LMFDB - Embedded newform 550.2.ba.g.399.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(49,550)] 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([5, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.ba (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,4,0,-2,0,0,48,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 56x^{12} - 141x^{10} + 551x^{8} - 1245x^{6} + 1400x^{4} + 125x^{2} + 625 $ x^16 - 11x^14 + 56x^12 - 141x^10 + 551x^8 - 1245x^6 + 1400x^4 + 125*x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			399.4
Root			$1.39494 + 0.453245i$ of defining polynomial
Character	$\chi$	$=$	550.399
Dual form			550.2.ba.g.499.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 + 0.809017i) q^{2} +(3.20812 - 1.04238i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.72899 + 1.98273i) q^{6} +(0.177866 + 0.0577923i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(6.77845 - 4.92483i) q^{9} +(-0.359735 + 3.29706i) q^{11} +3.37322i q^{12} +(-1.79219 - 2.46673i) q^{13} +(0.0577923 + 0.177866i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-1.73256 + 2.38467i) q^{17} +(7.96855 + 2.58914i) q^{18} +(-1.66209 - 5.11538i) q^{19} +0.630859 q^{21} +(-2.87882 + 1.64693i) q^{22} +0.115585i q^{23} +(-2.72899 + 1.98273i) q^{24} +(0.942208 - 2.89982i) q^{26} +(10.6644 - 14.6782i) q^{27} +(-0.109927 + 0.151302i) q^{28} +(-3.14256 + 9.67180i) q^{29} +(-6.22732 + 4.52442i) q^{31} -1.00000i q^{32} +(2.28272 + 10.9524i) q^{33} -2.94761 q^{34} +(2.58914 + 7.96855i) q^{36} +(6.41625 + 2.08477i) q^{37} +(3.16148 - 4.35140i) q^{38} +(-8.32083 - 6.04544i) q^{39} +(-1.44887 - 4.45917i) q^{41} +(0.370810 + 0.510376i) q^{42} -2.27719i q^{43} +(-3.02452 - 1.36098i) q^{44} +(-0.0935099 + 0.0679389i) q^{46} +(6.04544 - 1.96428i) q^{47} +(-3.20812 - 1.04238i) q^{48} +(-5.63482 - 4.09394i) q^{49} +(-3.07254 + 9.45631i) q^{51} +(2.89982 - 0.942208i) q^{52} +(-4.73399 - 6.51578i) q^{53} +18.1433 q^{54} -0.187020 q^{56} +(-10.6644 - 14.6782i) q^{57} +(-9.67180 + 3.14256i) q^{58} +(0.479439 - 1.47556i) q^{59} +(-0.711544 - 0.516967i) q^{61} +(-7.32066 - 2.37863i) q^{62} +(1.49028 - 0.484220i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-7.51889 + 8.28439i) q^{66} +9.03490i q^{67} +(-1.73256 - 2.38467i) q^{68} +(0.120483 + 0.370810i) q^{69} +(0.533268 + 0.387442i) q^{71} +(-4.92483 + 6.77845i) q^{72} +(2.21796 + 0.720659i) q^{73} +(2.08477 + 6.41625i) q^{74} +5.37863 q^{76} +(-0.254529 + 0.565646i) q^{77} -10.2851i q^{78} +(-7.45799 + 5.41855i) q^{79} +(11.1449 - 34.3003i) q^{81} +(2.75592 - 3.79320i) q^{82} +(1.86814 - 2.57128i) q^{83} +(-0.194946 + 0.599983i) q^{84} +(1.84229 - 1.33850i) q^{86} +34.3041i q^{87} +(-0.676718 - 3.24685i) q^{88} +6.69658 q^{89} +(-0.176211 - 0.542323i) q^{91} +(-0.109927 - 0.0357176i) q^{92} +(-15.2619 + 21.0061i) q^{93} +(5.14256 + 3.73629i) q^{94} +(-1.04238 - 3.20812i) q^{96} +(5.20431 + 7.16312i) q^{97} -6.96502i q^{98} +(13.7990 + 24.1206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 2 q^{6} + 48 q^{9} + 10 q^{11} + 4 q^{14} - 4 q^{16} - 34 q^{19} - 80 q^{21} + 2 q^{24} + 12 q^{26} - 4 q^{29} - 4 q^{31} - 4 q^{34} + 22 q^{36} - 48 q^{39} + 12 q^{41} - 20 q^{44} - 12 q^{46}+ \cdots + 144 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 2 * q^6 + 48 * q^9 + 10 * q^11 + 4 * q^14 - 4 * q^16 - 34 * q^19 - 80 * q^21 + 2 * q^24 + 12 * q^26 - 4 * q^29 - 4 * q^31 - 4 * q^34 + 22 * q^36 - 48 * q^39 + 12 * q^41 - 20 * q^44 - 12 * q^46 + 12 * q^49 - 34 * q^51 + 12 * q^54 - 24 * q^56 + 24 * q^59 - 4 * q^61 + 4 * q^64 - 54 * q^66 - 40 * q^69 + 40 * q^71 - 16 * q^74 + 4 * q^76 - 28 * q^79 + 70 * q^81 + 52 * q^86 - 4 * q^89 - 104 * q^91 + 36 * q^94 + 8 * q^96 + 144 * 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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	3.20812	−	1.04238i	1.85221	−	0.601820i	0.855788	−	0.517327i	$-0.173073\pi$
$3$	3.20812	−	1.04238i	1.85221	−	0.601820i	0.996424	−	0.0844926i	$-0.0269269\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	2.72899	+	1.98273i	1.11411	+	0.809446i
$7$	0.177866	+	0.0577923i	0.0672272	+	0.0218434i	0.342438	−	0.939541i	$-0.388747\pi$
$7$	0.177866	+	0.0577923i	0.0672272	+	0.0218434i	−0.275210	+	0.961384i	$0.588747\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	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
$12$			3.37322i			0.973765i
$13$	−1.79219	−	2.46673i	−0.497063	−	0.684148i	0.484608	−	0.874731i	$-0.338962\pi$
$13$	−1.79219	−	2.46673i	−0.497063	−	0.684148i	−0.981671	+	0.190583i	$0.938962\pi$
$14$	0.0577923	+	0.177866i	0.0154456	+	0.0475368i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.73256	+	2.38467i	−0.420208	+	0.578367i	−0.965671	−	0.259768i	$-0.916354\pi$
$17$	−1.73256	+	2.38467i	−0.420208	+	0.578367i	0.545463	+	0.838135i	$0.316354\pi$
$18$	7.96855	+	2.58914i	1.87820	+	0.610266i
$19$	−1.66209	−	5.11538i	−0.381309	−	1.17355i	−0.939123	−	0.343582i	$-0.888360\pi$
$19$	−1.66209	−	5.11538i	−0.381309	−	1.17355i	0.557814	−	0.829966i	$-0.311640\pi$
$20$		0			0
$21$	0.630859			0.137665
$22$	−2.87882	+	1.64693i	−0.613767	+	0.351127i
$23$			0.115585i			0.0241011i	0.999927	+	0.0120505i	$0.00383589\pi$
$23$			0.115585i			0.0241011i	−0.999927	+	0.0120505i	$0.996164\pi$
$24$	−2.72899	+	1.98273i	−0.557054	+	0.404723i
$25$		0			0
$26$	0.942208	−	2.89982i	0.184782	−	0.568701i
$27$	10.6644	−	14.6782i	2.05236	−	2.82483i
$28$	−0.109927	+	0.151302i	−0.0207743	+	0.0285934i
$29$	−3.14256	+	9.67180i	−0.583558	+	1.79601i	0.0214257	+	0.999770i	$0.493179\pi$
$29$	−3.14256	+	9.67180i	−0.583558	+	1.79601i	−0.604984	+	0.796238i	$0.706821\pi$
$30$		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	$0.542938\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.28272	+	10.9524i	0.397371	+	1.90656i
$34$	−2.94761			−0.505511
$35$		0			0
$36$	2.58914	+	7.96855i	0.431523	+	1.32809i
$37$	6.41625	+	2.08477i	1.05482	+	0.342733i	0.784560	−	0.620053i	$-0.212889\pi$
$37$	6.41625	+	2.08477i	1.05482	+	0.342733i	0.270265	+	0.962786i	$0.412889\pi$
$38$	3.16148	−	4.35140i	0.512859	−	0.705890i
$39$	−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	$-0.219315\pi$
$42$	0.370810	+	0.510376i	0.0572172	+	0.0787527i
$43$		−	2.27719i		−	0.347268i	−0.984810	−	0.173634i	$-0.944449\pi$
$43$		−	2.27719i		−	0.347268i	0.984810	−	0.173634i	$-0.0555510\pi$
$44$	−3.02452	−	1.36098i	−0.455964	−	0.205175i
$45$		0			0
$46$	−0.0935099	+	0.0679389i	−0.0137873	+	0.0100170i
$47$	6.04544	−	1.96428i	0.881818	−	0.286520i	0.167106	−	0.985939i	$-0.446558\pi$
$47$	6.04544	−	1.96428i	0.881818	−	0.286520i	0.714712	+	0.699419i	$0.246558\pi$
$48$	−3.20812	−	1.04238i	−0.463053	−	0.150455i
$49$	−5.63482	−	4.09394i	−0.804975	−	0.584848i
$50$		0			0
$51$	−3.07254	+	9.45631i	−0.430242	+	1.32415i
$52$	2.89982	−	0.942208i	0.402132	−	0.130661i
$53$	−4.73399	−	6.51578i	−0.650264	−	0.895011i	0.348847	−	0.937180i	$-0.386573\pi$
$53$	−4.73399	−	6.51578i	−0.650264	−	0.895011i	−0.999111	+	0.0421685i	$0.986573\pi$
$54$	18.1433			2.46899
$55$		0			0
$56$	−0.187020			−0.0249916
$57$	−10.6644	−	14.6782i	−1.41253	−	1.94418i
$58$	−9.67180	+	3.14256i	−1.26997	+	0.412638i
$59$	0.479439	−	1.47556i	0.0624177	−	0.192102i	−0.914985	−	0.403488i	$-0.867798\pi$
$59$	0.479439	−	1.47556i	0.0624177	−	0.192102i	0.977403	+	0.211386i	$0.0677977\pi$
$60$		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	$0.717932\pi$
$62$	−7.32066	−	2.37863i	−0.929725	−	0.302086i
$63$	1.49028	−	0.484220i	0.187757	−	0.0610060i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		0			0
$66$	−7.51889	+	8.28439i	−0.925511	+	1.01974i
$67$			9.03490i			1.10379i	0.833914	+	0.551894i	$0.186095\pi$
$67$			9.03490i			1.10379i	−0.833914	+	0.551894i	$0.813905\pi$
$68$	−1.73256	−	2.38467i	−0.210104	−	0.289183i
$69$	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	$0.687547\pi$
$72$	−4.92483	+	6.77845i	−0.580397	+	0.798848i
$73$	2.21796	+	0.720659i	0.259592	+	0.0843467i	0.435922	−	0.899985i	$-0.356422\pi$
$73$	2.21796	+	0.720659i	0.259592	+	0.0843467i	−0.176329	+	0.984331i	$0.556422\pi$
$74$	2.08477	+	6.41625i	0.242349	+	0.745874i
$75$		0			0
$76$	5.37863			0.616971
$77$	−0.254529	+	0.565646i	−0.0290063	+	0.0644613i
$78$		−	10.2851i		−	1.16456i
$79$	−7.45799	+	5.41855i	−0.839089	+	0.609634i	−0.922116	−	0.386913i	$-0.873541\pi$
$79$	−7.45799	+	5.41855i	−0.839089	+	0.609634i	0.0830269	+	0.996547i	$0.473541\pi$
$80$		0			0
$81$	11.1449	−	34.3003i	1.23832	−	3.81115i
$82$	2.75592	−	3.79320i	0.304340	−	0.418889i
$83$	1.86814	−	2.57128i	0.205055	−	0.282235i	−0.694087	−	0.719891i	$-0.744192\pi$
$83$	1.86814	−	2.57128i	0.205055	−	0.282235i	0.899142	+	0.437657i	$0.144192\pi$
$84$	−0.194946	+	0.599983i	−0.0212704	+	0.0654635i
$85$		0			0
$86$	1.84229	−	1.33850i	0.198659	−	0.144334i
$87$			34.3041i			3.67778i
$88$	−0.676718	−	3.24685i	−0.0721384	−	0.346116i
$89$	6.69658			0.709836			0.354918	−	0.934897i	$-0.384509\pi$
$89$	6.69658			0.709836			0.354918	+	0.934897i	$0.384509\pi$
$90$		0			0
$91$	−0.176211	−	0.542323i	−0.0184720	−	0.0568509i
$92$	−0.109927	−	0.0357176i	−0.0114607	−	0.00372382i
$93$	−15.2619	+	21.0061i	−1.58258	+	2.17824i
$94$	5.14256	+	3.73629i	0.530414	+	0.385369i
$95$		0			0
$96$	−1.04238	−	3.20812i	−0.106388	−	0.327428i
$97$	5.20431	+	7.16312i	0.528418	+	0.727305i	0.986888	−	0.161405i	$-0.0516026\pi$
$97$	5.20431	+	7.16312i	0.528418	+	0.727305i	−0.458471	+	0.888710i	$0.651603\pi$
$98$		−	6.96502i		−	0.703574i
$99$	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	$0.535792\pi$
$102$	−9.45631	+	3.07254i	−0.936314	+	0.304227i
$103$	−6.77198	−	2.20035i	−0.667263	−	0.216807i	−0.0442526	−	0.999020i	$-0.514091\pi$
$103$	−6.77198	−	2.20035i	−0.667263	−	0.216807i	−0.623011	+	0.782213i	$0.714091\pi$
$104$	2.46673	+	1.79219i	0.241883	+	0.175738i
$105$		0			0
$106$	2.48881	−	7.65976i	0.241734	−	0.743982i
$107$	2.72739	−	0.886182i	0.263666	−	0.0856704i	−0.174200	−	0.984710i	$-0.555734\pi$
$107$	2.72739	−	0.886182i	0.263666	−	0.0856704i	0.437867	+	0.899040i	$0.355734\pi$
$108$	10.6644	+	14.6782i	1.02618	+	1.41241i
$109$	−11.0316			−1.05663			−0.528316	−	0.849048i	$-0.677176\pi$
$109$	−11.0316			−1.05663			−0.528316	+	0.849048i	$0.677176\pi$
$110$		0			0
$111$	22.7573			2.16002
$112$	−0.109927	−	0.151302i	−0.0103872	−	0.0142967i
$113$	7.48507	−	2.43205i	0.704136	−	0.228788i	0.0650044	−	0.997885i	$-0.479294\pi$
$113$	7.48507	−	2.43205i	0.704136	−	0.228788i	0.639132	+	0.769097i	$0.279294\pi$
$114$	5.60659	−	17.2553i	0.525105	−	1.61611i
$115$		0			0
$116$	−8.22732	−	5.97750i	−0.763888	−	0.554997i
$117$	−24.2965	−	7.89441i	−2.24621	−	0.729838i
$118$	1.47556	−	0.479439i	0.135836	−	0.0441359i
$119$	−0.445980	+	0.324024i	−0.0408829	+	0.0297032i
$120$		0			0
$121$	−10.7412	−	2.37214i	−0.976471	−	0.215649i
$122$		−	0.879517i		−	0.0796277i
$123$	−9.29633	−	12.7953i	−0.838222	−	1.15371i
$124$	−2.37863	−	7.32066i	−0.213607	−	0.657415i
$125$		0			0
$126$	1.26770	+	0.921041i	0.112936	+	0.0820529i
$127$	5.32918	−	7.33498i	0.472888	−	0.650874i	−0.504231	−	0.863569i	$-0.668224\pi$
$127$	5.32918	−	7.33498i	0.472888	−	0.650874i	0.977119	+	0.212695i	$0.0682239\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−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	$0.583346\pi$
$132$	−11.1217	−	1.21347i	−0.968020	−	0.105619i
$133$		−	1.00591i		−	0.0872234i
$134$	−7.30939	+	5.31058i	−0.631435	+	0.458764i
$135$		0			0
$136$	0.910862	−	2.80335i	0.0781058	−	0.240385i
$137$	5.94988	−	8.18931i	0.508333	−	0.699660i	−0.475304	−	0.879822i	$-0.657662\pi$
$137$	5.94988	−	8.18931i	0.508333	−	0.699660i	0.983637	+	0.180161i	$0.0576620\pi$
$138$	−0.229173	+	0.315430i	−0.0195085	+	0.0268512i
$139$	5.29537	−	16.2975i	0.449148	−	1.38233i	−0.428723	−	0.903436i	$-0.641036\pi$
$139$	5.29537	−	16.2975i	0.449148	−	1.38233i	0.877870	−	0.478898i	$-0.158964\pi$
$140$		0			0
$141$	17.3470	−	12.6033i	1.46088	−	1.06139i
$142$			0.659156i			0.0553151i
$143$	8.77767	−	5.02157i	0.734026	−	0.419925i
$144$	−8.37863			−0.698219
$145$		0			0
$146$	0.720659	+	2.21796i	0.0596421	+	0.183560i
$147$	−22.3447	−	7.26022i	−1.84296	−	0.598813i
$148$	−3.96546	+	5.45799i	−0.325959	+	0.448644i
$149$	18.9571	+	13.7731i	1.55303	+	1.12834i	0.941450	+	0.337154i	$0.109464\pi$
$149$	18.9571	+	13.7731i	1.55303	+	1.12834i	0.611576	+	0.791185i	$0.290536\pi$
$150$		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	$0.736665\pi$
$152$	3.16148	+	4.35140i	0.256430	+	0.352945i
$153$			24.6969i			1.99663i
$154$	−0.607226	+	0.126560i	−0.0489316	+	0.0101985i
$155$		0			0
$156$	8.32083	−	6.04544i	0.666200	−	0.484023i
$157$	2.87291	−	0.933464i	0.229283	−	0.0744985i	−0.192122	−	0.981371i	$-0.561537\pi$
$157$	2.87291	−	0.933464i	0.229283	−	0.0744985i	0.421405	+	0.906872i	$0.361537\pi$
$158$	−8.76739	−	2.84870i	−0.697496	−	0.226630i
$159$	−21.9792	−	15.9688i	−1.74306	−	1.26641i
$160$		0			0
$161$	−0.00667990	+	0.0205586i	−0.000526450	+	0.00162025i
$162$	34.3003	−	11.1449i	2.69489	−	0.875622i
$163$	−1.26868	−	1.74619i	−0.0993709	−	0.136772i	0.756436	−	0.654068i	$-0.226939\pi$
$163$	−1.26868	−	1.74619i	−0.0993709	−	0.136772i	−0.855807	+	0.517295i	$0.826939\pi$
$164$	4.68865			0.366122
$165$		0			0
$166$	3.17828			0.246682
$167$	−3.30686	−	4.55150i	−0.255892	−	0.352205i	0.661672	−	0.749794i	$-0.269847\pi$
$167$	−3.30686	−	4.55150i	−0.255892	−	0.352205i	−0.917564	+	0.397588i	$0.869847\pi$
$168$	−0.599983	+	0.194946i	−0.0462897	+	0.0150404i
$169$	1.14438	−	3.52205i	0.0880296	−	0.270927i
$170$		0			0
$171$	−36.4588	−	26.4888i	−2.78807	−	2.02565i
$172$	2.16574	+	0.703690i	0.165136	+	0.0536559i
$173$	14.7962	−	4.80758i	1.12493	−	0.365513i	0.313285	−	0.949659i	$-0.398570\pi$
$173$	14.7962	−	4.80758i	1.12493	−	0.365513i	0.811649	+	0.584146i	$0.198570\pi$
$174$	−27.7526	+	20.1634i	−2.10392	+	1.52859i
$175$		0			0
$176$	2.22899	−	2.45593i	0.168017	−	0.185123i
$177$		−	5.23355i		−	0.393377i
$178$	3.93615	+	5.41765i	0.295027	+	0.406070i
$179$	5.36885	+	16.5236i	0.401287	+	1.23503i	0.923956	+	0.382498i	$0.124936\pi$
$179$	5.36885	+	16.5236i	0.401287	+	1.23503i	−0.522670	+	0.852535i	$0.675064\pi$
$180$		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	$0.871951\pi$
$182$	0.335174	−	0.461328i	0.0248448	−	0.0341959i
$183$	−2.82160	−	0.916793i	−0.208579	−	0.0677713i
$184$	−0.0357176	−	0.109927i	−0.00263314	−	0.00810396i
$185$		0			0
$186$	−25.9650			−1.90385
$187$	−7.23912	−	6.57021i	−0.529377	−	0.480461i
$188$			6.35655i			0.463599i
$189$	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	$0.145897\pi$
$192$	1.98273	−	2.72899i	0.143091	−	0.196948i
$193$	4.66953	−	6.42705i	0.336120	−	0.462629i	−0.607183	−	0.794562i	$-0.707701\pi$
$193$	4.66953	−	6.42705i	0.336120	−	0.462629i	0.943303	+	0.331933i	$0.107701\pi$
$194$	−2.73607	+	8.42075i	−0.196438	+	0.604575i
$195$		0			0
$196$	5.63482	−	4.09394i	0.402487	−	0.292424i
$197$		−	5.54948i		−	0.395384i	−0.980264	−	0.197692i	$-0.936655\pi$
$197$		−	5.54948i		−	0.395384i	0.980264	−	0.197692i	$-0.0633446\pi$
$198$	−11.4031	+	25.3414i	−0.810383	+	1.80093i
$199$	−4.31846			−0.306127			−0.153064	−	0.988216i	$-0.548914\pi$
$199$	−4.31846			−0.306127			−0.153064	+	0.988216i	$0.548914\pi$
$200$		0			0
$201$	9.41783	+	28.9851i	0.664282	+	2.04445i
$202$	−12.9004	−	4.19161i	−0.907672	−	0.294920i
$203$	−1.11791	+	1.53867i	−0.0784620	+	0.107994i
$204$	−8.04401	−	5.84432i	−0.563194	−	0.409184i
$205$		0			0
$206$	−2.20035	−	6.77198i	−0.153306	−	0.471826i
$207$	0.569235	+	0.783484i	0.0395646	+	0.0544559i
$208$			3.04905i			0.211413i
$209$	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	$0.380781\pi$
$212$	7.65976	−	2.48881i	0.526074	−	0.170932i
$213$	2.11465	+	0.687093i	0.144894	+	0.0470788i
$214$	2.32005	+	1.68562i	0.158596	+	0.115226i
$215$		0			0
$216$	−5.60659	+	17.2553i	−0.381480	+	1.17407i
$217$	−1.36911	+	0.444850i	−0.0929411	+	0.0301984i
$218$	−6.48419	−	8.92472i	−0.439165	−	0.604458i
$219$	7.86669			0.531582
$220$		0			0
$221$	8.98741			0.604559
$222$	13.3764	+	18.4110i	0.897764	+	1.23567i
$223$	−15.6840	+	5.09603i	−1.05028	+	0.341256i	−0.782777	−	0.622302i	$-0.786197\pi$
$223$	−15.6840	+	5.09603i	−1.05028	+	0.341256i	−0.267500	+	0.963558i	$0.586197\pi$
$224$	0.0577923	−	0.177866i	0.00386141	−	0.0118842i
$225$		0			0
$226$	6.36718	+	4.62603i	0.423539	+	0.307719i
$227$	11.0794	+	3.59992i	0.735367	+	0.238935i	0.652673	−	0.757640i	$-0.273648\pi$
$227$	11.0794	+	3.59992i	0.735367	+	0.238935i	0.0826941	+	0.996575i	$0.473648\pi$
$228$	17.2553	−	5.60659i	1.14276	−	0.371305i
$229$	16.0236	−	11.6419i	1.05887	−	0.769315i	0.0849922	−	0.996382i	$-0.472913\pi$
$229$	16.0236	−	11.6419i	1.05887	−	0.769315i	0.973879	+	0.227066i	$0.0729135\pi$
$230$		0			0
$231$	−0.226942	+	2.07998i	−0.0149317	+	0.136853i
$232$		−	10.1695i		−	0.667662i
$233$	−3.16632	−	4.35807i	−0.207433	−	0.285506i	0.692607	−	0.721316i	$-0.256462\pi$
$233$	−3.16632	−	4.35807i	−0.207433	−	0.285506i	−0.900039	+	0.435809i	$0.856462\pi$
$234$	−7.89441	−	24.2965i	−0.516073	−	1.58831i
$235$		0			0
$236$	1.25519	+	0.911947i	0.0817058	+	0.0593627i
$237$	−18.2780	+	25.1574i	−1.18728	+	1.63415i
$238$	−0.524281	−	0.170349i	−0.0339841	−	0.0110421i
$239$	−2.76883	−	8.52159i	−0.179101	−	0.551216i	0.820696	−	0.571365i	$-0.193586\pi$
$239$	−2.76883	−	8.52159i	−0.179101	−	0.551216i	−0.999797	+	0.0201493i	$0.993586\pi$
$240$		0			0
$241$	10.6881			0.688484			0.344242	−	0.938881i	$-0.388136\pi$
$241$	10.6881			0.688484			0.344242	+	0.938881i	$0.388136\pi$
$242$	−4.39441	−	10.0841i	−0.282483	−	0.648231i
$243$		−	67.2270i		−	4.31262i
$244$	0.711544	−	0.516967i	0.0455519	−	0.0330954i
$245$		0			0
$246$	4.88737	−	15.0418i	0.311607	−	0.959029i
$247$	−9.63950	+	13.2676i	−0.613346	+	0.844199i
$248$	4.52442	−	6.22732i	0.287301	−	0.395435i
$249$	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	$0.375485\pi$
$252$			1.56697i			0.0987098i
$253$	−0.381089	−	0.0415798i	−0.0239589	−	0.00261410i
$254$	9.06654			0.568885
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.09895	+	2.95643i	0.567577	+	0.184417i	0.578728	−	0.815521i	$-0.303549\pi$
$257$	9.09895	+	2.95643i	0.567577	+	0.184417i	−0.0111506	+	0.999938i	$0.503549\pi$
$258$	4.51505	−	6.21444i	0.281095	−	0.386894i
$259$	1.02075	+	0.741620i	0.0634264	+	0.0460820i
$260$		0			0
$261$	26.3303	+	81.0364i	1.62981	+	5.01603i
$262$	−3.48294	−	4.79386i	−0.215177	−	0.296166i
$263$			20.8985i			1.28866i	0.764749	+	0.644328i	$0.222863\pi$
$263$			20.8985i			1.28866i	−0.764749	+	0.644328i	$0.777137\pi$
$264$	−5.55546	−	9.71091i	−0.341915	−	0.597665i
$265$		0			0
$266$	0.813798	−	0.591259i	0.0498971	−	0.0362524i
$267$	21.4835	−	6.98040i	1.31477	−	0.427193i
$268$	−8.59270	−	2.79194i	−0.524883	−	0.170545i
$269$	16.6766	+	12.1162i	1.01679	+	0.738740i	0.965622	−	0.259950i	$-0.0837062\pi$
$269$	16.6766	+	12.1162i	1.01679	+	0.738740i	0.0511662	+	0.998690i	$0.483706\pi$
$270$		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	$0.0198343\pi$
$272$	2.80335	−	0.910862i	0.169978	−	0.0552291i
$273$	−1.13062	−	1.55616i	−0.0684280	−	0.0941831i
$274$	10.1225			0.611525
$275$		0			0
$276$	−0.389892			−0.0234688
$277$	7.50725	+	10.3328i	0.451067	+	0.620840i	0.972626	−	0.232375i	$-0.0746495\pi$
$277$	7.50725	+	10.3328i	0.451067	+	0.620840i	−0.521559	+	0.853215i	$0.674650\pi$
$278$	16.2975	−	5.29537i	0.977458	−	0.317595i
$279$	−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	$0.468415\pi$
$282$	20.3926	+	6.62596i	1.21436	+	0.394570i
$283$	10.6844	−	3.47159i	0.635124	−	0.206364i	0.0262805	−	0.999655i	$-0.491634\pi$
$283$	10.6844	−	3.47159i	0.635124	−	0.206364i	0.608844	+	0.793290i	$0.291634\pi$
$284$	−0.533268	+	0.387442i	−0.0316436	+	0.0229905i
$285$		0			0
$286$	9.22192	+	4.14968i	0.545304	+	0.245376i
$287$		−	0.876871i		−	0.0517600i
$288$	−4.92483	−	6.77845i	−0.290199	−	0.399424i
$289$	2.56842	+	7.90479i	0.151084	+	0.464987i
$290$		0			0
$291$	24.1628	+	17.5553i	1.41645	+	1.02911i
$292$	−1.37077	+	1.88671i	−0.0802185	+	0.110411i
$293$	24.3503	+	7.91189i	1.42256	+	0.462218i	0.916415	−	0.400230i	$-0.131070\pi$
$293$	24.3503	+	7.91189i	1.42256	+	0.462218i	0.506146	+	0.862448i	$0.331070\pi$
$294$	−7.26022	−	22.3447i	−0.423425	−	1.30317i
$295$		0			0
$296$	−6.74644			−0.392129
$297$	44.5587	+	40.4413i	2.58556	+	2.34664i
$298$			23.4323i			1.35739i
$299$	0.285116	−	0.207149i	0.0164887	−	0.0119797i
$300$		0			0
$301$	0.131604	−	0.405036i	0.00758553	−	0.0233459i
$302$	−7.09149	+	9.76059i	−0.408069	+	0.561659i
$303$	−26.8944	+	37.0170i	−1.54504	+	2.12657i
$304$	−1.66209	+	5.11538i	−0.0953272	+	0.293387i
$305$		0			0
$306$	−19.9802	+	14.5165i	−1.14219	+	0.829853i
$307$			19.3732i			1.10569i	0.833285	+	0.552844i	$0.186457\pi$
$307$			19.3732i			1.10569i	−0.833285	+	0.552844i	$0.813543\pi$
$308$	−0.459307	−	0.416866i	−0.0261715	−	0.0237531i
$309$	−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	$-0.264770\pi$
$312$	9.78173	+	3.17828i	0.553781	+	0.179934i
$313$	12.6740	−	17.4443i	0.716377	−	0.986009i	−0.283259	−	0.959043i	$-0.591416\pi$
$313$	12.6740	−	17.4443i	0.716377	−	0.986009i	0.999636	−	0.0269652i	$-0.00858432\pi$
$314$	2.44384	+	1.77555i	0.137914	+	0.100200i
$315$		0			0
$316$	−2.84870	−	8.76739i	−0.160252	−	0.493204i
$317$	−12.0507	−	16.5864i	−0.676836	−	0.931585i	0.323054	−	0.946380i	$-0.395290\pi$
$317$	−12.0507	−	16.5864i	−0.676836	−	0.931585i	−0.999891	+	0.0147955i	$0.995290\pi$
$318$		−	27.1678i		−	1.52349i
$319$	−30.7580	−	13.8405i	−1.72212	−	0.774918i
$320$		0			0
$321$	7.82606	−	5.68596i	0.436808	−	0.317360i
$322$	−0.0205586	+	0.00667990i	−0.00114569	+	0.000372256i
$323$	15.0781	+	4.89919i	0.838971	+	0.272598i
$324$	29.1776	+	21.1988i	1.62098	+	1.17771i
$325$		0			0
$326$	0.666986	−	2.05277i	0.0369409	−	0.113692i
$327$	−35.3906	+	11.4991i	−1.95711	+	0.635902i
$328$	2.75592	+	3.79320i	0.152170	+	0.209444i
$329$	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	$0.421651\pi$
$332$	1.86814	+	2.57128i	0.102528	+	0.141117i
$333$	53.7594	−	17.4675i	2.94599	−	0.957212i
$334$	1.73852	−	5.35061i	0.0951274	−	0.292772i
$335$		0			0
$336$	−0.510376	−	0.370810i	−0.0278433	−	0.0202293i
$337$	−3.61099	−	1.17328i	−0.196703	−	0.0639127i	0.209009	−	0.977914i	$-0.432976\pi$
$337$	−3.61099	−	1.17328i	−0.196703	−	0.0639127i	−0.405712	+	0.914001i	$0.632976\pi$
$338$	3.52205	−	1.14438i	0.191574	−	0.0622463i
$339$	21.4779	−	15.6046i	1.16652	−	0.847526i
$340$		0			0
$341$	−12.6771	−	22.1594i	−0.686502	−	1.20000i
$342$		−	45.0655i		−	2.43686i
$343$	−1.53514	−	2.11294i	−0.0828898	−	0.114088i
$344$	0.703690	+	2.16574i	0.0379404	+	0.116769i
$345$		0			0
$346$	12.5864	+	9.14455i	0.676649	+	0.491614i
$347$	12.0539	−	16.5907i	0.647086	−	0.890637i	−0.351883	−	0.936044i	$-0.614458\pi$
$347$	12.0539	−	16.5907i	0.647086	−	0.890637i	0.998969	+	0.0454069i	$0.0144584\pi$
$348$	−32.6251	−	10.6005i	−1.74889	−	0.568249i
$349$	−4.37529	−	13.4657i	−0.234204	−	0.720805i	−0.997226	−	0.0744327i	$-0.976285\pi$
$349$	−4.37529	−	13.4657i	−0.234204	−	0.720805i	0.763022	−	0.646372i	$-0.223715\pi$
$350$		0			0
$351$	−55.3198			−2.95275
$352$	3.29706	+	0.359735i	0.175734	+	0.0191739i
$353$			22.1366i			1.17821i	0.808056	+	0.589105i	$0.200520\pi$
$353$			22.1366i			1.17821i	−0.808056	+	0.589105i	$0.799480\pi$
$354$	4.23403	−	3.07620i	0.225036	−	0.163498i
$355$		0			0
$356$	−2.06936	+	6.36882i	−0.109676	+	0.337547i
$357$	−1.09300	+	1.50439i	−0.0578479	+	0.0796208i
$358$	−10.2122	+	14.0558i	−0.539729	+	0.742874i
$359$	2.55974	−	7.87806i	0.135098	−	0.415788i	−0.860507	−	0.509438i	$-0.829853\pi$
$359$	2.55974	−	7.87806i	0.135098	−	0.415788i	0.995605	+	0.0936498i	$0.0298534\pi$
$360$		0			0
$361$	−8.03323	+	5.83648i	−0.422802	+	0.307183i
$362$		−	13.8386i		−	0.727342i
$363$	−36.9317	+	3.58632i	−1.93841	+	0.188233i
$364$	0.570232			0.0298883
$365$		0			0
$366$	−0.916793	−	2.82160i	−0.0479215	−	0.147487i
$367$	−22.5390	−	7.32336i	−1.17652	−	0.382276i	−0.345450	−	0.938437i	$-0.612274\pi$
$367$	−22.5390	−	7.32336i	−1.17652	−	0.382276i	−0.831075	+	0.556161i	$0.812274\pi$
$368$	0.0679389	−	0.0935099i	0.00354156	−	0.00487454i
$369$	−31.7818	−	23.0908i	−1.65449	−	1.20206i
$370$		0			0
$371$	−0.465456	−	1.43253i	−0.0241653	−	0.0743731i
$372$	−15.2619	−	21.0061i	−0.791290	−	1.08912i
$373$			27.6907i			1.43377i	0.697191	+	0.716885i	$0.254433\pi$
$373$			27.6907i			1.43377i	−0.697191	+	0.716885i	$0.745567\pi$
$374$	1.06036	−	9.71845i	0.0548299	−	0.502529i
$375$		0			0
$376$	−5.14256	+	3.73629i	−0.265207	+	0.192684i
$377$	29.4898	−	9.58181i	1.51880	−	0.493488i
$378$	3.22708	+	1.04854i	0.165983	+	0.0539312i
$379$	12.8168	+	9.31197i	0.658356	+	0.478324i	0.866108	−	0.499858i	$-0.166614\pi$
$379$	12.8168	+	9.31197i	0.658356	+	0.478324i	−0.207751	+	0.978182i	$0.566614\pi$
$380$		0			0
$381$	9.45080	−	29.0866i	0.484179	−	1.49015i
$382$	−3.77731	+	1.22732i	−0.193264	+	0.0627954i
$383$	−0.793887	−	1.09269i	−0.0405657	−	0.0558340i	0.788252	−	0.615352i	$-0.210986\pi$
$383$	−0.793887	−	1.09269i	−0.0405657	−	0.0558340i	−0.828818	+	0.559518i	$0.810986\pi$
$384$	3.37322			0.172139
$385$		0			0
$386$	7.94427			0.404353
$387$	−11.2148	−	15.4358i	−0.570079	−	0.784647i
$388$	−8.42075	+	2.73607i	−0.427499	+	0.138903i
$389$	1.45465	−	4.47695i	0.0737536	−	0.226990i	−0.907383	−	0.420304i	$-0.861923\pi$
$389$	1.45465	−	4.47695i	0.0737536	−	0.226990i	0.981137	+	0.193314i	$0.0619235\pi$
$390$		0			0
$391$	−0.275631	−	0.200258i	−0.0139393	−	0.0101275i
$392$	6.62413	+	2.15231i	0.334569	+	0.108708i
$393$	−19.0099	+	6.17668i	−0.958921	+	0.311572i
$394$	4.48962	−	3.26190i	0.226184	−	0.164332i
$395$		0			0
$396$	−27.2042	+	5.66997i	−1.36706	+	0.284927i
$397$		−	23.2196i		−	1.16536i	−0.812702	−	0.582679i	$-0.802005\pi$
$397$		−	23.2196i		−	1.16536i	0.812702	−	0.582679i	$-0.197995\pi$
$398$	−2.53833	−	3.49371i	−0.127235	−	0.175124i
$399$	−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	$0.653225\pi$
$402$	−17.9138	+	24.6562i	−0.893458	+	1.22974i
$403$	22.3210	+	7.25255i	1.11189	+	0.361275i
$404$	−4.19161	−	12.9004i	−0.208540	−	0.641821i
$405$		0			0
$406$	−1.90190			−0.0943899
$407$	−9.18174	+	20.4048i	−0.455122	+	1.01143i
$408$		−	9.94295i		−	0.492249i
$409$	−21.1843	+	15.3913i	−1.04750	+	0.761051i	−0.971735	−	0.236075i	$-0.924139\pi$
$409$	−21.1843	+	15.3913i	−1.04750	+	0.761051i	−0.0757616	+	0.997126i	$0.524139\pi$
$410$		0			0
$411$	10.5516	−	32.4744i	0.520471	−	1.60184i
$412$	4.18532	−	5.76059i	0.206196	−	0.283804i
$413$	0.170552	−	0.234745i	0.00839233	−	0.0115510i
$414$	−0.299264	+	0.921041i	−0.0147080	+	0.0452667i
$415$		0			0
$416$	−2.46673	+	1.79219i	−0.120941	+	0.0878691i
$417$		−	57.8042i		−	2.83068i
$418$	13.2095	+	11.9889i	0.646099	+	0.586397i
$419$	6.68865			0.326762			0.163381	−	0.986563i	$-0.447760\pi$
$419$	6.68865			0.326762			0.163381	+	0.986563i	$0.447760\pi$
$420$		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	$0.688811\pi$
$422$	−6.93687	−	2.25393i	−0.337682	−	0.109719i
$423$	31.3050	−	43.0876i	1.52210	−	2.09499i
$424$	6.51578	+	4.73399i	0.316434	+	0.229903i
$425$		0			0
$426$	0.687093	+	2.11465i	0.0332897	+	0.102455i
$427$	−0.0966830	−	0.133073i	−0.00467882	−	0.00643984i
$428$			2.86774i			0.138618i
$429$	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	$0.0192604\pi$
$432$	−17.2553	+	5.60659i	−0.830196	+	0.269747i
$433$	−9.90223	−	3.21743i	−0.475871	−	0.154620i	0.0612546	−	0.998122i	$-0.480490\pi$
$433$	−9.90223	−	3.21743i	−0.475871	−	0.154620i	−0.537125	+	0.843502i	$0.680490\pi$
$434$	−1.16463	−	0.846155i	−0.0559042	−	0.0406168i
$435$		0			0
$436$	3.40894	−	10.4916i	0.163259	−	0.502458i
$437$	0.591259	−	0.192112i	0.0282837	−	0.00918994i
$438$	4.62393	+	6.36429i	0.220940	+	0.304097i
$439$	−31.4256			−1.49986			−0.749931	−	0.661517i	$-0.769913\pi$
$439$	−31.4256			−1.49986			−0.749931	+	0.661517i	$0.769913\pi$
$440$		0			0
$441$	−58.3573			−2.77892
$442$	5.28267	+	7.27097i	0.251271	+	0.345845i
$443$	−39.1057	+	12.7062i	−1.85797	+	0.603690i	−0.862792	+	0.505559i	$0.831286\pi$
$443$	−39.1057	+	12.7062i	−1.85797	+	0.603690i	−0.995173	+	0.0981312i	$0.968714\pi$
$444$	−7.03238	+	21.6434i	−0.333742	+	1.02715i
$445$		0			0
$446$	−13.3416	−	9.69323i	−0.631742	−	0.458988i
$447$	75.1736	+	24.4254i	3.55559	+	1.15528i
$448$	0.177866	−	0.0577923i	0.00840340	−	0.00273043i
$449$	−9.28984	+	6.74946i	−0.438414	+	0.318527i	−0.785005	−	0.619490i	$-0.787339\pi$
$449$	−9.28984	+	6.74946i	−0.438414	+	0.318527i	0.346590	+	0.938017i	$0.387339\pi$
$450$		0			0
$451$	15.2234	−	3.17290i	0.716840	−	0.149406i
$452$			7.87027i			0.370186i
$453$	23.9212	+	32.9246i	1.12391	+	1.54693i
$454$	3.59992	+	11.0794i	0.168953	+	0.519983i
$455$		0			0
$456$	14.6782	+	10.6644i	0.687371	+	0.499405i
$457$	10.8664	−	14.9563i	0.508309	−	0.699627i	−0.475324	−	0.879811i	$-0.657669\pi$
$457$	10.8664	−	14.9563i	0.508309	−	0.699627i	0.983633	+	0.180184i	$0.0576692\pi$
$458$	18.8369	+	6.12048i	0.880191	+	0.285991i
$459$	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	$0.550017\pi$
$462$	−1.81613	+	1.03898i	−0.0844941	+	0.0483378i
$463$			25.2817i			1.17494i	0.809246	+	0.587470i	$0.199876\pi$
$463$			25.2817i			1.17494i	−0.809246	+	0.587470i	$0.800124\pi$
$464$	8.22732	−	5.97750i	0.381944	−	0.277499i
$465$		0			0
$466$	1.66463	−	5.12321i	0.0771126	−	0.237328i
$467$	−11.7224	+	16.1346i	−0.542450	+	0.746618i	−0.988964	−	0.148159i	$-0.952665\pi$
$467$	−11.7224	+	16.1346i	−0.542450	+	0.746618i	0.446514	+	0.894777i	$0.352665\pi$
$468$	15.0161	−	20.6678i	0.694117	−	0.955370i
$469$	−0.522148	+	1.60700i	−0.0241105	+	0.0742046i
$470$		0			0
$471$	8.24361	−	5.98934i	0.379846	−	0.275974i
$472$			1.55150i			0.0714135i
$473$	7.50803	+	0.819185i	0.345219	+	0.0376662i
$474$	−31.0963			−1.42830
$475$		0			0
$476$	−0.170349	−	0.524281i	−0.00780794	−	0.0240304i
$477$	−64.1783	−	20.8528i	−2.93852	−	0.954783i
$478$	5.26663	−	7.24889i	0.240890	−	0.331557i
$479$	6.64419	+	4.82729i	0.303581	+	0.220564i	0.729137	−	0.684368i	$-0.239922\pi$
$479$	6.64419	+	4.82729i	0.303581	+	0.220564i	−0.425556	+	0.904932i	$0.639922\pi$
$480$		0			0
$481$	−6.35655	−	19.5635i	−0.289834	−	0.892017i
$482$	6.28233	+	8.64689i	0.286153	+	0.393855i
$483$			0.0729176i			0.00331787i
$484$	5.57524	−	9.48244i	0.253420	−	0.431020i
$485$		0			0
$486$	54.3878	−	39.5151i	2.46708	−	1.79244i
$487$	−26.6169	+	8.64835i	−1.20613	+	0.391894i	−0.842011	−	0.539460i	$-0.818628\pi$
$487$	−26.6169	+	8.64835i	−1.20613	+	0.391894i	−0.364115	+	0.931354i	$0.618628\pi$
$488$	0.836470	+	0.271786i	0.0378652	+	0.0123032i
$489$	−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	$0.995471\pi$
$492$	15.0418	−	4.88737i	0.678136	−	0.220340i
$493$	−17.6194	−	24.2510i	−0.793536	−	1.09221i
$494$	−16.3997			−0.737857
$495$		0			0
$496$	7.69740			0.345623
$497$	0.0724593	+	0.0997317i	0.00325024	+	0.00447358i
$498$	10.1963	−	3.31298i	0.456907	−	0.148458i
$499$	−1.51667	+	4.66783i	−0.0678955	+	0.208961i	−0.979248	−	0.202666i	$-0.935039\pi$
$499$	−1.51667	+	4.66783i	−0.0678955	+	0.208961i	0.911352	+	0.411627i	$0.135039\pi$
$500$		0			0
$501$	−15.3532	−	11.1548i	−0.685931	−	0.498358i
$502$	−7.07951	−	2.30027i	−0.315974	−	0.102666i
$503$	−6.24866	+	2.03031i	−0.278614	+	0.0905272i	−0.444991	−	0.895535i	$-0.646793\pi$
$503$	−6.24866	+	2.03031i	−0.278614	+	0.0905272i	0.166377	+	0.986062i	$0.446793\pi$
$504$	−1.26770	+	0.921041i	−0.0564680	+	0.0410264i
$505$		0			0
$506$	−0.190360	−	0.332748i	−0.00846252	−	0.0147924i
$507$		−	12.4921i		−	0.554792i
$508$	5.32918	+	7.33498i	0.236444	+	0.325437i
$509$	−0.849203	−	2.61358i	−0.0376403	−	0.115845i	0.930471	−	0.366366i	$-0.119398\pi$
$509$	−0.849203	−	2.61358i	−0.0376403	−	0.115845i	−0.968111	+	0.250521i	$0.919398\pi$
$510$		0			0
$511$	0.352852	+	0.256362i	0.0156092	+	0.0113408i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−92.8098	−	30.1557i	−4.09765	−	1.33141i
$514$	2.95643	+	9.09895i	0.130402	+	0.401338i
$515$		0			0
$516$	7.68147			0.338158
$517$	4.30160	+	20.6388i	0.189184	+	0.907693i
$518$			1.26172i			0.0554367i
$519$	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	$0.154294\pi$
$522$	−50.0832	+	68.9337i	−2.19208	+	3.01714i
$523$	15.2841	−	21.0367i	0.668326	−	0.919871i	−0.331395	−	0.943492i	$-0.607519\pi$
$523$	15.2841	−	21.0367i	0.668326	−	0.919871i	0.999721	+	0.0236208i	$0.00751943\pi$
$524$	1.83109	−	5.63552i	0.0799916	−	0.246189i
$525$		0			0
$526$	−16.9072	+	12.2838i	−0.737190	+	0.535600i
$527$		−	22.6889i		−	0.988346i
$528$	4.59087	−	10.2024i	0.199792	−	0.444002i
$529$	22.9866			0.999419
$530$		0			0
$531$	−4.01704	−	12.3632i	−0.174325	−	0.536516i
$532$	0.956677	+	0.310843i	0.0414772	+	0.0134768i
$533$	−8.40293	+	11.5656i	−0.363971	+	0.500964i
$534$	18.2749	+	13.2775i	0.790833	+	0.574574i
$535$		0			0
$536$	−2.79194	−	8.59270i	−0.120593	−	0.371148i
$537$	34.4479	+	47.4134i	1.48654	+	2.04604i
$538$			20.6134i			0.888706i
$539$	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	$0.138382\pi$
$542$	7.80295	−	2.53533i	0.335165	−	0.108902i
$543$	−44.3961	−	14.4252i	−1.90522	−	0.619043i
$544$	2.38467	+	1.73256i	0.102242	+	0.0742830i
$545$		0			0
$546$	0.594400	−	1.82938i	0.0254380	−	0.0782901i
$547$	−32.8110	+	10.6609i	−1.40290	+	0.455828i	−0.910126	−	0.414331i	$-0.864015\pi$
$547$	−32.8110	+	10.6609i	−1.40290	+	0.455828i	−0.492770	+	0.870160i	$0.664015\pi$
$548$	5.94988	+	8.18931i	0.254166	+	0.349830i
$549$	−7.36914			−0.314507
$550$		0			0
$551$	54.6981			2.33022
$552$	−0.229173	−	0.315430i	−0.00975425	−	0.0134256i
$553$	−1.63968	+	0.532763i	−0.0697261	+	0.0226554i
$554$	−3.94679	+	12.1470i	−0.167683	+	0.516076i
$555$		0			0
$556$	13.8635	+	10.0724i	0.587942	+	0.427165i
$557$	−17.7396	−	5.76393i	−0.751649	−	0.244226i	−0.0919585	−	0.995763i	$-0.529313\pi$
$557$	−17.7396	−	5.76393i	−0.751649	−	0.244226i	−0.659691	+	0.751537i	$0.729313\pi$
$558$	−61.3371	+	19.9296i	−2.59660	+	0.843688i
$559$	−5.61722	+	4.08115i	−0.237583	+	0.172614i
$560$		0			0
$561$	−30.0727	−	13.5321i	−1.26967	−	0.571326i
$562$			22.2962i			0.940507i
$563$	−22.7708	−	31.3413i	−0.959675	−	1.32088i	−0.947093	−	0.320958i	$-0.895995\pi$
$563$	−22.7708	−	31.3413i	−0.959675	−	1.32088i	−0.0125815	−	0.999921i	$-0.504005\pi$
$564$	6.62596	+	20.3926i	0.279003	+	0.858684i
$565$		0			0
$566$	9.08873	+	6.60335i	0.382028	+	0.277559i
$567$	3.96459	−	5.45679i	0.166497	−	0.229164i
$568$	−0.626894	−	0.203690i	−0.0263039	−	0.00854666i
$569$	8.05198	+	24.7814i	0.337557	+	1.03889i	0.965449	+	0.260592i	$0.0839178\pi$
$569$	8.05198	+	24.7814i	0.337557	+	1.03889i	−0.627892	+	0.778300i	$0.716082\pi$
$570$		0			0
$571$	−39.8951			−1.66956			−0.834778	−	0.550586i	$-0.814404\pi$
$571$	−39.8951			−1.66956			−0.834778	+	0.550586i	$0.814404\pi$
$572$	2.06335	+	9.89981i	0.0862729	+	0.413932i
$573$			13.3974i			0.559686i
$574$	0.709403	−	0.515412i	0.0296099	−	0.0215129i
$575$		0			0
$576$	2.58914	−	7.96855i	0.107881	−	0.332023i
$577$	−4.66683	+	6.42334i	−0.194283	+	0.267407i	−0.895033	−	0.445999i	$-0.852848\pi$
$577$	−4.66683	+	6.42334i	−0.194283	+	0.267407i	0.700751	+	0.713406i	$0.252848\pi$
$578$	−4.88543	+	6.72421i	−0.203207	+	0.279690i
$579$	8.28097	−	25.4862i	0.344146	−	1.05917i
$580$		0			0
$581$	0.480880	−	0.349380i	0.0199503	−	0.0144947i
$582$			29.8669i			1.23802i
$583$	23.1859	−	13.2643i	0.960261	−	0.549351i
$584$	−2.33210			−0.0965030
$585$		0			0
$586$	7.91189	+	24.3503i	0.326837	+	1.00590i
$587$	−11.2727	−	3.66271i	−0.465273	−	0.151176i	0.0669934	−	0.997753i	$-0.478659\pi$
$587$	−11.2727	−	3.66271i	−0.465273	−	0.151176i	−0.532266	+	0.846577i	$0.678659\pi$
$588$	13.8098	−	19.0075i	0.569505	−	0.783856i
$589$	33.4944	+	24.3351i	1.38011	+	1.00271i
$590$		0			0
$591$	−5.78468	−	17.8034i	−0.237950	−	0.732335i
$592$	−3.96546	−	5.45799i	−0.162979	−	0.224322i
$593$		−	29.4865i		−	1.21087i	−0.795896	−	0.605433i	$-0.793000\pi$
$593$		−	29.4865i		−	1.21087i	0.795896	−	0.605433i	$-0.207000\pi$
$594$	−6.52678	+	59.8195i	−0.267797	+	2.45442i
$595$		0			0
$596$	−18.9571	+	13.7731i	−0.776513	+	0.564170i
$597$	−13.8541	+	4.50149i	−0.567013	+	0.184234i
$598$	0.335174	+	0.108905i	0.0137063	+	0.00445344i
$599$	−22.4696	−	16.3251i	−0.918084	−	0.667027i	0.0249627	−	0.999688i	$-0.492053\pi$
$599$	−22.4696	−	16.3251i	−0.918084	−	0.667027i	−0.943046	+	0.332662i	$0.892053\pi$
$600$		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	$-0.104414\pi$
$602$	0.405036	−	0.131604i	0.0165080	−	0.00536378i
$603$	44.4954	+	61.2426i	1.81199	+	2.49399i
$604$	−12.0648			−0.490908
$605$		0			0
$606$	−45.7555			−1.85869
$607$	−6.33323	−	8.71695i	−0.257058	−	0.353810i	0.660909	−	0.750466i	$-0.270171\pi$
$607$	−6.33323	−	8.71695i	−0.257058	−	0.353810i	−0.917967	+	0.396656i	$0.870171\pi$
$608$	−5.11538	+	1.66209i	−0.207456	+	0.0674065i
$609$	−1.98251	+	6.10154i	−0.0803354	+	0.247247i
$610$		0			0
$611$	−15.6799	−	11.3921i	−0.634341	−	0.460876i
$612$	−23.4882	−	7.63177i	−0.949454	−	0.308496i
$613$	43.0821	−	13.9982i	1.74007	−	0.565383i	0.745226	−	0.666812i	$-0.232341\pi$
$613$	43.0821	−	13.9982i	1.74007	−	0.565383i	0.994843	+	0.101429i	$0.0323414\pi$
$614$	−15.6733	+	11.3873i	−0.632522	+	0.459554i
$615$		0			0
$616$	0.0672776	−	0.616615i	0.00271069	−	0.0248441i
$617$			7.32134i			0.294746i	0.989081	+	0.147373i	$0.0470818\pi$
$617$			7.32134i			0.294746i	−0.989081	+	0.147373i	$0.952918\pi$
$618$	−14.1180	−	19.4318i	−0.567909	−	0.781660i
$619$	−8.99572	−	27.6860i	−0.361569	−	1.11279i	−0.952102	−	0.305781i	$-0.901083\pi$
$619$	−8.99572	−	27.6860i	−0.361569	−	1.11279i	0.590533	−	0.807013i	$-0.298917\pi$
$620$		0			0
$621$	1.69658	+	1.23264i	0.0680813	+	0.0494640i
$622$	10.2585	−	14.1197i	0.411330	−	0.566147i
$623$	1.19110	+	0.387011i	0.0477203	+	0.0155053i
$624$	3.17828	+	9.78173i	0.127233	+	0.391582i
$625$		0			0
$626$	21.5623			0.861803
$627$	52.2313	−	29.8807i	2.08592	−	1.19332i
$628$			3.02075i			0.120541i
$629$	−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	$0.753353\pi$
$632$	5.41855	−	7.45799i	0.215538	−	0.296663i
$633$	−14.4618	+	19.9049i	−0.574803	+	0.791149i
$634$	6.33544	−	19.4985i	0.251612	−	0.774384i
$635$		0			0
$636$	21.9792	−	15.9688i	0.871531	−	0.633204i
$637$			21.2367i			0.841428i
$638$	−6.88191	−	33.0190i	−0.272457	−	1.30723i
$639$	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	$-0.313030\pi$
$642$	9.20008	+	2.98929i	0.363098	+	0.117978i
$643$	−20.0465	+	27.5916i	−0.790556	+	1.08811i	0.203483	+	0.979079i	$0.434774\pi$
$643$	−20.0465	+	27.5916i	−0.790556	+	1.08811i	−0.994039	+	0.109028i	$0.965226\pi$
$644$	−0.0174882	−	0.0127059i	−0.000689132	−	0.000500683i
$645$		0			0
$646$	4.89919	+	15.0781i	0.192756	+	0.593242i
$647$	10.8268	+	14.9018i	0.425646	+	0.585851i	0.966947	−	0.254978i	$-0.0820681\pi$
$647$	10.8268	+	14.9018i	0.425646	+	0.585851i	−0.541301	+	0.840829i	$0.682068\pi$
$648$			36.0655i			1.41679i
$649$	4.69254	+	2.11155i	0.184198	+	0.0828856i
$650$		0			0
$651$	−3.92856	+	2.85427i	−0.153973	+	0.111868i
$652$	2.05277	−	0.666986i	0.0803927	−	0.0261212i
$653$	−16.4359	−	5.34034i	−0.643185	−	0.208984i	−0.0307784	−	0.999526i	$-0.509799\pi$
$653$	−16.4359	−	5.34034i	−0.643185	−	0.208984i	−0.612407	+	0.790543i	$0.709799\pi$
$654$	−30.1051	−	21.8726i	−1.17720	−	0.855287i
$655$		0			0
$656$	−1.44887	+	4.45917i	−0.0565690	+	0.174101i
$657$	18.5834	−	6.03813i	0.725009	−	0.235570i
$658$	0.698760	+	0.961760i	0.0272405	+	0.0374933i
$659$	−9.78298			−0.381091			−0.190545	−	0.981678i	$-0.561026\pi$
$659$	−9.78298			−0.381091			−0.190545	+	0.981678i	$0.561026\pi$
$660$		0			0
$661$	4.62985			0.180080			0.0900401	−	0.995938i	$-0.471300\pi$
$661$	4.62985			0.180080			0.0900401	+	0.995938i	$0.471300\pi$
$662$	5.21137	+	7.17283i	0.202546	+	0.278780i
$663$	28.8327	−	9.36832i	1.11977	−	0.363836i
$664$	−0.982141	+	3.02272i	−0.0381145	+	0.117304i
$665$		0			0
$666$	45.7304	+	33.2251i	1.77202	+	1.28745i
$667$	−1.11791	−	0.363231i	−0.0432857	−	0.0140644i
$668$	5.35061	−	1.73852i	0.207021	−	0.0672653i
$669$	−45.0041	+	32.6974i	−1.73996	+	1.26416i
$670$		0			0
$671$	1.96044	−	2.16003i	0.0756818	−	0.0833870i
$672$		−	0.630859i		−	0.0243359i
$673$	−21.4100	−	29.4683i	−0.825293	−	1.13592i	−0.988781	−	0.149374i	$-0.952274\pi$
$673$	−21.4100	−	29.4683i	−0.825293	−	1.13592i	0.163487	−	0.986545i	$-0.447726\pi$
$674$	−1.17328	−	3.61099i	−0.0451931	−	0.139090i
$675$		0			0
$676$	2.99604	+	2.17675i	0.115232	+	0.0837211i
$677$	25.7149	−	35.3935i	0.988304	−	1.36028i	0.0560698	−	0.998427i	$-0.482143\pi$
$677$	25.7149	−	35.3935i	0.988304	−	1.36028i	0.932234	−	0.361856i	$-0.117857\pi$
$678$	25.2488	+	8.20383i	0.969674	+	0.315066i
$679$	0.511699	+	1.57485i	0.0196372	+	0.0604371i
$680$		0			0
$681$	39.2967			1.50585
$682$	10.4760	−	23.2810i	0.401145	−	0.891474i
$683$			19.5734i			0.748953i	0.927236	+	0.374477i	$0.122178\pi$
$683$			19.5734i			0.748953i	−0.927236	+	0.374477i	$0.877822\pi$
$684$	36.4588	−	26.4888i	1.39404	−	1.01283i
$685$		0			0
$686$	0.807071	−	2.48391i	0.0308141	−	0.0948361i
$687$	39.2705	−	54.0513i	1.49826	−	2.06218i
$688$	−1.33850	+	1.84229i	−0.0510298	+	0.0702365i
$689$	−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	$0.453769\pi$
$692$			15.5576i			0.591413i
$693$	1.06040	+	5.08772i	0.0402811	+	0.193266i
$694$	20.5073			0.778445
$695$		0			0
$696$	−10.6005	−	32.6251i	−0.401813	−	1.23665i
$697$	13.1439	+	4.27072i	0.497861	+	0.161765i
$698$	8.32229	−	11.4546i	0.315003	−	0.433565i
$699$	−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	$0.974635\pi$
$702$	−32.5162	−	44.7547i	−1.22724	−	1.68916i
$703$		−	36.2866i		−	1.36857i
$704$	1.64693	+	2.87882i	0.0620710	+	0.108500i
$705$		0			0
$706$	−17.9089	+	13.0116i	−0.674009	+	0.489696i
$707$	−2.41264	+	0.783913i	−0.0907366	+	0.0294821i
$708$	4.97740	+	1.61725i	0.187062	+	0.0607801i
$709$	2.09099	+	1.51919i	0.0785287	+	0.0570544i	0.626357	−	0.779536i	$-0.284545\pi$
$709$	2.09099	+	1.51919i	0.0785287	+	0.0570544i	−0.547828	+	0.836591i	$0.684545\pi$
$710$		0			0
$711$	−23.8682	+	73.4587i	−0.895126	+	2.75492i
$712$	−6.36882	+	2.06936i	−0.238682	+	0.0775524i
$713$	−0.522953	−	0.719783i	−0.0195847	−	0.0269561i
$714$	−1.85953			−0.0695911
$715$		0			0
$716$	−17.3740			−0.649295
$717$	−17.7655	−	24.4521i	−0.663465	−	0.913181i
$718$	7.87806	−	2.55974i	0.294007	−	0.0955285i
$719$	12.3660	−	38.0587i	0.461175	−	1.41935i	−0.402554	−	0.915396i	$-0.631878\pi$
$719$	12.3660	−	38.0587i	0.461175	−	1.41935i	0.863730	−	0.503956i	$-0.168122\pi$
$720$		0			0
$721$	−1.07734	−	0.782737i	−0.0401224	−	0.0291506i
$722$	−9.44363	−	3.06842i	−0.351455	−	0.114195i
$723$	34.2889	−	11.1411i	1.27522	−	0.414343i
$724$	11.1957	−	8.13414i	0.416084	−	0.302303i
$725$		0			0
$726$	−24.6093	−	27.7704i	−0.913337	−	1.03066i
$727$		−	47.6224i		−	1.76622i	−0.469169	−	0.883108i	$-0.655446\pi$
$727$		−	47.6224i		−	1.76622i	0.469169	−	0.883108i	$-0.344554\pi$
$728$	0.335174	+	0.461328i	0.0124224	+	0.0170979i
$729$	−36.6417	−	112.772i	−1.35710	−	4.17673i
$730$		0			0
$731$	5.43034	+	3.94537i	0.200848	+	0.145925i
$732$	1.74384	−	2.40020i	0.0644543	−	0.0887138i
$733$	−41.1492	−	13.3702i	−1.51988	−	0.493839i	−0.574139	−	0.818758i	$-0.694663\pi$
$733$	−41.1492	−	13.3702i	−1.51988	−	0.493839i	−0.945742	+	0.324918i	$0.894663\pi$
$734$	−7.32336	−	22.5390i	−0.270310	−	0.831929i
$735$		0			0
$736$	0.115585			0.00426050
$737$	−29.7886	−	3.25017i	−1.09728	−	0.119722i
$738$		−	39.2845i		−	1.44608i
$739$	−36.8236	+	26.7539i	−1.35458	+	0.984160i	−0.355810	+	0.934558i	$0.615795\pi$
$739$	−36.8236	+	26.7539i	−1.35458	+	0.984160i	−0.998769	+	0.0496014i	$0.984205\pi$
$740$		0			0
$741$	−17.0948	+	52.6123i	−0.627992	+	1.93276i
$742$	0.885350	−	1.21858i	0.0325022	−	0.0447355i
$743$	−24.7265	+	34.0331i	−0.907128	+	1.24855i	0.0610105	+	0.998137i	$0.480568\pi$
$743$	−24.7265	+	34.0331i	−0.907128	+	1.24855i	−0.968138	+	0.250417i	$0.919432\pi$
$744$	8.02363	−	24.6942i	0.294161	−	0.905333i
$745$		0			0
$746$	−22.4023	+	16.2762i	−0.820205	+	0.595914i
$747$		−	26.6296i		−	0.974326i
$748$	8.48565	−	4.85451i	0.310266	−	0.177498i
$749$	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	$0.923889\pi$
$752$	−6.04544	−	1.96428i	−0.220454	−	0.0716300i
$753$	−14.7591	+	20.3142i	−0.537852	+	0.740290i
$754$	25.0855	+	18.2257i	0.913560	+	0.663740i
$755$		0			0
$756$	1.04854	+	3.22708i	0.0381351	+	0.117368i
$757$	2.88717	+	3.97384i	0.104936	+	0.144432i	0.858255	−	0.513223i	$-0.171549\pi$
$757$	2.88717	+	3.97384i	0.104936	+	0.144432i	−0.753319	+	0.657655i	$0.771549\pi$
$758$			15.8425i			0.575425i
$759$	−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	$0.475250\pi$
$762$	29.0866	−	9.45080i	1.05370	−	0.342366i
$763$	−1.96214	−	0.637539i	−0.0710344	−	0.0230805i
$764$	−3.21318	−	2.33451i	−0.116249	−	0.0844596i
$765$		0			0
$766$	0.417371	−	1.28454i	0.0150802	−	0.0464122i
$767$	−4.49906	+	1.46183i	−0.162452	+	0.0527837i
$768$	1.98273	+	2.72899i	0.0715456	+	0.0984741i
$769$	35.9976			1.29811			0.649053	−	0.760743i	$-0.275165\pi$
$769$	35.9976			1.29811			0.649053	+	0.760743i	$0.275165\pi$
$770$		0			0
$771$	32.2723			1.16226
$772$	4.66953	+	6.42705i	0.168060	+	0.231315i
$773$	−8.47960	+	2.75519i	−0.304990	+	0.0990972i	−0.457514	−	0.889203i	$-0.651260\pi$
$773$	−8.47960	+	2.75519i	−0.304990	+	0.0990972i	0.152524	+	0.988300i	$0.451260\pi$
$774$	5.89596	−	18.1459i	0.211926	−	0.652241i
$775$		0			0
$776$	−7.16312	−	5.20431i	−0.257141	−	0.186824i
$777$	4.04775	+	1.31519i	0.145212	+	0.0471823i
$778$	4.47695	−	1.45465i	0.160506	−	0.0521516i
$779$	−20.4022	+	14.8231i	−0.730985	+	0.531091i
$780$		0			0
$781$	−1.46925	+	1.61884i	−0.0525740	+	0.0579266i
$782$		−	0.340698i		−	0.0121834i
$783$	108.452	+	149.271i	3.87574	+	5.33450i
$784$	2.15231	+	6.62413i	0.0768682	+	0.236576i
$785$		0			0
$786$	−16.1708	−	11.7487i	−0.576792	−	0.419064i
$787$	−10.0575	+	13.8429i	−0.358510	+	0.493446i	−0.949733	−	0.313062i	$-0.898645\pi$
$787$	−10.0575	+	13.8429i	−0.358510	+	0.493446i	0.591223	+	0.806508i	$0.298645\pi$
$788$	5.27787	+	1.71488i	0.188016	+	0.0610902i
$789$	21.7842	+	67.0450i	0.775539	+	2.38686i
$790$		0			0
$791$	1.47190			0.0523346
$792$	−20.5773	−	18.6759i	−0.731183	−	0.663619i
$793$			2.68169i			0.0952296i
$794$	18.7850	−	13.6481i	0.666656	−	0.484354i
$795$		0			0
$796$	1.33448	−	4.10710i	0.0472993	−	0.145572i
$797$	−19.3705	+	26.6612i	−0.686139	+	0.944389i	−0.999987	−	0.00508424i	$-0.998382\pi$
$797$	−19.3705	+	26.6612i	−0.686139	+	0.944389i	0.313848	+	0.949473i	$0.398382\pi$
$798$	1.99445	−	2.74512i	0.0706027	−	0.0971762i
$799$	−5.78994	+	17.8196i	−0.204833	+	0.630412i
$800$		0			0
$801$	45.3924	−	32.9795i	1.60386	−	1.16527i
$802$			5.86409i			0.207068i
$803$	−3.17393	+	7.05349i	−0.112006	+	0.248912i
$804$	−30.4767			−1.07483
$805$		0			0
$806$	7.25255	+	22.3210i	0.255460	+	0.786225i
$807$	66.1303	+	21.4870i	2.32790	+	0.756379i
$808$	7.97291	−	10.9738i	0.280486	−	0.386056i
$809$	−33.1781	−	24.1053i	−1.16648	−	0.847498i	−0.175897	−	0.984409i	$-0.556283\pi$
$809$	−33.1781	−	24.1053i	−1.16648	−	0.847498i	−0.990583	+	0.136911i	$0.956283\pi$
$810$		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	$0.959969\pi$
$812$	−1.11791	−	1.53867i	−0.0392310	−	0.0539968i
$813$		−	27.6756i		−	0.970627i
$814$	−21.9047	+	4.56544i	−0.767760	+	0.160019i
$815$		0			0
$816$	8.04401	−	5.84432i	0.281597	−	0.204592i
$817$	−11.6487	+	3.78489i	−0.407536	+	0.132416i
$818$	−24.9036	−	8.09168i	−0.870735	−	0.282919i
$819$	−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	$0.0627934\pi$
$822$	32.4744	−	10.5516i	1.13267	−	0.368028i
$823$	−22.2772	−	30.6620i	−0.776535	−	1.06881i	−0.995656	−	0.0931110i	$-0.970319\pi$
$823$	−22.2772	−	30.6620i	−0.776535	−	1.06881i	0.219121	−	0.975698i	$-0.429681\pi$
$824$	7.12048			0.248054
$825$		0			0
$826$	0.290161			0.0100960
$827$	19.3271	+	26.6015i	0.672071	+	0.925026i	0.999805	−	0.0197438i	$-0.00628505\pi$
$827$	19.3271	+	26.6015i	0.672071	+	0.925026i	−0.327734	+	0.944770i	$0.606285\pi$
$828$	−0.921041	+	0.299264i	−0.0320084	+	0.0104002i
$829$	−4.15827	+	12.7978i	−0.144423	+	0.444487i	−0.996936	−	0.0782180i	$-0.975077\pi$
$829$	−4.15827	+	12.7978i	−0.144423	+	0.444487i	0.852514	+	0.522705i	$0.175077\pi$
$830$		0			0
$831$	34.8550	+	25.3236i	1.20911	+	0.878466i
$832$	−2.89982	−	0.942208i	−0.100533	−	0.0326652i
$833$	19.5254	−	6.34418i	0.676514	−	0.219813i
$834$	46.7646	−	33.9764i	1.61932	−	1.17651i
$835$		0			0
$836$	−1.93488	+	17.7336i	−0.0669193	+	0.613331i
$837$			139.656i			4.82722i
$838$	3.93149	+	5.41123i	0.135811	+	0.186928i
$839$	13.3324	+	41.0329i	0.460285	+	1.41661i	0.864817	+	0.502088i	$0.167435\pi$
$839$	13.3324	+	41.0329i	0.460285	+	1.41661i	−0.404532	+	0.914524i	$0.632565\pi$
$840$		0			0
$841$	−60.2065	−	43.7426i	−2.07609	−	1.50837i
$842$	−14.8548	+	20.4459i	−0.511931	+	0.704612i
$843$	71.5289	+	23.2411i	2.46358	+	0.800467i
$844$	−2.25393	−	6.93687i	−0.0775834	−	0.238777i
$845$		0			0
$846$	53.2592			1.83109
$847$	−1.77340	−	1.04268i	−0.0609349	−	0.0358269i
$848$			8.05395i			0.276574i
$849$	30.6583	−	22.2746i	1.05219	−	0.764461i
$850$		0			0
$851$	−0.240967	+	0.741620i	−0.00826024	+	0.0254224i
$852$	−1.30693	+	1.79883i	−0.0447746	+	0.0616270i
$853$	28.0908	−	38.6637i	0.961811	−	1.32382i	0.0157338	−	0.999876i	$-0.494992\pi$
$853$	28.0908	−	38.6637i	0.961811	−	1.32382i	0.946077	−	0.323942i	$-0.105008\pi$
$854$	0.0508293	−	0.156436i	0.00173934	−	0.00535314i
$855$		0			0
$856$	−2.32005	+	1.68562i	−0.0792978	+	0.0576132i
$857$			3.49798i			0.119489i	0.998214	+	0.0597444i	$0.0190285\pi$
$857$			3.49798i			0.119489i	−0.998214	+	0.0597444i	$0.980971\pi$
$858$	33.9106	+	3.69992i	1.15769	+	0.126313i
$859$	−26.4442			−0.902263			−0.451131	−	0.892458i	$-0.648979\pi$
$859$	−26.4442			−0.902263			−0.451131	+	0.892458i	$0.648979\pi$
$860$		0			0
$861$	−0.914035	−	2.81311i	−0.0311502	−	0.0958705i
$862$	30.4851	+	9.90521i	1.03833	+	0.337373i
$863$	29.4811	−	40.5772i	1.00355	−	1.38126i	0.0804231	−	0.996761i	$-0.474373\pi$
$863$	29.4811	−	40.5772i	1.00355	−	1.38126i	0.923124	−	0.384503i	$-0.125627\pi$
$864$	−14.6782	−	10.6644i	−0.499364	−	0.362809i
$865$		0			0
$866$	−3.21743	−	9.90223i	−0.109333	−	0.336491i
$867$	16.4796	+	22.6823i	0.559678	+	0.770330i
$868$		−	1.43957i		−	0.0488620i
$869$	−15.1824	−	26.5387i	−0.515026	−	0.900262i
$870$		0			0
$871$	22.2867	−	16.1922i	0.755155	−	0.548652i
$872$	10.4916	−	3.40894i	0.355292	−	0.115441i
$873$	70.5543	+	22.9245i	2.38790	+	0.775876i
$874$	0.502955	+	0.365418i	0.0170127	+	0.0123604i
$875$		0			0
$876$	−2.43094	+	7.48167i	−0.0821339	+	0.252782i
$877$	21.4583	−	6.97221i	0.724594	−	0.235435i	0.0765800	−	0.997063i	$-0.475600\pi$
$877$	21.4583	−	6.97221i	0.724594	−	0.235435i	0.648014	+	0.761629i	$0.275600\pi$
$878$	−18.4715	−	25.4238i	−0.623383	−	0.858013i
$879$	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	$0.458522\pi$
$882$	−34.3016	−	47.2121i	−1.15499	−	1.58971i
$883$	−31.4225	+	10.2098i	−1.05745	+	0.343586i	−0.785588	−	0.618750i	$-0.787639\pi$
$883$	−31.4225	+	10.2098i	−1.05745	+	0.343586i	−0.271862	+	0.962336i	$0.587639\pi$
$884$	−2.77726	+	8.54754i	−0.0934095	+	0.287485i
$885$		0			0
$886$	−33.2653	−	24.1686i	−1.11757	−	0.811961i
$887$	−17.5934	−	5.71644i	−0.590729	−	0.191939i	−0.00162748	−	0.999999i	$-0.500518\pi$
$887$	−17.5934	−	5.71644i	−0.590729	−	0.191939i	−0.589101	+	0.808059i	$0.700518\pi$
$888$	−21.6434	+	7.03238i	−0.726306	+	0.235991i
$889$	1.37179	−	0.996661i	0.0460083	−	0.0334270i
$890$		0			0
$891$	109.081	+	49.0843i	3.65435	+	1.64438i
$892$		−	16.4911i		−	0.552163i
$893$	−20.0961	−	27.6599i	−0.672490	−	0.925603i
$894$	24.4254	+	75.1736i	0.816907	+	2.51418i
$895$		0			0
$896$	0.151302	+	0.109927i	0.00505465	+	0.00367242i
$897$	0.698760	−	0.961760i	0.0233309	−	0.0321122i
$898$	−10.9209	−	3.54840i	−0.364434	−	0.118412i
$899$	−24.1895	−	74.4477i	−0.806765	−	2.48297i
$900$		0			0
$901$	23.7399			0.790891
$902$	11.5150	+	10.4510i	0.383407	+	0.347979i
$903$		−	1.43659i		−	0.0478066i
$904$	−6.36718	+	4.62603i	−0.211769	+	0.153859i
$905$		0			0
$906$	−12.5761	+	38.7052i	−0.417813	+	1.28590i
$907$	30.0515	−	41.3623i	0.997843	−	1.37341i	0.0712035	−	0.997462i	$-0.477316\pi$
$907$	30.0515	−	41.3623i	0.997843	−	1.37341i	0.926639	−	0.375951i	$-0.122684\pi$
$908$	−6.84746	+	9.42472i	−0.227241	+	0.312770i
$909$	−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	$0.173973\pi$
$912$			18.1433i			0.600785i
$913$	7.80562	+	7.08436i	0.258328	+	0.234458i
$914$	18.4870			0.611496
$915$		0			0
$916$	6.12048	+	18.8369i	0.202226	+	0.622389i
$917$	−1.05395	−	0.342450i	−0.0348046	−	0.0113087i
$918$	−31.4344	+	43.2657i	−1.03749	+	1.42798i
$919$	13.1742	+	9.57161i	0.434577	+	0.315738i	0.783476	−	0.621422i	$-0.213445\pi$
$919$	13.1742	+	9.57161i	0.434577	+	0.315738i	−0.348900	+	0.937160i	$0.613445\pi$
$920$		0			0
$921$	20.1943	+	62.1517i	0.665425	+	2.04797i
$922$	−3.94979	−	5.43642i	−0.130079	−	0.179039i
$923$		−	2.00980i		−	0.0661533i
$924$	−1.90805	−	0.858584i	−0.0627702	−	0.0282453i
$925$		0			0
$926$	−20.4533	+	14.8602i	−0.672138	+	0.488337i
$927$	−56.7399	+	18.4359i	−1.86358	+	0.605515i
$928$	9.67180	+	3.14256i	0.317492	+	0.103160i
$929$	−10.7933	−	7.84178i	−0.354116	−	0.257280i	0.396478	−	0.918044i	$-0.370232\pi$
$929$	−10.7933	−	7.84178i	−0.354116	−	0.257280i	−0.750594	+	0.660764i	$0.770232\pi$
$930$		0			0
$931$	−11.5765	+	35.6287i	−0.379404	+	1.16768i
$932$	5.12321	−	1.66463i	0.167816	−	0.0545269i
$933$	−34.6043	−	47.6288i	−1.13289	−	1.55930i
$934$	−19.9434			−0.652568
$935$		0			0
$936$	25.5468			0.835024
$937$	9.35641	+	12.8780i	0.305660	+	0.420706i	0.934022	−	0.357216i	$-0.116274\pi$
$937$	9.35641	+	12.8780i	0.305660	+	0.420706i	−0.628361	+	0.777922i	$0.716274\pi$
$938$	−1.60700	+	0.522148i	−0.0524706	+	0.0170487i
$939$	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	$0.584080\pi$
$942$	9.69095	+	3.14878i	0.315748	+	0.102593i
$943$	0.515412	−	0.167467i	0.0167841	−	0.00545349i
$944$	−1.25519	+	0.911947i	−0.0408529	+	0.0296814i
$945$		0			0
$946$	3.75037	+	6.55563i	0.121935	+	0.213142i
$947$			24.6072i			0.799627i	0.916596	+	0.399814i	$0.130925\pi$
$947$			24.6072i			0.799627i	−0.916596	+	0.399814i	$0.869075\pi$
$948$	−18.2780	−	25.1574i	−0.593640	−	0.817076i
$949$	−2.19732	−	6.76266i	−0.0713281	−	0.219525i
$950$		0			0
$951$	−55.9496	−	40.6498i	−1.81429	−	1.31816i
$952$	0.324024	−	0.445980i	0.0105017	−	0.0144543i
$953$	10.3741	+	3.37076i	0.336051	+	0.109190i	0.472182	−	0.881501i	$-0.343467\pi$
$953$	10.3741	+	3.37076i	0.336051	+	0.109190i	−0.136131	+	0.990691i	$0.543467\pi$
$954$	−20.8528	−	64.1783i	−0.675134	−	2.07785i
$955$		0			0
$956$	8.96012			0.289791
$957$	−113.103	−	12.3404i	−3.65609	−	0.398908i
$958$			8.21267i			0.265339i
$959$	1.53156	−	1.11275i	0.0494568	−	0.0359324i
$960$		0			0
$961$	8.72970	−	26.8673i	0.281603	−	0.866686i
$962$	12.0909	−	16.6417i	0.389826	−	0.536549i
$963$	14.1232	−	19.4389i	0.455113	−	0.626409i
$964$	−3.30282	+	10.1650i	−0.106377	+	0.327394i
$965$		0			0
$966$	−0.0589916	+	0.0428599i	−0.00189802	+	0.00137899i
$967$			21.5493i			0.692980i	0.938054	+	0.346490i	$0.112626\pi$
$967$			21.5493i			0.692980i	−0.938054	+	0.346490i	$0.887374\pi$
$968$	10.9485	−	1.06317i	0.351898	−	0.0341717i
$969$	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	$0.632768\pi$
$972$	63.9367	+	20.7743i	2.05077	+	0.666336i
$973$	1.88374	−	2.59274i	0.0603899	−	0.0831195i
$974$	−22.6417	−	16.4501i	−0.725486	−	0.527096i
$975$		0			0
$976$	0.271786	+	0.836470i	0.00869964	+	0.0267748i
$977$	−18.8859	−	25.9943i	−0.604215	−	0.831630i	0.391871	−	0.920020i	$-0.371828\pi$
$977$	−18.8859	−	25.9943i	−0.604215	−	0.831630i	−0.996086	+	0.0883901i	$0.971828\pi$
$978$		−	7.28080i		−	0.232814i
$979$	−2.40899	+	22.0790i	−0.0769918	+	0.705648i
$980$		0			0
$981$	−74.7769	+	54.3286i	−2.38744	+	1.73458i
$982$	−13.5935	+	4.41679i	−0.433786	+	0.140946i
$983$	−27.1905	−	8.83474i	−0.867244	−	0.281785i	−0.158593	−	0.987344i	$-0.550696\pi$
$983$	−27.1905	−	8.83474i	−0.867244	−	0.281785i	−0.708651	+	0.705560i	$0.750696\pi$
$984$	12.7953	+	9.29633i	0.407899	+	0.296356i
$985$		0			0
$986$	9.26304	−	28.5087i	0.294995	−	0.907902i
$987$	3.81382	−	1.23919i	0.121395	−	0.0394437i
$988$	−9.63950	−	13.2676i	−0.306673	−	0.422099i
$989$	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	$0.451521\pi$
$992$	4.52442	+	6.22732i	0.143650	+	0.197718i
$993$	28.4436	−	9.24188i	0.902630	−	0.293282i
$994$	−0.0380941	+	0.117242i	−0.00120827	+	0.00371868i
$995$		0			0
$996$	8.67349	+	6.30166i	0.274830	+	0.199676i
$997$	33.0302	+	10.7321i	1.04608	+	0.339891i	0.781127	−	0.624372i	$-0.214645\pi$
$997$	33.0302	+	10.7321i	1.04608	+	0.339891i	0.264949	+	0.964263i	$0.414645\pi$
$998$	−4.66783	+	1.51667i	−0.147758	+	0.0480094i
$999$	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.ba.g.399.4		16
5.2	odd	4		550.2.h.k.201.1	✓	8
5.3	odd	4		550.2.h.m.201.2	yes	8
5.4	even	2	inner	550.2.ba.g.399.1		16
11.4	even	5	inner	550.2.ba.g.499.1		16
55.2	even	20		6050.2.a.cz.1.1		4
55.4	even	10	inner	550.2.ba.g.499.4		16
55.13	even	20		6050.2.a.dn.1.4		4
55.37	odd	20		550.2.h.k.301.1	yes	8
55.42	odd	20		6050.2.a.dg.1.1		4
55.48	odd	20		550.2.h.m.301.2	yes	8
55.53	odd	20		6050.2.a.df.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.k.201.1	✓	8	5.2	odd	4
550.2.h.k.301.1	yes	8	55.37	odd	20
550.2.h.m.201.2	yes	8	5.3	odd	4
550.2.h.m.301.2	yes	8	55.48	odd	20
550.2.ba.g.399.1		16	5.4	even	2	inner
550.2.ba.g.399.4		16	1.1	even	1	trivial
550.2.ba.g.499.1		16	11.4	even	5	inner
550.2.ba.g.499.4		16	55.4	even	10	inner
6050.2.a.cz.1.1		4	55.2	even	20
6050.2.a.df.1.4		4	55.53	odd	20
6050.2.a.dg.1.1		4	55.42	odd	20
6050.2.a.dn.1.4		4	55.13	even	20

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.ba (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(3.20812 - 1.04238i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.72899 + 1.98273i) q^{6} +(0.177866 + 0.0577923i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(6.77845 - 4.92483i) q^{9} +(-0.359735 + 3.29706i) q^{11} +3.37322i q^{12} +(-1.79219 - 2.46673i) q^{13} +(0.0577923 + 0.177866i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-1.73256 + 2.38467i) q^{17} +(7.96855 + 2.58914i) q^{18} +(-1.66209 - 5.11538i) q^{19} +0.630859 q^{21} +(-2.87882 + 1.64693i) q^{22} +0.115585i q^{23} +(-2.72899 + 1.98273i) q^{24} +(0.942208 - 2.89982i) q^{26} +(10.6644 - 14.6782i) q^{27} +(-0.109927 + 0.151302i) q^{28} +(-3.14256 + 9.67180i) q^{29} +(-6.22732 + 4.52442i) q^{31} -1.00000i q^{32} +(2.28272 + 10.9524i) q^{33} -2.94761 q^{34} +(2.58914 + 7.96855i) q^{36} +(6.41625 + 2.08477i) q^{37} +(3.16148 - 4.35140i) q^{38} +(-8.32083 - 6.04544i) q^{39} +(-1.44887 - 4.45917i) q^{41} +(0.370810 + 0.510376i) q^{42} -2.27719i q^{43} +(-3.02452 - 1.36098i) q^{44} +(-0.0935099 + 0.0679389i) q^{46} +(6.04544 - 1.96428i) q^{47} +(-3.20812 - 1.04238i) q^{48} +(-5.63482 - 4.09394i) q^{49} +(-3.07254 + 9.45631i) q^{51} +(2.89982 - 0.942208i) q^{52} +(-4.73399 - 6.51578i) q^{53} +18.1433 q^{54} -0.187020 q^{56} +(-10.6644 - 14.6782i) q^{57} +(-9.67180 + 3.14256i) q^{58} +(0.479439 - 1.47556i) q^{59} +(-0.711544 - 0.516967i) q^{61} +(-7.32066 - 2.37863i) q^{62} +(1.49028 - 0.484220i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-7.51889 + 8.28439i) q^{66} +9.03490i q^{67} +(-1.73256 - 2.38467i) q^{68} +(0.120483 + 0.370810i) q^{69} +(0.533268 + 0.387442i) q^{71} +(-4.92483 + 6.77845i) q^{72} +(2.21796 + 0.720659i) q^{73} +(2.08477 + 6.41625i) q^{74} +5.37863 q^{76} +(-0.254529 + 0.565646i) q^{77} -10.2851i q^{78} +(-7.45799 + 5.41855i) q^{79} +(11.1449 - 34.3003i) q^{81} +(2.75592 - 3.79320i) q^{82} +(1.86814 - 2.57128i) q^{83} +(-0.194946 + 0.599983i) q^{84} +(1.84229 - 1.33850i) q^{86} +34.3041i q^{87} +(-0.676718 - 3.24685i) q^{88} +6.69658 q^{89} +(-0.176211 - 0.542323i) q^{91} +(-0.109927 - 0.0357176i) q^{92} +(-15.2619 + 21.0061i) q^{93} +(5.14256 + 3.73629i) q^{94} +(-1.04238 - 3.20812i) q^{96} +(5.20431 + 7.16312i) q^{97} -6.96502i q^{98} +(13.7990 + 24.1206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 2 q^{6} + 48 q^{9} + 10 q^{11} + 4 q^{14} - 4 q^{16} - 34 q^{19} - 80 q^{21} + 2 q^{24} + 12 q^{26} - 4 q^{29} - 4 q^{31} - 4 q^{34} + 22 q^{36} - 48 q^{39} + 12 q^{41} - 20 q^{44} - 12 q^{46}+ \cdots + 144 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 2 * q^6 + 48 * q^9 + 10 * q^11 + 4 * q^14 - 4 * q^16 - 34 * q^19 - 80 * q^21 + 2 * q^24 + 12 * q^26 - 4 * q^29 - 4 * q^31 - 4 * q^34 + 22 * q^36 - 48 * q^39 + 12 * q^41 - 20 * q^44 - 12 * q^46 + 12 * q^49 - 34 * q^51 + 12 * q^54 - 24 * q^56 + 24 * q^59 - 4 * q^61 + 4 * q^64 - 54 * q^66 - 40 * q^69 + 40 * q^71 - 16 * q^74 + 4 * q^76 - 28 * q^79 + 70 * q^81 + 52 * q^86 - 4 * q^89 - 104 * q^91 + 36 * q^94 + 8 * q^96 + 144 * q^99

Introduction

L-functions

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