LMFDB - Embedded newform 546.2.by.a.115.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.2
Character	$\chi$	$=$	546.115
Dual form			546.2.by.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.43558 - 0.384662i) q^{5} +(0.258819 + 0.965926i) q^{6} +(1.74877 - 1.98539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.43558 - 0.384662i) q^{5} +(0.258819 + 0.965926i) q^{6} +(1.74877 - 1.98539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +1.48622 q^{10} +(-0.00182246 + 0.00182246i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.56197 + 0.558913i) q^{13} +(-1.17533 + 2.37036i) q^{14} +(-0.384662 + 1.43558i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.27930 - 5.67992i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-1.18975 + 1.18975i) q^{19} +(-1.43558 + 0.384662i) q^{20} +(-1.98539 - 1.74877i) q^{21} +(0.00128868 - 0.00223205i) q^{22} +(0.438397 + 0.253109i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-2.41720 - 1.39557i) q^{25} +(-3.58525 + 0.382036i) q^{26} +1.00000i q^{27} +(0.521786 - 2.59379i) q^{28} +(-0.810496 - 1.40382i) q^{29} -1.48622i q^{30} +(-2.18986 - 8.17269i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.00182246 + 0.00182246i) q^{33} +(4.63763 + 4.63763i) q^{34} +(-3.27421 + 2.17750i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(1.20072 + 4.48115i) q^{37} +(0.841283 - 1.45715i) q^{38} +(0.558913 - 3.56197i) q^{39} +(1.28711 - 0.743111i) q^{40} +(-3.86453 - 1.03550i) q^{41} +(2.37036 + 1.17533i) q^{42} +(-5.25932 - 3.03647i) q^{43} +(-0.000667068 + 0.00248953i) q^{44} +(1.43558 + 0.384662i) q^{45} +(-0.488969 - 0.131019i) q^{46} +(-0.507333 + 1.89339i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.883577 - 6.94401i) q^{49} +(2.69604 + 0.722402i) q^{50} +(-5.67992 + 3.27930i) q^{51} +(3.36421 - 1.29695i) q^{52} +(3.92998 - 6.80692i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(0.00331733 - 0.00191526i) q^{55} +(0.167315 + 2.64046i) q^{56} +(1.18975 + 1.18975i) q^{57} +(1.14622 + 1.14622i) q^{58} +(-0.944794 + 3.52602i) q^{59} +(0.384662 + 1.43558i) q^{60} -12.2476i q^{61} +(4.23049 + 7.32743i) q^{62} +(-1.74877 + 1.98539i) q^{63} -1.00000i q^{64} +(-4.89850 - 2.17252i) q^{65} +(-0.00223205 - 0.00128868i) q^{66} +(2.46681 + 2.46681i) q^{67} +(-5.67992 - 3.27930i) q^{68} +(0.253109 - 0.438397i) q^{69} +(2.59907 - 2.95074i) q^{70} +(-11.1394 + 2.98479i) q^{71} +(0.707107 - 0.707107i) q^{72} +(5.87443 - 1.57405i) q^{73} +(-2.31961 - 4.01769i) q^{74} +(-1.39557 + 2.41720i) q^{75} +(-0.435480 + 1.62523i) q^{76} +(0.000431231 + 0.00680539i) q^{77} +(0.382036 + 3.58525i) q^{78} +(2.83157 + 4.90442i) q^{79} +(-1.05092 + 1.05092i) q^{80} +1.00000 q^{81} +4.00086 q^{82} +(8.65678 - 8.65678i) q^{83} +(-2.59379 - 0.521786i) q^{84} +(2.52285 + 9.41540i) q^{85} +(5.86601 + 1.57179i) q^{86} +(-1.40382 + 0.810496i) q^{87} -0.00257735i q^{88} +(12.9152 - 3.46061i) q^{89} -1.48622 q^{90} +(7.33874 - 6.09450i) q^{91} +0.506218 q^{92} +(-8.17269 + 2.18986i) q^{93} -1.96018i q^{94} +(2.16564 - 1.25033i) q^{95} +(0.965926 + 0.258819i) q^{96} +(4.02482 + 15.0208i) q^{97} +(2.65071 + 6.47871i) q^{98} +(0.00182246 - 0.00182246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.43558	−	0.384662i	−0.642011	−	0.172026i	−0.0768967	−	0.997039i	$-0.524501\pi$
$5$	−1.43558	−	0.384662i	−0.642011	−	0.172026i	−0.565114	+	0.825013i	$0.691168\pi$
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	1.74877	−	1.98539i	0.660975	−	0.750408i
$7$	1.74877	−	1.98539i	0.660975	−	0.750408i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	1.48622			0.469985
$11$	−0.00182246	+	0.00182246i	−0.000549494	+	0.000549494i	−0.707381	−	0.706832i	$-0.750124\pi$
$11$	−0.00182246	+	0.00182246i	−0.000549494	+	0.000549494i	0.706832	+	0.707381i	$0.250124\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	3.56197	+	0.558913i	0.987912	+	0.155015i
$13$	3.56197	+	0.558913i	0.987912	+	0.155015i
$14$	−1.17533	+	2.37036i	−0.314120	+	0.633505i
$15$	−0.384662	+	1.43558i	−0.0993194	+	0.370665i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.27930	−	5.67992i	−0.795347	−	1.37758i	−0.922618	−	0.385714i	$-0.873955\pi$
$17$	−3.27930	−	5.67992i	−0.795347	−	1.37758i	0.127271	−	0.991868i	$-0.459378\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−1.18975	+	1.18975i	−0.272948	+	0.272948i	−0.830286	−	0.557338i	$-0.811823\pi$
$19$	−1.18975	+	1.18975i	−0.272948	+	0.272948i	0.557338	+	0.830286i	$0.311823\pi$
$20$	−1.43558	+	0.384662i	−0.321005	+	0.0860131i
$21$	−1.98539	−	1.74877i	−0.433248	−	0.381614i
$22$	0.00128868	−	0.00223205i	0.000274747	−	0.000475875i
$23$	0.438397	+	0.253109i	0.0914122	+	0.0527768i	0.545009	−	0.838430i	$-0.316526\pi$
$23$	0.438397	+	0.253109i	0.0914122	+	0.0527768i	−0.453597	+	0.891207i	$0.649859\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−2.41720	−	1.39557i	−0.483441	−	0.279115i
$26$	−3.58525	+	0.382036i	−0.703126	+	0.0749235i
$27$			1.00000i			0.192450i
$28$	0.521786	−	2.59379i	0.0986083	−	0.490180i
$29$	−0.810496	−	1.40382i	−0.150505	−	0.260683i	0.780908	−	0.624646i	$-0.214757\pi$
$29$	−0.810496	−	1.40382i	−0.150505	−	0.260683i	−0.931413	+	0.363963i	$0.881423\pi$
$30$		−	1.48622i		−	0.271346i
$31$	−2.18986	−	8.17269i	−0.393311	−	1.46786i	−0.824637	−	0.565662i	$-0.808621\pi$
$31$	−2.18986	−	8.17269i	−0.393311	−	1.46786i	0.431326	−	0.902196i	$-0.358046\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.00182246	+	0.00182246i	0.000317250	+	0.000317250i
$34$	4.63763	+	4.63763i	0.795347	+	0.795347i
$35$	−3.27421	+	2.17750i	−0.553443	+	0.368065i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	1.20072	+	4.48115i	0.197397	+	0.736697i	0.991633	+	0.129087i	$0.0412047\pi$
$37$	1.20072	+	4.48115i	0.197397	+	0.736697i	−0.794236	+	0.607609i	$0.792129\pi$
$38$	0.841283	−	1.45715i	0.136474	−	0.236380i
$39$	0.558913	−	3.56197i	0.0894978	−	0.570371i
$40$	1.28711	−	0.743111i	0.203509	−	0.117496i
$41$	−3.86453	−	1.03550i	−0.603538	−	0.161718i	−0.0559051	−	0.998436i	$-0.517804\pi$
$41$	−3.86453	−	1.03550i	−0.603538	−	0.161718i	−0.547633	+	0.836718i	$0.684471\pi$
$42$	2.37036	+	1.17533i	0.365754	+	0.181357i
$43$	−5.25932	−	3.03647i	−0.802039	−	0.463057i	0.0421447	−	0.999112i	$-0.486581\pi$
$43$	−5.25932	−	3.03647i	−0.802039	−	0.463057i	−0.844184	+	0.536054i	$0.819914\pi$
$44$	−0.000667068		0.00248953i	−0.000100564		0.000375311i
$45$	1.43558	+	0.384662i	0.214004	+	0.0573421i
$46$	−0.488969	−	0.131019i	−0.0720945	−	0.0193177i
$47$	−0.507333	+	1.89339i	−0.0740021	+	0.276180i	−0.993005	−	0.118071i	$-0.962329\pi$
$47$	−0.507333	+	1.89339i	−0.0740021	+	0.276180i	0.919003	+	0.394250i	$0.128996\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−0.883577	−	6.94401i	−0.126225	−	0.992002i
$50$	2.69604	+	0.722402i	0.381278	+	0.102163i
$51$	−5.67992	+	3.27930i	−0.795347	+	0.459194i
$52$	3.36421	−	1.29695i	0.466532	−	0.179855i
$53$	3.92998	−	6.80692i	0.539824	−	0.935002i	−0.459089	−	0.888390i	$-0.651824\pi$
$53$	3.92998	−	6.80692i	0.539824	−	0.935002i	0.998913	−	0.0466119i	$-0.0148424\pi$
$54$	−0.258819	−	0.965926i	−0.0352208	−	0.131446i
$55$	0.00331733	−	0.00191526i	0.000447308	−	0.000258254i
$56$	0.167315	+	2.64046i	0.0223584	+	0.352846i
$57$	1.18975	+	1.18975i	0.157587	+	0.157587i
$58$	1.14622	+	1.14622i	0.150505	+	0.150505i
$59$	−0.944794	+	3.52602i	−0.123002	+	0.459048i	−0.999761	−	0.0218817i	$-0.993034\pi$
$59$	−0.944794	+	3.52602i	−0.123002	+	0.459048i	0.876759	+	0.480930i	$0.159701\pi$
$60$	0.384662	+	1.43558i	0.0496597	+	0.185333i
$61$		−	12.2476i		−	1.56815i	−0.620666	−	0.784075i	$-0.713138\pi$
$61$		−	12.2476i		−	1.56815i	0.620666	−	0.784075i	$-0.286862\pi$
$62$	4.23049	+	7.32743i	0.537273	+	0.930584i
$63$	−1.74877	+	1.98539i	−0.220325	+	0.250136i
$64$		−	1.00000i		−	0.125000i
$65$	−4.89850	−	2.17252i	−0.607584	−	0.269468i
$66$	−0.00223205	−	0.00128868i	−0.000274747	−	0.000158625i
$67$	2.46681	+	2.46681i	0.301369	+	0.301369i	0.841549	−	0.540180i	$-0.181644\pi$
$67$	2.46681	+	2.46681i	0.301369	+	0.301369i	−0.540180	+	0.841549i	$0.681644\pi$
$68$	−5.67992	−	3.27930i	−0.688791	−	0.397674i
$69$	0.253109	−	0.438397i	0.0304707	−	0.0527768i
$70$	2.59907	−	2.95074i	0.310648	−	0.352680i
$71$	−11.1394	+	2.98479i	−1.32200	+	0.354230i	−0.849728	−	0.527221i	$-0.823234\pi$
$71$	−11.1394	+	2.98479i	−1.32200	+	0.354230i	−0.472275	+	0.881451i	$0.656567\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	5.87443	−	1.57405i	0.687550	−	0.184228i	0.101903	−	0.994794i	$-0.467507\pi$
$73$	5.87443	−	1.57405i	0.687550	−	0.184228i	0.585647	+	0.810566i	$0.300840\pi$
$74$	−2.31961	−	4.01769i	−0.269650	−	0.467047i
$75$	−1.39557	+	2.41720i	−0.161147	+	0.279115i
$76$	−0.435480	+	1.62523i	−0.0499530	+	0.186427i
$77$	0.000431231		0.00680539i	4.91433e−5		0.000775546i
$78$	0.382036	+	3.58525i	0.0432571	+	0.405950i
$79$	2.83157	+	4.90442i	0.318576	+	0.551790i	0.980191	−	0.198054i	$-0.0634620\pi$
$79$	2.83157	+	4.90442i	0.318576	+	0.551790i	−0.661615	+	0.749844i	$0.730129\pi$
$80$	−1.05092	+	1.05092i	−0.117496	+	0.117496i
$81$	1.00000			0.111111
$82$	4.00086			0.441821
$83$	8.65678	−	8.65678i	0.950205	−	0.950205i	−0.0486129	−	0.998818i	$-0.515480\pi$
$83$	8.65678	−	8.65678i	0.950205	−	0.950205i	0.998818	+	0.0486129i	$0.0154801\pi$
$84$	−2.59379	−	0.521786i	−0.283006	−	0.0569315i
$85$	2.52285	+	9.41540i	0.273641	+	1.02124i
$86$	5.86601	+	1.57179i	0.632548	+	0.169491i
$87$	−1.40382	+	0.810496i	−0.150505	+	0.0868943i
$88$		−	0.00257735i		−	0.000274747i
$89$	12.9152	−	3.46061i	1.36900	−	0.366824i	0.501890	−	0.864932i	$-0.332638\pi$
$89$	12.9152	−	3.46061i	1.36900	−	0.366824i	0.867115	+	0.498108i	$0.165972\pi$
$90$	−1.48622			−0.156662
$91$	7.33874	−	6.09450i	0.769309	−	0.638877i
$92$	0.506218			0.0527768
$93$	−8.17269	+	2.18986i	−0.847468	+	0.227078i
$94$		−	1.96018i		−	0.202178i
$95$	2.16564	−	1.25033i	0.222190	−	0.128282i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	4.02482	+	15.0208i	0.408659	+	1.52514i	0.797206	+	0.603707i	$0.206310\pi$
$97$	4.02482	+	15.0208i	0.408659	+	1.52514i	−0.388548	+	0.921429i	$0.627023\pi$
$98$	2.65071	+	6.47871i	0.267762	+	0.654449i
$99$	0.00182246	−	0.00182246i	0.000183165	−	0.000183165i
$100$	−2.79115			−0.279115
$101$	1.32389			0.131732			0.0658661	−	0.997828i	$-0.479019\pi$
$101$	1.32389			0.131732			0.0658661	+	0.997828i	$0.479019\pi$
$102$	4.63763	−	4.63763i	0.459194	−	0.459194i
$103$	−1.66947	−	2.89160i	−0.164498	−	0.284918i	0.771979	−	0.635648i	$-0.219267\pi$
$103$	−1.66947	−	2.89160i	−0.164498	−	0.284918i	−0.936477	+	0.350730i	$0.885934\pi$
$104$	−2.91390	+	2.12348i	−0.285732	+	0.208224i
$105$	2.17750	+	3.27421i	0.212503	+	0.319530i
$106$	−2.03430	+	7.59213i	−0.197589	+	0.737413i
$107$	0.275709	−	0.477542i	0.0266538	−	0.0461658i	−0.852391	−	0.522905i	$-0.824848\pi$
$107$	0.275709	−	0.477542i	0.0266538	−	0.0461658i	0.879045	+	0.476739i	$0.158181\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	4.36620	−	1.16992i	0.418206	−	0.112058i	−0.0435786	−	0.999050i	$-0.513876\pi$
$109$	4.36620	−	1.16992i	0.418206	−	0.112058i	0.461785	+	0.886992i	$0.347209\pi$
$110$	−0.00270859	+	0.00270859i	−0.000258254	+	0.000258254i
$111$	4.48115	−	1.20072i	0.425332	−	0.113967i
$112$	−0.845014	−	2.50718i	−0.0798463	−	0.236906i
$113$	−6.23223	+	10.7945i	−0.586279	+	1.01546i	0.408436	+	0.912787i	$0.366074\pi$
$113$	−6.23223	+	10.7945i	−0.586279	+	1.01546i	−0.994715	+	0.102678i	$0.967259\pi$
$114$	−1.45715	−	0.841283i	−0.136474	−	0.0787934i
$115$	−0.531993	−	0.531993i	−0.0496086	−	0.0496086i
$116$	−1.40382	−	0.810496i	−0.130342	−	0.0752527i
$117$	−3.56197	−	0.558913i	−0.329304	−	0.0516716i
$118$		−	3.65040i		−	0.336047i
$119$	−17.0116	−	3.42219i	−1.55945	−	0.313711i
$120$	−0.743111	−	1.28711i	−0.0678364	−	0.117496i
$121$			11.0000i			0.999999i
$122$	3.16992	+	11.8303i	0.286991	+	1.07107i
$123$	−1.03550	+	3.86453i	−0.0933677	+	0.348453i
$124$	−5.98282	−	5.98282i	−0.537273	−	0.537273i
$125$	8.18785	+	8.18785i	0.732344	+	0.732344i
$126$	1.17533	−	2.37036i	0.104707	−	0.211168i
$127$	−2.75083	+	1.58819i	−0.244097	+	0.140929i	−0.617058	−	0.786917i	$-0.711676\pi$
$127$	−2.75083	+	1.58819i	−0.244097	+	0.140929i	0.372961	+	0.927847i	$0.378342\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−3.03647	+	5.25932i	−0.267346	+	0.463057i
$130$	5.29387	+	0.830669i	0.464303	+	0.0728545i
$131$	9.73459	−	5.62027i	0.850515	−	0.491045i	−0.0103096	−	0.999947i	$-0.503282\pi$
$131$	9.73459	−	5.62027i	0.850515	−	0.491045i	0.860825	+	0.508902i	$0.169948\pi$
$132$	0.00248953		0.000667068i	0.000216686		5.80608e-5i
$133$	0.281519	+	4.44274i	0.0244108	+	0.385235i
$134$	−3.02122	−	1.74430i	−0.260993	−	0.150685i
$135$	0.384662	−	1.43558i	0.0331065	−	0.123555i
$136$	6.33512	+	1.69749i	0.543232	+	0.145559i
$137$	10.7015	+	2.86746i	0.914293	+	0.244984i	0.685144	−	0.728407i	$-0.259739\pi$
$137$	10.7015	+	2.86746i	0.914293	+	0.244984i	0.229149	+	0.973391i	$0.426406\pi$
$138$	−0.131019	+	0.488969i	−0.0111531	+	0.0416238i
$139$	−7.06294	−	4.07779i	−0.599071	−	0.345874i	0.169605	−	0.985512i	$-0.445751\pi$
$139$	−7.06294	−	4.07779i	−0.599071	−	0.345874i	−0.768676	+	0.639638i	$0.779084\pi$
$140$	−1.74680	+	3.52288i	−0.147631	+	0.297738i
$141$	1.89339	+	0.507333i	0.159452	+	0.0427252i
$142$	9.98731	−	5.76618i	0.838116	−	0.483887i
$143$	−0.00751016	+	0.00547296i	−0.000628031	+	0.000457672i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.623535	+	2.32706i	0.0517818	+	0.193252i
$146$	−5.26687	+	3.04083i	−0.435889	+	0.251661i
$147$	−6.94401	+	0.883577i	−0.572732	+	0.0728762i
$148$	3.28043	+	3.28043i	0.269650	+	0.269650i
$149$	10.0773	+	10.0773i	0.825562	+	0.825562i	0.986899	−	0.161338i	$-0.0515808\pi$
$149$	10.0773	+	10.0773i	0.825562	+	0.825562i	−0.161338	+	0.986899i	$0.551581\pi$
$150$	0.722402	−	2.69604i	0.0589838	−	0.220131i
$151$	3.91497	+	14.6109i	0.318596	+	1.18902i	0.920595	+	0.390519i	$0.127704\pi$
$151$	3.91497	+	14.6109i	0.318596	+	1.18902i	−0.601999	+	0.798497i	$0.705629\pi$
$152$		−	1.68257i		−	0.136474i
$153$	3.27930	+	5.67992i	0.265116	+	0.459194i
$154$	−0.00217790	−	0.00646189i	−0.000175500	−	0.000520714i
$155$			12.5749i			1.01004i
$156$	−1.29695	−	3.36421i	−0.103839	−	0.269352i
$157$	−2.73438	−	1.57869i	−0.218227	−	0.125993i	0.386902	−	0.922121i	$-0.373545\pi$
$157$	−2.73438	−	1.57869i	−0.218227	−	0.125993i	−0.605129	+	0.796127i	$0.706878\pi$
$158$	−4.00444	−	4.00444i	−0.318576	−	0.318576i
$159$	−6.80692	−	3.92998i	−0.539824	−	0.311667i
$160$	0.743111	−	1.28711i	0.0587481	−	0.101755i
$161$	1.26918	−	0.427761i	0.100025	−	0.0337123i
$162$	−0.965926	+	0.258819i	−0.0758903	+	0.0203347i
$163$	0.789338	−	0.789338i	0.0618257	−	0.0618257i	−0.675518	−	0.737344i	$-0.736080\pi$
$163$	0.789338	−	0.789338i	0.0618257	−	0.0618257i	0.737344	+	0.675518i	$0.236080\pi$
$164$	−3.86453	+	1.03550i	−0.301769	+	0.0808588i
$165$	−0.00191526	−	0.00331733i	−0.000149103	−	0.000258254i
$166$	−6.12127	+	10.6023i	−0.475102	+	0.822901i
$167$	−5.96371	+	22.2569i	−0.461486	+	1.72229i	0.206798	+	0.978384i	$0.433696\pi$
$167$	−5.96371	+	22.2569i	−0.461486	+	1.72229i	−0.668285	+	0.743906i	$0.732971\pi$
$168$	2.64046	−	0.167315i	0.203716	−	0.0129086i
$169$	12.3752	+	3.98166i	0.951941	+	0.306282i
$170$	−4.87377	−	8.44161i	−0.373801	−	0.647442i
$171$	1.18975	−	1.18975i	0.0909828	−	0.0909828i
$172$	−6.07294			−0.463057
$173$	8.97093			0.682047			0.341023	−	0.940055i	$-0.389226\pi$
$173$	8.97093			0.682047			0.341023	+	0.940055i	$0.389226\pi$
$174$	1.14622	−	1.14622i	0.0868943	−	0.0868943i
$175$	−6.99790	+	2.35856i	−0.528992	+	0.178290i
$176$	0.000667068		0.00248953i	5.02822e−5		0.000187656i
$177$	3.52602	+	0.944794i	0.265032	+	0.0710150i
$178$	−11.5794	+	6.68538i	−0.867914	+	0.501091i
$179$		−	13.6961i		−	1.02369i	−0.859077	−	0.511846i	$-0.828962\pi$
$179$		−	13.6961i		−	1.02369i	0.859077	−	0.511846i	$-0.171038\pi$
$180$	1.43558	−	0.384662i	0.107002	−	0.0286710i
$181$	24.4159			1.81482			0.907408	−	0.420251i	$-0.138058\pi$
$181$	24.4159			1.81482			0.907408	+	0.420251i	$0.138058\pi$
$182$	−5.51131	+	7.78624i	−0.408525	+	0.577154i
$183$	−12.2476			−0.905371
$184$	−0.488969	+	0.131019i	−0.0360472	+	0.00965883i
$185$		−	6.89492i		−	0.506925i
$186$	7.32743	−	4.23049i	0.537273	−	0.310195i
$187$	0.0163279	+	0.00437503i	0.00119401	+	0.000319934i
$188$	0.507333	+	1.89339i	0.0370011	+	0.138090i
$189$	1.98539	+	1.74877i	0.144416	+	0.127205i
$190$	−1.76824	+	1.76824i	−0.128282	+	0.128282i
$191$	12.2419			0.885792			0.442896	−	0.896573i	$-0.353951\pi$
$191$	12.2419			0.885792			0.442896	+	0.896573i	$0.353951\pi$
$192$	−1.00000			−0.0721688
$193$	−9.84276	+	9.84276i	−0.708497	+	0.708497i	−0.966219	−	0.257722i	$-0.917028\pi$
$193$	−9.84276	+	9.84276i	−0.708497	+	0.708497i	0.257722	+	0.966219i	$0.417028\pi$
$194$	−7.77536	−	13.4673i	−0.558238	−	0.966897i
$195$	−2.17252	+	4.89850i	−0.155577	+	0.350789i
$196$	−4.23721	−	5.57190i	−0.302658	−	0.397993i
$197$	0.885599	−	3.30510i	0.0630963	−	0.235479i	−0.927175	−	0.374628i	$-0.877770\pi$
$197$	0.885599	−	3.30510i	0.0630963	−	0.235479i	0.990271	+	0.139150i	$0.0444370\pi$
$198$	−0.00128868	+	0.00223205i	−9.15823e−5	+	0.000158625i
$199$	−10.7287	−	18.5826i	−0.760534	−	1.31728i	−0.942575	−	0.333993i	$-0.891604\pi$
$199$	−10.7287	−	18.5826i	−0.760534	−	1.31728i	0.182041	−	0.983291i	$-0.441730\pi$
$200$	2.69604	−	0.722402i	0.190639	−	0.0510815i
$201$	2.46681	−	2.46681i	0.173996	−	0.173996i
$202$	−1.27878	+	0.342648i	−0.0899747	+	0.0241087i
$203$	−4.20451	−	0.845812i	−0.295099	−	0.0593643i
$204$	−3.27930	+	5.67992i	−0.229597	+	0.397674i
$205$	5.14953	+	2.97308i	0.359659	+	0.207649i
$206$	2.36098	+	2.36098i	0.164498	+	0.164498i
$207$	−0.438397	−	0.253109i	−0.0304707	−	0.0175923i
$208$	2.26502	−	2.80530i	0.157051	−	0.194512i
$209$		−	0.00433657i		−	0.000299967i
$210$	−2.95074	−	2.59907i	−0.203620	−	0.179353i
$211$	−5.48542	−	9.50102i	−0.377632	−	0.654077i	0.613086	−	0.790017i	$-0.289928\pi$
$211$	−5.48542	−	9.50102i	−0.377632	−	0.654077i	−0.990717	+	0.135939i	$0.956595\pi$
$212$		−	7.85995i		−	0.539824i
$213$	2.98479	+	11.1394i	0.204515	+	0.763259i
$214$	−0.142718	+	0.532629i	−0.00975598	+	0.0364098i
$215$	6.38216	+	6.38216i	0.435260	+	0.435260i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−20.0556	−	9.94444i	−1.36146	−	0.675073i
$218$	−3.91463	+	2.26011i	−0.265132	+	0.153074i
$219$	−1.57405	−	5.87443i	−0.106364	−	0.396957i
$220$	0.00191526	−	0.00331733i	0.000129127	−	0.000223654i
$221$	−8.50618	−	22.0645i	−0.572188	−	1.48422i
$222$	−4.01769	+	2.31961i	−0.269650	+	0.155682i
$223$	−14.7002	−	3.93891i	−0.984400	−	0.263769i	−0.269503	−	0.962999i	$-0.586860\pi$
$223$	−14.7002	−	3.93891i	−0.984400	−	0.263769i	−0.714896	+	0.699230i	$0.753526\pi$
$224$	1.46513	+	2.20304i	0.0978929	+	0.147197i
$225$	2.41720	+	1.39557i	0.161147	+	0.0930382i
$226$	3.22604	−	12.0397i	0.214593	−	0.800872i
$227$	10.8869	+	2.91714i	0.722590	+	0.193618i	0.601327	−	0.799003i	$-0.294639\pi$
$227$	10.8869	+	2.91714i	0.722590	+	0.193618i	0.121263	+	0.992620i	$0.461305\pi$
$228$	1.62523	+	0.435480i	0.107634	+	0.0288404i
$229$	3.07218	−	11.4655i	0.203015	−	0.757663i	−0.787030	−	0.616915i	$-0.788382\pi$
$229$	3.07218	−	11.4655i	0.203015	−	0.757663i	0.990045	−	0.140749i	$-0.0449510\pi$
$230$	0.651556	+	0.376176i	0.0429623	+	0.0248043i
$231$	0.00680539		0.000431231i	0.000447762		2.83729e-5i
$232$	1.56576	+	0.419544i	0.102797	+	0.0275444i
$233$	25.2033	−	14.5511i	1.65112	−	0.953275i	0.674508	−	0.738268i	$-0.264356\pi$
$233$	25.2033	−	14.5511i	1.65112	−	0.953275i	0.976613	−	0.215007i	$-0.0689773\pi$
$234$	3.58525	−	0.382036i	0.234375	−	0.0249745i
$235$	1.45663	−	2.52296i	0.0950204	−	0.164580i
$236$	0.944794	+	3.52602i	0.0615008	+	0.229524i
$237$	4.90442	−	2.83157i	0.318576	−	0.183930i
$238$	17.3177	−	1.09735i	1.12254	−	0.0711309i
$239$	−13.7110	−	13.7110i	−0.886894	−	0.886894i	0.107330	−	0.994223i	$-0.465770\pi$
$239$	−13.7110	−	13.7110i	−0.886894	−	0.886894i	−0.994223	+	0.107330i	$0.965770\pi$
$240$	1.05092	+	1.05092i	0.0678364	+	0.0678364i
$241$	4.95603	−	18.4962i	0.319246	−	1.19144i	−0.600725	−	0.799456i	$-0.705121\pi$
$241$	4.95603	−	18.4962i	0.319246	−	1.19144i	0.919971	−	0.391987i	$-0.128212\pi$
$242$	−2.84701	−	10.6252i	−0.183013	−	0.683012i
$243$		−	1.00000i		−	0.0641500i
$244$	−6.12382	−	10.6068i	−0.392037	−	0.679029i
$245$	−1.40266	+	10.3086i	−0.0896124	+	0.658590i
$246$		−	4.00086i		−	0.255085i
$247$	−4.90284	+	3.57290i	−0.311960	+	0.227338i
$248$	7.32743	+	4.23049i	0.465292	+	0.268637i
$249$	−8.65678	−	8.65678i	−0.548601	−	0.548601i
$250$	−10.0280	−	5.78968i	−0.634228	−	0.366172i
$251$	15.3883	−	26.6532i	0.971298	−	1.68234i	0.279652	−	0.960101i	$-0.409781\pi$
$251$	15.3883	−	26.6532i	0.971298	−	1.68234i	0.691646	−	0.722237i	$-0.256886\pi$
$252$	−0.521786	+	2.59379i	−0.0328694	+	0.163393i
$253$	−0.00126025		0.000337682i	−7.92309e−5		2.12299e-5i
$254$	2.24605	−	2.24605i	0.140929	−	0.140929i
$255$	9.41540	−	2.52285i	0.589615	−	0.157987i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.375374	−	0.650167i	0.0234152	−	0.0405563i	−0.854080	−	0.520141i	$-0.825879\pi$
$257$	0.375374	−	0.650167i	0.0234152	−	0.0405563i	0.877496	+	0.479585i	$0.159213\pi$
$258$	1.57179	−	5.86601i	0.0978555	−	0.365202i
$259$	10.9966	+	5.45262i	0.683298	+	0.338809i
$260$	−5.32848	+	0.567791i	−0.330458	+	0.0352129i
$261$	0.810496	+	1.40382i	0.0501685	+	0.0868943i
$262$	−7.94826	+	7.94826i	−0.491045	+	0.491045i
$263$	−15.4971			−0.955594			−0.477797	−	0.878470i	$-0.658565\pi$
$263$	−15.4971			−0.955594			−0.477797	+	0.878470i	$0.658565\pi$
$264$	−0.00257735			−0.000158625
$265$	−8.26016	+	8.26016i	−0.507417	+	0.507417i
$266$	−1.42179	−	4.21850i	−0.0871757	−	0.258653i
$267$	−3.46061	−	12.9152i	−0.211786	−	0.790395i
$268$	3.36973	+	0.902916i	0.205839	+	0.0551544i
$269$	10.3830	−	5.99464i	0.633064	−	0.365499i	−0.148874	−	0.988856i	$-0.547565\pi$
$269$	10.3830	−	5.99464i	0.633064	−	0.365499i	0.781938	+	0.623357i	$0.214232\pi$
$270$			1.48622i			0.0904486i
$271$	−11.9419	+	3.19982i	−0.725419	+	0.194375i	−0.602588	−	0.798052i	$-0.705864\pi$
$271$	−11.9419	+	3.19982i	−0.725419	+	0.194375i	−0.122831	+	0.992428i	$0.539197\pi$
$272$	−6.55860			−0.397674
$273$	−6.09450	−	7.33874i	−0.368856	−	0.444161i
$274$	−11.0790			−0.669309
$275$	0.00694865	−	0.00186188i	0.000419019	−	0.000112276i
$276$		−	0.506218i		−	0.0304707i
$277$	−17.6936	+	10.2154i	−1.06311	+	0.613785i	−0.926290	−	0.376812i	$-0.877020\pi$
$277$	−17.6936	+	10.2154i	−1.06311	+	0.613785i	−0.136816	+	0.990596i	$0.543687\pi$
$278$	7.87768	+	2.11082i	0.472472	+	0.126599i
$279$	2.18986	+	8.17269i	0.131104	+	0.489286i
$280$	0.775490	−	3.85494i	0.0463444	−	0.230377i
$281$	6.90403	−	6.90403i	0.411860	−	0.411860i	−0.470526	−	0.882386i	$-0.655936\pi$
$281$	6.90403	−	6.90403i	0.411860	−	0.411860i	0.882386	+	0.470526i	$0.155936\pi$
$282$	−1.96018			−0.116727
$283$	−9.46217			−0.562468			−0.281234	−	0.959639i	$-0.590744\pi$
$283$	−9.46217			−0.562468			−0.281234	+	0.959639i	$0.590744\pi$
$284$	−8.15460	+	8.15460i	−0.483887	+	0.483887i
$285$	−1.25033	−	2.16564i	−0.0740634	−	0.128282i
$286$	0.00583775	−	0.00723025i	0.000345193	−	0.000427533i
$287$	−8.81407	+	5.86176i	−0.520278	+	0.346009i
$288$	0.258819	−	0.965926i	0.0152511	−	0.0569177i
$289$	−13.0076	+	22.5299i	−0.765155	+	1.32529i
$290$	−1.20458	−	2.08639i	−0.0707352	−	0.122517i
$291$	15.0208	−	4.02482i	0.880537	−	0.235939i
$292$	4.30038	−	4.30038i	0.251661	−	0.251661i
$293$	5.63626	−	1.51023i	0.329274	−	0.0882286i	−0.0903950	−	0.995906i	$-0.528813\pi$
$293$	5.63626	−	1.51023i	0.329274	−	0.0882286i	0.419669	+	0.907677i	$0.362146\pi$
$294$	6.47871	−	2.65071i	0.377846	−	0.154593i
$295$	2.71265	−	4.69845i	0.157937	−	0.273555i
$296$	−4.01769	−	2.31961i	−0.233523	−	0.134825i
$297$	−0.00182246	−	0.00182246i	−0.000105750	−	0.000105750i
$298$	−12.3421	−	7.12570i	−0.714957	−	0.412781i
$299$	1.42009	+	1.14659i	0.0821260	+	0.0663091i
$300$			2.79115i			0.161147i
$301$	−15.2260	+	5.13172i	−0.877609	+	0.295787i
$302$	−7.56314	−	13.0997i	−0.435210	−	0.753806i
$303$		−	1.32389i		−	0.0760556i
$304$	0.435480	+	1.62523i	0.0249765	+	0.0932136i
$305$	−4.71121	+	17.5825i	−0.269763	+	1.00677i
$306$	−4.63763	−	4.63763i	−0.265116	−	0.265116i
$307$	21.2225	+	21.2225i	1.21123	+	1.21123i	0.970621	+	0.240612i	$0.0773481\pi$
$307$	21.2225	+	21.2225i	1.21123	+	1.21123i	0.240612	+	0.970621i	$0.422652\pi$
$308$	0.00377615	+	0.00567802i	0.000215166	+	0.000323535i
$309$	−2.89160	+	1.66947i	−0.164498	+	0.0949727i
$310$	−3.25462	−	12.1464i	−0.184850	−	0.689870i
$311$	−4.96799	+	8.60482i	−0.281709	+	0.487934i	−0.971806	−	0.235783i	$-0.924235\pi$
$311$	−4.96799	+	8.60482i	−0.281709	+	0.487934i	0.690097	+	0.723717i	$0.257568\pi$
$312$	2.12348	+	2.91390i	0.120218	+	0.164967i
$313$	20.8321	−	12.0274i	1.17750	−	0.679829i	0.222064	−	0.975032i	$-0.428721\pi$
$313$	20.8321	−	12.0274i	1.17750	−	0.679829i	0.955435	+	0.295203i	$0.0953873\pi$
$314$	3.04980	+	0.817192i	0.172110	+	0.0461168i
$315$	3.27421	−	2.17750i	0.184481	−	0.122688i
$316$	4.90442	+	2.83157i	0.275895	+	0.159288i
$317$	2.78864	−	10.4074i	0.156626	−	0.584536i	−0.842335	−	0.538955i	$-0.818819\pi$
$317$	2.78864	−	10.4074i	0.156626	−	0.584536i	0.998961	−	0.0455810i	$-0.0145139\pi$
$318$	7.59213	+	2.03430i	0.425745	+	0.114078i
$319$	0.00403551	+	0.00108131i	0.000225945	+	6.05419e-5i
$320$	−0.384662	+	1.43558i	−0.0215033	+	0.0802514i
$321$	−0.477542	−	0.275709i	−0.0266538	−	0.0153886i
$322$	−1.11522	+	0.741673i	−0.0621488	+	0.0413318i
$323$	10.6593	+	2.85614i	0.593097	+	0.158920i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−7.83000	−	6.32199i	−0.434330	−	0.350681i
$326$	−0.558146	+	0.966737i	−0.0309129	+	0.0535426i
$327$	−1.16992	−	4.36620i	−0.0646967	−	0.241451i
$328$	3.46484	−	2.00043i	0.191314	−	0.110455i
$329$	2.87192	+	4.31837i	0.158334	+	0.238080i
$330$	0.00270859	+	0.00270859i	0.000149103	+	0.000149103i
$331$	1.00169	+	1.00169i	0.0550580	+	0.0550580i	0.734100	−	0.679042i	$-0.237604\pi$
$331$	1.00169	+	1.00169i	0.0550580	+	0.0550580i	−0.679042	+	0.734100i	$0.737604\pi$
$332$	3.16860	−	11.8254i	0.173900	−	0.649002i
$333$	−1.20072	−	4.48115i	−0.0657991	−	0.245566i
$334$		−	23.0420i		−	1.26080i
$335$	−2.59242	−	4.49020i	−0.141639	−	0.245326i
$336$	−2.50718	+	0.845014i	−0.136778	+	0.0460993i
$337$			32.9805i			1.79656i	0.439419	+	0.898282i	$0.355184\pi$
$337$			32.9805i			1.79656i	−0.439419	+	0.898282i	$0.644816\pi$
$338$	−12.9841	−	0.643045i	−0.706241	−	0.0349770i
$339$	10.7945	+	6.23223i	0.586279	+	0.338488i
$340$	6.89255	+	6.89255i	0.373801	+	0.373801i
$341$	0.0188854	+	0.0109035i	0.00102270	+	0.000590456i
$342$	−0.841283	+	1.45715i	−0.0454914	+	0.0787934i
$343$	−15.3318	−	10.3893i	−0.827838	−	0.560967i
$344$	5.86601	−	1.57179i	0.316274	−	0.0847454i
$345$	−0.531993	+	0.531993i	−0.0286415	+	0.0286415i
$346$	−8.66525	+	2.32185i	−0.465847	+	0.124823i
$347$	10.2151	+	17.6930i	0.548374	+	0.949812i	0.998386	+	0.0567897i	$0.0180865\pi$
$347$	10.2151	+	17.6930i	0.548374	+	0.949812i	−0.450012	+	0.893023i	$0.648580\pi$
$348$	−0.810496	+	1.40382i	−0.0434472	+	0.0752527i
$349$	2.53200	−	9.44955i	0.135535	−	0.505823i	−0.864460	−	0.502701i	$-0.832340\pi$
$349$	2.53200	−	9.44955i	0.135535	−	0.505823i	0.999995	−	0.00312188i	$-0.000993728\pi$
$350$	6.14902	−	4.08938i	0.328679	−	0.218587i
$351$	−0.558913	+	3.56197i	−0.0298326	+	0.190124i
$352$	−0.00128868	−	0.00223205i	−6.86867e−5	−	0.000118969i
$353$	21.1688	−	21.1688i	1.12670	−	1.12670i	0.135990	−	0.990710i	$-0.456579\pi$
$353$	21.1688	−	21.1688i	1.12670	−	1.12670i	0.990710	−	0.135990i	$-0.0434215\pi$
$354$	−3.65040			−0.194017
$355$	17.1396			0.909677
$356$	9.45456	−	9.45456i	0.501091	−	0.501091i
$357$	−3.42219	+	17.0116i	−0.181121	+	0.900351i
$358$	3.54481	+	13.2294i	0.187349	+	0.699195i
$359$	−4.78988	−	1.28344i	−0.252800	−	0.0677376i	0.130193	−	0.991489i	$-0.458440\pi$
$359$	−4.78988	−	1.28344i	−0.252800	−	0.0677376i	−0.382994	+	0.923751i	$0.625107\pi$
$360$	−1.28711	+	0.743111i	−0.0678364	+	0.0391654i
$361$			16.1690i			0.850998i
$362$	−23.5839	+	6.31929i	−1.23954	+	0.332134i
$363$	11.0000			0.577350
$364$	3.30829	−	8.94736i	0.173401	−	0.468969i
$365$	−9.03869			−0.473107
$366$	11.8303	−	3.16992i	0.618380	−	0.165694i
$367$			15.9499i			0.832580i	0.909232	+	0.416290i	$0.136670\pi$
$367$			15.9499i			0.832580i	−0.909232	+	0.416290i	$0.863330\pi$
$368$	0.438397	−	0.253109i	0.0228530	−	0.0131942i
$369$	3.86453	+	1.03550i	0.201179	+	0.0539059i
$370$	1.78454	+	6.65998i	0.0927737	+	0.346236i
$371$	−6.64177	−	19.7063i	−0.344824	−	1.02310i
$372$	−5.98282	+	5.98282i	−0.310195	+	0.310195i
$373$	−31.8381			−1.64851			−0.824257	−	0.566216i	$-0.808407\pi$
$373$	−31.8381			−1.64851			−0.824257	+	0.566216i	$0.808407\pi$
$374$	−0.0169038			−0.000874077
$375$	8.18785	−	8.18785i	0.422819	−	0.422819i
$376$	−0.980092	−	1.69757i	−0.0505444	−	0.0875455i
$377$	−2.10235	−	5.45336i	−0.108276	−	0.280862i
$378$	−2.37036	−	1.17533i	−0.121918	−	0.0604524i
$379$	−1.69445	+	6.32378i	−0.0870382	+	0.324831i	−0.995692	−	0.0927186i	$-0.970444\pi$
$379$	−1.69445	+	6.32378i	−0.0870382	+	0.324831i	0.908654	+	0.417550i	$0.137111\pi$
$380$	1.25033	−	2.16564i	0.0641408	−	0.111095i
$381$	1.58819	+	2.75083i	0.0813657	+	0.140929i
$382$	−11.8248	+	3.16843i	−0.605007	+	0.162111i
$383$	−19.9178	+	19.9178i	−1.01775	+	1.01775i	−0.0179127	+	0.999840i	$0.505702\pi$
$383$	−19.9178	+	19.9178i	−1.01775	+	1.01775i	−0.999840	+	0.0179127i	$0.994298\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	0.00199871	−	0.00993556i	0.000101864	−	0.000506363i
$386$	6.95988	−	12.0549i	0.354249	−	0.613576i
$387$	5.25932	+	3.03647i	0.267346	+	0.154352i
$388$	10.9960	+	10.9960i	0.558238	+	0.558238i
$389$	−12.1096	−	6.99146i	−0.613979	−	0.354481i	0.160542	−	0.987029i	$-0.448676\pi$
$389$	−12.1096	−	6.99146i	−0.613979	−	0.354481i	−0.774521	+	0.632548i	$0.782009\pi$
$390$	0.830669	−	5.29387i	0.0420626	−	0.268066i
$391$		−	3.32008i		−	0.167904i
$392$	5.53494	+	4.28537i	0.279557	+	0.216444i
$393$	−5.62027	−	9.73459i	−0.283505	−	0.491045i
$394$			3.42169i			0.172382i
$395$	−2.17839	−	8.12988i	−0.109607	−	0.409059i
$396$	0.000667068	−	0.00248953i	3.35214e−5	−	0.000125104i
$397$	24.6542	+	24.6542i	1.23736	+	1.23736i	0.961077	+	0.276281i	$0.0891020\pi$
$397$	24.6542	+	24.6542i	1.23736	+	1.23736i	0.276281	+	0.961077i	$0.410898\pi$
$398$	15.1726	+	15.1726i	0.760534	+	0.760534i
$399$	4.44274	−	0.281519i	0.222415	−	0.0140936i
$400$	−2.41720	+	1.39557i	−0.120860	+	0.0697786i
$401$	−4.50898	−	16.8278i	−0.225168	−	0.840338i	−0.982337	−	0.187119i	$-0.940085\pi$
$401$	−4.50898	−	16.8278i	−0.225168	−	0.840338i	0.757169	−	0.653219i	$-0.226582\pi$
$402$	−1.74430	+	3.02122i	−0.0869978	+	0.150685i
$403$	−3.23240	−	30.3348i	−0.161018	−	1.51108i
$404$	1.14652	−	0.661946i	0.0570417	−	0.0329330i
$405$	−1.43558	−	0.384662i	−0.0713345	−	0.0191140i
$406$	4.28016	−	0.271217i	0.212421	−	0.0134603i
$407$	−0.0103550	−	0.00597847i	−0.000513279	−	0.000296342i
$408$	1.69749	−	6.33512i	0.0840383	−	0.313635i
$409$	−21.4764	−	5.75458i	−1.06194	−	0.284546i	−0.314762	−	0.949171i	$-0.601925\pi$
$409$	−21.4764	−	5.75458i	−1.06194	−	0.284546i	−0.747177	+	0.664625i	$0.768591\pi$
$410$	−5.74355	−	1.53898i	−0.283654	−	0.0760048i
$411$	2.86746	−	10.7015i	0.141442	−	0.527867i
$412$	−2.89160	−	1.66947i	−0.142459	−	0.0822488i
$413$	5.34830	+	8.04200i	0.263173	+	0.395721i
$414$	0.488969	+	0.131019i	0.0240315	+	0.00643922i
$415$	−15.7574	+	9.09756i	−0.773502	+	0.446582i
$416$	−1.46177	+	3.29594i	−0.0716694	+	0.161597i
$417$	−4.07779	+	7.06294i	−0.199690	+	0.345874i
$418$	0.00112239	+	0.00418880i	5.48977e−5	+	0.000204881i
$419$	−28.1431	+	16.2484i	−1.37488	+	0.793788i	−0.991538	−	0.129818i	$-0.958561\pi$
$419$	−28.1431	+	16.2484i	−1.37488	+	0.793788i	−0.383344	+	0.923606i	$0.625227\pi$
$420$	3.52288	+	1.74680i	0.171899	+	0.0852350i
$421$	−2.16390	−	2.16390i	−0.105462	−	0.105462i	0.652407	−	0.757869i	$-0.273759\pi$
$421$	−2.16390	−	2.16390i	−0.105462	−	0.105462i	−0.757869	+	0.652407i	$0.773759\pi$
$422$	7.75755	+	7.75755i	0.377632	+	0.377632i
$423$	0.507333	−	1.89339i	0.0246674	−	0.0920599i
$424$	2.03430	+	7.59213i	0.0987946	+	0.368706i
$425$			18.3060i			0.887972i
$426$	−5.76618	−	9.98731i	−0.279372	−	0.483887i
$427$	−24.3164	−	21.4184i	−1.17675	−	1.03651i
$428$		−	0.551419i		−	0.0266538i
$429$	0.00547296	+	0.00751016i	0.000264237	+	0.000362594i
$430$	−7.81652	−	4.51287i	−0.376946	−	0.217630i
$431$	2.14294	+	2.14294i	0.103222	+	0.103222i	0.756832	−	0.653610i	$-0.226746\pi$
$431$	2.14294	+	2.14294i	0.103222	+	0.103222i	−0.653610	+	0.756832i	$0.726746\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−0.383442	+	0.664141i	−0.0184271	+	0.0319166i	−0.875092	−	0.483957i	$-0.839199\pi$
$433$	−0.383442	+	0.664141i	−0.0184271	+	0.0319166i	0.856665	+	0.515873i	$0.172533\pi$
$434$	21.9460	+	4.41483i	1.05344	+	0.211918i
$435$	2.32706	−	0.623535i	0.111574	−	0.0298962i
$436$	3.19628	−	3.19628i	0.153074	−	0.153074i
$437$	−0.822722	+	0.220448i	−0.0393561	+	0.0105454i
$438$	3.04083	+	5.26687i	0.145296	+	0.251661i
$439$	2.62079	−	4.53935i	0.125084	−	0.216651i	−0.796682	−	0.604399i	$-0.793413\pi$
$439$	2.62079	−	4.53935i	0.125084	−	0.216651i	0.921766	+	0.387747i	$0.126747\pi$
$440$	−0.000991411		0.00370000i	−4.72637e−5		0.000176390i
$441$	0.883577	+	6.94401i	0.0420751	+	0.330667i
$442$	13.9271	+	19.1111i	0.662443	+	0.909024i
$443$	−2.68880	−	4.65713i	−0.127749	−	0.221267i	0.795055	−	0.606537i	$-0.207442\pi$
$443$	−2.68880	−	4.65713i	−0.127749	−	0.221267i	−0.922804	+	0.385270i	$0.874108\pi$
$444$	3.28043	−	3.28043i	0.155682	−	0.155682i
$445$	−19.8719			−0.942019
$446$	15.2188			0.720631
$447$	10.0773	−	10.0773i	0.476638	−	0.476638i
$448$	−1.98539	−	1.74877i	−0.0938010	−	0.0826218i
$449$	4.11387	+	15.3532i	0.194145	+	0.724560i	0.992486	+	0.122355i	$0.0390446\pi$
$449$	4.11387	+	15.3532i	0.194145	+	0.724560i	−0.798341	+	0.602206i	$0.794289\pi$
$450$	−2.69604	−	0.722402i	−0.127093	−	0.0340543i
$451$	0.00893013	−	0.00515581i	0.000420503	−	0.000242778i
$452$			12.4645i			0.586279i
$453$	14.6109	−	3.91497i	0.686478	−	0.183941i
$454$	−11.2710			−0.528973
$455$	−12.8797	+	5.92620i	−0.603808	+	0.277824i
$456$	−1.68257			−0.0787934
$457$	27.3394	−	7.32557i	1.27888	−	0.342676i	0.445456	−	0.895304i	$-0.353042\pi$
$457$	27.3394	−	7.32557i	1.27888	−	0.342676i	0.833428	+	0.552628i	$0.186375\pi$
$458$			11.8700i			0.554648i
$459$	5.67992	−	3.27930i	0.265116	−	0.153065i
$460$	−0.726716	−	0.194723i	−0.0338833	−	0.00907900i
$461$	−5.27351	−	19.6810i	−0.245612	−	0.916637i	−0.973075	−	0.230489i	$-0.925967\pi$
$461$	−5.27351	−	19.6810i	−0.245612	−	0.916637i	0.727463	−	0.686147i	$-0.240699\pi$
$462$	−0.00646189	+	0.00217790i	−0.000300634	+	0.000101325i
$463$	21.1675	−	21.1675i	0.983735	−	0.983735i	−0.0161346	−	0.999870i	$-0.505136\pi$
$463$	21.1675	−	21.1675i	0.983735	−	0.983735i	0.999870	+	0.0161346i	$0.00513603\pi$
$464$	−1.62099			−0.0752527
$465$	12.5749			0.583147
$466$	−20.5784	+	20.5784i	−0.953275	+	0.953275i
$467$	15.6076	+	27.0331i	0.722232	+	1.25094i	0.960103	+	0.279646i	$0.0902170\pi$
$467$	15.6076	+	27.0331i	0.722232	+	1.25094i	−0.237871	+	0.971297i	$0.576450\pi$
$468$	−3.36421	+	1.29695i	−0.155511	+	0.0599516i
$469$	9.21150	−	0.583696i	0.425347	−	0.0269526i
$470$	−0.754009	+	2.81400i	−0.0347799	+	0.129800i
$471$	−1.57869	+	2.73438i	−0.0727424	+	0.125993i
$472$	−1.82520	−	3.16134i	−0.0840117	−	0.145513i
$473$	0.0151188	−	0.00405107i	0.000695162	−	0.000186268i
$474$	−4.00444	+	4.00444i	−0.183930	+	0.183930i
$475$	4.53627	−	1.21549i	0.208138	−	0.0557705i
$476$	−16.4436	+	5.54211i	−0.753691	+	0.254022i
$477$	−3.92998	+	6.80692i	−0.179941	+	0.311667i
$478$	16.7925	+	9.69517i	0.768072	+	0.443447i
$479$	22.5481	+	22.5481i	1.03025	+	1.03025i	0.999528	+	0.0307200i	$0.00978001\pi$
$479$	22.5481	+	22.5481i	1.03025	+	1.03025i	0.0307200	+	0.999528i	$0.490220\pi$
$480$	−1.28711	−	0.743111i	−0.0587481	−	0.0339182i
$481$	1.77235	+	16.6328i	0.0808124	+	0.758391i
$482$			19.1486i			0.872196i
$483$	−0.427761	−	1.26918i	−0.0194638	−	0.0577496i
$484$	5.50000	+	9.52627i	0.250000	+	0.433012i
$485$		−	23.1118i		−	1.04945i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	−4.01597	+	14.9878i	−0.181981	+	0.679163i	0.813276	+	0.581879i	$0.197682\pi$
$487$	−4.01597	+	14.9878i	−0.181981	+	0.679163i	−0.995257	+	0.0972839i	$0.968985\pi$
$488$	8.66039	+	8.66039i	0.392037	+	0.392037i
$489$	−0.789338	−	0.789338i	−0.0356951	−	0.0356951i
$490$	−1.31319	−	10.3203i	−0.0593239	−	0.466225i
$491$	−2.26552	+	1.30800i	−0.102241	+	0.0590291i	−0.550249	−	0.835001i	$-0.685467\pi$
$491$	−2.26552	+	1.30800i	−0.102241	+	0.0590291i	0.448007	+	0.894030i	$0.352134\pi$
$492$	1.03550	+	3.86453i	0.0466839	+	0.174227i
$493$	−5.31572	+	9.20710i	−0.239408	+	0.414667i
$494$	3.81104	−	4.72010i	0.171467	−	0.212367i
$495$	−0.00331733	+	0.00191526i	−0.000149103	+	8.60845e-5i
$496$	−8.17269	−	2.18986i	−0.366964	−	0.0983278i
$497$	−13.5543	+	27.3358i	−0.607994	+	1.22618i
$498$	10.6023	+	6.12127i	0.475102	+	0.274300i
$499$	−4.93132	+	18.4039i	−0.220756	+	0.823874i	0.763304	+	0.646039i	$0.223576\pi$
$499$	−4.93132	+	18.4039i	−0.220756	+	0.823874i	−0.984060	+	0.177834i	$0.943091\pi$
$500$	11.1848	+	2.99696i	0.500200	+	0.134028i
$501$	22.2569	+	5.96371i	0.994364	+	0.266439i
$502$	−7.96555	+	29.7278i	−0.355520	+	1.32682i
$503$	0.589071	+	0.340100i	0.0262654	+	0.0151643i	0.513075	−	0.858344i	$-0.328506\pi$
$503$	0.589071	+	0.340100i	0.0262654	+	0.0151643i	−0.486810	+	0.873508i	$0.661840\pi$
$504$	−0.167315	−	2.64046i	−0.00745281	−	0.117615i
$505$	−1.90055	−	0.509251i	−0.0845735	−	0.0226614i
$506$	0.00112990		0.000652351i	5.02304e−5		2.90005e-5i
$507$	3.98166	−	12.3752i	0.176832	−	0.549603i
$508$	−1.58819	+	2.75083i	−0.0704647	+	0.122048i
$509$	−3.02255	−	11.2803i	−0.133972	−	0.499991i	0.866028	−	0.499996i	$-0.166665\pi$
$509$	−3.02255	−	11.2803i	−0.133972	−	0.499991i	−1.00000		4.94009e-6i	$0.999998\pi$
$510$	−8.44161	+	4.87377i	−0.373801	+	0.215814i
$511$	7.14794	−	14.4157i	0.316206	−	0.637714i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.18975	−	1.18975i	−0.0525289	−	0.0525289i
$514$	−0.194308	+	0.725167i	−0.00857056	+	0.0319858i
$515$	1.28436	+	4.79331i	0.0565958	+	0.211218i
$516$			6.07294i			0.267346i
$517$	−0.00252604	−	0.00437524i	−0.000111095	−	0.000192423i
$518$	−12.0332	−	2.42068i	−0.528707	−	0.106359i
$519$		−	8.97093i		−	0.393780i
$520$	4.99996	−	1.92756i	0.219263	−	0.0845289i
$521$	11.7132	+	6.76262i	0.513164	+	0.296276i	0.734133	−	0.679005i	$-0.237589\pi$
$521$	11.7132	+	6.76262i	0.513164	+	0.296276i	−0.220969	+	0.975281i	$0.570922\pi$
$522$	−1.14622	−	1.14622i	−0.0501685	−	0.0501685i
$523$	−0.0410699	−	0.0237117i	−0.00179586	−	0.00103684i	0.499102	−	0.866543i	$-0.333663\pi$
$523$	−0.0410699	−	0.0237117i	−0.00179586	−	0.00103684i	−0.500898	+	0.865507i	$0.666997\pi$
$524$	5.62027	−	9.73459i	0.245523	−	0.425258i
$525$	2.35856	+	6.99790i	0.102936	+	0.305414i
$526$	14.9691	−	4.01095i	0.652683	−	0.174886i
$527$	−39.2389	+	39.2389i	−1.70928	+	1.70928i
$528$	0.00248953		0.000667068i	0.000108343		2.90304e-5i
$529$	−11.3719	−	19.6967i	−0.494429	−	0.856377i
$530$	5.84081	−	10.1166i	0.253709	−	0.439436i
$531$	0.944794	−	3.52602i	0.0410006	−	0.153016i
$532$	2.46517	+	3.70677i	0.106879	+	0.160709i
$533$	−13.1866	−	5.84835i	−0.571174	−	0.253320i
$534$	6.68538	+	11.5794i	0.289305	+	0.501091i
$535$	−0.579495	+	0.579495i	−0.0250538	+	0.0250538i
$536$	−3.48860			−0.150685
$537$	−13.6961			−0.591029
$538$	−8.47770	+	8.47770i	−0.365499	+	0.365499i
$539$	0.0142655	+	0.0110449i	0.000614459	+	0.000475739i
$540$	−0.384662	−	1.43558i	−0.0165532	−	0.0617775i
$541$	−21.6571	−	5.80300i	−0.931112	−	0.249491i	−0.238783	−	0.971073i	$-0.576748\pi$
$541$	−21.6571	−	5.80300i	−0.931112	−	0.249491i	−0.692329	+	0.721582i	$0.743415\pi$
$542$	10.7068	−	6.18158i	0.459897	−	0.265522i
$543$		−	24.4159i		−	1.04778i
$544$	6.33512	−	1.69749i	0.271616	−	0.0727793i
$545$	−6.71805			−0.287770
$546$	7.78624	+	5.51131i	0.333220	+	0.235862i
$547$	41.1865			1.76101			0.880504	−	0.474040i	$-0.157205\pi$
$547$	41.1865			1.76101			0.880504	+	0.474040i	$0.157205\pi$
$548$	10.7015	−	2.86746i	0.457146	−	0.122492i
$549$			12.2476i			0.522716i
$550$	−0.00622999	+	0.00359688i	−0.000265648	+	0.000153372i
$551$	2.63449	+	0.705911i	0.112233	+	0.0300728i
$552$	0.131019	+	0.488969i	0.00557653	+	0.0208119i
$553$	14.6890	+	2.95494i	0.624638	+	0.125657i
$554$	14.4468	−	14.4468i	0.613785	−	0.613785i
$555$	−6.89492			−0.292673
$556$	−8.15558			−0.345874
$557$	17.3396	−	17.3396i	0.734703	−	0.734703i	−0.236845	−	0.971547i	$-0.576113\pi$
$557$	17.3396	−	17.3396i	0.734703	−	0.734703i	0.971547	+	0.236845i	$0.0761133\pi$
$558$	−4.23049	−	7.32743i	−0.179091	−	0.310195i
$559$	−17.0364	−	13.7553i	−0.720563	−	0.581788i
$560$	0.248667	+	3.92430i	0.0105081	+	0.165832i
$561$	0.00437503	−	0.0163279i	0.000184714	−	0.000689362i
$562$	−4.88189	+	8.45568i	−0.205930	+	0.356681i
$563$	6.81039	+	11.7959i	0.287024	+	0.497140i	0.973098	−	0.230392i	$-0.0740008\pi$
$563$	6.81039	+	11.7959i	0.287024	+	0.497140i	−0.686074	+	0.727532i	$0.740667\pi$
$564$	1.89339	−	0.507333i	0.0797262	−	0.0213626i
$565$	13.0991	−	13.0991i	0.551084	−	0.551084i
$566$	9.13975	−	2.44899i	0.384172	−	0.102939i
$567$	1.74877	−	1.98539i	0.0734416	−	0.0833787i
$568$	5.76618	−	9.98731i	0.241943	−	0.419058i
$569$	15.3506	+	8.86269i	0.643532	+	0.371543i	0.785974	−	0.618260i	$-0.212162\pi$
$569$	15.3506	+	8.86269i	0.643532	+	0.371543i	−0.142442	+	0.989803i	$0.545495\pi$
$570$	1.76824	+	1.76824i	0.0740634	+	0.0740634i
$571$	29.4847	+	17.0230i	1.23390	+	0.712391i	0.967840	−	0.251567i	$-0.0809458\pi$
$571$	29.4847	+	17.0230i	1.23390	+	0.712391i	0.266057	+	0.963957i	$0.414279\pi$
$572$	−0.00376751	+	0.00849480i	−0.000157527	+	0.000355186i
$573$		−	12.2419i		−	0.511412i
$574$	6.99660	−	7.94328i	0.292032	−	0.331546i
$575$	−0.706463	−	1.22363i	−0.0294616	−	0.0510289i
$576$			1.00000i			0.0416667i
$577$	3.33179	+	12.4344i	0.138704	+	0.517652i	0.999955	+	0.00947158i	$0.00301494\pi$
$577$	3.33179	+	12.4344i	0.138704	+	0.517652i	−0.861251	+	0.508180i	$0.830318\pi$
$578$	6.73324	−	25.1288i	0.280066	−	1.04522i
$579$	9.84276	+	9.84276i	0.409051	+	0.409051i
$580$	1.70353	+	1.70353i	0.0707352	+	0.0707352i
$581$	−2.04836	−	32.3259i	−0.0849804	−	1.34110i
$582$	−13.4673	+	7.77536i	−0.558238	+	0.322299i
$583$	0.00524312	+	0.0195676i	0.000217148	+	0.000810407i
$584$	−3.04083	+	5.26687i	−0.125830	+	0.217945i
$585$	4.89850	+	2.17252i	0.202528	+	0.0898226i
$586$	−5.05333	+	2.91754i	−0.208751	+	0.120523i
$587$	−33.2879	−	8.91948i	−1.37394	−	0.368146i	−0.505024	−	0.863105i	$-0.668516\pi$
$587$	−33.2879	−	8.91948i	−1.37394	−	0.368146i	−0.868916	+	0.494959i	$0.835183\pi$
$588$	−5.57190	+	4.23721i	−0.229781	+	0.174739i
$589$	12.3289	+	7.11809i	0.508003	+	0.293296i
$590$	−1.40417	+	5.24044i	−0.0578089	+	0.215746i
$591$	−3.30510	−	0.885599i	−0.135954	−	0.0364287i
$592$	4.48115	+	1.20072i	0.184174	+	0.0493493i
$593$	0.939093	−	3.50474i	0.0385639	−	0.143923i	−0.943960	−	0.330061i	$-0.892931\pi$
$593$	0.939093	−	3.50474i	0.0385639	−	0.143923i	0.982524	+	0.186139i	$0.0595973\pi$
$594$	0.00223205	+	0.00128868i	9.15823e−5	+	5.28751e-5i
$595$	23.1052	+	11.4566i	0.947219	+	0.469673i
$596$	13.7658	+	3.68853i	0.563869	+	0.151088i
$597$	−18.5826	+	10.7287i	−0.760534	+	0.439095i
$598$	−1.66846	−	0.739976i	−0.0682285	−	0.0302599i
$599$	8.93093	−	15.4688i	0.364908	−	0.632039i	−0.623853	−	0.781541i	$-0.714434\pi$
$599$	8.93093	−	15.4688i	0.364908	−	0.632039i	0.988761	+	0.149502i	$0.0477671\pi$
$600$	−0.722402	−	2.69604i	−0.0294919	−	0.110065i
$601$	23.7119	−	13.6900i	0.967227	−	0.558429i	0.0688371	−	0.997628i	$-0.478071\pi$
$601$	23.7119	−	13.6900i	0.967227	−	0.558429i	0.898390	+	0.439199i	$0.144738\pi$
$602$	13.3790	−	8.89763i	0.545285	−	0.362640i
$603$	−2.46681	−	2.46681i	−0.100456	−	0.100456i
$604$	10.6959	+	10.6959i	0.435210	+	0.435210i
$605$	4.23128	−	15.7914i	0.172026	−	0.642010i
$606$	0.342648	+	1.27878i	0.0139191	+	0.0519469i
$607$		−	16.3441i		−	0.663386i	−0.943387	−	0.331693i	$-0.892380\pi$
$607$		−	16.3441i		−	0.663386i	0.943387	−	0.331693i	$-0.107620\pi$
$608$	−0.841283	−	1.45715i	−0.0341185	−	0.0590951i
$609$	−0.845812	+	4.20451i	−0.0342740	+	0.170375i
$610$		−	18.2027i		−	0.737006i
$611$	−2.86535	+	6.46065i	−0.115920	+	0.261370i
$612$	5.67992	+	3.27930i	0.229597	+	0.132558i
$613$	12.4485	+	12.4485i	0.502788	+	0.502788i	0.912303	−	0.409515i	$-0.134302\pi$
$613$	12.4485	+	12.4485i	0.502788	+	0.502788i	−0.409515	+	0.912303i	$0.634302\pi$
$614$	−25.9922	−	15.0066i	−1.04896	−	0.605617i
$615$	2.97308	−	5.14953i	0.119886	−	0.207649i
$616$	−0.00511706	−	0.00450721i	−0.000206172	−	0.000181601i
$617$	−42.4346	+	11.3703i	−1.70835	+	0.457751i	−0.975019	−	0.222119i	$-0.928703\pi$
$617$	−42.4346	+	11.3703i	−1.70835	+	0.457751i	−0.733332	+	0.679871i	$0.762036\pi$
$618$	2.36098	−	2.36098i	0.0949727	−	0.0949727i
$619$	−31.3967	+	8.41271i	−1.26194	+	0.338135i	−0.826937	−	0.562295i	$-0.809919\pi$
$619$	−31.3967	+	8.41271i	−1.26194	+	0.338135i	−0.435001	+	0.900430i	$0.643252\pi$
$620$	6.28745	+	10.8902i	0.252510	+	0.437360i
$621$	−0.253109	+	0.438397i	−0.0101569	+	0.0175923i
$622$	2.57162	−	9.59743i	0.103113	−	0.384822i
$623$	15.7150	−	31.6935i	0.629610	−	1.26977i
$624$	−2.80530	−	2.26502i	−0.112302	−	0.0906733i
$625$	−1.62689	−	2.81786i	−0.0650756	−	0.112714i
$626$	−17.0093	+	17.0093i	−0.679829	+	0.679829i
$627$	−0.00433657			−0.000173186
$628$	−3.15739			−0.125993
$629$	21.5150	−	21.5150i	0.857861	−	0.857861i
$630$	−2.59907	+	2.95074i	−0.103549	+	0.117560i
$631$	−8.03971	−	30.0046i	−0.320056	−	1.19446i	−0.919189	−	0.393816i	$-0.871155\pi$
$631$	−8.03971	−	30.0046i	−0.320056	−	1.19446i	0.599134	−	0.800649i	$-0.295512\pi$
$632$	−5.47016	−	1.46573i	−0.217591	−	0.0583035i
$633$	−9.50102	+	5.48542i	−0.377632	+	0.218026i
$634$			10.7745i			0.427910i
$635$	4.55996	−	1.22184i	0.180956	−	0.0484871i
$636$	−7.85995			−0.311667
$637$	0.733828	−	25.2282i	0.0290753	−	0.999577i
$638$	−0.00417787			−0.000165404
$639$	11.1394	−	2.98479i	0.440668	−	0.118077i
$640$		−	1.48622i		−	0.0587481i
$641$	−24.2737	+	14.0144i	−0.958754	+	0.553537i	−0.895789	−	0.444479i	$-0.853389\pi$
$641$	−24.2737	+	14.0144i	−0.958754	+	0.553537i	−0.0629647	+	0.998016i	$0.520056\pi$
$642$	0.532629	+	0.142718i	0.0210212	+	0.00563262i
$643$	−3.37434	−	12.5932i	−0.133071	−	0.496628i	0.866927	−	0.498435i	$-0.166092\pi$
$643$	−3.37434	−	12.5932i	−0.133071	−	0.496628i	−0.999998	+	0.00180669i	$0.999425\pi$
$644$	0.885260	−	1.00504i	0.0348841	−	0.0396042i
$645$	6.38216	−	6.38216i	0.251297	−	0.251297i
$646$	−11.0353			−0.434177
$647$	−20.8635			−0.820228			−0.410114	−	0.912034i	$-0.634511\pi$
$647$	−20.8635			−0.820228			−0.410114	+	0.912034i	$0.634511\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−0.00470419	−	0.00814789i	−0.000184656	−	0.000319833i
$650$	9.19945	+	4.08002i	0.360832	+	0.160032i
$651$	−9.94444	+	20.0556i	−0.389753	+	0.786040i
$652$	0.288918	−	1.07826i	0.0113149	−	0.0422277i
$653$	−18.5074	+	32.0557i	−0.724249	+	1.25444i	0.235033	+	0.971987i	$0.424480\pi$
$653$	−18.5074	+	32.0557i	−0.724249	+	1.25444i	−0.959282	+	0.282449i	$0.908853\pi$
$654$	2.26011	+	3.91463i	0.0883774	+	0.153074i
$655$	−16.1367	+	4.32381i	−0.630512	+	0.168945i
$656$	−2.82903	+	2.82903i	−0.110455	+	0.110455i
$657$	−5.87443	+	1.57405i	−0.229183	+	0.0614095i
$658$	−3.89174	−	3.42792i	−0.151716	−	0.133634i
$659$	−13.2560	+	22.9600i	−0.516380	+	0.894396i	0.483439	+	0.875378i	$0.339387\pi$
$659$	−13.2560	+	22.9600i	−0.516380	+	0.894396i	−0.999819	+	0.0190181i	$0.993946\pi$
$660$	−0.00331733	−	0.00191526i	−0.000129127	−	7.45514e-5i
$661$	−22.4464	−	22.4464i	−0.873063	−	0.873063i	0.119742	−	0.992805i	$-0.461793\pi$
$661$	−22.4464	−	22.4464i	−0.873063	−	0.873063i	−0.992805	+	0.119742i	$0.961793\pi$
$662$	−1.22682	−	0.708303i	−0.0476816	−	0.0275290i
$663$	−22.0645	+	8.50618i	−0.856915	+	0.330353i
$664$			12.2425i			0.475102i
$665$	1.30481	−	6.48620i	0.0505985	−	0.251524i
$666$	2.31961	+	4.01769i	0.0898832	+	0.155682i
$667$		−	0.820575i		−	0.0317728i
$668$	5.96371	+	22.2569i	0.230743	+	0.861145i
$669$	−3.93891	+	14.7002i	−0.152287	+	0.568344i
$670$	3.66623	+	3.66623i	0.141639	+	0.141639i
$671$	0.0223209	+	0.0223209i	0.000861688	+	0.000861688i
$672$	2.20304	−	1.46513i	0.0849843	−	0.0565185i
$673$	28.7827	−	16.6177i	1.10949	−	0.640564i	0.170793	−	0.985307i	$-0.445367\pi$
$673$	28.7827	−	16.6177i	1.10949	−	0.640564i	0.938697	+	0.344743i	$0.112034\pi$
$674$	−8.53599	−	31.8568i	−0.328794	−	1.22708i
$675$	1.39557	−	2.41720i	0.0537156	−	0.0930382i
$676$	12.7081	−	2.73940i	0.488773	−	0.105361i
$677$	−24.9834	+	14.4242i	−0.960192	+	0.554367i	−0.896232	−	0.443586i	$-0.853706\pi$
$677$	−24.9834	+	14.4242i	−0.960192	+	0.554367i	−0.0639597	+	0.997952i	$0.520373\pi$
$678$	−12.0397	−	3.22604i	−0.462384	−	0.123895i
$679$	36.8608	+	18.2772i	1.41459	+	0.701415i
$680$	−8.44161	−	4.87377i	−0.323721	−	0.186900i
$681$	2.91714	−	10.8869i	0.111785	−	0.417188i
$682$	−0.0210639	−	0.00564406i	−0.000806578	−	0.000216122i
$683$	36.6594	+	9.82287i	1.40273	+	0.375862i	0.879326	−	0.476220i	$-0.157993\pi$
$683$	36.6594	+	9.82287i	1.40273	+	0.375862i	0.523409	+	0.852082i	$0.324660\pi$
$684$	0.435480	−	1.62523i	0.0166510	−	0.0621424i
$685$	−14.2599	−	8.23295i	−0.544842	−	0.314565i
$686$	17.4983	+	6.06710i	0.668088	+	0.231643i
$687$	−11.4655	−	3.07218i	−0.437437	−	0.117211i
$688$	−5.25932	+	3.03647i	−0.200510	+	0.115764i
$689$	17.8029	−	22.0495i	0.678237	−	0.840019i
$690$	0.376176	−	0.651556i	0.0143208	−	0.0248043i
$691$	3.07332	+	11.4698i	0.116915	+	0.436331i	0.999423	−	0.0339655i	$-0.0108136\pi$
$691$	3.07332	+	11.4698i	0.116915	+	0.436331i	−0.882508	+	0.470297i	$0.844147\pi$
$692$	7.76905	−	4.48546i	0.295335	−	0.170512i
$693$	−0.000431231	−	0.00680539i	−1.63811e−5	−	0.000258515i
$694$	−14.4463	−	14.4463i	−0.548374	−	0.548374i
$695$	8.57084	+	8.57084i	0.325110	+	0.325110i
$696$	0.419544	−	1.56576i	0.0159028	−	0.0593499i
$697$	6.79142	+	25.3459i	0.257243	+	0.960045i
$698$			9.78290i			0.370288i
$699$	−14.5511	−	25.2033i	−0.550373	−	0.953275i
$700$	−4.88108	+	5.54152i	−0.184488	+	0.209450i
$701$		−	0.635868i		−	0.0240164i	−0.999928	−	0.0120082i	$-0.996178\pi$
$701$		−	0.635868i		−	0.0240164i	0.999928	−	0.0120082i	$-0.00382242\pi$
$702$	−0.382036	−	3.58525i	−0.0144190	−	0.135317i
$703$	−6.76003	−	3.90291i	−0.254959	−	0.147201i
$704$	0.00182246	+	0.00182246i	6.86867e−5	+	6.86867e-5i
$705$	−2.52296	−	1.45663i	−0.0950204	−	0.0548600i
$706$	−14.9686	+	25.9263i	−0.563350	+	0.975751i
$707$	2.31519	−	2.62845i	0.0870716	−	0.0988529i
$708$	3.52602	−	0.944794i	0.132516	−	0.0355075i
$709$	−5.26972	+	5.26972i	−0.197908	+	0.197908i	−0.799103	−	0.601194i	$-0.794692\pi$
$709$	−5.26972	+	5.26972i	−0.197908	+	0.197908i	0.601194	+	0.799103i	$0.294692\pi$
$710$	−16.5556	+	4.43606i	−0.621321	+	0.166482i
$711$	−2.83157	−	4.90442i	−0.106192	−	0.183930i
$712$	−6.68538	+	11.5794i	−0.250545	+	0.433957i
$713$	1.10855	−	4.13716i	0.0415154	−	0.154938i
$714$	−1.09735	−	17.3177i	−0.0410674	−	0.648099i
$715$	0.0128867	−	0.00496799i	0.000481934	−	0.000185792i
$716$	−6.84804	−	11.8611i	−0.255923	−	0.443272i
$717$	−13.7110	+	13.7110i	−0.512048	+	0.512048i
$718$	4.95885			0.185063
$719$	0.0974892			0.00363573			0.00181787	−	0.999998i	$-0.499421\pi$
$719$	0.0974892			0.00363573			0.00181787	+	0.999998i	$0.499421\pi$
$720$	1.05092	−	1.05092i	0.0391654	−	0.0391654i
$721$	−8.66049	−	1.74221i	−0.322534	−	0.0648833i
$722$	−4.18484	−	15.6180i	−0.155744	−	0.581243i
$723$	−18.4962	−	4.95603i	−0.687880	−	0.184317i
$724$	21.1447	−	12.2079i	0.785838	−	0.453704i
$725$			4.52443i			0.168033i
$726$	−10.6252	+	2.84701i	−0.394337	+	0.105662i
$727$	19.9405			0.739551			0.369775	−	0.929121i	$-0.379435\pi$
$727$	19.9405			0.739551			0.369775	+	0.929121i	$0.379435\pi$
$728$	−0.879814	+	9.49873i	−0.0326081	+	0.352046i
$729$	−1.00000			−0.0370370
$730$	8.73070	−	2.33938i	0.323138	−	0.0865845i
$731$			39.8300i			1.47317i
$732$	−10.6068	+	6.12382i	−0.392037	+	0.226343i
$733$	−46.4631	−	12.4498i	−1.71616	−	0.459842i	−0.739235	−	0.673447i	$-0.764813\pi$
$733$	−46.4631	−	12.4498i	−1.71616	−	0.459842i	−0.976920	+	0.213605i	$0.931479\pi$
$734$	−4.12815	−	15.4065i	−0.152373	−	0.568663i
$735$	10.3086	+	1.40266i	0.380237	+	0.0517377i
$736$	−0.357950	+	0.357950i	−0.0131942	+	0.0131942i
$737$	−0.00899136			−0.000331201
$738$	−4.00086			−0.147274
$739$	7.04963	−	7.04963i	0.259325	−	0.259325i	−0.565455	−	0.824779i	$-0.691299\pi$
$739$	7.04963	−	7.04963i	0.259325	−	0.259325i	0.824779	+	0.565455i	$0.191299\pi$
$740$	−3.44746	−	5.97118i	−0.126731	−	0.219505i
$741$	3.57290	+	4.90284i	0.131254	+	0.180110i
$742$	11.5158	+	17.3158i	0.422759	+	0.635684i
$743$	10.2022	−	38.0753i	0.374284	−	1.39685i	−0.480104	−	0.877211i	$-0.659401\pi$
$743$	10.2022	−	38.0753i	0.374284	−	1.39685i	0.854388	−	0.519635i	$-0.173932\pi$
$744$	4.23049	−	7.32743i	0.155097	−	0.268637i
$745$	−10.5904	−	18.3431i	−0.388001	−	0.672038i
$746$	30.7532	−	8.24031i	1.12596	−	0.301699i
$747$	−8.65678	+	8.65678i	−0.316735	+	0.316735i
$748$	0.0163279	−	0.00437503i	0.000597005	−	0.000159967i
$749$	−0.465957	−	1.38251i	−0.0170257	−	0.0505156i
$750$	−5.78968	+	10.0280i	−0.211409	+	0.366172i
$751$	20.3904	+	11.7724i	0.744058	+	0.429582i	0.823543	−	0.567254i	$-0.191994\pi$
$751$	20.3904	+	11.7724i	0.744058	+	0.429582i	−0.0794852	+	0.996836i	$0.525328\pi$
$752$	1.38606	+	1.38606i	0.0505444	+	0.0505444i
$753$	−26.6532	−	15.3883i	−0.971298	−	0.560779i
$754$	3.44215	+	4.72342i	0.125356	+	0.172017i
$755$		−	22.4810i		−	0.818168i
$756$	2.59379	+	0.521786i	0.0943352	+	0.0189772i
$757$	−10.3994	−	18.0123i	−0.377972	−	0.654667i	0.612795	−	0.790242i	$-0.290045\pi$
$757$	−10.3994	−	18.0123i	−0.377972	−	0.654667i	−0.990767	+	0.135575i	$0.956712\pi$
$758$		−	6.54686i		−	0.237793i
$759$	0.000337682		0.00126025i	1.22571e−5		4.57440e-5i
$760$	−0.647220	+	2.41546i	−0.0234771	+	0.0876179i
$761$	−11.1029	−	11.1029i	−0.402481	−	0.402481i	0.476625	−	0.879106i	$-0.341860\pi$
$761$	−11.1029	−	11.1029i	−0.402481	−	0.402481i	−0.879106	+	0.476625i	$0.841860\pi$
$762$	−2.24605	−	2.24605i	−0.0813657	−	0.0813657i
$763$	5.31275	−	10.7146i	0.192334	−	0.387893i
$764$	10.6018	−	6.12094i	0.383559	−	0.221448i
$765$	−2.52285	−	9.41540i	−0.0912138	−	0.340414i
$766$	14.0840	−	24.3942i	0.508876	−	0.881399i
$767$	−5.33606	+	12.0315i	−0.192674	+	0.434432i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−11.9936	−	3.21367i	−0.432500	−	0.115888i	0.0359997	−	0.999352i	$-0.488538\pi$
$769$	−11.9936	−	3.21367i	−0.432500	−	0.115888i	−0.468499	+	0.883464i	$0.655205\pi$
$770$	0.000640904		0.0101143i	2.30966e−5		0.000364495i
$771$	−0.650167	−	0.375374i	−0.0234152	−	0.0135188i
$772$	−3.60270	+	13.4455i	−0.129664	+	0.483912i
$773$	−12.5100	−	3.35204i	−0.449953	−	0.120565i	0.0267244	−	0.999643i	$-0.491492\pi$
$773$	−12.5100	−	3.35204i	−0.449953	−	0.120565i	−0.476677	+	0.879078i	$0.658159\pi$
$774$	−5.86601	−	1.57179i	−0.210849	−	0.0564969i
$775$	−6.11223	+	22.8112i	−0.219558	+	0.819401i
$776$	−13.4673	−	7.77536i	−0.483449	−	0.279119i
$777$	5.45262	−	10.9966i	0.195612	−	0.394502i
$778$	13.5065	+	3.61904i	0.484230	+	0.129749i
$779$	5.82983	−	3.36585i	0.208875	−	0.120594i
$780$	0.567791	+	5.32848i	0.0203302	+	0.190790i
$781$	0.0148615	−	0.0257408i	0.000531785	−	0.000921079i
$782$	0.859300	+	3.20695i	0.0307285	+	0.114680i
$783$	1.40382	−	0.810496i	0.0501685	−	0.0289648i
$784$	−6.45548	−	2.70681i	−0.230553	−	0.0966716i
$785$	3.31815	+	3.31815i	0.118430	+	0.118430i
$786$	7.94826	+	7.94826i	0.283505	+	0.283505i
$787$	8.48809	−	31.6780i	0.302568	−	1.12920i	−0.632451	−	0.774600i	$-0.717951\pi$
$787$	8.48809	−	31.6780i	0.302568	−	1.12920i	0.935019	−	0.354598i	$-0.115382\pi$
$788$	−0.885599	−	3.30510i	−0.0315482	−	0.117739i
$789$			15.4971i			0.551713i
$790$	4.20833	+	7.28905i	0.149726	+	0.259333i
$791$	10.5326	+	31.2506i	0.374498	+	1.11115i
$792$			0.00257735i			9.15823e-5i
$793$	6.84537	−	43.6257i	0.243086	−	1.54919i
$794$	−30.1951	−	17.4331i	−1.07158	−	0.618679i
$795$	8.26016	+	8.26016i	0.292958	+	0.292958i
$796$	−18.5826	−	10.7287i	−0.658642	−	0.380267i
$797$	−11.8237	+	20.4793i	−0.418817	+	0.725413i	−0.995821	−	0.0913290i	$-0.970889\pi$
$797$	−11.8237	+	20.4793i	−0.418817	+	0.725413i	0.577004	+	0.816742i	$0.304222\pi$
$798$	−4.21850	+	1.42179i	−0.149333	+	0.0503309i
$799$	12.4180	−	3.32740i	0.439318	−	0.117715i
$800$	1.97364	−	1.97364i	0.0697786	−	0.0697786i
$801$	−12.9152	+	3.46061i	−0.456335	+	0.122275i
$802$	8.71069	+	15.0874i	0.307585	+	0.532753i
$803$	−0.00783729	+	0.0135746i	−0.000276572	+	0.000479037i
$804$	0.902916	−	3.36973i	0.0318434	−	0.118841i
$805$	−1.98655	+	0.125880i	−0.0700167	+	0.00443668i
$806$	10.9735	+	28.4645i	0.386524	+	1.00262i
$807$	−5.99464	−	10.3830i	−0.211021	−	0.365499i
$808$	−0.936133	+	0.936133i	−0.0329330	+	0.0329330i
$809$	36.4762			1.28243			0.641217	−	0.767359i	$-0.278430\pi$
$809$	36.4762			1.28243			0.641217	+	0.767359i	$0.278430\pi$
$810$	1.48622			0.0522205
$811$	−28.7062	+	28.7062i	−1.00801	+	1.00801i	−0.00804163	+	0.999968i	$0.502560\pi$
$811$	−28.7062	+	28.7062i	−1.00801	+	1.00801i	−0.999968	+	0.00804163i	$0.997440\pi$
$812$	−4.06412	+	1.36976i	−0.142623	+	0.0480692i
$813$	3.19982	+	11.9419i	0.112223	+	0.418821i
$814$	0.0115495	+	0.00309468i	0.000404810	+	0.000108469i
$815$	−1.43679	+	0.829529i	−0.0503284	+	0.0290571i
$816$			6.55860i			0.229597i
$817$	9.86995	−	2.64465i	0.345306	−	0.0925244i
$818$	22.2340			0.777394
$819$	−7.33874	+	6.09450i	−0.256436	+	0.212959i
$820$	5.94616			0.207649
$821$	36.0110	−	9.64911i	1.25679	−	0.336756i	0.431835	−	0.901953i	$-0.357866\pi$
$821$	36.0110	−	9.64911i	1.25679	−	0.336756i	0.824956	+	0.565196i	$0.191200\pi$
$822$			11.0790i			0.386426i
$823$	−20.5318	+	11.8540i	−0.715692	+	0.413205i	−0.813165	−	0.582033i	$-0.802257\pi$
$823$	−20.5318	+	11.8540i	−0.715692	+	0.413205i	0.0974727	+	0.995238i	$0.468924\pi$
$824$	3.22516	+	0.864180i	0.112354	+	0.0301051i
$825$	−0.00186188	−	0.00694865i	−6.48225e−5	−	0.000241921i
$826$	−7.24749	−	6.38373i	−0.252172	−	0.222118i
$827$	29.5127	−	29.5127i	1.02626	−	1.02626i	0.0266107	−	0.999646i	$-0.491529\pi$
$827$	29.5127	−	29.5127i	1.02626	−	1.02626i	0.999646	−	0.0266107i	$-0.00847145\pi$
$828$	−0.506218			−0.0175923
$829$	−4.21677			−0.146455			−0.0732273	−	0.997315i	$-0.523330\pi$
$829$	−4.21677			−0.146455			−0.0732273	+	0.997315i	$0.523330\pi$
$830$	12.8659	−	12.8659i	0.446582	−	0.446582i
$831$	10.2154	+	17.6936i	0.354369	+	0.613785i
$832$	0.558913	−	3.56197i	0.0193768	−	0.123489i
$833$	−36.5439	+	27.7901i	−1.26617	+	0.962871i
$834$	2.11082	−	7.87768i	0.0730917	−	0.272782i
$835$	17.1228	−	29.6575i	0.592558	−	1.02634i
$836$	−0.00216828	−	0.00375558i	−7.49917e−5	−	0.000129889i
$837$	8.17269	−	2.18986i	0.282489	−	0.0756928i
$838$	22.9788	−	22.9788i	0.793788	−	0.793788i
$839$	−54.6675	+	14.6481i	−1.88733	+	0.505709i	−0.888422	+	0.459027i	$0.848198\pi$
$839$	−54.6675	+	14.6481i	−1.88733	+	0.505709i	−0.998910	+	0.0466822i	$0.985135\pi$
$840$	−3.85494	−	0.775490i	−0.133008	−	0.0267569i
$841$	13.1862	−	22.8392i	0.454696	−	0.787557i
$842$	2.65023	+	1.53011i	0.0913329	+	0.0527311i
$843$	−6.90403	−	6.90403i	−0.237788	−	0.237788i
$844$	−9.50102	−	5.48542i	−0.327039	−	0.188816i
$845$	−16.2340	−	10.4763i	−0.558468	−	0.360395i
$846$			1.96018i			0.0673925i
$847$	21.8393	+	19.2365i	0.750408	+	0.660974i
$848$	−3.92998	−	6.80692i	−0.134956	−	0.233750i
$849$			9.46217i			0.324741i
$850$	−4.73794	−	17.6822i	−0.162510	−	0.606496i
$851$	−0.607826	+	2.26844i	−0.0208360	+	0.0777610i
$852$	8.15460	+	8.15460i	0.279372	+	0.279372i
$853$	28.8339	+	28.8339i	0.987254	+	0.987254i	0.999920	−	0.0126661i	$-0.00403186\pi$
$853$	28.8339	+	28.8339i	0.987254	+	0.987254i	−0.0126661	+	0.999920i	$0.504032\pi$
$854$	29.0313	+	14.3950i	0.993431	+	0.492587i
$855$	−2.16564	+	1.25033i	−0.0740634	+	0.0427605i
$856$	0.142718	+	0.532629i	0.00487799	+	0.0182049i
$857$	2.00576	−	3.47407i	0.0685154	−	0.118672i	−0.829733	−	0.558161i	$-0.811507\pi$
$857$	2.00576	−	3.47407i	0.0685154	−	0.118672i	0.898248	+	0.439489i	$0.144840\pi$
$858$	−0.00723025	−	0.00583775i	−0.000246837	−	0.000199298i
$859$	23.1820	−	13.3841i	0.790959	−	0.456661i	−0.0493408	−	0.998782i	$-0.515712\pi$
$859$	23.1820	−	13.3841i	0.790959	−	0.456661i	0.840300	+	0.542121i	$0.182379\pi$
$860$	8.71819	+	2.33603i	0.297288	+	0.0796580i
$861$	5.86176	+	8.81407i	0.199768	+	0.300383i
$862$	−2.62456	−	1.51529i	−0.0893929	−	0.0516110i
$863$	−0.0926917	+	0.345930i	−0.00315526	+	0.0117756i	−0.967486	−	0.252926i	$-0.918607\pi$
$863$	−0.0926917	+	0.345930i	−0.00315526	+	0.0117756i	0.964330	+	0.264702i	$0.0852736\pi$
$864$	−0.965926	−	0.258819i	−0.0328615	−	0.00880520i
$865$	−12.8785	−	3.45078i	−0.437881	−	0.117330i
$866$	0.198484	−	0.740753i	0.00674477	−	0.0251718i
$867$	22.5299	+	13.0076i	0.765155	+	0.441762i
$868$	−22.3409	+	1.41565i	−0.758298	+	0.0480504i
$869$	−0.0140985	−	0.00377770i	−0.000478261	−	0.000128150i
$870$	−2.08639	+	1.20458i	−0.0707352	+	0.0408390i
$871$	7.40798	+	10.1654i	0.251010	+	0.344443i
$872$	−2.26011	+	3.91463i	−0.0765370	+	0.132566i
$873$	−4.02482	−	15.0208i	−0.136220	−	0.508379i
$874$	0.737633	−	0.425872i	0.0249508	−	0.0144053i
$875$	30.5748	−	1.93740i	1.03362	−	0.0654962i
$876$	−4.30038	−	4.30038i	−0.145296	−	0.145296i
$877$	27.3872	+	27.3872i	0.924800	+	0.924800i	0.997364	−	0.0725639i	$-0.0231181\pi$
$877$	27.3872	+	27.3872i	0.924800	+	0.924800i	−0.0725639	+	0.997364i	$0.523118\pi$
$878$	−1.35662	+	5.06299i	−0.0457838	+	0.170867i
$879$	−1.51023	−	5.63626i	−0.0509388	−	0.190106i
$880$		−	0.00383052i		−	0.000129127i
$881$	−14.9309	−	25.8610i	−0.503034	−	0.871281i	−0.999994	−	0.00350714i	$-0.998884\pi$
$881$	−14.9309	−	25.8610i	−0.503034	−	0.871281i	0.496960	−	0.867774i	$-0.334450\pi$
$882$	−2.65071	−	6.47871i	−0.0892541	−	0.218150i
$883$			7.07937i			0.238240i	0.992880	+	0.119120i	$0.0380073\pi$
$883$			7.07937i			0.238240i	−0.992880	+	0.119120i	$0.961993\pi$
$884$	−18.3988	−	14.8553i	−0.618820	−	0.499639i
$885$	−4.69845	−	2.71265i	−0.157937	−	0.0911848i
$886$	3.80253	+	3.80253i	0.127749	+	0.127749i
$887$	11.6565	+	6.72991i	0.391389	+	0.225968i	0.682762	−	0.730641i	$-0.260779\pi$
$887$	11.6565	+	6.72991i	0.391389	+	0.225968i	−0.291373	+	0.956609i	$0.594112\pi$
$888$	−2.31961	+	4.01769i	−0.0778412	+	0.134825i
$889$	−1.65740	+	8.23888i	−0.0555873	+	0.276323i
$890$	19.1948	−	5.14323i	0.643411	−	0.172401i
$891$	−0.00182246	+	0.00182246i	−6.10549e−5	+	6.10549e-5i
$892$	−14.7002	+	3.93891i	−0.492200	+	0.131885i
$893$	−1.64907	−	2.85627i	−0.0551841	−	0.0955816i
$894$	−7.12570	+	12.3421i	−0.238319	+	0.412781i
$895$	−5.26837	+	19.6618i	−0.176102	+	0.657222i
$896$	2.37036	+	1.17533i	0.0791881	+	0.0392650i
$897$	1.14659	−	1.42009i	0.0382836	−	0.0474155i
$898$	−7.94738	−	13.7653i	−0.265208	−	0.459353i
$899$	−9.69811	+	9.69811i	−0.323450	+	0.323450i
$900$	2.79115			0.0930382
$901$	−51.5503			−1.71739
$902$	−0.00729142	+	0.00729142i	−0.000242778	+	0.000242778i
$903$	5.13172	+	15.2260i	0.170773	+	0.506688i
$904$	−3.22604	−	12.0397i	−0.107296	−	0.400436i
$905$	−35.0509	−	9.39186i	−1.16513	−	0.312196i
$906$	−13.0997	+	7.56314i	−0.435210	+	0.251269i
$907$		−	24.5465i		−	0.815053i	−0.913193	−	0.407526i	$-0.866391\pi$
$907$		−	24.5465i		−	0.815053i	0.913193	−	0.407526i	$-0.133609\pi$
$908$	10.8869	−	2.91714i	0.361295	−	0.0968088i
$909$	−1.32389			−0.0439107
$910$	10.9070	−	9.05777i	0.361563	−	0.300262i
$911$	−19.2902			−0.639114			−0.319557	−	0.947567i	$-0.603534\pi$
$911$	−19.2902			−0.639114			−0.319557	+	0.947567i	$0.603534\pi$
$912$	1.62523	−	0.435480i	0.0538169	−	0.0144202i
$913$			0.0315533i			0.00104426i
$914$	−24.5118	+	14.1519i	−0.810780	+	0.468104i
$915$	17.5825	+	4.71121i	0.581258	+	0.155748i
$916$	−3.07218	−	11.4655i	−0.101508	−	0.378832i
$917$	5.86516	−	29.1556i	0.193684	−	0.962802i
$918$	−4.63763	+	4.63763i	−0.153065	+	0.153065i
$919$	46.7443			1.54195			0.770976	−	0.636864i	$-0.219769\pi$
$919$	46.7443			1.54195			0.770976	+	0.636864i	$0.219769\pi$
$920$	0.752351			0.0248043
$921$	21.2225	−	21.2225i	0.699306	−	0.699306i
$922$	10.1876	+	17.6455i	0.335512	+	0.581124i
$923$	−41.3464	+	4.40578i	−1.36093	+	0.145018i
$924$	0.00567802	−	0.00377615i	0.000186793	−	0.000124226i
$925$	3.35139	−	12.5075i	0.110193	−	0.411245i
$926$	−14.9677	+	25.9247i	−0.491868	+	0.851940i
$927$	1.66947	+	2.89160i	0.0548325	+	0.0949727i
$928$	1.56576	−	0.419544i	0.0513986	−	0.0137722i
$929$	−12.8971	+	12.8971i	−0.423141	+	0.423141i	−0.886284	−	0.463143i	$-0.846722\pi$
$929$	−12.8971	+	12.8971i	−0.423141	+	0.423141i	0.463143	+	0.886284i	$0.346722\pi$
$930$	−12.1464	+	3.25462i	−0.398297	+	0.106723i
$931$	9.31291	+	7.21043i	0.305218	+	0.236312i
$932$	14.5511	−	25.2033i	0.476637	−	0.825560i
$933$	8.60482	+	4.96799i	0.281709	+	0.162645i
$934$	−22.0724	−	22.0724i	−0.722232	−	0.722232i
$935$	−0.0217570	−	0.0125614i	−0.000711531	−	0.000410802i
$936$	2.91390	−	2.12348i	0.0952439	−	0.0694081i
$937$		−	34.8058i		−	1.13706i	−0.822663	−	0.568529i	$-0.807513\pi$
$937$		−	34.8058i		−	1.13706i	0.822663	−	0.568529i	$-0.192487\pi$
$938$	−8.74655	+	2.94792i	−0.285585	+	0.0962529i
$939$	−12.0274	−	20.8321i	−0.392499	−	0.679829i
$940$		−	2.91327i		−	0.0950204i
$941$	10.0110	+	37.3615i	0.326349	+	1.21795i	0.912949	+	0.408073i	$0.133799\pi$
$941$	10.0110	+	37.3615i	0.326349	+	1.21795i	−0.586601	+	0.809876i	$0.699534\pi$
$942$	0.817192	−	3.04980i	0.0266255	−	0.0993679i
$943$	−1.43211	−	1.43211i	−0.0466358	−	0.0466358i
$944$	2.58122	+	2.58122i	0.0840117	+	0.0840117i
$945$	−2.17750	−	3.27421i	−0.0708342	−	0.106510i
$946$	−0.0135551	+	0.00782606i	−0.000440715	+	0.000254447i
$947$	−4.21245	−	15.7211i	−0.136886	−	0.510866i	−0.999983	−	0.00582760i	$-0.998145\pi$
$947$	−4.21245	−	15.7211i	−0.136886	−	0.510866i	0.863097	−	0.505038i	$-0.168522\pi$
$948$	2.83157	−	4.90442i	0.0919650	−	0.159288i
$949$	21.8043	−	2.32341i	0.707797	−	0.0754212i
$950$	−4.06711	+	2.34814i	−0.131954	+	0.0761839i
$951$	−10.4074	−	2.78864i	−0.337482	−	0.0904280i
$952$	14.4489	−	9.60918i	0.468291	−	0.311435i
$953$	9.44672	+	5.45406i	0.306009	+	0.176674i	0.645139	−	0.764065i	$-0.276799\pi$
$953$	9.44672	+	5.45406i	0.306009	+	0.176674i	−0.339130	+	0.940739i	$0.610133\pi$
$954$	2.03430	−	7.59213i	0.0658631	−	0.245804i
$955$	−17.5742	−	4.70899i	−0.568688	−	0.152379i
$956$	−18.7296	−	5.01859i	−0.605760	−	0.162313i
$957$	0.00108131	−	0.00403551i	3.49539e−5	−	0.000130450i
$958$	−27.6156	−	15.9439i	−0.892221	−	0.515124i
$959$	24.4076	−	16.2322i	0.788162	−	0.524165i
$960$	1.43558	+	0.384662i	0.0463331	+	0.0124149i
$961$	−35.1505	+	20.2941i	−1.13389	+	0.654650i
$962$	−6.01685	−	15.6073i	−0.193991	−	0.503201i
$963$	−0.275709	+	0.477542i	−0.00888461	+	0.0153886i
$964$	−4.95603	−	18.4962i	−0.159623	−	0.595721i
$965$	17.9162	−	10.3439i	0.576743	−	0.332983i
$966$	0.741673	+	1.11522i	0.0238629	+	0.0358816i
$967$	−13.7989	−	13.7989i	−0.443744	−	0.443744i	0.449524	−	0.893268i	$-0.351594\pi$
$967$	−13.7989	−	13.7989i	−0.443744	−	0.443744i	−0.893268	+	0.449524i	$0.851594\pi$
$968$	−7.77817	−	7.77817i	−0.250000	−	0.250000i
$969$	2.85614	−	10.6593i	0.0917525	−	0.342425i
$970$	5.98178	+	22.3243i	0.192063	+	0.716790i
$971$			43.2771i			1.38883i	0.719575	+	0.694414i	$0.244336\pi$
$971$			43.2771i			1.38883i	−0.719575	+	0.694414i	$0.755664\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−20.4475	+	6.89158i	−0.655517	+	0.220934i
$974$		−	15.5165i		−	0.497182i
$975$	−6.32199	+	7.83000i	−0.202466	+	0.250761i
$976$	−10.6068	−	6.12382i	−0.339514	−	0.196019i
$977$	18.3628	+	18.3628i	0.587479	+	0.587479i	0.936948	−	0.349469i	$-0.113638\pi$
$977$	18.3628	+	18.3628i	0.587479	+	0.587479i	−0.349469	+	0.936948i	$0.613638\pi$
$978$	0.966737	+	0.558146i	0.0309129	+	0.0178475i
$979$	−0.0172306	+	0.0298443i	−0.000550692	+	0.000953827i
$980$	3.93955	+	9.62880i	0.125844	+	0.307581i
$981$	−4.36620	+	1.16992i	−0.139402	+	0.0373527i
$982$	1.84979	−	1.84979i	0.0590291	−	0.0590291i
$983$	−41.0023	+	10.9865i	−1.30777	+	0.350416i	−0.844383	−	0.535740i	$-0.820033\pi$
$983$	−41.0023	+	10.9865i	−1.30777	+	0.350416i	−0.463387	+	0.886156i	$0.653366\pi$
$984$	−2.00043	−	3.46484i	−0.0637713	−	0.110455i
$985$	−2.54270	+	4.40408i	−0.0810170	+	0.140326i
$986$	2.75162	−	10.2692i	0.0876295	−	0.327038i
$987$	4.31837	−	2.87192i	0.137455	−	0.0914142i
$988$	−2.45953	+	5.54564i	−0.0782481	+	0.176430i
$989$	−1.53711	−	2.66236i	−0.0488774	−	0.0846581i
$990$	0.00270859	−	0.00270859i	8.60845e−5	−	8.60845e-5i
$991$	−44.1709			−1.40313			−0.701567	−	0.712604i	$-0.747516\pi$
$991$	−44.1709			−1.40313			−0.701567	+	0.712604i	$0.747516\pi$
$992$	8.46099			0.268637
$993$	1.00169	−	1.00169i	0.0317877	−	0.0317877i
$994$	6.01742	−	29.9125i	0.190861	−	0.948766i
$995$	8.25382	+	30.8037i	0.261664	+	0.976543i
$996$	−11.8254	−	3.16860i	−0.374701	−	0.100401i
$997$	35.3804	−	20.4269i	1.12051	−	0.646925i	0.178977	−	0.983853i	$-0.442721\pi$
$997$	35.3804	−	20.4269i	1.12051	−	0.646925i	0.941530	+	0.336928i	$0.109388\pi$
$998$		−	19.0532i		−	0.603117i
$999$	−4.48115	+	1.20072i	−0.141777	+	0.0379891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.115.2	yes	32
7.5	odd	6		546.2.cg.a.271.6	yes	32
13.6	odd	12		546.2.cg.a.409.6	yes	32
91.19	even	12	inner	546.2.by.a.19.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.2	✓	32	91.19	even	12	inner
546.2.by.a.115.2	yes	32	1.1	even	1	trivial
546.2.cg.a.271.6	yes	32	7.5	odd	6
546.2.cg.a.409.6	yes	32	13.6	odd	12

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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.43558 - 0.384662i) q^{5} +(0.258819 + 0.965926i) q^{6} +(1.74877 - 1.98539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.43558 - 0.384662i) q^{5} +(0.258819 + 0.965926i) q^{6} +(1.74877 - 1.98539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +1.48622 q^{10} +(-0.00182246 + 0.00182246i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.56197 + 0.558913i) q^{13} +(-1.17533 + 2.37036i) q^{14} +(-0.384662 + 1.43558i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.27930 - 5.67992i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-1.18975 + 1.18975i) q^{19} +(-1.43558 + 0.384662i) q^{20} +(-1.98539 - 1.74877i) q^{21} +(0.00128868 - 0.00223205i) q^{22} +(0.438397 + 0.253109i) q^{23} +(0.707107 + 0.707107i) q^{24} +(-2.41720 - 1.39557i) q^{25} +(-3.58525 + 0.382036i) q^{26} +1.00000i q^{27} +(0.521786 - 2.59379i) q^{28} +(-0.810496 - 1.40382i) q^{29} -1.48622i q^{30} +(-2.18986 - 8.17269i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.00182246 + 0.00182246i) q^{33} +(4.63763 + 4.63763i) q^{34} +(-3.27421 + 2.17750i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(1.20072 + 4.48115i) q^{37} +(0.841283 - 1.45715i) q^{38} +(0.558913 - 3.56197i) q^{39} +(1.28711 - 0.743111i) q^{40} +(-3.86453 - 1.03550i) q^{41} +(2.37036 + 1.17533i) q^{42} +(-5.25932 - 3.03647i) q^{43} +(-0.000667068 + 0.00248953i) q^{44} +(1.43558 + 0.384662i) q^{45} +(-0.488969 - 0.131019i) q^{46} +(-0.507333 + 1.89339i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.883577 - 6.94401i) q^{49} +(2.69604 + 0.722402i) q^{50} +(-5.67992 + 3.27930i) q^{51} +(3.36421 - 1.29695i) q^{52} +(3.92998 - 6.80692i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(0.00331733 - 0.00191526i) q^{55} +(0.167315 + 2.64046i) q^{56} +(1.18975 + 1.18975i) q^{57} +(1.14622 + 1.14622i) q^{58} +(-0.944794 + 3.52602i) q^{59} +(0.384662 + 1.43558i) q^{60} -12.2476i q^{61} +(4.23049 + 7.32743i) q^{62} +(-1.74877 + 1.98539i) q^{63} -1.00000i q^{64} +(-4.89850 - 2.17252i) q^{65} +(-0.00223205 - 0.00128868i) q^{66} +(2.46681 + 2.46681i) q^{67} +(-5.67992 - 3.27930i) q^{68} +(0.253109 - 0.438397i) q^{69} +(2.59907 - 2.95074i) q^{70} +(-11.1394 + 2.98479i) q^{71} +(0.707107 - 0.707107i) q^{72} +(5.87443 - 1.57405i) q^{73} +(-2.31961 - 4.01769i) q^{74} +(-1.39557 + 2.41720i) q^{75} +(-0.435480 + 1.62523i) q^{76} +(0.000431231 + 0.00680539i) q^{77} +(0.382036 + 3.58525i) q^{78} +(2.83157 + 4.90442i) q^{79} +(-1.05092 + 1.05092i) q^{80} +1.00000 q^{81} +4.00086 q^{82} +(8.65678 - 8.65678i) q^{83} +(-2.59379 - 0.521786i) q^{84} +(2.52285 + 9.41540i) q^{85} +(5.86601 + 1.57179i) q^{86} +(-1.40382 + 0.810496i) q^{87} -0.00257735i q^{88} +(12.9152 - 3.46061i) q^{89} -1.48622 q^{90} +(7.33874 - 6.09450i) q^{91} +0.506218 q^{92} +(-8.17269 + 2.18986i) q^{93} -1.96018i q^{94} +(2.16564 - 1.25033i) q^{95} +(0.965926 + 0.258819i) q^{96} +(4.02482 + 15.0208i) q^{97} +(2.65071 + 6.47871i) q^{98} +(0.00182246 - 0.00182246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more