LMFDB - Embedded newform 494.2.g.b.419.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [494,2,Mod(191,494)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(494, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("494.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.g (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:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1
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			419.2
Root			$-0.136945 - 0.237196i$ of defining polynomial
Character	$\chi$	$=$	494.419
Dual form			494.2.g.b.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.636945 + 1.10322i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.37720 q^{5} +(0.636945 - 1.10322i) q^{6} +(-0.136945 + 0.237196i) q^{7} +1.00000 q^{8} +(0.688601 - 1.19269i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.636945 + 1.10322i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.37720 q^{5} +(0.636945 - 1.10322i) q^{6} +(-0.136945 + 0.237196i) q^{7} +1.00000 q^{8} +(0.688601 - 1.19269i) q^{9} +(-1.18860 - 2.05872i) q^{10} +(2.18860 + 3.79077i) q^{11} -1.27389 q^{12} +(-0.910836 - 3.48861i) q^{13} +0.273891 q^{14} +(1.51415 + 2.62258i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.273891 + 0.474392i) q^{17} -1.37720 q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.18860 + 2.05872i) q^{20} -0.348907 q^{21} +(2.18860 - 3.79077i) q^{22} +(2.28804 + 3.96300i) q^{23} +(0.636945 + 1.10322i) q^{24} +0.651093 q^{25} +(-2.56580 + 2.53311i) q^{26} +5.57608 q^{27} +(-0.136945 - 0.237196i) q^{28} +(-0.839695 - 1.45439i) q^{29} +(1.51415 - 2.62258i) q^{30} +2.85772 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.78804 + 4.82902i) q^{33} +0.547781 q^{34} +(-0.325547 + 0.563863i) q^{35} +(0.688601 + 1.19269i) q^{36} +(4.02830 + 6.97721i) q^{37} +1.00000 q^{38} +(3.26855 - 3.22691i) q^{39} +2.37720 q^{40} +(-4.51415 - 7.81873i) q^{41} +(0.174453 + 0.302162i) q^{42} +(0.226109 - 0.391633i) q^{43} -4.37720 q^{44} +(1.63695 - 2.83527i) q^{45} +(2.28804 - 3.96300i) q^{46} +0.472765 q^{47} +(0.636945 - 1.10322i) q^{48} +(3.46249 + 5.99721i) q^{49} +(-0.325547 - 0.563863i) q^{50} -0.697813 q^{51} +(3.47664 + 0.955496i) q^{52} -2.85772 q^{53} +(-2.78804 - 4.82902i) q^{54} +(5.20275 + 9.01143i) q^{55} +(-0.136945 + 0.237196i) q^{56} -1.27389 q^{57} +(-0.839695 + 1.45439i) q^{58} +(6.76468 - 11.7168i) q^{59} -3.02830 q^{60} +(-2.09944 + 3.63633i) q^{61} +(-1.42886 - 2.47486i) q^{62} +(0.188601 + 0.326667i) q^{63} +1.00000 q^{64} +(-2.16524 - 8.29313i) q^{65} +5.57608 q^{66} +(-5.02830 - 8.70926i) q^{67} +(-0.273891 - 0.474392i) q^{68} +(-2.91471 + 5.04843i) q^{69} +0.651093 q^{70} +(1.50000 - 2.59808i) q^{71} +(0.688601 - 1.19269i) q^{72} -11.1132 q^{73} +(4.02830 - 6.97721i) q^{74} +(0.414711 + 0.718300i) q^{75} +(-0.500000 - 0.866025i) q^{76} -1.19887 q^{77} +(-4.42886 - 1.21720i) q^{78} +2.36945 q^{79} +(-1.18860 - 2.05872i) q^{80} +(1.48585 + 2.57357i) q^{81} +(-4.51415 + 7.81873i) q^{82} -16.7643 q^{83} +(0.174453 - 0.302162i) q^{84} +(-0.651093 + 1.12773i) q^{85} -0.452219 q^{86} +(1.06968 - 1.85274i) q^{87} +(2.18860 + 3.79077i) q^{88} +(1.02336 + 1.77251i) q^{89} -3.27389 q^{90} +(0.952219 + 0.261701i) q^{91} -4.57608 q^{92} +(1.82021 + 3.15270i) q^{93} +(-0.236383 - 0.409427i) q^{94} +(-1.18860 + 2.05872i) q^{95} -1.27389 q^{96} +(2.72611 - 4.72176i) q^{97} +(3.46249 - 5.99721i) q^{98} +6.02830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 8 q^{11} - 4 q^{12} - 2 q^{14} - 3 q^{15} - 3 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 2 q^{20} - 16 q^{21} + 8 q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{25} + 2 q^{27} + q^{28} + 14 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - q^{33} - 4 q^{34} + 5 q^{35} - q^{36} + 6 q^{38} - 13 q^{39} + 4 q^{40} - 15 q^{41} + 8 q^{42} + 5 q^{43} - 16 q^{44} + 8 q^{45} - 2 q^{46} - 22 q^{47} + 2 q^{48} + 12 q^{49} + 5 q^{50} - 32 q^{51} + 10 q^{53} - q^{54} + 14 q^{55} + q^{56} - 4 q^{57} + 14 q^{58} + 4 q^{59} + 6 q^{60} - 2 q^{61} + 5 q^{62} - 4 q^{63} + 6 q^{64} + 13 q^{65} + 2 q^{66} - 6 q^{67} + 2 q^{68} - 16 q^{69} - 10 q^{70} + 9 q^{71} - q^{72} + 30 q^{73} + q^{75} - 3 q^{76} + 14 q^{77} - 13 q^{78} - 4 q^{79} - 2 q^{80} + 21 q^{81} - 15 q^{82} + 10 q^{83} + 8 q^{84} + 10 q^{85} - 10 q^{86} - 5 q^{87} + 8 q^{88} + 27 q^{89} - 16 q^{90} + 13 q^{91} + 4 q^{92} - 25 q^{93} + 11 q^{94} - 2 q^{95} - 4 q^{96} + 20 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9 - 2 * q^10 + 8 * q^11 - 4 * q^12 - 2 * q^14 - 3 * q^15 - 3 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 2 * q^20 - 16 * q^21 + 8 * q^22 - 2 * q^23 + 2 * q^24 - 10 * q^25 + 2 * q^27 + q^28 + 14 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - q^33 - 4 * q^34 + 5 * q^35 - q^36 + 6 * q^38 - 13 * q^39 + 4 * q^40 - 15 * q^41 + 8 * q^42 + 5 * q^43 - 16 * q^44 + 8 * q^45 - 2 * q^46 - 22 * q^47 + 2 * q^48 + 12 * q^49 + 5 * q^50 - 32 * q^51 + 10 * q^53 - q^54 + 14 * q^55 + q^56 - 4 * q^57 + 14 * q^58 + 4 * q^59 + 6 * q^60 - 2 * q^61 + 5 * q^62 - 4 * q^63 + 6 * q^64 + 13 * q^65 + 2 * q^66 - 6 * q^67 + 2 * q^68 - 16 * q^69 - 10 * q^70 + 9 * q^71 - q^72 + 30 * q^73 + q^75 - 3 * q^76 + 14 * q^77 - 13 * q^78 - 4 * q^79 - 2 * q^80 + 21 * q^81 - 15 * q^82 + 10 * q^83 + 8 * q^84 + 10 * q^85 - 10 * q^86 - 5 * q^87 + 8 * q^88 + 27 * q^89 - 16 * q^90 + 13 * q^91 + 4 * q^92 - 25 * q^93 + 11 * q^94 - 2 * q^95 - 4 * q^96 + 20 * q^97 + 12 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.636945	+	1.10322i	0.367741	+	0.636945i	0.989212	−	0.146492i	$-0.0467981\pi$
$3$	0.636945	+	1.10322i	0.367741	+	0.636945i	−0.621471	+	0.783437i	$0.713465\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.37720			1.06312			0.531559	−	0.847021i	$-0.321606\pi$
$5$	2.37720			1.06312			0.531559	+	0.847021i	$0.321606\pi$
$6$	0.636945	−	1.10322i	0.260032	−	0.450388i
$7$	−0.136945	+	0.237196i	−0.0517604	+	0.0896517i	−0.890745	−	0.454504i	$-0.849817\pi$
$7$	−0.136945	+	0.237196i	−0.0517604	+	0.0896517i	0.838984	+	0.544156i	$0.183150\pi$
$8$	1.00000			0.353553
$9$	0.688601	−	1.19269i	0.229534	−	0.397564i
$10$	−1.18860	−	2.05872i	−0.375869	−	0.651024i
$11$	2.18860	+	3.79077i	0.659888	+	1.14296i	0.980644	+	0.195798i	$0.0627297\pi$
$11$	2.18860	+	3.79077i	0.659888	+	1.14296i	−0.320756	+	0.947162i	$0.603937\pi$
$12$	−1.27389			−0.367741
$13$	−0.910836	−	3.48861i	−0.252620	−	0.967565i
$13$	−0.910836	−	3.48861i	−0.252620	−	0.967565i
$14$	0.273891			0.0732003
$15$	1.51415	+	2.62258i	0.390951	+	0.677148i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.273891	+	0.474392i	−0.0664282	+	0.115057i	−0.897327	−	0.441367i	$-0.854494\pi$
$17$	−0.273891	+	0.474392i	−0.0664282	+	0.115057i	0.830898	+	0.556424i	$0.187827\pi$
$18$	−1.37720			−0.324610
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	−1.18860	+	2.05872i	−0.265779	+	0.460343i
$21$	−0.348907			−0.0761377
$22$	2.18860	−	3.79077i	0.466611	−	0.808195i
$23$	2.28804	+	3.96300i	0.477089	+	0.826342i	0.999655	−	0.0262562i	$-0.00835858\pi$
$23$	2.28804	+	3.96300i	0.477089	+	0.826342i	−0.522566	+	0.852599i	$0.675025\pi$
$24$	0.636945	+	1.10322i	0.130016	+	0.225194i
$25$	0.651093			0.130219
$26$	−2.56580	+	2.53311i	−0.503196	+	0.496784i
$27$	5.57608			1.07312
$28$	−0.136945	−	0.237196i	−0.0258802	−	0.0448259i
$29$	−0.839695	−	1.45439i	−0.155927	−	0.270074i	0.777469	−	0.628921i	$-0.216503\pi$
$29$	−0.839695	−	1.45439i	−0.155927	−	0.270074i	−0.933396	+	0.358847i	$0.883170\pi$
$30$	1.51415	−	2.62258i	0.276444	−	0.478816i
$31$	2.85772			0.513261			0.256631	−	0.966510i	$-0.417388\pi$
$31$	2.85772			0.513261			0.256631	+	0.966510i	$0.417388\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.78804	+	4.82902i	−0.485335	+	0.840625i
$34$	0.547781			0.0939437
$35$	−0.325547	+	0.563863i	−0.0550274	+	0.0953103i
$36$	0.688601	+	1.19269i	0.114767	+	0.198782i
$37$	4.02830	+	6.97721i	0.662248	+	1.14705i	0.980024	+	0.198881i	$0.0637307\pi$
$37$	4.02830	+	6.97721i	0.662248	+	1.14705i	−0.317776	+	0.948166i	$0.602936\pi$
$38$	1.00000			0.162221
$39$	3.26855	−	3.22691i	0.523387	−	0.516718i
$40$	2.37720			0.375869
$41$	−4.51415	−	7.81873i	−0.704991	−	1.22108i	−0.966695	−	0.255933i	$-0.917617\pi$
$41$	−4.51415	−	7.81873i	−0.704991	−	1.22108i	0.261703	−	0.965148i	$-0.415716\pi$
$42$	0.174453	+	0.302162i	0.0269187	+	0.0466246i
$43$	0.226109	−	0.391633i	0.0344814	−	0.0597235i	−0.848270	−	0.529564i	$-0.822355\pi$
$43$	0.226109	−	0.391633i	0.0344814	−	0.0597235i	0.882751	+	0.469841i	$0.155689\pi$
$44$	−4.37720			−0.659888
$45$	1.63695	−	2.83527i	0.244021	−	0.422657i
$46$	2.28804	−	3.96300i	0.337353	−	0.584312i
$47$	0.472765			0.0689599			0.0344799	−	0.999405i	$-0.489023\pi$
$47$	0.472765			0.0689599			0.0344799	+	0.999405i	$0.489023\pi$
$48$	0.636945	−	1.10322i	0.0919351	−	0.159236i
$49$	3.46249	+	5.99721i	0.494642	+	0.856745i
$50$	−0.325547	−	0.563863i	−0.0460393	−	0.0797423i
$51$	−0.697813			−0.0977134
$52$	3.47664	+	0.955496i	0.482123	+	0.132504i
$53$	−2.85772			−0.392538			−0.196269	−	0.980550i	$-0.562883\pi$
$53$	−2.85772			−0.392538			−0.196269	+	0.980550i	$0.562883\pi$
$54$	−2.78804	−	4.82902i	−0.379404	−	0.657147i
$55$	5.20275	+	9.01143i	0.701539	+	1.21510i
$56$	−0.136945	+	0.237196i	−0.0183001	+	0.0316967i
$57$	−1.27389			−0.168731
$58$	−0.839695	+	1.45439i	−0.110257	+	0.190971i
$59$	6.76468	−	11.7168i	0.880686	−	1.52539i	0.0301067	−	0.999547i	$-0.490415\pi$
$59$	6.76468	−	11.7168i	0.880686	−	1.52539i	0.850579	−	0.525846i	$-0.176251\pi$
$60$	−3.02830			−0.390951
$61$	−2.09944	+	3.63633i	−0.268805	+	0.465585i	−0.968554	−	0.248805i	$-0.919962\pi$
$61$	−2.09944	+	3.63633i	−0.268805	+	0.465585i	0.699748	+	0.714390i	$0.253296\pi$
$62$	−1.42886	−	2.47486i	−0.181465	−	0.314307i
$63$	0.188601	+	0.326667i	0.0237615	+	0.0411562i
$64$	1.00000			0.125000
$65$	−2.16524	−	8.29313i	−0.268565	−	1.02864i
$66$	5.57608			0.686368
$67$	−5.02830	−	8.70926i	−0.614304	−	1.06401i	−0.990506	−	0.137468i	$-0.956103\pi$
$67$	−5.02830	−	8.70926i	−0.614304	−	1.06401i	0.376202	−	0.926538i	$-0.377230\pi$
$68$	−0.273891	−	0.474392i	−0.0332141	−	0.0575285i
$69$	−2.91471	+	5.04843i	−0.350890	+	0.607759i
$70$	0.651093			0.0778205
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	0.941201	+	0.337846i	$0.109698\pi$
$72$	0.688601	−	1.19269i	0.0811525	−	0.140560i
$73$	−11.1132			−1.30070			−0.650350	−	0.759635i	$-0.725378\pi$
$73$	−11.1132			−1.30070			−0.650350	+	0.759635i	$0.725378\pi$
$74$	4.02830	−	6.97721i	0.468280	−	0.811085i
$75$	0.414711	+	0.718300i	0.0478867	+	0.0829422i
$76$	−0.500000	−	0.866025i	−0.0573539	−	0.0993399i
$77$	−1.19887			−0.136624
$78$	−4.42886	−	1.21720i	−0.501470	−	0.137821i
$79$	2.36945			0.266584			0.133292	−	0.991077i	$-0.457445\pi$
$79$	2.36945			0.266584			0.133292	+	0.991077i	$0.457445\pi$
$80$	−1.18860	−	2.05872i	−0.132890	−	0.230172i
$81$	1.48585	+	2.57357i	0.165095	+	0.285952i
$82$	−4.51415	+	7.81873i	−0.498504	+	0.863435i
$83$	−16.7643			−1.84012			−0.920059	−	0.391779i	$-0.871860\pi$
$83$	−16.7643			−1.84012			−0.920059	+	0.391779i	$0.871860\pi$
$84$	0.174453	−	0.302162i	0.0190344	−	0.0329686i
$85$	−0.651093	+	1.12773i	−0.0706210	+	0.122319i
$86$	−0.452219			−0.0487640
$87$	1.06968	−	1.85274i	0.114682	−	0.198634i
$88$	2.18860	+	3.79077i	0.233306	+	0.404097i
$89$	1.02336	+	1.77251i	0.108476	+	0.187886i	0.915153	−	0.403107i	$-0.132070\pi$
$89$	1.02336	+	1.77251i	0.108476	+	0.187886i	−0.806677	+	0.590992i	$0.798736\pi$
$90$	−3.27389			−0.345098
$91$	0.952219	+	0.261701i	0.0998197	+	0.0274338i
$92$	−4.57608			−0.477089
$93$	1.82021	+	3.15270i	0.188747	+	0.326919i
$94$	−0.236383	−	0.409427i	−0.0243810	−	0.0422291i
$95$	−1.18860	+	2.05872i	−0.121948	+	0.211220i
$96$	−1.27389			−0.130016
$97$	2.72611	−	4.72176i	0.276794	−	0.479422i	−0.693792	−	0.720176i	$-0.744061\pi$
$97$	2.72611	−	4.72176i	0.276794	−	0.479422i	0.970586	+	0.240754i	$0.0773945\pi$
$98$	3.46249	−	5.99721i	0.349765	−	0.605810i
$99$	6.02830			0.605867
$100$	−0.325547	+	0.563863i	−0.0325547	+	0.0563863i
$101$	−4.07608	−	7.05997i	−0.405585	−	0.702494i	0.588804	−	0.808275i	$-0.299599\pi$
$101$	−4.07608	−	7.05997i	−0.405585	−	0.702494i	−0.994389	+	0.105782i	$0.966265\pi$
$102$	0.348907	+	0.604324i	0.0345469	+	0.0598370i
$103$	−16.3510			−1.61111			−0.805557	−	0.592518i	$-0.798134\pi$
$103$	−16.3510			−1.61111			−0.805557	+	0.592518i	$0.798134\pi$
$104$	−0.910836	−	3.48861i	−0.0893148	−	0.342086i
$105$	−0.829422			−0.0809433
$106$	1.42886	+	2.47486i	0.138783	+	0.240379i
$107$	3.51415	+	6.08668i	0.339726	+	0.588422i	0.984381	−	0.176051i	$-0.0563325\pi$
$107$	3.51415	+	6.08668i	0.339726	+	0.588422i	−0.644655	+	0.764473i	$0.722999\pi$
$108$	−2.78804	+	4.82902i	−0.268279	+	0.464673i
$109$	−4.64334			−0.444752			−0.222376	−	0.974961i	$-0.571381\pi$
$109$	−4.64334			−0.444752			−0.222376	+	0.974961i	$0.571381\pi$
$110$	5.20275	−	9.01143i	0.496063	−	0.859206i
$111$	−5.13161	+	8.88821i	−0.487071	+	0.843631i
$112$	0.273891			0.0258802
$113$	−5.32942	+	9.23083i	−0.501350	+	0.868363i	0.498649	+	0.866804i	$0.333830\pi$
$113$	−5.32942	+	9.23083i	−0.501350	+	0.868363i	−0.999999	+	0.00155935i	$0.999504\pi$
$114$	0.636945	+	1.10322i	0.0596554	+	0.103326i
$115$	5.43913	+	9.42085i	0.507202	+	0.878499i
$116$	1.67939			0.155927
$117$	−4.78804	−	1.31591i	−0.442654	−	0.121656i
$118$	−13.5294			−1.24548
$119$	−0.0750160	−	0.129932i	−0.00687671	−	0.0119108i
$120$	1.51415	+	2.62258i	0.138222	+	0.239408i
$121$	−4.07995	+	7.06668i	−0.370905	+	0.642426i
$122$	4.19887			0.380148
$123$	5.75053	−	9.96021i	0.518508	−	0.898082i
$124$	−1.42886	+	2.47486i	−0.128315	+	0.222249i
$125$	−10.3382			−0.924680
$126$	0.188601	−	0.326667i	0.0168020	−	0.0291018i
$127$	8.07995	+	13.9949i	0.716980	+	1.24185i	0.962191	+	0.272376i	$0.0878094\pi$
$127$	8.07995	+	13.9949i	0.716980	+	1.24185i	−0.245211	+	0.969470i	$0.578857\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.576077			0.0507208
$130$	−6.09944	+	6.02172i	−0.534956	+	0.528140i
$131$	−15.9250			−1.39137			−0.695686	−	0.718346i	$-0.744900\pi$
$131$	−15.9250			−1.39137			−0.695686	+	0.718346i	$0.744900\pi$
$132$	−2.78804	−	4.82902i	−0.242668	−	0.420313i
$133$	−0.136945	−	0.237196i	−0.0118747	−	0.0205675i
$134$	−5.02830	+	8.70926i	−0.434379	+	0.752366i
$135$	13.2555			1.14085
$136$	−0.273891	+	0.474392i	−0.0234859	+	0.0406788i
$137$	6.59023	−	11.4146i	0.563041	−	0.975216i	−0.434188	−	0.900822i	$-0.642965\pi$
$137$	6.59023	−	11.4146i	0.563041	−	0.975216i	0.997229	−	0.0743933i	$-0.0237020\pi$
$138$	5.82942			0.496233
$139$	−1.25053	+	2.16598i	−0.106069	+	0.183716i	−0.914174	−	0.405321i	$-0.867160\pi$
$139$	−1.25053	+	2.16598i	−0.106069	+	0.183716i	0.808106	+	0.589038i	$0.200493\pi$
$140$	−0.325547	−	0.563863i	−0.0275137	−	0.0476552i
$141$	0.301125	+	0.521565i	0.0253593	+	0.0439237i
$142$	−3.00000			−0.251754
$143$	11.2310	−	11.0879i	0.939187	−	0.927220i
$144$	−1.37720			−0.114767
$145$	−1.99612	−	3.45739i	−0.165769	−	0.287121i
$146$	5.55659	+	9.62430i	0.459867	+	0.796513i
$147$	−4.41084	+	7.63979i	−0.363800	+	0.630119i
$148$	−8.05659			−0.662248
$149$	4.71196	−	8.16136i	0.386019	−	0.668604i	−0.605891	−	0.795548i	$-0.707183\pi$
$149$	4.71196	−	8.16136i	0.386019	−	0.668604i	0.991910	+	0.126943i	$0.0405166\pi$
$150$	0.414711	−	0.718300i	0.0338610	−	0.0586490i
$151$	−11.8217			−0.962034			−0.481017	−	0.876711i	$-0.659732\pi$
$151$	−11.8217			−0.962034			−0.481017	+	0.876711i	$0.659732\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	0.377203	+	0.653335i	0.0304950	+	0.0528190i
$154$	0.599437	+	1.03826i	0.0483040	+	0.0836650i
$155$	6.79338			0.545657
$156$	1.16031	+	4.44410i	0.0928988	+	0.355813i
$157$	1.13161			0.0903122			0.0451561	−	0.998980i	$-0.485621\pi$
$157$	1.13161			0.0903122			0.0451561	+	0.998980i	$0.485621\pi$
$158$	−1.18473	−	2.05201i	−0.0942518	−	0.163249i
$159$	−1.82021	−	3.15270i	−0.144352	−	0.250025i
$160$	−1.18860	+	2.05872i	−0.0939672	+	0.162756i
$161$	−1.25334			−0.0987774
$162$	1.48585	−	2.57357i	0.116740	−	0.202199i
$163$	−0.688601	+	1.19269i	−0.0539354	+	0.0934189i	−0.891733	−	0.452563i	$-0.850510\pi$
$163$	−0.688601	+	1.19269i	−0.0539354	+	0.0934189i	0.837797	+	0.545982i	$0.183843\pi$
$164$	9.02830			0.704991
$165$	−6.62773	+	11.4796i	−0.515968	+	0.893683i
$166$	8.38214	+	14.5183i	0.650580	+	1.12684i
$167$	0.208086	+	0.360416i	0.0161022	+	0.0278898i	0.873964	−	0.485990i	$-0.161541\pi$
$167$	0.208086	+	0.360416i	0.0161022	+	0.0278898i	−0.857862	+	0.513880i	$0.828208\pi$
$168$	−0.348907			−0.0269187
$169$	−11.3408	+	6.35510i	−0.872366	+	0.488854i
$170$	1.30219			0.0998732
$171$	0.688601	+	1.19269i	0.0526587	+	0.0912075i
$172$	0.226109	+	0.391633i	0.0172407	+	0.0298617i
$173$	2.10971	−	3.65413i	0.160398	−	0.277818i	−0.774613	−	0.632435i	$-0.782055\pi$
$173$	2.10971	−	3.65413i	0.160398	−	0.277818i	0.935012	+	0.354617i	$0.115389\pi$
$174$	−2.13936			−0.162184
$175$	−0.0891642	+	0.154437i	−0.00674018	+	0.0116743i
$176$	2.18860	−	3.79077i	0.164972	−	0.285740i
$177$	17.2349			1.29546
$178$	1.02336	−	1.77251i	0.0767041	−	0.132855i
$179$	−10.4572	−	18.1123i	−0.781604	−	1.35378i	−0.931007	−	0.365002i	$-0.881068\pi$
$179$	−10.4572	−	18.1123i	−0.781604	−	1.35378i	0.149402	−	0.988777i	$-0.452265\pi$
$180$	1.63695	+	2.83527i	0.122011	+	0.211329i
$181$	6.87051			0.510681			0.255341	−	0.966851i	$-0.417812\pi$
$181$	6.87051			0.510681			0.255341	+	0.966851i	$0.417812\pi$
$182$	−0.249469	−	0.955496i	−0.0184919	−	0.0708261i
$183$	−5.34891			−0.395403
$184$	2.28804	+	3.96300i	0.168676	+	0.292156i
$185$	9.57608	+	16.5863i	0.704047	+	1.21945i
$186$	1.82021	−	3.15270i	0.133464	−	0.231167i
$187$	−2.39775			−0.175341
$188$	−0.236383	+	0.409427i	−0.0172400	+	0.0298605i
$189$	−0.763617	+	1.32262i	−0.0555450	+	0.0962068i
$190$	2.37720			0.172460
$191$	−6.16524	+	10.6785i	−0.446101	+	0.772670i	−0.998128	−	0.0611563i	$-0.980521\pi$
$191$	−6.16524	+	10.6785i	−0.446101	+	0.772670i	0.552027	+	0.833826i	$0.313855\pi$
$192$	0.636945	+	1.10322i	0.0459676	+	0.0796182i
$193$	−10.1560	−	17.5908i	−0.731047	−	1.26621i	−0.956436	−	0.291942i	$-0.905699\pi$
$193$	−10.1560	−	17.5908i	−0.731047	−	1.26621i	0.225389	−	0.974269i	$-0.427635\pi$
$194$	−5.45222			−0.391447
$195$	7.77002	−	7.67101i	0.556422	−	0.549332i
$196$	−6.92498			−0.494642
$197$	−12.5424	−	21.7242i	−0.893612	−	1.54778i	−0.835513	−	0.549471i	$-0.814829\pi$
$197$	−12.5424	−	21.7242i	−0.893612	−	1.54778i	−0.0580993	−	0.998311i	$-0.518504\pi$
$198$	−3.01415	−	5.22066i	−0.214206	−	0.371016i
$199$	5.67018	−	9.82104i	0.401948	−	0.696195i	−0.592013	−	0.805929i	$-0.701667\pi$
$199$	5.67018	−	9.82104i	0.401948	−	0.696195i	0.993961	+	0.109734i	$0.0349998\pi$
$200$	0.651093			0.0460393
$201$	6.40550	−	11.0946i	0.451809	−	0.782556i
$202$	−4.07608	+	7.05997i	−0.286792	+	0.496738i
$203$	0.459969			0.0322835
$204$	0.348907	−	0.604324i	0.0244283	−	0.0423111i
$205$	−10.7310	−	18.5867i	−0.749489	−	1.29815i
$206$	8.17551	+	14.1604i	0.569615	+	0.986602i
$207$	6.30219			0.438032
$208$	−2.56580	+	2.53311i	−0.177907	+	0.175640i
$209$	−4.37720			−0.302777
$210$	0.414711	+	0.718300i	0.0286178	+	0.0495674i
$211$	3.75587	+	6.50535i	0.258565	+	0.447847i	0.965858	−	0.259073i	$-0.0834172\pi$
$211$	3.75587	+	6.50535i	0.258565	+	0.447847i	−0.707293	+	0.706920i	$0.750084\pi$
$212$	1.42886	−	2.47486i	0.0981344	−	0.169974i
$213$	3.82167			0.261857
$214$	3.51415	−	6.08668i	0.240222	−	0.416077i
$215$	0.537508	−	0.930991i	0.0366577	−	0.0634931i
$216$	5.57608			0.379404
$217$	−0.391351	+	0.677840i	−0.0265666	+	0.0460148i
$218$	2.32167	+	4.02125i	0.157243	+	0.272354i
$219$	−7.07849	−	12.2603i	−0.478320	−	0.828475i
$220$	−10.4055			−0.701539
$221$	1.90444	+	0.523403i	0.128106	+	0.0352079i
$222$	10.2632			0.688822
$223$	0.575016	+	0.995957i	0.0385059	+	0.0666942i	0.884636	−	0.466282i	$-0.154407\pi$
$223$	0.575016	+	0.995957i	0.0385059	+	0.0666942i	−0.846130	+	0.532976i	$0.821073\pi$
$224$	−0.136945	−	0.237196i	−0.00915004	−	0.0158483i
$225$	0.448344	−	0.776554i	0.0298896	−	0.0517703i
$226$	10.6588			0.709016
$227$	8.99079	−	15.5725i	0.596740	−	1.03358i	−0.396559	−	0.918009i	$-0.629796\pi$
$227$	8.99079	−	15.5725i	0.596740	−	1.03358i	0.993299	−	0.115574i	$-0.0368708\pi$
$228$	0.636945	−	1.10322i	0.0421827	−	0.0730626i
$229$	16.7437			1.10646			0.553228	−	0.833030i	$-0.313396\pi$
$229$	16.7437			1.10646			0.553228	+	0.833030i	$0.313396\pi$
$230$	5.43913	−	9.42085i	0.358646	−	0.621193i
$231$	−0.763617	−	1.32262i	−0.0502423	−	0.0870223i
$232$	−0.839695	−	1.45439i	−0.0551287	−	0.0954857i
$233$	−0.253344			−0.0165971			−0.00829857	−	0.999966i	$-0.502642\pi$
$233$	−0.253344			−0.0165971			−0.00829857	+	0.999966i	$0.502642\pi$
$234$	1.25441	+	4.80452i	0.0820031	+	0.314081i
$235$	1.12386			0.0733124
$236$	6.76468	+	11.7168i	0.440343	+	0.762697i
$237$	1.50921	+	2.61403i	0.0980338	+	0.169800i
$238$	−0.0750160	+	0.129932i	−0.00486257	+	0.00842221i
$239$	24.1025			1.55906			0.779531	−	0.626364i	$-0.215458\pi$
$239$	24.1025			1.55906			0.779531	+	0.626364i	$0.215458\pi$
$240$	1.51415	−	2.62258i	0.0977378	−	0.169287i
$241$	−1.03751	+	1.79702i	−0.0668318	+	0.115756i	−0.897505	−	0.441004i	$-0.854622\pi$
$241$	−1.03751	+	1.79702i	−0.0668318	+	0.115756i	0.830673	+	0.556760i	$0.187956\pi$
$242$	8.15990			0.524539
$243$	6.47130	−	11.2086i	0.415134	−	0.719034i
$244$	−2.09944	−	3.63633i	−0.134403	−	0.232792i
$245$	8.23105	+	14.2566i	0.525862	+	0.910820i
$246$	−11.5011			−0.733281
$247$	3.47664	+	0.955496i	0.221213	+	0.0607968i
$248$	2.85772			0.181465
$249$	−10.6779	−	18.4947i	−0.676686	−	1.17205i
$250$	5.16912	+	8.95317i	0.326924	+	0.566248i
$251$	3.78804	−	6.56108i	0.239099	−	0.414131i	−0.721357	−	0.692563i	$-0.756481\pi$
$251$	3.78804	−	6.56108i	0.239099	−	0.414131i	0.960456	+	0.278432i	$0.0898147\pi$
$252$	−0.377203			−0.0237615
$253$	−10.0152	+	17.3469i	−0.629651	+	1.09059i
$254$	8.07995	−	13.9949i	0.506981	−	0.878117i
$255$	−1.65884			−0.103881
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.03217	−	6.98393i	−0.251520	−	0.435645i	0.712425	−	0.701749i	$-0.247597\pi$
$257$	−4.03217	−	6.98393i	−0.251520	−	0.435645i	−0.963944	+	0.266103i	$0.914264\pi$
$258$	−0.288039	−	0.498898i	−0.0179325	−	0.0310600i
$259$	−2.20662			−0.137113
$260$	8.26468	+	2.27141i	0.512554	+	0.140867i
$261$	−2.31286			−0.143162
$262$	7.96249	+	13.7914i	0.491924	+	0.852038i
$263$	8.00388	+	13.8631i	0.493540	+	0.854836i	0.999972	−	0.00744328i	$-0.00236929\pi$
$263$	8.00388	+	13.8631i	0.493540	+	0.854836i	−0.506432	+	0.862280i	$0.669036\pi$
$264$	−2.78804	+	4.82902i	−0.171592	+	0.297206i
$265$	−6.79338			−0.417314
$266$	−0.136945	+	0.237196i	−0.00839665	+	0.0145434i
$267$	−1.30365	+	2.25799i	−0.0797820	+	0.138186i
$268$	10.0566			0.614304
$269$	7.84463	−	13.5873i	0.478296	−	0.828432i	−0.521395	−	0.853316i	$-0.674588\pi$
$269$	7.84463	−	13.5873i	0.478296	−	0.828432i	0.999690	+	0.0248833i	$0.00792142\pi$
$270$	−6.62773	−	11.4796i	−0.403351	−	0.698624i
$271$	10.6897	+	18.5150i	0.649351	+	1.12471i	0.983278	+	0.182110i	$0.0582926\pi$
$271$	10.6897	+	18.5150i	0.649351	+	1.12471i	−0.333927	+	0.942599i	$0.608374\pi$
$272$	0.547781			0.0332141
$273$	0.317797	+	1.21720i	0.0192339	+	0.0736682i
$274$	−13.1805			−0.796260
$275$	1.42498	+	2.46814i	0.0859298	+	0.148835i
$276$	−2.91471	−	5.04843i	−0.175445	−	0.303880i
$277$	3.38254	−	5.85873i	0.203237	−	0.352017i	−0.746333	−	0.665573i	$-0.768187\pi$
$277$	3.38254	−	5.85873i	0.203237	−	0.352017i	0.949570	+	0.313556i	$0.101520\pi$
$278$	2.50106			0.150004
$279$	1.96783	−	3.40838i	0.117811	−	0.204054i
$280$	−0.325547	+	0.563863i	−0.0194551	+	0.0336973i
$281$	25.3227			1.51063			0.755314	−	0.655363i	$-0.227484\pi$
$281$	25.3227			1.51063			0.755314	+	0.655363i	$0.227484\pi$
$282$	0.301125	−	0.521565i	0.0179318	−	0.0310587i
$283$	7.94688	+	13.7644i	0.472393	+	0.818209i	0.999501	−	0.0315895i	$-0.0100569\pi$
$283$	7.94688	+	13.7644i	0.472393	+	0.818209i	−0.527108	+	0.849798i	$0.676724\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$	−3.02830			−0.179381
$286$	−15.2180	−	4.18240i	−0.899857	−	0.247311i
$287$	2.47277			0.145963
$288$	0.688601	+	1.19269i	0.0405762	+	0.0702801i
$289$	8.34997	+	14.4626i	0.491175	+	0.850739i
$290$	−1.99612	+	3.45739i	−0.117216	+	0.203025i
$291$	6.94553			0.407154
$292$	5.55659	−	9.62430i	0.325175	−	0.563220i
$293$	−16.6507	+	28.8398i	−0.972744	+	1.68484i	−0.285556	+	0.958362i	$0.592178\pi$
$293$	−16.6507	+	28.8398i	−0.972744	+	1.68484i	−0.687188	+	0.726480i	$0.741155\pi$
$294$	8.82167			0.514490
$295$	16.0810	−	27.8531i	0.936273	−	1.62167i
$296$	4.02830	+	6.97721i	0.234140	+	0.405542i
$297$	12.2038	+	21.1376i	0.708137	+	1.22653i
$298$	−9.42392			−0.545913
$299$	11.7413	−	11.5917i	0.679018	−	0.670366i
$300$	−0.829422			−0.0478867
$301$	0.0619292	+	0.107265i	0.00356954	+	0.00618263i
$302$	5.91084	+	10.2379i	0.340130	+	0.589123i
$303$	5.19248	−	8.99363i	0.298300	−	0.516671i
$304$	1.00000			0.0573539
$305$	−4.99079	+	8.64430i	−0.285772	+	0.494971i
$306$	0.377203	−	0.653335i	0.0215633	−	0.0373486i
$307$	8.65884			0.494186			0.247093	−	0.968992i	$-0.420525\pi$
$307$	8.65884			0.494186			0.247093	+	0.968992i	$0.420525\pi$
$308$	0.599437	−	1.03826i	0.0341561	−	0.0591601i
$309$	−10.4147	−	18.0388i	−0.592472	−	1.02619i
$310$	−3.39669	−	5.88324i	−0.192919	−	0.334145i
$311$	8.93273			0.506529			0.253264	−	0.967397i	$-0.418496\pi$
$311$	8.93273			0.506529			0.253264	+	0.967397i	$0.418496\pi$
$312$	3.26855	−	3.22691i	0.185045	−	0.182688i
$313$	−11.6150			−0.656521			−0.328261	−	0.944587i	$-0.606462\pi$
$313$	−11.6150			−0.656521			−0.328261	+	0.944587i	$0.606462\pi$
$314$	−0.565804	−	0.980002i	−0.0319302	−	0.0553047i
$315$	0.448344	+	0.776554i	0.0252613	+	0.0437539i
$316$	−1.18473	+	2.05201i	−0.0666461	+	0.115434i
$317$	−32.5958			−1.83076			−0.915382	−	0.402587i	$-0.868111\pi$
$317$	−32.5958			−1.83076			−0.915382	+	0.402587i	$0.868111\pi$
$318$	−1.82021	+	3.15270i	−0.102072	+	0.176794i
$319$	3.67551	−	6.36618i	0.205789	−	0.356438i
$320$	2.37720			0.132890
$321$	−4.47664	+	7.75377i	−0.249862	+	0.432773i
$322$	0.626672	+	1.08543i	0.0349231	+	0.0604885i
$323$	−0.273891	−	0.474392i	−0.0152397	−	0.0263959i
$324$	−2.97170			−0.165095
$325$	−0.593039	−	2.27141i	−0.0328959	−	0.125995i
$326$	1.37720			0.0762762
$327$	−2.95756	−	5.12264i	−0.163553	−	0.283282i
$328$	−4.51415	−	7.81873i	−0.249252	−	0.431717i
$329$	−0.0647429	+	0.112138i	−0.00356939	+	0.00618237i
$330$	13.2555			0.729689
$331$	−3.66912	+	6.35510i	−0.201673	+	0.349308i	−0.949068	−	0.315073i	$-0.897971\pi$
$331$	−3.66912	+	6.35510i	−0.201673	+	0.349308i	0.747395	+	0.664380i	$0.231304\pi$
$332$	8.38214	−	14.5183i	0.460030	−	0.796795i
$333$	11.0956			0.608033
$334$	0.208086	−	0.360416i	0.0113860	−	0.0197211i
$335$	−11.9533	−	20.7037i	−0.653077	−	1.13116i
$336$	0.174453	+	0.302162i	0.00951721	+	0.0164843i
$337$	3.48052			0.189596			0.0947979	−	0.995497i	$-0.469780\pi$
$337$	3.48052			0.189596			0.0947979	+	0.995497i	$0.469780\pi$
$338$	11.1741	+	6.64383i	0.607788	+	0.361377i
$339$	−13.5782			−0.737467
$340$	−0.651093	−	1.12773i	−0.0353105	−	0.0611596i
$341$	6.25441	+	10.8329i	0.338695	+	0.586637i
$342$	0.688601	−	1.19269i	0.0372353	−	0.0644934i
$343$	−3.81392			−0.205932
$344$	0.226109	−	0.391633i	0.0121910	−	0.0211154i
$345$	−6.92886	+	12.0011i	−0.373037	+	0.646119i
$346$	−4.21942			−0.226837
$347$	−6.48545	+	11.2331i	−0.348157	+	0.603026i	−0.985922	−	0.167205i	$-0.946526\pi$
$347$	−6.48545	+	11.2331i	−0.348157	+	0.603026i	0.637765	+	0.770231i	$0.279859\pi$
$348$	1.06968	+	1.85274i	0.0573408	+	0.0993172i
$349$	8.25294	+	14.2945i	0.441770	+	0.765168i	0.997821	−	0.0659802i	$-0.0210174\pi$
$349$	8.25294	+	14.2945i	0.441770	+	0.765168i	−0.556051	+	0.831148i	$0.687684\pi$
$350$	0.178328			0.00953205
$351$	−5.07889	−	19.4527i	−0.271091	−	1.03831i
$352$	−4.37720			−0.233306
$353$	−11.7208	−	20.3010i	−0.623834	−	1.08051i	−0.988765	−	0.149477i	$-0.952241\pi$
$353$	−11.7208	−	20.3010i	−0.623834	−	1.08051i	0.364931	−	0.931034i	$-0.381092\pi$
$354$	−8.61746	−	14.9259i	−0.458013	−	0.793302i
$355$	3.56580	−	6.17615i	0.189253	−	0.327796i
$356$	−2.04672			−0.108476
$357$	0.0955622	−	0.165519i	0.00505769	−	0.00876017i
$358$	−10.4572	+	18.1123i	−0.552678	+	0.957266i
$359$	−18.6794			−0.985860			−0.492930	−	0.870069i	$-0.664074\pi$
$359$	−18.6794			−0.985860			−0.492930	+	0.870069i	$0.664074\pi$
$360$	1.63695	−	2.83527i	0.0862746	−	0.149432i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−3.43526	−	5.95004i	−0.180553	−	0.312727i
$363$	−10.3948			−0.545587
$364$	−0.702750	+	0.693795i	−0.0368341	+	0.0363647i
$365$	−26.4183			−1.38280
$366$	2.67445	+	4.63229i	0.139796	+	0.242134i
$367$	11.1989	+	19.3970i	0.584576	+	1.01252i	0.994928	+	0.100589i	$0.0320726\pi$
$367$	11.1989	+	19.3970i	0.584576	+	1.01252i	−0.410352	+	0.911927i	$0.634594\pi$
$368$	2.28804	−	3.96300i	0.119272	−	0.206586i
$369$	−12.4338			−0.647278
$370$	9.57608	−	16.5863i	0.497837	−	0.862278i
$371$	0.391351	−	0.677840i	0.0203179	−	0.0351917i
$372$	−3.64042			−0.188747
$373$	−16.6779	+	28.8870i	−0.863550	+	1.49571i	0.00492901	+	0.999988i	$0.498431\pi$
$373$	−16.6779	+	28.8870i	−0.863550	+	1.49571i	−0.868479	+	0.495725i	$0.834902\pi$
$374$	1.19887	+	2.07651i	0.0619923	+	0.107374i
$375$	−6.58489	−	11.4054i	−0.340042	−	0.588970i
$376$	0.472765			0.0243810
$377$	−4.30899	+	4.25408i	−0.221924	+	0.219096i
$378$	1.52723			0.0785525
$379$	17.4168	+	30.1668i	0.894643	+	1.54957i	0.834246	+	0.551392i	$0.185903\pi$
$379$	17.4168	+	30.1668i	0.894643	+	1.54957i	0.0603964	+	0.998174i	$0.480764\pi$
$380$	−1.18860	−	2.05872i	−0.0609740	−	0.105610i
$381$	−10.2930	+	17.8280i	−0.527325	+	0.913354i
$382$	12.3305			0.630882
$383$	−9.09169	+	15.7473i	−0.464564	+	0.804648i	−0.999182	−	0.0404461i	$-0.987122\pi$
$383$	−9.09169	+	15.7473i	−0.464564	+	0.804648i	0.534618	+	0.845094i	$0.320455\pi$
$384$	0.636945	−	1.10322i	0.0325040	−	0.0562985i
$385$	−2.84997			−0.145248
$386$	−10.1560	+	17.5908i	−0.516928	+	0.895346i
$387$	−0.311399	−	0.539358i	−0.0158293	−	0.0274171i
$388$	2.72611	+	4.72176i	0.138397	+	0.239711i
$389$	0.894565			0.0453562			0.0226781	−	0.999743i	$-0.492781\pi$
$389$	0.894565			0.0453562			0.0226781	+	0.999743i	$0.492781\pi$
$390$	−10.5283	−	2.89353i	−0.533121	−	0.146519i
$391$	−2.50669			−0.126769
$392$	3.46249	+	5.99721i	0.174882	+	0.302905i
$393$	−10.1433	−	17.5688i	−0.511664	−	0.886228i
$394$	−12.5424	+	21.7242i	−0.631879	+	1.09445i
$395$	5.63267			0.283410
$396$	−3.01415	+	5.22066i	−0.151467	+	0.262348i
$397$	−18.6624	+	32.3243i	−0.936640	+	1.62231i	−0.164958	+	0.986301i	$0.552749\pi$
$397$	−18.6624	+	32.3243i	−0.936640	+	1.62231i	−0.771682	+	0.636008i	$0.780584\pi$
$398$	−11.3404			−0.568441
$399$	0.174453	−	0.302162i	0.00873359	−	0.0151270i
$400$	−0.325547	−	0.563863i	−0.0162773	−	0.0281932i
$401$	−7.42498	−	12.8604i	−0.370786	−	0.642220i	0.618901	−	0.785469i	$-0.287578\pi$
$401$	−7.42498	−	12.8604i	−0.370786	−	0.642220i	−0.989687	+	0.143249i	$0.954245\pi$
$402$	−12.8110			−0.638955
$403$	−2.60291	−	9.96945i	−0.129660	−	0.496614i
$404$	8.15215			0.405585
$405$	3.53217	+	6.11790i	0.175515	+	0.304001i
$406$	−0.229984	−	0.398345i	−0.0114139	−	0.0197695i
$407$	−17.6327	+	30.5407i	−0.874019	+	1.51385i
$408$	−0.697813			−0.0345469
$409$	14.7023	−	25.4652i	0.726984	−	1.25917i	−0.231168	−	0.972914i	$-0.574255\pi$
$409$	14.7023	−	25.4652i	0.726984	−	1.25917i	0.958152	−	0.286260i	$-0.0924121\pi$
$410$	−10.7310	+	18.5867i	−0.529969	+	0.917933i
$411$	16.7905			0.828212
$412$	8.17551	−	14.1604i	0.402779	−	0.697633i
$413$	1.85278	+	3.20911i	0.0911694	+	0.157910i
$414$	−3.15109	−	5.45785i	−0.154868	−	0.268239i
$415$	−39.8521			−1.95626
$416$	3.47664	+	0.955496i	0.170456	+	0.0468471i
$417$	−3.18608			−0.156023
$418$	2.18860	+	3.79077i	0.107048	+	0.185413i
$419$	12.4610	+	21.5831i	0.608761	+	1.05441i	0.991445	+	0.130526i	$0.0416666\pi$
$419$	12.4610	+	21.5831i	0.608761	+	1.05441i	−0.382684	+	0.923879i	$0.625000\pi$
$420$	0.414711	−	0.718300i	0.0202358	−	0.0350495i
$421$	5.12174			0.249618			0.124809	−	0.992181i	$-0.460168\pi$
$421$	5.12174			0.249618			0.124809	+	0.992181i	$0.460168\pi$
$422$	3.75587	−	6.50535i	0.182833	−	0.316676i
$423$	0.325547	−	0.563863i	0.0158286	−	0.0274160i
$424$	−2.85772			−0.138783
$425$	−0.178328	+	0.308874i	−0.00865019	+	0.0149826i
$426$	−1.91084	−	3.30966i	−0.0925803	−	0.160354i
$427$	−0.575016	−	0.995957i	−0.0278270	−	0.0481977i
$428$	−7.02830			−0.339726
$429$	19.3860	+	5.32792i	0.935966	+	0.257235i
$430$	−1.07502			−0.0518419
$431$	−10.1560	−	17.5908i	−0.489199	−	0.847317i	0.510724	−	0.859745i	$-0.329377\pi$
$431$	−10.1560	−	17.5908i	−0.489199	−	0.847317i	−0.999923	+	0.0124276i	$0.996044\pi$
$432$	−2.78804	−	4.82902i	−0.134140	−	0.232337i
$433$	13.9353	−	24.1366i	0.669686	−	1.15993i	−0.308306	−	0.951287i	$-0.599762\pi$
$433$	13.9353	−	24.1366i	0.669686	−	1.15993i	0.977992	−	0.208643i	$-0.0669045\pi$
$434$	0.782702			0.0375709
$435$	2.54284	−	4.40434i	0.121920	−	0.211172i
$436$	2.32167	−	4.02125i	0.111188	−	0.192583i
$437$	−4.57608			−0.218903
$438$	−7.07849	+	12.2603i	−0.338223	+	0.585820i
$439$	2.94195	+	5.09560i	0.140411	+	0.243200i	0.927652	−	0.373447i	$-0.121824\pi$
$439$	2.94195	+	5.09560i	0.140411	+	0.243200i	−0.787240	+	0.616646i	$0.788491\pi$
$440$	5.20275	+	9.01143i	0.248031	+	0.429603i
$441$	9.53711			0.454148
$442$	−0.498939	−	1.91099i	−0.0237321	−	0.0908967i
$443$	−24.0878			−1.14445			−0.572223	−	0.820098i	$-0.693919\pi$
$443$	−24.0878			−1.14445			−0.572223	+	0.820098i	$0.693919\pi$
$444$	−5.13161	−	8.88821i	−0.243535	−	0.421816i
$445$	2.43273	+	4.21362i	0.115323	+	0.199745i
$446$	0.575016	−	0.995957i	0.0272278	−	0.0471599i
$447$	12.0050			0.567819
$448$	−0.136945	+	0.237196i	−0.00647006	+	0.0112065i
$449$	9.20129	−	15.9371i	0.434236	−	0.752118i	−0.562997	−	0.826459i	$-0.690352\pi$
$449$	9.20129	−	15.9371i	0.434236	−	0.752118i	0.997233	+	0.0743406i	$0.0236852\pi$
$450$	−0.896688			−0.0422703
$451$	19.7593	−	34.2242i	0.930431	−	1.61155i
$452$	−5.32942	−	9.23083i	−0.250675	−	0.434182i
$453$	−7.52976	−	13.0419i	−0.353779	−	0.612763i
$454$	−17.9816			−0.843917
$455$	2.26362	+	0.622117i	0.106120	+	0.0291653i
$456$	−1.27389			−0.0596554
$457$	0.912298	+	1.58015i	0.0426755	+	0.0739161i	0.886574	−	0.462586i	$-0.153079\pi$
$457$	0.912298	+	1.58015i	0.0426755	+	0.0739161i	−0.843899	+	0.536503i	$0.819745\pi$
$458$	−8.37187	−	14.5005i	−0.391192	−	0.677564i
$459$	−1.52723	+	2.64525i	−0.0712852	+	0.123470i
$460$	−10.8783			−0.507202
$461$	10.9865	−	19.0292i	0.511693	−	0.886278i	−0.488215	−	0.872723i	$-0.662352\pi$
$461$	10.9865	−	19.0292i	0.511693	−	0.886278i	0.999908	−	0.0135549i	$-0.00431478\pi$
$462$	−0.763617	+	1.32262i	−0.0355267	+	0.0615340i
$463$	6.74373			0.313408			0.156704	−	0.987646i	$-0.449913\pi$
$463$	6.74373			0.313408			0.156704	+	0.987646i	$0.449913\pi$
$464$	−0.839695	+	1.45439i	−0.0389819	+	0.0675186i
$465$	4.32701	+	7.49460i	0.200660	+	0.347554i
$466$	0.126672	+	0.219403i	0.00586798	+	0.0101636i
$467$	24.0227			1.11164			0.555818	−	0.831304i	$-0.312405\pi$
$467$	24.0227			1.11164			0.555818	+	0.831304i	$0.312405\pi$
$468$	3.53363	−	3.48861i	0.163342	−	0.161261i
$469$	2.75441			0.127187
$470$	−0.561929	−	0.973290i	−0.0259199	−	0.0448945i
$471$	0.720773	+	1.24841i	0.0332115	+	0.0575239i
$472$	6.76468	−	11.7168i	0.311370	−	0.539308i
$473$	1.97945			0.0910154
$474$	1.50921	−	2.61403i	0.0693204	−	0.120066i
$475$	−0.325547	+	0.563863i	−0.0149371	+	0.0258718i
$476$	0.150032			0.00687671
$477$	−1.96783	+	3.40838i	−0.0901007	+	0.156059i
$478$	−12.0513	−	20.8734i	−0.551212	−	0.954727i
$479$	7.10331	+	12.3033i	0.324559	+	0.562152i	0.981423	−	0.191857i	$-0.0614509\pi$
$479$	7.10331	+	12.3033i	0.324559	+	0.562152i	−0.656864	+	0.754009i	$0.728118\pi$
$480$	−3.02830			−0.138222
$481$	20.6716	−	20.4082i	0.942546	−	0.930536i
$482$	2.07502			0.0945144
$483$	−0.798312	−	1.38272i	−0.0363244	−	0.0629158i
$484$	−4.07995	−	7.06668i	−0.185452	−	0.321213i
$485$	6.48052	−	11.2246i	0.294265	−	0.509682i
$486$	−12.9426			−0.587089
$487$	−6.00106	+	10.3941i	−0.271934	+	0.471004i	−0.969357	−	0.245656i	$-0.920997\pi$
$487$	−6.00106	+	10.3941i	−0.271934	+	0.471004i	0.697423	+	0.716660i	$0.254330\pi$
$488$	−2.09944	+	3.63633i	−0.0950371	+	0.164609i
$489$	−1.75441			−0.0793370
$490$	8.23105	−	14.2566i	0.371841	−	0.644047i
$491$	14.2023	+	24.5992i	0.640943	+	1.11015i	0.985223	+	0.171279i	$0.0547899\pi$
$491$	14.2023	+	24.5992i	0.640943	+	1.11015i	−0.344280	+	0.938867i	$0.611877\pi$
$492$	5.75053	+	9.96021i	0.259254	+	0.449041i
$493$	0.919938			0.0414319
$494$	−0.910836	−	3.48861i	−0.0409804	−	0.156960i
$495$	14.3305			0.644107
$496$	−1.42886	−	2.47486i	−0.0641577	−	0.111124i
$497$	0.410836	+	0.711589i	0.0184285	+	0.0319191i
$498$	−10.6779	+	18.4947i	−0.478489	+	0.828768i
$499$	0.452219			0.0202441			0.0101220	−	0.999949i	$-0.496778\pi$
$499$	0.452219			0.0202441			0.0101220	+	0.999949i	$0.496778\pi$
$500$	5.16912	−	8.95317i	0.231170	−	0.400398i
$501$	−0.265079	+	0.459131i	−0.0118429	+	0.0205124i
$502$	−7.57608			−0.338137
$503$	0.785625	−	1.36074i	0.0350293	−	0.0606725i	−0.847979	−	0.530029i	$-0.822181\pi$
$503$	0.785625	−	1.36074i	0.0350293	−	0.0606725i	0.883009	+	0.469357i	$0.155514\pi$
$504$	0.188601	+	0.326667i	0.00840098	+	0.0145509i
$505$	−9.68966	−	16.7830i	−0.431184	−	0.746833i
$506$	20.0304			0.890461
$507$	−14.2345	−	8.46352i	−0.632177	−	0.375878i
$508$	−16.1599			−0.716980
$509$	15.2711	+	26.4503i	0.676879	+	1.17239i	0.975916	+	0.218147i	$0.0700011\pi$
$509$	15.2711	+	26.4503i	0.676879	+	1.17239i	−0.299037	+	0.954241i	$0.596666\pi$
$510$	0.829422	+	1.43660i	0.0367274	+	0.0636137i
$511$	1.52190	−	2.63601i	0.0673248	−	0.116610i
$512$	1.00000			0.0441942
$513$	−2.78804	+	4.82902i	−0.123095	+	0.213207i
$514$	−4.03217	+	6.98393i	−0.177851	+	0.308048i
$515$	−38.8697			−1.71280
$516$	−0.288039	+	0.498898i	−0.0126802	+	0.0219627i
$517$	1.03469	+	1.79214i	0.0455058	+	0.0788184i
$518$	1.10331	+	1.91099i	0.0484768	+	0.0839642i
$519$	5.37508			0.235940
$520$	−2.16524	−	8.29313i	−0.0949521	−	0.363678i
$521$	0.405499			0.0177652			0.00888262	−	0.999961i	$-0.497173\pi$
$521$	0.405499			0.0177652			0.00888262	+	0.999961i	$0.497173\pi$
$522$	1.15643	+	2.00300i	0.0506156	+	0.0876687i
$523$	1.37479	+	2.38121i	0.0601153	+	0.104123i	0.894517	−	0.447034i	$-0.147520\pi$
$523$	1.37479	+	2.38121i	0.0601153	+	0.104123i	−0.834401	+	0.551157i	$0.814186\pi$
$524$	7.96249	−	13.7914i	0.347843	−	0.602482i
$525$	−0.227171			−0.00991455
$526$	8.00388	−	13.8631i	0.348986	−	0.604461i
$527$	−0.782702	+	1.35568i	−0.0340950	+	0.0590543i
$528$	5.57608			0.242668
$529$	1.02976	−	1.78359i	0.0447721	−	0.0775475i
$530$	3.39669	+	5.88324i	0.147543	+	0.255551i
$531$	−9.31633	−	16.1364i	−0.404295	−	0.700259i
$532$	0.273891			0.0118747
$533$	−23.1648	+	22.8697i	−1.00338	+	0.990595i
$534$	2.60730			0.112829
$535$	8.35384	+	14.4693i	0.361168	+	0.625562i
$536$	−5.02830	−	8.70926i	−0.217189	−	0.376183i
$537$	13.3213	−	23.0731i	0.574855	−	0.995679i
$538$	−15.6893			−0.676412
$539$	−15.1560	+	26.2510i	−0.652816	+	1.13071i
$540$	−6.62773	+	11.4796i	−0.285212	+	0.494002i
$541$	24.0128			1.03239			0.516195	−	0.856471i	$-0.327348\pi$
$541$	24.0128			1.03239			0.516195	+	0.856471i	$0.327348\pi$
$542$	10.6897	−	18.5150i	0.459160	−	0.795289i
$543$	4.37614	+	7.57970i	0.187798	+	0.325276i
$544$	−0.273891	−	0.474392i	−0.0117430	−	0.0203394i
$545$	−11.0382			−0.472823
$546$	0.895226	−	0.883819i	0.0383121	−	0.0378240i
$547$	−43.2525			−1.84935			−0.924673	−	0.380763i	$-0.875661\pi$
$547$	−43.2525			−1.84935			−0.924673	+	0.380763i	$0.875661\pi$
$548$	6.59023	+	11.4146i	0.281520	+	0.487608i
$549$	2.89135	+	5.00797i	0.123400	+	0.213735i
$550$	1.42498	−	2.46814i	0.0607615	−	0.105242i
$551$	1.67939			0.0715444
$552$	−2.91471	+	5.04843i	−0.124058	+	0.214875i
$553$	−0.324485	+	0.562025i	−0.0137985	+	0.0238997i
$554$	−6.76508			−0.287421
$555$	−12.1989	+	21.1291i	−0.517813	+	0.896879i
$556$	−1.25053	−	2.16598i	−0.0530343	−	0.0918581i
$557$	−14.0424	−	24.3222i	−0.594997	−	1.03057i	−0.993547	−	0.113419i	$-0.963820\pi$
$557$	−14.0424	−	24.3222i	−0.594997	−	1.03057i	0.398550	−	0.917147i	$-0.369514\pi$
$558$	−3.93566			−0.166610
$559$	−1.57220	−	0.432094i	−0.0664971	−	0.0182756i
$560$	0.651093			0.0275137
$561$	−1.52723	−	2.64525i	−0.0644799	−	0.111682i
$562$	−12.6614	−	21.9301i	−0.534088	−	0.925067i
$563$	−17.5834	+	30.4554i	−0.741053	+	1.28354i	0.210963	+	0.977494i	$0.432340\pi$
$563$	−17.5834	+	30.4554i	−0.741053	+	1.28354i	−0.952016	+	0.306048i	$0.900993\pi$
$564$	−0.602251			−0.0253593
$565$	−12.6691	+	21.9436i	−0.532994	+	0.923172i
$566$	7.94688	−	13.7644i	0.334032	−	0.578561i
$567$	−0.813922			−0.0341815
$568$	1.50000	−	2.59808i	0.0629386	−	0.109013i
$569$	13.3461	+	23.1161i	0.559497	+	0.969078i	0.997538	+	0.0701228i	$0.0223391\pi$
$569$	13.3461	+	23.1161i	0.559497	+	0.969078i	−0.438041	+	0.898955i	$0.644328\pi$
$570$	1.51415	+	2.62258i	0.0634207	+	0.109848i
$571$	18.1882			0.761153			0.380576	−	0.924750i	$-0.375726\pi$
$571$	18.1882			0.761153			0.380576	+	0.924750i	$0.375726\pi$
$572$	3.98691	+	15.2703i	0.166701	+	0.638485i
$573$	−15.7077			−0.656198
$574$	−1.23638	−	2.14148i	−0.0516056	−	0.0893835i
$575$	1.48973	+	2.58028i	0.0621259	+	0.107605i
$576$	0.688601	−	1.19269i	0.0286917	−	0.0496955i
$577$	27.1076			1.12850			0.564251	−	0.825603i	$-0.309165\pi$
$577$	27.1076			1.12850			0.564251	+	0.825603i	$0.309165\pi$
$578$	8.34997	−	14.4626i	0.347313	−	0.601564i
$579$	12.9377	−	22.4087i	0.537671	−	0.931274i
$580$	3.99225			0.165769
$581$	2.29579	−	3.97642i	0.0952454	−	0.164970i
$582$	−3.47277	−	6.01501i	−0.143951	−	0.249330i
$583$	−6.25441	−	10.8329i	−0.259031	−	0.448655i
$584$	−11.1132			−0.459867
$585$	−11.3821	−	3.12819i	−0.470594	−	0.129335i
$586$	33.3014			1.37567
$587$	−8.17698	−	14.1629i	−0.337500	−	0.584567i	0.646462	−	0.762946i	$-0.276248\pi$
$587$	−8.17698	−	14.1629i	−0.337500	−	0.584567i	−0.983962	+	0.178379i	$0.942915\pi$
$588$	−4.41084	−	7.63979i	−0.181900	−	0.315060i
$589$	−1.42886	+	2.47486i	−0.0588751	+	0.101975i
$590$	−32.1620			−1.32409
$591$	15.9777	−	27.6742i	0.657235	−	1.13836i
$592$	4.02830	−	6.97721i	0.165562	−	0.286762i
$593$	37.0021			1.51950			0.759748	−	0.650218i	$-0.225323\pi$
$593$	37.0021			1.51950			0.759748	+	0.650218i	$0.225323\pi$
$594$	12.2038	−	21.1376i	0.500728	−	0.867287i
$595$	−0.178328	−	0.308874i	−0.00731075	−	0.0126626i
$596$	4.71196	+	8.16136i	0.193009	+	0.334302i
$597$	14.4464			0.591251
$598$	−15.9094	−	4.37243i	−0.650583	−	0.178802i
$599$	17.5830			0.718423			0.359211	−	0.933256i	$-0.383046\pi$
$599$	17.5830			0.718423			0.359211	+	0.933256i	$0.383046\pi$
$600$	0.414711	+	0.718300i	0.0169305	+	0.0293245i
$601$	−18.4465	−	31.9502i	−0.752448	−	1.30328i	−0.946633	−	0.322313i	$-0.895540\pi$
$601$	−18.4465	−	31.9502i	−0.752448	−	1.30328i	0.194186	−	0.980965i	$-0.437794\pi$
$602$	0.0619292	−	0.107265i	0.00252405	−	0.00437178i
$603$	−13.8500			−0.564014
$604$	5.91084	−	10.2379i	0.240508	−	0.416573i
$605$	−9.69887	+	16.7989i	−0.394315	+	0.682974i
$606$	−10.3850			−0.421860
$607$	11.4483	−	19.8291i	0.464674	−	0.804839i	−0.534513	−	0.845160i	$-0.679505\pi$
$607$	11.4483	−	19.8291i	0.464674	−	0.804839i	0.999187	+	0.0403215i	$0.0128382\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$	0.292975	+	0.507448i	0.0118719	+	0.0205628i
$610$	9.98158			0.404142
$611$	−0.430611	−	1.64929i	−0.0174207	−	0.0667232i
$612$	−0.754406			−0.0304950
$613$	12.4557	+	21.5739i	0.503081	+	0.871361i	0.999994	+	0.00356098i	$0.00113350\pi$
$613$	12.4557	+	21.5739i	0.503081	+	0.871361i	−0.496913	+	0.867800i	$0.665533\pi$
$614$	−4.32942	−	7.49878i	−0.174721	−	0.302626i
$615$	13.6702	−	23.6774i	0.551235	−	0.954767i
$616$	−1.19887			−0.0483040
$617$	3.82701	−	6.62857i	0.154070	−	0.266856i	−0.778650	−	0.627458i	$-0.784095\pi$
$617$	3.82701	−	6.62857i	0.154070	−	0.266856i	0.932720	+	0.360602i	$0.117429\pi$
$618$	−10.4147	+	18.0388i	−0.418941	+	0.725627i
$619$	−10.4140			−0.418576			−0.209288	−	0.977854i	$-0.567115\pi$
$619$	−10.4140			−0.418576			−0.209288	+	0.977854i	$0.567115\pi$
$620$	−3.39669	+	5.88324i	−0.136414	+	0.236276i
$621$	12.7583	+	22.0980i	0.511972	+	0.886762i
$622$	−4.46637	−	7.73597i	−0.179085	−	0.310184i
$623$	−0.560577			−0.0224591
$624$	−4.42886	−	1.21720i	−0.177296	−	0.0487269i
$625$	−27.8315			−1.11326
$626$	5.80752	+	10.0589i	0.232115	+	0.402036i
$627$	−2.78804	−	4.82902i	−0.111344	−	0.192853i
$628$	−0.565804	+	0.980002i	−0.0225780	+	0.0391063i
$629$	−4.41325			−0.175968
$630$	0.448344	−	0.776554i	0.0178624	−	0.0309387i
$631$	−14.4250	+	24.9848i	−0.574250	+	0.994629i	0.421873	+	0.906655i	$0.361373\pi$
$631$	−14.4250	+	24.9848i	−0.574250	+	0.994629i	−0.996123	+	0.0879745i	$0.971961\pi$
$632$	2.36945			0.0942518
$633$	−4.78456	+	8.28711i	−0.190169	+	0.329383i
$634$	16.2979	+	28.2288i	0.647273	+	1.12111i
$635$	19.2077	+	33.2687i	0.762234	+	1.32023i
$636$	3.64042			0.144352
$637$	17.7682	−	17.5417i	0.704000	−	0.695029i
$638$	−7.35103			−0.291030
$639$	−2.06580	−	3.57808i	−0.0817220	−	0.141547i
$640$	−1.18860	−	2.05872i	−0.0469836	−	0.0813780i
$641$	3.06087	−	5.30158i	0.120897	−	0.209400i	−0.799225	−	0.601032i	$-0.794756\pi$
$641$	3.06087	−	5.30158i	0.120897	−	0.209400i	0.920122	+	0.391633i	$0.128090\pi$
$642$	8.95328			0.353358
$643$	−15.5039	+	26.8535i	−0.611413	+	1.05900i	0.379589	+	0.925155i	$0.376065\pi$
$643$	−15.5039	+	26.8535i	−0.611413	+	1.05900i	−0.991002	+	0.133844i	$0.957268\pi$
$644$	0.626672	−	1.08543i	0.0246943	−	0.0427719i
$645$	1.36945			0.0539222
$646$	−0.273891	+	0.474392i	−0.0107761	+	0.0186647i
$647$	16.6171	+	28.7816i	0.653284	+	1.13152i	0.982321	+	0.187204i	$0.0599426\pi$
$647$	16.6171	+	28.7816i	0.653284	+	1.13152i	−0.329037	+	0.944317i	$0.606724\pi$
$648$	1.48585	+	2.57357i	0.0583698	+	0.101099i
$649$	59.2207			2.32462
$650$	−1.67058	+	1.64929i	−0.0655255	+	0.0646905i
$651$	−0.997077			−0.0390785
$652$	−0.688601	−	1.19269i	−0.0269677	−	0.0467094i
$653$	11.7023	+	20.2691i	0.457948	+	0.793190i	0.998852	−	0.0478945i	$-0.0152511\pi$
$653$	11.7023	+	20.2691i	0.457948	+	0.793190i	−0.540904	+	0.841084i	$0.681918\pi$
$654$	−2.95756	+	5.12264i	−0.115650	+	0.200311i
$655$	−37.8569			−1.47919
$656$	−4.51415	+	7.81873i	−0.176248	+	0.305270i
$657$	−7.65256	+	13.2546i	−0.298555	+	0.517112i
$658$	0.129486			0.00504789
$659$	−6.36159	+	11.0186i	−0.247812	+	0.429224i	−0.962919	−	0.269792i	$-0.913045\pi$
$659$	−6.36159	+	11.0186i	−0.247812	+	0.429224i	0.715106	+	0.699016i	$0.246378\pi$
$660$	−6.62773	−	11.4796i	−0.257984	−	0.446842i
$661$	−20.1921	−	34.9737i	−0.785381	−	1.36032i	−0.928771	−	0.370653i	$-0.879134\pi$
$661$	−20.1921	−	34.9737i	−0.785381	−	1.36032i	0.143391	−	0.989666i	$-0.454199\pi$
$662$	7.33823			0.285209
$663$	0.635593	+	2.43440i	0.0246844	+	0.0945441i
$664$	−16.7643			−0.650580
$665$	−0.325547	−	0.563863i	−0.0126242	−	0.0218657i
$666$	−5.54778	−	9.60904i	−0.214972	−	0.372343i
$667$	3.84251	−	6.65542i	0.148783	−	0.257699i
$668$	−0.416173			−0.0161022
$669$	−0.732507	+	1.26874i	−0.0283204	+	0.0490523i
$670$	−11.9533	+	20.7037i	−0.461796	+	0.799853i
$671$	−18.3793			−0.709526
$672$	0.174453	−	0.302162i	0.00672968	−	0.0116562i
$673$	3.58489	+	6.20921i	0.138187	+	0.239347i	0.926811	−	0.375529i	$-0.122539\pi$
$673$	3.58489	+	6.20921i	0.138187	+	0.239347i	−0.788623	+	0.614877i	$0.789206\pi$
$674$	−1.74026	−	3.01421i	−0.0670322	−	0.116103i
$675$	3.63055			0.139740
$676$	0.166703	−	12.9989i	0.00641166	−	0.499959i
$677$	−24.6220			−0.946300			−0.473150	−	0.880982i	$-0.656883\pi$
$677$	−24.6220			−0.946300			−0.473150	+	0.880982i	$0.656883\pi$
$678$	6.78910	+	11.7591i	0.260734	+	0.451604i
$679$	0.746656	+	1.29325i	0.0286540	+	0.0496302i
$680$	−0.651093	+	1.12773i	−0.0249683	+	0.0432464i
$681$	22.9066			0.877781
$682$	6.25441	−	10.8329i	0.239494	−	0.414815i
$683$	13.0336	−	22.5749i	0.498718	−	0.863805i	−0.501281	−	0.865285i	$-0.667138\pi$
$683$	13.0336	−	22.5749i	0.498718	−	0.863805i	0.999999	+	0.00147957i	$0.000470963\pi$
$684$	−1.37720			−0.0526587
$685$	15.6663	−	27.1348i	0.598579	−	1.03677i
$686$	1.90696	+	3.30295i	0.0728081	+	0.126107i
$687$	10.6648	+	18.4720i	0.406889	+	0.704753i
$688$	−0.452219			−0.0172407
$689$	2.60291	+	9.96945i	0.0991630	+	0.379806i
$690$	13.8577			0.527554
$691$	−9.54244	−	16.5280i	−0.363012	−	0.628755i	0.625443	−	0.780270i	$-0.284918\pi$
$691$	−9.54244	−	16.5280i	−0.363012	−	0.628755i	−0.988455	+	0.151515i	$0.951585\pi$
$692$	2.10971	+	3.65413i	0.0801992	+	0.138909i
$693$	−0.825547	+	1.42989i	−0.0313599	+	0.0543170i
$694$	12.9709			0.492369
$695$	−2.97277	+	5.14898i	−0.112763	+	0.195312i
$696$	1.06968	−	1.85274i	0.0405461	−	0.0702279i
$697$	4.94553			0.187325
$698$	8.25294	−	14.2945i	0.312379	−	0.541055i
$699$	−0.161367	−	0.279495i	−0.00610344	−	0.0105715i
$700$	−0.0891642	−	0.154437i	−0.00337009	−	0.00583716i
$701$	23.1834			0.875624			0.437812	−	0.899067i	$-0.355754\pi$
$701$	23.1834			0.875624			0.437812	+	0.899067i	$0.355754\pi$
$702$	−14.3071	+	14.1248i	−0.539988	+	0.533107i
$703$	−8.05659			−0.303860
$704$	2.18860	+	3.79077i	0.0824860	+	0.142870i
$705$	0.715836	+	1.23986i	0.0269600	+	0.0466960i
$706$	−11.7208	+	20.3010i	−0.441117	+	0.764037i
$707$	2.23280			0.0839730
$708$	−8.61746	+	14.9259i	−0.323864	+	0.560949i
$709$	−9.67018	+	16.7492i	−0.363171	+	0.629031i	−0.988481	−	0.151346i	$-0.951639\pi$
$709$	−9.67018	+	16.7492i	−0.363171	+	0.629031i	0.625310	+	0.780377i	$0.284973\pi$
$710$	−7.13161			−0.267645
$711$	1.63161	−	2.82603i	0.0611901	−	0.105984i
$712$	1.02336	+	1.77251i	0.0383520	+	0.0664277i
$713$	6.53857	+	11.3251i	0.244871	+	0.424130i
$714$	−0.191124			−0.00715265
$715$	26.6985	−	26.3583i	0.998466	−	0.985744i
$716$	20.9143			0.781604
$717$	15.3520	+	26.5904i	0.573330	+	0.993037i
$718$	9.33969	+	16.1768i	0.348554	+	0.603714i
$719$	−24.9501	+	43.2148i	−0.930480	+	1.61164i	−0.147979	+	0.988990i	$0.547277\pi$
$719$	−24.9501	+	43.2148i	−0.930480	+	1.61164i	−0.782501	+	0.622649i	$0.786056\pi$
$720$	−3.27389			−0.122011
$721$	2.23920	−	3.87840i	0.0833920	−	0.144439i
$722$	−0.500000	+	0.866025i	−0.0186081	+	0.0322301i
$723$	−2.64334			−0.0983070
$724$	−3.43526	+	5.95004i	−0.127670	+	0.221131i
$725$	−0.546720	−	0.946946i	−0.0203047	−	0.0351687i
$726$	5.19741	+	9.00218i	0.192894	+	0.334102i
$727$	3.20100			0.118718			0.0593592	−	0.998237i	$-0.481094\pi$
$727$	3.20100			0.118718			0.0593592	+	0.998237i	$0.481094\pi$
$728$	0.952219	+	0.261701i	0.0352916	+	0.00969930i
$729$	25.4026			0.940836
$730$	13.2091	+	22.8789i	0.488892	+	0.846787i
$731$	0.123858	+	0.214529i	0.00458107	+	0.00793465i
$732$	2.67445	−	4.63229i	0.0988506	−	0.171214i
$733$	25.6823			0.948598			0.474299	−	0.880364i	$-0.342702\pi$
$733$	25.6823			0.948598			0.474299	+	0.880364i	$0.342702\pi$
$734$	11.1989	−	19.3970i	0.413358	−	0.715957i
$735$	−10.4855	+	18.1613i	−0.386762	+	0.669891i
$736$	−4.57608			−0.168676
$737$	22.0099	−	38.1222i	0.810744	−	1.40425i
$738$	6.21690	+	10.7680i	0.228847	+	0.396375i
$739$	−18.2799	−	31.6617i	−0.672437	−	1.16469i	−0.977211	−	0.212270i	$-0.931914\pi$
$739$	−18.2799	−	31.6617i	−0.672437	−	1.16469i	0.304775	−	0.952425i	$-0.401419\pi$
$740$	−19.1522			−0.704047
$741$	1.16031	+	4.44410i	0.0426249	+	0.163258i
$742$	−0.782702			−0.0287339
$743$	−12.8500	−	22.2568i	−0.471420	−	0.816523i	0.528046	−	0.849216i	$-0.322925\pi$
$743$	−12.8500	−	22.2568i	−0.471420	−	0.816523i	−0.999465	+	0.0326932i	$0.989592\pi$
$744$	1.82021	+	3.15270i	0.0667321	+	0.115583i
$745$	11.2013	−	19.4012i	0.410383	−	0.710805i
$746$	33.3559			1.22124
$747$	−11.5439	+	19.9946i	−0.422369	+	0.731565i
$748$	1.19887	−	2.07651i	0.0438352	−	0.0759248i
$749$	−1.92498			−0.0703374
$750$	−6.58489	+	11.4054i	−0.240446	+	0.416465i
$751$	23.1663	+	40.1252i	0.845350	+	1.46419i	0.885317	+	0.464989i	$0.153942\pi$
$751$	23.1663	+	40.1252i	0.845350	+	1.46419i	−0.0399662	+	0.999201i	$0.512725\pi$
$752$	−0.236383	−	0.409427i	−0.00861998	−	0.0149303i
$753$	9.65109			0.351705
$754$	5.83863	+	1.60465i	0.212630	+	0.0584379i
$755$	−28.1025			−1.02276
$756$	−0.763617	−	1.32262i	−0.0277725	−	0.0481034i
$757$	14.3255	+	24.8126i	0.520671	+	0.901828i	0.999711	+	0.0240354i	$0.00765145\pi$
$757$	14.3255	+	24.8126i	0.520671	+	0.901828i	−0.479040	+	0.877793i	$0.659015\pi$
$758$	17.4168	−	30.1668i	0.632608	−	1.09571i
$759$	−25.5166			−0.926193
$760$	−1.18860	+	2.05872i	−0.0431151	+	0.0746776i
$761$	15.5502	−	26.9337i	0.563694	−	0.976347i	−0.433476	−	0.901165i	$-0.642713\pi$
$761$	15.5502	−	26.9337i	0.563694	−	0.976347i	0.997170	−	0.0751816i	$-0.0239536\pi$
$762$	20.5860			0.745750
$763$	0.635884	−	1.10138i	0.0230205	−	0.0398728i
$764$	−6.16524	−	10.6785i	−0.223051	−	0.386335i
$765$	0.896688	+	1.55311i	0.0324198	+	0.0561528i
$766$	18.1834			0.656992
$767$	−47.0367	−	12.9273i	−1.69840	−	0.466776i
$768$	−1.27389			−0.0459676
$769$	−24.7150	−	42.8077i	−0.891247	−	1.54369i	−0.838382	−	0.545083i	$-0.816498\pi$
$769$	−24.7150	−	42.8077i	−0.891247	−	1.54369i	−0.0528652	−	0.998602i	$-0.516835\pi$
$770$	1.42498	+	2.46814i	0.0513529	+	0.0889458i
$771$	5.13654	−	8.89676i	0.184988	−	0.320409i
$772$	20.3121			0.731047
$773$	−4.49225	+	7.78081i	−0.161575	+	0.279856i	−0.935434	−	0.353502i	$-0.884991\pi$
$773$	−4.49225	+	7.78081i	−0.161575	+	0.279856i	0.773859	+	0.633358i	$0.218324\pi$
$774$	−0.311399	+	0.539358i	−0.0111930	+	0.0193868i
$775$	1.86064			0.0668362
$776$	2.72611	−	4.72176i	0.0978616	−	0.169501i
$777$	−1.40550	−	2.43440i	−0.0504220	−	0.0873335i
$778$	−0.447283	−	0.774716i	−0.0160359	−	0.0277749i
$779$	9.02830			0.323472
$780$	2.75828	+	10.5645i	0.0987623	+	0.378271i
$781$	13.1316			0.469886
$782$	1.25334	+	2.17086i	0.0448195	+	0.0776297i
$783$	−4.68220	−	8.10981i	−0.167328	−	0.289821i
$784$	3.46249	−	5.99721i	0.123660	−	0.214186i
$785$	2.69006			0.0960125
$786$	−10.1433	+	17.5688i	−0.361801	+	0.626658i
$787$	12.5201	−	21.6855i	0.446295	−	0.773006i	−0.551846	−	0.833946i	$-0.686077\pi$
$787$	12.5201	−	21.6855i	0.446295	−	0.773006i	0.998141	+	0.0609401i	$0.0194099\pi$
$788$	25.0849			0.893612
$789$	−10.1961	+	17.6601i	−0.362989	+	0.628716i
$790$	−2.81633	−	4.87804i	−0.100201	−	0.173553i
$791$	−1.45968	−	2.52824i	−0.0519002	−	0.0898938i
$792$	6.02830			0.214206
$793$	14.5980	+	4.01201i	0.518389	+	0.142471i
$794$	37.3249			1.32461
$795$	−4.32701	−	7.49460i	−0.153463	−	0.265806i
$796$	5.67018	+	9.82104i	0.200974	+	0.348097i
$797$	7.03071	−	12.1775i	0.249041	−	0.431351i	−0.714219	−	0.699922i	$-0.753218\pi$
$797$	7.03071	−	12.1775i	0.249041	−	0.431351i	0.963260	+	0.268571i	$0.0865514\pi$
$798$	−0.348907			−0.0123512
$799$	−0.129486	+	0.224276i	−0.00458088	+	0.00793432i
$800$	−0.325547	+	0.563863i	−0.0115098	+	0.0199356i
$801$	2.81875			0.0995956
$802$	−7.42498	+	12.8604i	−0.262185	+	0.454118i
$803$	−24.3223	−	42.1275i	−0.858316	−	1.48665i
$804$	6.40550	+	11.0946i	0.225905	+	0.391278i
$805$	−2.97945			−0.105012
$806$	−7.33235	+	7.23892i	−0.258271	+	0.254980i
$807$	19.9864			0.703555
$808$	−4.07608	−	7.05997i	−0.143396	−	0.248369i
$809$	−1.93420	−	3.35013i	−0.0680027	−	0.117784i	0.830019	−	0.557735i	$-0.188329\pi$
$809$	−1.93420	−	3.35013i	−0.0680027	−	0.117784i	−0.898022	+	0.439951i	$0.854996\pi$
$810$	3.53217	−	6.11790i	0.124108	−	0.214961i
$811$	21.7467			0.763628			0.381814	−	0.924239i	$-0.375299\pi$
$811$	21.7467			0.763628			0.381814	+	0.924239i	$0.375299\pi$
$812$	−0.229984	+	0.398345i	−0.00807087	+	0.0139792i
$813$	−13.6175	+	23.5861i	−0.477585	+	0.827202i
$814$	35.2653			1.23605
$815$	−1.63695	+	2.83527i	−0.0573397	+	0.0993153i
$816$	0.348907	+	0.604324i	0.0122142	+	0.0211556i
$817$	0.226109	+	0.391633i	0.00791057	+	0.0137015i
$818$	−29.4047			−1.02811
$819$	0.967829	−	0.955496i	0.0338187	−	0.0333877i
$820$	21.4621			0.749489
$821$	−18.2463	−	31.6034i	−0.636799	−	1.10297i	−0.986131	−	0.165969i	$-0.946925\pi$
$821$	−18.2463	−	31.6034i	−0.636799	−	1.10297i	0.349332	−	0.936999i	$-0.386408\pi$
$822$	−8.39523	−	14.5410i	−0.292817	−	0.507174i
$823$	11.0195	−	19.0863i	0.384115	−	0.665307i	−0.607531	−	0.794296i	$-0.707840\pi$
$823$	11.0195	−	19.0863i	0.384115	−	0.665307i	0.991646	+	0.128989i	$0.0411732\pi$
$824$	−16.3510			−0.569615
$825$	−1.81527	+	3.14415i	−0.0631997	+	0.109465i
$826$	1.85278	−	3.20911i	0.0644665	−	0.111659i
$827$	−3.61292			−0.125634			−0.0628168	−	0.998025i	$-0.520008\pi$
$827$	−3.61292			−0.125634			−0.0628168	+	0.998025i	$0.520008\pi$
$828$	−3.15109	+	5.45785i	−0.109508	+	0.189674i
$829$	1.13307	+	1.96254i	0.0393532	+	0.0681617i	0.885031	−	0.465532i	$-0.154137\pi$
$829$	1.13307	+	1.96254i	0.0393532	+	0.0681617i	−0.845678	+	0.533694i	$0.820804\pi$
$830$	19.9260	+	34.5129i	0.691643	+	1.19796i
$831$	8.61797			0.298954
$832$	−0.910836	−	3.48861i	−0.0315776	−	0.120946i
$833$	−3.79338			−0.131433
$834$	1.59304	+	2.75922i	0.0551624	+	0.0955441i
$835$	0.494663	+	0.856782i	0.0171185	+	0.0296502i
$836$	2.18860	−	3.79077i	0.0756944	−	0.131106i
$837$	15.9349			0.550789
$838$	12.4610	−	21.5831i	0.430459	−	0.745577i
$839$	11.9685	−	20.7300i	0.413198	−	0.715680i	−0.582039	−	0.813161i	$-0.697745\pi$
$839$	11.9685	−	20.7300i	0.413198	−	0.715680i	0.995237	+	0.0974805i	$0.0310784\pi$
$840$	−0.829422			−0.0286178
$841$	13.0898	−	22.6722i	0.451373	−	0.781801i
$842$	−2.56087	−	4.43555i	−0.0882533	−	0.152859i
$843$	16.1292	+	27.9366i	0.555519	+	0.962187i
$844$	−7.51173			−0.258565
$845$	−26.9593	+	15.1074i	−0.927427	+	0.519709i
$846$	−0.651093			−0.0223851
$847$	−1.11746	−	1.93550i	−0.0383964	−	0.0665045i
$848$	1.42886	+	2.47486i	0.0490672	+	0.0849869i
$849$	−10.1235	+	17.5343i	−0.347436	+	0.601777i
$850$	0.356657			0.0122332
$851$	−18.4338	+	31.9283i	−0.631902	+	1.09449i
$852$	−1.91084	+	3.30966i	−0.0654642	+	0.113387i
$853$	−44.1484			−1.51161			−0.755807	−	0.654795i	$-0.772755\pi$
$853$	−44.1484			−1.51161			−0.755807	+	0.654795i	$0.772755\pi$
$854$	−0.575016	+	0.995957i	−0.0196766	+	0.0340809i
$855$	1.63695	+	2.83527i	0.0559823	+	0.0969643i
$856$	3.51415	+	6.08668i	0.120111	+	0.208039i
$857$	29.5344			1.00888			0.504438	−	0.863448i	$-0.331700\pi$
$857$	29.5344			1.00888			0.504438	+	0.863448i	$0.331700\pi$
$858$	−5.07889	−	19.4527i	−0.173390	−	0.664106i
$859$	22.2808			0.760212			0.380106	−	0.924943i	$-0.375887\pi$
$859$	22.2808			0.760212			0.380106	+	0.924943i	$0.375887\pi$
$860$	0.537508	+	0.930991i	0.0183289	+	0.0317465i
$861$	1.57502	+	2.72801i	0.0536764	+	0.0929703i
$862$	−10.1560	+	17.5908i	−0.345916	+	0.599144i
$863$	26.2427			0.893311			0.446655	−	0.894706i	$-0.352615\pi$
$863$	26.2427			0.893311			0.446655	+	0.894706i	$0.352615\pi$
$864$	−2.78804	+	4.82902i	−0.0948510	+	0.164287i
$865$	5.01521	−	8.68660i	0.170522	−	0.295353i
$866$	−27.8705			−0.947079
$867$	−10.6369	+	18.4237i	−0.361250	+	0.625703i
$868$	−0.391351	−	0.677840i	−0.0132833	−	0.0230074i
$869$	5.18579	+	8.98205i	0.175916	+	0.304695i
$870$	−5.08569			−0.172421
$871$	−25.8032	+	25.4745i	−0.874310	+	0.863169i
$872$	−4.64334			−0.157243
$873$	−3.75441	−	6.50282i	−0.127067	−	0.220087i
$874$	2.28804	+	3.96300i	0.0773941	+	0.134050i
$875$	1.41577	−	2.45219i	0.0478618	−	0.0828991i
$876$	14.1570			0.478320
$877$	−21.1341	+	36.6054i	−0.713649	+	1.23608i	0.249829	+	0.968290i	$0.419625\pi$
$877$	−21.1341	+	36.6054i	−0.713649	+	1.23608i	−0.963478	+	0.267786i	$0.913708\pi$
$878$	2.94195	−	5.09560i	0.0992859	−	0.171968i
$879$	−42.4223			−1.43087
$880$	5.20275	−	9.01143i	0.175385	−	0.303775i
$881$	−15.9363	−	27.6025i	−0.536908	−	0.929952i	−0.999068	−	0.0431558i	$-0.986259\pi$
$881$	−15.9363	−	27.6025i	−0.536908	−	0.929952i	0.462160	−	0.886796i	$-0.347075\pi$
$882$	−4.76855	−	8.25938i	−0.160566	−	0.278108i
$883$	20.3121			0.683555			0.341778	−	0.939781i	$-0.388971\pi$
$883$	20.3121			0.683555			0.341778	+	0.939781i	$0.388971\pi$
$884$	−1.40550	+	1.38759i	−0.0472721	+	0.0466697i
$885$	40.9709			1.37722
$886$	12.0439	+	20.8607i	0.404623	+	0.700827i
$887$	−21.2788	−	36.8560i	−0.714473	−	1.23750i	−0.963162	−	0.268920i	$-0.913333\pi$
$887$	−21.2788	−	36.8560i	−0.714473	−	1.23750i	0.248689	−	0.968583i	$-0.420000\pi$
$888$	−5.13161	+	8.88821i	−0.172206	+	0.298269i
$889$	−4.42605			−0.148445
$890$	2.43273	−	4.21362i	0.0815454	−	0.141241i
$891$	−6.50388	+	11.2650i	−0.217888	+	0.377393i
$892$	−1.15003			−0.0385059
$893$	−0.236383	+	0.409427i	−0.00791024	+	0.0137009i
$894$	−6.00252	−	10.3967i	−0.200754	−	0.347717i
$895$	−24.8588	−	43.0567i	−0.830937	−	1.43923i
$896$	0.273891			0.00915004
$897$	20.2668	+	5.56999i	0.676689	+	0.185977i
$898$	−18.4026			−0.614102
$899$	−2.39961	−	4.15625i	−0.0800315	−	0.138619i
$900$	0.448344	+	0.776554i	0.0149448	+	0.0258851i
$901$	0.782702	−	1.35568i	0.0260756	−	0.0451642i
$902$	−39.5187			−1.31583
$903$	−0.0788911	+	0.136643i	−0.00262533	+	0.00454721i
$904$	−5.32942	+	9.23083i	−0.177254	+	0.307013i
$905$	16.3326			0.542914
$906$	−7.52976	+	13.0419i	−0.250159	+	0.433289i
$907$	−2.38601	−	4.13270i	−0.0792263	−	0.137224i	0.823690	−	0.567040i	$-0.191912\pi$
$907$	−2.38601	−	4.13270i	−0.0792263	−	0.137224i	−0.902916	+	0.429816i	$0.858578\pi$
$908$	8.99079	+	15.5725i	0.298370	+	0.516792i
$909$	−11.2272			−0.372382
$910$	−0.593039	−	2.27141i	−0.0196591	−	0.0752965i
$911$	−1.66367			−0.0551199			−0.0275599	−	0.999620i	$-0.508774\pi$
$911$	−1.66367			−0.0551199			−0.0275599	+	0.999620i	$0.508774\pi$
$912$	0.636945	+	1.10322i	0.0210914	+	0.0365313i
$913$	−36.6903	−	63.5495i	−1.21427	−	2.10318i
$914$	0.912298	−	1.58015i	0.0301761	−	0.0522666i
$915$	−12.7154			−0.420359
$916$	−8.37187	+	14.5005i	−0.276614	+	0.479110i
$917$	2.18085	−	3.77735i	0.0720181	−	0.124739i
$918$	3.05447			0.100813
$919$	−6.98264	+	12.0943i	−0.230336	+	0.398954i	−0.957907	−	0.287079i	$-0.907316\pi$
$919$	−6.98264	+	12.0943i	−0.230336	+	0.398954i	0.727571	+	0.686032i	$0.240649\pi$
$920$	5.43913	+	9.42085i	0.179323	+	0.310596i
$921$	5.51521	+	9.55262i	0.181732	+	0.314770i
$922$	−21.9730			−0.723643
$923$	−10.4299	−	2.86649i	−0.343305	−	0.0943516i
$924$	1.52723			0.0502423
$925$	2.62280	+	4.54282i	0.0862370	+	0.149367i
$926$	−3.37187	−	5.84024i	−0.110806	−	0.191922i
$927$	−11.2593	+	19.5018i	−0.369805	+	0.640522i
$928$	1.67939			0.0551287
$929$	24.1571	−	41.8413i	0.792568	−	1.37277i	−0.131803	−	0.991276i	$-0.542077\pi$
$929$	24.1571	−	41.8413i	0.792568	−	1.37277i	0.924372	−	0.381493i	$-0.124590\pi$
$930$	4.32701	−	7.49460i	0.141888	−	0.245758i
$931$	−6.92498			−0.226957
$932$	0.126672	−	0.219403i	0.00414929	−	0.00718677i
$933$	5.68966	+	9.85478i	0.186271	+	0.322631i
$934$	−12.0113	−	20.8042i	−0.393023	−	0.680736i
$935$	−5.69994			−0.186408
$936$	−4.78804	−	1.31591i	−0.156502	−	0.0430119i
$937$	40.6524			1.32806			0.664028	−	0.747707i	$-0.268845\pi$
$937$	40.6524			1.32806			0.664028	+	0.747707i	$0.268845\pi$
$938$	−1.37720	−	2.38539i	−0.0449673	−	0.0778856i
$939$	−7.39815	−	12.8140i	−0.241429	−	0.418168i
$940$	−0.561929	+	0.973290i	−0.0183281	+	0.0317452i
$941$	47.7643			1.55707			0.778535	−	0.627601i	$-0.215963\pi$
$941$	47.7643			1.55707			0.778535	+	0.627601i	$0.215963\pi$
$942$	0.720773	−	1.24841i	0.0234840	−	0.0406756i
$943$	20.6571	−	35.7791i	0.672687	−	1.16513i
$944$	−13.5294			−0.440343
$945$	−1.81527	+	3.14415i	−0.0590509	+	0.102279i
$946$	−0.989727	−	1.71426i	−0.0321788	−	0.0557353i
$947$	2.41219	+	4.17803i	0.0783856	+	0.135768i	0.902554	−	0.430578i	$-0.141690\pi$
$947$	2.41219	+	4.17803i	0.0783856	+	0.135768i	−0.824168	+	0.566345i	$0.808357\pi$
$948$	−3.01842			−0.0980338
$949$	10.1223	+	38.7695i	0.328583	+	1.25851i
$950$	0.651093			0.0211243
$951$	−20.7618	−	35.9604i	−0.673246	−	1.16610i
$952$	−0.0750160	−	0.129932i	−0.00243128	−	0.00421111i
$953$	25.2891	−	43.8020i	0.819194	−	1.41889i	−0.0870823	−	0.996201i	$-0.527754\pi$
$953$	25.2891	−	43.8020i	0.819194	−	1.41889i	0.906277	−	0.422685i	$-0.138912\pi$
$954$	3.93566			0.127422
$955$	−14.6560	+	25.3850i	−0.474258	+	0.821439i
$956$	−12.0513	+	20.8734i	−0.389765	+	0.675094i
$957$	9.36441			0.302708
$958$	7.10331	−	12.3033i	0.229498	−	0.397502i
$959$	1.80500	+	3.12635i	0.0582865	+	0.100955i
$960$	1.51415	+	2.62258i	0.0488689	+	0.0846435i
$961$	−22.8334			−0.736563
$962$	−28.0099	−	7.69805i	−0.903075	−	0.248195i
$963$	9.67939			0.311914
$964$	−1.03751	−	1.79702i	−0.0334159	−	0.0578780i
$965$	−24.1429	−	41.8168i	−0.777189	−	1.34613i
$966$	−0.798312	+	1.38272i	−0.0256853	+	0.0444882i
$967$	28.2555			0.908635			0.454317	−	0.890840i	$-0.349883\pi$
$967$	28.2555			0.908635			0.454317	+	0.890840i	$0.349883\pi$
$968$	−4.07995	+	7.06668i	−0.131135	+	0.227132i
$969$	0.348907	−	0.604324i	0.0112085	−	0.0194137i
$970$	−12.9610			−0.416154
$971$	−10.6847	+	18.5065i	−0.342889	+	0.593901i	−0.984968	−	0.172737i	$-0.944739\pi$
$971$	−10.6847	+	18.5065i	−0.342889	+	0.593901i	0.642079	+	0.766639i	$0.278072\pi$
$972$	6.47130	+	11.2086i	0.207567	+	0.359517i
$973$	−0.342509	−	0.593242i	−0.0109803	−	0.0190185i
$974$	12.0021			0.384573
$975$	2.12813	−	2.10102i	0.0681548	−	0.0672864i
$976$	4.19887			0.134403
$977$	25.5729	+	44.2935i	0.818148	+	1.41707i	0.907045	+	0.421034i	$0.138333\pi$
$977$	25.5729	+	44.2935i	0.818148	+	1.41707i	−0.0888966	+	0.996041i	$0.528334\pi$
$978$	0.877203	+	1.51936i	0.0280499	+	0.0485838i
$979$	−4.47945	+	7.75864i	−0.143164	+	0.247967i
$980$	−16.4621			−0.525862
$981$	−3.19741	+	5.53808i	−0.102086	+	0.176817i
$982$	14.2023	−	24.5992i	0.453215	−	0.784992i
$983$	−15.1004			−0.481628			−0.240814	−	0.970571i	$-0.577414\pi$
$983$	−15.1004			−0.481628			−0.240814	+	0.970571i	$0.577414\pi$
$984$	5.75053	−	9.96021i	0.183320	−	0.317520i
$985$	−29.8159	−	51.6427i	−0.950015	−	1.64547i
$986$	−0.459969	−	0.796690i	−0.0146484	−	0.0253718i
$987$	−0.164951			−0.00525044
$988$	−2.56580	+	2.53311i	−0.0816291	+	0.0805890i
$989$	2.06939			0.0658027
$990$	−7.16524	−	12.4106i	−0.227726	−	0.394434i
$991$	−10.9246	−	18.9219i	−0.347031	−	0.601075i	0.638690	−	0.769464i	$-0.279477\pi$
$991$	−10.9246	−	18.9219i	−0.347031	−	0.601075i	−0.985721	+	0.168389i	$0.946143\pi$
$992$	−1.42886	+	2.47486i	−0.0453663	+	0.0785768i
$993$	−9.34811			−0.296653
$994$	0.410836	−	0.711589i	0.0130309	−	0.0225702i
$995$	13.4792	−	23.3466i	0.427318	−	0.740137i
$996$	21.3559			0.676686
$997$	7.01948	−	12.1581i	0.222309	−	0.385051i	−0.733199	−	0.680014i	$-0.761974\pi$
$997$	7.01948	−	12.1581i	0.222309	−	0.385051i	0.955509	+	0.294963i	$0.0953072\pi$
$998$	−0.226109	−	0.391633i	−0.00715737	−	0.0123969i
$999$	22.4621	+	38.9055i	0.710669	+	1.23092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.g.b.419.2	yes	6
13.3	even	3		6422.2.a.u.1.2		3
13.9	even	3	inner	494.2.g.b.191.2	✓	6
13.10	even	6		6422.2.a.m.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.g.b.191.2	✓	6	13.9	even	3	inner
494.2.g.b.419.2	yes	6	1.1	even	1	trivial
6422.2.a.m.1.2		3	13.10	even	6
6422.2.a.u.1.2		3	13.3	even	3

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:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.636945 + 1.10322i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.37720 q^{5} +(0.636945 - 1.10322i) q^{6} +(-0.136945 + 0.237196i) q^{7} +1.00000 q^{8} +(0.688601 - 1.19269i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.636945 + 1.10322i) q^{3} +(-0.500000 + 0.866025i) q^{4} +2.37720 q^{5} +(0.636945 - 1.10322i) q^{6} +(-0.136945 + 0.237196i) q^{7} +1.00000 q^{8} +(0.688601 - 1.19269i) q^{9} +(-1.18860 - 2.05872i) q^{10} +(2.18860 + 3.79077i) q^{11} -1.27389 q^{12} +(-0.910836 - 3.48861i) q^{13} +0.273891 q^{14} +(1.51415 + 2.62258i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.273891 + 0.474392i) q^{17} -1.37720 q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.18860 + 2.05872i) q^{20} -0.348907 q^{21} +(2.18860 - 3.79077i) q^{22} +(2.28804 + 3.96300i) q^{23} +(0.636945 + 1.10322i) q^{24} +0.651093 q^{25} +(-2.56580 + 2.53311i) q^{26} +5.57608 q^{27} +(-0.136945 - 0.237196i) q^{28} +(-0.839695 - 1.45439i) q^{29} +(1.51415 - 2.62258i) q^{30} +2.85772 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.78804 + 4.82902i) q^{33} +0.547781 q^{34} +(-0.325547 + 0.563863i) q^{35} +(0.688601 + 1.19269i) q^{36} +(4.02830 + 6.97721i) q^{37} +1.00000 q^{38} +(3.26855 - 3.22691i) q^{39} +2.37720 q^{40} +(-4.51415 - 7.81873i) q^{41} +(0.174453 + 0.302162i) q^{42} +(0.226109 - 0.391633i) q^{43} -4.37720 q^{44} +(1.63695 - 2.83527i) q^{45} +(2.28804 - 3.96300i) q^{46} +0.472765 q^{47} +(0.636945 - 1.10322i) q^{48} +(3.46249 + 5.99721i) q^{49} +(-0.325547 - 0.563863i) q^{50} -0.697813 q^{51} +(3.47664 + 0.955496i) q^{52} -2.85772 q^{53} +(-2.78804 - 4.82902i) q^{54} +(5.20275 + 9.01143i) q^{55} +(-0.136945 + 0.237196i) q^{56} -1.27389 q^{57} +(-0.839695 + 1.45439i) q^{58} +(6.76468 - 11.7168i) q^{59} -3.02830 q^{60} +(-2.09944 + 3.63633i) q^{61} +(-1.42886 - 2.47486i) q^{62} +(0.188601 + 0.326667i) q^{63} +1.00000 q^{64} +(-2.16524 - 8.29313i) q^{65} +5.57608 q^{66} +(-5.02830 - 8.70926i) q^{67} +(-0.273891 - 0.474392i) q^{68} +(-2.91471 + 5.04843i) q^{69} +0.651093 q^{70} +(1.50000 - 2.59808i) q^{71} +(0.688601 - 1.19269i) q^{72} -11.1132 q^{73} +(4.02830 - 6.97721i) q^{74} +(0.414711 + 0.718300i) q^{75} +(-0.500000 - 0.866025i) q^{76} -1.19887 q^{77} +(-4.42886 - 1.21720i) q^{78} +2.36945 q^{79} +(-1.18860 - 2.05872i) q^{80} +(1.48585 + 2.57357i) q^{81} +(-4.51415 + 7.81873i) q^{82} -16.7643 q^{83} +(0.174453 - 0.302162i) q^{84} +(-0.651093 + 1.12773i) q^{85} -0.452219 q^{86} +(1.06968 - 1.85274i) q^{87} +(2.18860 + 3.79077i) q^{88} +(1.02336 + 1.77251i) q^{89} -3.27389 q^{90} +(0.952219 + 0.261701i) q^{91} -4.57608 q^{92} +(1.82021 + 3.15270i) q^{93} +(-0.236383 - 0.409427i) q^{94} +(-1.18860 + 2.05872i) q^{95} -1.27389 q^{96} +(2.72611 - 4.72176i) q^{97} +(3.46249 - 5.99721i) q^{98} +6.02830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 8 q^{11} - 4 q^{12} - 2 q^{14} - 3 q^{15} - 3 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 2 q^{20} - 16 q^{21} + 8 q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{25} + 2 q^{27} + q^{28} + 14 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - q^{33} - 4 q^{34} + 5 q^{35} - q^{36} + 6 q^{38} - 13 q^{39} + 4 q^{40} - 15 q^{41} + 8 q^{42} + 5 q^{43} - 16 q^{44} + 8 q^{45} - 2 q^{46} - 22 q^{47} + 2 q^{48} + 12 q^{49} + 5 q^{50} - 32 q^{51} + 10 q^{53} - q^{54} + 14 q^{55} + q^{56} - 4 q^{57} + 14 q^{58} + 4 q^{59} + 6 q^{60} - 2 q^{61} + 5 q^{62} - 4 q^{63} + 6 q^{64} + 13 q^{65} + 2 q^{66} - 6 q^{67} + 2 q^{68} - 16 q^{69} - 10 q^{70} + 9 q^{71} - q^{72} + 30 q^{73} + q^{75} - 3 q^{76} + 14 q^{77} - 13 q^{78} - 4 q^{79} - 2 q^{80} + 21 q^{81} - 15 q^{82} + 10 q^{83} + 8 q^{84} + 10 q^{85} - 10 q^{86} - 5 q^{87} + 8 q^{88} + 27 q^{89} - 16 q^{90} + 13 q^{91} + 4 q^{92} - 25 q^{93} + 11 q^{94} - 2 q^{95} - 4 q^{96} + 20 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9 - 2 * q^10 + 8 * q^11 - 4 * q^12 - 2 * q^14 - 3 * q^15 - 3 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 2 * q^20 - 16 * q^21 + 8 * q^22 - 2 * q^23 + 2 * q^24 - 10 * q^25 + 2 * q^27 + q^28 + 14 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - q^33 - 4 * q^34 + 5 * q^35 - q^36 + 6 * q^38 - 13 * q^39 + 4 * q^40 - 15 * q^41 + 8 * q^42 + 5 * q^43 - 16 * q^44 + 8 * q^45 - 2 * q^46 - 22 * q^47 + 2 * q^48 + 12 * q^49 + 5 * q^50 - 32 * q^51 + 10 * q^53 - q^54 + 14 * q^55 + q^56 - 4 * q^57 + 14 * q^58 + 4 * q^59 + 6 * q^60 - 2 * q^61 + 5 * q^62 - 4 * q^63 + 6 * q^64 + 13 * q^65 + 2 * q^66 - 6 * q^67 + 2 * q^68 - 16 * q^69 - 10 * q^70 + 9 * q^71 - q^72 + 30 * q^73 + q^75 - 3 * q^76 + 14 * q^77 - 13 * q^78 - 4 * q^79 - 2 * q^80 + 21 * q^81 - 15 * q^82 + 10 * q^83 + 8 * q^84 + 10 * q^85 - 10 * q^86 - 5 * q^87 + 8 * q^88 + 27 * q^89 - 16 * q^90 + 13 * q^91 + 4 * q^92 - 25 * q^93 + 11 * q^94 - 2 * q^95 - 4 * q^96 + 20 * q^97 + 12 * q^98 + 12 * q^99

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