LMFDB - Embedded newform 1710.2.l.n.1261.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1710.1261
Dual form			1710.2.l.n.1531.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.44949 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.44949 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +3.00000 q^{11} +(2.44949 - 4.24264i) q^{13} +(1.72474 + 2.98735i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.22474 - 5.58542i) q^{17} +(3.17423 - 2.98735i) q^{19} -1.00000 q^{20} +(1.50000 + 2.59808i) q^{22} +(1.94949 - 3.37662i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.89898 q^{26} +(-1.72474 + 2.98735i) q^{28} +(-2.67423 + 4.63191i) q^{29} +8.89898 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.22474 - 5.58542i) q^{34} +(1.72474 + 2.98735i) q^{35} -0.101021 q^{37} +(4.17423 + 1.25529i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-5.17423 - 8.96204i) q^{41} +(-3.89898 - 6.75323i) q^{43} +(-1.50000 + 2.59808i) q^{44} +3.89898 q^{46} +(-5.44949 + 9.43879i) q^{47} +4.89898 q^{49} -1.00000 q^{50} +(2.44949 + 4.24264i) q^{52} +(-1.27526 + 2.20881i) q^{53} +(1.50000 + 2.59808i) q^{55} -3.44949 q^{56} -5.34847 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-3.77526 + 6.53893i) q^{61} +(4.44949 + 7.70674i) q^{62} +1.00000 q^{64} +4.89898 q^{65} +(-3.67423 + 6.36396i) q^{67} +6.44949 q^{68} +(-1.72474 + 2.98735i) q^{70} +(5.67423 + 9.82806i) q^{71} +(-2.77526 - 4.80688i) q^{73} +(-0.0505103 - 0.0874863i) q^{74} +(1.00000 + 4.24264i) q^{76} +10.3485 q^{77} +(1.44949 + 2.51059i) q^{79} +(0.500000 - 0.866025i) q^{80} +(5.17423 - 8.96204i) q^{82} +7.79796 q^{83} +(3.22474 - 5.58542i) q^{85} +(3.89898 - 6.75323i) q^{86} -3.00000 q^{88} +(-0.275255 + 0.476756i) q^{89} +(8.44949 - 14.6349i) q^{91} +(1.94949 + 3.37662i) q^{92} -10.8990 q^{94} +(4.17423 + 1.25529i) q^{95} +(6.77526 + 11.7351i) q^{97} +(2.44949 + 4.24264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8} - 2 q^{10} + 12 q^{11} + 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 2 q^{23} - 2 q^{25} - 2 q^{28} + 4 q^{29} + 16 q^{31} + 2 q^{32} + 8 q^{34} + 2 q^{35} - 20 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} + 4 q^{43} - 6 q^{44} - 4 q^{46} - 12 q^{47} - 4 q^{50} - 10 q^{53} + 6 q^{55} - 4 q^{56} + 8 q^{58} - 12 q^{59} - 20 q^{61} + 8 q^{62} + 4 q^{64} + 16 q^{68} - 2 q^{70} + 8 q^{71} - 16 q^{73} - 10 q^{74} + 4 q^{76} + 12 q^{77} - 4 q^{79} + 2 q^{80} + 6 q^{82} - 8 q^{83} + 8 q^{85} - 4 q^{86} - 12 q^{88} - 6 q^{89} + 24 q^{91} - 2 q^{92} - 24 q^{94} + 2 q^{95} + 32 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8 - 2 * q^10 + 12 * q^11 + 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 2 * q^23 - 2 * q^25 - 2 * q^28 + 4 * q^29 + 16 * q^31 + 2 * q^32 + 8 * q^34 + 2 * q^35 - 20 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 + 4 * q^43 - 6 * q^44 - 4 * q^46 - 12 * q^47 - 4 * q^50 - 10 * q^53 + 6 * q^55 - 4 * q^56 + 8 * q^58 - 12 * q^59 - 20 * q^61 + 8 * q^62 + 4 * q^64 + 16 * q^68 - 2 * q^70 + 8 * q^71 - 16 * q^73 - 10 * q^74 + 4 * q^76 + 12 * q^77 - 4 * q^79 + 2 * q^80 + 6 * q^82 - 8 * q^83 + 8 * q^85 - 4 * q^86 - 12 * q^88 - 6 * q^89 + 24 * q^91 - 2 * q^92 - 24 * q^94 + 2 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	3.44949			1.30378			0.651892	−	0.758312i	$-0.273975\pi$
$7$	3.44949			1.30378			0.651892	+	0.758312i	$0.273975\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	−0.295806	−	0.955248i	$-0.595588\pi$
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	0.975172	−	0.221449i	$-0.0710785\pi$
$14$	1.72474	+	2.98735i	0.460957	+	0.798402i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.22474	−	5.58542i	−0.782116	−	1.35466i	−0.930707	−	0.365765i	$-0.880807\pi$
$17$	−3.22474	−	5.58542i	−0.782116	−	1.35466i	0.148592	−	0.988899i	$-0.452526\pi$
$18$		0			0
$19$	3.17423	−	2.98735i	0.728219	−	0.685344i
$19$	3.17423	−	2.98735i	0.728219	−	0.685344i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	1.94949	−	3.37662i	0.406497	−	0.704073i	−0.587998	−	0.808863i	$-0.700084\pi$
$23$	1.94949	−	3.37662i	0.406497	−	0.704073i	0.994494	+	0.104790i	$0.0334169\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.89898			0.960769
$27$		0			0
$28$	−1.72474	+	2.98735i	−0.325946	+	0.564555i
$29$	−2.67423	+	4.63191i	−0.496593	+	0.860124i	−0.999992	−	0.00392972i	$-0.998749\pi$
$29$	−2.67423	+	4.63191i	−0.496593	+	0.860124i	0.503399	+	0.864054i	$0.332082\pi$
$30$		0			0
$31$	8.89898			1.59830			0.799152	−	0.601129i	$-0.205282\pi$
$31$	8.89898			1.59830			0.799152	+	0.601129i	$0.205282\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.22474	−	5.58542i	0.553039	−	0.957892i
$35$	1.72474	+	2.98735i	0.291535	+	0.504954i
$36$		0			0
$37$	−0.101021			−0.0166077			−0.00830384	−	0.999966i	$-0.502643\pi$
$37$	−0.101021			−0.0166077			−0.00830384	+	0.999966i	$0.502643\pi$
$38$	4.17423	+	1.25529i	0.677150	+	0.203636i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−5.17423	−	8.96204i	−0.808080	−	1.39964i	−0.914192	−	0.405281i	$-0.867174\pi$
$41$	−5.17423	−	8.96204i	−0.808080	−	1.39964i	0.106113	−	0.994354i	$-0.466160\pi$
$42$		0			0
$43$	−3.89898	−	6.75323i	−0.594589	−	1.02986i	−0.993605	−	0.112914i	$-0.963982\pi$
$43$	−3.89898	−	6.75323i	−0.594589	−	1.02986i	0.399016	−	0.916944i	$-0.369352\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	3.89898			0.574873
$47$	−5.44949	+	9.43879i	−0.794890	+	1.37679i	0.128019	+	0.991772i	$0.459138\pi$
$47$	−5.44949	+	9.43879i	−0.794890	+	1.37679i	−0.922909	+	0.385018i	$0.874195\pi$
$48$		0			0
$49$	4.89898			0.699854
$50$	−1.00000			−0.141421
$51$		0			0
$52$	2.44949	+	4.24264i	0.339683	+	0.588348i
$53$	−1.27526	+	2.20881i	−0.175170	+	0.303403i	−0.940220	−	0.340568i	$-0.889381\pi$
$53$	−1.27526	+	2.20881i	−0.175170	+	0.303403i	0.765050	+	0.643971i	$0.222714\pi$
$54$		0			0
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	−3.44949			−0.460957
$57$		0			0
$58$	−5.34847			−0.702288
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	−3.77526	+	6.53893i	−0.483372	+	0.837225i	−0.999818	−	0.0190952i	$-0.993921\pi$
$61$	−3.77526	+	6.53893i	−0.483372	+	0.837225i	0.516446	+	0.856320i	$0.327255\pi$
$62$	4.44949	+	7.70674i	0.565086	+	0.978757i
$63$		0			0
$64$	1.00000			0.125000
$65$	4.89898			0.607644
$66$		0			0
$67$	−3.67423	+	6.36396i	−0.448879	+	0.777482i	−0.998313	−	0.0580554i	$-0.981510\pi$
$67$	−3.67423	+	6.36396i	−0.448879	+	0.777482i	0.549434	+	0.835537i	$0.314843\pi$
$68$	6.44949			0.782116
$69$		0			0
$70$	−1.72474	+	2.98735i	−0.206146	+	0.357056i
$71$	5.67423	+	9.82806i	0.673408	+	1.16638i	0.976932	+	0.213553i	$0.0685035\pi$
$71$	5.67423	+	9.82806i	0.673408	+	1.16638i	−0.303524	+	0.952824i	$0.598163\pi$
$72$		0			0
$73$	−2.77526	−	4.80688i	−0.324819	−	0.562603i	0.656657	−	0.754190i	$-0.271970\pi$
$73$	−2.77526	−	4.80688i	−0.324819	−	0.562603i	−0.981476	+	0.191587i	$0.938637\pi$
$74$	−0.0505103	−	0.0874863i	−0.00587170	−	0.0101701i
$75$		0			0
$76$	1.00000	+	4.24264i	0.114708	+	0.486664i
$77$	10.3485			1.17932
$78$		0			0
$79$	1.44949	+	2.51059i	0.163080	+	0.282463i	0.935972	−	0.352075i	$-0.114524\pi$
$79$	1.44949	+	2.51059i	0.163080	+	0.282463i	−0.772892	+	0.634538i	$0.781190\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	5.17423	−	8.96204i	0.571399	−	0.989691i
$83$	7.79796			0.855937			0.427969	−	0.903794i	$-0.359229\pi$
$83$	7.79796			0.855937			0.427969	+	0.903794i	$0.359229\pi$
$84$		0			0
$85$	3.22474	−	5.58542i	0.349773	−	0.605824i
$86$	3.89898	−	6.75323i	0.420438	−	0.728220i
$87$		0			0
$88$	−3.00000			−0.319801
$89$	−0.275255	+	0.476756i	−0.0291770	+	0.0505360i	−0.880245	−	0.474519i	$-0.842622\pi$
$89$	−0.275255	+	0.476756i	−0.0291770	+	0.0505360i	0.851068	+	0.525055i	$0.175955\pi$
$90$		0			0
$91$	8.44949	−	14.6349i	0.885747	−	1.53416i
$92$	1.94949	+	3.37662i	0.203248	+	0.352036i
$93$		0			0
$94$	−10.8990			−1.12414
$95$	4.17423	+	1.25529i	0.428267	+	0.128791i
$96$		0			0
$97$	6.77526	+	11.7351i	0.687923	+	1.19152i	0.972509	+	0.232867i	$0.0748106\pi$
$97$	6.77526	+	11.7351i	0.687923	+	1.19152i	−0.284586	+	0.958651i	$0.591856\pi$
$98$	2.44949	+	4.24264i	0.247436	+	0.428571i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−5.44949	+	9.43879i	−0.542244	+	0.939195i	0.456530	+	0.889708i	$0.349092\pi$
$101$	−5.44949	+	9.43879i	−0.542244	+	0.939195i	−0.998775	+	0.0494871i	$0.984241\pi$
$102$		0			0
$103$	−13.2474			−1.30531			−0.652655	−	0.757655i	$-0.726345\pi$
$103$	−13.2474			−1.30531			−0.652655	+	0.757655i	$0.726345\pi$
$104$	−2.44949	+	4.24264i	−0.240192	+	0.416025i
$105$		0			0
$106$	−2.55051			−0.247727
$107$	17.3485			1.67714			0.838570	−	0.544794i	$-0.183392\pi$
$107$	17.3485			1.67714			0.838570	+	0.544794i	$0.183392\pi$
$108$		0			0
$109$	6.67423	+	11.5601i	0.639276	+	1.10726i	0.985592	+	0.169140i	$0.0540991\pi$
$109$	6.67423	+	11.5601i	0.639276	+	1.10726i	−0.346316	+	0.938118i	$0.612568\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$		0			0
$112$	−1.72474	−	2.98735i	−0.162973	−	0.282278i
$113$	14.4495			1.35929			0.679647	−	0.733539i	$-0.262133\pi$
$113$	14.4495			1.35929			0.679647	+	0.733539i	$0.262133\pi$
$114$		0			0
$115$	3.89898			0.363582
$116$	−2.67423	−	4.63191i	−0.248296	−	0.430062i
$117$		0			0
$118$	3.00000	−	5.19615i	0.276172	−	0.478345i
$119$	−11.1237	−	19.2669i	−1.01971	−	1.76619i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	−7.55051			−0.683591
$123$		0			0
$124$	−4.44949	+	7.70674i	−0.399576	+	0.692086i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.17423	+	12.4261i	−0.636610	+	1.10264i	0.349561	+	0.936914i	$0.386331\pi$
$127$	−7.17423	+	12.4261i	−0.636610	+	1.10264i	−0.986172	+	0.165728i	$0.947003\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	2.44949	+	4.24264i	0.214834	+	0.372104i
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	0.793028	−	0.609185i	$-0.208503\pi$
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$132$		0			0
$133$	10.9495	−	10.3048i	0.949441	−	0.893541i
$134$	−7.34847			−0.634811
$135$		0			0
$136$	3.22474	+	5.58542i	0.276520	+	0.478946i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−7.34847	+	12.7279i	−0.623289	+	1.07957i	0.365580	+	0.930780i	$0.380871\pi$
$139$	−7.34847	+	12.7279i	−0.623289	+	1.07957i	−0.988869	+	0.148788i	$0.952463\pi$
$140$	−3.44949			−0.291535
$141$		0			0
$142$	−5.67423	+	9.82806i	−0.476171	+	0.824753i
$143$	7.34847	−	12.7279i	0.614510	−	1.06436i
$144$		0			0
$145$	−5.34847			−0.444166
$146$	2.77526	−	4.80688i	0.229682	−	0.397820i
$147$		0			0
$148$	0.0505103	−	0.0874863i	0.00415192	−	0.00719133i
$149$	9.22474	+	15.9777i	0.755721	+	1.30895i	0.945015	+	0.327026i	$0.106046\pi$
$149$	9.22474	+	15.9777i	0.755721	+	1.30895i	−0.189295	+	0.981920i	$0.560620\pi$
$150$		0			0
$151$	−19.3485			−1.57456			−0.787278	−	0.616598i	$-0.788510\pi$
$151$	−19.3485			−1.57456			−0.787278	+	0.616598i	$0.788510\pi$
$152$	−3.17423	+	2.98735i	−0.257464	+	0.242306i
$153$		0			0
$154$	5.17423	+	8.96204i	0.416952	+	0.722182i
$155$	4.44949	+	7.70674i	0.357392	+	0.619020i
$156$		0			0
$157$	−0.601021	−	1.04100i	−0.0479667	−	0.0830807i	0.841045	−	0.540965i	$-0.181941\pi$
$157$	−0.601021	−	1.04100i	−0.0479667	−	0.0830807i	−0.889012	+	0.457884i	$0.848607\pi$
$158$	−1.44949	+	2.51059i	−0.115315	+	0.199732i
$159$		0			0
$160$	1.00000			0.0790569
$161$	6.72474	−	11.6476i	0.529984	−	0.917959i
$162$		0			0
$163$	−12.6969			−0.994501			−0.497250	−	0.867607i	$-0.665657\pi$
$163$	−12.6969			−0.994501			−0.497250	+	0.867607i	$0.665657\pi$
$164$	10.3485			0.808080
$165$		0			0
$166$	3.89898	+	6.75323i	0.302619	+	0.524152i
$167$	9.84847	−	17.0580i	0.762097	−	1.31999i	−0.179670	−	0.983727i	$-0.557503\pi$
$167$	9.84847	−	17.0580i	0.762097	−	1.31999i	0.941768	−	0.336265i	$-0.109164\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	6.44949			0.494653
$171$		0			0
$172$	7.79796			0.594589
$173$	−4.72474	−	8.18350i	−0.359216	−	0.622180i	0.628614	−	0.777717i	$-0.283622\pi$
$173$	−4.72474	−	8.18350i	−0.359216	−	0.622180i	−0.987830	+	0.155537i	$0.950289\pi$
$174$		0			0
$175$	−1.72474	+	2.98735i	−0.130378	+	0.225822i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−0.550510			−0.0412625
$179$	1.20204			0.0898448			0.0449224	−	0.998990i	$-0.485696\pi$
$179$	1.20204			0.0898448			0.0449224	+	0.998990i	$0.485696\pi$
$180$		0			0
$181$	8.57321	−	14.8492i	0.637242	−	1.10374i	−0.348793	−	0.937200i	$-0.613409\pi$
$181$	8.57321	−	14.8492i	0.637242	−	1.10374i	0.986035	−	0.166536i	$-0.0532582\pi$
$182$	16.8990			1.25264
$183$		0			0
$184$	−1.94949	+	3.37662i	−0.143718	+	0.248927i
$185$	−0.0505103	−	0.0874863i	−0.00371359	−	0.00643212i
$186$		0			0
$187$	−9.67423	−	16.7563i	−0.707450	−	1.22534i
$188$	−5.44949	−	9.43879i	−0.397445	−	0.688395i
$189$		0			0
$190$	1.00000	+	4.24264i	0.0725476	+	0.307794i
$191$	−15.7980			−1.14310			−0.571550	−	0.820567i	$-0.693658\pi$
$191$	−15.7980			−1.14310			−0.571550	+	0.820567i	$0.693658\pi$
$192$		0			0
$193$	3.32577	+	5.76039i	0.239394	+	0.414642i	0.960541	−	0.278140i	$-0.0897180\pi$
$193$	3.32577	+	5.76039i	0.239394	+	0.414642i	−0.721147	+	0.692782i	$0.756385\pi$
$194$	−6.77526	+	11.7351i	−0.486435	+	0.842530i
$195$		0			0
$196$	−2.44949	+	4.24264i	−0.174964	+	0.303046i
$197$	−11.4495			−0.815742			−0.407871	−	0.913039i	$-0.633729\pi$
$197$	−11.4495			−0.815742			−0.407871	+	0.913039i	$0.633729\pi$
$198$		0			0
$199$	−0.775255	+	1.34278i	−0.0549564	+	0.0951872i	−0.892195	−	0.451651i	$-0.850835\pi$
$199$	−0.775255	+	1.34278i	−0.0549564	+	0.0951872i	0.837238	+	0.546838i	$0.184169\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−10.8990			−0.766850
$203$	−9.22474	+	15.9777i	−0.647450	+	1.12142i
$204$		0			0
$205$	5.17423	−	8.96204i	0.361384	−	0.625936i
$206$	−6.62372	−	11.4726i	−0.461497	−	0.799336i
$207$		0			0
$208$	−4.89898			−0.339683
$209$	9.52270	−	8.96204i	0.658699	−	0.619917i
$210$		0			0
$211$	5.82577	+	10.0905i	0.401062	+	0.694660i	0.993854	−	0.110695i	$-0.0353078\pi$
$211$	5.82577	+	10.0905i	0.401062	+	0.694660i	−0.592792	+	0.805355i	$0.701974\pi$
$212$	−1.27526	−	2.20881i	−0.0875849	−	0.151701i
$213$		0			0
$214$	8.67423	+	15.0242i	0.592958	+	1.02703i
$215$	3.89898	−	6.75323i	0.265908	−	0.460567i
$216$		0			0
$217$	30.6969			2.08384
$218$	−6.67423	+	11.5601i	−0.452036	+	0.782950i
$219$		0			0
$220$	−3.00000			−0.202260
$221$	−31.5959			−2.12537
$222$		0			0
$223$	−0.724745	−	1.25529i	−0.0485325	−	0.0840608i	0.840739	−	0.541441i	$-0.182121\pi$
$223$	−0.724745	−	1.25529i	−0.0485325	−	0.0840608i	−0.889271	+	0.457380i	$0.848788\pi$
$224$	1.72474	−	2.98735i	0.115239	−	0.199600i
$225$		0			0
$226$	7.22474	+	12.5136i	0.480583	+	0.832394i
$227$	−3.34847			−0.222246			−0.111123	−	0.993807i	$-0.535445\pi$
$227$	−3.34847			−0.222246			−0.111123	+	0.993807i	$0.535445\pi$
$228$		0			0
$229$	−20.6969			−1.36769			−0.683846	−	0.729626i	$-0.739694\pi$
$229$	−20.6969			−1.36769			−0.683846	+	0.729626i	$0.739694\pi$
$230$	1.94949	+	3.37662i	0.128546	+	0.222647i
$231$		0			0
$232$	2.67423	−	4.63191i	0.175572	−	0.304100i
$233$	−4.10102	−	7.10318i	−0.268667	−	0.465345i	0.699851	−	0.714289i	$-0.253250\pi$
$233$	−4.10102	−	7.10318i	−0.268667	−	0.465345i	−0.968518	+	0.248944i	$0.919916\pi$
$234$		0			0
$235$	−10.8990			−0.710971
$236$	6.00000			0.390567
$237$		0			0
$238$	11.1237	−	19.2669i	0.721044	−	1.24888i
$239$	10.2020			0.659915			0.329958	−	0.943996i	$-0.392966\pi$
$239$	10.2020			0.659915			0.329958	+	0.943996i	$0.392966\pi$
$240$		0			0
$241$	11.3485	−	19.6561i	0.731019	−	1.26616i	−0.225429	−	0.974260i	$-0.572378\pi$
$241$	11.3485	−	19.6561i	0.731019	−	1.26616i	0.956448	−	0.291903i	$-0.0942883\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	−3.77526	−	6.53893i	−0.241686	−	0.418612i
$245$	2.44949	+	4.24264i	0.156492	+	0.271052i
$246$		0			0
$247$	−4.89898	−	20.7846i	−0.311715	−	1.32249i
$248$	−8.89898			−0.565086
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−10.8990	+	18.8776i	−0.687937	+	1.19154i	0.284566	+	0.958656i	$0.408150\pi$
$251$	−10.8990	+	18.8776i	−0.687937	+	1.19154i	−0.972504	+	0.232886i	$0.925183\pi$
$252$		0			0
$253$	5.84847	−	10.1298i	0.367690	−	0.636858i
$254$	−14.3485			−0.900303
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.89898	+	3.28913i	−0.118455	+	0.205170i	−0.919156	−	0.393895i	$-0.871127\pi$
$257$	−1.89898	+	3.28913i	−0.118455	+	0.205170i	0.800701	+	0.599065i	$0.204461\pi$
$258$		0			0
$259$	−0.348469			−0.0216528
$260$	−2.44949	+	4.24264i	−0.151911	+	0.263117i
$261$		0			0
$262$	1.50000	−	2.59808i	0.0926703	−	0.160510i
$263$	9.94949	+	17.2330i	0.613512	+	1.06263i	0.990644	+	0.136474i	$0.0435770\pi$
$263$	9.94949	+	17.2330i	0.613512	+	1.06263i	−0.377132	+	0.926160i	$0.623090\pi$
$264$		0			0
$265$	−2.55051			−0.156677
$266$	14.3990	+	4.33013i	0.882858	+	0.265497i
$267$		0			0
$268$	−3.67423	−	6.36396i	−0.224440	−	0.388741i
$269$	0.123724	+	0.214297i	0.00754361	+	0.0130659i	0.869773	−	0.493453i	$-0.164265\pi$
$269$	0.123724	+	0.214297i	0.00754361	+	0.0130659i	−0.862229	+	0.506519i	$0.830932\pi$
$270$		0			0
$271$	2.55051	+	4.41761i	0.154932	+	0.268351i	0.933034	−	0.359787i	$-0.117151\pi$
$271$	2.55051	+	4.41761i	0.154932	+	0.268351i	−0.778102	+	0.628138i	$0.783817\pi$
$272$	−3.22474	+	5.58542i	−0.195529	+	0.338666i
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$		0			0
$277$	−3.10102			−0.186322			−0.0931611	−	0.995651i	$-0.529697\pi$
$277$	−3.10102			−0.186322			−0.0931611	+	0.995651i	$0.529697\pi$
$278$	−14.6969			−0.881464
$279$		0			0
$280$	−1.72474	−	2.98735i	−0.103073	−	0.178528i
$281$	−0.174235	+	0.301783i	−0.0103940	+	0.0180029i	−0.871176	−	0.490972i	$-0.836642\pi$
$281$	−0.174235	+	0.301783i	−0.0103940	+	0.0180029i	0.860782	+	0.508974i	$0.169975\pi$
$282$		0			0
$283$	−8.34847	−	14.4600i	−0.496265	−	0.859556i	0.503726	−	0.863864i	$-0.331962\pi$
$283$	−8.34847	−	14.4600i	−0.496265	−	0.859556i	−0.999991	+	0.00430747i	$0.998629\pi$
$284$	−11.3485			−0.673408
$285$		0			0
$286$	14.6969			0.869048
$287$	−17.8485	−	30.9145i	−1.05356	−	1.82482i
$288$		0			0
$289$	−12.2980	+	21.3007i	−0.723409	+	1.25298i
$290$	−2.67423	−	4.63191i	−0.157036	−	0.271995i
$291$		0			0
$292$	5.55051			0.324819
$293$	6.55051			0.382685			0.191342	−	0.981523i	$-0.438716\pi$
$293$	6.55051			0.382685			0.191342	+	0.981523i	$0.438716\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$	0.101021			0.00587170
$297$		0			0
$298$	−9.22474	+	15.9777i	−0.534375	+	0.925565i
$299$	−9.55051	−	16.5420i	−0.552320	−	0.956647i
$300$		0			0
$301$	−13.4495	−	23.2952i	−0.775216	−	1.34271i
$302$	−9.67423	−	16.7563i	−0.556690	−	0.964215i
$303$		0			0
$304$	−4.17423	−	1.25529i	−0.239409	−	0.0719961i
$305$	−7.55051			−0.432341
$306$		0			0
$307$	−7.12372	−	12.3387i	−0.406572	−	0.704204i	0.587931	−	0.808911i	$-0.299943\pi$
$307$	−7.12372	−	12.3387i	−0.406572	−	0.704204i	−0.994503	+	0.104707i	$0.966609\pi$
$308$	−5.17423	+	8.96204i	−0.294829	+	0.510659i
$309$		0			0
$310$	−4.44949	+	7.70674i	−0.252714	+	0.437714i
$311$	−9.79796			−0.555591			−0.277796	−	0.960640i	$-0.589604\pi$
$311$	−9.79796			−0.555591			−0.277796	+	0.960640i	$0.589604\pi$
$312$		0			0
$313$	3.79796	−	6.57826i	0.214673	−	0.371825i	−0.738498	−	0.674256i	$-0.764465\pi$
$313$	3.79796	−	6.57826i	0.214673	−	0.371825i	0.953171	+	0.302430i	$0.0977980\pi$
$314$	0.601021	−	1.04100i	0.0339175	−	0.0587469i
$315$		0			0
$316$	−2.89898			−0.163080
$317$	2.27526	−	3.94086i	0.127791	−	0.221341i	−0.795029	−	0.606571i	$-0.792545\pi$
$317$	2.27526	−	3.94086i	0.127791	−	0.221341i	0.922820	+	0.385230i	$0.125878\pi$
$318$		0			0
$319$	−8.02270	+	13.8957i	−0.449185	+	0.778012i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	13.4495			0.749511
$323$	−26.9217	−	8.09601i	−1.49796	−	0.450474i
$324$		0			0
$325$	2.44949	+	4.24264i	0.135873	+	0.235339i
$326$	−6.34847	−	10.9959i	−0.351609	−	0.609005i
$327$		0			0
$328$	5.17423	+	8.96204i	0.285699	+	0.494846i
$329$	−18.7980	+	32.5590i	−1.03637	+	1.79504i
$330$		0			0
$331$	3.65153			0.200706			0.100353	−	0.994952i	$-0.468003\pi$
$331$	3.65153			0.200706			0.100353	+	0.994952i	$0.468003\pi$
$332$	−3.89898	+	6.75323i	−0.213984	+	0.370632i
$333$		0			0
$334$	19.6969			1.07777
$335$	−7.34847			−0.401490
$336$		0			0
$337$	−11.2474	−	19.4812i	−0.612688	−	1.06121i	−0.990785	−	0.135440i	$-0.956755\pi$
$337$	−11.2474	−	19.4812i	−0.612688	−	1.06121i	0.378098	−	0.925766i	$-0.376578\pi$
$338$	5.50000	−	9.52628i	0.299161	−	0.518161i
$339$		0			0
$340$	3.22474	+	5.58542i	0.174886	+	0.302912i
$341$	26.6969			1.44572
$342$		0			0
$343$	−7.24745			−0.391325
$344$	3.89898	+	6.75323i	0.210219	+	0.364110i
$345$		0			0
$346$	4.72474	−	8.18350i	0.254004	−	0.439948i
$347$	−3.89898	−	6.75323i	−0.209308	−	0.362532i	0.742189	−	0.670191i	$-0.233788\pi$
$347$	−3.89898	−	6.75323i	−0.209308	−	0.362532i	−0.951497	+	0.307659i	$0.900455\pi$
$348$		0			0
$349$	24.0454			1.28712			0.643561	−	0.765395i	$-0.277456\pi$
$349$	24.0454			1.28712			0.643561	+	0.765395i	$0.277456\pi$
$350$	−3.44949			−0.184383
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	20.6515			1.09917			0.549585	−	0.835438i	$-0.314786\pi$
$353$	20.6515			1.09917			0.549585	+	0.835438i	$0.314786\pi$
$354$		0			0
$355$	−5.67423	+	9.82806i	−0.301157	+	0.521619i
$356$	−0.275255	−	0.476756i	−0.0145885	−	0.0252680i
$357$		0			0
$358$	0.601021	+	1.04100i	0.0317649	+	0.0550185i
$359$	10.7753	+	18.6633i	0.568696	+	0.985011i	0.996695	+	0.0812316i	$0.0258853\pi$
$359$	10.7753	+	18.6633i	0.568696	+	0.985011i	−0.427999	+	0.903779i	$0.640781\pi$
$360$		0			0
$361$	1.15153	−	18.9651i	0.0606069	−	0.998162i
$362$	17.1464			0.901196
$363$		0			0
$364$	8.44949	+	14.6349i	0.442874	+	0.767080i
$365$	2.77526	−	4.80688i	0.145263	−	0.251604i
$366$		0			0
$367$	−5.55051	+	9.61377i	−0.289734	+	0.501834i	−0.973746	−	0.227636i	$-0.926900\pi$
$367$	−5.55051	+	9.61377i	−0.289734	+	0.501834i	0.684012	+	0.729471i	$0.260234\pi$
$368$	−3.89898			−0.203248
$369$		0			0
$370$	0.0505103	−	0.0874863i	0.00262590	−	0.00454820i
$371$	−4.39898	+	7.61926i	−0.228384	+	0.395572i
$372$		0			0
$373$	5.89898			0.305438			0.152719	−	0.988270i	$-0.451197\pi$
$373$	5.89898			0.305438			0.152719	+	0.988270i	$0.451197\pi$
$374$	9.67423	−	16.7563i	0.500243	−	0.866446i
$375$		0			0
$376$	5.44949	−	9.43879i	0.281036	−	0.486769i
$377$	13.1010	+	22.6916i	0.674737	+	1.16868i
$378$		0			0
$379$	22.6969			1.16586			0.582932	−	0.812521i	$-0.301906\pi$
$379$	22.6969			1.16586			0.582932	+	0.812521i	$0.301906\pi$
$380$	−3.17423	+	2.98735i	−0.162835	+	0.153248i
$381$		0			0
$382$	−7.89898	−	13.6814i	−0.404147	−	0.700003i
$383$	−9.24745	−	16.0171i	−0.472523	−	0.818433i	0.526983	−	0.849876i	$-0.323323\pi$
$383$	−9.24745	−	16.0171i	−0.472523	−	0.818433i	−0.999506	+	0.0314428i	$0.989990\pi$
$384$		0			0
$385$	5.17423	+	8.96204i	0.263703	+	0.456748i
$386$	−3.32577	+	5.76039i	−0.169277	+	0.293196i
$387$		0			0
$388$	−13.5505			−0.687923
$389$	5.57321	−	9.65309i	0.282573	−	0.489431i	−0.689445	−	0.724338i	$-0.742145\pi$
$389$	5.57321	−	9.65309i	0.282573	−	0.489431i	0.972018	+	0.234907i	$0.0754787\pi$
$390$		0			0
$391$	−25.1464			−1.27171
$392$	−4.89898			−0.247436
$393$		0			0
$394$	−5.72474	−	9.91555i	−0.288408	−	0.499538i
$395$	−1.44949	+	2.51059i	−0.0729317	+	0.126321i
$396$		0			0
$397$	18.7474	+	32.4715i	0.940907	+	1.62970i	0.763745	+	0.645518i	$0.223358\pi$
$397$	18.7474	+	32.4715i	0.940907	+	1.62970i	0.177162	+	0.984182i	$0.443308\pi$
$398$	−1.55051			−0.0777201
$399$		0			0
$400$	1.00000			0.0500000
$401$	7.89898	+	13.6814i	0.394456	+	0.683218i	0.993032	−	0.117848i	$-0.0375996\pi$
$401$	7.89898	+	13.6814i	0.394456	+	0.683218i	−0.598575	+	0.801066i	$0.704266\pi$
$402$		0			0
$403$	21.7980	−	37.7552i	1.08583	−	1.88072i
$404$	−5.44949	−	9.43879i	−0.271122	−	0.469598i
$405$		0			0
$406$	−18.4495			−0.915633
$407$	−0.303062			−0.0150222
$408$		0			0
$409$	−19.7474	+	34.2036i	−0.976448	+	1.69126i	−0.301379	+	0.953505i	$0.597447\pi$
$409$	−19.7474	+	34.2036i	−0.976448	+	1.69126i	−0.675070	+	0.737754i	$0.735886\pi$
$410$	10.3485			0.511074
$411$		0			0
$412$	6.62372	−	11.4726i	0.326327	−	0.565216i
$413$	−10.3485	−	17.9241i	−0.509215	−	0.881986i
$414$		0			0
$415$	3.89898	+	6.75323i	0.191393	+	0.331503i
$416$	−2.44949	−	4.24264i	−0.120096	−	0.208013i
$417$		0			0
$418$	12.5227	+	3.76588i	0.612505	+	0.184195i
$419$	−12.1010			−0.591174			−0.295587	−	0.955316i	$-0.595515\pi$
$419$	−12.1010			−0.591174			−0.295587	+	0.955316i	$0.595515\pi$
$420$		0			0
$421$	16.6742	+	28.8806i	0.812652	+	1.40756i	0.911001	+	0.412403i	$0.135311\pi$
$421$	16.6742	+	28.8806i	0.812652	+	1.40756i	−0.0983489	+	0.995152i	$0.531356\pi$
$422$	−5.82577	+	10.0905i	−0.283594	+	0.491199i
$423$		0			0
$424$	1.27526	−	2.20881i	0.0619319	−	0.107269i
$425$	6.44949			0.312846
$426$		0			0
$427$	−13.0227	+	22.5560i	−0.630213	+	1.09156i
$428$	−8.67423	+	15.0242i	−0.419285	+	0.726223i
$429$		0			0
$430$	7.79796			0.376051
$431$	12.6742	−	21.9524i	0.610496	−	1.05741i	−0.380660	−	0.924715i	$-0.624303\pi$
$431$	12.6742	−	21.9524i	0.610496	−	1.05741i	0.991157	−	0.132696i	$-0.0423634\pi$
$432$		0			0
$433$	5.67423	−	9.82806i	0.272686	−	0.472307i	−0.696862	−	0.717205i	$-0.745421\pi$
$433$	5.67423	−	9.82806i	0.272686	−	0.472307i	0.969549	+	0.244898i	$0.0787546\pi$
$434$	15.3485	+	26.5843i	0.736750	+	1.27609i
$435$		0			0
$436$	−13.3485			−0.639276
$437$	−3.89898	−	16.5420i	−0.186513	−	0.791310i
$438$		0			0
$439$	5.67423	+	9.82806i	0.270816	+	0.469068i	0.969071	−	0.246782i	$-0.0793730\pi$
$439$	5.67423	+	9.82806i	0.270816	+	0.469068i	−0.698255	+	0.715849i	$0.746040\pi$
$440$	−1.50000	−	2.59808i	−0.0715097	−	0.123858i
$441$		0			0
$442$	−15.7980	−	27.3629i	−0.751432	−	1.30152i
$443$	13.1237	−	22.7310i	0.623527	−	1.07998i	−0.365297	−	0.930891i	$-0.619032\pi$
$443$	13.1237	−	22.7310i	0.623527	−	1.07998i	0.988824	−	0.149089i	$-0.0476342\pi$
$444$		0			0
$445$	−0.550510			−0.0260967
$446$	0.724745	−	1.25529i	0.0343177	−	0.0594399i
$447$		0			0
$448$	3.44949			0.162973
$449$	−33.2474			−1.56904			−0.784522	−	0.620101i	$-0.787092\pi$
$449$	−33.2474			−1.56904			−0.784522	+	0.620101i	$0.787092\pi$
$450$		0			0
$451$	−15.5227	−	26.8861i	−0.730936	−	1.26602i
$452$	−7.22474	+	12.5136i	−0.339823	+	0.588591i
$453$		0			0
$454$	−1.67423	−	2.89986i	−0.0785757	−	0.136097i
$455$	16.8990			0.792236
$456$		0			0
$457$	32.0454			1.49902			0.749510	−	0.661992i	$-0.230289\pi$
$457$	32.0454			1.49902			0.749510	+	0.661992i	$0.230289\pi$
$458$	−10.3485	−	17.9241i	−0.483552	−	0.837537i
$459$		0			0
$460$	−1.94949	+	3.37662i	−0.0908954	+	0.157435i
$461$	−4.10102	−	7.10318i	−0.191004	−	0.330828i	0.754580	−	0.656209i	$-0.227841\pi$
$461$	−4.10102	−	7.10318i	−0.191004	−	0.330828i	−0.945583	+	0.325381i	$0.894508\pi$
$462$		0			0
$463$	−30.3485			−1.41041			−0.705206	−	0.709002i	$-0.749146\pi$
$463$	−30.3485			−1.41041			−0.705206	+	0.709002i	$0.749146\pi$
$464$	5.34847			0.248296
$465$		0			0
$466$	4.10102	−	7.10318i	0.189976	−	0.329048i
$467$	15.7526			0.728941			0.364471	−	0.931215i	$-0.381250\pi$
$467$	15.7526			0.728941			0.364471	+	0.931215i	$0.381250\pi$
$468$		0			0
$469$	−12.6742	+	21.9524i	−0.585242	+	1.01367i
$470$	−5.44949	−	9.43879i	−0.251366	−	0.435379i
$471$		0			0
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	−11.6969	−	20.2597i	−0.537826	−	0.931542i
$474$		0			0
$475$	1.00000	+	4.24264i	0.0458831	+	0.194666i
$476$	22.2474			1.01971
$477$		0			0
$478$	5.10102	+	8.83523i	0.233315	+	0.404114i
$479$	−17.0227	+	29.4842i	−0.777787	+	1.34717i	0.155427	+	0.987847i	$0.450325\pi$
$479$	−17.0227	+	29.4842i	−0.777787	+	1.34717i	−0.933215	+	0.359320i	$0.883009\pi$
$480$		0			0
$481$	−0.247449	+	0.428594i	−0.0112827	+	0.0195422i
$482$	22.6969			1.03382
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−6.77526	+	11.7351i	−0.307648	+	0.532863i
$486$		0			0
$487$	6.14643			0.278521			0.139261	−	0.990256i	$-0.455527\pi$
$487$	6.14643			0.278521			0.139261	+	0.990256i	$0.455527\pi$
$488$	3.77526	−	6.53893i	0.170898	−	0.296004i
$489$		0			0
$490$	−2.44949	+	4.24264i	−0.110657	+	0.191663i
$491$	−17.3990	−	30.1359i	−0.785205	−	1.36001i	−0.928877	−	0.370389i	$-0.879224\pi$
$491$	−17.3990	−	30.1359i	−0.785205	−	1.36001i	0.143672	−	0.989625i	$-0.454109\pi$
$492$		0			0
$493$	34.4949			1.55357
$494$	15.5505	−	14.6349i	0.699651	−	0.658457i
$495$		0			0
$496$	−4.44949	−	7.70674i	−0.199788	−	0.346043i
$497$	19.5732	+	33.9018i	0.877979	+	1.52070i
$498$		0			0
$499$	−7.72474	−	13.3797i	−0.345807	−	0.598955i	0.639693	−	0.768631i	$-0.279062\pi$
$499$	−7.72474	−	13.3797i	−0.345807	−	0.598955i	−0.985500	+	0.169675i	$0.945728\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−21.7980			−0.972891
$503$	15.8485	−	27.4504i	0.706648	−	1.22395i	−0.259445	−	0.965758i	$-0.583540\pi$
$503$	15.8485	−	27.4504i	0.706648	−	1.22395i	0.966093	−	0.258193i	$-0.0831270\pi$
$504$		0			0
$505$	−10.8990			−0.484998
$506$	11.6969			0.519992
$507$		0			0
$508$	−7.17423	−	12.4261i	−0.318305	−	0.551321i
$509$	3.44949	−	5.97469i	0.152896	−	0.264824i	−0.779395	−	0.626533i	$-0.784473\pi$
$509$	3.44949	−	5.97469i	0.152896	−	0.264824i	0.932291	+	0.361709i	$0.117807\pi$
$510$		0			0
$511$	−9.57321	−	16.5813i	−0.423494	−	0.733513i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.79796			−0.167521
$515$	−6.62372	−	11.4726i	−0.291876	−	0.505544i
$516$		0			0
$517$	−16.3485	+	28.3164i	−0.719005	+	1.24535i
$518$	−0.174235	−	0.301783i	−0.00765543	−	0.0132596i
$519$		0			0
$520$	−4.89898			−0.214834
$521$	−10.8990			−0.477493			−0.238746	−	0.971082i	$-0.576736\pi$
$521$	−10.8990			−0.477493			−0.238746	+	0.971082i	$0.576736\pi$
$522$		0			0
$523$	15.5732	−	26.9736i	0.680969	−	1.17947i	−0.293716	−	0.955893i	$-0.594892\pi$
$523$	15.5732	−	26.9736i	0.680969	−	1.17947i	0.974685	−	0.223580i	$-0.0717745\pi$
$524$	3.00000			0.131056
$525$		0			0
$526$	−9.94949	+	17.2330i	−0.433818	+	0.751395i
$527$	−28.6969	−	49.7046i	−1.25006	−	2.16516i
$528$		0			0
$529$	3.89898	+	6.75323i	0.169521	+	0.293619i
$530$	−1.27526	−	2.20881i	−0.0553935	−	0.0959444i
$531$		0			0
$532$	3.44949	+	14.6349i	0.149554	+	0.634505i
$533$	−50.6969			−2.19593
$534$		0			0
$535$	8.67423	+	15.0242i	0.375020	+	0.649553i
$536$	3.67423	−	6.36396i	0.158703	−	0.274881i
$537$		0			0
$538$	−0.123724	+	0.214297i	−0.00533414	+	0.00923899i
$539$	14.6969			0.633042
$540$		0			0
$541$	−14.4495	+	25.0273i	−0.621232	+	1.07601i	0.368025	+	0.929816i	$0.380034\pi$
$541$	−14.4495	+	25.0273i	−0.621232	+	1.07601i	−0.989257	+	0.146189i	$0.953299\pi$
$542$	−2.55051	+	4.41761i	−0.109554	+	0.189753i
$543$		0			0
$544$	−6.44949			−0.276520
$545$	−6.67423	+	11.5601i	−0.285893	+	0.495181i
$546$		0			0
$547$	16.3485	−	28.3164i	0.699010	−	1.21072i	−0.269800	−	0.962916i	$-0.586958\pi$
$547$	16.3485	−	28.3164i	0.699010	−	1.21072i	0.968810	−	0.247805i	$-0.0797091\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$		0			0
$550$	−3.00000			−0.127920
$551$	5.34847	+	22.6916i	0.227852	+	0.966696i
$552$		0			0
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$	−1.55051	−	2.68556i	−0.0658749	−	0.114099i
$555$		0			0
$556$	−7.34847	−	12.7279i	−0.311645	−	0.539784i
$557$	−1.82577	+	3.16232i	−0.0773602	+	0.133992i	−0.902110	−	0.431506i	$-0.857982\pi$
$557$	−1.82577	+	3.16232i	−0.0773602	+	0.133992i	0.824750	+	0.565497i	$0.191316\pi$
$558$		0			0
$559$	−38.2020			−1.61577
$560$	1.72474	−	2.98735i	0.0728838	−	0.126238i
$561$		0			0
$562$	−0.348469			−0.0146993
$563$	29.3939			1.23880			0.619402	−	0.785074i	$-0.287375\pi$
$563$	29.3939			1.23880			0.619402	+	0.785074i	$0.287375\pi$
$564$		0			0
$565$	7.22474	+	12.5136i	0.303947	+	0.526452i
$566$	8.34847	−	14.4600i	0.350912	−	0.607798i
$567$		0			0
$568$	−5.67423	−	9.82806i	−0.238086	−	0.412376i
$569$	2.55051			0.106923			0.0534615	−	0.998570i	$-0.482975\pi$
$569$	2.55051			0.106923			0.0534615	+	0.998570i	$0.482975\pi$
$570$		0			0
$571$	−27.7980			−1.16331			−0.581654	−	0.813436i	$-0.697594\pi$
$571$	−27.7980			−1.16331			−0.581654	+	0.813436i	$0.697594\pi$
$572$	7.34847	+	12.7279i	0.307255	+	0.532181i
$573$		0			0
$574$	17.8485	−	30.9145i	0.744981	−	1.29034i
$575$	1.94949	+	3.37662i	0.0812993	+	0.140815i
$576$		0			0
$577$	−23.1464			−0.963598			−0.481799	−	0.876282i	$-0.660017\pi$
$577$	−23.1464			−0.963598			−0.481799	+	0.876282i	$0.660017\pi$
$578$	−24.5959			−1.02306
$579$		0			0
$580$	2.67423	−	4.63191i	0.111042	−	0.192330i
$581$	26.8990			1.11596
$582$		0			0
$583$	−3.82577	+	6.62642i	−0.158447	+	0.274438i
$584$	2.77526	+	4.80688i	0.114841	+	0.198910i
$585$		0			0
$586$	3.27526	+	5.67291i	0.135300	+	0.234346i
$587$	8.24745	+	14.2850i	0.340409	+	0.589605i	0.984509	−	0.175336i	$-0.0561013\pi$
$587$	8.24745	+	14.2850i	0.340409	+	0.589605i	−0.644100	+	0.764941i	$0.722768\pi$
$588$		0			0
$589$	28.2474	−	26.5843i	1.16392	−	1.09539i
$590$	6.00000			0.247016
$591$		0			0
$592$	0.0505103	+	0.0874863i	0.00207596	+	0.00359567i
$593$	−0.426786	+	0.739215i	−0.0175260	+	0.0303559i	−0.874655	−	0.484745i	$-0.838912\pi$
$593$	−0.426786	+	0.739215i	−0.0175260	+	0.0303559i	0.857129	+	0.515101i	$0.172246\pi$
$594$		0			0
$595$	11.1237	−	19.2669i	0.456028	−	0.789864i
$596$	−18.4495			−0.755721
$597$		0			0
$598$	9.55051	−	16.5420i	0.390549	−	0.676451i
$599$	5.32577	−	9.22450i	0.217605	−	0.376903i	−0.736470	−	0.676470i	$-0.763509\pi$
$599$	5.32577	−	9.22450i	0.217605	−	0.376903i	0.954075	+	0.299567i	$0.0968423\pi$
$600$		0			0
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$	13.4495	−	23.2952i	0.548160	−	0.949441i
$603$		0			0
$604$	9.67423	−	16.7563i	0.393639	−	0.681803i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	24.5505			0.996474			0.498237	−	0.867041i	$-0.333981\pi$
$607$	24.5505			0.996474			0.498237	+	0.867041i	$0.333981\pi$
$608$	−1.00000	−	4.24264i	−0.0405554	−	0.172062i
$609$		0			0
$610$	−3.77526	−	6.53893i	−0.152856	−	0.264754i
$611$	26.6969	+	46.2405i	1.08004	+	1.87069i
$612$		0			0
$613$	18.7474	+	32.4715i	0.757202	+	1.31151i	0.944272	+	0.329166i	$0.106768\pi$
$613$	18.7474	+	32.4715i	0.757202	+	1.31151i	−0.187070	+	0.982347i	$0.559899\pi$
$614$	7.12372	−	12.3387i	0.287490	−	0.497947i
$615$		0			0
$616$	−10.3485			−0.416952
$617$	−11.7980	+	20.4347i	−0.474968	+	0.822669i	−0.999589	−	0.0286672i	$-0.990874\pi$
$617$	−11.7980	+	20.4347i	−0.474968	+	0.822669i	0.524621	+	0.851336i	$0.324207\pi$
$618$		0			0
$619$	−21.0454			−0.845886			−0.422943	−	0.906156i	$-0.639003\pi$
$619$	−21.0454			−0.845886			−0.422943	+	0.906156i	$0.639003\pi$
$620$	−8.89898			−0.357392
$621$		0			0
$622$	−4.89898	−	8.48528i	−0.196431	−	0.340229i
$623$	−0.949490	+	1.64456i	−0.0380405	+	0.0658881i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.59592			0.303594
$627$		0			0
$628$	1.20204			0.0479667
$629$	0.325765	+	0.564242i	0.0129891	+	0.0224978i
$630$		0			0
$631$	0.876276	−	1.51775i	0.0348840	−	0.0604208i	−0.848056	−	0.529906i	$-0.822227\pi$
$631$	0.876276	−	1.51775i	0.0348840	−	0.0604208i	0.882940	+	0.469485i	$0.155560\pi$
$632$	−1.44949	−	2.51059i	−0.0576576	−	0.0998659i
$633$		0			0
$634$	4.55051			0.180724
$635$	−14.3485			−0.569402
$636$		0			0
$637$	12.0000	−	20.7846i	0.475457	−	0.823516i
$638$	−16.0454			−0.635244
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−20.3485	−	35.2446i	−0.803716	−	1.39208i	−0.917154	−	0.398532i	$-0.869520\pi$
$641$	−20.3485	−	35.2446i	−0.803716	−	1.39208i	0.113438	−	0.993545i	$-0.463814\pi$
$642$		0			0
$643$	2.12372	+	3.67840i	0.0837515	+	0.145062i	0.904859	−	0.425712i	$-0.139976\pi$
$643$	2.12372	+	3.67840i	0.0837515	+	0.145062i	−0.821107	+	0.570774i	$0.806643\pi$
$644$	6.72474	+	11.6476i	0.264992	+	0.458980i
$645$		0			0
$646$	−6.44949	−	27.3629i	−0.253752	−	1.07658i
$647$	−9.89898			−0.389169			−0.194585	−	0.980886i	$-0.562336\pi$
$647$	−9.89898			−0.389169			−0.194585	+	0.980886i	$0.562336\pi$
$648$		0			0
$649$	−9.00000	−	15.5885i	−0.353281	−	0.611900i
$650$	−2.44949	+	4.24264i	−0.0960769	+	0.166410i
$651$		0			0
$652$	6.34847	−	10.9959i	0.248625	−	0.430632i
$653$	25.6515			1.00382			0.501911	−	0.864919i	$-0.332630\pi$
$653$	25.6515			1.00382			0.501911	+	0.864919i	$0.332630\pi$
$654$		0			0
$655$	1.50000	−	2.59808i	0.0586098	−	0.101515i
$656$	−5.17423	+	8.96204i	−0.202020	+	0.349909i
$657$		0			0
$658$	−37.5959			−1.46564
$659$	−8.29796	+	14.3725i	−0.323243	+	0.559873i	−0.981155	−	0.193222i	$-0.938106\pi$
$659$	−8.29796	+	14.3725i	−0.323243	+	0.559873i	0.657913	+	0.753094i	$0.271440\pi$
$660$		0			0
$661$	−2.89898	+	5.02118i	−0.112757	+	0.195301i	−0.916881	−	0.399161i	$-0.869302\pi$
$661$	−2.89898	+	5.02118i	−0.112757	+	0.195301i	0.804124	+	0.594462i	$0.202635\pi$
$662$	1.82577	+	3.16232i	0.0709604	+	0.122907i
$663$		0			0
$664$	−7.79796			−0.302619
$665$	14.3990	+	4.33013i	0.558368	+	0.167915i
$666$		0			0
$667$	10.4268	+	18.0597i	0.403727	+	0.699275i
$668$	9.84847	+	17.0580i	0.381049	+	0.659996i
$669$		0			0
$670$	−3.67423	−	6.36396i	−0.141948	−	0.245861i
$671$	−11.3258	+	19.6168i	−0.437226	+	0.757298i
$672$		0			0
$673$	8.49490			0.327454			0.163727	−	0.986506i	$-0.447648\pi$
$673$	8.49490			0.327454			0.163727	+	0.986506i	$0.447648\pi$
$674$	11.2474	−	19.4812i	0.433236	−	0.750386i
$675$		0			0
$676$	11.0000			0.423077
$677$	23.9444			0.920258			0.460129	−	0.887852i	$-0.347803\pi$
$677$	23.9444			0.920258			0.460129	+	0.887852i	$0.347803\pi$
$678$		0			0
$679$	23.3712	+	40.4801i	0.896903	+	1.55348i
$680$	−3.22474	+	5.58542i	−0.123663	+	0.214191i
$681$		0			0
$682$	13.3485	+	23.1202i	0.511139	+	0.885319i
$683$	42.2474			1.61655			0.808277	−	0.588803i	$-0.200400\pi$
$683$	42.2474			1.61655			0.808277	+	0.588803i	$0.200400\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$	−3.62372	−	6.27647i	−0.138354	−	0.239637i
$687$		0			0
$688$	−3.89898	+	6.75323i	−0.148647	+	0.257465i
$689$	6.24745	+	10.8209i	0.238009	+	0.412243i
$690$		0			0
$691$	−26.5505			−1.01003			−0.505015	−	0.863111i	$-0.668513\pi$
$691$	−26.5505			−1.01003			−0.505015	+	0.863111i	$0.668513\pi$
$692$	9.44949			0.359216
$693$		0			0
$694$	3.89898	−	6.75323i	0.148003	−	0.256349i
$695$	−14.6969			−0.557487
$696$		0			0
$697$	−33.3712	+	57.8006i	−1.26402	+	2.18935i
$698$	12.0227	+	20.8239i	0.455066	+	0.788198i
$699$		0			0
$700$	−1.72474	−	2.98735i	−0.0651892	−	0.112911i
$701$	11.8990	+	20.6096i	0.449418	+	0.778415i	0.998348	−	0.0574531i	$-0.0182980\pi$
$701$	11.8990	+	20.6096i	0.449418	+	0.778415i	−0.548930	+	0.835868i	$0.684965\pi$
$702$		0			0
$703$	−0.320663	+	0.301783i	−0.0120940	+	0.0113820i
$704$	3.00000			0.113067
$705$		0			0
$706$	10.3258	+	17.8848i	0.388615	+	0.673101i
$707$	−18.7980	+	32.5590i	−0.706970	+	1.22451i
$708$		0			0
$709$	4.47219	−	7.74607i	0.167957	−	0.290910i	−0.769745	−	0.638352i	$-0.779616\pi$
$709$	4.47219	−	7.74607i	0.167957	−	0.290910i	0.937701	+	0.347442i	$0.112950\pi$
$710$	−11.3485			−0.425900
$711$		0			0
$712$	0.275255	−	0.476756i	0.0103156	−	0.0178672i
$713$	17.3485	−	30.0484i	0.649705	−	1.12532i
$714$		0			0
$715$	14.6969			0.549634
$716$	−0.601021	+	1.04100i	−0.0224612	+	0.0389039i
$717$		0			0
$718$	−10.7753	+	18.6633i	−0.402129	+	0.696508i
$719$	−2.65153	−	4.59259i	−0.0988854	−	0.171275i	0.812338	−	0.583187i	$-0.198194\pi$
$719$	−2.65153	−	4.59259i	−0.0988854	−	0.171275i	−0.911224	+	0.411912i	$0.864861\pi$
$720$		0			0
$721$	−45.6969			−1.70184
$722$	17.0000	−	8.48528i	0.632674	−	0.315789i
$723$		0			0
$724$	8.57321	+	14.8492i	0.318621	+	0.551868i
$725$	−2.67423	−	4.63191i	−0.0993186	−	0.172025i
$726$		0			0
$727$	−13.8990	−	24.0737i	−0.515485	−	0.892846i	−0.999838	−	0.0179734i	$-0.994279\pi$
$727$	−13.8990	−	24.0737i	−0.515485	−	0.892846i	0.484354	−	0.874872i	$-0.339055\pi$
$728$	−8.44949	+	14.6349i	−0.313159	+	0.542407i
$729$		0			0
$730$	5.55051			0.205434
$731$	−25.1464	+	43.5549i	−0.930074	+	1.61094i
$732$		0			0
$733$	36.5959			1.35170			0.675851	−	0.737039i	$-0.263776\pi$
$733$	36.5959			1.35170			0.675851	+	0.737039i	$0.263776\pi$
$734$	−11.1010			−0.409746
$735$		0			0
$736$	−1.94949	−	3.37662i	−0.0718591	−	0.124464i
$737$	−11.0227	+	19.0919i	−0.406027	+	0.703259i
$738$		0			0
$739$	7.97219	+	13.8082i	0.293262	+	0.507944i	0.974579	−	0.224044i	$-0.0719259\pi$
$739$	7.97219	+	13.8082i	0.293262	+	0.507944i	−0.681317	+	0.731988i	$0.738593\pi$
$740$	0.101021			0.00371359
$741$		0			0
$742$	−8.79796			−0.322983
$743$	4.84847	+	8.39780i	0.177873	+	0.308085i	0.941152	−	0.337984i	$-0.109745\pi$
$743$	4.84847	+	8.39780i	0.177873	+	0.308085i	−0.763279	+	0.646069i	$0.776412\pi$
$744$		0			0
$745$	−9.22474	+	15.9777i	−0.337969	+	0.585379i
$746$	2.94949	+	5.10867i	0.107988	+	0.187042i
$747$		0			0
$748$	19.3485			0.707450
$749$	59.8434			2.18663
$750$		0			0
$751$	−26.4949	+	45.8905i	−0.966813	+	1.67457i	−0.262148	+	0.965028i	$0.584431\pi$
$751$	−26.4949	+	45.8905i	−0.966813	+	1.67457i	−0.704664	+	0.709541i	$0.748902\pi$
$752$	10.8990			0.397445
$753$		0			0
$754$	−13.1010	+	22.6916i	−0.477111	+	0.826381i
$755$	−9.67423	−	16.7563i	−0.352081	−	0.609823i
$756$		0			0
$757$	−27.1969	−	47.1065i	−0.988490	−	1.71211i	−0.625265	−	0.780412i	$-0.715009\pi$
$757$	−27.1969	−	47.1065i	−0.988490	−	1.71211i	−0.363224	−	0.931702i	$-0.618324\pi$
$758$	11.3485	+	19.6561i	0.412195	+	0.713943i
$759$		0			0
$760$	−4.17423	−	1.25529i	−0.151415	−	0.0455343i
$761$	−16.5505			−0.599956			−0.299978	−	0.953946i	$-0.596979\pi$
$761$	−16.5505			−0.599956			−0.299978	+	0.953946i	$0.596979\pi$
$762$		0			0
$763$	23.0227	+	39.8765i	0.833478	+	1.44363i
$764$	7.89898	−	13.6814i	0.285775	−	0.494977i
$765$		0			0
$766$	9.24745	−	16.0171i	0.334124	−	0.578720i
$767$	−29.3939			−1.06135
$768$		0			0
$769$	7.10102	−	12.2993i	0.256069	−	0.443525i	−0.709116	−	0.705092i	$-0.750906\pi$
$769$	7.10102	−	12.2993i	0.256069	−	0.443525i	0.965185	+	0.261567i	$0.0842391\pi$
$770$	−5.17423	+	8.96204i	−0.186466	+	0.322969i
$771$		0			0
$772$	−6.65153			−0.239394
$773$	−0.477296	+	0.826701i	−0.0171671	+	0.0297344i	−0.874481	−	0.485059i	$-0.838798\pi$
$773$	−0.477296	+	0.826701i	−0.0171671	+	0.0297344i	0.857314	+	0.514794i	$0.172131\pi$
$774$		0			0
$775$	−4.44949	+	7.70674i	−0.159830	+	0.276834i
$776$	−6.77526	−	11.7351i	−0.243217	−	0.421265i
$777$		0			0
$778$	11.1464			0.399619
$779$	−43.1969	−	12.9904i	−1.54769	−	0.465429i
$780$		0			0
$781$	17.0227	+	29.4842i	0.609120	+	1.05503i
$782$	−12.5732	−	21.7774i	−0.449617	−	0.778760i
$783$		0			0
$784$	−2.44949	−	4.24264i	−0.0874818	−	0.151523i
$785$	0.601021	−	1.04100i	0.0214513	−	0.0371548i
$786$		0			0
$787$	−24.0454			−0.857126			−0.428563	−	0.903512i	$-0.640980\pi$
$787$	−24.0454			−0.857126			−0.428563	+	0.903512i	$0.640980\pi$
$788$	5.72474	−	9.91555i	0.203936	−	0.353227i
$789$		0			0
$790$	−2.89898			−0.103141
$791$	49.8434			1.77223
$792$		0			0
$793$	18.4949	+	32.0341i	0.656773	+	1.13756i
$794$	−18.7474	+	32.4715i	−0.665322	+	1.15237i
$795$		0			0
$796$	−0.775255	−	1.34278i	−0.0274782	−	0.0475936i
$797$	−1.65153			−0.0585002			−0.0292501	−	0.999572i	$-0.509312\pi$
$797$	−1.65153			−0.0585002			−0.0292501	+	0.999572i	$0.509312\pi$
$798$		0			0
$799$	70.2929			2.48678
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−7.89898	+	13.6814i	−0.278923	+	0.483108i
$803$	−8.32577	−	14.4206i	−0.293810	−	0.508894i
$804$		0			0
$805$	13.4495			0.474032
$806$	43.5959			1.53560
$807$		0			0
$808$	5.44949	−	9.43879i	0.191712	−	0.332056i
$809$	28.4949			1.00183			0.500914	−	0.865497i	$-0.332997\pi$
$809$	28.4949			1.00183			0.500914	+	0.865497i	$0.332997\pi$
$810$		0			0
$811$	21.4217	−	37.1034i	0.752217	−	1.30288i	−0.194529	−	0.980897i	$-0.562318\pi$
$811$	21.4217	−	37.1034i	0.752217	−	1.30288i	0.946746	−	0.321981i	$-0.104349\pi$
$812$	−9.22474	−	15.9777i	−0.323725	−	0.560708i
$813$		0			0
$814$	−0.151531	−	0.262459i	−0.00531115	−	0.00919918i
$815$	−6.34847	−	10.9959i	−0.222377	−	0.385169i
$816$		0			0
$817$	−32.5505	−	9.78874i	−1.13880	−	0.342465i
$818$	−39.4949			−1.38091
$819$		0			0
$820$	5.17423	+	8.96204i	0.180692	+	0.312968i
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	−0.607714	−	0.794156i	$-0.707913\pi$
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	0.991616	+	0.129217i	$0.0412465\pi$
$822$		0			0
$823$	18.0732	−	31.3037i	0.629993	−	1.09118i	−0.357560	−	0.933890i	$-0.616391\pi$
$823$	18.0732	−	31.3037i	0.629993	−	1.09118i	0.987553	−	0.157289i	$-0.0502754\pi$
$824$	13.2474			0.461497
$825$		0			0
$826$	10.3485	−	17.9241i	0.360069	−	0.623658i
$827$	6.57321	−	11.3851i	0.228573	−	0.395900i	−0.728812	−	0.684713i	$-0.759927\pi$
$827$	6.57321	−	11.3851i	0.228573	−	0.395900i	0.957385	+	0.288813i	$0.0932607\pi$
$828$		0			0
$829$	32.8990			1.14263			0.571314	−	0.820731i	$-0.306434\pi$
$829$	32.8990			1.14263			0.571314	+	0.820731i	$0.306434\pi$
$830$	−3.89898	+	6.75323i	−0.135336	+	0.234408i
$831$		0			0
$832$	2.44949	−	4.24264i	0.0849208	−	0.147087i
$833$	−15.7980	−	27.3629i	−0.547367	−	0.948067i
$834$		0			0
$835$	19.6969			0.681641
$836$	3.00000	+	12.7279i	0.103757	+	0.440204i
$837$		0			0
$838$	−6.05051	−	10.4798i	−0.209011	−	0.362018i
$839$	2.75255	+	4.76756i	0.0950286	+	0.164594i	0.909621	−	0.415440i	$-0.136372\pi$
$839$	2.75255	+	4.76756i	0.0950286	+	0.164594i	−0.814592	+	0.580034i	$0.803039\pi$
$840$		0			0
$841$	0.196938	+	0.341107i	0.00679098	+	0.0117623i
$842$	−16.6742	+	28.8806i	−0.574632	+	0.995292i
$843$		0			0
$844$	−11.6515			−0.401062
$845$	5.50000	−	9.52628i	0.189206	−	0.327714i
$846$		0			0
$847$	−6.89898			−0.237052
$848$	2.55051			0.0875849
$849$		0			0
$850$	3.22474	+	5.58542i	0.110608	+	0.191578i
$851$	−0.196938	+	0.341107i	−0.00675096	+	0.0116930i
$852$		0			0
$853$	−21.6969	−	37.5802i	−0.742889	−	1.28672i	−0.951175	−	0.308653i	$-0.900122\pi$
$853$	−21.6969	−	37.5802i	−0.742889	−	1.28672i	0.208286	−	0.978068i	$-0.433212\pi$
$854$	−26.0454			−0.891256
$855$		0			0
$856$	−17.3485			−0.592958
$857$	−2.20204	−	3.81405i	−0.0752203	−	0.130285i	0.825962	−	0.563726i	$-0.190633\pi$
$857$	−2.20204	−	3.81405i	−0.0752203	−	0.130285i	−0.901182	+	0.433441i	$0.857299\pi$
$858$		0			0
$859$	5.52270	−	9.56560i	0.188432	−	0.326374i	−0.756295	−	0.654230i	$-0.772993\pi$
$859$	5.52270	−	9.56560i	0.188432	−	0.326374i	0.944728	+	0.327856i	$0.106326\pi$
$860$	3.89898	+	6.75323i	0.132954	+	0.230283i
$861$		0			0
$862$	25.3485			0.863372
$863$	−29.0000			−0.987171			−0.493586	−	0.869697i	$-0.664314\pi$
$863$	−29.0000			−0.987171			−0.493586	+	0.869697i	$0.664314\pi$
$864$		0			0
$865$	4.72474	−	8.18350i	0.160646	−	0.278247i
$866$	11.3485			0.385637
$867$		0			0
$868$	−15.3485	+	26.5843i	−0.520961	+	0.902331i
$869$	4.34847	+	7.53177i	0.147512	+	0.255498i
$870$		0			0
$871$	18.0000	+	31.1769i	0.609907	+	1.05639i
$872$	−6.67423	−	11.5601i	−0.226018	−	0.391475i
$873$		0			0
$874$	12.3763	−	11.6476i	0.418634	−	0.393986i
$875$	−3.44949			−0.116614
$876$		0			0
$877$	7.74745	+	13.4190i	0.261613	+	0.453127i	0.966671	−	0.256023i	$-0.0824123\pi$
$877$	7.74745	+	13.4190i	0.261613	+	0.453127i	−0.705058	+	0.709150i	$0.749079\pi$
$878$	−5.67423	+	9.82806i	−0.191496	+	0.331681i
$879$		0			0
$880$	1.50000	−	2.59808i	0.0505650	−	0.0875811i
$881$	7.04541			0.237366			0.118683	−	0.992932i	$-0.462133\pi$
$881$	7.04541			0.237366			0.118683	+	0.992932i	$0.462133\pi$
$882$		0			0
$883$	3.47219	−	6.01402i	0.116849	−	0.202388i	−0.801669	−	0.597769i	$-0.796054\pi$
$883$	3.47219	−	6.01402i	0.116849	−	0.202388i	0.918517	+	0.395381i	$0.129387\pi$
$884$	15.7980	−	27.3629i	0.531343	−	0.920313i
$885$		0			0
$886$	26.2474			0.881800
$887$	−12.1010	+	20.9596i	−0.406313	+	0.703754i	−0.994473	−	0.104990i	$-0.966519\pi$
$887$	−12.1010	+	20.9596i	−0.406313	+	0.703754i	0.588161	+	0.808744i	$0.299852\pi$
$888$		0			0
$889$	−24.7474	+	42.8638i	−0.830003	+	1.43761i
$890$	−0.275255	−	0.476756i	−0.00922657	−	0.0159809i
$891$		0			0
$892$	1.44949			0.0485325
$893$	10.8990	+	46.2405i	0.364720	+	1.54738i
$894$		0			0
$895$	0.601021	+	1.04100i	0.0200899	+	0.0347967i
$896$	1.72474	+	2.98735i	0.0576197	+	0.0998002i
$897$		0			0
$898$	−16.6237	−	28.7931i	−0.554741	−	0.960839i
$899$	−23.7980	+	41.2193i	−0.793706	+	1.37474i
$900$		0			0
$901$	16.4495			0.548012
$902$	15.5227	−	26.8861i	0.516850	−	0.895210i
$903$		0			0
$904$	−14.4495			−0.480583
$905$	17.1464			0.569967
$906$		0			0
$907$	−0.797959	−	1.38211i	−0.0264958	−	0.0458921i	0.852473	−	0.522770i	$-0.175102\pi$
$907$	−0.797959	−	1.38211i	−0.0264958	−	0.0458921i	−0.878969	+	0.476878i	$0.841768\pi$
$908$	1.67423	−	2.89986i	0.0555614	−	0.0962352i
$909$		0			0
$910$	8.44949	+	14.6349i	0.280098	+	0.485144i
$911$	−34.0908			−1.12948			−0.564740	−	0.825269i	$-0.691023\pi$
$911$	−34.0908			−1.12948			−0.564740	+	0.825269i	$0.691023\pi$
$912$		0			0
$913$	23.3939			0.774224
$914$	16.0227	+	27.7521i	0.529984	+	0.917959i
$915$		0			0
$916$	10.3485	−	17.9241i	0.341923	−	0.592228i
$917$	−5.17423	−	8.96204i	−0.170868	−	0.295953i
$918$		0			0
$919$	−20.4495			−0.674566			−0.337283	−	0.941403i	$-0.609508\pi$
$919$	−20.4495			−0.674566			−0.337283	+	0.941403i	$0.609508\pi$
$920$	−3.89898			−0.128546
$921$		0			0
$922$	4.10102	−	7.10318i	0.135060	−	0.233931i
$923$	55.5959			1.82996
$924$		0			0
$925$	0.0505103	−	0.0874863i	0.00166077	−	0.00287653i
$926$	−15.1742	−	26.2825i	−0.498656	−	0.863698i
$927$		0			0
$928$	2.67423	+	4.63191i	0.0877861	+	0.152050i
$929$	19.7247	+	34.1643i	0.647148	+	1.12089i	0.983801	+	0.179264i	$0.0573717\pi$
$929$	19.7247	+	34.1643i	0.647148	+	1.12089i	−0.336653	+	0.941629i	$0.609295\pi$
$930$		0			0
$931$	15.5505	−	14.6349i	0.509647	−	0.479641i
$932$	8.20204			0.268667
$933$		0			0
$934$	7.87628	+	13.6421i	0.257720	+	0.446383i
$935$	9.67423	−	16.7563i	0.316381	−	0.547988i
$936$		0			0
$937$	−9.02270	+	15.6278i	−0.294759	+	0.510537i	−0.974929	−	0.222517i	$-0.928573\pi$
$937$	−9.02270	+	15.6278i	−0.294759	+	0.510537i	0.680170	+	0.733055i	$0.261906\pi$
$938$	−25.3485			−0.827657
$939$		0			0
$940$	5.44949	−	9.43879i	0.177743	−	0.307859i
$941$	−10.2247	+	17.7098i	−0.333317	+	0.577322i	−0.983160	−	0.182746i	$-0.941501\pi$
$941$	−10.2247	+	17.7098i	−0.333317	+	0.577322i	0.649843	+	0.760069i	$0.274835\pi$
$942$		0			0
$943$	−40.3485			−1.31393
$944$	−3.00000	+	5.19615i	−0.0976417	+	0.169120i
$945$		0			0
$946$	11.6969	−	20.2597i	0.380300	−	0.658699i
$947$	−9.77526	−	16.9312i	−0.317653	−	0.550191i	0.662345	−	0.749199i	$-0.269561\pi$
$947$	−9.77526	−	16.9312i	−0.317653	−	0.550191i	−0.979998	+	0.199008i	$0.936228\pi$
$948$		0			0
$949$	−27.1918			−0.882684
$950$	−3.17423	+	2.98735i	−0.102986	+	0.0969223i
$951$		0			0
$952$	11.1237	+	19.2669i	0.360522	+	0.624442i
$953$	8.69694	+	15.0635i	0.281721	+	0.487956i	0.971809	−	0.235770i	$-0.0757613\pi$
$953$	8.69694	+	15.0635i	0.281721	+	0.487956i	−0.690087	+	0.723726i	$0.742428\pi$
$954$		0			0
$955$	−7.89898	−	13.6814i	−0.255605	−	0.442721i
$956$	−5.10102	+	8.83523i	−0.164979	+	0.285752i
$957$		0			0
$958$	−34.0454			−1.09996
$959$	−20.6969	+	35.8481i	−0.668339	+	1.15760i
$960$		0			0
$961$	48.1918			1.55458
$962$	−0.494897			−0.0159561
$963$		0			0
$964$	11.3485	+	19.6561i	0.365510	+	0.633081i
$965$	−3.32577	+	5.76039i	−0.107060	+	0.185434i
$966$		0			0
$967$	−1.55051	−	2.68556i	−0.0498610	−	0.0863619i	0.840018	−	0.542559i	$-0.182545\pi$
$967$	−1.55051	−	2.68556i	−0.0498610	−	0.0863619i	−0.889879	+	0.456197i	$0.849211\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$	−13.5505			−0.435081
$971$	16.3485	+	28.3164i	0.524647	+	0.908716i	0.999588	+	0.0286981i	$0.00913614\pi$
$971$	16.3485	+	28.3164i	0.524647	+	0.908716i	−0.474941	+	0.880018i	$0.657531\pi$
$972$		0			0
$973$	−25.3485	+	43.9048i	−0.812635	+	1.40752i
$974$	3.07321	+	5.32296i	0.0984721	+	0.170559i
$975$		0			0
$976$	7.55051			0.241686
$977$	−44.9444			−1.43790			−0.718949	−	0.695063i	$-0.755377\pi$
$977$	−44.9444			−1.43790			−0.718949	+	0.695063i	$0.755377\pi$
$978$		0			0
$979$	−0.825765	+	1.43027i	−0.0263916	+	0.0457116i
$980$	−4.89898			−0.156492
$981$		0			0
$982$	17.3990	−	30.1359i	0.555224	−	0.961676i
$983$	27.0959	+	46.9315i	0.864226	+	1.49688i	0.867814	+	0.496889i	$0.165524\pi$
$983$	27.0959	+	46.9315i	0.864226	+	1.49688i	−0.00358852	+	0.999994i	$0.501142\pi$
$984$		0			0
$985$	−5.72474	−	9.91555i	−0.182406	−	0.315936i
$986$	17.2474	+	29.8735i	0.549271	+	0.951365i
$987$		0			0
$988$	20.4495	+	6.14966i	0.650585	+	0.195647i
$989$	−30.4041			−0.966794
$990$		0			0
$991$	−3.32577	−	5.76039i	−0.105646	−	0.182985i	0.808356	−	0.588694i	$-0.200358\pi$
$991$	−3.32577	−	5.76039i	−0.105646	−	0.182985i	−0.914002	+	0.405709i	$0.867025\pi$
$992$	4.44949	−	7.70674i	0.141271	−	0.244689i
$993$		0			0
$994$	−19.5732	+	33.9018i	−0.620825	+	1.07530i
$995$	−1.55051			−0.0491545
$996$		0			0
$997$	7.29796	−	12.6404i	0.231129	−	0.400327i	−0.727012	−	0.686625i	$-0.759091\pi$
$997$	7.29796	−	12.6404i	0.231129	−	0.400327i	0.958141	+	0.286298i	$0.0924248\pi$
$998$	7.72474	−	13.3797i	0.244523	−	0.423525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.n.1261.2		4
3.2	odd	2		570.2.i.f.121.2	✓	4
19.11	even	3	inner	1710.2.l.n.1531.2		4
57.11	odd	6		570.2.i.f.391.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.f.121.2	✓	4	3.2	odd	2
570.2.i.f.391.2	yes	4	57.11	odd	6
1710.2.l.n.1261.2		4	1.1	even	1	trivial
1710.2.l.n.1531.2		4	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.44949 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.44949 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +3.00000 q^{11} +(2.44949 - 4.24264i) q^{13} +(1.72474 + 2.98735i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.22474 - 5.58542i) q^{17} +(3.17423 - 2.98735i) q^{19} -1.00000 q^{20} +(1.50000 + 2.59808i) q^{22} +(1.94949 - 3.37662i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.89898 q^{26} +(-1.72474 + 2.98735i) q^{28} +(-2.67423 + 4.63191i) q^{29} +8.89898 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.22474 - 5.58542i) q^{34} +(1.72474 + 2.98735i) q^{35} -0.101021 q^{37} +(4.17423 + 1.25529i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-5.17423 - 8.96204i) q^{41} +(-3.89898 - 6.75323i) q^{43} +(-1.50000 + 2.59808i) q^{44} +3.89898 q^{46} +(-5.44949 + 9.43879i) q^{47} +4.89898 q^{49} -1.00000 q^{50} +(2.44949 + 4.24264i) q^{52} +(-1.27526 + 2.20881i) q^{53} +(1.50000 + 2.59808i) q^{55} -3.44949 q^{56} -5.34847 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-3.77526 + 6.53893i) q^{61} +(4.44949 + 7.70674i) q^{62} +1.00000 q^{64} +4.89898 q^{65} +(-3.67423 + 6.36396i) q^{67} +6.44949 q^{68} +(-1.72474 + 2.98735i) q^{70} +(5.67423 + 9.82806i) q^{71} +(-2.77526 - 4.80688i) q^{73} +(-0.0505103 - 0.0874863i) q^{74} +(1.00000 + 4.24264i) q^{76} +10.3485 q^{77} +(1.44949 + 2.51059i) q^{79} +(0.500000 - 0.866025i) q^{80} +(5.17423 - 8.96204i) q^{82} +7.79796 q^{83} +(3.22474 - 5.58542i) q^{85} +(3.89898 - 6.75323i) q^{86} -3.00000 q^{88} +(-0.275255 + 0.476756i) q^{89} +(8.44949 - 14.6349i) q^{91} +(1.94949 + 3.37662i) q^{92} -10.8990 q^{94} +(4.17423 + 1.25529i) q^{95} +(6.77526 + 11.7351i) q^{97} +(2.44949 + 4.24264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 4 q^{7} - 4 q^{8} - 2 q^{10} + 12 q^{11} + 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 2 q^{23} - 2 q^{25} - 2 q^{28} + 4 q^{29} + 16 q^{31} + 2 q^{32} + 8 q^{34} + 2 q^{35} - 20 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} + 4 q^{43} - 6 q^{44} - 4 q^{46} - 12 q^{47} - 4 q^{50} - 10 q^{53} + 6 q^{55} - 4 q^{56} + 8 q^{58} - 12 q^{59} - 20 q^{61} + 8 q^{62} + 4 q^{64} + 16 q^{68} - 2 q^{70} + 8 q^{71} - 16 q^{73} - 10 q^{74} + 4 q^{76} + 12 q^{77} - 4 q^{79} + 2 q^{80} + 6 q^{82} - 8 q^{83} + 8 q^{85} - 4 q^{86} - 12 q^{88} - 6 q^{89} + 24 q^{91} - 2 q^{92} - 24 q^{94} + 2 q^{95} + 32 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 4 * q^7 - 4 * q^8 - 2 * q^10 + 12 * q^11 + 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 2 * q^23 - 2 * q^25 - 2 * q^28 + 4 * q^29 + 16 * q^31 + 2 * q^32 + 8 * q^34 + 2 * q^35 - 20 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 + 4 * q^43 - 6 * q^44 - 4 * q^46 - 12 * q^47 - 4 * q^50 - 10 * q^53 + 6 * q^55 - 4 * q^56 + 8 * q^58 - 12 * q^59 - 20 * q^61 + 8 * q^62 + 4 * q^64 + 16 * q^68 - 2 * q^70 + 8 * q^71 - 16 * q^73 - 10 * q^74 + 4 * q^76 + 12 * q^77 - 4 * q^79 + 2 * q^80 + 6 * q^82 - 8 * q^83 + 8 * q^85 - 4 * q^86 - 12 * q^88 - 6 * q^89 + 24 * q^91 - 2 * q^92 - 24 * q^94 + 2 * q^95 + 32 * q^97

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