LMFDB - Embedded newform 663.2.z.d.511.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [663,2,Mod(205,663)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(663, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("663.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 663 = 3 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	663.z (of order $6$, 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:	$5.29408165401$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 602x^{10} + 1212x^{8} + 1259x^{6} + 665x^{4} + 168x^{2} + 16 $ x^16 + 20x^14 + 156x^12 + 602x^10 + 1212x^8 + 1259x^6 + 665x^4 + 168*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			511.5
Root			$0.513139i$ of defining polynomial
Character	$\chi$	$=$	663.511
Dual form			663.2.z.d.205.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.444391 + 0.256569i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.868344 - 1.50402i) q^{4} +4.12599i q^{5} +(-0.444391 + 0.256569i) q^{6} +(0.528206 - 0.304960i) q^{7} -1.91744i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.444391 + 0.256569i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.868344 - 1.50402i) q^{4} +4.12599i q^{5} +(-0.444391 + 0.256569i) q^{6} +(0.528206 - 0.304960i) q^{7} -1.91744i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.05860 + 1.83355i) q^{10} +(0.581272 + 0.335598i) q^{11} +1.73669 q^{12} +(1.46481 + 3.29459i) q^{13} +0.312974 q^{14} +(-3.57321 - 2.06300i) q^{15} +(-1.24473 + 2.15594i) q^{16} +(-0.500000 - 0.866025i) q^{17} -0.513139i q^{18} +(-5.71550 + 3.29984i) q^{19} +(6.20556 - 3.58278i) q^{20} +0.609920i q^{21} +(0.172208 + 0.298273i) q^{22} +(-2.11645 + 3.66580i) q^{23} +(1.66055 + 0.958720i) q^{24} -12.0238 q^{25} +(-0.194345 + 1.83991i) q^{26} +1.00000 q^{27} +(-0.917330 - 0.529621i) q^{28} +(3.62460 - 6.27800i) q^{29} +(-1.05860 - 1.83355i) q^{30} +6.63092i q^{31} +(-4.42740 + 2.55616i) q^{32} +(-0.581272 + 0.335598i) q^{33} -0.513139i q^{34} +(1.25826 + 2.17937i) q^{35} +(-0.868344 + 1.50402i) q^{36} +(-9.10722 - 5.25806i) q^{37} -3.38656 q^{38} +(-3.58560 - 0.378738i) q^{39} +7.91134 q^{40} +(0.203888 + 0.117715i) q^{41} +(-0.156487 + 0.271043i) q^{42} +(-1.18023 - 2.04422i) q^{43} -1.16566i q^{44} +(3.57321 - 2.06300i) q^{45} +(-1.88107 + 1.08603i) q^{46} +8.71486i q^{47} +(-1.24473 - 2.15594i) q^{48} +(-3.31400 + 5.74001i) q^{49} +(-5.34328 - 3.08494i) q^{50} +1.00000 q^{51} +(3.68317 - 5.06393i) q^{52} -0.835075 q^{53} +(0.444391 + 0.256569i) q^{54} +(-1.38467 + 2.39832i) q^{55} +(-0.584743 - 1.01280i) q^{56} -6.59969i q^{57} +(3.22148 - 1.85992i) q^{58} +(10.2351 - 5.90925i) q^{59} +7.16556i q^{60} +(-1.27676 - 2.21142i) q^{61} +(-1.70129 + 2.94672i) q^{62} +(-0.528206 - 0.304960i) q^{63} +2.35560 q^{64} +(-13.5935 + 6.04378i) q^{65} -0.344416 q^{66} +(12.2877 + 7.09433i) q^{67} +(-0.868344 + 1.50402i) q^{68} +(-2.11645 - 3.66580i) q^{69} +1.29133i q^{70} +(11.0529 - 6.38141i) q^{71} +(-1.66055 + 0.958720i) q^{72} +13.7741i q^{73} +(-2.69811 - 4.67327i) q^{74} +(6.01190 - 10.4129i) q^{75} +(9.92604 + 5.73080i) q^{76} +0.409375 q^{77} +(-1.49624 - 1.08826i) q^{78} +2.65316 q^{79} +(-8.89539 - 5.13575i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0604041 + 0.104623i) q^{82} +9.26795i q^{83} +(0.917330 - 0.529621i) q^{84} +(3.57321 - 2.06300i) q^{85} -1.21125i q^{86} +(3.62460 + 6.27800i) q^{87} +(0.643488 - 1.11455i) q^{88} +(1.30421 + 0.752984i) q^{89} +2.11721 q^{90} +(1.77844 + 1.29352i) q^{91} +7.35123 q^{92} +(-5.74255 - 3.31546i) q^{93} +(-2.23597 + 3.87281i) q^{94} +(-13.6151 - 23.5821i) q^{95} -5.11232i q^{96} +(8.12871 - 4.69311i) q^{97} +(-2.94542 + 1.70054i) q^{98} -0.671195i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) $ 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/663\mathbb{Z}\right)^\times$.

$n$	$443$	$547$	$613$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.444391	+	0.256569i	0.314232	+	0.181422i	0.648819	−	0.760943i	$-0.275263\pi$
$2$	0.444391	+	0.256569i	0.314232	+	0.181422i	−0.334587	+	0.942365i	$0.608597\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.868344	−	1.50402i	−0.434172	−	0.752008i
$5$			4.12599i			1.84520i	0.385758	+	0.922600i	$0.373940\pi$
$5$			4.12599i			1.84520i	−0.385758	+	0.922600i	$0.626060\pi$
$6$	−0.444391	+	0.256569i	−0.181422	+	0.104744i
$7$	0.528206	−	0.304960i	0.199643	−	0.115264i	−0.396846	−	0.917885i	$-0.629895\pi$
$7$	0.528206	−	0.304960i	0.199643	−	0.115264i	0.596489	+	0.802621i	$0.296562\pi$
$8$		−	1.91744i		−	0.677917i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.05860	+	1.83355i	−0.334760	+	0.579821i
$11$	0.581272	+	0.335598i	0.175260	+	0.101186i	0.585064	−	0.810987i	$-0.301069\pi$
$11$	0.581272	+	0.335598i	0.175260	+	0.101186i	−0.409804	+	0.912174i	$0.634403\pi$
$12$	1.73669			0.501339
$13$	1.46481	+	3.29459i	0.406264	+	0.913756i
$13$	1.46481	+	3.29459i	0.406264	+	0.913756i
$14$	0.312974			0.0836457
$15$	−3.57321	−	2.06300i	−0.922600	−	0.532663i
$16$	−1.24473	+	2.15594i	−0.311183	+	0.538985i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$		−	0.513139i		−	0.120948i
$19$	−5.71550	+	3.29984i	−1.31122	+	0.757036i	−0.982299	−	0.187320i	$-0.940020\pi$
$19$	−5.71550	+	3.29984i	−1.31122	+	0.757036i	−0.328926	+	0.944356i	$0.606687\pi$
$20$	6.20556	−	3.58278i	1.38761	−	0.801134i
$21$			0.609920i			0.133095i
$22$	0.172208	+	0.298273i	0.0367149	+	0.0635921i
$23$	−2.11645	+	3.66580i	−0.441311	+	0.764372i	−0.997787	−	0.0664910i	$-0.978820\pi$
$23$	−2.11645	+	3.66580i	−0.441311	+	0.764372i	0.556476	+	0.830863i	$0.312153\pi$
$24$	1.66055	+	0.958720i	0.338959	+	0.195698i
$25$	−12.0238			−2.40476
$26$	−0.194345	+	1.83991i	−0.0381142	+	0.360837i
$27$	1.00000			0.192450
$28$	−0.917330	−	0.529621i	−0.173359	−	0.100089i
$29$	3.62460	−	6.27800i	0.673072	−	1.16579i	−0.303957	−	0.952686i	$-0.598308\pi$
$29$	3.62460	−	6.27800i	0.673072	−	1.16579i	0.977029	−	0.213109i	$-0.0683588\pi$
$30$	−1.05860	−	1.83355i	−0.193274	−	0.334760i
$31$			6.63092i			1.19095i	0.803374	+	0.595475i	$0.203036\pi$
$31$			6.63092i			1.19095i	−0.803374	+	0.595475i	$0.796964\pi$
$32$	−4.42740	+	2.55616i	−0.782661	+	0.451870i
$33$	−0.581272	+	0.335598i	−0.101186	+	0.0584200i
$34$		−	0.513139i		−	0.0880026i
$35$	1.25826	+	2.17937i	0.212685	+	0.368382i
$36$	−0.868344	+	1.50402i	−0.144724	+	0.250669i
$37$	−9.10722	−	5.25806i	−1.49722	−	0.864419i	−0.497223	−	0.867623i	$-0.665647\pi$
$37$	−9.10722	−	5.25806i	−1.49722	−	0.864419i	−0.999995	+	0.00320364i	$0.998980\pi$
$38$	−3.38656			−0.549372
$39$	−3.58560	−	0.378738i	−0.574156	−	0.0606466i
$40$	7.91134			1.25089
$41$	0.203888	+	0.117715i	0.0318420	+	0.0183840i	0.515836	−	0.856687i	$-0.327481\pi$
$41$	0.203888	+	0.117715i	0.0318420	+	0.0183840i	−0.483995	+	0.875071i	$0.660815\pi$
$42$	−0.156487	+	0.271043i	−0.0241464	+	0.0418229i
$43$	−1.18023	−	2.04422i	−0.179984	−	0.311741i	0.761891	−	0.647705i	$-0.224271\pi$
$43$	−1.18023	−	2.04422i	−0.179984	−	0.311741i	−0.941875	+	0.335964i	$0.890938\pi$
$44$		−	1.16566i		−	0.175729i
$45$	3.57321	−	2.06300i	0.532663	−	0.307533i
$46$	−1.88107	+	1.08603i	−0.277348	+	0.160127i
$47$			8.71486i			1.27119i	0.772021	+	0.635597i	$0.219246\pi$
$47$			8.71486i			1.27119i	−0.772021	+	0.635597i	$0.780754\pi$
$48$	−1.24473	−	2.15594i	−0.179662	−	0.311183i
$49$	−3.31400	+	5.74001i	−0.473428	+	0.820002i
$50$	−5.34328	−	3.08494i	−0.755653	−	0.436277i
$51$	1.00000			0.140028
$52$	3.68317	−	5.06393i	0.510763	−	0.702241i
$53$	−0.835075			−0.114706			−0.0573532	−	0.998354i	$-0.518266\pi$
$53$	−0.835075			−0.114706			−0.0573532	+	0.998354i	$0.518266\pi$
$54$	0.444391	+	0.256569i	0.0604740	+	0.0349147i
$55$	−1.38467	+	2.39832i	−0.186709	+	0.323390i
$56$	−0.584743	−	1.01280i	−0.0781395	−	0.135342i
$57$		−	6.59969i		−	0.874150i
$58$	3.22148	−	1.85992i	0.423001	−	0.244220i
$59$	10.2351	−	5.90925i	1.33250	−	0.769319i	0.346818	−	0.937933i	$-0.387262\pi$
$59$	10.2351	−	5.90925i	1.33250	−	0.769319i	0.985682	+	0.168613i	$0.0539290\pi$
$60$			7.16556i			0.925070i
$61$	−1.27676	−	2.21142i	−0.163473	−	0.283143i	0.772639	−	0.634845i	$-0.218936\pi$
$61$	−1.27676	−	2.21142i	−0.163473	−	0.283143i	−0.936112	+	0.351702i	$0.885603\pi$
$62$	−1.70129	+	2.94672i	−0.216064	+	0.374234i
$63$	−0.528206	−	0.304960i	−0.0665477	−	0.0384214i
$64$	2.35560			0.294450
$65$	−13.5935	+	6.04378i	−1.68606	+	0.749638i
$66$	−0.344416			−0.0423947
$67$	12.2877	+	7.09433i	1.50119	+	0.866710i	0.999999	+	0.00137053i	$0.000436253\pi$
$67$	12.2877	+	7.09433i	1.50119	+	0.866710i	0.501186	+	0.865339i	$0.332897\pi$
$68$	−0.868344	+	1.50402i	−0.105302	+	0.182389i
$69$	−2.11645	−	3.66580i	−0.254791	−	0.441311i
$70$			1.29133i			0.154343i
$71$	11.0529	−	6.38141i	1.31174	−	0.757335i	0.329357	−	0.944205i	$-0.393168\pi$
$71$	11.0529	−	6.38141i	1.31174	−	0.757335i	0.982384	+	0.186871i	$0.0598346\pi$
$72$	−1.66055	+	0.958720i	−0.195698	+	0.112986i
$73$			13.7741i			1.61214i	0.591822	+	0.806068i	$0.298409\pi$
$73$			13.7741i			1.61214i	−0.591822	+	0.806068i	$0.701591\pi$
$74$	−2.69811	−	4.67327i	−0.313649	−	0.543256i
$75$	6.01190	−	10.4129i	0.694195	−	1.20238i
$76$	9.92604	+	5.73080i	1.13859	+	0.657368i
$77$	0.409375			0.0466527
$78$	−1.49624	−	1.08826i	−0.169416	−	0.123222i
$79$	2.65316			0.298504			0.149252	−	0.988799i	$-0.452313\pi$
$79$	2.65316			0.298504			0.149252	+	0.988799i	$0.452313\pi$
$80$	−8.89539	−	5.13575i	−0.994535	−	0.574195i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.0604041	+	0.104623i	0.00667051	+	0.0115537i
$83$			9.26795i			1.01729i	0.860976	+	0.508645i	$0.169853\pi$
$83$			9.26795i			1.01729i	−0.860976	+	0.508645i	$0.830147\pi$
$84$	0.917330	−	0.529621i	0.100089	−	0.0577863i
$85$	3.57321	−	2.06300i	0.387569	−	0.223763i
$86$		−	1.21125i		−	0.130612i
$87$	3.62460	+	6.27800i	0.388598	+	0.673072i
$88$	0.643488	−	1.11455i	0.0685961	−	0.118812i
$89$	1.30421	+	0.752984i	0.138246	+	0.0798161i	0.567528	−	0.823354i	$-0.307900\pi$
$89$	1.30421	+	0.752984i	0.138246	+	0.0798161i	−0.429282	+	0.903171i	$0.641233\pi$
$90$	2.11721			0.223173
$91$	1.77844	+	1.29352i	0.186431	+	0.135597i
$92$	7.35123			0.766419
$93$	−5.74255	−	3.31546i	−0.595475	−	0.343797i
$94$	−2.23597	+	3.87281i	−0.230622	+	0.399450i
$95$	−13.6151	−	23.5821i	−1.39688	−	2.41947i
$96$		−	5.11232i		−	0.521774i
$97$	8.12871	−	4.69311i	0.825346	−	0.476513i	−0.0269108	−	0.999638i	$-0.508567\pi$
$97$	8.12871	−	4.69311i	0.825346	−	0.476513i	0.852256	+	0.523124i	$0.175234\pi$
$98$	−2.94542	+	1.70054i	−0.297533	+	0.171781i
$99$		−	0.671195i		−	0.0674576i
$100$	10.4408	+	18.0840i	1.04408	+	1.80840i
$101$	−2.07626	+	3.59620i	−0.206596	+	0.357835i	−0.950640	−	0.310296i	$-0.899572\pi$
$101$	−2.07626	+	3.59620i	−0.206596	+	0.357835i	0.744044	+	0.668131i	$0.232905\pi$
$102$	0.444391	+	0.256569i	0.0440013	+	0.0254042i
$103$	5.23862			0.516176			0.258088	−	0.966121i	$-0.416908\pi$
$103$	5.23862			0.516176			0.258088	+	0.966121i	$0.416908\pi$
$104$	6.31718	−	2.80868i	0.619451	−	0.275413i
$105$	−2.51653			−0.245588
$106$	−0.371100	−	0.214255i	−0.0360444	−	0.0208103i
$107$	−0.0735498	+	0.127392i	−0.00711033	+	0.0123155i	−0.869559	−	0.493830i	$-0.835597\pi$
$107$	−0.0735498	+	0.127392i	−0.00711033	+	0.0123155i	0.862448	+	0.506145i	$0.168930\pi$
$108$	−0.868344	−	1.50402i	−0.0835565	−	0.144724i
$109$		−	14.1799i		−	1.35819i	−0.734051	−	0.679095i	$-0.762373\pi$
$109$		−	14.1799i		−	1.35819i	0.734051	−	0.679095i	$-0.237627\pi$
$110$	−1.23067	+	0.710529i	−0.117340	+	0.0677463i
$111$	9.10722	−	5.25806i	0.864419	−	0.499073i
$112$			1.51837i			0.143473i
$113$	−0.850293	−	1.47275i	−0.0799888	−	0.138545i	0.823256	−	0.567670i	$-0.192155\pi$
$113$	−0.850293	−	1.47275i	−0.0799888	−	0.138545i	−0.903245	+	0.429126i	$0.858822\pi$
$114$	1.69328	−	2.93284i	0.158590	−	0.274686i
$115$	−15.1251	−	8.73246i	−1.41042	−	0.814306i
$116$	−12.5896			−1.16892
$117$	2.12080	−	2.91586i	0.196068	−	0.269571i
$118$	6.06453			0.558286
$119$	−0.528206	−	0.304960i	−0.0484206	−	0.0279556i
$120$	−3.95567	+	6.85142i	−0.361102	+	0.625446i
$121$	−5.27475	−	9.13613i	−0.479523	−	0.830557i
$122$		−	1.31031i		−	0.118630i
$123$	−0.203888	+	0.117715i	−0.0183840	+	0.0106140i
$124$	9.97302	−	5.75792i	0.895604	−	0.517077i
$125$		−	28.9802i		−	2.59207i
$126$	−0.156487	−	0.271043i	−0.0139410	−	0.0241464i
$127$	5.35691	−	9.27844i	0.475349	−	0.823328i	−0.524253	−	0.851563i	$-0.675655\pi$
$127$	5.35691	−	9.27844i	0.475349	−	0.823328i	0.999601	+	0.0282347i	$0.00898859\pi$
$128$	9.90161	+	5.71670i	0.875187	+	0.505289i
$129$	2.36046			0.207827
$130$	−7.59147	−	0.801866i	−0.665816	−	0.0703283i
$131$	1.46444			0.127949			0.0639745	−	0.997952i	$-0.479622\pi$
$131$	1.46444			0.127949			0.0639745	+	0.997952i	$0.479622\pi$
$132$	1.00949	+	0.582828i	0.0878647	+	0.0507287i
$133$	−2.01264	+	3.48600i	−0.174518	+	0.302274i
$134$	3.64037	+	6.30531i	0.314480	+	0.544696i
$135$			4.12599i			0.355109i
$136$	−1.66055	+	0.958720i	−0.142391	+	0.0822096i
$137$	14.1692	−	8.18060i	1.21056	−	0.698916i	0.247677	−	0.968843i	$-0.420333\pi$
$137$	14.1692	−	8.18060i	1.21056	−	0.698916i	0.962881	+	0.269927i	$0.0869996\pi$
$138$		−	2.17207i		−	0.184899i
$139$	0.996275	+	1.72560i	0.0845029	+	0.146363i	0.905179	−	0.425030i	$-0.139736\pi$
$139$	0.996275	+	1.72560i	0.0845029	+	0.146363i	−0.820676	+	0.571393i	$0.806403\pi$
$140$	2.18521	−	3.78489i	0.184684	−	0.319882i
$141$	−7.54729	−	4.35743i	−0.635597	−	0.366962i
$142$	6.54910			0.549589
$143$	−0.254207	+	2.40664i	−0.0212578	+	0.201253i
$144$	2.48946			0.207455
$145$	25.9030	+	14.9551i	2.15112	+	1.24195i
$146$	−3.53401	+	6.12109i	−0.292477	+	0.506585i
$147$	−3.31400	−	5.74001i	−0.273334	−	0.473428i
$148$			18.2632i			1.50123i
$149$	−2.09903	+	1.21188i	−0.171959	+	0.0992808i	−0.583509	−	0.812106i	$-0.698321\pi$
$149$	−2.09903	+	1.21188i	−0.171959	+	0.0992808i	0.411550	+	0.911387i	$0.364988\pi$
$150$	5.34328	−	3.08494i	0.436277	−	0.251884i
$151$			5.57610i			0.453776i	0.973921	+	0.226888i	$0.0728552\pi$
$151$			5.57610i			0.453776i	−0.973921	+	0.226888i	$0.927145\pi$
$152$	6.32725	+	10.9591i	0.513208	+	0.888902i
$153$	−0.500000	+	0.866025i	−0.0404226	+	0.0700140i
$154$	0.181923	+	0.105033i	0.0146598	+	0.00846382i
$155$	−27.3591			−2.19754
$156$	2.54391	+	5.72168i	0.203676	+	0.458101i
$157$	−22.2748			−1.77772			−0.888860	−	0.458180i	$-0.848502\pi$
$157$	−22.2748			−1.77772			−0.888860	+	0.458180i	$0.848502\pi$
$158$	1.17904	+	0.680721i	0.0937996	+	0.0541552i
$159$	0.417537	−	0.723196i	0.0331129	−	0.0573532i
$160$	−10.5467	−	18.2674i	−0.833790	−	1.44417i
$161$			2.58173i			0.203469i
$162$	−0.444391	+	0.256569i	−0.0349147	+	0.0201580i
$163$	−7.95240	+	4.59132i	−0.622880	+	0.359620i	−0.777989	−	0.628277i	$-0.783760\pi$
$163$	−7.95240	+	4.59132i	−0.622880	+	0.359620i	0.155109	+	0.987897i	$0.450427\pi$
$164$		−	0.408868i		−	0.0319272i
$165$	−1.38467	−	2.39832i	−0.107797	−	0.186709i
$166$	−2.37787	+	4.11860i	−0.184559	+	0.319665i
$167$	19.0071	+	10.9737i	1.47081	+	0.849173i	0.999463	−	0.0327746i	$-0.0104344\pi$
$167$	19.0071	+	10.9737i	1.47081	+	0.849173i	0.471348	+	0.881947i	$0.343768\pi$
$168$	1.16949			0.0902277
$169$	−8.70869	+	9.65188i	−0.669899	+	0.742452i
$170$	2.11721			0.162382
$171$	5.71550	+	3.29984i	0.437075	+	0.252345i
$172$	−2.04970	+	3.55018i	−0.156288	+	0.270698i
$173$	−0.126118	−	0.218443i	−0.00958860	−	0.0166079i	0.861191	−	0.508281i	$-0.169719\pi$
$173$	−0.126118	−	0.218443i	−0.00958860	−	0.0166079i	−0.870780	+	0.491673i	$0.836386\pi$
$174$			3.71985i			0.282001i
$175$	−6.35105	+	3.66678i	−0.480094	+	0.277183i
$176$	−1.44706	+	0.835458i	−0.109076	+	0.0629750i
$177$			11.8185i			0.888333i
$178$	0.386385	+	0.669239i	0.0289608	+	0.0501616i
$179$	−4.14622	+	7.18146i	−0.309903	+	0.536767i	−0.978341	−	0.207000i	$-0.933630\pi$
$179$	−4.14622	+	7.18146i	−0.309903	+	0.536767i	0.668438	+	0.743768i	$0.266963\pi$
$180$	−6.20556	−	3.58278i	−0.462535	−	0.267045i
$181$	20.9596			1.55791			0.778956	−	0.627078i	$-0.215749\pi$
$181$	20.9596			1.55791			0.778956	+	0.627078i	$0.215749\pi$
$182$	0.458446	+	1.03112i	0.0339823	+	0.0764318i
$183$	2.55352			0.188762
$184$	7.02895	+	4.05817i	0.518181	+	0.299172i
$185$	21.6947	−	37.5763i	1.59503	−	2.76267i
$186$	−1.70129	−	2.94672i	−0.124745	−	0.216064i
$187$		−	0.671195i		−	0.0490826i
$188$	13.1073	−	7.56750i	0.955948	−	0.551917i
$189$	0.528206	−	0.304960i	0.0384214	−	0.0221826i
$190$		−	13.9729i		−	1.01370i
$191$	6.98353	+	12.0958i	0.505311	+	0.875224i	0.999981	+	0.00614301i	$0.00195539\pi$
$191$	6.98353	+	12.0958i	0.505311	+	0.875224i	−0.494671	+	0.869081i	$0.664711\pi$
$192$	−1.17780	+	2.04001i	−0.0850003	+	0.147225i
$193$	21.5712	+	12.4542i	1.55273	+	0.896470i	0.997918	+	0.0644963i	$0.0205441\pi$
$193$	21.5712	+	12.4542i	1.55273	+	0.896470i	0.554814	+	0.831974i	$0.312789\pi$
$194$	4.81644			0.345800
$195$	1.56267	−	14.7942i	0.111905	−	1.05943i
$196$	11.5108			0.822198
$197$	−9.45867	−	5.46097i	−0.673903	−	0.389078i	0.123651	−	0.992326i	$-0.460540\pi$
$197$	−9.45867	−	5.46097i	−0.673903	−	0.389078i	−0.797554	+	0.603248i	$0.793873\pi$
$198$	0.172208	−	0.298273i	0.0122383	−	0.0211974i
$199$	3.01445	+	5.22118i	0.213689	+	0.370120i	0.952866	−	0.303391i	$-0.0981188\pi$
$199$	3.01445	+	5.22118i	0.213689	+	0.370120i	−0.739177	+	0.673511i	$0.764785\pi$
$200$			23.0549i			1.63023i
$201$	−12.2877	+	7.09433i	−0.866710	+	0.500395i
$202$	−1.84535	+	1.06541i	−0.129838	+	0.0749621i
$203$		−	4.42144i		−	0.310324i
$204$	−0.868344	−	1.50402i	−0.0607963	−	0.105302i
$205$	−0.485690	+	0.841241i	−0.0339221	+	0.0587548i
$206$	2.32800	+	1.34407i	0.162199	+	0.0936457i
$207$	4.23290			0.294207
$208$	−8.92623	−	0.942854i	−0.618923	−	0.0653751i
$209$	−4.42968			−0.306407
$210$	−1.11832	−	0.645663i	−0.0771715	−	0.0445550i
$211$	−0.176620	+	0.305915i	−0.0121590	+	0.0210601i	−0.872041	−	0.489433i	$-0.837204\pi$
$211$	−0.176620	+	0.305915i	−0.0121590	+	0.0210601i	0.859882	+	0.510493i	$0.170537\pi$
$212$	0.725133	+	1.25597i	0.0498023	+	0.0862601i
$213$			12.7628i			0.874495i
$214$	−0.0653698	+	0.0377413i	−0.00446859	+	0.00257994i
$215$	8.43444	−	4.86963i	0.575224	−	0.332106i
$216$		−	1.91744i		−	0.130465i
$217$	2.02217	+	3.50250i	0.137274	+	0.237765i
$218$	3.63813	−	6.30143i	0.246405	−	0.426787i
$219$	−11.9287	−	6.88705i	−0.806068	−	0.465384i
$220$	4.80949			0.324256
$221$	2.12080	−	2.91586i	0.142660	−	0.196142i
$222$	5.39623			0.362171
$223$	−9.27775	−	5.35651i	−0.621284	−	0.358699i	0.156085	−	0.987744i	$-0.450113\pi$
$223$	−9.27775	−	5.35651i	−0.621284	−	0.358699i	−0.777369	+	0.629045i	$0.783446\pi$
$224$	−1.55905	+	2.70036i	−0.104169	+	0.180425i
$225$	6.01190	+	10.4129i	0.400794	+	0.694195i
$226$		−	0.872637i		−	0.0580469i
$227$	19.8180	−	11.4419i	1.31537	−	0.759428i	0.332389	−	0.943142i	$-0.392145\pi$
$227$	19.8180	−	11.4419i	1.31537	−	0.759428i	0.982980	+	0.183714i	$0.0588120\pi$
$228$	−9.92604	+	5.73080i	−0.657368	+	0.379532i
$229$		−	15.6119i		−	1.03166i	−0.856690	−	0.515831i	$-0.827483\pi$
$229$		−	15.6119i		−	1.03166i	0.856690	−	0.515831i	$-0.172517\pi$
$230$	−4.48097	−	7.76126i	−0.295466	−	0.511762i
$231$	−0.204688	+	0.354529i	−0.0134675	+	0.0233263i
$232$	−12.0377	−	6.94996i	−0.790312	−	0.456287i
$233$	15.2014			0.995879			0.497939	−	0.867212i	$-0.334090\pi$
$233$	15.2014			0.995879			0.497939	+	0.867212i	$0.334090\pi$
$234$	1.69058	−	0.751649i	0.110517	−	0.0491368i
$235$	−35.9575			−2.34561
$236$	−17.7752	−	10.2625i	−1.15707	−	0.668034i
$237$	−1.32658	+	2.29771i	−0.0861707	+	0.149252i
$238$	−0.156487	−	0.271043i	−0.0101435	−	0.0175691i
$239$			17.9147i			1.15881i	0.815040	+	0.579404i	$0.196715\pi$
$239$			17.9147i			1.15881i	−0.815040	+	0.579404i	$0.803285\pi$
$240$	8.89539	−	5.13575i	0.574195	−	0.331512i
$241$	−24.9501	+	14.4049i	−1.60718	+	0.927904i	−0.617179	+	0.786823i	$0.711725\pi$
$241$	−24.9501	+	14.4049i	−1.60718	+	0.927904i	−0.989998	+	0.141081i	$0.954942\pi$
$242$		−	5.41336i		−	0.347984i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.21734	+	3.84054i	−0.141951	+	0.245866i
$245$	−23.6833	−	13.6735i	−1.51307	−	0.873570i
$246$	−0.120808			−0.00770244
$247$	−19.2437	−	13.9966i	−1.22445	−	0.890583i
$248$	12.7144			0.807365
$249$	−8.02628	−	4.63397i	−0.508645	−	0.293666i
$250$	7.43543	−	12.8785i	0.470258	−	0.814510i
$251$	4.63654	+	8.03072i	0.292656	+	0.506895i	0.974437	−	0.224662i	$-0.0721277\pi$
$251$	4.63654	+	8.03072i	0.292656	+	0.506895i	−0.681781	+	0.731556i	$0.738794\pi$
$252$			1.05924i			0.0667259i
$253$	−2.46047	+	1.42055i	−0.154688	+	0.0893093i
$254$	4.76113	−	2.74884i	0.298740	−	0.172477i
$255$			4.12599i			0.258380i
$256$	0.577861	+	1.00088i	0.0361163	+	0.0625552i
$257$	3.79318	−	6.56998i	0.236612	−	0.409824i	−0.723128	−	0.690714i	$-0.757296\pi$
$257$	3.79318	−	6.56998i	0.236612	−	0.409824i	0.959740	+	0.280890i	$0.0906296\pi$
$258$	1.04897	+	0.605623i	0.0653060	+	0.0377044i
$259$	−6.41399			−0.398546
$260$	20.8937	+	15.1967i	1.29578	+	0.942460i
$261$	−7.24920			−0.448715
$262$	0.650786	+	0.375731i	0.0402057	+	0.0232128i
$263$	−13.5480	+	23.4659i	−0.835408	+	1.44697i	0.0582892	+	0.998300i	$0.481435\pi$
$263$	−13.5480	+	23.4659i	−0.835408	+	1.44697i	−0.893698	+	0.448670i	$0.851898\pi$
$264$	0.643488	+	1.11455i	0.0396040	+	0.0685961i
$265$		−	3.44551i		−	0.211656i
$266$	−1.78880	+	1.03276i	−0.109678	+	0.0633228i
$267$	−1.30421	+	0.752984i	−0.0798161	+	0.0460819i
$268$		−	24.6413i		−	1.50521i
$269$	−11.3702	−	19.6937i	−0.693251	−	1.20075i	−0.970767	−	0.240025i	$-0.922844\pi$
$269$	−11.3702	−	19.6937i	−0.693251	−	1.20075i	0.277516	−	0.960721i	$-0.410489\pi$
$270$	−1.05860	+	1.83355i	−0.0644245	+	0.111587i
$271$	−16.5497	−	9.55495i	−1.00532	−	0.580422i	−0.0955025	−	0.995429i	$-0.530446\pi$
$271$	−16.5497	−	9.55495i	−1.00532	−	0.580422i	−0.909818	+	0.415007i	$0.863779\pi$
$272$	2.48946			0.150946
$273$	−2.00944	+	0.893414i	−0.121617	+	0.0540719i
$274$	8.39557			0.507195
$275$	−6.98910	−	4.03516i	−0.421459	−	0.243329i
$276$	−3.67562	+	6.36636i	−0.221246	+	0.383210i
$277$	−3.59979	−	6.23501i	−0.216290	−	0.374626i	0.737381	−	0.675477i	$-0.236062\pi$
$277$	−3.59979	−	6.23501i	−0.216290	−	0.374626i	−0.953671	+	0.300852i	$0.902729\pi$
$278$			1.02245i			0.0613227i
$279$	5.74255	−	3.31546i	0.343797	−	0.198492i
$280$	4.17882	−	2.41264i	0.249732	−	0.144183i
$281$			6.14581i			0.366628i	0.983054	+	0.183314i	$0.0586825\pi$
$281$			6.14581i			0.366628i	−0.983054	+	0.183314i	$0.941317\pi$
$282$	−2.23597	−	3.87281i	−0.133150	−	0.230622i
$283$	0.615925	−	1.06681i	0.0366129	−	0.0634154i	−0.847138	−	0.531372i	$-0.821676\pi$
$283$	0.615925	−	1.06681i	0.0366129	−	0.0634154i	0.883751	+	0.467957i	$0.155010\pi$
$284$	−19.1955	−	11.0825i	−1.13904	−	0.657627i
$285$	27.2303			1.61298
$286$	−0.730438	+	1.00427i	−0.0431917	+	0.0593836i
$287$	0.143593			0.00847604
$288$	4.42740	+	2.55616i	0.260887	+	0.150623i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	7.67403	+	13.2918i	0.450635	+	0.780522i
$291$			9.38623i			0.550230i
$292$	20.7165	−	11.9607i	1.21234	−	0.699945i
$293$	−5.13711	+	2.96591i	−0.300113	+	0.173270i	−0.642494	−	0.766291i	$-0.722100\pi$
$293$	−5.13711	+	2.96591i	−0.300113	+	0.173270i	0.342381	+	0.939561i	$0.388767\pi$
$294$		−	3.40108i		−	0.198355i
$295$	24.3815	+	42.2300i	1.41955	+	2.45873i
$296$	−10.0820	+	17.4625i	−0.586005	+	1.01499i
$297$	0.581272	+	0.335598i	0.0337288	+	0.0194733i
$298$	−1.24372			−0.0720468
$299$	−15.1775	−	1.60316i	−0.877738	−	0.0927131i
$300$	−20.8816			−1.20560
$301$	−1.24681	−	0.719847i	−0.0718650	−	0.0414913i
$302$	−1.43066	+	2.47797i	−0.0823250	+	0.142591i
$303$	−2.07626	−	3.59620i	−0.119278	−	0.206596i
$304$		−	16.4297i		−	0.942307i
$305$	9.12429	−	5.26791i	0.522455	−	0.301640i
$306$	−0.444391	+	0.256569i	−0.0254042	+	0.0146671i
$307$		−	2.52272i		−	0.143979i	−0.997405	−	0.0719896i	$-0.977065\pi$
$307$		−	2.52272i		−	0.143979i	0.997405	−	0.0719896i	$-0.0229348\pi$
$308$	−0.355479	−	0.615707i	−0.0202553	−	0.0350832i
$309$	−2.61931	+	4.53677i	−0.149007	+	0.258088i
$310$	−12.1582	−	7.01952i	−0.690537	−	0.398682i
$311$	−4.58303			−0.259880			−0.129940	−	0.991522i	$-0.541478\pi$
$311$	−4.58303			−0.259880			−0.129940	+	0.991522i	$0.541478\pi$
$312$	−0.726207	+	6.87518i	−0.0411134	+	0.389230i
$313$	3.82997			0.216483			0.108241	−	0.994125i	$-0.465478\pi$
$313$	3.82997			0.216483			0.108241	+	0.994125i	$0.465478\pi$
$314$	−9.89871	−	5.71502i	−0.558616	−	0.322517i
$315$	1.25826	−	2.17937i	0.0708951	−	0.122794i
$316$	−2.30386	−	3.99040i	−0.129602	−	0.224478i
$317$		−	15.0204i		−	0.843631i	−0.906682	−	0.421815i	$-0.861393\pi$
$317$		−	15.0204i		−	0.843631i	0.906682	−	0.421815i	$-0.138607\pi$
$318$	0.371100	−	0.214255i	0.0208103	−	0.0120148i
$319$	4.21376	−	2.43282i	0.235925	−	0.136212i
$320$			9.71918i			0.543319i
$321$	−0.0735498	−	0.127392i	−0.00410515	−	0.00711033i
$322$	−0.662394	+	1.14730i	−0.0369138	+	0.0639365i
$323$	5.71550	+	3.29984i	0.318019	+	0.183608i
$324$	1.73669			0.0964827
$325$	−17.6125	−	39.6136i	−0.976968	−	2.19736i
$326$	−4.71197			−0.260972
$327$	12.2802	+	7.08996i	0.679095	+	0.392076i
$328$	0.225711	−	0.390943i	0.0124628	−	0.0215862i
$329$	2.65769	+	4.60325i	0.146523	+	0.253785i
$330$		−	1.42106i		−	0.0782267i
$331$	−6.32492	+	3.65169i	−0.347649	+	0.200715i	−0.663649	−	0.748044i	$-0.730993\pi$
$331$	−6.32492	+	3.65169i	−0.347649	+	0.200715i	0.316000	+	0.948759i	$0.397660\pi$
$332$	13.9391	−	8.04777i	0.765010	−	0.441679i
$333$			10.5161i			0.576279i
$334$	5.63105	+	9.75326i	0.308117	+	0.533675i
$335$	−29.2711	+	50.6991i	−1.59925	+	2.76999i
$336$	−1.31495	−	0.759187i	−0.0717364	−	0.0414170i
$337$	16.5304			0.900470			0.450235	−	0.892910i	$-0.351340\pi$
$337$	16.5304			0.900470			0.450235	+	0.892910i	$0.351340\pi$
$338$	−6.34644	+	2.05483i	−0.345201	+	0.111768i
$339$	1.70059			0.0923631
$340$	−6.20556	−	3.58278i	−0.336544	−	0.194304i
$341$	−2.22532	+	3.85437i	−0.120508	+	0.208726i
$342$	1.69328	+	2.93284i	0.0915620	+	0.158590i
$343$			8.31199i			0.448805i
$344$	−3.91967	+	2.26302i	−0.211335	+	0.122014i
$345$	15.1251	−	8.73246i	0.814306	−	0.470140i
$346$		−	0.129432i		−	0.00695833i
$347$	14.0697	+	24.3695i	0.755302	+	1.30822i	0.945224	+	0.326422i	$0.105843\pi$
$347$	14.0697	+	24.3695i	0.755302	+	1.30822i	−0.189922	+	0.981799i	$0.560824\pi$
$348$	6.29481	−	10.9029i	0.337437	−	0.584458i
$349$	−3.79947	−	2.19363i	−0.203381	−	0.117422i	0.394850	−	0.918745i	$-0.370796\pi$
$349$	−3.79947	−	2.19363i	−0.203381	−	0.117422i	−0.598232	+	0.801323i	$0.704130\pi$
$350$	−3.76314			−0.201148
$351$	1.46481	+	3.29459i	0.0781855	+	0.175852i
$352$	−3.43136			−0.182892
$353$	−14.6138	−	8.43731i	−0.777817	−	0.449073i	0.0578393	−	0.998326i	$-0.481579\pi$
$353$	−14.6138	−	8.43731i	−0.777817	−	0.449073i	−0.835656	+	0.549253i	$0.814912\pi$
$354$	−3.03227	+	5.25204i	−0.161163	+	0.279143i
$355$	26.3297	+	45.6043i	1.39743	+	2.42043i
$356$		−	2.61540i		−	0.138616i
$357$	0.528206	−	0.304960i	0.0279556	−	0.0161402i
$358$	−3.68509	+	2.12759i	−0.194763	+	0.112446i
$359$		−	9.09023i		−	0.479764i	−0.970802	−	0.239882i	$-0.922891\pi$
$359$		−	9.09023i		−	0.479764i	0.970802	−	0.239882i	$-0.0771088\pi$
$360$	−3.95567	−	6.85142i	−0.208482	−	0.361102i
$361$	12.2779	−	21.2660i	0.646207	−	1.11926i
$362$	9.31425	+	5.37758i	0.489546	+	0.282640i
$363$	10.5495			0.553705
$364$	0.401174	−	3.79802i	0.0210273	−	0.199070i
$365$	−56.8318			−2.97471
$366$	1.13476	+	0.655156i	0.0593151	+	0.0342456i
$367$	−0.413045	+	0.715414i	−0.0215607	+	0.0373443i	−0.876604	−	0.481212i	$-0.840197\pi$
$367$	−0.413045	+	0.715414i	−0.0215607	+	0.0373443i	0.855044	+	0.518556i	$0.173530\pi$
$368$	−5.26883	−	9.12588i	−0.274657	−	0.475719i
$369$		−	0.235430i		−	0.0122560i
$370$	19.2819	−	11.1324i	1.00242	−	0.578745i
$371$	−0.441092	+	0.254664i	−0.0229003	+	0.0132215i
$372$			11.5158i			0.597069i
$373$	11.0591	+	19.1550i	0.572621	+	0.991809i	0.996296	+	0.0859942i	$0.0274067\pi$
$373$	11.0591	+	19.1550i	0.572621	+	0.991809i	−0.423675	+	0.905814i	$0.639260\pi$
$374$	0.172208	−	0.298273i	0.00890467	−	0.0154233i
$375$	25.0976	+	14.4901i	1.29603	+	0.748265i
$376$	16.7102			0.861764
$377$	25.9928	+	2.74555i	1.33870	+	0.141403i
$378$	0.312974			0.0160976
$379$	1.27036	+	0.733443i	0.0652540	+	0.0376744i	0.532272	−	0.846573i	$-0.321338\pi$
$379$	1.27036	+	0.733443i	0.0652540	+	0.0376744i	−0.467018	+	0.884248i	$0.654672\pi$
$380$	−23.6452	+	40.9548i	−1.21298	+	2.10093i
$381$	5.35691	+	9.27844i	0.274443	+	0.475349i
$382$			7.16704i			0.366698i
$383$	0.494619	−	0.285569i	0.0252739	−	0.0145919i	−0.487310	−	0.873229i	$-0.662022\pi$
$383$	0.494619	−	0.285569i	0.0252739	−	0.0145919i	0.512584	+	0.858637i	$0.328688\pi$
$384$	−9.90161	+	5.71670i	−0.505289	+	0.291729i
$385$			1.68908i			0.0860835i
$386$	6.39072	+	11.0690i	0.325279	+	0.563400i
$387$	−1.18023	+	2.04422i	−0.0599946	+	0.103914i
$388$	−14.1170	−	8.15048i	−0.716684	−	0.413778i
$389$	22.7869			1.15534			0.577671	−	0.816270i	$-0.303962\pi$
$389$	22.7869			1.15534			0.577671	+	0.816270i	$0.303962\pi$
$390$	4.49017	−	6.17347i	0.227369	−	0.312606i
$391$	4.23290			0.214067
$392$	11.0061	+	6.35439i	0.555894	+	0.320945i
$393$	−0.732222	+	1.26824i	−0.0369357	+	0.0639745i
$394$	−2.80223	−	4.85361i	−0.141175	−	0.244522i
$395$			10.9469i			0.550800i
$396$	−1.00949	+	0.582828i	−0.0507287	+	0.0292882i
$397$	−22.6603	+	13.0829i	−1.13729	+	0.656612i	−0.945757	−	0.324875i	$-0.894678\pi$
$397$	−22.6603	+	13.0829i	−1.13729	+	0.656612i	−0.191529	+	0.981487i	$0.561345\pi$
$398$			3.09367i			0.155071i
$399$	−2.01264	−	3.48600i	−0.100758	−	0.174518i
$400$	14.9664	−	25.9226i	0.748321	−	1.29613i
$401$	−11.0180	−	6.36122i	−0.550210	−	0.317664i	0.198997	−	0.980000i	$-0.436232\pi$
$401$	−11.0180	−	6.36122i	−0.550210	−	0.317664i	−0.749207	+	0.662336i	$0.769565\pi$
$402$	−7.28075			−0.363131
$403$	−21.8462	+	9.71302i	−1.08824	+	0.483840i
$404$	7.21165			0.358793
$405$	−3.57321	−	2.06300i	−0.177554	−	0.102511i
$406$	1.13441	−	1.96485i	0.0562996	−	0.0975137i
$407$	−3.52918	−	6.11272i	−0.174935	−	0.302996i
$408$		−	1.91744i		−	0.0949274i
$409$	−14.0431	+	8.10777i	−0.694385	+	0.400904i	−0.805253	−	0.592932i	$-0.797970\pi$
$409$	−14.0431	+	8.10777i	−0.694385	+	0.400904i	0.110867	+	0.993835i	$0.464637\pi$
$410$	−0.431673	+	0.249227i	−0.0213188	+	0.0123084i
$411$			16.3612i			0.807038i
$412$	−4.54892	−	7.87896i	−0.224109	−	0.388169i
$413$	3.60417	−	6.24261i	0.177350	−	0.307179i
$414$	1.88107	+	1.08603i	0.0924493	+	0.0533756i
$415$	−38.2395			−1.87710
$416$	−14.9068	−	10.8422i	−0.730865	−	0.531583i
$417$	−1.99255			−0.0975756
$418$	−1.96851	−	1.13652i	−0.0962830	−	0.0555890i
$419$	−2.17770	+	3.77189i	−0.106388	+	0.184269i	−0.914304	−	0.405028i	$-0.867262\pi$
$419$	−2.17770	+	3.77189i	−0.106388	+	0.184269i	0.807917	+	0.589297i	$0.200595\pi$
$420$	2.18521	+	3.78489i	0.106627	+	0.184684i
$421$		−	9.35435i		−	0.455903i	−0.973672	−	0.227951i	$-0.926797\pi$
$421$		−	9.35435i		−	0.455903i	0.973672	−	0.227951i	$-0.0732028\pi$
$422$	−0.156977	+	0.0906306i	−0.00764151	+	0.00441183i
$423$	7.54729	−	4.35743i	0.366962	−	0.211866i
$424$			1.60121i			0.0777614i
$425$	6.01190	+	10.4129i	0.291620	+	0.505101i
$426$	−3.27455	+	5.67169i	−0.158653	+	0.274794i
$427$	−1.34879	−	0.778723i	−0.0652724	−	0.0376850i
$428$	0.255466			0.0123484
$429$	−1.95711	−	1.42347i	−0.0944901	−	0.0687258i
$430$	4.99759			0.241005
$431$	−19.9723	−	11.5310i	−0.962031	−	0.555429i	−0.0652336	−	0.997870i	$-0.520779\pi$
$431$	−19.9723	−	11.5310i	−0.962031	−	0.555429i	−0.896798	+	0.442441i	$0.854113\pi$
$432$	−1.24473	+	2.15594i	−0.0598872	+	0.103728i
$433$	13.2651	+	22.9758i	0.637479	+	1.10415i	0.985984	+	0.166839i	$0.0533559\pi$
$433$	13.2651	+	22.9758i	0.637479	+	1.10415i	−0.348506	+	0.937307i	$0.613311\pi$
$434$			2.07530i			0.0996178i
$435$	−25.9030	+	14.9551i	−1.24195	+	0.717041i
$436$	−21.3268	+	12.3130i	−1.02137	+	0.589688i
$437$		−	27.9358i		−	1.33635i
$438$	−3.53401	−	6.12109i	−0.168862	−	0.292477i
$439$	1.56875	−	2.71715i	0.0748722	−	0.129682i	−0.826158	−	0.563438i	$-0.809478\pi$
$439$	1.56875	−	2.71715i	0.0748722	−	0.129682i	0.901031	+	0.433755i	$0.142812\pi$
$440$	4.59864	+	2.65503i	0.219232	+	0.126573i
$441$	6.62800			0.315619
$442$	1.69058	−	0.751649i	0.0804129	−	0.0357523i
$443$	−14.2320			−0.676185			−0.338092	−	0.941113i	$-0.609782\pi$
$443$	−14.2320			−0.676185			−0.338092	+	0.941113i	$0.609782\pi$
$444$	−15.8164	−	9.13161i	−0.750613	−	0.433367i
$445$	−3.10680	+	5.38114i	−0.147277	+	0.255091i
$446$	−2.74863	−	4.76078i	−0.130152	−	0.225429i
$447$		−	2.42375i		−	0.114640i
$448$	1.24424	−	0.718363i	0.0587849	−	0.0339395i
$449$	24.0124	−	13.8636i	1.13322	−	0.654262i	0.188474	−	0.982078i	$-0.439646\pi$
$449$	24.0124	−	13.8636i	1.13322	−	0.654262i	0.944742	+	0.327816i	$0.106313\pi$
$450$			6.16988i			0.290851i
$451$	0.0790096	+	0.136849i	0.00372042	+	0.00644395i
$452$	−1.47669	+	2.55771i	−0.0694578	+	0.120305i
$453$	−4.82904	−	2.78805i	−0.226888	−	0.130994i
$454$	11.7426			0.551108
$455$	−5.33704	+	7.33782i	−0.250204	+	0.344002i
$456$	−12.6545			−0.592601
$457$	13.3301	+	7.69616i	0.623558	+	0.360011i	0.778253	−	0.627951i	$-0.216106\pi$
$457$	13.3301	+	7.69616i	0.623558	+	0.360011i	−0.154695	+	0.987962i	$0.549440\pi$
$458$	4.00553	−	6.93779i	0.187166	−	0.324181i
$459$	−0.500000	−	0.866025i	−0.0233380	−	0.0404226i
$460$			30.3311i			1.41420i
$461$	−14.8879	+	8.59552i	−0.693397	+	0.400333i	−0.804884	−	0.593433i	$-0.797772\pi$
$461$	−14.8879	+	8.59552i	−0.693397	+	0.400333i	0.111486	+	0.993766i	$0.464439\pi$
$462$	−0.181923	+	0.105033i	−0.00846382	+	0.00488659i
$463$		−	32.9254i		−	1.53017i	−0.643928	−	0.765086i	$-0.722696\pi$
$463$		−	32.9254i		−	1.53017i	0.643928	−	0.765086i	$-0.277304\pi$
$464$	9.02332	+	15.6288i	0.418897	+	0.725551i
$465$	13.6796	−	23.6937i	0.634375	−	1.09877i
$466$	6.75538	+	3.90022i	0.312937	+	0.180674i
$467$	2.68389			0.124196			0.0620979	−	0.998070i	$-0.480221\pi$
$467$	2.68389			0.124196			0.0620979	+	0.998070i	$0.480221\pi$
$468$	−6.22708	−	0.657749i	−0.287847	−	0.0304045i
$469$	8.65394			0.399602
$470$	−15.9792	−	9.22558i	−0.737065	−	0.425544i
$471$	11.1374	−	19.2905i	0.513183	−	0.888860i
$472$	−11.3306	−	19.6252i	−0.521535	−	0.903325i
$473$		−	1.58433i		−	0.0728477i
$474$	−1.17904	+	0.680721i	−0.0541552	+	0.0312665i
$475$	68.7220	−	39.6767i	3.15318	−	1.82049i
$476$			1.05924i			0.0485502i
$477$	0.417537	+	0.723196i	0.0191177	+	0.0331129i
$478$	−4.59638	+	7.96116i	−0.210233	+	0.364135i
$479$	9.23893	+	5.33410i	0.422137	+	0.243721i	0.695991	−	0.718050i	$-0.254965\pi$
$479$	9.23893	+	5.33410i	0.422137	+	0.243721i	−0.273854	+	0.961771i	$0.588298\pi$
$480$	21.0934			0.962777
$481$	3.98285	−	37.7066i	0.181602	−	1.71927i
$482$	−14.7835			−0.673369
$483$	−2.23585	−	1.29087i	−0.101735	−	0.0587364i
$484$	−9.16060	+	15.8666i	−0.416391	+	0.721210i
$485$	19.3637	+	33.5390i	0.879262	+	1.52293i
$486$		−	0.513139i		−	0.0232765i
$487$	18.6270	−	10.7543i	0.844071	−	0.487325i	−0.0145749	−	0.999894i	$-0.504639\pi$
$487$	18.6270	−	10.7543i	0.844071	−	0.487325i	0.858646	+	0.512569i	$0.171306\pi$
$488$	−4.24026	+	2.44812i	−0.191948	+	0.110821i
$489$		−	9.18264i		−	0.415253i
$490$	−7.01642	−	12.1528i	−0.316970	−	0.549007i
$491$	12.6003	−	21.8243i	0.568643	−	0.984918i	−0.428058	−	0.903751i	$-0.640802\pi$
$491$	12.6003	−	21.8243i	0.568643	−	0.984918i	0.996701	−	0.0811668i	$-0.0258647\pi$
$492$	0.354090	+	0.204434i	0.0159636	+	0.00921660i
$493$	−7.24920			−0.326488
$494$	−4.96065	−	11.1573i	−0.223190	−	0.501992i
$495$	2.76935			0.124473
$496$	−14.2959	−	8.25372i	−0.641903	−	0.370603i
$497$	3.89215	−	6.74141i	0.174587	−	0.302393i
$498$	−2.37787	−	4.11860i	−0.106555	−	0.184559i
$499$		−	25.3384i		−	1.13430i	−0.823614	−	0.567151i	$-0.808046\pi$
$499$		−	25.3384i		−	1.13430i	0.823614	−	0.567151i	$-0.191954\pi$
$500$	−43.5867	+	25.1648i	−1.94925	+	1.12540i
$501$	−19.0071	+	10.9737i	−0.849173	+	0.490270i
$502$			4.75838i			0.212377i
$503$	−6.43593	−	11.1474i	−0.286964	−	0.497036i	0.686120	−	0.727489i	$-0.259313\pi$
$503$	−6.43593	−	11.1474i	−0.286964	−	0.497036i	−0.973084	+	0.230453i	$0.925979\pi$
$504$	−0.584743	+	1.01280i	−0.0260465	+	0.0451139i
$505$	−14.8379	−	8.56665i	−0.660277	−	0.381211i
$506$	−1.45788			−0.0648107
$507$	−4.00443	−	12.3679i	−0.177843	−	0.549277i
$508$	−18.6066			−0.825533
$509$	30.5349	+	17.6294i	1.35344	+	0.781407i	0.988729	−	0.149714i	$-0.0478354\pi$
$509$	30.5349	+	17.6294i	1.35344	+	0.781407i	0.364708	+	0.931122i	$0.381169\pi$
$510$	−1.05860	+	1.83355i	−0.0468757	+	0.0811912i
$511$	4.20055	+	7.27557i	0.185821	+	0.321852i
$512$		−	22.2737i		−	0.984369i
$513$	−5.71550	+	3.29984i	−0.252345	+	0.145692i
$514$	3.37131	−	1.94643i	0.148702	−	0.0858532i
$515$			21.6145i			0.952448i
$516$	−2.04970	−	3.55018i	−0.0902328	−	0.156288i
$517$	−2.92469	+	5.06571i	−0.128628	+	0.222790i
$518$	−2.85032	−	1.64563i	−0.125236	−	0.0723050i
$519$	0.252237			0.0110720
$520$	11.5886	+	26.0647i	0.508193	+	1.14301i
$521$	−4.91401			−0.215287			−0.107643	−	0.994190i	$-0.534330\pi$
$521$	−4.91401			−0.215287			−0.107643	+	0.994190i	$0.534330\pi$
$522$	−3.22148	−	1.85992i	−0.141000	−	0.0814067i
$523$	1.65011	−	2.85807i	0.0721542	−	0.124975i	−0.827691	−	0.561184i	$-0.810346\pi$
$523$	1.65011	−	2.85807i	0.0721542	−	0.124975i	0.899845	+	0.436209i	$0.143679\pi$
$524$	−1.27164	−	2.20255i	−0.0555519	−	0.0962187i
$525$		−	7.33356i		−	0.320063i
$526$	−12.0413	+	6.95203i	−0.525024	+	0.303123i
$527$	5.74255	−	3.31546i	0.250149	−	0.144424i
$528$		−	1.67092i		−	0.0727173i
$529$	2.54127	+	4.40160i	0.110490	+	0.191374i
$530$	0.884013	−	1.53116i	0.0383991	−	0.0665091i
$531$	−10.2351	−	5.90925i	−0.444167	−	0.256440i
$532$	6.99066			0.303084
$533$	−0.0891661	+	0.844158i	−0.00386221	+	0.0365645i
$534$	−0.772770			−0.0334410
$535$	−0.525619	−	0.303466i	−0.0227245	−	0.0131200i
$536$	13.6029	−	23.5610i	0.587558	−	1.01768i
$537$	−4.14622	−	7.18146i	−0.178922	−	0.309903i
$538$		−	11.6689i		−	0.503084i
$539$	−3.85267	+	2.22434i	−0.165946	+	0.0958091i
$540$	6.20556	−	3.58278i	0.267045	−	0.154178i
$541$		−	13.7158i		−	0.589690i	−0.955545	−	0.294845i	$-0.904732\pi$
$541$		−	13.7158i		−	0.589690i	0.955545	−	0.294845i	$-0.0952679\pi$
$542$	−4.90302	−	8.49228i	−0.210603	−	0.364775i
$543$	−10.4798	+	18.1515i	−0.449731	+	0.778956i
$544$	4.42740	+	2.55616i	0.189823	+	0.109594i
$545$	58.5062			2.50613
$546$	−1.12220	−	0.118535i	−0.0480257	−	0.00507283i
$547$	−26.1911			−1.11985			−0.559925	−	0.828543i	$-0.689170\pi$
$547$	−26.1911			−1.11985			−0.559925	+	0.828543i	$0.689170\pi$
$548$	−24.6075	−	14.2072i	−1.05118	−	0.606899i
$549$	−1.27676	+	2.21142i	−0.0544909	+	0.0943810i
$550$	−2.07060	−	3.58638i	−0.0882906	−	0.152924i
$551$			47.8425i			2.03816i
$552$	−7.02895	+	4.05817i	−0.299172	+	0.172727i
$553$	1.40142	−	0.809109i	0.0595943	−	0.0344068i
$554$		−	3.69438i		−	0.156959i
$555$	21.6947	+	37.5763i	0.920889	+	1.59503i
$556$	1.73022	−	2.99683i	0.0733776	−	0.127094i
$557$	30.8740	+	17.8251i	1.30817	+	0.755273i	0.981791	−	0.189965i	$-0.0608374\pi$
$557$	30.8740	+	17.8251i	1.30817	+	0.755273i	0.326381	+	0.945238i	$0.394171\pi$
$558$	3.40258			0.144043
$559$	5.00607	−	6.88277i	0.211734	−	0.291110i
$560$	−6.26480			−0.264736
$561$	0.581272	+	0.335598i	0.0245413	+	0.0141689i
$562$	−1.57683	+	2.73114i	−0.0665144	+	0.115206i
$563$	−7.66741	−	13.2803i	−0.323143	−	0.559700i	0.657992	−	0.753025i	$-0.271406\pi$
$563$	−7.66741	−	13.2803i	−0.323143	−	0.559700i	−0.981135	+	0.193325i	$0.938073\pi$
$564$			15.1350i			0.637299i
$565$	6.07656	−	3.50830i	0.255643	−	0.147595i
$566$	0.547423	−	0.316055i	0.0230099	−	0.0132848i
$567$			0.609920i			0.0256142i
$568$	−12.2360	−	21.1933i	−0.513410	−	0.889253i
$569$	9.15198	−	15.8517i	0.383671	−	0.664538i	−0.607913	−	0.794004i	$-0.707993\pi$
$569$	9.15198	−	15.8517i	0.383671	−	0.664538i	0.991584	+	0.129466i	$0.0413263\pi$
$570$	12.1009	+	6.98645i	0.506850	+	0.292630i
$571$	−25.0255			−1.04728			−0.523642	−	0.851939i	$-0.675427\pi$
$571$	−25.0255			−1.04728			−0.523642	+	0.851939i	$0.675427\pi$
$572$	3.84037	−	1.70746i	0.160574	−	0.0713925i
$573$	−13.9671			−0.583482
$574$	0.0638116	+	0.0368416i	0.00266344	+	0.00153774i
$575$	25.4478	−	44.0769i	1.06125	−	1.83813i
$576$	−1.17780	−	2.04001i	−0.0490750	−	0.0850003i
$577$			0.529134i			0.0220281i	0.999939	+	0.0110141i	$0.00350596\pi$
$577$			0.529134i			0.0220281i	−0.999939	+	0.0110141i	$0.996494\pi$
$578$	−0.444391	+	0.256569i	−0.0184842	+	0.0106719i
$579$	−21.5712	+	12.4542i	−0.896470	+	0.517577i
$580$		−	51.9446i		−	2.15688i
$581$	2.82635	+	4.89539i	0.117257	+	0.203095i
$582$	−2.40822	+	4.17116i	−0.0998239	+	0.172900i
$583$	−0.485406	−	0.280249i	−0.0201035	−	0.0116067i
$584$	26.4110			1.09290
$585$	12.0308	+	8.75040i	0.497412	+	0.361784i
$586$	−3.04385			−0.125740
$587$	28.5633	+	16.4911i	1.17894	+	0.680659i	0.955768	−	0.294122i	$-0.0950271\pi$
$587$	28.5633	+	16.4911i	1.17894	+	0.680659i	0.223167	+	0.974780i	$0.428360\pi$
$588$	−5.75538	+	9.96862i	−0.237348	+	0.411099i
$589$	−21.8810	−	37.8990i	−0.901591	−	1.56160i
$590$			25.0222i			1.03015i
$591$	9.45867	−	5.46097i	0.389078	−	0.224634i
$592$	22.6721	−	13.0897i	0.931818	−	0.537985i
$593$			13.4919i			0.554048i	0.960863	+	0.277024i	$0.0893481\pi$
$593$			13.4919i			0.554048i	−0.960863	+	0.277024i	$0.910652\pi$
$594$	0.172208	+	0.298273i	0.00706579	+	0.0122383i
$595$	1.25826	−	2.17937i	0.0515837	−	0.0893457i
$596$	3.64536	+	2.10465i	0.149320	+	0.0862099i
$597$	−6.02890			−0.246747
$598$	−6.33343	−	4.60652i	−0.258993	−	0.188374i
$599$	3.29638			0.134686			0.0673432	−	0.997730i	$-0.478548\pi$
$599$	3.29638			0.134686			0.0673432	+	0.997730i	$0.478548\pi$
$600$	−19.9662	−	11.5275i	−0.815115	−	0.470607i
$601$	−4.42768	+	7.66897i	−0.180609	+	0.312824i	−0.942088	−	0.335366i	$-0.891140\pi$
$601$	−4.42768	+	7.66897i	−0.180609	+	0.312824i	0.761479	+	0.648189i	$0.224473\pi$
$602$	−0.369382	−	0.639788i	−0.0150549	−	0.0260758i
$603$		−	14.1887i		−	0.577807i
$604$	8.38654	−	4.84197i	0.341243	−	0.197017i
$605$	37.6956	−	21.7636i	1.53254	−	0.884815i
$606$		−	2.13082i		−	0.0865588i
$607$	−7.89651	−	13.6772i	−0.320509	−	0.555139i	0.660084	−	0.751192i	$-0.270521\pi$
$607$	−7.89651	−	13.6772i	−0.320509	−	0.555139i	−0.980593	+	0.196053i	$0.937187\pi$
$608$	16.8699	−	29.2195i	0.684163	−	1.18501i
$609$	3.82908	+	2.21072i	0.155162	+	0.0895828i
$610$	5.40634			0.218896
$611$	−28.7119	+	12.7656i	−1.16156	+	0.516440i
$612$	1.73669			0.0702015
$613$	11.6600	+	6.73190i	0.470943	+	0.271899i	0.716634	−	0.697449i	$-0.245682\pi$
$613$	11.6600	+	6.73190i	0.470943	+	0.271899i	−0.245692	+	0.969348i	$0.579015\pi$
$614$	0.647252	−	1.12107i	0.0261210	−	0.0452429i
$615$	−0.485690	−	0.841241i	−0.0195849	−	0.0339221i
$616$		−	0.784953i		−	0.0316266i
$617$	6.62095	−	3.82260i	0.266549	−	0.153892i	−0.360769	−	0.932655i	$-0.617486\pi$
$617$	6.62095	−	3.82260i	0.266549	−	0.153892i	0.627318	+	0.778763i	$0.284152\pi$
$618$	−2.32800	+	1.34407i	−0.0936457	+	0.0540664i
$619$			0.0332037i			0.00133457i	1.00000		0.000667284i	$0.000212403\pi$
$619$			0.0332037i			0.00133457i	−1.00000		0.000667284i	$0.999788\pi$
$620$	23.7572	+	41.1486i	0.954110	+	1.65257i
$621$	−2.11645	+	3.66580i	−0.0849303	+	0.147104i
$622$	−2.03666	−	1.17586i	−0.0816625	−	0.0471479i
$623$	0.918520			0.0367997
$624$	5.27965	−	7.25892i	0.211355	−	0.290589i
$625$	59.4529			2.37812
$626$	1.70201	+	0.982654i	0.0680259	+	0.0392748i
$627$	2.21484	−	3.83621i	0.0884522	−	0.153204i
$628$	19.3422	+	33.5016i	0.771836	+	1.33686i
$629$			10.5161i			0.419305i
$630$	1.11832	−	0.645663i	0.0445550	−	0.0257238i
$631$	−32.3657	+	18.6864i	−1.28846	+	0.743892i	−0.978379	−	0.206818i	$-0.933689\pi$
$631$	−32.3657	+	18.6864i	−1.28846	+	0.743892i	−0.310080	+	0.950710i	$0.600356\pi$
$632$		−	5.08728i		−	0.202361i
$633$	−0.176620	−	0.305915i	−0.00702002	−	0.0121590i
$634$	3.85378	−	6.67494i	0.153053	−	0.265096i
$635$	38.2827	+	22.1026i	1.51920	+	0.877113i
$636$	−1.45027			−0.0575068
$637$	−23.7654	−	2.51027i	−0.941618	−	0.0994606i
$638$	2.49674			0.0988471
$639$	−11.0529	−	6.38141i	−0.437247	−	0.252445i
$640$	−23.5870	+	40.8539i	−0.932360	+	1.61489i
$641$	0.779446	+	1.35004i	0.0307862	+	0.0533233i	0.881008	−	0.473101i	$-0.156866\pi$
$641$	0.779446	+	1.35004i	0.0307862	+	0.0533233i	−0.850222	+	0.526425i	$0.823532\pi$
$642$		−	0.0754825i		−	0.00297906i
$643$	15.5974	−	9.00517i	0.615102	−	0.355129i	−0.159858	−	0.987140i	$-0.551103\pi$
$643$	15.5974	−	9.00517i	0.615102	−	0.355129i	0.774960	+	0.632011i	$0.217770\pi$
$644$	3.88297	−	2.24183i	0.153010	−	0.0883406i
$645$			9.73926i			0.383483i
$646$	1.69328	+	2.93284i	0.0666211	+	0.115391i
$647$	−0.662404	+	1.14732i	−0.0260418	+	0.0451057i	−0.878753	−	0.477278i	$-0.841624\pi$
$647$	−0.662404	+	1.14732i	−0.0260418	+	0.0451057i	0.852711	+	0.522383i	$0.174957\pi$
$648$	1.66055	+	0.958720i	0.0652326	+	0.0376621i
$649$	7.93252			0.311379
$650$	2.33677	−	22.1228i	0.0916555	−	0.867726i
$651$	−4.04433			−0.158510
$652$	13.8108	+	7.97369i	0.540874	+	0.312274i
$653$	0.0841004	−	0.145666i	0.00329110	−	0.00570036i	−0.864375	−	0.502847i	$-0.832286\pi$
$653$	0.0841004	−	0.145666i	0.00329110	−	0.00570036i	0.867666	+	0.497147i	$0.165619\pi$
$654$	3.63813	+	6.30143i	0.142262	+	0.246405i
$655$			6.04228i			0.236091i
$656$	−0.507572	+	0.293047i	−0.0198174	+	0.0114416i
$657$	11.9287	−	6.88705i	0.465384	−	0.268689i
$658$			2.72752i			0.106330i
$659$	0.420142	+	0.727707i	0.0163664	+	0.0283474i	0.874093	−	0.485759i	$-0.161457\pi$
$659$	0.420142	+	0.727707i	0.0163664	+	0.0283474i	−0.857726	+	0.514107i	$0.828124\pi$
$660$	−2.40475	+	4.16514i	−0.0936046	+	0.162128i
$661$	−20.3604	−	11.7551i	−0.791926	−	0.457219i	0.0487139	−	0.998813i	$-0.484488\pi$
$661$	−20.3604	−	11.7551i	−0.791926	−	0.457219i	−0.840640	+	0.541594i	$0.817821\pi$
$662$	−3.74765			−0.145657
$663$	1.46481	+	3.29459i	0.0568883	+	0.127951i
$664$	17.7707			0.689638
$665$	−14.3832	−	8.30414i	−0.557756	−	0.322021i
$666$	−2.69811	+	4.67327i	−0.104550	+	0.181085i
$667$	15.3426	+	26.5741i	0.594067	+	1.02896i
$668$		−	38.1159i		−	1.47475i
$669$	9.27775	−	5.35651i	0.358699	−	0.207095i
$670$	−26.0157	+	15.0202i	−1.00507	+	0.580279i
$671$		−	1.71391i		−	0.0661649i
$672$	−1.55905	−	2.70036i	−0.0601418	−	0.104169i
$673$	−17.4183	+	30.1694i	−0.671426	+	1.16294i	0.306074	+	0.952008i	$0.400985\pi$
$673$	−17.4183	+	30.1694i	−0.671426	+	1.16294i	−0.977500	+	0.210936i	$0.932349\pi$
$674$	7.34598	+	4.24120i	0.282957	+	0.163365i
$675$	−12.0238			−0.462797
$676$	22.0787	+	4.71686i	0.849182	+	0.181418i
$677$	14.7181			0.565662			0.282831	−	0.959170i	$-0.408726\pi$
$677$	14.7181			0.565662			0.282831	+	0.959170i	$0.408726\pi$
$678$	0.755726	+	0.436318i	0.0290235	+	0.0167567i
$679$	2.86242	−	4.95786i	0.109850	−	0.190265i
$680$	−3.95567	−	6.85142i	−0.151693	−	0.262740i
$681$			22.8839i			0.876912i
$682$	−1.97783	+	1.14190i	−0.0757349	+	0.0437256i
$683$	39.9707	−	23.0771i	1.52943	−	0.883020i	0.530049	−	0.847967i	$-0.322173\pi$
$683$	39.9707	−	23.0771i	1.52943	−	0.883020i	0.999385	−	0.0350528i	$-0.0111599\pi$
$684$		−	11.4616i		−	0.438245i
$685$	33.7531	+	58.4621i	1.28964	+	2.23372i
$686$	−2.13260	+	3.69378i	−0.0814231	+	0.141029i
$687$	13.5203	+	7.80594i	0.515831	+	0.297815i
$688$	5.87629			0.224031
$689$	−1.22322	−	2.75123i	−0.0466011	−	0.104814i
$690$	8.96193			0.341175
$691$	−5.69773	−	3.28958i	−0.216752	−	0.125142i	0.387694	−	0.921788i	$-0.373272\pi$
$691$	−5.69773	−	3.28958i	−0.216752	−	0.125142i	−0.604445	+	0.796647i	$0.706605\pi$
$692$	−0.219028	+	0.379368i	−0.00832621	+	0.0144214i
$693$	−0.204688	−	0.354529i	−0.00777544	−	0.0134675i
$694$			14.4394i			0.548113i
$695$	−7.11980	+	4.11062i	−0.270070	+	0.155925i
$696$	12.0377	−	6.94996i	0.456287	−	0.263437i
$697$		−	0.235430i		−	0.00891754i
$698$	−1.12564	−	1.94966i	−0.0426059	−	0.0737956i
$699$	−7.60071	+	13.1648i	−0.287485	+	0.497939i
$700$	11.0298	+	6.36806i	0.416887	+	0.240690i
$701$	1.70603			0.0644360			0.0322180	−	0.999481i	$-0.489743\pi$
$701$	1.70603			0.0644360			0.0322180	+	0.999481i	$0.489743\pi$
$702$	−0.194345	+	1.83991i	−0.00733508	+	0.0694430i
$703$	69.4031			2.61759
$704$	1.36924	+	0.790533i	0.0516053	+	0.0297943i
$705$	17.9787	−	31.1401i	0.677118	−	1.17280i
$706$	−4.32951	−	7.49893i	−0.162943	−	0.282226i
$707$			2.53271i			0.0952524i
$708$	17.7752	−	10.2625i	0.668034	−	0.385690i
$709$	15.2111	−	8.78214i	0.571265	−	0.329820i	−0.186389	−	0.982476i	$-0.559679\pi$
$709$	15.2111	−	8.78214i	0.571265	−	0.329820i	0.757655	+	0.652656i	$0.226345\pi$
$710$			27.0215i			1.01410i
$711$	−1.32658	−	2.29771i	−0.0497507	−	0.0861707i
$712$	1.44380	−	2.50074i	0.0541087	−	0.0937191i
$713$	−24.3077	−	14.0340i	−0.910329	−	0.525579i
$714$	0.312974			0.0117127
$715$	−9.92978	−	1.04886i	−0.371353	−	0.0392250i
$716$	14.4014			0.538205
$717$	−15.5146	−	8.95737i	−0.579404	−	0.334519i
$718$	2.33228	−	4.03962i	0.0870398	−	0.150757i
$719$	−12.0167	−	20.8136i	−0.448148	−	0.776215i	0.550118	−	0.835087i	$-0.314583\pi$
$719$	−12.0167	−	20.8136i	−0.448148	−	0.776215i	−0.998266	+	0.0588722i	$0.981250\pi$
$720$			10.2715i			0.382797i
$721$	2.76707	−	1.59757i	0.103051	−	0.0594966i
$722$	10.9124	−	6.30029i	0.406118	−	0.234472i
$723$		−	28.8099i		−	1.07145i
$724$	−18.2001	−	31.5235i	−0.676402	−	1.17156i
$725$	−43.5815	+	75.4854i	−1.61858	+	2.80346i
$726$	4.68810	+	2.70668i	0.173992	+	0.100454i
$727$	−7.96846			−0.295534			−0.147767	−	0.989022i	$-0.547209\pi$
$727$	−7.96846			−0.295534			−0.147767	+	0.989022i	$0.547209\pi$
$728$	2.48024	−	3.41005i	0.0919239	−	0.126385i
$729$	1.00000			0.0370370
$730$	−25.2556	−	14.5813i	−0.934751	−	0.539679i
$731$	−1.18023	+	2.04422i	−0.0436525	+	0.0756083i
$732$	−2.21734	−	3.84054i	−0.0819552	−	0.141951i
$733$			17.9747i			0.663911i	0.943295	+	0.331955i	$0.107708\pi$
$733$			17.9747i			0.663911i	−0.943295	+	0.331955i	$0.892292\pi$
$734$	−0.367107	+	0.211949i	−0.0135502	+	0.00782319i
$735$	23.6833	−	13.6735i	0.873570	−	0.504356i
$736$		−	21.6400i		−	0.797659i
$737$	4.76168	+	8.24747i	0.175399	+	0.303799i
$738$	0.0604041	−	0.104623i	0.00222350	−	0.00385122i
$739$	−6.68598	−	3.86015i	−0.245948	−	0.141998i	0.371960	−	0.928249i	$-0.378686\pi$
$739$	−6.68598	−	3.86015i	−0.245948	−	0.141998i	−0.617907	+	0.786251i	$0.712019\pi$
$740$	−75.3539			−2.77006
$741$	21.7433	−	9.66726i	0.798760	−	0.355136i
$742$	−0.261356			−0.00959470
$743$	45.0997	+	26.0383i	1.65455	+	0.955252i	0.975169	+	0.221463i	$0.0710832\pi$
$743$	45.0997	+	26.0383i	1.65455	+	0.955252i	0.679377	+	0.733789i	$0.262250\pi$
$744$	−6.35720	+	11.0110i	−0.233066	+	0.403683i
$745$	−5.00019	−	8.66058i	−0.183193	−	0.317299i
$746$			11.3498i			0.415544i
$747$	8.02628	−	4.63397i	0.293666	−	0.169548i
$748$	−1.00949	+	0.582828i	−0.0369106	+	0.0213103i
$749$			0.0897190i			0.00327826i
$750$	7.43543	+	12.8785i	0.271503	+	0.470258i
$751$	−20.1743	+	34.9429i	−0.736171	+	1.27509i	0.218037	+	0.975940i	$0.430035\pi$
$751$	−20.1743	+	34.9429i	−0.736171	+	1.27509i	−0.954208	+	0.299145i	$0.903299\pi$
$752$	−18.7887	−	10.8477i	−0.685154	−	0.395574i
$753$	−9.27308			−0.337930
$754$	10.8465	+	7.88905i	0.395008	+	0.287302i
$755$	−23.0069			−0.837308
$756$	−0.917330	−	0.529621i	−0.0333630	−	0.0192621i
$757$	20.8744	−	36.1555i	0.758692	−	1.31409i	−0.184825	−	0.982771i	$-0.559172\pi$
$757$	20.8744	−	36.1555i	0.758692	−	1.31409i	0.943518	−	0.331322i	$-0.107495\pi$
$758$	0.376358	+	0.651871i	0.0136699	+	0.0236770i
$759$		−	2.84110i		−	0.103126i
$760$	−45.2173	+	26.1062i	−1.64020	+	0.946971i
$761$	−36.6260	+	21.1460i	−1.32769	+	0.766543i	−0.984942	−	0.172884i	$-0.944691\pi$
$761$	−36.6260	+	21.1460i	−1.32769	+	0.766543i	−0.342749	+	0.939427i	$0.611358\pi$
$762$			5.49767i			0.199160i
$763$	−4.32431	−	7.48992i	−0.156550	−	0.271153i
$764$	12.1282	−	21.0067i	0.438784	−	0.759995i
$765$	−3.57321	−	2.06300i	−0.129190	−	0.0745878i
$766$	0.293073			0.0105891
$767$	34.4611	+	25.0647i	1.24432	+	0.905033i
$768$	−1.15572			−0.0417035
$769$	−8.23825	−	4.75636i	−0.297079	−	0.171519i	0.344051	−	0.938951i	$-0.388201\pi$
$769$	−8.23825	−	4.75636i	−0.297079	−	0.171519i	−0.641130	+	0.767432i	$0.721534\pi$
$770$	−0.433366	+	0.750612i	−0.0156174	+	0.0270502i
$771$	3.79318	+	6.56998i	0.136608	+	0.236612i
$772$		−	43.2580i		−	1.55689i
$773$	−4.13782	+	2.38897i	−0.148827	+	0.0859254i	−0.572564	−	0.819860i	$-0.694051\pi$
$773$	−4.13782	+	2.38897i	−0.148827	+	0.0859254i	0.423737	+	0.905785i	$0.360718\pi$
$774$	−1.04897	+	0.605623i	−0.0377044	+	0.0217687i
$775$		−	79.7290i		−	2.86395i
$776$	−8.99876	−	15.5863i	−0.323037	−	0.559516i
$777$	3.20699	−	5.55468i	0.115050	−	0.199273i
$778$	10.1263	+	5.84642i	0.363046	+	0.209604i
$779$	−1.55376			−0.0556693
$780$	−23.6076	+	10.4962i	−0.845288	+	0.375823i
$781$	8.56635			0.306528
$782$	1.88107	+	1.08603i	0.0672668	+	0.0388365i
$783$	3.62460	−	6.27800i	0.129533	−	0.224357i
$784$	−8.25008	−	14.2896i	−0.294646	−	0.510341i
$785$		−	91.9055i		−	3.28025i
$786$	−0.650786	+	0.375731i	−0.0232128	+	0.0134019i
$787$	0.910095	−	0.525443i	0.0324414	−	0.0187300i	−0.483692	−	0.875239i	$-0.660704\pi$
$787$	0.910095	−	0.525443i	0.0324414	−	0.0187300i	0.516133	+	0.856508i	$0.327371\pi$
$788$			18.9680i			0.675707i
$789$	−13.5480	−	23.4659i	−0.482323	−	0.835408i
$790$	−2.80865	+	4.86472i	−0.0999272	+	0.173079i
$791$	−0.898260	−	0.518611i	−0.0319385	−	0.0184397i
$792$	−1.28698			−0.0457307
$793$	5.41551	−	7.44571i	0.192310	−	0.264405i
$794$	−13.4267			−0.476496
$795$	2.98390	+	1.72276i	0.105828	+	0.0610999i
$796$	5.23516	−	9.06757i	0.185555	−	0.321392i
$797$	−24.0900	−	41.7251i	−0.853311	−	1.47798i	−0.878203	−	0.478288i	$-0.841257\pi$
$797$	−24.0900	−	41.7251i	−0.853311	−	1.47798i	0.0248915	−	0.999690i	$-0.492076\pi$
$798$		−	2.06553i		−	0.0731189i
$799$	7.54729	−	4.35743i	0.267004	−	0.154155i
$800$	53.2342	−	30.7348i	1.88211	−	1.08664i
$801$		−	1.50597i		−	0.0532107i
$802$	−3.26419	−	5.65374i	−0.115262	−	0.199640i
$803$	−4.62256	+	8.00650i	−0.163126	+	0.282543i
$804$	21.3400	+	12.3206i	0.752603	+	0.434515i
$805$	−10.6522			−0.375441
$806$	−12.2003	−	1.28869i	−0.429738	−	0.0453921i
$807$	22.7403			0.800497
$808$	6.89549	+	3.98111i	0.242582	+	0.140055i
$809$	−12.2517	+	21.2206i	−0.430748	+	0.746078i	−0.996938	−	0.0781973i	$-0.975084\pi$
$809$	−12.2517	+	21.2206i	−0.430748	+	0.746078i	0.566190	+	0.824275i	$0.308417\pi$
$810$	−1.05860	−	1.83355i	−0.0371955	−	0.0644245i
$811$		−	35.6986i		−	1.25355i	−0.779201	−	0.626774i	$-0.784375\pi$
$811$		−	35.6986i		−	1.25355i	0.779201	−	0.626774i	$-0.215625\pi$
$812$	−6.64991	+	3.83933i	−0.233366	+	0.134734i
$813$	16.5497	−	9.55495i	0.580422	−	0.335107i
$814$		−	3.62192i		−	0.126948i
$815$	−18.9438	−	32.8115i	−0.663571	−	1.14934i
$816$	−1.24473	+	2.15594i	−0.0435743	+	0.0754730i
$817$	13.4912	+	7.78916i	0.471998	+	0.272508i
$818$	−8.32083			−0.290931
$819$	0.231000	−	2.18693i	0.00807178	−	0.0764176i
$820$	1.68699			0.0589121
$821$	35.1493	+	20.2934i	1.22672	+	0.708246i	0.966342	−	0.257261i	$-0.0828201\pi$
$821$	35.1493	+	20.2934i	1.22672	+	0.708246i	0.260376	+	0.965507i	$0.416153\pi$
$822$	−4.19778	+	7.27077i	−0.146415	+	0.253597i
$823$	5.77589	+	10.0041i	0.201335	+	0.348722i	0.948959	−	0.315400i	$-0.102139\pi$
$823$	5.77589	+	10.0041i	0.201335	+	0.348722i	−0.747624	+	0.664122i	$0.768805\pi$
$824$		−	10.0447i		−	0.349925i
$825$	6.98910	−	4.03516i	0.243329	−	0.140486i
$826$	3.20332	−	1.84944i	0.111458	−	0.0643503i
$827$		−	32.3091i		−	1.12350i	−0.827308	−	0.561749i	$-0.810129\pi$
$827$		−	32.3091i		−	1.12350i	0.827308	−	0.561749i	$-0.189871\pi$
$828$	−3.67562	−	6.36636i	−0.127737	−	0.221246i
$829$	−19.7242	+	34.1633i	−0.685049	+	1.18654i	0.288372	+	0.957519i	$0.406886\pi$
$829$	−19.7242	+	34.1633i	−0.685049	+	1.18654i	−0.973421	+	0.229022i	$0.926447\pi$
$830$	−16.9933	−	9.81108i	−0.589846	−	0.340548i
$831$	7.19957			0.249750
$832$	3.45049	+	7.76074i	0.119624	+	0.269055i
$833$	6.62800			0.229647
$834$	−0.885471	−	0.511227i	−0.0306614	−	0.0177023i
$835$	−45.2775	+	78.4230i	−1.56689	+	2.71394i
$836$	3.84649	+	6.66231i	0.133033	+	0.230421i
$837$			6.63092i			0.229198i
$838$	−1.93550	+	1.11746i	−0.0668608	+	0.0386021i
$839$	−44.5359	+	25.7128i	−1.53755	+	0.887705i	−0.538569	+	0.842581i	$0.681035\pi$
$839$	−44.5359	+	25.7128i	−1.53755	+	0.887705i	−0.998981	+	0.0451242i	$0.985632\pi$
$840$			4.82529i			0.166488i
$841$	−11.7755	−	20.3957i	−0.406051	−	0.703301i
$842$	2.40004	−	4.15699i	0.0827108	−	0.143259i
$843$	−5.32243	−	3.07290i	−0.183314	−	0.105836i
$844$	0.613468			0.0211164
$845$	−39.8236	−	35.9320i	−1.36997	−	1.23610i
$846$	4.47194			0.153748
$847$	−5.57231	−	3.21717i	−0.191467	−	0.110543i
$848$	1.03944	−	1.80037i	0.0356947	−	0.0618250i
$849$	0.615925	+	1.06681i	0.0211385	+	0.0366129i
$850$			6.16988i			0.211625i
$851$	38.5500	−	22.2568i	1.32148	−	0.762955i
$852$	19.1955	−	11.0825i	0.657627	−	0.379681i
$853$			41.5674i			1.42324i	0.702564	+	0.711621i	$0.252039\pi$
$853$			41.5674i			1.42324i	−0.702564	+	0.711621i	$0.747961\pi$
$854$	−0.399593	−	0.692115i	−0.0136738	−	0.0236837i
$855$	−13.6151	+	23.5821i	−0.465628	+	0.806491i
$856$	0.244267	+	0.141027i	0.00834886	+	0.00482022i
$857$	−45.4421			−1.55227			−0.776136	−	0.630565i	$-0.782823\pi$
$857$	−45.4421			−1.55227			−0.776136	+	0.630565i	$0.782823\pi$
$858$	−0.504503	−	1.13471i	−0.0172234	−	0.0387384i
$859$	−19.3469			−0.660108			−0.330054	−	0.943962i	$-0.607067\pi$
$859$	−19.3469			−0.660108			−0.330054	+	0.943962i	$0.607067\pi$
$860$	−14.6480	−	8.45703i	−0.499493	−	0.288382i
$861$	−0.0717966	+	0.124355i	−0.00244682	+	0.00423802i
$862$	−5.91701	−	10.2486i	−0.201534	−	0.349067i
$863$		−	55.5628i		−	1.89138i	−0.325069	−	0.945690i	$-0.605388\pi$
$863$		−	55.5628i		−	1.89138i	0.325069	−	0.945690i	$-0.394612\pi$
$864$	−4.42740	+	2.55616i	−0.150623	+	0.0869623i
$865$	0.901296	−	0.520363i	0.0306450	−	0.0176929i
$866$			13.6136i			0.462610i
$867$	−0.500000	−	0.866025i	−0.0169809	−	0.0294118i
$868$	3.51187	−	6.08274i	0.119201	−	0.206462i
$869$	1.54221	+	0.890395i	0.0523159	+	0.0302046i
$870$	−15.3481			−0.520348
$871$	−5.37378	+	50.8749i	−0.182083	+	1.72383i
$872$	−27.1891			−0.920740
$873$	−8.12871	−	4.69311i	−0.275115	−	0.158838i
$874$	7.16748	−	12.4144i	0.242444	−	0.419925i
$875$	−8.83779	−	15.3075i	−0.298772	−	0.517488i
$876$			23.9213i			0.808227i
$877$	10.4999	−	6.06212i	0.354557	−	0.204703i	−0.312134	−	0.950038i	$-0.601044\pi$
$877$	10.4999	−	6.06212i	0.354557	−	0.204703i	0.666690	+	0.745335i	$0.267710\pi$
$878$	1.39427	−	0.804985i	0.0470545	−	0.0271669i
$879$		−	5.93182i		−	0.200075i
$880$	−3.44709	−	5.97054i	−0.116201	−	0.201267i
$881$	13.2745	−	22.9921i	0.447229	−	0.774623i	−0.550976	−	0.834521i	$-0.685744\pi$
$881$	13.2745	−	22.9921i	0.447229	−	0.774623i	0.998204	+	0.0598985i	$0.0190777\pi$
$882$	2.94542	+	1.70054i	0.0991776	+	0.0572602i
$883$	−0.925998			−0.0311623			−0.0155811	−	0.999879i	$-0.504960\pi$
$883$	−0.925998			−0.0311623			−0.0155811	+	0.999879i	$0.504960\pi$
$884$	−6.22708	−	0.657749i	−0.209439	−	0.0221225i
$885$	−48.7631			−1.63915
$886$	−6.32460	−	3.65151i	−0.212479	−	0.122675i
$887$	−20.9951	+	36.3646i	−0.704946	+	1.22100i	0.261765	+	0.965132i	$0.415696\pi$
$887$	−20.9951	+	36.3646i	−0.704946	+	1.22100i	−0.966711	+	0.255871i	$0.917638\pi$
$888$	−10.0820	−	17.4625i	−0.338330	−	0.586005i
$889$		−	6.53457i		−	0.219162i
$890$	−2.76127	+	1.59422i	−0.0925581	+	0.0534385i
$891$	−0.581272	+	0.335598i	−0.0194733	+	0.0112429i
$892$			18.6052i			0.622948i
$893$	−28.7577	−	49.8098i	−0.962339	−	1.66682i
$894$	0.621861	−	1.07709i	0.0207981	−	0.0360234i
$895$	−29.6306	−	17.1073i	−0.990443	−	0.571833i
$896$	6.97345			0.232967
$897$	8.97713	−	12.3425i	0.299738	−	0.412105i
$898$	14.2279			0.474790
$899$	41.6289	+	24.0345i	1.38840	+	0.801594i
$900$	10.4408	−	18.0840i	0.348027	−	0.602800i
$901$	0.417537	+	0.723196i	0.0139102	+	0.0240932i
$902$			0.0810858i			0.00269986i
$903$	1.24681	−	0.719847i	0.0414913	−	0.0239550i
$904$	−2.82391	+	1.63039i	−0.0939219	+	0.0542258i
$905$			86.4790i			2.87466i
$906$	−1.43066	−	2.47797i	−0.0475304	−	0.0823250i
$907$	1.18082	−	2.04523i	0.0392083	−	0.0679108i	−0.845755	−	0.533571i	$-0.820850\pi$
$907$	1.18082	−	2.04523i	0.0392083	−	0.0679108i	0.884964	+	0.465660i	$0.154183\pi$
$908$	−34.4177	−	19.8711i	−1.14219	−	0.659445i
$909$	4.15253			0.137731
$910$	−4.25440	+	1.89154i	−0.141032	+	0.0627040i
$911$	−39.8007			−1.31866			−0.659328	−	0.751856i	$-0.729159\pi$
$911$	−39.8007			−1.31866			−0.659328	+	0.751856i	$0.729159\pi$
$912$	14.2285	+	8.21484i	0.471154	+	0.272021i
$913$	−3.11030	+	5.38720i	−0.102936	+	0.178290i
$914$	3.94920	+	6.84021i	0.130628	+	0.226254i
$915$			10.5358i			0.348304i
$916$	−23.4805	+	13.5565i	−0.775819	+	0.447919i
$917$	0.773528	−	0.446597i	0.0255441	−	0.0147479i
$918$		−	0.513139i		−	0.0169361i
$919$	29.7692	+	51.5617i	0.981994	+	1.70086i	0.654598	+	0.755977i	$0.272838\pi$
$919$	29.7692	+	51.5617i	0.981994	+	1.70086i	0.327396	+	0.944887i	$0.393829\pi$
$920$	−16.7440	+	29.0014i	−0.552032	+	0.956148i
$921$	2.18474	+	1.26136i	0.0719896	+	0.0415632i
$922$	−8.82139			−0.290517
$923$	37.2146	+	27.0674i	1.22493	+	0.890934i
$924$	0.710958			0.0233888
$925$	109.503	+	63.2219i	3.60045	+	2.07872i
$926$	8.44765	−	14.6318i	0.277607	−	0.480829i
$927$	−2.61931	−	4.53677i	−0.0860294	−	0.149007i
$928$			37.0603i			1.21656i
$929$	−9.22771	+	5.32762i	−0.302751	+	0.174793i	−0.643678	−	0.765296i	$-0.722592\pi$
$929$	−9.22771	+	5.32762i	−0.302751	+	0.174793i	0.340927	+	0.940090i	$0.389259\pi$
$930$	12.1582	−	7.01952i	0.398682	−	0.230179i
$931$		−	43.7427i		−	1.43361i
$932$	−13.2001	−	22.8632i	−0.432383	−	0.748909i
$933$	2.29151	−	3.96902i	0.0750208	−	0.129940i
$934$	1.19270	+	0.688605i	0.0390263	+	0.0225318i
$935$	2.76935			0.0905673
$936$	−5.59098	−	4.06650i	−0.182747	−	0.132918i
$937$	−0.664857			−0.0217199			−0.0108600	−	0.999941i	$-0.503457\pi$
$937$	−0.664857			−0.0217199			−0.0108600	+	0.999941i	$0.503457\pi$
$938$	3.84574	+	2.22034i	0.125568	+	0.0724966i
$939$	−1.91499	+	3.31685i	−0.0624932	+	0.108241i
$940$	31.2235	+	54.0806i	1.01840	+	1.76391i
$941$		−	10.5927i		−	0.345311i	−0.984982	−	0.172655i	$-0.944765\pi$
$941$		−	10.5927i		−	0.345311i	0.984982	−	0.172655i	$-0.0552347\pi$
$942$	9.89871	−	5.71502i	0.322517	−	0.186205i
$943$	−0.863039	+	0.498276i	−0.0281044	+	0.0162261i
$944$			29.4217i			0.957596i
$945$	1.25826	+	2.17937i	0.0409313	+	0.0708951i
$946$	0.406491	−	0.704063i	0.0132162	−	0.0228911i
$947$	9.91614	+	5.72508i	0.322231	+	0.186040i	0.652387	−	0.757886i	$-0.273768\pi$
$947$	9.91614	+	5.72508i	0.322231	+	0.186040i	−0.330156	+	0.943927i	$0.607101\pi$
$948$	4.60772			0.149652
$949$	−45.3801	+	20.1764i	−1.47310	+	0.654953i
$950$	40.7193			1.32111
$951$	13.0081	+	7.51021i	0.421815	+	0.243535i
$952$	−0.584743	+	1.01280i	−0.0189516	+	0.0328252i
$953$	−22.7587	−	39.4193i	−0.737228	−	1.27692i	−0.953739	−	0.300636i	$-0.902801\pi$
$953$	−22.7587	−	39.4193i	−0.737228	−	1.27692i	0.216511	−	0.976280i	$-0.430532\pi$
$954$			0.428509i			0.0138735i
$955$	−49.9073	+	28.8140i	−1.61496	+	0.932399i
$956$	26.9441	−	15.5562i	0.871433	−	0.503122i
$957$			4.86563i			0.157284i
$958$	2.73713	+	4.74085i	0.0884328	+	0.153170i
$959$	4.98951	−	8.64209i	0.161120	−	0.279068i
$960$	−8.41705	−	4.85959i	−0.271659	−	0.156843i
$961$	−12.9692			−0.418360
$962$	11.4443	−	15.7346i	0.368979	−	0.507304i
$963$	0.147100			0.00474022
$964$	43.3305	+	25.0169i	1.39558	+	0.805740i
$965$	−51.3858	+	89.0028i	−1.65417	+	2.86510i
$966$	−0.662394	−	1.14730i	−0.0213122	−	0.0369138i
$967$		−	1.50314i		−	0.0483378i	−0.999708	−	0.0241689i	$-0.992306\pi$
$967$		−	1.50314i		−	0.0483378i	0.999708	−	0.0241689i	$-0.00769395\pi$
$968$	−17.5180	+	10.1140i	−0.563049	+	0.325077i
$969$	−5.71550	+	3.29984i	−0.183608	+	0.106006i
$970$			19.8726i			0.638070i
$971$	15.9840	+	27.6851i	0.512951	+	0.888457i	0.999887	+	0.0150196i	$0.00478108\pi$
$971$	15.9840	+	27.6851i	0.512951	+	0.888457i	−0.486936	+	0.873438i	$0.661886\pi$
$972$	−0.868344	+	1.50402i	−0.0278522	+	0.0482413i
$973$	1.05248	+	0.607648i	0.0337409	+	0.0194803i
$974$	11.0369			0.353646
$975$	43.1126	+	4.55387i	1.38071	+	0.145841i
$976$	6.35691			0.203480
$977$	−6.59095	−	3.80529i	−0.210863	−	0.121742i	0.390849	−	0.920455i	$-0.372181\pi$
$977$	−6.59095	−	3.80529i	−0.210863	−	0.121742i	−0.601712	+	0.798713i	$0.705515\pi$
$978$	2.35598	−	4.08069i	0.0753361	−	0.130486i
$979$	0.505399	+	0.875377i	0.0161526	+	0.0279772i
$980$			47.4933i			1.51712i
$981$	−12.2802	+	7.08996i	−0.392076	+	0.226365i
$982$	11.1989	−	6.46569i	0.357372	−	0.206329i
$983$			31.2654i			0.997211i	0.866829	+	0.498605i	$0.166154\pi$
$983$			31.2654i			0.997211i	−0.866829	+	0.498605i	$0.833846\pi$
$984$	0.225711	+	0.390943i	0.00719541	+	0.0124628i
$985$	22.5319	−	39.0264i	0.717926	−	1.24348i
$986$	−3.22148	−	1.85992i	−0.102593	−	0.0592321i
$987$	−5.31537			−0.169190
$988$	−4.34094	+	41.0968i	−0.138104	+	1.30746i
$989$	9.99162			0.317715
$990$	1.23067	+	0.710529i	0.0391134	+	0.0225821i
$991$	−20.5509	+	35.5952i	−0.652820	+	1.13072i	0.329615	+	0.944115i	$0.393081\pi$
$991$	−20.5509	+	35.5952i	−0.652820	+	1.13072i	−0.982436	+	0.186602i	$0.940252\pi$
$992$	−16.9497	−	29.3578i	−0.538154	−	0.932110i
$993$		−	7.30339i		−	0.231766i
$994$	3.45928	−	1.99721i	0.109722	−	0.0633478i
$995$	−21.5426	+	12.4376i	−0.682945	+	0.394299i
$996$			16.0955i			0.510007i
$997$	−1.64109	−	2.84246i	−0.0519740	−	0.0900216i	0.838868	−	0.544335i	$-0.183218\pi$
$997$	−1.64109	−	2.84246i	−0.0519740	−	0.0900216i	−0.890842	+	0.454313i	$0.849885\pi$
$998$	6.50105	−	11.2602i	0.205787	−	0.356434i
$999$	−9.10722	−	5.25806i	−0.288140	−	0.166358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	663.2.z.d.511.5	yes	16
13.6	odd	12		8619.2.a.bn.1.8		16
13.7	odd	12		8619.2.a.bn.1.9		16
13.10	even	6	inner	663.2.z.d.205.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.z.d.205.5	✓	16	13.10	even	6	inner
663.2.z.d.511.5	yes	16	1.1	even	1	trivial
8619.2.a.bn.1.8		16	13.6	odd	12
8619.2.a.bn.1.9		16	13.7	odd	12

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:	\( N \)	\(=\)	\( 663 = 3 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	663.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.444391 + 0.256569i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.868344 - 1.50402i) q^{4} +4.12599i q^{5} +(-0.444391 + 0.256569i) q^{6} +(0.528206 - 0.304960i) q^{7} -1.91744i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.444391 + 0.256569i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.868344 - 1.50402i) q^{4} +4.12599i q^{5} +(-0.444391 + 0.256569i) q^{6} +(0.528206 - 0.304960i) q^{7} -1.91744i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.05860 + 1.83355i) q^{10} +(0.581272 + 0.335598i) q^{11} +1.73669 q^{12} +(1.46481 + 3.29459i) q^{13} +0.312974 q^{14} +(-3.57321 - 2.06300i) q^{15} +(-1.24473 + 2.15594i) q^{16} +(-0.500000 - 0.866025i) q^{17} -0.513139i q^{18} +(-5.71550 + 3.29984i) q^{19} +(6.20556 - 3.58278i) q^{20} +0.609920i q^{21} +(0.172208 + 0.298273i) q^{22} +(-2.11645 + 3.66580i) q^{23} +(1.66055 + 0.958720i) q^{24} -12.0238 q^{25} +(-0.194345 + 1.83991i) q^{26} +1.00000 q^{27} +(-0.917330 - 0.529621i) q^{28} +(3.62460 - 6.27800i) q^{29} +(-1.05860 - 1.83355i) q^{30} +6.63092i q^{31} +(-4.42740 + 2.55616i) q^{32} +(-0.581272 + 0.335598i) q^{33} -0.513139i q^{34} +(1.25826 + 2.17937i) q^{35} +(-0.868344 + 1.50402i) q^{36} +(-9.10722 - 5.25806i) q^{37} -3.38656 q^{38} +(-3.58560 - 0.378738i) q^{39} +7.91134 q^{40} +(0.203888 + 0.117715i) q^{41} +(-0.156487 + 0.271043i) q^{42} +(-1.18023 - 2.04422i) q^{43} -1.16566i q^{44} +(3.57321 - 2.06300i) q^{45} +(-1.88107 + 1.08603i) q^{46} +8.71486i q^{47} +(-1.24473 - 2.15594i) q^{48} +(-3.31400 + 5.74001i) q^{49} +(-5.34328 - 3.08494i) q^{50} +1.00000 q^{51} +(3.68317 - 5.06393i) q^{52} -0.835075 q^{53} +(0.444391 + 0.256569i) q^{54} +(-1.38467 + 2.39832i) q^{55} +(-0.584743 - 1.01280i) q^{56} -6.59969i q^{57} +(3.22148 - 1.85992i) q^{58} +(10.2351 - 5.90925i) q^{59} +7.16556i q^{60} +(-1.27676 - 2.21142i) q^{61} +(-1.70129 + 2.94672i) q^{62} +(-0.528206 - 0.304960i) q^{63} +2.35560 q^{64} +(-13.5935 + 6.04378i) q^{65} -0.344416 q^{66} +(12.2877 + 7.09433i) q^{67} +(-0.868344 + 1.50402i) q^{68} +(-2.11645 - 3.66580i) q^{69} +1.29133i q^{70} +(11.0529 - 6.38141i) q^{71} +(-1.66055 + 0.958720i) q^{72} +13.7741i q^{73} +(-2.69811 - 4.67327i) q^{74} +(6.01190 - 10.4129i) q^{75} +(9.92604 + 5.73080i) q^{76} +0.409375 q^{77} +(-1.49624 - 1.08826i) q^{78} +2.65316 q^{79} +(-8.89539 - 5.13575i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0604041 + 0.104623i) q^{82} +9.26795i q^{83} +(0.917330 - 0.529621i) q^{84} +(3.57321 - 2.06300i) q^{85} -1.21125i q^{86} +(3.62460 + 6.27800i) q^{87} +(0.643488 - 1.11455i) q^{88} +(1.30421 + 0.752984i) q^{89} +2.11721 q^{90} +(1.77844 + 1.29352i) q^{91} +7.35123 q^{92} +(-5.74255 - 3.31546i) q^{93} +(-2.23597 + 3.87281i) q^{94} +(-13.6151 - 23.5821i) q^{95} -5.11232i q^{96} +(8.12871 - 4.69311i) q^{97} +(-2.94542 + 1.70054i) q^{98} -0.671195i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 4 q^{4} - 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} - 2 q^{13} - 26 q^{14} - 3 q^{15} - 8 q^{17} + 27 q^{20} + q^{22} - 21 q^{23} + 14 q^{25} + 2 q^{26} + 16 q^{27} - 33 q^{28} + 29 q^{29} + q^{30} - 15 q^{32} - 3 q^{33} + 15 q^{35} + 4 q^{36} - 18 q^{37} + 62 q^{38} + q^{39} + 4 q^{40} + 12 q^{41} + 13 q^{42} - 3 q^{43} + 3 q^{45} - 9 q^{46} + 2 q^{49} - 36 q^{50} + 16 q^{51} - 8 q^{52} - 26 q^{53} + 9 q^{55} - 37 q^{56} + 30 q^{58} - 3 q^{59} + 29 q^{61} - 20 q^{62} + 36 q^{64} - 16 q^{65} - 2 q^{66} + 33 q^{67} + 4 q^{68} - 21 q^{69} + 27 q^{71} + 17 q^{74} - 7 q^{75} - 48 q^{76} - 8 q^{77} - q^{78} - 14 q^{79} - 39 q^{80} - 8 q^{81} - 3 q^{82} + 33 q^{84} + 3 q^{85} + 29 q^{87} - 5 q^{88} - 3 q^{89} - 2 q^{90} - 70 q^{91} - 64 q^{92} - 6 q^{93} - 25 q^{94} - 27 q^{95} + 6 q^{97} + 102 q^{98}+O(q^{100}) \) 16 * q - 8 * q^3 + 4 * q^4 - 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 - 2 * q^13 - 26 * q^14 - 3 * q^15 - 8 * q^17 + 27 * q^20 + q^22 - 21 * q^23 + 14 * q^25 + 2 * q^26 + 16 * q^27 - 33 * q^28 + 29 * q^29 + q^30 - 15 * q^32 - 3 * q^33 + 15 * q^35 + 4 * q^36 - 18 * q^37 + 62 * q^38 + q^39 + 4 * q^40 + 12 * q^41 + 13 * q^42 - 3 * q^43 + 3 * q^45 - 9 * q^46 + 2 * q^49 - 36 * q^50 + 16 * q^51 - 8 * q^52 - 26 * q^53 + 9 * q^55 - 37 * q^56 + 30 * q^58 - 3 * q^59 + 29 * q^61 - 20 * q^62 + 36 * q^64 - 16 * q^65 - 2 * q^66 + 33 * q^67 + 4 * q^68 - 21 * q^69 + 27 * q^71 + 17 * q^74 - 7 * q^75 - 48 * q^76 - 8 * q^77 - q^78 - 14 * q^79 - 39 * q^80 - 8 * q^81 - 3 * q^82 + 33 * q^84 + 3 * q^85 + 29 * q^87 - 5 * q^88 - 3 * q^89 - 2 * q^90 - 70 * q^91 - 64 * q^92 - 6 * q^93 - 25 * q^94 - 27 * q^95 + 6 * q^97 + 102 * q^98

Introduction

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