LMFDB - Embedded newform 770.2.n.i.141.2

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 11 x^{10} - 21 x^{9} + 61 x^{8} - 34 x^{7} + 141 x^{6} + 192 x^{5} + 289 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 11x^10 - 21x^9 + 61x^8 - 34x^7 + 141x^6 + 192x^5 + 289x^4 - 55x^3 + 222x^2 - 24*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.2
Root			$-1.00857 + 0.732772i$ of defining polynomial
Character	$\chi$	$=$	770.141
Dual form			770.2.n.i.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.338879 - 0.246210i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.129440 - 0.398376i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.872831 + 2.68630i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.338879 - 0.246210i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.129440 - 0.398376i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.872831 + 2.68630i) q^{9} +1.00000 q^{10} +(-1.19466 + 3.09399i) q^{11} -0.418877 q^{12} +(-1.63801 + 5.04129i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(0.338879 + 0.246210i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.456166 + 1.40393i) q^{17} +(2.28510 + 1.66022i) q^{18} +(-0.770581 + 0.559860i) q^{19} +(0.309017 - 0.951057i) q^{20} -0.418877 q^{21} +(2.57339 + 2.09228i) q^{22} +2.37872 q^{23} +(-0.129440 + 0.398376i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(4.28838 + 3.11569i) q^{26} +(0.753930 + 2.32036i) q^{27} +(0.309017 + 0.951057i) q^{28} +(-4.83605 - 3.51359i) q^{29} +(0.338879 - 0.246210i) q^{30} +(0.724120 - 2.22861i) q^{31} +1.00000 q^{32} +(0.356927 + 1.34263i) q^{33} +1.47618 q^{34} +(0.309017 - 0.951057i) q^{35} +(2.28510 - 1.66022i) q^{36} +(-0.0181241 - 0.0131679i) q^{37} +(0.294336 + 0.905872i) q^{38} +(0.686127 + 2.11168i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(1.23930 - 0.900404i) q^{41} +(-0.129440 + 0.398376i) q^{42} +3.83101 q^{43} +(2.78510 - 1.80089i) q^{44} -2.82454 q^{45} +(0.735065 - 2.26230i) q^{46} +(1.21711 - 0.884279i) q^{47} +(0.338879 + 0.246210i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(0.500248 + 0.363451i) q^{51} +(4.28838 - 3.11569i) q^{52} +(-3.50695 + 10.7933i) q^{53} +2.43977 q^{54} +(-3.31173 - 0.180091i) q^{55} +1.00000 q^{56} +(-0.123291 + 0.379449i) q^{57} +(-4.83605 + 3.51359i) q^{58} +(-0.622026 - 0.451928i) q^{59} +(-0.129440 - 0.398376i) q^{60} +(2.49071 + 7.66562i) q^{61} +(-1.89577 - 1.37736i) q^{62} +(2.28510 - 1.66022i) q^{63} +(0.309017 - 0.951057i) q^{64} -5.30073 q^{65} +(1.38721 + 0.0754362i) q^{66} +12.1841 q^{67} +(0.456166 - 1.40393i) q^{68} +(0.806097 - 0.585664i) q^{69} +(-0.809017 - 0.587785i) q^{70} +(-3.68805 - 11.3507i) q^{71} +(-0.872831 - 2.68630i) q^{72} +(-5.89369 - 4.28201i) q^{73} +(-0.0181241 + 0.0131679i) q^{74} +(-0.129440 + 0.398376i) q^{75} +0.952490 q^{76} +(2.78510 - 1.80089i) q^{77} +2.22035 q^{78} +(-3.95872 + 12.1837i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-6.02852 - 4.37998i) q^{81} +(-0.473371 - 1.45689i) q^{82} +(1.89590 + 5.83498i) q^{83} +(0.338879 + 0.246210i) q^{84} +(-1.19426 + 0.867679i) q^{85} +(1.18385 - 3.64350i) q^{86} -2.50392 q^{87} +(-0.852104 - 3.20530i) q^{88} +13.4596 q^{89} +(-0.872831 + 2.68630i) q^{90} +(4.28838 - 3.11569i) q^{91} +(-1.92442 - 1.39818i) q^{92} +(-0.303317 - 0.933515i) q^{93} +(-0.464893 - 1.43079i) q^{94} +(-0.770581 - 0.559860i) q^{95} +(0.338879 - 0.246210i) q^{96} +(5.71255 - 17.5814i) q^{97} +1.00000 q^{98} +(-7.26865 - 5.90974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * 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
$3$	0.338879	−	0.246210i	0.195652	−	0.142149i	−0.485646	−	0.874155i	$-0.661416\pi$
$3$	0.338879	−	0.246210i	0.195652	−	0.142149i	0.681298	+	0.732006i	$0.261416\pi$
$4$	−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
$6$	−0.129440	−	0.398376i	−0.0528437	−	0.162636i
$7$	−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
$9$	−0.872831	+	2.68630i	−0.290944	+	0.895433i
$10$	1.00000			0.316228
$11$	−1.19466	+	3.09399i	−0.360203	+	0.932874i
$11$	−1.19466	+	3.09399i	−0.360203	+	0.932874i
$12$	−0.418877			−0.120919
$13$	−1.63801	+	5.04129i	−0.454303	+	1.39820i	0.417648	+	0.908609i	$0.362855\pi$
$13$	−1.63801	+	5.04129i	−0.454303	+	1.39820i	−0.871951	+	0.489593i	$0.837145\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	0.338879	+	0.246210i	0.0874981	+	0.0635711i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.456166	+	1.40393i	0.110637	+	0.340504i	0.991012	−	0.133773i	$-0.0427094\pi$
$17$	0.456166	+	1.40393i	0.110637	+	0.340504i	−0.880375	+	0.474277i	$0.842709\pi$
$18$	2.28510	+	1.66022i	0.538604	+	0.391319i
$19$	−0.770581	+	0.559860i	−0.176783	+	0.128441i	−0.672658	−	0.739953i	$-0.734848\pi$
$19$	−0.770581	+	0.559860i	−0.176783	+	0.128441i	0.495875	+	0.868394i	$0.334848\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$	−0.418877			−0.0914065
$22$	2.57339	+	2.09228i	0.548649	+	0.446076i
$23$	2.37872			0.495997			0.247999	−	0.968760i	$-0.420227\pi$
$23$	2.37872			0.495997			0.247999	+	0.968760i	$0.420227\pi$
$24$	−0.129440	+	0.398376i	−0.0264219	+	0.0813181i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	4.28838	+	3.11569i	0.841020	+	0.611037i
$27$	0.753930	+	2.32036i	0.145094	+	0.446553i
$28$	0.309017	+	0.951057i	0.0583987	+	0.179733i
$29$	−4.83605	−	3.51359i	−0.898031	−	0.652458i	0.0399282	−	0.999203i	$-0.487287\pi$
$29$	−4.83605	−	3.51359i	−0.898031	−	0.652458i	−0.937960	+	0.346745i	$0.887287\pi$
$30$	0.338879	−	0.246210i	0.0618705	−	0.0449516i
$31$	0.724120	−	2.22861i	0.130056	−	0.400271i	−0.864733	−	0.502233i	$-0.832512\pi$
$31$	0.724120	−	2.22861i	0.130056	−	0.400271i	0.994788	+	0.101962i	$0.0325121\pi$
$32$	1.00000			0.176777
$33$	0.356927	+	1.34263i	0.0621330	+	0.233721i
$34$	1.47618			0.253163
$35$	0.309017	−	0.951057i	0.0522334	−	0.160758i
$36$	2.28510	−	1.66022i	0.380850	−	0.276704i
$37$	−0.0181241	−	0.0131679i	−0.00297958	−	0.00216479i	0.586294	−	0.810098i	$-0.300586\pi$
$37$	−0.0181241	−	0.0131679i	−0.00297958	−	0.00216479i	−0.589274	+	0.807933i	$0.700586\pi$
$38$	0.294336	+	0.905872i	0.0477476	+	0.146952i
$39$	0.686127	+	2.11168i	0.109868	+	0.338140i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	1.23930	−	0.900404i	0.193546	−	0.140620i	−0.486792	−	0.873518i	$-0.661833\pi$
$41$	1.23930	−	0.900404i	0.193546	−	0.140620i	0.680338	+	0.732898i	$0.261833\pi$
$42$	−0.129440	+	0.398376i	−0.0199731	+	0.0614707i
$43$	3.83101			0.584223			0.292112	−	0.956384i	$-0.405642\pi$
$43$	3.83101			0.584223			0.292112	+	0.956384i	$0.405642\pi$
$44$	2.78510	−	1.80089i	0.419870	−	0.271494i
$45$	−2.82454			−0.421058
$46$	0.735065	−	2.26230i	0.108379	−	0.333557i
$47$	1.21711	−	0.884279i	0.177533	−	0.128985i	−0.495470	−	0.868625i	$-0.665004\pi$
$47$	1.21711	−	0.884279i	0.177533	−	0.128985i	0.673003	+	0.739640i	$0.265004\pi$
$48$	0.338879	+	0.246210i	0.0489129	+	0.0355373i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	0.500248	+	0.363451i	0.0700487	+	0.0508933i
$52$	4.28838	−	3.11569i	0.594691	−	0.432068i
$53$	−3.50695	+	10.7933i	−0.481717	+	1.48257i	0.354964	+	0.934880i	$0.384493\pi$
$53$	−3.50695	+	10.7933i	−0.481717	+	1.48257i	−0.836680	+	0.547692i	$0.815507\pi$
$54$	2.43977			0.332010
$55$	−3.31173	−	0.180091i	−0.446554	−	0.0242835i
$56$	1.00000			0.133631
$57$	−0.123291	+	0.379449i	−0.0163302	+	0.0502593i
$58$	−4.83605	+	3.51359i	−0.635004	+	0.461357i
$59$	−0.622026	−	0.451928i	−0.0809809	−	0.0588361i	0.546558	−	0.837421i	$-0.315938\pi$
$59$	−0.622026	−	0.451928i	−0.0809809	−	0.0588361i	−0.627539	+	0.778585i	$0.715938\pi$
$60$	−0.129440	−	0.398376i	−0.0167107	−	0.0514301i
$61$	2.49071	+	7.66562i	0.318903	+	0.981483i	0.974118	+	0.226040i	$0.0725781\pi$
$61$	2.49071	+	7.66562i	0.318903	+	0.981483i	−0.655215	+	0.755443i	$0.727422\pi$
$62$	−1.89577	−	1.37736i	−0.240763	−	0.174925i
$63$	2.28510	−	1.66022i	0.287896	−	0.209169i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−5.30073			−0.657474
$66$	1.38721	+	0.0754362i	0.170754	+	0.00928556i
$67$	12.1841			1.48852			0.744260	−	0.667890i	$-0.232802\pi$
$67$	12.1841			1.48852			0.744260	+	0.667890i	$0.232802\pi$
$68$	0.456166	−	1.40393i	0.0553183	−	0.170252i
$69$	0.806097	−	0.585664i	0.0970427	−	0.0705057i
$70$	−0.809017	−	0.587785i	−0.0966960	−	0.0702538i
$71$	−3.68805	−	11.3507i	−0.437691	−	1.34708i	−0.890303	−	0.455368i	$-0.849508\pi$
$71$	−3.68805	−	11.3507i	−0.437691	−	1.34708i	0.452612	−	0.891707i	$-0.350492\pi$
$72$	−0.872831	−	2.68630i	−0.102864	−	0.316583i
$73$	−5.89369	−	4.28201i	−0.689804	−	0.501172i	0.186792	−	0.982400i	$-0.440191\pi$
$73$	−5.89369	−	4.28201i	−0.689804	−	0.501172i	−0.876596	+	0.481228i	$0.840191\pi$
$74$	−0.0181241	+	0.0131679i	−0.00210688	+	0.00153074i
$75$	−0.129440	+	0.398376i	−0.0149465	+	0.0460005i
$76$	0.952490			0.109258
$77$	2.78510	−	1.80089i	0.317392	−	0.205230i
$78$	2.22035			0.251406
$79$	−3.95872	+	12.1837i	−0.445390	+	1.37077i	0.436664	+	0.899624i	$0.356160\pi$
$79$	−3.95872	+	12.1837i	−0.445390	+	1.37077i	−0.882055	+	0.471147i	$0.843840\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−6.02852	−	4.37998i	−0.669836	−	0.486664i
$82$	−0.473371	−	1.45689i	−0.0522750	−	0.160886i
$83$	1.89590	+	5.83498i	0.208102	+	0.640472i	0.999572	+	0.0292639i	$0.00931633\pi$
$83$	1.89590	+	5.83498i	0.208102	+	0.640472i	−0.791470	+	0.611209i	$0.790684\pi$
$84$	0.338879	+	0.246210i	0.0369747	+	0.0268637i
$85$	−1.19426	+	0.867679i	−0.129535	+	0.0941130i
$86$	1.18385	−	3.64350i	0.127657	−	0.392889i
$87$	−2.50392			−0.268448
$88$	−0.852104	−	3.20530i	−0.0908346	−	0.341686i
$89$	13.4596			1.42671			0.713357	−	0.700801i	$-0.247174\pi$
$89$	13.4596			1.42671			0.713357	+	0.700801i	$0.247174\pi$
$90$	−0.872831	+	2.68630i	−0.0920045	+	0.283161i
$91$	4.28838	−	3.11569i	0.449544	−	0.326613i
$92$	−1.92442	−	1.39818i	−0.200635	−	0.145770i
$93$	−0.303317	−	0.933515i	−0.0314525	−	0.0968010i
$94$	−0.464893	−	1.43079i	−0.0479501	−	0.147575i
$95$	−0.770581	−	0.559860i	−0.0790599	−	0.0574404i
$96$	0.338879	−	0.246210i	0.0345867	−	0.0251287i
$97$	5.71255	−	17.5814i	0.580022	−	1.78512i	−0.0383814	−	0.999263i	$-0.512220\pi$
$97$	5.71255	−	17.5814i	0.580022	−	1.78512i	0.618403	−	0.785861i	$-0.287780\pi$
$98$	1.00000			0.101015
$99$	−7.26865	−	5.90974i	−0.730527	−	0.593952i
$100$	1.00000			0.100000
$101$	2.75684	−	8.48467i	0.274316	−	0.844257i	−0.715084	−	0.699038i	$-0.753612\pi$
$101$	2.75684	−	8.48467i	0.274316	−	0.844257i	0.989400	−	0.145218i	$-0.0463884\pi$
$102$	0.500248	−	0.363451i	0.0495319	−	0.0359870i
$103$	9.98216	+	7.25246i	0.983571	+	0.714606i	0.958504	−	0.285079i	$-0.0920199\pi$
$103$	9.98216	+	7.25246i	0.983571	+	0.714606i	0.0250674	+	0.999686i	$0.492020\pi$
$104$	−1.63801	−	5.04129i	−0.160621	−	0.494339i
$105$	−0.129440	−	0.398376i	−0.0126321	−	0.0388775i
$106$	9.18132	+	6.67062i	0.891768	+	0.647908i
$107$	−7.81283	+	5.67636i	−0.755295	+	0.548754i	−0.897464	−	0.441088i	$-0.854593\pi$
$107$	−7.81283	+	5.67636i	−0.755295	+	0.548754i	0.142168	+	0.989842i	$0.454593\pi$
$108$	0.753930	−	2.32036i	0.0725469	−	0.223276i
$109$	−5.91826			−0.566867			−0.283433	−	0.958992i	$-0.591474\pi$
$109$	−5.91826			−0.566867			−0.283433	+	0.958992i	$0.591474\pi$
$110$	−1.19466	+	3.09399i	−0.113906	+	0.295001i
$111$	−0.00938394			−0.000890684
$112$	0.309017	−	0.951057i	0.0291994	−	0.0898664i
$113$	−10.1901	+	7.40356i	−0.958607	+	0.696469i	−0.952827	−	0.303515i	$-0.901840\pi$
$113$	−10.1901	+	7.40356i	−0.958607	+	0.696469i	−0.00578010	+	0.999983i	$0.501840\pi$
$114$	0.322779	+	0.234513i	0.0302310	+	0.0219641i
$115$	0.735065	+	2.26230i	0.0685451	+	0.210960i
$116$	1.84721	+	5.68511i	0.171509	+	0.527850i
$117$	−12.1127	−	8.80039i	−1.11982	−	0.813597i
$118$	−0.622026	+	0.451928i	−0.0572621	+	0.0416034i
$119$	0.456166	−	1.40393i	0.0418167	−	0.128698i
$120$	−0.418877			−0.0382381
$121$	−8.14558	−	7.39253i	−0.740507	−	0.672048i
$122$	8.06011			0.729729
$123$	0.198284	−	0.610256i	0.0178787	−	0.0550249i
$124$	−1.89577	+	1.37736i	−0.170245	+	0.123690i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	−0.872831	−	2.68630i	−0.0777580	−	0.239315i
$127$	−0.785541	−	2.41765i	−0.0697055	−	0.214531i	0.910135	−	0.414311i	$-0.135977\pi$
$127$	−0.785541	−	2.41765i	−0.0697055	−	0.214531i	−0.979841	+	0.199780i	$0.935977\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	1.29825	−	0.943232i	0.114304	−	0.0830469i
$130$	−1.63801	+	5.04129i	−0.143663	+	0.442150i
$131$	7.80495			0.681921			0.340961	−	0.940078i	$-0.389248\pi$
$131$	7.80495			0.681921			0.340961	+	0.940078i	$0.389248\pi$
$132$	0.500415	−	1.29600i	0.0435556	−	0.112803i
$133$	0.952490			0.0825914
$134$	3.76508	−	11.5877i	0.325254	−	1.00103i
$135$	−1.97381	+	1.43406i	−0.169879	+	0.123424i
$136$	−1.19426	−	0.867679i	−0.102407	−	0.0744029i
$137$	6.10226	+	18.7808i	0.521351	+	1.60455i	0.771420	+	0.636326i	$0.219547\pi$
$137$	6.10226	+	18.7808i	0.521351	+	1.60455i	−0.250069	+	0.968228i	$0.580453\pi$
$138$	−0.307902	−	0.947624i	−0.0262103	−	0.0806671i
$139$	−10.7595	−	7.81723i	−0.912608	−	0.663049i	0.0290648	−	0.999578i	$-0.490747\pi$
$139$	−10.7595	−	7.81723i	−0.912608	−	0.663049i	−0.941673	+	0.336529i	$0.890747\pi$
$140$	−0.809017	+	0.587785i	−0.0683744	+	0.0496769i
$141$	0.194733	−	0.599327i	0.0163995	−	0.0504724i
$142$	−11.9348			−1.00155
$143$	−13.6408	−	11.0906i	−1.14070	−	0.927445i
$144$	−2.82454			−0.235378
$145$	1.84721	−	5.68511i	0.153402	−	0.472123i
$146$	−5.89369	+	4.28201i	−0.487765	+	0.354382i
$147$	0.338879	+	0.246210i	0.0279503	+	0.0203070i
$148$	0.00692279	+	0.0213061i	0.000569049	+	0.00175135i
$149$	1.22185	+	3.76046i	0.100098	+	0.308069i	0.988549	−	0.150903i	$-0.0482180\pi$
$149$	1.22185	+	3.76046i	0.100098	+	0.308069i	−0.888451	+	0.458971i	$0.848218\pi$
$150$	0.338879	+	0.246210i	0.0276693	+	0.0201030i
$151$	7.61740	−	5.53437i	0.619896	−	0.450381i	−0.232989	−	0.972479i	$-0.574851\pi$
$151$	7.61740	−	5.53437i	0.619896	−	0.450381i	0.852885	+	0.522099i	$0.174851\pi$
$152$	0.294336	−	0.905872i	0.0238738	−	0.0734759i
$153$	−4.16954			−0.337088
$154$	−0.852104	−	3.20530i	−0.0686645	−	0.258290i
$155$	2.34330			0.188218
$156$	0.686127	−	2.11168i	0.0549341	−	0.169070i
$157$	6.97674	−	5.06890i	0.556804	−	0.404542i	−0.273484	−	0.961877i	$-0.588176\pi$
$157$	6.97674	−	5.06890i	0.556804	−	0.404542i	0.830288	+	0.557335i	$0.188176\pi$
$158$	10.3641	+	7.52993i	0.824520	+	0.599049i
$159$	1.46898	+	4.52106i	0.116498	+	0.358543i
$160$	0.309017	+	0.951057i	0.0244299	+	0.0751876i
$161$	−1.92442	−	1.39818i	−0.151666	−	0.110192i
$162$	−6.02852	+	4.37998i	−0.473645	+	0.344124i
$163$	−3.39625	+	10.4526i	−0.266015	+	0.818710i	0.725443	+	0.688282i	$0.241635\pi$
$163$	−3.39625	+	10.4526i	−0.266015	+	0.818710i	−0.991458	+	0.130427i	$0.958365\pi$
$164$	−1.53186			−0.119618
$165$	−1.16662	+	0.754352i	−0.0908209	+	0.0587262i
$166$	6.13526			0.476189
$167$	1.31722	−	4.05398i	0.101929	−	0.313707i	−0.887068	−	0.461639i	$-0.847262\pi$
$167$	1.31722	−	4.05398i	0.101929	−	0.313707i	0.988998	+	0.147932i	$0.0472617\pi$
$168$	0.338879	−	0.246210i	0.0261451	−	0.0189955i
$169$	−12.2143	−	8.87420i	−0.939561	−	0.682631i
$170$	0.456166	+	1.40393i	0.0349863	+	0.107677i
$171$	−0.831364	−	2.55867i	−0.0635760	−	0.195667i
$172$	−3.09935	−	2.25181i	−0.236323	−	0.171699i
$173$	−17.6975	+	12.8580i	−1.34552	+	0.977575i	−0.346295	+	0.938126i	$0.612560\pi$
$173$	−17.6975	+	12.8580i	−1.34552	+	0.977575i	−0.999222	+	0.0394490i	$0.987440\pi$
$174$	−0.773752	+	2.38136i	−0.0586580	+	0.180531i
$175$	1.00000			0.0755929
$176$	−3.31173	−	0.180091i	−0.249631	−	0.0135749i
$177$	−0.322061			−0.0242076
$178$	4.15924	−	12.8008i	0.311748	−	0.959463i
$179$	−9.72018	+	7.06212i	−0.726520	+	0.527848i	−0.888461	−	0.458953i	$-0.848225\pi$
$179$	−9.72018	+	7.06212i	−0.726520	+	0.527848i	0.161941	+	0.986801i	$0.448225\pi$
$180$	2.28510	+	1.66022i	0.170321	+	0.123746i
$181$	−6.50856	−	20.0313i	−0.483777	−	1.48891i	−0.833744	−	0.552151i	$-0.813807\pi$
$181$	−6.50856	−	20.0313i	−0.483777	−	1.48891i	0.349967	−	0.936762i	$-0.386193\pi$
$182$	−1.63801	−	5.04129i	−0.121418	−	0.373685i
$183$	2.73140	+	1.98448i	0.201911	+	0.146697i
$184$	−1.92442	+	1.39818i	−0.141870	+	0.103075i
$185$	0.00692279	−	0.0213061i	0.000508973	−	0.00156646i
$186$	−0.981556			−0.0719711
$187$	−4.88873	−	0.265848i	−0.357499	−	0.0194407i
$188$	−1.50443			−0.109722
$189$	0.753930	−	2.32036i	0.0548403	−	0.168781i
$190$	−0.770581	+	0.559860i	−0.0559038	+	0.0406165i
$191$	6.15609	+	4.47266i	0.445439	+	0.323630i	0.787792	−	0.615941i	$-0.211224\pi$
$191$	6.15609	+	4.47266i	0.445439	+	0.323630i	−0.342353	+	0.939571i	$0.611224\pi$
$192$	−0.129440	−	0.398376i	−0.00934154	−	0.0287503i
$193$	6.37403	+	19.6173i	0.458813	+	1.41208i	0.866600	+	0.499004i	$0.166301\pi$
$193$	6.37403	+	19.6173i	0.458813	+	1.41208i	−0.407787	+	0.913077i	$0.633699\pi$
$194$	−14.9557	−	10.8659i	−1.07375	−	0.780128i
$195$	−1.79630	+	1.30509i	−0.128636	+	0.0934595i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−10.1376			−0.722273			−0.361136	−	0.932513i	$-0.617611\pi$
$197$	−10.1376			−0.722273			−0.361136	+	0.932513i	$0.617611\pi$
$198$	−7.86664	+	5.08669i	−0.559058	+	0.361495i
$199$	22.6636			1.60658			0.803290	−	0.595588i	$-0.203081\pi$
$199$	22.6636			1.60658			0.803290	+	0.595588i	$0.203081\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	4.12892	−	2.99984i	0.291232	−	0.211592i
$202$	−7.21750	−	5.24382i	−0.507821	−	0.368954i
$203$	1.84721	+	5.68511i	0.129648	+	0.399017i
$204$	−0.191078	−	0.588076i	−0.0133781	−	0.0411736i
$205$	1.23930	+	0.900404i	0.0865565	+	0.0628870i
$206$	9.98216	−	7.25246i	0.695490	−	0.505303i
$207$	−2.07622	+	6.38995i	−0.144307	+	0.444132i
$208$	−5.30073			−0.367539
$209$	−0.811621	−	3.05301i	−0.0561410	−	0.211181i
$210$	−0.418877			−0.0289053
$211$	4.10285	−	12.6273i	0.282452	−	0.869297i	−0.704699	−	0.709506i	$-0.748918\pi$
$211$	4.10285	−	12.6273i	0.282452	−	0.869297i	0.987151	−	0.159791i	$-0.0510819\pi$
$212$	9.18132	−	6.67062i	0.630575	−	0.458140i
$213$	−4.04445	−	2.93846i	−0.277121	−	0.201340i
$214$	2.98424	+	9.18454i	0.203998	+	0.627842i
$215$	1.18385	+	3.64350i	0.0807376	+	0.248485i
$216$	−1.97381	−	1.43406i	−0.134301	−	0.0975754i
$217$	−1.89577	+	1.37736i	−0.128693	+	0.0935011i
$218$	−1.82884	+	5.62860i	−0.123865	+	0.381217i
$219$	−3.05152			−0.206203
$220$	2.57339	+	2.09228i	0.173498	+	0.141062i
$221$	−7.82485			−0.526356
$222$	−0.00289980	+	0.00892466i	−0.000194622	+	0.000598984i
$223$	8.58781	−	6.23941i	0.575082	−	0.417822i	−0.261866	−	0.965104i	$-0.584338\pi$
$223$	8.58781	−	6.23941i	0.575082	−	0.417822i	0.836948	+	0.547283i	$0.184338\pi$
$224$	−0.809017	−	0.587785i	−0.0540547	−	0.0392731i
$225$	−0.872831	−	2.68630i	−0.0581888	−	0.179087i
$226$	3.89228	+	11.9792i	0.258911	+	0.796846i
$227$	19.7340	+	14.3376i	1.30979	+	0.951621i	1.00000		0.000817631i	$0.000260260\pi$
$227$	19.7340	+	14.3376i	1.30979	+	0.951621i	0.309795	+	0.950804i	$0.399740\pi$
$228$	0.322779	−	0.234513i	0.0213765	−	0.0155310i
$229$	3.48585	−	10.7283i	0.230351	−	0.708949i	−0.767353	−	0.641225i	$-0.778426\pi$
$229$	3.48585	−	10.7283i	0.230351	−	0.708949i	0.997704	−	0.0677235i	$-0.0215736\pi$
$230$	2.37872			0.156848
$231$	0.500415	−	1.29600i	0.0329249	−	0.0852707i
$232$	5.97768			0.392454
$233$	2.83864	−	8.73644i	0.185966	−	0.572343i	−0.813998	−	0.580868i	$-0.802713\pi$
$233$	2.83864	−	8.73644i	0.185966	−	0.572343i	0.999964	+	0.00852421i	$0.00271337\pi$
$234$	−12.1127	+	8.80039i	−0.791832	+	0.575300i
$235$	1.21711	+	0.884279i	0.0793953	+	0.0576840i
$236$	0.237593	+	0.731235i	0.0154660	+	0.0475994i
$237$	1.65822	+	5.10347i	0.107713	+	0.331506i
$238$	−1.19426	−	0.867679i	−0.0774123	−	0.0562433i
$239$	2.46982	−	1.79443i	0.159759	−	0.116072i	−0.505033	−	0.863100i	$-0.668520\pi$
$239$	2.46982	−	1.79443i	0.159759	−	0.116072i	0.664793	+	0.747028i	$0.268520\pi$
$240$	−0.129440	+	0.398376i	−0.00835533	+	0.0257151i
$241$	−5.27801			−0.339987			−0.169993	−	0.985445i	$-0.554375\pi$
$241$	−5.27801			−0.339987			−0.169993	+	0.985445i	$0.554375\pi$
$242$	−9.54784	+	5.46249i	−0.613758	+	0.351142i
$243$	−10.4406			−0.669767
$244$	2.49071	−	7.66562i	0.159452	−	0.490741i
$245$	−0.809017	+	0.587785i	−0.0516862	+	0.0375522i
$246$	−0.519115	−	0.377159i	−0.0330975	−	0.0240468i
$247$	−1.56019	−	4.80178i	−0.0992727	−	0.305530i
$248$	0.724120	+	2.22861i	0.0459817	+	0.141517i
$249$	2.07911	+	1.51056i	0.131758	+	0.0957280i
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−0.654501	+	2.01435i	−0.0413117	+	0.127144i	−0.969585	−	0.244754i	$-0.921293\pi$
$251$	−0.654501	+	2.01435i	−0.0413117	+	0.127144i	0.928274	+	0.371898i	$0.121293\pi$
$252$	−2.82454			−0.177929
$253$	−2.84176	+	7.35974i	−0.178660	+	0.462703i
$254$	−2.54206			−0.159503
$255$	−0.191078	+	0.588076i	−0.0119657	+	0.0368268i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	21.7021	+	15.7675i	1.35374	+	0.983549i	0.998816	+	0.0486543i	$0.0154933\pi$
$257$	21.7021	+	15.7675i	1.35374	+	0.983549i	0.354924	+	0.934895i	$0.384507\pi$
$258$	−0.495886	−	1.52618i	−0.0308725	−	0.0950159i
$259$	0.00692279	+	0.0213061i	0.000430161	+	0.00132390i
$260$	4.28838	+	3.11569i	0.265954	+	0.193227i
$261$	13.6596	−	9.92429i	0.845509	−	0.614298i
$262$	2.41186	−	7.42295i	0.149005	−	0.458591i
$263$	−8.68185			−0.535346			−0.267673	−	0.963510i	$-0.586255\pi$
$263$	−8.68185			−0.535346			−0.267673	+	0.963510i	$0.586255\pi$
$264$	−1.07794	−	0.876410i	−0.0663423	−	0.0539393i
$265$	−11.3487			−0.697147
$266$	0.294336	−	0.905872i	0.0180469	−	0.0555426i
$267$	4.56117	−	3.31388i	0.279139	−	0.202806i
$268$	−9.85712	−	7.16162i	−0.602119	−	0.437465i
$269$	−3.54222	−	10.9018i	−0.215973	−	0.664696i	−0.999083	−	0.0428134i	$-0.986368\pi$
$269$	−3.54222	−	10.9018i	−0.215973	−	0.664696i	0.783110	−	0.621883i	$-0.213632\pi$
$270$	0.753930	+	2.32036i	0.0458827	+	0.141212i
$271$	−13.9078	−	10.1046i	−0.844836	−	0.613809i	0.0788816	−	0.996884i	$-0.474865\pi$
$271$	−13.9078	−	10.1046i	−0.844836	−	0.613809i	−0.923717	+	0.383075i	$0.874865\pi$
$272$	−1.19426	+	0.867679i	−0.0724125	+	0.0526108i
$273$	0.686127	−	2.11168i	0.0415263	−	0.127805i
$274$	19.7473			1.19298
$275$	−0.852104	−	3.20530i	−0.0513838	−	0.193287i
$276$	−0.996391			−0.0599757
$277$	4.69876	−	14.4613i	0.282321	−	0.868894i	−0.704868	−	0.709339i	$-0.748994\pi$
$277$	4.69876	−	14.4613i	0.282321	−	0.868894i	0.987189	−	0.159556i	$-0.0510062\pi$
$278$	−10.7595	+	7.81723i	−0.645312	+	0.468846i
$279$	5.35468	+	3.89040i	0.320576	+	0.232912i
$280$	0.309017	+	0.951057i	0.0184673	+	0.0568365i
$281$	−0.740017	−	2.27754i	−0.0441457	−	0.135867i	0.926554	−	0.376161i	$-0.122756\pi$
$281$	−0.740017	−	2.27754i	−0.0441457	−	0.135867i	−0.970700	+	0.240294i	$0.922756\pi$
$282$	−0.509818	−	0.370405i	−0.0303592	−	0.0220573i
$283$	9.72599	−	7.06634i	0.578150	−	0.420050i	−0.259907	−	0.965634i	$-0.583692\pi$
$283$	9.72599	−	7.06634i	0.578150	−	0.420050i	0.838057	+	0.545583i	$0.183692\pi$
$284$	−3.68805	+	11.3507i	−0.218846	+	0.673538i
$285$	−0.398977			−0.0236333
$286$	−14.7631	+	9.54602i	−0.872958	+	0.564468i
$287$	−1.53186			−0.0904228
$288$	−0.872831	+	2.68630i	−0.0514321	+	0.158292i
$289$	11.9903	−	8.71149i	0.705314	−	0.512441i
$290$	−4.83605	−	3.51359i	−0.283982	−	0.206325i
$291$	−2.39286	−	7.36446i	−0.140272	−	0.431712i
$292$	2.25119	+	6.92844i	0.131741	+	0.405456i
$293$	−9.09532	−	6.60814i	−0.531354	−	0.386052i	0.289510	−	0.957175i	$-0.406508\pi$
$293$	−9.09532	−	6.60814i	−0.531354	−	0.386052i	−0.820864	+	0.571124i	$0.806508\pi$
$294$	0.338879	−	0.246210i	0.0197638	−	0.0143593i
$295$	0.237593	−	0.731235i	0.0138332	−	0.0425742i
$296$	0.0224026			0.00130213
$297$	−8.07986	−	0.439381i	−0.468841	−	0.0254955i
$298$	3.95398			0.229048
$299$	−3.89638	+	11.9918i	−0.225333	+	0.693504i
$300$	0.338879	−	0.246210i	0.0195652	−	0.0142149i
$301$	−3.09935	−	2.25181i	−0.178644	−	0.129792i
$302$	−2.90959	−	8.95480i	−0.167428	−	0.515291i
$303$	−1.15478	−	3.55404i	−0.0663402	−	0.204174i
$304$	−0.770581	−	0.559860i	−0.0441958	−	0.0321102i
$305$	−6.52077	+	4.73762i	−0.373378	+	0.271275i
$306$	−1.28846	+	3.96547i	−0.0736564	+	0.226691i
$307$	25.1111			1.43317			0.716584	−	0.697501i	$-0.245705\pi$
$307$	25.1111			1.43317			0.716584	+	0.697501i	$0.245705\pi$
$308$	−3.31173	−	0.180091i	−0.188703	−	0.0102617i
$309$	5.16837			0.294018
$310$	0.724120	−	2.22861i	0.0411272	−	0.126577i
$311$	2.12573	−	1.54443i	0.120539	−	0.0875766i	−0.525883	−	0.850557i	$-0.676265\pi$
$311$	2.12573	−	1.54443i	0.120539	−	0.0875766i	0.646421	+	0.762981i	$0.276265\pi$
$312$	−1.79630	−	1.30509i	−0.101696	−	0.0738862i
$313$	1.20552	+	3.71021i	0.0681400	+	0.209713i	0.979328	−	0.202276i	$-0.0648339\pi$
$313$	1.20552	+	3.71021i	0.0681400	+	0.209713i	−0.911188	+	0.411990i	$0.864834\pi$
$314$	−2.66488	−	8.20165i	−0.150388	−	0.462846i
$315$	2.28510	+	1.66022i	0.128751	+	0.0935430i
$316$	10.3641	−	7.52993i	0.583024	−	0.423592i
$317$	−8.52346	+	26.2325i	−0.478725	+	1.47336i	0.362142	+	0.932123i	$0.382046\pi$
$317$	−8.52346	+	26.2325i	−0.478725	+	1.47336i	−0.840867	+	0.541242i	$0.817954\pi$
$318$	4.75372			0.266576
$319$	16.6485	−	10.7651i	0.932135	−	0.602733i
$320$	1.00000			0.0559017
$321$	−1.25003	+	3.84719i	−0.0697698	+	0.214729i
$322$	−1.92442	+	1.39818i	−0.107244	+	0.0779173i
$323$	−1.13752	−	0.826456i	−0.0632933	−	0.0459853i
$324$	2.30269	+	7.08695i	0.127927	+	0.393720i
$325$	−1.63801	−	5.04129i	−0.0908607	−	0.279640i
$326$	8.89150	+	6.46005i	0.492455	+	0.357789i
$327$	−2.00557	+	1.45714i	−0.110909	+	0.0805798i
$328$	−0.473371	+	1.45689i	−0.0261375	+	0.0804430i
$329$	−1.50443			−0.0829417
$330$	0.356927	+	1.34263i	0.0196482	+	0.0739091i
$331$	33.4595			1.83910			0.919551	−	0.392972i	$-0.128553\pi$
$331$	33.4595			1.83910			0.919551	+	0.392972i	$0.128553\pi$
$332$	1.89590	−	5.83498i	0.104051	−	0.320236i
$333$	0.0511922	−	0.0371933i	0.00280532	−	0.00203818i
$334$	−3.44852	−	2.50550i	−0.188695	−	0.137095i
$335$	3.76508	+	11.5877i	0.205709	+	0.633106i
$336$	−0.129440	−	0.398376i	−0.00706154	−	0.0217332i
$337$	−12.8856	−	9.36196i	−0.701925	−	0.509978i	0.178634	−	0.983916i	$-0.442832\pi$
$337$	−12.8856	−	9.36196i	−0.701925	−	0.509978i	−0.880559	+	0.473937i	$0.842832\pi$
$338$	−12.2143	+	8.87420i	−0.664370	+	0.482693i
$339$	−1.63039	+	5.01782i	−0.0885506	+	0.272531i
$340$	1.47618			0.0800573
$341$	6.03023	+	4.90285i	0.326555	+	0.265504i
$342$	−2.69035			−0.145477
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−3.09935	+	2.25181i	−0.167106	+	0.121409i
$345$	0.806097	+	0.585664i	0.0433988	+	0.0315311i
$346$	6.75984	+	20.8047i	0.363412	+	1.11847i
$347$	5.89602	+	18.1461i	0.316515	+	0.974133i	0.975126	+	0.221650i	$0.0711441\pi$
$347$	5.89602	+	18.1461i	0.316515	+	0.974133i	−0.658611	+	0.752483i	$0.728856\pi$
$348$	2.02571	+	1.47176i	0.108589	+	0.0788949i
$349$	14.0324	−	10.1952i	0.751140	−	0.545735i	−0.145040	−	0.989426i	$-0.546331\pi$
$349$	14.0324	−	10.1952i	0.751140	−	0.545735i	0.896180	+	0.443691i	$0.146331\pi$
$350$	0.309017	−	0.951057i	0.0165177	−	0.0508361i
$351$	−12.9325			−0.690288
$352$	−1.19466	+	3.09399i	−0.0636755	+	0.164910i
$353$	−23.2547			−1.23772			−0.618861	−	0.785501i	$-0.712405\pi$
$353$	−23.2547			−1.23772			−0.618861	+	0.785501i	$0.712405\pi$
$354$	−0.0995222	+	0.306298i	−0.00528955	+	0.0162795i
$355$	9.65545	−	7.01509i	0.512458	−	0.372322i
$356$	−10.8890	−	7.91135i	−0.577118	−	0.419301i
$357$	−0.191078	−	0.588076i	−0.0101129	−	0.0311243i
$358$	3.71278	+	11.4268i	0.196226	+	0.603923i
$359$	0.161926	+	0.117646i	0.00854612	+	0.00620912i	0.592050	−	0.805901i	$-0.298319\pi$
$359$	0.161926	+	0.117646i	0.00854612	+	0.00620912i	−0.583504	+	0.812110i	$0.698319\pi$
$360$	2.28510	−	1.66022i	0.120435	−	0.0875015i
$361$	−5.59097	+	17.2072i	−0.294262	+	0.905644i
$362$	−21.0621			−1.10700
$363$	−4.58048	−	0.499649i	−0.240413	−	0.0262248i
$364$	−5.30073			−0.277834
$365$	2.25119	−	6.92844i	0.117833	−	0.362651i
$366$	2.73140	−	1.98448i	0.142773	−	0.103730i
$367$	−10.5470	−	7.66285i	−0.550549	−	0.399998i	0.277439	−	0.960743i	$-0.410514\pi$
$367$	−10.5470	−	7.66285i	−0.550549	−	0.399998i	−0.827988	+	0.560746i	$0.810514\pi$
$368$	0.735065	+	2.26230i	0.0383179	+	0.117930i
$369$	1.33706	+	4.11503i	0.0696043	+	0.214220i
$370$	−0.0181241	−	0.0131679i	−0.000942227	−	0.000684568i
$371$	9.18132	−	6.67062i	0.476670	−	0.346321i
$372$	−0.303317	+	0.933515i	−0.0157263	+	0.0484005i
$373$	16.1910			0.838336			0.419168	−	0.907909i	$-0.362322\pi$
$373$	16.1910			0.838336			0.419168	+	0.907909i	$0.362322\pi$
$374$	−1.76354	+	4.56730i	−0.0911903	+	0.236170i
$375$	−0.418877			−0.0216307
$376$	−0.464893	+	1.43079i	−0.0239750	+	0.0737876i
$377$	25.6346	−	18.6246i	1.32025	−	0.959216i
$378$	−1.97381	−	1.43406i	−0.101522	−	0.0737601i
$379$	11.7604	+	36.1949i	0.604093	+	1.85921i	0.502908	+	0.864340i	$0.332263\pi$
$379$	11.7604	+	36.1949i	0.604093	+	1.85921i	0.101185	+	0.994868i	$0.467737\pi$
$380$	0.294336	+	0.905872i	0.0150991	+	0.0464703i
$381$	−0.861451	−	0.625881i	−0.0441335	−	0.0320649i
$382$	6.15609	−	4.47266i	0.314973	−	0.228841i
$383$	−1.01047	+	3.10990i	−0.0516325	+	0.158908i	−0.973548	−	0.228483i	$-0.926624\pi$
$383$	−1.01047	+	3.10990i	−0.0516325	+	0.158908i	0.921916	+	0.387391i	$0.126624\pi$
$384$	−0.418877			−0.0213757
$385$	2.57339	+	2.09228i	0.131152	+	0.106633i
$386$	20.6268			1.04988
$387$	−3.34382	+	10.2912i	−0.169976	+	0.523133i
$388$	−14.9557	+	10.8659i	−0.759259	+	0.551634i
$389$	24.2783	+	17.6392i	1.23096	+	0.894344i	0.996962	−	0.0778928i	$-0.0248192\pi$
$389$	24.2783	+	17.6392i	1.23096	+	0.894344i	0.233998	+	0.972237i	$0.424819\pi$
$390$	0.686127	+	2.11168i	0.0347434	+	0.106929i
$391$	1.08509	+	3.33957i	0.0548754	+	0.168889i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	2.64493	−	1.92165i	0.133419	−	0.0969347i
$394$	−3.13269	+	9.64141i	−0.157822	+	0.485727i
$395$	−12.8107			−0.644575
$396$	2.40680	+	9.05349i	0.120946	+	0.454955i
$397$	15.5047			0.778158			0.389079	−	0.921204i	$-0.372793\pi$
$397$	15.5047			0.778158			0.389079	+	0.921204i	$0.372793\pi$
$398$	7.00344	−	21.5544i	0.351050	−	1.08042i
$399$	0.322779	−	0.234513i	0.0161592	−	0.0117403i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−1.76285	−	5.42551i	−0.0880328	−	0.270937i	0.897343	−	0.441335i	$-0.145495\pi$
$401$	−1.76285	−	5.42551i	−0.0880328	−	0.270937i	−0.985375	+	0.170398i	$0.945495\pi$
$402$	−1.57711	−	4.85384i	−0.0786590	−	0.242088i
$403$	10.0490	+	7.30100i	0.500574	+	0.363689i
$404$	−7.21750	+	5.24382i	−0.359084	+	0.260890i
$405$	2.30269	−	7.08695i	0.114422	−	0.352153i
$406$	5.97768			0.296667
$407$	0.0623936	−	0.0403446i	0.00309273	−	0.00199981i
$408$	−0.618340			−0.0306124
$409$	0.398004	−	1.22493i	0.0196800	−	0.0605690i	−0.940734	−	0.339145i	$-0.889862\pi$
$409$	0.398004	−	1.22493i	0.0196800	−	0.0605690i	0.960414	+	0.278576i	$0.0898623\pi$
$410$	1.23930	−	0.900404i	0.0612047	−	0.0444678i
$411$	6.69195	+	4.86199i	0.330090	+	0.239824i
$412$	−3.81285	−	11.7347i	−0.187845	−	0.578129i
$413$	0.237593	+	0.731235i	0.0116912	+	0.0359817i
$414$	5.43562	+	3.94921i	0.267146	+	0.194093i
$415$	−4.96353	+	3.60622i	−0.243650	+	0.177022i
$416$	−1.63801	+	5.04129i	−0.0803103	+	0.247170i
$417$	−5.57084			−0.272805
$418$	−3.15439	−	0.171535i	−0.154286	−	0.00839007i
$419$	36.2889			1.77283			0.886414	−	0.462893i	$-0.153189\pi$
$419$	36.2889			1.77283			0.886414	+	0.462893i	$0.153189\pi$
$420$	−0.129440	+	0.398376i	−0.00631603	+	0.0194388i
$421$	10.8442	−	7.87877i	0.528514	−	0.383988i	−0.291288	−	0.956635i	$-0.594084\pi$
$421$	10.8442	−	7.87877i	0.528514	−	0.383988i	0.819802	+	0.572648i	$0.194084\pi$
$422$	−10.7414	−	7.80408i	−0.522883	−	0.379897i
$423$	1.31311	+	4.04134i	0.0638456	+	0.196497i
$424$	−3.50695	−	10.7933i	−0.170313	−	0.524168i
$425$	−1.19426	−	0.867679i	−0.0579300	−	0.0420886i
$426$	−4.04445	+	2.93846i	−0.195954	+	0.142369i
$427$	2.49071	−	7.66562i	0.120534	−	0.370966i
$428$	9.65719			0.466798
$429$	−7.35321	−	0.399867i	−0.355017	−	0.0193057i
$430$	3.83101			0.184748
$431$	0.737575	−	2.27002i	0.0355277	−	0.109343i	−0.931720	−	0.363178i	$-0.881692\pi$
$431$	0.737575	−	2.27002i	0.0355277	−	0.109343i	0.967248	+	0.253834i	$0.0816918\pi$
$432$	−1.97381	+	1.43406i	−0.0949652	+	0.0689962i
$433$	18.3387	+	13.3238i	0.881300	+	0.640302i	0.933595	−	0.358330i	$-0.116654\pi$
$433$	18.3387	+	13.3238i	0.881300	+	0.640302i	−0.0522952	+	0.998632i	$0.516654\pi$
$434$	0.724120	+	2.22861i	0.0347589	+	0.106977i
$435$	−0.773752	−	2.38136i	−0.0370986	−	0.114178i
$436$	4.78798	+	3.47867i	0.229303	+	0.166598i
$437$	−1.83300	+	1.33175i	−0.0876841	+	0.0637062i
$438$	−0.942971	+	2.90217i	−0.0450569	+	0.138671i
$439$	17.7876			0.848958			0.424479	−	0.905438i	$-0.360457\pi$
$439$	17.7876			0.848958			0.424479	+	0.905438i	$0.360457\pi$
$440$	2.78510	−	1.80089i	0.132775	−	0.0858541i
$441$	−2.82454			−0.134502
$442$	−2.41801	+	7.44187i	−0.115013	+	0.353974i
$443$	19.4904	−	14.1606i	0.926015	−	0.672789i	−0.0189990	−	0.999820i	$-0.506048\pi$
$443$	19.4904	−	14.1606i	0.926015	−	0.672789i	0.945014	+	0.327030i	$0.106048\pi$
$444$	0.00759177	+	0.00551574i	0.000360289	+	0.000261766i
$445$	4.15924	+	12.8008i	0.197167	+	0.606817i
$446$	−3.28025	−	10.0956i	−0.155324	−	0.478039i
$447$	1.33992	+	0.973509i	0.0633760	+	0.0460454i
$448$	−0.809017	+	0.587785i	−0.0382225	+	0.0277702i
$449$	−1.87559	+	5.77248i	−0.0885147	+	0.272420i	−0.985509	−	0.169621i	$-0.945746\pi$
$449$	−1.87559	+	5.77248i	−0.0885147	+	0.272420i	0.896995	+	0.442041i	$0.145746\pi$
$450$	−2.82454			−0.133150
$451$	1.30530	+	4.91006i	0.0614644	+	0.231206i
$452$	12.5957			0.592452
$453$	1.21876	−	3.75096i	0.0572624	−	0.176235i
$454$	19.7340	−	14.3376i	0.926164	−	0.672898i
$455$	4.28838	+	3.11569i	0.201042	+	0.146066i
$456$	−0.123291	−	0.379449i	−0.00577361	−	0.0177693i
$457$	1.52056	+	4.67982i	0.0711290	+	0.218913i	0.980301	−	0.197507i	$-0.0632846\pi$
$457$	1.52056	+	4.67982i	0.0711290	+	0.218913i	−0.909172	+	0.416420i	$0.863285\pi$
$458$	−9.12607	−	6.63048i	−0.426433	−	0.309822i
$459$	−2.91371	+	2.11694i	−0.136000	+	0.0988101i
$460$	0.735065	−	2.26230i	0.0342726	−	0.105480i
$461$	−33.6918			−1.56918			−0.784591	−	0.620013i	$-0.787127\pi$
$461$	−33.6918			−1.56918			−0.784591	+	0.620013i	$0.787127\pi$
$462$	−1.07794	−	0.876410i	−0.0501501	−	0.0407743i
$463$	2.26163			0.105107			0.0525533	−	0.998618i	$-0.483264\pi$
$463$	2.26163			0.105107			0.0525533	+	0.998618i	$0.483264\pi$
$464$	1.84721	−	5.68511i	0.0857544	−	0.263925i
$465$	0.794095	−	0.576944i	0.0368253	−	0.0267551i
$466$	−7.43166	−	5.39942i	−0.344265	−	0.250123i
$467$	4.13848	+	12.7369i	0.191506	+	0.589395i	1.00000		0.000890122i	$0.000283335\pi$
$467$	4.13848	+	12.7369i	0.191506	+	0.589395i	−0.808493	+	0.588505i	$0.799717\pi$
$468$	4.62664	+	14.2393i	0.213867	+	0.658213i
$469$	−9.85712	−	7.16162i	−0.455159	−	0.330693i
$470$	1.21711	−	0.884279i	0.0561409	−	0.0407888i
$471$	1.11626	−	3.43548i	0.0514344	−	0.158299i
$472$	0.768866			0.0353899
$473$	−4.57675	+	11.8531i	−0.210439	+	0.545006i
$474$	5.36610			0.246473
$475$	0.294336	−	0.905872i	0.0135050	−	0.0415643i
$476$	−1.19426	+	0.867679i	−0.0547387	+	0.0397700i
$477$	−25.9330	−	18.8414i	−1.18739	−	0.862690i
$478$	−0.943388	−	2.90345i	−0.0431496	−	0.132801i
$479$	5.14937	+	15.8481i	0.235281	+	0.724120i	0.997084	+	0.0763114i	$0.0243143\pi$
$479$	5.14937	+	15.8481i	0.235281	+	0.724120i	−0.761803	+	0.647809i	$0.775686\pi$
$480$	0.338879	+	0.246210i	0.0154676	+	0.0112379i
$481$	0.0960708	−	0.0697995i	0.00438045	−	0.00318259i
$482$	−1.63099	+	5.01969i	−0.0742898	+	0.228640i
$483$	−0.996391			−0.0453374
$484$	2.24469	+	10.7685i	0.102032	+	0.489479i
$485$	18.4862			0.839416
$486$	−3.22633	+	9.92963i	−0.146349	+	0.450417i
$487$	10.2712	−	7.46249i	0.465434	−	0.338158i	−0.330225	−	0.943902i	$-0.607125\pi$
$487$	10.2712	−	7.46249i	0.465434	−	0.338158i	0.795659	+	0.605745i	$0.207125\pi$
$488$	−6.52077	−	4.73762i	−0.295181	−	0.214462i
$489$	1.42261	+	4.37835i	0.0643328	+	0.197996i
$490$	0.309017	+	0.951057i	0.0139600	+	0.0429644i
$491$	−12.4906	−	9.07493i	−0.563691	−	0.409546i	0.269117	−	0.963108i	$-0.413268\pi$
$491$	−12.4906	−	9.07493i	−0.563691	−	0.409546i	−0.832808	+	0.553562i	$0.813268\pi$
$492$	−0.519115	+	0.377159i	−0.0234035	+	0.0170036i
$493$	2.72682	−	8.39228i	0.122810	−	0.377969i
$494$	−5.04889			−0.227160
$495$	3.37436	−	8.73911i	0.151666	−	0.392794i
$496$	2.34330			0.105217
$497$	−3.68805	+	11.3507i	−0.165432	+	0.509147i
$498$	2.07911	−	1.51056i	0.0931672	−	0.0676899i
$499$	4.82943	+	3.50878i	0.216195	+	0.157075i	0.690612	−	0.723225i	$-0.257341\pi$
$499$	4.82943	+	3.50878i	0.216195	+	0.157075i	−0.474417	+	0.880300i	$0.657341\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−0.551753	−	1.69812i	−0.0246505	−	0.0758664i
$502$	1.71351	+	1.24493i	0.0764775	+	0.0555642i
$503$	0.812961	−	0.590651i	0.0362481	−	0.0263358i	−0.569514	−	0.821982i	$-0.692868\pi$
$503$	0.812961	−	0.590651i	0.0362481	−	0.0263358i	0.605762	+	0.795646i	$0.292868\pi$
$504$	−0.872831	+	2.68630i	−0.0388790	+	0.119657i
$505$	8.92131			0.396993
$506$	6.12138	+	4.97696i	0.272128	+	0.221253i
$507$	−6.32408			−0.280862
$508$	−0.785541	+	2.41765i	−0.0348527	+	0.107266i
$509$	−15.5698	+	11.3121i	−0.690119	+	0.501401i	−0.876699	−	0.481039i	$-0.840260\pi$
$509$	−15.5698	+	11.3121i	−0.690119	+	0.501401i	0.186580	+	0.982440i	$0.440260\pi$
$510$	0.500248	+	0.363451i	0.0221513	+	0.0160939i
$511$	2.25119	+	6.92844i	0.0995867	+	0.306496i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.88004	−	1.36593i	−0.0830057	−	0.0603072i
$514$	21.7021	−	15.7675i	0.957238	−	0.695474i
$515$	−3.81285	+	11.7347i	−0.168014	+	0.517094i
$516$	−1.60472			−0.0706439
$517$	1.28193	+	4.82213i	0.0563791	+	0.212077i
$518$	0.0224026			0.000984314
$519$	−2.83155	+	8.71460i	−0.124291	+	0.382528i
$520$	4.28838	−	3.11569i	0.188058	−	0.136632i
$521$	−3.25548	−	2.36525i	−0.142625	−	0.103623i	0.514185	−	0.857680i	$-0.328095\pi$
$521$	−3.25548	−	2.36525i	−0.142625	−	0.103623i	−0.656810	+	0.754056i	$0.728095\pi$
$522$	−5.21751	−	16.0578i	−0.228364	−	0.702833i
$523$	−0.331253	−	1.01949i	−0.0144847	−	0.0445792i	0.943553	−	0.331222i	$-0.107461\pi$
$523$	−0.331253	−	1.01949i	−0.0144847	−	0.0445792i	−0.958038	+	0.286643i	$0.907461\pi$
$524$	−6.31433	−	4.58763i	−0.275843	−	0.200412i
$525$	0.338879	−	0.246210i	0.0147899	−	0.0107455i
$526$	−2.68284	+	8.25693i	−0.116977	+	0.360019i
$527$	3.45914			0.150683
$528$	−1.16662	+	0.754352i	−0.0507704	+	0.0328289i
$529$	−17.3417			−0.753987
$530$	−3.50695	+	10.7933i	−0.152332	+	0.468830i
$531$	1.75694	−	1.27649i	0.0762446	−	0.0553950i
$532$	−0.770581	−	0.559860i	−0.0334089	−	0.0242730i
$533$	2.50921	+	7.72255i	0.108686	+	0.334501i
$534$	−1.74221	−	5.36198i	−0.0753929	−	0.232035i
$535$	−7.81283	−	5.67636i	−0.337778	−	0.245410i
$536$	−9.85712	+	7.16162i	−0.425763	+	0.309335i
$537$	−1.55520	+	4.78641i	−0.0671117	+	0.206549i
$538$	−11.4629			−0.494199
$539$	−3.31173	−	0.180091i	−0.142646	−	0.00775709i
$540$	2.43977			0.104991
$541$	−9.84871	+	30.3112i	−0.423429	+	1.30318i	0.481061	+	0.876687i	$0.340251\pi$
$541$	−9.84871	+	30.3112i	−0.423429	+	1.30318i	−0.904490	+	0.426494i	$0.859749\pi$
$542$	−13.9078	+	10.1046i	−0.597389	+	0.434029i
$543$	−7.13751	−	5.18570i	−0.306300	−	0.222540i
$544$	0.456166	+	1.40393i	0.0195580	+	0.0601932i
$545$	−1.82884	−	5.62860i	−0.0783391	−	0.241103i
$546$	−1.79630	−	1.30509i	−0.0768747	−	0.0558527i
$547$	6.15532	−	4.47210i	0.263183	−	0.191213i	−0.448366	−	0.893850i	$-0.647994\pi$
$547$	6.15532	−	4.47210i	0.263183	−	0.191213i	0.711549	+	0.702637i	$0.247994\pi$
$548$	6.10226	−	18.7808i	0.260676	−	0.802277i
$549$	−22.7661			−0.971635
$550$	−3.31173	−	0.180091i	−0.141213	−	0.00767913i
$551$	5.69369			0.242559
$552$	−0.307902	+	0.947624i	−0.0131052	+	0.0403336i
$553$	10.3641	−	7.52993i	0.440725	−	0.320205i
$554$	−12.3015	−	8.93757i	−0.522641	−	0.379721i
$555$	−0.00289980	−	0.00892466i	−0.000123090	−	0.000378831i
$556$	4.10976	+	12.6485i	0.174293	+	0.536418i
$557$	−20.3489	−	14.7843i	−0.862210	−	0.626432i	0.0662757	−	0.997801i	$-0.478888\pi$
$557$	−20.3489	−	14.7843i	−0.862210	−	0.626432i	−0.928485	+	0.371369i	$0.878888\pi$
$558$	5.35468	−	3.89040i	0.226682	−	0.164694i
$559$	−6.27524	+	19.3132i	−0.265415	+	0.816862i
$560$	1.00000			0.0422577
$561$	−1.72214	+	1.11356i	−0.0727088	+	0.0470146i
$562$	−2.39475			−0.101016
$563$	11.2380	−	34.5870i	0.473626	−	1.45767i	−0.374177	−	0.927357i	$-0.622075\pi$
$563$	11.2380	−	34.5870i	0.473626	−	1.45767i	0.847802	−	0.530312i	$-0.177925\pi$
$564$	−0.509818	+	0.370405i	−0.0214672	+	0.0155968i
$565$	−10.1901	−	7.40356i	−0.428702	−	0.311470i
$566$	−3.71500	−	11.4336i	−0.156153	−	0.480589i
$567$	2.30269	+	7.08695i	0.0967039	+	0.297624i
$568$	9.65545	+	7.01509i	0.405134	+	0.294347i
$569$	−19.2037	+	13.9523i	−0.805060	+	0.584910i	−0.912394	−	0.409313i	$-0.865769\pi$
$569$	−19.2037	+	13.9523i	−0.805060	+	0.584910i	0.107334	+	0.994223i	$0.465769\pi$
$570$	−0.123291	+	0.379449i	−0.00516407	+	0.0158934i
$571$	−42.7475			−1.78893			−0.894464	−	0.447139i	$-0.852443\pi$
$571$	−42.7475			−1.78893			−0.894464	+	0.447139i	$0.852443\pi$
$572$	4.51677	+	16.9904i	0.188856	+	0.710404i
$573$	3.18738			0.133155
$574$	−0.473371	+	1.45689i	−0.0197581	+	0.0608092i
$575$	−1.92442	+	1.39818i	−0.0802540	+	0.0583080i
$576$	2.28510	+	1.66022i	0.0952126	+	0.0691760i
$577$	7.93426	+	24.4192i	0.330308	+	1.01658i	0.968987	+	0.247110i	$0.0794809\pi$
$577$	7.93426	+	24.4192i	0.330308	+	1.01658i	−0.638680	+	0.769473i	$0.720519\pi$
$578$	−4.57990	−	14.0955i	−0.190499	−	0.586295i
$579$	6.98999	+	5.07852i	0.290494	+	0.211056i
$580$	−4.83605	+	3.51359i	−0.200806	+	0.145894i
$581$	1.89590	−	5.83498i	0.0786552	−	0.242076i
$582$	−7.74345			−0.320976
$583$	−29.2047	−	23.7448i	−1.20954	−	0.983408i
$584$	7.28500			0.301455
$585$	4.62664	−	14.2393i	0.191288	−	0.588724i
$586$	−9.09532	+	6.60814i	−0.375724	+	0.272980i
$587$	30.6145	+	22.2427i	1.26359	+	0.918055i	0.998928	−	0.0462846i	$-0.0147381\pi$
$587$	30.6145	+	22.2427i	1.26359	+	0.918055i	0.264667	+	0.964340i	$0.414738\pi$
$588$	−0.129440	−	0.398376i	−0.00533802	−	0.0164287i
$589$	0.689717	+	2.12273i	0.0284193	+	0.0874656i
$590$	−0.622026	−	0.451928i	−0.0256084	−	0.0186056i
$591$	−3.43541	+	2.49597i	−0.141314	+	0.102671i
$592$	0.00692279	−	0.0213061i	0.000284525	−	0.000875677i
$593$	8.15354			0.334826			0.167413	−	0.985887i	$-0.446459\pi$
$593$	8.15354			0.334826			0.167413	+	0.985887i	$0.446459\pi$
$594$	−2.91469	+	7.54862i	−0.119591	+	0.309724i
$595$	1.47618			0.0605177
$596$	1.22185	−	3.76046i	0.0500488	−	0.154034i
$597$	7.68021	−	5.58000i	0.314330	−	0.228374i
$598$	10.2008	+	7.41135i	0.417144	+	0.303073i
$599$	−3.10370	−	9.55221i	−0.126814	−	0.390293i	0.867413	−	0.497588i	$-0.165781\pi$
$599$	−3.10370	−	9.55221i	−0.126814	−	0.390293i	−0.994227	+	0.107295i	$0.965781\pi$
$600$	−0.129440	−	0.398376i	−0.00528437	−	0.0162636i
$601$	−15.7141	−	11.4169i	−0.640990	−	0.465707i	0.219200	−	0.975680i	$-0.429655\pi$
$601$	−15.7141	−	11.4169i	−0.640990	−	0.465707i	−0.860190	+	0.509973i	$0.829655\pi$
$602$	−3.09935	+	2.25181i	−0.126320	+	0.0917769i
$603$	−10.6346	+	32.7301i	−0.433076	+	1.33287i
$604$	−9.41563			−0.383117
$605$	4.51359	−	10.0313i	0.183504	−	0.407831i
$606$	−3.73694			−0.151803
$607$	4.59976	−	14.1566i	0.186698	−	0.574598i	−0.813275	−	0.581879i	$-0.802318\pi$
$607$	4.59976	−	14.1566i	0.186698	−	0.574598i	0.999973	+	0.00728090i	$0.00231760\pi$
$608$	−0.770581	+	0.559860i	−0.0312512	+	0.0227053i
$609$	2.02571	+	1.47176i	0.0820859	+	0.0596389i
$610$	2.49071	+	7.66562i	0.100846	+	0.310372i
$611$	2.46427	+	7.58425i	0.0996938	+	0.306826i
$612$	3.37323	+	2.45080i	0.136355	+	0.0990676i
$613$	14.6488	−	10.6430i	0.591660	−	0.429866i	−0.251249	−	0.967923i	$-0.580841\pi$
$613$	14.6488	−	10.6430i	0.591660	−	0.429866i	0.842909	+	0.538056i	$0.180841\pi$
$614$	7.75977	−	23.8821i	0.313159	−	0.963803i
$615$	0.641661			0.0258743
$616$	−1.19466	+	3.09399i	−0.0481342	+	0.124661i
$617$	−33.3189			−1.34137			−0.670684	−	0.741743i	$-0.733999\pi$
$617$	−33.3189			−1.34137			−0.670684	+	0.741743i	$0.733999\pi$
$618$	1.59711	−	4.91541i	0.0642454	−	0.197727i
$619$	10.5716	−	7.68070i	0.424907	−	0.308713i	−0.354702	−	0.934979i	$-0.615418\pi$
$619$	10.5716	−	7.68070i	0.424907	−	0.308713i	0.779609	+	0.626266i	$0.215418\pi$
$620$	−1.89577	−	1.37736i	−0.0761360	−	0.0553160i
$621$	1.79339	+	5.51948i	0.0719661	+	0.221489i
$622$	−0.811955	−	2.49894i	−0.0325564	−	0.100198i
$623$	−10.8890	−	7.91135i	−0.436260	−	0.316961i
$624$	−1.79630	+	1.30509i	−0.0719097	+	0.0522455i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	3.90115			0.155921
$627$	−1.02672	−	0.834772i	−0.0410034	−	0.0333376i
$628$	−8.62372			−0.344124
$629$	0.0102193	−	0.0314518i	0.000407470	−	0.00125407i
$630$	2.28510	−	1.66022i	0.0910407	−	0.0661449i
$631$	−31.8074	−	23.1094i	−1.26623	−	0.919972i	−0.267186	−	0.963645i	$-0.586094\pi$
$631$	−31.8074	−	23.1094i	−1.26623	−	0.919972i	−0.999046	+	0.0436732i	$0.986094\pi$
$632$	−3.95872	−	12.1837i	−0.157469	−	0.484641i
$633$	−1.71859	−	5.28927i	−0.0683078	−	0.210230i
$634$	22.3147	+	16.2126i	0.886230	+	0.643884i
$635$	2.05657	−	1.49419i	0.0816126	−	0.0592950i
$636$	1.46898	−	4.52106i	0.0582489	−	0.179272i
$637$	−5.30073			−0.210022
$638$	−5.09361	−	19.1602i	−0.201658	−	0.758561i
$639$	33.7103			1.33356
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	−26.7079	+	19.4044i	−1.05490	+	0.766428i	−0.973138	−	0.230224i	$-0.926054\pi$
$641$	−26.7079	+	19.4044i	−1.05490	+	0.766428i	−0.0817596	+	0.996652i	$0.526054\pi$
$642$	3.27262	+	2.37770i	0.129160	+	0.0938402i
$643$	0.0398262	+	0.122572i	0.00157059	+	0.00483378i	0.951839	−	0.306599i	$-0.0991911\pi$
$643$	0.0398262	+	0.122572i	0.00157059	+	0.00483378i	−0.950268	+	0.311433i	$0.899191\pi$
$644$	0.735065	+	2.26230i	0.0289656	+	0.0891470i
$645$	1.29825	+	0.943232i	0.0511184	+	0.0371397i
$646$	−1.13752	+	0.826456i	−0.0447551	+	0.0325165i
$647$	9.88369	−	30.4189i	0.388568	−	1.19589i	−0.545291	−	0.838247i	$-0.683581\pi$
$647$	9.88369	−	30.4189i	0.388568	−	1.19589i	0.933859	−	0.357642i	$-0.116419\pi$
$648$	7.45166			0.292729
$649$	2.14137	−	1.38464i	0.0840562	−	0.0543520i
$650$	−5.30073			−0.207912
$651$	−0.303317	+	0.933515i	−0.0118879	+	0.0365873i
$652$	8.89150	−	6.46005i	0.348218	−	0.252995i
$653$	24.2866	+	17.6452i	0.950407	+	0.690511i	0.950903	−	0.309489i	$-0.100158\pi$
$653$	24.2866	+	17.6452i	0.950407	+	0.690511i	−0.000496442		1.00000i	$0.500158\pi$
$654$	0.766061	+	2.35769i	0.0299554	+	0.0921931i
$655$	2.41186	+	7.42295i	0.0942392	+	0.290038i
$656$	1.23930	+	0.900404i	0.0483866	+	0.0351549i
$657$	16.6470	−	12.0947i	0.649460	−	0.471860i
$658$	−0.464893	+	1.43079i	−0.0181234	+	0.0557782i
$659$	−19.3178			−0.752515			−0.376258	−	0.926515i	$-0.622789\pi$
$659$	−19.3178			−0.752515			−0.376258	+	0.926515i	$0.622789\pi$
$660$	1.38721	+	0.0754362i	0.0539970	+	0.00293635i
$661$	−0.389498			−0.0151497			−0.00757487	−	0.999971i	$-0.502411\pi$
$661$	−0.389498			−0.0151497			−0.00757487	+	0.999971i	$0.502411\pi$
$662$	10.3396	−	31.8219i	0.401858	−	1.23679i
$663$	−2.65168	+	1.92655i	−0.102983	+	0.0748212i
$664$	−4.96353	−	3.60622i	−0.192622	−	0.139948i
$665$	0.294336	+	0.905872i	0.0114139	+	0.0351282i
$666$	−0.0195537	−	0.0601801i	−0.000757690	−	0.00233193i
$667$	−11.5036	−	8.35785i	−0.445421	−	0.323617i
$668$	−3.44852	+	2.50550i	−0.133427	+	0.0969407i
$669$	1.37402	−	4.22881i	0.0531228	−	0.163495i
$670$	12.1841			0.470712
$671$	−26.6929	−	1.45156i	−1.03047	−	0.0560368i
$672$	−0.418877			−0.0161585
$673$	9.80809	−	30.1862i	0.378074	−	1.16359i	−0.563307	−	0.826248i	$-0.690471\pi$
$673$	9.80809	−	30.1862i	0.378074	−	1.16359i	0.941381	−	0.337345i	$-0.109529\pi$
$674$	−12.8856	+	9.36196i	−0.496336	+	0.360609i
$675$	−1.97381	−	1.43406i	−0.0759721	−	0.0551970i
$676$	4.66544	+	14.3588i	0.179440	+	0.552260i
$677$	13.0314	+	40.1066i	0.500839	+	1.54142i	0.807656	+	0.589655i	$0.200736\pi$
$677$	13.0314	+	40.1066i	0.500839	+	1.54142i	−0.306817	+	0.951769i	$0.599264\pi$
$678$	4.26841	+	3.10118i	0.163927	+	0.119100i
$679$	−14.9557	+	10.8659i	−0.573946	+	0.416996i
$680$	0.456166	−	1.40393i	0.0174932	−	0.0538384i
$681$	10.2175			0.391536
$682$	6.52633	−	4.22003i	0.249906	−	0.161593i
$683$	−22.4212			−0.857923			−0.428961	−	0.903323i	$-0.641120\pi$
$683$	−22.4212			−0.857923			−0.428961	+	0.903323i	$0.641120\pi$
$684$	−0.831364	+	2.55867i	−0.0317880	+	0.0978333i
$685$	−15.9759	+	11.6072i	−0.610409	+	0.443488i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	−1.46014	−	4.49386i	−0.0557079	−	0.171451i
$688$	1.18385	+	3.64350i	0.0451337	+	0.138907i
$689$	−48.6676	−	35.3591i	−1.85409	−	1.34707i
$690$	0.806097	−	0.585664i	0.0306876	−	0.0222958i
$691$	−6.59469	+	20.2964i	−0.250874	+	0.772110i	0.743741	+	0.668468i	$0.233050\pi$
$691$	−6.59469	+	20.2964i	−0.250874	+	0.772110i	−0.994615	+	0.103642i	$0.966950\pi$
$692$	21.8753			0.831575
$693$	2.40680	+	9.05349i	0.0914269	+	0.343914i
$694$	19.0799			0.724264
$695$	4.10976	−	12.6485i	0.155892	−	0.479787i
$696$	2.02571	−	1.47176i	0.0767843	−	0.0557871i
$697$	1.82944	+	1.32916i	0.0692948	+	0.0503456i
$698$	−5.35992	−	16.4961i	−0.202876	−	0.624388i
$699$	−1.18904	−	3.65950i	−0.0449737	−	0.138415i
$700$	−0.809017	−	0.587785i	−0.0305780	−	0.0222162i
$701$	18.1943	−	13.2189i	0.687189	−	0.499272i	−0.188546	−	0.982064i	$-0.560377\pi$
$701$	18.1943	−	13.2189i	0.687189	−	0.499272i	0.875735	+	0.482792i	$0.160377\pi$
$702$	−3.99638	+	12.2996i	−0.150833	+	0.464218i
$703$	0.0213383			0.000804788
$704$	2.57339	+	2.09228i	0.0969884	+	0.0788559i
$705$	0.630170			0.0237336
$706$	−7.18609	+	22.1165i	−0.270452	+	0.832366i
$707$	−7.21750	+	5.24382i	−0.271442	+	0.197214i
$708$	0.260553	+	0.189303i	0.00979216	+	0.00711442i
$709$	−11.9417	−	36.7528i	−0.448480	−	1.38028i	−0.878622	−	0.477518i	$-0.841536\pi$
$709$	−11.9417	−	36.7528i	−0.448480	−	1.38028i	0.430142	−	0.902761i	$-0.358464\pi$
$710$	−3.68805	−	11.3507i	−0.138410	−	0.425983i
$711$	−29.2737	−	21.2686i	−1.09785	−	0.797635i
$712$	−10.8890	+	7.91135i	−0.408084	+	0.296490i
$713$	1.72248	−	5.30124i	0.0645073	−	0.198533i
$714$	−0.618340			−0.0231408
$715$	6.33256	−	16.4004i	0.236824	−	0.613340i
$716$	12.0148			0.449014
$717$	0.395164	−	1.21619i	0.0147577	−	0.0454194i
$718$	0.161926	−	0.117646i	0.00604302	−	0.00439051i
$719$	−13.8528	−	10.0646i	−0.516622	−	0.375348i	0.298708	−	0.954345i	$-0.403444\pi$
$719$	−13.8528	−	10.0646i	−0.516622	−	0.375348i	−0.815330	+	0.578997i	$0.803444\pi$
$720$	−0.872831	−	2.68630i	−0.0325285	−	0.100112i
$721$	−3.81285	−	11.7347i	−0.141998	−	0.437024i
$722$	14.6374	+	10.6347i	0.544746	+	0.395781i
$723$	−1.78861	+	1.29950i	−0.0665190	+	0.0483289i
$724$	−6.50856	+	20.0313i	−0.241889	+	0.744456i
$725$	5.97768			0.222006
$726$	−1.89064	+	4.20189i	−0.0701682	+	0.155947i
$727$	−21.9967			−0.815811			−0.407906	−	0.913024i	$-0.633741\pi$
$727$	−21.9967			−0.815811			−0.407906	+	0.913024i	$0.633741\pi$
$728$	−1.63801	+	5.04129i	−0.0607089	+	0.186843i
$729$	14.5475	−	10.5693i	0.538795	−	0.391457i
$730$	−5.89369	−	4.28201i	−0.218135	−	0.158484i
$731$	1.74757	+	5.37848i	0.0646364	+	0.198930i
$732$	−1.04330	−	3.21096i	−0.0385616	−	0.118680i
$733$	−10.5417	−	7.65898i	−0.389366	−	0.282891i	0.375830	−	0.926689i	$-0.377358\pi$
$733$	−10.5417	−	7.65898i	−0.389366	−	0.282891i	−0.765196	+	0.643798i	$0.777358\pi$
$734$	−10.5470	+	7.66285i	−0.389297	+	0.282841i
$735$	−0.129440	+	0.398376i	−0.00477447	+	0.0146943i
$736$	2.37872			0.0876807
$737$	−14.5558	+	37.6974i	−0.536170	+	1.38860i
$738$	4.32680			0.159272
$739$	−5.35908	+	16.4936i	−0.197137	+	0.606725i	0.802808	+	0.596238i	$0.203338\pi$
$739$	−5.35908	+	16.4936i	−0.197137	+	0.606725i	−0.999945	+	0.0104876i	$0.996662\pi$
$740$	−0.0181241	+	0.0131679i	−0.000666255	+	0.000484062i
$741$	−1.71096	−	1.24309i	−0.0628538	−	0.0456659i
$742$	−3.50695	−	10.7933i	−0.128744	−	0.396234i
$743$	−8.44918	−	26.0039i	−0.309970	−	0.953990i	−0.977776	−	0.209654i	$-0.932766\pi$
$743$	−8.44918	−	26.0039i	−0.309970	−	0.953990i	0.667805	−	0.744336i	$-0.267234\pi$
$744$	0.794095	+	0.576944i	0.0291129	+	0.0211518i
$745$	−3.19884	+	2.32409i	−0.117196	+	0.0851481i
$746$	5.00328	−	15.3985i	0.183183	−	0.563780i
$747$	−17.3293			−0.634046
$748$	3.79880	+	3.08860i	0.138898	+	0.112930i
$749$	9.65719			0.352866
$750$	−0.129440	+	0.398376i	−0.00472649	+	0.0145466i
$751$	30.4820	−	22.1465i	1.11231	−	0.808137i	0.129280	−	0.991608i	$-0.458733\pi$
$751$	30.4820	−	22.1465i	1.11231	−	0.808137i	0.983025	+	0.183471i	$0.0587333\pi$
$752$	1.21711	+	0.884279i	0.0443833	+	0.0322464i
$753$	0.274156	+	0.843764i	0.00999078	+	0.0307485i
$754$	−9.79153	−	30.1352i	−0.356587	−	1.09746i
$755$	7.61740	+	5.53437i	0.277226	+	0.201416i
$756$	−1.97381	+	1.43406i	−0.0717869	+	0.0521562i
$757$	−2.62553	+	8.08054i	−0.0954264	+	0.293692i	−0.987365	−	0.158465i	$-0.949345\pi$
$757$	−2.62553	+	8.08054i	−0.0954264	+	0.293692i	0.891938	+	0.452157i	$0.149345\pi$
$758$	38.0576			1.38231
$759$	0.849029	+	3.19373i	0.0308178	+	0.115925i
$760$	0.952490			0.0345505
$761$	4.55876	−	14.0304i	0.165255	−	0.508603i	−0.833800	−	0.552067i	$-0.813839\pi$
$761$	4.55876	−	14.0304i	0.165255	−	0.508603i	0.999055	+	0.0434639i	$0.0138394\pi$
$762$	−0.861451	+	0.625881i	−0.0312071	+	0.0226733i
$763$	4.78798	+	3.47867i	0.173336	+	0.125936i
$764$	−2.35142	−	7.23692i	−0.0850713	−	0.261823i
$765$	−1.28846	−	3.96547i	−0.0465844	−	0.143372i
$766$	2.64544	+	1.92202i	0.0955836	+	0.0694455i
$767$	3.29719	−	2.39555i	0.119055	−	0.0864982i
$768$	−0.129440	+	0.398376i	−0.00467077	+	0.0143752i
$769$	39.2157			1.41415			0.707077	−	0.707136i	$-0.250013\pi$
$769$	39.2157			1.41415			0.707077	+	0.707136i	$0.250013\pi$
$770$	2.78510	−	1.80089i	0.100368	−	0.0648996i
$771$	11.2365			0.404672
$772$	6.37403	−	19.6173i	0.229406	−	0.706040i
$773$	−1.02581	+	0.745296i	−0.0368959	+	0.0268064i	−0.606080	−	0.795403i	$-0.707259\pi$
$773$	−1.02581	+	0.745296i	−0.0368959	+	0.0268064i	0.569184	+	0.822210i	$0.307259\pi$
$774$	8.75424	+	6.36033i	0.314665	+	0.228617i
$775$	0.724120	+	2.22861i	0.0260112	+	0.0800541i
$776$	5.71255	+	17.5814i	0.205069	+	0.631137i
$777$	0.00759177	+	0.00551574i	0.000272353	+	0.000197876i
$778$	24.2783	−	17.6392i	0.870420	−	0.632397i
$779$	−0.450881	+	1.38767i	−0.0161545	+	0.0497184i
$780$	2.22035			0.0795014
$781$	39.5248	+	2.14935i	1.41431	+	0.0769099i
$782$	3.51143			0.125568
$783$	4.50675	−	13.8704i	0.161058	−	0.495686i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	6.97674	+	5.06890i	0.249010	+	0.180917i
$786$	−1.01027	−	3.10930i	−0.0360353	−	0.110905i
$787$	7.64659	+	23.5338i	0.272572	+	0.838889i	0.989852	+	0.142104i	$0.0453868\pi$
$787$	7.64659	+	23.5338i	0.272572	+	0.838889i	−0.717280	+	0.696785i	$0.754613\pi$
$788$	8.20148	+	5.95872i	0.292166	+	0.212271i
$789$	−2.94209	+	2.13756i	−0.104741	+	0.0760990i
$790$	−3.95872	+	12.1837i	−0.140845	+	0.433476i
$791$	12.5957			0.447851
$792$	9.35412	+	0.508676i	0.332384	+	0.0180750i
$793$	−42.7245			−1.51719
$794$	4.79121	−	14.7458i	0.170034	−	0.523310i
$795$	−3.84584	+	2.79417i	−0.136398	+	0.0990990i
$796$	−18.3352	−	13.3213i	−0.649875	−	0.472162i
$797$	−7.52049	−	23.1457i	−0.266389	−	0.819862i	−0.991370	−	0.131093i	$-0.958151\pi$
$797$	−7.52049	−	23.1457i	−0.266389	−	0.819862i	0.724981	−	0.688769i	$-0.241849\pi$
$798$	−0.123291	−	0.379449i	−0.00436444	−	0.0134324i
$799$	1.79667	+	1.30536i	0.0635617	+	0.0461803i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	−11.7480	+	36.1565i	−0.415093	+	1.27753i
$802$	−5.70472			−0.201441
$803$	20.2895	−	13.1195i	0.715999	−	0.462976i
$804$	−5.10363			−0.179991
$805$	0.735065	−	2.26230i	0.0259076	−	0.0797355i
$806$	10.0490	−	7.30100i	0.353960	−	0.257167i
$807$	−3.88452	−	2.82227i	−0.136742	−	0.0993486i
$808$	2.75684	+	8.48467i	0.0969852	+	0.298490i
$809$	−12.8336	−	39.4978i	−0.451206	−	1.38867i	−0.875532	−	0.483160i	$-0.839489\pi$
$809$	−12.8336	−	39.4978i	−0.451206	−	1.38867i	0.424326	−	0.905509i	$-0.360511\pi$
$810$	−6.02852	−	4.37998i	−0.211821	−	0.153897i
$811$	−36.0647	+	26.2025i	−1.26640	+	0.920096i	−0.999053	−	0.0435039i	$-0.986148\pi$
$811$	−36.0647	+	26.2025i	−1.26640	+	0.920096i	−0.267350	+	0.963600i	$0.586148\pi$
$812$	1.84721	−	5.68511i	0.0648242	−	0.199508i
$813$	−7.20089			−0.252546
$814$	−0.0190894	−	0.0718070i	−0.000669082	−	0.00251683i
$815$	−10.9905			−0.384980
$816$	−0.191078	+	0.588076i	−0.00668905	+	0.0205868i
$817$	−2.95210	+	2.14483i	−0.103281	+	0.0750380i
$818$	−1.04199	−	0.757049i	−0.0364323	−	0.0264696i
$819$	4.62664	+	14.2393i	0.161668	+	0.497563i
$820$	−0.473371	−	1.45689i	−0.0165308	−	0.0508766i
$821$	14.6120	+	10.6162i	0.509962	+	0.370509i	0.812809	−	0.582530i	$-0.197937\pi$
$821$	14.6120	+	10.6162i	0.509962	+	0.370509i	−0.302847	+	0.953039i	$0.597937\pi$
$822$	6.69195	−	4.86199i	0.233409	−	0.169581i
$823$	17.2597	−	53.1200i	0.601636	−	1.85165i	0.0831945	−	0.996533i	$-0.473488\pi$
$823$	17.2597	−	53.1200i	0.601636	−	1.85165i	0.518442	−	0.855113i	$-0.326512\pi$
$824$	−12.3386			−0.429836
$825$	−1.07794	−	0.876410i	−0.0375289	−	0.0305127i
$826$	0.768866			0.0267523
$827$	−14.9679	+	46.0664i	−0.520484	+	1.60188i	0.252593	+	0.967573i	$0.418717\pi$
$827$	−14.9679	+	46.0664i	−0.520484	+	1.60188i	−0.773077	+	0.634312i	$0.781283\pi$
$828$	5.43562	−	3.94921i	0.188901	−	0.137244i
$829$	−12.6866	−	9.21739i	−0.440625	−	0.320133i	0.345258	−	0.938508i	$-0.387791\pi$
$829$	−12.6866	−	9.21739i	−0.440625	−	0.320133i	−0.785883	+	0.618375i	$0.787791\pi$
$830$	1.89590	+	5.83498i	0.0658077	+	0.202535i
$831$	−1.96820	−	6.05750i	−0.0682762	−	0.210132i
$832$	4.28838	+	3.11569i	0.148673	+	0.108017i
$833$	−1.19426	+	0.867679i	−0.0413786	+	0.0300633i
$834$	−1.72149	+	5.29819i	−0.0596102	+	0.183461i
$835$	4.26261			0.147514
$836$	−1.13790	+	2.94700i	−0.0393551	+	0.101924i
$837$	5.71711			0.197612
$838$	11.2139	−	34.5128i	0.387377	−	1.19222i
$839$	18.4409	−	13.3981i	0.636652	−	0.462554i	−0.222047	−	0.975036i	$-0.571274\pi$
$839$	18.4409	−	13.3981i	0.636652	−	0.462554i	0.858698	+	0.512482i	$0.171274\pi$
$840$	0.338879	+	0.246210i	0.0116924	+	0.00849505i
$841$	2.08052	+	6.40317i	0.0717419	+	0.220799i
$842$	−4.14211	−	12.7481i	−0.142747	−	0.439329i
$843$	−0.811529	−	0.589610i	−0.0279505	−	0.0203073i
$844$	−10.7414	+	7.80408i	−0.369734	+	0.268627i
$845$	4.66544	−	14.3588i	0.160496	−	0.493956i
$846$	4.24931			0.146094
$847$	2.24469	+	10.7685i	0.0771286	+	0.370011i
$848$	−11.3487			−0.389717
$849$	1.55613	−	4.78927i	0.0534061	−	0.164367i
$850$	−1.19426	+	0.867679i	−0.0409627	+	0.0297612i
$851$	−0.0431121	−	0.0313228i	−0.00147786	−	0.00107373i
$852$	1.54484	+	4.75453i	0.0529254	+	0.162888i
$853$	4.14215	+	12.7482i	0.141824	+	0.436490i	0.996589	−	0.0825254i	$-0.0262986\pi$
$853$	4.14215	+	12.7482i	0.141824	+	0.436490i	−0.854765	+	0.519016i	$0.826299\pi$
$854$	−6.52077	−	4.73762i	−0.223136	−	0.162118i
$855$	2.17654	−	1.58135i	0.0744360	−	0.0540809i
$856$	2.98424	−	9.18454i	0.101999	−	0.313921i
$857$	6.20533			0.211970			0.105985	−	0.994368i	$-0.466200\pi$
$857$	6.20533			0.211970			0.105985	+	0.994368i	$0.466200\pi$
$858$	−2.65256	+	6.86976i	−0.0905571	+	0.234530i
$859$	−34.2020			−1.16696			−0.583479	−	0.812128i	$-0.698309\pi$
$859$	−34.2020			−1.16696			−0.583479	+	0.812128i	$0.698309\pi$
$860$	1.18385	−	3.64350i	0.0403688	−	0.124242i
$861$	−0.519115	+	0.377159i	−0.0176914	+	0.0128535i
$862$	−1.93100	−	1.40295i	−0.0657700	−	0.0477847i
$863$	−4.00549	−	12.3276i	−0.136349	−	0.419638i	0.859449	−	0.511222i	$-0.170807\pi$
$863$	−4.00549	−	12.3276i	−0.136349	−	0.419638i	−0.995797	+	0.0915840i	$0.970807\pi$
$864$	0.753930	+	2.32036i	0.0256492	+	0.0789402i
$865$	−17.6975	−	12.8580i	−0.601733	−	0.437185i
$866$	18.3387	−	13.3238i	0.623173	−	0.452762i
$867$	1.91842	−	5.90428i	0.0651529	−	0.200520i
$868$	2.34330			0.0795368
$869$	−32.9669	−	26.8036i	−1.11833	−	0.909249i
$870$	−2.50392			−0.0848907
$871$	−19.9577	+	61.4234i	−0.676240	+	2.08125i
$872$	4.78798	−	3.47867i	0.162141	−	0.117803i
$873$	42.2429	+	30.6913i	1.42971	+	1.03874i
$874$	0.700142	+	2.15482i	0.0236827	+	0.0728877i
$875$	0.309017	+	0.951057i	0.0104467	+	0.0321516i
$876$	2.46873	+	1.79364i	0.0834107	+	0.0606014i
$877$	−4.89848	+	3.55895i	−0.165410	+	0.120177i	−0.667411	−	0.744690i	$-0.732597\pi$
$877$	−4.89848	+	3.55895i	−0.165410	+	0.120177i	0.502001	+	0.864867i	$0.332597\pi$
$878$	5.49668	−	16.9170i	0.185504	−	0.570923i
$879$	−4.70920			−0.158837
$880$	−0.852104	−	3.20530i	−0.0287244	−	0.108050i
$881$	−19.9937			−0.673605			−0.336803	−	0.941575i	$-0.609346\pi$
$881$	−19.9937			−0.673605			−0.336803	+	0.941575i	$0.609346\pi$
$882$	−0.872831	+	2.68630i	−0.0293898	+	0.0904524i
$883$	5.99261	−	4.35388i	0.201667	−	0.146520i	−0.482368	−	0.875969i	$-0.660223\pi$
$883$	5.99261	−	4.35388i	0.201667	−	0.146520i	0.684036	+	0.729449i	$0.260223\pi$
$884$	6.33043	+	4.59933i	0.212916	+	0.154692i
$885$	−0.0995222	−	0.306298i	−0.00334540	−	0.0102961i
$886$	−7.44465	−	22.9123i	−0.250108	−	0.769753i
$887$	−46.7849	−	33.9912i	−1.57088	−	1.14131i	−0.926303	−	0.376778i	$-0.877032\pi$
$887$	−46.7849	−	33.9912i	−1.57088	−	1.14131i	−0.644581	−	0.764536i	$-0.722968\pi$
$888$	0.00759177	−	0.00551574i	0.000254763	−	0.000185096i
$889$	−0.785541	+	2.41765i	−0.0263462	+	0.0810852i
$890$	13.4596			0.451166
$891$	20.7536	−	13.4196i	0.695273	−	0.449574i
$892$	−10.6151			−0.355420
$893$	−0.442806	+	1.36282i	−0.0148179	+	0.0456050i
$894$	1.33992	−	0.973509i	0.0448136	−	0.0325590i
$895$	−9.72018	−	7.06212i	−0.324910	−	0.236061i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	1.63210	+	5.02310i	0.0544943	+	0.167716i
$898$	4.91037	+	3.56759i	0.163861	+	0.119052i
$899$	−11.3323	+	8.23341i	−0.377954	+	0.274600i
$900$	−0.872831	+	2.68630i	−0.0290944	+	0.0895433i
$901$	−16.7528			−0.558117
$902$	5.07311	+	0.275875i	0.168916	+	0.00918563i
$903$	−1.60472			−0.0534018
$904$	3.89228	−	11.9792i	0.129455	−	0.398423i
$905$	17.0396	−	12.3800i	0.566416	−	0.411525i
$906$	−3.19076	−	2.31822i	−0.106006	−	0.0770177i
$907$	−4.88400	−	15.0314i	−0.162171	−	0.499110i	0.836646	−	0.547744i	$-0.184513\pi$
$907$	−4.88400	−	15.0314i	−0.162171	−	0.499110i	−0.998817	+	0.0486340i	$0.984513\pi$
$908$	−7.53773	−	23.1988i	−0.250148	−	0.769878i
$909$	20.3861	+	14.8114i	0.676165	+	0.491263i
$910$	4.28838	−	3.11569i	0.142158	−	0.103284i
$911$	−11.1357	+	34.2723i	−0.368943	+	1.13549i	0.578531	+	0.815660i	$0.303626\pi$
$911$	−11.1357	+	34.2723i	−0.368943	+	1.13549i	−0.947475	+	0.319831i	$0.896374\pi$
$912$	−0.398977			−0.0132114
$913$	−20.3183	−	1.10491i	−0.672439	−	0.0365671i
$914$	4.92065			0.162761
$915$	−1.04330	+	3.21096i	−0.0344905	+	0.106151i
$916$	−9.12607	+	6.63048i	−0.301534	+	0.219077i
$917$	−6.31433	−	4.58763i	−0.208518	−	0.151497i
$918$	1.11294	+	3.42527i	0.0367325	+	0.113051i
$919$	−12.5047	−	38.4855i	−0.412492	−	1.26952i	−0.914475	−	0.404643i	$-0.867396\pi$
$919$	−12.5047	−	38.4855i	−0.412492	−	1.26952i	0.501982	−	0.864878i	$-0.332604\pi$
$920$	−1.92442	−	1.39818i	−0.0634464	−	0.0460965i
$921$	8.50963	−	6.18261i	0.280402	−	0.203724i
$922$	−10.4113	+	32.0428i	−0.342879	+	1.05527i
$923$	63.2630			2.08233
$924$	−1.16662	+	0.754352i	−0.0383788	+	0.0248164i
$925$	0.0224026			0.000736593
$926$	0.698881	−	2.15093i	0.0229667	−	0.0706841i
$927$	−28.1950	+	20.4849i	−0.926046	+	0.672812i
$928$	−4.83605	−	3.51359i	−0.158751	−	0.115339i
$929$	9.15611	+	28.1796i	0.300402	+	0.924543i	0.981353	+	0.192214i	$0.0615668\pi$
$929$	9.15611	+	28.1796i	0.300402	+	0.924543i	−0.680951	+	0.732329i	$0.738433\pi$
$930$	−0.303317	−	0.933515i	−0.00994617	−	0.0306112i
$931$	−0.770581	−	0.559860i	−0.0252548	−	0.0183487i
$932$	−7.43166	+	5.39942i	−0.243432	+	0.176864i
$933$	0.340109	−	1.04675i	0.0111347	−	0.0342690i
$934$	13.3924			0.438213
$935$	−1.25786	−	4.73161i	−0.0411365	−	0.154740i
$936$	14.9721			0.489379
$937$	−2.56064	+	7.88083i	−0.0836523	+	0.257455i	−0.984131	−	0.177446i	$-0.943217\pi$
$937$	−2.56064	+	7.88083i	−0.0836523	+	0.257455i	0.900478	+	0.434901i	$0.143217\pi$
$938$	−9.85712	+	7.16162i	−0.321846	+	0.233835i
$939$	1.32202	+	0.960501i	0.0431424	+	0.0313448i
$940$	−0.464893	−	1.43079i	−0.0151631	−	0.0466674i
$941$	9.53598	+	29.3487i	0.310864	+	0.956741i	0.977424	+	0.211289i	$0.0677662\pi$
$941$	9.53598	+	29.3487i	0.310864	+	0.956741i	−0.666560	+	0.745452i	$0.732234\pi$
$942$	−2.92240	−	2.12325i	−0.0952168	−	0.0691791i
$943$	2.94795	−	2.14181i	0.0959984	−	0.0697469i
$944$	0.237593	−	0.731235i	0.00773299	−	0.0237997i
$945$	2.43977			0.0793657
$946$	9.85868	+	8.01555i	0.320533	+	0.260608i
$947$	12.2671			0.398627			0.199313	−	0.979936i	$-0.436129\pi$
$947$	12.2671			0.398627			0.199313	+	0.979936i	$0.436129\pi$
$948$	1.65822	−	5.10347i	0.0538564	−	0.165753i
$949$	31.2408	−	22.6978i	1.01412	−	0.736801i
$950$	−0.770581	−	0.559860i	−0.0250009	−	0.0181643i
$951$	3.57028	+	10.9882i	0.115774	+	0.356317i
$952$	0.456166	+	1.40393i	0.0147844	+	0.0455018i
$953$	5.80849	+	4.22012i	0.188156	+	0.136703i	0.677875	−	0.735177i	$-0.262901\pi$
$953$	5.80849	+	4.22012i	0.188156	+	0.136703i	−0.489720	+	0.871880i	$0.662901\pi$
$954$	−25.9330	+	18.8414i	−0.839612	+	0.610014i
$955$	−2.35142	+	7.23692i	−0.0760901	+	0.234181i
$956$	−3.05287			−0.0987368
$957$	2.99132	−	7.74710i	0.0966958	−	0.250428i
$958$	16.6637			0.538380
$959$	6.10226	−	18.7808i	0.197052	−	0.606464i
$960$	0.338879	−	0.246210i	0.0109373	−	0.00794639i
$961$	20.6372	+	14.9938i	0.665715	+	0.483670i
$962$	−0.0366958	−	0.112938i	−0.00118312	−	0.00364127i
$963$	−8.42910	−	25.9421i	−0.271624	−	0.835973i
$964$	4.27000	+	3.10234i	0.137527	+	0.0999195i
$965$	−16.6874	+	12.1241i	−0.537187	+	0.390290i
$966$	−0.307902	+	0.947624i	−0.00990658	+	0.0304893i
$967$	5.07937			0.163341			0.0816707	−	0.996659i	$-0.473974\pi$
$967$	5.07937			0.163341			0.0816707	+	0.996659i	$0.473974\pi$
$968$	10.9351	+	1.19283i	0.351469	+	0.0383390i
$969$	−0.588963			−0.0189202
$970$	5.71255	−	17.5814i	0.183419	−	0.564506i
$971$	32.6128	−	23.6946i	1.04660	−	0.760397i	0.0750338	−	0.997181i	$-0.476094\pi$
$971$	32.6128	−	23.6946i	1.04660	−	0.760397i	0.971562	+	0.236784i	$0.0760935\pi$
$972$	8.44665	+	6.13685i	0.270926	+	0.196840i
$973$	4.10976	+	12.6485i	0.131753	+	0.405494i
$974$	−3.92326	−	12.0746i	−0.125709	−	0.386894i
$975$	−1.79630	−	1.30509i	−0.0575278	−	0.0417964i
$976$	−6.52077	+	4.73762i	−0.208725	+	0.151647i
$977$	−8.69026	+	26.7459i	−0.278026	+	0.855676i	0.710377	+	0.703821i	$0.248524\pi$
$977$	−8.69026	+	26.7459i	−0.278026	+	0.855676i	−0.988403	+	0.151854i	$0.951476\pi$
$978$	4.60367			0.147209
$979$	−16.0796	+	41.6439i	−0.513907	+	1.33094i
$980$	1.00000			0.0319438
$981$	5.16565	−	15.8982i	0.164926	−	0.507591i
$982$	−12.4906	+	9.07493i	−0.398590	+	0.289593i
$983$	−18.7429	−	13.6175i	−0.597805	−	0.434331i	0.247294	−	0.968940i	$-0.420459\pi$
$983$	−18.7429	−	13.6175i	−0.597805	−	0.434331i	−0.845099	+	0.534610i	$0.820459\pi$
$984$	0.198284	+	0.610256i	0.00632107	+	0.0194542i
$985$	−3.13269	−	9.64141i	−0.0998157	−	0.307201i
$986$	−7.13890	−	5.18671i	−0.227349	−	0.165179i
$987$	−0.509818	+	0.370405i	−0.0162277	+	0.0117901i
$988$	−1.56019	+	4.80178i	−0.0496364	+	0.152765i
$989$	9.11289			0.289773
$990$	−7.26865	−	5.90974i	−0.231013	−	0.187824i
$991$	−33.5898			−1.06701			−0.533507	−	0.845795i	$-0.679126\pi$
$991$	−33.5898			−1.06701			−0.533507	+	0.845795i	$0.679126\pi$
$992$	0.724120	−	2.22861i	0.0229908	−	0.0707585i
$993$	11.3387	−	8.23806i	0.359823	−	0.261427i
$994$	9.65545	+	7.01509i	0.306252	+	0.222505i
$995$	7.00344	+	21.5544i	0.222024	+	0.683319i
$996$	−0.794150	−	2.44414i	−0.0251636	−	0.0774456i
$997$	18.3030	+	13.2979i	0.579662	+	0.421149i	0.838602	−	0.544744i	$-0.183373\pi$
$997$	18.3030	+	13.2979i	0.579662	+	0.421149i	−0.258940	+	0.965893i	$0.583373\pi$
$998$	4.82943	−	3.50878i	0.152873	−	0.111069i
$999$	0.0168900	−	0.0519820i	0.000534376	−	0.00164464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.i.141.2	yes	12
11.4	even	5		8470.2.a.de.1.3		6
11.5	even	5	inner	770.2.n.i.71.2	✓	12
11.7	odd	10		8470.2.a.cy.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.i.71.2	✓	12	11.5	even	5	inner
770.2.n.i.141.2	yes	12	1.1	even	1	trivial
8470.2.a.cy.1.3		6	11.7	odd	10
8470.2.a.de.1.3		6	11.4	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.338879 - 0.246210i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.129440 - 0.398376i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.872831 + 2.68630i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.338879 - 0.246210i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.129440 - 0.398376i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.872831 + 2.68630i) q^{9} +1.00000 q^{10} +(-1.19466 + 3.09399i) q^{11} -0.418877 q^{12} +(-1.63801 + 5.04129i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(0.338879 + 0.246210i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.456166 + 1.40393i) q^{17} +(2.28510 + 1.66022i) q^{18} +(-0.770581 + 0.559860i) q^{19} +(0.309017 - 0.951057i) q^{20} -0.418877 q^{21} +(2.57339 + 2.09228i) q^{22} +2.37872 q^{23} +(-0.129440 + 0.398376i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(4.28838 + 3.11569i) q^{26} +(0.753930 + 2.32036i) q^{27} +(0.309017 + 0.951057i) q^{28} +(-4.83605 - 3.51359i) q^{29} +(0.338879 - 0.246210i) q^{30} +(0.724120 - 2.22861i) q^{31} +1.00000 q^{32} +(0.356927 + 1.34263i) q^{33} +1.47618 q^{34} +(0.309017 - 0.951057i) q^{35} +(2.28510 - 1.66022i) q^{36} +(-0.0181241 - 0.0131679i) q^{37} +(0.294336 + 0.905872i) q^{38} +(0.686127 + 2.11168i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(1.23930 - 0.900404i) q^{41} +(-0.129440 + 0.398376i) q^{42} +3.83101 q^{43} +(2.78510 - 1.80089i) q^{44} -2.82454 q^{45} +(0.735065 - 2.26230i) q^{46} +(1.21711 - 0.884279i) q^{47} +(0.338879 + 0.246210i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(0.500248 + 0.363451i) q^{51} +(4.28838 - 3.11569i) q^{52} +(-3.50695 + 10.7933i) q^{53} +2.43977 q^{54} +(-3.31173 - 0.180091i) q^{55} +1.00000 q^{56} +(-0.123291 + 0.379449i) q^{57} +(-4.83605 + 3.51359i) q^{58} +(-0.622026 - 0.451928i) q^{59} +(-0.129440 - 0.398376i) q^{60} +(2.49071 + 7.66562i) q^{61} +(-1.89577 - 1.37736i) q^{62} +(2.28510 - 1.66022i) q^{63} +(0.309017 - 0.951057i) q^{64} -5.30073 q^{65} +(1.38721 + 0.0754362i) q^{66} +12.1841 q^{67} +(0.456166 - 1.40393i) q^{68} +(0.806097 - 0.585664i) q^{69} +(-0.809017 - 0.587785i) q^{70} +(-3.68805 - 11.3507i) q^{71} +(-0.872831 - 2.68630i) q^{72} +(-5.89369 - 4.28201i) q^{73} +(-0.0181241 + 0.0131679i) q^{74} +(-0.129440 + 0.398376i) q^{75} +0.952490 q^{76} +(2.78510 - 1.80089i) q^{77} +2.22035 q^{78} +(-3.95872 + 12.1837i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-6.02852 - 4.37998i) q^{81} +(-0.473371 - 1.45689i) q^{82} +(1.89590 + 5.83498i) q^{83} +(0.338879 + 0.246210i) q^{84} +(-1.19426 + 0.867679i) q^{85} +(1.18385 - 3.64350i) q^{86} -2.50392 q^{87} +(-0.852104 - 3.20530i) q^{88} +13.4596 q^{89} +(-0.872831 + 2.68630i) q^{90} +(4.28838 - 3.11569i) q^{91} +(-1.92442 - 1.39818i) q^{92} +(-0.303317 - 0.933515i) q^{93} +(-0.464893 - 1.43079i) q^{94} +(-0.770581 - 0.559860i) q^{95} +(0.338879 - 0.246210i) q^{96} +(5.71255 - 17.5814i) q^{97} +1.00000 q^{98} +(-7.26865 - 5.90974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * q^99

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