LMFDB - Embedded newform 550.2.h.k.201.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(201,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.201"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,4,-2,0,-1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.1
Root			$0.453245 - 1.39494i$ of defining polynomial
Character	$\chi$	$=$	550.201
Dual form			550.2.h.k.301.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(-1.04238 - 3.20812i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.72899 + 1.98273i) q^{6} +(-0.0577923 + 0.177866i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-6.77845 + 4.92483i) q^{9} +(-0.359735 + 3.29706i) q^{11} -3.37322 q^{12} +(-2.46673 + 1.79219i) q^{13} +(-0.0577923 - 0.177866i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-2.38467 - 1.73256i) q^{17} +(2.58914 - 7.96855i) q^{18} +(1.66209 + 5.11538i) q^{19} +0.630859 q^{21} +(-1.64693 - 2.87882i) q^{22} +0.115585 q^{23} +(2.72899 - 1.98273i) q^{24} +(0.942208 - 2.89982i) q^{26} +(14.6782 + 10.6644i) q^{27} +(0.151302 + 0.109927i) q^{28} +(3.14256 - 9.67180i) q^{29} +(-6.22732 + 4.52442i) q^{31} +1.00000 q^{32} +(10.9524 - 2.28272i) q^{33} +2.94761 q^{34} +(2.58914 + 7.96855i) q^{36} +(-2.08477 + 6.41625i) q^{37} +(-4.35140 - 3.16148i) q^{38} +(8.32083 + 6.04544i) q^{39} +(-1.44887 - 4.45917i) q^{41} +(-0.510376 + 0.370810i) q^{42} -2.27719 q^{43} +(3.02452 + 1.36098i) q^{44} +(-0.0935099 + 0.0679389i) q^{46} +(1.96428 + 6.04544i) q^{47} +(-1.04238 + 3.20812i) q^{48} +(5.63482 + 4.09394i) q^{49} +(-3.07254 + 9.45631i) q^{51} +(0.942208 + 2.89982i) q^{52} +(-6.51578 + 4.73399i) q^{53} -18.1433 q^{54} -0.187020 q^{56} +(14.6782 - 10.6644i) q^{57} +(3.14256 + 9.67180i) q^{58} +(-0.479439 + 1.47556i) q^{59} +(-0.711544 - 0.516967i) q^{61} +(2.37863 - 7.32066i) q^{62} +(-0.484220 - 1.49028i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.51889 + 8.28439i) q^{66} -9.03490 q^{67} +(-2.38467 + 1.73256i) q^{68} +(-0.120483 - 0.370810i) q^{69} +(0.533268 + 0.387442i) q^{71} +(-6.77845 - 4.92483i) q^{72} +(0.720659 - 2.21796i) q^{73} +(-2.08477 - 6.41625i) q^{74} +5.37863 q^{76} +(-0.565646 - 0.254529i) q^{77} -10.2851 q^{78} +(7.45799 - 5.41855i) q^{79} +(11.1449 - 34.3003i) q^{81} +(3.79320 + 2.75592i) q^{82} +(-2.57128 - 1.86814i) q^{83} +(0.194946 - 0.599983i) q^{84} +(1.84229 - 1.33850i) q^{86} -34.3041 q^{87} +(-3.24685 + 0.676718i) q^{88} -6.69658 q^{89} +(-0.176211 - 0.542323i) q^{91} +(0.0357176 - 0.109927i) q^{92} +(21.0061 + 15.2619i) q^{93} +(-5.14256 - 3.73629i) q^{94} +(-1.04238 - 3.20812i) q^{96} +(-7.16312 + 5.20431i) q^{97} -6.96502 q^{98} +(-13.7990 - 24.1206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} - 2 q^{7} - 2 q^{8} - 24 q^{9} + 5 q^{11} - 6 q^{12} - 4 q^{13} - 2 q^{14} - 2 q^{16} - 18 q^{17} + 11 q^{18} + 17 q^{19} - 40 q^{21} - 5 q^{22} + 4 q^{23} - q^{24}+ \cdots - 72 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 - 2 * q^7 - 2 * q^8 - 24 * q^9 + 5 * q^11 - 6 * q^12 - 4 * q^13 - 2 * q^14 - 2 * q^16 - 18 * q^17 + 11 * q^18 + 17 * q^19 - 40 * q^21 - 5 * q^22 + 4 * q^23 - q^24 + 6 * q^26 + 19 * q^27 + 8 * q^28 + 2 * q^29 - 2 * q^31 + 8 * q^32 + 23 * q^33 + 2 * q^34 + 11 * q^36 + 8 * q^37 - 18 * q^38 + 24 * q^39 + 6 * q^41 + 20 * q^42 + 16 * q^43 + 10 * q^44 - 6 * q^46 + 12 * q^47 + 4 * q^48 - 6 * q^49 - 17 * q^51 + 6 * q^52 - 8 * q^53 - 6 * q^54 - 12 * q^56 + 19 * q^57 + 2 * q^58 - 12 * q^59 - 2 * q^61 - 22 * q^62 - 48 * q^63 - 2 * q^64 - 27 * q^66 - 34 * q^67 - 18 * q^68 + 20 * q^69 + 20 * q^71 - 24 * q^72 - 26 * q^73 + 8 * q^74 + 2 * q^76 + 26 * q^77 - 36 * q^78 + 14 * q^79 + 35 * q^81 - 9 * q^82 - 9 * q^83 + 26 * q^86 - 56 * q^87 - 5 * q^88 + 2 * q^89 - 52 * q^91 + 4 * q^92 + 32 * q^93 - 18 * q^94 + 4 * q^96 - 26 * q^97 + 64 * q^98 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−1.04238	−	3.20812i	−0.601820	−	1.85221i	−0.517327	−	0.855788i	$-0.673073\pi$
$3$	−1.04238	−	3.20812i	−0.601820	−	1.85221i	−0.0844926	−	0.996424i	$-0.526927\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	2.72899	+	1.98273i	1.11411	+	0.809446i
$7$	−0.0577923	+	0.177866i	−0.0218434	+	0.0672272i	−0.961384	−	0.275210i	$-0.911253\pi$
$7$	−0.0577923	+	0.177866i	−0.0218434	+	0.0672272i	0.939541	+	0.342438i	$0.111253\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−6.77845	+	4.92483i	−2.25948	+	1.64161i
$10$		0			0
$11$	−0.359735	+	3.29706i	−0.108464	+	0.994100i
$11$	−0.359735	+	3.29706i	−0.108464	+	0.994100i
$12$	−3.37322			−0.973765
$13$	−2.46673	+	1.79219i	−0.684148	+	0.497063i	−0.874731	−	0.484608i	$-0.838962\pi$
$13$	−2.46673	+	1.79219i	−0.684148	+	0.497063i	0.190583	+	0.981671i	$0.438962\pi$
$14$	−0.0577923	−	0.177866i	−0.0154456	−	0.0475368i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.38467	−	1.73256i	−0.578367	−	0.420208i	0.259768	−	0.965671i	$-0.416354\pi$
$17$	−2.38467	−	1.73256i	−0.578367	−	0.420208i	−0.838135	+	0.545463i	$0.816354\pi$
$18$	2.58914	−	7.96855i	0.610266	−	1.87820i
$19$	1.66209	+	5.11538i	0.381309	+	1.17355i	0.939123	+	0.343582i	$0.111640\pi$
$19$	1.66209	+	5.11538i	0.381309	+	1.17355i	−0.557814	+	0.829966i	$0.688360\pi$
$20$		0			0
$21$	0.630859			0.137665
$22$	−1.64693	−	2.87882i	−0.351127	−	0.613767i
$23$	0.115585			0.0241011			0.0120505	−	0.999927i	$-0.496164\pi$
$23$	0.115585			0.0241011			0.0120505	+	0.999927i	$0.496164\pi$
$24$	2.72899	−	1.98273i	0.557054	−	0.404723i
$25$		0			0
$26$	0.942208	−	2.89982i	0.184782	−	0.568701i
$27$	14.6782	+	10.6644i	2.82483	+	2.05236i
$28$	0.151302	+	0.109927i	0.0285934	+	0.0207743i
$29$	3.14256	−	9.67180i	0.583558	−	1.79601i	−0.0214257	−	0.999770i	$-0.506821\pi$
$29$	3.14256	−	9.67180i	0.583558	−	1.79601i	0.604984	−	0.796238i	$-0.293179\pi$
$30$		0			0
$31$	−6.22732	+	4.52442i	−1.11846	+	0.812609i	−0.983975	−	0.178307i	$-0.942938\pi$
$31$	−6.22732	+	4.52442i	−1.11846	+	0.812609i	−0.134485	+	0.990916i	$0.542938\pi$
$32$	1.00000			0.176777
$33$	10.9524	−	2.28272i	1.90656	−	0.397371i
$34$	2.94761			0.505511
$35$		0			0
$36$	2.58914	+	7.96855i	0.431523	+	1.32809i
$37$	−2.08477	+	6.41625i	−0.342733	+	1.05482i	0.620053	+	0.784560i	$0.287111\pi$
$37$	−2.08477	+	6.41625i	−0.342733	+	1.05482i	−0.962786	+	0.270265i	$0.912889\pi$
$38$	−4.35140	−	3.16148i	−0.705890	−	0.512859i
$39$	8.32083	+	6.04544i	1.33240	+	0.968045i
$40$		0			0
$41$	−1.44887	−	4.45917i	−0.226276	−	0.696406i	−0.998160	−	0.0606419i	$-0.980685\pi$
$41$	−1.44887	−	4.45917i	−0.226276	−	0.696406i	0.771884	−	0.635764i	$-0.219315\pi$
$42$	−0.510376	+	0.370810i	−0.0787527	+	0.0572172i
$43$	−2.27719			−0.347268			−0.173634	−	0.984810i	$-0.555551\pi$
$43$	−2.27719			−0.347268			−0.173634	+	0.984810i	$0.555551\pi$
$44$	3.02452	+	1.36098i	0.455964	+	0.205175i
$45$		0			0
$46$	−0.0935099	+	0.0679389i	−0.0137873	+	0.0100170i
$47$	1.96428	+	6.04544i	0.286520	+	0.881818i	0.985939	+	0.167106i	$0.0534422\pi$
$47$	1.96428	+	6.04544i	0.286520	+	0.881818i	−0.699419	+	0.714712i	$0.746558\pi$
$48$	−1.04238	+	3.20812i	−0.150455	+	0.463053i
$49$	5.63482	+	4.09394i	0.804975	+	0.584848i
$50$		0			0
$51$	−3.07254	+	9.45631i	−0.430242	+	1.32415i
$52$	0.942208	+	2.89982i	0.130661	+	0.402132i
$53$	−6.51578	+	4.73399i	−0.895011	+	0.650264i	−0.937180	−	0.348847i	$-0.886573\pi$
$53$	−6.51578	+	4.73399i	−0.895011	+	0.650264i	0.0421685	+	0.999111i	$0.486573\pi$
$54$	−18.1433			−2.46899
$55$		0			0
$56$	−0.187020			−0.0249916
$57$	14.6782	−	10.6644i	1.94418	−	1.41253i
$58$	3.14256	+	9.67180i	0.412638	+	1.26997i
$59$	−0.479439	+	1.47556i	−0.0624177	+	0.192102i	−0.977403	−	0.211386i	$-0.932202\pi$
$59$	−0.479439	+	1.47556i	−0.0624177	+	0.192102i	0.914985	+	0.403488i	$0.132202\pi$
$60$		0			0
$61$	−0.711544	−	0.516967i	−0.0911039	−	0.0661908i	0.541301	−	0.840829i	$-0.317932\pi$
$61$	−0.711544	−	0.516967i	−0.0911039	−	0.0661908i	−0.632405	+	0.774638i	$0.717932\pi$
$62$	2.37863	−	7.32066i	0.302086	−	0.929725i
$63$	−0.484220	−	1.49028i	−0.0610060	−	0.187757i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$	−7.51889	+	8.28439i	−0.925511	+	1.01974i
$67$	−9.03490			−1.10379			−0.551894	−	0.833914i	$-0.686095\pi$
$67$	−9.03490			−1.10379			−0.551894	+	0.833914i	$0.686095\pi$
$68$	−2.38467	+	1.73256i	−0.289183	+	0.210104i
$69$	−0.120483	−	0.370810i	−0.0145045	−	0.0446402i
$70$		0			0
$71$	0.533268	+	0.387442i	0.0632873	+	0.0459809i	0.618979	−	0.785407i	$-0.287547\pi$
$71$	0.533268	+	0.387442i	0.0632873	+	0.0459809i	−0.555692	+	0.831388i	$0.687547\pi$
$72$	−6.77845	−	4.92483i	−0.798848	−	0.580397i
$73$	0.720659	−	2.21796i	0.0843467	−	0.259592i	−0.899985	−	0.435922i	$-0.856422\pi$
$73$	0.720659	−	2.21796i	0.0843467	−	0.259592i	0.984331	+	0.176329i	$0.0564224\pi$
$74$	−2.08477	−	6.41625i	−0.242349	−	0.745874i
$75$		0			0
$76$	5.37863			0.616971
$77$	−0.565646	−	0.254529i	−0.0644613	−	0.0290063i
$78$	−10.2851			−1.16456
$79$	7.45799	−	5.41855i	0.839089	−	0.609634i	−0.0830269	−	0.996547i	$-0.526459\pi$
$79$	7.45799	−	5.41855i	0.839089	−	0.609634i	0.922116	+	0.386913i	$0.126459\pi$
$80$		0			0
$81$	11.1449	−	34.3003i	1.23832	−	3.81115i
$82$	3.79320	+	2.75592i	0.418889	+	0.304340i
$83$	−2.57128	−	1.86814i	−0.282235	−	0.205055i	0.437657	−	0.899142i	$-0.355808\pi$
$83$	−2.57128	−	1.86814i	−0.282235	−	0.205055i	−0.719891	+	0.694087i	$0.755808\pi$
$84$	0.194946	−	0.599983i	0.0212704	−	0.0654635i
$85$		0			0
$86$	1.84229	−	1.33850i	0.198659	−	0.144334i
$87$	−34.3041			−3.67778
$88$	−3.24685	+	0.676718i	−0.346116	+	0.0721384i
$89$	−6.69658			−0.709836			−0.354918	−	0.934897i	$-0.615491\pi$
$89$	−6.69658			−0.709836			−0.354918	+	0.934897i	$0.615491\pi$
$90$		0			0
$91$	−0.176211	−	0.542323i	−0.0184720	−	0.0568509i
$92$	0.0357176	−	0.109927i	0.00372382	−	0.0114607i
$93$	21.0061	+	15.2619i	2.17824	+	1.58258i
$94$	−5.14256	−	3.73629i	−0.530414	−	0.385369i
$95$		0			0
$96$	−1.04238	−	3.20812i	−0.106388	−	0.327428i
$97$	−7.16312	+	5.20431i	−0.727305	+	0.528418i	−0.888710	−	0.458471i	$-0.848397\pi$
$97$	−7.16312	+	5.20431i	−0.727305	+	0.528418i	0.161405	+	0.986888i	$0.448397\pi$
$98$	−6.96502			−0.703574
$99$	−13.7990	−	24.1206i	−1.38685	−	2.42421i
$100$		0			0
$101$	−10.9738	+	7.97291i	−1.09193	+	0.793334i	−0.979724	−	0.200351i	$-0.935792\pi$
$101$	−10.9738	+	7.97291i	−1.09193	+	0.793334i	−0.112206	+	0.993685i	$0.535792\pi$
$102$	−3.07254	−	9.45631i	−0.304227	−	0.936314i
$103$	−2.20035	+	6.77198i	−0.216807	+	0.667263i	0.782213	+	0.623011i	$0.214091\pi$
$103$	−2.20035	+	6.77198i	−0.216807	+	0.667263i	−0.999020	+	0.0442526i	$0.985909\pi$
$104$	−2.46673	−	1.79219i	−0.241883	−	0.175738i
$105$		0			0
$106$	2.48881	−	7.65976i	0.241734	−	0.743982i
$107$	0.886182	+	2.72739i	0.0856704	+	0.263666i	0.984710	−	0.174200i	$-0.0557341\pi$
$107$	0.886182	+	2.72739i	0.0856704	+	0.263666i	−0.899040	+	0.437867i	$0.855734\pi$
$108$	14.6782	−	10.6644i	1.41241	−	1.02618i
$109$	11.0316			1.05663			0.528316	−	0.849048i	$-0.322824\pi$
$109$	11.0316			1.05663			0.528316	+	0.849048i	$0.322824\pi$
$110$		0			0
$111$	22.7573			2.16002
$112$	0.151302	−	0.109927i	0.0142967	−	0.0103872i
$113$	−2.43205	−	7.48507i	−0.228788	−	0.704136i	−0.997885	−	0.0650044i	$-0.979294\pi$
$113$	−2.43205	−	7.48507i	−0.228788	−	0.704136i	0.769097	−	0.639132i	$-0.220706\pi$
$114$	−5.60659	+	17.2553i	−0.525105	+	1.61611i
$115$		0			0
$116$	−8.22732	−	5.97750i	−0.763888	−	0.554997i
$117$	7.89441	−	24.2965i	0.729838	−	2.24621i
$118$	−0.479439	−	1.47556i	−0.0441359	−	0.135836i
$119$	0.445980	−	0.324024i	0.0408829	−	0.0297032i
$120$		0			0
$121$	−10.7412	−	2.37214i	−0.976471	−	0.215649i
$122$	0.879517			0.0796277
$123$	−12.7953	+	9.29633i	−1.15371	+	0.838222i
$124$	2.37863	+	7.32066i	0.213607	+	0.657415i
$125$		0			0
$126$	1.26770	+	0.921041i	0.112936	+	0.0820529i
$127$	7.33498	+	5.32918i	0.650874	+	0.472888i	0.863569	−	0.504231i	$-0.168224\pi$
$127$	7.33498	+	5.32918i	0.650874	+	0.472888i	−0.212695	+	0.977119i	$0.568224\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	2.37370	+	7.30551i	0.208993	+	0.643214i
$130$		0			0
$131$	−5.92554			−0.517717			−0.258858	−	0.965915i	$-0.583346\pi$
$131$	−5.92554			−0.517717			−0.258858	+	0.965915i	$0.583346\pi$
$132$	1.21347	−	11.1217i	0.105619	−	0.968020i
$133$	−1.00591			−0.0872234
$134$	7.30939	−	5.31058i	0.631435	−	0.458764i
$135$		0			0
$136$	0.910862	−	2.80335i	0.0781058	−	0.240385i
$137$	8.18931	+	5.94988i	0.699660	+	0.508333i	0.879822	−	0.475304i	$-0.157662\pi$
$137$	8.18931	+	5.94988i	0.699660	+	0.508333i	−0.180161	+	0.983637i	$0.557662\pi$
$138$	0.315430	+	0.229173i	0.0268512	+	0.0195085i
$139$	−5.29537	+	16.2975i	−0.449148	+	1.38233i	0.428723	+	0.903436i	$0.358964\pi$
$139$	−5.29537	+	16.2975i	−0.449148	+	1.38233i	−0.877870	+	0.478898i	$0.841036\pi$
$140$		0			0
$141$	17.3470	−	12.6033i	1.46088	−	1.06139i
$142$	−0.659156			−0.0553151
$143$	−5.02157	−	8.77767i	−0.419925	−	0.734026i
$144$	8.37863			0.698219
$145$		0			0
$146$	0.720659	+	2.21796i	0.0596421	+	0.183560i
$147$	7.26022	−	22.3447i	0.598813	−	1.84296i
$148$	5.45799	+	3.96546i	0.448644	+	0.325959i
$149$	−18.9571	−	13.7731i	−1.55303	−	1.12834i	−0.941450	−	0.337154i	$-0.890536\pi$
$149$	−18.9571	−	13.7731i	−1.55303	−	1.12834i	−0.611576	−	0.791185i	$-0.709464\pi$
$150$		0			0
$151$	3.72821	+	11.4743i	0.303398	+	0.933762i	0.980270	+	0.197662i	$0.0633349\pi$
$151$	3.72821	+	11.4743i	0.303398	+	0.933762i	−0.676872	+	0.736100i	$0.736665\pi$
$152$	−4.35140	+	3.16148i	−0.352945	+	0.256430i
$153$	24.6969			1.99663
$154$	0.607226	−	0.126560i	0.0489316	−	0.0101985i
$155$		0			0
$156$	8.32083	−	6.04544i	0.666200	−	0.484023i
$157$	0.933464	+	2.87291i	0.0744985	+	0.229283i	0.981371	−	0.192122i	$-0.0615370\pi$
$157$	0.933464	+	2.87291i	0.0744985	+	0.229283i	−0.906872	+	0.421405i	$0.861537\pi$
$158$	−2.84870	+	8.76739i	−0.226630	+	0.697496i
$159$	21.9792	+	15.9688i	1.74306	+	1.26641i
$160$		0			0
$161$	−0.00667990	+	0.0205586i	−0.000526450	+	0.00162025i
$162$	11.1449	+	34.3003i	0.875622	+	2.69489i
$163$	−1.74619	+	1.26868i	−0.136772	+	0.0993709i	−0.654068	−	0.756436i	$-0.726939\pi$
$163$	−1.74619	+	1.26868i	−0.136772	+	0.0993709i	0.517295	+	0.855807i	$0.326939\pi$
$164$	−4.68865			−0.366122
$165$		0			0
$166$	3.17828			0.246682
$167$	4.55150	−	3.30686i	0.352205	−	0.255892i	−0.397588	−	0.917564i	$-0.630153\pi$
$167$	4.55150	−	3.30686i	0.352205	−	0.255892i	0.749794	+	0.661672i	$0.230153\pi$
$168$	0.194946	+	0.599983i	0.0150404	+	0.0462897i
$169$	−1.14438	+	3.52205i	−0.0880296	+	0.270927i
$170$		0			0
$171$	−36.4588	−	26.4888i	−2.78807	−	2.02565i
$172$	−0.703690	+	2.16574i	−0.0536559	+	0.165136i
$173$	−4.80758	−	14.7962i	−0.365513	−	1.12493i	−0.949659	−	0.313285i	$-0.898570\pi$
$173$	−4.80758	−	14.7962i	−0.365513	−	1.12493i	0.584146	−	0.811649i	$-0.301430\pi$
$174$	27.7526	−	20.1634i	2.10392	−	1.52859i
$175$		0			0
$176$	2.22899	−	2.45593i	0.168017	−	0.185123i
$177$	5.23355			0.393377
$178$	5.41765	−	3.93615i	0.406070	−	0.295027i
$179$	−5.36885	−	16.5236i	−0.401287	−	1.23503i	−0.923956	−	0.382498i	$-0.875064\pi$
$179$	−5.36885	−	16.5236i	−0.401287	−	1.23503i	0.522670	−	0.852535i	$-0.324936\pi$
$180$		0			0
$181$	−11.1957	−	8.13414i	−0.832169	−	0.604606i	0.0880032	−	0.996120i	$-0.471951\pi$
$181$	−11.1957	−	8.13414i	−0.832169	−	0.604606i	−0.920172	+	0.391514i	$0.871951\pi$
$182$	0.461328	+	0.335174i	0.0341959	+	0.0248448i
$183$	−0.916793	+	2.82160i	−0.0677713	+	0.208579i
$184$	0.0357176	+	0.109927i	0.00263314	+	0.00810396i
$185$		0			0
$186$	−25.9650			−1.90385
$187$	6.57021	−	7.23912i	0.480461	−	0.529377i
$188$	6.35655			0.463599
$189$	−2.74512	+	1.99445i	−0.199678	+	0.145075i
$190$		0			0
$191$	−1.22732	+	3.77731i	−0.0888060	+	0.273317i	−0.985590	−	0.169152i	$-0.945897\pi$
$191$	−1.22732	+	3.77731i	−0.0888060	+	0.273317i	0.896784	+	0.442469i	$0.145897\pi$
$192$	2.72899	+	1.98273i	0.196948	+	0.143091i
$193$	−6.42705	−	4.66953i	−0.462629	−	0.336120i	0.331933	−	0.943303i	$-0.392299\pi$
$193$	−6.42705	−	4.66953i	−0.462629	−	0.336120i	−0.794562	+	0.607183i	$0.792299\pi$
$194$	2.73607	−	8.42075i	0.196438	−	0.604575i
$195$		0			0
$196$	5.63482	−	4.09394i	0.402487	−	0.292424i
$197$	5.54948			0.395384			0.197692	−	0.980264i	$-0.436655\pi$
$197$	5.54948			0.395384			0.197692	+	0.980264i	$0.436655\pi$
$198$	25.3414	+	11.4031i	1.80093	+	0.810383i
$199$	4.31846			0.306127			0.153064	−	0.988216i	$-0.451086\pi$
$199$	4.31846			0.306127			0.153064	+	0.988216i	$0.451086\pi$
$200$		0			0
$201$	9.41783	+	28.9851i	0.664282	+	2.04445i
$202$	4.19161	−	12.9004i	0.294920	−	0.907672i
$203$	1.53867	+	1.11791i	0.107994	+	0.0784620i
$204$	8.04401	+	5.84432i	0.563194	+	0.409184i
$205$		0			0
$206$	−2.20035	−	6.77198i	−0.153306	−	0.471826i
$207$	−0.783484	+	0.569235i	−0.0544559	+	0.0395646i
$208$	3.04905			0.211413
$209$	−17.4636	+	3.63982i	−1.20798	+	0.251771i
$210$		0			0
$211$	−5.90086	+	4.28722i	−0.406232	+	0.295145i	−0.772074	−	0.635532i	$-0.780781\pi$
$211$	−5.90086	+	4.28722i	−0.406232	+	0.295145i	0.365843	+	0.930677i	$0.380781\pi$
$212$	2.48881	+	7.65976i	0.170932	+	0.526074i
$213$	0.687093	−	2.11465i	0.0470788	−	0.144894i
$214$	−2.32005	−	1.68562i	−0.158596	−	0.115226i
$215$		0			0
$216$	−5.60659	+	17.2553i	−0.381480	+	1.17407i
$217$	−0.444850	−	1.36911i	−0.0301984	−	0.0929411i
$218$	−8.92472	+	6.48419i	−0.604458	+	0.439165i
$219$	−7.86669			−0.531582
$220$		0			0
$221$	8.98741			0.604559
$222$	−18.4110	+	13.3764i	−1.23567	+	0.897764i
$223$	5.09603	+	15.6840i	0.341256	+	1.05028i	0.963558	+	0.267500i	$0.0861974\pi$
$223$	5.09603	+	15.6840i	0.341256	+	1.05028i	−0.622302	+	0.782777i	$0.713803\pi$
$224$	−0.0577923	+	0.177866i	−0.00386141	+	0.0118842i
$225$		0			0
$226$	6.36718	+	4.62603i	0.423539	+	0.307719i
$227$	−3.59992	+	11.0794i	−0.238935	+	0.735367i	0.757640	+	0.652673i	$0.226352\pi$
$227$	−3.59992	+	11.0794i	−0.238935	+	0.735367i	−0.996575	+	0.0826941i	$0.973648\pi$
$228$	−5.60659	−	17.2553i	−0.371305	−	1.14276i
$229$	−16.0236	+	11.6419i	−1.05887	+	0.769315i	−0.973879	−	0.227066i	$-0.927087\pi$
$229$	−16.0236	+	11.6419i	−1.05887	+	0.769315i	−0.0849922	+	0.996382i	$0.527087\pi$
$230$		0			0
$231$	−0.226942	+	2.07998i	−0.0149317	+	0.136853i
$232$	10.1695			0.667662
$233$	−4.35807	+	3.16632i	−0.285506	+	0.207433i	−0.721316	−	0.692607i	$-0.756462\pi$
$233$	−4.35807	+	3.16632i	−0.285506	+	0.207433i	0.435809	+	0.900039i	$0.356462\pi$
$234$	7.89441	+	24.2965i	0.516073	+	1.58831i
$235$		0			0
$236$	1.25519	+	0.911947i	0.0817058	+	0.0593627i
$237$	−25.1574	−	18.2780i	−1.63415	−	1.18728i
$238$	−0.170349	+	0.524281i	−0.0110421	+	0.0339841i
$239$	2.76883	+	8.52159i	0.179101	+	0.551216i	0.999797	−	0.0201493i	$-0.00641415\pi$
$239$	2.76883	+	8.52159i	0.179101	+	0.551216i	−0.820696	+	0.571365i	$0.806414\pi$
$240$		0			0
$241$	10.6881			0.688484			0.344242	−	0.938881i	$-0.388136\pi$
$241$	10.6881			0.688484			0.344242	+	0.938881i	$0.388136\pi$
$242$	10.0841	−	4.39441i	0.648231	−	0.282483i
$243$	−67.2270			−4.31262
$244$	−0.711544	+	0.516967i	−0.0455519	+	0.0330954i
$245$		0			0
$246$	4.88737	−	15.0418i	0.311607	−	0.959029i
$247$	−13.2676	−	9.63950i	−0.844199	−	0.613346i
$248$	−6.22732	−	4.52442i	−0.395435	−	0.287301i
$249$	−3.31298	+	10.1963i	−0.209952	+	0.646165i
$250$		0			0
$251$	−6.02219	+	4.37538i	−0.380117	+	0.276171i	−0.761394	−	0.648290i	$-0.775485\pi$
$251$	−6.02219	+	4.37538i	−0.380117	+	0.276171i	0.381276	+	0.924461i	$0.375485\pi$
$252$	−1.56697			−0.0987098
$253$	−0.0415798	+	0.381089i	−0.00261410	+	0.0239589i
$254$	−9.06654			−0.568885
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−2.95643	+	9.09895i	−0.184417	+	0.567577i	−0.999938	−	0.0111506i	$-0.996451\pi$
$257$	−2.95643	+	9.09895i	−0.184417	+	0.567577i	0.815521	+	0.578728i	$0.196451\pi$
$258$	−6.21444	−	4.51505i	−0.386894	−	0.281095i
$259$	−1.02075	−	0.741620i	−0.0634264	−	0.0460820i
$260$		0			0
$261$	26.3303	+	81.0364i	1.62981	+	5.01603i
$262$	4.79386	−	3.48294i	0.296166	−	0.215177i
$263$	20.8985			1.28866			0.644328	−	0.764749i	$-0.277137\pi$
$263$	20.8985			1.28866			0.644328	+	0.764749i	$0.277137\pi$
$264$	5.55546	+	9.71091i	0.341915	+	0.597665i
$265$		0			0
$266$	0.813798	−	0.591259i	0.0498971	−	0.0362524i
$267$	6.98040	+	21.4835i	0.427193	+	1.31477i
$268$	−2.79194	+	8.59270i	−0.170545	+	0.524883i
$269$	−16.6766	−	12.1162i	−1.01679	−	0.738740i	−0.0511662	−	0.998690i	$-0.516294\pi$
$269$	−16.6766	−	12.1162i	−1.01679	−	0.738740i	−0.965622	+	0.259950i	$0.916294\pi$
$270$		0			0
$271$	2.53533	−	7.80295i	0.154010	−	0.473996i	−0.844049	−	0.536266i	$-0.819834\pi$
$271$	2.53533	−	7.80295i	0.154010	−	0.473996i	0.998059	+	0.0622709i	$0.0198343\pi$
$272$	0.910862	+	2.80335i	0.0552291	+	0.169978i
$273$	−1.55616	+	1.13062i	−0.0941831	+	0.0684280i
$274$	−10.1225			−0.611525
$275$		0			0
$276$	−0.389892			−0.0234688
$277$	−10.3328	+	7.50725i	−0.620840	+	0.451067i	−0.853215	−	0.521559i	$-0.825350\pi$
$277$	−10.3328	+	7.50725i	−0.620840	+	0.451067i	0.232375	+	0.972626i	$0.425350\pi$
$278$	−5.29537	−	16.2975i	−0.317595	−	0.977458i
$279$	19.9296	−	61.3371i	1.19316	−	3.67215i
$280$		0			0
$281$	18.0380	+	13.1054i	1.07606	+	0.781800i	0.976991	−	0.213281i	$-0.0684150\pi$
$281$	18.0380	+	13.1054i	1.07606	+	0.781800i	0.0990644	+	0.995081i	$0.468415\pi$
$282$	−6.62596	+	20.3926i	−0.394570	+	1.21436i
$283$	−3.47159	−	10.6844i	−0.206364	−	0.635124i	−0.999655	−	0.0262805i	$-0.991634\pi$
$283$	−3.47159	−	10.6844i	−0.206364	−	0.635124i	0.793290	−	0.608844i	$-0.208366\pi$
$284$	0.533268	−	0.387442i	0.0316436	−	0.0229905i
$285$		0			0
$286$	9.22192	+	4.14968i	0.545304	+	0.245376i
$287$	0.876871			0.0517600
$288$	−6.77845	+	4.92483i	−0.399424	+	0.290199i
$289$	−2.56842	−	7.90479i	−0.151084	−	0.464987i
$290$		0			0
$291$	24.1628	+	17.5553i	1.41645	+	1.02911i
$292$	−1.88671	−	1.37077i	−0.110411	−	0.0802185i
$293$	7.91189	−	24.3503i	0.462218	−	1.42256i	−0.400230	−	0.916415i	$-0.631070\pi$
$293$	7.91189	−	24.3503i	0.462218	−	1.42256i	0.862448	−	0.506146i	$-0.168930\pi$
$294$	7.26022	+	22.3447i	0.423425	+	1.30317i
$295$		0			0
$296$	−6.74644			−0.392129
$297$	−40.4413	+	44.5587i	−2.34664	+	2.58556i
$298$	23.4323			1.35739
$299$	−0.285116	+	0.207149i	−0.0164887	+	0.0119797i
$300$		0			0
$301$	0.131604	−	0.405036i	0.00758553	−	0.0233459i
$302$	−9.76059	−	7.09149i	−0.561659	−	0.408069i
$303$	37.0170	+	26.8944i	2.12657	+	1.54504i
$304$	1.66209	−	5.11538i	0.0953272	−	0.293387i
$305$		0			0
$306$	−19.9802	+	14.5165i	−1.14219	+	0.829853i
$307$	−19.3732			−1.10569			−0.552844	−	0.833285i	$-0.686457\pi$
$307$	−19.3732			−1.10569			−0.552844	+	0.833285i	$0.686457\pi$
$308$	−0.416866	+	0.459307i	−0.0237531	+	0.0261715i
$309$	24.0190			1.36639
$310$		0			0
$311$	−5.39323	−	16.5987i	−0.305822	−	0.941224i	−0.979369	−	0.202079i	$-0.935230\pi$
$311$	−5.39323	−	16.5987i	−0.305822	−	0.941224i	0.673547	−	0.739144i	$-0.264770\pi$
$312$	−3.17828	+	9.78173i	−0.179934	+	0.553781i
$313$	−17.4443	−	12.6740i	−0.986009	−	0.716377i	−0.0269652	−	0.999636i	$-0.508584\pi$
$313$	−17.4443	−	12.6740i	−0.986009	−	0.716377i	−0.959043	+	0.283259i	$0.908584\pi$
$314$	−2.44384	−	1.77555i	−0.137914	−	0.100200i
$315$		0			0
$316$	−2.84870	−	8.76739i	−0.160252	−	0.493204i
$317$	16.5864	−	12.0507i	0.931585	−	0.676836i	−0.0147955	−	0.999891i	$-0.504710\pi$
$317$	16.5864	−	12.0507i	0.931585	−	0.676836i	0.946380	+	0.323054i	$0.104710\pi$
$318$	−27.1678			−1.52349
$319$	30.7580	+	13.8405i	1.72212	+	0.774918i
$320$		0			0
$321$	7.82606	−	5.68596i	0.436808	−	0.317360i
$322$	−0.00667990	−	0.0205586i	−0.000372256	−	0.00114569i
$323$	4.89919	−	15.0781i	0.272598	−	0.838971i
$324$	−29.1776	−	21.1988i	−1.62098	−	1.17771i
$325$		0			0
$326$	0.666986	−	2.05277i	0.0369409	−	0.113692i
$327$	−11.4991	−	35.3906i	−0.635902	−	1.95711i
$328$	3.79320	−	2.75592i	0.209444	−	0.152170i
$329$	−1.18880			−0.0655407
$330$		0			0
$331$	8.86611			0.487325			0.243663	−	0.969860i	$-0.421651\pi$
$331$	8.86611			0.487325			0.243663	+	0.969860i	$0.421651\pi$
$332$	−2.57128	+	1.86814i	−0.141117	+	0.102528i
$333$	−17.4675	−	53.7594i	−0.957212	−	2.94599i
$334$	−1.73852	+	5.35061i	−0.0951274	+	0.292772i
$335$		0			0
$336$	−0.510376	−	0.370810i	−0.0278433	−	0.0202293i
$337$	1.17328	−	3.61099i	0.0639127	−	0.196703i	−0.914001	−	0.405712i	$-0.867024\pi$
$337$	1.17328	−	3.61099i	0.0639127	−	0.196703i	0.977914	+	0.209009i	$0.0670237\pi$
$338$	−1.14438	−	3.52205i	−0.0622463	−	0.191574i
$339$	−21.4779	+	15.6046i	−1.16652	+	0.847526i
$340$		0			0
$341$	−12.6771	−	22.1594i	−0.686502	−	1.20000i
$342$	45.0655			2.43686
$343$	−2.11294	+	1.53514i	−0.114088	+	0.0828898i
$344$	−0.703690	−	2.16574i	−0.0379404	−	0.116769i
$345$		0			0
$346$	12.5864	+	9.14455i	0.676649	+	0.491614i
$347$	16.5907	+	12.0539i	0.890637	+	0.647086i	0.936044	−	0.351883i	$-0.114458\pi$
$347$	16.5907	+	12.0539i	0.890637	+	0.647086i	−0.0454069	+	0.998969i	$0.514458\pi$
$348$	−10.6005	+	32.6251i	−0.568249	+	1.74889i
$349$	4.37529	+	13.4657i	0.234204	+	0.720805i	0.997226	+	0.0744327i	$0.0237146\pi$
$349$	4.37529	+	13.4657i	0.234204	+	0.720805i	−0.763022	+	0.646372i	$0.776285\pi$
$350$		0			0
$351$	−55.3198			−2.95275
$352$	−0.359735	+	3.29706i	−0.0191739	+	0.175734i
$353$	22.1366			1.17821			0.589105	−	0.808056i	$-0.299480\pi$
$353$	22.1366			1.17821			0.589105	+	0.808056i	$0.299480\pi$
$354$	−4.23403	+	3.07620i	−0.225036	+	0.163498i
$355$		0			0
$356$	−2.06936	+	6.36882i	−0.109676	+	0.337547i
$357$	−1.50439	−	1.09300i	−0.0796208	−	0.0578479i
$358$	14.0558	+	10.2122i	0.742874	+	0.539729i
$359$	−2.55974	+	7.87806i	−0.135098	+	0.415788i	−0.995605	−	0.0936498i	$-0.970147\pi$
$359$	−2.55974	+	7.87806i	−0.135098	+	0.415788i	0.860507	+	0.509438i	$0.170147\pi$
$360$		0			0
$361$	−8.03323	+	5.83648i	−0.422802	+	0.307183i
$362$	13.8386			0.727342
$363$	3.58632	+	36.9317i	0.188233	+	1.93841i
$364$	−0.570232			−0.0298883
$365$		0			0
$366$	−0.916793	−	2.82160i	−0.0479215	−	0.147487i
$367$	7.32336	−	22.5390i	0.382276	−	1.17652i	−0.556161	−	0.831075i	$-0.687726\pi$
$367$	7.32336	−	22.5390i	0.382276	−	1.17652i	0.938437	−	0.345450i	$-0.112274\pi$
$368$	−0.0935099	−	0.0679389i	−0.00487454	−	0.00354156i
$369$	31.7818	+	23.0908i	1.65449	+	1.20206i
$370$		0			0
$371$	−0.465456	−	1.43253i	−0.0241653	−	0.0743731i
$372$	21.0061	−	15.2619i	1.08912	−	0.791290i
$373$	27.6907			1.43377			0.716885	−	0.697191i	$-0.245567\pi$
$373$	27.6907			1.43377			0.716885	+	0.697191i	$0.245567\pi$
$374$	−1.06036	+	9.71845i	−0.0548299	+	0.502529i
$375$		0			0
$376$	−5.14256	+	3.73629i	−0.265207	+	0.192684i
$377$	9.58181	+	29.4898i	0.493488	+	1.51880i
$378$	1.04854	−	3.22708i	0.0539312	−	0.165983i
$379$	−12.8168	−	9.31197i	−0.658356	−	0.478324i	0.207751	−	0.978182i	$-0.433386\pi$
$379$	−12.8168	−	9.31197i	−0.658356	−	0.478324i	−0.866108	+	0.499858i	$0.833386\pi$
$380$		0			0
$381$	9.45080	−	29.0866i	0.484179	−	1.49015i
$382$	−1.22732	−	3.77731i	−0.0627954	−	0.193264i
$383$	−1.09269	+	0.793887i	−0.0558340	+	0.0405657i	−0.615352	−	0.788252i	$-0.710986\pi$
$383$	−1.09269	+	0.793887i	−0.0558340	+	0.0405657i	0.559518	+	0.828818i	$0.310986\pi$
$384$	−3.37322			−0.172139
$385$		0			0
$386$	7.94427			0.404353
$387$	15.4358	−	11.2148i	0.784647	−	0.570079i
$388$	2.73607	+	8.42075i	0.138903	+	0.427499i
$389$	−1.45465	+	4.47695i	−0.0737536	+	0.226990i	−0.981137	−	0.193314i	$-0.938077\pi$
$389$	−1.45465	+	4.47695i	−0.0737536	+	0.226990i	0.907383	+	0.420304i	$0.138077\pi$
$390$		0			0
$391$	−0.275631	−	0.200258i	−0.0139393	−	0.0101275i
$392$	−2.15231	+	6.62413i	−0.108708	+	0.334569i
$393$	6.17668	+	19.0099i	0.311572	+	0.958921i
$394$	−4.48962	+	3.26190i	−0.226184	+	0.164332i
$395$		0			0
$396$	−27.2042	+	5.66997i	−1.36706	+	0.284927i
$397$	23.2196			1.16536			0.582679	−	0.812702i	$-0.302005\pi$
$397$	23.2196			1.16536			0.582679	+	0.812702i	$0.302005\pi$
$398$	−3.49371	+	2.53833i	−0.175124	+	0.127235i
$399$	1.04854	+	3.22708i	0.0524928	+	0.161556i
$400$		0			0
$401$	4.74415	+	3.44683i	0.236912	+	0.172126i	0.699906	−	0.714235i	$-0.253225\pi$
$401$	4.74415	+	3.44683i	0.236912	+	0.172126i	−0.462995	+	0.886361i	$0.653225\pi$
$402$	−24.6562	−	17.9138i	−1.22974	−	0.893458i
$403$	7.25255	−	22.3210i	0.361275	−	1.11189i
$404$	4.19161	+	12.9004i	0.208540	+	0.641821i
$405$		0			0
$406$	−1.90190			−0.0943899
$407$	−20.4048	−	9.18174i	−1.01143	−	0.455122i
$408$	−9.94295			−0.492249
$409$	21.1843	−	15.3913i	1.04750	−	0.761051i	0.0757616	−	0.997126i	$-0.475861\pi$
$409$	21.1843	−	15.3913i	1.04750	−	0.761051i	0.971735	+	0.236075i	$0.0758612\pi$
$410$		0			0
$411$	10.5516	−	32.4744i	0.520471	−	1.60184i
$412$	5.76059	+	4.18532i	0.283804	+	0.206196i
$413$	−0.234745	−	0.170552i	−0.0115510	−	0.00839233i
$414$	0.299264	−	0.921041i	0.0147080	−	0.0452667i
$415$		0			0
$416$	−2.46673	+	1.79219i	−0.120941	+	0.0878691i
$417$	57.8042			2.83068
$418$	11.9889	−	13.2095i	0.586397	−	0.646099i
$419$	−6.68865			−0.326762			−0.163381	−	0.986563i	$-0.552240\pi$
$419$	−6.68865			−0.326762			−0.163381	+	0.986563i	$0.552240\pi$
$420$		0			0
$421$	7.80964	+	24.0356i	0.380619	+	1.17142i	0.939609	+	0.342249i	$0.111189\pi$
$421$	7.80964	+	24.0356i	0.380619	+	1.17142i	−0.558991	+	0.829174i	$0.688811\pi$
$422$	2.25393	−	6.93687i	0.109719	−	0.337682i
$423$	−43.0876	−	31.3050i	−2.09499	−	1.52210i
$424$	−6.51578	−	4.73399i	−0.316434	−	0.229903i
$425$		0			0
$426$	0.687093	+	2.11465i	0.0332897	+	0.102455i
$427$	0.133073	−	0.0966830i	0.00643984	−	0.00467882i
$428$	2.86774			0.138618
$429$	−22.9255	+	25.2595i	−1.10685	+	1.21954i
$430$		0			0
$431$	25.9322	−	18.8408i	1.24911	−	0.907531i	0.250940	−	0.968003i	$-0.419260\pi$
$431$	25.9322	−	18.8408i	1.24911	−	0.907531i	0.998170	+	0.0604715i	$0.0192604\pi$
$432$	−5.60659	−	17.2553i	−0.269747	−	0.830196i
$433$	−3.21743	+	9.90223i	−0.154620	+	0.475871i	−0.998122	−	0.0612546i	$-0.980490\pi$
$433$	−3.21743	+	9.90223i	−0.154620	+	0.475871i	0.843502	+	0.537125i	$0.180490\pi$
$434$	1.16463	+	0.846155i	0.0559042	+	0.0406168i
$435$		0			0
$436$	3.40894	−	10.4916i	0.163259	−	0.502458i
$437$	0.192112	+	0.591259i	0.00918994	+	0.0282837i
$438$	6.36429	−	4.62393i	0.304097	−	0.220940i
$439$	31.4256			1.49986			0.749931	−	0.661517i	$-0.230087\pi$
$439$	31.4256			1.49986			0.749931	+	0.661517i	$0.230087\pi$
$440$		0			0
$441$	−58.3573			−2.77892
$442$	−7.27097	+	5.28267i	−0.345845	+	0.251271i
$443$	12.7062	+	39.1057i	0.603690	+	1.85797i	0.505559	+	0.862792i	$0.331286\pi$
$443$	12.7062	+	39.1057i	0.603690	+	1.85797i	0.0981312	+	0.995173i	$0.468714\pi$
$444$	7.03238	−	21.6434i	0.333742	−	1.02715i
$445$		0			0
$446$	−13.3416	−	9.69323i	−0.631742	−	0.458988i
$447$	−24.4254	+	75.1736i	−1.15528	+	3.55559i
$448$	−0.0577923	−	0.177866i	−0.00273043	−	0.00840340i
$449$	9.28984	−	6.74946i	0.438414	−	0.318527i	−0.346590	−	0.938017i	$-0.612661\pi$
$449$	9.28984	−	6.74946i	0.438414	−	0.318527i	0.785005	+	0.619490i	$0.212661\pi$
$450$		0			0
$451$	15.2234	−	3.17290i	0.716840	−	0.149406i
$452$	−7.87027			−0.370186
$453$	32.9246	−	23.9212i	1.54693	−	1.12391i
$454$	−3.59992	−	11.0794i	−0.168953	−	0.519983i
$455$		0			0
$456$	14.6782	+	10.6644i	0.687371	+	0.499405i
$457$	14.9563	+	10.8664i	0.699627	+	0.508309i	0.879811	−	0.475324i	$-0.157669\pi$
$457$	14.9563	+	10.8664i	0.699627	+	0.508309i	−0.180184	+	0.983633i	$0.557669\pi$
$458$	6.12048	−	18.8369i	0.285991	−	0.880191i
$459$	−16.5260	−	50.8619i	−0.771370	−	2.37403i
$460$		0			0
$461$	−6.71978			−0.312971			−0.156486	−	0.987680i	$-0.550017\pi$
$461$	−6.71978			−0.312971			−0.156486	+	0.987680i	$0.550017\pi$
$462$	−1.03898	−	1.81613i	−0.0483378	−	0.0844941i
$463$	25.2817			1.17494			0.587470	−	0.809246i	$-0.300124\pi$
$463$	25.2817			1.17494			0.587470	+	0.809246i	$0.300124\pi$
$464$	−8.22732	+	5.97750i	−0.381944	+	0.277499i
$465$		0			0
$466$	1.66463	−	5.12321i	0.0771126	−	0.237328i
$467$	−16.1346	−	11.7224i	−0.746618	−	0.542450i	0.148159	−	0.988964i	$-0.452665\pi$
$467$	−16.1346	−	11.7224i	−0.746618	−	0.542450i	−0.894777	+	0.446514i	$0.852665\pi$
$468$	−20.6678	−	15.0161i	−0.955370	−	0.694117i
$469$	0.522148	−	1.60700i	0.0241105	−	0.0742046i
$470$		0			0
$471$	8.24361	−	5.98934i	0.379846	−	0.275974i
$472$	−1.55150			−0.0714135
$473$	0.819185	−	7.50803i	0.0376662	−	0.345219i
$474$	31.0963			1.42830
$475$		0			0
$476$	−0.170349	−	0.524281i	−0.00780794	−	0.0240304i
$477$	20.8528	−	64.1783i	0.954783	−	2.93852i
$478$	−7.24889	−	5.26663i	−0.331557	−	0.240890i
$479$	−6.64419	−	4.82729i	−0.303581	−	0.220564i	0.425556	−	0.904932i	$-0.360078\pi$
$479$	−6.64419	−	4.82729i	−0.303581	−	0.220564i	−0.729137	+	0.684368i	$0.760078\pi$
$480$		0			0
$481$	−6.35655	−	19.5635i	−0.289834	−	0.892017i
$482$	−8.64689	+	6.28233i	−0.393855	+	0.286153i
$483$	0.0729176			0.00331787
$484$	−5.57524	+	9.48244i	−0.253420	+	0.431020i
$485$		0			0
$486$	54.3878	−	39.5151i	2.46708	−	1.79244i
$487$	−8.64835	−	26.6169i	−0.391894	−	1.20613i	−0.931354	−	0.364115i	$-0.881372\pi$
$487$	−8.64835	−	26.6169i	−0.391894	−	1.20613i	0.539460	−	0.842011i	$-0.318628\pi$
$488$	0.271786	−	0.836470i	0.0123032	−	0.0378652i
$489$	5.89029	+	4.27955i	0.266368	+	0.193528i
$490$		0			0
$491$	−4.41679	+	13.5935i	−0.199327	+	0.613466i	0.800572	+	0.599237i	$0.204529\pi$
$491$	−4.41679	+	13.5935i	−0.199327	+	0.613466i	−0.999899	+	0.0142287i	$0.995471\pi$
$492$	4.88737	+	15.0418i	0.220340	+	0.678136i
$493$	−24.2510	+	17.6194i	−1.09221	+	0.793536i
$494$	16.3997			0.737857
$495$		0			0
$496$	7.69740			0.345623
$497$	−0.0997317	+	0.0724593i	−0.00447358	+	0.00325024i
$498$	−3.31298	−	10.1963i	−0.148458	−	0.456907i
$499$	1.51667	−	4.66783i	0.0678955	−	0.208961i	−0.911352	−	0.411627i	$-0.864961\pi$
$499$	1.51667	−	4.66783i	0.0678955	−	0.208961i	0.979248	+	0.202666i	$0.0649606\pi$
$500$		0			0
$501$	−15.3532	−	11.1548i	−0.685931	−	0.498358i
$502$	2.30027	−	7.07951i	0.102666	−	0.315974i
$503$	2.03031	+	6.24866i	0.0905272	+	0.278614i	0.986062	−	0.166377i	$-0.0532069\pi$
$503$	2.03031	+	6.24866i	0.0905272	+	0.278614i	−0.895535	+	0.444991i	$0.853207\pi$
$504$	1.26770	−	0.921041i	0.0564680	−	0.0410264i
$505$		0			0
$506$	−0.190360	−	0.332748i	−0.00846252	−	0.0147924i
$507$	12.4921			0.554792
$508$	7.33498	−	5.32918i	0.325437	−	0.236444i
$509$	0.849203	+	2.61358i	0.0376403	+	0.115845i	0.968111	−	0.250521i	$-0.0806019\pi$
$509$	0.849203	+	2.61358i	0.0376403	+	0.115845i	−0.930471	+	0.366366i	$0.880602\pi$
$510$		0			0
$511$	0.352852	+	0.256362i	0.0156092	+	0.0113408i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−30.1557	+	92.8098i	−1.33141	+	4.09765i
$514$	−2.95643	−	9.09895i	−0.130402	−	0.401338i
$515$		0			0
$516$	7.68147			0.338158
$517$	−20.6388	+	4.30160i	−0.907693	+	0.189184i
$518$	1.26172			0.0554367
$519$	−42.4567	+	30.8466i	−1.86364	+	1.35402i
$520$		0			0
$521$	−2.39458	+	7.36975i	−0.104908	+	0.322875i	−0.989709	−	0.143095i	$-0.954294\pi$
$521$	−2.39458	+	7.36975i	−0.104908	+	0.322875i	0.884801	+	0.465970i	$0.154294\pi$
$522$	−68.9337	−	50.0832i	−3.01714	−	2.19208i
$523$	−21.0367	−	15.2841i	−0.919871	−	0.668326i	0.0236208	−	0.999721i	$-0.492481\pi$
$523$	−21.0367	−	15.2841i	−0.919871	−	0.668326i	−0.943492	+	0.331395i	$0.892481\pi$
$524$	−1.83109	+	5.63552i	−0.0799916	+	0.246189i
$525$		0			0
$526$	−16.9072	+	12.2838i	−0.737190	+	0.535600i
$527$	22.6889			0.988346
$528$	−10.2024	−	4.59087i	−0.444002	−	0.199792i
$529$	−22.9866			−0.999419
$530$		0			0
$531$	−4.01704	−	12.3632i	−0.174325	−	0.536516i
$532$	−0.310843	+	0.956677i	−0.0134768	+	0.0414772i
$533$	11.5656	+	8.40293i	0.500964	+	0.363971i
$534$	−18.2749	−	13.2775i	−0.790833	−	0.574574i
$535$		0			0
$536$	−2.79194	−	8.59270i	−0.120593	−	0.371148i
$537$	−47.4134	+	34.4479i	−2.04604	+	1.48654i
$538$	20.6134			0.888706
$539$	−15.5250	+	17.1056i	−0.668709	+	0.736790i
$540$		0			0
$541$	18.2979	−	13.2942i	0.786690	−	0.571564i	−0.120289	−	0.992739i	$-0.538382\pi$
$541$	18.2979	−	13.2942i	0.786690	−	0.571564i	0.906979	+	0.421175i	$0.138382\pi$
$542$	2.53533	+	7.80295i	0.108902	+	0.335165i
$543$	−14.4252	+	44.3961i	−0.619043	+	1.90522i
$544$	−2.38467	−	1.73256i	−0.102242	−	0.0742830i
$545$		0			0
$546$	0.594400	−	1.82938i	0.0254380	−	0.0782901i
$547$	−10.6609	−	32.8110i	−0.455828	−	1.40290i	−0.870160	−	0.492770i	$-0.835985\pi$
$547$	−10.6609	−	32.8110i	−0.455828	−	1.40290i	0.414331	−	0.910126i	$-0.364015\pi$
$548$	8.18931	−	5.94988i	0.349830	−	0.254166i
$549$	7.36914			0.314507
$550$		0			0
$551$	54.6981			2.33022
$552$	0.315430	−	0.229173i	0.0134256	−	0.00975425i
$553$	0.532763	+	1.63968i	0.0226554	+	0.0697261i
$554$	3.94679	−	12.1470i	0.167683	−	0.516076i
$555$		0			0
$556$	13.8635	+	10.0724i	0.587942	+	0.427165i
$557$	5.76393	−	17.7396i	0.244226	−	0.751649i	−0.751537	−	0.659691i	$-0.770687\pi$
$557$	5.76393	−	17.7396i	0.244226	−	0.751649i	0.995763	−	0.0919585i	$-0.0293127\pi$
$558$	19.9296	+	61.3371i	0.843688	+	2.59660i
$559$	5.61722	−	4.08115i	0.237583	−	0.172614i
$560$		0			0
$561$	−30.0727	−	13.5321i	−1.26967	−	0.571326i
$562$	−22.2962			−0.940507
$563$	−31.3413	+	22.7708i	−1.32088	+	0.959675i	−0.320958	+	0.947093i	$0.604005\pi$
$563$	−31.3413	+	22.7708i	−1.32088	+	0.959675i	−0.999921	+	0.0125815i	$0.995995\pi$
$564$	−6.62596	−	20.3926i	−0.279003	−	0.858684i
$565$		0			0
$566$	9.08873	+	6.60335i	0.382028	+	0.277559i
$567$	5.45679	+	3.96459i	0.229164	+	0.166497i
$568$	−0.203690	+	0.626894i	−0.00854666	+	0.0263039i
$569$	−8.05198	−	24.7814i	−0.337557	−	1.03889i	−0.965449	−	0.260592i	$-0.916082\pi$
$569$	−8.05198	−	24.7814i	−0.337557	−	1.03889i	0.627892	−	0.778300i	$-0.283918\pi$
$570$		0			0
$571$	−39.8951			−1.66956			−0.834778	−	0.550586i	$-0.814404\pi$
$571$	−39.8951			−1.66956			−0.834778	+	0.550586i	$0.814404\pi$
$572$	−9.89981	+	2.06335i	−0.413932	+	0.0862729i
$573$	13.3974			0.559686
$574$	−0.709403	+	0.515412i	−0.0296099	+	0.0215129i
$575$		0			0
$576$	2.58914	−	7.96855i	0.107881	−	0.332023i
$577$	−6.42334	−	4.66683i	−0.267407	−	0.194283i	0.445999	−	0.895033i	$-0.352848\pi$
$577$	−6.42334	−	4.66683i	−0.267407	−	0.194283i	−0.713406	+	0.700751i	$0.752848\pi$
$578$	6.72421	+	4.88543i	0.279690	+	0.203207i
$579$	−8.28097	+	25.4862i	−0.344146	+	1.05917i
$580$		0			0
$581$	0.480880	−	0.349380i	0.0199503	−	0.0144947i
$582$	−29.8669			−1.23802
$583$	−13.2643	−	23.1859i	−0.549351	−	0.960261i
$584$	2.33210			0.0965030
$585$		0			0
$586$	7.91189	+	24.3503i	0.326837	+	1.00590i
$587$	3.66271	−	11.2727i	0.151176	−	0.465273i	−0.846577	−	0.532266i	$-0.821341\pi$
$587$	3.66271	−	11.2727i	0.151176	−	0.465273i	0.997753	+	0.0669934i	$0.0213406\pi$
$588$	−19.0075	−	13.8098i	−0.783856	−	0.569505i
$589$	−33.4944	−	24.3351i	−1.38011	−	1.00271i
$590$		0			0
$591$	−5.78468	−	17.8034i	−0.237950	−	0.732335i
$592$	5.45799	−	3.96546i	0.224322	−	0.162979i
$593$	−29.4865			−1.21087			−0.605433	−	0.795896i	$-0.707000\pi$
$593$	−29.4865			−1.21087			−0.605433	+	0.795896i	$0.707000\pi$
$594$	6.52678	−	59.8195i	0.267797	−	2.45442i
$595$		0			0
$596$	−18.9571	+	13.7731i	−0.776513	+	0.564170i
$597$	−4.50149	−	13.8541i	−0.184234	−	0.567013i
$598$	0.108905	−	0.335174i	0.00445344	−	0.0137063i
$599$	22.4696	+	16.3251i	0.918084	+	0.667027i	0.943046	−	0.332662i	$-0.107947\pi$
$599$	22.4696	+	16.3251i	0.918084	+	0.667027i	−0.0249627	+	0.999688i	$0.507947\pi$
$600$		0			0
$601$	9.07483	−	27.9295i	0.370170	−	1.13927i	−0.576510	−	0.817090i	$-0.695586\pi$
$601$	9.07483	−	27.9295i	0.370170	−	1.13927i	0.946680	−	0.322176i	$-0.104414\pi$
$602$	0.131604	+	0.405036i	0.00536378	+	0.0165080i
$603$	61.2426	−	44.4954i	2.49399	−	1.81199i
$604$	12.0648			0.490908
$605$		0			0
$606$	−45.7555			−1.85869
$607$	8.71695	−	6.33323i	0.353810	−	0.257058i	−0.396656	−	0.917967i	$-0.629829\pi$
$607$	8.71695	−	6.33323i	0.353810	−	0.257058i	0.750466	+	0.660909i	$0.229829\pi$
$608$	1.66209	+	5.11538i	0.0674065	+	0.207456i
$609$	1.98251	−	6.10154i	0.0803354	−	0.247247i
$610$		0			0
$611$	−15.6799	−	11.3921i	−0.634341	−	0.460876i
$612$	7.63177	−	23.4882i	0.308496	−	0.949454i
$613$	−13.9982	−	43.0821i	−0.565383	−	1.74007i	−0.666812	−	0.745226i	$-0.732341\pi$
$613$	−13.9982	−	43.0821i	−0.565383	−	1.74007i	0.101429	−	0.994843i	$-0.467659\pi$
$614$	15.6733	−	11.3873i	0.632522	−	0.459554i
$615$		0			0
$616$	0.0672776	−	0.616615i	0.00271069	−	0.0248441i
$617$	−7.32134			−0.294746			−0.147373	−	0.989081i	$-0.547082\pi$
$617$	−7.32134			−0.294746			−0.147373	+	0.989081i	$0.547082\pi$
$618$	−19.4318	+	14.1180i	−0.781660	+	0.567909i
$619$	8.99572	+	27.6860i	0.361569	+	1.11279i	0.952102	+	0.305781i	$0.0989174\pi$
$619$	8.99572	+	27.6860i	0.361569	+	1.11279i	−0.590533	+	0.807013i	$0.701083\pi$
$620$		0			0
$621$	1.69658	+	1.23264i	0.0680813	+	0.0494640i
$622$	14.1197	+	10.2585i	0.566147	+	0.411330i
$623$	0.387011	−	1.19110i	0.0155053	−	0.0477203i
$624$	−3.17828	−	9.78173i	−0.127233	−	0.391582i
$625$		0			0
$626$	21.5623			0.861803
$627$	29.8807	+	52.2313i	1.19332	+	2.08592i
$628$	3.02075			0.120541
$629$	16.0880	−	11.6886i	0.641472	−	0.466056i
$630$		0			0
$631$	−13.7577	+	42.3419i	−0.547686	+	1.68560i	0.166831	+	0.985985i	$0.446647\pi$
$631$	−13.7577	+	42.3419i	−0.547686	+	1.68560i	−0.714517	+	0.699618i	$0.753353\pi$
$632$	7.45799	+	5.41855i	0.296663	+	0.215538i
$633$	19.9049	+	14.4618i	0.791149	+	0.574803i
$634$	−6.33544	+	19.4985i	−0.251612	+	0.774384i
$635$		0			0
$636$	21.9792	−	15.9688i	0.871531	−	0.633204i
$637$	−21.2367			−0.841428
$638$	−33.0190	+	6.88191i	−1.30723	+	0.272457i
$639$	−5.52282			−0.218479
$640$		0			0
$641$	−9.70763	−	29.8770i	−0.383428	−	1.18007i	−0.937614	−	0.347678i	$-0.886970\pi$
$641$	−9.70763	−	29.8770i	−0.383428	−	1.18007i	0.554186	−	0.832393i	$-0.313030\pi$
$642$	−2.98929	+	9.20008i	−0.117978	+	0.363098i
$643$	27.5916	+	20.0465i	1.08811	+	0.790556i	0.979079	−	0.203483i	$-0.0652261\pi$
$643$	27.5916	+	20.0465i	1.08811	+	0.790556i	0.109028	+	0.994039i	$0.465226\pi$
$644$	0.0174882	+	0.0127059i	0.000689132	+	0.000500683i
$645$		0			0
$646$	4.89919	+	15.0781i	0.192756	+	0.593242i
$647$	−14.9018	+	10.8268i	−0.585851	+	0.425646i	−0.840829	−	0.541301i	$-0.817932\pi$
$647$	−14.9018	+	10.8268i	−0.585851	+	0.425646i	0.254978	+	0.966947i	$0.417932\pi$
$648$	36.0655			1.41679
$649$	−4.69254	−	2.11155i	−0.184198	−	0.0828856i
$650$		0			0
$651$	−3.92856	+	2.85427i	−0.153973	+	0.111868i
$652$	0.666986	+	2.05277i	0.0261212	+	0.0803927i
$653$	−5.34034	+	16.4359i	−0.208984	+	0.643185i	0.790543	+	0.612407i	$0.209799\pi$
$653$	−5.34034	+	16.4359i	−0.208984	+	0.643185i	−0.999526	+	0.0307784i	$0.990201\pi$
$654$	30.1051	+	21.8726i	1.17720	+	0.855287i
$655$		0			0
$656$	−1.44887	+	4.45917i	−0.0565690	+	0.174101i
$657$	6.03813	+	18.5834i	0.235570	+	0.725009i
$658$	0.961760	−	0.698760i	0.0374933	−	0.0272405i
$659$	9.78298			0.381091			0.190545	−	0.981678i	$-0.438974\pi$
$659$	9.78298			0.381091			0.190545	+	0.981678i	$0.438974\pi$
$660$		0			0
$661$	4.62985			0.180080			0.0900401	−	0.995938i	$-0.471300\pi$
$661$	4.62985			0.180080			0.0900401	+	0.995938i	$0.471300\pi$
$662$	−7.17283	+	5.21137i	−0.278780	+	0.202546i
$663$	−9.36832	−	28.8327i	−0.363836	−	1.11977i
$664$	0.982141	−	3.02272i	0.0381145	−	0.117304i
$665$		0			0
$666$	45.7304	+	33.2251i	1.77202	+	1.28745i
$667$	0.363231	−	1.11791i	0.0140644	−	0.0432857i
$668$	−1.73852	−	5.35061i	−0.0672653	−	0.207021i
$669$	45.0041	−	32.6974i	1.73996	−	1.26416i
$670$		0			0
$671$	1.96044	−	2.16003i	0.0756818	−	0.0833870i
$672$	0.630859			0.0243359
$673$	−29.4683	+	21.4100i	−1.13592	+	0.825293i	−0.986545	−	0.163487i	$-0.947726\pi$
$673$	−29.4683	+	21.4100i	−1.13592	+	0.825293i	−0.149374	+	0.988781i	$0.547726\pi$
$674$	1.17328	+	3.61099i	0.0451931	+	0.139090i
$675$		0			0
$676$	2.99604	+	2.17675i	0.115232	+	0.0837211i
$677$	35.3935	+	25.7149i	1.36028	+	0.988304i	0.998427	+	0.0560698i	$0.0178570\pi$
$677$	35.3935	+	25.7149i	1.36028	+	0.988304i	0.361856	+	0.932234i	$0.382143\pi$
$678$	8.20383	−	25.2488i	0.315066	−	0.969674i
$679$	−0.511699	−	1.57485i	−0.0196372	−	0.0604371i
$680$		0			0
$681$	39.2967			1.50585
$682$	23.2810	+	10.4760i	0.891474	+	0.401145i
$683$	19.5734			0.748953			0.374477	−	0.927236i	$-0.377822\pi$
$683$	19.5734			0.748953			0.374477	+	0.927236i	$0.377822\pi$
$684$	−36.4588	+	26.4888i	−1.39404	+	1.01283i
$685$		0			0
$686$	0.807071	−	2.48391i	0.0308141	−	0.0948361i
$687$	54.0513	+	39.2705i	2.06218	+	1.49826i
$688$	1.84229	+	1.33850i	0.0702365	+	0.0510298i
$689$	7.58849	−	23.3550i	0.289098	−	0.889754i
$690$		0			0
$691$	−19.7570	+	14.3543i	−0.751592	+	0.546063i	−0.896320	−	0.443408i	$-0.853769\pi$
$691$	−19.7570	+	14.3543i	−0.751592	+	0.546063i	0.144728	+	0.989471i	$0.453769\pi$
$692$	−15.5576			−0.591413
$693$	5.08772	−	1.06040i	0.193266	−	0.0402811i
$694$	−20.5073			−0.778445
$695$		0			0
$696$	−10.6005	−	32.6251i	−0.401813	−	1.23665i
$697$	−4.27072	+	13.1439i	−0.161765	+	0.497861i
$698$	−11.4546	−	8.32229i	−0.433565	−	0.315003i
$699$	14.7007	+	10.6807i	0.556032	+	0.403981i
$700$		0			0
$701$	−3.80171	−	11.7005i	−0.143589	−	0.441921i	0.853238	−	0.521522i	$-0.174635\pi$
$701$	−3.80171	−	11.7005i	−0.143589	−	0.441921i	−0.996827	+	0.0796009i	$0.974635\pi$
$702$	44.7547	−	32.5162i	1.68916	−	1.22724i
$703$	−36.2866			−1.36857
$704$	−1.64693	−	2.87882i	−0.0620710	−	0.108500i
$705$		0			0
$706$	−17.9089	+	13.0116i	−0.674009	+	0.489696i
$707$	−0.783913	−	2.41264i	−0.0294821	−	0.0907366i
$708$	1.61725	−	4.97740i	0.0607801	−	0.187062i
$709$	−2.09099	−	1.51919i	−0.0785287	−	0.0570544i	0.547828	−	0.836591i	$-0.315455\pi$
$709$	−2.09099	−	1.51919i	−0.0785287	−	0.0570544i	−0.626357	+	0.779536i	$0.715455\pi$
$710$		0			0
$711$	−23.8682	+	73.4587i	−0.895126	+	2.75492i
$712$	−2.06936	−	6.36882i	−0.0775524	−	0.238682i
$713$	−0.719783	+	0.522953i	−0.0269561	+	0.0195847i
$714$	1.85953			0.0695911
$715$		0			0
$716$	−17.3740			−0.649295
$717$	24.4521	−	17.7655i	0.913181	−	0.663465i
$718$	−2.55974	−	7.87806i	−0.0955285	−	0.294007i
$719$	−12.3660	+	38.0587i	−0.461175	+	1.41935i	0.402554	+	0.915396i	$0.368122\pi$
$719$	−12.3660	+	38.0587i	−0.461175	+	1.41935i	−0.863730	+	0.503956i	$0.831878\pi$
$720$		0			0
$721$	−1.07734	−	0.782737i	−0.0401224	−	0.0291506i
$722$	3.06842	−	9.44363i	0.114195	−	0.351455i
$723$	−11.1411	−	34.2889i	−0.414343	−	1.27522i
$724$	−11.1957	+	8.13414i	−0.416084	+	0.302303i
$725$		0			0
$726$	−24.6093	−	27.7704i	−0.913337	−	1.03066i
$727$	47.6224			1.76622			0.883108	−	0.469169i	$-0.155446\pi$
$727$	47.6224			1.76622			0.883108	+	0.469169i	$0.155446\pi$
$728$	0.461328	−	0.335174i	0.0170979	−	0.0124224i
$729$	36.6417	+	112.772i	1.35710	+	4.17673i
$730$		0			0
$731$	5.43034	+	3.94537i	0.200848	+	0.145925i
$732$	2.40020	+	1.74384i	0.0887138	+	0.0644543i
$733$	−13.3702	+	41.1492i	−0.493839	+	1.51988i	0.324918	+	0.945742i	$0.394663\pi$
$733$	−13.3702	+	41.1492i	−0.493839	+	1.51988i	−0.818758	+	0.574139i	$0.805337\pi$
$734$	7.32336	+	22.5390i	0.270310	+	0.831929i
$735$		0			0
$736$	0.115585			0.00426050
$737$	3.25017	−	29.7886i	0.119722	−	1.09728i
$738$	−39.2845			−1.44608
$739$	36.8236	−	26.7539i	1.35458	−	0.984160i	0.355810	−	0.934558i	$-0.384205\pi$
$739$	36.8236	−	26.7539i	1.35458	−	0.984160i	0.998769	−	0.0496014i	$-0.0157951\pi$
$740$		0			0
$741$	−17.0948	+	52.6123i	−0.627992	+	1.93276i
$742$	1.21858	+	0.885350i	0.0447355	+	0.0325022i
$743$	34.0331	+	24.7265i	1.24855	+	0.907128i	0.998137	−	0.0610105i	$-0.0194323\pi$
$743$	34.0331	+	24.7265i	1.24855	+	0.907128i	0.250417	+	0.968138i	$0.419432\pi$
$744$	−8.02363	+	24.6942i	−0.294161	+	0.905333i
$745$		0			0
$746$	−22.4023	+	16.2762i	−0.820205	+	0.595914i
$747$	26.6296			0.974326
$748$	−4.85451	−	8.48565i	−0.177498	−	0.310266i
$749$	−0.536325			−0.0195969
$750$		0			0
$751$	−1.26991	−	3.90839i	−0.0463398	−	0.142619i	0.925209	−	0.379457i	$-0.123889\pi$
$751$	−1.26991	−	3.90839i	−0.0463398	−	0.142619i	−0.971549	+	0.236837i	$0.923889\pi$
$752$	1.96428	−	6.04544i	0.0716300	−	0.220454i
$753$	20.3142	+	14.7591i	0.740290	+	0.537852i
$754$	−25.0855	−	18.2257i	−0.913560	−	0.663740i
$755$		0			0
$756$	1.04854	+	3.22708i	0.0381351	+	0.117368i
$757$	−3.97384	+	2.88717i	−0.144432	+	0.104936i	−0.657655	−	0.753319i	$-0.728451\pi$
$757$	−3.97384	+	2.88717i	−0.144432	+	0.104936i	0.513223	+	0.858255i	$0.328451\pi$
$758$	15.8425			0.575425
$759$	1.26592	−	0.263847i	0.0459501	−	0.00957705i
$760$		0			0
$761$	−23.3518	+	16.9661i	−0.846503	+	0.615021i	−0.924180	−	0.381958i	$-0.875250\pi$
$761$	−23.3518	+	16.9661i	−0.846503	+	0.615021i	0.0776764	+	0.996979i	$0.475250\pi$
$762$	9.45080	+	29.0866i	0.342366	+	1.05370i
$763$	−0.637539	+	1.96214i	−0.0230805	+	0.0710344i
$764$	3.21318	+	2.33451i	0.116249	+	0.0844596i
$765$		0			0
$766$	0.417371	−	1.28454i	0.0150802	−	0.0464122i
$767$	−1.46183	−	4.49906i	−0.0527837	−	0.162452i
$768$	2.72899	−	1.98273i	0.0984741	−	0.0715456i
$769$	−35.9976			−1.29811			−0.649053	−	0.760743i	$-0.724835\pi$
$769$	−35.9976			−1.29811			−0.649053	+	0.760743i	$0.724835\pi$
$770$		0			0
$771$	32.2723			1.16226
$772$	−6.42705	+	4.66953i	−0.231315	+	0.168060i
$773$	2.75519	+	8.47960i	0.0990972	+	0.304990i	0.988300	−	0.152524i	$-0.0487401\pi$
$773$	2.75519	+	8.47960i	0.0990972	+	0.304990i	−0.889203	+	0.457514i	$0.848740\pi$
$774$	−5.89596	+	18.1459i	−0.211926	+	0.652241i
$775$		0			0
$776$	−7.16312	−	5.20431i	−0.257141	−	0.186824i
$777$	−1.31519	+	4.04775i	−0.0471823	+	0.145212i
$778$	−1.45465	−	4.47695i	−0.0521516	−	0.160506i
$779$	20.4022	−	14.8231i	0.730985	−	0.531091i
$780$		0			0
$781$	−1.46925	+	1.61884i	−0.0525740	+	0.0579266i
$782$	0.340698			0.0121834
$783$	149.271	−	108.452i	5.33450	−	3.87574i
$784$	−2.15231	−	6.62413i	−0.0768682	−	0.236576i
$785$		0			0
$786$	−16.1708	−	11.7487i	−0.576792	−	0.419064i
$787$	−13.8429	−	10.0575i	−0.493446	−	0.358510i	0.313062	−	0.949733i	$-0.398645\pi$
$787$	−13.8429	−	10.0575i	−0.493446	−	0.358510i	−0.806508	+	0.591223i	$0.798645\pi$
$788$	1.71488	−	5.27787i	0.0610902	−	0.188016i
$789$	−21.7842	−	67.0450i	−0.775539	−	2.38686i
$790$		0			0
$791$	1.47190			0.0523346
$792$	18.6759	−	20.5773i	0.663619	−	0.731183i
$793$	2.68169			0.0952296
$794$	−18.7850	+	13.6481i	−0.666656	+	0.484354i
$795$		0			0
$796$	1.33448	−	4.10710i	0.0472993	−	0.145572i
$797$	−26.6612	−	19.3705i	−0.944389	−	0.686139i	0.00508424	−	0.999987i	$-0.498382\pi$
$797$	−26.6612	−	19.3705i	−0.944389	−	0.686139i	−0.949473	+	0.313848i	$0.898382\pi$
$798$	−2.74512	−	1.99445i	−0.0971762	−	0.0706027i
$799$	5.78994	−	17.8196i	0.204833	−	0.630412i
$800$		0			0
$801$	45.3924	−	32.9795i	1.60386	−	1.16527i
$802$	−5.86409			−0.207068
$803$	7.05349	+	3.17393i	0.248912	+	0.112006i
$804$	30.4767			1.07483
$805$		0			0
$806$	7.25255	+	22.3210i	0.255460	+	0.786225i
$807$	−21.4870	+	66.1303i	−0.756379	+	2.32790i
$808$	−10.9738	−	7.97291i	−0.386056	−	0.280486i
$809$	33.1781	+	24.1053i	1.16648	+	0.847498i	0.990583	−	0.136911i	$-0.0437173\pi$
$809$	33.1781	+	24.1053i	1.16648	+	0.847498i	0.175897	+	0.984409i	$0.443717\pi$
$810$		0			0
$811$	−3.29631	−	10.1450i	−0.115749	−	0.356239i	0.876353	−	0.481669i	$-0.159969\pi$
$811$	−3.29631	−	10.1450i	−0.115749	−	0.356239i	−0.992103	+	0.125430i	$0.959969\pi$
$812$	1.53867	−	1.11791i	0.0539968	−	0.0392310i
$813$	−27.6756			−0.970627
$814$	21.9047	−	4.56544i	0.767760	−	0.160019i
$815$		0			0
$816$	8.04401	−	5.84432i	0.281597	−	0.204592i
$817$	−3.78489	−	11.6487i	−0.132416	−	0.407536i
$818$	−8.09168	+	24.9036i	−0.282919	+	0.870735i
$819$	3.86529	+	2.80830i	0.135064	+	0.0981299i
$820$		0			0
$821$	2.06521	−	6.35607i	0.0720764	−	0.221828i	−0.908529	−	0.417823i	$-0.862793\pi$
$821$	2.06521	−	6.35607i	0.0720764	−	0.221828i	0.980605	+	0.195994i	$0.0627934\pi$
$822$	10.5516	+	32.4744i	0.368028	+	1.13267i
$823$	−30.6620	+	22.2772i	−1.06881	+	0.776535i	−0.975698	−	0.219121i	$-0.929681\pi$
$823$	−30.6620	+	22.2772i	−1.06881	+	0.776535i	−0.0931110	+	0.995656i	$0.529681\pi$
$824$	−7.12048			−0.248054
$825$		0			0
$826$	0.290161			0.0100960
$827$	−26.6015	+	19.3271i	−0.925026	+	0.672071i	−0.944770	−	0.327734i	$-0.893715\pi$
$827$	−26.6015	+	19.3271i	−0.925026	+	0.672071i	0.0197438	+	0.999805i	$0.493715\pi$
$828$	0.299264	+	0.921041i	0.0104002	+	0.0320084i
$829$	4.15827	−	12.7978i	0.144423	−	0.444487i	−0.852514	−	0.522705i	$-0.824923\pi$
$829$	4.15827	−	12.7978i	0.144423	−	0.444487i	0.996936	+	0.0782180i	$0.0249230\pi$
$830$		0			0
$831$	34.8550	+	25.3236i	1.20911	+	0.878466i
$832$	0.942208	−	2.89982i	0.0326652	−	0.100533i
$833$	−6.34418	−	19.5254i	−0.219813	−	0.676514i
$834$	−46.7646	+	33.9764i	−1.61932	+	1.17651i
$835$		0			0
$836$	−1.93488	+	17.7336i	−0.0669193	+	0.613331i
$837$	−139.656			−4.82722
$838$	5.41123	−	3.93149i	0.186928	−	0.135811i
$839$	−13.3324	−	41.0329i	−0.460285	−	1.41661i	−0.864817	−	0.502088i	$-0.832565\pi$
$839$	−13.3324	−	41.0329i	−0.460285	−	1.41661i	0.404532	−	0.914524i	$-0.367435\pi$
$840$		0			0
$841$	−60.2065	−	43.7426i	−2.07609	−	1.50837i
$842$	−20.4459	−	14.8548i	−0.704612	−	0.511931i
$843$	23.2411	−	71.5289i	0.800467	−	2.46358i
$844$	2.25393	+	6.93687i	0.0775834	+	0.238777i
$845$		0			0
$846$	53.2592			1.83109
$847$	1.04268	−	1.77340i	0.0358269	−	0.0609349i
$848$	8.05395			0.276574
$849$	−30.6583	+	22.2746i	−1.05219	+	0.764461i
$850$		0			0
$851$	−0.240967	+	0.741620i	−0.00826024	+	0.0254224i
$852$	−1.79883	−	1.30693i	−0.0616270	−	0.0447746i
$853$	−38.6637	−	28.0908i	−1.32382	−	0.961811i	−0.999876	−	0.0157338i	$-0.994992\pi$
$853$	−38.6637	−	28.0908i	−1.32382	−	0.961811i	−0.323942	−	0.946077i	$-0.605008\pi$
$854$	−0.0508293	+	0.156436i	−0.00173934	+	0.00535314i
$855$		0			0
$856$	−2.32005	+	1.68562i	−0.0792978	+	0.0576132i
$857$	−3.49798			−0.119489			−0.0597444	−	0.998214i	$-0.519029\pi$
$857$	−3.49798			−0.119489			−0.0597444	+	0.998214i	$0.519029\pi$
$858$	3.69992	−	33.9106i	0.126313	−	1.15769i
$859$	26.4442			0.902263			0.451131	−	0.892458i	$-0.351021\pi$
$859$	26.4442			0.902263			0.451131	+	0.892458i	$0.351021\pi$
$860$		0			0
$861$	−0.914035	−	2.81311i	−0.0311502	−	0.0958705i
$862$	−9.90521	+	30.4851i	−0.337373	+	1.03833i
$863$	−40.5772	−	29.4811i	−1.38126	−	1.00355i	−0.996761	−	0.0804231i	$-0.974373\pi$
$863$	−40.5772	−	29.4811i	−1.38126	−	1.00355i	−0.384503	−	0.923124i	$-0.625627\pi$
$864$	14.6782	+	10.6644i	0.499364	+	0.362809i
$865$		0			0
$866$	−3.21743	−	9.90223i	−0.109333	−	0.336491i
$867$	−22.6823	+	16.4796i	−0.770330	+	0.559678i
$868$	−1.43957			−0.0488620
$869$	15.1824	+	26.5387i	0.515026	+	0.900262i
$870$		0			0
$871$	22.2867	−	16.1922i	0.755155	−	0.548652i
$872$	3.40894	+	10.4916i	0.115441	+	0.355292i
$873$	22.9245	−	70.5543i	0.775876	−	2.38790i
$874$	−0.502955	−	0.365418i	−0.0170127	−	0.0123604i
$875$		0			0
$876$	−2.43094	+	7.48167i	−0.0821339	+	0.252782i
$877$	6.97221	+	21.4583i	0.235435	+	0.724594i	0.997063	+	0.0765800i	$0.0244001\pi$
$877$	6.97221	+	21.4583i	0.235435	+	0.724594i	−0.761629	+	0.648014i	$0.775600\pi$
$878$	−25.4238	+	18.4715i	−0.858013	+	0.623383i
$879$	−86.3660			−2.91305
$880$		0			0
$881$	7.71364			0.259879			0.129940	−	0.991522i	$-0.458522\pi$
$881$	7.71364			0.259879			0.129940	+	0.991522i	$0.458522\pi$
$882$	47.2121	−	34.3016i	1.58971	−	1.15499i
$883$	10.2098	+	31.4225i	0.343586	+	1.05745i	0.962336	+	0.271862i	$0.0876394\pi$
$883$	10.2098	+	31.4225i	0.343586	+	1.05745i	−0.618750	+	0.785588i	$0.712361\pi$
$884$	2.77726	−	8.54754i	0.0934095	−	0.287485i
$885$		0			0
$886$	−33.2653	−	24.1686i	−1.11757	−	0.811961i
$887$	5.71644	−	17.5934i	0.191939	−	0.590729i	−0.808059	−	0.589101i	$-0.799482\pi$
$887$	5.71644	−	17.5934i	0.191939	−	0.590729i	0.999999	−	0.00162748i	$-0.000518043\pi$
$888$	7.03238	+	21.6434i	0.235991	+	0.726306i
$889$	−1.37179	+	0.996661i	−0.0460083	+	0.0334270i
$890$		0			0
$891$	109.081	+	49.0843i	3.65435	+	1.64438i
$892$	16.4911			0.552163
$893$	−27.6599	+	20.0961i	−0.925603	+	0.672490i
$894$	−24.4254	−	75.1736i	−0.816907	−	2.51418i
$895$		0			0
$896$	0.151302	+	0.109927i	0.00505465	+	0.00367242i
$897$	0.961760	+	0.698760i	0.0321122	+	0.0233309i
$898$	−3.54840	+	10.9209i	−0.118412	+	0.364434i
$899$	24.1895	+	74.4477i	0.806765	+	2.48297i
$900$		0			0
$901$	23.7399			0.790891
$902$	−10.4510	+	11.5150i	−0.347979	+	0.383407i
$903$	−1.43659			−0.0478066
$904$	6.36718	−	4.62603i	0.211769	−	0.153859i
$905$		0			0
$906$	−12.5761	+	38.7052i	−0.417813	+	1.28590i
$907$	41.3623	+	30.0515i	1.37341	+	0.997843i	0.997462	+	0.0712035i	$0.0226840\pi$
$907$	41.3623	+	30.0515i	1.37341	+	0.997843i	0.375951	+	0.926639i	$0.377316\pi$
$908$	9.42472	+	6.84746i	0.312770	+	0.227241i
$909$	35.1199	−	108.088i	1.16485	−	3.58505i
$910$		0			0
$911$	18.8345	−	13.6840i	0.624014	−	0.453373i	−0.230307	−	0.973118i	$-0.573973\pi$
$911$	18.8345	−	13.6840i	0.624014	−	0.453373i	0.854321	+	0.519745i	$0.173973\pi$
$912$	−18.1433			−0.600785
$913$	7.08436	−	7.80562i	0.234458	−	0.258328i
$914$	−18.4870			−0.611496
$915$		0			0
$916$	6.12048	+	18.8369i	0.202226	+	0.622389i
$917$	0.342450	−	1.05395i	0.0113087	−	0.0348046i
$918$	43.2657	+	31.4344i	1.42798	+	1.03749i
$919$	−13.1742	−	9.57161i	−0.434577	−	0.315738i	0.348900	−	0.937160i	$-0.386555\pi$
$919$	−13.1742	−	9.57161i	−0.434577	−	0.315738i	−0.783476	+	0.621422i	$0.786555\pi$
$920$		0			0
$921$	20.1943	+	62.1517i	0.665425	+	2.04797i
$922$	5.43642	−	3.94979i	0.179039	−	0.130079i
$923$	−2.00980			−0.0661533
$924$	1.90805	+	0.858584i	0.0627702	+	0.0282453i
$925$		0			0
$926$	−20.4533	+	14.8602i	−0.672138	+	0.488337i
$927$	−18.4359	−	56.7399i	−0.605515	−	1.86358i
$928$	3.14256	−	9.67180i	0.103160	−	0.317492i
$929$	10.7933	+	7.84178i	0.354116	+	0.257280i	0.750594	−	0.660764i	$-0.229768\pi$
$929$	10.7933	+	7.84178i	0.354116	+	0.257280i	−0.396478	+	0.918044i	$0.629768\pi$
$930$		0			0
$931$	−11.5765	+	35.6287i	−0.379404	+	1.16768i
$932$	1.66463	+	5.12321i	0.0545269	+	0.167816i
$933$	−47.6288	+	34.6043i	−1.55930	+	1.13289i
$934$	19.9434			0.652568
$935$		0			0
$936$	25.5468			0.835024
$937$	−12.8780	+	9.35641i	−0.420706	+	0.305660i	−0.777922	−	0.628361i	$-0.783726\pi$
$937$	−12.8780	+	9.35641i	−0.420706	+	0.305660i	0.357216	+	0.934022i	$0.383726\pi$
$938$	0.522148	+	1.60700i	0.0170487	+	0.0524706i
$939$	−22.4762	+	69.1746i	−0.733482	+	2.25743i
$940$		0			0
$941$	17.6786	+	12.8442i	0.576305	+	0.418710i	0.837390	−	0.546605i	$-0.184080\pi$
$941$	17.6786	+	12.8442i	0.576305	+	0.418710i	−0.261085	+	0.965316i	$0.584080\pi$
$942$	−3.14878	+	9.69095i	−0.102593	+	0.315748i
$943$	−0.167467	−	0.515412i	−0.00545349	−	0.0167841i
$944$	1.25519	−	0.911947i	0.0408529	−	0.0296814i
$945$		0			0
$946$	3.75037	+	6.55563i	0.121935	+	0.213142i
$947$	−24.6072			−0.799627			−0.399814	−	0.916596i	$-0.630925\pi$
$947$	−24.6072			−0.799627			−0.399814	+	0.916596i	$0.630925\pi$
$948$	−25.1574	+	18.2780i	−0.817076	+	0.593640i
$949$	2.19732	+	6.76266i	0.0713281	+	0.219525i
$950$		0			0
$951$	−55.9496	−	40.6498i	−1.81429	−	1.31816i
$952$	0.445980	+	0.324024i	0.0144543	+	0.0105017i
$953$	3.37076	−	10.3741i	0.109190	−	0.336051i	−0.881501	−	0.472182i	$-0.843467\pi$
$953$	3.37076	−	10.3741i	0.109190	−	0.336051i	0.990691	+	0.136131i	$0.0434667\pi$
$954$	20.8528	+	64.1783i	0.675134	+	2.07785i
$955$		0			0
$956$	8.96012			0.289791
$957$	12.3404	−	113.103i	0.398908	−	3.65609i
$958$	8.21267			0.265339
$959$	−1.53156	+	1.11275i	−0.0494568	+	0.0359324i
$960$		0			0
$961$	8.72970	−	26.8673i	0.281603	−	0.866686i
$962$	16.6417	+	12.0909i	0.536549	+	0.389826i
$963$	−19.4389	−	14.1232i	−0.626409	−	0.455113i
$964$	3.30282	−	10.1650i	0.106377	−	0.327394i
$965$		0			0
$966$	−0.0589916	+	0.0428599i	−0.00189802	+	0.00137899i
$967$	−21.5493			−0.692980			−0.346490	−	0.938054i	$-0.612626\pi$
$967$	−21.5493			−0.692980			−0.346490	+	0.938054i	$0.612626\pi$
$968$	−1.06317	−	10.9485i	−0.0341717	−	0.351898i
$969$	−53.4794			−1.71801
$970$		0			0
$971$	14.3347	+	44.1177i	0.460023	+	1.41580i	0.865136	+	0.501538i	$0.167232\pi$
$971$	14.3347	+	44.1177i	0.460023	+	1.41580i	−0.405113	+	0.914267i	$0.632768\pi$
$972$	−20.7743	+	63.9367i	−0.666336	+	2.05077i
$973$	−2.59274	−	1.88374i	−0.0831195	−	0.0603899i
$974$	22.6417	+	16.4501i	0.725486	+	0.527096i
$975$		0			0
$976$	0.271786	+	0.836470i	0.00869964	+	0.0267748i
$977$	25.9943	−	18.8859i	0.831630	−	0.604215i	−0.0883901	−	0.996086i	$-0.528172\pi$
$977$	25.9943	−	18.8859i	0.831630	−	0.604215i	0.920020	+	0.391871i	$0.128172\pi$
$978$	−7.28080			−0.232814
$979$	2.40899	−	22.0790i	0.0769918	−	0.705648i
$980$		0			0
$981$	−74.7769	+	54.3286i	−2.38744	+	1.73458i
$982$	−4.41679	−	13.5935i	−0.140946	−	0.433786i
$983$	−8.83474	+	27.1905i	−0.281785	+	0.867244i	0.705560	+	0.708651i	$0.250696\pi$
$983$	−8.83474	+	27.1905i	−0.281785	+	0.867244i	−0.987344	+	0.158593i	$0.949304\pi$
$984$	−12.7953	−	9.29633i	−0.407899	−	0.296356i
$985$		0			0
$986$	9.26304	−	28.5087i	0.294995	−	0.907902i
$987$	1.23919	+	3.81382i	0.0394437	+	0.121395i
$988$	−13.2676	+	9.63950i	−0.422099	+	0.306673i
$989$	−0.263208			−0.00836953
$990$		0			0
$991$	9.55188			0.303425			0.151713	−	0.988425i	$-0.451521\pi$
$991$	9.55188			0.303425			0.151713	+	0.988425i	$0.451521\pi$
$992$	−6.22732	+	4.52442i	−0.197718	+	0.143650i
$993$	−9.24188	−	28.4436i	−0.293282	−	0.902630i
$994$	0.0380941	−	0.117242i	0.00120827	−	0.00371868i
$995$		0			0
$996$	8.67349	+	6.30166i	0.274830	+	0.199676i
$997$	−10.7321	+	33.0302i	−0.339891	+	1.04608i	0.624372	+	0.781127i	$0.285355\pi$
$997$	−10.7321	+	33.0302i	−0.339891	+	1.04608i	−0.964263	+	0.264949i	$0.914645\pi$
$998$	1.51667	+	4.66783i	0.0480094	+	0.147758i
$999$	−99.0259	+	71.9465i	−3.13304	+	2.27629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.h.k.201.1	✓	8
5.2	odd	4		550.2.ba.g.399.1		16
5.3	odd	4		550.2.ba.g.399.4		16
5.4	even	2		550.2.h.m.201.2	yes	8
11.2	odd	10		6050.2.a.cz.1.1		4
11.4	even	5	inner	550.2.h.k.301.1	yes	8
11.9	even	5		6050.2.a.dg.1.1		4
55.4	even	10		550.2.h.m.301.2	yes	8
55.9	even	10		6050.2.a.df.1.4		4
55.24	odd	10		6050.2.a.dn.1.4		4
55.37	odd	20		550.2.ba.g.499.4		16
55.48	odd	20		550.2.ba.g.499.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.k.201.1	✓	8	1.1	even	1	trivial
550.2.h.k.301.1	yes	8	11.4	even	5	inner
550.2.h.m.201.2	yes	8	5.4	even	2
550.2.h.m.301.2	yes	8	55.4	even	10
550.2.ba.g.399.1		16	5.2	odd	4
550.2.ba.g.399.4		16	5.3	odd	4
550.2.ba.g.499.1		16	55.48	odd	20
550.2.ba.g.499.4		16	55.37	odd	20
6050.2.a.cz.1.1		4	11.2	odd	10
6050.2.a.df.1.4		4	55.9	even	10
6050.2.a.dg.1.1		4	11.9	even	5
6050.2.a.dn.1.4		4	55.24	odd	10

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-1.04238 - 3.20812i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.72899 + 1.98273i) q^{6} +(-0.0577923 + 0.177866i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-6.77845 + 4.92483i) q^{9} +(-0.359735 + 3.29706i) q^{11} -3.37322 q^{12} +(-2.46673 + 1.79219i) q^{13} +(-0.0577923 - 0.177866i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-2.38467 - 1.73256i) q^{17} +(2.58914 - 7.96855i) q^{18} +(1.66209 + 5.11538i) q^{19} +0.630859 q^{21} +(-1.64693 - 2.87882i) q^{22} +0.115585 q^{23} +(2.72899 - 1.98273i) q^{24} +(0.942208 - 2.89982i) q^{26} +(14.6782 + 10.6644i) q^{27} +(0.151302 + 0.109927i) q^{28} +(3.14256 - 9.67180i) q^{29} +(-6.22732 + 4.52442i) q^{31} +1.00000 q^{32} +(10.9524 - 2.28272i) q^{33} +2.94761 q^{34} +(2.58914 + 7.96855i) q^{36} +(-2.08477 + 6.41625i) q^{37} +(-4.35140 - 3.16148i) q^{38} +(8.32083 + 6.04544i) q^{39} +(-1.44887 - 4.45917i) q^{41} +(-0.510376 + 0.370810i) q^{42} -2.27719 q^{43} +(3.02452 + 1.36098i) q^{44} +(-0.0935099 + 0.0679389i) q^{46} +(1.96428 + 6.04544i) q^{47} +(-1.04238 + 3.20812i) q^{48} +(5.63482 + 4.09394i) q^{49} +(-3.07254 + 9.45631i) q^{51} +(0.942208 + 2.89982i) q^{52} +(-6.51578 + 4.73399i) q^{53} -18.1433 q^{54} -0.187020 q^{56} +(14.6782 - 10.6644i) q^{57} +(3.14256 + 9.67180i) q^{58} +(-0.479439 + 1.47556i) q^{59} +(-0.711544 - 0.516967i) q^{61} +(2.37863 - 7.32066i) q^{62} +(-0.484220 - 1.49028i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.51889 + 8.28439i) q^{66} -9.03490 q^{67} +(-2.38467 + 1.73256i) q^{68} +(-0.120483 - 0.370810i) q^{69} +(0.533268 + 0.387442i) q^{71} +(-6.77845 - 4.92483i) q^{72} +(0.720659 - 2.21796i) q^{73} +(-2.08477 - 6.41625i) q^{74} +5.37863 q^{76} +(-0.565646 - 0.254529i) q^{77} -10.2851 q^{78} +(7.45799 - 5.41855i) q^{79} +(11.1449 - 34.3003i) q^{81} +(3.79320 + 2.75592i) q^{82} +(-2.57128 - 1.86814i) q^{83} +(0.194946 - 0.599983i) q^{84} +(1.84229 - 1.33850i) q^{86} -34.3041 q^{87} +(-3.24685 + 0.676718i) q^{88} -6.69658 q^{89} +(-0.176211 - 0.542323i) q^{91} +(0.0357176 - 0.109927i) q^{92} +(21.0061 + 15.2619i) q^{93} +(-5.14256 - 3.73629i) q^{94} +(-1.04238 - 3.20812i) q^{96} +(-7.16312 + 5.20431i) q^{97} -6.96502 q^{98} +(-13.7990 - 24.1206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} - 2 q^{7} - 2 q^{8} - 24 q^{9} + 5 q^{11} - 6 q^{12} - 4 q^{13} - 2 q^{14} - 2 q^{16} - 18 q^{17} + 11 q^{18} + 17 q^{19} - 40 q^{21} - 5 q^{22} + 4 q^{23} - q^{24}+ \cdots - 72 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 - 2 * q^7 - 2 * q^8 - 24 * q^9 + 5 * q^11 - 6 * q^12 - 4 * q^13 - 2 * q^14 - 2 * q^16 - 18 * q^17 + 11 * q^18 + 17 * q^19 - 40 * q^21 - 5 * q^22 + 4 * q^23 - q^24 + 6 * q^26 + 19 * q^27 + 8 * q^28 + 2 * q^29 - 2 * q^31 + 8 * q^32 + 23 * q^33 + 2 * q^34 + 11 * q^36 + 8 * q^37 - 18 * q^38 + 24 * q^39 + 6 * q^41 + 20 * q^42 + 16 * q^43 + 10 * q^44 - 6 * q^46 + 12 * q^47 + 4 * q^48 - 6 * q^49 - 17 * q^51 + 6 * q^52 - 8 * q^53 - 6 * q^54 - 12 * q^56 + 19 * q^57 + 2 * q^58 - 12 * q^59 - 2 * q^61 - 22 * q^62 - 48 * q^63 - 2 * q^64 - 27 * q^66 - 34 * q^67 - 18 * q^68 + 20 * q^69 + 20 * q^71 - 24 * q^72 - 26 * q^73 + 8 * q^74 + 2 * q^76 + 26 * q^77 - 36 * q^78 + 14 * q^79 + 35 * q^81 - 9 * q^82 - 9 * q^83 + 26 * q^86 - 56 * q^87 - 5 * q^88 + 2 * q^89 - 52 * q^91 + 4 * q^92 + 32 * q^93 - 18 * q^94 + 4 * q^96 - 26 * q^97 + 64 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more