LMFDB - Embedded newform 122.2.f.a.75.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(75,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("122.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.f (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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.110502144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 11x^{6} - 14x^{5} + 7x^{4} + 18x^{3} - 18x^{2} - 36x + 36 $ x^8 - 4x^7 + 11x^6 - 14x^5 + 7x^4 + 18x^3 - 18x^2 - 36*x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			75.2
Root			$-0.991555 - 0.533636i$ of defining polynomial
Character	$\chi$	$=$	122.75
Dual form			122.2.f.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +1.25106 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.99156 - 3.44948i) q^{5} +(-1.08345 + 0.625530i) q^{6} +(4.15633 - 2.39966i) q^{7} +1.00000i q^{8} -1.43485 q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +1.25106 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.99156 - 3.44948i) q^{5} +(-1.08345 + 0.625530i) q^{6} +(4.15633 - 2.39966i) q^{7} +1.00000i q^{8} -1.43485 q^{9} +(3.44948 + 1.99156i) q^{10} +5.15001i q^{11} +(0.625530 - 1.08345i) q^{12} +(-0.125530 - 0.217424i) q^{13} +(-2.39966 + 4.15633i) q^{14} +(-2.49156 - 4.31550i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.55038 + 2.04981i) q^{17} +(1.24262 - 0.717424i) q^{18} +(0.441741 - 0.765118i) q^{19} -3.98311 q^{20} +(5.19982 - 3.00212i) q^{21} +(-2.57501 - 4.46004i) q^{22} -0.451738i q^{23} +1.25106i q^{24} +(-5.43259 + 9.40952i) q^{25} +(0.217424 + 0.125530i) q^{26} -5.54826 q^{27} -4.79932i q^{28} +(-2.07572 - 1.19842i) q^{29} +(4.31550 + 2.49156i) q^{30} +(0.575716 + 0.332390i) q^{31} +(0.866025 + 0.500000i) q^{32} +6.44297i q^{33} -4.09963 q^{34} +(-16.5551 - 9.55812i) q^{35} +(-0.717424 + 1.24262i) q^{36} +9.33380i q^{37} +0.883483i q^{38} +(-0.157046 - 0.272011i) q^{39} +(3.44948 - 1.99156i) q^{40} +3.96198 q^{41} +(-3.00212 + 5.19982i) q^{42} +(-0.590342 + 0.340834i) q^{43} +(4.46004 + 2.57501i) q^{44} +(2.85758 + 4.94948i) q^{45} +(0.225869 + 0.391216i) q^{46} +(-1.40811 + 2.43891i) q^{47} +(-0.625530 - 1.08345i) q^{48} +(8.01675 - 13.8854i) q^{49} -10.8652i q^{50} +(4.44174 + 2.56444i) q^{51} -0.251060 q^{52} -3.83168i q^{53} +(4.80494 - 2.77413i) q^{54} +(17.7648 - 10.2565i) q^{55} +(2.39966 + 4.15633i) q^{56} +(0.552645 - 0.957209i) q^{57} +2.39683 q^{58} +(6.30861 - 3.64228i) q^{59} -4.98311 q^{60} +(-3.46410 + 7.00000i) q^{61} -0.664779 q^{62} +(-5.96371 + 3.44315i) q^{63} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-3.22149 - 5.57978i) q^{66} +(-8.67855 + 5.01056i) q^{67} +(3.55038 - 2.04981i) q^{68} -0.565151i q^{69} +19.1162 q^{70} +(-5.35630 - 3.09246i) q^{71} -1.43485i q^{72} +(0.447355 - 0.774842i) q^{73} +(-4.66690 - 8.08331i) q^{74} +(-6.79649 + 11.7719i) q^{75} +(-0.441741 - 0.765118i) q^{76} +(12.3583 + 21.4052i) q^{77} +(0.272011 + 0.157046i) q^{78} +(5.28342 - 3.05038i) q^{79} +(-1.99156 + 3.44948i) q^{80} -2.63666 q^{81} +(-3.43118 + 1.98099i) q^{82} +(2.89348 + 5.01165i) q^{83} -6.00424i q^{84} -16.3293i q^{85} +(0.340834 - 0.590342i) q^{86} +(-2.59685 - 1.49929i) q^{87} -5.15001 q^{88} -7.71516i q^{89} +(-4.94948 - 2.85758i) q^{90} +(-1.04349 - 0.602459i) q^{91} +(-0.391216 - 0.225869i) q^{92} +(0.720255 + 0.415840i) q^{93} -2.81621i q^{94} -3.51901 q^{95} +(1.08345 + 0.625530i) q^{96} +(-6.59963 + 11.4309i) q^{97} +16.0335i q^{98} -7.38949i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9	$ 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9} + 6 q^{10} + 4 q^{13} - 10 q^{14} - 8 q^{15} - 4 q^{16} - 12 q^{18} + 4 q^{19} - 8 q^{20} - 24 q^{21} + 6 q^{22} + 2 q^{25} - 6 q^{26} - 36 q^{27} - 24 q^{29} + 6 q^{30} + 12 q^{31} - 8 q^{34} - 18 q^{35} + 2 q^{36} - 14 q^{39} + 6 q^{40} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 6 q^{44} + 4 q^{45} + 6 q^{46} - 14 q^{47} + 38 q^{49} + 36 q^{51} + 8 q^{52} + 18 q^{54} + 42 q^{55} + 10 q^{56} + 6 q^{57} - 4 q^{58} + 6 q^{59} - 16 q^{60} + 4 q^{62} + 6 q^{63} - 8 q^{64} - 4 q^{65} - 20 q^{66} + 30 q^{67} + 52 q^{70} - 6 q^{71} + 2 q^{73} - 8 q^{74} - 22 q^{75} - 4 q^{76} - 8 q^{77} + 18 q^{78} + 12 q^{79} - 4 q^{80} + 8 q^{81} - 36 q^{82} + 32 q^{83} + 10 q^{86} - 12 q^{87} + 12 q^{88} - 18 q^{90} + 36 q^{91} + 18 q^{92} + 12 q^{93} - 32 q^{95} - 6 q^{96} - 28 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9 + 6 * q^10 + 4 * q^13 - 10 * q^14 - 8 * q^15 - 4 * q^16 - 12 * q^18 + 4 * q^19 - 8 * q^20 - 24 * q^21 + 6 * q^22 + 2 * q^25 - 6 * q^26 - 36 * q^27 - 24 * q^29 + 6 * q^30 + 12 * q^31 - 8 * q^34 - 18 * q^35 + 2 * q^36 - 14 * q^39 + 6 * q^40 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 6 * q^44 + 4 * q^45 + 6 * q^46 - 14 * q^47 + 38 * q^49 + 36 * q^51 + 8 * q^52 + 18 * q^54 + 42 * q^55 + 10 * q^56 + 6 * q^57 - 4 * q^58 + 6 * q^59 - 16 * q^60 + 4 * q^62 + 6 * q^63 - 8 * q^64 - 4 * q^65 - 20 * q^66 + 30 * q^67 + 52 * q^70 - 6 * q^71 + 2 * q^73 - 8 * q^74 - 22 * q^75 - 4 * q^76 - 8 * q^77 + 18 * q^78 + 12 * q^79 - 4 * q^80 + 8 * q^81 - 36 * q^82 + 32 * q^83 + 10 * q^86 - 12 * q^87 + 12 * q^88 - 18 * q^90 + 36 * q^91 + 18 * q^92 + 12 * q^93 - 32 * q^95 - 6 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.25106			0.722300			0.361150	−	0.932508i	$-0.382384\pi$
$3$	1.25106			0.722300			0.361150	+	0.932508i	$0.382384\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.99156	−	3.44948i	−0.890651	−	1.54265i	−0.839097	−	0.543982i	$-0.816916\pi$
$5$	−1.99156	−	3.44948i	−0.890651	−	1.54265i	−0.0515538	−	0.998670i	$-0.516417\pi$
$6$	−1.08345	+	0.625530i	−0.442317	+	0.255372i
$7$	4.15633	−	2.39966i	1.57095	−	0.906987i	0.574894	−	0.818228i	$-0.305043\pi$
$7$	4.15633	−	2.39966i	1.57095	−	0.906987i	0.996053	−	0.0887586i	$-0.0282900\pi$
$8$			1.00000i			0.353553i
$9$	−1.43485			−0.478283
$10$	3.44948	+	1.99156i	1.09082	+	0.629785i
$11$			5.15001i			1.55279i	0.630249	+	0.776393i	$0.282953\pi$
$11$			5.15001i			1.55279i	−0.630249	+	0.776393i	$0.717047\pi$
$12$	0.625530	−	1.08345i	0.180575	−	0.312765i
$13$	−0.125530	−	0.217424i	−0.0348158	−	0.0603027i	0.848092	−	0.529848i	$-0.177751\pi$
$13$	−0.125530	−	0.217424i	−0.0348158	−	0.0603027i	−0.882908	+	0.469546i	$0.844418\pi$
$14$	−2.39966	+	4.15633i	−0.641336	+	1.11083i
$15$	−2.49156	−	4.31550i	−0.643317	−	1.11426i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.55038	+	2.04981i	0.861094	+	0.497153i	0.864379	−	0.502842i	$-0.167712\pi$
$17$	3.55038	+	2.04981i	0.861094	+	0.497153i	−0.00328438	+	0.999995i	$0.501045\pi$
$18$	1.24262	−	0.717424i	0.292887	−	0.169099i
$19$	0.441741	−	0.765118i	0.101342	−	0.175530i	−0.810896	−	0.585191i	$-0.801020\pi$
$19$	0.441741	−	0.765118i	0.101342	−	0.175530i	0.912238	+	0.409661i	$0.134353\pi$
$20$	−3.98311			−0.890651
$21$	5.19982	−	3.00212i	1.13469	−	0.655116i
$22$	−2.57501	−	4.46004i	−0.548993	−	0.950884i
$23$		−	0.451738i		−	0.0941939i	−0.998890	−	0.0470969i	$-0.985003\pi$
$23$		−	0.451738i		−	0.0941939i	0.998890	−	0.0470969i	$-0.0149970\pi$
$24$			1.25106i			0.255372i
$25$	−5.43259	+	9.40952i	−1.08652	+	1.88190i
$26$	0.217424	+	0.125530i	0.0426404	+	0.0246185i
$27$	−5.54826			−1.06776
$28$		−	4.79932i		−	0.906987i
$29$	−2.07572	−	1.19842i	−0.385451	−	0.222540i	0.294736	−	0.955579i	$-0.404768\pi$
$29$	−2.07572	−	1.19842i	−0.385451	−	0.222540i	−0.680187	+	0.733038i	$0.738101\pi$
$30$	4.31550	+	2.49156i	0.787899	+	0.454894i
$31$	0.575716	+	0.332390i	0.103402	+	0.0596990i	0.550809	−	0.834631i	$-0.314319\pi$
$31$	0.575716	+	0.332390i	0.103402	+	0.0596990i	−0.447407	+	0.894330i	$0.647653\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$			6.44297i			1.12158i
$34$	−4.09963			−0.703080
$35$	−16.5551	−	9.55812i	−2.79833	−	1.61562i
$36$	−0.717424	+	1.24262i	−0.119571	+	0.207103i
$37$			9.33380i			1.53447i	0.641368	+	0.767234i	$0.278367\pi$
$37$			9.33380i			1.53447i	−0.641368	+	0.767234i	$0.721633\pi$
$38$			0.883483i			0.143320i
$39$	−0.157046	−	0.272011i	−0.0251474	−	0.0435566i
$40$	3.44948	−	1.99156i	0.545410	−	0.314893i
$41$	3.96198			0.618758			0.309379	−	0.950939i	$-0.399879\pi$
$41$	3.96198			0.618758			0.309379	+	0.950939i	$0.399879\pi$
$42$	−3.00212	+	5.19982i	−0.463237	+	0.802350i
$43$	−0.590342	+	0.340834i	−0.0900264	+	0.0519767i	−0.544337	−	0.838866i	$-0.683219\pi$
$43$	−0.590342	+	0.340834i	−0.0900264	+	0.0519767i	0.454311	+	0.890843i	$0.349886\pi$
$44$	4.46004	+	2.57501i	0.672376	+	0.388197i
$45$	2.85758	+	4.94948i	0.425983	+	0.737824i
$46$	0.225869	+	0.391216i	0.0333026	+	0.0576817i
$47$	−1.40811	+	2.43891i	−0.205393	+	0.355752i	−0.950258	−	0.311464i	$-0.899181\pi$
$47$	−1.40811	+	2.43891i	−0.205393	+	0.355752i	0.744865	+	0.667216i	$0.232514\pi$
$48$	−0.625530	−	1.08345i	−0.0902875	−	0.156383i
$49$	8.01675	−	13.8854i	1.14525	−	1.98363i
$50$		−	10.8652i		−	1.53657i
$51$	4.44174	+	2.56444i	0.621968	+	0.359094i
$52$	−0.251060			−0.0348158
$53$		−	3.83168i		−	0.526322i	−0.964752	−	0.263161i	$-0.915235\pi$
$53$		−	3.83168i		−	0.526322i	0.964752	−	0.263161i	$-0.0847650\pi$
$54$	4.80494	−	2.77413i	0.653869	−	0.377511i
$55$	17.7648	−	10.2565i	2.39541	−	1.38299i
$56$	2.39966	+	4.15633i	0.320668	+	0.555414i
$57$	0.552645	−	0.957209i	0.0731996	−	0.126785i
$58$	2.39683			0.314719
$59$	6.30861	−	3.64228i	0.821311	−	0.474184i	−0.0295575	−	0.999563i	$-0.509410\pi$
$59$	6.30861	−	3.64228i	0.821311	−	0.474184i	0.850868	+	0.525379i	$0.176076\pi$
$60$	−4.98311			−0.643317
$61$	−3.46410	+	7.00000i	−0.443533	+	0.896258i
$61$	−3.46410	+	7.00000i	−0.443533	+	0.896258i
$62$	−0.664779			−0.0844271
$63$	−5.96371	+	3.44315i	−0.751357	+	0.433796i
$64$	−1.00000			−0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	−3.22149	−	5.57978i	−0.396538	−	0.686823i
$67$	−8.67855	+	5.01056i	−1.06025	+	0.612138i	−0.925502	−	0.378742i	$-0.876357\pi$
$67$	−8.67855	+	5.01056i	−1.06025	+	0.612138i	−0.134751	+	0.990879i	$0.543024\pi$
$68$	3.55038	−	2.04981i	0.430547	−	0.248576i
$69$		−	0.565151i		−	0.0680362i
$70$	19.1162			2.28483
$71$	−5.35630	−	3.09246i	−0.635676	−	0.367008i	0.147271	−	0.989096i	$-0.452951\pi$
$71$	−5.35630	−	3.09246i	−0.635676	−	0.367008i	−0.782947	+	0.622088i	$0.786284\pi$
$72$		−	1.43485i		−	0.169099i
$73$	0.447355	−	0.774842i	0.0523590	−	0.0906884i	−0.838658	−	0.544658i	$-0.816659\pi$
$73$	0.447355	−	0.774842i	0.0523590	−	0.0906884i	0.891017	+	0.453970i	$0.149993\pi$
$74$	−4.66690	−	8.08331i	−0.542516	−	0.939665i
$75$	−6.79649	+	11.7719i	−0.784791	+	1.35930i
$76$	−0.441741	−	0.765118i	−0.0506712	−	0.0877651i
$77$	12.3583	+	21.4052i	1.40836	+	2.43935i
$78$	0.272011	+	0.157046i	0.0307992	+	0.0177819i
$79$	5.28342	−	3.05038i	0.594431	−	0.343195i	−0.172417	−	0.985024i	$-0.555158\pi$
$79$	5.28342	−	3.05038i	0.594431	−	0.343195i	0.766848	+	0.641829i	$0.221824\pi$
$80$	−1.99156	+	3.44948i	−0.222663	+	0.385663i
$81$	−2.63666			−0.292963
$82$	−3.43118	+	1.98099i	−0.378910	+	0.218764i
$83$	2.89348	+	5.01165i	0.317601	+	0.550100i	0.979987	−	0.199062i	$-0.0637895\pi$
$83$	2.89348	+	5.01165i	0.317601	+	0.550100i	−0.662386	+	0.749162i	$0.730456\pi$
$84$		−	6.00424i		−	0.655116i
$85$		−	16.3293i		−	1.77116i
$86$	0.340834	−	0.590342i	0.0367531	−	0.0636583i
$87$	−2.59685	−	1.49929i	−0.278411	−	0.160741i
$88$	−5.15001			−0.548993
$89$		−	7.71516i		−	0.817806i	−0.912578	−	0.408903i	$-0.865912\pi$
$89$		−	7.71516i		−	0.817806i	0.912578	−	0.408903i	$-0.134088\pi$
$90$	−4.94948	−	2.85758i	−0.521720	−	0.301215i
$91$	−1.04349	−	0.602459i	−0.109387	−	0.0631549i
$92$	−0.391216	−	0.225869i	−0.0407871	−	0.0235485i
$93$	0.720255	+	0.415840i	0.0746870	+	0.0431205i
$94$		−	2.81621i		−	0.290470i
$95$	−3.51901			−0.361043
$96$	1.08345	+	0.625530i	0.110579	+	0.0638429i
$97$	−6.59963	+	11.4309i	−0.670091	+	1.16063i	0.307787	+	0.951455i	$0.400411\pi$
$97$	−6.59963	+	11.4309i	−0.670091	+	1.16063i	−0.977878	+	0.209176i	$0.932922\pi$
$98$			16.0335i			1.61963i
$99$		−	7.38949i		−	0.742671i
$100$	5.43259	+	9.40952i	0.543259	+	0.940952i
$101$	−2.21757	+	1.28031i	−0.220656	+	0.127396i	−0.606254	−	0.795271i	$-0.707329\pi$
$101$	−2.21757	+	1.28031i	−0.220656	+	0.127396i	0.385598	+	0.922667i	$0.373995\pi$
$102$	−5.12888			−0.507835
$103$	5.80918	−	10.0618i	0.572395	−	0.991417i	−0.423924	−	0.905698i	$-0.639348\pi$
$103$	5.80918	−	10.0618i	0.572395	−	0.991417i	0.996319	−	0.0857198i	$-0.0273190\pi$
$104$	0.217424	−	0.125530i	0.0213202	−	0.0123092i
$105$	−20.7115	−	11.9578i	−2.02123	−	1.16696i
$106$	1.91584	+	3.31833i	0.186083	+	0.322305i
$107$	−7.36305	−	12.7532i	−0.711813	−	1.23290i	−0.964176	−	0.265264i	$-0.914541\pi$
$107$	−7.36305	−	12.7532i	−0.711813	−	1.23290i	0.252363	−	0.967633i	$-0.418792\pi$
$108$	−2.77413	+	4.80494i	−0.266941	+	0.462355i
$109$	0.372918	+	0.645913i	0.0357191	+	0.0618672i	0.883332	−	0.468747i	$-0.155295\pi$
$109$	0.372918	+	0.645913i	0.0357191	+	0.0618672i	−0.847613	+	0.530615i	$0.821961\pi$
$110$	−10.2565	+	17.7648i	−0.977922	+	1.69381i
$111$			11.6771i			1.10835i
$112$	−4.15633	−	2.39966i	−0.392737	−	0.226747i
$113$	−0.0337783			−0.00317759			−0.00158880	−	0.999999i	$-0.500506\pi$
$113$	−0.0337783			−0.00317759			−0.00158880	+	0.999999i	$0.500506\pi$
$114$			1.10529i			0.103520i
$115$	−1.55826	+	0.899661i	−0.145308	+	0.0838938i
$116$	−2.07572	+	1.19842i	−0.192725	+	0.111270i
$117$	0.180117	+	0.311971i	0.0166518	+	0.0288417i
$118$	−3.64228	+	6.30861i	−0.335299	+	0.580754i
$119$	19.6754			1.80364
$120$	4.31550	−	2.49156i	0.393950	−	0.227447i
$121$	−15.5226			−1.41115
$122$	−0.500000	−	7.79423i	−0.0452679	−	0.705656i
$123$	4.95668			0.446928
$124$	0.575716	−	0.332390i	0.0517008	−	0.0298495i
$125$	23.3616			2.08953
$126$	3.44315	−	5.96371i	0.306740	−	0.531290i
$127$	0.932018	+	1.61430i	0.0827032	+	0.143246i	0.904410	−	0.426664i	$-0.140311\pi$
$127$	0.932018	+	1.61430i	0.0827032	+	0.143246i	−0.821707	+	0.569910i	$0.806978\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−0.738554	+	0.426404i	−0.0650260	+	0.0375428i
$130$		−	1.00000i		−	0.0877058i
$131$	5.83980			0.510226			0.255113	−	0.966911i	$-0.417887\pi$
$131$	5.83980			0.510226			0.255113	+	0.966911i	$0.417887\pi$
$132$	5.57978	+	3.22149i	0.485657	+	0.280394i
$133$		−	4.24012i		−	0.367665i
$134$	5.01056	−	8.67855i	0.432847	−	0.749713i
$135$	11.0497	+	19.1386i	0.951004	+	1.64719i
$136$	−2.04981	+	3.55038i	−0.175770	+	0.304443i
$137$	3.34758	+	5.79819i	0.286003	+	0.495372i	0.972852	−	0.231428i	$-0.0743398\pi$
$137$	3.34758	+	5.79819i	0.286003	+	0.495372i	−0.686849	+	0.726801i	$0.741006\pi$
$138$	0.282576	+	0.489435i	0.0240544	+	0.0416635i
$139$	−15.9745	−	9.22290i	−1.35494	−	0.782276i	−0.366005	−	0.930613i	$-0.619275\pi$
$139$	−15.9745	−	9.22290i	−1.35494	−	0.782276i	−0.988937	+	0.148337i	$0.952608\pi$
$140$	−16.5551	+	9.55812i	−1.39916	+	0.807808i
$141$	−1.76162	+	3.05122i	−0.148356	+	0.256959i
$142$	6.18492			0.519027
$143$	1.11974	−	0.646481i	0.0936372	−	0.0540615i
$144$	0.717424	+	1.24262i	0.0597854	+	0.103551i
$145$			9.54684i			0.792822i
$146$			0.894710i			0.0740467i
$147$	10.0294	−	17.3715i	0.827214	−	1.43278i
$148$	8.08331	+	4.66690i	0.664444	+	0.383617i
$149$	−18.6338			−1.52654			−0.763271	−	0.646078i	$-0.776408\pi$
$149$	−18.6338			−1.52654			−0.763271	+	0.646078i	$0.776408\pi$
$150$		−	13.5930i		−	1.10986i
$151$	3.34758	+	1.93273i	0.272423	+	0.157283i	0.629988	−	0.776605i	$-0.283060\pi$
$151$	3.34758	+	1.93273i	0.272423	+	0.157283i	−0.357565	+	0.933888i	$0.616393\pi$
$152$	0.765118	+	0.441741i	0.0620593	+	0.0358300i
$153$	−5.09426	−	2.94117i	−0.411847	−	0.237780i
$154$	−21.4052	−	12.3583i	−1.72488	−	0.995859i
$155$		−	2.64789i		−	0.212684i
$156$	−0.314091			−0.0251474
$157$	−8.28734	−	4.78470i	−0.661401	−	0.381860i	0.131409	−	0.991328i	$-0.458050\pi$
$157$	−8.28734	−	4.78470i	−0.661401	−	0.381860i	−0.792811	+	0.609468i	$0.791383\pi$
$158$	−3.05038	+	5.28342i	−0.242675	+	0.420326i
$159$		−	4.79366i		−	0.380162i
$160$		−	3.98311i		−	0.314893i
$161$	−1.08402	−	1.87757i	−0.0854326	−	0.147974i
$162$	2.28342	−	1.31833i	0.179402	−	0.103578i
$163$	−0.367577			−0.0287909			−0.0143954	−	0.999896i	$-0.504582\pi$
$163$	−0.367577			−0.0287909			−0.0143954	+	0.999896i	$0.504582\pi$
$164$	1.98099	−	3.43118i	0.154689	−	0.267930i
$165$	22.2249	−	12.8315i	1.73020	−	0.998934i
$166$	−5.01165	−	2.89348i	−0.388980	−	0.224578i
$167$	−1.39683	−	2.41938i	−0.108090	−	0.187217i	0.806906	−	0.590679i	$-0.201140\pi$
$167$	−1.39683	−	2.41938i	−0.108090	−	0.187217i	−0.914996	+	0.403462i	$0.867807\pi$
$168$	3.00212	+	5.19982i	0.231619	+	0.401175i
$169$	6.46848	−	11.2037i	0.497576	−	0.861826i
$170$	8.16464	+	14.1416i	0.626199	+	1.08461i
$171$	−0.633832	+	1.09783i	−0.0484703	+	0.0839531i
$172$			0.681669i			0.0519767i
$173$	−6.70251	−	3.86970i	−0.509583	−	0.294208i	0.223079	−	0.974800i	$-0.428389\pi$
$173$	−6.70251	−	3.86970i	−0.509583	−	0.294208i	−0.732662	+	0.680593i	$0.761722\pi$
$174$	2.99858			0.227322
$175$			52.1455i			3.94183i
$176$	4.46004	−	2.57501i	0.336188	−	0.194098i
$177$	7.89245	−	4.55671i	0.593233	−	0.342503i
$178$	3.85758	+	6.68153i	0.289138	+	0.500802i
$179$	−3.03066	+	5.24926i	−0.226522	+	0.392348i	−0.956775	−	0.290829i	$-0.906069\pi$
$179$	−3.03066	+	5.24926i	−0.226522	+	0.392348i	0.730253	+	0.683177i	$0.239402\pi$
$180$	5.71516			0.425983
$181$	11.3763	−	6.56811i	0.845594	−	0.488204i	−0.0135677	−	0.999908i	$-0.504319\pi$
$181$	11.3763	−	6.56811i	0.845594	−	0.488204i	0.859162	+	0.511704i	$0.170986\pi$
$182$	1.20492			0.0893145
$183$	−4.33380	+	8.75742i	−0.320364	+	0.647367i
$184$	0.451738			0.0333026
$185$	32.1967	−	18.5888i	2.36715	−	1.36667i
$186$	−0.831679			−0.0609817
$187$	−10.5566	+	18.2845i	−0.771972	+	1.33710i
$188$	1.40811	+	2.43891i	0.102697	+	0.177876i
$189$	−23.0604	+	13.3139i	−1.67740	+	0.968447i
$190$	3.04755	−	1.75950i	0.221093	−	0.127648i
$191$		−	21.5792i		−	1.56142i	−0.624896	−	0.780708i	$-0.714859\pi$
$191$		−	21.5792i		−	1.56142i	0.624896	−	0.780708i	$-0.285141\pi$
$192$	−1.25106			−0.0902875
$193$	1.23388	+	0.712379i	0.0888163	+	0.0512781i	0.543750	−	0.839247i	$-0.317004\pi$
$193$	1.23388	+	0.712379i	0.0888163	+	0.0512781i	−0.454934	+	0.890525i	$0.650337\pi$
$194$		−	13.1993i		−	0.947651i
$195$	−0.625530	+	1.08345i	−0.0447951	+	0.0775875i
$196$	−8.01675	−	13.8854i	−0.572625	−	0.991815i
$197$	13.5637	−	23.4931i	0.966376	−	1.67381i	0.260503	−	0.965473i	$-0.416112\pi$
$197$	13.5637	−	23.4931i	0.966376	−	1.67381i	0.705873	−	0.708339i	$-0.250555\pi$
$198$	3.69474	+	6.39948i	0.262574	+	0.454791i
$199$	−6.79681	−	11.7724i	−0.481813	−	0.834525i	0.517969	−	0.855399i	$-0.326688\pi$
$199$	−6.79681	−	11.7724i	−0.481813	−	0.834525i	−0.999782	+	0.0208744i	$0.993355\pi$
$200$	−9.40952	−	5.43259i	−0.665353	−	0.384142i
$201$	−10.8574	+	6.26852i	−0.765821	+	0.442147i
$202$	1.28031	−	2.21757i	0.0900825	−	0.156027i
$203$	−11.5032			−0.807364
$204$	4.44174	−	2.56444i	0.310984	−	0.179547i
$205$	−7.89051	−	13.6668i	−0.551097	−	0.954528i
$206$			11.6184i			0.809489i
$207$			0.648176i			0.0450513i
$208$	−0.125530	+	0.217424i	−0.00870394	+	0.0150757i
$209$	3.94037	+	2.27497i	0.272561	+	0.157363i
$210$	23.9156			1.65033
$211$			14.7613i			1.01621i	0.861295	+	0.508105i	$0.169654\pi$
$211$			14.7613i			1.01621i	−0.861295	+	0.508105i	$0.830346\pi$
$212$	−3.31833	−	1.91584i	−0.227904	−	0.131580i
$213$	−6.70106	−	3.86886i	−0.459149	−	0.265090i
$214$	12.7532	+	7.36305i	0.871789	+	0.503328i
$215$	2.35140	+	1.35758i	0.160364	+	0.0925862i
$216$		−	5.54826i		−	0.377511i
$217$	3.19049			0.216585
$218$	−0.645913	−	0.372918i	−0.0437467	−	0.0252572i
$219$	0.559668	−	0.969374i	0.0378189	−	0.0655042i
$220$		−	20.5131i		−	1.38299i
$221$		−	1.02925i		−	0.0692350i
$222$	−5.83857	−	10.1127i	−0.391859	−	0.678720i
$223$	−8.59685	+	4.96339i	−0.575687	+	0.332373i	−0.759418	−	0.650603i	$-0.774516\pi$
$223$	−8.59685	+	4.96339i	−0.575687	+	0.332373i	0.183730	+	0.982977i	$0.441183\pi$
$224$	4.79932			0.320668
$225$	7.79494	−	13.5012i	0.519663	−	0.900082i
$226$	0.0292529	−	0.0168891i	0.00194587	−	0.00112345i
$227$	1.95413	+	1.12822i	0.129700	+	0.0748825i	0.563446	−	0.826153i	$-0.309475\pi$
$227$	1.95413	+	1.12822i	0.129700	+	0.0748825i	−0.433746	+	0.901035i	$0.642809\pi$
$228$	−0.552645	−	0.957209i	−0.0365998	−	0.0633927i
$229$	7.35913	+	12.7464i	0.486305	+	0.842305i	0.999876	−	0.0157419i	$-0.00501100\pi$
$229$	7.35913	+	12.7464i	0.486305	+	0.842305i	−0.513571	+	0.858047i	$0.671678\pi$
$230$	0.899661	−	1.55826i	0.0593219	−	0.102749i
$231$	15.4609	+	26.7792i	1.01726	+	1.76194i
$232$	1.19842	−	2.07572i	0.0786798	−	0.136277i
$233$			26.7261i			1.75089i	0.483322	+	0.875443i	$0.339430\pi$
$233$			26.7261i			1.75089i	−0.483322	+	0.875443i	$0.660570\pi$
$234$	−0.311971	−	0.180117i	−0.0203942	−	0.0117746i
$235$	11.2173			0.731735
$236$		−	7.28455i		−	0.474184i
$237$	6.60987	−	3.81621i	0.429357	−	0.247890i
$238$	−17.0394	+	9.83772i	−1.10450	+	0.637685i
$239$	0.213042	+	0.368999i	0.0137805	+	0.0238685i	0.872833	−	0.488018i	$-0.162280\pi$
$239$	0.213042	+	0.368999i	0.0137805	+	0.0238685i	−0.859053	+	0.511887i	$0.828947\pi$
$240$	−2.49156	+	4.31550i	−0.160829	+	0.278564i
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	13.4430	−	7.76130i	0.864147	−	0.498915i
$243$	13.3462			0.856157
$244$	4.33013	+	6.50000i	0.277208	+	0.416120i
$245$	−63.8632			−4.08007
$246$	−4.29261	+	2.47834i	−0.273687	+	0.158013i
$247$	−0.221807			−0.0141133
$248$	−0.332390	+	0.575716i	−0.0211068	+	0.0365580i
$249$	3.61992	+	6.26988i	0.229403	+	0.397337i
$250$	−20.2318	+	11.6808i	−1.27957	+	0.738760i
$251$	22.3307	−	12.8926i	1.40950	−	0.813775i	0.414160	−	0.910204i	$-0.364075\pi$
$251$	22.3307	−	12.8926i	1.40950	−	0.813775i	0.995340	+	0.0964286i	$0.0307420\pi$
$252$			6.88630i			0.433796i
$253$	2.32645			0.146263
$254$	−1.61430	−	0.932018i	−0.101290	−	0.0584800i
$255$		−	20.4289i		−	1.27931i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.91712	+	6.78465i	0.244343	+	0.423215i	0.961947	−	0.273237i	$-0.0880943\pi$
$257$	3.91712	+	6.78465i	0.244343	+	0.423215i	−0.717604	+	0.696452i	$0.754761\pi$
$258$	0.426404	−	0.738554i	0.0265468	−	0.0459803i
$259$	22.3980	+	38.7944i	1.39174	+	2.41057i
$260$	0.500000	+	0.866025i	0.0310087	+	0.0537086i
$261$	2.97834	+	1.71954i	0.184355	+	0.106437i
$262$	−5.05742	+	2.91990i	−0.312448	+	0.180392i
$263$	−10.6592	+	18.4622i	−0.657272	+	1.13843i	0.324047	+	0.946041i	$0.394957\pi$
$263$	−10.6592	+	18.4622i	−0.657272	+	1.13843i	−0.981319	+	0.192388i	$0.938377\pi$
$264$	−6.44297			−0.396538
$265$	−13.2173	+	7.63100i	−0.811931	+	0.468769i
$266$	2.12006	+	3.67205i	0.129989	+	0.225148i
$267$		−	9.65213i		−	0.590701i
$268$			10.0211i			0.612138i
$269$	−8.57609	+	14.8542i	−0.522894	+	0.905678i	0.476751	+	0.879038i	$0.341814\pi$
$269$	−8.57609	+	14.8542i	−0.522894	+	0.905678i	−0.999645	+	0.0266402i	$0.991519\pi$
$270$	−19.1386	−	11.0497i	−1.16474	−	0.672462i
$271$	11.6980			0.710602			0.355301	−	0.934752i	$-0.384378\pi$
$271$	11.6980			0.710602			0.355301	+	0.934752i	$0.384378\pi$
$272$		−	4.09963i		−	0.248576i
$273$	−1.30547	−	0.753712i	−0.0790105	−	0.0456168i
$274$	−5.79819	−	3.34758i	−0.350281	−	0.202235i
$275$	−48.4591	−	27.9779i	−2.92219	−	1.68713i
$276$	−0.489435	−	0.282576i	−0.0294605	−	0.0170091i
$277$		−	9.06047i		−	0.544391i	−0.962242	−	0.272196i	$-0.912250\pi$
$277$		−	9.06047i		−	0.544391i	0.962242	−	0.272196i	$-0.0877498\pi$
$278$	18.4458			1.10631
$279$	−0.826065	−	0.476929i	−0.0494552	−	0.0285530i
$280$	9.55812	−	16.5551i	0.571207	−	0.989359i
$281$			3.76583i			0.224651i	0.993671	+	0.112325i	$0.0358299\pi$
$281$			3.76583i			0.224651i	−0.993671	+	0.112325i	$0.964170\pi$
$282$		−	3.52325i		−	0.209806i
$283$	−11.0882	−	19.2053i	−0.659126	−	1.14164i	−0.980842	−	0.194803i	$-0.937593\pi$
$283$	−11.0882	−	19.2053i	−0.659126	−	1.14164i	0.321717	−	0.946836i	$-0.395740\pi$
$284$	−5.35630	+	3.09246i	−0.317838	+	0.183504i
$285$	−4.40249			−0.260781
$286$	−0.646481	+	1.11974i	−0.0382272	+	0.0662115i
$287$	16.4673	−	9.50741i	0.972035	−	0.561205i
$288$	−1.24262	−	0.717424i	−0.0732218	−	0.0422746i
$289$	−0.0965242	−	0.167185i	−0.00567789	−	0.00983440i
$290$	−4.77342	−	8.26781i	−0.280305	−	0.485502i
$291$	−8.25653	+	14.3007i	−0.484006	+	0.838324i
$292$	−0.447355	−	0.774842i	−0.0261795	−	0.0453442i
$293$	−12.2963	+	21.2979i	−0.718360	+	1.24424i	0.243289	+	0.969954i	$0.421774\pi$
$293$	−12.2963	+	21.2979i	−0.718360	+	1.24424i	−0.961649	+	0.274283i	$0.911560\pi$
$294$			20.0589i			1.16986i
$295$	−25.1279	−	14.5076i	−1.46300	−	0.844665i
$296$	−9.33380			−0.542516
$297$		−	28.5736i		−	1.65801i
$298$	16.1374	−	9.31691i	0.934812	−	0.539714i
$299$	−0.0982188	+	0.0567067i	−0.00568014	+	0.00327943i
$300$	6.79649	+	11.7719i	0.392396	+	0.679649i
$301$	−1.63577	+	2.83324i	−0.0942844	+	0.163305i
$302$	−3.86546			−0.222432
$303$	−2.77431	+	1.60175i	−0.159380	+	0.0920180i
$304$	−0.883483			−0.0506712
$305$	31.0453	−	1.99156i	1.77765	−	0.114036i
$306$	5.88235			0.336271
$307$	−13.8193	+	7.97859i	−0.788710	+	0.455362i	−0.839508	−	0.543347i	$-0.817157\pi$
$307$	−13.8193	+	7.97859i	−0.788710	+	0.455362i	0.0507982	+	0.998709i	$0.483823\pi$
$308$	24.7166			1.40836
$309$	7.26763	−	12.5879i	0.413441	−	0.716101i
$310$	1.32395	+	2.29314i	0.0751950	+	0.130242i
$311$	16.2366	−	9.37418i	0.920691	−	0.531561i	0.0368356	−	0.999321i	$-0.488272\pi$
$311$	16.2366	−	9.37418i	0.920691	−	0.531561i	0.883855	+	0.467760i	$0.154939\pi$
$312$	0.272011	−	0.157046i	0.0153996	−	0.00889096i
$313$		−	12.1345i		−	0.685885i	−0.939356	−	0.342942i	$-0.888576\pi$
$313$		−	12.1345i		−	0.685885i	0.939356	−	0.342942i	$-0.111424\pi$
$314$	9.56939			0.540032
$315$	23.7541	+	13.7145i	1.33839	+	0.772722i
$316$		−	6.10076i		−	0.343195i
$317$	−17.0743	+	29.5735i	−0.958988	+	1.66102i	−0.234022	+	0.972231i	$0.575189\pi$
$317$	−17.0743	+	29.5735i	−0.958988	+	1.66102i	−0.724966	+	0.688784i	$0.758145\pi$
$318$	2.39683	+	4.15143i	0.134408	+	0.232801i
$319$	6.17185	−	10.6900i	0.345557	−	0.598523i
$320$	1.99156	+	3.44948i	0.111331	+	0.192832i
$321$	−9.21162	−	15.9550i	−0.514143	−	0.890521i
$322$	1.87757	+	1.08402i	0.104633	+	0.0604100i
$323$	3.13670	−	1.81098i	0.174531	−	0.100765i
$324$	−1.31833	+	2.28342i	−0.0732406	+	0.126856i
$325$	2.72781			0.151312
$326$	0.318331	−	0.183789i	0.0176307	−	0.0101791i
$327$	0.466543	+	0.808076i	0.0257999	+	0.0446867i
$328$			3.96198i			0.218764i
$329$			13.5159i			0.745156i
$330$	−12.8315	+	22.2249i	−0.706353	+	1.22344i
$331$	−12.8471	−	7.41725i	−0.706138	−	0.407689i	0.103492	−	0.994630i	$-0.466999\pi$
$331$	−12.8471	−	7.41725i	−0.706138	−	0.407689i	−0.809629	+	0.586941i	$0.800332\pi$
$332$	5.78696			0.317601
$333$		−	13.3926i		−	0.733909i
$334$	2.41938	+	1.39683i	0.132383	+	0.0764312i
$335$	34.5676	+	19.9576i	1.88863	+	1.09040i
$336$	−5.19982	−	3.00212i	−0.283674	−	0.163779i
$337$	19.8896	+	11.4832i	1.08345	+	0.625532i	0.931826	−	0.362906i	$-0.118215\pi$
$337$	19.8896	+	11.4832i	1.08345	+	0.625532i	0.151627	+	0.988438i	$0.451549\pi$
$338$			12.9370i			0.703678i
$339$	−0.0422587			−0.00229518
$340$	−14.1416	−	8.16464i	−0.766934	−	0.442790i
$341$	−1.71181	+	2.96494i	−0.0926997	+	0.160561i
$342$		−	1.26766i		−	0.0685474i
$343$		−	43.3546i		−	2.34093i
$344$	−0.340834	−	0.590342i	−0.0183766	−	0.0318291i
$345$	−1.94948	+	1.12553i	−0.104956	+	0.0605965i
$346$	7.73940			0.416072
$347$	4.32522	−	7.49151i	0.232190	−	0.402165i	−0.726262	−	0.687418i	$-0.758744\pi$
$347$	4.32522	−	7.49151i	0.232190	−	0.402165i	0.958452	+	0.285253i	$0.0920775\pi$
$348$	−2.59685	+	1.49929i	−0.139206	+	0.0803703i
$349$	−12.6138	−	7.28258i	−0.675201	−	0.389827i	0.122844	−	0.992426i	$-0.460799\pi$
$349$	−12.6138	−	7.28258i	−0.675201	−	0.389827i	−0.798044	+	0.602599i	$0.794132\pi$
$350$	−26.0727	−	45.1593i	−1.39365	−	2.41387i
$351$	0.696473	+	1.20633i	0.0371750	+	0.0643890i
$352$	−2.57501	+	4.46004i	−0.137248	+	0.237721i
$353$	14.5803	+	25.2539i	0.776033	+	1.34413i	0.934212	+	0.356718i	$0.116104\pi$
$353$	14.5803	+	25.2539i	0.776033	+	1.34413i	−0.158179	+	0.987410i	$0.550562\pi$
$354$	−4.55671	+	7.89245i	−0.242186	+	0.419479i
$355$			24.6352i			1.30750i
$356$	−6.68153	−	3.85758i	−0.354120	−	0.204451i
$357$	24.6152			1.30277
$358$		−	6.06132i		−	0.320351i
$359$	8.41481	−	4.85829i	0.444117	−	0.256411i	−0.261226	−	0.965278i	$-0.584127\pi$
$359$	8.41481	−	4.85829i	0.444117	−	0.256411i	0.705342	+	0.708867i	$0.250793\pi$
$360$	−4.94948	+	2.85758i	−0.260860	+	0.150608i
$361$	9.10973	+	15.7785i	0.479459	+	0.830448i
$362$	−6.56811	+	11.3763i	−0.345212	+	0.597925i
$363$	−19.4197			−1.01927
$364$	−1.04349	+	0.602459i	−0.0546937	+	0.0315774i
$365$	−3.56373			−0.186534
$366$	−0.625530	−	9.75105i	−0.0326970	−	0.509695i
$367$	−3.21472			−0.167807			−0.0839036	−	0.996474i	$-0.526739\pi$
$367$	−3.21472			−0.167807			−0.0839036	+	0.996474i	$0.526739\pi$
$368$	−0.391216	+	0.225869i	−0.0203936	+	0.0117742i
$369$	−5.68484			−0.295941
$370$	−18.5888	+	32.1967i	−0.966385	+	1.67383i
$371$	−9.19473	−	15.9257i	−0.477367	−	0.826823i
$372$	0.720255	−	0.415840i	0.0373435	−	0.0215603i
$373$	5.15734	−	2.97759i	0.267037	−	0.154174i	−0.360503	−	0.932758i	$-0.617395\pi$
$373$	5.15734	−	2.97759i	0.267037	−	0.154174i	0.627540	+	0.778584i	$0.284062\pi$
$374$		−	21.1131i		−	1.09173i
$375$	29.2268			1.50927
$376$	−2.43891	−	1.40811i	−0.125777	−	0.0726175i
$377$			0.601748i			0.0309916i
$378$	13.3139	−	23.0604i	0.684796	−	1.18610i
$379$	−5.49902	−	9.52458i	−0.282465	−	0.489245i	0.689526	−	0.724261i	$-0.257819\pi$
$379$	−5.49902	−	9.52458i	−0.282465	−	0.489245i	−0.971991	+	0.235016i	$0.924486\pi$
$380$	−1.75950	+	3.04755i	−0.0902607	+	0.156336i
$381$	1.16601	+	2.01959i	0.0597365	+	0.103467i
$382$	10.7896	+	18.6881i	0.552044	+	0.956168i
$383$	15.2606	+	8.81073i	0.779782	+	0.450207i	0.836353	−	0.548191i	$-0.184683\pi$
$383$	15.2606	+	8.81073i	0.779782	+	0.450207i	−0.0565712	+	0.998399i	$0.518017\pi$
$384$	1.08345	−	0.625530i	0.0552896	−	0.0319214i
$385$	49.2244	−	85.2592i	2.50871	−	4.34521i
$386$	−1.42476			−0.0725182
$387$	0.847052	−	0.489046i	0.0430581	−	0.0248596i
$388$	6.59963	+	11.4309i	0.335045	+	0.580316i
$389$		−	26.4973i		−	1.34347i	−0.740793	−	0.671733i	$-0.765550\pi$
$389$		−	26.4973i		−	1.34347i	0.740793	−	0.671733i	$-0.234450\pi$
$390$		−	1.25106i		−	0.0633499i
$391$	0.925979	−	1.60384i	0.0468288	−	0.0811098i
$392$	13.8854	+	8.01675i	0.701319	+	0.404907i
$393$	7.30594			0.368536
$394$			27.1275i			1.36666i
$395$	−21.0444	−	12.1500i	−1.05886	−	0.611333i
$396$	−6.39948	−	3.69474i	−0.321586	−	0.185668i
$397$	22.1919	+	12.8125i	1.11378	+	0.643042i	0.939806	−	0.341708i	$-0.111005\pi$
$397$	22.1919	+	12.8125i	1.11378	+	0.643042i	0.173976	+	0.984750i	$0.444339\pi$
$398$	11.7724	+	6.79681i	0.590098	+	0.340693i
$399$		−	5.30464i		−	0.265564i
$400$	10.8652			0.543259
$401$	27.9804	+	16.1545i	1.39728	+	0.806717i	0.994106	−	0.108409i	$-0.0345755\pi$
$401$	27.9804	+	16.1545i	1.39728	+	0.806717i	0.403169	+	0.915126i	$0.367909\pi$
$402$	6.26852	−	10.8574i	0.312645	−	0.541517i
$403$		−	0.166900i		−	0.00831386i
$404$			2.56063i			0.127396i
$405$	5.25106	+	9.09510i	0.260927	+	0.451939i
$406$	9.96203	−	5.75158i	0.494407	−	0.285446i
$407$	−48.0692			−2.38270
$408$	−2.56444	+	4.44174i	−0.126959	+	0.219899i
$409$	−25.3987	+	14.6639i	−1.25588	+	0.725084i	−0.972272	−	0.233855i	$-0.924866\pi$
$409$	−25.3987	+	14.6639i	−1.25588	+	0.725084i	−0.283612	+	0.958939i	$0.591533\pi$
$410$	13.6668	+	7.89051i	0.674953	+	0.389684i
$411$	4.18803	+	7.25388i	0.206580	+	0.357807i
$412$	−5.80918	−	10.0618i	−0.286198	−	0.495709i
$413$	17.4805	−	30.2770i	0.860157	−	1.48984i
$414$	−0.324088	−	0.561337i	−0.0159280	−	0.0275882i
$415$	11.5250	−	19.9620i	0.565742	−	0.979895i
$416$		−	0.251060i		−	0.0123092i
$417$	−19.9851	−	11.5384i	−0.978674	−	0.565038i
$418$	−4.54994			−0.222545
$419$			18.7396i			0.915490i	0.889084	+	0.457745i	$0.151343\pi$
$419$			18.7396i			0.915490i	−0.889084	+	0.457745i	$0.848657\pi$
$420$	−20.7115	+	11.9578i	−1.01062	+	0.583480i
$421$	21.2372	−	12.2613i	1.03504	−	0.597579i	0.116614	−	0.993177i	$-0.462796\pi$
$421$	21.2372	−	12.2613i	1.03504	−	0.597579i	0.918424	+	0.395598i	$0.129463\pi$
$422$	−7.38065	−	12.7837i	−0.359285	−	0.622299i
$423$	2.02042	−	3.49947i	0.0982361	−	0.170150i
$424$	3.83168			0.186083
$425$	−38.5755	+	22.2716i	−1.87119	+	1.08033i
$426$	7.73771			0.374893
$427$	2.39966	+	37.4070i	0.116128	+	1.81025i
$428$	−14.7261			−0.711813
$429$	1.40086	−	0.808786i	0.0676341	−	0.0390486i
$430$	−2.71516			−0.130937
$431$	−9.85771	+	17.0741i	−0.474829	+	0.822428i	−0.999584	−	0.0288248i	$-0.990824\pi$
$431$	−9.85771	+	17.0741i	−0.474829	+	0.822428i	0.524755	+	0.851253i	$0.324157\pi$
$432$	2.77413	+	4.80494i	0.133470	+	0.231178i
$433$	−29.4873	+	17.0245i	−1.41707	+	0.818144i	−0.996040	−	0.0889037i	$-0.971664\pi$
$433$	−29.4873	+	17.0245i	−1.41707	+	0.818144i	−0.421027	+	0.907048i	$0.638330\pi$
$434$	−2.76305	+	1.59525i	−0.132630	+	0.0765742i
$435$			11.9437i			0.572655i
$436$	0.745836			0.0357191
$437$	−0.345633	−	0.199551i	−0.0165339	−	0.00954583i
$438$			1.11934i			0.0534840i
$439$	18.5733	−	32.1699i	0.886455	−	1.53539i	0.0424185	−	0.999100i	$-0.486494\pi$
$439$	18.5733	−	32.1699i	0.886455	−	1.53539i	0.844037	−	0.536285i	$-0.180173\pi$
$440$	10.2565	+	17.7648i	0.488961	+	0.846905i
$441$	−11.5028	+	19.9235i	−0.547753	+	0.948737i
$442$	0.514626	+	0.891359i	0.0244783	+	0.0423976i
$443$	−15.5428	−	26.9209i	−0.738460	−	1.27905i	−0.953189	−	0.302376i	$-0.902220\pi$
$443$	−15.5428	−	26.9209i	−0.738460	−	1.27905i	0.214729	−	0.976674i	$-0.431113\pi$
$444$	10.1127	+	5.83857i	0.479928	+	0.277086i
$445$	−26.6133	+	15.3652i	−1.26159	+	0.728379i
$446$	4.96339	−	8.59685i	0.235023	−	0.407072i
$447$	−23.3120			−1.10262
$448$	−4.15633	+	2.39966i	−0.196368	+	0.113373i
$449$	−8.80795	−	15.2558i	−0.415673	−	0.719966i	0.579826	−	0.814740i	$-0.303120\pi$
$449$	−8.80795	−	15.2558i	−0.415673	−	0.719966i	−0.995499	+	0.0947741i	$0.969787\pi$
$450$			15.5899i			0.734914i
$451$			20.4042i			0.960798i
$452$	−0.0168891	+	0.0292529i	−0.000794399	+	0.00137594i
$453$	4.18803	+	2.41796i	0.196771	+	0.113606i
$454$	−2.25644			−0.105900
$455$			4.79932i			0.224996i
$456$	0.957209	+	0.552645i	0.0448254	+	0.0258800i
$457$	15.3047	+	8.83617i	0.715923	+	0.413338i	0.813250	−	0.581914i	$-0.197696\pi$
$457$	15.3047	+	8.83617i	0.715923	+	0.413338i	−0.0973272	+	0.995252i	$0.531029\pi$
$458$	−12.7464	−	7.35913i	−0.595600	−	0.343870i
$459$	−19.6985	−	11.3729i	−0.919445	−	0.530842i
$460$			1.79932i			0.0838938i
$461$	20.8044			0.968958			0.484479	−	0.874803i	$-0.339009\pi$
$461$	20.8044			0.968958			0.484479	+	0.874803i	$0.339009\pi$
$462$	−26.7792	−	15.4609i	−1.24588	−	0.719308i
$463$	3.82607	−	6.62694i	0.177812	−	0.307980i	−0.763319	−	0.646022i	$-0.776431\pi$
$463$	3.82607	−	6.62694i	0.177812	−	0.307980i	0.941131	+	0.338042i	$0.109765\pi$
$464$			2.39683i			0.111270i
$465$		−	3.31267i		−	0.153621i
$466$	−13.3631	−	23.1455i	−0.619031	−	1.07219i
$467$	4.32965	−	2.49973i	0.200352	−	0.115674i	−0.396467	−	0.918049i	$-0.629764\pi$
$467$	4.32965	−	2.49973i	0.200352	−	0.115674i	0.596820	+	0.802375i	$0.296431\pi$
$468$	0.360233			0.0166518
$469$	−24.0473	+	41.6512i	−1.11040	+	1.92327i
$470$	−9.71445	+	5.60864i	−0.448094	+	0.258707i
$471$	−10.3680	−	5.98594i	−0.477730	−	0.275818i
$472$	3.64228	+	6.30861i	0.167649	+	0.290377i
$473$	−1.75530	−	3.04027i	−0.0807088	−	0.139792i
$474$	−3.81621	+	6.60987i	−0.175284	+	0.303601i
$475$	4.79960	+	8.31314i	0.220221	+	0.381433i
$476$	9.83772	−	17.0394i	0.450911	−	0.781001i
$477$			5.49788i			0.251731i
$478$	−0.368999	−	0.213042i	−0.0168776	−	0.00974429i
$479$	3.34448			0.152813			0.0764066	−	0.997077i	$-0.475655\pi$
$479$	3.34448			0.152813			0.0764066	+	0.997077i	$0.475655\pi$
$480$		−	4.98311i		−	0.227447i
$481$	2.02940	−	1.17167i	0.0925325	−	0.0534236i
$482$	15.5885	−	9.00000i	0.710035	−	0.409939i
$483$	−1.35617	−	2.34896i	−0.0617079	−	0.106881i
$484$	−7.76130	+	13.4430i	−0.352787	+	0.611044i
$485$	52.5741			2.38727
$486$	−11.5581	+	6.67308i	−0.524287	+	0.302697i
$487$	−19.4847			−0.882934			−0.441467	−	0.897277i	$-0.645542\pi$
$487$	−19.4847			−0.882934			−0.441467	+	0.897277i	$0.645542\pi$
$488$	−7.00000	−	3.46410i	−0.316875	−	0.156813i
$489$	−0.459861			−0.0207957
$490$	55.3071	−	31.9316i	2.49852	−	1.44252i
$491$	−0.861217			−0.0388662			−0.0194331	−	0.999811i	$-0.506186\pi$
$491$	−0.861217			−0.0388662			−0.0194331	+	0.999811i	$0.506186\pi$
$492$	2.47834	−	4.29261i	0.111732	−	0.193526i
$493$	−4.91306	−	8.50966i	−0.221273	−	0.383256i
$494$	0.192091	−	0.110904i	0.00864257	−	0.00498979i
$495$	−25.4898	+	14.7166i	−1.14568	+	0.661461i
$496$		−	0.664779i		−	0.0298495i
$497$	−29.6834			−1.33148
$498$	−6.26988	−	3.61992i	−0.280960	−	0.162212i
$499$		−	12.1880i		−	0.545611i	−0.962069	−	0.272806i	$-0.912048\pi$
$499$		−	12.1880i		−	0.545611i	0.962069	−	0.272806i	$-0.0879516\pi$
$500$	11.6808	−	20.2318i	0.522382	−	0.904792i
$501$	−1.74752	−	3.02679i	−0.0780734	−	0.135227i
$502$	−12.8926	+	22.3307i	−0.575426	+	0.996667i
$503$	−11.7768	−	20.3980i	−0.525102	−	0.909504i	−0.999573	−	0.0292325i	$-0.990694\pi$
$503$	−11.7768	−	20.3980i	−0.525102	−	0.909504i	0.474470	−	0.880272i	$-0.342640\pi$
$504$	−3.44315	−	5.96371i	−0.153370	−	0.265645i
$505$	8.83282	+	5.09963i	0.393055	+	0.226930i
$506$	−2.01477	+	1.16323i	−0.0895674	+	0.0517118i
$507$	8.09246	−	14.0166i	0.359399	−	0.622497i
$508$	1.86404			0.0827032
$509$	−22.3819	+	12.9222i	−0.992061	+	0.572766i	−0.905890	−	0.423514i	$-0.860796\pi$
$509$	−22.3819	+	12.9222i	−0.992061	+	0.572766i	−0.0861710	+	0.996280i	$0.527463\pi$
$510$	10.2145	+	17.6919i	0.452303	+	0.783413i
$511$		−	4.29400i		−	0.189955i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.45090	+	4.24508i	−0.108210	+	0.187425i
$514$	−6.78465	−	3.91712i	−0.299258	−	0.172777i
$515$	−46.2772			−2.03922
$516$			0.852808i			0.0375428i
$517$	−12.5604	−	7.25176i	−0.552406	−	0.318932i
$518$	−38.7944	−	22.3980i	−1.70453	−	0.984110i
$519$	−8.38525	−	4.84122i	−0.368071	−	0.212506i
$520$	−0.866025	−	0.500000i	−0.0379777	−	0.0219265i
$521$			39.1951i			1.71717i	0.512673	+	0.858584i	$0.328655\pi$
$521$			39.1951i			1.71717i	−0.512673	+	0.858584i	$0.671345\pi$
$522$	−3.43909			−0.150525
$523$	36.8752	+	21.2899i	1.61244	+	0.930942i	0.988803	+	0.149226i	$0.0476781\pi$
$523$	36.8752	+	21.2899i	1.61244	+	0.930942i	0.623635	+	0.781716i	$0.285655\pi$
$524$	2.91990	−	5.05742i	0.127556	−	0.220934i
$525$			65.2371i			2.84718i
$526$		−	21.3183i		−	0.929523i
$527$	1.36267	+	2.36022i	0.0593590	+	0.102813i
$528$	5.57978	−	3.22149i	0.242829	−	0.140197i
$529$	22.7959			0.991128
$530$	7.63100	−	13.2173i	0.331470	−	0.574122i
$531$	−9.05190	+	5.22612i	−0.392819	+	0.226794i
$532$	−3.67205	−	2.12006i	−0.159204	−	0.0919162i
$533$	−0.497348	−	0.861431i	−0.0215425	−	0.0373127i
$534$	4.82607	+	8.35899i	0.208844	+	0.361729i
$535$	−29.3279	+	50.7973i	−1.26795	+	2.19616i
$536$	−5.01056	−	8.67855i	−0.216423	−	0.374856i
$537$	−3.79154	+	6.56714i	−0.163617	+	0.283393i
$538$		−	17.1522i		−	0.739483i
$539$	71.5100	+	41.2863i	3.08015	+	1.77833i
$540$	22.0993			0.951004
$541$		−	13.7959i		−	0.593133i	−0.955012	−	0.296567i	$-0.904158\pi$
$541$		−	13.7959i		−	0.593133i	0.955012	−	0.296567i	$-0.0958417\pi$
$542$	−10.1308	+	5.84899i	−0.435153	+	0.251236i
$543$	14.2324	−	8.21710i	0.610772	−	0.352630i
$544$	2.04981	+	3.55038i	0.0878851	+	0.152221i
$545$	1.48537	−	2.57274i	0.0636264	−	0.110204i
$546$	1.50742			0.0645118
$547$	34.2154	−	19.7543i	1.46294	−	0.844632i	0.463798	−	0.885941i	$-0.346486\pi$
$547$	34.2154	−	19.7543i	1.46294	−	0.844632i	0.999146	+	0.0413093i	$0.0131529\pi$
$548$	6.69517			0.286003
$549$	4.97046	−	10.0439i	0.212134	−	0.428665i
$550$	55.9557			2.38596
$551$	−1.83386	+	1.05878i	−0.0781250	+	0.0451055i
$552$	0.565151			0.0240544
$553$	14.6398	−	25.3568i	0.622546	−	1.07828i
$554$	4.53024	+	7.84660i	0.192471	+	0.333370i
$555$	40.2800	−	23.2557i	1.70979	−	0.987149i
$556$	−15.9745	+	9.22290i	−0.677471	+	0.391138i
$557$		−	23.3712i		−	0.990272i	−0.868816	−	0.495136i	$-0.835118\pi$
$557$		−	23.3712i		−	0.990272i	0.868816	−	0.495136i	$-0.164882\pi$
$558$	0.953858			0.0403800
$559$	0.148211	+	0.0855699i	0.00626867	+	0.00361922i
$560$			19.1162i			0.807808i
$561$	−13.2069	+	22.8750i	−0.557596	+	0.965784i
$562$	−1.88291	−	3.26130i	−0.0794260	−	0.137570i
$563$	−9.00661	+	15.5999i	−0.379583	+	0.657457i	−0.991002	−	0.133850i	$-0.957266\pi$
$563$	−9.00661	+	15.5999i	−0.379583	+	0.657457i	0.611418	+	0.791308i	$0.290599\pi$
$564$	1.76162	+	3.05122i	0.0741778	+	0.128480i
$565$	0.0672713	+	0.116517i	0.00283013	+	0.00490192i
$566$	19.2053	+	11.0882i	0.807261	+	0.466072i
$567$	−10.9589	+	6.32710i	−0.460229	+	0.265713i
$568$	3.09246	−	5.35630i	0.129757	−	0.224745i
$569$	−9.79169			−0.410489			−0.205245	−	0.978711i	$-0.565799\pi$
$569$	−9.79169			−0.410489			−0.205245	+	0.978711i	$0.565799\pi$
$570$	3.81267	−	2.20125i	0.159695	−	0.0922000i
$571$	−21.0742	−	36.5015i	−0.881926	−	1.52754i	−0.849197	−	0.528076i	$-0.822914\pi$
$571$	−21.0742	−	36.5015i	−0.881926	−	1.52754i	−0.0327287	−	0.999464i	$-0.510420\pi$
$572$		−	1.29296i		−	0.0540615i
$573$		−	26.9969i		−	1.12781i
$574$	−9.50741	+	16.4673i	−0.396832	+	0.687333i
$575$	4.25063	+	2.45411i	0.177264	+	0.102343i
$576$	1.43485			0.0597854
$577$		−	21.1810i		−	0.881778i	−0.897562	−	0.440889i	$-0.854663\pi$
$577$		−	21.1810i		−	0.881778i	0.897562	−	0.440889i	$-0.145337\pi$
$578$	0.167185	+	0.0965242i	0.00695397	+	0.00401488i
$579$	1.54365	+	0.891229i	0.0641520	+	0.0370382i
$580$	8.26781	+	4.77342i	0.343302	+	0.198205i
$581$	24.0525	+	13.8867i	0.997867	+	0.576119i
$582$		−	16.5131i		−	0.684488i
$583$	19.7332			0.817265
$584$	0.774842	+	0.447355i	0.0320632	+	0.0185117i
$585$	0.717424	−	1.24262i	0.0296618	−	0.0513758i
$586$		−	24.5927i		−	1.01591i
$587$			15.0839i			0.622578i	0.950315	+	0.311289i	$0.100761\pi$
$587$			15.0839i			0.622578i	−0.950315	+	0.311289i	$0.899239\pi$
$588$	−10.0294	−	17.3715i	−0.413607	−	0.716388i
$589$	0.508635	−	0.293661i	0.0209579	−	0.0121001i
$590$	29.0152			1.19454
$591$	16.9690	−	29.3912i	0.698013	−	1.20899i
$592$	8.08331	−	4.66690i	0.332222	−	0.191808i
$593$	−31.1106	−	17.9617i	−1.27756	−	0.737598i	−0.301159	−	0.953574i	$-0.597374\pi$
$593$	−31.1106	−	17.9617i	−1.27756	−	0.737598i	−0.976399	+	0.215975i	$0.930707\pi$
$594$	14.2868	+	24.7455i	0.586195	+	1.01532i
$595$	−39.1847	−	67.8699i	−1.60642	−	2.78240i
$596$	−9.31691	+	16.1374i	−0.381636	+	0.661012i
$597$	−8.50322	−	14.7280i	−0.348014	−	0.602777i
$598$	0.0567067	−	0.0982188i	0.00231891	−	0.00401647i
$599$		−	1.66620i		−	0.0680791i	−0.999420	−	0.0340396i	$-0.989163\pi$
$599$		−	1.66620i		−	0.0680791i	0.999420	−	0.0340396i	$-0.0108372\pi$
$600$	−11.7719	−	6.79649i	−0.480585	−	0.277466i
$601$	−14.3895			−0.586958			−0.293479	−	0.955965i	$-0.594813\pi$
$601$	−14.3895			−0.586958			−0.293479	+	0.955965i	$0.594813\pi$
$602$		−	3.27155i		−	0.133338i
$603$	12.4524	−	7.18940i	0.507101	−	0.292775i
$604$	3.34758	−	1.93273i	0.136211	−	0.0786416i
$605$	30.9141	+	53.5448i	1.25684	+	2.17691i
$606$	1.60175	−	2.77431i	0.0650666	−	0.112699i
$607$	24.3647			0.988934			0.494467	−	0.869196i	$-0.335363\pi$
$607$	24.3647			0.988934			0.494467	+	0.869196i	$0.335363\pi$
$608$	0.765118	−	0.441741i	0.0310296	−	0.0179150i
$609$	−14.3911			−0.583159
$610$	−25.8902	+	17.2474i	−1.04826	+	0.698326i
$611$	0.707038			0.0286037
$612$	−5.09426	+	2.94117i	−0.205923	+	0.118890i
$613$	4.79657			0.193732			0.0968659	−	0.995297i	$-0.469118\pi$
$613$	4.79657			0.193732			0.0968659	+	0.995297i	$0.469118\pi$
$614$	7.97859	−	13.8193i	0.321990	−	0.557702i
$615$	−9.87150	−	17.0979i	−0.398057	−	0.689455i
$616$	−21.4052	+	12.3583i	−0.862439	+	0.497929i
$617$	31.8077	−	18.3642i	1.28053	−	0.739314i	0.303585	−	0.952804i	$-0.401816\pi$
$617$	31.8077	−	18.3642i	1.28053	−	0.739314i	0.976945	+	0.213490i	$0.0684831\pi$
$618$			14.5353i			0.584694i
$619$	29.2643			1.17623			0.588115	−	0.808777i	$-0.299870\pi$
$619$	29.2643			1.17623			0.588115	+	0.808777i	$0.299870\pi$
$620$	−2.29314	−	1.32395i	−0.0920947	−	0.0531709i
$621$			2.50636i			0.100577i
$622$	−9.37418	+	16.2366i	−0.375871	+	0.651027i
$623$	−18.5138	−	32.0668i	−0.741739	−	1.28473i
$624$	−0.157046	+	0.272011i	−0.00628686	+	0.0108892i
$625$	−19.3631	−	33.5378i	−0.774522	−	1.34151i
$626$	6.06727	+	10.5088i	0.242497	+	0.420017i
$627$	4.92964	+	2.84613i	0.196871	+	0.113663i
$628$	−8.28734	+	4.78470i	−0.330701	+	0.190930i
$629$	−19.1326	+	33.1386i	−0.762865	+	1.32132i
$630$	−27.4289			−1.09279
$631$	−24.2685	+	14.0114i	−0.966112	+	0.557785i	−0.898049	−	0.439896i	$-0.855015\pi$
$631$	−24.2685	+	14.0114i	−0.966112	+	0.557785i	−0.0680636	+	0.997681i	$0.521682\pi$
$632$	3.05038	+	5.28342i	0.121338	+	0.210163i
$633$			18.4673i			0.734008i
$634$		−	34.1486i		−	1.35621i
$635$	3.71233	−	6.42995i	0.147319	−	0.255165i
$636$	−4.15143	−	2.39683i	−0.164615	−	0.0950405i
$637$	−4.02537			−0.159491
$638$			12.3437i			0.488692i
$639$	7.68548	+	4.43722i	0.304033	+	0.175534i
$640$	−3.44948	−	1.99156i	−0.136352	−	0.0787231i
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	0.278093	−	0.960554i	$-0.410298\pi$
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	−0.692818	+	0.721113i	$0.743631\pi$
$642$	15.9550	+	9.21162i	0.629693	+	0.363554i
$643$			0.0886859i			0.00349743i	0.999998	+	0.00174872i	$0.000556634\pi$
$643$			0.0886859i			0.00349743i	−0.999998	+	0.00174872i	$0.999443\pi$
$644$	−2.16804			−0.0854326
$645$	2.94174	+	1.69842i	0.115831	+	0.0668750i
$646$	−1.81098	+	3.13670i	−0.0712519	+	0.123412i
$647$			17.1812i			0.675464i	0.941242	+	0.337732i	$0.109660\pi$
$647$			17.1812i			0.675464i	−0.941242	+	0.337732i	$0.890340\pi$
$648$		−	2.63666i		−	0.103578i
$649$	18.7578	+	32.4894i	0.736307	+	1.27532i
$650$	−2.36235	+	1.36391i	−0.0926591	+	0.0534968i
$651$	3.99150			0.156439
$652$	−0.183789	+	0.318331i	−0.00719772	+	0.0124668i
$653$	6.69346	−	3.86447i	0.261935	−	0.151229i	−0.363282	−	0.931679i	$-0.618344\pi$
$653$	6.69346	−	3.86447i	0.261935	−	0.151229i	0.625217	+	0.780451i	$0.285010\pi$
$654$	−0.808076	−	0.466543i	−0.0315983	−	0.0182433i
$655$	−11.6303	−	20.1443i	−0.454433	−	0.787101i
$656$	−1.98099	−	3.43118i	−0.0773447	−	0.133965i
$657$	−0.641887	+	1.11178i	−0.0250424	+	0.0433747i
$658$	−6.75795	−	11.7051i	−0.263452	−	0.456313i
$659$	4.09415	−	7.09127i	0.159485	−	0.276237i	−0.775198	−	0.631718i	$-0.782350\pi$
$659$	4.09415	−	7.09127i	0.159485	−	0.276237i	0.934683	+	0.355482i	$0.115683\pi$
$660$		−	25.6631i		−	0.998934i
$661$	42.8984	+	24.7674i	1.66855	+	0.963339i	0.968419	+	0.249327i	$0.0802095\pi$
$661$	42.8984	+	24.7674i	1.66855	+	0.963339i	0.700134	+	0.714012i	$0.253124\pi$
$662$	14.8345			0.576559
$663$		−	1.28766i		−	0.0500085i
$664$	−5.01165	+	2.89348i	−0.194490	+	0.112289i
$665$	−14.6262	+	8.44443i	−0.567179	+	0.327461i
$666$	6.69630	+	11.5983i	0.259476	+	0.449426i
$667$	−0.541370	+	0.937680i	−0.0209619	+	0.0363071i
$668$	−2.79366			−0.108090
$669$	−10.7552	+	6.20950i	−0.415819	+	0.240073i
$670$	−39.9153			−1.54206
$671$	−36.0501	−	17.8402i	−1.39170	−	0.688712i
$672$	6.00424			0.231619
$673$	−30.2155	+	17.4449i	−1.16472	+	0.672453i	−0.952431	−	0.304753i	$-0.901426\pi$
$673$	−30.2155	+	17.4449i	−1.16472	+	0.672453i	−0.212291	+	0.977206i	$0.568093\pi$
$674$	−22.9665			−0.884636
$675$	30.1414	−	52.2065i	1.16014	−	2.00943i
$676$	−6.46848	−	11.2037i	−0.248788	−	0.430913i
$677$	39.0206	−	22.5285i	1.49968	−	0.865842i	0.499682	−	0.866209i	$-0.333450\pi$
$677$	39.0206	−	22.5285i	1.49968	−	0.865842i	1.00000		0.000367190i	$0.000116880\pi$
$678$	0.0365971	−	0.0211293i	0.00140550	−	0.000811467i
$679$			63.3475i			2.43105i
$680$	16.3293			0.626199
$681$	2.44474	+	1.41147i	0.0936825	+	0.0540876i
$682$		−	3.42362i		−	0.131097i
$683$	−16.6885	+	28.9054i	−0.638570	+	1.10603i	0.347177	+	0.937800i	$0.387140\pi$
$683$	−16.6885	+	28.9054i	−0.638570	+	1.10603i	−0.985747	+	0.168235i	$0.946193\pi$
$684$	0.633832	+	1.09783i	0.0242352	+	0.0419765i
$685$	13.3338	−	23.0948i	0.509458	−	0.882408i
$686$	21.6773	+	37.5462i	0.827644	+	1.43352i
$687$	9.20672	+	15.9465i	0.351258	+	0.608397i
$688$	0.590342	+	0.340834i	0.0225066	+	0.0129942i
$689$	−0.833100	+	0.480991i	−0.0317386	+	0.0183243i
$690$	1.12553	−	1.94948i	0.0428482	−	0.0742153i
$691$	30.7427			1.16951			0.584754	−	0.811211i	$-0.301191\pi$
$691$	30.7427			1.16951			0.584754	+	0.811211i	$0.301191\pi$
$692$	−6.70251	+	3.86970i	−0.254791	+	0.147104i
$693$	−17.7323	−	30.7132i	−0.673593	−	1.16670i
$694$			8.65045i			0.328367i
$695$			73.4716i			2.78694i
$696$	1.49929	−	2.59685i	0.0568304	−	0.0984332i
$697$	14.0665	+	8.12133i	0.532809	+	0.307617i
$698$	14.5652			0.551299
$699$			33.4360i			1.26466i
$700$	45.1593	+	26.0727i	1.70686	+	0.985457i
$701$	−31.0621	−	17.9337i	−1.17320	−	0.677347i	−0.218768	−	0.975777i	$-0.570204\pi$
$701$	−31.0621	−	17.9337i	−1.17320	−	0.677347i	−0.954432	+	0.298429i	$0.903537\pi$
$702$	−1.20633	−	0.696473i	−0.0455299	−	0.0262867i
$703$	7.14146	+	4.12312i	0.269345	+	0.155507i
$704$		−	5.15001i		−	0.194098i
$705$	14.0335			0.528532
$706$	−25.2539	−	14.5803i	−0.950442	−	0.548738i
$707$	−6.14463	+	10.6428i	−0.231093	+	0.400264i
$708$		−	9.11341i		−	0.342503i
$709$		−	6.42637i		−	0.241347i	−0.992692	−	0.120674i	$-0.961495\pi$
$709$		−	6.42637i		−	0.241347i	0.992692	−	0.120674i	$-0.0385055\pi$
$710$	−12.3176	−	21.3347i	−0.462272	−	0.800679i
$711$	−7.58090	+	4.37684i	−0.284306	+	0.164144i
$712$	7.71516			0.289138
$713$	0.150153	−	0.260073i	0.00562328	−	0.00973980i
$714$	−21.3173	+	12.3076i	−0.797782	+	0.460599i
$715$	−4.46004	−	2.57501i	−0.166796	−	0.0962997i
$716$	3.03066	+	5.24926i	0.113261	+	0.196174i
$717$	0.266528	+	0.461640i	0.00995366	+	0.0172402i
$718$	−4.85829	+	8.41481i	−0.181310	+	0.314038i
$719$	−2.53377	−	4.38861i	−0.0944935	−	0.163668i	0.814904	−	0.579597i	$-0.196790\pi$
$719$	−2.53377	−	4.38861i	−0.0944935	−	0.163668i	−0.909397	+	0.415929i	$0.863457\pi$
$720$	2.85758	−	4.94948i	0.106496	−	0.184456i
$721$		−	55.7602i		−	2.07662i
$722$	−15.7785	−	9.10973i	−0.587215	−	0.339029i
$723$	−22.5191			−0.837494
$724$		−	13.1362i		−	0.488204i
$725$	22.5530	−	13.0210i	0.837598	−	0.483587i
$726$	16.8180	−	9.70986i	0.624173	−	0.360367i
$727$	−11.1060	−	19.2361i	−0.411897	−	0.713427i	0.583200	−	0.812328i	$-0.301800\pi$
$727$	−11.1060	−	19.2361i	−0.411897	−	0.713427i	−0.995097	+	0.0989020i	$0.968467\pi$
$728$	0.602459	−	1.04349i	0.0223286	−	0.0386743i
$729$	24.6068			0.911364
$730$	3.08628	−	1.78186i	0.114228	−	0.0659498i
$731$	−2.79459			−0.103362
$732$	5.41725	+	8.13189i	0.200227	+	0.300563i
$733$	14.0332			0.518328			0.259164	−	0.965833i	$-0.416553\pi$
$733$	14.0332			0.518328			0.259164	+	0.965833i	$0.416553\pi$
$734$	2.78403	−	1.60736i	0.102761	−	0.0593288i
$735$	−79.8967			−2.94703
$736$	0.225869	−	0.391216i	0.00832564	−	0.0144204i
$737$	−25.8045	−	44.6946i	−0.950520	−	1.64635i
$738$	4.92322	−	2.84242i	0.181226	−	0.104631i
$739$	17.6510	−	10.1908i	0.649303	−	0.374876i	−0.138886	−	0.990308i	$-0.544352\pi$
$739$	17.6510	−	10.1908i	0.649303	−	0.374876i	0.788189	+	0.615433i	$0.211019\pi$
$740$		−	37.1776i		−	1.36667i
$741$	−0.277494			−0.0101940
$742$	15.9257	+	9.19473i	0.584652	+	0.337549i
$743$		−	46.4930i		−	1.70566i	−0.522185	−	0.852832i	$-0.674883\pi$
$743$		−	46.4930i		−	1.70566i	0.522185	−	0.852832i	$-0.325117\pi$
$744$	−0.415840	+	0.720255i	−0.0152454	+	0.0264058i
$745$	37.1103	+	64.2769i	1.35962	+	2.35492i
$746$	−2.97759	+	5.15734i	−0.109017	+	0.188824i
$747$	−4.15171	−	7.19096i	−0.151903	−	0.263104i
$748$	10.5566	+	18.2845i	0.385986	+	0.668548i
$749$	−61.2066	−	35.3377i	−2.23644	−	1.29121i
$750$	−25.3112	+	14.6134i	−0.924233	+	0.533606i
$751$	−3.42400	+	5.93054i	−0.124943	+	0.216408i	−0.921711	−	0.387878i	$-0.873208\pi$
$751$	−3.42400	+	5.93054i	−0.124943	+	0.216408i	0.796767	+	0.604286i	$0.206542\pi$
$752$	2.81621			0.102697
$753$	27.9370	−	16.1294i	1.01808	−	0.587790i
$754$	−0.300874	−	0.521129i	−0.0109572	−	0.0189784i
$755$		−	15.3965i		−	0.560338i
$756$			26.6279i			0.968447i
$757$	−8.94396	+	15.4914i	−0.325074	+	0.563044i	−0.981527	−	0.191322i	$-0.938722\pi$
$757$	−8.94396	+	15.4914i	−0.325074	+	0.563044i	0.656454	+	0.754366i	$0.272056\pi$
$758$	9.52458	+	5.49902i	0.345948	+	0.199733i
$759$	2.91053			0.105646
$760$		−	3.51901i		−	0.127648i
$761$	−16.4382	−	9.49057i	−0.595883	−	0.344033i	0.171538	−	0.985178i	$-0.445127\pi$
$761$	−16.4382	−	9.49057i	−0.595883	−	0.344033i	−0.767420	+	0.641145i	$0.778460\pi$
$762$	−2.01959	−	1.16601i	−0.0731620	−	0.0422401i
$763$	3.09994	+	1.78975i	0.112226	+	0.0647934i
$764$	−18.6881	−	10.7896i	−0.676113	−	0.390354i
$765$			23.4300i			0.847115i
$766$	−17.6215			−0.636689
$767$	−1.58384	−	0.914430i	−0.0571891	−	0.0330182i
$768$	−0.625530	+	1.08345i	−0.0225719	+	0.0390956i
$769$		−	27.8464i		−	1.00417i	−0.864820	−	0.502083i	$-0.832567\pi$
$769$		−	27.8464i		−	1.00417i	0.864820	−	0.502083i	$-0.167433\pi$
$770$			98.4488i			3.54785i
$771$	4.90055	+	8.48800i	0.176489	+	0.305688i
$772$	1.23388	−	0.712379i	0.0444082	−	0.0256391i
$773$	8.40249			0.302217			0.151108	−	0.988517i	$-0.451716\pi$
$773$	8.40249			0.302217			0.151108	+	0.988517i	$0.451716\pi$
$774$	−0.489046	+	0.847052i	−0.0175784	+	0.0304467i
$775$	−6.25525	+	3.61147i	−0.224695	+	0.129728i
$776$	−11.4309	−	6.59963i	−0.410345	−	0.236913i
$777$	28.0212	+	48.5341i	1.00525	+	1.74115i
$778$	13.2487	+	22.9473i	0.474987	+	0.822702i
$779$	1.75017	−	3.03138i	0.0627064	−	0.108611i
$780$	0.625530	+	1.08345i	0.0223976	+	0.0387937i
$781$	15.9262	−	27.5850i	0.569885	−	0.987069i
$782$			1.85196i			0.0662259i
$783$	11.5166	+	6.64912i	0.411570	+	0.237620i
$784$	−16.0335			−0.572625
$785$			38.1159i			1.36042i
$786$	−6.32713	+	3.65297i	−0.225681	+	0.130297i
$787$	31.0770	−	17.9423i	1.10777	−	0.639574i	0.169522	−	0.985526i	$-0.445778\pi$
$787$	31.0770	−	17.9423i	1.10777	−	0.639574i	0.938252	+	0.345953i	$0.112444\pi$
$788$	−13.5637	−	23.4931i	−0.483188	−	0.836906i
$789$	−13.3353	+	23.0973i	−0.474748	+	0.822287i
$790$	24.3000			0.864556
$791$	−0.140394	+	0.0810564i	−0.00499183	+	0.00288204i
$792$	7.38949			0.262574
$793$	1.95682	−	0.125530i	0.0694887	−	0.00445770i
$794$	−25.6251			−0.909399
$795$	−16.5356	+	9.54684i	−0.586458	+	0.338592i
$796$	−13.5936			−0.481813
$797$	−6.97103	+	12.0742i	−0.246927	+	0.427689i	−0.962672	−	0.270672i	$-0.912754\pi$
$797$	−6.97103	+	12.0742i	−0.246927	+	0.427689i	0.715745	+	0.698362i	$0.246087\pi$
$798$	2.65232	+	4.59395i	0.0938911	+	0.162624i
$799$	−9.99863	+	5.77271i	−0.353726	+	0.204224i
$800$	−9.40952	+	5.43259i	−0.332677	+	0.192071i
$801$			11.0701i			0.391142i
$802$	−32.3090			−1.14087
$803$	3.99044	+	2.30388i	0.140820	+	0.0813023i
$804$			12.5370i			0.442147i
$805$	−4.31776	+	7.47859i	−0.152181	+	0.263586i
$806$	0.0834498	+	0.144539i	0.00293939	+	0.00509118i
$807$	−10.7292	+	18.5835i	−0.377686	+	0.654171i
$808$	−1.28031	−	2.21757i	−0.0450413	−	0.0780137i
$809$	10.7686	+	18.6518i	0.378605	+	0.655764i	0.990860	−	0.134897i	$-0.0430704\pi$
$809$	10.7686	+	18.6518i	0.378605	+	0.655764i	−0.612254	+	0.790661i	$0.709737\pi$
$810$	−9.09510	−	5.25106i	−0.319569	−	0.184503i
$811$	37.8423	−	21.8483i	1.32882	−	0.767197i	0.343706	−	0.939077i	$-0.388318\pi$
$811$	37.8423	−	21.8483i	1.32882	−	0.767197i	0.985118	+	0.171880i	$0.0549842\pi$
$812$	−5.75158	+	9.96203i	−0.201841	+	0.349599i
$813$	14.6349			0.513268
$814$	41.6291	−	24.0346i	1.45910	−	0.842412i
$815$	0.732051	+	1.26795i	0.0256426	+	0.0444143i
$816$		−	5.12888i		−	0.179547i
$817$			0.602242i			0.0210698i
$818$	14.6639	−	25.3987i	0.512712	−	0.888044i
$819$	1.49725	+	0.864438i	0.0523181	+	0.0302059i
$820$	−15.7810			−0.551097
$821$		−	29.7859i		−	1.03953i	−0.854308	−	0.519767i	$-0.826019\pi$
$821$		−	29.7859i		−	1.03953i	0.854308	−	0.519767i	$-0.173981\pi$
$822$	−7.25388	−	4.18803i	−0.253008	−	0.146074i
$823$	−9.75564	−	5.63242i	−0.340060	−	0.196334i	0.320238	−	0.947337i	$-0.396237\pi$
$823$	−9.75564	−	5.63242i	−0.340060	−	0.196334i	−0.660299	+	0.751003i	$0.729570\pi$
$824$	10.0618	+	5.80918i	0.350519	+	0.202372i
$825$	−60.6252	−	35.0020i	−2.11070	−	1.21861i
$826$			34.9609i			1.21645i
$827$	−40.5848			−1.41127			−0.705636	−	0.708575i	$-0.749338\pi$
$827$	−40.5848			−1.41127			−0.705636	+	0.708575i	$0.749338\pi$
$828$	0.561337	+	0.324088i	0.0195078	+	0.0112628i
$829$	−6.85394	+	11.8714i	−0.238047	+	0.412310i	−0.960154	−	0.279472i	$-0.909841\pi$
$829$	−6.85394	+	11.8714i	−0.238047	+	0.412310i	0.722107	+	0.691782i	$0.243174\pi$
$830$			23.0501i			0.800081i
$831$		−	11.3352i		−	0.393214i
$832$	0.125530	+	0.217424i	0.00435197	+	0.00753783i
$833$	56.9250	−	32.8657i	1.97234	−	1.13873i
$834$	23.0768			0.799084
$835$	−5.56373	+	9.63666i	−0.192541	+	0.333490i
$836$	3.94037	−	2.27497i	0.136280	−	0.0786816i
$837$	−3.19422	−	1.84419i	−0.110408	−	0.0637444i
$838$	−9.36980	−	16.2290i	−0.323674	−	0.560621i
$839$	3.93315	+	6.81242i	0.135788	+	0.235191i	0.925898	−	0.377774i	$-0.123310\pi$
$839$	3.93315	+	6.81242i	0.135788	+	0.235191i	−0.790110	+	0.612964i	$0.789977\pi$
$840$	11.9578	−	20.7115i	0.412583	−	0.714614i
$841$	−11.6276	−	20.1396i	−0.400952	−	0.694469i
$842$	−12.2613	+	21.2372i	−0.422552	+	0.731882i
$843$			4.71128i			0.162265i
$844$	12.7837	+	7.38065i	0.440032	+	0.254053i
$845$	−51.5294			−1.77266
$846$			4.04084i			0.138927i
$847$	−64.5172	+	37.2490i	−2.21684	+	1.27989i
$848$	−3.31833	+	1.91584i	−0.113952	+	0.0657902i
$849$	−13.8720	−	24.0270i	−0.476086	−	0.824606i
$850$	22.2716	−	38.5755i	0.763909	−	1.32313i
$851$	4.21643			0.144537
$852$	−6.70106	+	3.86886i	−0.229574	+	0.132545i
$853$	4.99356			0.170976			0.0854881	−	0.996339i	$-0.472755\pi$
$853$	4.99356			0.170976			0.0854881	+	0.996339i	$0.472755\pi$
$854$	−20.7817	−	31.1956i	−0.711134	−	1.06749i
$855$	5.04925			0.172681
$856$	12.7532	−	7.36305i	0.435895	−	0.251664i
$857$	−18.3949			−0.628357			−0.314178	−	0.949364i	$-0.601729\pi$
$857$	−18.3949			−0.628357			−0.314178	+	0.949364i	$0.601729\pi$
$858$	−0.808786	+	1.40086i	−0.0276115	+	0.0478245i
$859$	17.3737	+	30.0922i	0.592784	+	1.02673i	0.993856	+	0.110685i	$0.0353044\pi$
$859$	17.3737	+	30.0922i	0.592784	+	1.02673i	−0.401072	+	0.916047i	$0.631362\pi$
$860$	2.35140	−	1.35758i	0.0801820	−	0.0462931i
$861$	20.6016	−	11.8943i	0.702101	−	0.405358i
$862$		−	19.7154i		−	0.671510i
$863$	7.17114			0.244108			0.122054	−	0.992523i	$-0.461052\pi$
$863$	7.17114			0.244108			0.122054	+	0.992523i	$0.461052\pi$
$864$	−4.80494	−	2.77413i	−0.163467	−	0.0943779i
$865$			30.8269i			1.04814i
$866$	17.0245	−	29.4873i	0.578515	−	1.00202i
$867$	−0.120758	−	0.209158i	−0.00410114	−	0.00710339i
$868$	1.59525	−	2.76305i	0.0541462	−	0.0937839i
$869$	15.7095	+	27.2097i	0.532908	+	0.923024i
$870$	−5.97184	−	10.3435i	−0.202464	−	0.350678i
$871$	2.17884	+	1.25795i	0.0738271	+	0.0426241i
$872$	−0.645913	+	0.372918i	−0.0218734	+	0.0126286i
$873$	9.46947	−	16.4016i	0.320493	−	0.555110i
$874$	0.399103			0.0134998
$875$	97.0988	−	56.0600i	3.28254	−	1.89517i
$876$	−0.559668	−	0.969374i	−0.0189094	−	0.0327521i
$877$			30.0352i			1.01422i	0.861883	+	0.507108i	$0.169285\pi$
$877$			30.0352i			1.01422i	−0.861883	+	0.507108i	$0.830715\pi$
$878$			37.1466i			1.25364i
$879$	−15.3835	+	26.6450i	−0.518872	+	0.898712i
$880$	−17.7648	−	10.2565i	−0.598852	−	0.345748i
$881$	38.5314			1.29815			0.649077	−	0.760722i	$-0.275155\pi$
$881$	38.5314			1.29815			0.649077	+	0.760722i	$0.275155\pi$
$882$		−	23.0056i		−	0.774640i
$883$	42.4128	+	24.4870i	1.42730	+	0.824054i	0.996907	−	0.0785858i	$-0.0250405\pi$
$883$	42.4128	+	24.4870i	1.42730	+	0.824054i	0.430396	+	0.902640i	$0.358374\pi$
$884$	−0.891359	−	0.514626i	−0.0299797	−	0.0173088i
$885$	−31.4365	−	18.1499i	−1.05673	−	0.610101i
$886$	26.9209	+	15.5428i	0.904425	+	0.522170i
$887$		−	49.2250i		−	1.65281i	−0.563073	−	0.826407i	$-0.690381\pi$
$887$		−	49.2250i		−	1.65281i	0.563073	−	0.826407i	$-0.309619\pi$
$888$	−11.6771			−0.391859
$889$	7.74756	+	4.47305i	0.259845	+	0.150021i
$890$	15.3652	−	26.6133i	0.515042	−	0.892078i
$891$		−	13.5788i		−	0.454908i
$892$			9.92678i			0.332373i
$893$	1.24404	+	2.15474i	0.0416301	+	0.0721055i
$894$	20.1888	−	11.6560i	0.675215	−	0.389835i
$895$	24.1429			0.807009
$896$	2.39966	−	4.15633i	0.0801670	−	0.138853i
$897$	−0.122878	+	0.0709434i	−0.00410277	+	0.00236873i
$898$	15.2558	+	8.80795i	0.509093	+	0.293925i
$899$	−0.796682	−	1.37989i	−0.0265708	−	0.0460220i
$900$	−7.79494	−	13.5012i	−0.259831	−	0.450041i
$901$	7.85423	−	13.6039i	0.261662	−	0.453212i
$902$	−10.2021	−	17.6706i	−0.339694	−	0.588366i
$903$	−2.04645	+	3.54456i	−0.0681016	+	0.117955i
$904$		−	0.0337783i		−	0.00112345i
$905$	−45.3131	−	26.1615i	−1.50626	−	0.869638i
$906$	−4.83592			−0.160663
$907$			28.4606i			0.945019i	0.881326	+	0.472510i	$0.156652\pi$
$907$			28.4606i			0.945019i	−0.881326	+	0.472510i	$0.843348\pi$
$908$	1.95413	−	1.12822i	0.0648501	−	0.0374412i
$909$	3.18187	−	1.83706i	0.105536	−	0.0609313i
$910$	−2.39966	−	4.15633i	−0.0795480	−	0.137781i
$911$	−11.2665	+	19.5142i	−0.373277	+	0.646534i	−0.990067	−	0.140593i	$-0.955099\pi$
$911$	−11.2665	+	19.5142i	−0.373277	+	0.646534i	0.616791	+	0.787127i	$0.288432\pi$
$912$	−1.10529			−0.0365998
$913$	−25.8101	+	14.9014i	−0.854188	+	0.493166i
$914$	−17.6723			−0.584549
$915$	38.8395	−	2.49156i	1.28399	−	0.0823683i
$916$	14.7183			0.486305
$917$	24.2722	−	14.0135i	0.801538	−	0.462768i
$918$	22.7458			0.750724
$919$	3.31904	−	5.74875i	0.109485	−	0.189634i	−0.806077	−	0.591811i	$-0.798413\pi$
$919$	3.31904	−	5.74875i	0.109485	−	0.189634i	0.915562	+	0.402177i	$0.131746\pi$
$920$	−0.899661	−	1.55826i	−0.0296609	−	0.0513743i
$921$	−17.2888	+	9.98169i	−0.569685	+	0.328908i
$922$	−18.0172	+	10.4022i	−0.593363	+	0.342578i
$923$			1.55279i			0.0511106i
$924$	30.9219			1.01726
$925$	−87.8265	−	50.7067i	−2.88772	−	1.66722i
$926$			7.65213i			0.251465i
$927$	−8.33529	+	14.4371i	−0.273767	+	0.474178i
$928$	−1.19842	−	2.07572i	−0.0393399	−	0.0681387i
$929$	−0.451738	+	0.782433i	−0.0148210	+	0.0256708i	−0.873341	−	0.487110i	$-0.838051\pi$
$929$	−0.451738	+	0.782433i	−0.0148210	+	0.0256708i	0.858520	+	0.512780i	$0.171385\pi$
$930$	1.65633	+	2.86886i	0.0543134	+	0.0940735i
$931$	−7.08266	−	12.2675i	−0.232125	−	0.402052i
$932$	23.1455	+	13.3631i	0.758156	+	0.437721i
$933$	20.3129	−	11.7277i	0.665015	−	0.383947i
$934$	−2.49973	+	4.32965i	−0.0817936	+	0.141671i
$935$	84.0959			2.75023
$936$	−0.311971	+	0.180117i	−0.0101971	+	0.00588730i
$937$	−9.69467	−	16.7917i	−0.316711	−	0.548560i	0.663089	−	0.748541i	$-0.269245\pi$
$937$	−9.69467	−	16.7917i	−0.316711	−	0.548560i	−0.979800	+	0.199981i	$0.935912\pi$
$938$		−	48.0946i		−	1.57035i
$939$		−	15.1810i		−	0.495415i
$940$	5.60864	−	9.71445i	0.182934	−	0.316850i
$941$	31.5992	+	18.2438i	1.03011	+	0.594732i	0.917015	−	0.398853i	$-0.130592\pi$
$941$	31.5992	+	18.2438i	1.03011	+	0.594732i	0.113091	+	0.993585i	$0.463925\pi$
$942$	11.9719			0.390065
$943$		−	1.78978i		−	0.0582832i
$944$	−6.30861	−	3.64228i	−0.205328	−	0.118546i
$945$	91.8523	+	53.0309i	2.98795	+	1.72510i
$946$	3.04027	+	1.75530i	0.0988477	+	0.0570697i
$947$	38.8857	+	22.4507i	1.26362	+	0.729550i	0.973772	−	0.227524i	$-0.0730631\pi$
$947$	38.8857	+	22.4507i	1.26362	+	0.729550i	0.289844	+	0.957074i	$0.406396\pi$
$948$		−	7.63242i		−	0.247890i
$949$	−0.224626			−0.00729167
$950$	−8.31314	−	4.79960i	−0.269714	−	0.155719i
$951$	−21.3610	+	36.9983i	−0.692677	+	1.19975i
$952$			19.6754i			0.637685i
$953$			16.8679i			0.546406i	0.961956	+	0.273203i	$0.0880830\pi$
$953$			16.8679i			0.546406i	−0.961956	+	0.273203i	$0.911917\pi$
$954$	−2.74894	−	4.76130i	−0.0890002	−	0.154153i
$955$	−74.4369	+	42.9762i	−2.40872	+	1.39068i
$956$	0.426083			0.0137805
$957$	7.72136	−	13.3738i	0.249596	−	0.432313i
$958$	−2.89640	+	1.67224i	−0.0935786	+	0.0540276i
$959$	27.8274	+	16.0661i	0.898592	+	0.518803i
$960$	2.49156	+	4.31550i	0.0804146	+	0.139282i
$961$	−15.2790	−	26.4641i	−0.492872	−	0.853679i
$962$	−1.17167	+	2.02940i	−0.0377762	+	0.0654303i
$963$	10.5649	+	18.2989i	0.340448	+	0.589673i
$964$	−9.00000	+	15.5885i	−0.289870	+	0.502070i
$965$		−	5.67497i		−	0.182684i
$966$	2.34896	+	1.35617i	0.0755765	+	0.0436341i
$967$	38.1254			1.22603			0.613014	−	0.790072i	$-0.289957\pi$
$967$	38.1254			1.22603			0.613014	+	0.790072i	$0.289957\pi$
$968$		−	15.5226i		−	0.498915i
$969$	3.92420	−	2.26564i	0.126064	−	0.0727828i
$970$	−45.5305	+	26.2871i	−1.46190	+	0.844026i
$971$	−13.4964	−	23.3764i	−0.433119	−	0.750184i	0.564021	−	0.825760i	$-0.309254\pi$
$971$	−13.4964	−	23.3764i	−0.433119	−	0.750184i	−0.997140	+	0.0755764i	$0.975920\pi$
$972$	6.67308	−	11.5581i	0.214039	−	0.370727i
$973$	−88.5273			−2.83805
$974$	16.8742	−	9.74233i	0.540685	−	0.312164i
$975$	3.41265			0.109292
$976$	7.79423	−	0.500000i	0.249487	−	0.0160046i
$977$	37.0278			1.18462			0.592312	−	0.805709i	$-0.298215\pi$
$977$	37.0278			1.18462			0.592312	+	0.805709i	$0.298215\pi$
$978$	0.398252	−	0.229931i	0.0127347	−	0.00735237i
$979$	39.7332			1.26988
$980$	−31.9316	+	55.3071i	−1.02002	+	1.76672i
$981$	−0.535081	−	0.926787i	−0.0170838	−	0.0295900i
$982$	0.745836	−	0.430609i	0.0238006	−	0.0137413i
$983$	−4.40503	+	2.54324i	−0.140498	+	0.0811168i	−0.568602	−	0.822613i	$-0.692515\pi$
$983$	−4.40503	+	2.54324i	−0.140498	+	0.0811168i	0.428103	+	0.903730i	$0.359182\pi$
$984$			4.95668i			0.158013i
$985$	−108.052			−3.44281
$986$	8.50966	+	4.91306i	0.271003	+	0.156464i
$987$			16.9092i			0.538226i
$988$	−0.110904	+	0.192091i	−0.00352831	+	0.00611122i
$989$	0.153968	+	0.266680i	0.00489589	+	0.00847993i
$990$	14.7166	−	25.4898i	0.467723	−	0.810121i
$991$	−27.5465	−	47.7120i	−0.875044	−	1.51562i	−0.856716	−	0.515788i	$-0.827499\pi$
$991$	−27.5465	−	47.7120i	−0.875044	−	1.51562i	−0.0183274	−	0.999832i	$-0.505834\pi$
$992$	0.332390	+	0.575716i	0.0105534	+	0.0182790i
$993$	−16.0724	−	9.27942i	−0.510043	−	0.294474i
$994$	25.7066	−	14.8417i	0.815364	−	0.470751i
$995$	−27.0725	+	46.8909i	−0.858255	+	1.48654i
$996$	7.23983			0.229403
$997$	−28.9843	+	16.7341i	−0.917942	+	0.529974i	−0.882978	−	0.469415i	$-0.844465\pi$
$997$	−28.9843	+	16.7341i	−0.917942	+	0.529974i	−0.0349637	+	0.999389i	$0.511132\pi$
$998$	6.09401	+	10.5551i	0.192903	+	0.334117i
$999$		−	51.7864i		−	1.63845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.f.a.75.2	✓	8
3.2	odd	2		1098.2.o.a.685.4		8
4.3	odd	2		976.2.ba.b.929.2		8
61.29	odd	12		7442.2.a.m.1.2		4
61.32	odd	12		7442.2.a.l.1.2		4
61.48	even	6	inner	122.2.f.a.109.2	yes	8
183.170	odd	6		1098.2.o.a.109.4		8
244.231	odd	6		976.2.ba.b.353.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.f.a.75.2	✓	8	1.1	even	1	trivial
122.2.f.a.109.2	yes	8	61.48	even	6	inner
976.2.ba.b.353.2		8	244.231	odd	6
976.2.ba.b.929.2		8	4.3	odd	2
1098.2.o.a.109.4		8	183.170	odd	6
1098.2.o.a.685.4		8	3.2	odd	2
7442.2.a.l.1.2		4	61.32	odd	12
7442.2.a.m.1.2		4	61.29	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +1.25106 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.99156 - 3.44948i) q^{5} +(-1.08345 + 0.625530i) q^{6} +(4.15633 - 2.39966i) q^{7} +1.00000i q^{8} -1.43485 q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +1.25106 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.99156 - 3.44948i) q^{5} +(-1.08345 + 0.625530i) q^{6} +(4.15633 - 2.39966i) q^{7} +1.00000i q^{8} -1.43485 q^{9} +(3.44948 + 1.99156i) q^{10} +5.15001i q^{11} +(0.625530 - 1.08345i) q^{12} +(-0.125530 - 0.217424i) q^{13} +(-2.39966 + 4.15633i) q^{14} +(-2.49156 - 4.31550i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.55038 + 2.04981i) q^{17} +(1.24262 - 0.717424i) q^{18} +(0.441741 - 0.765118i) q^{19} -3.98311 q^{20} +(5.19982 - 3.00212i) q^{21} +(-2.57501 - 4.46004i) q^{22} -0.451738i q^{23} +1.25106i q^{24} +(-5.43259 + 9.40952i) q^{25} +(0.217424 + 0.125530i) q^{26} -5.54826 q^{27} -4.79932i q^{28} +(-2.07572 - 1.19842i) q^{29} +(4.31550 + 2.49156i) q^{30} +(0.575716 + 0.332390i) q^{31} +(0.866025 + 0.500000i) q^{32} +6.44297i q^{33} -4.09963 q^{34} +(-16.5551 - 9.55812i) q^{35} +(-0.717424 + 1.24262i) q^{36} +9.33380i q^{37} +0.883483i q^{38} +(-0.157046 - 0.272011i) q^{39} +(3.44948 - 1.99156i) q^{40} +3.96198 q^{41} +(-3.00212 + 5.19982i) q^{42} +(-0.590342 + 0.340834i) q^{43} +(4.46004 + 2.57501i) q^{44} +(2.85758 + 4.94948i) q^{45} +(0.225869 + 0.391216i) q^{46} +(-1.40811 + 2.43891i) q^{47} +(-0.625530 - 1.08345i) q^{48} +(8.01675 - 13.8854i) q^{49} -10.8652i q^{50} +(4.44174 + 2.56444i) q^{51} -0.251060 q^{52} -3.83168i q^{53} +(4.80494 - 2.77413i) q^{54} +(17.7648 - 10.2565i) q^{55} +(2.39966 + 4.15633i) q^{56} +(0.552645 - 0.957209i) q^{57} +2.39683 q^{58} +(6.30861 - 3.64228i) q^{59} -4.98311 q^{60} +(-3.46410 + 7.00000i) q^{61} -0.664779 q^{62} +(-5.96371 + 3.44315i) q^{63} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-3.22149 - 5.57978i) q^{66} +(-8.67855 + 5.01056i) q^{67} +(3.55038 - 2.04981i) q^{68} -0.565151i q^{69} +19.1162 q^{70} +(-5.35630 - 3.09246i) q^{71} -1.43485i q^{72} +(0.447355 - 0.774842i) q^{73} +(-4.66690 - 8.08331i) q^{74} +(-6.79649 + 11.7719i) q^{75} +(-0.441741 - 0.765118i) q^{76} +(12.3583 + 21.4052i) q^{77} +(0.272011 + 0.157046i) q^{78} +(5.28342 - 3.05038i) q^{79} +(-1.99156 + 3.44948i) q^{80} -2.63666 q^{81} +(-3.43118 + 1.98099i) q^{82} +(2.89348 + 5.01165i) q^{83} -6.00424i q^{84} -16.3293i q^{85} +(0.340834 - 0.590342i) q^{86} +(-2.59685 - 1.49929i) q^{87} -5.15001 q^{88} -7.71516i q^{89} +(-4.94948 - 2.85758i) q^{90} +(-1.04349 - 0.602459i) q^{91} +(-0.391216 - 0.225869i) q^{92} +(0.720255 + 0.415840i) q^{93} -2.81621i q^{94} -3.51901 q^{95} +(1.08345 + 0.625530i) q^{96} +(-6.59963 + 11.4309i) q^{97} +16.0335i q^{98} -7.38949i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9	\( 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9} + 6 q^{10} + 4 q^{13} - 10 q^{14} - 8 q^{15} - 4 q^{16} - 12 q^{18} + 4 q^{19} - 8 q^{20} - 24 q^{21} + 6 q^{22} + 2 q^{25} - 6 q^{26} - 36 q^{27} - 24 q^{29} + 6 q^{30} + 12 q^{31} - 8 q^{34} - 18 q^{35} + 2 q^{36} - 14 q^{39} + 6 q^{40} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 6 q^{44} + 4 q^{45} + 6 q^{46} - 14 q^{47} + 38 q^{49} + 36 q^{51} + 8 q^{52} + 18 q^{54} + 42 q^{55} + 10 q^{56} + 6 q^{57} - 4 q^{58} + 6 q^{59} - 16 q^{60} + 4 q^{62} + 6 q^{63} - 8 q^{64} - 4 q^{65} - 20 q^{66} + 30 q^{67} + 52 q^{70} - 6 q^{71} + 2 q^{73} - 8 q^{74} - 22 q^{75} - 4 q^{76} - 8 q^{77} + 18 q^{78} + 12 q^{79} - 4 q^{80} + 8 q^{81} - 36 q^{82} + 32 q^{83} + 10 q^{86} - 12 q^{87} + 12 q^{88} - 18 q^{90} + 36 q^{91} + 18 q^{92} + 12 q^{93} - 32 q^{95} - 6 q^{96} - 28 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9 + 6 * q^10 + 4 * q^13 - 10 * q^14 - 8 * q^15 - 4 * q^16 - 12 * q^18 + 4 * q^19 - 8 * q^20 - 24 * q^21 + 6 * q^22 + 2 * q^25 - 6 * q^26 - 36 * q^27 - 24 * q^29 + 6 * q^30 + 12 * q^31 - 8 * q^34 - 18 * q^35 + 2 * q^36 - 14 * q^39 + 6 * q^40 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 6 * q^44 + 4 * q^45 + 6 * q^46 - 14 * q^47 + 38 * q^49 + 36 * q^51 + 8 * q^52 + 18 * q^54 + 42 * q^55 + 10 * q^56 + 6 * q^57 - 4 * q^58 + 6 * q^59 - 16 * q^60 + 4 * q^62 + 6 * q^63 - 8 * q^64 - 4 * q^65 - 20 * q^66 + 30 * q^67 + 52 * q^70 - 6 * q^71 + 2 * q^73 - 8 * q^74 - 22 * q^75 - 4 * q^76 - 8 * q^77 + 18 * q^78 + 12 * q^79 - 4 * q^80 + 8 * q^81 - 36 * q^82 + 32 * q^83 + 10 * q^86 - 12 * q^87 + 12 * q^88 - 18 * q^90 + 36 * q^91 + 18 * q^92 + 12 * q^93 - 32 * q^95 - 6 * q^96 - 28 * q^97

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