LMFDB - Embedded newform 546.2.bg.a.467.7

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			467.7
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.a.311.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.924091 - 1.46494i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23425 + 1.86729i) q^{5} +(1.73072 - 0.0678152i) q^{6} +(-0.481958 + 2.60148i) q^{7} +1.00000 q^{8} +(-1.29211 + 2.70748i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.924091 - 1.46494i) 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} +(-1.29211 + 2.70748i) q^{9} +(-3.23425 + 1.86729i) q^{10} +(-0.664055 - 1.15018i) q^{11} +(-0.806632 + 1.53276i) 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} +(-1.69869 - 2.47274i) q^{18} +(-2.36598 + 4.09800i) q^{19} -3.73459i q^{20} +(4.25640 - 1.69797i) q^{21} +1.32811 q^{22} +(1.00204 + 0.578526i) q^{23} +(-0.924091 - 1.46494i) q^{24} +(4.47357 + 7.74844i) q^{25} +(-2.87145 - 2.18055i) q^{26} +(5.16033 - 0.609089i) q^{27} +(2.49393 - 0.883354i) q^{28} +6.29862i q^{29} +(5.72421 + 3.01244i) q^{30} +(-1.66752 - 2.88823i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.07130 + 2.03567i) 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} +(5.65845 - 2.64233i) q^{39} +(3.23425 + 1.86729i) q^{40} +4.38044i q^{41} +(-0.657716 + 4.53513i) q^{42} -9.54856 q^{43} +(-0.664055 + 1.15018i) q^{44} +(-9.23466 + 6.34391i) 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} +(-4.02077 + 7.64024i) q^{51} +(3.32413 - 1.39647i) q^{52} +(1.36514 - 0.788163i) q^{53} +(-2.05268 + 4.77352i) 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} +(-5.47095 + 3.45110i) q^{60} +(4.85105 + 2.80076i) q^{61} +3.33504 q^{62} +(-6.42072 - 4.66630i) q^{63} +1.00000 q^{64} +(-8.14345 + 10.7237i) q^{65} +(-1.22729 - 1.94560i) 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} +(-1.29211 + 2.70748i) q^{72} +(7.21154 + 12.4907i) q^{73} +(-7.87543 + 4.54688i) q^{74} +(7.21704 - 13.7138i) 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} +(-5.66090 - 6.99673i) q^{81} +(-3.79357 - 2.19022i) q^{82} -6.74642i q^{83} +(-3.59868 - 2.83716i) q^{84} -18.6156i q^{85} +(4.77428 - 8.26929i) q^{86} +(9.22711 - 5.82050i) q^{87} +(-0.664055 - 1.15018i) q^{88} +(-2.55804 - 1.47689i) q^{89} +(-0.876652 - 11.1694i) q^{90} +(-9.08738 - 2.90163i) q^{91} -1.15705i q^{92} +(-2.69015 + 5.11180i) q^{93} +(-6.95231 + 4.01392i) q^{94} +(-15.3043 + 8.83595i) q^{95} +(-0.806632 + 1.53276i) 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
$3$	−0.924091	−	1.46494i	−0.533524	−	0.845785i
$3$	−0.924091	−	1.46494i	−0.533524	−	0.845785i
$4$	−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
$9$	−1.29211	+	2.70748i	−0.430704	+	0.902493i
$10$	−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	$0.897499\pi$
$12$	−0.806632	+	1.53276i	−0.232855	+	0.442469i
$13$	−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	$-0.960049\pi$
$17$	−2.49232	−	4.31682i	−0.604476	−	1.04698i	0.387658	−	0.921803i	$-0.373284\pi$
$18$	−1.69869	−	2.47274i	−0.400385	−	0.582831i
$19$	−2.36598	+	4.09800i	−0.542793	+	0.940145i	0.455949	+	0.890006i	$0.349300\pi$
$19$	−2.36598	+	4.09800i	−0.542793	+	0.940145i	−0.998742	+	0.0501391i	$0.984034\pi$
$20$		−	3.73459i		−	0.835079i
$21$	4.25640	−	1.69797i	0.928822	−	0.370527i
$22$	1.32811			0.283154
$23$	1.00204	+	0.578526i	0.208939	+	0.120631i	0.600818	−	0.799386i	$-0.294842\pi$
$23$	1.00204	+	0.578526i	0.208939	+	0.120631i	−0.391879	+	0.920017i	$0.628175\pi$
$24$	−0.924091	−	1.46494i	−0.188629	−	0.299030i
$25$	4.47357	+	7.74844i	0.894713	+	1.54969i
$26$	−2.87145	−	2.18055i	−0.563137	−	0.427641i
$27$	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	$0.198832\pi$
$29$			6.29862i			1.16962i	−0.811169	+	0.584812i	$0.801168\pi$
$30$	5.72421	+	3.01244i	1.04509	+	0.549993i
$31$	−1.66752	−	2.88823i	−0.299495	−	0.518741i	0.676525	−	0.736419i	$-0.263485\pi$
$31$	−1.66752	−	2.88823i	−0.299495	−	0.518741i	−0.976021	+	0.217679i	$0.930152\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.07130	+	2.03567i	−0.186489	+	0.354365i
$34$	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	0.979486	−	0.201514i	$-0.0645861\pi$
$37$	7.87543	+	4.54688i	1.29471	+	0.747503i	0.315227	+	0.949016i	$0.397919\pi$
$38$	−2.36598	−	4.09800i	−0.383812	−	0.664783i
$39$	5.65845	−	2.64233i	0.906077	−	0.423112i
$40$	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	$0.888877\pi$
$42$	−0.657716	+	4.53513i	−0.101488	+	0.699786i
$43$	−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
$45$	−9.23466	+	6.34391i	−1.37662	+	0.945694i
$46$	−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
$51$	−4.02077	+	7.64024i	−0.563020	+	1.06985i
$52$	3.32413	−	1.39647i	0.460974	−	0.193656i
$53$	1.36514	−	0.788163i	0.187516	−	0.108263i	−0.403303	−	0.915066i	$-0.632138\pi$
$53$	1.36514	−	0.788163i	0.187516	−	0.108263i	0.590819	+	0.806804i	$0.298805\pi$
$54$	−2.05268	+	4.77352i	−0.279334	+	0.649594i
$55$		−	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	$0.0864283\pi$
$60$	−5.47095	+	3.45110i	−0.706297	+	0.445535i
$61$	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
$63$	−6.42072	−	4.66630i	−0.808935	−	0.587898i
$64$	1.00000			0.125000
$65$	−8.14345	+	10.7237i	−1.01007	+	1.33011i
$66$	−1.22729	−	1.94560i	−0.151070	−	0.239487i
$67$	3.51817	−	2.03122i	0.429813	−	0.248153i	−0.269454	−	0.963013i	$-0.586843\pi$
$67$	3.51817	−	2.03122i	0.429813	−	0.248153i	0.699267	+	0.714861i	$0.253510\pi$
$68$	−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	$0.701167\pi$
$72$	−1.29211	+	2.70748i	−0.152277	+	0.319080i
$73$	7.21154	+	12.4907i	0.844046	+	1.46193i	0.886447	+	0.462830i	$0.153166\pi$
$73$	7.21154	+	12.4907i	0.844046	+	1.46193i	−0.0424005	+	0.999101i	$0.513501\pi$
$74$	−7.87543	+	4.54688i	−0.915500	+	0.528564i
$75$	7.21704	−	13.7138i	0.833352	−	1.58353i
$76$	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
$81$	−5.66090	−	6.99673i	−0.628988	−	0.777415i
$82$	−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	$-0.120731\pi$
$84$	−3.59868	−	2.83716i	−0.392648	−	0.309560i
$85$		−	18.6156i		−	2.01914i
$86$	4.77428	−	8.26929i	0.514824	−	0.891701i
$87$	9.22711	−	5.82050i	0.989251	−	0.624023i
$88$	−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
$91$	−9.08738	−	2.90163i	−0.952617	−	0.304174i
$92$		−	1.15705i		−	0.120631i
$93$	−2.69015	+	5.11180i	−0.278955	+	0.530069i
$94$	−6.95231	+	4.01392i	−0.717076	+	0.414004i
$95$	−15.3043	+	8.83595i	−1.57019	+	0.906550i
$96$	−0.806632	+	1.53276i	−0.0823265	+	0.156436i
$97$	9.79404			0.994434			0.497217	−	0.867626i	$-0.334355\pi$
$97$	9.79404			0.994434			0.497217	+	0.867626i	$0.334355\pi$
$98$	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	0.533062	−	0.846076i	$-0.321041\pi$
$101$	−4.68518	−	8.11497i	−0.466193	−	0.807470i	−0.999254	+	0.0386068i	$0.987708\pi$
$102$	−4.60626	−	7.30220i	−0.456087	−	0.723026i
$103$	−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
$105$	16.9368	+	2.45630i	1.65287	+	0.239710i
$106$			1.57633i			0.153106i
$107$	−5.15442	−	2.97590i	−0.498296	−	0.287691i	0.229714	−	0.973258i	$-0.426221\pi$
$107$	−5.15442	−	2.97590i	−0.498296	−	0.287691i	−0.728010	+	0.685567i	$0.759554\pi$
$108$	−3.10765	−	4.16443i	−0.299034	−	0.400723i
$109$	−10.3694	+	5.98679i	−0.993211	+	0.573431i	−0.906233	−	0.422780i	$-0.861054\pi$
$109$	−10.3694	+	5.98679i	−0.993211	+	0.573431i	−0.0869783	+	0.996210i	$0.527721\pi$
$110$	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	$-0.977905\pi$
$113$		−	1.47456i		−	0.138714i	0.997592	−	0.0693572i	$-0.0220948\pi$
$114$	−3.81695	+	7.25294i	−0.357490	+	0.679300i
$115$	2.16055	+	3.74219i	0.201473	+	0.348961i
$116$	5.45477	−	3.14931i	0.506462	−	0.292406i
$117$	−9.09979	−	5.84755i	−0.841276	−	0.540606i
$118$			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
$123$	6.41709	−	4.04792i	0.578609	−	0.364989i
$124$	−1.66752	+	2.88823i	−0.149748	+	0.259370i
$125$			14.7409i			1.31847i
$126$	7.25149	−	3.22736i	0.646014	−	0.287516i
$127$	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
$129$	8.82373	+	13.9881i	0.776887	+	1.23158i
$130$	−5.21524	−	12.4143i	−0.457407	−	1.08880i
$131$	0.258515	−	0.447761i	0.0225865	−	0.0391210i	−0.854511	−	0.519433i	$-0.826143\pi$
$131$	0.258515	−	0.447761i	0.0225865	−	0.0391210i	0.877098	+	0.480312i	$0.159477\pi$
$132$	2.29859	−	0.0900661i	0.200067	−	0.00783925i
$133$	−9.52057	−	8.13012i	−0.825538	−	0.704971i
$134$			4.06244i			0.350941i
$135$	17.8271	+	7.66590i	1.53431	+	0.659776i
$136$	−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	$0.852219\pi$
$138$	1.77348	+	0.933314i	0.150969	+	0.0794490i
$139$			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
$143$	4.41482	−	1.85467i	0.369186	−	0.155095i
$144$	−1.69869	−	2.47274i	−0.141558	−	0.206062i
$145$	−11.7614	+	20.3713i	−0.976729	+	1.69174i
$146$	−14.4231			−1.19366
$147$	2.36583	+	11.8913i	0.195130	+	0.980777i
$148$		−	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	$0.0561738\pi$
$150$	8.26796	+	13.1070i	0.675076	+	1.07018i
$151$	−1.12265	+	0.648163i	−0.0913600	+	0.0527467i	−0.544984	−	0.838446i	$-0.683464\pi$
$151$	−1.12265	+	0.648163i	−0.0913600	+	0.0527467i	0.453624	+	0.891193i	$0.350131\pi$
$152$	−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
$156$	−5.11755	−	3.57920i	−0.409732	−	0.286565i
$157$	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
$159$	−2.41613	−	1.27151i	−0.191611	−	0.100838i
$160$		−	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	0.254192	−	0.967154i	$-0.418190\pi$
$163$	−5.82554	−	3.36338i	−0.456292	−	0.263440i	−0.710484	+	0.703714i	$0.751524\pi$
$164$	3.79357	−	2.19022i	0.296228	−	0.171027i
$165$	−7.26603	+	4.58344i	−0.565660	+	0.356820i
$166$	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	$0.982772\pi$
$168$	4.25640	−	1.69797i	0.328388	−	0.131001i
$169$	−12.5901	−	3.23854i	−0.968473	−	0.249119i
$170$	16.1215	+	9.30778i	1.23647	+	0.713874i
$171$	−8.03813	−	11.7009i	−0.614691	−	0.894791i
$172$	4.77428	+	8.26929i	0.364035	+	0.630528i
$173$	11.0767	−	19.1854i	0.842145	−	1.45864i	−0.0459336	−	0.998944i	$-0.514626\pi$
$173$	11.0767	−	19.1854i	0.842145	−	1.45864i	0.888078	−	0.459693i	$-0.152040\pi$
$174$	0.427142	+	10.9012i	0.0323816	+	0.826415i
$175$	−22.3135	+	7.90348i	−1.68674	+	0.597447i
$176$	1.32811			0.100110
$177$	−16.4873	−	8.67665i	−1.23926	−	0.652177i
$178$	2.55804	−	1.47689i	0.191734	−	0.110697i
$179$	−21.0472	+	12.1516i	−1.57314	+	0.908253i	−0.577359	+	0.816490i	$0.695917\pi$
$179$	−21.0472	+	12.1516i	−1.57314	+	0.908253i	−0.995781	+	0.0917629i	$0.970750\pi$
$180$	10.1113	+	4.82550i	0.753653	+	0.359672i
$181$		−	14.4139i		−	1.07137i	−0.844417	−	0.535687i	$-0.820053\pi$
$181$		−	14.4139i		−	1.07137i	0.844417	−	0.535687i	$-0.179947\pi$
$182$	7.05658	−	6.41909i	0.523068	−	0.475815i
$183$	−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
$186$	−3.08188	−	4.88564i	−0.225974	−	0.358232i
$187$	−3.31007	+	5.73321i	−0.242057	+	0.419254i
$188$		−	8.02784i		−	0.585490i
$189$	−0.902527	+	13.7181i	−0.0656491	+	0.997843i
$190$		−	17.6719i		−	1.28205i
$191$	0.358267	+	0.206846i	0.0259233	+	0.0149668i	0.512906	−	0.858445i	$-0.328569\pi$
$191$	0.358267	+	0.206846i	0.0259233	+	0.0149668i	−0.486982	+	0.873412i	$0.661902\pi$
$192$	−0.924091	−	1.46494i	−0.0666905	−	0.105723i
$193$	−6.58304	+	3.80072i	−0.473857	+	0.273582i	−0.717853	−	0.696195i	$-0.754875\pi$
$193$	−6.58304	+	3.80072i	−0.473857	+	0.273582i	0.243996	+	0.969776i	$0.421542\pi$
$194$	−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	$0.423849\pi$
$198$	−1.71607	+	3.59583i	−0.121956	+	0.255545i
$199$	−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
$201$	−6.22673	−	3.27689i	−0.439200	−	0.231134i
$202$	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
$207$	−2.86109	+	1.96547i	−0.198859	+	0.136610i
$208$	−2.87145	−	2.18055i	−0.199099	−	0.151194i
$209$	6.28456			0.434712
$210$	−10.5956	+	13.4396i	−0.731168	+	0.927419i
$211$	−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
$213$	9.19975	+	14.5842i	0.630356	+	0.999291i
$214$	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
$219$	11.6341	−	22.1071i	0.786160	−	1.49386i
$220$	−4.29544	+	2.47997i	−0.289598	+	0.167200i
$221$	16.5696	−	6.96090i	1.11459	−	0.468241i
$222$	13.9385	+	7.33532i	0.935493	+	0.492314i
$223$	21.3728			1.43123			0.715616	−	0.698494i	$-0.246146\pi$
$223$	21.3728			1.43123			0.715616	+	0.698494i	$0.246146\pi$
$224$	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	$0.165092\pi$
$228$	−4.37276	−	6.93205i	−0.289593	−	0.459086i
$229$	10.7812	−	18.6737i	0.712445	−	1.23399i	−0.251492	−	0.967859i	$-0.580921\pi$
$229$	10.7812	−	18.6737i	0.712445	−	1.23399i	0.963937	−	0.266131i	$-0.0857454\pi$
$230$	−4.32111			−0.284925
$231$	−4.77944	−	3.76807i	−0.314464	−	0.247921i
$232$			6.29862i			0.413525i
$233$	−23.8631	−	13.7774i	−1.56332	−	0.902586i	−0.996917	−	0.0784603i	$-0.975000\pi$
$233$	−23.8631	−	13.7774i	−1.56332	−	0.902586i	−0.566407	−	0.824126i	$-0.691667\pi$
$234$	9.61402	−	4.95687i	0.628488	−	0.324041i
$235$	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	$0.627968\pi$
$240$	5.72421	+	3.01244i	0.369496	+	0.194452i
$241$	1.76152	+	3.05105i	0.113470	+	0.196535i	0.917167	−	0.398503i	$-0.130470\pi$
$241$	1.76152	+	3.05105i	0.113470	+	0.196535i	−0.803697	+	0.595038i	$0.797137\pi$
$242$	4.61806	+	7.99872i	0.296860	+	0.514177i
$243$	−5.01862	+	14.7585i	−0.321945	+	0.946758i
$244$		−	5.60151i		−	0.358600i
$245$	−16.4548	−	20.3138i	−1.05126	−	1.29780i
$246$	0.297060	+	7.58132i	0.0189399	+	0.483367i
$247$	−13.5876	−	10.3183i	−0.864556	−	0.656535i
$248$	−1.66752	−	2.88823i	−0.105887	−	0.183403i
$249$	−9.88312	+	6.23431i	−0.626317	+	0.395083i
$250$	−12.7660	−	7.37045i	−0.807392	−	0.466148i
$251$	18.9499			1.19611			0.598053	−	0.801457i	$-0.295941\pi$
$251$	18.9499			1.19611			0.598053	+	0.801457i	$0.295941\pi$
$252$	−0.830772	+	7.89366i	−0.0523337	+	0.497254i
$253$		−	1.53669i		−	0.0966110i
$254$	−5.30202	+	9.18338i	−0.332679	+	0.576216i
$255$	−27.2707	+	17.2025i	−1.70776	+	1.07726i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.299289	+	0.518384i	−0.0186692	+	0.0323359i	−0.875209	−	0.483745i	$-0.839276\pi$
$257$	−0.299289	+	0.518384i	−0.0186692	+	0.0323359i	0.856540	+	0.516081i	$0.172610\pi$
$258$	−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
$261$	−17.0534	−	8.13852i	−1.05558	−	0.503762i
$262$	0.258515	+	0.447761i	0.0159711	+	0.0276627i
$263$	23.1551	−	13.3686i	1.42781	−	0.824344i	0.430859	−	0.902419i	$-0.358211\pi$
$263$	23.1551	−	13.3686i	1.42781	−	0.824344i	0.996947	+	0.0780752i	$0.0248774\pi$
$264$	−1.07130	+	2.03567i	−0.0659337	+	0.125287i
$265$	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	0.637052	−	0.770820i	$-0.280153\pi$
$269$	−5.72442	−	9.91498i	−0.349024	−	0.604527i	−0.986076	+	0.166293i	$0.946820\pi$
$270$	−15.5524	+	11.6058i	−0.946491	+	0.706306i
$271$	−12.6383	+	21.8902i	−0.767723	+	1.32974i	0.171072	+	0.985259i	$0.445277\pi$
$271$	−12.6383	+	21.8902i	−0.767723	+	1.32974i	−0.938795	+	0.344477i	$0.888056\pi$
$272$	4.98464			0.302238
$273$	4.14685	+	15.9939i	0.250979	+	0.967993i
$274$	1.38807			0.0838562
$275$	5.94139	−	10.2908i	0.358279	−	0.620558i
$276$	−1.69501	+	1.06922i	−0.102028	+	0.0643595i
$277$	−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	$0.734431\pi$
$282$	12.3047	+	6.47551i	0.732736	+	0.385611i
$283$	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
$285$	27.0867	+	14.2547i	1.60448	+	0.844377i
$286$	−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
$291$	−9.05058	−	14.3477i	−0.530555	−	0.841077i
$292$	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	$0.859666\pi$
$294$	−11.4811	−	3.89678i	−0.669590	−	0.227265i
$295$	40.1716			2.33888
$296$	7.87543	+	4.54688i	0.457750	+	0.264282i
$297$	−4.12730	−	5.53083i	−0.239491	−	0.320931i
$298$	4.15260	+	7.19252i	0.240554	+	0.416651i
$299$	−2.52301	+	3.32241i	−0.145909	+	0.192140i
$300$	−15.4850	+	0.606752i	−0.894027	+	0.0350308i
$301$	4.60200	−	24.8404i	0.265255	−	1.43178i
$302$		−	1.29633i		−	0.0745952i
$303$	−7.55843	+	14.3625i	−0.434220	+	0.825103i
$304$	−2.36598	−	4.09800i	−0.135698	−	0.235036i
$305$	10.4597	+	18.1167i	0.598918	+	1.03736i
$306$	−6.44070	+	13.4958i	−0.368191	+	0.771504i
$307$	5.52889			0.315550			0.157775	−	0.987475i	$-0.449568\pi$
$307$	5.52889			0.315550			0.157775	+	0.987475i	$0.449568\pi$
$308$	−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	$0.0842982\pi$
$311$	12.5077	+	21.6640i	0.709247	+	1.22845i	−0.255890	+	0.966706i	$0.582368\pi$
$312$	5.65845	−	2.64233i	0.320347	−	0.149593i
$313$	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
$315$	−12.0528	−	27.0813i	−0.679101	−	1.52586i
$316$	−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	$0.306788\pi$
$318$	2.30923	−	1.45667i	0.129495	−	0.0816860i
$319$	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
$324$	−3.22890	+	8.40085i	−0.179383	+	0.466714i
$325$	−29.7415	+	12.4944i	−1.64976	+	0.693065i
$326$	5.82554	−	3.36338i	0.322647	−	0.186280i
$327$	18.3526	+	9.65827i	1.01490	+	0.534104i
$328$			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	0.993207	−	0.116360i	$-0.0371225\pi$
$331$	25.2714	+	14.5904i	1.38904	+	0.801963i	0.395833	+	0.918322i	$0.370456\pi$
$332$	−5.84258	+	3.37321i	−0.320653	+	0.185129i
$333$	−22.4865	+	15.4475i	−1.23225	+	0.846517i
$334$	−1.21086	−	0.699090i	−0.0662553	−	0.0382525i
$335$	15.1715			0.828908
$336$	−0.657716	+	4.53513i	−0.0358813	+	0.247412i
$337$	21.8314			1.18923			0.594615	−	0.804011i	$-0.297305\pi$
$337$	21.8314			1.18923			0.594615	+	0.804011i	$0.297305\pi$
$338$	9.09973	−	9.28412i	0.494960	−	0.504989i
$339$	−2.16014	+	1.36262i	−0.117323	+	0.0740075i
$340$	−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
$345$	3.48554	−	6.62321i	0.187655	−	0.356582i
$346$	11.0767	+	19.1854i	0.595486	+	1.03141i
$347$	24.0903	−	13.9086i	1.29324	−	0.746651i	0.314011	−	0.949419i	$-0.398327\pi$
$347$	24.0903	−	13.9086i	1.29324	−	0.746651i	0.979227	+	0.202768i	$0.0649938\pi$
$348$	−9.65426	−	5.08067i	−0.517522	−	0.272352i
$349$	4.54691			0.243391			0.121695	−	0.992567i	$-0.461167\pi$
$349$	4.54691			0.243391			0.121695	+	0.992567i	$0.461167\pi$
$350$	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	$0.262209\pi$
$354$	15.7579	−	9.94012i	0.837521	−	0.528311i
$355$	−32.1984	−	18.5897i	−1.70891	−	0.986641i
$356$			2.95378i			0.156550i
$357$	−17.9381	−	14.1422i	−0.949386	−	0.748486i
$358$		−	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	$0.289021\pi$
$360$	−9.23466	+	6.34391i	−0.486710	+	0.334353i
$361$	−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
$364$	2.03081	+	9.32072i	0.106443	+	0.488538i
$365$			53.8642i			2.81938i
$366$	8.58576	+	4.51836i	0.448785	+	0.236178i
$367$	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
$369$	−11.8599	−	5.66001i	−0.617404	−	0.294648i
$370$	−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
$375$	21.5946	−	13.6219i	1.11514	−	0.703434i
$376$	6.95231	+	4.01392i	0.358538	+	0.207002i
$377$	−22.5303	−	2.85130i	−1.16037	−	0.146850i
$378$	−11.4289	−	7.64065i	−0.587841	−	0.392992i
$379$			18.0896i			0.929201i	0.885520	+	0.464601i	$0.153802\pi$
$379$			18.0896i			0.929201i	−0.885520	+	0.464601i	$0.846198\pi$
$380$	15.3043	+	8.83595i	0.785095	+	0.453275i
$381$	−9.79911	−	15.5343i	−0.502023	−	0.795847i
$382$	−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
$387$	12.3378	−	25.8525i	0.627166	−	1.31416i
$388$	−4.89702	−	8.48189i	−0.248609	−	0.430603i
$389$	27.5356	−	15.8977i	1.39611	−	0.806045i	0.402128	−	0.915583i	$-0.368271\pi$
$389$	27.5356	−	15.8977i	1.39611	−	0.806045i	0.993983	+	0.109539i	$0.0349373\pi$
$390$	−13.3668	+	19.1119i	−0.676855	+	0.967771i
$391$		−	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
$396$	−2.25605	−	3.28407i	−0.113371	−	0.165031i
$397$	13.5400	−	23.4520i	0.679555	−	1.17702i	−0.295560	−	0.955324i	$-0.595506\pi$
$397$	13.5400	−	23.4520i	0.679555	−	1.17702i	0.975115	−	0.221700i	$-0.0711605\pi$
$398$		−	15.1263i		−	0.758212i
$399$	−3.11228	+	21.4600i	−0.155809	+	1.07435i
$400$	−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	$0.0442766\pi$
$402$	5.95123	−	3.75406i	0.296821	−	0.187235i
$403$	11.0861	−	4.65728i	0.552238	−	0.231996i
$404$	−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
$408$	−4.02077	+	7.64024i	−0.199058	+	0.378248i
$409$	9.71830	+	16.8326i	0.480539	+	0.832318i	0.999751	−	0.0223276i	$-0.00710770\pi$
$409$	9.71830	+	16.8326i	0.480539	+	0.832318i	−0.519212	+	0.854646i	$0.673774\pi$
$410$	−8.17956	−	14.1674i	−0.403960	−	0.699679i
$411$	−1.11966	+	2.12757i	−0.0552287	+	0.104945i
$412$			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
$416$	3.32413	−	1.39647i	0.162979	−	0.0684677i
$417$	18.9027	−	11.9239i	0.925672	−	0.583917i
$418$	−3.14228	+	5.44259i	−0.153694	+	0.266206i
$419$	11.9628			0.584422			0.292211	−	0.956354i	$-0.405609\pi$
$419$	11.9628			0.584422			0.292211	+	0.956354i	$0.405609\pi$
$420$	−6.34120	−	15.8959i	−0.309419	−	0.775639i
$421$			8.12436i			0.395957i	0.980206	+	0.197979i	$0.0634377\pi$
$421$			8.12436i			0.395957i	−0.980206	+	0.197979i	$0.936562\pi$
$422$	5.11771	−	8.86413i	0.249126	−	0.431499i
$423$	−19.8508	+	13.6368i	−0.965177	+	0.663045i
$424$	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
$429$	−6.79667	−	4.75357i	−0.328147	−	0.229504i
$430$	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	$0.909838\pi$
$432$	−2.05268	+	4.77352i	−0.0987595	+	0.229666i
$433$		−	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
$438$	13.3282	+	21.1290i	0.636847	+	1.00958i
$439$	−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
$441$	15.2338	−	14.4544i	0.725420	−	0.688307i
$442$	−2.25648	+	17.8301i	−0.107330	+	0.848093i
$443$	0.915950	+	0.528824i	0.0435181	+	0.0251252i	0.521601	−	0.853189i	$-0.325335\pi$
$443$	0.915950	+	0.528824i	0.0435181	+	0.0251252i	−0.478083	+	0.878315i	$0.658668\pi$
$444$	−13.3218	+	8.40346i	−0.632226	+	0.398811i
$445$	−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	$0.442594\pi$
$450$	11.5607	−	24.2242i	0.544976	−	1.14194i
$451$	5.03828	−	2.90885i	0.237243	−	0.136972i
$452$	−1.27700	+	0.737278i	−0.0600651	+	0.0346786i
$453$	1.98695	+	1.04566i	0.0933552	+	0.0491293i
$454$			15.1954i			0.713156i
$455$	−23.9726	−	26.3534i	−1.12385	−	1.23547i
$456$	8.18971	−	0.320899i	0.383518	−	0.0150275i
$457$	−9.27260	−	5.35354i	−0.433754	−	0.250428i	0.267191	−	0.963644i	$-0.413905\pi$
$457$	−9.27260	−	5.35354i	−0.433754	−	0.250428i	−0.700945	+	0.713216i	$0.747238\pi$
$458$	10.7812	+	18.6737i	0.503775	+	0.872563i
$459$	−15.4905	−	20.7582i	−0.723035	−	0.968909i
$460$	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	$0.928851\pi$
$462$	5.65296	−	2.25509i	0.263000	−	0.104916i
$463$			17.7463i			0.824742i	0.911016	+	0.412371i	$0.135299\pi$
$463$			17.7463i			0.824742i	−0.911016	+	0.412371i	$0.864701\pi$
$464$	−5.45477	−	3.14931i	−0.253231	−	0.146203i
$465$	−18.2458	+	11.5095i	−0.846130	+	0.533742i
$466$	23.8631	−	13.7774i	1.10544	−	0.638225i
$467$	−2.60380	+	4.50991i	−0.120489	+	0.208694i	−0.919961	−	0.392010i	$-0.871780\pi$
$467$	−2.60380	+	4.50991i	−0.120489	+	0.208694i	0.799471	+	0.600704i	$0.205113\pi$
$468$	−0.514232	+	10.8044i	−0.0237704	+	0.499435i
$469$	3.58857	+	10.1314i	0.165705	+	0.467826i
$470$	−29.9807			−1.38290
$471$	−27.0261	−	14.2228i	−1.24530	−	0.655352i
$472$	9.31553	−	5.37832i	0.428782	−	0.247557i
$473$	6.34077	+	10.9825i	0.291549	+	0.504977i
$474$	11.6560	−	22.1487i	0.535378	−	1.01732i
$475$	−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	$0.466184\pi$
$480$	−5.47095	+	3.45110i	−0.249714	+	0.157520i
$481$	−19.8294	+	26.1123i	−0.904142	+	1.19062i
$482$	−3.52305			−0.160470
$483$	5.24738	+	0.761011i	0.238764	+	0.0346272i
$484$	−9.23612			−0.419824
$485$	31.6763	+	18.2883i	1.43835	+	0.830431i
$486$	−10.2719	−	11.7255i	−0.465944	−	0.531880i
$487$	−18.9701	+	10.9524i	−0.859616	+	0.496299i	−0.863884	−	0.503691i	$-0.831975\pi$
$487$	−18.9701	+	10.9524i	−0.859616	+	0.496299i	0.00426783	+	0.999991i	$0.498642\pi$
$488$	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	$0.0258893\pi$
$491$			3.60049i			0.162488i	−0.996694	+	0.0812438i	$0.974111\pi$
$492$	−6.71415	−	3.53340i	−0.302697	−	0.159298i
$493$	27.1900	−	15.6982i	1.22458	−	0.707010i
$494$	15.7297	−	6.60805i	0.707711	−	0.297310i
$495$	13.4289	+	6.40880i	0.603586	+	0.288054i
$496$	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	0.337873	−	0.941192i	$-0.390293\pi$
$499$	−6.88661	−	3.97599i	−0.308287	−	0.177990i	−0.646160	+	0.763202i	$0.723626\pi$
$500$	12.7660	−	7.37045i	0.570913	−	0.329617i
$501$	2.04825	−	1.29205i	0.0915092	−	0.0577243i
$502$	−9.47494	+	16.4111i	−0.422887	+	0.732462i
$503$	10.7862			0.480934			0.240467	−	0.970657i	$-0.422699\pi$
$503$	10.7862			0.480934			0.240467	+	0.970657i	$0.422699\pi$
$504$	−6.42072	−	4.66630i	−0.286002	−	0.207853i
$505$		−	34.9944i		−	1.55723i
$506$	1.33081	+	0.768346i	0.0591619	+	0.0341571i
$507$	6.89017	+	21.4365i	0.306003	+	0.952031i
$508$	−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
$513$	−9.71319	+	22.5881i	−0.428848	+	0.997289i
$514$	−0.299289	−	0.518384i	−0.0132011	−	0.0228650i
$515$	−0.336360	−	0.582592i	−0.0148218	−	0.0256721i
$516$	7.70217	−	14.6356i	0.339069	−	0.644297i
$517$		−	10.6619i		−	0.468908i
$518$	−8.03301	−	22.6792i	−0.352950	−	0.996467i
$519$	−38.3413	+	1.50234i	−1.68300	+	0.0659452i
$520$	−8.14345	+	10.7237i	−0.357114	+	0.470264i
$521$	−1.55866	−	2.69969i	−0.0682863	−	0.118275i	0.829861	−	0.557971i	$-0.188420\pi$
$521$	−1.55866	−	2.69969i	−0.0682863	−	0.118275i	−0.898147	+	0.439695i	$0.855086\pi$
$522$	15.5749	−	10.6994i	0.681693	−	0.468300i
$523$	−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
$525$	32.1979	+	25.3845i	1.40523	+	1.10787i
$526$			26.7372i			1.16580i
$527$	−8.31197	+	14.3968i	−0.362075	+	0.627132i
$528$	−1.22729	−	1.94560i	−0.0534112	−	0.0846716i
$529$	−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
$534$	−4.52742	−	2.38261i	−0.195921	−	0.103106i
$535$	−11.1138	−	19.2496i	−0.480490	−	0.832233i
$536$	3.51817	−	2.03122i	0.151962	−	0.0877352i
$537$	37.2509	+	19.6037i	1.60750	+	0.845963i
$538$	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	0.493824	−	0.869562i	$-0.335599\pi$
$541$	−0.286703	−	0.165528i	−0.0123263	−	0.00711660i	−0.506150	+	0.862445i	$0.668932\pi$
$542$	−12.6383	−	21.8902i	−0.542862	−	0.940265i
$543$	−21.1155	+	13.3197i	−0.906151	+	0.571604i
$544$	−2.49232	+	4.31682i	−0.106857	+	0.185082i
$545$	−44.7164			−1.91544
$546$	−15.9245	−	4.40566i	−0.681506	−	0.188545i
$547$	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
$549$	−13.8511	+	9.51523i	−0.591150	+	0.406100i
$550$	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
$555$	27.3944	−	52.0546i	1.16283	−	2.20960i
$556$	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	$0.692262\pi$
$558$	−4.30924	+	9.02954i	−0.182425	+	0.382251i
$559$	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	$-0.923542\pi$
$563$	−16.4117	−	28.4259i	−0.691670	−	1.19801i	0.279621	−	0.960111i	$-0.409791\pi$
$564$	−11.7603	+	7.41845i	−0.495199	+	0.312373i
$565$	2.75343	−	4.76907i	0.115838	−	0.200636i
$566$			7.47391i			0.314152i
$567$	20.9302	−	11.3546i	0.878986	−	0.476848i
$568$	−9.95545			−0.417722
$569$	−36.2966	−	20.9559i	−1.52163	−	0.878515i	−0.999674	−	0.0255443i	$-0.991868\pi$
$569$	−36.2966	−	20.9559i	−1.52163	−	0.878515i	−0.521959	−	0.852971i	$-0.674799\pi$
$570$	−25.8883	+	16.3304i	−1.08434	+	0.684007i
$571$	−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	$0.886741\pi$
$572$	−3.81360	−	2.89601i	−0.159455	−	0.121088i
$573$	−0.0280546	−	0.715985i	−0.00117200	−	0.0299107i
$574$	7.52616	−	8.81332i	0.314136	−	0.367861i
$575$			10.3523i			0.431720i
$576$	−1.29211	+	2.70748i	−0.0538380	+	0.112812i
$577$	−6.63093	−	11.4851i	−0.276049	−	0.478131i	0.694350	−	0.719637i	$-0.255692\pi$
$577$	−6.63093	−	11.4851i	−0.276049	−	0.478131i	−0.970399	+	0.241506i	$0.922359\pi$
$578$	−3.92330	−	6.79535i	−0.163188	−	0.282649i
$579$	11.6512	+	6.13156i	0.484205	+	0.254819i
$580$	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
$585$	−18.5119	−	35.9044i	−0.765372	−	1.48446i
$586$	−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	$0.937496\pi$
$588$	9.11525	−	7.99451i	0.375906	−	0.329688i
$589$	15.7813			0.650255
$590$	−20.0858	+	34.7896i	−0.826920	+	1.43227i
$591$	−6.14689	−	9.74453i	−0.252849	−	0.400836i
$592$	−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
$597$	23.1849	+	12.2013i	0.948895	+	0.499367i
$598$	−1.61579	−	3.84619i	−0.0660745	−	0.157283i
$599$	3.32776	−	1.92128i	0.135969	−	0.0785016i	−0.430473	−	0.902604i	$-0.641653\pi$
$599$	3.32776	−	1.92128i	0.135969	−	0.0785016i	0.566441	+	0.824102i	$0.308320\pi$
$600$	7.21704	−	13.7138i	0.294634	−	0.559863i
$601$			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
$606$	−8.65907	−	13.7270i	−0.351750	−	0.557623i
$607$	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
$609$	10.6948	+	26.8094i	0.433377	+	1.08637i
$610$	−20.9193			−0.846999
$611$	−17.5051	+	23.0515i	−0.708180	+	0.932564i
$612$	−8.46735	−	12.3257i	−0.342273	−	0.498237i
$613$	7.85345	−	4.53419i	0.317198	−	0.183134i	−0.332945	−	0.942946i	$-0.608042\pi$
$613$	7.85345	−	4.53419i	0.317198	−	0.183134i	0.650143	+	0.759812i	$0.274709\pi$
$614$	−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	$0.903680\pi$
$618$	−0.276099	−	0.145300i	−0.0111063	−	0.00584484i
$619$	−20.7977	−	36.0226i	−0.835929	−	1.44787i	−0.893272	−	0.449517i	$-0.851596\pi$
$619$	−20.7977	−	36.0226i	−0.835929	−	1.44787i	0.0573430	−	0.998355i	$-0.481737\pi$
$620$	−10.7863	+	6.22749i	−0.433189	+	0.250102i
$621$	5.52321	+	2.37505i	0.221639	+	0.0953076i
$622$	−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
$627$	−5.80751	−	9.20652i	−0.231930	−	0.367673i
$628$	−15.2700	−	8.81616i	−0.609341	−	0.351803i
$629$		−	45.3291i		−	1.80739i
$630$	29.4795	+	3.10259i	1.17449	+	0.123610i
$631$		−	2.35427i		−	0.0937218i	−0.998901	−	0.0468609i	$-0.985078\pi$
$631$		−	2.35427i		−	0.0937218i	0.998901	−	0.0468609i	$-0.0149218\pi$
$632$	7.22510	−	12.5142i	0.287399	−	0.497790i
$633$	9.45846	+	14.9943i	0.375940	+	0.595970i
$634$	−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
$637$	11.9283	−	22.2422i	0.472616	−	0.881269i
$638$			8.36526i			0.331184i
$639$	12.8636	−	26.9542i	0.508874	−	1.06629i
$640$	−3.23425	+	1.86729i	−0.127845	+	0.0738112i
$641$	−14.3753	+	8.29956i	−0.567789	+	0.327813i	−0.756266	−	0.654265i	$-0.772978\pi$
$641$	−14.3753	+	8.29956i	−0.567789	+	0.327813i	0.188477	+	0.982078i	$0.439645\pi$
$642$	−9.12268	−	4.80092i	−0.360043	−	0.189477i
$643$	−5.87699			−0.231766			−0.115883	−	0.993263i	$-0.536970\pi$
$643$	−5.87699			−0.231766			−0.115883	+	0.993263i	$0.536970\pi$
$644$	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	$0.0332783\pi$
$647$	14.9475	+	25.8898i	0.587645	+	1.01783i	−0.406895	+	0.913475i	$0.633388\pi$
$648$	−5.66090	−	6.99673i	−0.222381	−	0.274858i
$649$	−12.3721	−	7.14301i	−0.485645	−	0.280388i
$650$	4.05025	−	32.0041i	0.158864	−	1.25530i
$651$	−12.0017	−	9.46204i	−0.470385	−	0.370847i
$652$			6.72676i			0.263440i
$653$	6.48294	+	3.74293i	0.253697	+	0.146472i	0.621456	−	0.783449i	$-0.286541\pi$
$653$	6.48294	+	3.74293i	0.253697	+	0.146472i	−0.367759	+	0.929921i	$0.619875\pi$
$654$	−17.5406	+	11.0647i	−0.685892	+	0.432663i
$655$	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	$-0.780330\pi$
$659$		−	32.6856i		−	1.27325i	0.771174	−	0.636624i	$-0.219670\pi$
$660$	7.60239	+	4.00085i	0.295923	+	0.155733i
$661$	−2.68538	−	4.65121i	−0.104449	−	0.180911i	0.809064	−	0.587721i	$-0.199975\pi$
$661$	−2.68538	−	4.65121i	−0.104449	−	0.180911i	−0.913513	+	0.406809i	$0.866641\pi$
$662$	−25.2714	+	14.5904i	−0.982200	+	0.567073i
$663$	−25.5091	−	17.8410i	−0.990693	−	0.692887i
$664$		−	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
$669$	−19.7505	−	31.3100i	−0.763597	−	1.21051i
$670$	−7.58576	+	13.1389i	−0.293063	+	0.507601i
$671$		−	7.43942i		−	0.287196i
$672$	−3.59868	−	2.83716i	−0.138822	−	0.109446i
$673$	−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
$675$	27.8046	+	37.2597i	1.07020	+	1.43413i
$676$	3.49042	+	12.5227i	0.134247	+	0.481641i
$677$	−17.5946	+	30.4747i	−0.676214	+	1.17124i	0.299898	+	0.953971i	$0.403047\pi$
$677$	−17.5946	+	30.4747i	−0.676214	+	1.17124i	−0.976112	+	0.217266i	$0.930286\pi$
$678$	−0.0999973	−	2.55205i	−0.00384037	−	0.0980107i
$679$	−4.72032	+	25.4790i	−0.181149	+	0.977796i
$680$		−	18.6156i		−	0.713874i
$681$	−23.2909	−	12.2571i	−0.892509	−	0.469693i
$682$	−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	$0.638083\pi$
$684$	−6.11422	+	12.8117i	−0.233783	+	0.489867i
$685$		−	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
$689$	2.20130	+	5.23992i	0.0838627	+	0.199625i
$690$	3.99310	+	6.33017i	0.152015	+	0.240986i
$691$	11.4256	−	19.7898i	0.434651	−	0.752838i	−0.562616	−	0.826719i	$-0.690205\pi$
$691$	11.4256	−	19.7898i	0.434651	−	0.752838i	0.997267	+	0.0738803i	$0.0235383\pi$
$692$	−22.1534			−0.842145
$693$	−1.10336	+	10.4836i	−0.0419131	+	0.398241i
$694$			27.8171i			1.05592i
$695$	−24.0944	+	41.7328i	−0.913954	+	1.58302i
$696$	9.22711	−	5.82050i	0.349753	−	0.220625i
$697$	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	$-0.796772\pi$
$701$		−	31.5577i		−	1.19192i	0.803015	−	0.595959i	$-0.203228\pi$
$702$	−16.1458	−	9.50338i	−0.609383	−	0.358682i
$703$	−37.2662	+	21.5156i	−1.40552	+	0.811478i
$704$	−0.664055	−	1.15018i	−0.0250275	−	0.0433489i
$705$	24.1833	−	45.9531i	0.910797	−	1.73069i
$706$			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	0.742169	−	0.670213i	$-0.233797\pi$
$709$	14.1878	+	8.19131i	0.532833	+	0.307631i	−0.209336	+	0.977844i	$0.567130\pi$
$710$	32.1984	−	18.5897i	1.20838	−	0.697661i
$711$	24.5464	+	35.7316i	0.920563	+	1.34004i
$712$	−2.55804	−	1.47689i	−0.0958668	−	0.0553487i
$713$		−	3.85881i		−	0.144513i
$714$	21.2166	−	8.46375i	0.794011	−	0.316748i
$715$	17.7418	+	2.24530i	0.663506	+	0.0839695i
$716$	21.0472	+	12.1516i	0.786570	+	0.454126i
$717$	11.1798	+	17.7231i	0.417516	+	0.661880i
$718$	−7.10506	−	12.3063i	−0.265158	−	0.459268i
$719$	8.08537	−	14.0043i	0.301533	−	0.522271i	−0.674950	−	0.737863i	$-0.735835\pi$
$719$	8.08537	−	14.0043i	0.301533	−	0.522271i	0.976483	+	0.215592i	$0.0691682\pi$
$720$	−0.876652	−	11.1694i	−0.0326709	−	0.416259i
$721$	0.309490	−	0.362421i	0.0115260	−	0.0134973i
$722$	3.39143			0.126216
$723$	2.84180	−	5.39998i	0.105688	−	0.200827i
$724$	−12.4828	+	7.20693i	−0.463918	+	0.267843i
$725$	−48.8045	+	28.1773i	−1.81255	+	1.04648i
$726$	7.45015	−	14.1567i	0.276501	−	0.525406i
$727$			16.3582i			0.606692i	0.952880	+	0.303346i	$0.0981038\pi$
$727$			16.3582i			0.606692i	−0.952880	+	0.303346i	$0.901896\pi$
$728$	−9.08738	−	2.90163i	−0.336801	−	0.107542i
$729$	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
$732$	−8.20589	+	5.17631i	−0.303298	+	0.191322i
$733$	25.9026	−	44.8646i	0.956734	−	1.65711i	0.226386	−	0.974038i	$-0.427309\pi$
$733$	25.9026	−	44.8646i	0.956734	−	1.65711i	0.730348	−	0.683075i	$-0.239358\pi$
$734$			2.37849i			0.0877918i
$735$	−14.5529	+	42.8771i	−0.536790	+	1.58154i
$736$		−	1.15705i		−	0.0426495i
$737$	−4.67252	−	2.69768i	−0.172115	−	0.0993704i
$738$	10.8317	−	7.44101i	0.398720	−	0.273907i
$739$	−13.0157	+	7.51460i	−0.478789	+	0.276429i	−0.719912	−	0.694066i	$-0.755818\pi$
$739$	−13.0157	+	7.51460i	−0.478789	+	0.276429i	0.241123	+	0.970495i	$0.422484\pi$
$740$	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	$0.634934\pi$
$744$	−2.69015	+	5.11180i	−0.0986255	+	0.187408i
$745$	26.8611	−	15.5082i	0.984114	−	0.568178i
$746$	−11.7785	−	20.4010i	−0.431243	−	0.746934i
$747$	18.2658	+	8.71713i	0.668311	+	0.318943i
$748$	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
$753$	−17.5114	−	27.7605i	−0.638152	−	1.01165i
$754$	13.7344	−	18.0862i	0.500179	−	0.658659i
$755$	−4.84124			−0.176191
$756$	12.3315	−	6.07742i	0.448491	−	0.221034i
$757$	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
$759$	−2.25116	+	1.42004i	−0.0817121	+	0.0515443i
$760$	−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
$765$	50.4012	+	24.0534i	1.82226	+	0.869651i
$766$	6.97099	−	4.02470i	0.251872	−	0.145418i
$767$	15.0214	+	35.7565i	0.542390	+	1.29109i
$768$	−0.806632	+	1.53276i	−0.0291068	+	0.0553086i
$769$	22.9273			0.826779			0.413390	−	0.910554i	$-0.364345\pi$
$769$	22.9273			0.826779			0.413390	+	0.910554i	$0.364345\pi$
$770$	−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	$0.601920\pi$
$774$	16.2200	+	23.6111i	0.583017	+	0.848684i
$775$	14.9195	−	25.8413i	0.535924	−	0.928248i
$776$	9.79404			0.351586
$777$	41.2414	+	5.98111i	1.47953	+	0.214571i
$778$			31.7954i			1.13992i
$779$	−17.9510	−	10.3640i	−0.643162	−	0.371330i
$780$	−9.86802	−	21.1320i	−0.353332	−	0.756646i
$781$	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
$786$	0.417052	−	0.792481i	0.0148758	−	0.0282669i
$787$	6.06775	+	10.5097i	0.216292	+	0.374629i	0.953671	−	0.300850i	$-0.0972703\pi$
$787$	6.06775	+	10.5097i	0.216292	+	0.374629i	−0.737379	+	0.675479i	$0.763937\pi$
$788$	−3.32591	−	5.76064i	−0.118481	−	0.205214i
$789$	−40.9817	−	21.5671i	−1.45899	−	0.767809i
$790$			53.9655i			1.92001i
$791$	3.83603	+	0.710674i	0.136394	+	0.0252686i
$792$	3.97212	−	0.311759i	0.141143	−	0.0110779i
$793$	−12.2144	+	16.0844i	−0.433745	+	0.571175i
$794$	13.5400	+	23.4520i	0.480518	+	0.832282i
$795$	−5.44006	−	8.62401i	−0.192939	−	0.305862i
$796$	13.0997	+	7.56314i	0.464308	+	0.268068i
$797$	29.6346			1.04971			0.524856	−	0.851191i	$-0.324119\pi$
$797$	29.6346			1.04971			0.524856	+	0.851191i	$0.324119\pi$
$798$	−17.0288	−	13.4253i	−0.602813	−	0.475252i
$799$		−	40.0159i		−	1.41566i
$800$	4.47357	−	7.74844i	0.158164	−	0.273949i
$801$	7.30392	−	5.01755i	0.258071	−	0.177286i
$802$	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
$807$	−9.23499	+	17.5483i	−0.325087	+	0.617729i
$808$	−4.68518	−	8.11497i	−0.164824	−	0.285484i
$809$	2.60344	−	1.50310i	0.0915320	−	0.0528460i	−0.453535	−	0.891238i	$-0.649837\pi$
$809$	2.60344	−	1.50310i	0.0915320	−	0.0528460i	0.545067	+	0.838392i	$0.316504\pi$
$810$	31.3737	+	12.0586i	1.10236	+	0.423696i
$811$	−26.5609			−0.932679			−0.466339	−	0.884606i	$-0.654427\pi$
$811$	−26.5609			−0.932679			−0.466339	+	0.884606i	$0.654427\pi$
$812$	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
$816$	−4.60626	−	7.30220i	−0.161251	−	0.255628i
$817$	22.5917	−	39.1299i	0.790383	−	1.36898i
$818$	−19.4366			−0.679585
$819$	19.5980	−	20.8547i	0.684810	−	0.728721i
$820$	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	$-0.0130151\pi$
$822$	−1.28270	−	2.03344i	−0.0447393	−	0.0709243i
$823$	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	$0.589408\pi$
$828$	3.13269	+	1.49504i	0.108869	+	0.0519562i
$829$	−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
$831$	−3.70590	+	7.04194i	−0.128556	+	0.244282i
$832$	−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
$837$	−10.3641	−	13.8885i	−0.358237	−	0.480058i
$838$	−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	$-0.0348634\pi$
$840$	16.9368	+	2.45630i	0.584376	+	0.0847502i
$841$	−10.6726			−0.368021
$842$	−7.03591	−	4.06218i	−0.242473	−	0.139992i
$843$	20.8097	+	32.9892i	0.716724	+	1.13621i
$844$	5.11771	+	8.86413i	0.176159	+	0.305116i
$845$	−34.6723	−	33.9837i	−1.19276	−	1.16908i
$846$	−1.88444	−	24.0097i	−0.0647885	−	0.825470i
$847$	18.5828	+	15.8689i	0.638513	+	0.545260i
$848$			1.57633i			0.0541313i
$849$	−11.4557	−	6.02869i	−0.393158	−	0.206904i
$850$	22.2991	+	38.6232i	0.764853	+	1.32476i
$851$	5.26097	+	9.11227i	0.180344	+	0.312365i
$852$	8.03038	−	15.2593i	0.275116	−	0.522775i
$853$	−56.4541			−1.93295			−0.966475	−	0.256760i	$-0.917345\pi$
$853$	−56.4541			−1.93295			−0.966475	+	0.256760i	$0.917345\pi$
$854$	−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	$-0.947001\pi$
$857$	−18.6366	−	32.2796i	−0.636615	−	1.10265i	0.349556	−	0.936916i	$-0.386333\pi$
$858$	7.51505	−	3.50931i	0.256560	−	0.119806i
$859$	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
$861$	7.43784	+	18.6449i	0.253481	+	0.635416i
$862$	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	$0.955152\pi$
$864$	−3.10765	−	4.16443i	−0.105724	−	0.141677i
$865$	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
$870$	−18.9742	+	36.0547i	−0.643285	+	1.22237i
$871$	5.67308	+	13.5041i	0.192225	+	0.457568i
$872$	−10.3694	+	5.98679i	−0.351153	+	0.202738i
$873$	−12.6550	+	26.5172i	−0.428307	+	0.897470i
$874$		−	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	0.658397	−	0.752671i	$-0.271235\pi$
$877$	9.94338	+	5.74081i	0.335764	+	0.193853i	−0.322633	+	0.946524i	$0.604568\pi$
$878$	17.7811	−	10.2659i	0.600083	−	0.346458i
$879$	21.4012	−	13.4999i	0.721843	−	0.455341i
$880$	4.29544	+	2.47997i	0.144799	+	0.0835998i
$881$	5.83608			0.196622			0.0983112	−	0.995156i	$-0.468656\pi$
$881$	5.83608			0.196622			0.0983112	+	0.995156i	$0.468656\pi$
$882$	4.90100	+	20.4201i	0.165025	+	0.687580i
$883$	−1.68447			−0.0566871			−0.0283435	−	0.999598i	$-0.509023\pi$
$883$	−1.68447			−0.0566871			−0.0283435	+	0.999598i	$0.509023\pi$
$884$	−14.3131	−	10.8692i	−0.481402	−	0.365572i
$885$	−37.1222	−	58.8491i	−1.24785	−	1.97819i
$886$	−0.915950	+	0.528824i	−0.0307719	+	0.0177662i
$887$	−27.8345	+	48.2107i	−0.934591	+	1.61876i	−0.159228	+	0.987242i	$0.550901\pi$
$887$	−27.8345	+	48.2107i	−0.934591	+	1.61876i	−0.775362	+	0.631517i	$0.782433\pi$
$888$	−0.616695	−	15.7388i	−0.0206949	−	0.528159i
$889$	−5.11071	+	27.5863i	−0.171408	+	0.925213i
$890$	11.0311			0.369764
$891$	−4.28833	+	11.1572i	−0.143665	+	0.373782i
$892$	−10.6864	−	18.5094i	−0.357808	−	0.619741i
$893$	−32.8981	+	18.9937i	−1.10089	+	0.635600i
$894$	6.69924	−	12.7299i	0.224056	−	0.425750i
$895$	−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
$900$	15.1984	+	22.1239i	0.506614	+	0.737465i
$901$	−6.80472	−	3.92871i	−0.226698	−	0.130884i
$902$			5.81770i			0.193708i
$903$	−40.6424	+	16.2131i	−1.35250	+	0.539539i
$904$		−	1.47456i		−	0.0490430i
$905$	26.9149	−	46.6180i	0.894681	−	1.54963i
$906$	−1.89904	+	1.19792i	−0.0630915	+	0.0397983i
$907$	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
$910$	34.8090	−	7.58422i	1.15391	−	0.251414i
$911$			1.50513i			0.0498672i	0.999689	+	0.0249336i	$0.00793743\pi$
$911$			1.50513i			0.0498672i	−0.999689	+	0.0249336i	$0.992063\pi$
$912$	−3.81695	+	7.25294i	−0.126392	+	0.240169i
$913$	−7.75958	+	4.48000i	−0.256805	+	0.148266i
$914$	9.27260	−	5.35354i	0.306710	−	0.177079i
$915$	16.8742	−	32.0642i	0.557843	−	1.06001i
$916$	−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
$921$	−5.10920	−	8.09951i	−0.168354	−	0.266888i
$922$	−8.24337	−	4.75931i	−0.271481	−	0.156740i
$923$	4.50670	−	35.6109i	0.148340	−	1.17215i
$924$	−0.873519	+	6.02315i	−0.0287367	+	0.198147i
$925$			81.3631i			2.67520i
$926$	−15.3688	−	8.87316i	−0.505049	−	0.291590i
$927$	0.445420	−	0.305989i	0.0146295	−	0.0100500i
$928$	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
$933$	20.1782	−	38.3426i	0.660605	−	1.25528i
$934$	−2.60380	−	4.50991i	−0.0851988	−	0.147569i
$935$	−21.4112	+	12.3618i	−0.700221	+	0.404273i
$936$	−9.09979	−	5.84755i	−0.297436	−	0.191133i
$937$		−	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	$0.230688\pi$
$942$	25.8303	−	16.2939i	0.841598	−	0.530883i
$943$	−2.53420	+	4.38935i	−0.0825247	+	0.142937i
$944$			10.7566i			0.350099i
$945$	−28.5346	+	42.6823i	−0.928232	+	1.38846i
$946$	−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	$-0.0815444\pi$
$948$	13.3533	+	21.1687i	0.433695	+	0.687528i
$949$	−47.9442	+	20.1414i	−1.55634	+	0.653818i
$950$	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	$0.451826\pi$
$953$			61.0356i			1.97714i	−0.150767	+	0.988569i	$0.548174\pi$
$954$	−4.26787	−	2.03679i	−0.138177	−	0.0659435i
$955$	0.772483	+	1.33798i	0.0249970	+	0.0432960i
$956$	6.04907	+	10.4773i	0.195641	+	0.338860i
$957$	−12.8219	−	6.74769i	−0.414474	−	0.218122i
$958$		−	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
$962$	−12.6992	−	30.2289i	−0.409438	−	0.974618i
$963$	14.7173	−	10.1103i	0.474258	−	0.325799i
$964$	1.76152	−	3.05105i	0.0567348	−	0.0982676i
$965$	−28.3882			−0.913849
$966$	−3.28274	+	4.16386i	−0.105621	+	0.133970i
$967$			31.0756i			0.999325i	0.866220	+	0.499662i	$0.166543\pi$
$967$			31.0756i			0.999325i	−0.866220	+	0.499662i	$0.833457\pi$
$968$	4.61806	−	7.99872i	0.148430	−	0.257089i
$969$	−21.7966	−	34.5537i	−0.700208	−	1.11003i
$970$	−31.6763	+	18.2883i	−1.01707	+	0.587203i
$971$	−25.3208	+	43.8569i	−0.812583	+	1.40743i	0.0984680	+	0.995140i	$0.468606\pi$
$971$	−25.3208	+	43.8569i	−0.812583	+	1.40743i	−0.911051	+	0.412294i	$0.864728\pi$
$972$	15.2906	−	3.03300i	0.490445	−	0.0972834i
$973$	−33.5680	−	6.21890i	−1.07614	−	0.199369i
$974$		−	21.9047i		−	0.701873i
$975$	45.7874	+	32.0235i	1.46637	+	1.02557i
$976$	−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	$0.955827\pi$
$978$	−10.3105	−	5.42601i	−0.329693	−	0.173505i
$979$			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	$0.621017\pi$
$984$	6.41709	−	4.04792i	0.204569	−	0.129043i
$985$	21.5136	+	12.4209i	0.685481	+	0.395763i
$986$			31.3963i			0.999863i
$987$	36.4073	+	5.28003i	1.15886	+	0.168065i
$988$	−2.14210	+	16.9263i	−0.0681491	+	0.538498i
$989$	−9.56799	−	5.52408i	−0.304245	−	0.175656i
$990$	−12.2647	+	8.42541i	−0.389796	+	0.267777i
$991$	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
$996$	10.3406	+	5.44188i	0.327655	+	0.172433i
$997$	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
$999$	43.4093	+	18.6666i	1.37341	+	0.590584i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.924091 - 1.46494i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23425 + 1.86729i) q^{5} +(1.73072 - 0.0678152i) q^{6} +(-0.481958 + 2.60148i) q^{7} +1.00000 q^{8} +(-1.29211 + 2.70748i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.924091 - 1.46494i) 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} +(-1.29211 + 2.70748i) q^{9} +(-3.23425 + 1.86729i) q^{10} +(-0.664055 - 1.15018i) q^{11} +(-0.806632 + 1.53276i) 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} +(-1.69869 - 2.47274i) q^{18} +(-2.36598 + 4.09800i) q^{19} -3.73459i q^{20} +(4.25640 - 1.69797i) q^{21} +1.32811 q^{22} +(1.00204 + 0.578526i) q^{23} +(-0.924091 - 1.46494i) q^{24} +(4.47357 + 7.74844i) q^{25} +(-2.87145 - 2.18055i) q^{26} +(5.16033 - 0.609089i) q^{27} +(2.49393 - 0.883354i) q^{28} +6.29862i q^{29} +(5.72421 + 3.01244i) q^{30} +(-1.66752 - 2.88823i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.07130 + 2.03567i) 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} +(5.65845 - 2.64233i) q^{39} +(3.23425 + 1.86729i) q^{40} +4.38044i q^{41} +(-0.657716 + 4.53513i) q^{42} -9.54856 q^{43} +(-0.664055 + 1.15018i) q^{44} +(-9.23466 + 6.34391i) 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} +(-4.02077 + 7.64024i) q^{51} +(3.32413 - 1.39647i) q^{52} +(1.36514 - 0.788163i) q^{53} +(-2.05268 + 4.77352i) 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} +(-5.47095 + 3.45110i) q^{60} +(4.85105 + 2.80076i) q^{61} +3.33504 q^{62} +(-6.42072 - 4.66630i) q^{63} +1.00000 q^{64} +(-8.14345 + 10.7237i) q^{65} +(-1.22729 - 1.94560i) 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} +(-1.29211 + 2.70748i) q^{72} +(7.21154 + 12.4907i) q^{73} +(-7.87543 + 4.54688i) q^{74} +(7.21704 - 13.7138i) 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} +(-5.66090 - 6.99673i) q^{81} +(-3.79357 - 2.19022i) q^{82} -6.74642i q^{83} +(-3.59868 - 2.83716i) q^{84} -18.6156i q^{85} +(4.77428 - 8.26929i) q^{86} +(9.22711 - 5.82050i) q^{87} +(-0.664055 - 1.15018i) q^{88} +(-2.55804 - 1.47689i) q^{89} +(-0.876652 - 11.1694i) q^{90} +(-9.08738 - 2.90163i) q^{91} -1.15705i q^{92} +(-2.69015 + 5.11180i) q^{93} +(-6.95231 + 4.01392i) q^{94} +(-15.3043 + 8.83595i) q^{95} +(-0.806632 + 1.53276i) 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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