LMFDB - Embedded newform 847.2.f.l.372.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.l.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.118034 + 0.363271i) q^{2} +(1.30902 - 0.951057i) q^{3} +(1.50000 + 1.08981i) q^{4} +(0.309017 + 0.951057i) q^{5} +(0.190983 + 0.587785i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})$	\(q+(-0.118034 + 0.363271i) q^{2} +(1.30902 - 0.951057i) q^{3} +(1.50000 + 1.08981i) q^{4} +(0.309017 + 0.951057i) q^{5} +(0.190983 + 0.587785i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.118034 + 0.363271i) q^{9} -0.381966 q^{10} +3.00000 q^{12} +(-0.381966 + 1.17557i) q^{13} +(0.309017 - 0.224514i) q^{14} +(1.30902 + 0.951057i) q^{15} +(0.972136 + 2.99193i) q^{16} +(0.954915 + 2.93893i) q^{17} +(-0.118034 - 0.0857567i) q^{18} +(1.42705 - 1.03681i) q^{19} +(-0.572949 + 1.76336i) q^{20} -1.61803 q^{21} +5.09017 q^{23} +(-0.736068 + 2.26538i) q^{24} +(3.23607 - 2.35114i) q^{25} +(-0.381966 - 0.277515i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-0.572949 - 1.76336i) q^{28} +(3.73607 + 2.71441i) q^{29} +(-0.500000 + 0.363271i) q^{30} +(-1.30902 + 4.02874i) q^{31} -4.14590 q^{32} -1.18034 q^{34} +(0.309017 - 0.951057i) q^{35} +(-0.572949 + 0.416272i) q^{36} +(-5.23607 - 3.80423i) q^{37} +(0.208204 + 0.640786i) q^{38} +(0.618034 + 1.90211i) q^{39} +(-1.19098 - 0.865300i) q^{40} +(9.04508 - 6.57164i) q^{41} +(0.190983 - 0.587785i) q^{42} -12.5623 q^{43} -0.381966 q^{45} +(-0.600813 + 1.84911i) q^{46} +(5.35410 - 3.88998i) q^{47} +(4.11803 + 2.99193i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.472136 + 1.45309i) q^{50} +(4.04508 + 2.93893i) q^{51} +(-1.85410 + 1.34708i) q^{52} +(-0.736068 + 2.26538i) q^{53} -2.09017 q^{54} +1.47214 q^{56} +(0.881966 - 2.71441i) q^{57} +(-1.42705 + 1.03681i) q^{58} +(-8.97214 - 6.51864i) q^{59} +(0.927051 + 2.85317i) q^{60} +(-2.35410 - 7.24518i) q^{61} +(-1.30902 - 0.951057i) q^{62} +(0.309017 - 0.224514i) q^{63} +(-1.45492 + 4.47777i) q^{64} -1.23607 q^{65} -8.32624 q^{67} +(-1.77051 + 5.44907i) q^{68} +(6.66312 - 4.84104i) q^{69} +(0.309017 + 0.224514i) q^{70} +(-4.97214 - 15.3027i) q^{71} +(-0.173762 - 0.534785i) q^{72} +(11.5172 + 8.36775i) q^{73} +(2.00000 - 1.45309i) q^{74} +(2.00000 - 6.15537i) q^{75} +3.27051 q^{76} -0.763932 q^{78} +(1.97214 - 6.06961i) q^{79} +(-2.54508 + 1.84911i) q^{80} +(6.23607 + 4.53077i) q^{81} +(1.31966 + 4.06150i) q^{82} +(0.836881 + 2.57565i) q^{83} +(-2.42705 - 1.76336i) q^{84} +(-2.50000 + 1.81636i) q^{85} +(1.48278 - 4.56352i) q^{86} +7.47214 q^{87} +6.85410 q^{89} +(0.0450850 - 0.138757i) q^{90} +(1.00000 - 0.726543i) q^{91} +(7.63525 + 5.54734i) q^{92} +(2.11803 + 6.51864i) q^{93} +(0.781153 + 2.40414i) q^{94} +(1.42705 + 1.03681i) q^{95} +(-5.42705 + 3.94298i) q^{96} +(2.16312 - 6.65740i) q^{97} -0.381966 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - q^7 - 7 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - q^{7} - 7 q^{8} + 4 q^{9} - 6 q^{10} + 12 q^{12} - 6 q^{13} - q^{14} + 3 q^{15} - 14 q^{16} + 15 q^{17} + 4 q^{18} - q^{19} - 9 q^{20} - 2 q^{21} - 2 q^{23} + 6 q^{24} + 4 q^{25} - 6 q^{26} + 9 q^{27} - 9 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{31} - 30 q^{32} + 40 q^{34} - q^{35} - 9 q^{36} - 12 q^{37} - 26 q^{38} - 2 q^{39} - 7 q^{40} + 25 q^{41} + 3 q^{42} - 10 q^{43} - 6 q^{45} - 27 q^{46} + 8 q^{47} + 12 q^{48} - q^{49} - 16 q^{50} + 5 q^{51} + 6 q^{52} + 6 q^{53} + 14 q^{54} - 12 q^{56} + 8 q^{57} + q^{58} - 18 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{62} - q^{63} - 17 q^{64} + 4 q^{65} - 2 q^{67} + 60 q^{68} + 11 q^{69} - q^{70} - 2 q^{71} - 32 q^{72} + 17 q^{73} + 8 q^{74} + 8 q^{75} - 54 q^{76} - 12 q^{78} - 10 q^{79} + q^{80} + 16 q^{81} + 50 q^{82} + 19 q^{83} - 3 q^{84} - 10 q^{85} + 35 q^{86} + 12 q^{87} + 14 q^{89} - 11 q^{90} + 4 q^{91} - 3 q^{92} + 4 q^{93} - 17 q^{94} - q^{95} - 15 q^{96} - 7 q^{97} - 6 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - q^7 - 7 * q^8 + 4 * q^9 - 6 * q^10 + 12 * q^12 - 6 * q^13 - q^14 + 3 * q^15 - 14 * q^16 + 15 * q^17 + 4 * q^18 - q^19 - 9 * q^20 - 2 * q^21 - 2 * q^23 + 6 * q^24 + 4 * q^25 - 6 * q^26 + 9 * q^27 - 9 * q^28 + 6 * q^29 - 2 * q^30 - 3 * q^31 - 30 * q^32 + 40 * q^34 - q^35 - 9 * q^36 - 12 * q^37 - 26 * q^38 - 2 * q^39 - 7 * q^40 + 25 * q^41 + 3 * q^42 - 10 * q^43 - 6 * q^45 - 27 * q^46 + 8 * q^47 + 12 * q^48 - q^49 - 16 * q^50 + 5 * q^51 + 6 * q^52 + 6 * q^53 + 14 * q^54 - 12 * q^56 + 8 * q^57 + q^58 - 18 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^62 - q^63 - 17 * q^64 + 4 * q^65 - 2 * q^67 + 60 * q^68 + 11 * q^69 - q^70 - 2 * q^71 - 32 * q^72 + 17 * q^73 + 8 * q^74 + 8 * q^75 - 54 * q^76 - 12 * q^78 - 10 * q^79 + q^80 + 16 * q^81 + 50 * q^82 + 19 * q^83 - 3 * q^84 - 10 * q^85 + 35 * q^86 + 12 * q^87 + 14 * q^89 - 11 * q^90 + 4 * q^91 - 3 * q^92 + 4 * q^93 - 17 * q^94 - q^95 - 15 * q^96 - 7 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.118034	+	0.363271i	−0.0834626	+	0.256872i	−0.984076	−	0.177750i	$-0.943118\pi$
$2$	−0.118034	+	0.363271i	−0.0834626	+	0.256872i	0.900613	+	0.434622i	$0.143118\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	−0.141846	−	0.989889i	$-0.545304\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	0.897607	+	0.440796i	$0.145304\pi$
$4$	1.50000	+	1.08981i	0.750000	+	0.544907i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i	0.996074	−	0.0885298i	$-0.0282169\pi$
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i	−0.857877	+	0.513855i	$0.828217\pi$
$6$	0.190983	+	0.587785i	0.0779685	+	0.239962i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−1.19098	+	0.865300i	−0.421076	+	0.305930i
$9$	−0.118034	+	0.363271i	−0.0393447	+	0.121090i
$10$	−0.381966			−0.120788
$11$		0			0
$11$		0			0
$12$	3.00000			0.866025
$13$	−0.381966	+	1.17557i	−0.105938	+	0.326045i	−0.989950	−	0.141421i	$-0.954833\pi$
$13$	−0.381966	+	1.17557i	−0.105938	+	0.326045i	0.884011	+	0.467466i	$0.154833\pi$
$14$	0.309017	−	0.224514i	0.0825883	−	0.0600039i
$15$	1.30902	+	0.951057i	0.337987	+	0.245562i
$16$	0.972136	+	2.99193i	0.243034	+	0.747982i
$17$	0.954915	+	2.93893i	0.231601	+	0.712794i	0.997554	+	0.0698980i	$0.0222674\pi$
$17$	0.954915	+	2.93893i	0.231601	+	0.712794i	−0.765953	+	0.642896i	$0.777733\pi$
$18$	−0.118034	−	0.0857567i	−0.0278209	−	0.0202131i
$19$	1.42705	−	1.03681i	0.327388	−	0.237861i	−0.411934	−	0.911214i	$-0.635146\pi$
$19$	1.42705	−	1.03681i	0.327388	−	0.237861i	0.739321	+	0.673353i	$0.235146\pi$
$20$	−0.572949	+	1.76336i	−0.128115	+	0.394298i
$21$	−1.61803			−0.353084
$22$		0			0
$23$	5.09017			1.06137			0.530687	−	0.847568i	$-0.321934\pi$
$23$	5.09017			1.06137			0.530687	+	0.847568i	$0.321934\pi$
$24$	−0.736068	+	2.26538i	−0.150249	+	0.462420i
$25$	3.23607	−	2.35114i	0.647214	−	0.470228i
$26$	−0.381966	−	0.277515i	−0.0749097	−	0.0544251i
$27$	1.69098	+	5.20431i	0.325430	+	1.00157i
$28$	−0.572949	−	1.76336i	−0.108277	−	0.333243i
$29$	3.73607	+	2.71441i	0.693770	+	0.504054i	0.877897	−	0.478849i	$-0.158946\pi$
$29$	3.73607	+	2.71441i	0.693770	+	0.504054i	−0.184127	+	0.982902i	$0.558946\pi$
$30$	−0.500000	+	0.363271i	−0.0912871	+	0.0663240i
$31$	−1.30902	+	4.02874i	−0.235106	+	0.723583i	0.762001	+	0.647576i	$0.224217\pi$
$31$	−1.30902	+	4.02874i	−0.235106	+	0.723583i	−0.997107	+	0.0760071i	$0.975783\pi$
$32$	−4.14590			−0.732898
$33$		0			0
$34$	−1.18034			−0.202427
$35$	0.309017	−	0.951057i	0.0522334	−	0.160758i
$36$	−0.572949	+	0.416272i	−0.0954915	+	0.0693786i
$37$	−5.23607	−	3.80423i	−0.860804	−	0.625411i	0.0672994	−	0.997733i	$-0.478562\pi$
$37$	−5.23607	−	3.80423i	−0.860804	−	0.625411i	−0.928104	+	0.372322i	$0.878562\pi$
$38$	0.208204	+	0.640786i	0.0337751	+	0.103949i
$39$	0.618034	+	1.90211i	0.0989646	+	0.304582i
$40$	−1.19098	−	0.865300i	−0.188311	−	0.136816i
$41$	9.04508	−	6.57164i	1.41260	−	1.02632i	0.419668	−	0.907678i	$-0.362147\pi$
$41$	9.04508	−	6.57164i	1.41260	−	1.02632i	0.992937	−	0.118640i	$-0.0378533\pi$
$42$	0.190983	−	0.587785i	0.0294693	−	0.0906972i
$43$	−12.5623			−1.91573			−0.957867	−	0.287213i	$-0.907271\pi$
$43$	−12.5623			−1.91573			−0.957867	+	0.287213i	$0.907271\pi$
$44$		0			0
$45$	−0.381966			−0.0569401
$46$	−0.600813	+	1.84911i	−0.0885851	+	0.272637i
$47$	5.35410	−	3.88998i	0.780976	−	0.567412i	−0.124296	−	0.992245i	$-0.539667\pi$
$47$	5.35410	−	3.88998i	0.780976	−	0.567412i	0.905272	+	0.424833i	$0.139667\pi$
$48$	4.11803	+	2.99193i	0.594387	+	0.431847i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.472136	+	1.45309i	0.0667701	+	0.205497i
$51$	4.04508	+	2.93893i	0.566425	+	0.411532i
$52$	−1.85410	+	1.34708i	−0.257118	+	0.186807i
$53$	−0.736068	+	2.26538i	−0.101107	+	0.311174i	−0.988797	−	0.149267i	$-0.952309\pi$
$53$	−0.736068	+	2.26538i	−0.101107	+	0.311174i	0.887690	+	0.460441i	$0.152309\pi$
$54$	−2.09017			−0.284436
$55$		0			0
$56$	1.47214			0.196722
$57$	0.881966	−	2.71441i	0.116819	−	0.359533i
$58$	−1.42705	+	1.03681i	−0.187381	+	0.136140i
$59$	−8.97214	−	6.51864i	−1.16807	−	0.848654i	−0.177296	−	0.984158i	$-0.556735\pi$
$59$	−8.97214	−	6.51864i	−1.16807	−	0.848654i	−0.990777	+	0.135503i	$0.956735\pi$
$60$	0.927051	+	2.85317i	0.119682	+	0.368343i
$61$	−2.35410	−	7.24518i	−0.301412	−	0.927650i	−0.980992	−	0.194049i	$-0.937838\pi$
$61$	−2.35410	−	7.24518i	−0.301412	−	0.927650i	0.679580	−	0.733601i	$-0.262162\pi$
$62$	−1.30902	−	0.951057i	−0.166245	−	0.120784i
$63$	0.309017	−	0.224514i	0.0389325	−	0.0282861i
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	−1.23607			−0.153315
$66$		0			0
$67$	−8.32624			−1.01721			−0.508606	−	0.860999i	$-0.669839\pi$
$67$	−8.32624			−1.01721			−0.508606	+	0.860999i	$0.669839\pi$
$68$	−1.77051	+	5.44907i	−0.214706	+	0.660797i
$69$	6.66312	−	4.84104i	0.802145	−	0.582793i
$70$	0.309017	+	0.224514i	0.0369346	+	0.0268346i
$71$	−4.97214	−	15.3027i	−0.590084	−	1.81609i	−0.577816	−	0.816167i	$-0.696095\pi$
$71$	−4.97214	−	15.3027i	−0.590084	−	1.81609i	−0.0122679	−	0.999925i	$-0.503905\pi$
$72$	−0.173762	−	0.534785i	−0.0204781	−	0.0630250i
$73$	11.5172	+	8.36775i	1.34799	+	0.979371i	0.999109	+	0.0422036i	$0.0134378\pi$
$73$	11.5172	+	8.36775i	1.34799	+	0.979371i	0.348880	+	0.937168i	$0.386562\pi$
$74$	2.00000	−	1.45309i	0.232495	−	0.168918i
$75$	2.00000	−	6.15537i	0.230940	−	0.710761i
$76$	3.27051			0.375153
$77$		0			0
$78$	−0.763932			−0.0864983
$79$	1.97214	−	6.06961i	0.221883	−	0.682885i	−0.776710	−	0.629858i	$-0.783113\pi$
$79$	1.97214	−	6.06961i	0.221883	−	0.682885i	0.998593	−	0.0530267i	$-0.0168868\pi$
$80$	−2.54508	+	1.84911i	−0.284549	+	0.206737i
$81$	6.23607	+	4.53077i	0.692896	+	0.503419i
$82$	1.31966	+	4.06150i	0.145732	+	0.448517i
$83$	0.836881	+	2.57565i	0.0918596	+	0.282715i	0.986423	−	0.164227i	$-0.0525130\pi$
$83$	0.836881	+	2.57565i	0.0918596	+	0.282715i	−0.894563	+	0.446942i	$0.852513\pi$
$84$	−2.42705	−	1.76336i	−0.264813	−	0.192398i
$85$	−2.50000	+	1.81636i	−0.271163	+	0.197012i
$86$	1.48278	−	4.56352i	0.159892	−	0.492098i
$87$	7.47214			0.801097
$88$		0			0
$89$	6.85410			0.726533			0.363267	−	0.931685i	$-0.381661\pi$
$89$	6.85410			0.726533			0.363267	+	0.931685i	$0.381661\pi$
$90$	0.0450850	−	0.138757i	0.00475237	−	0.0146263i
$91$	1.00000	−	0.726543i	0.104828	−	0.0761624i
$92$	7.63525	+	5.54734i	0.796030	+	0.578350i
$93$	2.11803	+	6.51864i	0.219630	+	0.675951i
$94$	0.781153	+	2.40414i	0.0805698	+	0.247968i
$95$	1.42705	+	1.03681i	0.146412	+	0.106375i
$96$	−5.42705	+	3.94298i	−0.553896	+	0.402429i
$97$	2.16312	−	6.65740i	0.219631	−	0.675956i	−0.779161	−	0.626824i	$-0.784354\pi$
$97$	2.16312	−	6.65740i	0.219631	−	0.675956i	0.998792	−	0.0491321i	$-0.0156455\pi$
$98$	−0.381966			−0.0385844
$99$		0			0
$100$	7.41641			0.741641
$101$	−4.57295	+	14.0741i	−0.455025	+	1.40042i	0.416080	+	0.909328i	$0.363404\pi$
$101$	−4.57295	+	14.0741i	−0.455025	+	1.40042i	−0.871105	+	0.491096i	$0.836596\pi$
$102$	−1.54508	+	1.12257i	−0.152986	+	0.111151i
$103$	−7.16312	−	5.20431i	−0.705803	−	0.512796i	0.176014	−	0.984388i	$-0.443680\pi$
$103$	−7.16312	−	5.20431i	−0.705803	−	0.512796i	−0.881817	+	0.471592i	$0.843680\pi$
$104$	−0.562306	−	1.73060i	−0.0551386	−	0.169699i
$105$	−0.500000	−	1.53884i	−0.0487950	−	0.150176i
$106$	−0.736068	−	0.534785i	−0.0714932	−	0.0519429i
$107$	−2.19098	+	1.59184i	−0.211810	+	0.153889i	−0.688632	−	0.725111i	$-0.741789\pi$
$107$	−2.19098	+	1.59184i	−0.211810	+	0.153889i	0.476822	+	0.879000i	$0.341789\pi$
$108$	−3.13525	+	9.64932i	−0.301690	+	0.928506i
$109$	−1.52786			−0.146343			−0.0731714	−	0.997319i	$-0.523312\pi$
$109$	−1.52786			−0.146343			−0.0731714	+	0.997319i	$0.523312\pi$
$110$		0			0
$111$	−10.4721			−0.993971
$112$	0.972136	−	2.99193i	0.0918582	−	0.282711i
$113$	−0.118034	+	0.0857567i	−0.0111037	+	0.00806731i	−0.593323	−	0.804964i	$-0.702184\pi$
$113$	−0.118034	+	0.0857567i	−0.0111037	+	0.00806731i	0.582220	+	0.813032i	$0.302184\pi$
$114$	0.881966	+	0.640786i	0.0826037	+	0.0600151i
$115$	1.57295	+	4.84104i	0.146678	+	0.451429i
$116$	2.64590	+	8.14324i	0.245665	+	0.756081i
$117$	−0.381966	−	0.277515i	−0.0353128	−	0.0256562i
$118$	3.42705	−	2.48990i	0.315486	−	0.229214i
$119$	0.954915	−	2.93893i	0.0875369	−	0.269411i
$120$	−2.38197			−0.217443
$121$		0			0
$122$	2.90983			0.263444
$123$	5.59017	−	17.2048i	0.504049	−	1.55130i
$124$	−6.35410	+	4.61653i	−0.570615	+	0.414576i
$125$	7.28115	+	5.29007i	0.651246	+	0.473158i
$126$	0.0450850	+	0.138757i	0.00401649	+	0.0123615i
$127$	0.909830	+	2.80017i	0.0807344	+	0.248475i	0.983274	−	0.182132i	$-0.0582997\pi$
$127$	0.909830	+	2.80017i	0.0807344	+	0.248475i	−0.902540	+	0.430606i	$0.858300\pi$
$128$	−8.16312	−	5.93085i	−0.721525	−	0.524218i
$129$	−16.4443	+	11.9475i	−1.44784	+	1.05192i
$130$	0.145898	−	0.449028i	0.0127961	−	0.0393824i
$131$	18.9443			1.65517			0.827584	−	0.561341i	$-0.189715\pi$
$131$	18.9443			1.65517			0.827584	+	0.561341i	$0.189715\pi$
$132$		0			0
$133$	−1.76393			−0.152952
$134$	0.982779	−	3.02468i	0.0848992	−	0.261293i
$135$	−4.42705	+	3.21644i	−0.381020	+	0.276827i
$136$	−3.68034	−	2.67392i	−0.315587	−	0.229287i
$137$	−4.73607	−	14.5761i	−0.404630	−	1.24532i	−0.921204	−	0.389080i	$-0.872793\pi$
$137$	−4.73607	−	14.5761i	−0.404630	−	1.24532i	0.516575	−	0.856242i	$-0.327207\pi$
$138$	0.972136	+	2.99193i	0.0827537	+	0.254690i
$139$	−9.66312	−	7.02067i	−0.819615	−	0.595485i	0.0969872	−	0.995286i	$-0.469079\pi$
$139$	−9.66312	−	7.02067i	−0.819615	−	0.595485i	−0.916602	+	0.399800i	$0.869079\pi$
$140$	1.50000	−	1.08981i	0.126773	−	0.0921061i
$141$	3.30902	−	10.1841i	0.278670	−	0.857657i
$142$	6.14590			0.515752
$143$		0			0
$144$	−1.20163			−0.100136
$145$	−1.42705	+	4.39201i	−0.118510	+	0.364737i
$146$	−4.39919	+	3.19620i	−0.364079	+	0.264519i
$147$	1.30902	+	0.951057i	0.107966	+	0.0784418i
$148$	−3.70820	−	11.4127i	−0.304812	−	0.938116i
$149$	−2.73607	−	8.42075i	−0.224147	−	0.689855i	−0.998377	−	0.0569500i	$-0.981862\pi$
$149$	−2.73607	−	8.42075i	−0.224147	−	0.689855i	0.774230	−	0.632905i	$-0.218138\pi$
$150$	2.00000	+	1.45309i	0.163299	+	0.118644i
$151$	−0.0450850	+	0.0327561i	−0.00366896	+	0.00266566i	−0.589618	−	0.807682i	$-0.700722\pi$
$151$	−0.0450850	+	0.0327561i	−0.00366896	+	0.00266566i	0.585949	+	0.810348i	$0.300722\pi$
$152$	−0.802439	+	2.46965i	−0.0650864	+	0.200315i
$153$	−1.18034			−0.0954248
$154$		0			0
$155$	−4.23607			−0.340249
$156$	−1.14590	+	3.52671i	−0.0917453	+	0.282363i
$157$	−16.0902	+	11.6902i	−1.28414	+	0.932979i	−0.999670	−	0.0257072i	$-0.991816\pi$
$157$	−16.0902	+	11.6902i	−1.28414	+	0.932979i	−0.284466	+	0.958686i	$0.591816\pi$
$158$	1.97214	+	1.43284i	0.156895	+	0.113991i
$159$	1.19098	+	3.66547i	0.0944511	+	0.290691i
$160$	−1.28115	−	3.94298i	−0.101284	−	0.311720i
$161$	−4.11803	−	2.99193i	−0.324547	−	0.235797i
$162$	−2.38197	+	1.73060i	−0.187145	+	0.135969i
$163$	−2.69098	+	8.28199i	−0.210774	+	0.648696i	0.788653	+	0.614839i	$0.210779\pi$
$163$	−2.69098	+	8.28199i	−0.210774	+	0.648696i	−0.999427	+	0.0338568i	$0.989221\pi$
$164$	20.7295			1.61870
$165$		0			0
$166$	−1.03444			−0.0802883
$167$	2.00000	−	6.15537i	0.154765	−	0.476317i	−0.843372	−	0.537330i	$-0.819433\pi$
$167$	2.00000	−	6.15537i	0.154765	−	0.476317i	0.998137	+	0.0610130i	$0.0194331\pi$
$168$	1.92705	−	1.40008i	0.148675	−	0.108019i
$169$	9.28115	+	6.74315i	0.713935	+	0.518704i
$170$	−0.364745	−	1.12257i	−0.0279747	−	0.0860972i
$171$	0.208204	+	0.640786i	0.0159218	+	0.0490021i
$172$	−18.8435	−	13.6906i	−1.43680	−	1.04390i
$173$	12.4443	−	9.04129i	0.946120	−	0.687397i	−0.00376565	−	0.999993i	$-0.501199\pi$
$173$	12.4443	−	9.04129i	0.946120	−	0.687397i	0.949886	+	0.312596i	$0.101199\pi$
$174$	−0.881966	+	2.71441i	−0.0668617	+	0.205779i
$175$	−4.00000			−0.302372
$176$		0			0
$177$	−17.9443			−1.34877
$178$	−0.809017	+	2.48990i	−0.0606384	+	0.186626i
$179$	3.04508	−	2.21238i	0.227600	−	0.165361i	−0.468141	−	0.883654i	$-0.655076\pi$
$179$	3.04508	−	2.21238i	0.227600	−	0.165361i	0.695741	+	0.718293i	$0.255076\pi$
$180$	−0.572949	−	0.416272i	−0.0427051	−	0.0310271i
$181$	−2.29180	−	7.05342i	−0.170348	−	0.524277i	0.829043	−	0.559185i	$-0.188886\pi$
$181$	−2.29180	−	7.05342i	−0.170348	−	0.524277i	−0.999391	+	0.0349086i	$0.988886\pi$
$182$	0.145898	+	0.449028i	0.0108147	+	0.0332842i
$183$	−9.97214	−	7.24518i	−0.737162	−	0.535579i
$184$	−6.06231	+	4.40452i	−0.446919	+	0.324706i
$185$	2.00000	−	6.15537i	0.147043	−	0.452552i
$186$	−2.61803			−0.191964
$187$		0			0
$188$	12.2705			0.894919
$189$	1.69098	−	5.20431i	0.123001	−	0.378558i
$190$	−0.545085	+	0.396027i	−0.0395446	+	0.0287308i
$191$	−12.7533	−	9.26581i	−0.922796	−	0.670450i	0.0214227	−	0.999771i	$-0.493180\pi$
$191$	−12.7533	−	9.26581i	−0.922796	−	0.670450i	−0.944218	+	0.329320i	$0.893180\pi$
$192$	2.35410	+	7.24518i	0.169893	+	0.522876i
$193$	−4.73607	−	14.5761i	−0.340910	−	1.04921i	−0.963737	−	0.266853i	$-0.914016\pi$
$193$	−4.73607	−	14.5761i	−0.340910	−	1.04921i	0.622828	−	0.782359i	$-0.285984\pi$
$194$	2.16312	+	1.57160i	0.155303	+	0.112834i
$195$	−1.61803	+	1.17557i	−0.115870	+	0.0841844i
$196$	−0.572949	+	1.76336i	−0.0409249	+	0.125954i
$197$	−4.29180			−0.305778			−0.152889	−	0.988243i	$-0.548858\pi$
$197$	−4.29180			−0.305778			−0.152889	+	0.988243i	$0.548858\pi$
$198$		0			0
$199$	−8.23607			−0.583839			−0.291920	−	0.956443i	$-0.594294\pi$
$199$	−8.23607			−0.583839			−0.291920	+	0.956443i	$0.594294\pi$
$200$	−1.81966	+	5.60034i	−0.128669	+	0.396004i
$201$	−10.8992	+	7.91872i	−0.768769	+	0.558544i
$202$	−4.57295	−	3.32244i	−0.321752	−	0.233766i
$203$	−1.42705	−	4.39201i	−0.100159	−	0.308259i
$204$	2.86475	+	8.81678i	0.200572	+	0.617298i
$205$	9.04508	+	6.57164i	0.631736	+	0.458983i
$206$	2.73607	−	1.98787i	0.190631	−	0.138501i
$207$	−0.600813	+	1.84911i	−0.0417594	+	0.128522i
$208$	−3.88854			−0.269622
$209$		0			0
$210$	0.618034			0.0426484
$211$	4.82624	−	14.8536i	0.332252	−	1.02257i	−0.635808	−	0.771847i	$-0.719333\pi$
$211$	4.82624	−	14.8536i	0.332252	−	1.02257i	0.968060	−	0.250719i	$-0.0806670\pi$
$212$	−3.57295	+	2.59590i	−0.245391	+	0.178287i
$213$	−21.0623	−	15.3027i	−1.44317	−	1.04852i
$214$	−0.319660	−	0.983813i	−0.0218515	−	0.0672520i
$215$	−3.88197	−	11.9475i	−0.264748	−	0.814810i
$216$	−6.51722	−	4.73504i	−0.443441	−	0.322179i
$217$	3.42705	−	2.48990i	0.232643	−	0.169025i
$218$	0.180340	−	0.555029i	0.0122142	−	0.0375913i
$219$	23.0344			1.55652
$220$		0			0
$221$	−3.81966			−0.256938
$222$	1.23607	−	3.80423i	0.0829595	−	0.255323i
$223$	−1.64590	+	1.19581i	−0.110217	+	0.0800777i	−0.641529	−	0.767099i	$-0.721699\pi$
$223$	−1.64590	+	1.19581i	−0.110217	+	0.0800777i	0.531311	+	0.847177i	$0.321699\pi$
$224$	3.35410	+	2.43690i	0.224105	+	0.162822i
$225$	0.472136	+	1.45309i	0.0314757	+	0.0968723i
$226$	−0.0172209	−	0.0530006i	−0.00114552	−	0.00352555i
$227$	12.9721	+	9.42481i	0.860991	+	0.625547i	0.928154	−	0.372195i	$-0.121395\pi$
$227$	12.9721	+	9.42481i	0.860991	+	0.625547i	−0.0671635	+	0.997742i	$0.521395\pi$
$228$	4.28115	−	3.11044i	0.283526	−	0.205994i
$229$	2.09017	−	6.43288i	0.138122	−	0.425097i	−0.857940	−	0.513749i	$-0.828256\pi$
$229$	2.09017	−	6.43288i	0.138122	−	0.425097i	0.996063	+	0.0886526i	$0.0282561\pi$
$230$	−1.94427			−0.128201
$231$		0			0
$232$	−6.79837			−0.446335
$233$	−9.09017	+	27.9767i	−0.595517	+	1.83281i	−0.0433803	+	0.999059i	$0.513813\pi$
$233$	−9.09017	+	27.9767i	−0.595517	+	1.83281i	−0.552137	+	0.833754i	$0.686187\pi$
$234$	0.145898	−	0.106001i	0.00953765	−	0.00692951i
$235$	5.35410	+	3.88998i	0.349263	+	0.253754i
$236$	−6.35410	−	19.5559i	−0.413617	−	1.27298i
$237$	−3.19098	−	9.82084i	−0.207277	−	0.637932i
$238$	0.954915	+	0.693786i	0.0618979	+	0.0449715i
$239$	13.8262	−	10.0453i	0.894345	−	0.649780i	−0.0426623	−	0.999090i	$-0.513584\pi$
$239$	13.8262	−	10.0453i	0.894345	−	0.649780i	0.937007	+	0.349310i	$0.113584\pi$
$240$	−1.57295	+	4.84104i	−0.101533	+	0.312488i
$241$	16.2705			1.04808			0.524038	−	0.851695i	$-0.324425\pi$
$241$	16.2705			1.04808			0.524038	+	0.851695i	$0.324425\pi$
$242$		0			0
$243$	−3.94427			−0.253025
$244$	4.36475	−	13.4333i	0.279424	−	0.859979i
$245$	−0.809017	+	0.587785i	−0.0516862	+	0.0375522i
$246$	5.59017	+	4.06150i	0.356416	+	0.258952i
$247$	0.673762	+	2.07363i	0.0428705	+	0.131942i
$248$	−1.92705	−	5.93085i	−0.122368	−	0.376610i
$249$	3.54508	+	2.57565i	0.224661	+	0.163226i
$250$	−2.78115	+	2.02063i	−0.175896	+	0.127796i
$251$	7.10739	−	21.8743i	0.448615	−	1.38069i	−0.429856	−	0.902897i	$-0.641436\pi$
$251$	7.10739	−	21.8743i	0.448615	−	1.38069i	0.878471	−	0.477796i	$-0.158564\pi$
$252$	0.708204			0.0446127
$253$		0			0
$254$	−1.12461			−0.0705644
$255$	−1.54508	+	4.75528i	−0.0967570	+	0.297787i
$256$	−4.50000	+	3.26944i	−0.281250	+	0.204340i
$257$	6.92705	+	5.03280i	0.432098	+	0.313937i	0.782487	−	0.622667i	$-0.213951\pi$
$257$	6.92705	+	5.03280i	0.432098	+	0.313937i	−0.350390	+	0.936604i	$0.613951\pi$
$258$	−2.39919	−	7.38394i	−0.149367	−	0.459704i
$259$	2.00000	+	6.15537i	0.124274	+	0.382476i
$260$	−1.85410	−	1.34708i	−0.114987	−	0.0835426i
$261$	−1.42705	+	1.03681i	−0.0883322	+	0.0641771i
$262$	−2.23607	+	6.88191i	−0.138145	+	0.425166i
$263$	−17.1246			−1.05595			−0.527974	−	0.849260i	$-0.677048\pi$
$263$	−17.1246			−1.05595			−0.527974	+	0.849260i	$0.677048\pi$
$264$		0			0
$265$	−2.38197			−0.146323
$266$	0.208204	−	0.640786i	0.0127658	−	0.0392891i
$267$	8.97214	−	6.51864i	0.549086	−	0.398934i
$268$	−12.4894	−	9.07405i	−0.762909	−	0.554286i
$269$	5.20820	+	16.0292i	0.317550	+	0.977318i	0.974692	+	0.223551i	$0.0717650\pi$
$269$	5.20820	+	16.0292i	0.317550	+	0.977318i	−0.657142	+	0.753766i	$0.728235\pi$
$270$	−0.645898	−	1.98787i	−0.0393081	−	0.120978i
$271$	3.88197	+	2.82041i	0.235813	+	0.171328i	0.699416	−	0.714715i	$-0.253444\pi$
$271$	3.88197	+	2.82041i	0.235813	+	0.171328i	−0.463603	+	0.886043i	$0.653444\pi$
$272$	−7.86475	+	5.71407i	−0.476870	+	0.346466i
$273$	0.618034	−	1.90211i	0.0374051	−	0.115121i
$274$	5.85410			0.353659
$275$		0			0
$276$	15.2705			0.919177
$277$	7.11803	−	21.9071i	0.427681	−	1.31627i	−0.472722	−	0.881211i	$-0.656729\pi$
$277$	7.11803	−	21.9071i	0.427681	−	1.31627i	0.900403	−	0.435056i	$-0.143271\pi$
$278$	3.69098	−	2.68166i	0.221370	−	0.160835i
$279$	−1.30902	−	0.951057i	−0.0783688	−	0.0569383i
$280$	0.454915	+	1.40008i	0.0271864	+	0.0836711i
$281$	−7.78115	−	23.9479i	−0.464185	−	1.42861i	−0.860005	−	0.510286i	$-0.829540\pi$
$281$	−7.78115	−	23.9479i	−0.464185	−	1.42861i	0.395820	−	0.918328i	$-0.370460\pi$
$282$	3.30902	+	2.40414i	0.197049	+	0.143165i
$283$	−9.66312	+	7.02067i	−0.574413	+	0.417335i	−0.836706	−	0.547653i	$-0.815521\pi$
$283$	−9.66312	+	7.02067i	−0.574413	+	0.417335i	0.262293	+	0.964988i	$0.415521\pi$
$284$	9.21885	−	28.3727i	0.547038	−	1.68361i
$285$	2.85410			0.169062
$286$		0			0
$287$	−11.1803			−0.659955
$288$	0.489357	−	1.50609i	0.0288356	−	0.0887469i
$289$	6.02786	−	4.37950i	0.354580	−	0.257618i
$290$	−1.42705	−	1.03681i	−0.0837993	−	0.0608838i
$291$	−3.50000	−	10.7719i	−0.205174	−	0.631460i
$292$	8.15654	+	25.1033i	0.477325	+	1.46906i
$293$	8.89919	+	6.46564i	0.519896	+	0.377727i	0.816565	−	0.577254i	$-0.195876\pi$
$293$	8.89919	+	6.46564i	0.519896	+	0.377727i	−0.296669	+	0.954980i	$0.595876\pi$
$294$	−0.500000	+	0.363271i	−0.0291606	+	0.0211864i
$295$	3.42705	−	10.5474i	0.199531	−	0.614092i
$296$	9.52786			0.553796
$297$		0			0
$298$	3.38197			0.195912
$299$	−1.94427	+	5.98385i	−0.112440	+	0.346055i
$300$	9.70820	−	7.05342i	0.560503	−	0.407230i
$301$	10.1631	+	7.38394i	0.585792	+	0.425603i
$302$	−0.00657781	−	0.0202444i	−0.000378510	−	0.00116494i
$303$	7.39919	+	22.7724i	0.425072	+	1.30824i
$304$	4.48936	+	3.26171i	0.257482	+	0.187072i
$305$	6.16312	−	4.47777i	0.352899	−	0.256396i
$306$	0.139320	−	0.428784i	0.00796441	−	0.0245119i
$307$	−23.1803			−1.32297			−0.661486	−	0.749958i	$-0.730074\pi$
$307$	−23.1803			−1.32297			−0.661486	+	0.749958i	$0.730074\pi$
$308$		0			0
$309$	−14.3262			−0.814991
$310$	0.500000	−	1.53884i	0.0283981	−	0.0874003i
$311$	−7.28115	+	5.29007i	−0.412876	+	0.299972i	−0.774765	−	0.632249i	$-0.782132\pi$
$311$	−7.28115	+	5.29007i	−0.412876	+	0.299972i	0.361889	+	0.932221i	$0.382132\pi$
$312$	−2.38197	−	1.73060i	−0.134852	−	0.0979759i
$313$	5.66312	+	17.4293i	0.320098	+	0.985162i	0.973605	+	0.228241i	$0.0732973\pi$
$313$	5.66312	+	17.4293i	0.320098	+	0.985162i	−0.653506	+	0.756921i	$0.726703\pi$
$314$	−2.34752	−	7.22494i	−0.132478	−	0.407727i
$315$	0.309017	+	0.224514i	0.0174111	+	0.0126499i
$316$	9.57295	−	6.95515i	0.538520	−	0.391258i
$317$	−1.37132	+	4.22050i	−0.0770212	+	0.237047i	−0.982153	−	0.188085i	$-0.939772\pi$
$317$	−1.37132	+	4.22050i	−0.0770212	+	0.237047i	0.905132	+	0.425131i	$0.139772\pi$
$318$	−1.47214			−0.0825533
$319$		0			0
$320$	−4.70820			−0.263197
$321$	−1.35410	+	4.16750i	−0.0755786	+	0.232607i
$322$	1.57295	−	1.14281i	0.0876570	−	0.0636866i
$323$	4.40983	+	3.20393i	0.245370	+	0.178271i
$324$	4.41641	+	13.5923i	0.245356	+	0.755128i
$325$	1.52786	+	4.70228i	0.0847506	+	0.260836i
$326$	−2.69098	−	1.95511i	−0.149040	−	0.108284i
$327$	−2.00000	+	1.45309i	−0.110600	+	0.0803558i
$328$	−5.08610	+	15.6534i	−0.280833	+	0.864316i
$329$	−6.61803			−0.364864
$330$		0			0
$331$	6.18034			0.339702			0.169851	−	0.985470i	$-0.445671\pi$
$331$	6.18034			0.339702			0.169851	+	0.985470i	$0.445671\pi$
$332$	−1.55166	+	4.77553i	−0.0851586	+	0.262091i
$333$	2.00000	−	1.45309i	0.109599	−	0.0796286i
$334$	2.00000	+	1.45309i	0.109435	+	0.0795093i
$335$	−2.57295	−	7.91872i	−0.140575	−	0.432646i
$336$	−1.57295	−	4.84104i	−0.0858114	−	0.264100i
$337$	−20.9894	−	15.2497i	−1.14336	−	0.830702i	−0.155779	−	0.987792i	$-0.549789\pi$
$337$	−20.9894	−	15.2497i	−1.14336	−	0.830702i	−0.987584	+	0.157090i	$0.949789\pi$
$338$	−3.54508	+	2.57565i	−0.192827	+	0.140097i
$339$	−0.0729490	+	0.224514i	−0.00396205	+	0.0121939i
$340$	−5.72949			−0.310725
$341$		0			0
$342$	−0.257354			−0.0139161
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	14.9615	−	10.8702i	0.806670	−	0.586080i
$345$	6.66312	+	4.84104i	0.358730	+	0.260633i
$346$	1.81559	+	5.58783i	0.0976070	+	0.300403i
$347$	0.725425	+	2.23263i	0.0389428	+	0.119854i	0.968638	−	0.248476i	$-0.0799297\pi$
$347$	0.725425	+	2.23263i	0.0389428	+	0.119854i	−0.929695	+	0.368330i	$0.879930\pi$
$348$	11.2082	+	8.14324i	0.600823	+	0.436523i
$349$	−26.5344	+	19.2784i	−1.42036	+	1.03195i	−0.428643	+	0.903474i	$0.641008\pi$
$349$	−26.5344	+	19.2784i	−1.42036	+	1.03195i	−0.991713	+	0.128475i	$0.958992\pi$
$350$	0.472136	−	1.45309i	0.0252367	−	0.0776707i
$351$	−6.76393			−0.361032
$352$		0			0
$353$	24.0902			1.28219			0.641095	−	0.767461i	$-0.278480\pi$
$353$	24.0902			1.28219			0.641095	+	0.767461i	$0.278480\pi$
$354$	2.11803	−	6.51864i	0.112572	−	0.346462i
$355$	13.0172	−	9.45756i	0.690882	−	0.501955i
$356$	10.2812	+	7.46969i	0.544900	+	0.395893i
$357$	−1.54508	−	4.75528i	−0.0817746	−	0.251676i
$358$	0.444272	+	1.36733i	0.0234805	+	0.0722655i
$359$	12.6353	+	9.18005i	0.666863	+	0.484505i	0.868974	−	0.494858i	$-0.164780\pi$
$359$	12.6353	+	9.18005i	0.666863	+	0.484505i	−0.202110	+	0.979363i	$0.564780\pi$
$360$	0.454915	−	0.330515i	0.0239761	−	0.0174197i
$361$	−4.90983	+	15.1109i	−0.258412	+	0.795311i
$362$	2.83282			0.148889
$363$		0			0
$364$	2.29180			0.120123
$365$	−4.39919	+	13.5393i	−0.230264	+	0.708680i
$366$	3.80902	−	2.76741i	0.199101	−	0.144655i
$367$	−26.5623	−	19.2986i	−1.38654	−	1.00738i	−0.996235	−	0.0866960i	$-0.972369\pi$
$367$	−26.5623	−	19.2986i	−1.38654	−	1.00738i	−0.390306	−	0.920685i	$-0.627631\pi$
$368$	4.94834	+	15.2294i	0.257950	+	0.793888i
$369$	1.31966	+	4.06150i	0.0686988	+	0.211433i
$370$	2.00000	+	1.45309i	0.103975	+	0.0755423i
$371$	1.92705	−	1.40008i	0.100048	−	0.0726888i
$372$	−3.92705	+	12.0862i	−0.203608	+	0.626641i
$373$	−15.4377			−0.799334			−0.399667	−	0.916661i	$-0.630874\pi$
$373$	−15.4377			−0.799334			−0.399667	+	0.916661i	$0.630874\pi$
$374$		0			0
$375$	14.5623			0.751994
$376$	−3.01064	+	9.26581i	−0.155262	+	0.477847i
$377$	−4.61803	+	3.35520i	−0.237841	+	0.172801i
$378$	1.69098	+	1.22857i	0.0869748	+	0.0631909i
$379$	9.90983	+	30.4993i	0.509034	+	1.56664i	0.793882	+	0.608072i	$0.208057\pi$
$379$	9.90983	+	30.4993i	0.509034	+	1.56664i	−0.284848	+	0.958573i	$0.591943\pi$
$380$	1.01064	+	3.11044i	0.0518449	+	0.159562i
$381$	3.85410	+	2.80017i	0.197452	+	0.143457i
$382$	4.87132	−	3.53922i	0.249239	−	0.181082i
$383$	−10.6910	+	32.9035i	−0.546284	+	1.68129i	0.171634	+	0.985161i	$0.445095\pi$
$383$	−10.6910	+	32.9035i	−0.546284	+	1.68129i	−0.717918	+	0.696128i	$0.754905\pi$
$384$	−16.3262			−0.833145
$385$		0			0
$386$	5.85410			0.297966
$387$	1.48278	−	4.56352i	0.0753739	−	0.231977i
$388$	10.5000	−	7.62870i	0.533057	−	0.387288i
$389$	27.6525	+	20.0907i	1.40204	+	1.01864i	0.994421	+	0.105485i	$0.0336396\pi$
$389$	27.6525	+	20.0907i	1.40204	+	1.01864i	0.407615	+	0.913154i	$0.366360\pi$
$390$	−0.236068	−	0.726543i	−0.0119538	−	0.0367899i
$391$	4.86068	+	14.9596i	0.245815	+	0.756541i
$392$	−1.19098	−	0.865300i	−0.0601537	−	0.0437042i
$393$	24.7984	−	18.0171i	1.25091	−	0.908841i
$394$	0.506578	−	1.55909i	0.0255210	−	0.0785456i
$395$	6.38197			0.321112
$396$		0			0
$397$	−0.819660			−0.0411376			−0.0205688	−	0.999788i	$-0.506548\pi$
$397$	−0.819660			−0.0411376			−0.0205688	+	0.999788i	$0.506548\pi$
$398$	0.972136	−	2.99193i	0.0487288	−	0.149972i
$399$	−2.30902	+	1.67760i	−0.115595	+	0.0839850i
$400$	10.1803	+	7.39645i	0.509017	+	0.369822i
$401$	−5.41641	−	16.6700i	−0.270483	−	0.832460i	−0.990379	−	0.138379i	$-0.955811\pi$
$401$	−5.41641	−	16.6700i	−0.270483	−	0.832460i	0.719897	−	0.694081i	$-0.244189\pi$
$402$	−1.59017	−	4.89404i	−0.0793105	−	0.244093i
$403$	−4.23607	−	3.07768i	−0.211014	−	0.153310i
$404$	−22.1976	+	16.1275i	−1.10437	+	0.802372i
$405$	−2.38197	+	7.33094i	−0.118361	+	0.364277i
$406$	1.76393			0.0875425
$407$		0			0
$408$	−7.36068			−0.364408
$409$	−5.47214	+	16.8415i	−0.270580	+	0.832759i	0.719775	+	0.694207i	$0.244245\pi$
$409$	−5.47214	+	16.8415i	−0.270580	+	0.832759i	−0.990355	+	0.138552i	$0.955755\pi$
$410$	−3.45492	+	2.51014i	−0.170626	+	0.123967i
$411$	−20.0623	−	14.5761i	−0.989601	−	0.718987i
$412$	−5.07295	−	15.6129i	−0.249926	−	0.769194i
$413$	3.42705	+	10.5474i	0.168634	+	0.519003i
$414$	−0.600813	−	0.436516i	−0.0295284	−	0.0214536i
$415$	−2.19098	+	1.59184i	−0.107551	+	0.0781405i
$416$	1.58359	−	4.87380i	0.0776420	−	0.238957i
$417$	−19.3262			−0.946410
$418$		0			0
$419$	29.8885			1.46015			0.730075	−	0.683367i	$-0.239485\pi$
$419$	29.8885			1.46015			0.730075	+	0.683367i	$0.239485\pi$
$420$	0.927051	−	2.85317i	0.0452355	−	0.139220i
$421$	−0.618034	+	0.449028i	−0.0301211	+	0.0218843i	−0.602744	−	0.797935i	$-0.705926\pi$
$421$	−0.618034	+	0.449028i	−0.0301211	+	0.0218843i	0.572623	+	0.819819i	$0.305926\pi$
$422$	4.82624	+	3.50647i	0.234938	+	0.170692i
$423$	0.781153	+	2.40414i	0.0379810	+	0.116893i
$424$	−1.08359	−	3.33495i	−0.0526239	−	0.161960i
$425$	10.0000	+	7.26543i	0.485071	+	0.352425i
$426$	8.04508	−	5.84510i	0.389786	−	0.283196i
$427$	−2.35410	+	7.24518i	−0.113923	+	0.350619i
$428$	−5.02129			−0.242713
$429$		0			0
$430$	4.79837			0.231398
$431$	−4.28115	+	13.1760i	−0.206216	+	0.634667i	0.793445	+	0.608641i	$0.208285\pi$
$431$	−4.28115	+	13.1760i	−0.206216	+	0.634667i	−0.999661	+	0.0260258i	$0.991715\pi$
$432$	−13.9271	+	10.1186i	−0.670066	+	0.486831i
$433$	7.25329	+	5.26982i	0.348571	+	0.253252i	0.748269	−	0.663395i	$-0.230885\pi$
$433$	7.25329	+	5.26982i	0.348571	+	0.253252i	−0.399698	+	0.916647i	$0.630885\pi$
$434$	0.500000	+	1.53884i	0.0240008	+	0.0738668i
$435$	2.30902	+	7.10642i	0.110709	+	0.340727i
$436$	−2.29180	−	1.66509i	−0.109757	−	0.0797432i
$437$	7.26393	−	5.27756i	0.347481	−	0.252460i
$438$	−2.71885	+	8.36775i	−0.129912	+	0.399827i
$439$	3.38197			0.161412			0.0807062	−	0.996738i	$-0.474282\pi$
$439$	3.38197			0.161412			0.0807062	+	0.996738i	$0.474282\pi$
$440$		0			0
$441$	−0.381966			−0.0181889
$442$	0.450850	−	1.38757i	0.0214447	−	0.0660001i
$443$	−2.50000	+	1.81636i	−0.118779	+	0.0862977i	−0.645589	−	0.763685i	$-0.723388\pi$
$443$	−2.50000	+	1.81636i	−0.118779	+	0.0862977i	0.526810	+	0.849983i	$0.323388\pi$
$444$	−15.7082	−	11.4127i	−0.745478	−	0.541622i
$445$	2.11803	+	6.51864i	0.100404	+	0.309013i
$446$	−0.240133	−	0.739054i	−0.0113706	−	0.0349952i
$447$	−11.5902	−	8.42075i	−0.548196	−	0.398288i
$448$	3.80902	−	2.76741i	0.179959	−	0.130748i
$449$	3.80902	−	11.7229i	0.179759	−	0.553240i	−0.820060	−	0.572277i	$-0.806060\pi$
$449$	3.80902	−	11.7229i	0.179759	−	0.553240i	0.999819	+	0.0190372i	$0.00606009\pi$
$450$	−0.583592			−0.0275108
$451$		0			0
$452$	−0.270510			−0.0127237
$453$	−0.0278640	+	0.0857567i	−0.00130917	+	0.00402920i
$454$	−4.95492	+	3.59996i	−0.232546	+	0.168954i
$455$	1.00000	+	0.726543i	0.0468807	+	0.0340608i
$456$	1.29837	+	3.99598i	0.0608019	+	0.187129i
$457$	−0.0450850	−	0.138757i	−0.00210899	−	0.00649079i	0.949996	−	0.312261i	$-0.101086\pi$
$457$	−0.0450850	−	0.138757i	−0.00210899	−	0.00649079i	−0.952105	+	0.305770i	$0.901086\pi$
$458$	2.09017	+	1.51860i	0.0976672	+	0.0709594i
$459$	−13.6803	+	9.93935i	−0.638544	+	0.463929i
$460$	−2.91641	+	8.97578i	−0.135978	+	0.418498i
$461$	−18.5066			−0.861937			−0.430969	−	0.902367i	$-0.641828\pi$
$461$	−18.5066			−0.861937			−0.430969	+	0.902367i	$0.641828\pi$
$462$		0			0
$463$	22.2361			1.03340			0.516699	−	0.856167i	$-0.327161\pi$
$463$	22.2361			1.03340			0.516699	+	0.856167i	$0.327161\pi$
$464$	−4.48936	+	13.8168i	−0.208413	+	0.641430i
$465$	−5.54508	+	4.02874i	−0.257147	+	0.186828i
$466$	−9.09017	−	6.60440i	−0.421094	−	0.305943i
$467$	−1.39261	−	4.28601i	−0.0644423	−	0.198333i	0.913651	−	0.406499i	$-0.133251\pi$
$467$	−1.39261	−	4.28601i	−0.0644423	−	0.198333i	−0.978093	+	0.208166i	$0.933251\pi$
$468$	−0.270510	−	0.832544i	−0.0125043	−	0.0384843i
$469$	6.73607	+	4.89404i	0.311043	+	0.225986i
$470$	−2.04508	+	1.48584i	−0.0943327	+	0.0685367i
$471$	−9.94427	+	30.6053i	−0.458208	+	1.41022i
$472$	16.3262			0.751476
$473$		0			0
$474$	3.94427			0.181166
$475$	2.18034	−	6.71040i	0.100041	−	0.307894i
$476$	4.63525	−	3.36771i	0.212457	−	0.154359i
$477$	−0.736068	−	0.534785i	−0.0337022	−	0.0244861i
$478$	2.01722	+	6.20837i	0.0922655	+	0.283964i
$479$	6.72542	+	20.6987i	0.307293	+	0.945749i	0.978812	+	0.204762i	$0.0656420\pi$
$479$	6.72542	+	20.6987i	0.307293	+	0.945749i	−0.671519	+	0.740987i	$0.734358\pi$
$480$	−5.42705	−	3.94298i	−0.247710	−	0.179972i
$481$	6.47214	−	4.70228i	0.295104	−	0.214406i
$482$	−1.92047	+	5.91061i	−0.0874752	+	0.269221i
$483$	−8.23607			−0.374754
$484$		0			0
$485$	7.00000			0.317854
$486$	0.465558	−	1.43284i	0.0211181	−	0.0649950i
$487$	26.3713	−	19.1599i	1.19500	−	0.868217i	0.201215	−	0.979547i	$-0.435511\pi$
$487$	26.3713	−	19.1599i	1.19500	−	0.868217i	0.993784	+	0.111330i	$0.0355110\pi$
$488$	9.07295	+	6.59188i	0.410713	+	0.298401i
$489$	4.35410	+	13.4005i	0.196899	+	0.605994i
$490$	−0.118034	−	0.363271i	−0.00533223	−	0.0164109i
$491$	−17.9164	−	13.0170i	−0.808556	−	0.587450i	0.104855	−	0.994487i	$-0.466562\pi$
$491$	−17.9164	−	13.0170i	−0.808556	−	0.587450i	−0.913412	+	0.407037i	$0.866562\pi$
$492$	27.1353	−	19.7149i	1.22335	−	0.888817i
$493$	−4.40983	+	13.5721i	−0.198609	+	0.611255i
$494$	−0.832816			−0.0374702
$495$		0			0
$496$	−13.3262			−0.598366
$497$	−4.97214	+	15.3027i	−0.223031	+	0.686418i
$498$	−1.35410	+	0.983813i	−0.0606788	+	0.0440857i
$499$	8.16312	+	5.93085i	0.365431	+	0.265501i	0.755314	−	0.655363i	$-0.227484\pi$
$499$	8.16312	+	5.93085i	0.365431	+	0.265501i	−0.389883	+	0.920865i	$0.627484\pi$
$500$	5.15654	+	15.8702i	0.230608	+	0.709737i
$501$	−3.23607	−	9.95959i	−0.144577	−	0.444962i
$502$	7.10739	+	5.16382i	0.317218	+	0.230473i
$503$	28.1803	−	20.4742i	1.25650	−	0.912900i	0.257919	−	0.966167i	$-0.416963\pi$
$503$	28.1803	−	20.4742i	1.25650	−	0.912900i	0.998580	+	0.0532664i	$0.0169633\pi$
$504$	−0.173762	+	0.534785i	−0.00773998	+	0.0238212i
$505$	−14.7984			−0.658519
$506$		0			0
$507$	18.5623			0.824381
$508$	−1.68692	+	5.19180i	−0.0748449	+	0.230349i
$509$	8.69098	−	6.31437i	0.385221	−	0.279879i	−0.378273	−	0.925694i	$-0.623482\pi$
$509$	8.69098	−	6.31437i	0.385221	−	0.279879i	0.763494	+	0.645814i	$0.223482\pi$
$510$	−1.54508	−	1.12257i	−0.0684175	−	0.0497082i
$511$	−4.39919	−	13.5393i	−0.194609	−	0.598944i
$512$	−6.89261	−	21.2133i	−0.304613	−	0.937503i
$513$	7.80902	+	5.67358i	0.344777	+	0.250495i
$514$	−2.64590	+	1.92236i	−0.116706	+	0.0847916i
$515$	2.73607	−	8.42075i	0.120566	−	0.371063i
$516$	−37.6869			−1.65907
$517$		0			0
$518$	−2.47214			−0.108619
$519$	7.69098	−	23.6704i	0.337597	−	1.03902i
$520$	1.47214	−	1.06957i	0.0645574	−	0.0469037i
$521$	9.89919	+	7.19218i	0.433691	+	0.315095i	0.783123	−	0.621867i	$-0.213625\pi$
$521$	9.89919	+	7.19218i	0.433691	+	0.315095i	−0.349432	+	0.936962i	$0.613625\pi$
$522$	−0.208204	−	0.640786i	−0.00911284	−	0.0280464i
$523$	5.11803	+	15.7517i	0.223796	+	0.688773i	0.998412	+	0.0563409i	$0.0179434\pi$
$523$	5.11803	+	15.7517i	0.223796	+	0.688773i	−0.774616	+	0.632432i	$0.782057\pi$
$524$	28.4164	+	20.6457i	1.24138	+	0.901913i
$525$	−5.23607	+	3.80423i	−0.228521	+	0.166030i
$526$	2.02129	−	6.22088i	0.0881323	−	0.271243i
$527$	−13.0902			−0.570217
$528$		0			0
$529$	2.90983			0.126514
$530$	0.281153	−	0.865300i	0.0122125	−	0.0375862i
$531$	3.42705	−	2.48990i	0.148721	−	0.108052i
$532$	−2.64590	−	1.92236i	−0.114714	−	0.0833448i
$533$	4.27051	+	13.1433i	0.184976	+	0.569299i
$534$	1.30902	+	4.02874i	0.0566467	+	0.174341i
$535$	−2.19098	−	1.59184i	−0.0947245	−	0.0688213i
$536$	9.91641	−	7.20469i	0.428324	−	0.311195i
$537$	1.88197	−	5.79210i	0.0812128	−	0.249947i
$538$	−6.43769			−0.277549
$539$		0			0
$540$	−10.1459			−0.436610
$541$	0.218847	−	0.673542i	0.00940897	−	0.0289578i	−0.946242	−	0.323460i	$-0.895154\pi$
$541$	0.218847	−	0.673542i	0.00940897	−	0.0289578i	0.955651	+	0.294502i	$0.0951539\pi$
$542$	−1.48278	+	1.07730i	−0.0636908	+	0.0462741i
$543$	−9.70820	−	7.05342i	−0.416619	−	0.302691i
$544$	−3.95898	−	12.1845i	−0.169740	−	0.522406i
$545$	−0.472136	−	1.45309i	−0.0202241	−	0.0622433i
$546$	0.618034	+	0.449028i	0.0264494	+	0.0192166i
$547$	1.39919	−	1.01657i	0.0598249	−	0.0434653i	−0.557471	−	0.830196i	$-0.688228\pi$
$547$	1.39919	−	1.01657i	0.0598249	−	0.0434653i	0.617296	+	0.786731i	$0.288228\pi$
$548$	8.78115	−	27.0256i	0.375112	−	1.15448i
$549$	2.90983			0.124189
$550$		0			0
$551$	8.14590			0.347027
$552$	−3.74671	+	11.5312i	−0.159471	+	0.490800i
$553$	−5.16312	+	3.75123i	−0.219558	+	0.159518i
$554$	7.11803	+	5.17155i	0.302416	+	0.219718i
$555$	−3.23607	−	9.95959i	−0.137363	−	0.422761i
$556$	−6.84346	−	21.0620i	−0.290227	−	0.893228i
$557$	7.89919	+	5.73910i	0.334699	+	0.243173i	0.742422	−	0.669933i	$-0.233677\pi$
$557$	7.89919	+	5.73910i	0.334699	+	0.243173i	−0.407723	+	0.913106i	$0.633677\pi$
$558$	0.500000	−	0.363271i	0.0211667	−	0.0153785i
$559$	4.79837	−	14.7679i	0.202950	−	0.624615i
$560$	3.14590			0.132938
$561$		0			0
$562$	9.61803			0.405712
$563$	−9.88197	+	30.4136i	−0.416475	+	1.28178i	0.494450	+	0.869206i	$0.335370\pi$
$563$	−9.88197	+	30.4136i	−0.416475	+	1.28178i	−0.910925	+	0.412573i	$0.864630\pi$
$564$	16.0623	−	11.6699i	0.676345	−	0.491393i
$565$	−0.118034	−	0.0857567i	−0.00496573	−	0.00360781i
$566$	−1.40983	−	4.33901i	−0.0592596	−	0.182382i
$567$	−2.38197	−	7.33094i	−0.100033	−	0.307870i
$568$	19.1631	+	13.9228i	0.804067	+	0.584189i
$569$	−30.1803	+	21.9273i	−1.26523	+	0.919240i	−0.999002	−	0.0446710i	$-0.985776\pi$
$569$	−30.1803	+	21.9273i	−1.26523	+	0.919240i	−0.266224	+	0.963911i	$0.585776\pi$
$570$	−0.336881	+	1.03681i	−0.0141104	+	0.0434273i
$571$	34.3050			1.43562			0.717809	−	0.696240i	$-0.245145\pi$
$571$	34.3050			1.43562			0.717809	+	0.696240i	$0.245145\pi$
$572$		0			0
$573$	−25.5066			−1.06555
$574$	1.31966	−	4.06150i	0.0550815	−	0.169524i
$575$	16.4721	−	11.9677i	0.686936	−	0.499088i
$576$	−1.45492	−	1.05706i	−0.0606215	−	0.0440441i
$577$	2.98278	+	9.18005i	0.124175	+	0.382170i	0.993750	−	0.111630i	$-0.0356072\pi$
$577$	2.98278	+	9.18005i	0.124175	+	0.382170i	−0.869575	+	0.493801i	$0.835607\pi$
$578$	0.879454	+	2.70668i	0.0365804	+	0.112583i
$579$	−20.0623	−	14.5761i	−0.833761	−	0.605763i
$580$	−6.92705	+	5.03280i	−0.287630	+	0.208976i
$581$	0.836881	−	2.57565i	0.0347197	−	0.106856i
$582$	4.32624			0.179328
$583$		0			0
$584$	−20.9574			−0.867225
$585$	0.145898	−	0.449028i	0.00603214	−	0.0185650i
$586$	−3.39919	+	2.46965i	−0.140419	+	0.102020i
$587$	−0.809017	−	0.587785i	−0.0333917	−	0.0242605i	0.570964	−	0.820975i	$-0.306569\pi$
$587$	−0.809017	−	0.587785i	−0.0333917	−	0.0242605i	−0.604356	+	0.796714i	$0.706569\pi$
$588$	0.927051	+	2.85317i	0.0382309	+	0.117663i
$589$	2.30902	+	7.10642i	0.0951414	+	0.292815i
$590$	3.42705	+	2.48990i	0.141089	+	0.102507i
$591$	−5.61803	+	4.08174i	−0.231095	+	0.167900i
$592$	6.29180	−	19.3642i	0.258591	−	0.795862i
$593$	11.1246			0.456833			0.228417	−	0.973564i	$-0.426645\pi$
$593$	11.1246			0.456833			0.228417	+	0.973564i	$0.426645\pi$
$594$		0			0
$595$	3.09017			0.126685
$596$	5.07295	−	15.6129i	0.207796	−	0.639531i
$597$	−10.7812	+	7.83297i	−0.441243	+	0.320582i
$598$	−1.94427	−	1.41260i	−0.0795072	−	0.0577654i
$599$	−4.94427	−	15.2169i	−0.202017	−	0.621746i	−0.999823	−	0.0188306i	$-0.994006\pi$
$599$	−4.94427	−	15.2169i	−0.202017	−	0.621746i	0.797805	−	0.602915i	$-0.205994\pi$
$600$	2.94427	+	9.06154i	0.120199	+	0.369936i
$601$	−11.0902	−	8.05748i	−0.452377	−	0.328671i	0.338156	−	0.941090i	$-0.390197\pi$
$601$	−11.0902	−	8.05748i	−0.452377	−	0.328671i	−0.790534	+	0.612419i	$0.790197\pi$
$602$	−3.88197	+	2.82041i	−0.158217	+	0.114951i
$603$	0.982779	−	3.02468i	0.0400219	−	0.123175i
$604$	−0.103326			−0.00420426
$605$		0			0
$606$	−9.14590			−0.371527
$607$	6.24265	−	19.2129i	0.253381	−	0.779827i	−0.740763	−	0.671766i	$-0.765536\pi$
$607$	6.24265	−	19.2129i	0.253381	−	0.779827i	0.994144	−	0.108061i	$-0.0344641\pi$
$608$	−5.91641	+	4.29852i	−0.239942	+	0.174328i
$609$	−6.04508	−	4.39201i	−0.244959	−	0.177973i
$610$	0.899187	+	2.76741i	0.0364070	+	0.112049i
$611$	2.52786	+	7.77997i	0.102266	+	0.314744i
$612$	−1.77051	−	1.28635i	−0.0715686	−	0.0519976i
$613$	0.718847	−	0.522273i	0.0290340	−	0.0210944i	−0.573174	−	0.819434i	$-0.694288\pi$
$613$	0.718847	−	0.522273i	0.0290340	−	0.0210944i	0.602208	+	0.798340i	$0.294288\pi$
$614$	2.73607	−	8.42075i	0.110419	−	0.339834i
$615$	18.0902			0.729466
$616$		0			0
$617$	9.41641			0.379090			0.189545	−	0.981872i	$-0.439299\pi$
$617$	9.41641			0.379090			0.189545	+	0.981872i	$0.439299\pi$
$618$	1.69098	−	5.20431i	0.0680213	−	0.209348i
$619$	32.1246	−	23.3399i	1.29120	−	0.938110i	0.291368	−	0.956611i	$-0.405889\pi$
$619$	32.1246	−	23.3399i	1.29120	−	0.938110i	0.999829	+	0.0185013i	$0.00588948\pi$
$620$	−6.35410	−	4.61653i	−0.255187	−	0.185404i
$621$	8.60739	+	26.4908i	0.345403	+	1.06304i
$622$	−1.06231	−	3.26944i	−0.0425946	−	0.131093i
$623$	−5.54508	−	4.02874i	−0.222159	−	0.161408i
$624$	−5.09017	+	3.69822i	−0.203770	+	0.148047i
$625$	3.39919	−	10.4616i	0.135967	−	0.418465i
$626$	−7.00000			−0.279776
$627$		0			0
$628$	−36.8754			−1.47149
$629$	6.18034	−	19.0211i	0.246426	−	0.758422i
$630$	−0.118034	+	0.0857567i	−0.00470259	+	0.00341663i
$631$	−14.4271	−	10.4819i	−0.574332	−	0.417277i	0.262344	−	0.964974i	$-0.415504\pi$
$631$	−14.4271	−	10.4819i	−0.574332	−	0.417277i	−0.836676	+	0.547698i	$0.815504\pi$
$632$	2.90325	+	8.93529i	0.115485	+	0.355427i
$633$	−7.80902	−	24.0337i	−0.310381	−	0.955253i
$634$	−1.37132	−	0.996324i	−0.0544622	−	0.0395691i
$635$	−2.38197	+	1.73060i	−0.0945254	+	0.0686768i
$636$	−2.20820	+	6.79615i	−0.0875610	+	0.269485i
$637$	−1.23607			−0.0489748
$638$		0			0
$639$	6.14590			0.243128
$640$	3.11803	−	9.59632i	0.123251	−	0.379328i
$641$	−25.6074	+	18.6049i	−1.01143	+	0.734848i	−0.964509	−	0.264051i	$-0.914941\pi$
$641$	−25.6074	+	18.6049i	−1.01143	+	0.734848i	−0.0469224	+	0.998899i	$0.514941\pi$
$642$	−1.35410	−	0.983813i	−0.0534421	−	0.0388280i
$643$	0.489357	+	1.50609i	0.0192984	+	0.0593942i	0.960242	−	0.279169i	$-0.0900590\pi$
$643$	0.489357	+	1.50609i	0.0192984	+	0.0593942i	−0.940944	+	0.338563i	$0.890059\pi$
$644$	−2.91641	−	8.97578i	−0.114923	−	0.353695i
$645$	−16.4443	−	11.9475i	−0.647493	−	0.470431i
$646$	−1.68441	+	1.22379i	−0.0662720	+	0.0481495i
$647$	1.90983	−	5.87785i	0.0750832	−	0.231082i	−0.906470	−	0.422269i	$-0.861234\pi$
$647$	1.90983	−	5.87785i	0.0750832	−	0.231082i	0.981554	+	0.191187i	$0.0612337\pi$
$648$	−11.3475			−0.445773
$649$		0			0
$650$	−1.88854			−0.0740748
$651$	2.11803	−	6.51864i	0.0830123	−	0.255486i
$652$	−13.0623	+	9.49032i	−0.511559	+	0.371670i
$653$	−14.7533	−	10.7189i	−0.577341	−	0.419463i	0.260424	−	0.965494i	$-0.416138\pi$
$653$	−14.7533	−	10.7189i	−0.577341	−	0.419463i	−0.837764	+	0.546032i	$0.816138\pi$
$654$	−0.291796	−	0.898056i	−0.0114101	−	0.0351168i
$655$	5.85410	+	18.0171i	0.228739	+	0.703985i
$656$	28.4549	+	20.6737i	1.11098	+	0.807173i
$657$	−4.39919	+	3.19620i	−0.171629	+	0.124695i
$658$	0.781153	−	2.40414i	0.0304525	−	0.0937232i
$659$	31.4721			1.22598			0.612990	−	0.790091i	$-0.289967\pi$
$659$	31.4721			1.22598			0.612990	+	0.790091i	$0.289967\pi$
$660$		0			0
$661$	−34.5623			−1.34432			−0.672159	−	0.740407i	$-0.734633\pi$
$661$	−34.5623			−1.34432			−0.672159	+	0.740407i	$0.734633\pi$
$662$	−0.729490	+	2.24514i	−0.0283524	+	0.0872598i
$663$	−5.00000	+	3.63271i	−0.194184	+	0.141083i
$664$	−3.22542	−	2.34341i	−0.125171	−	0.0909419i
$665$	−0.545085	−	1.67760i	−0.0211375	−	0.0650545i
$666$	0.291796	+	0.898056i	0.0113069	+	0.0347990i
$667$	19.0172	+	13.8168i	0.736350	+	0.534989i
$668$	9.70820	−	7.05342i	0.375622	−	0.272905i
$669$	−1.01722	+	3.13068i	−0.0393280	+	0.121039i
$670$	3.18034			0.122867
$671$		0			0
$672$	6.70820			0.258775
$673$	−2.03444	+	6.26137i	−0.0784220	+	0.241358i	−0.982580	−	0.185840i	$-0.940499\pi$
$673$	−2.03444	+	6.26137i	−0.0784220	+	0.241358i	0.904158	+	0.427198i	$0.140499\pi$
$674$	8.01722	−	5.82485i	0.308812	−	0.224365i
$675$	17.7082	+	12.8658i	0.681589	+	0.495203i
$676$	6.57295	+	20.2295i	0.252806	+	0.778056i
$677$	−11.2082	−	34.4953i	−0.430766	−	1.32576i	−0.897363	−	0.441292i	$-0.854520\pi$
$677$	−11.2082	−	34.4953i	−0.430766	−	1.32576i	0.466597	−	0.884470i	$-0.345480\pi$
$678$	−0.0729490	−	0.0530006i	−0.00280159	−	0.00203547i
$679$	−5.66312	+	4.11450i	−0.217331	+	0.157900i
$680$	1.40576	−	4.32650i	0.0539086	−	0.165914i
$681$	25.9443			0.994187
$682$		0			0
$683$	0.493422			0.0188803			0.00944014	−	0.999955i	$-0.496995\pi$
$683$	0.493422			0.0188803			0.00944014	+	0.999955i	$0.496995\pi$
$684$	−0.386031	+	1.18808i	−0.0147603	+	0.0454275i
$685$	12.3992	−	9.00854i	0.473749	−	0.344198i
$686$	0.309017	+	0.224514i	0.0117983	+	0.00857198i
$687$	−3.38197	−	10.4086i	−0.129030	−	0.397114i
$688$	−12.2123	−	37.5855i	−0.465588	−	1.43293i
$689$	−2.38197	−	1.73060i	−0.0907457	−	0.0659306i
$690$	−2.54508	+	1.84911i	−0.0968897	+	0.0703945i
$691$	5.72949	−	17.6336i	0.217960	−	0.670812i	−0.780970	−	0.624568i	$-0.785275\pi$
$691$	5.72949	−	17.6336i	0.217960	−	0.670812i	0.998930	−	0.0462437i	$-0.0147251\pi$
$692$	28.5197			1.08416
$693$		0			0
$694$	−0.896674			−0.0340373
$695$	3.69098	−	11.3597i	0.140007	−	0.430897i
$696$	−8.89919	+	6.46564i	−0.337323	+	0.245079i
$697$	27.9508	+	20.3075i	1.05871	+	0.769201i
$698$	−3.87132	−	11.9147i	−0.146532	−	0.450978i
$699$	14.7082	+	45.2672i	0.556315	+	1.71216i
$700$	−6.00000	−	4.35926i	−0.226779	−	0.164764i
$701$	−14.9721	+	10.8779i	−0.565490	+	0.410852i	−0.833464	−	0.552574i	$-0.813646\pi$
$701$	−14.9721	+	10.8779i	−0.565490	+	0.410852i	0.267974	+	0.963426i	$0.413646\pi$
$702$	0.798374	−	2.45714i	0.0301327	−	0.0927389i
$703$	−11.4164			−0.430578
$704$		0			0
$705$	10.7082			0.403294
$706$	−2.84346	+	8.75127i	−0.107015	+	0.329358i
$707$	11.9721	−	8.69827i	0.450259	−	0.327132i
$708$	−26.9164	−	19.5559i	−1.01158	−	0.734956i
$709$	−2.17376	−	6.69015i	−0.0816373	−	0.251254i	0.901904	−	0.431936i	$-0.142169\pi$
$709$	−2.17376	−	6.69015i	−0.0816373	−	0.251254i	−0.983542	+	0.180682i	$0.942169\pi$
$710$	1.89919	+	5.84510i	0.0712752	+	0.219363i
$711$	1.97214	+	1.43284i	0.0739609	+	0.0537357i
$712$	−8.16312	+	5.93085i	−0.305926	+	0.222268i
$713$	−6.66312	+	20.5070i	−0.249536	+	0.767992i
$714$	1.90983			0.0714736
$715$		0			0
$716$	6.97871			0.260807
$717$	8.54508	−	26.2991i	0.319122	−	0.982157i
$718$	−4.82624	+	3.50647i	−0.180114	+	0.130860i
$719$	2.33688	+	1.69784i	0.0871510	+	0.0633189i	0.630507	−	0.776183i	$-0.282847\pi$
$719$	2.33688	+	1.69784i	0.0871510	+	0.0633189i	−0.543357	+	0.839502i	$0.682847\pi$
$720$	−0.371323	−	1.14281i	−0.0138384	−	0.0425902i
$721$	2.73607	+	8.42075i	0.101896	+	0.313605i
$722$	−4.90983	−	3.56720i	−0.182725	−	0.132757i
$723$	21.2984	−	15.4742i	0.792095	−	0.575491i
$724$	4.24922	−	13.0778i	0.157921	−	0.486031i
$725$	18.4721			0.686038
$726$		0			0
$727$	−12.4508			−0.461776			−0.230888	−	0.972980i	$-0.574163\pi$
$727$	−12.4508			−0.461776			−0.230888	+	0.972980i	$0.574163\pi$
$728$	−0.562306	+	1.73060i	−0.0208404	+	0.0641403i
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$	−4.39919	−	3.19620i	−0.162821	−	0.118297i
$731$	−11.9959	−	36.9197i	−0.443686	−	1.36552i
$732$	−7.06231	−	21.7355i	−0.261030	−	0.803369i
$733$	−42.8328	−	31.1199i	−1.58207	−	1.14944i	−0.914278	−	0.405087i	$-0.867241\pi$
$733$	−42.8328	−	31.1199i	−1.58207	−	1.14944i	−0.667788	−	0.744352i	$-0.732759\pi$
$734$	10.1459	−	7.37143i	0.374492	−	0.272084i
$735$	−0.500000	+	1.53884i	−0.0184428	+	0.0567610i
$736$	−21.1033			−0.777879
$737$		0			0
$738$	−1.63119			−0.0600449
$739$	−3.51722	+	10.8249i	−0.129383	+	0.398200i	−0.994674	−	0.103070i	$-0.967134\pi$
$739$	−3.51722	+	10.8249i	−0.129383	+	0.398200i	0.865291	+	0.501270i	$0.167134\pi$
$740$	9.70820	−	7.05342i	0.356881	−	0.259289i
$741$	2.85410	+	2.07363i	0.104848	+	0.0761766i
$742$	0.281153	+	0.865300i	0.0103214	+	0.0317662i
$743$	−4.60739	−	14.1801i	−0.169029	−	0.520217i	0.830282	−	0.557344i	$-0.188179\pi$
$743$	−4.60739	−	14.1801i	−0.169029	−	0.520217i	−0.999311	+	0.0371268i	$0.988179\pi$
$744$	−8.16312	−	5.93085i	−0.299274	−	0.217436i
$745$	7.16312	−	5.20431i	0.262436	−	0.190671i
$746$	1.82217	−	5.60807i	0.0667145	−	0.205326i
$747$	−1.03444			−0.0378482
$748$		0			0
$749$	2.70820			0.0989556
$750$	−1.71885	+	5.29007i	−0.0627634	+	0.193166i
$751$	−33.4164	+	24.2784i	−1.21938	+	0.885933i	−0.996049	−	0.0888092i	$-0.971694\pi$
$751$	−33.4164	+	24.2784i	−1.21938	+	0.885933i	−0.223333	+	0.974742i	$0.571694\pi$
$752$	16.8435	+	12.2375i	0.614218	+	0.446255i
$753$	−11.5000	−	35.3934i	−0.419083	−	1.28981i
$754$	−0.673762	−	2.07363i	−0.0245370	−	0.0755170i
$755$	−0.0450850	−	0.0327561i	−0.00164081	−	0.00119212i
$756$	8.20820	−	5.96361i	0.298529	−	0.216894i
$757$	−4.56231	+	14.0413i	−0.165820	+	0.510341i	−0.999096	−	0.0425164i	$-0.986463\pi$
$757$	−4.56231	+	14.0413i	−0.165820	+	0.510341i	0.833276	+	0.552857i	$0.186463\pi$
$758$	−12.2492			−0.444912
$759$		0			0
$760$	−2.59675			−0.0941939
$761$	4.72949	−	14.5559i	0.171444	−	0.527650i	−0.828009	−	0.560714i	$-0.810527\pi$
$761$	4.72949	−	14.5559i	0.171444	−	0.527650i	0.999453	+	0.0330643i	$0.0105266\pi$
$762$	−1.47214	+	1.06957i	−0.0533299	+	0.0387464i
$763$	1.23607	+	0.898056i	0.0447487	+	0.0325118i
$764$	−9.03193	−	27.7974i	−0.326764	−	1.00568i
$765$	−0.364745	−	1.12257i	−0.0131874	−	0.0405866i
$766$	−10.6910	−	7.76745i	−0.386281	−	0.280650i
$767$	11.0902	−	8.05748i	0.400443	−	0.290939i
$768$	−2.78115	+	8.55951i	−0.100356	+	0.308865i
$769$	48.5623			1.75120			0.875601	−	0.483035i	$-0.160466\pi$
$769$	48.5623			1.75120			0.875601	+	0.483035i	$0.160466\pi$
$770$		0			0
$771$	13.8541			0.498943
$772$	8.78115	−	27.0256i	0.316041	−	0.972673i
$773$	−32.5517	+	23.6502i	−1.17080	+	0.850637i	−0.991105	−	0.133085i	$-0.957512\pi$
$773$	−32.5517	+	23.6502i	−1.17080	+	0.850637i	−0.179697	+	0.983722i	$0.557512\pi$
$774$	1.48278	+	1.07730i	0.0532974	+	0.0387228i
$775$	5.23607	+	16.1150i	0.188085	+	0.578866i
$776$	3.18441	+	9.80059i	0.114313	+	0.351821i
$777$	8.47214	+	6.15537i	0.303936	+	0.220823i
$778$	−10.5623	+	7.67396i	−0.378677	+	0.275125i
$779$	6.09424	−	18.7561i	0.218349	−	0.672008i
$780$	−3.70820			−0.132775
$781$		0			0
$782$	−6.00813			−0.214850
$783$	−7.80902	+	24.0337i	−0.279072	+	0.858894i
$784$	−2.54508	+	1.84911i	−0.0908959	+	0.0660397i
$785$	−16.0902	−	11.6902i	−0.574283	−	0.417241i
$786$	3.61803	+	11.1352i	0.129051	+	0.397178i
$787$	6.35410	+	19.5559i	0.226499	+	0.697093i	0.998136	+	0.0610295i	$0.0194384\pi$
$787$	6.35410	+	19.5559i	0.226499	+	0.697093i	−0.771637	+	0.636064i	$0.780562\pi$
$788$	−6.43769	−	4.67726i	−0.229333	−	0.166620i
$789$	−22.4164	+	16.2865i	−0.798045	+	0.579814i
$790$	−0.753289	+	2.31838i	−0.0268008	+	0.0824844i
$791$	0.145898			0.00518754
$792$		0			0
$793$	9.41641			0.334386
$794$	0.0967478	−	0.297759i	0.00343345	−	0.0105671i
$795$	−3.11803	+	2.26538i	−0.110585	+	0.0803449i
$796$	−12.3541	−	8.97578i	−0.437880	−	0.318138i
$797$	9.96149	+	30.6583i	0.352854	+	1.08597i	0.957243	+	0.289284i	$0.0934173\pi$
$797$	9.96149	+	30.6583i	0.352854	+	1.08597i	−0.604389	+	0.796689i	$0.706583\pi$
$798$	−0.336881	−	1.03681i	−0.0119255	−	0.0367028i
$799$	16.5451	+	12.0207i	0.585323	+	0.425262i
$800$	−13.4164	+	9.74759i	−0.474342	+	0.344629i
$801$	−0.809017	+	2.48990i	−0.0285852	+	0.0879762i
$802$	6.69505			0.236410
$803$		0			0
$804$	−24.9787			−0.880931
$805$	1.57295	−	4.84104i	0.0554392	−	0.170624i
$806$	1.61803	−	1.17557i	0.0569928	−	0.0414077i
$807$	22.0623	+	16.0292i	0.776630	+	0.564255i
$808$	−6.73200	−	20.7190i	−0.236831	−	0.728891i
$809$	10.0451	+	30.9156i	0.353166	+	1.08693i	0.957065	+	0.289873i	$0.0936132\pi$
$809$	10.0451	+	30.9156i	0.353166	+	1.08693i	−0.603899	+	0.797061i	$0.706387\pi$
$810$	−2.38197	−	1.73060i	−0.0836938	−	0.0608071i
$811$	−0.944272	+	0.686054i	−0.0331579	+	0.0240906i	−0.604241	−	0.796802i	$-0.706523\pi$
$811$	−0.944272	+	0.686054i	−0.0331579	+	0.0240906i	0.571083	+	0.820892i	$0.306523\pi$
$812$	2.64590	−	8.14324i	0.0928528	−	0.285772i
$813$	7.76393			0.272293
$814$		0			0
$815$	−8.70820			−0.305035
$816$	−4.86068	+	14.9596i	−0.170158	+	0.523692i
$817$	−17.9271	+	13.0248i	−0.627188	+	0.455679i
$818$	−5.47214	−	3.97574i	−0.191329	−	0.139008i
$819$	0.145898	+	0.449028i	0.00509809	+	0.0156903i
$820$	6.40576	+	19.7149i	0.223699	+	0.688475i
$821$	−45.8435	−	33.3072i	−1.59995	−	1.16243i	−0.887613	−	0.460590i	$-0.847638\pi$
$821$	−45.8435	−	33.3072i	−1.59995	−	1.16243i	−0.712335	−	0.701840i	$-0.752362\pi$
$822$	7.66312	−	5.56758i	0.267282	−	0.194192i
$823$	−9.85410	+	30.3278i	−0.343492	+	1.05716i	0.618894	+	0.785475i	$0.287581\pi$
$823$	−9.85410	+	30.3278i	−0.343492	+	1.05716i	−0.962386	+	0.271686i	$0.912419\pi$
$824$	13.0344			0.454076
$825$		0			0
$826$	−4.23607			−0.147392
$827$	−6.05573	+	18.6376i	−0.210578	+	0.648093i	0.788860	+	0.614573i	$0.210672\pi$
$827$	−6.05573	+	18.6376i	−0.210578	+	0.648093i	−0.999438	+	0.0335201i	$0.989328\pi$
$828$	−2.91641	+	2.11889i	−0.101352	+	0.0736367i
$829$	38.8156	+	28.2012i	1.34812	+	0.979467i	0.999103	+	0.0423517i	$0.0134850\pi$
$829$	38.8156	+	28.2012i	1.34812	+	0.979467i	0.349019	+	0.937116i	$0.386515\pi$
$830$	−0.319660	−	0.983813i	−0.0110956	−	0.0341486i
$831$	−11.5172	−	35.4464i	−0.399528	−	1.22962i
$832$	−4.70820	−	3.42071i	−0.163228	−	0.118592i
$833$	−2.50000	+	1.81636i	−0.0866199	+	0.0629330i
$834$	2.28115	−	7.02067i	0.0789899	−	0.243106i
$835$	6.47214			0.223978
$836$		0			0
$837$	−23.1803			−0.801230
$838$	−3.52786	+	10.8576i	−0.121868	+	0.375071i
$839$	−24.7533	+	17.9843i	−0.854578	+	0.620888i	−0.926405	−	0.376530i	$-0.877117\pi$
$839$	−24.7533	+	17.9843i	−0.854578	+	0.620888i	0.0718262	+	0.997417i	$0.477117\pi$
$840$	1.92705	+	1.40008i	0.0664896	+	0.0483075i
$841$	−2.37132	−	7.29818i	−0.0817698	−	0.251661i
$842$	−0.0901699	−	0.277515i	−0.00310746	−	0.00956378i
$843$	−32.9615	−	23.9479i	−1.13525	−	0.824810i
$844$	23.4271	−	17.0207i	0.806392	−	0.585878i
$845$	−3.54508	+	10.9106i	−0.121955	+	0.375338i
$846$	−0.965558			−0.0331966
$847$		0			0
$848$	−7.49342			−0.257325
$849$	−5.97214	+	18.3803i	−0.204963	+	0.630812i
$850$	−3.81966	+	2.77515i	−0.131013	+	0.0951867i
$851$	−26.6525	−	19.3642i	−0.913635	−	0.663795i
$852$	−14.9164	−	45.9080i	−0.511028	−	1.57278i
$853$	−10.7877	−	33.2012i	−0.369365	−	1.13679i	−0.947202	−	0.320636i	$-0.896103\pi$
$853$	−10.7877	−	33.2012i	−0.369365	−	1.13679i	0.577838	−	0.816152i	$-0.303897\pi$
$854$	−2.35410	−	1.71036i	−0.0805557	−	0.0585271i
$855$	−0.545085	+	0.396027i	−0.0186415	+	0.0135439i
$856$	1.23200	−	3.79171i	0.0421090	−	0.129598i
$857$	−15.0902			−0.515470			−0.257735	−	0.966216i	$-0.582976\pi$
$857$	−15.0902			−0.515470			−0.257735	+	0.966216i	$0.582976\pi$
$858$		0			0
$859$	21.5623			0.735696			0.367848	−	0.929886i	$-0.380095\pi$
$859$	21.5623			0.735696			0.367848	+	0.929886i	$0.380095\pi$
$860$	7.19756	−	22.1518i	0.245435	−	0.755371i
$861$	−14.6353	+	10.6331i	−0.498768	+	0.362376i
$862$	−4.28115	−	3.11044i	−0.145817	−	0.105942i
$863$	−14.8156	−	45.5977i	−0.504329	−	1.55216i	−0.801896	−	0.597463i	$-0.796175\pi$
$863$	−14.8156	−	45.5977i	−0.504329	−	1.55216i	0.297567	−	0.954701i	$-0.403825\pi$
$864$	−7.01064	−	21.5765i	−0.238507	−	0.734049i
$865$	12.4443	+	9.04129i	0.423118	+	0.307413i
$866$	−2.77051	+	2.01289i	−0.0941458	+	0.0684009i
$867$	3.72542	−	11.4657i	0.126522	−	0.389395i
$868$	7.85410			0.266586
$869$		0			0
$870$	−2.85410			−0.0967631
$871$	3.18034	−	9.78808i	0.107762	−	0.331656i
$872$	1.81966	−	1.32206i	0.0616215	−	0.0447706i
$873$	2.16312	+	1.57160i	0.0732105	+	0.0531905i
$874$	1.05979	+	3.26171i	0.0358480	+	0.110329i
$875$	−2.78115	−	8.55951i	−0.0940201	−	0.289364i
$876$	34.5517	+	25.1033i	1.16739	+	0.848160i
$877$	−10.5172	+	7.64121i	−0.355141	+	0.258025i	−0.751023	−	0.660276i	$-0.770439\pi$
$877$	−10.5172	+	7.64121i	−0.355141	+	0.258025i	0.395881	+	0.918302i	$0.370439\pi$
$878$	−0.399187	+	1.22857i	−0.0134719	+	0.0414623i
$879$	17.7984			0.600324
$880$		0			0
$881$	14.1459			0.476587			0.238294	−	0.971193i	$-0.423412\pi$
$881$	14.1459			0.476587			0.238294	+	0.971193i	$0.423412\pi$
$882$	0.0450850	−	0.138757i	0.00151809	−	0.00467220i
$883$	−25.5902	+	18.5923i	−0.861178	+	0.625682i	−0.928205	−	0.372069i	$-0.878649\pi$
$883$	−25.5902	+	18.5923i	−0.861178	+	0.625682i	0.0670273	+	0.997751i	$0.478649\pi$
$884$	−5.72949	−	4.16272i	−0.192704	−	0.140007i
$885$	−5.54508	−	17.0660i	−0.186396	−	0.573668i
$886$	−0.364745	−	1.12257i	−0.0122539	−	0.0377135i
$887$	−46.2877	−	33.6300i	−1.55419	−	1.12919i	−0.940578	−	0.339577i	$-0.889716\pi$
$887$	−46.2877	−	33.6300i	−1.55419	−	1.12919i	−0.613612	−	0.789608i	$-0.710284\pi$
$888$	12.4721	−	9.06154i	0.418537	−	0.304085i
$889$	0.909830	−	2.80017i	0.0305147	−	0.0939147i
$890$	−2.61803			−0.0877567
$891$		0			0
$892$	−3.77206			−0.126298
$893$	3.60739	−	11.1024i	0.120717	−	0.371528i
$894$	4.42705	−	3.21644i	0.148063	−	0.107574i
$895$	3.04508	+	2.21238i	0.101786	+	0.0739518i
$896$	3.11803	+	9.59632i	0.104166	+	0.320591i
$897$	3.14590	+	9.68208i	0.105038	+	0.323275i
$898$	3.80902	+	2.76741i	0.127109	+	0.0923498i
$899$	−15.8262	+	11.4984i	−0.527835	+	0.383494i
$900$	−0.875388	+	2.69417i	−0.0291796	+	0.0898056i
$901$	−7.36068			−0.245220
$902$		0			0
$903$	20.3262			0.676415
$904$	0.0663712	−	0.204270i	0.00220747	−	0.00679390i
$905$	6.00000	−	4.35926i	0.199447	−	0.144907i
$906$	−0.0278640	−	0.0202444i	−0.000925721	−	0.000672576i
$907$	−4.87132	−	14.9924i	−0.161750	−	0.497814i	0.837032	−	0.547153i	$-0.184289\pi$
$907$	−4.87132	−	14.9924i	−0.161750	−	0.497814i	−0.998782	+	0.0493391i	$0.984289\pi$
$908$	9.18692	+	28.2744i	0.304879	+	0.938320i
$909$	−4.57295	−	3.32244i	−0.151675	−	0.110198i
$910$	−0.381966	+	0.277515i	−0.0126620	+	0.00919952i
$911$	−13.9615	+	42.9691i	−0.462565	+	1.42363i	0.399454	+	0.916753i	$0.369200\pi$
$911$	−13.9615	+	42.9691i	−0.462565	+	1.42363i	−0.862019	+	0.506875i	$0.830800\pi$
$912$	8.97871			0.297315
$913$		0			0
$914$	0.0557281			0.00184332
$915$	3.80902	−	11.7229i	0.125922	−	0.387549i
$916$	10.1459	−	7.37143i	0.335230	−	0.243559i
$917$	−15.3262	−	11.1352i	−0.506117	−	0.367715i
$918$	−1.99593	−	6.14286i	−0.0658757	−	0.202744i
$919$	−4.60081	−	14.1598i	−0.151767	−	0.467090i	0.846052	−	0.533100i	$-0.178973\pi$
$919$	−4.60081	−	14.1598i	−0.151767	−	0.467090i	−0.997819	+	0.0660099i	$0.978973\pi$
$920$	−6.06231	−	4.40452i	−0.199868	−	0.145213i
$921$	−30.3435	+	22.0458i	−0.999851	+	0.726434i
$922$	2.18441	−	6.72291i	0.0719396	−	0.221407i
$923$	19.8885			0.654639
$924$		0			0
$925$	−25.8885			−0.851210
$926$	−2.62461	+	8.07772i	−0.0862501	+	0.265450i
$927$	2.73607	−	1.98787i	0.0898643	−	0.0652902i
$928$	−15.4894	−	11.2537i	−0.508463	−	0.369420i
$929$	7.41641	+	22.8254i	0.243324	+	0.748876i	0.995908	+	0.0903783i	$0.0288076\pi$
$929$	7.41641	+	22.8254i	0.243324	+	0.748876i	−0.752583	+	0.658497i	$0.771192\pi$
$930$	−0.809017	−	2.48990i	−0.0265287	−	0.0816470i
$931$	1.42705	+	1.03681i	0.0467697	+	0.0339802i
$932$	−44.1246	+	32.0584i	−1.44535	+	1.05011i
$933$	−4.50000	+	13.8496i	−0.147323	+	0.453415i
$934$	1.72136			0.0563246
$935$		0			0
$936$	0.695048			0.0227184
$937$	−15.9828	+	49.1899i	−0.522135	+	1.60697i	0.247779	+	0.968817i	$0.420299\pi$
$937$	−15.9828	+	49.1899i	−0.522135	+	1.60697i	−0.769913	+	0.638148i	$0.779701\pi$
$938$	−2.57295	+	1.86936i	−0.0840098	+	0.0610367i
$939$	23.9894	+	17.4293i	0.782863	+	0.568783i
$940$	3.79180	+	11.6699i	0.123675	+	0.380632i
$941$	8.36475	+	25.7440i	0.272683	+	0.839232i	0.989823	+	0.142303i	$0.0454507\pi$
$941$	8.36475	+	25.7440i	0.272683	+	0.839232i	−0.717140	+	0.696929i	$0.754549\pi$
$942$	−9.94427	−	7.22494i	−0.324002	−	0.235401i
$943$	46.0410	−	33.4508i	1.49930	−	1.08931i
$944$	10.7812	−	33.1810i	0.350897	−	1.07995i
$945$	5.47214			0.178009
$946$		0			0
$947$	6.29180			0.204456			0.102228	−	0.994761i	$-0.467403\pi$
$947$	6.29180			0.204456			0.102228	+	0.994761i	$0.467403\pi$
$948$	5.91641	−	18.2088i	0.192156	−	0.591395i
$949$	−14.2361	+	10.3431i	−0.462122	+	0.335752i
$950$	2.18034	+	1.58411i	0.0707396	+	0.0513953i
$951$	2.21885	+	6.82891i	0.0719510	+	0.221443i
$952$	1.40576	+	4.32650i	0.0455611	+	0.140223i
$953$	5.04508	+	3.66547i	0.163426	+	0.118736i	0.666493	−	0.745512i	$-0.267795\pi$
$953$	5.04508	+	3.66547i	0.163426	+	0.118736i	−0.503066	+	0.864248i	$0.667795\pi$
$954$	0.281153	−	0.204270i	0.00910266	−	0.00661347i
$955$	4.87132	−	14.9924i	0.157632	−	0.485142i
$956$	31.6869			1.02483
$957$		0			0
$958$	−8.31308			−0.268583
$959$	−4.73607	+	14.5761i	−0.152936	+	0.470687i
$960$	−6.16312	+	4.47777i	−0.198914	+	0.144519i
$961$	10.5623	+	7.67396i	0.340720	+	0.247547i
$962$	0.944272	+	2.90617i	0.0304445	+	0.0936987i
$963$	−0.319660	−	0.983813i	−0.0103009	−	0.0317029i
$964$	24.4058	+	17.7318i	0.786057	+	0.571104i
$965$	12.3992	−	9.00854i	0.399144	−	0.289995i
$966$	0.972136	−	2.99193i	0.0312780	−	0.0962637i
$967$	27.4508			0.882760			0.441380	−	0.897320i	$-0.354489\pi$
$967$	27.4508			0.882760			0.441380	+	0.897320i	$0.354489\pi$
$968$		0			0
$969$	8.81966			0.283328
$970$	−0.826238	+	2.54290i	−0.0265289	+	0.0816476i
$971$	22.8541	−	16.6045i	0.733423	−	0.532863i	−0.157221	−	0.987563i	$-0.550254\pi$
$971$	22.8541	−	16.6045i	0.733423	−	0.532863i	0.890644	+	0.454700i	$0.150254\pi$
$972$	−5.91641	−	4.29852i	−0.189769	−	0.137875i
$973$	3.69098	+	11.3597i	0.118327	+	0.364175i
$974$	3.84752	+	11.8415i	0.123283	+	0.379425i
$975$	6.47214	+	4.70228i	0.207274	+	0.150594i
$976$	19.3885	−	14.0866i	0.620612	−	0.450901i
$977$	−3.34346	+	10.2901i	−0.106967	+	0.329210i	−0.990187	−	0.139749i	$-0.955371\pi$
$977$	−3.34346	+	10.2901i	−0.106967	+	0.329210i	0.883220	+	0.468958i	$0.155371\pi$
$978$	−5.38197			−0.172096
$979$		0			0
$980$	−1.85410			−0.0592271
$981$	0.180340	−	0.555029i	0.00575781	−	0.0177207i
$982$	6.84346	−	4.97206i	0.218384	−	0.158665i
$983$	10.0172	+	7.27794i	0.319500	+	0.232130i	0.735962	−	0.677023i	$-0.236730\pi$
$983$	10.0172	+	7.27794i	0.319500	+	0.232130i	−0.416462	+	0.909153i	$0.636730\pi$
$984$	8.22949	+	25.3278i	0.262347	+	0.807420i
$985$	−1.32624	−	4.08174i	−0.0422575	−	0.130055i
$986$	−4.40983	−	3.20393i	−0.140438	−	0.102034i
$987$	−8.66312	+	6.29412i	−0.275750	+	0.200344i
$988$	−1.24922	+	3.84471i	−0.0397431	+	0.122317i
$989$	−63.9443			−2.03331
$990$		0			0
$991$	−0.729490			−0.0231730			−0.0115865	−	0.999933i	$-0.503688\pi$
$991$	−0.729490			−0.0231730			−0.0115865	+	0.999933i	$0.503688\pi$
$992$	5.42705	−	16.7027i	0.172309	−	0.530313i
$993$	8.09017	−	5.87785i	0.256734	−	0.186528i
$994$	−4.97214	−	3.61247i	−0.157707	−	0.114581i
$995$	−2.54508	−	7.83297i	−0.0806846	−	0.248322i
$996$	2.51064	+	7.72696i	0.0795528	+	0.244838i
$997$	45.1976	+	32.8380i	1.43142	+	1.03999i	0.989750	+	0.142811i	$0.0456142\pi$
$997$	45.1976	+	32.8380i	1.43142	+	1.03999i	0.441671	+	0.897177i	$0.354386\pi$
$998$	−3.11803	+	2.26538i	−0.0986996	+	0.0717095i
$999$	10.9443	−	33.6830i	0.346261	−	1.06568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.l.372.1		4
11.2	odd	10		847.2.f.j.729.1		4
11.3	even	5		847.2.f.d.323.1		4
11.4	even	5		847.2.a.d.1.2	✓	2
11.5	even	5	inner	847.2.f.l.148.1		4
11.6	odd	10		847.2.f.c.148.1		4
11.7	odd	10		847.2.a.h.1.1	yes	2
11.8	odd	10		847.2.f.j.323.1		4
11.9	even	5		847.2.f.d.729.1		4
11.10	odd	2		847.2.f.c.372.1		4
33.26	odd	10		7623.2.a.bx.1.1		2
33.29	even	10		7623.2.a.t.1.2		2
77.48	odd	10		5929.2.a.i.1.2		2
77.62	even	10		5929.2.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.d.1.2	✓	2	11.4	even	5
847.2.a.h.1.1	yes	2	11.7	odd	10
847.2.f.c.148.1		4	11.6	odd	10
847.2.f.c.372.1		4	11.10	odd	2
847.2.f.d.323.1		4	11.3	even	5
847.2.f.d.729.1		4	11.9	even	5
847.2.f.j.323.1		4	11.8	odd	10
847.2.f.j.729.1		4	11.2	odd	10
847.2.f.l.148.1		4	11.5	even	5	inner
847.2.f.l.372.1		4	1.1	even	1	trivial
5929.2.a.i.1.2		2	77.48	odd	10
5929.2.a.s.1.1		2	77.62	even	10
7623.2.a.t.1.2		2	33.29	even	10
7623.2.a.bx.1.1		2	33.26	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)

\(f(q)\)	\(=\)	\(q+(-0.118034 + 0.363271i) q^{2} +(1.30902 - 0.951057i) q^{3} +(1.50000 + 1.08981i) q^{4} +(0.309017 + 0.951057i) q^{5} +(0.190983 + 0.587785i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.118034 + 0.363271i) q^{9} +O(q^{10})\)	\(q+(-0.118034 + 0.363271i) q^{2} +(1.30902 - 0.951057i) q^{3} +(1.50000 + 1.08981i) q^{4} +(0.309017 + 0.951057i) q^{5} +(0.190983 + 0.587785i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(-0.118034 + 0.363271i) q^{9} -0.381966 q^{10} +3.00000 q^{12} +(-0.381966 + 1.17557i) q^{13} +(0.309017 - 0.224514i) q^{14} +(1.30902 + 0.951057i) q^{15} +(0.972136 + 2.99193i) q^{16} +(0.954915 + 2.93893i) q^{17} +(-0.118034 - 0.0857567i) q^{18} +(1.42705 - 1.03681i) q^{19} +(-0.572949 + 1.76336i) q^{20} -1.61803 q^{21} +5.09017 q^{23} +(-0.736068 + 2.26538i) q^{24} +(3.23607 - 2.35114i) q^{25} +(-0.381966 - 0.277515i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-0.572949 - 1.76336i) q^{28} +(3.73607 + 2.71441i) q^{29} +(-0.500000 + 0.363271i) q^{30} +(-1.30902 + 4.02874i) q^{31} -4.14590 q^{32} -1.18034 q^{34} +(0.309017 - 0.951057i) q^{35} +(-0.572949 + 0.416272i) q^{36} +(-5.23607 - 3.80423i) q^{37} +(0.208204 + 0.640786i) q^{38} +(0.618034 + 1.90211i) q^{39} +(-1.19098 - 0.865300i) q^{40} +(9.04508 - 6.57164i) q^{41} +(0.190983 - 0.587785i) q^{42} -12.5623 q^{43} -0.381966 q^{45} +(-0.600813 + 1.84911i) q^{46} +(5.35410 - 3.88998i) q^{47} +(4.11803 + 2.99193i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.472136 + 1.45309i) q^{50} +(4.04508 + 2.93893i) q^{51} +(-1.85410 + 1.34708i) q^{52} +(-0.736068 + 2.26538i) q^{53} -2.09017 q^{54} +1.47214 q^{56} +(0.881966 - 2.71441i) q^{57} +(-1.42705 + 1.03681i) q^{58} +(-8.97214 - 6.51864i) q^{59} +(0.927051 + 2.85317i) q^{60} +(-2.35410 - 7.24518i) q^{61} +(-1.30902 - 0.951057i) q^{62} +(0.309017 - 0.224514i) q^{63} +(-1.45492 + 4.47777i) q^{64} -1.23607 q^{65} -8.32624 q^{67} +(-1.77051 + 5.44907i) q^{68} +(6.66312 - 4.84104i) q^{69} +(0.309017 + 0.224514i) q^{70} +(-4.97214 - 15.3027i) q^{71} +(-0.173762 - 0.534785i) q^{72} +(11.5172 + 8.36775i) q^{73} +(2.00000 - 1.45309i) q^{74} +(2.00000 - 6.15537i) q^{75} +3.27051 q^{76} -0.763932 q^{78} +(1.97214 - 6.06961i) q^{79} +(-2.54508 + 1.84911i) q^{80} +(6.23607 + 4.53077i) q^{81} +(1.31966 + 4.06150i) q^{82} +(0.836881 + 2.57565i) q^{83} +(-2.42705 - 1.76336i) q^{84} +(-2.50000 + 1.81636i) q^{85} +(1.48278 - 4.56352i) q^{86} +7.47214 q^{87} +6.85410 q^{89} +(0.0450850 - 0.138757i) q^{90} +(1.00000 - 0.726543i) q^{91} +(7.63525 + 5.54734i) q^{92} +(2.11803 + 6.51864i) q^{93} +(0.781153 + 2.40414i) q^{94} +(1.42705 + 1.03681i) q^{95} +(-5.42705 + 3.94298i) q^{96} +(2.16312 - 6.65740i) q^{97} -0.381966 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - q^7 - 7 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - q^{5} + 3 q^{6} - q^{7} - 7 q^{8} + 4 q^{9} - 6 q^{10} + 12 q^{12} - 6 q^{13} - q^{14} + 3 q^{15} - 14 q^{16} + 15 q^{17} + 4 q^{18} - q^{19} - 9 q^{20} - 2 q^{21} - 2 q^{23} + 6 q^{24} + 4 q^{25} - 6 q^{26} + 9 q^{27} - 9 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{31} - 30 q^{32} + 40 q^{34} - q^{35} - 9 q^{36} - 12 q^{37} - 26 q^{38} - 2 q^{39} - 7 q^{40} + 25 q^{41} + 3 q^{42} - 10 q^{43} - 6 q^{45} - 27 q^{46} + 8 q^{47} + 12 q^{48} - q^{49} - 16 q^{50} + 5 q^{51} + 6 q^{52} + 6 q^{53} + 14 q^{54} - 12 q^{56} + 8 q^{57} + q^{58} - 18 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{62} - q^{63} - 17 q^{64} + 4 q^{65} - 2 q^{67} + 60 q^{68} + 11 q^{69} - q^{70} - 2 q^{71} - 32 q^{72} + 17 q^{73} + 8 q^{74} + 8 q^{75} - 54 q^{76} - 12 q^{78} - 10 q^{79} + q^{80} + 16 q^{81} + 50 q^{82} + 19 q^{83} - 3 q^{84} - 10 q^{85} + 35 q^{86} + 12 q^{87} + 14 q^{89} - 11 q^{90} + 4 q^{91} - 3 q^{92} + 4 q^{93} - 17 q^{94} - q^{95} - 15 q^{96} - 7 q^{97} - 6 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - q^5 + 3 * q^6 - q^7 - 7 * q^8 + 4 * q^9 - 6 * q^10 + 12 * q^12 - 6 * q^13 - q^14 + 3 * q^15 - 14 * q^16 + 15 * q^17 + 4 * q^18 - q^19 - 9 * q^20 - 2 * q^21 - 2 * q^23 + 6 * q^24 + 4 * q^25 - 6 * q^26 + 9 * q^27 - 9 * q^28 + 6 * q^29 - 2 * q^30 - 3 * q^31 - 30 * q^32 + 40 * q^34 - q^35 - 9 * q^36 - 12 * q^37 - 26 * q^38 - 2 * q^39 - 7 * q^40 + 25 * q^41 + 3 * q^42 - 10 * q^43 - 6 * q^45 - 27 * q^46 + 8 * q^47 + 12 * q^48 - q^49 - 16 * q^50 + 5 * q^51 + 6 * q^52 + 6 * q^53 + 14 * q^54 - 12 * q^56 + 8 * q^57 + q^58 - 18 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^62 - q^63 - 17 * q^64 + 4 * q^65 - 2 * q^67 + 60 * q^68 + 11 * q^69 - q^70 - 2 * q^71 - 32 * q^72 + 17 * q^73 + 8 * q^74 + 8 * q^75 - 54 * q^76 - 12 * q^78 - 10 * q^79 + q^80 + 16 * q^81 + 50 * q^82 + 19 * q^83 - 3 * q^84 - 10 * q^85 + 35 * q^86 + 12 * q^87 + 14 * q^89 - 11 * q^90 + 4 * q^91 - 3 * q^92 + 4 * q^93 - 17 * q^94 - q^95 - 15 * q^96 - 7 * q^97 - 6 * q^98

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