LMFDB - Embedded newform 847.2.f.x.729.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.3
Root			$0.901622 - 0.655067i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.x.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.901622 - 0.655067i) q^{2} +(-0.883423 - 2.71890i) q^{3} +(-0.234224 + 0.720867i) q^{4} +(-2.79603 - 2.03143i) q^{5} +(-2.57757 - 1.87272i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.949813 + 2.92322i) q^{8} +(-4.18492 + 3.04052i) q^{9} +O(q^{10})$	\(q+(0.901622 - 0.655067i) q^{2} +(-0.883423 - 2.71890i) q^{3} +(-0.234224 + 0.720867i) q^{4} +(-2.79603 - 2.03143i) q^{5} +(-2.57757 - 1.87272i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.949813 + 2.92322i) q^{8} +(-4.18492 + 3.04052i) q^{9} -3.85168 q^{10} +2.16688 q^{12} +(-1.66629 + 1.21063i) q^{13} +(0.344389 + 1.05992i) q^{14} +(-3.05318 + 9.39672i) q^{15} +(1.54487 + 1.12241i) q^{16} +(1.56442 + 1.13662i) q^{17} +(-1.78147 + 5.48280i) q^{18} +(-0.501522 - 1.54353i) q^{19} +(2.11929 - 1.53975i) q^{20} +2.85882 q^{21} -0.807136 q^{23} +(7.10886 - 5.16489i) q^{24} +(2.14596 + 6.60459i) q^{25} +(-0.709322 + 2.18307i) q^{26} +(5.02542 + 3.65118i) q^{27} +(-0.613206 - 0.445520i) q^{28} +(-2.46400 + 7.58342i) q^{29} +(3.40267 + 10.4723i) q^{30} +(-0.637845 + 0.463421i) q^{31} -4.01918 q^{32} +2.15508 q^{34} +(2.79603 - 2.03143i) q^{35} +(-1.21160 - 3.72893i) q^{36} +(3.10926 - 9.56931i) q^{37} +(-1.46330 - 1.06315i) q^{38} +(4.76363 + 3.46098i) q^{39} +(3.28263 - 10.1029i) q^{40} +(0.657011 + 2.02207i) q^{41} +(2.57757 - 1.87272i) q^{42} -3.08043 q^{43} +17.8777 q^{45} +(-0.727732 + 0.528728i) q^{46} +(2.33812 + 7.19600i) q^{47} +(1.68695 - 5.19190i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(6.26129 + 4.54910i) q^{50} +(1.70830 - 5.25761i) q^{51} +(-0.482420 - 1.48474i) q^{52} +(-8.75554 + 6.36127i) q^{53} +6.92280 q^{54} -3.07366 q^{56} +(-3.75363 + 2.72717i) q^{57} +(2.74605 + 8.45147i) q^{58} +(-1.01872 + 3.13529i) q^{59} +(-6.05866 - 4.40187i) q^{60} +(-0.871010 - 0.632826i) q^{61} +(-0.271523 + 0.835662i) q^{62} +(-1.59850 - 4.91966i) q^{63} +(-6.71351 + 4.87765i) q^{64} +7.11832 q^{65} +2.40314 q^{67} +(-1.18577 + 0.861515i) q^{68} +(0.713042 + 2.19452i) q^{69} +(1.19024 - 3.66317i) q^{70} +(2.57963 + 1.87421i) q^{71} +(-12.8630 - 9.34552i) q^{72} +(-0.378940 + 1.16626i) q^{73} +(-3.46516 - 10.6647i) q^{74} +(16.0614 - 11.6693i) q^{75} +1.23015 q^{76} +6.56217 q^{78} +(-7.67096 + 5.57328i) q^{79} +(-2.03939 - 6.27659i) q^{80} +(0.692124 - 2.13014i) q^{81} +(1.91697 + 1.39276i) q^{82} +(-13.0004 - 9.44536i) q^{83} +(-0.669603 + 2.06083i) q^{84} +(-2.06520 - 6.35602i) q^{85} +(-2.77738 + 2.01789i) q^{86} +22.7953 q^{87} -4.43830 q^{89} +(16.1190 - 11.7111i) q^{90} +(-0.636468 - 1.95885i) q^{91} +(0.189050 - 0.581837i) q^{92} +(1.82348 + 1.32484i) q^{93} +(6.82196 + 4.95645i) q^{94} +(-1.73330 + 5.33455i) q^{95} +(3.55063 + 10.9277i) q^{96} +(-5.23278 + 3.80184i) q^{97} -1.11447 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.901622	−	0.655067i	0.637543	−	0.463202i	−0.221462	−	0.975169i	$-0.571083\pi$
$2$	0.901622	−	0.655067i	0.637543	−	0.463202i	0.859005	+	0.511967i	$0.171083\pi$
$3$	−0.883423	−	2.71890i	−0.510045	−	1.56976i	−0.792121	−	0.610364i	$-0.791023\pi$
$3$	−0.883423	−	2.71890i	−0.510045	−	1.56976i	0.282076	−	0.959392i	$-0.408977\pi$
$4$	−0.234224	+	0.720867i	−0.117112	+	0.360433i
$5$	−2.79603	−	2.03143i	−1.25042	−	0.908484i	−0.252174	−	0.967682i	$-0.581146\pi$
$5$	−2.79603	−	2.03143i	−1.25042	−	0.908484i	−0.998246	+	0.0591979i	$0.981146\pi$
$6$	−2.57757	−	1.87272i	−1.05229	−	0.764534i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.949813	+	2.92322i	0.335810	+	1.03352i
$9$	−4.18492	+	3.04052i	−1.39497	+	1.01351i
$10$	−3.85168			−1.21801
$11$		0			0
$11$		0			0
$12$	2.16688			0.625525
$13$	−1.66629	+	1.21063i	−0.462147	+	0.335769i	−0.794373	−	0.607430i	$-0.792200\pi$
$13$	−1.66629	+	1.21063i	−0.462147	+	0.335769i	0.332226	+	0.943200i	$0.392200\pi$
$14$	0.344389	+	1.05992i	0.0920419	+	0.283276i
$15$	−3.05318	+	9.39672i	−0.788328	+	2.42622i
$16$	1.54487	+	1.12241i	0.386217	+	0.280603i
$17$	1.56442	+	1.13662i	0.379427	+	0.275670i	0.761109	−	0.648624i	$-0.224655\pi$
$17$	1.56442	+	1.13662i	0.379427	+	0.275670i	−0.381682	+	0.924294i	$0.624655\pi$
$18$	−1.78147	+	5.48280i	−0.419897	+	1.29231i
$19$	−0.501522	−	1.54353i	−0.115057	−	0.354109i	0.876902	−	0.480669i	$-0.159606\pi$
$19$	−0.501522	−	1.54353i	−0.115057	−	0.354109i	−0.991959	+	0.126560i	$0.959606\pi$
$20$	2.11929	−	1.53975i	0.473887	−	0.344299i
$21$	2.85882			0.623845
$22$		0			0
$23$	−0.807136			−0.168299			−0.0841497	−	0.996453i	$-0.526817\pi$
$23$	−0.807136			−0.168299			−0.0841497	+	0.996453i	$0.526817\pi$
$24$	7.10886	−	5.16489i	1.45109	−	1.05428i
$25$	2.14596	+	6.60459i	0.429192	+	1.32092i
$26$	−0.709322	+	2.18307i	−0.139109	+	0.428135i
$27$	5.02542	+	3.65118i	0.967142	+	0.702670i
$28$	−0.613206	−	0.445520i	−0.115885	−	0.0841954i
$29$	−2.46400	+	7.58342i	−0.457554	+	1.40821i	0.410557	+	0.911835i	$0.365334\pi$
$29$	−2.46400	+	7.58342i	−0.457554	+	1.40821i	−0.868111	+	0.496371i	$0.834666\pi$
$30$	3.40267	+	10.4723i	0.621239	+	1.91198i
$31$	−0.637845	+	0.463421i	−0.114560	+	0.0832330i	−0.643590	−	0.765370i	$-0.722556\pi$
$31$	−0.637845	+	0.463421i	−0.114560	+	0.0832330i	0.529030	+	0.848603i	$0.322556\pi$
$32$	−4.01918			−0.710497
$33$		0			0
$34$	2.15508			0.369592
$35$	2.79603	−	2.03143i	0.472615	−	0.343375i
$36$	−1.21160	−	3.72893i	−0.201934	−	0.621488i
$37$	3.10926	−	9.56931i	0.511159	−	1.57318i	−0.279005	−	0.960290i	$-0.590005\pi$
$37$	3.10926	−	9.56931i	0.511159	−	1.57318i	0.790164	−	0.612895i	$-0.209995\pi$
$38$	−1.46330	−	1.06315i	−0.237378	−	0.172465i
$39$	4.76363	+	3.46098i	0.762792	+	0.554200i
$40$	3.28263	−	10.1029i	0.519029	−	1.59741i
$41$	0.657011	+	2.02207i	0.102608	+	0.315795i	0.989162	−	0.146831i	$-0.0469074\pi$
$41$	0.657011	+	2.02207i	0.102608	+	0.315795i	−0.886554	+	0.462626i	$0.846907\pi$
$42$	2.57757	−	1.87272i	0.397728	−	0.288967i
$43$	−3.08043			−0.469761			−0.234880	−	0.972024i	$-0.575470\pi$
$43$	−3.08043			−0.469761			−0.234880	+	0.972024i	$0.575470\pi$
$44$		0			0
$45$	17.8777			2.66506
$46$	−0.727732	+	0.528728i	−0.107298	+	0.0779567i
$47$	2.33812	+	7.19600i	0.341050	+	1.04964i	0.963665	+	0.267115i	$0.0860705\pi$
$47$	2.33812	+	7.19600i	0.341050	+	1.04964i	−0.622615	+	0.782529i	$0.713930\pi$
$48$	1.68695	−	5.19190i	0.243490	−	0.749387i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	6.26129	+	4.54910i	0.885481	+	0.643339i
$51$	1.70830	−	5.25761i	0.239210	−	0.736213i
$52$	−0.482420	−	1.48474i	−0.0668996	−	0.205896i
$53$	−8.75554	+	6.36127i	−1.20267	+	0.873788i	−0.994544	−	0.104315i	$-0.966735\pi$
$53$	−8.75554	+	6.36127i	−1.20267	+	0.873788i	−0.208122	+	0.978103i	$0.566735\pi$
$54$	6.92280			0.942073
$55$		0			0
$56$	−3.07366			−0.410735
$57$	−3.75363	+	2.72717i	−0.497181	+	0.361223i
$58$	2.74605	+	8.45147i	0.360574	+	1.10973i
$59$	−1.01872	+	3.13529i	−0.132626	+	0.408180i	−0.995213	−	0.0977281i	$-0.968842\pi$
$59$	−1.01872	+	3.13529i	−0.132626	+	0.408180i	0.862587	+	0.505908i	$0.168842\pi$
$60$	−6.05866	−	4.40187i	−0.782169	−	0.568279i
$61$	−0.871010	−	0.632826i	−0.111521	−	0.0810250i	0.530627	−	0.847606i	$-0.321957\pi$
$61$	−0.871010	−	0.632826i	−0.111521	−	0.0810250i	−0.642148	+	0.766581i	$0.721957\pi$
$62$	−0.271523	+	0.835662i	−0.0344835	+	0.106129i
$63$	−1.59850	−	4.91966i	−0.201392	−	0.619819i
$64$	−6.71351	+	4.87765i	−0.839189	+	0.609707i
$65$	7.11832			0.882919
$66$		0			0
$67$	2.40314			0.293590			0.146795	−	0.989167i	$-0.453104\pi$
$67$	2.40314			0.293590			0.146795	+	0.989167i	$0.453104\pi$
$68$	−1.18577	+	0.861515i	−0.143796	+	0.104474i
$69$	0.713042	+	2.19452i	0.0858402	+	0.264189i
$70$	1.19024	−	3.66317i	0.142260	−	0.437832i
$71$	2.57963	+	1.87421i	0.306145	+	0.222428i	0.730241	−	0.683190i	$-0.239408\pi$
$71$	2.57963	+	1.87421i	0.306145	+	0.222428i	−0.424095	+	0.905618i	$0.639408\pi$
$72$	−12.8630	−	9.34552i	−1.51592	−	1.10138i
$73$	−0.378940	+	1.16626i	−0.0443516	+	0.136500i	−0.970780	−	0.239970i	$-0.922862\pi$
$73$	−0.378940	+	1.16626i	−0.0443516	+	0.136500i	0.926429	+	0.376470i	$0.122862\pi$
$74$	−3.46516	−	10.6647i	−0.402817	−	1.23974i
$75$	16.0614	−	11.6693i	1.85461	−	1.34745i
$76$	1.23015			0.141107
$77$		0			0
$78$	6.56217			0.743020
$79$	−7.67096	+	5.57328i	−0.863050	+	0.627043i	−0.928713	−	0.370799i	$-0.879084\pi$
$79$	−7.67096	+	5.57328i	−0.863050	+	0.627043i	0.0656630	+	0.997842i	$0.479084\pi$
$80$	−2.03939	−	6.27659i	−0.228010	−	0.701744i
$81$	0.692124	−	2.13014i	0.0769027	−	0.236682i
$82$	1.91697	+	1.39276i	0.211694	+	0.153805i
$83$	−13.0004	−	9.44536i	−1.42698	−	1.03676i	−0.990569	−	0.137016i	$-0.956249\pi$
$83$	−13.0004	−	9.44536i	−1.42698	−	1.03676i	−0.436412	−	0.899747i	$-0.643751\pi$
$84$	−0.669603	+	2.06083i	−0.0730597	+	0.224855i
$85$	−2.06520	−	6.35602i	−0.224002	−	0.689407i
$86$	−2.77738	+	2.01789i	−0.299493	+	0.217594i
$87$	22.7953			2.44391
$88$		0			0
$89$	−4.43830			−0.470459			−0.235230	−	0.971940i	$-0.575584\pi$
$89$	−4.43830			−0.470459			−0.235230	+	0.971940i	$0.575584\pi$
$90$	16.1190	−	11.7111i	1.69909	−	1.23446i
$91$	−0.636468	−	1.95885i	−0.0667199	−	0.205343i
$92$	0.189050	−	0.581837i	0.0197099	−	0.0606607i
$93$	1.82348	+	1.32484i	0.189086	+	0.137379i
$94$	6.82196	+	4.95645i	0.703632	+	0.511218i
$95$	−1.73330	+	5.33455i	−0.177833	+	0.547313i
$96$	3.55063	+	10.9277i	0.362385	+	1.11531i
$97$	−5.23278	+	3.80184i	−0.531308	+	0.386018i	−0.820847	−	0.571148i	$-0.806498\pi$
$97$	−5.23278	+	3.80184i	−0.531308	+	0.386018i	0.289539	+	0.957166i	$0.406498\pi$
$98$	−1.11447			−0.112578
$99$		0			0
$100$	−5.26366			−0.526366
$101$	−12.4952	+	9.07828i	−1.24332	+	0.903323i	−0.997815	−	0.0660728i	$-0.978953\pi$
$101$	−12.4952	+	9.07828i	−1.24332	+	0.903323i	−0.245503	+	0.969396i	$0.578953\pi$
$102$	−1.90384	−	5.85943i	−0.188509	−	0.580170i
$103$	2.75276	−	8.47213i	0.271238	−	0.834784i	−0.718953	−	0.695059i	$-0.755378\pi$
$103$	2.75276	−	8.47213i	0.271238	−	0.834784i	0.990190	−	0.139725i	$-0.0446218\pi$
$104$	−5.12162	−	3.72107i	−0.502216	−	0.364881i
$105$	−7.99333	−	5.80749i	−0.780069	−	0.566753i
$106$	−3.72713	+	11.4709i	−0.362011	+	1.11416i
$107$	−1.08533	−	3.34029i	−0.104922	−	0.322918i	0.884790	−	0.465990i	$-0.154302\pi$
$107$	−1.08533	−	3.34029i	−0.104922	−	0.322918i	−0.989712	+	0.143072i	$0.954302\pi$
$108$	−3.80909	+	2.76746i	−0.366530	+	0.266299i
$109$	−3.87655			−0.371306			−0.185653	−	0.982615i	$-0.559440\pi$
$109$	−3.87655			−0.371306			−0.185653	+	0.982615i	$0.559440\pi$
$110$		0			0
$111$	−28.7648			−2.73023
$112$	−1.54487	+	1.12241i	−0.145976	+	0.106058i
$113$	3.29224	+	10.1325i	0.309708	+	0.953183i	0.977878	+	0.209175i	$0.0670777\pi$
$113$	3.29224	+	10.1325i	0.309708	+	0.953183i	−0.668170	+	0.744008i	$0.732922\pi$
$114$	−1.59788	+	4.91776i	−0.149655	+	0.460591i
$115$	2.25677	+	1.63964i	0.210445	+	0.152897i
$116$	−4.88951	−	3.55243i	−0.453979	−	0.329835i
$117$	3.29235	−	10.1328i	0.304378	−	0.936778i
$118$	1.13533	+	3.49417i	0.104515	+	0.321665i
$119$	−1.56442	+	1.13662i	−0.143410	+	0.104194i
$120$	−30.3687			−2.77227
$121$		0			0
$122$	−1.19987			−0.108631
$123$	4.91739	−	3.57269i	0.443386	−	0.322139i
$124$	−0.184667	−	0.568346i	−0.0165836	−	0.0510389i
$125$	2.07667	−	6.39134i	0.185743	−	0.571659i
$126$	−4.66395	−	3.38856i	−0.415498	−	0.301877i
$127$	15.7361	+	11.4330i	1.39635	+	1.01451i	0.995134	+	0.0985289i	$0.0314137\pi$
$127$	15.7361	+	11.4330i	1.39635	+	1.01451i	0.401220	+	0.915982i	$0.368586\pi$
$128$	−0.373878	+	1.15068i	−0.0330464	+	0.101706i
$129$	2.72132	+	8.37537i	0.239599	+	0.737410i
$130$	6.41804	−	4.66298i	0.562899	−	0.408970i
$131$	−5.11284			−0.446711			−0.223355	−	0.974737i	$-0.571701\pi$
$131$	−5.11284			−0.446711			−0.223355	+	0.974737i	$0.571701\pi$
$132$		0			0
$133$	1.62296			0.140728
$134$	2.16672	−	1.57422i	0.187176	−	0.135992i
$135$	−6.63407	−	20.4176i	−0.570970	−	1.75727i
$136$	−1.83668	+	5.65272i	−0.157494	+	0.484717i
$137$	−7.36247	−	5.34915i	−0.629019	−	0.457009i	0.227042	−	0.973885i	$-0.427095\pi$
$137$	−7.36247	−	5.34915i	−0.629019	−	0.457009i	−0.856060	+	0.516876i	$0.827095\pi$
$138$	2.08045	+	1.51154i	0.177100	+	0.128671i
$139$	4.02234	−	12.3795i	0.341171	−	1.05002i	−0.622431	−	0.782675i	$-0.713855\pi$
$139$	4.02234	−	12.3795i	0.341171	−	1.05002i	0.963602	−	0.267341i	$-0.0861450\pi$
$140$	0.809496	+	2.49137i	0.0684149	+	0.210559i
$141$	17.4996	−	12.7142i	1.47373	−	1.07073i
$142$	3.55358			0.298210
$143$		0			0
$144$	−9.87786			−0.823155
$145$	22.2946	−	16.1980i	1.85147	−	1.34517i
$146$	0.422316	+	1.29975i	0.0349511	+	0.107568i
$147$	−0.883423	+	2.71890i	−0.0728635	+	0.224251i
$148$	6.16994	+	4.48272i	0.507166	+	0.368477i
$149$	−2.54557	−	1.84947i	−0.208541	−	0.151514i	0.478612	−	0.878026i	$-0.341140\pi$
$149$	−2.54557	−	1.84947i	−0.208541	−	0.151514i	−0.687153	+	0.726512i	$0.741140\pi$
$150$	6.83715	−	21.0426i	0.558251	−	1.71812i
$151$	−0.885940	−	2.72664i	−0.0720968	−	0.221891i	0.908515	−	0.417853i	$-0.137217\pi$
$151$	−0.885940	−	2.72664i	−0.0720968	−	0.221891i	−0.980612	+	0.195962i	$0.937217\pi$
$152$	4.03572	−	2.93212i	0.327340	−	0.237827i
$153$	−10.0029			−0.808684
$154$		0			0
$155$	2.72484			0.218864
$156$	−3.61066	+	2.62330i	−0.289084	+	0.210032i
$157$	−6.64062	−	20.4377i	−0.529979	−	1.63111i	−0.754254	−	0.656582i	$-0.772001\pi$
$157$	−6.64062	−	20.4377i	−0.529979	−	1.63111i	0.224275	−	0.974526i	$-0.427999\pi$
$158$	−3.26544	+	10.0500i	−0.259784	+	0.799534i
$159$	25.0305	+	18.1857i	1.98505	+	1.44222i
$160$	11.2377	+	8.16468i	0.888420	+	0.645475i
$161$	0.249419	−	0.767632i	0.0196569	−	0.0604978i
$162$	−0.771349	−	2.37397i	−0.0606029	−	0.186517i
$163$	6.65210	−	4.83304i	0.521033	−	0.378553i	−0.295960	−	0.955200i	$-0.595639\pi$
$163$	6.65210	−	4.83304i	0.521033	−	0.378553i	0.816993	+	0.576648i	$0.195639\pi$
$164$	−1.61153			−0.125840
$165$		0			0
$166$	−17.9088			−1.38999
$167$	−17.5626	+	12.7600i	−1.35904	+	0.987397i	−0.360529	+	0.932748i	$0.617404\pi$
$167$	−17.5626	+	12.7600i	−1.35904	+	0.987397i	−0.998506	+	0.0546489i	$0.982596\pi$
$168$	2.71534	+	8.35696i	0.209493	+	0.644754i
$169$	−2.70632	+	8.32919i	−0.208178	+	0.640707i
$170$	−6.02565	−	4.37789i	−0.462146	−	0.335769i
$171$	6.79195	+	4.93464i	0.519393	+	0.377361i
$172$	0.721509	−	2.22058i	0.0550146	−	0.169317i
$173$	2.48624	+	7.65185i	0.189025	+	0.581760i	0.999994	−	0.00332915i	$-0.00105970\pi$
$173$	2.48624	+	7.65185i	0.189025	+	0.581760i	−0.810969	+	0.585089i	$0.801060\pi$
$174$	20.5527	−	14.9324i	1.55810	−	1.13203i
$175$	−6.94447			−0.524953
$176$		0			0
$177$	9.42449			0.708388
$178$	−4.00167	+	2.90739i	−0.299938	+	0.217918i
$179$	−1.11892	−	3.44369i	−0.0836322	−	0.257393i	0.900493	−	0.434871i	$-0.143206\pi$
$179$	−1.11892	−	3.44369i	−0.0836322	−	0.257393i	−0.984125	+	0.177478i	$0.943206\pi$
$180$	−4.18739	+	12.8875i	−0.312110	+	0.960575i
$181$	−12.7970	−	9.29753i	−0.951190	−	0.691080i	−0.000102207	−	1.00000i	$-0.500033\pi$
$181$	−12.7970	−	9.29753i	−0.951190	−	0.691080i	−0.951088	+	0.308920i	$0.900033\pi$
$182$	−1.85703	−	1.34921i	−0.137652	−	0.100010i
$183$	−0.951118	+	2.92724i	−0.0703087	+	0.216388i
$184$	−0.766628	−	2.35944i	−0.0565165	−	0.173940i
$185$	−28.1330	+	20.4398i	−2.06838	+	1.50276i
$186$	2.51195			0.184185
$187$		0			0
$188$	−5.73500			−0.418268
$189$	−5.02542	+	3.65118i	−0.365545	+	0.265584i
$190$	1.93170	+	5.94518i	0.140141	+	0.431308i
$191$	0.132593	−	0.408080i	0.00959411	−	0.0295276i	−0.946145	−	0.323744i	$-0.895058\pi$
$191$	0.132593	−	0.408080i	0.00959411	−	0.0295276i	0.955739	+	0.294216i	$0.0950585\pi$
$192$	19.1927	+	13.9443i	1.38511	+	1.00634i
$193$	−12.2767	−	8.91954i	−0.883696	−	0.642042i	0.0505310	−	0.998722i	$-0.483909\pi$
$193$	−12.2767	−	8.91954i	−0.883696	−	0.642042i	−0.934227	+	0.356680i	$0.883909\pi$
$194$	−2.22753	+	6.85564i	−0.159927	+	0.492206i
$195$	−6.28849	−	19.3540i	−0.450328	−	1.38597i
$196$	0.613206	−	0.445520i	0.0438004	−	0.0318229i
$197$	20.8082			1.48252			0.741262	−	0.671216i	$-0.234228\pi$
$197$	20.8082			1.48252			0.741262	+	0.671216i	$0.234228\pi$
$198$		0			0
$199$	8.44567			0.598698			0.299349	−	0.954144i	$-0.403231\pi$
$199$	8.44567			0.598698			0.299349	+	0.954144i	$0.403231\pi$
$200$	−17.2684	+	12.5462i	−1.22106	+	0.887153i
$201$	−2.12299	−	6.53389i	−0.149744	−	0.460865i
$202$	−5.31906	+	16.3704i	−0.374247	+	1.15182i
$203$	−6.45084	−	4.68681i	−0.452760	−	0.328950i
$204$	3.38991	+	2.46292i	0.237341	+	0.172439i
$205$	2.27068	−	6.98844i	0.158591	−	0.488094i
$206$	−3.06786	−	9.44190i	−0.213748	−	0.657849i
$207$	3.37779	−	2.45411i	0.234773	−	0.170573i
$208$	−3.93303			−0.272707
$209$		0			0
$210$	−11.0113			−0.759849
$211$	−7.97632	+	5.79513i	−0.549112	+	0.398953i	−0.827458	−	0.561528i	$-0.810214\pi$
$211$	−7.97632	+	5.79513i	−0.549112	+	0.398953i	0.278346	+	0.960481i	$0.410214\pi$
$212$	−2.53487	−	7.80154i	−0.174096	−	0.535812i
$213$	2.81688	−	8.66946i	0.193009	−	0.594022i
$214$	−3.16667	−	2.30072i	−0.216469	−	0.157274i
$215$	8.61295	+	6.25768i	0.587399	+	0.426770i
$216$	−5.90001	+	18.1584i	−0.401445	+	1.23552i
$217$	−0.243635	−	0.749832i	−0.0165390	−	0.0509019i
$218$	−3.49518	+	2.53940i	−0.236724	+	0.171990i
$219$	3.50570			0.236893
$220$		0			0
$221$	−3.98281			−0.267913
$222$	−25.9350	+	18.8429i	−1.74064	+	1.26465i
$223$	5.37562	+	16.5445i	0.359978	+	1.10790i	0.953066	+	0.302762i	$0.0979087\pi$
$223$	5.37562	+	16.5445i	0.359978	+	1.10790i	−0.593088	+	0.805138i	$0.702091\pi$
$224$	1.24199	−	3.82246i	0.0829842	−	0.255399i
$225$	−29.0620	−	21.1148i	−1.93747	−	1.40765i
$226$	9.60581	+	6.97903i	0.638969	+	0.464238i
$227$	3.90334	−	12.0133i	0.259074	−	0.797348i	−0.733926	−	0.679230i	$-0.762314\pi$
$227$	3.90334	−	12.0133i	0.259074	−	0.797348i	0.993000	−	0.118118i	$-0.0376861\pi$
$228$	−1.08674	−	3.34464i	−0.0719711	−	0.221504i
$229$	−3.69997	+	2.68819i	−0.244501	+	0.177640i	−0.703286	−	0.710907i	$-0.748285\pi$
$229$	−3.69997	+	2.68819i	−0.244501	+	0.177640i	0.458785	+	0.888547i	$0.348285\pi$
$230$	3.10883			0.204990
$231$		0			0
$232$	−24.5084			−1.60905
$233$	19.3006	−	14.0227i	1.26443	−	0.918659i	0.265460	−	0.964122i	$-0.414476\pi$
$233$	19.3006	−	14.0227i	1.26443	−	0.918659i	0.998966	+	0.0454624i	$0.0144761\pi$
$234$	−3.66921	−	11.2927i	−0.239864	−	0.738225i
$235$	8.08073	−	24.8699i	0.527129	−	1.62234i
$236$	−2.02152	−	1.46872i	−0.131590	−	0.0956054i
$237$	21.9299	+	15.9330i	1.42450	+	1.03496i
$238$	−0.665955	+	2.04960i	−0.0431675	+	0.132856i
$239$	−2.73114	−	8.40558i	−0.176663	−	0.543711i	0.823043	−	0.567979i	$-0.192275\pi$
$239$	−2.73114	−	8.40558i	−0.176663	−	0.543711i	−0.999705	+	0.0242677i	$0.992275\pi$
$240$	−15.2638	+	11.0898i	−0.985271	+	0.715841i
$241$	−18.9464			−1.22045			−0.610224	−	0.792229i	$-0.708921\pi$
$241$	−18.9464			−1.22045			−0.610224	+	0.792229i	$0.708921\pi$
$242$		0			0
$243$	12.2322			0.784696
$244$	0.660194	−	0.479659i	0.0422646	−	0.0307070i
$245$	1.06799	+	3.28693i	0.0682312	+	0.209994i
$246$	2.09328	−	6.44244i	0.133462	−	0.410755i
$247$	2.70433	+	1.96481i	0.172072	+	0.125018i
$248$	−1.96052	−	1.42440i	−0.124493	−	0.0904495i
$249$	−14.1961	+	43.6911i	−0.899640	+	2.76881i
$250$	−2.31438	−	7.12294i	−0.146374	−	0.450494i
$251$	2.31938	−	1.68513i	0.146398	−	0.106364i	−0.512175	−	0.858881i	$-0.671160\pi$
$251$	2.31938	−	1.68513i	0.146398	−	0.106364i	0.658573	+	0.752516i	$0.271160\pi$
$252$	3.92083			0.246989
$253$		0			0
$254$	21.6774			1.36016
$255$	−15.4569	+	11.2301i	−0.967950	+	0.703257i
$256$	−4.71199	−	14.5020i	−0.294500	−	0.906377i
$257$	6.92689	−	21.3188i	0.432087	−	1.32983i	−0.463955	−	0.885859i	$-0.653570\pi$
$257$	6.92689	−	21.3188i	0.432087	−	1.32983i	0.896042	−	0.443969i	$-0.146430\pi$
$258$	7.94003	+	5.76877i	0.494325	+	0.359148i
$259$	8.14014	+	5.91416i	0.505804	+	0.367488i
$260$	−1.66728	+	5.13136i	−0.103400	+	0.318234i
$261$	−12.7459	−	39.2278i	−0.788951	−	2.42814i
$262$	−4.60985	+	3.34925i	−0.284797	+	0.206917i
$263$	−0.990706			−0.0610895			−0.0305448	−	0.999533i	$-0.509724\pi$
$263$	−0.990706			−0.0610895			−0.0305448	+	0.999533i	$0.509724\pi$
$264$		0			0
$265$	37.4032			2.29766
$266$	1.46330	−	1.06315i	0.0897205	−	0.0651858i
$267$	3.92090	+	12.0673i	0.239955	+	0.738506i
$268$	−0.562873	+	1.73234i	−0.0343829	+	0.105820i
$269$	5.81713	+	4.22639i	0.354677	+	0.257688i	0.750828	−	0.660497i	$-0.229655\pi$
$269$	5.81713	+	4.22639i	0.354677	+	0.257688i	−0.396152	+	0.918185i	$0.629655\pi$
$270$	−19.3563	−	14.0632i	−1.17799	−	0.855858i
$271$	8.39423	−	25.8348i	0.509913	−	1.56935i	−0.282438	−	0.959285i	$-0.591143\pi$
$271$	8.39423	−	25.8348i	0.509913	−	1.56935i	0.792351	−	0.610065i	$-0.208857\pi$
$272$	1.14107	+	3.51185i	0.0691874	+	0.212937i
$273$	−4.76363	+	3.46098i	−0.288308	+	0.209468i
$274$	−10.1422			−0.612714
$275$		0			0
$276$	−1.74897			−0.105275
$277$	16.9777	−	12.3350i	1.02009	−	0.741140i	0.0537900	−	0.998552i	$-0.482870\pi$
$277$	16.9777	−	12.3350i	1.02009	−	0.741140i	0.966302	+	0.257412i	$0.0828698\pi$
$278$	−4.48277	−	13.7965i	−0.268859	−	0.827462i
$279$	1.26029	−	3.87876i	0.0754513	−	0.232215i
$280$	8.59403	+	6.24393i	0.513592	+	0.373146i
$281$	−22.7803	−	16.5509i	−1.35896	−	0.987341i	−0.998510	−	0.0545621i	$-0.982624\pi$
$281$	−22.7803	−	16.5509i	−1.35896	−	0.987341i	−0.360448	−	0.932779i	$-0.617376\pi$
$282$	7.44939	−	22.9269i	0.443605	−	1.36527i
$283$	8.09369	+	24.9098i	0.481120	+	1.48074i	0.837523	+	0.546403i	$0.184003\pi$
$283$	8.09369	+	24.9098i	0.481120	+	1.48074i	−0.356403	+	0.934332i	$0.615997\pi$
$284$	−1.95527	+	1.42058i	−0.116024	+	0.0842961i
$285$	16.0353			0.949851
$286$		0			0
$287$	−2.12613			−0.125502
$288$	16.8199	−	12.2204i	0.991123	−	0.720093i
$289$	−4.09778	−	12.6117i	−0.241046	−	0.741863i
$290$	9.49056	−	29.2089i	0.557305	−	1.71521i
$291$	14.9596	+	10.8688i	0.876945	+	0.637138i
$292$	−0.751959	−	0.546331i	−0.0440051	−	0.0319716i
$293$	1.37941	−	4.24538i	0.0805858	−	0.248017i	−0.902644	−	0.430388i	$-0.858377\pi$
$293$	1.37941	−	4.24538i	0.0805858	−	0.248017i	0.983230	+	0.182370i	$0.0583769\pi$
$294$	0.984546	+	3.03012i	0.0574199	+	0.176720i
$295$	9.21748	−	6.69689i	0.536663	−	0.389908i
$296$	30.9264			1.79756
$297$		0			0
$298$	−3.50667			−0.203136
$299$	1.34493	−	0.977145i	0.0777790	−	0.0565098i
$300$	4.65004	+	14.3114i	0.268470	+	0.826267i
$301$	0.951904	−	2.92966i	0.0548669	−	0.168863i
$302$	−2.58492	−	1.87805i	−0.148745	−	0.108070i
$303$	35.7215	+	25.9532i	2.05214	+	1.49097i
$304$	0.957688	−	2.94746i	0.0549271	−	0.169048i
$305$	1.14982	+	3.53879i	0.0658387	+	0.202631i
$306$	−9.01881	+	6.55255i	−0.515571	+	0.374584i
$307$	−12.8841			−0.735334			−0.367667	−	0.929957i	$-0.619843\pi$
$307$	−12.8841			−0.735334			−0.367667	+	0.929957i	$0.619843\pi$
$308$		0			0
$309$	−25.4667			−1.44875
$310$	2.45678	−	1.78495i	0.139536	−	0.101379i
$311$	8.28779	+	25.5072i	0.469957	+	1.44638i	0.852639	+	0.522500i	$0.175001\pi$
$311$	8.28779	+	25.5072i	0.469957	+	1.44638i	−0.382682	+	0.923880i	$0.624999\pi$
$312$	−5.59266	+	17.2124i	−0.316622	+	0.974463i
$313$	−2.90331	−	2.10938i	−0.164105	−	0.119229i	0.502702	−	0.864460i	$-0.332339\pi$
$313$	−2.90331	−	2.10938i	−0.164105	−	0.119229i	−0.666807	+	0.745231i	$0.732339\pi$
$314$	−19.3754	−	14.0771i	−1.09342	−	0.794415i
$315$	−5.52453	+	17.0027i	−0.311272	+	0.957996i
$316$	−2.22087	−	6.83513i	−0.124934	−	0.384506i
$317$	13.6870	−	9.94418i	0.768738	−	0.558521i	−0.132840	−	0.991138i	$-0.542410\pi$
$317$	13.6870	−	9.94418i	0.768738	−	0.558521i	0.901578	+	0.432617i	$0.142410\pi$
$318$	34.4809			1.93359
$319$		0			0
$320$	28.6798			1.60325
$321$	−8.12311	+	5.90178i	−0.453388	+	0.329405i
$322$	−0.277969	−	0.855500i	−0.0154906	−	0.0476751i
$323$	0.969808	−	2.98476i	0.0539616	−	0.166077i
$324$	1.37343	+	0.997859i	0.0763019	+	0.0554366i
$325$	−11.5715	−	8.40721i	−0.641873	−	0.466348i
$326$	2.83172	−	8.71515i	0.156835	−	0.482687i
$327$	3.42463	+	10.5399i	0.189383	+	0.582860i
$328$	−5.28693	+	3.84118i	−0.291922	+	0.212094i
$329$	−7.56632			−0.417145
$330$		0			0
$331$	−1.23826			−0.0680610			−0.0340305	−	0.999421i	$-0.510834\pi$
$331$	−1.23826			−0.0680610			−0.0340305	+	0.999421i	$0.510834\pi$
$332$	9.85385	−	7.15924i	0.540800	−	0.392914i
$333$	16.0837	+	49.5005i	0.881381	+	2.71261i
$334$	−7.47620	+	23.0094i	−0.409079	+	1.25902i
$335$	−6.71924	−	4.88181i	−0.367111	−	0.266722i
$336$	4.41650	+	3.20877i	0.240940	+	0.175053i
$337$	6.32885	−	19.4782i	0.344754	−	1.06104i	−0.616961	−	0.786994i	$-0.711636\pi$
$337$	6.32885	−	19.4782i	0.344754	−	1.06104i	0.961715	−	0.274051i	$-0.0883637\pi$
$338$	3.01610	+	9.28261i	0.164054	+	0.504907i
$339$	24.6407	−	17.9025i	1.33830	−	0.972332i
$340$	5.06556			0.274719
$341$		0			0
$342$	9.35630			0.505931
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−2.92583	−	9.00478i	−0.157750	−	0.485505i
$345$	2.46433	−	7.58443i	0.132675	−	0.408332i
$346$	7.25412	+	5.27043i	0.389984	+	0.283340i
$347$	22.0618	+	16.0288i	1.18434	+	0.860472i	0.992654	−	0.120985i	$-0.0386052\pi$
$347$	22.0618	+	16.0288i	1.18434	+	0.860472i	0.191684	+	0.981457i	$0.438605\pi$
$348$	−5.33920	+	16.4324i	−0.286211	+	0.880868i
$349$	−2.46730	−	7.59356i	−0.132071	−	0.406474i	0.863052	−	0.505116i	$-0.168550\pi$
$349$	−2.46730	−	7.59356i	−0.132071	−	0.406474i	−0.995123	+	0.0986418i	$0.968550\pi$
$350$	−6.26129	+	4.54910i	−0.334680	+	0.243159i
$351$	−12.7941			−0.682897
$352$		0			0
$353$	5.93472			0.315873			0.157937	−	0.987449i	$-0.449516\pi$
$353$	5.93472			0.315873			0.157937	+	0.987449i	$0.449516\pi$
$354$	8.49733	−	6.17367i	0.451628	−	0.328127i
$355$	−3.40538	−	10.4807i	−0.180739	−	0.556256i
$356$	1.03956	−	3.19942i	0.0550964	−	0.169569i
$357$	4.47239	+	3.24938i	0.236704	+	0.171976i
$358$	−3.26469	−	2.37194i	−0.172544	−	0.125361i
$359$	−8.78235	+	27.0293i	−0.463515	+	1.42655i	0.397326	+	0.917677i	$0.369938\pi$
$359$	−8.78235	+	27.0293i	−0.463515	+	1.42655i	−0.860841	+	0.508874i	$0.830062\pi$
$360$	16.9805	+	52.2606i	0.894951	+	2.75438i
$361$	13.2404	−	9.61969i	0.696862	−	0.506300i
$362$	−17.6285			−0.926535
$363$		0			0
$364$	1.56114			0.0818261
$365$	3.42870	−	2.49109i	0.179466	−	0.130390i
$366$	1.05999	+	3.26231i	0.0554065	+	0.170524i
$367$	−9.39456	+	28.9135i	−0.490392	+	1.50927i	0.333625	+	0.942706i	$0.391728\pi$
$367$	−9.39456	+	28.9135i	−0.490392	+	1.50927i	−0.824017	+	0.566565i	$0.808272\pi$
$368$	−1.24692	−	0.905939i	−0.0650001	−	0.0472253i
$369$	−8.89769	−	6.46455i	−0.463195	−	0.336531i
$370$	−11.9759	+	36.8580i	−0.622596	+	1.91615i
$371$	−3.34432	−	10.2928i	−0.173628	−	0.534373i
$372$	−1.38213	+	1.00418i	−0.0716603	+	0.0520643i
$373$	−14.4226			−0.746772			−0.373386	−	0.927676i	$-0.621803\pi$
$373$	−14.4226			−0.746772			−0.373386	+	0.927676i	$0.621803\pi$
$374$		0			0
$375$	−19.2120			−0.992103
$376$	−18.8147	+	13.6697i	−0.970296	+	0.704961i
$377$	−5.07499	−	15.6192i	−0.261375	−	0.804430i
$378$	−2.13926	+	6.58397i	−0.110032	+	0.338643i
$379$	18.1278	+	13.1706i	0.931163	+	0.676529i	0.946277	−	0.323356i	$-0.104811\pi$
$379$	18.1278	+	13.1706i	0.931163	+	0.676529i	−0.0151144	+	0.999886i	$0.504811\pi$
$380$	−3.43952	−	2.49896i	−0.176444	−	0.128194i
$381$	17.1834	−	52.8850i	0.880331	−	2.70938i
$382$	−0.147771	−	0.454792i	−0.00756061	−	0.0232692i
$383$	−27.2465	+	19.7957i	−1.39223	+	1.01152i	−0.396615	+	0.917985i	$0.629815\pi$
$383$	−27.2465	+	19.7957i	−1.39223	+	1.01152i	−0.995616	+	0.0935305i	$0.970185\pi$
$384$	3.45887			0.176510
$385$		0			0
$386$	−16.9118			−0.860790
$387$	12.8913	−	9.36610i	0.655303	−	0.476106i
$388$	−1.51498	−	4.66262i	−0.0769112	−	0.236708i
$389$	0.750241	−	2.30900i	0.0380387	−	0.117071i	−0.930234	−	0.366967i	$-0.880396\pi$
$389$	0.750241	−	2.30900i	0.0380387	−	0.117071i	0.968273	+	0.249896i	$0.0803963\pi$
$390$	−18.3480	−	13.3306i	−0.929087	−	0.675021i
$391$	−1.26270	−	0.917404i	−0.0638574	−	0.0463951i
$392$	0.949813	−	2.92322i	0.0479728	−	0.147645i
$393$	4.51680	+	13.9013i	0.227842	+	0.701227i
$394$	18.7611	−	13.6308i	0.945173	−	0.686708i
$395$	32.7699			1.64883
$396$		0			0
$397$	−5.89696			−0.295960			−0.147980	−	0.988990i	$-0.547277\pi$
$397$	−5.89696			−0.295960			−0.147980	+	0.988990i	$0.547277\pi$
$398$	7.61481	−	5.53248i	0.381696	−	0.277318i
$399$	−1.43376	−	4.41266i	−0.0717778	−	0.220909i
$400$	−4.09784	+	12.6119i	−0.204892	+	0.630593i
$401$	−9.09302	−	6.60646i	−0.454084	−	0.329911i	0.337122	−	0.941461i	$-0.390546\pi$
$401$	−9.09302	−	6.60646i	−0.454084	−	0.329911i	−0.791206	+	0.611550i	$0.790546\pi$
$402$	−6.19427	−	4.50040i	−0.308942	−	0.224460i
$403$	0.501804	−	1.54439i	0.0249966	−	0.0769317i
$404$	−3.61756	−	11.1337i	−0.179981	−	0.553923i
$405$	−6.26243	+	4.54992i	−0.311183	+	0.226087i
$406$	−8.88640			−0.441025
$407$		0			0
$408$	16.9917			0.841216
$409$	23.7320	−	17.2423i	1.17347	−	0.852578i	0.182052	−	0.983289i	$-0.441726\pi$
$409$	23.7320	−	17.2423i	1.17347	−	0.852578i	0.991421	+	0.130711i	$0.0417260\pi$
$410$	−2.53060	−	7.78839i	−0.124977	−	0.384641i
$411$	−8.03961	+	24.7434i	−0.396565	+	1.22050i
$412$	5.46251	+	3.96875i	0.269119	+	0.195526i
$413$	−2.66704	−	1.93771i	−0.131236	−	0.0953487i
$414$	1.43789	−	4.42536i	0.0706683	−	0.217495i
$415$	17.1619	+	52.8189i	0.842445	+	2.59278i
$416$	6.69713	−	4.86575i	0.328354	−	0.238563i
$417$	−37.2120			−1.82228
$418$		0			0
$419$	−20.2858			−0.991027			−0.495514	−	0.868600i	$-0.665020\pi$
$419$	−20.2858			−0.991027			−0.495514	+	0.868600i	$0.665020\pi$
$420$	6.05866	−	4.40187i	0.295632	−	0.214789i
$421$	−0.945600	−	2.91026i	−0.0460857	−	0.141837i	0.925366	−	0.379075i	$-0.123758\pi$
$421$	−0.945600	−	2.91026i	−0.0460857	−	0.141837i	−0.971452	+	0.237238i	$0.923758\pi$
$422$	−3.39542	+	10.4500i	−0.165287	+	0.508700i
$423$	−31.6644	−	23.0055i	−1.53958	−	1.11857i
$424$	−26.9116	−	19.5524i	−1.30694	−	0.949548i
$425$	−4.14971	+	12.7715i	−0.201290	+	0.619508i
$426$	−3.13932	−	9.66183i	−0.152100	−	0.468117i
$427$	0.871010	−	0.632826i	0.0421511	−	0.0306246i
$428$	2.66211			0.128678
$429$		0			0
$430$	11.8648			0.572173
$431$	6.10158	−	4.43306i	0.293903	−	0.213533i	−0.431056	−	0.902325i	$-0.641859\pi$
$431$	6.10158	−	4.43306i	0.293903	−	0.213533i	0.724959	+	0.688792i	$0.241859\pi$
$432$	3.66548	+	11.2812i	0.176355	+	0.542766i
$433$	−9.93848	+	30.5875i	−0.477613	+	1.46994i	0.364788	+	0.931091i	$0.381141\pi$
$433$	−9.93848	+	30.5875i	−0.477613	+	1.46994i	−0.842401	+	0.538851i	$0.818859\pi$
$434$	−0.710857	−	0.516468i	−0.0341222	−	0.0247912i
$435$	−63.7362	−	46.3071i	−3.05592	−	2.22025i
$436$	0.907980	−	2.79447i	0.0434844	−	0.133831i
$437$	0.404796	+	1.24584i	0.0193640	+	0.0595964i
$438$	3.16082	−	2.29647i	0.151030	−	0.109729i
$439$	4.66725			0.222756			0.111378	−	0.993778i	$-0.464474\pi$
$439$	4.66725			0.222756			0.111378	+	0.993778i	$0.464474\pi$
$440$		0			0
$441$	5.17284			0.246326
$442$	−3.59099	+	2.60901i	−0.170806	+	0.124098i
$443$	5.33893	+	16.4315i	0.253660	+	0.780686i	0.994091	+	0.108553i	$0.0346218\pi$
$443$	5.33893	+	16.4315i	0.253660	+	0.780686i	−0.740430	+	0.672133i	$0.765378\pi$
$444$	6.73739	−	20.7356i	0.319743	−	0.984066i
$445$	12.4096	+	9.01611i	0.588272	+	0.427404i
$446$	15.6845	+	11.3955i	0.742684	+	0.539591i
$447$	−2.77969	+	8.55501i	−0.131475	+	0.404638i
$448$	−2.56433	−	7.89221i	−0.121153	−	0.372872i
$449$	13.5430	−	9.83957i	0.639134	−	0.464358i	−0.220418	−	0.975405i	$-0.570742\pi$
$449$	13.5430	−	9.83957i	0.639134	−	0.464358i	0.859553	+	0.511047i	$0.170742\pi$
$450$	−40.0346			−1.88725
$451$		0			0
$452$	−8.07529			−0.379829
$453$	−6.63080	+	4.81756i	−0.311542	+	0.226349i
$454$	−4.35015	−	13.3884i	−0.204162	−	0.628347i
$455$	−2.19968	+	6.76992i	−0.103123	+	0.317379i
$456$	−11.5374	−	8.38241i	−0.540288	−	0.392542i
$457$	−17.5536	−	12.7534i	−0.821121	−	0.596580i	0.0959121	−	0.995390i	$-0.469423\pi$
$457$	−17.5536	−	12.7534i	−0.821121	−	0.596580i	−0.917033	+	0.398810i	$0.869423\pi$
$458$	−1.57503	+	4.84746i	−0.0735965	+	0.226507i
$459$	3.71187	+	11.4240i	0.173255	+	0.533224i
$460$	−1.71055	+	1.24279i	−0.0797549	+	0.0579453i
$461$	6.07778			0.283070			0.141535	−	0.989933i	$-0.454796\pi$
$461$	6.07778			0.283070			0.141535	+	0.989933i	$0.454796\pi$
$462$		0			0
$463$	−5.14719			−0.239210			−0.119605	−	0.992822i	$-0.538163\pi$
$463$	−5.14719			−0.239210			−0.119605	+	0.992822i	$0.538163\pi$
$464$	−12.3183	+	8.94975i	−0.571862	+	0.415482i
$465$	−2.40719	−	7.40856i	−0.111631	−	0.343564i
$466$	8.21605	−	25.2864i	0.380601	−	1.17137i
$467$	3.17076	+	2.30369i	0.146725	+	0.106602i	0.658726	−	0.752383i	$-0.271096\pi$
$467$	3.17076	+	2.30369i	0.146725	+	0.106602i	−0.512001	+	0.858985i	$0.671096\pi$
$468$	6.53325	+	4.74669i	0.302000	+	0.219416i
$469$	−0.742611	+	2.28552i	−0.0342906	+	0.105536i
$470$	−9.00570	−	27.7167i	−0.415402	−	1.27848i
$471$	−49.7016	+	36.1103i	−2.29013	+	1.66388i
$472$	−10.1327			−0.466397
$473$		0			0
$474$	30.2096			1.38757
$475$	9.11811	−	6.62469i	0.418368	−	0.303962i
$476$	−0.452925	−	1.39396i	−0.0207598	−	0.0638921i
$477$	17.2996	−	53.2428i	0.792096	−	2.43782i
$478$	−7.96867	−	5.78958i	−0.364478	−	0.264809i
$479$	−12.2266	−	8.88315i	−0.558648	−	0.405882i	0.272316	−	0.962208i	$-0.412210\pi$
$479$	−12.2266	−	8.88315i	−0.558648	−	0.405882i	−0.830964	+	0.556326i	$0.812210\pi$
$480$	12.2713	−	37.7671i	0.560104	−	1.72382i
$481$	6.40399	+	19.7095i	0.291997	+	0.898674i
$482$	−17.0825	+	12.4112i	−0.778088	+	0.565314i
$483$	−2.30745			−0.104993
$484$		0			0
$485$	22.3541			1.01505
$486$	11.0288	−	8.01291i	0.500278	−	0.363473i
$487$	7.74916	+	23.8495i	0.351148	+	1.08072i	0.958210	+	0.286067i	$0.0923480\pi$
$487$	7.74916	+	23.8495i	0.351148	+	1.08072i	−0.607062	+	0.794655i	$0.707652\pi$
$488$	1.02259	−	3.14722i	0.0462907	−	0.142468i
$489$	−19.0172	−	13.8168i	−0.859985	−	0.624816i
$490$	3.11608	+	2.26396i	0.140770	+	0.102275i
$491$	−11.5019	+	35.3991i	−0.519071	+	1.59754i	0.256679	+	0.966497i	$0.417372\pi$
$491$	−11.5019	+	35.3991i	−0.519071	+	1.59754i	−0.775750	+	0.631040i	$0.782628\pi$
$492$	1.42367	+	4.38159i	0.0641838	+	0.197538i
$493$	−12.4742	+	9.06302i	−0.561809	+	0.408178i
$494$	3.72536			0.167612
$495$		0			0
$496$	−1.50554			−0.0676006
$497$	−2.57963	+	1.87421i	−0.115712	+	0.0840698i
$498$	15.8211	+	48.6922i	0.708959	+	2.18195i
$499$	−9.83087	+	30.2563i	−0.440090	+	1.35446i	0.447689	+	0.894189i	$0.352247\pi$
$499$	−9.83087	+	30.2563i	−0.440090	+	1.35446i	−0.887780	+	0.460269i	$0.847753\pi$
$500$	4.12090	+	2.99401i	0.184292	+	0.133896i
$501$	50.2083	+	36.4785i	2.24314	+	1.62974i
$502$	0.987334	−	3.03870i	0.0440669	−	0.135624i
$503$	5.93493	+	18.2658i	0.264626	+	0.814434i	0.991779	+	0.127959i	$0.0408426\pi$
$503$	5.93493	+	18.2658i	0.264626	+	0.814434i	−0.727154	+	0.686474i	$0.759157\pi$
$504$	12.8630	−	9.34552i	0.572964	−	0.416283i
$505$	53.3788			2.37532
$506$		0			0
$507$	25.0370			1.11193
$508$	−11.9274	+	8.66577i	−0.529193	+	0.384481i
$509$	0.777328	+	2.39237i	0.0344545	+	0.106040i	0.966805	−	0.255516i	$-0.0822455\pi$
$509$	0.777328	+	2.39237i	0.0344545	+	0.106040i	−0.932350	+	0.361556i	$0.882246\pi$
$510$	−6.57984	+	20.2506i	−0.291360	+	0.896714i
$511$	−0.992078	−	0.720787i	−0.0438869	−	0.0318857i
$512$	−15.7059	−	11.4110i	−0.694109	−	0.504300i
$513$	3.11533	−	9.58801i	0.137545	−	0.423321i
$514$	−7.71978	−	23.7590i	−0.340505	−	1.04797i
$515$	−24.9073	+	18.0962i	−1.09755	+	0.797416i
$516$	−6.67492			−0.293847
$517$		0			0
$518$	11.2135			0.492693
$519$	18.6082	−	13.5196i	0.816809	−	0.593447i
$520$	6.76107	+	20.8084i	0.296493	+	0.912510i
$521$	4.60335	−	14.1677i	0.201677	−	0.620697i	−0.798157	−	0.602450i	$-0.794191\pi$
$521$	4.60335	−	14.1677i	0.201677	−	0.620697i	0.999834	−	0.0182471i	$-0.00580856\pi$
$522$	−37.1888	−	27.0193i	−1.62771	−	1.18260i
$523$	−8.01333	−	5.82203i	−0.350399	−	0.254579i	0.398638	−	0.917109i	$-0.369483\pi$
$523$	−8.01333	−	5.82203i	−0.350399	−	0.254579i	−0.749036	+	0.662529i	$0.769483\pi$
$524$	1.19755	−	3.68567i	0.0523151	−	0.161009i
$525$	6.13491	+	18.8813i	0.267749	+	0.824048i
$526$	−0.893242	+	0.648979i	−0.0389472	+	0.0282968i
$527$	−1.52459			−0.0664122
$528$		0			0
$529$	−22.3485			−0.971675
$530$	33.7236	−	24.5016i	1.46486	−	1.06428i
$531$	−5.26966	−	16.2183i	−0.228684	−	0.703816i
$532$	−0.380136	+	1.16994i	−0.0164810	+	0.0507232i
$533$	−3.54276	−	2.57397i	−0.153454	−	0.111491i
$534$	11.4401	+	8.31169i	0.495060	+	0.359682i
$535$	−3.75097	+	11.5443i	−0.162169	+	0.499104i
$536$	2.28253	+	7.02491i	0.0985904	+	0.303430i
$537$	−8.37456	+	6.08447i	−0.361389	+	0.262564i
$538$	8.01342			0.345483
$539$		0			0
$540$	16.2722			0.700245
$541$	−17.8052	+	12.9362i	−0.765503	+	0.556171i	−0.900593	−	0.434663i	$-0.856868\pi$
$541$	−17.8052	+	12.9362i	−0.765503	+	0.556171i	0.135090	+	0.990833i	$0.456868\pi$
$542$	−9.35508	−	28.7920i	−0.401835	−	1.23672i
$543$	−13.9739	+	43.0073i	−0.599678	+	1.84562i
$544$	−6.28768	−	4.56826i	−0.269582	−	0.195863i
$545$	10.8389	+	7.87494i	0.464289	+	0.337325i
$546$	−2.02782	+	6.24100i	−0.0867828	+	0.267090i
$547$	3.35724	+	10.3325i	0.143545	+	0.441787i	0.996821	−	0.0796728i	$-0.0253875\pi$
$547$	3.35724	+	10.3325i	0.143545	+	0.441787i	−0.853276	+	0.521460i	$0.825388\pi$
$548$	5.58049	−	4.05446i	0.238387	−	0.173198i
$549$	5.56922			0.237689
$550$		0			0
$551$	12.9410			0.551303
$552$	−5.73781	+	4.16876i	−0.244218	+	0.177434i
$553$	−2.93004	−	9.01775i	−0.124598	−	0.383474i
$554$	7.22721	−	22.2431i	0.307055	−	0.945018i
$555$	80.4270	+	58.4337i	3.41394	+	2.48037i
$556$	7.98184	+	5.79915i	0.338506	+	0.245939i
$557$	−10.3869	+	31.9675i	−0.440105	+	1.35451i	0.447658	+	0.894205i	$0.352258\pi$
$557$	−10.3869	+	31.9675i	−0.440105	+	1.35451i	−0.887763	+	0.460300i	$0.847742\pi$
$558$	−1.40455	−	4.32275i	−0.0594592	−	0.182997i
$559$	5.13290	−	3.72927i	0.217098	−	0.157731i
$560$	6.59959			0.278884
$561$		0			0
$562$	−31.3811			−1.32373
$563$	−1.66130	+	1.20701i	−0.0700155	+	0.0508693i	−0.622242	−	0.782825i	$-0.713778\pi$
$563$	−1.66130	+	1.20701i	−0.0700155	+	0.0508693i	0.552227	+	0.833694i	$0.313778\pi$
$564$	5.06643	+	15.5929i	0.213335	+	0.656578i
$565$	11.3782	−	35.0186i	0.478686	−	1.47324i
$566$	23.6151	+	17.1573i	0.992615	+	0.721177i
$567$	1.81200	+	1.31650i	0.0760971	+	0.0552877i
$568$	−3.02857	+	9.32098i	−0.127076	+	0.391099i
$569$	−1.01177	−	3.11391i	−0.0424156	−	0.130542i	0.927606	−	0.373559i	$-0.121863\pi$
$569$	−1.01177	−	3.11391i	−0.0424156	−	0.130542i	−0.970022	+	0.243017i	$0.921863\pi$
$570$	14.4578	−	10.5042i	0.605571	−	0.439973i
$571$	43.8897			1.83673			0.918363	−	0.395738i	$-0.129511\pi$
$571$	43.8897			1.83673			0.918363	+	0.395738i	$0.129511\pi$
$572$		0			0
$573$	−1.22666			−0.0512446
$574$	−1.91697	+	1.39276i	−0.0800128	+	0.0581327i
$575$	−1.73208	−	5.33080i	−0.0722328	−	0.222310i
$576$	13.2649	−	40.8251i	0.552704	−	1.70105i
$577$	35.5081	+	25.7981i	1.47822	+	1.07399i	0.978125	+	0.208020i	$0.0667019\pi$
$577$	35.5081	+	25.7981i	1.47822	+	1.07399i	0.500096	+	0.865970i	$0.333298\pi$
$578$	−11.9561	−	8.68664i	−0.497310	−	0.361317i
$579$	−13.4058	+	41.2588i	−0.557126	+	1.71466i
$580$	6.45466	+	19.8654i	0.268015	+	0.824866i
$581$	13.0004	−	9.44536i	0.539348	−	0.391859i
$582$	20.6076			0.854214
$583$		0			0
$584$	−3.76915			−0.155969
$585$	−29.7896	+	21.6434i	−1.23165	+	0.894844i
$586$	−1.53730	−	4.73133i	−0.0635054	−	0.195449i
$587$	0.862670	−	2.65503i	0.0356062	−	0.109585i	−0.931674	−	0.363296i	$-0.881651\pi$
$587$	0.862670	−	2.65503i	0.0356062	−	0.109585i	0.967280	+	0.253711i	$0.0816513\pi$
$588$	−1.75304	−	1.27366i	−0.0722943	−	0.0525249i
$589$	1.03520	+	0.752114i	0.0426545	+	0.0309903i
$590$	3.92378	−	12.0761i	0.161539	−	0.497167i
$591$	−18.3825	−	56.5754i	−0.756153	−	2.32720i
$592$	15.5441	−	11.2935i	0.638859	−	0.464158i
$593$	−23.2526			−0.954871			−0.477435	−	0.878667i	$-0.658434\pi$
$593$	−23.2526			−0.954871			−0.477435	+	0.878667i	$0.658434\pi$
$594$		0			0
$595$	6.68312			0.273981
$596$	1.92945	−	1.40183i	0.0790334	−	0.0574211i
$597$	−7.46111	−	22.9629i	−0.305363	−	0.939810i
$598$	0.572519	−	1.76203i	0.0234120	−	0.0720549i
$599$	−8.46187	−	6.14791i	−0.345743	−	0.251197i	0.401338	−	0.915930i	$-0.368545\pi$
$599$	−8.46187	−	6.14791i	−0.345743	−	0.251197i	−0.747081	+	0.664733i	$0.768545\pi$
$600$	49.3673	+	35.8674i	2.01541	+	1.46428i
$601$	−6.89406	+	21.2177i	−0.281215	+	0.865489i	0.706293	+	0.707919i	$0.250366\pi$
$601$	−6.89406	+	21.2177i	−0.281215	+	0.865489i	−0.987508	+	0.157570i	$0.949634\pi$
$602$	−1.06087	−	3.26501i	−0.0432376	−	0.133072i
$603$	−10.0569	+	7.30679i	−0.409550	+	0.297556i
$604$	2.17306			0.0884204
$605$		0			0
$606$	49.2083			1.99895
$607$	15.3619	−	11.1611i	0.623522	−	0.453015i	−0.230628	−	0.973042i	$-0.574078\pi$
$607$	15.3619	−	11.1611i	0.623522	−	0.453015i	0.854150	+	0.520027i	$0.174078\pi$
$608$	2.01571	+	6.20370i	0.0817477	+	0.251593i
$609$	−7.04413	+	21.6796i	−0.285443	+	0.878502i
$610$	3.35485	+	2.43744i	0.135834	+	0.0986892i
$611$	−12.6077	−	9.16004i	−0.510053	−	0.370576i
$612$	2.34291	−	7.21074i	0.0947066	−	0.291477i
$613$	−6.23030	−	19.1749i	−0.251639	−	0.774467i	−0.994473	−	0.104991i	$-0.966519\pi$
$613$	−6.23030	−	19.1749i	−0.251639	−	0.774467i	0.742834	−	0.669476i	$-0.233481\pi$
$614$	−11.6166	+	8.43995i	−0.468807	+	0.340608i
$615$	−21.0068			−0.847077
$616$		0			0
$617$	7.03919			0.283387			0.141694	−	0.989911i	$-0.454745\pi$
$617$	7.03919			0.283387			0.141694	+	0.989911i	$0.454745\pi$
$618$	−22.9614	+	16.6824i	−0.923641	+	0.671064i
$619$	−9.60520	−	29.5618i	−0.386066	−	1.18819i	−0.935704	−	0.352785i	$-0.885235\pi$
$619$	−9.60520	−	29.5618i	−0.386066	−	1.18819i	0.549639	−	0.835402i	$-0.314765\pi$
$620$	−0.638222	+	1.96425i	−0.0256316	+	0.0788860i
$621$	−4.05619	−	2.94700i	−0.162769	−	0.118259i
$622$	24.1814	+	17.5688i	0.969585	+	0.704445i
$623$	1.37151	−	4.22108i	0.0549484	−	0.169114i
$624$	3.47453	+	10.6935i	0.139093	+	0.428083i
$625$	9.30098	−	6.75756i	0.372039	−	0.270302i
$626$	−3.99947			−0.159851
$627$		0			0
$628$	16.2883			0.649973
$629$	15.7408	−	11.4364i	0.627628	−	0.455998i
$630$	6.15690	+	18.9490i	0.245297	+	0.754946i
$631$	6.78971	−	20.8966i	0.270294	−	0.831880i	−0.720132	−	0.693837i	$-0.755919\pi$
$631$	6.78971	−	20.8966i	0.270294	−	0.831880i	0.990426	−	0.138043i	$-0.0440812\pi$
$632$	−23.5779	−	17.1303i	−0.937879	−	0.681409i
$633$	22.8028	+	16.5672i	0.906331	+	0.658488i
$634$	5.82639	−	17.9318i	0.231396	−	0.712163i
$635$	−20.7733	−	63.9337i	−0.824364	−	2.53713i
$636$	−18.9722	+	13.7841i	−0.752298	+	0.546576i
$637$	2.05965			0.0816064
$638$		0			0
$639$	−16.4941			−0.652496
$640$	3.38290	−	2.45782i	0.133721	−	0.0971538i
$641$	−4.10713	−	12.6404i	−0.162222	−	0.499267i	0.836599	−	0.547816i	$-0.184540\pi$
$641$	−4.10713	−	12.6404i	−0.162222	−	0.499267i	−0.998821	+	0.0485485i	$0.984540\pi$
$642$	−3.45791	+	10.6424i	−0.136473	+	0.420020i
$643$	−11.8848	−	8.63480i	−0.468690	−	0.340523i	0.328241	−	0.944594i	$-0.393544\pi$
$643$	−11.8848	−	8.63480i	−0.468690	−	0.340523i	−0.796930	+	0.604071i	$0.793544\pi$
$644$	0.494940	+	0.359595i	0.0195034	+	0.0141700i
$645$	9.40510	−	28.9459i	0.370325	−	1.13974i
$646$	−1.08082	−	3.32642i	−0.0425242	−	0.130876i
$647$	4.97160	−	3.61208i	0.195454	−	0.142005i	−0.485754	−	0.874095i	$-0.661455\pi$
$647$	4.97160	−	3.61208i	0.195454	−	0.142005i	0.681208	+	0.732090i	$0.261455\pi$
$648$	6.88426			0.270439
$649$		0			0
$650$	−15.9404			−0.625236
$651$	−1.82348	+	1.32484i	−0.0714679	+	0.0519245i
$652$	1.92589	+	5.92729i	0.0754238	+	0.232131i
$653$	−12.5674	+	38.6786i	−0.491802	+	1.51361i	0.330079	+	0.943953i	$0.392924\pi$
$653$	−12.5674	+	38.6786i	−0.491802	+	1.51361i	−0.821882	+	0.569658i	$0.807076\pi$
$654$	9.99209	+	7.25968i	0.390722	+	0.283876i
$655$	14.2956	+	10.3864i	0.558576	+	0.405829i
$656$	−1.25460	+	3.86127i	−0.0489841	+	0.150757i
$657$	−1.96020	−	6.03286i	−0.0764745	−	0.235364i
$658$	−6.82196	+	4.95645i	−0.265948	+	0.193222i
$659$	−18.0090			−0.701531			−0.350765	−	0.936463i	$-0.614079\pi$
$659$	−18.0090			−0.701531			−0.350765	+	0.936463i	$0.614079\pi$
$660$		0			0
$661$	−17.1420			−0.666745			−0.333373	−	0.942795i	$-0.608187\pi$
$661$	−17.1420			−0.666745			−0.333373	+	0.942795i	$0.608187\pi$
$662$	−1.11644	+	0.811145i	−0.0433919	+	0.0315260i
$663$	3.51851	+	10.8289i	0.136647	+	0.420558i
$664$	15.2629	−	46.9744i	0.592316	−	1.82296i
$665$	−4.53784	−	3.29693i	−0.175970	−	0.127850i
$666$	46.9276	+	34.0949i	1.81841	+	1.32115i
$667$	1.98878	−	6.12085i	0.0770060	−	0.237000i
$668$	−5.08466	−	15.6490i	−0.196732	−	0.605478i
$669$	40.2338	−	29.2315i	1.55553	−	1.13016i
$670$	−9.25613			−0.357596
$671$		0			0
$672$	−11.4901			−0.443240
$673$	−18.7632	+	13.6322i	−0.723268	+	0.525485i	−0.887426	−	0.460949i	$-0.847509\pi$
$673$	−18.7632	+	13.6322i	−0.723268	+	0.525485i	0.164159	+	0.986434i	$0.447509\pi$
$674$	−7.05329	−	21.7078i	−0.271683	−	0.836153i
$675$	−13.3302	+	41.0261i	−0.513079	+	1.57910i
$676$	−5.37035	−	3.90179i	−0.206552	−	0.150069i
$677$	−22.3050	−	16.2056i	−0.857252	−	0.622830i	0.0698841	−	0.997555i	$-0.477737\pi$
$677$	−22.3050	−	16.2056i	−0.857252	−	0.622830i	−0.927136	+	0.374725i	$0.877737\pi$
$678$	10.4893	−	32.2826i	0.402838	−	1.23981i
$679$	−1.99874	−	6.15150i	−0.0767047	−	0.236073i
$680$	16.6185	−	12.0741i	0.637291	−	0.463019i
$681$	−36.1111			−1.38378
$682$		0			0
$683$	21.9351			0.839322			0.419661	−	0.907681i	$-0.362149\pi$
$683$	21.9351			0.839322			0.419661	+	0.907681i	$0.362149\pi$
$684$	−5.14806	+	3.74028i	−0.196841	+	0.143013i
$685$	9.71923	+	29.9127i	0.371353	+	1.14291i
$686$	0.344389	−	1.05992i	0.0131488	−	0.0404680i
$687$	10.5775	+	7.68503i	0.403558	+	0.293202i
$688$	−4.75885	−	3.45751i	−0.181430	−	0.131816i
$689$	6.88814	−	21.1995i	0.262417	−	0.807637i
$690$	−2.74641	−	8.45259i	−0.104554	−	0.321785i
$691$	20.7647	−	15.0865i	0.789928	−	0.573916i	−0.118014	−	0.993012i	$-0.537653\pi$
$691$	20.7647	−	15.0865i	0.789928	−	0.573916i	0.907942	+	0.419096i	$0.137653\pi$
$692$	−6.09830			−0.231823
$693$		0			0
$694$	30.3913			1.15364
$695$	−36.3947	+	26.4423i	−1.38053	+	1.00301i
$696$	21.6513	+	66.6357i	0.820689	+	2.52582i
$697$	−1.27048	+	3.91014i	−0.0481229	+	0.148107i
$698$	−7.19886	−	5.23028i	−0.272481	−	0.197969i
$699$	−55.1770	−	40.0884i	−2.08699	−	1.51628i
$700$	1.62656	−	5.00604i	0.0614782	−	0.189211i
$701$	5.69007	+	17.5122i	0.214911	+	0.661428i	0.999160	+	0.0409817i	$0.0130485\pi$
$701$	5.69007	+	17.5122i	0.214911	+	0.661428i	−0.784249	+	0.620446i	$0.786951\pi$
$702$	−11.5354	+	8.38097i	−0.435376	+	0.316319i
$703$	−16.3298			−0.615892
$704$		0			0
$705$	−74.7575			−2.81553
$706$	5.35087	−	3.88764i	0.201383	−	0.146313i
$707$	−4.77274	−	14.6890i	−0.179497	−	0.552436i
$708$	−2.20744	+	6.79380i	−0.0829607	+	0.255327i
$709$	−19.1430	−	13.9082i	−0.718930	−	0.522334i	0.167112	−	0.985938i	$-0.446556\pi$
$709$	−19.1430	−	13.9082i	−0.718930	−	0.522334i	−0.886042	+	0.463604i	$0.846556\pi$
$710$	−9.93591	−	7.21886i	−0.372888	−	0.270919i
$711$	15.1567	−	46.6474i	0.568419	−	1.74941i
$712$	−4.21556	−	12.9741i	−0.157985	−	0.486227i
$713$	0.514827	−	0.374044i	0.0192804	−	0.0140081i
$714$	6.16097			0.230569
$715$		0			0
$716$	2.74452			0.102568
$717$	−20.4411	+	14.8514i	−0.763389	+	0.554634i
$718$	9.78763	+	30.1232i	0.365271	+	1.12419i
$719$	3.43696	−	10.5779i	0.128177	−	0.394488i	−0.866289	−	0.499542i	$-0.833502\pi$
$719$	3.43696	−	10.5779i	0.128177	−	0.394488i	0.994467	+	0.105054i	$0.0335015\pi$
$720$	27.6187	+	20.0662i	1.02929	+	0.747823i
$721$	7.20682	+	5.23606i	0.268396	+	0.195001i
$722$	5.63627	−	17.3467i	0.209760	−	0.645576i
$723$	16.7377	+	51.5135i	0.622483	+	1.91581i
$724$	9.69964	−	7.04720i	0.360484	−	0.261907i
$725$	−55.3730			−2.05650
$726$		0			0
$727$	42.4803			1.57551			0.787753	−	0.615991i	$-0.211244\pi$
$727$	42.4803			1.57551			0.787753	+	0.615991i	$0.211244\pi$
$728$	5.12162	−	3.72107i	0.189820	−	0.137912i
$729$	−12.8826	−	39.6485i	−0.477133	−	1.46846i
$730$	1.45956	−	4.49205i	0.0540206	−	0.166258i
$731$	−4.81908	−	3.50127i	−0.178240	−	0.129499i
$732$	−1.88738	−	1.37126i	−0.0697594	−	0.0506832i
$733$	−6.85660	+	21.1025i	−0.253254	+	0.779437i	0.740914	+	0.671600i	$0.234393\pi$
$733$	−6.85660	+	21.1025i	−0.253254	+	0.779437i	−0.994169	+	0.107837i	$0.965607\pi$
$734$	10.4699	+	32.2231i	0.386452	+	1.18938i
$735$	7.99333	−	5.80749i	0.294838	−	0.214213i
$736$	3.24402			0.119576
$737$		0			0
$738$	−12.2571			−0.451189
$739$	23.8240	−	17.3092i	0.876381	−	0.636728i	−0.0559106	−	0.998436i	$-0.517806\pi$
$739$	23.8240	−	17.3092i	0.876381	−	0.636728i	0.932292	+	0.361708i	$0.117806\pi$
$740$	−8.14496	−	25.0676i	−0.299415	−	0.921504i
$741$	2.95305	−	9.08855i	0.108483	−	0.333876i
$742$	−9.75776	−	7.08943i	−0.358219	−	0.260261i
$743$	13.6772	+	9.93704i	0.501766	+	0.364555i	0.809691	−	0.586856i	$-0.199635\pi$
$743$	13.6772	+	9.93704i	0.501766	+	0.364555i	−0.307925	+	0.951411i	$0.599635\pi$
$744$	−2.14083	+	6.58879i	−0.0784866	+	0.241557i
$745$	3.36042	+	10.3423i	0.123116	+	0.378913i
$746$	−13.0037	+	9.44774i	−0.476099	+	0.345906i
$747$	83.1244			3.04136
$748$		0			0
$749$	3.51219			0.128333
$750$	−17.3220	+	12.5851i	−0.632508	+	0.459544i
$751$	−0.479429	−	1.47553i	−0.0174946	−	0.0538429i	0.941928	−	0.335815i	$-0.109012\pi$
$751$	−0.479429	−	1.47553i	−0.0174946	−	0.0538429i	−0.959423	+	0.281972i	$0.909012\pi$
$752$	−4.46479	+	13.7412i	−0.162814	+	0.501090i
$753$	−6.63069	−	4.81748i	−0.241636	−	0.175559i
$754$	−14.8074	−	10.7582i	−0.539252	−	0.391789i
$755$	−3.06188	+	9.42349i	−0.111433	+	0.342956i
$756$	−1.45494	−	4.47785i	−0.0529157	−	0.162858i
$757$	−10.1505	+	7.37474i	−0.368925	+	0.268040i	−0.756765	−	0.653687i	$-0.773221\pi$
$757$	−10.1505	+	7.37474i	−0.368925	+	0.268040i	0.387840	+	0.921727i	$0.373221\pi$
$758$	24.9721			0.907027
$759$		0			0
$760$	−17.2404			−0.625375
$761$	−7.30895	+	5.31026i	−0.264949	+	0.192497i	−0.712326	−	0.701849i	$-0.752358\pi$
$761$	−7.30895	+	5.31026i	−0.264949	+	0.192497i	0.447377	+	0.894346i	$0.352358\pi$
$762$	−19.1503	−	58.9386i	−0.693742	−	2.13512i
$763$	1.19792	−	3.68682i	0.0433676	−	0.133472i
$764$	0.263115	+	0.191164i	0.00951916	+	0.00691608i
$765$	27.9683	+	20.3201i	1.01120	+	0.734677i
$766$	−11.5985	+	35.6966i	−0.419072	+	1.28977i
$767$	−2.09820	−	6.45761i	−0.0757617	−	0.233171i
$768$	−35.2668	+	25.6229i	−1.27258	+	0.924585i
$769$	16.1383			0.581963			0.290981	−	0.956729i	$-0.406018\pi$
$769$	16.1383			0.581963			0.290981	+	0.956729i	$0.406018\pi$
$770$		0			0
$771$	−64.0829			−2.30789
$772$	9.30529	−	6.76069i	0.334905	−	0.243323i
$773$	−5.69007	−	17.5122i	−0.204657	−	0.629871i	−0.999727	−	0.0233530i	$-0.992566\pi$
$773$	−5.69007	−	17.5122i	−0.204657	−	0.629871i	0.795070	−	0.606518i	$-0.207434\pi$
$774$	5.48769	−	16.8894i	0.197251	−	0.607076i
$775$	−4.42950	−	3.21822i	−0.159112	−	0.115602i
$776$	−16.0838	−	11.6855i	−0.577374	−	0.419487i
$777$	8.88880	−	27.3569i	0.318884	−	0.981424i
$778$	−0.836118	−	2.57331i	−0.0299763	−	0.0922575i
$779$	2.79162	−	2.02823i	0.100020	−	0.0726689i
$780$	15.4246			0.552288
$781$		0			0
$782$	−1.73944			−0.0622022
$783$	−40.0711	+	29.1133i	−1.43202	+	1.04043i
$784$	−0.590087	−	1.81610i	−0.0210745	−	0.0648608i
$785$	−22.9505	+	70.6344i	−0.819139	+	2.52105i
$786$	13.1787	+	9.57490i	0.470069	+	0.341525i
$787$	38.0133	+	27.6183i	1.35503	+	0.984486i	0.998744	+	0.0501080i	$0.0159565\pi$
$787$	38.0133	+	27.6183i	1.35503	+	0.984486i	0.356284	+	0.934378i	$0.384043\pi$
$788$	−4.87378	+	14.9999i	−0.173621	+	0.534351i
$789$	0.875212	+	2.69363i	0.0311584	+	0.0958957i
$790$	29.5461	−	21.4665i	1.05120	−	0.763744i
$791$	−10.6539			−0.378810
$792$		0			0
$793$	2.21748			0.0787450
$794$	−5.31683	+	3.86291i	−0.188687	+	0.137089i
$795$	−33.0429	−	101.696i	−1.17191	−	3.60677i
$796$	−1.97818	+	6.08821i	−0.0701147	+	0.215791i
$797$	2.52781	+	1.83656i	0.0895395	+	0.0650543i	0.631654	−	0.775250i	$-0.282376\pi$
$797$	2.52781	+	1.83656i	0.0895395	+	0.0650543i	−0.542115	+	0.840304i	$0.682376\pi$
$798$	−4.18330	−	3.03935i	−0.148087	−	0.107592i
$799$	−4.52129	+	13.9151i	−0.159952	+	0.492281i
$800$	−8.62499	−	26.5450i	−0.304940	−	0.938507i
$801$	18.5739	−	13.4947i	0.656277	−	0.476813i
$802$	−12.5261			−0.442314
$803$		0			0
$804$	5.20732			0.183648
$805$	−2.25677	+	1.63964i	−0.0795408	+	0.0577897i
$806$	−0.559243	−	1.72117i	−0.0196985	−	0.0606258i
$807$	6.35214	−	19.5499i	0.223606	−	0.688188i
$808$	−38.4059	−	27.9036i	−1.35112	−	0.981643i
$809$	−26.4756	−	19.2357i	−0.930833	−	0.676290i	0.0153636	−	0.999882i	$-0.495109\pi$
$809$	−26.4756	−	19.2357i	−0.930833	−	0.676290i	−0.946197	+	0.323592i	$0.895109\pi$
$810$	−2.66584	+	8.20462i	−0.0936682	+	0.288281i
$811$	−10.0929	−	31.0627i	−0.354410	−	1.09076i	−0.956351	−	0.292220i	$-0.905606\pi$
$811$	−10.0929	−	31.0627i	−0.354410	−	1.09076i	0.601941	−	0.798540i	$-0.294394\pi$
$812$	4.88951	−	3.55243i	0.171588	−	0.124666i
$813$	−77.6578			−2.72358
$814$		0			0
$815$	−28.4174			−0.995419
$816$	8.54031	−	6.20490i	0.298970	−	0.217215i
$817$	1.54490	+	4.75472i	0.0540493	+	0.166347i
$818$	10.1024	−	31.0921i	0.353224	−	1.08711i
$819$	8.61947	+	6.26241i	0.301189	+	0.218826i
$820$	4.50589	+	3.27372i	0.157352	+	0.114323i
$821$	2.29644	−	7.06770i	0.0801461	−	0.246664i	−0.902953	−	0.429740i	$-0.858605\pi$
$821$	2.29644	−	7.06770i	0.0801461	−	0.246664i	0.983099	+	0.183075i	$0.0586053\pi$
$822$	8.95988	+	27.5757i	0.312512	+	0.961812i
$823$	−5.30607	+	3.85509i	−0.184958	+	0.134380i	−0.676411	−	0.736524i	$-0.736466\pi$
$823$	−5.30607	+	3.85509i	−0.184958	+	0.134380i	0.491453	+	0.870904i	$0.336466\pi$
$824$	27.3805			0.953846
$825$		0			0
$826$	−3.67399			−0.127835
$827$	19.2982	−	14.0209i	0.671063	−	0.487556i	−0.199318	−	0.979935i	$-0.563873\pi$
$827$	19.2982	−	14.0209i	0.671063	−	0.487556i	0.870381	+	0.492379i	$0.163873\pi$
$828$	0.977928	+	3.00975i	0.0339853	+	0.104596i
$829$	−8.07867	+	24.8636i	−0.280584	+	0.863549i	0.707104	+	0.707110i	$0.250001\pi$
$829$	−8.07867	+	24.8636i	−0.280584	+	0.863549i	−0.987688	+	0.156439i	$0.949999\pi$
$830$	50.0735	+	36.3805i	1.73808	+	1.26279i
$831$	−48.5362	−	35.2636i	−1.68370	−	1.22328i
$832$	5.28164	−	16.2552i	0.183108	−	0.563548i
$833$	−0.597555	−	1.83909i	−0.0207041	−	0.0637205i
$834$	−33.5512	+	24.3764i	−1.16178	+	0.844085i
$835$	75.0265			2.59640
$836$		0			0
$837$	−4.89747			−0.169281
$838$	−18.2901	+	13.2886i	−0.631823	+	0.459046i
$839$	10.5959	+	32.6107i	0.365810	+	1.12585i	0.949472	+	0.313851i	$0.101619\pi$
$839$	10.5959	+	32.6107i	0.365810	+	1.12585i	−0.583662	+	0.811997i	$0.698381\pi$
$840$	9.38443	−	28.8823i	0.323794	−	0.996535i
$841$	−27.9754	−	20.3253i	−0.964670	−	0.700874i
$842$	−2.75899	−	2.00452i	−0.0950810	−	0.0690804i
$843$	−24.8754	+	76.5587i	−0.856755	+	2.63682i
$844$	−2.30928	−	7.10722i	−0.0794885	−	0.244641i
$845$	24.4871	−	17.7909i	0.842383	−	0.612027i
$846$	−43.6195			−1.49967
$847$		0			0
$848$	−20.6661			−0.709678
$849$	60.5771	−	44.0118i	2.07900	−	1.51048i
$850$	4.62471	+	14.2334i	0.158626	+	0.488201i
$851$	−2.50959	+	7.72373i	−0.0860277	+	0.264766i
$852$	5.58975	+	4.06119i	0.191502	+	0.139134i
$853$	17.3002	+	12.5693i	0.592347	+	0.430365i	0.843154	−	0.537672i	$-0.180696\pi$
$853$	17.3002	+	12.5693i	0.592347	+	0.430365i	−0.250807	+	0.968037i	$0.580696\pi$
$854$	0.370779	−	1.14114i	0.0126878	−	0.0390490i
$855$	−8.96608	−	27.5948i	−0.306634	−	0.943721i
$856$	8.73356	−	6.34530i	0.298507	−	0.216878i
$857$	−42.8697			−1.46440			−0.732200	−	0.681090i	$-0.761506\pi$
$857$	−42.8697			−1.46440			−0.732200	+	0.681090i	$0.761506\pi$
$858$		0			0
$859$	−30.3915			−1.03695			−0.518473	−	0.855094i	$-0.673499\pi$
$859$	−30.3915			−1.03695			−0.518473	+	0.855094i	$0.673499\pi$
$860$	−6.52831	+	4.74310i	−0.222614	+	0.161738i
$861$	1.87828	+	5.78074i	0.0640115	+	0.197007i
$862$	2.59737	−	7.99389i	0.0884668	−	0.272273i
$863$	−9.56130	−	6.94669i	−0.325471	−	0.236468i	0.413036	−	0.910715i	$-0.364468\pi$
$863$	−9.56130	−	6.94669i	−0.325471	−	0.236468i	−0.738506	+	0.674247i	$0.764468\pi$
$864$	−20.1980	−	14.6747i	−0.687151	−	0.499244i
$865$	8.59263	−	26.4454i	0.292158	−	0.899170i
$866$	11.0761	+	34.0887i	0.376381	+	1.15838i
$867$	−30.6698	+	22.2829i	−1.04160	+	0.756766i
$868$	0.597594			0.0202837
$869$		0			0
$870$	−87.8003			−2.97671
$871$	−4.00434	+	2.90932i	−0.135682	+	0.0985786i
$872$	−3.68200	−	11.3320i	−0.124688	−	0.383750i
$873$	10.3392	−	31.8207i	0.349928	−	1.07697i
$874$	1.18108	+	0.858104i	0.0399506	+	0.0290258i
$875$	5.43680	+	3.95007i	0.183797	+	0.133537i
$876$	−0.821118	+	2.52714i	−0.0277430	+	0.0853842i
$877$	2.84446	+	8.75436i	0.0960507	+	0.295614i	0.987526	−	0.157455i	$-0.0503291\pi$
$877$	2.84446	+	8.75436i	0.0960507	+	0.295614i	−0.891475	+	0.453069i	$0.850329\pi$
$878$	4.20810	−	3.05736i	0.142016	−	0.103181i
$879$	−12.7613			−0.430429
$880$		0			0
$881$	−41.9030			−1.41175			−0.705874	−	0.708338i	$-0.749445\pi$
$881$	−41.9030			−1.41175			−0.705874	+	0.708338i	$0.749445\pi$
$882$	4.66395	−	3.38856i	0.157043	−	0.114099i
$883$	−4.95906	−	15.2624i	−0.166886	−	0.513621i	0.832285	−	0.554348i	$-0.187032\pi$
$883$	−4.95906	−	15.2624i	−0.166886	−	0.513621i	−0.999170	+	0.0407275i	$0.987032\pi$
$884$	0.932869	−	2.87108i	0.0313758	−	0.0965647i
$885$	−26.3511	−	19.1452i	−0.885783	−	0.643559i
$886$	15.5775	+	11.3177i	0.523335	+	0.380225i
$887$	10.4597	−	32.1917i	0.351203	−	1.08089i	−0.606976	−	0.794720i	$-0.707618\pi$
$887$	10.4597	−	32.1917i	0.351203	−	1.08089i	0.958179	−	0.286171i	$-0.0923825\pi$
$888$	−27.3211	−	84.0858i	−0.916838	−	2.82174i
$889$	−15.7361	+	11.4330i	−0.527772	+	0.383449i
$890$	17.0949			0.573024
$891$		0			0
$892$	−13.1855			−0.441482
$893$	9.93459	−	7.21790i	0.332448	−	0.241538i
$894$	3.09787	+	9.53427i	0.103608	+	0.318874i
$895$	−3.86708	+	11.9017i	−0.129262	+	0.397829i
$896$	−0.978825	−	0.711158i	−0.0327002	−	0.0237581i
$897$	−3.84490	−	2.79348i	−0.128377	−	0.0932716i
$898$	5.76510	−	17.7432i	0.192384	−	0.592097i
$899$	−1.94267	−	5.97892i	−0.0647916	−	0.199408i
$900$	22.0280	−	16.0043i	0.734266	−	0.533476i
$901$	−20.9277			−0.697202
$902$		0			0
$903$	−8.80638			−0.293058
$904$	−26.4925	+	19.2479i	−0.881127	+	0.640176i
$905$	16.8933	+	51.9923i	0.561553	+	1.72828i
$906$	−2.82266	+	8.68724i	−0.0937765	+	0.288614i
$907$	35.6787	+	25.9221i	1.18469	+	0.860730i	0.992693	−	0.120665i	$-0.0385027\pi$
$907$	35.6787	+	25.9221i	1.18469	+	0.860730i	0.192000	+	0.981395i	$0.438503\pi$
$908$	7.74570	+	5.62758i	0.257050	+	0.186758i
$909$	24.6886	−	75.9837i	0.818869	−	2.52022i
$910$	2.45147	+	7.54486i	0.0812655	+	0.250110i
$911$	−40.1075	+	29.1398i	−1.32882	+	0.965446i	−0.329045	+	0.944314i	$0.606727\pi$
$911$	−40.1075	+	29.1398i	−1.32882	+	0.965446i	−0.999777	+	0.0211316i	$0.993273\pi$
$912$	−8.85988			−0.293380
$913$		0			0
$914$	−24.1810			−0.799837
$915$	8.60584	−	6.25251i	0.284500	−	0.206702i
$916$	−1.07120	−	3.29682i	−0.0353935	−	0.108930i
$917$	1.57995	−	4.86260i	0.0521746	−	0.160577i
$918$	10.8302	+	7.86857i	0.357448	+	0.259701i
$919$	−33.0019	−	23.9773i	−1.08863	−	0.790939i	−0.109466	−	0.993991i	$-0.534914\pi$
$919$	−33.0019	−	23.9773i	−1.08863	−	0.790939i	−0.979168	+	0.203052i	$0.934914\pi$
$920$	−2.64953	+	8.15440i	−0.0873523	+	0.268843i
$921$	11.3821	+	35.0305i	0.375053	+	1.15430i
$922$	5.47986	−	3.98135i	0.180470	−	0.131119i
$923$	−6.56740			−0.216169
$924$		0			0
$925$	69.8737			2.29743
$926$	−4.64082	+	3.37176i	−0.152507	+	0.110803i
$927$	14.2396	+	43.8250i	0.467690	+	1.43940i
$928$	9.90326	−	30.4791i	0.325090	−	1.00053i
$929$	−33.4876	−	24.3301i	−1.09869	−	0.798246i	−0.117846	−	0.993032i	$-0.537599\pi$
$929$	−33.4876	−	24.3301i	−1.09869	−	0.798246i	−0.980846	+	0.194786i	$0.937599\pi$
$930$	−7.02348	−	5.10286i	−0.230309	−	0.167329i
$931$	−0.501522	+	1.54353i	−0.0164367	+	0.0505870i
$932$	5.58785	+	17.1976i	0.183036	+	0.563327i
$933$	62.0298	−	45.0673i	2.03077	−	1.47544i
$934$	4.36790			0.142922
$935$		0			0
$936$	32.7476			1.07039
$937$	1.29155	−	0.938364i	0.0421930	−	0.0306550i	−0.566489	−	0.824069i	$-0.691699\pi$
$937$	1.29155	−	0.938364i	0.0421930	−	0.0306550i	0.608682	+	0.793414i	$0.291699\pi$
$938$	0.827615	+	2.54714i	0.0270226	+	0.0831670i
$939$	−3.17033	+	9.75727i	−0.103460	+	0.318416i
$940$	16.0352	+	11.6503i	0.523011	+	0.379990i
$941$	5.75039	+	4.17790i	0.187457	+	0.136196i	0.677556	−	0.735471i	$-0.263039\pi$
$941$	5.75039	+	4.17790i	0.187457	+	0.136196i	−0.490099	+	0.871667i	$0.663039\pi$
$942$	−21.1574	+	65.1158i	−0.689345	+	2.12159i
$943$	−0.530297	−	1.63209i	−0.0172689	−	0.0531481i
$944$	−5.09287	+	3.70019i	−0.165759	+	0.120431i
$945$	21.4683			0.698364
$946$		0			0
$947$	−2.45986			−0.0799347			−0.0399674	−	0.999201i	$-0.512725\pi$
$947$	−2.45986			−0.0799347			−0.0399674	+	0.999201i	$0.512725\pi$
$948$	−16.6221	+	12.0766i	−0.539859	+	0.392231i
$949$	−0.780485	−	2.40209i	−0.0253356	−	0.0779750i
$950$	3.88147	−	11.9459i	0.125932	−	0.387578i
$951$	−39.1286	−	28.4286i	−1.26883	−	0.921861i
$952$	−4.80849	−	3.49357i	−0.155844	−	0.113227i
$953$	8.83790	−	27.2003i	0.286288	−	0.881103i	−0.699722	−	0.714415i	$-0.746693\pi$
$953$	8.83790	−	27.2003i	0.286288	−	0.881103i	0.986010	−	0.166688i	$-0.0533071\pi$
$954$	−19.2799	−	59.3373i	−0.624209	−	1.92112i
$955$	−1.19972	+	0.871648i	−0.0388221	+	0.0282059i
$956$	6.69900			0.216661
$957$		0			0
$958$	−16.8428			−0.544168
$959$	7.36247	−	5.34915i	0.237747	−	0.172733i
$960$	−25.3364	−	77.9774i	−0.817728	−	2.51671i
$961$	−9.38744	+	28.8916i	−0.302821	+	0.931986i
$962$	18.6850	+	13.5754i	0.602428	+	0.437690i
$963$	14.6982	+	10.6789i	0.473644	+	0.344122i
$964$	4.43771	−	13.6579i	0.142929	−	0.439890i
$965$	16.2065	+	49.8785i	0.521706	+	1.60565i
$966$	−2.08045	+	1.51154i	−0.0669374	+	0.0486329i
$967$	0.213338			0.00686047			0.00343024	−	0.999994i	$-0.498908\pi$
$967$	0.213338			0.00686047			0.00343024	+	0.999994i	$0.498908\pi$
$968$		0			0
$969$	−8.97201			−0.288223
$970$	20.1550	−	14.6435i	0.647138	−	0.470173i
$971$	−0.255927	−	0.787664i	−0.00821310	−	0.0252773i	0.946866	−	0.321628i	$-0.104230\pi$
$971$	−0.255927	−	0.787664i	−0.00821310	−	0.0252773i	−0.955079	+	0.296351i	$0.904230\pi$
$972$	−2.86507	+	8.81779i	−0.0918973	+	0.282831i
$973$	10.5306	+	7.65095i	0.337597	+	0.245278i
$974$	22.6098	+	16.4270i	0.724465	+	0.526354i
$975$	−12.6358	+	38.8890i	−0.404669	+	1.24544i
$976$	−0.635304	−	1.95526i	−0.0203356	−	0.0625865i
$977$	−7.89369	+	5.73510i	−0.252542	+	0.183482i	−0.706852	−	0.707361i	$-0.749886\pi$
$977$	−7.89369	+	5.73510i	−0.252542	+	0.183482i	0.454311	+	0.890843i	$0.349886\pi$
$978$	−26.1972			−0.837694
$979$		0			0
$980$	−2.61958			−0.0836795
$981$	16.2230	−	11.7867i	0.517961	−	0.376321i
$982$	12.8184	+	39.4511i	0.409052	+	1.25893i
$983$	13.9428	−	42.9114i	0.444705	−	1.36866i	−0.438101	−	0.898926i	$-0.644349\pi$
$983$	13.9428	−	42.9114i	0.444705	−	1.36866i	0.882807	−	0.469737i	$-0.155651\pi$
$984$	15.1144	+	10.9812i	0.481829	+	0.350069i
$985$	−58.1803	−	42.2704i	−1.85378	−	1.34685i
$986$	−5.31011	+	16.3428i	−0.169108	+	0.520462i
$987$	6.68426	+	20.5720i	0.212762	+	0.654815i
$988$	−2.04978	+	1.48926i	−0.0652123	+	0.0473795i
$989$	2.48632			0.0790604
$990$		0			0
$991$	53.5405			1.70077			0.850384	−	0.526162i	$-0.176369\pi$
$991$	53.5405			1.70077			0.850384	+	0.526162i	$0.176369\pi$
$992$	2.56361	−	1.86257i	0.0813947	−	0.0591367i
$993$	1.09391	+	3.36671i	0.0347142	+	0.106839i
$994$	−1.09812	+	3.37966i	−0.0348302	+	0.107196i
$995$	−23.6143	−	17.1568i	−0.748624	−	0.543907i
$996$	−28.1704	−	20.4670i	−0.892612	−	0.648521i
$997$	9.62918	−	29.6356i	0.304959	−	0.938568i	−0.674733	−	0.738062i	$-0.735741\pi$
$997$	9.62918	−	29.6356i	0.304959	−	0.938568i	0.979692	−	0.200506i	$-0.0642587\pi$
$998$	10.9562	+	33.7196i	0.346812	+	1.06738i
$999$	50.5646	−	36.7373i	1.59979	−	1.16232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.x.729.3		16
11.2	odd	10		847.2.a.p.1.6		8
11.3	even	5		847.2.f.v.148.2		16
11.4	even	5	inner	847.2.f.x.323.3		16
11.5	even	5		847.2.f.v.372.2		16
11.6	odd	10		847.2.f.w.372.3		16
11.7	odd	10		77.2.f.b.15.2	✓	16
11.8	odd	10		847.2.f.w.148.3		16
11.9	even	5		847.2.a.o.1.3		8
11.10	odd	2		77.2.f.b.36.2	yes	16
33.2	even	10		7623.2.a.ct.1.3		8
33.20	odd	10		7623.2.a.cw.1.6		8
33.29	even	10		693.2.m.i.631.3		16
33.32	even	2		693.2.m.i.190.3		16
77.10	even	6		539.2.q.f.520.2		32
77.13	even	10		5929.2.a.bt.1.6		8
77.18	odd	30		539.2.q.g.422.3		32
77.20	odd	10		5929.2.a.bs.1.3		8
77.32	odd	6		539.2.q.g.520.2		32
77.40	even	30		539.2.q.f.312.2		32
77.51	odd	30		539.2.q.g.312.2		32
77.54	even	6		539.2.q.f.410.3		32
77.62	even	10		539.2.f.e.246.2		16
77.65	odd	6		539.2.q.g.410.3		32
77.73	even	30		539.2.q.f.422.3		32
77.76	even	2		539.2.f.e.344.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.2	✓	16	11.7	odd	10
77.2.f.b.36.2	yes	16	11.10	odd	2
539.2.f.e.246.2		16	77.62	even	10
539.2.f.e.344.2		16	77.76	even	2
539.2.q.f.312.2		32	77.40	even	30
539.2.q.f.410.3		32	77.54	even	6
539.2.q.f.422.3		32	77.73	even	30
539.2.q.f.520.2		32	77.10	even	6
539.2.q.g.312.2		32	77.51	odd	30
539.2.q.g.410.3		32	77.65	odd	6
539.2.q.g.422.3		32	77.18	odd	30
539.2.q.g.520.2		32	77.32	odd	6
693.2.m.i.190.3		16	33.32	even	2
693.2.m.i.631.3		16	33.29	even	10
847.2.a.o.1.3		8	11.9	even	5
847.2.a.p.1.6		8	11.2	odd	10
847.2.f.v.148.2		16	11.3	even	5
847.2.f.v.372.2		16	11.5	even	5
847.2.f.w.148.3		16	11.8	odd	10
847.2.f.w.372.3		16	11.6	odd	10
847.2.f.x.323.3		16	11.4	even	5	inner
847.2.f.x.729.3		16	1.1	even	1	trivial
5929.2.a.bs.1.3		8	77.20	odd	10
5929.2.a.bt.1.6		8	77.13	even	10
7623.2.a.ct.1.3		8	33.2	even	10
7623.2.a.cw.1.6		8	33.20	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.901622 - 0.655067i) q^{2} +(-0.883423 - 2.71890i) q^{3} +(-0.234224 + 0.720867i) q^{4} +(-2.79603 - 2.03143i) q^{5} +(-2.57757 - 1.87272i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.949813 + 2.92322i) q^{8} +(-4.18492 + 3.04052i) q^{9} +O(q^{10})\)	\(q+(0.901622 - 0.655067i) q^{2} +(-0.883423 - 2.71890i) q^{3} +(-0.234224 + 0.720867i) q^{4} +(-2.79603 - 2.03143i) q^{5} +(-2.57757 - 1.87272i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.949813 + 2.92322i) q^{8} +(-4.18492 + 3.04052i) q^{9} -3.85168 q^{10} +2.16688 q^{12} +(-1.66629 + 1.21063i) q^{13} +(0.344389 + 1.05992i) q^{14} +(-3.05318 + 9.39672i) q^{15} +(1.54487 + 1.12241i) q^{16} +(1.56442 + 1.13662i) q^{17} +(-1.78147 + 5.48280i) q^{18} +(-0.501522 - 1.54353i) q^{19} +(2.11929 - 1.53975i) q^{20} +2.85882 q^{21} -0.807136 q^{23} +(7.10886 - 5.16489i) q^{24} +(2.14596 + 6.60459i) q^{25} +(-0.709322 + 2.18307i) q^{26} +(5.02542 + 3.65118i) q^{27} +(-0.613206 - 0.445520i) q^{28} +(-2.46400 + 7.58342i) q^{29} +(3.40267 + 10.4723i) q^{30} +(-0.637845 + 0.463421i) q^{31} -4.01918 q^{32} +2.15508 q^{34} +(2.79603 - 2.03143i) q^{35} +(-1.21160 - 3.72893i) q^{36} +(3.10926 - 9.56931i) q^{37} +(-1.46330 - 1.06315i) q^{38} +(4.76363 + 3.46098i) q^{39} +(3.28263 - 10.1029i) q^{40} +(0.657011 + 2.02207i) q^{41} +(2.57757 - 1.87272i) q^{42} -3.08043 q^{43} +17.8777 q^{45} +(-0.727732 + 0.528728i) q^{46} +(2.33812 + 7.19600i) q^{47} +(1.68695 - 5.19190i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(6.26129 + 4.54910i) q^{50} +(1.70830 - 5.25761i) q^{51} +(-0.482420 - 1.48474i) q^{52} +(-8.75554 + 6.36127i) q^{53} +6.92280 q^{54} -3.07366 q^{56} +(-3.75363 + 2.72717i) q^{57} +(2.74605 + 8.45147i) q^{58} +(-1.01872 + 3.13529i) q^{59} +(-6.05866 - 4.40187i) q^{60} +(-0.871010 - 0.632826i) q^{61} +(-0.271523 + 0.835662i) q^{62} +(-1.59850 - 4.91966i) q^{63} +(-6.71351 + 4.87765i) q^{64} +7.11832 q^{65} +2.40314 q^{67} +(-1.18577 + 0.861515i) q^{68} +(0.713042 + 2.19452i) q^{69} +(1.19024 - 3.66317i) q^{70} +(2.57963 + 1.87421i) q^{71} +(-12.8630 - 9.34552i) q^{72} +(-0.378940 + 1.16626i) q^{73} +(-3.46516 - 10.6647i) q^{74} +(16.0614 - 11.6693i) q^{75} +1.23015 q^{76} +6.56217 q^{78} +(-7.67096 + 5.57328i) q^{79} +(-2.03939 - 6.27659i) q^{80} +(0.692124 - 2.13014i) q^{81} +(1.91697 + 1.39276i) q^{82} +(-13.0004 - 9.44536i) q^{83} +(-0.669603 + 2.06083i) q^{84} +(-2.06520 - 6.35602i) q^{85} +(-2.77738 + 2.01789i) q^{86} +22.7953 q^{87} -4.43830 q^{89} +(16.1190 - 11.7111i) q^{90} +(-0.636468 - 1.95885i) q^{91} +(0.189050 - 0.581837i) q^{92} +(1.82348 + 1.32484i) q^{93} +(6.82196 + 4.95645i) q^{94} +(-1.73330 + 5.33455i) q^{95} +(3.55063 + 10.9277i) q^{96} +(-5.23278 + 3.80184i) q^{97} -1.11447 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

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