LMFDB - Embedded newform 950.2.l.m.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	950.101
Dual form			950.2.l.m.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-2.74319 - 0.998438i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.74319 + 0.998438i) q^{6} +(0.366794 - 0.635305i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(4.23006 + 3.54944i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-2.74319 - 0.998438i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.74319 + 0.998438i) q^{6} +(0.366794 - 0.635305i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(4.23006 + 3.54944i) q^{9} +(2.78239 + 4.81925i) q^{11} +(-1.45962 + 2.52813i) q^{12} +(2.81127 - 1.02322i) q^{13} +(-0.127386 - 0.722442i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(1.79794 - 1.50865i) q^{17} +5.52195 q^{18} +(4.10449 - 1.46738i) q^{19} +(-1.64050 + 1.37654i) q^{21} +(5.22919 + 1.90327i) q^{22} +(-0.521278 + 2.95631i) q^{23} +(0.506920 + 2.87489i) q^{24} +(1.49585 - 2.59088i) q^{26} +(-3.68109 - 6.37584i) q^{27} +(-0.561960 - 0.471541i) q^{28} +(-6.50377 - 5.45731i) q^{29} +(0.667440 - 1.15604i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-2.82090 - 15.9981i) q^{33} +(0.407560 - 2.31139i) q^{34} +(4.23006 - 3.54944i) q^{36} +4.27315 q^{37} +(2.20101 - 3.76239i) q^{38} -8.73346 q^{39} +(6.72682 + 2.44836i) q^{41} +(-0.371870 + 2.10898i) q^{42} +(0.0151416 + 0.0858725i) q^{43} +(5.22919 - 1.90327i) q^{44} +(1.50096 + 2.59974i) q^{46} +(-8.49186 - 7.12551i) q^{47} +(2.23627 + 1.87645i) q^{48} +(3.23092 + 5.59613i) q^{49} +(-6.43838 + 2.34338i) q^{51} +(-0.519502 - 2.94624i) q^{52} +(1.91640 - 10.8685i) q^{53} +(-6.91819 - 2.51802i) q^{54} -0.733587 q^{56} +(-12.7245 - 0.0727909i) q^{57} -8.49007 q^{58} +(-0.740001 + 0.620934i) q^{59} +(1.76164 - 9.99073i) q^{61} +(-0.231799 - 1.31460i) q^{62} +(3.80654 - 1.38547i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-12.4443 - 10.4420i) q^{66} +(-0.0888429 - 0.0745481i) q^{67} +(-1.17352 - 2.03260i) q^{68} +(4.38166 - 7.58925i) q^{69} +(-0.207583 - 1.17726i) q^{71} +(0.958877 - 5.43806i) q^{72} +(11.3670 + 4.13725i) q^{73} +(3.27342 - 2.74673i) q^{74} +(-0.732346 - 4.29694i) q^{76} +4.08226 q^{77} +(-6.69022 + 5.61376i) q^{78} +(-1.74198 - 0.634030i) q^{79} +(0.855411 + 4.85128i) q^{81} +(6.72682 - 2.44836i) q^{82} +(-8.09936 + 14.0285i) q^{83} +(1.07076 + 1.85461i) q^{84} +(0.0667970 + 0.0560493i) q^{86} +(12.3923 + 21.4640i) q^{87} +(2.78239 - 4.81925i) q^{88} +(15.2730 - 5.55893i) q^{89} +(0.381100 - 2.16132i) q^{91} +(2.82088 + 1.02672i) q^{92} +(-2.98515 + 2.50483i) q^{93} -11.0853 q^{94} +2.91924 q^{96} +(3.04266 - 2.55309i) q^{97} +(6.07215 + 2.21008i) q^{98} +(-5.33595 + 30.2617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 12 q^{7} - 15 q^{8}+O(q^{10}) $ 30 * q + 12 * q^7 - 15 * q^8	$ 30 q + 12 q^{7} - 15 q^{8} + 6 q^{11} + 6 q^{14} + 30 q^{18} + 24 q^{19} + 24 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 18 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{33} - 24 q^{37} + 12 q^{38} - 24 q^{39} - 3 q^{41} - 12 q^{42} - 6 q^{43} - 3 q^{44} - 48 q^{47} + 15 q^{49} - 90 q^{51} + 18 q^{53} + 18 q^{54} - 24 q^{56} + 42 q^{57} - 36 q^{58} - 18 q^{59} - 60 q^{61} + 24 q^{62} + 21 q^{63} - 15 q^{64} - 78 q^{66} + 30 q^{67} + 12 q^{68} + 24 q^{69} - 30 q^{73} - 9 q^{74} - 3 q^{76} - 78 q^{77} - 6 q^{79} + 60 q^{81} - 3 q^{82} + 42 q^{83} - 6 q^{84} + 12 q^{86} + 54 q^{87} + 6 q^{88} - 30 q^{89} - 6 q^{91} + 6 q^{92} - 72 q^{93} - 78 q^{94} + 42 q^{97} - 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q + 12 * q^7 - 15 * q^8 + 6 * q^11 + 6 * q^14 + 30 * q^18 + 24 * q^19 + 24 * q^21 - 3 * q^22 - 3 * q^23 + 3 * q^26 + 18 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^33 - 24 * q^37 + 12 * q^38 - 24 * q^39 - 3 * q^41 - 12 * q^42 - 6 * q^43 - 3 * q^44 - 48 * q^47 + 15 * q^49 - 90 * q^51 + 18 * q^53 + 18 * q^54 - 24 * q^56 + 42 * q^57 - 36 * q^58 - 18 * q^59 - 60 * q^61 + 24 * q^62 + 21 * q^63 - 15 * q^64 - 78 * q^66 + 30 * q^67 + 12 * q^68 + 24 * q^69 - 30 * q^73 - 9 * q^74 - 3 * q^76 - 78 * q^77 - 6 * q^79 + 60 * q^81 - 3 * q^82 + 42 * q^83 - 6 * q^84 + 12 * q^86 + 54 * q^87 + 6 * q^88 - 30 * q^89 - 6 * q^91 + 6 * q^92 - 72 * q^93 - 78 * q^94 + 42 * q^97 - 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−2.74319	−	0.998438i	−1.58378	−	0.576449i	−0.607758	−	0.794122i	$-0.707931\pi$
$3$	−2.74319	−	0.998438i	−1.58378	−	0.576449i	−0.976022	+	0.217673i	$0.930153\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−2.74319	+	0.998438i	−1.11990	+	0.407611i
$7$	0.366794	−	0.635305i	0.138635	−	0.240123i	−0.788345	−	0.615233i	$-0.789062\pi$
$7$	0.366794	−	0.635305i	0.138635	−	0.240123i	0.926980	+	0.375110i	$0.122395\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	4.23006	+	3.54944i	1.41002	+	1.18315i
$10$		0			0
$11$	2.78239	+	4.81925i	0.838923	+	1.45306i	0.890796	+	0.454404i	$0.150148\pi$
$11$	2.78239	+	4.81925i	0.838923	+	1.45306i	−0.0518725	+	0.998654i	$0.516519\pi$
$12$	−1.45962	+	2.52813i	−0.421356	+	0.729810i
$13$	2.81127	−	1.02322i	0.779706	−	0.283790i	0.0786559	−	0.996902i	$-0.474937\pi$
$13$	2.81127	−	1.02322i	0.779706	−	0.283790i	0.701050	+	0.713112i	$0.252715\pi$
$14$	−0.127386	−	0.722442i	−0.0340454	−	0.193081i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.79794	−	1.50865i	0.436064	−	0.365901i	−0.398170	−	0.917312i	$-0.630355\pi$
$17$	1.79794	−	1.50865i	0.436064	−	0.365901i	0.834234	+	0.551410i	$0.185910\pi$
$18$	5.52195			1.30154
$19$	4.10449	−	1.46738i	0.941634	−	0.336639i
$19$	4.10449	−	1.46738i	0.941634	−	0.336639i
$20$		0			0
$21$	−1.64050	+	1.37654i	−0.357986	+	0.300386i
$22$	5.22919	+	1.90327i	1.11487	+	0.405778i
$23$	−0.521278	+	2.95631i	−0.108694	+	0.616434i	0.880987	+	0.473141i	$0.156880\pi$
$23$	−0.521278	+	2.95631i	−0.108694	+	0.616434i	−0.989680	+	0.143292i	$0.954231\pi$
$24$	0.506920	+	2.87489i	0.103475	+	0.586834i
$25$		0			0
$26$	1.49585	−	2.59088i	0.293359	−	0.508113i
$27$	−3.68109	−	6.37584i	−0.708427	−	1.22703i
$28$	−0.561960	−	0.471541i	−0.106201	−	0.0891128i
$29$	−6.50377	−	5.45731i	−1.20772	−	1.01340i	−0.999375	−	0.0353424i	$-0.988748\pi$
$29$	−6.50377	−	5.45731i	−1.20772	−	1.01340i	−0.208345	−	0.978055i	$-0.566808\pi$
$30$		0			0
$31$	0.667440	−	1.15604i	0.119876	−	0.207631i	−0.799843	−	0.600210i	$-0.795084\pi$
$31$	0.667440	−	1.15604i	0.119876	−	0.207631i	0.919718	+	0.392579i	$0.128417\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−2.82090	−	15.9981i	−0.491056	−	2.78492i
$34$	0.407560	−	2.31139i	0.0698959	−	0.396400i
$35$		0			0
$36$	4.23006	−	3.54944i	0.705010	−	0.591574i
$37$	4.27315			0.702501			0.351251	−	0.936281i	$-0.385757\pi$
$37$	4.27315			0.702501			0.351251	+	0.936281i	$0.385757\pi$
$38$	2.20101	−	3.76239i	0.357051	−	0.610340i
$39$	−8.73346			−1.39847
$40$		0			0
$41$	6.72682	+	2.44836i	1.05055	+	0.382370i	0.808871	−	0.587986i	$-0.200079\pi$
$41$	6.72682	+	2.44836i	1.05055	+	0.382370i	0.241681	+	0.970356i	$0.422301\pi$
$42$	−0.371870	+	2.10898i	−0.0573808	+	0.325423i
$43$	0.0151416	+	0.0858725i	0.00230908	+	0.0130954i	0.985941	−	0.167097i	$-0.0534392\pi$
$43$	0.0151416	+	0.0858725i	0.00230908	+	0.0130954i	−0.983631	+	0.180192i	$0.942328\pi$
$44$	5.22919	−	1.90327i	0.788330	−	0.286929i
$45$		0			0
$46$	1.50096	+	2.59974i	0.221304	+	0.383310i
$47$	−8.49186	−	7.12551i	−1.23866	−	1.03936i	−0.997627	−	0.0688472i	$-0.978068\pi$
$47$	−8.49186	−	7.12551i	−1.23866	−	1.03936i	−0.241037	−	0.970516i	$-0.577488\pi$
$48$	2.23627	+	1.87645i	0.322777	+	0.270842i
$49$	3.23092	+	5.59613i	0.461561	+	0.799447i
$50$		0			0
$51$	−6.43838	+	2.34338i	−0.901553	+	0.328139i
$52$	−0.519502	−	2.94624i	−0.0720419	−	0.408570i
$53$	1.91640	−	10.8685i	0.263238	−	1.49290i	−0.510768	−	0.859719i	$-0.670639\pi$
$53$	1.91640	−	10.8685i	0.263238	−	1.49290i	0.774006	−	0.633178i	$-0.218250\pi$
$54$	−6.91819	−	2.51802i	−0.941447	−	0.342659i
$55$		0			0
$56$	−0.733587			−0.0980297
$57$	−12.7245	−	0.0727909i	−1.68540	−	0.00964140i
$58$	−8.49007			−1.11480
$59$	−0.740001	+	0.620934i	−0.0963399	+	0.0808387i	−0.689685	−	0.724109i	$-0.742251\pi$
$59$	−0.740001	+	0.620934i	−0.0963399	+	0.0808387i	0.593346	+	0.804948i	$0.297807\pi$
$60$		0			0
$61$	1.76164	−	9.99073i	0.225554	−	1.27918i	−0.636068	−	0.771633i	$-0.719440\pi$
$61$	1.76164	−	9.99073i	0.225554	−	1.27918i	0.861623	−	0.507550i	$-0.169449\pi$
$62$	−0.231799	−	1.31460i	−0.0294385	−	0.166954i
$63$	3.80654	−	1.38547i	0.479579	−	0.174552i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−12.4443	−	10.4420i	−1.53179	−	1.28533i
$67$	−0.0888429	−	0.0745481i	−0.0108539	−	0.00910750i	0.637345	−	0.770579i	$-0.280033\pi$
$67$	−0.0888429	−	0.0745481i	−0.0108539	−	0.00910750i	−0.648198	+	0.761471i	$0.724477\pi$
$68$	−1.17352	−	2.03260i	−0.142310	−	0.246489i
$69$	4.38166	−	7.58925i	0.527490	−	0.913639i
$70$		0			0
$71$	−0.207583	−	1.17726i	−0.0246356	−	0.139715i	0.970009	−	0.243068i	$-0.0781539\pi$
$71$	−0.207583	−	1.17726i	−0.0246356	−	0.139715i	−0.994645	+	0.103353i	$0.967043\pi$
$72$	0.958877	−	5.43806i	0.113005	−	0.640882i
$73$	11.3670	+	4.13725i	1.33041	+	0.484228i	0.906778	−	0.421608i	$-0.138534\pi$
$73$	11.3670	+	4.13725i	1.33041	+	0.484228i	0.423628	+	0.905836i	$0.360756\pi$
$74$	3.27342	−	2.74673i	0.380528	−	0.319301i
$75$		0			0
$76$	−0.732346	−	4.29694i	−0.0840059	−	0.492892i
$77$	4.08226			0.465216
$78$	−6.69022	+	5.61376i	−0.757518	+	0.635633i
$79$	−1.74198	−	0.634030i	−0.195988	−	0.0713340i	0.242161	−	0.970236i	$-0.422144\pi$
$79$	−1.74198	−	0.634030i	−0.195988	−	0.0713340i	−0.438150	+	0.898902i	$0.644366\pi$
$80$		0			0
$81$	0.855411	+	4.85128i	0.0950457	+	0.539031i
$82$	6.72682	−	2.44836i	0.742853	−	0.270376i
$83$	−8.09936	+	14.0285i	−0.889020	+	1.53983i	−0.0479841	+	0.998848i	$0.515280\pi$
$83$	−8.09936	+	14.0285i	−0.889020	+	1.53983i	−0.841036	+	0.540979i	$0.818054\pi$
$84$	1.07076	+	1.85461i	0.116829	+	0.202354i
$85$		0			0
$86$	0.0667970	+	0.0560493i	0.00720290	+	0.00604395i
$87$	12.3923	+	21.4640i	1.32859	+	2.30119i
$88$	2.78239	−	4.81925i	0.296604	−	0.513733i
$89$	15.2730	−	5.55893i	1.61894	−	0.589246i	0.635760	−	0.771887i	$-0.280687\pi$
$89$	15.2730	−	5.55893i	1.61894	−	0.589246i	0.983180	+	0.182642i	$0.0584648\pi$
$90$		0			0
$91$	0.381100	−	2.16132i	0.0399501	−	0.226568i
$92$	2.82088	+	1.02672i	0.294097	+	0.107043i
$93$	−2.98515	+	2.50483i	−0.309545	+	0.259739i
$94$	−11.0853			−1.14336
$95$		0			0
$96$	2.91924			0.297944
$97$	3.04266	−	2.55309i	0.308935	−	0.259227i	−0.475117	−	0.879923i	$-0.657594\pi$
$97$	3.04266	−	2.55309i	0.308935	−	0.259227i	0.784052	+	0.620696i	$0.213150\pi$
$98$	6.07215	+	2.21008i	0.613380	+	0.223252i
$99$	−5.33595	+	30.2617i	−0.536283	+	3.04141i
$100$		0			0
$101$	7.24642	−	2.63748i	0.721046	−	0.262439i	0.0446761	−	0.999002i	$-0.485774\pi$
$101$	7.24642	−	2.63748i	0.721046	−	0.262439i	0.676370	+	0.736562i	$0.263552\pi$
$102$	−3.42579	+	5.93364i	−0.339204	+	0.587518i
$103$	0.169642	+	0.293829i	0.0167153	+	0.0289518i	0.874262	−	0.485454i	$-0.161346\pi$
$103$	0.169642	+	0.293829i	0.0167153	+	0.0289518i	−0.857547	+	0.514406i	$0.828012\pi$
$104$	−2.29177	−	1.92302i	−0.224726	−	0.188568i
$105$		0			0
$106$	−5.51806	−	9.55756i	−0.535961	−	0.928312i
$107$	−0.0434930	+	0.0753321i	−0.00420463	+	0.00728263i	−0.868120	−	0.496354i	$-0.834672\pi$
$107$	−0.0434930	+	0.0753321i	−0.00420463	+	0.00728263i	0.863915	+	0.503637i	$0.168005\pi$
$108$	−6.91819	+	2.51802i	−0.665703	+	0.242296i
$109$	−0.536758	−	3.04411i	−0.0514121	−	0.291573i	0.948251	−	0.317521i	$-0.102850\pi$
$109$	−0.536758	−	3.04411i	−0.0514121	−	0.291573i	−0.999663	+	0.0259486i	$0.991739\pi$
$110$		0			0
$111$	−11.7220	−	4.26648i	−1.11261	−	0.404956i
$112$	−0.561960	+	0.471541i	−0.0531003	+	0.0445564i
$113$	4.33262			0.407579			0.203789	−	0.979015i	$-0.434674\pi$
$113$	4.33262			0.407579			0.203789	+	0.979015i	$0.434674\pi$
$114$	−9.79429	+	8.12336i	−0.917319	+	0.760823i
$115$		0			0
$116$	−6.50377	+	5.45731i	−0.603860	+	0.506699i
$117$	15.5237	+	5.65017i	1.43517	+	0.522358i
$118$	−0.167744	+	0.951326i	−0.0154421	+	0.0875767i
$119$	−0.298981	−	1.69560i	−0.0274075	−	0.155436i
$120$		0			0
$121$	−9.98343	+	17.2918i	−0.907584	+	1.57198i
$122$	−5.07243	−	8.78570i	−0.459236	−	0.795420i
$123$	−16.0084	−	13.4326i	−1.44343	−	1.21118i
$124$	−1.02258	−	0.858044i	−0.0918301	−	0.0770546i
$125$		0			0
$126$	2.02542	−	3.50813i	0.180439	−	0.312529i
$127$	2.15310	−	0.783665i	0.191057	−	0.0695391i	−0.244720	−	0.969594i	$-0.578696\pi$
$127$	2.15310	−	0.783665i	0.191057	−	0.0695391i	0.435777	+	0.900055i	$0.356474\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	0.0442021	−	0.250682i	0.00389178	−	0.0220714i
$130$		0			0
$131$	−4.06852	+	3.41389i	−0.355468	+	0.298273i	−0.802981	−	0.596004i	$-0.796754\pi$
$131$	−4.06852	+	3.41389i	−0.355468	+	0.298273i	0.447513	+	0.894277i	$0.352310\pi$
$132$	−16.2449			−1.41394
$133$	0.573268	−	3.14582i	0.0497086	−	0.272778i
$134$	−0.115976			−0.0100188
$135$		0			0
$136$	−2.20550	−	0.802736i	−0.189120	−	0.0688341i
$137$	−1.51134	+	8.57122i	−0.129122	+	0.732289i	0.849651	+	0.527345i	$0.176812\pi$
$137$	−1.51134	+	8.57122i	−0.129122	+	0.732289i	−0.978774	+	0.204944i	$0.934299\pi$
$138$	−1.52173	−	8.63018i	−0.129539	−	0.734650i
$139$	21.6733	−	7.88844i	1.83831	−	0.669088i	0.848033	−	0.529943i	$-0.177787\pi$
$139$	21.6733	−	7.88844i	1.83831	−	0.669088i	0.990272	−	0.139146i	$-0.0444356\pi$
$140$		0			0
$141$	16.1804	+	28.0252i	1.36263	+	2.36015i
$142$	−0.915747	−	0.768403i	−0.0768478	−	0.0644830i
$143$	12.7532	+	10.7012i	1.06648	+	0.894880i
$144$	−2.76098	−	4.78215i	−0.230081	−	0.398513i
$145$		0			0
$146$	11.3670	−	4.13725i	0.940740	−	0.342401i
$147$	−3.27564	−	18.5771i	−0.270171	−	1.53221i
$148$	0.742024	−	4.20823i	0.0609940	−	0.345914i
$149$	−15.4164	−	5.61111i	−1.26296	−	0.459680i	−0.378199	−	0.925724i	$-0.623456\pi$
$149$	−15.4164	−	5.61111i	−1.26296	−	0.459680i	−0.884761	+	0.466045i	$0.845679\pi$
$150$		0			0
$151$	−0.916548			−0.0745876			−0.0372938	−	0.999304i	$-0.511874\pi$
$151$	−0.916548			−0.0745876			−0.0372938	+	0.999304i	$0.511874\pi$
$152$	−3.32303	−	2.82090i	−0.269533	−	0.228805i
$153$	12.9603			1.04778
$154$	3.12719	−	2.62402i	0.251996	−	0.211450i
$155$		0			0
$156$	−1.51655	+	8.60078i	−0.121421	+	0.688613i
$157$	−2.87960	−	16.3310i	−0.229817	−	1.30336i	−0.853259	−	0.521487i	$-0.825378\pi$
$157$	−2.87960	−	16.3310i	−0.229817	−	1.30336i	0.623443	−	0.781869i	$-0.285734\pi$
$158$	−1.74198	+	0.634030i	−0.138585	+	0.0504407i
$159$	−16.1085	+	27.9008i	−1.27749	+	2.21268i
$160$		0			0
$161$	1.68696	+	1.41553i	0.132951	+	0.111559i
$162$	3.77363	+	3.16645i	0.296484	+	0.248780i
$163$	5.14215	+	8.90646i	0.402764	+	0.697608i	0.994058	−	0.108848i	$-0.0347161\pi$
$163$	5.14215	+	8.90646i	0.402764	+	0.697608i	−0.591294	+	0.806456i	$0.701383\pi$
$164$	3.57927	−	6.19947i	0.279494	−	0.484097i
$165$		0			0
$166$	2.81288	+	15.9526i	0.218322	+	1.23816i
$167$	−3.56484	+	20.2172i	−0.275855	+	1.56445i	0.460377	+	0.887724i	$0.347714\pi$
$167$	−3.56484	+	20.2172i	−0.275855	+	1.56445i	−0.736232	+	0.676729i	$0.763397\pi$
$168$	2.01237	+	0.732442i	0.155257	+	0.0565091i
$169$	−3.10232	+	2.60315i	−0.238640	+	0.200243i
$170$		0			0
$171$	22.5706	+	8.36155i	1.72602	+	0.639424i
$172$	0.0871972			0.00664873
$173$	−9.16166	+	7.68754i	−0.696548	+	0.584473i	−0.920789	−	0.390061i	$-0.872454\pi$
$173$	−9.16166	+	7.68754i	−0.696548	+	0.584473i	0.224241	+	0.974534i	$0.428010\pi$
$174$	23.2899	+	8.47682i	1.76560	+	0.642626i
$175$		0			0
$176$	−0.966315	−	5.48025i	−0.0728387	−	0.413089i
$177$	2.64992	−	0.964494i	0.199181	−	0.0724958i
$178$	8.12662	−	14.0757i	0.609116	−	1.05502i
$179$	−4.60425	−	7.97480i	−0.344138	−	0.596065i	0.641059	−	0.767492i	$-0.278495\pi$
$179$	−4.60425	−	7.97480i	−0.344138	−	0.596065i	−0.985197	+	0.171427i	$0.945162\pi$
$180$		0			0
$181$	−12.6692	−	10.6307i	−0.941691	−	0.790172i	0.0361881	−	0.999345i	$-0.488478\pi$
$181$	−12.6692	−	10.6307i	−0.941691	−	0.790172i	−0.977879	+	0.209173i	$0.932923\pi$
$182$	−1.09733	−	1.90064i	−0.0813397	−	0.140885i
$183$	−14.8076	+	25.6476i	−1.09461	+	1.89592i
$184$	2.82088	−	1.02672i	0.207958	−	0.0756905i
$185$		0			0
$186$	−0.676678	+	3.83763i	−0.0496164	+	0.281389i
$187$	12.2731	+	4.46706i	0.897500	+	0.326663i
$188$	−8.49186	+	7.12551i	−0.619332	+	0.519682i
$189$	−5.40081			−0.392851
$190$		0			0
$191$	19.0304			1.37699			0.688496	−	0.725240i	$-0.258271\pi$
$191$	19.0304			1.37699			0.688496	+	0.725240i	$0.258271\pi$
$192$	2.23627	−	1.87645i	0.161389	−	0.135421i
$193$	9.24973	+	3.36663i	0.665810	+	0.242335i	0.652743	−	0.757579i	$-0.273618\pi$
$193$	9.24973	+	3.36663i	0.665810	+	0.242335i	0.0130674	+	0.999915i	$0.495840\pi$
$194$	0.689714	−	3.91156i	0.0495186	−	0.280834i
$195$		0			0
$196$	6.07215	−	2.21008i	0.433725	−	0.157863i
$197$	−8.59680	+	14.8901i	−0.612497	+	1.06088i	0.378322	+	0.925674i	$0.376501\pi$
$197$	−8.59680	+	14.8901i	−0.612497	+	1.06088i	−0.990818	+	0.135201i	$0.956832\pi$
$198$	15.3643	+	26.6117i	1.09189	+	1.89121i
$199$	−9.93399	−	8.33561i	−0.704202	−	0.590896i	0.218764	−	0.975778i	$-0.429798\pi$
$199$	−9.93399	−	8.33561i	−0.704202	−	0.590896i	−0.922966	+	0.384882i	$0.874242\pi$
$200$		0			0
$201$	0.169281	+	0.293204i	0.0119402	+	0.0206810i
$202$	3.85574	−	6.67834i	0.271289	−	0.469886i
$203$	−5.85260	+	2.13017i	−0.410772	+	0.149509i
$204$	1.18976	+	6.74749i	0.0833002	+	0.472419i
$205$		0			0
$206$	0.318823	+	0.116042i	0.0222134	+	0.00808503i
$207$	−12.6983	+	10.6551i	−0.882593	+	0.740583i
$208$	−2.99169			−0.207436
$209$	18.4919	+	15.6977i	1.27911	+	1.08583i
$210$		0			0
$211$	−0.114083	+	0.0957271i	−0.00785380	+	0.00659012i	−0.646706	−	0.762739i	$-0.723854\pi$
$211$	−0.114083	+	0.0957271i	−0.00785380	+	0.00659012i	0.638852	+	0.769329i	$0.279410\pi$
$212$	−10.3706	−	3.77457i	−0.712253	−	0.259239i
$213$	−0.605985	+	3.43671i	−0.0415214	+	0.235479i
$214$	0.0151050	+	0.0856645i	0.00103255	+	0.00585590i
$215$		0			0
$216$	−3.68109	+	6.37584i	−0.250467	+	0.433821i
$217$	−0.489625	−	0.848056i	−0.0332379	−	0.0575698i
$218$	−2.36790	−	1.98690i	−0.160374	−	0.134570i
$219$	−27.0510	−	22.6985i	−1.82794	−	1.53382i
$220$		0			0
$221$	3.51081	−	6.08091i	0.236163	−	0.409046i
$222$	−11.7220	+	4.26648i	−0.786732	+	0.286347i
$223$	0.160642	+	0.911048i	0.0107574	+	0.0610083i	0.989714	−	0.143061i	$-0.0456944\pi$
$223$	0.160642	+	0.911048i	0.0107574	+	0.0610083i	−0.978957	+	0.204069i	$0.934583\pi$
$224$	−0.127386	+	0.722442i	−0.00851134	+	0.0482702i
$225$		0			0
$226$	3.31898	−	2.78496i	0.220775	−	0.185253i
$227$	10.5087			0.697489			0.348744	−	0.937218i	$-0.386608\pi$
$227$	10.5087			0.697489			0.348744	+	0.937218i	$0.386608\pi$
$228$	−2.28126	+	12.5185i	−0.151080	+	0.829058i
$229$	1.65736			0.109522			0.0547608	−	0.998499i	$-0.482560\pi$
$229$	1.65736			0.109522			0.0547608	+	0.998499i	$0.482560\pi$
$230$		0			0
$231$	−11.1984	−	4.07588i	−0.736800	−	0.268173i
$232$	−1.47429	+	8.36109i	−0.0967916	+	0.548932i
$233$	2.42768	+	13.7681i	0.159043	+	0.901977i	0.954996	+	0.296619i	$0.0958590\pi$
$233$	2.42768	+	13.7681i	0.159043	+	0.901977i	−0.795953	+	0.605358i	$0.793030\pi$
$234$	15.5237	−	5.65017i	1.01482	−	0.369363i
$235$		0			0
$236$	0.483001	+	0.836582i	0.0314407	+	0.0544569i
$237$	4.14555	+	3.47853i	0.269282	+	0.225955i
$238$	−1.31895	−	1.10673i	−0.0854945	−	0.0717384i
$239$	3.19315	+	5.53069i	0.206548	+	0.357751i	0.950625	−	0.310343i	$-0.100444\pi$
$239$	3.19315	+	5.53069i	0.206548	+	0.357751i	−0.744077	+	0.668094i	$0.767111\pi$
$240$		0			0
$241$	−7.33975	+	2.67145i	−0.472795	+	0.172083i	−0.567418	−	0.823430i	$-0.692058\pi$
$241$	−7.33975	+	2.67145i	−0.472795	+	0.172083i	0.0946233	+	0.995513i	$0.469835\pi$
$242$	3.46721	+	19.6635i	0.222881	+	1.26402i
$243$	−1.33814	+	7.58897i	−0.0858418	+	0.486833i
$244$	−9.53305	−	3.46975i	−0.610291	−	0.222128i
$245$		0			0
$246$	−20.8975			−1.33237
$247$	10.0374	−	8.32498i	0.638663	−	0.529705i
$248$	−1.33488			−0.0847649
$249$	36.2246	−	30.3961i	2.29564	−	1.92627i
$250$		0			0
$251$	0.460441	−	2.61129i	0.0290628	−	0.164823i	−0.966822	−	0.255451i	$-0.917776\pi$
$251$	0.460441	−	2.61129i	0.0290628	−	0.164823i	0.995885	+	0.0906275i	$0.0288873\pi$
$252$	−0.703420	−	3.98929i	−0.0443113	−	0.251302i
$253$	−15.6976	+	5.71346i	−0.986899	+	0.359202i
$254$	1.14564	−	1.98431i	0.0718840	−	0.124507i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	6.82951	+	5.73064i	0.426013	+	0.357467i	0.830445	−	0.557101i	$-0.188086\pi$
$257$	6.82951	+	5.73064i	0.426013	+	0.357467i	−0.404432	+	0.914568i	$0.632531\pi$
$258$	−0.127275	−	0.220446i	−0.00792378	−	0.0137244i
$259$	1.56736	−	2.71475i	0.0973912	−	0.168687i
$260$		0			0
$261$	−8.14094	−	46.1696i	−0.503911	−	2.85782i
$262$	−0.922258	+	5.23038i	−0.0569773	+	0.323134i
$263$	−17.1765	−	6.25175i	−1.05915	−	0.385499i	−0.247042	−	0.969005i	$-0.579458\pi$
$263$	−17.1765	−	6.25175i	−1.05915	−	0.385499i	−0.812109	+	0.583506i	$0.801681\pi$
$264$	−12.4443	+	10.4420i	−0.765897	+	0.642664i
$265$		0			0
$266$	−1.58295	−	2.77833i	−0.0970568	−	0.170350i
$267$	−47.4471			−2.90371
$268$	−0.0888429	+	0.0745481i	−0.00542695	+	0.00455375i
$269$	19.8430	+	7.22226i	1.20985	+	0.440349i	0.866651	−	0.498914i	$-0.166268\pi$
$269$	19.8430	+	7.22226i	1.20985	+	0.440349i	0.343198	+	0.939263i	$0.388490\pi$
$270$		0			0
$271$	0.209616	+	1.18879i	0.0127333	+	0.0722139i	0.990512	−	0.137424i	$-0.0438824\pi$
$271$	0.209616	+	1.18879i	0.0127333	+	0.0722139i	−0.977779	+	0.209638i	$0.932771\pi$
$272$	−2.20550	+	0.802736i	−0.133728	+	0.0486730i
$273$	−3.20338	+	5.54841i	−0.193877	+	0.335805i
$274$	4.35172	+	7.53741i	0.262897	+	0.455351i
$275$		0			0
$276$	−6.71309	−	5.63295i	−0.404080	−	0.339064i
$277$	0.820174	+	1.42058i	0.0492795	+	0.0853546i	0.889613	−	0.456715i	$-0.150974\pi$
$277$	0.820174	+	1.42058i	0.0492795	+	0.0853546i	−0.840333	+	0.542070i	$0.817641\pi$
$278$	11.5321	−	19.9742i	0.691651	−	1.19797i
$279$	6.92661	−	2.52108i	0.414685	−	0.150933i
$280$		0			0
$281$	3.66817	−	20.8032i	0.218825	−	1.24102i	−0.655320	−	0.755351i	$-0.727466\pi$
$281$	3.66817	−	20.8032i	0.218825	−	1.24102i	0.874145	−	0.485665i	$-0.161422\pi$
$282$	30.4091	+	11.0680i	1.81084	+	0.659091i
$283$	17.9155	−	15.0329i	1.06497	−	0.893615i	0.0703816	−	0.997520i	$-0.477578\pi$
$283$	17.9155	−	15.0329i	1.06497	−	0.893615i	0.994587	+	0.103905i	$0.0331339\pi$
$284$	−1.19542			−0.0709353
$285$		0			0
$286$	16.6481			0.984424
$287$	4.02281	−	3.37554i	0.237459	−	0.199252i
$288$	−5.18894	−	1.88862i	−0.305761	−	0.111288i
$289$	−1.99546	+	11.3168i	−0.117380	+	0.665695i
$290$		0			0
$291$	−10.8957	+	3.96570i	−0.638716	+	0.232474i
$292$	6.04825	−	10.4759i	0.353947	−	0.613055i
$293$	−10.2867	−	17.8171i	−0.600955	−	1.04088i	−0.992677	−	0.120801i	$-0.961454\pi$
$293$	−10.2867	−	17.8171i	−0.600955	−	1.04088i	0.391722	−	0.920084i	$-0.371880\pi$
$294$	−14.4504	−	12.1253i	−0.842766	−	0.707164i
$295$		0			0
$296$	−2.13657	−	3.70066i	−0.124186	−	0.215096i
$297$	20.4845	−	35.4802i	1.18863	−	2.05877i
$298$	−15.4164	+	5.61111i	−0.893048	+	0.325043i
$299$	1.55950	+	8.84437i	0.0901883	+	0.511483i
$300$		0			0
$301$	0.0601091	+	0.0218779i	0.00346463	+	0.00126102i
$302$	−0.702116	+	0.589146i	−0.0404023	+	0.0339015i
$303$	−22.5116			−1.29326
$304$	−4.35883	−	0.0249349i	−0.249996	−	0.00143011i
$305$		0			0
$306$	9.92814	−	8.33070i	0.567554	−	0.476234i
$307$	−5.17393	−	1.88316i	−0.295292	−	0.107477i	0.190126	−	0.981760i	$-0.439110\pi$
$307$	−5.17393	−	1.88316i	−0.295292	−	0.107477i	−0.485418	+	0.874282i	$0.661333\pi$
$308$	0.708876	−	4.02024i	0.0403920	−	0.229074i
$309$	−0.171990	−	0.975404i	−0.00978417	−	0.0554888i
$310$		0			0
$311$	−10.6100	+	18.3771i	−0.601638	+	1.04207i	0.390935	+	0.920418i	$0.372152\pi$
$311$	−10.6100	+	18.3771i	−0.601638	+	1.04207i	−0.992573	+	0.121650i	$0.961182\pi$
$312$	4.36673	+	7.56340i	0.247217	+	0.428193i
$313$	−3.94257	−	3.30821i	−0.222847	−	0.186991i	0.524528	−	0.851393i	$-0.324242\pi$
$313$	−3.94257	−	3.30821i	−0.222847	−	0.186991i	−0.747375	+	0.664402i	$0.768686\pi$
$314$	−12.7033	−	10.6593i	−0.716887	−	0.601539i
$315$		0			0
$316$	−0.926890	+	1.60542i	−0.0521417	+	0.0903120i
$317$	−15.0211	+	5.46722i	−0.843668	+	0.307070i	−0.727456	−	0.686155i	$-0.759297\pi$
$317$	−15.0211	+	5.46722i	−0.843668	+	0.307070i	−0.116212	+	0.993224i	$0.537075\pi$
$318$	5.59443	+	31.7276i	0.313720	+	1.77920i
$319$	8.20409	−	46.5277i	0.459341	−	2.60505i
$320$		0			0
$321$	0.194524	−	0.163225i	0.0108573	−	0.00911032i
$322$	2.20217			0.122722
$323$	5.16586	−	8.83049i	0.287436	−	0.491341i
$324$	4.92612			0.273673
$325$		0			0
$326$	9.66408	+	3.51744i	0.535244	+	0.194813i
$327$	−1.56693	+	8.88648i	−0.0866512	+	0.491423i
$328$	−1.24307	−	7.04978i	−0.0686368	−	0.389259i
$329$	−7.64163	+	2.78133i	−0.421297	+	0.153340i
$330$		0			0
$331$	−11.9292	−	20.6621i	−0.655691	−	1.13569i	−0.981720	−	0.190330i	$-0.939044\pi$
$331$	−11.9292	−	20.6621i	−0.655691	−	1.13569i	0.326029	−	0.945360i	$-0.394289\pi$
$332$	12.4089	+	10.4123i	0.681029	+	0.571451i
$333$	18.0757	+	15.1673i	0.990541	+	0.831163i
$334$	10.2645	+	17.7787i	0.561650	+	0.972807i
$335$		0			0
$336$	2.01237	−	0.732442i	0.109784	−	0.0399580i
$337$	0.468549	+	2.65728i	0.0255235	+	0.144751i	0.994906	−	0.100803i	$-0.0321412\pi$
$337$	0.468549	+	2.65728i	0.0255235	+	0.144751i	−0.969383	+	0.245554i	$0.921030\pi$
$338$	−0.703238	+	3.98826i	−0.0382511	+	0.216933i
$339$	−11.8852	−	4.32586i	−0.645515	−	0.234948i
$340$		0			0
$341$	7.42832			0.402266
$342$	22.6648	−	8.10278i	1.22557	−	0.438148i
$343$	9.87544			0.533224
$344$	0.0667970	−	0.0560493i	0.00360145	−	0.00302198i
$345$		0			0
$346$	−2.07678	+	11.7780i	−0.111648	+	0.633189i
$347$	−5.22111	−	29.6104i	−0.280284	−	1.58957i	−0.721661	−	0.692246i	$-0.756621\pi$
$347$	−5.22111	−	29.6104i	−0.280284	−	1.58957i	0.441378	−	0.897321i	$-0.354490\pi$
$348$	23.2899	−	8.47682i	1.24847	−	0.454405i
$349$	0.996459	−	1.72592i	0.0533392	−	0.0923862i	−0.838123	−	0.545481i	$-0.816347\pi$
$349$	0.996459	−	1.72592i	0.0533392	−	0.0923862i	0.891462	+	0.453095i	$0.149680\pi$
$350$		0			0
$351$	−16.8724	−	14.1576i	−0.900583	−	0.755679i
$352$	−4.26287	−	3.57698i	−0.227212	−	0.190653i
$353$	−3.87236	−	6.70712i	−0.206105	−	0.356984i	0.744379	−	0.667757i	$-0.232745\pi$
$353$	−3.87236	−	6.70712i	−0.206105	−	0.356984i	−0.950484	+	0.310773i	$0.899412\pi$
$354$	1.41000	−	2.44218i	0.0749404	−	0.129801i
$355$		0			0
$356$	−2.82234	−	16.0063i	−0.149584	−	0.848333i
$357$	−0.872796	+	4.94987i	−0.0461932	+	0.261975i
$358$	−8.65317	−	3.14949i	−0.457334	−	0.166456i
$359$	−9.47498	+	7.95045i	−0.500070	+	0.419609i	−0.857619	−	0.514286i	$-0.828057\pi$
$359$	−9.47498	+	7.95045i	−0.500070	+	0.419609i	0.357549	+	0.933894i	$0.383613\pi$
$360$		0			0
$361$	14.6936	−	12.0456i	0.773348	−	0.633981i
$362$	−16.5384			−0.869239
$363$	44.6512	−	37.4668i	2.34358	−	1.96650i
$364$	−2.06231	−	0.750620i	−0.108094	−	0.0393432i
$365$		0			0
$366$	5.14264	+	29.1653i	0.268810	+	1.52450i
$367$	13.0187	−	4.73842i	0.679570	−	0.247343i	0.0209071	−	0.999781i	$-0.493345\pi$
$367$	13.0187	−	4.73842i	0.679570	−	0.247343i	0.658663	+	0.752438i	$0.271122\pi$
$368$	1.50096	−	2.59974i	0.0782429	−	0.135521i
$369$	19.7645	+	34.2332i	1.02890	+	1.78211i
$370$		0			0
$371$	−6.20186	−	5.20398i	−0.321984	−	0.270177i
$372$	1.94842	+	3.37475i	0.101021	+	0.174973i
$373$	−4.39509	+	7.61253i	−0.227569	+	0.394162i	−0.957087	−	0.289800i	$-0.906411\pi$
$373$	−4.39509	+	7.61253i	−0.227569	+	0.394162i	0.729518	+	0.683962i	$0.239745\pi$
$374$	12.2731	−	4.46706i	0.634629	−	0.230986i
$375$		0			0
$376$	−1.92495	+	10.9169i	−0.0992716	+	0.562997i
$377$	−23.8679	−	8.68720i	−1.22926	−	0.447414i
$378$	−4.13726	+	3.47157i	−0.212798	+	0.178558i
$379$	−27.5192			−1.41357			−0.706784	−	0.707429i	$-0.749855\pi$
$379$	−27.5192			−1.41357			−0.706784	+	0.707429i	$0.749855\pi$
$380$		0			0
$381$	−6.68881			−0.342678
$382$	14.5781	−	12.2325i	0.745882	−	0.625870i
$383$	14.3392	+	5.21906i	0.732701	+	0.266681i	0.681308	−	0.731997i	$-0.261412\pi$
$383$	14.3392	+	5.21906i	0.732701	+	0.266681i	0.0513935	+	0.998678i	$0.483634\pi$
$384$	0.506920	−	2.87489i	0.0258687	−	0.146709i
$385$		0			0
$386$	9.24973	−	3.36663i	0.470799	−	0.171357i
$387$	−0.240750	+	0.416991i	−0.0122380	+	0.0211968i
$388$	−1.98595	−	3.43977i	−0.100821	−	0.174628i
$389$	9.95924	+	8.35679i	0.504953	+	0.423706i	0.859349	−	0.511389i	$-0.170869\pi$
$389$	9.95924	+	8.35679i	0.504953	+	0.423706i	−0.354396	+	0.935096i	$0.615313\pi$
$390$		0			0
$391$	3.52282	+	6.10170i	0.178156	+	0.308576i
$392$	3.23092	−	5.59613i	0.163186	−	0.282647i
$393$	14.5693	−	5.30278i	0.734922	−	0.267490i
$394$	2.98564	+	16.9324i	0.150414	+	0.853041i
$395$		0			0
$396$	28.8753	+	10.5098i	1.45104	+	0.528136i
$397$	6.29863	−	5.28518i	0.316119	−	0.265256i	−0.470896	−	0.882189i	$-0.656069\pi$
$397$	6.29863	−	5.28518i	0.316119	−	0.265256i	0.787016	+	0.616933i	$0.211625\pi$
$398$	−12.9679			−0.650022
$399$	−4.71349	+	8.05721i	−0.235970	+	0.403365i
$400$		0			0
$401$	−5.67113	+	4.75864i	−0.283203	+	0.237635i	−0.773312	−	0.634026i	$-0.781401\pi$
$401$	−5.67113	+	4.75864i	−0.283203	+	0.237635i	0.490109	+	0.871661i	$0.336957\pi$
$402$	0.318144	+	0.115795i	0.0158676	+	0.00577534i
$403$	0.693472	−	3.93287i	0.0345443	−	0.195910i
$404$	−1.33908	−	7.59432i	−0.0666219	−	0.377832i
$405$		0			0
$406$	−3.11410	+	5.39379i	−0.154550	+	0.267689i
$407$	11.8896	+	20.5934i	0.589345	+	1.02077i
$408$	5.24861	+	4.40411i	0.259845	+	0.218036i
$409$	−13.5495	−	11.3693i	−0.669978	−	0.562178i	0.243081	−	0.970006i	$-0.421842\pi$
$409$	−13.5495	−	11.3693i	−0.669978	−	0.562178i	−0.913059	+	0.407828i	$0.866286\pi$
$410$		0			0
$411$	12.7037	−	22.0035i	0.626628	−	1.08535i
$412$	0.318823	−	0.116042i	0.0157073	−	0.00571698i
$413$	0.123055	+	0.697881i	0.00605515	+	0.0343405i
$414$	−2.87847	+	16.3246i	−0.141469	+	0.802311i
$415$		0			0
$416$	−2.29177	+	1.92302i	−0.112363	+	0.0942839i
$417$	−67.3300			−3.29717
$418$	24.2559	+	0.138757i	1.18640	+	0.00678685i
$419$	3.57271			0.174538			0.0872692	−	0.996185i	$-0.472186\pi$
$419$	3.57271			0.174538			0.0872692	+	0.996185i	$0.472186\pi$
$420$		0			0
$421$	−1.21414	−	0.441909i	−0.0591733	−	0.0215373i	0.312264	−	0.949995i	$-0.398913\pi$
$421$	−1.21414	−	0.441909i	−0.0591733	−	0.0215373i	−0.371437	+	0.928458i	$0.621135\pi$
$422$	−0.0258605	+	0.146662i	−0.00125887	+	0.00713941i
$423$	−10.6295	−	60.2827i	−0.516823	−	2.93105i
$424$	−10.3706	+	3.77457i	−0.503639	+	0.183309i
$425$		0			0
$426$	1.74486	+	3.02219i	0.0845389	+	0.146426i
$427$	−5.70101	−	4.78371i	−0.275891	−	0.231500i
$428$	0.0666351	+	0.0559135i	0.00322093	+	0.00270268i
$429$	−24.2999	−	42.0887i	−1.17321	−	2.03206i
$430$		0			0
$431$	−16.1748	+	5.88713i	−0.779111	+	0.283573i	−0.700802	−	0.713356i	$-0.747174\pi$
$431$	−16.1748	+	5.88713i	−0.779111	+	0.283573i	−0.0783089	+	0.996929i	$0.524952\pi$
$432$	1.27843	+	7.25034i	0.0615085	+	0.348832i
$433$	−5.51828	+	31.2957i	−0.265192	+	1.50398i	0.503297	+	0.864113i	$0.332120\pi$
$433$	−5.51828	+	31.2957i	−0.265192	+	1.50398i	−0.768489	+	0.639863i	$0.778991\pi$
$434$	−0.920194	−	0.334923i	−0.0441707	−	0.0160768i
$435$		0			0
$436$	−3.09107			−0.148035
$437$	2.19844	+	12.8991i	0.105166	+	0.617045i
$438$	−35.3126			−1.68730
$439$	−18.5800	+	15.5905i	−0.886776	+	0.744093i	−0.967561	−	0.252638i	$-0.918702\pi$
$439$	−18.5800	+	15.5905i	−0.886776	+	0.744093i	0.0807848	+	0.996732i	$0.474257\pi$
$440$		0			0
$441$	−6.19612	+	35.1400i	−0.295053	+	1.67333i
$442$	−1.21929	−	6.91495i	−0.0579958	−	0.328911i
$443$	−32.3624	+	11.7790i	−1.53759	+	0.559635i	−0.965465	−	0.260534i	$-0.916102\pi$
$443$	−32.3624	+	11.7790i	−1.53759	+	0.559635i	−0.572121	+	0.820169i	$0.693879\pi$
$444$	−6.23717	+	10.8031i	−0.296003	+	0.512692i
$445$		0			0
$446$	0.708670	+	0.594644i	0.0335565	+	0.0281572i
$447$	36.6877	+	30.7846i	1.73527	+	1.45606i
$448$	0.366794	+	0.635305i	0.0173294	+	0.0300153i
$449$	−4.97484	+	8.61668i	−0.234777	+	0.406646i	−0.959208	−	0.282702i	$-0.908769\pi$
$449$	−4.97484	+	8.61668i	−0.234777	+	0.406646i	0.724431	+	0.689348i	$0.242103\pi$
$450$		0			0
$451$	6.91740	+	39.2305i	0.325728	+	1.84729i
$452$	0.752352	−	4.26680i	0.0353877	−	0.200693i
$453$	2.51426	+	0.915117i	0.118130	+	0.0429959i
$454$	8.05015	−	6.75488i	0.377812	−	0.317022i
$455$		0			0
$456$	6.29919	+	11.0561i	0.294987	+	0.517749i
$457$	−9.30248			−0.435152			−0.217576	−	0.976043i	$-0.569815\pi$
$457$	−9.30248			−0.435152			−0.217576	+	0.976043i	$0.569815\pi$
$458$	1.26961	−	1.06533i	0.0593252	−	0.0497797i
$459$	−16.2373	−	5.90989i	−0.757892	−	0.275850i
$460$		0			0
$461$	0.521031	+	2.95492i	0.0242669	+	0.137624i	0.994534	−	0.104412i	$-0.0332960\pi$
$461$	0.521031	+	2.95492i	0.0242669	+	0.137624i	−0.970267	+	0.242036i	$0.922185\pi$
$462$	−11.1984	+	4.07588i	−0.520996	+	0.189627i
$463$	2.69707	−	4.67146i	0.125343	−	0.217101i	−0.796524	−	0.604607i	$-0.793330\pi$
$463$	2.69707	−	4.67146i	0.125343	−	0.217101i	0.921867	+	0.387506i	$0.126663\pi$
$464$	4.24504	+	7.35262i	0.197071	+	0.341337i
$465$		0			0
$466$	10.7097	+	8.98648i	0.496116	+	0.416290i
$467$	1.58194	+	2.73999i	0.0732033	+	0.126792i	0.900304	−	0.435263i	$-0.143344\pi$
$467$	1.58194	+	2.73999i	0.0732033	+	0.126792i	−0.827100	+	0.562054i	$0.810011\pi$
$468$	8.25999	−	14.3067i	0.381818	−	0.661328i
$469$	−0.0799478	+	0.0290986i	−0.00369165	+	0.00134365i
$470$		0			0
$471$	−8.40623	+	47.6741i	−0.387339	+	2.19671i
$472$	0.907745	+	0.330392i	0.0417824	+	0.0152075i
$473$	−0.371711	+	0.311902i	−0.0170913	+	0.0143413i
$474$	5.41163			0.248564
$475$		0			0
$476$	−1.72176			−0.0789168
$477$	46.6835	−	39.1721i	2.13749	−	1.79357i
$478$	6.00115	+	2.18424i	0.274486	+	0.0999049i
$479$	−2.88027	+	16.3348i	−0.131603	+	0.746356i	0.845563	+	0.533876i	$0.179265\pi$
$479$	−2.88027	+	16.3348i	−0.131603	+	0.746356i	−0.977165	+	0.212480i	$0.931846\pi$
$480$		0			0
$481$	12.0130	−	4.37236i	0.547744	−	0.199363i
$482$	−3.90540	+	6.76435i	−0.177886	+	0.308108i
$483$	−3.21433	−	5.56738i	−0.146257	−	0.253324i
$484$	15.2955	+	12.8344i	0.695250	+	0.583384i
$485$		0			0
$486$	3.85302	+	6.67363i	0.174777	+	0.302722i
$487$	−1.51374	+	2.62188i	−0.0685941	+	0.118809i	−0.898283	−	0.439418i	$-0.855185\pi$
$487$	−1.51374	+	2.62188i	−0.0685941	+	0.118809i	0.829689	+	0.558227i	$0.188518\pi$
$488$	−9.53305	+	3.46975i	−0.431541	+	0.157068i
$489$	−5.21332	−	29.5662i	−0.235755	−	1.33703i
$490$		0			0
$491$	−17.4638	−	6.35629i	−0.788128	−	0.286855i	−0.0835706	−	0.996502i	$-0.526632\pi$
$491$	−17.4638	−	6.35629i	−0.788128	−	0.286855i	−0.704558	+	0.709647i	$0.748855\pi$
$492$	−16.0084	+	13.4326i	−0.721714	+	0.605590i
$493$	−19.9266			−0.897448
$494$	2.33788	−	12.8292i	0.105186	−	0.577213i
$495$		0			0
$496$	−1.02258	+	0.858044i	−0.0459151	+	0.0385273i
$497$	−0.824061	−	0.299934i	−0.0369642	−	0.0134539i
$498$	8.21146	−	46.5695i	0.367964	−	2.08683i
$499$	5.37449	+	30.4802i	0.240595	+	1.36448i	0.830504	+	0.557013i	$0.188053\pi$
$499$	5.37449	+	30.4802i	0.240595	+	1.36448i	−0.589909	+	0.807470i	$0.700836\pi$
$500$		0			0
$501$	29.9646	−	51.9003i	1.33872	−	2.31873i
$502$	−1.32579	−	2.29633i	−0.0591728	−	0.102490i
$503$	18.3281	+	15.3791i	0.817209	+	0.685720i	0.952317	−	0.305111i	$-0.0986936\pi$
$503$	18.3281	+	15.3791i	0.817209	+	0.685720i	−0.135108	+	0.990831i	$0.543138\pi$
$504$	−3.10312	−	2.60383i	−0.138224	−	0.115984i
$505$		0			0
$506$	−8.35252	+	14.4670i	−0.371315	+	0.643136i
$507$	11.1093	−	4.04346i	0.493382	−	0.179576i
$508$	−0.397877	−	2.25647i	−0.0176530	−	0.100115i
$509$	−5.57074	+	31.5932i	−0.246919	+	1.40035i	0.569076	+	0.822285i	$0.307301\pi$
$509$	−5.57074	+	31.5932i	−0.246919	+	1.40035i	−0.815994	+	0.578060i	$0.803810\pi$
$510$		0			0
$511$	6.79776	−	5.70400i	0.300715	−	0.252330i
$512$	1.00000			0.0441942
$513$	−24.4648	−	20.7680i	−1.08015	−	0.916930i
$514$	8.91529			0.393237
$515$		0			0
$516$	−0.239198	−	0.0870611i	−0.0105301	−	0.00383265i
$517$	10.7119	−	60.7503i	0.471110	−	2.67180i
$518$	−0.544340	−	3.08710i	−0.0239169	−	0.135640i
$519$	32.8077	−	11.9410i	1.44010	−	0.524152i
$520$		0			0
$521$	22.2334	+	38.5093i	0.974062	+	1.68713i	0.682996	+	0.730422i	$0.260677\pi$
$521$	22.2334	+	38.5093i	0.974062	+	1.68713i	0.291066	+	0.956703i	$0.405990\pi$
$522$	−35.9135	−	30.1350i	−1.57189	−	1.31897i
$523$	−24.4267	−	20.4965i	−1.06811	−	0.896248i	−0.0732275	−	0.997315i	$-0.523330\pi$
$523$	−24.4267	−	20.4965i	−1.06811	−	0.896248i	−0.994880	+	0.101067i	$0.967774\pi$
$524$	2.65553	+	4.59952i	0.116008	+	0.200931i
$525$		0			0
$526$	−17.1765	+	6.25175i	−0.748933	+	0.272589i
$527$	−0.544043	−	3.08542i	−0.0236989	−	0.134403i
$528$	−2.82090	+	15.9981i	−0.122764	+	0.696230i
$529$	13.1449	+	4.78435i	0.571517	+	0.208015i
$530$		0			0
$531$	−5.33422			−0.231485
$532$	−2.99849	−	1.11083i	−0.130001	−	0.0481604i
$533$	21.4161			0.927635
$534$	−36.3466	+	30.4984i	−1.57287	+	1.31979i
$535$		0			0
$536$	−0.0201391	+	0.114214i	−0.000869875	+	0.00493331i
$537$	4.66798	+	26.4734i	0.201438	+	1.14241i
$538$	19.8430	−	7.22226i	0.855492	−	0.311374i
$539$	−17.9794	+	31.1413i	−0.774428	+	1.34135i
$540$		0			0
$541$	−14.8145	−	12.4308i	−0.636925	−	0.534444i	0.266147	−	0.963932i	$-0.414249\pi$
$541$	−14.8145	−	12.4308i	−0.636925	−	0.534444i	−0.903072	+	0.429489i	$0.858694\pi$
$542$	0.924715	+	0.775928i	0.0397199	+	0.0333290i
$543$	24.1398	+	41.8113i	1.03594	+	1.79430i
$544$	−1.17352	+	2.03260i	−0.0503143	+	0.0871470i
$545$		0			0
$546$	1.11252	+	6.30942i	0.0476115	+	0.270018i
$547$	1.26379	−	7.16729i	0.0540356	−	0.306451i	−0.945797	−	0.324759i	$-0.894717\pi$
$547$	1.26379	−	7.16729i	0.0540356	−	0.306451i	0.999832	+	0.0183078i	$0.00582789\pi$
$548$	8.17857	+	2.97675i	0.349371	+	0.127161i
$549$	42.9134	−	36.0086i	1.83150	−	1.53681i
$550$		0			0
$551$	−34.7026	−	12.8560i	−1.47838	−	0.547684i
$552$	−8.76331			−0.372991
$553$	−1.04175	+	0.874133i	−0.0442998	+	0.0371719i
$554$	1.54142	+	0.561032i	0.0654888	+	0.0238360i
$555$		0			0
$556$	−4.00506	−	22.7138i	−0.169853	−	0.963282i
$557$	−25.4454	+	9.26137i	−1.07816	+	0.392417i	−0.819221	−	0.573478i	$-0.805594\pi$
$557$	−25.4454	+	9.26137i	−1.07816	+	0.392417i	−0.258935	+	0.965895i	$0.583372\pi$
$558$	3.68557	−	6.38360i	0.156023	−	0.270239i
$559$	0.130434	+	0.225918i	0.00551675	+	0.00955530i
$560$		0			0
$561$	−29.2074	−	24.5079i	−1.23314	−	1.03473i
$562$	−10.5621	−	18.2940i	−0.445534	−	0.771688i
$563$	22.0565	−	38.2030i	0.929572	−	1.61007i	0.145534	−	0.989353i	$-0.453510\pi$
$563$	22.0565	−	38.2030i	0.929572	−	1.61007i	0.784038	−	0.620712i	$-0.213157\pi$
$564$	30.4091	−	11.0680i	1.28046	−	0.466048i
$565$		0			0
$566$	4.06112	−	23.0318i	0.170702	−	0.968098i
$567$	3.39580	+	1.23597i	0.142610	+	0.0519059i
$568$	−0.915747	+	0.768403i	−0.0384239	+	0.0322415i
$569$	−17.7134			−0.742583			−0.371291	−	0.928516i	$-0.621085\pi$
$569$	−17.7134			−0.742583			−0.371291	+	0.928516i	$0.621085\pi$
$570$		0			0
$571$	5.51193			0.230667			0.115334	−	0.993327i	$-0.463206\pi$
$571$	5.51193			0.230667			0.115334	+	0.993327i	$0.463206\pi$
$572$	12.7532	−	10.7012i	0.533238	−	0.447440i
$573$	−52.2040	−	19.0007i	−2.18085	−	0.793765i
$574$	0.911897	−	5.17163i	0.0380619	−	0.215859i
$575$		0			0
$576$	−5.18894	+	1.88862i	−0.216206	+	0.0786925i
$577$	−13.5486	+	23.4668i	−0.564034	+	0.976936i	0.433105	+	0.901344i	$0.357418\pi$
$577$	−13.5486	+	23.4668i	−0.564034	+	0.976936i	−0.997139	+	0.0755923i	$0.975915\pi$
$578$	5.74569	+	9.95183i	0.238989	+	0.413942i
$579$	−22.0124	−	18.4706i	−0.914803	−	0.767611i
$580$		0			0
$581$	5.94158	+	10.2911i	0.246498	+	0.426948i
$582$	−5.79747	+	10.0415i	−0.240313	+	0.416234i
$583$	57.7099	−	21.0047i	2.39010	−	0.869926i
$584$	−2.10054	−	11.9127i	−0.0869208	−	0.492953i
$585$		0			0
$586$	−19.3327	−	7.03651i	−0.798625	−	0.290676i
$587$	3.90544	−	3.27706i	0.161195	−	0.135259i	−0.558623	−	0.829422i	$-0.688670\pi$
$587$	3.90544	−	3.27706i	0.161195	−	0.135259i	0.719817	+	0.694163i	$0.244226\pi$
$588$	−18.8637			−0.777925
$589$	1.04315	−	5.72433i	0.0429824	−	0.235867i
$590$		0			0
$591$	38.4495	−	32.2629i	1.58160	−	1.32712i
$592$	−4.01545	−	1.46150i	−0.165034	−	0.0600674i
$593$	−0.333949	+	1.89392i	−0.0137136	+	0.0777738i	−0.990897	−	0.134626i	$-0.957017\pi$
$593$	−0.333949	+	1.89392i	−0.0137136	+	0.0777738i	0.977183	+	0.212400i	$0.0681279\pi$
$594$	−7.11419	−	40.3466i	−0.291899	−	1.65544i
$595$		0			0
$596$	−8.20289	+	14.2078i	−0.336003	+	0.581975i
$597$	18.9282	+	32.7846i	0.774680	+	1.34178i
$598$	6.87970	+	5.77275i	0.281332	+	0.236065i
$599$	27.5856	+	23.1471i	1.12712	+	0.945765i	0.998942	−	0.0459861i	$-0.0146430\pi$
$599$	27.5856	+	23.1471i	1.12712	+	0.945765i	0.128177	+	0.991751i	$0.459087\pi$
$600$		0			0
$601$	−0.567781	+	0.983425i	−0.0231603	+	0.0401148i	−0.877373	−	0.479809i	$-0.840706\pi$
$601$	−0.567781	+	0.983425i	−0.0231603	+	0.0401148i	0.854213	+	0.519923i	$0.174039\pi$
$602$	0.0601091	−	0.0218779i	0.00244986	−	0.000891678i
$603$	−0.111207	−	0.630686i	−0.00452870	−	0.0256835i
$604$	−0.159157	+	0.902623i	−0.00647600	+	0.0367272i
$605$		0			0
$606$	−17.2449	+	14.4702i	−0.700527	+	0.587812i
$607$	39.3421			1.59685			0.798423	−	0.602097i	$-0.205668\pi$
$607$	39.3421			1.59685			0.798423	+	0.602097i	$0.205668\pi$
$608$	−3.35508	+	2.78270i	−0.136067	+	0.112853i
$609$	18.1816			0.736757
$610$		0			0
$611$	−31.1639	−	11.3427i	−1.26075	−	0.458877i
$612$	2.25053	−	12.7634i	0.0909721	−	0.515929i
$613$	−0.431556	−	2.44748i	−0.0174304	−	0.0988527i	0.974851	−	0.222856i	$-0.0715379\pi$
$613$	−0.431556	−	2.44748i	−0.0174304	−	0.0988527i	−0.992282	+	0.124003i	$0.960427\pi$
$614$	−5.17393	+	1.88316i	−0.208803	+	0.0759980i
$615$		0			0
$616$	−2.04113	−	3.53534i	−0.0822394	−	0.142443i
$617$	7.78203	+	6.52990i	0.313293	+	0.262884i	0.785851	−	0.618415i	$-0.212225\pi$
$617$	7.78203	+	6.52990i	0.313293	+	0.262884i	−0.472559	+	0.881299i	$0.656670\pi$
$618$	−0.758729	−	0.636650i	−0.0305206	−	0.0256098i
$619$	9.34967	+	16.1941i	0.375795	+	0.650896i	0.990446	−	0.137903i	$-0.0440364\pi$
$619$	9.34967	+	16.1941i	0.375795	+	0.650896i	−0.614651	+	0.788799i	$0.710703\pi$
$620$		0			0
$621$	20.7678	−	7.55888i	0.833385	−	0.303327i
$622$	3.68482	+	20.8976i	0.147748	+	0.837919i
$623$	2.07044	−	11.7420i	0.0829502	−	0.470434i
$624$	8.20677	+	2.98702i	0.328534	+	0.119576i
$625$		0			0
$626$	−5.14665			−0.205702
$627$	−35.0537	−	61.5248i	−1.39991	−	2.45707i
$628$	−16.5829			−0.661731
$629$	7.68286	−	6.44669i	0.306336	−	0.257046i
$630$		0			0
$631$	−3.28011	+	18.6024i	−0.130579	+	0.740551i	0.847258	+	0.531182i	$0.178252\pi$
$631$	−3.28011	+	18.6024i	−0.130579	+	0.740551i	−0.977837	+	0.209369i	$0.932859\pi$
$632$	0.321906	+	1.82562i	0.0128047	+	0.0726192i
$633$	0.408529	−	0.148692i	0.0162376	−	0.00590999i
$634$	−7.99255	+	13.8435i	−0.317425	+	0.549796i
$635$		0			0
$636$	24.6797	+	20.7087i	0.978614	+	0.821154i
$637$	14.8091	+	12.4263i	0.586756	+	0.492347i
$638$	−23.6227	−	40.9158i	−0.935233	−	1.61987i
$639$	3.30054	−	5.71670i	0.130567	−	0.226149i
$640$		0			0
$641$	−0.336382	−	1.90772i	−0.0132863	−	0.0753503i	0.977444	−	0.211196i	$-0.0677359\pi$
$641$	−0.336382	−	1.90772i	−0.0132863	−	0.0753503i	−0.990730	+	0.135846i	$0.956625\pi$
$642$	0.0440950	−	0.250075i	0.00174029	−	0.00986967i
$643$	−18.4085	−	6.70014i	−0.725960	−	0.264228i	−0.0475063	−	0.998871i	$-0.515127\pi$
$643$	−18.4085	−	6.70014i	−0.725960	−	0.264228i	−0.678454	+	0.734643i	$0.737350\pi$
$644$	1.68696	−	1.41553i	0.0664755	−	0.0557795i
$645$		0			0
$646$	−1.71885	−	10.0851i	−0.0676272	−	0.396793i
$647$	26.5987			1.04570			0.522851	−	0.852424i	$-0.324869\pi$
$647$	26.5987			1.04570			0.522851	+	0.852424i	$0.324869\pi$
$648$	3.77363	−	3.16645i	0.148242	−	0.124390i
$649$	−5.05141	−	1.83856i	−0.198285	−	0.0721699i
$650$		0			0
$651$	0.496402	+	2.81524i	0.0194555	+	0.110338i
$652$	9.66408	−	3.51744i	0.378475	−	0.137753i
$653$	−17.0971	+	29.6131i	−0.669062	+	1.15885i	0.309105	+	0.951028i	$0.399971\pi$
$653$	−17.0971	+	29.6131i	−0.669062	+	1.15885i	−0.978167	+	0.207821i	$0.933363\pi$
$654$	4.51178	+	7.81464i	0.176425	+	0.305576i
$655$		0			0
$656$	−5.48375	−	4.60142i	−0.214105	−	0.179655i
$657$	33.3982	+	57.8474i	1.30299	+	2.25684i
$658$	−4.06603	+	7.04257i	−0.158510	+	0.274548i
$659$	−31.5982	+	11.5008i	−1.23089	+	0.448007i	−0.873902	−	0.486102i	$-0.838418\pi$
$659$	−31.5982	+	11.5008i	−1.23089	+	0.448007i	−0.356988	+	0.934109i	$0.616196\pi$
$660$		0			0
$661$	1.33128	−	7.55004i	0.0517806	−	0.293663i	−0.947910	−	0.318539i	$-0.896808\pi$
$661$	1.33128	−	7.55004i	0.0517806	−	0.293663i	0.999691	+	0.0248760i	$0.00791908\pi$
$662$	−22.4197	−	8.16009i	−0.871364	−	0.317151i
$663$	−15.7022	+	13.1757i	−0.609824	+	0.511703i
$664$	16.1987			0.628632
$665$		0			0
$666$	23.5961			0.914332
$667$	19.5238	−	16.3824i	0.755964	−	0.634329i
$668$	19.2910	+	7.02136i	0.746392	+	0.271664i
$669$	0.468953	−	2.65957i	0.0181308	−	0.102825i
$670$		0			0
$671$	53.0494	−	19.3084i	2.04795	−	0.745392i
$672$	1.07076	−	1.85461i	0.0413054	−	0.0715430i
$673$	−7.77922	−	13.4740i	−0.299867	−	0.519385i	0.676238	−	0.736683i	$-0.263609\pi$
$673$	−7.77922	−	13.4740i	−0.299867	−	0.519385i	−0.976105	+	0.217298i	$0.930276\pi$
$674$	2.06699	+	1.73441i	0.0796176	+	0.0668071i
$675$		0			0
$676$	2.02489	+	3.50722i	0.0778805	+	0.134893i
$677$	−9.18956	+	15.9168i	−0.353183	+	0.611732i	−0.986805	−	0.161911i	$-0.948234\pi$
$677$	−9.18956	+	15.9168i	−0.353183	+	0.611732i	0.633622	+	0.773643i	$0.281567\pi$
$678$	−11.8852	+	4.32586i	−0.456448	+	0.166134i
$679$	−0.505965	−	2.86947i	−0.0194172	−	0.110120i
$680$		0			0
$681$	−28.8274	−	10.4923i	−1.10467	−	0.402067i
$682$	5.69042	−	4.77483i	0.217898	−	0.182838i
$683$	22.7386			0.870069			0.435035	−	0.900414i	$-0.356736\pi$
$683$	22.7386			0.870069			0.435035	+	0.900414i	$0.356736\pi$
$684$	12.1539	−	20.7757i	0.464715	−	0.794380i
$685$		0			0
$686$	7.56503	−	6.34781i	0.288834	−	0.242361i
$687$	−4.54646	−	1.65478i	−0.173458	−	0.0631336i
$688$	0.0151416	−	0.0858725i	0.000577270	−	0.00327386i
$689$	−5.73328	−	32.5150i	−0.218421	−	1.23872i
$690$		0			0
$691$	14.6303	−	25.3404i	0.556563	−	0.963995i	−0.441217	−	0.897400i	$-0.645453\pi$
$691$	14.6303	−	25.3404i	0.556563	−	0.963995i	0.997780	−	0.0665947i	$-0.0212135\pi$
$692$	5.97985	+	10.3574i	0.227320	+	0.393729i
$693$	17.2682	+	14.4897i	0.655965	+	0.550420i
$694$	−23.0328	−	19.3268i	−0.874312	−	0.733635i
$695$		0			0
$696$	12.3923	−	21.4640i	0.469728	−	0.813593i
$697$	15.7881	−	5.74641i	0.598018	−	0.217661i
$698$	−0.346066	−	1.96264i	−0.0130988	−	0.0742870i
$699$	7.08699	−	40.1923i	0.268055	−	1.52021i
$700$		0			0
$701$	4.83573	−	4.05766i	0.182643	−	0.153256i	−0.546882	−	0.837209i	$-0.684185\pi$
$701$	4.83573	−	4.05766i	0.182643	−	0.153256i	0.729525	+	0.683954i	$0.239741\pi$
$702$	−22.0254			−0.831295
$703$	17.5391	−	6.27031i	0.661499	−	0.236489i
$704$	−5.56479			−0.209731
$705$		0			0
$706$	−7.27765	−	2.64885i	−0.273898	−	0.0996907i
$707$	0.982335	−	5.57110i	0.0369445	−	0.209523i
$708$	−0.489686	−	2.77715i	−0.0184035	−	0.104372i
$709$	−21.5058	+	7.82748i	−0.807669	+	0.293967i	−0.712660	−	0.701509i	$-0.752510\pi$
$709$	−21.5058	+	7.82748i	−0.807669	+	0.293967i	−0.0950081	+	0.995476i	$0.530288\pi$
$710$		0			0
$711$	−5.11825	−	8.86506i	−0.191949	−	0.332466i
$712$	−12.4507	−	10.4474i	−0.466610	−	0.391532i
$713$	3.06969	+	2.57578i	0.114961	+	0.0964636i
$714$	2.51312	+	4.35284i	0.0940510	+	0.162901i
$715$		0			0
$716$	−8.65317	+	3.14949i	−0.323384	+	0.117702i
$717$	−3.23734	−	18.3599i	−0.120901	−	0.685662i
$718$	−2.14780	+	12.1808i	−0.0801553	+	0.454583i
$719$	−32.7211	−	11.9095i	−1.22029	−	0.444149i	−0.350029	−	0.936739i	$-0.613828\pi$
$719$	−32.7211	−	11.9095i	−1.22029	−	0.444149i	−0.870262	+	0.492590i	$0.836050\pi$
$720$		0			0
$721$	0.248894			0.00926931
$722$	3.51317	−	18.6724i	0.130747	−	0.694914i
$723$	22.8016			0.848000
$724$	−12.6692	+	10.6307i	−0.470845	+	0.395086i
$725$		0			0
$726$	10.1216	−	57.4025i	0.375648	−	2.13041i
$727$	1.59841	+	9.06506i	0.0592819	+	0.336204i	0.999996	−	0.00299748i	$-0.000954128\pi$
$727$	1.59841	+	9.06506i	0.0592819	+	0.336204i	−0.940714	+	0.339202i	$0.889843\pi$
$728$	−2.06231	+	0.750620i	−0.0764343	+	0.0278198i
$729$	18.6371	−	32.2804i	0.690262	−	1.19557i
$730$		0			0
$731$	0.156775	+	0.131550i	0.00579855	+	0.00486556i
$732$	22.6866	+	19.0363i	0.838521	+	0.703603i
$733$	14.3663	+	24.8831i	0.530631	+	0.919079i	0.999361	+	0.0357380i	$0.0113782\pi$
$733$	14.3663	+	24.8831i	0.530631	+	0.919079i	−0.468731	+	0.883341i	$0.655288\pi$
$734$	6.92710	−	11.9981i	0.255684	−	0.442858i
$735$		0			0
$736$	−0.521278	−	2.95631i	−0.0192145	−	0.108971i
$737$	0.112070	−	0.635578i	0.00412814	−	0.0234118i
$738$	37.1452	+	13.5197i	1.36733	+	0.497669i
$739$	12.4609	−	10.4560i	0.458382	−	0.384628i	−0.384153	−	0.923269i	$-0.625507\pi$
$739$	12.4609	−	10.4560i	0.458382	−	0.384628i	0.842535	+	0.538641i	$0.181062\pi$
$740$		0			0
$741$	−35.8464	+	12.8153i	−1.31685	+	0.470781i
$742$	−8.09595			−0.297212
$743$	−6.80257	+	5.70804i	−0.249562	+	0.209408i	−0.758984	−	0.651110i	$-0.774304\pi$
$743$	−6.80257	+	5.70804i	−0.249562	+	0.209408i	0.509422	+	0.860517i	$0.329859\pi$
$744$	3.66182	+	1.33279i	0.134249	+	0.0488626i
$745$		0			0
$746$	1.52640	+	8.65665i	0.0558855	+	0.316942i
$747$	−84.0541	+	30.5932i	−3.07538	+	1.11935i
$748$	6.53040	−	11.3110i	0.238775	−	0.413570i
$749$	0.0319059	+	0.0552626i	0.00116582	+	0.00201925i
$750$		0			0
$751$	23.5083	+	19.7258i	0.857830	+	0.719805i	0.961499	−	0.274807i	$-0.0886140\pi$
$751$	23.5083	+	19.7258i	0.857830	+	0.719805i	−0.103669	+	0.994612i	$0.533058\pi$
$752$	5.54267	+	9.60018i	0.202120	+	0.350083i
$753$	−3.87029	+	6.70354i	−0.141041	+	0.244291i
$754$	−23.8679	+	8.68720i	−0.869217	+	0.316369i
$755$		0			0
$756$	−0.937840	+	5.31876i	−0.0341089	+	0.193441i
$757$	2.04287	+	0.743546i	0.0742495	+	0.0270246i	0.378878	−	0.925447i	$-0.376310\pi$
$757$	2.04287	+	0.743546i	0.0742495	+	0.0270246i	−0.304628	+	0.952471i	$0.598532\pi$
$758$	−21.0810	+	17.6890i	−0.765695	+	0.642495i
$759$	48.7660			1.77009
$760$		0			0
$761$	−48.5504			−1.75995			−0.879976	−	0.475019i	$-0.842441\pi$
$761$	−48.5504			−1.75995			−0.879976	+	0.475019i	$0.842441\pi$
$762$	−5.12392	+	4.29948i	−0.185620	+	0.155754i
$763$	−2.13082	−	0.775554i	−0.0771407	−	0.0280769i
$764$	3.30460	−	18.7413i	0.119556	−	0.678036i
$765$		0			0
$766$	14.3392	−	5.21906i	0.518098	−	0.188572i
$767$	−1.44499	+	2.50280i	−0.0521756	+	0.0903707i
$768$	−1.45962	−	2.52813i	−0.0526695	−	0.0912262i
$769$	−10.4556	−	8.77332i	−0.377040	−	0.316374i	0.434499	−	0.900672i	$-0.356925\pi$
$769$	−10.4556	−	8.77332i	−0.377040	−	0.316374i	−0.811539	+	0.584298i	$0.801370\pi$
$770$		0			0
$771$	−13.0129	−	22.5391i	−0.468649	−	0.811724i
$772$	4.92168	−	8.52460i	0.177135	−	0.306807i
$773$	−15.1266	+	5.50563i	−0.544066	+	0.198024i	−0.599408	−	0.800444i	$-0.704597\pi$
$773$	−15.1266	+	5.50563i	−0.544066	+	0.198024i	0.0553423	+	0.998467i	$0.482375\pi$
$774$	0.0836115	+	0.474184i	0.00300535	+	0.0170442i
$775$		0			0
$776$	−3.73237	−	1.35847i	−0.133984	−	0.0487663i
$777$	−7.01008	+	5.88216i	−0.251485	+	0.211021i
$778$	13.0009			0.466104
$779$	31.2028	+	0.178497i	1.11796	+	0.00639533i
$780$		0			0
$781$	5.09594	−	4.27600i	0.182347	−	0.153007i
$782$	6.62073	+	2.40975i	0.236757	+	0.0861724i
$783$	−10.8540	+	61.5559i	−0.387889	+	2.19983i
$784$	−1.12209	−	6.36368i	−0.0400746	−	0.227274i
$785$		0			0
$786$	7.75214	−	13.4271i	0.276510	−	0.478929i
$787$	9.59592	+	16.6206i	0.342057	+	0.592461i	0.984815	−	0.173609i	$-0.0555429\pi$
$787$	9.59592	+	16.6206i	0.342057	+	0.592461i	−0.642757	+	0.766070i	$0.722210\pi$
$788$	13.1711	+	11.0518i	0.469200	+	0.393705i
$789$	40.8765	+	34.2994i	1.45524	+	1.22109i
$790$		0			0
$791$	1.58918	−	2.75254i	0.0565047	−	0.0978690i
$792$	28.8753	−	10.5098i	1.02604	−	0.373448i
$793$	−5.27027	−	29.8892i	−0.187153	−	1.06140i
$794$	1.42778	−	8.09737i	0.0506702	−	0.287365i
$795$		0			0
$796$	−9.93399	+	8.33561i	−0.352101	+	0.295448i
$797$	−48.8300			−1.72965			−0.864824	−	0.502075i	$-0.832570\pi$
$797$	−48.8300			−1.72965			−0.864824	+	0.502075i	$0.832570\pi$
$798$	1.56833	+	9.20196i	0.0555183	+	0.325746i
$799$	−26.0178			−0.920442
$800$		0			0
$801$	84.3370	+	30.6962i	2.97990	+	1.08460i
$802$	−1.28554	+	7.29067i	−0.0453940	+	0.257442i
$803$	11.6890	+	66.2918i	0.412497	+	2.33939i
$804$	0.318144	−	0.115795i	0.0112201	−	0.00408378i
$805$		0			0
$806$	−1.99677	−	3.45851i	−0.0703333	−	0.121821i
$807$	−47.2221	−	39.6240i	−1.66230	−	1.39483i
$808$	−5.90734	−	4.95684i	−0.207819	−	0.174381i
$809$	15.1960	+	26.3203i	0.534264	+	0.925373i	0.999199	+	0.0400279i	$0.0127447\pi$
$809$	15.1960	+	26.3203i	0.534264	+	0.925373i	−0.464934	+	0.885345i	$0.653922\pi$
$810$		0			0
$811$	4.66334	−	1.69732i	0.163752	−	0.0596009i	−0.258843	−	0.965919i	$-0.583341\pi$
$811$	4.66334	−	1.69732i	0.163752	−	0.0596009i	0.422595	+	0.906318i	$0.361119\pi$
$812$	1.08152	+	6.13359i	0.0379538	+	0.215247i
$813$	0.611919	−	3.47036i	0.0214609	−	0.121711i
$814$	22.3451	+	8.13295i	0.783195	+	0.285060i
$815$		0			0
$816$	6.85158			0.239853
$817$	0.188156	+	0.330244i	0.00658274	+	0.0115538i
$818$	−17.6876			−0.618431
$819$	9.28357	−	7.78984i	0.324394	−	0.272199i
$820$		0			0
$821$	−6.43511	+	36.4953i	−0.224587	+	1.27370i	0.638886	+	0.769301i	$0.279395\pi$
$821$	−6.43511	+	36.4953i	−0.224587	+	1.27370i	−0.863473	+	0.504395i	$0.831716\pi$
$822$	−4.41196	−	25.0214i	−0.153885	−	0.872723i
$823$	−3.35328	+	1.22049i	−0.116888	+	0.0425437i	−0.399802	−	0.916602i	$-0.630921\pi$
$823$	−3.35328	+	1.22049i	−0.116888	+	0.0425437i	0.282914	+	0.959145i	$0.408699\pi$
$824$	0.169642	−	0.293829i	0.00590976	−	0.0102360i
$825$		0			0
$826$	0.542855	+	0.455509i	0.0188883	+	0.0158492i
$827$	11.3320	+	9.50865i	0.394051	+	0.330648i	0.818189	−	0.574949i	$-0.194978\pi$
$827$	11.3320	+	9.50865i	0.394051	+	0.330648i	−0.424138	+	0.905598i	$0.639423\pi$
$828$	8.28823	+	14.3556i	0.288036	+	0.498893i
$829$	−4.45536	+	7.71690i	−0.154741	+	0.268019i	−0.932965	−	0.359968i	$-0.882788\pi$
$829$	−4.45536	+	7.71690i	−0.154741	+	0.268019i	0.778224	+	0.627987i	$0.216121\pi$
$830$		0			0
$831$	−0.831526	−	4.71582i	−0.0288453	−	0.163590i
$832$	−0.519502	+	2.94624i	−0.0180105	+	0.102142i
$833$	14.2516	+	5.18716i	0.493789	+	0.179724i
$834$	−51.5778	+	43.2789i	−1.78599	+	1.49863i
$835$		0			0
$836$	18.6703	−	15.4851i	0.645727	−	0.535564i
$837$	−9.82763			−0.339693
$838$	2.73686	−	2.29649i	0.0945431	−	0.0793311i
$839$	−53.2639	−	19.3865i	−1.83888	−	0.669296i	−0.990067	−	0.140595i	$-0.955098\pi$
$839$	−53.2639	−	19.3865i	−1.83888	−	0.669296i	−0.848808	−	0.528701i	$-0.822679\pi$
$840$		0			0
$841$	7.48100	+	42.4268i	0.257965	+	1.46299i
$842$	−1.21414	+	0.441909i	−0.0418419	+	0.0152292i
$843$	−30.8332	+	53.4047i	−1.06195	+	1.83935i
$844$	0.0744624	+	0.128973i	0.00256310	+	0.00443942i
$845$		0			0
$846$	−46.8916	−	39.3468i	−1.61217	−	1.35277i
$847$	7.32371	+	12.6850i	0.251646	+	0.435863i
$848$	−5.51806	+	9.55756i	−0.189491	+	0.328208i
$849$	−64.1552	+	23.3506i	−2.20180	+	0.801389i
$850$		0			0
$851$	−2.22750	+	12.6328i	−0.0763576	+	0.433045i
$852$	3.27927	+	1.19356i	0.112346	+	0.0408906i
$853$	25.9989	−	21.8157i	0.890185	−	0.746954i	−0.0780621	−	0.996948i	$-0.524873\pi$
$853$	25.9989	−	21.8157i	0.890185	−	0.746954i	0.968247	+	0.249994i	$0.0804288\pi$
$854$	−7.44214			−0.254665
$855$		0			0
$856$	0.0869860			0.00297312
$857$	18.2831	−	15.3414i	0.624539	−	0.524051i	−0.274688	−	0.961534i	$-0.588574\pi$
$857$	18.2831	−	15.3414i	0.624539	−	0.524051i	0.899227	+	0.437483i	$0.144130\pi$
$858$	−45.6689	−	16.6221i	−1.55911	−	0.567470i
$859$	3.24518	−	18.4043i	0.110724	−	0.627948i	−0.878055	−	0.478560i	$-0.841159\pi$
$859$	3.24518	−	18.4043i	0.110724	−	0.627948i	0.988779	−	0.149387i	$-0.0477301\pi$
$860$		0			0
$861$	−14.4056	+	5.24321i	−0.490941	+	0.178688i
$862$	−8.60641	+	14.9067i	−0.293135	+	0.507725i
$863$	−2.11860	−	3.66952i	−0.0721179	−	0.124912i	0.827711	−	0.561154i	$-0.189642\pi$
$863$	−2.11860	−	3.66952i	−0.0721179	−	0.124912i	−0.899829	+	0.436242i	$0.856309\pi$
$864$	5.63976	+	4.73232i	0.191869	+	0.160997i
$865$		0			0
$866$	15.8893	+	27.5210i	0.539939	+	0.935202i
$867$	16.7731	−	29.0518i	0.569643	−	0.986650i
$868$	−0.920194	+	0.334923i	−0.0312334	+	0.0113680i
$869$	−1.79134	−	10.1592i	−0.0607669	−	0.344626i
$870$		0			0
$871$	−0.326040	−	0.118669i	−0.0110475	−	0.00402095i
$872$	−2.36790	+	1.98690i	−0.0801870	+	0.0672849i
$873$	21.9327			0.742309
$874$	9.97546	+	8.46811i	0.337425	+	0.286438i
$875$		0			0
$876$	−27.0510	+	22.6985i	−0.913969	+	0.766911i
$877$	−14.1333	−	5.14410i	−0.477247	−	0.173704i	0.0921853	−	0.995742i	$-0.470615\pi$
$877$	−14.1333	−	5.14410i	−0.477247	−	0.173704i	−0.569432	+	0.822038i	$0.692837\pi$
$878$	−4.21175	+	23.8860i	−0.142140	+	0.806114i
$879$	10.4291	+	59.1462i	0.351764	+	1.99495i
$880$		0			0
$881$	−18.2867	+	31.6735i	−0.616095	+	1.06711i	0.374097	+	0.927390i	$0.377953\pi$
$881$	−18.2867	+	31.6735i	−0.616095	+	1.06711i	−0.990191	+	0.139717i	$0.955381\pi$
$882$	17.8410	+	30.9016i	0.600738	+	1.04051i
$883$	−24.0194	−	20.1546i	−0.808316	−	0.678258i	0.141889	−	0.989883i	$-0.454682\pi$
$883$	−24.0194	−	20.1546i	−0.808316	−	0.678258i	−0.950205	+	0.311625i	$0.899127\pi$
$884$	−5.37888	−	4.51342i	−0.180911	−	0.151803i
$885$		0			0
$886$	−17.2197	+	29.8254i	−0.578507	+	1.00200i
$887$	−2.34126	+	0.852151i	−0.0786120	+	0.0286124i	−0.381027	−	0.924564i	$-0.624429\pi$
$887$	−2.34126	+	0.852151i	−0.0786120	+	0.0286124i	0.302415	+	0.953176i	$0.402207\pi$
$888$	2.16615	+	12.2848i	0.0726911	+	0.412252i
$889$	0.291878	−	1.65532i	0.00978926	−	0.0555177i
$890$		0			0
$891$	−20.9994	+	17.6206i	−0.703507	+	0.590313i
$892$	0.925102			0.0309747
$893$	−45.3105	−	16.7858i	−1.51626	−	0.561716i
$894$	47.8924			1.60176
$895$		0			0
$896$	0.689346	+	0.250902i	0.0230294	+	0.00838203i
$897$	4.55256	−	25.8188i	0.152005	−	0.862066i
$898$	1.72774	+	9.79852i	0.0576556	+	0.326981i
$899$	−10.6497	+	3.87619i	−0.355189	+	0.129278i
$900$		0			0
$901$	−12.9511	−	22.4320i	−0.431464	−	0.747318i
$902$	30.5159	+	25.6059i	1.01607	+	0.852583i
$903$	−0.143047	−	0.120030i	−0.00476030	−	0.00399436i
$904$	−2.16631	−	3.75216i	−0.0720505	−	0.124795i
$905$		0			0
$906$	2.51426	−	0.915117i	0.0835308	−	0.0304027i
$907$	1.67857	+	9.51966i	0.0557361	+	0.316095i	0.999911	−	0.0133499i	$-0.00424952\pi$
$907$	1.67857	+	9.51966i	0.0557361	+	0.316095i	−0.944175	+	0.329445i	$0.893138\pi$
$908$	1.82482	−	10.3491i	0.0605588	−	0.343446i
$909$	40.0144	+	14.5641i	1.32719	+	0.483059i
$910$		0			0
$911$	19.8973			0.659227			0.329613	−	0.944116i	$-0.393082\pi$
$911$	19.8973			0.659227			0.329613	+	0.944116i	$0.393082\pi$
$912$	11.9322	+	4.42042i	0.395114	+	0.146375i
$913$	−90.1424			−2.98328
$914$	−7.12611	+	5.97952i	−0.235711	+	0.197785i
$915$		0			0
$916$	0.287798	−	1.63218i	0.00950912	−	0.0539289i
$917$	0.676556	+	3.83694i	0.0223419	+	0.126707i
$918$	−16.2373	+	5.90989i	−0.535911	+	0.195056i
$919$	10.9604	−	18.9840i	0.361551	−	0.626224i	−0.626666	−	0.779288i	$-0.715581\pi$
$919$	10.9604	−	18.9840i	0.361551	−	0.626224i	0.988216	+	0.153064i	$0.0489142\pi$
$920$		0			0
$921$	12.3128	+	10.3317i	0.405722	+	0.340441i
$922$	2.29852	+	1.92868i	0.0756976	+	0.0635178i
$923$	−1.78817	−	3.09720i	−0.0588583	−	0.101946i
$924$	−5.95854	+	10.3205i	−0.196022	+	0.339519i
$925$		0			0
$926$	−0.936682	−	5.31219i	−0.0307813	−	0.174569i
$927$	−0.325332	+	1.84505i	−0.0106853	+	0.0605993i
$928$	7.97806	+	2.90378i	0.261893	+	0.0953211i
$929$	−15.6858	+	13.1619i	−0.514634	+	0.431829i	−0.862756	−	0.505620i	$-0.831264\pi$
$929$	−15.6858	+	13.1619i	−0.514634	+	0.431829i	0.348122	+	0.937449i	$0.386819\pi$
$930$		0			0
$931$	21.4729	+	18.2282i	0.703746	+	0.597407i
$932$	13.9805			0.457946
$933$	47.4536	−	39.8183i	1.55356	−	1.30359i
$934$	2.97307	+	1.08211i	0.0972817	+	0.0354077i
$935$		0			0
$936$	−2.86866	−	16.2690i	−0.0937652	−	0.531769i
$937$	46.5738	−	16.9515i	1.52150	−	0.553780i	0.559977	−	0.828508i	$-0.310810\pi$
$937$	46.5738	−	16.9515i	1.52150	−	0.553780i	0.961522	+	0.274728i	$0.0885879\pi$
$938$	−0.0425393	+	0.0736803i	−0.00138896	+	0.00240575i
$939$	7.51216	+	13.0114i	0.245150	+	0.424612i
$940$		0			0
$941$	14.6060	+	12.2559i	0.476142	+	0.399530i	0.849029	−	0.528346i	$-0.177188\pi$
$941$	14.6060	+	12.2559i	0.476142	+	0.399530i	−0.372887	+	0.927877i	$0.621632\pi$
$942$	24.2048	+	41.9239i	0.788634	+	1.36595i
$943$	−10.7447	+	18.6103i	−0.349894	+	0.606035i
$944$	0.907745	−	0.330392i	0.0295446	−	0.0107533i
$945$		0			0
$946$	−0.0842600	+	0.477862i	−0.00273953	+	0.0155366i
$947$	13.1482	+	4.78556i	0.427260	+	0.155510i	0.546694	−	0.837332i	$-0.315886\pi$
$947$	13.1482	+	4.78556i	0.427260	+	0.155510i	−0.119435	+	0.992842i	$0.538108\pi$
$948$	4.14555	−	3.47853i	0.134641	−	0.112977i
$949$	36.1890			1.17475
$950$		0			0
$951$	46.6643			1.51319
$952$	−1.31895	+	1.10673i	−0.0427473	+	0.0358692i
$953$	50.3604	+	18.3297i	1.63133	+	0.593757i	0.985493	−	0.169715i	$-0.0542847\pi$
$953$	50.3604	+	18.3297i	1.63133	+	0.593757i	0.645841	+	0.763472i	$0.276507\pi$
$954$	10.5823	−	60.0151i	0.342614	−	1.94306i
$955$		0			0
$956$	6.00115	−	2.18424i	0.194091	−	0.0706434i
$957$	−68.9604	+	119.443i	−2.22917	+	3.86104i
$958$	8.29339	+	14.3646i	0.267947	+	0.464098i
$959$	4.89099	+	4.10403i	0.157938	+	0.132526i
$960$		0			0
$961$	14.6090	+	25.3036i	0.471260	+	0.816246i
$962$	6.39197	−	11.0712i	0.206085	−	0.356950i
$963$	−0.451365	+	0.164283i	−0.0145450	+	0.00529396i
$964$	1.35633	+	7.69213i	0.0436845	+	0.247747i
$965$		0			0
$966$	−6.04096	−	2.19873i	−0.194365	−	0.0707429i
$967$	−38.0876	+	31.9593i	−1.22482	+	1.02774i	−0.226257	+	0.974068i	$0.572649\pi$
$967$	−38.0876	+	31.9593i	−1.22482	+	1.02774i	−0.998558	+	0.0536747i	$0.982907\pi$
$968$	19.9669			0.641759
$969$	−22.9876	+	19.0659i	−0.738469	+	0.612484i
$970$		0			0
$971$	−34.1205	+	28.6305i	−1.09498	+	0.918795i	−0.997077	−	0.0764008i	$-0.975657\pi$
$971$	−34.1205	+	28.6305i	−1.09498	+	0.918795i	−0.0979005	+	0.995196i	$0.531213\pi$
$972$	7.24132	+	2.63562i	0.232265	+	0.0845377i
$973$	2.93806	−	16.6626i	0.0941900	−	0.534178i
$974$	0.525717	+	2.98149i	0.0168450	+	0.0955330i
$975$		0			0
$976$	−5.07243	+	8.78570i	−0.162364	+	0.281224i
$977$	−11.5975	−	20.0874i	−0.371036	−	0.642654i	0.618689	−	0.785636i	$-0.287664\pi$
$977$	−11.5975	−	20.0874i	−0.371036	−	0.642654i	−0.989725	+	0.142982i	$0.954331\pi$
$978$	−22.9984	−	19.2980i	−0.735409	−	0.617081i
$979$	69.2855	+	58.1374i	2.21437	+	1.85808i
$980$		0			0
$981$	8.53437	−	14.7820i	0.272481	−	0.471952i
$982$	−17.4638	+	6.35629i	−0.557291	+	0.202837i
$983$	−8.07304	−	45.7845i	−0.257490	−	1.46030i	−0.789599	−	0.613623i	$-0.789712\pi$
$983$	−8.07304	−	45.7845i	−0.257490	−	1.46030i	0.532109	−	0.846676i	$-0.321400\pi$
$984$	−3.62881	+	20.5800i	−0.115682	+	0.656066i
$985$		0			0
$986$	−15.2646	+	12.8086i	−0.486125	+	0.407907i
$987$	23.7394			0.755634
$988$	−6.45553	−	11.3305i	−0.205378	−	0.360471i
$989$	−0.261759			−0.00832345
$990$		0			0
$991$	−57.2846	−	20.8499i	−1.81971	−	0.662318i	−0.995359	−	0.0962325i	$-0.969321\pi$
$991$	−57.2846	−	20.8499i	−1.81971	−	0.662318i	−0.824346	−	0.566086i	$-0.808457\pi$
$992$	−0.231799	+	1.31460i	−0.00735964	+	0.0417386i
$993$	12.0944	+	68.5905i	0.383803	+	2.17665i
$994$	−0.824061	+	0.299934i	−0.0261376	+	0.00951332i
$995$		0			0
$996$	−23.6440	−	40.9525i	−0.749187	−	1.29763i
$997$	−23.5181	−	19.7341i	−0.744827	−	0.624984i	0.189303	−	0.981919i	$-0.439377\pi$
$997$	−23.5181	−	19.7341i	−0.744827	−	0.624984i	−0.934129	+	0.356935i	$0.883822\pi$
$998$	23.7094	+	19.8946i	0.750509	+	0.629751i
$999$	−15.7299	−	27.2449i	−0.497671	−	0.861991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.m.101.1		30
5.2	odd	4		190.2.p.a.139.6	yes	60
5.3	odd	4		190.2.p.a.139.5	✓	60
5.4	even	2		950.2.l.l.101.5		30
19.16	even	9	inner	950.2.l.m.301.1		30
95.54	even	18		950.2.l.l.301.5		30
95.73	odd	36		190.2.p.a.149.6	yes	60
95.92	odd	36		190.2.p.a.149.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.139.5	✓	60	5.3	odd	4
190.2.p.a.139.6	yes	60	5.2	odd	4
190.2.p.a.149.5	yes	60	95.92	odd	36
190.2.p.a.149.6	yes	60	95.73	odd	36
950.2.l.l.101.5		30	5.4	even	2
950.2.l.l.301.5		30	95.54	even	18
950.2.l.m.101.1		30	1.1	even	1	trivial
950.2.l.m.301.1		30	19.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-2.74319 - 0.998438i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.74319 + 0.998438i) q^{6} +(0.366794 - 0.635305i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(4.23006 + 3.54944i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-2.74319 - 0.998438i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.74319 + 0.998438i) q^{6} +(0.366794 - 0.635305i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(4.23006 + 3.54944i) q^{9} +(2.78239 + 4.81925i) q^{11} +(-1.45962 + 2.52813i) q^{12} +(2.81127 - 1.02322i) q^{13} +(-0.127386 - 0.722442i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(1.79794 - 1.50865i) q^{17} +5.52195 q^{18} +(4.10449 - 1.46738i) q^{19} +(-1.64050 + 1.37654i) q^{21} +(5.22919 + 1.90327i) q^{22} +(-0.521278 + 2.95631i) q^{23} +(0.506920 + 2.87489i) q^{24} +(1.49585 - 2.59088i) q^{26} +(-3.68109 - 6.37584i) q^{27} +(-0.561960 - 0.471541i) q^{28} +(-6.50377 - 5.45731i) q^{29} +(0.667440 - 1.15604i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-2.82090 - 15.9981i) q^{33} +(0.407560 - 2.31139i) q^{34} +(4.23006 - 3.54944i) q^{36} +4.27315 q^{37} +(2.20101 - 3.76239i) q^{38} -8.73346 q^{39} +(6.72682 + 2.44836i) q^{41} +(-0.371870 + 2.10898i) q^{42} +(0.0151416 + 0.0858725i) q^{43} +(5.22919 - 1.90327i) q^{44} +(1.50096 + 2.59974i) q^{46} +(-8.49186 - 7.12551i) q^{47} +(2.23627 + 1.87645i) q^{48} +(3.23092 + 5.59613i) q^{49} +(-6.43838 + 2.34338i) q^{51} +(-0.519502 - 2.94624i) q^{52} +(1.91640 - 10.8685i) q^{53} +(-6.91819 - 2.51802i) q^{54} -0.733587 q^{56} +(-12.7245 - 0.0727909i) q^{57} -8.49007 q^{58} +(-0.740001 + 0.620934i) q^{59} +(1.76164 - 9.99073i) q^{61} +(-0.231799 - 1.31460i) q^{62} +(3.80654 - 1.38547i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-12.4443 - 10.4420i) q^{66} +(-0.0888429 - 0.0745481i) q^{67} +(-1.17352 - 2.03260i) q^{68} +(4.38166 - 7.58925i) q^{69} +(-0.207583 - 1.17726i) q^{71} +(0.958877 - 5.43806i) q^{72} +(11.3670 + 4.13725i) q^{73} +(3.27342 - 2.74673i) q^{74} +(-0.732346 - 4.29694i) q^{76} +4.08226 q^{77} +(-6.69022 + 5.61376i) q^{78} +(-1.74198 - 0.634030i) q^{79} +(0.855411 + 4.85128i) q^{81} +(6.72682 - 2.44836i) q^{82} +(-8.09936 + 14.0285i) q^{83} +(1.07076 + 1.85461i) q^{84} +(0.0667970 + 0.0560493i) q^{86} +(12.3923 + 21.4640i) q^{87} +(2.78239 - 4.81925i) q^{88} +(15.2730 - 5.55893i) q^{89} +(0.381100 - 2.16132i) q^{91} +(2.82088 + 1.02672i) q^{92} +(-2.98515 + 2.50483i) q^{93} -11.0853 q^{94} +2.91924 q^{96} +(3.04266 - 2.55309i) q^{97} +(6.07215 + 2.21008i) q^{98} +(-5.33595 + 30.2617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 12 q^{7} - 15 q^{8}+O(q^{10}) \) 30 * q + 12 * q^7 - 15 * q^8	\( 30 q + 12 q^{7} - 15 q^{8} + 6 q^{11} + 6 q^{14} + 30 q^{18} + 24 q^{19} + 24 q^{21} - 3 q^{22} - 3 q^{23} + 3 q^{26} + 18 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{33} - 24 q^{37} + 12 q^{38} - 24 q^{39} - 3 q^{41} - 12 q^{42} - 6 q^{43} - 3 q^{44} - 48 q^{47} + 15 q^{49} - 90 q^{51} + 18 q^{53} + 18 q^{54} - 24 q^{56} + 42 q^{57} - 36 q^{58} - 18 q^{59} - 60 q^{61} + 24 q^{62} + 21 q^{63} - 15 q^{64} - 78 q^{66} + 30 q^{67} + 12 q^{68} + 24 q^{69} - 30 q^{73} - 9 q^{74} - 3 q^{76} - 78 q^{77} - 6 q^{79} + 60 q^{81} - 3 q^{82} + 42 q^{83} - 6 q^{84} + 12 q^{86} + 54 q^{87} + 6 q^{88} - 30 q^{89} - 6 q^{91} + 6 q^{92} - 72 q^{93} - 78 q^{94} + 42 q^{97} - 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q + 12 * q^7 - 15 * q^8 + 6 * q^11 + 6 * q^14 + 30 * q^18 + 24 * q^19 + 24 * q^21 - 3 * q^22 - 3 * q^23 + 3 * q^26 + 18 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^33 - 24 * q^37 + 12 * q^38 - 24 * q^39 - 3 * q^41 - 12 * q^42 - 6 * q^43 - 3 * q^44 - 48 * q^47 + 15 * q^49 - 90 * q^51 + 18 * q^53 + 18 * q^54 - 24 * q^56 + 42 * q^57 - 36 * q^58 - 18 * q^59 - 60 * q^61 + 24 * q^62 + 21 * q^63 - 15 * q^64 - 78 * q^66 + 30 * q^67 + 12 * q^68 + 24 * q^69 - 30 * q^73 - 9 * q^74 - 3 * q^76 - 78 * q^77 - 6 * q^79 + 60 * q^81 - 3 * q^82 + 42 * q^83 - 6 * q^84 + 12 * q^86 + 54 * q^87 + 6 * q^88 - 30 * q^89 - 6 * q^91 + 6 * q^92 - 72 * q^93 - 78 * q^94 + 42 * q^97 - 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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