LMFDB - Embedded newform 546.2.bg.a.467.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			467.12
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.a.311.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.806632 + 1.53276i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23425 + 1.86729i) q^{5} +(-1.73072 - 0.0678152i) q^{6} +(0.481958 - 2.60148i) q^{7} +1.00000 q^{8} +(-1.69869 + 2.47274i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.806632 + 1.53276i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23425 + 1.86729i) q^{5} +(-1.73072 - 0.0678152i) q^{6} +(0.481958 - 2.60148i) q^{7} +1.00000 q^{8} +(-1.69869 + 2.47274i) q^{9} +(-3.23425 + 1.86729i) q^{10} +(-0.664055 - 1.15018i) q^{11} +(0.924091 - 1.46494i) q^{12} +(0.452687 + 3.57702i) q^{13} +(2.01197 + 1.71813i) q^{14} +(-0.253262 + 6.46353i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.49232 + 4.31682i) q^{17} +(-1.29211 - 2.70748i) q^{18} +(2.36598 - 4.09800i) q^{19} -3.73459i q^{20} +(4.37621 - 1.35971i) q^{21} +1.32811 q^{22} +(-1.00204 - 0.578526i) q^{23} +(0.806632 + 1.53276i) q^{24} +(4.47357 + 7.74844i) q^{25} +(-3.32413 - 1.39647i) q^{26} +(-5.16033 - 0.609089i) q^{27} +(-2.49393 + 0.883354i) q^{28} -6.29862i q^{29} +(-5.47095 - 3.45110i) q^{30} +(1.66752 + 2.88823i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.22729 - 1.94560i) q^{33} -4.98464 q^{34} +(6.41650 - 7.51388i) q^{35} +(2.99080 + 0.234739i) q^{36} +(-7.87543 - 4.54688i) q^{37} +(2.36598 + 4.09800i) q^{38} +(-5.11755 + 3.57920i) q^{39} +(3.23425 + 1.86729i) q^{40} +4.38044i q^{41} +(-1.01056 + 4.46976i) q^{42} -9.54856 q^{43} +(-0.664055 + 1.15018i) q^{44} +(-10.1113 + 4.82550i) q^{45} +(1.00204 - 0.578526i) q^{46} +(6.95231 + 4.01392i) q^{47} +(-1.73072 - 0.0678152i) q^{48} +(-6.53543 - 2.50761i) q^{49} -8.94713 q^{50} +(-4.60626 + 7.30220i) q^{51} +(2.87145 - 2.18055i) q^{52} +(-1.36514 + 0.788163i) q^{53} +(3.10765 - 4.16443i) q^{54} -4.95994i q^{55} +(0.481958 - 2.60148i) q^{56} +(8.18971 + 0.320899i) q^{57} +(5.45477 + 3.14931i) q^{58} +(9.31553 - 5.37832i) q^{59} +(5.72421 - 3.01244i) q^{60} +(4.85105 + 2.80076i) q^{61} -3.33504 q^{62} +(5.61410 + 5.61087i) q^{63} +1.00000 q^{64} +(-5.21524 + 12.4143i) q^{65} +(1.07130 + 2.03567i) q^{66} +(-3.51817 + 2.03122i) q^{67} +(2.49232 - 4.31682i) q^{68} +(0.0784657 - 2.00253i) q^{69} +(3.29896 + 9.31379i) q^{70} -9.95545 q^{71} +(-1.69869 + 2.47274i) q^{72} +(-7.21154 - 12.4907i) q^{73} +(7.87543 - 4.54688i) q^{74} +(-8.26796 + 13.1070i) q^{75} -4.73196 q^{76} +(-3.31221 + 1.17319i) q^{77} +(-0.540899 - 6.22153i) q^{78} +(7.22510 - 12.5142i) q^{79} +(-3.23425 + 1.86729i) q^{80} +(-3.22890 - 8.40085i) q^{81} +(-3.79357 - 2.19022i) q^{82} -6.74642i q^{83} +(-3.36565 - 3.11005i) q^{84} +18.6156i q^{85} +(4.77428 - 8.26929i) q^{86} +(9.65426 - 5.08067i) q^{87} +(-0.664055 - 1.15018i) q^{88} +(-2.55804 - 1.47689i) q^{89} +(0.876652 - 11.1694i) q^{90} +(9.52374 + 0.546316i) q^{91} +1.15705i q^{92} +(-3.08188 + 4.88564i) q^{93} +(-6.95231 + 4.01392i) q^{94} +(15.3043 - 8.83595i) q^{95} +(0.924091 - 1.46494i) q^{96} -9.79404 q^{97} +(5.43937 - 4.40604i) q^{98} +(3.97212 + 0.311759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9 - 14 * q^15 - 18 * q^16 + 4 * q^18 + 23 * q^21 + 14 * q^25 - 6 * q^26 + 7 * q^30 - 18 * q^32 + 24 * q^33 - 8 * q^36 - 10 * q^39 - 16 * q^42 - 16 * q^43 - 9 * q^45 + 72 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^54 - 8 * q^57 + 24 * q^59 + 7 * q^60 - 36 * q^61 - 39 * q^63 + 36 * q^64 + 18 * q^65 - 24 * q^66 - 72 * q^71 + 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 - 7 * q^84 + 8 * q^86 - 24 * q^87 - 72 * q^89 - 2 * q^91 - 14 * q^93 - 72 * q^94 - 12 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.806632	+	1.53276i	0.465709	+	0.884938i
$3$	0.806632	+	1.53276i	0.465709	+	0.884938i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.23425	+	1.86729i	1.44640	+	0.835079i	0.998265	−	0.0588875i	$-0.0187553\pi$
$5$	3.23425	+	1.86729i	1.44640	+	0.835079i	0.448134	+	0.893966i	$0.352089\pi$
$6$	−1.73072	−	0.0678152i	−0.706565	−	0.0276854i
$7$	0.481958	−	2.60148i	0.182163	−	0.983268i
$7$	0.481958	−	2.60148i	0.182163	−	0.983268i
$8$	1.00000			0.353553
$9$	−1.69869	+	2.47274i	−0.566230	+	0.824247i
$10$	−3.23425	+	1.86729i	−1.02276	+	0.590490i
$11$	−0.664055	−	1.15018i	−0.200220	−	0.346791i	0.748379	−	0.663271i	$-0.230832\pi$
$11$	−0.664055	−	1.15018i	−0.200220	−	0.346791i	−0.948599	+	0.316480i	$0.897499\pi$
$12$	0.924091	−	1.46494i	0.266762	−	0.422892i
$13$	0.452687	+	3.57702i	0.125553	+	0.992087i
$13$	0.452687	+	3.57702i	0.125553	+	0.992087i
$14$	2.01197	+	1.71813i	0.537722	+	0.459189i
$15$	−0.253262	+	6.46353i	−0.0653919	+	1.66888i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.49232	+	4.31682i	0.604476	+	1.04698i	0.992134	+	0.125180i	$0.0399508\pi$
$17$	2.49232	+	4.31682i	0.604476	+	1.04698i	−0.387658	+	0.921803i	$0.626716\pi$
$18$	−1.29211	−	2.70748i	−0.304554	−	0.638159i
$19$	2.36598	−	4.09800i	0.542793	−	0.940145i	−0.455949	−	0.890006i	$-0.650700\pi$
$19$	2.36598	−	4.09800i	0.542793	−	0.940145i	0.998742	−	0.0501391i	$-0.0159665\pi$
$20$		−	3.73459i		−	0.835079i
$21$	4.37621	−	1.35971i	0.954966	−	0.296714i
$22$	1.32811			0.283154
$23$	−1.00204	−	0.578526i	−0.208939	−	0.120631i	0.391879	−	0.920017i	$-0.371825\pi$
$23$	−1.00204	−	0.578526i	−0.208939	−	0.120631i	−0.600818	+	0.799386i	$0.705158\pi$
$24$	0.806632	+	1.53276i	0.164653	+	0.312873i
$25$	4.47357	+	7.74844i	0.894713	+	1.54969i
$26$	−3.32413	−	1.39647i	−0.651916	−	0.273871i
$27$	−5.16033	−	0.609089i	−0.993106	−	0.117219i
$28$	−2.49393	+	0.883354i	−0.471308	+	0.166938i
$29$		−	6.29862i		−	1.16962i	−0.811169	−	0.584812i	$-0.801168\pi$
$29$		−	6.29862i		−	1.16962i	0.811169	−	0.584812i	$-0.198832\pi$
$30$	−5.47095	−	3.45110i	−0.998855	−	0.630081i
$31$	1.66752	+	2.88823i	0.299495	+	0.518741i	0.976021	−	0.217679i	$-0.0698485\pi$
$31$	1.66752	+	2.88823i	0.299495	+	0.518741i	−0.676525	+	0.736419i	$0.736515\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.22729	−	1.94560i	0.213645	−	0.338686i
$34$	−4.98464			−0.854858
$35$	6.41650	−	7.51388i	1.08459	−	1.27008i
$36$	2.99080	+	0.234739i	0.498467	+	0.0391231i
$37$	−7.87543	−	4.54688i	−1.29471	−	0.747503i	−0.315227	−	0.949016i	$-0.602081\pi$
$37$	−7.87543	−	4.54688i	−1.29471	−	0.747503i	−0.979486	+	0.201514i	$0.935414\pi$
$38$	2.36598	+	4.09800i	0.383812	+	0.664783i
$39$	−5.11755	+	3.57920i	−0.819464	+	0.573130i
$40$	3.23425	+	1.86729i	0.511379	+	0.295245i
$41$			4.38044i			0.684109i	0.939680	+	0.342055i	$0.111123\pi$
$41$			4.38044i			0.684109i	−0.939680	+	0.342055i	$0.888877\pi$
$42$	−1.01056	+	4.46976i	−0.155932	+	0.689699i
$43$	−9.54856			−1.45614			−0.728071	−	0.685502i	$-0.759583\pi$
$43$	−9.54856			−1.45614			−0.728071	+	0.685502i	$0.759583\pi$
$44$	−0.664055	+	1.15018i	−0.100110	+	0.173396i
$45$	−10.1113	+	4.82550i	−1.50731	+	0.719343i
$46$	1.00204	−	0.578526i	0.147742	−	0.0852990i
$47$	6.95231	+	4.01392i	1.01410	+	0.585490i	0.912389	−	0.409324i	$-0.134235\pi$
$47$	6.95231	+	4.01392i	1.01410	+	0.585490i	0.101710	+	0.994814i	$0.467569\pi$
$48$	−1.73072	−	0.0678152i	−0.249808	−	0.00978828i
$49$	−6.53543	−	2.50761i	−0.933633	−	0.358230i
$50$	−8.94713			−1.26532
$51$	−4.60626	+	7.30220i	−0.645005	+	1.02251i
$52$	2.87145	−	2.18055i	0.398198	−	0.302388i
$53$	−1.36514	+	0.788163i	−0.187516	+	0.108263i	−0.590819	−	0.806804i	$-0.701195\pi$
$53$	−1.36514	+	0.788163i	−0.187516	+	0.108263i	0.403303	+	0.915066i	$0.367862\pi$
$54$	3.10765	−	4.16443i	0.422898	−	0.566707i
$55$		−	4.95994i		−	0.668798i
$56$	0.481958	−	2.60148i	0.0644044	−	0.347638i
$57$	8.18971	+	0.320899i	1.08475	+	0.0425041i
$58$	5.45477	+	3.14931i	0.716246	+	0.413525i
$59$	9.31553	−	5.37832i	1.21278	−	0.700198i	0.249415	−	0.968397i	$-0.419762\pi$
$59$	9.31553	−	5.37832i	1.21278	−	0.700198i	0.963364	+	0.268199i	$0.0864283\pi$
$60$	5.72421	−	3.01244i	0.738993	−	0.388904i
$61$	4.85105	+	2.80076i	0.621113	+	0.358600i	0.777302	−	0.629127i	$-0.216588\pi$
$61$	4.85105	+	2.80076i	0.621113	+	0.358600i	−0.156189	+	0.987727i	$0.549921\pi$
$62$	−3.33504			−0.423550
$63$	5.61410	+	5.61087i	0.707310	+	0.706904i
$64$	1.00000			0.125000
$65$	−5.21524	+	12.4143i	−0.646871	+	1.53980i
$66$	1.07130	+	2.03567i	0.131867	+	0.250574i
$67$	−3.51817	+	2.03122i	−0.429813	+	0.248153i	−0.699267	−	0.714861i	$-0.746490\pi$
$67$	−3.51817	+	2.03122i	−0.429813	+	0.248153i	0.269454	+	0.963013i	$0.413157\pi$
$68$	2.49232	−	4.31682i	0.302238	−	0.523491i
$69$	0.0784657	−	2.00253i	0.00944616	−	0.241077i
$70$	3.29896	+	9.31379i	0.394301	+	1.11321i
$71$	−9.95545			−1.18150			−0.590748	−	0.806856i	$-0.701167\pi$
$71$	−9.95545			−1.18150			−0.590748	+	0.806856i	$0.701167\pi$
$72$	−1.69869	+	2.47274i	−0.200193	+	0.291415i
$73$	−7.21154	−	12.4907i	−0.844046	−	1.46193i	−0.886447	−	0.462830i	$-0.846834\pi$
$73$	−7.21154	−	12.4907i	−0.844046	−	1.46193i	0.0424005	−	0.999101i	$-0.486499\pi$
$74$	7.87543	−	4.54688i	0.915500	−	0.528564i
$75$	−8.26796	+	13.1070i	−0.954702	+	1.51347i
$76$	−4.73196			−0.542793
$77$	−3.31221	+	1.17319i	−0.377462	+	0.133698i
$78$	−0.540899	−	6.22153i	−0.0612448	−	0.704449i
$79$	7.22510	−	12.5142i	0.812888	−	1.40796i	−0.0979473	−	0.995192i	$-0.531228\pi$
$79$	7.22510	−	12.5142i	0.812888	−	1.40796i	0.910835	−	0.412771i	$-0.135439\pi$
$80$	−3.23425	+	1.86729i	−0.361600	+	0.208770i
$81$	−3.22890	−	8.40085i	−0.358767	−	0.933427i
$82$	−3.79357	−	2.19022i	−0.418930	−	0.241869i
$83$		−	6.74642i		−	0.740516i	−0.928929	−	0.370258i	$-0.879269\pi$
$83$		−	6.74642i		−	0.740516i	0.928929	−	0.370258i	$-0.120731\pi$
$84$	−3.36565	−	3.11005i	−0.367223	−	0.339334i
$85$			18.6156i			2.01914i
$86$	4.77428	−	8.26929i	0.514824	−	0.891701i
$87$	9.65426	−	5.08067i	1.03504	−	0.544705i
$88$	−0.664055	−	1.15018i	−0.0707885	−	0.122609i
$89$	−2.55804	−	1.47689i	−0.271152	−	0.156550i	0.358259	−	0.933622i	$-0.383371\pi$
$89$	−2.55804	−	1.47689i	−0.271152	−	0.156550i	−0.629411	+	0.777072i	$0.716704\pi$
$90$	0.876652	−	11.1694i	0.0924072	−	1.17736i
$91$	9.52374	+	0.546316i	0.998359	+	0.0572695i
$92$			1.15705i			0.120631i
$93$	−3.08188	+	4.88564i	−0.319576	+	0.506617i
$94$	−6.95231	+	4.01392i	−0.717076	+	0.414004i
$95$	15.3043	−	8.83595i	1.57019	−	0.906550i
$96$	0.924091	−	1.46494i	0.0943146	−	0.149515i
$97$	−9.79404			−0.994434			−0.497217	−	0.867626i	$-0.665645\pi$
$97$	−9.79404			−0.994434			−0.497217	+	0.867626i	$0.665645\pi$
$98$	5.43937	−	4.40604i	0.549460	−	0.445078i
$99$	3.97212	+	0.311759i	0.399213	+	0.0313329i
$100$	4.47357	−	7.74844i	0.447357	−	0.774844i
$101$	4.68518	+	8.11497i	0.466193	+	0.807470i	0.999254	−	0.0386068i	$-0.0122920\pi$
$101$	4.68518	+	8.11497i	0.466193	+	0.807470i	−0.533062	+	0.846076i	$0.678959\pi$
$102$	−4.02077	−	7.64024i	−0.398115	−	0.756496i
$103$	−0.155999	−	0.0900661i	−0.0153710	−	0.00887448i	0.492295	−	0.870429i	$-0.336158\pi$
$103$	−0.155999	−	0.0900661i	−0.0153710	−	0.00887448i	−0.507666	+	0.861554i	$0.669492\pi$
$104$	0.452687	+	3.57702i	0.0443896	+	0.350756i
$105$	16.6927	+	3.77401i	1.62904	+	0.368305i
$106$		−	1.57633i		−	0.153106i
$107$	5.15442	+	2.97590i	0.498296	+	0.287691i	0.728010	−	0.685567i	$-0.240446\pi$
$107$	5.15442	+	2.97590i	0.498296	+	0.287691i	−0.229714	+	0.973258i	$0.573779\pi$
$108$	2.05268	+	4.77352i	0.197519	+	0.459332i
$109$	10.3694	−	5.98679i	0.993211	−	0.573431i	0.0869783	−	0.996210i	$-0.472279\pi$
$109$	10.3694	−	5.98679i	0.993211	−	0.573431i	0.906233	+	0.422780i	$0.138946\pi$
$110$	4.29544	+	2.47997i	0.409554	+	0.236456i
$111$	0.616695	−	15.7388i	0.0585341	−	1.49386i
$112$	2.01197	+	1.71813i	0.190113	+	0.162348i
$113$			1.47456i			0.138714i	0.997592	+	0.0693572i	$0.0220948\pi$
$113$			1.47456i			0.138714i	−0.997592	+	0.0693572i	$0.977905\pi$
$114$	−4.37276	+	6.93205i	−0.409547	+	0.649246i
$115$	−2.16055	−	3.74219i	−0.201473	−	0.348961i
$116$	−5.45477	+	3.14931i	−0.506462	+	0.292406i
$117$	−9.61402	−	4.95687i	−0.888817	−	0.458263i
$118$			10.7566i			0.990230i
$119$	12.4313	−	4.40320i	1.13958	−	0.403640i
$120$	−0.253262	+	6.46353i	−0.0231195	+	0.590037i
$121$	4.61806	−	7.99872i	0.419824	−	0.727156i
$122$	−4.85105	+	2.80076i	−0.439193	+	0.253568i
$123$	−6.71415	+	3.53340i	−0.605394	+	0.318596i
$124$	1.66752	−	2.88823i	0.149748	−	0.259370i
$125$			14.7409i			1.31847i
$126$	−7.66621	+	2.05651i	−0.682960	+	0.183209i
$127$	10.6040			0.940957			0.470479	−	0.882411i	$-0.344081\pi$
$127$	10.6040			0.940957			0.470479	+	0.882411i	$0.344081\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−7.70217	−	14.6356i	−0.678138	−	1.28859i
$130$	−8.14345	−	10.7237i	−0.714227	−	0.940528i
$131$	−0.258515	+	0.447761i	−0.0225865	+	0.0391210i	−0.877098	−	0.480312i	$-0.840523\pi$
$131$	−0.258515	+	0.447761i	−0.0225865	+	0.0391210i	0.854511	+	0.519433i	$0.173857\pi$
$132$	−2.29859	−	0.0900661i	−0.200067	−	0.00783925i
$133$	−9.52057	−	8.13012i	−0.825538	−	0.704971i
$134$		−	4.06244i		−	0.350941i
$135$	−15.5524	−	11.6058i	−1.33854	−	0.998868i
$136$	2.49232	+	4.31682i	0.213714	+	0.370164i
$137$	−0.694033	−	1.20210i	−0.0592953	−	0.102702i	0.834854	−	0.550471i	$-0.185552\pi$
$137$	−0.694033	−	1.20210i	−0.0592953	−	0.102702i	−0.894149	+	0.447769i	$0.852219\pi$
$138$	1.69501	+	1.06922i	0.144289	+	0.0910181i
$139$			12.9034i			1.09445i	0.836985	+	0.547226i	$0.184316\pi$
$139$			12.9034i			1.09445i	−0.836985	+	0.547226i	$0.815684\pi$
$140$	−9.71546	−	1.79991i	−0.821107	−	0.152120i
$141$	−0.544410	+	13.8940i	−0.0458476	+	1.17008i
$142$	4.97773	−	8.62168i	0.417722	−	0.723515i
$143$	3.81360	−	2.89601i	0.318909	−	0.242176i
$144$	−1.29211	−	2.70748i	−0.107676	−	0.225623i
$145$	11.7614	−	20.3713i	0.976729	−	1.69174i
$146$	14.4231			1.19366
$147$	−1.42813	−	12.0400i	−0.117790	−	0.993039i
$148$			9.09376i			0.747503i
$149$	4.15260	−	7.19252i	0.340194	−	0.589234i	−0.644274	−	0.764795i	$-0.722840\pi$
$149$	4.15260	−	7.19252i	0.340194	−	0.589234i	0.984469	+	0.175561i	$0.0561738\pi$
$150$	−7.21704	−	13.7138i	−0.589269	−	1.11973i
$151$	1.12265	−	0.648163i	0.0913600	−	0.0527467i	−0.453624	−	0.891193i	$-0.649869\pi$
$151$	1.12265	−	0.648163i	0.0913600	−	0.0527467i	0.544984	+	0.838446i	$0.316536\pi$
$152$	2.36598	−	4.09800i	0.191906	−	0.332391i
$153$	−14.9081	−	1.17009i	−1.20525	−	0.0945959i
$154$	0.640093	−	3.45506i	0.0515802	−	0.278416i
$155$			12.4550i			1.00041i
$156$	5.65845	+	2.64233i	0.453039	+	0.211556i
$157$	15.2700	−	8.81616i	1.21868	−	0.703606i	0.254046	−	0.967192i	$-0.418239\pi$
$157$	15.2700	−	8.81616i	1.21868	−	0.703606i	0.964636	+	0.263586i	$0.0849053\pi$
$158$	7.22510	+	12.5142i	0.574798	+	0.995580i
$159$	−2.30923	−	1.45667i	−0.183134	−	0.115521i
$160$		−	3.73459i		−	0.295245i
$161$	−1.98796	+	2.32795i	−0.156674	+	0.183469i
$162$	8.88980	+	1.40411i	0.698448	+	0.110318i
$163$	5.82554	+	3.36338i	0.456292	+	0.263440i	0.710484	−	0.703714i	$-0.248476\pi$
$163$	5.82554	+	3.36338i	0.456292	+	0.263440i	−0.254192	+	0.967154i	$0.581810\pi$
$164$	3.79357	−	2.19022i	0.296228	−	0.171027i
$165$	7.60239	−	4.00085i	0.591845	−	0.311465i
$166$	5.84258	+	3.37321i	0.453472	+	0.261812i
$167$			1.39818i			0.108194i	0.998536	+	0.0540972i	$0.0172281\pi$
$167$			1.39818i			0.108194i	−0.998536	+	0.0540972i	$0.982772\pi$
$168$	4.37621	−	1.35971i	0.337632	−	0.104904i
$169$	−12.5901	+	3.23854i	−0.968473	+	0.249119i
$170$	−16.1215	−	9.30778i	−1.23647	−	0.713874i
$171$	6.11422	+	12.8117i	0.467566	+	0.979734i
$172$	4.77428	+	8.26929i	0.364035	+	0.630528i
$173$	−11.0767	+	19.1854i	−0.842145	+	1.45864i	0.0459336	+	0.998944i	$0.485374\pi$
$173$	−11.0767	+	19.1854i	−0.842145	+	1.45864i	−0.888078	+	0.459693i	$0.847960\pi$
$174$	−0.427142	+	10.9012i	−0.0323816	+	0.826415i
$175$	22.3135	−	7.90348i	1.68674	−	0.597447i
$176$	1.32811			0.100110
$177$	15.7579	+	9.94012i	1.18443	+	0.747145i
$178$	2.55804	−	1.47689i	0.191734	−	0.110697i
$179$	21.0472	−	12.1516i	1.57314	−	0.908253i	0.577359	−	0.816490i	$-0.304083\pi$
$179$	21.0472	−	12.1516i	1.57314	−	0.908253i	0.995781	−	0.0917629i	$-0.0292502\pi$
$180$	9.23466	+	6.34391i	0.688311	+	0.472847i
$181$		−	14.4139i		−	1.07137i	−0.844417	−	0.535687i	$-0.820053\pi$
$181$		−	14.4139i		−	1.07137i	0.844417	−	0.535687i	$-0.179947\pi$
$182$	−5.23499	+	7.97464i	−0.388043	+	0.591120i
$183$	−0.379868	+	9.69466i	−0.0280806	+	0.716650i
$184$	−1.00204	−	0.578526i	−0.0738711	−	0.0426495i
$185$	−16.9807	−	29.4115i	−1.24845	−	2.16237i
$186$	−2.69015	−	5.11180i	−0.197251	−	0.374815i
$187$	3.31007	−	5.73321i	0.242057	−	0.419254i
$188$		−	8.02784i		−	0.585490i
$189$	−4.07160	+	13.1310i	−0.296165	+	0.955137i
$190$			17.6719i			1.28205i
$191$	−0.358267	−	0.206846i	−0.0259233	−	0.0149668i	0.486982	−	0.873412i	$-0.338098\pi$
$191$	−0.358267	−	0.206846i	−0.0259233	−	0.0149668i	−0.512906	+	0.858445i	$0.671431\pi$
$192$	0.806632	+	1.53276i	0.0582136	+	0.110617i
$193$	6.58304	−	3.80072i	0.473857	−	0.273582i	−0.243996	−	0.969776i	$-0.578458\pi$
$193$	6.58304	−	3.80072i	0.473857	−	0.273582i	0.717853	+	0.696195i	$0.245125\pi$
$194$	4.89702	−	8.48189i	0.351586	−	0.608964i
$195$	−23.2348	+	2.02003i	−1.66388	+	0.144658i
$196$	1.09606	+	6.91366i	0.0782901	+	0.493833i
$197$	6.65182			0.473922			0.236961	−	0.971519i	$-0.423849\pi$
$197$	6.65182			0.473922			0.236961	+	0.971519i	$0.423849\pi$
$198$	−2.25605	+	3.28407i	−0.160330	+	0.233389i
$199$	−13.0997	+	7.56314i	−0.928616	+	0.536137i	−0.886374	−	0.462971i	$-0.846783\pi$
$199$	−13.0997	+	7.56314i	−0.928616	+	0.536137i	−0.0422423	+	0.999107i	$0.513450\pi$
$200$	4.47357	+	7.74844i	0.316329	+	0.547898i
$201$	−5.95123	−	3.75406i	−0.419768	−	0.264791i
$202$	−9.37036			−0.659296
$203$	−16.3858	−	3.03567i	−1.15005	−	0.213062i
$204$	8.62702	+	0.338034i	0.604012	+	0.0236671i
$205$	−8.17956	+	14.1674i	−0.571285	+	0.989495i
$206$	0.155999	−	0.0900661i	0.0108690	−	0.00627520i
$207$	3.13269	−	1.49504i	0.217737	−	0.103912i
$208$	−3.32413	−	1.39647i	−0.230487	−	0.0968279i
$209$	−6.28456			−0.434712
$210$	−11.6147	+	12.5693i	−0.801493	+	0.867365i
$211$	−10.2354			−0.704635			−0.352318	−	0.935880i	$-0.614606\pi$
$211$	−10.2354			−0.704635			−0.352318	+	0.935880i	$0.614606\pi$
$212$	1.36514	+	0.788163i	0.0937581	+	0.0541313i
$213$	−8.03038	−	15.2593i	−0.550233	−	1.04555i
$214$	−5.15442	+	2.97590i	−0.352349	+	0.203429i
$215$	−30.8824	−	17.8300i	−2.10616	−	1.21599i
$216$	−5.16033	−	0.609089i	−0.351116	−	0.0414433i
$217$	8.31735	−	2.94602i	0.564618	−	0.199989i
$218$			11.9736i			0.810953i
$219$	13.3282	−	21.1290i	0.900638	−	1.42776i
$220$	−4.29544	+	2.47997i	−0.289598	+	0.167200i
$221$	−14.3131	+	10.8692i	−0.962804	+	0.731144i
$222$	13.3218	+	8.40346i	0.894103	+	0.564004i
$223$	−21.3728			−1.43123			−0.715616	−	0.698494i	$-0.753854\pi$
$223$	−21.3728			−1.43123			−0.715616	+	0.698494i	$0.753854\pi$
$224$	−2.49393	+	0.883354i	−0.166633	+	0.0590216i
$225$	−26.7591	−	2.10024i	−1.78394	−	0.140016i
$226$	−1.27700	−	0.737278i	−0.0849449	−	0.0490430i
$227$	13.1596	−	7.59771i	0.873434	−	0.504278i	0.00494636	−	0.999988i	$-0.498426\pi$
$227$	13.1596	−	7.59771i	0.873434	−	0.504278i	0.868488	+	0.495710i	$0.165092\pi$
$228$	−3.81695	−	7.25294i	−0.252784	−	0.480338i
$229$	−10.7812	+	18.6737i	−0.712445	+	1.23399i	0.251492	+	0.967859i	$0.419079\pi$
$229$	−10.7812	+	18.6737i	−0.712445	+	1.23399i	−0.963937	+	0.266131i	$0.914255\pi$
$230$	4.32111			0.284925
$231$	−4.46995	−	4.13049i	−0.294101	−	0.271766i
$232$		−	6.29862i		−	0.413525i
$233$	23.8631	+	13.7774i	1.56332	+	0.902586i	0.996917	+	0.0784603i	$0.0250004\pi$
$233$	23.8631	+	13.7774i	1.56332	+	0.902586i	0.566407	+	0.824126i	$0.308333\pi$
$234$	9.09979	−	5.84755i	0.594872	−	0.382266i
$235$	14.9903	+	25.9640i	0.977861	+	1.69371i
$236$	−9.31553	−	5.37832i	−0.606389	−	0.350099i
$237$	25.0093	+	0.979944i	1.62453	+	0.0636542i
$238$	−2.40239	+	12.9674i	−0.155724	+	0.840555i
$239$	−12.0981			−0.782563			−0.391282	−	0.920271i	$-0.627968\pi$
$239$	−12.0981			−0.782563			−0.391282	+	0.920271i	$0.627968\pi$
$240$	−5.47095	−	3.45110i	−0.353148	−	0.222767i
$241$	−1.76152	−	3.05105i	−0.113470	−	0.196535i	0.803697	−	0.595038i	$-0.202863\pi$
$241$	−1.76152	−	3.05105i	−0.113470	−	0.196535i	−0.917167	+	0.398503i	$0.869530\pi$
$242$	4.61806	+	7.99872i	0.296860	+	0.514177i
$243$	10.2719	−	11.7255i	0.658944	−	0.752192i
$244$		−	5.60151i		−	0.358600i
$245$	−16.4548	−	20.3138i	−1.05126	−	1.29780i
$246$	0.297060	−	7.58132i	0.0189399	−	0.483367i
$247$	15.7297	+	6.60805i	1.00085	+	0.420460i
$248$	1.66752	+	2.88823i	0.105887	+	0.183403i
$249$	10.3406	−	5.44188i	0.655311	−	0.344865i
$250$	−12.7660	−	7.37045i	−0.807392	−	0.466148i
$251$	−18.9499			−1.19611			−0.598053	−	0.801457i	$-0.704059\pi$
$251$	−18.9499			−1.19611			−0.598053	+	0.801457i	$0.704059\pi$
$252$	2.05211	−	7.66739i	0.129271	−	0.483000i
$253$			1.53669i			0.0966110i
$254$	−5.30202	+	9.18338i	−0.332679	+	0.576216i
$255$	−28.5331	+	15.0159i	−1.78681	+	0.940332i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.299289	−	0.518384i	0.0186692	−	0.0323359i	−0.856540	−	0.516081i	$-0.827390\pi$
$257$	0.299289	−	0.518384i	0.0186692	−	0.0323359i	0.875209	+	0.483745i	$0.160724\pi$
$258$	16.5259	+	0.647537i	1.02886	+	0.0403139i
$259$	−15.6243	+	18.2964i	−0.970844	+	1.13688i
$260$	13.3587	−	1.69060i	0.828471	−	0.104846i
$261$	15.5749	+	10.6994i	0.964060	+	0.662277i
$262$	−0.258515	−	0.447761i	−0.0159711	−	0.0276627i
$263$	−23.1551	+	13.3686i	−1.42781	+	0.824344i	−0.996947	−	0.0780752i	$-0.975123\pi$
$263$	−23.1551	+	13.3686i	−1.42781	+	0.824344i	−0.430859	+	0.902419i	$0.641789\pi$
$264$	1.22729	−	1.94560i	0.0755348	−	0.119744i
$265$	−5.88693			−0.361631
$266$	11.8012	−	4.17999i	0.723576	−	0.256292i
$267$	0.200311	−	5.11217i	0.0122588	−	0.312860i
$268$	3.51817	+	2.03122i	0.214907	+	0.124076i
$269$	5.72442	+	9.91498i	0.349024	+	0.604527i	0.986076	−	0.166293i	$-0.0531799\pi$
$269$	5.72442	+	9.91498i	0.349024	+	0.604527i	−0.637052	+	0.770820i	$0.719847\pi$
$270$	17.8271	−	7.66590i	1.08492	−	0.466532i
$271$	12.6383	−	21.8902i	0.767723	−	1.32974i	−0.171072	−	0.985259i	$-0.554723\pi$
$271$	12.6383	−	21.8902i	0.767723	−	1.32974i	0.938795	−	0.344477i	$-0.111944\pi$
$272$	−4.98464			−0.302238
$273$	6.84478	+	15.0383i	0.414265	+	0.910156i
$274$	1.38807			0.0838562
$275$	5.94139	−	10.2908i	0.358279	−	0.620558i
$276$	−1.77348	+	0.933314i	−0.106751	+	0.0561789i
$277$	−2.29715	−	3.97877i	−0.138022	−	0.239061i	0.788726	−	0.614745i	$-0.210741\pi$
$277$	−2.29715	−	3.97877i	−0.138022	−	0.239061i	−0.926748	+	0.375684i	$0.877408\pi$
$278$	−11.1747	−	6.45170i	−0.670213	−	0.386947i
$279$	−9.97443	−	0.782862i	−0.597154	−	0.0468687i
$280$	6.41650	−	7.51388i	0.383459	−	0.449040i
$281$	−22.5191			−1.34338			−0.671689	−	0.740834i	$-0.734431\pi$
$281$	−22.5191			−1.34338			−0.671689	+	0.740834i	$0.734431\pi$
$282$	−11.7603	−	7.41845i	−0.700317	−	0.441763i
$283$	6.47259	−	3.73695i	0.384756	−	0.222139i	−0.295130	−	0.955457i	$-0.595363\pi$
$283$	6.47259	−	3.73695i	0.384756	−	0.222139i	0.679885	+	0.733318i	$0.262030\pi$
$284$	4.97773	+	8.62168i	0.295374	+	0.511602i
$285$	25.8883	+	16.3304i	1.53349	+	0.967332i
$286$	0.601218	+	4.75068i	0.0355508	+	0.280913i
$287$	11.3956	+	2.11119i	0.672663	+	0.124619i
$288$	2.99080	+	0.234739i	0.176235	+	0.0138321i
$289$	−3.92330	+	6.79535i	−0.230782	+	0.399726i
$290$	11.7614	+	20.3713i	0.690651	+	1.19624i
$291$	−7.90018	−	15.0119i	−0.463117	−	0.880012i
$292$	−7.21154	+	12.4907i	−0.422023	+	0.730966i
$293$			14.6089i			0.853460i	0.904379	+	0.426730i	$0.140334\pi$
$293$			14.6089i			0.853460i	−0.904379	+	0.426730i	$0.859666\pi$
$294$	11.1410	+	4.78318i	0.649754	+	0.278961i
$295$	40.1716			2.33888
$296$	−7.87543	−	4.54688i	−0.457750	−	0.264282i
$297$	2.72618	+	6.33976i	0.158189	+	0.367870i
$298$	4.15260	+	7.19252i	0.240554	+	0.416651i
$299$	1.61579	−	3.84619i	0.0934435	−	0.222431i
$300$	15.4850	+	0.606752i	0.894027	+	0.0350308i
$301$	−4.60200	+	24.8404i	−0.265255	+	1.43178i
$302$			1.29633i			0.0745952i
$303$	−8.65907	+	13.7270i	−0.497450	+	0.788598i
$304$	2.36598	+	4.09800i	0.135698	+	0.235036i
$305$	10.4597	+	18.1167i	0.598918	+	1.03736i
$306$	8.46735	−	12.3257i	0.484046	−	0.704614i
$307$	−5.52889			−0.315550			−0.157775	−	0.987475i	$-0.550432\pi$
$307$	−5.52889			−0.315550			−0.157775	+	0.987475i	$0.550432\pi$
$308$	2.67212	+	2.28187i	0.152258	+	0.130021i
$309$	0.0122157	−	0.311759i	0.000694927	−	0.0177353i
$310$	−10.7863	−	6.22749i	−0.612622	−	0.353698i
$311$	−12.5077	−	21.6640i	−0.709247	−	1.22845i	−0.965137	−	0.261746i	$-0.915702\pi$
$311$	−12.5077	−	21.6640i	−0.709247	−	1.22845i	0.255890	−	0.966706i	$-0.417632\pi$
$312$	−5.11755	+	3.57920i	−0.289724	+	0.202632i
$313$	12.4242	+	7.17314i	0.702260	+	0.405450i	0.808189	−	0.588924i	$-0.200448\pi$
$313$	12.4242	+	7.17314i	0.702260	+	0.405450i	−0.105929	+	0.994374i	$0.533782\pi$
$314$			17.6323i			0.995049i
$315$	7.68023	+	28.6301i	0.432732	+	1.61312i
$316$	−14.4502			−0.812888
$317$	−7.58692	+	13.1409i	−0.426124	+	0.738068i	−0.996525	−	0.0832983i	$-0.973455\pi$
$317$	−7.58692	+	13.1409i	−0.426124	+	0.738068i	0.570401	+	0.821367i	$0.306788\pi$
$318$	2.41613	−	1.27151i	0.135490	−	0.0713030i
$319$	−7.24453	+	4.18263i	−0.405616	+	0.234182i
$320$	3.23425	+	1.86729i	0.180800	+	0.104385i
$321$	−0.403623	+	10.3009i	−0.0225280	+	0.574942i
$322$	−1.02209	−	2.88560i	−0.0569586	−	0.160808i
$323$	23.5871			1.31242
$324$	−5.66090	+	6.99673i	−0.314494	+	0.388707i
$325$	−25.6912	+	19.5097i	−1.42509	+	1.08220i
$326$	−5.82554	+	3.36338i	−0.322647	+	0.186280i
$327$	17.5406	+	11.0647i	0.969998	+	0.611878i
$328$			4.38044i			0.241869i
$329$	13.7929	−	16.1518i	0.760425	−	0.890477i
$330$	−0.336360	+	8.58428i	−0.0185160	+	0.472549i
$331$	−25.2714	−	14.5904i	−1.38904	−	0.801963i	−0.395833	−	0.918322i	$-0.629544\pi$
$331$	−25.2714	−	14.5904i	−1.38904	−	0.801963i	−0.993207	+	0.116360i	$0.962878\pi$
$332$	−5.84258	+	3.37321i	−0.320653	+	0.185129i
$333$	24.6212	−	11.7502i	1.34923	−	0.643904i
$334$	−1.21086	−	0.699090i	−0.0662553	−	0.0382525i
$335$	−15.1715			−0.828908
$336$	−1.01056	+	4.46976i	−0.0551303	+	0.243846i
$337$	21.8314			1.18923			0.594615	−	0.804011i	$-0.297305\pi$
$337$	21.8314			1.18923			0.594615	+	0.804011i	$0.297305\pi$
$338$	3.49042	−	12.5227i	0.189854	−	0.681143i
$339$	−2.26014	+	1.18942i	−0.122754	+	0.0646006i
$340$	16.1215	−	9.30778i	0.874313	−	0.504785i
$341$	2.21465	−	3.83588i	0.119930	−	0.207725i
$342$	−14.1524	−	1.11077i	−0.765271	−	0.0600638i
$343$	−9.67332	+	15.7933i	−0.522310	+	0.852756i
$344$	−9.54856			−0.514824
$345$	3.99310	−	6.33017i	0.214981	−	0.340805i
$346$	−11.0767	−	19.1854i	−0.595486	−	1.03141i
$347$	−24.0903	+	13.9086i	−1.29324	+	0.746651i	−0.979227	−	0.202768i	$-0.935006\pi$
$347$	−24.0903	+	13.9086i	−1.29324	+	0.746651i	−0.314011	+	0.949419i	$0.601673\pi$
$348$	−9.22711	−	5.82050i	−0.494625	−	0.312011i
$349$	−4.54691			−0.243391			−0.121695	−	0.992567i	$-0.538833\pi$
$349$	−4.54691			−0.243391			−0.121695	+	0.992567i	$0.538833\pi$
$350$	−4.31214	+	23.2758i	−0.230494	+	1.24414i
$351$	−0.157289	−	18.7343i	−0.00839546	−	0.999965i
$352$	−0.664055	+	1.15018i	−0.0353943	+	0.0613047i
$353$	7.21102	−	4.16329i	0.383804	−	0.221589i	−0.295668	−	0.955291i	$-0.595542\pi$
$353$	7.21102	−	4.16329i	0.383804	−	0.221589i	0.679472	+	0.733701i	$0.262209\pi$
$354$	−16.4873	+	8.67665i	−0.876292	+	0.461159i
$355$	−32.1984	−	18.5897i	−1.70891	−	0.986641i
$356$			2.95378i			0.156550i
$357$	16.7765	+	15.5025i	0.887909	+	0.820477i
$358$			24.3032i			1.28446i
$359$	−7.10506	+	12.3063i	−0.374991	+	0.649503i	−0.990326	−	0.138763i	$-0.955687\pi$
$359$	−7.10506	+	12.3063i	−0.374991	+	0.649503i	0.615335	+	0.788266i	$0.289021\pi$
$360$	−10.1113	+	4.82550i	−0.532913	+	0.254326i
$361$	−1.69571	−	2.93706i	−0.0892481	−	0.154582i
$362$	12.4828	+	7.20693i	0.656080	+	0.378788i
$363$	15.9852	+	0.626350i	0.839004	+	0.0328748i
$364$	−4.28874	−	8.52095i	−0.224791	−	0.446619i
$365$		−	53.8642i		−	2.81938i
$366$	−8.20589	−	5.17631i	−0.428929	−	0.270570i
$367$	2.05984	−	1.18925i	0.107523	−	0.0620782i	−0.445274	−	0.895394i	$-0.646894\pi$
$367$	2.05984	−	1.18925i	0.107523	−	0.0620782i	0.552797	+	0.833316i	$0.313561\pi$
$368$	1.00204	−	0.578526i	0.0522347	−	0.0301577i
$369$	−10.8317	−	7.44101i	−0.563875	−	0.387363i
$370$	33.9614			1.76557
$371$	1.39245	+	3.93125i	0.0722926	+	0.204100i
$372$	5.77202	+	0.226166i	0.299265	+	0.0117262i
$373$	−11.7785	+	20.4010i	−0.609869	+	1.05632i	0.381392	+	0.924413i	$0.375445\pi$
$373$	−11.7785	+	20.4010i	−0.609869	+	1.05632i	−0.991262	+	0.131911i	$0.957889\pi$
$374$	3.31007	+	5.73321i	0.171160	+	0.296457i
$375$	−22.5942	+	11.8905i	−1.16676	+	0.614022i
$376$	6.95231	+	4.01392i	0.358538	+	0.207002i
$377$	22.5303	−	2.85130i	1.16037	−	0.146850i
$378$	−9.33594	−	10.0916i	−0.480189	−	0.519055i
$379$		−	18.0896i		−	0.929201i	−0.885520	−	0.464601i	$-0.846198\pi$
$379$		−	18.0896i		−	0.929201i	0.885520	−	0.464601i	$-0.153802\pi$
$380$	−15.3043	−	8.83595i	−0.785095	−	0.453275i
$381$	8.55356	+	16.2534i	0.438212	+	0.832689i
$382$	0.358267	−	0.206846i	0.0183306	−	0.0105831i
$383$	−6.97099	−	4.02470i	−0.356201	−	0.205653i	0.311212	−	0.950340i	$-0.399265\pi$
$383$	−6.97099	−	4.02470i	−0.356201	−	0.205653i	−0.667413	+	0.744688i	$0.732598\pi$
$384$	−1.73072	−	0.0678152i	−0.0883206	−	0.00346068i
$385$	−12.9032	−	2.39048i	−0.657608	−	0.121830i
$386$			7.60143i			0.386903i
$387$	16.2200	−	23.6111i	0.824511	−	1.20022i
$388$	4.89702	+	8.48189i	0.248609	+	0.430603i
$389$	−27.5356	+	15.8977i	−1.39611	+	0.806045i	−0.993983	−	0.109539i	$-0.965063\pi$
$389$	−27.5356	+	15.8977i	−1.39611	+	0.806045i	−0.402128	+	0.915583i	$0.631729\pi$
$390$	9.86802	−	21.1320i	0.499686	−	1.07006i
$391$		−	5.76748i		−	0.291674i
$392$	−6.53543	−	2.50761i	−0.330089	−	0.126654i
$393$	−0.894835	−	0.0350625i	−0.0451384	−	0.00176867i
$394$	−3.32591	+	5.76064i	−0.167557	+	0.290217i
$395$	46.7355	−	26.9828i	2.35152	−	1.35765i
$396$	−1.71607	−	3.59583i	−0.0862356	−	0.180697i
$397$	−13.5400	+	23.4520i	−0.679555	+	1.17702i	0.295560	+	0.955324i	$0.404494\pi$
$397$	−13.5400	+	23.4520i	−0.679555	+	1.17702i	−0.975115	+	0.221700i	$0.928840\pi$
$398$		−	15.1263i		−	0.758212i
$399$	4.78191	−	21.1507i	0.239395	−	1.05886i
$400$	−8.94713			−0.447357
$401$	7.51128	−	13.0099i	0.375095	−	0.649684i	−0.615246	−	0.788335i	$-0.710943\pi$
$401$	7.51128	−	13.0099i	0.375095	−	0.649684i	0.990341	+	0.138651i	$0.0442766\pi$
$402$	6.22673	−	3.27689i	0.310561	−	0.163436i
$403$	−9.57638	+	7.27221i	−0.477033	+	0.362254i
$404$	4.68518	−	8.11497i	0.233096	−	0.403735i
$405$	5.24378	−	33.1997i	0.260566	−	1.64971i
$406$	10.8218	−	12.6726i	0.537079	−	0.628933i
$407$			12.0775i			0.598660i
$408$	−4.60626	+	7.30220i	−0.228044	+	0.361513i
$409$	−9.71830	−	16.8326i	−0.480539	−	0.832318i	0.519212	−	0.854646i	$-0.326226\pi$
$409$	−9.71830	−	16.8326i	−0.480539	−	0.832318i	−0.999751	+	0.0223276i	$0.992892\pi$
$410$	−8.17956	−	14.1674i	−0.403960	−	0.699679i
$411$	1.28270	−	2.03344i	0.0632709	−	0.100302i
$412$			0.180132i			0.00887448i
$413$	−9.50193	−	26.8263i	−0.467559	−	1.32004i
$414$	−0.271605	+	3.46051i	−0.0133486	+	0.170075i
$415$	12.5976	−	21.8196i	0.618389	−	1.07108i
$416$	2.87145	−	2.18055i	0.140784	−	0.106910i
$417$	−19.7778	+	10.4083i	−0.968523	+	0.509697i
$418$	3.14228	−	5.44259i	0.153694	−	0.266206i
$419$	−11.9628			−0.584422			−0.292211	−	0.956354i	$-0.594391\pi$
$419$	−11.9628			−0.584422			−0.292211	+	0.956354i	$0.594391\pi$
$420$	−5.07797	−	16.3433i	−0.247780	−	0.797472i
$421$		−	8.12436i		−	0.395957i	−0.980206	−	0.197979i	$-0.936562\pi$
$421$		−	8.12436i		−	0.395957i	0.980206	−	0.197979i	$-0.0634377\pi$
$422$	5.11771	−	8.86413i	0.249126	−	0.431499i
$423$	−21.7352	+	10.3729i	−1.05680	+	0.504346i
$424$	−1.36514	+	0.788163i	−0.0662970	+	0.0382766i
$425$	−22.2991	+	38.6232i	−1.08166	+	1.87350i
$426$	17.2301	+	0.675131i	0.834803	+	0.0327102i
$427$	9.62412	−	11.2701i	0.465744	−	0.545397i
$428$		−	5.95181i		−	0.287691i
$429$	7.51505	+	3.50931i	0.362830	+	0.169431i
$430$	30.8824	−	17.8300i	1.48928	−	0.859837i
$431$	−4.94182	−	8.55948i	−0.238039	−	0.412296i	0.722112	−	0.691776i	$-0.243171\pi$
$431$	−4.94182	−	8.55948i	−0.238039	−	0.412296i	−0.960152	+	0.279480i	$0.909838\pi$
$432$	3.10765	−	4.16443i	0.149517	−	0.200361i
$433$		−	14.2606i		−	0.685321i	−0.939459	−	0.342661i	$-0.888672\pi$
$433$		−	14.2606i		−	0.685321i	0.939459	−	0.342661i	$-0.111328\pi$
$434$	−1.60735	+	8.67604i	−0.0771551	+	0.416463i
$435$	40.7113	+	1.59520i	1.95196	+	0.0764840i
$436$	−10.3694	−	5.98679i	−0.496605	−	0.286715i
$437$	−4.74159	+	2.73756i	−0.226821	+	0.130955i
$438$	11.6341	+	22.1071i	0.555899	+	1.05632i
$439$	−17.7811	−	10.2659i	−0.848646	−	0.489966i	0.0115480	−	0.999933i	$-0.496324\pi$
$439$	−17.7811	−	10.2659i	−0.848646	−	0.489966i	−0.860194	+	0.509968i	$0.829657\pi$
$440$		−	4.95994i		−	0.236456i
$441$	17.3024	−	11.9008i	0.823922	−	0.566704i
$442$	−2.25648	−	17.8301i	−0.107330	−	0.848093i
$443$	−0.915950	−	0.528824i	−0.0435181	−	0.0251252i	0.478083	−	0.878315i	$-0.341332\pi$
$443$	−0.915950	−	0.528824i	−0.0435181	−	0.0251252i	−0.521601	+	0.853189i	$0.674665\pi$
$444$	−13.9385	+	7.33532i	−0.661493	+	0.348119i
$445$	−5.51556	−	9.55324i	−0.261463	−	0.452867i
$446$	10.6864	−	18.5094i	0.506017	−	0.876447i
$447$	14.3740	+	0.563219i	0.679867	+	0.0266394i
$448$	0.481958	−	2.60148i	0.0227704	−	0.122909i
$449$	7.60160			0.358742			0.179371	−	0.983782i	$-0.442594\pi$
$449$	7.60160			0.358742			0.179371	+	0.983782i	$0.442594\pi$
$450$	15.1984	−	22.1239i	0.716460	−	1.04293i
$451$	5.03828	−	2.90885i	0.237243	−	0.136972i
$452$	1.27700	−	0.737278i	0.0600651	−	0.0346786i
$453$	1.89904	+	1.19792i	0.0892248	+	0.0562833i
$454$			15.1954i			0.713156i
$455$	29.7820	+	19.5505i	1.39620	+	0.916543i
$456$	8.18971	+	0.320899i	0.383518	+	0.0150275i
$457$	9.27260	+	5.35354i	0.433754	+	0.250428i	0.700945	−	0.713216i	$-0.252762\pi$
$457$	9.27260	+	5.35354i	0.433754	+	0.250428i	−0.267191	+	0.963644i	$0.586095\pi$
$458$	−10.7812	−	18.6737i	−0.503775	−	0.872563i
$459$	−10.2319	−	23.7943i	−0.477582	−	1.11062i
$460$	−2.16055	+	3.74219i	−0.100736	+	0.174480i
$461$			9.51862i			0.443326i	0.975123	+	0.221663i	$0.0711485\pi$
$461$			9.51862i			0.443326i	−0.975123	+	0.221663i	$0.928851\pi$
$462$	5.81208	−	1.80585i	0.270403	−	0.0840158i
$463$		−	17.7463i		−	0.824742i	−0.911016	−	0.412371i	$-0.864701\pi$
$463$		−	17.7463i		−	0.824742i	0.911016	−	0.412371i	$-0.135299\pi$
$464$	5.45477	+	3.14931i	0.253231	+	0.146203i
$465$	−19.0905	+	10.0466i	−0.885299	+	0.465899i
$466$	−23.8631	+	13.7774i	−1.10544	+	0.638225i
$467$	2.60380	−	4.50991i	0.120489	−	0.208694i	−0.799471	−	0.600704i	$-0.794887\pi$
$467$	2.60380	−	4.50991i	0.120489	−	0.208694i	0.919961	+	0.392010i	$0.128220\pi$
$468$	0.514232	+	10.8044i	0.0237704	+	0.499435i
$469$	3.58857	+	10.1314i	0.165705	+	0.467826i
$470$	−29.9807			−1.38290
$471$	25.8303	+	16.2939i	1.19020	+	0.750782i
$472$	9.31553	−	5.37832i	0.428782	−	0.247557i
$473$	6.34077	+	10.9825i	0.291549	+	0.504977i
$474$	−13.3533	+	21.1687i	−0.613338	+	0.972311i
$475$	42.3375			1.94258
$476$	−10.0289	−	8.56425i	−0.459676	−	0.392542i
$477$	0.370025	−	4.71448i	0.0169423	−	0.215861i
$478$	6.04907	−	10.4773i	0.276678	−	0.479220i
$479$	−15.3659	+	8.87151i	−0.702086	+	0.405350i	−0.808124	−	0.589012i	$-0.799517\pi$
$479$	−15.3659	+	8.87151i	−0.702086	+	0.405350i	0.106038	+	0.994362i	$0.466184\pi$
$480$	5.72421	−	3.01244i	0.261273	−	0.137498i
$481$	12.6992	−	30.2289i	0.579033	−	1.37832i
$482$	3.52305			0.160470
$483$	−5.17174	−	1.16927i	−0.235323	−	0.0532034i
$484$	−9.23612			−0.419824
$485$	−31.6763	−	18.2883i	−1.43835	−	0.830431i
$486$	5.01862	+	14.7585i	0.227649	+	0.669459i
$487$	18.9701	−	10.9524i	0.859616	−	0.496299i	−0.00426783	−	0.999991i	$-0.501358\pi$
$487$	18.9701	−	10.9524i	0.859616	−	0.496299i	0.863884	+	0.503691i	$0.168025\pi$
$488$	4.85105	+	2.80076i	0.219597	+	0.126784i
$489$	−0.456176	+	11.6421i	−0.0206290	+	0.526476i
$490$	25.8196	−	4.09333i	1.16641	−	0.184918i
$491$		−	3.60049i		−	0.162488i	−0.996694	−	0.0812438i	$-0.974111\pi$
$491$		−	3.60049i		−	0.162488i	0.996694	−	0.0812438i	$-0.0258893\pi$
$492$	6.41709	+	4.04792i	0.289305	+	0.182494i
$493$	27.1900	−	15.6982i	1.22458	−	0.707010i
$494$	−13.5876	+	10.3183i	−0.611334	+	0.464241i
$495$	12.2647	+	8.42541i	0.551255	+	0.378694i
$496$	−3.33504			−0.149748
$497$	−4.79811	+	25.8990i	−0.215225	+	1.16173i
$498$	−0.457510	+	11.6762i	−0.0205015	+	0.523223i
$499$	6.88661	+	3.97599i	0.308287	+	0.177990i	0.646160	−	0.763202i	$-0.276374\pi$
$499$	6.88661	+	3.97599i	0.308287	+	0.177990i	−0.337873	+	0.941192i	$0.609707\pi$
$500$	12.7660	−	7.37045i	0.570913	−	0.329617i
$501$	−2.14307	+	1.12782i	−0.0957454	+	0.0503871i
$502$	9.47494	−	16.4111i	0.422887	−	0.732462i
$503$	−10.7862			−0.480934			−0.240467	−	0.970657i	$-0.577301\pi$
$503$	−10.7862			−0.480934			−0.240467	+	0.970657i	$0.577301\pi$
$504$	5.61410	+	5.61087i	0.250072	+	0.249928i
$505$			34.9944i			1.55723i
$506$	−1.33081	−	0.768346i	−0.0591619	−	0.0341571i
$507$	−15.1195	−	16.6853i	−0.671481	−	0.741022i
$508$	−5.30202	−	9.18338i	−0.235239	−	0.407446i
$509$	14.3853	+	8.30537i	0.637618	+	0.368129i	0.783696	−	0.621144i	$-0.213332\pi$
$509$	14.3853	+	8.30537i	0.637618	+	0.368129i	−0.146078	+	0.989273i	$0.546665\pi$
$510$	1.26242	−	32.2184i	0.0559008	−	1.42665i
$511$	−35.9701	+	12.7407i	−1.59122	+	0.563614i
$512$	1.00000			0.0441942
$513$	−14.7053	+	19.7059i	−0.649254	+	0.870038i
$514$	0.299289	+	0.518384i	0.0132011	+	0.0228650i
$515$	−0.336360	−	0.582592i	−0.0148218	−	0.0256721i
$516$	−8.82373	+	13.9881i	−0.388443	+	0.615791i
$517$		−	10.6619i		−	0.468908i
$518$	−8.03301	−	22.6792i	−0.352950	−	0.996467i
$519$	−38.3413	−	1.50234i	−1.68300	−	0.0659452i
$520$	−5.21524	+	12.4143i	−0.228704	+	0.544401i
$521$	1.55866	+	2.69969i	0.0682863	+	0.118275i	0.898147	−	0.439695i	$-0.144914\pi$
$521$	1.55866	+	2.69969i	0.0682863	+	0.118275i	−0.829861	+	0.557971i	$0.811580\pi$
$522$	−17.0534	+	8.13852i	−0.746407	+	0.356213i
$523$	−10.9887	−	6.34431i	−0.480501	−	0.277417i	0.240124	−	0.970742i	$-0.422812\pi$
$523$	−10.9887	−	6.34431i	−0.480501	−	0.277417i	−0.720625	+	0.693325i	$0.756145\pi$
$524$	0.517030			0.0225865
$525$	30.1129	+	27.8260i	1.31424	+	1.21443i
$526$		−	26.7372i		−	1.16580i
$527$	−8.31197	+	14.3968i	−0.362075	+	0.627132i
$528$	1.07130	+	2.03567i	0.0466222	+	0.0885912i
$529$	−10.8306	−	18.7592i	−0.470896	−	0.815616i
$530$	2.94346	−	5.09823i	0.127856	−	0.221453i
$531$	−2.52500	+	32.1710i	−0.109576	+	1.39610i
$532$	−2.28061	+	12.3101i	−0.0988768	+	0.533711i
$533$	−15.6689	+	1.98297i	−0.678696	+	0.0858918i
$534$	4.32711	+	2.72956i	0.187252	+	0.118120i
$535$	11.1138	+	19.2496i	0.480490	+	0.832233i
$536$	−3.51817	+	2.03122i	−0.151962	+	0.0877352i
$537$	35.6028	+	22.4584i	1.53637	+	0.969150i
$538$	−11.4488			−0.493594
$539$	1.45569	+	9.18210i	0.0627010	+	0.395501i
$540$	−2.27470	+	19.2717i	−0.0978874	+	0.829322i
$541$	0.286703	+	0.165528i	0.0123263	+	0.00711660i	0.506150	−	0.862445i	$-0.331068\pi$
$541$	0.286703	+	0.165528i	0.0123263	+	0.00711660i	−0.493824	+	0.869562i	$0.664401\pi$
$542$	12.6383	+	21.8902i	0.542862	+	0.940265i
$543$	22.0929	−	11.6267i	0.948099	−	0.498948i
$544$	2.49232	−	4.31682i	0.106857	−	0.185082i
$545$	44.7164			1.91544
$546$	−16.4459	−	1.59138i	−0.703819	−	0.0681046i
$547$	21.1593			0.904707			0.452354	−	0.891839i	$-0.350584\pi$
$547$	21.1593			0.904707			0.452354	+	0.891839i	$0.350584\pi$
$548$	−0.694033	+	1.20210i	−0.0296476	+	0.0513512i
$549$	−15.1660	+	7.23778i	−0.647268	+	0.308901i
$550$	5.94139	+	10.2908i	0.253342	+	0.438801i
$551$	−25.8117	−	14.9024i	−1.09962	−	0.634864i
$552$	0.0784657	−	2.00253i	0.00333972	−	0.0852335i
$553$	−29.0734	−	24.8273i	−1.23633	−	1.05577i
$554$	4.59429			0.195193
$555$	31.3835	−	49.7515i	1.33215	−	2.11184i
$556$	11.1747	−	6.45170i	0.473912	−	0.273613i
$557$	10.1206	+	17.5294i	0.428823	+	0.742743i	0.996769	−	0.0803231i	$-0.0255952\pi$
$557$	10.1206	+	17.5294i	0.428823	+	0.742743i	−0.567946	+	0.823066i	$0.692262\pi$
$558$	5.66519	−	8.24668i	0.239827	−	0.349110i
$559$	−4.32251	−	34.1554i	−0.182823	−	1.44462i
$560$	3.29896	+	9.31379i	0.139407	+	0.393580i
$561$	11.4576	+	0.448947i	0.483742	+	0.0189545i
$562$	11.2596	−	19.5021i	0.474956	−	0.822647i
$563$	16.4117	+	28.4259i	0.691670	+	1.19801i	0.971290	+	0.237897i	$0.0764580\pi$
$563$	16.4117	+	28.4259i	0.691670	+	1.19801i	−0.279621	+	0.960111i	$0.590209\pi$
$564$	12.3047	−	6.47551i	0.518123	−	0.272668i
$565$	−2.75343	+	4.76907i	−0.115838	+	0.200636i
$566$			7.47391i			0.314152i
$567$	−23.4109	+	4.35107i	−0.983164	+	0.182728i
$568$	−9.95545			−0.417722
$569$	36.2966	+	20.9559i	1.52163	+	0.878515i	0.999674	+	0.0255443i	$0.00813190\pi$
$569$	36.2966	+	20.9559i	1.52163	+	0.878515i	0.521959	+	0.852971i	$0.325201\pi$
$570$	−27.0867	+	14.2547i	−1.13454	+	0.597064i
$571$	−3.99051	−	6.91177i	−0.166998	−	0.289248i	0.770365	−	0.637603i	$-0.220074\pi$
$571$	−3.99051	−	6.91177i	−0.166998	−	0.289248i	−0.937363	+	0.348354i	$0.886741\pi$
$572$	−4.41482	−	1.85467i	−0.184593	−	0.0775476i
$573$	0.0280546	−	0.715985i	0.00117200	−	0.0299107i
$574$	−7.52616	+	8.81332i	−0.314136	+	0.367861i
$575$		−	10.3523i		−	0.431720i
$576$	−1.69869	+	2.47274i	−0.0707788	+	0.103031i
$577$	6.63093	+	11.4851i	0.276049	+	0.478131i	0.970399	−	0.241506i	$-0.0776414\pi$
$577$	6.63093	+	11.4851i	0.276049	+	0.478131i	−0.694350	+	0.719637i	$0.744308\pi$
$578$	−3.92330	−	6.79535i	−0.163188	−	0.282649i
$579$	11.1357	+	7.02442i	0.462782	+	0.291925i
$580$	−23.5227			−0.976729
$581$	−17.5507	−	3.25149i	−0.728126	−	0.134895i
$582$	16.9508	+	0.664185i	0.702632	+	0.0275314i
$583$	1.81306	+	1.04677i	0.0750891	+	0.0433527i
$584$	−7.21154	−	12.4907i	−0.298415	−	0.516871i
$585$	−21.8382	−	33.9839i	−0.902897	−	1.40506i
$586$	−12.6517	−	7.30444i	−0.522635	−	0.301744i
$587$			9.45396i			0.390207i	0.980783	+	0.195103i	$0.0625043\pi$
$587$			9.45396i			0.390207i	−0.980783	+	0.195103i	$0.937496\pi$
$588$	−9.71284	+	7.25677i	−0.400551	+	0.299264i
$589$	15.7813			0.650255
$590$	−20.0858	+	34.7896i	−0.826920	+	1.43227i
$591$	5.36557	+	10.1956i	0.220710	+	0.419392i
$592$	7.87543	−	4.54688i	0.323678	−	0.186876i
$593$	30.1356	+	17.3988i	1.23752	+	0.714482i	0.968587	−	0.248677i	$-0.0799956\pi$
$593$	30.1356	+	17.3988i	1.23752	+	0.714482i	0.268933	+	0.963159i	$0.413329\pi$
$594$	−6.85349	−	0.808938i	−0.281202	−	0.0331911i
$595$	48.4280	+	8.97191i	1.98536	+	0.367813i
$596$	−8.30520			−0.340194
$597$	−22.1591	−	13.9781i	−0.906912	−	0.572084i
$598$	2.52301	+	3.32241i	0.103173	+	0.135864i
$599$	−3.32776	+	1.92128i	−0.135969	+	0.0785016i	−0.566441	−	0.824102i	$-0.691680\pi$
$599$	−3.32776	+	1.92128i	−0.135969	+	0.0785016i	0.430473	+	0.902604i	$0.358347\pi$
$600$	−8.26796	+	13.1070i	−0.337538	+	0.535092i
$601$			24.4368i			0.996796i	0.866948	+	0.498398i	$0.166078\pi$
$601$			24.4368i			0.996796i	−0.866948	+	0.498398i	$0.833922\pi$
$602$	−19.2114	−	16.4057i	−0.782999	−	0.668645i
$603$	0.953611	−	12.1499i	0.0388340	−	0.494784i
$604$	−1.12265	−	0.648163i	−0.0456800	−	0.0263734i
$605$	29.8719	−	17.2465i	1.21447	−	0.701172i
$606$	−7.55843	−	14.3625i	−0.307040	−	0.583436i
$607$	25.3256	+	14.6218i	1.02794	+	0.593479i	0.916393	−	0.400281i	$-0.131087\pi$
$607$	25.3256	+	14.6218i	1.02794	+	0.593479i	0.111543	+	0.993760i	$0.464421\pi$
$608$	−4.73196			−0.191906
$609$	−8.56432	−	27.5641i	−0.347044	−	1.11695i
$610$	−20.9193			−0.846999
$611$	−11.2107	+	26.6856i	−0.453534	+	1.07958i
$612$	6.44070	+	13.4958i	0.260350	+	0.545535i
$613$	−7.85345	+	4.53419i	−0.317198	+	0.183134i	−0.650143	−	0.759812i	$-0.725291\pi$
$613$	−7.85345	+	4.53419i	−0.317198	+	0.183134i	0.332945	+	0.942946i	$0.391958\pi$
$614$	2.76445	−	4.78816i	0.111564	−	0.193234i
$615$	−28.3131	−	1.10940i	−1.14169	−	0.0447352i
$616$	−3.31221	+	1.17319i	−0.133453	+	0.0472692i
$617$	−47.4218			−1.90913			−0.954565	−	0.298002i	$-0.903680\pi$
$617$	−47.4218			−1.90913			−0.954565	+	0.298002i	$0.903680\pi$
$618$	0.263883	+	0.166459i	0.0106149	+	0.00669594i
$619$	20.7977	+	36.0226i	0.835929	+	1.44787i	0.893272	+	0.449517i	$0.148404\pi$
$619$	20.7977	+	36.0226i	0.835929	+	1.44787i	−0.0573430	+	0.998355i	$0.518263\pi$
$620$	10.7863	−	6.22749i	0.433189	−	0.250102i
$621$	4.81846	+	3.59571i	0.193358	+	0.144291i
$622$	25.0154			1.00303
$623$	−5.07497	+	5.94291i	−0.203324	+	0.238098i
$624$	−0.540899	−	6.22153i	−0.0216533	−	0.249061i
$625$	−5.15775	+	8.93348i	−0.206310	+	0.357339i
$626$	−12.4242	+	7.17314i	−0.496573	+	0.286696i
$627$	−5.06933	−	9.63271i	−0.202449	−	0.384693i
$628$	−15.2700	−	8.81616i	−0.609341	−	0.351803i
$629$		−	45.3291i		−	1.80739i
$630$	−28.6345	−	7.66378i	−1.14083	−	0.305332i
$631$			2.35427i			0.0937218i	0.998901	+	0.0468609i	$0.0149218\pi$
$631$			2.35427i			0.0937218i	−0.998901	+	0.0468609i	$0.985078\pi$
$632$	7.22510	−	12.5142i	0.287399	−	0.497790i
$633$	−8.25621	−	15.6884i	−0.328155	−	0.623558i
$634$	−7.58692	−	13.1409i	−0.301315	−	0.521893i
$635$	34.2961	+	19.8009i	1.36100	+	0.785773i
$636$	−0.106899	+	2.72818i	−0.00423882	+	0.108180i
$637$	6.01127	−	24.5125i	0.238175	−	0.971222i
$638$		−	8.36526i		−	0.331184i
$639$	16.9112	−	24.6173i	0.668998	−	0.973844i
$640$	−3.23425	+	1.86729i	−0.127845	+	0.0738112i
$641$	14.3753	−	8.29956i	0.567789	−	0.327813i	−0.188477	−	0.982078i	$-0.560355\pi$
$641$	14.3753	−	8.29956i	0.567789	−	0.327813i	0.756266	+	0.654265i	$0.227022\pi$
$642$	−8.71905	−	5.50001i	−0.344114	−	0.217068i
$643$	5.87699			0.231766			0.115883	−	0.993263i	$-0.463030\pi$
$643$	5.87699			0.231766			0.115883	+	0.993263i	$0.463030\pi$
$644$	3.01005	+	0.557650i	0.118613	+	0.0219745i
$645$	2.41828	−	61.7174i	0.0952198	−	2.43012i
$646$	−11.7935	+	20.4270i	−0.464011	+	0.803690i
$647$	−14.9475	−	25.8898i	−0.587645	−	1.01783i	−0.994540	−	0.104356i	$-0.966722\pi$
$647$	−14.9475	−	25.8898i	−0.587645	−	1.01783i	0.406895	−	0.913475i	$-0.366612\pi$
$648$	−3.22890	−	8.40085i	−0.126843	−	0.330016i
$649$	−12.3721	−	7.14301i	−0.485645	−	0.280388i
$650$	−4.05025	−	32.0041i	−0.158864	−	1.25530i
$651$	11.2246	+	10.3721i	0.439925	+	0.406516i
$652$		−	6.72676i		−	0.263440i
$653$	−6.48294	−	3.74293i	−0.253697	−	0.146472i	0.367759	−	0.929921i	$-0.380125\pi$
$653$	−6.48294	−	3.74293i	−0.253697	−	0.146472i	−0.621456	+	0.783449i	$0.713459\pi$
$654$	−18.3526	+	9.65827i	−0.717643	+	0.377668i
$655$	−1.67220	+	0.965446i	−0.0653383	+	0.0377231i
$656$	−3.79357	−	2.19022i	−0.148114	−	0.0855137i
$657$	43.1365	+	3.38565i	1.68292	+	0.132087i
$658$	7.09142	+	20.0209i	0.276452	+	0.780495i
$659$			32.6856i			1.27325i	0.771174	+	0.636624i	$0.219670\pi$
$659$			32.6856i			1.27325i	−0.771174	+	0.636624i	$0.780330\pi$
$660$	−7.26603	−	4.58344i	−0.282830	−	0.178410i
$661$	2.68538	+	4.65121i	0.104449	+	0.180911i	0.913513	−	0.406809i	$-0.133359\pi$
$661$	2.68538	+	4.65121i	0.104449	+	0.180911i	−0.809064	+	0.587721i	$0.800025\pi$
$662$	25.2714	−	14.5904i	0.982200	−	0.567073i
$663$	−28.2053	−	13.1711i	−1.09540	−	0.511522i
$664$		−	6.74642i		−	0.261812i
$665$	−15.6105	−	44.0725i	−0.605351	−	1.70906i
$666$	−2.13466	+	27.1976i	−0.0827163	+	1.05389i
$667$	−3.64391	+	6.31144i	−0.141093	+	0.244380i
$668$	1.21086	−	0.699090i	0.0468496	−	0.0270486i
$669$	−17.2400	−	32.7594i	−0.666537	−	1.26655i
$670$	7.58576	−	13.1389i	0.293063	−	0.507601i
$671$		−	7.43942i		−	0.287196i
$672$	−3.36565	−	3.11005i	−0.129833	−	0.119973i
$673$	−27.9654			−1.07799			−0.538994	−	0.842310i	$-0.681195\pi$
$673$	−27.9654			−1.07799			−0.538994	+	0.842310i	$0.681195\pi$
$674$	−10.9157	+	18.9065i	−0.420456	+	0.728251i
$675$	−18.3656	−	42.7093i	−0.706892	−	1.64388i
$676$	9.09973	+	9.28412i	0.349990	+	0.357081i
$677$	17.5946	−	30.4747i	0.676214	−	1.17124i	−0.299898	−	0.953971i	$-0.596953\pi$
$677$	17.5946	−	30.4747i	0.676214	−	1.17124i	0.976112	−	0.217266i	$-0.0697139\pi$
$678$	0.0999973	−	2.55205i	0.00384037	−	0.0980107i
$679$	−4.72032	+	25.4790i	−0.181149	+	0.977796i
$680$			18.6156i			0.713874i
$681$	22.2604	+	14.0419i	0.853021	+	0.538089i
$682$	2.21465	+	3.83588i	0.0848032	+	0.146884i
$683$	15.0441	+	26.0572i	0.575648	+	0.997052i	0.995971	+	0.0896770i	$0.0285835\pi$
$683$	15.0441	+	26.0572i	0.575648	+	0.997052i	−0.420323	+	0.907375i	$0.638083\pi$
$684$	8.03813	−	11.7009i	0.307346	−	0.447395i
$685$		−	5.18385i		−	0.198065i
$686$	−8.84070	−	16.2740i	−0.337540	−	0.621343i
$687$	−37.3187	−	1.46227i	−1.42380	−	0.0557889i
$688$	4.77428	−	8.26929i	0.182018	−	0.315264i
$689$	−3.43726	−	4.52634i	−0.130949	−	0.172440i
$690$	3.48554	+	6.62321i	0.132692	+	0.252141i
$691$	−11.4256	+	19.7898i	−0.434651	+	0.752838i	−0.997267	−	0.0738803i	$-0.976462\pi$
$691$	−11.4256	+	19.7898i	−0.434651	+	0.752838i	0.562616	+	0.826719i	$0.309795\pi$
$692$	22.1534			0.842145
$693$	2.72543	−	10.1831i	0.103530	−	0.386825i
$694$		−	27.8171i		−	1.05592i
$695$	−24.0944	+	41.7328i	−0.913954	+	1.58302i
$696$	9.65426	−	5.08067i	0.365944	−	0.192582i
$697$	−18.9096	+	10.9174i	−0.716251	+	0.413528i
$698$	2.27346	−	3.93774i	0.0860516	−	0.149046i
$699$	−1.86863	+	47.6896i	−0.0706781	+	1.80379i
$700$	−18.0014	−	15.3723i	−0.680388	−	0.581020i
$701$			31.5577i			1.19192i	0.803015	+	0.595959i	$0.203228\pi$
$701$			31.5577i			1.19192i	−0.803015	+	0.595959i	$0.796772\pi$
$702$	16.3031	+	9.23095i	0.615319	+	0.348400i
$703$	−37.2662	+	21.5156i	−1.40552	+	0.811478i
$704$	−0.664055	−	1.15018i	−0.0250275	−	0.0433489i
$705$	−27.7049	+	43.9199i	−1.04343	+	1.65412i
$706$			8.32657i			0.313375i
$707$	23.3690	−	8.27734i	0.878882	−	0.311302i
$708$	0.729464	−	18.6168i	0.0274150	−	0.699661i
$709$	−14.1878	−	8.19131i	−0.532833	−	0.307631i	0.209336	−	0.977844i	$-0.432870\pi$
$709$	−14.1878	−	8.19131i	−0.532833	−	0.307631i	−0.742169	+	0.670213i	$0.766203\pi$
$710$	32.1984	−	18.5897i	1.20838	−	0.697661i
$711$	18.6713	+	39.1236i	0.700228	+	1.46725i
$712$	−2.55804	−	1.47689i	−0.0958668	−	0.0553487i
$713$		−	3.85881i		−	0.144513i
$714$	−21.8138	+	6.77768i	−0.816361	+	0.253648i
$715$	17.7418	−	2.24530i	0.663506	−	0.0839695i
$716$	−21.0472	−	12.1516i	−0.786570	−	0.454126i
$717$	−9.75874	−	18.5435i	−0.364447	−	0.692520i
$718$	−7.10506	−	12.3063i	−0.265158	−	0.459268i
$719$	−8.08537	+	14.0043i	−0.301533	+	0.522271i	−0.976483	−	0.215592i	$-0.930832\pi$
$719$	−8.08537	+	14.0043i	−0.301533	+	0.522271i	0.674950	+	0.737863i	$0.264165\pi$
$720$	0.876652	−	11.1694i	0.0326709	−	0.416259i
$721$	−0.309490	+	0.362421i	−0.0115260	+	0.0134973i
$722$	3.39143			0.126216
$723$	3.25562	−	5.16106i	0.121078	−	0.191942i
$724$	−12.4828	+	7.20693i	−0.463918	+	0.267843i
$725$	48.8045	−	28.1773i	1.81255	−	1.04648i
$726$	−8.53502	+	13.5304i	−0.316764	+	0.502160i
$727$			16.3582i			0.606692i	0.952880	+	0.303346i	$0.0981038\pi$
$727$			16.3582i			0.606692i	−0.952880	+	0.303346i	$0.901896\pi$
$728$	9.52374	+	0.546316i	0.352973	+	0.0202478i
$729$	26.2580	+	6.28621i	0.972519	+	0.232822i
$730$	46.6478	+	26.9321i	1.72651	+	0.996802i
$731$	−23.7980	−	41.2194i	−0.880202	−	1.52455i
$732$	8.58576	−	4.51836i	0.317339	−	0.167003i
$733$	−25.9026	+	44.8646i	−0.956734	+	1.65711i	−0.226386	+	0.974038i	$0.572691\pi$
$733$	−25.9026	+	44.8646i	−0.956734	+	1.65711i	−0.730348	+	0.683075i	$0.760642\pi$
$734$			2.37849i			0.0877918i
$735$	17.8632	−	41.6069i	0.658894	−	1.53469i
$736$			1.15705i			0.0426495i
$737$	4.67252	+	2.69768i	0.172115	+	0.0993704i
$738$	11.8599	−	5.66001i	0.436571	−	0.208348i
$739$	13.0157	−	7.51460i	0.478789	−	0.276429i	−0.241123	−	0.970495i	$-0.577516\pi$
$739$	13.0157	−	7.51460i	0.478789	−	0.276429i	0.719912	+	0.694066i	$0.244182\pi$
$740$	−16.9807	+	29.4115i	−0.624224	+	1.08119i
$741$	2.55951	+	29.4400i	0.0940260	+	1.08151i
$742$	−4.10079	−	0.759723i	−0.150545	−	0.0278903i
$743$	−22.4238			−0.822651			−0.411326	−	0.911489i	$-0.634934\pi$
$743$	−22.4238			−0.822651			−0.411326	+	0.911489i	$0.634934\pi$
$744$	−3.08188	+	4.88564i	−0.112987	+	0.179116i
$745$	26.8611	−	15.5082i	0.984114	−	0.568178i
$746$	−11.7785	−	20.4010i	−0.431243	−	0.746934i
$747$	16.6822	+	11.4601i	0.610368	+	0.419303i
$748$	−6.62015			−0.242057
$749$	10.2260	−	11.9749i	0.373649	−	0.437552i
$750$	0.999657	−	25.5124i	0.0365023	−	0.931581i
$751$	−13.6135	+	23.5793i	−0.496765	+	0.860422i	−0.999993	−	0.00373163i	$-0.998812\pi$
$751$	−13.6135	+	23.5793i	−0.496765	+	0.860422i	0.503228	+	0.864154i	$0.332146\pi$
$752$	−6.95231	+	4.01392i	−0.253525	+	0.146373i
$753$	−15.2856	−	29.0456i	−0.557037	−	1.05848i
$754$	−8.79585	+	20.9375i	−0.320326	+	0.762497i
$755$	4.84124			0.176191
$756$	13.4075	−	3.03937i	0.487628	−	0.110541i
$757$	4.76540			0.173201			0.0866007	−	0.996243i	$-0.472400\pi$
$757$	4.76540			0.173201			0.0866007	+	0.996243i	$0.472400\pi$
$758$	15.6661	+	9.04481i	0.569017	+	0.328522i
$759$	−2.35538	+	1.23954i	−0.0854947	+	0.0449926i
$760$	15.3043	−	8.83595i	0.555146	−	0.320514i
$761$	29.7410	+	17.1710i	1.07811	+	0.622448i	0.930386	−	0.366580i	$-0.119471\pi$
$761$	29.7410	+	17.1710i	1.07811	+	0.622448i	0.147725	+	0.989028i	$0.452805\pi$
$762$	−18.3527	−	0.719116i	−0.664847	−	0.0260508i
$763$	−10.5769	−	29.8613i	−0.382910	−	1.08105i
$764$			0.413691i			0.0149668i
$765$	−46.0314	−	31.6221i	−1.66427	−	1.14330i
$766$	6.97099	−	4.02470i	0.251872	−	0.145418i
$767$	23.4554	+	30.8871i	0.846925	+	1.11527i
$768$	0.924091	−	1.46494i	0.0333453	−	0.0528615i
$769$	−22.9273			−0.826779			−0.413390	−	0.910554i	$-0.635655\pi$
$769$	−22.9273			−0.826779			−0.413390	+	0.910554i	$0.635655\pi$
$770$	8.52182	−	9.97926i	0.307105	−	0.359628i
$771$	1.03597	+	0.0405927i	0.0373097	+	0.00146191i
$772$	−6.58304	−	3.80072i	−0.236929	−	0.136791i
$773$	−35.9806	+	20.7734i	−1.29413	+	0.747168i	−0.979384	−	0.202007i	$-0.935253\pi$
$773$	−35.9806	+	20.7734i	−1.29413	+	0.747168i	−0.314748	+	0.949175i	$0.601920\pi$
$774$	12.3378	+	25.8525i	0.443473	+	0.929250i
$775$	−14.9195	+	25.8413i	−0.535924	+	0.928248i
$776$	−9.79404			−0.351586
$777$	−40.6470	−	9.18975i	−1.45820	−	0.329681i
$778$		−	31.7954i		−	1.13992i
$779$	17.9510	+	10.3640i	0.643162	+	0.371330i
$780$	13.3668	+	19.1119i	0.478609	+	0.684317i
$781$	6.61097	+	11.4505i	0.236559	+	0.409732i
$782$	4.99478	+	2.88374i	0.178613	+	0.103122i
$783$	−3.83642	+	32.5030i	−0.137103	+	1.16156i
$784$	5.43937	−	4.40604i	0.194263	−	0.157359i
$785$	65.8494			2.35027
$786$	0.477782	−	0.757418i	0.0170419	−	0.0270162i
$787$	−6.06775	−	10.5097i	−0.216292	−	0.374629i	0.737379	−	0.675479i	$-0.236063\pi$
$787$	−6.06775	−	10.5097i	−0.216292	−	0.374629i	−0.953671	+	0.300850i	$0.902730\pi$
$788$	−3.32591	−	5.76064i	−0.118481	−	0.205214i
$789$	−39.1685	−	24.7076i	−1.39444	−	0.879615i
$790$			53.9655i			1.92001i
$791$	3.83603	+	0.710674i	0.136394	+	0.0252686i
$792$	3.97212	+	0.311759i	0.141143	+	0.0110779i
$793$	−7.82235	+	18.6202i	−0.277780	+	0.661222i
$794$	−13.5400	−	23.4520i	−0.480518	−	0.832282i
$795$	−4.74858	−	9.02323i	−0.168415	−	0.320021i
$796$	13.0997	+	7.56314i	0.464308	+	0.268068i
$797$	−29.6346			−1.04971			−0.524856	−	0.851191i	$-0.675881\pi$
$797$	−29.6346			−1.04971			−0.524856	+	0.851191i	$0.675881\pi$
$798$	15.9261	+	14.7166i	0.563778	+	0.520963i
$799$			40.0159i			1.41566i
$800$	4.47357	−	7.74844i	0.158164	−	0.273949i
$801$	7.99729	−	3.81661i	0.282570	−	0.134853i
$802$	7.51128	+	13.0099i	0.265233	+	0.459396i
$803$	−9.57771	+	16.5891i	−0.337990	+	0.585416i
$804$	−0.275495	+	7.03095i	−0.00971596	+	0.247962i
$805$	−10.7765	+	3.81707i	−0.379823	+	0.134534i
$806$	−1.50973	−	11.9295i	−0.0531779	−	0.420198i
$807$	−10.5798	+	16.7719i	−0.372425	+	0.590398i
$808$	4.68518	+	8.11497i	0.164824	+	0.285484i
$809$	−2.60344	+	1.50310i	−0.0915320	+	0.0528460i	−0.545067	−	0.838392i	$-0.683496\pi$
$809$	−2.60344	+	1.50310i	−0.0915320	+	0.0528460i	0.453535	+	0.891238i	$0.350163\pi$
$810$	26.1299	+	21.1411i	0.918111	+	0.742823i
$811$	26.5609			0.932679			0.466339	−	0.884606i	$-0.345573\pi$
$811$	26.5609			0.932679			0.466339	+	0.884606i	$0.345573\pi$
$812$	5.56391	+	15.7083i	0.195255	+	0.551254i
$813$	43.7469	+	1.71414i	1.53427	+	0.0601175i
$814$	−10.4594	−	6.03876i	−0.366603	−	0.211658i
$815$	12.5608	+	21.7560i	0.439986	+	0.762079i
$816$	−4.02077	−	7.64024i	−0.140755	−	0.267462i
$817$	−22.5917	+	39.1299i	−0.790383	+	1.36898i
$818$	19.4366			0.679585
$819$	−17.5288	+	22.6217i	−0.612505	+	0.790467i
$820$	16.3591			0.571285
$821$	15.3289	−	26.5504i	0.534982	−	0.926617i	−0.464182	−	0.885740i	$-0.653652\pi$
$821$	15.3289	−	26.5504i	0.534982	−	0.926617i	0.999164	−	0.0408767i	$-0.0130151\pi$
$822$	1.11966	+	2.12757i	0.0390526	+	0.0742075i
$823$	14.7584	+	25.5624i	0.514447	+	0.891048i	0.999859	+	0.0167629i	$0.00533605\pi$
$823$	14.7584	+	25.5624i	0.514447	+	0.891048i	−0.485413	+	0.874285i	$0.661331\pi$
$824$	−0.155999	−	0.0900661i	−0.00543448	−	0.00313760i
$825$	20.5658	+	0.805833i	0.716009	+	0.0280555i
$826$	27.9832	+	5.18425i	0.973661	+	0.180383i
$827$	−15.9435			−0.554408			−0.277204	−	0.960811i	$-0.589408\pi$
$827$	−15.9435			−0.554408			−0.277204	+	0.960811i	$0.589408\pi$
$828$	−2.86109	−	1.96547i	−0.0994297	−	0.0683049i
$829$	−34.3579	+	19.8365i	−1.19330	+	0.688952i	−0.959053	−	0.283226i	$-0.908595\pi$
$829$	−34.3579	+	19.8365i	−1.19330	+	0.688952i	−0.234246	+	0.972177i	$0.575262\pi$
$830$	12.5976	+	21.8196i	0.437267	+	0.757369i
$831$	4.24554	−	6.73037i	0.147276	−	0.233474i
$832$	0.452687	+	3.57702i	0.0156941	+	0.124011i
$833$	−5.46346	−	34.4621i	−0.189298	−	1.19404i
$834$	0.875047	−	22.3322i	0.0303004	−	0.773302i
$835$	−2.61081	+	4.52206i	−0.0903509	+	0.156492i
$836$	3.14228	+	5.44259i	0.108678	+	0.188236i
$837$	−6.84576	−	15.9199i	−0.236624	−	0.550271i
$838$	5.98141	−	10.3601i	0.206625	−	0.357884i
$839$		−	6.33231i		−	0.218616i	−0.994008	−	0.109308i	$-0.965137\pi$
$839$		−	6.33231i		−	0.218616i	0.994008	−	0.109308i	$-0.0348634\pi$
$840$	16.6927	+	3.77401i	0.575953	+	0.130216i
$841$	−10.6726			−0.368021
$842$	7.03591	+	4.06218i	0.242473	+	0.139992i
$843$	−18.1646	−	34.5163i	−0.625623	−	1.18881i
$844$	5.11771	+	8.86413i	0.176159	+	0.305116i
$845$	−46.7669	−	13.0353i	−1.60883	−	0.448426i
$846$	1.88444	−	24.0097i	0.0647885	−	0.825470i
$847$	−18.5828	−	15.8689i	−0.638513	−	0.545260i
$848$		−	1.57633i		−	0.0541313i
$849$	10.9488	+	6.90657i	0.375763	+	0.237033i
$850$	−22.2991	−	38.6232i	−0.764853	−	1.32476i
$851$	5.26097	+	9.11227i	0.180344	+	0.312365i
$852$	−9.19975	+	14.5842i	−0.315178	+	0.499645i
$853$	56.4541			1.93295			0.966475	−	0.256760i	$-0.0826551\pi$
$853$	56.4541			1.93295			0.966475	+	0.256760i	$0.0826551\pi$
$854$	4.94812	+	13.9698i	0.169321	+	0.478036i
$855$	−4.14828	+	52.8532i	−0.141868	+	1.80754i
$856$	5.15442	+	2.97590i	0.176174	+	0.101714i
$857$	18.6366	+	32.2796i	0.636615	+	1.10265i	0.986171	+	0.165734i	$0.0529992\pi$
$857$	18.6366	+	32.2796i	0.636615	+	1.10265i	−0.349556	+	0.936916i	$0.613667\pi$
$858$	−6.79667	+	4.75357i	−0.232035	+	0.162284i
$859$	21.9122	+	12.6510i	0.747634	+	0.431646i	0.824838	−	0.565369i	$-0.191266\pi$
$859$	21.9122	+	12.6510i	0.747634	+	0.431646i	−0.0772046	+	0.997015i	$0.524599\pi$
$860$			35.6599i			1.21599i
$861$	5.95614	+	19.1697i	0.202985	+	0.653301i
$862$	9.88364			0.336638
$863$	−18.1156	+	31.3771i	−0.616661	+	1.06809i	0.373430	+	0.927658i	$0.378182\pi$
$863$	−18.1156	+	31.3771i	−0.616661	+	1.06809i	−0.990091	+	0.140429i	$0.955152\pi$
$864$	2.05268	+	4.77352i	0.0698335	+	0.162399i
$865$	−71.6494	+	41.3668i	−2.43615	+	1.40651i
$866$	12.3501	+	7.13030i	0.419672	+	0.242298i
$867$	−13.5803	−	0.532118i	−0.461210	−	0.0180717i
$868$	−6.71000	−	5.73002i	−0.227752	−	0.194490i
$869$	−19.1915			−0.651026
$870$	−21.7372	+	34.4595i	−0.736958	+	1.16828i
$871$	−8.85834	−	11.6651i	−0.300153	−	0.395256i
$872$	10.3694	−	5.98679i	0.351153	−	0.202738i
$873$	16.6370	−	24.2181i	0.563079	−	0.819659i
$874$		−	5.47512i		−	0.185199i
$875$	38.3482	+	7.10450i	1.29641	+	0.240176i
$876$	−24.9623	−	0.978104i	−0.843399	−	0.0330471i
$877$	−9.94338	−	5.74081i	−0.335764	−	0.193853i	0.322633	−	0.946524i	$-0.395432\pi$
$877$	−9.94338	−	5.74081i	−0.335764	−	0.193853i	−0.658397	+	0.752671i	$0.728765\pi$
$878$	17.7811	−	10.2659i	0.600083	−	0.346458i
$879$	−22.3919	+	11.7840i	−0.755259	+	0.397464i
$880$	4.29544	+	2.47997i	0.144799	+	0.0835998i
$881$	−5.83608			−0.196622			−0.0983112	−	0.995156i	$-0.531344\pi$
$881$	−5.83608			−0.196622			−0.0983112	+	0.995156i	$0.531344\pi$
$882$	1.65520	+	20.9347i	0.0557334	+	0.704907i
$883$	−1.68447			−0.0566871			−0.0283435	−	0.999598i	$-0.509023\pi$
$883$	−1.68447			−0.0566871			−0.0283435	+	0.999598i	$0.509023\pi$
$884$	16.5696	+	6.96090i	0.557296	+	0.234121i
$885$	32.4037	+	61.5734i	1.08924	+	2.06977i
$886$	0.915950	−	0.528824i	0.0307719	−	0.0177662i
$887$	27.8345	−	48.2107i	0.934591	−	1.61876i	0.159228	−	0.987242i	$-0.449099\pi$
$887$	27.8345	−	48.2107i	0.934591	−	1.61876i	0.775362	−	0.631517i	$-0.217567\pi$
$888$	0.616695	−	15.7388i	0.0206949	−	0.528159i
$889$	5.11071	−	27.5863i	0.171408	−	0.925213i
$890$	11.0311			0.369764
$891$	−7.51829	+	9.29243i	−0.251872	+	0.311308i
$892$	10.6864	+	18.5094i	0.357808	+	0.619741i
$893$	32.8981	−	18.9937i	1.10089	−	0.635600i
$894$	−7.67476	+	12.1666i	−0.256683	+	0.406913i
$895$	90.7624			3.03385
$896$	2.01197	+	1.71813i	0.0672153	+	0.0573987i
$897$	7.19863	−	0.625848i	0.240355	−	0.0208965i
$898$	−3.80080	+	6.58318i	−0.126834	+	0.219684i
$899$	18.1918	−	10.5031i	0.606732	−	0.350297i
$900$	11.5607	+	24.2242i	0.385356	+	0.807473i
$901$	−6.80472	−	3.92871i	−0.226698	−	0.130884i
$902$			5.81770i			0.193708i
$903$	−41.7864	+	12.9833i	−1.39057	+	0.432057i
$904$			1.47456i			0.0490430i
$905$	26.9149	−	46.6180i	0.894681	−	1.54963i
$906$	−1.98695	+	1.04566i	−0.0660121	+	0.0347396i
$907$	2.07089	+	3.58688i	0.0687627	+	0.119100i	0.898357	−	0.439266i	$-0.144762\pi$
$907$	2.07089	+	3.58688i	0.0687627	+	0.119100i	−0.829594	+	0.558367i	$0.811428\pi$
$908$	−13.1596	−	7.59771i	−0.436717	−	0.252139i
$909$	−28.0249	−	2.19959i	−0.929527	−	0.0729557i
$910$	−31.8222	+	16.0167i	−1.05490	+	0.530948i
$911$		−	1.50513i		−	0.0498672i	−0.999689	−	0.0249336i	$-0.992063\pi$
$911$		−	1.50513i		−	0.0498672i	0.999689	−	0.0249336i	$-0.00793743\pi$
$912$	−4.37276	+	6.93205i	−0.144797	+	0.229543i
$913$	−7.75958	+	4.48000i	−0.256805	+	0.148266i
$914$	−9.27260	+	5.35354i	−0.306710	+	0.177079i
$915$	−19.3314	+	30.6456i	−0.639075	+	1.01311i
$916$	21.5625			0.712445
$917$	1.04025	+	0.888324i	0.0343520	+	0.0293350i
$918$	25.7224	+	3.03609i	0.848965	+	0.100206i
$919$	−18.6222	+	32.2546i	−0.614289	+	1.06398i	0.376220	+	0.926531i	$0.377224\pi$
$919$	−18.6222	+	32.2546i	−0.614289	+	1.06398i	−0.990509	+	0.137450i	$0.956109\pi$
$920$	−2.16055	−	3.74219i	−0.0712313	−	0.123376i
$921$	−4.45978	−	8.47445i	−0.146955	−	0.279243i
$922$	−8.24337	−	4.75931i	−0.271481	−	0.156740i
$923$	−4.50670	−	35.6109i	−0.148340	−	1.17215i
$924$	−1.34213	+	5.93634i	−0.0441528	+	0.195291i
$925$		−	81.3631i		−	2.67520i
$926$	15.3688	+	8.87316i	0.505049	+	0.291590i
$927$	0.487704	−	0.232751i	0.0160183	−	0.00764454i
$928$	−5.45477	+	3.14931i	−0.179061	+	0.103381i
$929$	−34.7114	−	20.0407i	−1.13885	−	0.657513i	−0.192701	−	0.981257i	$-0.561725\pi$
$929$	−34.7114	−	20.0407i	−1.13885	−	0.657513i	−0.946145	+	0.323745i	$0.895058\pi$
$930$	0.844637	−	21.5561i	0.0276967	−	0.706853i
$931$	−25.7389	+	20.8492i	−0.843558	+	0.683306i
$932$		−	27.5547i		−	0.902586i
$933$	23.1165	−	36.6461i	0.756801	−	1.19974i
$934$	2.60380	+	4.50991i	0.0851988	+	0.147569i
$935$	21.4112	−	12.3618i	0.700221	−	0.404273i
$936$	−9.61402	−	4.95687i	−0.314244	−	0.162020i
$937$		−	26.4374i		−	0.863673i	−0.901952	−	0.431836i	$-0.857866\pi$
$937$		−	26.4374i		−	0.863673i	0.901952	−	0.431836i	$-0.142134\pi$
$938$	−10.5684	−	1.95792i	−0.345069	−	0.0639285i
$939$	−0.972896	+	24.8294i	−0.0317493	+	0.810278i
$940$	14.9903	−	25.9640i	0.488931	−	0.846853i
$941$	16.8380	−	9.72143i	0.548903	−	0.316909i	−0.199776	−	0.979842i	$-0.564022\pi$
$941$	16.8380	−	9.72143i	0.548903	−	0.316909i	0.748680	+	0.662932i	$0.230688\pi$
$942$	−27.0261	+	14.2228i	−0.880557	+	0.463403i
$943$	2.53420	−	4.38935i	0.0825247	−	0.142937i
$944$			10.7566i			0.350099i
$945$	−37.6879	+	34.8659i	−1.22599	+	1.13419i
$946$	−12.6815			−0.412312
$947$	21.6374	−	37.4771i	0.703122	−	1.21784i	−0.264244	−	0.964456i	$-0.585122\pi$
$947$	21.6374	−	37.4771i	0.703122	−	1.21784i	0.967365	−	0.253386i	$-0.0815444\pi$
$948$	−11.6560	−	22.1487i	−0.378569	−	0.719355i
$949$	41.4151	−	31.4502i	1.34439	−	1.02092i
$950$	−21.1687	+	36.6653i	−0.686804	+	1.18958i
$951$	−26.2617	−	1.02902i	−0.851594	−	0.0333682i
$952$	12.4313	−	4.40320i	0.402902	−	0.142708i
$953$		−	61.0356i		−	1.97714i	−0.150767	−	0.988569i	$-0.548174\pi$
$953$		−	61.0356i		−	1.97714i	0.150767	−	0.988569i	$-0.451826\pi$
$954$	3.89785	+	2.67769i	0.126197	+	0.0866935i
$955$	−0.772483	−	1.33798i	−0.0249970	−	0.0432960i
$956$	6.04907	+	10.4773i	0.195641	+	0.338860i
$957$	−12.2546	−	7.73026i	−0.396136	−	0.249884i
$958$		−	17.7430i		−	0.573251i
$959$	−3.46174	+	1.22615i	−0.111785	+	0.0395946i
$960$	−0.253262	+	6.46353i	−0.00817399	+	0.208610i
$961$	9.93877	−	17.2145i	0.320605	−	0.555305i
$962$	19.8294	+	26.1123i	0.639325	+	0.841893i
$963$	−16.1144	+	7.69040i	−0.519279	+	0.247820i
$964$	−1.76152	+	3.05105i	−0.0567348	+	0.0982676i
$965$	28.3882			0.913849
$966$	3.59849	−	3.89423i	0.115779	−	0.125295i
$967$		−	31.0756i		−	0.999325i	−0.866220	−	0.499662i	$-0.833457\pi$
$967$		−	31.0756i		−	0.999325i	0.866220	−	0.499662i	$-0.166543\pi$
$968$	4.61806	−	7.99872i	0.148430	−	0.257089i
$969$	19.0261	+	36.1533i	0.611206	+	1.16141i
$970$	31.6763	−	18.2883i	1.01707	−	0.587203i
$971$	25.3208	−	43.8569i	0.812583	−	1.40743i	−0.0984680	−	0.995140i	$-0.531394\pi$
$971$	25.3208	−	43.8569i	0.812583	−	1.40743i	0.911051	−	0.412294i	$-0.135272\pi$
$972$	−15.2906	−	3.03300i	−0.490445	−	0.0972834i
$973$	33.5680	+	6.21890i	1.07614	+	0.199369i
$974$			21.9047i			0.701873i
$975$	−50.6269	−	23.6413i	−1.62136	−	0.757127i
$976$	−4.85105	+	2.80076i	−0.155278	+	0.0896500i
$977$	−11.7338	−	20.3235i	−0.375396	−	0.650206i	0.614990	−	0.788535i	$-0.289160\pi$
$977$	−11.7338	−	20.3235i	−0.375396	−	0.650206i	−0.990386	+	0.138329i	$0.955827\pi$
$978$	−9.85431	−	6.21613i	−0.315106	−	0.198770i
$979$			3.92294i			0.125378i
$980$	−9.36489	+	24.4071i	−0.299150	+	0.779657i
$981$	−2.81066	+	35.8106i	−0.0897376	+	1.14334i
$982$	3.11811	+	1.80024i	0.0995030	+	0.0574481i
$983$	−42.6658	+	24.6331i	−1.36083	+	0.785675i	−0.989734	−	0.142920i	$-0.954351\pi$
$983$	−42.6658	+	24.6331i	−1.36083	+	0.785675i	−0.371095	+	0.928595i	$0.621017\pi$
$984$	−6.71415	+	3.53340i	−0.214039	+	0.112641i
$985$	21.5136	+	12.4209i	0.685481	+	0.395763i
$986$			31.3963i			0.999863i
$987$	35.8825	+	8.11258i	1.14215	+	0.258226i
$988$	−2.14210	−	16.9263i	−0.0681491	−	0.538498i
$989$	9.56799	+	5.52408i	0.304245	+	0.175656i
$990$	−13.4289	+	6.40880i	−0.426800	+	0.203685i
$991$	2.66048	+	4.60809i	0.0845131	+	0.146381i	0.905184	−	0.425021i	$-0.139733\pi$
$991$	2.66048	+	4.60809i	0.0845131	+	0.146381i	−0.820671	+	0.571402i	$0.806400\pi$
$992$	1.66752	−	2.88823i	0.0529437	−	0.0917013i
$993$	1.97891	−	50.5040i	0.0627987	−	1.60270i
$994$	−20.0301	−	17.1048i	−0.635316	−	0.542530i
$995$	−56.4904			−1.79087
$996$	−9.88312	−	6.23431i	−0.313159	−	0.197542i
$997$	20.5432	−	11.8606i	0.650608	−	0.375629i	−0.138081	−	0.990421i	$-0.544093\pi$
$997$	20.5432	−	11.8606i	0.650608	−	0.375629i	0.788689	+	0.614792i	$0.210760\pi$
$998$	−6.88661	+	3.97599i	−0.217992	+	0.125858i
$999$	37.8704	+	28.2602i	1.19817	+	0.894115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.a.467.12	yes	36
3.2	odd	2		546.2.bg.b.467.7	yes	36
7.3	odd	6	inner	546.2.bg.a.311.7	✓	36
13.12	even	2		546.2.bg.b.467.12	yes	36
21.17	even	6		546.2.bg.b.311.12	yes	36
39.38	odd	2	inner	546.2.bg.a.467.7	yes	36
91.38	odd	6		546.2.bg.b.311.7	yes	36
273.38	even	6	inner	546.2.bg.a.311.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.7	✓	36	7.3	odd	6	inner
546.2.bg.a.311.12	yes	36	273.38	even	6	inner
546.2.bg.a.467.7	yes	36	39.38	odd	2	inner
546.2.bg.a.467.12	yes	36	1.1	even	1	trivial
546.2.bg.b.311.7	yes	36	91.38	odd	6
546.2.bg.b.311.12	yes	36	21.17	even	6
546.2.bg.b.467.7	yes	36	3.2	odd	2
546.2.bg.b.467.12	yes	36	13.12	even	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.806632 + 1.53276i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23425 + 1.86729i) q^{5} +(-1.73072 - 0.0678152i) q^{6} +(0.481958 - 2.60148i) q^{7} +1.00000 q^{8} +(-1.69869 + 2.47274i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.806632 + 1.53276i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23425 + 1.86729i) q^{5} +(-1.73072 - 0.0678152i) q^{6} +(0.481958 - 2.60148i) q^{7} +1.00000 q^{8} +(-1.69869 + 2.47274i) q^{9} +(-3.23425 + 1.86729i) q^{10} +(-0.664055 - 1.15018i) q^{11} +(0.924091 - 1.46494i) q^{12} +(0.452687 + 3.57702i) q^{13} +(2.01197 + 1.71813i) q^{14} +(-0.253262 + 6.46353i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.49232 + 4.31682i) q^{17} +(-1.29211 - 2.70748i) q^{18} +(2.36598 - 4.09800i) q^{19} -3.73459i q^{20} +(4.37621 - 1.35971i) q^{21} +1.32811 q^{22} +(-1.00204 - 0.578526i) q^{23} +(0.806632 + 1.53276i) q^{24} +(4.47357 + 7.74844i) q^{25} +(-3.32413 - 1.39647i) q^{26} +(-5.16033 - 0.609089i) q^{27} +(-2.49393 + 0.883354i) q^{28} -6.29862i q^{29} +(-5.47095 - 3.45110i) q^{30} +(1.66752 + 2.88823i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.22729 - 1.94560i) q^{33} -4.98464 q^{34} +(6.41650 - 7.51388i) q^{35} +(2.99080 + 0.234739i) q^{36} +(-7.87543 - 4.54688i) q^{37} +(2.36598 + 4.09800i) q^{38} +(-5.11755 + 3.57920i) q^{39} +(3.23425 + 1.86729i) q^{40} +4.38044i q^{41} +(-1.01056 + 4.46976i) q^{42} -9.54856 q^{43} +(-0.664055 + 1.15018i) q^{44} +(-10.1113 + 4.82550i) q^{45} +(1.00204 - 0.578526i) q^{46} +(6.95231 + 4.01392i) q^{47} +(-1.73072 - 0.0678152i) q^{48} +(-6.53543 - 2.50761i) q^{49} -8.94713 q^{50} +(-4.60626 + 7.30220i) q^{51} +(2.87145 - 2.18055i) q^{52} +(-1.36514 + 0.788163i) q^{53} +(3.10765 - 4.16443i) q^{54} -4.95994i q^{55} +(0.481958 - 2.60148i) q^{56} +(8.18971 + 0.320899i) q^{57} +(5.45477 + 3.14931i) q^{58} +(9.31553 - 5.37832i) q^{59} +(5.72421 - 3.01244i) q^{60} +(4.85105 + 2.80076i) q^{61} -3.33504 q^{62} +(5.61410 + 5.61087i) q^{63} +1.00000 q^{64} +(-5.21524 + 12.4143i) q^{65} +(1.07130 + 2.03567i) q^{66} +(-3.51817 + 2.03122i) q^{67} +(2.49232 - 4.31682i) q^{68} +(0.0784657 - 2.00253i) q^{69} +(3.29896 + 9.31379i) q^{70} -9.95545 q^{71} +(-1.69869 + 2.47274i) q^{72} +(-7.21154 - 12.4907i) q^{73} +(7.87543 - 4.54688i) q^{74} +(-8.26796 + 13.1070i) q^{75} -4.73196 q^{76} +(-3.31221 + 1.17319i) q^{77} +(-0.540899 - 6.22153i) q^{78} +(7.22510 - 12.5142i) q^{79} +(-3.23425 + 1.86729i) q^{80} +(-3.22890 - 8.40085i) q^{81} +(-3.79357 - 2.19022i) q^{82} -6.74642i q^{83} +(-3.36565 - 3.11005i) q^{84} +18.6156i q^{85} +(4.77428 - 8.26929i) q^{86} +(9.65426 - 5.08067i) q^{87} +(-0.664055 - 1.15018i) q^{88} +(-2.55804 - 1.47689i) q^{89} +(0.876652 - 11.1694i) q^{90} +(9.52374 + 0.546316i) q^{91} +1.15705i q^{92} +(-3.08188 + 4.88564i) q^{93} +(-6.95231 + 4.01392i) q^{94} +(15.3043 - 8.83595i) q^{95} +(0.924091 - 1.46494i) q^{96} -9.79404 q^{97} +(5.43937 - 4.40604i) q^{98} +(3.97212 + 0.311759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9 - 14 * q^15 - 18 * q^16 + 4 * q^18 + 23 * q^21 + 14 * q^25 - 6 * q^26 + 7 * q^30 - 18 * q^32 + 24 * q^33 - 8 * q^36 - 10 * q^39 - 16 * q^42 - 16 * q^43 - 9 * q^45 + 72 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^54 - 8 * q^57 + 24 * q^59 + 7 * q^60 - 36 * q^61 - 39 * q^63 + 36 * q^64 + 18 * q^65 - 24 * q^66 - 72 * q^71 + 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 - 7 * q^84 + 8 * q^86 - 24 * q^87 - 72 * q^89 - 2 * q^91 - 14 * q^93 - 72 * q^94 - 12 * q^98 + 72 * q^99

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