LMFDB - Embedded newform 273.2.cg.b.115.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.4
Character	$\chi$	$=$	273.115
Dual form			273.2.cg.b.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46932 + 0.393703i) q^{2} -1.00000i q^{3} +(0.271846 - 0.156950i) q^{4} +(-3.59085 - 0.962166i) q^{5} +(0.393703 + 1.46932i) q^{6} +(2.64173 + 0.145891i) q^{7} +(1.81360 - 1.81360i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.46932 + 0.393703i) q^{2} -1.00000i q^{3} +(0.271846 - 0.156950i) q^{4} +(-3.59085 - 0.962166i) q^{5} +(0.393703 + 1.46932i) q^{6} +(2.64173 + 0.145891i) q^{7} +(1.81360 - 1.81360i) q^{8} -1.00000 q^{9} +5.65491 q^{10} +(-1.41093 + 1.41093i) q^{11} +(-0.156950 - 0.271846i) q^{12} +(-1.45921 + 3.29708i) q^{13} +(-3.93898 + 0.825695i) q^{14} +(-0.962166 + 3.59085i) q^{15} +(-2.26463 + 3.92246i) q^{16} +(2.36075 + 4.08893i) q^{17} +(1.46932 - 0.393703i) q^{18} +(-3.15258 + 3.15258i) q^{19} +(-1.12717 + 0.302024i) q^{20} +(0.145891 - 2.64173i) q^{21} +(1.51761 - 2.62859i) q^{22} +(-1.80957 - 1.04476i) q^{23} +(-1.81360 - 1.81360i) q^{24} +(7.63832 + 4.40999i) q^{25} +(0.845973 - 5.41895i) q^{26} +1.00000i q^{27} +(0.741039 - 0.374959i) q^{28} +(5.10970 + 8.85026i) q^{29} -5.65491i q^{30} +(-0.591623 - 2.20797i) q^{31} +(0.455541 - 1.70010i) q^{32} +(1.41093 + 1.41093i) q^{33} +(-5.07852 - 5.07852i) q^{34} +(-9.34567 - 3.06565i) q^{35} +(-0.271846 + 0.156950i) q^{36} +(0.166900 + 0.622880i) q^{37} +(3.39097 - 5.87333i) q^{38} +(3.29708 + 1.45921i) q^{39} +(-8.25733 + 4.76737i) q^{40} +(-8.81239 - 2.36127i) q^{41} +(0.825695 + 3.93898i) q^{42} +(0.0966425 + 0.0557966i) q^{43} +(-0.162109 + 0.604999i) q^{44} +(3.59085 + 0.962166i) q^{45} +(3.07017 + 0.822648i) q^{46} +(-1.16024 + 4.33009i) q^{47} +(3.92246 + 2.26463i) q^{48} +(6.95743 + 0.770807i) q^{49} +(-12.9594 - 3.47245i) q^{50} +(4.08893 - 2.36075i) q^{51} +(0.120797 + 1.12532i) q^{52} +(-2.18989 + 3.79299i) q^{53} +(-0.393703 - 1.46932i) q^{54} +(6.42397 - 3.70888i) q^{55} +(5.05561 - 4.52644i) q^{56} +(3.15258 + 3.15258i) q^{57} +(-10.9921 - 10.9921i) q^{58} +(0.438963 - 1.63823i) q^{59} +(0.302024 + 1.12717i) q^{60} -6.75131i q^{61} +(1.73857 + 3.01128i) q^{62} +(-2.64173 - 0.145891i) q^{63} -6.38120i q^{64} +(8.41213 - 10.4353i) q^{65} +(-2.62859 - 1.51761i) q^{66} +(-2.10721 - 2.10721i) q^{67} +(1.28352 + 0.741039i) q^{68} +(-1.04476 + 1.80957i) q^{69} +(14.9387 + 0.825000i) q^{70} +(14.4800 - 3.87990i) q^{71} +(-1.81360 + 1.81360i) q^{72} +(-10.1535 + 2.72063i) q^{73} +(-0.490459 - 0.849500i) q^{74} +(4.40999 - 7.63832i) q^{75} +(-0.362217 + 1.35181i) q^{76} +(-3.93312 + 3.52144i) q^{77} +(-5.41895 - 0.845973i) q^{78} +(-0.0273492 - 0.0473702i) q^{79} +(11.9060 - 11.9060i) q^{80} +1.00000 q^{81} +13.8778 q^{82} +(-9.05174 + 9.05174i) q^{83} +(-0.374959 - 0.741039i) q^{84} +(-4.54286 - 16.9542i) q^{85} +(-0.163966 - 0.0439346i) q^{86} +(8.85026 - 5.10970i) q^{87} +5.11770i q^{88} +(-6.91330 + 1.85241i) q^{89} -5.65491 q^{90} +(-4.33584 + 8.49709i) q^{91} -0.655900 q^{92} +(-2.20797 + 0.591623i) q^{93} -6.81908i q^{94} +(14.3537 - 8.28714i) q^{95} +(-1.70010 - 0.455541i) q^{96} +(-3.20050 - 11.9444i) q^{97} +(-10.5262 + 1.60660i) q^{98} +(1.41093 - 1.41093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.46932	+	0.393703i	−1.03897	+	0.278390i	−0.737685	−	0.675145i	$-0.764081\pi$
$2$	−1.46932	+	0.393703i	−1.03897	+	0.278390i	−0.301281	+	0.953535i	$0.597414\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.271846	−	0.156950i	0.135923	−	0.0784751i
$5$	−3.59085	−	0.962166i	−1.60588	−	0.430294i	−0.659067	−	0.752085i	$-0.729048\pi$
$5$	−3.59085	−	0.962166i	−1.60588	−	0.430294i	−0.946811	+	0.321791i	$0.895715\pi$
$6$	0.393703	+	1.46932i	0.160729	+	0.599847i
$7$	2.64173	+	0.145891i	0.998479	+	0.0551416i
$7$	2.64173	+	0.145891i	0.998479	+	0.0551416i
$8$	1.81360	−	1.81360i	0.641203	−	0.641203i
$9$	−1.00000			−0.333333
$10$	5.65491			1.78824
$11$	−1.41093	+	1.41093i	−0.425410	+	0.425410i	−0.887062	−	0.461651i	$-0.847257\pi$
$11$	−1.41093	+	1.41093i	−0.425410	+	0.425410i	0.461651	+	0.887062i	$0.347257\pi$
$12$	−0.156950	−	0.271846i	−0.0453076	−	0.0784751i
$13$	−1.45921	+	3.29708i	−0.404711	+	0.914444i
$13$	−1.45921	+	3.29708i	−0.404711	+	0.914444i
$14$	−3.93898	+	0.825695i	−1.05274	+	0.220676i
$15$	−0.962166	+	3.59085i	−0.248430	+	0.927154i
$16$	−2.26463	+	3.92246i	−0.566158	+	0.980615i
$17$	2.36075	+	4.08893i	0.572565	+	0.991712i	0.996301	+	0.0859265i	$0.0273850\pi$
$17$	2.36075	+	4.08893i	0.572565	+	0.991712i	−0.423736	+	0.905786i	$0.639282\pi$
$18$	1.46932	−	0.393703i	0.346322	−	0.0927966i
$19$	−3.15258	+	3.15258i	−0.723251	+	0.723251i	−0.969266	−	0.246015i	$-0.920879\pi$
$19$	−3.15258	+	3.15258i	−0.723251	+	0.723251i	0.246015	+	0.969266i	$0.420879\pi$
$20$	−1.12717	+	0.302024i	−0.252043	+	0.0675346i
$21$	0.145891	−	2.64173i	0.0318360	−	0.576472i
$22$	1.51761	−	2.62859i	0.323557	−	0.560416i
$23$	−1.80957	−	1.04476i	−0.377322	−	0.217847i	0.299330	−	0.954150i	$-0.403237\pi$
$23$	−1.80957	−	1.04476i	−0.377322	−	0.217847i	−0.676653	+	0.736302i	$0.736570\pi$
$24$	−1.81360	−	1.81360i	−0.370199	−	0.370199i
$25$	7.63832	+	4.40999i	1.52766	+	0.881997i
$26$	0.845973	−	5.41895i	0.165909	−	1.06274i
$27$			1.00000i			0.192450i
$28$	0.741039	−	0.374959i	0.140043	−	0.0708607i
$29$	5.10970	+	8.85026i	0.948847	+	1.64345i	0.747859	+	0.663858i	$0.231082\pi$
$29$	5.10970	+	8.85026i	0.948847	+	1.64345i	0.200988	+	0.979594i	$0.435585\pi$
$30$		−	5.65491i		−	1.03244i
$31$	−0.591623	−	2.20797i	−0.106259	−	0.396563i	0.892226	−	0.451589i	$-0.149142\pi$
$31$	−0.591623	−	2.20797i	−0.106259	−	0.396563i	−0.998485	+	0.0550260i	$0.982476\pi$
$32$	0.455541	−	1.70010i	0.0805290	−	0.300538i
$33$	1.41093	+	1.41093i	0.245611	+	0.245611i
$34$	−5.07852	−	5.07852i	−0.870958	−	0.870958i
$35$	−9.34567	−	3.06565i	−1.57971	−	0.518189i
$36$	−0.271846	+	0.156950i	−0.0453076	+	0.0261584i
$37$	0.166900	+	0.622880i	0.0274382	+	0.102401i	0.978287	−	0.207255i	$-0.0664529\pi$
$37$	0.166900	+	0.622880i	0.0274382	+	0.102401i	−0.950849	+	0.309656i	$0.899786\pi$
$38$	3.39097	−	5.87333i	0.550087	−	0.952779i
$39$	3.29708	+	1.45921i	0.527955	+	0.233660i
$40$	−8.25733	+	4.76737i	−1.30560	+	0.753788i
$41$	−8.81239	−	2.36127i	−1.37626	−	0.368769i	−0.506501	−	0.862239i	$-0.669061\pi$
$41$	−8.81239	−	2.36127i	−1.37626	−	0.368769i	−0.869763	+	0.493471i	$0.835728\pi$
$42$	0.825695	+	3.93898i	0.127407	+	0.607797i
$43$	0.0966425	+	0.0557966i	0.0147378	+	0.00850890i	0.507351	−	0.861740i	$-0.330625\pi$
$43$	0.0966425	+	0.0557966i	0.0147378	+	0.00850890i	−0.492613	+	0.870249i	$0.663958\pi$
$44$	−0.162109	+	0.604999i	−0.0244389	+	0.0912071i
$45$	3.59085	+	0.962166i	0.535292	+	0.143431i
$46$	3.07017	+	0.822648i	0.452671	+	0.121293i
$47$	−1.16024	+	4.33009i	−0.169239	+	0.631609i	0.828222	+	0.560400i	$0.189352\pi$
$47$	−1.16024	+	4.33009i	−0.169239	+	0.631609i	−0.997461	+	0.0712092i	$0.977314\pi$
$48$	3.92246	+	2.26463i	0.566158	+	0.326872i
$49$	6.95743	+	0.770807i	0.993919	+	0.110115i
$50$	−12.9594	−	3.47245i	−1.83273	−	0.491078i
$51$	4.08893	−	2.36075i	0.572565	−	0.330571i
$52$	0.120797	+	1.12532i	0.0167516	+	0.156054i
$53$	−2.18989	+	3.79299i	−0.300804	+	0.521008i	−0.976318	−	0.216339i	$-0.930588\pi$
$53$	−2.18989	+	3.79299i	−0.300804	+	0.521008i	0.675514	+	0.737347i	$0.263922\pi$
$54$	−0.393703	−	1.46932i	−0.0535762	−	0.199949i
$55$	6.42397	−	3.70888i	0.866208	−	0.500105i
$56$	5.05561	−	4.52644i	0.675584	−	0.604871i
$57$	3.15258	+	3.15258i	0.417569	+	0.417569i
$58$	−10.9921	−	10.9921i	−1.44334	−	1.44334i
$59$	0.438963	−	1.63823i	0.0571481	−	0.213280i	−0.931447	−	0.363877i	$-0.881453\pi$
$59$	0.438963	−	1.63823i	0.0571481	−	0.213280i	0.988595	+	0.150597i	$0.0481196\pi$
$60$	0.302024	+	1.12717i	0.0389911	+	0.145517i
$61$		−	6.75131i		−	0.864416i	−0.901774	−	0.432208i	$-0.857735\pi$
$61$		−	6.75131i		−	0.864416i	0.901774	−	0.432208i	$-0.142265\pi$
$62$	1.73857	+	3.01128i	0.220798	+	0.382433i
$63$	−2.64173	−	0.145891i	−0.332826	−	0.0183805i
$64$		−	6.38120i		−	0.797649i
$65$	8.41213	−	10.4353i	1.04340	−	1.29434i
$66$	−2.62859	−	1.51761i	−0.323557	−	0.186805i
$67$	−2.10721	−	2.10721i	−0.257436	−	0.257436i	0.566574	−	0.824011i	$-0.308268\pi$
$67$	−2.10721	−	2.10721i	−0.257436	−	0.257436i	−0.824011	+	0.566574i	$0.808268\pi$
$68$	1.28352	+	0.741039i	0.155649	+	0.0898642i
$69$	−1.04476	+	1.80957i	−0.125774	+	0.217847i
$70$	14.9387	+	0.825000i	1.78552	+	0.0986064i
$71$	14.4800	−	3.87990i	1.71846	−	0.460459i	0.740985	−	0.671521i	$-0.234359\pi$
$71$	14.4800	−	3.87990i	1.71846	−	0.460459i	0.977473	+	0.211062i	$0.0676921\pi$
$72$	−1.81360	+	1.81360i	−0.213734	+	0.213734i
$73$	−10.1535	+	2.72063i	−1.18838	+	0.318426i	−0.798246	−	0.602332i	$-0.794238\pi$
$73$	−10.1535	+	2.72063i	−1.18838	+	0.318426i	−0.390135	+	0.920758i	$0.627572\pi$
$74$	−0.490459	−	0.849500i	−0.0570147	−	0.0987524i
$75$	4.40999	−	7.63832i	0.509221	−	0.881997i
$76$	−0.362217	+	1.35181i	−0.0415492	+	0.155064i
$77$	−3.93312	+	3.52144i	−0.448221	+	0.401305i
$78$	−5.41895	−	0.845973i	−0.613575	−	0.0957876i
$79$	−0.0273492	−	0.0473702i	−0.00307703	−	0.00532957i	0.864483	−	0.502662i	$-0.167646\pi$
$79$	−0.0273492	−	0.0473702i	−0.00307703	−	0.00532957i	−0.867560	+	0.497333i	$0.834313\pi$
$80$	11.9060	−	11.9060i	1.33113	−	1.33113i
$81$	1.00000			0.111111
$82$	13.8778			1.53255
$83$	−9.05174	+	9.05174i	−0.993558	+	0.993558i	−0.999979	−	0.00642168i	$-0.997956\pi$
$83$	−9.05174	+	9.05174i	−0.993558	+	0.993558i	0.00642168	+	0.999979i	$0.497956\pi$
$84$	−0.374959	−	0.741039i	−0.0409114	−	0.0808540i
$85$	−4.54286	−	16.9542i	−0.492742	−	1.83894i
$86$	−0.163966	−	0.0439346i	−0.0176809	−	0.00473759i
$87$	8.85026	−	5.10970i	0.948847	−	0.547817i
$88$			5.11770i			0.545549i
$89$	−6.91330	+	1.85241i	−0.732808	+	0.196355i	−0.605879	−	0.795556i	$-0.707179\pi$
$89$	−6.91330	+	1.85241i	−0.732808	+	0.196355i	−0.126929	+	0.991912i	$0.540512\pi$
$90$	−5.65491			−0.596080
$91$	−4.33584	+	8.49709i	−0.454520	+	0.890737i
$92$	−0.655900			−0.0683823
$93$	−2.20797	+	0.591623i	−0.228955	+	0.0613484i
$94$		−	6.81908i		−	0.703334i
$95$	14.3537	−	8.28714i	1.47266	−	0.850243i
$96$	−1.70010	−	0.455541i	−0.173516	−	0.0464934i
$97$	−3.20050	−	11.9444i	−0.324962	−	1.21277i	−0.914350	−	0.404924i	$-0.867298\pi$
$97$	−3.20050	−	11.9444i	−0.324962	−	1.21277i	0.589388	−	0.807850i	$-0.299369\pi$
$98$	−10.5262	+	1.60660i	−1.06330	+	0.162291i
$99$	1.41093	−	1.41093i	0.141803	−	0.141803i
$100$	2.76859			0.276859
$101$	−3.33743			−0.332086			−0.166043	−	0.986118i	$-0.553099\pi$
$101$	−3.33743			−0.332086			−0.166043	+	0.986118i	$0.553099\pi$
$102$	−5.07852	+	5.07852i	−0.502848	+	0.502848i
$103$	9.27777	+	16.0696i	0.914166	+	1.58338i	0.808118	+	0.589021i	$0.200486\pi$
$103$	9.27777	+	16.0696i	0.914166	+	1.58338i	0.106048	+	0.994361i	$0.466180\pi$
$104$	3.33315	+	8.62598i	0.326842	+	0.845847i
$105$	−3.06565	+	9.34567i	−0.299177	+	0.912044i
$106$	1.72433	−	6.43528i	0.167482	−	0.625050i
$107$	−2.66439	+	4.61486i	−0.257576	+	0.446135i	−0.965592	−	0.260061i	$-0.916257\pi$
$107$	−2.66439	+	4.61486i	−0.257576	+	0.446135i	0.708016	+	0.706197i	$0.249591\pi$
$108$	0.156950	+	0.271846i	0.0151025	+	0.0261584i
$109$	−10.8027	+	2.89458i	−1.03471	+	0.277251i	−0.735921	−	0.677067i	$-0.763251\pi$
$109$	−10.8027	+	2.89458i	−1.03471	+	0.277251i	−0.298793	+	0.954318i	$0.596584\pi$
$110$	−7.97866	+	7.97866i	−0.760736	+	0.760736i
$111$	0.622880	−	0.166900i	0.0591212	−	0.0158415i
$112$	−6.55479	+	10.0317i	−0.619370	+	0.947904i
$113$	1.28775	−	2.23045i	0.121142	−	0.209823i	−0.799077	−	0.601229i	$-0.794678\pi$
$113$	1.28775	−	2.23045i	0.121142	−	0.209823i	0.920218	+	0.391406i	$0.128011\pi$
$114$	−5.87333	−	3.39097i	−0.550087	−	0.317593i
$115$	5.49268	+	5.49268i	0.512195	+	0.512195i
$116$	2.77810	+	1.60394i	0.257940	+	0.148922i
$117$	1.45921	−	3.29708i	0.134904	−	0.304815i
$118$			2.57990i			0.237499i
$119$	5.63991	+	11.1463i	0.517010	+	1.02178i
$120$	4.76737	+	8.25733i	0.435200	+	0.753788i
$121$			7.01857i			0.638052i
$122$	2.65801	+	9.91982i	0.240645	+	0.898099i
$123$	−2.36127	+	8.81239i	−0.212909	+	0.794586i
$124$	−0.507371	−	0.507371i	−0.0455632	−	0.0455632i
$125$	−10.0415	−	10.0415i	−0.898140	−	0.898140i
$126$	3.93898	−	0.825695i	0.350912	−	0.0735587i
$127$	−15.9822	+	9.22735i	−1.41819	+	0.818795i	−0.996140	−	0.0877754i	$-0.972024\pi$
$127$	−15.9822	+	9.22735i	−1.41819	+	0.818795i	−0.422054	+	0.906570i	$0.638691\pi$
$128$	3.42338	+	12.7762i	0.302587	+	1.12927i
$129$	0.0557966	−	0.0966425i	0.00491262	−	0.00850890i
$130$	−8.25169	+	18.6447i	−0.723721	+	1.63525i
$131$	5.76722	−	3.32971i	0.503885	−	0.290918i	−0.226432	−	0.974027i	$-0.572706\pi$
$131$	5.76722	−	3.32971i	0.503885	−	0.290918i	0.730316	+	0.683109i	$0.239373\pi$
$132$	0.604999	+	0.162109i	0.0526584	+	0.0141098i
$133$	−8.78818	+	7.86832i	−0.762032	+	0.682270i
$134$	3.92577	+	2.26654i	0.339135	+	0.195800i
$135$	0.962166	−	3.59085i	0.0828100	−	0.309051i
$136$	11.6971	+	3.13423i	1.00302	+	0.268758i
$137$	15.4237	+	4.13276i	1.31773	+	0.353085i	0.848128	−	0.529792i	$-0.177730\pi$
$137$	15.4237	+	4.13276i	1.31773	+	0.353085i	0.469604	+	0.882877i	$0.344397\pi$
$138$	0.822648	−	3.07017i	0.0700285	−	0.261350i
$139$	−9.32621	−	5.38449i	−0.791038	−	0.456706i	0.0492896	−	0.998785i	$-0.484304\pi$
$139$	−9.32621	−	5.38449i	−0.791038	−	0.456706i	−0.840328	+	0.542078i	$0.817638\pi$
$140$	−3.02173	+	0.633421i	−0.255383	+	0.0535339i
$141$	4.33009	+	1.16024i	0.364660	+	0.0977102i
$142$	−19.7482	+	11.4016i	−1.65723	+	0.956803i
$143$	−2.59310	−	6.71077i	−0.216846	−	0.561182i
$144$	2.26463	−	3.92246i	0.188719	−	0.326872i
$145$	−9.83275	−	36.6963i	−0.816565	−	3.04746i
$146$	13.8476	−	7.99494i	1.14604	−	0.661666i
$147$	0.770807	−	6.95743i	0.0635751	−	0.573839i
$148$	0.143132	+	0.143132i	0.0117654	+	0.0117654i
$149$	1.87483	+	1.87483i	0.153592	+	0.153592i	0.779720	−	0.626128i	$-0.215361\pi$
$149$	1.87483	+	1.87483i	0.153592	+	0.153592i	−0.626128	+	0.779720i	$0.715361\pi$
$150$	−3.47245	+	12.9594i	−0.283524	+	1.05813i
$151$	0.927335	+	3.46086i	0.0754655	+	0.281641i	0.993338	−	0.115233i	$-0.0367615\pi$
$151$	0.927335	+	3.46086i	0.0754655	+	0.281641i	−0.917873	+	0.396874i	$0.870095\pi$
$152$			11.4350i			0.927502i
$153$	−2.36075	−	4.08893i	−0.190855	−	0.330571i
$154$	4.39261	−	6.72260i	0.353967	−	0.541722i
$155$			8.49772i			0.682553i
$156$	1.12532	−	0.120797i	0.0900976	−	0.00967153i
$157$	−8.63943	−	4.98798i	−0.689502	−	0.398084i	0.113924	−	0.993490i	$-0.463658\pi$
$157$	−8.63943	−	4.98798i	−0.689502	−	0.398084i	−0.803425	+	0.595406i	$0.796991\pi$
$158$	0.0588345	+	0.0588345i	0.00468062	+	0.00468062i
$159$	3.79299	+	2.18989i	0.300804	+	0.173669i
$160$	−3.27156	+	5.66651i	−0.258639	+	0.447977i
$161$	−4.62798	−	3.02396i	−0.364736	−	0.238322i
$162$	−1.46932	+	0.393703i	−0.115441	+	0.0309322i
$163$	−0.822174	+	0.822174i	−0.0643977	+	0.0643977i	−0.738572	−	0.674174i	$-0.764500\pi$
$163$	−0.822174	+	0.822174i	−0.0643977	+	0.0643977i	0.674174	+	0.738572i	$0.264500\pi$
$164$	−2.76621	+	0.741204i	−0.216005	+	0.0578783i
$165$	−3.70888	−	6.42397i	−0.288736	−	0.500105i
$166$	9.73620	−	16.8636i	0.755676	−	1.30887i
$167$	1.15161	−	4.29785i	0.0891139	−	0.332578i	−0.906947	−	0.421244i	$-0.861594\pi$
$167$	1.15161	−	4.29785i	0.0891139	−	0.332578i	0.996061	+	0.0886660i	$0.0282604\pi$
$168$	−4.52644	−	5.05561i	−0.349222	−	0.390049i
$169$	−8.74143	−	9.62224i	−0.672417	−	0.740172i
$170$	13.3498	+	23.1226i	1.02388	+	1.77342i
$171$	3.15258	−	3.15258i	0.241084	−	0.241084i
$172$	0.0350291			0.00267095
$173$	−19.6085			−1.49081			−0.745403	−	0.666614i	$-0.767743\pi$
$173$	−19.6085			−1.49081			−0.745403	+	0.666614i	$0.767743\pi$
$174$	−10.9921	+	10.9921i	−0.833313	+	0.833313i
$175$	19.5350	+	12.7643i	1.47671	+	0.964893i
$176$	−2.33907	−	8.72953i	−0.176314	−	0.658013i
$177$	−1.63823	−	0.438963i	−0.123137	−	0.0329945i
$178$	9.42854	−	5.44357i	0.706699	−	0.408013i
$179$		−	23.0627i		−	1.72379i	−0.507088	−	0.861894i	$-0.669278\pi$
$179$		−	23.0627i		−	1.72379i	0.507088	−	0.861894i	$-0.330722\pi$
$180$	1.12717	−	0.302024i	0.0840142	−	0.0225115i
$181$	20.5419			1.52686			0.763432	−	0.645888i	$-0.223513\pi$
$181$	20.5419			1.52686			0.763432	+	0.645888i	$0.223513\pi$
$182$	3.02540	−	14.1920i	0.224258	−	1.05198i
$183$	−6.75131			−0.499071
$184$	−5.17661	+	1.38707i	−0.381624	+	0.102256i
$185$		−	2.39726i		−	0.176250i
$186$	3.01128	−	1.73857i	0.220798	−	0.127478i
$187$	−9.10002	−	2.43834i	−0.665460	−	0.178309i
$188$	0.364201	+	1.35922i	0.0265621	+	0.0991311i
$189$	−0.145891	+	2.64173i	−0.0106120	+	0.192157i
$190$	−17.8276	+	17.8276i	−1.29335	+	1.29335i
$191$	22.9816			1.66289			0.831443	−	0.555609i	$-0.187515\pi$
$191$	22.9816			1.66289			0.831443	+	0.555609i	$0.187515\pi$
$192$	−6.38120			−0.460523
$193$	−5.51721	+	5.51721i	−0.397137	+	0.397137i	−0.877222	−	0.480085i	$-0.840606\pi$
$193$	−5.51721	+	5.51721i	−0.397137	+	0.397137i	0.480085	+	0.877222i	$0.340606\pi$
$194$	9.40512	+	16.2901i	0.675248	+	1.16956i
$195$	−10.4353	−	8.41213i	−0.747288	−	0.602405i
$196$	2.01233	−	0.882429i	0.143738	−	0.0630307i
$197$	−2.60698	+	9.72938i	−0.185740	+	0.693190i	0.808731	+	0.588178i	$0.200155\pi$
$197$	−2.60698	+	9.72938i	−0.185740	+	0.693190i	−0.994471	+	0.105012i	$0.966512\pi$
$198$	−1.51761	+	2.62859i	−0.107852	+	0.186805i
$199$	3.84516	+	6.66002i	0.272576	+	0.472116i	0.969521	−	0.245009i	$-0.0787909\pi$
$199$	3.84516	+	6.66002i	0.272576	+	0.472116i	−0.696944	+	0.717125i	$0.745458\pi$
$200$	21.8508	−	5.85489i	1.54508	−	0.414004i
$201$	−2.10721	+	2.10721i	−0.148631	+	0.148631i
$202$	4.90374	−	1.31395i	0.345026	−	0.0924495i
$203$	12.2072	+	24.1254i	0.856781	+	1.69327i
$204$	0.741039	−	1.28352i	0.0518831	−	0.0898642i
$205$	29.3720	+	16.9580i	2.05143	+	1.18439i
$206$	−19.9586	−	19.9586i	−1.39058	−	1.39058i
$207$	1.80957	+	1.04476i	0.125774	+	0.0726157i
$208$	−9.62808	−	13.1904i	−0.667587	−	0.914587i
$209$		−	8.89611i		−	0.615357i
$210$	0.825000	−	14.9387i	0.0569304	−	1.03087i
$211$	4.74990	+	8.22707i	0.326997	+	0.566375i	0.981914	−	0.189325i	$-0.0606301\pi$
$211$	4.74990	+	8.22707i	0.326997	+	0.566375i	−0.654918	+	0.755700i	$0.727297\pi$
$212$			1.37481i			0.0944224i
$213$	−3.87990	−	14.4800i	−0.265846	−	0.992152i
$214$	2.09796	−	7.82968i	0.143413	−	0.535226i
$215$	−0.293343	−	0.293343i	−0.0200059	−	0.0200059i
$216$	1.81360	+	1.81360i	0.123400	+	0.123400i
$217$	−1.24078	−	5.91916i	−0.0842299	−	0.401818i
$218$	14.7331	−	8.50613i	0.997848	−	0.576108i
$219$	2.72063	+	10.1535i	0.183843	+	0.686112i
$220$	1.16422	−	2.01649i	0.0784916	−	0.135951i
$221$	−16.9263	+	1.81696i	−1.13859	+	0.122222i
$222$	−0.849500	+	0.490459i	−0.0570147	+	0.0329175i
$223$	16.5658	+	4.43878i	1.10933	+	0.297243i	0.766556	−	0.642177i	$-0.221969\pi$
$223$	16.5658	+	4.43878i	1.10933	+	0.297243i	0.342769	+	0.939420i	$0.388635\pi$
$224$	1.45144	−	4.42474i	0.0969786	−	0.295641i
$225$	−7.63832	−	4.40999i	−0.509221	−	0.293999i
$226$	−1.01398	+	3.78424i	−0.0674492	+	0.251724i
$227$	6.00538	+	1.60914i	0.398591	+	0.106802i	0.452546	−	0.891741i	$-0.350516\pi$
$227$	6.00538	+	1.60914i	0.398591	+	0.106802i	−0.0539546	+	0.998543i	$0.517183\pi$
$228$	1.35181	+	0.362217i	0.0895260	+	0.0239884i
$229$	−1.25618	+	4.68814i	−0.0830110	+	0.309801i	−0.994930	−	0.100569i	$-0.967934\pi$
$229$	−1.25618	+	4.68814i	−0.0830110	+	0.309801i	0.911919	+	0.410370i	$0.134600\pi$
$230$	−10.2330	−	5.90802i	−0.674743	−	0.389563i
$231$	3.52144	+	3.93312i	0.231694	+	0.258780i
$232$	25.3177	+	6.78386i	1.66219	+	0.445382i
$233$	−11.3722	+	6.56573i	−0.745016	+	0.430135i	−0.823890	−	0.566749i	$-0.808201\pi$
$233$	−11.3722	+	6.56573i	−0.745016	+	0.430135i	0.0788741	+	0.996885i	$0.474867\pi$
$234$	−0.845973	+	5.41895i	−0.0553030	+	0.354248i
$235$	8.33253	−	14.4324i	0.543554	−	0.941464i
$236$	−0.137790	−	0.514241i	−0.00896940	−	0.0334742i
$237$	−0.0473702	+	0.0273492i	−0.00307703	+	0.00177652i
$238$	−12.6751	−	14.1570i	−0.821607	−	0.917659i
$239$	6.23607	+	6.23607i	0.403378	+	0.403378i	0.879422	−	0.476044i	$-0.157930\pi$
$239$	6.23607	+	6.23607i	0.403378	+	0.403378i	−0.476044	+	0.879422i	$0.657930\pi$
$240$	−11.9060	−	11.9060i	−0.768530	−	0.768530i
$241$	2.36670	−	8.83265i	0.152453	−	0.568961i	−0.846857	−	0.531820i	$-0.821508\pi$
$241$	2.36670	−	8.83265i	0.152453	−	0.568961i	0.999310	−	0.0371409i	$-0.0118250\pi$
$242$	−2.76323	−	10.3125i	−0.177627	−	0.662914i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.05962	−	1.83531i	−0.0678351	−	0.117494i
$245$	−24.2415	−	9.46206i	−1.54873	−	0.604509i
$246$		−	13.8778i		−	0.884819i
$247$	−5.79403	−	14.9946i	−0.368665	−	0.954081i
$248$	−5.07732	−	2.93139i	−0.322410	−	0.186144i
$249$	9.05174	+	9.05174i	0.573631	+	0.573631i
$250$	18.7075	+	10.8008i	1.18317	+	0.683103i
$251$	6.74060	−	11.6751i	0.425463	−	0.736924i	−0.571000	−	0.820950i	$-0.693445\pi$
$251$	6.74060	−	11.6751i	0.425463	−	0.736924i	0.996464	+	0.0840260i	$0.0267779\pi$
$252$	−0.741039	+	0.374959i	−0.0466811	+	0.0236202i
$253$	4.02725	−	1.07910i	0.253191	−	0.0678424i
$254$	19.8502	−	19.8502i	1.24551	−	1.24551i
$255$	−16.9542	+	4.54286i	−1.06171	+	0.284485i
$256$	−3.67887	−	6.37199i	−0.229929	−	0.398249i
$257$	4.92529	−	8.53085i	0.307231	−	0.532140i	−0.670524	−	0.741887i	$-0.733931\pi$
$257$	4.92529	−	8.53085i	0.307231	−	0.532140i	0.977756	+	0.209747i	$0.0672642\pi$
$258$	−0.0439346	+	0.163966i	−0.00273525	+	0.0102081i
$259$	0.350032	+	1.66983i	0.0217499	+	0.103758i
$260$	0.648977	−	4.15708i	0.0402479	−	0.257811i
$261$	−5.10970	−	8.85026i	−0.316282	−	0.547817i
$262$	−7.16297	+	7.16297i	−0.442530	+	0.442530i
$263$	−10.0381			−0.618973			−0.309486	−	0.950904i	$-0.600157\pi$
$263$	−10.0381			−0.618973			−0.309486	+	0.950904i	$0.600157\pi$
$264$	5.11770			0.314973
$265$	11.5130	−	11.5130i	0.707240	−	0.707240i
$266$	9.81487	−	15.0210i	0.601788	−	0.920997i
$267$	1.85241	+	6.91330i	0.113366	+	0.423087i
$268$	−0.903561	−	0.242108i	−0.0551938	−	0.0147891i
$269$	−26.1996	+	15.1263i	−1.59742	+	0.922268i	−0.605433	+	0.795896i	$0.707000\pi$
$269$	−26.1996	+	15.1263i	−1.59742	+	0.922268i	−0.991983	+	0.126372i	$0.959667\pi$
$270$			5.65491i			0.344147i
$271$	16.9184	−	4.53326i	1.02772	−	0.275376i	0.294702	−	0.955589i	$-0.404779\pi$
$271$	16.9184	−	4.53326i	1.02772	−	0.275376i	0.733014	+	0.680213i	$0.238113\pi$
$272$	−21.3849			−1.29665
$273$	8.49709	+	4.33584i	0.514267	+	0.262417i
$274$	−24.2893			−1.46737
$275$	−16.9993	+	4.55494i	−1.02509	+	0.274673i
$276$			0.655900i			0.0394805i
$277$	15.4484	−	8.91911i	0.928202	−	0.535897i	0.0419593	−	0.999119i	$-0.486640\pi$
$277$	15.4484	−	8.91911i	0.928202	−	0.535897i	0.886242	+	0.463222i	$0.153307\pi$
$278$	15.8231	+	4.23978i	0.949004	+	0.254285i
$279$	0.591623	+	2.20797i	0.0354195	+	0.132188i
$280$	−22.5091	+	11.3894i	−1.34518	+	0.680648i
$281$	0.156351	−	0.156351i	0.00932711	−	0.00932711i	−0.702428	−	0.711755i	$-0.747901\pi$
$281$	0.156351	−	0.156351i	0.00932711	−	0.00932711i	0.711755	+	0.702428i	$0.247901\pi$
$282$	−6.81908			−0.406070
$283$	−25.7108			−1.52835			−0.764176	−	0.645008i	$-0.776854\pi$
$283$	−25.7108			−1.52835			−0.764176	+	0.645008i	$0.776854\pi$
$284$	3.32737	−	3.32737i	0.197443	−	0.197443i
$285$	−8.28714	−	14.3537i	−0.490888	−	0.850243i
$286$	6.45213	+	8.83935i	0.381523	+	0.522681i
$287$	−22.9354	−	7.52348i	−1.35384	−	0.444097i
$288$	−0.455541	+	1.70010i	−0.0268430	+	0.100179i
$289$	−2.64625	+	4.58345i	−0.155662	+	0.269615i
$290$	28.8949	+	50.0474i	1.69677	+	2.93889i
$291$	−11.9444	+	3.20050i	−0.700195	+	0.187617i
$292$	−2.33319	+	2.33319i	−0.136540	+	0.136540i
$293$	15.5701	−	4.17200i	0.909615	−	0.243731i	0.226474	−	0.974017i	$-0.427280\pi$
$293$	15.5701	−	4.17200i	0.909615	−	0.243731i	0.683141	+	0.730286i	$0.260613\pi$
$294$	1.60660	+	10.5262i	0.0936987	+	0.613898i
$295$	−3.15250	+	5.46029i	−0.183546	+	0.317910i
$296$	1.43234	+	0.826963i	0.0832532	+	0.0480663i
$297$	−1.41093	−	1.41093i	−0.0818702	−	0.0818702i
$298$	−3.49286	−	2.01660i	−0.202336	−	0.116819i
$299$	6.08519	−	4.44179i	0.351916	−	0.256875i
$300$		−	2.76859i		−	0.159845i
$301$	0.247163	+	0.161499i	0.0142462	+	0.00930862i
$302$	−2.72510	−	4.72002i	−0.156812	−	0.271606i
$303$			3.33743i			0.191730i
$304$	−5.22643	−	19.5053i	−0.299756	−	1.11871i
$305$	−6.49588	+	24.2429i	−0.371953	+	1.38815i
$306$	5.07852	+	5.07852i	0.290319	+	0.290319i
$307$	21.2119	+	21.2119i	1.21063	+	1.21063i	0.970820	+	0.239809i	$0.0770849\pi$
$307$	21.2119	+	21.2119i	1.21063	+	1.21063i	0.239809	+	0.970820i	$0.422915\pi$
$308$	−0.516511	+	1.57459i	−0.0294310	+	0.0897207i
$309$	16.0696	−	9.27777i	0.914166	−	0.527794i
$310$	−3.34558	−	12.4859i	−0.190016	−	0.709149i
$311$	12.0212	−	20.8214i	0.681660	−	1.18067i	−0.292813	−	0.956170i	$-0.594591\pi$
$311$	12.0212	−	20.8214i	0.681660	−	1.18067i	0.974474	−	0.224501i	$-0.0720752\pi$
$312$	8.62598	−	3.33315i	0.488350	−	0.188703i
$313$	20.0578	−	11.5804i	1.13373	−	0.654562i	0.188863	−	0.982003i	$-0.439520\pi$
$313$	20.0578	−	11.5804i	1.13373	−	0.654562i	0.944872	+	0.327441i	$0.106186\pi$
$314$	14.6579	+	3.92756i	0.827191	+	0.221645i
$315$	9.34567	+	3.06565i	0.526569	+	0.172730i
$316$	−0.0148695	−	0.00858493i	−0.000836477	−	0.000482940i
$317$	5.29442	−	19.7590i	0.297364	−	1.10978i	−0.641958	−	0.766740i	$-0.721877\pi$
$317$	5.29442	−	19.7590i	0.297364	−	1.10978i	0.939322	−	0.343038i	$-0.111456\pi$
$318$	−6.43528	−	1.72433i	−0.360873	−	0.0966955i
$319$	−19.6965	−	5.27765i	−1.10279	−	0.295492i
$320$	−6.13977	+	22.9139i	−0.343223	+	1.28093i
$321$	4.61486	+	2.66439i	0.257576	+	0.148712i
$322$	7.99052	+	2.62112i	0.445294	+	0.146069i
$323$	−20.3331	−	5.44825i	−1.13137	−	0.303149i
$324$	0.271846	−	0.156950i	0.0151025	−	0.00871945i
$325$	−25.6860	+	18.7490i	−1.42480	+	1.04001i
$326$	0.884344	−	1.53173i	0.0489793	−	0.0848346i
$327$	2.89458	+	10.8027i	0.160071	+	0.597392i
$328$	−20.2645	+	11.6997i	−1.11892	+	0.646009i
$329$	−3.69677	+	11.2696i	−0.203809	+	0.621316i
$330$	7.97866	+	7.97866i	0.439211	+	0.439211i
$331$	−14.8316	−	14.8316i	−0.815218	−	0.815218i	0.170193	−	0.985411i	$-0.445561\pi$
$331$	−14.8316	−	14.8316i	−0.815218	−	0.815218i	−0.985411	+	0.170193i	$0.945561\pi$
$332$	−1.04000	+	3.88135i	−0.0570776	+	0.213017i
$333$	−0.166900	−	0.622880i	−0.00914608	−	0.0341336i
$334$			6.76830i			0.370345i
$335$	5.53918	+	9.59414i	0.302638	+	0.524184i
$336$	10.0317	+	6.55479i	0.547273	+	0.357593i
$337$		−	30.0384i		−	1.63629i	−0.575009	−	0.818147i	$-0.695001\pi$
$337$		−	30.0384i		−	1.63629i	0.575009	−	0.818147i	$-0.304999\pi$
$338$	16.6322	+	10.6966i	0.904675	+	0.581819i
$339$	−2.23045	−	1.28775i	−0.121142	−	0.0699411i
$340$	−3.89592	−	3.89592i	−0.211286	−	0.211286i
$341$	3.95001	+	2.28054i	0.213905	+	0.123498i
$342$	−3.39097	+	5.87333i	−0.183362	+	0.317593i
$343$	18.2672	+	3.05129i	0.986335	+	0.164754i
$344$	0.276463	−	0.0740780i	0.0149059	−	0.00399402i
$345$	5.49268	−	5.49268i	0.295716	−	0.295716i
$346$	28.8111	−	7.71992i	1.54890	−	0.415026i
$347$	−0.955000	−	1.65411i	−0.0512671	−	0.0887972i	0.839253	−	0.543741i	$-0.182993\pi$
$347$	−0.955000	−	1.65411i	−0.0512671	−	0.0887972i	−0.890520	+	0.454944i	$0.849659\pi$
$348$	1.60394	−	2.77810i	0.0859800	−	0.148922i
$349$	−0.864466	+	3.22623i	−0.0462738	+	0.172696i	−0.985195	−	0.171435i	$-0.945160\pi$
$349$	−0.864466	+	3.22623i	−0.0462738	+	0.172696i	0.938922	+	0.344131i	$0.111826\pi$
$350$	−33.7285	−	11.0639i	−1.80286	−	0.591391i
$351$	−3.29708	−	1.45921i	−0.175985	−	0.0778867i
$352$	1.75598	+	3.04145i	0.0935942	+	0.162110i
$353$	−7.04763	+	7.04763i	−0.375108	+	0.375108i	−0.869334	−	0.494226i	$-0.835452\pi$
$353$	−7.04763	+	7.04763i	−0.375108	+	0.375108i	0.494226	+	0.869334i	$0.335452\pi$
$354$	2.57990			0.137120
$355$	−55.7286			−2.95777
$356$	−1.58861	+	1.58861i	−0.0841963	+	0.0841963i
$357$	11.1463	−	5.63991i	0.589922	−	0.298496i
$358$	9.07986	+	33.8865i	0.479885	+	1.79096i
$359$	13.3711	+	3.58279i	0.705702	+	0.189092i	0.593783	−	0.804625i	$-0.297634\pi$
$359$	13.3711	+	3.58279i	0.705702	+	0.189092i	0.111919	+	0.993717i	$0.464300\pi$
$360$	8.25733	−	4.76737i	0.435200	−	0.251263i
$361$		−	0.877521i		−	0.0461853i
$362$	−30.1826	+	8.08739i	−1.58636	+	0.425064i
$363$	7.01857			0.368380
$364$	0.154940	+	2.99041i	0.00812106	+	0.156740i
$365$	39.0775			2.04541
$366$	9.91982	−	2.65801i	0.518517	−	0.138936i
$367$			26.2338i			1.36939i	0.728827	+	0.684697i	$0.240066\pi$
$367$			26.2338i			1.36939i	−0.728827	+	0.684697i	$0.759934\pi$
$368$	8.19604	−	4.73199i	0.427248	−	0.246672i
$369$	8.81239	+	2.36127i	0.458755	+	0.122923i
$370$	0.943806	+	3.52233i	0.0490661	+	0.183117i
$371$	−6.33844	+	9.70056i	−0.329075	+	0.503628i
$372$	−0.507371	+	0.507371i	−0.0263059	+	0.0263059i
$373$	14.3805			0.744596			0.372298	−	0.928113i	$-0.378570\pi$
$373$	14.3805			0.744596			0.372298	+	0.928113i	$0.378570\pi$
$374$	14.3308			0.741029
$375$	−10.0415	+	10.0415i	−0.518541	+	0.518541i
$376$	5.74882	+	9.95725i	0.296473	+	0.513506i
$377$	−36.6361	+	3.93270i	−1.88685	+	0.202545i
$378$	−0.825695	−	3.93898i	−0.0424692	−	0.202599i
$379$	0.297354	−	1.10974i	0.0152740	−	0.0570035i	−0.957868	−	0.287208i	$-0.907273\pi$
$379$	0.297354	−	1.10974i	0.0152740	−	0.0570035i	0.973142	+	0.230205i	$0.0739395\pi$
$380$	2.60134	−	4.50565i	0.133446	−	0.231135i
$381$	9.22735	+	15.9822i	0.472732	+	0.818795i
$382$	−33.7672	+	9.04790i	−1.72768	+	0.462931i
$383$	14.5999	−	14.5999i	0.746019	−	0.746019i	−0.227710	−	0.973729i	$-0.573124\pi$
$383$	14.5999	−	14.5999i	0.746019	−	0.746019i	0.973729	+	0.227710i	$0.0731237\pi$
$384$	12.7762	−	3.42338i	0.651983	−	0.174698i
$385$	17.5115	−	8.86065i	0.892467	−	0.451580i
$386$	5.93440	−	10.2787i	0.302053	−	0.523171i
$387$	−0.0966425	−	0.0557966i	−0.00491262	−	0.00283630i
$388$	−2.74472	−	2.74472i	−0.139342	−	0.139342i
$389$	−25.6552	−	14.8121i	−1.30077	−	0.751001i	−0.320236	−	0.947338i	$-0.603762\pi$
$389$	−25.6552	−	14.8121i	−1.30077	−	0.751001i	−0.980537	+	0.196337i	$0.937095\pi$
$390$	18.6447	+	8.25169i	0.944110	+	0.417841i
$391$		−	9.86564i		−	0.498927i
$392$	14.0159	−	11.2200i	0.707910	−	0.566697i
$393$	−3.32971	−	5.76722i	−0.167962	−	0.290918i
$394$		−	15.3219i		−	0.771908i
$395$	0.0526290	+	0.196414i	0.00264805	+	0.00988266i
$396$	0.162109	−	0.604999i	0.00814629	−	0.0304024i
$397$	13.3468	+	13.3468i	0.669857	+	0.669857i	0.957683	−	0.287826i	$-0.0929323\pi$
$397$	13.3468	+	13.3468i	0.669857	+	0.669857i	−0.287826	+	0.957683i	$0.592932\pi$
$398$	−8.27184	−	8.27184i	−0.414630	−	0.414630i
$399$	7.86832	+	8.78818i	0.393909	+	0.439960i
$400$	−34.5960	+	19.9740i	−1.72980	+	0.998700i
$401$	−2.33975	−	8.73208i	−0.116842	−	0.436059i	0.882576	−	0.470169i	$-0.155807\pi$
$401$	−2.33975	−	8.73208i	−0.116842	−	0.436059i	−0.999418	+	0.0341098i	$0.989140\pi$
$402$	2.26654	−	3.92577i	0.113045	−	0.195800i
$403$	8.14314	+	1.27126i	0.405638	+	0.0633258i
$404$	−0.907265	+	0.523810i	−0.0451381	+	0.0260605i
$405$	−3.59085	−	0.962166i	−0.178431	−	0.0478104i
$406$	−27.4346	−	30.6419i	−1.36156	−	1.52073i
$407$	−1.11432	−	0.643354i	−0.0552349	−	0.0318899i
$408$	3.13423	−	11.6971i	0.155168	−	0.579094i
$409$	−8.35698	−	2.23925i	−0.413226	−	0.110724i	0.0462157	−	0.998931i	$-0.485284\pi$
$409$	−8.35698	−	2.23925i	−0.413226	−	0.110724i	−0.459442	+	0.888208i	$0.651951\pi$
$410$	−49.8333	−	13.3528i	−2.46109	−	0.659447i
$411$	4.13276	−	15.4237i	0.203854	−	0.760793i
$412$	5.04424	+	2.91229i	0.248512	+	0.143478i
$413$	1.39862	−	4.26372i	0.0688217	−	0.209804i
$414$	−3.07017	−	0.822648i	−0.150890	−	0.0404310i
$415$	41.2127	−	23.7942i	2.02305	−	1.16801i
$416$	4.94064	+	3.98275i	0.242235	+	0.195271i
$417$	−5.38449	+	9.32621i	−0.263679	+	0.456706i
$418$	3.50243	+	13.0712i	0.171309	+	0.639335i
$419$	−3.98045	+	2.29811i	−0.194457	+	0.112270i	−0.594068	−	0.804415i	$-0.702479\pi$
$419$	−3.98045	+	2.29811i	−0.194457	+	0.112270i	0.399610	+	0.916685i	$0.369146\pi$
$420$	0.633421	+	3.02173i	0.0309078	+	0.147446i
$421$	16.2204	+	16.2204i	0.790532	+	0.790532i	0.981581	−	0.191049i	$-0.0611888\pi$
$421$	16.2204	+	16.2204i	0.790532	+	0.790532i	−0.191049	+	0.981581i	$0.561189\pi$
$422$	−10.2181	−	10.2181i	−0.497411	−	0.497411i
$423$	1.16024	−	4.33009i	0.0564130	−	0.210536i
$424$	2.90739	+	10.8505i	0.141195	+	0.526948i
$425$			41.6435i			2.02000i
$426$	11.4016	+	19.7482i	0.552410	+	0.956803i
$427$	0.984954	−	17.8351i	0.0476653	−	0.863101i
$428$			1.67271i			0.0808533i
$429$	−6.71077	+	2.59310i	−0.323999	+	0.125196i
$430$	0.546505	+	0.315525i	0.0263548	+	0.0152160i
$431$	−8.20333	−	8.20333i	−0.395141	−	0.395141i	0.481374	−	0.876515i	$-0.340138\pi$
$431$	−8.20333	−	8.20333i	−0.395141	−	0.395141i	−0.876515	+	0.481374i	$0.840138\pi$
$432$	−3.92246	−	2.26463i	−0.188719	−	0.108957i
$433$	−0.155556	+	0.269431i	−0.00747554	+	0.0129480i	−0.869739	−	0.493512i	$-0.835713\pi$
$433$	−0.155556	+	0.269431i	−0.00747554	+	0.0129480i	0.862263	+	0.506460i	$0.169046\pi$
$434$	4.15349	+	8.20863i	0.199374	+	0.394027i
$435$	−36.6963	+	9.83275i	−1.75945	+	0.471444i
$436$	−2.48237	+	2.48237i	−0.118884	+	0.118884i
$437$	8.99851	−	2.41114i	0.430457	−	0.115341i
$438$	−7.99494	−	13.8476i	−0.382013	−	0.661666i
$439$	10.2875	−	17.8185i	0.490996	−	0.850430i	−0.508950	−	0.860796i	$-0.669966\pi$
$439$	10.2875	−	17.8185i	0.490996	−	0.850430i	0.999946	+	0.0103658i	$0.00329959\pi$
$440$	4.92408	−	18.3769i	0.234746	−	0.876084i
$441$	−6.95743	−	0.770807i	−0.331306	−	0.0367051i
$442$	24.1549	−	9.33365i	1.14893	−	0.443956i
$443$	13.6460	+	23.6355i	0.648340	+	1.12296i	0.983519	+	0.180804i	$0.0578699\pi$
$443$	13.6460	+	23.6355i	0.648340	+	1.12296i	−0.335179	+	0.942154i	$0.608797\pi$
$444$	0.143132	−	0.143132i	0.00679275	−	0.00679275i
$445$	26.6069			1.26129
$446$	−26.0879			−1.23530
$447$	1.87483	−	1.87483i	0.0886766	−	0.0886766i
$448$	0.930958	−	16.8574i	0.0439836	−	0.796436i
$449$	−1.99206	−	7.43447i	−0.0940111	−	0.350854i	0.902857	−	0.429942i	$-0.141466\pi$
$449$	−1.99206	−	7.43447i	−0.0940111	−	0.350854i	−0.996868	+	0.0790877i	$0.974799\pi$
$450$	12.9594	+	3.47245i	0.610910	+	0.163693i
$451$	15.7652	−	9.10205i	0.742355	−	0.428599i
$452$		−	0.808452i		−	0.0380264i
$453$	3.46086	−	0.927335i	0.162606	−	0.0435700i
$454$	−9.45734			−0.443855
$455$	23.7450	−	26.3400i	1.11318	−	1.23484i
$456$	11.4350			0.535494
$457$	−22.7366	+	6.09225i	−1.06357	+	0.284983i	−0.747850	−	0.663868i	$-0.768914\pi$
$457$	−22.7366	+	6.09225i	−1.06357	+	0.284983i	−0.315723	+	0.948852i	$0.602247\pi$
$458$		−	7.38294i		−	0.344982i
$459$	−4.08893	+	2.36075i	−0.190855	+	0.110190i
$460$	2.35524	+	0.631084i	0.109814	+	0.0294245i
$461$	8.59300	+	32.0695i	0.400216	+	1.49363i	0.812711	+	0.582666i	$0.197991\pi$
$461$	8.59300	+	32.0695i	0.400216	+	1.49363i	−0.412495	+	0.910960i	$0.635343\pi$
$462$	−6.72260	−	4.39261i	−0.312764	−	0.204363i
$463$	−4.66625	+	4.66625i	−0.216859	+	0.216859i	−0.807173	−	0.590314i	$-0.799004\pi$
$463$	−4.66625	+	4.66625i	−0.216859	+	0.216859i	0.590314	+	0.807173i	$0.299004\pi$
$464$	−46.2864			−2.14879
$465$	8.49772			0.394072
$466$	14.1244	−	14.1244i	0.654301	−	0.654301i
$467$	7.16204	+	12.4050i	0.331420	+	0.574036i	0.982790	−	0.184724i	$-0.0591391\pi$
$467$	7.16204	+	12.4050i	0.331420	+	0.574036i	−0.651371	+	0.758760i	$0.725806\pi$
$468$	−0.120797	−	1.12532i	−0.00558386	−	0.0520179i
$469$	−5.25924	−	5.87408i	−0.242849	−	0.271240i
$470$	−6.56108	+	24.4863i	−0.302640	+	1.12947i
$471$	−4.98798	+	8.63943i	−0.229834	+	0.398084i
$472$	−2.17499	−	3.76719i	−0.100112	−	0.173399i
$473$	−0.215080	+	0.0576306i	−0.00988941	+	0.00264986i
$474$	0.0588345	−	0.0588345i	0.00270236	−	0.00270236i
$475$	−37.9833	+	10.1776i	−1.74279	+	0.466979i
$476$	3.28259	+	2.14488i	0.150457	+	0.0983102i
$477$	2.18989	−	3.79299i	0.100268	−	0.173669i
$478$	−11.6179	−	6.70762i	−0.531392	−	0.306799i
$479$	10.4665	+	10.4665i	0.478227	+	0.478227i	0.904564	−	0.426337i	$-0.140196\pi$
$479$	10.4665	+	10.4665i	0.478227	+	0.478227i	−0.426337	+	0.904564i	$0.640196\pi$
$480$	5.66651	+	3.27156i	0.258639	+	0.149326i
$481$	−2.29723	−	0.358629i	−0.104744	−	0.0163521i
$482$			13.9098i			0.633572i
$483$	−3.02396	+	4.62798i	−0.137595	+	0.210580i
$484$	1.10157	+	1.90797i	0.0500712	+	0.0867259i
$485$			45.9701i			2.08740i
$486$	0.393703	+	1.46932i	0.0178587	+	0.0666497i
$487$	−8.58118	+	32.0254i	−0.388851	+	1.45121i	0.443156	+	0.896444i	$0.353859\pi$
$487$	−8.58118	+	32.0254i	−0.388851	+	1.45121i	−0.832007	+	0.554766i	$0.812808\pi$
$488$	−12.2441	−	12.2441i	−0.554266	−	0.554266i
$489$	0.822174	+	0.822174i	0.0371800	+	0.0371800i
$490$	39.3437	+	4.35885i	1.77737	+	0.196913i
$491$	−17.1631	+	9.90909i	−0.774558	+	0.447191i	−0.834498	−	0.551011i	$-0.814242\pi$
$491$	−17.1631	+	9.90909i	−0.774558	+	0.447191i	0.0599403	+	0.998202i	$0.480909\pi$
$492$	0.741204	+	2.76621i	0.0334161	+	0.124710i
$493$	−24.1254	+	41.7864i	−1.08655	+	1.88197i
$494$	14.4167	+	19.7507i	0.648637	+	0.888625i
$495$	−6.42397	+	3.70888i	−0.288736	+	0.166702i
$496$	10.0005	+	2.67962i	0.449034	+	0.120318i
$497$	38.8182	−	8.13714i	1.74123	−	0.365000i
$498$	−16.8636	−	9.73620i	−0.755676	−	0.436290i
$499$	−6.00770	+	22.4211i	−0.268942	+	1.00370i	0.690852	+	0.722997i	$0.257236\pi$
$499$	−6.00770	+	22.4211i	−0.268942	+	1.00370i	−0.959793	+	0.280708i	$0.909431\pi$
$500$	−4.30576	−	1.15372i	−0.192559	−	0.0515961i
$501$	−4.29785	−	1.15161i	−0.192014	−	0.0514499i
$502$	−5.30759	+	19.8082i	−0.236889	+	0.884083i
$503$	24.2350	+	13.9921i	1.08059	+	0.623877i	0.931055	−	0.364880i	$-0.118890\pi$
$503$	24.2350	+	13.9921i	1.08059	+	0.623877i	0.149532	+	0.988757i	$0.452223\pi$
$504$	−5.05561	+	4.52644i	−0.225195	+	0.201624i
$505$	11.9842	+	3.21116i	0.533290	+	0.142895i
$506$	−5.49247	+	3.17108i	−0.244170	+	0.140972i
$507$	−9.62224	+	8.74143i	−0.427339	+	0.388220i
$508$	−2.89647	+	5.01683i	−0.128510	+	0.222586i
$509$	−2.81831	−	10.5181i	−0.124920	−	0.466206i	0.874917	−	0.484273i	$-0.160916\pi$
$509$	−2.81831	−	10.5181i	−0.124920	−	0.466206i	−0.999837	+	0.0180663i	$0.994249\pi$
$510$	23.1226	−	13.3498i	1.02388	−	0.591140i
$511$	−27.2197	+	5.70585i	−1.20413	+	0.252412i
$512$	−10.7916	−	10.7916i	−0.476925	−	0.476925i
$513$	−3.15258	−	3.15258i	−0.139190	−	0.139190i
$514$	−3.87820	+	14.4736i	−0.171060	+	0.638405i
$515$	−17.8535	−	66.6302i	−0.786719	−	2.93608i
$516$		−	0.0350291i		−	0.00154207i
$517$	−4.47242	−	7.74646i	−0.196697	−	0.340689i
$518$	−1.17172	−	2.31570i	−0.0514826	−	0.101746i
$519$			19.6085i			0.860718i
$520$	−3.66923	−	34.1816i	−0.160906	−	1.49896i
$521$	−19.3656	−	11.1808i	−0.848424	−	0.489838i	0.0116948	−	0.999932i	$-0.496277\pi$
$521$	−19.3656	−	11.1808i	−0.848424	−	0.489838i	−0.860119	+	0.510094i	$0.829611\pi$
$522$	10.9921	+	10.9921i	0.481113	+	0.481113i
$523$	15.6632	+	9.04313i	0.684902	+	0.395428i	0.801699	−	0.597727i	$-0.203929\pi$
$523$	15.6632	+	9.04313i	0.684902	+	0.395428i	−0.116797	+	0.993156i	$0.537263\pi$
$524$	1.04520	−	1.81033i	0.0456596	−	0.0790847i
$525$	12.7643	−	19.5350i	0.557081	−	0.852576i
$526$	14.7491	−	3.95201i	0.643091	−	0.172316i
$527$	7.63156	−	7.63156i	0.332436	−	0.332436i
$528$	−8.72953	+	2.33907i	−0.379904	+	0.101795i
$529$	−9.31696	−	16.1374i	−0.405085	−	0.701628i
$530$	−12.3836	+	21.4490i	−0.537910	+	0.931687i
$531$	−0.438963	+	1.63823i	−0.0190494	+	0.0710932i
$532$	−1.15410	+	3.51827i	−0.0500364	+	0.152537i
$533$	20.6444	−	25.6095i	0.894208	−	1.10927i
$534$	−5.44357	−	9.42854i	−0.235566	−	0.408013i
$535$	14.0077	−	14.0077i	0.605605	−	0.605605i
$536$	−7.64324			−0.330138
$537$	−23.0627			−0.995230
$538$	32.5402	−	32.5402i	1.40291	−	1.40291i
$539$	−10.9040	+	8.72887i	−0.469667	+	0.375979i
$540$	−0.302024	−	1.12717i	−0.0129970	−	0.0485056i
$541$	−10.0627	−	2.69630i	−0.432630	−	0.115923i	0.0359302	−	0.999354i	$-0.488561\pi$
$541$	−10.0627	−	2.69630i	−0.432630	−	0.115923i	−0.468561	+	0.883431i	$0.655227\pi$
$542$	−23.0737	+	13.3216i	−0.991100	+	0.572212i
$543$		−	20.5419i		−	0.881536i
$544$	8.02702	−	2.15083i	0.344156	−	0.0922162i
$545$	41.5761			1.78092
$546$	−14.1920	−	3.02540i	−0.607360	−	0.129475i
$547$	22.4723			0.960845			0.480422	−	0.877037i	$-0.340483\pi$
$547$	22.4723			0.960845			0.480422	+	0.877037i	$0.340483\pi$
$548$	4.84149	−	1.29727i	0.206818	−	0.0554168i
$549$			6.75131i			0.288139i
$550$	23.1841	−	13.3853i	0.988572	−	0.570752i
$551$	−44.0099	−	11.7924i	−1.87488	−	0.502374i
$552$	1.38707	+	5.17661i	0.0590375	+	0.220331i
$553$	−0.0653383	−	0.129129i	−0.00277847	−	0.00549113i
$554$	−19.1871	+	19.1871i	−0.815181	+	0.815181i
$555$	−2.39726			−0.101758
$556$	−3.38038			−0.143360
$557$	15.2428	−	15.2428i	0.645859	−	0.645859i	−0.306131	−	0.951990i	$-0.599034\pi$
$557$	15.2428	−	15.2428i	0.645859	−	0.645859i	0.951990	+	0.306131i	$0.0990344\pi$
$558$	−1.73857	−	3.01128i	−0.0735993	−	0.127478i
$559$	−0.324987	+	0.237219i	−0.0137455	+	0.0100333i
$560$	33.1894	−	29.7155i	1.40251	−	1.25571i
$561$	−2.43834	+	9.10002i	−0.102947	+	0.384203i
$562$	−0.168174	+	0.291285i	−0.00709397	+	0.0122871i
$563$	1.96849	+	3.40952i	0.0829618	+	0.143694i	0.904521	−	0.426429i	$-0.140229\pi$
$563$	1.96849	+	3.40952i	0.0829618	+	0.143694i	−0.821559	+	0.570123i	$0.806895\pi$
$564$	1.35922	−	0.364201i	0.0572334	−	0.0153356i
$565$	−6.77019	+	6.77019i	−0.284824	+	0.284824i
$566$	37.7774	−	10.1224i	1.58790	−	0.425478i
$567$	2.64173	+	0.145891i	0.110942	+	0.00612684i
$568$	19.2243	−	33.2974i	0.806633	−	1.39713i
$569$	−27.7198	−	16.0040i	−1.16207	−	0.670924i	−0.210274	−	0.977642i	$-0.567436\pi$
$569$	−27.7198	−	16.0040i	−1.16207	−	0.670924i	−0.951800	+	0.306718i	$0.900769\pi$
$570$	17.8276	+	17.8276i	0.746715	+	0.746715i
$571$	7.22374	+	4.17063i	0.302304	+	0.174535i	0.643477	−	0.765465i	$-0.277491\pi$
$571$	7.22374	+	4.17063i	0.302304	+	0.174535i	−0.341173	+	0.940000i	$0.610824\pi$
$572$	−1.75818	−	1.41731i	−0.0735131	−	0.0592605i
$573$		−	22.9816i		−	0.960068i
$574$	36.6615	+	2.02465i	1.53022	+	0.0845073i
$575$	−9.21474	−	15.9604i	−0.384281	−	0.665594i
$576$			6.38120i			0.265883i
$577$	6.49388	+	24.2355i	0.270344	+	1.00894i	0.958898	+	0.283752i	$0.0915792\pi$
$577$	6.49388	+	24.2355i	0.270344	+	1.00894i	−0.688554	+	0.725185i	$0.741754\pi$
$578$	2.08368	−	7.77638i	0.0866695	−	0.323455i
$579$	5.51721	+	5.51721i	0.229287	+	0.229287i
$580$	−8.43248	−	8.43248i	−0.350140	−	0.350140i
$581$	−25.2328	+	22.5917i	−1.04683	+	0.937260i
$582$	16.2901	−	9.40512i	0.675248	−	0.389855i
$583$	−2.26187	−	8.44140i	−0.0936769	−	0.349607i
$584$	−13.4803	+	23.3485i	−0.557818	+	0.966169i
$585$	−8.41213	+	10.4353i	−0.347799	+	0.431447i
$586$	−21.2349	+	12.2600i	−0.877207	+	0.506456i
$587$	−20.0251	−	5.36570i	−0.826524	−	0.221466i	−0.179327	−	0.983790i	$-0.557392\pi$
$587$	−20.0251	−	5.36570i	−0.826524	−	0.221466i	−0.647197	+	0.762323i	$0.724059\pi$
$588$	−0.882429	−	2.01233i	−0.0363908	−	0.0829869i
$589$	8.82593	+	5.09565i	0.363666	+	0.209963i
$590$	2.48230	−	9.26405i	0.102194	−	0.381395i
$591$	9.72938	+	2.60698i	0.400213	+	0.107237i
$592$	−2.82119	−	0.755936i	−0.115950	−	0.0310688i
$593$	−0.0561154	+	0.209425i	−0.00230438	+	0.00860007i	−0.967068	−	0.254516i	$-0.918084\pi$
$593$	−0.0561154	+	0.209425i	−0.00230438	+	0.00860007i	0.964764	+	0.263117i	$0.0847504\pi$
$594$	2.62859	+	1.51761i	0.107852	+	0.0622685i
$595$	−9.52753	−	45.4511i	−0.390591	−	1.86331i
$596$	0.803921	+	0.215410i	0.0329299	+	0.00882354i
$597$	6.66002	−	3.84516i	0.272576	−	0.157372i
$598$	−7.19234	+	8.92216i	−0.294117	+	0.364854i
$599$	0.450193	−	0.779757i	0.0183944	−	0.0318600i	−0.856682	−	0.515845i	$-0.827478\pi$
$599$	0.450193	−	0.779757i	0.0183944	−	0.0318600i	0.875076	+	0.483985i	$0.160811\pi$
$600$	−5.85489	−	21.8508i	−0.239025	−	0.892054i
$601$	−24.7998	+	14.3182i	−1.01161	+	0.584051i	−0.911661	−	0.410942i	$-0.865200\pi$
$601$	−24.7998	+	14.3182i	−1.01161	+	0.584051i	−0.0999444	+	0.994993i	$0.531866\pi$
$602$	−0.426744	−	0.139984i	−0.0173928	−	0.00570533i
$603$	2.10721	+	2.10721i	0.0858121	+	0.0858121i
$604$	0.795275	+	0.795275i	0.0323593	+	0.0323593i
$605$	6.75303	−	25.2027i	0.274550	−	1.02463i
$606$	−1.31395	−	4.90374i	−0.0533758	−	0.199201i
$607$			23.5452i			0.955671i	0.878449	+	0.477835i	$0.158578\pi$
$607$			23.5452i			0.955671i	−0.878449	+	0.477835i	$0.841422\pi$
$608$	3.92358	+	6.79584i	0.159122	+	0.275608i
$609$	24.1254	−	12.2072i	0.977611	−	0.494663i
$610$		−	38.1781i		−	1.54578i
$611$	−12.5836	−	10.1439i	−0.509078	−	0.410379i
$612$	−1.28352	−	0.741039i	−0.0518831	−	0.0299547i
$613$	20.4541	+	20.4541i	0.826132	+	0.826132i	0.986979	−	0.160848i	$-0.0514228\pi$
$613$	20.4541	+	20.4541i	0.826132	+	0.826132i	−0.160848	+	0.986979i	$0.551423\pi$
$614$	−39.5183	−	22.8159i	−1.59483	−	0.920775i
$615$	16.9580	−	29.3720i	0.683811	−	1.18439i
$616$	−0.746626	+	13.5196i	−0.0300824	+	0.544719i
$617$	−17.9700	+	4.81504i	−0.723444	+	0.193846i	−0.601708	−	0.798716i	$-0.705513\pi$
$617$	−17.9700	+	4.81504i	−0.723444	+	0.193846i	−0.121736	+	0.992563i	$0.538846\pi$
$618$	−19.9586	+	19.9586i	−0.802854	+	0.802854i
$619$	40.9411	−	10.9701i	1.64556	−	0.440927i	0.687198	−	0.726471i	$-0.258841\pi$
$619$	40.9411	−	10.9701i	1.64556	−	0.440927i	0.958366	+	0.285543i	$0.0921740\pi$
$620$	1.33372	+	2.31007i	0.0535634	+	0.0927745i
$621$	1.04476	−	1.80957i	0.0419247	−	0.0726157i
$622$	−9.46557	+	35.3260i	−0.379535	+	1.41644i
$623$	−18.5333	+	3.88498i	−0.742521	+	0.155648i
$624$	−13.1904	+	9.62808i	−0.528037	+	0.385432i
$625$	4.34603	+	7.52754i	0.173841	+	0.301102i
$626$	−24.9121	+	24.9121i	−0.995688	+	0.995688i
$627$	−8.89611			−0.355277
$628$	−3.13146			−0.124959
$629$	−2.15291	+	2.15291i	−0.0858420	+	0.0858420i
$630$	−14.9387	−	0.825000i	−0.595173	−	0.0328688i
$631$	0.481180	+	1.79579i	0.0191555	+	0.0714893i	0.974842	−	0.222897i	$-0.0715514\pi$
$631$	0.481180	+	1.79579i	0.0191555	+	0.0714893i	−0.955686	+	0.294386i	$0.904885\pi$
$632$	−0.135511	−	0.0363100i	−0.00539034	−	0.00144434i
$633$	8.22707	−	4.74990i	0.326997	−	0.188792i
$634$			31.1168i			1.23580i
$635$	66.2681	−	17.7565i	2.62977	−	0.704644i
$636$	1.37481			0.0545148
$637$	−12.6937	+	21.8144i	−0.502945	+	0.864319i
$638$	31.0182			1.22802
$639$	−14.4800	+	3.87990i	−0.572819	+	0.153486i
$640$		−	49.1713i		−	1.94367i
$641$	21.5514	−	12.4427i	0.851231	−	0.491458i	−0.00983531	−	0.999952i	$-0.503131\pi$
$641$	21.5514	−	12.4427i	0.851231	−	0.491458i	0.861066	+	0.508493i	$0.169797\pi$
$642$	−7.82968	−	2.09796i	−0.309013	−	0.0827997i
$643$	2.77769	+	10.3665i	0.109541	+	0.408814i	0.998821	−	0.0485507i	$-0.0154602\pi$
$643$	2.77769	+	10.3665i	0.109541	+	0.408814i	−0.889279	+	0.457364i	$0.848794\pi$
$644$	−1.73271	−	0.0956898i	−0.0682782	−	0.00377071i
$645$	−0.293343	+	0.293343i	−0.0115504	+	0.0115504i
$646$	32.0209			1.25984
$647$	−13.4344			−0.528163			−0.264081	−	0.964500i	$-0.585069\pi$
$647$	−13.4344			−0.528163			−0.264081	+	0.964500i	$0.585069\pi$
$648$	1.81360	−	1.81360i	0.0712448	−	0.0712448i
$649$	1.69208	+	2.93077i	0.0664199	+	0.115043i
$650$	30.3593	−	37.6610i	1.19079	−	1.47718i
$651$	−5.91916	+	1.24078i	−0.231990	+	0.0486301i
$652$	−0.0944641	+	0.352545i	−0.00369950	+	0.0138067i
$653$	10.8493	−	18.7915i	0.424566	−	0.735370i	−0.571814	−	0.820383i	$-0.693760\pi$
$653$	10.8493	−	18.7915i	0.424566	−	0.735370i	0.996380	+	0.0850136i	$0.0270934\pi$
$654$	−8.50613	−	14.7331i	−0.332616	−	0.576108i
$655$	−23.9130	+	6.40746i	−0.934357	+	0.250360i
$656$	29.2188	−	29.2188i	1.14080	−	1.14080i
$657$	10.1535	−	2.72063i	0.396127	−	0.106142i
$658$	0.994841	−	18.0141i	0.0387829	−	0.702264i
$659$	−6.28037	+	10.8779i	−0.244648	+	0.423744i	−0.962033	−	0.272934i	$-0.912006\pi$
$659$	−6.28037	+	10.8779i	−0.244648	+	0.423744i	0.717384	+	0.696678i	$0.245339\pi$
$660$	−2.01649	−	1.16422i	−0.0784916	−	0.0453172i
$661$	−3.54671	−	3.54671i	−0.137951	−	0.137951i	0.634759	−	0.772710i	$-0.281099\pi$
$661$	−3.54671	−	3.54671i	−0.137951	−	0.137951i	−0.772710	+	0.634759i	$0.781099\pi$
$662$	27.6316	+	15.9531i	1.07393	+	0.620035i
$663$	1.81696	+	16.9263i	0.0705649	+	0.657365i
$664$			32.8324i			1.27414i
$665$	39.1277	−	19.7983i	1.51731	−	0.767744i
$666$	0.490459	+	0.849500i	0.0190049	+	0.0329175i
$667$		−	21.3536i		−	0.826814i
$668$	−0.361489	−	1.34910i	−0.0139864	−	0.0521981i
$669$	4.43878	−	16.5658i	0.171613	−	0.640469i
$670$	−11.9161	−	11.9161i	−0.460358	−	0.460358i
$671$	9.52560	+	9.52560i	0.367732	+	0.367732i
$672$	−4.42474	−	1.45144i	−0.170688	−	0.0559906i
$673$	−24.8578	+	14.3517i	−0.958198	+	0.553216i	−0.895618	−	0.444824i	$-0.853266\pi$
$673$	−24.8578	+	14.3517i	−0.958198	+	0.553216i	−0.0625799	+	0.998040i	$0.519933\pi$
$674$	11.8262	+	44.1360i	0.455528	+	1.70005i
$675$	−4.40999	+	7.63832i	−0.169740	+	0.293999i
$676$	−3.88653	−	1.24380i	−0.149482	−	0.0478383i
$677$	−24.1896	+	13.9659i	−0.929683	+	0.536753i	−0.886711	−	0.462324i	$-0.847016\pi$
$677$	−24.1896	+	13.9659i	−0.929683	+	0.536753i	−0.0429716	+	0.999076i	$0.513682\pi$
$678$	3.78424	+	1.01398i	0.145333	+	0.0389418i
$679$	−6.71227	−	32.0209i	−0.257593	−	1.22885i
$680$	−38.9870	−	22.5091i	−1.49508	−	0.863186i
$681$	1.60914	−	6.00538i	0.0616623	−	0.230127i
$682$	−6.70169	−	1.79571i	−0.256621	−	0.0687613i
$683$	34.0427	+	9.12171i	1.30261	+	0.349033i	0.842435	−	0.538797i	$-0.181121\pi$
$683$	34.0427	+	9.12171i	1.30261	+	0.349033i	0.460172	+	0.887830i	$0.347788\pi$
$684$	0.362217	−	1.35181i	0.0138497	−	0.0516879i
$685$	−51.4077	−	29.6802i	−1.96419	−	1.13402i
$686$	−28.0416	+	2.70852i	−1.07063	+	0.103412i
$687$	4.68814	+	1.25618i	0.178864	+	0.0479264i
$688$	−0.437720	+	0.252718i	−0.0166879	+	0.00963477i
$689$	−9.31029	−	12.7550i	−0.354694	−	0.485926i
$690$	−5.90802	+	10.2330i	−0.224914	+	0.389563i
$691$	−2.33123	−	8.70025i	−0.0886840	−	0.330973i	0.907302	−	0.420479i	$-0.138138\pi$
$691$	−2.33123	−	8.70025i	−0.0886840	−	0.330973i	−0.995986	+	0.0895057i	$0.971471\pi$
$692$	−5.33048	+	3.07756i	−0.202635	+	0.116991i
$693$	3.93312	−	3.52144i	0.149407	−	0.133768i
$694$	2.05443	+	2.05443i	0.0779849	+	0.0779849i
$695$	28.3082	+	28.3082i	1.07379	+	1.07379i
$696$	6.78386	−	25.3177i	0.257142	−	0.959666i
$697$	−11.1487	−	41.6076i	−0.422288	−	1.57600i
$698$		−	5.08071i		−	0.192308i
$699$	6.56573	+	11.3722i	0.248339	+	0.430135i
$700$	7.31386	+	0.403912i	0.276438	+	0.0152664i
$701$			10.4155i			0.393389i	0.980465	+	0.196695i	$0.0630207\pi$
$701$			10.4155i			0.393389i	−0.980465	+	0.196695i	$0.936979\pi$
$702$	5.41895	+	0.845973i	0.204525	+	0.0319292i
$703$	−2.48985	−	1.43751i	−0.0939063	−	0.0542168i
$704$	9.00339	+	9.00339i	0.339328	+	0.339328i
$705$	−14.4324	−	8.33253i	−0.543554	−	0.313821i
$706$	7.58055	−	13.1299i	0.285298	−	0.494150i
$707$	−8.81657	−	0.486900i	−0.331581	−	0.0183118i
$708$	−0.514241	+	0.137790i	−0.0193264	+	0.00517848i
$709$	18.9866	−	18.9866i	0.713058	−	0.713058i	−0.254116	−	0.967174i	$-0.581784\pi$
$709$	18.9866	−	18.9866i	0.713058	−	0.713058i	0.967174	+	0.254116i	$0.0817845\pi$
$710$	81.8831	−	21.9405i	3.07302	−	0.823412i
$711$	0.0273492	+	0.0473702i	0.00102568	+	0.00177652i
$712$	−9.17840	+	15.8975i	−0.343975	+	0.595782i
$713$	−1.23621	+	4.61358i	−0.0462963	+	0.172780i
$714$	−14.1570	+	12.6751i	−0.529811	+	0.474355i
$715$	2.85456	+	26.5923i	0.106754	+	0.994497i
$716$	−3.61970	−	6.26950i	−0.135274	−	0.234302i
$717$	6.23607	−	6.23607i	0.232890	−	0.232890i
$718$	−21.0570			−0.785842
$719$	36.9778			1.37904			0.689519	−	0.724267i	$-0.257822\pi$
$719$	36.9778			1.37904			0.689519	+	0.724267i	$0.257822\pi$
$720$	−11.9060	+	11.9060i	−0.443711	+	0.443711i
$721$	22.1649	+	43.8049i	0.825465	+	1.63138i
$722$	0.345482	+	1.28936i	0.0128575	+	0.0479849i
$723$	−8.83265	−	2.36670i	−0.328490	−	0.0880186i
$724$	5.58422	−	3.22405i	0.207536	−	0.119821i
$725$			90.1348i			3.34752i
$726$	−10.3125	+	2.76323i	−0.382734	+	0.102553i
$727$	−32.7889			−1.21607			−0.608037	−	0.793909i	$-0.708043\pi$
$727$	−32.7889			−1.21607			−0.608037	+	0.793909i	$0.708043\pi$
$728$	7.54682	+	23.2737i	0.279704	+	0.862582i
$729$	−1.00000			−0.0370370
$730$	−57.4173	+	15.3849i	−2.12511	+	0.569421i
$731$			0.526887i			0.0194876i
$732$	−1.83531	+	1.05962i	−0.0678351	+	0.0391646i
$733$	11.9130	+	3.19209i	0.440018	+	0.117902i	0.472025	−	0.881585i	$-0.343523\pi$
$733$	11.9130	+	3.19209i	0.440018	+	0.117902i	−0.0320071	+	0.999488i	$0.510190\pi$
$734$	−10.3283	−	38.5459i	−0.381226	−	1.42275i
$735$	−9.46206	+	24.2415i	−0.349013	+	0.894160i
$736$	−2.60053	+	2.60053i	−0.0958568	+	0.0958568i
$737$	5.94622			0.219032
$738$	−13.8778			−0.510851
$739$	−3.35344	+	3.35344i	−0.123358	+	0.123358i	−0.766091	−	0.642733i	$-0.777801\pi$
$739$	−3.35344	+	3.35344i	−0.123358	+	0.123358i	0.642733	+	0.766091i	$0.277801\pi$
$740$	−0.376250	−	0.651683i	−0.0138312	−	0.0239564i
$741$	−14.9946	+	5.79403i	−0.550839	+	0.212849i
$742$	5.49405	−	16.7487i	0.201693	−	0.614863i
$743$	−6.39444	+	23.8644i	−0.234589	+	0.875499i	0.743745	+	0.668464i	$0.233048\pi$
$743$	−6.39444	+	23.8644i	−0.234589	+	0.875499i	−0.978334	+	0.207035i	$0.933619\pi$
$744$	−2.93139	+	5.07732i	−0.107470	+	0.186144i
$745$	−4.92835	−	8.53615i	−0.180561	−	0.312740i
$746$	−21.1296	+	5.66166i	−0.773609	+	0.207288i
$747$	9.05174	−	9.05174i	0.331186	−	0.331186i
$748$	−2.85650	+	0.765397i	−0.104444	+	0.0279857i
$749$	−7.71185	+	11.8025i	−0.281785	+	0.431253i
$750$	10.8008	−	18.7075i	0.394390	−	0.683103i
$751$	15.6847	+	9.05557i	0.572343	+	0.330443i	0.758085	−	0.652156i	$-0.226135\pi$
$751$	15.6847	+	9.05557i	0.572343	+	0.330443i	−0.185741	+	0.982599i	$0.559469\pi$
$752$	−14.3571	−	14.3571i	−0.523549	−	0.523549i
$753$	−11.6751	−	6.74060i	−0.425463	−	0.245641i
$754$	52.2818	−	20.2021i	1.90399	−	0.735718i
$755$		−	13.3197i		−	0.484753i
$756$	0.374959	+	0.741039i	0.0136371	+	0.0269513i
$757$	−20.3244	−	35.2029i	−0.738704	−	1.27947i	−0.953079	−	0.302722i	$-0.902105\pi$
$757$	−20.3244	−	35.2029i	−0.738704	−	1.27947i	0.214375	−	0.976751i	$-0.431229\pi$
$758$			1.74763i			0.0634768i
$759$	−1.07910	−	4.02725i	−0.0391688	−	0.146180i
$760$	11.0024	−	41.0614i	0.399098	−	1.48945i
$761$	−18.2921	−	18.2921i	−0.663087	−	0.663087i	0.293019	−	0.956107i	$-0.405340\pi$
$761$	−18.2921	−	18.2921i	−0.663087	−	0.663087i	−0.956107	+	0.293019i	$0.905340\pi$
$762$	−19.8502	−	19.8502i	−0.719096	−	0.719096i
$763$	−28.9602	+	6.07068i	−1.04843	+	0.219773i
$764$	6.24743	−	3.60696i	0.226024	−	0.130495i
$765$	4.54286	+	16.9542i	0.164247	+	0.612980i
$766$	−15.7039	+	27.1999i	−0.567404	+	0.982773i
$767$	4.76083	+	3.83781i	0.171904	+	0.138575i
$768$	−6.37199	+	3.67887i	−0.229929	+	0.132750i
$769$	−3.03465	−	0.813131i	−0.109432	−	0.0293223i	0.203687	−	0.979036i	$-0.434707\pi$
$769$	−3.03465	−	0.813131i	−0.109432	−	0.0293223i	−0.313120	+	0.949714i	$0.601374\pi$
$770$	−22.2415	+	19.9134i	−0.801527	+	0.717630i
$771$	−8.53085	−	4.92529i	−0.307231	−	0.177380i
$772$	−0.633902	+	2.36575i	−0.0228146	+	0.0851454i
$773$	41.1448	+	11.0247i	1.47987	+	0.396531i	0.906304	−	0.422626i	$-0.138892\pi$
$773$	41.1448	+	11.0247i	1.47987	+	0.396531i	0.573570	+	0.819157i	$0.305558\pi$
$774$	0.163966	+	0.0439346i	0.00589364	+	0.00157920i
$775$	5.21810	−	19.4742i	0.187440	−	0.699534i
$776$	−27.4668	−	15.8580i	−0.986001	−	0.569268i
$777$	1.66983	−	0.350032i	0.0599047	−	0.0125573i
$778$	43.5273	+	11.6631i	1.56053	+	0.418142i
$779$	35.2259	−	20.3377i	1.26210	−	0.728672i
$780$	−4.15708	−	0.648977i	−0.148847	−	0.0232371i
$781$	−14.9559	+	25.9044i	−0.535166	+	0.926934i
$782$	3.88413	+	14.4958i	0.138896	+	0.518368i
$783$	−8.85026	+	5.10970i	−0.316282	+	0.182606i
$784$	−18.7795	+	25.5447i	−0.670696	+	0.912309i
$785$	26.2236	+	26.2236i	0.935962	+	0.935962i
$786$	7.16297	+	7.16297i	0.255495	+	0.255495i
$787$	−5.08037	+	18.9602i	−0.181096	+	0.675859i	0.814337	+	0.580392i	$0.197101\pi$
$787$	−5.08037	+	18.9602i	−0.181096	+	0.675859i	−0.995433	+	0.0954662i	$0.969566\pi$
$788$	0.818332	+	3.05406i	0.0291519	+	0.108796i
$789$			10.0381i			0.357364i
$790$	−0.154657	−	0.267875i	−0.00550247	−	0.00953055i
$791$	3.72729	−	5.70437i	0.132527	−	0.202824i
$792$		−	5.11770i		−	0.181850i
$793$	22.2596	+	9.85156i	0.790461	+	0.349839i
$794$	−24.8654	−	14.3560i	−0.882440	−	0.509477i
$795$	−11.5130	−	11.5130i	−0.408325	−	0.408325i
$796$	2.09058	+	1.20700i	0.0740987	+	0.0427809i
$797$	−5.96514	+	10.3319i	−0.211296	+	0.365976i	−0.952120	−	0.305723i	$-0.901102\pi$
$797$	−5.96514	+	10.3319i	−0.211296	+	0.365976i	0.740824	+	0.671699i	$0.234435\pi$
$798$	−15.0210	−	9.81487i	−0.531738	−	0.347443i
$799$	−20.4445	+	5.47809i	−0.723275	+	0.193801i
$800$	10.9770	−	10.9770i	0.388095	−	0.388095i
$801$	6.91330	−	1.85241i	0.244269	−	0.0654518i
$802$	6.87569	+	11.9090i	0.242789	+	0.420523i
$803$	10.4873	−	18.1645i	0.370088	−	0.641011i
$804$	−0.242108	+	0.903561i	−0.00853851	+	0.0318661i
$805$	13.7088	+	15.3115i	0.483173	+	0.539659i
$806$	−12.4654	+	1.33810i	−0.439074	+	0.0471324i
$807$	15.1263	+	26.1996i	0.532472	+	0.922268i
$808$	−6.05274	+	6.05274i	−0.212935	+	0.212935i
$809$	−4.89567			−0.172123			−0.0860614	−	0.996290i	$-0.527428\pi$
$809$	−4.89567			−0.172123			−0.0860614	+	0.996290i	$0.527428\pi$
$810$	5.65491			0.198693
$811$	18.6293	−	18.6293i	0.654164	−	0.654164i	−0.299829	−	0.953993i	$-0.596930\pi$
$811$	18.6293	−	18.6293i	0.654164	−	0.654164i	0.953993	+	0.299829i	$0.0969295\pi$
$812$	7.10497	+	4.64246i	0.249336	+	0.162918i
$813$	−4.53326	−	16.9184i	−0.158988	−	0.593353i
$814$	1.89058	+	0.506581i	0.0662649	+	0.0177556i
$815$	3.74337	−	2.16124i	0.131125	−	0.0757048i
$816$			21.3849i			0.748622i
$817$	−0.480577	+	0.128770i	−0.0168132	+	0.00450510i
$818$	13.1607			0.460152
$819$	4.33584	−	8.49709i	0.151507	−	0.296912i
$820$	10.6462			0.371782
$821$	11.7259	−	3.14195i	0.409237	−	0.109655i	−0.0483266	−	0.998832i	$-0.515389\pi$
$821$	11.7259	−	3.14195i	0.409237	−	0.109655i	0.457564	+	0.889177i	$0.348722\pi$
$822$			24.2893i			0.847188i
$823$	13.6800	−	7.89813i	0.476854	−	0.275312i	−0.242251	−	0.970214i	$-0.577886\pi$
$823$	13.6800	−	7.89813i	0.476854	−	0.275312i	0.719104	+	0.694902i	$0.244552\pi$
$824$	45.9698	+	12.3176i	1.60144	+	0.429103i
$825$	4.55494	+	16.9993i	0.158583	+	0.591839i
$826$	−0.376385	+	6.81540i	−0.0130961	+	0.237138i
$827$	25.0121	−	25.0121i	0.869756	−	0.869756i	−0.122689	−	0.992445i	$-0.539152\pi$
$827$	25.0121	−	25.0121i	0.869756	−	0.869756i	0.992445	+	0.122689i	$0.0391518\pi$
$828$	0.655900			0.0227941
$829$	12.2047			0.423885			0.211943	−	0.977282i	$-0.432021\pi$
$829$	12.2047			0.423885			0.211943	+	0.977282i	$0.432021\pi$
$830$	−51.1868	+	51.1868i	−1.77672	+	1.77672i
$831$	−8.91911	−	15.4484i	−0.309401	−	0.535897i
$832$	21.0393	+	9.31149i	0.729406	+	0.322818i
$833$	13.2730	+	30.2682i	0.459881	+	1.04873i
$834$	4.23978	−	15.8231i	0.146811	−	0.547908i
$835$	−8.27049	+	14.3249i	−0.286212	+	0.495734i
$836$	−1.39625	−	2.41837i	−0.0482902	−	0.0836411i
$837$	2.20797	−	0.591623i	0.0763185	−	0.0204495i
$838$	4.94377	−	4.94377i	0.170780	−	0.170780i
$839$	−31.9263	+	8.55462i	−1.10222	+	0.295338i	−0.763667	−	0.645610i	$-0.776603\pi$
$839$	−31.9263	+	8.55462i	−1.10222	+	0.295338i	−0.338550	+	0.940948i	$0.609936\pi$
$840$	11.3894	+	22.5091i	0.392972	+	0.776639i
$841$	−37.7180	+	65.3295i	−1.30062	+	2.25274i
$842$	−30.2189	−	17.4469i	−1.04141	−	0.601259i
$843$	−0.156351	−	0.156351i	−0.00538501	−	0.00538501i
$844$	2.58248	+	1.49100i	0.0888926	+	0.0513222i
$845$	22.1310	+	42.9627i	0.761329	+	1.47796i
$846$			6.81908i			0.234445i
$847$	−1.02395	+	18.5412i	−0.0351832	+	0.637081i
$848$	−9.91858	−	17.1795i	−0.340605	−	0.589946i
$849$			25.7108i			0.882394i
$850$	−16.3951	−	61.1875i	−0.562349	−	2.09871i
$851$	0.348741	−	1.30152i	0.0119547	−	0.0446155i
$852$	−3.32737	−	3.32737i	−0.113994	−	0.113994i
$853$	−34.9288	−	34.9288i	−1.19594	−	1.19594i	−0.975372	−	0.220568i	$-0.929209\pi$
$853$	−34.9288	−	34.9288i	−1.19594	−	1.19594i	−0.220568	−	0.975372i	$-0.570791\pi$
$854$	5.57452	+	26.5932i	0.190756	+	0.910002i
$855$	−14.3537	+	8.28714i	−0.490888	+	0.283414i
$856$	3.53736	+	13.2016i	0.120905	+	0.451222i
$857$	−15.4917	+	26.8324i	−0.529186	+	0.916577i	0.470235	+	0.882541i	$0.344169\pi$
$857$	−15.4917	+	26.8324i	−0.529186	+	0.916577i	−0.999421	+	0.0340353i	$0.989164\pi$
$858$	8.83935	−	6.45213i	0.301770	−	0.220272i
$859$	3.82146	−	2.20632i	0.130387	−	0.0752788i	−0.433388	−	0.901207i	$-0.642682\pi$
$859$	3.82146	−	2.20632i	0.130387	−	0.0752788i	0.563775	+	0.825929i	$0.309349\pi$
$860$	−0.125784	−	0.0337038i	−0.00428921	−	0.00114929i
$861$	−7.52348	+	22.9354i	−0.256400	+	0.781637i
$862$	15.2830	+	8.82364i	0.520541	+	0.300534i
$863$	−3.29472	+	12.2961i	−0.112154	+	0.418563i	−0.999058	−	0.0433897i	$-0.986184\pi$
$863$	−3.29472	+	12.2961i	−0.112154	+	0.418563i	0.886905	+	0.461953i	$0.152851\pi$
$864$	1.70010	+	0.455541i	0.0578386	+	0.0154978i
$865$	70.4112	+	18.8666i	2.39405	+	0.641484i
$866$	0.122486	−	0.457122i	0.00416223	−	0.0155337i
$867$	4.58345	+	2.64625i	0.155662	+	0.0898715i
$868$	−1.26631	−	1.41436i	−0.0429815	−	0.0480063i
$869$	0.105424	+	0.0282482i	0.00357625	+	0.000958254i
$870$	50.0474	−	28.8949i	1.69677	−	0.979629i
$871$	10.0225	−	3.87277i	0.339598	−	0.131224i
$872$	−14.3422	+	24.8414i	−0.485688	+	0.841236i
$873$	3.20050	+	11.9444i	0.108321	+	0.404258i
$874$	−12.2724	+	7.08548i	−0.415120	+	0.239670i
$875$	−25.0619	−	27.9919i	−0.847248	−	0.946298i
$876$	2.33319	+	2.33319i	0.0788311	+	0.0788311i
$877$	−18.0242	−	18.0242i	−0.608633	−	0.608633i	0.333955	−	0.942589i	$-0.391616\pi$
$877$	−18.0242	−	18.0242i	−0.608633	−	0.608633i	−0.942589	+	0.333955i	$0.891616\pi$
$878$	−8.10044	+	30.2313i	−0.273377	+	1.02026i
$879$	−4.17200	−	15.5701i	−0.140718	−	0.525167i
$880$			33.5970i			1.13256i
$881$	11.9538	+	20.7046i	0.402735	+	0.697557i	0.994055	−	0.108880i	$-0.0347263\pi$
$881$	11.9538	+	20.7046i	0.402735	+	0.697557i	−0.591320	+	0.806437i	$0.701393\pi$
$882$	10.5262	−	1.60660i	0.354434	−	0.0540970i
$883$		−	43.3376i		−	1.45843i	−0.684287	−	0.729213i	$-0.739887\pi$
$883$		−	43.3376i		−	1.45843i	0.684287	−	0.729213i	$-0.260113\pi$
$884$	−4.31618	+	3.15053i	−0.145169	+	0.105964i
$885$	5.46029	+	3.15250i	0.183546	+	0.105970i
$886$	−29.3557	−	29.3557i	−0.986223	−	0.986223i
$887$	−22.4737	−	12.9752i	−0.754594	−	0.435665i	0.0727576	−	0.997350i	$-0.476820\pi$
$887$	−22.4737	−	12.9752i	−0.754594	−	0.435665i	−0.827351	+	0.561685i	$0.810153\pi$
$888$	0.826963	−	1.43234i	0.0277511	−	0.0480663i
$889$	−43.5669	+	22.0445i	−1.46119	+	0.739348i
$890$	−39.0941	+	10.4752i	−1.31044	+	0.351131i
$891$	−1.41093	+	1.41093i	−0.0472678	+	0.0472678i
$892$	5.20000	−	1.39333i	0.174109	−	0.0466523i
$893$	−9.99320	−	17.3087i	−0.334410	−	0.579214i
$894$	−2.01660	+	3.49286i	−0.0674453	+	0.116819i
$895$	−22.1902	+	82.8148i	−0.741735	+	2.76819i
$896$	7.17969	+	34.2507i	0.239857	+	1.14424i
$897$	−4.44179	−	6.08519i	−0.148307	−	0.203179i
$898$	5.85394	+	10.1393i	0.195349	+	0.338354i
$899$	16.5181	−	16.5181i	0.550908	−	0.550908i
$900$	−2.76859			−0.0922864
$901$	−20.6791			−0.688919
$902$	−19.5806	+	19.5806i	−0.651963	+	0.651963i
$903$	0.161499	−	0.247163i	0.00537434	−	0.00822507i
$904$	−1.70968	−	6.38060i	−0.0568630	−	0.212216i
$905$	−73.7628	−	19.7647i	−2.45196	−	0.657000i
$906$	−4.72002	+	2.72510i	−0.156812	+	0.0905355i
$907$			9.57765i			0.318021i	0.987277	+	0.159010i	$0.0508303\pi$
$907$			9.57765i			0.318021i	−0.987277	+	0.159010i	$0.949170\pi$
$908$	1.88509	−	0.505109i	0.0625589	−	0.0167626i
$909$	3.33743			0.110695
$910$	−24.5188	+	48.0503i	−0.812790	+	1.59285i
$911$	21.2966			0.705588			0.352794	−	0.935701i	$-0.385232\pi$
$911$	21.2966			0.705588			0.352794	+	0.935701i	$0.385232\pi$
$912$	−19.5053	+	5.22643i	−0.645885	+	0.173064i
$913$		−	25.5427i		−	0.845339i
$914$	31.0088	−	17.9029i	1.02568	−	0.592176i
$915$	24.2429	+	6.49588i	0.801447	+	0.214747i
$916$	0.394317	+	1.47161i	0.0130286	+	0.0486234i
$917$	15.7212	−	7.95479i	0.519160	−	0.262690i
$918$	5.07852	−	5.07852i	0.167616	−	0.167616i
$919$	6.13994			0.202538			0.101269	−	0.994859i	$-0.467710\pi$
$919$	6.13994			0.202538			0.101269	+	0.994859i	$0.467710\pi$
$920$	19.9230			0.656842
$921$	21.2119	−	21.2119i	0.698957	−	0.698957i
$922$	−25.2517	−	43.7373i	−0.831621	−	1.44041i
$923$	−8.33698	+	53.4032i	−0.274415	+	1.75779i
$924$	1.57459	+	0.516511i	0.0518003	+	0.0169920i
$925$	−1.47206	+	5.49379i	−0.0484009	+	0.180635i
$926$	5.01909	−	8.69332i	0.164938	−	0.285680i
$927$	−9.27777	−	16.0696i	−0.304722	−	0.527794i
$928$	17.3740	−	4.65535i	0.570330	−	0.152819i
$929$	18.3867	−	18.3867i	0.603249	−	0.603249i	−0.337924	−	0.941173i	$-0.609725\pi$
$929$	18.3867	−	18.3867i	0.603249	−	0.603249i	0.941173	+	0.337924i	$0.109725\pi$
$930$	−12.4859	+	3.34558i	−0.409427	+	0.109706i
$931$	−24.3639	+	19.5038i	−0.798494	+	0.639212i
$932$	−2.06098	+	3.56973i	−0.0675098	+	0.116930i
$933$	−20.8214	−	12.0212i	−0.681660	−	0.393557i
$934$	−15.4072	−	15.4072i	−0.504139	−	0.504139i
$935$	30.3307	+	17.5115i	0.991921	+	0.572686i
$936$	−3.33315	−	8.62598i	−0.108947	−	0.281949i
$937$		−	13.4306i		−	0.438759i	−0.975640	−	0.219380i	$-0.929597\pi$
$937$		−	13.4306i		−	0.438759i	0.975640	−	0.219380i	$-0.0704033\pi$
$938$	10.0401	+	6.56032i	0.327822	+	0.214202i
$939$	−11.5804	−	20.0578i	−0.377912	−	0.654562i
$940$		−	5.23117i		−	0.170622i
$941$	−9.81563	−	36.6324i	−0.319981	−	1.19418i	−0.919262	−	0.393645i	$-0.871214\pi$
$941$	−9.81563	−	36.6324i	−0.319981	−	1.19418i	0.599282	−	0.800538i	$-0.295453\pi$
$942$	3.92756	−	14.6579i	0.127967	−	0.477579i
$943$	13.4797	+	13.4797i	0.438960	+	0.438960i
$944$	5.43181	+	5.43181i	0.176790	+	0.176790i
$945$	3.06565	−	9.34567i	0.0997256	−	0.304015i
$946$	0.293332	−	0.169356i	0.00953706	−	0.00550622i
$947$	−1.58573	−	5.91802i	−0.0515292	−	0.192310i	0.935363	−	0.353688i	$-0.115073\pi$
$947$	−1.58573	−	5.91802i	−0.0515292	−	0.192310i	−0.986893	+	0.161379i	$0.948406\pi$
$948$	−0.00858493	+	0.0148695i	−0.000278826	+	0.000482940i
$949$	5.84598	−	37.4469i	0.189769	−	1.21558i
$950$	51.8026	−	29.9082i	1.68070	−	0.970351i
$951$	−19.7590	−	5.29442i	−0.640731	−	0.171683i
$952$	30.4433	+	9.98629i	0.986674	+	0.323657i
$953$	16.2411	+	9.37683i	0.526102	+	0.303745i	0.739428	−	0.673236i	$-0.235096\pi$
$953$	16.2411	+	9.37683i	0.526102	+	0.303745i	−0.213326	+	0.976981i	$0.568430\pi$
$954$	−1.72433	+	6.43528i	−0.0558272	+	0.208350i
$955$	−82.5233	−	22.1121i	−2.67039	−	0.715529i
$956$	2.67400	+	0.716497i	0.0864834	+	0.0231732i
$957$	−5.27765	+	19.6965i	−0.170602	+	0.636696i
$958$	−19.4994	−	11.2580i	−0.629995	−	0.363728i
$959$	40.1421	+	13.1678i	1.29626	+	0.425210i
$960$	22.9139	+	6.13977i	0.739544	+	0.198160i
$961$	22.3217	−	12.8874i	0.720054	−	0.415724i
$962$	3.51655	−	0.377484i	0.113378	−	0.0121706i
$963$	2.66439	−	4.61486i	0.0858588	−	0.148712i
$964$	−0.742908	−	2.77257i	−0.0239275	−	0.0892985i
$965$	25.1199	−	14.5030i	0.808639	−	0.466868i
$966$	2.62112	−	7.99052i	0.0843332	−	0.257091i
$967$	−37.6662	−	37.6662i	−1.21126	−	1.21126i	−0.970611	−	0.240652i	$-0.922639\pi$
$967$	−37.6662	−	37.6662i	−1.21126	−	1.21126i	−0.240652	−	0.970611i	$-0.577361\pi$
$968$	12.7289	+	12.7289i	0.409121	+	0.409121i
$969$	−5.44825	+	20.3331i	−0.175023	+	0.653194i
$970$	−18.0986	−	67.5448i	−0.581110	−	2.16873i
$971$		−	26.2439i		−	0.842207i	−0.907012	−	0.421104i	$-0.861643\pi$
$971$		−	26.2439i		−	0.842207i	0.907012	−	0.421104i	$-0.138357\pi$
$972$	−0.156950	−	0.271846i	−0.00503418	−	0.00871945i
$973$	−23.8517	−	15.5849i	−0.764651	−	0.499630i
$974$		−	50.4340i		−	1.61601i
$975$	18.7490	+	25.6860i	0.600450	+	0.822609i
$976$	26.4817	+	15.2892i	0.847660	+	0.489397i
$977$	−0.0635239	−	0.0635239i	−0.00203231	−	0.00203231i	0.706090	−	0.708122i	$-0.250457\pi$
$977$	−0.0635239	−	0.0635239i	−0.00203231	−	0.00203231i	−0.708122	+	0.706090i	$0.750457\pi$
$978$	−1.53173	−	0.884344i	−0.0489793	−	0.0282782i
$979$	7.14054	−	12.3678i	0.228213	−	0.395276i
$980$	−8.07500	+	1.23248i	−0.257947	+	0.0393702i
$981$	10.8027	−	2.89458i	0.344905	−	0.0924169i
$982$	21.3168	−	21.3168i	0.680245	−	0.680245i
$983$	20.0941	−	5.38419i	0.640902	−	0.171729i	0.0762899	−	0.997086i	$-0.475693\pi$
$983$	20.0941	−	5.38419i	0.640902	−	0.171729i	0.564612	+	0.825357i	$0.309026\pi$
$984$	11.6997	+	20.2645i	0.372973	+	0.646009i
$985$	18.7226	−	32.4284i	0.596550	−	1.03326i
$986$	18.9965	−	70.8958i	0.604971	−	2.25778i
$987$	11.2696	+	3.69677i	0.358717	+	0.117669i
$988$	−3.92848	−	3.16683i	−0.124982	−	0.100750i
$989$	−0.116588	−	0.201936i	−0.00370728	−	0.00642120i
$990$	7.97866	−	7.97866i	0.253579	−	0.253579i
$991$	20.5308			0.652181			0.326090	−	0.945339i	$-0.394269\pi$
$991$	20.5308			0.652181			0.326090	+	0.945339i	$0.394269\pi$
$992$	−4.02328			−0.127739
$993$	−14.8316	+	14.8316i	−0.470666	+	0.470666i
$994$	−53.8327	+	27.2389i	−1.70747	+	0.863965i
$995$	−7.39937	−	27.6148i	−0.234576	−	0.875449i
$996$	3.88135	+	1.04000i	0.122985	+	0.0329538i
$997$	49.2601	−	28.4403i	1.56008	−	0.900714i	0.562836	−	0.826569i	$-0.309710\pi$
$997$	49.2601	−	28.4403i	1.56008	−	0.900714i	0.997247	−	0.0741457i	$-0.0236230\pi$
$998$		−	35.3089i		−	1.11768i
$999$	−0.622880	+	0.166900i	−0.0197071	+	0.00528049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.115.4	yes	40
3.2	odd	2		819.2.gh.d.388.7		40
7.5	odd	6		273.2.bt.b.271.7	yes	40
13.6	odd	12		273.2.bt.b.136.7	✓	40
21.5	even	6		819.2.et.d.271.4		40
39.32	even	12		819.2.et.d.136.4		40
91.19	even	12	inner	273.2.cg.b.19.4	yes	40
273.110	odd	12		819.2.gh.d.19.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.7	✓	40	13.6	odd	12
273.2.bt.b.271.7	yes	40	7.5	odd	6
273.2.cg.b.19.4	yes	40	91.19	even	12	inner
273.2.cg.b.115.4	yes	40	1.1	even	1	trivial
819.2.et.d.136.4		40	39.32	even	12
819.2.et.d.271.4		40	21.5	even	6
819.2.gh.d.19.7		40	273.110	odd	12
819.2.gh.d.388.7		40	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46932 + 0.393703i) q^{2} -1.00000i q^{3} +(0.271846 - 0.156950i) q^{4} +(-3.59085 - 0.962166i) q^{5} +(0.393703 + 1.46932i) q^{6} +(2.64173 + 0.145891i) q^{7} +(1.81360 - 1.81360i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.46932 + 0.393703i) q^{2} -1.00000i q^{3} +(0.271846 - 0.156950i) q^{4} +(-3.59085 - 0.962166i) q^{5} +(0.393703 + 1.46932i) q^{6} +(2.64173 + 0.145891i) q^{7} +(1.81360 - 1.81360i) q^{8} -1.00000 q^{9} +5.65491 q^{10} +(-1.41093 + 1.41093i) q^{11} +(-0.156950 - 0.271846i) q^{12} +(-1.45921 + 3.29708i) q^{13} +(-3.93898 + 0.825695i) q^{14} +(-0.962166 + 3.59085i) q^{15} +(-2.26463 + 3.92246i) q^{16} +(2.36075 + 4.08893i) q^{17} +(1.46932 - 0.393703i) q^{18} +(-3.15258 + 3.15258i) q^{19} +(-1.12717 + 0.302024i) q^{20} +(0.145891 - 2.64173i) q^{21} +(1.51761 - 2.62859i) q^{22} +(-1.80957 - 1.04476i) q^{23} +(-1.81360 - 1.81360i) q^{24} +(7.63832 + 4.40999i) q^{25} +(0.845973 - 5.41895i) q^{26} +1.00000i q^{27} +(0.741039 - 0.374959i) q^{28} +(5.10970 + 8.85026i) q^{29} -5.65491i q^{30} +(-0.591623 - 2.20797i) q^{31} +(0.455541 - 1.70010i) q^{32} +(1.41093 + 1.41093i) q^{33} +(-5.07852 - 5.07852i) q^{34} +(-9.34567 - 3.06565i) q^{35} +(-0.271846 + 0.156950i) q^{36} +(0.166900 + 0.622880i) q^{37} +(3.39097 - 5.87333i) q^{38} +(3.29708 + 1.45921i) q^{39} +(-8.25733 + 4.76737i) q^{40} +(-8.81239 - 2.36127i) q^{41} +(0.825695 + 3.93898i) q^{42} +(0.0966425 + 0.0557966i) q^{43} +(-0.162109 + 0.604999i) q^{44} +(3.59085 + 0.962166i) q^{45} +(3.07017 + 0.822648i) q^{46} +(-1.16024 + 4.33009i) q^{47} +(3.92246 + 2.26463i) q^{48} +(6.95743 + 0.770807i) q^{49} +(-12.9594 - 3.47245i) q^{50} +(4.08893 - 2.36075i) q^{51} +(0.120797 + 1.12532i) q^{52} +(-2.18989 + 3.79299i) q^{53} +(-0.393703 - 1.46932i) q^{54} +(6.42397 - 3.70888i) q^{55} +(5.05561 - 4.52644i) q^{56} +(3.15258 + 3.15258i) q^{57} +(-10.9921 - 10.9921i) q^{58} +(0.438963 - 1.63823i) q^{59} +(0.302024 + 1.12717i) q^{60} -6.75131i q^{61} +(1.73857 + 3.01128i) q^{62} +(-2.64173 - 0.145891i) q^{63} -6.38120i q^{64} +(8.41213 - 10.4353i) q^{65} +(-2.62859 - 1.51761i) q^{66} +(-2.10721 - 2.10721i) q^{67} +(1.28352 + 0.741039i) q^{68} +(-1.04476 + 1.80957i) q^{69} +(14.9387 + 0.825000i) q^{70} +(14.4800 - 3.87990i) q^{71} +(-1.81360 + 1.81360i) q^{72} +(-10.1535 + 2.72063i) q^{73} +(-0.490459 - 0.849500i) q^{74} +(4.40999 - 7.63832i) q^{75} +(-0.362217 + 1.35181i) q^{76} +(-3.93312 + 3.52144i) q^{77} +(-5.41895 - 0.845973i) q^{78} +(-0.0273492 - 0.0473702i) q^{79} +(11.9060 - 11.9060i) q^{80} +1.00000 q^{81} +13.8778 q^{82} +(-9.05174 + 9.05174i) q^{83} +(-0.374959 - 0.741039i) q^{84} +(-4.54286 - 16.9542i) q^{85} +(-0.163966 - 0.0439346i) q^{86} +(8.85026 - 5.10970i) q^{87} +5.11770i q^{88} +(-6.91330 + 1.85241i) q^{89} -5.65491 q^{90} +(-4.33584 + 8.49709i) q^{91} -0.655900 q^{92} +(-2.20797 + 0.591623i) q^{93} -6.81908i q^{94} +(14.3537 - 8.28714i) q^{95} +(-1.70010 - 0.455541i) q^{96} +(-3.20050 - 11.9444i) q^{97} +(-10.5262 + 1.60660i) q^{98} +(1.41093 - 1.41093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Introduction

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