LMFDB - Embedded newform 252.2.ba.a.155.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.6
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24454 + 0.671660i) q^{2} +(-0.586217 - 1.62983i) q^{3} +(1.09775 - 1.67181i) q^{4} +(-2.16781 + 1.25159i) q^{5} +(1.82426 + 1.63465i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.243298 + 2.81794i) q^{8} +(-2.31270 + 1.91087i) q^{9} +O(q^{10})$	\(q+(-1.24454 + 0.671660i) q^{2} +(-0.586217 - 1.62983i) q^{3} +(1.09775 - 1.67181i) q^{4} +(-2.16781 + 1.25159i) q^{5} +(1.82426 + 1.63465i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.243298 + 2.81794i) q^{8} +(-2.31270 + 1.91087i) q^{9} +(1.85728 - 3.01367i) q^{10} +(0.351433 - 0.608700i) q^{11} +(-3.36829 - 0.809097i) q^{12} +(1.55324 + 2.69030i) q^{13} +(1.41363 + 0.0405943i) q^{14} +(3.31068 + 2.79946i) q^{15} +(-1.58991 - 3.67045i) q^{16} +7.91554i q^{17} +(1.59479 - 3.93150i) q^{18} +2.37413i q^{19} +(-0.287291 + 4.99809i) q^{20} +(-0.307237 + 1.70458i) q^{21} +(-0.0285324 + 0.993594i) q^{22} +(0.346619 + 0.600362i) q^{23} +(4.73540 - 1.25539i) q^{24} +(0.632931 - 1.09627i) q^{25} +(-3.74003 - 2.30492i) q^{26} +(4.47014 + 2.64912i) q^{27} +(-1.78658 + 0.898958i) q^{28} +(-8.70126 - 5.02368i) q^{29} +(-6.00055 - 1.26039i) q^{30} +(-7.34846 + 4.24264i) q^{31} +(4.44399 + 3.50014i) q^{32} +(-1.19809 - 0.215946i) q^{33} +(-5.31655 - 9.85118i) q^{34} +2.50317 q^{35} +(0.655856 + 5.96405i) q^{36} +2.85107 q^{37} +(-1.59460 - 2.95469i) q^{38} +(3.47419 - 4.10862i) q^{39} +(-2.99947 - 6.41327i) q^{40} +(5.82034 - 3.36037i) q^{41} +(-0.762533 - 2.32778i) q^{42} +(-3.17043 - 1.83045i) q^{43} +(-0.631847 - 1.25573i) q^{44} +(2.62187 - 7.03694i) q^{45} +(-0.834620 - 0.514363i) q^{46} +(-3.67787 + 6.37026i) q^{47} +(-5.05018 + 4.74296i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.0513868 + 1.78946i) q^{50} +(12.9010 - 4.64022i) q^{51} +(6.20273 + 0.356534i) q^{52} +0.889576i q^{53} +(-7.34256 - 0.294523i) q^{54} +1.75939i q^{55} +(1.61967 - 2.31876i) q^{56} +(3.86942 - 1.39175i) q^{57} +(14.2032 + 0.407865i) q^{58} +(-3.63052 - 6.28824i) q^{59} +(8.31446 - 2.46173i) q^{60} +(-2.39732 + 4.15228i) q^{61} +(6.29583 - 10.2158i) q^{62} +(2.95829 - 0.498512i) q^{63} +(-7.88161 - 1.37120i) q^{64} +(-6.73427 - 3.88803i) q^{65} +(1.63612 - 0.535959i) q^{66} +(7.40811 - 4.27707i) q^{67} +(13.2333 + 8.68925i) q^{68} +(0.775295 - 0.916874i) q^{69} +(-3.11529 + 1.68128i) q^{70} -6.34514 q^{71} +(-4.82205 - 6.98197i) q^{72} +8.20222 q^{73} +(-3.54826 + 1.91495i) q^{74} +(-2.15777 - 0.388920i) q^{75} +(3.96909 + 2.60619i) q^{76} +(-0.608700 + 0.351433i) q^{77} +(-1.56416 + 7.44681i) q^{78} +(-2.27268 - 1.31214i) q^{79} +(8.04049 + 5.96693i) q^{80} +(1.69715 - 8.83853i) q^{81} +(-4.98660 + 8.09139i) q^{82} +(6.50432 - 11.2658i) q^{83} +(2.51247 + 2.38484i) q^{84} +(-9.90697 - 17.1594i) q^{85} +(5.17515 + 0.148611i) q^{86} +(-3.08692 + 17.1266i) q^{87} +(1.62978 + 1.13841i) q^{88} +1.71842i q^{89} +(1.46341 + 10.5187i) q^{90} -3.10649i q^{91} +(1.38419 + 0.0795635i) q^{92} +(11.2226 + 9.48965i) q^{93} +(0.298601 - 10.3983i) q^{94} +(-2.97142 - 5.14665i) q^{95} +(3.09949 - 9.29479i) q^{96} +(-6.81083 + 11.7967i) q^{97} +(-1.20394 - 0.741971i) q^{98} +(0.350387 + 2.07928i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.24454	+	0.671660i	−0.880021	+	0.474935i
$2$	−1.24454	+	0.671660i	−0.880021	+	0.474935i
$3$	−0.586217	−	1.62983i	−0.338453	−	0.940983i
$3$	−0.586217	−	1.62983i	−0.338453	−	0.940983i
$4$	1.09775	−	1.67181i	0.548873	−	0.835906i
$5$	−2.16781	+	1.25159i	−0.969474	+	0.559726i	−0.899076	−	0.437793i	$-0.855760\pi$
$5$	−2.16781	+	1.25159i	−0.969474	+	0.559726i	−0.0703980	+	0.997519i	$0.522427\pi$
$6$	1.82426	+	1.63465i	0.744751	+	0.667342i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	−0.243298	+	2.81794i	−0.0860189	+	0.996294i
$9$	−2.31270	+	1.91087i	−0.770900	+	0.636957i
$10$	1.85728	−	3.01367i	0.587324	−	0.953008i
$11$	0.351433	−	0.608700i	0.105961	−	0.183530i	−0.808169	−	0.588950i	$-0.799541\pi$
$11$	0.351433	−	0.608700i	0.105961	−	0.183530i	0.914130	+	0.405420i	$0.132875\pi$
$12$	−3.36829	−	0.809097i	−0.972341	−	0.233566i
$13$	1.55324	+	2.69030i	0.430792	+	0.746154i	0.996942	−	0.0781487i	$-0.0249009\pi$
$13$	1.55324	+	2.69030i	0.430792	+	0.746154i	−0.566150	+	0.824302i	$0.691568\pi$
$14$	1.41363	+	0.0405943i	0.377809	+	0.0108493i
$15$	3.31068	+	2.79946i	0.854814	+	0.722818i
$16$	−1.58991	−	3.67045i	−0.397476	−	0.917612i
$17$			7.91554i			1.91980i	0.280343	+	0.959900i	$0.409552\pi$
$17$			7.91554i			1.91980i	−0.280343	+	0.959900i	$0.590448\pi$
$18$	1.59479	−	3.93150i	0.375895	−	0.926662i
$19$			2.37413i			0.544662i	0.962204	+	0.272331i	$0.0877945\pi$
$19$			2.37413i			0.544662i	−0.962204	+	0.272331i	$0.912205\pi$
$20$	−0.287291	+	4.99809i	−0.0642401	+	1.11761i
$21$	−0.307237	+	1.70458i	−0.0670445	+	0.371971i
$22$	−0.0285324	+	0.993594i	−0.00608312	+	0.211835i
$23$	0.346619	+	0.600362i	0.0722751	+	0.125184i	0.899898	−	0.436100i	$-0.143641\pi$
$23$	0.346619	+	0.600362i	0.0722751	+	0.125184i	−0.827623	+	0.561284i	$0.810307\pi$
$24$	4.73540	−	1.25539i	0.966609	−	0.256256i
$25$	0.632931	−	1.09627i	0.126586	−	0.219254i
$26$	−3.74003	−	2.30492i	−0.733481	−	0.452033i
$27$	4.47014	+	2.64912i	0.860279	+	0.509824i
$28$	−1.78658	+	0.898958i	−0.337632	+	0.169887i
$29$	−8.70126	−	5.02368i	−1.61578	−	0.932873i	−0.987994	−	0.154490i	$-0.950627\pi$
$29$	−8.70126	−	5.02368i	−1.61578	−	0.932873i	−0.627789	−	0.778383i	$-0.716040\pi$
$30$	−6.00055	−	1.26039i	−1.09555	−	0.230114i
$31$	−7.34846	+	4.24264i	−1.31982	+	0.762000i	−0.983700	−	0.179818i	$-0.942449\pi$
$31$	−7.34846	+	4.24264i	−1.31982	+	0.762000i	−0.336123	+	0.941818i	$0.609116\pi$
$32$	4.44399	+	3.50014i	0.785594	+	0.618743i
$33$	−1.19809	−	0.215946i	−0.208561	−	0.0375914i
$34$	−5.31655	−	9.85118i	−0.911780	−	1.68946i
$35$	2.50317			0.423113
$36$	0.655856	+	5.96405i	0.109309	+	0.994008i
$37$	2.85107			0.468712			0.234356	−	0.972151i	$-0.424702\pi$
$37$	2.85107			0.468712			0.234356	+	0.972151i	$0.424702\pi$
$38$	−1.59460	−	2.95469i	−0.258679	−	0.479314i
$39$	3.47419	−	4.10862i	0.556316	−	0.657906i
$40$	−2.99947	−	6.41327i	−0.474258	−	1.01403i
$41$	5.82034	−	3.36037i	0.908984	−	0.524802i	0.0288798	−	0.999583i	$-0.490806\pi$
$41$	5.82034	−	3.36037i	0.908984	−	0.524802i	0.880104	+	0.474781i	$0.157473\pi$
$42$	−0.762533	−	2.32778i	−0.117661	−	0.359184i
$43$	−3.17043	−	1.83045i	−0.483485	−	0.279140i	0.238383	−	0.971171i	$-0.423383\pi$
$43$	−3.17043	−	1.83045i	−0.483485	−	0.279140i	−0.721868	+	0.692031i	$0.756716\pi$
$44$	−0.631847	−	1.25573i	−0.0952545	−	0.189308i
$45$	2.62187	−	7.03694i	0.390846	−	1.04901i
$46$	−0.834620	−	0.514363i	−0.123058	−	0.0758387i
$47$	−3.67787	+	6.37026i	−0.536473	+	0.929198i	0.462618	+	0.886558i	$0.346910\pi$
$47$	−3.67787	+	6.37026i	−0.536473	+	0.929198i	−0.999091	+	0.0426400i	$0.986423\pi$
$48$	−5.05018	+	4.74296i	−0.728931	+	0.684587i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−0.0513868	+	1.78946i	−0.00726719	+	0.253068i
$51$	12.9010	−	4.64022i	1.80650	−	0.649761i
$52$	6.20273	+	0.356534i	0.860164	+	0.0494423i
$53$			0.889576i			0.122193i	0.998132	+	0.0610964i	$0.0194597\pi$
$53$			0.889576i			0.122193i	−0.998132	+	0.0610964i	$0.980540\pi$
$54$	−7.34256	−	0.294523i	−0.999196	−	0.0400795i
$55$			1.75939i			0.237237i
$56$	1.61967	−	2.31876i	0.216438	−	0.309858i
$57$	3.86942	−	1.39175i	0.512518	−	0.184342i
$58$	14.2032	+	0.407865i	1.86498	+	0.0535553i
$59$	−3.63052	−	6.28824i	−0.472653	−	0.818660i	0.526857	−	0.849954i	$-0.323370\pi$
$59$	−3.63052	−	6.28824i	−0.472653	−	0.818660i	−0.999510	+	0.0312945i	$0.990037\pi$
$60$	8.31446	−	2.46173i	1.07339	−	0.317808i
$61$	−2.39732	+	4.15228i	−0.306946	+	0.531645i	−0.977693	−	0.210041i	$-0.932640\pi$
$61$	−2.39732	+	4.15228i	−0.306946	+	0.531645i	0.670747	+	0.741686i	$0.265974\pi$
$62$	6.29583	−	10.2158i	0.799571	−	1.29741i
$63$	2.95829	−	0.498512i	0.372710	−	0.0628066i
$64$	−7.88161	−	1.37120i	−0.985201	−	0.171400i
$65$	−6.73427	−	3.88803i	−0.835283	−	0.482251i
$66$	1.63612	−	0.535959i	0.201392	−	0.0659719i
$67$	7.40811	−	4.27707i	0.905044	−	0.522528i	0.0262109	−	0.999656i	$-0.491656\pi$
$67$	7.40811	−	4.27707i	0.905044	−	0.522528i	0.878833	+	0.477129i	$0.158323\pi$
$68$	13.2333	+	8.68925i	1.60477	+	1.05373i
$69$	0.775295	−	0.916874i	0.0933345	−	0.110379i
$70$	−3.11529	+	1.68128i	−0.372348	+	0.200951i
$71$	−6.34514			−0.753030			−0.376515	−	0.926411i	$-0.622878\pi$
$71$	−6.34514			−0.753030			−0.376515	+	0.926411i	$0.622878\pi$
$72$	−4.82205	−	6.98197i	−0.568284	−	0.822833i
$73$	8.20222			0.959998			0.479999	−	0.877269i	$-0.340637\pi$
$73$	8.20222			0.959998			0.479999	+	0.877269i	$0.340637\pi$
$74$	−3.54826	+	1.91495i	−0.412477	+	0.222608i
$75$	−2.15777	−	0.388920i	−0.249158	−	0.0449086i
$76$	3.96909	+	2.60619i	0.455286	+	0.298950i
$77$	−0.608700	+	0.351433i	−0.0693678	+	0.0400495i
$78$	−1.56416	+	7.44681i	−0.177107	+	0.843185i
$79$	−2.27268	−	1.31214i	−0.255697	−	0.147627i	0.366673	−	0.930350i	$-0.380497\pi$
$79$	−2.27268	−	1.31214i	−0.255697	−	0.147627i	−0.622370	+	0.782723i	$0.713830\pi$
$80$	8.04049	+	5.96693i	0.898954	+	0.667123i
$81$	1.69715	−	8.83853i	0.188573	−	0.982059i
$82$	−4.98660	+	8.09139i	−0.550678	+	0.893545i
$83$	6.50432	−	11.2658i	0.713942	−	1.23658i	−0.249425	−	0.968394i	$-0.580241\pi$
$83$	6.50432	−	11.2658i	0.713942	−	1.23658i	0.963366	−	0.268189i	$-0.0864252\pi$
$84$	2.51247	+	2.38484i	0.274133	+	0.260208i
$85$	−9.90697	−	17.1594i	−1.07456	−	1.86120i
$86$	5.17515	+	0.148611i	0.558051	+	0.0160252i
$87$	−3.08692	+	17.1266i	−0.330952	+	1.83616i
$88$	1.62978	+	1.13841i	0.173735	+	0.121355i
$89$			1.71842i			0.182152i	0.995844	+	0.0910760i	$0.0290306\pi$
$89$			1.71842i			0.182152i	−0.995844	+	0.0910760i	$0.970969\pi$
$90$	1.46341	+	10.5187i	0.154257	+	1.10877i
$91$		−	3.10649i		−	0.325648i
$92$	1.38419	+	0.0795635i	0.144312	+	0.00829507i
$93$	11.2226	+	9.48965i	1.16373	+	0.984031i
$94$	0.298601	−	10.3983i	0.0307984	−	1.07250i
$95$	−2.97142	−	5.14665i	−0.304861	−	0.528035i
$96$	3.09949	−	9.29479i	0.316340	−	0.948646i
$97$	−6.81083	+	11.7967i	−0.691535	+	1.19777i	0.279800	+	0.960058i	$0.409732\pi$
$97$	−6.81083	+	11.7967i	−0.691535	+	1.19777i	−0.971335	+	0.237716i	$0.923601\pi$
$98$	−1.20394	−	0.741971i	−0.121617	−	0.0749504i
$99$	0.350387	+	2.07928i	0.0352153	+	0.208976i
$100$	−1.13796	−	2.26157i	−0.113796	−	0.226157i
$101$	2.23784	+	1.29202i	0.222673	+	0.128560i	0.607187	−	0.794559i	$-0.292298\pi$
$101$	2.23784	+	1.29202i	0.222673	+	0.128560i	−0.384514	+	0.923119i	$0.625631\pi$
$102$	−12.9391	+	14.4400i	−1.28116	+	1.42977i
$103$	−11.6579	+	6.73069i	−1.14869	+	0.663195i	−0.948567	−	0.316576i	$-0.897467\pi$
$103$	−11.6579	+	6.73069i	−1.14869	+	0.663195i	−0.200120	+	0.979771i	$0.564133\pi$
$104$	−7.95900	+	3.72241i	−0.780444	+	0.365012i
$105$	−1.46740	−	4.07975i	−0.143204	−	0.398142i
$106$	−0.597493	−	1.10711i	−0.0580336	−	0.107532i
$107$	−17.0371			−1.64703			−0.823517	−	0.567291i	$-0.807991\pi$
$107$	−17.0371			−1.64703			−0.823517	+	0.567291i	$0.807991\pi$
$108$	9.33592	−	4.56516i	0.898349	−	0.439283i
$109$	−2.43459			−0.233191			−0.116596	−	0.993179i	$-0.537198\pi$
$109$	−2.43459			−0.233191			−0.116596	+	0.993179i	$0.537198\pi$
$110$	−1.18171	−	2.18963i	−0.112672	−	0.208773i
$111$	−1.67134	−	4.64675i	−0.158637	−	0.441050i
$112$	−0.458326	+	3.97366i	−0.0433078	+	0.375475i
$113$	−4.13789	+	2.38901i	−0.389260	+	0.224739i	−0.681839	−	0.731502i	$-0.738820\pi$
$113$	−4.13789	+	2.38901i	−0.389260	+	0.224739i	0.292580	+	0.956241i	$0.405486\pi$
$114$	−3.88086	+	4.33103i	−0.363476	+	0.405638i
$115$	−1.50281	−	0.867647i	−0.140138	−	0.0809085i
$116$	−17.9504	+	9.03215i	−1.66665	+	0.838614i
$117$	−8.73299	−	3.25380i	−0.807365	−	0.300814i
$118$	8.74188	+	5.38748i	0.804755	+	0.495958i
$119$	3.95777	−	6.85506i	0.362808	−	0.628402i
$120$	−8.69421	+	8.64820i	−0.793669	+	0.789469i
$121$	5.25299	+	9.09844i	0.477544	+	0.827131i
$122$	0.194635	−	6.77786i	0.0176214	−	0.613638i
$123$	−8.88882	−	7.51626i	−0.801478	−	0.677718i
$124$	−0.973861	+	16.9426i	−0.0874553	+	1.52149i
$125$		−	9.34718i		−	0.836037i
$126$	−3.34687	+	2.60738i	−0.298163	+	0.232284i
$127$			4.91393i			0.436041i	0.975944	+	0.218020i	$0.0699599\pi$
$127$			4.91393i			0.436041i	−0.975944	+	0.218020i	$0.930040\pi$
$128$	10.7299	−	3.58725i	0.948402	−	0.317071i
$129$	−1.12476	+	6.24030i	−0.0990296	+	0.549427i
$130$	10.9925	+	0.315664i	0.964105	+	0.0276855i
$131$	2.61968	+	4.53741i	0.228882	+	0.396435i	0.957477	−	0.288509i	$-0.0931596\pi$
$131$	2.61968	+	4.53741i	0.228882	+	0.396435i	−0.728595	+	0.684945i	$0.759826\pi$
$132$	−1.67623	+	1.76593i	−0.145897	+	0.153705i
$133$	1.18706	−	2.05605i	0.102931	−	0.178282i
$134$	−6.34693	+	10.2987i	−0.548291	+	0.889672i
$135$	−13.0060	−	0.148038i	−1.11938	−	0.0127411i
$136$	−22.3055	−	1.92584i	−1.91268	−	0.165139i
$137$	9.03659	+	5.21728i	0.772048	+	0.445742i	0.833605	−	0.552361i	$-0.186273\pi$
$137$	9.03659	+	5.21728i	0.772048	+	0.445742i	−0.0615566	+	0.998104i	$0.519606\pi$
$138$	−0.349056	+	1.66182i	−0.0297137	+	0.141463i
$139$	−10.2848	+	5.93796i	−0.872349	+	0.503651i	−0.868128	−	0.496340i	$-0.834677\pi$
$139$	−10.2848	+	5.93796i	−0.872349	+	0.503651i	−0.00422072	+	0.999991i	$0.501344\pi$
$140$	2.74785	−	4.18483i	0.232235	−	0.353683i
$141$	12.5385	+	2.25995i	1.05593	+	0.190322i
$142$	7.89677	−	4.26178i	0.662682	−	0.357640i
$143$	2.18344			0.182589
$144$	10.6907	+	5.45054i	0.890894	+	0.454212i
$145$	25.1502			2.08861
$146$	−10.2080	+	5.50910i	−0.844818	+	0.455937i
$147$	1.11837	−	1.32259i	0.0922413	−	0.109086i
$148$	3.12975	−	4.76644i	0.257264	−	0.391799i
$149$	15.3300	−	8.85079i	1.25588	−	0.725085i	0.283612	−	0.958939i	$-0.408467\pi$
$149$	15.3300	−	8.85079i	1.25588	−	0.725085i	0.972272	+	0.233854i	$0.0751337\pi$
$150$	2.94665	−	0.965262i	0.240593	−	0.0788133i
$151$	18.1796	+	10.4960i	1.47944	+	0.854152i	0.999729	−	0.0232767i	$-0.00740988\pi$
$151$	18.1796	+	10.4960i	1.47944	+	0.854152i	0.479706	+	0.877429i	$0.340743\pi$
$152$	−6.69015	−	0.577621i	−0.542643	−	0.0468512i
$153$	−15.1256	−	18.3063i	−1.22283	−	1.47997i
$154$	0.521507	−	0.846211i	0.0420242	−	0.0681896i
$155$	10.6200	−	18.3945i	0.853022	−	1.47748i
$156$	−3.05506	−	10.3184i	−0.244600	−	0.826134i
$157$	−0.841990	−	1.45837i	−0.0671981	−	0.116391i	0.830469	−	0.557065i	$-0.188073\pi$
$157$	−0.841990	−	1.45837i	−0.0671981	−	0.116391i	−0.897667	+	0.440675i	$0.854739\pi$
$158$	3.70975	+	0.106530i	0.295132	+	0.00847510i
$159$	1.44986	−	0.521485i	0.114981	−	0.0413564i
$160$	−14.0144	−	2.02560i	−1.10794	−	0.160137i
$161$		−	0.693239i		−	0.0546349i
$162$	3.82431	+	12.1398i	0.300467	+	0.953792i
$163$			14.9299i			1.16940i	0.811249	+	0.584700i	$0.198788\pi$
$163$			14.9299i			1.16940i	−0.811249	+	0.584700i	$0.801212\pi$
$164$	0.771345	−	13.4193i	0.0602319	−	1.04787i
$165$	2.86752	−	1.03139i	0.223236	−	0.0802934i
$166$	−0.528076	+	18.3894i	−0.0409867	+	1.42729i
$167$	−1.17066	−	2.02764i	−0.0905885	−	0.156904i	0.817170	−	0.576396i	$-0.195541\pi$
$167$	−1.17066	−	2.02764i	−0.0905885	−	0.156904i	−0.907759	+	0.419492i	$0.862208\pi$
$168$	−4.72867	−	1.28050i	−0.364825	−	0.0987926i
$169$	1.67487	−	2.90097i	0.128836	−	0.223151i
$170$	23.8549	+	14.7014i	1.82958	+	1.12754i
$171$	−4.53665	−	5.49064i	−0.346926	−	0.419880i
$172$	−6.54048	+	3.29099i	−0.498707	+	0.250935i
$173$	0.875908	+	0.505706i	0.0665940	+	0.0384481i	0.532927	−	0.846161i	$-0.321092\pi$
$173$	0.875908	+	0.505706i	0.0665940	+	0.0384481i	−0.466333	+	0.884609i	$0.654425\pi$
$174$	−7.66143	−	23.3880i	−0.580812	−	1.77304i
$175$	−1.09627	+	0.632931i	−0.0828702	+	0.0478451i
$176$	−2.79295	−	0.322142i	−0.210526	−	0.0242824i
$177$	−8.12050	+	9.60341i	−0.610374	+	0.721836i
$178$	−1.15419	−	2.13864i	−0.0865104	−	0.160298i
$179$	11.8651			0.886837			0.443419	−	0.896315i	$-0.353765\pi$
$179$	11.8651			0.886837			0.443419	+	0.896315i	$0.353765\pi$
$180$	−8.88628	−	12.1081i	−0.662344	−	0.902481i
$181$	−11.7216			−0.871262			−0.435631	−	0.900125i	$-0.643475\pi$
$181$	−11.7216			−0.871262			−0.435631	+	0.900125i	$0.643475\pi$
$182$	2.08650	+	3.86614i	0.154662	+	0.286577i
$183$	8.17287	+	1.47309i	0.604156	+	0.108894i
$184$	−1.77612	+	0.830687i	−0.130937	+	0.0612390i
$185$	−6.18057	+	3.56835i	−0.454404	+	0.262350i
$186$	−20.3407	−	4.27247i	−1.49145	−	0.313273i
$187$	4.81819	+	2.78178i	0.352341	+	0.203424i
$188$	6.61250	+	13.1416i	0.482266	+	0.958452i
$189$	−2.54669	−	4.52928i	−0.185245	−	0.329457i
$190$	7.15484	+	4.40942i	0.519067	+	0.319893i
$191$	−3.38132	+	5.85662i	−0.244664	+	0.423770i	−0.962037	−	0.272919i	$-0.912011\pi$
$191$	−3.38132	+	5.85662i	−0.244664	+	0.423770i	0.717373	+	0.696689i	$0.245344\pi$
$192$	2.38551	+	13.6495i	0.172159	+	0.985069i
$193$	−1.38307	−	2.39554i	−0.0995553	−	0.172435i	0.811945	−	0.583733i	$-0.198409\pi$
$193$	−1.38307	−	2.39554i	−0.0995553	−	0.172435i	−0.911501	+	0.411299i	$0.865075\pi$
$194$	0.552962	−	19.2560i	0.0397003	−	1.38250i
$195$	−2.38909	+	13.2550i	−0.171086	+	0.949207i
$196$	1.99670	+	0.114771i	0.142622	+	0.00819791i
$197$			17.2636i			1.22998i	0.788536	+	0.614989i	$0.210839\pi$
$197$			17.2636i			1.22998i	−0.788536	+	0.614989i	$0.789161\pi$
$198$	−1.83264	−	2.35240i	−0.130240	−	0.167178i
$199$		−	14.4922i		−	1.02732i	−0.857993	−	0.513662i	$-0.828289\pi$
$199$		−	14.4922i		−	1.02732i	0.857993	−	0.513662i	$-0.171711\pi$
$200$	2.93523	+	2.05029i	0.207552	+	0.144977i
$201$	−11.3137	−	9.56667i	−0.798004	−	0.674781i
$202$	−3.65287	−	0.104897i	−0.257015	−	0.00738052i
$203$	5.02368	+	8.70126i	0.352593	+	0.610709i
$204$	6.40444	−	26.6618i	0.448400	−	1.86670i
$205$	−8.41159	+	14.5693i	−0.587491	+	1.01756i
$206$	9.98796	−	16.2067i	0.695894	−	1.12918i
$207$	−1.94884	−	0.726113i	−0.135454	−	0.0504683i
$208$	7.40509	−	9.97842i	0.513450	−	0.691879i
$209$	1.44513	+	0.834347i	0.0999618	+	0.0577130i
$210$	4.56644	+	4.09180i	0.315114	+	0.282361i
$211$	22.1795	−	12.8053i	1.52690	−	0.881555i	0.527407	−	0.849612i	$-0.323164\pi$
$211$	22.1795	−	12.8053i	1.52690	−	0.881555i	0.999490	−	0.0319420i	$-0.0101692\pi$
$212$	1.48720	+	0.976529i	0.102142	+	0.0670683i
$213$	3.71963	+	10.3415i	0.254865	+	0.708589i
$214$	21.2033	−	11.4431i	1.44942	−	0.782235i
$215$	9.16384			0.624968
$216$	−8.55266	+	11.9521i	−0.581935	+	0.813235i
$217$	8.48527			0.576018
$218$	3.02994	−	1.63522i	0.205213	−	0.110751i
$219$	−4.80828	−	13.3682i	−0.324914	−	0.903342i
$220$	2.94138	+	1.93137i	0.198307	+	0.130213i
$221$	−21.2951	+	12.2948i	−1.43247	+	0.827035i
$222$	5.20109	+	4.66049i	0.349074	+	0.312791i
$223$	13.2137	+	7.62891i	0.884853	+	0.510870i	0.872255	−	0.489051i	$-0.162657\pi$
$223$	13.2137	+	7.62891i	0.884853	+	0.510870i	0.0125973	+	0.999921i	$0.495990\pi$
$224$	−2.09854	−	5.25320i	−0.140215	−	0.350994i
$225$	0.631048	+	3.74479i	0.0420699	+	0.249653i
$226$	3.54515	−	5.75247i	0.235820	−	0.382648i
$227$	−3.88279	+	6.72519i	−0.257710	+	0.446367i	−0.965628	−	0.259928i	$-0.916301\pi$
$227$	−3.88279	+	6.72519i	−0.257710	+	0.446367i	0.707918	+	0.706295i	$0.249635\pi$
$228$	1.92090	−	7.99674i	0.127215	−	0.529597i
$229$	−5.70048	−	9.87351i	−0.376698	−	0.652460i	0.613882	−	0.789398i	$-0.289607\pi$
$229$	−5.70048	−	9.87351i	−0.376698	−	0.652460i	−0.990580	+	0.136938i	$0.956274\pi$
$230$	2.45307	+	0.0704431i	0.161750	+	0.00464488i
$231$	0.929607	+	0.786062i	0.0611637	+	0.0517191i
$232$	16.2734	−	23.2974i	1.06840	−	1.52955i
$233$		−	19.4113i		−	1.27167i	−0.771824	−	0.635837i	$-0.780655\pi$
$233$		−	19.4113i		−	1.27167i	0.771824	−	0.635837i	$-0.219345\pi$
$234$	13.0540	−	1.81612i	0.853365	−	0.118724i
$235$		−	18.4127i		−	1.20111i
$236$	−14.4981	−	0.833354i	−0.943749	−	0.0542467i
$237$	−0.806272	+	4.47329i	−0.0523730	+	0.290571i
$238$	−0.321326	+	11.1896i	−0.0208284	+	0.725317i
$239$	3.57434	+	6.19093i	0.231205	+	0.400458i	0.958163	−	0.286224i	$-0.0924000\pi$
$239$	3.57434	+	6.19093i	0.231205	+	0.400458i	−0.726958	+	0.686682i	$0.759067\pi$
$240$	5.01162	−	16.6026i	0.323499	−	1.07169i
$241$	−1.19735	+	2.07386i	−0.0771279	+	0.133589i	−0.902010	−	0.431716i	$-0.857908\pi$
$241$	−1.19735	+	2.07386i	−0.0771279	+	0.133589i	0.824882	+	0.565305i	$0.191242\pi$
$242$	−12.6486	−	7.79513i	−0.813083	−	0.501090i
$243$	−15.4002	+	2.41522i	−0.987924	+	0.154937i
$244$	4.31018	+	8.56602i	0.275931	+	0.548383i
$245$	−2.16781	−	1.25159i	−0.138496	−	0.0799609i
$246$	16.1108	+	3.38400i	1.02719	+	0.215756i
$247$	−6.38710	+	3.68759i	−0.406401	+	0.234636i
$248$	−10.1676	−	21.7398i	−0.645646	−	1.38048i
$249$	−22.1743	−	3.99673i	−1.40524	−	0.253283i
$250$	6.27813	+	11.6329i	0.397064	+	0.735730i
$251$	3.05973			0.193129			0.0965644	−	0.995327i	$-0.469215\pi$
$251$	3.05973			0.193129			0.0965644	+	0.995327i	$0.469215\pi$
$252$	2.41404	−	5.49294i	0.152070	−	0.346023i
$253$	0.487254			0.0306334
$254$	−3.30049	−	6.11557i	−0.207091	−	0.383725i
$255$	−22.1593	+	26.2058i	−1.38767	+	1.64107i
$256$	−10.9444	+	11.6713i	−0.684025	+	0.729459i
$257$	17.1928	−	9.92624i	1.07245	−	0.619182i	0.143603	−	0.989635i	$-0.454131\pi$
$257$	17.1928	−	9.92624i	1.07245	−	0.619182i	0.928851	+	0.370453i	$0.120798\pi$
$258$	−2.79155	−	8.52174i	−0.173794	−	0.530540i
$259$	−2.46909	−	1.42553i	−0.153422	−	0.0885783i
$260$	−13.8926	+	6.99035i	−0.861581	+	0.433523i
$261$	29.7230	−	5.00873i	1.83981	−	0.310032i
$262$	−6.30788	−	3.88745i	−0.389702	−	0.240167i
$263$	−9.51239	+	16.4759i	−0.586559	+	1.01595i	0.408120	+	0.912928i	$0.366184\pi$
$263$	−9.51239	+	16.4759i	−0.586559	+	1.01595i	−0.994679	+	0.103022i	$0.967149\pi$
$264$	0.900019	−	3.32362i	0.0553923	−	0.204555i
$265$	−1.11338	−	1.92843i	−0.0683944	−	0.118463i
$266$	−0.0963760	+	3.35614i	−0.00590919	+	0.205778i
$267$	2.80073	−	1.00737i	0.171402	−	0.0616498i
$268$	0.981765	−	17.0801i	0.0599708	−	1.04333i
$269$			27.0790i			1.65103i	0.564378	+	0.825517i	$0.309116\pi$
$269$			27.0790i			1.65103i	−0.564378	+	0.825517i	$0.690884\pi$
$270$	16.2859	−	8.55138i	0.991128	−	0.520420i
$271$		−	29.1249i		−	1.76921i	−0.466337	−	0.884607i	$-0.654427\pi$
$271$		−	29.1249i		−	1.76921i	0.466337	−	0.884607i	$-0.345573\pi$
$272$	29.0536	−	12.5850i	1.76163	−	0.763075i
$273$	−5.06305	+	1.82107i	−0.306430	+	0.110216i
$274$	−14.7506	−	0.423583i	−0.891117	−	0.0255896i
$275$	−0.444866	−	0.770531i	−0.0268264	−	0.0464648i
$276$	−0.681762	−	2.30264i	−0.0410373	−	0.138603i
$277$	8.22279	−	14.2423i	0.494060	−	0.855737i	−0.505917	−	0.862582i	$-0.668846\pi$
$277$	8.22279	−	14.2423i	0.494060	−	0.855737i	0.999977	+	0.00684565i	$0.00217905\pi$
$278$	8.81158	−	14.2979i	0.528484	−	0.857532i
$279$	8.88766	−	23.8539i	0.532090	−	1.42810i
$280$	−0.609017	+	7.05379i	−0.0363957	+	0.421545i
$281$	5.47490	+	3.16093i	0.326605	+	0.188566i	0.654333	−	0.756207i	$-0.272950\pi$
$281$	5.47490	+	3.16093i	0.326605	+	0.188566i	−0.327728	+	0.944772i	$0.606283\pi$
$282$	−17.1225	+	5.60899i	−1.01963	+	0.334011i
$283$	−7.14839	+	4.12712i	−0.424927	+	0.245332i	−0.697183	−	0.716893i	$-0.745564\pi$
$283$	−7.14839	+	4.12712i	−0.424927	+	0.245332i	0.272256	+	0.962225i	$0.412230\pi$
$284$	−6.96536	+	10.6079i	−0.413318	+	0.629462i
$285$	−6.64628	+	7.85997i	−0.393691	+	0.465584i
$286$	−2.71738	+	1.46653i	−0.160682	+	0.0867178i
$287$	−6.72075			−0.396713
$288$	−16.9659	+	0.397124i	−0.999726	+	0.0234007i
$289$	−45.6557			−2.68563
$290$	−31.3004	+	16.8924i	−1.83802	+	0.991956i
$291$	23.2193	+	4.18508i	1.36114	+	0.245333i
$292$	9.00396	−	13.7126i	0.526917	−	0.802467i
$293$	6.70404	−	3.87058i	0.391654	−	0.226122i	−0.291222	−	0.956655i	$-0.594062\pi$
$293$	6.70404	−	3.87058i	0.391654	−	0.226122i	0.682877	+	0.730534i	$0.260729\pi$
$294$	−0.503516	+	2.39718i	−0.0293656	+	0.139806i
$295$	15.7405	+	9.08781i	0.916450	+	0.529113i
$296$	−0.693659	+	8.03414i	−0.0403181	+	0.466975i
$297$	3.18348	−	1.78998i	0.184724	−	0.103865i
$298$	−13.1341	+	21.3117i	−0.760836	+	1.23455i
$299$	−1.07677	+	1.86502i	−0.0622711	+	0.107857i
$300$	−3.01888	+	3.18045i	−0.174295	+	0.183623i
$301$	1.83045	+	3.17043i	0.105505	+	0.182740i
$302$	−29.6749	−	0.852155i	−1.70760	−	0.0490360i
$303$	0.793909	−	4.40470i	0.0456089	−	0.253043i
$304$	8.71411	−	3.77464i	0.499788	−	0.216490i
$305$		−	12.0018i		−	0.687222i
$306$	31.1199	+	12.6236i	1.77901	+	0.721643i
$307$		−	14.7032i		−	0.839154i	−0.907720	−	0.419577i	$-0.862178\pi$
$307$		−	14.7032i		−	0.839154i	0.907720	−	0.419577i	$-0.137822\pi$
$308$	−0.0806685	+	1.40342i	−0.00459651	+	0.0799671i
$309$	17.8040	+	15.0548i	1.01283	+	0.856436i
$310$	−0.862226	+	30.0256i	−0.0489712	+	1.70534i
$311$	6.26710	+	10.8549i	0.355375	+	0.615527i	0.987182	−	0.159599i	$-0.0510200\pi$
$311$	6.26710	+	10.8549i	0.355375	+	0.615527i	−0.631807	+	0.775125i	$0.717687\pi$
$312$	10.7326	+	10.7897i	0.607614	+	0.610846i
$313$	−11.6110	+	20.1108i	−0.656292	+	1.13673i	0.325276	+	0.945619i	$0.394543\pi$
$313$	−11.6110	+	20.1108i	−0.656292	+	1.13673i	−0.981568	+	0.191112i	$0.938790\pi$
$314$	2.02742	+	1.24946i	0.114414	+	0.0705113i
$315$	−5.78908	+	4.78323i	−0.326178	+	0.269505i
$316$	−4.68847	+	2.35911i	−0.263747	+	0.132710i
$317$	5.93134	+	3.42446i	0.333137	+	0.192337i	0.657233	−	0.753687i	$-0.271727\pi$
$317$	5.93134	+	3.42446i	0.333137	+	0.192337i	−0.324096	+	0.946024i	$0.605060\pi$
$318$	−1.45414	+	1.62282i	−0.0815443	+	0.0910032i
$319$	−6.11582	+	3.53097i	−0.342420	+	0.197697i
$320$	18.8020	−	6.89201i	1.05106	−	0.385275i
$321$	9.98741	+	27.7675i	0.557443	+	1.54983i
$322$	0.465620	+	0.862761i	0.0259480	+	0.0480798i
$323$	−18.7925			−1.04564
$324$	−12.9133	−	12.5398i	−0.717406	−	0.696655i
$325$	3.93239			0.218129
$326$	−10.0278	−	18.5808i	−0.555389	−	1.02910i
$327$	1.42720	+	3.96797i	0.0789242	+	0.219429i
$328$	8.05326	+	17.2190i	0.444667	+	0.950758i
$329$	6.37026	−	3.67787i	0.351204	−	0.202768i
$330$	−2.87599	+	3.20959i	−0.158318	+	0.176682i
$331$	6.98234	+	4.03126i	0.383784	+	0.221578i	0.679463	−	0.733709i	$-0.262213\pi$
$331$	6.98234	+	4.03126i	0.383784	+	0.221578i	−0.295679	+	0.955287i	$0.595546\pi$
$332$	−11.6942	−	23.2410i	−0.641803	−	1.27552i
$333$	−6.59366	+	5.44801i	−0.361330	+	0.298549i
$334$	2.81882	+	1.73719i	0.154239	+	0.0950550i
$335$	−10.7062	+	18.5438i	−0.584944	+	1.01315i
$336$	6.74507	−	1.58243i	0.367974	−	0.0863286i
$337$	−8.08375	−	14.0015i	−0.440350	−	0.762708i	0.557365	−	0.830267i	$-0.311812\pi$
$337$	−8.08375	−	14.0015i	−0.440350	−	0.762708i	−0.997715	+	0.0675590i	$0.978479\pi$
$338$	−0.135981	+	4.73530i	−0.00739637	+	0.257567i
$339$	6.31939	+	5.34358i	0.343222	+	0.290223i
$340$	−39.5626	−	2.27406i	−2.14558	−	0.123328i
$341$			5.96401i			0.322969i
$342$	9.33387	+	3.78622i	0.504718	+	0.204736i
$343$		−	1.00000i		−	0.0539949i
$344$	5.92945	−	8.48873i	0.319695	−	0.457682i
$345$	−0.533146	+	2.95795i	−0.0287036	+	0.159251i
$346$	−1.42976	−	0.0410575i	−0.0768645	−	0.00220727i
$347$	3.82900	+	6.63203i	0.205552	+	0.356026i	0.950308	−	0.311310i	$-0.100768\pi$
$347$	3.82900	+	6.63203i	0.205552	+	0.356026i	−0.744757	+	0.667336i	$0.767434\pi$
$348$	25.2437	+	23.9614i	1.35321	+	1.28446i
$349$	4.40927	−	7.63708i	0.236023	−	0.408803i	−0.723547	−	0.690275i	$-0.757489\pi$
$349$	4.40927	−	7.63708i	0.236023	−	0.408803i	0.959569	+	0.281472i	$0.0908227\pi$
$350$	0.939234	−	1.52403i	0.0502042	−	0.0814627i
$351$	−0.183718	+	16.1407i	−0.00980613	+	0.861528i
$352$	3.69230	−	1.47499i	0.196800	−	0.0786174i
$353$	−2.81435	−	1.62487i	−0.149793	−	0.0864830i	0.423230	−	0.906022i	$-0.360896\pi$
$353$	−2.81435	−	1.62487i	−0.149793	−	0.0864830i	−0.573023	+	0.819539i	$0.694229\pi$
$354$	3.65605	−	17.4060i	0.194317	−	0.925119i
$355$	13.7551	−	7.94149i	0.730043	−	0.421490i
$356$	2.87287	+	1.88639i	0.152262	+	0.0999783i
$357$	−13.4927	−	2.43194i	−0.714109	−	0.128712i
$358$	−14.7665	+	7.96929i	−0.780435	+	0.421190i
$359$	28.4033			1.49907			0.749533	−	0.661967i	$-0.230278\pi$
$359$	28.4033			1.49907			0.749533	+	0.661967i	$0.230278\pi$
$360$	19.1918	+	9.10037i	1.01150	+	0.479632i
$361$	13.3635			0.703343
$362$	14.5880	−	7.87295i	0.766729	−	0.413793i
$363$	11.7495	−	13.8951i	0.616691	−	0.729306i
$364$	−5.19346	−	3.41013i	−0.272211	−	0.178740i
$365$	−17.7809	+	10.2658i	−0.930692	+	0.537336i
$366$	−11.1609	+	3.65607i	−0.583387	+	0.191106i
$367$	−4.00164	−	2.31035i	−0.208884	−	0.120599i	0.391909	−	0.920004i	$-0.371815\pi$
$367$	−4.00164	−	2.31035i	−0.208884	−	0.120599i	−0.600793	+	0.799405i	$0.705148\pi$
$368$	1.65251	−	2.22677i	0.0861429	−	0.116078i
$369$	−7.03945	+	18.8934i	−0.366459	+	0.983553i
$370$	5.29523	−	8.59218i	0.275286	−	0.446686i
$371$	0.444788	−	0.770396i	0.0230923	−	0.0399970i
$372$	28.1844	−	8.34480i	1.46130	−	0.432658i
$373$	−13.7859	−	23.8779i	−0.713808	−	1.23635i	−0.963417	−	0.268005i	$-0.913636\pi$
$373$	−13.7859	−	23.8779i	−0.713808	−	1.23635i	0.249609	−	0.968347i	$-0.419698\pi$
$374$	−7.86483	−	0.225849i	−0.406681	−	0.0116784i
$375$	−15.2343	+	5.47948i	−0.786697	+	0.282959i
$376$	−17.0562	−	11.9139i	−0.879607	−	0.614413i
$377$		−	31.2120i		−	1.60750i
$378$	6.21159	+	3.92635i	0.319490	+	0.201949i
$379$		−	20.5766i		−	1.05695i	−0.848949	−	0.528475i	$-0.822764\pi$
$379$		−	20.5766i		−	1.05695i	0.848949	−	0.528475i	$-0.177236\pi$
$380$	−11.8661	−	0.682064i	−0.608718	−	0.0349892i
$381$	8.00888	−	2.88063i	0.410307	−	0.147579i
$382$	0.274525	−	9.55988i	0.0140459	−	0.489126i
$383$	0.0457558	+	0.0792514i	0.00233801	+	0.00404955i	0.867192	−	0.497974i	$-0.165922\pi$
$383$	0.0457558	+	0.0792514i	0.00233801	+	0.00404955i	−0.864854	+	0.502023i	$0.832589\pi$
$384$	−12.1367	−	15.3851i	−0.619348	−	0.785117i
$385$	0.879697	−	1.52368i	0.0448335	−	0.0776539i
$386$	3.33027	+	2.05239i	0.169506	+	0.104464i
$387$	10.8300	−	1.82500i	0.550519	−	0.0927699i
$388$	12.2453	+	24.3362i	0.621661	+	1.23548i
$389$	−1.65481	−	0.955404i	−0.0839021	−	0.0484409i	0.457462	−	0.889229i	$-0.348759\pi$
$389$	−1.65481	−	0.955404i	−0.0839021	−	0.0484409i	−0.541364	+	0.840788i	$0.682092\pi$
$390$	−5.92950	−	18.1009i	−0.300252	−	0.916577i
$391$	−4.75219	+	2.74368i	−0.240329	+	0.138754i
$392$	−2.56206	+	1.19827i	−0.129404	+	0.0605217i
$393$	5.85951	−	6.92954i	0.295573	−	0.349549i
$394$	−11.5952	−	21.4851i	−0.584160	−	1.08241i
$395$	6.56900			0.330522
$396$	3.86081	+	1.69674i	0.194013	+	0.0852646i
$397$	30.4353			1.52750			0.763751	−	0.645511i	$-0.223355\pi$
$397$	30.4353			1.52750			0.763751	+	0.645511i	$0.223355\pi$
$398$	9.73382	+	18.0361i	0.487912	+	0.904066i
$399$	−4.04690	−	0.729419i	−0.202598	−	0.0365166i
$400$	−5.03010	−	0.580178i	−0.251505	−	0.0290089i
$401$	18.9221	−	10.9247i	0.944922	−	0.545551i	0.0534223	−	0.998572i	$-0.482987\pi$
$401$	18.9221	−	10.9247i	0.944922	−	0.545551i	0.891500	+	0.453021i	$0.149654\pi$
$402$	20.5058	+	4.30715i	1.02274	+	0.214821i
$403$	−22.8279	−	13.1797i	−1.13714	−	0.656527i
$404$	4.61658	−	2.32294i	0.229684	−	0.115570i
$405$	7.38307	+	21.2844i	0.366868	+	1.05763i
$406$	−12.0964	−	7.45484i	−0.600336	−	0.369978i
$407$	1.00196	−	1.73544i	0.0496653	−	0.0860228i
$408$	9.93710	+	37.4832i	0.491960	+	1.85570i
$409$	2.23786	+	3.87609i	0.110655	+	0.191660i	0.916035	−	0.401099i	$-0.131372\pi$
$409$	2.23786	+	3.87609i	0.110655	+	0.191660i	−0.805379	+	0.592760i	$0.798038\pi$
$410$	0.682925	−	23.7818i	0.0337273	−	1.17450i
$411$	3.20588	−	17.7866i	0.158134	−	0.877347i
$412$	−1.54497	+	26.8784i	−0.0761154	+	1.32420i
$413$			7.26104i			0.357292i
$414$	2.91311	−	0.405283i	0.143171	−	0.0199186i
$415$			32.5628i			1.59845i
$416$	−2.51381	+	17.3922i	−0.123249	+	0.852723i
$417$	15.7070	+	13.2816i	0.769176	+	0.650404i
$418$	−2.35892	−	0.0677394i	−0.115378	−	0.00331324i
$419$	11.4022	+	19.7492i	0.557033	+	0.964809i	0.997742	+	0.0671595i	$0.0213936\pi$
$419$	11.4022	+	19.7492i	0.557033	+	0.964809i	−0.440709	+	0.897650i	$0.645273\pi$
$420$	−8.43140	−	2.02531i	−0.411410	−	0.0988249i
$421$	−14.0510	+	24.3370i	−0.684803	+	1.18611i	0.288696	+	0.957421i	$0.406778\pi$
$421$	−14.0510	+	24.3370i	−0.684803	+	1.18611i	−0.973499	+	0.228693i	$0.926555\pi$
$422$	−19.0024	+	30.8337i	−0.925020	+	1.50096i
$423$	−3.66693	−	21.7604i	−0.178292	−	1.05803i
$424$	−2.50678	−	0.216432i	−0.121740	−	0.0105109i
$425$	8.67756	+	5.00999i	0.420924	+	0.243020i
$426$	−11.5752	−	10.3721i	−0.560820	−	0.502528i
$427$	4.15228	−	2.39732i	0.200943	−	0.116015i
$428$	−18.7024	+	28.4827i	−0.904013	+	1.37677i
$429$	−1.27997	−	3.55865i	−0.0617976	−	0.171813i
$430$	−11.4047	+	6.15498i	−0.549985	+	0.296819i
$431$	0.610755			0.0294190			0.0147095	−	0.999892i	$-0.495318\pi$
$431$	0.610755			0.0294190			0.0147095	+	0.999892i	$0.495318\pi$
$432$	2.61638	−	20.6193i	0.125881	−	0.992045i
$433$	10.5169			0.505410			0.252705	−	0.967543i	$-0.418680\pi$
$433$	10.5169			0.505410			0.252705	+	0.967543i	$0.418680\pi$
$434$	−10.5602	+	5.69922i	−0.506908	+	0.273571i
$435$	−14.7435	−	40.9906i	−0.706897	−	1.96535i
$436$	−2.67256	+	4.07017i	−0.127993	+	0.194926i
$437$	−1.42534	+	0.822918i	−0.0681830	+	0.0393655i
$438$	14.9630	+	13.4077i	0.714960	+	0.640647i
$439$	−32.6334	−	18.8409i	−1.55751	−	0.899227i	−0.997495	−	0.0707423i	$-0.977463\pi$
$439$	−32.6334	−	18.8409i	−1.55751	−	0.899227i	−0.560012	−	0.828485i	$-0.689203\pi$
$440$	−4.95787	−	0.428057i	−0.236357	−	0.0204068i
$441$	−2.81121	−	1.04742i	−0.133867	−	0.0498772i
$442$	18.2447	−	29.6044i	0.867812	−	1.40814i
$443$	−20.7455	+	35.9322i	−0.985647	+	1.70719i	−0.346622	+	0.938005i	$0.612671\pi$
$443$	−20.7455	+	35.9322i	−0.985647	+	1.70719i	−0.639025	+	0.769186i	$0.720662\pi$
$444$	−9.60321	−	2.30679i	−0.455748	−	0.109475i
$445$	−2.15075	−	3.72520i	−0.101955	−	0.176592i
$446$	−21.5689	−	0.619381i	−1.02132	−	0.0293285i
$447$	−23.4120	−	19.7969i	−1.10735	−	0.936359i
$448$	6.14008	+	5.12830i	0.290091	+	0.242289i
$449$		−	31.9656i		−	1.50855i	−0.656559	−	0.754275i	$-0.727989\pi$
$449$		−	31.9656i		−	1.50855i	0.656559	−	0.754275i	$-0.272011\pi$
$450$	−3.30059	−	4.23668i	−0.155591	−	0.199719i
$451$		−	4.72379i		−	0.222434i
$452$	−0.548377	+	9.54030i	−0.0257935	+	0.448738i
$453$	6.44951	−	35.7826i	0.303025	−	1.68121i
$454$	0.315238	−	10.9777i	0.0147949	−	0.515208i
$455$	3.88803	+	6.73427i	0.182274	+	0.315707i
$456$	2.98046	+	11.2424i	0.139573	+	0.526475i
$457$	−14.8515	+	25.7236i	−0.694724	+	1.20330i	0.275549	+	0.961287i	$0.411140\pi$
$457$	−14.8515	+	25.7236i	−0.694724	+	1.20330i	−0.970274	+	0.242011i	$0.922193\pi$
$458$	13.7261	+	8.45918i	0.641378	+	0.395271i
$459$	−20.9692	+	35.3835i	−0.978761	+	1.65156i
$460$	−3.10025	+	1.55996i	−0.144550	+	0.0727333i
$461$	−8.96753	−	5.17741i	−0.417659	−	0.241136i	0.276416	−	0.961038i	$-0.410853\pi$
$461$	−8.96753	−	5.17741i	−0.417659	−	0.241136i	−0.694075	+	0.719902i	$0.744187\pi$
$462$	−1.68490	−	0.353904i	−0.0783885	−	0.0164651i
$463$	−13.7219	+	7.92236i	−0.637712	+	0.368183i	−0.783733	−	0.621098i	$-0.786687\pi$
$463$	−13.7219	+	7.92236i	−0.637712	+	0.368183i	0.146021	+	0.989282i	$0.453353\pi$
$464$	−4.60497	+	39.9247i	−0.213780	+	1.85346i
$465$	−36.2055	−	6.52573i	−1.67899	−	0.302624i
$466$	13.0378	+	24.1580i	0.603963	+	1.11910i
$467$	27.9844			1.29496			0.647481	−	0.762081i	$-0.275822\pi$
$467$	27.9844			1.29496			0.647481	+	0.762081i	$0.275822\pi$
$468$	−15.0263	+	11.0281i	−0.694593	+	0.509772i
$469$	−8.55414			−0.394994
$470$	12.3671	+	22.9153i	0.570450	+	1.05700i
$471$	−1.88331	+	2.22722i	−0.0867782	+	0.102625i
$472$	18.6032	−	8.70068i	0.856282	−	0.400481i
$473$	−2.22839	+	1.28656i	−0.102461	+	0.0591560i
$474$	−2.00109	−	6.10871i	−0.0919132	−	0.280583i
$475$	2.60268	+	1.50266i	0.119419	+	0.0689467i
$476$	−7.11573	−	14.1418i	−0.326149	−	0.648186i
$477$	−1.69986	−	2.05732i	−0.0778314	−	0.0941983i
$478$	−8.60659	−	5.30411i	−0.393656	−	0.242604i
$479$	−11.5844	+	20.0648i	−0.529306	+	0.916785i	0.470110	+	0.882608i	$0.344214\pi$
$479$	−11.5844	+	20.0648i	−0.529306	+	0.916785i	−0.999416	+	0.0341768i	$0.989119\pi$
$480$	4.91413	+	24.0286i	0.224298	+	1.09675i
$481$	4.42840	+	7.67021i	0.201918	+	0.349731i
$482$	0.0972109	−	3.38521i	0.00442783	−	0.154192i
$483$	−1.12986	+	0.406388i	−0.0514105	+	0.0184913i
$484$	20.9773	+	1.20578i	0.953515	+	0.0548081i
$485$		−	34.0973i		−	1.54828i
$486$	17.5439	−	13.3495i	0.795809	−	0.605547i
$487$		−	13.8456i		−	0.627406i	−0.949521	−	0.313703i	$-0.898430\pi$
$487$		−	13.8456i		−	0.627406i	0.949521	−	0.313703i	$-0.101570\pi$
$488$	−11.1176	−	7.76576i	−0.503272	−	0.351539i
$489$	24.3332	−	8.75216i	1.10039	−	0.395787i
$490$	3.53856	+	0.101614i	0.159856	+	0.00459047i
$491$	−1.97999	−	3.42944i	−0.0893557	−	0.154769i	0.817883	−	0.575384i	$-0.195147\pi$
$491$	−1.97999	−	3.42944i	−0.0893557	−	0.154769i	−0.907239	+	0.420616i	$0.861814\pi$
$492$	−22.3234	+	6.60948i	−1.00642	+	0.297979i
$493$	39.7651	−	68.8752i	1.79093	−	3.10198i
$494$	5.47218	−	8.87931i	0.246205	−	0.399499i
$495$	−3.36197	−	4.06895i	−0.151109	−	0.182886i
$496$	27.2557	+	20.2268i	1.22382	+	0.908209i
$497$	5.49505	+	3.17257i	0.246487	+	0.142309i
$498$	30.2812	−	9.91951i	1.35693	−	0.444504i
$499$	18.6834	−	10.7868i	0.836382	−	0.482886i	−0.0196506	−	0.999807i	$-0.506255\pi$
$499$	18.6834	−	10.7868i	0.836382	−	0.482886i	0.856033	+	0.516921i	$0.172922\pi$
$500$	−15.6267	−	10.2608i	−0.698848	−	0.458879i
$501$	−2.61846	+	3.09662i	−0.116984	+	0.138347i
$502$	−3.80795	+	2.05510i	−0.169957	+	0.0917236i
$503$	−24.7621			−1.10409			−0.552044	−	0.833815i	$-0.686152\pi$
$503$	−24.7621			−1.10409			−0.552044	+	0.833815i	$0.686152\pi$
$504$	0.685032	+	8.45758i	0.0305138	+	0.376731i
$505$	−6.46827			−0.287834
$506$	−0.606406	+	0.327269i	−0.0269580	+	0.0145489i
$507$	−5.70992	−	1.02916i	−0.253587	−	0.0457068i
$508$	8.21516	+	5.39425i	0.364489	+	0.239331i
$509$	−22.5133	+	12.9980i	−0.997882	+	0.576128i	−0.907621	−	0.419790i	$-0.862104\pi$
$509$	−22.5133	+	12.9980i	−0.997882	+	0.576128i	−0.0902614	+	0.995918i	$0.528770\pi$
$510$	9.97663	−	47.4976i	0.441773	−	2.10323i
$511$	−7.10333	−	4.10111i	−0.314233	−	0.181422i
$512$	5.78155	−	21.8763i	0.255511	−	0.966806i
$513$	−6.28936	+	10.6127i	−0.277682	+	0.468561i
$514$	−14.7300	+	23.9013i	−0.649711	+	1.05424i
$515$	16.8481	−	29.1817i	0.742415	−	1.28590i
$516$	9.19790	+	8.73065i	0.404915	+	0.384345i
$517$	2.58505	+	4.47744i	0.113690	+	0.196918i
$518$	4.03035	+	0.115737i	0.177084	+	0.00508519i
$519$	0.310743	−	1.72404i	0.0136401	−	0.0756767i
$520$	12.5947	−	18.0308i	0.552314	−	0.790705i
$521$			16.4772i			0.721880i	0.932589	+	0.360940i	$0.117544\pi$
$521$			16.4772i			0.721880i	−0.932589	+	0.360940i	$0.882456\pi$
$522$	−33.6272	+	26.1973i	−1.47182	+	1.14662i
$523$			35.6352i			1.55822i	0.626888	+	0.779110i	$0.284329\pi$
$523$			35.6352i			1.55822i	−0.626888	+	0.779110i	$0.715671\pi$
$524$	10.4614	+	0.601324i	0.457010	+	0.0262690i
$525$	1.67422	+	1.41570i	0.0730691	+	0.0617862i
$526$	0.772297	−	26.8940i	0.0336738	−	1.17263i
$527$	−33.5827	−	58.1670i	−1.46289	−	2.53380i
$528$	1.11224	+	4.74088i	0.0484039	+	0.206320i
$529$	11.2597	−	19.5024i	0.489553	−	0.847930i
$530$	2.68089	+	1.65219i	0.116451	+	0.0717667i
$531$	20.4123	+	7.60537i	0.885819	+	0.330045i
$532$	−2.13424	−	4.24157i	−0.0925310	−	0.183895i
$533$	18.0808	+	10.4390i	0.783166	+	0.452161i
$534$	−2.80901	+	3.13484i	−0.121558	+	0.135658i
$535$	36.9331	−	21.3233i	1.59676	−	0.921888i
$536$	10.2502	+	21.9162i	0.442740	+	0.946637i
$537$	−6.95551	−	19.3381i	−0.300152	−	0.834499i
$538$	−18.1878	−	33.7008i	−0.784134	−	1.45294i
$539$	0.702866			0.0302746
$540$	−14.5248	+	21.5811i	−0.625048	+	0.928702i
$541$	16.0235			0.688903			0.344452	−	0.938804i	$-0.388065\pi$
$541$	16.0235			0.688903			0.344452	+	0.938804i	$0.388065\pi$
$542$	19.5621	+	36.2471i	0.840262	+	1.55695i
$543$	6.87142	+	19.1043i	0.294881	+	0.819843i
$544$	−27.7055	+	35.1766i	−1.18786	+	1.50818i
$545$	5.27773	−	3.04710i	0.226073	−	0.130523i
$546$	5.07801	−	5.66704i	0.217319	−	0.242527i
$547$	9.75181	+	5.63021i	0.416957	+	0.240730i	0.693775	−	0.720192i	$-0.255946\pi$
$547$	9.75181	+	5.63021i	0.416957	+	0.240730i	−0.276817	+	0.960923i	$0.589280\pi$
$548$	18.6422	−	9.38023i	0.796355	−	0.400703i
$549$	−2.39019	−	14.1840i	−0.102011	−	0.605356i
$550$	1.07119	+	0.660156i	0.0456756	+	0.0281491i
$551$	11.9268	−	20.6579i	0.508100	−	0.880056i
$552$	2.39507	+	2.40781i	0.101941	+	0.102483i
$553$	1.31214	+	2.27268i	0.0557977	+	0.0966444i
$554$	−0.667597	+	23.2480i	−0.0283635	+	0.987712i
$555$	9.43896	+	7.98145i	0.400662	+	0.338794i
$556$	−1.36301	+	23.7127i	−0.0578044	+	1.00564i
$557$			25.2666i			1.07058i	0.844669	+	0.535289i	$0.179797\pi$
$557$			25.2666i			1.07058i	−0.844669	+	0.535289i	$0.820203\pi$
$558$	4.96068	+	35.6565i	0.210002	+	1.50946i
$559$		−	11.3725i		−	0.481006i
$560$	−3.97980	−	9.18776i	−0.168177	−	0.388254i
$561$	1.70933	−	9.48356i	0.0721680	−	0.400396i
$562$	−8.93679	−	0.256632i	−0.376976	−	0.0108254i
$563$	−6.29010	−	10.8948i	−0.265096	−	0.459160i	0.702493	−	0.711691i	$-0.252070\pi$
$563$	−6.29010	−	10.8948i	−0.265096	−	0.459160i	−0.967589	+	0.252531i	$0.918737\pi$
$564$	17.5423	−	18.4811i	0.738663	−	0.778195i
$565$	5.98010	−	10.3578i	0.251585	−	0.435758i
$566$	6.12441	−	9.93764i	0.257428	−	0.417710i
$567$	−5.88905	+	6.80582i	−0.247317	+	0.285817i
$568$	1.54376	−	17.8803i	0.0647748	−	0.750239i
$569$	−9.64118	−	5.56634i	−0.404179	−	0.233353i	0.284107	−	0.958793i	$-0.408303\pi$
$569$	−9.64118	−	5.56634i	−0.404179	−	0.233353i	−0.688286	+	0.725440i	$0.741636\pi$
$570$	2.99231	−	14.2461i	0.125334	−	0.596702i
$571$	−38.6886	+	22.3369i	−1.61907	+	0.934769i	−0.631906	+	0.775045i	$0.717727\pi$
$571$	−38.6886	+	22.3369i	−1.61907	+	0.934769i	−0.987162	+	0.159724i	$0.948939\pi$
$572$	2.39687	−	3.65031i	0.100218	−	0.152627i
$573$	11.5275	+	2.07773i	0.481568	+	0.0867985i
$574$	8.36422	−	4.51405i	0.349116	−	0.188413i
$575$	0.877545			0.0365962
$576$	20.8480	−	11.8896i	0.868666	−	0.495398i
$577$	0.773772			0.0322125			0.0161063	−	0.999870i	$-0.494873\pi$
$577$	0.773772			0.0322125			0.0161063	+	0.999870i	$0.494873\pi$
$578$	56.8203	−	30.6651i	2.36341	−	1.27550i
$579$	−3.09355	+	3.65847i	−0.128564	+	0.152041i
$580$	27.6086	−	42.0464i	1.14638	−	1.74588i
$581$	−11.2658	+	6.50432i	−0.467385	+	0.269845i
$582$	−31.7082	+	10.3870i	−1.31435	+	0.430553i
$583$	0.541485	+	0.312627i	0.0224260	+	0.0129477i
$584$	−1.99559	+	23.1134i	−0.0825779	+	0.956439i
$585$	23.0039	−	3.87646i	0.951093	−	0.160272i
$586$	−5.74372	+	9.31992i	−0.237271	+	0.385002i
$587$	3.95356	−	6.84776i	0.163181	−	0.282637i	−0.772827	−	0.634617i	$-0.781158\pi$
$587$	3.95356	−	6.84776i	0.163181	−	0.282637i	0.936008	+	0.351979i	$0.114491\pi$
$588$	−0.983445	−	3.32157i	−0.0405566	−	0.136979i
$589$	−10.0726	−	17.4462i	−0.415032	−	0.718857i
$590$	−25.6936	−	0.737826i	−1.05779	−	0.0303758i
$591$	28.1367	−	10.1202i	1.15739	−	0.416289i
$592$	−4.53292	−	10.4647i	−0.186302	−	0.430096i
$593$			13.0459i			0.535732i	0.963456	+	0.267866i	$0.0863184\pi$
$593$			13.0459i			0.535732i	−0.963456	+	0.267866i	$0.913682\pi$
$594$	−2.75970	+	4.36592i	−0.113232	+	0.179136i
$595$			19.8139i			0.812292i
$596$	2.03162	−	35.3448i	0.0832185	−	1.44778i
$597$	−23.6198	+	8.49557i	−0.966695	+	0.347700i
$598$	0.0874213	−	3.04430i	0.00357492	−	0.124491i
$599$	5.35898	+	9.28202i	0.218962	+	0.379253i	0.954491	−	0.298240i	$-0.0963996\pi$
$599$	5.35898	+	9.28202i	0.218962	+	0.379253i	−0.735529	+	0.677493i	$0.763066\pi$
$600$	1.62093	−	5.98585i	0.0661744	−	0.244371i
$601$	−2.22698	+	3.85725i	−0.0908406	+	0.157341i	−0.907865	−	0.419262i	$-0.862289\pi$
$601$	−2.22698	+	3.85725i	−0.0908406	+	0.157341i	0.817024	+	0.576603i	$0.195622\pi$
$602$	−4.40750	−	2.71628i	−0.179636	−	0.110707i
$603$	−8.95979	+	24.0475i	−0.364871	+	0.979290i
$604$	37.5039	−	18.8709i	1.52601	−	0.767847i
$605$	−22.7750	−	13.1491i	−0.925934	−	0.534588i
$606$	1.97041	+	6.01505i	0.0800424	+	0.244345i
$607$	29.7000	−	17.1473i	1.20549	−	0.695988i	0.243717	−	0.969846i	$-0.421633\pi$
$607$	29.7000	−	17.1473i	1.20549	−	0.695988i	0.961770	+	0.273858i	$0.0882999\pi$
$608$	−8.30976	+	10.5506i	−0.337005	+	0.427883i
$609$	11.2366	−	13.2886i	0.455331	−	0.538480i
$610$	8.06113	+	14.9367i	0.326386	+	0.604769i
$611$	−22.8505			−0.924433
$612$	−47.2086	+	5.19145i	−1.90830	+	0.209852i
$613$	−27.5606			−1.11316			−0.556581	−	0.830794i	$-0.687887\pi$
$613$	−27.5606			−1.11316			−0.556581	+	0.830794i	$0.687887\pi$
$614$	9.87553	+	18.2986i	0.398544	+	0.738473i
$615$	28.6765	+	5.16870i	1.15635	+	0.208422i
$616$	−0.842223	−	1.80079i	−0.0339341	−	0.0725557i
$617$	21.8157	−	12.5953i	0.878268	−	0.507068i	0.00818075	−	0.999967i	$-0.497396\pi$
$617$	21.8157	−	12.5953i	0.878268	−	0.507068i	0.870087	+	0.492899i	$0.164063\pi$
$618$	−32.2694	−	6.77802i	−1.29806	−	0.272652i
$619$	2.44808	+	1.41340i	0.0983968	+	0.0568094i	0.548391	−	0.836222i	$-0.315241\pi$
$619$	2.44808	+	1.41340i	0.0983968	+	0.0568094i	−0.449994	+	0.893032i	$0.648574\pi$
$620$	−19.0939	−	37.9472i	−0.766831	−	1.52399i
$621$	−0.0409982	+	3.60194i	−0.00164520	+	0.144541i
$622$	−15.0905	−	9.30001i	−0.605072	−	0.372897i
$623$	0.859209	−	1.48819i	0.0344235	−	0.0596232i
$624$	−20.6041	−	6.21952i	−0.824825	−	0.248980i
$625$	14.8635	+	25.7443i	0.594538	+	1.02977i
$626$	0.942680	−	32.8273i	0.0376771	−	1.31204i
$627$	0.512684	−	2.84443i	0.0204746	−	0.113595i
$628$	−3.36241	−	0.193271i	−0.134175	−	0.00771237i
$629$			22.5677i			0.899834i
$630$	3.99202	−	9.84120i	0.159046	−	0.392083i
$631$			35.3279i			1.40638i	0.711002	+	0.703190i	$0.248242\pi$
$631$			35.3279i			1.40638i	−0.711002	+	0.703190i	$0.751758\pi$
$632$	4.25046	−	6.08506i	0.169074	−	0.242051i
$633$	−33.8725	−	28.6421i	−1.34631	−	1.13842i
$634$	−9.68185	−	0.278027i	−0.384515	−	0.0110419i
$635$	−6.15020	−	10.6525i	−0.244063	−	0.422730i
$636$	0.719754	−	2.99635i	0.0285401	−	0.118813i
$637$	−1.55324	+	2.69030i	−0.0615417	+	0.106593i
$638$	5.23976	−	8.50218i	0.207444	−	0.336605i
$639$	14.6744	−	12.1247i	0.580510	−	0.479647i
$640$	−18.7707	+	21.2059i	−0.741978	+	0.838237i
$641$	17.8094	+	10.2823i	0.703431	+	0.406126i	0.808624	−	0.588326i	$-0.200213\pi$
$641$	17.8094	+	10.2823i	0.703431	+	0.406126i	−0.105193	+	0.994452i	$0.533546\pi$
$642$	−31.0800	−	27.8496i	−1.22663	−	1.09914i
$643$	−16.6218	+	9.59659i	−0.655499	+	0.378453i	−0.790560	−	0.612385i	$-0.790210\pi$
$643$	−16.6218	+	9.59659i	−0.655499	+	0.378453i	0.135061	+	0.990837i	$0.456877\pi$
$644$	−1.15896	−	0.761000i	−0.0456696	−	0.0299876i
$645$	−5.37200	−	14.9355i	−0.211522	−	0.588085i
$646$	23.3879	−	12.6222i	0.920186	−	0.496612i
$647$	30.9160			1.21544			0.607718	−	0.794153i	$-0.292085\pi$
$647$	30.9160			1.21544			0.607718	+	0.794153i	$0.292085\pi$
$648$	24.4936	+	6.93288i	0.962198	+	0.272349i
$649$	−5.10354			−0.200331
$650$	−4.89400	+	2.64122i	−0.191958	+	0.103597i
$651$	−4.97421	−	13.8296i	−0.194955	−	0.542023i
$652$	24.9600	+	16.3893i	0.977508	+	0.641853i
$653$	−14.2740	+	8.24109i	−0.558584	+	0.322499i	−0.752577	−	0.658504i	$-0.771190\pi$
$653$	−14.2740	+	8.24109i	−0.558584	+	0.322499i	0.193993	+	0.981003i	$0.437856\pi$
$654$	−4.44133	−	3.97970i	−0.173670	−	0.155618i
$655$	−11.3579	−	6.55749i	−0.443790	−	0.256222i
$656$	−21.5879	−	16.0206i	−0.842864	−	0.625498i
$657$	−18.9693	+	15.6734i	−0.740062	+	0.611477i
$658$	−5.45775	+	8.85589i	−0.212765	+	0.345239i
$659$	−13.7838	+	23.8743i	−0.536942	+	0.930010i	0.462125	+	0.886815i	$0.347087\pi$
$659$	−13.7838	+	23.8743i	−0.536942	+	0.930010i	−0.999067	+	0.0431955i	$0.986246\pi$
$660$	1.42352	−	5.92615i	0.0554105	−	0.230675i
$661$	5.86138	+	10.1522i	0.227981	+	0.394875i	0.957210	−	0.289395i	$-0.0934542\pi$
$661$	5.86138	+	10.1522i	0.227981	+	0.394875i	−0.729229	+	0.684270i	$0.760121\pi$
$662$	−11.3974	−	0.327292i	−0.442973	−	0.0127206i
$663$	32.5219	+	27.5001i	1.26305	+	1.06801i
$664$	30.1639	+	21.0698i	1.17059	+	0.817665i
$665$			5.94284i			0.230454i
$666$	4.54684	−	11.2089i	0.176186	−	0.434338i
$667$		−	6.96521i		−	0.269694i
$668$	−4.67493	−	0.268715i	−0.180878	−	0.0103969i
$669$	4.68777	−	26.0082i	0.181239	−	1.00554i
$670$	0.869225	−	30.2693i	0.0335811	−	1.16941i
$671$	1.68500	+	2.91850i	0.0650486	+	0.112667i
$672$	−7.33163	+	6.49978i	−0.282824	+	0.250735i
$673$	−3.04565	+	5.27522i	−0.117401	+	0.203345i	−0.918737	−	0.394870i	$-0.870790\pi$
$673$	−3.04565	+	5.27522i	−0.117401	+	0.203345i	0.801336	+	0.598215i	$0.204123\pi$
$674$	19.4647	+	11.9958i	0.749754	+	0.462062i
$675$	5.73345	−	3.22376i	0.220680	−	0.124083i
$676$	−3.01128	−	5.98460i	−0.115818	−	0.230177i
$677$	25.8756	+	14.9393i	0.994481	+	0.574164i	0.906611	−	0.421968i	$-0.138661\pi$
$677$	25.8756	+	14.9393i	0.994481	+	0.574164i	0.0878702	+	0.996132i	$0.471994\pi$
$678$	−11.4538	−	2.40581i	−0.439880	−	0.0923945i
$679$	11.7967	−	6.81083i	0.452716	−	0.261376i
$680$	50.7645	−	23.7424i	1.94673	−	0.910481i
$681$	13.2371	+	2.38587i	0.507246	+	0.0914268i
$682$	−4.00579	−	7.42244i	−0.153390	−	0.284220i
$683$	−5.57818			−0.213443			−0.106722	−	0.994289i	$-0.534035\pi$
$683$	−5.57818			−0.213443			−0.106722	+	0.994289i	$0.534035\pi$
$684$	−14.1594	+	1.55708i	−0.541398	+	0.0595366i
$685$	−26.1195			−0.997974
$686$	0.671660	+	1.24454i	0.0256441	+	0.0475167i
$687$	−12.7504	+	15.0788i	−0.486460	+	0.575294i
$688$	−1.67788	+	14.5471i	−0.0639687	+	0.554604i
$689$	−2.39322	+	1.38173i	−0.0911745	+	0.0526396i
$690$	−1.32322	−	4.03938i	−0.0503741	−	0.153776i
$691$	−6.59535	−	3.80783i	−0.250899	−	0.144857i	0.369277	−	0.929319i	$-0.379605\pi$
$691$	−6.59535	−	3.80783i	−0.250899	−	0.144857i	−0.620176	+	0.784463i	$0.712939\pi$
$692$	1.80697	−	0.909216i	0.0686907	−	0.0345632i
$693$	0.736197	−	1.97591i	0.0279658	−	0.0750585i
$694$	−9.21981	−	5.68202i	−0.349979	−	0.215687i
$695$	14.8637	−	25.7447i	0.563813	−	0.976553i
$696$	−47.5106	−	12.8656i	−1.80089	−	0.487670i
$697$	26.5992	+	46.0711i	1.00751	+	1.74507i
$698$	−0.357982	+	12.4662i	−0.0135498	+	0.471851i
$699$	−31.6371	+	11.3792i	−1.19662	+	0.430401i
$700$	−0.145284	+	2.52755i	−0.00549122	+	0.0955326i
$701$		−	13.6591i		−	0.515896i	−0.966159	−	0.257948i	$-0.916954\pi$
$701$		−	13.6591i		−	0.515896i	0.966159	−	0.257948i	$-0.0830463\pi$
$702$	−10.6124	−	20.2111i	−0.400540	−	0.762820i
$703$			6.76879i			0.255290i
$704$	−3.60451	+	4.31565i	−0.135850	+	0.162652i
$705$	−30.0096	+	10.7938i	−1.13023	+	0.406519i
$706$	4.59393	+	0.131921i	0.172895	+	0.00496490i
$707$	−1.29202	−	2.23784i	−0.0485913	−	0.0841625i
$708$	7.14083	+	24.1181i	0.268369	+	0.906412i
$709$	−11.1244	+	19.2680i	−0.417784	+	0.723624i	−0.995716	−	0.0924613i	$-0.970527\pi$
$709$	−11.1244	+	19.2680i	−0.417784	+	0.723624i	0.577932	+	0.816085i	$0.303860\pi$
$710$	−11.7847	+	19.1222i	−0.442272	+	0.717643i
$711$	7.76336	−	1.30823i	0.291149	−	0.0490625i
$712$	−4.84241	−	0.418088i	−0.181477	−	0.0156685i
$713$	−5.09424	−	2.94116i	−0.190781	−	0.110147i
$714$	18.4256	−	6.03586i	0.689561	−	0.225886i
$715$	−4.73329	+	2.73277i	−0.177015	+	0.102200i
$716$	13.0248	−	19.8362i	0.486761	−	0.741312i
$717$	7.99484	−	9.45479i	0.298573	−	0.353096i
$718$	−35.3489	+	19.0773i	−1.31921	+	0.711959i
$719$	17.7827			0.663184			0.331592	−	0.943423i	$-0.392414\pi$
$719$	17.7827			0.663184			0.331592	+	0.943423i	$0.392414\pi$
$720$	−29.9973	+	1.56461i	−1.11793	+	0.0583097i
$721$	13.4614			0.501328
$722$	−16.6314	+	8.97574i	−0.618957	+	0.334043i
$723$	4.08195	+	0.735737i	0.151810	+	0.0273624i
$724$	−12.8674	+	19.5964i	−0.478212	+	0.728293i
$725$	−11.0146	+	6.35929i	−0.409072	+	0.236178i
$726$	−5.28992	+	25.1847i	−0.196328	+	0.934693i
$727$	45.2123	+	26.1034i	1.67683	+	0.968120i	0.963660	+	0.267131i	$0.0860758\pi$
$727$	45.2123	+	26.1034i	1.67683	+	0.968120i	0.713173	+	0.700988i	$0.247258\pi$
$728$	8.75390	+	0.755802i	0.324441	+	0.0280119i
$729$	12.9643	+	23.6839i	0.480158	+	0.877182i
$730$	15.2338	−	24.7188i	0.563829	−	0.914885i
$731$	14.4890	−	25.0956i	0.535894	−	0.928195i
$732$	11.4345	−	12.0464i	0.422630	−	0.445248i
$733$	−5.30936	−	9.19609i	−0.196106	−	0.339665i	0.751157	−	0.660124i	$-0.229496\pi$
$733$	−5.30936	−	9.19609i	−0.196106	−	0.339665i	−0.947262	+	0.320459i	$0.896163\pi$
$734$	6.53196	+	0.187574i	0.241099	+	0.00692348i
$735$	−0.769066	+	4.26686i	−0.0283674	+	0.157386i
$736$	−0.560977	+	3.88122i	−0.0206779	+	0.143064i
$737$		−	6.01242i		−	0.221470i
$738$	−3.92910	−	28.2417i	−0.144632	−	1.03959i
$739$			25.7536i			0.947362i	0.880696	+	0.473681i	$0.157075\pi$
$739$			25.7536i			0.947362i	−0.880696	+	0.473681i	$0.842925\pi$
$740$	−0.819084	+	14.2499i	−0.0301101	+	0.523836i
$741$	9.75438	+	8.24816i	0.358336	+	0.303004i
$742$	−0.0361117	+	1.25753i	−0.00132570	+	0.0461655i
$743$	−1.97016	−	3.41241i	−0.0722780	−	0.125189i	0.827621	−	0.561287i	$-0.189694\pi$
$743$	−1.97016	−	3.41241i	−0.0722780	−	0.125189i	−0.899899	+	0.436098i	$0.856360\pi$
$744$	−29.4717	+	29.3158i	−1.08049	+	1.07477i
$745$	−22.1550	+	38.3737i	−0.811698	+	1.40590i
$746$	33.1949	+	20.4575i	1.21535	+	0.749003i
$747$	6.48496	+	38.4833i	0.237272	+	1.40803i
$748$	9.93976	−	5.00141i	0.363434	−	0.182870i
$749$	14.7545	+	8.51853i	0.539119	+	0.311260i
$750$	15.2793	−	17.0517i	0.557923	−	0.622640i
$751$	−10.3540	+	5.97786i	−0.377821	+	0.218135i	−0.676870	−	0.736103i	$-0.736664\pi$
$751$	−10.3540	+	5.97786i	−0.377821	+	0.218135i	0.299049	+	0.954238i	$0.403331\pi$
$752$	29.2292	+	3.37133i	1.06588	+	0.122940i
$753$	−1.79367	−	4.98685i	−0.0653649	−	0.181731i
$754$	20.9638	+	38.8444i	0.763457	+	1.41463i
$755$	−52.5466			−1.91237
$756$	−10.3677	−	0.714413i	−0.377070	−	0.0259829i
$757$	1.73758			0.0631534			0.0315767	−	0.999501i	$-0.489947\pi$
$757$	1.73758			0.0631534			0.0315767	+	0.999501i	$0.489947\pi$
$758$	13.8205	+	25.6084i	0.501983	+	0.930138i
$759$	−0.285637	−	0.794142i	−0.0103680	−	0.0288255i
$760$	15.2259	−	7.12113i	0.552302	−	0.258310i
$761$	−25.7786	+	14.8833i	−0.934473	+	0.539518i	−0.888223	−	0.459412i	$-0.848060\pi$
$761$	−25.7786	+	14.8833i	−0.934473	+	0.539518i	−0.0462496	+	0.998930i	$0.514727\pi$
$762$	−8.03254	+	8.96429i	−0.290988	+	0.324742i
$763$	2.10842	+	1.21729i	0.0763298	+	0.0440690i
$764$	6.07933	+	12.0820i	0.219942	+	0.437112i
$765$	55.7012	+	20.7535i	2.01388	+	0.750346i
$766$	−0.110175	−	0.0678989i	−0.00398077	−	0.00245329i
$767$	11.2782	−	19.5343i	0.407231	−	0.705344i
$768$	25.4381	+	10.9956i	0.917918	+	0.396769i
$769$	11.5167	+	19.9475i	0.415303	+	0.719327i	0.995460	−	0.0951782i	$-0.0303421\pi$
$769$	11.5167	+	19.9475i	0.415303	+	0.719327i	−0.580157	+	0.814505i	$0.697009\pi$
$770$	−0.0714214	+	2.48713i	−0.00257385	+	0.0896301i
$771$	−26.2568	−	22.2024i	−0.945615	−	0.799598i
$772$	−5.52315	−	0.317471i	−0.198783	−	0.0114260i
$773$			1.33102i			0.0478734i	0.999713	+	0.0239367i	$0.00762002\pi$
$773$			1.33102i			0.0478734i	−0.999713	+	0.0239367i	$0.992380\pi$
$774$	−12.2525	+	9.54534i	−0.440408	+	0.343100i
$775$			10.7412i			0.385835i
$776$	−31.5854	−	22.0627i	−1.13385	−	0.792003i
$777$	−0.875952	+	4.85988i	−0.0314246	+	0.174347i
$778$	2.70118	+	0.0775679i	0.0968419	+	0.00278094i
$779$	7.97795	+	13.8182i	0.285840	+	0.495089i
$780$	19.5372	+	18.5447i	0.699543	+	0.664006i
$781$	−2.22989	+	3.86229i	−0.0797919	+	0.138204i
$782$	4.07146	−	6.60646i	0.145595	−	0.236247i
$783$	−25.5875	−	45.5073i	−0.914423	−	1.62630i
$784$	2.38375	−	3.21212i	0.0851339	−	0.114719i
$785$	3.65055	+	2.10764i	0.130294	+	0.0752250i
$786$	−2.63810	+	12.5597i	−0.0940977	+	0.447988i
$787$	−1.23901	+	0.715343i	−0.0441659	+	0.0254992i	−0.521920	−	0.852994i	$-0.674784\pi$
$787$	−1.23901	+	0.715343i	−0.0441659	+	0.0254992i	0.477754	+	0.878493i	$0.341451\pi$
$788$	28.8614	+	18.9510i	1.02815	+	0.675102i
$789$	32.4293	+	5.84511i	1.15451	+	0.208091i
$790$	−8.17536	+	4.41213i	−0.290866	+	0.156977i
$791$	4.77802			0.169887
$792$	−5.94455	+	0.481486i	−0.211230	+	0.0171089i
$793$	−14.8945			−0.528919
$794$	−37.8778	+	20.4421i	−1.34423	+	0.725465i
$795$	−2.49034	+	2.94510i	−0.0883231	+	0.104452i
$796$	−24.2282	−	15.9087i	−0.858746	−	0.563871i
$797$	−29.9747	+	17.3059i	−1.06176	+	0.613007i	−0.925918	−	0.377724i	$-0.876707\pi$
$797$	−29.9747	+	17.3059i	−1.06176	+	0.613007i	−0.135841	+	0.990731i	$0.543373\pi$
$798$	5.52643	−	1.81035i	0.195634	−	0.0640856i
$799$	−50.4240	−	29.1123i	−1.78387	−	1.02992i
$800$	6.64983	−	2.65646i	0.235107	−	0.0939202i
$801$	−3.28367	−	3.97418i	−0.116023	−	0.140421i
$802$	−16.2116	+	26.3053i	−0.572450	+	0.928873i
$803$	2.88253	−	4.99269i	0.101722	−	0.176188i
$804$	−28.4132	+	8.41253i	−1.00206	+	0.296687i
$805$	0.867647	+	1.50281i	0.0305805	+	0.0529671i
$806$	37.2624	+	1.07004i	1.31251	+	0.0376906i
$807$	44.1341	−	15.8741i	1.55359	−	0.558796i
$808$	−4.18529	+	5.99175i	−0.147238	+	0.210789i
$809$		−	21.7895i		−	0.766078i	−0.923732	−	0.383039i	$-0.874878\pi$
$809$		−	21.7895i		−	0.766078i	0.923732	−	0.383039i	$-0.125122\pi$
$810$	−23.4844	−	21.5303i	−0.825157	−	0.756498i
$811$			14.6383i			0.514020i	0.966409	+	0.257010i	$0.0827374\pi$
$811$			14.6383i			0.514020i	−0.966409	+	0.257010i	$0.917263\pi$
$812$	20.0616	+	1.15314i	0.704024	+	0.0404673i
$813$	−47.4687	+	17.0735i	−1.66480	+	0.598795i
$814$	−0.0813476	+	2.83280i	−0.00285123	+	0.0992896i
$815$	−18.6860	−	32.3652i	−0.654544	−	1.13370i
$816$	−37.5431	−	39.9749i	−1.31427	−	1.39940i
$817$	4.34571	−	7.52699i	0.152037	−	0.263336i
$818$	−5.38851	−	3.32086i	−0.188405	−	0.116111i
$819$	5.93609	+	7.18437i	0.207424	+	0.251042i
$820$	15.1233	+	30.0560i	0.528129	+	1.04960i
$821$	−15.6555	−	9.03872i	−0.546382	−	0.315454i	0.201280	−	0.979534i	$-0.435490\pi$
$821$	−15.6555	−	9.03872i	−0.546382	−	0.315454i	−0.747661	+	0.664080i	$0.768823\pi$
$822$	7.95669	+	24.2893i	0.277521	+	0.847187i
$823$	10.4800	−	6.05062i	0.365309	−	0.210911i	−0.306098	−	0.952000i	$-0.599024\pi$
$823$	10.4800	−	6.05062i	0.365309	−	0.210911i	0.671407	+	0.741089i	$0.265690\pi$
$824$	−16.1304	−	34.4889i	−0.561928	−	1.20148i
$825$	−0.995047	+	1.17676i	−0.0346431	+	0.0409694i
$826$	−4.87695	−	9.03663i	−0.169691	−	0.314425i
$827$	−50.7180			−1.76364			−0.881819	−	0.471588i	$-0.843681\pi$
$827$	−50.7180			−1.76364			−0.881819	+	0.471588i	$0.843681\pi$
$828$	−3.35326	+	2.46100i	−0.116534	+	0.0855258i
$829$	−14.5505			−0.505359			−0.252679	−	0.967550i	$-0.581312\pi$
$829$	−14.5505			−0.505359			−0.252679	+	0.967550i	$0.581312\pi$
$830$	−21.8711	−	40.5257i	−0.759159	−	1.40667i
$831$	−28.0329	−	5.05269i	−0.972450	−	0.175276i
$832$	−8.55312	−	23.3337i	−0.296526	−	0.808950i
$833$	−6.85506	+	3.95777i	−0.237514	+	0.137129i
$834$	−28.4687	−	5.97971i	−0.985790	−	0.207060i
$835$	5.07554	+	2.93036i	0.175646	+	0.101409i
$836$	2.98126	−	1.50008i	0.103109	−	0.0518815i
$837$	−44.0879	−	0.501820i	−1.52390	−	0.0173454i
$838$	−27.4552	−	16.9202i	−0.948423	−	0.584498i
$839$	7.34607	−	12.7238i	0.253615	−	0.439273i	−0.710904	−	0.703289i	$-0.751714\pi$
$839$	7.34607	−	12.7238i	0.253615	−	0.439273i	0.964518	+	0.264016i	$0.0850472\pi$
$840$	11.8535	−	3.14246i	0.408985	−	0.108425i
$841$	35.9746	+	62.3099i	1.24050	+	2.14862i
$842$	1.14078	−	39.7258i	0.0393138	−	1.36904i
$843$	1.94231	−	10.7762i	0.0668967	−	0.371150i
$844$	2.93935	−	51.1369i	0.101177	−	1.76020i
$845$			8.38499i			0.288452i
$846$	19.1792	+	24.6187i	0.659395	+	0.846409i
$847$		−	10.5060i		−	0.360990i
$848$	3.26515	−	1.41434i	0.112126	−	0.0485687i
$849$	10.9170	+	9.23127i	0.374671	+	0.316816i
$850$	−14.1646	−	0.406754i	−0.485840	−	0.0139516i
$851$	0.988234	+	1.71167i	0.0338762	+	0.0586754i
$852$	21.3723	+	5.13384i	0.732202	+	0.175882i
$853$	0.885883	−	1.53439i	0.0303321	−	0.0525367i	−0.850461	−	0.526038i	$-0.823677\pi$
$853$	0.885883	−	1.53439i	0.0303321	−	0.0525367i	0.880793	+	0.473502i	$0.157010\pi$
$854$	−3.55749	+	5.77248i	−0.121735	+	0.197530i
$855$	16.7066	+	6.22466i	0.571353	+	0.212879i
$856$	4.14508	−	48.0095i	0.141676	−	1.64093i
$857$	0.277829	+	0.160404i	0.00949045	+	0.00547931i	0.504738	−	0.863273i	$-0.331589\pi$
$857$	0.277829	+	0.160404i	0.00949045	+	0.00547931i	−0.495247	+	0.868752i	$0.664923\pi$
$858$	3.98317	+	3.56916i	0.135983	+	0.121849i
$859$	−27.9931	+	16.1618i	−0.955112	+	0.551434i	−0.894665	−	0.446737i	$-0.852586\pi$
$859$	−27.9931	+	16.1618i	−0.955112	+	0.551434i	−0.0604467	+	0.998171i	$0.519253\pi$
$860$	10.0596	−	15.3202i	0.343028	−	0.522415i
$861$	3.93982	+	10.9537i	0.134269	+	0.373300i
$862$	−0.760107	+	0.410219i	−0.0258893	+	0.0139721i
$863$	18.8459			0.641522			0.320761	−	0.947160i	$-0.396061\pi$
$863$	18.8459			0.641522			0.320761	+	0.947160i	$0.396061\pi$
$864$	10.5930	+	27.4188i	0.360380	+	0.932806i
$865$	−2.53174			−0.0860816
$866$	−13.0887	+	7.06378i	−0.444772	+	0.240037i
$867$	26.7642	+	74.4111i	0.908959	+	2.52713i
$868$	9.31468	−	14.1858i	0.316161	−	0.481497i
$869$	−1.59739	+	0.922256i	−0.0541879	+	0.0312854i
$870$	45.8806	+	41.1118i	1.55550	+	1.39382i
$871$	23.0132	+	13.2867i	0.779772	+	0.450201i
$872$	0.592331	−	6.86054i	0.0200589	−	0.232327i
$873$	−6.79056	−	40.2968i	−0.229826	−	1.36384i
$874$	1.22116	−	1.98149i	0.0413064	−	0.0670250i
$875$	−4.67359	+	8.09490i	−0.157996	+	0.273657i
$876$	−27.6274	−	6.63639i	−0.933445	−	0.224223i
$877$	−20.0001	−	34.6412i	−0.675355	−	1.16975i	−0.976365	−	0.216129i	$-0.930657\pi$
$877$	−20.0001	−	34.6412i	−0.675355	−	1.16975i	0.301010	−	0.953621i	$-0.402676\pi$
$878$	53.2681	+	1.52967i	1.79771	+	0.0516237i
$879$	−10.2384	−	8.65746i	−0.345333	−	0.292009i
$880$	6.45777	−	2.79727i	0.217691	−	0.0942960i
$881$		−	4.11680i		−	0.138699i	−0.997592	−	0.0693493i	$-0.977908\pi$
$881$		−	4.11680i		−	0.138699i	0.997592	−	0.0693493i	$-0.0220923\pi$
$882$	4.20217	−	0.584622i	0.141494	−	0.0196853i
$883$			58.6257i			1.97291i	0.164027	+	0.986456i	$0.447551\pi$
$883$			58.6257i			1.97291i	−0.164027	+	0.986456i	$0.552449\pi$
$884$	−2.82215	+	49.0980i	−0.0949193	+	1.65134i
$885$	5.58422	−	30.9819i	0.187711	−	1.04144i
$886$	1.68430	−	58.6529i	0.0565850	−	1.97048i
$887$	−14.3027	−	24.7730i	−0.480238	−	0.831797i	0.519505	−	0.854468i	$-0.326117\pi$
$887$	−14.3027	−	24.7730i	−0.480238	−	0.831797i	−0.999743	+	0.0226703i	$0.992783\pi$
$888$	13.5009	−	3.57920i	0.453061	−	0.120110i
$889$	2.45696	−	4.25559i	0.0824040	−	0.142728i
$890$	5.17875	+	3.19158i	0.173592	+	0.106982i
$891$	−4.78358	−	4.13921i	−0.160256	−	0.138669i
$892$	27.2594	−	13.7161i	0.912711	−	0.459250i
$893$	−15.1238	−	8.73173i	−0.506099	−	0.292196i
$894$	42.4339	+	8.91302i	1.41920	+	0.298096i
$895$	−25.7212	+	14.8502i	−0.859766	+	0.496386i
$896$	−11.0860	−	2.25832i	−0.370358	−	0.0754452i
$897$	3.67088	+	0.661645i	0.122567	+	0.0220917i
$898$	21.4700	+	39.7824i	0.716463	+	1.32756i
$899$	85.2545			2.84340
$900$	6.95331	+	3.05584i	0.231777	+	0.101861i
$901$	−7.04147			−0.234586
$902$	3.17278	+	5.87893i	0.105642	+	0.195747i
$903$	4.09422	−	4.84187i	0.136247	−	0.161128i
$904$	−5.72536	−	12.2416i	−0.190423	−	0.407149i
$905$	25.4103	−	14.6706i	0.844666	−	0.487668i
$906$	16.0071	+	48.8647i	0.531800	+	1.62342i
$907$	9.05264	+	5.22654i	0.300588	+	0.173545i	0.642707	−	0.766112i	$-0.277811\pi$
$907$	9.05264	+	5.22654i	0.300588	+	0.173545i	−0.342119	+	0.939657i	$0.611145\pi$
$908$	6.98093	+	13.8739i	0.231670	+	0.460420i
$909$	−7.64432	+	1.28817i	−0.253546	+	0.0427259i
$910$	−9.36194	−	5.76961i	−0.310345	−	0.191261i
$911$	7.21831	−	12.5025i	0.239153	−	0.414226i	−0.721318	−	0.692604i	$-0.756463\pi$
$911$	7.21831	−	12.5025i	0.239153	−	0.414226i	0.960472	+	0.278378i	$0.0897968\pi$
$912$	−11.2604	−	11.9898i	−0.372868	−	0.397021i
$913$	−4.57167	−	7.91836i	−0.151300	−	0.262059i
$914$	1.20577	−	41.9891i	0.0398834	−	1.38888i
$915$	−19.5609	+	7.03567i	−0.646664	+	0.232592i
$916$	−22.7643	−	1.30850i	−0.752155	−	0.0432339i
$917$		−	5.23935i		−	0.173019i
$918$	2.33131	−	58.1203i	0.0769445	−	1.91826i
$919$			12.1505i			0.400810i	0.979713	+	0.200405i	$0.0642257\pi$
$919$			12.1505i			0.400810i	−0.979713	+	0.200405i	$0.935774\pi$
$920$	2.81061	−	4.02373i	0.0926631	−	0.132659i
$921$	−23.9637	+	8.61925i	−0.789630	+	0.284014i
$922$	14.6379	+	0.420346i	0.482073	+	0.0138434i
$923$	−9.85555	−	17.0703i	−0.324399	−	0.561876i
$924$	2.33462	−	0.691231i	0.0768034	−	0.0227398i
$925$	1.80453	−	3.12554i	0.0593325	−	0.102767i
$926$	11.7563	−	19.0761i	0.386337	−	0.626881i
$927$	14.0997	−	37.8428i	0.463096	−	1.24292i
$928$	−21.0848	−	52.7808i	−0.692142	−	1.73261i
$929$	−38.7325	−	22.3622i	−1.27077	−	0.733680i	−0.295638	−	0.955300i	$-0.595532\pi$
$929$	−38.7325	−	22.3622i	−1.27077	−	0.733680i	−0.975133	+	0.221620i	$0.928866\pi$
$930$	49.4422	−	16.1963i	1.62127	−	0.531096i
$931$	−2.05605	+	1.18706i	−0.0673844	+	0.0389044i
$932$	−32.4520	−	21.3086i	−1.06300	−	0.697988i
$933$	14.0178	−	16.5777i	0.458923	−	0.542728i
$934$	−34.8276	+	18.7960i	−1.13959	+	0.615023i
$935$	−13.9266			−0.455447
$936$	11.2937	−	23.8174i	0.369148	−	0.778497i
$937$	−28.8712			−0.943180			−0.471590	−	0.881818i	$-0.656320\pi$
$937$	−28.8712			−0.943180			−0.471590	+	0.881818i	$0.656320\pi$
$938$	10.6460	−	5.74547i	0.347603	−	0.187596i
$939$	39.5838	+	7.13465i	1.29177	+	0.232830i
$940$	−30.7825	−	20.2124i	−1.00401	−	0.659257i
$941$	31.0674	−	17.9368i	1.01277	−	0.584723i	0.100768	−	0.994910i	$-0.467870\pi$
$941$	31.0674	−	17.9368i	1.01277	−	0.584723i	0.912001	+	0.410187i	$0.134537\pi$
$942$	0.847910	−	4.03680i	0.0276264	−	0.131526i
$943$	4.03488	+	2.32954i	0.131394	+	0.0758603i
$944$	−17.3085	+	23.3233i	−0.563344	+	0.759110i
$945$	11.1895	+	6.63121i	0.363995	+	0.215713i
$946$	1.90918	−	3.09789i	0.0620728	−	0.100721i
$947$	8.81974	−	15.2762i	0.286603	−	0.496411i	−0.686394	−	0.727230i	$-0.740807\pi$
$947$	8.81974	−	15.2762i	0.286603	−	0.496411i	0.972997	+	0.230819i	$0.0741406\pi$
$948$	6.59341	+	6.25847i	0.214144	+	0.203266i
$949$	12.7400	+	22.0664i	0.413559	+	0.716306i
$950$	−4.24841	−	0.121999i	−0.137837	−	0.00395816i
$951$	2.10424	−	11.6746i	0.0682347	−	0.378574i
$952$	18.3542	+	12.8206i	0.594864	+	0.415518i
$953$			9.66882i			0.313204i	0.987662	+	0.156602i	$0.0500540\pi$
$953$			9.66882i			0.313204i	−0.987662	+	0.156602i	$0.949946\pi$
$954$	3.49737	+	1.41868i	0.113231	+	0.0459316i
$955$		−	16.9280i		−	0.547779i
$956$	14.2738	+	0.820458i	0.461647	+	0.0265355i
$957$	9.34009	+	7.89784i	0.301922	+	0.255301i
$958$	0.940523	−	32.7522i	0.0303869	−	1.05818i
$959$	−5.21728	−	9.03659i	−0.168475	−	0.291807i
$960$	−22.2549	−	26.6039i	−0.718273	−	0.858637i
$961$	20.4999	−	35.5069i	0.661288	−	1.14538i
$962$	−10.6631	−	6.57148i	−0.343791	−	0.211873i
$963$	39.4016	−	32.5556i	1.26970	−	1.04909i
$964$	2.15273	+	4.27831i	0.0693347	+	0.137795i
$965$	5.99645	+	3.46205i	0.193033	+	0.111447i
$966$	1.13320	−	1.26465i	0.0364601	−	0.0406894i
$967$	2.67131	−	1.54228i	0.0859036	−	0.0495964i	−0.456433	−	0.889758i	$-0.650873\pi$
$967$	2.67131	−	1.54228i	0.0859036	−	0.0495964i	0.542336	+	0.840161i	$0.317540\pi$
$968$	−26.9169	+	12.5890i	−0.865143	+	0.404626i
$969$	11.0165	+	30.6286i	0.353900	+	0.983932i
$970$	22.9018	+	42.4354i	0.735333	+	1.36252i
$971$	−24.5223			−0.786958			−0.393479	−	0.919334i	$-0.628729\pi$
$971$	−24.5223			−0.786958			−0.393479	+	0.919334i	$0.628729\pi$
$972$	−12.8677	+	28.3976i	−0.412733	+	0.910852i
$973$	11.8759			0.380724
$974$	9.29956	+	17.2314i	0.297977	+	0.552130i
$975$	−2.30523	−	6.40912i	−0.0738265	−	0.205256i
$976$	19.0523	+	2.19751i	0.609848	+	0.0703406i
$977$	9.43845	−	5.44929i	0.301963	−	0.174338i	−0.341362	−	0.939932i	$-0.610888\pi$
$977$	9.43845	−	5.44929i	0.301963	−	0.174338i	0.643324	+	0.765594i	$0.277555\pi$
$978$	−24.4051	+	27.2360i	−0.780390	+	0.870913i
$979$	1.04600	+	0.603909i	0.0334304	+	0.0193010i
$980$	−4.47212	+	2.25024i	−0.142857	+	0.0718814i
$981$	5.63047	−	4.65218i	0.179767	−	0.148533i
$982$	4.76759	+	2.93819i	0.152140	+	0.0937615i
$983$	−14.8209	+	25.6706i	−0.472715	+	0.818766i	−0.999512	−	0.0312247i	$-0.990059\pi$
$983$	−14.8209	+	25.6706i	−0.472715	+	0.818766i	0.526798	+	0.849991i	$0.323393\pi$
$984$	23.3430	−	23.2195i	0.744148	−	0.740211i
$985$	−21.6068	−	37.4241i	−0.688450	−	1.19243i
$986$	−3.22847	+	112.426i	−0.102815	+	3.58038i
$987$	−9.72866	−	8.22642i	−0.309667	−	0.261850i
$988$	−0.846455	+	14.7261i	−0.0269293	+	0.468499i
$989$		−	2.53787i		−	0.0806996i
$990$	6.91705	+	2.80586i	0.219838	+	0.0891760i
$991$		−	20.5496i		−	0.652779i	−0.945235	−	0.326390i	$-0.894168\pi$
$991$		−	20.5496i		−	0.652779i	0.945235	−	0.326390i	$-0.105832\pi$
$992$	−47.5063	−	6.86638i	−1.50833	−	0.218008i
$993$	2.47710	−	13.7432i	0.0786084	−	0.436128i
$994$	−8.96969	−	0.257577i	−0.284501	−	0.00816983i
$995$	18.1382	+	31.4163i	0.575020	+	0.995963i
$996$	−31.0235	+	32.6839i	−0.983019	+	1.03563i
$997$	6.42074	−	11.1210i	0.203347	−	0.352207i	−0.746258	−	0.665657i	$-0.768151\pi$
$997$	6.42074	−	11.1210i	0.203347	−	0.352207i	0.949605	+	0.313450i	$0.101485\pi$
$998$	−16.0071	+	25.9735i	−0.506695	+	0.822177i
$999$	12.7447	+	7.55283i	0.403223	+	0.238961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.6	✓	72
3.2	odd	2		756.2.ba.a.575.31		72
4.3	odd	2	inner	252.2.ba.a.155.17	yes	72
9.4	even	3		756.2.ba.a.71.20		72
9.5	odd	6	inner	252.2.ba.a.239.17	yes	72
12.11	even	2		756.2.ba.a.575.20		72
36.23	even	6	inner	252.2.ba.a.239.6	yes	72
36.31	odd	6		756.2.ba.a.71.31		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.6	✓	72	1.1	even	1	trivial
252.2.ba.a.155.17	yes	72	4.3	odd	2	inner
252.2.ba.a.239.6	yes	72	36.23	even	6	inner
252.2.ba.a.239.17	yes	72	9.5	odd	6	inner
756.2.ba.a.71.20		72	9.4	even	3
756.2.ba.a.71.31		72	36.31	odd	6
756.2.ba.a.575.20		72	12.11	even	2
756.2.ba.a.575.31		72	3.2	odd	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24454 + 0.671660i) q^{2} +(-0.586217 - 1.62983i) q^{3} +(1.09775 - 1.67181i) q^{4} +(-2.16781 + 1.25159i) q^{5} +(1.82426 + 1.63465i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.243298 + 2.81794i) q^{8} +(-2.31270 + 1.91087i) q^{9} +O(q^{10})\)	\(q+(-1.24454 + 0.671660i) q^{2} +(-0.586217 - 1.62983i) q^{3} +(1.09775 - 1.67181i) q^{4} +(-2.16781 + 1.25159i) q^{5} +(1.82426 + 1.63465i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.243298 + 2.81794i) q^{8} +(-2.31270 + 1.91087i) q^{9} +(1.85728 - 3.01367i) q^{10} +(0.351433 - 0.608700i) q^{11} +(-3.36829 - 0.809097i) q^{12} +(1.55324 + 2.69030i) q^{13} +(1.41363 + 0.0405943i) q^{14} +(3.31068 + 2.79946i) q^{15} +(-1.58991 - 3.67045i) q^{16} +7.91554i q^{17} +(1.59479 - 3.93150i) q^{18} +2.37413i q^{19} +(-0.287291 + 4.99809i) q^{20} +(-0.307237 + 1.70458i) q^{21} +(-0.0285324 + 0.993594i) q^{22} +(0.346619 + 0.600362i) q^{23} +(4.73540 - 1.25539i) q^{24} +(0.632931 - 1.09627i) q^{25} +(-3.74003 - 2.30492i) q^{26} +(4.47014 + 2.64912i) q^{27} +(-1.78658 + 0.898958i) q^{28} +(-8.70126 - 5.02368i) q^{29} +(-6.00055 - 1.26039i) q^{30} +(-7.34846 + 4.24264i) q^{31} +(4.44399 + 3.50014i) q^{32} +(-1.19809 - 0.215946i) q^{33} +(-5.31655 - 9.85118i) q^{34} +2.50317 q^{35} +(0.655856 + 5.96405i) q^{36} +2.85107 q^{37} +(-1.59460 - 2.95469i) q^{38} +(3.47419 - 4.10862i) q^{39} +(-2.99947 - 6.41327i) q^{40} +(5.82034 - 3.36037i) q^{41} +(-0.762533 - 2.32778i) q^{42} +(-3.17043 - 1.83045i) q^{43} +(-0.631847 - 1.25573i) q^{44} +(2.62187 - 7.03694i) q^{45} +(-0.834620 - 0.514363i) q^{46} +(-3.67787 + 6.37026i) q^{47} +(-5.05018 + 4.74296i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.0513868 + 1.78946i) q^{50} +(12.9010 - 4.64022i) q^{51} +(6.20273 + 0.356534i) q^{52} +0.889576i q^{53} +(-7.34256 - 0.294523i) q^{54} +1.75939i q^{55} +(1.61967 - 2.31876i) q^{56} +(3.86942 - 1.39175i) q^{57} +(14.2032 + 0.407865i) q^{58} +(-3.63052 - 6.28824i) q^{59} +(8.31446 - 2.46173i) q^{60} +(-2.39732 + 4.15228i) q^{61} +(6.29583 - 10.2158i) q^{62} +(2.95829 - 0.498512i) q^{63} +(-7.88161 - 1.37120i) q^{64} +(-6.73427 - 3.88803i) q^{65} +(1.63612 - 0.535959i) q^{66} +(7.40811 - 4.27707i) q^{67} +(13.2333 + 8.68925i) q^{68} +(0.775295 - 0.916874i) q^{69} +(-3.11529 + 1.68128i) q^{70} -6.34514 q^{71} +(-4.82205 - 6.98197i) q^{72} +8.20222 q^{73} +(-3.54826 + 1.91495i) q^{74} +(-2.15777 - 0.388920i) q^{75} +(3.96909 + 2.60619i) q^{76} +(-0.608700 + 0.351433i) q^{77} +(-1.56416 + 7.44681i) q^{78} +(-2.27268 - 1.31214i) q^{79} +(8.04049 + 5.96693i) q^{80} +(1.69715 - 8.83853i) q^{81} +(-4.98660 + 8.09139i) q^{82} +(6.50432 - 11.2658i) q^{83} +(2.51247 + 2.38484i) q^{84} +(-9.90697 - 17.1594i) q^{85} +(5.17515 + 0.148611i) q^{86} +(-3.08692 + 17.1266i) q^{87} +(1.62978 + 1.13841i) q^{88} +1.71842i q^{89} +(1.46341 + 10.5187i) q^{90} -3.10649i q^{91} +(1.38419 + 0.0795635i) q^{92} +(11.2226 + 9.48965i) q^{93} +(0.298601 - 10.3983i) q^{94} +(-2.97142 - 5.14665i) q^{95} +(3.09949 - 9.29479i) q^{96} +(-6.81083 + 11.7967i) q^{97} +(-1.20394 - 0.741971i) q^{98} +(0.350387 + 2.07928i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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