LMFDB - Embedded newform 845.2.n.e.484.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(484,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("845.484");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not 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:	$6.74735897080$
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:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			484.2
Root			$-1.02826 - 0.593667i$ of defining polynomial
Character	$\chi$	$=$	845.484
Dual form			845.2.n.e.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02826 + 0.593667i) q^{2} +(-0.298874 + 0.172555i) q^{3} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 + 1.71029i) q^{5} +(0.204880 - 0.354863i) q^{6} +(1.75765 + 1.01478i) q^{7} -3.07548i q^{8} +(-1.44045 + 2.49493i) q^{9} +O(q^{10})$	\(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} -2.40976 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} -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} +(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} -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} +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} -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} +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} + 18 q^{29} + 4 q^{30} + 16 q^{31} - 16 q^{34} + 10 q^{35} - 2 q^{36} + 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} + 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} + 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 + 18 * q^29 + 4 * q^30 + 16 * q^31 - 16 * q^34 + 10 * q^35 - 2 * q^36 + 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 + 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 + 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.02826	+	0.593667i	−0.727090	+	0.419786i	−0.817357	−	0.576132i	$-0.804561\pi$
$2$	−1.02826	+	0.593667i	−0.727090	+	0.419786i	0.0902665	+	0.995918i	$0.471228\pi$
$3$	−0.298874	+	0.172555i	−0.172555	+	0.0996247i	−0.583790	−	0.811905i	$-0.698431\pi$
$3$	−0.298874	+	0.172555i	−0.172555	+	0.0996247i	0.411235	+	0.911529i	$0.365098\pi$
$4$	−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	$-0.208035\pi$
$7$	1.75765	+	1.01478i	0.664328	+	0.383550i	−0.129596	+	0.991567i	$0.541368\pi$
$8$		−	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	0.994867	+	0.101191i	$0.0322653\pi$
$11$	1.94045	+	3.36096i	0.585068	+	1.01337i	−0.409799	+	0.912176i	$0.634401\pi$
$12$		−	0.203698i		−	0.0588024i
$13$		0			0
$13$		0			0
$14$	−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	0.947605	−	0.319445i	$-0.103497\pi$
$17$	4.71996	+	2.72507i	1.14476	+	0.660927i	0.197155	+	0.980372i	$0.436830\pi$
$18$		−	3.42059i		−	0.806240i
$19$	−2.94045	+	5.09301i	−0.674585	+	1.16842i	0.302005	+	0.953306i	$0.402344\pi$
$19$	−2.94045	+	5.09301i	−0.674585	+	1.16842i	−0.976590	+	0.215110i	$0.930989\pi$
$20$	−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	−0.468516	−	0.883455i	$-0.655211\pi$
$23$	0.298874	−	0.172555i	0.0623195	−	0.0359802i	0.530836	+	0.847475i	$0.321878\pi$
$24$	0.530689	+	0.919180i	0.108326	+	0.187627i
$25$	−0.850210	−	4.92718i	−0.170042	−	0.985437i
$26$		0			0
$27$		−	2.02956i		−	0.390588i
$28$	−1.03743	+	0.598962i	−0.196056	+	0.113193i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	0.311800	+	0.861568i	0.0569267	+	0.157300i
$31$	−1.18048			−0.212020			−0.106010	−	0.994365i	$-0.533808\pi$
$31$	−1.18048			−0.212020			−0.106010	+	0.994365i	$0.533808\pi$
$32$	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	$-0.814530\pi$
$37$	−4.71996	+	2.72507i	−0.775957	+	0.447999i	0.0590384	+	0.998256i	$0.481197\pi$
$38$		−	6.98259i		−	1.13273i
$39$		0			0
$40$	5.25997	+	4.43007i	0.831674	+	0.700456i
$41$	0.0902394	+	0.156299i	0.0140930	+	0.0244098i	0.872986	−	0.487745i	$-0.162181\pi$
$41$	0.0902394	+	0.156299i	0.0140930	+	0.0244098i	−0.858893	+	0.512155i	$0.828847\pi$
$42$	0.720215	−	0.415816i	0.111132	−	0.0641618i
$43$	−1.15990	−	0.669668i	−0.176883	−	0.102123i	0.408944	−	0.912559i	$-0.365897\pi$
$43$	−1.15990	−	0.669668i	−0.176883	−	0.102123i	−0.585827	+	0.810436i	$0.699230\pi$
$44$	−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			0
$53$		−	2.42636i		−	0.333286i	−0.986017	−	0.166643i	$-0.946707\pi$
$53$		−	2.42636i		−	0.333286i	0.986017	−	0.166643i	$-0.0532928\pi$
$54$	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	$-0.681306\pi$
$59$	3.53069	−	6.11533i	0.459657	−	0.796149i	0.998943	+	0.0459741i	$0.0146392\pi$
$60$	0.348383	+	0.293416i	0.0449760	+	0.0378798i
$61$	−3.38090	+	5.85589i	−0.432880	+	0.749770i	−0.997120	−	0.0758409i	$-0.975836\pi$
$61$	−3.38090	+	5.85589i	−0.432880	+	0.749770i	0.564240	+	0.825611i	$0.309169\pi$
$62$	1.21384	−	0.700811i	0.154158	−	0.0890031i
$63$	−5.06361	+	2.92347i	−0.637954	+	0.368323i
$64$	−8.76180			−1.09522
$65$		0			0
$66$	1.59024			0.195745
$67$	3.81417	−	2.20211i	0.465975	−	0.269031i	−0.248578	−	0.968612i	$-0.579963\pi$
$67$	3.81417	−	2.20211i	0.465975	−	0.269031i	0.714553	+	0.699581i	$0.246630\pi$
$68$	−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	$-0.868934\pi$
$71$	−0.940450	+	1.62891i	−0.111611	+	0.193316i	0.804809	+	0.593534i	$0.202268\pi$
$72$	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			0
$79$	−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	−0.983406	−	0.181420i	$-0.941931\pi$
$89$	−6.12093	−	10.6018i	−0.648817	−	1.12378i	0.334589	−	0.942364i	$-0.391403\pi$
$90$	5.85021	+	4.92718i	0.616666	+	0.519371i
$91$		0			0
$92$			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	$-0.428569\pi$
$97$	−5.02801	−	2.90292i	−0.510517	−	0.294747i	−0.733046	+	0.680179i	$0.761902\pi$
$98$	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	0.975133	−	0.221619i	$-0.0711340\pi$
$101$	2.97114	+	5.14616i	0.295639	+	0.512062i	−0.679494	+	0.733681i	$0.737801\pi$
$102$	1.93405	−	1.11663i	0.191500	−	0.110563i
$103$			6.43378i			0.633939i	0.948436	+	0.316970i	$0.102665\pi$
$103$			6.43378i			0.633939i	−0.948436	+	0.316970i	$0.897335\pi$
$104$		0			0
$105$	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	0.480387	−	0.877057i	$-0.340496\pi$
$107$	15.3106	−	8.83959i	1.48013	−	0.854555i	0.999747	+	0.0225015i	$0.00716305\pi$
$108$	1.03743	+	0.598962i	0.0998270	+	0.0576352i
$109$	5.76180			0.551880			0.275940	−	0.961175i	$-0.411011\pi$
$109$	5.76180			0.551880			0.275940	+	0.961175i	$0.411011\pi$
$110$	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	0.293415	−	0.955985i	$-0.405208\pi$
$113$	−4.12222	−	2.37996i	−0.387785	−	0.223888i	−0.681200	+	0.732097i	$0.738542\pi$
$114$	1.20488	+	2.08691i	0.112847	+	0.195457i
$115$	−0.135393	+	0.759719i	−0.0126255	+	0.0708442i
$116$	−1.77072			−0.164407
$117$		0			0
$118$			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	−0.977545	−	0.210728i	$-0.932417\pi$
$127$	−14.4679	+	8.35307i	−1.28382	+	0.741215i	−0.306277	+	0.951942i	$0.599083\pi$
$128$	3.43760	−	1.98470i	0.303844	−	0.175424i
$129$	0.462218			0.0406961
$130$		0			0
$131$	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	$-0.306407\pi$
$137$	1.71288	+	0.988931i	0.146341	+	0.0844901i	−0.425042	+	0.905174i	$0.639741\pi$
$138$		−	0.141412i		−	0.0120378i
$139$	4.35021	−	7.53478i	0.368980	−	0.639092i	−0.620426	−	0.784265i	$-0.713040\pi$
$139$	4.35021	−	7.53478i	0.368980	−	0.639092i	0.989406	+	0.145173i	$0.0463737\pi$
$140$	0.469969	−	2.63709i	0.0397196	−	0.222875i
$141$	2.11910	+	3.67039i	0.178460	+	0.309103i
$142$		−	2.23325i		−	0.187411i
$143$		0			0
$144$	−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	−0.104603	+	0.994514i	$0.533357\pi$
$149$	−11.1516	+	19.3152i	−0.913576	+	1.58236i	−0.808973	+	0.587846i	$0.799976\pi$
$150$	−1.92267	−	0.707775i	−0.156985	−	0.0577896i
$151$	19.1626			1.55943			0.779717	−	0.626132i	$-0.215363\pi$
$151$	19.1626			1.55943			0.779717	+	0.626132i	$0.215363\pi$
$152$	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			0
$157$		−	6.20265i		−	0.495025i	−0.968885	−	0.247513i	$-0.920387\pi$
$157$		−	6.20265i		−	0.495025i	0.968885	−	0.247513i	$-0.0796132\pi$
$158$	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	$-0.488155\pi$
$163$	−10.3365	−	5.96781i	−0.809621	−	0.467435i	−0.846824	+	0.531873i	$0.821488\pi$
$164$	−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	$-0.641645\pi$
$167$	1.75765	−	1.01478i	0.136011	−	0.0785259i	0.566461	+	0.824088i	$0.308312\pi$
$168$			2.15413i			0.166195i
$169$		0			0
$170$	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	0.543444	−	0.839445i	$-0.317120\pi$
$173$	1.15990	+	0.669668i	0.0881855	+	0.0509139i	−0.455259	+	0.890359i	$0.650453\pi$
$174$	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	0.944972	+	0.327151i	$0.106089\pi$
$179$	10.1120	+	17.5145i	0.755807	+	1.30910i	−0.189165	+	0.981945i	$0.560578\pi$
$180$	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	$0.236372\pi$
$182$		0			0
$183$		−	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	−0.892502	−	0.451044i	$-0.851052\pi$
$191$	−0.768891	+	1.33176i	−0.0556350	+	0.0963626i	0.836867	+	0.547407i	$0.184385\pi$
$192$	2.61867	−	1.51189i	0.188986	−	0.109111i
$193$	18.3625	−	10.6016i	1.32176	−	0.763118i	0.337750	−	0.941236i	$-0.390334\pi$
$193$	18.3625	−	10.6016i	1.32176	−	0.763118i	0.984009	+	0.178117i	$0.0570007\pi$
$194$	6.89347			0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$	8.01675	−	4.62847i	0.571170	−	0.329765i	−0.186447	−	0.982465i	$-0.559697\pi$
$197$	8.01675	−	4.62847i	0.571170	−	0.329765i	0.757616	+	0.652700i	$0.226364\pi$
$198$	11.4964	−	6.63748i	0.817017	−	0.471705i
$199$	−8.70225	+	15.0727i	−0.616886	+	1.06848i	0.373164	+	0.927765i	$0.378273\pi$
$199$	−8.70225	+	15.0727i	−0.616886	+	1.06848i	−0.990050	+	0.140713i	$0.955061\pi$
$200$	−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
$208$		0			0
$209$	−22.8232			−1.57871
$210$	−0.326265	+	1.83074i	−0.0225144	+	0.126333i
$211$	3.64087	+	6.30617i	0.250648	+	0.434135i	0.963704	−	0.266972i	$-0.0860231\pi$
$211$	3.64087	+	6.30617i	0.250648	+	0.434135i	−0.713057	+	0.701107i	$0.752690\pi$
$212$	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
$221$		0			0
$222$			2.23325i			0.149886i
$223$	−16.8589	+	9.73351i	−1.12896	+	0.651804i	−0.943672	−	0.330881i	$-0.892654\pi$
$223$	−16.8589	+	9.73351i	−1.12896	+	0.651804i	−0.185285	+	0.982685i	$0.559321\pi$
$224$	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	$-0.282287\pi$
$227$	4.16698	+	2.40581i	0.276572	+	0.159679i	−0.355298	+	0.934753i	$0.615621\pi$
$228$	1.03743	+	0.598962i	0.0687057	+	0.0396672i
$229$	1.52360			0.100682			0.0503410	−	0.998732i	$-0.483969\pi$
$229$	1.52360			0.100682			0.0503410	+	0.998732i	$0.483969\pi$
$230$	−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	$0.151235\pi$
$233$			13.9652i			0.914889i	−0.889238	+	0.457445i	$0.848765\pi$
$234$		0			0
$235$	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	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	1.79314	−	0.648935i	0.115747	−	0.0418886i
$241$	−8.73294	+	15.1259i	−0.562538	+	0.974344i	0.434736	+	0.900558i	$0.356842\pi$
$241$	−8.73294	+	15.1259i	−0.562538	+	0.974344i	−0.997274	+	0.0737864i	$0.976492\pi$
$242$		−	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
$247$		0			0
$248$			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	−0.974633	−	0.223809i	$-0.928151\pi$
$251$	−4.64979	+	8.05367i	−0.293492	+	0.508343i	0.681141	+	0.732152i	$0.261484\pi$
$252$		−	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	−0.176141	−	0.984365i	$-0.556361\pi$
$257$	9.43076	−	5.44485i	0.588274	−	0.339640i	0.764415	+	0.644725i	$0.223028\pi$
$258$	−0.475281	+	0.274404i	−0.0295897	+	0.0170836i
$259$	−11.0614			−0.687321
$260$		0			0
$261$	−8.64270			−0.534970
$262$	−10.2826	+	5.93667i	−0.635262	+	0.366769i
$263$	11.6399	−	6.72031i	0.717749	−	0.414392i	−0.0961749	−	0.995364i	$-0.530661\pi$
$263$	11.6399	−	6.72031i	0.717749	−	0.414392i	0.813923	+	0.580972i	$0.197327\pi$
$264$	−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	−0.804819	−	0.593520i	$-0.797738\pi$
$269$	1.83027	−	3.17012i	0.111593	−	0.193286i	0.916413	+	0.400234i	$0.131071\pi$
$270$	−5.30481	−	0.945395i	−0.322840	−	0.0575349i
$271$	11.0018	+	19.0557i	0.668313	+	1.15755i	0.978376	+	0.206837i	$0.0663168\pi$
$271$	11.0018	+	19.0557i	0.668313	+	1.15755i	−0.310062	+	0.950716i	$0.600350\pi$
$272$			13.4681i			0.816621i
$273$		0			0
$274$	−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	0.219943	−	0.975513i	$-0.429413\pi$
$277$	−8.56973	−	4.94774i	−0.514905	−	0.297281i	−0.734848	+	0.678232i	$0.762746\pi$
$278$			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	$-0.538655\pi$
$281$	−4.06138			−0.242281			−0.121141	+	0.992635i	$0.538655\pi$
$282$	−4.35798	−	2.51608i	−0.259514	−	0.149830i
$283$	5.27294	−	3.04434i	0.313444	−	0.180967i	−0.335023	−	0.942210i	$-0.608744\pi$
$283$	5.27294	−	3.04434i	0.313444	−	0.180967i	0.648467	+	0.761243i	$0.275411\pi$
$284$	−0.555090	−	0.961445i	−0.0329386	−	0.0570513i
$285$	3.47114	+	2.92347i	0.205613	+	0.173172i
$286$		0			0
$287$			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	$-0.240998\pi$
$293$	8.48019	+	4.89604i	0.495418	+	0.286030i	−0.231401	+	0.972858i	$0.574331\pi$
$294$	−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			0
$300$	−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	$0.430508\pi$
$312$		0			0
$313$		−	26.1425i		−	1.47766i	−0.673891	−	0.738831i	$-0.735378\pi$
$313$		−	26.1425i		−	1.47766i	0.673891	−	0.738831i	$-0.264622\pi$
$314$	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
$325$		0			0
$326$	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	$-0.946825\pi$
$331$	−6.35021	+	10.9989i	−0.349039	+	0.604553i	0.637040	+	0.770831i	$0.280159\pi$
$332$	−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	$-0.863237\pi$
$337$		−	15.2939i		−	0.833113i	0.909110	−	0.416556i	$-0.136763\pi$
$338$		0			0
$339$	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	0.187733	−	0.982220i	$-0.439886\pi$
$347$	−10.5998	−	6.11981i	−0.569029	−	0.328529i	−0.756761	+	0.653691i	$0.773219\pi$
$348$	0.529222	−	0.305546i	0.0283693	−	0.0163790i
$349$	−9.35021	−	16.1950i	−0.500505	−	0.866901i	−1.00000		0.000583538i	$-0.999814\pi$
$349$	−9.35021	−	16.1950i	−0.500505	−	0.866901i	0.499495	−	0.866317i	$-0.333519\pi$
$350$	2.04880	+	11.8733i	0.109513	+	0.634656i
$351$		0			0
$352$			12.4844i			0.665422i
$353$	1.13348	−	0.654413i	0.0603288	−	0.0348309i	−0.469532	−	0.882915i	$-0.655577\pi$
$353$	1.13348	−	0.654413i	0.0603288	−	0.0348309i	0.529861	+	0.848084i	$0.322244\pi$
$354$	−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	$-0.782780\pi$
$359$	−29.4082			−1.55210			−0.776051	+	0.630670i	$0.782780\pi$
$360$	−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
$364$		0			0
$365$	−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	−0.511429	+	0.859326i	$0.670884\pi$
$367$	−28.9531	+	16.7161i	−1.51134	+	0.872573i	−0.999912	+	0.0132473i	$0.995783\pi$
$368$	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	−0.998438	−	0.0558628i	$-0.982209\pi$
$373$	−29.8589	−	17.2391i	−1.54604	−	0.892604i	−0.547598	−	0.836742i	$-0.684458\pi$
$374$	−12.5569	−	21.7492i	−0.649303	−	1.12463i
$375$	−3.85839	−	0.0211863i	−0.199246	−	0.00109406i
$376$	−37.7691			−1.94779
$377$		0			0
$378$			4.89075i			0.251553i
$379$	8.70225	+	15.0727i	0.447004	+	0.774234i	0.998189	−	0.0601487i	$-0.0191575\pi$
$379$	8.70225	+	15.0727i	0.447004	+	0.774234i	−0.551185	+	0.834383i	$0.685824\pi$
$380$	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	$-0.347543\pi$
$383$	−1.51271	−	0.873366i	−0.0772961	−	0.0446269i	−0.538150	+	0.842849i	$0.680877\pi$
$384$	−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	$0.688748\pi$
$390$		0			0
$391$	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	$-0.524620\pi$
$397$	−19.5132	−	11.2660i	−0.979339	−	0.565422i	−0.902071	+	0.431588i	$0.857953\pi$
$398$		−	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	$-0.196148\pi$
$401$	−1.85204	−	3.20782i	−0.0924863	−	0.160191i	−0.908557	+	0.417761i	$0.862815\pi$
$402$		−	1.80468i		−	0.0900091i
$403$		0			0
$404$	−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	$-0.725150\pi$
$409$	6.74186	−	11.6772i	0.333363	−	0.577402i	0.983169	+	0.182698i	$0.0584831\pi$
$410$	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
$416$		0			0
$417$			3.00260i			0.147038i
$418$	23.4682	−	13.5494i	1.14787	−	0.662721i
$419$	8.41159	+	14.5693i	0.410933	+	0.711757i	0.994992	−	0.0999544i	$-0.0318697\pi$
$419$	8.41159	+	14.5693i	0.410933	+	0.711757i	−0.584059	+	0.811711i	$0.698536\pi$
$420$	0.314582	+	0.869253i	0.0153500	+	0.0424152i
$421$	−17.1013			−0.833464			−0.416732	−	0.909029i	$-0.636825\pi$
$421$	−17.1013			−0.833464			−0.416732	+	0.909029i	$0.636825\pi$
$422$	−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
$429$		0			0
$430$	−2.29066	+	2.71978i	−0.110465	+	0.131159i
$431$	4.83027	+	8.36627i	0.232666	+	0.402989i	0.958592	−	0.284784i	$-0.0919218\pi$
$431$	4.83027	+	8.36627i	0.232666	+	0.402989i	−0.725926	+	0.687773i	$0.758588\pi$
$432$	4.34339	−	2.50766i	0.208972	−	0.120650i
$433$	21.4538	+	12.3863i	1.03100	+	0.595249i	0.917272	−	0.398262i	$-0.130387\pi$
$433$	21.4538	+	12.3863i	1.03100	+	0.595249i	0.113730	+	0.993512i	$0.463720\pi$
$434$	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	0.937896	−	0.346915i	$-0.112771\pi$
$439$	3.53069	+	6.11533i	0.168511	+	0.291869i	−0.769386	+	0.638784i	$0.779438\pi$
$440$	−4.68257	+	26.2749i	−0.223233	+	1.25261i
$441$	8.29958			0.395218
$442$		0			0
$443$			38.2438i			1.81702i	0.417865	+	0.908509i	$0.362778\pi$
$443$			38.2438i			1.81702i	−0.417865	+	0.908509i	$0.637222\pi$
$444$	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	$-0.738185\pi$
$449$	6.24003	−	10.8080i	0.294485	−	0.510063i	0.974865	+	0.222796i	$0.0715185\pi$
$450$	−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
$455$		0			0
$456$	−6.24186			−0.292302
$457$	−7.12930	+	4.11610i	−0.333495	+	0.192543i	−0.657392	−	0.753549i	$-0.728340\pi$
$457$	−7.12930	+	4.11610i	−0.333495	+	0.192543i	0.323897	+	0.946092i	$0.395007\pi$
$458$	−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	$-0.867060\pi$
$461$	−2.27072	+	3.93300i	−0.105758	+	0.183178i	0.808290	+	0.588785i	$0.200394\pi$
$462$	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	$-0.725688\pi$
$467$		−	32.8043i		−	1.51800i	0.651091	−	0.759000i	$-0.274312\pi$
$468$		0			0
$469$	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	0.967135	+	0.254263i	$0.0818329\pi$
$479$	15.4027	+	26.6782i	0.703766	+	1.21896i	−0.263369	+	0.964695i	$0.584834\pi$
$480$	1.59916	−	1.89874i	0.0729913	−	0.0866650i
$481$		0			0
$482$		−	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	$-0.502145\pi$
$487$	−19.3341	−	11.1626i	−0.876113	−	0.505824i	−0.869375	+	0.494153i	$0.835478\pi$
$488$	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	0.719964	−	0.694011i	$-0.244158\pi$
$491$	−5.34129	−	9.25139i	−0.241049	−	0.417509i	−0.961013	+	0.276502i	$0.910825\pi$
$492$	0.0318378	−	0.0183815i	0.00143536	−	0.000828704i
$493$			16.3504i			0.736386i
$494$		0			0
$495$	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	$-0.361595\pi$
$499$	18.8195			0.842477			0.421239	+	0.906950i	$0.361595\pi$
$500$	−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	0.386284	−	0.922380i	$-0.373758\pi$
$503$	−4.92013	−	2.84064i	−0.219378	−	0.126658i	−0.605662	+	0.795722i	$0.707092\pi$
$504$	8.99108	+	15.5730i	0.400495	+	0.693677i
$505$	−13.0812	−	2.33127i	−0.582107	−	0.103740i
$506$	−1.59024			−0.0706948
$507$		0			0
$508$		−	9.86062i		−	0.437494i
$509$	−13.9622	−	24.1833i	−0.618864	−	1.07190i	−0.989693	−	0.143203i	$-0.954260\pi$
$509$	−13.9622	−	24.1833i	−0.618864	−	1.07190i	0.370829	−	0.928701i	$-0.379074\pi$
$510$	−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
$520$		0			0
$521$	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	−0.865873	−	0.500265i	$-0.833236\pi$
$523$	−19.7948	+	11.4285i	−0.865567	+	0.499735i	0.000305526		1.00000i	$0.499903\pi$
$524$	−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			0
$534$	−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	$-0.434674\pi$
$541$	9.48006			0.407580			0.203790	+	0.979015i	$0.434674\pi$
$542$	−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
$546$		0			0
$547$			33.3911i			1.42770i	0.700299	+	0.713850i	$0.253050\pi$
$547$			33.3911i			1.42770i	−0.700299	+	0.713850i	$0.746950\pi$
$548$	−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	$-0.371461\pi$
$557$	32.7053	−	18.8824i	1.38577	−	0.800073i	0.992835	+	0.119495i	$0.0381274\pi$
$558$			4.03793i			0.170939i
$559$		0			0
$560$	−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	0.891631	−	0.452762i	$-0.149561\pi$
$563$	22.4307	+	12.9504i	0.945343	+	0.545794i	0.0537120	+	0.998556i	$0.482895\pi$
$564$	−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	0.546878	−	0.837213i	$-0.315816\pi$
$569$	−10.7725	−	18.6586i	−0.451609	−	0.782209i	−0.998486	+	0.0550035i	$0.982483\pi$
$570$	−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	$0.514794\pi$
$572$		0			0
$573$		−	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
$585$		0			0
$586$	−11.6265			−0.480285
$587$	−1.58391	+	0.914469i	−0.0653748	+	0.0377442i	−0.532331	−	0.846536i	$-0.678684\pi$
$587$	−1.58391	+	0.914469i	−0.0653748	+	0.0377442i	0.466956	+	0.884280i	$0.345351\pi$
$588$	−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			0
$599$	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	0.819944	+	0.572444i	$0.194005\pi$
$601$	22.2041	+	38.4586i	0.905723	+	1.56876i	0.0857795	+	0.996314i	$0.472662\pi$
$602$	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	0.975684	−	0.219183i	$-0.0703392\pi$
$607$	31.3808	+	18.1177i	1.27371	+	0.735375i	0.298024	+	0.954558i	$0.403672\pi$
$608$	−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
$611$		0			0
$612$		−	9.26754i		−	0.374618i
$613$	−2.90838	+	1.67915i	−0.117468	+	0.0678203i	−0.557583	−	0.830121i	$-0.688271\pi$
$613$	−2.90838	+	1.67915i	−0.117468	+	0.0678203i	0.440115	+	0.897942i	$0.354938\pi$
$614$	−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	$-0.193123\pi$
$617$	18.3441	+	10.5910i	0.738507	+	0.426377i	−0.0830194	+	0.996548i	$0.526456\pi$
$618$	2.28311	+	1.31815i	0.0918402	+	0.0530240i
$619$	25.4082			1.02124			0.510620	−	0.859807i	$-0.329416\pi$
$619$	25.4082			1.02124			0.510620	+	0.859807i	$0.329416\pi$
$620$	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
$624$		0			0
$625$	−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	0.00145375	−	0.999999i	$-0.499537\pi$
$631$	21.7725	−	37.7112i	0.866751	−	1.50126i	0.865298	−	0.501258i	$-0.167129\pi$
$632$			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
$637$		0			0
$638$		−	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	−0.215993	+	0.976395i	$0.569299\pi$
$641$	−24.1427	+	41.8164i	−0.953579	+	1.65165i	−0.737586	+	0.675253i	$0.764035\pi$
$642$		−	7.24423i		−	0.285907i
$643$	36.6710	+	21.1720i	1.44616	+	0.834943i	0.998250	−	0.0591344i	$-0.0188341\pi$
$643$	36.6710	+	21.1720i	1.44616	+	0.834943i	0.447913	+	0.894077i	$0.352167\pi$
$644$	−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	−0.954008	−	0.299781i	$-0.903086\pi$
$647$	−29.7958	+	17.2026i	−1.17139	+	0.676305i	−0.217386	+	0.976086i	$0.569753\pi$
$648$	−21.1538	+	12.2131i	−0.830999	+	0.479778i
$649$	27.4045			1.07572
$650$		0			0
$651$	0.826831			0.0324061
$652$	6.10104	−	3.52244i	0.238935	−	0.137949i
$653$	12.4114	−	7.16573i	0.485696	−	0.280417i	−0.237091	−	0.971487i	$-0.576194\pi$
$653$	12.4114	−	7.16573i	0.485696	−	0.280417i	0.722787	+	0.691071i	$0.242861\pi$
$654$	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	−0.553487	−	0.832858i	$-0.686703\pi$
$659$	11.4116	−	19.7655i	0.444532	−	0.769953i	0.998020	+	0.0629051i	$0.0200365\pi$
$660$	−0.310140	+	1.74026i	−0.0120722	+	0.0677394i
$661$	7.20934	+	12.4869i	0.280411	+	0.485686i	0.971486	−	0.237097i	$-0.0761960\pi$
$661$	7.20934	+	12.4869i	0.280411	+	0.485686i	−0.691075	+	0.722783i	$0.742863\pi$
$662$		−	15.0796i		−	0.586087i
$663$		0			0
$664$	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	0.194193	−	0.980963i	$-0.437791\pi$
$673$	29.5956	−	17.0871i	1.14083	−	0.658657i	0.946636	+	0.322306i	$0.104458\pi$
$674$	9.07949	+	15.7261i	0.349729	+	0.605748i
$675$	−10.0000	+	1.72555i	−0.384900	+	0.0664164i
$676$		0			0
$677$			5.84695i			0.224716i	0.993668	+	0.112358i	$0.0358404\pi$
$677$			5.84695i			0.224716i	−0.993668	+	0.112358i	$0.964160\pi$
$678$	−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	$-0.263666\pi$
$683$	9.82834	+	5.67439i	0.376071	+	0.217125i	−0.300036	+	0.953928i	$0.596999\pi$
$684$	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
$689$		0			0
$690$	0.241857	+	0.203698i	0.00920733	+	0.00775463i
$691$	−9.41159	−	16.3013i	−0.358034	−	0.620133i	0.629599	−	0.776921i	$-0.283219\pi$
$691$	−9.41159	−	16.3013i	−0.358034	−	0.620133i	−0.987632	+	0.156788i	$0.949886\pi$
$692$	−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	$0.382135\pi$
$702$		0			0
$703$		−	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	$-0.978700\pi$
$709$	−11.7419	+	20.3375i	−0.440975	+	0.763791i	0.556787	+	0.830655i	$0.312034\pi$
$710$	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
$715$		0			0
$716$	−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	−0.967059	−	0.254553i	$-0.918072\pi$
$719$	−7.05429	+	12.2184i	−0.263080	+	0.455669i	0.703978	+	0.710221i	$0.251405\pi$
$720$	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	$0.155954\pi$
$727$			25.3762i			0.941153i	−0.882359	+	0.470576i	$0.844046\pi$
$728$		0			0
$729$	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	$-0.158381\pi$
$739$	0.707513	+	1.22545i	0.0260263	+	0.0450788i	−0.852719	+	0.522370i	$0.825048\pi$
$740$	5.50183	+	4.63377i	0.202251	+	0.170341i
$741$		0			0
$742$			5.84695i			0.214648i
$743$	−25.8748	+	14.9389i	−0.949256	+	0.548053i	−0.892850	−	0.450355i	$-0.851298\pi$
$743$	−25.8748	+	14.9389i	−0.949256	+	0.548053i	−0.0564064	+	0.998408i	$0.517964\pi$
$744$	−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	0.988719	−	0.149780i	$-0.0478565\pi$
$751$	9.99291	+	17.3082i	0.364646	+	0.631586i	−0.624073	+	0.781366i	$0.714523\pi$
$752$	26.2816	−	15.1737i	0.958391	−	0.553328i
$753$		−	3.20938i		−	0.116956i
$754$		0			0
$755$	−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	−0.744269	−	0.667880i	$-0.767202\pi$
$757$	−14.8024	+	8.54617i	−0.538003	+	0.310616i	0.206266	+	0.978496i	$0.433869\pi$
$758$	−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	0.174773	+	0.984609i	$0.444081\pi$
$761$	−21.1120	+	36.5671i	−0.765310	+	1.32556i	−0.940083	+	0.340947i	$0.889252\pi$
$762$			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
$767$		0			0
$768$			4.42107i			0.159531i
$769$	11.8827	+	20.5815i	0.428502	+	0.742187i	0.996740	−	0.0806767i	$-0.0257081\pi$
$769$	11.8827	+	20.5815i	0.428502	+	0.742187i	−0.568238	+	0.822864i	$0.692375\pi$
$770$	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	$-0.331707\pi$
$773$	0.246026	+	0.142043i	0.00884894	+	0.00510894i	−0.495569	+	0.868569i	$0.665040\pi$
$774$	−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
$780$		0			0
$781$	−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	$-0.191796\pi$
$787$	20.9008	+	12.0671i	0.745032	+	0.430145i	−0.0788638	+	0.996885i	$0.525129\pi$
$788$			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
$793$		0			0
$794$	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	0.923641	−	0.383259i	$-0.125198\pi$
$797$	29.7430	+	17.1721i	1.05355	+	0.608267i	0.129909	+	0.991526i	$0.458532\pi$
$798$			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
$806$		0			0
$807$			1.26329i			0.0444698i
$808$	15.8269	−	9.13767i	0.556789	−	0.321462i
$809$	−23.8431	−	41.2975i	−0.838279	−	1.45194i	−0.891332	−	0.453351i	$-0.850229\pi$
$809$	−23.8431	−	41.2975i	−0.838279	−	1.45194i	0.0530528	−	0.998592i	$-0.483105\pi$
$810$	−19.8279	+	7.17570i	−0.696682	+	0.252128i
$811$	−24.5992			−0.863793			−0.431897	−	0.901923i	$-0.642155\pi$
$811$	−24.5992			−0.863793			−0.431897	+	0.901923i	$0.642155\pi$
$812$	−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
$819$		0			0
$820$	0.153445	−	0.182190i	0.00535853	−	0.00636236i
$821$	8.64979	+	14.9819i	0.301880	+	0.522871i	0.976562	−	0.215237i	$-0.0690526\pi$
$821$	8.64979	+	14.9819i	0.301880	+	0.522871i	−0.674682	+	0.738109i	$0.735719\pi$
$822$	0.701870	−	0.405225i	0.0244805	−	0.0141338i
$823$	−28.2000	−	16.2813i	−0.982990	−	0.567529i	−0.0798182	−	0.996809i	$-0.525434\pi$
$823$	−28.2000	−	16.2813i	−0.982990	−	0.567529i	−0.903171	+	0.429280i	$0.858767\pi$
$824$	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	0.711922	−	0.702258i	$-0.247825\pi$
$829$	−7.26180	−	12.5778i	−0.252213	−	0.436845i	−0.964135	+	0.265413i	$0.914492\pi$
$830$	20.4800	+	3.64984i	0.710870	+	0.126688i
$831$	3.41503			0.118466
$832$		0			0
$833$		−	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	$-0.837816\pi$
$839$	−0.407933	+	0.706561i	−0.0140834	+	0.0243932i	0.858898	+	0.512147i	$0.171150\pi$
$840$	−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
$845$		0			0
$846$	−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	$0.245329\pi$
$857$			40.7886i			1.39331i	−0.717406	+	0.696656i	$0.754671\pi$
$858$		0			0
$859$	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
$871$		0			0
$872$		−	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	$-0.0451258\pi$
$877$	40.3520	+	23.2972i	1.36259	+	0.786691i	0.372621	+	0.927984i	$0.378459\pi$
$878$	−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	0.592254	−	0.805751i	$-0.298238\pi$
$881$	−11.9223	−	20.6501i	−0.401674	−	0.695719i	−0.993928	+	0.110032i	$0.964905\pi$
$882$	−8.53413	+	4.92718i	−0.287359	+	0.165907i
$883$			37.2496i			1.25355i	0.779201	+	0.626774i	$0.215625\pi$
$883$			37.2496i			1.25355i	−0.779201	+	0.626774i	$0.784375\pi$
$884$		0			0
$885$	−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	−0.0231673	−	0.999732i	$-0.507375\pi$
$887$	24.7505	−	14.2897i	0.831042	−	0.479802i	0.854209	+	0.519929i	$0.174042\pi$
$888$	−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			0
$898$			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	−0.404939	−	0.914344i	$-0.632707\pi$
$907$	5.55457	−	3.20693i	0.184436	−	0.106484i	0.589375	+	0.807859i	$0.299374\pi$
$908$	−2.45952	+	1.42000i	−0.0816220	+	0.0471245i
$909$	−17.1191			−0.567805
$910$		0			0
$911$	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	−0.566037	−	0.824380i	$-0.691524\pi$
$919$	13.0632	−	22.6261i	0.430915	−	0.746367i	0.996952	+	0.0780125i	$0.0248574\pi$
$920$	2.33650	+	0.416399i	0.0770321	+	0.0137283i
$921$	−3.81426	−	6.60649i	−0.125684	−	0.217691i
$922$		−	5.39220i		−	0.177583i
$923$		0			0
$924$	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	$-0.704854\pi$
$929$	11.9711	−	20.7346i	0.392760	−	0.680281i	0.992813	+	0.119680i	$0.0381869\pi$
$930$	−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
$936$		0			0
$937$		−	18.5046i		−	0.604518i	−0.953226	−	0.302259i	$-0.902259\pi$
$937$		−	18.5046i		−	0.604518i	0.953226	−	0.302259i	$-0.0977407\pi$
$938$	−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	$-0.424698\pi$
$941$	14.3788			0.468735			0.234368	+	0.972148i	$0.424698\pi$
$942$	−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	−0.660807	+	0.750555i	$0.729786\pi$
$947$	−50.5056	+	29.1594i	−1.64121	+	0.947554i	−0.980404	+	0.196998i	$0.936881\pi$
$948$			2.27744i			0.0739677i
$949$		0			0
$950$	−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	0.293791	−	0.955870i	$-0.405083\pi$
$953$	−11.9507	−	6.89975i	−0.387122	−	0.223505i	−0.680912	+	0.732365i	$0.738417\pi$
$954$	−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
$962$		0			0
$963$			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	0.258092	+	0.966120i	$0.416906\pi$
$971$	−22.0506	+	38.1928i	−0.707638	+	1.22567i	−0.965731	+	0.259545i	$0.916427\pi$
$972$	−4.51337	+	2.60580i	−0.144767	+	0.0835810i
$973$	15.2923	−	8.82900i	0.490248	−	0.283045i
$974$	26.5074			0.849351
$975$		0			0
$976$	−16.7093			−0.534853
$977$	19.3314	−	11.1610i	0.618466	−	0.357071i	−0.157806	−	0.987470i	$-0.550442\pi$
$977$	19.3314	−	11.1610i	0.618466	−	0.357071i	0.776271	+	0.630399i	$0.217109\pi$
$978$	−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
$988$		0			0
$989$	−0.462218			−0.0146977
$990$	−5.20802	+	29.2233i	−0.165522	+	0.928776i
$991$	−14.8250	−	25.6777i	−0.470932	−	0.815678i	0.528515	−	0.848924i	$-0.322749\pi$
$991$	−14.8250	−	25.6777i	−0.470932	−	0.815678i	−0.999447	+	0.0332459i	$0.989416\pi$
$992$	−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	0.164040	−	0.986454i	$-0.447547\pi$
$997$	−19.2052	−	11.0881i	−0.608233	−	0.351164i	−0.772274	+	0.635290i	$0.780881\pi$
$998$	−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	845.2.n.e.484.2		12
5.4	even	2	inner	845.2.n.e.484.5		12
13.2	odd	12		845.2.d.d.844.3		12
13.3	even	3		845.2.b.e.339.2		6
13.4	even	6		65.2.n.a.9.2	✓	12
13.5	odd	4		845.2.l.f.699.9		24
13.6	odd	12		845.2.l.f.654.10		24
13.7	odd	12		845.2.l.f.654.4		24
13.8	odd	4		845.2.l.f.699.3		24
13.9	even	3	inner	845.2.n.e.529.5		12
13.10	even	6		845.2.b.d.339.5		6
13.11	odd	12		845.2.d.d.844.9		12
13.12	even	2		65.2.n.a.29.5	yes	12
39.17	odd	6		585.2.bs.a.334.5		12
39.38	odd	2		585.2.bs.a.289.2		12
52.43	odd	6		1040.2.dh.a.529.3		12
52.51	odd	2		1040.2.dh.a.289.4		12
65.3	odd	12		4225.2.a.bq.1.2		6
65.4	even	6		65.2.n.a.9.5	yes	12
65.9	even	6	inner	845.2.n.e.529.2		12
65.12	odd	4		325.2.e.e.276.5		12
65.17	odd	12		325.2.e.e.126.5		12
65.19	odd	12		845.2.l.f.654.3		24
65.23	odd	12		4225.2.a.br.1.5		6
65.24	odd	12		845.2.d.d.844.4		12
65.29	even	6		845.2.b.e.339.5		6
65.34	odd	4		845.2.l.f.699.10		24
65.38	odd	4		325.2.e.e.276.2		12
65.42	odd	12		4225.2.a.bq.1.5		6
65.43	odd	12		325.2.e.e.126.2		12
65.44	odd	4		845.2.l.f.699.4		24
65.49	even	6		845.2.b.d.339.2		6
65.54	odd	12		845.2.d.d.844.10		12
65.59	odd	12		845.2.l.f.654.9		24
65.62	odd	12		4225.2.a.br.1.2		6
65.64	even	2		65.2.n.a.29.2	yes	12
195.134	odd	6		585.2.bs.a.334.2		12
195.194	odd	2		585.2.bs.a.289.5		12
260.199	odd	6		1040.2.dh.a.529.4		12
260.259	odd	2		1040.2.dh.a.289.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	13.4	even	6
65.2.n.a.9.5	yes	12	65.4	even	6
65.2.n.a.29.2	yes	12	65.64	even	2
65.2.n.a.29.5	yes	12	13.12	even	2
325.2.e.e.126.2		12	65.43	odd	12
325.2.e.e.126.5		12	65.17	odd	12
325.2.e.e.276.2		12	65.38	odd	4
325.2.e.e.276.5		12	65.12	odd	4
585.2.bs.a.289.2		12	39.38	odd	2
585.2.bs.a.289.5		12	195.194	odd	2
585.2.bs.a.334.2		12	195.134	odd	6
585.2.bs.a.334.5		12	39.17	odd	6
845.2.b.d.339.2		6	65.49	even	6
845.2.b.d.339.5		6	13.10	even	6
845.2.b.e.339.2		6	13.3	even	3
845.2.b.e.339.5		6	65.29	even	6
845.2.d.d.844.3		12	13.2	odd	12
845.2.d.d.844.4		12	65.24	odd	12
845.2.d.d.844.9		12	13.11	odd	12
845.2.d.d.844.10		12	65.54	odd	12
845.2.l.f.654.3		24	65.19	odd	12
845.2.l.f.654.4		24	13.7	odd	12
845.2.l.f.654.9		24	65.59	odd	12
845.2.l.f.654.10		24	13.6	odd	12
845.2.l.f.699.3		24	13.8	odd	4
845.2.l.f.699.4		24	65.44	odd	4
845.2.l.f.699.9		24	13.5	odd	4
845.2.l.f.699.10		24	65.34	odd	4
845.2.n.e.484.2		12	1.1	even	1	trivial
845.2.n.e.484.5		12	5.4	even	2	inner
845.2.n.e.529.2		12	65.9	even	6	inner
845.2.n.e.529.5		12	13.9	even	3	inner
1040.2.dh.a.289.3		12	260.259	odd	2
1040.2.dh.a.289.4		12	52.51	odd	2
1040.2.dh.a.529.3		12	52.43	odd	6
1040.2.dh.a.529.4		12	260.199	odd	6
4225.2.a.bq.1.2		6	65.3	odd	12
4225.2.a.bq.1.5		6	65.42	odd	12
4225.2.a.br.1.2		6	65.62	odd	12
4225.2.a.br.1.5		6	65.23	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not 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} -2.40976 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} -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} +(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} -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} +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} -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} +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	\( 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} + 4 q^{15} - 16 q^{16} - 12 q^{19} + q^{20} + 8 q^{21} - 32 q^{24} - 2 q^{25} + 18 q^{29} + 4 q^{30} + 16 q^{31} - 16 q^{34} + 10 q^{35} - 2 q^{36} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 29 q^{45} - 10 q^{46} + 6 q^{49} + 31 q^{50} + 24 q^{51} + 22 q^{54} - 26 q^{55} - 16 q^{56} + 4 q^{59} + 96 q^{60} + 6 q^{61} - 12 q^{64} + 4 q^{66} - 24 q^{69} - 20 q^{70} + 12 q^{71} + 8 q^{74} + 2 q^{75} + 10 q^{76} - 104 q^{79} - 33 q^{80} + 14 q^{81} - 90 q^{84} - 21 q^{85} + 4 q^{86} - 20 q^{89} + 62 q^{90} + 56 q^{94} + 20 q^{95} - 12 q^{96} - 104 q^{99}+O(q^{100}) \) 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 + 18 * q^29 + 4 * q^30 + 16 * q^31 - 16 * q^34 + 10 * q^35 - 2 * q^36 + 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 + 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 + 56 * q^94 + 20 * q^95 - 12 * q^96 - 104 * q^99

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