LMFDB - Embedded newform 950.2.l.l.101.5

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			101.5
Character	$\chi$	$=$	950.101
Dual form			950.2.l.l.301.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(2.74319 + 0.998438i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.74319 + 0.998438i) q^{6} +(-0.366794 + 0.635305i) q^{7} +(0.500000 + 0.866025i) q^{8} +(4.23006 + 3.54944i) q^{9} +O(q^{10})$	\(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	0.976022	−	0.217673i	$-0.0698468\pi$
$3$	2.74319	+	0.998438i	1.58378	+	0.576449i	0.607758	+	0.794122i	$0.292069\pi$
$4$	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	−0.926980	−	0.375110i	$-0.877605\pi$
$7$	−0.366794	+	0.635305i	−0.138635	+	0.240123i	0.788345	+	0.615233i	$0.210938\pi$
$8$	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	−0.701050	−	0.713112i	$-0.747285\pi$
$13$	−2.81127	+	1.02322i	−0.779706	+	0.283790i	−0.0786559	+	0.996902i	$0.525063\pi$
$14$	−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	−0.834234	−	0.551410i	$-0.814090\pi$
$17$	−1.79794	+	1.50865i	−0.436064	+	0.365901i	0.398170	+	0.917312i	$0.369645\pi$
$18$	−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	$-0.843120\pi$
$23$	0.521278	−	2.95631i	0.108694	−	0.616434i	0.989680	−	0.143292i	$-0.0457689\pi$
$24$	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	$-0.614243\pi$
$37$	−4.27315			−0.702501			−0.351251	+	0.936281i	$0.614243\pi$
$38$	−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	0.983631	−	0.180192i	$-0.0576719\pi$
$43$	−0.0151416	−	0.0858725i	−0.00230908	−	0.0130954i	−0.985941	+	0.167097i	$0.946561\pi$
$44$	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	$0.0219321\pi$
$47$	8.49186	+	7.12551i	1.23866	+	1.03936i	0.241037	+	0.970516i	$0.422512\pi$
$48$	−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	$0.329361\pi$
$53$	−1.91640	+	10.8685i	−0.263238	+	1.49290i	−0.774006	+	0.633178i	$0.781750\pi$
$54$	−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	0.648198	−	0.761471i	$-0.275523\pi$
$67$	0.0888429	+	0.0745481i	0.0108539	+	0.00910750i	−0.637345	+	0.770579i	$0.719967\pi$
$68$	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	−0.423628	−	0.905836i	$-0.639244\pi$
$73$	−11.3670	−	4.13725i	−1.33041	−	0.484228i	−0.906778	+	0.421608i	$0.861466\pi$
$74$	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	$-0.484720\pi$
$83$	8.09936	−	14.0285i	0.889020	−	1.53983i	0.841036	−	0.540979i	$-0.181946\pi$
$84$	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	−0.784052	−	0.620696i	$-0.786850\pi$
$97$	−3.04266	+	2.55309i	−0.308935	+	0.259227i	0.475117	+	0.879923i	$0.342406\pi$
$98$	−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	0.857547	−	0.514406i	$-0.171988\pi$
$103$	−0.169642	−	0.293829i	−0.0167153	−	0.0289518i	−0.874262	+	0.485454i	$0.838654\pi$
$104$	−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	−0.863915	−	0.503637i	$-0.831995\pi$
$107$	0.0434930	−	0.0753321i	0.00420463	−	0.00728263i	0.868120	+	0.496354i	$0.165328\pi$
$108$	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	$-0.565326\pi$
$113$	−4.33262			−0.407579			−0.203789	+	0.979015i	$0.565326\pi$
$114$	−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	−0.435777	−	0.900055i	$-0.643526\pi$
$127$	−2.15310	+	0.783665i	−0.191057	+	0.0695391i	0.244720	+	0.969594i	$0.421304\pi$
$128$	−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	$-0.823188\pi$
$137$	1.51134	−	8.57122i	0.129122	−	0.732289i	0.978774	−	0.204944i	$-0.0657013\pi$
$138$	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	$0.174622\pi$
$157$	2.87960	+	16.3310i	0.229817	+	1.30336i	−0.623443	+	0.781869i	$0.714266\pi$
$158$	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	0.591294	−	0.806456i	$-0.298617\pi$
$163$	−5.14215	−	8.90646i	−0.402764	−	0.697608i	−0.994058	+	0.108848i	$0.965284\pi$
$164$	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	$-0.652286\pi$
$167$	3.56484	−	20.2172i	0.275855	−	1.56445i	0.736232	−	0.676729i	$-0.236603\pi$
$168$	−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	−0.224241	−	0.974534i	$-0.571990\pi$
$173$	9.16166	−	7.68754i	0.696548	−	0.584473i	0.920789	+	0.390061i	$0.127546\pi$
$174$	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	−0.0130674	−	0.999915i	$-0.504160\pi$
$193$	−9.24973	−	3.36663i	−0.665810	−	0.242335i	−0.652743	+	0.757579i	$0.726382\pi$
$194$	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	$-0.623499\pi$
$197$	8.59680	−	14.8901i	0.612497	−	1.06088i	0.990818	−	0.135201i	$-0.0431680\pi$
$198$	−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	0.978957	−	0.204069i	$-0.0654167\pi$
$223$	−0.160642	−	0.911048i	−0.0107574	−	0.0610083i	−0.989714	+	0.143061i	$0.954306\pi$
$224$	−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	$-0.613392\pi$
$227$	−10.5087			−0.697489			−0.348744	+	0.937218i	$0.613392\pi$
$228$	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	$-0.904141\pi$
$233$	−2.42768	−	13.7681i	−0.159043	−	0.901977i	0.795953	−	0.605358i	$-0.206970\pi$
$234$	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	0.404432	−	0.914568i	$-0.367469\pi$
$257$	−6.82951	−	5.73064i	−0.426013	−	0.357467i	−0.830445	+	0.557101i	$0.811914\pi$
$258$	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	0.812109	−	0.583506i	$-0.198319\pi$
$263$	17.1765	+	6.25175i	1.05915	+	0.385499i	0.247042	+	0.969005i	$0.420542\pi$
$264$	−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	0.840333	−	0.542070i	$-0.182359\pi$
$277$	−0.820174	−	1.42058i	−0.0492795	−	0.0853546i	−0.889613	+	0.456715i	$0.849026\pi$
$278$	−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	−0.994587	−	0.103905i	$-0.966866\pi$
$283$	−17.9155	+	15.0329i	−1.06497	+	0.893615i	−0.0703816	+	0.997520i	$0.522422\pi$
$284$	−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	$0.0385463\pi$
$293$	10.2867	+	17.8171i	0.600955	+	1.04088i	−0.391722	+	0.920084i	$0.628120\pi$
$294$	−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	0.485418	−	0.874282i	$-0.338667\pi$
$307$	5.17393	+	1.88316i	0.295292	+	0.107477i	−0.190126	+	0.981760i	$0.560890\pi$
$308$	−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	0.747375	−	0.664402i	$-0.231314\pi$
$313$	3.94257	+	3.30821i	0.222847	+	0.186991i	−0.524528	+	0.851393i	$0.675758\pi$
$314$	−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	0.116212	−	0.993224i	$-0.462925\pi$
$317$	15.0211	−	5.46722i	0.843668	−	0.307070i	0.727456	+	0.686155i	$0.240703\pi$
$318$	−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	0.969383	−	0.245554i	$-0.0789699\pi$
$337$	−0.468549	−	2.65728i	−0.0255235	−	0.144751i	−0.994906	+	0.100803i	$0.967859\pi$
$338$	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	$0.243379\pi$
$347$	5.22111	+	29.6104i	0.280284	+	1.58957i	−0.441378	+	0.897321i	$0.645510\pi$
$348$	−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	0.950484	−	0.310773i	$-0.100588\pi$
$353$	3.87236	+	6.70712i	0.206105	+	0.356984i	−0.744379	+	0.667757i	$0.767255\pi$
$354$	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	−0.658663	−	0.752438i	$-0.728878\pi$
$367$	−13.0187	+	4.73842i	−0.679570	+	0.247343i	−0.0209071	+	0.999781i	$0.506655\pi$
$368$	−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	−0.729518	−	0.683962i	$-0.760255\pi$
$373$	4.39509	−	7.61253i	0.227569	−	0.394162i	0.957087	+	0.289800i	$0.0935888\pi$
$374$	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	−0.0513935	−	0.998678i	$-0.516366\pi$
$383$	−14.3392	−	5.21906i	−0.732701	−	0.266681i	−0.681308	+	0.731997i	$0.738588\pi$
$384$	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	−0.787016	−	0.616933i	$-0.788375\pi$
$397$	−6.29863	+	5.28518i	−0.316119	+	0.265256i	0.470896	+	0.882189i	$0.343931\pi$
$398$	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	$-0.667880\pi$
$433$	5.51828	−	31.2957i	0.265192	−	1.50398i	0.768489	−	0.639863i	$-0.221009\pi$
$434$	−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	0.572121	−	0.820169i	$-0.306121\pi$
$443$	32.3624	−	11.7790i	1.53759	−	0.559635i	0.965465	+	0.260534i	$0.0838985\pi$
$444$	−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	$-0.430185\pi$
$457$	9.30248			0.435152			0.217576	+	0.976043i	$0.430185\pi$
$458$	−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	−0.921867	−	0.387506i	$-0.873337\pi$
$463$	−2.69707	+	4.67146i	−0.125343	+	0.217101i	0.796524	+	0.604607i	$0.206670\pi$
$464$	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	0.827100	−	0.562054i	$-0.189989\pi$
$467$	−1.58194	−	2.73999i	−0.0732033	−	0.126792i	−0.900304	+	0.435263i	$0.856656\pi$
$468$	−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	−0.829689	−	0.558227i	$-0.811482\pi$
$487$	1.51374	−	2.62188i	0.0685941	−	0.118809i	0.898283	+	0.439418i	$0.144815\pi$
$488$	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	0.135108	−	0.990831i	$-0.456862\pi$
$503$	−18.3281	−	15.3791i	−0.817209	−	0.685720i	−0.952317	+	0.305111i	$0.901306\pi$
$504$	−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	0.994880	−	0.101067i	$-0.0322256\pi$
$523$	24.4267	+	20.4965i	1.06811	+	0.896248i	0.0732275	+	0.997315i	$0.476670\pi$
$524$	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	−0.999832	−	0.0183078i	$-0.994172\pi$
$547$	−1.26379	+	7.16729i	−0.0540356	+	0.306451i	0.945797	+	0.324759i	$0.105283\pi$
$548$	−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	0.258935	−	0.965895i	$-0.416628\pi$
$557$	25.4454	−	9.26137i	1.07816	−	0.392417i	0.819221	+	0.573478i	$0.194406\pi$
$558$	−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	$0.546490\pi$
$563$	−22.0565	+	38.2030i	−0.929572	+	1.61007i	−0.784038	+	0.620712i	$0.786843\pi$
$564$	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	$-0.642582\pi$
$577$	13.5486	−	23.4668i	0.564034	−	0.976936i	0.997139	−	0.0755923i	$-0.0240848\pi$
$578$	−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	−0.719817	−	0.694163i	$-0.755774\pi$
$587$	−3.90544	+	3.27706i	−0.161195	+	0.135259i	0.558623	+	0.829422i	$0.311330\pi$
$588$	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	−0.977183	−	0.212400i	$-0.931872\pi$
$593$	0.333949	−	1.89392i	0.0137136	−	0.0777738i	0.990897	+	0.134626i	$0.0429832\pi$
$594$	−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	$-0.794332\pi$
$607$	−39.3421			−1.59685			−0.798423	+	0.602097i	$0.794332\pi$
$608$	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	0.992282	−	0.124003i	$-0.0395732\pi$
$613$	0.431556	+	2.44748i	0.0174304	+	0.0988527i	−0.974851	+	0.222856i	$0.928462\pi$
$614$	−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	0.472559	−	0.881299i	$-0.343330\pi$
$617$	−7.78203	−	6.52990i	−0.313293	−	0.262884i	−0.785851	+	0.618415i	$0.787775\pi$
$618$	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	0.678454	−	0.734643i	$-0.262650\pi$
$643$	18.4085	+	6.70014i	0.725960	+	0.264228i	0.0475063	+	0.998871i	$0.484873\pi$
$644$	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	$-0.675131\pi$
$647$	−26.5987			−1.04570			−0.522851	+	0.852424i	$0.675131\pi$
$648$	−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	$-0.600029\pi$
$653$	17.0971	−	29.6131i	0.669062	−	1.15885i	0.978167	−	0.207821i	$-0.0666372\pi$
$654$	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	0.976105	−	0.217298i	$-0.0697243\pi$
$673$	7.77922	+	13.4740i	0.299867	+	0.519385i	−0.676238	+	0.736683i	$0.736391\pi$
$674$	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	−0.633622	−	0.773643i	$-0.718433\pi$
$677$	9.18956	−	15.9168i	0.353183	−	0.611732i	0.986805	+	0.161911i	$0.0517658\pi$
$678$	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	$-0.643264\pi$
$683$	−22.7386			−0.870069			−0.435035	+	0.900414i	$0.643264\pi$
$684$	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	0.940714	−	0.339202i	$-0.110157\pi$
$727$	−1.59841	−	9.06506i	−0.0592819	−	0.336204i	−0.999996	+	0.00299748i	$0.999046\pi$
$728$	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	$-0.988622\pi$
$733$	−14.3663	−	24.8831i	−0.530631	−	0.919079i	0.468731	−	0.883341i	$-0.344712\pi$
$734$	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	−0.509422	−	0.860517i	$-0.670141\pi$
$743$	6.80257	−	5.70804i	0.249562	−	0.209408i	0.758984	+	0.651110i	$0.225696\pi$
$744$	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	0.304628	−	0.952471i	$-0.401468\pi$
$757$	−2.04287	−	0.743546i	−0.0742495	−	0.0270246i	−0.378878	+	0.925447i	$0.623690\pi$
$758$	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	−0.0553423	−	0.998467i	$-0.517625\pi$
$773$	15.1266	−	5.50563i	0.544066	−	0.198024i	0.599408	+	0.800444i	$0.295403\pi$
$774$	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	0.642757	−	0.766070i	$-0.277790\pi$
$787$	−9.59592	−	16.6206i	−0.342057	−	0.592461i	−0.984815	+	0.173609i	$0.944457\pi$
$788$	−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	$-0.167430\pi$
$797$	48.8300			1.72965			0.864824	+	0.502075i	$0.167430\pi$
$798$	−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	−0.282914	−	0.959145i	$-0.591301\pi$
$823$	3.35328	−	1.22049i	0.116888	−	0.0425437i	0.399802	+	0.916602i	$0.369079\pi$
$824$	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	0.424138	−	0.905598i	$-0.360577\pi$
$827$	−11.3320	−	9.50865i	−0.394051	−	0.330648i	−0.818189	+	0.574949i	$0.805022\pi$
$828$	−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	−0.968247	−	0.249994i	$-0.919571\pi$
$853$	−25.9989	+	21.8157i	−0.890185	+	0.746954i	0.0780621	+	0.996948i	$0.475127\pi$
$854$	−7.44214			−0.254665
$855$		0			0
$856$	0.0869860			0.00297312
$857$	−18.2831	+	15.3414i	−0.624539	+	0.524051i	−0.899227	−	0.437483i	$-0.855870\pi$
$857$	−18.2831	+	15.3414i	−0.624539	+	0.524051i	0.274688	+	0.961534i	$0.411426\pi$
$858$	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	0.899829	−	0.436242i	$-0.143691\pi$
$863$	2.11860	+	3.66952i	0.0721179	+	0.124912i	−0.827711	+	0.561154i	$0.810358\pi$
$864$	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	0.569432	−	0.822038i	$-0.307163\pi$
$877$	14.1333	+	5.14410i	0.477247	+	0.173704i	−0.0921853	+	0.995742i	$0.529385\pi$
$878$	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	0.950205	−	0.311625i	$-0.100873\pi$
$883$	24.0194	+	20.1546i	0.808316	+	0.678258i	−0.141889	+	0.989883i	$0.545318\pi$
$884$	−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	−0.302415	−	0.953176i	$-0.597793\pi$
$887$	2.34126	−	0.852151i	0.0786120	−	0.0286124i	0.381027	+	0.924564i	$0.375571\pi$
$888$	−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	0.944175	−	0.329445i	$-0.106862\pi$
$907$	−1.67857	−	9.51966i	−0.0557361	−	0.316095i	−0.999911	+	0.0133499i	$0.995750\pi$
$908$	−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	−0.961522	−	0.274728i	$-0.911412\pi$
$937$	−46.5738	+	16.9515i	−1.52150	+	0.553780i	−0.559977	+	0.828508i	$0.689190\pi$
$938$	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	0.119435	−	0.992842i	$-0.461892\pi$
$947$	−13.1482	−	4.78556i	−0.427260	−	0.155510i	−0.546694	+	0.837332i	$0.684114\pi$
$948$	−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	−0.645841	−	0.763472i	$-0.723493\pi$
$953$	−50.3604	−	18.3297i	−1.63133	−	0.593757i	−0.985493	+	0.169715i	$0.945715\pi$
$954$	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	$-0.427351\pi$
$967$	38.0876	−	31.9593i	1.22482	−	1.02774i	0.998558	−	0.0536747i	$-0.0170934\pi$
$968$	−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	0.989725	−	0.142982i	$-0.0456692\pi$
$977$	11.5975	+	20.0874i	0.371036	+	0.642654i	−0.618689	+	0.785636i	$0.712336\pi$
$978$	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	$0.210288\pi$
$983$	8.07304	+	45.7845i	0.257490	+	1.46030i	−0.532109	+	0.846676i	$0.678600\pi$
$984$	−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	0.934129	−	0.356935i	$-0.116178\pi$
$997$	23.5181	+	19.7341i	0.744827	+	0.624984i	−0.189303	+	0.981919i	$0.560623\pi$
$998$	−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.l.101.5		30
5.2	odd	4		190.2.p.a.139.5	✓	60
5.3	odd	4		190.2.p.a.139.6	yes	60
5.4	even	2		950.2.l.m.101.1		30
19.16	even	9	inner	950.2.l.l.301.5		30
95.54	even	18		950.2.l.m.301.1		30
95.73	odd	36		190.2.p.a.149.5	yes	60
95.92	odd	36		190.2.p.a.149.6	yes	60

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

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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