LMFDB - Embedded newform 122.2.c.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(13,122)]

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([4]))

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

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

chi := DirichletCharacter("122.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.c (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.2
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	122.13
Dual form			122.2.c.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +2.30278 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.15139 + 1.99426i) q^{5} +(1.15139 - 1.99426i) q^{6} +(0.348612 - 0.603814i) q^{7} -1.00000 q^{8} +2.30278 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +2.30278 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.15139 + 1.99426i) q^{5} +(1.15139 - 1.99426i) q^{6} +(0.348612 - 0.603814i) q^{7} -1.00000 q^{8} +2.30278 q^{9} +(1.15139 + 1.99426i) q^{10} -5.60555 q^{11} +(-1.15139 - 1.99426i) q^{12} +(0.651388 - 1.12824i) q^{13} +(-0.348612 - 0.603814i) q^{14} +(-2.65139 + 4.59234i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.197224 + 0.341603i) q^{17} +(1.15139 - 1.99426i) q^{18} +(-2.15139 - 3.72631i) q^{19} +2.30278 q^{20} +(0.802776 - 1.39045i) q^{21} +(-2.80278 + 4.85455i) q^{22} +7.60555 q^{23} -2.30278 q^{24} +(-0.151388 - 0.262211i) q^{25} +(-0.651388 - 1.12824i) q^{26} -1.60555 q^{27} -0.697224 q^{28} +(2.15139 + 3.72631i) q^{29} +(2.65139 + 4.59234i) q^{30} +(1.95416 + 3.38471i) q^{31} +(0.500000 + 0.866025i) q^{32} -12.9083 q^{33} +0.394449 q^{34} +(0.802776 + 1.39045i) q^{35} +(-1.15139 - 1.99426i) q^{36} -0.394449 q^{37} -4.30278 q^{38} +(1.50000 - 2.59808i) q^{39} +(1.15139 - 1.99426i) q^{40} -10.8167 q^{41} +(-0.802776 - 1.39045i) q^{42} +(5.10555 - 8.84307i) q^{43} +(2.80278 + 4.85455i) q^{44} +(-2.65139 + 4.59234i) q^{45} +(3.80278 - 6.58660i) q^{46} +(5.80278 + 10.0507i) q^{47} +(-1.15139 + 1.99426i) q^{48} +(3.25694 + 5.64118i) q^{49} -0.302776 q^{50} +(0.454163 + 0.786634i) q^{51} -1.30278 q^{52} +0.605551 q^{53} +(-0.802776 + 1.39045i) q^{54} +(6.45416 - 11.1789i) q^{55} +(-0.348612 + 0.603814i) q^{56} +(-4.95416 - 8.58086i) q^{57} +4.30278 q^{58} +(5.40833 - 9.36750i) q^{59} +5.30278 q^{60} +(-3.60555 - 6.92820i) q^{61} +3.90833 q^{62} +(0.802776 - 1.39045i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(-6.45416 + 11.1789i) q^{66} +(5.95416 - 10.3129i) q^{67} +(0.197224 - 0.341603i) q^{68} +17.5139 q^{69} +1.60555 q^{70} +(-6.80278 - 11.7828i) q^{71} -2.30278 q^{72} +(-0.651388 - 1.12824i) q^{73} +(-0.197224 + 0.341603i) q^{74} +(-0.348612 - 0.603814i) q^{75} +(-2.15139 + 3.72631i) q^{76} +(-1.95416 + 3.38471i) q^{77} +(-1.50000 - 2.59808i) q^{78} +(-2.90833 + 5.03737i) q^{79} +(-1.15139 - 1.99426i) q^{80} -10.6056 q^{81} +(-5.40833 + 9.36750i) q^{82} +(-6.45416 + 11.1789i) q^{83} -1.60555 q^{84} -0.908327 q^{85} +(-5.10555 - 8.84307i) q^{86} +(4.95416 + 8.58086i) q^{87} +5.60555 q^{88} +4.69722 q^{89} +(2.65139 + 4.59234i) q^{90} +(-0.454163 - 0.786634i) q^{91} +(-3.80278 - 6.58660i) q^{92} +(4.50000 + 7.79423i) q^{93} +11.6056 q^{94} +9.90833 q^{95} +(1.15139 + 1.99426i) q^{96} +(0.105551 + 0.182820i) q^{97} +6.51388 q^{98} -12.9083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + q^{6} + 5 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + q^6 + 5 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + q^{6} + 5 q^{7} - 4 q^{8} + 2 q^{9} + q^{10} - 8 q^{11} - q^{12} - q^{13} - 5 q^{14} - 7 q^{15} - 2 q^{16} + 8 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} - 4 q^{21} - 4 q^{22} + 16 q^{23} - 2 q^{24} + 3 q^{25} + q^{26} + 8 q^{27} - 10 q^{28} + 5 q^{29} + 7 q^{30} - 3 q^{31} + 2 q^{32} - 30 q^{33} + 16 q^{34} - 4 q^{35} - q^{36} - 16 q^{37} - 10 q^{38} + 6 q^{39} + q^{40} + 4 q^{42} + 6 q^{43} + 4 q^{44} - 7 q^{45} + 8 q^{46} + 16 q^{47} - q^{48} - 5 q^{49} + 6 q^{50} - 9 q^{51} + 2 q^{52} - 12 q^{53} + 4 q^{54} + 15 q^{55} - 5 q^{56} - 9 q^{57} + 10 q^{58} + 14 q^{60} - 6 q^{62} - 4 q^{63} + 4 q^{64} + 6 q^{65} - 15 q^{66} + 13 q^{67} + 8 q^{68} + 34 q^{69} - 8 q^{70} - 20 q^{71} - 2 q^{72} + q^{73} - 8 q^{74} - 5 q^{75} - 5 q^{76} + 3 q^{77} - 6 q^{78} + 10 q^{79} - q^{80} - 28 q^{81} - 15 q^{83} + 8 q^{84} + 18 q^{85} - 6 q^{86} + 9 q^{87} + 8 q^{88} + 26 q^{89} + 7 q^{90} + 9 q^{91} - 8 q^{92} + 18 q^{93} + 32 q^{94} + 18 q^{95} + q^{96} - 14 q^{97} - 10 q^{98} - 30 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + q^6 + 5 * q^7 - 4 * q^8 + 2 * q^9 + q^10 - 8 * q^11 - q^12 - q^13 - 5 * q^14 - 7 * q^15 - 2 * q^16 + 8 * q^17 + q^18 - 5 * q^19 + 2 * q^20 - 4 * q^21 - 4 * q^22 + 16 * q^23 - 2 * q^24 + 3 * q^25 + q^26 + 8 * q^27 - 10 * q^28 + 5 * q^29 + 7 * q^30 - 3 * q^31 + 2 * q^32 - 30 * q^33 + 16 * q^34 - 4 * q^35 - q^36 - 16 * q^37 - 10 * q^38 + 6 * q^39 + q^40 + 4 * q^42 + 6 * q^43 + 4 * q^44 - 7 * q^45 + 8 * q^46 + 16 * q^47 - q^48 - 5 * q^49 + 6 * q^50 - 9 * q^51 + 2 * q^52 - 12 * q^53 + 4 * q^54 + 15 * q^55 - 5 * q^56 - 9 * q^57 + 10 * q^58 + 14 * q^60 - 6 * q^62 - 4 * q^63 + 4 * q^64 + 6 * q^65 - 15 * q^66 + 13 * q^67 + 8 * q^68 + 34 * q^69 - 8 * q^70 - 20 * q^71 - 2 * q^72 + q^73 - 8 * q^74 - 5 * q^75 - 5 * q^76 + 3 * q^77 - 6 * q^78 + 10 * q^79 - q^80 - 28 * q^81 - 15 * q^83 + 8 * q^84 + 18 * q^85 - 6 * q^86 + 9 * q^87 + 8 * q^88 + 26 * q^89 + 7 * q^90 + 9 * q^91 - 8 * q^92 + 18 * q^93 + 32 * q^94 + 18 * q^95 + q^96 - 14 * q^97 - 10 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$63$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	2.30278			1.32951			0.664754	−	0.747062i	$-0.268536\pi$
$3$	2.30278			1.32951			0.664754	+	0.747062i	$0.268536\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.15139	+	1.99426i	−0.514916	+	0.891861i	0.484934	+	0.874551i	$0.338844\pi$
$5$	−1.15139	+	1.99426i	−0.514916	+	0.891861i	−0.999850	+	0.0173104i	$0.994490\pi$
$6$	1.15139	−	1.99426i	0.470052	−	0.814154i
$7$	0.348612	−	0.603814i	0.131763	−	0.228220i	−0.792593	−	0.609751i	$-0.791270\pi$
$7$	0.348612	−	0.603814i	0.131763	−	0.228220i	0.924356	+	0.381531i	$0.124603\pi$
$8$	−1.00000			−0.353553
$9$	2.30278			0.767592
$10$	1.15139	+	1.99426i	0.364101	+	0.630641i
$11$	−5.60555			−1.69014			−0.845069	−	0.534658i	$-0.820441\pi$
$11$	−5.60555			−1.69014			−0.845069	+	0.534658i	$0.820441\pi$
$12$	−1.15139	−	1.99426i	−0.332377	−	0.575694i
$13$	0.651388	−	1.12824i	0.180662	−	0.312917i	−0.761444	−	0.648231i	$-0.775509\pi$
$13$	0.651388	−	1.12824i	0.180662	−	0.312917i	0.942106	+	0.335314i	$0.108843\pi$
$14$	−0.348612	−	0.603814i	−0.0931705	−	0.161376i
$15$	−2.65139	+	4.59234i	−0.684585	+	1.18574i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.197224	+	0.341603i	0.0478339	+	0.0828508i	0.888951	−	0.458002i	$-0.151435\pi$
$17$	0.197224	+	0.341603i	0.0478339	+	0.0828508i	−0.841117	+	0.540853i	$0.818102\pi$
$18$	1.15139	−	1.99426i	0.271385	−	0.470052i
$19$	−2.15139	−	3.72631i	−0.493562	−	0.854875i	0.506410	−	0.862293i	$-0.330972\pi$
$19$	−2.15139	−	3.72631i	−0.493562	−	0.854875i	−0.999972	+	0.00741783i	$0.997639\pi$
$20$	2.30278			0.514916
$21$	0.802776	−	1.39045i	0.175180	−	0.303421i
$22$	−2.80278	+	4.85455i	−0.597554	+	1.03499i
$23$	7.60555			1.58587			0.792934	−	0.609308i	$-0.208553\pi$
$23$	7.60555			1.58587			0.792934	+	0.609308i	$0.208553\pi$
$24$	−2.30278			−0.470052
$25$	−0.151388	−	0.262211i	−0.0302776	−	0.0524423i
$26$	−0.651388	−	1.12824i	−0.127748	−	0.221265i
$27$	−1.60555			−0.308988
$28$	−0.697224			−0.131763
$29$	2.15139	+	3.72631i	0.399503	+	0.691959i	0.993665	−	0.112387i	$-0.0358495\pi$
$29$	2.15139	+	3.72631i	0.399503	+	0.691959i	−0.594162	+	0.804345i	$0.702516\pi$
$30$	2.65139	+	4.59234i	0.484075	+	0.838442i
$31$	1.95416	+	3.38471i	0.350978	+	0.607912i	0.986421	−	0.164236i	$-0.0525158\pi$
$31$	1.95416	+	3.38471i	0.350978	+	0.607912i	−0.635443	+	0.772148i	$0.719182\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−12.9083			−2.24705
$34$	0.394449			0.0676474
$35$	0.802776	+	1.39045i	0.135694	+	0.235029i
$36$	−1.15139	−	1.99426i	−0.191898	−	0.332377i
$37$	−0.394449			−0.0648470			−0.0324235	−	0.999474i	$-0.510323\pi$
$37$	−0.394449			−0.0648470			−0.0324235	+	0.999474i	$0.510323\pi$
$38$	−4.30278			−0.698002
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$	1.15139	−	1.99426i	0.182050	−	0.315321i
$41$	−10.8167			−1.68928			−0.844639	−	0.535337i	$-0.820185\pi$
$41$	−10.8167			−1.68928			−0.844639	+	0.535337i	$0.820185\pi$
$42$	−0.802776	−	1.39045i	−0.123871	−	0.214551i
$43$	5.10555	−	8.84307i	0.778589	−	1.34856i	−0.154166	−	0.988045i	$-0.549269\pi$
$43$	5.10555	−	8.84307i	0.778589	−	1.34856i	0.932755	−	0.360511i	$-0.117398\pi$
$44$	2.80278	+	4.85455i	0.422534	+	0.731851i
$45$	−2.65139	+	4.59234i	−0.395246	+	0.684585i
$46$	3.80278	−	6.58660i	0.560689	−	0.971141i
$47$	5.80278	+	10.0507i	0.846422	+	1.46605i	0.884381	+	0.466766i	$0.154581\pi$
$47$	5.80278	+	10.0507i	0.846422	+	1.46605i	−0.0379589	+	0.999279i	$0.512086\pi$
$48$	−1.15139	+	1.99426i	−0.166189	+	0.287847i
$49$	3.25694	+	5.64118i	0.465277	+	0.805883i
$50$	−0.302776			−0.0428189
$51$	0.454163	+	0.786634i	0.0635956	+	0.110151i
$52$	−1.30278			−0.180662
$53$	0.605551			0.0831789			0.0415894	−	0.999135i	$-0.486758\pi$
$53$	0.605551			0.0831789			0.0415894	+	0.999135i	$0.486758\pi$
$54$	−0.802776	+	1.39045i	−0.109244	+	0.189216i
$55$	6.45416	−	11.1789i	0.870279	−	1.50737i
$56$	−0.348612	+	0.603814i	−0.0465853	+	0.0806880i
$57$	−4.95416	−	8.58086i	−0.656195	−	1.13656i
$58$	4.30278			0.564982
$59$	5.40833	−	9.36750i	0.704104	−	1.21954i	−0.262910	−	0.964820i	$-0.584682\pi$
$59$	5.40833	−	9.36750i	0.704104	−	1.21954i	0.967014	−	0.254724i	$-0.0819845\pi$
$60$	5.30278			0.684585
$61$	−3.60555	−	6.92820i	−0.461644	−	0.887066i
$61$	−3.60555	−	6.92820i	−0.461644	−	0.887066i
$62$	3.90833			0.496358
$63$	0.802776	−	1.39045i	0.101140	−	0.175180i
$64$	1.00000			0.125000
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$	−6.45416	+	11.1789i	−0.794453	+	1.37603i
$67$	5.95416	−	10.3129i	0.727417	−	1.25992i	−0.230555	−	0.973059i	$-0.574054\pi$
$67$	5.95416	−	10.3129i	0.727417	−	1.25992i	0.957971	−	0.286864i	$-0.0926126\pi$
$68$	0.197224	−	0.341603i	0.0239170	−	0.0414254i
$69$	17.5139			2.10842
$70$	1.60555			0.191900
$71$	−6.80278	−	11.7828i	−0.807341	−	1.39836i	−0.914699	−	0.404135i	$-0.867573\pi$
$71$	−6.80278	−	11.7828i	−0.807341	−	1.39836i	0.107358	−	0.994220i	$-0.465761\pi$
$72$	−2.30278			−0.271385
$73$	−0.651388	−	1.12824i	−0.0762392	−	0.132050i	0.825385	−	0.564570i	$-0.190958\pi$
$73$	−0.651388	−	1.12824i	−0.0762392	−	0.132050i	−0.901624	+	0.432520i	$0.857625\pi$
$74$	−0.197224	+	0.341603i	−0.0229269	+	0.0397105i
$75$	−0.348612	−	0.603814i	−0.0402543	−	0.0697224i
$76$	−2.15139	+	3.72631i	−0.246781	+	0.427437i
$77$	−1.95416	+	3.38471i	−0.222698	+	0.385724i
$78$	−1.50000	−	2.59808i	−0.169842	−	0.294174i
$79$	−2.90833	+	5.03737i	−0.327212	+	0.566748i	−0.981958	−	0.189101i	$-0.939443\pi$
$79$	−2.90833	+	5.03737i	−0.327212	+	0.566748i	0.654745	+	0.755850i	$0.272776\pi$
$80$	−1.15139	−	1.99426i	−0.128729	−	0.222965i
$81$	−10.6056			−1.17839
$82$	−5.40833	+	9.36750i	−0.597250	+	1.03447i
$83$	−6.45416	+	11.1789i	−0.708436	+	1.22705i	0.257000	+	0.966411i	$0.417266\pi$
$83$	−6.45416	+	11.1789i	−0.708436	+	1.22705i	−0.965437	+	0.260637i	$0.916068\pi$
$84$	−1.60555			−0.175180
$85$	−0.908327			−0.0985219
$86$	−5.10555	−	8.84307i	−0.550546	−	0.953573i
$87$	4.95416	+	8.58086i	0.531142	+	0.919965i
$88$	5.60555			0.597554
$89$	4.69722			0.497905			0.248952	−	0.968516i	$-0.419914\pi$
$89$	4.69722			0.497905			0.248952	+	0.968516i	$0.419914\pi$
$90$	2.65139	+	4.59234i	0.279481	+	0.484075i
$91$	−0.454163	−	0.786634i	−0.0476093	−	0.0824617i
$92$	−3.80278	−	6.58660i	−0.396467	−	0.686701i
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$	11.6056			1.19702
$95$	9.90833			1.01657
$96$	1.15139	+	1.99426i	0.117513	+	0.203539i
$97$	0.105551	+	0.182820i	0.0107171	+	0.0185626i	0.871334	−	0.490690i	$-0.163255\pi$
$97$	0.105551	+	0.182820i	0.0107171	+	0.0185626i	−0.860617	+	0.509253i	$0.829922\pi$
$98$	6.51388			0.658001
$99$	−12.9083			−1.29734
$100$	−0.151388	+	0.262211i	−0.0151388	+	0.0262211i
$101$	−4.69722	+	8.13583i	−0.467391	+	0.809545i	−0.999306	−	0.0372525i	$-0.988139\pi$
$101$	−4.69722	+	8.13583i	−0.467391	+	0.809545i	0.531915	+	0.846798i	$0.321473\pi$
$102$	0.908327			0.0899378
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	−0.651388	+	1.12824i	−0.0638738	+	0.110633i
$105$	1.84861	+	3.20189i	0.180406	+	0.312472i
$106$	0.302776	−	0.524423i	0.0294082	−	0.0509364i
$107$	2.60555	−	4.51295i	0.251888	−	0.436283i	−0.712158	−	0.702020i	$-0.752282\pi$
$107$	2.60555	−	4.51295i	0.251888	−	0.436283i	0.964046	+	0.265737i	$0.0856152\pi$
$108$	0.802776	+	1.39045i	0.0772471	+	0.133796i
$109$	−1.54584	+	2.67747i	−0.148064	+	0.256455i	−0.930512	−	0.366261i	$-0.880638\pi$
$109$	−1.54584	+	2.67747i	−0.148064	+	0.256455i	0.782448	+	0.622716i	$0.213971\pi$
$110$	−6.45416	−	11.1789i	−0.615380	−	1.06587i
$111$	−0.908327			−0.0862146
$112$	0.348612	+	0.603814i	0.0329408	+	0.0570551i
$113$	−16.6056			−1.56212			−0.781059	−	0.624457i	$-0.785320\pi$
$113$	−16.6056			−1.56212			−0.781059	+	0.624457i	$0.785320\pi$
$114$	−9.90833			−0.928000
$115$	−8.75694	+	15.1675i	−0.816589	+	1.41437i
$116$	2.15139	−	3.72631i	0.199751	−	0.345979i
$117$	1.50000	−	2.59808i	0.138675	−	0.240192i
$118$	−5.40833	−	9.36750i	−0.497877	−	0.862348i
$119$	0.275019			0.0252110
$120$	2.65139	−	4.59234i	0.242037	−	0.419221i
$121$	20.4222			1.85656
$122$	−7.80278	−	0.341603i	−0.706430	−	0.0309272i
$123$	−24.9083			−2.24591
$124$	1.95416	−	3.38471i	0.175489	−	0.303956i
$125$	−10.8167			−0.967471
$126$	−0.802776	−	1.39045i	−0.0715169	−	0.123871i
$127$	−2.54584	+	4.40952i	−0.225906	+	0.391281i	−0.956591	−	0.291434i	$-0.905868\pi$
$127$	−2.54584	+	4.40952i	−0.225906	+	0.391281i	0.730685	+	0.682715i	$0.239201\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	11.7569	−	20.3636i	1.03514	−	1.79292i
$130$	3.00000			0.263117
$131$	12.8167			1.11980			0.559898	−	0.828561i	$-0.310840\pi$
$131$	12.8167			1.11980			0.559898	+	0.828561i	$0.310840\pi$
$132$	6.45416	+	11.1789i	0.561763	+	0.973002i
$133$	−3.00000			−0.260133
$134$	−5.95416	−	10.3129i	−0.514361	−	0.890900i
$135$	1.84861	−	3.20189i	0.159103	−	0.275575i
$136$	−0.197224	−	0.341603i	−0.0169118	−	0.0292922i
$137$	−5.30278	+	9.18468i	−0.453047	+	0.784700i	−0.998574	−	0.0533934i	$-0.982996\pi$
$137$	−5.30278	+	9.18468i	−0.453047	+	0.784700i	0.545527	+	0.838093i	$0.316330\pi$
$138$	8.75694	−	15.1675i	0.745440	−	1.29114i
$139$	−0.802776	−	1.39045i	−0.0680905	−	0.117936i	0.829970	−	0.557808i	$-0.188357\pi$
$139$	−0.802776	−	1.39045i	−0.0680905	−	0.117936i	−0.898061	+	0.439871i	$0.855024\pi$
$140$	0.802776	−	1.39045i	0.0678469	−	0.117514i
$141$	13.3625	+	23.1445i	1.12532	+	1.94912i
$142$	−13.6056			−1.14175
$143$	−3.65139	+	6.32439i	−0.305344	+	0.528872i
$144$	−1.15139	+	1.99426i	−0.0959490	+	0.166189i
$145$	−9.90833			−0.822842
$146$	−1.30278			−0.107818
$147$	7.50000	+	12.9904i	0.618590	+	1.07143i
$148$	0.197224	+	0.341603i	0.0162117	+	0.0280796i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	−0.697224			−0.0569281
$151$	−0.394449	−	0.683205i	−0.0320998	−	0.0555985i	0.849529	−	0.527542i	$-0.176886\pi$
$151$	−0.394449	−	0.683205i	−0.0320998	−	0.0555985i	−0.881629	+	0.471943i	$0.843553\pi$
$152$	2.15139	+	3.72631i	0.174501	+	0.302244i
$153$	0.454163	+	0.786634i	0.0367169	+	0.0635956i
$154$	1.95416	+	3.38471i	0.157471	+	0.272748i
$155$	−9.00000			−0.722897
$156$	−3.00000			−0.240192
$157$	−2.45416	−	4.25074i	−0.195864	−	0.339246i	0.751320	−	0.659938i	$-0.229418\pi$
$157$	−2.45416	−	4.25074i	−0.195864	−	0.339246i	−0.947183	+	0.320693i	$0.896084\pi$
$158$	2.90833	+	5.03737i	0.231374	+	0.400752i
$159$	1.39445			0.110587
$160$	−2.30278			−0.182050
$161$	2.65139	−	4.59234i	0.208959	−	0.361927i
$162$	−5.30278	+	9.18468i	−0.416625	+	0.721616i
$163$	−6.60555			−0.517387			−0.258693	−	0.965959i	$-0.583292\pi$
$163$	−6.60555			−0.517387			−0.258693	+	0.965959i	$0.583292\pi$
$164$	5.40833	+	9.36750i	0.422319	+	0.731479i
$165$	14.8625	−	25.7426i	1.15704	−	2.00406i
$166$	6.45416	+	11.1789i	0.500940	+	0.867654i
$167$	3.69722	−	6.40378i	0.286100	−	0.495539i	−0.686775	−	0.726870i	$-0.740974\pi$
$167$	3.69722	−	6.40378i	0.286100	−	0.495539i	0.972875	+	0.231330i	$0.0743078\pi$
$168$	−0.802776	+	1.39045i	−0.0619355	+	0.107275i
$169$	5.65139	+	9.78849i	0.434722	+	0.752961i
$170$	−0.454163	+	0.786634i	−0.0348327	+	0.0603321i
$171$	−4.95416	−	8.58086i	−0.378854	−	0.656195i
$172$	−10.2111			−0.778589
$173$	−5.60555	−	9.70910i	−0.426182	−	0.738169i	0.570348	−	0.821403i	$-0.306808\pi$
$173$	−5.60555	−	9.70910i	−0.426182	−	0.738169i	−0.996530	+	0.0832341i	$0.973475\pi$
$174$	9.90833			0.751148
$175$	−0.211103			−0.0159579
$176$	2.80278	−	4.85455i	0.211267	−	0.365925i
$177$	12.4542	−	21.5712i	0.936112	−	1.62139i
$178$	2.34861	−	4.06792i	0.176036	−	0.304903i
$179$	7.16527	+	12.4106i	0.535557	+	0.927612i	0.999136	+	0.0415566i	$0.0132317\pi$
$179$	7.16527	+	12.4106i	0.535557	+	0.927612i	−0.463579	+	0.886056i	$0.653435\pi$
$180$	5.30278			0.395246
$181$	−1.55971	+	2.70151i	−0.115933	+	0.200801i	−0.918152	−	0.396228i	$-0.870319\pi$
$181$	−1.55971	+	2.70151i	−0.115933	+	0.200801i	0.802220	+	0.597029i	$0.203652\pi$
$182$	−0.908327			−0.0673297
$183$	−8.30278	−	15.9541i	−0.613759	−	1.17936i
$184$	−7.60555			−0.560689
$185$	0.454163	−	0.786634i	0.0333908	−	0.0578345i
$186$	9.00000			0.659912
$187$	−1.10555	−	1.91487i	−0.0808459	−	0.140029i
$188$	5.80278	−	10.0507i	0.423211	−	0.733023i
$189$	−0.559715	+	0.969454i	−0.0407133	+	0.0705174i
$190$	4.95416	−	8.58086i	0.359413	−	0.622521i
$191$	8.81665			0.637951			0.318975	−	0.947763i	$-0.396661\pi$
$191$	8.81665			0.637951			0.318975	+	0.947763i	$0.396661\pi$
$192$	2.30278			0.166189
$193$	7.75694	+	13.4354i	0.558357	+	0.967102i	0.997634	+	0.0687506i	$0.0219013\pi$
$193$	7.75694	+	13.4354i	0.558357	+	0.967102i	−0.439277	+	0.898352i	$0.644765\pi$
$194$	0.211103			0.0151563
$195$	3.45416	+	5.98279i	0.247358	+	0.428436i
$196$	3.25694	−	5.64118i	0.232639	−	0.402942i
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	0.687618	−	0.726073i	$-0.258656\pi$
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	−0.972606	+	0.232458i	$0.925323\pi$
$198$	−6.45416	+	11.1789i	−0.458677	+	0.794453i
$199$	−11.1056	+	19.2354i	−0.787252	+	1.36356i	0.140393	+	0.990096i	$0.455163\pi$
$199$	−11.1056	+	19.2354i	−0.787252	+	1.36356i	−0.927645	+	0.373464i	$0.878170\pi$
$200$	0.151388	+	0.262211i	0.0107047	+	0.0185411i
$201$	13.7111	−	23.7483i	0.967107	−	1.67508i
$202$	4.69722	+	8.13583i	0.330496	+	0.572435i
$203$	3.00000			0.210559
$204$	0.454163	−	0.786634i	0.0317978	−	0.0550754i
$205$	12.4542	−	21.5712i	0.869837	−	1.50660i
$206$	5.00000			0.348367
$207$	17.5139			1.21730
$208$	0.651388	+	1.12824i	0.0451656	+	0.0782291i
$209$	12.0597	+	20.8880i	0.834188	+	1.44486i
$210$	3.69722			0.255133
$211$	−19.6972			−1.35601			−0.678006	−	0.735056i	$-0.737156\pi$
$211$	−19.6972			−1.35601			−0.678006	+	0.735056i	$0.737156\pi$
$212$	−0.302776	−	0.524423i	−0.0207947	−	0.0360175i
$213$	−15.6653	−	27.1330i	−1.07337	−	1.85913i
$214$	−2.60555	−	4.51295i	−0.178112	−	0.308499i
$215$	11.7569	+	20.3636i	0.801817	+	1.38879i
$216$	1.60555			0.109244
$217$	2.72498			0.184984
$218$	1.54584	+	2.67747i	0.104697	+	0.181341i
$219$	−1.50000	−	2.59808i	−0.101361	−	0.175562i
$220$	−12.9083			−0.870279
$221$	0.513878			0.0345672
$222$	−0.454163	+	0.786634i	−0.0304815	+	0.0527954i
$223$	−6.04584	+	10.4717i	−0.404859	+	0.701237i	−0.994305	−	0.106571i	$-0.966013\pi$
$223$	−6.04584	+	10.4717i	−0.404859	+	0.701237i	0.589446	+	0.807808i	$0.299346\pi$
$224$	0.697224			0.0465853
$225$	−0.348612	−	0.603814i	−0.0232408	−	0.0402543i
$226$	−8.30278	+	14.3808i	−0.552292	+	0.956599i
$227$	−9.86249	−	17.0823i	−0.654596	−	1.13379i	−0.981995	−	0.188908i	$-0.939505\pi$
$227$	−9.86249	−	17.0823i	−0.654596	−	1.13379i	0.327398	−	0.944886i	$-0.393828\pi$
$228$	−4.95416	+	8.58086i	−0.328097	+	0.568282i
$229$	5.54584	−	9.60567i	0.366479	−	0.634761i	−0.622533	−	0.782593i	$-0.713896\pi$
$229$	5.54584	−	9.60567i	0.366479	−	0.634761i	0.989012	+	0.147833i	$0.0472298\pi$
$230$	8.75694	+	15.1675i	0.577415	+	1.00011i
$231$	−4.50000	+	7.79423i	−0.296078	+	0.512823i
$232$	−2.15139	−	3.72631i	−0.141246	−	0.244644i
$233$	22.6056			1.48094			0.740469	−	0.672090i	$-0.234603\pi$
$233$	22.6056			1.48094			0.740469	+	0.672090i	$0.234603\pi$
$234$	−1.50000	−	2.59808i	−0.0980581	−	0.169842i
$235$	−26.7250			−1.74335
$236$	−10.8167			−0.704104
$237$	−6.69722	+	11.5999i	−0.435031	+	0.753497i
$238$	0.137510	−	0.238174i	0.00891343	−	0.0154385i
$239$	10.3028	−	17.8449i	0.666431	−	1.15429i	−0.312464	−	0.949930i	$-0.601154\pi$
$239$	10.3028	−	17.8449i	0.666431	−	1.15429i	0.978895	−	0.204363i	$-0.0655123\pi$
$240$	−2.65139	−	4.59234i	−0.171146	−	0.296434i
$241$	10.7889			0.694974			0.347487	−	0.937685i	$-0.387035\pi$
$241$	10.7889			0.694974			0.347487	+	0.937685i	$0.387035\pi$
$242$	10.2111	−	17.6861i	0.656395	−	1.13691i
$243$	−19.6056			−1.25770
$244$	−4.19722	+	6.58660i	−0.268700	+	0.421664i
$245$	−15.0000			−0.958315
$246$	−12.4542	+	21.5712i	−0.794048	+	1.37533i
$247$	−5.60555			−0.356673
$248$	−1.95416	−	3.38471i	−0.124090	−	0.214929i
$249$	−14.8625	+	25.7426i	−0.941872	+	1.63137i
$250$	−5.40833	+	9.36750i	−0.342053	+	0.592453i
$251$	0.440285	−	0.762596i	0.0277906	−	0.0481347i	−0.851796	−	0.523874i	$-0.824486\pi$
$251$	0.440285	−	0.762596i	0.0277906	−	0.0481347i	0.879586	+	0.475740i	$0.157820\pi$
$252$	−1.60555			−0.101140
$253$	−42.6333			−2.68033
$254$	2.54584	+	4.40952i	0.159740	+	0.276678i
$255$	−2.09167			−0.130986
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.2569	+	17.7655i	−0.639810	+	1.10818i	0.345664	+	0.938358i	$0.387654\pi$
$257$	−10.2569	+	17.7655i	−0.639810	+	1.10818i	−0.985474	+	0.169826i	$0.945680\pi$
$258$	−11.7569	−	20.3636i	−0.731955	−	1.26778i
$259$	−0.137510	+	0.238174i	−0.00854443	+	0.0147994i
$260$	1.50000	−	2.59808i	0.0930261	−	0.161126i
$261$	4.95416	+	8.58086i	0.306655	+	0.531142i
$262$	6.40833	−	11.0995i	0.395908	−	0.685732i
$263$	−14.9222	−	25.8460i	−0.920143	−	1.59373i	−0.799193	−	0.601075i	$-0.794739\pi$
$263$	−14.9222	−	25.8460i	−0.920143	−	1.59373i	−0.120950	−	0.992659i	$-0.538594\pi$
$264$	12.9083			0.794453
$265$	−0.697224	+	1.20763i	−0.0428302	+	0.0741840i
$266$	−1.50000	+	2.59808i	−0.0919709	+	0.159298i
$267$	10.8167			0.661968
$268$	−11.9083			−0.727417
$269$	8.51388	+	14.7465i	0.519100	+	0.899108i	0.999754	+	0.0221974i	$0.00706623\pi$
$269$	8.51388	+	14.7465i	0.519100	+	0.899108i	−0.480653	+	0.876911i	$0.659600\pi$
$270$	−1.84861	−	3.20189i	−0.112503	−	0.194861i
$271$	19.5139			1.18538			0.592692	−	0.805429i	$-0.298065\pi$
$271$	19.5139			1.18538			0.592692	+	0.805429i	$0.298065\pi$
$272$	−0.394449			−0.0239170
$273$	−1.04584	−	1.81144i	−0.0632969	−	0.109633i
$274$	5.30278	+	9.18468i	0.320352	+	0.554867i
$275$	0.848612	+	1.46984i	0.0511732	+	0.0886347i
$276$	−8.75694	−	15.1675i	−0.527106	−	0.912974i
$277$	−6.00000			−0.360505			−0.180253	−	0.983620i	$-0.557691\pi$
$277$	−6.00000			−0.360505			−0.180253	+	0.983620i	$0.557691\pi$
$278$	−1.60555			−0.0962946
$279$	4.50000	+	7.79423i	0.269408	+	0.466628i
$280$	−0.802776	−	1.39045i	−0.0479750	−	0.0830952i
$281$	−18.2111			−1.08638			−0.543192	−	0.839609i	$-0.682784\pi$
$281$	−18.2111			−1.08638			−0.543192	+	0.839609i	$0.682784\pi$
$282$	26.7250			1.59145
$283$	4.36249	−	7.55605i	0.259323	−	0.449161i	−0.706738	−	0.707476i	$-0.749834\pi$
$283$	4.36249	−	7.55605i	0.259323	−	0.449161i	0.966061	+	0.258315i	$0.0831672\pi$
$284$	−6.80278	+	11.7828i	−0.403670	+	0.699178i
$285$	22.8167			1.35154
$286$	3.65139	+	6.32439i	0.215911	+	0.373969i
$287$	−3.77082	+	6.53125i	−0.222584	+	0.385527i
$288$	1.15139	+	1.99426i	0.0678462	+	0.117513i
$289$	8.42221	−	14.5877i	0.495424	−	0.858099i
$290$	−4.95416	+	8.58086i	−0.290918	+	0.503886i
$291$	0.243061	+	0.420994i	0.0142485	+	0.0246791i
$292$	−0.651388	+	1.12824i	−0.0381196	+	0.0660251i
$293$	1.80278	+	3.12250i	0.105319	+	0.182418i	0.913869	−	0.406010i	$-0.133080\pi$
$293$	1.80278	+	3.12250i	0.105319	+	0.182418i	−0.808549	+	0.588428i	$0.799747\pi$
$294$	15.0000			0.874818
$295$	12.4542	+	21.5712i	0.725109	+	1.25593i
$296$	0.394449			0.0229269
$297$	9.00000			0.522233
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	4.95416	−	8.58086i	0.286507	−	0.496244i
$300$	−0.348612	+	0.603814i	−0.0201271	+	0.0348612i
$301$	−3.55971	−	6.16561i	−0.205179	−	0.355380i
$302$	−0.788897			−0.0453959
$303$	−10.8167	+	18.7350i	−0.621401	+	1.07630i
$304$	4.30278			0.246781
$305$	17.9680	+	0.786634i	1.02885	+	0.0450425i
$306$	0.908327			0.0519256
$307$	3.09167	−	5.35493i	0.176451	−	0.305622i	−0.764211	−	0.644966i	$-0.776872\pi$
$307$	3.09167	−	5.35493i	0.176451	−	0.305622i	0.940663	+	0.339344i	$0.110205\pi$
$308$	3.90833			0.222698
$309$	5.75694	+	9.97131i	0.327501	+	0.567248i
$310$	−4.50000	+	7.79423i	−0.255583	+	0.442682i
$311$	16.3625	−	28.3407i	0.927832	−	1.60705i	0.140889	−	0.990025i	$-0.455004\pi$
$311$	16.3625	−	28.3407i	0.927832	−	1.60705i	0.786943	−	0.617026i	$-0.211663\pi$
$312$	−1.50000	+	2.59808i	−0.0849208	+	0.147087i
$313$	−9.02776			−0.510279			−0.255139	−	0.966904i	$-0.582121\pi$
$313$	−9.02776			−0.510279			−0.255139	+	0.966904i	$0.582121\pi$
$314$	−4.90833			−0.276993
$315$	1.84861	+	3.20189i	0.104157	+	0.180406i
$316$	5.81665			0.327212
$317$	−6.45416	−	11.1789i	−0.362502	−	0.627872i	0.625870	−	0.779927i	$-0.284744\pi$
$317$	−6.45416	−	11.1789i	−0.362502	−	0.627872i	−0.988372	+	0.152056i	$0.951411\pi$
$318$	0.697224	−	1.20763i	0.0390984	−	0.0677204i
$319$	−12.0597	−	20.8880i	−0.675214	−	1.16951i
$320$	−1.15139	+	1.99426i	−0.0643645	+	0.111483i
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$	−2.65139	−	4.59234i	−0.147756	−	0.255921i
$323$	0.848612	−	1.46984i	0.0472180	−	0.0817841i
$324$	5.30278	+	9.18468i	0.294599	+	0.510260i
$325$	−0.394449			−0.0218801
$326$	−3.30278	+	5.72058i	−0.182924	+	0.316833i
$327$	−3.55971	+	6.16561i	−0.196853	+	0.340959i
$328$	10.8167			0.597250
$329$	8.09167			0.446108
$330$	−14.8625	−	25.7426i	−0.818153	−	1.41708i
$331$	4.54584	+	7.87362i	0.249862	+	0.432773i	0.963487	−	0.267754i	$-0.0862815\pi$
$331$	4.54584	+	7.87362i	0.249862	+	0.432773i	−0.713626	+	0.700527i	$0.752948\pi$
$332$	12.9083			0.708436
$333$	−0.908327			−0.0497760
$334$	−3.69722	−	6.40378i	−0.202303	−	0.350399i
$335$	13.7111	+	23.7483i	0.749118	+	1.29751i
$336$	0.802776	+	1.39045i	0.0437950	+	0.0758552i
$337$	−8.80278	−	15.2469i	−0.479518	−	0.830549i	0.520206	−	0.854041i	$-0.325855\pi$
$337$	−8.80278	−	15.2469i	−0.479518	−	0.830549i	−0.999724	+	0.0234915i	$0.992522\pi$
$338$	11.3028			0.614790
$339$	−38.2389			−2.07685
$340$	0.454163	+	0.786634i	0.0246305	+	0.0426612i
$341$	−10.9542	−	18.9732i	−0.593201	−	1.02745i
$342$	−9.90833			−0.535781
$343$	9.42221			0.508751
$344$	−5.10555	+	8.84307i	−0.275273	+	0.476787i
$345$	−20.1653	+	34.9273i	−1.08566	+	1.88042i
$346$	−11.2111			−0.602713
$347$	−4.45416	−	7.71484i	−0.239112	−	0.414154i	0.721348	−	0.692573i	$-0.243523\pi$
$347$	−4.45416	−	7.71484i	−0.239112	−	0.414154i	−0.960460	+	0.278419i	$0.910190\pi$
$348$	4.95416	−	8.58086i	0.265571	−	0.459983i
$349$	10.4542	+	18.1071i	0.559599	+	0.969253i	0.997530	+	0.0702446i	$0.0223780\pi$
$349$	10.4542	+	18.1071i	0.559599	+	0.969253i	−0.437931	+	0.899008i	$0.644289\pi$
$350$	−0.105551	+	0.182820i	−0.00564195	+	0.00977215i
$351$	−1.04584	+	1.81144i	−0.0558226	+	0.0966876i
$352$	−2.80278	−	4.85455i	−0.149388	−	0.258748i
$353$	−2.09167	+	3.62288i	−0.111329	+	0.192827i	−0.916306	−	0.400478i	$-0.868844\pi$
$353$	−2.09167	+	3.62288i	−0.111329	+	0.192827i	0.804978	+	0.593305i	$0.202177\pi$
$354$	−12.4542	−	21.5712i	−0.661931	−	1.14650i
$355$	31.3305			1.66285
$356$	−2.34861	−	4.06792i	−0.124476	−	0.215599i
$357$	0.633308			0.0335182
$358$	14.3305			0.757392
$359$	14.1056	−	24.4315i	0.744463	−	1.28945i	−0.205983	−	0.978556i	$-0.566039\pi$
$359$	14.1056	−	24.4315i	0.744463	−	1.28945i	0.950445	−	0.310891i	$-0.100628\pi$
$360$	2.65139	−	4.59234i	0.139740	−	0.242037i
$361$	0.243061	−	0.420994i	0.0127927	−	0.0221576i
$362$	1.55971	+	2.70151i	0.0819768	+	0.141988i
$363$	47.0278			2.46832
$364$	−0.454163	+	0.786634i	−0.0238046	+	0.0412308i
$365$	3.00000			0.157027
$366$	−17.9680	−	0.786634i	−0.939205	−	0.0411180i
$367$	−17.6056			−0.919002			−0.459501	−	0.888177i	$-0.651972\pi$
$367$	−17.6056			−0.919002			−0.459501	+	0.888177i	$0.651972\pi$
$368$	−3.80278	+	6.58660i	−0.198233	+	0.343350i
$369$	−24.9083			−1.29668
$370$	−0.454163	−	0.786634i	−0.0236108	−	0.0408952i
$371$	0.211103	−	0.365640i	0.0109599	−	0.0189831i
$372$	4.50000	−	7.79423i	0.233314	−	0.404112i
$373$	−5.16527	+	8.94650i	−0.267447	+	0.463232i	−0.968202	−	0.250170i	$-0.919513\pi$
$373$	−5.16527	+	8.94650i	−0.267447	+	0.463232i	0.700755	+	0.713402i	$0.252847\pi$
$374$	−2.21110			−0.114333
$375$	−24.9083			−1.28626
$376$	−5.80278	−	10.0507i	−0.299255	−	0.518325i
$377$	5.60555			0.288701
$378$	0.559715	+	0.969454i	0.0287886	+	0.0498634i
$379$	0.697224	−	1.20763i	0.0358140	−	0.0620317i	−0.847563	−	0.530695i	$-0.821931\pi$
$379$	0.697224	−	1.20763i	0.0358140	−	0.0620317i	0.883377	+	0.468663i	$0.155264\pi$
$380$	−4.95416	−	8.58086i	−0.254143	−	0.440189i
$381$	−5.86249	+	10.1541i	−0.300344	+	0.520212i
$382$	4.40833	−	7.63545i	0.225550	−	0.390663i
$383$	18.3167	+	31.7254i	0.935937	+	1.62109i	0.772954	+	0.634462i	$0.218778\pi$
$383$	18.3167	+	31.7254i	0.935937	+	1.62109i	0.162983	+	0.986629i	$0.447888\pi$
$384$	1.15139	−	1.99426i	0.0587565	−	0.101769i
$385$	−4.50000	−	7.79423i	−0.229341	−	0.397231i
$386$	15.5139			0.789636
$387$	11.7569	−	20.3636i	0.597639	−	1.03514i
$388$	0.105551	−	0.182820i	0.00535855	−	0.00928129i
$389$	11.7889			0.597721			0.298860	−	0.954297i	$-0.403394\pi$
$389$	11.7889			0.597721			0.298860	+	0.954297i	$0.403394\pi$
$390$	6.90833			0.349817
$391$	1.50000	+	2.59808i	0.0758583	+	0.131390i
$392$	−3.25694	−	5.64118i	−0.164500	−	0.284923i
$393$	29.5139			1.48878
$394$	−8.00000			−0.403034
$395$	−6.69722	−	11.5999i	−0.336974	−	0.583656i
$396$	6.45416	+	11.1789i	0.324334	+	0.561763i
$397$	19.4542	+	33.6956i	0.976376	+	1.69113i	0.675316	+	0.737529i	$0.264007\pi$
$397$	19.4542	+	33.6956i	0.976376	+	1.69113i	0.301061	+	0.953605i	$0.402659\pi$
$398$	11.1056	+	19.2354i	0.556671	+	0.964182i
$399$	−6.90833			−0.345849
$400$	0.302776			0.0151388
$401$	−11.8625	−	20.5464i	−0.592385	−	1.02604i	−0.993910	−	0.110192i	$-0.964853\pi$
$401$	−11.8625	−	20.5464i	−0.592385	−	1.02604i	0.401526	−	0.915848i	$-0.368480\pi$
$402$	−13.7111	−	23.7483i	−0.683848	−	1.18446i
$403$	5.09167			0.253634
$404$	9.39445			0.467391
$405$	12.2111	−	21.1503i	0.606775	−	1.05096i
$406$	1.50000	−	2.59808i	0.0744438	−	0.128940i
$407$	2.21110			0.109600
$408$	−0.454163	−	0.786634i	−0.0224844	−	0.0389442i
$409$	−5.10555	+	8.84307i	−0.252453	+	0.437262i	−0.964201	−	0.265174i	$-0.914571\pi$
$409$	−5.10555	+	8.84307i	−0.252453	+	0.437262i	0.711747	+	0.702435i	$0.247904\pi$
$410$	−12.4542	−	21.5712i	−0.615067	−	1.06533i
$411$	−12.2111	+	21.1503i	−0.602329	+	1.04326i
$412$	2.50000	−	4.33013i	0.123166	−	0.213330i
$413$	−3.77082	−	6.53125i	−0.185550	−	0.321382i
$414$	8.75694	−	15.1675i	0.430380	−	0.745440i
$415$	−14.8625	−	25.7426i	−0.729571	−	1.26365i
$416$	1.30278			0.0638738
$417$	−1.84861	−	3.20189i	−0.0905269	−	0.156797i
$418$	24.1194			1.17972
$419$	−15.7889			−0.771338			−0.385669	−	0.922637i	$-0.626029\pi$
$419$	−15.7889			−0.771338			−0.385669	+	0.922637i	$0.626029\pi$
$420$	1.84861	−	3.20189i	0.0902030	−	0.156236i
$421$	−18.0139	+	31.2010i	−0.877943	+	1.52064i	−0.0243481	+	0.999704i	$0.507751\pi$
$421$	−18.0139	+	31.2010i	−0.877943	+	1.52064i	−0.853595	+	0.520938i	$0.825582\pi$
$422$	−9.84861	+	17.0583i	−0.479423	+	0.830385i
$423$	13.3625	+	23.1445i	0.649707	+	1.12532i
$424$	−0.605551			−0.0294082
$425$	0.0597147	−	0.103429i	0.00289659	−	0.00501704i
$426$	−31.3305			−1.51797
$427$	−5.44029	−	0.238174i	−0.263274	−	0.0115260i
$428$	−5.21110			−0.251888
$429$	−8.40833	+	14.5636i	−0.405958	+	0.703140i
$430$	23.5139			1.13394
$431$	0.954163	+	1.65266i	0.0459604	+	0.0796058i	0.888090	−	0.459669i	$-0.152032\pi$
$431$	0.954163	+	1.65266i	0.0459604	+	0.0796058i	−0.842130	+	0.539275i	$0.818699\pi$
$432$	0.802776	−	1.39045i	0.0386236	−	0.0668980i
$433$	5.95416	−	10.3129i	0.286139	−	0.495607i	−0.686746	−	0.726898i	$-0.740961\pi$
$433$	5.95416	−	10.3129i	0.286139	−	0.495607i	0.972885	+	0.231291i	$0.0742948\pi$
$434$	1.36249	−	2.35990i	0.0654016	−	0.113279i
$435$	−22.8167			−1.09397
$436$	3.09167			0.148064
$437$	−16.3625	−	28.3407i	−0.782724	−	1.35572i
$438$	−3.00000			−0.143346
$439$	11.4083	+	19.7598i	0.544490	+	0.943084i	0.998639	+	0.0521582i	$0.0166100\pi$
$439$	11.4083	+	19.7598i	0.544490	+	0.943084i	−0.454149	+	0.890926i	$0.650057\pi$
$440$	−6.45416	+	11.1789i	−0.307690	+	0.532935i
$441$	7.50000	+	12.9904i	0.357143	+	0.618590i
$442$	0.256939	−	0.445032i	0.0122213	−	0.0211680i
$443$	−5.01388	+	8.68429i	−0.238217	+	0.412603i	−0.960203	−	0.279304i	$-0.909896\pi$
$443$	−5.01388	+	8.68429i	−0.238217	+	0.412603i	0.721986	+	0.691908i	$0.243229\pi$
$444$	0.454163	+	0.786634i	0.0215536	+	0.0373320i
$445$	−5.40833	+	9.36750i	−0.256379	+	0.444062i
$446$	6.04584	+	10.4717i	0.286279	+	0.495849i
$447$	13.8167			0.653505
$448$	0.348612	−	0.603814i	0.0164704	−	0.0285275i
$449$	19.6791	−	34.0853i	0.928716	−	1.60858i	0.143243	−	0.989687i	$-0.454247\pi$
$449$	19.6791	−	34.0853i	0.928716	−	1.60858i	0.785473	−	0.618896i	$-0.212420\pi$
$450$	−0.697224			−0.0328675
$451$	60.6333			2.85511
$452$	8.30278	+	14.3808i	0.390530	+	0.676417i
$453$	−0.908327	−	1.57327i	−0.0426769	−	0.0739186i
$454$	−19.7250			−0.925739
$455$	2.09167			0.0980591
$456$	4.95416	+	8.58086i	0.232000	+	0.401836i
$457$	2.25694	+	3.90913i	0.105575	+	0.182862i	0.913973	−	0.405775i	$-0.132998\pi$
$457$	2.25694	+	3.90913i	0.105575	+	0.182862i	−0.808398	+	0.588636i	$0.799665\pi$
$458$	−5.54584	−	9.60567i	−0.259140	−	0.448844i
$459$	−0.316654	−	0.548461i	−0.0147801	−	0.0255999i
$460$	17.5139			0.816589
$461$	−6.60555			−0.307651			−0.153826	−	0.988098i	$-0.549159\pi$
$461$	−6.60555			−0.307651			−0.153826	+	0.988098i	$0.549159\pi$
$462$	4.50000	+	7.79423i	0.209359	+	0.362620i
$463$	3.80278	+	6.58660i	0.176730	+	0.306105i	0.940759	−	0.339077i	$-0.110115\pi$
$463$	3.80278	+	6.58660i	0.176730	+	0.306105i	−0.764029	+	0.645182i	$0.776781\pi$
$464$	−4.30278			−0.199751
$465$	−20.7250			−0.961098
$466$	11.3028	−	19.5770i	0.523591	−	0.906886i
$467$	4.45416	−	7.71484i	0.206114	−	0.357000i	−0.744373	−	0.667764i	$-0.767252\pi$
$467$	4.45416	−	7.71484i	0.206114	−	0.357000i	0.950487	+	0.310764i	$0.100585\pi$
$468$	−3.00000			−0.138675
$469$	−4.15139	−	7.19041i	−0.191693	−	0.332022i
$470$	−13.3625	+	23.1445i	−0.616366	+	1.06758i
$471$	−5.65139	−	9.78849i	−0.260402	−	0.451030i
$472$	−5.40833	+	9.36750i	−0.248938	+	0.431174i
$473$	−28.6194	+	49.5703i	−1.31592	+	2.27925i
$474$	6.69722	+	11.5999i	0.307614	+	0.532803i
$475$	−0.651388	+	1.12824i	−0.0298877	+	0.0517671i
$476$	−0.137510	−	0.238174i	−0.00630274	−	0.0109167i
$477$	1.39445			0.0638474
$478$	−10.3028	−	17.8449i	−0.471238	−	0.816208i
$479$	−33.3028			−1.52164			−0.760821	−	0.648961i	$-0.775204\pi$
$479$	−33.3028			−1.52164			−0.760821	+	0.648961i	$0.775204\pi$
$480$	−5.30278			−0.242037
$481$	−0.256939	+	0.445032i	−0.0117154	+	0.0202917i
$482$	5.39445	−	9.34346i	0.245710	−	0.425583i
$483$	6.10555	−	10.5751i	0.277812	−	0.481185i
$484$	−10.2111	−	17.6861i	−0.464141	−	0.803916i
$485$	−0.486122			−0.0220737
$486$	−9.80278	+	16.9789i	−0.444663	+	0.770179i
$487$	−21.5416			−0.976145			−0.488072	−	0.872803i	$-0.662300\pi$
$487$	−21.5416			−0.976145			−0.488072	+	0.872803i	$0.662300\pi$
$488$	3.60555	+	6.92820i	0.163216	+	0.313625i
$489$	−15.2111			−0.687870
$490$	−7.50000	+	12.9904i	−0.338815	+	0.586846i
$491$	5.02776			0.226899			0.113450	−	0.993544i	$-0.463810\pi$
$491$	5.02776			0.226899			0.113450	+	0.993544i	$0.463810\pi$
$492$	12.4542	+	21.5712i	0.561477	+	0.972507i
$493$	−0.848612	+	1.46984i	−0.0382196	+	0.0661982i
$494$	−2.80278	+	4.85455i	−0.126103	+	0.218417i
$495$	14.8625	−	25.7426i	0.668019	−	1.15704i
$496$	−3.90833			−0.175489
$497$	−9.48612			−0.425511
$498$	14.8625	+	25.7426i	0.666004	+	1.15355i
$499$	−31.2389			−1.39844			−0.699222	−	0.714905i	$-0.746470\pi$
$499$	−31.2389			−1.39844			−0.699222	+	0.714905i	$0.746470\pi$
$500$	5.40833	+	9.36750i	0.241868	+	0.418927i
$501$	8.51388	−	14.7465i	0.380372	−	0.658824i
$502$	−0.440285	−	0.762596i	−0.0196509	−	0.0340363i
$503$	2.10555	−	3.64692i	0.0938819	−	0.162608i	−0.815260	−	0.579096i	$-0.803406\pi$
$503$	2.10555	−	3.64692i	0.0938819	−	0.162608i	0.909141	+	0.416488i	$0.136739\pi$
$504$	−0.802776	+	1.39045i	−0.0357585	+	0.0619355i
$505$	−10.8167	−	18.7350i	−0.481335	−	0.833696i
$506$	−21.3167	+	36.9215i	−0.947641	+	1.64136i
$507$	13.0139	+	22.5407i	0.577967	+	1.00107i
$508$	5.09167			0.225906
$509$	−5.89445	+	10.2095i	−0.261267	+	0.452527i	−0.966579	−	0.256370i	$-0.917474\pi$
$509$	−5.89445	+	10.2095i	−0.261267	+	0.452527i	0.705312	+	0.708897i	$0.250807\pi$
$510$	−1.04584	+	1.81144i	−0.0463104	+	0.0802120i
$511$	−0.908327			−0.0401820
$512$	−1.00000			−0.0441942
$513$	3.45416	+	5.98279i	0.152505	+	0.264146i
$514$	10.2569	+	17.7655i	0.452414	+	0.783604i
$515$	−11.5139			−0.507362
$516$	−23.5139			−1.03514
$517$	−32.5278	−	56.3397i	−1.43057	−	2.47782i
$518$	0.137510	+	0.238174i	0.00604183	+	0.0104648i
$519$	−12.9083	−	22.3579i	−0.566613	−	0.981402i
$520$	−1.50000	−	2.59808i	−0.0657794	−	0.113933i
$521$	4.90833			0.215038			0.107519	−	0.994203i	$-0.465709\pi$
$521$	4.90833			0.215038			0.107519	+	0.994203i	$0.465709\pi$
$522$	9.90833			0.433676
$523$	6.01388	+	10.4163i	0.262969	+	0.455475i	0.967029	−	0.254665i	$-0.0819651\pi$
$523$	6.01388	+	10.4163i	0.262969	+	0.455475i	−0.704061	+	0.710140i	$0.748632\pi$
$524$	−6.40833	−	11.0995i	−0.279949	−	0.484886i
$525$	−0.486122			−0.0212161
$526$	−29.8444			−1.30128
$527$	−0.770817	+	1.33509i	−0.0335773	+	0.0581576i
$528$	6.45416	−	11.1789i	0.280881	−	0.486501i
$529$	34.8444			1.51497
$530$	0.697224	+	1.20763i	0.0302855	+	0.0524560i
$531$	12.4542	−	21.5712i	0.540465	−	0.936112i
$532$	1.50000	+	2.59808i	0.0650332	+	0.112641i
$533$	−7.04584	+	12.2037i	−0.305189	+	0.528603i
$534$	5.40833	−	9.36750i	0.234041	−	0.405371i
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	−5.95416	+	10.3129i	−0.257181	+	0.445450i
$537$	16.5000	+	28.5788i	0.712028	+	1.23327i
$538$	17.0278			0.734119
$539$	−18.2569	−	31.6219i	−0.786382	−	1.36205i
$540$	−3.69722			−0.159103
$541$	39.2389			1.68701			0.843505	−	0.537121i	$-0.180488\pi$
$541$	39.2389			1.68701			0.843505	+	0.537121i	$0.180488\pi$
$542$	9.75694	−	16.8995i	0.419096	−	0.725896i
$543$	−3.59167	+	6.22096i	−0.154133	+	0.266967i
$544$	−0.197224	+	0.341603i	−0.00845592	+	0.0146461i
$545$	−3.55971	−	6.16561i	−0.152481	−	0.264106i
$546$	−2.09167			−0.0895153
$547$	3.80278	−	6.58660i	0.162595	−	0.281623i	−0.773204	−	0.634158i	$-0.781347\pi$
$547$	3.80278	−	6.58660i	0.162595	−	0.281623i	0.935799	+	0.352535i	$0.114680\pi$
$548$	10.6056			0.453047
$549$	−8.30278	−	15.9541i	−0.354354	−	0.680904i
$550$	1.69722			0.0723699
$551$	9.25694	−	16.0335i	0.394359	−	0.683050i
$552$	−17.5139			−0.745440
$553$	2.02776	+	3.51218i	0.0862290	+	0.149353i
$554$	−3.00000	+	5.19615i	−0.127458	+	0.220763i
$555$	1.04584	−	1.81144i	0.0443933	−	0.0768914i
$556$	−0.802776	+	1.39045i	−0.0340453	+	0.0589681i
$557$	−5.02776			−0.213033			−0.106516	−	0.994311i	$-0.533970\pi$
$557$	−5.02776			−0.213033			−0.106516	+	0.994311i	$0.533970\pi$
$558$	9.00000			0.381000
$559$	−6.65139	−	11.5205i	−0.281324	−	0.487267i
$560$	−1.60555			−0.0678469
$561$	−2.54584	−	4.40952i	−0.107485	−	0.186170i
$562$	−9.10555	+	15.7713i	−0.384094	+	0.665271i
$563$	9.66527	+	16.7407i	0.407342	+	0.705538i	0.994591	−	0.103869i	$-0.0331222\pi$
$563$	9.66527	+	16.7407i	0.407342	+	0.705538i	−0.587249	+	0.809407i	$0.699789\pi$
$564$	13.3625	−	23.1445i	0.562662	−	0.974560i
$565$	19.1194	−	33.1158i	0.804360	−	1.39319i
$566$	−4.36249	−	7.55605i	−0.183369	−	0.317605i
$567$	−3.69722	+	6.40378i	−0.155269	+	0.268934i
$568$	6.80278	+	11.7828i	0.285438	+	0.494393i
$569$	−4.42221			−0.185388			−0.0926942	−	0.995695i	$-0.529548\pi$
$569$	−4.42221			−0.185388			−0.0926942	+	0.995695i	$0.529548\pi$
$570$	11.4083	−	19.7598i	0.477842	−	0.827647i
$571$	3.98612	−	6.90417i	0.166814	−	0.288930i	−0.770484	−	0.637459i	$-0.779985\pi$
$571$	3.98612	−	6.90417i	0.166814	−	0.288930i	0.937298	+	0.348529i	$0.113319\pi$
$572$	7.30278			0.305344
$573$	20.3028			0.848161
$574$	3.77082	+	6.53125i	0.157391	+	0.272609i
$575$	−1.15139	−	1.99426i	−0.0480162	−	0.0831665i
$576$	2.30278			0.0959490
$577$	−7.39445			−0.307835			−0.153917	−	0.988084i	$-0.549189\pi$
$577$	−7.39445			−0.307835			−0.153917	+	0.988084i	$0.549189\pi$
$578$	−8.42221	−	14.5877i	−0.350318	−	0.606768i
$579$	17.8625	+	30.9387i	0.742340	+	1.28577i
$580$	4.95416	+	8.58086i	0.205710	+	0.356301i
$581$	4.50000	+	7.79423i	0.186691	+	0.323359i
$582$	0.486122			0.0201504
$583$	−3.39445			−0.140584
$584$	0.651388	+	1.12824i	0.0269546	+	0.0466868i
$585$	3.45416	+	5.98279i	0.142812	+	0.247358i
$586$	3.60555			0.148944
$587$	−17.7250			−0.731588			−0.365794	−	0.930696i	$-0.619203\pi$
$587$	−17.7250			−0.731588			−0.365794	+	0.930696i	$0.619203\pi$
$588$	7.50000	−	12.9904i	0.309295	−	0.535714i
$589$	8.40833	−	14.5636i	0.346459	−	0.600085i
$590$	24.9083			1.02546
$591$	−9.21110	−	15.9541i	−0.378894	−	0.656264i
$592$	0.197224	−	0.341603i	0.00810587	−	0.0140398i
$593$	9.51388	+	16.4785i	0.390688	+	0.676692i	0.992540	−	0.121916i	$-0.0389038\pi$
$593$	9.51388	+	16.4785i	0.390688	+	0.676692i	−0.601852	+	0.798607i	$0.705570\pi$
$594$	4.50000	−	7.79423i	0.184637	−	0.319801i
$595$	−0.316654	+	0.548461i	−0.0129815	+	0.0224847i
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$	−25.5736	+	44.2948i	−1.04666	+	1.81286i
$598$	−4.95416	−	8.58086i	−0.202591	−	0.350898i
$599$	−13.5778			−0.554774			−0.277387	−	0.960758i	$-0.589468\pi$
$599$	−13.5778			−0.554774			−0.277387	+	0.960758i	$0.589468\pi$
$600$	0.348612	+	0.603814i	0.0142320	+	0.0246506i
$601$	4.00000			0.163163			0.0815817	−	0.996667i	$-0.474003\pi$
$601$	4.00000			0.163163			0.0815817	+	0.996667i	$0.474003\pi$
$602$	−7.11943			−0.290166
$603$	13.7111	−	23.7483i	0.558359	−	0.967107i
$604$	−0.394449	+	0.683205i	−0.0160499	+	0.0277992i
$605$	−23.5139	+	40.7272i	−0.955975	+	1.65580i
$606$	10.8167	+	18.7350i	0.439397	+	0.761057i
$607$	18.2389			0.740292			0.370146	−	0.928974i	$-0.379308\pi$
$607$	18.2389			0.740292			0.370146	+	0.928974i	$0.379308\pi$
$608$	2.15139	−	3.72631i	0.0872503	−	0.151122i
$609$	6.90833			0.279940
$610$	9.66527	−	15.1675i	0.391335	−	0.614113i
$611$	15.1194			0.611667
$612$	0.454163	−	0.786634i	0.0183585	−	0.0317978i
$613$	36.5416			1.47590			0.737951	−	0.674854i	$-0.235793\pi$
$613$	36.5416			1.47590			0.737951	+	0.674854i	$0.235793\pi$
$614$	−3.09167	−	5.35493i	−0.124770	−	0.216108i
$615$	28.6791	−	49.6737i	1.15645	−	2.00304i
$616$	1.95416	−	3.38471i	0.0787355	−	0.136374i
$617$	16.9083	−	29.2861i	0.680704	−	1.17901i	−0.294063	−	0.955786i	$-0.595007\pi$
$617$	16.9083	−	29.2861i	0.680704	−	1.17901i	0.974766	−	0.223227i	$-0.0716592\pi$
$618$	11.5139			0.463156
$619$	−1.39445			−0.0560476			−0.0280238	−	0.999607i	$-0.508921\pi$
$619$	−1.39445			−0.0560476			−0.0280238	+	0.999607i	$0.508921\pi$
$620$	4.50000	+	7.79423i	0.180724	+	0.313024i
$621$	−12.2111			−0.490015
$622$	−16.3625	−	28.3407i	−0.656076	−	1.13636i
$623$	1.63751	−	2.83625i	0.0656054	−	0.113632i
$624$	1.50000	+	2.59808i	0.0600481	+	0.104006i
$625$	13.2111	−	22.8823i	0.528444	−	0.915292i
$626$	−4.51388	+	7.81827i	−0.180411	+	0.312481i
$627$	27.7708	+	48.1005i	1.10906	+	1.92095i
$628$	−2.45416	+	4.25074i	−0.0979318	+	0.169623i
$629$	−0.0777949	−	0.134745i	−0.00310189	−	0.00537262i
$630$	3.69722			0.147301
$631$	−11.3167	+	19.6010i	−0.450509	+	0.780304i	−0.998418	−	0.0562338i	$-0.982091\pi$
$631$	−11.3167	+	19.6010i	−0.450509	+	0.780304i	0.547909	+	0.836538i	$0.315424\pi$
$632$	2.90833	−	5.03737i	0.115687	−	0.200376i
$633$	−45.3583			−1.80283
$634$	−12.9083			−0.512655
$635$	−5.86249	−	10.1541i	−0.232646	−	0.402954i
$636$	−0.697224	−	1.20763i	−0.0276467	−	0.0478856i
$637$	8.48612			0.336232
$638$	−24.1194			−0.954897
$639$	−15.6653	−	27.1330i	−0.619708	−	1.07337i
$640$	1.15139	+	1.99426i	0.0455126	+	0.0788301i
$641$	−20.9222	−	36.2383i	−0.826377	−	1.43133i	−0.900862	−	0.434106i	$-0.857065\pi$
$641$	−20.9222	−	36.2383i	−0.826377	−	1.43133i	0.0744846	−	0.997222i	$-0.476269\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	10.5139			0.414627			0.207313	−	0.978275i	$-0.433528\pi$
$643$	10.5139			0.414627			0.207313	+	0.978275i	$0.433528\pi$
$644$	−5.30278			−0.208959
$645$	27.0736	+	46.8928i	1.06602	+	1.84640i
$646$	−0.848612	−	1.46984i	−0.0333882	−	0.0578301i
$647$	10.3028			0.405044			0.202522	−	0.979278i	$-0.435086\pi$
$647$	10.3028			0.405044			0.202522	+	0.979278i	$0.435086\pi$
$648$	10.6056			0.416625
$649$	−30.3167	+	52.5100i	−1.19003	+	2.06120i
$650$	−0.197224	+	0.341603i	−0.00773578	+	0.0133988i
$651$	6.27502			0.245937
$652$	3.30278	+	5.72058i	0.129347	+	0.224035i
$653$	2.19722	−	3.80570i	0.0859840	−	0.148929i	−0.819826	−	0.572613i	$-0.805930\pi$
$653$	2.19722	−	3.80570i	0.0859840	−	0.148929i	0.905810	+	0.423684i	$0.139263\pi$
$654$	3.55971	+	6.16561i	0.139196	+	0.241094i
$655$	−14.7569	+	25.5598i	−0.576601	+	0.998703i
$656$	5.40833	−	9.36750i	0.211160	−	0.365739i
$657$	−1.50000	−	2.59808i	−0.0585206	−	0.101361i
$658$	4.04584	−	7.00759i	0.157723	−	0.273184i
$659$	−2.10555	−	3.64692i	−0.0820206	−	0.142064i	0.822097	−	0.569347i	$-0.192804\pi$
$659$	−2.10555	−	3.64692i	−0.0820206	−	0.142064i	−0.904118	+	0.427283i	$0.859471\pi$
$660$	−29.7250			−1.15704
$661$	8.19722	+	14.1980i	0.318835	+	0.552239i	0.980245	−	0.197786i	$-0.0633751\pi$
$661$	8.19722	+	14.1980i	0.318835	+	0.552239i	−0.661410	+	0.750024i	$0.730042\pi$
$662$	9.09167			0.353358
$663$	1.18335			0.0459574
$664$	6.45416	−	11.1789i	0.250470	−	0.433827i
$665$	3.45416	−	5.98279i	0.133947	−	0.232003i
$666$	−0.454163	+	0.786634i	−0.0175985	+	0.0304815i
$667$	16.3625	+	28.3407i	0.633558	+	1.09735i
$668$	−7.39445			−0.286100
$669$	−13.9222	+	24.1140i	−0.538264	+	0.932300i
$670$	27.4222			1.05941
$671$	20.2111	+	38.8364i	0.780241	+	1.49926i
$672$	1.60555			0.0619355
$673$	13.8944	−	24.0659i	0.535592	−	0.927672i	−0.463543	−	0.886075i	$-0.653422\pi$
$673$	13.8944	−	24.0659i	0.535592	−	0.927672i	0.999134	−	0.0415974i	$-0.0132447\pi$
$674$	−17.6056			−0.678140
$675$	0.243061	+	0.420994i	0.00935542	+	0.0162041i
$676$	5.65139	−	9.78849i	0.217361	−	0.376480i
$677$	−19.8167	+	34.3235i	−0.761616	+	1.31916i	0.180401	+	0.983593i	$0.442260\pi$
$677$	−19.8167	+	34.3235i	−0.761616	+	1.31916i	−0.942017	+	0.335564i	$0.891073\pi$
$678$	−19.1194	+	33.1158i	−0.734277	+	1.27181i
$679$	0.147186			0.00564847
$680$	0.908327			0.0348327
$681$	−22.7111	−	39.3368i	−0.870291	−	1.50739i
$682$	−21.9083			−0.838913
$683$	−18.9222	−	32.7742i	−0.724038	−	1.25407i	−0.959369	−	0.282155i	$-0.908951\pi$
$683$	−18.9222	−	32.7742i	−0.724038	−	1.25407i	0.235331	−	0.971915i	$-0.424383\pi$
$684$	−4.95416	+	8.58086i	−0.189427	+	0.328097i
$685$	−12.2111	−	21.1503i	−0.466562	−	0.808110i
$686$	4.71110	−	8.15987i	0.179871	−	0.311545i
$687$	12.7708	−	22.1197i	0.487237	−	0.843919i
$688$	5.10555	+	8.84307i	0.194647	+	0.337139i
$689$	0.394449	−	0.683205i	0.0150273	−	0.0260280i
$690$	20.1653	+	34.9273i	0.767679	+	1.32966i
$691$	−34.4500			−1.31054			−0.655269	−	0.755395i	$-0.727445\pi$
$691$	−34.4500			−1.31054			−0.655269	+	0.755395i	$0.727445\pi$
$692$	−5.60555	+	9.70910i	−0.213091	+	0.369085i
$693$	−4.50000	+	7.79423i	−0.170941	+	0.296078i
$694$	−8.90833			−0.338155
$695$	3.69722			0.140244
$696$	−4.95416	−	8.58086i	−0.187787	−	0.325257i
$697$	−2.13331	−	3.69500i	−0.0808048	−	0.139958i
$698$	20.9083			0.791392
$699$	52.0555			1.96892
$700$	0.105551	+	0.182820i	0.00398946	+	0.00690995i
$701$	2.86249	+	4.95798i	0.108115	+	0.187260i	0.915007	−	0.403439i	$-0.132185\pi$
$701$	2.86249	+	4.95798i	0.108115	+	0.187260i	−0.806892	+	0.590699i	$0.798852\pi$
$702$	1.04584	+	1.81144i	0.0394726	+	0.0683685i
$703$	0.848612	+	1.46984i	0.0320060	+	0.0554360i
$704$	−5.60555			−0.211267
$705$	−61.5416			−2.31779
$706$	2.09167	+	3.62288i	0.0787212	+	0.136349i
$707$	3.27502	+	5.67250i	0.123170	+	0.213336i
$708$	−24.9083			−0.936112
$709$	30.1472			1.13220			0.566101	−	0.824336i	$-0.308451\pi$
$709$	30.1472			1.13220			0.566101	+	0.824336i	$0.308451\pi$
$710$	15.6653	−	27.1330i	0.587907	−	1.01828i
$711$	−6.69722	+	11.5999i	−0.251166	+	0.435031i
$712$	−4.69722			−0.176036
$713$	14.8625	+	25.7426i	0.556605	+	0.964068i
$714$	0.316654	−	0.548461i	0.0118505	−	0.0205256i
$715$	−8.40833	−	14.5636i	−0.314454	−	0.544650i
$716$	7.16527	−	12.4106i	0.267779	−	0.463806i
$717$	23.7250	−	41.0929i	0.886026	−	1.53464i
$718$	−14.1056	−	24.4315i	−0.526414	−	0.911777i
$719$	3.05971	−	5.29958i	0.114108	−	0.197641i	−0.803315	−	0.595555i	$-0.796932\pi$
$719$	3.05971	−	5.29958i	0.114108	−	0.197641i	0.917423	+	0.397914i	$0.130266\pi$
$720$	−2.65139	−	4.59234i	−0.0988114	−	0.171146i
$721$	3.48612			0.129830
$722$	−0.243061	−	0.420994i	−0.00904579	−	0.0156678i
$723$	24.8444			0.923974
$724$	3.11943			0.115933
$725$	0.651388	−	1.12824i	0.0241919	−	0.0419017i
$726$	23.5139	−	40.7272i	0.872682	−	1.51153i
$727$	15.1653	−	26.2670i	0.562449	−	0.974190i	−0.434833	−	0.900511i	$-0.643193\pi$
$727$	15.1653	−	26.2670i	0.562449	−	0.974190i	0.997282	−	0.0736786i	$-0.0234739\pi$
$728$	0.454163	+	0.786634i	0.0168324	+	0.0291546i
$729$	−13.3305			−0.493723
$730$	1.50000	−	2.59808i	0.0555175	−	0.0961591i
$731$	4.02776			0.148972
$732$	−9.66527	+	15.1675i	−0.357239	+	0.560606i
$733$	17.8167			0.658073			0.329037	−	0.944317i	$-0.393276\pi$
$733$	17.8167			0.658073			0.329037	+	0.944317i	$0.393276\pi$
$734$	−8.80278	+	15.2469i	−0.324916	+	0.562772i
$735$	−34.5416			−1.27409
$736$	3.80278	+	6.58660i	0.140172	+	0.242785i
$737$	−33.3764	+	57.8096i	−1.22943	+	2.12944i
$738$	−12.4542	+	21.5712i	−0.458444	+	0.794048i
$739$	14.0139	−	24.2727i	0.515509	−	0.892888i	−0.484329	−	0.874886i	$-0.660936\pi$
$739$	14.0139	−	24.2727i	0.515509	−	0.892888i	0.999838	−	0.0180016i	$-0.00573040\pi$
$740$	−0.908327			−0.0333908
$741$	−12.9083			−0.474199
$742$	−0.211103	−	0.365640i	−0.00774982	−	0.0134231i
$743$	11.3028			0.414659			0.207329	−	0.978271i	$-0.433523\pi$
$743$	11.3028			0.414659			0.207329	+	0.978271i	$0.433523\pi$
$744$	−4.50000	−	7.79423i	−0.164978	−	0.285750i
$745$	−6.90833	+	11.9656i	−0.253102	+	0.438385i
$746$	5.16527	+	8.94650i	0.189114	+	0.327555i
$747$	−14.8625	+	25.7426i	−0.543790	+	0.941872i
$748$	−1.10555	+	1.91487i	−0.0404230	+	0.0700146i
$749$	−1.81665	−	3.14654i	−0.0663791	−	0.114972i
$750$	−12.4542	+	21.5712i	−0.454762	+	0.787670i
$751$	−2.25694	−	3.90913i	−0.0823569	−	0.142646i	0.821905	−	0.569625i	$-0.192911\pi$
$751$	−2.25694	−	3.90913i	−0.0823569	−	0.142646i	−0.904262	+	0.426978i	$0.859578\pi$
$752$	−11.6056			−0.423211
$753$	1.01388	−	1.75609i	0.0369478	−	0.0639954i
$754$	2.80278	−	4.85455i	0.102071	−	0.176792i
$755$	1.81665			0.0661148
$756$	1.11943			0.0407133
$757$	−4.00000	−	6.92820i	−0.145382	−	0.251810i	0.784133	−	0.620593i	$-0.213108\pi$
$757$	−4.00000	−	6.92820i	−0.145382	−	0.251810i	−0.929516	+	0.368783i	$0.879775\pi$
$758$	−0.697224	−	1.20763i	−0.0253243	−	0.0438630i
$759$	−98.1749			−3.56352
$760$	−9.90833			−0.359413
$761$	−23.6653	−	40.9894i	−0.857865	−	1.48587i	−0.873961	−	0.485996i	$-0.838457\pi$
$761$	−23.6653	−	40.9894i	−0.857865	−	1.48587i	0.0160960	−	0.999870i	$-0.494876\pi$
$762$	5.86249	+	10.1541i	0.212376	+	0.367845i
$763$	1.07779	+	1.86680i	0.0390188	+	0.0675825i
$764$	−4.40833	−	7.63545i	−0.159488	−	0.276241i
$765$	−2.09167			−0.0756246
$766$	36.6333			1.32362
$767$	−7.04584	−	12.2037i	−0.254410	−	0.440652i
$768$	−1.15139	−	1.99426i	−0.0415471	−	0.0719617i
$769$	−9.39445			−0.338772			−0.169386	−	0.985550i	$-0.554179\pi$
$769$	−9.39445			−0.338772			−0.169386	+	0.985550i	$0.554179\pi$
$770$	−9.00000			−0.324337
$771$	−23.6194	+	40.9101i	−0.850633	+	1.47334i
$772$	7.75694	−	13.4354i	0.279178	−	0.483551i
$773$	32.2111			1.15855			0.579276	−	0.815131i	$-0.303335\pi$
$773$	32.2111			1.15855			0.579276	+	0.815131i	$0.303335\pi$
$774$	−11.7569	−	20.3636i	−0.422594	−	0.731955i
$775$	0.591673	−	1.02481i	0.0212535	−	0.0368122i
$776$	−0.105551	−	0.182820i	−0.00378907	−	0.00656286i
$777$	−0.316654	+	0.548461i	−0.0113599	+	0.0196759i
$778$	5.89445	−	10.2095i	0.211326	−	0.366028i
$779$	23.2708	+	40.3062i	0.833764	+	1.44412i
$780$	3.45416	−	5.98279i	0.123679	−	0.214218i
$781$	38.1333	+	66.0488i	1.36452	+	2.36341i
$782$	3.00000			0.107280
$783$	−3.45416	−	5.98279i	−0.123442	−	0.213807i
$784$	−6.51388			−0.232639
$785$	11.3028			0.403413
$786$	14.7569	−	25.5598i	0.526363	−	0.911687i
$787$	−21.6194	+	37.4460i	−0.770649	+	1.33480i	0.166558	+	0.986032i	$0.446735\pi$
$787$	−21.6194	+	37.4460i	−0.770649	+	1.33480i	−0.937207	+	0.348772i	$0.886599\pi$
$788$	−4.00000	+	6.92820i	−0.142494	+	0.246807i
$789$	−34.3625	−	59.5176i	−1.22334	−	2.11888i
$790$	−13.3944			−0.476553
$791$	−5.78890	+	10.0267i	−0.205829	+	0.356507i
$792$	12.9083			0.458677
$793$	−10.1653	−	0.445032i	−0.360979	−	0.0158035i
$794$	38.9083			1.38080
$795$	−1.60555	+	2.78090i	−0.0569430	+	0.0986282i
$796$	22.2111			0.787252
$797$	3.98612	+	6.90417i	0.141196	+	0.244558i	0.927947	−	0.372712i	$-0.121572\pi$
$797$	3.98612	+	6.90417i	0.141196	+	0.244558i	−0.786751	+	0.617270i	$0.788239\pi$
$798$	−3.45416	+	5.98279i	−0.122276	+	0.211788i
$799$	−2.28890	+	3.96449i	−0.0809754	+	0.140253i
$800$	0.151388	−	0.262211i	0.00535237	−	0.00927057i
$801$	10.8167			0.382188
$802$	−23.7250			−0.837758
$803$	3.65139	+	6.32439i	0.128855	+	0.223183i
$804$	−27.4222			−0.967107
$805$	6.10555	+	10.5751i	0.215192	+	0.372724i
$806$	2.54584	−	4.40952i	0.0896733	−	0.155319i
$807$	19.6056	+	33.9578i	0.690148	+	1.19537i
$808$	4.69722	−	8.13583i	0.165248	−	0.286218i
$809$	4.60555	−	7.97705i	0.161923	−	0.280458i	−0.773636	−	0.633631i	$-0.781564\pi$
$809$	4.60555	−	7.97705i	0.161923	−	0.280458i	0.935558	+	0.353173i	$0.114897\pi$
$810$	−12.2111	−	21.1503i	−0.429054	−	0.743144i
$811$	−17.4222	+	30.1761i	−0.611776	+	1.05963i	0.379165	+	0.925329i	$0.376211\pi$
$811$	−17.4222	+	30.1761i	−0.611776	+	1.05963i	−0.990941	+	0.134298i	$0.957122\pi$
$812$	−1.50000	−	2.59808i	−0.0526397	−	0.0911746i
$813$	44.9361			1.57598
$814$	1.10555	−	1.91487i	0.0387496	−	0.0671162i
$815$	7.60555	−	13.1732i	0.266411	−	0.461437i
$816$	−0.908327			−0.0317978
$817$	−43.9361			−1.53713
$818$	5.10555	+	8.84307i	0.178511	+	0.309191i
$819$	−1.04584	−	1.81144i	−0.0365445	−	0.0632969i
$820$	−24.9083			−0.869837
$821$	7.78890			0.271834			0.135917	−	0.990720i	$-0.456602\pi$
$821$	7.78890			0.271834			0.135917	+	0.990720i	$0.456602\pi$
$822$	12.2111	+	21.1503i	0.425911	+	0.737700i
$823$	−13.2111	−	22.8823i	−0.460510	−	0.797627i	0.538476	−	0.842641i	$-0.319000\pi$
$823$	−13.2111	−	22.8823i	−0.460510	−	0.797627i	−0.998986	+	0.0450138i	$0.985667\pi$
$824$	−2.50000	−	4.33013i	−0.0870916	−	0.150847i
$825$	1.95416	+	3.38471i	0.0680352	+	0.117840i
$826$	−7.54163			−0.262407
$827$	35.0278			1.21803			0.609017	−	0.793157i	$-0.291564\pi$
$827$	35.0278			1.21803			0.609017	+	0.793157i	$0.291564\pi$
$828$	−8.75694	−	15.1675i	−0.304325	−	0.527106i
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	0.788165	−	0.615465i	$-0.211032\pi$
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	−0.927090	+	0.374838i	$0.877698\pi$
$830$	−29.7250			−1.03177
$831$	−13.8167			−0.479294
$832$	0.651388	−	1.12824i	0.0225828	−	0.0391146i
$833$	−1.28470	+	2.22516i	−0.0445121	+	0.0770971i
$834$	−3.69722			−0.128024
$835$	8.51388	+	14.7465i	0.294635	+	0.510323i
$836$	12.0597	−	20.8880i	0.417094	−	0.722428i
$837$	−3.13751	−	5.43433i	−0.108448	−	0.187838i
$838$	−7.89445	+	13.6736i	−0.272709	+	0.472346i
$839$	−2.15139	+	3.72631i	−0.0742742	+	0.128647i	−0.900770	−	0.434296i	$-0.856997\pi$
$839$	−2.15139	+	3.72631i	−0.0742742	+	0.128647i	0.826496	+	0.562942i	$0.190331\pi$
$840$	−1.84861	−	3.20189i	−0.0637832	−	0.110476i
$841$	5.24306	−	9.08125i	0.180795	−	0.313146i
$842$	18.0139	+	31.2010i	0.620799	+	1.07526i
$843$	−41.9361			−1.44436
$844$	9.84861	+	17.0583i	0.339003	+	0.587171i
$845$	−26.0278			−0.895382
$846$	26.7250			0.918824
$847$	7.11943	−	12.3312i	0.244626	−	0.423706i
$848$	−0.302776	+	0.524423i	−0.0103974	+	0.0180088i
$849$	10.0458	−	17.3999i	0.344772	−	0.597163i
$850$	−0.0597147	−	0.103429i	−0.00204820	−	0.00354758i
$851$	−3.00000			−0.102839
$852$	−15.6653	+	27.1330i	−0.536683	+	0.929563i
$853$	−42.1194			−1.44214			−0.721071	−	0.692861i	$-0.756350\pi$
$853$	−42.1194			−1.44214			−0.721071	+	0.692861i	$0.756350\pi$
$854$	−2.92641	+	4.59234i	−0.100140	+	0.157147i
$855$	22.8167			0.780313
$856$	−2.60555	+	4.51295i	−0.0890559	+	0.154249i
$857$	45.1749			1.54315			0.771573	−	0.636140i	$-0.219470\pi$
$857$	45.1749			1.54315			0.771573	+	0.636140i	$0.219470\pi$
$858$	8.40833	+	14.5636i	0.287056	+	0.497195i
$859$	7.34861	−	12.7282i	0.250731	−	0.434280i	−0.712996	−	0.701168i	$-0.752662\pi$
$859$	7.34861	−	12.7282i	0.250731	−	0.434280i	0.963727	+	0.266889i	$0.0859956\pi$
$860$	11.7569	−	20.3636i	0.400908	−	0.694394i
$861$	−8.68335	+	15.0400i	−0.295928	+	0.512562i
$862$	1.90833			0.0649979
$863$	42.7250			1.45438			0.727188	−	0.686439i	$-0.240827\pi$
$863$	42.7250			1.45438			0.727188	+	0.686439i	$0.240827\pi$
$864$	−0.802776	−	1.39045i	−0.0273110	−	0.0473040i
$865$	25.8167			0.877793
$866$	−5.95416	−	10.3129i	−0.202331	−	0.350447i
$867$	19.3944	−	33.5922i	0.658670	−	1.14085i
$868$	−1.36249	−	2.35990i	−0.0462459	−	0.0801003i
$869$	16.3028	−	28.2372i	0.553034	−	0.957883i
$870$	−11.4083	+	19.7598i	−0.386779	+	0.669920i
$871$	−7.75694	−	13.4354i	−0.262834	−	0.455242i
$872$	1.54584	−	2.67747i	0.0523486	−	0.0906705i
$873$	0.243061	+	0.420994i	0.00822637	+	0.0142485i
$874$	−32.7250			−1.10694
$875$	−3.77082	+	6.53125i	−0.127477	+	0.220796i
$876$	−1.50000	+	2.59808i	−0.0506803	+	0.0877809i
$877$	7.84441			0.264887			0.132443	−	0.991191i	$-0.457718\pi$
$877$	7.84441			0.264887			0.132443	+	0.991191i	$0.457718\pi$
$878$	22.8167			0.770025
$879$	4.15139	+	7.19041i	0.140023	+	0.242527i
$880$	6.45416	+	11.1789i	0.217570	+	0.376842i
$881$	44.3583			1.49447			0.747234	−	0.664561i	$-0.231381\pi$
$881$	44.3583			1.49447			0.747234	+	0.664561i	$0.231381\pi$
$882$	15.0000			0.505076
$883$	9.46804	+	16.3991i	0.318625	+	0.551875i	0.980201	−	0.198003i	$-0.0634456\pi$
$883$	9.46804	+	16.3991i	0.318625	+	0.551875i	−0.661576	+	0.749878i	$0.730112\pi$
$884$	−0.256939	−	0.445032i	−0.00864180	−	0.0149680i
$885$	28.6791	+	49.6737i	0.964039	+	1.66976i
$886$	5.01388	+	8.68429i	0.168445	+	0.291754i
$887$	−15.6056			−0.523983			−0.261992	−	0.965070i	$-0.584379\pi$
$887$	−15.6056			−0.523983			−0.261992	+	0.965070i	$0.584379\pi$
$888$	0.908327			0.0304815
$889$	1.77502	+	3.07442i	0.0595322	+	0.103113i
$890$	5.40833	+	9.36750i	0.181288	+	0.313999i
$891$	59.4500			1.99165
$892$	12.0917			0.404859
$893$	24.9680	−	43.2459i	0.835524	−	1.44717i
$894$	6.90833	−	11.9656i	0.231049	−	0.400189i
$895$	−33.0000			−1.10307
$896$	−0.348612	−	0.603814i	−0.0116463	−	0.0201720i
$897$	11.4083	−	19.7598i	0.380913	−	0.659761i
$898$	−19.6791	−	34.0853i	−0.656702	−	1.13744i
$899$	−8.40833	+	14.5636i	−0.280433	+	0.485725i
$900$	−0.348612	+	0.603814i	−0.0116204	+	0.0201271i
$901$	0.119429	+	0.206858i	0.00397877	+	0.00689144i
$902$	30.3167	−	52.5100i	1.00943	−	1.74839i
$903$	−8.19722	−	14.1980i	−0.272787	−	0.472480i
$904$	16.6056			0.552292
$905$	−3.59167	−	6.22096i	−0.119391	−	0.206792i
$906$	−1.81665			−0.0603543
$907$	5.66947			0.188252			0.0941258	−	0.995560i	$-0.469994\pi$
$907$	5.66947			0.188252			0.0941258	+	0.995560i	$0.469994\pi$
$908$	−9.86249	+	17.0823i	−0.327298	+	0.566897i
$909$	−10.8167	+	18.7350i	−0.358766	+	0.621401i
$910$	1.04584	−	1.81144i	0.0346691	−	0.0600487i
$911$	−9.81665	−	17.0029i	−0.325240	−	0.563333i	0.656321	−	0.754482i	$-0.272112\pi$
$911$	−9.81665	−	17.0029i	−0.325240	−	0.563333i	−0.981561	+	0.191149i	$0.938779\pi$
$912$	9.90833			0.328097
$913$	36.1791	−	62.6641i	1.19735	−	2.07388i
$914$	4.51388			0.149306
$915$	41.3764	+	1.81144i	1.36786	+	0.0598844i
$916$	−11.0917			−0.366479
$917$	4.46804	−	7.73888i	0.147548	−	0.255560i
$918$	−0.633308			−0.0209023
$919$	−25.1791	−	43.6116i	−0.830583	−	1.43861i	−0.897576	−	0.440859i	$-0.854674\pi$
$919$	−25.1791	−	43.6116i	−0.830583	−	1.43861i	0.0669930	−	0.997753i	$-0.478659\pi$
$920$	8.75694	−	15.1675i	0.288708	−	0.500056i
$921$	7.11943	−	12.3312i	0.234593	−	0.406327i
$922$	−3.30278	+	5.72058i	−0.108771	+	0.188397i
$923$	−17.7250			−0.583425
$924$	9.00000			0.296078
$925$	0.0597147	+	0.103429i	0.00196341	+	0.00340072i
$926$	7.60555			0.249934
$927$	5.75694	+	9.97131i	0.189083	+	0.327501i
$928$	−2.15139	+	3.72631i	−0.0706228	+	0.122322i
$929$	11.6972	+	20.2602i	0.383773	+	0.664715i	0.991598	−	0.129356i	$-0.0412910\pi$
$929$	11.6972	+	20.2602i	0.383773	+	0.664715i	−0.607825	+	0.794071i	$0.707958\pi$
$930$	−10.3625	+	17.9484i	−0.339799	+	0.588550i
$931$	14.0139	−	24.2727i	0.459286	−	0.795507i
$932$	−11.3028	−	19.5770i	−0.370235	−	0.641265i
$933$	37.6791	−	65.2622i	1.23356	−	2.13659i
$934$	−4.45416	−	7.71484i	−0.145745	−	0.252437i
$935$	5.09167			0.166516
$936$	−1.50000	+	2.59808i	−0.0490290	+	0.0849208i
$937$	−13.9083	+	24.0899i	−0.454365	+	0.786984i	−0.998651	−	0.0519159i	$-0.983467\pi$
$937$	−13.9083	+	24.0899i	−0.454365	+	0.786984i	0.544286	+	0.838900i	$0.316801\pi$
$938$	−8.30278			−0.271095
$939$	−20.7889			−0.678420
$940$	13.3625	+	23.1445i	0.435836	+	0.754891i
$941$	7.07359	+	12.2518i	0.230593	+	0.399398i	0.957983	−	0.286826i	$-0.0926002\pi$
$941$	7.07359	+	12.2518i	0.230593	+	0.399398i	−0.727390	+	0.686224i	$0.759267\pi$
$942$	−11.3028			−0.368264
$943$	−82.2666			−2.67897
$944$	5.40833	+	9.36750i	0.176026	+	0.304886i
$945$	−1.28890	−	2.23244i	−0.0419278	−	0.0726211i
$946$	28.6194	+	49.5703i	0.930498	+	1.61167i
$947$	1.25694	+	2.17708i	0.0408450	+	0.0707457i	0.885725	−	0.464210i	$-0.153662\pi$
$947$	1.25694	+	2.17708i	0.0408450	+	0.0707457i	−0.844880	+	0.534956i	$0.820328\pi$
$948$	13.3944			0.435031
$949$	−1.69722			−0.0550942
$950$	0.651388	+	1.12824i	0.0211338	+	0.0366048i
$951$	−14.8625	−	25.7426i	−0.481949	−	0.834761i
$952$	−0.275019			−0.00891343
$953$	3.48612			0.112927			0.0564633	−	0.998405i	$-0.482018\pi$
$953$	3.48612			0.112927			0.0564633	+	0.998405i	$0.482018\pi$
$954$	0.697224	−	1.20763i	0.0225735	−	0.0390984i
$955$	−10.1514	+	17.5827i	−0.328491	+	0.568963i
$956$	−20.6056			−0.666431
$957$	−27.7708	−	48.1005i	−0.897703	−	1.55487i
$958$	−16.6514	+	28.8410i	−0.537982	+	0.931812i
$959$	3.69722	+	6.40378i	0.119390	+	0.206789i
$960$	−2.65139	+	4.59234i	−0.0855732	+	0.148217i
$961$	7.86249	−	13.6182i	0.253629	−	0.439298i
$962$	0.256939	+	0.445032i	0.00828405	+	0.0143484i
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	−5.39445	−	9.34346i	−0.173743	−	0.300933i
$965$	−35.7250			−1.15003
$966$	−6.10555	−	10.5751i	−0.196443	−	0.340249i
$967$	−61.9361			−1.99173			−0.995865	−	0.0908446i	$-0.971043\pi$
$967$	−61.9361			−1.99173			−0.995865	+	0.0908446i	$0.971043\pi$
$968$	−20.4222			−0.656395
$969$	1.95416	−	3.38471i	0.0627768	−	0.108733i
$970$	−0.243061	+	0.420994i	−0.00780422	+	0.0135173i
$971$	−9.66527	+	16.7407i	−0.310173	+	0.537236i	−0.978400	−	0.206722i	$-0.933720\pi$
$971$	−9.66527	+	16.7407i	−0.310173	+	0.537236i	0.668227	+	0.743958i	$0.267054\pi$
$972$	9.80278	+	16.9789i	0.314424	+	0.544599i
$973$	−1.11943			−0.0358873
$974$	−10.7708	+	18.6556i	−0.345119	+	0.597764i
$975$	−0.908327			−0.0290897
$976$	7.80278	+	0.341603i	0.249761	+	0.0109344i
$977$	19.9361			0.637812			0.318906	−	0.947786i	$-0.396685\pi$
$977$	19.9361			0.637812			0.318906	+	0.947786i	$0.396685\pi$
$978$	−7.60555	+	13.1732i	−0.243199	+	0.421233i
$979$	−26.3305			−0.841527
$980$	7.50000	+	12.9904i	0.239579	+	0.414963i
$981$	−3.55971	+	6.16561i	−0.113653	+	0.196853i
$982$	2.51388	−	4.35416i	0.0802211	−	0.138947i
$983$	−29.7250	+	51.4852i	−0.948080	+	1.64212i	−0.198615	+	0.980078i	$0.563644\pi$
$983$	−29.7250	+	51.4852i	−0.948080	+	1.64212i	−0.749464	+	0.662045i	$0.769689\pi$
$984$	24.9083			0.794048
$985$	18.4222			0.586980
$986$	0.848612	+	1.46984i	0.0270253	+	0.0468092i
$987$	18.6333			0.593105
$988$	2.80278	+	4.85455i	0.0891682	+	0.154444i
$989$	38.8305	−	67.2565i	1.23474	−	2.13863i
$990$	−14.8625	−	25.7426i	−0.472361	−	0.818153i
$991$	−15.0139	+	26.0048i	−0.476932	+	0.826070i	−0.999651	−	0.0264354i	$-0.991584\pi$
$991$	−15.0139	+	26.0048i	−0.476932	+	0.826070i	0.522719	+	0.852505i	$0.324918\pi$
$992$	−1.95416	+	3.38471i	−0.0620448	+	0.107465i
$993$	10.4680	+	18.1312i	0.332193	+	0.575376i
$994$	−4.74306	+	8.21522i	−0.150441	+	0.260571i
$995$	−25.5736	−	44.2948i	−0.810737	−	1.40424i
$996$	29.7250			0.941872
$997$	12.4403	−	21.5472i	0.393988	−	0.682407i	−0.598984	−	0.800761i	$-0.704429\pi$
$997$	12.4403	−	21.5472i	0.393988	−	0.682407i	0.992971	+	0.118354i	$0.0377619\pi$
$998$	−15.6194	+	27.0536i	−0.494424	+	0.856368i
$999$	0.633308			0.0200370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.c.a.13.2	✓	4
3.2	odd	2		1098.2.f.c.379.2		4
4.3	odd	2		976.2.i.c.257.1		4
61.13	even	3		7442.2.a.e.1.2		2
61.47	even	3	inner	122.2.c.a.47.2	yes	4
61.48	even	6		7442.2.a.h.1.2		2
183.47	odd	6		1098.2.f.c.901.2		4
244.47	odd	6		976.2.i.c.657.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.c.a.13.2	✓	4	1.1	even	1	trivial
122.2.c.a.47.2	yes	4	61.47	even	3	inner
976.2.i.c.257.1		4	4.3	odd	2
976.2.i.c.657.1		4	244.47	odd	6
1098.2.f.c.379.2		4	3.2	odd	2
1098.2.f.c.901.2		4	183.47	odd	6
7442.2.a.e.1.2		2	61.13	even	3
7442.2.a.h.1.2		2	61.48	even	6

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.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +2.30278 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.15139 + 1.99426i) q^{5} +(1.15139 - 1.99426i) q^{6} +(0.348612 - 0.603814i) q^{7} -1.00000 q^{8} +2.30278 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +2.30278 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.15139 + 1.99426i) q^{5} +(1.15139 - 1.99426i) q^{6} +(0.348612 - 0.603814i) q^{7} -1.00000 q^{8} +2.30278 q^{9} +(1.15139 + 1.99426i) q^{10} -5.60555 q^{11} +(-1.15139 - 1.99426i) q^{12} +(0.651388 - 1.12824i) q^{13} +(-0.348612 - 0.603814i) q^{14} +(-2.65139 + 4.59234i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.197224 + 0.341603i) q^{17} +(1.15139 - 1.99426i) q^{18} +(-2.15139 - 3.72631i) q^{19} +2.30278 q^{20} +(0.802776 - 1.39045i) q^{21} +(-2.80278 + 4.85455i) q^{22} +7.60555 q^{23} -2.30278 q^{24} +(-0.151388 - 0.262211i) q^{25} +(-0.651388 - 1.12824i) q^{26} -1.60555 q^{27} -0.697224 q^{28} +(2.15139 + 3.72631i) q^{29} +(2.65139 + 4.59234i) q^{30} +(1.95416 + 3.38471i) q^{31} +(0.500000 + 0.866025i) q^{32} -12.9083 q^{33} +0.394449 q^{34} +(0.802776 + 1.39045i) q^{35} +(-1.15139 - 1.99426i) q^{36} -0.394449 q^{37} -4.30278 q^{38} +(1.50000 - 2.59808i) q^{39} +(1.15139 - 1.99426i) q^{40} -10.8167 q^{41} +(-0.802776 - 1.39045i) q^{42} +(5.10555 - 8.84307i) q^{43} +(2.80278 + 4.85455i) q^{44} +(-2.65139 + 4.59234i) q^{45} +(3.80278 - 6.58660i) q^{46} +(5.80278 + 10.0507i) q^{47} +(-1.15139 + 1.99426i) q^{48} +(3.25694 + 5.64118i) q^{49} -0.302776 q^{50} +(0.454163 + 0.786634i) q^{51} -1.30278 q^{52} +0.605551 q^{53} +(-0.802776 + 1.39045i) q^{54} +(6.45416 - 11.1789i) q^{55} +(-0.348612 + 0.603814i) q^{56} +(-4.95416 - 8.58086i) q^{57} +4.30278 q^{58} +(5.40833 - 9.36750i) q^{59} +5.30278 q^{60} +(-3.60555 - 6.92820i) q^{61} +3.90833 q^{62} +(0.802776 - 1.39045i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(-6.45416 + 11.1789i) q^{66} +(5.95416 - 10.3129i) q^{67} +(0.197224 - 0.341603i) q^{68} +17.5139 q^{69} +1.60555 q^{70} +(-6.80278 - 11.7828i) q^{71} -2.30278 q^{72} +(-0.651388 - 1.12824i) q^{73} +(-0.197224 + 0.341603i) q^{74} +(-0.348612 - 0.603814i) q^{75} +(-2.15139 + 3.72631i) q^{76} +(-1.95416 + 3.38471i) q^{77} +(-1.50000 - 2.59808i) q^{78} +(-2.90833 + 5.03737i) q^{79} +(-1.15139 - 1.99426i) q^{80} -10.6056 q^{81} +(-5.40833 + 9.36750i) q^{82} +(-6.45416 + 11.1789i) q^{83} -1.60555 q^{84} -0.908327 q^{85} +(-5.10555 - 8.84307i) q^{86} +(4.95416 + 8.58086i) q^{87} +5.60555 q^{88} +4.69722 q^{89} +(2.65139 + 4.59234i) q^{90} +(-0.454163 - 0.786634i) q^{91} +(-3.80278 - 6.58660i) q^{92} +(4.50000 + 7.79423i) q^{93} +11.6056 q^{94} +9.90833 q^{95} +(1.15139 + 1.99426i) q^{96} +(0.105551 + 0.182820i) q^{97} +6.51388 q^{98} -12.9083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + q^{6} + 5 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + q^6 + 5 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + q^{6} + 5 q^{7} - 4 q^{8} + 2 q^{9} + q^{10} - 8 q^{11} - q^{12} - q^{13} - 5 q^{14} - 7 q^{15} - 2 q^{16} + 8 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} - 4 q^{21} - 4 q^{22} + 16 q^{23} - 2 q^{24} + 3 q^{25} + q^{26} + 8 q^{27} - 10 q^{28} + 5 q^{29} + 7 q^{30} - 3 q^{31} + 2 q^{32} - 30 q^{33} + 16 q^{34} - 4 q^{35} - q^{36} - 16 q^{37} - 10 q^{38} + 6 q^{39} + q^{40} + 4 q^{42} + 6 q^{43} + 4 q^{44} - 7 q^{45} + 8 q^{46} + 16 q^{47} - q^{48} - 5 q^{49} + 6 q^{50} - 9 q^{51} + 2 q^{52} - 12 q^{53} + 4 q^{54} + 15 q^{55} - 5 q^{56} - 9 q^{57} + 10 q^{58} + 14 q^{60} - 6 q^{62} - 4 q^{63} + 4 q^{64} + 6 q^{65} - 15 q^{66} + 13 q^{67} + 8 q^{68} + 34 q^{69} - 8 q^{70} - 20 q^{71} - 2 q^{72} + q^{73} - 8 q^{74} - 5 q^{75} - 5 q^{76} + 3 q^{77} - 6 q^{78} + 10 q^{79} - q^{80} - 28 q^{81} - 15 q^{83} + 8 q^{84} + 18 q^{85} - 6 q^{86} + 9 q^{87} + 8 q^{88} + 26 q^{89} + 7 q^{90} + 9 q^{91} - 8 q^{92} + 18 q^{93} + 32 q^{94} + 18 q^{95} + q^{96} - 14 q^{97} - 10 q^{98} - 30 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + q^6 + 5 * q^7 - 4 * q^8 + 2 * q^9 + q^10 - 8 * q^11 - q^12 - q^13 - 5 * q^14 - 7 * q^15 - 2 * q^16 + 8 * q^17 + q^18 - 5 * q^19 + 2 * q^20 - 4 * q^21 - 4 * q^22 + 16 * q^23 - 2 * q^24 + 3 * q^25 + q^26 + 8 * q^27 - 10 * q^28 + 5 * q^29 + 7 * q^30 - 3 * q^31 + 2 * q^32 - 30 * q^33 + 16 * q^34 - 4 * q^35 - q^36 - 16 * q^37 - 10 * q^38 + 6 * q^39 + q^40 + 4 * q^42 + 6 * q^43 + 4 * q^44 - 7 * q^45 + 8 * q^46 + 16 * q^47 - q^48 - 5 * q^49 + 6 * q^50 - 9 * q^51 + 2 * q^52 - 12 * q^53 + 4 * q^54 + 15 * q^55 - 5 * q^56 - 9 * q^57 + 10 * q^58 + 14 * q^60 - 6 * q^62 - 4 * q^63 + 4 * q^64 + 6 * q^65 - 15 * q^66 + 13 * q^67 + 8 * q^68 + 34 * q^69 - 8 * q^70 - 20 * q^71 - 2 * q^72 + q^73 - 8 * q^74 - 5 * q^75 - 5 * q^76 + 3 * q^77 - 6 * q^78 + 10 * q^79 - q^80 - 28 * q^81 - 15 * q^83 + 8 * q^84 + 18 * q^85 - 6 * q^86 + 9 * q^87 + 8 * q^88 + 26 * q^89 + 7 * q^90 + 9 * q^91 - 8 * q^92 + 18 * q^93 + 32 * q^94 + 18 * q^95 + q^96 - 14 * q^97 - 10 * q^98 - 30 * q^99

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