LMFDB - Embedded newform 315.2.l.b.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	315.151
Dual form			315.2.l.b.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71927 q^{2} +(-0.324473 + 1.70139i) q^{3} +0.955889 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.557856 - 2.92514i) q^{6} +(-2.52983 + 0.774581i) q^{7} +1.79511 q^{8} +(-2.78943 - 1.10411i) q^{9} +O(q^{10})$	\(q-1.71927 q^{2} +(-0.324473 + 1.70139i) q^{3} +0.955889 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.557856 - 2.92514i) q^{6} +(-2.52983 + 0.774581i) q^{7} +1.79511 q^{8} +(-2.78943 - 1.10411i) q^{9} +(-0.859635 + 1.48893i) q^{10} +(-2.30123 - 3.98585i) q^{11} +(-0.310160 + 1.62634i) q^{12} +(0.944711 + 1.63629i) q^{13} +(4.34945 - 1.33171i) q^{14} +(1.31121 + 1.13170i) q^{15} -4.99805 q^{16} +(0.371733 - 0.643861i) q^{17} +(4.79579 + 1.89826i) q^{18} +(-0.518230 - 0.897600i) q^{19} +(0.477944 - 0.827824i) q^{20} +(-0.497003 - 4.55554i) q^{21} +(3.95644 + 6.85276i) q^{22} +(2.38562 - 4.13202i) q^{23} +(-0.582464 + 3.05418i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.62421 - 2.81322i) q^{26} +(2.78361 - 4.38766i) q^{27} +(-2.41823 + 0.740414i) q^{28} +(4.71667 - 8.16951i) q^{29} +(-2.25432 - 1.94569i) q^{30} +1.17974 q^{31} +5.00279 q^{32} +(7.52817 - 2.62199i) q^{33} +(-0.639110 + 1.10697i) q^{34} +(-0.594106 + 2.57818i) q^{35} +(-2.66639 - 1.05540i) q^{36} +(-2.82154 - 4.88706i) q^{37} +(0.890976 + 1.54322i) q^{38} +(-3.09049 + 1.07639i) q^{39} +(0.897555 - 1.55461i) q^{40} +(-3.72949 - 6.45966i) q^{41} +(0.854482 + 7.83221i) q^{42} +(-1.26959 + 2.19900i) q^{43} +(-2.19972 - 3.81003i) q^{44} +(-2.35090 + 1.86367i) q^{45} +(-4.10153 + 7.10406i) q^{46} -1.91984 q^{47} +(1.62173 - 8.50362i) q^{48} +(5.80005 - 3.91911i) q^{49} +(0.859635 + 1.48893i) q^{50} +(0.974839 + 0.841377i) q^{51} +(0.903039 + 1.56411i) q^{52} +(-3.94471 + 6.83244i) q^{53} +(-4.78577 + 7.54356i) q^{54} -4.60247 q^{55} +(-4.54132 + 1.39046i) q^{56} +(1.69532 - 0.590462i) q^{57} +(-8.10923 + 14.0456i) q^{58} -5.10165 q^{59} +(1.25337 + 1.08177i) q^{60} +4.07757 q^{61} -2.02829 q^{62} +(7.91201 + 0.632556i) q^{63} +1.39497 q^{64} +1.88942 q^{65} +(-12.9429 + 4.50790i) q^{66} -7.45782 q^{67} +(0.355335 - 0.615459i) q^{68} +(6.25610 + 5.39960i) q^{69} +(1.02143 - 4.43260i) q^{70} -6.30656 q^{71} +(-5.00734 - 1.98199i) q^{72} +(3.33632 - 5.77867i) q^{73} +(4.85100 + 8.40217i) q^{74} +(1.63568 - 0.569692i) q^{75} +(-0.495370 - 0.858006i) q^{76} +(8.90909 + 8.30103i) q^{77} +(5.31339 - 1.85060i) q^{78} -5.21220 q^{79} +(-2.49903 + 4.32844i) q^{80} +(6.56189 + 6.15967i) q^{81} +(6.41199 + 11.1059i) q^{82} +(-8.45847 + 14.6505i) q^{83} +(-0.475079 - 4.35459i) q^{84} +(-0.371733 - 0.643861i) q^{85} +(2.18277 - 3.78067i) q^{86} +(12.3691 + 10.6757i) q^{87} +(-4.13096 - 7.15504i) q^{88} +(8.48148 + 14.6904i) q^{89} +(4.04184 - 3.20415i) q^{90} +(-3.65739 - 3.40777i) q^{91} +(2.28039 - 3.94975i) q^{92} +(-0.382794 + 2.00720i) q^{93} +3.30072 q^{94} -1.03646 q^{95} +(-1.62327 + 8.51167i) q^{96} +(5.80321 - 10.0515i) q^{97} +(-9.97185 + 6.73801i) q^{98} +(2.01833 + 13.6591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.71927			−1.21571			−0.607854	−	0.794049i	$-0.707969\pi$
$2$	−1.71927			−1.21571			−0.607854	+	0.794049i	$0.707969\pi$
$3$	−0.324473	+	1.70139i	−0.187334	+	0.982296i
$3$	−0.324473	+	1.70139i	−0.187334	+	0.982296i
$4$	0.955889			0.477944
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.557856	−	2.92514i	0.227744	−	1.19418i
$7$	−2.52983	+	0.774581i	−0.956185	+	0.292764i
$7$	−2.52983	+	0.774581i	−0.956185	+	0.292764i
$8$	1.79511			0.634667
$9$	−2.78943	−	1.10411i	−0.929812	−	0.368036i
$10$	−0.859635	+	1.48893i	−0.271840	+	0.470841i
$11$	−2.30123	−	3.98585i	−0.693848	−	1.20178i	−0.970568	−	0.240829i	$-0.922581\pi$
$11$	−2.30123	−	3.98585i	−0.693848	−	1.20178i	0.276720	−	0.960951i	$-0.410753\pi$
$12$	−0.310160	+	1.62634i	−0.0895354	+	0.469483i
$13$	0.944711	+	1.63629i	0.262016	+	0.453825i	0.966777	−	0.255619i	$-0.0822794\pi$
$13$	0.944711	+	1.63629i	0.262016	+	0.453825i	−0.704762	+	0.709444i	$0.748946\pi$
$14$	4.34945	−	1.33171i	1.16244	−	0.355916i
$15$	1.31121	+	1.13170i	0.338552	+	0.292202i
$16$	−4.99805			−1.24951
$17$	0.371733	−	0.643861i	0.0901585	−	0.156159i	−0.817419	−	0.576043i	$-0.804596\pi$
$17$	0.371733	−	0.643861i	0.0901585	−	0.156159i	0.907578	+	0.419884i	$0.137929\pi$
$18$	4.79579	+	1.89826i	1.13038	+	0.447424i
$19$	−0.518230	−	0.897600i	−0.118890	−	0.205924i	0.800438	−	0.599415i	$-0.204600\pi$
$19$	−0.518230	−	0.897600i	−0.118890	−	0.205924i	−0.919328	+	0.393492i	$0.871267\pi$
$20$	0.477944	−	0.827824i	0.106872	−	0.185107i
$21$	−0.497003	−	4.55554i	−0.108455	−	0.994101i
$22$	3.95644	+	6.85276i	0.843516	+	1.46101i
$23$	2.38562	−	4.13202i	0.497437	−	0.861586i	−0.502559	−	0.864543i	$-0.667608\pi$
$23$	2.38562	−	4.13202i	0.497437	−	0.861586i	0.999996	+	0.00295696i	$0.000941229\pi$
$24$	−0.582464	+	3.05418i	−0.118895	+	0.623431i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.62421	−	2.81322i	−0.318535	−	0.551718i
$27$	2.78361	−	4.38766i	0.535706	−	0.844405i
$28$	−2.41823	+	0.740414i	−0.457003	+	0.139925i
$29$	4.71667	−	8.16951i	0.875864	−	1.51704i	0.0200242	−	0.999799i	$-0.493626\pi$
$29$	4.71667	−	8.16951i	0.875864	−	1.51704i	0.855840	−	0.517241i	$-0.173041\pi$
$30$	−2.25432	−	1.94569i	−0.411581	−	0.355233i
$31$	1.17974			0.211888			0.105944	−	0.994372i	$-0.466214\pi$
$31$	1.17974			0.211888			0.105944	+	0.994372i	$0.466214\pi$
$32$	5.00279			0.884376
$33$	7.52817	−	2.62199i	1.31049	−	0.456429i
$34$	−0.639110	+	1.10697i	−0.109606	+	0.189844i
$35$	−0.594106	+	2.57818i	−0.100422	+	0.435793i
$36$	−2.66639	−	1.05540i	−0.444398	−	0.175901i
$37$	−2.82154	−	4.88706i	−0.463859	−	0.803427i	0.535290	−	0.844668i	$-0.320202\pi$
$37$	−2.82154	−	4.88706i	−0.463859	−	0.803427i	−0.999149	+	0.0412409i	$0.986869\pi$
$38$	0.890976	+	1.54322i	0.144535	+	0.250343i
$39$	−3.09049	+	1.07639i	−0.494875	+	0.172360i
$40$	0.897555	−	1.55461i	0.141916	−	0.245805i
$41$	−3.72949	−	6.45966i	−0.582448	−	1.00883i	−0.995188	−	0.0979806i	$-0.968762\pi$
$41$	−3.72949	−	6.45966i	−0.582448	−	1.00883i	0.412741	−	0.910849i	$-0.364572\pi$
$42$	0.854482	+	7.83221i	0.131849	+	1.20854i
$43$	−1.26959	+	2.19900i	−0.193611	+	0.335344i	−0.946444	−	0.322867i	$-0.895353\pi$
$43$	−1.26959	+	2.19900i	−0.193611	+	0.335344i	0.752833	+	0.658211i	$0.228687\pi$
$44$	−2.19972	−	3.81003i	−0.331621	−	0.574384i
$45$	−2.35090	+	1.86367i	−0.350452	+	0.277819i
$46$	−4.10153	+	7.10406i	−0.604738	+	1.04744i
$47$	−1.91984			−0.280037			−0.140019	−	0.990149i	$-0.544716\pi$
$47$	−1.91984			−0.280037			−0.140019	+	0.990149i	$0.544716\pi$
$48$	1.62173	−	8.50362i	0.234077	−	1.22739i
$49$	5.80005	−	3.91911i	0.828578	−	0.559873i
$50$	0.859635	+	1.48893i	0.121571	+	0.210567i
$51$	0.974839	+	0.841377i	0.136505	+	0.117816i
$52$	0.903039	+	1.56411i	0.125229	+	0.216903i
$53$	−3.94471	+	6.83244i	−0.541848	+	0.938507i	0.456950	+	0.889492i	$0.348942\pi$
$53$	−3.94471	+	6.83244i	−0.541848	+	0.938507i	−0.998798	+	0.0490154i	$0.984392\pi$
$54$	−4.78577	+	7.54356i	−0.651261	+	1.02655i
$55$	−4.60247			−0.620596
$56$	−4.54132	+	1.39046i	−0.606859	+	0.185808i
$57$	1.69532	−	0.590462i	0.224550	−	0.0782086i
$58$	−8.10923	+	14.0456i	−1.06479	+	1.84428i
$59$	−5.10165			−0.664178			−0.332089	−	0.943248i	$-0.607753\pi$
$59$	−5.10165			−0.664178			−0.332089	+	0.943248i	$0.607753\pi$
$60$	1.25337	+	1.08177i	0.161809	+	0.139656i
$61$	4.07757			0.522080			0.261040	−	0.965328i	$-0.415935\pi$
$61$	4.07757			0.522080			0.261040	+	0.965328i	$0.415935\pi$
$62$	−2.02829			−0.257594
$63$	7.91201	+	0.632556i	0.996819	+	0.0796945i
$64$	1.39497			0.174371
$65$	1.88942			0.234354
$66$	−12.9429	+	4.50790i	−1.59317	+	0.554885i
$67$	−7.45782			−0.911117			−0.455559	−	0.890206i	$-0.650560\pi$
$67$	−7.45782			−0.911117			−0.455559	+	0.890206i	$0.650560\pi$
$68$	0.355335	−	0.615459i	0.0430908	−	0.0746354i
$69$	6.25610	+	5.39960i	0.753146	+	0.650035i
$70$	1.02143	−	4.43260i	0.122084	−	0.529797i
$71$	−6.30656			−0.748451			−0.374225	−	0.927338i	$-0.622091\pi$
$71$	−6.30656			−0.748451			−0.374225	+	0.927338i	$0.622091\pi$
$72$	−5.00734	−	1.98199i	−0.590121	−	0.233580i
$73$	3.33632	−	5.77867i	0.390486	−	0.676342i	−0.602027	−	0.798475i	$-0.705640\pi$
$73$	3.33632	−	5.77867i	0.390486	−	0.676342i	0.992514	+	0.122133i	$0.0389736\pi$
$74$	4.85100	+	8.40217i	0.563917	+	0.976732i
$75$	1.63568	−	0.569692i	0.188872	−	0.0657824i
$76$	−0.495370	−	0.858006i	−0.0568228	−	0.0984200i
$77$	8.90909	+	8.30103i	1.01528	+	0.945990i
$78$	5.31339	−	1.85060i	0.601623	−	0.209540i
$79$	−5.21220			−0.586418			−0.293209	−	0.956048i	$-0.594723\pi$
$79$	−5.21220			−0.586418			−0.293209	+	0.956048i	$0.594723\pi$
$80$	−2.49903	+	4.32844i	−0.279400	+	0.483935i
$81$	6.56189	+	6.15967i	0.729099	+	0.684408i
$82$	6.41199	+	11.1059i	0.708086	+	1.22644i
$83$	−8.45847	+	14.6505i	−0.928438	+	1.60810i	−0.142501	+	0.989795i	$0.545514\pi$
$83$	−8.45847	+	14.6505i	−0.928438	+	1.60810i	−0.785937	+	0.618307i	$0.787819\pi$
$84$	−0.475079	−	4.35459i	−0.0518354	−	0.475125i
$85$	−0.371733	−	0.643861i	−0.0403201	−	0.0698365i
$86$	2.18277	−	3.78067i	0.235374	−	0.407681i
$87$	12.3691	+	10.6757i	1.32610	+	1.14455i
$88$	−4.13096	−	7.15504i	−0.440362	−	0.762730i
$89$	8.48148	+	14.6904i	0.899035	+	1.55717i	0.828730	+	0.559649i	$0.189064\pi$
$89$	8.48148	+	14.6904i	0.899035	+	1.55717i	0.0703049	+	0.997526i	$0.477603\pi$
$90$	4.04184	−	3.20415i	0.426047	−	0.337747i
$91$	−3.65739	−	3.40777i	−0.383399	−	0.357231i
$92$	2.28039	−	3.94975i	0.237747	−	0.411790i
$93$	−0.382794	+	2.00720i	−0.0396939	+	0.208137i
$94$	3.30072			0.340444
$95$	−1.03646			−0.106338
$96$	−1.62327	+	8.51167i	−0.165674	+	0.868719i
$97$	5.80321	−	10.0515i	0.589227	−	1.02057i	−0.405107	−	0.914269i	$-0.632766\pi$
$97$	5.80321	−	10.0515i	0.589227	−	1.02057i	0.994334	−	0.106302i	$-0.0339009\pi$
$98$	−9.97185	+	6.73801i	−1.00731	+	0.680642i
$99$	2.01833	+	13.6591i	0.202850	+	1.37279i
$100$	−0.477944	−	0.827824i	−0.0477944	−	0.0827824i
$101$	−9.46492	−	16.3937i	−0.941794	−	1.63124i	−0.762046	−	0.647523i	$-0.775805\pi$
$101$	−9.46492	−	16.3937i	−0.941794	−	1.63124i	−0.179749	−	0.983713i	$-0.557528\pi$
$102$	−1.67601	−	1.44655i	−0.165950	−	0.143230i
$103$	−4.16009	+	7.20549i	−0.409906	+	0.709978i	−0.994879	−	0.101075i	$-0.967772\pi$
$103$	−4.16009	+	7.20549i	−0.409906	+	0.709978i	0.584973	+	0.811053i	$0.301105\pi$
$104$	1.69586	+	2.93732i	0.166293	+	0.288028i
$105$	−4.19372	−	1.84736i	−0.409265	−	0.180283i
$106$	6.78202	−	11.7468i	0.658728	−	1.14095i
$107$	−4.96262	−	8.59551i	−0.479754	−	0.830959i	0.519976	−	0.854181i	$-0.325941\pi$
$107$	−4.96262	−	8.59551i	−0.479754	−	0.830959i	−0.999730	+	0.0232218i	$0.992608\pi$
$108$	2.66082	−	4.19411i	0.256038	−	0.403578i
$109$	−2.68358	+	4.64809i	−0.257040	+	0.445206i	−0.965448	−	0.260597i	$-0.916081\pi$
$109$	−2.68358	+	4.64809i	−0.257040	+	0.445206i	0.708408	+	0.705803i	$0.249414\pi$
$110$	7.91288			0.754464
$111$	9.23029	−	3.21482i	0.876100	−	0.305137i
$112$	12.6442	−	3.87140i	1.19477	−	0.365813i
$113$	−7.54586	−	13.0698i	−0.709855	−	1.22951i	−0.964911	−	0.262579i	$-0.915427\pi$
$113$	−7.54586	−	13.0698i	−0.709855	−	1.22951i	0.255055	−	0.966926i	$-0.417906\pi$
$114$	−2.91471	+	1.01516i	−0.272987	+	0.0950788i
$115$	−2.38562	−	4.13202i	−0.222461	−	0.385313i
$116$	4.50861	−	7.80915i	0.418614	−	0.725061i
$117$	−0.828574	−	5.60738i	−0.0766017	−	0.518403i
$118$	8.77111			0.807446
$119$	−0.441698	+	1.91679i	−0.0404904	+	0.175712i
$120$	2.35376	+	2.03152i	0.214868	+	0.185451i
$121$	−5.09135	+	8.81847i	−0.462850	+	0.801680i
$122$	−7.01045			−0.634696
$123$	12.2005	−	4.24932i	1.10008	−	0.383148i
$124$	1.12770			0.101271
$125$	−1.00000			−0.0894427
$126$	−13.6029	−	1.08753i	−1.21184	−	0.0968852i
$127$	−21.1638			−1.87798			−0.938991	−	0.343940i	$-0.888238\pi$
$127$	−21.1638			−1.87798			−0.938991	+	0.343940i	$0.888238\pi$
$128$	−12.4039			−1.09636
$129$	−3.32940	−	2.87358i	−0.293137	−	0.253005i
$130$	−3.24843			−0.284906
$131$	7.11044	−	12.3156i	0.621242	−	1.07602i	−0.368013	−	0.929821i	$-0.619962\pi$
$131$	7.11044	−	12.3156i	0.621242	−	1.07602i	0.989255	−	0.146202i	$-0.0467048\pi$
$132$	7.19609	−	2.50633i	0.626339	−	0.218148i
$133$	2.00630	+	1.86936i	0.173968	+	0.162094i
$134$	12.8220			1.10765
$135$	−2.40802	−	4.60450i	−0.207249	−	0.396293i
$136$	0.667302	−	1.15580i	0.0572206	−	0.0991090i
$137$	0.279292	+	0.483748i	0.0238615	+	0.0413293i	0.877710	−	0.479193i	$-0.159071\pi$
$137$	0.279292	+	0.483748i	0.0238615	+	0.0413293i	−0.853848	+	0.520522i	$0.825737\pi$
$138$	−10.7559	−	9.28337i	−0.915605	−	0.790253i
$139$	−6.91228	−	11.9724i	−0.586292	−	1.01549i	−0.994713	−	0.102694i	$-0.967254\pi$
$139$	−6.91228	−	11.9724i	−0.586292	−	1.01549i	0.408421	−	0.912794i	$-0.366080\pi$
$140$	−0.567899	+	2.46446i	−0.0479963	+	0.208285i
$141$	0.622936	−	3.26639i	0.0524606	−	0.275080i
$142$	10.8427			0.909897
$143$	4.34800	−	7.53096i	0.363598	−	0.629771i
$144$	13.9417	+	5.51839i	1.16181	+	0.459866i
$145$	−4.71667	−	8.16951i	−0.391698	−	0.678441i
$146$	−5.73603	+	9.93509i	−0.474717	+	0.822234i
$147$	4.78597	+	11.1398i	0.394740	+	0.918793i
$148$	−2.69708	−	4.67148i	−0.221699	−	0.383994i
$149$	−2.95113	+	5.11150i	−0.241766	+	0.418751i	−0.961217	−	0.275792i	$-0.911060\pi$
$149$	−2.95113	+	5.11150i	−0.241766	+	0.418751i	0.719451	+	0.694543i	$0.244393\pi$
$150$	−2.81218	+	0.979454i	−0.229613	+	0.0799721i
$151$	10.1855	+	17.6417i	0.828881	+	1.43566i	0.898917	+	0.438119i	$0.144355\pi$
$151$	10.1855	+	17.6417i	0.828881	+	1.43566i	−0.0700359	+	0.997544i	$0.522311\pi$
$152$	−0.930279	−	1.61129i	−0.0754556	−	0.130693i
$153$	−1.74782	+	1.38557i	−0.141303	+	0.112017i
$154$	−15.3171	−	14.2717i	−1.23429	−	1.15005i
$155$	0.589871	−	1.02169i	0.0473796	−	0.0820638i
$156$	−2.95417	+	1.02891i	−0.236523	+	0.0823786i
$157$	19.4336			1.55097			0.775486	−	0.631365i	$-0.217505\pi$
$157$	19.4336			1.55097			0.775486	+	0.631365i	$0.217505\pi$
$158$	8.96118			0.712913
$159$	−10.3447	−	8.92842i	−0.820386	−	0.708070i
$160$	2.50139	−	4.33254i	0.197752	−	0.342517i
$161$	−2.83463	+	12.3012i	−0.223400	+	0.969467i
$162$	−11.2817	−	10.5901i	−0.886372	−	0.832040i
$163$	9.70630	+	16.8118i	0.760256	+	1.31680i	0.942718	+	0.333590i	$0.108260\pi$
$163$	9.70630	+	16.8118i	0.760256	+	1.31680i	−0.182462	+	0.983213i	$0.558407\pi$
$164$	−3.56497	−	6.17471i	−0.278378	−	0.482164i
$165$	1.49337	−	7.83058i	0.116259	−	0.609610i
$166$	14.5424	−	25.1882i	1.12871	−	1.95498i
$167$	−2.54026	−	4.39986i	−0.196571	−	0.340471i	0.750843	−	0.660480i	$-0.229647\pi$
$167$	−2.54026	−	4.39986i	−0.196571	−	0.340471i	−0.947414	+	0.320009i	$0.896314\pi$
$168$	−0.892174	−	8.17770i	−0.0688328	−	0.630923i
$169$	4.71504	−	8.16669i	0.362695	−	0.628207i
$170$	0.639110	+	1.10697i	0.0490175	+	0.0849007i
$171$	0.454521	+	3.07598i	0.0347581	+	0.235226i
$172$	−1.21359	+	2.10200i	−0.0925353	+	0.160276i
$173$	11.2759			0.857294			0.428647	−	0.903472i	$-0.358990\pi$
$173$	11.2759			0.857294			0.428647	+	0.903472i	$0.358990\pi$
$174$	−21.2658	−	18.3544i	−1.61215	−	1.39144i
$175$	1.93572	+	1.80360i	0.146327	+	0.136340i
$176$	11.5017	+	19.9215i	0.866972	+	1.50164i
$177$	1.65534	−	8.67987i	0.124423	−	0.652419i
$178$	−14.5819	−	25.2567i	−1.09296	−	1.89307i
$179$	4.78541	−	8.28858i	0.357679	−	0.619517i	−0.629894	−	0.776681i	$-0.716902\pi$
$179$	4.78541	−	8.28858i	0.357679	−	0.619517i	0.987573	+	0.157164i	$0.0502350\pi$
$180$	−2.24720	+	1.78146i	−0.167496	+	0.132782i
$181$	0.422168			0.0313795			0.0156898	−	0.999877i	$-0.495006\pi$
$181$	0.422168			0.0313795			0.0156898	+	0.999877i	$0.495006\pi$
$182$	6.28805	+	5.85888i	0.466101	+	0.434289i
$183$	−1.32306	+	6.93753i	−0.0978035	+	0.512837i
$184$	4.28246	−	7.41743i	0.315707	−	0.546820i
$185$	−5.64309			−0.414888
$186$	0.658126	−	3.45091i	0.0482562	−	0.253033i
$187$	−3.42178			−0.250225
$188$	−1.83515			−0.133842
$189$	−3.64345	+	13.2561i	−0.265022	+	0.964242i
$190$	1.78195			0.129276
$191$	8.95130			0.647693			0.323847	−	0.946110i	$-0.395024\pi$
$191$	8.95130			0.647693			0.323847	+	0.946110i	$0.395024\pi$
$192$	−0.452630	+	2.37338i	−0.0326657	+	0.171284i
$193$	−22.7000			−1.63398			−0.816990	−	0.576651i	$-0.804359\pi$
$193$	−22.7000			−1.63398			−0.816990	+	0.576651i	$0.804359\pi$
$194$	−9.97729	+	17.2812i	−0.716327	+	1.24072i
$195$	−0.613066	+	3.21464i	−0.0439026	+	0.230205i
$196$	5.54420	−	3.74624i	0.396014	−	0.267588i
$197$	3.56585			0.254056			0.127028	−	0.991899i	$-0.459456\pi$
$197$	3.56585			0.254056			0.127028	+	0.991899i	$0.459456\pi$
$198$	−3.47006	−	23.4837i	−0.246606	−	1.66891i
$199$	8.23861	−	14.2697i	0.584020	−	1.01155i	−0.410977	−	0.911646i	$-0.634812\pi$
$199$	8.23861	−	14.2697i	0.584020	−	1.01155i	0.994997	−	0.0999063i	$-0.0318543\pi$
$200$	−0.897555	−	1.55461i	−0.0634667	−	0.109928i
$201$	2.41986	−	12.6886i	0.170684	−	0.894987i
$202$	16.2727	+	28.1852i	1.14495	+	1.98311i
$203$	−5.60441	+	24.3209i	−0.393352	+	1.70699i
$204$	0.931837	+	0.804263i	0.0652417	+	0.0563097i
$205$	−7.45897			−0.520957
$206$	7.15232	−	12.3882i	0.498326	−	0.863125i
$207$	−11.2167	+	8.89202i	−0.779617	+	0.618038i
$208$	−4.72172	−	8.17826i	−0.327392	−	0.567060i
$209$	−2.38513	+	4.13117i	−0.164983	+	0.285759i
$210$	7.21013	+	3.17610i	0.497547	+	0.219172i
$211$	13.1358	+	22.7518i	0.904304	+	1.56630i	0.821849	+	0.569705i	$0.192943\pi$
$211$	13.1358	+	22.7518i	0.904304	+	1.56630i	0.0824548	+	0.996595i	$0.473724\pi$
$212$	−3.77070	+	6.53105i	−0.258973	+	0.448554i
$213$	2.04631	−	10.7299i	0.140211	−	0.735200i
$214$	8.53208	+	14.7780i	0.583241	+	1.01020i
$215$	1.26959	+	2.19900i	0.0865855	+	0.149971i
$216$	4.99688	−	7.87632i	0.339995	−	0.535916i
$217$	−2.98454	+	0.913806i	−0.202604	+	0.0620332i
$218$	4.61379	−	7.99132i	0.312485	−	0.541240i
$219$	8.74921	+	7.55138i	0.591217	+	0.510275i
$220$	−4.39945			−0.296611
$221$	1.40472			0.0944918
$222$	−15.8694	+	5.52715i	−1.06508	+	0.370958i
$223$	1.65477	−	2.86615i	0.110812	−	0.191932i	−0.805286	−	0.592886i	$-0.797988\pi$
$223$	1.65477	−	2.86615i	0.110812	−	0.191932i	0.916098	+	0.400955i	$0.131322\pi$
$224$	−12.6562	+	3.87506i	−0.845627	+	0.258914i
$225$	0.438533	+	2.96778i	0.0292355	+	0.197852i
$226$	12.9734	+	22.4705i	0.862976	+	1.49472i
$227$	−8.60251	−	14.9000i	−0.570968	−	0.988946i	−0.996467	−	0.0839872i	$-0.973235\pi$
$227$	−8.60251	−	14.9000i	−0.570968	−	0.988946i	0.425498	−	0.904959i	$-0.360099\pi$
$228$	1.62053	−	0.564416i	0.107322	−	0.0373794i
$229$	2.03962	−	3.53273i	0.134782	−	0.233450i	−0.790732	−	0.612162i	$-0.790300\pi$
$229$	2.03962	−	3.53273i	0.134782	−	0.233450i	0.925514	+	0.378713i	$0.123633\pi$
$230$	4.10153	+	7.10406i	0.270447	+	0.468428i
$231$	−17.0140	+	12.4644i	−1.11944	+	0.820094i
$232$	8.46694	−	14.6652i	0.555882	−	0.962816i
$233$	9.57801	+	16.5896i	0.627476	+	1.08682i	0.988056	+	0.154092i	$0.0492453\pi$
$233$	9.57801	+	16.5896i	0.627476	+	1.08682i	−0.360580	+	0.932728i	$0.617421\pi$
$234$	1.42454	+	9.64060i	0.0931252	+	0.630226i
$235$	−0.959920	+	1.66263i	−0.0626183	+	0.108458i
$236$	−4.87661			−0.317440
$237$	1.69122	−	8.86797i	0.109856	−	0.576036i
$238$	0.759398	−	3.29549i	0.0492245	−	0.213615i
$239$	−0.0833779	−	0.144415i	−0.00539327	−	0.00934141i	0.863316	−	0.504663i	$-0.168383\pi$
$239$	−0.0833779	−	0.144415i	−0.00539327	−	0.00934141i	−0.868709	+	0.495322i	$0.835050\pi$
$240$	−6.55349	−	5.65627i	−0.423026	−	0.365111i
$241$	11.3477	+	19.6548i	0.730969	+	1.26608i	0.956469	+	0.291832i	$0.0942650\pi$
$241$	11.3477	+	19.6548i	0.730969	+	1.26608i	−0.225500	+	0.974243i	$0.572402\pi$
$242$	8.75340	−	15.1613i	0.562690	−	0.974608i
$243$	−12.6091	+	9.16568i	−0.808877	+	0.587978i
$244$	3.89771			0.249525
$245$	−0.494028	−	6.98255i	−0.0315623	−	0.446098i
$246$	−20.9759	+	7.30572i	−1.33738	+	0.465796i
$247$	0.979155	−	1.69595i	0.0623021	−	0.107910i
$248$	2.11777			0.134478
$249$	−22.1816	−	19.1448i	−1.40570	−	1.21325i
$250$	1.71927			0.108736
$251$	13.3004			0.839511			0.419756	−	0.907637i	$-0.362116\pi$
$251$	13.3004			0.839511			0.419756	+	0.907637i	$0.362116\pi$
$252$	7.56300	+	0.604653i	0.476424	+	0.0380895i
$253$	−21.9595			−1.38058
$254$	36.3863			2.28308
$255$	1.21607	−	0.423547i	0.0761535	−	0.0265235i
$256$	18.5357			1.15848
$257$	−6.23155	+	10.7934i	−0.388713	+	0.673271i	−0.992277	−	0.124044i	$-0.960414\pi$
$257$	−6.23155	+	10.7934i	−0.388713	+	0.673271i	0.603563	+	0.797315i	$0.293747\pi$
$258$	5.72414	+	4.94047i	0.356369	+	0.307580i
$259$	10.9234	+	10.1779i	0.678750	+	0.632424i
$260$	1.80608			0.112008
$261$	−22.1769	+	17.5806i	−1.37271	+	1.08821i
$262$	−12.2248	+	21.1739i	−0.755248	+	1.30813i
$263$	−2.69633	−	4.67018i	−0.166263	−	0.287976i	0.770840	−	0.637029i	$-0.219837\pi$
$263$	−2.69633	−	4.67018i	−0.166263	−	0.287976i	−0.937103	+	0.349053i	$0.886503\pi$
$264$	13.5139	−	4.70675i	0.831722	−	0.289681i
$265$	3.94471	+	6.83244i	0.242322	+	0.419713i
$266$	−3.44936	−	3.21394i	−0.211494	−	0.197059i
$267$	−27.7460	+	9.66366i	−1.69803	+	0.591406i
$268$	−7.12884			−0.435463
$269$	11.5676	−	20.0357i	0.705289	−	1.22160i	−0.261298	−	0.965258i	$-0.584150\pi$
$269$	11.5676	−	20.0357i	0.705289	−	1.22160i	0.966587	−	0.256339i	$-0.0825162\pi$
$270$	4.14003	+	7.91638i	0.251954	+	0.481776i
$271$	−3.01396	−	5.22033i	−0.183085	−	0.317113i	0.759845	−	0.650105i	$-0.225275\pi$
$271$	−3.01396	−	5.22033i	−0.183085	−	0.317113i	−0.942930	+	0.332992i	$0.891942\pi$
$272$	−1.85794	+	3.21805i	−0.112654	+	0.195123i
$273$	6.98466	−	5.11692i	0.422731	−	0.309690i
$274$	−0.480178	−	0.831693i	−0.0290086	−	0.0502444i
$275$	−2.30123	+	3.98585i	−0.138770	+	0.240356i
$276$	5.98013	+	5.16141i	0.359962	+	0.310681i
$277$	−4.98378	−	8.63216i	−0.299446	−	0.518656i	0.676563	−	0.736385i	$-0.263469\pi$
$277$	−4.98378	−	8.63216i	−0.299446	−	0.518656i	−0.976009	+	0.217728i	$0.930135\pi$
$278$	11.8841	+	20.5838i	0.712760	+	1.23454i
$279$	−3.29081	−	1.30256i	−0.197016	−	0.0779823i
$280$	−1.06649	+	4.62812i	−0.0637347	+	0.276583i
$281$	−11.8821	+	20.5804i	−0.708828	+	1.22773i	0.256464	+	0.966554i	$0.417443\pi$
$281$	−11.8821	+	20.5804i	−0.708828	+	1.22773i	−0.965292	+	0.261173i	$0.915891\pi$
$282$	−1.07099	+	5.61581i	−0.0637768	+	0.334416i
$283$	18.0998			1.07592			0.537961	−	0.842970i	$-0.319195\pi$
$283$	18.0998			1.07592			0.537961	+	0.842970i	$0.319195\pi$
$284$	−6.02837			−0.357718
$285$	0.336303	−	1.76342i	0.0199209	−	0.104456i
$286$	−7.47539	+	12.9478i	−0.442029	+	0.765617i
$287$	14.4385	+	13.4530i	0.852277	+	0.794107i
$288$	−13.9549	−	5.52361i	−0.822303	−	0.325482i
$289$	8.22363	+	14.2437i	0.483743	+	0.837867i
$290$	8.10923	+	14.0456i	0.476190	+	0.824786i
$291$	15.2184	+	13.1349i	0.892120	+	0.769983i
$292$	3.18915	−	5.52376i	0.186631	−	0.323254i
$293$	−10.7702	−	18.6545i	−0.629200	−	1.08981i	−0.987713	−	0.156281i	$-0.950049\pi$
$293$	−10.7702	−	18.6545i	−0.629200	−	1.08981i	0.358513	−	0.933525i	$-0.383284\pi$
$294$	−8.22838	−	19.1523i	−0.479889	−	1.11698i
$295$	−2.55082	+	4.41816i	−0.148515	+	0.257235i
$296$	−5.06498	−	8.77280i	−0.294396	−	0.509909i
$297$	−23.8943	−	0.998037i	−1.38649	−	0.0579120i
$298$	5.07379	−	8.78806i	0.293917	−	0.509078i
$299$	9.01491			0.521345
$300$	1.56353	−	0.544562i	0.0902704	−	0.0314403i
$301$	1.50855	−	6.54649i	0.0869512	−	0.377333i
$302$	−17.5116	−	30.3309i	−1.00768	−	1.74535i
$303$	30.9632	−	10.7842i	1.77879	−	0.619535i
$304$	2.59014	+	4.48625i	0.148555	+	0.257304i
$305$	2.03879	−	3.53128i	0.116741	−	0.202201i
$306$	3.00497	−	2.38218i	0.171783	−	0.136180i
$307$	4.40118			0.251189			0.125594	−	0.992082i	$-0.459916\pi$
$307$	4.40118			0.251189			0.125594	+	0.992082i	$0.459916\pi$
$308$	8.51610	+	7.93486i	0.485250	+	0.452130i
$309$	−10.9095	−	9.41591i	−0.620619	−	0.535652i
$310$	−1.01415	+	1.75655i	−0.0575997	+	0.0997656i
$311$	−14.1325			−0.801380			−0.400690	−	0.916214i	$-0.631230\pi$
$311$	−14.1325			−0.801380			−0.400690	+	0.916214i	$0.631230\pi$
$312$	−5.54777	+	1.93224i	−0.314081	+	0.109391i
$313$	−8.26589			−0.467216			−0.233608	−	0.972331i	$-0.575053\pi$
$313$	−8.26589			−0.467216			−0.233608	+	0.972331i	$0.575053\pi$
$314$	−33.4116			−1.88553
$315$	4.50381	−	6.53572i	0.253761	−	0.368246i
$316$	−4.98228			−0.280275
$317$	0.134195			0.00753715			0.00376858	−	0.999993i	$-0.498800\pi$
$317$	0.134195			0.00753715			0.00376858	+	0.999993i	$0.498800\pi$
$318$	17.7853	+	15.3504i	0.997349	+	0.860805i
$319$	−43.4166			−2.43087
$320$	0.697485	−	1.20808i	0.0389906	−	0.0675337i
$321$	16.2345	−	5.65433i	0.906122	−	0.315594i
$322$	4.87349	−	21.1490i	0.271589	−	1.17859i
$323$	−0.770572			−0.0428758
$324$	6.27244	+	5.88796i	0.348469	+	0.327109i
$325$	0.944711	−	1.63629i	0.0524032	−	0.0907649i
$326$	−16.6878	−	28.9040i	−0.924249	−	1.60085i
$327$	−7.03745	−	6.07398i	−0.389172	−	0.335892i
$328$	−6.69483	−	11.5958i	−0.369660	−	0.640271i
$329$	4.85686	−	1.48707i	0.267768	−	0.0819850i
$330$	−2.56751	+	13.4629i	−0.141337	+	0.741107i
$331$	0.441708			0.0242785			0.0121392	−	0.999926i	$-0.496136\pi$
$331$	0.441708			0.0242785			0.0121392	+	0.999926i	$0.496136\pi$
$332$	−8.08536	+	14.0042i	−0.443742	+	0.768583i
$333$	2.47468	+	16.7474i	0.135612	+	0.917753i
$334$	4.36739	+	7.56454i	0.238973	+	0.413913i
$335$	−3.72891	+	6.45866i	−0.203732	+	0.352874i
$336$	2.48405	+	22.7689i	0.135516	+	1.24214i
$337$	−6.10063	−	10.5666i	−0.332323	−	0.575600i	0.650644	−	0.759383i	$-0.274499\pi$
$337$	−6.10063	−	10.5666i	−0.332323	−	0.575600i	−0.982967	+	0.183783i	$0.941166\pi$
$338$	−8.10643	+	14.0407i	−0.440931	+	0.763716i
$339$	24.6852	−	8.59763i	1.34072	−	0.466959i
$340$	−0.355335	−	0.615459i	−0.0192708	−	0.0333780i
$341$	−2.71486	−	4.70228i	−0.147018	−	0.254643i
$342$	−0.781444	−	5.28844i	−0.0422557	−	0.285966i
$343$	−11.6374	+	14.4073i	−0.628363	+	0.777920i
$344$	−2.27906	+	3.94744i	−0.122879	+	0.212832i
$345$	7.80424	−	2.71814i	0.420166	−	0.146340i
$346$	−19.3864			−1.04222
$347$	4.82105			0.258808			0.129404	−	0.991592i	$-0.458694\pi$
$347$	4.82105			0.258808			0.129404	+	0.991592i	$0.458694\pi$
$348$	11.8235	+	10.2047i	0.633804	+	0.547032i
$349$	−6.69861	+	11.6023i	−0.358569	+	0.621059i	−0.987722	−	0.156222i	$-0.950068\pi$
$349$	−6.69861	+	11.6023i	−0.358569	+	0.621059i	0.629153	+	0.777281i	$0.283402\pi$
$350$	−3.32803	−	3.10088i	−0.177890	−	0.165749i
$351$	9.80918	+	0.409718i	0.523575	+	0.0218691i
$352$	−11.5126	−	19.9404i	−0.613622	−	1.06283i
$353$	16.2099	+	28.0764i	0.862767	+	1.49436i	0.869248	+	0.494377i	$0.164604\pi$
$353$	16.2099	+	28.0764i	0.862767	+	1.49436i	−0.00648100	+	0.999979i	$0.502063\pi$
$354$	−2.84598	+	14.9230i	−0.151262	+	0.793151i
$355$	−3.15328	+	5.46164i	−0.167359	+	0.289874i
$356$	8.10735	+	14.0423i	0.429689	+	0.744243i
$357$	−3.11789	−	1.37345i	−0.165016	−	0.0726905i
$358$	−8.22742	+	14.2503i	−0.434832	+	0.753152i
$359$	−17.6749	−	30.6138i	−0.932846	−	1.61574i	−0.778430	−	0.627731i	$-0.783984\pi$
$359$	−17.6749	−	30.6138i	−0.932846	−	1.61574i	−0.154416	−	0.988006i	$-0.549350\pi$
$360$	−4.22013	+	3.34549i	−0.222420	+	0.176323i
$361$	8.96288	−	15.5242i	0.471730	−	0.817061i
$362$	−0.725821			−0.0381483
$363$	−13.3516	−	11.5237i	−0.700779	−	0.604838i
$364$	−3.49606	−	3.25745i	−0.183243	−	0.170737i
$365$	−3.33632	−	5.77867i	−0.174631	−	0.302469i
$366$	2.27470	−	11.9275i	0.118900	−	0.623460i
$367$	9.33497	+	16.1686i	0.487282	+	0.843996i	0.999893	−	0.0146242i	$-0.00465521\pi$
$367$	9.33497	+	16.1686i	0.487282	+	0.843996i	−0.512611	+	0.858621i	$0.671322\pi$
$368$	−11.9235	+	20.6521i	−0.621554	+	1.07656i
$369$	3.27100	+	22.1365i	0.170282	+	1.15238i
$370$	9.70199			0.504382
$371$	4.68715	−	20.3404i	0.243345	−	1.05602i
$372$	−0.365909	+	1.91866i	−0.0189715	+	0.0994778i
$373$	5.80962	−	10.0626i	0.300811	−	0.521020i	−0.675509	−	0.737352i	$-0.736076\pi$
$373$	5.80962	−	10.0626i	0.300811	−	0.521020i	0.976320	+	0.216332i	$0.0694094\pi$
$374$	5.88296			0.304201
$375$	0.324473	−	1.70139i	0.0167557	−	0.0878592i
$376$	−3.44632			−0.177731
$377$	17.8236			0.917961
$378$	6.26408	−	22.7909i	0.322189	−	1.17224i
$379$	30.8650			1.58543			0.792714	−	0.609593i	$-0.208667\pi$
$379$	30.8650			1.58543			0.792714	+	0.609593i	$0.208667\pi$
$380$	−0.990739			−0.0508239
$381$	6.86707	−	36.0078i	0.351811	−	1.84474i
$382$	−15.3897			−0.787405
$383$	13.7713	−	23.8527i	0.703683	−	1.21881i	−0.263482	−	0.964664i	$-0.584871\pi$
$383$	13.7713	−	23.8527i	0.703683	−	1.21881i	0.967165	−	0.254150i	$-0.0817957\pi$
$384$	4.02473	−	21.1038i	0.205386	−	1.07695i
$385$	11.6434	−	3.56498i	0.593405	−	0.181688i
$386$	39.0274			1.98644
$387$	5.96938	−	4.73220i	0.303441	−	0.240551i
$388$	5.54722	−	9.60807i	0.281618	−	0.487776i
$389$	−9.56351	−	16.5645i	−0.484889	−	0.839853i	0.514960	−	0.857214i	$-0.327807\pi$
$389$	−9.56351	−	16.5645i	−0.484889	−	0.839853i	−0.999849	+	0.0173614i	$0.994473\pi$
$390$	1.05403	−	5.52683i	0.0533727	−	0.279862i
$391$	−1.77363	−	3.07202i	−0.0896964	−	0.155359i
$392$	10.4117	−	7.03524i	0.525871	−	0.355333i
$393$	18.6465	+	16.0937i	0.940593	+	0.811819i
$394$	−6.13065			−0.308858
$395$	−2.60610	+	4.51390i	−0.131127	+	0.227119i
$396$	1.92930	+	13.0566i	0.0969510	+	0.656117i
$397$	−5.02935	−	8.71109i	−0.252416	−	0.437197i	0.711775	−	0.702408i	$-0.247892\pi$
$397$	−5.02935	−	8.71109i	−0.252416	−	0.437197i	−0.964190	+	0.265211i	$0.914558\pi$
$398$	−14.1644	+	24.5335i	−0.709997	+	1.22975i
$399$	−3.83150	+	2.80693i	−0.191815	+	0.140522i
$400$	2.49903	+	4.32844i	0.124951	+	0.216422i
$401$	7.85979	−	13.6135i	0.392499	−	0.679828i	−0.600279	−	0.799790i	$-0.704944\pi$
$401$	7.85979	−	13.6135i	0.392499	−	0.679828i	0.992778	+	0.119962i	$0.0382773\pi$
$402$	−4.16039	+	21.8152i	−0.207501	+	1.08804i
$403$	1.11452	+	1.93040i	0.0555180	+	0.0961600i
$404$	−9.04741	−	15.6706i	−0.450125	−	0.779640i
$405$	8.61538	−	2.60293i	0.428102	−	0.129341i
$406$	9.63549	−	41.8142i	0.478201	−	2.07520i
$407$	−12.9861	+	22.4925i	−0.643695	+	1.11491i
$408$	1.74994	+	1.51036i	0.0866350	+	0.0747741i
$409$	−12.4895			−0.617566			−0.308783	−	0.951132i	$-0.599922\pi$
$409$	−12.4895			−0.617566			−0.308783	+	0.951132i	$0.599922\pi$
$410$	12.8240			0.633331
$411$	−0.913664	+	0.318220i	−0.0450677	+	0.0156967i
$412$	−3.97658	+	6.88764i	−0.195912	+	0.339330i
$413$	12.9063	−	3.95164i	0.635077	−	0.194448i
$414$	19.2846	−	15.2878i	0.947786	−	0.751354i
$415$	8.45847	+	14.6505i	0.415210	+	0.719165i
$416$	4.72619	+	8.18600i	0.231720	+	0.401352i
$417$	22.6126	−	7.87574i	1.10734	−	0.385677i
$418$	4.10069	−	7.10260i	0.200571	−	0.347400i
$419$	1.57397	+	2.72619i	0.0768934	+	0.133183i	0.901908	−	0.431928i	$-0.142167\pi$
$419$	1.57397	+	2.72619i	0.0768934	+	0.133183i	−0.825015	+	0.565111i	$0.808833\pi$
$420$	−4.00873	−	1.76587i	−0.195606	−	0.0861654i
$421$	2.08259	−	3.60716i	0.101499	−	0.175802i	−0.810803	−	0.585319i	$-0.800969\pi$
$421$	2.08259	−	3.60716i	0.101499	−	0.175802i	0.912303	+	0.409517i	$0.134303\pi$
$422$	−22.5839	−	39.1165i	−1.09937	−	1.90416i
$423$	5.35527	+	2.11971i	0.260382	+	0.103064i
$424$	−7.08118	+	12.2650i	−0.343893	+	0.595640i
$425$	−0.743466			−0.0360634
$426$	−3.51815	+	18.4476i	−0.170455	+	0.893788i
$427$	−10.3156	+	3.15841i	−0.499205	+	0.152846i
$428$	−4.74371	−	8.21635i	−0.229296	−	0.397152i
$429$	11.4023	+	9.84123i	0.550507	+	0.475139i
$430$	−2.18277	−	3.78067i	−0.105263	−	0.182320i
$431$	5.66305	−	9.80869i	0.272780	−	0.472468i	−0.696793	−	0.717272i	$-0.745390\pi$
$431$	5.66305	−	9.80869i	0.272780	−	0.472468i	0.969573	+	0.244804i	$0.0787237\pi$
$432$	−13.9126	+	21.9297i	−0.669372	+	1.05510i
$433$	40.8240			1.96188			0.980938	−	0.194319i	$-0.0622497\pi$
$433$	40.8240			1.96188			0.980938	+	0.194319i	$0.0622497\pi$
$434$	5.13124	−	1.57108i	0.246307	−	0.0754142i
$435$	15.4299	−	5.37410i	0.739809	−	0.257668i
$436$	−2.56520	+	4.44306i	−0.122851	+	0.212784i
$437$	−4.94520			−0.236561
$438$	−15.0422	−	12.9829i	−0.718746	−	0.620345i
$439$	−16.9278			−0.807918			−0.403959	−	0.914777i	$-0.632366\pi$
$439$	−16.9278			−0.807918			−0.403959	+	0.914777i	$0.632366\pi$
$440$	−8.26193			−0.393872
$441$	−20.5060	+	4.52824i	−0.976475	+	0.215630i
$442$	−2.41510			−0.114874
$443$	9.33503			0.443521			0.221760	−	0.975101i	$-0.428820\pi$
$443$	9.33503			0.443521			0.221760	+	0.975101i	$0.428820\pi$
$444$	8.82313	−	3.07301i	0.418727	−	0.145839i
$445$	16.9630			0.804121
$446$	−2.84500	+	4.92768i	−0.134715	+	0.233333i
$447$	−7.73909	−	6.67955i	−0.366046	−	0.315932i
$448$	−3.52903	+	1.08052i	−0.166731	+	0.0510497i
$449$	−35.6523			−1.68254			−0.841268	−	0.540618i	$-0.818191\pi$
$449$	−35.6523			−1.68254			−0.841268	+	0.540618i	$0.818191\pi$
$450$	−0.753956	−	5.10241i	−0.0355418	−	0.240530i
$451$	−17.1648	+	29.7304i	−0.808260	+	1.39995i
$452$	−7.21301	−	12.4933i	−0.339271	−	0.587635i
$453$	−33.3203	+	11.6051i	−1.56553	+	0.545257i
$454$	14.7900	+	25.6171i	0.694131	+	1.20227i
$455$	−4.77991	+	1.46351i	−0.224086	+	0.0686105i
$456$	3.04328	−	1.05994i	0.142515	−	0.0496364i
$457$	−12.8930			−0.603108			−0.301554	−	0.953449i	$-0.597505\pi$
$457$	−12.8930			−0.603108			−0.301554	+	0.953449i	$0.597505\pi$
$458$	−3.50667	+	6.07372i	−0.163856	+	0.283806i
$459$	−1.79028	−	3.42329i	−0.0835631	−	0.159786i
$460$	−2.28039	−	3.94975i	−0.106324	−	0.184158i
$461$	−18.5507	+	32.1308i	−0.863992	+	1.49648i	0.00405225	+	0.999992i	$0.498710\pi$
$461$	−18.5507	+	32.1308i	−0.863992	+	1.49648i	−0.868044	+	0.496487i	$0.834623\pi$
$462$	29.2517	−	21.4296i	1.36091	−	0.996994i
$463$	−11.4001	−	19.7456i	−0.529810	−	0.917658i	−0.999395	−	0.0347706i	$-0.988930\pi$
$463$	−11.4001	−	19.7456i	−0.529810	−	0.917658i	0.469585	−	0.882887i	$-0.344403\pi$
$464$	−23.5742	+	40.8317i	−1.09440	+	1.89556i
$465$	1.54689	+	1.33511i	0.0717352	+	0.0619142i
$466$	−16.4672	−	28.5220i	−0.762827	−	1.32126i
$467$	5.78367	+	10.0176i	0.267636	+	0.463559i	0.968251	−	0.249980i	$-0.0804242\pi$
$467$	5.78367	+	10.0176i	0.267636	+	0.463559i	−0.700615	+	0.713540i	$0.747091\pi$
$468$	−0.792024	−	5.36003i	−0.0366113	−	0.247768i
$469$	18.8670	−	5.77669i	0.871196	−	0.266743i
$470$	1.65036	−	2.85851i	0.0761255	−	0.131853i
$471$	−6.30568	+	33.0641i	−0.290550	+	1.52351i
$472$	−9.15801			−0.421532
$473$	11.6865			0.537347
$474$	−2.90766	+	15.2464i	−0.133553	+	0.700292i
$475$	−0.518230	+	0.897600i	−0.0237780	+	0.0411847i
$476$	−0.422214	+	1.83224i	−0.0193521	+	0.0839806i
$477$	18.5473	−	14.7033i	0.849220	−	0.673216i
$478$	0.143349	+	0.248288i	0.00655664	+	0.0113564i
$479$	−2.74988	−	4.76294i	−0.125645	−	0.217624i	0.796340	−	0.604850i	$-0.206767\pi$
$479$	−2.74988	−	4.76294i	−0.125645	−	0.217624i	−0.921985	+	0.387225i	$0.873434\pi$
$480$	6.55969	+	5.66163i	0.299408	+	0.258417i
$481$	5.33109	−	9.23372i	0.243077	−	0.421021i
$482$	−19.5097	−	33.7919i	−0.888644	−	1.53918i
$483$	−20.0093	−	8.81419i	−0.910453	−	0.401060i
$484$	−4.86676	+	8.42948i	−0.221216	+	0.383158i
$485$	−5.80321	−	10.0515i	−0.263510	−	0.456413i
$486$	21.6785	−	15.7583i	0.983357	−	0.714810i
$487$	0.825893	−	1.43049i	0.0374248	−	0.0648217i	−0.846706	−	0.532061i	$-0.821418\pi$
$487$	0.825893	−	1.43049i	0.0374248	−	0.0648217i	0.884131	+	0.467239i	$0.154751\pi$
$488$	7.31969			0.331347
$489$	−31.7528	+	11.0592i	−1.43591	+	0.500114i
$490$	0.849368	+	12.0049i	0.0383705	+	0.542325i
$491$	4.06248	+	7.03643i	0.183337	+	0.317549i	0.943015	−	0.332750i	$-0.107977\pi$
$491$	4.06248	+	7.03643i	0.183337	+	0.317549i	−0.759678	+	0.650300i	$0.774643\pi$
$492$	11.6623	−	4.06187i	0.525778	−	0.183123i
$493$	−3.50669	−	6.07376i	−0.157933	−	0.273548i
$494$	−1.68343	+	2.91579i	−0.0757412	+	0.131188i
$495$	12.8383	+	5.08162i	0.577038	+	0.228402i
$496$	−5.89642			−0.264757
$497$	15.9545	−	4.88494i	0.715657	−	0.219120i
$498$	38.1362	+	32.9151i	1.70892	+	1.47496i
$499$	−5.83729	+	10.1105i	−0.261313	+	0.452607i	−0.966591	−	0.256323i	$-0.917489\pi$
$499$	−5.83729	+	10.1105i	−0.261313	+	0.452607i	0.705278	+	0.708931i	$0.250822\pi$
$500$	−0.955889			−0.0427486
$501$	8.31010	−	2.89433i	0.371268	−	0.129309i
$502$	−22.8669			−1.02060
$503$	5.08007			0.226509			0.113255	−	0.993566i	$-0.463872\pi$
$503$	5.08007			0.226509			0.113255	+	0.993566i	$0.463872\pi$
$504$	14.2029	+	1.13551i	0.632648	+	0.0505795i
$505$	−18.9298			−0.842367
$506$	37.7543			1.67838
$507$	12.3648	+	10.6720i	0.549140	+	0.473959i
$508$	−20.2302			−0.897571
$509$	10.3876	−	17.9919i	0.460424	−	0.797478i	−0.538558	−	0.842588i	$-0.681031\pi$
$509$	10.3876	−	17.9919i	0.460424	−	0.797478i	0.998982	+	0.0451108i	$0.0143641\pi$
$510$	−2.09076	+	0.728191i	−0.0925803	+	0.0322448i
$511$	−3.96425	+	17.2033i	−0.175368	+	0.761028i
$512$	−7.06009			−0.312015
$513$	−5.38091	−	0.224754i	−0.237573	−	0.00992315i
$514$	10.7137	−	18.5567i	0.472562	−	0.818501i
$515$	4.16009	+	7.20549i	0.183315	+	0.317512i
$516$	−3.18254	−	2.74683i	−0.140103	−	0.120922i
$517$	4.41800	+	7.65220i	0.194303	+	0.336543i
$518$	−18.7803	−	17.4985i	−0.825161	−	0.768842i
$519$	−3.65874	+	19.1847i	−0.160601	+	0.842117i
$520$	3.39172			0.148737
$521$	−7.15028	+	12.3846i	−0.313259	+	0.542581i	−0.979066	−	0.203543i	$-0.934754\pi$
$521$	−7.15028	+	12.3846i	−0.313259	+	0.542581i	0.665807	+	0.746124i	$0.268088\pi$
$522$	38.1280	−	30.2258i	1.66882	−	1.32295i
$523$	−9.31897	−	16.1409i	−0.407490	−	0.705794i	0.587118	−	0.809502i	$-0.300263\pi$
$523$	−9.31897	−	16.1409i	−0.407490	−	0.705794i	−0.994608	+	0.103708i	$0.966929\pi$
$524$	6.79679	−	11.7724i	0.296919	−	0.514279i
$525$	−3.69672	+	2.70819i	−0.161338	+	0.118195i
$526$	4.63572	+	8.02930i	0.202127	+	0.350094i
$527$	0.438549	−	0.759590i	0.0191035	−	0.0330882i
$528$	−37.6262	+	13.1048i	−1.63747	+	0.570315i
$529$	0.117595	+	0.203681i	0.00511283	+	0.00885568i
$530$	−6.78202	−	11.7468i	−0.294592	−	0.510249i
$531$	14.2307	+	5.63276i	0.617560	+	0.244441i
$532$	1.91779	+	1.78690i	0.0831469	+	0.0774720i
$533$	7.04658	−	12.2050i	0.305221	−	0.528658i
$534$	47.7028	−	16.6144i	2.06430	−	0.718977i
$535$	−9.92524			−0.429105
$536$	−13.3876			−0.578256
$537$	12.5493	+	10.8313i	0.541544	+	0.467403i
$538$	−19.8878	+	34.4467i	−0.857425	+	1.48510i
$539$	−28.9683	−	14.0993i	−1.24775	−	0.607302i
$540$	−2.30180	−	4.40139i	−0.0990535	−	0.189406i
$541$	−14.3876	−	24.9200i	−0.618570	−	1.07139i	−0.989747	−	0.142832i	$-0.954379\pi$
$541$	−14.3876	−	24.9200i	−0.618570	−	1.07139i	0.371177	−	0.928562i	$-0.378954\pi$
$542$	5.18181	+	8.97516i	0.222578	+	0.385516i
$543$	−0.136982	+	0.718272i	−0.00587846	+	0.0308240i
$544$	1.85970	−	3.22110i	0.0797340	−	0.138103i
$545$	2.68358	+	4.64809i	0.114952	+	0.199102i
$546$	−12.0085	+	8.79736i	−0.513917	+	0.376492i
$547$	16.5643	−	28.6902i	0.708239	−	1.22671i	−0.257271	−	0.966339i	$-0.582823\pi$
$547$	16.5643	−	28.6902i	0.708239	−	1.22671i	0.965510	−	0.260367i	$-0.0838434\pi$
$548$	0.266972	+	0.462409i	0.0114045	+	0.0197531i
$549$	−11.3741	−	4.50208i	−0.485436	−	0.192144i
$550$	3.95644	−	6.85276i	0.168703	−	0.292203i
$551$	−9.77727			−0.416526
$552$	11.2304	+	9.69287i	0.477997	+	0.412556i
$553$	13.1860	−	4.03727i	0.560724	−	0.171682i
$554$	8.56846	+	14.8410i	0.364039	+	0.630534i
$555$	1.83103	−	9.60108i	0.0777228	−	0.407543i
$556$	−6.60737	−	11.4443i	−0.280215	−	0.485347i
$557$	−3.56430	+	6.17354i	−0.151024	+	0.261581i	−0.931604	−	0.363474i	$-0.881590\pi$
$557$	−3.56430	+	6.17354i	−0.151024	+	0.261581i	0.780580	+	0.625056i	$0.214924\pi$
$558$	5.65780	+	2.23946i	0.239514	+	0.0948037i
$559$	−4.79760			−0.202917
$560$	2.96938	−	12.8859i	0.125479	−	0.544529i
$561$	1.11027	−	5.82177i	0.0468758	−	0.245795i
$562$	20.4286	−	35.3833i	0.861728	−	1.49256i
$563$	29.0206			1.22307			0.611537	−	0.791216i	$-0.290552\pi$
$563$	29.0206			1.22307			0.611537	+	0.791216i	$0.290552\pi$
$564$	0.595457	−	3.12231i	0.0250733	−	0.131473i
$565$	−15.0917			−0.634914
$566$	−31.1184			−1.30801
$567$	−21.3716	−	10.5002i	−0.897524	−	0.440966i
$568$	−11.3210			−0.475017
$569$	−21.2762			−0.891943			−0.445971	−	0.895047i	$-0.647142\pi$
$569$	−21.2762			−0.891943			−0.445971	+	0.895047i	$0.647142\pi$
$570$	−0.578195	+	3.03179i	−0.0242179	+	0.126988i
$571$	−10.6504			−0.445705			−0.222853	−	0.974852i	$-0.571537\pi$
$571$	−10.6504			−0.445705			−0.222853	+	0.974852i	$0.571537\pi$
$572$	4.15621	−	7.19876i	0.173780	−	0.300995i
$573$	−2.90445	+	15.2296i	−0.121335	+	0.636227i
$574$	−24.8236	−	23.1294i	−1.03612	−	0.965402i
$575$	−4.77125			−0.198975
$576$	−3.89118	−	1.54020i	−0.162132	−	0.0641749i
$577$	−10.2383	+	17.7333i	−0.426227	+	0.738248i	−0.996534	−	0.0831842i	$-0.973491\pi$
$577$	−10.2383	+	17.7333i	−0.426227	+	0.738248i	0.570307	+	0.821432i	$0.306824\pi$
$578$	−14.1386	−	24.4888i	−0.588090	−	1.01860i
$579$	7.36552	−	38.6215i	0.306101	−	1.60505i
$580$	−4.50861	−	7.80915i	−0.187210	−	0.324257i
$581$	10.0505	−	43.6150i	0.416963	−	1.80946i
$582$	−26.1646	−	22.5825i	−1.08456	−	0.936074i
$583$	36.3108			1.50384
$584$	5.98905	−	10.3733i	0.247829	−	0.429252i
$585$	−5.27042	−	2.08613i	−0.217905	−	0.0862507i
$586$	18.5168	+	32.0721i	0.764923	+	1.32489i
$587$	6.61348	−	11.4549i	0.272967	−	0.472794i	−0.696653	−	0.717408i	$-0.745328\pi$
$587$	6.61348	−	11.4549i	0.272967	−	0.472794i	0.969620	+	0.244615i	$0.0786615\pi$
$588$	4.57486	+	10.6484i	0.188664	+	0.439132i
$589$	−0.611377	−	1.05894i	−0.0251914	−	0.0436327i
$590$	4.38555	−	7.59600i	0.180550	−	0.312722i
$591$	−1.15702	+	6.06689i	−0.0475935	+	0.249558i
$592$	14.1022	+	24.4258i	0.579598	+	1.00389i
$593$	6.01696	+	10.4217i	0.247087	+	0.427967i	0.962716	−	0.270513i	$-0.0871934\pi$
$593$	6.01696	+	10.4217i	0.247087	+	0.427967i	−0.715629	+	0.698480i	$0.753860\pi$
$594$	41.0807	+	1.71589i	1.68556	+	0.0704040i
$595$	1.43914	+	1.34092i	0.0589991	+	0.0549723i
$596$	−2.82095	+	4.88603i	−0.115551	+	0.200140i
$597$	21.6051	+	18.6472i	0.884237	+	0.763179i
$598$	−15.4991			−0.633804
$599$	24.7789			1.01244			0.506220	−	0.862404i	$-0.331042\pi$
$599$	24.7789			1.01244			0.506220	+	0.862404i	$0.331042\pi$
$600$	2.93623	−	1.02266i	0.119871	−	0.0417499i
$601$	−11.2423	+	19.4722i	−0.458581	+	0.794286i	−0.998886	−	0.0471831i	$-0.984976\pi$
$601$	−11.2423	+	19.4722i	−0.458581	+	0.794286i	0.540305	+	0.841469i	$0.318309\pi$
$602$	−2.59360	+	11.2552i	−0.105707	+	0.458727i
$603$	20.8031	+	8.23423i	0.847167	+	0.335324i
$604$	9.73616	+	16.8635i	0.396159	+	0.686167i
$605$	5.09135	+	8.81847i	0.206993	+	0.358522i
$606$	−53.2340	+	18.5409i	−2.16248	+	0.753173i
$607$	−7.23803	+	12.5366i	−0.293782	+	0.508846i	−0.974701	−	0.223513i	$-0.928247\pi$
$607$	−7.23803	+	12.5366i	−0.293782	+	0.508846i	0.680918	+	0.732359i	$0.261581\pi$
$608$	−2.59259	−	4.49050i	−0.105143	−	0.182114i
$609$	−39.5608	−	17.4267i	−1.60308	−	0.706167i
$610$	−3.50522	+	6.07123i	−0.141922	+	0.245817i
$611$	−1.81369	−	3.14141i	−0.0733742	−	0.127088i
$612$	−1.67072	+	1.32445i	−0.0675348	+	0.0535379i
$613$	16.3703	−	28.3542i	0.661190	−	1.14521i	−0.319114	−	0.947716i	$-0.603385\pi$
$613$	16.3703	−	28.3542i	0.661190	−	1.14521i	0.980303	−	0.197498i	$-0.0632815\pi$
$614$	−7.56681			−0.305372
$615$	2.42023	−	12.6906i	0.0975932	−	0.511734i
$616$	15.9928	+	14.9012i	0.644368	+	0.600388i
$617$	13.8291	+	23.9527i	0.556738	+	0.964299i	0.997766	+	0.0668057i	$0.0212808\pi$
$617$	13.8291	+	23.9527i	0.556738	+	0.964299i	−0.441028	+	0.897494i	$0.645386\pi$
$618$	18.7564	+	16.1885i	0.754491	+	0.651196i
$619$	11.4743	+	19.8740i	0.461190	+	0.798805i	0.999021	−	0.0442479i	$-0.0140892\pi$
$619$	11.4743	+	19.8740i	0.461190	+	0.798805i	−0.537830	+	0.843053i	$0.680756\pi$
$620$	0.563851	−	0.976619i	0.0226448	−	0.0392219i
$621$	−11.4892	−	21.9692i	−0.461048	−	0.881595i
$622$	24.2976			0.974243
$623$	−32.8355	−	30.5945i	−1.31553	−	1.22574i
$624$	15.4464	−	5.37985i	0.618353	−	0.215366i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.2113			0.567998
$627$	−6.25481	−	5.39849i	−0.249793	−	0.215595i
$628$	18.5764			0.741278
$629$	−4.19545			−0.167283
$630$	−7.74327	+	11.2367i	−0.308499	+	0.447680i
$631$	11.7247			0.466755			0.233377	−	0.972386i	$-0.425022\pi$
$631$	11.7247			0.466755			0.233377	+	0.972386i	$0.425022\pi$
$632$	−9.35647			−0.372180
$633$	−42.9719	+	14.9667i	−1.70798	+	0.594872i
$634$	−0.230718			−0.00916297
$635$	−10.5819	+	18.3284i	−0.419930	+	0.727340i
$636$	−9.88835	−	8.53457i	−0.392099	−	0.338418i
$637$	11.8922	+	5.78812i	0.471185	+	0.229334i
$638$	74.6449			2.95522
$639$	17.5917	+	6.96311i	0.695918	+	0.275457i
$640$	−6.20195	+	10.7421i	−0.245154	+	0.424619i
$641$	10.2353	+	17.7281i	0.404271	+	0.700217i	0.994236	−	0.107211i	$-0.0341921\pi$
$641$	10.2353	+	17.7281i	0.404271	+	0.700217i	−0.589966	+	0.807428i	$0.700859\pi$
$642$	−27.9115	+	9.72131i	−1.10158	+	0.383670i
$643$	−6.02670	−	10.4386i	−0.237670	−	0.411656i	0.722375	−	0.691501i	$-0.243050\pi$
$643$	−6.02670	−	10.4386i	−0.237670	−	0.411656i	−0.960045	+	0.279845i	$0.909717\pi$
$644$	−2.70959	+	11.7585i	−0.106773	+	0.463351i
$645$	−4.15330	+	1.44655i	−0.163536	+	0.0569580i
$646$	1.32482			0.0521244
$647$	−1.33773	+	2.31702i	−0.0525916	+	0.0910913i	−0.891123	−	0.453762i	$-0.850081\pi$
$647$	−1.33773	+	2.31702i	−0.0525916	+	0.0910913i	0.838531	+	0.544854i	$0.183415\pi$
$648$	11.7793	+	11.0573i	0.462735	+	0.434371i
$649$	11.7401	+	20.3344i	0.460838	+	0.798196i
$650$	−1.62421	+	2.81322i	−0.0637069	+	0.110344i
$651$	−0.586335	−	5.37437i	−0.0229803	−	0.210638i
$652$	9.27814	+	16.0702i	0.363360	+	0.629358i
$653$	2.28406	−	3.95611i	0.0893822	−	0.154814i	−0.817868	−	0.575406i	$-0.804844\pi$
$653$	2.28406	−	3.95611i	0.0893822	−	0.154814i	0.907250	+	0.420591i	$0.138177\pi$
$654$	12.0993	+	10.4428i	0.473119	+	0.408346i
$655$	−7.11044	−	12.3156i	−0.277828	−	0.481212i
$656$	18.6402	+	32.2857i	0.727776	+	1.26055i
$657$	−15.6867	+	12.4356i	−0.611997	+	0.485158i
$658$	−8.35026	+	2.55668i	−0.325527	+	0.0996697i
$659$	9.40458	−	16.2892i	0.366350	−	0.634537i	−0.622641	−	0.782507i	$-0.713940\pi$
$659$	9.40458	−	16.2892i	0.366350	−	0.634537i	0.988992	+	0.147970i	$0.0472738\pi$
$660$	1.42750	−	7.48516i	0.0555654	−	0.291359i
$661$	−2.89274			−0.112515			−0.0562573	−	0.998416i	$-0.517917\pi$
$661$	−2.89274			−0.112515			−0.0562573	+	0.998416i	$0.517917\pi$
$662$	−0.759416			−0.0295155
$663$	−0.455794	+	2.38998i	−0.0177016	+	0.0928190i
$664$	−15.1839	+	26.2992i	−0.589249	+	1.02061i
$665$	2.62206	−	0.802822i	0.101679	−	0.0311321i
$666$	−4.25464	−	28.7933i	−0.164864	−	1.11572i
$667$	−22.5044	−	38.9788i	−0.871374	−	1.50926i
$668$	−2.42820	−	4.20577i	−0.0939500	−	0.162726i
$669$	4.33950	+	3.74539i	0.167775	+	0.144805i
$670$	6.41100	−	11.1042i	0.247678	−	0.428992i
$671$	−9.38345	−	16.2526i	−0.362244	−	0.627425i
$672$	−2.48640	−	22.7904i	−0.0959149	−	0.879159i
$673$	−12.6582	+	21.9247i	−0.487939	+	0.845136i	−0.999904	−	0.0138710i	$-0.995585\pi$
$673$	−12.6582	+	21.9247i	−0.487939	+	0.845136i	0.511965	+	0.859007i	$0.328918\pi$
$674$	10.4886	+	18.1669i	0.404007	+	0.699761i
$675$	−5.19163	−	0.216848i	−0.199826	−	0.00834649i
$676$	4.50705	−	7.80645i	0.173348	−	0.300248i
$677$	2.69033			0.103398			0.0516989	−	0.998663i	$-0.483536\pi$
$677$	2.69033			0.103398			0.0516989	+	0.998663i	$0.483536\pi$
$678$	−42.4406	+	14.7817i	−1.62992	+	0.567686i
$679$	−6.89545	+	29.9235i	−0.264623	+	1.14836i
$680$	−0.667302	−	1.15580i	−0.0255898	−	0.0443229i
$681$	28.1419	−	9.80156i	1.07840	−	0.375596i
$682$	4.66758	+	8.08449i	0.178731	+	0.309571i
$683$	−6.32531	+	10.9558i	−0.242031	+	0.419210i	−0.961293	−	0.275529i	$-0.911147\pi$
$683$	−6.32531	+	10.9558i	−0.242031	+	0.419210i	0.719262	+	0.694739i	$0.244480\pi$
$684$	0.434472	+	2.94029i	0.0166124	+	0.112425i
$685$	0.558584			0.0213424
$686$	20.0079	−	24.7700i	0.763905	−	0.945723i
$687$	5.34874	+	4.61647i	0.204067	+	0.176129i
$688$	6.34549	−	10.9907i	0.241920	−	0.419017i
$689$	−14.9065			−0.567891
$690$	−13.4176	+	4.67322i	−0.510799	+	0.177906i
$691$	20.6396			0.785166			0.392583	−	0.919717i	$-0.371582\pi$
$691$	20.6396			0.785166			0.392583	+	0.919717i	$0.371582\pi$
$692$	10.7785			0.409739
$693$	−15.6861	−	32.9918i	−0.595866	−	1.25325i
$694$	−8.28869			−0.314634
$695$	−13.8246			−0.524396
$696$	22.2038	+	19.1640i	0.841634	+	0.726409i
$697$	−5.54549			−0.210051
$698$	11.5167	−	19.9476i	0.435915	−	0.755026i
$699$	−31.3331	+	10.9130i	−1.18513	+	0.412768i
$700$	1.85033	+	1.72404i	0.0699360	+	0.0651627i
$701$	−19.3708			−0.731626			−0.365813	−	0.930688i	$-0.619209\pi$
$701$	−19.3708			−0.731626			−0.365813	+	0.930688i	$0.619209\pi$
$702$	−16.8646	−	0.704416i	−0.636514	−	0.0265865i
$703$	−2.92442	+	5.06524i	−0.110296	+	0.191039i
$704$	−3.21015	−	5.56015i	−0.120987	−	0.209556i
$705$	−2.51731	−	2.17267i	−0.0948074	−	0.0818276i
$706$	−27.8692	−	48.2709i	−1.04887	−	1.81670i
$707$	36.6429	+	34.1419i	1.37810	+	1.28404i
$708$	1.58233	−	8.29699i	0.0594674	−	0.311820i
$709$	14.1845			0.532711			0.266355	−	0.963875i	$-0.414181\pi$
$709$	14.1845			0.532711			0.266355	+	0.963875i	$0.414181\pi$
$710$	5.42134	−	9.39003i	0.203459	−	0.352402i
$711$	14.5391	+	5.75483i	0.545258	+	0.215823i
$712$	15.2252	+	26.3708i	0.570588	+	0.988287i
$713$	2.81442	−	4.87472i	0.105401	−	0.182560i
$714$	5.36049	+	2.36132i	0.200611	+	0.0883704i
$715$	−4.34800	−	7.53096i	−0.162606	−	0.281642i
$716$	4.57432	−	7.92296i	0.170950	−	0.296095i
$717$	0.272759	−	0.0949994i	0.0101864	−	0.00354782i
$718$	30.3879	+	52.6335i	1.13407	+	1.96426i
$719$	1.47355	+	2.55226i	0.0549542	+	0.0951834i	0.892194	−	0.451653i	$-0.149165\pi$
$719$	1.47355	+	2.55226i	0.0549542	+	0.0951834i	−0.837240	+	0.546836i	$0.815832\pi$
$720$	11.7499	−	9.31471i	0.437894	−	0.347139i
$721$	4.94307	−	21.4510i	0.184090	−	0.798876i
$722$	−15.4096	+	26.6902i	−0.573486	+	0.993307i
$723$	−37.1224	+	12.9294i	−1.38060	+	0.480849i
$724$	0.403546			0.0149977
$725$	−9.43334			−0.350346
$726$	22.9551	+	19.8124i	0.851942	+	0.735306i
$727$	−7.45252	+	12.9082i	−0.276399	+	0.478737i	−0.970487	−	0.241153i	$-0.922474\pi$
$727$	−7.45252	+	12.9082i	−0.276399	+	0.478737i	0.694088	+	0.719890i	$0.255808\pi$
$728$	−6.56542	−	6.11732i	−0.243331	−	0.226723i
$729$	−11.5030	−	24.4270i	−0.426039	−	0.904705i
$730$	5.73603	+	9.93509i	0.212300	+	0.367714i
$731$	0.943900	+	1.63488i	0.0349114	+	0.0604683i
$732$	−1.26470	+	6.63151i	−0.0467446	+	0.245108i
$733$	0.648040	−	1.12244i	0.0239359	−	0.0414582i	−0.853809	−	0.520586i	$-0.825714\pi$
$733$	0.648040	−	1.12244i	0.0239359	−	0.0414582i	0.877745	+	0.479128i	$0.159047\pi$
$734$	−16.0493	−	27.7983i	−0.592392	−	1.02605i
$735$	12.0403	+	1.42511i	0.444114	+	0.0525661i
$736$	11.9348	−	20.6716i	0.439921	−	0.761966i
$737$	17.1622	+	29.7258i	0.632177	+	1.09496i
$738$	−5.62374	−	38.0587i	−0.207013	−	1.40096i
$739$	8.55467	−	14.8171i	0.314689	−	0.545057i	−0.664683	−	0.747126i	$-0.731433\pi$
$739$	8.55467	−	14.8171i	0.314689	−	0.545057i	0.979371	+	0.202069i	$0.0647665\pi$
$740$	−5.39416			−0.198293
$741$	2.56775	+	2.21621i	0.0943287	+	0.0814145i
$742$	−8.05848	+	34.9706i	−0.295836	+	1.28381i
$743$	−1.23227	−	2.13436i	−0.0452076	−	0.0783019i	0.842536	−	0.538640i	$-0.181062\pi$
$743$	−1.23227	−	2.13436i	−0.0452076	−	0.0783019i	−0.887744	+	0.460338i	$0.847728\pi$
$744$	−0.687157	+	3.60314i	−0.0251924	+	0.132097i
$745$	2.95113	+	5.11150i	0.108121	+	0.187271i
$746$	−9.98831	+	17.3003i	−0.365698	+	0.633407i
$747$	39.7701	−	31.5276i	1.45511	−	1.15353i
$748$	−3.27084			−0.119594
$749$	19.2125	+	17.9012i	0.702009	+	0.654095i
$750$	−0.557856	+	2.92514i	−0.0203700	+	0.106811i
$751$	−16.1069	+	27.8980i	−0.587751	+	1.01801i	0.406776	+	0.913528i	$0.366653\pi$
$751$	−16.1069	+	27.8980i	−0.587751	+	1.01801i	−0.994526	+	0.104486i	$0.966680\pi$
$752$	9.59546			0.349911
$753$	−4.31560	+	22.6291i	−0.157269	+	0.824649i
$754$	−30.6435			−1.11597
$755$	20.3709			0.741374
$756$	−3.48273	+	12.6714i	−0.126666	+	0.460854i
$757$	15.0178			0.545831			0.272915	−	0.962038i	$-0.412012\pi$
$757$	15.0178			0.545831			0.272915	+	0.962038i	$0.412012\pi$
$758$	−53.0653			−1.92742
$759$	7.12526	−	37.3616i	0.258631	−	1.35614i
$760$	−1.86056			−0.0674895
$761$	−21.0710	+	36.4961i	−0.763825	+	1.32298i	0.177041	+	0.984203i	$0.443348\pi$
$761$	−21.0710	+	36.4961i	−0.763825	+	1.32298i	−0.940866	+	0.338780i	$0.889986\pi$
$762$	−11.8064	+	61.9071i	−0.427699	+	2.24266i
$763$	3.18866	−	13.8375i	0.115437	−	0.500951i
$764$	8.55644			0.309561
$765$	0.326034	+	2.20644i	0.0117878	+	0.0797740i
$766$	−23.6767	+	41.0092i	−0.855472	+	1.48172i
$767$	−4.81958	−	8.34776i	−0.174025	−	0.301420i
$768$	−6.01433	+	31.5364i	−0.217024	+	1.13797i
$769$	14.9534	+	25.9000i	0.539233	+	0.933979i	0.998946	+	0.0459114i	$0.0146192\pi$
$769$	14.9534	+	25.9000i	0.539233	+	0.933979i	−0.459712	+	0.888068i	$0.652047\pi$
$770$	−20.0182	+	6.12917i	−0.721407	+	0.220880i
$771$	−16.3417	−	14.1044i	−0.588533	−	0.507959i
$772$	−21.6987			−0.780952
$773$	3.44462	−	5.96625i	0.123894	−	0.214591i	−0.797406	−	0.603443i	$-0.793795\pi$
$773$	3.44462	−	5.96625i	0.123894	−	0.214591i	0.921300	+	0.388852i	$0.127128\pi$
$774$	−10.2630	+	8.13593i	−0.368895	+	0.292440i
$775$	−0.589871	−	1.02169i	−0.0211888	−	0.0367001i
$776$	10.4174	−	18.0435i	0.373963	−	0.647723i
$777$	−20.8609	+	15.2826i	−0.748380	+	0.548259i
$778$	16.4423	+	28.4788i	0.589483	+	1.02102i
$779$	−3.86546	+	6.69517i	−0.138494	+	0.239879i
$780$	−0.586023	+	3.07284i	−0.0209830	+	0.110025i
$781$	14.5129	+	25.1370i	0.519311	+	0.899473i
$782$	3.04935	+	5.28163i	0.109045	+	0.188871i
$783$	−22.7156	−	43.4359i	−0.811791	−	1.55227i
$784$	−28.9890	+	19.5879i	−1.03532	+	0.699569i
$785$	9.71681	−	16.8300i	0.346808	−	0.600689i
$786$	−32.0584	−	27.6694i	−1.14349	−	0.986935i
$787$	−28.9946			−1.03355			−0.516774	−	0.856122i	$-0.672867\pi$
$787$	−28.9946			−1.03355			−0.516774	+	0.856122i	$0.672867\pi$
$788$	3.40855			0.121425
$789$	8.82067	−	3.07216i	0.314024	−	0.109372i
$790$	4.48059	−	7.76061i	0.159412	−	0.276110i
$791$	29.2134	+	27.2195i	1.03871	+	0.967814i
$792$	3.62313	+	24.5195i	0.128742	+	0.871264i
$793$	3.85213	+	6.67209i	0.136793	+	0.236933i
$794$	8.64681	+	14.9767i	0.306864	+	0.531504i
$795$	−12.9046	+	4.49454i	−0.457678	+	0.159405i
$796$	7.87520	−	13.6402i	0.279129	−	0.483466i
$797$	18.2990	+	31.6948i	0.648184	+	1.12269i	0.983556	+	0.180602i	$0.0578047\pi$
$797$	18.2990	+	31.6948i	0.648184	+	1.12269i	−0.335372	+	0.942086i	$0.608862\pi$
$798$	6.58737	−	4.82587i	0.233191	−	0.170834i
$799$	−0.713668	+	1.23611i	−0.0252478	+	0.0437304i
$800$	−2.50139	−	4.33254i	−0.0884376	−	0.153178i
$801$	−7.43881	−	50.3422i	−0.262837	−	1.77876i
$802$	−13.5131	+	23.4054i	−0.477164	+	0.826472i
$803$	−30.7106			−1.08375
$804$	2.31311	−	12.1289i	0.0815773	−	0.427754i
$805$	9.23580	+	8.60544i	0.325519	+	0.303302i
$806$	−1.91615	−	3.31888i	−0.0674936	−	0.116902i
$807$	30.3351	+	26.1820i	1.06784	+	0.921650i
$808$	−16.9906	−	29.4285i	−0.597726	−	1.03529i
$809$	−6.95113	+	12.0397i	−0.244389	+	0.423294i	−0.961960	−	0.273192i	$-0.911921\pi$
$809$	−6.95113	+	12.0397i	−0.244389	+	0.423294i	0.717571	+	0.696485i	$0.245254\pi$
$810$	−14.8122	+	4.47514i	−0.520446	+	0.157241i
$811$	23.2445			0.816224			0.408112	−	0.912932i	$-0.366187\pi$
$811$	23.2445			0.816224			0.408112	+	0.912932i	$0.366187\pi$
$812$	−5.35719	+	23.2481i	−0.188001	+	0.815847i
$813$	9.85975	−	3.43406i	0.345797	−	0.120438i
$814$	22.3265	−	38.6707i	0.782545	−	1.35541i
$815$	19.4126			0.679994
$816$	−4.87230	−	4.20525i	−0.170565	−	0.147213i
$817$	2.63176			0.0920737
$818$	21.4728			0.750780
$819$	6.43952	+	13.5439i	0.225015	+	0.473262i
$820$	−7.12995			−0.248989
$821$	40.8589			1.42598			0.712992	−	0.701172i	$-0.247339\pi$
$821$	40.8589			1.42598			0.712992	+	0.701172i	$0.247339\pi$
$822$	1.57084	−	0.547107i	0.0547892	−	0.0190825i
$823$	−16.7182			−0.582760			−0.291380	−	0.956607i	$-0.594114\pi$
$823$	−16.7182			−0.582760			−0.291380	+	0.956607i	$0.594114\pi$
$824$	−7.46782	+	12.9346i	−0.260154	+	0.450599i
$825$	−6.03479	−	5.20859i	−0.210104	−	0.181340i
$826$	−22.1894	+	6.79394i	−0.772067	+	0.236391i
$827$	4.44830			0.154682			0.0773412	−	0.997005i	$-0.475357\pi$
$827$	4.44830			0.154682			0.0773412	+	0.997005i	$0.475357\pi$
$828$	−10.7220	+	8.49978i	−0.372614	+	0.295388i
$829$	18.5305	−	32.0957i	0.643590	−	1.11473i	−0.341036	−	0.940050i	$-0.610778\pi$
$829$	18.5305	−	32.0957i	0.643590	−	1.11473i	0.984625	−	0.174680i	$-0.0558890\pi$
$830$	−14.5424	−	25.1882i	−0.504774	−	0.874294i
$831$	16.3037	−	5.67844i	0.565571	−	0.196983i
$832$	1.31784	+	2.28257i	0.0456880	+	0.0791340i
$833$	−0.367293	−	5.19129i	−0.0127260	−	0.179867i
$834$	−38.8771	+	13.5405i	−1.34620	+	0.468870i
$835$	−5.08052			−0.175818
$836$	−2.27992	+	3.94894i	−0.0788528	+	0.136577i
$837$	3.28394	−	5.17630i	0.113510	−	0.178919i
$838$	−2.70608	−	4.68706i	−0.0934798	−	0.161912i
$839$	0.692323	−	1.19914i	0.0239016	−	0.0413988i	−0.853827	−	0.520557i	$-0.825724\pi$
$839$	0.692323	−	1.19914i	0.0239016	−	0.0413988i	0.877729	+	0.479158i	$0.159058\pi$
$840$	−7.52818	−	3.31620i	−0.259747	−	0.114420i
$841$	−29.9940	−	51.9511i	−1.03427	−	1.79142i
$842$	−3.58054	+	6.20168i	−0.123394	+	0.213724i
$843$	−31.1599	−	26.8939i	−1.07320	−	0.926275i
$844$	12.5563	+	21.7482i	0.432207	+	0.748604i
$845$	−4.71504	−	8.16669i	−0.162202	−	0.280943i
$846$	−9.20715	−	3.64435i	−0.316548	−	0.125295i
$847$	6.04960	−	26.2529i	0.207867	−	0.902060i
$848$	19.7159	−	34.1489i	0.677046	−	1.17268i
$849$	−5.87289	+	30.7948i	−0.201557	+	1.05687i
$850$	1.27822			0.0438426
$851$	−26.9246			−0.922963
$852$	1.95604	−	10.2566i	0.0670128	−	0.351385i
$853$	15.3741	−	26.6288i	0.526401	−	0.911752i	−0.473126	−	0.880995i	$-0.656875\pi$
$853$	15.3741	−	26.6288i	0.526401	−	0.911752i	0.999527	−	0.0307579i	$-0.00979208\pi$
$854$	17.7352	−	5.43016i	0.606887	−	0.185816i
$855$	2.89114	+	1.14436i	0.0988747	+	0.0391364i
$856$	−8.90844	−	15.4299i	−0.304484	−	0.527382i
$857$	7.13463	+	12.3575i	0.243714	+	0.422126i	0.961769	−	0.273861i	$-0.0883007\pi$
$857$	7.13463	+	12.3575i	0.243714	+	0.422126i	−0.718055	+	0.695986i	$0.754967\pi$
$858$	−19.6036	−	16.9197i	−0.669255	−	0.577630i
$859$	23.2027	−	40.1882i	0.791665	−	1.37120i	−0.133271	−	0.991080i	$-0.542548\pi$
$859$	23.2027	−	40.1882i	0.791665	−	1.37120i	0.924935	−	0.380124i	$-0.124119\pi$
$860$	1.21359	+	2.10200i	0.0413831	+	0.0716776i
$861$	−27.5737	+	20.2003i	−0.939709	+	0.688425i
$862$	−9.73631	+	16.8638i	−0.331620	+	0.574383i
$863$	−11.3378	−	19.6376i	−0.385943	−	0.668473i	0.605957	−	0.795498i	$-0.292791\pi$
$863$	−11.3378	−	19.6376i	−0.385943	−	0.668473i	−0.991900	+	0.127025i	$0.959457\pi$
$864$	13.9258	−	21.9505i	0.473765	−	0.746771i
$865$	5.63797	−	9.76525i	0.191697	−	0.332029i
$866$	−70.1875			−2.38507
$867$	−26.9025	+	9.36987i	−0.913655	+	0.318217i
$868$	−2.85289	+	0.873497i	−0.0968334	+	0.0296484i
$869$	11.9945	+	20.7751i	0.406885	+	0.704746i
$870$	−26.5282	+	9.23953i	−0.899391	+	0.313249i
$871$	−7.04548	−	12.2031i	−0.238727	−	0.413488i
$872$	−4.81731	+	8.34383i	−0.163135	+	0.282558i
$873$	−27.2856	+	21.6305i	−0.923477	+	0.732082i
$874$	8.50214			0.287589
$875$	2.52983	−	0.774581i	0.0855238	−	0.0261856i
$876$	8.36327	+	7.21828i	0.282569	+	0.243883i
$877$	11.1131	−	19.2485i	0.375264	−	0.649976i	−0.615103	−	0.788447i	$-0.710885\pi$
$877$	11.1131	−	19.2485i	0.375264	−	0.649976i	0.990366	+	0.138471i	$0.0442188\pi$
$878$	29.1034			0.982192
$879$	35.2331	−	12.2714i	1.18838	−	0.413903i
$880$	23.0034			0.775444
$881$	−4.26806			−0.143795			−0.0718973	−	0.997412i	$-0.522905\pi$
$881$	−4.26806			−0.143795			−0.0718973	+	0.997412i	$0.522905\pi$
$882$	35.2553	−	7.78526i	1.18711	−	0.262143i
$883$	−18.2078			−0.612741			−0.306370	−	0.951912i	$-0.599115\pi$
$883$	−18.2078			−0.612741			−0.306370	+	0.951912i	$0.599115\pi$
$884$	1.34276			0.0451618
$885$	−6.68932	−	5.77351i	−0.224859	−	0.194074i
$886$	−16.0494			−0.539191
$887$	13.1258	−	22.7346i	0.440721	−	0.763352i	−0.557022	−	0.830498i	$-0.688056\pi$
$887$	13.1258	−	22.7346i	0.440721	−	0.763352i	0.997743	+	0.0671462i	$0.0213894\pi$
$888$	16.5694	−	5.77096i	0.556032	−	0.193661i
$889$	53.5407	−	16.3931i	1.79570	−	0.549806i
$890$	−29.1639			−0.977576
$891$	9.45109	−	40.3296i	0.316623	−	1.35109i
$892$	1.58178	−	2.73972i	0.0529618	−	0.0917326i
$893$	0.994918	+	1.72325i	0.0332937	+	0.0576663i
$894$	13.3056	+	11.4840i	0.445005	+	0.384081i
$895$	−4.78541	−	8.28858i	−0.159959	−	0.277057i
$896$	31.3797	−	9.60783i	1.04832	−	0.320975i
$897$	−2.92509	+	15.3378i	−0.0976659	+	0.512116i
$898$	61.2959			2.04547
$899$	5.56446	−	9.63792i	0.185585	−	0.321443i
$900$	0.419188	+	2.83686i	0.0139729	+	0.0945621i
$901$	2.93276	+	5.07969i	0.0977044	+	0.169229i
$902$	29.5110	−	51.1145i	0.982608	−	1.70193i
$903$	10.6486	+	4.69078i	0.354364	+	0.156099i
$904$	−13.5456	−	23.4618i	−0.450522	−	0.780326i
$905$	0.211084	−	0.365608i	0.00701667	−	0.0121532i
$906$	57.2866	−	19.9524i	1.90322	−	0.662873i
$907$	−7.46852	−	12.9359i	−0.247988	−	0.429528i	0.714979	−	0.699146i	$-0.246436\pi$
$907$	−7.46852	−	12.9359i	−0.247988	−	0.429528i	−0.962968	+	0.269617i	$0.913103\pi$
$908$	−8.22304	−	14.2427i	−0.272891	−	0.472661i
$909$	8.30135	+	56.1795i	0.275338	+	1.86336i
$910$	8.21796	−	2.51617i	0.272423	−	0.0834103i
$911$	−9.19315	+	15.9230i	−0.304583	+	0.527553i	−0.977168	−	0.212467i	$-0.931850\pi$
$911$	−9.19315	+	15.9230i	−0.304583	+	0.527553i	0.672586	+	0.740019i	$0.265184\pi$
$912$	−8.47328	+	2.95116i	−0.280578	+	0.0977228i
$913$	77.8597			2.57678
$914$	22.1665			0.733203
$915$	5.34655	+	4.61457i	0.176751	+	0.152553i
$916$	1.94965	−	3.37690i	0.0644184	−	0.111576i
$917$	−8.44871	+	36.6640i	−0.279001	+	1.21075i
$918$	3.07797	+	5.88556i	0.101588	+	0.194253i
$919$	−2.59097	−	4.48768i	−0.0854681	−	0.148035i	0.820122	−	0.572188i	$-0.193905\pi$
$919$	−2.59097	−	4.48768i	−0.0854681	−	0.148035i	−0.905591	+	0.424153i	$0.860572\pi$
$920$	−4.28246	−	7.41743i	−0.141188	−	0.244545i
$921$	−1.42806	+	7.48811i	−0.0470563	+	0.246742i
$922$	31.8937	−	55.2414i	1.05036	−	1.81928i
$923$	−5.95788	−	10.3193i	−0.196106	−	0.339665i
$924$	−16.2635	+	11.9145i	−0.535030	+	0.391959i
$925$	−2.82154	+	4.88706i	−0.0927718	+	0.160685i
$926$	19.5999	+	33.9481i	0.644094	+	1.11560i
$927$	19.5599	−	15.5061i	0.642432	−	0.509286i
$928$	23.5965	−	40.8703i	0.774593	−	1.34163i
$929$	25.8879			0.849354			0.424677	−	0.905345i	$-0.360388\pi$
$929$	25.8879			0.849354			0.424677	+	0.905345i	$0.360388\pi$
$930$	−2.65952	−	2.29541i	−0.0872090	−	0.0752695i
$931$	−6.52355	−	3.17512i	−0.213801	−	0.104060i
$932$	9.15551	+	15.8578i	0.299899	+	0.519440i
$933$	4.58561	−	24.0448i	0.150126	−	0.787192i
$934$	−9.94368	−	17.2230i	−0.325367	−	0.563553i
$935$	−1.71089	+	2.96335i	−0.0559521	+	0.0969118i
$936$	−1.48738	−	10.0659i	−0.0486165	−	0.329013i
$937$	45.6581			1.49158			0.745792	−	0.666178i	$-0.232071\pi$
$937$	45.6581			1.49158			0.745792	+	0.666178i	$0.232071\pi$
$938$	−32.4374	+	9.93168i	−1.05912	+	0.324281i
$939$	2.68206	−	14.0635i	0.0875256	−	0.458944i
$940$	−0.917577	+	1.58929i	−0.0299280	+	0.0518369i
$941$	−39.5929			−1.29069			−0.645346	−	0.763890i	$-0.723287\pi$
$941$	−39.5929			−1.29069			−0.645346	+	0.763890i	$0.723287\pi$
$942$	10.8412	−	56.8461i	0.353224	−	1.85215i
$943$	−35.5886			−1.15892
$944$	25.4983			0.829899
$945$	9.65843	+	9.78339i	0.314189	+	0.318254i
$946$	−20.0923			−0.653256
$947$	−47.2360			−1.53496			−0.767482	−	0.641070i	$-0.778491\pi$
$947$	−47.2360			−1.53496			−0.767482	+	0.641070i	$0.778491\pi$
$948$	1.61661	−	8.47679i	0.0525052	−	0.275313i
$949$	12.6074			0.409254
$950$	0.890976	−	1.54322i	0.0289071	−	0.0500686i
$951$	−0.0435427	+	0.228318i	−0.00141197	+	0.00740371i
$952$	−0.792896	+	3.44085i	−0.0256979	+	0.111519i
$953$	−61.6657			−1.99755			−0.998773	−	0.0495191i	$-0.984231\pi$
$953$	−61.6657			−1.99755			−0.998773	+	0.0495191i	$0.984231\pi$
$954$	−31.8877	+	25.2789i	−1.03240	+	0.818434i
$955$	4.47565	−	7.75205i	0.144829	−	0.250850i
$956$	−0.0797000	−	0.138044i	−0.00257768	−	0.00446468i
$957$	14.0875	−	73.8685i	0.455385	−	2.38783i
$958$	4.72779	+	8.18878i	0.152748	+	0.264567i
$959$	−1.08126	−	1.00746i	−0.0349158	−	0.0325327i
$960$	1.82910	+	1.57868i	0.0590338	+	0.0509517i
$961$	−29.6082			−0.955104
$962$	−9.16558	+	15.8753i	−0.295510	+	0.511839i
$963$	4.35254	+	29.4559i	0.140259	+	0.949202i
$964$	10.8471	+	18.7878i	0.349362	+	0.605114i
$965$	−11.3500	+	19.6588i	−0.365369	+	0.632838i
$966$	34.4013	+	15.1540i	1.10684	+	0.487571i
$967$	21.1947	+	36.7103i	0.681576	+	1.18052i	0.974500	+	0.224389i	$0.0720385\pi$
$967$	21.1947	+	36.7103i	0.681576	+	1.18052i	−0.292924	+	0.956136i	$0.594628\pi$
$968$	−9.13953	+	15.8301i	−0.293756	+	0.508799i
$969$	0.250030	−	1.31104i	0.00803211	−	0.0421167i
$970$	9.97729	+	17.2812i	0.320351	+	0.554865i
$971$	1.17376	+	2.03301i	0.0376677	+	0.0652424i	0.884245	−	0.467024i	$-0.154674\pi$
$971$	1.17376	+	2.03301i	0.0376677	+	0.0652424i	−0.846577	+	0.532266i	$0.821340\pi$
$972$	−12.0529	+	8.76137i	−0.386598	+	0.281021i
$973$	26.7605	+	24.9340i	0.857902	+	0.799349i
$974$	−1.41993	+	2.45940i	−0.0454976	+	0.0788042i
$975$	2.47743	+	2.13825i	0.0793411	+	0.0684788i
$976$	−20.3799			−0.652346
$977$	4.45628			0.142569			0.0712846	−	0.997456i	$-0.477290\pi$
$977$	4.45628			0.142569			0.0712846	+	0.997456i	$0.477290\pi$
$978$	54.5917	−	19.0138i	1.74565	−	0.607993i
$979$	39.0357	−	67.6119i	1.24759	−	2.16088i
$980$	−0.472236	−	6.67454i	−0.0150850	−	0.213210i
$981$	12.6176	−	10.0026i	0.402850	−	0.319358i
$982$	−6.98450	−	12.0975i	−0.222884	−	0.386047i
$983$	10.8186	+	18.7383i	0.345059	+	0.597660i	0.985365	−	0.170460i	$-0.0545255\pi$
$983$	10.8186	+	18.7383i	0.345059	+	0.597660i	−0.640305	+	0.768120i	$0.721192\pi$
$984$	21.9012	−	7.62798i	0.698185	−	0.243171i
$985$	1.78292	−	3.08811i	0.0568087	−	0.0983955i
$986$	6.02894	+	10.4424i	0.192001	+	0.332555i
$987$	0.954166	+	8.74592i	0.0303714	+	0.278386i
$988$	0.935963	−	1.62114i	0.0297769	−	0.0515752i
$989$	6.05754	+	10.4920i	0.192619	+	0.333625i
$990$	−22.0725	−	8.73667i	−0.701509	−	0.277670i
$991$	26.4853	−	45.8739i	0.841333	−	1.45723i	−0.0474349	−	0.998874i	$-0.515105\pi$
$991$	26.4853	−	45.8739i	0.841333	−	1.45723i	0.888768	−	0.458357i	$-0.151562\pi$
$992$	5.90200			0.187389
$993$	−0.143322	+	0.751517i	−0.00454820	+	0.0238487i
$994$	−27.4301	+	8.39853i	−0.870029	+	0.266385i
$995$	−8.23861	−	14.2697i	−0.261182	−	0.452380i
$996$	−21.2032	−	18.3003i	−0.671848	−	0.579868i
$997$	−13.5044	−	23.3903i	−0.427688	−	0.740777i	0.568979	−	0.822352i	$-0.307338\pi$
$997$	−13.5044	−	23.3903i	−0.427688	−	0.740777i	−0.996667	+	0.0815748i	$0.974005\pi$
$998$	10.0359	−	17.3826i	0.317680	−	0.550238i
$999$	−29.2968	−	1.22369i	−0.926910	−	0.0387160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.151.2	yes	24
3.2	odd	2		945.2.l.b.46.11		24
7.2	even	3		315.2.k.b.16.11	✓	24
9.4	even	3		315.2.k.b.256.11	yes	24
9.5	odd	6		945.2.k.b.361.2		24
21.2	odd	6		945.2.k.b.856.2		24
63.23	odd	6		945.2.l.b.226.11		24
63.58	even	3	inner	315.2.l.b.121.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.11	✓	24	7.2	even	3
315.2.k.b.256.11	yes	24	9.4	even	3
315.2.l.b.121.2	yes	24	63.58	even	3	inner
315.2.l.b.151.2	yes	24	1.1	even	1	trivial
945.2.k.b.361.2		24	9.5	odd	6
945.2.k.b.856.2		24	21.2	odd	6
945.2.l.b.46.11		24	3.2	odd	2
945.2.l.b.226.11		24	63.23	odd	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.71927 q^{2} +(-0.324473 + 1.70139i) q^{3} +0.955889 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.557856 - 2.92514i) q^{6} +(-2.52983 + 0.774581i) q^{7} +1.79511 q^{8} +(-2.78943 - 1.10411i) q^{9} +O(q^{10})\)	\(q-1.71927 q^{2} +(-0.324473 + 1.70139i) q^{3} +0.955889 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.557856 - 2.92514i) q^{6} +(-2.52983 + 0.774581i) q^{7} +1.79511 q^{8} +(-2.78943 - 1.10411i) q^{9} +(-0.859635 + 1.48893i) q^{10} +(-2.30123 - 3.98585i) q^{11} +(-0.310160 + 1.62634i) q^{12} +(0.944711 + 1.63629i) q^{13} +(4.34945 - 1.33171i) q^{14} +(1.31121 + 1.13170i) q^{15} -4.99805 q^{16} +(0.371733 - 0.643861i) q^{17} +(4.79579 + 1.89826i) q^{18} +(-0.518230 - 0.897600i) q^{19} +(0.477944 - 0.827824i) q^{20} +(-0.497003 - 4.55554i) q^{21} +(3.95644 + 6.85276i) q^{22} +(2.38562 - 4.13202i) q^{23} +(-0.582464 + 3.05418i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.62421 - 2.81322i) q^{26} +(2.78361 - 4.38766i) q^{27} +(-2.41823 + 0.740414i) q^{28} +(4.71667 - 8.16951i) q^{29} +(-2.25432 - 1.94569i) q^{30} +1.17974 q^{31} +5.00279 q^{32} +(7.52817 - 2.62199i) q^{33} +(-0.639110 + 1.10697i) q^{34} +(-0.594106 + 2.57818i) q^{35} +(-2.66639 - 1.05540i) q^{36} +(-2.82154 - 4.88706i) q^{37} +(0.890976 + 1.54322i) q^{38} +(-3.09049 + 1.07639i) q^{39} +(0.897555 - 1.55461i) q^{40} +(-3.72949 - 6.45966i) q^{41} +(0.854482 + 7.83221i) q^{42} +(-1.26959 + 2.19900i) q^{43} +(-2.19972 - 3.81003i) q^{44} +(-2.35090 + 1.86367i) q^{45} +(-4.10153 + 7.10406i) q^{46} -1.91984 q^{47} +(1.62173 - 8.50362i) q^{48} +(5.80005 - 3.91911i) q^{49} +(0.859635 + 1.48893i) q^{50} +(0.974839 + 0.841377i) q^{51} +(0.903039 + 1.56411i) q^{52} +(-3.94471 + 6.83244i) q^{53} +(-4.78577 + 7.54356i) q^{54} -4.60247 q^{55} +(-4.54132 + 1.39046i) q^{56} +(1.69532 - 0.590462i) q^{57} +(-8.10923 + 14.0456i) q^{58} -5.10165 q^{59} +(1.25337 + 1.08177i) q^{60} +4.07757 q^{61} -2.02829 q^{62} +(7.91201 + 0.632556i) q^{63} +1.39497 q^{64} +1.88942 q^{65} +(-12.9429 + 4.50790i) q^{66} -7.45782 q^{67} +(0.355335 - 0.615459i) q^{68} +(6.25610 + 5.39960i) q^{69} +(1.02143 - 4.43260i) q^{70} -6.30656 q^{71} +(-5.00734 - 1.98199i) q^{72} +(3.33632 - 5.77867i) q^{73} +(4.85100 + 8.40217i) q^{74} +(1.63568 - 0.569692i) q^{75} +(-0.495370 - 0.858006i) q^{76} +(8.90909 + 8.30103i) q^{77} +(5.31339 - 1.85060i) q^{78} -5.21220 q^{79} +(-2.49903 + 4.32844i) q^{80} +(6.56189 + 6.15967i) q^{81} +(6.41199 + 11.1059i) q^{82} +(-8.45847 + 14.6505i) q^{83} +(-0.475079 - 4.35459i) q^{84} +(-0.371733 - 0.643861i) q^{85} +(2.18277 - 3.78067i) q^{86} +(12.3691 + 10.6757i) q^{87} +(-4.13096 - 7.15504i) q^{88} +(8.48148 + 14.6904i) q^{89} +(4.04184 - 3.20415i) q^{90} +(-3.65739 - 3.40777i) q^{91} +(2.28039 - 3.94975i) q^{92} +(-0.382794 + 2.00720i) q^{93} +3.30072 q^{94} -1.03646 q^{95} +(-1.62327 + 8.51167i) q^{96} +(5.80321 - 10.0515i) q^{97} +(-9.97185 + 6.73801i) q^{98} +(2.01833 + 13.6591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more