LMFDB - Embedded newform 847.2.f.q.323.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$0.453245 + 1.39494i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.q.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18661 - 0.862123i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.0467549 + 0.143897i) q^{4} +(-0.377594 + 0.274338i) q^{5} +(1.91998 - 1.39494i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.837913 + 2.57883i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})$	\(q+(-1.18661 - 0.862123i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.0467549 + 0.143897i) q^{4} +(-0.377594 + 0.274338i) q^{5} +(1.91998 - 1.39494i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.837913 + 2.57883i) q^{8} +(0.309017 + 0.224514i) q^{9} +0.684570 q^{10} -0.244812 q^{12} +(-1.28012 - 0.930062i) q^{13} +(0.453245 - 1.39494i) q^{14} +(-0.233366 - 0.718226i) q^{15} +(3.46236 - 2.51555i) q^{16} +(4.22899 - 3.07254i) q^{17} +(-0.173124 - 0.532822i) q^{18} +(-1.30464 + 4.01528i) q^{19} +(-0.0571308 - 0.0415079i) q^{20} -1.61803 q^{21} -1.80505 q^{23} +(-3.54946 - 2.57883i) q^{24} +(-1.47777 + 4.54811i) q^{25} +(0.717177 + 2.20724i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(-0.122406 + 0.0889332i) q^{28} +(-0.840363 - 2.58637i) q^{29} +(-0.342285 + 1.05345i) q^{30} +(-1.04675 - 0.760512i) q^{31} -0.854102 q^{32} -7.66708 q^{34} +(-0.377594 - 0.274338i) q^{35} +(-0.0178588 + 0.0549637i) q^{36} +(-0.600175 - 1.84715i) q^{37} +(5.00978 - 3.63982i) q^{38} +(2.07128 - 1.50487i) q^{39} +(-0.391081 - 1.20362i) q^{40} +(0.321724 - 0.990166i) q^{41} +(1.91998 + 1.39494i) q^{42} -8.70820 q^{43} -0.178276 q^{45} +(2.14190 + 1.55618i) q^{46} +(-1.97626 + 6.08229i) q^{47} +(2.13986 + 6.58580i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(5.67457 - 4.12281i) q^{50} +(2.61366 + 8.04402i) q^{51} +(0.0739811 - 0.227690i) q^{52} +(10.6826 + 7.76137i) q^{53} +8.02616 q^{54} -2.71154 q^{56} +(-5.52656 - 4.01528i) q^{57} +(-1.23259 + 3.79351i) q^{58} +(-2.65875 - 8.18278i) q^{59} +(0.0924396 - 0.0671613i) q^{60} +(-12.3295 + 8.95793i) q^{61} +(0.586436 + 1.80486i) q^{62} +(-0.118034 + 0.363271i) q^{63} +(-5.91123 - 4.29476i) q^{64} +0.738517 q^{65} -4.67583 q^{67} +(0.639856 + 0.464883i) q^{68} +(0.902527 - 2.77769i) q^{69} +(0.211544 + 0.651065i) q^{70} +(-7.88234 + 5.72685i) q^{71} +(-0.837913 + 0.608780i) q^{72} +(4.11611 + 12.6681i) q^{73} +(-0.880296 + 2.70927i) q^{74} +(-6.25993 - 4.54811i) q^{75} -0.638786 q^{76} -3.75519 q^{78} +(2.89815 + 2.10563i) q^{79} +(-0.617255 + 1.89971i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(-1.23541 + 0.897575i) q^{82} +(-13.9627 + 10.1445i) q^{83} +(-0.0756511 - 0.232830i) q^{84} +(-0.753927 + 2.32035i) q^{85} +(10.3333 + 7.50755i) q^{86} +4.40020 q^{87} -8.91982 q^{89} +(0.211544 + 0.153696i) q^{90} +(0.488963 - 1.50487i) q^{91} +(-0.0843952 - 0.259742i) q^{92} +(1.69369 - 1.23053i) q^{93} +(7.58873 - 5.51353i) q^{94} +(-0.608919 - 1.87406i) q^{95} +(0.427051 - 1.31433i) q^{96} +(2.18727 + 1.58915i) q^{97} +1.46673 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 - 3 * q^8 - 2 * q^9	\( 8 q + q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{8} - 2 q^{9} + 28 q^{10} - 14 q^{12} - 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} + 11 q^{17} - 4 q^{18} + 9 q^{19} + 21 q^{20} - 4 q^{21} - 16 q^{23} - 21 q^{24} + 5 q^{25} + 21 q^{26} - 22 q^{27} - 7 q^{28} + 9 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} - 2 q^{36} + 6 q^{37} + 35 q^{38} + 5 q^{39} + 16 q^{40} + 22 q^{41} - 3 q^{42} - 16 q^{43} + 18 q^{45} - 29 q^{46} + 7 q^{47} + 4 q^{48} - 2 q^{49} + 34 q^{50} - 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 18 q^{56} + 3 q^{57} - 39 q^{58} + 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + 8 q^{63} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} + 8 q^{69} - 2 q^{70} - 14 q^{71} - 3 q^{72} - 3 q^{73} + 9 q^{74} + 5 q^{75} + 52 q^{76} - 18 q^{78} + 9 q^{79} - 33 q^{80} - 28 q^{81} + 31 q^{82} - 23 q^{83} - 4 q^{84} + 10 q^{85} - 17 q^{86} - 12 q^{87} - 34 q^{89} - 2 q^{90} + 5 q^{91} - 34 q^{92} + 8 q^{93} + 30 q^{94} - 24 q^{95} - 10 q^{96} + 30 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 - 3 * q^8 - 2 * q^9 + 28 * q^10 - 14 * q^12 - 5 * q^13 + q^14 + 6 * q^15 - 3 * q^16 + 11 * q^17 - 4 * q^18 + 9 * q^19 + 21 * q^20 - 4 * q^21 - 16 * q^23 - 21 * q^24 + 5 * q^25 + 21 * q^26 - 22 * q^27 - 7 * q^28 + 9 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 - 2 * q^36 + 6 * q^37 + 35 * q^38 + 5 * q^39 + 16 * q^40 + 22 * q^41 - 3 * q^42 - 16 * q^43 + 18 * q^45 - 29 * q^46 + 7 * q^47 + 4 * q^48 - 2 * q^49 + 34 * q^50 - 3 * q^51 - 21 * q^52 + 2 * q^53 - 4 * q^54 - 18 * q^56 + 3 * q^57 - 39 * q^58 + 25 * q^59 - 38 * q^60 - 7 * q^61 + 5 * q^62 + 8 * q^63 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 + 8 * q^69 - 2 * q^70 - 14 * q^71 - 3 * q^72 - 3 * q^73 + 9 * q^74 + 5 * q^75 + 52 * q^76 - 18 * q^78 + 9 * q^79 - 33 * q^80 - 28 * q^81 + 31 * q^82 - 23 * q^83 - 4 * q^84 + 10 * q^85 - 17 * q^86 - 12 * q^87 - 34 * q^89 - 2 * q^90 + 5 * q^91 - 34 * q^92 + 8 * q^93 + 30 * q^94 - 24 * q^95 - 10 * q^96 + 30 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.18661	−	0.862123i	−0.839061	−	0.609613i	0.0830475	−	0.996546i	$-0.473535\pi$
$2$	−1.18661	−	0.862123i	−0.839061	−	0.609613i	−0.922108	+	0.386932i	$0.873535\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	0.696598	+	0.717462i	$0.254696\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	−0.985273	+	0.170989i	$0.945304\pi$
$4$	0.0467549	+	0.143897i	0.0233775	+	0.0719485i
$5$	−0.377594	+	0.274338i	−0.168865	+	0.122688i	−0.669008	−	0.743255i	$-0.733281\pi$
$5$	−0.377594	+	0.274338i	−0.168865	+	0.122688i	0.500143	+	0.865943i	$0.333281\pi$
$6$	1.91998	−	1.39494i	0.783827	−	0.569484i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.837913	+	2.57883i	−0.296247	+	0.911755i
$9$	0.309017	+	0.224514i	0.103006	+	0.0748380i
$10$	0.684570			0.216480
$11$		0			0
$11$		0			0
$12$	−0.244812			−0.0706712
$13$	−1.28012	−	0.930062i	−0.355042	−	0.257953i	0.395939	−	0.918277i	$-0.370419\pi$
$13$	−1.28012	−	0.930062i	−0.355042	−	0.257953i	−0.750981	+	0.660324i	$0.770419\pi$
$14$	0.453245	−	1.39494i	0.121135	−	0.372815i
$15$	−0.233366	−	0.718226i	−0.0602548	−	0.185445i
$16$	3.46236	−	2.51555i	0.865590	−	0.628888i
$17$	4.22899	−	3.07254i	1.02568	−	0.745201i	0.0582418	−	0.998303i	$-0.481451\pi$
$17$	4.22899	−	3.07254i	1.02568	−	0.745201i	0.967440	+	0.253101i	$0.0814505\pi$
$18$	−0.173124	−	0.532822i	−0.0408058	−	0.125587i
$19$	−1.30464	+	4.01528i	−0.299306	+	0.921169i	0.682435	+	0.730946i	$0.260921\pi$
$19$	−1.30464	+	4.01528i	−0.299306	+	0.921169i	−0.981741	+	0.190223i	$0.939079\pi$
$20$	−0.0571308	−	0.0415079i	−0.0127748	−	0.00928146i
$21$	−1.61803			−0.353084
$22$		0			0
$23$	−1.80505			−0.376380			−0.188190	−	0.982133i	$-0.560262\pi$
$23$	−1.80505			−0.376380			−0.188190	+	0.982133i	$0.560262\pi$
$24$	−3.54946	−	2.57883i	−0.724530	−	0.526402i
$25$	−1.47777	+	4.54811i	−0.295554	+	0.909621i
$26$	0.717177	+	2.20724i	0.140650	+	0.432876i
$27$	−4.42705	+	3.21644i	−0.851986	+	0.619004i
$28$	−0.122406	+	0.0889332i	−0.0231326	+	0.0168068i
$29$	−0.840363	−	2.58637i	−0.156051	−	0.480277i	0.842215	−	0.539143i	$-0.181252\pi$
$29$	−0.840363	−	2.58637i	−0.156051	−	0.480277i	−0.998266	+	0.0588657i	$0.981252\pi$
$30$	−0.342285	+	1.05345i	−0.0624924	+	0.192332i
$31$	−1.04675	−	0.760512i	−0.188003	−	0.136592i	0.489803	−	0.871833i	$-0.337069\pi$
$31$	−1.04675	−	0.760512i	−0.188003	−	0.136592i	−0.677805	+	0.735241i	$0.737069\pi$
$32$	−0.854102			−0.150985
$33$		0			0
$34$	−7.66708			−1.31489
$35$	−0.377594	−	0.274338i	−0.0638250	−	0.0463716i
$36$	−0.0178588	+	0.0549637i	−0.00297647	+	0.00916062i
$37$	−0.600175	−	1.84715i	−0.0986682	−	0.303669i	0.889524	−	0.456888i	$-0.151036\pi$
$37$	−0.600175	−	1.84715i	−0.0986682	−	0.303669i	−0.988192	+	0.153219i	$0.951036\pi$
$38$	5.00978	−	3.63982i	0.812693	−	0.590456i
$39$	2.07128	−	1.50487i	0.331670	−	0.240972i
$40$	−0.391081	−	1.20362i	−0.0618353	−	0.190309i
$41$	0.321724	−	0.990166i	0.0502449	−	0.154638i	−0.922786	−	0.385313i	$-0.874093\pi$
$41$	0.321724	−	0.990166i	0.0502449	−	0.154638i	0.973031	+	0.230675i	$0.0740935\pi$
$42$	1.91998	+	1.39494i	0.296259	+	0.215245i
$43$	−8.70820			−1.32799			−0.663994	−	0.747738i	$-0.731140\pi$
$43$	−8.70820			−1.32799			−0.663994	+	0.747738i	$0.731140\pi$
$44$		0			0
$45$	−0.178276			−0.0265758
$46$	2.14190	+	1.55618i	0.315805	+	0.229446i
$47$	−1.97626	+	6.08229i	−0.288266	+	0.887193i	0.697134	+	0.716941i	$0.254458\pi$
$47$	−1.97626	+	6.08229i	−0.288266	+	0.887193i	−0.985401	+	0.170252i	$0.945542\pi$
$48$	2.13986	+	6.58580i	0.308862	+	0.950578i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	5.67457	−	4.12281i	0.802505	−	0.583054i
$51$	2.61366	+	8.04402i	0.365986	+	1.12639i
$52$	0.0739811	−	0.227690i	0.0102593	−	0.0315750i
$53$	10.6826	+	7.76137i	1.46737	+	1.06611i	0.981366	+	0.192149i	$0.0615458\pi$
$53$	10.6826	+	7.76137i	1.46737	+	1.06611i	0.486004	+	0.873957i	$0.338454\pi$
$54$	8.02616			1.09222
$55$		0			0
$56$	−2.71154			−0.362345
$57$	−5.52656	−	4.01528i	−0.732011	−	0.531837i
$58$	−1.23259	+	3.79351i	−0.161847	+	0.498112i
$59$	−2.65875	−	8.18278i	−0.346139	−	1.06531i	−0.960971	−	0.276649i	$-0.910776\pi$
$59$	−2.65875	−	8.18278i	−0.346139	−	1.06531i	0.614832	−	0.788658i	$-0.289224\pi$
$60$	0.0924396	−	0.0671613i	0.0119339	−	0.00867048i
$61$	−12.3295	+	8.95793i	−1.57864	+	1.14695i	−0.660399	+	0.750915i	$0.729613\pi$
$61$	−12.3295	+	8.95793i	−1.57864	+	1.14695i	−0.918237	+	0.396031i	$0.870387\pi$
$62$	0.586436	+	1.80486i	0.0744774	+	0.229218i
$63$	−0.118034	+	0.363271i	−0.0148709	+	0.0457679i
$64$	−5.91123	−	4.29476i	−0.738904	−	0.536845i
$65$	0.738517			0.0916018
$66$		0			0
$67$	−4.67583			−0.571243			−0.285622	−	0.958342i	$-0.592200\pi$
$67$	−4.67583			−0.571243			−0.285622	+	0.958342i	$0.592200\pi$
$68$	0.639856	+	0.464883i	0.0775939	+	0.0563753i
$69$	0.902527	−	2.77769i	0.108651	−	0.334395i
$70$	0.211544	+	0.651065i	0.0252843	+	0.0778172i
$71$	−7.88234	+	5.72685i	−0.935461	+	0.679652i	−0.947324	−	0.320277i	$-0.896224\pi$
$71$	−7.88234	+	5.72685i	−0.935461	+	0.679652i	0.0118626	+	0.999930i	$0.496224\pi$
$72$	−0.837913	+	0.608780i	−0.0987490	+	0.0717454i
$73$	4.11611	+	12.6681i	0.481754	+	1.48269i	0.836627	+	0.547773i	$0.184524\pi$
$73$	4.11611	+	12.6681i	0.481754	+	1.48269i	−0.354873	+	0.934915i	$0.615476\pi$
$74$	−0.880296	+	2.70927i	−0.102332	+	0.314947i
$75$	−6.25993	−	4.54811i	−0.722835	−	0.525170i
$76$	−0.638786			−0.0732737
$77$		0			0
$78$	−3.75519			−0.425191
$79$	2.89815	+	2.10563i	0.326068	+	0.236902i	0.738760	−	0.673968i	$-0.235412\pi$
$79$	2.89815	+	2.10563i	0.326068	+	0.236902i	−0.412692	+	0.910870i	$0.635412\pi$
$80$	−0.617255	+	1.89971i	−0.0690112	+	0.212395i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	−1.23541	+	0.897575i	−0.136428	+	0.0991206i
$83$	−13.9627	+	10.1445i	−1.53261	+	1.11351i	−0.577842	+	0.816148i	$0.696105\pi$
$83$	−13.9627	+	10.1445i	−1.53261	+	1.11351i	−0.954766	+	0.297357i	$0.903895\pi$
$84$	−0.0756511	−	0.232830i	−0.00825421	−	0.0254038i
$85$	−0.753927	+	2.32035i	−0.0817748	+	0.251677i
$86$	10.3333	+	7.50755i	1.11426	+	0.809559i
$87$	4.40020			0.471750
$88$		0			0
$89$	−8.91982			−0.945499			−0.472750	−	0.881197i	$-0.656738\pi$
$89$	−8.91982			−0.945499			−0.472750	+	0.881197i	$0.656738\pi$
$90$	0.211544	+	0.153696i	0.0222987	+	0.0162009i
$91$	0.488963	−	1.50487i	0.0512572	−	0.157753i
$92$	−0.0843952	−	0.259742i	−0.00879881	−	0.0270799i
$93$	1.69369	−	1.23053i	0.175627	−	0.127600i
$94$	7.58873	−	5.51353i	0.782718	−	0.568678i
$95$	−0.608919	−	1.87406i	−0.0624738	−	0.192275i
$96$	0.427051	−	1.31433i	0.0435857	−	0.134143i
$97$	2.18727	+	1.58915i	0.222084	+	0.161353i	0.693264	−	0.720684i	$-0.256172\pi$
$97$	2.18727	+	1.58915i	0.222084	+	0.161353i	−0.471180	+	0.882037i	$0.656172\pi$
$98$	1.46673			0.148162
$99$		0			0
$100$	−0.723551			−0.0723551
$101$	0.144637	+	0.105085i	0.0143919	+	0.0104563i	0.594958	−	0.803757i	$-0.297169\pi$
$101$	0.144637	+	0.105085i	0.0143919	+	0.0104563i	−0.580566	+	0.814213i	$0.697169\pi$
$102$	3.83354	−	11.7984i	0.379577	−	1.16822i
$103$	5.21535	+	16.0512i	0.513884	+	1.58157i	0.785304	+	0.619111i	$0.212507\pi$
$103$	5.21535	+	16.0512i	0.513884	+	1.58157i	−0.271420	+	0.962461i	$0.587493\pi$
$104$	3.47110	−	2.52190i	0.340370	−	0.247293i
$105$	0.610960	−	0.443888i	0.0596236	−	0.0433191i
$106$	−5.98484	−	18.4195i	−0.581299	−	1.78906i
$107$	4.78241	−	14.7188i	0.462333	−	1.42292i	−0.399972	−	0.916527i	$-0.630980\pi$
$107$	4.78241	−	14.7188i	0.462333	−	1.42292i	0.862305	−	0.506389i	$-0.169020\pi$
$108$	−0.669822	−	0.486655i	−0.0644537	−	0.0468284i
$109$	−11.0349			−1.05695			−0.528476	−	0.848948i	$-0.677236\pi$
$109$	−11.0349			−1.05695			−0.528476	+	0.848948i	$0.677236\pi$
$110$		0			0
$111$	3.14256			0.298278
$112$	3.46236	+	2.51555i	0.327162	+	0.237697i
$113$	0.546984	−	1.68344i	0.0514559	−	0.158365i	−0.922027	−	0.387127i	$-0.873468\pi$
$113$	0.546984	−	1.68344i	0.0514559	−	0.158365i	0.973482	+	0.228762i	$0.0734676\pi$
$114$	3.09621	+	9.52916i	0.289987	+	0.892488i
$115$	0.681577	−	0.495195i	0.0635574	−	0.0461772i
$116$	0.332880	−	0.241851i	0.0309071	−	0.0224553i
$117$	−0.186767	−	0.574810i	−0.0172666	−	0.0531412i
$118$	−3.89967	+	12.0019i	−0.358994	+	1.10487i
$119$	4.22899	+	3.07254i	0.387671	+	0.281660i
$120$	2.04773			0.186931
$121$		0			0
$122$	22.3532			2.02376
$123$	1.36285	+	0.990166i	0.122884	+	0.0892802i
$124$	0.0604944	−	0.186183i	0.00543255	−	0.0167197i
$125$	−1.41086	−	4.34219i	−0.126191	−	0.388377i
$126$	0.453245	−	0.329302i	0.0403783	−	0.0293365i
$127$	−6.90919	+	5.01982i	−0.613092	+	0.445437i	−0.850502	−	0.525972i	$-0.823702\pi$
$127$	−6.90919	+	5.01982i	−0.613092	+	0.445437i	0.237410	+	0.971410i	$0.423702\pi$
$128$	3.83958	+	11.8170i	0.339374	+	1.04449i
$129$	4.35410	−	13.4005i	0.383357	−	1.17985i
$130$	−0.876333	−	0.636693i	−0.0768595	−	0.0558417i
$131$	9.66708			0.844617			0.422308	−	0.906452i	$-0.361220\pi$
$131$	9.66708			0.844617			0.422308	+	0.906452i	$0.361220\pi$
$132$		0			0
$133$	−4.22192			−0.366087
$134$	5.54839	+	4.03114i	0.479308	+	0.348237i
$135$	0.789236	−	2.42902i	0.0679266	−	0.209057i
$136$	4.38004	+	13.4804i	0.375586	+	1.15593i
$137$	11.3350	−	8.23535i	0.968413	−	0.703593i	0.0133236	−	0.999911i	$-0.495759\pi$
$137$	11.3350	−	8.23535i	0.968413	−	0.703593i	0.955089	+	0.296318i	$0.0957589\pi$
$138$	−3.46566	+	2.51795i	−0.295017	+	0.214342i
$139$	−2.95966	−	9.10889i	−0.251035	−	0.772606i	−0.994585	−	0.103926i	$-0.966860\pi$
$139$	−2.95966	−	9.10889i	−0.251035	−	0.772606i	0.743550	−	0.668680i	$-0.233140\pi$
$140$	0.0218220	−	0.0671613i	0.00184430	−	0.00567616i
$141$	−8.37155	−	6.08229i	−0.705012	−	0.512221i
$142$	14.2905			1.19923
$143$		0			0
$144$	1.63470			0.136225
$145$	1.02686	+	0.746054i	0.0852757	+	0.0619564i
$146$	6.03723	−	18.5807i	0.499645	−	1.53775i
$147$	−0.500000	−	1.53884i	−0.0412393	−	0.126922i
$148$	0.237738	−	0.172727i	0.0195419	−	0.0141980i
$149$	12.1049	−	8.79474i	0.991674	−	0.720493i	0.0313866	−	0.999507i	$-0.490008\pi$
$149$	12.1049	−	8.79474i	0.991674	−	0.720493i	0.960287	+	0.279014i	$0.0900077\pi$
$150$	3.50707	+	10.7937i	0.286351	+	0.881299i
$151$	0.887599	−	2.73175i	0.0722318	−	0.222307i	−0.908423	−	0.418053i	$-0.862713\pi$
$151$	0.887599	−	2.73175i	0.0722318	−	0.222307i	0.980655	+	0.195746i	$0.0627128\pi$
$152$	−9.26156	−	6.72892i	−0.751212	−	0.545787i
$153$	1.99666			0.161420
$154$		0			0
$155$	0.603886			0.0485053
$156$	0.313389	+	0.227690i	0.0250912	+	0.0182298i
$157$	−5.83496	+	17.9582i	−0.465680	+	1.43322i	0.392444	+	0.919776i	$0.371630\pi$
$157$	−5.83496	+	17.9582i	−0.465680	+	1.43322i	−0.858125	+	0.513441i	$0.828370\pi$
$158$	−1.62367	−	4.99713i	−0.129172	−	0.397551i
$159$	−17.2848	+	12.5582i	−1.37078	+	0.995927i
$160$	0.322504	−	0.234313i	0.0254962	−	0.0185240i
$161$	−0.557792	−	1.71671i	−0.0439602	−	0.135296i
$162$	−3.49371	+	10.7525i	−0.274491	+	0.844798i
$163$	−9.38067	−	6.81545i	−0.734751	−	0.533827i	0.156312	−	0.987708i	$-0.450039\pi$
$163$	−9.38067	−	6.81545i	−0.734751	−	0.533827i	−0.891063	+	0.453880i	$0.850039\pi$
$164$	0.157524			0.0123006
$165$		0			0
$166$	25.3142			1.96476
$167$	5.11696	+	3.71769i	0.395963	+	0.287684i	0.767894	−	0.640576i	$-0.221305\pi$
$167$	5.11696	+	3.71769i	0.395963	+	0.287684i	−0.371932	+	0.928260i	$0.621305\pi$
$168$	1.35577	−	4.17264i	0.104600	−	0.321926i
$169$	−3.24353	−	9.98255i	−0.249502	−	0.767889i
$170$	2.89504	−	2.10337i	0.222040	−	0.161321i
$171$	−1.30464	+	0.947880i	−0.0997687	+	0.0724862i
$172$	−0.407152	−	1.25308i	−0.0310450	−	0.0955467i
$173$	−0.413793	+	1.27352i	−0.0314601	+	0.0968243i	−0.965554	−	0.260204i	$-0.916210\pi$
$173$	−0.413793	+	1.27352i	−0.0314601	+	0.0968243i	0.934093	+	0.357029i	$0.116210\pi$
$174$	−5.22132	−	3.79351i	−0.395827	−	0.287585i
$175$	−4.78216			−0.361497
$176$		0			0
$177$	13.9214			1.04639
$178$	10.5844	+	7.68999i	0.793331	+	0.576389i
$179$	5.49705	−	16.9182i	0.410868	−	1.26452i	−0.505026	−	0.863104i	$-0.668517\pi$
$179$	5.49705	−	16.9182i	0.410868	−	1.26452i	0.915895	−	0.401419i	$-0.131483\pi$
$180$	−0.00833527	−	0.0256533i	−0.000621274	−	0.00191209i
$181$	0.779712	−	0.566494i	0.0579555	−	0.0421072i	−0.558430	−	0.829551i	$-0.688596\pi$
$181$	0.779712	−	0.566494i	0.0579555	−	0.0421072i	0.616386	+	0.787444i	$0.288596\pi$
$182$	−1.87759	+	1.36415i	−0.139177	+	0.101118i
$183$	−7.62007	−	23.4522i	−0.563292	−	1.73363i
$184$	1.51248	−	4.65493i	0.111501	−	0.343166i
$185$	0.733366	+	0.532822i	0.0539181	+	0.0391738i
$186$	−3.07062			−0.225149
$187$		0			0
$188$	−0.967622			−0.0705711
$189$	−4.42705	−	3.21644i	−0.322021	−	0.233962i
$190$	−0.893121	+	2.74874i	−0.0647938	+	0.199415i
$191$	−4.97173	−	15.3014i	−0.359742	−	1.10717i	−0.953209	−	0.302313i	$-0.902241\pi$
$191$	−4.97173	−	15.3014i	−0.359742	−	1.10717i	0.593467	−	0.804858i	$-0.297759\pi$
$192$	9.56458	−	6.94907i	0.690264	−	0.501506i
$193$	9.82750	−	7.14010i	0.707399	−	0.513955i	−0.174935	−	0.984580i	$-0.555971\pi$
$193$	9.82750	−	7.14010i	0.707399	−	0.513955i	0.882333	+	0.470625i	$0.155971\pi$
$194$	−1.22540	−	3.77140i	−0.0879787	−	0.270771i
$195$	−0.369259	+	1.13646i	−0.0264432	+	0.0813837i
$196$	−0.122406	−	0.0889332i	−0.00874329	−	0.00635237i
$197$	2.30179			0.163996			0.0819978	−	0.996633i	$-0.473870\pi$
$197$	2.30179			0.163996			0.0819978	+	0.996633i	$0.473870\pi$
$198$		0			0
$199$	20.2797			1.43759			0.718795	−	0.695222i	$-0.244694\pi$
$199$	20.2797			1.43759			0.718795	+	0.695222i	$0.244694\pi$
$200$	−10.4906	−	7.62184i	−0.741794	−	0.538945i
$201$	2.33791	−	7.19536i	0.164904	−	0.507521i
$202$	−0.0810316	−	0.249390i	−0.00570136	−	0.0175470i
$203$	2.20010	−	1.59846i	0.154417	−	0.112190i
$204$	−1.03531	+	0.752196i	−0.0724861	+	0.0526642i
$205$	0.150159	+	0.462142i	0.0104876	+	0.0322774i
$206$	7.64952	−	23.5428i	0.532967	−	1.64030i
$207$	−0.557792	−	0.405260i	−0.0387692	−	0.0281675i
$208$	−6.77186			−0.469544
$209$		0			0
$210$	−1.10766			−0.0764357
$211$	4.34062	+	3.15364i	0.298820	+	0.217106i	0.727085	−	0.686548i	$-0.240875\pi$
$211$	4.34062	+	3.15364i	0.298820	+	0.217106i	−0.428264	+	0.903654i	$0.640875\pi$
$212$	−0.617372	+	1.90008i	−0.0424013	+	0.130498i
$213$	−4.87155	−	14.9931i	−0.333793	−	1.02731i
$214$	−18.3642	+	13.3424i	−1.25535	+	0.912068i
$215$	3.28817	−	2.38899i	0.224251	−	0.162928i
$216$	−4.58517	−	14.1117i	−0.311982	−	0.960181i
$217$	0.399825	−	1.23053i	0.0271419	−	0.0835341i
$218$	13.0941	+	9.51344i	0.886847	+	0.644332i
$219$	−21.5522			−1.45637
$220$		0			0
$221$	−8.27128			−0.556387
$222$	−3.72899	−	2.70927i	−0.250274	−	0.181834i
$223$	−7.85614	+	24.1787i	−0.526086	+	1.61913i	0.236072	+	0.971736i	$0.424140\pi$
$223$	−7.85614	+	24.1787i	−0.526086	+	1.61913i	−0.762158	+	0.647391i	$0.775860\pi$
$224$	−0.263932	−	0.812299i	−0.0176347	−	0.0542740i
$225$	−1.47777	+	1.07366i	−0.0985179	+	0.0715775i
$226$	−2.10039	+	1.52602i	−0.139716	+	0.101510i
$227$	6.70869	+	20.6472i	0.445271	+	1.37040i	0.882186	+	0.470901i	$0.156071\pi$
$227$	6.70869	+	20.6472i	0.445271	+	1.37040i	−0.436915	+	0.899503i	$0.643929\pi$
$228$	0.319393	−	0.982990i	0.0211523	−	0.0651001i
$229$	−16.6097	−	12.0676i	−1.09760	−	0.797451i	−0.116931	−	0.993140i	$-0.537306\pi$
$229$	−16.6097	−	12.0676i	−1.09760	−	0.797451i	−0.980666	+	0.195689i	$0.937306\pi$
$230$	−1.23569			−0.0814787
$231$		0			0
$232$	7.37396			0.484124
$233$	0.561503	+	0.407956i	0.0367853	+	0.0267261i	0.606026	−	0.795445i	$-0.292763\pi$
$233$	0.561503	+	0.407956i	0.0367853	+	0.0267261i	−0.569241	+	0.822171i	$0.692763\pi$
$234$	−0.273937	+	0.843092i	−0.0179078	+	0.0551147i
$235$	−0.922381	−	2.83880i	−0.0601695	−	0.185183i
$236$	1.05317	−	0.765171i	0.0685554	−	0.0498084i
$237$	−4.68931	+	3.40699i	−0.304604	+	0.221307i
$238$	−2.36926	−	7.29183i	−0.153576	−	0.472659i
$239$	−0.107093	+	0.329599i	−0.00692728	+	0.0213200i	−0.954460	−	0.298338i	$-0.903568\pi$
$239$	−0.107093	+	0.329599i	−0.00692728	+	0.0213200i	0.947533	+	0.319658i	$0.103568\pi$
$240$	−2.61473	−	1.89971i	−0.168780	−	0.122626i
$241$	10.4372			0.672317			0.336158	−	0.941806i	$-0.390872\pi$
$241$	10.4372			0.672317			0.336158	+	0.941806i	$0.390872\pi$
$242$		0			0
$243$	−3.94427			−0.253025
$244$	−1.86549	−	1.35536i	−0.119426	−	0.0867677i
$245$	0.144228	−	0.443888i	0.00921439	−	0.0283590i
$246$	−0.763523	−	2.34988i	−0.0486805	−	0.149823i
$247$	5.40457	−	3.92665i	0.343884	−	0.249847i
$248$	2.83832	−	2.06216i	0.180234	−	0.130947i
$249$	−8.62944	−	26.5587i	−0.546869	−	1.68309i
$250$	−2.06936	+	6.36882i	−0.130878	+	0.402800i
$251$	5.65909	+	4.11157i	0.357199	+	0.259520i	0.751883	−	0.659297i	$-0.229146\pi$
$251$	5.65909	+	4.11157i	0.357199	+	0.259520i	−0.394684	+	0.918817i	$0.629146\pi$
$252$	−0.0577923			−0.00364057
$253$		0			0
$254$	12.5262			0.785965
$255$	−3.19369	−	2.32035i	−0.199996	−	0.145306i
$256$	1.11586	−	3.43426i	0.0697412	−	0.214641i
$257$	−3.07423	−	9.46152i	−0.191765	−	0.590193i	−0.999999	−	0.00133144i	$-0.999576\pi$
$257$	−3.07423	−	9.46152i	−0.191765	−	0.590193i	0.808234	−	0.588862i	$-0.200424\pi$
$258$	−16.7196	+	12.1475i	−1.04091	+	0.756268i
$259$	1.57128	−	1.14160i	0.0976345	−	0.0709356i
$260$	0.0345293	+	0.106270i	0.00214142	+	0.00659061i
$261$	0.320990	−	0.987905i	0.0198688	−	0.0611498i
$262$	−11.4711	−	8.33422i	−0.708685	−	0.514890i
$263$	−14.1803			−0.874397			−0.437199	−	0.899365i	$-0.644029\pi$
$263$	−14.1803			−0.874397			−0.437199	+	0.899365i	$0.644029\pi$
$264$		0			0
$265$	−6.16293			−0.378586
$266$	5.00978	+	3.63982i	0.307169	+	0.223171i
$267$	4.45991	−	13.7262i	0.272942	−	0.840029i
$268$	−0.218618	−	0.672837i	−0.0133542	−	0.0411001i
$269$	14.8884	−	10.8171i	0.907762	−	0.659528i	−0.0326859	−	0.999466i	$-0.510406\pi$
$269$	14.8884	−	10.8171i	0.907762	−	0.659528i	0.940448	+	0.339938i	$0.110406\pi$
$270$	−3.03063	+	2.20188i	−0.184438	+	0.134002i
$271$	−0.225765	−	0.694833i	−0.0137142	−	0.0422081i	0.943965	−	0.330045i	$-0.107064\pi$
$271$	−0.225765	−	0.694833i	−0.0137142	−	0.0422081i	−0.957679	+	0.287837i	$0.907064\pi$
$272$	6.91316	−	21.2765i	0.419172	−	1.29008i
$273$	2.07128	+	1.50487i	0.125360	+	0.0910790i
$274$	−20.5501			−1.24148
$275$		0			0
$276$	0.441899			0.0265992
$277$	12.1874	+	8.85463i	0.732267	+	0.532023i	0.890280	−	0.455414i	$-0.150509\pi$
$277$	12.1874	+	8.85463i	0.732267	+	0.532023i	−0.158013	+	0.987437i	$0.550509\pi$
$278$	−4.34102	+	13.3603i	−0.260357	+	0.801297i
$279$	−0.152719	−	0.470022i	−0.00914308	−	0.0281395i
$280$	1.02386	−	0.743880i	0.0611875	−	0.0444553i
$281$	−8.65334	+	6.28702i	−0.516215	+	0.375052i	−0.815176	−	0.579213i	$-0.803360\pi$
$281$	−8.65334	+	6.28702i	−0.516215	+	0.375052i	0.298961	+	0.954265i	$0.403360\pi$
$282$	4.69009	+	14.4346i	0.279291	+	0.859569i
$283$	−2.81481	+	8.66308i	−0.167323	+	0.514967i	−0.999200	−	0.0399931i	$-0.987266\pi$
$283$	−2.81481	+	8.66308i	−0.167323	+	0.514967i	0.831877	+	0.554960i	$0.187266\pi$
$284$	−1.19261	−	0.866485i	−0.0707687	−	0.0514164i
$285$	3.18834			0.188861
$286$		0			0
$287$	1.04112			0.0614555
$288$	−0.263932	−	0.191758i	−0.0155523	−	0.0112994i
$289$	3.19057	−	9.81958i	0.187681	−	0.577622i
$290$	−0.575287	−	1.77055i	−0.0337820	−	0.103970i
$291$	−3.53908	+	2.57129i	−0.207465	+	0.150732i
$292$	−1.63045	+	1.18459i	−0.0954149	+	0.0693230i
$293$	−3.67390	−	11.3071i	−0.214632	−	0.660569i	−0.999180	−	0.0405002i	$-0.987105\pi$
$293$	−3.67390	−	11.3071i	−0.214632	−	0.660569i	0.784548	−	0.620068i	$-0.212895\pi$
$294$	−0.733366	+	2.25707i	−0.0427708	+	0.131635i
$295$	3.24878	+	2.36037i	0.189151	+	0.137426i
$296$	5.26638			0.306102
$297$		0			0
$298$	−21.9460			−1.27130
$299$	2.31069	+	1.67881i	0.133630	+	0.0970882i
$300$	0.361776	−	1.11343i	0.0208871	−	0.0642840i
$301$	−2.69098	−	8.28199i	−0.155106	−	0.477366i
$302$	−3.40834	+	2.47630i	−0.196128	+	0.142495i
$303$	−0.234027	+	0.170031i	−0.0134445	+	0.00976802i
$304$	5.58350	+	17.1843i	0.320236	+	0.985585i
$305$	2.19806	−	6.76492i	0.125860	−	0.387358i
$306$	−2.36926	−	1.72137i	−0.135442	−	0.0984040i
$307$	−2.22072			−0.126743			−0.0633716	−	0.997990i	$-0.520185\pi$
$307$	−2.22072			−0.126743			−0.0633716	+	0.997990i	$0.520185\pi$
$308$		0			0
$309$	−27.3079			−1.55349
$310$	−0.716577	−	0.520624i	−0.0406989	−	0.0295695i
$311$	−6.61685	+	20.3646i	−0.375207	+	1.15477i	0.568132	+	0.822937i	$0.307666\pi$
$311$	−6.61685	+	20.3646i	−0.375207	+	1.15477i	−0.943339	+	0.331831i	$0.892334\pi$
$312$	2.14526	+	6.60243i	0.121451	+	0.373789i
$313$	25.5283	−	18.5474i	1.44295	−	1.04836i	0.455531	−	0.890220i	$-0.349450\pi$
$313$	25.5283	−	18.5474i	1.44295	−	1.04836i	0.987416	−	0.158142i	$-0.0505505\pi$
$314$	22.4060	−	16.2789i	1.26444	−	0.918671i
$315$	−0.0550902	−	0.169550i	−0.00310398	−	0.00955307i
$316$	−0.167491	+	0.515484i	−0.00942211	+	0.0289983i
$317$	10.6796	+	7.75915i	0.599824	+	0.435798i	0.845816	−	0.533474i	$-0.179114\pi$
$317$	10.6796	+	7.75915i	0.599824	+	0.435798i	−0.245992	+	0.969272i	$0.579114\pi$
$318$	31.3370			1.75729
$319$		0			0
$320$	3.41026			0.190639
$321$	20.2586	+	14.7188i	1.13073	+	0.821521i
$322$	−0.818132	+	2.51795i	−0.0455927	+	0.140320i
$323$	6.81980	+	20.9892i	0.379464	+	1.16787i
$324$	0.943531	−	0.685515i	0.0524184	−	0.0380842i
$325$	6.12174	−	4.44771i	0.339573	−	0.246714i
$326$	5.25544	+	16.1746i	0.291072	+	0.895827i
$327$	5.51745	−	16.9810i	0.305116	−	0.939050i
$328$	2.28389	+	1.65935i	0.126107	+	0.0916220i
$329$	−6.39530			−0.352584
$330$		0			0
$331$	9.47653			0.520877			0.260439	−	0.965490i	$-0.416133\pi$
$331$	9.47653			0.520877			0.260439	+	0.965490i	$0.416133\pi$
$332$	−2.11259	−	1.53489i	−0.115944	−	0.0842379i
$333$	0.229247	−	0.705548i	0.0125626	−	0.0386638i
$334$	−2.86674	−	8.82291i	−0.156861	−	0.482768i
$335$	1.76556	−	1.28276i	0.0964631	−	0.0700845i
$336$	−5.60222	+	4.07025i	−0.305626	+	0.222050i
$337$	5.93346	+	18.2613i	0.323216	+	0.994758i	0.972239	+	0.233989i	$0.0751779\pi$
$337$	5.93346	+	18.2613i	0.323216	+	0.994758i	−0.649023	+	0.760769i	$0.724822\pi$
$338$	−4.75738	+	14.6417i	−0.258768	+	0.796405i
$339$	2.31706	+	1.68344i	0.125845	+	0.0914321i
$340$	−0.369141			−0.0200195
$341$		0			0
$342$	2.36530			0.127901
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	7.29672	−	22.4570i	0.393413	−	1.21080i
$345$	0.421238	+	1.29644i	0.0226787	+	0.0697978i
$346$	1.58895	−	1.15444i	0.0854223	−	0.0620629i
$347$	2.46613	−	1.79175i	0.132389	−	0.0961862i	−0.519620	−	0.854397i	$-0.673926\pi$
$347$	2.46613	−	1.79175i	0.132389	−	0.0961862i	0.652009	+	0.758211i	$0.273926\pi$
$348$	0.205731	+	0.633175i	0.0110283	+	0.0339417i
$349$	−5.99373	+	18.4468i	−0.320837	+	0.987435i	0.652448	+	0.757834i	$0.273742\pi$
$349$	−5.99373	+	18.4468i	−0.320837	+	0.987435i	−0.973285	+	0.229601i	$0.926258\pi$
$350$	5.67457	+	4.12281i	0.303318	+	0.220374i
$351$	8.65865			0.462165
$352$		0			0
$353$	−10.7585			−0.572619			−0.286309	−	0.958137i	$-0.592428\pi$
$353$	−10.7585			−0.572619			−0.286309	+	0.958137i	$0.592428\pi$
$354$	−16.5193	−	12.0019i	−0.877989	−	0.637896i
$355$	1.40523	−	4.32485i	0.0745818	−	0.229539i
$356$	−0.417046	−	1.28353i	−0.0221034	−	0.0680272i
$357$	−6.84266	+	4.97148i	−0.362152	+	0.263119i
$358$	−21.1084	+	15.3361i	−1.11561	+	0.810541i
$359$	−0.187643	−	0.577506i	−0.00990342	−	0.0304796i	0.945983	−	0.324217i	$-0.105101\pi$
$359$	−0.187643	−	0.577506i	−0.00990342	−	0.0304796i	−0.955886	+	0.293738i	$0.905101\pi$
$360$	0.149380	−	0.459743i	0.00787299	−	0.0242306i
$361$	0.950914	+	0.690879i	0.0500481	+	0.0363621i
$362$	−1.41360			−0.0742973
$363$		0			0
$364$	0.239408			0.0125484
$365$	−5.02956	−	3.65419i	−0.263259	−	0.191269i
$366$	−11.1766	+	34.3981i	−0.584211	+	1.79802i
$367$	8.54829	+	26.3089i	0.446217	+	1.37332i	0.881143	+	0.472849i	$0.156774\pi$
$367$	8.54829	+	26.3089i	0.446217	+	1.37332i	−0.434926	+	0.900466i	$0.643226\pi$
$368$	−6.24975	+	4.54071i	−0.325791	+	0.236701i
$369$	0.321724	−	0.233746i	0.0167483	−	0.0121684i
$370$	−0.410862	−	1.26450i	−0.0213597	−	0.0657384i
$371$	−4.08039	+	12.5582i	−0.211843	+	0.651987i
$372$	0.256258	+	0.186183i	0.0132864	+	0.00965311i
$373$	29.4513			1.52493			0.762465	−	0.647029i	$-0.223989\pi$
$373$	29.4513			1.52493			0.762465	+	0.647029i	$0.223989\pi$
$374$		0			0
$375$	7.38737			0.381482
$376$	−14.0293	−	10.1929i	−0.723504	−	0.525657i
$377$	−1.32972	+	4.09246i	−0.0684840	+	0.210772i
$378$	2.48022	+	7.63333i	0.127569	+	0.392616i
$379$	−20.5034	+	14.8966i	−1.05319	+	0.765188i	−0.972817	−	0.231577i	$-0.925612\pi$
$379$	−20.5034	+	14.8966i	−1.05319	+	0.765188i	−0.0803745	+	0.996765i	$0.525612\pi$
$380$	0.241202	−	0.175243i	0.0123734	−	0.00898979i
$381$	−4.27012	−	13.1421i	−0.218765	−	0.673288i
$382$	−7.29219	+	22.4431i	−0.373101	+	1.14829i
$383$	25.8337	+	18.7693i	1.32004	+	0.959065i	0.999932	+	0.0116837i	$0.00371913\pi$
$383$	25.8337	+	18.7693i	1.32004	+	0.959065i	0.320108	+	0.947381i	$0.396281\pi$
$384$	−20.1043			−1.02594
$385$		0			0
$386$	−17.8171			−0.906865
$387$	−2.69098	−	1.95511i	−0.136790	−	0.0993840i
$388$	−0.126407	+	0.389042i	−0.00641737	+	0.0197506i
$389$	5.48558	+	16.8829i	0.278130	+	0.855996i	0.988374	+	0.152040i	$0.0485844\pi$
$389$	5.48558	+	16.8829i	0.278130	+	0.855996i	−0.710244	+	0.703955i	$0.751416\pi$
$390$	1.41794	−	1.03019i	0.0718000	−	0.0521657i
$391$	−7.63356	+	5.54611i	−0.386046	+	0.280479i
$392$	−0.837913	−	2.57883i	−0.0423210	−	0.130251i
$393$	−4.83354	+	14.8761i	−0.243820	+	0.750400i
$394$	−2.73133	−	1.98442i	−0.137602	−	0.0999738i
$395$	−1.67198			−0.0841265
$396$		0			0
$397$	−13.3047			−0.667742			−0.333871	−	0.942619i	$-0.608355\pi$
$397$	−13.3047			−0.667742			−0.333871	+	0.942619i	$0.608355\pi$
$398$	−24.0641	−	17.4836i	−1.20623	−	0.876374i
$399$	2.11096	−	6.49687i	0.105680	−	0.325250i
$400$	6.32443	+	19.4646i	0.316221	+	0.973229i
$401$	2.82317	−	2.05115i	0.140982	−	0.102430i	−0.515059	−	0.857155i	$-0.672230\pi$
$401$	2.82317	−	2.05115i	0.140982	−	0.102430i	0.656041	+	0.754725i	$0.272230\pi$
$402$	−8.97748	+	6.52252i	−0.447756	+	0.325314i
$403$	0.632649	+	1.94709i	0.0315145	+	0.0969917i
$404$	−0.00835890	+	0.0257260i	−0.000415871	+	0.00127992i
$405$	2.91057	+	2.11465i	0.144627	+	0.105078i
$406$	−3.98873			−0.197958
$407$		0			0
$408$	−22.9342			−1.13541
$409$	−23.9675	−	17.4134i	−1.18512	−	0.861039i	−0.192379	−	0.981321i	$-0.561620\pi$
$409$	−23.9675	−	17.4134i	−1.18512	−	0.861039i	−0.992740	+	0.120282i	$0.961620\pi$
$410$	0.220243	−	0.677838i	0.0108770	−	0.0334760i
$411$	7.00540	+	21.5604i	0.345551	+	1.06350i
$412$	−2.06587	+	1.50095i	−0.101778	+	0.0739463i
$413$	6.96069	−	5.05724i	0.342513	−	0.248850i
$414$	0.312499	+	0.961771i	0.0153585	+	0.0472685i
$415$	2.48922	−	7.66102i	0.122191	−	0.376065i
$416$	1.09335	+	0.794368i	0.0536061	+	0.0389471i
$417$	15.4970			0.758890
$418$		0			0
$419$	−11.6452			−0.568907			−0.284454	−	0.958690i	$-0.591812\pi$
$419$	−11.6452			−0.568907			−0.284454	+	0.958690i	$0.591812\pi$
$420$	0.0924396	+	0.0671613i	0.00451059	+	0.00327713i
$421$	6.14475	−	18.9116i	0.299477	−	0.921696i	−0.682204	−	0.731162i	$-0.738978\pi$
$421$	6.14475	−	18.9116i	0.299477	−	0.921696i	0.981681	−	0.190533i	$-0.0610217\pi$
$422$	−2.43179	−	7.48429i	−0.118378	−	0.364330i
$423$	−1.97626	+	1.43583i	−0.0960888	+	0.0698126i
$424$	−28.9664	+	21.0453i	−1.40673	+	1.02205i
$425$	7.72478	+	23.7744i	0.374707	+	1.15323i
$426$	−7.14526	+	21.9908i	−0.346189	+	1.06546i
$427$	−12.3295	−	8.95793i	−0.596668	−	0.433505i
$428$	2.34159			0.113185
$429$		0			0
$430$	−5.96138			−0.287483
$431$	24.4698	+	17.7784i	1.17867	+	0.856354i	0.992021	−	0.126073i	$-0.0402372\pi$
$431$	24.4698	+	17.7784i	1.17867	+	0.856354i	0.186649	+	0.982427i	$0.440237\pi$
$432$	−7.23692	+	22.2730i	−0.348186	+	1.07161i
$433$	−1.76362	−	5.42786i	−0.0847542	−	0.260846i	0.899694	−	0.436521i	$-0.143789\pi$
$433$	−1.76362	−	5.42786i	−0.0847542	−	0.260846i	−0.984448	+	0.175674i	$0.943789\pi$
$434$	−1.53531	+	1.11547i	−0.0736972	+	0.0535441i
$435$	−1.66149	+	1.20714i	−0.0796622	+	0.0578780i
$436$	−0.515936	−	1.58789i	−0.0247089	−	0.0760461i
$437$	2.35495	−	7.24780i	0.112653	−	0.346709i
$438$	25.5741	+	18.5807i	1.22198	+	0.887820i
$439$	−6.84875			−0.326873			−0.163436	−	0.986554i	$-0.552258\pi$
$439$	−6.84875			−0.326873			−0.163436	+	0.986554i	$0.552258\pi$
$440$		0			0
$441$	−0.381966			−0.0181889
$442$	9.81479	+	7.13086i	0.466842	+	0.339181i
$443$	0.0311165	−	0.0957668i	0.00147839	−	0.00455002i	−0.950315	−	0.311291i	$-0.899239\pi$
$443$	0.0311165	−	0.0957668i	0.00147839	−	0.00455002i	0.951793	+	0.306741i	$0.0992386\pi$
$444$	0.146930	+	0.452204i	0.00697300	+	0.0214607i
$445$	3.36807	−	2.44705i	0.159662	−	0.116001i
$446$	30.1672	−	21.9178i	1.42846	−	1.03784i
$447$	7.48125	+	23.0249i	0.353851	+	1.08904i
$448$	2.25789	−	6.94907i	0.106675	−	0.328313i
$449$	24.9216	+	18.1066i	1.17612	+	0.854502i	0.991729	−	0.128351i	$-0.0409683\pi$
$449$	24.9216	+	18.1066i	1.17612	+	0.854502i	0.184392	+	0.982853i	$0.440968\pi$
$450$	2.67917			0.126297
$451$		0			0
$452$	0.267817			0.0125970
$453$	3.75993	+	2.73175i	0.176657	+	0.128349i
$454$	9.83984	−	30.2839i	0.461807	−	1.42129i
$455$	0.228214	+	0.702372i	0.0106989	+	0.0329277i
$456$	14.9855	−	10.8876i	0.701761	−	0.509859i
$457$	18.7171	−	13.5987i	0.875547	−	0.636122i	−0.0565223	−	0.998401i	$-0.518001\pi$
$457$	18.7171	−	13.5987i	0.875547	−	0.636122i	0.932070	+	0.362279i	$0.118001\pi$
$458$	9.30542	+	28.6392i	0.434814	+	1.33822i
$459$	−8.83932	+	27.2046i	−0.412584	+	1.26980i
$460$	0.103124	+	0.0749241i	0.00480819	+	0.00349335i
$461$	2.77839			0.129403			0.0647013	−	0.997905i	$-0.479391\pi$
$461$	2.77839			0.129403			0.0647013	+	0.997905i	$0.479391\pi$
$462$		0			0
$463$	−26.0950			−1.21274			−0.606369	−	0.795184i	$-0.707374\pi$
$463$	−26.0950			−1.21274			−0.606369	+	0.795184i	$0.707374\pi$
$464$	−9.41578	−	6.84097i	−0.437117	−	0.317584i
$465$	−0.301943	+	0.929285i	−0.0140023	+	0.0430945i
$466$	−0.314577	−	0.968169i	−0.0145725	−	0.0448496i
$467$	2.15060	−	1.56250i	0.0995180	−	0.0723041i	−0.536913	−	0.843637i	$-0.680410\pi$
$467$	2.15060	−	1.56250i	0.0995180	−	0.0723041i	0.636431	+	0.771333i	$0.280410\pi$
$468$	0.0739811	−	0.0537504i	0.00341978	−	0.00248461i
$469$	−1.44491	−	4.44698i	−0.0667197	−	0.205342i
$470$	−1.35289	+	4.16375i	−0.0624040	+	0.192060i
$471$	−24.7173	−	17.9582i	−1.13891	−	0.827468i
$472$	23.3298			1.07384
$473$		0			0
$474$	8.50163			0.390493
$475$	−16.3340	−	11.8673i	−0.749454	−	0.544510i
$476$	−0.244403	+	0.752196i	−0.0112022	+	0.0344768i
$477$	1.55857	+	4.79679i	0.0713621	+	0.219630i
$478$	0.411233	−	0.298778i	0.0188093	−	0.0136658i
$479$	−6.70047	+	4.86818i	−0.306152	+	0.222433i	−0.730244	−	0.683187i	$-0.760593\pi$
$479$	−6.70047	+	4.86818i	−0.306152	+	0.222433i	0.424091	+	0.905619i	$0.360593\pi$
$480$	0.199318	+	0.613439i	0.00909759	+	0.0279995i
$481$	−0.949667	+	2.92277i	−0.0433011	+	0.133267i
$482$	−12.3848	−	8.99812i	−0.564114	−	0.409853i
$483$	2.92064			0.132894
$484$		0			0
$485$	−1.26186			−0.0572983
$486$	4.68032	+	3.40045i	0.212303	+	0.154247i
$487$	−6.05536	+	18.6365i	−0.274395	+	0.844500i	0.714984	+	0.699141i	$0.246434\pi$
$487$	−6.05536	+	18.6365i	−0.274395	+	0.844500i	−0.989379	+	0.145360i	$0.953566\pi$
$488$	−12.7699	−	39.3018i	−0.578067	−	1.77911i
$489$	15.1782	−	11.0276i	0.686384	−	0.498687i
$490$	−0.553829	+	0.402380i	−0.0250194	+	0.0181777i
$491$	8.86312	+	27.2779i	0.399987	+	1.23103i	0.925009	+	0.379945i	$0.124057\pi$
$491$	8.86312	+	27.2779i	0.399987	+	1.23103i	−0.525022	+	0.851089i	$0.675943\pi$
$492$	−0.0787620	+	0.242405i	−0.00355087	+	0.0109284i
$493$	−11.5006	−	8.35569i	−0.517962	−	0.376321i
$494$	−9.79837			−0.440850
$495$		0			0
$496$	−5.53735			−0.248634
$497$	−7.88234	−	5.72685i	−0.353571	−	0.256884i
$498$	−12.6571	+	38.9545i	−0.567177	+	1.74559i
$499$	8.63700	+	26.5819i	0.386645	+	1.18997i	0.935280	+	0.353909i	$0.115148\pi$
$499$	8.63700	+	26.5819i	0.386645	+	1.18997i	−0.548635	+	0.836062i	$0.684852\pi$
$500$	0.558863	−	0.406037i	0.0249931	−	0.0181585i
$501$	−8.27942	+	6.01535i	−0.369897	+	0.268746i
$502$	−3.17046	−	9.75767i	−0.141505	−	0.435506i
$503$	2.50222	−	7.70104i	0.111568	−	0.343373i	−0.879647	−	0.475626i	$-0.842221\pi$
$503$	2.50222	−	7.70104i	0.111568	−	0.343373i	0.991216	+	0.132254i	$0.0422214\pi$
$504$	−0.837913	−	0.608780i	−0.0373236	−	0.0271172i
$505$	−0.0834428			−0.00371316
$506$		0			0
$507$	16.9833			0.754256
$508$	−1.04538	−	0.759510i	−0.0463811	−	0.0336978i
$509$	5.03702	−	15.5024i	0.223262	−	0.687130i	−0.775201	−	0.631714i	$-0.782352\pi$
$509$	5.03702	−	15.5024i	0.223262	−	0.687130i	0.998463	−	0.0554159i	$-0.0176485\pi$
$510$	1.78924	+	5.50670i	0.0792287	+	0.243841i
$511$	−10.7761	+	7.82931i	−0.476707	+	0.346348i
$512$	15.8195	−	11.4935i	0.699129	−	0.507947i
$513$	−7.13919	−	21.9722i	−0.315203	−	0.970096i
$514$	−4.50908	+	13.8775i	−0.198887	+	0.612111i
$515$	−6.37274	−	4.63007i	−0.280816	−	0.204025i
$516$	2.13187			0.0938505
$517$		0			0
$518$	−2.84870			−0.125165
$519$	−1.75286	−	1.27352i	−0.0769419	−	0.0559015i
$520$	−0.618813	+	1.90451i	−0.0271368	+	0.0835184i
$521$	2.37512	+	7.30987i	0.104056	+	0.320251i	0.989508	−	0.144480i	$-0.0461509\pi$
$521$	2.37512	+	7.30987i	0.104056	+	0.320251i	−0.885452	+	0.464731i	$0.846151\pi$
$522$	−1.23259	+	0.895526i	−0.0539488	+	0.0391961i
$523$	21.1339	−	15.3547i	0.924121	−	0.671413i	−0.0204256	−	0.999791i	$-0.506502\pi$
$523$	21.1339	−	15.3547i	0.924121	−	0.671413i	0.944546	+	0.328378i	$0.106502\pi$
$524$	0.451984	+	1.39106i	0.0197450	+	0.0607689i
$525$	2.39108	−	7.35899i	0.104355	−	0.321173i
$526$	16.8265	+	12.2252i	0.733672	+	0.533044i
$527$	−6.76343			−0.294619
$528$		0			0
$529$	−19.7418			−0.858338
$530$	7.31300	+	5.31320i	0.317656	+	0.230791i
$531$	1.01555	−	3.12554i	0.0440712	−	0.135637i
$532$	−0.197396	−	0.607521i	−0.00855819	−	0.0263394i
$533$	−1.33276	+	0.968308i	−0.0577283	+	0.0419421i
$534$	−17.1258	+	12.4427i	−0.741108	+	0.538446i
$535$	2.23210	+	6.86971i	0.0965023	+	0.297004i
$536$	3.91794	−	12.0582i	0.169229	−	0.520834i
$537$	23.2859	+	16.9182i	1.00486	+	0.730073i
$538$	−26.9924			−1.16372
$539$		0			0
$540$	0.386429			0.0166292
$541$	−20.9355	−	15.2105i	−0.900086	−	0.653951i	0.0384021	−	0.999262i	$-0.487773\pi$
$541$	−20.9355	−	15.2105i	−0.900086	−	0.653951i	−0.938488	+	0.345312i	$0.887773\pi$
$542$	−0.331137	+	1.01913i	−0.0142235	+	0.0437756i
$543$	0.481889	+	1.48310i	0.0206798	+	0.0636459i
$544$	−3.61199	+	2.62427i	−0.154863	+	0.112514i
$545$	4.16671	−	3.02729i	0.178482	−	0.129675i
$546$	−1.16042	−	3.57140i	−0.0496613	−	0.152842i
$547$	11.7726	−	36.2322i	0.503359	−	1.54918i	−0.300154	−	0.953891i	$-0.597038\pi$
$547$	11.7726	−	36.2322i	0.503359	−	1.54918i	0.803513	−	0.595288i	$-0.202962\pi$
$548$	1.71501	+	1.24603i	0.0732615	+	0.0532276i
$549$	−5.82122			−0.248444
$550$		0			0
$551$	11.4814			0.489123
$552$	6.40696	+	4.65493i	0.272698	+	0.198127i
$553$	−1.10700	+	3.40699i	−0.0470743	+	0.144880i
$554$	−6.82786	−	21.0140i	−0.290088	−	0.892799i
$555$	−1.18661	+	0.862123i	−0.0503688	+	0.0365951i
$556$	1.17236	−	0.851771i	0.0497192	−	0.0361231i
$557$	−10.6741	−	32.8516i	−0.452277	−	1.39197i	−0.874303	−	0.485381i	$-0.838681\pi$
$557$	−10.6741	−	32.8516i	−0.452277	−	1.39197i	0.422026	−	0.906584i	$-0.361319\pi$
$558$	−0.223999	+	0.689397i	−0.00948261	+	0.0291845i
$559$	11.1476	+	8.09917i	0.471491	+	0.342558i
$560$	−1.99748			−0.0844088
$561$		0			0
$562$	15.6883			0.661773
$563$	15.7612	+	11.4512i	0.664256	+	0.482610i	0.868098	−	0.496394i	$-0.165343\pi$
$563$	15.7612	+	11.4512i	0.664256	+	0.482610i	−0.203842	+	0.979004i	$0.565343\pi$
$564$	0.483811	−	1.48902i	0.0203721	−	0.0626990i
$565$	0.255295	+	0.785717i	0.0107403	+	0.0330553i
$566$	10.8087	−	7.85300i	0.454325	−	0.330086i
$567$	6.23607	−	4.53077i	0.261890	−	0.190274i
$568$	−8.16387	−	25.1258i	−0.342549	−	1.05426i
$569$	−5.29308	+	16.2904i	−0.221897	+	0.682930i	0.776694	+	0.629878i	$0.216895\pi$
$569$	−5.29308	+	16.2904i	−0.221897	+	0.682930i	−0.998592	+	0.0530524i	$0.983105\pi$
$570$	−3.78332	−	2.74874i	−0.158466	−	0.115132i
$571$	3.85581			0.161360			0.0806802	−	0.996740i	$-0.474291\pi$
$571$	3.85581			0.161360			0.0806802	+	0.996740i	$0.474291\pi$
$572$		0			0
$573$	26.0323			1.08751
$574$	−1.23541	−	0.897575i	−0.0515649	−	0.0374641i
$575$	2.66745	−	8.20958i	0.111240	−	0.342363i
$576$	−0.862437	−	2.65431i	−0.0359349	−	0.110596i
$577$	7.91368	−	5.74963i	0.329451	−	0.239360i	−0.410747	−	0.911750i	$-0.634732\pi$
$577$	7.91368	−	5.74963i	0.329451	−	0.239360i	0.740198	+	0.672389i	$0.234732\pi$
$578$	−12.2517	+	8.90135i	−0.509602	+	0.370247i
$579$	6.07373	+	18.6930i	0.252416	+	0.776855i
$580$	−0.0593443	+	0.182643i	−0.00246414	+	0.00758384i
$581$	−13.9627	−	10.1445i	−0.579272	−	0.420865i
$582$	6.41628			0.265964
$583$		0			0
$584$	−36.1178			−1.49457
$585$	0.228214	+	0.165807i	0.00943551	+	0.00685530i
$586$	−5.38863	+	16.5845i	−0.222602	+	0.685099i
$587$	−1.88467	−	5.80041i	−0.0777886	−	0.239409i	0.904599	−	0.426264i	$-0.140170\pi$
$587$	−1.88467	−	5.80041i	−0.0777886	−	0.239409i	−0.982387	+	0.186855i	$0.940170\pi$
$588$	0.198057	−	0.143897i	0.00816774	−	0.00593421i
$589$	4.41932	−	3.21082i	0.182095	−	0.132300i
$590$	−1.82010	−	5.60169i	−0.0749323	−	0.230618i
$591$	−1.15089	+	3.54209i	−0.0473414	+	0.145702i
$592$	−6.72462	−	4.88572i	−0.276380	−	0.200802i
$593$	−13.2330			−0.543413			−0.271706	−	0.962380i	$-0.587588\pi$
$593$	−13.2330			−0.543413			−0.271706	+	0.962380i	$0.587588\pi$
$594$		0			0
$595$	−2.43976			−0.100020
$596$	1.83150	+	1.33066i	0.0750212	+	0.0545061i
$597$	−10.1399	+	31.2073i	−0.414997	+	1.27723i
$598$	−1.29454	−	3.98419i	−0.0529378	−	0.162926i
$599$	4.79355	−	3.48271i	0.195859	−	0.142300i	−0.485534	−	0.874218i	$-0.661375\pi$
$599$	4.79355	−	3.48271i	0.195859	−	0.142300i	0.681393	+	0.731918i	$0.261375\pi$
$600$	16.9741	−	12.3324i	0.692964	−	0.503468i
$601$	−3.93712	−	12.1172i	−0.160599	−	0.494272i	0.838086	−	0.545538i	$-0.183674\pi$
$601$	−3.93712	−	12.1172i	−0.160599	−	0.494272i	−0.998685	+	0.0512657i	$0.983674\pi$
$602$	−3.94695	+	12.1475i	−0.160866	+	0.495094i
$603$	−1.44491	−	1.04979i	−0.0588413	−	0.0427507i
$604$	0.434590			0.0176832
$605$		0			0
$606$	0.424287			0.0172355
$607$	6.76452	+	4.91471i	0.274563	+	0.199482i	0.716543	−	0.697543i	$-0.245724\pi$
$607$	6.76452	+	4.91471i	0.274563	+	0.199482i	−0.441979	+	0.897025i	$0.645724\pi$
$608$	1.11430	−	3.42946i	0.0451908	−	0.139083i
$609$	1.35974	+	4.18483i	0.0550992	+	0.169578i
$610$	−8.44044	+	6.13234i	−0.341743	+	0.248291i
$611$	8.18675	−	5.94802i	0.331201	−	0.240631i
$612$	0.0933537	+	0.287313i	0.00377360	+	0.0116139i
$613$	2.06514	−	6.35585i	0.0834102	−	0.256710i	−0.900650	−	0.434545i	$-0.856909\pi$
$613$	2.06514	−	6.35585i	0.0834102	−	0.256710i	0.984060	+	0.177835i	$0.0569092\pi$
$614$	2.63513	+	1.91453i	0.106345	+	0.0772643i
$615$	−0.786243			−0.0317044
$616$		0			0
$617$	11.8669			0.477741			0.238871	−	0.971051i	$-0.423223\pi$
$617$	11.8669			0.477741			0.238871	+	0.971051i	$0.423223\pi$
$618$	32.4039	+	23.5428i	1.30348	+	0.947031i
$619$	6.37213	−	19.6114i	0.256118	−	0.788249i	−0.737490	−	0.675358i	$-0.763989\pi$
$619$	6.37213	−	19.6114i	0.256118	−	0.788249i	0.993607	−	0.112891i	$-0.0360109\pi$
$620$	0.0282346	+	0.0868973i	0.00113393	+	0.00348988i
$621$	7.99107	−	5.80585i	0.320670	−	0.232981i
$622$	25.4084	−	18.4603i	1.01878	−	0.740189i
$623$	−2.75638	−	8.48325i	−0.110432	−	0.339874i
$624$	3.38593	−	10.4208i	0.135546	−	0.417167i
$625$	−17.6203	−	12.8019i	−0.704812	−	0.512076i
$626$	−46.2824			−1.84982
$627$		0			0
$628$	−2.85694			−0.114004
$629$	−8.21358	−	5.96752i	−0.327497	−	0.237941i
$630$	−0.0808026	+	0.248685i	−0.00321925	+	0.00990784i
$631$	−4.78342	−	14.7219i	−0.190425	−	0.586068i	0.809575	−	0.587017i	$-0.199698\pi$
$631$	−4.78342	−	14.7219i	−0.190425	−	0.586068i	−1.00000		0.000949112i	$0.999698\pi$
$632$	−7.85847	+	5.70952i	−0.312593	+	0.227112i
$633$	−7.02326	+	5.10270i	−0.279150	+	0.202814i
$634$	−5.98314	−	18.4142i	−0.237621	−	0.731321i
$635$	1.23174	−	3.79091i	0.0488801	−	0.150438i
$636$	−2.61523	−	1.90008i	−0.103701	−	0.0753430i
$637$	1.58232			0.0626937
$638$		0			0
$639$	−3.72153			−0.147222
$640$	−4.69166	−	3.40869i	−0.185454	−	0.134740i
$641$	−7.28615	+	22.4245i	−0.287786	+	0.885713i	0.697764	+	0.716327i	$0.254178\pi$
$641$	−7.28615	+	22.4245i	−0.287786	+	0.885713i	−0.985550	+	0.169385i	$0.945822\pi$
$642$	−11.3497	−	34.9309i	−0.447938	−	1.37861i
$643$	−23.2031	+	16.8581i	−0.915042	+	0.664817i	−0.942285	−	0.334812i	$-0.891327\pi$
$643$	−23.2031	+	16.8581i	−0.915042	+	0.664817i	0.0272428	+	0.999629i	$0.491327\pi$
$644$	0.220949	−	0.160529i	0.00870663	−	0.00632574i
$645$	2.03220	+	6.25446i	0.0800177	+	0.246269i
$646$	10.0028	−	30.7855i	0.393556	−	1.21124i
$647$	−4.39104	−	3.19028i	−0.172630	−	0.125423i	0.498115	−	0.867111i	$-0.334026\pi$
$647$	−4.39104	−	3.19028i	−0.172630	−	0.125423i	−0.670745	+	0.741688i	$0.734026\pi$
$648$	20.9011			0.821074
$649$		0			0
$650$	−11.0986			−0.435323
$651$	1.69369	+	1.23053i	0.0663808	+	0.0482284i
$652$	0.542130	−	1.66851i	0.0212315	−	0.0653437i
$653$	−3.81392	−	11.7380i	−0.149250	−	0.459344i	0.848283	−	0.529543i	$-0.177637\pi$
$653$	−3.81392	−	11.7380i	−0.149250	−	0.459344i	−0.997533	+	0.0701988i	$0.977637\pi$
$654$	−21.1868	+	15.3931i	−0.828468	+	0.601917i
$655$	−3.65023	+	2.65205i	−0.142626	+	0.103624i
$656$	−1.37689	−	4.23762i	−0.0537584	−	0.165451i
$657$	−1.57221	+	4.83878i	−0.0613379	+	0.188779i
$658$	7.58873	+	5.51353i	0.295839	+	0.214940i
$659$	−16.2115			−0.631512			−0.315756	−	0.948840i	$-0.602258\pi$
$659$	−16.2115			−0.631512			−0.315756	+	0.948840i	$0.602258\pi$
$660$		0			0
$661$	43.7050			1.69993			0.849964	−	0.526840i	$-0.176623\pi$
$661$	43.7050			1.69993			0.849964	+	0.526840i	$0.176623\pi$
$662$	−11.2450	−	8.16994i	−0.437048	−	0.317534i
$663$	4.13564	−	12.7282i	0.160615	−	0.494322i
$664$	−14.4614	−	44.5078i	−0.561213	−	1.72724i
$665$	1.59417	−	1.15823i	0.0618193	−	0.0449144i
$666$	−0.880296	+	0.639573i	−0.0341108	+	0.0247829i
$667$	1.51690	+	4.66854i	0.0587346	+	0.180766i
$668$	−0.295721	+	0.910136i	−0.0114418	+	0.0352142i
$669$	−33.2792	−	24.1787i	−1.28665	−	0.934803i
$670$	−3.20093			−0.123663
$671$		0			0
$672$	1.38197			0.0533105
$673$	−4.74166	−	3.44502i	−0.182778	−	0.132796i	0.492634	−	0.870237i	$-0.336034\pi$
$673$	−4.74166	−	3.44502i	−0.182778	−	0.132796i	−0.675412	+	0.737441i	$0.736034\pi$
$674$	8.70280	−	26.7845i	0.335219	−	1.03170i
$675$	−8.08655	−	24.8879i	−0.311252	−	0.957934i
$676$	1.28481	−	0.933467i	0.0494157	−	0.0359026i
$677$	−16.6074	+	12.0660i	−0.638275	+	0.463734i	−0.859257	−	0.511544i	$-0.829074\pi$
$677$	−16.6074	+	12.0660i	−0.638275	+	0.463734i	0.220982	+	0.975278i	$0.429074\pi$
$678$	−1.29811	−	3.99519i	−0.0498538	−	0.153434i
$679$	−0.835464	+	2.57129i	−0.0320622	+	0.0986772i
$680$	−5.35206	−	3.88850i	−0.205242	−	0.149117i
$681$	−35.1271			−1.34607
$682$		0			0
$683$	38.7055			1.48103			0.740513	−	0.672042i	$-0.234583\pi$
$683$	38.7055			1.48103			0.740513	+	0.672042i	$0.234583\pi$
$684$	−0.197396	−	0.143416i	−0.00754761	−	0.00548366i
$685$	−2.02075	+	6.21923i	−0.0772090	+	0.237625i
$686$	0.453245	+	1.39494i	0.0173050	+	0.0532592i
$687$	26.8750	−	19.5258i	1.02535	−	0.744957i
$688$	−30.1509	+	21.9059i	−1.14949	+	0.835156i
$689$	−6.45647	−	19.8710i	−0.245972	−	0.757024i
$690$	0.617843	−	1.90153i	0.0235209	−	0.0723898i
$691$	18.7126	+	13.5955i	0.711860	+	0.517197i	0.883773	−	0.467916i	$-0.154995\pi$
$691$	18.7126	+	13.5955i	0.711860	+	0.517197i	−0.171913	+	0.985112i	$0.554995\pi$
$692$	−0.202603			−0.00770182
$693$		0			0
$694$	−4.47105			−0.169719
$695$	3.61646	+	2.62751i	0.137180	+	0.0996673i
$696$	−3.68698	+	11.3474i	−0.139755	+	0.430121i
$697$	−1.68176	−	5.17592i	−0.0637011	−	0.196052i
$698$	23.0156	−	16.7218i	0.871155	−	0.632931i
$699$	−0.908531	+	0.660086i	−0.0343638	+	0.0249668i
$700$	−0.223590	−	0.688138i	−0.00845090	−	0.0260092i
$701$	−10.9734	+	33.7727i	−0.414460	+	1.27558i	0.498273	+	0.867020i	$0.333968\pi$
$701$	−10.9734	+	33.7727i	−0.414460	+	1.27558i	−0.912733	+	0.408557i	$0.866032\pi$
$702$	−10.2744	−	7.46482i	−0.387784	−	0.281742i
$703$	8.19985			0.309263
$704$		0			0
$705$	4.82965			0.181895
$706$	12.7662	+	9.27518i	0.480462	+	0.349076i
$707$	−0.0552464	+	0.170031i	−0.00207775	+	0.00639467i
$708$	0.650893	+	2.00324i	0.0244621	+	0.0752865i
$709$	−35.4386	+	25.7476i	−1.33092	+	0.966972i	−0.331197	+	0.943562i	$0.607453\pi$
$709$	−35.4386	+	25.7476i	−1.33092	+	0.966972i	−0.999726	+	0.0234107i	$0.992547\pi$
$710$	−5.39601	+	3.92043i	−0.202509	+	0.147131i
$711$	0.422835	+	1.30135i	0.0158576	+	0.0488045i
$712$	7.47403	−	23.0027i	0.280101	−	0.862063i
$713$	1.88945	+	1.37277i	0.0707604	+	0.0514105i
$714$	12.4056			0.464268
$715$		0			0
$716$	2.69149			0.100586
$717$	−0.453654	−	0.329599i	−0.0169420	−	0.0123091i
$718$	−0.275222	+	0.847046i	−0.0102712	+	0.0316115i
$719$	4.90115	+	15.0842i	0.182782	+	0.562546i	0.999903	−	0.0139205i	$-0.00443118\pi$
$719$	4.90115	+	15.0842i	0.182782	+	0.562546i	−0.817121	+	0.576466i	$0.804431\pi$
$720$	−0.617255	+	0.448462i	−0.0230037	+	0.0167132i
$721$	−13.6540	+	9.92019i	−0.508500	+	0.369447i
$722$	−0.532741	−	1.63961i	−0.0198266	−	0.0610199i
$723$	−5.21858	+	16.0611i	−0.194081	+	0.597320i
$724$	0.117972	+	0.0857118i	0.00438440	+	0.00318545i
$725$	13.0049			0.482992
$726$		0			0
$727$	13.7719			0.510770			0.255385	−	0.966839i	$-0.417798\pi$
$727$	13.7719			0.510770			0.255385	+	0.966839i	$0.417798\pi$
$728$	3.47110	+	2.52190i	0.128648	+	0.0934680i
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$	2.81777	+	8.67220i	0.104290	+	0.320972i
$731$	−36.8269	+	26.7563i	−1.36209	+	0.989619i
$732$	3.01842	−	2.19301i	0.111564	−	0.0810560i
$733$	6.04675	+	18.6100i	0.223342	+	0.687376i	0.998456	+	0.0555542i	$0.0176926\pi$
$733$	6.04675	+	18.6100i	0.223342	+	0.687376i	−0.775114	+	0.631822i	$0.782307\pi$
$734$	12.5380	−	38.5881i	0.462788	−	1.42431i
$735$	0.610960	+	0.443888i	0.0225356	+	0.0163731i
$736$	1.54170			0.0568278
$737$		0			0
$738$	−0.583280			−0.0214708
$739$	−9.02392	−	6.55626i	−0.331950	−	0.241176i	0.409307	−	0.912397i	$-0.365770\pi$
$739$	−9.02392	−	6.55626i	−0.331950	−	0.241176i	−0.741258	+	0.671220i	$0.765770\pi$
$740$	−0.0423829	+	0.130441i	−0.00155803	+	0.00479511i
$741$	3.34021	+	10.2801i	0.122706	+	0.377649i
$742$	15.6685	−	11.3838i	0.575210	−	0.417914i
$743$	16.7102	−	12.1407i	0.613038	−	0.445398i	−0.237445	−	0.971401i	$-0.576310\pi$
$743$	16.7102	−	12.1407i	0.613038	−	0.445398i	0.850483	+	0.526003i	$0.176310\pi$
$744$	1.75418	+	5.39881i	0.0643113	+	0.197930i
$745$	−2.15801	+	6.64168i	−0.0790635	+	0.243332i
$746$	−34.9472	−	25.3907i	−1.27951	−	0.929618i
$747$	−6.59231			−0.241200
$748$		0			0
$749$	15.4762			0.565489
$750$	−8.76593	−	6.36882i	−0.320087	−	0.232557i
$751$	8.21957	−	25.2972i	0.299936	−	0.923109i	−0.681582	−	0.731742i	$-0.738708\pi$
$751$	8.21957	−	25.2972i	0.299936	−	0.923109i	0.981518	−	0.191367i	$-0.0612922\pi$
$752$	8.45780	+	26.0304i	0.308424	+	0.949233i
$753$	−9.15661	+	6.65266i	−0.333685	+	0.242437i
$754$	5.10606	−	3.70977i	0.185952	−	0.135102i
$755$	0.414271	+	1.27499i	0.0150769	+	0.0464018i
$756$	0.255849	−	0.787424i	0.00930515	−	0.0286383i
$757$	−17.0702	−	12.4022i	−0.620427	−	0.450767i	0.232644	−	0.972562i	$-0.425262\pi$
$757$	−17.0702	−	12.4022i	−0.620427	−	0.450767i	−0.853071	+	0.521796i	$0.825262\pi$
$758$	37.1723			1.35016
$759$		0			0
$760$	5.34311			0.193815
$761$	−6.47006	−	4.70077i	−0.234539	−	0.170403i	0.464308	−	0.885674i	$-0.346303\pi$
$761$	−6.47006	−	4.70077i	−0.234539	−	0.170403i	−0.698847	+	0.715271i	$0.746303\pi$
$762$	−6.26311	+	19.2759i	−0.226889	+	0.698292i
$763$	−3.40997	−	10.4948i	−0.123449	−	0.379938i
$764$	1.96937	−	1.43083i	0.0712494	−	0.0517657i
$765$	−0.753927	+	0.547760i	−0.0272583	+	0.0198043i
$766$	−14.4731	−	44.5436i	−0.522935	−	1.60943i
$767$	−4.20698	+	12.9477i	−0.151905	+	0.467516i
$768$	4.72685	+	3.43426i	0.170566	+	0.123923i
$769$	52.0476			1.87689			0.938443	−	0.345435i	$-0.112269\pi$
$769$	52.0476			1.87689			0.938443	+	0.345435i	$0.112269\pi$
$770$		0			0
$771$	16.0969			0.579716
$772$	1.48692	+	1.08031i	0.0535155	+	0.0388813i
$773$	−0.488554	+	1.50361i	−0.0175721	+	0.0540812i	−0.959458	−	0.281851i	$-0.909051\pi$
$773$	−0.488554	+	1.50361i	−0.0175721	+	0.0540812i	0.941886	+	0.335933i	$0.109051\pi$
$774$	1.50760	+	4.63992i	0.0541896	+	0.166778i
$775$	5.00575	−	3.63689i	0.179812	−	0.130641i
$776$	−5.93089	+	4.30904i	−0.212906	+	0.154686i
$777$	0.971104	+	2.98875i	0.0348382	+	0.107221i
$778$	8.04587	−	24.7626i	0.288458	−	0.887784i
$779$	3.55606	+	2.58363i	0.127409	+	0.0925681i
$780$	−0.180798			−0.00647361
$781$		0			0
$782$	13.8395			0.494899
$783$	12.0392	+	8.74702i	0.430247	+	0.312593i
$784$	−1.32250	+	4.07025i	−0.0472323	+	0.145366i
$785$	−2.72336	−	8.38164i	−0.0972009	−	0.299154i
$786$	18.5606	−	13.4850i	0.662034	−	0.480996i
$787$	18.9235	−	13.7487i	0.674549	−	0.490089i	−0.196996	−	0.980404i	$-0.563118\pi$
$787$	18.9235	−	13.7487i	0.674549	−	0.490089i	0.871545	+	0.490316i	$0.163118\pi$
$788$	0.107620	+	0.331220i	0.00383380	+	0.0117992i
$789$	7.09017	−	21.8213i	0.252417	−	0.776859i
$790$	1.98399	+	1.44145i	0.0705872	+	0.0512846i
$791$	1.77008			0.0629367
$792$		0			0
$793$	24.1147			0.856339
$794$	15.7875	+	11.4703i	0.560276	+	0.407064i
$795$	3.08146	−	9.48377i	0.109288	−	0.336355i
$796$	0.948177	+	2.91819i	0.0336072	+	0.103432i
$797$	37.3376	−	27.1274i	1.32257	−	0.960900i	0.322669	−	0.946512i	$-0.395420\pi$
$797$	37.3376	−	27.1274i	1.32257	−	0.960900i	0.999896	−	0.0143887i	$-0.00458021\pi$
$798$	−8.10599	+	5.88935i	−0.286949	+	0.208481i
$799$	10.3305	+	31.7941i	0.365468	+	1.12479i
$800$	1.26217	−	3.88455i	0.0446243	−	0.137339i
$801$	−2.75638	−	2.00262i	−0.0973918	−	0.0707593i
$802$	−5.11834			−0.180735
$803$		0			0
$804$	1.14470			0.0403704
$805$	0.681577	+	0.495195i	0.0240224	+	0.0174533i
$806$	0.927927	−	2.85587i	0.0326848	−	0.100594i
$807$	9.20154	+	28.3194i	0.323910	+	0.996891i
$808$	−0.392189	+	0.284942i	−0.0137972	+	0.0100242i
$809$	27.3044	−	19.8378i	0.959972	−	0.697461i	0.00682787	−	0.999977i	$-0.497827\pi$
$809$	27.3044	−	19.8378i	0.959972	−	0.697461i	0.953144	+	0.302516i	$0.0978266\pi$
$810$	−1.63062	−	5.01854i	−0.0572943	−	0.176334i
$811$	9.50690	−	29.2592i	0.333833	−	1.02743i	−0.633462	−	0.773774i	$-0.718367\pi$
$811$	9.50690	−	29.2592i	0.333833	−	1.02743i	0.967294	−	0.253657i	$-0.0816334\pi$
$812$	0.332880	+	0.241851i	0.0116818	+	0.00848731i
$813$	1.18212			0.0414588
$814$		0			0
$815$	5.41182			0.189568
$816$	29.2846	+	21.2765i	1.02517	+	0.744827i
$817$	11.3611	−	34.9659i	0.397475	−	1.22330i
$818$	13.4276	+	41.3259i	0.469485	+	1.44493i
$819$	0.488963	−	0.355252i	0.0170857	−	0.0124135i
$820$	−0.0594801	+	0.0432148i	−0.00207714	+	0.00150913i
$821$	−3.73242	−	11.4872i	−0.130262	−	0.400906i	0.864561	−	0.502528i	$-0.167597\pi$
$821$	−3.73242	−	11.4872i	−0.130262	−	0.400906i	−0.994823	+	0.101622i	$0.967597\pi$
$822$	10.2750	−	31.6233i	0.358383	−	1.10299i
$823$	20.0787	+	14.5880i	0.699900	+	0.508507i	0.879900	−	0.475159i	$-0.157610\pi$
$823$	20.0787	+	14.5880i	0.699900	+	0.508507i	−0.179999	+	0.983667i	$0.557610\pi$
$824$	−45.7634			−1.59424
$825$		0			0
$826$	−12.6196			−0.439092
$827$	4.18529	+	3.04079i	0.145537	+	0.105739i	0.658171	−	0.752868i	$-0.271330\pi$
$827$	4.18529	+	3.04079i	0.145537	+	0.105739i	−0.512634	+	0.858607i	$0.671330\pi$
$828$	0.0322361	−	0.0992125i	0.00112028	−	0.00344787i
$829$	9.75057	+	30.0092i	0.338651	+	1.04226i	0.964895	+	0.262635i	$0.0845914\pi$
$829$	9.75057	+	30.0092i	0.338651	+	1.04226i	−0.626244	+	0.779627i	$0.715409\pi$
$830$	−9.55847	+	6.94464i	−0.331779	+	0.241052i
$831$	−19.7196	+	14.3271i	−0.684064	+	0.497001i
$832$	3.57270	+	10.9956i	0.123861	+	0.381205i
$833$	−1.61533	+	4.97148i	−0.0559679	+	0.172252i
$834$	−18.3889	−	13.3603i	−0.636755	−	0.462629i
$835$	−2.95204			−0.102160
$836$		0			0
$837$	7.08018			0.244727
$838$	13.8184	+	10.0396i	0.477348	+	0.346813i
$839$	−1.80355	+	5.55077i	−0.0622656	+	0.191634i	−0.977350	−	0.211628i	$-0.932124\pi$
$839$	−1.80355	+	5.55077i	−0.0622656	+	0.191634i	0.915085	+	0.403262i	$0.132124\pi$
$840$	0.632782	+	1.94750i	0.0218330	+	0.0671952i
$841$	17.4784	−	12.6988i	0.602703	−	0.437889i
$842$	−23.5956	+	17.1432i	−0.813157	+	0.590793i
$843$	−5.34806	−	16.4596i	−0.184197	−	0.566900i
$844$	−0.250854	+	0.772050i	−0.00863475	+	0.0265750i
$845$	3.96333	+	2.87953i	0.136343	+	0.0990588i
$846$	3.58291			0.123183
$847$		0			0
$848$	56.5112			1.94060
$849$	−11.9237	−	8.66308i	−0.409221	−	0.297316i
$850$	11.3302	−	34.8707i	0.388622	−	1.19606i
$851$	1.08335	+	3.33420i	0.0371367	+	0.114295i
$852$	1.92969	−	1.40200i	0.0661101	−	0.0480318i
$853$	−16.4604	+	11.9592i	−0.563593	+	0.409475i	−0.832772	−	0.553616i	$-0.813248\pi$
$853$	−16.4604	+	11.9592i	−0.563593	+	0.409475i	0.269179	+	0.963090i	$0.413248\pi$
$854$	6.90752	+	21.2592i	0.236371	+	0.727474i
$855$	0.232586	−	0.715828i	0.00795429	−	0.0244808i
$856$	33.9499	+	24.6661i	1.16039	+	0.843069i
$857$	15.1087			0.516104			0.258052	−	0.966131i	$-0.416919\pi$
$857$	15.1087			0.516104			0.258052	+	0.966131i	$0.416919\pi$
$858$		0			0
$859$	−33.9641			−1.15884			−0.579420	−	0.815029i	$-0.696721\pi$
$859$	−33.9641			−1.15884			−0.579420	+	0.815029i	$0.696721\pi$
$860$	0.497507	+	0.361460i	0.0169648	+	0.0123257i
$861$	−0.520561	+	1.60212i	−0.0177407	+	0.0546002i
$862$	−13.7090	−	42.1920i	−0.466931	−	1.43707i
$863$	2.24691	−	1.63248i	0.0764859	−	0.0555702i	−0.548885	−	0.835898i	$-0.684948\pi$
$863$	2.24691	−	1.63248i	0.0764859	−	0.0555702i	0.625371	+	0.780327i	$0.284948\pi$
$864$	3.78115	−	2.74717i	0.128637	−	0.0934606i
$865$	−0.193130	−	0.594395i	−0.00656663	−	0.0202100i
$866$	−2.58676	+	7.96122i	−0.0879016	+	0.270533i
$867$	13.5155	+	9.81958i	0.459010	+	0.333490i
$868$	0.195764			0.00664466
$869$		0			0
$870$	3.01224			0.102125
$871$	5.98562	+	4.34881i	0.202815	+	0.147354i
$872$	9.24629	−	28.4571i	0.313119	−	0.963681i
$873$	0.319119	+	0.982147i	0.0108005	+	0.0332406i
$874$	−9.04292	+	6.57006i	−0.305881	+	0.222236i
$875$	3.69369	−	2.68362i	0.124869	−	0.0907229i
$876$	−1.00767	−	3.10130i	−0.0340461	−	0.104783i
$877$	−15.3514	+	47.2469i	−0.518381	+	1.59541i	0.258662	+	0.965968i	$0.416718\pi$
$877$	−15.3514	+	47.2469i	−0.518381	+	1.59541i	−0.777044	+	0.629446i	$0.783282\pi$
$878$	8.12680	+	5.90446i	0.274266	+	0.199266i
$879$	19.2368			0.648841
$880$		0			0
$881$	−27.3064			−0.919975			−0.459988	−	0.887925i	$-0.652146\pi$
$881$	−27.3064			−0.919975			−0.459988	+	0.887925i	$0.652146\pi$
$882$	0.453245	+	0.329302i	0.0152616	+	0.0110882i
$883$	−5.50388	+	16.9392i	−0.185220	+	0.570049i	−0.999952	−	0.00978852i	$-0.996884\pi$
$883$	−5.50388	+	16.9392i	−0.185220	+	0.570049i	0.814732	+	0.579838i	$0.196884\pi$
$884$	−0.386723	−	1.19021i	−0.0130069	−	0.0400312i
$885$	−5.25663	+	3.81916i	−0.176700	+	0.128380i
$886$	−0.119486	+	0.0868116i	−0.00401421	+	0.00291649i
$887$	5.09040	+	15.6666i	0.170919	+	0.526034i	0.999424	−	0.0339479i	$-0.0108080\pi$
$887$	5.09040	+	15.6666i	0.170919	+	0.526034i	−0.828505	+	0.559982i	$0.810808\pi$
$888$	−2.63319	+	8.10413i	−0.0883641	+	0.271957i
$889$	−6.90919	−	5.01982i	−0.231727	−	0.168359i
$890$	−6.10625			−0.204682
$891$		0			0
$892$	−3.84656			−0.128792
$893$	−21.8438	−	15.8705i	−0.730975	−	0.531084i
$894$	10.9730	−	33.7714i	0.366992	−	1.12948i
$895$	2.56565	+	7.89625i	0.0857601	+	0.263942i
$896$	−10.0522	+	7.30332i	−0.335819	+	0.243987i
$897$	−3.73877	+	2.71638i	−0.124834	+	0.0906971i
$898$	−13.9621	−	42.9709i	−0.465921	−	1.43396i
$899$	−1.08731	+	3.34640i	−0.0362639	+	0.111609i
$900$	−0.223590	−	0.162447i	−0.00745299	−	0.00541491i
$901$	69.0238			2.29952
$902$		0			0
$903$	14.0902			0.468891
$904$	3.88299	+	2.82116i	0.129146	+	0.0938304i
$905$	−0.139004	+	0.427809i	−0.00462064	+	0.0142209i
$906$	−2.10647	−	6.48305i	−0.0699828	−	0.215385i
$907$	−23.0470	+	16.7446i	−0.765264	+	0.555997i	−0.900520	−	0.434814i	$-0.856814\pi$
$907$	−23.0470	+	16.7446i	−0.765264	+	0.555997i	0.135257	+	0.990811i	$0.456814\pi$
$908$	−2.65741	+	1.93072i	−0.0881891	+	0.0640731i
$909$	0.0211022	+	0.0649460i	0.000699917	+	0.00215412i
$910$	0.334729	−	1.03019i	0.0110962	−	0.0341505i
$911$	9.08955	+	6.60394i	0.301150	+	0.218798i	0.728090	−	0.685482i	$-0.240408\pi$
$911$	9.08955	+	6.60394i	0.301150	+	0.218798i	−0.426940	+	0.904280i	$0.640408\pi$
$912$	−29.2356			−0.968088
$913$		0			0
$914$	−33.9337			−1.12243
$915$	9.31112	+	6.76492i	0.307816	+	0.223641i
$916$	0.959910	−	2.95430i	0.0317163	−	0.0976128i
$917$	2.98729	+	9.19394i	0.0986491	+	0.303611i
$918$	33.9426	−	24.6607i	1.12027	−	0.813925i
$919$	0.631403	−	0.458741i	0.0208281	−	0.0151325i	−0.577323	−	0.816516i	$-0.695902\pi$
$919$	0.631403	−	0.458741i	0.0208281	−	0.0151325i	0.598151	+	0.801384i	$0.295902\pi$
$920$	0.705922	+	2.17260i	0.0232735	+	0.0716286i
$921$	1.11036	−	3.41734i	0.0365876	−	0.112605i
$922$	−3.29687	−	2.39532i	−0.108577	−	0.0788856i
$923$	15.4167			0.507446
$924$		0			0
$925$	9.28795			0.305386
$926$	30.9646	+	22.4971i	1.01756	+	0.739301i
$927$	−1.99209	+	6.13101i	−0.0654287	+	0.201369i
$928$	0.717755	+	2.20902i	0.0235615	+	0.0725148i
$929$	−21.5169	+	15.6329i	−0.705946	+	0.512899i	−0.881863	−	0.471505i	$-0.843711\pi$
$929$	−21.5169	+	15.6329i	−0.705946	+	0.512899i	0.175918	+	0.984405i	$0.443711\pi$
$930$	1.15945	−	0.842387i	0.0380198	−	0.0276230i
$931$	−1.30464	−	4.01528i	−0.0427580	−	0.131596i
$932$	−0.0324505	+	0.0998725i	−0.00106295	+	0.00327143i
$933$	−28.0294	−	20.3646i	−0.917642	−	0.666706i
$934$	−3.89900			−0.127579
$935$		0			0
$936$	1.63883			0.0535669
$937$	33.9542	+	24.6691i	1.10923	+	0.805906i	0.982543	−	0.186036i	$-0.0595642\pi$
$937$	33.9542	+	24.6691i	1.10923	+	0.805906i	0.126691	+	0.991942i	$0.459564\pi$
$938$	−2.11930	+	6.52252i	−0.0691974	+	0.212968i
$939$	15.7774	+	48.5578i	0.514875	+	1.58462i
$940$	0.365368	−	0.265456i	0.0119170	−	0.00865821i
$941$	−39.6685	+	28.8209i	−1.29316	+	0.939533i	−0.999864	−	0.0164899i	$-0.994751\pi$
$941$	−39.6685	+	28.8209i	−1.29316	+	0.939533i	−0.293292	+	0.956023i	$0.594751\pi$
$942$	13.8477	+	42.6187i	0.451181	+	1.38859i
$943$	−0.580730	+	1.78730i	−0.0189112	+	0.0582026i
$944$	−29.7897	−	21.6435i	−0.969574	−	0.704437i
$945$	2.55402			0.0830823
$946$		0			0
$947$	−27.2953			−0.886978			−0.443489	−	0.896280i	$-0.646259\pi$
$947$	−27.2953			−0.886978			−0.443489	+	0.896280i	$0.646259\pi$
$948$	−0.709503	−	0.515484i	−0.0230436	−	0.0167422i
$949$	6.51299	−	20.0449i	0.211421	−	0.650686i
$950$	9.15097	+	28.1638i	0.296897	+	0.913754i
$951$	−17.2799	+	12.5546i	−0.560339	+	0.407110i
$952$	−11.4671	+	8.33134i	−0.371651	+	0.270020i
$953$	−6.10023	−	18.7746i	−0.197606	−	0.608169i	−0.999936	−	0.0112883i	$-0.996407\pi$
$953$	−6.10023	−	18.7746i	−0.197606	−	0.608169i	0.802330	−	0.596880i	$-0.203593\pi$
$954$	2.28601	−	7.03561i	0.0740122	−	0.227786i
$955$	6.07505	+	4.41378i	0.196584	+	0.142827i
$956$	−0.0524354			−0.00169588
$957$		0			0
$958$	12.1478			0.392478
$959$	11.3350	+	8.23535i	0.366026	+	0.265933i
$960$	−1.70513	+	5.24785i	−0.0550329	+	0.169374i
$961$	−9.06221	−	27.8906i	−0.292329	−	0.899697i
$962$	3.64668	−	2.64947i	0.117574	−	0.0854222i
$963$	4.78241	−	3.47463i	0.154111	−	0.111968i
$964$	0.487989	+	1.50188i	0.0157171	+	0.0483721i
$965$	−1.75200	+	5.39211i	−0.0563990	+	0.173578i
$966$	−3.46566	−	2.51795i	−0.111506	−	0.0810137i
$967$	12.6734			0.407551			0.203775	−	0.979018i	$-0.434679\pi$
$967$	12.6734			0.407551			0.203775	+	0.979018i	$0.434679\pi$
$968$		0			0
$969$	−35.7089			−1.14714
$970$	1.49734	+	1.08788i	0.0480768	+	0.0349298i
$971$	5.16170	−	15.8861i	0.165647	−	0.509809i	−0.833436	−	0.552615i	$-0.813630\pi$
$971$	5.16170	−	15.8861i	0.165647	−	0.509809i	0.999083	+	0.0428065i	$0.0136299\pi$
$972$	−0.184414	−	0.567569i	−0.00591509	−	0.0182048i
$973$	7.74848	−	5.62960i	0.248405	−	0.180477i
$974$	23.2523	−	16.8938i	0.745052	−	0.541312i
$975$	3.78345	+	11.6443i	0.121167	+	0.372914i
$976$	−20.1552	+	62.0312i	−0.645151	+	1.98557i
$977$	−22.1227	−	16.0731i	−0.707769	−	0.514224i	0.174684	−	0.984625i	$-0.444110\pi$
$977$	−22.1227	−	16.0731i	−0.707769	−	0.514224i	−0.882453	+	0.470400i	$0.844110\pi$
$978$	−27.5178			−0.879924
$979$		0			0
$980$	0.0706175			0.00225579
$981$	−3.40997	−	2.47749i	−0.108872	−	0.0791001i
$982$	12.9998	−	40.0093i	0.414841	−	1.27675i
$983$	−16.9979	−	52.3143i	−0.542150	−	1.66857i	−0.727671	−	0.685926i	$-0.759397\pi$
$983$	−16.9979	−	52.3143i	−0.542150	−	1.66857i	0.185521	−	0.982640i	$-0.440603\pi$
$984$	−3.69542	+	2.68488i	−0.117806	+	0.0855908i
$985$	−0.869141	+	0.631468i	−0.0276931	+	0.0201202i
$986$	6.44313	+	19.8299i	0.205191	+	0.631513i
$987$	3.19765	−	9.84135i	0.101782	−	0.313254i
$988$	0.817723	+	0.594110i	0.0260152	+	0.0189012i
$989$	15.7188			0.499828
$990$		0			0
$991$	53.2327			1.69099			0.845497	−	0.533980i	$-0.179304\pi$
$991$	53.2327			1.69099			0.845497	+	0.533980i	$0.179304\pi$
$992$	0.894035	+	0.649555i	0.0283857	+	0.0206234i
$993$	−4.73826	+	14.5829i	−0.150364	+	0.462774i
$994$	4.41601	+	13.5911i	0.140067	+	0.431083i
$995$	−7.65750	+	5.56350i	−0.242759	+	0.176375i
$996$	3.41825	−	2.48350i	0.108311	−	0.0786927i
$997$	−10.1217	−	31.1515i	−0.320558	−	0.986577i	−0.973406	−	0.229087i	$-0.926426\pi$
$997$	−10.1217	−	31.1515i	−0.320558	−	0.986577i	0.652848	−	0.757489i	$-0.273574\pi$
$998$	12.6682	−	38.9886i	0.401004	−	1.23416i
$999$	8.59825	+	6.24700i	0.272037	+	0.197646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.q.323.1		8
11.2	odd	10		847.2.f.p.148.1		8
11.3	even	5	inner	847.2.f.q.729.1		8
11.4	even	5		847.2.f.s.372.2		8
11.5	even	5		847.2.a.k.1.4		4
11.6	odd	10		847.2.a.l.1.1		4
11.7	odd	10		847.2.f.p.372.1		8
11.8	odd	10		77.2.f.a.36.2	yes	8
11.9	even	5		847.2.f.s.148.2		8
11.10	odd	2		77.2.f.a.15.2	✓	8
33.5	odd	10		7623.2.a.co.1.1		4
33.8	even	10		693.2.m.g.190.1		8
33.17	even	10		7623.2.a.ch.1.4		4
33.32	even	2		693.2.m.g.631.1		8
77.6	even	10		5929.2.a.bi.1.1		4
77.10	even	6		539.2.q.b.422.1		16
77.19	even	30		539.2.q.b.410.1		16
77.27	odd	10		5929.2.a.bb.1.4		4
77.30	odd	30		539.2.q.c.410.1		16
77.32	odd	6		539.2.q.c.422.1		16
77.41	even	10		539.2.f.d.344.2		8
77.52	even	30		539.2.q.b.520.2		16
77.54	even	6		539.2.q.b.312.2		16
77.65	odd	6		539.2.q.c.312.2		16
77.74	odd	30		539.2.q.c.520.2		16
77.76	even	2		539.2.f.d.246.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.2	✓	8	11.10	odd	2
77.2.f.a.36.2	yes	8	11.8	odd	10
539.2.f.d.246.2		8	77.76	even	2
539.2.f.d.344.2		8	77.41	even	10
539.2.q.b.312.2		16	77.54	even	6
539.2.q.b.410.1		16	77.19	even	30
539.2.q.b.422.1		16	77.10	even	6
539.2.q.b.520.2		16	77.52	even	30
539.2.q.c.312.2		16	77.65	odd	6
539.2.q.c.410.1		16	77.30	odd	30
539.2.q.c.422.1		16	77.32	odd	6
539.2.q.c.520.2		16	77.74	odd	30
693.2.m.g.190.1		8	33.8	even	10
693.2.m.g.631.1		8	33.32	even	2
847.2.a.k.1.4		4	11.5	even	5
847.2.a.l.1.1		4	11.6	odd	10
847.2.f.p.148.1		8	11.2	odd	10
847.2.f.p.372.1		8	11.7	odd	10
847.2.f.q.323.1		8	1.1	even	1	trivial
847.2.f.q.729.1		8	11.3	even	5	inner
847.2.f.s.148.2		8	11.9	even	5
847.2.f.s.372.2		8	11.4	even	5
5929.2.a.bb.1.4		4	77.27	odd	10
5929.2.a.bi.1.1		4	77.6	even	10
7623.2.a.ch.1.4		4	33.17	even	10
7623.2.a.co.1.1		4	33.5	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)

\(f(q)\)	\(=\)	\(q+(-1.18661 - 0.862123i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.0467549 + 0.143897i) q^{4} +(-0.377594 + 0.274338i) q^{5} +(1.91998 - 1.39494i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.837913 + 2.57883i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})\)	\(q+(-1.18661 - 0.862123i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.0467549 + 0.143897i) q^{4} +(-0.377594 + 0.274338i) q^{5} +(1.91998 - 1.39494i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.837913 + 2.57883i) q^{8} +(0.309017 + 0.224514i) q^{9} +0.684570 q^{10} -0.244812 q^{12} +(-1.28012 - 0.930062i) q^{13} +(0.453245 - 1.39494i) q^{14} +(-0.233366 - 0.718226i) q^{15} +(3.46236 - 2.51555i) q^{16} +(4.22899 - 3.07254i) q^{17} +(-0.173124 - 0.532822i) q^{18} +(-1.30464 + 4.01528i) q^{19} +(-0.0571308 - 0.0415079i) q^{20} -1.61803 q^{21} -1.80505 q^{23} +(-3.54946 - 2.57883i) q^{24} +(-1.47777 + 4.54811i) q^{25} +(0.717177 + 2.20724i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(-0.122406 + 0.0889332i) q^{28} +(-0.840363 - 2.58637i) q^{29} +(-0.342285 + 1.05345i) q^{30} +(-1.04675 - 0.760512i) q^{31} -0.854102 q^{32} -7.66708 q^{34} +(-0.377594 - 0.274338i) q^{35} +(-0.0178588 + 0.0549637i) q^{36} +(-0.600175 - 1.84715i) q^{37} +(5.00978 - 3.63982i) q^{38} +(2.07128 - 1.50487i) q^{39} +(-0.391081 - 1.20362i) q^{40} +(0.321724 - 0.990166i) q^{41} +(1.91998 + 1.39494i) q^{42} -8.70820 q^{43} -0.178276 q^{45} +(2.14190 + 1.55618i) q^{46} +(-1.97626 + 6.08229i) q^{47} +(2.13986 + 6.58580i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(5.67457 - 4.12281i) q^{50} +(2.61366 + 8.04402i) q^{51} +(0.0739811 - 0.227690i) q^{52} +(10.6826 + 7.76137i) q^{53} +8.02616 q^{54} -2.71154 q^{56} +(-5.52656 - 4.01528i) q^{57} +(-1.23259 + 3.79351i) q^{58} +(-2.65875 - 8.18278i) q^{59} +(0.0924396 - 0.0671613i) q^{60} +(-12.3295 + 8.95793i) q^{61} +(0.586436 + 1.80486i) q^{62} +(-0.118034 + 0.363271i) q^{63} +(-5.91123 - 4.29476i) q^{64} +0.738517 q^{65} -4.67583 q^{67} +(0.639856 + 0.464883i) q^{68} +(0.902527 - 2.77769i) q^{69} +(0.211544 + 0.651065i) q^{70} +(-7.88234 + 5.72685i) q^{71} +(-0.837913 + 0.608780i) q^{72} +(4.11611 + 12.6681i) q^{73} +(-0.880296 + 2.70927i) q^{74} +(-6.25993 - 4.54811i) q^{75} -0.638786 q^{76} -3.75519 q^{78} +(2.89815 + 2.10563i) q^{79} +(-0.617255 + 1.89971i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(-1.23541 + 0.897575i) q^{82} +(-13.9627 + 10.1445i) q^{83} +(-0.0756511 - 0.232830i) q^{84} +(-0.753927 + 2.32035i) q^{85} +(10.3333 + 7.50755i) q^{86} +4.40020 q^{87} -8.91982 q^{89} +(0.211544 + 0.153696i) q^{90} +(0.488963 - 1.50487i) q^{91} +(-0.0843952 - 0.259742i) q^{92} +(1.69369 - 1.23053i) q^{93} +(7.58873 - 5.51353i) q^{94} +(-0.608919 - 1.87406i) q^{95} +(0.427051 - 1.31433i) q^{96} +(2.18727 + 1.58915i) q^{97} +1.46673 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 - 3 * q^8 - 2 * q^9	\( 8 q + q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 3 q^{8} - 2 q^{9} + 28 q^{10} - 14 q^{12} - 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} + 11 q^{17} - 4 q^{18} + 9 q^{19} + 21 q^{20} - 4 q^{21} - 16 q^{23} - 21 q^{24} + 5 q^{25} + 21 q^{26} - 22 q^{27} - 7 q^{28} + 9 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} - 2 q^{36} + 6 q^{37} + 35 q^{38} + 5 q^{39} + 16 q^{40} + 22 q^{41} - 3 q^{42} - 16 q^{43} + 18 q^{45} - 29 q^{46} + 7 q^{47} + 4 q^{48} - 2 q^{49} + 34 q^{50} - 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 18 q^{56} + 3 q^{57} - 39 q^{58} + 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + 8 q^{63} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} + 8 q^{69} - 2 q^{70} - 14 q^{71} - 3 q^{72} - 3 q^{73} + 9 q^{74} + 5 q^{75} + 52 q^{76} - 18 q^{78} + 9 q^{79} - 33 q^{80} - 28 q^{81} + 31 q^{82} - 23 q^{83} - 4 q^{84} + 10 q^{85} - 17 q^{86} - 12 q^{87} - 34 q^{89} - 2 q^{90} + 5 q^{91} - 34 q^{92} + 8 q^{93} + 30 q^{94} - 24 q^{95} - 10 q^{96} + 30 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 - 3 * q^8 - 2 * q^9 + 28 * q^10 - 14 * q^12 - 5 * q^13 + q^14 + 6 * q^15 - 3 * q^16 + 11 * q^17 - 4 * q^18 + 9 * q^19 + 21 * q^20 - 4 * q^21 - 16 * q^23 - 21 * q^24 + 5 * q^25 + 21 * q^26 - 22 * q^27 - 7 * q^28 + 9 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 - 2 * q^36 + 6 * q^37 + 35 * q^38 + 5 * q^39 + 16 * q^40 + 22 * q^41 - 3 * q^42 - 16 * q^43 + 18 * q^45 - 29 * q^46 + 7 * q^47 + 4 * q^48 - 2 * q^49 + 34 * q^50 - 3 * q^51 - 21 * q^52 + 2 * q^53 - 4 * q^54 - 18 * q^56 + 3 * q^57 - 39 * q^58 + 25 * q^59 - 38 * q^60 - 7 * q^61 + 5 * q^62 + 8 * q^63 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 + 8 * q^69 - 2 * q^70 - 14 * q^71 - 3 * q^72 - 3 * q^73 + 9 * q^74 + 5 * q^75 + 52 * q^76 - 18 * q^78 + 9 * q^79 - 33 * q^80 - 28 * q^81 + 31 * q^82 - 23 * q^83 - 4 * q^84 + 10 * q^85 - 17 * q^86 - 12 * q^87 - 34 * q^89 - 2 * q^90 + 5 * q^91 - 34 * q^92 + 8 * q^93 + 30 * q^94 - 24 * q^95 - 10 * q^96 + 30 * q^97 - 4 * q^98

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