LMFDB - Embedded newform 1183.2.e.g.170.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1183,2,Mod(170,1183)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1183.170"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1183, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.5
Root			$-1.02197 - 1.77010i$ of defining polynomial
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.g.508.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.777343 - 1.34640i) q^{2} +(0.244626 + 0.423704i) q^{3} +(-0.208526 - 0.361177i) q^{4} +(-0.595756 + 1.03188i) q^{5} +0.760633 q^{6} +(-2.10390 - 1.60425i) q^{7} +2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +(0.926214 + 1.60425i) q^{10} +(1.05807 + 1.83263i) q^{11} +(0.102021 - 0.176706i) q^{12} +(-3.79541 + 1.58563i) q^{14} -0.582949 q^{15} +(2.33009 - 4.03583i) q^{16} +(0.453151 + 0.784881i) q^{17} +(-2.14596 - 3.71691i) q^{18} +(3.34514 - 5.79395i) q^{19} +0.496921 q^{20} +(0.165059 - 1.28387i) q^{21} +3.28993 q^{22} +(-1.79866 + 3.11538i) q^{23} +(0.602021 + 1.04273i) q^{24} +(1.79015 + 3.10063i) q^{25} +2.81840 q^{27} +(-0.140701 + 1.09441i) q^{28} +8.51545 q^{29} +(-0.453151 + 0.784881i) q^{30} +(-2.64390 - 4.57937i) q^{31} +(-1.16156 - 2.01189i) q^{32} +(-0.517662 + 0.896617i) q^{33} +1.40902 q^{34} +(2.90880 - 1.21523i) q^{35} -1.15133 q^{36} +(2.49579 - 4.32284i) q^{37} +(-5.20065 - 9.00778i) q^{38} +(-1.46615 + 2.53944i) q^{40} -1.53636 q^{41} +(-1.60029 - 1.22024i) q^{42} +5.43273 q^{43} +(0.441269 - 0.764301i) q^{44} +(1.64466 + 2.84864i) q^{45} +(2.79636 + 4.84344i) q^{46} +(-1.59337 + 2.75979i) q^{47} +2.28000 q^{48} +(1.85277 + 6.75035i) q^{49} +5.56625 q^{50} +(-0.221705 + 0.384004i) q^{51} +(1.41239 + 2.44632i) q^{53} +(2.19086 - 3.79469i) q^{54} -2.52140 q^{55} +(-5.17767 - 3.94804i) q^{56} +3.27323 q^{57} +(6.61943 - 11.4652i) q^{58} +(-5.12298 - 8.87327i) q^{59} +(0.121560 + 0.210548i) q^{60} +(4.13423 - 7.16069i) q^{61} -8.22088 q^{62} +(-6.73945 + 2.81558i) q^{63} +5.70861 q^{64} +(0.804802 + 1.39396i) q^{66} +(-1.87182 - 3.24208i) q^{67} +(0.188987 - 0.327336i) q^{68} -1.76000 q^{69} +(0.624956 - 4.86105i) q^{70} +2.53020 q^{71} +(3.39694 - 5.88368i) q^{72} +(-2.86522 - 4.96271i) q^{73} +(-3.88018 - 6.72066i) q^{74} +(-0.875834 + 1.51699i) q^{75} -2.79019 q^{76} +(0.713925 - 5.55307i) q^{77} +(-3.03620 + 5.25885i) q^{79} +(2.77632 + 4.80873i) q^{80} +(-3.45150 - 5.97817i) q^{81} +(-1.19428 + 2.06856i) q^{82} +11.6309 q^{83} +(-0.498124 + 0.208104i) q^{84} -1.07987 q^{85} +(4.22310 - 7.31462i) q^{86} +(2.08310 + 3.60803i) q^{87} +(2.60390 + 4.51008i) q^{88} +(-8.87557 + 15.3729i) q^{89} +5.11387 q^{90} +1.50027 q^{92} +(1.29353 - 2.24046i) q^{93} +(2.47719 + 4.29061i) q^{94} +(3.98577 + 6.90356i) q^{95} +(0.568297 - 0.984319i) q^{96} -6.20434 q^{97} +(10.5289 + 2.75277i) q^{98} +5.84188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21}+ \cdots + 20 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 5 * q^12 - 2 * q^14 - 4 * q^15 + 8 * q^16 + 5 * q^17 - 3 * q^18 + q^19 - 2 * q^20 + 9 * q^21 + 10 * q^22 - q^23 + 11 * q^24 + 7 * q^25 - 8 * q^27 - 8 * q^28 - 6 * q^29 - 5 * q^30 - 16 * q^31 - 8 * q^32 - 16 * q^33 - 32 * q^34 - 28 * q^35 + 42 * q^36 + 13 * q^37 - 17 * q^38 - 5 * q^40 - 16 * q^41 - 52 * q^42 + 22 * q^43 - 21 * q^44 + 7 * q^45 - 16 * q^46 + q^47 - 42 * q^48 + 6 * q^49 + 12 * q^50 - 20 * q^51 - 2 * q^53 + 18 * q^54 - 18 * q^55 + 9 * q^56 - 42 * q^57 + 8 * q^58 - 13 * q^59 - 20 * q^60 - 5 * q^61 - 10 * q^62 - 8 * q^63 - 30 * q^64 + 18 * q^66 + 11 * q^67 + 29 * q^68 - 46 * q^69 + 39 * q^70 + 12 * q^71 - 25 * q^72 + 30 * q^73 - 3 * q^74 - 3 * q^75 - 18 * q^76 + 11 * q^77 + 7 * q^79 + 7 * q^80 - 6 * q^81 + q^82 + 54 * q^83 - 41 * q^84 - 2 * q^85 + 7 * q^86 + 16 * q^87 - 4 * q^89 - 16 * q^90 + 54 * q^92 + 7 * q^93 + 45 * q^94 - 6 * q^95 - 19 * q^96 - 70 * q^97 + 82 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.777343	−	1.34640i	0.549665	−	0.952047i	−0.448632	−	0.893716i	$-0.648089\pi$
$2$	0.777343	−	1.34640i	0.549665	−	0.952047i	0.998297	−	0.0583310i	$-0.0185779\pi$
$3$	0.244626	+	0.423704i	0.141235	+	0.244626i	0.927962	−	0.372675i	$-0.121559\pi$
$3$	0.244626	+	0.423704i	0.141235	+	0.244626i	−0.786727	+	0.617301i	$0.788226\pi$
$4$	−0.208526	−	0.361177i	−0.104263	−	0.180588i
$5$	−0.595756	+	1.03188i	−0.266430	+	0.461470i	−0.967937	−	0.251192i	$-0.919177\pi$
$5$	−0.595756	+	1.03188i	−0.266430	+	0.461470i	0.701507	+	0.712662i	$0.252511\pi$
$6$	0.760633			0.310527
$7$	−2.10390	−	1.60425i	−0.795199	−	0.606349i
$7$	−2.10390	−	1.60425i	−0.795199	−	0.606349i
$8$	2.46099			0.870091
$9$	1.38032	−	2.39078i	0.460105	−	0.796926i
$10$	0.926214	+	1.60425i	0.292894	+	0.507308i
$11$	1.05807	+	1.83263i	0.319020	+	0.552559i	0.980284	−	0.197595i	$-0.0633130\pi$
$11$	1.05807	+	1.83263i	0.319020	+	0.552559i	−0.661264	+	0.750153i	$0.729980\pi$
$12$	0.102021	−	0.176706i	0.0294511	−	0.0510107i
$13$		0			0
$13$		0			0
$14$	−3.79541	+	1.58563i	−1.01437	+	0.423778i
$15$	−0.582949			−0.150517
$16$	2.33009	−	4.03583i	0.582521	−	1.00896i
$17$	0.453151	+	0.784881i	0.109905	+	0.190362i	0.915732	−	0.401790i	$-0.131612\pi$
$17$	0.453151	+	0.784881i	0.109905	+	0.190362i	−0.805826	+	0.592152i	$0.798279\pi$
$18$	−2.14596	−	3.71691i	−0.505808	−	0.876084i
$19$	3.34514	−	5.79395i	0.767428	−	1.32922i	−0.171525	−	0.985180i	$-0.554870\pi$
$19$	3.34514	−	5.79395i	0.767428	−	1.32922i	0.938953	−	0.344045i	$-0.111797\pi$
$20$	0.496921			0.111115
$21$	0.165059	−	1.28387i	0.0360189	−	0.280164i
$22$	3.28993			0.701416
$23$	−1.79866	+	3.11538i	−0.375048	+	0.649601i	−0.990334	−	0.138702i	$-0.955707\pi$
$23$	−1.79866	+	3.11538i	−0.375048	+	0.649601i	0.615287	+	0.788303i	$0.289040\pi$
$24$	0.602021	+	1.04273i	0.122887	+	0.212847i
$25$	1.79015	+	3.10063i	0.358030	+	0.620126i
$26$		0			0
$27$	2.81840			0.542401
$28$	−0.140701	+	1.09441i	−0.0265900	+	0.206823i
$29$	8.51545			1.58128			0.790639	−	0.612282i	$-0.209748\pi$
$29$	8.51545			1.58128			0.790639	+	0.612282i	$0.209748\pi$
$30$	−0.453151	+	0.784881i	−0.0827337	+	0.143299i
$31$	−2.64390	−	4.57937i	−0.474859	−	0.822479i	0.524727	−	0.851271i	$-0.324168\pi$
$31$	−2.64390	−	4.57937i	−0.474859	−	0.822479i	−0.999585	+	0.0287913i	$0.990834\pi$
$32$	−1.16156	−	2.01189i	−0.205337	−	0.355655i
$33$	−0.517662	+	0.896617i	−0.0901134	+	0.156081i
$34$	1.40902			0.241644
$35$	2.90880	−	1.21523i	0.491677	−	0.205411i
$36$	−1.15133			−0.191888
$37$	2.49579	−	4.32284i	0.410306	−	0.710670i	−0.584617	−	0.811309i	$-0.698755\pi$
$37$	2.49579	−	4.32284i	0.410306	−	0.710670i	0.994923	+	0.100639i	$0.0320886\pi$
$38$	−5.20065	−	9.00778i	−0.843656	−	1.46126i
$39$		0			0
$40$	−1.46615	+	2.53944i	−0.231818	+	0.401521i
$41$	−1.53636			−0.239939			−0.119970	−	0.992778i	$-0.538280\pi$
$41$	−1.53636			−0.239939			−0.119970	+	0.992778i	$0.538280\pi$
$42$	−1.60029	−	1.22024i	−0.246931	−	0.188288i
$43$	5.43273			0.828483			0.414242	−	0.910167i	$-0.364047\pi$
$43$	5.43273			0.828483			0.414242	+	0.910167i	$0.364047\pi$
$44$	0.441269	−	0.764301i	0.0665238	−	0.115223i
$45$	1.64466	+	2.84864i	0.245172	+	0.424650i
$46$	2.79636	+	4.84344i	0.412301	+	0.714126i
$47$	−1.59337	+	2.75979i	−0.232416	+	0.402557i	−0.958519	−	0.285030i	$-0.907997\pi$
$47$	−1.59337	+	2.75979i	−0.232416	+	0.402557i	0.726102	+	0.687587i	$0.241330\pi$
$48$	2.28000			0.329089
$49$	1.85277	+	6.75035i	0.264682	+	0.964336i
$50$	5.56625			0.787186
$51$	−0.221705	+	0.384004i	−0.0310449	+	0.0537714i
$52$		0			0
$53$	1.41239	+	2.44632i	0.194006	+	0.336029i	0.946574	−	0.322486i	$-0.104518\pi$
$53$	1.41239	+	2.44632i	0.194006	+	0.336029i	−0.752568	+	0.658514i	$0.771185\pi$
$54$	2.19086	−	3.79469i	0.298139	−	0.516391i
$55$	−2.52140			−0.339986
$56$	−5.17767	−	3.94804i	−0.691895	−	0.527579i
$57$	3.27323			0.433550
$58$	6.61943	−	11.4652i	0.869173	−	1.50545i
$59$	−5.12298	−	8.87327i	−0.666956	−	1.15520i	−0.978751	−	0.205052i	$-0.934264\pi$
$59$	−5.12298	−	8.87327i	−0.666956	−	1.15520i	0.311795	−	0.950149i	$-0.399070\pi$
$60$	0.121560	+	0.210548i	0.0156933	+	0.0271816i
$61$	4.13423	−	7.16069i	0.529333	−	0.916832i	−0.470081	−	0.882623i	$-0.655775\pi$
$61$	4.13423	−	7.16069i	0.529333	−	0.916832i	0.999415	−	0.0342093i	$-0.0108913\pi$
$62$	−8.22088			−1.04405
$63$	−6.73945	+	2.81558i	−0.849091	+	0.354730i
$64$	5.70861			0.713576
$65$		0			0
$66$	0.804802	+	1.39396i	0.0990643	+	0.171584i
$67$	−1.87182	−	3.24208i	−0.228679	−	0.396083i	0.728738	−	0.684793i	$-0.240107\pi$
$67$	−1.87182	−	3.24208i	−0.228679	−	0.396083i	−0.957417	+	0.288709i	$0.906774\pi$
$68$	0.188987	−	0.327336i	0.0229181	−	0.0396953i
$69$	−1.76000			−0.211879
$70$	0.624956	−	4.86105i	0.0746965	−	0.581007i
$71$	2.53020			0.300280			0.150140	−	0.988665i	$-0.452028\pi$
$71$	2.53020			0.300280			0.150140	+	0.988665i	$0.452028\pi$
$72$	3.39694	−	5.88368i	0.400334	−	0.693398i
$73$	−2.86522	−	4.96271i	−0.335349	−	0.580841i	0.648203	−	0.761468i	$-0.275521\pi$
$73$	−2.86522	−	4.96271i	−0.335349	−	0.580841i	−0.983552	+	0.180627i	$0.942187\pi$
$74$	−3.88018	−	6.72066i	−0.451061	−	0.781261i
$75$	−0.875834	+	1.51699i	−0.101133	+	0.175167i
$76$	−2.79019			−0.320057
$77$	0.713925	−	5.55307i	0.0813593	−	0.632831i
$78$		0			0
$79$	−3.03620	+	5.25885i	−0.341599	+	0.591667i	−0.984730	−	0.174089i	$-0.944302\pi$
$79$	−3.03620	+	5.25885i	−0.341599	+	0.591667i	0.643131	+	0.765756i	$0.277635\pi$
$80$	2.77632	+	4.80873i	0.310402	+	0.537633i
$81$	−3.45150	−	5.97817i	−0.383500	−	0.664241i
$82$	−1.19428	+	2.06856i	−0.131886	+	0.228434i
$83$	11.6309			1.27665			0.638327	−	0.769766i	$-0.279627\pi$
$83$	11.6309			1.27665			0.638327	+	0.769766i	$0.279627\pi$
$84$	−0.498124	+	0.208104i	−0.0543498	+	0.0227060i
$85$	−1.07987			−0.117128
$86$	4.22310	−	7.31462i	0.455388	−	0.788755i
$87$	2.08310	+	3.60803i	0.223331	+	0.386821i
$88$	2.60390	+	4.51008i	0.277576	+	0.480776i
$89$	−8.87557	+	15.3729i	−0.940808	+	1.62953i	−0.176875	+	0.984233i	$0.556599\pi$
$89$	−8.87557	+	15.3729i	−0.940808	+	1.62953i	−0.763934	+	0.645295i	$0.776735\pi$
$90$	5.11387			0.539049
$91$		0			0
$92$	1.50027			0.156414
$93$	1.29353	−	2.24046i	0.134133	−	0.232325i
$94$	2.47719	+	4.29061i	0.255502	+	0.442543i
$95$	3.98577	+	6.90356i	0.408932	+	0.708291i
$96$	0.568297	−	0.984319i	0.0580015	−	0.100462i
$97$	−6.20434			−0.629955			−0.314978	−	0.949099i	$-0.601997\pi$
$97$	−6.20434			−0.629955			−0.314978	+	0.949099i	$0.601997\pi$
$98$	10.5289	+	2.75277i	1.06358	+	0.278072i
$99$	5.84188			0.587131
$100$	0.746584	−	1.29312i	0.0746584	−	0.129312i
$101$	3.61133	+	6.25501i	0.359341	+	0.622397i	0.987851	−	0.155405i	$-0.0496682\pi$
$101$	3.61133	+	6.25501i	0.359341	+	0.622397i	−0.628510	+	0.777802i	$0.716335\pi$
$102$	0.344682	+	0.597007i	0.0341286	+	0.0591125i
$103$	−4.96322	+	8.59656i	−0.489041	+	0.847044i	−0.999921	−	0.0126084i	$-0.995987\pi$
$103$	−4.96322	+	8.59656i	−0.489041	+	0.847044i	0.510879	+	0.859652i	$0.329320\pi$
$104$		0			0
$105$	1.22646	+	0.935195i	0.119691	+	0.0912657i
$106$	4.39164			0.426553
$107$	1.10003	−	1.90531i	0.106344	−	0.184193i	−0.807942	−	0.589261i	$-0.799419\pi$
$107$	1.10003	−	1.90531i	0.106344	−	0.184193i	0.914287	+	0.405068i	$0.132752\pi$
$108$	−0.587708	−	1.01794i	−0.0565523	−	0.0979514i
$109$	6.87291	+	11.9042i	0.658305	+	1.14022i	0.981054	+	0.193734i	$0.0620598\pi$
$109$	6.87291	+	11.9042i	0.658305	+	1.14022i	−0.322749	+	0.946485i	$0.604607\pi$
$110$	−1.96000	+	3.39481i	−0.186878	+	0.323683i
$111$	2.44214			0.231798
$112$	−11.3767	+	4.75293i	−1.07500	+	0.449110i
$113$	−16.0947			−1.51406			−0.757032	−	0.653378i	$-0.773351\pi$
$113$	−16.0947			−1.51406			−0.757032	+	0.653378i	$0.773351\pi$
$114$	2.54442	−	4.40707i	0.238307	−	0.412760i
$115$	−2.14313	−	3.71201i	−0.199848	−	0.346147i
$116$	−1.77569	−	3.07558i	−0.164869	−	0.285561i
$117$		0			0
$118$	−15.9293			−1.46641
$119$	0.305761	−	2.37828i	0.0280290	−	0.218016i
$120$	−1.43463			−0.130963
$121$	3.26098	−	5.64818i	0.296453	−	0.513471i
$122$	−6.42743	−	11.1326i	−0.581912	−	1.00790i
$123$	−0.375834	−	0.650963i	−0.0338878	−	0.0586954i
$124$	−1.10264	+	1.90983i	−0.0990202	+	0.171508i
$125$	−10.2235			−0.914420
$126$	−1.44797	+	11.2627i	−0.128996	+	1.00336i
$127$	−15.6784			−1.39123			−0.695617	−	0.718413i	$-0.744869\pi$
$127$	−15.6784			−1.39123			−0.695617	+	0.718413i	$0.744869\pi$
$128$	6.76067	−	11.7098i	0.597565	−	1.03501i
$129$	1.32899	+	2.30187i	0.117011	+	0.202668i
$130$		0			0
$131$	4.76884	−	8.25988i	0.416656	−	0.721669i	−0.578945	−	0.815367i	$-0.696535\pi$
$131$	4.76884	−	8.25988i	0.416656	−	0.721669i	0.995601	+	0.0936976i	$0.0298687\pi$
$132$	0.431783			0.0375819
$133$	−16.3328	+	6.82345i	−1.41623	+	0.591668i
$134$	−5.82018			−0.502787
$135$	−1.67908	+	2.90825i	−0.144512	+	0.250302i
$136$	1.11520	+	1.93158i	0.0956277	+	0.165632i
$137$	−1.38231	−	2.39422i	−0.118098	−	0.204552i	0.800916	−	0.598777i	$-0.204346\pi$
$137$	−1.38231	−	2.39422i	−0.118098	−	0.204552i	−0.919014	+	0.394225i	$0.871013\pi$
$138$	−1.36812	+	2.36966i	−0.116462	+	0.201719i
$139$	−22.7967			−1.93359			−0.966795	−	0.255554i	$-0.917742\pi$
$139$	−22.7967			−1.93359			−0.966795	+	0.255554i	$0.917742\pi$
$140$	−1.04547	−	0.797185i	−0.0883585	−	0.0673745i
$141$	−1.55911			−0.131301
$142$	1.96684	−	3.40666i	0.165053	−	0.285881i
$143$		0			0
$144$	−6.43251	−	11.1414i	−0.536043	−	0.928453i
$145$	−5.07312	+	8.78691i	−0.421300	+	0.729713i
$146$	−8.90904			−0.737317
$147$	−2.40692	+	2.43634i	−0.198519	+	0.200946i
$148$	−2.08175			−0.171119
$149$	−7.20581	+	12.4808i	−0.590323	+	1.02247i	0.403866	+	0.914818i	$0.367666\pi$
$149$	−7.20581	+	12.4808i	−0.590323	+	1.02247i	−0.994189	+	0.107651i	$0.965667\pi$
$150$	1.36165	+	2.35844i	0.111178	+	0.192566i
$151$	7.62901	+	13.2138i	0.620840	+	1.07533i	0.989330	+	0.145695i	$0.0465417\pi$
$151$	7.62901	+	13.2138i	0.620840	+	1.07533i	−0.368489	+	0.929632i	$0.620125\pi$
$152$	8.23236	−	14.2589i	0.667732	−	1.15655i
$153$	2.50197			0.202272
$154$	−6.92168	−	5.27787i	−0.557765	−	0.425303i
$155$	6.30048			0.506067
$156$		0			0
$157$	5.70745	+	9.88559i	0.455504	+	0.788956i	0.998717	−	0.0506387i	$-0.0161257\pi$
$157$	5.70745	+	9.88559i	0.455504	+	0.788956i	−0.543213	+	0.839595i	$0.682792\pi$
$158$	4.72034	+	8.17587i	0.375530	+	0.650437i
$159$	−0.691012	+	1.19687i	−0.0548008	+	0.0949178i
$160$	2.76803			0.218832
$161$	8.78205	−	3.66893i	0.692122	−	0.289152i
$162$	−10.7320			−0.843185
$163$	−7.20385	+	12.4774i	−0.564249	+	0.977308i	0.432870	+	0.901456i	$0.357501\pi$
$163$	−7.20385	+	12.4774i	−0.564249	+	0.977308i	−0.997119	+	0.0758514i	$0.975833\pi$
$164$	0.320371	+	0.554899i	0.0250168	+	0.0433303i
$165$	−0.616800	−	1.06833i	−0.0480178	−	0.0831693i
$166$	9.04118	−	15.6598i	0.701731	−	1.21543i
$167$	−7.77190			−0.601407			−0.300704	−	0.953718i	$-0.597222\pi$
$167$	−7.77190			−0.601407			−0.300704	+	0.953718i	$0.597222\pi$
$168$	0.406210	−	3.15959i	0.0313398	−	0.243768i
$169$		0			0
$170$	−0.839430	+	1.45394i	−0.0643813	+	0.111512i
$171$	−9.23471	−	15.9950i	−0.706196	−	1.22317i
$172$	−1.13286	−	1.96218i	−0.0863800	−	0.149615i
$173$	−3.04731	+	5.27809i	−0.231682	+	0.401286i	−0.958303	−	0.285753i	$-0.907756\pi$
$173$	−3.04731	+	5.27809i	−0.231682	+	0.401286i	0.726621	+	0.687039i	$0.241090\pi$
$174$	6.47713			0.491030
$175$	1.20789	−	9.39526i	0.0913080	−	0.710215i
$176$	9.86157			0.743344
$177$	2.50643	−	4.34126i	0.188395	−	0.326309i
$178$	13.7987	+	23.9001i	1.03426	+	1.79139i
$179$	−9.26488	−	16.0472i	−0.692490	−	1.19943i	−0.971020	−	0.239000i	$-0.923181\pi$
$179$	−9.26488	−	16.0472i	−0.692490	−	1.19943i	0.278530	−	0.960428i	$-0.410153\pi$
$180$	0.685909	−	1.18803i	0.0511246	−	0.0885504i
$181$	−5.60520			−0.416631			−0.208316	−	0.978062i	$-0.566798\pi$
$181$	−5.60520			−0.416631			−0.208316	+	0.978062i	$0.566798\pi$
$182$		0			0
$183$	4.04535			0.299041
$184$	−4.42650	+	7.66692i	−0.326326	+	0.565212i
$185$	2.97377	+	5.15071i	0.218636	+	0.378688i
$186$	−2.01104	−	3.48322i	−0.147456	−	0.255402i
$187$	−0.958931	+	1.66092i	−0.0701240	+	0.121458i
$188$	1.32903			0.0969295
$189$	−5.92962	−	4.52141i	−0.431317	−	0.328884i
$190$	12.3933			0.899102
$191$	−0.251851	+	0.436219i	−0.0182233	+	0.0315637i	−0.874993	−	0.484135i	$-0.839134\pi$
$191$	−0.251851	+	0.436219i	−0.0182233	+	0.0315637i	0.856770	+	0.515699i	$0.172468\pi$
$192$	1.39647	+	2.41876i	0.100782	+	0.174559i
$193$	−1.85622	−	3.21507i	−0.133614	−	0.231426i	0.791453	−	0.611230i	$-0.209325\pi$
$193$	−1.85622	−	3.21507i	−0.133614	−	0.231426i	−0.925067	+	0.379804i	$0.875991\pi$
$194$	−4.82290	+	8.35351i	−0.346264	+	0.599747i
$195$		0			0
$196$	2.05172	−	2.07680i	0.146552	−	0.148343i
$197$	7.44451			0.530399			0.265200	−	0.964194i	$-0.414562\pi$
$197$	7.44451			0.530399			0.265200	+	0.964194i	$0.414562\pi$
$198$	4.54115	−	7.86550i	0.322725	−	0.558977i
$199$	−3.75278	−	6.50001i	−0.266028	−	0.460773i	0.701805	−	0.712369i	$-0.252378\pi$
$199$	−3.75278	−	6.50001i	−0.266028	−	0.460773i	−0.967832	+	0.251596i	$0.919045\pi$
$200$	4.40554	+	7.63062i	0.311519	+	0.539566i
$201$	0.915789	−	1.58619i	0.0645948	−	0.111881i
$202$	11.2290			0.790068
$203$	−17.9156	−	13.6609i	−1.25743	−	0.958807i
$204$	0.184925			0.0129473
$205$	0.915297	−	1.58534i	0.0639271	−	0.110725i
$206$	7.71626	+	13.3650i	0.537617	+	0.931181i
$207$	4.96545	+	8.60042i	0.345123	+	0.597770i
$208$		0			0
$209$	14.1576			0.979299
$210$	2.21253	−	0.924342i	0.152679	−	0.0637857i
$211$	3.79063			0.260957			0.130479	−	0.991451i	$-0.458349\pi$
$211$	3.79063			0.260957			0.130479	+	0.991451i	$0.458349\pi$
$212$	0.589037	−	1.02024i	0.0404553	−	0.0700706i
$213$	0.618953	+	1.07206i	0.0424100	+	0.0734562i
$214$	−1.71020	−	2.96216i	−0.116907	−	0.202489i
$215$	−3.23658	+	5.60592i	−0.220733	+	0.382320i
$216$	6.93605			0.471938
$217$	−1.78395	+	13.8760i	−0.121103	+	0.941965i
$218$	21.3704			1.44739
$219$	1.40181	−	2.42801i	0.0947258	−	0.164070i
$220$	0.525777	+	0.910673i	0.0354479	+	0.0613975i
$221$		0			0
$222$	1.89838	−	3.28809i	0.127411	−	0.220682i
$223$	−4.86879			−0.326039			−0.163019	−	0.986623i	$-0.552123\pi$
$223$	−4.86879			−0.326039			−0.163019	+	0.986623i	$0.552123\pi$
$224$	−0.783757	+	6.09624i	−0.0523669	+	0.407322i
$225$	9.88390			0.658926
$226$	−12.5111	+	21.6699i	−0.832228	+	1.44146i
$227$	12.0884	+	20.9376i	0.802332	+	1.38968i	0.918077	+	0.396402i	$0.129741\pi$
$227$	12.0884	+	20.9376i	0.802332	+	1.38968i	−0.115745	+	0.993279i	$0.536925\pi$
$228$	−0.682552	−	1.18222i	−0.0452031	−	0.0782941i
$229$	−10.8561	+	18.8034i	−0.717394	+	1.24256i	0.244635	+	0.969615i	$0.421332\pi$
$229$	−10.8561	+	18.8034i	−0.717394	+	1.24256i	−0.962029	+	0.272947i	$0.912002\pi$
$230$	−6.66379			−0.439397
$231$	2.52750	−	1.05593i	0.166298	−	0.0694752i
$232$	20.9564			1.37586
$233$	−1.89842	+	3.28816i	−0.124370	+	0.215414i	−0.921486	−	0.388411i	$-0.873024\pi$
$233$	−1.89842	+	3.28816i	−0.124370	+	0.215414i	0.797117	+	0.603825i	$0.206358\pi$
$234$		0			0
$235$	−1.89851	−	3.28832i	−0.123845	−	0.214507i
$236$	−2.13655	+	3.70061i	−0.139077	+	0.240889i
$237$	−2.97093			−0.192983
$238$	−2.96443	−	2.26041i	−0.192155	−	0.146521i
$239$	−21.9100			−1.41724			−0.708619	−	0.705592i	$-0.750681\pi$
$239$	−21.9100			−1.41724			−0.708619	+	0.705592i	$0.750681\pi$
$240$	−1.35832	+	2.35268i	−0.0876792	+	0.151865i
$241$	−10.3744	−	17.9690i	−0.668273	−	1.15748i	−0.978387	−	0.206783i	$-0.933701\pi$
$241$	−10.3744	−	17.9690i	−0.668273	−	1.15748i	0.310114	−	0.950699i	$-0.399633\pi$
$242$	−5.06980	−	8.78115i	−0.325899	−	0.564474i
$243$	5.91625	−	10.2472i	0.379527	−	0.657361i
$244$	−3.44837			−0.220759
$245$	−8.06935	−	2.10972i	−0.515532	−	0.134785i
$246$	−1.16861			−0.0745077
$247$		0			0
$248$	−6.50661	−	11.2698i	−0.413170	−	0.715632i
$249$	2.84521	+	4.92805i	0.180308	+	0.312302i
$250$	−7.94719	+	13.7649i	−0.502624	+	0.870571i
$251$	13.2578			0.836827			0.418413	−	0.908257i	$-0.362586\pi$
$251$	13.2578			0.836827			0.418413	+	0.908257i	$0.362586\pi$
$252$	2.42227	+	1.84701i	0.152589	+	0.116351i
$253$	−7.61245			−0.478591
$254$	−12.1875	+	21.1094i	−0.764713	+	1.32452i
$255$	−0.264164	−	0.457546i	−0.0165426	−	0.0286526i
$256$	−4.80213	−	8.31753i	−0.300133	−	0.519845i
$257$	6.58555	−	11.4065i	0.410795	−	0.711518i	−0.584182	−	0.811623i	$-0.698584\pi$
$257$	6.58555	−	11.4065i	0.410795	−	0.711518i	0.994977	+	0.100105i	$0.0319178\pi$
$258$	4.13231			0.257266
$259$	−12.1858	+	5.09094i	−0.757189	+	0.316336i
$260$		0			0
$261$	11.7540	−	20.3585i	0.727555	−	1.26016i
$262$	−7.41406	−	12.8415i	−0.458042	−	0.793352i
$263$	9.57028	+	16.5762i	0.590129	+	1.02213i	0.994215	+	0.107412i	$0.0342564\pi$
$263$	9.57028	+	16.5762i	0.590129	+	1.02213i	−0.404086	+	0.914721i	$0.632410\pi$
$264$	−1.27396	+	2.20657i	−0.0784069	+	0.135805i
$265$	−3.36575			−0.206756
$266$	−3.50910	+	27.2946i	−0.215157	+	1.67354i
$267$	−8.68477			−0.531499
$268$	−0.780643	+	1.35211i	−0.0476854	+	0.0825935i
$269$	14.2411	+	24.6663i	0.868296	+	1.50393i	0.863737	+	0.503943i	$0.168118\pi$
$269$	14.2411	+	24.6663i	0.868296	+	1.50393i	0.00455867	+	0.999990i	$0.498549\pi$
$270$	2.61044	+	4.52141i	0.158866	+	0.275164i
$271$	8.97371	−	15.5429i	0.545114	−	0.944165i	−0.453486	−	0.891263i	$-0.649820\pi$
$271$	8.97371	−	15.5429i	0.545114	−	0.944165i	0.998600	−	0.0529014i	$-0.0168469\pi$
$272$	4.22353			0.256089
$273$		0			0
$274$	−4.29811			−0.259658
$275$	−3.78821	+	6.56137i	−0.228437	+	0.395665i
$276$	0.367005	+	0.635671i	0.0220911	+	0.0382629i
$277$	−6.71943	−	11.6384i	−0.403732	−	0.699284i	0.590441	−	0.807081i	$-0.298954\pi$
$277$	−6.71943	−	11.6384i	−0.403732	−	0.699284i	−0.994173	+	0.107797i	$0.965620\pi$
$278$	−17.7209	+	30.6934i	−1.06283	+	1.84087i
$279$	−14.5977			−0.873940
$280$	7.15853	−	2.99066i	0.427804	−	0.178726i
$281$	29.9530			1.78685			0.893424	−	0.449214i	$-0.148296\pi$
$281$	29.9530			1.78685			0.893424	+	0.449214i	$0.148296\pi$
$282$	−1.21197	+	2.09919i	−0.0721716	+	0.125005i
$283$	4.94561	+	8.56604i	0.293986	+	0.509199i	0.974748	−	0.223306i	$-0.0716848\pi$
$283$	4.94561	+	8.56604i	0.293986	+	0.509199i	−0.680763	+	0.732504i	$0.738351\pi$
$284$	−0.527613	−	0.913852i	−0.0313080	−	0.0542271i
$285$	−1.95005	+	3.37758i	−0.115511	+	0.200070i
$286$		0			0
$287$	3.23235	+	2.46471i	0.190800	+	0.145487i
$288$	−6.41330			−0.377907
$289$	8.08931	−	14.0111i	0.475842	−	0.824182i
$290$	7.88712	+	13.6609i	0.463148	+	0.802195i
$291$	−1.51774	−	2.62881i	−0.0889716	−	0.154103i
$292$	−1.19494	+	2.06970i	−0.0699288	+	0.121120i
$293$	−7.91058			−0.462141			−0.231071	−	0.972937i	$-0.574223\pi$
$293$	−7.91058			−0.462141			−0.231071	+	0.972937i	$0.574223\pi$
$294$	1.40928	+	5.13454i	0.0821908	+	0.299452i
$295$	12.2082			0.710788
$296$	6.14212	−	10.6385i	0.357003	−	0.618348i
$297$	2.98206	+	5.16508i	0.173037	+	0.299708i
$298$	11.2028	+	19.4038i	0.648959	+	1.12403i
$299$		0			0
$300$	0.730535			0.0421775
$301$	−11.4299	−	8.71545i	−0.658809	−	0.502350i
$302$	23.7214			1.36502
$303$	−1.76685	+	3.06027i	−0.101503	+	0.175808i
$304$	−15.5889	−	27.0008i	−0.894086	−	1.54860i
$305$	4.92598	+	8.53204i	0.282061	+	0.488543i
$306$	1.94489	−	3.36865i	0.111182	−	0.192573i
$307$	−1.27238			−0.0726187			−0.0363094	−	0.999341i	$-0.511560\pi$
$307$	−1.27238			−0.0726187			−0.0363094	+	0.999341i	$0.511560\pi$
$308$	−2.15451	+	0.900105i	−0.122765	+	0.0512882i
$309$	−4.85653			−0.276278
$310$	4.89763	−	8.48295i	0.278167	−	0.481799i
$311$	−12.3817	−	21.4458i	−0.702103	−	1.21608i	−0.967727	−	0.252002i	$-0.918911\pi$
$311$	−12.3817	−	21.4458i	−0.702103	−	1.21608i	0.265624	−	0.964077i	$-0.414422\pi$
$312$		0			0
$313$	−1.18826	+	2.05812i	−0.0671642	+	0.116332i	−0.897652	−	0.440705i	$-0.854728\pi$
$313$	−1.18826	+	2.05812i	−0.0671642	+	0.116332i	0.830488	+	0.557037i	$0.188062\pi$
$314$	17.7466			1.00150
$315$	1.10972	−	8.63169i	0.0625259	−	0.486341i
$316$	2.53250			0.142464
$317$	−9.88979	+	17.1296i	−0.555466	+	0.962096i	0.442401	+	0.896817i	$0.354127\pi$
$317$	−9.88979	+	17.1296i	−0.555466	+	0.962096i	−0.997867	+	0.0652782i	$0.979207\pi$
$318$	1.07431	+	1.86076i	0.0602442	+	0.104346i
$319$	9.00993	+	15.6057i	0.504459	+	0.873749i
$320$	−3.40093	+	5.89059i	−0.190118	+	0.329294i
$321$	1.07638			0.0600779
$322$	1.88682	−	14.6762i	0.105149	−	0.817870i
$323$	6.06342			0.337378
$324$	−1.43945	+	2.49320i	−0.0799695	+	0.138511i
$325$		0			0
$326$	11.1997	+	19.3985i	0.620295	+	1.07438i
$327$	−3.36258	+	5.82416i	−0.185951	+	0.322077i
$328$	−3.78097			−0.208769
$329$	7.77967	−	3.25016i	0.428907	−	0.179187i
$330$	−1.91786			−0.105575
$331$	1.96386	−	3.40151i	0.107944	−	0.186964i	−0.806993	−	0.590561i	$-0.798907\pi$
$331$	1.96386	−	3.40151i	0.107944	−	0.186964i	0.914937	+	0.403596i	$0.132240\pi$
$332$	−2.42533	−	4.20080i	−0.133107	−	0.230549i
$333$	−6.88997	−	11.9338i	−0.377568	−	0.653967i
$334$	−6.04143	+	10.4641i	−0.330572	+	0.572568i
$335$	4.46058			0.243708
$336$	−4.79688	−	3.65768i	−0.261691	−	0.199543i
$337$	−7.14099			−0.388995			−0.194497	−	0.980903i	$-0.562308\pi$
$337$	−7.14099			−0.388995			−0.194497	+	0.980903i	$0.562308\pi$
$338$		0			0
$339$	−3.93718	−	6.81940i	−0.213838	−	0.370379i
$340$	0.225181	+	0.390024i	0.0122121	+	0.0211520i
$341$	5.59486	−	9.69059i	0.302979	−	0.524775i
$342$	−28.7142			−1.55268
$343$	6.93120	−	17.1744i	0.374250	−	0.927328i
$344$	13.3699			0.720856
$345$	1.04853	−	1.81611i	0.0564509	−	0.0977759i
$346$	4.73761	+	8.20578i	0.254695	+	0.441145i
$347$	−5.03498	−	8.72085i	−0.270292	−	0.468160i	0.698644	−	0.715469i	$-0.253787\pi$
$347$	−5.03498	−	8.72085i	−0.270292	−	0.468160i	−0.968937	+	0.247309i	$0.920454\pi$
$348$	0.868758	−	1.50473i	0.0465703	−	0.0806622i
$349$	6.28837			0.336609			0.168304	−	0.985735i	$-0.446171\pi$
$349$	6.28837			0.336609			0.168304	+	0.985735i	$0.446171\pi$
$350$	−11.7108	−	8.92964i	−0.625969	−	0.477310i
$351$		0			0
$352$	2.45803	−	4.25743i	0.131013	−	0.226922i
$353$	17.0836	+	29.5897i	0.909269	+	1.57490i	0.815083	+	0.579345i	$0.196692\pi$
$353$	17.0836	+	29.5897i	0.909269	+	1.57490i	0.0941861	+	0.995555i	$0.469975\pi$
$354$	−3.89671	−	6.74930i	−0.207108	−	0.358721i
$355$	−1.50738	+	2.61087i	−0.0800036	+	0.138570i
$356$	7.40313			0.392365
$357$	1.08248	−	0.452236i	0.0572911	−	0.0239349i
$358$	−28.8080			−1.52255
$359$	9.34327	−	16.1830i	0.493119	−	0.854107i	−0.506850	−	0.862034i	$-0.669190\pi$
$359$	9.34327	−	16.1830i	0.493119	−	0.854107i	0.999969	+	0.00792750i	$0.00252343\pi$
$360$	4.04750	+	7.01047i	0.213322	+	0.369484i
$361$	−12.8799	−	22.3087i	−0.677891	−	1.17414i
$362$	−4.35716	+	7.54683i	−0.229007	+	0.396653i
$363$	3.19088			0.167478
$364$		0			0
$365$	6.82788			0.357388
$366$	3.14463	−	5.44666i	0.164372	−	0.284701i
$367$	15.5305	+	26.8997i	0.810687	+	1.40415i	0.912384	+	0.409336i	$0.134240\pi$
$367$	15.5305	+	26.8997i	0.810687	+	1.40415i	−0.101696	+	0.994816i	$0.532427\pi$
$368$	8.38209	+	14.5182i	0.436946	+	0.756813i
$369$	−2.12067	+	3.67310i	−0.110397	+	0.191214i
$370$	9.24655			0.480705
$371$	0.952998	−	7.41264i	0.0494772	−	0.384845i
$372$	−1.07894			−0.0559404
$373$	1.46852	−	2.54355i	0.0760371	−	0.131700i	−0.825500	−	0.564403i	$-0.809107\pi$
$373$	1.46852	−	2.54355i	0.0760371	−	0.131700i	0.901537	+	0.432702i	$0.142440\pi$
$374$	1.49084	+	2.58221i	0.0770894	+	0.133523i
$375$	−2.50094	−	4.33175i	−0.129148	−	0.223691i
$376$	−3.92126	+	6.79182i	−0.202223	+	0.350261i
$377$		0			0
$378$	−10.6970	+	4.46894i	−0.550193	+	0.229858i
$379$	−10.0851			−0.518036			−0.259018	−	0.965872i	$-0.583399\pi$
$379$	−10.0851			−0.518036			−0.259018	+	0.965872i	$0.583399\pi$
$380$	1.66227	−	2.87914i	0.0852727	−	0.147697i
$381$	−3.83534	−	6.64301i	−0.196491	−	0.340332i
$382$	0.391550	+	0.678184i	0.0200334	+	0.0346989i
$383$	1.84466	−	3.19504i	0.0942576	−	0.163259i	−0.815041	−	0.579403i	$-0.803286\pi$
$383$	1.84466	−	3.19504i	0.0942576	−	0.163259i	0.909299	+	0.416144i	$0.136619\pi$
$384$	6.61534			0.337588
$385$	5.30477	+	4.04496i	0.270356	+	0.206150i
$386$	−5.77168			−0.293771
$387$	7.49888	−	12.9884i	0.381190	−	0.660240i
$388$	1.29376	+	2.24086i	0.0656809	+	0.113763i
$389$	−11.3333	−	19.6299i	−0.574623	−	0.995277i	−0.996082	−	0.0884295i	$-0.971815\pi$
$389$	−11.3333	−	19.6299i	−0.574623	−	0.995277i	0.421459	−	0.906847i	$-0.361518\pi$
$390$		0			0
$391$	−3.26027			−0.164879
$392$	4.55965	+	16.6125i	0.230297	+	0.839060i
$393$	4.66633			0.235385
$394$	5.78694	−	10.0233i	0.291542	−	0.504965i
$395$	−3.61767	−	6.26598i	−0.182025	−	0.315276i
$396$	−1.21818	−	2.10995i	−0.0612160	−	0.106029i
$397$	−14.5680	+	25.2325i	−0.731146	+	1.26638i	0.225248	+	0.974302i	$0.427681\pi$
$397$	−14.5680	+	25.2325i	−0.731146	+	1.26638i	−0.956394	+	0.292080i	$0.905652\pi$
$398$	−11.6688			−0.584904
$399$	−6.88654	−	5.25108i	−0.344758	−	0.262883i
$400$	16.6848			0.834241
$401$	4.06026	−	7.03258i	0.202760	−	0.351190i	−0.746657	−	0.665209i	$-0.768342\pi$
$401$	4.06026	−	7.03258i	0.202760	−	0.351190i	0.949417	+	0.314019i	$0.101676\pi$
$402$	−1.42377	−	2.46603i	−0.0710110	−	0.122995i
$403$		0			0
$404$	1.50611	−	2.60866i	0.0749318	−	0.129786i
$405$	8.22499			0.408703
$406$	−32.3196	+	13.5024i	−1.60399	+	0.670111i
$407$	10.5629			0.523583
$408$	−0.545614	+	0.945031i	−0.0270119	+	0.0467860i
$409$	−4.16131	−	7.20759i	−0.205763	−	0.356393i	0.744612	−	0.667497i	$-0.232634\pi$
$409$	−4.16131	−	7.20759i	−0.205763	−	0.356393i	−0.950376	+	0.311105i	$0.899301\pi$
$410$	−1.42300	−	2.46471i	−0.0702769	−	0.121723i
$411$	0.676295	−	1.17138i	0.0333592	−	0.0577798i
$412$	4.13984			0.203955
$413$	−3.45670	+	26.8870i	−0.170093	+	1.32302i
$414$	15.4395			0.758808
$415$	−6.92915	+	12.0016i	−0.340139	+	0.589138i
$416$		0			0
$417$	−5.57666	−	9.65905i	−0.273090	−	0.473006i
$418$	11.0053	−	19.0617i	0.538286	−	0.932339i
$419$	−13.0166			−0.635905			−0.317952	−	0.948107i	$-0.602995\pi$
$419$	−13.0166			−0.635905			−0.317952	+	0.948107i	$0.602995\pi$
$420$	0.0820216	−	0.637983i	0.00400224	−	0.0311304i
$421$	8.89681			0.433604			0.216802	−	0.976216i	$-0.430437\pi$
$421$	8.89681			0.433604			0.216802	+	0.976216i	$0.430437\pi$
$422$	2.94662	−	5.10369i	0.143439	−	0.248444i
$423$	4.39870	+	7.61877i	0.213872	+	0.370437i
$424$	3.47587	+	6.02038i	0.168803	+	0.292376i
$425$	−1.62242	+	2.81011i	−0.0786988	+	0.136310i
$426$	1.92456			0.0932451
$427$	−20.1855	+	8.43303i	−0.976846	+	0.408103i
$428$	−0.917539			−0.0443509
$429$		0			0
$430$	5.03187	+	8.71545i	0.242658	+	0.420296i
$431$	−4.47872	−	7.75736i	−0.215732	−	0.373659i	0.737767	−	0.675056i	$-0.235880\pi$
$431$	−4.47872	−	7.75736i	−0.215732	−	0.373659i	−0.953499	+	0.301397i	$0.902547\pi$
$432$	6.56711	−	11.3746i	0.315960	−	0.547259i
$433$	−0.172909			−0.00830950			−0.00415475	−	0.999991i	$-0.501323\pi$
$433$	−0.172909			−0.00830950			−0.00415475	+	0.999991i	$0.501323\pi$
$434$	17.2959	+	13.1883i	0.830229	+	0.633060i
$435$	−4.96407			−0.238009
$436$	2.86636	−	4.96467i	0.137274	−	0.237765i
$437$	12.0336	+	20.8428i	0.575644	+	0.997045i
$438$	−2.17938	−	3.77480i	−0.104135	−	0.180367i
$439$	−4.77080	+	8.26327i	−0.227698	+	0.394384i	−0.957125	−	0.289674i	$-0.906453\pi$
$439$	−4.77080	+	8.26327i	−0.227698	+	0.394384i	0.729428	+	0.684058i	$0.239787\pi$
$440$	−6.20515			−0.295819
$441$	18.6960	+	4.88806i	0.890286	+	0.232765i
$442$		0			0
$443$	6.93676	−	12.0148i	0.329576	−	0.570842i	−0.652852	−	0.757485i	$-0.726428\pi$
$443$	6.93676	−	12.0148i	0.329576	−	0.570842i	0.982428	+	0.186644i	$0.0597610\pi$
$444$	−0.509249	−	0.882045i	−0.0241679	−	0.0418600i
$445$	−10.5753	−	18.3170i	−0.501319	−	0.868310i
$446$	−3.78473	+	6.55534i	−0.179212	+	0.310404i
$447$	−7.05091			−0.333496
$448$	−12.0103	−	9.15803i	−0.567434	−	0.432676i
$449$	21.2913			1.00480			0.502398	−	0.864636i	$-0.332451\pi$
$449$	21.2913			1.00480			0.502398	+	0.864636i	$0.332451\pi$
$450$	7.68318	−	13.3077i	0.362189	−	0.627329i
$451$	−1.62558	−	2.81558i	−0.0765455	−	0.132581i
$452$	3.35616	+	5.81304i	0.157861	+	0.273423i
$453$	−3.73251	+	6.46489i	−0.175368	+	0.303747i
$454$	37.5872			1.76406
$455$		0			0
$456$	8.05539			0.377228
$457$	4.84282	−	8.38801i	0.226538	−	0.392375i	−0.730242	−	0.683189i	$-0.760593\pi$
$457$	4.84282	−	8.38801i	0.226538	−	0.392375i	0.956780	+	0.290814i	$0.0939261\pi$
$458$	16.8779	+	29.2334i	0.788652	+	1.36599i
$459$	1.27716	+	2.21211i	0.0596128	+	0.103252i
$460$	−0.893795	+	1.54810i	−0.0416734	+	0.0721804i
$461$	1.37436			0.0640101			0.0320051	−	0.999488i	$-0.489811\pi$
$461$	1.37436			0.0640101			0.0320051	+	0.999488i	$0.489811\pi$
$462$	0.543035	−	4.22385i	0.0252643	−	0.196511i
$463$	−31.7710			−1.47653			−0.738263	−	0.674513i	$-0.764354\pi$
$463$	−31.7710			−1.47653			−0.738263	+	0.674513i	$0.764354\pi$
$464$	19.8417	−	34.3669i	0.921128	−	1.59544i
$465$	1.54126	+	2.66954i	0.0714742	+	0.123797i
$466$	2.95145	+	5.11206i	0.136723	+	0.236812i
$467$	14.5605	−	25.2195i	0.673778	−	1.16702i	−0.303046	−	0.952976i	$-0.598004\pi$
$467$	14.5605	−	25.2195i	0.673778	−	1.16702i	0.976824	−	0.214042i	$-0.0686629\pi$
$468$		0			0
$469$	−1.26299	+	9.82387i	−0.0583197	+	0.453624i
$470$	−5.90319			−0.272294
$471$	−2.79238	+	4.83654i	−0.128666	+	0.222856i
$472$	−12.6076	−	21.8370i	−0.580312	−	1.00513i
$473$	5.74820	+	9.95618i	0.264303	+	0.457786i
$474$	−2.30943	+	4.00006i	−0.106076	+	0.183729i
$475$	23.9532			1.09905
$476$	−0.922738	+	0.385498i	−0.0422936	+	0.0176693i
$477$	7.79816			0.357053
$478$	−17.0316	+	29.4995i	−0.779005	+	1.34928i
$479$	4.86092	+	8.41936i	0.222101	+	0.384690i	0.955446	−	0.295167i	$-0.0953752\pi$
$479$	4.86092	+	8.41936i	0.222101	+	0.384690i	−0.733345	+	0.679857i	$0.762042\pi$
$480$	0.677132	+	1.17283i	0.0309067	+	0.0535320i
$481$		0			0
$482$	−32.2578			−1.46930
$483$	3.70286	+	2.82348i	0.168486	+	0.128473i
$484$	−2.71999			−0.123636
$485$	3.69627	−	6.40213i	0.167839	−	0.290706i
$486$	−9.19791	−	15.9313i	−0.417226	−	0.722656i
$487$	−8.55666	−	14.8206i	−0.387739	−	0.671584i	0.604406	−	0.796676i	$-0.293411\pi$
$487$	−8.55666	−	14.8206i	−0.387739	−	0.671584i	−0.992145	+	0.125093i	$0.960077\pi$
$488$	10.1743	−	17.6224i	0.460568	−	0.797728i
$489$	−7.04899			−0.318766
$490$	−9.11318	+	9.22457i	−0.411692	+	0.416724i
$491$	−25.7213			−1.16079			−0.580394	−	0.814336i	$-0.697101\pi$
$491$	−25.7213			−1.16079			−0.580394	+	0.814336i	$0.697101\pi$
$492$	−0.156742	+	0.271485i	−0.00706647	+	0.0122395i
$493$	3.85879	+	6.68361i	0.173791	+	0.301015i
$494$		0			0
$495$	−3.48033	+	6.02812i	−0.156429	+	0.270944i
$496$	−24.6421			−1.10646
$497$	−5.32329	−	4.05908i	−0.238782	−	0.182075i
$498$	8.84682			0.396435
$499$	2.70198	−	4.67996i	0.120957	−	0.209504i	−0.799188	−	0.601081i	$-0.794737\pi$
$499$	2.70198	−	4.67996i	0.120957	−	0.209504i	0.920145	+	0.391577i	$0.128070\pi$
$500$	2.13187	+	3.69250i	0.0953400	+	0.165134i
$501$	−1.90121	−	3.29299i	−0.0849396	−	0.147120i
$502$	10.3059	−	17.8503i	0.459974	−	0.796699i
$503$	−12.6169			−0.562562			−0.281281	−	0.959625i	$-0.590759\pi$
$503$	−12.6169			−0.562562			−0.281281	+	0.959625i	$0.590759\pi$
$504$	−16.5857	+	6.92912i	−0.738786	+	0.308647i
$505$	−8.60589			−0.382957
$506$	−5.91749	+	10.2494i	−0.263064	+	0.455641i
$507$		0			0
$508$	3.26935	+	5.66268i	0.145054	+	0.251241i
$509$	−0.979379	+	1.69633i	−0.0434102	+	0.0751887i	−0.886914	−	0.461934i	$-0.847156\pi$
$509$	−0.979379	+	1.69633i	−0.0434102	+	0.0751887i	0.843504	+	0.537123i	$0.180489\pi$
$510$	−0.821385			−0.0363715
$511$	−1.93329	+	15.0376i	−0.0855236	+	0.665222i
$512$	12.1111			0.535240
$513$	9.42794	−	16.3297i	0.416254	−	0.720973i
$514$	−10.2385	−	17.7335i	−0.451599	−	0.782193i
$515$	−5.91374	−	10.2429i	−0.260590	−	0.451356i
$516$	0.554255	−	0.959998i	0.0243997	−	0.0422615i
$517$	−6.74357			−0.296582
$518$	−2.61812	+	20.3644i	−0.115034	+	0.894758i
$519$	−2.98180			−0.130886
$520$		0			0
$521$	19.5477	+	33.8576i	0.856401	+	1.48333i	0.875339	+	0.483509i	$0.160638\pi$
$521$	19.5477	+	33.8576i	0.856401	+	1.48333i	−0.0189387	+	0.999821i	$0.506029\pi$
$522$	−18.2738	−	31.6512i	−0.799823	−	1.38533i
$523$	4.35634	−	7.54540i	0.190489	−	0.329937i	−0.754923	−	0.655813i	$-0.772326\pi$
$523$	4.35634	−	7.54540i	0.190489	−	0.329937i	0.945413	+	0.325876i	$0.105659\pi$
$524$	−3.97770			−0.173767
$525$	4.27629	−	1.78653i	0.186633	−	0.0779707i
$526$	29.7576			1.29749
$527$	2.39618	−	4.15030i	0.104379	−	0.180790i
$528$	2.41239	+	4.17839i	0.104986	+	0.181841i
$529$	5.02961	+	8.71154i	0.218679	+	0.378763i
$530$	−2.61634	+	4.53164i	−0.113647	+	0.196842i
$531$	−28.2854			−1.22748
$532$	5.87028	+	4.47616i	0.254509	+	0.194066i
$533$		0			0
$534$	−6.75105	+	11.6932i	−0.292147	+	0.506013i
$535$	1.31070	+	2.27020i	0.0566665	+	0.0981493i
$536$	−4.60652	−	7.97873i	−0.198971	−	0.344629i
$537$	4.53286	−	7.85114i	0.195607	−	0.338802i
$538$	44.2809			1.90909
$539$	−10.4105	+	10.5378i	−0.448413	+	0.453894i
$540$	1.40052			0.0602689
$541$	−10.7497	+	18.6190i	−0.462165	+	0.800493i	−0.999069	−	0.0431505i	$-0.986260\pi$
$541$	−10.7497	+	18.6190i	−0.462165	+	0.800493i	0.536904	+	0.843644i	$0.319594\pi$
$542$	−13.9513	−	24.1644i	−0.599260	−	1.03795i
$543$	−1.37118	−	2.37495i	−0.0588428	−	0.101919i
$544$	1.05273	−	1.82338i	0.0451353	−	0.0781767i
$545$	−16.3783			−0.701569
$546$		0			0
$547$	−30.2968			−1.29540			−0.647699	−	0.761896i	$-0.724269\pi$
$547$	−30.2968			−1.29540			−0.647699	+	0.761896i	$0.724269\pi$
$548$	−0.576493	+	0.998514i	−0.0246265	+	0.0426544i
$549$	−11.4131	−	19.7680i	−0.487098	−	0.843679i
$550$	5.88947	+	10.2009i	0.251128	+	0.434967i
$551$	28.4854	−	49.3381i	1.21352	−	2.10187i
$552$	−4.33134			−0.184354
$553$	14.8244	−	6.19327i	0.630396	−	0.263365i
$554$	−20.8932			−0.887668
$555$	−1.45492	+	2.51999i	−0.0617579	+	0.106968i
$556$	4.75369	+	8.23364i	0.201601	+	0.349184i
$557$	−8.84201	−	15.3148i	−0.374648	−	0.648909i	0.615626	−	0.788038i	$-0.288903\pi$
$557$	−8.84201	−	15.3148i	−0.374648	−	0.648909i	−0.990274	+	0.139129i	$0.955570\pi$
$558$	−11.3474	+	19.6543i	−0.480374	+	0.832033i
$559$		0			0
$560$	1.87330	−	14.5710i	0.0791616	−	0.615737i
$561$	−0.938317			−0.0396158
$562$	23.2838	−	40.3287i	0.982167	−	1.70116i
$563$	20.8695	+	36.1471i	0.879545	+	1.52342i	0.851841	+	0.523801i	$0.175486\pi$
$563$	20.8695	+	36.1471i	0.879545	+	1.52342i	0.0277042	+	0.999616i	$0.491180\pi$
$564$	0.325115	+	0.563116i	0.0136898	+	0.0237115i
$565$	9.58852	−	16.6078i	0.403392	−	0.698696i
$566$	15.3777			0.646375
$567$	−2.32887	+	18.1145i	−0.0978035	+	0.760738i
$568$	6.22681			0.261271
$569$	−2.73388	+	4.73521i	−0.114610	+	0.198510i	−0.917624	−	0.397450i	$-0.869895\pi$
$569$	−2.73388	+	4.73521i	−0.114610	+	0.198510i	0.803014	+	0.595960i	$0.203229\pi$
$570$	3.03171	+	5.25108i	0.126984	+	0.219943i
$571$	−4.67621	−	8.09944i	−0.195693	−	0.338951i	0.751434	−	0.659808i	$-0.229362\pi$
$571$	−4.67621	−	8.09944i	−0.195693	−	0.338951i	−0.947128	+	0.320857i	$0.896029\pi$
$572$		0			0
$573$	−0.246437			−0.0102951
$574$	5.83112	−	2.43611i	0.243386	−	0.101681i
$575$	−12.8795			−0.537113
$576$	7.87968	−	13.6480i	0.328320	−	0.568667i
$577$	−1.68462	−	2.91786i	−0.0701318	−	0.121472i	0.828827	−	0.559505i	$-0.189009\pi$
$577$	−1.68462	−	2.91786i	−0.0701318	−	0.121472i	−0.898959	+	0.438033i	$0.855675\pi$
$578$	−12.5763	−	21.7829i	−0.523107	−	0.906048i
$579$	0.908159	−	1.57298i	0.0377418	−	0.0653707i
$580$	4.23151			0.175704
$581$	−24.4702	−	18.6588i	−1.01519	−	0.774098i
$582$	−4.71923			−0.195618
$583$	−2.98881	+	5.17676i	−0.123784	+	0.214400i
$584$	−7.05128	−	12.2132i	−0.291784	−	0.505385i
$585$		0			0
$586$	−6.14924	+	10.6508i	−0.254023	+	0.439980i
$587$	13.1528			0.542873			0.271437	−	0.962456i	$-0.412501\pi$
$587$	13.1528			0.542873			0.271437	+	0.962456i	$0.412501\pi$
$588$	1.38185	+	0.361284i	0.0569866	+	0.0148991i
$589$	−35.3769			−1.45768
$590$	9.48995	−	16.4371i	0.390695	−	0.676704i
$591$	1.82112	+	3.15427i	0.0749108	+	0.129749i
$592$	−11.6308	−	20.1452i	−0.478024	−	0.827961i
$593$	19.2958	−	33.4213i	0.792384	−	1.37245i	−0.132102	−	0.991236i	$-0.542173\pi$
$593$	19.2958	−	33.4213i	0.792384	−	1.37245i	0.924487	−	0.381214i	$-0.124494\pi$
$594$	9.27234			0.380449
$595$	2.27194	+	1.73238i	0.0931403	+	0.0710207i
$596$	6.01038			0.246195
$597$	1.83605	−	3.18014i	0.0751447	−	0.130154i
$598$		0			0
$599$	−9.20762	−	15.9481i	−0.376213	−	0.651620i	0.614295	−	0.789077i	$-0.289441\pi$
$599$	−9.20762	−	15.9481i	−0.376213	−	0.651620i	−0.990508	+	0.137457i	$0.956107\pi$
$600$	−2.15542	+	3.73329i	−0.0879946	+	0.152411i
$601$	−41.4037			−1.68889			−0.844445	−	0.535642i	$-0.820070\pi$
$601$	−41.4037			−1.68889			−0.844445	+	0.535642i	$0.820070\pi$
$602$	−20.6194	+	8.61431i	−0.840385	+	0.351093i
$603$	−10.3348			−0.420865
$604$	3.18169	−	5.51085i	0.129461	−	0.224233i
$605$	3.88549	+	6.72987i	0.157968	+	0.273608i
$606$	2.74690	+	4.75777i	0.111585	+	0.193271i
$607$	−6.15255	+	10.6565i	−0.249724	+	0.432535i	−0.963449	−	0.267891i	$-0.913673\pi$
$607$	−6.15255	+	10.6565i	−0.249724	+	0.432535i	0.713725	+	0.700426i	$0.247007\pi$
$608$	−15.5424			−0.630327
$609$	1.40556	−	10.9327i	0.0569560	−	0.443017i
$610$	15.3167			0.620155
$611$		0			0
$612$	−0.521725	−	0.903654i	−0.0210895	−	0.0365280i
$613$	13.1112	+	22.7093i	0.529556	+	0.917219i	0.999406	+	0.0344720i	$0.0109749\pi$
$613$	13.1112	+	22.7093i	0.529556	+	0.917219i	−0.469849	+	0.882747i	$0.655692\pi$
$614$	−0.989078	+	1.71313i	−0.0399160	+	0.0691365i
$615$	0.895620			0.0361149
$616$	1.75696	−	13.6661i	0.0707900	−	0.550621i
$617$	18.8252			0.757873			0.378936	−	0.925423i	$-0.376290\pi$
$617$	18.8252			0.757873			0.378936	+	0.925423i	$0.376290\pi$
$618$	−3.77519	+	6.53882i	−0.151860	+	0.263030i
$619$	−7.90415	−	13.6904i	−0.317695	−	0.550263i	0.662312	−	0.749228i	$-0.269575\pi$
$619$	−7.90415	−	13.6904i	−0.317695	−	0.550263i	−0.980007	+	0.198965i	$0.936242\pi$
$620$	−1.31381	−	2.27559i	−0.0527639	−	0.0913898i
$621$	−5.06935	+	8.78038i	−0.203426	+	0.352344i
$622$	−38.4994			−1.54369
$623$	43.3353	−	18.1045i	1.73619	−	0.725340i
$624$		0			0
$625$	−2.86003	+	4.95371i	−0.114401	+	0.198149i
$626$	1.84737	+	3.19973i	0.0738356	+	0.127887i
$627$	3.46331	+	5.99862i	0.138311	+	0.239562i
$628$	2.38030	−	4.12280i	0.0949843	−	0.164518i
$629$	4.52389			0.180379
$630$	−10.7591	−	8.20392i	−0.428651	−	0.326852i
$631$	16.6763			0.663875			0.331937	−	0.943301i	$-0.392298\pi$
$631$	16.6763			0.663875			0.331937	+	0.943301i	$0.392298\pi$
$632$	−7.47206	+	12.9420i	−0.297222	+	0.514804i
$633$	0.927285	+	1.60610i	0.0368563	+	0.0638369i
$634$	15.3755	+	26.6312i	0.610640	+	1.05766i
$635$	9.34050	−	16.1782i	0.370667	−	0.642013i
$636$	0.576375			0.0228548
$637$		0			0
$638$	28.0152			1.10913
$639$	3.49248	−	6.04916i	0.138161	−	0.239301i
$640$	8.05542	+	13.9524i	0.318418	+	0.551517i
$641$	−24.6232	−	42.6487i	−0.972559	−	1.68452i	−0.687767	−	0.725932i	$-0.741409\pi$
$641$	−24.6232	−	42.6487i	−0.972559	−	1.68452i	−0.284792	−	0.958589i	$-0.591925\pi$
$642$	0.836720	−	1.44924i	0.0330227	−	0.0571970i
$643$	−42.8711			−1.69067			−0.845335	−	0.534236i	$-0.820599\pi$
$643$	−42.8711			−1.69067			−0.845335	+	0.534236i	$0.820599\pi$
$644$	−3.15642	−	2.40681i	−0.124380	−	0.0948415i
$645$	−3.16700			−0.124701
$646$	4.71336	−	8.16378i	0.185445	−	0.321200i
$647$	−2.12929	−	3.68804i	−0.0837112	−	0.144992i	0.821130	−	0.570741i	$-0.193344\pi$
$647$	−2.12929	−	3.68804i	−0.0837112	−	0.144992i	−0.904841	+	0.425749i	$0.860011\pi$
$648$	−8.49410	−	14.7122i	−0.333680	−	0.577950i
$649$	10.8409	−	18.7771i	0.425544	−	0.737064i
$650$		0			0
$651$	−6.31572	+	2.63856i	−0.247533	+	0.103413i
$652$	6.00875			0.235321
$653$	1.04776	−	1.81477i	0.0410020	−	0.0710176i	−0.844796	−	0.535088i	$-0.820278\pi$
$653$	1.04776	−	1.81477i	0.0410020	−	0.0710176i	0.885798	+	0.464071i	$0.153612\pi$
$654$	5.22776	+	9.05475i	0.204422	+	0.354069i
$655$	5.68213	+	9.84174i	0.222019	+	0.384549i
$656$	−3.57986	+	6.20049i	−0.139770	+	0.242089i
$657$	−15.8196			−0.617183
$658$	1.67146	−	13.0010i	0.0651604	−	0.506833i
$659$	25.4518			0.991463			0.495732	−	0.868476i	$-0.334900\pi$
$659$	25.4518			0.991463			0.495732	+	0.868476i	$0.334900\pi$
$660$	−0.257237	+	0.445548i	−0.0100129	+	0.0173429i
$661$	13.9054	+	24.0848i	0.540857	+	0.936792i	0.998855	+	0.0478387i	$0.0152333\pi$
$661$	13.9054	+	24.0848i	0.540857	+	0.936792i	−0.457998	+	0.888953i	$0.651433\pi$
$662$	−3.05319	−	5.28829i	−0.118666	−	0.205535i
$663$		0			0
$664$	28.6234			1.11080
$665$	2.68937	−	20.9186i	0.104289	−	0.811187i
$666$	−21.4235			−0.830143
$667$	−15.3164	+	26.5288i	−0.593055	+	1.02720i
$668$	1.62064	+	2.80703i	0.0627044	+	0.108607i
$669$	−1.19103	−	2.06293i	−0.0460480	−	0.0797574i
$670$	3.46740	−	6.00572i	0.133957	−	0.232021i
$671$	17.4972			0.675472
$672$	−2.77473	+	1.15922i	−0.107038	+	0.0447178i
$673$	15.5207			0.598278			0.299139	−	0.954210i	$-0.403301\pi$
$673$	15.5207			0.598278			0.299139	+	0.954210i	$0.403301\pi$
$674$	−5.55100	+	9.61462i	−0.213817	+	0.370341i
$675$	5.04536	+	8.73881i	0.194196	+	0.336357i
$676$		0			0
$677$	−17.2813	+	29.9321i	−0.664175	+	1.15038i	0.315334	+	0.948981i	$0.397884\pi$
$677$	−17.2813	+	29.9321i	−0.664175	+	1.15038i	−0.979508	+	0.201403i	$0.935450\pi$
$678$	−12.2422			−0.470158
$679$	13.0533	+	9.95331i	0.500940	+	0.381973i
$680$	−2.65755			−0.101912
$681$	−5.91425	+	10.2438i	−0.226634	+	0.392542i
$682$	−8.69826	−	15.0658i	−0.333074	−	0.576900i
$683$	23.5032	+	40.7087i	0.899325	+	1.55768i	0.828359	+	0.560198i	$0.189275\pi$
$683$	23.5032	+	40.7087i	0.899325	+	1.55768i	0.0709661	+	0.997479i	$0.477392\pi$
$684$	−3.85135	+	6.67073i	−0.147260	+	0.255062i
$685$	3.29407			0.125860
$686$	−17.7356	−	22.6825i	−0.677148	−	0.866023i
$687$	−10.6228			−0.405284
$688$	12.6587	−	21.9255i	0.482609	−	0.835904i
$689$		0			0
$690$	−1.63013	−	2.82348i	−0.0620582	−	0.107488i
$691$	9.50301	−	16.4597i	0.361512	−	0.626156i	−0.626698	−	0.779262i	$-0.715594\pi$
$691$	9.50301	−	16.4597i	0.361512	−	0.626156i	0.988210	+	0.153106i	$0.0489275\pi$
$692$	2.54177			0.0966235
$693$	−12.2907	−	9.37183i	−0.466886	−	0.356006i
$694$	−15.6556			−0.594280
$695$	13.5813	−	23.5234i	0.515166	−	0.892294i
$696$	5.12648	+	8.87933i	0.194319	+	0.336570i
$697$	−0.696205	−	1.20586i	−0.0263706	−	0.0456753i
$698$	4.88822	−	8.46665i	0.185022	−	0.320467i
$699$	−1.85761			−0.0702612
$700$	−3.64523	+	1.52289i	−0.137777	+	0.0575598i
$701$	−45.4648			−1.71718			−0.858591	−	0.512662i	$-0.828659\pi$
$701$	−45.4648			−1.71718			−0.858591	+	0.512662i	$0.828659\pi$
$702$		0			0
$703$	−16.6976	−	28.9210i	−0.629760	−	1.09078i
$704$	6.04010	+	10.4618i	0.227645	+	0.394293i
$705$	0.928851	−	1.60882i	0.0349826	−	0.0605916i
$706$	53.1193			1.99917
$707$	2.43672	−	18.9534i	0.0916423	−	0.712815i
$708$	−2.09062			−0.0785702
$709$	−4.89390	+	8.47648i	−0.183794	+	0.318341i	−0.943170	−	0.332312i	$-0.892171\pi$
$709$	−4.89390	+	8.47648i	−0.183794	+	0.318341i	0.759375	+	0.650653i	$0.225505\pi$
$710$	2.34351	+	4.05908i	0.0879504	+	0.152334i
$711$	8.38183	+	14.5178i	0.314343	+	0.544459i
$712$	−21.8427	+	37.8326i	−0.818589	+	1.41784i
$713$	19.0220			0.712378
$714$	0.232572	−	1.80900i	0.00870377	−	0.0677000i
$715$		0			0
$716$	−3.86393	+	6.69252i	−0.144402	+	0.250111i
$717$	−5.35974	−	9.28334i	−0.200163	−	0.346693i
$718$	−14.5259	−	25.1595i	−0.542100	−	0.938945i
$719$	13.9201	−	24.1104i	0.519133	−	0.899165i	−0.480620	−	0.876929i	$-0.659588\pi$
$719$	13.9201	−	24.1104i	0.519133	−	0.899165i	0.999753	−	0.0222358i	$-0.00707846\pi$
$720$	15.3288			0.571271
$721$	24.2331	−	10.1240i	0.902489	−	0.377039i
$722$	−40.0485			−1.49045
$723$	5.07568	−	8.79134i	0.188767	−	0.326953i
$724$	1.16883	+	2.02447i	0.0434391	+	0.0752388i
$725$	15.2439	+	26.4033i	0.566145	+	0.980592i
$726$	2.48041	−	4.29619i	0.0920566	−	0.159447i
$727$	−14.5650			−0.540186			−0.270093	−	0.962834i	$-0.587055\pi$
$727$	−14.5650			−0.540186			−0.270093	+	0.962834i	$0.587055\pi$
$728$		0			0
$729$	−14.9199			−0.552589
$730$	5.30761	−	9.19305i	0.196444	−	0.340250i
$731$	2.46185	+	4.26405i	0.0910547	+	0.157711i
$732$	−0.843560	−	1.46109i	−0.0311789	−	0.0540034i
$733$	8.83030	−	15.2945i	0.326155	−	0.564916i	−0.655591	−	0.755116i	$-0.727580\pi$
$733$	8.83030	−	15.2945i	0.326155	−	0.564916i	0.981745	+	0.190200i	$0.0609136\pi$
$734$	48.2902			1.78243
$735$	−1.08007	−	3.93511i	−0.0398390	−	0.145149i
$736$	8.35705			0.308045
$737$	3.96102	−	6.86069i	0.145906	−	0.252717i
$738$	3.29697	+	5.71052i	0.121363	+	0.210207i
$739$	4.48279	+	7.76443i	0.164902	+	0.285619i	0.936621	−	0.350345i	$-0.113936\pi$
$739$	4.48279	+	7.76443i	0.164902	+	0.285619i	−0.771718	+	0.635964i	$0.780602\pi$
$740$	1.24021	−	2.14811i	0.0455911	−	0.0789661i
$741$		0			0
$742$	−9.23955	−	7.04528i	−0.339195	−	0.258640i
$743$	26.3679			0.967343			0.483671	−	0.875250i	$-0.339303\pi$
$743$	26.3679			0.967343			0.483671	+	0.875250i	$0.339303\pi$
$744$	3.18337	−	5.51376i	0.116708	−	0.202144i
$745$	−8.58580	−	14.8710i	−0.314560	−	0.544833i
$746$	−2.28309	−	3.95442i	−0.0835898	−	0.144782i
$747$	16.0543	−	27.8068i	0.587395	−	1.01740i
$748$	0.799847			0.0292453
$749$	−5.37095	+	2.24385i	−0.196250	+	0.0819887i
$750$	−7.77635			−0.283952
$751$	10.1438	−	17.5696i	0.370152	−	0.641123i	−0.619436	−	0.785047i	$-0.712639\pi$
$751$	10.1438	−	17.5696i	0.370152	−	0.641123i	0.989589	+	0.143924i	$0.0459721\pi$
$752$	7.42536	+	12.8611i	0.270775	+	0.468996i
$753$	3.24321	+	5.61740i	0.118189	+	0.204709i
$754$		0			0
$755$	−18.1801			−0.661642
$756$	−0.396552	+	3.08447i	−0.0144225	+	0.112181i
$757$	24.9984			0.908584			0.454292	−	0.890853i	$-0.349892\pi$
$757$	24.9984			0.908584			0.454292	+	0.890853i	$0.349892\pi$
$758$	−7.83957	+	13.5785i	−0.284746	+	0.493195i
$759$	−1.86220	−	3.22543i	−0.0675936	−	0.117076i
$760$	9.80895	+	16.9896i	0.355808	+	0.616277i
$761$	10.0711	−	17.4436i	0.365077	−	0.632332i	−0.623712	−	0.781655i	$-0.714376\pi$
$761$	10.0711	−	17.4436i	0.365077	−	0.632332i	0.988789	+	0.149323i	$0.0477094\pi$
$762$	−11.9255			−0.432016
$763$	4.63745	−	36.0711i	0.167887	−	1.30586i
$764$	0.210070			0.00760006
$765$	−1.49056	+	2.58173i	−0.0538914	+	0.0933426i
$766$	−2.86786	−	4.96729i	−0.103620	−	0.179475i
$767$		0			0
$768$	2.34945	−	4.06936i	0.0847784	−	0.146840i
$769$	−8.67220			−0.312727			−0.156364	−	0.987700i	$-0.549977\pi$
$769$	−8.67220			−0.312727			−0.156364	+	0.987700i	$0.549977\pi$
$770$	9.56976	−	3.99802i	0.344870	−	0.144079i
$771$	6.44398			0.232074
$772$	−0.774139	+	1.34085i	−0.0278619	+	0.0482582i
$773$	1.17283	+	2.03141i	0.0421839	+	0.0730647i	0.886346	−	0.463023i	$-0.153235\pi$
$773$	1.17283	+	2.03141i	0.0421839	+	0.0730647i	−0.844163	+	0.536087i	$0.819902\pi$
$774$	−11.6584	−	20.1930i	−0.419053	−	0.725821i
$775$	9.46596	−	16.3955i	0.340027	−	0.588945i
$776$	−15.2688			−0.548119
$777$	−5.13801	−	3.91780i	−0.184325	−	0.140550i
$778$	−35.2396			−1.26340
$779$	−5.13935	+	8.90161i	−0.184136	+	0.318933i
$780$		0			0
$781$	2.67713	+	4.63693i	0.0957953	+	0.165922i
$782$	−2.53435	+	4.38962i	−0.0906281	+	0.156973i
$783$	23.9999			0.857687
$784$	31.5604	+	8.25143i	1.12716	+	0.294694i
$785$	−13.6010			−0.485440
$786$	3.62734	−	6.28274i	0.129383	−	0.224098i
$787$	−17.0583	−	29.5459i	−0.608063	−	1.05320i	−0.991559	−	0.129654i	$-0.958613\pi$
$787$	−17.0583	−	29.5459i	−0.608063	−	1.05320i	0.383496	−	0.923543i	$-0.374720\pi$
$788$	−1.55237	−	2.68878i	−0.0553009	−	0.0957840i
$789$	−4.68228	+	8.10994i	−0.166693	+	0.288721i
$790$	−11.2487			−0.400210
$791$	33.8616	+	25.8199i	1.20398	+	0.918051i
$792$	14.3768			0.510858
$793$		0			0
$794$	22.6486	+	39.2286i	0.803770	+	1.39217i
$795$	−0.823349	−	1.42608i	−0.0292012	−	0.0505779i
$796$	−1.56510	+	2.71084i	−0.0554736	+	0.0960830i
$797$	−34.0844			−1.20733			−0.603666	−	0.797237i	$-0.706294\pi$
$797$	−34.0844			−1.20733			−0.603666	+	0.797237i	$0.706294\pi$
$798$	−12.4232	+	5.19014i	−0.439778	+	0.183729i
$799$	−2.88815			−0.102175
$800$	4.15875	−	7.20316i	0.147034	−	0.254670i
$801$	24.5022	+	42.4390i	0.865742	+	1.49951i
$802$	−6.31243	−	10.9335i	−0.222900	−	0.386074i
$803$	6.06320	−	10.5018i	0.213966	−	0.370600i
$804$	−0.763862			−0.0269393
$805$	−1.44606	+	11.2478i	−0.0509670	+	0.396433i
$806$		0			0
$807$	−6.96748	+	12.0680i	−0.245267	+	0.424815i
$808$	8.88745	+	15.3935i	0.312659	+	0.541542i
$809$	13.2603	+	22.9675i	0.466206	+	0.807493i	0.999255	−	0.0385914i	$-0.0122871\pi$
$809$	13.2603	+	22.9675i	0.466206	+	0.807493i	−0.533049	+	0.846085i	$0.678954\pi$
$810$	6.39365	−	11.0741i	0.224650	−	0.389105i
$811$	−52.5463			−1.84515			−0.922575	−	0.385818i	$-0.873919\pi$
$811$	−52.5463			−1.84515			−0.922575	+	0.385818i	$0.873919\pi$
$812$	−1.19813	+	9.31936i	−0.0420462	+	0.327045i
$813$	8.78080			0.307956
$814$	8.21099	−	14.2219i	0.287795	−	0.498476i
$815$	−8.58347	−	14.8670i	−0.300666	−	0.520768i
$816$	1.03318	+	1.78953i	0.0361686	+	0.0626459i
$817$	18.1732	−	31.4770i	0.635801	−	1.10124i
$818$	−12.9391			−0.452403
$819$		0			0
$820$	−0.763451			−0.0266609
$821$	−15.3773	+	26.6343i	−0.536671	+	0.929542i	0.462409	+	0.886667i	$0.346985\pi$
$821$	−15.3773	+	26.6343i	−0.536671	+	0.929542i	−0.999080	+	0.0428753i	$0.986348\pi$
$822$	−1.05143	−	1.82113i	−0.0366728	−	0.0635191i
$823$	14.8519	+	25.7243i	0.517705	+	0.896691i	0.999789	+	0.0205659i	$0.00654678\pi$
$823$	14.8519	+	25.7243i	0.517705	+	0.896691i	−0.482084	+	0.876125i	$0.660120\pi$
$824$	−12.2144	+	21.1560i	−0.425510	+	0.737006i
$825$	−3.70677			−0.129053
$826$	33.5136	+	25.5545i	1.16609	+	0.889155i
$827$	−14.8351			−0.515866			−0.257933	−	0.966163i	$-0.583041\pi$
$827$	−14.8351			−0.515866			−0.257933	+	0.966163i	$0.583041\pi$
$828$	2.07085	−	3.58681i	0.0719670	−	0.124650i
$829$	−7.29244	−	12.6309i	−0.253277	−	0.438688i	0.711149	−	0.703041i	$-0.248175\pi$
$829$	−7.29244	−	12.6309i	−0.253277	−	0.438688i	−0.964426	+	0.264353i	$0.914842\pi$
$830$	10.7727	+	18.6588i	0.373925	+	0.647657i
$831$	3.28749	−	5.69411i	0.114042	−	0.197526i
$832$		0			0
$833$	−4.45864	+	4.51314i	−0.154483	+	0.156371i
$834$	−17.3399			−0.600432
$835$	4.63015	−	8.01966i	0.160233	−	0.277532i
$836$	−2.95221	−	5.11339i	−0.102104	−	0.176850i
$837$	−7.45157	−	12.9065i	−0.257564	−	0.446114i
$838$	−10.1184	+	17.5256i	−0.349534	+	0.605411i
$839$	−36.8086			−1.27077			−0.635386	−	0.772194i	$-0.719159\pi$
$839$	−36.8086			−1.27077			−0.635386	+	0.772194i	$0.719159\pi$
$840$	3.01832	+	2.30150i	0.104142	+	0.0794095i
$841$	43.5128			1.50044
$842$	6.91588	−	11.9787i	0.238337	−	0.412812i
$843$	7.32728	+	12.6912i	0.252365	+	0.437109i
$844$	−0.790442	−	1.36909i	−0.0272082	−	0.0471259i
$845$		0			0
$846$	13.6772			0.470232
$847$	−15.9219	+	6.65177i	−0.547081	+	0.228558i
$848$	13.1639			0.452051
$849$	−2.41965	+	4.19095i	−0.0830421	+	0.143833i
$850$	2.52235	+	4.36884i	0.0865160	+	0.149850i
$851$	8.97819	+	15.5507i	0.307768	+	0.533070i
$852$	0.258135	−	0.447103i	0.00884357	−	0.0153175i
$853$	4.10728			0.140630			0.0703152	−	0.997525i	$-0.477599\pi$
$853$	4.10728			0.140630			0.0703152	+	0.997525i	$0.477599\pi$
$854$	−4.33686	+	33.7331i	−0.148404	+	1.15432i
$855$	22.0065			0.752607
$856$	2.70717	−	4.68895i	0.0925291	−	0.160265i
$857$	19.1656	+	33.1958i	0.654684	+	1.13395i	0.981973	+	0.189022i	$0.0605318\pi$
$857$	19.1656	+	33.1958i	0.654684	+	1.13395i	−0.327288	+	0.944925i	$0.606135\pi$
$858$		0			0
$859$	19.7185	−	34.1534i	0.672785	−	1.16530i	−0.304326	−	0.952568i	$-0.598431\pi$
$859$	19.7185	−	34.1534i	0.672785	−	1.16530i	0.977111	−	0.212730i	$-0.0682356\pi$
$860$	2.69964			0.0920569
$861$	−0.253591	+	1.97249i	−0.00864236	+	0.0672223i
$862$	−13.9260			−0.474322
$863$	−19.3220	+	33.4667i	−0.657728	+	1.13922i	0.323474	+	0.946237i	$0.395149\pi$
$863$	−19.3220	+	33.4667i	−0.657728	+	1.13922i	−0.981202	+	0.192982i	$0.938184\pi$
$864$	−3.27375	−	5.67030i	−0.111375	−	0.192907i
$865$	−3.63090	−	6.28891i	−0.123454	−	0.213829i
$866$	−0.134410	+	0.232805i	−0.00456744	+	0.00791104i
$867$	7.91541			0.268821
$868$	5.38369	−	2.24918i	0.182734	−	0.0763421i
$869$	−12.8500			−0.435908
$870$	−3.85879	+	6.68361i	−0.130825	+	0.226596i
$871$		0			0
$872$	16.9142	+	29.2962i	0.572786	+	0.992094i
$873$	−8.56395	+	14.8332i	−0.289846	+	0.502028i
$874$	37.4169			1.26564
$875$	21.5093	+	16.4011i	0.727145	+	0.554458i
$876$	−1.16926			−0.0395055
$877$	−29.0371	+	50.2937i	−0.980512	+	1.69830i	−0.320118	+	0.947378i	$0.603723\pi$
$877$	−29.0371	+	50.2937i	−0.980512	+	1.69830i	−0.660394	+	0.750919i	$0.729611\pi$
$878$	7.41710	+	12.8468i	0.250315	+	0.433558i
$879$	−1.93513	−	3.35175i	−0.0652704	−	0.113052i
$880$	−5.87508	+	10.1759i	−0.198049	+	0.343031i
$881$	21.6236			0.728519			0.364259	−	0.931298i	$-0.381322\pi$
$881$	21.6236			0.728519			0.364259	+	0.931298i	$0.381322\pi$
$882$	21.1145	−	21.3726i	0.710962	−	0.719652i
$883$	−22.7329			−0.765022			−0.382511	−	0.923951i	$-0.624941\pi$
$883$	−22.7329			−0.765022			−0.382511	+	0.923951i	$0.624941\pi$
$884$		0			0
$885$	2.98644	+	5.17266i	0.100388	+	0.173877i
$886$	−10.7845	−	18.6793i	−0.362312	−	0.627543i
$887$	8.16585	−	14.1437i	0.274182	−	0.474898i	−0.695746	−	0.718288i	$-0.744926\pi$
$887$	8.16585	−	14.1437i	0.274182	−	0.474898i	0.969929	+	0.243390i	$0.0782595\pi$
$888$	6.01008			0.201685
$889$	32.9858	+	25.1521i	1.10631	+	0.843574i
$890$	−32.8827			−1.10223
$891$	7.30385	−	12.6506i	0.244688	−	0.423812i
$892$	1.01527	+	1.75850i	0.0339937	+	0.0588788i
$893$	10.6601	+	18.4638i	0.356726	+	0.617867i
$894$	−5.48098	+	9.49333i	−0.183311	+	0.317504i
$895$	22.0784			0.738000
$896$	−33.0093	+	13.7905i	−1.10276	+	0.460708i
$897$		0			0
$898$	16.5506	−	28.6665i	0.552301	−	0.956614i
$899$	−22.5140	−	38.9954i	−0.750884	−	1.30057i
$900$	−2.06105	−	3.56984i	−0.0687015	−	0.118995i
$901$	−1.28005	+	2.21711i	−0.0426446	+	0.0738627i
$902$	−5.05453			−0.168297
$903$	0.896723	−	6.97492i	0.0298411	−	0.232111i
$904$	−39.6089			−1.31737
$905$	3.33933	−	5.78389i	0.111003	−	0.192263i
$906$	5.80288	+	10.0509i	0.192788	+	0.333918i
$907$	−7.20480	−	12.4791i	−0.239232	−	0.414361i	0.721262	−	0.692662i	$-0.243562\pi$
$907$	−7.20480	−	12.4791i	−0.239232	−	0.414361i	−0.960494	+	0.278301i	$0.910229\pi$
$908$	5.04146	−	8.73207i	0.167307	−	0.289784i
$909$	19.9391			0.661339
$910$		0			0
$911$	−1.32236			−0.0438118			−0.0219059	−	0.999760i	$-0.506973\pi$
$911$	−1.32236			−0.0438118			−0.0219059	+	0.999760i	$0.506973\pi$
$912$	7.62691	−	13.2102i	0.252552	−	0.437433i
$913$	12.3063	+	21.3151i	0.407278	+	0.705426i
$914$	−7.52907	−	13.0407i	−0.249039	−	0.431349i
$915$	−2.41004	+	4.17432i	−0.0796735	+	0.137999i
$916$	9.05513			0.299190
$917$	−23.2841	+	9.72753i	−0.768907	+	0.321231i
$918$	3.97117			0.131068
$919$	13.7229	−	23.7688i	0.452677	−	0.784059i	−0.545875	−	0.837867i	$-0.683802\pi$
$919$	13.7229	−	23.7688i	0.452677	−	0.784059i	0.998551	+	0.0538078i	$0.0171358\pi$
$920$	−5.27422	−	9.13522i	−0.173886	−	0.301179i
$921$	−0.311258	−	0.539114i	−0.0102563	−	0.0177644i
$922$	1.06835	−	1.85043i	0.0351841	−	0.0609407i
$923$		0			0
$924$	−0.908428	−	0.692688i	−0.0298851	−	0.0227878i
$925$	17.8714			0.587607
$926$	−24.6970	+	42.7765i	−0.811594	+	1.40572i
$927$	13.7016	+	23.7319i	0.450021	+	0.779459i
$928$	−9.89123	−	17.1321i	−0.324696	−	0.562389i
$929$	−14.3194	+	24.8020i	−0.469805	+	0.813727i	−0.999404	−	0.0345217i	$-0.989009\pi$
$929$	−14.3194	+	24.8020i	−0.469805	+	0.813727i	0.529599	+	0.848248i	$0.322343\pi$
$930$	4.79235			0.157147
$931$	45.3090	+	11.8460i	1.48494	+	0.388237i
$932$	1.58348			0.0518685
$933$	6.05778	−	10.4924i	0.198323	−	0.343505i
$934$	−22.6370	−	39.2084i	−0.740704	−	1.28294i
$935$	−1.14258	−	1.97900i	−0.0373663	−	0.0647203i
$936$		0			0
$937$	27.9990			0.914688			0.457344	−	0.889290i	$-0.348801\pi$
$937$	27.9990			0.914688			0.457344	+	0.889290i	$0.348801\pi$
$938$	12.2451	+	9.33701i	0.399815	+	0.304864i
$939$	−1.16271			−0.0379437
$940$	−0.791778	+	1.37140i	−0.0258249	+	0.0447301i
$941$	14.4502	+	25.0284i	0.471062	+	0.815903i	0.999452	−	0.0330983i	$-0.0105375\pi$
$941$	14.4502	+	25.0284i	0.471062	+	0.815903i	−0.528390	+	0.849002i	$0.677204\pi$
$942$	4.34127	+	7.51931i	0.141446	+	0.244992i
$943$	2.76340	−	4.78635i	0.0899887	−	0.155865i
$944$	−47.7480			−1.55406
$945$	8.19816	−	3.42500i	0.266686	−	0.111415i
$946$	17.8733			0.581111
$947$	15.0617	−	26.0877i	0.489441	−	0.847736i	−0.510486	−	0.859886i	$-0.670534\pi$
$947$	15.0617	−	26.0877i	0.489441	−	0.847736i	0.999926	+	0.0121504i	$0.00386769\pi$
$948$	0.619515	+	1.07303i	0.0201209	+	0.0348505i
$949$		0			0
$950$	18.6199	−	32.2506i	0.604109	−	1.04635i
$951$	−9.67719			−0.313805
$952$	0.752474	−	5.85292i	0.0243878	−	0.189694i
$953$	4.93022			0.159705			0.0798527	−	0.996807i	$-0.474555\pi$
$953$	4.93022			0.159705			0.0798527	+	0.996807i	$0.474555\pi$
$954$	6.06185	−	10.4994i	0.196260	−	0.339932i
$955$	−0.300084	−	0.519760i	−0.00971048	−	0.0168190i
$956$	4.56879	+	7.91337i	0.147765	+	0.255937i
$957$	−4.40812	+	7.63509i	−0.142494	+	0.246808i
$958$	15.1144			0.488325
$959$	−0.932701	+	7.25477i	−0.0301185	+	0.234269i
$960$	−3.32783			−0.107405
$961$	1.51957	−	2.63197i	0.0490184	−	0.0849024i
$962$		0			0
$963$	−3.03678	−	5.25986i	−0.0978590	−	0.169497i
$964$	−4.32665	+	7.49398i	−0.139352	+	0.241365i
$965$	4.42341			0.142395
$966$	6.67992	−	2.79071i	0.214923	−	0.0897896i
$967$	−29.1431			−0.937180			−0.468590	−	0.883416i	$-0.655238\pi$
$967$	−29.1431			−0.937180			−0.468590	+	0.883416i	$0.655238\pi$
$968$	8.02523	−	13.9001i	0.257941	−	0.446767i
$969$	1.48327	+	2.56910i	0.0476495	+	0.0825313i
$970$	−5.74654	−	9.95331i	−0.184510	−	0.319581i
$971$	−7.28843	+	12.6239i	−0.233897	+	0.405121i	−0.958952	−	0.283570i	$-0.908481\pi$
$971$	−7.28843	+	12.6239i	−0.233897	+	0.405121i	0.725055	+	0.688691i	$0.241814\pi$
$972$	−4.93476			−0.158282
$973$	47.9619	+	36.5716i	1.53759	+	1.17243i
$974$	−26.6058			−0.852506
$975$		0			0
$976$	−19.2662	−	33.3700i	−0.616696	−	1.06815i
$977$	26.2609	+	45.4852i	0.840161	+	1.45520i	0.889758	+	0.456432i	$0.150873\pi$
$977$	26.2609	+	45.4852i	0.840161	+	1.45520i	−0.0495974	+	0.998769i	$0.515794\pi$
$978$	−5.47948	+	9.49074i	−0.175215	+	0.303481i
$979$	−37.5639			−1.20055
$980$	0.920681	+	3.35439i	0.0294101	+	0.107152i
$981$	37.9472			1.21156
$982$	−19.9943	+	34.6312i	−0.638044	+	1.10513i
$983$	−3.01884	−	5.22879i	−0.0962862	−	0.166773i	0.813858	−	0.581063i	$-0.197363\pi$
$983$	−3.01884	−	5.22879i	−0.0962862	−	0.166773i	−0.910145	+	0.414291i	$0.864030\pi$
$984$	−0.924923	−	1.60201i	−0.0294855	−	0.0510703i
$985$	−4.43511	+	7.68183i	−0.141314	+	0.244764i
$986$	11.9984			0.382107
$987$	3.28022	+	2.50121i	0.104410	+	0.0796143i
$988$		0			0
$989$	−9.77166	+	16.9250i	−0.310721	+	0.538184i
$990$	5.41083	+	9.37183i	0.171967	+	0.297856i
$991$	−15.6742	−	27.1485i	−0.497907	−	0.862400i	0.502090	−	0.864815i	$-0.332564\pi$
$991$	−15.6742	−	27.1485i	−0.497907	−	0.862400i	−0.999997	+	0.00241558i	$0.999231\pi$
$992$	−6.14212	+	10.6385i	−0.195012	+	0.337771i
$993$	1.92165			0.0609816
$994$	−9.60316	+	4.01197i	−0.304594	+	0.127252i
$995$	8.94296			0.283511
$996$	1.18660	−	2.05525i	0.0375988	−	0.0651230i
$997$	−2.74017	−	4.74611i	−0.0867819	−	0.150311i	0.819367	−	0.573269i	$-0.194325\pi$
$997$	−2.74017	−	4.74611i	−0.0867819	−	0.150311i	−0.906149	+	0.422958i	$0.860992\pi$
$998$	−4.20073	−	7.27588i	−0.132972	−	0.230314i
$999$	7.03414	−	12.1835i	0.222550	−	0.385468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.g.170.5		12
7.2	even	3		8281.2.a.ce.1.2		6
7.4	even	3	inner	1183.2.e.g.508.5		12
7.5	odd	6		8281.2.a.cf.1.2		6
13.4	even	6		91.2.h.b.16.5	yes	12
13.10	even	6		91.2.g.b.9.2	✓	12
13.12	even	2		1183.2.e.h.170.2		12
39.17	odd	6		819.2.s.d.289.2		12
39.23	odd	6		819.2.n.d.100.5		12
91.4	even	6		91.2.g.b.81.2	yes	12
91.10	odd	6		637.2.h.l.165.5		12
91.12	odd	6		8281.2.a.ca.1.5		6
91.17	odd	6		637.2.g.l.263.2		12
91.23	even	6		637.2.f.k.295.2		12
91.25	even	6		1183.2.e.h.508.2		12
91.30	even	6		637.2.f.k.393.2		12
91.51	even	6		8281.2.a.bz.1.5		6
91.62	odd	6		637.2.g.l.373.2		12
91.69	odd	6		637.2.h.l.471.5		12
91.75	odd	6		637.2.f.j.295.2		12
91.82	odd	6		637.2.f.j.393.2		12
91.88	even	6		91.2.h.b.74.5	yes	12
273.95	odd	6		819.2.n.d.172.5		12
273.179	odd	6		819.2.s.d.802.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.2	✓	12	13.10	even	6
91.2.g.b.81.2	yes	12	91.4	even	6
91.2.h.b.16.5	yes	12	13.4	even	6
91.2.h.b.74.5	yes	12	91.88	even	6
637.2.f.j.295.2		12	91.75	odd	6
637.2.f.j.393.2		12	91.82	odd	6
637.2.f.k.295.2		12	91.23	even	6
637.2.f.k.393.2		12	91.30	even	6
637.2.g.l.263.2		12	91.17	odd	6
637.2.g.l.373.2		12	91.62	odd	6
637.2.h.l.165.5		12	91.10	odd	6
637.2.h.l.471.5		12	91.69	odd	6
819.2.n.d.100.5		12	39.23	odd	6
819.2.n.d.172.5		12	273.95	odd	6
819.2.s.d.289.2		12	39.17	odd	6
819.2.s.d.802.2		12	273.179	odd	6
1183.2.e.g.170.5		12	1.1	even	1	trivial
1183.2.e.g.508.5		12	7.4	even	3	inner
1183.2.e.h.170.2		12	13.12	even	2
1183.2.e.h.508.2		12	91.25	even	6
8281.2.a.bz.1.5		6	91.51	even	6
8281.2.a.ca.1.5		6	91.12	odd	6
8281.2.a.ce.1.2		6	7.2	even	3
8281.2.a.cf.1.2		6	7.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.777343 - 1.34640i) q^{2} +(0.244626 + 0.423704i) q^{3} +(-0.208526 - 0.361177i) q^{4} +(-0.595756 + 1.03188i) q^{5} +0.760633 q^{6} +(-2.10390 - 1.60425i) q^{7} +2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +(0.926214 + 1.60425i) q^{10} +(1.05807 + 1.83263i) q^{11} +(0.102021 - 0.176706i) q^{12} +(-3.79541 + 1.58563i) q^{14} -0.582949 q^{15} +(2.33009 - 4.03583i) q^{16} +(0.453151 + 0.784881i) q^{17} +(-2.14596 - 3.71691i) q^{18} +(3.34514 - 5.79395i) q^{19} +0.496921 q^{20} +(0.165059 - 1.28387i) q^{21} +3.28993 q^{22} +(-1.79866 + 3.11538i) q^{23} +(0.602021 + 1.04273i) q^{24} +(1.79015 + 3.10063i) q^{25} +2.81840 q^{27} +(-0.140701 + 1.09441i) q^{28} +8.51545 q^{29} +(-0.453151 + 0.784881i) q^{30} +(-2.64390 - 4.57937i) q^{31} +(-1.16156 - 2.01189i) q^{32} +(-0.517662 + 0.896617i) q^{33} +1.40902 q^{34} +(2.90880 - 1.21523i) q^{35} -1.15133 q^{36} +(2.49579 - 4.32284i) q^{37} +(-5.20065 - 9.00778i) q^{38} +(-1.46615 + 2.53944i) q^{40} -1.53636 q^{41} +(-1.60029 - 1.22024i) q^{42} +5.43273 q^{43} +(0.441269 - 0.764301i) q^{44} +(1.64466 + 2.84864i) q^{45} +(2.79636 + 4.84344i) q^{46} +(-1.59337 + 2.75979i) q^{47} +2.28000 q^{48} +(1.85277 + 6.75035i) q^{49} +5.56625 q^{50} +(-0.221705 + 0.384004i) q^{51} +(1.41239 + 2.44632i) q^{53} +(2.19086 - 3.79469i) q^{54} -2.52140 q^{55} +(-5.17767 - 3.94804i) q^{56} +3.27323 q^{57} +(6.61943 - 11.4652i) q^{58} +(-5.12298 - 8.87327i) q^{59} +(0.121560 + 0.210548i) q^{60} +(4.13423 - 7.16069i) q^{61} -8.22088 q^{62} +(-6.73945 + 2.81558i) q^{63} +5.70861 q^{64} +(0.804802 + 1.39396i) q^{66} +(-1.87182 - 3.24208i) q^{67} +(0.188987 - 0.327336i) q^{68} -1.76000 q^{69} +(0.624956 - 4.86105i) q^{70} +2.53020 q^{71} +(3.39694 - 5.88368i) q^{72} +(-2.86522 - 4.96271i) q^{73} +(-3.88018 - 6.72066i) q^{74} +(-0.875834 + 1.51699i) q^{75} -2.79019 q^{76} +(0.713925 - 5.55307i) q^{77} +(-3.03620 + 5.25885i) q^{79} +(2.77632 + 4.80873i) q^{80} +(-3.45150 - 5.97817i) q^{81} +(-1.19428 + 2.06856i) q^{82} +11.6309 q^{83} +(-0.498124 + 0.208104i) q^{84} -1.07987 q^{85} +(4.22310 - 7.31462i) q^{86} +(2.08310 + 3.60803i) q^{87} +(2.60390 + 4.51008i) q^{88} +(-8.87557 + 15.3729i) q^{89} +5.11387 q^{90} +1.50027 q^{92} +(1.29353 - 2.24046i) q^{93} +(2.47719 + 4.29061i) q^{94} +(3.98577 + 6.90356i) q^{95} +(0.568297 - 0.984319i) q^{96} -6.20434 q^{97} +(10.5289 + 2.75277i) q^{98} +5.84188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21}+ \cdots + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 5 * q^12 - 2 * q^14 - 4 * q^15 + 8 * q^16 + 5 * q^17 - 3 * q^18 + q^19 - 2 * q^20 + 9 * q^21 + 10 * q^22 - q^23 + 11 * q^24 + 7 * q^25 - 8 * q^27 - 8 * q^28 - 6 * q^29 - 5 * q^30 - 16 * q^31 - 8 * q^32 - 16 * q^33 - 32 * q^34 - 28 * q^35 + 42 * q^36 + 13 * q^37 - 17 * q^38 - 5 * q^40 - 16 * q^41 - 52 * q^42 + 22 * q^43 - 21 * q^44 + 7 * q^45 - 16 * q^46 + q^47 - 42 * q^48 + 6 * q^49 + 12 * q^50 - 20 * q^51 - 2 * q^53 + 18 * q^54 - 18 * q^55 + 9 * q^56 - 42 * q^57 + 8 * q^58 - 13 * q^59 - 20 * q^60 - 5 * q^61 - 10 * q^62 - 8 * q^63 - 30 * q^64 + 18 * q^66 + 11 * q^67 + 29 * q^68 - 46 * q^69 + 39 * q^70 + 12 * q^71 - 25 * q^72 + 30 * q^73 - 3 * q^74 - 3 * q^75 - 18 * q^76 + 11 * q^77 + 7 * q^79 + 7 * q^80 - 6 * q^81 + q^82 + 54 * q^83 - 41 * q^84 - 2 * q^85 + 7 * q^86 + 16 * q^87 - 4 * q^89 - 16 * q^90 + 54 * q^92 + 7 * q^93 + 45 * q^94 - 6 * q^95 - 19 * q^96 - 70 * q^97 + 82 * q^98 + 20 * q^99

Introduction

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