LMFDB - Embedded newform 770.2.n.e.141.1

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			141.1
Root			$2.51217 - 1.82520i$ of defining polynomial
Character	$\chi$	$=$	770.141
Dual form			770.2.n.e.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-1.55261 + 1.12804i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.593044 - 1.82520i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.211078 - 0.649631i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.55261 + 1.12804i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.593044 - 1.82520i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.211078 - 0.649631i) q^{9} +1.00000 q^{10} +(-0.0276194 + 3.31651i) q^{11} +1.91913 q^{12} +(-0.268582 + 0.826612i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(1.55261 + 1.12804i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.28403 - 3.95183i) q^{17} +(0.552609 + 0.401494i) q^{18} +(-6.11739 + 4.44455i) q^{19} +(-0.309017 + 0.951057i) q^{20} -1.91913 q^{21} +(-3.14565 - 1.05113i) q^{22} -2.00000 q^{23} +(-0.593044 + 1.82520i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.703158 - 0.510874i) q^{26} +(-1.37405 - 4.22888i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(0.967486 + 0.702919i) q^{29} +(-1.55261 + 1.12804i) q^{30} +(2.38197 - 7.33094i) q^{31} -1.00000 q^{32} +(-3.69826 - 5.18040i) q^{33} +4.15520 q^{34} +(0.309017 - 0.951057i) q^{35} +(-0.552609 + 0.401494i) q^{36} +(-5.51153 - 4.00436i) q^{37} +(-2.33664 - 7.19143i) q^{38} +(-0.515445 - 1.58638i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(7.97902 - 5.79710i) q^{41} +(0.593044 - 1.82520i) q^{42} -6.62654 q^{43} +(1.97174 - 2.66688i) q^{44} -0.683063 q^{45} +(0.618034 - 1.90211i) q^{46} +(-8.69925 + 6.32037i) q^{47} +(-1.55261 - 1.12804i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(6.45140 + 4.68722i) q^{51} +(0.703158 - 0.510874i) q^{52} +(-0.487185 + 1.49940i) q^{53} +4.44651 q^{54} +(3.16272 - 0.998590i) q^{55} +1.00000 q^{56} +(4.48431 - 13.8013i) q^{57} +(-0.967486 + 0.702919i) q^{58} +(6.01217 + 4.36810i) q^{59} +(-0.593044 - 1.82520i) q^{60} +(-2.39127 - 7.35956i) q^{61} +(6.23607 + 4.53077i) q^{62} +(0.552609 - 0.401494i) q^{63} +(0.309017 - 0.951057i) q^{64} +0.869151 q^{65} +(6.06968 - 1.91643i) q^{66} +3.56151 q^{67} +(-1.28403 + 3.95183i) q^{68} +(3.10522 - 2.25607i) q^{69} +(0.809017 + 0.587785i) q^{70} +(-0.690738 - 2.12587i) q^{71} +(-0.211078 - 0.649631i) q^{72} +(-13.7848 - 10.0152i) q^{73} +(5.51153 - 4.00436i) q^{74} +(0.593044 - 1.82520i) q^{75} +7.56151 q^{76} +(-1.97174 + 2.66688i) q^{77} +1.66801 q^{78} +(-0.967486 + 2.97761i) q^{79} +(0.809017 - 0.587785i) q^{80} +(8.56151 + 6.22030i) q^{81} +(3.04771 + 9.37990i) q^{82} +(-2.54306 - 7.82675i) q^{83} +(1.55261 + 1.12804i) q^{84} +(-3.36163 + 2.44236i) q^{85} +(2.04771 - 6.30222i) q^{86} -2.29505 q^{87} +(1.92705 + 2.69935i) q^{88} -9.89429 q^{89} +(0.211078 - 0.649631i) q^{90} +(-0.703158 + 0.510874i) q^{91} +(1.61803 + 1.17557i) q^{92} +(4.57130 + 14.0690i) q^{93} +(-3.32282 - 10.2266i) q^{94} +(6.11739 + 4.44455i) q^{95} +(1.55261 - 1.12804i) q^{96} +(4.57295 - 14.0741i) q^{97} -1.00000 q^{98} +(2.14868 + 0.717985i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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
$3$	−1.55261	+	1.12804i	−0.896399	+	0.651272i	−0.937539	−	0.347881i	$-0.886901\pi$
$3$	−1.55261	+	1.12804i	−0.896399	+	0.651272i	0.0411392	+	0.999153i	$0.486901\pi$
$4$	−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
$6$	−0.593044	−	1.82520i	−0.242109	−	0.745136i
$7$	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
$9$	0.211078	−	0.649631i	0.0703593	−	0.216544i
$10$	1.00000			0.316228
$11$	−0.0276194	+	3.31651i	−0.00832756	+	0.999965i
$11$	−0.0276194	+	3.31651i	−0.00832756	+	0.999965i
$12$	1.91913			0.554005
$13$	−0.268582	+	0.826612i	−0.0744913	+	0.229261i	−0.981369	−	0.192134i	$-0.938459\pi$
$13$	−0.268582	+	0.826612i	−0.0744913	+	0.229261i	0.906877	+	0.421395i	$0.138459\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	1.55261	+	1.12804i	0.400882	+	0.291258i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.28403	−	3.95183i	−0.311422	−	0.958459i	−0.977202	−	0.212311i	$-0.931901\pi$
$17$	−1.28403	−	3.95183i	−0.311422	−	0.958459i	0.665780	−	0.746148i	$-0.268099\pi$
$18$	0.552609	+	0.401494i	0.130251	+	0.0946331i
$19$	−6.11739	+	4.44455i	−1.40343	+	1.01965i	−0.409189	+	0.912450i	$0.634188\pi$
$19$	−6.11739	+	4.44455i	−1.40343	+	1.01965i	−0.994238	+	0.107199i	$0.965812\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	−1.91913			−0.418789
$22$	−3.14565	−	1.05113i	−0.670656	−	0.224101i
$23$	−2.00000			−0.417029			−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000			−0.417029			−0.208514	+	0.978019i	$0.566863\pi$
$24$	−0.593044	+	1.82520i	−0.121055	+	0.372568i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−0.703158	−	0.510874i	−0.137901	−	0.100191i
$27$	−1.37405	−	4.22888i	−0.264435	−	0.813848i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	0.967486	+	0.702919i	0.179658	+	0.130529i	0.673979	−	0.738750i	$-0.264584\pi$
$29$	0.967486	+	0.702919i	0.179658	+	0.130529i	−0.494322	+	0.869279i	$0.664584\pi$
$30$	−1.55261	+	1.12804i	−0.283466	+	0.205950i
$31$	2.38197	−	7.33094i	0.427814	−	1.31668i	−0.472460	−	0.881352i	$-0.656634\pi$
$31$	2.38197	−	7.33094i	0.427814	−	1.31668i	0.900274	−	0.435323i	$-0.143366\pi$
$32$	−1.00000			−0.176777
$33$	−3.69826	−	5.18040i	−0.643785	−	0.901792i
$34$	4.15520			0.712611
$35$	0.309017	−	0.951057i	0.0522334	−	0.160758i
$36$	−0.552609	+	0.401494i	−0.0921016	+	0.0669157i
$37$	−5.51153	−	4.00436i	−0.906091	−	0.658313i	0.0339325	−	0.999424i	$-0.489197\pi$
$37$	−5.51153	−	4.00436i	−0.906091	−	0.658313i	−0.940023	+	0.341111i	$0.889197\pi$
$38$	−2.33664	−	7.19143i	−0.379052	−	1.16660i
$39$	−0.515445	−	1.58638i	−0.0825372	−	0.254023i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	7.97902	−	5.79710i	1.24611	−	0.905354i	0.248124	−	0.968728i	$-0.420186\pi$
$41$	7.97902	−	5.79710i	1.24611	−	0.905354i	0.997990	+	0.0633739i	$0.0201861\pi$
$42$	0.593044	−	1.82520i	0.0915087	−	0.281635i
$43$	−6.62654			−1.01054			−0.505269	−	0.862962i	$-0.668607\pi$
$43$	−6.62654			−1.01054			−0.505269	+	0.862962i	$0.668607\pi$
$44$	1.97174	−	2.66688i	0.297251	−	0.402047i
$45$	−0.683063			−0.101825
$46$	0.618034	−	1.90211i	0.0911241	−	0.280451i
$47$	−8.69925	+	6.32037i	−1.26892	+	0.921921i	−0.999159	−	0.0410073i	$-0.986943\pi$
$47$	−8.69925	+	6.32037i	−1.26892	+	0.921921i	−0.269757	+	0.962928i	$0.586943\pi$
$48$	−1.55261	−	1.12804i	−0.224100	−	0.162818i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$	6.45140	+	4.68722i	0.903377	+	0.656342i
$52$	0.703158	−	0.510874i	0.0975104	−	0.0708455i
$53$	−0.487185	+	1.49940i	−0.0669200	+	0.205958i	−0.978925	−	0.204221i	$-0.934534\pi$
$53$	−0.487185	+	1.49940i	−0.0669200	+	0.205958i	0.912005	+	0.410179i	$0.134534\pi$
$54$	4.44651			0.605093
$55$	3.16272	−	0.998590i	0.426461	−	0.134650i
$56$	1.00000			0.133631
$57$	4.48431	−	13.8013i	0.593961	−	1.82803i
$58$	−0.967486	+	0.702919i	−0.127037	+	0.0922978i
$59$	6.01217	+	4.36810i	0.782718	+	0.568678i	0.905794	−	0.423719i	$-0.139276\pi$
$59$	6.01217	+	4.36810i	0.782718	+	0.568678i	−0.123075	+	0.992397i	$0.539276\pi$
$60$	−0.593044	−	1.82520i	−0.0765617	−	0.235633i
$61$	−2.39127	−	7.35956i	−0.306170	−	0.942295i	−0.979238	−	0.202714i	$-0.935024\pi$
$61$	−2.39127	−	7.35956i	−0.306170	−	0.942295i	0.673068	−	0.739581i	$-0.264976\pi$
$62$	6.23607	+	4.53077i	0.791981	+	0.575408i
$63$	0.552609	−	0.401494i	0.0696222	−	0.0505835i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.869151			0.107805
$66$	6.06968	−	1.91643i	0.747126	−	0.235896i
$67$	3.56151			0.435108			0.217554	−	0.976048i	$-0.430192\pi$
$67$	3.56151			0.435108			0.217554	+	0.976048i	$0.430192\pi$
$68$	−1.28403	+	3.95183i	−0.155711	+	0.479230i
$69$	3.10522	−	2.25607i	0.373824	−	0.271599i
$70$	0.809017	+	0.587785i	0.0966960	+	0.0702538i
$71$	−0.690738	−	2.12587i	−0.0819756	−	0.252295i	0.901666	−	0.432434i	$-0.142345\pi$
$71$	−0.690738	−	2.12587i	−0.0819756	−	0.252295i	−0.983641	+	0.180139i	$0.942345\pi$
$72$	−0.211078	−	0.649631i	−0.0248758	−	0.0765598i
$73$	−13.7848	−	10.0152i	−1.61338	−	1.17219i	−0.851218	−	0.524812i	$-0.824136\pi$
$73$	−13.7848	−	10.0152i	−1.61338	−	1.17219i	−0.762167	−	0.647381i	$-0.775864\pi$
$74$	5.51153	−	4.00436i	0.640703	−	0.465498i
$75$	0.593044	−	1.82520i	0.0684788	−	0.210756i
$76$	7.56151			0.867365
$77$	−1.97174	+	2.66688i	−0.224701	+	0.303919i
$78$	1.66801			0.188865
$79$	−0.967486	+	2.97761i	−0.108851	+	0.335008i	−0.990615	−	0.136683i	$-0.956356\pi$
$79$	−0.967486	+	2.97761i	−0.108851	+	0.335008i	0.881764	+	0.471690i	$0.156356\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	8.56151	+	6.22030i	0.951279	+	0.691145i
$82$	3.04771	+	9.37990i	0.336564	+	1.03584i
$83$	−2.54306	−	7.82675i	−0.279138	−	0.859097i	−0.988095	−	0.153846i	$-0.950834\pi$
$83$	−2.54306	−	7.82675i	−0.279138	−	0.859097i	0.708957	−	0.705251i	$-0.249166\pi$
$84$	1.55261	+	1.12804i	0.169404	+	0.123079i
$85$	−3.36163	+	2.44236i	−0.364620	+	0.264912i
$86$	2.04771	−	6.30222i	0.220811	−	0.679586i
$87$	−2.29505			−0.246055
$88$	1.92705	+	2.69935i	0.205424	+	0.287751i
$89$	−9.89429			−1.04879			−0.524396	−	0.851474i	$-0.675709\pi$
$89$	−9.89429			−1.04879			−0.524396	+	0.851474i	$0.675709\pi$
$90$	0.211078	−	0.649631i	0.0222496	−	0.0684771i
$91$	−0.703158	+	0.510874i	−0.0737110	+	0.0535541i
$92$	1.61803	+	1.17557i	0.168692	+	0.122562i
$93$	4.57130	+	14.0690i	0.474022	+	1.45889i
$94$	−3.32282	−	10.2266i	−0.342722	−	1.05479i
$95$	6.11739	+	4.44455i	0.627631	+	0.456001i
$96$	1.55261	−	1.12804i	0.158463	−	0.115130i
$97$	4.57295	−	14.0741i	0.464313	−	1.42901i	−0.395532	−	0.918452i	$-0.629440\pi$
$97$	4.57295	−	14.0741i	0.464313	−	1.42901i	0.859845	−	0.510555i	$-0.170560\pi$
$98$	−1.00000			−0.101015
$99$	2.14868	+	0.717985i	0.215950	+	0.0721602i
$100$	1.00000			0.100000
$101$	−5.44125	+	16.7464i	−0.541424	+	1.66633i	0.187919	+	0.982185i	$0.439826\pi$
$101$	−5.44125	+	16.7464i	−0.541424	+	1.66633i	−0.729343	+	0.684148i	$0.760174\pi$
$102$	−6.45140	+	4.68722i	−0.638784	+	0.464104i
$103$	3.92601	+	2.85242i	0.386842	+	0.281057i	0.764160	−	0.645027i	$-0.223154\pi$
$103$	3.92601	+	2.85242i	0.386842	+	0.281057i	−0.377318	+	0.926084i	$0.623154\pi$
$104$	0.268582	+	0.826612i	0.0263367	+	0.0810559i
$105$	0.593044	+	1.82520i	0.0578752	+	0.178121i
$106$	−1.27547	−	0.926680i	−0.123884	−	0.0900072i
$107$	4.83233	−	3.51089i	0.467159	−	0.339411i	−0.329174	−	0.944269i	$-0.606770\pi$
$107$	4.83233	−	3.51089i	0.467159	−	0.339411i	0.796333	+	0.604858i	$0.206770\pi$
$108$	−1.37405	+	4.22888i	−0.132218	+	0.406924i
$109$	−19.3651			−1.85484			−0.927422	−	0.374016i	$-0.877981\pi$
$109$	−19.3651			−1.85484			−0.927422	+	0.374016i	$0.877981\pi$
$110$	−0.0276194	+	3.31651i	−0.00263341	+	0.316217i
$111$	13.0743			1.24096
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	−10.9163	+	7.93112i	−1.02692	+	0.746097i	−0.967689	−	0.252147i	$-0.918863\pi$
$113$	−10.9163	+	7.93112i	−1.02692	+	0.746097i	−0.0592261	+	0.998245i	$0.518863\pi$
$114$	11.7401	+	8.52967i	1.09956	+	0.798876i
$115$	0.618034	+	1.90211i	0.0576320	+	0.177373i
$116$	−0.369547	−	1.13735i	−0.0343115	−	0.105600i
$117$	0.480301	+	0.348959i	0.0444038	+	0.0322613i
$118$	−6.01217	+	4.36810i	−0.553466	+	0.402116i
$119$	1.28403	−	3.95183i	0.117707	−	0.362264i
$120$	1.91913			0.175192
$121$	−10.9985	−	0.183200i	−0.999861	−	0.0166545i
$122$	7.73830			0.700593
$123$	−5.84896	+	18.0013i	−0.527383	+	1.62312i
$124$	−6.23607	+	4.53077i	−0.560015	+	0.406875i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	0.211078	+	0.649631i	0.0188043	+	0.0578738i
$127$	−0.828961	−	2.55128i	−0.0735584	−	0.226389i	0.907517	−	0.420015i	$-0.137975\pi$
$127$	−0.828961	−	2.55128i	−0.0735584	−	0.226389i	−0.981075	+	0.193626i	$0.937975\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	10.2884	−	7.47498i	0.905846	−	0.658136i
$130$	−0.268582	+	0.826612i	−0.0235562	+	0.0724986i
$131$	1.19986			0.104832			0.0524159	−	0.998625i	$-0.483308\pi$
$131$	1.19986			0.104832			0.0524159	+	0.998625i	$0.483308\pi$
$132$	−0.0530052	+	6.36482i	−0.00461351	+	0.553986i
$133$	−7.56151			−0.655666
$134$	−1.10057	+	3.38720i	−0.0950746	+	0.292610i
$135$	−3.59730	+	2.61359i	−0.309606	+	0.224942i
$136$	−3.36163	−	2.44236i	−0.288257	−	0.209431i
$137$	−1.43947	−	4.43023i	−0.122982	−	0.378500i	0.870546	−	0.492087i	$-0.163766\pi$
$137$	−1.43947	−	4.43023i	−0.122982	−	0.378500i	−0.993528	+	0.113587i	$0.963766\pi$
$138$	1.18609	+	3.65040i	0.100967	+	0.310743i
$139$	10.2104	+	7.41832i	0.866038	+	0.629213i	0.929521	−	0.368769i	$-0.120221\pi$
$139$	10.2104	+	7.41832i	0.866038	+	0.629213i	−0.0634829	+	0.997983i	$0.520221\pi$
$140$	−0.809017	+	0.587785i	−0.0683744	+	0.0496769i
$141$	6.37692	−	19.6261i	0.537034	−	1.65282i
$142$	2.23528			0.187580
$143$	−2.73405	−	0.913587i	−0.228633	−	0.0763979i
$144$	0.683063			0.0569219
$145$	0.369547	−	1.13735i	0.0306892	−	0.0944516i
$146$	13.7848	−	10.0152i	1.14084	−	0.828865i
$147$	−1.55261	−	1.12804i	−0.128057	−	0.0930389i
$148$	2.10522	+	6.47920i	0.173048	+	0.532587i
$149$	4.98253	+	15.3347i	0.408185	+	1.25626i	0.918206	+	0.396103i	$0.129638\pi$
$149$	4.98253	+	15.3347i	0.408185	+	1.25626i	−0.510021	+	0.860162i	$0.670362\pi$
$150$	1.55261	+	1.12804i	0.126770	+	0.0921038i
$151$	−7.93660	+	5.76627i	−0.645871	+	0.469253i	−0.861862	−	0.507143i	$-0.830702\pi$
$151$	−7.93660	+	5.76627i	−0.645871	+	0.469253i	0.215991	+	0.976395i	$0.430702\pi$
$152$	−2.33664	+	7.19143i	−0.189526	+	0.583302i
$153$	−2.83826			−0.229460
$154$	−1.92705	−	2.69935i	−0.155286	−	0.217520i
$155$	−7.70820			−0.619138
$156$	−0.515445	+	1.58638i	−0.0412686	+	0.127012i
$157$	2.21860	−	1.61191i	0.177064	−	0.128644i	−0.495723	−	0.868480i	$-0.665097\pi$
$157$	2.21860	−	1.61191i	0.177064	−	0.128644i	0.672787	+	0.739836i	$0.265097\pi$
$158$	−2.53291	−	1.84027i	−0.201508	−	0.146404i
$159$	−0.934971	−	2.87755i	−0.0741480	−	0.228204i
$160$	0.309017	+	0.951057i	0.0244299	+	0.0751876i
$161$	−1.61803	−	1.17557i	−0.127519	−	0.0926479i
$162$	−8.56151	+	6.22030i	−0.672656	+	0.488713i
$163$	−2.89864	+	8.92110i	−0.227039	+	0.698754i	0.771039	+	0.636788i	$0.219737\pi$
$163$	−2.89864	+	8.92110i	−0.227039	+	0.698754i	−0.998078	+	0.0619665i	$0.980263\pi$
$164$	−9.86261			−0.770141
$165$	−3.78403	+	5.11809i	−0.294586	+	0.398443i
$166$	8.22953			0.638735
$167$	−3.70820	+	11.4127i	−0.286949	+	0.883140i	0.698858	+	0.715260i	$0.253692\pi$
$167$	−3.70820	+	11.4127i	−0.286949	+	0.883140i	−0.985808	+	0.167879i	$0.946308\pi$
$168$	−1.55261	+	1.12804i	−0.119786	+	0.0870299i
$169$	9.90607	+	7.19718i	0.762005	+	0.553629i
$170$	−1.28403	−	3.95183i	−0.0984804	−	0.303091i
$171$	1.59607	+	4.91220i	0.122054	+	0.375645i
$172$	5.36099	+	3.89498i	0.408771	+	0.296990i
$173$	−7.40078	+	5.37698i	−0.562671	+	0.408804i	−0.832435	−	0.554122i	$-0.813054\pi$
$173$	−7.40078	+	5.37698i	−0.562671	+	0.408804i	0.269765	+	0.962926i	$0.413054\pi$
$174$	0.709208	−	2.18272i	0.0537649	−	0.165471i
$175$	−1.00000			−0.0755929
$176$	−3.16272	+	0.998590i	−0.238399	+	0.0752716i
$177$	−14.2619			−1.07199
$178$	3.05750	−	9.41003i	0.229170	−	0.705312i
$179$	−3.00529	+	2.18347i	−0.224626	+	0.163200i	−0.694407	−	0.719583i	$-0.744333\pi$
$179$	−3.00529	+	2.18347i	−0.224626	+	0.163200i	0.469781	+	0.882783i	$0.344333\pi$
$180$	0.552609	+	0.401494i	0.0411891	+	0.0299256i
$181$	−6.62654	−	20.3944i	−0.492547	−	1.51590i	−0.820745	−	0.571295i	$-0.806441\pi$
$181$	−6.62654	−	20.3944i	−0.492547	−	1.51590i	0.328198	−	0.944609i	$-0.393559\pi$
$182$	−0.268582	−	0.826612i	−0.0199086	−	0.0612725i
$183$	12.0146	+	8.72909i	0.888142	+	0.645273i
$184$	−1.61803	+	1.17557i	−0.119283	+	0.0866642i
$185$	−2.10522	+	6.47920i	−0.154779	+	0.476360i
$186$	−14.7931			−1.08468
$187$	13.1417	−	4.14934i	0.961019	−	0.303430i
$188$	10.7529			0.784233
$189$	1.37405	−	4.22888i	0.0999471	−	0.307606i
$190$	−6.11739	+	4.44455i	−0.443802	+	0.322441i
$191$	17.7112	+	12.8679i	1.28154	+	0.931090i	0.999598	−	0.0283425i	$-0.00902290\pi$
$191$	17.7112	+	12.8679i	1.28154	+	0.931090i	0.281938	+	0.959433i	$0.409023\pi$
$192$	0.593044	+	1.82520i	0.0427993	+	0.131723i
$193$	1.26042	+	3.87917i	0.0907268	+	0.279228i	0.986116	−	0.166055i	$-0.0531029\pi$
$193$	1.26042	+	3.87917i	0.0907268	+	0.279228i	−0.895390	+	0.445283i	$0.853103\pi$
$194$	11.9721	+	8.69827i	0.859549	+	0.624499i
$195$	−1.34945	+	0.980434i	−0.0966362	+	0.0702103i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	14.2275			1.01366			0.506832	−	0.862045i	$-0.330816\pi$
$197$	14.2275			1.01366			0.506832	+	0.862045i	$0.330816\pi$
$198$	−1.34682	+	1.82165i	−0.0957145	+	0.129459i
$199$	−8.75085			−0.620331			−0.310166	−	0.950682i	$-0.600385\pi$
$199$	−8.75085			−0.620331			−0.310166	+	0.950682i	$0.600385\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	−5.52964	+	4.01752i	−0.390031	+	0.283374i
$202$	−14.2454	−	10.3499i	−1.00230	−	0.728214i
$203$	0.369547	+	1.13735i	0.0259371	+	0.0798261i
$204$	−2.46422	−	7.58408i	−0.172530	−	0.530992i
$205$	−7.97902	−	5.79710i	−0.557279	−	0.404887i
$206$	−3.92601	+	2.85242i	−0.273538	+	0.198737i
$207$	−0.422156	+	1.29926i	−0.0293419	+	0.0903050i
$208$	−0.869151			−0.0602648
$209$	−14.5714	−	20.4112i	−1.00793	−	1.41187i
$210$	−1.91913			−0.132433
$211$	−6.10911	+	18.8019i	−0.420568	+	1.29438i	0.486606	+	0.873622i	$0.338235\pi$
$211$	−6.10911	+	18.8019i	−0.420568	+	1.29438i	−0.907174	+	0.420755i	$0.861765\pi$
$212$	1.27547	−	0.926680i	0.0875994	−	0.0636447i
$213$	3.47051	+	2.52147i	0.237795	+	0.172769i
$214$	1.84579	+	5.68074i	0.126175	+	0.388328i
$215$	2.04771	+	6.30222i	0.139653	+	0.429808i
$216$	−3.59730	−	2.61359i	−0.244765	−	0.177832i
$217$	6.23607	−	4.53077i	0.423332	−	0.307569i
$218$	5.98416	−	18.4173i	0.405298	−	1.24738i
$219$	32.6999			2.20965
$220$	−3.14565	−	1.05113i	−0.212080	−	0.0708669i
$221$	3.61149			0.242935
$222$	−4.04019	+	12.4344i	−0.271160	+	0.834544i
$223$	−8.83698	+	6.42044i	−0.591768	+	0.429945i	−0.842947	−	0.537996i	$-0.819182\pi$
$223$	−8.83698	+	6.42044i	−0.591768	+	0.429945i	0.251179	+	0.967941i	$0.419182\pi$
$224$	−0.809017	−	0.587785i	−0.0540547	−	0.0392731i
$225$	0.211078	+	0.649631i	0.0140719	+	0.0433088i
$226$	−4.16964	−	12.8328i	−0.277360	−	0.853627i
$227$	15.8299	+	11.5011i	1.05066	+	0.763352i	0.972339	−	0.233576i	$-0.0750426\pi$
$227$	15.8299	+	11.5011i	1.05066	+	0.763352i	0.0783255	+	0.996928i	$0.475043\pi$
$228$	−11.7401	+	8.52967i	−0.777506	+	0.564891i
$229$	−4.59240	+	14.1340i	−0.303475	+	0.933999i	0.676767	+	0.736197i	$0.263380\pi$
$229$	−4.59240	+	14.1340i	−0.303475	+	0.933999i	−0.980242	+	0.197802i	$0.936620\pi$
$230$	−2.00000			−0.131876
$231$	0.0530052	−	6.36482i	0.00348749	−	0.418774i
$232$	1.19588			0.0785132
$233$	1.41463	−	4.35379i	0.0926756	−	0.285226i	−0.893965	−	0.448136i	$-0.852088\pi$
$233$	1.41463	−	4.35379i	0.0926756	−	0.285226i	0.986641	+	0.162910i	$0.0520880\pi$
$234$	−0.480301	+	0.348959i	−0.0313982	+	0.0228122i
$235$	8.69925	+	6.32037i	0.567476	+	0.412296i
$236$	−2.29645	−	7.06774i	−0.149486	−	0.460070i
$237$	−1.85673	−	5.71443i	−0.120608	−	0.371192i
$238$	3.36163	+	2.44236i	0.217902	+	0.158315i
$239$	13.7112	−	9.96175i	0.886902	−	0.644372i	−0.0481662	−	0.998839i	$-0.515338\pi$
$239$	13.7112	−	9.96175i	0.886902	−	0.644372i	0.935068	+	0.354467i	$0.115338\pi$
$240$	−0.593044	+	1.82520i	−0.0382808	+	0.117816i
$241$	27.4289			1.76685			0.883425	−	0.468572i	$-0.155231\pi$
$241$	27.4289			1.76685			0.883425	+	0.468572i	$0.155231\pi$
$242$	3.57295	−	10.4036i	0.229678	−	0.668766i
$243$	−6.96990			−0.447119
$244$	−2.39127	+	7.35956i	−0.153085	+	0.471148i
$245$	0.809017	−	0.587785i	0.0516862	−	0.0375522i
$246$	−15.3128	−	11.1254i	−0.976307	−	0.709329i
$247$	−2.03089	−	6.25043i	−0.129222	−	0.397706i
$248$	−2.38197	−	7.33094i	−0.151255	−	0.465515i
$249$	12.7772	+	9.28321i	0.809725	+	0.588300i
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	1.61149	−	4.95967i	0.101717	−	0.313052i	−0.887229	−	0.461329i	$-0.847373\pi$
$251$	1.61149	−	4.95967i	0.101717	−	0.313052i	0.988946	+	0.148277i	$0.0473728\pi$
$252$	−0.683063			−0.0430289
$253$	0.0552388	−	6.63302i	0.00347283	−	0.417014i
$254$	2.68257			0.168320
$255$	2.46422	−	7.58408i	0.154315	−	0.474933i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.43497	+	1.04257i	0.0895110	+	0.0650336i	0.631641	−	0.775261i	$-0.282382\pi$
$257$	1.43497	+	1.04257i	0.0895110	+	0.0650336i	−0.542130	+	0.840295i	$0.682382\pi$
$258$	3.92983	+	12.0948i	0.244661	+	0.752988i
$259$	−2.10522	−	6.47920i	−0.130812	−	0.402598i
$260$	−0.703158	−	0.510874i	−0.0436080	−	0.0316831i
$261$	0.660853	−	0.480138i	0.0409058	−	0.0297198i
$262$	−0.370776	+	1.14113i	−0.0229066	+	0.0704993i
$263$	−14.0317			−0.865231			−0.432615	−	0.901579i	$-0.642409\pi$
$263$	−14.0317			−0.865231			−0.432615	+	0.901579i	$0.642409\pi$
$264$	−6.03692	−	2.01725i	−0.371547	−	0.124153i
$265$	1.57656			0.0968475
$266$	2.33664	−	7.19143i	0.143268	−	0.440935i
$267$	15.3620	−	11.1611i	0.940137	−	0.683050i
$268$	−2.88133	−	2.09341i	−0.176005	−	0.127875i
$269$	−4.33804	−	13.3511i	−0.264495	−	0.814031i	−0.991809	−	0.127727i	$-0.959232\pi$
$269$	−4.33804	−	13.3511i	−0.264495	−	0.814031i	0.727315	−	0.686304i	$-0.240768\pi$
$270$	−1.37405	−	4.22888i	−0.0836218	−	0.257361i
$271$	−17.4452	−	12.6747i	−1.05972	−	0.769933i	−0.0856850	−	0.996322i	$-0.527308\pi$
$271$	−17.4452	−	12.6747i	−1.05972	−	0.769933i	−0.974037	+	0.226389i	$0.927308\pi$
$272$	3.36163	−	2.44236i	0.203829	−	0.148090i
$273$	0.515445	−	1.58638i	0.0311961	−	0.0960118i
$274$	4.65822			0.281414
$275$	−1.92705	−	2.69935i	−0.116206	−	0.162777i
$276$	−3.83826			−0.231036
$277$	−3.23528	+	9.95716i	−0.194389	+	0.598268i	0.805594	+	0.592468i	$0.201846\pi$
$277$	−3.23528	+	9.95716i	−0.194389	+	0.598268i	−0.999983	+	0.00579994i	$0.998154\pi$
$278$	−10.2104	+	7.41832i	−0.612381	+	0.444921i
$279$	−4.25963	−	3.09480i	−0.255017	−	0.185281i
$280$	−0.309017	−	0.951057i	−0.0184673	−	0.0568365i
$281$	8.51006	+	26.1913i	0.507668	+	1.56244i	0.796239	+	0.604982i	$0.206820\pi$
$281$	8.51006	+	26.1913i	0.507668	+	1.56244i	−0.288572	+	0.957458i	$0.593180\pi$
$282$	16.6950	+	12.1296i	0.994172	+	0.722308i
$283$	10.2364	−	7.43719i	0.608492	−	0.442095i	−0.240391	−	0.970676i	$-0.577276\pi$
$283$	10.2364	−	7.43719i	0.608492	−	0.442095i	0.848883	+	0.528581i	$0.177276\pi$
$284$	−0.690738	+	2.12587i	−0.0409878	+	0.126147i
$285$	−14.5115			−0.859589
$286$	1.71374	−	2.31792i	0.101336	−	0.137061i
$287$	9.86261			0.582172
$288$	−0.211078	+	0.649631i	−0.0124379	+	0.0382799i
$289$	−0.214937	+	0.156161i	−0.0126433	+	0.00918592i
$290$	0.967486	+	0.702919i	0.0568127	+	0.0412769i
$291$	8.77609	+	27.0100i	0.514463	+	1.58336i
$292$	5.26531	+	16.2050i	0.308129	+	0.948324i
$293$	21.3749	+	15.5298i	1.24874	+	0.907261i	0.998148	−	0.0608329i	$-0.0193757\pi$
$293$	21.3749	+	15.5298i	1.24874	+	0.907261i	0.250589	+	0.968094i	$0.419376\pi$
$294$	1.55261	−	1.12804i	0.0905500	−	0.0657884i
$295$	2.29645	−	7.06774i	0.133704	−	0.411499i
$296$	−6.81263			−0.395976
$297$	14.0631	−	4.44024i	0.816022	−	0.257649i
$298$	−16.1238			−0.934028
$299$	0.537165	−	1.65322i	0.0310650	−	0.0956084i
$300$	−1.55261	+	1.12804i	−0.0896399	+	0.0651272i
$301$	−5.36099	−	3.89498i	−0.309002	−	0.224503i
$302$	−3.03151	−	9.33003i	−0.174444	−	0.536883i
$303$	−10.4425	−	32.1386i	−0.599904	−	1.84631i
$304$	−6.11739	−	4.44455i	−0.350857	−	0.254912i
$305$	−6.26042	+	4.54846i	−0.358470	+	0.260444i
$306$	0.877071	−	2.69935i	0.0501388	−	0.154311i
$307$	−24.8324			−1.41726			−0.708630	−	0.705580i	$-0.750687\pi$
$307$	−24.8324			−1.41726			−0.708630	+	0.705580i	$0.750687\pi$
$308$	3.16272	−	0.998590i	0.180213	−	0.0569000i
$309$	−9.31320			−0.529809
$310$	2.38197	−	7.33094i	0.135287	−	0.416369i
$311$	−4.64446	+	3.37439i	−0.263363	+	0.191344i	−0.711628	−	0.702556i	$-0.752042\pi$
$311$	−4.64446	+	3.37439i	−0.263363	+	0.191344i	0.448265	+	0.893901i	$0.352042\pi$
$312$	−1.34945	−	0.980434i	−0.0763977	−	0.0555061i
$313$	−6.72711	−	20.7039i	−0.380239	−	1.17025i	−0.939876	−	0.341517i	$-0.889059\pi$
$313$	−6.72711	−	20.7039i	−0.380239	−	1.17025i	0.559637	−	0.828738i	$-0.310941\pi$
$314$	0.847431	+	2.60812i	0.0478233	+	0.147185i
$315$	−0.552609	−	0.401494i	−0.0311360	−	0.0226216i
$316$	2.53291	−	1.84027i	0.142487	−	0.103523i
$317$	2.12076	−	6.52702i	0.119114	−	0.366594i	−0.873669	−	0.486520i	$-0.838266\pi$
$317$	2.12076	−	6.52702i	0.119114	−	0.366594i	0.992783	+	0.119927i	$0.0382659\pi$
$318$	3.02563			0.169669
$319$	−2.35796	+	3.18926i	−0.132020	+	0.178564i
$320$	−1.00000			−0.0559017
$321$	−3.54230	+	10.9021i	−0.197712	+	0.608495i
$322$	1.61803	−	1.17557i	0.0901695	−	0.0655120i
$323$	25.4190	+	18.4680i	1.41435	+	1.02759i
$324$	−3.27021	−	10.0647i	−0.181678	−	0.559148i
$325$	−0.268582	−	0.826612i	−0.0148983	−	0.0458522i
$326$	−7.58874	−	5.51354i	−0.420301	−	0.305367i
$327$	30.0665	−	21.8446i	1.66268	−	1.20801i
$328$	3.04771	−	9.37990i	0.168282	−	0.517918i
$329$	−10.7529			−0.592824
$330$	−3.69826	−	5.18040i	−0.203583	−	0.285172i
$331$	−20.6399			−1.13447			−0.567235	−	0.823556i	$-0.691987\pi$
$331$	−20.6399			−1.13447			−0.567235	+	0.823556i	$0.691987\pi$
$332$	−2.54306	+	7.82675i	−0.139569	+	0.429549i
$333$	−3.76472	+	2.73523i	−0.206306	+	0.149890i
$334$	−9.70820	−	7.05342i	−0.531209	−	0.385946i
$335$	−1.10057	−	3.38720i	−0.0601305	−	0.185063i
$336$	−0.593044	−	1.82520i	−0.0323532	−	0.0995729i
$337$	−0.0206837	−	0.0150276i	−0.00112671	−	0.000818605i	0.587222	−	0.809426i	$-0.300222\pi$
$337$	−0.0206837	−	0.0150276i	−0.00112671	−	0.000818605i	−0.588348	+	0.808607i	$0.700222\pi$
$338$	−9.90607	+	7.19718i	−0.538819	+	0.391475i
$339$	8.00208	−	24.6279i	0.434613	−	1.33760i
$340$	4.15520			0.225347
$341$	24.2473	+	8.10229i	1.31307	+	0.438764i
$342$	−5.16499			−0.279291
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−5.36099	+	3.89498i	−0.289045	+	0.210003i
$345$	−3.10522	−	2.25607i	−0.167179	−	0.121463i
$346$	−2.82685	−	8.70014i	−0.151972	−	0.467722i
$347$	8.57191	+	26.3816i	0.460164	+	1.41624i	0.864964	+	0.501835i	$0.167341\pi$
$347$	8.57191	+	26.3816i	0.460164	+	1.41624i	−0.404799	+	0.914406i	$0.632659\pi$
$348$	1.85673	+	1.34899i	0.0995312	+	0.0723137i
$349$	−6.28398	+	4.56558i	−0.336373	+	0.244390i	−0.743130	−	0.669147i	$-0.766660\pi$
$349$	−6.28398	+	4.56558i	−0.336373	+	0.244390i	0.406757	+	0.913537i	$0.366660\pi$
$350$	0.309017	−	0.951057i	0.0165177	−	0.0508361i
$351$	3.86468			0.206282
$352$	0.0276194	−	3.31651i	0.00147212	−	0.176771i
$353$	−23.1303			−1.23110			−0.615550	−	0.788098i	$-0.711066\pi$
$353$	−23.1303			−1.23110			−0.615550	+	0.788098i	$0.711066\pi$
$354$	4.40718	−	13.5639i	0.234239	−	0.720914i
$355$	−1.80838	+	1.31386i	−0.0959787	+	0.0697326i
$356$	8.00465	+	5.81572i	0.424246	+	0.308232i
$357$	2.46422	+	7.58408i	0.130420	+	0.401392i
$358$	−1.14792	−	3.53293i	−0.0606694	−	0.186721i
$359$	10.2017	+	7.41198i	0.538426	+	0.391189i	0.823500	−	0.567316i	$-0.192018\pi$
$359$	10.2017	+	7.41198i	0.538426	+	0.391189i	−0.285074	+	0.958505i	$0.592018\pi$
$360$	−0.552609	+	0.401494i	−0.0291251	+	0.0211606i
$361$	11.7972	−	36.3080i	0.620905	−	1.91095i
$362$	21.4439			1.12707
$363$	17.2830	−	12.1222i	0.907122	−	0.636253i
$364$	0.869151			0.0455559
$365$	−5.26531	+	16.2050i	−0.275599	+	0.848207i
$366$	−12.0146	+	8.72909i	−0.628011	+	0.456277i
$367$	−2.84252	−	2.06521i	−0.148378	−	0.107803i	0.511120	−	0.859510i	$-0.329231\pi$
$367$	−2.84252	−	2.06521i	−0.148378	−	0.107803i	−0.659498	+	0.751707i	$0.729231\pi$
$368$	−0.618034	−	1.90211i	−0.0322172	−	0.0991545i
$369$	−2.08178	−	6.40706i	−0.108373	−	0.333538i
$370$	−5.51153	−	4.00436i	−0.286531	−	0.208177i
$371$	−1.27547	+	0.926680i	−0.0662189	+	0.0481109i
$372$	4.57130	−	14.0690i	0.237011	−	0.729445i
$373$	−8.48915			−0.439552			−0.219776	−	0.975550i	$-0.570533\pi$
$373$	−8.48915			−0.439552			−0.219776	+	0.975550i	$0.570533\pi$
$374$	−0.114764	+	13.7808i	−0.00593431	+	0.712586i
$375$	−1.91913			−0.0991035
$376$	−3.32282	+	10.2266i	−0.171361	+	0.527396i
$377$	−0.840891	+	0.610943i	−0.0433081	+	0.0314652i
$378$	3.59730	+	2.61359i	0.185025	+	0.134429i
$379$	−5.89314	−	18.1372i	−0.302710	−	0.931646i	−0.980522	−	0.196410i	$-0.937072\pi$
$379$	−5.89314	−	18.1372i	−0.302710	−	0.931646i	0.677812	−	0.735236i	$-0.262928\pi$
$380$	−2.33664	−	7.19143i	−0.119867	−	0.368912i
$381$	4.16499	+	3.02604i	0.213379	+	0.155029i
$382$	−17.7112	+	12.8679i	−0.906183	+	0.658380i
$383$	0.412472	−	1.26946i	0.0210763	−	0.0648662i	−0.939965	−	0.341270i	$-0.889143\pi$
$383$	0.412472	−	1.26946i	0.0210763	−	0.0648662i	0.961041	+	0.276404i	$0.0891428\pi$
$384$	−1.91913			−0.0979352
$385$	3.14565	+	1.05113i	0.160317	+	0.0535703i
$386$	−4.07880			−0.207605
$387$	−1.39872	+	4.30481i	−0.0711008	+	0.218826i
$388$	−11.9721	+	8.69827i	−0.607793	+	0.441588i
$389$	0.956347	+	0.694827i	0.0484887	+	0.0352291i	0.611766	−	0.791039i	$-0.290460\pi$
$389$	0.956347	+	0.694827i	0.0484887	+	0.0352291i	−0.563277	+	0.826268i	$0.690460\pi$
$390$	−0.515445	−	1.58638i	−0.0261006	−	0.0803292i
$391$	2.56805	+	7.90366i	0.129872	+	0.399705i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$	−1.86291	+	1.35348i	−0.0939712	+	0.0682741i
$394$	−4.39653	+	13.5311i	−0.221494	+	0.681688i
$395$	3.13085			0.157530
$396$	−1.31630	−	1.84382i	−0.0661464	−	0.0926556i
$397$	−15.9540			−0.800708			−0.400354	−	0.916361i	$-0.631113\pi$
$397$	−15.9540			−0.800708			−0.400354	+	0.916361i	$0.631113\pi$
$398$	2.70416	−	8.32256i	0.135547	−	0.417172i
$399$	11.7401	−	8.52967i	0.587739	−	0.427017i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−3.65057	−	11.2353i	−0.182301	−	0.561064i	0.817591	−	0.575800i	$-0.195309\pi$
$401$	−3.65057	−	11.2353i	−0.182301	−	0.561064i	−0.999891	+	0.0147360i	$0.995309\pi$
$402$	−2.11213	−	6.50048i	−0.105344	−	0.324215i
$403$	5.42008	+	3.93792i	0.269994	+	0.196162i
$404$	14.2454	−	10.3499i	0.708734	−	0.514925i
$405$	3.27021	−	10.0647i	0.162498	−	0.500117i
$406$	−1.19588			−0.0593504
$407$	13.4327	−	18.1685i	0.665836	−	0.900577i
$408$	7.97437			0.394790
$409$	−5.31694	+	16.3639i	−0.262906	+	0.809140i	0.729263	+	0.684234i	$0.239863\pi$
$409$	−5.31694	+	16.3639i	−0.262906	+	0.809140i	−0.992168	+	0.124907i	$0.960137\pi$
$410$	7.97902	−	5.79710i	0.394056	−	0.286298i
$411$	7.23240	+	5.25465i	0.356748	+	0.259193i
$412$	−1.49960	−	4.61531i	−0.0738802	−	0.227380i
$413$	2.29645	+	7.06774i	0.113001	+	0.347781i
$414$	−1.10522	−	0.802988i	−0.0543185	−	0.0394647i
$415$	−6.65783	+	4.83720i	−0.326820	+	0.237449i
$416$	0.268582	−	0.826612i	0.0131683	−	0.0405280i
$417$	−24.2210			−1.18611
$418$	23.9150	−	7.55085i	1.16972	−	0.369324i
$419$	−7.07910			−0.345837			−0.172918	−	0.984936i	$-0.555320\pi$
$419$	−7.07910			−0.345837			−0.172918	+	0.984936i	$0.555320\pi$
$420$	0.593044	−	1.82520i	0.0289376	−	0.0890607i
$421$	12.8433	−	9.33121i	0.625945	−	0.454775i	−0.229048	−	0.973415i	$-0.573561\pi$
$421$	12.8433	−	9.33121i	0.625945	−	0.454775i	0.854993	+	0.518640i	$0.173561\pi$
$422$	−15.9939	−	11.6202i	−0.778569	−	0.565663i
$423$	2.26969	+	6.98539i	0.110356	+	0.339642i
$424$	0.487185	+	1.49940i	0.0236598	+	0.0728173i
$425$	3.36163	+	2.44236i	0.163063	+	0.118472i
$426$	−3.47051	+	2.52147i	−0.168147	+	0.122166i
$427$	2.39127	−	7.35956i	0.115722	−	0.356154i
$428$	−5.97309			−0.288720
$429$	5.27547	−	1.66566i	0.254702	−	0.0804189i
$430$	−6.62654			−0.319560
$431$	−5.39843	+	16.6147i	−0.260033	+	0.800300i	0.732763	+	0.680484i	$0.238230\pi$
$431$	−5.39843	+	16.6147i	−0.260033	+	0.800300i	−0.992796	+	0.119816i	$0.961770\pi$
$432$	3.59730	−	2.61359i	0.173075	−	0.125746i
$433$	−14.7153	−	10.6913i	−0.707174	−	0.513792i	0.175087	−	0.984553i	$-0.443979\pi$
$433$	−14.7153	−	10.6913i	−0.707174	−	0.513792i	−0.882261	+	0.470761i	$0.843979\pi$
$434$	2.38197	+	7.33094i	0.114338	+	0.351896i
$435$	0.709208	+	2.18272i	0.0340039	+	0.104653i
$436$	15.6667	+	11.3825i	0.750300	+	0.545125i
$437$	12.2348	−	8.88909i	0.585269	−	0.425223i
$438$	−10.1048	+	31.0994i	−0.482827	+	1.48599i
$439$	−16.5826			−0.791445			−0.395722	−	0.918370i	$-0.629506\pi$
$439$	−16.5826			−0.791445			−0.395722	+	0.918370i	$0.629506\pi$
$440$	1.97174	−	2.66688i	0.0939990	−	0.127138i
$441$	0.683063			0.0325268
$442$	−1.11601	+	3.43474i	−0.0530833	+	0.163374i
$443$	30.0923	−	21.8633i	1.42973	−	1.03876i	0.439659	−	0.898165i	$-0.355099\pi$
$443$	30.0923	−	21.8633i	1.42973	−	1.03876i	0.990068	−	0.140592i	$-0.0449006\pi$
$444$	−10.5774	−	7.68490i	−0.501979	−	0.364709i
$445$	3.05750	+	9.41003i	0.144940	+	0.446078i
$446$	−3.37543	−	10.3885i	−0.159831	−	0.491909i
$447$	−25.0340	−	18.1883i	−1.18407	−	0.860275i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	3.26718	−	10.0554i	0.154188	−	0.474541i	−0.843890	−	0.536516i	$-0.819740\pi$
$449$	3.26718	−	10.0554i	0.154188	−	0.474541i	0.998078	+	0.0619750i	$0.0197399\pi$
$450$	−0.683063			−0.0321999
$451$	19.0058	+	26.6226i	0.894946	+	1.25361i
$452$	13.4932			0.634668
$453$	5.81786	−	17.9055i	0.273347	−	0.841276i
$454$	−15.8299	+	11.5011i	−0.742932	+	0.539772i
$455$	0.703158	+	0.510874i	0.0329645	+	0.0239501i
$456$	−4.48431	−	13.8013i	−0.209997	−	0.646305i
$457$	−0.485711	−	1.49486i	−0.0227206	−	0.0699268i	0.939053	−	0.343772i	$-0.111705\pi$
$457$	−0.485711	−	1.49486i	−0.0227206	−	0.0699268i	−0.961774	+	0.273845i	$0.911705\pi$
$458$	−12.0231	−	8.73527i	−0.561801	−	0.408172i
$459$	−14.9475	+	10.8600i	−0.697689	+	0.506901i
$460$	0.618034	−	1.90211i	0.0288160	−	0.0886865i
$461$	15.9056			0.740796			0.370398	−	0.928873i	$-0.379221\pi$
$461$	15.9056			0.740796			0.370398	+	0.928873i	$0.379221\pi$
$462$	6.03692	+	2.01725i	0.280863	+	0.0938508i
$463$	22.1265			1.02831			0.514153	−	0.857698i	$-0.328106\pi$
$463$	22.1265			1.02831			0.514153	+	0.857698i	$0.328106\pi$
$464$	−0.369547	+	1.13735i	−0.0171558	+	0.0528000i
$465$	11.9678	−	8.69514i	0.554995	−	0.403227i
$466$	3.70355	+	2.69079i	0.171564	+	0.124648i
$467$	1.02352	+	3.15006i	0.0473627	+	0.145767i	0.971941	−	0.235225i	$-0.0755826\pi$
$467$	1.02352	+	3.15006i	0.0473627	+	0.145767i	−0.924578	+	0.380992i	$0.875583\pi$
$468$	−0.183459	−	0.564628i	−0.00848038	−	0.0260999i
$469$	2.88133	+	2.09341i	0.133047	+	0.0966645i
$470$	−8.69925	+	6.32037i	−0.401266	+	0.291537i
$471$	−1.62633	+	5.00533i	−0.0749373	+	0.230633i
$472$	7.43146			0.342061
$473$	0.183021	−	21.9770i	0.00841532	−	1.01050i
$474$	6.00851			0.275980
$475$	2.33664	−	7.19143i	0.107212	−	0.329965i
$476$	−3.36163	+	2.44236i	−0.154080	+	0.111946i
$477$	0.871223	+	0.632981i	0.0398906	+	0.0289822i
$478$	5.23720	+	16.1185i	0.239544	+	0.737241i
$479$	−8.14742	−	25.0752i	−0.372265	−	1.14571i	−0.945305	−	0.326187i	$-0.894236\pi$
$479$	−8.14742	−	25.0752i	−0.372265	−	1.14571i	0.573040	−	0.819527i	$-0.305764\pi$
$480$	−1.55261	−	1.12804i	−0.0708666	−	0.0514876i
$481$	4.79035	−	3.48040i	0.218421	−	0.158692i
$482$	−8.47599	+	26.0864i	−0.386071	+	1.18820i
$483$	3.83826			0.174647
$484$	8.79027	+	6.61295i	0.399558	+	0.300589i
$485$	−14.7984			−0.671960
$486$	2.15382	−	6.62877i	0.0976992	−	0.300687i
$487$	−10.0889	+	7.33001i	−0.457171	+	0.332154i	−0.792421	−	0.609975i	$-0.791179\pi$
$487$	−10.0889	+	7.33001i	−0.457171	+	0.332154i	0.335249	+	0.942129i	$0.391179\pi$
$488$	−6.26042	−	4.54846i	−0.283396	−	0.205899i
$489$	−5.56287	−	17.1207i	−0.251562	−	0.774227i
$490$	0.309017	+	0.951057i	0.0139600	+	0.0429644i
$491$	−29.6872	−	21.5690i	−1.33977	−	0.973397i	−0.999453	−	0.0330845i	$-0.989467\pi$
$491$	−29.6872	−	21.5690i	−1.33977	−	0.973397i	−0.340313	−	0.940312i	$-0.610533\pi$
$492$	15.3128	−	11.1254i	0.690354	−	0.501571i
$493$	1.53554	−	4.72591i	0.0691572	−	0.212844i
$494$	6.57210			0.295693
$495$	0.0188658	−	2.26538i	0.000847954	−	0.101821i
$496$	7.70820			0.346109
$497$	0.690738	−	2.12587i	0.0309838	−	0.0953585i
$498$	−12.7772	+	9.28321i	−0.572562	+	0.415991i
$499$	−17.8656	−	12.9801i	−0.799776	−	0.581071i	0.111073	−	0.993812i	$-0.464571\pi$
$499$	−17.8656	−	12.9801i	−0.799776	−	0.581071i	−0.910848	+	0.412741i	$0.864571\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−7.11653	−	21.9024i	−0.317943	−	0.978528i
$502$	4.21895	+	3.06524i	0.188301	+	0.136809i
$503$	−17.5166	+	12.7265i	−0.781026	+	0.567448i	−0.905287	−	0.424801i	$-0.860344\pi$
$503$	−17.5166	+	12.7265i	−0.781026	+	0.567448i	0.124261	+	0.992250i	$0.460344\pi$
$504$	0.211078	−	0.649631i	0.00940216	−	0.0289369i
$505$	17.6082			0.783557
$506$	6.29131	+	2.10225i	0.279683	+	0.0934565i
$507$	−23.4989			−1.04362
$508$	−0.828961	+	2.55128i	−0.0367792	+	0.113195i
$509$	−8.73909	+	6.34932i	−0.387353	+	0.281429i	−0.764370	−	0.644778i	$-0.776950\pi$
$509$	−8.73909	+	6.34932i	−0.387353	+	0.281429i	0.377017	+	0.926206i	$0.376950\pi$
$510$	6.45140	+	4.68722i	0.285673	+	0.207553i
$511$	−5.26531	−	16.2050i	−0.232924	−	0.716865i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	27.2010	+	19.7627i	1.20095	+	0.872545i
$514$	−1.43497	+	1.04257i	−0.0632939	+	0.0459857i
$515$	1.49960	−	4.61531i	0.0660805	−	0.203375i
$516$	−12.7172			−0.559844
$517$	−20.7213	−	29.0257i	−0.911322	−	1.27655i
$518$	6.81263			0.299330
$519$	5.42509	−	16.6967i	0.238135	−	0.732904i
$520$	0.703158	−	0.510874i	0.0308355	−	0.0224033i
$521$	−20.9808	−	15.2434i	−0.919185	−	0.667827i	0.0241357	−	0.999709i	$-0.492317\pi$
$521$	−20.9808	−	15.2434i	−0.919185	−	0.667827i	−0.943321	+	0.331881i	$0.892317\pi$
$522$	0.252424	+	0.776880i	0.0110483	+	0.0340031i
$523$	7.34808	+	22.6151i	0.321309	+	0.988887i	0.973079	+	0.230471i	$0.0740266\pi$
$523$	7.34808	+	22.6151i	0.321309	+	0.988887i	−0.651770	+	0.758416i	$0.725973\pi$
$524$	−0.970704	−	0.705258i	−0.0424054	−	0.0308093i
$525$	1.55261	−	1.12804i	0.0677614	−	0.0492316i
$526$	4.33603	−	13.3449i	0.189060	−	0.581866i
$527$	−32.0291			−1.39521
$528$	3.78403	−	5.11809i	0.164679	−	0.222736i
$529$	−19.0000			−0.826087
$530$	−0.487185	+	1.49940i	−0.0211620	+	0.0651298i
$531$	4.10669	−	2.98369i	0.178215	−	0.129481i
$532$	6.11739	+	4.44455i	0.265223	+	0.192696i
$533$	2.64892	+	8.15255i	0.114738	+	0.353126i
$534$	5.86775	+	18.0591i	0.253922	+	0.781493i
$535$	−4.83233	−	3.51089i	−0.208920	−	0.151789i
$536$	2.88133	−	2.09341i	0.124454	−	0.0904213i
$537$	2.20301	−	6.78016i	0.0950667	−	0.292585i
$538$	14.0382			0.605229
$539$	−3.16272	+	0.998590i	−0.136228	+	0.0430123i
$540$	4.44651			0.191347
$541$	−10.2312	+	31.4883i	−0.439872	+	1.35379i	0.448139	+	0.893964i	$0.352087\pi$
$541$	−10.2312	+	31.4883i	−0.439872	+	1.35379i	−0.888011	+	0.459822i	$0.847913\pi$
$542$	17.4452	−	12.6747i	0.749337	−	0.544425i
$543$	33.2941	+	24.1896i	1.42879	+	1.03807i
$544$	1.28403	+	3.95183i	0.0550522	+	0.169433i
$545$	5.98416	+	18.4173i	0.256333	+	0.788913i
$546$	1.34945	+	0.980434i	0.0577512	+	0.0419587i
$547$	−21.1991	+	15.4020i	−0.906406	+	0.658543i	−0.940103	−	0.340889i	$-0.889272\pi$
$547$	−21.1991	+	15.4020i	−0.906406	+	0.658543i	0.0336973	+	0.999432i	$0.489272\pi$
$548$	−1.43947	+	4.43023i	−0.0614911	+	0.189250i
$549$	−5.28575			−0.225590
$550$	3.16272	−	0.998590i	0.134859	−	0.0425800i
$551$	−9.04265			−0.385230
$552$	1.18609	−	3.65040i	0.0504833	−	0.155371i
$553$	−2.53291	+	1.84027i	−0.107710	+	0.0782561i
$554$	−8.47006	−	6.15386i	−0.359859	−	0.261453i
$555$	−4.04019	−	12.4344i	−0.171497	−	0.527812i
$556$	−3.90004	−	12.0031i	−0.165399	−	0.509044i
$557$	0.838261	+	0.609033i	0.0355183	+	0.0258055i	0.605403	−	0.795919i	$-0.293012\pi$
$557$	0.838261	+	0.609033i	0.0355183	+	0.0258055i	−0.569884	+	0.821725i	$0.693012\pi$
$558$	4.25963	−	3.09480i	0.180324	−	0.131013i
$559$	1.77977	−	5.47758i	0.0752764	−	0.231677i
$560$	1.00000			0.0422577
$561$	−15.7234	+	21.2667i	−0.663842	+	0.897880i
$562$	−27.5391			−1.16167
$563$	5.11941	−	15.7559i	0.215758	−	0.664034i	−0.783341	−	0.621592i	$-0.786486\pi$
$563$	5.11941	−	15.7559i	0.215758	−	0.664034i	0.999099	−	0.0424418i	$-0.0135137\pi$
$564$	−16.6950	+	12.1296i	−0.702986	+	0.510749i
$565$	10.9163	+	7.93112i	0.459250	+	0.333665i
$566$	3.90996	+	12.0336i	0.164348	+	0.505811i
$567$	3.27021	+	10.0647i	0.137336	+	0.422676i
$568$	−1.80838	−	1.31386i	−0.0758778	−	0.0551284i
$569$	23.1698	−	16.8338i	0.971328	−	0.705711i	0.0155743	−	0.999879i	$-0.495042\pi$
$569$	23.1698	−	16.8338i	0.971328	−	0.705711i	0.955754	+	0.294168i	$0.0950424\pi$
$570$	4.48431	−	13.8013i	0.187827	−	0.578072i
$571$	16.0059			0.669828			0.334914	−	0.942249i	$-0.391293\pi$
$571$	16.0059			0.669828			0.334914	+	0.942249i	$0.391293\pi$
$572$	1.67490	+	2.34614i	0.0700310	+	0.0980970i
$573$	−42.0140			−1.75516
$574$	−3.04771	+	9.37990i	−0.127209	+	0.391509i
$575$	1.61803	−	1.17557i	0.0674767	−	0.0490247i
$576$	−0.552609	−	0.401494i	−0.0230254	−	0.0167289i
$577$	10.8606	+	33.4255i	0.452132	+	1.39152i	0.874469	+	0.485081i	$0.161210\pi$
$577$	10.8606	+	33.4255i	0.452132	+	1.39152i	−0.422337	+	0.906439i	$0.638790\pi$
$578$	−0.0820985	−	0.252673i	−0.00341485	−	0.0105098i
$579$	−6.33278	−	4.60103i	−0.263181	−	0.191212i
$580$	−0.967486	+	0.702919i	−0.0401727	+	0.0291871i
$581$	2.54306	−	7.82675i	0.105504	−	0.324708i
$582$	−28.4000			−1.17722
$583$	−4.95932	−	1.65717i	−0.205394	−	0.0686328i
$584$	−17.0389			−0.705075
$585$	0.183459	−	0.564628i	0.00758508	−	0.0233445i
$586$	−21.3749	+	15.5298i	−0.882991	+	0.641530i
$587$	−24.4796	−	17.7854i	−1.01038	−	0.734084i	−0.0460911	−	0.998937i	$-0.514676\pi$
$587$	−24.4796	−	17.7854i	−1.01038	−	0.734084i	−0.964289	+	0.264853i	$0.914676\pi$
$588$	0.593044	+	1.82520i	0.0244567	+	0.0752701i
$589$	18.0113	+	55.4330i	0.742141	+	2.28408i
$590$	6.01217	+	4.36810i	0.247517	+	0.179832i
$591$	−22.0897	+	16.0491i	−0.908648	+	0.660171i
$592$	2.10522	−	6.47920i	0.0865240	−	0.266293i
$593$	16.7760			0.688907			0.344454	−	0.938803i	$-0.388064\pi$
$593$	16.7760			0.688907			0.344454	+	0.938803i	$0.388064\pi$
$594$	−0.122810	+	14.7469i	−0.00503895	+	0.605072i
$595$	−4.15520			−0.170347
$596$	4.98253	−	15.3347i	0.204093	−	0.628132i
$597$	13.5867	−	9.87128i	0.556065	−	0.404005i
$598$	1.40632	+	1.02175i	0.0575085	+	0.0417824i
$599$	−6.99408	−	21.5256i	−0.285770	−	0.879511i	−0.986167	−	0.165757i	$-0.946993\pi$
$599$	−6.99408	−	21.5256i	−0.285770	−	0.879511i	0.700396	−	0.713754i	$-0.253007\pi$
$600$	−0.593044	−	1.82520i	−0.0242109	−	0.0745136i
$601$	25.6648	+	18.6466i	1.04689	+	0.760611i	0.971619	−	0.236552i	$-0.0760175\pi$
$601$	25.6648	+	18.6466i	1.04689	+	0.760611i	0.0752721	+	0.997163i	$0.476017\pi$
$602$	5.36099	−	3.89498i	0.218497	−	0.158748i
$603$	0.751757	−	2.31367i	0.0306139	−	0.0942200i
$604$	9.81017			0.399170
$605$	3.22448	+	10.5168i	0.131094	+	0.427568i
$606$	33.7925			1.37273
$607$	4.72588	−	14.5448i	0.191818	−	0.590354i	−0.808181	−	0.588934i	$-0.799548\pi$
$607$	4.72588	−	14.5448i	0.191818	−	0.590354i	0.999999	−	0.00142029i	$-0.000452093\pi$
$608$	6.11739	−	4.44455i	0.248093	−	0.180250i
$609$	−1.85673	−	1.34899i	−0.0752386	−	0.0546640i
$610$	−2.39127	−	7.35956i	−0.0968196	−	0.297980i
$611$	−2.88803	−	8.88844i	−0.116837	−	0.359588i
$612$	2.29620	+	1.66829i	0.0928185	+	0.0674366i
$613$	−7.87973	+	5.72496i	−0.318259	+	0.231229i	−0.735432	−	0.677598i	$-0.763021\pi$
$613$	−7.87973	+	5.72496i	−0.318259	+	0.231229i	0.417173	+	0.908827i	$0.363021\pi$
$614$	7.67364	−	23.6170i	0.309683	−	0.953106i
$615$	18.9276			0.763236
$616$	−0.0276194	+	3.31651i	−0.00111282	+	0.133626i
$617$	30.2611			1.21827			0.609133	−	0.793068i	$-0.291518\pi$
$617$	30.2611			1.21827			0.609133	+	0.793068i	$0.291518\pi$
$618$	2.87794	−	8.85738i	0.115768	−	0.356296i
$619$	21.8637	−	15.8849i	0.878777	−	0.638469i	−0.0541507	−	0.998533i	$-0.517245\pi$
$619$	21.8637	−	15.8849i	0.878777	−	0.638469i	0.932928	+	0.360064i	$0.117245\pi$
$620$	6.23607	+	4.53077i	0.250447	+	0.181960i
$621$	2.74809	+	8.45776i	0.110277	+	0.339398i
$622$	−1.77402	−	5.45989i	−0.0711319	−	0.218921i
$623$	−8.00465	−	5.81572i	−0.320700	−	0.233002i
$624$	1.34945	−	0.980434i	0.0540213	−	0.0392488i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	21.7694			0.870080
$627$	45.6483	+	15.2534i	1.82302	+	0.609164i
$628$	−2.74234			−0.109431
$629$	−8.74760	+	26.9224i	−0.348790	+	1.07346i
$630$	0.552609	−	0.401494i	0.0220165	−	0.0159959i
$631$	−8.78219	−	6.38063i	−0.349613	−	0.254009i	0.399093	−	0.916910i	$-0.369325\pi$
$631$	−8.78219	−	6.38063i	−0.349613	−	0.254009i	−0.748707	+	0.662901i	$0.769325\pi$
$632$	0.967486	+	2.97761i	0.0384845	+	0.118443i
$633$	−11.7242	−	36.0833i	−0.465994	−	1.43418i
$634$	5.55221	+	4.03392i	0.220507	+	0.160207i
$635$	−2.17025	+	1.57678i	−0.0861236	+	0.0625725i
$636$	−0.934971	+	2.87755i	−0.0370740	+	0.114102i
$637$	−0.869151			−0.0344370
$638$	−2.30452	−	3.22809i	−0.0912367	−	0.127801i
$639$	−1.52683			−0.0604006
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	12.9951	−	9.44152i	0.513277	−	0.372918i	−0.300788	−	0.953691i	$-0.597250\pi$
$641$	12.9951	−	9.44152i	0.513277	−	0.372918i	0.814065	+	0.580773i	$0.197250\pi$
$642$	−9.27387	−	6.73786i	−0.366011	−	0.265922i
$643$	13.6596	+	42.0399i	0.538682	+	1.65789i	0.735557	+	0.677463i	$0.236921\pi$
$643$	13.6596	+	42.0399i	0.538682	+	1.65789i	−0.196875	+	0.980429i	$0.563079\pi$
$644$	0.618034	+	1.90211i	0.0243540	+	0.0749538i
$645$	−10.2884	−	7.47498i	−0.405107	−	0.294327i
$646$	−25.4190	+	18.4680i	−1.00010	+	0.726613i
$647$	−13.7876	+	42.4339i	−0.542047	+	1.66825i	0.185861	+	0.982576i	$0.440492\pi$
$647$	−13.7876	+	42.4339i	−0.542047	+	1.66825i	−0.727909	+	0.685674i	$0.759508\pi$
$648$	10.5826			0.415724
$649$	−14.6529	+	19.8188i	−0.575177	+	0.777956i
$650$	0.869151			0.0340909
$651$	−4.57130	+	14.0690i	−0.179164	+	0.551409i
$652$	7.58874	−	5.51354i	0.297198	−	0.215927i
$653$	−5.48511	−	3.98517i	−0.214649	−	0.155952i	0.475266	−	0.879842i	$-0.342352\pi$
$653$	−5.48511	−	3.98517i	−0.214649	−	0.155952i	−0.689915	+	0.723891i	$0.742352\pi$
$654$	11.4844	+	35.3453i	0.449075	+	1.38211i
$655$	−0.370776	−	1.14113i	−0.0144874	−	0.0445877i
$656$	7.97902	+	5.79710i	0.311528	+	0.226339i
$657$	−9.41586	+	6.84102i	−0.367348	+	0.266894i
$658$	3.32282	−	10.2266i	0.129537	−	0.398674i
$659$	−2.83294			−0.110356			−0.0551778	−	0.998477i	$-0.517573\pi$
$659$	−2.83294			−0.110356			−0.0551778	+	0.998477i	$0.517573\pi$
$660$	6.06968	−	1.91643i	0.236262	−	0.0745968i
$661$	36.4484			1.41768			0.708839	−	0.705370i	$-0.249219\pi$
$661$	36.4484			1.41768			0.708839	+	0.705370i	$0.249219\pi$
$662$	6.37808	−	19.6297i	0.247891	−	0.762930i
$663$	−5.60724	+	4.07390i	−0.217767	+	0.158217i
$664$	−6.65783	−	4.83720i	−0.258374	−	0.187720i
$665$	2.33664	+	7.19143i	0.0906109	+	0.278872i
$666$	−1.43800	−	4.42570i	−0.0557212	−	0.171492i
$667$	−1.93497	−	1.40584i	−0.0749224	−	0.0544343i
$668$	9.70820	−	7.05342i	0.375622	−	0.272905i
$669$	6.47788	−	19.9369i	0.250449	−	0.770804i
$670$	3.56151			0.137593
$671$	24.4741	−	7.72739i	0.944812	−	0.298313i
$672$	1.91913			0.0740321
$673$	−1.58703	+	4.88436i	−0.0611753	+	0.188278i	−0.976974	−	0.213360i	$-0.931559\pi$
$673$	−1.58703	+	4.88436i	−0.0611753	+	0.188278i	0.915798	+	0.401639i	$0.131559\pi$
$674$	0.0206837	−	0.0150276i	0.000796706	−	0.000578841i
$675$	3.59730	+	2.61359i	0.138460	+	0.100597i
$676$	−3.78378	−	11.6453i	−0.145530	−	0.447896i
$677$	8.76081	+	26.9630i	0.336705	+	1.03627i	0.965876	+	0.259005i	$0.0833947\pi$
$677$	8.76081	+	26.9630i	0.336705	+	1.03627i	−0.629170	+	0.777267i	$0.716605\pi$
$678$	20.9497	+	15.2209i	0.804569	+	0.584554i
$679$	11.9721	−	8.69827i	0.459448	−	0.333809i
$680$	−1.28403	+	3.95183i	−0.0492402	+	0.151546i
$681$	−37.5512			−1.43896
$682$	−15.1986	+	20.5568i	−0.581984	+	0.787162i
$683$	25.0913			0.960094			0.480047	−	0.877243i	$-0.340620\pi$
$683$	25.0913			0.960094			0.480047	+	0.877243i	$0.340620\pi$
$684$	1.59607	−	4.91220i	0.0610272	−	0.187823i
$685$	−3.76858	+	2.73804i	−0.143990	+	0.104615i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	−8.81342	−	27.1249i	−0.336253	−	1.03488i
$688$	−2.04771	−	6.30222i	−0.0780684	−	0.240270i
$689$	−1.10857	−	0.805425i	−0.0422332	−	0.0306843i
$690$	3.10522	−	2.25607i	0.118214	−	0.0858872i
$691$	−15.2638	+	46.9771i	−0.580662	+	1.78709i	0.0353728	+	0.999374i	$0.488738\pi$
$691$	−15.2638	+	46.9771i	−0.580662	+	1.78709i	−0.616035	+	0.787719i	$0.711262\pi$
$692$	9.14787			0.347750
$693$	1.31630	+	1.84382i	0.0500020	+	0.0700411i
$694$	−27.7393			−1.05297
$695$	3.90004	−	12.0031i	0.147937	−	0.455303i
$696$	−1.85673	+	1.34899i	−0.0703792	+	0.0511335i
$697$	−33.1544	−	24.0881i	−1.25581	−	0.912402i
$698$	−2.40026	−	7.38726i	−0.0908514	−	0.279612i
$699$	2.71486	+	8.35549i	0.102686	+	0.316034i
$700$	0.809017	+	0.587785i	0.0305780	+	0.0222162i
$701$	−41.6222	+	30.2403i	−1.57205	+	1.14216i	−0.646889	+	0.762584i	$0.723930\pi$
$701$	−41.6222	+	30.2403i	−1.57205	+	1.14216i	−0.925160	+	0.379576i	$0.876070\pi$
$702$	−1.19425	+	3.67553i	−0.0450742	+	0.138724i
$703$	51.5138			1.94288
$704$	3.14565	+	1.05113i	0.118556	+	0.0396158i
$705$	−20.6361			−0.777202
$706$	7.14764	−	21.9982i	0.269005	−	0.827912i
$707$	−14.2454	+	10.3499i	−0.535752	+	0.389247i
$708$	11.5381	+	8.38296i	0.433630	+	0.315051i
$709$	−12.1815	−	37.4907i	−0.457485	−	1.40799i	−0.868193	−	0.496227i	$-0.834718\pi$
$709$	−12.1815	−	37.4907i	−0.457485	−	1.40799i	0.410708	−	0.911767i	$-0.365282\pi$
$710$	−0.690738	−	2.12587i	−0.0259229	−	0.0797826i
$711$	1.73014	+	1.25702i	0.0648852	+	0.0471419i
$712$	−8.00465	+	5.81572i	−0.299987	+	0.217953i
$713$	−4.76393	+	14.6619i	−0.178411	+	0.549092i
$714$	−7.97437			−0.298433
$715$	−0.0240054	+	2.88255i	−0.000897752	+	0.107801i
$716$	3.71474			0.138826
$717$	−10.0509	+	30.9334i	−0.375357	+	1.15523i
$718$	−10.2017	+	7.41198i	−0.380725	+	0.276613i
$719$	−20.0145	−	14.5414i	−0.746413	−	0.542301i	0.148300	−	0.988942i	$-0.452620\pi$
$719$	−20.0145	−	14.5414i	−0.746413	−	0.542301i	−0.894713	+	0.446641i	$0.852620\pi$
$720$	−0.211078	−	0.649631i	−0.00786641	−	0.0242103i
$721$	1.49960	+	4.61531i	0.0558482	+	0.171883i
$722$	30.8854	+	22.4396i	1.14944	+	0.835115i
$723$	−42.5864	+	30.9408i	−1.58380	+	1.15070i
$724$	−6.62654	+	20.3944i	−0.246274	+	0.757952i
$725$	−1.19588			−0.0444138
$726$	6.18820	+	20.1831i	0.229666	+	0.749064i
$727$	−51.2679			−1.90142			−0.950710	−	0.310081i	$-0.899644\pi$
$727$	−51.2679			−1.90142			−0.950710	+	0.310081i	$0.899644\pi$
$728$	−0.268582	+	0.826612i	−0.00995432	+	0.0306363i
$729$	−14.8630	+	10.7986i	−0.550482	+	0.399948i
$730$	−13.7848	−	10.0152i	−0.510197	−	0.370680i
$731$	8.50866	+	26.1870i	0.314704	+	0.968560i
$732$	−4.58915	−	14.1240i	−0.169620	−	0.522037i
$733$	0.227836	+	0.165532i	0.00841530	+	0.00611408i	0.591985	−	0.805949i	$-0.298344\pi$
$733$	0.227836	+	0.165532i	0.00841530	+	0.00611408i	−0.583570	+	0.812063i	$0.698344\pi$
$734$	2.84252	−	2.06521i	0.104919	−	0.0762282i
$735$	−0.593044	+	1.82520i	−0.0218748	+	0.0673236i
$736$	2.00000			0.0737210
$737$	−0.0983669	+	11.8118i	−0.00362339	+	0.435093i
$738$	6.73678			0.247984
$739$	0.447603	−	1.37758i	0.0164654	−	0.0506751i	−0.942486	−	0.334245i	$-0.891519\pi$
$739$	0.447603	−	1.37758i	0.0164654	−	0.0506751i	0.958952	+	0.283570i	$0.0915187\pi$
$740$	5.51153	−	4.00436i	0.202608	−	0.147203i
$741$	10.2039	+	7.41357i	0.374850	+	0.272344i
$742$	−0.487185	−	1.49940i	−0.0178851	−	0.0550447i
$743$	−3.37872	−	10.3986i	−0.123953	−	0.381488i	0.869756	−	0.493482i	$-0.164276\pi$
$743$	−3.37872	−	10.3986i	−0.123953	−	0.381488i	−0.993709	+	0.111994i	$0.964276\pi$
$744$	11.9678	+	8.69514i	0.438762	+	0.318779i
$745$	13.0444	−	9.47734i	0.477911	−	0.347223i
$746$	2.62329	−	8.07367i	0.0960456	−	0.295598i
$747$	−5.62128			−0.205672
$748$	−13.0708	−	4.36764i	−0.477916	−	0.159697i
$749$	5.97309			0.218252
$750$	0.593044	−	1.82520i	0.0216549	−	0.0666469i
$751$	31.9020	−	23.1781i	1.16412	−	0.845782i	0.173826	−	0.984776i	$-0.444387\pi$
$751$	31.9020	−	23.1781i	1.16412	−	0.845782i	0.990293	+	0.138994i	$0.0443869\pi$
$752$	−8.69925	−	6.32037i	−0.317229	−	0.230480i
$753$	3.09267	+	9.51825i	0.112703	+	0.346864i
$754$	−0.321192	−	0.988527i	−0.0116971	−	0.0360000i
$755$	7.93660	+	5.76627i	0.288842	+	0.209856i
$756$	−3.59730	+	2.61359i	−0.130832	+	0.0950554i
$757$	−6.85130	+	21.0861i	−0.249015	+	0.766389i	0.745935	+	0.666018i	$0.232003\pi$
$757$	−6.85130	+	21.0861i	−0.249015	+	0.766389i	−0.994950	+	0.100370i	$0.967997\pi$
$758$	19.0706			0.692675
$759$	7.39653	+	10.3608i	0.268477	+	0.376073i
$760$	7.56151			0.274285
$761$	−8.99236	+	27.6756i	−0.325973	+	1.00324i	0.645027	+	0.764160i	$0.276846\pi$
$761$	−8.99236	+	27.6756i	−0.325973	+	1.00324i	−0.971000	+	0.239081i	$0.923154\pi$
$762$	−4.16499	+	3.02604i	−0.150882	+	0.109622i
$763$	−15.6667	−	11.3825i	−0.567174	−	0.412076i
$764$	−6.76507	−	20.8207i	−0.244752	−	0.753268i
$765$	0.877071	+	2.69935i	0.0317106	+	0.0975951i
$766$	1.07986	+	0.784568i	0.0390171	+	0.0283476i
$767$	−5.22549	+	3.79654i	−0.188681	+	0.137085i
$768$	0.593044	−	1.82520i	0.0213996	−	0.0658613i
$769$	36.2631			1.30768			0.653840	−	0.756633i	$-0.273157\pi$
$769$	36.2631			1.30768			0.653840	+	0.756633i	$0.273157\pi$
$770$	−1.97174	+	2.66688i	−0.0710566	+	0.0961076i
$771$	−3.40400			−0.122592
$772$	1.26042	−	3.87917i	0.0453634	−	0.139614i
$773$	3.44274	−	2.50130i	0.123827	−	0.0899654i	−0.524148	−	0.851627i	$-0.675616\pi$
$773$	3.44274	−	2.50130i	0.123827	−	0.0899654i	0.647975	+	0.761662i	$0.275616\pi$
$774$	−3.66189	−	2.66052i	−0.131624	−	0.0956304i
$775$	2.38197	+	7.33094i	0.0855627	+	0.263335i
$776$	−4.57295	−	14.0741i	−0.164159	−	0.505230i
$777$	10.5774	+	7.68490i	0.379460	+	0.275694i
$778$	−0.956347	+	0.694827i	−0.0342867	+	0.0249108i
$779$	−23.0453	+	70.9262i	−0.825685	+	2.54120i
$780$	1.66801			0.0597245
$781$	7.06956	−	2.23213i	0.252969	−	0.0798717i
$782$	−8.31040			−0.297179
$783$	1.64319	−	5.05722i	0.0587229	−	0.180730i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	−2.21860	−	1.61191i	−0.0791853	−	0.0575315i
$786$	−0.711567	−	2.18998i	−0.0253808	−	0.0781140i
$787$	−2.57108	−	7.91297i	−0.0916491	−	0.282067i	0.894717	−	0.446634i	$-0.147377\pi$
$787$	−2.57108	−	7.91297i	−0.0916491	−	0.282067i	−0.986366	+	0.164567i	$0.947377\pi$
$788$	−11.5103	−	8.36269i	−0.410036	−	0.297908i
$789$	21.7857	−	15.8283i	0.775592	−	0.563501i
$790$	−0.967486	+	2.97761i	−0.0344216	+	0.105939i
$791$	−13.4932			−0.479764
$792$	2.16034	−	0.682100i	0.0767643	−	0.0242374i
$793$	6.72575			0.238838
$794$	4.93006	−	15.1732i	0.174961	−	0.538475i
$795$	−2.44779	+	1.77842i	−0.0868140	+	0.0630741i
$796$	7.07959	+	5.14362i	0.250929	+	0.182311i
$797$	0.813015	+	2.50220i	0.0287985	+	0.0886325i	0.964423	−	0.264365i	$-0.0851624\pi$
$797$	0.813015	+	2.50220i	0.0287985	+	0.0886325i	−0.935624	+	0.352998i	$0.885162\pi$
$798$	4.48431	+	13.8013i	0.158743	+	0.488560i
$799$	36.1471	+	26.2624i	1.27879	+	0.929097i
$800$	0.809017	−	0.587785i	0.0286031	−	0.0207813i
$801$	−2.08847	+	6.42764i	−0.0737924	+	0.227110i
$802$	11.8135			0.417149
$803$	33.5963	−	45.4407i	1.18559	−	1.60357i
$804$	6.83501			0.241052
$805$	−0.618034	+	1.90211i	−0.0217828	+	0.0670407i
$806$	−5.42008	+	3.93792i	−0.190914	+	0.138707i
$807$	21.7958	+	15.8356i	0.767249	+	0.557439i
$808$	5.44125	+	16.7464i	0.191422	+	0.589138i
$809$	−3.02786	−	9.31881i	−0.106454	−	0.327632i	0.883615	−	0.468214i	$-0.155102\pi$
$809$	−3.02786	−	9.31881i	−0.106454	−	0.327632i	−0.990069	+	0.140582i	$0.955102\pi$
$810$	8.56151	+	6.22030i	0.300821	+	0.218559i
$811$	−22.2532	+	16.1679i	−0.781416	+	0.567732i	−0.905404	−	0.424552i	$-0.860432\pi$
$811$	−22.2532	+	16.1679i	−0.781416	+	0.567732i	0.123988	+	0.992284i	$0.460432\pi$
$812$	0.369547	−	1.13735i	0.0129685	−	0.0399131i
$813$	41.3831			1.45137
$814$	13.1283	+	18.3897i	0.460146	+	0.644557i
$815$	9.38020			0.328574
$816$	−2.46422	+	7.58408i	−0.0862648	+	0.265496i
$817$	40.5372	−	29.4520i	1.41822	−	1.03039i
$818$	−13.9199	−	10.1134i	−0.486699	−	0.353607i
$819$	0.183459	+	0.564628i	0.00641056	+	0.0197297i
$820$	3.04771	+	9.37990i	0.106431	+	0.327560i
$821$	−35.6889	−	25.9295i	−1.24555	−	0.904945i	−0.247595	−	0.968864i	$-0.579640\pi$
$821$	−35.6889	−	25.9295i	−1.24555	−	0.904945i	−0.997955	+	0.0639186i	$0.979640\pi$
$822$	−7.23240	+	5.25465i	−0.252259	+	0.183277i
$823$	8.21694	−	25.2891i	0.286424	−	0.881524i	−0.699544	−	0.714590i	$-0.746613\pi$
$823$	8.21694	−	25.2891i	0.286424	−	0.881524i	0.985968	−	0.166934i	$-0.0533867\pi$
$824$	4.85282			0.169056
$825$	6.03692	+	2.01725i	0.210179	+	0.0702315i
$826$	−7.43146			−0.258573
$827$	−11.3796	+	35.0229i	−0.395708	+	1.21787i	0.532700	+	0.846304i	$0.321177\pi$
$827$	−11.3796	+	35.0229i	−0.395708	+	1.21787i	−0.928408	+	0.371561i	$0.878823\pi$
$828$	1.10522	−	0.802988i	0.0384090	−	0.0279058i
$829$	35.8767	+	26.0659i	1.24605	+	0.905307i	0.997986	−	0.0634366i	$-0.0202061\pi$
$829$	35.8767	+	26.0659i	1.24605	+	0.905307i	0.248063	+	0.968744i	$0.420206\pi$
$830$	−2.54306	−	7.82675i	−0.0882710	−	0.271670i
$831$	−6.20892	−	19.1091i	−0.215385	−	0.662887i
$832$	0.703158	+	0.510874i	0.0243776	+	0.0177114i
$833$	3.36163	−	2.44236i	0.116473	−	0.0846229i
$834$	7.48469	−	23.0355i	0.259174	−	0.797654i
$835$	12.0000			0.415277
$836$	−0.208844	+	25.0778i	−0.00722304	+	0.867335i
$837$	−34.2746			−1.18470
$838$	2.18756	−	6.73262i	0.0755681	−	0.232575i
$839$	−14.9552	+	10.8656i	−0.516310	+	0.375121i	−0.815212	−	0.579163i	$-0.803380\pi$
$839$	−14.9552	+	10.8656i	−0.516310	+	0.375121i	0.298902	+	0.954284i	$0.403380\pi$
$840$	1.55261	+	1.12804i	0.0535701	+	0.0389210i
$841$	−8.51956	−	26.2205i	−0.293778	−	0.904156i
$842$	4.90571	+	15.0982i	0.169062	+	0.520319i
$843$	−42.7575	−	31.0652i	−1.47265	−	1.06994i
$844$	15.9939	−	11.6202i	0.550531	−	0.399984i
$845$	3.78378	−	11.6453i	0.130166	−	0.400610i
$846$	−7.34488			−0.252522
$847$	−8.79027	−	6.61295i	−0.302037	−	0.227224i
$848$	−1.57656			−0.0541394
$849$	−7.50373	+	23.0941i	−0.257527	+	0.792587i
$850$	−3.36163	+	2.44236i	−0.115303	+	0.0837724i
$851$	11.0231	+	8.00873i	0.377866	+	0.274536i
$852$	−1.32562	−	4.07983i	−0.0454149	−	0.139773i
$853$	−6.26253	−	19.2741i	−0.214425	−	0.659932i	−0.999194	−	0.0401438i	$-0.987218\pi$
$853$	−6.26253	−	19.2741i	−0.214425	−	0.659932i	0.784769	−	0.619788i	$-0.212782\pi$
$854$	6.26042	+	4.54846i	0.214227	+	0.155645i
$855$	4.17856	−	3.03590i	0.142904	−	0.103826i
$856$	1.84579	−	5.68074i	0.0630877	−	0.194164i
$857$	−34.4745			−1.17763			−0.588813	−	0.808269i	$-0.700404\pi$
$857$	−34.4745			−1.17763			−0.588813	+	0.808269i	$0.700404\pi$
$858$	−0.0460695	+	5.53198i	−0.00157279	+	0.188859i
$859$	7.96220			0.271667			0.135833	−	0.990732i	$-0.456629\pi$
$859$	7.96220			0.271667			0.135833	+	0.990732i	$0.456629\pi$
$860$	2.04771	−	6.30222i	0.0698265	−	0.214904i
$861$	−15.3128	+	11.1254i	−0.521858	+	0.379152i
$862$	−14.1333	−	10.2684i	−0.481381	−	0.349744i
$863$	−9.23804	−	28.4318i	−0.314466	−	0.967828i	−0.975974	−	0.217889i	$-0.930083\pi$
$863$	−9.23804	−	28.4318i	−0.314466	−	0.967828i	0.661507	−	0.749939i	$-0.269917\pi$
$864$	1.37405	+	4.22888i	0.0467460	+	0.143869i
$865$	7.40078	+	5.37698i	0.251634	+	0.182823i
$866$	14.7153	−	10.6913i	0.500047	−	0.363306i
$867$	0.157558	−	0.484913i	0.00535094	−	0.0164685i
$868$	−7.70820			−0.261633
$869$	−9.84857	−	3.29092i	−0.334090	−	0.111637i
$870$	−2.29505			−0.0778094
$871$	−0.956560	+	2.94399i	−0.0324118	+	0.0997532i
$872$	−15.6667	+	11.3825i	−0.530543	+	0.385462i
$873$	−8.17772	−	5.94146i	−0.276774	−	0.201088i
$874$	4.67327	+	14.3829i	0.158076	+	0.486507i
$875$	0.309017	+	0.951057i	0.0104467	+	0.0321516i
$876$	−26.4548	−	19.2205i	−0.893824	−	0.649401i
$877$	−2.03296	+	1.47703i	−0.0686483	+	0.0498759i	−0.621580	−	0.783351i	$-0.713509\pi$
$877$	−2.03296	+	1.47703i	−0.0686483	+	0.0498759i	0.552932	+	0.833226i	$0.313509\pi$
$878$	5.12431	−	15.7710i	0.172937	−	0.532246i
$879$	−50.7051			−1.71024
$880$	1.92705	+	2.69935i	0.0649609	+	0.0909950i
$881$	31.5748			1.06378			0.531890	−	0.846813i	$-0.321482\pi$
$881$	31.5748			1.06378			0.531890	+	0.846813i	$0.321482\pi$
$882$	−0.211078	+	0.649631i	−0.00710737	+	0.0218742i
$883$	−17.5096	+	12.7215i	−0.589246	+	0.428113i	−0.842046	−	0.539406i	$-0.818649\pi$
$883$	−17.5096	+	12.7215i	−0.589246	+	0.428113i	0.252799	+	0.967519i	$0.418649\pi$
$884$	−2.92176	−	2.12278i	−0.0982694	−	0.0713969i
$885$	4.40718	+	13.5639i	0.148146	+	0.455946i
$886$	11.4942	+	35.3756i	0.386156	+	1.18847i
$887$	27.7966	+	20.1954i	0.933320	+	0.678097i	0.946803	−	0.321812i	$-0.104292\pi$
$887$	27.7966	+	20.1954i	0.933320	+	0.678097i	−0.0134834	+	0.999909i	$0.504292\pi$
$888$	10.5774	−	7.68490i	0.354953	−	0.257888i
$889$	0.828961	−	2.55128i	0.0278025	−	0.0855671i
$890$	−9.89429			−0.331657
$891$	−20.8662	+	28.2225i	−0.699043	+	0.945491i
$892$	10.9231			0.365733
$893$	25.1255	−	77.3284i	0.840794	−	2.58770i
$894$	25.0340	−	18.1883i	0.837262	−	0.608306i
$895$	3.00529	+	2.18347i	0.100456	+	0.0729854i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	1.03089	+	3.17275i	0.0344204	+	0.105935i
$898$	8.55359	+	6.21455i	0.285437	+	0.207382i
$899$	7.45758	−	5.41825i	0.248724	−	0.180709i
$900$	0.211078	−	0.649631i	0.00703593	−	0.0216544i
$901$	6.55093			0.218243
$902$	−31.1927	+	9.84871i	−1.03860	+	0.327926i
$903$	12.7172			0.423202
$904$	−4.16964	+	12.8328i	−0.138680	+	0.426814i
$905$	−17.3485	+	12.6044i	−0.576684	+	0.418986i
$906$	15.2314	+	11.0662i	0.506028	+	0.367651i
$907$	4.90670	+	15.1013i	0.162924	+	0.501429i	0.998877	−	0.0473716i	$-0.0150845\pi$
$907$	4.90670	+	15.1013i	0.162924	+	0.501429i	−0.835953	+	0.548801i	$0.815084\pi$
$908$	−6.04647	−	18.6091i	−0.200659	−	0.617565i
$909$	9.73048	+	7.06961i	0.322740	+	0.234484i
$910$	−0.703158	+	0.510874i	−0.0233095	+	0.0169353i
$911$	6.00062	−	18.4680i	0.198809	−	0.611873i	−0.801102	−	0.598528i	$-0.795752\pi$
$911$	6.00062	−	18.4680i	0.198809	−	0.611873i	0.999911	−	0.0133440i	$-0.00424767\pi$
$912$	14.5115			0.480525
$913$	26.0277	−	8.21793i	0.861392	−	0.271974i
$914$	1.57179			0.0519903
$915$	4.58915	−	14.1240i	0.151713	−	0.466924i
$916$	12.0231	−	8.73527i	0.397253	−	0.288621i
$917$	0.970704	+	0.705258i	0.0320555	+	0.0232897i
$918$	−5.70943	−	17.5718i	−0.188439	−	0.579957i
$919$	−9.95915	−	30.6511i	−0.328522	−	1.01109i	−0.969826	−	0.243800i	$-0.921606\pi$
$919$	−9.95915	−	30.6511i	−0.328522	−	1.01109i	0.641304	−	0.767287i	$-0.278394\pi$
$920$	1.61803	+	1.17557i	0.0533450	+	0.0387574i
$921$	38.5550	−	28.0119i	1.27043	−	0.923023i
$922$	−4.91509	+	15.1271i	−0.161870	+	0.498184i
$923$	1.94279			0.0639478
$924$	−3.78403	+	5.11809i	−0.124485	+	0.168373i
$925$	6.81263			0.223998
$926$	−6.83747	+	21.0436i	−0.224693	+	0.691535i
$927$	2.68171	−	1.94838i	0.0880791	−	0.0639932i
$928$	−0.967486	−	0.702919i	−0.0317593	−	0.0230745i
$929$	9.29547	+	28.6085i	0.304974	+	0.938615i	0.979687	+	0.200534i	$0.0642677\pi$
$929$	9.29547	+	28.6085i	0.304974	+	0.938615i	−0.674712	+	0.738081i	$0.735732\pi$
$930$	4.57130	+	14.0690i	0.149899	+	0.461342i
$931$	−6.11739	−	4.44455i	−0.200489	−	0.145664i
$932$	−3.70355	+	2.69079i	−0.121314	+	0.0881397i
$933$	3.40458	−	10.4782i	0.111461	−	0.343042i
$934$	−3.31217			−0.108377
$935$	−8.00728	−	11.2163i	−0.261866	−	0.366813i
$936$	0.593685			0.0194052
$937$	1.59671	−	4.91417i	0.0521622	−	0.160539i	−0.921582	−	0.388184i	$-0.873103\pi$
$937$	1.59671	−	4.91417i	0.0521622	−	0.160539i	0.973744	+	0.227645i	$0.0731026\pi$
$938$	−2.88133	+	2.09341i	−0.0940786	+	0.0683521i
$939$	33.7994	+	24.5567i	1.10300	+	0.801377i
$940$	−3.32282	−	10.2266i	−0.108378	−	0.333554i
$941$	6.45225	+	19.8580i	0.210337	+	0.647352i	0.999452	+	0.0331059i	$0.0105398\pi$
$941$	6.45225	+	19.8580i	0.210337	+	0.647352i	−0.789114	+	0.614246i	$0.789460\pi$
$942$	−4.25779	−	3.09346i	−0.138726	−	0.100791i
$943$	−15.9580	+	11.5942i	−0.519665	+	0.377559i
$944$	−2.29645	+	7.06774i	−0.0747430	+	0.230035i
$945$	−4.44651			−0.144645
$946$	20.8448	+	6.96533i	0.677723	+	0.226462i
$947$	22.5179			0.731733			0.365867	−	0.930667i	$-0.380773\pi$
$947$	22.5179			0.731733			0.365867	+	0.930667i	$0.380773\pi$
$948$	−1.85673	+	5.71443i	−0.0603038	+	0.185596i
$949$	11.9810	−	8.70474i	0.388921	−	0.282568i
$950$	6.11739	+	4.44455i	0.198474	+	0.144200i
$951$	4.07001	+	12.5262i	0.131979	+	0.406190i
$952$	−1.28403	−	3.95183i	−0.0416156	−	0.128080i
$953$	−3.02177	−	2.19545i	−0.0978848	−	0.0711175i	0.537766	−	0.843094i	$-0.319268\pi$
$953$	−3.02177	−	2.19545i	−0.0978848	−	0.0711175i	−0.635651	+	0.771976i	$0.719268\pi$
$954$	−0.871223	+	0.632981i	−0.0282069	+	0.0204935i
$955$	6.76507	−	20.8207i	0.218912	−	0.673743i
$956$	−16.9479			−0.548136
$957$	0.0633878	−	7.61154i	0.00204904	−	0.246046i
$958$	26.3656			0.851834
$959$	1.43947	−	4.43023i	0.0464829	−	0.143060i
$960$	1.55261	−	1.12804i	0.0501103	−	0.0364072i
$961$	−22.9894	−	16.7027i	−0.741592	−	0.538798i
$962$	1.82975	+	5.63140i	0.0589936	+	0.181564i
$963$	−1.26079	−	3.88031i	−0.0406283	−	0.125041i
$964$	−22.1904	−	16.1223i	−0.714706	−	0.519264i
$965$	3.29982	−	2.39746i	0.106225	−	0.0771769i
$966$	−1.18609	+	3.65040i	−0.0381618	+	0.117450i
$967$	17.0337			0.547767			0.273884	−	0.961763i	$-0.411692\pi$
$967$	17.0337			0.547767			0.273884	+	0.961763i	$0.411692\pi$
$968$	−9.00563	+	6.31653i	−0.289452	+	0.203021i
$969$	−60.2983			−1.93706
$970$	4.57295	−	14.0741i	0.146829	−	0.451892i
$971$	−25.4688	+	18.5042i	−0.817332	+	0.593827i	−0.915947	−	0.401299i	$-0.868559\pi$
$971$	−25.4688	+	18.5042i	−0.817332	+	0.593827i	0.0986149	+	0.995126i	$0.468559\pi$
$972$	5.63877	+	4.09681i	0.180864	+	0.131405i
$973$	3.90004	+	12.0031i	0.125030	+	0.384801i
$974$	−3.85361	−	11.8602i	−0.123478	−	0.380025i
$975$	1.34945	+	0.980434i	0.0432170	+	0.0313990i
$976$	6.26042	−	4.54846i	0.200391	−	0.145593i
$977$	8.26163	−	25.4267i	0.264313	−	0.813472i	−0.727538	−	0.686068i	$-0.759335\pi$
$977$	8.26163	−	25.4267i	0.264313	−	0.813472i	0.991851	−	0.127404i	$-0.0406646\pi$
$978$	18.0018			0.575635
$979$	0.273274	−	32.8145i	0.00873389	−	1.04876i
$980$	−1.00000			−0.0319438
$981$	−4.08756	+	12.5802i	−0.130506	+	0.401655i
$982$	29.6872	−	21.5690i	0.947357	−	0.688295i
$983$	−18.3396	−	13.3245i	−0.584941	−	0.424985i	0.255561	−	0.966793i	$-0.417740\pi$
$983$	−18.3396	−	13.3245i	−0.584941	−	0.424985i	−0.840502	+	0.541808i	$0.817740\pi$
$984$	5.84896	+	18.0013i	0.186458	+	0.573859i
$985$	−4.39653	−	13.5311i	−0.140085	−	0.431137i
$986$	4.02009	+	2.92077i	0.128026	+	0.0930163i
$987$	16.6950	−	12.1296i	0.531407	−	0.386090i
$988$	−2.03089	+	6.25043i	−0.0646112	+	0.198853i
$989$	13.2531			0.421424
$990$	2.14868	+	0.717985i	0.0682895	+	0.0228191i
$991$	5.56237			0.176695			0.0883473	−	0.996090i	$-0.471841\pi$
$991$	5.56237			0.176695			0.0883473	+	0.996090i	$0.471841\pi$
$992$	−2.38197	+	7.33094i	−0.0756275	+	0.232758i
$993$	32.0457	−	23.2825i	1.01694	−	0.738849i
$994$	1.80838	+	1.31386i	0.0573582	+	0.0416732i
$995$	2.70416	+	8.32256i	0.0857277	+	0.263843i
$996$	−4.88047	−	15.0205i	−0.154644	−	0.475944i
$997$	−32.3688	−	23.5173i	−1.02513	−	0.744802i	−0.0578031	−	0.998328i	$-0.518410\pi$
$997$	−32.3688	−	23.5173i	−1.02513	−	0.744802i	−0.967328	+	0.253526i	$0.918410\pi$
$998$	17.8656	−	12.9801i	0.565527	−	0.410879i
$999$	−9.36087	+	28.8098i	−0.296165	+	0.911501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.e.141.1	yes	8
11.4	even	5		8470.2.a.cq.1.3		4
11.5	even	5	inner	770.2.n.e.71.1	✓	8
11.7	odd	10		8470.2.a.ct.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.e.71.1	✓	8	11.5	even	5	inner
770.2.n.e.141.1	yes	8	1.1	even	1	trivial
8470.2.a.cq.1.3		4	11.4	even	5
8470.2.a.ct.1.3		4	11.7	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.55261 + 1.12804i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.593044 - 1.82520i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.211078 - 0.649631i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.55261 + 1.12804i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.593044 - 1.82520i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.211078 - 0.649631i) q^{9} +1.00000 q^{10} +(-0.0276194 + 3.31651i) q^{11} +1.91913 q^{12} +(-0.268582 + 0.826612i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(1.55261 + 1.12804i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.28403 - 3.95183i) q^{17} +(0.552609 + 0.401494i) q^{18} +(-6.11739 + 4.44455i) q^{19} +(-0.309017 + 0.951057i) q^{20} -1.91913 q^{21} +(-3.14565 - 1.05113i) q^{22} -2.00000 q^{23} +(-0.593044 + 1.82520i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.703158 - 0.510874i) q^{26} +(-1.37405 - 4.22888i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(0.967486 + 0.702919i) q^{29} +(-1.55261 + 1.12804i) q^{30} +(2.38197 - 7.33094i) q^{31} -1.00000 q^{32} +(-3.69826 - 5.18040i) q^{33} +4.15520 q^{34} +(0.309017 - 0.951057i) q^{35} +(-0.552609 + 0.401494i) q^{36} +(-5.51153 - 4.00436i) q^{37} +(-2.33664 - 7.19143i) q^{38} +(-0.515445 - 1.58638i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(7.97902 - 5.79710i) q^{41} +(0.593044 - 1.82520i) q^{42} -6.62654 q^{43} +(1.97174 - 2.66688i) q^{44} -0.683063 q^{45} +(0.618034 - 1.90211i) q^{46} +(-8.69925 + 6.32037i) q^{47} +(-1.55261 - 1.12804i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(6.45140 + 4.68722i) q^{51} +(0.703158 - 0.510874i) q^{52} +(-0.487185 + 1.49940i) q^{53} +4.44651 q^{54} +(3.16272 - 0.998590i) q^{55} +1.00000 q^{56} +(4.48431 - 13.8013i) q^{57} +(-0.967486 + 0.702919i) q^{58} +(6.01217 + 4.36810i) q^{59} +(-0.593044 - 1.82520i) q^{60} +(-2.39127 - 7.35956i) q^{61} +(6.23607 + 4.53077i) q^{62} +(0.552609 - 0.401494i) q^{63} +(0.309017 - 0.951057i) q^{64} +0.869151 q^{65} +(6.06968 - 1.91643i) q^{66} +3.56151 q^{67} +(-1.28403 + 3.95183i) q^{68} +(3.10522 - 2.25607i) q^{69} +(0.809017 + 0.587785i) q^{70} +(-0.690738 - 2.12587i) q^{71} +(-0.211078 - 0.649631i) q^{72} +(-13.7848 - 10.0152i) q^{73} +(5.51153 - 4.00436i) q^{74} +(0.593044 - 1.82520i) q^{75} +7.56151 q^{76} +(-1.97174 + 2.66688i) q^{77} +1.66801 q^{78} +(-0.967486 + 2.97761i) q^{79} +(0.809017 - 0.587785i) q^{80} +(8.56151 + 6.22030i) q^{81} +(3.04771 + 9.37990i) q^{82} +(-2.54306 - 7.82675i) q^{83} +(1.55261 + 1.12804i) q^{84} +(-3.36163 + 2.44236i) q^{85} +(2.04771 - 6.30222i) q^{86} -2.29505 q^{87} +(1.92705 + 2.69935i) q^{88} -9.89429 q^{89} +(0.211078 - 0.649631i) q^{90} +(-0.703158 + 0.510874i) q^{91} +(1.61803 + 1.17557i) q^{92} +(4.57130 + 14.0690i) q^{93} +(-3.32282 - 10.2266i) q^{94} +(6.11739 + 4.44455i) q^{95} +(1.55261 - 1.12804i) q^{96} +(4.57295 - 14.0741i) q^{97} -1.00000 q^{98} +(2.14868 + 0.717985i) 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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