LMFDB - Embedded newform 546.2.bz.b.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.6
Character	$\chi$	$=$	546.73
Dual form			546.2.bz.b.187.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-4.17716 - 1.11927i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.344270 - 2.62326i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-4.17716 - 1.11927i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.344270 - 2.62326i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.16226 + 3.74514i) q^{10} +(1.30811 + 4.88192i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-3.28713 + 1.48147i) q^{13} +(-2.62298 - 0.346409i) q^{14} +(-3.05790 - 3.05790i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.53445 + 2.65775i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-3.43041 - 0.919175i) q^{19} +(3.05790 + 3.05790i) q^{20} +(1.01348 - 2.44394i) q^{21} +5.05414 q^{22} +(-3.27981 + 1.89360i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(11.8658 + 6.85072i) q^{25} +(0.580218 + 3.55856i) q^{26} +1.00000i q^{27} +(-1.01348 + 2.44394i) q^{28} -5.32331 q^{29} +(-3.74514 + 2.16226i) q^{30} +(-2.08124 - 7.76730i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.30811 + 4.88192i) q^{33} +(2.17004 + 2.17004i) q^{34} +(-1.49805 + 11.3431i) q^{35} -1.00000i q^{36} +(-3.74857 - 1.00443i) q^{37} +(-1.77571 + 3.07562i) q^{38} +(-3.58748 - 0.360575i) q^{39} +(3.74514 - 2.16226i) q^{40} +(-2.16181 + 2.16181i) q^{41} +(-2.09836 - 1.61149i) q^{42} -8.74410i q^{43} +(1.30811 - 4.88192i) q^{44} +(-1.11927 - 4.17716i) q^{45} +(0.980199 + 3.65815i) q^{46} +(2.31434 - 8.63722i) q^{47} +1.00000i q^{48} +(-6.76296 + 1.80622i) q^{49} +(9.68839 - 9.68839i) q^{50} +(-2.65775 + 1.53445i) q^{51} +(3.58748 + 0.360575i) q^{52} +(-0.196202 + 0.339831i) q^{53} +(0.965926 + 0.258819i) q^{54} -21.8567i q^{55} +(2.09836 + 1.61149i) q^{56} +(-2.51123 - 2.51123i) q^{57} +(-1.37777 + 5.14192i) q^{58} +(0.810898 - 0.217280i) q^{59} +(1.11927 + 4.17716i) q^{60} +(3.31015 - 1.91111i) q^{61} -8.04130 q^{62} +(2.09967 - 1.60978i) q^{63} -1.00000i q^{64} +(15.3891 - 2.50916i) q^{65} +(4.37701 + 2.52707i) q^{66} +(-5.85964 + 1.57009i) q^{67} +(2.65775 - 1.53445i) q^{68} -3.78720 q^{69} +(10.5689 + 4.38282i) q^{70} +(1.51564 + 1.51564i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(-2.38419 + 0.638842i) q^{73} +(-1.94040 + 3.36088i) q^{74} +(6.85072 + 11.8658i) q^{75} +(2.51123 + 2.51123i) q^{76} +(12.3562 - 5.11220i) q^{77} +(-1.27680 + 3.37191i) q^{78} +(6.16264 + 10.6740i) q^{79} +(-1.11927 - 4.17716i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.52863 + 2.64767i) q^{82} +(-6.36325 + 6.36325i) q^{83} +(-2.09967 + 1.60978i) q^{84} +(9.38439 - 9.38439i) q^{85} +(-8.44615 - 2.26314i) q^{86} +(-4.61012 - 2.66166i) q^{87} +(-4.37701 - 2.52707i) q^{88} +(1.74994 - 6.53086i) q^{89} -4.32452 q^{90} +(5.01794 + 8.11297i) q^{91} +3.78720 q^{92} +(2.08124 - 7.76730i) q^{93} +(-7.74392 - 4.47096i) q^{94} +(13.3006 + 7.67909i) q^{95} +(0.965926 + 0.258819i) q^{96} +(9.94940 - 9.94940i) q^{97} +(-0.00570888 + 7.00000i) q^{98} +(-3.57382 + 3.57382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−4.17716	−	1.11927i	−1.86808	−	0.500552i	−0.999991	−	0.00414924i	$-0.998679\pi$
$5$	−4.17716	−	1.11927i	−1.86808	−	0.500552i	−0.868093	−	0.496402i	$-0.834654\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−0.344270	−	2.62326i	−0.130122	−	0.991498i
$7$	−0.344270	−	2.62326i	−0.130122	−	0.991498i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.16226	+	3.74514i	−0.683766	+	1.18432i
$11$	1.30811	+	4.88192i	0.394409	+	1.47196i	0.822784	+	0.568354i	$0.192420\pi$
$11$	1.30811	+	4.88192i	0.394409	+	1.47196i	−0.428375	+	0.903601i	$0.640914\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−3.28713	+	1.48147i	−0.911687	+	0.410886i
$13$	−3.28713	+	1.48147i	−0.911687	+	0.410886i
$14$	−2.62298	−	0.346409i	−0.701020	−	0.0925818i
$15$	−3.05790	−	3.05790i	−0.789545	−	0.789545i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.53445	+	2.65775i	−0.372159	+	0.644599i	−0.989897	−	0.141785i	$-0.954716\pi$
$17$	−1.53445	+	2.65775i	−0.372159	+	0.644599i	0.617738	+	0.786384i	$0.288049\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−3.43041	−	0.919175i	−0.786990	−	0.210873i	−0.157126	−	0.987579i	$-0.550223\pi$
$19$	−3.43041	−	0.919175i	−0.786990	−	0.210873i	−0.629864	+	0.776705i	$0.716889\pi$
$20$	3.05790	+	3.05790i	0.683766	+	0.683766i
$21$	1.01348	−	2.44394i	0.221160	−	0.533312i
$22$	5.05414			1.07755
$23$	−3.27981	+	1.89360i	−0.683888	+	0.394843i	−0.801318	−	0.598238i	$-0.795868\pi$
$23$	−3.27981	+	1.89360i	−0.683888	+	0.394843i	0.117430	+	0.993081i	$0.462534\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	11.8658	+	6.85072i	2.37316	+	1.37014i
$26$	0.580218	+	3.55856i	0.113790	+	0.697891i
$27$			1.00000i			0.192450i
$28$	−1.01348	+	2.44394i	−0.191530	+	0.461862i
$29$	−5.32331			−0.988514			−0.494257	−	0.869316i	$-0.664560\pi$
$29$	−5.32331			−0.988514			−0.494257	+	0.869316i	$0.664560\pi$
$30$	−3.74514	+	2.16226i	−0.683766	+	0.394773i
$31$	−2.08124	−	7.76730i	−0.373802	−	1.39505i	−0.855087	−	0.518484i	$-0.826497\pi$
$31$	−2.08124	−	7.76730i	−0.373802	−	1.39505i	0.481285	−	0.876564i	$-0.340170\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−1.30811	+	4.88192i	−0.227712	+	0.849834i
$34$	2.17004	+	2.17004i	0.372159	+	0.372159i
$35$	−1.49805	+	11.3431i	−0.253217	+	1.91733i
$36$		−	1.00000i		−	0.166667i
$37$	−3.74857	−	1.00443i	−0.616262	−	0.165127i	−0.0628338	−	0.998024i	$-0.520014\pi$
$37$	−3.74857	−	1.00443i	−0.616262	−	0.165127i	−0.553428	+	0.832897i	$0.686680\pi$
$38$	−1.77571	+	3.07562i	−0.288058	+	0.498932i
$39$	−3.58748	−	0.360575i	−0.574456	−	0.0577382i
$40$	3.74514	−	2.16226i	0.592159	−	0.341883i
$41$	−2.16181	+	2.16181i	−0.337618	+	0.337618i	−0.855470	−	0.517852i	$-0.826732\pi$
$41$	−2.16181	+	2.16181i	−0.337618	+	0.337618i	0.517852	+	0.855470i	$0.326732\pi$
$42$	−2.09836	−	1.61149i	−0.323784	−	0.248658i
$43$		−	8.74410i		−	1.33346i	−0.745298	−	0.666731i	$-0.767693\pi$
$43$		−	8.74410i		−	1.33346i	0.745298	−	0.666731i	$-0.232307\pi$
$44$	1.30811	−	4.88192i	0.197205	−	0.735978i
$45$	−1.11927	−	4.17716i	−0.166851	−	0.622695i
$46$	0.980199	+	3.65815i	0.144522	+	0.539365i
$47$	2.31434	−	8.63722i	0.337581	−	1.25987i	−0.563463	−	0.826141i	$-0.690531\pi$
$47$	2.31434	−	8.63722i	0.337581	−	1.25987i	0.901044	−	0.433727i	$-0.142802\pi$
$48$			1.00000i			0.144338i
$49$	−6.76296	+	1.80622i	−0.966137	+	0.258031i
$50$	9.68839	−	9.68839i	1.37014	−	1.37014i
$51$	−2.65775	+	1.53445i	−0.372159	+	0.214866i
$52$	3.58748	+	0.360575i	0.497493	+	0.0500028i
$53$	−0.196202	+	0.339831i	−0.0269504	+	0.0466794i	−0.879186	−	0.476479i	$-0.841913\pi$
$53$	−0.196202	+	0.339831i	−0.0269504	+	0.0466794i	0.852236	+	0.523158i	$0.175246\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$		−	21.8567i		−	2.94716i
$56$	2.09836	+	1.61149i	0.280405	+	0.215344i
$57$	−2.51123	−	2.51123i	−0.332621	−	0.332621i
$58$	−1.37777	+	5.14192i	−0.180911	+	0.675168i
$59$	0.810898	−	0.217280i	0.105570	−	0.0282874i	−0.205647	−	0.978626i	$-0.565930\pi$
$59$	0.810898	−	0.217280i	0.105570	−	0.0282874i	0.311217	+	0.950339i	$0.399263\pi$
$60$	1.11927	+	4.17716i	0.144497	+	0.539269i
$61$	3.31015	−	1.91111i	0.423821	−	0.244693i	−0.272890	−	0.962045i	$-0.587979\pi$
$61$	3.31015	−	1.91111i	0.423821	−	0.244693i	0.696711	+	0.717352i	$0.254646\pi$
$62$	−8.04130			−1.02125
$63$	2.09967	−	1.60978i	0.264534	−	0.202813i
$64$		−	1.00000i		−	0.125000i
$65$	15.3891	−	2.50916i	1.90878	−	0.311223i
$66$	4.37701	+	2.52707i	0.538773	+	0.311061i
$67$	−5.85964	+	1.57009i	−0.715869	+	0.191817i	−0.598328	−	0.801251i	$-0.704168\pi$
$67$	−5.85964	+	1.57009i	−0.715869	+	0.191817i	−0.117541	+	0.993068i	$0.537501\pi$
$68$	2.65775	−	1.53445i	0.322299	−	0.186080i
$69$	−3.78720			−0.455925
$70$	10.5689	+	4.38282i	1.26322	+	0.523847i
$71$	1.51564	+	1.51564i	0.179873	+	0.179873i	0.791300	−	0.611427i	$-0.209404\pi$
$71$	1.51564	+	1.51564i	0.179873	+	0.179873i	−0.611427	+	0.791300i	$0.709404\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	−2.38419	+	0.638842i	−0.279048	+	0.0747708i	−0.395629	−	0.918410i	$-0.629473\pi$
$73$	−2.38419	+	0.638842i	−0.279048	+	0.0747708i	0.116580	+	0.993181i	$0.462807\pi$
$74$	−1.94040	+	3.36088i	−0.225567	+	0.390694i
$75$	6.85072	+	11.8658i	0.791053	+	1.37014i
$76$	2.51123	+	2.51123i	0.288058	+	0.288058i
$77$	12.3562	−	5.11220i	1.40812	−	0.582590i
$78$	−1.27680	+	3.37191i	−0.144569	+	0.381794i
$79$	6.16264	+	10.6740i	0.693351	+	1.20092i	0.970734	+	0.240159i	$0.0771996\pi$
$79$	6.16264	+	10.6740i	0.693351	+	1.20092i	−0.277383	+	0.960759i	$0.589467\pi$
$80$	−1.11927	−	4.17716i	−0.125138	−	0.467021i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.52863	+	2.64767i	0.168809	+	0.292386i
$83$	−6.36325	+	6.36325i	−0.698457	+	0.698457i	−0.964078	−	0.265620i	$-0.914423\pi$
$83$	−6.36325	+	6.36325i	−0.698457	+	0.698457i	0.265620	+	0.964078i	$0.414423\pi$
$84$	−2.09967	+	1.60978i	−0.229093	+	0.175641i
$85$	9.38439	−	9.38439i	1.01788	−	1.01788i
$86$	−8.44615	−	2.26314i	−0.910772	−	0.244041i
$87$	−4.61012	−	2.66166i	−0.494257	−	0.285359i
$88$	−4.37701	−	2.52707i	−0.466591	−	0.269386i
$89$	1.74994	−	6.53086i	0.185493	−	0.692269i	−0.809031	−	0.587765i	$-0.800008\pi$
$89$	1.74994	−	6.53086i	0.185493	−	0.692269i	0.994524	−	0.104504i	$-0.0333255\pi$
$90$	−4.32452			−0.455844
$91$	5.01794	+	8.11297i	0.526023	+	0.850470i
$92$	3.78720			0.394843
$93$	2.08124	−	7.76730i	0.215815	−	0.805431i
$94$	−7.74392	−	4.47096i	−0.798725	−	0.461144i
$95$	13.3006	+	7.67909i	1.36461	+	0.787858i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	9.94940	−	9.94940i	1.01021	−	1.01021i	0.0102613	−	0.999947i	$-0.496734\pi$
$97$	9.94940	−	9.94940i	1.01021	−	1.01021i	0.999947	−	0.0102613i	$-0.00326632\pi$
$98$	−0.00570888	+	7.00000i	−0.000576684	+	0.707107i
$99$	−3.57382	+	3.57382i	−0.359182	+	0.359182i
$100$	−6.85072	−	11.8658i	−0.685072	−	1.18658i
$101$	−7.16340	+	12.4074i	−0.712785	+	1.23458i	0.251023	+	0.967981i	$0.419233\pi$
$101$	−7.16340	+	12.4074i	−0.712785	+	1.23458i	−0.963808	+	0.266598i	$0.914100\pi$
$102$	0.794291	+	2.96433i	0.0786465	+	0.293513i
$103$	2.27100	+	3.93349i	0.223768	+	0.387578i	0.955949	−	0.293532i	$-0.0948307\pi$
$103$	2.27100	+	3.93349i	0.223768	+	0.387578i	−0.732181	+	0.681110i	$0.761497\pi$
$104$	1.27680	−	3.37191i	0.125200	−	0.330643i
$105$	−6.96890	+	9.07439i	−0.680095	+	0.885570i
$106$	0.277471	+	0.277471i	0.0269504	+	0.0269504i
$107$	−2.78119	−	4.81717i	−0.268868	−	0.465693i	0.699702	−	0.714435i	$-0.253316\pi$
$107$	−2.78119	−	4.81717i	−0.268868	−	0.465693i	−0.968570	+	0.248742i	$0.919983\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	2.04723	−	0.548553i	0.196089	−	0.0525419i	−0.159438	−	0.987208i	$-0.550968\pi$
$109$	2.04723	−	0.548553i	0.196089	−	0.0525419i	0.355527	+	0.934666i	$0.384301\pi$
$110$	−21.1120	−	5.65693i	−2.01295	−	0.539367i
$111$	−2.74415	−	2.74415i	−0.260463	−	0.260463i
$112$	2.09967	−	1.60978i	0.198400	−	0.152109i
$113$	0.946359			0.0890259			0.0445130	−	0.999009i	$-0.485826\pi$
$113$	0.946359			0.0890259			0.0445130	+	0.999009i	$0.485826\pi$
$114$	−3.07562	+	1.77571i	−0.288058	+	0.166311i
$115$	15.8197	−	4.23889i	1.47520	−	0.395278i
$116$	4.61012	+	2.66166i	0.428039	+	0.247128i
$117$	−2.92656	−	2.10601i	−0.270560	−	0.194700i
$118$		−	0.839504i		−	0.0772826i
$119$	7.50023	+	3.11028i	0.687545	+	0.285119i
$120$	4.32452			0.394773
$121$	−12.5957	+	7.27216i	−1.14507	+	0.661105i
$122$	−0.989266	−	3.69199i	−0.0895639	−	0.334257i
$123$	−2.95309	+	0.791277i	−0.266271	+	0.0713471i
$124$	−2.08124	+	7.76730i	−0.186901	+	0.697524i
$125$	−26.6081	−	26.6081i	−2.37990	−	2.37990i
$126$	−1.01149	−	2.44477i	−0.0901105	−	0.217797i
$127$			8.81327i			0.782051i	0.920380	+	0.391026i	$0.127880\pi$
$127$			8.81327i			0.782051i	−0.920380	+	0.391026i	$0.872120\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	4.37205	−	7.57261i	0.384937	−	0.666731i
$130$	1.55931	−	15.5141i	0.136761	−	1.36068i
$131$	−5.07556	+	2.93038i	−0.443454	+	0.256028i	−0.705062	−	0.709146i	$-0.749081\pi$
$131$	−5.07556	+	2.93038i	−0.443454	+	0.256028i	0.261608	+	0.965174i	$0.415747\pi$
$132$	3.57382	−	3.57382i	0.311061	−	0.311061i
$133$	−1.23025	+	9.31529i	−0.106676	+	0.807738i
$134$			6.06635i			0.524053i
$135$	1.11927	−	4.17716i	0.0963312	−	0.359513i
$136$	−0.794291	−	2.96433i	−0.0681099	−	0.254190i
$137$	−4.94358	−	18.4497i	−0.422359	−	1.57627i	−0.769624	−	0.638498i	$-0.779556\pi$
$137$	−4.94358	−	18.4497i	−0.422359	−	1.57627i	0.347265	−	0.937767i	$-0.387111\pi$
$138$	−0.980199	+	3.65815i	−0.0834401	+	0.311403i
$139$		−	7.94250i		−	0.673674i	−0.941563	−	0.336837i	$-0.890643\pi$
$139$		−	7.94250i		−	0.673674i	0.941563	−	0.336837i	$-0.109357\pi$
$140$	6.96890	−	9.07439i	0.588980	−	0.766926i
$141$	6.32289	−	6.32289i	0.532483	−	0.532483i
$142$	1.85627	−	1.07172i	0.155775	−	0.0899365i
$143$	−11.5323	−	14.1096i	−0.964384	−	1.17990i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	22.2363	+	5.95821i	1.84663	+	0.494802i
$146$			2.46830i			0.204278i
$147$	−6.76000	−	1.81725i	−0.557555	−	0.149884i
$148$	2.74415	+	2.74415i	0.225567	+	0.225567i
$149$	−2.90466	+	10.8404i	−0.237959	+	0.888076i	0.738833	+	0.673888i	$0.235377\pi$
$149$	−2.90466	+	10.8404i	−0.237959	+	0.888076i	−0.976792	+	0.214188i	$0.931290\pi$
$150$	13.2346	−	3.54620i	1.08060	−	0.289546i
$151$	4.65772	+	17.3829i	0.379040	+	1.41460i	0.847351	+	0.531033i	$0.178196\pi$
$151$	4.65772	+	17.3829i	0.379040	+	1.41460i	−0.468311	+	0.883564i	$0.655137\pi$
$152$	3.07562	−	1.77571i	0.249466	−	0.144029i
$153$	−3.06890			−0.248106
$154$	−1.73999	−	13.2583i	−0.140212	−	1.06838i
$155$			34.7747i			2.79317i
$156$	2.92656	+	2.10601i	0.234312	+	0.168615i
$157$	5.46279	+	3.15395i	0.435978	+	0.251712i	0.701890	−	0.712285i	$-0.252340\pi$
$157$	5.46279	+	3.15395i	0.435978	+	0.251712i	−0.265912	+	0.963997i	$0.585673\pi$
$158$	11.9053	−	3.19001i	0.947135	−	0.253784i
$159$	−0.339831	+	0.196202i	−0.0269504	+	0.0155598i
$160$	−4.32452			−0.341883
$161$	6.09654	+	7.95188i	0.480475	+	0.626696i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−6.68755	−	1.79192i	−0.523809	−	0.140354i	−0.0127812	−	0.999918i	$-0.504068\pi$
$163$	−6.68755	−	1.79192i	−0.523809	−	0.140354i	−0.511028	+	0.859564i	$0.670735\pi$
$164$	2.95309	−	0.791277i	0.230597	−	0.0617884i
$165$	10.9284	−	18.9285i	0.850771	−	1.47358i
$166$	4.49950	+	7.79336i	0.349229	+	0.604882i
$167$	4.14832	+	4.14832i	0.321006	+	0.321006i	0.849153	−	0.528147i	$-0.177113\pi$
$167$	4.14832	+	4.14832i	0.321006	+	0.321006i	−0.528147	+	0.849153i	$0.677113\pi$
$168$	1.01149	+	2.44477i	0.0780380	+	0.188618i
$169$	8.61049	−	9.73958i	0.662345	−	0.749199i
$170$	−6.63577	−	11.4935i	−0.508940	−	0.881510i
$171$	−0.919175	−	3.43041i	−0.0702911	−	0.262330i
$172$	−4.37205	+	7.57261i	−0.333366	+	0.577406i
$173$	−2.77271	−	4.80247i	−0.210805	−	0.365125i	0.741162	−	0.671327i	$-0.234275\pi$
$173$	−2.77271	−	4.80247i	−0.210805	−	0.365125i	−0.951967	+	0.306202i	$0.900942\pi$
$174$	−3.76415	+	3.76415i	−0.285359	+	0.285359i
$175$	13.8862	−	33.4855i	1.04970	−	2.53127i
$176$	−3.57382	+	3.57382i	−0.269386	+	0.269386i
$177$	0.810898	+	0.217280i	0.0609509	+	0.0163317i
$178$	−5.85541	−	3.38062i	−0.438881	−	0.253388i
$179$	−12.3602	−	7.13614i	−0.923842	−	0.533380i	−0.0389831	−	0.999240i	$-0.512412\pi$
$179$	−12.3602	−	7.13614i	−0.923842	−	0.533380i	−0.884859	+	0.465860i	$0.845745\pi$
$180$	−1.11927	+	4.17716i	−0.0834253	+	0.311347i
$181$	−21.8025			−1.62057			−0.810284	−	0.586037i	$-0.800687\pi$
$181$	−21.8025			−1.62057			−0.810284	+	0.586037i	$0.800687\pi$
$182$	9.13527	−	2.74717i	0.677151	−	0.203634i
$183$	3.82223			0.282547
$184$	0.980199	−	3.65815i	0.0722612	−	0.269683i
$185$	14.5342	+	8.39131i	1.06857	+	0.616941i
$186$	−6.96397	−	4.02065i	−0.510623	−	0.294808i
$187$	−14.9822	−	4.01446i	−1.09560	−	0.293566i
$188$	−6.32289	+	6.32289i	−0.461144	+	0.461144i
$189$	2.62326	−	0.344270i	0.190814	−	0.0250420i
$190$	10.8599	−	10.8599i	0.787858	−	0.787858i
$191$	−4.59279	−	7.95494i	−0.332323	−	0.575600i	0.650644	−	0.759383i	$-0.274499\pi$
$191$	−4.59279	−	7.95494i	−0.332323	−	0.575600i	−0.982967	+	0.183783i	$0.941166\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−3.34768	−	12.4937i	−0.240971	−	0.899318i	−0.975366	−	0.220594i	$-0.929200\pi$
$193$	−3.34768	−	12.4937i	−0.240971	−	0.899318i	0.734394	−	0.678723i	$-0.237466\pi$
$194$	−7.03529	−	12.1855i	−0.505104	−	0.874866i
$195$	14.5819	+	5.52153i	1.04423	+	0.395405i
$196$	6.76000	+	1.81725i	0.482857	+	0.129803i
$197$	−12.6310	−	12.6310i	−0.899924	−	0.899924i	0.0955052	−	0.995429i	$-0.469553\pi$
$197$	−12.6310	−	12.6310i	−0.899924	−	0.899924i	−0.995429	+	0.0955052i	$0.969553\pi$
$198$	2.52707	+	4.37701i	0.179591	+	0.311061i
$199$	3.93845	−	6.82160i	0.279190	−	0.483571i	−0.691994	−	0.721903i	$-0.743268\pi$
$199$	3.93845	−	6.82160i	0.279190	−	0.483571i	0.971184	+	0.238333i	$0.0766008\pi$
$200$	−13.2346	+	3.54620i	−0.935826	+	0.250754i
$201$	−5.85964	−	1.57009i	−0.413307	−	0.110745i
$202$	10.1306	+	10.1306i	0.712785	+	0.712785i
$203$	1.83266	+	13.9644i	0.128627	+	0.980110i
$204$	3.06890			0.214866
$205$	11.4499	−	6.61059i	0.799694	−	0.461703i
$206$	4.38724	−	1.17556i	0.305673	−	0.0819049i
$207$	−3.27981	−	1.89360i	−0.227963	−	0.131614i
$208$	−2.92656	−	2.10601i	−0.202920	−	0.146025i
$209$		−	17.9494i		−	1.24158i
$210$	6.96150	+	9.08007i	0.480389	+	0.626584i
$211$	25.0075			1.72158			0.860792	−	0.508956i	$-0.169968\pi$
$211$	25.0075			1.72158			0.860792	+	0.508956i	$0.169968\pi$
$212$	0.339831	−	0.196202i	0.0233397	−	0.0134752i
$213$	0.554762	+	2.07040i	0.0380116	+	0.141861i
$214$	−5.37285	+	1.43965i	−0.367281	+	0.0984126i
$215$	−9.78698	+	36.5255i	−0.667467	+	2.49102i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−19.6591	+	8.13368i	−1.33455	+	0.552150i
$218$		−	2.11945i		−	0.143547i
$219$	−2.38419	−	0.638842i	−0.161109	−	0.0431689i
$220$	−10.9284	+	18.9285i	−0.736790	+	1.27616i
$221$	1.10657	−	11.0096i	0.0744360	−	0.740587i
$222$	−3.36088	+	1.94040i	−0.225567	+	0.130231i
$223$	−19.8721	+	19.8721i	−1.33074	+	1.33074i	−0.426025	+	0.904712i	$0.640086\pi$
$223$	−19.8721	+	19.8721i	−1.33074	+	1.33074i	−0.904712	+	0.426025i	$0.859914\pi$
$224$	−1.01149	−	2.44477i	−0.0675829	−	0.163348i
$225$			13.7014i			0.913430i
$226$	0.244936	−	0.914112i	0.0162929	−	0.0608058i
$227$	1.29127	+	4.81907i	0.0857043	+	0.319853i	0.995447	−	0.0953205i	$-0.0303876\pi$
$227$	1.29127	+	4.81907i	0.0857043	+	0.319853i	−0.909742	+	0.415173i	$0.863721\pi$
$228$	0.919175	+	3.43041i	0.0608739	+	0.227184i
$229$	−3.90349	+	14.5680i	−0.257950	+	0.962682i	0.708476	+	0.705735i	$0.249383\pi$
$229$	−3.90349	+	14.5680i	−0.257950	+	0.962682i	−0.966426	+	0.256947i	$0.917283\pi$
$230$		−	16.3778i		−	1.07992i
$231$	13.2569	+	1.75080i	0.872239	+	0.115194i
$232$	3.76415	−	3.76415i	0.247128	−	0.247128i
$233$	3.02978	−	1.74924i	0.198487	−	0.114597i	−0.397462	−	0.917619i	$-0.630109\pi$
$233$	3.02978	−	1.74924i	0.198487	−	0.114597i	0.595950	+	0.803022i	$0.296776\pi$
$234$	−2.79169	+	2.28176i	−0.182499	+	0.149164i
$235$	−19.3347	+	33.4887i	−1.26126	+	2.18456i
$236$	−0.810898	−	0.217280i	−0.0527850	−	0.0141437i
$237$			12.3253i			0.800612i
$238$	4.94550	−	6.43966i	0.320569	−	0.417421i
$239$	−1.92190	−	1.92190i	−0.124318	−	0.124318i	0.642211	−	0.766528i	$-0.278017\pi$
$239$	−1.92190	−	1.92190i	−0.124318	−	0.124318i	−0.766528	+	0.642211i	$0.778017\pi$
$240$	1.11927	−	4.17716i	0.0722484	−	0.269635i
$241$	−25.6445	+	6.87142i	−1.65191	+	0.442627i	−0.960146	−	0.279499i	$-0.909832\pi$
$241$	−25.6445	+	6.87142i	−1.65191	+	0.442627i	−0.691761	+	0.722126i	$0.743165\pi$
$242$	3.76435	+	14.0487i	0.241981	+	0.903087i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−3.82223			−0.244693
$245$	30.2716	+	0.0246882i	1.93398	+	0.00157727i
$246$			3.05726i			0.194924i
$247$	12.6379	−	2.06060i	0.804133	−	0.131113i
$248$	6.96397	+	4.02065i	0.442212	+	0.255312i
$249$	−8.69236	+	2.32911i	−0.550856	+	0.147601i
$250$	−32.5882	+	18.8148i	−2.06106	+	1.18995i
$251$	20.5164			1.29498			0.647491	−	0.762073i	$-0.275818\pi$
$251$	20.5164			1.29498			0.647491	+	0.762073i	$0.275818\pi$
$252$	−2.62326	+	0.344270i	−0.165250	+	0.0216870i
$253$	−13.5348	−	13.5348i	−0.850922	−	0.850922i
$254$	8.51296	+	2.28104i	0.534151	+	0.143125i
$255$	12.8193	−	3.43493i	0.802777	−	0.215103i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.846985	+	1.46702i	0.0528335	+	0.0915102i	0.891233	−	0.453547i	$-0.149841\pi$
$257$	0.846985	+	1.46702i	0.0528335	+	0.0915102i	−0.838399	+	0.545057i	$0.816508\pi$
$258$	−6.18301	−	6.18301i	−0.384937	−	0.384937i
$259$	−1.34435	+	10.1793i	−0.0835338	+	0.632509i
$260$	−14.5819	−	5.52153i	−0.904331	−	0.342431i
$261$	−2.66166	−	4.61012i	−0.164752	−	0.285359i
$262$	1.51687	+	5.66105i	0.0937128	+	0.349741i
$263$	2.89731	−	5.01829i	0.178656	−	0.309441i	−0.762765	−	0.646676i	$-0.776159\pi$
$263$	2.89731	−	5.01829i	0.178656	−	0.309441i	0.941420	+	0.337235i	$0.109492\pi$
$264$	−2.52707	−	4.37701i	−0.155530	−	0.269386i
$265$	1.19993	−	1.19993i	0.0737110	−	0.0737110i
$266$	8.67947	+	3.59930i	0.532172	+	0.220687i
$267$	4.78092	−	4.78092i	0.292588	−	0.292588i
$268$	5.85964	+	1.57009i	0.357935	+	0.0959083i
$269$	−1.51888	−	0.876924i	−0.0926076	−	0.0534670i	0.452981	−	0.891520i	$-0.350361\pi$
$269$	−1.51888	−	0.876924i	−0.0926076	−	0.0534670i	−0.545589	+	0.838053i	$0.683694\pi$
$270$	−3.74514	−	2.16226i	−0.227922	−	0.131591i
$271$	−0.220922	+	0.824491i	−0.0134200	+	0.0500842i	−0.972311	−	0.233690i	$-0.924920\pi$
$271$	−0.220922	+	0.824491i	−0.0134200	+	0.0500842i	0.958891	+	0.283774i	$0.0915866\pi$
$272$	−3.06890			−0.186080
$273$	0.289180	+	9.53501i	0.0175020	+	0.577085i
$274$	−19.1005			−1.15391
$275$	−17.9230	+	66.8894i	−1.08080	+	4.03358i
$276$	3.27981	+	1.89360i	0.197421	+	0.113981i
$277$	24.2821	+	14.0193i	1.45897	+	0.842338i	0.998961	−	0.0455757i	$-0.0145122\pi$
$277$	24.2821	+	14.0193i	1.45897	+	0.842338i	0.460011	+	0.887913i	$0.347846\pi$
$278$	−7.67186	−	2.05567i	−0.460128	−	0.123291i
$279$	5.68606	−	5.68606i	0.340415	−	0.340415i
$280$	−6.96150	−	9.08007i	−0.416029	−	0.542638i
$281$	16.0574	−	16.0574i	0.957904	−	0.957904i	−0.0412451	−	0.999149i	$-0.513132\pi$
$281$	16.0574	−	16.0574i	0.957904	−	0.957904i	0.999149	+	0.0412451i	$0.0131325\pi$
$282$	−4.47096	−	7.74392i	−0.266242	−	0.461144i
$283$	−9.51588	+	16.4820i	−0.565661	+	0.979753i	0.431327	+	0.902196i	$0.358045\pi$
$283$	−9.51588	+	16.4820i	−0.565661	+	0.979753i	−0.996988	+	0.0775574i	$0.975288\pi$
$284$	−0.554762	−	2.07040i	−0.0329190	−	0.122856i
$285$	7.67909	+	13.3006i	0.454870	+	0.787858i
$286$	−16.6136	+	7.48756i	−0.982384	+	0.442749i
$287$	6.41523	+	4.92674i	0.378679	+	0.290816i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	3.79091	+	6.56605i	0.222995	+	0.386238i
$290$	11.5104	−	19.9366i	0.675912	−	1.17071i
$291$	13.5911	−	3.64173i	0.796726	−	0.213482i
$292$	2.38419	+	0.638842i	0.139524	+	0.0373854i
$293$	−5.11821	−	5.11821i	−0.299009	−	0.299009i	0.541617	−	0.840626i	$-0.317813\pi$
$293$	−5.11821	−	5.11821i	−0.299009	−	0.299009i	−0.840626	+	0.541617i	$0.817813\pi$
$294$	−3.50494	+	6.05932i	−0.204412	+	0.353387i
$295$	−3.63045			−0.211373
$296$	3.36088	−	1.94040i	0.195347	−	0.112784i
$297$	−4.88192	+	1.30811i	−0.283278	+	0.0759041i
$298$	9.71919	+	5.61138i	0.563018	+	0.325059i
$299$	7.97586	−	11.0835i	0.461256	−	0.640973i
$300$		−	13.7014i		−	0.791053i
$301$	−22.9380	+	3.01033i	−1.32213	+	0.173513i
$302$	17.9961			1.03556
$303$	−12.4074	+	7.16340i	−0.712785	+	0.411526i
$304$	−0.919175	−	3.43041i	−0.0527183	−	0.196747i
$305$	−15.9661	+	4.27810i	−0.914215	+	0.244963i
$306$	−0.794291	+	2.96433i	−0.0454066	+	0.169460i
$307$	20.9825	+	20.9825i	1.19753	+	1.19753i	0.974902	+	0.222632i	$0.0714649\pi$
$307$	20.9825	+	20.9825i	1.19753	+	1.19753i	0.222632	+	0.974902i	$0.428535\pi$
$308$	−13.2569	−	1.75080i	−0.755381	−	0.0997612i
$309$			4.54200i			0.258386i
$310$	33.5898	+	9.00036i	1.90777	+	0.511186i
$311$	−7.61836	+	13.1954i	−0.431997	+	0.748242i	−0.997045	−	0.0768167i	$-0.975524\pi$
$311$	−7.61836	+	13.1954i	−0.431997	+	0.748242i	0.565048	+	0.825058i	$0.308858\pi$
$312$	2.79169	−	2.28176i	0.158049	−	0.129179i
$313$	17.7961	−	10.2746i	1.00590	−	0.580754i	0.0959082	−	0.995390i	$-0.469424\pi$
$313$	17.7961	−	10.2746i	1.00590	−	0.580754i	0.909987	+	0.414636i	$0.136091\pi$
$314$	4.46035	−	4.46035i	0.251712	−	0.251712i
$315$	−10.5724	+	4.37420i	−0.595690	+	0.246458i
$316$		−	12.3253i		−	0.693351i
$317$	1.26668	−	4.72731i	0.0711437	−	0.265512i	−0.921188	−	0.389119i	$-0.872780\pi$
$317$	1.26668	−	4.72731i	0.0711437	−	0.265512i	0.992331	+	0.123607i	$0.0394462\pi$
$318$	0.101561	+	0.379032i	0.00569528	+	0.0212551i
$319$	−6.96346	−	25.9880i	−0.389879	−	1.45505i
$320$	−1.11927	+	4.17716i	−0.0625689	+	0.233510i
$321$		−	5.56239i		−	0.310462i
$322$	9.25882	−	3.83071i	0.515974	−	0.213477i
$323$	7.70674	−	7.70674i	0.428814	−	0.428814i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−49.1536	−	4.94040i	−2.72655	−	0.274044i
$326$	−3.46173	+	5.99589i	−0.191727	+	0.332082i
$327$	2.04723	+	0.548553i	0.113212	+	0.0303351i
$328$		−	3.05726i		−	0.168809i
$329$	−23.4544	−	3.09756i	−1.29308	−	0.170774i
$330$	−15.4550	−	15.4550i	−0.850771	−	0.850771i
$331$	−0.629186	+	2.34816i	−0.0345832	+	0.129066i	−0.981059	−	0.193708i	$-0.937949\pi$
$331$	−0.629186	+	2.34816i	−0.0345832	+	0.129066i	0.946476	+	0.322774i	$0.104615\pi$
$332$	8.69236	−	2.32911i	0.477055	−	0.127827i
$333$	−1.00443	−	3.74857i	−0.0550423	−	0.205421i
$334$	5.08063	−	2.93330i	0.278000	−	0.160503i
$335$	26.2340			1.43332
$336$	2.62326	−	0.344270i	0.143110	−	0.0187815i
$337$		−	34.8264i		−	1.89712i	−0.316603	−	0.948558i	$-0.602542\pi$
$337$		−	34.8264i		−	1.89712i	0.316603	−	0.948558i	$-0.397458\pi$
$338$	−7.17916	−	10.8379i	−0.390495	−	0.589503i
$339$	0.819571	+	0.473179i	0.0445130	+	0.0256996i
$340$	−12.8193	+	3.43493i	−0.695225	+	0.186285i
$341$	35.1969	−	20.3209i	1.90602	−	1.10044i
$342$	−3.55142			−0.192039
$343$	7.06646	+	17.1191i	0.381553	+	0.924347i
$344$	6.18301	+	6.18301i	0.333366	+	0.333366i
$345$	15.8197	+	4.23889i	0.851706	+	0.228214i
$346$	−5.35646	+	1.43526i	−0.287965	+	0.0771600i
$347$	−9.22831	+	15.9839i	−0.495401	+	0.858061i	−0.999986	−	0.00530181i	$-0.998312\pi$
$347$	−9.22831	+	15.9839i	−0.495401	+	0.858061i	0.504584	+	0.863362i	$0.331646\pi$
$348$	2.66166	+	4.61012i	0.142680	+	0.247128i
$349$	15.7836	+	15.7836i	0.844877	+	0.844877i	0.989489	−	0.144611i	$-0.0461932\pi$
$349$	15.7836	+	15.7836i	0.844877	+	0.844877i	−0.144611	+	0.989489i	$0.546193\pi$
$350$	−28.7506	−	22.0797i	−1.53678	−	1.18021i
$351$	−1.48147	−	3.28713i	−0.0790751	−	0.175454i
$352$	2.52707	+	4.37701i	0.134693	+	0.233296i
$353$	7.35880	+	27.4634i	0.391669	+	1.46173i	0.827380	+	0.561643i	$0.189831\pi$
$353$	7.35880	+	27.4634i	0.391669	+	1.46173i	−0.435710	+	0.900087i	$0.643503\pi$
$354$	0.419752	−	0.727032i	0.0223096	−	0.0386413i
$355$	−4.63466	−	8.02746i	−0.245982	−	0.426054i
$356$	−4.78092	+	4.78092i	−0.253388	+	0.253388i
$357$	4.94025	+	6.44369i	0.261466	+	0.341036i
$358$	−10.0920	+	10.0920i	−0.533380	+	0.533380i
$359$	4.44850	+	1.19197i	0.234783	+	0.0629099i	0.374292	−	0.927311i	$-0.377886\pi$
$359$	4.44850	+	1.19197i	0.234783	+	0.0629099i	−0.139509	+	0.990221i	$0.544552\pi$
$360$	3.74514	+	2.16226i	0.197386	+	0.113961i
$361$	−5.53166	−	3.19371i	−0.291140	−	0.168090i
$362$	−5.64291	+	21.0596i	−0.296585	+	1.10687i
$363$	−14.5443			−0.763379
$364$	−0.289180	−	9.53501i	−0.0151571	−	0.499770i
$365$	10.6742			0.558713
$366$	0.989266	−	3.69199i	0.0517097	−	0.192983i
$367$	−16.5388	−	9.54868i	−0.863318	−	0.498437i	0.00180371	−	0.999998i	$-0.499426\pi$
$367$	−16.5388	−	9.54868i	−0.863318	−	0.498437i	−0.865122	+	0.501561i	$0.832759\pi$
$368$	−3.27981	−	1.89360i	−0.170972	−	0.0987107i
$369$	−2.95309	−	0.791277i	−0.153732	−	0.0411922i
$370$	11.8671	−	11.8671i	0.616941	−	0.616941i
$371$	0.959010	+	0.397693i	0.0497893	+	0.0206472i
$372$	−5.68606	+	5.68606i	−0.294808	+	0.294808i
$373$	0.714755	+	1.23799i	0.0370086	+	0.0641008i	0.883936	−	0.467607i	$-0.154884\pi$
$373$	0.714755	+	1.23799i	0.0370086	+	0.0641008i	−0.846928	+	0.531708i	$0.821550\pi$
$374$	−7.75534	+	13.4326i	−0.401019	+	0.694585i
$375$	−9.73925	−	36.3474i	−0.502933	−	1.87697i
$376$	4.47096	+	7.74392i	0.230572	+	0.399362i
$377$	17.4984	−	7.88633i	0.901215	−	0.406167i
$378$	0.346409	−	2.62298i	0.0178174	−	0.134911i
$379$	15.4767	+	15.4767i	0.794986	+	0.794986i	0.982300	−	0.187314i	$-0.0599782\pi$
$379$	15.4767	+	15.4767i	0.794986	+	0.794986i	−0.187314	+	0.982300i	$0.559978\pi$
$380$	−7.67909	−	13.3006i	−0.393929	−	0.682305i
$381$	−4.40663	+	7.63251i	−0.225759	+	0.391026i
$382$	−8.87259	+	2.37740i	−0.453961	+	0.121638i
$383$	8.38668	+	2.24720i	0.428539	+	0.114827i	0.466640	−	0.884447i	$-0.345464\pi$
$383$	8.38668	+	2.24720i	0.428539	+	0.114827i	−0.0381012	+	0.999274i	$0.512131\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−57.3358	+	7.52461i	−2.92210	+	0.383490i
$386$	−12.9345			−0.658346
$387$	7.57261	−	4.37205i	0.384937	−	0.222244i
$388$	−13.5911	+	3.64173i	−0.689985	+	0.184881i
$389$	23.5167	+	13.5774i	1.19235	+	0.688401i	0.958838	−	0.283954i	$-0.0916464\pi$
$389$	23.5167	+	13.5774i	1.19235	+	0.688401i	0.233507	+	0.972355i	$0.424980\pi$
$390$	9.10746	−	12.6559i	0.461174	−	0.640859i
$391$		−	11.6226i		−	0.587778i
$392$	3.50494	−	6.05932i	0.177026	−	0.306042i
$393$	−5.86075			−0.295636
$394$	−15.4698	+	8.93149i	−0.779357	+	0.449962i
$395$	−13.7953	−	51.4847i	−0.694116	−	2.59047i
$396$	4.88192	−	1.30811i	0.245326	−	0.0657349i
$397$	−0.500084	+	1.86634i	−0.0250985	+	0.0936688i	−0.977339	−	0.211680i	$-0.932106\pi$
$397$	−0.500084	+	1.86634i	−0.0250985	+	0.0936688i	0.952240	+	0.305349i	$0.0987731\pi$
$398$	−5.56982	−	5.56982i	−0.279190	−	0.279190i
$399$	−5.72307	+	7.45215i	−0.286512	+	0.373074i
$400$			13.7014i			0.685072i
$401$	2.17838	+	0.583696i	0.108783	+	0.0291484i	0.312800	−	0.949819i	$-0.398733\pi$
$401$	2.17838	+	0.583696i	0.108783	+	0.0291484i	−0.204017	+	0.978967i	$0.565400\pi$
$402$	−3.03317	+	5.25361i	−0.151281	+	0.262026i
$403$	18.3483	+	22.4488i	0.913996	+	1.11826i
$404$	12.4074	−	7.16340i	0.617290	−	0.356392i
$405$	3.05790	−	3.05790i	0.151948	−	0.151948i
$406$	13.9629	+	1.84405i	0.692968	+	0.0915184i
$407$		−	19.6141i		−	0.972237i
$408$	0.794291	−	2.96433i	0.0393233	−	0.146756i
$409$	0.401283	+	1.49761i	0.0198422	+	0.0740520i	0.975137	−	0.221603i	$-0.0711288\pi$
$409$	0.401283	+	1.49761i	0.0198422	+	0.0740520i	−0.955295	+	0.295655i	$0.904462\pi$
$410$	−3.42189	−	12.7707i	−0.168995	−	0.630699i
$411$	4.94358	−	18.4497i	0.243849	−	0.910057i
$412$		−	4.54200i		−	0.223768i
$413$	−0.849148	−	2.05239i	−0.0417839	−	0.100992i
$414$	−2.67795	+	2.67795i	−0.131614	+	0.131614i
$415$	33.7025	−	19.4582i	1.65439	−	0.955163i
$416$	−2.79169	+	2.28176i	−0.136874	+	0.111873i
$417$	3.97125	−	6.87840i	0.194473	−	0.336837i
$418$	−17.3378	−	4.64564i	−0.848018	−	0.227226i
$419$			30.2063i			1.47567i	0.674979	+	0.737837i	$0.264153\pi$
$419$			30.2063i			1.47567i	−0.674979	+	0.737837i	$0.735847\pi$
$420$	10.5724	−	4.37420i	0.515882	−	0.213439i
$421$	−14.4147	−	14.4147i	−0.702531	−	0.702531i	0.262423	−	0.964953i	$-0.415479\pi$
$421$	−14.4147	−	14.4147i	−0.702531	−	0.702531i	−0.964953	+	0.262423i	$0.915479\pi$
$422$	6.47241	−	24.1554i	0.315072	−	1.17586i
$423$	8.63722	−	2.31434i	0.419956	−	0.112527i
$424$	−0.101561	−	0.379032i	−0.00493226	−	0.0184074i
$425$	−36.4150	+	21.0242i	−1.76639	+	1.01982i
$426$	2.14343			0.103850
$427$	−6.15293	−	8.02543i	−0.297761	−	0.388378i
$428$			5.56239i			0.268868i
$429$	−2.93250	−	17.9855i	−0.141583	−	0.868346i
$430$	32.7479	+	18.9070i	1.57924	+	0.911776i
$431$	21.4988	−	5.76058i	1.03556	−	0.277478i	0.299288	−	0.954163i	$-0.403251\pi$
$431$	21.4988	−	5.76058i	1.03556	−	0.277478i	0.736272	+	0.676685i	$0.236584\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−21.4850			−1.03251			−0.516253	−	0.856436i	$-0.672673\pi$
$433$	−21.4850			−1.03251			−0.516253	+	0.856436i	$0.672673\pi$
$434$	2.76838	+	21.0944i	0.132886	+	1.01256i
$435$	16.2781	+	16.2781i	0.780476	+	0.780476i
$436$	−2.04723	−	0.548553i	−0.0980445	−	0.0262709i
$437$	12.9916	−	3.48110i	0.621474	−	0.166524i
$438$	−1.23415	+	2.13761i	−0.0589699	+	0.102139i
$439$	−9.71370	−	16.8246i	−0.463610	−	0.802995i	0.535528	−	0.844517i	$-0.320113\pi$
$439$	−9.71370	−	16.8246i	−0.463610	−	0.802995i	−0.999138	+	0.0415221i	$0.986779\pi$
$440$	15.4550	+	15.4550i	0.736790	+	0.736790i
$441$	−4.94571	−	4.95378i	−0.235510	−	0.235894i
$442$	−10.3481	−	3.91837i	−0.492208	−	0.186378i
$443$	−16.0878	−	27.8649i	−0.764356	−	1.32390i	−0.940586	−	0.339555i	$-0.889724\pi$
$443$	−16.0878	−	27.8649i	−0.764356	−	1.32390i	0.176230	−	0.984349i	$-0.443610\pi$
$444$	1.00443	+	3.74857i	0.0476680	+	0.177899i
$445$	−14.6196	+	25.3218i	−0.693033	+	1.20037i
$446$	14.0517	+	24.3383i	0.665368	+	1.15245i
$447$	−7.93569	+	7.93569i	−0.375345	+	0.375345i
$448$	−2.62326	+	0.344270i	−0.123937	+	0.0162652i
$449$	−20.8928	+	20.8928i	−0.985993	+	0.985993i	−0.999903	−	0.0139102i	$-0.995572\pi$
$449$	−20.8928	+	20.8928i	−0.985993	+	0.985993i	0.0139102	+	0.999903i	$0.495572\pi$
$450$	13.2346	+	3.54620i	0.623884	+	0.167169i
$451$	−13.3817	−	7.72591i	−0.630118	−	0.363799i
$452$	−0.819571	−	0.473179i	−0.0385494	−	0.0222565i
$453$	−4.65772	+	17.3829i	−0.218839	+	0.816718i
$454$	4.98907			0.234149
$455$	−11.8802	−	39.5056i	−0.556951	−	1.85205i
$456$	3.55142			0.166311
$457$	6.78023	−	25.3042i	0.317166	−	1.18368i	−0.604790	−	0.796385i	$-0.706743\pi$
$457$	6.78023	−	25.3042i	0.317166	−	1.18368i	0.921956	−	0.387294i	$-0.126590\pi$
$458$	13.0613	+	7.54096i	0.610316	+	0.352366i
$459$	−2.65775	−	1.53445i	−0.124053	−	0.0716221i
$460$	−15.8197	−	4.23889i	−0.737599	−	0.197639i
$461$	8.48338	−	8.48338i	0.395110	−	0.395110i	−0.481394	−	0.876504i	$-0.659869\pi$
$461$	8.48338	−	8.48338i	0.395110	−	0.395110i	0.876504	+	0.481394i	$0.159869\pi$
$462$	5.12228	−	12.3520i	0.238310	−	0.574668i
$463$	−6.85359	+	6.85359i	−0.318513	+	0.318513i	−0.848196	−	0.529683i	$-0.822311\pi$
$463$	−6.85359	+	6.85359i	−0.318513	+	0.318513i	0.529683	+	0.848196i	$0.322311\pi$
$464$	−2.66166	−	4.61012i	−0.123564	−	0.214020i
$465$	−17.3874	+	30.1158i	−0.806320	+	1.39659i
$466$	−0.905475	−	3.37928i	−0.0419453	−	0.156542i
$467$	−4.02663	−	6.97432i	−0.186330	−	0.322733i	0.757694	−	0.652610i	$-0.226326\pi$
$467$	−4.02663	−	6.97432i	−0.186330	−	0.322733i	−0.944024	+	0.329877i	$0.892993\pi$
$468$	1.48147	+	3.28713i	0.0684810	+	0.151948i
$469$	6.13604	+	14.8308i	0.283336	+	0.684823i
$470$	27.3434	+	27.3434i	1.26126	+	1.26126i
$471$	3.15395	+	5.46279i	0.145326	+	0.251712i
$472$	−0.419752	+	0.727032i	−0.0193206	+	0.0334643i
$473$	42.6880	−	11.4382i	1.96280	−	0.525930i
$474$	11.9053	+	3.19001i	0.546828	+	0.146522i
$475$	−34.4075	−	34.4075i	−1.57873	−	1.57873i
$476$	−4.94025	−	6.44369i	−0.226436	−	0.295346i
$477$	−0.392403			−0.0179669
$478$	−2.35384	+	1.35899i	−0.107662	+	0.0621588i
$479$	−38.4032	+	10.2901i	−1.75469	+	0.470168i	−0.985617	−	0.168995i	$-0.945948\pi$
$479$	−38.4032	+	10.2901i	−1.75469	+	0.470168i	−0.769072	+	0.639162i	$0.779281\pi$
$480$	−3.74514	−	2.16226i	−0.170942	−	0.0986931i
$481$	13.8101	−	2.25172i	0.629686	−	0.102669i
$482$			26.5491i			1.20928i
$483$	1.30382	+	9.93480i	0.0593258	+	0.452049i
$484$	14.5443			0.661105
$485$	−52.6963	+	30.4242i	−2.39282	+	1.38149i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	−16.6988	+	4.47444i	−0.756697	+	0.202756i	−0.616487	−	0.787365i	$-0.711445\pi$
$487$	−16.6988	+	4.47444i	−0.756697	+	0.202756i	−0.140210	+	0.990122i	$0.544778\pi$
$488$	−0.989266	+	3.69199i	−0.0447820	+	0.167129i
$489$	−4.89563	−	4.89563i	−0.221388	−	0.221388i
$490$	7.85872	−	29.2337i	0.355021	−	1.32065i
$491$			17.0033i			0.767349i	0.923468	+	0.383675i	$0.125342\pi$
$491$			17.0033i			0.767349i	−0.923468	+	0.383675i	$0.874658\pi$
$492$	2.95309	+	0.791277i	0.133135	+	0.0356735i
$493$	8.16837	−	14.1480i	0.367885	−	0.637195i
$494$	1.28055	−	12.7406i	0.0576148	−	0.573228i
$495$	18.9285	−	10.9284i	0.850771	−	0.491193i
$496$	5.68606	−	5.68606i	0.255312	−	0.255312i
$497$	3.45412	−	4.49769i	0.154938	−	0.201749i
$498$			8.99899i			0.403255i
$499$	0.616787	−	2.30188i	0.0276112	−	0.103046i	−0.950745	−	0.309974i	$-0.899680\pi$
$499$	0.616787	−	2.30188i	0.0276112	−	0.103046i	0.978356	+	0.206927i	$0.0663464\pi$
$500$	9.73925	+	36.3474i	0.435552	+	1.62550i
$501$	1.51839	+	5.66671i	0.0678366	+	0.253170i
$502$	5.31003	−	19.8173i	0.236998	−	0.884489i
$503$		−	18.3368i		−	0.817597i	−0.912625	−	0.408798i	$-0.865948\pi$
$503$		−	18.3368i		−	0.817597i	0.912625	−	0.408798i	$-0.134052\pi$
$504$	−0.346409	+	2.62298i	−0.0154303	+	0.116837i
$505$	43.8098	−	43.8098i	1.94951	−	1.94951i
$506$	−16.5766	+	9.57051i	−0.736920	+	0.425461i
$507$	12.3267	−	4.12948i	0.547448	−	0.183397i
$508$	4.40663	−	7.63251i	0.195513	−	0.338638i
$509$	3.72497	+	0.998103i	0.165106	+	0.0442401i	0.340425	−	0.940272i	$-0.389429\pi$
$509$	3.72497	+	0.998103i	0.165106	+	0.0442401i	−0.175319	+	0.984512i	$0.556096\pi$
$510$		−	13.2715i		−	0.587673i
$511$	2.49665	+	6.03441i	0.110445	+	0.266947i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.919175	−	3.43041i	0.0405826	−	0.151456i
$514$	1.63625	−	0.438432i	0.0721719	−	0.0193384i
$515$	−5.08372	−	18.9727i	−0.224015	−	0.836036i
$516$	−7.57261	+	4.37205i	−0.333366	+	0.192469i
$517$	45.1937			1.98761
$518$	9.48447	+	3.93313i	0.416724	+	0.172812i
$519$		−	5.54541i		−	0.243417i
$520$	−9.10746	+	12.6559i	−0.399388	+	0.555000i
$521$	−0.194810	−	0.112474i	−0.00853478	−	0.00492756i	0.495727	−	0.868479i	$-0.334902\pi$
$521$	−0.194810	−	0.112474i	−0.00853478	−	0.00492756i	−0.504261	+	0.863551i	$0.668235\pi$
$522$	−5.14192	+	1.37777i	−0.225056	+	0.0603035i
$523$	23.1348	−	13.3569i	1.01161	−	0.584056i	0.0999505	−	0.994992i	$-0.468132\pi$
$523$	23.1348	−	13.3569i	1.01161	−	0.584056i	0.911664	+	0.410937i	$0.134798\pi$
$524$	5.86075			0.256028
$525$	28.7685	−	22.0563i	1.25556	−	0.962614i
$526$	−4.09741	−	4.09741i	−0.178656	−	0.178656i
$527$	23.8371	+	6.38713i	1.03836	+	0.278228i
$528$	−4.88192	+	1.30811i	−0.212458	+	0.0569281i
$529$	−4.32856	+	7.49729i	−0.188198	+	0.325969i
$530$	−0.848477	−	1.46960i	−0.0368555	−	0.0638356i
$531$	0.593619	+	0.593619i	0.0257609	+	0.0257609i
$532$	5.72307	−	7.45215i	0.248126	−	0.323092i
$533$	3.90350	−	10.3088i	0.169079	−	0.446524i
$534$	−3.38062	−	5.85541i	−0.146294	−	0.253388i
$535$	6.22580	+	23.2350i	0.269165	+	1.00454i
$536$	3.03317	−	5.25361i	0.131013	−	0.226921i
$537$	−7.13614	−	12.3602i	−0.307947	−	0.533380i
$538$	−1.24016	+	1.24016i	−0.0534670	+	0.0534670i
$539$	−17.6645	−	30.6535i	−0.760864	−	1.32034i
$540$	−3.05790	+	3.05790i	−0.131591	+	0.131591i
$541$	−11.4098	−	3.05726i	−0.490547	−	0.131442i	0.00506241	−	0.999987i	$-0.498389\pi$
$541$	−11.4098	−	3.05726i	−0.490547	−	0.131442i	−0.495609	+	0.868546i	$0.665055\pi$
$542$	0.739218	+	0.426788i	0.0317521	+	0.0183321i
$543$	−18.8815	−	10.9013i	−0.810284	−	0.467818i
$544$	−0.794291	+	2.96433i	−0.0340549	+	0.127095i
$545$	−9.16559			−0.392611
$546$	9.28496	+	2.18852i	0.397359	+	0.0936598i
$547$	5.62368			0.240451			0.120226	−	0.992747i	$-0.461638\pi$
$547$	5.62368			0.240451			0.120226	+	0.992747i	$0.461638\pi$
$548$	−4.94358	+	18.4497i	−0.211179	+	0.788133i
$549$	3.31015	+	1.91111i	0.141274	+	0.0815644i
$550$	59.9714	+	34.6245i	2.55719	+	1.47639i
$551$	18.2611	+	4.89306i	0.777950	+	0.208451i
$552$	2.67795	−	2.67795i	0.113981	−	0.113981i
$553$	25.8790	−	19.8409i	1.10049	−	0.843722i
$554$	19.8263	−	19.8263i	0.842338	−	0.842338i
$555$	8.39131	+	14.5342i	0.356191	+	0.616941i
$556$	−3.97125	+	6.87840i	−0.168418	+	0.291709i
$557$	−0.417785	−	1.55919i	−0.0177021	−	0.0660652i	0.956510	−	0.291700i	$-0.0942210\pi$
$557$	−0.417785	−	1.55919i	−0.0177021	−	0.0660652i	−0.974212	+	0.225635i	$0.927554\pi$
$558$	−4.02065	−	6.96397i	−0.170208	−	0.294808i
$559$	12.9541	+	28.7430i	0.547901	+	1.21570i
$560$	−10.5724	+	4.37420i	−0.446767	+	0.184844i
$561$	−10.9677	−	10.9677i	−0.463057	−	0.463057i
$562$	−11.3543	−	19.6662i	−0.478952	−	0.829569i
$563$	17.2369	−	29.8552i	0.726449	−	1.25825i	−0.231925	−	0.972734i	$-0.574502\pi$
$563$	17.2369	−	29.8552i	0.726449	−	1.25825i	0.958375	−	0.285514i	$-0.0921642\pi$
$564$	−8.63722	+	2.31434i	−0.363693	+	0.0974512i
$565$	−3.95309	−	1.05923i	−0.166308	−	0.0445621i
$566$	13.4575	+	13.4575i	0.565661	+	0.565661i
$567$	2.44394	+	1.01348i	0.102636	+	0.0425622i
$568$	−2.14343			−0.0899365
$569$	7.99782	−	4.61755i	0.335286	−	0.193578i	−0.322899	−	0.946433i	$-0.604658\pi$
$569$	7.99782	−	4.61755i	0.335286	−	0.193578i	0.658186	+	0.752856i	$0.271324\pi$
$570$	14.8349	−	3.97499i	0.621364	−	0.166494i
$571$	−35.9780	−	20.7719i	−1.50563	−	0.869278i	−0.999979	−	0.00654130i	$-0.997918\pi$
$571$	−35.9780	−	20.7719i	−1.50563	−	0.869278i	−0.505654	−	0.862736i	$-0.668749\pi$
$572$	2.93250	+	17.9855i	0.122614	+	0.752010i
$573$		−	9.18558i		−	0.383733i
$574$	6.41924	−	4.92150i	0.267934	−	0.205420i
$575$	−51.8901			−2.16397
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	−0.946225	−	3.53136i	−0.0393919	−	0.147012i	0.943429	−	0.331575i	$-0.107580\pi$
$577$	−0.946225	−	3.53136i	−0.0393919	−	0.147012i	−0.982821	+	0.184562i	$0.940913\pi$
$578$	7.32348	−	1.96232i	0.304617	−	0.0816218i
$579$	3.34768	−	12.4937i	0.139125	−	0.519221i
$580$	−16.2781	−	16.2781i	−0.675912	−	0.675912i
$581$	18.8831	+	14.5018i	0.783404	+	0.601635i
$582$		−	14.0706i		−	0.583244i
$583$	−1.91568	−	0.513305i	−0.0793394	−	0.0212589i
$584$	1.23415	−	2.13761i	0.0510694	−	0.0884548i
$585$	9.86753	+	12.0727i	0.407972	+	0.499146i
$586$	−6.26851	+	3.61912i	−0.258950	+	0.149505i
$587$	3.35996	−	3.35996i	0.138681	−	0.138681i	−0.634358	−	0.773039i	$-0.718736\pi$
$587$	3.35996	−	3.35996i	0.138681	−	0.138681i	0.773039	+	0.634358i	$0.218736\pi$
$588$	4.94571	+	4.95378i	0.203958	+	0.204291i
$589$			28.5580i			1.17671i
$590$	−0.939629	+	3.50674i	−0.0386839	+	0.144370i
$591$	−4.62328	−	17.2543i	−0.190176	−	0.709747i
$592$	−1.00443	−	3.74857i	−0.0412817	−	0.154065i
$593$	−9.35039	+	34.8961i	−0.383974	+	1.43301i	0.455803	+	0.890081i	$0.349352\pi$
$593$	−9.35039	+	34.8961i	−0.383974	+	1.43301i	−0.839777	+	0.542931i	$0.817315\pi$
$594$			5.05414i			0.207374i
$595$	−27.8484	−	21.3869i	−1.14167	−	0.876778i
$596$	7.93569	−	7.93569i	0.325059	−	0.325059i
$597$	6.82160	−	3.93845i	0.279190	−	0.161190i
$598$	−8.64149	−	10.5727i	−0.353377	−	0.432350i
$599$	−16.4120	+	28.4265i	−0.670578	+	1.16148i	0.307163	+	0.951657i	$0.400620\pi$
$599$	−16.4120	+	28.4265i	−0.670578	+	1.16148i	−0.977740	+	0.209818i	$0.932713\pi$
$600$	−13.2346	−	3.54620i	−0.540300	−	0.144773i
$601$		−	18.2200i		−	0.743208i	−0.928391	−	0.371604i	$-0.878808\pi$
$601$		−	18.2200i		−	0.743208i	0.928391	−	0.371604i	$-0.121192\pi$
$602$	−3.02904	+	22.9356i	−0.123454	+	0.934783i
$603$	−4.28956	−	4.28956i	−0.174684	−	0.174684i
$604$	4.65772	−	17.3829i	0.189520	−	0.707299i
$605$	60.7540	−	16.2790i	2.47000	−	0.661835i
$606$	3.70805	+	13.8386i	0.150629	+	0.562155i
$607$	−6.49995	+	3.75275i	−0.263825	+	0.152319i	−0.626078	−	0.779760i	$-0.715341\pi$
$607$	−6.49995	+	3.75275i	−0.263825	+	0.152319i	0.362253	+	0.932080i	$0.382008\pi$
$608$	−3.55142			−0.144029
$609$	−5.39508	+	13.0099i	−0.218620	+	0.527186i
$610$			16.5293i			0.669252i
$611$	5.18826	+	31.8203i	0.209895	+	1.28731i
$612$	2.65775	+	1.53445i	0.107433	+	0.0620266i
$613$	19.6002	−	5.25185i	0.791644	−	0.212120i	0.159732	−	0.987160i	$-0.448937\pi$
$613$	19.6002	−	5.25185i	0.791644	−	0.212120i	0.631912	+	0.775040i	$0.282270\pi$
$614$	25.6982	−	14.8369i	1.03710	−	0.598767i
$615$	13.2212			0.533129
$616$	−5.12228	+	12.3520i	−0.206382	+	0.497677i
$617$	−2.58793	−	2.58793i	−0.104186	−	0.104186i	0.653092	−	0.757278i	$-0.273471\pi$
$617$	−2.58793	−	2.58793i	−0.104186	−	0.104186i	−0.757278	+	0.653092i	$0.773471\pi$
$618$	4.38724	+	1.17556i	0.176481	+	0.0472878i
$619$	−42.2811	+	11.3292i	−1.69942	+	0.455359i	−0.972794	−	0.231671i	$-0.925581\pi$
$619$	−42.2811	+	11.3292i	−1.69942	+	0.455359i	−0.726629	+	0.687030i	$0.758914\pi$
$620$	17.3874	−	30.1158i	0.698293	−	1.20948i
$621$	−1.89360	−	3.27981i	−0.0759875	−	0.131614i
$622$	10.7740	+	10.7740i	0.431997	+	0.431997i
$623$	−17.7346	−	2.34216i	−0.710521	−	0.0938366i
$624$	−1.48147	−	3.28713i	−0.0593063	−	0.131591i
$625$	47.1112	+	81.5990i	1.88445	+	3.26396i
$626$	−5.31852	−	19.8490i	−0.212571	−	0.793325i
$627$	8.97469	−	15.5446i	0.358414	−	0.620792i
$628$	−3.15395	−	5.46279i	−0.125856	−	0.217989i
$629$	8.42152	−	8.42152i	0.335788	−	0.335788i
$630$	1.48880	+	11.3443i	0.0593153	+	0.451969i
$631$	−24.8517	+	24.8517i	−0.989329	+	0.989329i	−0.999944	−	0.0106143i	$-0.996621\pi$
$631$	−24.8517	+	24.8517i	−0.989329	+	0.989329i	0.0106143	+	0.999944i	$0.496621\pi$
$632$	−11.9053	−	3.19001i	−0.473567	−	0.126892i
$633$	21.6571	+	12.5037i	0.860792	+	0.496979i
$634$	−4.23839	−	2.44703i	−0.168328	−	0.0971842i
$635$	9.86440	−	36.8145i	0.391457	−	1.46094i
$636$	0.392403			0.0155598
$637$	19.5549	−	15.9564i	0.774792	−	0.632216i
$638$	−26.9048			−1.06517
$639$	−0.554762	+	2.07040i	−0.0219460	+	0.0819037i
$640$	3.74514	+	2.16226i	0.148040	+	0.0854708i
$641$	−38.0315	−	21.9575i	−1.50215	−	0.867269i	−0.999997	−	0.00249346i	$-0.999206\pi$
$641$	−38.0315	−	21.9575i	−1.50215	−	0.867269i	−0.502158	−	0.864776i	$-0.667460\pi$
$642$	−5.37285	−	1.43965i	−0.212050	−	0.0568185i
$643$	−2.33993	+	2.33993i	−0.0922780	+	0.0922780i	−0.751739	−	0.659461i	$-0.770785\pi$
$643$	−2.33993	+	2.33993i	−0.0922780	+	0.0922780i	0.659461	+	0.751739i	$0.270785\pi$
$644$	−1.30382	−	9.93480i	−0.0513777	−	0.391486i
$645$	−26.7385	+	26.7385i	−1.05283	+	1.05283i
$646$	−5.44949	−	9.43879i	−0.214407	−	0.371364i
$647$	15.6515	−	27.1093i	0.615326	−	1.06578i	−0.375002	−	0.927024i	$-0.622358\pi$
$647$	15.6515	−	27.1093i	0.615326	−	1.06578i	0.990327	−	0.138751i	$-0.0443088\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	2.12148	+	3.67452i	0.0832755	+	0.144237i
$650$	−17.4940	+	46.2001i	−0.686169	+	1.81212i
$651$	−21.0921	−	2.78558i	−0.826666	−	0.109176i
$652$	4.89563	+	4.89563i	0.191727	+	0.191727i
$653$	−17.6786	−	30.6203i	−0.691818	−	1.19826i	−0.971242	−	0.238095i	$-0.923477\pi$
$653$	−17.6786	−	30.6203i	−0.691818	−	1.19826i	0.279424	−	0.960168i	$-0.409856\pi$
$654$	1.05972	−	1.83550i	0.0414385	−	0.0717736i
$655$	24.4813	−	6.55975i	0.956564	−	0.256311i
$656$	−2.95309	−	0.791277i	−0.115299	−	0.0308942i
$657$	−1.74535	−	1.74535i	−0.0680926	−	0.0680926i
$658$	−9.06246	+	21.8535i	−0.353292	+	0.851939i
$659$	−33.6180			−1.30957			−0.654785	−	0.755815i	$-0.727241\pi$
$659$	−33.6180			−1.30957			−0.654785	+	0.755815i	$0.727241\pi$
$660$	−18.9285	+	10.9284i	−0.736790	+	0.425386i
$661$	−16.8396	+	4.51215i	−0.654984	+	0.175502i	−0.570981	−	0.820963i	$-0.693437\pi$
$661$	−16.8396	+	4.51215i	−0.654984	+	0.175502i	−0.0840027	+	0.996466i	$0.526770\pi$
$662$	2.10530	+	1.21549i	0.0818248	+	0.0472415i
$663$	6.46313	−	8.98133i	0.251007	−	0.348806i
$664$		−	8.99899i		−	0.349229i
$665$	15.5652	−	37.5345i	0.603594	−	1.45553i
$666$	−3.88081			−0.150378
$667$	17.4594	−	10.0802i	0.676033	−	0.390308i
$668$	−1.51839	−	5.66671i	−0.0587482	−	0.219251i
$669$	−27.1458	+	7.27370i	−1.04952	+	0.281218i
$670$	6.78986	−	25.3401i	0.262315	−	0.978974i
$671$	13.6599	+	13.6599i	0.527336	+	0.527336i
$672$	0.346409	−	2.62298i	0.0133630	−	0.101183i
$673$			46.0164i			1.77380i	0.461958	+	0.886902i	$0.347147\pi$
$673$			46.0164i			1.77380i	−0.461958	+	0.886902i	$0.652853\pi$
$674$	−33.6397	−	9.01374i	−1.29575	−	0.347196i
$675$	−6.85072	+	11.8658i	−0.263684	+	0.456715i
$676$	−12.3267	+	4.12948i	−0.474104	+	0.158826i
$677$	20.1767	−	11.6490i	0.775452	−	0.447707i	−0.0593641	−	0.998236i	$-0.518907\pi$
$677$	20.1767	−	11.6490i	0.775452	−	0.447707i	0.834816	+	0.550529i	$0.185574\pi$
$678$	0.669177	−	0.669177i	0.0256996	−	0.0256996i
$679$	−29.5251	−	22.6746i	−1.13307	−	0.870170i
$680$			13.2715i			0.508940i
$681$	−1.29127	+	4.81907i	−0.0494814	+	0.184667i
$682$	−10.5189	−	39.2570i	−0.402789	−	1.50323i
$683$	−1.24268	−	4.63776i	−0.0475500	−	0.177459i	0.938067	−	0.346454i	$-0.112614\pi$
$683$	−1.24268	−	4.63776i	−0.0475500	−	0.177459i	−0.985617	+	0.168995i	$0.945948\pi$
$684$	−0.919175	+	3.43041i	−0.0351455	+	0.131165i
$685$			82.6006i			3.15601i
$686$	18.3648	−	2.39491i	0.701170	−	0.0914383i
$687$	−10.6645	+	10.6645i	−0.406877	+	0.406877i
$688$	7.57261	−	4.37205i	0.288703	−	0.166683i
$689$	0.141491	−	1.40774i	0.00539037	−	0.0536305i
$690$	8.18890	−	14.1836i	0.311746	−	0.539960i
$691$	11.9676	+	3.20671i	0.455269	+	0.121989i	0.479164	−	0.877725i	$-0.340940\pi$
$691$	11.9676	+	3.20671i	0.455269	+	0.121989i	−0.0238946	+	0.999714i	$0.507607\pi$
$692$			5.54541i			0.210805i
$693$	10.6054	+	8.14468i	0.402866	+	0.309391i
$694$	13.0508	+	13.0508i	0.495401	+	0.495401i
$695$	−8.88978	+	33.1771i	−0.337209	+	1.25848i
$696$	5.14192	−	1.37777i	0.194904	−	0.0522244i
$697$	−2.42835	−	9.06274i	−0.0919805	−	0.343276i
$698$	19.3309	−	11.1607i	0.731685	−	0.422439i
$699$	3.49849			0.132325
$700$	−28.7685	+	22.0563i	−1.08735	+	0.833648i
$701$			5.59447i			0.211300i	0.994403	+	0.105650i	$0.0336924\pi$
$701$			5.59447i			0.211300i	−0.994403	+	0.105650i	$0.966308\pi$
$702$	−3.55856	+	0.580218i	−0.134309	+	0.0218989i
$703$	11.9359	+	6.89119i	0.450171	+	0.259906i
$704$	4.88192	−	1.30811i	0.183994	−	0.0493012i
$705$	−33.4887	+	19.3347i	−1.26126	+	0.728188i
$706$	28.4322			1.07006
$707$	35.0139	+	14.5199i	1.31683	+	0.546079i
$708$	−0.593619	−	0.593619i	−0.0223096	−	0.0223096i
$709$	−17.3613	−	4.65196i	−0.652019	−	0.174708i	−0.0823775	−	0.996601i	$-0.526251\pi$
$709$	−17.3613	−	4.65196i	−0.652019	−	0.174708i	−0.569642	+	0.821893i	$0.692918\pi$
$710$	−8.95347	+	2.39908i	−0.336018	+	0.0900357i
$711$	−6.16264	+	10.6740i	−0.231117	+	0.400306i
$712$	3.38062	+	5.85541i	0.126694	+	0.219441i
$713$	21.5342	+	21.5342i	0.806463	+	0.806463i
$714$	7.50276	−	3.10416i	0.280784	−	0.116170i
$715$	32.3801	+	71.8459i	1.21095	+	2.68688i
$716$	7.13614	+	12.3602i	0.266690	+	0.461921i
$717$	−0.703465	−	2.62537i	−0.0262714	−	0.0980462i
$718$	2.30272	−	3.98842i	0.0859366	−	0.148847i
$719$	3.74178	+	6.48096i	0.139545	+	0.241699i	0.927324	−	0.374258i	$-0.122103\pi$
$719$	3.74178	+	6.48096i	0.139545	+	0.241699i	−0.787780	+	0.615957i	$0.788769\pi$
$720$	3.05790	−	3.05790i	0.113961	−	0.113961i
$721$	9.53672	−	7.31160i	0.355166	−	0.272298i
$722$	−4.51658	+	4.51658i	−0.168090	+	0.168090i
$723$	−25.6445	−	6.87142i	−0.953729	−	0.255551i
$724$	18.8815	+	10.9013i	0.701727	+	0.405142i
$725$	−63.1653	−	36.4685i	−2.34590	−	1.35441i
$726$	−3.76435	+	14.0487i	−0.139708	+	0.521397i
$727$	13.3542			0.495279			0.247640	−	0.968852i	$-0.420345\pi$
$727$	13.3542			0.495279			0.247640	+	0.968852i	$0.420345\pi$
$728$	−9.28496	−	2.18852i	−0.344123	−	0.0811118i
$729$	−1.00000			−0.0370370
$730$	2.76268	−	10.3105i	0.102252	−	0.381608i
$731$	23.2396	+	13.4174i	0.859548	+	0.496260i
$732$	−3.31015	−	1.91111i	−0.122347	−	0.0706368i
$733$	7.68035	+	2.05794i	0.283680	+	0.0760119i	0.397854	−	0.917449i	$-0.369755\pi$
$733$	7.68035	+	2.05794i	0.283680	+	0.0760119i	−0.114173	+	0.993461i	$0.536422\pi$
$734$	−13.5039	+	13.5039i	−0.498437	+	0.498437i
$735$	26.2036	+	15.1572i	0.966536	+	0.559081i
$736$	−2.67795	+	2.67795i	−0.0987107	+	0.0987107i
$737$	−15.3301	−	26.5525i	−0.564691	−	0.978073i
$738$	−1.52863	+	2.64767i	−0.0562697	+	0.0974619i
$739$	4.38445	+	16.3630i	0.161285	+	0.601922i	0.998485	+	0.0550259i	$0.0175241\pi$
$739$	4.38445	+	16.3630i	0.161285	+	0.601922i	−0.837200	+	0.546896i	$0.815809\pi$
$740$	−8.39131	−	14.5342i	−0.308471	−	0.534287i
$741$	11.9751	+	4.53444i	0.439915	+	0.166577i
$742$	0.632352	−	0.823402i	0.0232144	−	0.0302280i
$743$	−22.5162	−	22.5162i	−0.826038	−	0.826038i	0.160928	−	0.986966i	$-0.448551\pi$
$743$	−22.5162	−	22.5162i	−0.826038	−	0.826038i	−0.986966	+	0.160928i	$0.948551\pi$
$744$	4.02065	+	6.96397i	0.147404	+	0.255312i
$745$	24.2665	−	42.0308i	0.889056	−	1.53989i
$746$	1.38080	−	0.369985i	0.0505547	−	0.0135461i
$747$	−8.69236	−	2.32911i	−0.318037	−	0.0852177i
$748$	10.9677	+	10.9677i	0.401019	+	0.401019i
$749$	−11.6792	+	8.95419i	−0.426748	+	0.327179i
$750$	−37.6296			−1.37404
$751$	11.5378	−	6.66135i	0.421020	−	0.243076i	−0.274494	−	0.961589i	$-0.588510\pi$
$751$	11.5378	−	6.66135i	0.421020	−	0.243076i	0.695514	+	0.718513i	$0.255177\pi$
$752$	8.63722	−	2.31434i	0.314967	−	0.0843952i
$753$	17.7677	+	10.2582i	0.647491	+	0.373829i
$754$	−3.08868	−	18.9433i	−0.112483	−	0.689875i
$755$		−	77.8243i		−	2.83232i
$756$	−2.44394	−	1.01348i	−0.0888853	−	0.0368600i
$757$	−7.60210			−0.276303			−0.138152	−	0.990411i	$-0.544116\pi$
$757$	−7.60210			−0.276303			−0.138152	+	0.990411i	$0.544116\pi$
$758$	18.9550	−	10.9437i	0.688478	−	0.397493i
$759$	−4.95406	−	18.4888i	−0.179821	−	0.671101i
$760$	−14.8349	+	3.97499i	−0.538117	+	0.144188i
$761$	3.24500	−	12.1105i	0.117631	−	0.439006i	−0.881839	−	0.471550i	$-0.843695\pi$
$761$	3.24500	−	12.1105i	0.117631	−	0.439006i	0.999470	+	0.0325449i	$0.0103612\pi$
$762$	6.23192	+	6.23192i	0.225759	+	0.225759i
$763$	−2.14380	−	5.18156i	−0.0776106	−	0.187585i
$764$			9.18558i			0.332323i
$765$	12.8193	+	3.43493i	0.463483	+	0.124190i
$766$	4.34126	−	7.51929i	0.156856	−	0.271683i
$767$	−2.34364	+	1.91555i	−0.0846238	+	0.0691665i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−3.83908	+	3.83908i	−0.138441	+	0.138441i	−0.772931	−	0.634490i	$-0.781210\pi$
$769$	−3.83908	+	3.83908i	−0.138441	+	0.138441i	0.634490	+	0.772931i	$0.281210\pi$
$770$	−7.57137	+	57.3296i	−0.272853	+	2.06602i
$771$			1.69397i			0.0610068i
$772$	−3.34768	+	12.4937i	−0.120486	+	0.449659i
$773$	−7.29749	−	27.2346i	−0.262473	−	0.979561i	−0.963779	−	0.266701i	$-0.914066\pi$
$773$	−7.29749	−	27.2346i	−0.262473	−	0.979561i	0.701307	−	0.712860i	$-0.252600\pi$
$774$	−2.26314	−	8.44615i	−0.0813468	−	0.303591i
$775$	28.5160	−	106.423i	1.02433	−	3.82284i
$776$			14.0706i			0.505104i
$777$	−6.25387	+	8.14333i	−0.224356	+	0.292140i
$778$	19.2013	−	19.2013i	0.688401	−	0.688401i
$779$	9.40297	−	5.42881i	0.336896	−	0.194507i
$780$	−9.86753	−	12.0727i	−0.353314	−	0.432273i
$781$	−5.41661	+	9.38184i	−0.193821	+	0.335709i
$782$	−11.2265	−	3.00814i	−0.401460	−	0.107571i
$783$		−	5.32331i		−	0.190240i
$784$	−4.94571	−	4.95378i	−0.176632	−	0.176921i
$785$	−19.2889	−	19.2889i	−0.688449	−	0.688449i
$786$	−1.51687	+	5.66105i	−0.0541051	+	0.201923i
$787$	−20.0835	+	5.38137i	−0.715900	+	0.191825i	−0.598342	−	0.801241i	$-0.704173\pi$
$787$	−20.0835	+	5.38137i	−0.715900	+	0.191825i	−0.117559	+	0.993066i	$0.537507\pi$
$788$	4.62328	+	17.2543i	0.164697	+	0.614659i
$789$	5.01829	−	2.89731i	0.178656	−	0.103147i
$790$	−53.3008			−1.89636
$791$	−0.325803	−	2.48254i	−0.0115842	−	0.0882690i
$792$		−	5.05414i		−	0.179591i
$793$	−8.04964	+	11.1860i	−0.285851	+	0.397226i
$794$	1.67331	+	0.966087i	0.0593836	+	0.0342852i
$795$	1.63913	−	0.439204i	0.0581340	−	0.0155770i
$796$	−6.82160	+	3.93845i	−0.241785	+	0.139595i
$797$	−43.3441			−1.53533			−0.767664	−	0.640853i	$-0.778581\pi$
$797$	−43.3441			−1.53533			−0.767664	+	0.640853i	$0.778581\pi$
$798$	5.71699	+	7.45682i	0.202379	+	0.263969i
$799$	19.4043	+	19.4043i	0.686476	+	0.686476i
$800$	13.2346	+	3.54620i	0.467913	+	0.125377i
$801$	6.53086	−	1.74994i	0.230756	−	0.0618310i
$802$	1.12761	−	1.95309i	0.0398175	−	0.0689659i
$803$	−6.23756	−	10.8038i	−0.220119	−	0.381257i
$804$	4.28956	+	4.28956i	0.151281	+	0.151281i
$805$	−16.5660	−	40.0399i	−0.583873	−	1.41122i
$806$	26.4328	−	11.9130i	0.931056	−	0.419616i
$807$	−0.876924	−	1.51888i	−0.0308692	−	0.0534670i
$808$	−3.70805	−	13.8386i	−0.130449	−	0.486841i
$809$	−20.8189	+	36.0593i	−0.731952	+	1.26778i	0.224096	+	0.974567i	$0.428057\pi$
$809$	−20.8189	+	36.0593i	−0.731952	+	1.26778i	−0.956048	+	0.293211i	$0.905276\pi$
$810$	−2.16226	−	3.74514i	−0.0759740	−	0.131591i
$811$	−10.3627	+	10.3627i	−0.363884	+	0.363884i	−0.865241	−	0.501357i	$-0.832834\pi$
$811$	−10.3627	+	10.3627i	−0.363884	+	0.363884i	0.501357	+	0.865241i	$0.332834\pi$
$812$	5.39508	−	13.0099i	0.189330	−	0.456557i
$813$	−0.603569	+	0.603569i	−0.0211681	+	0.0211681i
$814$	−18.9458	−	5.07651i	−0.664050	−	0.177932i
$815$	25.9293	+	14.9703i	0.908265	+	0.524387i
$816$	−2.65775	−	1.53445i	−0.0930398	−	0.0537166i
$817$	−8.03736	+	29.9958i	−0.281192	+	1.04942i
$818$	1.55044			0.0542098
$819$	−4.51707	+	8.40215i	−0.157839	+	0.293595i
$820$	−13.2212			−0.461703
$821$	10.6332	−	39.6837i	0.371102	−	1.38497i	−0.487856	−	0.872924i	$-0.662221\pi$
$821$	10.6332	−	39.6837i	0.371102	−	1.38497i	0.858957	−	0.512047i	$-0.171113\pi$
$822$	−16.5416	−	9.55027i	−0.576953	−	0.333104i
$823$	−18.5957	−	10.7363i	−0.648207	−	0.374242i	0.139562	−	0.990213i	$-0.455431\pi$
$823$	−18.5957	−	10.7363i	−0.648207	−	0.374242i	−0.787769	+	0.615971i	$0.788764\pi$
$824$	−4.38724	−	1.17556i	−0.152837	−	0.0409525i
$825$	−48.9665	+	48.9665i	−1.70479	+	1.70479i
$826$	−2.20223	+	0.289016i	−0.0766255	+	0.0100562i
$827$	−36.4404	+	36.4404i	−1.26716	+	1.26716i	−0.319608	+	0.947550i	$0.603551\pi$
$827$	−36.4404	+	36.4404i	−1.26716	+	1.26716i	−0.947550	+	0.319608i	$0.896449\pi$
$828$	1.89360	+	3.27981i	0.0658071	+	0.113981i
$829$	1.57682	−	2.73113i	0.0547652	−	0.0948562i	−0.837343	−	0.546678i	$-0.815892\pi$
$829$	1.57682	−	2.73113i	0.0547652	−	0.0948562i	0.892108	+	0.451822i	$0.149226\pi$
$830$	−10.0723	−	37.5903i	−0.349614	−	1.30478i
$831$	14.0193	+	24.2821i	0.486324	+	0.842338i
$832$	1.48147	+	3.28713i	0.0513608	+	0.113961i
$833$	5.57696	−	20.7458i	0.193230	−	0.718799i
$834$	−5.61619	−	5.61619i	−0.194473	−	0.194473i
$835$	−12.6851	−	21.9713i	−0.438987	−	0.760347i
$836$	−8.97469	+	15.5446i	−0.310396	+	0.537622i
$837$	7.76730	−	2.08124i	0.268477	−	0.0719382i
$838$	29.1770	+	7.81796i	1.00790	+	0.270067i
$839$	4.20268	+	4.20268i	0.145093	+	0.145093i	0.775922	−	0.630829i	$-0.217285\pi$
$839$	4.20268	+	4.20268i	0.145093	+	0.145093i	−0.630829	+	0.775922i	$0.717285\pi$
$840$	−1.48880	−	11.3443i	−0.0513686	−	0.391416i
$841$	−0.662365			−0.0228402
$842$	−17.6544	+	10.1927i	−0.608409	+	0.351265i
$843$	21.9348	−	5.87741i	0.755475	−	0.202429i
$844$	−21.6571	−	12.5037i	−0.745468	−	0.430396i
$845$	−46.8686	+	31.0464i	−1.61233	+	1.06803i
$846$		−	8.94191i		−	0.307429i
$847$	23.4131	+	30.5383i	0.804483	+	1.04931i
$848$	−0.392403			−0.0134752
$849$	−16.4820	+	9.51588i	−0.565661	+	0.326584i
$850$	10.8829	+	40.6157i	0.373282	+	1.39311i
$851$	14.1966	−	3.80396i	0.486653	−	0.130398i
$852$	0.554762	−	2.07040i	0.0190058	−	0.0709307i
$853$	−16.1042	−	16.1042i	−0.551396	−	0.551396i	0.375448	−	0.926844i	$-0.377489\pi$
$853$	−16.1042	−	16.1042i	−0.551396	−	0.551396i	−0.926844	+	0.375448i	$0.877489\pi$
$854$	−9.34446	+	3.86614i	−0.319761	+	0.132297i
$855$			15.3582i			0.525239i
$856$	5.37285	+	1.43965i	0.183640	+	0.0492063i
$857$	20.3609	−	35.2661i	0.695515	−	1.20467i	−0.274492	−	0.961589i	$-0.588510\pi$
$857$	20.3609	−	35.2661i	0.695515	−	1.20467i	0.970007	−	0.243078i	$-0.0781570\pi$
$858$	−18.1316	−	1.82240i	−0.619003	−	0.0622156i
$859$	−10.3199	+	5.95819i	−0.352110	+	0.203291i	−0.665614	−	0.746296i	$-0.731830\pi$
$859$	−10.3199	+	5.95819i	−0.352110	+	0.203291i	0.313504	+	0.949587i	$0.398497\pi$
$860$	26.7385	−	26.7385i	0.911776	−	0.911776i
$861$	3.09238	+	7.47429i	0.105388	+	0.254723i
$862$		−	22.2572i		−	0.758083i
$863$	−2.55303	+	9.52803i	−0.0869060	+	0.324338i	−0.995668	−	0.0929764i	$-0.970362\pi$
$863$	−2.55303	+	9.52803i	−0.0869060	+	0.324338i	0.908762	+	0.417314i	$0.137029\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	6.20680	+	23.1641i	0.211038	+	0.787603i
$866$	−5.56074	+	20.7530i	−0.188962	+	0.705214i
$867$			7.58182i			0.257492i
$868$	21.0921	+	2.78558i	0.715914	+	0.0945488i
$869$	−44.0482	+	44.0482i	−1.49423	+	1.49423i
$870$	19.9366	−	11.5104i	0.675912	−	0.390238i
$871$	16.9354	−	13.8420i	0.573834	−	0.469017i
$872$	−1.05972	+	1.83550i	−0.0358868	+	0.0621577i
$873$	13.5911	+	3.64173i	0.459990	+	0.123254i
$874$		−	13.4499i		−	0.454951i
$875$	−60.6396	+	78.9603i	−2.04999	+	2.66935i
$876$	1.74535	+	1.74535i	0.0589699	+	0.0589699i
$877$	7.05053	−	26.3129i	0.238080	−	0.888525i	−0.738657	−	0.674082i	$-0.764540\pi$
$877$	7.05053	−	26.3129i	0.238080	−	0.888525i	0.976736	−	0.214443i	$-0.0687937\pi$
$878$	−18.7654	+	5.02818i	−0.633302	+	0.169693i
$879$	−1.87340	−	6.99161i	−0.0631881	−	0.235821i
$880$	18.9285	−	10.9284i	0.638078	−	0.368395i
$881$	−36.0053			−1.21305			−0.606524	−	0.795065i	$-0.707437\pi$
$881$	−36.0053			−1.21305			−0.606524	+	0.795065i	$0.707437\pi$
$882$	−6.06503	+	3.49505i	−0.204220	+	0.117685i
$883$		−	20.0695i		−	0.675392i	−0.941255	−	0.337696i	$-0.890352\pi$
$883$		−	20.0695i		−	0.675392i	0.941255	−	0.337696i	$-0.109648\pi$
$884$	−6.46313	+	8.98133i	−0.217379	+	0.302075i
$885$	−3.14406	−	1.81522i	−0.105686	−	0.0610181i
$886$	−31.0793	+	8.32768i	−1.04413	+	0.279774i
$887$	21.7505	−	12.5577i	0.730310	−	0.421645i	−0.0882255	−	0.996101i	$-0.528120\pi$
$887$	21.7505	−	12.5577i	0.730310	−	0.421645i	0.818536	+	0.574456i	$0.194786\pi$
$888$	3.88081			0.130231
$889$	23.1195	−	3.03415i	0.775402	−	0.101762i
$890$	20.6752	+	20.6752i	0.693033	+	0.693033i
$891$	−4.88192	−	1.30811i	−0.163551	−	0.0438232i
$892$	27.1458	−	7.27370i	0.908910	−	0.243542i
$893$	−15.8782	+	27.5019i	−0.531345	+	0.920317i
$894$	5.61138	+	9.71919i	0.187673	+	0.325059i
$895$	43.6431	+	43.6431i	1.45883	+	1.45883i
$896$	−0.346409	+	2.62298i	−0.0115727	+	0.0876275i
$897$	12.4490	−	5.61062i	0.415661	−	0.187333i
$898$	14.7735	+	25.5884i	0.492997	+	0.853895i
$899$	11.0791	+	41.3477i	0.369508	+	1.37902i
$900$	6.85072	−	11.8658i	0.228357	−	0.395527i
$901$	−0.602124	−	1.04291i	−0.0200597	−	0.0347443i
$902$	−10.9261	+	10.9261i	−0.363799	+	0.363799i
$903$	−21.3701	−	8.86198i	−0.711151	−	0.294908i
$904$	−0.669177	+	0.669177i	−0.0222565	+	0.0222565i
$905$	91.0727	+	24.4028i	3.02736	+	0.811178i
$906$	15.5850	+	8.99803i	0.517778	+	0.298940i
$907$	23.3950	+	13.5071i	0.776819	+	0.448497i	0.835302	−	0.549792i	$-0.185293\pi$
$907$	23.3950	+	13.5071i	0.776819	+	0.448497i	−0.0584825	+	0.998288i	$0.518626\pi$
$908$	1.29127	−	4.81907i	0.0428522	−	0.159926i
$909$	−14.3268			−0.475190
$910$	−41.2343	+	1.25056i	−1.36690	+	0.0414557i
$911$	−17.5249			−0.580626			−0.290313	−	0.956932i	$-0.593759\pi$
$911$	−17.5249			−0.580626			−0.290313	+	0.956932i	$0.593759\pi$
$912$	0.919175	−	3.43041i	0.0304369	−	0.113592i
$913$	−39.3887	−	22.7411i	−1.30358	−	0.752620i
$914$	−22.6871	−	13.0984i	−0.750422	−	0.433256i
$915$	−15.9661	−	4.27810i	−0.527822	−	0.141430i
$916$	10.6645	−	10.6645i	0.352366	−	0.352366i
$917$	9.43449	+	12.3057i	0.311554	+	0.406369i
$918$	−2.17004	+	2.17004i	−0.0716221	+	0.0716221i
$919$	−7.26157	−	12.5774i	−0.239537	−	0.414891i	0.721044	−	0.692889i	$-0.243662\pi$
$919$	−7.26157	−	12.5774i	−0.239537	−	0.414891i	−0.960582	+	0.277998i	$0.910329\pi$
$920$	−8.18890	+	14.1836i	−0.269980	+	0.467619i
$921$	7.68013	+	28.6626i	0.253069	+	0.944466i
$922$	−5.99865	−	10.3900i	−0.197555	−	0.342175i
$923$	−7.22747	−	2.73673i	−0.237895	−	0.0900805i
$924$	−10.6054	−	8.14468i	−0.348892	−	0.267940i
$925$	−37.5988	−	37.5988i	−1.23624	−	1.23624i
$926$	4.84622	+	8.39390i	0.159257	+	0.275841i
$927$	−2.27100	+	3.93349i	−0.0745895	+	0.129193i
$928$	−5.14192	+	1.37777i	−0.168792	+	0.0452277i
$929$	45.1151	+	12.0886i	1.48018	+	0.396613i	0.906408	−	0.422404i	$-0.138814\pi$
$929$	45.1151	+	12.0886i	1.48018	+	0.396613i	0.573770	+	0.819016i	$0.305480\pi$
$930$	24.5895	+	24.5895i	0.806320	+	0.806320i
$931$	24.8599	+	0.0202746i	0.814751	+	0.000664475i
$932$	−3.49849			−0.114597
$933$	−13.1954	+	7.61836i	−0.431997	+	0.249414i
$934$	−7.77884	+	2.08433i	−0.254532	+	0.0682015i
$935$	58.0897	+	33.5381i	1.89973	+	1.09681i
$936$	3.55856	−	0.580218i	0.116315	−	0.0189650i
$937$		−	23.2751i		−	0.760364i	−0.924912	−	0.380182i	$-0.875861\pi$
$937$		−	23.2751i		−	0.760364i	0.924912	−	0.380182i	$-0.124139\pi$
$938$	15.9136	−	2.08846i	0.519597	−	0.0681907i
$939$	20.5492			0.670597
$940$	33.4887	−	19.3347i	1.09228	−	0.630629i
$941$	−0.267660	−	0.998921i	−0.00872547	−	0.0325639i	0.961426	−	0.275064i	$-0.0886991\pi$
$941$	−0.267660	−	0.998921i	−0.00872547	−	0.0325639i	−0.970151	+	0.242500i	$0.922032\pi$
$942$	6.09295	−	1.63260i	0.198519	−	0.0531931i
$943$	2.99672	−	11.1839i	0.0975868	−	0.364199i
$944$	0.593619	+	0.593619i	0.0193206	+	0.0193206i
$945$	−11.3431	−	1.49805i	−0.368991	−	0.0487317i
$946$		−	44.1939i		−	1.43687i
$947$	−36.4557	−	9.76829i	−1.18465	−	0.317427i	−0.387882	−	0.921709i	$-0.626793\pi$
$947$	−36.4557	−	9.76829i	−1.18465	−	0.317427i	−0.796770	+	0.604282i	$0.793460\pi$
$948$	6.16264	−	10.6740i	0.200153	−	0.346675i
$949$	6.89073	−	5.63207i	0.223682	−	0.182825i
$950$	−42.1405	+	24.3298i	−1.36722	+	0.789363i
$951$	3.46063	−	3.46063i	0.112219	−	0.112219i
$952$	−7.50276	+	3.10416i	−0.243166	+	0.100606i
$953$		−	30.8085i		−	0.997986i	−0.866606	−	0.498993i	$-0.833703\pi$
$953$		−	30.8085i		−	0.997986i	0.866606	−	0.498993i	$-0.166297\pi$
$954$	−0.101561	+	0.379032i	−0.00328817	+	0.0122716i
$955$	10.2811	+	38.3697i	0.332689	+	1.24161i
$956$	0.703465	+	2.62537i	0.0227517	+	0.0849105i
$957$	6.96346	−	25.9880i	0.225097	−	0.840073i
$958$			39.7580i			1.28452i
$959$	−46.6964	+	19.3200i	−1.50791	+	0.623875i
$960$	−3.05790	+	3.05790i	−0.0986931	+	0.0986931i
$961$	−29.1526	+	16.8312i	−0.940406	+	0.542943i
$962$	1.39932	−	13.9223i	0.0451160	−	0.448873i
$963$	2.78119	−	4.81717i	0.0896227	−	0.155231i
$964$	25.6445	+	6.87142i	0.825953	+	0.221314i
$965$			55.9353i			1.80062i
$966$	9.93373	+	1.31192i	0.319613	+	0.0422104i
$967$	−5.65134	−	5.65134i	−0.181735	−	0.181735i	0.610377	−	0.792111i	$-0.291018\pi$
$967$	−5.65134	−	5.65134i	−0.181735	−	0.181735i	−0.792111	+	0.610377i	$0.791018\pi$
$968$	3.76435	−	14.0487i	0.120991	−	0.451543i
$969$	10.5276	−	2.82086i	0.338195	−	0.0906191i
$970$	15.7487	+	58.7751i	0.505662	+	1.88715i
$971$	−24.0319	+	13.8748i	−0.771220	+	0.445264i	−0.833310	−	0.552807i	$-0.813557\pi$
$971$	−24.0319	+	13.8748i	−0.771220	+	0.445264i	0.0620898	+	0.998071i	$0.480223\pi$
$972$	1.00000			0.0320750
$973$	−20.8352	+	2.73437i	−0.667946	+	0.0876597i
$974$			17.2879i			0.553941i
$975$	−40.0981	−	28.8553i	−1.28417	−	0.924110i
$976$	3.31015	+	1.91111i	0.105955	+	0.0611733i
$977$	15.8854	−	4.25648i	0.508219	−	0.136177i	0.00440737	−	0.999990i	$-0.498597\pi$
$977$	15.8854	−	4.25648i	0.508219	−	0.136177i	0.503812	+	0.863813i	$0.331930\pi$
$978$	−5.99589	+	3.46173i	−0.191727	+	0.110694i
$979$	34.1723			1.09215
$980$	−26.2036	−	15.1572i	−0.837045	−	0.484179i
$981$	1.49868	+	1.49868i	0.0478490	+	0.0478490i
$982$	16.4240	+	4.40078i	0.524109	+	0.140435i
$983$	11.3448	−	3.03983i	0.361843	−	0.0969555i	−0.0733171	−	0.997309i	$-0.523359\pi$
$983$	11.3448	−	3.03983i	0.361843	−	0.0969555i	0.435160	+	0.900353i	$0.356692\pi$
$984$	1.52863	−	2.64767i	0.0487309	−	0.0844045i
$985$	38.6244	+	66.8994i	1.23067	+	2.13159i
$986$	−11.5518	−	11.5518i	−0.367885	−	0.367885i
$987$	−18.7633	−	14.4098i	−0.597244	−	0.458668i
$988$	−11.9751	−	4.53444i	−0.380978	−	0.144260i
$989$	16.5578	+	28.6790i	0.526508	+	0.911938i
$990$	−5.65693	−	21.1120i	−0.179789	−	0.670982i
$991$	22.0543	−	38.1991i	0.700577	−	1.21344i	−0.267687	−	0.963506i	$-0.586259\pi$
$991$	22.0543	−	38.1991i	0.700577	−	1.21344i	0.968264	−	0.249930i	$-0.0804074\pi$
$992$	−4.02065	−	6.96397i	−0.127656	−	0.221106i
$993$	−1.71897	+	1.71897i	−0.0545498	+	0.0545498i
$994$	−3.45045	−	4.50051i	−0.109442	−	0.142747i
$995$	−24.0868	+	24.0868i	−0.763602	+	0.763602i
$996$	8.69236	+	2.32911i	0.275428	+	0.0738007i
$997$	40.4186	+	23.3357i	1.28007	+	0.739048i	0.976861	−	0.213876i	$-0.0686088\pi$
$997$	40.4186	+	23.3357i	1.28007	+	0.739048i	0.303209	+	0.952924i	$0.401942\pi$
$998$	−2.06381	−	1.19154i	−0.0653288	−	0.0377176i
$999$	1.00443	−	3.74857i	0.0317787	−	0.118600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.b.73.6	yes	40
7.5	odd	6		546.2.bz.a.229.1	yes	40
13.5	odd	4		546.2.bz.a.31.1	✓	40
91.5	even	12	inner	546.2.bz.b.187.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.31.1	✓	40	13.5	odd	4
546.2.bz.a.229.1	yes	40	7.5	odd	6
546.2.bz.b.73.6	yes	40	1.1	even	1	trivial
546.2.bz.b.187.6	yes	40	91.5	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-4.17716 - 1.11927i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.344270 - 2.62326i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-4.17716 - 1.11927i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.344270 - 2.62326i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.16226 + 3.74514i) q^{10} +(1.30811 + 4.88192i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-3.28713 + 1.48147i) q^{13} +(-2.62298 - 0.346409i) q^{14} +(-3.05790 - 3.05790i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.53445 + 2.65775i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-3.43041 - 0.919175i) q^{19} +(3.05790 + 3.05790i) q^{20} +(1.01348 - 2.44394i) q^{21} +5.05414 q^{22} +(-3.27981 + 1.89360i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(11.8658 + 6.85072i) q^{25} +(0.580218 + 3.55856i) q^{26} +1.00000i q^{27} +(-1.01348 + 2.44394i) q^{28} -5.32331 q^{29} +(-3.74514 + 2.16226i) q^{30} +(-2.08124 - 7.76730i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-1.30811 + 4.88192i) q^{33} +(2.17004 + 2.17004i) q^{34} +(-1.49805 + 11.3431i) q^{35} -1.00000i q^{36} +(-3.74857 - 1.00443i) q^{37} +(-1.77571 + 3.07562i) q^{38} +(-3.58748 - 0.360575i) q^{39} +(3.74514 - 2.16226i) q^{40} +(-2.16181 + 2.16181i) q^{41} +(-2.09836 - 1.61149i) q^{42} -8.74410i q^{43} +(1.30811 - 4.88192i) q^{44} +(-1.11927 - 4.17716i) q^{45} +(0.980199 + 3.65815i) q^{46} +(2.31434 - 8.63722i) q^{47} +1.00000i q^{48} +(-6.76296 + 1.80622i) q^{49} +(9.68839 - 9.68839i) q^{50} +(-2.65775 + 1.53445i) q^{51} +(3.58748 + 0.360575i) q^{52} +(-0.196202 + 0.339831i) q^{53} +(0.965926 + 0.258819i) q^{54} -21.8567i q^{55} +(2.09836 + 1.61149i) q^{56} +(-2.51123 - 2.51123i) q^{57} +(-1.37777 + 5.14192i) q^{58} +(0.810898 - 0.217280i) q^{59} +(1.11927 + 4.17716i) q^{60} +(3.31015 - 1.91111i) q^{61} -8.04130 q^{62} +(2.09967 - 1.60978i) q^{63} -1.00000i q^{64} +(15.3891 - 2.50916i) q^{65} +(4.37701 + 2.52707i) q^{66} +(-5.85964 + 1.57009i) q^{67} +(2.65775 - 1.53445i) q^{68} -3.78720 q^{69} +(10.5689 + 4.38282i) q^{70} +(1.51564 + 1.51564i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(-2.38419 + 0.638842i) q^{73} +(-1.94040 + 3.36088i) q^{74} +(6.85072 + 11.8658i) q^{75} +(2.51123 + 2.51123i) q^{76} +(12.3562 - 5.11220i) q^{77} +(-1.27680 + 3.37191i) q^{78} +(6.16264 + 10.6740i) q^{79} +(-1.11927 - 4.17716i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.52863 + 2.64767i) q^{82} +(-6.36325 + 6.36325i) q^{83} +(-2.09967 + 1.60978i) q^{84} +(9.38439 - 9.38439i) q^{85} +(-8.44615 - 2.26314i) q^{86} +(-4.61012 - 2.66166i) q^{87} +(-4.37701 - 2.52707i) q^{88} +(1.74994 - 6.53086i) q^{89} -4.32452 q^{90} +(5.01794 + 8.11297i) q^{91} +3.78720 q^{92} +(2.08124 - 7.76730i) q^{93} +(-7.74392 - 4.47096i) q^{94} +(13.3006 + 7.67909i) q^{95} +(0.965926 + 0.258819i) q^{96} +(9.94940 - 9.94940i) q^{97} +(-0.00570888 + 7.00000i) q^{98} +(-3.57382 + 3.57382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more