LMFDB - Embedded newform 1183.2.e.h.170.1

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)

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")

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);

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			170.1
Root			$0.217953 + 0.377506i$ of defining polynomial
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.h.508.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.929081 + 1.60921i) q^{2} +(-1.14703 - 1.98672i) q^{3} +(-0.726381 - 1.25813i) q^{4} +(0.0986811 - 0.170921i) q^{5} +4.26275 q^{6} +(-2.62662 + 0.317598i) q^{7} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +(0.183365 + 0.317598i) q^{10} +(2.09137 + 3.62236i) q^{11} +(-1.66637 + 2.88623i) q^{12} +(1.92926 - 4.52187i) q^{14} -0.452762 q^{15} +(2.39750 - 4.15260i) q^{16} +(-0.420653 - 0.728592i) q^{17} +(-2.10227 - 3.64125i) q^{18} +(-0.675876 + 1.17065i) q^{19} -0.286720 q^{20} +(3.64380 + 4.85406i) q^{21} -7.77220 q^{22} +(2.05760 - 3.56386i) q^{23} +(1.16637 + 2.02021i) q^{24} +(2.48052 + 4.29639i) q^{25} -1.69131 q^{27} +(2.30751 + 3.07393i) q^{28} -8.23861 q^{29} +(0.420653 - 0.728592i) q^{30} +(0.640350 + 1.10912i) q^{31} +(3.43809 + 5.95495i) q^{32} +(4.79774 - 8.30993i) q^{33} +1.56328 q^{34} +(-0.204914 + 0.480285i) q^{35} +3.28723 q^{36} +(-1.52242 + 2.63692i) q^{37} +(-1.25589 - 2.17526i) q^{38} +(-0.100344 + 0.173802i) q^{40} +5.39696 q^{41} +(-11.1966 + 1.35384i) q^{42} +5.32778 q^{43} +(3.03826 - 5.26242i) q^{44} +(0.223290 + 0.386750i) q^{45} +(3.82334 + 6.62223i) q^{46} +(5.83204 - 10.1014i) q^{47} -11.0001 q^{48} +(6.79826 - 1.66842i) q^{49} -9.21843 q^{50} +(-0.965006 + 1.67144i) q^{51} +(-2.32398 - 4.02525i) q^{53} +(1.57136 - 2.72168i) q^{54} +0.825514 q^{55} +(2.67089 - 0.322952i) q^{56} +3.10101 q^{57} +(7.65434 - 13.2577i) q^{58} +(-3.02905 - 5.24648i) q^{59} +(0.328878 + 0.569634i) q^{60} +(5.68285 - 9.84298i) q^{61} -2.37975 q^{62} +(2.34932 - 5.50644i) q^{63} -3.18704 q^{64} +(8.91498 + 15.4412i) q^{66} +(-6.69851 - 11.6022i) q^{67} +(-0.611109 + 1.05847i) q^{68} -9.44053 q^{69} +(-0.582500 - 0.775973i) q^{70} -5.97040 q^{71} +(1.15044 - 1.99263i) q^{72} +(-1.94273 - 3.36491i) q^{73} +(-2.82891 - 4.89982i) q^{74} +(5.69049 - 9.85622i) q^{75} +1.96377 q^{76} +(-6.64368 - 8.85034i) q^{77} +(5.36669 - 9.29537i) q^{79} +(-0.473177 - 0.819566i) q^{80} +(5.33411 + 9.23895i) q^{81} +(-5.01421 + 8.68486i) q^{82} +3.07390 q^{83} +(3.46025 - 8.11027i) q^{84} -0.166042 q^{85} +(-4.94994 + 8.57354i) q^{86} +(9.44997 + 16.3678i) q^{87} +(-2.12662 - 3.68341i) q^{88} +(5.99207 - 10.3786i) q^{89} -0.829819 q^{90} -5.97840 q^{92} +(1.46901 - 2.54439i) q^{93} +(10.8369 + 18.7700i) q^{94} +(0.133392 + 0.231042i) q^{95} +(7.88721 - 13.6611i) q^{96} +19.4727 q^{97} +(-3.63129 + 12.4900i) q^{98} -9.46448 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 $

$2$	−0.929081	+	1.60921i	−0.656959	+	1.13789i	0.324440	+	0.945906i	$0.394824\pi$
$2$	−0.929081	+	1.60921i	−0.656959	+	1.13789i	−0.981399	+	0.191980i	$0.938509\pi$
$3$	−1.14703	−	1.98672i	−0.662240	−	1.14703i	−0.980026	−	0.198871i	$-0.936272\pi$
$3$	−1.14703	−	1.98672i	−0.662240	−	1.14703i	0.317785	−	0.948163i	$-0.397061\pi$
$4$	−0.726381	−	1.25813i	−0.363191	−	0.629065i
$5$	0.0986811	−	0.170921i	0.0441315	−	0.0764381i	−0.843116	−	0.537732i	$-0.819281\pi$
$5$	0.0986811	−	0.170921i	0.0441315	−	0.0764381i	0.887247	+	0.461294i	$0.152615\pi$
$6$	4.26275			1.74026
$7$	−2.62662	+	0.317598i	−0.992769	+	0.120041i
$7$	−2.62662	+	0.317598i	−0.992769	+	0.120041i
$8$	−1.01686			−0.359513
$9$	−1.13137	+	1.95960i	−0.377125	+	0.653199i
$10$	0.183365	+	0.317598i	0.0579852	+	0.100433i
$11$	2.09137	+	3.62236i	0.630571	+	1.09218i	0.987435	+	0.158025i	$0.0505127\pi$
$11$	2.09137	+	3.62236i	0.630571	+	1.09218i	−0.356864	+	0.934156i	$0.616154\pi$
$12$	−1.66637	+	2.88623i	−0.481039	+	0.833184i
$13$		0			0
$13$		0			0
$14$	1.92926	−	4.52187i	0.515616	−	1.20852i
$15$	−0.452762			−0.116903
$16$	2.39750	−	4.15260i	0.599376	−	1.03815i
$17$	−0.420653	−	0.728592i	−0.102023	−	0.176709i	0.810495	−	0.585746i	$-0.199198\pi$
$17$	−0.420653	−	0.728592i	−0.102023	−	0.176709i	−0.912518	+	0.409036i	$0.865865\pi$
$18$	−2.10227	−	3.64125i	−0.495511	−	0.858250i
$19$	−0.675876	+	1.17065i	−0.155057	+	0.268566i	−0.933080	−	0.359670i	$-0.882889\pi$
$19$	−0.675876	+	1.17065i	−0.155057	+	0.268566i	0.778023	+	0.628236i	$0.216223\pi$
$20$	−0.286720			−0.0641126
$21$	3.64380	+	4.85406i	0.795143	+	1.05924i
$22$	−7.77220			−1.65704
$23$	2.05760	−	3.56386i	0.429038	−	0.743116i	−0.567750	−	0.823201i	$-0.692186\pi$
$23$	2.05760	−	3.56386i	0.429038	−	0.743116i	0.996788	+	0.0800850i	$0.0255192\pi$
$24$	1.16637	+	2.02021i	0.238084	+	0.412373i
$25$	2.48052	+	4.29639i	0.496105	+	0.859279i
$26$		0			0
$27$	−1.69131			−0.325492
$28$	2.30751	+	3.07393i	0.436078	+	0.580918i
$29$	−8.23861			−1.52987			−0.764936	−	0.644106i	$-0.777230\pi$
$29$	−8.23861			−1.52987			−0.764936	+	0.644106i	$0.777230\pi$
$30$	0.420653	−	0.728592i	0.0768003	−	0.133022i
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	0.917784	−	0.397080i	$-0.129977\pi$
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	−0.802774	+	0.596284i	$0.796643\pi$
$32$	3.43809	+	5.95495i	0.607774	+	1.05270i
$33$	4.79774	−	8.30993i	0.835180	−	1.44657i
$34$	1.56328			0.268100
$35$	−0.204914	+	0.480285i	−0.0346367	+	0.0811829i
$36$	3.28723			0.547872
$37$	−1.52242	+	2.63692i	−0.250285	+	0.433506i	−0.963604	−	0.267333i	$-0.913858\pi$
$37$	−1.52242	+	2.63692i	−0.250285	+	0.433506i	0.713319	+	0.700839i	$0.247191\pi$
$38$	−1.25589	−	2.17526i	−0.203732	−	0.352874i
$39$		0			0
$40$	−0.100344	+	0.173802i	−0.0158659	+	0.0274805i
$41$	5.39696			0.842863			0.421431	−	0.906860i	$-0.361528\pi$
$41$	5.39696			0.842863			0.421431	+	0.906860i	$0.361528\pi$
$42$	−11.1966	+	1.35384i	−1.72768	+	0.208902i
$43$	5.32778			0.812479			0.406239	−	0.913767i	$-0.366840\pi$
$43$	5.32778			0.812479			0.406239	+	0.913767i	$0.366840\pi$
$44$	3.03826	−	5.26242i	0.458035	−	0.793340i
$45$	0.223290	+	0.386750i	0.0332862	+	0.0576534i
$46$	3.82334	+	6.62223i	0.563721	+	0.976394i
$47$	5.83204	−	10.1014i	0.850690	−	1.47344i	−0.0298969	−	0.999553i	$-0.509518\pi$
$47$	5.83204	−	10.1014i	0.850690	−	1.47344i	0.880587	−	0.473885i	$-0.157149\pi$
$48$	−11.0001			−1.58772
$49$	6.79826	−	1.66842i	0.971180	−	0.238346i
$50$	−9.21843			−1.30368
$51$	−0.965006	+	1.67144i	−0.135128	+	0.234048i
$52$		0			0
$53$	−2.32398	−	4.02525i	−0.319223	−	0.552911i	0.661103	−	0.750295i	$-0.270089\pi$
$53$	−2.32398	−	4.02525i	−0.319223	−	0.552911i	−0.980326	+	0.197384i	$0.936755\pi$
$54$	1.57136	−	2.72168i	0.213835	−	0.370373i
$55$	0.825514			0.111312
$56$	2.67089	−	0.322952i	0.356913	−	0.0431562i
$57$	3.10101			0.410739
$58$	7.65434	−	13.2577i	1.00506	−	1.74082i
$59$	−3.02905	−	5.24648i	−0.394349	−	0.683033i	0.598669	−	0.800997i	$-0.295697\pi$
$59$	−3.02905	−	5.24648i	−0.394349	−	0.683033i	−0.993018	+	0.117964i	$0.962363\pi$
$60$	0.328878	+	0.569634i	0.0424580	+	0.0735394i
$61$	5.68285	−	9.84298i	0.727614	−	1.26026i	−0.230275	−	0.973126i	$-0.573962\pi$
$61$	5.68285	−	9.84298i	0.727614	−	1.26026i	0.957889	−	0.287139i	$-0.0927042\pi$
$62$	−2.37975			−0.302228
$63$	2.34932	−	5.50644i	0.295987	−	0.693746i
$64$	−3.18704			−0.398380
$65$		0			0
$66$	8.91498	+	15.4412i	1.09736	+	1.90068i
$67$	−6.69851	−	11.6022i	−0.818354	−	1.41743i	−0.906895	−	0.421357i	$-0.861554\pi$
$67$	−6.69851	−	11.6022i	−0.818354	−	1.41743i	0.0885411	−	0.996073i	$-0.471780\pi$
$68$	−0.611109	+	1.05847i	−0.0741078	+	0.128358i
$69$	−9.44053			−1.13651
$70$	−0.582500	−	0.775973i	−0.0696221	−	0.0927465i
$71$	−5.97040			−0.708556			−0.354278	−	0.935140i	$-0.615273\pi$
$71$	−5.97040			−0.708556			−0.354278	+	0.935140i	$0.615273\pi$
$72$	1.15044	−	1.99263i	0.135581	−	0.234833i
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	0.729651	−	0.683820i	$-0.239683\pi$
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	−0.957031	+	0.289986i	$0.906349\pi$
$74$	−2.82891	−	4.89982i	−0.328854	−	0.569592i
$75$	5.69049	−	9.85622i	0.657081	−	1.13810i
$76$	1.96377			0.225260
$77$	−6.64368	−	8.85034i	−0.757118	−	1.00859i
$78$		0			0
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	−0.388441	−	0.921474i	$-0.626986\pi$
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	0.992240	−	0.124337i	$-0.0396805\pi$
$80$	−0.473177	−	0.819566i	−0.0529028	−	0.0916303i
$81$	5.33411	+	9.23895i	0.592679	+	1.02655i
$82$	−5.01421	+	8.68486i	−0.553726	+	0.959082i
$83$	3.07390			0.337404			0.168702	−	0.985667i	$-0.446042\pi$
$83$	3.07390			0.337404			0.168702	+	0.985667i	$0.446042\pi$
$84$	3.46025	−	8.11027i	0.377544	−	0.884903i
$85$	−0.166042			−0.0180098
$86$	−4.94994	+	8.57354i	−0.533765	+	0.924509i
$87$	9.44997	+	16.3678i	1.01314	+	1.75482i
$88$	−2.12662	−	3.68341i	−0.226698	−	0.392653i
$89$	5.99207	−	10.3786i	0.635159	−	1.10013i	−0.351323	−	0.936254i	$-0.614268\pi$
$89$	5.99207	−	10.3786i	0.635159	−	1.10013i	0.986482	−	0.163873i	$-0.0523986\pi$
$90$	−0.829819			−0.0874706
$91$		0			0
$92$	−5.97840			−0.623291
$93$	1.46901	−	2.54439i	0.152329	−	0.263841i
$94$	10.8369	+	18.7700i	1.11774	+	1.93598i
$95$	0.133392	+	0.231042i	0.0136858	+	0.0237045i
$96$	7.88721	−	13.6611i	0.804986	−	1.39428i
$97$	19.4727			1.97716			0.988578	−	0.150709i	$-0.0481558\pi$
$97$	19.4727			1.97716			0.988578	+	0.150709i	$0.0481558\pi$
$98$	−3.63129	+	12.4900i	−0.366815	+	1.26168i
$99$	−9.46448			−0.951216
$100$	3.60361	−	6.24164i	0.360361	−	0.624164i
$101$	8.46697	+	14.6652i	0.842495	+	1.45924i	0.887779	+	0.460270i	$0.152247\pi$
$101$	8.46697	+	14.6652i	0.842495	+	1.45924i	−0.0452843	+	0.998974i	$0.514419\pi$
$102$	−1.79314	−	3.10580i	−0.177547	−	0.307520i
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	−0.630952	−	0.775822i	$-0.717335\pi$
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	0.987357	+	0.158509i	$0.0506688\pi$
$104$		0			0
$105$	1.18923	−	0.143797i	0.116057	−	0.0140331i
$106$	8.63667			0.838867
$107$	4.92625	−	8.53251i	0.476238	−	0.824869i	−0.523391	−	0.852093i	$-0.675333\pi$
$107$	4.92625	−	8.53251i	0.476238	−	0.824869i	0.999629	+	0.0272237i	$0.00866664\pi$
$108$	1.22853	+	2.12788i	0.118216	+	0.204756i
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	0.980179	+	0.198115i	$0.0634821\pi$
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	−0.318516	+	0.947917i	$0.603185\pi$
$110$	−0.766969	+	1.32843i	−0.0731277	+	0.126661i
$111$	6.98509			0.662995
$112$	−4.97847	+	11.6687i	−0.470421	+	1.10259i
$113$	−4.26864			−0.401560			−0.200780	−	0.979636i	$-0.564348\pi$
$113$	−4.26864			−0.401560			−0.200780	+	0.979636i	$0.564348\pi$
$114$	−2.88109	+	4.99019i	−0.269839	+	0.467374i
$115$	−0.406092	−	0.703371i	−0.0378682	−	0.0655897i
$116$	5.98437	+	10.3652i	0.555635	+	0.962388i
$117$		0			0
$118$	11.2569			1.03629
$119$	1.33629	+	1.78014i	0.122498	+	0.163185i
$120$	0.460394			0.0420280
$121$	−3.24765	+	5.62509i	−0.295240	+	0.511372i
$122$	10.5596	+	18.2898i	0.956026	+	1.65589i
$123$	−6.19049	−	10.7222i	−0.558178	−	0.966792i
$124$	0.930276	−	1.61129i	0.0835412	−	0.144698i
$125$	1.96593			0.175839
$126$	6.67833	+	8.89649i	0.594953	+	0.792562i
$127$	−2.19024			−0.194352			−0.0971761	−	0.995267i	$-0.530981\pi$
$127$	−2.19024			−0.194352			−0.0971761	+	0.995267i	$0.530981\pi$
$128$	−3.91516	+	6.78126i	−0.346055	+	0.599385i
$129$	−6.11114	−	10.5848i	−0.538056	−	0.931941i
$130$		0			0
$131$	−1.13806	+	1.97117i	−0.0994326	+	0.172222i	−0.911450	−	0.411411i	$-0.865036\pi$
$131$	−1.13806	+	1.97117i	−0.0994326	+	0.172222i	0.812017	+	0.583633i	$0.198369\pi$
$132$	−13.9400			−1.21332
$133$	1.40347	−	3.28951i	0.121696	−	0.285237i
$134$	24.8938			2.15050
$135$	−0.166900	+	0.289079i	−0.0143645	+	0.0248800i
$136$	0.427743	+	0.740873i	0.0366787	+	0.0635293i
$137$	−6.72399	−	11.6463i	−0.574469	−	0.995010i	−0.996099	−	0.0882417i	$-0.971875\pi$
$137$	−6.72399	−	11.6463i	−0.574469	−	0.995010i	0.421630	−	0.906768i	$-0.361458\pi$
$138$	8.77101	−	15.1918i	0.746638	−	1.29321i
$139$	4.04540			0.343126			0.171563	−	0.985173i	$-0.445118\pi$
$139$	4.04540			0.343126			0.171563	+	0.985173i	$0.445118\pi$
$140$	0.753106	−	0.0910619i	0.0636490	−	0.00769614i
$141$	−26.7582			−2.25344
$142$	5.54698	−	9.60765i	0.465492	−	0.806256i
$143$		0			0
$144$	5.42494	+	9.39628i	0.452079	+	0.783023i
$145$	−0.812996	+	1.40815i	−0.0675156	+	0.116940i
$146$	7.21982			0.597517
$147$	−11.1125	−	11.5925i	−0.916545	−	0.956135i
$148$	4.42344			0.363605
$149$	−7.67596	+	13.2952i	−0.628840	+	1.08918i	0.358945	+	0.933359i	$0.383136\pi$
$149$	−7.67596	+	13.2952i	−0.628840	+	1.08918i	−0.987785	+	0.155823i	$0.950197\pi$
$150$	10.5738	+	18.3144i	0.863351	+	1.49537i
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	0.714203	−	0.699939i	$-0.246789\pi$
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	−0.963266	+	0.268548i	$0.913456\pi$
$152$	0.687268	−	1.19038i	0.0557448	−	0.0965528i
$153$	1.90366			0.153902
$154$	20.4146	−	2.46844i	1.64506	−	0.198912i
$155$	0.252762			0.0203023
$156$		0			0
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	0.761199	−	0.648518i	$-0.224611\pi$
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	−0.942233	+	0.334959i	$0.891278\pi$
$158$	9.97217	+	17.2723i	0.793343	+	1.37411i
$159$	−5.33137	+	9.23421i	−0.422805	+	0.732320i
$160$	1.35710			0.107288
$161$	−4.27265	+	10.0144i	−0.336732	+	0.789245i
$162$	−19.8233			−1.55746
$163$	−0.911271	+	1.57837i	−0.0713762	+	0.123627i	−0.899505	−	0.436911i	$-0.856072\pi$
$163$	−0.911271	+	1.57837i	−0.0713762	+	0.123627i	0.828128	+	0.560538i	$0.189406\pi$
$164$	−3.92025	−	6.79007i	−0.306120	−	0.530215i
$165$	−0.946893	−	1.64007i	−0.0737155	−	0.127679i
$166$	−2.85590	+	4.94656i	−0.221661	+	0.383928i
$167$	−10.7079			−0.828606			−0.414303	−	0.910139i	$-0.635975\pi$
$167$	−10.7079			−0.828606			−0.414303	+	0.910139i	$0.635975\pi$
$168$	−3.70522	−	4.93588i	−0.285864	−	0.380812i
$169$		0			0
$170$	0.154266	−	0.267197i	0.0118317	−	0.0204931i
$171$	−1.52934	−	2.64889i	−0.116951	−	0.202566i
$172$	−3.87000	−	6.70303i	−0.295085	−	0.511102i
$173$	6.74634	−	11.6850i	0.512915	−	0.888395i	−0.486973	−	0.873417i	$-0.661899\pi$
$173$	6.74634	−	11.6850i	0.512915	−	0.888395i	0.999888	−	0.0149778i	$-0.00476775\pi$
$174$	−35.1191			−2.66237
$175$	−7.87992	−	10.4972i	−0.595666	−	0.793512i
$176$	20.0563			1.51180
$177$	−6.94886	+	12.0358i	−0.522308	+	0.904664i
$178$	11.1342	+	19.2851i	0.834547	+	1.44548i
$179$	−5.23458	−	9.06657i	−0.391251	−	0.677667i	0.601364	−	0.798975i	$-0.294624\pi$
$179$	−5.23458	−	9.06657i	−0.391251	−	0.677667i	−0.992615	+	0.121309i	$0.961291\pi$
$180$	0.324388	−	0.561857i	0.0241785	−	0.0418783i
$181$	12.5209			0.930674			0.465337	−	0.885133i	$-0.345933\pi$
$181$	12.5209			0.930674			0.465337	+	0.885133i	$0.345933\pi$
$182$		0			0
$183$	−26.0737			−1.92742
$184$	−2.09228	+	3.62393i	−0.154245	+	0.267160i
$185$	0.300469	+	0.520428i	0.0220909	+	0.0382626i
$186$	2.72965	+	4.72789i	0.200148	+	0.346666i
$187$	1.75948	−	3.04751i	0.128666	−	0.222856i
$188$	−16.9451			−1.23585
$189$	4.44242	−	0.537156i	0.323139	−	0.0390724i
$190$	−0.495729			−0.0359640
$191$	−6.55685	+	11.3568i	−0.474437	+	0.821749i	−0.999572	−	0.0292704i	$-0.990682\pi$
$191$	−6.55685	+	11.3568i	−0.474437	+	0.821749i	0.525135	+	0.851019i	$0.324015\pi$
$192$	3.65565	+	6.33176i	0.263823	+	0.456956i
$193$	−0.520786	−	0.902028i	−0.0374870	−	0.0649294i	0.846673	−	0.532113i	$-0.178602\pi$
$193$	−0.520786	−	0.902028i	−0.0374870	−	0.0649294i	−0.884160	+	0.467184i	$0.845269\pi$
$194$	−18.0917	+	31.3358i	−1.29891	+	2.24978i
$195$		0			0
$196$	−7.03722	−	7.34118i	−0.502658	−	0.524370i
$197$	1.47833			0.105327			0.0526635	−	0.998612i	$-0.483229\pi$
$197$	1.47833			0.105327			0.0526635	+	0.998612i	$0.483229\pi$
$198$	8.79326	−	15.2304i	0.624910	−	1.08238i
$199$	−7.04993	−	12.2108i	−0.499756	−	0.865603i	0.500244	−	0.865885i	$-0.333244\pi$
$199$	−7.04993	−	12.2108i	−0.499756	−	0.865603i	−1.00000		0.000281618i	$0.999910\pi$
$200$	−2.52233	−	4.36881i	−0.178356	−	0.308922i
$201$	−15.3668	+	26.6162i	−1.08389	+	1.87736i
$202$	−31.4660			−2.21394
$203$	21.6397	−	2.61657i	1.51881	−	0.183647i
$204$	2.80385			0.196309
$205$	0.532578	−	0.922451i	0.0371968	−	0.0644268i
$206$	6.72120	+	11.6415i	0.468288	+	0.811099i
$207$	4.65582	+	8.06412i	0.323602	+	0.560495i
$208$		0			0
$209$	−5.65402			−0.391097
$210$	−0.873495	+	2.04733i	−0.0602769	+	0.141279i
$211$	26.4692			1.82222			0.911108	−	0.412167i	$-0.135228\pi$
$211$	26.4692			1.82222			0.911108	+	0.412167i	$0.135228\pi$
$212$	−3.37619	+	5.84774i	−0.231878	+	0.401624i
$213$	6.84825	+	11.8615i	0.469234	+	0.812737i
$214$	9.15376	+	15.8548i	0.625738	+	1.08381i
$215$	0.525751	−	0.910628i	0.0358559	−	0.0621043i
$216$	1.71981			0.117019
$217$	−2.03421	−	2.70986i	−0.138091	−	0.183957i
$218$	−25.6722			−1.73874
$219$	−4.45676	+	7.71934i	−0.301160	+	0.521625i
$220$	−0.599638	−	1.03860i	−0.0404276	−	0.0700227i
$221$		0			0
$222$	−6.48971	+	11.2405i	−0.435561	+	0.754414i
$223$	−0.728048			−0.0487537			−0.0243769	−	0.999703i	$-0.507760\pi$
$223$	−0.728048			−0.0487537			−0.0243769	+	0.999703i	$0.507760\pi$
$224$	−10.9218	−	14.5495i	−0.729746	−	0.972126i
$225$	−11.2256			−0.748373
$226$	3.96591	−	6.86916i	0.263808	−	0.456929i
$227$	1.42598	+	2.46986i	0.0946454	+	0.163931i	0.909461	−	0.415790i	$-0.136495\pi$
$227$	1.42598	+	2.46986i	0.0946454	+	0.163931i	−0.814815	+	0.579721i	$0.803162\pi$
$228$	−2.25252	−	3.90147i	−0.149177	−	0.258381i
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	−0.913679	−	0.406436i	$-0.866772\pi$
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	0.808823	+	0.588052i	$0.200105\pi$
$230$	1.50917			0.0995116
$231$	−9.96262	+	23.3508i	−0.655492	+	1.53637i
$232$	8.37748			0.550009
$233$	−6.70354	+	11.6109i	−0.439163	+	0.760653i	−0.997625	−	0.0688769i	$-0.978058\pi$
$233$	−6.70354	+	11.6109i	−0.439163	+	0.760653i	0.558462	+	0.829530i	$0.311392\pi$
$234$		0			0
$235$	−1.15102	−	1.99363i	−0.0750845	−	0.130050i
$236$	−4.40050	+	7.62188i	−0.286448	+	0.496142i
$237$	−24.6231			−1.59944
$238$	−4.10614	+	0.496495i	−0.266162	+	0.0321830i
$239$	−15.5538			−1.00609			−0.503046	−	0.864259i	$-0.667788\pi$
$239$	−15.5538			−1.00609			−0.503046	+	0.864259i	$0.667788\pi$
$240$	−1.08550	+	1.88014i	−0.0700687	+	0.121363i
$241$	3.78787	+	6.56078i	0.243998	+	0.422617i	0.961849	−	0.273579i	$-0.0882076\pi$
$241$	3.78787	+	6.56078i	0.243998	+	0.422617i	−0.717851	+	0.696196i	$0.754874\pi$
$242$	−6.03465	−	10.4523i	−0.387922	−	0.671900i
$243$	9.69985	−	16.8006i	0.622245	−	1.07776i
$244$	−16.5117			−1.05705
$245$	0.385693	−	1.32661i	0.0246410	−	0.0847537i
$246$	23.0059			1.46680
$247$		0			0
$248$	−0.651143	−	1.12781i	−0.0413476	−	0.0716162i
$249$	−3.52587	−	6.10698i	−0.223443	−	0.387014i
$250$	−1.82651	+	3.16361i	−0.115519	+	0.200084i
$251$	1.27476			0.0804624			0.0402312	−	0.999190i	$-0.487191\pi$
$251$	1.27476			0.0804624			0.0402312	+	0.999190i	$0.487191\pi$
$252$	−8.63432	+	1.04402i	−0.543911	+	0.0657671i
$253$	17.2128			1.08216
$254$	2.03491	−	3.52456i	0.127682	−	0.221151i
$255$	0.190456	+	0.329879i	0.0119268	+	0.0206578i
$256$	−10.4620	−	18.1208i	−0.653878	−	1.13255i
$257$	4.24010	−	7.34406i	0.264490	−	0.458110i	−0.702940	−	0.711249i	$-0.748130\pi$
$257$	4.24010	−	7.34406i	0.264490	−	0.458110i	0.967430	+	0.253139i	$0.0814631\pi$
$258$	22.7110			1.41392
$259$	3.16135	−	7.40970i	0.196437	−	0.460416i
$260$		0			0
$261$	9.32095	−	16.1444i	0.576952	−	0.999311i
$262$	−2.11470	−	3.66276i	−0.130646	−	0.226286i
$263$	−6.39415	−	11.0750i	−0.394280	−	0.682913i	0.598729	−	0.800952i	$-0.295673\pi$
$263$	−6.39415	−	11.0750i	−0.394280	−	0.682913i	−0.993009	+	0.118038i	$0.962339\pi$
$264$	−4.87861	+	8.45000i	−0.300258	+	0.520062i
$265$	−0.917333			−0.0563513
$266$	3.98959	+	5.31471i	0.244618	+	0.325866i
$267$	−27.4925			−1.68251
$268$	−9.73135	+	16.8552i	−0.594437	+	1.02959i
$269$	2.35586	+	4.08047i	0.143639	+	0.248790i	0.928864	−	0.370420i	$-0.120786\pi$
$269$	2.35586	+	4.08047i	0.143639	+	0.248790i	−0.785225	+	0.619210i	$0.787453\pi$
$270$	−0.310127	−	0.537156i	−0.0188737	−	0.0326903i
$271$	9.00562	−	15.5982i	0.547052	−	0.947522i	−0.451422	−	0.892310i	$-0.649083\pi$
$271$	9.00562	−	15.5982i	0.547052	−	0.947522i	0.998475	−	0.0552119i	$-0.0175834\pi$
$272$	−4.03407			−0.244601
$273$		0			0
$274$	24.9885			1.50961
$275$	−10.3754	+	17.9707i	−0.625659	+	1.08367i
$276$	6.85742	+	11.8774i	0.412768	+	0.714936i
$277$	13.0604	+	22.6213i	0.784725	+	1.35918i	0.929163	+	0.369670i	$0.120529\pi$
$277$	13.0604	+	22.6213i	0.784725	+	1.35918i	−0.144438	+	0.989514i	$0.546137\pi$
$278$	−3.75850	+	6.50991i	−0.225420	+	0.390439i
$279$	−2.89790			−0.173493
$280$	0.208368	−	0.488380i	0.0124523	−	0.0291863i
$281$	−3.66197			−0.218455			−0.109227	−	0.994017i	$-0.534838\pi$
$281$	−3.66197			−0.218455			−0.109227	+	0.994017i	$0.534838\pi$
$282$	24.8605	−	43.0596i	1.48042	−	2.56416i
$283$	−3.82263	−	6.62099i	−0.227232	−	0.393577i	0.729755	−	0.683709i	$-0.239634\pi$
$283$	−3.82263	−	6.62099i	−0.227232	−	0.393577i	−0.956987	+	0.290132i	$0.906301\pi$
$284$	4.33678	+	7.51153i	0.257341	+	0.445727i
$285$	0.306011	−	0.530027i	0.0181265	−	0.0313961i
$286$		0			0
$287$	−14.1757	+	1.71406i	−0.836768	+	0.101178i
$288$	−15.5591			−0.916827
$289$	8.14610	−	14.1095i	0.479183	−	0.829968i
$290$	−1.51068	−	2.61657i	−0.0887100	−	0.153650i
$291$	−22.3359	−	38.6869i	−1.30935	−	2.26787i
$292$	−2.82233	+	4.88842i	−0.165164	+	0.286073i
$293$	−17.1534			−1.00211			−0.501056	−	0.865415i	$-0.667055\pi$
$293$	−17.1534			−1.00211			−0.501056	+	0.865415i	$0.667055\pi$
$294$	28.9793	−	7.11205i	1.69011	−	0.414783i
$295$	−1.19564			−0.0696130
$296$	1.54809	−	2.68136i	0.0899807	−	0.155851i
$297$	−3.53715	−	6.12652i	−0.205246	−	0.355497i
$298$	−14.2632	−	24.7045i	−0.826244	−	1.43110i
$299$		0			0
$300$	−16.5339			−0.954583
$301$	−13.9940	+	1.69209i	−0.806604	+	0.0975306i
$302$	11.3740			0.654498
$303$	19.4238	−	33.6430i	1.11587	−	1.93274i
$304$	3.24083	+	5.61328i	0.185874	+	0.321944i
$305$	−1.12158	−	1.94263i	−0.0642215	−	0.111235i
$306$	−1.76866	+	3.06340i	−0.101107	+	0.175123i
$307$	−28.0696			−1.60201			−0.801007	−	0.598655i	$-0.795702\pi$
$307$	−28.0696			−1.60201			−0.801007	+	0.598655i	$0.795702\pi$
$308$	−6.30902	+	14.7873i	−0.359490	+	0.842586i
$309$	−16.5959			−0.944105
$310$	−0.234836	+	0.406748i	−0.0133378	+	0.0231017i
$311$	11.7670	+	20.3811i	0.667248	+	1.15571i	0.978671	+	0.205436i	$0.0658611\pi$
$311$	11.7670	+	20.3811i	0.667248	+	1.15571i	−0.311423	+	0.950271i	$0.600806\pi$
$312$		0			0
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	−0.814820	−	0.579714i	$-0.803164\pi$
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	0.909457	+	0.415798i	$0.136498\pi$
$314$	8.42989			0.475726
$315$	−0.709330	−	0.944930i	−0.0399662	−	0.0532408i
$316$	−15.5930			−0.877177
$317$	3.63917	−	6.30323i	0.204396	−	0.354025i	−0.745544	−	0.666456i	$-0.767810\pi$
$317$	3.63917	−	6.30323i	0.204396	−	0.354025i	0.949940	+	0.312432i	$0.101144\pi$
$318$	−9.90655	−	17.1586i	−0.555532	−	0.962209i
$319$	−17.2300	−	29.8432i	−0.964694	−	1.67090i
$320$	−0.314501	+	0.544732i	−0.0175811	+	0.0304514i
$321$	−22.6023			−1.26154
$322$	−12.1457	−	16.1798i	−0.676852	−	0.901664i
$323$	1.13724			0.0632775
$324$	7.74919	−	13.4220i	0.430511	−	0.745666i
$325$		0			0
$326$	−1.69329	−	2.93286i	−0.0937826	−	0.162436i
$327$	15.8473	−	27.4484i	0.876359	−	1.51790i
$328$	−5.48792			−0.303020
$329$	−12.1104	+	28.3847i	−0.667666	+	1.56490i
$330$	3.51896			0.193712
$331$	7.16168	−	12.4044i	0.393642	−	0.681807i	−0.599285	−	0.800536i	$-0.704548\pi$
$331$	7.16168	−	12.4044i	0.393642	−	0.681807i	0.992927	+	0.118728i	$0.0378818\pi$
$332$	−2.23282	−	3.86736i	−0.122542	−	0.212249i
$333$	−3.44486	−	5.96668i	−0.188777	−	0.326972i
$334$	9.94855	−	17.2314i	0.544360	−	0.942860i
$335$	−2.64407			−0.144461
$336$	28.8930	−	3.49360i	1.57624	−	0.190592i
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$		0			0
$339$	4.89627	+	8.48060i	0.265929	+	0.460603i
$340$	0.120610	+	0.208902i	0.00654098	+	0.0113293i
$341$	−2.67841	+	4.63915i	−0.145044	+	0.251224i
$342$	5.68351			0.307329
$343$	−17.3266	+	6.54142i	−0.935547	+	0.353203i
$344$	−5.41758			−0.292096
$345$	−0.931602	+	1.61358i	−0.0501558	+	0.0868723i
$346$	12.5358	+	21.7126i	0.673928	+	1.16728i
$347$	3.85139	+	6.67080i	0.206753	+	0.358107i	0.950690	−	0.310143i	$-0.100377\pi$
$347$	3.85139	+	6.67080i	0.206753	+	0.358107i	−0.743937	+	0.668250i	$0.767044\pi$
$348$	13.7286	−	23.7786i	0.735928	−	1.27466i
$349$	22.3701			1.19744			0.598721	−	0.800958i	$-0.295676\pi$
$349$	22.3701			1.19744			0.598721	+	0.800958i	$0.295676\pi$
$350$	24.2133	−	2.92776i	1.29426	−	0.156495i
$351$		0			0
$352$	−14.3806	+	24.9080i	−0.766490	+	1.32760i
$353$	11.1311	+	19.2797i	0.592451	+	1.02616i	0.993901	+	0.110275i	$0.0351731\pi$
$353$	11.1311	+	19.2797i	0.592451	+	1.02616i	−0.401450	+	0.915881i	$0.631494\pi$
$354$	−12.9121	−	22.3644i	−0.686270	−	1.18865i
$355$	−0.589165	+	1.02046i	−0.0312697	+	0.0541606i
$356$	−17.4101			−0.922735
$357$	2.00386	−	4.69672i	0.106055	−	0.248577i
$358$	19.4534			1.02814
$359$	1.37921	−	2.38887i	0.0727920	−	0.126079i	−0.827332	−	0.561713i	$-0.810142\pi$
$359$	1.37921	−	2.38887i	0.0727920	−	0.126079i	0.900124	+	0.435634i	$0.143476\pi$
$360$	−0.227054	−	0.393269i	−0.0119668	−	0.0207271i
$361$	8.58638	+	14.8721i	0.451915	+	0.782740i
$362$	−11.6330	+	20.1489i	−0.611415	+	1.05900i
$363$	14.9006			0.782081
$364$		0			0
$365$	−0.766844			−0.0401385
$366$	24.2246	−	41.9582i	1.26624	−	2.19319i
$367$	7.07485	+	12.2540i	0.369304	+	0.639654i	0.989457	−	0.144827i	$-0.0462626\pi$
$367$	7.07485	+	12.2540i	0.369304	+	0.639654i	−0.620153	+	0.784481i	$0.712929\pi$
$368$	−9.86618	−	17.0887i	−0.514310	−	0.890812i
$369$	−6.10597	+	10.5759i	−0.317864	+	0.550557i
$370$	−1.11664			−0.0580514
$371$	7.38263	+	9.83472i	0.383287	+	0.510593i
$372$	−4.26823			−0.221298
$373$	2.52142	−	4.36723i	0.130554	−	0.226127i	−0.793336	−	0.608784i	$-0.791658\pi$
$373$	2.52142	−	4.36723i	0.130554	−	0.226127i	0.923890	+	0.382657i	$0.124991\pi$
$374$	3.26940	+	5.66276i	0.169056	+	0.292814i
$375$	−2.25499	−	3.90576i	−0.116447	−	0.201693i
$376$	−5.93034	+	10.2716i	−0.305834	+	0.529720i
$377$		0			0
$378$	−3.26297	+	7.64787i	−0.167829	+	0.393364i
$379$	−6.05964			−0.311263			−0.155631	−	0.987815i	$-0.549741\pi$
$379$	−6.05964			−0.311263			−0.155631	+	0.987815i	$0.549741\pi$
$380$	0.193787	−	0.335650i	0.00994109	−	0.0172185i
$381$	2.51228	+	4.35139i	0.128708	+	0.222929i
$382$	−12.1837	−	21.1028i	−0.623371	−	1.07971i
$383$	2.27052	−	3.93266i	0.116018	−	0.200950i	−0.802168	−	0.597098i	$-0.796320\pi$
$383$	2.27052	−	3.93266i	0.116018	−	0.200950i	0.918186	+	0.396149i	$0.129654\pi$
$384$	17.9633			0.916686
$385$	−2.16831	+	0.262182i	−0.110507	+	0.0133620i
$386$	1.93541			0.0985098
$387$	−6.02771	+	10.4403i	−0.306406	+	0.530710i
$388$	−14.1446	−	24.4992i	−0.718085	−	1.24376i
$389$	−2.25383	−	3.90374i	−0.114273	−	0.197927i	0.803216	−	0.595688i	$-0.203121\pi$
$389$	−2.25383	−	3.90374i	−0.114273	−	0.197927i	−0.917489	+	0.397761i	$0.869787\pi$
$390$		0			0
$391$	−3.46213			−0.175088
$392$	−6.91285	+	1.69654i	−0.349152	+	0.0856883i
$393$	5.22157			0.263393
$394$	−1.37349	+	2.37896i	−0.0691955	+	0.119850i
$395$	−1.05918	−	1.83456i	−0.0532932	−	0.0923065i
$396$	6.87482	+	11.9075i	0.345473	+	0.598376i
$397$	−2.00174	+	3.46712i	−0.100465	+	0.174010i	−0.911876	−	0.410465i	$-0.865366\pi$
$397$	−2.00174	+	3.46712i	−0.100465	+	0.174010i	0.811412	+	0.584475i	$0.198700\pi$
$398$	26.1998			1.31328
$399$	−8.14518	+	0.984875i	−0.407769	+	0.0493054i
$400$	23.7883			1.18941
$401$	−6.30674	+	10.9236i	−0.314944	+	0.545498i	−0.979426	−	0.201806i	$-0.935319\pi$
$401$	−6.30674	+	10.9236i	−0.314944	+	0.545498i	0.664482	+	0.747304i	$0.268652\pi$
$402$	−28.5541	−	49.4571i	−1.42415	−	2.46670i
$403$		0			0
$404$	12.3005	−	21.3051i	0.611972	−	1.05997i
$405$	2.10550			0.104623
$406$	−15.8944	+	37.2539i	−0.788826	+	1.84888i
$407$	−12.7358			−0.631290
$408$	0.981272	−	1.69961i	0.0485802	−	0.0841434i
$409$	−10.3476	−	17.9226i	−0.511657	−	0.886216i	−0.999909	−	0.0135128i	$-0.995699\pi$
$409$	−10.3476	−	17.9226i	−0.511657	−	0.886216i	0.488252	−	0.872703i	$-0.337635\pi$
$410$	0.989615	+	1.71406i	0.0488736	+	0.0846516i
$411$	−15.4253	+	26.7174i	−0.760873	+	1.31787i
$412$	−10.5096			−0.517773
$413$	9.62244	+	12.8185i	0.473490	+	0.630756i
$414$	−17.3025			−0.850373
$415$	0.303336	−	0.525393i	0.0148902	−	0.0257905i
$416$		0			0
$417$	−4.64021	−	8.03708i	−0.227232	−	0.393577i
$418$	5.25304	−	9.09854i	0.256935	−	0.445024i
$419$	−21.8175			−1.06586			−0.532928	−	0.846161i	$-0.678908\pi$
$419$	−21.8175			−1.06586			−0.532928	+	0.846161i	$0.678908\pi$
$420$	−1.04475	−	1.39176i	−0.0509787	−	0.0679109i
$421$	9.42727			0.459457			0.229728	−	0.973255i	$-0.426216\pi$
$421$	9.42727			0.459457			0.229728	+	0.973255i	$0.426216\pi$
$422$	−24.5920	+	42.5947i	−1.19712	+	2.07348i
$423$	13.1964	+	22.8569i	0.641632	+	1.11134i
$424$	2.36315	+	4.09310i	0.114765	+	0.198779i
$425$	2.08688	−	3.61458i	0.101228	−	0.175333i
$426$	−25.4503			−1.23307
$427$	−11.8006	+	27.6586i	−0.571070	+	1.33850i
$428$	−14.3133			−0.691861
$429$		0			0
$430$	0.976930	+	1.69209i	0.0471118	+	0.0816000i
$431$	−10.2138	−	17.6908i	−0.491980	−	0.852134i	0.507977	−	0.861370i	$-0.330393\pi$
$431$	−10.2138	−	17.6908i	−0.491980	−	0.852134i	−0.999957	+	0.00923613i	$0.997060\pi$
$432$	−4.05491	+	7.02332i	−0.195092	+	0.337909i
$433$	26.3486			1.26623			0.633117	−	0.774056i	$-0.281775\pi$
$433$	26.3486			1.26623			0.633117	+	0.774056i	$0.281775\pi$
$434$	6.25069	−	0.755803i	0.300043	−	0.0362797i
$435$	3.73014			0.178846
$436$	10.0356	−	17.3822i	0.480619	−	0.832457i
$437$	2.78136	+	4.81745i	0.133050	+	0.230450i
$438$	−8.28138	−	14.3438i	−0.395700	−	0.685372i
$439$	−12.5655	+	21.7641i	−0.599720	+	1.03875i	0.393142	+	0.919478i	$0.371388\pi$
$439$	−12.5655	+	21.7641i	−0.599720	+	1.03875i	−0.992862	+	0.119267i	$0.961945\pi$
$440$	−0.839429			−0.0400182
$441$	−4.42195	+	15.2095i	−0.210569	+	0.724260i
$442$		0			0
$443$	−9.25995	+	16.0387i	−0.439953	+	0.762022i	−0.997685	−	0.0679994i	$-0.978338\pi$
$443$	−9.25995	+	16.0387i	−0.439953	+	0.762022i	0.557732	+	0.830021i	$0.311672\pi$
$444$	−5.07384	−	8.78815i	−0.240794	−	0.417067i
$445$	−1.18261	−	2.04834i	−0.0560611	−	0.0971006i
$446$	0.676415	−	1.17159i	0.0320292	−	0.0554762i
$447$	35.2184			1.66577
$448$	8.37115	−	1.01220i	0.395500	−	0.0478219i
$449$	11.6431			0.549471			0.274736	−	0.961520i	$-0.411410\pi$
$449$	11.6431			0.549471			0.274736	+	0.961520i	$0.411410\pi$
$450$	10.4295	−	18.0644i	0.491651	−	0.851564i
$451$	11.2870	+	19.5497i	0.531485	+	0.920559i
$452$	3.10066	+	5.37050i	0.145843	+	0.252607i
$453$	−7.02109	+	12.1609i	−0.329880	+	0.571368i
$454$	−5.29939			−0.248713
$455$		0			0
$456$	−3.15328			−0.147666
$457$	−10.2592	+	17.7695i	−0.479906	+	0.831222i	−0.999734	−	0.0230490i	$-0.992663\pi$
$457$	−10.2592	+	17.7695i	−0.479906	+	0.831222i	0.519828	+	0.854271i	$0.325996\pi$
$458$	−2.94845	−	5.10687i	−0.137772	−	0.238629i
$459$	0.711453	+	1.23227i	0.0332078	+	0.0575176i
$460$	−0.589955	+	1.02183i	−0.0275068	+	0.0476431i
$461$	2.04075			0.0950473			0.0475236	−	0.998870i	$-0.484867\pi$
$461$	2.04075			0.0950473			0.0475236	+	0.998870i	$0.484867\pi$
$462$	−28.3203	−	37.7268i	−1.31758	−	1.75521i
$463$	3.03155			0.140888			0.0704441	−	0.997516i	$-0.477558\pi$
$463$	3.03155			0.140888			0.0704441	+	0.997516i	$0.477558\pi$
$464$	−19.7521	+	34.2116i	−0.916968	+	1.58824i
$465$	−0.289926	−	0.502167i	−0.0134450	−	0.0232874i
$466$	−12.4563	−	21.5749i	−0.577025	−	0.999436i
$467$	6.46371	−	11.1955i	0.299105	−	0.518065i	−0.676827	−	0.736142i	$-0.736645\pi$
$467$	6.46371	−	11.1955i	0.299105	−	0.518065i	0.975931	+	0.218078i	$0.0699787\pi$
$468$		0			0
$469$	21.2793	+	28.3470i	0.982585	+	1.30894i
$470$	4.27757			0.197310
$471$	−5.20373	+	9.01312i	−0.239775	+	0.415303i
$472$	3.08011	+	5.33491i	0.141774	+	0.245559i
$473$	11.1423	+	19.2991i	0.512326	+	0.887374i
$474$	22.8768	−	39.6238i	1.05077	−	1.81998i
$475$	−6.70611			−0.307697
$476$	1.26898	−	2.97429i	0.0581637	−	0.136326i
$477$	10.5172			0.481548
$478$	14.4507	−	25.0294i	0.660962	−	1.14482i
$479$	−18.2911	−	31.6810i	−0.835740	−	1.44754i	−0.893427	−	0.449209i	$-0.851706\pi$
$479$	−18.2911	−	31.6810i	−0.835740	−	1.44754i	0.0576873	−	0.998335i	$-0.481627\pi$
$480$	−1.55664	−	2.69618i	−0.0710505	−	0.123063i
$481$		0			0
$482$	−14.0769			−0.641187
$483$	24.7967	−	2.99830i	1.12829	−	0.136427i
$484$	9.43611			0.428914
$485$	1.92159	−	3.32829i	0.0872550	−	0.151130i
$486$	18.0239	+	31.2183i	0.817580	+	1.41609i
$487$	−18.3748	−	31.8261i	−0.832642	−	1.44218i	−0.895936	−	0.444183i	$-0.853494\pi$
$487$	−18.3748	−	31.8261i	−0.832642	−	1.44218i	0.0632939	−	0.997995i	$-0.479839\pi$
$488$	−5.77864	+	10.0089i	−0.261587	+	0.453081i
$489$	4.18103			0.189073
$490$	1.77645	+	1.85319i	0.0802520	+	0.0837184i
$491$	−8.19797			−0.369969			−0.184985	−	0.982741i	$-0.559224\pi$
$491$	−8.19797			−0.369969			−0.184985	+	0.982741i	$0.559224\pi$
$492$	−8.99331	+	15.5769i	−0.405450	+	0.702260i
$493$	3.46560	+	6.00259i	0.156083	+	0.270343i
$494$		0			0
$495$	−0.933965	+	1.61768i	−0.0419786	+	0.0727091i
$496$	6.14096			0.275737
$497$	15.6820	−	1.89619i	0.703432	−	0.0850556i
$498$	13.1033			0.587171
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.267211	−	0.963638i	$-0.413898\pi$
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.700929	−	0.713231i	$-0.252769\pi$
$500$	−1.42802	−	2.47340i	−0.0638629	−	0.110614i
$501$	12.2824	+	21.2737i	0.548736	+	0.950439i
$502$	−1.18436	+	2.05137i	−0.0528605	+	0.0915571i
$503$	0.0181922			0.000811149			0.000405575	−	1.00000i	$-0.499871\pi$
$503$	0.0181922			0.000811149			0.000405575		1.00000i	$0.499871\pi$
$504$	−2.38892	+	5.59925i	−0.106411	+	0.249411i
$505$	3.34212			0.148722
$506$	−15.9920	+	27.6990i	−0.710933	+	1.23137i
$507$		0			0
$508$	1.59095	+	2.75560i	0.0705869	+	0.122260i
$509$	−21.5503	+	37.3262i	−0.955200	+	1.65446i	−0.221292	+	0.975208i	$0.571027\pi$
$509$	−21.5503	+	37.3262i	−0.955200	+	1.65446i	−0.733909	+	0.679248i	$0.762306\pi$
$510$	−0.707795			−0.0313417
$511$	6.17151	+	8.22134i	0.273012	+	0.363691i
$512$	23.2197			1.02617
$513$	1.14311	−	1.97993i	0.0504697	−	0.0874161i
$514$	7.87878	+	13.6464i	0.347518	+	0.601919i
$515$	−0.713884	−	1.23648i	−0.0314575	−	0.0544859i
$516$	−8.87804	+	15.3772i	−0.390834	+	0.676944i
$517$	48.7877			2.14568
$518$	8.98664	+	11.9715i	0.394850	+	0.525997i
$519$	−30.9531			−1.35869
$520$		0			0
$521$	−10.4770	−	18.1467i	−0.459006	−	0.795022i	0.539903	−	0.841727i	$-0.318461\pi$
$521$	−10.4770	−	18.1467i	−0.459006	−	0.795022i	−0.998909	+	0.0467056i	$0.985128\pi$
$522$	17.3198	+	29.9988i	0.758068	+	1.31301i
$523$	17.3701	−	30.0860i	0.759543	−	1.31557i	−0.183541	−	0.983012i	$-0.558756\pi$
$523$	17.3701	−	30.0860i	0.759543	−	1.31557i	0.943084	−	0.332555i	$-0.107911\pi$
$524$	3.30666			0.144452
$525$	−11.8164	+	27.6958i	−0.515712	+	1.20875i
$526$	23.7627			1.03610
$527$	0.538730	−	0.933107i	0.0234674	−	0.0406468i
$528$	−23.0052	−	39.8462i	−1.00117	−	1.73408i
$529$	3.03260	+	5.25262i	0.131852	+	0.228375i
$530$	0.852276	−	1.47619i	0.0370205	−	0.0641214i
$531$	13.7080			0.594875
$532$	−5.15809	+	0.623691i	−0.223631	+	0.0270404i
$533$		0			0
$534$	25.5427	−	44.2413i	1.10534	−	1.91451i
$535$	−0.972255	−	1.68400i	−0.0420343	−	0.0728055i
$536$	6.81142	+	11.7977i	0.294209	+	0.509584i
$537$	−12.0085	+	20.7993i	−0.518205	+	0.897557i
$538$	−8.75513			−0.377460
$539$	20.2613	+	21.1365i	0.872715	+	0.910411i
$540$	0.484932			0.0208682
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	−0.828393	−	0.560148i	$-0.810744\pi$
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	0.899299	+	0.437335i	$0.144078\pi$
$542$	16.7339	+	28.9839i	0.718782	+	1.24497i
$543$	−14.3619	−	24.8756i	−0.616330	−	1.06752i
$544$	2.89249	−	5.00993i	0.124014	−	0.214799i
$545$	2.72674			0.116801
$546$		0			0
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	−9.76836	+	16.9193i	−0.417284	+	0.722756i
$549$	12.8589	+	22.2722i	0.548803	+	0.950554i
$550$	−19.2791	−	33.3924i	−0.822065	−	1.42386i
$551$	5.56828	−	9.64455i	0.237217	−	0.410871i
$552$	9.59965			0.408588
$553$	−11.1440	+	26.1199i	−0.473893	+	1.11073i
$554$	−48.5368			−2.06213
$555$	0.689297	−	1.19390i	0.0292590	−	0.0506781i
$556$	−2.93850	−	5.08963i	−0.124620	−	0.215848i
$557$	7.14329	+	12.3725i	0.302671	+	0.524241i	0.976740	−	0.214427i	$-0.0687884\pi$
$557$	7.14329	+	12.3725i	0.302671	+	0.524241i	−0.674069	+	0.738668i	$0.735455\pi$
$558$	2.69238	−	4.66334i	0.113978	−	0.197415i
$559$		0			0
$560$	1.50315	+	2.00241i	0.0635196	+	0.0846172i
$561$	−8.07273			−0.340831
$562$	3.40226	−	5.89289i	0.143516	−	0.248577i
$563$	−3.39392	−	5.87844i	−0.143037	−	0.247747i	0.785602	−	0.618732i	$-0.212353\pi$
$563$	−3.39392	−	5.87844i	−0.143037	−	0.247747i	−0.928639	+	0.370985i	$0.879020\pi$
$564$	19.4366	+	33.6652i	0.818430	+	1.41756i
$565$	−0.421234	+	0.729599i	−0.0177215	+	0.0306945i
$566$	14.2061			0.597128
$567$	−16.9449	−	22.5731i	−0.711621	−	0.947981i
$568$	6.07103			0.254735
$569$	8.66061	−	15.0006i	0.363072	−	0.628859i	−0.625393	−	0.780310i	$-0.715061\pi$
$569$	8.66061	−	15.0006i	0.363072	−	0.628859i	0.988465	+	0.151451i	$0.0483947\pi$
$570$	0.568618	+	0.984875i	0.0238168	+	0.0412519i
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	0.969440	−	0.245328i	$-0.0788957\pi$
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	−0.697180	+	0.716896i	$0.745562\pi$
$572$		0			0
$573$	30.0837			1.25676
$574$	10.4121	−	24.4043i	0.434593	−	1.01862i
$575$	20.4157			0.851392
$576$	3.60574	−	6.24532i	0.150239	−	0.260222i
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	0.873539	−	0.486755i	$-0.161820\pi$
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	−0.858311	+	0.513129i	$0.828486\pi$
$578$	15.1368	+	26.2177i	0.629607	+	1.09051i
$579$	−1.19472	+	2.06931i	−0.0496508	+	0.0859978i
$580$	2.36218			0.0980842
$581$	−8.07396	+	0.976265i	−0.334964	+	0.0405023i
$582$	83.0073			3.44076
$583$	9.72061	−	16.8366i	0.402586	−	0.697300i
$584$	1.97548	+	3.42163i	0.0817459	+	0.141588i
$585$		0			0
$586$	15.9369	−	27.6035i	0.658347	−	1.14029i
$587$	−8.52284			−0.351775			−0.175888	−	0.984410i	$-0.556280\pi$
$587$	−8.52284			−0.351775			−0.175888	+	0.984410i	$0.556280\pi$
$588$	−6.51296	+	22.4016i	−0.268590	+	0.923825i
$589$	−1.73119			−0.0713323
$590$	1.11085	−	1.92404i	0.0457329	−	0.0792117i
$591$	−1.69570	−	2.93704i	−0.0697517	−	0.120814i
$592$	7.30004	+	12.6440i	0.300030	+	0.519667i
$593$	15.6547	−	27.1147i	0.642860	−	1.11347i	−0.341932	−	0.939725i	$-0.611081\pi$
$593$	15.6547	−	27.1147i	0.642860	−	1.11347i	0.984791	−	0.173741i	$-0.0555854\pi$
$594$	13.1452			0.539353
$595$	0.436129	−	0.0527346i	0.0178795	−	0.00216191i
$596$	22.3027			0.913554
$597$	−16.1730	+	28.0125i	−0.661917	+	1.14647i
$598$		0			0
$599$	0.375116	+	0.649720i	0.0153268	+	0.0265468i	0.873587	−	0.486668i	$-0.161788\pi$
$599$	0.375116	+	0.649720i	0.0153268	+	0.0265468i	−0.858260	+	0.513215i	$0.828454\pi$
$600$	−5.78641	+	10.0224i	−0.236229	+	0.409161i
$601$	−9.55305			−0.389677			−0.194838	−	0.980835i	$-0.562418\pi$
$601$	−9.55305			−0.389677			−0.194838	+	0.980835i	$0.562418\pi$
$602$	10.2787	−	24.0915i	0.418927	−	0.981897i
$603$	30.3141			1.23449
$604$	−4.44624	+	7.70111i	−0.180915	+	0.313354i
$605$	0.640963	+	1.11018i	0.0260588	+	0.0451352i
$606$	36.0925	+	62.5141i	1.46616	+	2.53946i
$607$	−11.1197	+	19.2599i	−0.451336	+	0.781737i	−0.998469	−	0.0553087i	$-0.982386\pi$
$607$	−11.1197	+	19.2599i	−0.451336	+	0.781737i	0.547133	+	0.837045i	$0.315719\pi$
$608$	−9.29489			−0.376958
$609$	−30.0199	−	39.9908i	−1.21647	−	1.62051i
$610$	4.16815			0.168764
$611$		0			0
$612$	−1.38278	−	2.39505i	−0.0558957	−	0.0968143i
$613$	4.13993	+	7.17057i	0.167210	+	0.289617i	0.937438	−	0.348152i	$-0.113191\pi$
$613$	4.13993	+	7.17057i	0.167210	+	0.289617i	−0.770228	+	0.637769i	$0.779857\pi$
$614$	26.0789	−	45.1699i	1.05246	−	1.82291i
$615$	−2.44354			−0.0985330
$616$	6.75567	+	8.99952i	0.272194	+	0.362601i
$617$	20.3312			0.818503			0.409252	−	0.912422i	$-0.365790\pi$
$617$	20.3312			0.818503			0.409252	+	0.912422i	$0.365790\pi$
$618$	15.4189	−	26.7063i	0.620238	−	1.07428i
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	0.807354	−	0.590067i	$-0.200899\pi$
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	−0.914690	+	0.404156i	$0.867565\pi$
$620$	−0.183601	−	0.318007i	−0.00737361	−	0.0127715i
$621$	−3.48003	+	6.02758i	−0.139649	+	0.241879i
$622$	−43.7301			−1.75342
$623$	−12.4427	+	29.1636i	−0.498506	+	1.16842i
$624$		0			0
$625$	−12.2086	+	21.1459i	−0.488345	+	0.845838i
$626$	3.11112	+	5.38862i	0.124345	+	0.215372i
$627$	6.48536	+	11.2330i	0.259000	+	0.448601i
$628$	−3.29536	+	5.70773i	−0.131499	+	0.227763i
$629$	2.56165			0.102140
$630$	2.17962	−	0.263549i	0.0868381	−	0.0105001i
$631$	6.46662			0.257432			0.128716	−	0.991681i	$-0.458914\pi$
$631$	6.46662			0.257432			0.128716	+	0.991681i	$0.458914\pi$
$632$	−5.45714	+	9.45205i	−0.217074	+	0.375982i
$633$	−30.3611	−	52.5870i	−1.20675	−	2.09014i
$634$	6.76217	+	11.7124i	0.268560	+	0.465160i
$635$	−0.216135	+	0.374357i	−0.00857707	+	0.0148559i
$636$	15.4904			0.614236
$637$		0			0
$638$	64.0322			2.53506
$639$	6.75475	−	11.6996i	0.267214	−	0.462828i
$640$	0.772706	+	1.33837i	0.0305439	+	0.0529035i
$641$	−11.6644	−	20.2034i	−0.460717	−	0.797985i	0.538280	−	0.842766i	$-0.319074\pi$
$641$	−11.6644	−	20.2034i	−0.460717	−	0.797985i	−0.998997	+	0.0447808i	$0.985741\pi$
$642$	20.9993	−	36.3719i	0.828778	−	1.43549i
$643$	−3.58878			−0.141527			−0.0707637	−	0.997493i	$-0.522544\pi$
$643$	−3.58878			−0.141527			−0.0707637	+	0.997493i	$0.522544\pi$
$644$	15.7030	−	1.89873i	0.618784	−	0.0748204i
$645$	−2.41222			−0.0949810
$646$	−1.05658	+	1.83006i	−0.0415707	+	0.0720026i
$647$	19.8262	+	34.3400i	0.779448	+	1.35004i	0.932260	+	0.361788i	$0.117834\pi$
$647$	19.8262	+	34.3400i	0.779448	+	1.35004i	−0.152812	+	0.988255i	$0.548833\pi$
$648$	−5.42402	−	9.39467i	−0.213076	−	0.369058i
$649$	12.6697	−	21.9446i	0.497331	−	0.861402i
$650$		0			0
$651$	−3.05042	+	7.14970i	−0.119556	+	0.280219i
$652$	2.64772			0.103693
$653$	−9.06777	+	15.7058i	−0.354849	+	0.614617i	−0.987092	−	0.160153i	$-0.948801\pi$
$653$	−9.06777	+	15.7058i	−0.354849	+	0.614617i	0.632243	+	0.774770i	$0.282135\pi$
$654$	29.4469	+	51.0035i	1.15146	+	1.99439i
$655$	0.224610	+	0.389035i	0.00877623	+	0.0152009i
$656$	12.9392	−	22.4114i	0.505192	−	0.875017i
$657$	8.79183			0.343002
$658$	−34.4256	−	45.8599i	−1.34205	−	1.78780i
$659$	13.4810			0.525147			0.262573	−	0.964912i	$-0.415429\pi$
$659$	13.4810			0.525147			0.262573	+	0.964912i	$0.415429\pi$
$660$	−1.37561	+	2.38263i	−0.0535456	+	0.0927437i
$661$	−5.15611	−	8.93064i	−0.200549	−	0.347362i	0.748156	−	0.663523i	$-0.230939\pi$
$661$	−5.15611	−	8.93064i	−0.200549	−	0.347362i	−0.948706	+	0.316161i	$0.897606\pi$
$662$	13.3076	+	23.0494i	0.517213	+	0.895839i
$663$		0			0
$664$	−3.12571			−0.121301
$665$	−0.423750	−	0.564495i	−0.0164323	−	0.0218902i
$666$	12.8022			0.496076
$667$	−16.9517	+	29.3613i	−0.656374	+	1.13687i
$668$	7.77805	+	13.4720i	0.300942	+	0.521247i
$669$	0.835096	+	1.44643i	0.0322867	+	0.0559222i
$670$	2.45655	−	4.25487i	0.0949049	−	0.164380i
$671$	47.5397			1.83525
$672$	−16.3780	+	38.3874i	−0.631795	+	1.48082i
$673$	−9.23056			−0.355812			−0.177906	−	0.984048i	$-0.556932\pi$
$673$	−9.23056			−0.355812			−0.177906	+	0.984048i	$0.556932\pi$
$674$	−15.9618	+	27.6467i	−0.614827	+	1.06491i
$675$	−4.19533	−	7.26652i	−0.161478	−	0.279689i
$676$		0			0
$677$	10.5467	−	18.2674i	0.405343	−	0.702075i	−0.589018	−	0.808120i	$-0.700485\pi$
$677$	10.5467	−	18.2674i	0.405343	−	0.702075i	0.994361	+	0.106045i	$0.0338187\pi$
$678$	−18.1961			−0.698818
$679$	−51.1475	+	6.18450i	−1.96286	+	0.237340i
$680$	0.168841			0.00647474
$681$	3.27129	−	5.66604i	0.125356	−	0.217123i
$682$	−4.97693	−	8.62029i	−0.190576	−	0.330088i
$683$	19.1106	+	33.1005i	0.731246	+	1.26656i	0.956351	+	0.292221i	$0.0943944\pi$
$683$	19.1106	+	33.1005i	0.731246	+	1.26656i	−0.225104	+	0.974335i	$0.572272\pi$
$684$	−2.22176	+	3.84821i	−0.0849512	+	0.147140i
$685$	−2.65412			−0.101409
$686$	5.57122	−	33.9597i	0.212710	−	1.29659i
$687$	7.28027			0.277760
$688$	12.7734	−	22.1241i	0.486980	−	0.843474i
$689$		0			0
$690$	−1.73107	−	2.99830i	−0.0659006	−	0.114143i
$691$	13.1161	−	22.7178i	0.498960	−	0.864224i	−0.501039	−	0.865425i	$-0.667049\pi$
$691$	13.1161	−	22.7178i	0.498960	−	0.864224i	0.999999	+	0.00120019i	$0.000382034\pi$
$692$	−19.6017			−0.745144
$693$	24.8596	−	3.00590i	0.944338	−	0.114185i
$694$	−14.3130			−0.543314
$695$	0.399204	−	0.691442i	0.0151427	−	0.0262279i
$696$	−9.60925	−	16.6437i	−0.364238	−	0.630878i
$697$	−2.27024	−	3.93218i	−0.0859916	−	0.148942i
$698$	−20.7836	+	35.9982i	−0.786670	+	1.36255i
$699$	30.7567			1.16333
$700$	−7.48299	+	17.5389i	−0.282830	+	0.662909i
$701$	−46.7346			−1.76514			−0.882570	−	0.470180i	$-0.844189\pi$
$701$	−46.7346			−1.76514			−0.882570	+	0.470180i	$0.844189\pi$
$702$		0			0
$703$	−2.05794	−	3.56446i	−0.0776167	−	0.134436i
$704$	−6.66528	−	11.5446i	−0.251207	−	0.435104i
$705$	−2.64053	+	4.57353i	−0.0994480	+	0.172249i
$706$	−41.3669			−1.55687
$707$	−26.8972	−	35.8309i	−1.01157	−	1.34756i
$708$	20.1901			0.758789
$709$	23.7232	−	41.0898i	0.890944	−	1.54316i	0.0521988	−	0.998637i	$-0.483377\pi$
$709$	23.7232	−	41.0898i	0.890944	−	1.54316i	0.838745	−	0.544524i	$-0.183290\pi$
$710$	−1.09476	−	1.89619i	−0.0410858	−	0.0711626i
$711$	12.1435	+	21.0331i	0.455415	+	0.788802i
$712$	−6.09307	+	10.5535i	−0.228348	+	0.395510i
$713$	5.27032			0.197375
$714$	5.69629	+	7.58827i	0.213178	+	0.283984i
$715$		0			0
$716$	−7.60461	+	13.1716i	−0.284197	+	0.492244i
$717$	17.8408	+	30.9011i	0.666275	+	1.15402i
$718$	2.56280	+	4.43890i	0.0956428	+	0.165658i
$719$	24.6190	−	42.6413i	0.918133	−	1.59025i	0.115884	−	0.993263i	$-0.463030\pi$
$719$	24.6190	−	42.6413i	0.918133	−	1.59025i	0.802249	−	0.596990i	$-0.203637\pi$
$720$	2.14136			0.0798037
$721$	−7.51104	+	17.6047i	−0.279726	+	0.655632i
$722$	−31.9098			−1.18756
$723$	8.68963	−	15.0509i	0.323171	−	0.559748i
$724$	−9.09498	−	15.7530i	−0.338012	−	0.585454i
$725$	−20.4361	−	35.3963i	−0.758977	−	1.31459i
$726$	−13.8439	+	23.9783i	−0.513795	+	0.889919i
$727$	−32.0495			−1.18865			−0.594325	−	0.804225i	$-0.702581\pi$
$727$	−32.0495			−1.18865			−0.594325	+	0.804225i	$0.702581\pi$
$728$		0			0
$729$	−12.4996			−0.462947
$730$	0.712460	−	1.23402i	0.0263693	−	0.0456730i
$731$	−2.24114	−	3.88178i	−0.0828917	−	0.143573i
$732$	18.9394	+	32.8041i	0.700022	+	1.21247i
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	0.478894	+	0.877873i	$0.341038\pi$
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	−0.999707	+	0.0242025i	$0.992295\pi$
$734$	−26.2924			−0.970472
$735$	−3.07800	+	0.755398i	−0.113534	+	0.0278633i
$736$	28.2968			1.04303
$737$	28.0181	−	48.5288i	1.03206	−	1.78758i
$738$	−11.3459	−	19.6516i	−0.417648	−	0.723387i
$739$	21.2685	+	36.8381i	0.782375	+	1.35511i	0.930555	+	0.366153i	$0.119325\pi$
$739$	21.2685	+	36.8381i	0.782375	+	1.35511i	−0.148180	+	0.988960i	$0.547342\pi$
$740$	0.436510	−	0.756058i	0.0160464	−	0.0277932i
$741$		0			0
$742$	−22.6852	+	2.74299i	−0.832801	+	0.100698i
$743$	15.9142			0.583836			0.291918	−	0.956443i	$-0.405706\pi$
$743$	15.9142			0.583836			0.291918	+	0.956443i	$0.405706\pi$
$744$	−1.49377	+	2.58728i	−0.0547641	+	0.0948543i
$745$	1.51495	+	2.62396i	0.0555033	+	0.0961346i
$746$	4.68521	+	8.11502i	0.171538	+	0.297112i
$747$	−3.47773	+	6.02360i	−0.127243	+	0.220392i
$748$	−5.11221			−0.186921
$749$	−10.2295	+	23.9762i	−0.373777	+	0.876072i
$750$	8.38028			0.306005
$751$	−9.09981	+	15.7613i	−0.332057	+	0.575139i	−0.982915	−	0.184060i	$-0.941076\pi$
$751$	−9.09981	+	15.7613i	−0.332057	+	0.575139i	0.650858	+	0.759199i	$0.274409\pi$
$752$	−27.9646	−	48.4362i	−1.01977	−	1.76629i
$753$	−1.46220	−	2.53260i	−0.0532855	−	0.0922931i
$754$		0			0
$755$	−1.20807			−0.0439662
$756$	−3.90270	−	5.19896i	−0.141940	−	0.189084i
$757$	−44.9004			−1.63193			−0.815967	−	0.578099i	$-0.803795\pi$
$757$	−44.9004			−1.63193			−0.815967	+	0.578099i	$0.803795\pi$
$758$	5.62989	−	9.75126i	0.204487	−	0.354182i
$759$	−19.7436	−	34.1970i	−0.716648	−	1.24127i
$760$	−0.135641	−	0.234937i	−0.00492021	−	0.00852205i
$761$	13.2444	−	22.9399i	0.480108	−	0.831572i	−0.519631	−	0.854391i	$-0.673931\pi$
$761$	13.2444	−	22.9399i	0.480108	−	0.831572i	0.999740	+	0.0228184i	$0.00726396\pi$
$762$	−9.33644			−0.338223
$763$	−21.9446	−	29.2334i	−0.794449	−	1.05832i
$764$	19.0511			0.689244
$765$	0.187856	−	0.325375i	0.00679193	−	0.0117640i
$766$	4.21900	+	7.30752i	0.152439	+	0.264031i
$767$		0			0
$768$	−24.0006	+	41.5703i	−0.866049	+	1.50004i
$769$	13.9625			0.503502			0.251751	−	0.967792i	$-0.418994\pi$
$769$	13.9625			0.503502			0.251751	+	0.967792i	$0.418994\pi$
$770$	1.59263	−	3.73287i	0.0573944	−	0.134523i
$771$	−19.4541			−0.700623
$772$	−0.756579	+	1.31043i	−0.0272299	+	0.0471635i
$773$	−6.40564	−	11.0949i	−0.230395	−	0.399056i	0.727529	−	0.686077i	$-0.240668\pi$
$773$	−6.40564	−	11.0949i	−0.230395	−	0.399056i	−0.957924	+	0.287021i	$0.907335\pi$
$774$	−11.2005	−	19.3998i	−0.402592	−	0.697310i
$775$	−3.17681	+	5.50239i	−0.114114	+	0.197652i
$776$	−19.8010			−0.710813
$777$	−18.3472	+	2.21845i	−0.658201	+	0.0795865i
$778$	8.37594			0.300292
$779$	−3.64767	+	6.31795i	−0.130691	+	0.226364i
$780$		0			0
$781$	−12.4863	−	21.6269i	−0.446795	−	0.773871i
$782$	3.21660	−	5.57132i	0.115025	−	0.199230i
$783$	13.9340			0.497961
$784$	9.37058	−	32.2305i	0.334664	−	1.15109i
$785$	−0.895370			−0.0319571
$786$	−4.85125	+	8.40262i	−0.173039	+	0.299712i
$787$	13.6599	+	23.6597i	0.486924	+	0.843377i	0.999887	−	0.0150334i	$-0.00478545\pi$
$787$	13.6599	+	23.6597i	0.486924	+	0.843377i	−0.512963	+	0.858411i	$0.671452\pi$
$788$	−1.07383	−	1.85993i	−0.0382537	−	0.0662574i
$789$	−14.6686	+	25.4068i	−0.522217	+	0.904506i
$790$	3.93626			0.140046
$791$	11.2121	−	1.35571i	0.398656	−	0.0482036i
$792$	9.62401			0.341974
$793$		0			0
$794$	−3.71956	−	6.44247i	−0.132002	−	0.228635i
$795$	1.05221	+	1.82248i	0.0373181	+	0.0646369i
$796$	−10.2419	+	17.7394i	−0.363013	+	0.628758i
$797$	−29.4003			−1.04141			−0.520707	−	0.853736i	$-0.674332\pi$
$797$	−29.4003			−1.04141			−0.520707	+	0.853736i	$0.674332\pi$
$798$	5.98265	−	14.0224i	0.211783	−	0.496386i
$799$	−9.81305			−0.347161
$800$	−17.0565	+	29.5428i	−0.603040	+	1.04450i
$801$	13.5586	+	23.4841i	0.479068	+	0.829770i
$802$	−11.7189	−	20.2978i	−0.413810	−	0.716740i
$803$	8.12594	−	14.0745i	0.286758	−	0.496680i
$804$	44.6487			1.57464
$805$	1.29004	+	1.71852i	0.0454679	+	0.0605697i
$806$		0			0
$807$	5.40450	−	9.36087i	0.190247	−	0.329518i
$808$	−8.60968	−	14.9124i	−0.302888	−	0.524617i
$809$	3.00617	+	5.20683i	0.105691	+	0.183063i	0.914020	−	0.405668i	$-0.132961\pi$
$809$	3.00617	+	5.20683i	0.105691	+	0.183063i	−0.808329	+	0.588731i	$0.799628\pi$
$810$	−1.95618	+	3.38821i	−0.0687332	+	0.119049i
$811$	8.44807			0.296652			0.148326	−	0.988939i	$-0.452612\pi$
$811$	8.44807			0.296652			0.148326	+	0.988939i	$0.452612\pi$
$812$	−19.0107	−	25.3249i	−0.667143	−	0.888730i
$813$	−41.3190			−1.44912
$814$	11.8326	−	20.4946i	0.414732	−	0.718337i
$815$	0.179850	+	0.311510i	0.00629989	+	0.0109117i
$816$	4.62721	+	8.01456i	0.161985	+	0.280566i
$817$	−3.60092	+	6.23697i	−0.125980	+	0.218204i
$818$	38.4551			1.34455
$819$		0			0
$820$	−1.54742			−0.0540382
$821$	17.1318	−	29.6731i	0.597903	−	1.03560i	−0.395228	−	0.918583i	$-0.629334\pi$
$821$	17.1318	−	29.6731i	0.597903	−	1.03560i	0.993130	−	0.117014i	$-0.0373324\pi$
$822$	−28.6627	−	49.6452i	−0.999725	−	1.73157i
$823$	3.11866	+	5.40168i	0.108710	+	0.188291i	0.915248	−	0.402891i	$-0.131995\pi$
$823$	3.11866	+	5.40168i	0.108710	+	0.188291i	−0.806538	+	0.591182i	$0.798661\pi$
$824$	−3.67809	+	6.37064i	−0.128132	+	0.221932i
$825$	47.6037			1.65735
$826$	−29.5677	+	3.57518i	−1.02879	+	0.124397i
$827$	19.5232			0.678889			0.339445	−	0.940626i	$-0.389761\pi$
$827$	19.5232			0.678889			0.339445	+	0.940626i	$0.389761\pi$
$828$	6.76380	−	11.7152i	0.235058	−	0.407133i
$829$	−16.3383	−	28.2988i	−0.567453	−	0.982857i	−0.996817	−	0.0797254i	$-0.974596\pi$
$829$	−16.3383	−	28.2988i	−0.567453	−	0.982857i	0.429364	−	0.903131i	$-0.358738\pi$
$830$	0.563647	+	0.976265i	0.0195645	+	0.0338866i
$831$	29.9615	−	51.8949i	1.03935	−	1.80021i
$832$		0			0
$833$	−4.07530	−	4.25133i	−0.141201	−	0.147300i
$834$	17.2445			0.597128
$835$	−1.05667	+	1.83021i	−0.0365677	+	0.0633370i
$836$	4.10698	+	7.11349i	0.142043	+	0.246025i
$837$	−1.08303	−	1.87586i	−0.0374349	−	0.0648392i
$838$	20.2702	−	35.1091i	0.700223	−	1.21282i
$839$	24.7427			0.854212			0.427106	−	0.904202i	$-0.359533\pi$
$839$	24.7427			0.854212			0.427106	+	0.904202i	$0.359533\pi$
$840$	−1.20928	+	0.146220i	−0.0417241	+	0.00504508i
$841$	38.8748			1.34051
$842$	−8.75869	+	15.1705i	−0.301844	+	0.522810i
$843$	4.20040	+	7.27531i	0.144669	+	0.250575i
$844$	−19.2267	−	33.3017i	−0.661812	−	1.14629i
$845$		0			0
$846$	−49.0422			−1.68610
$847$	6.74381	−	15.8064i	0.231720	−	0.543115i
$848$	−22.2870			−0.765339
$849$	−8.76938	+	15.1890i	−0.300964	+	0.521285i
$850$	3.87776	+	6.71647i	0.133006	+	0.230373i
$851$	6.26507	+	10.8514i	0.214764	+	0.371982i
$852$	9.94888	−	17.2320i	0.340843	−	0.590357i
$853$	18.2245			0.623994			0.311997	−	0.950083i	$-0.399002\pi$
$853$	18.2245			0.623994			0.311997	+	0.950083i	$0.399002\pi$
$854$	−33.5450	−	44.6868i	−1.14789	−	1.52915i
$855$	−0.603667			−0.0206450
$856$	−5.00928	+	8.67633i	−0.171214	+	0.296551i
$857$	−1.27340	−	2.20559i	−0.0434984	−	0.0753414i	0.843457	−	0.537197i	$-0.180517\pi$
$857$	−1.27340	−	2.20559i	−0.0434984	−	0.0753414i	−0.886955	+	0.461856i	$0.847184\pi$
$858$		0			0
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.124104	+	0.992269i	$0.539606\pi$
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.797278	+	0.603612i	$0.793728\pi$
$860$	−1.52758			−0.0520902
$861$	19.6654	+	26.1972i	0.670196	+	0.892797i
$862$	37.9577			1.29284
$863$	−0.621545	+	1.07655i	−0.0211576	+	0.0366461i	−0.876410	−	0.481565i	$-0.840069\pi$
$863$	−0.621545	+	1.07655i	−0.0211576	+	0.0366461i	0.855253	+	0.518211i	$0.173402\pi$
$864$	−5.81487	−	10.0716i	−0.197826	−	0.342644i
$865$	−1.33147	−	2.30618i	−0.0452715	−	0.0784125i
$866$	−24.4800	+	42.4006i	−0.831864	+	1.44083i
$867$	−37.3754			−1.26934
$868$	−1.93174	+	4.52769i	−0.0655675	+	0.153680i
$869$	44.8949			1.52295
$870$	−3.46560	+	6.00259i	−0.117495	+	0.203507i
$871$		0			0
$872$	−7.02440	−	12.1666i	−0.237876	−	0.412013i
$873$	−22.0309	+	38.1587i	−0.745634	+	1.29148i
$874$	−10.3364			−0.349635
$875$	−5.16376	+	0.624377i	−0.174567	+	0.0211078i
$876$	12.9492			0.437514
$877$	−0.401330	+	0.695125i	−0.0135520	+	0.0234727i	−0.872722	−	0.488218i	$-0.837647\pi$
$877$	−0.401330	+	0.695125i	−0.0135520	+	0.0234727i	0.859170	+	0.511690i	$0.170981\pi$
$878$	−23.3488	−	40.4412i	−0.787983	−	1.36483i
$879$	19.6755	+	34.0790i	0.663639	+	1.14946i
$880$	1.97917	−	3.42803i	0.0667179	−	0.115559i
$881$	−37.0636			−1.24870			−0.624352	−	0.781143i	$-0.714637\pi$
$881$	−37.0636			−1.24870			−0.624352	+	0.781143i	$0.714637\pi$
$882$	−20.3669	−	21.2467i	−0.685791	−	0.715413i
$883$	−22.8671			−0.769539			−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671			−0.769539			−0.384770	+	0.923013i	$0.625719\pi$
$884$		0			0
$885$	1.37144	+	2.37541i	0.0461005	+	0.0798484i
$886$	−17.2065	−	29.8025i	−0.578063	−	1.00123i
$887$	24.6287	−	42.6581i	0.826950	−	1.43232i	−0.0734699	−	0.997297i	$-0.523407\pi$
$887$	24.6287	−	42.6581i	0.826950	−	1.43232i	0.900420	−	0.435022i	$-0.143259\pi$
$888$	−7.10283			−0.238355
$889$	5.75292	−	0.695616i	0.192947	−	0.0233302i
$890$	4.39496			0.147319
$891$	−22.3112	+	38.6441i	−0.747452	+	1.29463i
$892$	0.528840	+	0.915978i	0.0177069	+	0.0306692i
$893$	7.88347	+	13.6546i	0.263810	+	0.456932i
$894$	−32.7207	+	56.6739i	−1.09434	+	1.89546i
$895$	−2.06622			−0.0690661
$896$	8.12993	−	19.0552i	0.271602	−	0.636591i
$897$		0			0
$898$	−10.8174	+	18.7362i	−0.360980	+	0.625236i
$899$	−5.27559	−	9.13760i	−0.175951	−	0.304756i
$900$	8.15406	+	14.1233i	0.271802	+	0.470775i
$901$	−1.95518	+	3.38647i	−0.0651365	+	0.112820i
$902$	−41.9462			−1.39666
$903$	19.4134	+	25.8614i	0.646036	+	0.860613i
$904$	4.34059			0.144366
$905$	1.23558	−	2.14009i	0.0410721	−	0.0711390i
$906$	−13.0463	−	22.5969i	−0.433435	−	0.750731i
$907$	2.50228	+	4.33407i	0.0830867	+	0.143910i	0.904574	−	0.426316i	$-0.140189\pi$
$907$	2.50228	+	4.33407i	0.0830867	+	0.143910i	−0.821488	+	0.570226i	$0.806855\pi$
$908$	2.07161	−	3.58813i	0.0687487	−	0.119076i
$909$	−38.3172			−1.27090
$910$		0			0
$911$	49.0582			1.62537			0.812685	−	0.582703i	$-0.198005\pi$
$911$	49.0582			1.62537			0.812685	+	0.582703i	$0.198005\pi$
$912$	7.43468	−	12.8772i	0.246187	−	0.426408i
$913$	6.42866	+	11.1348i	0.212757	+	0.368507i
$914$	−19.0633	−	33.0186i	−0.630557	−	1.09216i
$915$	−2.57298	+	4.45653i	−0.0850601	+	0.147328i
$916$	4.61037			0.152331
$917$	2.36320	−	5.53897i	0.0780399	−	0.182913i
$918$	−2.64399			−0.0872646
$919$	−14.8028	+	25.6392i	−0.488299	+	0.845758i	−0.999909	−	0.0134590i	$-0.995716\pi$
$919$	−14.8028	+	25.6392i	−0.488299	+	0.845758i	0.511611	+	0.859217i	$0.329049\pi$
$920$	0.412937	+	0.715227i	0.0136141	+	0.0235803i
$921$	32.1967	+	55.7664i	1.06092	+	1.83756i
$922$	−1.89602	+	3.28401i	−0.0624422	+	0.108153i
$923$		0			0
$924$	36.6150	−	4.42731i	1.20454	−	0.145648i
$925$	−15.1056			−0.496670
$926$	−2.81656	+	4.87842i	−0.0925578	+	0.160315i
$927$	8.18464	+	14.1762i	0.268819	+	0.465608i
$928$	−28.3251	−	49.0605i	−0.929817	−	1.61049i
$929$	−8.41525	+	14.5756i	−0.276095	+	0.478211i	−0.970411	−	0.241460i	$-0.922374\pi$
$929$	−8.41525	+	14.5756i	−0.276095	+	0.478211i	0.694316	+	0.719671i	$0.255707\pi$
$930$	1.07746			0.0353313
$931$	−2.64164	+	9.08604i	−0.0865764	+	0.297783i
$932$	19.4773			0.638000
$933$	26.9944	−	46.7557i	0.883757	−	1.53071i
$934$	12.0106	+	20.8030i	0.392999	+	0.680695i
$935$	−0.347255	−	0.601463i	−0.0113565	−	0.0196699i
$936$		0			0
$937$	44.0131			1.43784			0.718922	−	0.695091i	$-0.244636\pi$
$937$	44.0131			1.43784			0.718922	+	0.695091i	$0.244636\pi$
$938$	−65.3866	+	7.90624i	−2.13495	+	0.258148i
$939$	−7.68191			−0.250690
$940$	−1.67216	+	2.89627i	−0.0545400	+	0.0944660i
$941$	−26.5338	−	45.9578i	−0.864976	−	1.49818i	−0.867071	−	0.498184i	$-0.834000\pi$
$941$	−26.5338	−	45.9578i	−0.864976	−	1.49818i	0.00209573	−	0.999998i	$-0.499333\pi$
$942$	−9.66937	−	16.7478i	−0.315045	−	0.545674i
$943$	11.1048	−	19.2340i	0.361620	−	0.626345i
$944$	−29.0487			−0.945453
$945$	0.346572	−	0.812309i	0.0112740	−	0.0264244i
$946$	−41.4086			−1.34631
$947$	13.9409	−	24.1463i	0.453017	−	0.784649i	−0.545555	−	0.838075i	$-0.683681\pi$
$947$	13.9409	−	24.1463i	0.453017	−	0.784649i	0.998572	+	0.0534265i	$0.0170143\pi$
$948$	17.8857	+	30.9790i	0.580902	+	1.00615i
$949$		0			0
$950$	6.23051	−	10.7916i	0.202145	−	0.350125i
$951$	−16.6970			−0.541438
$952$	−1.35882	−	1.81014i	−0.0440396	−	0.0586670i
$953$	−36.3568			−1.17771			−0.588856	−	0.808238i	$-0.700421\pi$
$953$	−36.3568			−1.17771			−0.588856	+	0.808238i	$0.700421\pi$
$954$	−9.77130	+	16.9244i	−0.316357	+	0.547947i
$955$	1.29407	+	2.24140i	0.0418753	+	0.0725301i
$956$	11.2980	+	19.5687i	0.365403	+	0.632897i
$957$	−39.5267	+	68.4623i	−1.27772	+	2.21307i
$958$	67.9754			2.19619
$959$	21.3602	+	28.4548i	0.689757	+	0.918855i
$960$	1.44297			0.0465718
$961$	14.6799	−	25.4263i	0.473545	−	0.820205i
$962$		0			0
$963$	11.1469	+	19.3069i	0.359202	+	0.622157i
$964$	5.50287	−	9.53126i	0.177236	−	0.306981i
$965$	−0.205567			−0.00661744
$966$	−18.2132	+	42.6888i	−0.586000	+	1.37349i
$967$	−15.2681			−0.490988			−0.245494	−	0.969398i	$-0.578950\pi$
$967$	−15.2681			−0.490988			−0.245494	+	0.969398i	$0.578950\pi$
$968$	3.30239	−	5.71990i	0.106143	−	0.183845i
$969$	−1.30445	−	2.25937i	−0.0419049	−	0.0725815i
$970$	3.57063	+	6.18450i	0.114646	+	0.198572i
$971$	18.4460	−	31.9494i	0.591961	−	1.02531i	−0.402008	−	0.915636i	$-0.631687\pi$
$971$	18.4460	−	31.9494i	0.591961	−	1.02531i	0.993968	−	0.109669i	$-0.0349792\pi$
$972$	−28.1831			−0.903975
$973$	−10.6257	+	1.28481i	−0.340645	+	0.0411891i
$974$	68.2867			2.18805
$975$		0			0
$976$	−27.2493	−	47.1972i	−0.872229	−	1.51074i
$977$	0.221957	+	0.384441i	0.00710104	+	0.0122994i	0.869554	−	0.493838i	$-0.164406\pi$
$977$	0.221957	+	0.384441i	0.00710104	+	0.0122994i	−0.862453	+	0.506137i	$0.831073\pi$
$978$	−3.88452	+	6.72818i	−0.124213	+	0.215144i
$979$	50.1265			1.60205
$980$	−1.94920	+	0.478370i	−0.0622649	+	0.0152810i
$981$	−31.2619			−0.998117
$982$	7.61658	−	13.1923i	0.243055	−	0.420983i
$983$	−22.7802	−	39.4564i	−0.726575	−	1.25846i	−0.958323	−	0.285688i	$-0.907778\pi$
$983$	−22.7802	−	39.4564i	−0.726575	−	1.25846i	0.231748	−	0.972776i	$-0.425556\pi$
$984$	6.29483	+	10.9030i	0.200672	+	0.347574i
$985$	0.145884	−	0.252678i	0.00464824	−	0.00805099i
$986$	−12.8793			−0.410160
$987$	70.2835	−	8.49835i	2.23715	−	0.270505i
$988$		0			0
$989$	10.9624	−	18.9875i	0.348585	−	0.603766i
$990$	−1.73546	−	3.00590i	−0.0551565	−	0.0955338i
$991$	−26.8148	−	46.4445i	−0.851799	−	1.47536i	−0.879583	−	0.475745i	$-0.842178\pi$
$991$	−26.8148	−	46.4445i	−0.851799	−	1.47536i	0.0277842	−	0.999614i	$-0.491155\pi$
$992$	−4.40316	+	7.62650i	−0.139801	+	0.242142i
$993$	−32.8588			−1.04274
$994$	−11.5184	+	26.9974i	−0.365342	+	0.856304i
$995$	−2.78278			−0.0882200
$996$	−5.12225	+	8.87199i	−0.162305	+	0.281120i
$997$	−14.5426	−	25.1886i	−0.460569	−	0.797730i	0.538420	−	0.842677i	$-0.319021\pi$
$997$	−14.5426	−	25.1886i	−0.460569	−	0.797730i	−0.998989	+	0.0449470i	$0.985688\pi$
$998$	40.1857	+	69.6038i	1.27206	+	2.20327i
$999$	2.57489	−	4.45984i	0.0814658	−	0.141103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.h.170.1		12
7.2	even	3		8281.2.a.bz.1.6		6
7.4	even	3	inner	1183.2.e.h.508.1		12
7.5	odd	6		8281.2.a.ca.1.6		6
13.3	even	3		91.2.g.b.9.1	✓	12
13.9	even	3		91.2.h.b.16.6	yes	12
13.12	even	2		1183.2.e.g.170.6		12
39.29	odd	6		819.2.n.d.100.6		12
39.35	odd	6		819.2.s.d.289.1		12
91.3	odd	6		637.2.h.l.165.6		12
91.9	even	3		637.2.f.k.393.1		12
91.12	odd	6		8281.2.a.cf.1.1		6
91.16	even	3		637.2.f.k.295.1		12
91.25	even	6		1183.2.e.g.508.6		12
91.48	odd	6		637.2.h.l.471.6		12
91.51	even	6		8281.2.a.ce.1.1		6
91.55	odd	6		637.2.g.l.373.1		12
91.61	odd	6		637.2.f.j.393.1		12
91.68	odd	6		637.2.f.j.295.1		12
91.74	even	3		91.2.g.b.81.1	yes	12
91.81	even	3		91.2.h.b.74.6	yes	12
91.87	odd	6		637.2.g.l.263.1		12
273.74	odd	6		819.2.n.d.172.6		12
273.263	odd	6		819.2.s.d.802.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	13.3	even	3
91.2.g.b.81.1	yes	12	91.74	even	3
91.2.h.b.16.6	yes	12	13.9	even	3
91.2.h.b.74.6	yes	12	91.81	even	3
637.2.f.j.295.1		12	91.68	odd	6
637.2.f.j.393.1		12	91.61	odd	6
637.2.f.k.295.1		12	91.16	even	3
637.2.f.k.393.1		12	91.9	even	3
637.2.g.l.263.1		12	91.87	odd	6
637.2.g.l.373.1		12	91.55	odd	6
637.2.h.l.165.6		12	91.3	odd	6
637.2.h.l.471.6		12	91.48	odd	6
819.2.n.d.100.6		12	39.29	odd	6
819.2.n.d.172.6		12	273.74	odd	6
819.2.s.d.289.1		12	39.35	odd	6
819.2.s.d.802.1		12	273.263	odd	6
1183.2.e.g.170.6		12	13.12	even	2
1183.2.e.g.508.6		12	91.25	even	6
1183.2.e.h.170.1		12	1.1	even	1	trivial
1183.2.e.h.508.1		12	7.4	even	3	inner
8281.2.a.bz.1.6		6	7.2	even	3
8281.2.a.ca.1.6		6	7.5	odd	6
8281.2.a.ce.1.1		6	91.51	even	6
8281.2.a.cf.1.1		6	91.12	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+(-0.929081 + 1.60921i) q^{2} +(-1.14703 - 1.98672i) q^{3} +(-0.726381 - 1.25813i) q^{4} +(0.0986811 - 0.170921i) q^{5} +4.26275 q^{6} +(-2.62662 + 0.317598i) q^{7} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +(0.183365 + 0.317598i) q^{10} +(2.09137 + 3.62236i) q^{11} +(-1.66637 + 2.88623i) q^{12} +(1.92926 - 4.52187i) q^{14} -0.452762 q^{15} +(2.39750 - 4.15260i) q^{16} +(-0.420653 - 0.728592i) q^{17} +(-2.10227 - 3.64125i) q^{18} +(-0.675876 + 1.17065i) q^{19} -0.286720 q^{20} +(3.64380 + 4.85406i) q^{21} -7.77220 q^{22} +(2.05760 - 3.56386i) q^{23} +(1.16637 + 2.02021i) q^{24} +(2.48052 + 4.29639i) q^{25} -1.69131 q^{27} +(2.30751 + 3.07393i) q^{28} -8.23861 q^{29} +(0.420653 - 0.728592i) q^{30} +(0.640350 + 1.10912i) q^{31} +(3.43809 + 5.95495i) q^{32} +(4.79774 - 8.30993i) q^{33} +1.56328 q^{34} +(-0.204914 + 0.480285i) q^{35} +3.28723 q^{36} +(-1.52242 + 2.63692i) q^{37} +(-1.25589 - 2.17526i) q^{38} +(-0.100344 + 0.173802i) q^{40} +5.39696 q^{41} +(-11.1966 + 1.35384i) q^{42} +5.32778 q^{43} +(3.03826 - 5.26242i) q^{44} +(0.223290 + 0.386750i) q^{45} +(3.82334 + 6.62223i) q^{46} +(5.83204 - 10.1014i) q^{47} -11.0001 q^{48} +(6.79826 - 1.66842i) q^{49} -9.21843 q^{50} +(-0.965006 + 1.67144i) q^{51} +(-2.32398 - 4.02525i) q^{53} +(1.57136 - 2.72168i) q^{54} +0.825514 q^{55} +(2.67089 - 0.322952i) q^{56} +3.10101 q^{57} +(7.65434 - 13.2577i) q^{58} +(-3.02905 - 5.24648i) q^{59} +(0.328878 + 0.569634i) q^{60} +(5.68285 - 9.84298i) q^{61} -2.37975 q^{62} +(2.34932 - 5.50644i) q^{63} -3.18704 q^{64} +(8.91498 + 15.4412i) q^{66} +(-6.69851 - 11.6022i) q^{67} +(-0.611109 + 1.05847i) q^{68} -9.44053 q^{69} +(-0.582500 - 0.775973i) q^{70} -5.97040 q^{71} +(1.15044 - 1.99263i) q^{72} +(-1.94273 - 3.36491i) q^{73} +(-2.82891 - 4.89982i) q^{74} +(5.69049 - 9.85622i) q^{75} +1.96377 q^{76} +(-6.64368 - 8.85034i) q^{77} +(5.36669 - 9.29537i) q^{79} +(-0.473177 - 0.819566i) q^{80} +(5.33411 + 9.23895i) q^{81} +(-5.01421 + 8.68486i) q^{82} +3.07390 q^{83} +(3.46025 - 8.11027i) q^{84} -0.166042 q^{85} +(-4.94994 + 8.57354i) q^{86} +(9.44997 + 16.3678i) q^{87} +(-2.12662 - 3.68341i) q^{88} +(5.99207 - 10.3786i) q^{89} -0.829819 q^{90} -5.97840 q^{92} +(1.46901 - 2.54439i) q^{93} +(10.8369 + 18.7700i) q^{94} +(0.133392 + 0.231042i) q^{95} +(7.88721 - 13.6611i) q^{96} +19.4727 q^{97} +(-3.63129 + 12.4900i) q^{98} -9.46448 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

L-functions

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