LMFDB - Embedded newform 882.2.e.o.655.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (of order $3$, degree $2$, not 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.o.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.64400 + 0.545231i) q^{3} +1.00000 q^{4} +(0.794182 - 1.37556i) q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(2.40545 + 1.79272i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.64400 + 0.545231i) q^{3} +1.00000 q^{4} +(0.794182 - 1.37556i) q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(2.40545 + 1.79272i) q^{9} +(-0.794182 + 1.37556i) q^{10} +(0.794182 + 1.37556i) q^{11} +(1.64400 + 0.545231i) q^{12} +(-2.40545 - 4.16635i) q^{13} +(2.05563 - 1.82841i) q^{15} +1.00000 q^{16} +(2.69963 - 4.67589i) q^{17} +(-2.40545 - 1.79272i) q^{18} +(3.54944 + 6.14781i) q^{19} +(0.794182 - 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} +(-0.150186 + 0.260130i) q^{23} +(-1.64400 - 0.545231i) q^{24} +(1.23855 + 2.14523i) q^{25} +(2.40545 + 4.16635i) q^{26} +(2.97710 + 4.25874i) q^{27} +(4.13781 - 7.16689i) q^{29} +(-2.05563 + 1.82841i) q^{30} +2.71201 q^{31} -1.00000 q^{32} +(0.555632 + 2.69443i) q^{33} +(-2.69963 + 4.67589i) q^{34} +(2.40545 + 1.79272i) q^{36} +(0.500000 + 0.866025i) q^{37} +(-3.54944 - 6.14781i) q^{38} +(-1.68292 - 8.16100i) q^{39} +(-0.794182 + 1.37556i) q^{40} +(-2.93818 - 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} +(0.794182 + 1.37556i) q^{44} +(4.37636 - 1.88510i) q^{45} +(0.150186 - 0.260130i) q^{46} -2.66621 q^{47} +(1.64400 + 0.545231i) q^{48} +(-1.23855 - 2.14523i) q^{50} +(6.98762 - 6.21523i) q^{51} +(-2.40545 - 4.16635i) q^{52} +(2.44437 - 4.23377i) q^{53} +(-2.97710 - 4.25874i) q^{54} +2.52290 q^{55} +(2.48329 + 12.0422i) q^{57} +(-4.13781 + 7.16689i) q^{58} -6.47710 q^{59} +(2.05563 - 1.82841i) q^{60} +4.47710 q^{61} -2.71201 q^{62} +1.00000 q^{64} -7.64145 q^{65} +(-0.555632 - 2.69443i) q^{66} -10.0531 q^{67} +(2.69963 - 4.67589i) q^{68} +(-0.388736 + 0.345766i) q^{69} +12.7207 q^{71} +(-2.40545 - 1.79272i) q^{72} +(-8.02654 + 13.9024i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(0.866524 + 4.20205i) q^{75} +(3.54944 + 6.14781i) q^{76} +(1.68292 + 8.16100i) q^{78} +8.38688 q^{79} +(0.794182 - 1.37556i) q^{80} +(2.57234 + 8.62456i) q^{81} +(2.93818 + 5.08907i) q^{82} +(-1.18292 + 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(0.833104 - 1.44298i) q^{86} +(10.7101 - 9.52628i) q^{87} +(-0.794182 - 1.37556i) q^{88} +(-1.60507 - 2.78007i) q^{89} +(-4.37636 + 1.88510i) q^{90} +(-0.150186 + 0.260130i) q^{92} +(4.45853 + 1.47867i) q^{93} +2.66621 q^{94} +11.2756 q^{95} +(-1.64400 - 0.545231i) q^{96} +(-0.712008 + 1.23323i) q^{97} +(-0.555632 + 4.73259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9} + q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} + 6 q^{16} + 4 q^{17} - 8 q^{18} + 3 q^{19} - q^{20} + q^{22} - 7 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} - 12 q^{30} + 40 q^{31} - 6 q^{32} + 3 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} - 3 q^{38} - 5 q^{39} + q^{40} - 6 q^{43} - q^{44} - 9 q^{45} + 7 q^{46} - 18 q^{47} - 2 q^{48} - 2 q^{50} + 6 q^{51} - 8 q^{52} + 15 q^{53} - 7 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} - 28 q^{59} + 12 q^{60} + 16 q^{61} - 40 q^{62} + 6 q^{64} + 24 q^{65} - 3 q^{66} - 2 q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} - 8 q^{72} - 19 q^{73} - 3 q^{74} - 8 q^{75} + 3 q^{76} + 5 q^{78} - 10 q^{79} - q^{80} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} + 27 q^{87} + q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} - 38 q^{93} + 18 q^{94} + 8 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9 + q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 + 6 * q^16 + 4 * q^17 - 8 * q^18 + 3 * q^19 - q^20 + q^22 - 7 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 - 12 * q^30 + 40 * q^31 - 6 * q^32 + 3 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 - 3 * q^38 - 5 * q^39 + q^40 - 6 * q^43 - q^44 - 9 * q^45 + 7 * q^46 - 18 * q^47 - 2 * q^48 - 2 * q^50 + 6 * q^51 - 8 * q^52 + 15 * q^53 - 7 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 - 28 * q^59 + 12 * q^60 + 16 * q^61 - 40 * q^62 + 6 * q^64 + 24 * q^65 - 3 * q^66 - 2 * q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 - 8 * q^72 - 19 * q^73 - 3 * q^74 - 8 * q^75 + 3 * q^76 + 5 * q^78 - 10 * q^79 - q^80 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 + 27 * q^87 + q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 - 38 * q^93 + 18 * q^94 + 8 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.64400	+	0.545231i	0.949162	+	0.314789i
$3$	1.64400	+	0.545231i	0.949162	+	0.314789i
$4$	1.00000			0.500000
$5$	0.794182	−	1.37556i	0.355169	−	0.615171i	−0.631978	−	0.774986i	$-0.717757\pi$
$5$	0.794182	−	1.37556i	0.355169	−	0.615171i	0.987147	+	0.159816i	$0.0510900\pi$
$6$	−1.64400	−	0.545231i	−0.671159	−	0.222590i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	2.40545	+	1.79272i	0.801815	+	0.597572i
$10$	−0.794182	+	1.37556i	−0.251142	+	0.434991i
$11$	0.794182	+	1.37556i	0.239455	+	0.414748i	0.960558	−	0.278080i	$-0.0896979\pi$
$11$	0.794182	+	1.37556i	0.239455	+	0.414748i	−0.721103	+	0.692828i	$0.756365\pi$
$12$	1.64400	+	0.545231i	0.474581	+	0.157395i
$13$	−2.40545	−	4.16635i	−0.667151	−	1.15554i	−0.978697	−	0.205308i	$-0.934180\pi$
$13$	−2.40545	−	4.16635i	−0.667151	−	1.15554i	0.311547	−	0.950231i	$-0.399153\pi$
$14$		0			0
$15$	2.05563	−	1.82841i	0.530762	−	0.472093i
$16$	1.00000			0.250000
$17$	2.69963	−	4.67589i	0.654756	−	1.13407i	−0.327199	−	0.944955i	$-0.606105\pi$
$17$	2.69963	−	4.67589i	0.654756	−	1.13407i	0.981955	−	0.189115i	$-0.0605620\pi$
$18$	−2.40545	−	1.79272i	−0.566969	−	0.422547i
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	0.909831	+	0.414979i	$0.136211\pi$
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	−0.0955331	+	0.995426i	$0.530456\pi$
$20$	0.794182	−	1.37556i	0.177584	−	0.307585i
$21$		0			0
$22$	−0.794182	−	1.37556i	−0.169320	−	0.293271i
$23$	−0.150186	+	0.260130i	−0.0313159	+	0.0542408i	−0.881259	−	0.472634i	$-0.843303\pi$
$23$	−0.150186	+	0.260130i	−0.0313159	+	0.0542408i	0.849943	+	0.526875i	$0.176636\pi$
$24$	−1.64400	−	0.545231i	−0.335579	−	0.111295i
$25$	1.23855	+	2.14523i	0.247710	+	0.429046i
$26$	2.40545	+	4.16635i	0.471747	+	0.817089i
$27$	2.97710	+	4.25874i	0.572943	+	0.819595i
$28$		0			0
$29$	4.13781	−	7.16689i	0.768371	−	1.33086i	−0.170074	−	0.985431i	$-0.554401\pi$
$29$	4.13781	−	7.16689i	0.768371	−	1.33086i	0.938446	−	0.345427i	$-0.112266\pi$
$30$	−2.05563	+	1.82841i	−0.375305	+	0.333820i
$31$	2.71201			0.487091			0.243545	−	0.969889i	$-0.421689\pi$
$31$	2.71201			0.487091			0.243545	+	0.969889i	$0.421689\pi$
$32$	−1.00000			−0.176777
$33$	0.555632	+	2.69443i	0.0967231	+	0.469041i
$34$	−2.69963	+	4.67589i	−0.462982	+	0.801909i
$35$		0			0
$36$	2.40545	+	1.79272i	0.400908	+	0.298786i
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−3.54944	−	6.14781i	−0.575796	−	0.997307i
$39$	−1.68292	−	8.16100i	−0.269483	−	1.30681i
$40$	−0.794182	+	1.37556i	−0.125571	+	0.217496i
$41$	−2.93818	−	5.08907i	−0.458866	−	0.794780i	0.540035	−	0.841643i	$-0.318411\pi$
$41$	−2.93818	−	5.08907i	−0.458866	−	0.794780i	−0.998901	+	0.0468628i	$0.985078\pi$
$42$		0			0
$43$	−0.833104	+	1.44298i	−0.127047	+	0.220052i	−0.922531	−	0.385922i	$-0.873883\pi$
$43$	−0.833104	+	1.44298i	−0.127047	+	0.220052i	0.795484	+	0.605974i	$0.207217\pi$
$44$	0.794182	+	1.37556i	0.119727	+	0.207374i
$45$	4.37636	−	1.88510i	0.652389	−	0.281014i
$46$	0.150186	−	0.260130i	0.0221437	−	0.0383540i
$47$	−2.66621			−0.388906			−0.194453	−	0.980912i	$-0.562293\pi$
$47$	−2.66621			−0.388906			−0.194453	+	0.980912i	$0.562293\pi$
$48$	1.64400	+	0.545231i	0.237290	+	0.0786973i
$49$		0			0
$50$	−1.23855	−	2.14523i	−0.175157	−	0.303382i
$51$	6.98762	−	6.21523i	0.978463	−	0.870306i
$52$	−2.40545	−	4.16635i	−0.333575	−	0.577769i
$53$	2.44437	−	4.23377i	0.335760	−	0.581553i	−0.647871	−	0.761750i	$-0.724340\pi$
$53$	2.44437	−	4.23377i	0.335760	−	0.581553i	0.983630	+	0.180197i	$0.0576736\pi$
$54$	−2.97710	−	4.25874i	−0.405132	−	0.579541i
$55$	2.52290			0.340188
$56$		0			0
$57$	2.48329	+	12.0422i	0.328920	+	1.59503i
$58$	−4.13781	+	7.16689i	−0.543321	+	0.941059i
$59$	−6.47710			−0.843247			−0.421623	−	0.906771i	$-0.638540\pi$
$59$	−6.47710			−0.843247			−0.421623	+	0.906771i	$0.638540\pi$
$60$	2.05563	−	1.82841i	0.265381	−	0.236047i
$61$	4.47710			0.573234			0.286617	−	0.958045i	$-0.407469\pi$
$61$	4.47710			0.573234			0.286617	+	0.958045i	$0.407469\pi$
$62$	−2.71201			−0.344425
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.64145			−0.947805
$66$	−0.555632	−	2.69443i	−0.0683936	−	0.331662i
$67$	−10.0531			−1.22818			−0.614090	−	0.789236i	$-0.710477\pi$
$67$	−10.0531			−1.22818			−0.614090	+	0.789236i	$0.710477\pi$
$68$	2.69963	−	4.67589i	0.327378	−	0.567035i
$69$	−0.388736	+	0.345766i	−0.0467983	+	0.0416253i
$70$		0			0
$71$	12.7207			1.50967			0.754833	−	0.655917i	$-0.227718\pi$
$71$	12.7207			1.50967			0.754833	+	0.655917i	$0.227718\pi$
$72$	−2.40545	−	1.79272i	−0.283485	−	0.211274i
$73$	−8.02654	+	13.9024i	−0.939436	+	1.62715i	−0.172909	+	0.984938i	$0.555317\pi$
$73$	−8.02654	+	13.9024i	−0.939436	+	1.62715i	−0.766527	+	0.642213i	$0.778017\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	0.866524	+	4.20205i	0.100058	+	0.485211i
$76$	3.54944	+	6.14781i	0.407149	+	0.705203i
$77$		0			0
$78$	1.68292	+	8.16100i	0.190553	+	0.924051i
$79$	8.38688			0.943597			0.471799	−	0.881706i	$-0.343605\pi$
$79$	8.38688			0.943597			0.471799	+	0.881706i	$0.343605\pi$
$80$	0.794182	−	1.37556i	0.0887922	−	0.153793i
$81$	2.57234	+	8.62456i	0.285816	+	0.958285i
$82$	2.93818	+	5.08907i	0.324467	+	0.561994i
$83$	−1.18292	+	2.04887i	−0.129842	+	0.224893i	−0.923615	−	0.383321i	$-0.874780\pi$
$83$	−1.18292	+	2.04887i	−0.129842	+	0.224893i	0.793773	+	0.608214i	$0.208114\pi$
$84$		0			0
$85$	−4.28799	−	7.42702i	−0.465098	−	0.805573i
$86$	0.833104	−	1.44298i	0.0898359	−	0.155600i
$87$	10.7101	−	9.52628i	1.14825	−	1.02132i
$88$	−0.794182	−	1.37556i	−0.0846601	−	0.146636i
$89$	−1.60507	−	2.78007i	−0.170138	−	0.294687i	0.768330	−	0.640054i	$-0.221088\pi$
$89$	−1.60507	−	2.78007i	−0.170138	−	0.294687i	−0.938468	+	0.345367i	$0.887755\pi$
$90$	−4.37636	+	1.88510i	−0.461308	+	0.198707i
$91$		0			0
$92$	−0.150186	+	0.260130i	−0.0156580	+	0.0271204i
$93$	4.45853	+	1.47867i	0.462328	+	0.153331i
$94$	2.66621			0.274998
$95$	11.2756			1.15685
$96$	−1.64400	−	0.545231i	−0.167790	−	0.0556474i
$97$	−0.712008	+	1.23323i	−0.0722934	+	0.125216i	−0.899906	−	0.436084i	$-0.856365\pi$
$97$	−0.712008	+	1.23323i	−0.0722934	+	0.125216i	0.827613	+	0.561300i	$0.189698\pi$
$98$		0			0
$99$	−0.555632	+	4.73259i	−0.0558431	+	0.475643i
$100$	1.23855	+	2.14523i	0.123855	+	0.214523i
$101$	6.01671	+	10.4212i	0.598685	+	1.03695i	0.993015	+	0.117984i	$0.0376432\pi$
$101$	6.01671	+	10.4212i	0.598685	+	1.03695i	−0.394330	+	0.918969i	$0.629023\pi$
$102$	−6.98762	+	6.21523i	−0.691878	+	0.615399i
$103$	−3.04944	+	5.28179i	−0.300470	+	0.520430i	−0.976243	−	0.216680i	$-0.930477\pi$
$103$	−3.04944	+	5.28179i	−0.300470	+	0.520430i	0.675772	+	0.737111i	$0.263810\pi$
$104$	2.40545	+	4.16635i	0.235873	+	0.408545i
$105$		0			0
$106$	−2.44437	+	4.23377i	−0.237418	+	0.411220i
$107$	−1.54325	−	2.67299i	−0.149192	−	0.258408i	0.781737	−	0.623608i	$-0.214334\pi$
$107$	−1.54325	−	2.67299i	−0.149192	−	0.258408i	−0.930929	+	0.365200i	$0.881001\pi$
$108$	2.97710	+	4.25874i	0.286472	+	0.409798i
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	−0.806023	−	0.591884i	$-0.798384\pi$
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	0.915598	+	0.402095i	$0.131718\pi$
$110$	−2.52290			−0.240549
$111$	0.349814	+	1.69636i	0.0332029	+	0.161011i
$112$		0			0
$113$	−9.73236	−	16.8569i	−0.915543	−	1.58577i	−0.806104	−	0.591774i	$-0.798428\pi$
$113$	−9.73236	−	16.8569i	−0.915543	−	1.58577i	−0.109440	−	0.993993i	$-0.534906\pi$
$114$	−2.48329	−	12.0422i	−0.232581	−	1.12786i
$115$	0.238550	+	0.413181i	0.0222449	+	0.0385293i
$116$	4.13781	−	7.16689i	0.384186	−	0.665429i
$117$	1.68292	−	14.3342i	0.155586	−	1.32520i
$118$	6.47710			0.596265
$119$		0			0
$120$	−2.05563	+	1.82841i	−0.187653	+	0.166910i
$121$	4.23855	−	7.34138i	0.385323	−	0.667399i
$122$	−4.47710			−0.405338
$123$	−2.05563	−	9.96840i	−0.185350	−	0.898821i
$124$	2.71201			0.243545
$125$	11.8764			1.06225
$126$		0			0
$127$	−13.4400			−1.19260			−0.596302	−	0.802760i	$-0.703364\pi$
$127$	−13.4400			−1.19260			−0.596302	+	0.802760i	$0.703364\pi$
$128$	−1.00000			−0.0883883
$129$	−2.15638	+	1.91802i	−0.189858	+	0.168872i
$130$	7.64145			0.670199
$131$	−1.58836	+	2.75113i	−0.138776	+	0.240367i	−0.927034	−	0.374978i	$-0.877650\pi$
$131$	−1.58836	+	2.75113i	−0.138776	+	0.240367i	0.788258	+	0.615345i	$0.210983\pi$
$132$	0.555632	+	2.69443i	0.0483616	+	0.234520i
$133$		0			0
$134$	10.0531			0.868454
$135$	8.22253	−	0.712974i	0.707683	−	0.0613631i
$136$	−2.69963	+	4.67589i	−0.231491	+	0.400955i
$137$	10.6316	+	18.4145i	0.908320	+	1.57326i	0.816397	+	0.577491i	$0.195968\pi$
$137$	10.6316	+	18.4145i	0.908320	+	1.57326i	0.0919231	+	0.995766i	$0.470699\pi$
$138$	0.388736	−	0.345766i	0.0330914	−	0.0294336i
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	−0.998013	−	0.0630092i	$-0.979930\pi$
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	0.444439	−	0.895809i	$-0.353403\pi$
$140$		0			0
$141$	−4.38323	−	1.45370i	−0.369135	−	0.122424i
$142$	−12.7207			−1.06749
$143$	3.82072	−	6.61769i	0.319505	−	0.553399i
$144$	2.40545	+	1.79272i	0.200454	+	0.149393i
$145$	−6.57234	−	11.3836i	−0.545803	−	0.945359i
$146$	8.02654	−	13.9024i	0.664281	−	1.15057i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−2.60439	+	4.51093i	−0.213360	+	0.369550i	−0.952764	−	0.303712i	$-0.901774\pi$
$149$	−2.60439	+	4.51093i	−0.213360	+	0.369550i	0.739404	+	0.673262i	$0.235107\pi$
$150$	−0.866524	−	4.20205i	−0.0707514	−	0.343096i
$151$	0.261450	+	0.452845i	0.0212765	+	0.0368520i	0.876468	−	0.481461i	$-0.159894\pi$
$151$	0.261450	+	0.452845i	0.0212765	+	0.0368520i	−0.855191	+	0.518313i	$0.826560\pi$
$152$	−3.54944	−	6.14781i	−0.287898	−	0.498654i
$153$	14.8764	−	6.40794i	1.20268	−	0.518052i
$154$		0			0
$155$	2.15383	−	3.73054i	0.173000	−	0.299644i
$156$	−1.68292	−	8.16100i	−0.134741	−	0.653403i
$157$	−8.86398			−0.707422			−0.353711	−	0.935355i	$-0.615080\pi$
$157$	−8.86398			−0.707422			−0.353711	+	0.935355i	$0.615080\pi$
$158$	−8.38688			−0.667224
$159$	6.32691	−	5.62755i	0.501757	−	0.446294i
$160$	−0.794182	+	1.37556i	−0.0627856	+	0.108748i
$161$		0			0
$162$	−2.57234	−	8.62456i	−0.202102	−	0.677610i
$163$	10.9814	+	19.0204i	0.860132	+	1.48979i	0.871801	+	0.489860i	$0.162952\pi$
$163$	10.9814	+	19.0204i	0.860132	+	1.48979i	−0.0116689	+	0.999932i	$0.503714\pi$
$164$	−2.93818	−	5.08907i	−0.229433	−	0.397390i
$165$	4.14764	+	1.37556i	0.322893	+	0.107087i
$166$	1.18292	−	2.04887i	0.0918122	−	0.159023i
$167$	−1.65019	−	2.85821i	−0.127695	−	0.221175i	0.795088	−	0.606494i	$-0.207425\pi$
$167$	−1.65019	−	2.85821i	−0.127695	−	0.221175i	−0.922783	+	0.385319i	$0.874091\pi$
$168$		0			0
$169$	−5.07234	+	8.78555i	−0.390180	+	0.675812i
$170$	4.28799	+	7.42702i	0.328874	+	0.569626i
$171$	−2.48329	+	21.1514i	−0.189902	+	1.61749i
$172$	−0.833104	+	1.44298i	−0.0635236	+	0.110026i
$173$	−19.1075			−1.45272			−0.726360	−	0.687315i	$-0.758789\pi$
$173$	−19.1075			−1.45272			−0.726360	+	0.687315i	$0.758789\pi$
$174$	−10.7101	+	9.52628i	−0.811934	+	0.722185i
$175$		0			0
$176$	0.794182	+	1.37556i	0.0598637	+	0.103687i
$177$	−10.6483	−	3.53152i	−0.800377	−	0.265445i
$178$	1.60507	+	2.78007i	0.120305	+	0.208375i
$179$	−8.03706	+	13.9206i	−0.600718	+	1.04047i	0.391994	+	0.919968i	$0.371785\pi$
$179$	−8.03706	+	13.9206i	−0.600718	+	1.04047i	−0.992712	+	0.120507i	$0.961548\pi$
$180$	4.37636	−	1.88510i	0.326194	−	0.140507i
$181$	−8.05308			−0.598581			−0.299291	−	0.954162i	$-0.596750\pi$
$181$	−8.05308			−0.598581			−0.299291	+	0.954162i	$0.596750\pi$
$182$		0			0
$183$	7.36033	+	2.44105i	0.544092	+	0.180448i
$184$	0.150186	−	0.260130i	0.0110719	−	0.0191770i
$185$	1.58836			0.116779
$186$	−4.45853	−	1.47867i	−0.326915	−	0.108421i
$187$	8.57598			0.627138
$188$	−2.66621			−0.194453
$189$		0			0
$190$	−11.2756			−0.818019
$191$	−23.9629			−1.73389			−0.866946	−	0.498402i	$-0.833920\pi$
$191$	−23.9629			−1.73389			−0.866946	+	0.498402i	$0.833920\pi$
$192$	1.64400	+	0.545231i	0.118645	+	0.0393487i
$193$	9.76509			0.702907			0.351453	−	0.936205i	$-0.385688\pi$
$193$	9.76509			0.702907			0.351453	+	0.936205i	$0.385688\pi$
$194$	0.712008	−	1.23323i	0.0511192	−	0.0885410i
$195$	−12.5625	−	4.16635i	−0.899620	−	0.298359i
$196$		0			0
$197$	−18.2436			−1.29980			−0.649900	−	0.760020i	$-0.725189\pi$
$197$	−18.2436			−1.29980			−0.649900	+	0.760020i	$0.725189\pi$
$198$	0.555632	−	4.73259i	0.0394871	−	0.336330i
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	0.343601	+	0.939116i	$0.388353\pi$
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	−0.985098	+	0.171991i	$0.944980\pi$
$200$	−1.23855	−	2.14523i	−0.0875787	−	0.151691i
$201$	−16.5272	−	5.48125i	−1.16574	−	0.386618i
$202$	−6.01671	−	10.4212i	−0.423334	−	0.733236i
$203$		0			0
$204$	6.98762	−	6.21523i	0.489231	−	0.435153i
$205$	−9.33379			−0.651900
$206$	3.04944	−	5.28179i	0.212465	−	0.368000i
$207$	−0.827603	+	0.356487i	−0.0575224	+	0.0247776i
$208$	−2.40545	−	4.16635i	−0.166788	−	0.288885i
$209$	−5.63781	+	9.76497i	−0.389975	+	0.675457i
$210$		0			0
$211$	0.166208	+	0.287880i	0.0114422	+	0.0198185i	0.871690	−	0.490058i	$-0.163024\pi$
$211$	0.166208	+	0.287880i	0.0114422	+	0.0198185i	−0.860248	+	0.509877i	$0.829691\pi$
$212$	2.44437	−	4.23377i	0.167880	−	0.290776i
$213$	20.9127	+	6.93570i	1.43292	+	0.475227i
$214$	1.54325	+	2.67299i	0.105495	+	0.182722i
$215$	1.32327	+	2.29197i	0.0902464	+	0.156311i
$216$	−2.97710	−	4.25874i	−0.202566	−	0.289771i
$217$		0			0
$218$	−1.14400	+	1.98146i	−0.0774812	+	0.134201i
$219$	−20.7756	+	18.4791i	−1.40389	+	1.24870i
$220$	2.52290			0.170094
$221$	−25.9752			−1.74728
$222$	−0.349814	−	1.69636i	−0.0234780	−	0.113852i
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	−0.952348	−	0.305013i	$-0.901339\pi$
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	0.740323	+	0.672251i	$0.234672\pi$
$224$		0			0
$225$	−0.866524	+	7.38061i	−0.0577683	+	0.492040i
$226$	9.73236	+	16.8569i	0.647387	+	1.12131i
$227$	−11.6545	−	20.1862i	−0.773537	−	1.33981i	−0.935613	−	0.353028i	$-0.885152\pi$
$227$	−11.6545	−	20.1862i	−0.773537	−	1.33981i	0.162075	−	0.986778i	$-0.448181\pi$
$228$	2.48329	+	12.0422i	0.164460	+	0.797517i
$229$	−2.47710	+	4.29046i	−0.163691	+	0.283522i	−0.936190	−	0.351495i	$-0.885673\pi$
$229$	−2.47710	+	4.29046i	−0.163691	+	0.283522i	0.772498	+	0.635017i	$0.219007\pi$
$230$	−0.238550	−	0.413181i	−0.0157295	−	0.0272443i
$231$		0			0
$232$	−4.13781	+	7.16689i	−0.271660	+	0.470529i
$233$	−7.13781	−	12.3630i	−0.467613	−	0.809930i	0.531702	−	0.846932i	$-0.321553\pi$
$233$	−7.13781	−	12.3630i	−0.467613	−	0.809930i	−0.999315	+	0.0370017i	$0.988219\pi$
$234$	−1.68292	+	14.3342i	−0.110016	+	0.937057i
$235$	−2.11745	+	3.66754i	−0.138127	+	0.239244i
$236$	−6.47710			−0.421623
$237$	13.7880	+	4.57279i	0.895626	+	0.297034i
$238$		0			0
$239$	2.48762	+	4.30868i	0.160911	+	0.278706i	0.935196	−	0.354132i	$-0.115224\pi$
$239$	2.48762	+	4.30868i	0.160911	+	0.278706i	−0.774285	+	0.632837i	$0.781890\pi$
$240$	2.05563	−	1.82841i	0.132690	−	0.118023i
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$	−4.23855	+	7.34138i	−0.272464	+	0.471922i
$243$	−0.473458	+	15.5813i	−0.0303723	+	0.999539i
$244$	4.47710			0.286617
$245$		0			0
$246$	2.05563	+	9.96840i	0.131062	+	0.635562i
$247$	17.0760	−	29.5765i	1.08652	−	1.88191i
$248$	−2.71201			−0.172213
$249$	−3.06182	+	2.72338i	−0.194035	+	0.172587i
$250$	−11.8764			−0.751127
$251$	−2.43268			−0.153549			−0.0767746	−	0.997048i	$-0.524462\pi$
$251$	−2.43268			−0.153549			−0.0767746	+	0.997048i	$0.524462\pi$
$252$		0			0
$253$	−0.477100			−0.0299950
$254$	13.4400			0.843298
$255$	−3.00000	−	14.5479i	−0.187867	−	0.911027i
$256$	1.00000			0.0625000
$257$	−0.493810	+	0.855304i	−0.0308030	+	0.0533524i	−0.881016	−	0.473087i	$-0.843140\pi$
$257$	−0.493810	+	0.855304i	−0.0308030	+	0.0533524i	0.850213	+	0.526439i	$0.176473\pi$
$258$	2.15638	−	1.91802i	0.134250	−	0.119410i
$259$		0			0
$260$	−7.64145			−0.473902
$261$	22.8015	−	9.82166i	1.41138	−	0.607946i
$262$	1.58836	−	2.75113i	0.0981295	−	0.169965i
$263$	−8.59269	−	14.8830i	−0.529848	−	0.917724i	−0.999394	−	0.0348158i	$-0.988916\pi$
$263$	−8.59269	−	14.8830i	−0.529848	−	0.917724i	0.469545	−	0.882908i	$-0.344418\pi$
$264$	−0.555632	−	2.69443i	−0.0341968	−	0.165831i
$265$	−3.88255	−	6.72477i	−0.238503	−	0.413099i
$266$		0			0
$267$	−1.12296	−	5.44556i	−0.0687237	−	0.333263i
$268$	−10.0531			−0.614090
$269$	−11.4523	+	19.8360i	−0.698262	+	1.20942i	0.270807	+	0.962634i	$0.412709\pi$
$269$	−11.4523	+	19.8360i	−0.698262	+	1.20942i	−0.969069	+	0.246791i	$0.920624\pi$
$270$	−8.22253	+	0.712974i	−0.500407	+	0.0433902i
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	0.571021	−	0.820936i	$-0.306548\pi$
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	−0.996462	+	0.0840504i	$0.973214\pi$
$272$	2.69963	−	4.67589i	0.163689	−	0.283518i
$273$		0			0
$274$	−10.6316	−	18.4145i	−0.642279	−	1.11246i
$275$	−1.96727	+	3.40741i	−0.118631	+	0.205474i
$276$	−0.388736	+	0.345766i	−0.0233991	+	0.0208127i
$277$	−14.1476	−	24.5044i	−0.850049	−	1.47233i	−0.881163	−	0.472813i	$-0.843239\pi$
$277$	−14.1476	−	24.5044i	−0.850049	−	1.47233i	0.0311139	−	0.999516i	$-0.490095\pi$
$278$	6.52654	+	11.3043i	0.391436	+	0.677987i
$279$	6.52359	+	4.86186i	0.390557	+	0.291072i
$280$		0			0
$281$	−8.79782	+	15.2383i	−0.524834	+	0.909039i	0.474748	+	0.880122i	$0.342539\pi$
$281$	−8.79782	+	15.2383i	−0.524834	+	0.909039i	−0.999582	+	0.0289175i	$0.990794\pi$
$282$	4.38323	+	1.45370i	0.261018	+	0.0865665i
$283$	18.5229			1.10107			0.550536	−	0.834811i	$-0.314423\pi$
$283$	18.5229			1.10107			0.550536	+	0.834811i	$0.314423\pi$
$284$	12.7207			0.754833
$285$	18.5371	+	6.14781i	1.09804	+	0.364165i
$286$	−3.82072	+	6.61769i	−0.225924	+	0.391312i
$287$		0			0
$288$	−2.40545	−	1.79272i	−0.141742	−	0.105637i
$289$	−6.07598	−	10.5239i	−0.357411	−	0.619054i
$290$	6.57234	+	11.3836i	0.385941	+	0.668470i
$291$	−1.84294	+	1.63922i	−0.108035	+	0.0960929i
$292$	−8.02654	+	13.9024i	−0.469718	+	0.813575i
$293$	7.04256	+	12.1981i	0.411431	+	0.712619i	0.995046	−	0.0994108i	$-0.0316958\pi$
$293$	7.04256	+	12.1981i	0.411431	+	0.712619i	−0.583616	+	0.812030i	$0.698362\pi$
$294$		0			0
$295$	−5.14400	+	8.90966i	−0.299495	+	0.518741i
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$	−3.49381	+	7.47741i	−0.202731	+	0.433883i
$298$	2.60439	−	4.51093i	0.150868	−	0.261311i
$299$	1.44506			0.0835698
$300$	0.866524	+	4.20205i	0.0500288	+	0.242605i
$301$		0			0
$302$	−0.261450	−	0.452845i	−0.0150448	−	0.0260583i
$303$	4.20946	+	20.4130i	0.241827	+	1.17270i
$304$	3.54944	+	6.14781i	0.203574	+	0.352601i
$305$	3.55563	−	6.15854i	0.203595	−	0.352637i
$306$	−14.8764	+	6.40794i	−0.850425	+	0.366318i
$307$	5.85532			0.334180			0.167090	−	0.985942i	$-0.446563\pi$
$307$	5.85532			0.334180			0.167090	+	0.985942i	$0.446563\pi$
$308$		0			0
$309$	−7.89307	+	7.02059i	−0.449021	+	0.399387i
$310$	−2.15383	+	3.73054i	−0.122329	+	0.211880i
$311$	−0.810892			−0.0459815			−0.0229907	−	0.999736i	$-0.507319\pi$
$311$	−0.810892			−0.0459815			−0.0229907	+	0.999736i	$0.507319\pi$
$312$	1.68292	+	8.16100i	0.0952765	+	0.462025i
$313$	−10.5760			−0.597790			−0.298895	−	0.954286i	$-0.596618\pi$
$313$	−10.5760			−0.597790			−0.298895	+	0.954286i	$0.596618\pi$
$314$	8.86398			0.500223
$315$		0			0
$316$	8.38688			0.471799
$317$	12.1964			0.685018			0.342509	−	0.939515i	$-0.388723\pi$
$317$	12.1964			0.685018			0.342509	+	0.939515i	$0.388723\pi$
$318$	−6.32691	+	5.62755i	−0.354796	+	0.315578i
$319$	13.1447			0.735961
$320$	0.794182	−	1.37556i	0.0443961	−	0.0768963i
$321$	−1.07970	−	5.23582i	−0.0602631	−	0.292235i
$322$		0			0
$323$	38.3287			2.13267
$324$	2.57234	+	8.62456i	0.142908	+	0.479142i
$325$	5.95853	−	10.3205i	0.330520	−	0.572477i
$326$	−10.9814	−	19.0204i	−0.608205	−	1.05344i
$327$	2.96108	−	2.63377i	0.163748	−	0.145648i
$328$	2.93818	+	5.08907i	0.162234	+	0.280997i
$329$		0			0
$330$	−4.14764	−	1.37556i	−0.228320	−	0.0757223i
$331$	−15.6662			−0.861093			−0.430546	−	0.902568i	$-0.641679\pi$
$331$	−15.6662			−0.861093			−0.430546	+	0.902568i	$0.641679\pi$
$332$	−1.18292	+	2.04887i	−0.0649211	+	0.112447i
$333$	−0.349814	+	2.97954i	−0.0191697	+	0.163278i
$334$	1.65019	+	2.85821i	0.0902942	+	0.156394i
$335$	−7.98398	+	13.8287i	−0.436211	+	0.755540i
$336$		0			0
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	0.728200	−	0.685364i	$-0.240357\pi$
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	−0.957643	+	0.287958i	$0.907024\pi$
$338$	5.07234	−	8.78555i	0.275899	−	0.477871i
$339$	−6.80903	−	33.0191i	−0.369816	−	1.79335i
$340$	−4.28799	−	7.42702i	−0.232549	−	0.402787i
$341$	2.15383	+	3.73054i	0.116636	+	0.202020i
$342$	2.48329	−	21.1514i	0.134281	−	1.14374i
$343$		0			0
$344$	0.833104	−	1.44298i	0.0449179	−	0.0778002i
$345$	0.166896	+	0.809332i	0.00898539	+	0.0435730i
$346$	19.1075			1.02723
$347$	0.567323			0.0304555			0.0152277	−	0.999884i	$-0.495153\pi$
$347$	0.567323			0.0304555			0.0152277	+	0.999884i	$0.495153\pi$
$348$	10.7101	−	9.52628i	0.574124	−	0.510662i
$349$	0.00364189	−	0.00630794i	0.000194946	−	0.000337656i	−0.865928	−	0.500169i	$-0.833271\pi$
$349$	0.00364189	−	0.00630794i	0.000194946	−	0.000337656i	0.866123	+	0.499831i	$0.166605\pi$
$350$		0			0
$351$	10.5822	−	22.6478i	0.564835	−	1.20885i
$352$	−0.794182	−	1.37556i	−0.0423300	−	0.0733178i
$353$	3.32691	+	5.76238i	0.177074	+	0.306701i	0.940877	−	0.338748i	$-0.110004\pi$
$353$	3.32691	+	5.76238i	0.177074	+	0.306701i	−0.763803	+	0.645449i	$0.776670\pi$
$354$	10.6483	+	3.53152i	0.565952	+	0.187698i
$355$	10.1025	−	17.4981i	0.536186	−	0.928702i
$356$	−1.60507	−	2.78007i	−0.0850688	−	0.147343i
$357$		0			0
$358$	8.03706	−	13.9206i	0.424772	−	0.735727i
$359$	−0.398568	−	0.690339i	−0.0210356	−	0.0364347i	0.855316	−	0.518107i	$-0.173363\pi$
$359$	−0.398568	−	0.690339i	−0.0210356	−	0.0364347i	−0.876352	+	0.481672i	$0.840030\pi$
$360$	−4.37636	+	1.88510i	−0.230654	+	0.0993536i
$361$	−15.6971	+	27.1881i	−0.826162	+	1.43095i
$362$	8.05308			0.423261
$363$	10.9709	−	9.75822i	0.575823	−	0.512174i
$364$		0			0
$365$	12.7491	+	22.0820i	0.667317	+	1.15583i
$366$	−7.36033	−	2.44105i	−0.384731	−	0.127596i
$367$	−7.71634	−	13.3651i	−0.402790	−	0.697652i	0.591272	−	0.806472i	$-0.298626\pi$
$367$	−7.71634	−	13.3651i	−0.402790	−	0.697652i	−0.994061	+	0.108820i	$0.965293\pi$
$368$	−0.150186	+	0.260130i	−0.00782898	+	0.0135602i
$369$	2.05563	−	17.5088i	0.107012	−	0.911472i
$370$	−1.58836			−0.0825751
$371$		0			0
$372$	4.45853	+	1.47867i	0.231164	+	0.0766655i
$373$	−5.12110	+	8.87000i	−0.265160	+	0.459271i	−0.967606	−	0.252467i	$-0.918758\pi$
$373$	−5.12110	+	8.87000i	−0.265160	+	0.459271i	0.702445	+	0.711738i	$0.252092\pi$
$374$	−8.57598			−0.443454
$375$	19.5247	+	6.47536i	1.00825	+	0.334386i
$376$	2.66621			0.137499
$377$	−39.8131			−2.05048
$378$		0			0
$379$	25.0087			1.28461			0.642304	−	0.766450i	$-0.277979\pi$
$379$	25.0087			1.28461			0.642304	+	0.766450i	$0.277979\pi$
$380$	11.2756			0.578427
$381$	−22.0952	−	7.32788i	−1.13197	−	0.375419i
$382$	23.9629			1.22605
$383$	−3.13348	+	5.42734i	−0.160113	+	0.277324i	−0.934909	−	0.354887i	$-0.884519\pi$
$383$	−3.13348	+	5.42734i	−0.160113	+	0.277324i	0.774796	+	0.632211i	$0.217853\pi$
$384$	−1.64400	−	0.545231i	−0.0838948	−	0.0278237i
$385$		0			0
$386$	−9.76509			−0.497030
$387$	−4.59084	+	1.97749i	−0.233365	+	0.100521i
$388$	−0.712008	+	1.23323i	−0.0361467	+	0.0626080i
$389$	10.8171	+	18.7357i	0.548448	+	0.949940i	0.998381	+	0.0568774i	$0.0181144\pi$
$389$	10.8171	+	18.7357i	0.548448	+	0.949940i	−0.449933	+	0.893062i	$0.648552\pi$
$390$	12.5625	+	4.16635i	0.636127	+	0.210972i
$391$	0.810892	+	1.40451i	0.0410086	+	0.0710290i
$392$		0			0
$393$	−4.11126	+	3.65682i	−0.207386	+	0.184462i
$394$	18.2436			0.919098
$395$	6.66071	−	11.5367i	0.335137	−	0.580473i
$396$	−0.555632	+	4.73259i	−0.0279216	+	0.237821i
$397$	−2.05308	−	3.55605i	−0.103041	−	0.178473i	0.809895	−	0.586575i	$-0.199524\pi$
$397$	−2.05308	−	3.55605i	−0.103041	−	0.178473i	−0.912936	+	0.408102i	$0.866191\pi$
$398$	9.04944	−	15.6741i	0.453608	−	0.785671i
$399$		0			0
$400$	1.23855	+	2.14523i	0.0619275	+	0.107262i
$401$	−8.37085	+	14.4987i	−0.418021	+	0.724033i	−0.995740	−	0.0922024i	$-0.970609\pi$
$401$	−8.37085	+	14.4987i	−0.418021	+	0.724033i	0.577720	+	0.816235i	$0.303943\pi$
$402$	16.5272	+	5.48125i	0.824303	+	0.273380i
$403$	−6.52359	−	11.2992i	−0.324963	−	0.562853i
$404$	6.01671	+	10.4212i	0.299343	+	0.518476i
$405$	13.9065	+	3.31105i	0.691022	+	0.164527i
$406$		0			0
$407$	−0.794182	+	1.37556i	−0.0393661	+	0.0681842i
$408$	−6.98762	+	6.21523i	−0.345939	+	0.307700i
$409$	8.76509			0.433406			0.216703	−	0.976238i	$-0.430470\pi$
$409$	8.76509			0.433406			0.216703	+	0.976238i	$0.430470\pi$
$410$	9.33379			0.460963
$411$	7.43818	+	36.0701i	0.366898	+	1.77920i
$412$	−3.04944	+	5.28179i	−0.150235	+	0.260215i
$413$		0			0
$414$	0.827603	−	0.356487i	0.0406744	−	0.0175204i
$415$	1.87890	+	3.25436i	0.0922318	+	0.159750i
$416$	2.40545	+	4.16635i	0.117937	+	0.204272i
$417$	−4.56615	−	22.1427i	−0.223605	−	1.08433i
$418$	5.63781	−	9.76497i	0.275754	−	0.477620i
$419$	0.210149	+	0.363988i	0.0102664	+	0.0177820i	0.871113	−	0.491083i	$-0.163399\pi$
$419$	0.210149	+	0.363988i	0.0102664	+	0.0177820i	−0.860847	+	0.508865i	$0.830065\pi$
$420$		0			0
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	−0.774710	−	0.632316i	$-0.782104\pi$
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	0.934957	+	0.354761i	$0.115438\pi$
$422$	−0.166208	−	0.287880i	−0.00809086	−	0.0140138i
$423$	−6.41342	−	4.77975i	−0.311831	−	0.232399i
$424$	−2.44437	+	4.23377i	−0.118709	+	0.205610i
$425$	13.3745			0.648758
$426$	−20.9127	−	6.93570i	−1.01323	−	0.336036i
$427$		0			0
$428$	−1.54325	−	2.67299i	−0.0745959	−	0.129204i
$429$	9.88942	−	8.79628i	0.477466	−	0.424688i
$430$	−1.32327	−	2.29197i	−0.0638138	−	0.110529i
$431$	11.0439	−	19.1287i	0.531968	−	0.921395i	−0.467336	−	0.884080i	$-0.654786\pi$
$431$	11.0439	−	19.1287i	0.531968	−	0.921395i	0.999304	−	0.0373155i	$-0.0118806\pi$
$432$	2.97710	+	4.25874i	0.143236	+	0.204899i
$433$	9.43268			0.453306			0.226653	−	0.973976i	$-0.427222\pi$
$433$	9.43268			0.453306			0.226653	+	0.973976i	$0.427222\pi$
$434$		0			0
$435$	−4.59820	−	22.2981i	−0.220467	−	1.06911i
$436$	1.14400	−	1.98146i	0.0547875	−	0.0948947i
$437$	−2.13231			−0.102002
$438$	20.7756	−	18.4791i	0.992697	−	0.882967i
$439$	31.2064			1.48940			0.744701	−	0.667398i	$-0.232592\pi$
$439$	31.2064			1.48940			0.744701	+	0.667398i	$0.232592\pi$
$440$	−2.52290			−0.120275
$441$		0			0
$442$	25.9752			1.23552
$443$	13.0545			0.620236			0.310118	−	0.950698i	$-0.399631\pi$
$443$	13.0545			0.620236			0.310118	+	0.950698i	$0.399631\pi$
$444$	0.349814	+	1.69636i	0.0166014	+	0.0805056i
$445$	−5.09888			−0.241710
$446$	3.16621	−	5.48403i	0.149924	−	0.259676i
$447$	−6.74110	+	5.99596i	−0.318843	+	0.283599i
$448$		0			0
$449$	−9.91706			−0.468015			−0.234008	−	0.972235i	$-0.575184\pi$
$449$	−9.91706			−0.468015			−0.234008	+	0.972235i	$0.575184\pi$
$450$	0.866524	−	7.38061i	0.0408484	−	0.347925i
$451$	4.66690	−	8.08330i	0.219756	−	0.380628i
$452$	−9.73236	−	16.8569i	−0.457772	−	0.792884i
$453$	0.182918	+	0.887026i	0.00859423	+	0.0416761i
$454$	11.6545	+	20.1862i	0.546974	+	0.947386i
$455$		0			0
$456$	−2.48329	−	12.0422i	−0.116291	−	0.563930i
$457$	−24.5229			−1.14713			−0.573566	−	0.819159i	$-0.694441\pi$
$457$	−24.5229			−1.14713			−0.573566	+	0.819159i	$0.694441\pi$
$458$	2.47710	−	4.29046i	0.115747	−	0.200480i
$459$	27.9505	−	2.42358i	1.30462	−	0.113123i
$460$	0.238550	+	0.413181i	0.0111224	+	0.0192646i
$461$	−1.75526	+	3.04020i	−0.0817506	+	0.141596i	−0.904002	−	0.427528i	$-0.859384\pi$
$461$	−1.75526	+	3.04020i	−0.0817506	+	0.141596i	0.822251	+	0.569125i	$0.192718\pi$
$462$		0			0
$463$	8.69413	+	15.0587i	0.404050	+	0.699836i	0.994210	−	0.107451i	$-0.0342687\pi$
$463$	8.69413	+	15.0587i	0.404050	+	0.699836i	−0.590160	+	0.807286i	$0.700935\pi$
$464$	4.13781	−	7.16689i	0.192093	−	0.332715i
$465$	5.57489	−	4.95866i	0.258529	−	0.229952i
$466$	7.13781	+	12.3630i	0.330652	+	0.572707i
$467$	−6.69894	−	11.6029i	−0.309990	−	0.536918i	0.668370	−	0.743829i	$-0.266992\pi$
$467$	−6.69894	−	11.6029i	−0.309990	−	0.536918i	−0.978360	+	0.206911i	$0.933659\pi$
$468$	1.68292	−	14.3342i	0.0777929	−	0.662600i
$469$		0			0
$470$	2.11745	−	3.66754i	0.0976709	−	0.169171i
$471$	−14.5723	−	4.83292i	−0.671458	−	0.222689i
$472$	6.47710			0.298133
$473$	−2.64654			−0.121688
$474$	−13.7880	−	4.57279i	−0.633303	−	0.210035i
$475$	−8.79232	+	15.2287i	−0.403419	+	0.698743i
$476$		0			0
$477$	13.4697	−	5.80205i	0.616737	−	0.265658i
$478$	−2.48762	−	4.30868i	−0.113781	−	0.197075i
$479$	10.4029	+	18.0183i	0.475321	+	0.823279i	0.999600	−	0.0282667i	$-0.00899876\pi$
$479$	10.4029	+	18.0183i	0.475321	+	0.823279i	−0.524280	+	0.851546i	$0.675665\pi$
$480$	−2.05563	+	1.82841i	−0.0938263	+	0.0834550i
$481$	2.40545	−	4.16635i	0.109679	−	0.189969i
$482$	6.50000	+	11.2583i	0.296067	+	0.512803i
$483$		0			0
$484$	4.23855	−	7.34138i	0.192661	−	0.333699i
$485$	1.13093	+	1.95882i	0.0513528	+	0.0889456i
$486$	0.473458	−	15.5813i	0.0214765	−	0.706781i
$487$	16.2472	−	28.1410i	0.736231	−	1.27519i	−0.217950	−	0.975960i	$-0.569937\pi$
$487$	16.2472	−	28.1410i	0.736231	−	1.27519i	0.954181	−	0.299230i	$-0.0967298\pi$
$488$	−4.47710			−0.202669
$489$	7.68292	+	37.2569i	0.347434	+	1.68481i
$490$		0			0
$491$	−9.66071	−	16.7328i	−0.435982	−	0.755142i	0.561394	−	0.827549i	$-0.310265\pi$
$491$	−9.66071	−	16.7328i	−0.435982	−	0.755142i	−0.997375	+	0.0724067i	$0.976932\pi$
$492$	−2.05563	−	9.96840i	−0.0926751	−	0.449410i
$493$	−22.3411	−	38.6959i	−1.00619	−	1.74277i
$494$	−17.0760	+	29.5765i	−0.768285	+	1.33071i
$495$	6.06870	+	4.52284i	0.272768	+	0.203287i
$496$	2.71201			0.121773
$497$		0			0
$498$	3.06182	−	2.72338i	0.137204	−	0.122037i
$499$	5.57530	−	9.65670i	0.249585	−	0.432293i	−0.713826	−	0.700323i	$-0.753039\pi$
$499$	5.57530	−	9.65670i	0.249585	−	0.432293i	0.963411	+	0.268030i	$0.0863726\pi$
$500$	11.8764			0.531127
$501$	−1.15452	−	5.59861i	−0.0515800	−	0.250128i
$502$	2.43268			0.108576
$503$	40.7651			1.81763			0.908813	−	0.417204i	$-0.136990\pi$
$503$	40.7651			1.81763			0.908813	+	0.417204i	$0.136990\pi$
$504$		0			0
$505$	19.1135			0.850537
$506$	0.477100			0.0212097
$507$	−13.1291	+	11.6778i	−0.583082	+	0.518630i
$508$	−13.4400			−0.596302
$509$	0.722528	−	1.25146i	0.0320255	−	0.0554698i	−0.849568	−	0.527478i	$-0.823138\pi$
$509$	0.722528	−	1.25146i	0.0320255	−	0.0554698i	0.881594	+	0.472009i	$0.156471\pi$
$510$	3.00000	+	14.5479i	0.132842	+	0.644194i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−15.6149	+	33.4188i	−0.689415	+	1.47548i
$514$	0.493810	−	0.855304i	0.0217810	−	0.0377259i
$515$	4.84362	+	8.38940i	0.213436	+	0.369681i
$516$	−2.15638	+	1.91802i	−0.0949292	+	0.0844360i
$517$	−2.11745	−	3.66754i	−0.0931255	−	0.161298i
$518$		0			0
$519$	−31.4127	−	10.4180i	−1.37887	−	0.457301i
$520$	7.64145			0.335100
$521$	−9.64214	+	16.7007i	−0.422430	+	0.731670i	−0.996177	−	0.0873630i	$-0.972156\pi$
$521$	−9.64214	+	16.7007i	−0.422430	+	0.731670i	0.573747	+	0.819033i	$0.305489\pi$
$522$	−22.8015	+	9.82166i	−0.997993	+	0.429882i
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	0.918173	+	0.396180i	$0.129665\pi$
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	−0.115984	+	0.993251i	$0.537002\pi$
$524$	−1.58836	+	2.75113i	−0.0693880	+	0.120184i
$525$		0			0
$526$	8.59269	+	14.8830i	0.374659	+	0.648929i
$527$	7.32141	−	12.6811i	0.318926	−	0.552396i
$528$	0.555632	+	2.69443i	0.0241808	+	0.117260i
$529$	11.4549	+	19.8404i	0.498039	+	0.862628i
$530$	3.88255	+	6.72477i	0.168647	+	0.292105i
$531$	−15.5803	−	11.6116i	−0.676128	−	0.503900i
$532$		0			0
$533$	−14.1353	+	24.4830i	−0.612266	+	1.06048i
$534$	1.12296	+	5.44556i	0.0485950	+	0.235652i
$535$	−4.90249			−0.211953
$536$	10.0531			0.434227
$537$	−20.8028	+	18.5034i	−0.897709	+	0.798479i
$538$	11.4523	−	19.8360i	0.493745	−	0.855192i
$539$		0			0
$540$	8.22253	−	0.712974i	0.353841	−	0.0306815i
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	0.828967	−	0.559298i	$-0.188929\pi$
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	−0.898849	+	0.438258i	$0.855596\pi$
$542$	7.00364	+	12.1307i	0.300832	+	0.521057i
$543$	−13.2392	−	4.39079i	−0.568150	−	0.188427i
$544$	−2.69963	+	4.67589i	−0.115746	+	0.200477i
$545$	−1.81708	−	3.14728i	−0.0778352	−	0.134815i
$546$		0			0
$547$	−2.95853	+	5.12432i	−0.126498	+	0.219100i	−0.922317	−	0.386433i	$-0.873707\pi$
$547$	−2.95853	+	5.12432i	−0.126498	+	0.219100i	0.795820	+	0.605534i	$0.207040\pi$
$548$	10.6316	+	18.4145i	0.454160	+	0.786628i
$549$	10.7694	+	8.02617i	0.459628	+	0.342548i
$550$	1.96727	−	3.40741i	0.0838846	−	0.145292i
$551$	58.7476			2.50273
$552$	0.388736	−	0.345766i	0.0165457	−	0.0147168i
$553$		0			0
$554$	14.1476	+	24.5044i	0.601076	+	1.04109i
$555$	2.61126	+	0.866025i	0.110842	+	0.0367607i
$556$	−6.52654	−	11.3043i	−0.276787	−	0.479409i
$557$	12.8040	−	22.1772i	0.542523	−	0.939678i	−0.456235	−	0.889859i	$-0.650802\pi$
$557$	12.8040	−	22.1772i	0.542523	−	0.939678i	0.998758	−	0.0498188i	$-0.0158644\pi$
$558$	−6.52359	−	4.86186i	−0.276166	−	0.205819i
$559$	8.01594			0.339038
$560$		0			0
$561$	14.0989	+	4.67589i	0.595255	+	0.197416i
$562$	8.79782	−	15.2383i	0.371114	−	0.642788i
$563$	46.6377			1.96555			0.982773	−	0.184817i	$-0.0591692\pi$
$563$	46.6377			1.96555			0.982773	+	0.184817i	$0.0591692\pi$
$564$	−4.38323	−	1.45370i	−0.184567	−	0.0612118i
$565$	−30.9171			−1.30069
$566$	−18.5229			−0.778576
$567$		0			0
$568$	−12.7207			−0.533747
$569$	31.1978			1.30788			0.653939	−	0.756547i	$-0.273115\pi$
$569$	31.1978			1.30788			0.653939	+	0.756547i	$0.273115\pi$
$570$	−18.5371	−	6.14781i	−0.776432	−	0.257504i
$571$	−15.6762			−0.656030			−0.328015	−	0.944672i	$-0.606380\pi$
$571$	−15.6762			−0.656030			−0.328015	+	0.944672i	$0.606380\pi$
$572$	3.82072	−	6.61769i	0.159752	−	0.276699i
$573$	−39.3948	−	13.0653i	−1.64574	−	0.545811i
$574$		0			0
$575$	−0.744051			−0.0310291
$576$	2.40545	+	1.79272i	0.100227	+	0.0746965i
$577$	−6.99567	+	12.1169i	−0.291234	+	0.504431i	−0.974102	−	0.226110i	$-0.927399\pi$
$577$	−6.99567	+	12.1169i	−0.291234	+	0.504431i	0.682868	+	0.730542i	$0.260732\pi$
$578$	6.07598	+	10.5239i	0.252728	+	0.437737i
$579$	16.0538	+	5.32423i	0.667172	+	0.221268i
$580$	−6.57234	−	11.3836i	−0.272902	−	0.472680i
$581$		0			0
$582$	1.84294	−	1.63922i	0.0763921	−	0.0679480i
$583$	7.76509			0.321597
$584$	8.02654	−	13.9024i	0.332141	−	0.575285i
$585$	−18.3811	−	13.6989i	−0.759965	−	0.566382i
$586$	−7.04256	−	12.1981i	−0.290926	−	0.503898i
$587$	−1.44801	+	2.50803i	−0.0597658	+	0.103517i	−0.894360	−	0.447348i	$-0.852369\pi$
$587$	−1.44801	+	2.50803i	−0.0597658	+	0.103517i	0.834594	+	0.550865i	$0.185702\pi$
$588$		0			0
$589$	9.62612	+	16.6729i	0.396637	+	0.686996i
$590$	5.14400	−	8.90966i	0.211775	−	0.366805i
$591$	−29.9924	−	9.94696i	−1.23372	−	0.409163i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	2.04394	+	3.54021i	0.0839346	+	0.145379i	0.904937	−	0.425546i	$-0.139918\pi$
$593$	2.04394	+	3.54021i	0.0839346	+	0.145379i	−0.821002	+	0.570925i	$0.806585\pi$
$594$	3.49381	−	7.47741i	0.143353	−	0.306802i
$595$		0			0
$596$	−2.60439	+	4.51093i	−0.106680	+	0.184775i
$597$	−23.4233	+	20.8341i	−0.958650	+	0.852683i
$598$	−1.44506			−0.0590928
$599$	−19.7651			−0.807580			−0.403790	−	0.914852i	$-0.632307\pi$
$599$	−19.7651			−0.807580			−0.403790	+	0.914852i	$0.632307\pi$
$600$	−0.866524	−	4.20205i	−0.0353757	−	0.171548i
$601$	13.4320	−	23.2649i	0.547902	−	0.948994i	−0.450516	−	0.892768i	$-0.648760\pi$
$601$	13.4320	−	23.2649i	0.547902	−	0.948994i	0.998418	−	0.0562261i	$-0.0179068\pi$
$602$		0			0
$603$	−24.1822	−	18.0223i	−0.984773	−	0.733926i
$604$	0.261450	+	0.452845i	0.0106383	+	0.0184260i
$605$	−6.73236	−	11.6608i	−0.273709	−	0.474079i
$606$	−4.20946	−	20.4130i	−0.170998	−	0.829221i
$607$	−7.62110	+	13.2001i	−0.309331	+	0.535777i	−0.978216	−	0.207589i	$-0.933438\pi$
$607$	−7.62110	+	13.2001i	−0.309331	+	0.535777i	0.668885	+	0.743366i	$0.266772\pi$
$608$	−3.54944	−	6.14781i	−0.143949	−	0.249327i
$609$		0			0
$610$	−3.55563	+	6.15854i	−0.143963	+	0.249352i
$611$	6.41342	+	11.1084i	0.259459	+	0.449396i
$612$	14.8764	−	6.40794i	0.601341	−	0.259026i
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	−0.892189	−	0.451662i	$-0.850831\pi$
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	0.837246	+	0.546827i	$0.184165\pi$
$614$	−5.85532			−0.236301
$615$	−15.3447	−	5.08907i	−0.618759	−	0.205211i
$616$		0			0
$617$	−9.21812	−	15.9663i	−0.371108	−	0.642777i	0.618629	−	0.785684i	$-0.287689\pi$
$617$	−9.21812	−	15.9663i	−0.371108	−	0.642777i	−0.989736	+	0.142906i	$0.954355\pi$
$618$	7.89307	−	7.02059i	0.317506	−	0.282410i
$619$	0.0537728	+	0.0931373i	0.00216131	+	0.00374350i	0.867104	−	0.498127i	$-0.165979\pi$
$619$	0.0537728	+	0.0931373i	0.00216131	+	0.00374350i	−0.864943	+	0.501871i	$0.832645\pi$
$620$	2.15383	−	3.73054i	0.0864998	−	0.149822i
$621$	−1.55494	+	0.134829i	−0.0623977	+	0.00541050i
$622$	0.810892			0.0325138
$623$		0			0
$624$	−1.68292	−	8.16100i	−0.0673706	−	0.326701i
$625$	3.23924	−	5.61053i	0.129570	−	0.224421i
$626$	10.5760			0.422701
$627$	−14.5927	+	12.9797i	−0.582776	+	0.518358i
$628$	−8.86398			−0.353711
$629$	5.39926			0.215282
$630$		0			0
$631$	35.7266			1.42225			0.711126	−	0.703064i	$-0.248185\pi$
$631$	35.7266			1.42225			0.711126	+	0.703064i	$0.248185\pi$
$632$	−8.38688			−0.333612
$633$	0.116283	+	0.563895i	0.00462185	+	0.0224128i
$634$	−12.1964			−0.484381
$635$	−10.6738	+	18.4875i	−0.423576	+	0.733655i
$636$	6.32691	−	5.62755i	0.250878	−	0.223147i
$637$		0			0
$638$	−13.1447			−0.520403
$639$	30.5989	+	22.8045i	1.21047	+	0.902134i
$640$	−0.794182	+	1.37556i	−0.0313928	+	0.0543739i
$641$	−8.65638	−	14.9933i	−0.341906	−	0.592199i	0.642880	−	0.765967i	$-0.277739\pi$
$641$	−8.65638	−	14.9933i	−0.341906	−	0.592199i	−0.984787	+	0.173767i	$0.944406\pi$
$642$	1.07970	+	5.23582i	0.0426125	+	0.206641i
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	−0.996451	−	0.0841700i	$-0.973176\pi$
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	0.425332	−	0.905037i	$-0.360157\pi$
$644$		0			0
$645$	0.925798	+	4.48949i	0.0364533	+	0.176773i
$646$	−38.3287			−1.50802
$647$	−1.27816	+	2.21384i	−0.0502497	+	0.0870350i	−0.890056	−	0.455851i	$-0.849335\pi$
$647$	−1.27816	+	2.21384i	−0.0502497	+	0.0870350i	0.839807	+	0.542886i	$0.182668\pi$
$648$	−2.57234	−	8.62456i	−0.101051	−	0.338805i
$649$	−5.14400	−	8.90966i	−0.201920	−	0.349735i
$650$	−5.95853	+	10.3205i	−0.233713	+	0.404802i
$651$		0			0
$652$	10.9814	+	19.0204i	0.430066	+	0.744896i
$653$	−14.9883	+	25.9605i	−0.586538	+	1.01591i	0.408144	+	0.912918i	$0.366176\pi$
$653$	−14.9883	+	25.9605i	−0.586538	+	1.01591i	−0.994682	+	0.102996i	$0.967157\pi$
$654$	−2.96108	+	2.63377i	−0.115787	+	0.102989i
$655$	2.52290	+	4.36979i	0.0985779	+	0.170742i
$656$	−2.93818	−	5.08907i	−0.114717	−	0.198695i
$657$	−44.2304	+	19.0521i	−1.72559	+	0.743294i
$658$		0			0
$659$	−7.63162	+	13.2183i	−0.297286	+	0.514914i	−0.975514	−	0.219937i	$-0.929415\pi$
$659$	−7.63162	+	13.2183i	−0.297286	+	0.514914i	0.678228	+	0.734851i	$0.262748\pi$
$660$	4.14764	+	1.37556i	0.161447	+	0.0535437i
$661$	27.2522			1.05999			0.529994	−	0.848001i	$-0.322194\pi$
$661$	27.2522			1.05999			0.529994	+	0.848001i	$0.322194\pi$
$662$	15.6662			0.608884
$663$	−42.7032	−	14.1625i	−1.65845	−	0.550026i
$664$	1.18292	−	2.04887i	0.0459061	−	0.0795117i
$665$		0			0
$666$	0.349814	−	2.97954i	0.0135550	−	0.115455i
$667$	1.24288	+	2.15273i	0.0481245	+	0.0833541i
$668$	−1.65019	−	2.85821i	−0.0638476	−	0.110587i
$669$	−8.19530	+	7.28941i	−0.316849	+	0.281825i
$670$	7.98398	−	13.8287i	0.308448	−	0.534248i
$671$	3.55563	+	6.15854i	0.137264	+	0.237748i
$672$		0			0
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.0620280	−	0.998074i	$-0.480243\pi$
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.833344	−	0.552755i	$-0.186423\pi$
$674$	4.21201	+	7.29541i	0.162240	+	0.281009i
$675$	−5.44870	+	11.6612i	−0.209721	+	0.448841i
$676$	−5.07234	+	8.78555i	−0.195090	+	0.337906i
$677$	−5.09888			−0.195966			−0.0979830	−	0.995188i	$-0.531239\pi$
$677$	−5.09888			−0.195966			−0.0979830	+	0.995188i	$0.531239\pi$
$678$	6.80903	+	33.0191i	0.261499	+	1.26809i
$679$		0			0
$680$	4.28799	+	7.42702i	0.164437	+	0.284813i
$681$	−8.15383	−	39.5405i	−0.312455	−	1.51519i
$682$	−2.15383	−	3.73054i	−0.0824743	−	0.142850i
$683$	−7.77197	+	13.4614i	−0.297386	+	0.515088i	−0.975537	−	0.219835i	$-0.929448\pi$
$683$	−7.77197	+	13.4614i	−0.297386	+	0.515088i	0.678151	+	0.734923i	$0.262782\pi$
$684$	−2.48329	+	21.1514i	−0.0949510	+	0.808743i
$685$	33.7738			1.29043
$686$		0			0
$687$	−6.41164	+	5.70291i	−0.244619	+	0.217580i
$688$	−0.833104	+	1.44298i	−0.0317618	+	0.0550130i
$689$	−23.5192			−0.896009
$690$	−0.166896	−	0.809332i	−0.00635363	−	0.0308107i
$691$	−23.2967			−0.886246			−0.443123	−	0.896461i	$-0.646130\pi$
$691$	−23.2967			−0.886246			−0.443123	+	0.896461i	$0.646130\pi$
$692$	−19.1075			−0.726360
$693$		0			0
$694$	−0.567323			−0.0215353
$695$	−20.7330			−0.786449
$696$	−10.7101	+	9.52628i	−0.405967	+	0.361093i
$697$	−31.7280			−1.20178
$698$	−0.00364189	+	0.00630794i	−0.000137848	+	0.000238759i
$699$	−4.99381	−	24.2165i	−0.188883	−	0.915954i
$700$		0			0
$701$	−45.6464			−1.72404			−0.862020	−	0.506874i	$-0.830801\pi$
$701$	−45.6464			−1.72404			−0.862020	+	0.506874i	$0.830801\pi$
$702$	−10.5822	+	22.6478i	−0.399398	+	0.854787i
$703$	−3.54944	+	6.14781i	−0.133870	+	0.231869i
$704$	0.794182	+	1.37556i	0.0299319	+	0.0518435i
$705$	−5.48074	+	4.87492i	−0.206417	+	0.183600i
$706$	−3.32691	−	5.76238i	−0.125210	−	0.216870i
$707$		0			0
$708$	−10.6483	−	3.53152i	−0.400189	−	0.132723i
$709$	18.0014			0.676056			0.338028	−	0.941136i	$-0.390240\pi$
$709$	18.0014			0.676056			0.338028	+	0.941136i	$0.390240\pi$
$710$	−10.1025	+	17.4981i	−0.379141	+	0.656692i
$711$	20.1742	+	15.0353i	0.756591	+	0.563867i
$712$	1.60507	+	2.78007i	0.0601527	+	0.104188i
$713$	−0.407305	+	0.705474i	−0.0152537	+	0.0264202i
$714$		0			0
$715$	−6.06870	−	10.5113i	−0.226957	−	0.393100i
$716$	−8.03706	+	13.9206i	−0.300359	+	0.520237i
$717$	1.74041	+	8.43979i	0.0649968	+	0.315190i
$718$	0.398568	+	0.690339i	0.0148744	+	0.0257632i
$719$	−18.4389	−	31.9371i	−0.687654	−	1.19105i	−0.972595	−	0.232506i	$-0.925307\pi$
$719$	−18.4389	−	31.9371i	−0.687654	−	1.19105i	0.284941	−	0.958545i	$-0.408026\pi$
$720$	4.37636	−	1.88510i	0.163097	−	0.0702536i
$721$		0			0
$722$	15.6971	−	27.1881i	0.584185	−	1.01184i
$723$	−4.54758	−	22.0527i	−0.169126	−	0.820147i
$724$	−8.05308			−0.299291
$725$	20.4995			0.761333
$726$	−10.9709	+	9.75822i	−0.407169	+	0.362161i
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	0.431692	+	0.902021i	$0.357917\pi$
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	−0.997019	+	0.0771543i	$0.975417\pi$
$728$		0			0
$729$	−9.27375	+	25.3574i	−0.343472	+	0.939163i
$730$	−12.7491	−	22.0820i	−0.471864	−	0.817293i
$731$	4.49814	+	7.79101i	0.166370	+	0.288161i
$732$	7.36033	+	2.44105i	0.272046	+	0.0902240i
$733$	3.07530	−	5.32657i	0.113589	−	0.196741i	−0.803626	−	0.595135i	$-0.797099\pi$
$733$	3.07530	−	5.32657i	0.113589	−	0.196741i	0.917215	+	0.398393i	$0.130432\pi$
$734$	7.71634	+	13.3651i	0.284815	+	0.493314i
$735$		0			0
$736$	0.150186	−	0.260130i	0.00553593	−	0.00958851i
$737$	−7.98398	−	13.8287i	−0.294094	−	0.509385i
$738$	−2.05563	+	17.5088i	−0.0756689	+	0.644508i
$739$	−20.3912	+	35.3186i	−0.750103	+	1.29922i	0.197670	+	0.980269i	$0.436663\pi$
$739$	−20.3912	+	35.3186i	−0.750103	+	1.29922i	−0.947772	+	0.318947i	$0.896671\pi$
$740$	1.58836			0.0583894
$741$	44.1989	−	39.3132i	1.62369	−	1.44421i
$742$		0			0
$743$	7.25271	+	12.5621i	0.266076	+	0.460858i	0.967845	−	0.251547i	$-0.0809394\pi$
$743$	7.25271	+	12.5621i	0.266076	+	0.460858i	−0.701769	+	0.712405i	$0.747606\pi$
$744$	−4.45853	−	1.47867i	−0.163458	−	0.0542107i
$745$	4.13671	+	7.16500i	0.151557	+	0.262505i
$746$	5.12110	−	8.87000i	0.187497	−	0.324754i
$747$	−6.51849	+	2.80782i	−0.238499	+	0.102733i
$748$	8.57598			0.313569
$749$		0			0
$750$	−19.5247	−	6.47536i	−0.712941	−	0.236447i
$751$	−2.09455	+	3.62787i	−0.0764314	+	0.132383i	−0.901708	−	0.432346i	$-0.857686\pi$
$751$	−2.09455	+	3.62787i	−0.0764314	+	0.132383i	0.825276	+	0.564729i	$0.191019\pi$
$752$	−2.66621			−0.0972266
$753$	−3.99931	−	1.32637i	−0.145743	−	0.0483356i
$754$	39.8131			1.44991
$755$	0.830556			0.0302270
$756$		0			0
$757$	2.38688			0.0867525			0.0433763	−	0.999059i	$-0.486189\pi$
$757$	2.38688			0.0867525			0.0433763	+	0.999059i	$0.486189\pi$
$758$	−25.0087			−0.908355
$759$	−0.784350	−	0.260130i	−0.0284701	−	0.00944211i
$760$	−11.2756			−0.409009
$761$	1.81708	−	3.14728i	0.0658692	−	0.114089i	−0.831210	−	0.555959i	$-0.812351\pi$
$761$	1.81708	−	3.14728i	0.0658692	−	0.114089i	0.897079	+	0.441870i	$0.145685\pi$
$762$	22.0952	+	7.32788i	0.800426	+	0.265461i
$763$		0			0
$764$	−23.9629			−0.866946
$765$	3.00000	−	25.5524i	0.108465	−	0.923851i
$766$	3.13348	−	5.42734i	0.113217	−	0.196098i
$767$	15.5803	+	26.9859i	0.562573	+	0.974404i
$768$	1.64400	+	0.545231i	0.0593226	+	0.0196743i
$769$	19.9672	+	34.5842i	0.720035	+	1.24714i	0.960985	+	0.276600i	$0.0892078\pi$
$769$	19.9672	+	34.5842i	0.720035	+	1.24714i	−0.240950	+	0.970538i	$0.577459\pi$
$770$		0			0
$771$	−1.27816	+	1.13688i	−0.0460318	+	0.0409436i
$772$	9.76509			0.351453
$773$	−18.0698	+	31.2978i	−0.649925	+	1.12570i	0.333215	+	0.942851i	$0.391867\pi$
$773$	−18.0698	+	31.2978i	−0.649925	+	1.12570i	−0.983140	+	0.182853i	$0.941467\pi$
$774$	4.59084	−	1.97749i	0.165014	−	0.0710793i
$775$	3.35896	+	5.81788i	0.120657	+	0.208985i
$776$	0.712008	−	1.23323i	0.0255596	−	0.0442705i
$777$		0			0
$778$	−10.8171	−	18.7357i	−0.387811	−	0.671709i
$779$	20.8578	−	36.1267i	0.747308	−	1.29438i
$780$	−12.5625	−	4.16635i	−0.449810	−	0.149179i
$781$	10.1025	+	17.4981i	0.361497	+	0.626131i
$782$	−0.810892	−	1.40451i	−0.0289974	−	0.0502251i
$783$	42.8406	−	3.71470i	1.53100	−	0.132753i
$784$		0			0
$785$	−7.03961	+	12.1930i	−0.251254	+	0.435186i
$786$	4.11126	−	3.65682i	0.146644	−	0.130434i
$787$	44.6377			1.59116			0.795582	−	0.605846i	$-0.207165\pi$
$787$	44.6377			1.59116			0.795582	+	0.605846i	$0.207165\pi$
$788$	−18.2436			−0.649900
$789$	−6.01169	−	29.1526i	−0.214022	−	1.03786i
$790$	−6.66071	+	11.5367i	−0.236977	+	0.410457i
$791$		0			0
$792$	0.555632	−	4.73259i	0.0197435	−	0.168165i
$793$	−10.7694	−	18.6532i	−0.382433	−	0.662394i
$794$	2.05308	+	3.55605i	0.0728612	+	0.126199i
$795$	−2.71634	−	13.1724i	−0.0963386	−	0.467176i
$796$	−9.04944	+	15.6741i	−0.320749	+	0.555554i
$797$	−26.2836	−	45.5245i	−0.931012	−	1.61256i	−0.781595	−	0.623786i	$-0.785593\pi$
$797$	−26.2836	−	45.5245i	−0.931012	−	1.61256i	−0.149418	−	0.988774i	$-0.547740\pi$
$798$		0			0
$799$	−7.19777	+	12.4669i	−0.254639	+	0.441047i
$800$	−1.23855	−	2.14523i	−0.0437894	−	0.0758454i
$801$	1.12296	−	9.56475i	0.0396777	−	0.337954i
$802$	8.37085	−	14.4987i	0.295585	−	0.511969i
$803$	−25.4981			−0.899810
$804$	−16.5272	−	5.48125i	−0.582870	−	0.193309i
$805$		0			0
$806$	6.52359	+	11.2992i	0.229784	+	0.397997i
$807$	−29.6428	+	26.3662i	−1.04348	+	0.928134i
$808$	−6.01671	−	10.4212i	−0.211667	−	0.366618i
$809$	7.40290	−	12.8222i	0.260272	−	0.450804i	−0.706042	−	0.708170i	$-0.749521\pi$
$809$	7.40290	−	12.8222i	0.260272	−	0.450804i	0.966314	+	0.257365i	$0.0828544\pi$
$810$	−13.9065	−	3.31105i	−0.488626	−	0.116338i
$811$	−27.0704			−0.950571			−0.475285	−	0.879832i	$-0.657655\pi$
$811$	−27.0704			−0.950571			−0.475285	+	0.879832i	$0.657655\pi$
$812$		0			0
$813$	−4.89995	−	23.7614i	−0.171849	−	0.833348i
$814$	0.794182	−	1.37556i	0.0278361	−	0.0482135i
$815$	34.8850			1.22197
$816$	6.98762	−	6.21523i	0.244616	−	0.217577i
$817$	−11.8282			−0.413817
$818$	−8.76509			−0.306464
$819$		0			0
$820$	−9.33379			−0.325950
$821$	43.8182			1.52926			0.764632	−	0.644467i	$-0.222921\pi$
$821$	43.8182			1.52926			0.764632	+	0.644467i	$0.222921\pi$
$822$	−7.43818	−	36.0701i	−0.259436	−	1.25809i
$823$	31.3425			1.09253			0.546265	−	0.837613i	$-0.316049\pi$
$823$	31.3425			1.09253			0.546265	+	0.837613i	$0.316049\pi$
$824$	3.04944	−	5.28179i	0.106232	−	0.184000i
$825$	−5.09201	+	4.52915i	−0.177281	+	0.157685i
$826$		0			0
$827$	−14.7665			−0.513480			−0.256740	−	0.966480i	$-0.582648\pi$
$827$	−14.7665			−0.513480			−0.256740	+	0.966480i	$0.582648\pi$
$828$	−0.827603	+	0.356487i	−0.0287612	+	0.0123888i
$829$	15.0036	−	25.9871i	0.521098	−	0.902568i	−0.478601	−	0.878033i	$-0.658856\pi$
$829$	15.0036	−	25.9871i	0.521098	−	0.902568i	0.999699	−	0.0245357i	$-0.00781074\pi$
$830$	−1.87890	−	3.25436i	−0.0652177	−	0.112960i
$831$	−9.89809	−	47.9989i	−0.343361	−	1.66506i
$832$	−2.40545	−	4.16635i	−0.0833938	−	0.144442i
$833$		0			0
$834$	4.56615	+	22.1427i	0.158113	+	0.766739i
$835$	−5.24219			−0.181414
$836$	−5.63781	+	9.76497i	−0.194988	+	0.337728i
$837$	8.07392	+	11.5497i	0.279075	+	0.399217i
$838$	−0.210149	−	0.363988i	−0.00725946	−	0.0125738i
$839$	−18.0167	+	31.2059i	−0.622006	+	1.07735i	0.367106	+	0.930179i	$0.380349\pi$
$839$	−18.0167	+	31.2059i	−0.622006	+	1.07735i	−0.989112	+	0.147167i	$0.952985\pi$
$840$		0			0
$841$	−19.7429	−	34.1957i	−0.680789	−	1.17916i
$842$	−3.28799	+	5.69497i	−0.113312	+	0.196262i
$843$	−22.7720	+	20.2548i	−0.784308	+	0.697613i
$844$	0.166208	+	0.287880i	0.00572110	+	0.00990923i
$845$	8.05673	+	13.9547i	0.277160	+	0.480055i
$846$	6.41342	+	4.77975i	0.220498	+	0.164331i
$847$		0			0
$848$	2.44437	−	4.23377i	0.0839399	−	0.145388i
$849$	30.4516	+	10.0993i	1.04510	+	0.346606i
$850$	−13.3745			−0.458741
$851$	−0.300372			−0.0102966
$852$	20.9127	+	6.93570i	0.716458	+	0.237613i
$853$	12.2658	−	21.2450i	0.419972	−	0.727413i	−0.575964	−	0.817475i	$-0.695373\pi$
$853$	12.2658	−	21.2450i	0.419972	−	0.727413i	0.995936	+	0.0900617i	$0.0287064\pi$
$854$		0			0
$855$	27.1229	+	20.2140i	0.927583	+	0.691303i
$856$	1.54325	+	2.67299i	0.0527473	+	0.0913610i
$857$	14.5240	+	25.1563i	0.496130	+	0.859323i	0.999990	−	0.00446273i	$-0.00142053\pi$
$857$	14.5240	+	25.1563i	0.496130	+	0.859323i	−0.503860	+	0.863785i	$0.668087\pi$
$858$	−9.88942	+	8.79628i	−0.337619	+	0.300300i
$859$	12.6476	−	21.9064i	0.431532	−	0.747435i	−0.565474	−	0.824766i	$-0.691307\pi$
$859$	12.6476	−	21.9064i	0.431532	−	0.747435i	0.997005	+	0.0773313i	$0.0246399\pi$
$860$	1.32327	+	2.29197i	0.0451232	+	0.0781557i
$861$		0			0
$862$	−11.0439	+	19.1287i	−0.376158	+	0.651525i
$863$	−1.34981	−	2.33795i	−0.0459482	−	0.0795846i	0.842137	−	0.539264i	$-0.181298\pi$
$863$	−1.34981	−	2.33795i	−0.0459482	−	0.0795846i	−0.888085	+	0.459680i	$0.847964\pi$
$864$	−2.97710	−	4.25874i	−0.101283	−	0.144885i
$865$	−15.1749	+	26.2836i	−0.515961	+	0.893671i
$866$	−9.43268			−0.320535
$867$	−4.25093	−	20.6141i	−0.144369	−	0.700091i
$868$		0			0
$869$	6.66071	+	11.5367i	0.225949	+	0.391355i
$870$	4.59820	+	22.2981i	0.155893	+	0.755976i
$871$	24.1822	+	41.8847i	0.819381	+	1.41921i
$872$	−1.14400	+	1.98146i	−0.0387406	+	0.0671007i
$873$	−3.92353	+	1.69005i	−0.132792	+	0.0571995i
$874$	2.13231			0.0721263
$875$		0			0
$876$	−20.7756	+	18.4791i	−0.701943	+	0.624352i
$877$	5.54580	−	9.60561i	0.187268	−	0.324358i	−0.757070	−	0.653334i	$-0.773370\pi$
$877$	5.54580	−	9.60561i	0.187268	−	0.324358i	0.944339	+	0.328975i	$0.106703\pi$
$878$	−31.2064			−1.05317
$879$	4.92718	+	23.8934i	0.166190	+	0.805905i
$880$	2.52290			0.0850469
$881$	40.3942			1.36091			0.680457	−	0.732788i	$-0.261781\pi$
$881$	40.3942			1.36091			0.680457	+	0.732788i	$0.261781\pi$
$882$		0			0
$883$	−33.2581			−1.11923			−0.559613	−	0.828754i	$-0.689050\pi$
$883$	−33.2581			−1.11923			−0.559613	+	0.828754i	$0.689050\pi$
$884$	−25.9752			−0.873642
$885$	−13.3145	+	11.8428i	−0.447563	+	0.398091i
$886$	−13.0545			−0.438573
$887$	20.2836	−	35.1322i	0.681056	−	1.17962i	−0.293603	−	0.955928i	$-0.594854\pi$
$887$	20.2836	−	35.1322i	0.681056	−	1.17962i	0.974659	−	0.223696i	$-0.0718124\pi$
$888$	−0.349814	−	1.69636i	−0.0117390	−	0.0569260i
$889$		0			0
$890$	5.09888			0.170915
$891$	−9.82072	+	10.3879i	−0.329007	+	0.348007i
$892$	−3.16621	+	5.48403i	−0.106012	+	0.183619i
$893$	−9.46355	−	16.3913i	−0.316686	−	0.548516i
$894$	6.74110	−	5.99596i	0.225456	−	0.200535i
$895$	12.7658	+	22.1110i	0.426713	+	0.739089i
$896$		0			0
$897$	2.37567	+	0.787890i	0.0793212	+	0.0263069i
$898$	9.91706			0.330937
$899$	11.2218	−	19.4367i	0.374267	−	0.648249i
$900$	−0.866524	+	7.38061i	−0.0288841	+	0.246020i
$901$	−13.1978	−	22.8592i	−0.439681	−	0.761551i
$902$	−4.66690	+	8.08330i	−0.155391	+	0.269144i
$903$		0			0
$904$	9.73236	+	16.8569i	0.323693	+	0.560654i
$905$	−6.39561	+	11.0775i	−0.212597	+	0.368230i
$906$	−0.182918	−	0.887026i	−0.00607704	−	0.0294695i
$907$	−15.0567	−	26.0790i	−0.499950	−	0.865939i	0.500050	−	0.865997i	$-0.333315\pi$
$907$	−15.0567	−	26.0790i	−0.499950	−	0.865939i	−1.00000		5.72941e-5i	$0.999982\pi$
$908$	−11.6545	−	20.1862i	−0.386769	−	0.669903i
$909$	−4.20946	+	35.8540i	−0.139619	+	1.18920i
$910$		0			0
$911$	14.6113	−	25.3075i	0.484093	−	0.838473i	−0.515740	−	0.856745i	$-0.672483\pi$
$911$	14.6113	−	25.3075i	0.484093	−	0.838473i	0.999833	+	0.0182717i	$0.00581638\pi$
$912$	2.48329	+	12.0422i	0.0822299	+	0.398759i
$913$	−3.75781			−0.124365
$914$	24.5229			0.811145
$915$	9.20327	−	8.18597i	0.304251	−	0.270620i
$916$	−2.47710	+	4.29046i	−0.0818457	+	0.141761i
$917$		0			0
$918$	−27.9505	+	2.42358i	−0.922503	+	0.0799902i
$919$	−5.52359	−	9.56714i	−0.182206	−	0.315591i	0.760425	−	0.649426i	$-0.224991\pi$
$919$	−5.52359	−	9.56714i	−0.182206	−	0.315591i	−0.942632	+	0.333835i	$0.891657\pi$
$920$	−0.238550	−	0.413181i	−0.00786476	−	0.0136222i
$921$	9.62612	+	3.19250i	0.317191	+	0.105196i
$922$	1.75526	−	3.04020i	0.0578064	−	0.100124i
$923$	−30.5989	−	52.9988i	−1.00717	−	1.74448i
$924$		0			0
$925$	−1.23855	+	2.14523i	−0.0407233	+	0.0705348i
$926$	−8.69413	−	15.0587i	−0.285707	−	0.494859i
$927$	−16.8040	+	7.23828i	−0.551916	+	0.237736i
$928$	−4.13781	+	7.16689i	−0.135830	+	0.235265i
$929$	42.3338			1.38893			0.694463	−	0.719528i	$-0.255642\pi$
$929$	42.3338			1.38893			0.694463	+	0.719528i	$0.255642\pi$
$930$	−5.57489	+	4.95866i	−0.182808	+	0.162601i
$931$		0			0
$932$	−7.13781	−	12.3630i	−0.233807	−	0.404965i
$933$	−1.33310	−	0.442124i	−0.0436439	−	0.0144745i
$934$	6.69894	+	11.6029i	0.219196	+	0.379659i
$935$	6.81089	−	11.7968i	0.222740	−	0.385797i
$936$	−1.68292	+	14.3342i	−0.0550079	+	0.468529i
$937$	11.7651			0.384349			0.192174	−	0.981361i	$-0.438446\pi$
$937$	11.7651			0.384349			0.192174	+	0.981361i	$0.438446\pi$
$938$		0			0
$939$	−17.3869	−	5.76636i	−0.567399	−	0.188178i
$940$	−2.11745	+	3.66754i	−0.0690637	+	0.119622i
$941$	−14.5760			−0.475164			−0.237582	−	0.971368i	$-0.576355\pi$
$941$	−14.5760			−0.475164			−0.237582	+	0.971368i	$0.576355\pi$
$942$	14.5723	+	4.83292i	0.474793	+	0.157465i
$943$	1.76509			0.0574793
$944$	−6.47710			−0.210812
$945$		0			0
$946$	2.64654			0.0860466
$947$	6.24357			0.202889			0.101444	−	0.994841i	$-0.467654\pi$
$947$	6.24357			0.202889			0.101444	+	0.994841i	$0.467654\pi$
$948$	13.7880	+	4.57279i	0.447813	+	0.148517i
$949$	77.2297			2.50698
$950$	8.79232	−	15.2287i	0.285261	−	0.494086i
$951$	20.0508	+	6.64985i	0.650192	+	0.215636i
$952$		0			0
$953$	28.0173			0.907570			0.453785	−	0.891111i	$-0.350073\pi$
$953$	28.0173			0.907570			0.453785	+	0.891111i	$0.350073\pi$
$954$	−13.4697	+	5.80205i	−0.436099	+	0.187848i
$955$	−19.0309	+	32.9624i	−0.615825	+	1.06664i
$956$	2.48762	+	4.30868i	0.0804554	+	0.139353i
$957$	21.6098	+	7.16689i	0.698546	+	0.231673i
$958$	−10.4029	−	18.0183i	−0.336102	−	0.582146i
$959$		0			0
$960$	2.05563	−	1.82841i	0.0663452	−	0.0590116i
$961$	−23.6450			−0.762742
$962$	−2.40545	+	4.16635i	−0.0775547	+	0.134329i
$963$	1.07970	−	9.19635i	0.0347929	−	0.296348i
$964$	−6.50000	−	11.2583i	−0.209351	−	0.362606i
$965$	7.75526	−	13.4325i	0.249651	−	0.432408i
$966$		0			0
$967$	15.7837	+	27.3381i	0.507568	+	0.879134i	0.999962	+	0.00876132i	$0.00278885\pi$
$967$	15.7837	+	27.3381i	0.507568	+	0.879134i	−0.492393	+	0.870373i	$0.663878\pi$
$968$	−4.23855	+	7.34138i	−0.136232	+	0.235961i
$969$	63.0122	+	20.8980i	2.02424	+	0.671340i
$970$	−1.13093	−	1.95882i	−0.0363119	−	0.0628941i
$971$	−2.82141	−	4.88683i	−0.0905434	−	0.156826i	0.817196	−	0.576359i	$-0.195527\pi$
$971$	−2.82141	−	4.88683i	−0.0905434	−	0.156826i	−0.907740	+	0.419533i	$0.862194\pi$
$972$	−0.473458	+	15.5813i	−0.0151862	+	0.499769i
$973$		0			0
$974$	−16.2472	+	28.1410i	−0.520594	+	0.901696i
$975$	15.4228	−	13.7180i	0.493926	−	0.439329i
$976$	4.47710			0.143308
$977$	6.49304			0.207731			0.103865	−	0.994591i	$-0.466879\pi$
$977$	6.49304			0.207731			0.103865	+	0.994591i	$0.466879\pi$
$978$	−7.68292	−	37.2569i	−0.245673	−	1.19134i
$979$	2.54944	−	4.41576i	0.0814805	−	0.141128i
$980$		0			0
$981$	6.30401	−	2.71543i	0.201272	−	0.0866971i
$982$	9.66071	+	16.7328i	0.308286	+	0.533966i
$983$	−15.1531	−	26.2460i	−0.483310	−	0.837118i	0.516506	−	0.856283i	$-0.327232\pi$
$983$	−15.1531	−	26.2460i	−0.483310	−	0.837118i	−0.999816	+	0.0191658i	$0.993899\pi$
$984$	2.05563	+	9.96840i	0.0655312	+	0.317781i
$985$	−14.4887	+	25.0952i	−0.461649	+	0.799599i
$986$	22.3411	+	38.6959i	0.711485	+	1.23233i
$987$		0			0
$988$	17.0760	−	29.5765i	0.543259	−	0.940953i
$989$	−0.250241	−	0.433430i	−0.00795720	−	0.0137823i
$990$	−6.06870	−	4.52284i	−0.192876	−	0.143745i
$991$	11.1669	−	19.3416i	0.354728	−	0.614407i	−0.632343	−	0.774688i	$-0.717907\pi$
$991$	11.1669	−	19.3416i	0.354728	−	0.614407i	0.987071	+	0.160281i	$0.0512401\pi$
$992$	−2.71201			−0.0861063
$993$	−25.7552	−	8.54170i	−0.817316	−	0.271063i
$994$		0			0
$995$	14.3738	+	24.8962i	0.455680	+	0.789262i
$996$	−3.06182	+	2.72338i	−0.0970175	+	0.0862935i
$997$	−4.38255	−	7.59079i	−0.138797	−	0.240403i	0.788245	−	0.615362i	$-0.210990\pi$
$997$	−4.38255	−	7.59079i	−0.138797	−	0.240403i	−0.927041	+	0.374959i	$0.877657\pi$
$998$	−5.57530	+	9.65670i	−0.176483	+	0.305677i
$999$	−2.19963	+	4.70761i	−0.0695932	+	0.148942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.e.o.655.3		6
3.2	odd	2		2646.2.e.p.2125.1		6
7.2	even	3		882.2.h.p.79.1		6
7.3	odd	6		882.2.f.n.295.3		6
7.4	even	3		882.2.f.o.295.1		6
7.5	odd	6		126.2.h.d.79.3	yes	6
7.6	odd	2		126.2.e.c.25.1	✓	6
9.4	even	3		882.2.h.p.67.1		6
9.5	odd	6		2646.2.h.o.361.3		6
21.2	odd	6		2646.2.h.o.667.3		6
21.5	even	6		378.2.h.c.289.1		6
21.11	odd	6		2646.2.f.m.883.1		6
21.17	even	6		2646.2.f.l.883.3		6
21.20	even	2		378.2.e.d.235.3		6
28.19	even	6		1008.2.t.h.961.1		6
28.27	even	2		1008.2.q.g.529.3		6
63.4	even	3		882.2.f.o.589.1		6
63.5	even	6		378.2.e.d.37.3		6
63.11	odd	6		7938.2.a.bz.1.3		3
63.13	odd	6		126.2.h.d.67.3	yes	6
63.20	even	6		1134.2.g.l.487.3		6
63.23	odd	6		2646.2.e.p.1549.1		6
63.25	even	3		7938.2.a.bw.1.1		3
63.31	odd	6		882.2.f.n.589.3		6
63.32	odd	6		2646.2.f.m.1765.1		6
63.34	odd	6		1134.2.g.m.487.1		6
63.38	even	6		7938.2.a.ca.1.1		3
63.40	odd	6		126.2.e.c.121.1	yes	6
63.41	even	6		378.2.h.c.361.1		6
63.47	even	6		1134.2.g.l.163.3		6
63.52	odd	6		7938.2.a.bv.1.3		3
63.58	even	3	inner	882.2.e.o.373.3		6
63.59	even	6		2646.2.f.l.1765.3		6
63.61	odd	6		1134.2.g.m.163.1		6
84.47	odd	6		3024.2.t.h.289.1		6
84.83	odd	2		3024.2.q.g.2881.3		6
252.103	even	6		1008.2.q.g.625.3		6
252.131	odd	6		3024.2.q.g.2305.3		6
252.139	even	6		1008.2.t.h.193.1		6
252.167	odd	6		3024.2.t.h.1873.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.1	✓	6	7.6	odd	2
126.2.e.c.121.1	yes	6	63.40	odd	6
126.2.h.d.67.3	yes	6	63.13	odd	6
126.2.h.d.79.3	yes	6	7.5	odd	6
378.2.e.d.37.3		6	63.5	even	6
378.2.e.d.235.3		6	21.20	even	2
378.2.h.c.289.1		6	21.5	even	6
378.2.h.c.361.1		6	63.41	even	6
882.2.e.o.373.3		6	63.58	even	3	inner
882.2.e.o.655.3		6	1.1	even	1	trivial
882.2.f.n.295.3		6	7.3	odd	6
882.2.f.n.589.3		6	63.31	odd	6
882.2.f.o.295.1		6	7.4	even	3
882.2.f.o.589.1		6	63.4	even	3
882.2.h.p.67.1		6	9.4	even	3
882.2.h.p.79.1		6	7.2	even	3
1008.2.q.g.529.3		6	28.27	even	2
1008.2.q.g.625.3		6	252.103	even	6
1008.2.t.h.193.1		6	252.139	even	6
1008.2.t.h.961.1		6	28.19	even	6
1134.2.g.l.163.3		6	63.47	even	6
1134.2.g.l.487.3		6	63.20	even	6
1134.2.g.m.163.1		6	63.61	odd	6
1134.2.g.m.487.1		6	63.34	odd	6
2646.2.e.p.1549.1		6	63.23	odd	6
2646.2.e.p.2125.1		6	3.2	odd	2
2646.2.f.l.883.3		6	21.17	even	6
2646.2.f.l.1765.3		6	63.59	even	6
2646.2.f.m.883.1		6	21.11	odd	6
2646.2.f.m.1765.1		6	63.32	odd	6
2646.2.h.o.361.3		6	9.5	odd	6
2646.2.h.o.667.3		6	21.2	odd	6
3024.2.q.g.2305.3		6	252.131	odd	6
3024.2.q.g.2881.3		6	84.83	odd	2
3024.2.t.h.289.1		6	84.47	odd	6
3024.2.t.h.1873.1		6	252.167	odd	6
7938.2.a.bv.1.3		3	63.52	odd	6
7938.2.a.bw.1.1		3	63.25	even	3
7938.2.a.bz.1.3		3	63.11	odd	6
7938.2.a.ca.1.1		3	63.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.64400 + 0.545231i) q^{3} +1.00000 q^{4} +(0.794182 - 1.37556i) q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(2.40545 + 1.79272i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.64400 + 0.545231i) q^{3} +1.00000 q^{4} +(0.794182 - 1.37556i) q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(2.40545 + 1.79272i) q^{9} +(-0.794182 + 1.37556i) q^{10} +(0.794182 + 1.37556i) q^{11} +(1.64400 + 0.545231i) q^{12} +(-2.40545 - 4.16635i) q^{13} +(2.05563 - 1.82841i) q^{15} +1.00000 q^{16} +(2.69963 - 4.67589i) q^{17} +(-2.40545 - 1.79272i) q^{18} +(3.54944 + 6.14781i) q^{19} +(0.794182 - 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} +(-0.150186 + 0.260130i) q^{23} +(-1.64400 - 0.545231i) q^{24} +(1.23855 + 2.14523i) q^{25} +(2.40545 + 4.16635i) q^{26} +(2.97710 + 4.25874i) q^{27} +(4.13781 - 7.16689i) q^{29} +(-2.05563 + 1.82841i) q^{30} +2.71201 q^{31} -1.00000 q^{32} +(0.555632 + 2.69443i) q^{33} +(-2.69963 + 4.67589i) q^{34} +(2.40545 + 1.79272i) q^{36} +(0.500000 + 0.866025i) q^{37} +(-3.54944 - 6.14781i) q^{38} +(-1.68292 - 8.16100i) q^{39} +(-0.794182 + 1.37556i) q^{40} +(-2.93818 - 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} +(0.794182 + 1.37556i) q^{44} +(4.37636 - 1.88510i) q^{45} +(0.150186 - 0.260130i) q^{46} -2.66621 q^{47} +(1.64400 + 0.545231i) q^{48} +(-1.23855 - 2.14523i) q^{50} +(6.98762 - 6.21523i) q^{51} +(-2.40545 - 4.16635i) q^{52} +(2.44437 - 4.23377i) q^{53} +(-2.97710 - 4.25874i) q^{54} +2.52290 q^{55} +(2.48329 + 12.0422i) q^{57} +(-4.13781 + 7.16689i) q^{58} -6.47710 q^{59} +(2.05563 - 1.82841i) q^{60} +4.47710 q^{61} -2.71201 q^{62} +1.00000 q^{64} -7.64145 q^{65} +(-0.555632 - 2.69443i) q^{66} -10.0531 q^{67} +(2.69963 - 4.67589i) q^{68} +(-0.388736 + 0.345766i) q^{69} +12.7207 q^{71} +(-2.40545 - 1.79272i) q^{72} +(-8.02654 + 13.9024i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(0.866524 + 4.20205i) q^{75} +(3.54944 + 6.14781i) q^{76} +(1.68292 + 8.16100i) q^{78} +8.38688 q^{79} +(0.794182 - 1.37556i) q^{80} +(2.57234 + 8.62456i) q^{81} +(2.93818 + 5.08907i) q^{82} +(-1.18292 + 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(0.833104 - 1.44298i) q^{86} +(10.7101 - 9.52628i) q^{87} +(-0.794182 - 1.37556i) q^{88} +(-1.60507 - 2.78007i) q^{89} +(-4.37636 + 1.88510i) q^{90} +(-0.150186 + 0.260130i) q^{92} +(4.45853 + 1.47867i) q^{93} +2.66621 q^{94} +11.2756 q^{95} +(-1.64400 - 0.545231i) q^{96} +(-0.712008 + 1.23323i) q^{97} +(-0.555632 + 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9} + q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} + 6 q^{16} + 4 q^{17} - 8 q^{18} + 3 q^{19} - q^{20} + q^{22} - 7 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} - 12 q^{30} + 40 q^{31} - 6 q^{32} + 3 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} - 3 q^{38} - 5 q^{39} + q^{40} - 6 q^{43} - q^{44} - 9 q^{45} + 7 q^{46} - 18 q^{47} - 2 q^{48} - 2 q^{50} + 6 q^{51} - 8 q^{52} + 15 q^{53} - 7 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} - 28 q^{59} + 12 q^{60} + 16 q^{61} - 40 q^{62} + 6 q^{64} + 24 q^{65} - 3 q^{66} - 2 q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} - 8 q^{72} - 19 q^{73} - 3 q^{74} - 8 q^{75} + 3 q^{76} + 5 q^{78} - 10 q^{79} - q^{80} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} + 27 q^{87} + q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} - 38 q^{93} + 18 q^{94} + 8 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9 + q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 + 6 * q^16 + 4 * q^17 - 8 * q^18 + 3 * q^19 - q^20 + q^22 - 7 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 - 12 * q^30 + 40 * q^31 - 6 * q^32 + 3 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 - 3 * q^38 - 5 * q^39 + q^40 - 6 * q^43 - q^44 - 9 * q^45 + 7 * q^46 - 18 * q^47 - 2 * q^48 - 2 * q^50 + 6 * q^51 - 8 * q^52 + 15 * q^53 - 7 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 - 28 * q^59 + 12 * q^60 + 16 * q^61 - 40 * q^62 + 6 * q^64 + 24 * q^65 - 3 * q^66 - 2 * q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 - 8 * q^72 - 19 * q^73 - 3 * q^74 - 8 * q^75 + 3 * q^76 + 5 * q^78 - 10 * q^79 - q^80 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 + 27 * q^87 + q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 - 38 * q^93 + 18 * q^94 + 8 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

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