LMFDB - Embedded newform 65.2.n.a.9.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(9,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("65.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.n (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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
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			9.5
Root			$1.02826 - 0.593667i$ of defining polynomial
Character	$\chi$	$=$	65.9
Dual form			65.2.n.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02826 + 0.593667i) q^{2} +(-0.298874 - 0.172555i) q^{3} +(-0.295120 - 0.511162i) q^{4} +(1.44045 + 1.71029i) q^{5} +(-0.204880 - 0.354863i) q^{6} +(-1.75765 + 1.01478i) q^{7} -3.07548i q^{8} +(-1.44045 - 2.49493i) q^{9} +O(q^{10})$	\(q+(1.02826 + 0.593667i) q^{2} +(-0.298874 - 0.172555i) q^{3} +(-0.295120 - 0.511162i) q^{4} +(1.44045 + 1.71029i) q^{5} +(-0.204880 - 0.354863i) q^{6} +(-1.75765 + 1.01478i) q^{7} -3.07548i q^{8} +(-1.44045 - 2.49493i) q^{9} +(0.465813 + 2.61378i) q^{10} +(-1.94045 + 3.36096i) q^{11} +0.203698i q^{12} +(-2.96232 - 2.05540i) q^{13} -2.40976 q^{14} +(-0.135393 - 0.759719i) q^{15} +(1.23557 - 2.14007i) q^{16} +(4.71996 - 2.72507i) q^{17} -3.42059i q^{18} +(2.94045 + 5.09301i) q^{19} +(0.449133 - 1.24105i) q^{20} +0.700420 q^{21} +(-3.99058 + 2.30396i) q^{22} +(0.298874 + 0.172555i) q^{23} +(-0.530689 + 0.919180i) q^{24} +(-0.850210 + 4.92718i) q^{25} +(-1.82581 - 3.87212i) q^{26} +2.02956i q^{27} +(1.03743 + 0.598962i) q^{28} +(1.50000 - 2.59808i) q^{29} +(0.311800 - 0.861568i) q^{30} +1.18048 q^{31} +(-2.78591 + 1.60845i) q^{32} +(1.15990 - 0.669668i) q^{33} +6.47114 q^{34} +(-4.26737 - 1.54436i) q^{35} +(-0.850210 + 1.47261i) q^{36} +(4.71996 + 2.72507i) q^{37} +6.98259i q^{38} +(0.530689 + 1.12547i) q^{39} +(5.25997 - 4.43007i) q^{40} +(-0.0902394 + 0.156299i) q^{41} +(0.720215 + 0.415816i) q^{42} +(-1.15990 + 0.669668i) q^{43} +2.29066 q^{44} +(2.19217 - 6.05742i) q^{45} +(0.204880 + 0.354863i) q^{46} -12.2807i q^{47} +(-0.738559 + 0.426407i) q^{48} +(-1.44045 + 2.49493i) q^{49} +(-3.79934 + 4.56169i) q^{50} -1.88090 q^{51} +(-0.176407 + 2.12081i) q^{52} +2.42636i q^{53} +(-1.20488 + 2.08691i) q^{54} +(-8.54334 + 1.52255i) q^{55} +(3.12093 + 5.40561i) q^{56} -2.02956i q^{57} +(3.08478 - 1.78100i) q^{58} +(-3.53069 - 6.11533i) q^{59} +(-0.348383 + 0.293416i) q^{60} +(-3.38090 - 5.85589i) q^{61} +(1.21384 + 0.700811i) q^{62} +(5.06361 + 2.92347i) q^{63} -8.76180 q^{64} +(-0.751722 - 8.02714i) q^{65} +1.59024 q^{66} +(-3.81417 - 2.20211i) q^{67} +(-2.78591 - 1.60845i) q^{68} +(-0.0595504 - 0.103144i) q^{69} +(-3.47114 - 4.12140i) q^{70} +(0.940450 + 1.62891i) q^{71} +(-7.67311 + 4.43007i) q^{72} +8.86014i q^{73} +(3.23557 + 5.60417i) q^{74} +(1.10432 - 1.32590i) q^{75} +(1.73557 - 3.00609i) q^{76} -7.87651i q^{77} +(-0.122467 + 1.47233i) q^{78} -11.1805 q^{79} +(5.43992 - 0.969475i) q^{80} +(-3.97114 + 6.87821i) q^{81} +(-0.185579 + 0.107144i) q^{82} +7.83540i q^{83} +(-0.206708 - 0.358028i) q^{84} +(11.4595 + 4.14720i) q^{85} -1.59024 q^{86} +(-0.896622 + 0.517665i) q^{87} +(10.3365 + 5.96781i) q^{88} +(6.12093 - 10.6018i) q^{89} +(5.85021 - 4.92718i) q^{90} +(7.29249 + 0.606582i) q^{91} -0.203698i q^{92} +(-0.352814 - 0.203698i) q^{93} +(7.29066 - 12.6278i) q^{94} +(-4.47497 + 12.3653i) q^{95} +1.11018 q^{96} +(5.02801 - 2.90292i) q^{97} +(-2.96232 + 1.71029i) q^{98} +11.1805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 6 q^{5} - 10 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 6 * q^5 - 10 * q^6 + 6 * q^9	$ 12 q + 4 q^{4} - 6 q^{5} - 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} - 4 q^{15} - 16 q^{16} + 12 q^{19} - q^{20} - 8 q^{21} + 32 q^{24} - 2 q^{25} + 24 q^{26} + 18 q^{29} + 4 q^{30} - 16 q^{31} + 16 q^{34} + 10 q^{35} - 2 q^{36} - 32 q^{39} + 70 q^{40} + 14 q^{41} - 4 q^{44} - 29 q^{45} + 10 q^{46} + 6 q^{49} - 31 q^{50} + 24 q^{51} - 22 q^{54} - 26 q^{55} - 16 q^{56} - 4 q^{59} - 96 q^{60} + 6 q^{61} - 12 q^{64} + 23 q^{65} + 4 q^{66} - 24 q^{69} + 20 q^{70} - 12 q^{71} + 8 q^{74} + 2 q^{75} - 10 q^{76} - 104 q^{79} + 33 q^{80} + 14 q^{81} + 90 q^{84} + 21 q^{85} - 4 q^{86} + 20 q^{89} + 62 q^{90} - 44 q^{91} + 56 q^{94} + 20 q^{95} + 12 q^{96} + 104 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 - 6 * q^5 - 10 * q^6 + 6 * q^9 + 7 * q^10 - 44 * q^14 - 4 * q^15 - 16 * q^16 + 12 * q^19 - q^20 - 8 * q^21 + 32 * q^24 - 2 * q^25 + 24 * q^26 + 18 * q^29 + 4 * q^30 - 16 * q^31 + 16 * q^34 + 10 * q^35 - 2 * q^36 - 32 * q^39 + 70 * q^40 + 14 * q^41 - 4 * q^44 - 29 * q^45 + 10 * q^46 + 6 * q^49 - 31 * q^50 + 24 * q^51 - 22 * q^54 - 26 * q^55 - 16 * q^56 - 4 * q^59 - 96 * q^60 + 6 * q^61 - 12 * q^64 + 23 * q^65 + 4 * q^66 - 24 * q^69 + 20 * q^70 - 12 * q^71 + 8 * q^74 + 2 * q^75 - 10 * q^76 - 104 * q^79 + 33 * q^80 + 14 * q^81 + 90 * q^84 + 21 * q^85 - 4 * q^86 + 20 * q^89 + 62 * q^90 - 44 * q^91 + 56 * q^94 + 20 * q^95 + 12 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.02826	+	0.593667i	0.727090	+	0.419786i	0.817357	−	0.576132i	$-0.195439\pi$
$2$	1.02826	+	0.593667i	0.727090	+	0.419786i	−0.0902665	+	0.995918i	$0.528772\pi$
$3$	−0.298874	−	0.172555i	−0.172555	−	0.0996247i	0.411235	−	0.911529i	$-0.365098\pi$
$3$	−0.298874	−	0.172555i	−0.172555	−	0.0996247i	−0.583790	+	0.811905i	$0.698431\pi$
$4$	−0.295120	−	0.511162i	−0.147560	−	0.255581i
$5$	1.44045	+	1.71029i	0.644189	+	0.764867i
$5$	1.44045	+	1.71029i	0.644189	+	0.764867i
$6$	−0.204880	−	0.354863i	−0.0836420	−	0.144872i
$7$	−1.75765	+	1.01478i	−0.664328	+	0.383550i	−0.793924	−	0.608017i	$-0.791965\pi$
$7$	−1.75765	+	1.01478i	−0.664328	+	0.383550i	0.129596	+	0.991567i	$0.458632\pi$
$8$		−	3.07548i		−	1.08735i
$9$	−1.44045	−	2.49493i	−0.480150	−	0.831644i
$10$	0.465813	+	2.61378i	0.147303	+	0.826548i
$11$	−1.94045	+	3.36096i	−0.585068	+	1.01337i	0.409799	+	0.912176i	$0.365599\pi$
$11$	−1.94045	+	3.36096i	−0.585068	+	1.01337i	−0.994867	+	0.101191i	$0.967735\pi$
$12$			0.203698i			0.0588024i
$13$	−2.96232	−	2.05540i	−0.821599	−	0.570066i
$13$	−2.96232	−	2.05540i	−0.821599	−	0.570066i
$14$	−2.40976			−0.644036
$15$	−0.135393	−	0.759719i	−0.0349584	−	0.196159i
$16$	1.23557	−	2.14007i	0.308892	−	0.535017i
$17$	4.71996	−	2.72507i	1.14476	−	0.660927i	0.197155	−	0.980372i	$-0.436830\pi$
$17$	4.71996	−	2.72507i	1.14476	−	0.660927i	0.947605	+	0.319445i	$0.103497\pi$
$18$		−	3.42059i		−	0.806240i
$19$	2.94045	+	5.09301i	0.674585	+	1.16842i	0.976590	+	0.215110i	$0.0690109\pi$
$19$	2.94045	+	5.09301i	0.674585	+	1.16842i	−0.302005	+	0.953306i	$0.597656\pi$
$20$	0.449133	−	1.24105i	0.100429	−	0.277506i
$21$	0.700420			0.152844
$22$	−3.99058	+	2.30396i	−0.850794	+	0.491206i
$23$	0.298874	+	0.172555i	0.0623195	+	0.0359802i	0.530836	−	0.847475i	$-0.321878\pi$
$23$	0.298874	+	0.172555i	0.0623195	+	0.0359802i	−0.468516	+	0.883455i	$0.655211\pi$
$24$	−0.530689	+	0.919180i	−0.108326	+	0.187627i
$25$	−0.850210	+	4.92718i	−0.170042	+	0.985437i
$26$	−1.82581	−	3.87212i	−0.358071	−	0.759385i
$27$			2.02956i			0.390588i
$28$	1.03743	+	0.598962i	0.196056	+	0.113193i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	0.311800	−	0.861568i	0.0569267	−	0.157300i
$31$	1.18048			0.212020			0.106010	−	0.994365i	$-0.466192\pi$
$31$	1.18048			0.212020			0.106010	+	0.994365i	$0.466192\pi$
$32$	−2.78591	+	1.60845i	−0.492484	+	0.284336i
$33$	1.15990	−	0.669668i	0.201913	−	0.116574i
$34$	6.47114			1.10979
$35$	−4.26737	−	1.54436i	−0.721318	−	0.261044i
$36$	−0.850210	+	1.47261i	−0.141702	+	0.245435i
$37$	4.71996	+	2.72507i	0.775957	+	0.447999i	0.834996	−	0.550257i	$-0.185470\pi$
$37$	4.71996	+	2.72507i	0.775957	+	0.447999i	−0.0590384	+	0.998256i	$0.518803\pi$
$38$			6.98259i			1.13273i
$39$	0.530689	+	1.12547i	0.0849782	+	0.180219i
$40$	5.25997	−	4.43007i	0.831674	−	0.700456i
$41$	−0.0902394	+	0.156299i	−0.0140930	+	0.0244098i	−0.872986	−	0.487745i	$-0.837819\pi$
$41$	−0.0902394	+	0.156299i	−0.0140930	+	0.0244098i	0.858893	+	0.512155i	$0.171153\pi$
$42$	0.720215	+	0.415816i	0.111132	+	0.0641618i
$43$	−1.15990	+	0.669668i	−0.176883	+	0.102123i	−0.585827	−	0.810436i	$-0.699230\pi$
$43$	−1.15990	+	0.669668i	−0.176883	+	0.102123i	0.408944	+	0.912559i	$0.365897\pi$
$44$	2.29066			0.345330
$45$	2.19217	−	6.05742i	0.326790	−	0.902986i
$46$	0.204880	+	0.354863i	0.0302079	+	0.0523217i
$47$		−	12.2807i		−	1.79133i	−0.444731	−	0.895664i	$-0.646701\pi$
$47$		−	12.2807i		−	1.79133i	0.444731	−	0.895664i	$-0.353299\pi$
$48$	−0.738559	+	0.426407i	−0.106602	+	0.0615466i
$49$	−1.44045	+	2.49493i	−0.205779	+	0.356419i
$50$	−3.79934	+	4.56169i	−0.537308	+	0.645120i
$51$	−1.88090			−0.263379
$52$	−0.176407	+	2.12081i	−0.0244633	+	0.294104i
$53$			2.42636i			0.333286i	0.986017	+	0.166643i	$0.0532928\pi$
$53$			2.42636i			0.333286i	−0.986017	+	0.166643i	$0.946707\pi$
$54$	−1.20488	+	2.08691i	−0.163963	+	0.283993i
$55$	−8.54334	+	1.52255i	−1.15198	+	0.205301i
$56$	3.12093	+	5.40561i	0.417052	+	0.722355i
$57$		−	2.02956i		−	0.268821i
$58$	3.08478	−	1.78100i	0.405052	−	0.233857i
$59$	−3.53069	−	6.11533i	−0.459657	−	0.796149i	0.539286	−	0.842123i	$-0.318694\pi$
$59$	−3.53069	−	6.11533i	−0.459657	−	0.796149i	−0.998943	+	0.0459741i	$0.985361\pi$
$60$	−0.348383	+	0.293416i	−0.0449760	+	0.0378798i
$61$	−3.38090	−	5.85589i	−0.432880	−	0.749770i	0.564240	−	0.825611i	$-0.309169\pi$
$61$	−3.38090	−	5.85589i	−0.432880	−	0.749770i	−0.997120	+	0.0758409i	$0.975836\pi$
$62$	1.21384	+	0.700811i	0.154158	+	0.0890031i
$63$	5.06361	+	2.92347i	0.637954	+	0.368323i
$64$	−8.76180			−1.09522
$65$	−0.751722	−	8.02714i	−0.0932396	−	0.995644i
$66$	1.59024			0.195745
$67$	−3.81417	−	2.20211i	−0.465975	−	0.269031i	0.248578	−	0.968612i	$-0.420037\pi$
$67$	−3.81417	−	2.20211i	−0.465975	−	0.269031i	−0.714553	+	0.699581i	$0.753370\pi$
$68$	−2.78591	−	1.60845i	−0.337841	−	0.195053i
$69$	−0.0595504	−	0.103144i	−0.00716903	−	0.0124171i
$70$	−3.47114	−	4.12140i	−0.414880	−	0.492601i
$71$	0.940450	+	1.62891i	0.111611	+	0.193316i	0.916420	−	0.400218i	$-0.131066\pi$
$71$	0.940450	+	1.62891i	0.111611	+	0.193316i	−0.804809	+	0.593534i	$0.797732\pi$
$72$	−7.67311	+	4.43007i	−0.904284	+	0.522089i
$73$			8.86014i			1.03700i	0.855077	+	0.518501i	$0.173510\pi$
$73$			8.86014i			1.03700i	−0.855077	+	0.518501i	$0.826490\pi$
$74$	3.23557	+	5.60417i	0.376127	+	0.651472i
$75$	1.10432	−	1.32590i	0.127515	−	0.153102i
$76$	1.73557	−	3.00609i	0.199083	−	0.344823i
$77$		−	7.87651i		−	0.897611i
$78$	−0.122467	+	1.47233i	−0.0138666	+	0.166708i
$79$	−11.1805			−1.25790			−0.628951	−	0.777445i	$-0.716515\pi$
$79$	−11.1805			−1.25790			−0.628951	+	0.777445i	$0.716515\pi$
$80$	5.43992	−	0.969475i	0.608202	−	0.108391i
$81$	−3.97114	+	6.87821i	−0.441238	+	0.764246i
$82$	−0.185579	+	0.107144i	−0.0204938	+	0.0118321i
$83$			7.83540i			0.860047i	0.902818	+	0.430024i	$0.141495\pi$
$83$			7.83540i			0.860047i	−0.902818	+	0.430024i	$0.858505\pi$
$84$	−0.206708	−	0.358028i	−0.0225537	−	0.0390641i
$85$	11.4595	+	4.14720i	1.24296	+	0.449827i
$86$	−1.59024			−0.171480
$87$	−0.896622	+	0.517665i	−0.0961280	+	0.0554995i
$88$	10.3365	+	5.96781i	1.10188	+	0.636171i
$89$	6.12093	−	10.6018i	0.648817	−	1.12378i	−0.334589	−	0.942364i	$-0.608597\pi$
$89$	6.12093	−	10.6018i	0.648817	−	1.12378i	0.983406	−	0.181420i	$-0.0580693\pi$
$90$	5.85021	−	4.92718i	0.616666	−	0.519371i
$91$	7.29249	+	0.606582i	0.764460	+	0.0635870i
$92$		−	0.203698i		−	0.0212369i
$93$	−0.352814	−	0.203698i	−0.0365852	−	0.0211224i
$94$	7.29066	−	12.6278i	0.751974	−	1.30246i
$95$	−4.47497	+	12.3653i	−0.459122	+	1.26865i
$96$	1.11018			0.113307
$97$	5.02801	−	2.90292i	0.510517	−	0.294747i	−0.222529	−	0.974926i	$-0.571431\pi$
$97$	5.02801	−	2.90292i	0.510517	−	0.294747i	0.733046	+	0.680179i	$0.238098\pi$
$98$	−2.96232	+	1.71029i	−0.299239	+	0.172766i
$99$	11.1805			1.12368
$100$	2.76950	−	1.01951i	0.276950	−	0.101951i
$101$	2.97114	−	5.14616i	0.295639	−	0.512062i	−0.679494	−	0.733681i	$-0.737801\pi$
$101$	2.97114	−	5.14616i	0.295639	−	0.512062i	0.975133	+	0.221619i	$0.0711340\pi$
$102$	−1.93405	−	1.11663i	−0.191500	−	0.110563i
$103$		−	6.43378i		−	0.633939i	−0.948436	−	0.316970i	$-0.897335\pi$
$103$		−	6.43378i		−	0.633939i	0.948436	−	0.316970i	$-0.102665\pi$
$104$	−6.32135	+	9.11054i	−0.619859	+	0.893362i
$105$	1.00892	+	1.19792i	0.0984605	+	0.116905i
$106$	−1.44045	+	2.49493i	−0.139909	+	0.242329i
$107$	15.3106	+	8.83959i	1.48013	+	0.854555i	0.999747	−	0.0225015i	$-0.00716305\pi$
$107$	15.3106	+	8.83959i	1.48013	+	0.854555i	0.480387	+	0.877057i	$0.340496\pi$
$108$	1.03743	−	0.598962i	0.0998270	−	0.0576352i
$109$	−5.76180			−0.551880			−0.275940	−	0.961175i	$-0.588989\pi$
$109$	−5.76180			−0.551880			−0.275940	+	0.961175i	$0.588989\pi$
$110$	−9.68867	−	3.50632i	−0.923779	−	0.334314i
$111$	−0.940450	−	1.62891i	−0.0892635	−	0.154609i
$112$			5.01532i			0.473903i
$113$	−4.12222	+	2.37996i	−0.387785	+	0.223888i	−0.681200	−	0.732097i	$-0.738542\pi$
$113$	−4.12222	+	2.37996i	−0.387785	+	0.223888i	0.293415	+	0.955985i	$0.405208\pi$
$114$	1.20488	−	2.08691i	0.112847	−	0.195457i
$115$	0.135393	+	0.759719i	0.0126255	+	0.0708442i
$116$	−1.77072			−0.164407
$117$	−0.861026	+	10.3515i	−0.0796019	+	0.956995i
$118$		−	8.38421i		−	0.771829i
$119$	−5.53069	+	9.57943i	−0.506997	+	0.878145i
$120$	−2.33650	+	0.416399i	−0.213292	+	0.0380118i
$121$	−2.03069	−	3.51726i	−0.184608	−	0.319751i
$122$		−	8.02851i		−	0.726867i
$123$	0.0539404	−	0.0311425i	0.00486365	−	0.00280803i
$124$	−0.348383	−	0.603416i	−0.0312857	−	0.0541884i
$125$	−9.65162	+	5.64325i	−0.863267	+	0.504748i
$126$	3.47114	+	6.01219i	0.309234	+	0.535608i
$127$	−14.4679	−	8.35307i	−1.28382	−	0.741215i	−0.306277	−	0.951942i	$-0.599083\pi$
$127$	−14.4679	−	8.35307i	−1.28382	−	0.741215i	−0.977545	+	0.210728i	$0.932417\pi$
$128$	−3.43760	−	1.98470i	−0.303844	−	0.175424i
$129$	0.462218			0.0406961
$130$	3.99248	−	8.70026i	0.350163	−	0.763063i
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	−0.684619	−	0.395265i	−0.0595884	−	0.0344034i
$133$	−10.3365	−	5.96781i	−0.896292	−	0.517475i
$134$	−2.61464	−	4.52869i	−0.225871	−	0.391219i
$135$	−3.47114	+	2.92347i	−0.298748	+	0.251613i
$136$	−8.38090	−	14.5161i	−0.718656	−	1.24475i
$137$	−1.71288	+	0.988931i	−0.146341	+	0.0844901i	−0.571383	−	0.820684i	$-0.693593\pi$
$137$	−1.71288	+	0.988931i	−0.146341	+	0.0844901i	0.425042	+	0.905174i	$0.360259\pi$
$138$		−	0.141412i		−	0.0120378i
$139$	4.35021	+	7.53478i	0.368980	+	0.639092i	0.989406	−	0.145173i	$-0.0463737\pi$
$139$	4.35021	+	7.53478i	0.368980	+	0.639092i	−0.620426	+	0.784265i	$0.713040\pi$
$140$	0.469969	+	2.63709i	0.0397196	+	0.222875i
$141$	−2.11910	+	3.67039i	−0.178460	+	0.309103i
$142$			2.23325i			0.187411i
$143$	12.6563	−	5.96781i	1.05838	−	0.499053i
$144$	−7.11910			−0.593258
$145$	6.60415	−	1.17696i	0.548445	−	0.0977410i
$146$	−5.25997	+	9.11054i	−0.435318	+	0.753993i
$147$	0.861026	−	0.497113i	0.0710162	−	0.0410012i
$148$		−	3.21689i		−	0.264427i
$149$	11.1516	+	19.3152i	0.913576	+	1.58236i	0.808973	+	0.587846i	$0.200024\pi$
$149$	11.1516	+	19.3152i	0.913576	+	1.58236i	0.104603	+	0.994514i	$0.466643\pi$
$150$	1.92267	−	0.707775i	0.156985	−	0.0577896i
$151$	−19.1626			−1.55943			−0.779717	−	0.626132i	$-0.784637\pi$
$151$	−19.1626			−1.55943			−0.779717	+	0.626132i	$0.784637\pi$
$152$	15.6634	−	9.04329i	1.27047	−	0.733507i
$153$	−13.5977	−	7.85066i	−1.09931	−	0.634688i
$154$	4.67602	−	8.09910i	0.376804	−	0.652644i
$155$	1.70042	+	2.01897i	0.136581	+	0.162167i
$156$	0.418681	−	0.603416i	0.0335213	−	0.0483120i
$157$			6.20265i			0.495025i	0.968885	+	0.247513i	$0.0796132\pi$
$157$			6.20265i			0.495025i	−0.968885	+	0.247513i	$0.920387\pi$
$158$	−11.4964	−	6.63748i	−0.914608	−	0.528049i
$159$	0.418681	−	0.725176i	0.0332035	−	0.0575102i
$160$	−6.76387	−	2.44784i	−0.534731	−	0.193519i
$161$	−0.700420			−0.0552008
$162$	−8.16673	+	4.71507i	−0.641639	+	0.370451i
$163$	10.3365	−	5.96781i	0.809621	−	0.467435i	−0.0372032	−	0.999308i	$-0.511845\pi$
$163$	10.3365	−	5.96781i	0.809621	−	0.467435i	0.846824	+	0.531873i	$0.178512\pi$
$164$	0.106526			0.00831826
$165$	2.81611	+	1.01915i	0.219234	+	0.0793404i
$166$	−4.65162	+	8.05684i	−0.361036	+	0.625332i
$167$	−1.75765	−	1.01478i	−0.136011	−	0.0785259i	0.430451	−	0.902614i	$-0.358355\pi$
$167$	−1.75765	−	1.01478i	−0.136011	−	0.0785259i	−0.566461	+	0.824088i	$0.691688\pi$
$168$		−	2.15413i		−	0.166195i
$169$	4.55063	+	12.1775i	0.350048	+	0.936732i
$170$	9.32135	+	11.0675i	0.714915	+	0.848842i
$171$	8.47114	−	14.6724i	0.647804	−	1.12203i
$172$	0.684619	+	0.395265i	0.0522017	+	0.0301387i
$173$	1.15990	−	0.669668i	0.0881855	−	0.0509139i	−0.455259	−	0.890359i	$-0.650453\pi$
$173$	1.15990	−	0.669668i	0.0881855	−	0.0509139i	0.543444	+	0.839445i	$0.317120\pi$
$174$	−1.22928			−0.0931916
$175$	−3.50563	−	9.52303i	−0.265001	−	0.719873i
$176$	4.79512	+	8.30539i	0.361446	+	0.626042i
$177$			2.43695i			0.183173i
$178$	12.5878	−	7.26758i	0.943497	−	0.544728i
$179$	10.1120	−	17.5145i	0.755807	−	1.30910i	−0.189165	−	0.981945i	$-0.560578\pi$
$179$	10.1120	−	17.5145i	0.755807	−	1.30910i	0.944972	−	0.327151i	$-0.106089\pi$
$180$	−3.74328	+	0.667107i	−0.279007	+	0.0497232i
$181$	19.8232			1.47345			0.736723	−	0.676195i	$-0.236372\pi$
$181$	19.8232			1.47345			0.736723	+	0.676195i	$0.236372\pi$
$182$	7.13847	+	4.95303i	0.529139	+	0.367143i
$183$			2.33356i			0.172502i
$184$	0.530689	−	0.919180i	0.0391229	−	0.0677629i
$185$	2.13820	+	11.9979i	0.157203	+	0.882100i
$186$	−0.241857	−	0.418908i	−0.0177338	−	0.0307159i
$187$			21.1515i			1.54675i
$188$	−6.27745	+	3.62429i	−0.457830	+	0.264328i
$189$	−2.05955	−	3.56725i	−0.149810	−	0.259479i
$190$	−11.9423	+	10.0581i	−0.866384	+	0.729689i
$191$	−0.768891	−	1.33176i	−0.0556350	−	0.0963626i	0.836867	−	0.547407i	$-0.184385\pi$
$191$	−0.768891	−	1.33176i	−0.0556350	−	0.0963626i	−0.892502	+	0.451044i	$0.851052\pi$
$192$	2.61867	+	1.51189i	0.188986	+	0.109111i
$193$	−18.3625	−	10.6016i	−1.32176	−	0.763118i	−0.337750	−	0.941236i	$-0.609666\pi$
$193$	−18.3625	−	10.6016i	−1.32176	−	0.763118i	−0.984009	+	0.178117i	$0.942999\pi$
$194$	6.89347			0.494923
$195$	−1.16045	+	2.52882i	−0.0831017	+	0.181092i
$196$	1.70042			0.121459
$197$	−8.01675	−	4.62847i	−0.571170	−	0.329765i	0.186447	−	0.982465i	$-0.440303\pi$
$197$	−8.01675	−	4.62847i	−0.571170	−	0.329765i	−0.757616	+	0.652700i	$0.773636\pi$
$198$	11.4964	+	6.63748i	0.817017	+	0.471705i
$199$	−8.70225	−	15.0727i	−0.616886	−	1.06848i	−0.990050	−	0.140713i	$-0.955061\pi$
$199$	−8.70225	−	15.0727i	−0.616886	−	1.06848i	0.373164	−	0.927765i	$-0.378273\pi$
$200$	15.1534	+	2.61480i	1.07151	+	0.184894i
$201$	0.759971	+	1.31631i	0.0536042	+	0.0928452i
$202$	6.11021	−	3.52773i	0.429913	−	0.248210i
$203$			6.08867i			0.427341i
$204$	0.555090	+	0.961445i	0.0388641	+	0.0673146i
$205$	−0.397303	+	0.0708053i	−0.0277488	+	0.00494526i
$206$	3.81952	−	6.61560i	0.266119	−	0.460931i
$207$		−	0.994227i		−	0.0691036i
$208$	−8.05885	+	3.79997i	−0.558781	+	0.263480i
$209$	−22.8232			−1.57871
$210$	0.326265	+	1.83074i	0.0225144	+	0.126333i
$211$	3.64087	−	6.30617i	0.250648	−	0.434135i	−0.713057	−	0.701107i	$-0.752690\pi$
$211$	3.64087	−	6.30617i	0.250648	−	0.434135i	0.963704	+	0.266972i	$0.0860231\pi$
$212$	1.24026	−	0.716067i	0.0851817	−	0.0491797i
$213$		−	0.649117i		−	0.0444768i
$214$	10.4955	+	18.1788i	0.717460	+	1.24268i
$215$	−2.81611	−	1.01915i	−0.192057	−	0.0695052i
$216$	6.24186			0.424705
$217$	−2.07487	+	1.19792i	−0.140851	+	0.0813204i
$218$	−5.92463	−	3.42059i	−0.401267	−	0.231671i
$219$	1.52886	−	2.64807i	0.103311	−	0.178940i
$220$	3.29958	+	3.91770i	0.222458	+	0.264131i
$221$	−19.5831	−	1.62891i	−1.31731	−	0.109572i
$222$		−	2.23325i		−	0.149886i
$223$	16.8589	+	9.73351i	1.12896	+	0.651804i	0.943672	−	0.330881i	$-0.107346\pi$
$223$	16.8589	+	9.73351i	1.12896	+	0.651804i	0.185285	+	0.982685i	$0.440679\pi$
$224$	3.26443	−	5.65416i	0.218114	−	0.377784i
$225$	13.5177	−	4.97614i	0.901178	−	0.331743i
$226$	−5.65162			−0.375940
$227$	−4.16698	+	2.40581i	−0.276572	+	0.159679i	−0.631871	−	0.775074i	$-0.717713\pi$
$227$	−4.16698	+	2.40581i	−0.276572	+	0.159679i	0.355298	+	0.934753i	$0.384379\pi$
$228$	−1.03743	+	0.598962i	−0.0687057	+	0.0396672i
$229$	−1.52360			−0.100682			−0.0503410	−	0.998732i	$-0.516031\pi$
$229$	−1.52360			−0.100682			−0.0503410	+	0.998732i	$0.516031\pi$
$230$	−0.311800	+	0.861568i	−0.0205595	+	0.0568101i
$231$	−1.35913	+	2.35408i	−0.0894242	+	0.154887i
$232$	−7.99033	−	4.61322i	−0.524591	−	0.302873i
$233$		−	13.9652i		−	0.914889i	−0.889238	−	0.457445i	$-0.848765\pi$
$233$		−	13.9652i		−	0.914889i	0.889238	−	0.457445i	$-0.151235\pi$
$234$	−7.03069	+	10.1329i	−0.459611	+	0.662406i
$235$	21.0037	−	17.6898i	1.37013	−	1.15395i
$236$	−2.08395	+	3.60951i	−0.135654	+	0.234959i
$237$	3.34155	+	1.92925i	0.217057	+	0.125318i
$238$	−11.3740	+	6.56677i	−0.737266	+	0.425661i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	−1.79314	−	0.648935i	−0.115747	−	0.0418886i
$241$	8.73294	+	15.1259i	0.562538	+	0.974344i	0.997274	+	0.0737864i	$0.0235083\pi$
$241$	8.73294	+	15.1259i	0.562538	+	0.974344i	−0.434736	+	0.900558i	$0.643158\pi$
$242$		−	4.82221i		−	0.309983i
$243$	7.64668	−	4.41481i	0.490535	−	0.283210i
$244$	−1.99554	+	3.45638i	−0.127751	+	0.221272i
$245$	−6.34196	+	1.13023i	−0.405173	+	0.0722078i
$246$	0.0739531			0.00471508
$247$	1.75765	−	21.1309i	0.111836	−	1.34453i
$248$		−	3.63054i		−	0.230539i
$249$	1.35204	−	2.34180i	0.0856819	−	0.148405i
$250$	−13.2746	+	0.0728904i	−0.839559	+	0.00460999i
$251$	−4.64979	−	8.05367i	−0.293492	−	0.508343i	0.681141	−	0.732152i	$-0.261484\pi$
$251$	−4.64979	−	8.05367i	−0.293492	−	0.508343i	−0.974633	+	0.223809i	$0.928151\pi$
$252$		−	3.45110i		−	0.217399i
$253$	−1.15990	+	0.669668i	−0.0729223	+	0.0421017i
$254$	−9.91788	−	17.1783i	−0.622303	−	1.07786i
$255$	−2.70934	−	3.21689i	−0.169665	−	0.201449i
$256$	6.40530	+	11.0943i	0.400331	+	0.693394i
$257$	9.43076	+	5.44485i	0.588274	+	0.339640i	0.764415	−	0.644725i	$-0.223028\pi$
$257$	9.43076	+	5.44485i	0.588274	+	0.339640i	−0.176141	+	0.984365i	$0.556361\pi$
$258$	0.475281	+	0.274404i	0.0295897	+	0.0170836i
$259$	−11.0614			−0.687321
$260$	−3.88132	+	2.75322i	−0.240709	+	0.170747i
$261$	−8.64270			−0.534970
$262$	10.2826	+	5.93667i	0.635262	+	0.366769i
$263$	11.6399	+	6.72031i	0.717749	+	0.414392i	0.813923	−	0.580972i	$-0.197327\pi$
$263$	11.6399	+	6.72031i	0.717749	+	0.414392i	−0.0961749	+	0.995364i	$0.530661\pi$
$264$	−2.05955	−	3.56725i	−0.126757	−	0.219549i
$265$	−4.14979	+	3.49505i	−0.254920	+	0.214699i
$266$	−7.08578	−	12.2729i	−0.434457	−	0.752502i
$267$	−3.65877	+	2.11239i	−0.223913	+	0.129276i
$268$			2.59955i			0.158793i
$269$	1.83027	+	3.17012i	0.111593	+	0.193286i	0.916413	−	0.400234i	$-0.131071\pi$
$269$	1.83027	+	3.17012i	0.111593	+	0.193286i	−0.804819	+	0.593520i	$0.797738\pi$
$270$	−5.30481	+	0.945395i	−0.322840	+	0.0575349i
$271$	−11.0018	+	19.0557i	−0.668313	+	1.15755i	0.310062	+	0.950716i	$0.399650\pi$
$271$	−11.0018	+	19.0557i	−0.668313	+	1.15755i	−0.978376	+	0.206837i	$0.933683\pi$
$272$		−	13.4681i		−	0.816621i
$273$	−2.07487	−	1.43965i	−0.125577	−	0.0871314i
$274$	−2.34838			−0.141871
$275$	−14.9103	−	12.4185i	−0.899123	−	0.748862i
$276$	−0.0351490	+	0.0608799i	−0.00211572	+	0.00366454i
$277$	−8.56973	+	4.94774i	−0.514905	+	0.297281i	−0.734848	−	0.678232i	$-0.762746\pi$
$277$	−8.56973	+	4.94774i	−0.514905	+	0.297281i	0.219943	+	0.975513i	$0.429413\pi$
$278$			10.3303i			0.619570i
$279$	−1.70042	−	2.94521i	−0.101801	−	0.176325i
$280$	−4.74964	+	13.1242i	−0.283845	+	0.784321i
$281$	4.06138			0.242281			0.121141	−	0.992635i	$-0.461345\pi$
$281$	4.06138			0.242281			0.121141	+	0.992635i	$0.461345\pi$
$282$	−4.35798	+	2.51608i	−0.259514	+	0.149830i
$283$	5.27294	+	3.04434i	0.313444	+	0.180967i	0.648467	−	0.761243i	$-0.275411\pi$
$283$	5.27294	+	3.04434i	0.313444	+	0.180967i	−0.335023	+	0.942210i	$0.608744\pi$
$284$	0.555090	−	0.961445i	0.0329386	−	0.0570513i
$285$	3.47114	−	2.92347i	0.205613	−	0.173172i
$286$	16.5569	+	1.37719i	0.979031	+	0.0814348i
$287$		−	0.366292i		−	0.0216215i
$288$	8.02592	+	4.63377i	0.472932	+	0.273047i
$289$	6.35204	−	11.0021i	0.373649	−	0.647180i
$290$	7.48951	+	2.71044i	0.439799	+	0.159163i
$291$	−2.00366			−0.117456
$292$	4.52897	−	2.61480i	0.265038	−	0.153020i
$293$	−8.48019	+	4.89604i	−0.495418	+	0.286030i	−0.726819	−	0.686829i	$-0.759002\pi$
$293$	−8.48019	+	4.89604i	−0.495418	+	0.286030i	0.231401	+	0.972858i	$0.425669\pi$
$294$	1.18048			0.0688469
$295$	5.37324	−	14.8473i	0.312842	−	0.864446i
$296$	8.38090	−	14.5161i	0.487130	−	0.843734i
$297$	−6.82125	−	3.93825i	−0.395809	−	0.228521i
$298$			26.4814i			1.53402i
$299$	−0.530689	−	1.12547i	−0.0306905	−	0.0650876i
$300$	−1.00366	−	0.173186i	−0.0579461	−	0.00999888i
$301$	1.35913	−	2.35408i	0.0783390	−	0.135687i
$302$	−19.7042	−	11.3762i	−1.13385	−	0.654628i
$303$	−1.77599	+	1.02537i	−0.102028	+	0.0589059i
$304$	14.5325			0.833497
$305$	5.14528	−	14.2174i	0.294618	−	0.814088i
$306$	−9.32135	−	16.1450i	−0.532866	−	0.922951i
$307$			22.1046i			1.26158i	0.775955	+	0.630788i	$0.217268\pi$
$307$			22.1046i			1.26158i	−0.775955	+	0.630788i	$0.782732\pi$
$308$	−4.02617	+	2.32451i	−0.229412	+	0.132451i
$309$	−1.11018	+	1.92289i	−0.0631560	+	0.109389i
$310$	0.549883	+	3.08551i	0.0312313	+	0.175245i
$311$	7.63904			0.433170			0.216585	−	0.976264i	$-0.430508\pi$
$311$	7.63904			0.433170			0.216585	+	0.976264i	$0.430508\pi$
$312$	3.46136	−	1.63212i	0.195961	−	0.0924007i
$313$			26.1425i			1.47766i	0.673891	+	0.738831i	$0.264622\pi$
$313$			26.1425i			1.47766i	−0.673891	+	0.738831i	$0.735378\pi$
$314$	−3.68231	+	6.37794i	−0.207805	+	0.359928i
$315$	2.29387	+	12.8714i	0.129245	+	0.725220i
$316$	3.29958	+	5.71504i	0.185616	+	0.321496i
$317$		−	11.8428i		−	0.665159i	−0.943075	−	0.332580i	$-0.892081\pi$
$317$		−	11.8428i		−	0.665159i	0.943075	−	0.332580i	$-0.107919\pi$
$318$	0.861026	−	0.497113i	0.0482839	−	0.0278767i
$319$	5.82135	+	10.0829i	0.325933	+	0.564532i
$320$	−12.6209	−	14.9852i	−0.705531	−	0.837701i
$321$	−3.05063	−	5.28385i	−0.170270	−	0.294916i
$322$	−0.720215	−	0.415816i	−0.0401360	−	0.0231725i
$323$	27.7576	+	16.0259i	1.54448	+	0.891704i
$324$	4.68785			0.260436
$325$	12.6459	−	12.8484i	0.701471	−	0.712698i
$326$	14.1716			0.784890
$327$	1.72205	+	0.994227i	0.0952297	+	0.0549809i
$328$	0.480695	+	0.277529i	0.0265419	+	0.0153240i
$329$	12.4622	+	21.5852i	0.687064	+	1.19003i
$330$	2.29066	+	2.71978i	0.126097	+	0.149719i
$331$	6.35021	+	10.9989i	0.349039	+	0.604553i	0.986079	−	0.166277i	$-0.0531747\pi$
$331$	6.35021	+	10.9989i	0.349039	+	0.604553i	−0.637040	+	0.770831i	$0.719841\pi$
$332$	4.00516	−	2.31238i	0.219812	−	0.126908i
$333$		−	15.7013i		−	0.860427i
$334$	−1.20488	−	2.08691i	−0.0659281	−	0.114191i
$335$	−1.72786	−	9.69538i	−0.0944031	−	0.529715i
$336$	0.865418	−	1.49895i	0.0472124	−	0.0817743i
$337$			15.2939i			0.833113i	0.909110	+	0.416556i	$0.136763\pi$
$337$			15.2939i			0.833113i	−0.909110	+	0.416556i	$0.863237\pi$
$338$	−2.55015	+	15.2232i	−0.138710	+	0.828034i
$339$	1.64270			0.0892191
$340$	−1.26205	−	7.08161i	−0.0684441	−	0.384054i
$341$	−2.29066	+	3.96754i	−0.124046	+	0.214854i
$342$	17.4211	−	10.0581i	0.942024	−	0.543878i
$343$		−	20.0538i		−	1.08281i
$344$	2.05955	+	3.56725i	0.111044	+	0.192333i
$345$	0.0906278	−	0.250423i	0.00487924	−	0.0134823i
$346$	1.59024			0.0854918
$347$	−10.5998	+	6.11981i	−0.569029	+	0.328529i	−0.756761	−	0.653691i	$-0.773219\pi$
$347$	−10.5998	+	6.11981i	−0.569029	+	0.328529i	0.187733	+	0.982220i	$0.439886\pi$
$348$	0.529222	+	0.305546i	0.0283693	+	0.0163790i
$349$	9.35021	−	16.1950i	0.500505	−	0.866901i	−0.499495	−	0.866317i	$-0.666481\pi$
$349$	9.35021	−	16.1950i	0.500505	−	0.866901i	1.00000		0.000583538i	$-0.000185746\pi$
$350$	2.04880	−	11.8733i	0.109513	−	0.634656i
$351$	4.17156	−	6.01219i	0.222661	−	0.320907i
$352$		−	12.4844i		−	0.665422i
$353$	−1.13348	−	0.654413i	−0.0603288	−	0.0348309i	0.469532	−	0.882915i	$-0.344423\pi$
$353$	−1.13348	−	0.654413i	−0.0603288	−	0.0348309i	−0.529861	+	0.848084i	$0.677756\pi$
$354$	−1.44674	+	2.50582i	−0.0768932	+	0.133183i
$355$	−1.43124	+	3.95480i	−0.0759623	+	0.209899i
$356$	−7.22563			−0.382957
$357$	3.30596	−	1.90870i	0.174970	−	0.101019i
$358$	20.7956	−	12.0063i	1.09908	−	0.634554i
$359$	29.4082			1.55210			0.776051	−	0.630670i	$-0.217220\pi$
$359$	29.4082			1.55210			0.776051	+	0.630670i	$0.217220\pi$
$360$	−18.6294	−	6.74198i	−0.981858	−	0.355333i
$361$	−7.79249	+	13.4970i	−0.410131	+	0.710368i
$362$	20.3834	+	11.7684i	1.07133	+	0.618531i
$363$			1.40162i			0.0735661i
$364$	−1.84210	−	3.90666i	−0.0965520	−	0.204765i
$365$	−15.1534	+	12.7626i	−0.793168	+	0.668024i
$366$	−1.38536	+	2.39951i	−0.0724139	+	0.125425i
$367$	−28.9531	−	16.7161i	−1.51134	−	0.872573i	−0.999912	−	0.0132473i	$-0.995783\pi$
$367$	−28.9531	−	16.7161i	−1.51134	−	0.872573i	−0.511429	−	0.859326i	$-0.670884\pi$
$368$	0.738559	−	0.426407i	0.0385001	−	0.0222280i
$369$	0.519941			0.0270671
$370$	−4.92410	+	13.6063i	−0.255992	+	0.707358i
$371$	−2.46222	−	4.26469i	−0.127832	−	0.221412i
$372$			0.240461i			0.0124673i
$373$	−29.8589	+	17.2391i	−1.54604	+	0.892604i	−0.547598	+	0.836742i	$0.684458\pi$
$373$	−29.8589	+	17.2391i	−1.54604	+	0.892604i	−0.998438	+	0.0558628i	$0.982209\pi$
$374$	−12.5569	+	21.7492i	−0.649303	+	1.12463i
$375$	3.85839	−	0.0211863i	0.199246	−	0.00109406i
$376$	−37.7691			−1.94779
$377$	−9.78357	+	4.61322i	−0.503879	+	0.237593i
$378$		−	4.89075i		−	0.251553i
$379$	−8.70225	+	15.0727i	−0.447004	+	0.774234i	−0.998189	−	0.0601487i	$-0.980843\pi$
$379$	−8.70225	+	15.0727i	−0.447004	+	0.774234i	0.551185	+	0.834383i	$0.314176\pi$
$380$	7.64130	−	1.36179i	0.391991	−	0.0698585i
$381$	2.88273	+	4.99303i	0.147687	+	0.255801i
$382$		−	1.82586i		−	0.0934191i
$383$	1.51271	−	0.873366i	0.0772961	−	0.0446269i	−0.460854	−	0.887476i	$-0.652457\pi$
$383$	1.51271	−	0.873366i	0.0772961	−	0.0446269i	0.538150	+	0.842849i	$0.319123\pi$
$384$	0.684939	+	1.18635i	0.0349531	+	0.0605406i
$385$	13.4711	−	11.3457i	0.686553	−	0.578231i
$386$	−12.5876	−	21.8024i	−0.640692	−	1.10971i
$387$	3.34155	+	1.92925i	0.169861	+	0.0980692i
$388$	−2.96773	−	1.71342i	−0.150664	−	0.0869857i
$389$	−22.0435			−1.11765			−0.558826	−	0.829285i	$-0.688748\pi$
$389$	−22.0435			−1.11765			−0.558826	+	0.829285i	$0.688748\pi$
$390$	−2.69452	+	1.91136i	−0.136442	+	0.0967855i
$391$	1.88090			0.0951212
$392$	7.67311	+	4.43007i	0.387550	+	0.223752i
$393$	−2.98874	−	1.72555i	−0.150762	−	0.0870425i
$394$	−5.49554	−	9.51855i	−0.276861	−	0.479538i
$395$	−16.1049	−	19.1219i	−0.810326	−	0.962127i
$396$	−3.29958	−	5.71504i	−0.165810	−	0.287192i
$397$	19.5132	−	11.2660i	0.979339	−	0.565422i	0.0772687	−	0.997010i	$-0.475380\pi$
$397$	19.5132	−	11.2660i	0.979339	−	0.565422i	0.902071	+	0.431588i	$0.142047\pi$
$398$		−	20.6649i		−	1.03584i
$399$	2.05955	+	3.56725i	0.103106	+	0.178586i
$400$	9.49402	+	7.90739i	0.474701	+	0.395369i
$401$	1.85204	−	3.20782i	0.0924863	−	0.160191i	−0.816070	−	0.577953i	$-0.803852\pi$
$401$	1.85204	−	3.20782i	0.0924863	−	0.160191i	0.908557	+	0.417761i	$0.137185\pi$
$402$			1.80468i			0.0900091i
$403$	−3.49695	−	2.42636i	−0.174196	−	0.120866i
$404$	−3.50737			−0.174498
$405$	−17.4840	+	3.11591i	−0.868787	+	0.154831i
$406$	−3.61464	+	6.26074i	−0.179392	+	0.310715i
$407$	−18.3177	+	10.5757i	−0.907975	+	0.524220i
$408$			5.78466i			0.286384i
$409$	−6.74186	−	11.6772i	−0.333363	−	0.577402i	0.649806	−	0.760100i	$-0.274850\pi$
$409$	−6.74186	−	11.6772i	−0.333363	−	0.577402i	−0.983169	+	0.182698i	$0.941517\pi$
$410$	−0.450566	−	0.163059i	−0.0222519	−	0.00805292i
$411$	0.682580			0.0336692
$412$	−3.28871	+	1.89874i	−0.162023	+	0.0935440i
$413$	12.4114	+	7.16573i	0.610726	+	0.352603i
$414$	0.590239	−	1.02232i	0.0290087	−	0.0502445i
$415$	−13.4008	+	11.2865i	−0.657821	+	0.554033i
$416$	11.5587	+	0.961445i	0.566714	+	0.0471387i
$417$		−	3.00260i		−	0.147038i
$418$	−23.4682	−	13.5494i	−1.14787	−	0.662721i
$419$	8.41159	−	14.5693i	0.410933	−	0.711757i	−0.584059	−	0.811711i	$-0.698536\pi$
$419$	8.41159	−	14.5693i	0.410933	−	0.711757i	0.994992	+	0.0999544i	$0.0318697\pi$
$420$	0.314582	−	0.869253i	0.0153500	−	0.0424152i
$421$	17.1013			0.833464			0.416732	−	0.909029i	$-0.363175\pi$
$421$	17.1013			0.833464			0.416732	+	0.909029i	$0.363175\pi$
$422$	7.48753	−	4.32293i	0.364487	−	0.210437i
$423$	−30.6396	+	17.6898i	−1.48975	+	0.860106i
$424$	7.46222			0.362397
$425$	9.41397	+	25.5730i	0.456645	+	1.24047i
$426$	0.385359	−	0.667462i	0.0186707	−	0.0323386i
$427$	11.8849	+	6.86173i	0.575149	+	0.332062i
$428$		−	10.4349i		−	0.504392i
$429$	−4.81243	−	0.400293i	−0.232346	−	0.0193263i
$430$	−2.29066	−	2.71978i	−0.110465	−	0.131159i
$431$	−4.83027	+	8.36627i	−0.232666	+	0.402989i	−0.958592	−	0.284784i	$-0.908078\pi$
$431$	−4.83027	+	8.36627i	−0.232666	+	0.402989i	0.725926	+	0.687773i	$0.241412\pi$
$432$	4.34339	+	2.50766i	0.208972	+	0.120650i
$433$	21.4538	−	12.3863i	1.03100	−	0.595249i	0.113730	−	0.993512i	$-0.463720\pi$
$433$	21.4538	−	12.3863i	1.03100	−	0.595249i	0.917272	+	0.398262i	$0.130387\pi$
$434$	−2.84467			−0.136549
$435$	−2.17690	−	0.787817i	−0.104374	−	0.0377729i
$436$	1.70042	+	2.94521i	0.0814354	+	0.141050i
$437$			2.02956i			0.0970869i
$438$	3.14414	−	1.81527i	0.150233	−	0.0867369i
$439$	3.53069	−	6.11533i	0.168511	−	0.291869i	−0.769386	−	0.638784i	$-0.779438\pi$
$439$	3.53069	−	6.11533i	0.168511	−	0.291869i	0.937896	+	0.346915i	$0.112771\pi$
$440$	4.68257	+	26.2749i	0.223233	+	1.25261i
$441$	8.29958			0.395218
$442$	−19.1696	−	13.3008i	−0.911803	−	0.632655i
$443$		−	38.2438i		−	1.81702i	−0.417865	−	0.908509i	$-0.637222\pi$
$443$		−	38.2438i		−	1.81702i	0.417865	−	0.908509i	$-0.362778\pi$
$444$	−0.555090	+	0.961445i	−0.0263434	+	0.0456282i
$445$	26.9490	−	4.80271i	1.27751	−	0.227670i
$446$	11.5569	+	20.0172i	0.547236	+	0.947840i
$447$		−	7.69707i		−	0.364059i
$448$	15.4002	−	8.89128i	0.727589	−	0.420074i
$449$	−6.24003	−	10.8080i	−0.294485	−	0.510063i	0.680380	−	0.732860i	$-0.261815\pi$
$449$	−6.24003	−	10.8080i	−0.294485	−	0.510063i	−0.974865	+	0.222796i	$0.928481\pi$
$450$	16.8539	+	2.90822i	0.794499	+	0.137095i
$451$	−0.350210	−	0.606582i	−0.0164908	−	0.0285628i
$452$	2.43309	+	1.40475i	0.114443	+	0.0660738i
$453$	5.72721	+	3.30661i	0.269088	+	0.155358i
$454$	−5.71300			−0.268124
$455$	9.46703	+	13.3460i	0.443821	+	0.625672i
$456$	−6.24186			−0.292302
$457$	7.12930	+	4.11610i	0.333495	+	0.192543i	0.657392	−	0.753549i	$-0.271660\pi$
$457$	7.12930	+	4.11610i	0.333495	+	0.192543i	−0.323897	+	0.946092i	$0.604993\pi$
$458$	−1.56665	−	0.904508i	−0.0732050	−	0.0422649i
$459$	5.53069	+	9.57943i	0.258150	+	0.447130i
$460$	0.348383	−	0.293416i	0.0162434	−	0.0136806i
$461$	2.27072	+	3.93300i	0.105758	+	0.183178i	0.914048	−	0.405607i	$-0.132940\pi$
$461$	2.27072	+	3.93300i	0.105758	+	0.183178i	−0.808290	+	0.588785i	$0.799606\pi$
$462$	−2.79508	+	1.61374i	−0.130039	+	0.0750780i
$463$		−	1.98845i		−	0.0924113i	−0.998932	−	0.0462056i	$-0.985287\pi$
$463$		−	1.98845i		−	0.0924113i	0.998932	−	0.0462056i	$-0.0147130\pi$
$464$	−3.70671	−	6.42021i	−0.172080	−	0.298051i
$465$	−0.159829	−	0.896832i	−0.00741188	−	0.0415896i
$466$	8.29066	−	14.3598i	0.384057	−	0.665207i
$467$			32.8043i			1.51800i	0.651091	+	0.759000i	$0.274312\pi$
$467$			32.8043i			1.51800i	−0.651091	+	0.759000i	$0.725688\pi$
$468$	5.54539	−	2.61480i	0.256336	−	0.120869i
$469$	8.93862			0.412747
$470$	32.0991	−	5.72053i	1.48062	−	0.263868i
$471$	1.07030	−	1.85381i	0.0493167	−	0.0854191i
$472$	−18.8076	+	10.8586i	−0.865689	+	0.499806i
$473$		−	5.19783i		−	0.238997i
$474$	2.29066	+	3.96754i	0.105213	+	0.182235i
$475$	−27.5942	+	10.1580i	−1.26611	+	0.466081i
$476$	6.52886			0.299250
$477$	6.05360	−	3.49505i	0.277176	−	0.160027i
$478$	−4.11304	−	2.37467i	−0.188126	−	0.108615i
$479$	−15.4027	+	26.6782i	−0.703766	+	1.21896i	0.263369	+	0.964695i	$0.415166\pi$
$479$	−15.4027	+	26.6782i	−0.703766	+	1.21896i	−0.967135	+	0.254263i	$0.918167\pi$
$480$	1.59916	+	1.89874i	0.0729913	+	0.0866650i
$481$	−8.38090	−	17.7740i	−0.382136	−	0.810423i
$482$			20.7378i			0.944582i
$483$	0.209337	+	0.120861i	0.00952518	+	0.00549937i
$484$	−1.19859	+	2.07602i	−0.0544815	+	0.0943647i
$485$	12.2074	+	4.41786i	0.554312	+	0.200605i
$486$	10.4837			0.475551
$487$	19.3341	−	11.1626i	0.876113	−	0.505824i	0.00673807	−	0.999977i	$-0.497855\pi$
$487$	19.3341	−	11.1626i	0.876113	−	0.505824i	0.869375	+	0.494153i	$0.164522\pi$
$488$	−18.0097	+	10.3979i	−0.815259	+	0.470690i
$489$	−4.11910			−0.186272
$490$	−7.19217	−	2.60284i	−0.324909	−	0.117584i
$491$	−5.34129	+	9.25139i	−0.241049	+	0.417509i	−0.961013	−	0.276502i	$-0.910825\pi$
$491$	−5.34129	+	9.25139i	−0.241049	+	0.417509i	0.719964	+	0.694011i	$0.244158\pi$
$492$	−0.0318378	−	0.0183815i	−0.00143536	−	0.000828704i
$493$		−	16.3504i		−	0.736386i
$494$	14.3520	−	20.6846i	0.645729	−	0.930646i
$495$	16.1049	+	19.1219i	0.723862	+	0.859466i
$496$	1.45856	−	2.52631i	0.0654914	−	0.113434i
$497$	−3.30596	−	1.90870i	−0.148292	−	0.0856167i
$498$	2.78049	−	1.60532i	0.124597	−	0.0719361i
$499$	−18.8195			−0.842477			−0.421239	−	0.906950i	$-0.638405\pi$
$499$	−18.8195			−0.842477			−0.421239	+	0.906950i	$0.638405\pi$
$500$	5.73300	+	3.26811i	0.256388	+	0.146154i
$501$	0.350210	+	0.606582i	0.0156462	+	0.0271001i
$502$		−	11.0417i		−	0.492815i
$503$	−4.92013	+	2.84064i	−0.219378	+	0.126658i	−0.605662	−	0.795722i	$-0.707092\pi$
$503$	−4.92013	+	2.84064i	−0.219378	+	0.126658i	0.386284	+	0.922380i	$0.373758\pi$
$504$	8.99108	−	15.5730i	0.400495	−	0.693677i
$505$	13.0812	−	2.33127i	0.582107	−	0.103740i
$506$	−1.59024			−0.0706948
$507$	0.741225	−	4.42478i	0.0329190	−	0.196511i
$508$			9.86062i			0.437494i
$509$	13.9622	−	24.1833i	0.618864	−	1.07190i	−0.370829	−	0.928701i	$-0.620926\pi$
$509$	13.9622	−	24.1833i	0.618864	−	1.07190i	0.989693	−	0.143203i	$-0.0457403\pi$
$510$	−0.876148	−	4.91625i	−0.0387965	−	0.217695i
$511$	−8.99108	−	15.5730i	−0.397742	−	0.688909i
$512$			23.1492i			1.02306i
$513$	−10.3365	+	5.96781i	−0.456370	+	0.263485i
$514$	6.46485	+	11.1975i	0.285152	+	0.493898i
$515$	11.0037	−	9.26754i	0.484879	−	0.408376i
$516$	−0.136410	−	0.236269i	−0.00600511	−	0.0104011i
$517$	41.2750	+	23.8301i	1.81527	+	1.04805i
$518$	−11.3740	−	6.56677i	−0.499744	−	0.288527i
$519$	−0.462218			−0.0202891
$520$	−24.6873	+	2.31190i	−1.08261	+	0.101384i
$521$	6.29958			0.275990			0.137995	−	0.990433i	$-0.455934\pi$
$521$	6.29958			0.275990			0.137995	+	0.990433i	$0.455934\pi$
$522$	−8.88695	−	5.13088i	−0.388971	−	0.224573i
$523$	−19.7948	−	11.4285i	−0.865567	−	0.499735i	0.000305526	−	1.00000i	$-0.499903\pi$
$523$	−19.7948	−	11.4285i	−0.865567	−	0.499735i	−0.865873	+	0.500265i	$0.833236\pi$
$524$	−2.95120	−	5.11162i	−0.128924	−	0.223302i
$525$	−0.595504	+	3.45110i	−0.0259899	+	0.150618i
$526$	7.97925	+	13.8205i	0.347912	+	0.602601i
$527$	5.57182	−	3.21689i	0.242712	−	0.140130i
$528$		−	3.30969i		−	0.144036i
$529$	−11.4404	−	19.8154i	−0.497411	−	0.861541i
$530$	−6.34196	+	1.13023i	−0.275477	+	0.0490941i
$531$	−10.1716	+	17.6177i	−0.441408	+	0.764541i
$532$			7.04487i			0.305434i
$533$	0.588576	−	0.277529i	0.0254940	−	0.0120211i
$534$	−5.01623			−0.217074
$535$	6.93588	+	38.9186i	0.299864	+	1.68260i
$536$	−6.77255	+	11.7304i	−0.292529	+	0.506676i
$537$	−6.04443	+	3.48975i	−0.260837	+	0.150594i
$538$			4.34628i			0.187381i
$539$	−5.59024	−	9.68258i	−0.240789	−	0.417058i
$540$	2.51877	+	0.911540i	0.108391	+	0.0392265i
$541$	−9.48006			−0.407580			−0.203790	−	0.979015i	$-0.565326\pi$
$541$	−9.48006			−0.407580			−0.203790	+	0.979015i	$0.565326\pi$
$542$	−22.6255	+	13.0628i	−0.971848	+	0.561097i
$543$	−5.92463	−	3.42059i	−0.254250	−	0.146791i
$544$	−8.76626	+	15.1836i	−0.375850	+	0.650992i
$545$	−8.29958	−	9.85437i	−0.355515	−	0.422115i
$546$	−1.27883	−	2.71211i	−0.0547290	−	0.116068i
$547$		−	33.3911i		−	1.42770i	−0.700299	−	0.713850i	$-0.746950\pi$
$547$		−	33.3911i		−	1.42770i	0.700299	−	0.713850i	$-0.253050\pi$
$548$	1.01101	+	0.583706i	0.0431882	+	0.0249347i
$549$	−9.74003	+	16.8702i	−0.415694	+	0.720004i
$550$	−7.95921	−	21.6212i	−0.339382	−	0.921929i
$551$	17.6427			0.751604
$552$	−0.317218	+	0.183146i	−0.0135017	+	0.00779521i
$553$	19.6513	−	11.3457i	0.835660	−	0.482469i
$554$	−11.7492			−0.499177
$555$	1.43124	−	3.95480i	0.0607527	−	0.167872i
$556$	2.56767	−	4.44733i	0.108893	−	0.188609i
$557$	−32.7053	−	18.8824i	−1.38577	−	0.800073i	−0.392932	−	0.919567i	$-0.628539\pi$
$557$	−32.7053	−	18.8824i	−1.38577	−	0.800073i	−0.992835	+	0.119495i	$0.961873\pi$
$558$		−	4.03793i		−	0.170939i
$559$	4.81243	+	0.400293i	0.203544	+	0.0169306i
$560$	−8.57766	+	7.22431i	−0.362472	+	0.305283i
$561$	3.64979	−	6.32162i	0.154094	−	0.266899i
$562$	4.17616	+	2.41110i	0.176161	+	0.101706i
$563$	22.4307	−	12.9504i	0.945343	−	0.545794i	0.0537120	−	0.998556i	$-0.482895\pi$
$563$	22.4307	−	12.9504i	0.945343	−	0.545794i	0.891631	+	0.452762i	$0.149561\pi$
$564$	2.50155			0.105334
$565$	−10.0083	−	3.62198i	−0.421051	−	0.152378i
$566$	3.61464	+	6.26074i	0.151935	+	0.263159i
$567$		−	16.1193i		−	0.676947i
$568$	5.00967	−	2.89233i	0.210201	−	0.121360i
$569$	−10.7725	+	18.6586i	−0.451609	+	0.782209i	−0.998486	−	0.0550035i	$-0.982483\pi$
$569$	−10.7725	+	18.6586i	−0.451609	+	0.782209i	0.546878	+	0.837213i	$0.315816\pi$
$570$	5.30481	−	0.945395i	0.222194	−	0.0395982i
$571$	−2.22036			−0.0929192			−0.0464596	−	0.998920i	$-0.514794\pi$
$571$	−2.22036			−0.0929192			−0.0464596	+	0.998920i	$0.514794\pi$
$572$	−6.78566	−	4.70823i	−0.283723	−	0.196861i
$573$			0.530704i			0.0221705i
$574$	0.217455	−	0.376644i	0.00907641	−	0.0157208i
$575$	−1.10432	+	1.32590i	−0.0460532	+	0.0552938i
$576$	12.6209	+	21.8601i	0.525872	+	0.910837i
$577$		−	6.20265i		−	0.258220i	−0.991630	−	0.129110i	$-0.958788\pi$
$577$		−	6.20265i		−	0.258220i	0.991630	−	0.129110i	$-0.0412120\pi$
$578$	13.0631	−	7.54199i	0.543353	−	0.313705i
$579$	3.65871	+	6.33707i	0.152051	+	0.263360i
$580$	−2.55063	−	3.02845i	−0.105909	−	0.125749i
$581$	−7.95120	−	13.7719i	−0.329871	−	0.571354i
$582$	−2.06028	−	1.18950i	−0.0854014	−	0.0493065i
$583$	−8.15489	−	4.70823i	−0.337741	−	0.194995i
$584$	27.2492			1.12758
$585$	−18.9443	+	13.4382i	−0.783252	+	0.555600i
$586$	−11.6265			−0.480285
$587$	1.58391	+	0.914469i	0.0653748	+	0.0377442i	0.532331	−	0.846536i	$-0.321316\pi$
$587$	1.58391	+	0.914469i	0.0653748	+	0.0377442i	−0.466956	+	0.884280i	$0.654649\pi$
$588$	−0.508211	−	0.293416i	−0.0209583	−	0.0121003i
$589$	3.47114	+	6.01219i	0.143026	+	0.247728i
$590$	14.3395	−	12.0770i	0.590346	−	0.497204i
$591$	1.59733	+	2.76666i	0.0657055	+	0.113805i
$592$	11.6637	−	6.73403i	0.479374	−	0.276767i
$593$			0.0728761i			0.00299266i	0.999999	+	0.00149633i	$0.000476297\pi$
$593$			0.0728761i			0.00299266i	−0.999999	+	0.00149633i	$0.999524\pi$
$594$	−4.67602	−	8.09910i	−0.191859	−	0.332310i
$595$	−24.3503	+	4.33959i	−0.998266	+	0.177906i
$596$	6.58212	−	11.4006i	0.269614	−	0.466986i
$597$			6.00646i			0.245828i
$598$	0.122467	−	1.47233i	0.00500804	−	0.0602080i
$599$	14.5813			0.595777			0.297888	−	0.954601i	$-0.403718\pi$
$599$	14.5813			0.595777			0.297888	+	0.954601i	$0.403718\pi$
$600$	−4.07777	−	3.39630i	−0.166474	−	0.138653i
$601$	22.2041	−	38.4586i	0.905723	−	1.56876i	0.0857795	−	0.996314i	$-0.472662\pi$
$601$	22.2041	−	38.4586i	0.905723	−	1.56876i	0.819944	−	0.572444i	$-0.194005\pi$
$602$	2.79508	−	1.61374i	0.113919	−	0.0657712i
$603$			12.6881i			0.516700i
$604$	5.65527	+	9.79522i	0.230110	+	0.398562i
$605$	3.09044	−	8.53951i	0.125644	−	0.347180i
$606$	−2.43491			−0.0989115
$607$	31.3808	−	18.1177i	1.27371	−	0.735375i	0.298024	−	0.954558i	$-0.403672\pi$
$607$	31.3808	−	18.1177i	1.27371	−	0.735375i	0.975684	+	0.219183i	$0.0703392\pi$
$608$	−16.3836	−	9.45910i	−0.664445	−	0.383617i
$609$	1.05063	−	1.81975i	0.0425737	−	0.0737398i
$610$	13.7311	−	11.5647i	0.555956	−	0.468239i
$611$	−25.2419	+	36.3794i	−1.02118	+	1.47175i
$612$			9.26754i			0.374618i
$613$	2.90838	+	1.67915i	0.117468	+	0.0678203i	0.557583	−	0.830121i	$-0.311729\pi$
$613$	2.90838	+	1.67915i	0.117468	+	0.0678203i	−0.440115	+	0.897942i	$0.645062\pi$
$614$	−13.1228	+	22.7293i	−0.529591	+	0.917279i
$615$	0.130961	+	0.0473948i	0.00528087	+	0.00191114i
$616$	−24.2240			−0.976013
$617$	−18.3441	+	10.5910i	−0.738507	+	0.426377i	−0.821526	−	0.570171i	$-0.806877\pi$
$617$	−18.3441	+	10.5910i	−0.738507	+	0.426377i	0.0830194	+	0.996548i	$0.473544\pi$
$618$	−2.28311	+	1.31815i	−0.0918402	+	0.0530240i
$619$	−25.4082			−1.02124			−0.510620	−	0.859807i	$-0.670584\pi$
$619$	−25.4082			−1.02124			−0.510620	+	0.859807i	$0.670584\pi$
$620$	0.530192	−	1.46503i	0.0212930	−	0.0588369i
$621$	−0.350210	+	0.606582i	−0.0140534	+	0.0243413i
$622$	7.85493	+	4.53504i	0.314954	+	0.181839i
$623$			24.8455i			0.995416i
$624$	3.06428	+	0.254884i	0.122670	+	0.0102035i
$625$	−23.5543	−	8.37828i	−0.942171	−	0.335131i
$626$	−15.5199	+	26.8813i	−0.620302	+	1.07439i
$627$	6.82125	+	3.93825i	0.272415	+	0.157279i
$628$	3.17056	−	1.83052i	0.126519	−	0.0730459i
$629$	29.7041			1.18438
$630$	−5.28261	+	14.5969i	−0.210464	+	0.581555i
$631$	−21.7725	−	37.7112i	−0.866751	−	1.50126i	−0.865298	−	0.501258i	$-0.832871\pi$
$631$	−21.7725	−	37.7112i	−0.866751	−	1.50126i	−0.00145375	−	0.999999i	$-0.500463\pi$
$632$			34.3853i			1.36777i
$633$	−2.17632	+	1.25650i	−0.0865011	+	0.0499414i
$634$	7.03069	−	12.1775i	0.279224	−	0.483631i
$635$	−6.55413	−	36.7766i	−0.260093	−	1.45943i
$636$	−0.494244			−0.0195980
$637$	9.39516	−	4.43007i	0.372250	−	0.175526i
$638$			13.8238i			0.547288i
$639$	2.70934	−	4.69272i	0.107180	−	0.185641i
$640$	−1.55727	−	8.73816i	−0.0615565	−	0.345406i
$641$	−24.1427	−	41.8164i	−0.953579	−	1.65165i	−0.737586	−	0.675253i	$-0.764035\pi$
$641$	−24.1427	−	41.8164i	−0.953579	−	1.65165i	−0.215993	−	0.976395i	$-0.569299\pi$
$642$		−	7.24423i		−	0.285907i
$643$	−36.6710	+	21.1720i	−1.44616	+	0.834943i	−0.998250	−	0.0591344i	$-0.981166\pi$
$643$	−36.6710	+	21.1720i	−1.44616	+	0.834943i	−0.447913	+	0.894077i	$0.647833\pi$
$644$	0.206708	+	0.358028i	0.00814543	+	0.0141083i
$645$	0.665802	+	0.790529i	0.0262159	+	0.0311271i
$646$	19.0281	+	32.9576i	0.748649	+	1.29670i
$647$	−29.7958	−	17.2026i	−1.17139	−	0.676305i	−0.217386	−	0.976086i	$-0.569753\pi$
$647$	−29.7958	−	17.2026i	−1.17139	−	0.676305i	−0.954008	+	0.299781i	$0.903086\pi$
$648$	21.1538	+	12.2131i	0.830999	+	0.479778i
$649$	27.4045			1.07572
$650$	20.6310	−	5.70398i	0.809213	−	0.223729i
$651$	0.826831			0.0324061
$652$	−6.10104	−	3.52244i	−0.238935	−	0.137949i
$653$	12.4114	+	7.16573i	0.485696	+	0.280417i	0.722787	−	0.691071i	$-0.242861\pi$
$653$	12.4114	+	7.16573i	0.485696	+	0.280417i	−0.237091	+	0.971487i	$0.576194\pi$
$654$	1.18048	+	2.04465i	0.0461604	+	0.0799521i
$655$	14.4045	+	17.1029i	0.562830	+	0.668267i
$656$	0.222994	+	0.386237i	0.00870646	+	0.0150800i
$657$	22.1054	−	12.7626i	0.862416	−	0.497916i
$658$			29.5936i			1.15368i
$659$	11.4116	+	19.7655i	0.444532	+	0.769953i	0.998020	−	0.0629051i	$-0.0200365\pi$
$659$	11.4116	+	19.7655i	0.444532	+	0.769953i	−0.553487	+	0.832858i	$0.686703\pi$
$660$	−0.310140	−	1.74026i	−0.0120722	−	0.0677394i
$661$	−7.20934	+	12.4869i	−0.280411	+	0.485686i	−0.971486	−	0.237097i	$-0.923804\pi$
$661$	−7.20934	+	12.4869i	−0.280411	+	0.485686i	0.691075	+	0.722783i	$0.257137\pi$
$662$			15.0796i			0.586087i
$663$	5.57182	+	3.86601i	0.216391	+	0.150143i
$664$	24.0976			0.935168
$665$	−4.68257	−	26.2749i	−0.181582	−	1.01890i
$666$	9.32135	−	16.1450i	0.361195	−	0.625608i
$667$	0.896622	−	0.517665i	0.0347173	−	0.0200441i
$668$			1.19792i			0.0463491i
$669$	−3.35913	−	5.81818i	−0.129871	−	0.224944i
$670$	3.97913	−	10.9952i	0.153727	−	0.424780i
$671$	26.2419			1.01306
$672$	−1.95131	+	1.12659i	−0.0752733	+	0.0434591i
$673$	29.5956	+	17.0871i	1.14083	+	0.658657i	0.946636	−	0.322306i	$-0.104458\pi$
$673$	29.5956	+	17.0871i	1.14083	+	0.658657i	0.194193	+	0.980963i	$0.437791\pi$
$674$	−9.07949	+	15.7261i	−0.349729	+	0.605748i
$675$	−10.0000	−	1.72555i	−0.384900	−	0.0664164i
$676$	4.88170	−	5.91993i	0.187758	−	0.227690i
$677$		−	5.84695i		−	0.224716i	−0.993668	−	0.112358i	$-0.964160\pi$
$677$		−	5.84695i		−	0.224716i	0.993668	−	0.112358i	$-0.0358404\pi$
$678$	1.68912	+	0.975215i	0.0648703	+	0.0374529i
$679$	−5.89165	+	10.2046i	−0.226101	+	0.391618i
$680$	12.7546	−	35.2436i	0.489117	−	1.35153i
$681$	1.66054			0.0636319
$682$	−4.71079	+	2.71978i	−0.180386	+	0.104146i
$683$	−9.82834	+	5.67439i	−0.376071	+	0.217125i	−0.676107	−	0.736803i	$-0.736334\pi$
$683$	−9.82834	+	5.67439i	−0.376071	+	0.217125i	0.300036	+	0.953928i	$0.403001\pi$
$684$	−10.0000			−0.382360
$685$	−4.15868	−	1.50502i	−0.158895	−	0.0575039i
$686$	11.9053	−	20.6206i	0.454546	−	0.787298i
$687$	0.455363	+	0.262904i	0.0173732	+	0.0100304i
$688$			3.30969i			0.126181i
$689$	4.98715	−	7.18765i	0.189995	−	0.273828i
$690$	0.241857	−	0.203698i	0.00920733	−	0.00775463i
$691$	9.41159	−	16.3013i	0.358034	−	0.620133i	−0.629599	−	0.776921i	$-0.716781\pi$
$691$	9.41159	−	16.3013i	0.358034	−	0.620133i	0.987632	+	0.156788i	$0.0501140\pi$
$692$	−0.684619	−	0.395265i	−0.0260253	−	0.0150257i
$693$	−19.6513	+	11.3457i	−0.746493	+	0.430988i
$694$	−14.5325			−0.551647
$695$	−6.62044	+	18.2936i	−0.251128	+	0.693916i
$696$	1.59207	+	2.75754i	0.0603471	+	0.104524i
$697$			0.983636i			0.0372579i
$698$	19.2289	−	11.1018i	0.727825	−	0.420210i
$699$	−2.40976	+	4.17383i	−0.0911455	+	0.157869i
$700$	−3.83323	+	4.60238i	−0.144883	+	0.173954i
$701$	19.1626			0.723763			0.361881	−	0.932224i	$-0.382135\pi$
$701$	19.1626			0.723763			0.361881	+	0.932224i	$0.382135\pi$
$702$	7.85869	−	3.70558i	0.296607	−	0.139858i
$703$			32.0518i			1.20885i
$704$	17.0018	−	29.4480i	0.640780	−	1.10986i
$705$	−9.32990	+	1.66273i	−0.351385	+	0.0626219i
$706$	−0.777006	−	1.34581i	−0.0292430	−	0.0506504i
$707$			12.0602i			0.453570i
$708$	1.24568	−	0.719193i	0.0468154	−	0.0270289i
$709$	11.7419	+	20.3375i	0.440975	+	0.763791i	0.997762	−	0.0668645i	$-0.0212995\pi$
$709$	11.7419	+	20.3375i	0.440975	+	0.763791i	−0.556787	+	0.830655i	$0.687966\pi$
$710$	−3.81952	+	3.21689i	−0.143344	+	0.120728i
$711$	16.1049	+	27.8945i	0.603982	+	1.04613i
$712$	−32.6055	−	18.8248i	−1.22194	−	0.705488i
$713$	0.352814	+	0.203698i	0.0132130	+	0.00762853i
$714$	4.53252			0.169625
$715$	28.4375	+	13.0497i	1.06350	+	0.488033i
$716$	−11.9370			−0.446107
$717$	1.19550	+	0.690220i	0.0446466	+	0.0257767i
$718$	30.2393	+	17.4586i	1.12852	+	0.651551i
$719$	−7.05429	−	12.2184i	−0.263080	−	0.455669i	0.703978	−	0.710221i	$-0.251405\pi$
$719$	−7.05429	−	12.2184i	−0.263080	−	0.455669i	−0.967059	+	0.254553i	$0.918072\pi$
$720$	−10.2547	−	12.1758i	−0.382170	−	0.453764i
$721$	6.52886	+	11.3083i	0.243148	+	0.421144i
$722$	−16.0254	+	9.25228i	−0.596404	+	0.344334i
$723$		−	6.02765i		−	0.224171i
$724$	−5.85021	−	10.1329i	−0.217421	−	0.376585i
$725$	11.5259	+	9.59969i	0.428061	+	0.356523i
$726$	−0.832096	+	1.44123i	−0.0308820	+	0.0534892i
$727$		−	25.3762i		−	0.941153i	−0.882359	−	0.470576i	$-0.844046\pi$
$727$		−	25.3762i		−	0.941153i	0.882359	−	0.470576i	$-0.155954\pi$
$728$	1.86553	−	22.4279i	0.0691411	−	0.831233i
$729$	20.7796			0.769616
$730$	−23.1584	+	4.12717i	−0.857131	+	0.152754i
$731$	−3.64979	+	6.32162i	−0.134992	+	0.233814i
$732$	1.19283	−	0.688681i	0.0440883	−	0.0254544i
$733$		−	10.6692i		−	0.394074i	−0.980396	−	0.197037i	$-0.936868\pi$
$733$		−	10.6692i		−	0.394074i	0.980396	−	0.197037i	$-0.0631320\pi$
$734$	−19.8476	−	34.3770i	−0.732587	−	1.26888i
$735$	2.09047	+	0.756540i	0.0771083	+	0.0279054i
$736$	−1.11018			−0.0409218
$737$	14.8024	−	8.54617i	0.545254	−	0.314802i
$738$	0.534635	+	0.308672i	0.0196802	+	0.0113624i
$739$	−0.707513	+	1.22545i	−0.0260263	+	0.0450788i	−0.878745	−	0.477291i	$-0.841619\pi$
$739$	−0.707513	+	1.22545i	−0.0260263	+	0.0450788i	0.852719	+	0.522370i	$0.174952\pi$
$740$	5.50183	−	4.63377i	0.202251	−	0.170341i
$741$	−4.17156	+	6.01219i	−0.153246	+	0.220863i
$742$		−	5.84695i		−	0.214648i
$743$	25.8748	+	14.9389i	0.949256	+	0.548053i	0.892850	−	0.450355i	$-0.148702\pi$
$743$	25.8748	+	14.9389i	0.949256	+	0.548053i	0.0564064	+	0.998408i	$0.482036\pi$
$744$	−0.626467	+	1.08507i	−0.0229674	+	0.0397807i
$745$	−16.9713	+	46.8951i	−0.621779	+	1.71810i
$746$	−40.9370			−1.49881
$747$	19.5488	−	11.2865i	0.715253	−	0.412952i
$748$	10.8118	−	6.24221i	0.395320	−	0.228238i
$749$	−35.8809			−1.31106
$750$	3.98001	+	2.26881i	0.145329	+	0.0828453i
$751$	9.99291	−	17.3082i	0.364646	−	0.631586i	−0.624073	−	0.781366i	$-0.714523\pi$
$751$	9.99291	−	17.3082i	0.364646	−	0.631586i	0.988719	+	0.149780i	$0.0478565\pi$
$752$	−26.2816	−	15.1737i	−0.958391	−	0.553328i
$753$			3.20938i			0.116956i
$754$	−12.7988	−	1.06459i	−0.466104	−	0.0387701i
$755$	−27.6028	−	32.7737i	−1.00457	−	1.19276i
$756$	−1.21563	+	2.10553i	−0.0442120	+	0.0765774i
$757$	−14.8024	−	8.54617i	−0.538003	−	0.310616i	0.206266	−	0.978496i	$-0.433869\pi$
$757$	−14.8024	−	8.54617i	−0.538003	−	0.310616i	−0.744269	+	0.667880i	$0.767202\pi$
$758$	−17.8964	+	10.3325i	−0.650025	+	0.375292i
$759$	0.462218			0.0167775
$760$	38.0291	+	13.7627i	1.37946	+	0.499225i
$761$	21.1120	+	36.5671i	0.765310	+	1.32556i	0.940083	+	0.340947i	$0.110748\pi$
$761$	21.1120	+	36.5671i	0.765310	+	1.32556i	−0.174773	+	0.984609i	$0.555919\pi$
$762$			6.84552i			0.247987i
$763$	10.1272	−	5.84695i	0.366630	−	0.211674i
$764$	−0.453830	+	0.786056i	−0.0164190	+	0.0284385i
$765$	−6.15992	−	34.5646i	−0.222713	−	1.24969i
$766$	2.07395			0.0749350
$767$	−2.11046	+	25.3725i	−0.0762044	+	0.916149i
$768$		−	4.42107i		−	0.159531i
$769$	−11.8827	+	20.5815i	−0.428502	+	0.742187i	−0.996740	−	0.0806767i	$-0.974292\pi$
$769$	−11.8827	+	20.5815i	−0.428502	+	0.742187i	0.568238	+	0.822864i	$0.307625\pi$
$770$	20.5874	−	3.66898i	0.741919	−	0.132221i
$771$	−1.87907	−	3.25465i	−0.0676731	−	0.117213i
$772$			12.5149i			0.450422i
$773$	−0.246026	+	0.142043i	−0.00884894	+	0.00510894i	−0.504418	−	0.863460i	$-0.668293\pi$
$773$	−0.246026	+	0.142043i	−0.00884894	+	0.00510894i	0.495569	+	0.868569i	$0.334960\pi$
$774$	2.29066	+	3.96754i	0.0823361	+	0.142610i
$775$	−1.00366	+	5.81644i	−0.0360524	+	0.208933i
$776$	−8.92787	−	15.4635i	−0.320492	−	0.555108i
$777$	3.30596	+	1.90870i	0.118601	+	0.0684741i
$778$	−22.6665	−	13.0865i	−0.812634	−	0.469174i
$779$	−1.06138			−0.0380278
$780$	1.63511	−	0.153124i	0.0585462	−	0.00548272i
$781$	−7.29958			−0.261199
$782$	1.93405	+	1.11663i	0.0691617	+	0.0399305i
$783$	5.27294	+	3.04434i	0.188440	+	0.108796i
$784$	3.55955	+	6.16532i	0.127127	+	0.220190i
$785$	−10.6084	+	8.93460i	−0.378628	+	0.318890i
$786$	−2.04880	−	3.54863i	−0.0730784	−	0.126575i
$787$	−20.9008	+	12.0671i	−0.745032	+	0.430145i	−0.823896	−	0.566741i	$-0.808204\pi$
$787$	−20.9008	+	12.0671i	−0.745032	+	0.430145i	0.0788638	+	0.996885i	$0.474871\pi$
$788$			5.46381i			0.194640i
$789$	−2.31925	−	4.01705i	−0.0825674	−	0.143011i
$790$	−5.20802	−	29.2233i	−0.185293	−	1.03972i
$791$	4.83027	−	8.36627i	0.171745	−	0.297470i
$792$		−	34.3853i		−	1.22183i
$793$	−2.02093	+	24.2961i	−0.0717652	+	0.862780i
$794$	26.7529			0.949424
$795$	1.84335	−	0.328513i	0.0653770	−	0.0116511i
$796$	−5.13641	+	8.89652i	−0.182055	+	0.315329i
$797$	29.7430	−	17.1721i	1.05355	−	0.608267i	0.129909	−	0.991526i	$-0.458532\pi$
$797$	29.7430	−	17.1721i	1.05355	−	0.608267i	0.923641	+	0.383259i	$0.125198\pi$
$798$			4.89075i			0.173131i
$799$	−33.4659	−	57.9646i	−1.18394	−	2.05064i
$800$	−5.55650	−	15.0942i	−0.196452	−	0.533661i
$801$	−35.2676			−1.24612
$802$	3.80876	−	2.19899i	0.134492	−	0.0776489i
$803$	−29.7786	−	17.1927i	−1.05086	−	0.606716i
$804$	0.448565	−	0.776937i	0.0158197	−	0.0274004i
$805$	−1.00892	−	1.19792i	−0.0355598	−	0.0422213i
$806$	−2.15533	−	4.57096i	−0.0759182	−	0.161005i
$807$		−	1.26329i		−	0.0444698i
$808$	−15.8269	−	9.13767i	−0.556789	−	0.321462i
$809$	−23.8431	+	41.2975i	−0.838279	+	1.45194i	0.0530528	+	0.998592i	$0.483105\pi$
$809$	−23.8431	+	41.2975i	−0.838279	+	1.45194i	−0.891332	+	0.453351i	$0.850229\pi$
$810$	−19.8279	−	7.17570i	−0.696682	−	0.252128i
$811$	24.5992			0.863793			0.431897	−	0.901923i	$-0.357845\pi$
$811$	24.5992			0.863793			0.431897	+	0.901923i	$0.357845\pi$
$812$	3.11230	−	1.79689i	0.109220	−	0.0630584i
$813$	6.57632	−	3.79684i	0.230642	−	0.133161i
$814$	−25.1138			−0.880239
$815$	25.0960	+	9.08221i	0.879074	+	0.318136i
$816$	−2.32398	+	4.02525i	−0.0813556	+	0.140912i
$817$	−6.82125	−	3.93825i	−0.238645	−	0.137782i
$818$		−	16.0097i		−	0.559765i
$819$	−8.99108	−	19.0680i	−0.314174	−	0.666290i
$820$	0.153445	+	0.182190i	0.00535853	+	0.00636236i
$821$	−8.64979	+	14.9819i	−0.301880	+	0.522871i	−0.976562	−	0.215237i	$-0.930947\pi$
$821$	−8.64979	+	14.9819i	−0.301880	+	0.522871i	0.674682	+	0.738109i	$0.264281\pi$
$822$	0.701870	+	0.405225i	0.0244805	+	0.0141338i
$823$	−28.2000	+	16.2813i	−0.982990	+	0.567529i	−0.903171	−	0.429280i	$-0.858767\pi$
$823$	−28.2000	+	16.2813i	−0.982990	+	0.567529i	−0.0798182	+	0.996809i	$0.525434\pi$
$824$	−19.7869			−0.689311
$825$	2.31342	+	6.28440i	0.0805430	+	0.218795i
$826$	8.50812	+	14.7365i	0.296035	+	0.512748i
$827$			15.4702i			0.537951i	0.963147	+	0.268976i	$0.0866851\pi$
$827$			15.4702i			0.537951i	−0.963147	+	0.268976i	$0.913315\pi$
$828$	−0.508211	+	0.293416i	−0.0176616	+	0.0101969i
$829$	−7.26180	+	12.5778i	−0.252213	+	0.436845i	−0.964135	−	0.265413i	$-0.914492\pi$
$829$	−7.26180	+	12.5778i	−0.252213	+	0.436845i	0.711922	+	0.702258i	$0.247825\pi$
$830$	−20.4800	+	3.64984i	−0.710870	+	0.126688i
$831$	3.41503			0.118466
$832$	25.9552	+	18.0090i	0.899835	+	0.624351i
$833$			15.7013i			0.544018i
$834$	1.78254	−	3.08746i	0.0617245	−	0.106910i
$835$	−0.796234	−	4.46783i	−0.0275548	−	0.154616i
$836$	6.73557	+	11.6663i	0.232955	+	0.403489i
$837$			2.39585i			0.0828127i
$838$	17.2986	−	9.98736i	0.597571	−	0.345008i
$839$	0.407933	+	0.706561i	0.0140834	+	0.0243932i	0.872981	−	0.487754i	$-0.162184\pi$
$839$	0.407933	+	0.706561i	0.0140834	+	0.0243932i	−0.858898	+	0.512147i	$0.828850\pi$
$840$	3.68419	−	3.10291i	0.127117	−	0.107061i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	17.5846	+	10.1524i	0.606004	+	0.349876i
$843$	−1.21384	−	0.700811i	−0.0418069	−	0.0241372i
$844$	−4.29797			−0.147942
$845$	−14.2722	+	25.3240i	−0.490978	+	0.871172i
$846$	−42.0073			−1.44424
$847$	7.13847	+	4.12140i	0.245281	+	0.141613i
$848$	5.19258	+	2.99794i	0.178314	+	0.102950i
$849$	−1.05063	−	1.81975i	−0.0360575	−	0.0624535i
$850$	−5.50183	+	31.8845i	−0.188711	+	1.09363i
$851$	0.940450	+	1.62891i	0.0322382	+	0.0558382i
$852$	−0.331804	+	0.191567i	−0.0113674	+	0.00656299i
$853$			20.0856i			0.687719i	0.939021	+	0.343859i	$0.111734\pi$
$853$			20.0856i			0.687719i	−0.939021	+	0.343859i	$0.888266\pi$
$854$	8.14716	+	14.1113i	0.278790	+	0.482878i
$855$	37.2964	−	6.64678i	1.27551	−	0.227315i
$856$	27.1860	−	47.0875i	0.929197	−	1.60942i
$857$		−	40.7886i		−	1.39331i	−0.717406	−	0.696656i	$-0.754671\pi$
$857$		−	40.7886i		−	1.39331i	0.717406	−	0.696656i	$-0.245329\pi$
$858$	−4.71079	−	3.26858i	−0.160824	−	0.111588i
$859$	40.1301			1.36922			0.684610	−	0.728909i	$-0.259972\pi$
$859$	40.1301			1.36922			0.684610	+	0.728909i	$0.259972\pi$
$860$	0.310140	+	1.74026i	0.0105757	+	0.0593423i
$861$	−0.0632055	+	0.109475i	−0.00215404	+	0.00373090i
$862$	−9.93355	+	5.73514i	−0.338338	+	0.195340i
$863$		−	20.8275i		−	0.708977i	−0.935060	−	0.354489i	$-0.884655\pi$
$863$		−	20.8275i		−	0.708977i	0.935060	−	0.354489i	$-0.115345\pi$
$864$	−3.26443	−	5.65416i	−0.111058	−	0.192358i
$865$	2.81611	+	1.01915i	0.0957505	+	0.0346520i
$866$	29.4134			0.999509
$867$	−3.79692	+	2.19215i	−0.128950	+	0.0744494i
$868$	1.22467	+	0.707062i	0.0415679	+	0.0239993i
$869$	21.6952	−	37.5771i	0.735958	−	1.27472i
$870$	−1.77072	−	2.10243i	−0.0600330	−	0.0712792i
$871$	6.77255	+	14.3630i	0.229479	+	0.486672i
$872$			17.7203i			0.600084i
$873$	−14.4852	−	8.36303i	−0.490249	−	0.283046i
$874$	−1.20488	+	2.08691i	−0.0407557	+	0.0705909i
$875$	11.2375	−	19.7131i	0.379897	−	0.666424i
$876$	−1.80479			−0.0609782
$877$	−40.3520	+	23.2972i	−1.36259	+	0.786691i	−0.989968	−	0.141293i	$-0.954874\pi$
$877$	−40.3520	+	23.2972i	−1.36259	+	0.786691i	−0.372621	+	0.927984i	$0.621541\pi$
$878$	7.26094	−	4.19210i	0.245045	−	0.141477i
$879$	3.37935			0.113982
$880$	−7.29753	+	20.1646i	−0.246000	+	0.679747i
$881$	−11.9223	+	20.6501i	−0.401674	+	0.695719i	−0.993928	−	0.110032i	$-0.964905\pi$
$881$	−11.9223	+	20.6501i	−0.401674	+	0.695719i	0.592254	+	0.805751i	$0.298238\pi$
$882$	8.53413	+	4.92718i	0.287359	+	0.165907i
$883$		−	37.2496i		−	1.25355i	−0.779201	−	0.626774i	$-0.784375\pi$
$883$		−	37.2496i		−	1.25355i	0.779201	−	0.626774i	$-0.215625\pi$
$884$	4.94674	+	10.4909i	0.166377	+	0.352847i
$885$	−4.16790	+	3.51031i	−0.140103	+	0.117998i
$886$	22.7041	−	39.3246i	0.762758	−	1.32114i
$887$	24.7505	+	14.2897i	0.831042	+	0.479802i	0.854209	−	0.519929i	$-0.174042\pi$
$887$	24.7505	+	14.2897i	0.831042	+	0.479802i	−0.0231673	+	0.999732i	$0.507375\pi$
$888$	−5.00967	+	2.89233i	−0.168113	+	0.0970603i
$889$	33.9060			1.13717
$890$	30.5618	+	11.0603i	1.02443	+	0.370742i
$891$	−15.4116	−	26.6937i	−0.516308	−	0.894271i
$892$		−	11.4902i		−	0.384720i
$893$	62.5459	−	36.1109i	2.09302	−	1.20840i
$894$	4.56949	−	7.91459i	0.152827	−	0.264704i
$895$	44.5208	−	7.93427i	1.48817	−	0.265213i
$896$	8.05611			0.269136
$897$	−0.0355962	+	0.427946i	−0.00118852	+	0.0142887i
$898$		−	14.8180i		−	0.494483i
$899$	1.77072	−	3.06697i	0.0590568	−	0.102289i
$900$	−6.53295	−	5.44117i	−0.217765	−	0.181372i
$901$	6.61201	+	11.4523i	0.220278	+	0.381533i
$902$		−	0.831632i		−	0.0276903i
$903$	−0.812417	+	0.469049i	−0.0270356	+	0.0156090i
$904$	7.31952	+	12.6778i	0.243444	+	0.421657i
$905$	28.5543	+	33.9035i	0.949177	+	1.12699i
$906$	3.92605	+	6.80011i	0.130434	+	0.225919i
$907$	5.55457	+	3.20693i	0.184436	+	0.106484i	0.589375	−	0.807859i	$-0.299374\pi$
$907$	5.55457	+	3.20693i	0.184436	+	0.106484i	−0.404939	+	0.914344i	$0.632707\pi$
$908$	2.45952	+	1.42000i	0.0816220	+	0.0471245i
$909$	−17.1191			−0.567805
$910$	1.81147	+	19.3435i	0.0600497	+	0.641230i
$911$	22.2204			0.736193			0.368097	−	0.929788i	$-0.380010\pi$
$911$	22.2204			0.736193			0.368097	+	0.929788i	$0.380010\pi$
$912$	−4.34339	−	2.50766i	−0.143824	−	0.0830369i
$913$	−26.3345	−	15.2042i	−0.871543	−	0.503186i
$914$	4.88719	+	8.46486i	0.161654	+	0.279993i
$915$	−3.99108	+	3.36138i	−0.131941	+	0.111124i
$916$	0.449643	+	0.778805i	0.0148566	+	0.0257324i
$917$	−17.5765	+	10.1478i	−0.580426	+	0.335109i
$918$			13.1335i			0.433472i
$919$	13.0632	+	22.6261i	0.430915	+	0.746367i	0.996952	−	0.0780125i	$-0.0248574\pi$
$919$	13.0632	+	22.6261i	0.430915	+	0.746367i	−0.566037	+	0.824380i	$0.691524\pi$
$920$	2.33650	−	0.416399i	0.0770321	−	0.0137283i
$921$	3.81426	−	6.60649i	0.125684	−	0.217691i
$922$			5.39220i			0.177583i
$923$	0.562152	−	6.75834i	0.0185035	−	0.222453i
$924$	1.60442			0.0527817
$925$	−17.4399	+	20.9392i	−0.573420	+	0.688478i
$926$	1.18048	−	2.04465i	0.0387929	−	0.0671913i
$927$	−16.0518	+	9.26754i	−0.527212	+	0.304386i
$928$			9.65067i			0.316799i
$929$	−11.9711	−	20.7346i	−0.392760	−	0.680281i	0.600052	−	0.799961i	$-0.295146\pi$
$929$	−11.9711	−	20.7346i	−0.392760	−	0.680281i	−0.992813	+	0.119680i	$0.961813\pi$
$930$	0.368074	−	1.01706i	0.0120696	−	0.0333508i
$931$	−16.9423			−0.555261
$932$	−7.13847	+	4.12140i	−0.233828	+	0.135001i
$933$	−2.28311	−	1.31815i	−0.0747457	−	0.0431544i
$934$	−19.4748	+	33.7313i	−0.637235	+	1.10372i
$935$	−36.1752	+	30.4676i	−1.18306	+	0.996397i
$936$	31.8358	+	2.64807i	1.04058	+	0.0865547i
$937$			18.5046i			0.604518i	0.953226	+	0.302259i	$0.0977407\pi$
$937$			18.5046i			0.604518i	−0.953226	+	0.302259i	$0.902259\pi$
$938$	9.19124	+	5.30656i	0.300104	+	0.173265i
$939$	4.51102	−	7.81332i	0.147212	−	0.254978i
$940$	−15.2409	−	5.51568i	−0.497105	−	0.179902i
$941$	−14.3788			−0.468735			−0.234368	−	0.972148i	$-0.575302\pi$
$941$	−14.3788			−0.468735			−0.234368	+	0.972148i	$0.575302\pi$
$942$	2.20109	−	1.27080i	0.0717154	−	0.0414049i
$943$	−0.0539404	+	0.0311425i	−0.00175654	+	0.00101414i
$944$	−17.4496			−0.567938
$945$	3.13436	−	8.66087i	0.101961	−	0.281738i
$946$	3.08578	−	5.34473i	0.100327	−	0.173772i
$947$	50.5056	+	29.1594i	1.64121	+	0.947554i	0.980404	+	0.196998i	$0.0631194\pi$
$947$	50.5056	+	29.1594i	1.64121	+	0.947554i	0.660807	+	0.750555i	$0.270214\pi$
$948$		−	2.27744i		−	0.0739677i
$949$	18.2112	−	26.2465i	0.591160	−	0.851999i
$950$	−34.4045	−	5.93667i	−1.11623	−	0.192611i
$951$	−2.04354	+	3.53951i	−0.0662663	+	0.114777i
$952$	29.4613	+	17.0095i	0.954847	+	0.551281i
$953$	−11.9507	+	6.89975i	−0.387122	+	0.223505i	−0.680912	−	0.732365i	$-0.738417\pi$
$953$	−11.9507	+	6.89975i	−0.387122	+	0.223505i	0.293791	+	0.955870i	$0.405083\pi$
$954$	8.29958			0.268709
$955$	1.17015	−	3.23336i	0.0378651	−	0.104629i
$956$	1.18048	+	2.04465i	0.0381794	+	0.0661287i
$957$		−	4.01801i		−	0.129884i
$958$	−31.6759	+	18.2881i	−1.02340	+	0.590862i
$959$	2.00709	−	3.47639i	0.0648124	−	0.112258i
$960$	1.18629	+	6.65651i	0.0382873	+	0.214838i
$961$	−29.6065			−0.955047
$962$	1.93405	−	23.2517i	0.0623564	−	0.749666i
$963$		−	50.9319i		−	1.64126i
$964$	5.15452	−	8.92790i	0.166016	−	0.287548i
$965$	−8.31840	−	46.6763i	−0.267779	−	1.50256i
$966$	0.143502	+	0.248553i	0.00461711	+	0.00799707i
$967$		−	30.3474i		−	0.975906i	−0.872870	−	0.487953i	$-0.837744\pi$
$967$		−	30.3474i		−	0.975906i	0.872870	−	0.487953i	$-0.162256\pi$
$968$	−10.8172	+	6.24534i	−0.347679	+	0.200733i
$969$	−5.53069	−	9.57943i	−0.177671	−	0.307736i
$970$	9.92970	+	11.7899i	0.318824	+	0.378550i
$971$	−22.0506	−	38.1928i	−0.707638	−	1.22567i	−0.965731	−	0.259545i	$-0.916427\pi$
$971$	−22.0506	−	38.1928i	−0.707638	−	1.22567i	0.258092	−	0.966120i	$-0.416906\pi$
$972$	−4.51337	−	2.60580i	−0.144767	−	0.0835810i
$973$	−15.2923	−	8.82900i	−0.490248	−	0.283045i
$974$	26.5074			0.849351
$975$	−5.99659	+	1.65792i	−0.192045	+	0.0530958i
$976$	−16.7093			−0.534853
$977$	−19.3314	−	11.1610i	−0.618466	−	0.357071i	0.157806	−	0.987470i	$-0.449558\pi$
$977$	−19.3314	−	11.1610i	−0.618466	−	0.357071i	−0.776271	+	0.630399i	$0.782891\pi$
$978$	−4.23551	−	2.44537i	−0.135437	−	0.0781944i
$979$	23.7547	+	41.1444i	0.759204	+	1.31498i
$980$	2.44937	+	2.90822i	0.0782422	+	0.0928996i
$981$	8.29958	+	14.3753i	0.264985	+	0.458968i
$982$	−10.9845	+	6.34189i	−0.350529	+	0.202378i
$983$			4.03793i			0.128790i	0.997924	+	0.0643950i	$0.0205118\pi$
$983$			4.03793i			0.128790i	−0.997924	+	0.0643950i	$0.979488\pi$
$984$	−0.0957781	−	0.165893i	−0.00305330	−	0.00528846i
$985$	−3.63168	−	20.3781i	−0.115715	−	0.649300i
$986$	9.70671	−	16.8125i	0.309125	−	0.535419i
$987$		−	8.60167i		−	0.273794i
$988$	−11.3200	+	5.33770i	−0.360139	+	0.169815i
$989$	−0.462218			−0.0146977
$990$	5.20802	+	29.2233i	0.165522	+	0.928776i
$991$	−14.8250	+	25.6777i	−0.470932	+	0.815678i	−0.999447	−	0.0332459i	$-0.989416\pi$
$991$	−14.8250	+	25.6777i	−0.470932	+	0.815678i	0.528515	+	0.848924i	$0.322749\pi$
$992$	−3.28871	+	1.89874i	−0.104417	+	0.0602849i
$993$		−	4.38304i		−	0.139092i
$994$	−2.26626	−	3.92527i	−0.0718813	−	0.124502i
$995$	13.2437	−	36.5949i	0.419852	−	1.16014i
$996$	−1.59605			−0.0505728
$997$	−19.2052	+	11.0881i	−0.608233	+	0.351164i	−0.772274	−	0.635290i	$-0.780881\pi$
$997$	−19.2052	+	11.0881i	−0.608233	+	0.351164i	0.164040	+	0.986454i	$0.447547\pi$
$998$	−19.3514	−	11.1725i	−0.612557	−	0.353660i
$999$	−5.53069	+	9.57943i	−0.174983	+	0.303080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.n.a.9.5	yes	12
3.2	odd	2		585.2.bs.a.334.2		12
4.3	odd	2		1040.2.dh.a.529.4		12
5.2	odd	4		325.2.e.e.126.2		12
5.3	odd	4		325.2.e.e.126.5		12
5.4	even	2	inner	65.2.n.a.9.2	✓	12
13.2	odd	12		845.2.l.f.699.10		24
13.3	even	3	inner	65.2.n.a.29.2	yes	12
13.4	even	6		845.2.b.e.339.5		6
13.5	odd	4		845.2.l.f.654.9		24
13.6	odd	12		845.2.d.d.844.4		12
13.7	odd	12		845.2.d.d.844.10		12
13.8	odd	4		845.2.l.f.654.3		24
13.9	even	3		845.2.b.d.339.2		6
13.10	even	6		845.2.n.e.484.5		12
13.11	odd	12		845.2.l.f.699.4		24
13.12	even	2		845.2.n.e.529.2		12
15.14	odd	2		585.2.bs.a.334.5		12
20.19	odd	2		1040.2.dh.a.529.3		12
39.29	odd	6		585.2.bs.a.289.5		12
52.3	odd	6		1040.2.dh.a.289.3		12
65.3	odd	12		325.2.e.e.276.5		12
65.4	even	6		845.2.b.e.339.2		6
65.9	even	6		845.2.b.d.339.5		6
65.17	odd	12		4225.2.a.bq.1.2		6
65.19	odd	12		845.2.d.d.844.9		12
65.22	odd	12		4225.2.a.br.1.5		6
65.24	odd	12		845.2.l.f.699.9		24
65.29	even	6	inner	65.2.n.a.29.5	yes	12
65.34	odd	4		845.2.l.f.654.10		24
65.42	odd	12		325.2.e.e.276.2		12
65.43	odd	12		4225.2.a.bq.1.5		6
65.44	odd	4		845.2.l.f.654.4		24
65.48	odd	12		4225.2.a.br.1.2		6
65.49	even	6		845.2.n.e.484.2		12
65.54	odd	12		845.2.l.f.699.3		24
65.59	odd	12		845.2.d.d.844.3		12
65.64	even	2		845.2.n.e.529.5		12
195.29	odd	6		585.2.bs.a.289.2		12
260.159	odd	6		1040.2.dh.a.289.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	5.4	even	2	inner
65.2.n.a.9.5	yes	12	1.1	even	1	trivial
65.2.n.a.29.2	yes	12	13.3	even	3	inner
65.2.n.a.29.5	yes	12	65.29	even	6	inner
325.2.e.e.126.2		12	5.2	odd	4
325.2.e.e.126.5		12	5.3	odd	4
325.2.e.e.276.2		12	65.42	odd	12
325.2.e.e.276.5		12	65.3	odd	12
585.2.bs.a.289.2		12	195.29	odd	6
585.2.bs.a.289.5		12	39.29	odd	6
585.2.bs.a.334.2		12	3.2	odd	2
585.2.bs.a.334.5		12	15.14	odd	2
845.2.b.d.339.2		6	13.9	even	3
845.2.b.d.339.5		6	65.9	even	6
845.2.b.e.339.2		6	65.4	even	6
845.2.b.e.339.5		6	13.4	even	6
845.2.d.d.844.3		12	65.59	odd	12
845.2.d.d.844.4		12	13.6	odd	12
845.2.d.d.844.9		12	65.19	odd	12
845.2.d.d.844.10		12	13.7	odd	12
845.2.l.f.654.3		24	13.8	odd	4
845.2.l.f.654.4		24	65.44	odd	4
845.2.l.f.654.9		24	13.5	odd	4
845.2.l.f.654.10		24	65.34	odd	4
845.2.l.f.699.3		24	65.54	odd	12
845.2.l.f.699.4		24	13.11	odd	12
845.2.l.f.699.9		24	65.24	odd	12
845.2.l.f.699.10		24	13.2	odd	12
845.2.n.e.484.2		12	65.49	even	6
845.2.n.e.484.5		12	13.10	even	6
845.2.n.e.529.2		12	13.12	even	2
845.2.n.e.529.5		12	65.64	even	2
1040.2.dh.a.289.3		12	52.3	odd	6
1040.2.dh.a.289.4		12	260.159	odd	6
1040.2.dh.a.529.3		12	20.19	odd	2
1040.2.dh.a.529.4		12	4.3	odd	2
4225.2.a.bq.1.2		6	65.17	odd	12
4225.2.a.bq.1.5		6	65.43	odd	12
4225.2.a.br.1.2		6	65.48	odd	12
4225.2.a.br.1.5		6	65.22	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02826 + 0.593667i) q^{2} +(-0.298874 - 0.172555i) q^{3} +(-0.295120 - 0.511162i) q^{4} +(1.44045 + 1.71029i) q^{5} +(-0.204880 - 0.354863i) q^{6} +(-1.75765 + 1.01478i) q^{7} -3.07548i q^{8} +(-1.44045 - 2.49493i) q^{9} +O(q^{10})\)	\(q+(1.02826 + 0.593667i) q^{2} +(-0.298874 - 0.172555i) q^{3} +(-0.295120 - 0.511162i) q^{4} +(1.44045 + 1.71029i) q^{5} +(-0.204880 - 0.354863i) q^{6} +(-1.75765 + 1.01478i) q^{7} -3.07548i q^{8} +(-1.44045 - 2.49493i) q^{9} +(0.465813 + 2.61378i) q^{10} +(-1.94045 + 3.36096i) q^{11} +0.203698i q^{12} +(-2.96232 - 2.05540i) q^{13} -2.40976 q^{14} +(-0.135393 - 0.759719i) q^{15} +(1.23557 - 2.14007i) q^{16} +(4.71996 - 2.72507i) q^{17} -3.42059i q^{18} +(2.94045 + 5.09301i) q^{19} +(0.449133 - 1.24105i) q^{20} +0.700420 q^{21} +(-3.99058 + 2.30396i) q^{22} +(0.298874 + 0.172555i) q^{23} +(-0.530689 + 0.919180i) q^{24} +(-0.850210 + 4.92718i) q^{25} +(-1.82581 - 3.87212i) q^{26} +2.02956i q^{27} +(1.03743 + 0.598962i) q^{28} +(1.50000 - 2.59808i) q^{29} +(0.311800 - 0.861568i) q^{30} +1.18048 q^{31} +(-2.78591 + 1.60845i) q^{32} +(1.15990 - 0.669668i) q^{33} +6.47114 q^{34} +(-4.26737 - 1.54436i) q^{35} +(-0.850210 + 1.47261i) q^{36} +(4.71996 + 2.72507i) q^{37} +6.98259i q^{38} +(0.530689 + 1.12547i) q^{39} +(5.25997 - 4.43007i) q^{40} +(-0.0902394 + 0.156299i) q^{41} +(0.720215 + 0.415816i) q^{42} +(-1.15990 + 0.669668i) q^{43} +2.29066 q^{44} +(2.19217 - 6.05742i) q^{45} +(0.204880 + 0.354863i) q^{46} -12.2807i q^{47} +(-0.738559 + 0.426407i) q^{48} +(-1.44045 + 2.49493i) q^{49} +(-3.79934 + 4.56169i) q^{50} -1.88090 q^{51} +(-0.176407 + 2.12081i) q^{52} +2.42636i q^{53} +(-1.20488 + 2.08691i) q^{54} +(-8.54334 + 1.52255i) q^{55} +(3.12093 + 5.40561i) q^{56} -2.02956i q^{57} +(3.08478 - 1.78100i) q^{58} +(-3.53069 - 6.11533i) q^{59} +(-0.348383 + 0.293416i) q^{60} +(-3.38090 - 5.85589i) q^{61} +(1.21384 + 0.700811i) q^{62} +(5.06361 + 2.92347i) q^{63} -8.76180 q^{64} +(-0.751722 - 8.02714i) q^{65} +1.59024 q^{66} +(-3.81417 - 2.20211i) q^{67} +(-2.78591 - 1.60845i) q^{68} +(-0.0595504 - 0.103144i) q^{69} +(-3.47114 - 4.12140i) q^{70} +(0.940450 + 1.62891i) q^{71} +(-7.67311 + 4.43007i) q^{72} +8.86014i q^{73} +(3.23557 + 5.60417i) q^{74} +(1.10432 - 1.32590i) q^{75} +(1.73557 - 3.00609i) q^{76} -7.87651i q^{77} +(-0.122467 + 1.47233i) q^{78} -11.1805 q^{79} +(5.43992 - 0.969475i) q^{80} +(-3.97114 + 6.87821i) q^{81} +(-0.185579 + 0.107144i) q^{82} +7.83540i q^{83} +(-0.206708 - 0.358028i) q^{84} +(11.4595 + 4.14720i) q^{85} -1.59024 q^{86} +(-0.896622 + 0.517665i) q^{87} +(10.3365 + 5.96781i) q^{88} +(6.12093 - 10.6018i) q^{89} +(5.85021 - 4.92718i) q^{90} +(7.29249 + 0.606582i) q^{91} -0.203698i q^{92} +(-0.352814 - 0.203698i) q^{93} +(7.29066 - 12.6278i) q^{94} +(-4.47497 + 12.3653i) q^{95} +1.11018 q^{96} +(5.02801 - 2.90292i) q^{97} +(-2.96232 + 1.71029i) q^{98} +11.1805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 6 q^{5} - 10 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 6 * q^5 - 10 * q^6 + 6 * q^9	\( 12 q + 4 q^{4} - 6 q^{5} - 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} - 4 q^{15} - 16 q^{16} + 12 q^{19} - q^{20} - 8 q^{21} + 32 q^{24} - 2 q^{25} + 24 q^{26} + 18 q^{29} + 4 q^{30} - 16 q^{31} + 16 q^{34} + 10 q^{35} - 2 q^{36} - 32 q^{39} + 70 q^{40} + 14 q^{41} - 4 q^{44} - 29 q^{45} + 10 q^{46} + 6 q^{49} - 31 q^{50} + 24 q^{51} - 22 q^{54} - 26 q^{55} - 16 q^{56} - 4 q^{59} - 96 q^{60} + 6 q^{61} - 12 q^{64} + 23 q^{65} + 4 q^{66} - 24 q^{69} + 20 q^{70} - 12 q^{71} + 8 q^{74} + 2 q^{75} - 10 q^{76} - 104 q^{79} + 33 q^{80} + 14 q^{81} + 90 q^{84} + 21 q^{85} - 4 q^{86} + 20 q^{89} + 62 q^{90} - 44 q^{91} + 56 q^{94} + 20 q^{95} + 12 q^{96} + 104 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 - 6 * q^5 - 10 * q^6 + 6 * q^9 + 7 * q^10 - 44 * q^14 - 4 * q^15 - 16 * q^16 + 12 * q^19 - q^20 - 8 * q^21 + 32 * q^24 - 2 * q^25 + 24 * q^26 + 18 * q^29 + 4 * q^30 - 16 * q^31 + 16 * q^34 + 10 * q^35 - 2 * q^36 - 32 * q^39 + 70 * q^40 + 14 * q^41 - 4 * q^44 - 29 * q^45 + 10 * q^46 + 6 * q^49 - 31 * q^50 + 24 * q^51 - 22 * q^54 - 26 * q^55 - 16 * q^56 - 4 * q^59 - 96 * q^60 + 6 * q^61 - 12 * q^64 + 23 * q^65 + 4 * q^66 - 24 * q^69 + 20 * q^70 - 12 * q^71 + 8 * q^74 + 2 * q^75 - 10 * q^76 - 104 * q^79 + 33 * q^80 + 14 * q^81 + 90 * q^84 + 21 * q^85 - 4 * q^86 + 20 * q^89 + 62 * q^90 - 44 * q^91 + 56 * q^94 + 20 * q^95 + 12 * q^96 + 104 * q^99

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