534i	0.471460	−	0.881887i	$-0.343727\pi$
$180$		0			0
$181$	−13.6453			−1.01425			−0.507124	−	0.861873i	$-0.669291\pi$
$181$	−13.6453			−1.01425			−0.507124	+	0.861873i	$0.669291\pi$
$182$	0.237705	−	9.53643i	0.0176198	−	0.706887i
$183$		0			0
$184$	−2.16961			−0.159946
$185$	−6.84033	−	11.8478i	−0.502911	−	0.871067i
$186$		0			0
$187$	14.9873	+	25.9587i	1.09598	+	1.89829i
$188$	2.44070	+	4.22742i	0.178006	+	0.308316i
$189$		0			0
$190$	−18.3767			−1.33318
$191$	−1.21572	+	2.10569i	−0.0879666	+	0.152363i	−0.906652	−	0.421880i	$-0.861370\pi$
$191$	−1.21572	+	2.10569i	−0.0879666	+	0.152363i	0.818685	+	0.574243i	$0.194704\pi$
$192$		0			0
$193$	−1.75877	−	3.04628i	−0.126599	−	0.219276i	0.795758	−	0.605615i	$-0.207073\pi$
$193$	−1.75877	−	3.04628i	−0.126599	−	0.219276i	−0.922357	+	0.386339i	$0.873740\pi$
$194$	4.92513	+	8.53057i	0.353604	+	0.612460i
$195$		0			0
$196$	6.90136	+	1.17099i	0.492954	+	0.0836418i
$197$	−1.15702	+	2.00402i	−0.0824345	+	0.142781i	−0.904295	−	0.426908i	$-0.859603\pi$
$197$	−1.15702	+	2.00402i	−0.0824345	+	0.142781i	0.821861	+	0.569689i	$0.192936\pi$
$198$		0			0
$199$	5.69467			0.403684			0.201842	−	0.979418i	$-0.435307\pi$
$199$	5.69467			0.403684			0.201842	+	0.979418i	$0.435307\pi$
$200$	3.65372	−	6.32843i	0.258357	−	0.447488i
$201$		0			0
$202$	−6.91016	−	11.9687i	−0.486197	−	0.842118i
$203$	−3.71691	+	5.34495i	−0.260876	+	0.375142i
$204$		0			0
$205$	35.7345			2.49581
$206$	6.56658	+	11.3737i	0.457515	+	0.792440i
$207$		0			0
$208$	−0.213022	−	3.59925i	−0.0147704	−	0.249563i
$209$	33.5655			2.32178
$210$		0			0
$211$	0.291966	−	0.505700i	0.0200998	−	0.0348139i	−0.855801	−	0.517306i	$-0.826935\pi$
$211$	0.291966	−	0.505700i	0.0200998	−	0.0348139i	0.875900	+	0.482492i	$0.160268\pi$
$212$	1.05395	−	1.82549i	0.0723853	−	0.125375i
$213$		0			0
$214$	−9.76463			−0.667496
$215$	−4.18660	+	7.25141i	−0.285524	+	0.494542i
$216$		0			0
$217$	−13.4750	+	19.3772i	−0.914743	+	1.31541i
$218$	−1.14786	+	1.98816i	−0.0777430	+	0.134655i
$219$		0			0
$220$	−11.2399	+	19.4682i	−0.757797	+	1.31254i
$221$	0.996476	+	16.8366i	0.0670302	+	1.13255i
$222$		0			0
$223$	−7.25749	+	12.5703i	−0.485998	+	0.841773i	−0.999870	−	0.0160938i	$-0.994877\pi$
$223$	−7.25749	+	12.5703i	−0.485998	+	0.841773i	0.513873	+	0.857866i	$0.328210\pi$
$224$	2.63641	+	0.222079i	0.176153	+	0.0148383i
$225$		0			0
$226$	1.96268	+	3.39947i	0.130556	+	0.226129i
$227$	−20.2464			−1.34380			−0.671899	−	0.740643i	$-0.734521\pi$
$227$	−20.2464			−1.34380			−0.671899	+	0.740643i	$0.734521\pi$
$228$		0			0
$229$	−0.668929	−	1.15862i	−0.0442041	−	0.0765637i	0.843077	−	0.537793i	$-0.180742\pi$
$229$	−0.668929	−	1.15862i	−0.0442041	−	0.0765637i	−0.887281	+	0.461229i	$0.847409\pi$
$230$	3.80571	+	6.59168i	0.250941	+	0.434643i
$231$		0			0
$232$	−1.23033	+	2.13099i	−0.0807752	+	0.139907i
$233$	−6.97568	−	12.0822i	−0.456992	−	0.791534i	0.541808	−	0.840502i	$-0.317740\pi$
$233$	−6.97568	−	12.0822i	−0.456992	−	0.791534i	−0.998800	+	0.0489686i	$0.984407\pi$
$234$		0			0
$235$	8.56246	−	14.8306i	0.558553	−	0.967443i
$236$	11.7946			0.767761
$237$		0			0
$238$	−12.3326	−	1.03884i	−0.799406	−	0.0673382i
$239$	−9.05495			−0.585716			−0.292858	−	0.956156i	$-0.594606\pi$
$239$	−9.05495			−0.585716			−0.292858	+	0.956156i	$0.594606\pi$
$240$		0			0
$241$	20.1102			1.29541			0.647705	−	0.761891i	$-0.275729\pi$
$241$	20.1102			1.29541			0.647705	+	0.761891i	$0.275729\pi$
$242$	15.0301	−	26.0329i	0.966171	−	1.67346i
$243$		0			0
$244$	−4.67781	+	8.10220i	−0.299466	+	0.518690i
$245$	−8.54799	−	23.0217i	−0.546111	−	1.47080i
$246$		0			0
$247$	16.8857	+	8.46047i	1.07441	+	0.538327i
$248$	−4.46035	+	7.72555i	−0.283232	+	0.490573i
$249$		0			0
$250$	−8.09497			−0.511971
$251$	−4.09035	−	7.08469i	−0.258181	−	0.447182i	0.707574	−	0.706639i	$-0.249790\pi$
$251$	−4.09035	−	7.08469i	−0.258181	−	0.447182i	−0.965755	+	0.259457i	$0.916456\pi$
$252$		0			0
$253$	−6.95123	−	12.0399i	−0.437020	−	0.756941i
$254$	−3.51196	+	6.08289i	−0.220360	+	0.381674i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−9.75393			−0.608433			−0.304217	−	0.952603i	$-0.598395\pi$
$257$	−9.75393			−0.608433			−0.304217	+	0.952603i	$0.598395\pi$
$258$		0			0
$259$	−10.2810	−	0.866025i	−0.638832	−	0.0538122i
$260$	−10.5615	+	6.96065i	−0.654999	+	0.431681i
$261$		0			0
$262$	−4.56251	−	7.90250i	−0.281873	−	0.488218i
$263$	−1.47358	−	2.55232i	−0.0908648	−	0.157383i	0.817010	−	0.576623i	$-0.195630\pi$
$263$	−1.47358	−	2.55232i	−0.0908648	−	0.157383i	−0.907875	+	0.419240i	$0.862296\pi$
$264$		0			0
$265$	−7.39490			−0.454265
$266$	−7.91249	+	11.3782i	−0.485146	+	0.697645i
$267$		0			0
$268$	−3.64461	−	6.31265i	−0.222630	−	0.385607i
$269$	23.9353			1.45936			0.729679	−	0.683790i	$-0.239669\pi$
$269$	23.9353			1.45936			0.729679	+	0.683790i	$0.239669\pi$
$270$		0			0
$271$	19.3667			1.17644			0.588222	−	0.808700i	$-0.299828\pi$
$271$	19.3667			1.17644			0.588222	+	0.808700i	$0.299828\pi$
$272$	−4.67781			−0.283634
$273$		0			0
$274$	15.0674			0.910255
$275$	46.8248			2.82364
$276$		0			0
$277$	2.43419			0.146256			0.0731282	−	0.997323i	$-0.476702\pi$
$277$	2.43419			0.146256			0.0731282	+	0.997323i	$0.476702\pi$
$278$	−7.02519	−	12.1680i	−0.421343	−	0.729787i
$279$		0			0
$280$	−3.94981	−	8.39947i	−0.236046	−	0.501964i
$281$	2.80329			0.167230			0.0836152	−	0.996498i	$-0.473353\pi$
$281$	2.80329			0.167230			0.0836152	+	0.996498i	$0.473353\pi$
$282$		0			0
$283$	8.47705	+	14.6827i	0.503909	+	0.872795i	0.999990	+	0.00451916i	$0.00143850\pi$
$283$	8.47705	+	14.6827i	0.503909	+	0.872795i	−0.496081	+	0.868276i	$0.665228\pi$
$284$	−2.79339	−	4.83829i	−0.165757	−	0.287100i
$285$		0			0
$286$	19.2910	−	12.7138i	1.14070	−	0.751784i
$287$	15.3863	−	22.1257i	0.908224	−	1.30604i
$288$		0			0
$289$	4.88187			0.287169
$290$	8.63248			0.506917
$291$		0			0
$292$	4.23175	−	7.32961i	0.247645	−	0.428933i
$293$	−2.84568	−	4.92886i	−0.166246	−	0.287947i	0.770851	−	0.637016i	$-0.219831\pi$
$293$	−2.84568	−	4.92886i	−0.166246	−	0.287947i	−0.937097	+	0.349069i	$0.886498\pi$
$294$		0			0
$295$	−20.6888	−	35.8341i	−1.20455	−	2.08634i
$296$	−3.89962			−0.226661
$297$		0			0
$298$	−0.614668	+	1.06464i	−0.0356067	+	0.0616727i
$299$	−0.462175	−	7.80897i	−0.0267283	−	0.451605i
$300$		0			0
$301$	2.68720	+	5.71447i	0.154888	+	0.329376i
$302$	−8.17245	+	14.1551i	−0.470272	+	0.814535i
$303$		0			0
$304$	−2.61911	+	4.53642i	−0.150216	+	0.260182i
$305$	32.8213			1.87934
$306$		0			0
$307$	3.48603			0.198958			0.0994791	−	0.995040i	$-0.468282\pi$
$307$	3.48603			0.198958			0.0994791	+	0.995040i	$0.468282\pi$
$308$	7.21444	+	15.3419i	0.411081	+	0.874184i
$309$		0			0
$310$	31.2955			1.77747
$311$	−12.0016	+	20.7873i	−0.680546	+	1.17874i	0.294268	+	0.955723i	$0.404924\pi$
$311$	−12.0016	+	20.7873i	−0.680546	+	1.17874i	−0.974814	+	0.223018i	$0.928409\pi$
$312$		0			0
$313$	−8.77758	−	15.2032i	−0.496138	−	0.859337i	0.503852	−	0.863790i	$-0.331916\pi$
$313$	−8.77758	−	15.2032i	−0.496138	−	0.859337i	−0.999990	+	0.00445337i	$0.998582\pi$
$314$	7.98494	−	13.8303i	0.450616	−	0.780490i
$315$		0			0
$316$	0.893764	+	1.54804i	0.0502781	+	0.0870843i
$317$	1.42018	+	2.45983i	0.0797655	+	0.138158i	0.903149	−	0.429328i	$-0.141250\pi$
$317$	1.42018	+	2.45983i	0.0797655	+	0.138158i	−0.823383	+	0.567486i	$0.807916\pi$
$318$		0			0
$319$	−15.7675			−0.882809
$320$	−1.75410	−	3.03819i	−0.0980571	−	0.169840i
$321$		0			0
$322$	5.71999	+	0.481825i	0.318763	+	0.0268511i
$323$	12.2517	−	21.2205i	0.681701	−	1.18074i
$324$		0			0
$325$	23.5560	+	11.8026i	1.30665	+	0.654689i
$326$	3.89316	−	6.74316i	0.215622	−	0.373469i
$327$		0			0
$328$	5.09300	−	8.82134i	0.281214	−	0.487077i
$329$	−5.49588	−	11.6873i	−0.302998	−	0.644339i
$330$		0			0
$331$	9.43745	−	16.3461i	0.518729	−	0.898465i	−0.481034	−	0.876702i	$-0.659739\pi$
$331$	9.43745	−	16.3461i	0.518729	−	0.898465i	0.999763	−	0.0217633i	$-0.00692802\pi$
$332$	2.59218			0.142264
$333$		0			0
$334$	3.32333	−	5.75618i	0.181845	−	0.314964i
$335$	−12.7860	+	22.1460i	−0.698575	+	1.20997i
$336$		0			0
$337$	10.9560			0.596813			0.298407	−	0.954439i	$-0.403545\pi$
$337$	10.9560			0.596813			0.298407	+	0.954439i	$0.403545\pi$
$338$	12.9092	−	1.53344i	0.702170	−	0.0834082i
$339$		0			0
$340$	8.20533	+	14.2121i	0.444997	+	0.770757i
$341$	−57.1622			−3.09551
$342$		0			0
$343$	−17.9348	−	4.61985i	−0.968388	−	0.249449i
$344$	1.19338	+	2.06699i	0.0643426	+	0.111445i
$345$		0			0
$346$	7.30337	−	12.6498i	0.392632	−	0.680058i
$347$	32.1029			1.72338			0.861688	−	0.507438i	$-0.169408\pi$
$347$	32.1029			1.72338			0.861688	+	0.507438i	$0.169408\pi$
$348$		0			0
$349$	−9.04373	+	15.6642i	−0.484100	+	0.838485i	−0.999833	−	0.0182638i	$-0.994186\pi$
$349$	−9.04373	+	15.6642i	−0.484100	+	0.838485i	0.515734	+	0.856749i	$0.327519\pi$
$350$	−11.0381	+	15.8730i	−0.590013	+	0.848445i
$351$		0			0
$352$	3.20391	+	5.54934i	0.170769	+	0.295781i
$353$	−13.7323	−	23.7850i	−0.730894	−	1.26595i	−0.956501	−	0.291728i	$-0.905770\pi$
$353$	−13.7323	−	23.7850i	−0.730894	−	1.26595i	0.225607	−	0.974218i	$-0.427564\pi$
$354$		0			0
$355$	−9.79976	+	16.9737i	−0.520117	+	0.900869i
$356$	−7.00752			−0.371398
$357$		0			0
$358$	7.06425	+	12.2356i	0.373357	+	0.646673i
$359$	10.8390	+	18.7738i	0.572063	+	0.990842i	0.996354	+	0.0853162i	$0.0271900\pi$
$359$	10.8390	+	18.7738i	0.572063	+	0.990842i	−0.424291	+	0.905526i	$0.639477\pi$
$360$		0			0
$361$	−4.21943	−	7.30827i	−0.222075	−	0.384646i
$362$	13.6453			0.717181
$363$		0			0
$364$	−0.237705	+	9.53643i	−0.0124591	+	0.499845i
$365$	−29.6916			−1.55413
$366$		0			0
$367$	−7.66086	−	13.2690i	−0.399894	−	0.692636i	0.593819	−	0.804599i	$-0.297620\pi$
$367$	−7.66086	−	13.2690i	−0.399894	−	0.692636i	−0.993712	+	0.111963i	$0.964286\pi$
$368$	2.16961			0.113099
$369$		0			0
$370$	6.84033	+	11.8478i	0.355612	+	0.615937i
$371$	−3.18404	+	4.57868i	−0.165307	+	0.237713i
$372$		0			0
$373$	16.6792	−	28.8893i	0.863618	−	1.49583i	−0.00479550	−	0.999989i	$-0.501526\pi$
$373$	16.6792	−	28.8893i	0.863618	−	1.49583i	0.868413	−	0.495841i	$-0.165140\pi$
$374$	−14.9873	−	25.9587i	−0.774973	−	1.34229i
$375$		0			0
$376$	−2.44070	−	4.22742i	−0.125870	−	0.218012i
$377$	−7.93208	−	3.97432i	−0.408523	−	0.204688i
$378$		0			0
$379$	8.43868	−	14.6162i	0.433466	−	0.750785i	−0.563703	−	0.825977i	$-0.690624\pi$
$379$	8.43868	−	14.6162i	0.433466	−	0.750785i	0.997169	+	0.0751926i	$0.0239571\pi$
$380$	18.3767			0.942704
$381$		0			0
$382$	1.21572	−	2.10569i	0.0622018	−	0.107737i
$383$	10.7933	−	18.6945i	0.551512	−	0.955246i	−0.446654	−	0.894707i	$-0.647385\pi$
$383$	10.7933	−	18.6945i	0.551512	−	0.955246i	0.998166	−	0.0605395i	$-0.0192821\pi$
$384$		0			0
$385$	33.9566	−	48.8300i	1.73059	−	2.48861i
$386$	1.75877	+	3.04628i	0.0895191	+	0.155052i
$387$		0			0
$388$	−4.92513	−	8.53057i	−0.250036	−	0.433074i
$389$	−8.68908	+	15.0499i	−0.440554	+	0.763062i	−0.997731	−	0.0673322i	$-0.978551\pi$
$389$	−8.68908	+	15.0499i	−0.440554	+	0.763062i	0.557177	+	0.830394i	$0.311885\pi$
$390$		0			0
$391$	−10.1490			−0.513258
$392$	−6.90136	−	1.17099i	−0.348571	−	0.0591437i
$393$		0			0
$394$	1.15702	−	2.00402i	0.0582900	−	0.100961i
$395$	3.13550	−	5.43084i	0.157764	−	0.273255i
$396$		0			0
$397$	−2.93718	+	5.08734i	−0.147413	+	0.255326i	−0.930270	−	0.366874i	$-0.880428\pi$
$397$	−2.93718	+	5.08734i	−0.147413	+	0.255326i	0.782858	+	0.622201i	$0.213761\pi$
$398$	−5.69467			−0.285448
$399$		0			0
$400$	−3.65372	+	6.32843i	−0.182686	+	0.316422i
$401$	13.9771			0.697983			0.348992	−	0.937126i	$-0.386524\pi$
$401$	13.9771			0.697983			0.348992	+	0.937126i	$0.386524\pi$
$402$		0			0
$403$	−28.7563	−	14.4082i	−1.43246	−	0.717724i
$404$	6.91016	+	11.9687i	0.343793	+	0.595467i
$405$		0			0
$406$	3.71691	−	5.34495i	0.184467	−	0.265266i
$407$	−12.4940	−	21.6403i	−0.619307	−	1.07267i
$408$		0			0
$409$	−37.4897			−1.85375			−0.926873	−	0.375375i	$-0.877514\pi$
$409$	−37.4897			−1.85375			−0.926873	+	0.375375i	$0.877514\pi$
$410$	−35.7345			−1.76480
$411$		0			0
$412$	−6.56658	−	11.3737i	−0.323512	−	0.560340i
$413$	−31.0954	−	2.61933i	−1.53010	−	0.128889i
$414$		0			0
$415$	−4.54694	−	7.87553i	−0.223200	−	0.386594i
$416$	0.213022	+	3.59925i	0.0104443	+	0.176468i
$417$		0			0
$418$	−33.5655			−1.64174
$419$	16.9548	−	29.3665i	0.828294	−	1.43465i	−0.0710814	−	0.997471i	$-0.522645\pi$
$419$	16.9548	−	29.3665i	0.828294	−	1.43465i	0.899375	−	0.437177i	$-0.144022\pi$
$420$		0			0
$421$	−10.5503			−0.514192			−0.257096	−	0.966386i	$-0.582766\pi$
$421$	−10.5503			−0.514192			−0.257096	+	0.966386i	$0.582766\pi$
$422$	−0.291966	+	0.505700i	−0.0142127	+	0.0246171i
$423$		0			0
$424$	−1.05395	+	1.82549i	−0.0511842	+	0.0886536i
$425$	17.0914	−	29.6032i	0.829055	−	1.43597i
$426$		0			0
$427$	14.1320	−	20.3219i	0.683894	−	0.983446i
$428$	9.76463			0.471991
$429$		0			0
$430$	4.18660	−	7.25141i	0.201896	−	0.349694i
$431$	−12.8043	−	22.1777i	−0.616761	−	1.06826i	−0.990073	−	0.140555i	$-0.955111\pi$
$431$	−12.8043	−	22.1777i	−0.616761	−	1.06826i	0.373312	−	0.927706i	$-0.378222\pi$
$432$		0			0
$433$	3.68968	+	6.39071i	0.177315	+	0.307118i	0.940960	−	0.338518i	$-0.109926\pi$
$433$	3.68968	+	6.39071i	0.177315	+	0.307118i	−0.763645	+	0.645636i	$0.776592\pi$
$434$	13.4750	−	19.3772i	0.646821	−	0.930135i
$435$		0			0
$436$	1.14786	−	1.98816i	0.0549726	−	0.0952154i
$437$	−5.68244	+	9.84227i	−0.271828	+	0.470820i
$438$		0			0
$439$	−23.0510			−1.10016			−0.550082	−	0.835110i	$-0.685404\pi$
$439$	−23.0510			−1.10016			−0.550082	+	0.835110i	$0.685404\pi$
$440$	11.2399	−	19.4682i	0.535844	−	0.928108i
$441$		0			0
$442$	−0.996476	−	16.8366i	−0.0473975	−	0.800836i
$443$	−9.05605	−	15.6855i	−0.430266	−	0.745242i	0.566630	−	0.823972i	$-0.308247\pi$
$443$	−9.05605	−	15.6855i	−0.430266	−	0.745242i	−0.996896	+	0.0787300i	$0.974914\pi$
$444$		0			0
$445$	12.2919	+	21.2902i	0.582691	+	1.00925i
$446$	7.25749	−	12.5703i	0.343652	−	0.595223i
$447$		0			0
$448$	−2.63641	−	0.222079i	−0.124559	−	0.0104923i
$449$	9.23084	+	15.9883i	0.435630	+	0.754534i	0.997347	−	0.0727961i	$-0.0231922\pi$
$449$	9.23084	+	15.9883i	0.435630	+	0.754534i	−0.561717	+	0.827330i	$0.689859\pi$
$450$		0			0
$451$	65.2701			3.07345
$452$	−1.96268	−	3.39947i	−0.0923168	−	0.159897i
$453$		0			0
$454$	20.2464			0.950209
$455$	29.3904	−	16.0056i	1.37784	−	0.750356i
$456$		0			0
$457$	−17.8047			−0.832866			−0.416433	−	0.909166i	$-0.636720\pi$
$457$	−17.8047			−0.832866			−0.416433	+	0.909166i	$0.636720\pi$
$458$	0.668929	+	1.15862i	0.0312570	+	0.0541387i
$459$		0			0
$460$	−3.80571	−	6.59168i	−0.177442	−	0.307339i
$461$	2.51030	+	4.34797i	0.116916	+	0.202505i	0.918544	−	0.395318i	$-0.129366\pi$
$461$	2.51030	+	4.34797i	0.116916	+	0.202505i	−0.801628	+	0.597823i	$0.796032\pi$
$462$		0			0
$463$	−25.0075			−1.16220			−0.581099	−	0.813833i	$-0.697377\pi$
$463$	−25.0075			−1.16220			−0.581099	+	0.813833i	$0.697377\pi$
$464$	1.23033	−	2.13099i	0.0571167	−	0.0989290i
$465$		0			0
$466$	6.97568	+	12.0822i	0.323142	+	0.559699i
$467$	−12.9128	−	22.3656i	−0.597532	−	1.03496i	−0.993184	−	0.116555i	$-0.962815\pi$
$467$	−12.9128	−	22.3656i	−0.597532	−	1.03496i	0.395653	−	0.918400i	$-0.370518\pi$
$468$		0			0
$469$	8.20680	+	17.4522i	0.378955	+	0.805866i
$470$	−8.56246	+	14.8306i	−0.394957	+	0.684085i
$471$		0			0
$472$	−11.7946			−0.542889
$473$	−7.64695	+	13.2449i	−0.351607	+	0.609001i
$474$		0			0
$475$	−19.1390	−	33.1497i	−0.878156	−	1.52101i
$476$	12.3326	+	1.03884i	0.565265	+	0.0476153i
$477$		0			0
$478$	9.05495			0.414164
$479$	11.5569	+	20.0171i	0.528047	+	0.914604i	0.999465	+	0.0326944i	$0.0104088\pi$
$479$	11.5569	+	20.0171i	0.528047	+	0.914604i	−0.471418	+	0.881910i	$0.656258\pi$
$480$		0			0
$481$	−0.830706	−	14.0357i	−0.0378769	−	0.639974i
$482$	−20.1102			−0.915993
$483$		0			0
$484$	−15.0301	+	26.0329i	−0.683186	+	1.18331i
$485$	−17.2783	+	29.9269i	−0.784568	+	1.35891i
$486$		0			0
$487$	−16.2740			−0.737447			−0.368723	−	0.929539i	$-0.620205\pi$
$487$	−16.2740			−0.737447			−0.368723	+	0.929539i	$0.620205\pi$
$488$	4.67781	−	8.10220i	0.211754	−	0.366769i
$489$		0			0
$490$	8.54799	+	23.0217i	0.386159	+	1.04001i
$491$	19.0299	−	32.9608i	0.858809	−	1.48750i	−0.0142561	−	0.999898i	$-0.504538\pi$
$491$	19.0299	−	32.9608i	0.858809	−	1.48750i	0.873065	−	0.487603i	$-0.162129\pi$
$492$		0			0
$493$	−5.75525	+	9.96838i	−0.259203	+	0.448953i
$494$	−16.8857	−	8.46047i	−0.759722	−	0.380654i
$495$		0			0
$496$	4.46035	−	7.72555i	0.200275	−	0.346887i
$497$	6.29005	+	13.3761i	0.282147	+	0.600000i
$498$		0			0
$499$	17.1178	+	29.6489i	0.766297	+	1.32727i	0.939558	+	0.342389i	$0.111236\pi$
$499$	17.1178	+	29.6489i	0.766297	+	1.32727i	−0.173261	+	0.984876i	$0.555430\pi$
$500$	8.09497			0.362018
$501$		0			0
$502$	4.09035	+	7.08469i	0.182561	+	0.316205i
$503$	1.12053	+	1.94081i	0.0499619	+	0.0865365i	0.889925	−	0.456107i	$-0.150757\pi$
$503$	1.12053	+	1.94081i	0.0499619	+	0.0865365i	−0.839963	+	0.542644i	$0.817423\pi$
$504$		0			0
$505$	24.2422	−	41.9887i	1.07876	−	1.86847i
$506$	6.95123	+	12.0399i	0.309020	+	0.535238i
$507$		0			0
$508$	3.51196	−	6.08289i	0.155818	−	0.269884i
$509$	25.8328			1.14502			0.572509	−	0.819899i	$-0.305970\pi$
$509$	25.8328			1.14502			0.572509	+	0.819899i	$0.305970\pi$
$510$		0			0
$511$	−12.7844	+	18.3841i	−0.565549	+	0.813265i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	9.75393			0.430227
$515$	−23.0369	+	39.9010i	−1.01513	+	1.75825i
$516$		0			0
$517$	15.6396	−	27.0885i	0.687828	−	1.19135i
$518$	10.2810	+	0.866025i	0.451722	+	0.0380510i
$519$		0			0
$520$	10.5615	−	6.96065i	0.463154	−	0.305244i
$521$	12.1715	−	21.0817i	0.533245	−	0.923607i	−0.466001	−	0.884784i	$-0.654306\pi$
$521$	12.1715	−	21.0817i	0.533245	−	0.923607i	0.999246	−	0.0388230i	$-0.0123609\pi$
$522$		0			0
$523$	8.88709			0.388605			0.194303	−	0.980942i	$-0.437756\pi$
$523$	8.88709			0.388605			0.194303	+	0.980942i	$0.437756\pi$
$524$	4.56251	+	7.90250i	0.199314	+	0.345222i
$525$		0			0
$526$	1.47358	+	2.55232i	0.0642511	+	0.111286i
$527$	−20.8646	+	36.1386i	−0.908878	+	1.57422i
$528$		0			0
$529$	−18.2928			−0.795339
$530$	7.39490			0.321214
$531$		0			0
$532$	7.91249	−	11.3782i	0.343050	−	0.493310i
$533$	32.8351	+	16.4519i	1.42225	+	0.712609i
$534$		0			0
$535$	−17.1281	−	29.6668i	−0.740513	−	1.28261i
$536$	3.64461	+	6.31265i	0.157423	+	0.272665i
$537$		0			0
$538$	−23.9353			−1.03192
$539$	−15.6132	−	42.0497i	−0.672506	−	1.81121i
$540$		0			0
$541$	8.01702	+	13.8859i	0.344679	+	0.597001i	0.985295	−	0.170860i	$-0.0546545\pi$
$541$	8.01702	+	13.8859i	0.344679	+	0.597001i	−0.640617	+	0.767861i	$0.721321\pi$
$542$	−19.3667			−0.831871
$543$		0			0
$544$	4.67781			0.200559
$545$	−8.05385			−0.344989
$546$		0			0
$547$	−10.3955			−0.444481			−0.222240	−	0.974992i	$-0.571337\pi$
$547$	−10.3955			−0.444481			−0.222240	+	0.974992i	$0.571337\pi$
$548$	−15.0674			−0.643648
$549$		0			0
$550$	−46.8248			−1.99662
$551$	6.44473	+	11.1626i	0.274555	+	0.475543i
$552$		0			0
$553$	−2.01254	−	4.27977i	−0.0855821	−	0.181994i
$554$	−2.43419			−0.103419
$555$		0			0
$556$	7.02519	+	12.1680i	0.297934	+	0.516038i
$557$	16.1951	+	28.0508i	0.686209	+	1.18855i	0.973055	+	0.230572i	$0.0740598\pi$
$557$	16.1951	+	28.0508i	0.686209	+	1.18855i	−0.286846	+	0.957977i	$0.592607\pi$
$558$		0			0
$559$	−7.18540	+	4.73558i	−0.303910	+	0.200294i
$560$	3.94981	+	8.39947i	0.166910	+	0.354942i
$561$		0			0
$562$	−2.80329			−0.118250
$563$	2.43309			0.102543			0.0512713	−	0.998685i	$-0.483673\pi$
$563$	2.43309			0.102543			0.0512713	+	0.998685i	$0.483673\pi$
$564$		0			0
$565$	−6.88548	+	11.9260i	−0.289674	+	0.501730i
$566$	−8.47705	−	14.6827i	−0.356317	−	0.617159i
$567$		0			0
$568$	2.79339	+	4.83829i	0.117208	+	0.203010i
$569$	7.94066			0.332890			0.166445	−	0.986051i	$-0.446771\pi$
$569$	7.94066			0.332890			0.166445	+	0.986051i	$0.446771\pi$
$570$		0			0
$571$	18.0463	−	31.2571i	0.755214	−	1.30807i	−0.190054	−	0.981774i	$-0.560866\pi$
$571$	18.0463	−	31.2571i	0.755214	−	1.30807i	0.945268	−	0.326295i	$-0.105800\pi$
$572$	−19.2910	+	12.7138i	−0.806596	+	0.531591i
$573$		0			0
$574$	−15.3863	+	22.1257i	−0.642212	+	0.923507i
$575$	−7.92715	+	13.7302i	−0.330585	+	0.572590i
$576$		0			0
$577$	−16.3980	+	28.4021i	−0.682657	+	1.18240i	0.291510	+	0.956568i	$0.405842\pi$
$577$	−16.3980	+	28.4021i	−0.682657	+	1.18240i	−0.974167	+	0.225829i	$0.927491\pi$
$578$	−4.88187			−0.203059
$579$		0			0
$580$	−8.63248			−0.358444
$581$	−6.83406	−	0.575669i	−0.283524	−	0.0238828i
$582$		0			0
$583$	−13.5070			−0.559403
$584$	−4.23175	+	7.32961i	−0.175111	+	0.303301i
$585$		0			0
$586$	2.84568	+	4.92886i	0.117554	+	0.203609i
$587$	−10.9482	+	18.9629i	−0.451881	+	0.782681i	−0.998503	−	0.0546984i	$-0.982580\pi$
$587$	−10.9482	+	18.9629i	−0.451881	+	0.782681i	0.546622	+	0.837380i	$0.315914\pi$
$588$		0			0
$589$	23.3642	+	40.4680i	0.962707	+	1.66746i
$590$	20.6888	+	35.8341i	0.851746	+	1.47527i
$591$		0			0
$592$	3.89962			0.160274
$593$	−3.25002	−	5.62921i	−0.133463	−	0.231164i	0.791547	−	0.611109i	$-0.209276\pi$
$593$	−3.25002	−	5.62921i	−0.133463	−	0.231164i	−0.925009	+	0.379945i	$0.875943\pi$
$594$		0			0
$595$	−18.4765	−	39.2911i	−0.757461	−	1.61078i
$596$	0.614668	−	1.06464i	0.0251778	−	0.0436092i
$597$		0			0
$598$	0.462175	+	7.80897i	0.0188997	+	0.319333i
$599$	−1.40105	+	2.42668i	−0.0572452	+	0.0991516i	−0.893228	−	0.449604i	$-0.851565\pi$
$599$	−1.40105	+	2.42668i	−0.0572452	+	0.0991516i	0.835983	+	0.548756i	$0.184898\pi$
$600$		0			0
$601$	−11.8591	+	20.5405i	−0.483741	+	0.837864i	−0.999826	−	0.0186737i	$-0.994056\pi$
$601$	−11.8591	+	20.5405i	−0.483741	+	0.837864i	0.516085	+	0.856538i	$0.327389\pi$
$602$	−2.68720	−	5.71447i	−0.109522	−	0.232904i
$603$		0			0
$604$	8.17245	−	14.1551i	0.332532	−	0.575963i
$605$	105.457			4.28744
$606$		0			0
$607$	5.92151	−	10.2564i	0.240347	−	0.416293i	−0.720466	−	0.693490i	$-0.756072\pi$
$607$	5.92151	−	10.2564i	0.240347	−	0.416293i	0.960813	+	0.277197i	$0.0894055\pi$
$608$	2.61911	−	4.53642i	0.106219	−	0.183976i
$609$		0			0
$610$	−32.8213			−1.32890
$611$	14.6956	−	9.68523i	0.594521	−	0.391823i
$612$		0			0
$613$	8.09895	+	14.0278i	0.327114	+	0.566577i	0.981938	−	0.189204i	$-0.0605907\pi$
$613$	8.09895	+	14.0278i	0.327114	+	0.566577i	−0.654824	+	0.755781i	$0.727257\pi$
$614$	−3.48603			−0.140685
$615$		0			0
$616$	−7.21444	−	15.3419i	−0.290678	−	0.618142i
$617$	22.0973	+	38.2737i	0.889606	+	1.54084i	0.840342	+	0.542057i	$0.182354\pi$
$617$	22.0973	+	38.2737i	0.889606	+	1.54084i	0.0492637	+	0.998786i	$0.484313\pi$
$618$		0			0
$619$	−17.0272	+	29.4920i	−0.684383	+	1.18539i	0.289248	+	0.957254i	$0.406595\pi$
$619$	−17.0272	+	29.4920i	−0.684383	+	1.18539i	−0.973630	+	0.228131i	$0.926738\pi$
$620$	−31.2955			−1.25686
$621$		0			0
$622$	12.0016	−	20.7873i	0.481219	−	0.833496i
$623$	18.4747	+	1.55622i	0.740174	+	0.0623488i
$624$		0			0
$625$	4.06923	+	7.04812i	0.162769	+	0.281925i
$626$	8.77758	+	15.2032i	0.350823	+	0.607643i
$627$		0			0
$628$	−7.98494	+	13.8303i	−0.318634	+	0.551890i
$629$	−18.2417			−0.727344
$630$		0			0
$631$	−0.712707	−	1.23444i	−0.0283724	−	0.0491424i	0.851491	−	0.524370i	$-0.175699\pi$
$631$	−0.712707	−	1.23444i	−0.0283724	−	0.0491424i	−0.879863	+	0.475227i	$0.842366\pi$
$632$	−0.893764	−	1.54804i	−0.0355520	−	0.0615779i
$633$		0			0
$634$	−1.42018	−	2.45983i	−0.0564027	−	0.0976923i
$635$	−24.6413			−0.977859
$636$		0			0
$637$	2.74453	−	25.0892i	0.108742	−	0.994070i
$638$	15.7675			0.624240
$639$		0			0
$640$	1.75410	+	3.03819i	0.0693368	+	0.120095i
$641$	23.2001			0.916350			0.458175	−	0.888862i	$-0.348503\pi$
$641$	23.2001			0.916350			0.458175	+	0.888862i	$0.348503\pi$
$642$		0			0
$643$	3.41821	+	5.92052i	0.134801	+	0.233482i	0.925521	−	0.378695i	$-0.123627\pi$
$643$	3.41821	+	5.92052i	0.134801	+	0.233482i	−0.790720	+	0.612178i	$0.790294\pi$
$644$	−5.71999	−	0.481825i	−0.225399	−	0.0189866i
$645$		0			0
$646$	−12.2517	+	21.2205i	−0.482036	+	0.834910i
$647$	−21.2982	−	36.8896i	−0.837320	−	1.45028i	−0.892127	−	0.451784i	$-0.850788\pi$
$647$	−21.2982	−	36.8896i	−0.837320	−	1.45028i	0.0548069	−	0.998497i	$-0.482546\pi$
$648$		0			0
$649$	−37.7888	−	65.4521i	−1.48334	−	2.56922i
$650$	−23.5560	−	11.8026i	−0.923941	−	0.462935i
$651$		0			0
$652$	−3.89316	+	6.74316i	−0.152468	+	0.264082i
$653$	39.4447			1.54359			0.771794	−	0.635872i	$-0.219360\pi$
$653$	39.4447			1.54359			0.771794	+	0.635872i	$0.219360\pi$
$654$		0			0
$655$	16.0062	−	27.7235i	0.625413	−	1.08325i
$656$	−5.09300	+	8.82134i	−0.198848	+	0.344415i
$657$		0			0
$658$	5.49588	+	11.6873i	0.214252	+	0.455617i
$659$	−0.667872	−	1.15679i	−0.0260166	−	0.0450621i	0.852724	−	0.522362i	$-0.174949\pi$
$659$	−0.667872	−	1.15679i	−0.0260166	−	0.0450621i	−0.878741	+	0.477300i	$0.841616\pi$
$660$		0			0
$661$	6.44661	+	11.1659i	0.250744	+	0.434301i	0.963731	−	0.266876i	$-0.0859914\pi$
$661$	6.44661	+	11.1659i	0.250744	+	0.434301i	−0.712987	+	0.701177i	$0.752658\pi$
$662$	−9.43745	+	16.3461i	−0.366797	+	0.635311i
$663$		0			0
$664$	−2.59218			−0.100596
$665$	−48.4485	−	4.08108i	−1.87875	−	0.158257i
$666$		0			0
$667$	2.66934	−	4.62343i	0.103357	−	0.179020i
$668$	−3.32333	+	5.75618i	−0.128584	+	0.222713i
$669$		0			0
$670$	12.7860	−	22.1460i	0.493967	−	0.855576i
$671$	59.9491			2.31431
$672$		0			0
$673$	−13.8759	+	24.0338i	−0.534877	+	0.926434i	0.464292	+	0.885682i	$0.346309\pi$
$673$	−13.8759	+	24.0338i	−0.534877	+	0.926434i	−0.999169	+	0.0407519i	$0.987025\pi$
$674$	−10.9560			−0.422011
$675$		0			0
$676$	−12.9092	+	1.53344i	−0.496509	+	0.0589785i
$677$	1.50219	+	2.60188i	0.0577340	+	0.0999982i	0.893448	−	0.449167i	$-0.148279\pi$
$677$	1.50219	+	2.60188i	0.0577340	+	0.0999982i	−0.835714	+	0.549165i	$0.814946\pi$
$678$		0			0
$679$	11.0902	+	23.5839i	0.425604	+	0.905067i
$680$	−8.20533	−	14.2121i	−0.314660	−	0.545007i
$681$		0			0
$682$	57.1622			2.18885
$683$	14.8693			0.568959			0.284480	−	0.958682i	$-0.408179\pi$
$683$	14.8693			0.568959			0.284480	+	0.958682i	$0.408179\pi$
$684$		0			0
$685$	26.4297	+	45.7776i	1.00983	+	1.74907i
$686$	17.9348	+	4.61985i	0.684754	+	0.176387i
$687$		0			0
$688$	−1.19338	−	2.06699i	−0.0454971	−	0.0788033i
$689$	−6.79491	−	3.40455i	−0.258865	−	0.129703i
$690$		0			0
$691$	8.38107			0.318831			0.159415	−	0.987212i	$-0.449039\pi$
$691$	8.38107			0.318831			0.159415	+	0.987212i	$0.449039\pi$
$692$	−7.30337	+	12.6498i	−0.277633	+	0.480874i
$693$		0			0
$694$	−32.1029			−1.21861
$695$	24.6457	−	42.6877i	0.934867	−	1.61924i
$696$		0			0
$697$	23.8241	−	41.2645i	0.902401	−	1.56300i
$698$	9.04373	−	15.6642i	0.342310	−	0.592899i
$699$		0			0
$700$	11.0381	−	15.8730i	0.417203	−	0.599941i
$701$	−39.2809			−1.48362			−0.741809	−	0.670611i	$-0.766032\pi$
$701$	−39.2809			−1.48362			−0.741809	+	0.670611i	$0.766032\pi$
$702$		0			0
$703$	−10.2135	+	17.6904i	−0.385211	+	0.667204i
$704$	−3.20391	−	5.54934i	−0.120752	−	0.209148i
$705$		0			0
$706$	13.7323	+	23.7850i	0.516820	+	0.895159i
$707$	−15.5600	−	33.0892i	−0.585195	−	1.24445i
$708$		0			0
$709$	−9.66018	+	16.7319i	−0.362796	+	0.628381i	−0.988420	−	0.151744i	$-0.951511\pi$
$709$	−9.66018	+	16.7319i	−0.362796	+	0.628381i	0.625624	+	0.780125i	$0.284844\pi$
$710$	9.79976	−	16.9737i	0.367778	−	0.637011i
$711$		0			0
$712$	7.00752			0.262618
$713$	9.67721	−	16.7614i	0.362414	−	0.627720i
$714$		0			0
$715$	72.4652	+	36.3083i	2.71004	+	1.35785i
$716$	−7.06425	−	12.2356i	−0.264003	−	0.457267i
$717$		0			0
$718$	−10.8390	−	18.7738i	−0.404510	−	0.700631i
$719$	−14.2205	+	24.6306i	−0.530335	+	0.918567i	0.469039	+	0.883178i	$0.344600\pi$
$719$	−14.2205	+	24.6306i	−0.530335	+	0.918567i	−0.999374	+	0.0353892i	$0.988733\pi$
$720$		0			0
$721$	14.7864	+	31.4440i	0.550674	+	1.17103i
$722$	4.21943	+	7.30827i	0.157031	+	0.271986i
$723$		0			0
$724$	−13.6453			−0.507124
$725$	8.99057	+	15.5721i	0.333902	+	0.578334i
$726$		0			0
$727$	−48.4057			−1.79527			−0.897634	−	0.440741i	$-0.854716\pi$
$727$	−48.4057			−1.79527			−0.897634	+	0.440741i	$0.854716\pi$
$728$	0.237705	−	9.53643i	0.00880992	−	0.353444i
$729$		0			0
$730$	29.6916			1.09894
$731$	5.58239	+	9.66898i	0.206472	+	0.357620i
$732$		0			0
$733$	−3.69118	−	6.39332i	−0.136337	−	0.236143i	0.789770	−	0.613403i	$-0.210200\pi$
$733$	−3.69118	−	6.39332i	−0.136337	−	0.236143i	−0.926107	+	0.377260i	$0.876866\pi$
$734$	7.66086	+	13.2690i	0.282768	+	0.489768i
$735$		0			0
$736$	−2.16961			−0.0799729
$737$	−23.3540	+	40.4503i	−0.860256	+	1.49001i
$738$		0			0
$739$	−2.41213	−	4.17793i	−0.0887316	−	0.153688i	0.818244	−	0.574872i	$-0.194948\pi$
$739$	−2.41213	−	4.17793i	−0.0887316	−	0.153688i	−0.906975	+	0.421184i	$0.861615\pi$
$740$	−6.84033	−	11.8478i	−0.251455	−	0.435533i
$741$		0			0
$742$	3.18404	−	4.57868i	0.116890	−	0.168089i
$743$	−17.8556	+	30.9268i	−0.655059	+	1.13460i	0.326820	+	0.945087i	$0.394023\pi$
$743$	−17.8556	+	30.9268i	−0.655059	+	1.13460i	−0.981879	+	0.189509i	$0.939310\pi$
$744$		0			0
$745$	−4.31275			−0.158007
$746$	−16.6792	+	28.8893i	−0.610670	+	1.05771i
$747$		0			0
$748$	14.9873	+	25.9587i	0.547989	+	0.949145i
$749$	−25.7436	−	2.16852i	−0.940651	−	0.0792361i
$750$		0			0
$751$	13.0969			0.477913			0.238956	−	0.971030i	$-0.423195\pi$
$751$	13.0969			0.477913			0.238956	+	0.971030i	$0.423195\pi$
$752$	2.44070	+	4.22742i	0.0890032	+	0.154158i
$753$		0			0
$754$	7.93208	+	3.97432i	0.288869	+	0.144736i
$755$	−57.3411			−2.08686
$756$		0			0
$757$	−22.0344	+	38.1646i	−0.800852	+	1.38712i	0.118204	+	0.992989i	$0.462286\pi$
$757$	−22.0344	+	38.1646i	−0.800852	+	1.38712i	−0.919056	+	0.394127i	$0.871047\pi$
$758$	−8.43868	+	14.6162i	−0.306507	+	0.530885i
$759$		0			0
$760$	−18.3767			−0.666592
$761$	−4.30571	+	7.45771i	−0.156082	+	0.270342i	−0.933452	−	0.358701i	$-0.883220\pi$
$761$	−4.30571	+	7.45771i	−0.156082	+	0.270342i	0.777371	+	0.629043i	$0.216553\pi$
$762$		0			0
$763$	−3.46777	+	4.98669i	−0.125542	+	0.180530i
$764$	−1.21572	+	2.10569i	−0.0439833	+	0.0761814i
$765$		0			0
$766$	−10.7933	+	18.6945i	−0.389978	+	0.675461i
$767$	−2.51251	−	42.4517i	−0.0907213	−	1.53284i
$768$		0			0
$769$	−3.20391	+	5.54934i	−0.115536	+	0.200114i	−0.917994	−	0.396595i	$-0.870192\pi$
$769$	−3.20391	+	5.54934i	−0.115536	+	0.200114i	0.802458	+	0.596709i	$0.203525\pi$
$770$	−33.9566	+	48.8300i	−1.22371	+	1.75971i
$771$		0			0
$772$	−1.75877	−	3.04628i	−0.0632996	−	0.109638i
$773$	−12.5816			−0.452530			−0.226265	−	0.974066i	$-0.572652\pi$
$773$	−12.5816			−0.452530			−0.226265	+	0.974066i	$0.572652\pi$
$774$		0			0
$775$	32.5937	+	56.4540i	1.17080	+	2.02789i
$776$	4.92513	+	8.53057i	0.176802	+	0.306230i
$777$		0			0
$778$	8.68908	−	15.0499i	0.311519	−	0.539566i
$779$	−26.6782	−	46.2080i	−0.955846	−	1.65557i
$780$		0			0
$781$	−17.8995	+	31.0029i	−0.640496	+	1.10937i
$782$	10.1490			0.362928
$783$		0			0
$784$	6.90136	+	1.17099i	0.246477	+	0.0418209i
$785$	56.0255			1.99963
$786$		0			0
$787$	−19.2139			−0.684900			−0.342450	−	0.939536i	$-0.611257\pi$
$787$	−19.2139			−0.684900			−0.342450	+	0.939536i	$0.611257\pi$
$788$	−1.15702	+	2.00402i	−0.0412172	+	0.0713904i
$789$		0			0
$790$	−3.13550	+	5.43084i	−0.111556	+	0.193221i
$791$	4.41949	+	9.39827i	0.157139	+	0.334164i
$792$		0			0
$793$	30.1583	+	15.1107i	1.07095	+	0.536595i
$794$	2.93718	−	5.08734i	0.104237	−	0.180543i
$795$		0			0
$796$	5.69467			0.201842
$797$	8.43333	+	14.6070i	0.298724	+	0.517405i	0.975844	−	0.218467i	$-0.0701058\pi$
$797$	8.43333	+	14.6070i	0.298724	+	0.517405i	−0.677120	+	0.735872i	$0.736772\pi$
$798$		0			0
$799$	−11.4171	−	19.7750i	−0.403909	−	0.699591i
$800$	3.65372	−	6.32843i	0.129179	−	0.223744i
$801$		0			0
$802$	−13.9771			−0.493549
$803$	−54.2326			−1.91383
$804$		0			0
$805$	8.56955	+	18.2236i	0.302037	+	0.642296i
$806$	28.7563	+	14.4082i	1.01290	+	0.507507i
$807$		0			0
$808$	−6.91016	−	11.9687i	−0.243099	−	0.421059i
$809$	4.38025	+	7.58681i	0.154001	+	0.266738i	0.932695	−	0.360666i	$-0.117451\pi$
$809$	4.38025	+	7.58681i	0.154001	+	0.266738i	−0.778694	+	0.627404i	$0.784117\pi$
$810$		0			0
$811$	−32.7259			−1.14916			−0.574581	−	0.818448i	$-0.694835\pi$
$811$	−32.7259			−1.14916			−0.574581	+	0.818448i	$0.694835\pi$
$812$	−3.71691	+	5.34495i	−0.130438	+	0.187571i
$813$		0			0
$814$	12.4940	+	21.6403i	0.437916	+	0.758493i
$815$	27.3160			0.956837
$816$		0			0
$817$	12.5023			0.437401
$818$	37.4897			1.31080
$819$		0			0
$820$	35.7345			1.24790
$821$	−14.6951			−0.512863			−0.256432	−	0.966562i	$-0.582547\pi$
$821$	−14.6951			−0.512863			−0.256432	+	0.966562i	$0.582547\pi$
$822$		0			0
$823$	41.3989			1.44307			0.721537	−	0.692376i	$-0.243436\pi$
$823$	41.3989			1.44307			0.721537	+	0.692376i	$0.243436\pi$
$824$	6.56658	+	11.3737i	0.228758	+	0.396220i
$825$		0			0
$826$	31.0954	+	2.61933i	1.08195	+	0.0911381i
$827$	−37.8157			−1.31498			−0.657491	−	0.753462i	$-0.728382\pi$
$827$	−37.8157			−1.31498			−0.657491	+	0.753462i	$0.728382\pi$
$828$		0			0
$829$	−17.2120	−	29.8120i	−0.597796	−	1.03541i	−0.993146	−	0.116883i	$-0.962710\pi$
$829$	−17.2120	−	29.8120i	−0.597796	−	1.03541i	0.395349	−	0.918531i	$-0.370624\pi$
$830$	4.54694	+	7.87553i	0.157826	+	0.273363i
$831$		0			0
$832$	−0.213022	−	3.59925i	−0.00738521	−	0.124782i
$833$	−32.2832	−	5.47764i	−1.11855	−	0.189789i
$834$		0			0
$835$	23.3178			0.806946
$836$	33.5655			1.16089
$837$		0			0
$838$	−16.9548	+	29.3665i	−0.585692	+	1.01445i
$839$	0.709771	+	1.22936i	0.0245040	+	0.0424422i	0.878017	−	0.478629i	$-0.158866\pi$
$839$	0.709771	+	1.22936i	0.0245040	+	0.0424422i	−0.853513	+	0.521071i	$0.825533\pi$
$840$		0			0
$841$	11.4726	+	19.8711i	0.395606	+	0.685210i
$842$	10.5503			0.363588
$843$		0			0
$844$	0.291966	−	0.505700i	0.0100499	−	0.0174069i
$845$	27.3030	+	36.5309i	0.939251	+	1.25670i
$846$		0			0
$847$	45.4069	−	65.2956i	1.56020	−	2.24358i
$848$	1.05395	−	1.82549i	0.0361927	−	0.0626875i
$849$		0			0
$850$	−17.0914	+	29.6032i	−0.586230	+	1.01538i
$851$	8.46066			0.290028
$852$		0			0
$853$	36.8892			1.26306			0.631531	−	0.775351i	$-0.282427\pi$
$853$	36.8892			1.26306			0.631531	+	0.775351i	$0.282427\pi$
$854$	−14.1320	+	20.3219i	−0.483586	+	0.695401i
$855$		0			0
$856$	−9.76463			−0.333748
$857$	−13.9245	+	24.1180i	−0.475653	+	0.823855i	−0.999611	−	0.0278890i	$-0.991121\pi$
$857$	−13.9245	+	24.1180i	−0.475653	+	0.823855i	0.523958	+	0.851744i	$0.324455\pi$
$858$		0			0
$859$	−25.2862	−	43.7970i	−0.862754	−	1.49433i	−0.869260	−	0.494355i	$-0.835404\pi$
$859$	−25.2862	−	43.7970i	−0.862754	−	1.49433i	0.00650572	−	0.999979i	$-0.497929\pi$
$860$	−4.18660	+	7.25141i	−0.142762	+	0.247271i
$861$		0			0
$862$	12.8043	+	22.1777i	0.436116	+	0.755375i
$863$	−14.5501	−	25.2016i	−0.495293	−	0.857872i	0.504693	−	0.863299i	$-0.331606\pi$
$863$	−14.5501	−	25.2016i	−0.495293	−	0.857872i	−0.999985	+	0.00542701i	$0.998273\pi$
$864$		0			0
$865$	51.2433			1.74233
$866$	−3.68968	−	6.39071i	−0.125380	−	0.217165i
$867$		0			0
$868$	−13.4750	+	19.3772i	−0.457371	+	0.657705i
$869$	5.72708	−	9.91959i	0.194278	−	0.336499i
$870$		0			0
$871$	−21.9444	+	14.4626i	−0.743559	+	0.490047i
$872$	−1.14786	+	1.98816i	−0.0388715	+	0.0673275i
$873$		0			0
$874$	5.68244	−	9.84227i	0.192211	−	0.332920i
$875$	−21.3417	−	1.79773i	−0.721481	−	0.0607742i
$876$		0			0
$877$	−0.556332	+	0.963595i	−0.0187860	+	0.0325383i	−0.875266	−	0.483643i	$-0.839313\pi$
$877$	−0.556332	+	0.963595i	−0.0187860	+	0.0325383i	0.856480	+	0.516181i	$0.172647\pi$
$878$	23.0510			0.777934
$879$		0			0
$880$	−11.2399	+	19.4682i	−0.378899	+	0.656272i
$881$	8.14254	−	14.1033i	0.274329	−	0.475152i	−0.695636	−	0.718394i	$-0.744878\pi$
$881$	8.14254	−	14.1033i	0.274329	−	0.475152i	0.969966	+	0.243242i	$0.0782109\pi$
$882$		0			0
$883$	−37.0876			−1.24810			−0.624048	−	0.781386i	$-0.714513\pi$
$883$	−37.0876			−1.24810			−0.624048	+	0.781386i	$0.714513\pi$
$884$	0.996476	+	16.8366i	0.0335151	+	0.566276i
$885$		0			0
$886$	9.05605	+	15.6855i	0.304244	+	0.526966i
$887$	21.6055			0.725443			0.362722	−	0.931898i	$-0.381848\pi$
$887$	21.6055			0.725443			0.362722	+	0.931898i	$0.381848\pi$
$888$		0			0
$889$	−10.6099	+	15.2571i	−0.355843	+	0.511706i
$890$	−12.2919	−	21.2902i	−0.412025	−	0.713647i
$891$		0			0
$892$	−7.25749	+	12.5703i	−0.242999	+	0.420886i
$893$	−25.5698			−0.855661
$894$		0			0
$895$	−24.7828	+	42.9250i	−0.828396	+	1.43482i
$896$	2.63641	+	0.222079i	0.0880764	+	0.00741914i
$897$		0			0
$898$	−9.23084	−	15.9883i	−0.308037	−	0.533536i
$899$	−10.9754	−	19.0099i	−0.366050	−	0.634017i
$900$		0			0
$901$	−4.93016	+	8.53928i	−0.164247	+	0.284485i
$902$	−65.2701			−2.17326
$903$		0			0
$904$	1.96268	+	3.39947i	0.0652778	+	0.113065i
$905$	23.9352	+	41.4570i	0.795633	+	1.37808i
$906$		0			0
$907$	14.5270	+	25.1614i	0.482360	+	0.835472i	0.999795	−	0.0202508i	$-0.00644647\pi$
$907$	14.5270	+	25.1614i	0.482360	+	0.835472i	−0.517435	+	0.855722i	$0.673113\pi$
$908$	−20.2464			−0.671899
$909$		0			0
$910$	−29.3904	+	16.0056i	−0.974283	+	0.530582i
$911$	22.2791			0.738141			0.369071	−	0.929401i	$-0.379676\pi$
$911$	22.2791			0.738141			0.369071	+	0.929401i	$0.379676\pi$
$912$		0			0
$913$	−8.30511	−	14.3849i	−0.274859	−	0.476070i
$914$	17.8047			0.588926
$915$		0			0
$916$	−0.668929	−	1.15862i	−0.0221020	−	0.0382819i
$917$	−10.2737	−	21.8475i	−0.339267	−	0.721468i
$918$		0			0
$919$	17.5718	−	30.4352i	0.579639	−	1.00396i	−0.415882	−	0.909419i	$-0.636527\pi$
$919$	17.5718	−	30.4352i	0.579639	−	1.00396i	0.995521	−	0.0945453i	$-0.0301397\pi$
$920$	3.80571	+	6.59168i	0.125470	+	0.217321i
$921$		0			0
$922$	−2.51030	−	4.34797i	−0.0826723	−	0.143193i
$923$	−16.8192	+	11.0848i	−0.553610	+	0.364860i
$924$		0			0
$925$	−14.2481	+	24.6785i	−0.468476	+	0.811425i
$926$	25.0075			0.821798
$927$		0			0
$928$	−1.23033	+	2.13099i	−0.0403876	+	0.0699533i
$929$	−18.3722	+	31.8217i	−0.602774	+	1.04403i	0.389625	+	0.920973i	$0.372604\pi$
$929$	−18.3722	+	31.8217i	−0.602774	+	1.04403i	−0.992399	+	0.123061i	$0.960729\pi$
$930$		0			0
$931$	−23.3875	+	28.2406i	−0.766494	+	0.925547i
$932$	−6.97568	−	12.0822i	−0.228496	−	0.395767i
$933$		0			0
$934$	12.9128	+	22.3656i	0.422519	+	0.731824i
$935$	52.5783	−	91.0683i	1.71949	−	2.97825i
$936$		0			0
$937$	18.5284			0.605295			0.302647	−	0.953103i	$-0.402130\pi$
$937$	18.5284			0.605295			0.302647	+	0.953103i	$0.402130\pi$
$938$	−8.20680	−	17.4522i	−0.267961	−	0.569833i
$939$		0			0
$940$	8.56246	−	14.8306i	0.279277	−	0.483721i
$941$	−22.5985	+	39.1417i	−0.736689	+	1.27598i	0.217290	+	0.976107i	$0.430278\pi$
$941$	−22.5985	+	39.1417i	−0.736689	+	1.27598i	−0.953979	+	0.299875i	$0.903055\pi$
$942$		0			0
$943$	−11.0498	+	19.1389i	−0.359832	+	0.623247i
$944$	11.7946			0.383881
$945$		0			0
$946$	7.64695	−	13.2449i	0.248624	−	0.430629i
$947$	−28.8667			−0.938040			−0.469020	−	0.883187i	$-0.655393\pi$
$947$	−28.8667			−0.938040			−0.469020	+	0.883187i	$0.655393\pi$
$948$		0			0
$949$	−27.2826	−	13.6698i	−0.885630	−	0.443740i
$950$	19.1390	+	33.1497i	0.620950	+	1.07552i
$951$		0			0
$952$	−12.3326	−	1.03884i	−0.399703	−	0.0336691i
$953$	−8.36687	−	14.4919i	−0.271030	−	0.469437i	0.698096	−	0.716004i	$-0.254031\pi$
$953$	−8.36687	−	14.4919i	−0.271030	−	0.469437i	−0.969126	+	0.246567i	$0.920697\pi$
$954$		0			0
$955$	8.52999			0.276024
$956$	−9.05495			−0.292858
$957$		0			0
$958$	−11.5569	−	20.0171i	−0.373386	−	0.646723i
$959$	39.7239	+	3.34616i	1.28275	+	0.108053i
$960$		0			0
$961$	−24.2894	−	42.0704i	−0.783528	−	1.35711i
$962$	0.830706	+	14.0357i	0.0267830	+	0.452530i
$963$		0			0
$964$	20.1102			0.647705
$965$	−6.17012	+	10.6870i	−0.198623	+	0.344025i
$966$		0			0
$967$	−3.01759			−0.0970392			−0.0485196	−	0.998822i	$-0.515450\pi$
$967$	−3.01759			−0.0970392			−0.0485196	+	0.998822i	$0.515450\pi$
$968$	15.0301	−	26.0329i	0.483085	−	0.836728i
$969$		0			0
$970$	17.2783	−	29.9269i	0.554774	−	0.960896i
$971$	12.8401	−	22.2397i	0.412058	−	0.713706i	−0.583057	−	0.812432i	$-0.698143\pi$
$971$	12.8401	−	22.2397i	0.412058	−	0.713706i	0.995115	+	0.0987260i	$0.0314767\pi$
$972$		0			0
$973$	−15.8191	−	33.6400i	−0.507136	−	1.07845i
$974$	16.2740			0.521453
$975$		0			0
$976$	−4.67781	+	8.10220i	−0.149733	+	0.259345i
$977$	−20.3251	−	35.2041i	−0.650258	−	1.12628i	−0.983060	−	0.183283i	$-0.941327\pi$
$977$	−20.3251	−	35.2041i	−0.650258	−	1.12628i	0.332802	−	0.942997i	$-0.392006\pi$
$978$		0			0
$979$	22.4515	+	38.8871i	0.717552	+	1.24284i
$980$	−8.54799	−	23.0217i	−0.273056	−	0.735400i
$981$		0			0
$982$	−19.0299	+	32.9608i	−0.607270	+	1.05182i
$983$	2.39794	−	4.15335i	0.0764823	−	0.132471i	−0.825248	−	0.564771i	$-0.808964\pi$
$983$	2.39794	−	4.15335i	0.0764823	−	0.132471i	0.901730	+	0.432300i	$0.142298\pi$
$984$		0			0
$985$	8.11813			0.258665
$986$	5.75525	−	9.96838i	0.183284	−	0.317458i
$987$		0			0
$988$	16.8857	+	8.46047i	0.537205	+	0.269163i
$989$	−2.58916	−	4.48456i	−0.0823306	−	0.142601i
$990$		0			0
$991$	19.5715	+	33.8989i	0.621710	+	1.07683i	0.989167	+	0.146793i	$0.0468951\pi$
$991$	19.5715	+	33.8989i	0.621710	+	1.07683i	−0.367457	+	0.930040i	$0.619772\pi$
$992$	−4.46035	+	7.72555i	−0.141616	+	0.245286i
$993$		0			0
$994$	−6.29005	−	13.3761i	−0.199508	−	0.424264i
$995$	−9.98901	−	17.3015i	−0.316673	−	0.548494i
$996$		0			0
$997$	−57.4491			−1.81943			−0.909716	−	0.415232i	$-0.863701\pi$
$997$	−57.4491			−1.81943			−0.909716	+	0.415232i	$0.863701\pi$
$998$	−17.1178	−	29.6489i	−0.541854	−	0.938518i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.h.1621.1		8
3.2	odd	2		546.2.j.c.529.4	yes	8
7.2	even	3		1638.2.p.h.919.1		8
13.3	even	3		1638.2.p.h.991.1		8
21.2	odd	6		546.2.k.c.373.4	yes	8
39.29	odd	6		546.2.k.c.445.4	yes	8
91.16	even	3	inner	1638.2.m.h.289.1		8
273.107	odd	6		546.2.j.c.289.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.4	✓	8	273.107	odd	6
546.2.j.c.529.4	yes	8	3.2	odd	2
546.2.k.c.373.4	yes	8	21.2	odd	6
546.2.k.c.445.4	yes	8	39.29	odd	6
1638.2.m.h.289.1		8	91.16	even	3	inner
1638.2.m.h.1621.1		8	1.1	even	1	trivial
1638.2.p.h.919.1		8	7.2	even	3
1638.2.p.h.991.1		8	13.3	even	3

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.75410 - 3.03819i) q^{5} +(-2.63641 - 0.222079i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.75410 - 3.03819i) q^{5} +(-2.63641 - 0.222079i) q^{7} -1.00000 q^{8} +(1.75410 + 3.03819i) q^{10} +(-3.20391 - 5.54934i) q^{11} +(-0.213022 - 3.59925i) q^{13} +(2.63641 + 0.222079i) q^{14} +1.00000 q^{16} -4.67781 q^{17} +(-2.61911 + 4.53642i) q^{19} +(-1.75410 - 3.03819i) q^{20} +(3.20391 + 5.54934i) q^{22} +2.16961 q^{23} +(-3.65372 + 6.32843i) q^{25} +(0.213022 + 3.59925i) q^{26} +(-2.63641 - 0.222079i) q^{28} +(1.23033 - 2.13099i) q^{29} +(4.46035 - 7.72555i) q^{31} -1.00000 q^{32} +4.67781 q^{34} +(3.94981 + 8.39947i) q^{35} +3.89962 q^{37} +(2.61911 - 4.53642i) q^{38} +(1.75410 + 3.03819i) q^{40} +(-5.09300 + 8.82134i) q^{41} +(-1.19338 - 2.06699i) q^{43} +(-3.20391 - 5.54934i) q^{44} -2.16961 q^{46} +(2.44070 + 4.22742i) q^{47} +(6.90136 + 1.17099i) q^{49} +(3.65372 - 6.32843i) q^{50} +(-0.213022 - 3.59925i) q^{52} +(1.05395 - 1.82549i) q^{53} +(-11.2399 + 19.4682i) q^{55} +(2.63641 + 0.222079i) q^{56} +(-1.23033 + 2.13099i) q^{58} +11.7946 q^{59} +(-4.67781 + 8.10220i) q^{61} +(-4.46035 + 7.72555i) q^{62} +1.00000 q^{64} +(-10.5615 + 6.96065i) q^{65} +(-3.64461 - 6.31265i) q^{67} -4.67781 q^{68} +(-3.94981 - 8.39947i) q^{70} +(-2.79339 - 4.83829i) q^{71} +(4.23175 - 7.32961i) q^{73} -3.89962 q^{74} +(-2.61911 + 4.53642i) q^{76} +(7.21444 + 15.3419i) q^{77} +(0.893764 + 1.54804i) q^{79} +(-1.75410 - 3.03819i) q^{80} +(5.09300 - 8.82134i) q^{82} +2.59218 q^{83} +(8.20533 + 14.2121i) q^{85} +(1.19338 + 2.06699i) q^{86} +(3.20391 + 5.54934i) q^{88} -7.00752 q^{89} +(-0.237705 + 9.53643i) q^{91} +2.16961 q^{92} +(-2.44070 - 4.22742i) q^{94} +18.3767 q^{95} +(-4.92513 - 8.53057i) q^{97} +(-6.90136 - 1.17099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} + 2 q^{10} - 4 q^{11} + 3 q^{13} - 3 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{25} - 3 q^{26} + 3 q^{28} - 2 q^{29} + 14 q^{31} - 8 q^{32} + 4 q^{34} + 22 q^{35} + 12 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} - 8 q^{46} - 7 q^{47} + 5 q^{49} - 2 q^{50} + 3 q^{52} + q^{53} - 25 q^{55} - 3 q^{56} + 2 q^{58} + 32 q^{59} - 4 q^{61} - 14 q^{62} + 8 q^{64} - 10 q^{65} + 19 q^{67} - 4 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} - 12 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} - 2 q^{80} + 12 q^{82} + 64 q^{83} + 15 q^{85} + 4 q^{88} - 22 q^{89} - 38 q^{91} + 8 q^{92} + 7 q^{94} + 56 q^{95} + 11 q^{97} - 5 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 + 2 * q^10 - 4 * q^11 + 3 * q^13 - 3 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + 2 * q^25 - 3 * q^26 + 3 * q^28 - 2 * q^29 + 14 * q^31 - 8 * q^32 + 4 * q^34 + 22 * q^35 + 12 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 8 * q^46 - 7 * q^47 + 5 * q^49 - 2 * q^50 + 3 * q^52 + q^53 - 25 * q^55 - 3 * q^56 + 2 * q^58 + 32 * q^59 - 4 * q^61 - 14 * q^62 + 8 * q^64 - 10 * q^65 + 19 * q^67 - 4 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 - 12 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 - 2 * q^80 + 12 * q^82 + 64 * q^83 + 15 * q^85 + 4 * q^88 - 22 * q^89 - 38 * q^91 + 8 * q^92 + 7 * q^94 + 56 * q^95 + 11 * q^97 - 5 * q^98

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