LMFDB - Embedded newform 845.2.n.e.529.3

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			529.3
Root			$-0.286513 + 0.165418i$ of defining polynomial
Character	$\chi$	$=$	845.529
Dual form			845.2.n.e.484.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.286513 - 0.165418i) q^{2} +(2.33117 + 1.34590i) q^{3} +(-0.945274 - 1.63726i) q^{4} +(2.12291 + 0.702335i) q^{5} +(-0.445274 - 0.771236i) q^{6} +(2.90420 - 1.67674i) q^{7} +1.28714i q^{8} +(2.12291 + 3.67698i) q^{9} +O(q^{10})$	\(q+(-0.286513 - 0.165418i) q^{2} +(2.33117 + 1.34590i) q^{3} +(-0.945274 - 1.63726i) q^{4} +(2.12291 + 0.702335i) q^{5} +(-0.445274 - 0.771236i) q^{6} +(2.90420 - 1.67674i) q^{7} +1.28714i q^{8} +(2.12291 + 3.67698i) q^{9} +(-0.492061 - 0.552395i) q^{10} +(-1.62291 + 2.81095i) q^{11} -5.08898i q^{12} -1.10945 q^{14} +(4.00358 + 4.49448i) q^{15} +(-1.67763 + 2.90574i) q^{16} +(1.68772 - 0.974404i) q^{17} -1.40467i q^{18} +(0.622905 + 1.07890i) q^{19} +(-0.856821 - 4.13965i) q^{20} +9.02690 q^{21} +(0.929966 - 0.536916i) q^{22} +(-2.33117 - 1.34590i) q^{23} +(-1.73236 + 3.00053i) q^{24} +(4.01345 + 2.98198i) q^{25} +3.35348i q^{27} +(-5.49052 - 3.16995i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.403608 - 1.94999i) q^{30} -3.78109 q^{31} +(3.19071 - 1.84216i) q^{32} +(-7.56654 + 4.36854i) q^{33} -0.644737 q^{34} +(7.34297 - 1.51984i) q^{35} +(4.01345 - 6.95150i) q^{36} +(-1.68772 - 0.974404i) q^{37} -0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +(1.39055 - 2.40850i) q^{41} +(-2.58632 - 1.49321i) q^{42} +(-7.56654 + 4.36854i) q^{43} +6.13636 q^{44} +(1.92426 + 9.29687i) q^{45} +(0.445274 + 0.771236i) q^{46} -6.86960i q^{47} +(-7.82169 + 4.51586i) q^{48} +(2.12291 - 3.67698i) q^{49} +(-0.656632 - 1.51827i) q^{50} +5.24581 q^{51} -12.8336i q^{53} +(0.554726 - 0.960814i) q^{54} +(-5.41950 + 4.82757i) q^{55} +(2.15819 + 3.73809i) q^{56} +3.35348i q^{57} +(-0.859539 + 0.496255i) q^{58} +(1.26764 + 2.19562i) q^{59} +(3.57417 - 10.8034i) q^{60} +(3.74581 + 6.48793i) q^{61} +(1.08333 + 0.625462i) q^{62} +(12.3307 + 7.11911i) q^{63} +5.49162 q^{64} +2.89055 q^{66} +(3.47722 + 2.00758i) q^{67} +(-3.19071 - 1.84216i) q^{68} +(-3.62291 - 6.27506i) q^{69} +(-2.35526 - 0.779207i) q^{70} +(2.62291 + 4.54300i) q^{71} +(-4.73277 + 2.73247i) q^{72} +5.46493i q^{73} +(0.322368 + 0.558359i) q^{74} +(5.34259 + 12.3532i) q^{75} +(1.17763 - 2.03972i) q^{76} +10.8848i q^{77} -13.7811 q^{79} +(-5.60226 + 4.99036i) q^{80} +(1.85526 - 3.21341i) q^{81} +(-0.796819 + 0.460044i) q^{82} -8.61955i q^{83} +(-8.53289 - 14.7794i) q^{84} +(4.26722 - 0.883225i) q^{85} +2.89055 q^{86} +(6.99351 - 4.03771i) q^{87} +(-3.61808 - 2.08890i) q^{88} +(-5.15819 + 8.93425i) q^{89} +(0.986548 - 2.98198i) q^{90} +5.08898i q^{92} +(-8.81438 - 5.08898i) q^{93} +(-1.13636 + 1.96823i) q^{94} +(0.564617 + 2.72790i) q^{95} +9.91745 q^{96} +(-4.56055 + 2.63304i) q^{97} +(-1.21648 + 0.702335i) q^{98} -13.7811 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.286513	−	0.165418i	−0.202595	−	0.116968i	0.395270	−	0.918565i	$-0.370651\pi$
$2$	−0.286513	−	0.165418i	−0.202595	−	0.116968i	−0.597865	+	0.801597i	$0.703984\pi$
$3$	2.33117	+	1.34590i	1.34590	+	0.777057i	0.987666	−	0.156574i	$-0.0500450\pi$
$3$	2.33117	+	1.34590i	1.34590	+	0.777057i	0.358236	+	0.933631i	$0.383378\pi$
$4$	−0.945274	−	1.63726i	−0.472637	−	0.818631i
$5$	2.12291	+	0.702335i	0.949392	+	0.314094i
$5$	2.12291	+	0.702335i	0.949392	+	0.314094i
$6$	−0.445274	−	0.771236i	−0.181782	−	0.314856i
$7$	2.90420	−	1.67674i	1.09768	−	0.633748i	0.162072	−	0.986779i	$-0.448182\pi$
$7$	2.90420	−	1.67674i	1.09768	−	0.633748i	0.935611	+	0.353031i	$0.114849\pi$
$8$			1.28714i			0.455071i
$9$	2.12291	+	3.67698i	0.707635	+	1.22566i
$10$	−0.492061	−	0.552395i	−0.155603	−	0.174683i
$11$	−1.62291	+	2.81095i	−0.489324	+	0.847535i	−0.999925	−	0.0122837i	$-0.996090\pi$
$11$	−1.62291	+	2.81095i	−0.489324	+	0.847535i	0.510600	+	0.859818i	$0.329423\pi$
$12$		−	5.08898i		−	1.46906i
$13$		0			0
$13$		0			0
$14$	−1.10945			−0.296514
$15$	4.00358	+	4.49448i	1.03372	+	1.16047i
$16$	−1.67763	+	2.90574i	−0.419408	+	0.726436i
$17$	1.68772	−	0.974404i	0.409332	−	0.236328i	−0.281171	−	0.959658i	$-0.590723\pi$
$17$	1.68772	−	0.974404i	0.409332	−	0.236328i	0.690503	+	0.723330i	$0.257389\pi$
$18$		−	1.40467i		−	0.331084i
$19$	0.622905	+	1.07890i	0.142904	+	0.247517i	0.928589	−	0.371110i	$-0.121023\pi$
$19$	0.622905	+	1.07890i	0.142904	+	0.247517i	−0.785685	+	0.618627i	$0.787689\pi$
$20$	−0.856821	−	4.13965i	−0.191591	−	0.925654i
$21$	9.02690			1.96983
$22$	0.929966	−	0.536916i	0.198269	−	0.114471i
$23$	−2.33117	−	1.34590i	−0.486083	−	0.280640i	0.236865	−	0.971543i	$-0.423880\pi$
$23$	−2.33117	−	1.34590i	−0.486083	−	0.280640i	−0.722948	+	0.690903i	$0.757213\pi$
$24$	−1.73236	+	3.00053i	−0.353616	+	0.612481i
$25$	4.01345	+	2.98198i	0.802690	+	0.596396i
$26$		0			0
$27$			3.35348i			0.645377i
$28$	−5.49052	−	3.16995i	−1.03761	−	0.599065i
$29$	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	$0.0768152\pi$
$30$	−0.403608	−	1.94999i	−0.0736883	−	0.356018i
$31$	−3.78109			−0.679105			−0.339552	−	0.940587i	$-0.610276\pi$
$31$	−3.78109			−0.679105			−0.339552	+	0.940587i	$0.610276\pi$
$32$	3.19071	−	1.84216i	0.564043	−	0.325650i
$33$	−7.56654	+	4.36854i	−1.31717	+	0.760466i
$34$	−0.644737			−0.110571
$35$	7.34297	−	1.51984i	1.24119	−	0.256900i
$36$	4.01345	−	6.95150i	0.668909	−	1.15858i
$37$	−1.68772	−	0.974404i	−0.277459	−	0.160191i	0.354813	−	0.934937i	$-0.384544\pi$
$37$	−1.68772	−	0.974404i	−0.277459	−	0.160191i	−0.632273	+	0.774746i	$0.717878\pi$
$38$		−	0.412160i		−	0.0668611i
$39$		0			0
$40$	−0.904000	+	2.73247i	−0.142935	+	0.432041i
$41$	1.39055	−	2.40850i	0.217167	−	0.376144i	−0.736774	−	0.676139i	$-0.763652\pi$
$41$	1.39055	−	2.40850i	0.217167	−	0.376144i	0.953941	+	0.299995i	$0.0969851\pi$
$42$	−2.58632	−	1.49321i	−0.399078	−	0.230408i
$43$	−7.56654	+	4.36854i	−1.15389	+	0.666197i	−0.949831	−	0.312763i	$-0.898745\pi$
$43$	−7.56654	+	4.36854i	−1.15389	+	0.666197i	−0.204055	+	0.978959i	$0.565412\pi$
$44$	6.13636			0.925091
$45$	1.92426	+	9.29687i	0.286851	+	1.38590i
$46$	0.445274	+	0.771236i	0.0656520	+	0.113713i
$47$		−	6.86960i		−	1.00203i	−0.865437	−	0.501017i	$-0.832959\pi$
$47$		−	6.86960i		−	1.00203i	0.865437	−	0.501017i	$-0.167041\pi$
$48$	−7.82169	+	4.51586i	−1.12896	+	0.651808i
$49$	2.12291	−	3.67698i	0.303272	−	0.525283i
$50$	−0.656632	−	1.51827i	−0.0928618	−	0.214716i
$51$	5.24581			0.734560
$52$		0			0
$53$		−	12.8336i		−	1.76282i	−0.472347	−	0.881412i	$-0.656593\pi$
$53$		−	12.8336i		−	1.76282i	0.472347	−	0.881412i	$-0.343407\pi$
$54$	0.554726	−	0.960814i	0.0754887	−	0.130750i
$55$	−5.41950	+	4.82757i	−0.730766	+	0.650949i
$56$	2.15819	+	3.73809i	0.288400	+	0.499524i
$57$			3.35348i			0.444179i
$58$	−0.859539	+	0.496255i	−0.112863	+	0.0651614i
$59$	1.26764	+	2.19562i	0.165033	+	0.285845i	0.936667	−	0.350221i	$-0.113894\pi$
$59$	1.26764	+	2.19562i	0.165033	+	0.285845i	−0.771634	+	0.636067i	$0.780560\pi$
$60$	3.57417	−	10.8034i	0.461423	−	1.39472i
$61$	3.74581	+	6.48793i	0.479602	+	0.830695i	0.999726	−	0.0233957i	$-0.00744777\pi$
$61$	3.74581	+	6.48793i	0.479602	+	0.830695i	−0.520124	+	0.854090i	$0.674114\pi$
$62$	1.08333	+	0.625462i	0.137583	+	0.0794338i
$63$	12.3307	+	7.11911i	1.55352	+	0.896924i
$64$	5.49162			0.686453
$65$		0			0
$66$	2.89055			0.355802
$67$	3.47722	+	2.00758i	0.424810	+	0.245264i	0.697133	−	0.716942i	$-0.254459\pi$
$67$	3.47722	+	2.00758i	0.424810	+	0.245264i	−0.272323	+	0.962206i	$0.587792\pi$
$68$	−3.19071	−	1.84216i	−0.386930	−	0.223394i
$69$	−3.62291	−	6.27506i	−0.436147	−	0.755428i
$70$	−2.35526	−	0.779207i	−0.281508	−	0.0931331i
$71$	2.62291	+	4.54300i	0.311282	+	0.539155i	0.978640	−	0.205581i	$-0.0659084\pi$
$71$	2.62291	+	4.54300i	0.311282	+	0.539155i	−0.667359	+	0.744737i	$0.732575\pi$
$72$	−4.73277	+	2.73247i	−0.557762	+	0.322024i
$73$			5.46493i			0.639622i	0.947481	+	0.319811i	$0.103619\pi$
$73$			5.46493i			0.639622i	−0.947481	+	0.319811i	$0.896381\pi$
$74$	0.322368	+	0.558359i	0.0374746	+	0.0649079i
$75$	5.34259	+	12.3532i	0.616909	+	1.42643i
$76$	1.17763	−	2.03972i	0.135084	−	0.233972i
$77$			10.8848i			1.24043i
$78$		0			0
$79$	−13.7811			−1.55049			−0.775247	−	0.631658i	$-0.782375\pi$
$79$	−13.7811			−1.55049			−0.775247	+	0.631658i	$0.782375\pi$
$80$	−5.60226	+	4.99036i	−0.626351	+	0.557939i
$81$	1.85526	−	3.21341i	0.206140	−	0.357046i
$82$	−0.796819	+	0.460044i	−0.0879940	+	0.0508033i
$83$		−	8.61955i		−	0.946119i	−0.881031	−	0.473059i	$-0.843150\pi$
$83$		−	8.61955i		−	0.946119i	0.881031	−	0.473059i	$-0.156850\pi$
$84$	−8.53289	−	14.7794i	−0.931015	−	1.61257i
$85$	4.26722	−	0.883225i	0.462845	−	0.0957992i
$86$	2.89055			0.311696
$87$	6.99351	−	4.03771i	0.749783	−	0.432888i
$88$	−3.61808	−	2.08890i	−0.385688	−	0.222677i
$89$	−5.15819	+	8.93425i	−0.546767	+	0.947028i	0.451726	+	0.892156i	$0.350808\pi$
$89$	−5.15819	+	8.93425i	−0.546767	+	0.947028i	−0.998493	+	0.0548717i	$0.982525\pi$
$90$	0.986548	−	2.98198i	0.103991	−	0.314328i
$91$		0			0
$92$			5.08898i			0.530563i
$93$	−8.81438	−	5.08898i	−0.914008	−	0.527703i
$94$	−1.13636	+	1.96823i	−0.117206	+	0.203007i
$95$	0.564617	+	2.72790i	0.0579285	+	0.279876i
$96$	9.91745			1.01220
$97$	−4.56055	+	2.63304i	−0.463054	+	0.267344i	−0.713328	−	0.700831i	$-0.752813\pi$
$97$	−4.56055	+	2.63304i	−0.463054	+	0.267344i	0.250273	+	0.968175i	$0.419479\pi$
$98$	−1.21648	+	0.702335i	−0.122883	+	0.0709465i
$99$	−13.7811			−1.38505
$100$	1.08847	−	9.38986i	0.108847	−	0.938986i
$101$	−2.85526	+	4.94546i	−0.284109	+	0.492092i	−0.972393	−	0.233350i	$-0.925031\pi$
$101$	−2.85526	+	4.94546i	−0.284109	+	0.492092i	0.688283	+	0.725442i	$0.258365\pi$
$102$	−1.50299	−	0.867753i	−0.148818	−	0.0859203i
$103$		−	7.36863i		−	0.726052i	−0.931779	−	0.363026i	$-0.881744\pi$
$103$		−	7.36863i		−	0.726052i	0.931779	−	0.363026i	$-0.118256\pi$
$104$		0			0
$105$	19.1633	+	6.33991i	1.87014	+	0.618712i
$106$	−2.12291	+	3.67698i	−0.206195	+	0.357140i
$107$	7.42568	+	4.28722i	0.717868	+	0.414461i	0.813967	−	0.580911i	$-0.197303\pi$
$107$	7.42568	+	4.28722i	0.717868	+	0.414461i	−0.0960996	+	0.995372i	$0.530637\pi$
$108$	5.49052	−	3.16995i	0.528326	−	0.305029i
$109$	−8.49162			−0.813350			−0.406675	−	0.913573i	$-0.633312\pi$
$109$	−8.49162			−0.813350			−0.406675	+	0.913573i	$0.633312\pi$
$110$	2.35133	−	0.486675i	0.224190	−	0.0464026i
$111$	−2.62291	−	4.54300i	−0.248955	−	0.431203i
$112$			11.2518i			1.06320i
$113$	−6.35006	+	3.66621i	−0.597363	+	0.344888i	−0.768004	−	0.640446i	$-0.778750\pi$
$113$	−6.35006	+	3.66621i	−0.597363	+	0.344888i	0.170640	+	0.985333i	$0.445416\pi$
$114$	0.554726	−	0.960814i	0.0519549	−	0.0899885i
$115$	−4.00358	−	4.49448i	−0.373336	−	0.419113i
$116$	−5.67164			−0.526599
$117$		0			0
$118$		−	0.838765i		−	0.0772145i
$119$	3.26764	−	5.65972i	0.299544	−	0.518826i
$120$	−5.78501	+	5.15315i	−0.528097	+	0.470416i
$121$	0.232358	+	0.402456i	0.0211234	+	0.0365869i
$122$		−	2.47850i		−	0.224393i
$123$	6.48321	−	3.74308i	0.584571	−	0.337502i
$124$	3.57417	+	6.19064i	0.320970	+	0.555936i
$125$	6.42583	+	9.14925i	0.574744	+	0.818333i
$126$	−2.35526	−	4.07944i	−0.209824	−	0.363425i
$127$	−7.93599	−	4.58185i	−0.704205	−	0.406573i	0.104707	−	0.994503i	$-0.466610\pi$
$127$	−7.93599	−	4.58185i	−0.704205	−	0.406573i	−0.808912	+	0.587930i	$0.799943\pi$
$128$	−7.95484	−	4.59273i	−0.703115	−	0.405944i
$129$	−23.5185			−2.07069
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	14.3049	+	8.25894i	1.24508	+	0.718848i
$133$	3.61808	+	2.08890i	0.313727	+	0.181130i
$134$	−0.664179	−	1.15039i	−0.0573763	−	0.0993787i
$135$	−2.35526	+	7.11911i	−0.202709	+	0.612716i
$136$	1.25419	+	2.17232i	0.107546	+	0.186275i
$137$	14.5914	−	8.42435i	1.24663	−	0.719741i	0.276193	−	0.961102i	$-0.410927\pi$
$137$	14.5914	−	8.42435i	1.24663	−	0.719741i	0.970435	+	0.241361i	$0.0775938\pi$
$138$			2.39718i			0.204061i
$139$	−0.513452	−	0.889325i	−0.0435505	−	0.0754316i	0.843429	−	0.537241i	$-0.180534\pi$
$139$	−0.513452	−	0.889325i	−0.0435505	−	0.0754316i	−0.886979	+	0.461810i	$0.847200\pi$
$140$	−9.42949	−	10.5857i	−0.796937	−	0.894654i
$141$	9.24581	−	16.0142i	0.778638	−	1.34864i
$142$		−	1.73551i		−	0.145640i
$143$		0			0
$144$	−14.2458			−1.18715
$145$	5.00908	−	4.46197i	0.415981	−	0.370546i
$146$	0.904000	−	1.56577i	0.0748155	−	0.129584i
$147$	9.89771	−	5.71445i	0.816349	−	0.471319i
$148$			3.68431i			0.302849i
$149$	−7.92583	−	13.7279i	−0.649309	−	1.12464i	−0.983288	−	0.182056i	$-0.941725\pi$
$149$	−7.92583	−	13.7279i	−0.649309	−	1.12464i	0.333979	−	0.942581i	$-0.391609\pi$
$150$	0.512727	−	4.42312i	0.0418640	−	0.361146i
$151$	−14.5454			−1.18369			−0.591845	−	0.806052i	$-0.701600\pi$
$151$	−14.5454			−1.18369			−0.591845	+	0.806052i	$0.701600\pi$
$152$	−1.38869	+	0.801763i	−0.112638	+	0.0650316i
$153$	7.16573	+	4.13713i	0.579315	+	0.334468i
$154$	1.80054	−	3.11862i	0.145091	−	0.251306i
$155$	−8.02690	−	2.65559i	−0.644736	−	0.213302i
$156$		0			0
$157$		−	10.9210i		−	0.871588i	−0.900047	−	0.435794i	$-0.856468\pi$
$157$		−	10.9210i		−	0.871588i	0.900047	−	0.435794i	$-0.143532\pi$
$158$	3.94846	+	2.27964i	0.314123	+	0.181359i
$159$	17.2727	−	29.9172i	1.36982	−	2.37259i
$160$	8.06738	−	1.66978i	0.637783	−	0.132008i
$161$	−9.02690			−0.711420
$162$	−1.06311	+	0.613789i	−0.0835261	+	0.0482238i
$163$	3.61808	−	2.08890i	0.283390	−	0.163615i	−0.351567	−	0.936163i	$-0.614351\pi$
$163$	3.61808	−	2.08890i	0.283390	−	0.163615i	0.634957	+	0.772547i	$0.281018\pi$
$164$	−5.25779			−0.410564
$165$	−19.1312	+	3.95976i	−1.48936	+	0.308267i
$166$	−1.42583	+	2.46961i	−0.110666	+	0.191679i
$167$	2.90420	+	1.67674i	0.224733	+	0.129750i	0.608140	−	0.793830i	$-0.291916\pi$
$167$	2.90420	+	1.67674i	0.224733	+	0.129750i	−0.383407	+	0.923580i	$0.625249\pi$
$168$			11.6188i			0.896413i
$169$		0			0
$170$	−1.36872	−	0.452821i	−0.104976	−	0.0347298i
$171$	−2.64474	+	4.58082i	−0.202248	+	0.350304i
$172$	14.3049	+	8.25894i	1.09074	+	0.629738i
$173$	7.56654	−	4.36854i	0.575273	−	0.332134i	−0.183979	−	0.982930i	$-0.558898\pi$
$173$	7.56654	−	4.36854i	0.575273	−	0.332134i	0.759253	+	0.650796i	$0.225565\pi$
$174$	−2.67164			−0.202537
$175$	16.6559	+	1.93074i	1.25906	+	0.145950i
$176$	−5.44527	−	9.43149i	−0.410453	−	0.710925i
$177$			6.82449i			0.512960i
$178$	2.95577	−	1.70652i	0.221545	−	0.127909i
$179$	−9.00507	+	15.5972i	−0.673071	+	1.16579i	0.303958	+	0.952685i	$0.401692\pi$
$179$	−9.00507	+	15.5972i	−0.673071	+	1.16579i	−0.977029	+	0.213107i	$0.931642\pi$
$180$	13.4025	−	11.9386i	0.998960	−	0.889850i
$181$	1.04366			0.0775749			0.0387875	−	0.999247i	$-0.487650\pi$
$181$	1.04366			0.0775749			0.0387875	+	0.999247i	$0.487650\pi$
$182$		0			0
$183$			20.1660i			1.49071i
$184$	1.73236	−	3.00053i	0.127711	−	0.221202i
$185$	−2.89851	−	3.25391i	−0.213102	−	0.239232i
$186$	1.68362	+	2.91612i	0.123449	+	0.213820i
$187$			6.32546i			0.462564i
$188$	−11.2473	+	6.49365i	−0.820296	+	0.473598i
$189$	5.62291	+	9.73916i	0.409006	+	0.708419i
$190$	0.289474	−	0.874976i	0.0210006	−	0.0634774i
$191$	−12.7593	−	22.0997i	−0.923228	−	1.59908i	−0.794387	−	0.607412i	$-0.792208\pi$
$191$	−12.7593	−	22.0997i	−0.923228	−	1.59908i	−0.128841	−	0.991665i	$-0.541126\pi$
$192$	12.8019	+	7.39118i	0.923898	+	0.533413i
$193$	−17.1652	−	9.91035i	−1.23558	−	0.713362i	−0.267392	−	0.963588i	$-0.586162\pi$
$193$	−17.1652	−	9.91035i	−1.23558	−	0.713362i	−0.968188	+	0.250225i	$0.919495\pi$
$194$	1.74221			0.125083
$195$		0			0
$196$	−8.02690			−0.573350
$197$	−18.7512	−	10.8260i	−1.33596	−	0.771319i	−0.349758	−	0.936840i	$-0.613736\pi$
$197$	−18.7512	−	10.8260i	−1.33596	−	0.771319i	−0.986206	+	0.165521i	$0.947070\pi$
$198$	3.94846	+	2.27964i	0.280605	+	0.162007i
$199$	9.11453	+	15.7868i	0.646112	+	1.11910i	0.984044	+	0.177928i	$0.0569393\pi$
$199$	9.11453	+	15.7868i	0.646112	+	1.11910i	−0.337932	+	0.941171i	$0.609727\pi$
$200$	−3.83821	+	5.16586i	−0.271402	+	0.365281i
$201$	5.40400	+	9.36000i	0.381169	+	0.660204i
$202$	1.63614	−	0.944625i	0.115118	−	0.0664636i
$203$		−	10.0604i		−	0.706104i
$204$	−4.95873	−	8.58877i	−0.347180	−	0.601334i
$205$	4.64357	−	4.13638i	0.324321	−	0.288898i
$206$	−1.21891	+	2.11121i	−0.0849252	+	0.147095i
$207$		−	11.4289i		−	0.794363i
$208$		0			0
$209$	−4.04366			−0.279706
$210$	−4.44178	−	4.98642i	−0.306512	−	0.344096i
$211$	−9.64981	+	16.7140i	−0.664320	+	1.15064i	0.315149	+	0.949042i	$0.397946\pi$
$211$	−9.64981	+	16.7140i	−0.664320	+	1.15064i	−0.979469	+	0.201594i	$0.935388\pi$
$212$	−21.0119	+	12.1312i	−1.44310	+	0.833176i
$213$			14.1207i			0.967534i
$214$	−1.41837	−	2.45669i	−0.0969577	−	0.167936i
$215$	−19.1312	+	3.95976i	−1.30474	+	0.270053i
$216$	−4.31638			−0.293692
$217$	−10.9810	+	6.33991i	−0.745442	+	0.430381i
$218$	2.43296	+	1.40467i	0.164781	+	0.0951362i
$219$	−7.35526	+	12.7397i	−0.497023	+	0.860868i
$220$	13.0269	+	4.30978i	0.878274	+	0.290565i
$221$		0			0
$222$			1.73551i			0.116480i
$223$	10.7134	+	6.18537i	0.717421	+	0.414203i	0.813803	−	0.581141i	$-0.197394\pi$
$223$	10.7134	+	6.18537i	0.717421	+	0.414203i	−0.0963818	+	0.995344i	$0.530727\pi$
$224$	6.17763	−	10.7000i	0.412760	−	0.714922i
$225$	−2.44450	+	21.0878i	−0.162967	+	1.40586i
$226$	2.42583			0.161364
$227$	−5.33715	+	3.08141i	−0.354239	+	0.204520i	−0.666551	−	0.745460i	$-0.732230\pi$
$227$	−5.33715	+	3.08141i	−0.354239	+	0.204520i	0.312311	+	0.949980i	$0.398897\pi$
$228$	5.49052	−	3.16995i	0.363619	−	0.209935i
$229$	−26.9832			−1.78310			−0.891551	−	0.452920i	$-0.850382\pi$
$229$	−26.9832			−1.78310			−0.891551	+	0.452920i	$0.850382\pi$
$230$	0.403608	+	1.94999i	0.0266131	+	0.128579i
$231$	−14.6498	+	25.3742i	−0.963887	+	1.66950i
$232$	3.34408	+	1.93070i	0.219549	+	0.126757i
$233$			0.824319i			0.0540029i	0.999635	+	0.0270015i	$0.00859588\pi$
$233$			0.824319i			0.0540029i	−0.999635	+	0.0270015i	$0.991404\pi$
$234$		0			0
$235$	4.82476	−	14.5835i	0.314733	−	0.951323i
$236$	2.39654	−	4.15092i	0.156001	−	0.270202i
$237$	−32.1261	−	18.5480i	−2.08681	−	1.20482i
$238$	−1.87244	+	1.08106i	−0.121372	+	0.0700744i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	−19.7764	+	4.09329i	−1.27656	+	0.264221i
$241$	11.3469	+	19.6534i	0.730917	+	1.26599i	0.956492	+	0.291760i	$0.0942407\pi$
$241$	11.3469	+	19.6534i	0.730917	+	1.26599i	−0.225575	+	0.974226i	$0.572426\pi$
$242$		−	0.153745i		−	0.00988310i
$243$	17.3625	−	10.0242i	1.11380	−	0.643054i
$244$	7.08163	−	12.2657i	0.453355	−	0.785234i
$245$	7.08920	−	6.31489i	0.452912	−	0.403443i
$246$	−2.47670			−0.157908
$247$		0			0
$248$		−	4.86678i		−	0.309041i
$249$	11.6011	−	20.0936i	0.735188	−	1.27338i
$250$	−0.327631	−	3.68433i	−0.0207212	−	0.233017i
$251$	−9.51345	−	16.4778i	−0.600484	−	1.04007i	−0.992748	−	0.120216i	$-0.961641\pi$
$251$	−9.51345	−	16.4778i	−0.600484	−	1.04007i	0.392264	−	0.919853i	$-0.371692\pi$
$252$		−	26.9180i		−	1.69568i
$253$	7.56654	−	4.36854i	0.475704	−	0.274648i
$254$	1.51584	+	2.62552i	0.0951124	+	0.164739i
$255$	11.1364	+	3.68431i	0.697386	+	0.230721i
$256$	−3.97218	−	6.88001i	−0.248261	−	0.430001i
$257$	−1.82857	−	1.05573i	−0.114063	−	0.0658544i	0.441883	−	0.897073i	$-0.354311\pi$
$257$	−1.82857	−	1.05573i	−0.114063	−	0.0658544i	−0.555946	+	0.831218i	$0.687644\pi$
$258$	6.73836	+	3.89039i	0.419512	+	0.242205i
$259$	−6.53528			−0.406083
$260$		0			0
$261$	12.7374			0.788427
$262$	−2.86513	−	1.65418i	−0.177008	−	0.102196i
$263$	−25.9092	−	14.9587i	−1.59763	−	0.922391i	−0.991943	−	0.126687i	$-0.959566\pi$
$263$	−25.9092	−	14.9587i	−1.59763	−	0.922391i	−0.605685	−	0.795704i	$-0.707101\pi$
$264$	−5.62291	−	9.73916i	−0.346066	−	0.599404i
$265$	9.01345	−	27.2444i	0.553692	−	1.67361i
$266$	−0.691084	−	1.19699i	−0.0423731	−	0.0733923i
$267$	−24.0492	+	13.8848i	−1.47179	+	0.849738i
$268$		−	7.59083i		−	0.463684i
$269$	9.29455	+	16.0986i	0.566699	+	0.981551i	0.996889	+	0.0788127i	$0.0251129\pi$
$269$	9.29455	+	16.0986i	0.566699	+	0.981551i	−0.430191	+	0.902738i	$0.641554\pi$
$270$	1.85244	−	1.65011i	0.112736	−	0.100423i
$271$	2.91238	−	5.04439i	0.176914	−	0.306425i	−0.763908	−	0.645326i	$-0.776722\pi$
$271$	2.91238	−	5.04439i	0.176914	−	0.306425i	0.940822	+	0.338901i	$0.110055\pi$
$272$			6.53876i			0.396471i
$273$		0			0
$274$	−5.57417			−0.336748
$275$	−14.8957	+	6.44216i	−0.898242	+	0.388477i
$276$	−6.84927	+	11.8633i	−0.412278	+	0.714086i
$277$	11.7263	−	6.77017i	0.704564	−	0.406780i	−0.104481	−	0.994527i	$-0.533318\pi$
$277$	11.7263	−	6.77017i	0.704564	−	0.406780i	0.809045	+	0.587747i	$0.199985\pi$
$278$			0.339738i			0.0203761i
$279$	−8.02690	−	13.9030i	−0.480558	−	0.832351i
$280$	1.95624	+	9.45139i	0.116908	+	0.564829i
$281$	0.464716			0.0277226			0.0138613	−	0.999904i	$-0.495588\pi$
$281$	0.464716			0.0277226			0.0138613	+	0.999904i	$0.495588\pi$
$282$	−5.29809	+	3.05885i	−0.315496	+	0.182152i
$283$	8.71259	+	5.03022i	0.517910	+	0.299015i	0.736079	−	0.676896i	$-0.236675\pi$
$283$	8.71259	+	5.03022i	0.517910	+	0.299015i	−0.218169	+	0.975911i	$0.570009\pi$
$284$	4.95873	−	8.58877i	0.294246	−	0.509649i
$285$	−2.35526	+	7.11911i	−0.139514	+	0.421700i
$286$		0			0
$287$		−	9.32634i		−	0.550516i
$288$	13.5471	+	7.82145i	0.798273	+	0.460883i
$289$	−6.60107	+	11.4334i	−0.388298	+	0.672553i
$290$	−2.17326	+	0.449818i	−0.127618	+	0.0264142i
$291$	−14.1752			−0.830967
$292$	8.94752	−	5.16586i	0.523614	−	0.302309i
$293$	11.6481	−	6.72506i	0.680492	−	0.392882i	−0.119548	−	0.992828i	$-0.538145\pi$
$293$	11.6481	−	6.72506i	0.680492	−	0.392882i	0.800040	+	0.599946i	$0.204811\pi$
$294$	−3.78109			−0.220518
$295$	1.14902	+	5.55140i	0.0668987	+	0.323215i
$296$	1.25419	−	2.17232i	0.0728983	−	0.126264i
$297$	−9.42647	−	5.44238i	−0.546979	−	0.315799i
$298$			5.24431i			0.303795i
$299$		0			0
$300$	15.1752	−	20.4244i	0.876143	−	1.17920i
$301$	−14.6498	+	25.3742i	−0.844401	+	1.46255i
$302$	4.16745	+	2.40608i	0.239810	+	0.138454i
$303$	−13.3122	+	7.68581i	−0.764767	+	0.441538i
$304$	−4.18002			−0.239741
$305$	3.39530	+	16.4041i	0.194414	+	0.939295i
$306$	−1.36872	−	2.37068i	−0.0782442	−	0.135523i
$307$		−	24.6077i		−	1.40444i	−0.711961	−	0.702219i	$-0.752193\pi$
$307$		−	24.6077i		−	1.40444i	0.711961	−	0.702219i	$-0.247807\pi$
$308$	17.8212	−	10.2891i	1.01546	−	0.586274i
$309$	9.91745	−	17.1775i	0.564184	−	0.977196i
$310$	1.86053	+	2.08866i	0.105671	+	0.118628i
$311$	2.43781			0.138236			0.0691178	−	0.997609i	$-0.477982\pi$
$311$	2.43781			0.138236			0.0691178	+	0.997609i	$0.477982\pi$
$312$		0			0
$313$			19.2965i			1.09071i	0.838207	+	0.545353i	$0.183604\pi$
$313$			19.2965i			1.09071i	−0.838207	+	0.545353i	$0.816396\pi$
$314$	−1.80653	+	3.12900i	−0.101948	+	0.176579i
$315$	21.1768	+	23.7735i	1.19318	+	1.33948i
$316$	13.0269	+	22.5633i	0.732821	+	1.26928i
$317$			28.8217i			1.61879i	0.587265	+	0.809395i	$0.300205\pi$
$317$			28.8217i			1.61879i	−0.587265	+	0.809395i	$0.699795\pi$
$318$	−9.89771	+	5.71445i	−0.555036	+	0.320450i
$319$	4.86872	+	8.43286i	0.272596	+	0.472150i
$320$	11.6582	+	3.85695i	0.651713	+	0.215610i
$321$	11.5404	+	19.9885i	0.644120	+	1.11565i
$322$	2.58632	+	1.49321i	0.144130	+	0.0832136i
$323$	2.10258	+	1.21392i	0.116990	+	0.0675445i
$324$	−7.01492			−0.389718
$325$		0			0
$326$	−1.38217			−0.0765512
$327$	−19.7954	−	11.4289i	−1.09469	−	0.632019i
$328$	3.10006	+	1.78982i	0.171172	+	0.0988264i
$329$	−11.5185	−	19.9507i	−0.635037	−	1.09992i
$330$	6.13636	+	2.03013i	0.337795	+	0.111755i
$331$	−1.48655	−	2.57478i	−0.0817081	−	0.141522i	0.822276	−	0.569089i	$-0.192704\pi$
$331$	−1.48655	−	2.57478i	−0.0817081	−	0.141522i	−0.903984	+	0.427567i	$0.859371\pi$
$332$	−14.1125	+	8.14783i	−0.774522	+	0.447171i
$333$		−	8.27427i		−	0.453427i
$334$	−0.554726	−	0.960814i	−0.0303533	−	0.0525734i
$335$	5.97182	+	6.70407i	0.326276	+	0.366282i
$336$	−15.1438	+	26.2299i	−0.826163	+	1.43096i
$337$			1.90370i			0.103701i	0.998655	+	0.0518505i	$0.0165119\pi$
$337$			1.90370i			0.103701i	−0.998655	+	0.0518505i	$0.983488\pi$
$338$		0			0
$339$	−19.7374			−1.07199
$340$	−5.47976	−	6.15167i	−0.297182	−	0.333621i
$341$	6.13636	−	10.6285i	0.332302	−	0.575565i
$342$	1.51550	−	0.874976i	0.0819490	−	0.0473133i
$343$			9.23611i			0.498703i
$344$	−5.62291	−	9.73916i	−0.303167	−	0.525100i
$345$	−3.28390	−	15.8658i	−0.176799	−	0.854188i
$346$	−2.89055			−0.155397
$347$	−10.9420	+	6.31735i	−0.587396	+	0.339133i	−0.764067	−	0.645137i	$-0.776800\pi$
$347$	−10.9420	+	6.31735i	−0.587396	+	0.339133i	0.176671	+	0.984270i	$0.443467\pi$
$348$	−13.2216	−	7.63347i	−0.708750	−	0.409197i
$349$	−4.48655	+	7.77093i	−0.240159	+	0.415968i	−0.960760	−	0.277383i	$-0.910533\pi$
$349$	−4.48655	+	7.77093i	−0.240159	+	0.415968i	0.720600	+	0.693351i	$0.243866\pi$
$350$	−4.45274	−	3.30837i	−0.238009	−	0.176840i
$351$		0			0
$352$			11.9586i			0.637395i
$353$	29.6618	+	17.1252i	1.57874	+	0.911484i	0.995036	+	0.0995150i	$0.0317291\pi$
$353$	29.6618	+	17.1252i	1.57874	+	0.911484i	0.583701	+	0.811969i	$0.301604\pi$
$354$	1.12890	−	1.95530i	0.0600001	−	0.103923i
$355$	2.37747	+	11.4865i	0.126183	+	0.609641i
$356$	19.5036			1.03369
$357$	15.2349	−	8.79585i	0.806315	−	0.465526i
$358$	5.16014	−	2.97921i	0.272722	−	0.157456i
$359$	22.4043			1.18245			0.591227	−	0.806505i	$-0.298644\pi$
$359$	22.4043			1.18245			0.591227	+	0.806505i	$0.298644\pi$
$360$	−11.9663	+	2.47678i	−0.630681	+	0.130538i
$361$	8.72398	−	15.1104i	0.459157	−	0.795283i
$362$	−0.299023	−	0.172641i	−0.0157163	−	0.00907381i
$363$			1.25092i			0.0656565i
$364$		0			0
$365$	−3.83821	+	11.6015i	−0.200901	+	0.607252i
$366$	3.33582	−	5.77781i	0.174366	−	0.302011i
$367$	11.4273	+	6.59753i	0.596498	+	0.344388i	0.767663	−	0.640854i	$-0.221420\pi$
$367$	11.4273	+	6.59753i	0.596498	+	0.344388i	−0.171165	+	0.985242i	$0.554753\pi$
$368$	7.82169	−	4.51586i	0.407734	−	0.235405i
$369$	11.8080			0.614700
$370$	0.292203	+	1.41175i	0.0151909	+	0.0733935i
$371$	−21.5185	−	37.2712i	−1.11719	−	1.93502i
$372$			19.2419i			0.997647i
$373$	13.2168	−	7.63070i	0.684338	−	0.395103i	−0.117149	−	0.993114i	$-0.537376\pi$
$373$	13.2168	−	7.63070i	0.684338	−	0.395103i	0.801488	+	0.598012i	$0.204042\pi$
$374$	1.04635	−	1.81233i	0.0541053	−	0.0937131i
$375$	2.66572	+	29.9770i	0.137657	+	1.54801i
$376$	8.84210			0.455997
$377$		0			0
$378$		−	3.72052i		−	0.191363i
$379$	−9.11453	+	15.7868i	−0.468182	+	0.810915i	−0.999339	−	0.0363588i	$-0.988424\pi$
$379$	−9.11453	+	15.7868i	−0.468182	+	0.810915i	0.531157	+	0.847273i	$0.321757\pi$
$380$	3.93256	−	3.50304i	0.201736	−	0.179702i
$381$	−12.3334	−	21.3621i	−0.631861	−	1.09442i
$382$			8.44246i			0.431954i
$383$	1.24784	−	0.720440i	0.0637616	−	0.0368128i	−0.467780	−	0.883845i	$-0.654946\pi$
$383$	1.24784	−	0.720440i	0.0637616	−	0.0368128i	0.531542	+	0.847032i	$0.321613\pi$
$384$	−12.3627	−	21.4129i	−0.630883	−	1.09272i
$385$	−7.64474	+	23.1073i	−0.389612	+	1.17766i
$386$	3.27870	+	5.67888i	0.166882	+	0.289048i
$387$	−32.1261	−	18.5480i	−1.63306	−	0.942848i
$388$	8.62194	+	4.97788i	0.437713	+	0.252714i
$389$	18.7912			0.952754			0.476377	−	0.879241i	$-0.341950\pi$
$389$	18.7912			0.952754			0.476377	+	0.879241i	$0.341950\pi$
$390$		0			0
$391$	−5.24581			−0.265292
$392$	4.73277	+	2.73247i	0.239041	+	0.138010i
$393$	23.3117	+	13.4590i	1.17592	+	0.678918i
$394$	3.58163	+	6.20357i	0.180440	+	0.312531i
$395$	−29.2560	−	9.67894i	−1.47203	−	0.487000i
$396$	13.0269	+	22.5633i	0.654627	+	1.13385i
$397$	14.8027	−	8.54634i	0.742926	−	0.428928i	−0.0802063	−	0.996778i	$-0.525558\pi$
$397$	14.8027	−	8.54634i	0.742926	−	0.428928i	0.823132	+	0.567850i	$0.192225\pi$
$398$		−	6.03084i		−	0.302298i
$399$	5.62291	+	9.73916i	0.281497	+	0.487568i
$400$	−15.3980	+	6.65940i	−0.769898	+	0.332970i
$401$	11.1011	−	19.2276i	0.554361	−	0.960182i	−0.443592	−	0.896229i	$-0.646296\pi$
$401$	11.1011	−	19.2276i	0.554361	−	0.960182i	0.997953	−	0.0639527i	$-0.0203707\pi$
$402$		−	3.57568i		−	0.178339i
$403$		0			0
$404$	10.7960			0.537122
$405$	6.19544	−	5.51875i	0.307854	−	0.274229i
$406$	−1.66418	+	2.88244i	−0.0825918	+	0.143053i
$407$	5.47801	−	3.16273i	0.271535	−	0.156771i
$408$			6.75207i			0.334277i
$409$	4.81638	+	8.34221i	0.238155	+	0.412496i	0.960185	−	0.279366i	$-0.0901242\pi$
$409$	4.81638	+	8.34221i	0.238155	+	0.412496i	−0.722030	+	0.691862i	$0.756791\pi$
$410$	−2.01468	+	0.416996i	−0.0994978	+	0.0205939i
$411$	45.3534			2.23712
$412$	−12.0644	+	6.96537i	−0.594369	+	0.343159i
$413$	7.36296	+	4.25101i	0.362308	+	0.209178i
$414$	−1.89055	+	3.27452i	−0.0929153	+	0.160934i
$415$	6.05381	−	18.2985i	0.297170	−	0.898238i
$416$		0			0
$417$		−	2.76423i		−	0.135365i
$418$	1.15856	+	0.668896i	0.0566671	+	0.0327168i
$419$	−0.978168	+	1.69424i	−0.0477866	+	0.0827689i	−0.888929	−	0.458044i	$-0.848550\pi$
$419$	−0.978168	+	1.69424i	−0.0477866	+	0.0827689i	0.841143	+	0.540813i	$0.181883\pi$
$420$	−7.73444	−	37.3682i	−0.377402	−	1.82338i
$421$	12.0807			0.588778			0.294389	−	0.955686i	$-0.404884\pi$
$421$	12.0807			0.588778			0.294389	+	0.955686i	$0.404884\pi$
$422$	5.52959	−	3.19251i	0.269176	−	0.155409i
$423$	25.2594	−	14.5835i	1.22815	−	0.709075i
$424$	16.5185			0.802210
$425$	9.67923	+	1.12201i	0.469511	+	0.0544257i
$426$	2.33582	−	4.04576i	0.113171	−	0.196018i
$427$	21.7571	+	12.5615i	1.05290	+	0.607893i
$428$		−	16.2104i		−	0.783558i
$429$		0			0
$430$	6.13636	+	2.03013i	0.295921	+	0.0979016i
$431$	12.2945	−	21.2948i	0.592207	−	1.02573i	−0.401727	−	0.915759i	$-0.631590\pi$
$431$	12.2945	−	21.2948i	0.592207	−	1.02573i	0.993934	−	0.109974i	$-0.0350767\pi$
$432$	−9.74434	−	5.62590i	−0.468825	−	0.270676i
$433$	31.2400	−	18.0364i	1.50130	−	0.866775i	0.501299	−	0.865274i	$-0.332856\pi$
$433$	31.2400	−	18.0364i	1.50130	−	0.866775i	0.999999	−	0.00150085i	$-0.000477735\pi$
$434$	4.19495			0.201364
$435$	17.6824	−	3.65988i	0.847805	−	0.175478i
$436$	8.02690	+	13.9030i	0.384419	+	0.665833i
$437$		−	3.35348i		−	0.160419i
$438$	4.21475	−	2.43339i	0.201389	−	0.116272i
$439$	1.26764	−	2.19562i	0.0605013	−	0.104791i	−0.834188	−	0.551480i	$-0.814063\pi$
$439$	1.26764	−	2.19562i	0.0605013	−	0.104791i	0.894690	+	0.446688i	$0.147397\pi$
$440$	−6.21373	−	6.97563i	−0.296228	−	0.332550i
$441$	18.0269			0.858424
$442$		0			0
$443$			19.3579i			0.919721i	0.887991	+	0.459860i	$0.152101\pi$
$443$			19.3579i			0.919721i	−0.887991	+	0.459860i	$0.847899\pi$
$444$	−4.95873	+	8.58877i	−0.235331	+	0.407605i
$445$	−17.2252	+	15.3438i	−0.816552	+	0.727365i
$446$	−2.04635	−	3.54438i	−0.0968973	−	0.167831i
$447$		−	42.6696i		−	2.01820i
$448$	15.9487	−	9.20801i	0.753507	−	0.435038i
$449$	12.4040	+	21.4844i	0.585381	+	1.01391i	0.994828	+	0.101576i	$0.0323884\pi$
$449$	12.4040	+	21.4844i	0.585381	+	1.01391i	−0.409447	+	0.912334i	$0.634278\pi$
$450$	4.18869	−	5.63757i	0.197457	−	0.265758i
$451$	4.51345	+	7.81753i	0.212530	+	0.368113i
$452$	12.0051	+	6.93114i	0.564672	+	0.326013i
$453$	−33.9079	−	19.5767i	−1.59313	−	0.919795i
$454$	2.03888			0.0956896
$455$		0			0
$456$	−4.31638			−0.202133
$457$	6.55363	+	3.78374i	0.306566	+	0.176996i	0.645389	−	0.763854i	$-0.276695\pi$
$457$	6.55363	+	3.78374i	0.306566	+	0.176996i	−0.338823	+	0.940850i	$0.610029\pi$
$458$	7.73105	+	4.46352i	0.361248	+	0.208567i
$459$	3.26764	+	5.65972i	0.152520	+	0.264173i
$460$	−3.57417	+	10.8034i	−0.166646	+	0.503712i
$461$	−6.17164	−	10.6896i	−0.287442	−	0.497864i	0.685756	−	0.727831i	$-0.259472\pi$
$461$	−6.17164	−	10.6896i	−0.287442	−	0.497864i	−0.973198	+	0.229967i	$0.926138\pi$
$462$	8.39472	−	4.84669i	0.390558	−	0.225489i
$463$			22.8578i			1.06229i	0.847281	+	0.531146i	$0.178238\pi$
$463$			22.8578i			1.06229i	−0.847281	+	0.531146i	$0.821762\pi$
$464$	5.03289	+	8.71723i	0.233646	+	0.404687i
$465$	−15.1379	−	16.9941i	−0.702004	−	0.788081i
$466$	0.136357	−	0.236178i	0.00631664	−	0.0109407i
$467$		−	15.2976i		−	0.707889i	−0.935266	−	0.353945i	$-0.884840\pi$
$467$		−	15.2976i		−	0.707889i	0.935266	−	0.353945i	$-0.115160\pi$
$468$		0			0
$469$	13.4647			0.621743
$470$	−3.79473	+	3.38026i	−0.175038	+	0.155920i
$471$	14.6985	−	25.4586i	0.677273	−	1.17307i
$472$	−2.82606	+	1.63163i	−0.130080	+	0.0751017i
$473$		−	28.3589i		−	1.30394i
$474$	6.13636	+	10.6285i	0.281852	+	0.488182i
$475$	−0.717267	+	6.18762i	−0.0329105	+	0.283907i
$476$	−12.3553			−0.566303
$477$	47.1887	−	27.2444i	2.16062	−	1.24744i
$478$	−1.14605	−	0.661673i	−0.0524192	−	0.0302642i
$479$	−12.1414	+	21.0296i	−0.554756	+	0.960866i	0.443166	+	0.896439i	$0.353855\pi$
$479$	−12.1414	+	21.0296i	−0.554756	+	0.960866i	−0.997922	+	0.0644264i	$0.979478\pi$
$480$	21.0538	+	6.96537i	0.960971	+	0.317924i
$481$		0			0
$482$		−	7.50793i		−	0.341977i
$483$	−21.0433	−	12.1493i	−0.957501	−	0.552814i
$484$	0.439284	−	0.760862i	0.0199674	−	0.0345846i
$485$	−11.5309	+	2.38665i	−0.523591	+	0.108372i
$486$	−6.63276			−0.300868
$487$	−31.9462	+	18.4441i	−1.44762	+	0.835783i	−0.998339	−	0.0576081i	$-0.981653\pi$
$487$	−31.9462	+	18.4441i	−1.44762	+	0.835783i	−0.449280	+	0.893391i	$0.648319\pi$
$488$	−8.35085	+	4.82136i	−0.378025	+	0.218253i
$489$	11.2458			0.508553
$490$	−3.07574	+	0.636614i	−0.138948	+	0.0287593i
$491$	17.6767	−	30.6170i	0.797739	−	1.38172i	−0.123346	−	0.992364i	$-0.539363\pi$
$491$	17.6767	−	30.6170i	0.797739	−	1.38172i	0.921085	−	0.389361i	$-0.127304\pi$
$492$	−12.2568	−	7.07647i	−0.552580	−	0.319032i
$493$		−	5.84642i		−	0.263310i
$494$		0			0
$495$	−29.2560	−	9.67894i	−1.31496	−	0.435036i
$496$	6.34328	−	10.9869i	0.284822	−	0.493326i
$497$	15.2349	+	8.79585i	0.683377	+	0.394548i
$498$	−6.64771	+	3.83806i	−0.297891	+	0.171988i
$499$	16.2189			0.726058			0.363029	−	0.931778i	$-0.381743\pi$
$499$	16.2189			0.726058			0.363029	+	0.931778i	$0.381743\pi$
$500$	8.90554	−	19.1693i	0.398268	−	0.857278i
$501$	4.51345	+	7.81753i	0.201646	+	0.349261i
$502$			6.29480i			0.280950i
$503$	−17.5270	+	10.1192i	−0.781489	+	0.451193i	−0.836958	−	0.547268i	$-0.815668\pi$
$503$	−17.5270	+	10.1192i	−0.781489	+	0.451193i	0.0554688	+	0.998460i	$0.482335\pi$
$504$	−9.16326	+	15.8712i	−0.408164	+	0.706961i
$505$	−9.53482	+	8.49339i	−0.424294	+	0.377951i
$506$	−2.89055			−0.128500
$507$		0			0
$508$			17.3244i			0.768646i
$509$	10.0185	−	17.3526i	0.444063	−	0.769140i	−0.553923	−	0.832568i	$-0.686870\pi$
$509$	10.0185	−	17.3526i	0.444063	−	0.769140i	0.997986	+	0.0634276i	$0.0202032\pi$
$510$	−2.58126	−	2.89776i	−0.114300	−	0.128315i
$511$	9.16326	+	15.8712i	0.405359	+	0.702102i
$512$			20.9992i			0.928042i
$513$	−3.61808	+	2.08890i	−0.159742	+	0.0922271i
$514$	0.349273	+	0.604959i	0.0154058	+	0.0266836i
$515$	5.17524	−	15.6429i	0.228048	−	0.689308i
$516$	22.2314	+	38.5060i	0.978685	+	1.69513i
$517$	19.3101	+	11.1487i	0.849259	+	0.490320i
$518$	1.87244	+	1.08106i	0.0822704	+	0.0474988i
$519$	23.5185			1.03235
$520$		0			0
$521$	16.0269			0.702151			0.351076	−	0.936347i	$-0.385816\pi$
$521$	16.0269			0.702151			0.351076	+	0.936347i	$0.385816\pi$
$522$	−3.64944	−	2.10700i	−0.159732	−	0.0922210i
$523$	−10.1654	−	5.86898i	−0.444501	−	0.256633i	0.261004	−	0.965338i	$-0.415946\pi$
$523$	−10.1654	−	5.86898i	−0.444501	−	0.256633i	−0.705505	+	0.708705i	$0.749280\pi$
$524$	−9.45274	−	16.3726i	−0.412945	−	0.715241i
$525$	36.2291	+	26.9180i	1.58117	+	1.17480i
$526$	4.94887	+	8.57170i	0.215781	+	0.373744i
$527$	−6.38142	+	3.68431i	−0.277979	+	0.160491i
$528$		−	29.3152i		−	1.27578i
$529$	−7.87709	−	13.6435i	−0.342482	−	0.593197i
$530$	−7.08920	+	6.31489i	−0.307935	+	0.274301i
$531$	−5.38217	+	9.32219i	−0.233566	+	0.404548i
$532$		−	7.89832i		−	0.342436i
$533$		0			0
$534$	9.18722			0.397570
$535$	12.7530	+	14.3167i	0.551358	+	0.618964i
$536$	−2.58402	+	4.47565i	−0.111613	+	0.193319i
$537$	−41.9847	+	24.2399i	−1.81177	+	1.04603i
$538$		−	6.14995i		−	0.265143i
$539$	6.89055	+	11.9348i	0.296797	+	0.514067i
$540$	13.8822	−	2.87333i	0.597396	−	0.123648i
$541$	21.8080			0.937599			0.468800	−	0.883305i	$-0.344687\pi$
$541$	21.8080			0.937599			0.468800	+	0.883305i	$0.344687\pi$
$542$	−1.66887	+	0.963521i	−0.0716840	+	0.0413868i
$543$	2.43296	+	1.40467i	0.104408	+	0.0602801i
$544$	3.59001	−	6.21808i	0.153920	−	0.266598i
$545$	−18.0269	−	5.96396i	−0.772188	−	0.255468i
$546$		0			0
$547$		−	6.30924i		−	0.269764i	−0.990862	−	0.134882i	$-0.956935\pi$
$547$		−	6.30924i		−	0.269764i	0.990862	−	0.134882i	$-0.0430655\pi$
$548$	−27.5858	−	15.9266i	−1.17840	−	0.680352i
$549$	−15.9040	+	27.5465i	−0.678766	+	1.17566i
$550$	5.33345	+	0.618252i	0.227419	+	0.0263624i
$551$	3.73743			0.159220
$552$	8.07684	−	4.66317i	0.343773	−	0.198478i
$553$	−40.0230	+	23.1073i	−1.70195	+	0.982622i
$554$	−4.47964			−0.190322
$555$	−2.37747	−	11.4865i	−0.100918	−	0.487576i
$556$	−0.970706	+	1.68131i	−0.0411671	+	0.0713035i
$557$	31.0364	+	17.9189i	1.31506	+	0.759247i	0.982929	−	0.183987i	$-0.0589006\pi$
$557$	31.0364	+	17.9189i	1.31506	+	0.759247i	0.332126	+	0.943235i	$0.392234\pi$
$558$			5.31119i			0.224840i
$559$		0			0
$560$	−7.90253	+	23.8865i	−0.333943	+	1.00939i
$561$	−8.51345	+	14.7457i	−0.359438	+	0.622565i
$562$	−0.133147	−	0.0768725i	−0.00561647	−	0.00324267i
$563$	−4.33196	+	2.50106i	−0.182570	+	0.105407i	−0.588500	−	0.808497i	$-0.700281\pi$
$563$	−4.33196	+	2.50106i	−0.182570	+	0.105407i	0.405929	+	0.913904i	$0.366948\pi$
$564$	−34.9593			−1.47205
$565$	−16.0555	+	3.32315i	−0.675459	+	0.139806i
$566$	−1.66418	−	2.88244i	−0.0699507	−	0.121158i
$567$		−	12.4432i		−	0.522564i
$568$	−5.84746	+	3.37603i	−0.245354	+	0.141655i
$569$	−6.58402	+	11.4039i	−0.276017	+	0.478075i	−0.970391	−	0.241539i	$-0.922348\pi$
$569$	−6.58402	+	11.4039i	−0.276017	+	0.478075i	0.694375	+	0.719614i	$0.255681\pi$
$570$	1.85244	−	1.65011i	0.0775904	−	0.0691157i
$571$	19.8349			0.830065			0.415032	−	0.909807i	$-0.363770\pi$
$571$	19.8349			0.830065			0.415032	+	0.909807i	$0.363770\pi$
$572$		0			0
$573$		−	68.6909i		−	2.86960i
$574$	−1.54275	+	2.67212i	−0.0643930	+	0.111532i
$575$	−5.34259	−	12.3532i	−0.222801	−	0.515165i
$576$	11.6582	+	20.1926i	0.485758	+	0.841357i
$577$		−	10.9210i		−	0.454646i	−0.973819	−	0.227323i	$-0.927003\pi$
$577$		−	10.9210i		−	0.454646i	0.973819	−	0.227323i	$-0.0729972\pi$
$578$	3.78258	−	2.18388i	0.157335	−	0.0908373i
$579$	−26.6767	−	46.2054i	−1.10865	−	1.92023i
$580$	−12.0404	−	3.98339i	−0.499949	−	0.165401i
$581$	−14.4527	−	25.0329i	−0.599601	−	1.03854i
$582$	4.06139	+	2.34484i	0.168350	+	0.0971969i
$583$	36.0745	+	20.8276i	1.49406	+	0.862593i
$584$	−7.03411			−0.291073
$585$		0			0
$586$	−4.44979			−0.183819
$587$	35.0303	+	20.2247i	1.44585	+	0.834764i	0.998231	−	0.0594576i	$-0.0189371\pi$
$587$	35.0303	+	20.2247i	1.44585	+	0.834764i	0.447624	+	0.894222i	$0.352270\pi$
$588$	−18.7121	−	10.8034i	−0.771673	−	0.445526i
$589$	−2.35526	−	4.07944i	−0.0970469	−	0.168090i
$590$	0.589093	−	1.78062i	0.0242526	−	0.0733069i
$591$	−29.1414	−	50.4744i	−1.19872	−	2.07624i
$592$	5.66274	−	3.26938i	0.232737	−	0.134371i
$593$			1.47709i			0.0606569i	0.999540	+	0.0303284i	$0.00965532\pi$
$593$			1.47709i			0.0606569i	−0.999540	+	0.0303284i	$0.990345\pi$
$594$	1.80054	+	3.11862i	0.0738769	+	0.127959i
$595$	10.9119	−	9.72008i	0.447345	−	0.398484i
$596$	−14.9842	+	25.9533i	−0.613775	+	1.06309i
$597$			49.0690i			2.00826i
$598$		0			0
$599$	−2.27271			−0.0928606			−0.0464303	−	0.998922i	$-0.514785\pi$
$599$	−2.27271			−0.0928606			−0.0464303	+	0.998922i	$0.514785\pi$
$600$	−15.9003	+	6.87664i	−0.649125	+	0.280738i
$601$	−3.70215	+	6.41231i	−0.151014	+	0.261563i	−0.931600	−	0.363484i	$-0.881587\pi$
$601$	−3.70215	+	6.41231i	−0.151014	+	0.261563i	0.780587	+	0.625048i	$0.214920\pi$
$602$	8.39472	−	4.84669i	0.342143	−	0.197536i
$603$			17.0476i			0.694231i
$604$	13.7494	+	23.8147i	0.559456	+	0.969005i
$605$	0.210615	+	1.01757i	0.00856273	+	0.0413700i
$606$	5.08549			0.206584
$607$	−9.26059	+	5.34661i	−0.375876	+	0.217012i	−0.676022	−	0.736881i	$-0.736298\pi$
$607$	−9.26059	+	5.34661i	−0.375876	+	0.217012i	0.300146	+	0.953893i	$0.402964\pi$
$608$	3.97502	+	2.29498i	0.161208	+	0.0930736i
$609$	13.5404	−	23.4526i	0.548683	−	0.950347i
$610$	1.74074	−	5.26162i	0.0704804	−	0.213037i
$611$		0			0
$612$		−	15.6429i		−	0.632327i
$613$	−5.26673	−	3.04075i	−0.212721	−	0.122815i	0.389854	−	0.920877i	$-0.372525\pi$
$613$	−5.26673	−	3.04075i	−0.212721	−	0.122815i	−0.602575	+	0.798062i	$0.705859\pi$
$614$	−4.07057	+	7.05043i	−0.164275	+	0.284532i
$615$	16.3921	−	3.39283i	0.660994	−	0.136812i
$616$	−14.0101			−0.564485
$617$	−27.5732	+	15.9194i	−1.11006	+	0.640892i	−0.938844	−	0.344342i	$-0.888102\pi$
$617$	−27.5732	+	15.9194i	−1.11006	+	0.640892i	−0.171213	+	0.985234i	$0.554769\pi$
$618$	−5.68295	+	3.28106i	−0.228602	+	0.131983i
$619$	−26.4043			−1.06128			−0.530639	−	0.847598i	$-0.678048\pi$
$619$	−26.4043			−1.06128			−0.530639	+	0.847598i	$0.678048\pi$
$620$	3.23972	+	15.6524i	0.130110	+	0.628616i
$621$	4.51345	−	7.81753i	0.181119	−	0.313707i
$622$	−0.698464	−	0.403259i	−0.0280059	−	0.0161692i
$623$			34.5957i			1.38605i
$624$		0			0
$625$	7.21560	+	23.9361i	0.288624	+	0.957443i
$626$	3.19200	−	5.52871i	0.127578	−	0.220972i
$627$	−9.42647	−	5.44238i	−0.376457	−	0.217348i
$628$	−17.8805	+	10.3233i	−0.713509	+	0.411944i
$629$	−3.79785			−0.151430
$630$	−2.13487	−	10.3144i	−0.0850553	−	0.410937i
$631$	17.5840	+	30.4564i	0.700009	+	1.21245i	0.968463	+	0.249158i	$0.0801539\pi$
$631$	17.5840	+	30.4564i	0.700009	+	1.21245i	−0.268454	+	0.963293i	$0.586513\pi$
$632$		−	17.7381i		−	0.705585i
$633$	−44.9907	+	25.9754i	−1.78822	+	1.03243i
$634$	4.76764	−	8.25780i	0.189347	−	0.327959i
$635$	−13.6294	−	15.3005i	−0.540865	−	0.607184i
$636$	−65.3098			−2.58970
$637$		0			0
$638$		−	3.22150i		−	0.127540i
$639$	−11.1364	+	19.2887i	−0.440547	+	0.763051i
$640$	−13.6617	−	15.3369i	−0.540028	−	0.606244i
$641$	−2.76257	−	4.78491i	−0.109115	−	0.188993i	0.806297	−	0.591511i	$-0.201468\pi$
$641$	−2.76257	−	4.78491i	−0.109115	−	0.188993i	−0.915412	+	0.402518i	$0.868135\pi$
$642$		−	7.63594i		−	0.301367i
$643$	−27.8472	+	16.0776i	−1.09819	+	0.634039i	−0.935744	−	0.352679i	$-0.885271\pi$
$643$	−27.8472	+	16.0776i	−1.09819	+	0.634039i	−0.162444	+	0.986718i	$0.551938\pi$
$644$	8.53289	+	14.7794i	0.336243	+	0.582390i
$645$	−49.9276	−	16.5179i	−1.96590	−	0.650391i
$646$	−0.401610	−	0.695609i	−0.0158011	−	0.0273684i
$647$	11.9376	+	6.89216i	0.469314	+	0.270959i	0.715953	−	0.698149i	$-0.245993\pi$
$647$	11.9376	+	6.89216i	0.469314	+	0.270959i	−0.246638	+	0.969108i	$0.579326\pi$
$648$	4.13609	+	2.38797i	0.162481	+	0.0938085i
$649$	−8.22905			−0.323019
$650$		0			0
$651$	−34.1316			−1.33772
$652$	−6.84015	−	3.94916i	−0.267881	−	0.154661i
$653$	7.36296	+	4.25101i	0.288135	+	0.166355i	0.637100	−	0.770781i	$-0.280134\pi$
$653$	7.36296	+	4.25101i	0.288135	+	0.166355i	−0.348965	+	0.937136i	$0.613467\pi$
$654$	3.78109	+	6.54905i	0.147852	+	0.256088i
$655$	21.2291	+	7.02335i	0.829488	+	0.274425i
$656$	4.66565	+	8.08115i	0.182163	+	0.315516i
$657$	−20.0944	+	11.6015i	−0.783959	+	0.452619i
$658$			7.62150i			0.297117i
$659$	2.02183	+	3.50192i	0.0787594	+	0.136415i	0.902715	−	0.430239i	$-0.141571\pi$
$659$	2.02183	+	3.50192i	0.0787594	+	0.136415i	−0.823956	+	0.566654i	$0.808237\pi$
$660$	24.5674	+	27.5798i	0.956285	+	1.07354i
$661$	15.6364	−	27.0830i	0.608184	−	1.05341i	−0.383356	−	0.923601i	$-0.625232\pi$
$661$	15.6364	−	27.0830i	0.608184	−	1.05341i	0.991540	−	0.129805i	$-0.0414350\pi$
$662$			0.983609i			0.0382290i
$663$		0			0
$664$	11.0945			0.430551
$665$	6.21373	+	6.97563i	0.240958	+	0.270503i
$666$	−1.36872	+	2.37068i	−0.0530366	+	0.0918622i
$667$	−6.99351	+	4.03771i	−0.270790	+	0.156341i
$668$		−	6.33991i		−	0.245298i
$669$	16.6498	+	28.8383i	0.643719	+	1.11495i
$670$	−0.602029	−	2.90865i	−0.0232584	−	0.112371i
$671$	−24.3164			−0.938723
$672$	28.8022	−	16.6290i	1.11107	−	0.641477i
$673$	−27.7768	−	16.0370i	−1.07072	−	0.618179i	−0.142340	−	0.989818i	$-0.545463\pi$
$673$	−27.7768	−	16.0370i	−1.07072	−	0.618179i	−0.928377	+	0.371639i	$0.878796\pi$
$674$	0.314906	−	0.545433i	0.0121297	−	0.0210093i
$675$	−10.0000	+	13.4590i	−0.384900	+	0.518038i
$676$		0			0
$677$			14.2382i			0.547220i	0.961841	+	0.273610i	$0.0882177\pi$
$677$			14.2382i			0.547220i	−0.961841	+	0.273610i	$0.911782\pi$
$678$	5.65503	+	3.26493i	0.217180	+	0.125389i
$679$	−8.82983	+	15.2937i	−0.338858	+	0.586919i
$680$	1.13683	+	5.49249i	0.0435954	+	0.210627i
$681$	−16.5891			−0.635695
$682$	−3.51629	+	2.03013i	−0.134646	+	0.0777377i
$683$	−22.3302	+	12.8923i	−0.854440	+	0.493311i	−0.862146	−	0.506659i	$-0.830880\pi$
$683$	−22.3302	+	12.8923i	−0.854440	+	0.493311i	0.00770647	+	0.999970i	$0.497547\pi$
$684$	10.0000			0.382360
$685$	36.8929	−	7.63605i	1.40961	−	0.291759i
$686$	1.52782	−	2.64626i	0.0583325	−	0.101035i
$687$	−62.9025	−	36.3168i	−2.39988	−	1.38557i
$688$		−	29.3152i		−	1.11763i
$689$		0			0
$690$	−1.68362	+	5.08898i	−0.0640944	+	0.193734i
$691$	−0.0218318	+	0.0378138i	−0.000830522	+	0.00143851i	−0.866440	−	0.499281i	$-0.833598\pi$
$691$	−0.0218318	+	0.0378138i	−0.000830522	+	0.00143851i	0.865610	+	0.500719i	$0.166931\pi$
$692$	−14.3049	−	8.25894i	−0.543791	−	0.313958i
$693$	−40.0230	+	23.1073i	−1.52035	+	0.877774i
$694$	4.18002			0.158671
$695$	−0.465407	−	2.24857i	−0.0176539	−	0.0852931i
$696$	5.19707	+	9.00160i	0.196995	+	0.341205i
$697$		−	5.41982i		−	0.205290i
$698$	2.57091	−	1.48431i	0.0973103	−	0.0561821i
$699$	−1.10945	+	1.92163i	−0.0419634	+	0.0726827i
$700$	−12.5832	−	29.0951i	−0.475601	−	1.09969i
$701$	−14.5454			−0.549373			−0.274687	−	0.961534i	$-0.588574\pi$
$701$	−14.5454			−0.549373			−0.274687	+	0.961534i	$0.588574\pi$
$702$		0			0
$703$		−	2.42785i		−	0.0915679i
$704$	−8.91238	+	15.4367i	−0.335898	+	0.581792i
$705$	30.8753	−	27.5030i	1.16283	−	1.03582i
$706$	−5.66565	−	9.81320i	−0.213230	−	0.369325i
$707$			19.1501i			0.720214i
$708$	11.1735	−	6.45101i	0.419925	−	0.242444i
$709$	−9.81638	−	17.0025i	−0.368662	−	0.638541i	0.620695	−	0.784052i	$-0.286851\pi$
$709$	−9.81638	−	17.0025i	−0.368662	−	0.638541i	−0.989357	+	0.145511i	$0.953517\pi$
$710$	1.21891	−	3.68431i	0.0457447	−	0.138270i
$711$	−29.2560	−	50.6728i	−1.09718	−	1.90038i
$712$	−11.4996	−	6.63929i	−0.430965	−	0.248818i
$713$	8.81438	+	5.08898i	0.330101	+	0.190584i
$714$	−5.81998			−0.217807
$715$		0			0
$716$	34.0490			1.27247
$717$	9.32468	+	5.38361i	0.348237	+	0.201055i
$718$	−6.41912	−	3.70608i	−0.239559	−	0.138310i
$719$	23.7156	+	41.0766i	0.884443	+	1.53190i	0.846351	+	0.532625i	$0.178794\pi$
$719$	23.7156	+	41.0766i	0.884443	+	1.53190i	0.0380914	+	0.999274i	$0.487872\pi$
$720$	−30.2425	−	10.0053i	−1.12707	−	0.372876i
$721$	−12.3553	−	21.3999i	−0.460134	−	0.796976i
$722$	−4.99906	+	2.88621i	−0.186046	+	0.107414i
$723$			61.0872i			2.27186i
$724$	−0.986548	−	1.70875i	−0.0366648	−	0.0635052i
$725$	13.7676	−	5.95429i	0.511315	−	0.221137i
$726$	0.206926	−	0.358406i	0.00767973	−	0.0133017i
$727$			34.0951i			1.26452i	0.774757	+	0.632259i	$0.217872\pi$
$727$			34.0951i			1.26452i	−0.774757	+	0.632259i	$0.782128\pi$
$728$		0			0
$729$	42.8349			1.58648
$730$	3.01880	−	2.68908i	0.111731	−	0.0995272i
$731$	−8.51345	+	14.7457i	−0.314881	+	0.545391i
$732$	33.0170	−	19.0624i	1.22034	−	0.704565i
$733$		−	14.3920i		−	0.531580i	−0.964031	−	0.265790i	$-0.914367\pi$
$733$		−	14.3920i		−	0.531580i	0.964031	−	0.265790i	$-0.0856327\pi$
$734$	−2.18270	−	3.78055i	−0.0805651	−	0.139543i
$735$	25.0253	−	5.17972i	0.923074	−	0.191057i
$736$	−9.91745			−0.365562
$737$	−11.2864	+	6.51621i	−0.415740	+	0.240028i
$738$	−3.38314	−	1.95326i	−0.124535	−	0.0719004i
$739$	17.2240	−	29.8328i	0.633594	−	1.09742i	−0.353217	−	0.935541i	$-0.614912\pi$
$739$	17.2240	−	29.8328i	0.633594	−	1.09742i	0.986811	−	0.161876i	$-0.0517545\pi$
$740$	−2.58762	+	7.82145i	−0.0951228	+	0.287522i
$741$		0			0
$742$			14.2382i			0.522702i
$743$	−35.2589	−	20.3567i	−1.29352	−	0.746816i	−0.314246	−	0.949342i	$-0.601752\pi$
$743$	−35.2589	−	20.3567i	−1.29352	−	0.746816i	−0.979277	+	0.202526i	$0.935085\pi$
$744$	6.55021	−	11.3453i	0.240142	−	0.415939i
$745$	−7.18418	−	34.7097i	−0.263208	−	1.27167i
$746$	−5.04903			−0.184858
$747$	31.6939	−	18.2985i	1.15962	−	0.669507i
$748$	10.3564	−	5.97929i	0.378669	−	0.218625i
$749$	28.7542			1.05066
$750$	4.19498	−	9.02975i	0.153179	−	0.329720i
$751$	−16.2509	+	28.1474i	−0.593003	+	1.02711i	0.400822	+	0.916156i	$0.368725\pi$
$751$	−16.2509	+	28.1474i	−0.593003	+	1.02711i	−0.993825	+	0.110956i	$0.964609\pi$
$752$	19.9613	+	11.5247i	0.727914	+	0.420261i
$753$		−	51.2167i		−	1.86644i
$754$		0			0
$755$	−30.8786	−	10.2158i	−1.12379	−	0.371790i
$756$	10.6304	−	18.4123i	0.386623	−	0.669650i
$757$	11.2864	+	6.51621i	0.410211	+	0.236836i	0.690881	−	0.722969i	$-0.257223\pi$
$757$	11.2864	+	6.51621i	0.410211	+	0.236836i	−0.280669	+	0.959805i	$0.590556\pi$
$758$	5.22286	−	3.01542i	0.189703	−	0.109525i
$759$	23.5185			0.853668
$760$	−3.51117	+	0.726739i	−0.127364	+	0.0263616i
$761$	−1.99493	−	3.45532i	−0.0723161	−	0.125255i	0.827600	−	0.561318i	$-0.189706\pi$
$761$	−1.99493	−	3.45532i	−0.0723161	−	0.125255i	−0.899916	+	0.436063i	$0.856372\pi$
$762$			8.16070i			0.295631i
$763$	−24.6613	+	14.2382i	−0.892800	+	0.515458i
$764$	−24.1220	+	41.7805i	−0.872703	+	1.51157i
$765$	12.3065	+	13.8155i	0.444943	+	0.499500i
$766$	−0.476696			−0.0172237
$767$		0			0
$768$		−	21.3847i		−	0.771652i
$769$	−3.33343	+	5.77367i	−0.120207	+	0.208204i	−0.919849	−	0.392272i	$-0.871689\pi$
$769$	−3.33343	+	5.77367i	−0.120207	+	0.208204i	0.799642	+	0.600476i	$0.205022\pi$
$770$	6.01268	−	5.35596i	0.216682	−	0.193015i
$771$	−2.84181	−	4.92216i	−0.102345	−	0.177267i
$772$			37.4720i			1.34865i
$773$	41.8593	−	24.1675i	1.50557	−	0.869244i	0.505595	−	0.862771i	$-0.331273\pi$
$773$	41.8593	−	24.1675i	1.50557	−	0.869244i	0.999979	−	0.00647254i	$-0.00206029\pi$
$774$	6.13636	+	10.6285i	0.220567	+	0.382033i
$775$	−15.1752	−	11.2751i	−0.545111	−	0.405015i
$776$	−3.38907	−	5.87005i	−0.121661	−	0.210723i
$777$	−15.2349	−	8.79585i	−0.546548	−	0.315549i
$778$	−5.38393	−	3.10841i	−0.193023	−	0.111442i
$779$	3.46472			0.124136
$780$		0			0
$781$	−17.0269			−0.609271
$782$	1.50299	+	0.867753i	0.0537469	+	0.0310308i
$783$	8.71259	+	5.03022i	0.311363	+	0.179765i
$784$	7.12291	+	12.3372i	0.254389	+	0.440615i
$785$	7.67017	−	23.1842i	0.273760	−	0.827478i
$786$	−4.45274	−	7.71236i	−0.158824	−	0.275091i
$787$	24.2151	−	13.9806i	0.863176	−	0.498355i	−0.00189876	−	0.999998i	$-0.500604\pi$
$787$	24.2151	−	13.9806i	0.863176	−	0.498355i	0.865074	+	0.501643i	$0.167271\pi$
$788$			40.9341i			1.45822i
$789$	−40.2658	−	69.7424i	−1.43350	−	2.48290i
$790$	6.78113	+	7.61261i	0.241262	+	0.270845i
$791$	−12.2945	+	21.2948i	−0.437144	+	0.757155i
$792$		−	17.7381i		−	0.630297i
$793$		0			0
$794$	−5.65488			−0.200684
$795$	57.6802	−	51.3802i	2.04571	−	1.82227i
$796$	17.2314	−	29.8457i	0.610752	−	1.05785i
$797$	32.2529	−	18.6212i	1.14246	−	0.659597i	0.195418	−	0.980720i	$-0.437393\pi$
$797$	32.2529	−	18.6212i	1.14246	−	0.659597i	0.947038	+	0.321123i	$0.104060\pi$
$798$		−	3.72052i		−	0.131705i
$799$	−6.69377	−	11.5939i	−0.236808	−	0.410164i
$800$	18.2990	+	2.12122i	0.646969	+	0.0749965i
$801$	−43.8014			−1.54765
$802$	−6.36120	+	3.67264i	−0.224622	+	0.129685i
$803$	−15.3617	−	8.86907i	−0.542102	−	0.312983i
$804$	10.2165	−	17.6955i	0.360309	−	0.624073i
$805$	−19.1633	−	6.33991i	−0.675416	−	0.223452i
$806$		0			0
$807$			50.0382i			1.76143i
$808$	−6.36548	−	3.67511i	−0.223937	−	0.129290i
$809$	7.26434	−	12.5822i	0.255400	−	0.442367i	−0.709604	−	0.704601i	$-0.751126\pi$
$809$	7.26434	−	12.5822i	0.255400	−	0.442367i	0.965004	+	0.262234i	$0.0844594\pi$
$810$	−2.68797	+	0.556354i	−0.0944458	+	0.0195483i
$811$	−44.0538			−1.54694			−0.773469	−	0.633834i	$-0.781480\pi$
$811$	−44.0538			−1.54694			−0.773469	+	0.633834i	$0.781480\pi$
$812$	−16.4716	+	9.50986i	−0.578039	+	0.333731i
$813$	13.5785	−	7.83955i	0.476219	−	0.274945i
$814$	−2.09269			−0.0733489
$815$	9.14794	−	1.89343i	0.320438	−	0.0663240i
$816$	−8.80054	+	15.2430i	−0.308080	+	0.533611i
$817$	−9.42647	−	5.44238i	−0.329790	−	0.190405i
$818$		−	3.18687i		−	0.111426i
$819$		0			0
$820$	−11.1618	−	3.69273i	−0.389787	−	0.128956i
$821$	13.5135	−	23.4060i	0.471623	−	0.816875i	−0.527850	−	0.849337i	$-0.677002\pi$
$821$	13.5135	−	23.4060i	0.471623	−	0.816875i	0.999473	+	0.0324629i	$0.0103351\pi$
$822$	−12.9943	−	7.50229i	−0.453230	−	0.261672i
$823$	34.2914	−	19.7981i	1.19532	−	0.690120i	0.235814	−	0.971798i	$-0.424225\pi$
$823$	34.2914	−	19.7981i	1.19532	−	0.690120i	0.959509	+	0.281679i	$0.0908912\pi$
$824$	9.48442			0.330405
$825$	−43.3948	−	5.03032i	−1.51081	−	0.175133i
$826$	−1.40639	−	2.43594i	−0.0489345	−	0.0847571i
$827$			26.5639i			0.923716i	0.886954	+	0.461858i	$0.152817\pi$
$827$			26.5639i			0.923716i	−0.886954	+	0.461858i	$0.847183\pi$
$828$	−18.7121	+	10.8034i	−0.650290	+	0.375445i
$829$	6.99162	−	12.1098i	0.242829	−	0.420592i	−0.718690	−	0.695331i	$-0.755258\pi$
$829$	6.99162	−	12.1098i	0.242829	−	0.420592i	0.961519	+	0.274738i	$0.0885913\pi$
$830$	−4.76140	+	4.24134i	−0.165271	+	0.147219i
$831$	36.4480			1.26437
$832$		0			0
$833$		−	8.27427i		−	0.286686i
$834$	−0.457254	+	0.791986i	−0.0158334	+	0.0274242i
$835$	4.98770	+	5.59927i	0.172607	+	0.193771i
$836$	3.82237	+	6.62054i	0.132199	+	0.228976i
$837$		−	12.6798i		−	0.438278i
$838$	0.560515	−	0.323614i	0.0193627	−	0.0111791i
$839$	−7.19707	−	12.4657i	−0.248471	−	0.430364i	0.714631	−	0.699502i	$-0.246595\pi$
$839$	−7.19707	−	12.4657i	−0.248471	−	0.430364i	−0.963102	+	0.269138i	$0.913261\pi$
$840$	−8.16032	+	24.6657i	−0.281558	+	0.851048i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−3.46128	−	1.99837i	−0.119284	−	0.0688684i
$843$	1.08333	+	0.625462i	0.0373119	+	0.0215421i
$844$	36.4868			1.25593
$845$		0			0
$846$	−9.64952			−0.331757
$847$	1.34963	+	0.779207i	0.0463737	+	0.0267739i
$848$	37.2910	+	21.5300i	1.28058	+	0.739343i
$849$	13.5404	+	23.4526i	0.464704	+	0.804891i
$850$	−2.58762	−	1.92259i	−0.0887547	−	0.0659444i
$851$	2.62291	+	4.54300i	0.0899120	+	0.155732i
$852$	23.1193	−	13.3479i	0.792053	−	0.457292i
$853$		−	27.2633i		−	0.933478i	−0.884395	−	0.466739i	$-0.845429\pi$
$853$		−	27.2633i		−	0.933478i	0.884395	−	0.466739i	$-0.154571\pi$
$854$	−4.15580	−	7.19806i	−0.142209	−	0.246312i
$855$	−8.83179	+	7.86715i	−0.302041	+	0.269051i
$856$	−5.51823	+	9.55786i	−0.188609	+	0.326681i
$857$		−	50.6201i		−	1.72915i	−0.502503	−	0.864575i	$-0.667587\pi$
$857$		−	50.6201i		−	1.72915i	0.502503	−	0.864575i	$-0.332413\pi$
$858$		0			0
$859$	−1.27992			−0.0436702			−0.0218351	−	0.999762i	$-0.506951\pi$
$859$	−1.27992			−0.0436702			−0.0218351	+	0.999762i	$0.506951\pi$
$860$	24.5674	+	27.5798i	0.837742	+	0.940462i
$861$	12.5523	−	21.7413i	0.427782	−	0.740941i
$862$	−7.04509	+	4.06749i	−0.239957	+	0.138539i
$863$			8.38448i			0.285411i	0.989765	+	0.142706i	$0.0455802\pi$
$863$			8.38448i			0.285411i	−0.989765	+	0.142706i	$0.954420\pi$
$864$	6.17763	+	10.7000i	0.210167	+	0.364020i
$865$	19.1312	−	3.95976i	0.650481	−	0.134636i
$866$	−11.9342			−0.405541
$867$	−30.7765	+	17.7688i	−1.04522	+	0.603460i
$868$	20.7602	+	11.9859i	0.704646	+	0.406828i
$869$	22.3654	−	38.7380i	0.758695	−	1.31410i
$870$	−5.67164	−	1.87639i	−0.192287	−	0.0636155i
$871$		0			0
$872$		−	10.9299i		−	0.370132i
$873$	−19.3632	−	11.1794i	−0.655347	−	0.378365i
$874$	−0.554726	+	0.960814i	−0.0187639	+	0.0325000i
$875$	34.0028	+	15.7968i	1.14950	+	0.534028i
$876$	27.8109			0.939645
$877$	48.3989	−	27.9431i	1.63431	−	0.943572i	0.651573	−	0.758586i	$-0.274110\pi$
$877$	48.3989	−	27.9431i	1.63431	−	0.943572i	0.982741	−	0.184985i	$-0.0592237\pi$
$878$	−0.726391	+	0.419382i	−0.0245145	+	0.0141535i
$879$	36.2051			1.22117
$880$	−4.93574	−	23.8466i	−0.166384	−	0.803867i
$881$	−12.5975	+	21.8195i	−0.424420	+	0.735116i	−0.996366	−	0.0851746i	$-0.972855\pi$
$881$	−12.5975	+	21.8195i	−0.424420	+	0.735116i	0.571946	+	0.820291i	$0.306189\pi$
$882$	−5.16494	−	2.98198i	−0.173913	−	0.100408i
$883$			30.7868i			1.03606i	0.855363	+	0.518029i	$0.173334\pi$
$883$			30.7868i			1.03606i	−0.855363	+	0.518029i	$0.826666\pi$
$884$		0			0
$885$	−4.79307	+	14.4877i	−0.161117	+	0.487000i
$886$	3.20215	−	5.54628i	0.107578	−	0.186331i
$887$	10.8011	+	6.23603i	0.362666	+	0.209385i	0.670250	−	0.742136i	$-0.266187\pi$
$887$	10.8011	+	6.23603i	0.362666	+	0.209385i	−0.307584	+	0.951521i	$0.599520\pi$
$888$	5.84746	−	3.37603i	0.196228	−	0.113292i
$889$	−30.7302			−1.03066
$890$	7.47338	−	1.54683i	0.250508	−	0.0518499i
$891$	6.02183	+	10.4301i	0.201739	+	0.349422i
$892$		−	23.3875i		−	0.783071i
$893$	7.41163	−	4.27911i	0.248021	−	0.143195i
$894$	−7.05833	+	12.2254i	−0.236066	+	0.408878i
$895$	−30.0714	+	26.7869i	−1.00518	+	0.895387i
$896$	−30.8032			−1.02906
$897$		0			0
$898$		−	8.20739i		−	0.273884i
$899$	−5.67164	+	9.82357i	−0.189160	+	0.327634i
$900$	36.8370	−	15.9315i	1.22790	−	0.531050i
$901$	−12.5051	−	21.6594i	−0.416604	−	0.721580i
$902$		−	2.98643i		−	0.0994372i
$903$	−68.3024	+	39.4344i	−2.27296	+	1.31230i
$904$	−4.71891	−	8.17338i	−0.156948	−	0.271843i
$905$	2.21560	+	0.733001i	0.0736490	+	0.0243658i
$906$	6.47670	+	11.2180i	0.215174	+	0.372692i
$907$	33.6807	+	19.4455i	1.11835	+	0.645678i	0.940979	−	0.338466i	$-0.109908\pi$
$907$	33.6807	+	19.4455i	1.11835	+	0.645678i	0.177369	+	0.984144i	$0.443241\pi$
$908$	10.0901	+	5.82555i	0.334853	+	0.193328i
$909$	−24.2458			−0.804183
$910$		0			0
$911$	0.165096			0.00546989			0.00273494	−	0.999996i	$-0.499129\pi$
$911$	0.165096			0.00546989			0.00273494	+	0.999996i	$0.499129\pi$
$912$	−9.74434	−	5.62590i	−0.322667	−	0.186292i
$913$	24.2292	+	13.9887i	0.801868	+	0.462959i
$914$	−1.25180	−	2.16818i	−0.0414059	−	0.0717171i
$915$	−14.1633	+	42.8105i	−0.468223	+	1.41527i
$916$	25.5065	+	44.1786i	0.842760	+	1.45970i
$917$	29.0420	−	16.7674i	0.959050	−	0.553708i
$918$		−	2.16211i		−	0.0713603i
$919$	0.447663	+	0.775375i	0.0147670	+	0.0255773i	0.873314	−	0.487157i	$-0.161966\pi$
$919$	0.447663	+	0.775375i	0.0147670	+	0.0255773i	−0.858547	+	0.512734i	$0.828633\pi$
$920$	5.78501	−	5.15315i	0.190726	−	0.169894i
$921$	33.1196	−	57.3648i	1.09133	−	1.89024i
$922$			4.08361i			0.134486i
$923$		0			0
$924$	55.3923			1.82227
$925$	−3.86792	−	8.94346i	−0.127176	−	0.294059i
$926$	3.78109	−	6.54905i	0.124254	−	0.215215i
$927$	27.0943	−	15.6429i	0.889893	−	0.513780i
$928$		−	11.0529i		−	0.362831i
$929$	6.14474	+	10.6430i	0.201602	+	0.349185i	0.949045	−	0.315141i	$-0.102052\pi$
$929$	6.14474	+	10.6430i	0.201602	+	0.349185i	−0.747443	+	0.664326i	$0.768718\pi$
$930$	1.52608	+	7.37311i	0.0500421	+	0.241774i
$931$	5.28947			0.173356
$932$	1.34963	−	0.779207i	0.0442085	−	0.0255238i
$933$	5.68295	+	3.28106i	0.186052	+	0.107417i
$934$	−2.53051	+	4.38296i	−0.0828007	+	0.143415i
$935$	−4.44259	+	13.4284i	−0.145288	+	0.439154i
$936$		0			0
$937$		−	5.77242i		−	0.188577i	−0.995545	−	0.0942884i	$-0.969942\pi$
$937$		−	5.77242i		−	0.188577i	0.995545	−	0.0942884i	$-0.0300576\pi$
$938$	−3.85781	−	2.22731i	−0.125962	−	0.0727242i
$939$	−25.9713	+	44.9835i	−0.847540	+	1.46798i
$940$	−28.4377	+	5.88601i	−0.927537	+	0.191981i
$941$	55.8887			1.82192			0.910960	−	0.412495i	$-0.135342\pi$
$941$	55.8887			1.82192			0.910960	+	0.412495i	$0.135342\pi$
$942$	−8.42264	+	4.86282i	−0.274425	+	0.158439i
$943$	−6.48321	+	3.74308i	−0.211122	+	0.121891i
$944$	−8.50655			−0.276864
$945$	5.09675	+	24.6245i	0.165797	+	0.801034i
$946$	−4.69108	+	8.12520i	−0.152520	+	0.264173i
$947$	−1.64231	−	0.948188i	−0.0533679	−	0.0308120i	0.473079	−	0.881020i	$-0.343143\pi$
$947$	−1.64231	−	0.948188i	−0.0533679	−	0.0308120i	−0.526447	+	0.850208i	$0.676476\pi$
$948$			70.1318i			2.27777i
$949$		0			0
$950$	1.22905	−	1.65418i	0.0398757	−	0.0536688i
$951$	−38.7912	+	67.1884i	−1.25789	+	2.17873i
$952$	7.28483	+	4.20590i	0.236103	+	0.136314i
$953$	−29.1438	+	16.8262i	−0.944059	+	0.545053i	−0.891230	−	0.453551i	$-0.850157\pi$
$953$	−29.1438	+	16.8262i	−0.944059	+	0.545053i	−0.0528285	+	0.998604i	$0.516824\pi$
$954$	−18.0269			−0.583643
$955$	−11.5653	−	55.8768i	−0.374245	−	1.80813i
$956$	−3.78109	−	6.54905i	−0.122289	−	0.211811i
$957$			26.2113i			0.847290i
$958$	6.95735	−	4.01683i	0.224782	−	0.129778i
$959$	28.2509	−	48.9320i	0.912269	−	1.58010i
$960$	21.9861	+	24.6820i	0.709600	+	0.796608i
$961$	−16.7033			−0.538817
$962$		0			0
$963$			36.4054i			1.17315i
$964$	21.4518	−	37.1556i	0.690917	−	1.19670i
$965$	−29.4798	−	33.0945i	−0.948987	−	1.06535i
$966$	4.01944	+	6.96188i	0.129323	+	0.223995i
$967$			23.0493i			0.741216i	0.928789	+	0.370608i	$0.120851\pi$
$967$			23.0493i			0.741216i	−0.928789	+	0.370608i	$0.879149\pi$
$968$	−0.518015	+	0.299076i	−0.0166496	+	0.00961267i
$969$	3.26764	+	5.65972i	0.104972	+	0.181816i
$970$	3.69855	+	1.22361i	0.118753	+	0.0392879i
$971$	−7.45964	−	12.9205i	−0.239391	−	0.414638i	0.721148	−	0.692781i	$-0.243615\pi$
$971$	−7.45964	−	12.9205i	−0.239391	−	0.414638i	−0.960540	+	0.278143i	$0.910281\pi$
$972$	−32.8246	−	18.9513i	−1.05285	−	0.607862i
$973$	−2.98233	−	1.72185i	−0.0956092	−	0.0552000i
$974$	12.2040			0.391041
$975$		0			0
$976$	−25.1364			−0.804595
$977$	−20.2339	−	11.6821i	−0.647341	−	0.373742i	0.140096	−	0.990138i	$-0.455259\pi$
$977$	−20.2339	−	11.6821i	−0.647341	−	0.373742i	−0.787437	+	0.616396i	$0.788592\pi$
$978$	−3.22207	−	1.86026i	−0.103030	−	0.0594846i
$979$	−16.7425	−	28.9989i	−0.535093	−	0.926808i
$980$	−17.0404	−	5.63757i	−0.544334	−	0.180086i
$981$	−18.0269	−	31.2235i	−0.575555	−	0.996890i
$982$	−10.1292	+	5.84810i	−0.323236	+	0.186620i
$983$			5.31119i			0.169401i	0.996406	+	0.0847003i	$0.0269933\pi$
$983$			5.31119i			0.169401i	−0.996406	+	0.0847003i	$0.973007\pi$
$984$	4.81785	+	8.34476i	0.153587	+	0.266021i
$985$	−32.2035	−	36.1521i	−1.02609	−	1.15190i
$986$	−0.967105	+	1.67508i	−0.0307989	+	0.0533453i
$987$		−	62.0112i		−	1.97384i
$988$		0			0
$989$	23.5185			0.747846
$990$	6.78113	+	7.61261i	0.215519	+	0.241945i
$991$	12.0440	−	20.8607i	0.382589	−	0.662663i	−0.608843	−	0.793291i	$-0.708366\pi$
$991$	12.0440	−	20.8607i	0.382589	−	0.662663i	0.991432	+	0.130628i	$0.0416992\pi$
$992$	−12.0644	+	6.96537i	−0.383044	+	0.221151i
$993$		−	8.00299i		−	0.253967i
$994$	−2.90999	−	5.04025i	−0.0922993	−	0.159867i
$995$	8.26164	+	39.9154i	0.261912	+	1.26540i
$996$	−43.8648			−1.38991
$997$	17.6755	−	10.2050i	0.559790	−	0.323195i	−0.193271	−	0.981145i	$-0.561910\pi$
$997$	17.6755	−	10.2050i	0.559790	−	0.323195i	0.753061	+	0.657951i	$0.228576\pi$
$998$	−4.64692	−	2.68290i	−0.147096	−	0.0849258i
$999$	3.26764	−	5.65972i	0.103384	−	0.179066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.e.529.3		12
5.4	even	2	inner	845.2.n.e.529.4		12
13.2	odd	12		845.2.l.f.699.5		24
13.3	even	3	inner	845.2.n.e.484.4		12
13.4	even	6		845.2.b.d.339.3		6
13.5	odd	4		845.2.l.f.654.6		24
13.6	odd	12		845.2.d.d.844.7		12
13.7	odd	12		845.2.d.d.844.5		12
13.8	odd	4		845.2.l.f.654.8		24
13.9	even	3		845.2.b.e.339.4		6
13.10	even	6		65.2.n.a.29.3	yes	12
13.11	odd	12		845.2.l.f.699.7		24
13.12	even	2		65.2.n.a.9.4	yes	12
39.23	odd	6		585.2.bs.a.289.4		12
39.38	odd	2		585.2.bs.a.334.3		12
52.23	odd	6		1040.2.dh.a.289.6		12
52.51	odd	2		1040.2.dh.a.529.1		12
65.4	even	6		845.2.b.d.339.4		6
65.9	even	6		845.2.b.e.339.3		6
65.12	odd	4		325.2.e.e.126.3		12
65.17	odd	12		4225.2.a.br.1.4		6
65.19	odd	12		845.2.d.d.844.6		12
65.22	odd	12		4225.2.a.bq.1.3		6
65.23	odd	12		325.2.e.e.276.4		12
65.24	odd	12		845.2.l.f.699.6		24
65.29	even	6	inner	845.2.n.e.484.3		12
65.34	odd	4		845.2.l.f.654.5		24
65.38	odd	4		325.2.e.e.126.4		12
65.43	odd	12		4225.2.a.br.1.3		6
65.44	odd	4		845.2.l.f.654.7		24
65.48	odd	12		4225.2.a.bq.1.4		6
65.49	even	6		65.2.n.a.29.4	yes	12
65.54	odd	12		845.2.l.f.699.8		24
65.59	odd	12		845.2.d.d.844.8		12
65.62	odd	12		325.2.e.e.276.3		12
65.64	even	2		65.2.n.a.9.3	✓	12
195.179	odd	6		585.2.bs.a.289.3		12
195.194	odd	2		585.2.bs.a.334.4		12
260.179	odd	6		1040.2.dh.a.289.1		12
260.259	odd	2		1040.2.dh.a.529.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.3	✓	12	65.64	even	2
65.2.n.a.9.4	yes	12	13.12	even	2
65.2.n.a.29.3	yes	12	13.10	even	6
65.2.n.a.29.4	yes	12	65.49	even	6
325.2.e.e.126.3		12	65.12	odd	4
325.2.e.e.126.4		12	65.38	odd	4
325.2.e.e.276.3		12	65.62	odd	12
325.2.e.e.276.4		12	65.23	odd	12
585.2.bs.a.289.3		12	195.179	odd	6
585.2.bs.a.289.4		12	39.23	odd	6
585.2.bs.a.334.3		12	39.38	odd	2
585.2.bs.a.334.4		12	195.194	odd	2
845.2.b.d.339.3		6	13.4	even	6
845.2.b.d.339.4		6	65.4	even	6
845.2.b.e.339.3		6	65.9	even	6
845.2.b.e.339.4		6	13.9	even	3
845.2.d.d.844.5		12	13.7	odd	12
845.2.d.d.844.6		12	65.19	odd	12
845.2.d.d.844.7		12	13.6	odd	12
845.2.d.d.844.8		12	65.59	odd	12
845.2.l.f.654.5		24	65.34	odd	4
845.2.l.f.654.6		24	13.5	odd	4
845.2.l.f.654.7		24	65.44	odd	4
845.2.l.f.654.8		24	13.8	odd	4
845.2.l.f.699.5		24	13.2	odd	12
845.2.l.f.699.6		24	65.24	odd	12
845.2.l.f.699.7		24	13.11	odd	12
845.2.l.f.699.8		24	65.54	odd	12
845.2.n.e.484.3		12	65.29	even	6	inner
845.2.n.e.484.4		12	13.3	even	3	inner
845.2.n.e.529.3		12	1.1	even	1	trivial
845.2.n.e.529.4		12	5.4	even	2	inner
1040.2.dh.a.289.1		12	260.179	odd	6
1040.2.dh.a.289.6		12	52.23	odd	6
1040.2.dh.a.529.1		12	52.51	odd	2
1040.2.dh.a.529.6		12	260.259	odd	2
4225.2.a.bq.1.3		6	65.22	odd	12
4225.2.a.bq.1.4		6	65.48	odd	12
4225.2.a.br.1.3		6	65.43	odd	12
4225.2.a.br.1.4		6	65.17	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)

\(f(q)\)	\(=\)	\(q+(-0.286513 - 0.165418i) q^{2} +(2.33117 + 1.34590i) q^{3} +(-0.945274 - 1.63726i) q^{4} +(2.12291 + 0.702335i) q^{5} +(-0.445274 - 0.771236i) q^{6} +(2.90420 - 1.67674i) q^{7} +1.28714i q^{8} +(2.12291 + 3.67698i) q^{9} +O(q^{10})\)	\(q+(-0.286513 - 0.165418i) q^{2} +(2.33117 + 1.34590i) q^{3} +(-0.945274 - 1.63726i) q^{4} +(2.12291 + 0.702335i) q^{5} +(-0.445274 - 0.771236i) q^{6} +(2.90420 - 1.67674i) q^{7} +1.28714i q^{8} +(2.12291 + 3.67698i) q^{9} +(-0.492061 - 0.552395i) q^{10} +(-1.62291 + 2.81095i) q^{11} -5.08898i q^{12} -1.10945 q^{14} +(4.00358 + 4.49448i) q^{15} +(-1.67763 + 2.90574i) q^{16} +(1.68772 - 0.974404i) q^{17} -1.40467i q^{18} +(0.622905 + 1.07890i) q^{19} +(-0.856821 - 4.13965i) q^{20} +9.02690 q^{21} +(0.929966 - 0.536916i) q^{22} +(-2.33117 - 1.34590i) q^{23} +(-1.73236 + 3.00053i) q^{24} +(4.01345 + 2.98198i) q^{25} +3.35348i q^{27} +(-5.49052 - 3.16995i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.403608 - 1.94999i) q^{30} -3.78109 q^{31} +(3.19071 - 1.84216i) q^{32} +(-7.56654 + 4.36854i) q^{33} -0.644737 q^{34} +(7.34297 - 1.51984i) q^{35} +(4.01345 - 6.95150i) q^{36} +(-1.68772 - 0.974404i) q^{37} -0.412160i q^{38} +(-0.904000 + 2.73247i) q^{40} +(1.39055 - 2.40850i) q^{41} +(-2.58632 - 1.49321i) q^{42} +(-7.56654 + 4.36854i) q^{43} +6.13636 q^{44} +(1.92426 + 9.29687i) q^{45} +(0.445274 + 0.771236i) q^{46} -6.86960i q^{47} +(-7.82169 + 4.51586i) q^{48} +(2.12291 - 3.67698i) q^{49} +(-0.656632 - 1.51827i) q^{50} +5.24581 q^{51} -12.8336i q^{53} +(0.554726 - 0.960814i) q^{54} +(-5.41950 + 4.82757i) q^{55} +(2.15819 + 3.73809i) q^{56} +3.35348i q^{57} +(-0.859539 + 0.496255i) q^{58} +(1.26764 + 2.19562i) q^{59} +(3.57417 - 10.8034i) q^{60} +(3.74581 + 6.48793i) q^{61} +(1.08333 + 0.625462i) q^{62} +(12.3307 + 7.11911i) q^{63} +5.49162 q^{64} +2.89055 q^{66} +(3.47722 + 2.00758i) q^{67} +(-3.19071 - 1.84216i) q^{68} +(-3.62291 - 6.27506i) q^{69} +(-2.35526 - 0.779207i) q^{70} +(2.62291 + 4.54300i) q^{71} +(-4.73277 + 2.73247i) q^{72} +5.46493i q^{73} +(0.322368 + 0.558359i) q^{74} +(5.34259 + 12.3532i) q^{75} +(1.17763 - 2.03972i) q^{76} +10.8848i q^{77} -13.7811 q^{79} +(-5.60226 + 4.99036i) q^{80} +(1.85526 - 3.21341i) q^{81} +(-0.796819 + 0.460044i) q^{82} -8.61955i q^{83} +(-8.53289 - 14.7794i) q^{84} +(4.26722 - 0.883225i) q^{85} +2.89055 q^{86} +(6.99351 - 4.03771i) q^{87} +(-3.61808 - 2.08890i) q^{88} +(-5.15819 + 8.93425i) q^{89} +(0.986548 - 2.98198i) q^{90} +5.08898i q^{92} +(-8.81438 - 5.08898i) q^{93} +(-1.13636 + 1.96823i) q^{94} +(0.564617 + 2.72790i) q^{95} +9.91745 q^{96} +(-4.56055 + 2.63304i) q^{97} +(-1.21648 + 0.702335i) q^{98} -13.7811 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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