LMFDB - Embedded newform 770.2.n.e.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.2
Root			$-1.20316 - 0.874145i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.e.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.743592 + 0.540251i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.284027 - 0.874145i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.665993 - 2.04972i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.743592 + 0.540251i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.284027 - 0.874145i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.665993 - 2.04972i) q^{9} +1.00000 q^{10} +(3.14565 + 1.05113i) q^{11} -0.919131 q^{12} +(1.15055 + 3.54102i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-0.743592 + 0.540251i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.406956 + 1.25248i) q^{17} +(-1.74359 + 1.26679i) q^{18} +(2.19034 + 1.59138i) q^{19} +(-0.309017 - 0.951057i) q^{20} +0.919131 q^{21} +(0.0276194 - 3.31651i) q^{22} -2.00000 q^{23} +(0.284027 + 0.874145i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(3.01217 - 2.18847i) q^{26} +(1.46422 - 4.50639i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(2.38662 - 1.73398i) q^{29} +(0.743592 + 0.540251i) q^{30} +(2.38197 + 7.33094i) q^{31} -1.00000 q^{32} +(1.77121 + 2.48105i) q^{33} +1.31694 q^{34} +(0.309017 + 0.951057i) q^{35} +(1.74359 + 1.26679i) q^{36} +(6.51153 - 4.73091i) q^{37} +(0.836636 - 2.57490i) q^{38} +(-1.05750 + 3.25466i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-2.62492 - 1.90711i) q^{41} +(-0.284027 - 0.874145i) q^{42} +6.48064 q^{43} +(-3.16272 + 0.998590i) q^{44} +2.15520 q^{45} +(0.618034 + 1.90211i) q^{46} +(7.58121 + 5.50807i) q^{47} +(0.743592 - 0.540251i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-0.979265 + 0.711477i) q^{51} +(-3.01217 - 2.18847i) q^{52} +(4.10522 + 12.6346i) q^{53} -4.73830 q^{54} +(-1.97174 + 2.66688i) q^{55} +1.00000 q^{56} +(0.768978 + 2.36667i) q^{57} +(-2.38662 - 1.73398i) q^{58} +(2.29684 - 1.66875i) q^{59} +(0.284027 - 0.874145i) q^{60} +(0.446995 - 1.37571i) q^{61} +(6.23607 - 4.53077i) q^{62} +(-1.74359 - 1.26679i) q^{63} +(0.309017 + 0.951057i) q^{64} -3.72325 q^{65} +(1.81229 - 2.45121i) q^{66} -6.70741 q^{67} +(-0.406956 - 1.25248i) q^{68} +(-1.48718 - 1.08050i) q^{69} +(0.809017 - 0.587785i) q^{70} +(2.48253 - 7.64046i) q^{71} +(0.665993 - 2.04972i) q^{72} +(1.07656 - 0.782169i) q^{73} +(-6.51153 - 4.73091i) q^{74} +(-0.284027 - 0.874145i) q^{75} -2.70741 q^{76} +(3.16272 - 0.998590i) q^{77} +3.42216 q^{78} +(-2.38662 - 7.34525i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-1.70741 + 1.24051i) q^{81} +(-1.00263 + 3.08578i) q^{82} +(0.0881490 - 0.271295i) q^{83} +(-0.743592 + 0.540251i) q^{84} +(-1.06542 - 0.774076i) q^{85} +(-2.00263 - 6.16346i) q^{86} +2.71145 q^{87} +(1.92705 + 2.69935i) q^{88} -8.14015 q^{89} +(-0.665993 - 2.04972i) q^{90} +(3.01217 + 2.18847i) q^{91} +(1.61803 - 1.17557i) q^{92} +(-2.18934 + 6.73809i) q^{93} +(2.89577 - 8.91225i) q^{94} +(-2.19034 + 1.59138i) q^{95} +(-0.743592 - 0.540251i) q^{96} +(4.57295 + 14.0741i) q^{97} -1.00000 q^{98} +(0.0595253 - 7.14774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9} + 8 q^{10} + 8 q^{11} + 4 q^{12} + 8 q^{13} - 2 q^{14} + q^{15} - 2 q^{16} - 9 q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} - 4 q^{21} - 8 q^{22} - 16 q^{23} + q^{24} - 2 q^{25} + 7 q^{26} - 22 q^{27} + 2 q^{28} - q^{30} + 28 q^{31} - 8 q^{32} - q^{33} + 4 q^{34} - 2 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{38} - 13 q^{39} - 2 q^{40} + 8 q^{41} - q^{42} - 14 q^{43} - 7 q^{44} - 12 q^{45} - 4 q^{46} - q^{48} - 2 q^{49} + 2 q^{50} + 4 q^{51} - 7 q^{52} + 10 q^{53} - 28 q^{54} + 7 q^{55} + 8 q^{56} - 17 q^{57} + 31 q^{59} + q^{60} + 28 q^{61} + 32 q^{62} - 7 q^{63} - 2 q^{64} + 2 q^{65} + 36 q^{66} - 26 q^{67} - 9 q^{68} + 2 q^{69} + 2 q^{70} + 34 q^{71} + 13 q^{72} - 24 q^{73} - 4 q^{74} - q^{75} + 6 q^{76} + 7 q^{77} - 2 q^{78} + 2 q^{80} + 14 q^{81} - 3 q^{82} - 21 q^{83} + q^{84} - 11 q^{85} - 11 q^{86} - 52 q^{87} + 2 q^{88} - 14 q^{89} - 13 q^{90} + 7 q^{91} + 4 q^{92} + 14 q^{93} + 5 q^{94} + 9 q^{95} + q^{96} + 50 q^{97} - 8 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9 + 8 * q^10 + 8 * q^11 + 4 * q^12 + 8 * q^13 - 2 * q^14 + q^15 - 2 * q^16 - 9 * q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 - 4 * q^21 - 8 * q^22 - 16 * q^23 + q^24 - 2 * q^25 + 7 * q^26 - 22 * q^27 + 2 * q^28 - q^30 + 28 * q^31 - 8 * q^32 - q^33 + 4 * q^34 - 2 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^38 - 13 * q^39 - 2 * q^40 + 8 * q^41 - q^42 - 14 * q^43 - 7 * q^44 - 12 * q^45 - 4 * q^46 - q^48 - 2 * q^49 + 2 * q^50 + 4 * q^51 - 7 * q^52 + 10 * q^53 - 28 * q^54 + 7 * q^55 + 8 * q^56 - 17 * q^57 + 31 * q^59 + q^60 + 28 * q^61 + 32 * q^62 - 7 * q^63 - 2 * q^64 + 2 * q^65 + 36 * q^66 - 26 * q^67 - 9 * q^68 + 2 * q^69 + 2 * q^70 + 34 * q^71 + 13 * q^72 - 24 * q^73 - 4 * q^74 - q^75 + 6 * q^76 + 7 * q^77 - 2 * q^78 + 2 * q^80 + 14 * q^81 - 3 * q^82 - 21 * q^83 + q^84 - 11 * q^85 - 11 * q^86 - 52 * q^87 + 2 * q^88 - 14 * q^89 - 13 * q^90 + 7 * q^91 + 4 * q^92 + 14 * q^93 + 5 * q^94 + 9 * q^95 + q^96 + 50 * q^97 - 8 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.743592	+	0.540251i	0.429313	+	0.311914i	0.781374	−	0.624063i	$-0.214519\pi$
$3$	0.743592	+	0.540251i	0.429313	+	0.311914i	−0.352061	+	0.935977i	$0.614519\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	0.284027	−	0.874145i	0.115954	−	0.356868i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.665993	−	2.04972i	−0.221998	−	0.683239i
$10$	1.00000			0.316228
$11$	3.14565	+	1.05113i	0.948450	+	0.316926i
$11$	3.14565	+	1.05113i	0.948450	+	0.316926i
$12$	−0.919131			−0.265330
$13$	1.15055	+	3.54102i	0.319105	+	0.982103i	0.974032	+	0.226411i	$0.0726993\pi$
$13$	1.15055	+	3.54102i	0.319105	+	0.982103i	−0.654927	+	0.755692i	$0.727301\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	−0.743592	+	0.540251i	−0.191995	+	0.139492i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.406956	+	1.25248i	−0.0987013	+	0.303771i	−0.988201	−	0.153165i	$-0.951053\pi$
$17$	−0.406956	+	1.25248i	−0.0987013	+	0.303771i	0.889499	+	0.456937i	$0.151053\pi$
$18$	−1.74359	+	1.26679i	−0.410969	+	0.298586i
$19$	2.19034	+	1.59138i	0.502499	+	0.365087i	0.809971	−	0.586470i	$-0.199483\pi$
$19$	2.19034	+	1.59138i	0.502499	+	0.365087i	−0.307472	+	0.951557i	$0.599483\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	0.919131			0.200571
$22$	0.0276194	−	3.31651i	0.00588847	−	0.707082i
$23$	−2.00000			−0.417029			−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000			−0.417029			−0.208514	+	0.978019i	$0.566863\pi$
$24$	0.284027	+	0.874145i	0.0579768	+	0.178434i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	3.01217	−	2.18847i	0.590736	−	0.429195i
$27$	1.46422	−	4.50639i	0.281788	−	0.867256i
$28$	−0.309017	+	0.951057i	−0.0583987	+	0.179733i
$29$	2.38662	−	1.73398i	0.443184	−	0.321992i	−0.343715	−	0.939074i	$-0.611685\pi$
$29$	2.38662	−	1.73398i	0.443184	−	0.321992i	0.786899	+	0.617082i	$0.211685\pi$
$30$	0.743592	+	0.540251i	0.135761	+	0.0986360i
$31$	2.38197	+	7.33094i	0.427814	+	1.31668i	0.900274	+	0.435323i	$0.143366\pi$
$31$	2.38197	+	7.33094i	0.427814	+	1.31668i	−0.472460	+	0.881352i	$0.656634\pi$
$32$	−1.00000			−0.176777
$33$	1.77121	+	2.48105i	0.308328	+	0.431896i
$34$	1.31694			0.225853
$35$	0.309017	+	0.951057i	0.0522334	+	0.160758i
$36$	1.74359	+	1.26679i	0.290599	+	0.211132i
$37$	6.51153	−	4.73091i	1.07049	−	0.777756i	0.0944894	−	0.995526i	$-0.469878\pi$
$37$	6.51153	−	4.73091i	1.07049	−	0.777756i	0.976000	+	0.217770i	$0.0698781\pi$
$38$	0.836636	−	2.57490i	0.135720	−	0.417704i
$39$	−1.05750	+	3.25466i	−0.169336	+	0.521163i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	−2.62492	−	1.90711i	−0.409943	−	0.297841i	0.363636	−	0.931541i	$-0.381535\pi$
$41$	−2.62492	−	1.90711i	−0.409943	−	0.297841i	−0.773579	+	0.633700i	$0.781535\pi$
$42$	−0.284027	−	0.874145i	−0.0438263	−	0.134884i
$43$	6.48064			0.988289			0.494145	−	0.869380i	$-0.335481\pi$
$43$	6.48064			0.988289			0.494145	+	0.869380i	$0.335481\pi$
$44$	−3.16272	+	0.998590i	−0.476798	+	0.150543i
$45$	2.15520			0.321278
$46$	0.618034	+	1.90211i	0.0911241	+	0.280451i
$47$	7.58121	+	5.50807i	1.10583	+	0.803435i	0.982002	−	0.188868i	$-0.0604819\pi$
$47$	7.58121	+	5.50807i	1.10583	+	0.803435i	0.123831	+	0.992303i	$0.460482\pi$
$48$	0.743592	−	0.540251i	0.107328	−	0.0779786i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	−0.979265	+	0.711477i	−0.137124	+	0.0996268i
$52$	−3.01217	−	2.18847i	−0.417713	−	0.303487i
$53$	4.10522	+	12.6346i	0.563895	+	1.73549i	0.671211	+	0.741266i	$0.265774\pi$
$53$	4.10522	+	12.6346i	0.563895	+	1.73549i	−0.107316	+	0.994225i	$0.534226\pi$
$54$	−4.73830			−0.644801
$55$	−1.97174	+	2.66688i	−0.265869	+	0.359602i
$56$	1.00000			0.133631
$57$	0.768978	+	2.36667i	0.101854	+	0.313473i
$58$	−2.38662	−	1.73398i	−0.313378	−	0.227683i
$59$	2.29684	−	1.66875i	0.299023	−	0.217253i	−0.428149	−	0.903708i	$-0.640834\pi$
$59$	2.29684	−	1.66875i	0.299023	−	0.217253i	0.727172	+	0.686455i	$0.240834\pi$
$60$	0.284027	−	0.874145i	0.0366677	−	0.112852i
$61$	0.446995	−	1.37571i	0.0572318	−	0.176141i	−0.918354	−	0.395760i	$-0.870481\pi$
$61$	0.446995	−	1.37571i	0.0572318	−	0.176141i	0.975586	+	0.219618i	$0.0704813\pi$
$62$	6.23607	−	4.53077i	0.791981	−	0.575408i
$63$	−1.74359	−	1.26679i	−0.219672	−	0.159601i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−3.72325			−0.461813
$66$	1.81229	−	2.45121i	0.223077	−	0.301723i
$67$	−6.70741			−0.819441			−0.409720	−	0.912211i	$-0.634374\pi$
$67$	−6.70741			−0.819441			−0.409720	+	0.912211i	$0.634374\pi$
$68$	−0.406956	−	1.25248i	−0.0493507	−	0.151886i
$69$	−1.48718	−	1.08050i	−0.179036	−	0.130077i
$70$	0.809017	−	0.587785i	0.0966960	−	0.0702538i
$71$	2.48253	−	7.64046i	0.294623	−	0.906755i	−0.688725	−	0.725022i	$-0.741829\pi$
$71$	2.48253	−	7.64046i	0.294623	−	0.906755i	0.983348	−	0.181733i	$-0.0581706\pi$
$72$	0.665993	−	2.04972i	0.0784880	−	0.241561i
$73$	1.07656	−	0.782169i	0.126002	−	0.0915459i	−0.522999	−	0.852333i	$-0.675187\pi$
$73$	1.07656	−	0.782169i	0.126002	−	0.0915459i	0.649001	+	0.760787i	$0.275187\pi$
$74$	−6.51153	−	4.73091i	−0.756950	−	0.549957i
$75$	−0.284027	−	0.874145i	−0.0327966	−	0.100938i
$76$	−2.70741			−0.310561
$77$	3.16272	−	0.998590i	0.360426	−	0.113800i
$78$	3.42216			0.387483
$79$	−2.38662	−	7.34525i	−0.268515	−	0.826405i	−0.990863	−	0.134875i	$-0.956937\pi$
$79$	−2.38662	−	7.34525i	−0.268515	−	0.826405i	0.722347	−	0.691530i	$-0.243063\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−1.70741	+	1.24051i	−0.189712	+	0.137834i
$82$	−1.00263	+	3.08578i	−0.110722	+	0.340767i
$83$	0.0881490	−	0.271295i	0.00967561	−	0.0297785i	−0.946102	−	0.323868i	$-0.895017\pi$
$83$	0.0881490	−	0.271295i	0.00967561	−	0.0297785i	0.955778	+	0.294090i	$0.0950165\pi$
$84$	−0.743592	+	0.540251i	−0.0811326	+	0.0589463i
$85$	−1.06542	−	0.774076i	−0.115562	−	0.0839604i
$86$	−2.00263	−	6.16346i	−0.215949	−	0.664623i
$87$	2.71145			0.290698
$88$	1.92705	+	2.69935i	0.205424	+	0.287751i
$89$	−8.14015			−0.862854			−0.431427	−	0.902148i	$-0.641990\pi$
$89$	−8.14015			−0.862854			−0.431427	+	0.902148i	$0.641990\pi$
$90$	−0.665993	−	2.04972i	−0.0702018	−	0.216059i
$91$	3.01217	+	2.18847i	0.315762	+	0.229414i
$92$	1.61803	−	1.17557i	0.168692	−	0.122562i
$93$	−2.18934	+	6.73809i	−0.227024	+	0.698707i
$94$	2.89577	−	8.91225i	0.298675	−	0.919228i
$95$	−2.19034	+	1.59138i	−0.224724	+	0.163272i
$96$	−0.743592	−	0.540251i	−0.0758926	−	0.0551392i
$97$	4.57295	+	14.0741i	0.464313	+	1.42901i	0.859845	+	0.510555i	$0.170560\pi$
$97$	4.57295	+	14.0741i	0.464313	+	1.42901i	−0.395532	+	0.918452i	$0.629440\pi$
$98$	−1.00000			−0.101015
$99$	0.0595253	−	7.14774i	0.00598252	−	0.718375i
$100$	1.00000			0.100000
$101$	−4.35713	−	13.4099i	−0.433550	−	1.33433i	−0.894565	−	0.446938i	$-0.852514\pi$
$101$	−4.35713	−	13.4099i	−0.433550	−	1.33433i	0.461014	−	0.887393i	$-0.347486\pi$
$102$	0.979265	+	0.711477i	0.0969616	+	0.0704468i
$103$	−9.51618	+	6.91391i	−0.937658	+	0.681248i	−0.947856	−	0.318700i	$-0.896754\pi$
$103$	−9.51618	+	6.91391i	−0.937658	+	0.681248i	0.0101981	+	0.999948i	$0.496754\pi$
$104$	−1.15055	+	3.54102i	−0.112821	+	0.347226i
$105$	−0.284027	+	0.874145i	−0.0277182	+	0.0853078i
$106$	10.7476	−	7.80859i	1.04390	−	0.758437i
$107$	−16.0405	−	11.6541i	−1.55070	−	1.12665i	−0.943152	−	0.332362i	$-0.892154\pi$
$107$	−16.0405	−	11.6541i	−1.55070	−	1.12665i	−0.607545	−	0.794285i	$-0.707846\pi$
$108$	1.46422	+	4.50639i	0.140894	+	0.433628i
$109$	−0.995533			−0.0953548			−0.0476774	−	0.998863i	$-0.515182\pi$
$109$	−0.995533			−0.0953548			−0.0476774	+	0.998863i	$0.515182\pi$
$110$	3.14565	+	1.05113i	0.299926	+	0.100221i
$111$	7.39781			0.702169
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	−8.95507	−	6.50624i	−0.842422	−	0.612055i	0.0806243	−	0.996745i	$-0.474309\pi$
$113$	−8.95507	−	6.50624i	−0.842422	−	0.612055i	−0.923046	+	0.384689i	$0.874309\pi$
$114$	2.01321	−	1.46268i	0.188554	−	0.136993i
$115$	0.618034	−	1.90211i	0.0576320	−	0.177373i
$116$	−0.911606	+	2.80564i	−0.0846405	+	0.260497i
$117$	6.49184	−	4.71659i	0.600170	−	0.436049i
$118$	−2.29684	−	1.66875i	−0.211441	−	0.153621i
$119$	0.406956	+	1.25248i	0.0373056	+	0.114815i
$120$	−0.919131			−0.0839048
$121$	8.79027	+	6.61295i	0.799115	+	0.601178i
$122$	−1.44651			−0.130960
$123$	−0.921548	−	2.83623i	−0.0830931	−	0.255734i
$124$	−6.23607	−	4.53077i	−0.560015	−	0.406875i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	−0.665993	+	2.04972i	−0.0593314	+	0.182603i
$127$	2.00930	−	6.18399i	0.178297	−	0.548741i	−0.821472	−	0.570249i	$-0.806847\pi$
$127$	2.00930	−	6.18399i	0.178297	−	0.548741i	0.999769	+	0.0215082i	$0.00684681\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	4.81896	+	3.50118i	0.424286	+	0.308262i
$130$	1.15055	+	3.54102i	0.100910	+	0.310568i
$131$	−21.7622			−1.90137			−0.950684	−	0.310160i	$-0.899617\pi$
$131$	−21.7622			−1.90137			−0.950684	+	0.310160i	$0.899617\pi$
$132$	−2.89127	−	0.966122i	−0.251652	−	0.0840901i
$133$	2.70741			0.234762
$134$	2.07270	+	6.37913i	0.179054	+	0.551073i
$135$	3.83337	+	2.78510i	0.329924	+	0.239704i
$136$	−1.06542	+	0.774076i	−0.0913594	+	0.0663765i
$137$	−0.897411	+	2.76195i	−0.0766710	+	0.235969i	−0.982045	−	0.188645i	$-0.939590\pi$
$137$	−0.897411	+	2.76195i	−0.0766710	+	0.235969i	0.905374	+	0.424614i	$0.139590\pi$
$138$	−0.568054	+	1.74829i	−0.0483560	+	0.148824i
$139$	1.02563	−	0.745164i	0.0869928	−	0.0632040i	−0.543439	−	0.839449i	$-0.682878\pi$
$139$	1.02563	−	0.745164i	0.0869928	−	0.0632040i	0.630432	+	0.776245i	$0.282878\pi$
$140$	−0.809017	−	0.587785i	−0.0683744	−	0.0496769i
$141$	2.66159	+	8.19152i	0.224146	+	0.689851i
$142$	−8.03365			−0.674169
$143$	−0.102834	+	12.3482i	−0.00859941	+	1.03261i
$144$	−2.15520			−0.179600
$145$	0.911606	+	2.80564i	0.0757048	+	0.232995i
$146$	−1.07656	−	0.782169i	−0.0890970	−	0.0647328i
$147$	0.743592	−	0.540251i	0.0613305	−	0.0445592i
$148$	−2.48718	+	7.65477i	−0.204445	+	0.629218i
$149$	1.80926	−	5.56833i	0.148220	−	0.456176i	−0.849191	−	0.528087i	$-0.822910\pi$
$149$	1.80926	−	5.56833i	0.148220	−	0.456176i	0.997411	+	0.0719107i	$0.0229097\pi$
$150$	−0.743592	+	0.540251i	−0.0607141	+	0.0441113i
$151$	−8.27161	−	6.00967i	−0.673134	−	0.489060i	0.197939	−	0.980214i	$-0.436575\pi$
$151$	−8.27161	−	6.00967i	−0.673134	−	0.489060i	−0.871073	+	0.491154i	$0.836575\pi$
$152$	0.836636	+	2.57490i	0.0678602	+	0.208852i
$153$	2.83826			0.229460
$154$	−1.92705	−	2.69935i	−0.155286	−	0.217520i
$155$	−7.70820			−0.619138
$156$	−1.05750	−	3.25466i	−0.0846681	−	0.260582i
$157$	−0.954670	−	0.693609i	−0.0761910	−	0.0553560i	0.549038	−	0.835798i	$-0.314994\pi$
$157$	−0.954670	−	0.693609i	−0.0761910	−	0.0553560i	−0.625229	+	0.780442i	$0.714994\pi$
$158$	−6.24824	+	4.53961i	−0.497084	+	0.361152i
$159$	−3.77323	+	11.6128i	−0.299237	+	0.920956i
$160$	0.309017	−	0.951057i	0.0244299	−	0.0751876i
$161$	−1.61803	+	1.17557i	−0.127519	+	0.0926479i
$162$	1.70741	+	1.24051i	0.134147	+	0.0974635i
$163$	4.19701	+	12.9171i	0.328735	+	1.01174i	0.969726	+	0.244195i	$0.0785237\pi$
$163$	4.19701	+	12.9171i	0.328735	+	1.01174i	−0.640991	+	0.767549i	$0.721476\pi$
$164$	3.24458			0.253359
$165$	−2.90696	+	0.917835i	−0.226306	+	0.0714534i
$166$	−0.285256			−0.0221402
$167$	−3.70820	−	11.4127i	−0.286949	−	0.883140i	−0.985808	−	0.167879i	$-0.946308\pi$
$167$	−3.70820	−	11.4127i	−0.286949	−	0.883140i	0.698858	−	0.715260i	$-0.253692\pi$
$168$	0.743592	+	0.540251i	0.0573694	+	0.0416813i
$169$	−0.697867	+	0.507030i	−0.0536821	+	0.0390023i
$170$	−0.406956	+	1.25248i	−0.0312121	+	0.0960610i
$171$	1.80312	−	5.54943i	0.137888	−	0.424375i
$172$	−5.24295	+	3.80923i	−0.399771	+	0.290451i
$173$	10.0918	+	7.33210i	0.767263	+	0.557449i	0.901129	−	0.433550i	$-0.142739\pi$
$173$	10.0918	+	7.33210i	0.767263	+	0.557449i	−0.133867	+	0.990999i	$0.542739\pi$
$174$	−0.837885	−	2.57875i	−0.0635199	−	0.195494i
$175$	−1.00000			−0.0755929
$176$	1.97174	−	2.66688i	0.148626	−	0.201024i
$177$	2.60946			0.196139
$178$	2.51544	+	7.74174i	0.188541	+	0.580268i
$179$	−9.89390	−	7.18834i	−0.739505	−	0.537281i	0.153051	−	0.988218i	$-0.451090\pi$
$179$	−9.89390	−	7.18834i	−0.739505	−	0.537281i	−0.892556	+	0.450937i	$0.851090\pi$
$180$	−1.74359	+	1.26679i	−0.129960	+	0.0944213i
$181$	6.48064	−	19.9454i	0.481703	−	1.48253i	−0.354998	−	0.934867i	$-0.615518\pi$
$181$	6.48064	−	19.9454i	0.481703	−	1.48253i	0.836700	−	0.547661i	$-0.184482\pi$
$182$	1.15055	−	3.54102i	0.0852843	−	0.262478i
$183$	1.07561	−	0.781477i	0.0795114	−	0.0577684i
$184$	−1.61803	−	1.17557i	−0.119283	−	0.0866642i
$185$	2.48718	+	7.65477i	0.182861	+	0.562790i
$186$	7.08485			0.519486
$187$	−2.59666	+	3.51211i	−0.189886	+	0.256831i
$188$	−9.37090			−0.683443
$189$	−1.46422	−	4.50639i	−0.106506	−	0.327792i
$190$	2.19034	+	1.59138i	0.158904	+	0.115451i
$191$	−5.45789	+	3.96539i	−0.394919	+	0.286925i	−0.767468	−	0.641087i	$-0.778484\pi$
$191$	−5.45789	+	3.96539i	−0.394919	+	0.286925i	0.372549	+	0.928012i	$0.378484\pi$
$192$	−0.284027	+	0.874145i	−0.0204979	+	0.0630860i
$193$	−6.17025	+	18.9901i	−0.444144	+	1.36694i	0.439276	+	0.898352i	$0.355235\pi$
$193$	−6.17025	+	18.9901i	−0.444144	+	1.36694i	−0.883420	+	0.468583i	$0.844765\pi$
$194$	11.9721	−	8.69827i	0.859549	−	0.624499i
$195$	−2.76858	−	2.01149i	−0.198262	−	0.144046i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	−21.1717			−1.50842			−0.754212	−	0.656631i	$-0.771981\pi$
$197$	−21.1717			−1.50842			−0.754212	+	0.656631i	$0.771981\pi$
$198$	−6.81630	+	2.15216i	−0.484413	+	0.152947i
$199$	8.27872			0.586863			0.293431	−	0.955980i	$-0.405203\pi$
$199$	8.27872			0.586863			0.293431	+	0.955980i	$0.405203\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$	−4.98758	−	3.62369i	−0.351797	−	0.255595i
$202$	−11.4071	+	8.28775i	−0.802601	+	0.583124i
$203$	0.911606	−	2.80564i	0.0639822	−	0.196917i
$204$	0.374046	−	1.15119i	0.0261884	−	0.0805997i
$205$	2.62492	−	1.90711i	0.183332	−	0.133199i
$206$	9.51618	+	6.91391i	0.663024	+	0.481715i
$207$	1.33199	+	4.09943i	0.0925794	+	0.284930i
$208$	3.72325			0.258161
$209$	5.21732	+	7.30825i	0.360890	+	0.505522i
$210$	0.919131			0.0634260
$211$	−4.81794	−	14.8281i	−0.331681	−	1.02081i	−0.968334	−	0.249658i	$-0.919682\pi$
$211$	−4.81794	−	14.8281i	−0.331681	−	1.02081i	0.636653	−	0.771150i	$-0.280318\pi$
$212$	−10.7476	−	7.80859i	−0.738148	−	0.536296i
$213$	5.97376	−	4.34019i	0.409315	−	0.297385i
$214$	−6.12694	+	18.8568i	−0.418829	+	1.28902i
$215$	−2.00263	+	6.16346i	−0.136578	+	0.420344i
$216$	3.83337	−	2.78510i	0.260828	−	0.189502i
$217$	6.23607	+	4.53077i	0.423332	+	0.307569i
$218$	0.307637	+	0.946808i	0.0208358	+	0.0641259i
$219$	1.22309			0.0826489
$220$	0.0276194	−	3.31651i	0.00186210	−	0.223599i
$221$	−4.90329			−0.329831
$222$	−2.28605	−	7.03573i	−0.153429	−	0.472207i
$223$	13.4550	+	9.77564i	0.901014	+	0.654625i	0.938726	−	0.344663i	$-0.112007\pi$
$223$	13.4550	+	9.77564i	0.901014	+	0.654625i	−0.0377119	+	0.999289i	$0.512007\pi$
$224$	−0.809017	+	0.587785i	−0.0540547	+	0.0392731i
$225$	−0.665993	+	2.04972i	−0.0443995	+	0.136648i
$226$	−3.42053	+	10.5273i	−0.227530	+	0.700266i
$227$	0.968522	−	0.703672i	0.0642831	−	0.0467044i	−0.555180	−	0.831730i	$-0.687351\pi$
$227$	0.968522	−	0.703672i	0.0642831	−	0.0467044i	0.619463	+	0.785026i	$0.287351\pi$
$228$	−2.01321	−	1.46268i	−0.133328	−	0.0968686i
$229$	4.59240	+	14.1340i	0.303475	+	0.933999i	0.980242	+	0.197802i	$0.0633803\pi$
$229$	4.59240	+	14.1340i	0.303475	+	0.933999i	−0.676767	+	0.736197i	$0.736620\pi$
$230$	−2.00000			−0.131876
$231$	2.89127	+	0.966122i	0.190231	+	0.0635661i
$232$	2.95002			0.193678
$233$	1.95669	+	6.02208i	0.128187	+	0.394519i	0.994468	−	0.105037i	$-0.0334962\pi$
$233$	1.95669	+	6.02208i	0.128187	+	0.394519i	−0.866281	+	0.499557i	$0.833496\pi$
$234$	−6.49184	−	4.71659i	−0.424385	−	0.308333i
$235$	−7.58121	+	5.50807i	−0.494544	+	0.359307i
$236$	−0.877316	+	2.70010i	−0.0571084	+	0.175762i
$237$	2.19361	−	6.75124i	0.142490	−	0.438540i
$238$	1.06542	−	0.774076i	0.0690612	−	0.0501759i
$239$	−9.45789	−	6.87156i	−0.611780	−	0.444484i	0.238261	−	0.971201i	$-0.423423\pi$
$239$	−9.45789	−	6.87156i	−0.611780	−	0.444484i	−0.850041	+	0.526717i	$0.823423\pi$
$240$	0.284027	+	0.874145i	0.0183339	+	0.0564258i
$241$	−10.3945			−0.669566			−0.334783	−	0.942295i	$-0.608663\pi$
$241$	−10.3945			−0.669566			−0.334783	+	0.942295i	$0.608663\pi$
$242$	3.57295	−	10.4036i	0.229678	−	0.668766i
$243$	−16.1547			−1.03633
$244$	0.446995	+	1.37571i	0.0286159	+	0.0880707i
$245$	0.809017	+	0.587785i	0.0516862	+	0.0375522i
$246$	−2.41264	+	1.75289i	−0.153824	+	0.111760i
$247$	−3.11501	+	9.58701i	−0.198203	+	0.610007i
$248$	−2.38197	+	7.33094i	−0.151255	+	0.465515i
$249$	0.212114	−	0.154110i	0.0134422	−	0.00976633i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−6.90329	−	21.2461i	−0.435732	−	1.34104i	−0.892335	−	0.451374i	$-0.850934\pi$
$251$	−6.90329	−	21.2461i	−0.435732	−	1.34104i	0.456603	−	0.889671i	$-0.349066\pi$
$252$	2.15520			0.135765
$253$	−6.29131	−	2.10225i	−0.395531	−	0.132167i
$254$	−6.50223			−0.407986
$255$	−0.374046	−	1.15119i	−0.0234237	−	0.0720906i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	4.27323	−	3.10469i	0.266557	−	0.193665i	−0.446476	−	0.894796i	$-0.647321\pi$
$257$	4.27323	−	3.10469i	0.266557	−	0.193665i	0.713033	+	0.701131i	$0.247321\pi$
$258$	1.84068	−	5.66503i	0.114596	−	0.352689i
$259$	2.48718	−	7.65477i	0.154546	−	0.475644i
$260$	3.01217	−	2.18847i	0.186807	−	0.135723i
$261$	−5.14363	−	3.73707i	−0.318383	−	0.231319i
$262$	6.72488	+	20.6970i	0.415464	+	1.27867i
$263$	−25.3847			−1.56529			−0.782645	−	0.622469i	$-0.786130\pi$
$263$	−25.3847			−1.56529			−0.782645	+	0.622469i	$0.786130\pi$
$264$	−0.0253858	+	3.04831i	−0.00156239	+	0.187610i
$265$	−13.2848			−0.816077
$266$	−0.836636	−	2.57490i	−0.0512975	−	0.157877i
$267$	−6.05295	−	4.39773i	−0.370435	−	0.269137i
$268$	5.42641	−	3.94252i	0.331471	−	0.240828i
$269$	−4.75213	+	14.6256i	−0.289743	+	0.891736i	0.695194	+	0.718822i	$0.255318\pi$
$269$	−4.75213	+	14.6256i	−0.289743	+	0.891736i	−0.984937	+	0.172914i	$0.944682\pi$
$270$	1.46422	−	4.50639i	0.0891093	−	0.274250i
$271$	8.35505	−	6.07030i	0.507533	−	0.368745i	−0.304354	−	0.952559i	$-0.598440\pi$
$271$	8.35505	−	6.07030i	0.507533	−	0.368745i	0.811887	+	0.583814i	$0.198440\pi$
$272$	1.06542	+	0.774076i	0.0646009	+	0.0469353i
$273$	1.05750	+	3.25466i	0.0640031	+	0.196981i
$274$	2.90408			0.175442
$275$	−1.92705	−	2.69935i	−0.116206	−	0.162777i
$276$	1.83826			0.110650
$277$	7.03365	+	21.6473i	0.422611	+	1.30066i	0.905263	+	0.424851i	$0.139674\pi$
$277$	7.03365	+	21.6473i	0.422611	+	1.30066i	−0.482652	+	0.875812i	$0.660326\pi$
$278$	−1.02563	−	0.745164i	−0.0615132	−	0.0446920i
$279$	13.4400	−	9.76471i	0.804630	−	0.584598i
$280$	−0.309017	+	0.951057i	−0.0184673	+	0.0568365i
$281$	0.951432	−	2.92821i	0.0567577	−	0.174682i	−0.918659	−	0.395052i	$-0.870726\pi$
$281$	0.951432	−	2.92821i	0.0567577	−	0.174682i	0.975416	+	0.220370i	$0.0707265\pi$
$282$	6.96813	−	5.06264i	0.414946	−	0.301476i
$283$	−8.88231	−	6.45338i	−0.527999	−	0.383613i	0.291610	−	0.956537i	$-0.405809\pi$
$283$	−8.88231	−	6.45338i	−0.527999	−	0.383613i	−0.819609	+	0.572924i	$0.805809\pi$
$284$	2.48253	+	7.64046i	0.147311	+	0.453378i
$285$	−2.48847			−0.147404
$286$	11.7756	−	3.71800i	0.696307	−	0.219850i
$287$	−3.24458			−0.191521
$288$	0.665993	+	2.04972i	0.0392440	+	0.120781i
$289$	12.3502	+	8.97294i	0.726482	+	0.527820i
$290$	2.38662	−	1.73398i	0.140147	−	0.101823i
$291$	−4.20314	+	12.9359i	−0.246392	+	0.758318i
$292$	−0.411210	+	1.26558i	−0.0240643	+	0.0740622i
$293$	6.51361	−	4.73241i	0.380529	−	0.276470i	−0.381034	−	0.924561i	$-0.624432\pi$
$293$	6.51361	−	4.73241i	0.380529	−	0.276470i	0.761563	+	0.648090i	$0.224432\pi$
$294$	−0.743592	−	0.540251i	−0.0433672	−	0.0315081i
$295$	0.877316	+	2.70010i	0.0510793	+	0.157206i
$296$	8.04870			0.467821
$297$	9.34270	−	12.6365i	0.542118	−	0.733243i
$298$	−5.85489			−0.339165
$299$	−2.30110	−	7.08205i	−0.133076	−	0.409565i
$300$	0.743592	+	0.540251i	0.0429313	+	0.0311914i
$301$	5.24295	−	3.80923i	0.302199	−	0.219560i
$302$	−3.15947	+	9.72386i	−0.181807	+	0.559545i
$303$	4.00477	−	12.3254i	0.230068	−	0.708076i
$304$	2.19034	−	1.59138i	0.125625	−	0.0912717i
$305$	1.17025	+	0.850235i	0.0670082	+	0.0486843i
$306$	−0.877071	−	2.69935i	−0.0501388	−	0.154311i
$307$	27.5963			1.57501			0.787503	−	0.616311i	$-0.211373\pi$
$307$	27.5963			1.57501			0.787503	+	0.616311i	$0.211373\pi$
$308$	−1.97174	+	2.66688i	−0.112350	+	0.151960i
$309$	−10.8114			−0.615040
$310$	2.38197	+	7.33094i	0.135287	+	0.416369i
$311$	−24.0982	−	17.5084i	−1.36648	−	0.992808i	−0.998003	−	0.0631724i	$-0.979878\pi$
$311$	−24.0982	−	17.5084i	−1.36648	−	0.992808i	−0.368480	−	0.929636i	$-0.620122\pi$
$312$	−2.76858	+	2.01149i	−0.156740	+	0.113878i
$313$	9.55335	−	29.4022i	0.539987	−	1.66191i	−0.192632	−	0.981271i	$-0.561702\pi$
$313$	9.55335	−	29.4022i	0.539987	−	1.66191i	0.732619	−	0.680639i	$-0.238298\pi$
$314$	−0.364652	+	1.12228i	−0.0205785	+	0.0633341i
$315$	1.74359	−	1.26679i	0.0982403	−	0.0713758i
$316$	6.24824	+	4.53961i	0.351491	+	0.255373i
$317$	−0.717505	−	2.20825i	−0.0402991	−	0.124028i	0.928883	−	0.370373i	$-0.120770\pi$
$317$	−0.717505	−	2.20825i	−0.0402991	−	0.124028i	−0.969182	+	0.246345i	$0.920770\pi$
$318$	12.2104			0.684727
$319$	9.33010	−	2.94586i	0.522385	−	0.164937i
$320$	−1.00000			−0.0559017
$321$	−5.63146	−	17.3318i	−0.314317	−	0.967369i
$322$	1.61803	+	1.17557i	0.0901695	+	0.0655120i
$323$	−2.88454	+	2.09574i	−0.160500	+	0.116610i
$324$	0.652173	−	2.00718i	0.0362319	−	0.111510i
$325$	1.15055	−	3.54102i	0.0638209	−	0.196421i
$326$	10.9879	−	7.98319i	0.608565	−	0.442148i
$327$	−0.740271	−	0.537838i	−0.0409371	−	0.0297425i
$328$	−1.00263	−	3.08578i	−0.0553609	−	0.170383i
$329$	9.37090			0.516634
$330$	1.77121	+	2.48105i	0.0975020	+	0.136577i
$331$	−9.95686			−0.547279			−0.273639	−	0.961832i	$-0.588227\pi$
$331$	−9.95686			−0.547279			−0.273639	+	0.961832i	$0.588227\pi$
$332$	0.0881490	+	0.271295i	0.00483781	+	0.0148892i
$333$	−14.0337	−	10.1960i	−0.769039	−	0.558740i
$334$	−9.70820	+	7.05342i	−0.531209	+	0.385946i
$335$	2.07270	−	6.37913i	0.113244	−	0.348529i
$336$	0.284027	−	0.874145i	0.0154949	−	0.0476885i
$337$	16.8018	−	12.2072i	0.915254	−	0.664971i	−0.0270839	−	0.999633i	$-0.508622\pi$
$337$	16.8018	−	12.2072i	0.915254	−	0.664971i	0.942338	+	0.334662i	$0.108622\pi$
$338$	0.697867	+	0.507030i	0.0379590	+	0.0275788i
$339$	−3.14392	−	9.67598i	−0.170754	−	0.525527i
$340$	1.31694			0.0714210
$341$	−0.212896	+	25.5643i	−0.0115290	+	1.38439i
$342$	−5.83501			−0.315521
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	5.24295	+	3.80923i	0.282681	+	0.205380i
$345$	1.48718	−	1.08050i	0.0800673	−	0.0581723i
$346$	3.85471	−	11.8636i	0.207231	−	0.637790i
$347$	−4.87029	+	14.9892i	−0.261451	+	0.804662i	0.731039	+	0.682335i	$0.239036\pi$
$347$	−4.87029	+	14.9892i	−0.261451	+	0.804662i	−0.992490	+	0.122327i	$0.960964\pi$
$348$	−2.19361	+	1.59375i	−0.117590	+	0.0854341i
$349$	18.8463	+	13.6926i	1.00882	+	0.732949i	0.963961	−	0.266044i	$-0.0857166\pi$
$349$	18.8463	+	13.6926i	1.00882	+	0.732949i	0.0448574	+	0.998993i	$0.485717\pi$
$350$	0.309017	+	0.951057i	0.0165177	+	0.0508361i
$351$	17.6419			0.941655
$352$	−3.14565	−	1.05113i	−0.167664	−	0.0560252i
$353$	27.1303			1.44400			0.721999	−	0.691894i	$-0.243224\pi$
$353$	27.1303			1.44400			0.721999	+	0.691894i	$0.243224\pi$
$354$	−0.806368	−	2.48174i	−0.0428580	−	0.131903i
$355$	6.49936	+	4.72206i	0.344950	+	0.250621i
$356$	6.58552	−	4.78466i	0.349032	−	0.253586i
$357$	−0.374046	+	1.15119i	−0.0197966	+	0.0609277i
$358$	−3.77913	+	11.6310i	−0.199733	+	0.614716i
$359$	25.9401	−	18.8466i	1.36907	−	0.994685i	0.371258	−	0.928530i	$-0.378927\pi$
$359$	25.9401	−	18.8466i	1.36907	−	0.994685i	0.997809	−	0.0661555i	$-0.0210733\pi$
$360$	1.74359	+	1.26679i	0.0918954	+	0.0667659i
$361$	−3.60620	−	11.0988i	−0.189800	−	0.584145i
$362$	−20.9718			−1.10225
$363$	2.96372	+	9.66630i	0.155555	+	0.507349i
$364$	−3.72325			−0.195151
$365$	0.411210	+	1.26558i	0.0215237	+	0.0662433i
$366$	−1.07561	−	0.781477i	−0.0562231	−	0.0408484i
$367$	9.38760	−	6.82049i	0.490029	−	0.356027i	−0.315167	−	0.949036i	$-0.602060\pi$
$367$	9.38760	−	6.82049i	0.490029	−	0.356027i	0.805195	+	0.593010i	$0.202060\pi$
$368$	−0.618034	+	1.90211i	−0.0322172	+	0.0991545i
$369$	−2.16087	+	6.65046i	−0.112490	+	0.346209i
$370$	6.51153	−	4.73091i	0.338519	−	0.245948i
$371$	10.7476	+	7.80859i	0.557988	+	0.405402i
$372$	−2.18934	−	6.73809i	−0.113512	−	0.349354i
$373$	17.7252			0.917777			0.458889	−	0.888494i	$-0.348248\pi$
$373$	17.7252			0.917777			0.458889	+	0.888494i	$0.348248\pi$
$374$	4.14263	+	1.38427i	0.214210	+	0.0715787i
$375$	0.919131			0.0474637
$376$	2.89577	+	8.91225i	0.149338	+	0.459614i
$377$	8.88598	+	6.45604i	0.457651	+	0.332503i
$378$	−3.83337	+	2.78510i	−0.197167	+	0.143250i
$379$	−3.72490	+	11.4641i	−0.191335	+	0.588869i	0.808665	+	0.588270i	$0.200191\pi$
$379$	−3.72490	+	11.4641i	−0.191335	+	0.588869i	−1.00000		0.000599140i	$0.999809\pi$
$380$	0.836636	−	2.57490i	0.0429185	−	0.132090i
$381$	4.83501	−	3.51284i	0.247705	−	0.179968i
$382$	5.45789	+	3.96539i	0.279250	+	0.202887i
$383$	2.08753	+	6.42475i	0.106668	+	0.328289i	0.990118	−	0.140235i	$-0.0447858\pi$
$383$	2.08753	+	6.42475i	0.106668	+	0.328289i	−0.883451	+	0.468524i	$0.844786\pi$
$384$	0.919131			0.0469042
$385$	−0.0276194	+	3.31651i	−0.00140761	+	0.169025i
$386$	19.9673			1.01631
$387$	−4.31606	−	13.2835i	−0.219398	−	0.675237i
$388$	−11.9721	−	8.69827i	−0.607793	−	0.441588i
$389$	19.5330	−	14.1916i	0.990363	−	0.719541i	0.0303624	−	0.999539i	$-0.490334\pi$
$389$	19.5330	−	14.1916i	0.990363	−	0.719541i	0.960001	+	0.279998i	$0.0903339\pi$
$390$	−1.05750	+	3.25466i	−0.0535488	+	0.164806i
$391$	0.813912	−	2.50496i	0.0411613	−	0.126681i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	−16.1822	−	11.7570i	−0.816283	−	0.593064i
$394$	6.54242	+	20.1355i	0.329603	+	1.01441i
$395$	7.72325			0.388599
$396$	4.15318	+	5.81763i	0.208705	+	0.292347i
$397$	10.5163			0.527798			0.263899	−	0.964550i	$-0.414991\pi$
$397$	10.5163			0.527798			0.263899	+	0.964550i	$0.414991\pi$
$398$	−2.55826	−	7.87353i	−0.128234	−	0.394664i
$399$	2.01321	+	1.46268i	0.100787	+	0.0732258i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−11.4953	+	35.3790i	−0.574049	+	1.76674i	0.0653443	+	0.997863i	$0.479185\pi$
$401$	−11.4953	+	35.3790i	−0.574049	+	1.76674i	−0.639394	+	0.768880i	$0.720815\pi$
$402$	−1.90509	+	5.86325i	−0.0950171	+	0.292432i
$403$	−23.2185	+	16.8692i	−1.15659	+	0.840315i
$404$	11.4071	+	8.28775i	0.567525	+	0.412331i
$405$	−0.652173	−	2.00718i	−0.0324068	−	0.0997377i
$406$	−2.95002			−0.146407
$407$	25.4558	−	8.03735i	1.26180	−	0.398397i
$408$	−1.21044			−0.0599256
$409$	−8.15520	−	25.0991i	−0.403249	−	1.24107i	−0.922349	−	0.386358i	$-0.873733\pi$
$409$	−8.15520	−	25.0991i	−0.403249	−	1.24107i	0.519100	−	0.854713i	$-0.326267\pi$
$410$	−2.62492	−	1.90711i	−0.129635	−	0.0941857i
$411$	−2.15945	+	1.56893i	−0.106518	+	0.0773898i
$412$	3.63486	−	11.1869i	0.179077	−	0.551141i
$413$	0.877316	−	2.70010i	0.0431699	−	0.132863i
$414$	3.48718	−	2.53359i	0.171386	−	0.124519i
$415$	0.230777	+	0.167669i	0.0113284	+	0.00823057i
$416$	−1.15055	−	3.54102i	−0.0564103	−	0.173613i
$417$	1.16523			0.0570614
$418$	5.33831	−	7.22034i	0.261105	−	0.353158i
$419$	13.0447			0.637273			0.318637	−	0.947877i	$-0.396775\pi$
$419$	13.0447			0.637273			0.318637	+	0.947877i	$0.396775\pi$
$420$	−0.284027	−	0.874145i	−0.0138591	−	0.0426539i
$421$	10.8821	+	7.90632i	0.530362	+	0.385331i	0.820493	−	0.571656i	$-0.193699\pi$
$421$	10.8821	+	7.90632i	0.530362	+	0.385331i	−0.290131	+	0.956987i	$0.593699\pi$
$422$	−12.6135	+	9.16427i	−0.614017	+	0.446110i
$423$	6.24095	−	19.2077i	0.303445	−	0.933909i
$424$	−4.10522	+	12.6346i	−0.199367	+	0.613589i
$425$	1.06542	−	0.774076i	0.0516807	−	0.0375482i
$426$	−5.97376	−	4.34019i	−0.289430	−	0.210283i
$427$	−0.446995	−	1.37571i	−0.0216316	−	0.0665752i
$428$	19.8272			0.958383
$429$	−6.74760	+	9.12647i	−0.325777	+	0.440630i
$430$	6.48064			0.312524
$431$	−10.1188	−	31.1424i	−0.487405	−	1.50008i	−0.828467	−	0.560038i	$-0.810787\pi$
$431$	−10.1188	−	31.1424i	−0.487405	−	1.50008i	0.341062	−	0.940041i	$-0.389213\pi$
$432$	−3.83337	−	2.78510i	−0.184433	−	0.133998i
$433$	−7.28467	+	5.29262i	−0.350079	+	0.254347i	−0.748902	−	0.662681i	$-0.769419\pi$
$433$	−7.28467	+	5.29262i	−0.350079	+	0.254347i	0.398823	+	0.917028i	$0.369419\pi$
$434$	2.38197	−	7.33094i	0.114338	−	0.351896i
$435$	−0.837885	+	2.57875i	−0.0401735	+	0.123641i
$436$	0.805403	−	0.585160i	0.0385718	−	0.0280241i
$437$	−4.38069	−	3.18275i	−0.209557	−	0.152252i
$438$	−0.377956	−	1.16323i	−0.0180594	−	0.0555813i
$439$	−3.88952			−0.185637			−0.0928184	−	0.995683i	$-0.529588\pi$
$439$	−3.88952			−0.185637			−0.0928184	+	0.995683i	$0.529588\pi$
$440$	−3.16272	+	0.998590i	−0.150777	+	0.0476059i
$441$	−2.15520			−0.102629
$442$	1.51520	+	4.66331i	0.0720707	+	0.221811i
$443$	−4.55782	−	3.31145i	−0.216548	−	0.157332i	0.474223	−	0.880405i	$-0.342729\pi$
$443$	−4.55782	−	3.31145i	−0.216548	−	0.157332i	−0.690772	+	0.723073i	$0.742729\pi$
$444$	−5.98495	+	4.34832i	−0.284033	+	0.206362i
$445$	2.51544	−	7.74174i	0.119244	−	0.366994i
$446$	5.13936	−	15.8173i	0.243356	−	0.748972i
$447$	4.35365	−	3.16312i	0.205921	−	0.149610i
$448$	0.809017	+	0.587785i	0.0382225	+	0.0277702i
$449$	−1.73932	−	5.35307i	−0.0820835	−	0.252627i	0.901589	−	0.432593i	$-0.142401\pi$
$449$	−1.73932	−	5.35307i	−0.0820835	−	0.252627i	−0.983673	+	0.179966i	$0.942401\pi$
$450$	2.15520			0.101597
$451$	−6.25247	−	8.75824i	−0.294417	−	0.412409i
$452$	11.0691			0.520645
$453$	−2.90397	−	8.93750i	−0.136440	−	0.419920i
$454$	−0.968522	−	0.703672i	−0.0454550	−	0.0330250i
$455$	−3.01217	+	2.18847i	−0.141213	+	0.102597i
$456$	−0.768978	+	2.36667i	−0.0360107	+	0.110830i
$457$	−0.357748	+	1.10103i	−0.0167347	+	0.0515042i	−0.959075	−	0.283152i	$-0.908620\pi$
$457$	−0.357748	+	1.10103i	−0.0167347	+	0.0515042i	0.942340	+	0.334656i	$0.108620\pi$
$458$	12.0231	−	8.73527i	0.561801	−	0.408172i
$459$	5.04830	+	3.66781i	0.235635	+	0.171199i
$460$	0.618034	+	1.90211i	0.0288160	+	0.0886865i
$461$	−10.3088			−0.480129			−0.240065	−	0.970757i	$-0.577169\pi$
$461$	−10.3088			−0.480129			−0.240065	+	0.970757i	$0.577169\pi$
$462$	0.0253858	−	3.04831i	0.00118106	−	0.141820i
$463$	−29.4740			−1.36977			−0.684887	−	0.728649i	$-0.740149\pi$
$463$	−29.4740			−1.36977			−0.684887	+	0.728649i	$0.740149\pi$
$464$	−0.911606	−	2.80564i	−0.0423203	−	0.130248i
$465$	−5.73176	−	4.16437i	−0.265804	−	0.193118i
$466$	5.12268	−	3.72185i	0.237304	−	0.172411i
$467$	6.36503	−	19.5895i	0.294538	−	0.906496i	−0.688838	−	0.724916i	$-0.741879\pi$
$467$	6.36503	−	19.5895i	0.294538	−	0.906496i	0.983376	−	0.181580i	$-0.0581212\pi$
$468$	−2.47966	+	7.63161i	−0.114622	+	0.352771i
$469$	−5.42641	+	3.94252i	−0.250568	+	0.182049i
$470$	7.58121	+	5.50807i	0.349695	+	0.254069i
$471$	−0.335163	−	1.03152i	−0.0154435	−	0.0475301i
$472$	2.83905			0.130678
$473$	20.3859	+	6.81197i	0.937343	+	0.313215i
$474$	−7.09868			−0.326053
$475$	−0.836636	−	2.57490i	−0.0383875	−	0.118145i
$476$	−1.06542	−	0.774076i	−0.0488337	−	0.0354797i
$477$	23.1632	−	16.8291i	1.06057	−	0.770550i
$478$	−3.61259	+	11.1184i	−0.165236	+	0.508544i
$479$	1.29332	−	3.98042i	0.0590931	−	0.181870i	−0.917153	−	0.398536i	$-0.869518\pi$
$479$	1.29332	−	3.98042i	0.0590931	−	0.181870i	0.976246	+	0.216666i	$0.0695184\pi$
$480$	0.743592	−	0.540251i	0.0339402	−	0.0246590i
$481$	24.2441	+	17.6144i	1.10544	+	0.803146i
$482$	3.21206	+	9.88571i	0.146305	+	0.450282i
$483$	−1.83826			−0.0836438
$484$	−10.9985	−	0.183200i	−0.499931	−	0.00832727i
$485$	−14.7984			−0.671960
$486$	4.99208	+	15.3640i	0.226445	+	0.696927i
$487$	6.52658	+	4.74184i	0.295748	+	0.214873i	0.725757	−	0.687951i	$-0.241490\pi$
$487$	6.52658	+	4.74184i	0.295748	+	0.214873i	−0.430009	+	0.902824i	$0.641490\pi$
$488$	1.17025	−	0.850235i	0.0529746	−	0.0384883i
$489$	−3.85760	+	11.8725i	−0.174447	+	0.536892i
$490$	0.309017	−	0.951057i	0.0139600	−	0.0429644i
$491$	−19.0833	+	13.8648i	−0.861217	+	0.625711i	−0.928216	−	0.372043i	$-0.878658\pi$
$491$	−19.0833	+	13.8648i	−0.861217	+	0.625711i	0.0669990	+	0.997753i	$0.478658\pi$
$492$	2.41264	+	1.75289i	0.108770	+	0.0790263i
$493$	1.20053	+	3.69485i	0.0540691	+	0.166408i
$494$	10.0804			0.453538
$495$	6.77951	+	2.26538i	0.304716	+	0.101821i
$496$	7.70820			0.346109
$497$	−2.48253	−	7.64046i	−0.111357	−	0.342721i
$498$	−0.212114	−	0.154110i	−0.00950507	−	0.00690584i
$499$	−5.84257	+	4.24487i	−0.261549	+	0.190027i	−0.710830	−	0.703364i	$-0.751680\pi$
$499$	−5.84257	+	4.24487i	−0.261549	+	0.190027i	0.449281	+	0.893391i	$0.351680\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	3.40832	−	10.4897i	0.152273	−	0.468647i
$502$	−18.0730	+	13.1308i	−0.806640	+	0.586058i
$503$	−9.20884	−	6.69062i	−0.410602	−	0.298320i	0.363243	−	0.931694i	$-0.381669\pi$
$503$	−9.20884	−	6.69062i	−0.410602	−	0.298320i	−0.773846	+	0.633374i	$0.781669\pi$
$504$	−0.665993	−	2.04972i	−0.0296657	−	0.0913016i
$505$	14.1000			0.627440
$506$	−0.0552388	+	6.63302i	−0.00245566	+	0.294874i
$507$	−0.792852			−0.0352118
$508$	2.00930	+	6.18399i	0.0891483	+	0.274370i
$509$	−9.82321	−	7.13698i	−0.435406	−	0.316341i	0.348401	−	0.937346i	$-0.386725\pi$
$509$	−9.82321	−	7.13698i	−0.435406	−	0.316341i	−0.783807	+	0.621005i	$0.786725\pi$
$510$	−0.979265	+	0.711477i	−0.0433626	+	0.0315047i
$511$	0.411210	−	1.26558i	0.0181909	−	0.0559858i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	10.3785	−	7.54042i	0.458222	−	0.332918i
$514$	−4.27323	−	3.10469i	−0.188484	−	0.136942i
$515$	−3.63486	−	11.1869i	−0.160171	−	0.492956i
$516$	−5.95656			−0.262223
$517$	18.0582	+	25.2953i	0.794198	+	1.11249i
$518$	−8.04870			−0.353640
$519$	3.54298	+	10.9042i	0.155520	+	0.478640i
$520$	−3.01217	−	2.18847i	−0.132093	−	0.0959709i
$521$	−9.83480	+	7.14540i	−0.430870	+	0.313046i	−0.781997	−	0.623282i	$-0.785799\pi$
$521$	−9.83480	+	7.14540i	−0.430870	+	0.313046i	0.351126	+	0.936328i	$0.385799\pi$
$522$	−1.96469	+	6.04670i	−0.0859923	+	0.264657i
$523$	−9.06035	+	27.8849i	−0.396181	+	1.21932i	0.531856	+	0.846835i	$0.321495\pi$
$523$	−9.06035	+	27.8849i	−0.396181	+	1.21932i	−0.928038	+	0.372486i	$0.878505\pi$
$524$	17.6060	−	12.7915i	0.769120	−	0.558798i
$525$	−0.743592	−	0.540251i	−0.0324530	−	0.0235785i
$526$	7.84431	+	24.1423i	0.342028	+	1.05265i
$527$	−10.1512			−0.442194
$528$	2.90696	−	0.917835i	0.126509	−	0.0399436i
$529$	−19.0000			−0.826087
$530$	4.10522	+	12.6346i	0.178319	+	0.548810i
$531$	−4.95015	−	3.59650i	−0.214818	−	0.156075i
$532$	−2.19034	+	1.59138i	−0.0949634	+	0.0689949i
$533$	3.73304	−	11.4891i	0.161696	−	0.497649i
$534$	−2.31202	+	7.11567i	−0.100051	+	0.307925i
$535$	16.0405	−	11.6541i	0.693493	−	0.503852i
$536$	−5.42641	−	3.94252i	−0.234385	−	0.170291i
$537$	−3.47352	−	10.6904i	−0.149893	−	0.461324i
$538$	15.3782			0.663002
$539$	1.97174	−	2.66688i	0.0849289	−	0.114871i
$540$	−4.73830			−0.203904
$541$	0.786881	+	2.42177i	0.0338307	+	0.104120i	0.966546	−	0.256494i	$-0.0825673\pi$
$541$	0.786881	+	2.42177i	0.0338307	+	0.104120i	−0.932715	+	0.360614i	$0.882567\pi$
$542$	−8.35505	−	6.07030i	−0.358880	−	0.260742i
$543$	15.5945	−	11.3301i	0.669223	−	0.486219i
$544$	0.406956	−	1.25248i	0.0174481	−	0.0536997i
$545$	0.307637	−	0.946808i	0.0131777	−	0.0405568i
$546$	2.76858	−	2.01149i	0.118484	−	0.0860839i
$547$	−25.9985	−	18.8890i	−1.11162	−	0.807636i	−0.128699	−	0.991684i	$-0.541080\pi$
$547$	−25.9985	−	18.8890i	−1.11162	−	0.807636i	−0.982917	+	0.184048i	$0.941080\pi$
$548$	−0.897411	−	2.76195i	−0.0383355	−	0.117984i
$549$	−3.11751			−0.133052
$550$	−1.97174	+	2.66688i	−0.0840753	+	0.113716i
$551$	7.98692			0.340254
$552$	−0.568054	−	1.74829i	−0.0241780	−	0.0744122i
$553$	−6.24824	−	4.53961i	−0.265702	−	0.193044i
$554$	18.4143	−	13.3788i	0.782350	−	0.568411i
$555$	−2.28605	+	7.03573i	−0.0970373	+	0.298650i
$556$	−0.391756	+	1.20570i	−0.0166142	+	0.0511331i
$557$	−4.83826	+	3.51520i	−0.205004	+	0.148944i	−0.685550	−	0.728025i	$-0.740438\pi$
$557$	−4.83826	+	3.51520i	−0.205004	+	0.148944i	0.480547	+	0.876969i	$0.340438\pi$
$558$	−13.4400	−	9.76471i	−0.568959	−	0.413373i
$559$	7.45630	+	22.9481i	0.315368	+	0.970602i
$560$	1.00000			0.0422577
$561$	−3.82828	+	1.20873i	−0.161630	+	0.0510327i
$562$	−3.07890			−0.129876
$563$	−0.557109	−	1.71460i	−0.0234793	−	0.0722619i	0.938630	−	0.344925i	$-0.112096\pi$
$563$	−0.557109	−	1.71460i	−0.0234793	−	0.0722619i	−0.962110	+	0.272663i	$0.912096\pi$
$564$	−6.96813	−	5.06264i	−0.293411	−	0.213176i
$565$	8.95507	−	6.50624i	0.376742	−	0.273719i
$566$	−3.39274	+	10.4418i	−0.142608	+	0.438901i
$567$	−0.652173	+	2.00718i	−0.0273887	+	0.0842938i
$568$	6.49936	−	4.72206i	0.272707	−	0.198133i
$569$	24.3819	+	17.7145i	1.02214	+	0.742629i	0.966721	−	0.255834i	$-0.0823501\pi$
$569$	24.3819	+	17.7145i	1.02214	+	0.742629i	0.0554205	+	0.998463i	$0.482350\pi$
$570$	0.768978	+	2.36667i	0.0322090	+	0.0991290i
$571$	−30.3322			−1.26936			−0.634681	−	0.772774i	$-0.718869\pi$
$571$	−30.3322			−1.26936			−0.634681	+	0.772774i	$0.718869\pi$
$572$	−7.17490	−	10.0504i	−0.299998	−	0.420226i
$573$	−6.20075			−0.259040
$574$	1.00263	+	3.08578i	0.0418489	+	0.128798i
$575$	1.61803	+	1.17557i	0.0674767	+	0.0490247i
$576$	1.74359	−	1.26679i	0.0726497	−	0.0527831i
$577$	−4.87781	+	15.0124i	−0.203066	+	0.624973i	0.796721	+	0.604347i	$0.206566\pi$
$577$	−4.87781	+	15.0124i	−0.203066	+	0.624973i	−0.999787	+	0.0206258i	$0.993434\pi$
$578$	4.71735	−	14.5185i	0.196216	−	0.603891i
$579$	−14.8476	+	10.7874i	−0.617044	+	0.448308i
$580$	−2.38662	−	1.73398i	−0.0990988	−	0.0719995i
$581$	−0.0881490	−	0.271295i	−0.00365704	−	0.0112552i
$582$	13.6016			0.563806
$583$	−0.366917	+	44.0591i	−0.0151962	+	1.82474i
$584$	1.33071			0.0550650
$585$	2.47966	+	7.63161i	0.102521	+	0.315528i
$586$	−6.51361	−	4.73241i	−0.269075	−	0.195494i
$587$	−20.9713	+	15.2365i	−0.865577	+	0.628879i	−0.929397	−	0.369083i	$-0.879672\pi$
$587$	−20.9713	+	15.2365i	−0.865577	+	0.628879i	0.0638191	+	0.997961i	$0.479672\pi$
$588$	−0.284027	+	0.874145i	−0.0117131	+	0.0360491i
$589$	−6.44896	+	19.8479i	−0.265725	+	0.817817i
$590$	2.29684	−	1.66875i	0.0945595	−	0.0687015i
$591$	−15.7431	−	11.4381i	−0.647586	−	0.470499i
$592$	−2.48718	−	7.65477i	−0.102223	−	0.314609i
$593$	2.58469			0.106140			0.0530702	−	0.998591i	$-0.483099\pi$
$593$	2.58469			0.106140			0.0530702	+	0.998591i	$0.483099\pi$
$594$	−14.9051	−	4.98055i	−0.611562	−	0.204354i
$595$	−1.31694			−0.0539892
$596$	1.80926	+	5.56833i	0.0741102	+	0.228088i
$597$	6.15599	+	4.47259i	0.251948	+	0.183051i
$598$	−6.02435	+	4.37695i	−0.246354	+	0.178987i
$599$	2.47686	−	7.62299i	0.101202	−	0.311467i	−0.887618	−	0.460579i	$-0.847642\pi$
$599$	2.47686	−	7.62299i	0.101202	−	0.311467i	0.988820	+	0.149112i	$0.0476416\pi$
$600$	0.284027	−	0.874145i	0.0115954	−	0.0356868i
$601$	0.869598	−	0.631800i	0.0354717	−	0.0257717i	−0.569908	−	0.821708i	$-0.693021\pi$
$601$	0.869598	−	0.631800i	0.0354717	−	0.0257717i	0.605380	+	0.795937i	$0.293021\pi$
$602$	−5.24295	−	3.80923i	−0.213687	−	0.155253i
$603$	4.46709	+	13.7483i	0.181914	+	0.559874i
$604$	10.2243			0.416020
$605$	−9.00563	+	6.31653i	−0.366131	+	0.256803i
$606$	−12.9597			−0.526452
$607$	−3.91687	−	12.0549i	−0.158981	−	0.489292i	0.839562	−	0.543264i	$-0.182812\pi$
$607$	−3.91687	−	12.0549i	−0.158981	−	0.489292i	−0.998542	+	0.0539721i	$0.982812\pi$
$608$	−2.19034	−	1.59138i	−0.0888301	−	0.0645389i
$609$	2.19361	−	1.59375i	0.0888897	−	0.0645821i
$610$	0.446995	−	1.37571i	0.0180983	−	0.0557008i
$611$	−10.7817	+	33.1826i	−0.436180	+	1.34242i
$612$	−2.29620	+	1.66829i	−0.0928185	+	0.0674366i
$613$	−17.0645	−	12.3981i	−0.689230	−	0.500755i	0.187177	−	0.982326i	$-0.440066\pi$
$613$	−17.0645	−	12.3981i	−0.689230	−	0.500755i	−0.876407	+	0.481571i	$0.840066\pi$
$614$	−8.52774	−	26.2457i	−0.344152	−	1.05919i
$615$	2.98219			0.120254
$616$	3.14565	+	1.05113i	0.126742	+	0.0423511i
$617$	−15.4070			−0.620263			−0.310131	−	0.950694i	$-0.600373\pi$
$617$	−15.4070			−0.620263			−0.310131	+	0.950694i	$0.600373\pi$
$618$	3.34091	+	10.2823i	0.134391	+	0.413613i
$619$	−15.0826	−	10.9581i	−0.606219	−	0.440444i	0.241862	−	0.970311i	$-0.422242\pi$
$619$	−15.0826	−	10.9581i	−0.606219	−	0.440444i	−0.848081	+	0.529867i	$0.822242\pi$
$620$	6.23607	−	4.53077i	0.250447	−	0.181960i
$621$	−2.92843	+	9.01279i	−0.117514	+	0.361671i
$622$	−9.20469	+	28.3291i	−0.369074	+	1.13589i
$623$	−6.58552	+	4.78466i	−0.263843	+	0.191693i
$624$	2.76858	+	2.01149i	0.110832	+	0.0805242i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−30.9153			−1.23562
$627$	−0.0687299	+	8.25302i	−0.00274481	+	0.329594i
$628$	1.18004			0.0470886
$629$	3.27547	+	10.0808i	0.130601	+	0.401950i
$630$	−1.74359	−	1.26679i	−0.0694664	−	0.0504703i
$631$	−22.2244	+	16.1470i	−0.884739	+	0.642800i	−0.934501	−	0.355961i	$-0.884154\pi$
$631$	−22.2244	+	16.1470i	−0.884739	+	0.642800i	0.0497620	+	0.998761i	$0.484154\pi$
$632$	2.38662	−	7.34525i	0.0949345	−	0.292178i
$633$	4.42832	−	13.6290i	0.176010	−	0.541703i
$634$	−1.87845	+	1.36477i	−0.0746028	+	0.0542021i
$635$	5.26042	+	3.82192i	0.208753	+	0.151668i
$636$	−3.77323	−	11.6128i	−0.149618	−	0.460478i
$637$	3.72325			0.147521
$638$	−5.68484	−	7.96313i	−0.225065	−	0.315263i
$639$	−17.3141			−0.684936
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	26.2303	+	19.0574i	1.03603	+	0.752723i	0.969507	−	0.245062i	$-0.0788083\pi$
$641$	26.2303	+	19.0574i	1.03603	+	0.752723i	0.0665266	+	0.997785i	$0.478808\pi$
$642$	−14.7433	+	10.7117i	−0.581874	+	0.422756i
$643$	0.503527	−	1.54970i	0.0198572	−	0.0611140i	−0.940637	−	0.339414i	$-0.889771\pi$
$643$	0.503527	−	1.54970i	0.0198572	−	0.0611140i	0.960494	+	0.278300i	$0.0897711\pi$
$644$	0.618034	−	1.90211i	0.0243540	−	0.0749538i
$645$	−4.81896	+	3.50118i	−0.189746	+	0.137859i
$646$	2.88454	+	2.09574i	0.113491	+	0.0824559i
$647$	11.2147	+	34.5152i	0.440894	+	1.35693i	0.886924	+	0.461915i	$0.152837\pi$
$647$	11.2147	+	34.5152i	0.440894	+	1.35693i	−0.446030	+	0.895018i	$0.647163\pi$
$648$	−2.11048			−0.0829074
$649$	8.97914	−	2.83505i	0.352462	−	0.111285i
$650$	−3.72325			−0.146038
$651$	2.18934	+	6.73809i	0.0858069	+	0.264087i
$652$	−10.9879	−	7.98319i	−0.430320	−	0.312646i
$653$	25.9917	−	18.8841i	1.01713	−	0.738991i	0.0514401	−	0.998676i	$-0.483619\pi$
$653$	25.9917	−	18.8841i	1.01713	−	0.738991i	0.965693	+	0.259685i	$0.0836189\pi$
$654$	−0.282758	+	0.870240i	−0.0110567	+	0.0340291i
$655$	6.72488	−	20.6970i	0.262763	−	0.808700i
$656$	−2.62492	+	1.90711i	−0.102486	+	0.0744603i
$657$	−2.32021	−	1.68573i	−0.0905199	−	0.0657666i
$658$	−2.89577	−	8.91225i	−0.112889	−	0.347436i
$659$	24.7215			0.963012			0.481506	−	0.876443i	$-0.340090\pi$
$659$	24.7215			0.963012			0.481506	+	0.876443i	$0.340090\pi$
$660$	1.81229	−	2.45121i	0.0705432	−	0.0954132i
$661$	−24.3370			−0.946598			−0.473299	−	0.880902i	$-0.656937\pi$
$661$	−24.3370			−0.946598			−0.473299	+	0.880902i	$0.656937\pi$
$662$	3.07684	+	9.46954i	0.119585	+	0.368044i
$663$	−3.64605	−	2.64901i	−0.141601	−	0.102879i
$664$	0.230777	−	0.167669i	0.00895589	−	0.00650683i
$665$	−0.836636	+	2.57490i	−0.0324434	+	0.0998504i
$666$	−5.36038	+	16.4975i	−0.207710	+	0.639267i
$667$	−4.77323	+	3.46796i	−0.184820	+	0.134280i
$668$	9.70820	+	7.05342i	0.375622	+	0.272905i
$669$	4.72374	+	14.5382i	0.182630	+	0.562079i
$670$	−6.70741			−0.259130
$671$	2.85213	−	3.85765i	0.110105	−	0.148923i
$672$	−0.919131			−0.0354562
$673$	−13.5310	−	41.6442i	−0.521582	−	1.60526i	−0.770977	−	0.636863i	$-0.780232\pi$
$673$	−13.5310	−	41.6442i	−0.521582	−	1.60526i	0.249395	−	0.968402i	$-0.419768\pi$
$674$	−16.8018	−	12.2072i	−0.647183	−	0.470206i
$675$	−3.83337	+	2.78510i	−0.147546	+	0.107199i
$676$	0.266561	−	0.820392i	0.0102524	−	0.0315535i
$677$	6.46461	−	19.8960i	0.248455	−	0.764666i	−0.746594	−	0.665280i	$-0.768312\pi$
$677$	6.46461	−	19.8960i	0.248455	−	0.764666i	0.995049	−	0.0993862i	$-0.0316879\pi$
$678$	−8.23088	+	5.98008i	−0.316105	+	0.229664i
$679$	11.9721	+	8.69827i	0.459448	+	0.333809i
$680$	−0.406956	−	1.25248i	−0.0156060	−	0.0480305i
$681$	1.10035			0.0421653
$682$	24.3789	−	7.69734i	0.933517	−	0.294746i
$683$	−6.79955			−0.260178			−0.130089	−	0.991502i	$-0.541526\pi$
$683$	−6.79955			−0.260178			−0.130089	+	0.991502i	$0.541526\pi$
$684$	1.80312	+	5.54943i	0.0689439	+	0.212188i
$685$	−2.34945	−	1.70698i	−0.0897679	−	0.0652202i
$686$	−0.809017	+	0.587785i	−0.0308884	+	0.0224417i
$687$	−4.22102	+	12.9910i	−0.161042	+	0.495636i
$688$	2.00263	−	6.16346i	0.0763495	−	0.234980i
$689$	−40.0160	+	29.0734i	−1.52449	+	1.10761i
$690$	−1.48718	−	1.08050i	−0.0566162	−	0.0411340i
$691$	10.2015	+	31.3969i	0.388083	+	1.19440i	0.934219	+	0.356699i	$0.116098\pi$
$691$	10.2015	+	31.3969i	0.388083	+	1.19440i	−0.546137	+	0.837696i	$0.683902\pi$
$692$	−12.4741			−0.474194
$693$	−4.15318	−	5.81763i	−0.157766	−	0.220993i
$694$	15.7606			0.598263
$695$	0.391756	+	1.20570i	0.0148602	+	0.0457348i
$696$	2.19361	+	1.59375i	0.0831487	+	0.0604110i
$697$	3.45685	−	2.51155i	0.130938	−	0.0951317i
$698$	7.19864	−	22.1551i	0.272472	−	0.838584i
$699$	−1.79846	+	5.53508i	−0.0680238	+	0.209356i
$700$	0.809017	−	0.587785i	0.0305780	−	0.0222162i
$701$	27.6779	+	20.1092i	1.04538	+	0.759514i	0.971329	−	0.237740i	$-0.0764067\pi$
$701$	27.6779	+	20.1092i	1.04538	+	0.759514i	0.0740526	+	0.997254i	$0.476407\pi$
$702$	−5.45165	−	16.7784i	−0.205759	−	0.633261i
$703$	21.7911			0.821869
$704$	−0.0276194	+	3.31651i	−0.00104095	+	0.124996i
$705$	−8.61308			−0.324387
$706$	−8.38371	−	25.8024i	−0.315525	−	0.971086i
$707$	−11.4071	−	8.28775i	−0.429008	−	0.311693i
$708$	−2.11110	+	1.53380i	−0.0793399	+	0.0576438i
$709$	−3.33168	+	10.2539i	−0.125124	+	0.385092i	−0.993924	−	0.110072i	$-0.964892\pi$
$709$	−3.33168	+	10.2539i	−0.125124	+	0.385092i	0.868800	+	0.495164i	$0.164892\pi$
$710$	2.48253	−	7.64046i	0.0931679	−	0.286741i
$711$	−13.4662	+	9.78377i	−0.505022	+	0.366920i
$712$	−6.58552	−	4.78466i	−0.246803	−	0.179313i
$713$	−4.76393	−	14.6619i	−0.178411	−	0.549092i
$714$	1.21044			0.0452995
$715$	−11.7121	−	3.91361i	−0.438006	−	0.146361i
$716$	12.2295			0.457039
$717$	−3.32044	−	10.2193i	−0.124004	−	0.381646i
$718$	−25.9401	−	18.8466i	−0.968077	−	0.703349i
$719$	39.4309	−	28.6482i	1.47052	−	1.06840i	0.490061	−	0.871688i	$-0.336974\pi$
$719$	39.4309	−	28.6482i	1.47052	−	1.06840i	0.980462	−	0.196710i	$-0.0630256\pi$
$720$	0.665993	−	2.04972i	0.0248201	−	0.0763884i
$721$	−3.63486	+	11.1869i	−0.135369	+	0.416624i
$722$	−9.44116	+	6.85941i	−0.351364	+	0.255281i
$723$	−7.72924	−	5.61562i	−0.287453	−	0.208847i
$724$	6.48064	+	19.9454i	0.240851	+	0.741264i
$725$	−2.95002			−0.109561
$726$	8.27736	−	5.80572i	0.307201	−	0.215470i
$727$	11.9416			0.442891			0.221446	−	0.975173i	$-0.428922\pi$
$727$	11.9416			0.442891			0.221446	+	0.975173i	$0.428922\pi$
$728$	1.15055	+	3.54102i	0.0426422	+	0.131239i
$729$	−6.89028	−	5.00608i	−0.255196	−	0.185410i
$730$	1.07656	−	0.782169i	0.0398454	−	0.0289494i
$731$	−2.63734	+	8.11689i	−0.0975454	+	0.300214i
$732$	−0.410847	+	1.26446i	−0.0151853	+	0.0467356i
$733$	31.4976	−	22.8843i	1.16339	−	0.845252i	0.173187	−	0.984889i	$-0.444593\pi$
$733$	31.4976	−	22.8843i	1.16339	−	0.845252i	0.990203	+	0.139637i	$0.0445934\pi$
$734$	−9.38760	−	6.82049i	−0.346503	−	0.251749i
$735$	0.284027	+	0.874145i	0.0104765	+	0.0322433i
$736$	2.00000			0.0737210
$737$	−21.0992	−	7.05033i	−0.777199	−	0.259702i
$738$	6.99271			0.257405
$739$	−9.07222	−	27.9214i	−0.333727	−	1.02711i	−0.967346	−	0.253460i	$-0.918431\pi$
$739$	−9.07222	−	27.9214i	−0.333727	−	1.02711i	0.633619	−	0.773645i	$-0.281569\pi$
$740$	−6.51153	−	4.73091i	−0.239369	−	0.173912i
$741$	−7.49569	+	5.44594i	−0.275361	+	0.200062i
$742$	4.10522	−	12.6346i	0.150707	−	0.463829i
$743$	−8.38522	+	25.8070i	−0.307624	+	0.946769i	0.671061	+	0.741402i	$0.265839\pi$
$743$	−8.38522	+	25.8070i	−0.307624	+	0.946769i	−0.978685	+	0.205367i	$0.934161\pi$
$744$	−5.73176	+	4.16437i	−0.210137	+	0.152673i
$745$	4.73671	+	3.44142i	0.173540	+	0.126084i
$746$	−5.47739	−	16.8577i	−0.200542	−	0.617204i
$747$	−0.614784			−0.0224938
$748$	0.0363730	−	4.36764i	0.00132993	−	0.159697i
$749$	−19.8272			−0.724470
$750$	−0.284027	−	0.874145i	−0.0103712	−	0.0319193i
$751$	29.8128	+	21.6603i	1.08789	+	0.790395i	0.979041	−	0.203664i	$-0.0652850\pi$
$751$	29.8128	+	21.6603i	1.08789	+	0.790395i	0.108844	+	0.994059i	$0.465285\pi$
$752$	7.58121	−	5.50807i	0.276458	−	0.200859i
$753$	6.34503	−	19.5280i	0.231226	−	0.711639i
$754$	3.39414	−	10.4461i	0.123607	−	0.380424i
$755$	8.27161	−	6.00967i	0.301035	−	0.218714i
$756$	3.83337	+	2.78510i	0.139418	+	0.101293i
$757$	0.323438	+	0.995438i	0.0117555	+	0.0361798i	0.956762	−	0.290871i	$-0.0939451\pi$
$757$	0.323438	+	0.995438i	0.0117555	+	0.0361798i	−0.945007	+	0.327051i	$0.893945\pi$
$758$	12.0540			0.437822
$759$	−3.54242	−	4.96211i	−0.128582	−	0.180113i
$760$	−2.70741			−0.0982082
$761$	−0.812589	−	2.50089i	−0.0294563	−	0.0906573i	0.935248	−	0.353994i	$-0.115177\pi$
$761$	−0.812589	−	2.50089i	−0.0294563	−	0.0906573i	−0.964704	+	0.263337i	$0.915177\pi$
$762$	−4.83501	−	3.51284i	−0.175154	−	0.127257i
$763$	−0.805403	+	0.585160i	−0.0291575	+	0.0211842i
$764$	2.08473	−	6.41613i	0.0754228	−	0.232128i
$765$	−0.877071	+	2.69935i	−0.0317106	+	0.0975951i
$766$	5.46522	−	3.97071i	0.197466	−	0.143468i
$767$	8.55172	+	6.21319i	0.308785	+	0.224345i
$768$	−0.284027	−	0.874145i	−0.0102489	−	0.0315430i
$769$	−31.0270			−1.11886			−0.559431	−	0.828877i	$-0.688980\pi$
$769$	−31.0270			−1.11886			−0.559431	+	0.828877i	$0.688980\pi$
$770$	3.16272	−	0.998590i	0.113977	−	0.0359867i
$771$	4.85485			0.174843
$772$	−6.17025	−	18.9901i	−0.222072	−	0.683468i
$773$	7.15807	+	5.20064i	0.257458	+	0.187054i	0.709026	−	0.705183i	$-0.249135\pi$
$773$	7.15807	+	5.20064i	0.257458	+	0.187054i	−0.451568	+	0.892237i	$0.649135\pi$
$774$	−11.2996	+	8.20964i	−0.406156	+	0.295089i
$775$	2.38197	−	7.33094i	0.0855627	−	0.263335i
$776$	−4.57295	+	14.0741i	−0.164159	+	0.505230i
$777$	5.98495	−	4.34832i	0.214709	−	0.155995i
$778$	−19.5330	−	14.1916i	−0.700292	−	0.508792i
$779$	−2.71453	−	8.35447i	−0.0972582	−	0.299330i
$780$	3.42216			0.122533
$781$	15.8403	−	21.4248i	0.566809	−	0.766639i
$782$	−2.63387			−0.0941872
$783$	−4.31947	−	13.2939i	−0.154365	−	0.475087i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	0.954670	−	0.693609i	0.0340736	−	0.0247560i
$786$	−6.18104	+	19.0233i	−0.220470	+	0.678538i
$787$	−1.90106	+	5.85085i	−0.0677654	+	0.208560i	−0.979205	−	0.202874i	$-0.934972\pi$
$787$	−1.90106	+	5.85085i	−0.0677654	+	0.208560i	0.911440	+	0.411434i	$0.134972\pi$
$788$	17.1283	−	12.4444i	0.610170	−	0.443314i
$789$	−18.8759	−	13.7141i	−0.671999	−	0.488236i
$790$	−2.38662	−	7.34525i	−0.0849120	−	0.261332i
$791$	−11.0691			−0.393571
$792$	4.24949	−	5.74765i	0.150999	−	0.204234i
$793$	5.38571			0.191252
$794$	−3.24972	−	10.0016i	−0.115328	−	0.354943i
$795$	−9.87845	−	7.17712i	−0.350353	−	0.254546i
$796$	−6.69762	+	4.86611i	−0.237391	+	0.172475i
$797$	−14.6393	+	45.0550i	−0.518549	+	1.59593i	0.258182	+	0.966096i	$0.416877\pi$
$797$	−14.6393	+	45.0550i	−0.518549	+	1.59593i	−0.776731	+	0.629833i	$0.783123\pi$
$798$	0.768978	−	2.36667i	0.0272215	−	0.0837793i
$799$	−9.98398	+	7.25379i	−0.353208	+	0.256621i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$	5.42128	+	16.6850i	0.191552	+	0.589535i
$802$	37.1997			1.31357
$803$	4.20865	−	1.32883i	0.148520	−	0.0468934i
$804$	6.16499			0.217422
$805$	−0.618034	−	1.90211i	−0.0217828	−	0.0670407i
$806$	23.2185	+	16.8692i	0.817835	+	0.594192i
$807$	−11.4351	+	8.30811i	−0.402536	+	0.292459i
$808$	4.35713	−	13.4099i	0.153283	−	0.471757i
$809$	−3.02786	+	9.31881i	−0.106454	+	0.327632i	−0.990069	−	0.140582i	$-0.955102\pi$
$809$	−3.02786	+	9.31881i	−0.106454	+	0.327632i	0.883615	+	0.468214i	$0.155102\pi$
$810$	−1.70741	+	1.24051i	−0.0599924	+	0.0435870i
$811$	16.9893	+	12.3434i	0.596574	+	0.433436i	0.844661	−	0.535301i	$-0.179802\pi$
$811$	16.9893	+	12.3434i	0.596574	+	0.433436i	−0.248087	+	0.968738i	$0.579802\pi$
$812$	0.911606	+	2.80564i	0.0319911	+	0.0984585i
$813$	9.49224			0.332908
$814$	−15.5103	−	21.7262i	−0.543634	−	0.761504i
$815$	−13.5818			−0.475750
$816$	0.374046	+	1.15119i	0.0130942	+	0.0402999i
$817$	14.1948	+	10.3131i	0.496614	+	0.360811i
$818$	−21.3506	+	15.5121i	−0.746506	+	0.542368i
$819$	2.47966	−	7.63161i	0.0866463	−	0.266670i
$820$	−1.00263	+	3.08578i	−0.0350133	+	0.107760i
$821$	38.9528	−	28.3009i	1.35946	−	0.987707i	0.360983	−	0.932572i	$-0.382441\pi$
$821$	38.9528	−	28.3009i	1.35946	−	0.987707i	0.998479	−	0.0551346i	$-0.0175588\pi$
$822$	2.15945	+	1.56893i	0.0753196	+	0.0547229i
$823$	−10.9809	−	33.7956i	−0.382769	−	1.17804i	−0.938086	−	0.346403i	$-0.887403\pi$
$823$	−10.9809	−	33.7956i	−0.382769	−	1.17804i	0.555317	−	0.831639i	$-0.312597\pi$
$824$	−11.7627			−0.409771
$825$	0.0253858	−	3.04831i	0.000883821	−	0.106128i
$826$	−2.83905			−0.0987833
$827$	−13.6270	−	41.9394i	−0.473856	−	1.45838i	−0.847495	−	0.530803i	$-0.821890\pi$
$827$	−13.6270	−	41.9394i	−0.473856	−	1.45838i	0.373640	−	0.927574i	$-0.378110\pi$
$828$	−3.48718	−	2.53359i	−0.121188	−	0.0880483i
$829$	5.48400	−	3.98436i	0.190467	−	0.138382i	−0.488465	−	0.872583i	$-0.662443\pi$
$829$	5.48400	−	3.98436i	0.190467	−	0.138382i	0.678932	+	0.734201i	$0.262443\pi$
$830$	0.0881490	−	0.271295i	0.00305970	−	0.00941678i
$831$	−6.46484	+	19.8967i	−0.224263	+	0.690210i
$832$	−3.01217	+	2.18847i	−0.104428	+	0.0758717i
$833$	1.06542	+	0.774076i	0.0369148	+	0.0268202i
$834$	−0.360075	−	1.10820i	−0.0124684	−	0.0383737i
$835$	12.0000			0.415277
$836$	−8.51658	−	2.84583i	−0.294552	−	0.0984251i
$837$	36.5238			1.26245
$838$	−4.03102	−	12.4062i	−0.139249	−	0.428565i
$839$	43.4060	+	31.5363i	1.49854	+	1.08875i	0.970957	+	0.239253i	$0.0769024\pi$
$839$	43.4060	+	31.5363i	1.49854	+	1.08875i	0.527585	+	0.849502i	$0.323098\pi$
$840$	−0.743592	+	0.540251i	−0.0256564	+	0.0186404i
$841$	−6.27224	+	19.3040i	−0.216284	+	0.665654i
$842$	4.15660	−	12.7927i	0.143246	−	0.440865i
$843$	2.28945	−	1.66338i	0.0788527	−	0.0572899i
$844$	12.6135	+	9.16427i	0.434176	+	0.315447i
$845$	−0.266561	−	0.820392i	−0.00916999	−	0.0282223i
$846$	−20.1961			−0.694358
$847$	10.9985	+	0.183200i	0.377912	+	0.00629483i
$848$	13.2848			0.456201
$849$	−3.11837	−	9.59736i	−0.107022	−	0.329381i
$850$	−1.06542	−	0.774076i	−0.0365438	−	0.0265506i
$851$	−13.0231	+	9.46181i	−0.446425	+	0.324347i
$852$	−2.28177	+	7.02258i	−0.0781723	+	0.240590i
$853$	−2.67516	+	8.23330i	−0.0915958	+	0.281903i	−0.986352	−	0.164653i	$-0.947350\pi$
$853$	−2.67516	+	8.23330i	−0.0915958	+	0.281903i	0.894756	+	0.446556i	$0.147350\pi$
$854$	−1.17025	+	0.850235i	−0.0400450	+	0.0290944i
$855$	4.72062	+	3.42973i	0.161442	+	0.117294i
$856$	−6.12694	−	18.8568i	−0.209414	−	0.644511i
$857$	−46.7535			−1.59707			−0.798534	−	0.601950i	$-0.794391\pi$
$857$	−46.7535			−1.59707			−0.798534	+	0.601950i	$0.794391\pi$
$858$	10.7649	+	3.59712i	0.367508	+	0.122803i
$859$	−35.5377			−1.21253			−0.606265	−	0.795263i	$-0.707333\pi$
$859$	−35.5377			−1.21253			−0.606265	+	0.795263i	$0.707333\pi$
$860$	−2.00263	−	6.16346i	−0.0682891	−	0.210172i
$861$	−2.41264	−	1.75289i	−0.0822226	−	0.0597382i
$862$	−26.4913	+	19.2471i	−0.902299	+	0.655558i
$863$	12.3839	−	38.1138i	0.421554	−	1.29741i	−0.484701	−	0.874680i	$-0.661072\pi$
$863$	12.3839	−	38.1138i	0.421554	−	1.29741i	0.906256	−	0.422730i	$-0.138928\pi$
$864$	−1.46422	+	4.50639i	−0.0498136	+	0.153311i
$865$	−10.0918	+	7.33210i	−0.343130	+	0.249299i
$866$	7.28467	+	5.29262i	0.247543	+	0.179851i
$867$	4.33586	+	13.3444i	0.147254	+	0.453200i
$868$	−7.70820			−0.261633
$869$	0.213312	−	25.6142i	0.00723610	−	0.868904i
$870$	2.71145			0.0919269
$871$	−7.71720	−	23.7511i	−0.261487	−	0.804776i
$872$	−0.805403	−	0.585160i	−0.0272744	−	0.0198160i
$873$	25.8023	−	18.7465i	0.873277	−	0.634473i
$874$	−1.67327	+	5.14980i	−0.0565993	+	0.174195i
$875$	0.309017	−	0.951057i	0.0104467	−	0.0321516i
$876$	−0.989502	+	0.718915i	−0.0334322	+	0.0242899i
$877$	−30.0015	−	21.7974i	−1.01308	−	0.736044i	−0.0482255	−	0.998836i	$-0.515357\pi$
$877$	−30.0015	−	21.7974i	−1.01308	−	0.736044i	−0.964852	+	0.262792i	$0.915357\pi$
$878$	1.20193	+	3.69916i	0.0405631	+	0.124840i
$879$	7.40016			0.249601
$880$	1.92705	+	2.69935i	0.0649609	+	0.0909950i
$881$	−24.7764			−0.834737			−0.417369	−	0.908737i	$-0.637048\pi$
$881$	−24.7764			−0.834737			−0.417369	+	0.908737i	$0.637048\pi$
$882$	0.665993	+	2.04972i	0.0224252	+	0.0690175i
$883$	4.44734	+	3.23118i	0.149665	+	0.108738i	0.660098	−	0.751180i	$-0.270515\pi$
$883$	4.44734	+	3.23118i	0.149665	+	0.108738i	−0.510433	+	0.859918i	$0.670515\pi$
$884$	3.96685	−	2.88208i	0.133419	−	0.0969349i
$885$	−0.806368	+	2.48174i	−0.0271058	+	0.0834229i
$886$	−1.74093	+	5.35803i	−0.0584877	+	0.180007i
$887$	−18.2065	+	13.2278i	−0.611314	+	0.444145i	−0.849877	−	0.526982i	$-0.823324\pi$
$887$	−18.2065	+	13.2278i	−0.611314	+	0.444145i	0.238563	+	0.971127i	$0.423324\pi$
$888$	5.98495	+	4.34832i	0.200842	+	0.145920i
$889$	−2.00930	−	6.18399i	−0.0673898	−	0.207404i
$890$	−8.14015			−0.272858
$891$	−6.67486	+	2.10750i	−0.223616	+	0.0706040i
$892$	−16.6313			−0.556858
$893$	7.84003	+	24.1291i	0.262357	+	0.807451i
$894$	−4.35365	−	3.16312i	−0.145608	−	0.105790i
$895$	9.89390	−	7.18834i	0.330716	−	0.240280i
$896$	0.309017	−	0.951057i	0.0103235	−	0.0317726i
$897$	2.11501	−	6.50933i	0.0706181	−	0.217340i
$898$	−4.55359	+	3.30838i	−0.151955	+	0.110402i
$899$	18.3965	+	13.3659i	0.613558	+	0.445776i
$900$	−0.665993	−	2.04972i	−0.0221998	−	0.0683239i
$901$	−17.4952			−0.582850
$902$	−6.39746	+	8.65289i	−0.213012	+	0.288110i
$903$	5.95656			0.198222
$904$	−3.42053	−	10.5273i	−0.113765	−	0.350133i
$905$	16.9665	+	12.3269i	0.563987	+	0.409761i
$906$	−7.60269	+	5.52368i	−0.252582	+	0.183512i
$907$	−3.11490	+	9.58669i	−0.103429	+	0.318321i	−0.989358	−	0.145499i	$-0.953521\pi$
$907$	−3.11490	+	9.58669i	−0.103429	+	0.318321i	0.885930	+	0.463819i	$0.153521\pi$
$908$	−0.369942	+	1.13857i	−0.0122770	+	0.0377846i
$909$	−24.5846	+	17.8617i	−0.815419	+	0.592437i
$910$	3.01217	+	2.18847i	0.0998526	+	0.0725472i
$911$	5.04446	+	15.5253i	0.167131	+	0.514375i	0.999187	−	0.0403160i	$-0.0128365\pi$
$911$	5.04446	+	15.5253i	0.167131	+	0.514375i	−0.832056	+	0.554691i	$0.812836\pi$
$912$	2.48847			0.0824013
$913$	0.562451	−	0.760744i	0.0186144	−	0.0251769i
$914$	1.15770			0.0382932
$915$	0.410847	+	1.26446i	0.0135822	+	0.0418016i
$916$	−12.0231	−	8.73527i	−0.397253	−	0.288621i
$917$	−17.6060	+	12.7915i	−0.581400	+	0.422412i
$918$	1.92828	−	5.93464i	0.0636427	−	0.195872i
$919$	5.85834	−	18.0301i	0.193249	−	0.594758i	−0.806744	−	0.590901i	$-0.798772\pi$
$919$	5.85834	−	18.0301i	0.193249	−	0.594758i	0.999993	−	0.00385704i	$-0.00122774\pi$
$920$	1.61803	−	1.17557i	0.0533450	−	0.0387574i
$921$	20.5204	+	14.9090i	0.676171	+	0.491267i
$922$	3.18560	+	9.80426i	0.104912	+	0.322886i
$923$	29.9113			0.984543
$924$	−2.90696	+	0.917835i	−0.0956318	+	0.0301946i
$925$	−8.04870			−0.264640
$926$	9.10798	+	28.0315i	0.299307	+	0.921172i
$927$	20.5093	+	14.9009i	0.673613	+	0.489408i
$928$	−2.38662	+	1.73398i	−0.0783445	+	0.0569206i
$929$	−4.81675	+	14.8244i	−0.158033	+	0.486374i	−0.998456	−	0.0555568i	$-0.982307\pi$
$929$	−4.81675	+	14.8244i	−0.158033	+	0.486374i	0.840423	+	0.541931i	$0.182307\pi$
$930$	−2.18934	+	6.73809i	−0.0717912	+	0.220951i
$931$	2.19034	−	1.59138i	0.0717856	−	0.0521553i
$932$	−5.12268	−	3.72185i	−0.167799	−	0.121913i
$933$	−8.46031	−	26.0382i	−0.276978	−	0.852451i
$934$	−20.5977			−0.673976
$935$	−2.53781	−	3.55487i	−0.0829951	−	0.116257i
$936$	8.02435			0.262284
$937$	10.1115	+	31.1200i	0.330328	+	1.01665i	0.968978	+	0.247148i	$0.0794933\pi$
$937$	10.1115	+	31.1200i	0.330328	+	1.01665i	−0.638650	+	0.769498i	$0.720507\pi$
$938$	5.42641	+	3.94252i	0.177179	+	0.128728i
$939$	22.9884	−	16.7020i	0.750197	−	0.545050i
$940$	2.89577	−	8.91225i	0.0944495	−	0.290686i
$941$	−4.48670	+	13.8086i	−0.146262	+	0.450148i	−0.997171	−	0.0751646i	$-0.976052\pi$
$941$	−4.48670	+	13.8086i	−0.146262	+	0.450148i	0.850909	+	0.525313i	$0.176052\pi$
$942$	−0.877467	+	0.637517i	−0.0285894	+	0.0207714i
$943$	5.24984	+	3.81423i	0.170958	+	0.124208i
$944$	−0.877316	−	2.70010i	−0.0285542	−	0.0878808i
$945$	4.73830			0.154137
$946$	0.178991	−	21.4931i	0.00581952	−	0.698802i
$947$	16.5854			0.538954			0.269477	−	0.963007i	$-0.413149\pi$
$947$	16.5854			0.538954			0.269477	+	0.963007i	$0.413149\pi$
$948$	2.19361	+	6.75124i	0.0712452	+	0.219270i
$949$	4.00832	+	2.91221i	0.130115	+	0.0945344i
$950$	−2.19034	+	1.59138i	−0.0710641	+	0.0516311i
$951$	0.659481	−	2.02967i	0.0213851	−	0.0658166i
$952$	−0.406956	+	1.25248i	−0.0131895	+	0.0405932i
$953$	−23.8946	+	17.3605i	−0.774023	+	0.562361i	−0.903179	−	0.429264i	$-0.858773\pi$
$953$	−23.8946	+	17.3605i	−0.774023	+	0.562361i	0.129156	+	0.991624i	$0.458773\pi$
$954$	−23.1632	−	16.8291i	−0.749937	−	0.544861i
$955$	−2.08473	−	6.41613i	−0.0674602	−	0.207621i
$956$	11.6906			0.378101
$957$	8.52929	+	2.85008i	0.275713	+	0.0921300i
$958$	−4.18526			−0.135220
$959$	0.897411	+	2.76195i	0.0289789	+	0.0891879i
$960$	−0.743592	−	0.540251i	−0.0239993	−	0.0174365i
$961$	−22.9894	+	16.7027i	−0.741592	+	0.538798i
$962$	9.26042	−	28.5006i	0.298568	−	0.918897i
$963$	−13.2048	+	40.6401i	−0.425518	+	1.30961i
$964$	8.40929	−	6.10971i	0.270845	−	0.196780i
$965$	−16.1539	−	11.7365i	−0.520013	−	0.377812i
$966$	0.568054	+	1.74829i	0.0182768	+	0.0562503i
$967$	36.7434			1.18159			0.590794	−	0.806823i	$-0.298815\pi$
$967$	36.7434			1.18159			0.590794	+	0.806823i	$0.298815\pi$
$968$	3.22448	+	10.5168i	0.103639	+	0.338022i
$969$	−3.27715			−0.105277
$970$	4.57295	+	14.0741i	0.146829	+	0.451892i
$971$	18.0311	+	13.1004i	0.578645	+	0.420410i	0.838235	−	0.545309i	$-0.183588\pi$
$971$	18.0311	+	13.1004i	0.578645	+	0.420410i	−0.259590	+	0.965719i	$0.583588\pi$
$972$	13.0694	−	9.49550i	0.419202	−	0.304568i
$973$	0.391756	−	1.20570i	0.0125591	−	0.0386530i
$974$	2.49293	−	7.67246i	0.0798787	−	0.245841i
$975$	2.76858	−	2.01149i	0.0886656	−	0.0644193i
$976$	−1.17025	−	0.850235i	−0.0374587	−	0.0272153i
$977$	−12.5321	−	38.5700i	−0.400939	−	1.23396i	−0.924239	−	0.381814i	$-0.875299\pi$
$977$	−12.5321	−	38.5700i	−0.400939	−	1.23396i	0.523300	−	0.852148i	$-0.324701\pi$
$978$	12.4835			0.399177
$979$	−25.6061	−	8.55632i	−0.818374	−	0.273461i
$980$	−1.00000			−0.0319438
$981$	0.663018	+	2.04056i	0.0211685	+	0.0651500i
$982$	19.0833	+	13.8648i	0.608972	+	0.442444i
$983$	32.2560	−	23.4353i	1.02881	−	0.747471i	0.0607363	−	0.998154i	$-0.480655\pi$
$983$	32.2560	−	23.4353i	1.02881	−	0.747471i	0.968069	+	0.250683i	$0.0806551\pi$
$984$	0.921548	−	2.83623i	0.0293779	−	0.0904158i
$985$	6.54242	−	20.1355i	0.208459	−	0.641571i
$986$	3.14302	−	2.28354i	0.100094	−	0.0727227i
$987$	6.96813	+	5.06264i	0.221798	+	0.161146i
$988$	−3.11501	−	9.58701i	−0.0991016	−	0.305003i
$989$	−12.9613			−0.412145
$990$	0.0595253	−	7.14774i	0.00189184	−	0.227170i
$991$	35.5410			1.12900			0.564498	−	0.825435i	$-0.309070\pi$
$991$	35.5410			1.12900			0.564498	+	0.825435i	$0.309070\pi$
$992$	−2.38197	−	7.33094i	−0.0756275	−	0.232758i
$993$	−7.40385	−	5.37921i	−0.234954	−	0.170704i
$994$	−6.49936	+	4.72206i	−0.206147	+	0.149775i
$995$	−2.55826	+	7.87353i	−0.0811024	+	0.249608i
$996$	−0.0810205	+	0.249355i	−0.00256723	+	0.00790113i
$997$	−38.3804	+	27.8850i	−1.21552	+	0.883126i	−0.995720	−	0.0924192i	$-0.970540\pi$
$997$	−38.3804	+	27.8850i	−1.21552	+	0.883126i	−0.219799	+	0.975545i	$0.570540\pi$
$998$	5.84257	+	4.24487i	0.184943	+	0.134369i
$999$	−11.7850	−	36.2706i	−0.372862	−	1.14755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.e.71.2	✓	8
11.3	even	5		8470.2.a.cq.1.2		4
11.8	odd	10		8470.2.a.ct.1.2		4
11.9	even	5	inner	770.2.n.e.141.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.e.71.2	✓	8	1.1	even	1	trivial
770.2.n.e.141.2	yes	8	11.9	even	5	inner
8470.2.a.cq.1.2		4	11.3	even	5
8470.2.a.ct.1.2		4	11.8	odd	10

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.743592 + 0.540251i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.284027 - 0.874145i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.665993 - 2.04972i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.743592 + 0.540251i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.284027 - 0.874145i) q^{6} +(0.809017 - 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.665993 - 2.04972i) q^{9} +1.00000 q^{10} +(3.14565 + 1.05113i) q^{11} -0.919131 q^{12} +(1.15055 + 3.54102i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-0.743592 + 0.540251i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.406956 + 1.25248i) q^{17} +(-1.74359 + 1.26679i) q^{18} +(2.19034 + 1.59138i) q^{19} +(-0.309017 - 0.951057i) q^{20} +0.919131 q^{21} +(0.0276194 - 3.31651i) q^{22} -2.00000 q^{23} +(0.284027 + 0.874145i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(3.01217 - 2.18847i) q^{26} +(1.46422 - 4.50639i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(2.38662 - 1.73398i) q^{29} +(0.743592 + 0.540251i) q^{30} +(2.38197 + 7.33094i) q^{31} -1.00000 q^{32} +(1.77121 + 2.48105i) q^{33} +1.31694 q^{34} +(0.309017 + 0.951057i) q^{35} +(1.74359 + 1.26679i) q^{36} +(6.51153 - 4.73091i) q^{37} +(0.836636 - 2.57490i) q^{38} +(-1.05750 + 3.25466i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-2.62492 - 1.90711i) q^{41} +(-0.284027 - 0.874145i) q^{42} +6.48064 q^{43} +(-3.16272 + 0.998590i) q^{44} +2.15520 q^{45} +(0.618034 + 1.90211i) q^{46} +(7.58121 + 5.50807i) q^{47} +(0.743592 - 0.540251i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-0.979265 + 0.711477i) q^{51} +(-3.01217 - 2.18847i) q^{52} +(4.10522 + 12.6346i) q^{53} -4.73830 q^{54} +(-1.97174 + 2.66688i) q^{55} +1.00000 q^{56} +(0.768978 + 2.36667i) q^{57} +(-2.38662 - 1.73398i) q^{58} +(2.29684 - 1.66875i) q^{59} +(0.284027 - 0.874145i) q^{60} +(0.446995 - 1.37571i) q^{61} +(6.23607 - 4.53077i) q^{62} +(-1.74359 - 1.26679i) q^{63} +(0.309017 + 0.951057i) q^{64} -3.72325 q^{65} +(1.81229 - 2.45121i) q^{66} -6.70741 q^{67} +(-0.406956 - 1.25248i) q^{68} +(-1.48718 - 1.08050i) q^{69} +(0.809017 - 0.587785i) q^{70} +(2.48253 - 7.64046i) q^{71} +(0.665993 - 2.04972i) q^{72} +(1.07656 - 0.782169i) q^{73} +(-6.51153 - 4.73091i) q^{74} +(-0.284027 - 0.874145i) q^{75} -2.70741 q^{76} +(3.16272 - 0.998590i) q^{77} +3.42216 q^{78} +(-2.38662 - 7.34525i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-1.70741 + 1.24051i) q^{81} +(-1.00263 + 3.08578i) q^{82} +(0.0881490 - 0.271295i) q^{83} +(-0.743592 + 0.540251i) q^{84} +(-1.06542 - 0.774076i) q^{85} +(-2.00263 - 6.16346i) q^{86} +2.71145 q^{87} +(1.92705 + 2.69935i) q^{88} -8.14015 q^{89} +(-0.665993 - 2.04972i) q^{90} +(3.01217 + 2.18847i) q^{91} +(1.61803 - 1.17557i) q^{92} +(-2.18934 + 6.73809i) q^{93} +(2.89577 - 8.91225i) q^{94} +(-2.19034 + 1.59138i) q^{95} +(-0.743592 - 0.540251i) q^{96} +(4.57295 + 14.0741i) q^{97} -1.00000 q^{98} +(0.0595253 - 7.14774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9	\( 8 q + 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 13 q^{9} + 8 q^{10} + 8 q^{11} + 4 q^{12} + 8 q^{13} - 2 q^{14} + q^{15} - 2 q^{16} - 9 q^{17} - 7 q^{18} - 9 q^{19} + 2 q^{20} - 4 q^{21} - 8 q^{22} - 16 q^{23} + q^{24} - 2 q^{25} + 7 q^{26} - 22 q^{27} + 2 q^{28} - q^{30} + 28 q^{31} - 8 q^{32} - q^{33} + 4 q^{34} - 2 q^{35} + 7 q^{36} + 4 q^{37} - 6 q^{38} - 13 q^{39} - 2 q^{40} + 8 q^{41} - q^{42} - 14 q^{43} - 7 q^{44} - 12 q^{45} - 4 q^{46} - q^{48} - 2 q^{49} + 2 q^{50} + 4 q^{51} - 7 q^{52} + 10 q^{53} - 28 q^{54} + 7 q^{55} + 8 q^{56} - 17 q^{57} + 31 q^{59} + q^{60} + 28 q^{61} + 32 q^{62} - 7 q^{63} - 2 q^{64} + 2 q^{65} + 36 q^{66} - 26 q^{67} - 9 q^{68} + 2 q^{69} + 2 q^{70} + 34 q^{71} + 13 q^{72} - 24 q^{73} - 4 q^{74} - q^{75} + 6 q^{76} + 7 q^{77} - 2 q^{78} + 2 q^{80} + 14 q^{81} - 3 q^{82} - 21 q^{83} + q^{84} - 11 q^{85} - 11 q^{86} - 52 q^{87} + 2 q^{88} - 14 q^{89} - 13 q^{90} + 7 q^{91} + 4 q^{92} + 14 q^{93} + 5 q^{94} + 9 q^{95} + q^{96} + 50 q^{97} - 8 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 13 * q^9 + 8 * q^10 + 8 * q^11 + 4 * q^12 + 8 * q^13 - 2 * q^14 + q^15 - 2 * q^16 - 9 * q^17 - 7 * q^18 - 9 * q^19 + 2 * q^20 - 4 * q^21 - 8 * q^22 - 16 * q^23 + q^24 - 2 * q^25 + 7 * q^26 - 22 * q^27 + 2 * q^28 - q^30 + 28 * q^31 - 8 * q^32 - q^33 + 4 * q^34 - 2 * q^35 + 7 * q^36 + 4 * q^37 - 6 * q^38 - 13 * q^39 - 2 * q^40 + 8 * q^41 - q^42 - 14 * q^43 - 7 * q^44 - 12 * q^45 - 4 * q^46 - q^48 - 2 * q^49 + 2 * q^50 + 4 * q^51 - 7 * q^52 + 10 * q^53 - 28 * q^54 + 7 * q^55 + 8 * q^56 - 17 * q^57 + 31 * q^59 + q^60 + 28 * q^61 + 32 * q^62 - 7 * q^63 - 2 * q^64 + 2 * q^65 + 36 * q^66 - 26 * q^67 - 9 * q^68 + 2 * q^69 + 2 * q^70 + 34 * q^71 + 13 * q^72 - 24 * q^73 - 4 * q^74 - q^75 + 6 * q^76 + 7 * q^77 - 2 * q^78 + 2 * q^80 + 14 * q^81 - 3 * q^82 - 21 * q^83 + q^84 - 11 * q^85 - 11 * q^86 - 52 * q^87 + 2 * q^88 - 14 * q^89 - 13 * q^90 + 7 * q^91 + 4 * q^92 + 14 * q^93 + 5 * q^94 + 9 * q^95 + q^96 + 50 * q^97 - 8 * q^98 - 18 * q^99

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