LMFDB - Embedded newform 931.2.v.b.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(177,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([6, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("931.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.v (of order $9$, degree $6$, 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			275.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	931.275
Dual form			931.2.v.b.606.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26604 + 0.460802i) q^{2} +(2.70574 + 0.984808i) q^{3} +(-0.141559 - 0.118782i) q^{4} +(0.673648 - 0.565258i) q^{5} +(2.97178 + 2.49362i) q^{6} +(-1.47178 - 2.54920i) q^{8} +(4.05303 + 3.40090i) q^{9} +O(q^{10})$	\(q+(1.26604 + 0.460802i) q^{2} +(2.70574 + 0.984808i) q^{3} +(-0.141559 - 0.118782i) q^{4} +(0.673648 - 0.565258i) q^{5} +(2.97178 + 2.49362i) q^{6} +(-1.47178 - 2.54920i) q^{8} +(4.05303 + 3.40090i) q^{9} +(1.11334 - 0.405223i) q^{10} +(1.11334 - 1.92836i) q^{11} +(-0.266044 - 0.460802i) q^{12} +(1.97178 + 1.65452i) q^{13} +(2.37939 - 0.866025i) q^{15} +(-0.624485 - 3.54163i) q^{16} +(0.358441 - 0.300767i) q^{17} +(3.56418 + 6.17334i) q^{18} +(2.77719 - 3.35965i) q^{19} -0.162504 q^{20} +(2.29813 - 1.92836i) q^{22} +(-0.467911 + 2.65366i) q^{23} +(-1.47178 - 8.34689i) q^{24} +(-0.733956 + 4.16247i) q^{25} +(1.73396 + 3.00330i) q^{26} +(3.29813 + 5.71253i) q^{27} +(-1.19459 + 6.77487i) q^{29} +3.41147 q^{30} -7.10607 q^{31} +(-0.180922 + 1.02606i) q^{32} +(4.91147 - 4.12122i) q^{33} +(0.592396 - 0.215615i) q^{34} +(-0.169778 - 0.962858i) q^{36} +(-2.47178 + 4.28125i) q^{37} +(5.06418 - 2.97373i) q^{38} +(3.70574 + 6.41852i) q^{39} +(-2.43242 - 0.885328i) q^{40} +(1.89646 - 1.59132i) q^{41} +(-3.66637 - 1.33445i) q^{43} +(-0.386659 + 0.140732i) q^{44} +4.65270 q^{45} +(-1.81521 + 3.14403i) q^{46} +(-5.58512 - 4.68647i) q^{47} +(1.79813 - 10.1977i) q^{48} +(-2.84730 + 4.93166i) q^{50} +(1.26604 - 0.460802i) q^{51} +(-0.0825961 - 0.468426i) q^{52} +(-2.17365 - 1.82391i) q^{53} +(1.54323 + 8.75211i) q^{54} +(-0.340022 - 1.92836i) q^{55} +(10.8229 - 6.35532i) q^{57} +(-4.63429 + 8.02682i) q^{58} +(-4.83022 + 4.05304i) q^{59} +(-0.439693 - 0.160035i) q^{60} +(1.58512 - 8.98968i) q^{61} +(-8.99660 - 3.27449i) q^{62} +(-4.29813 + 7.44459i) q^{64} +2.26352 q^{65} +(8.11721 - 2.95442i) q^{66} +(-7.21213 + 2.62500i) q^{67} -0.0864665 q^{68} +(-3.87939 + 6.71929i) q^{69} +(8.74422 + 3.18264i) q^{71} +(2.70439 - 15.3374i) q^{72} +(-1.30541 - 0.475129i) q^{73} +(-5.10220 + 4.28125i) q^{74} +(-6.08512 + 10.5397i) q^{75} +(-0.792204 + 0.145708i) q^{76} +(1.73396 + 9.83375i) q^{78} +(-2.05690 - 11.6653i) q^{79} +(-2.42262 - 2.03282i) q^{80} +(0.541889 + 3.07321i) q^{81} +(3.13429 - 1.14079i) q^{82} +(7.41534 - 12.8438i) q^{83} +(0.0714517 - 0.405223i) q^{85} +(-4.02687 - 3.37895i) q^{86} +(-9.90420 + 17.1546i) q^{87} -6.55438 q^{88} +(9.67024 - 3.51968i) q^{89} +(5.89053 + 2.14398i) q^{90} +(0.381445 - 0.320070i) q^{92} +(-19.2271 - 6.99811i) q^{93} +(-4.91147 - 8.50692i) q^{94} +(-0.0282185 - 3.83305i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(1.64156 + 9.30975i) q^{97} +(11.0706 - 4.02936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 6 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 6 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 + 12 * q^9	$ 6 q + 3 q^{2} + 6 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} + 12 q^{9} + 3 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} - 6 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} - 12 q^{23} + 6 q^{24} - 9 q^{25} + 15 q^{26} + 6 q^{27} - 3 q^{29} - 18 q^{31} - 18 q^{32} + 9 q^{33} - 24 q^{36} + 12 q^{38} + 12 q^{39} + 9 q^{40} + 21 q^{41} - 3 q^{43} - 9 q^{44} + 30 q^{45} - 18 q^{46} - 12 q^{47} - 3 q^{48} - 15 q^{50} + 3 q^{51} + 6 q^{52} - 12 q^{53} - 6 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} - 12 q^{61} - 12 q^{62} - 12 q^{64} + 24 q^{65} + 18 q^{66} + 6 q^{67} + 30 q^{68} - 12 q^{69} - 6 q^{71} + 15 q^{72} - 12 q^{73} - 30 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 24 q^{79} + 12 q^{80} - 3 q^{81} + 9 q^{82} - 48 q^{86} - 21 q^{87} - 18 q^{88} + 15 q^{89} + 18 q^{90} + 42 q^{92} - 36 q^{93} - 9 q^{94} - 15 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 6 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 + 12 * q^9 + 3 * q^12 - 3 * q^13 + 3 * q^15 + 9 * q^16 - 6 * q^17 + 3 * q^18 + 6 * q^19 - 6 * q^20 - 12 * q^23 + 6 * q^24 - 9 * q^25 + 15 * q^26 + 6 * q^27 - 3 * q^29 - 18 * q^31 - 18 * q^32 + 9 * q^33 - 24 * q^36 + 12 * q^38 + 12 * q^39 + 9 * q^40 + 21 * q^41 - 3 * q^43 - 9 * q^44 + 30 * q^45 - 18 * q^46 - 12 * q^47 - 3 * q^48 - 15 * q^50 + 3 * q^51 + 6 * q^52 - 12 * q^53 - 6 * q^54 + 18 * q^55 + 24 * q^57 - 18 * q^58 - 6 * q^59 + 3 * q^60 - 12 * q^61 - 12 * q^62 - 12 * q^64 + 24 * q^65 + 18 * q^66 + 6 * q^67 + 30 * q^68 - 12 * q^69 - 6 * q^71 + 15 * q^72 - 12 * q^73 - 30 * q^74 - 15 * q^75 + 36 * q^76 + 15 * q^78 + 24 * q^79 + 12 * q^80 - 3 * q^81 + 9 * q^82 - 48 * q^86 - 21 * q^87 - 18 * q^88 + 15 * q^89 + 18 * q^90 + 42 * q^92 - 36 * q^93 - 9 * q^94 - 15 * q^95 - 9 * q^96 + 18 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	1.26604	+	0.460802i	0.895229	+	0.325837i	0.748339	−	0.663316i	$-0.230852\pi$
$2$	1.26604	+	0.460802i	0.895229	+	0.325837i	0.146889	+	0.989153i	$0.453074\pi$
$3$	2.70574	+	0.984808i	1.56216	+	0.568579i	0.971230	−	0.238145i	$-0.0765393\pi$
$3$	2.70574	+	0.984808i	1.56216	+	0.568579i	0.590928	+	0.806724i	$0.298762\pi$
$4$	−0.141559	−	0.118782i	−0.0707796	−	0.0593912i
$5$	0.673648	−	0.565258i	0.301265	−	0.252791i	−0.479606	−	0.877484i	$-0.659220\pi$
$5$	0.673648	−	0.565258i	0.301265	−	0.252791i	0.780870	+	0.624693i	$0.214776\pi$
$6$	2.97178	+	2.49362i	1.21322	+	1.01802i
$7$		0			0
$7$		0			0
$8$	−1.47178	−	2.54920i	−0.520353	−	0.901278i
$9$	4.05303	+	3.40090i	1.35101	+	1.13363i
$10$	1.11334	−	0.405223i	0.352069	−	0.128143i
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	−0.647931	−	0.761699i	$-0.724366\pi$
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	0.983616	+	0.180276i	$0.0576989\pi$
$12$	−0.266044	−	0.460802i	−0.0768004	−	0.133022i
$13$	1.97178	+	1.65452i	0.546874	+	0.458882i	0.873881	−	0.486140i	$-0.161596\pi$
$13$	1.97178	+	1.65452i	0.546874	+	0.458882i	−0.327007	+	0.945022i	$0.606040\pi$
$14$		0			0
$15$	2.37939	−	0.866025i	0.614355	−	0.223607i
$16$	−0.624485	−	3.54163i	−0.156121	−	0.885408i
$17$	0.358441	−	0.300767i	0.0869346	−	0.0729468i	−0.598285	−	0.801284i	$-0.704151\pi$
$17$	0.358441	−	0.300767i	0.0869346	−	0.0729468i	0.685219	+	0.728337i	$0.259706\pi$
$18$	3.56418	+	6.17334i	0.840085	+	1.45507i
$19$	2.77719	−	3.35965i	0.637131	−	0.770756i
$19$	2.77719	−	3.35965i	0.637131	−	0.770756i
$20$	−0.162504			−0.0363370
$21$		0			0
$22$	2.29813	−	1.92836i	0.489964	−	0.411128i
$23$	−0.467911	+	2.65366i	−0.0975662	+	0.553325i	0.896365	+	0.443318i	$0.146199\pi$
$23$	−0.467911	+	2.65366i	−0.0975662	+	0.553325i	−0.993931	+	0.110008i	$0.964912\pi$
$24$	−1.47178	−	8.34689i	−0.300426	−	1.70380i
$25$	−0.733956	+	4.16247i	−0.146791	+	0.832494i
$26$	1.73396	+	3.00330i	0.340057	+	0.588995i
$27$	3.29813	+	5.71253i	0.634726	+	1.09938i
$28$		0			0
$29$	−1.19459	+	6.77487i	−0.221830	+	1.25806i	0.646822	+	0.762641i	$0.276097\pi$
$29$	−1.19459	+	6.77487i	−0.221830	+	1.25806i	−0.868653	+	0.495421i	$0.835014\pi$
$30$	3.41147			0.622847
$31$	−7.10607			−1.27629			−0.638144	−	0.769917i	$-0.720297\pi$
$31$	−7.10607			−1.27629			−0.638144	+	0.769917i	$0.720297\pi$
$32$	−0.180922	+	1.02606i	−0.0319828	+	0.181384i
$33$	4.91147	−	4.12122i	0.854978	−	0.717412i
$34$	0.592396	−	0.215615i	0.101595	−	0.0369776i
$35$		0			0
$36$	−0.169778	−	0.962858i	−0.0282963	−	0.160476i
$37$	−2.47178	+	4.28125i	−0.406358	+	0.703833i	−0.994479	−	0.104940i	$-0.966535\pi$
$37$	−2.47178	+	4.28125i	−0.406358	+	0.703833i	0.588120	+	0.808774i	$0.299868\pi$
$38$	5.06418	−	2.97373i	0.821518	−	0.482402i
$39$	3.70574	+	6.41852i	0.593393	+	1.02779i
$40$	−2.43242	−	0.885328i	−0.384599	−	0.139983i
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	−0.482574	−	0.875855i	$-0.660298\pi$
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	0.778751	+	0.627333i	$0.215854\pi$
$42$		0			0
$43$	−3.66637	−	1.33445i	−0.559117	−	0.203502i	0.0469757	−	0.998896i	$-0.485042\pi$
$43$	−3.66637	−	1.33445i	−0.559117	−	0.203502i	−0.606093	+	0.795394i	$0.707264\pi$
$44$	−0.386659	+	0.140732i	−0.0582911	+	0.0212162i
$45$	4.65270			0.693584
$46$	−1.81521	+	3.14403i	−0.267638	+	0.463562i
$47$	−5.58512	−	4.68647i	−0.814674	−	0.683592i	0.137045	−	0.990565i	$-0.456240\pi$
$47$	−5.58512	−	4.68647i	−0.814674	−	0.683592i	−0.951718	+	0.306972i	$0.900684\pi$
$48$	1.79813	−	10.1977i	0.259538	−	1.47191i
$49$		0			0
$50$	−2.84730	+	4.93166i	−0.402669	+	0.697442i
$51$	1.26604	−	0.460802i	0.177282	−	0.0645253i
$52$	−0.0825961	−	0.468426i	−0.0114540	−	0.0649590i
$53$	−2.17365	−	1.82391i	−0.298574	−	0.250533i	0.481177	−	0.876624i	$-0.340210\pi$
$53$	−2.17365	−	1.82391i	−0.298574	−	0.250533i	−0.779750	+	0.626091i	$0.784654\pi$
$54$	1.54323	+	8.75211i	0.210007	+	1.19101i
$55$	−0.340022	−	1.92836i	−0.0458486	−	0.260020i
$56$		0			0
$57$	10.8229	−	6.35532i	1.43353	−	0.841783i
$58$	−4.63429	+	8.02682i	−0.608511	+	1.05397i
$59$	−4.83022	+	4.05304i	−0.628841	+	0.527661i	−0.900569	−	0.434714i	$-0.856850\pi$
$59$	−4.83022	+	4.05304i	−0.628841	+	0.527661i	0.271727	+	0.962374i	$0.412405\pi$
$60$	−0.439693	−	0.160035i	−0.0567641	−	0.0206604i
$61$	1.58512	−	8.98968i	0.202954	−	1.15101i	−0.697673	−	0.716417i	$-0.745781\pi$
$61$	1.58512	−	8.98968i	0.202954	−	1.15101i	0.900627	−	0.434593i	$-0.143108\pi$
$62$	−8.99660	−	3.27449i	−1.14257	−	0.415861i
$63$		0			0
$64$	−4.29813	+	7.44459i	−0.537267	+	0.930573i
$65$	2.26352			0.280755
$66$	8.11721	−	2.95442i	0.999160	−	0.363664i
$67$	−7.21213	+	2.62500i	−0.881102	+	0.320695i	−0.742655	−	0.669675i	$-0.766434\pi$
$67$	−7.21213	+	2.62500i	−0.881102	+	0.320695i	−0.138448	+	0.990370i	$0.544211\pi$
$68$	−0.0864665			−0.0104856
$69$	−3.87939	+	6.71929i	−0.467023	+	0.808908i
$70$		0			0
$71$	8.74422	+	3.18264i	1.03775	+	0.377709i	0.804026	−	0.594594i	$-0.202687\pi$
$71$	8.74422	+	3.18264i	1.03775	+	0.377709i	0.233722	+	0.972303i	$0.424909\pi$
$72$	2.70439	−	15.3374i	0.318716	−	1.80753i
$73$	−1.30541	−	0.475129i	−0.152786	−	0.0556097i	0.264495	−	0.964387i	$-0.414795\pi$
$73$	−1.30541	−	0.475129i	−0.152786	−	0.0556097i	−0.417281	+	0.908777i	$0.637017\pi$
$74$	−5.10220	+	4.28125i	−0.593118	+	0.497685i
$75$	−6.08512	+	10.5397i	−0.702649	+	1.21702i
$76$	−0.792204	+	0.145708i	−0.0908720	+	0.0167139i
$77$		0			0
$78$	1.73396	+	9.83375i	0.196332	+	1.11345i
$79$	−2.05690	−	11.6653i	−0.231420	−	1.31245i	−0.850024	−	0.526744i	$-0.823413\pi$
$79$	−2.05690	−	11.6653i	−0.231420	−	1.31245i	0.618604	−	0.785703i	$-0.287698\pi$
$80$	−2.42262	−	2.03282i	−0.270857	−	0.227276i
$81$	0.541889	+	3.07321i	0.0602099	+	0.341467i
$82$	3.13429	−	1.14079i	0.346124	−	0.125979i
$83$	7.41534	−	12.8438i	0.813940	−	1.40979i	−0.0961469	−	0.995367i	$-0.530652\pi$
$83$	7.41534	−	12.8438i	0.813940	−	1.40979i	0.910087	−	0.414418i	$-0.136015\pi$
$84$		0			0
$85$	0.0714517	−	0.405223i	0.00775003	−	0.0439526i
$86$	−4.02687	−	3.37895i	−0.434229	−	0.364361i
$87$	−9.90420	+	17.1546i	−1.06184	+	1.83916i
$88$	−6.55438			−0.698699
$89$	9.67024	−	3.51968i	1.02504	−	0.373085i	0.225852	−	0.974162i	$-0.427483\pi$
$89$	9.67024	−	3.51968i	1.02504	−	0.373085i	0.799192	+	0.601076i	$0.205261\pi$
$90$	5.89053	+	2.14398i	0.620916	+	0.225995i
$91$		0			0
$92$	0.381445	−	0.320070i	0.0397684	−	0.0333696i
$93$	−19.2271	−	6.99811i	−1.99376	−	0.725670i
$94$	−4.91147	−	8.50692i	−0.506580	−	0.877422i
$95$	−0.0282185	−	3.83305i	−0.00289516	−	0.393262i
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$	1.64156	+	9.30975i	0.166675	+	0.945261i	0.947320	+	0.320287i	$0.103779\pi$
$97$	1.64156	+	9.30975i	0.166675	+	0.945261i	−0.780645	+	0.624974i	$0.785109\pi$
$98$		0			0
$99$	11.0706	−	4.02936i	1.11263	−	0.404966i
$100$	0.598326	−	0.502055i	0.0598326	−	0.0502055i
$101$	−1.60607	+	9.10846i	−0.159810	+	0.906325i	0.794446	+	0.607334i	$0.207761\pi$
$101$	−1.60607	+	9.10846i	−0.159810	+	0.906325i	−0.954256	+	0.298991i	$0.903350\pi$
$102$	1.81521			0.179732
$103$	−5.50980			−0.542897			−0.271448	−	0.962453i	$-0.587503\pi$
$103$	−5.50980			−0.542897			−0.271448	+	0.962453i	$0.587503\pi$
$104$	1.31567	−	7.46156i	0.129012	−	0.731666i
$105$		0			0
$106$	−1.91147	−	3.31077i	−0.185659	−	0.321570i
$107$	−5.11721	−	8.86327i	−0.494699	−	0.856845i	0.505282	−	0.862954i	$-0.331389\pi$
$107$	−5.11721	−	8.86327i	−0.494699	−	0.856845i	−0.999981	+	0.00610974i	$0.998055\pi$
$108$	0.211667	−	1.20042i	0.0203677	−	0.115511i
$109$	−0.316552	−	1.79525i	−0.0303201	−	0.171954i	0.965887	−	0.258962i	$-0.0833805\pi$
$109$	−0.316552	−	1.79525i	−0.0303201	−	0.171954i	−0.996208	+	0.0870081i	$0.972269\pi$
$110$	0.458111	−	2.59808i	0.0436792	−	0.247717i
$111$	−10.9042	+	9.14971i	−1.03498	+	0.868452i
$112$		0			0
$113$	−17.6878			−1.66393			−0.831963	−	0.554830i	$-0.812783\pi$
$113$	−17.6878			−1.66393			−0.831963	+	0.554830i	$0.812783\pi$
$114$	16.6309	−	3.05888i	1.55762	−	0.286490i
$115$	1.18479	+	2.05212i	0.110482	+	0.191361i
$116$	0.973841	−	0.817150i	0.0904189	−	0.0758704i
$117$	2.36484	+	13.4117i	0.218629	+	1.23991i
$118$	−7.98293	+	2.90555i	−0.734888	+	0.267477i
$119$		0			0
$120$	−5.70961	−	4.79093i	−0.521213	−	0.437350i
$121$	3.02094	+	5.23243i	0.274631	+	0.475675i
$122$	6.14930	−	10.6509i	0.556731	−	0.964287i
$123$	6.69846	−	2.43804i	0.603980	−	0.219831i
$124$	1.00593	+	0.844075i	0.0903352	+	0.0758002i
$125$	4.05690	+	7.02676i	0.362861	+	0.628493i
$126$		0			0
$127$	8.88919	+	7.45891i	0.788788	+	0.661871i	0.945445	−	0.325782i	$-0.105627\pi$
$127$	8.88919	+	7.45891i	0.788788	+	0.661871i	−0.156657	+	0.987653i	$0.550072\pi$
$128$	−7.27584	+	6.10516i	−0.643100	+	0.539625i
$129$	−8.60607	−	7.22135i	−0.757722	−	0.635804i
$130$	2.86571	+	1.04303i	0.251340	+	0.0914802i
$131$	−1.73396	−	0.631108i	−0.151496	−	0.0551402i	0.265159	−	0.964205i	$-0.414576\pi$
$131$	−1.73396	−	0.631108i	−0.151496	−	0.0551402i	−0.416655	+	0.909065i	$0.636798\pi$
$132$	−1.18479			−0.103123
$133$		0			0
$134$	−10.3405			−0.893282
$135$	5.45084	+	1.98394i	0.469133	+	0.170751i
$136$	−1.29426	−	0.471073i	−0.110982	−	0.0403942i
$137$	0.195937	+	0.164411i	0.0167400	+	0.0140465i	0.651119	−	0.758975i	$-0.274300\pi$
$137$	0.195937	+	0.164411i	0.0167400	+	0.0140465i	−0.634379	+	0.773022i	$0.718744\pi$
$138$	−8.00774	+	6.71929i	−0.681664	+	0.571984i
$139$	3.26604	+	2.74054i	0.277022	+	0.232449i	0.770704	−	0.637193i	$-0.219905\pi$
$139$	3.26604	+	2.74054i	0.277022	+	0.232449i	−0.493682	+	0.869643i	$0.664349\pi$
$140$		0			0
$141$	−10.4966	−	18.1806i	−0.883973	−	1.53109i
$142$	9.60401	+	8.05872i	0.805950	+	0.676273i
$143$	5.38578	−	1.96026i	0.450382	−	0.163926i
$144$	9.51367	−	16.4782i	0.792806	−	1.37318i
$145$	3.02481	+	5.23913i	0.251197	+	0.435086i
$146$	−1.43376	−	1.20307i	−0.118659	−	0.0995668i
$147$		0			0
$148$	0.858441	−	0.312447i	0.0705634	−	0.0256830i
$149$	2.87551	+	16.3079i	0.235571	+	1.33599i	0.841407	+	0.540402i	$0.181728\pi$
$149$	2.87551	+	16.3079i	0.235571	+	1.33599i	−0.605836	+	0.795590i	$0.707161\pi$
$150$	−12.5608	+	10.5397i	−1.02558	+	0.860566i
$151$	2.18092	+	3.77747i	0.177481	+	0.307406i	0.941017	−	0.338359i	$-0.109872\pi$
$151$	2.18092	+	3.77747i	0.177481	+	0.307406i	−0.763536	+	0.645765i	$0.776539\pi$
$152$	−12.6518	−	2.13495i	−1.02620	−	0.173167i
$153$	2.47565			0.200145
$154$		0			0
$155$	−4.78699	+	4.01676i	−0.384500	+	0.322634i
$156$	0.237826	−	1.34878i	0.0190413	−	0.107989i
$157$	−1.67024	−	9.47243i	−0.133300	−	0.755982i	−0.976028	−	0.217643i	$-0.930163\pi$
$157$	−1.67024	−	9.47243i	−0.133300	−	0.755982i	0.842728	−	0.538339i	$-0.180948\pi$
$158$	2.77126	−	15.7166i	0.220470	−	1.25034i
$159$	−4.08512	−	7.07564i	−0.323971	−	0.561135i
$160$	0.458111	+	0.793471i	0.0362168	+	0.0627294i
$161$		0			0
$162$	−0.730085	+	4.14052i	−0.0573609	+	0.325310i
$163$	8.35504			0.654417			0.327209	−	0.944952i	$-0.393892\pi$
$163$	8.35504			0.654417			0.327209	+	0.944952i	$0.393892\pi$
$164$	−0.457482			−0.0357233
$165$	0.979055	−	5.55250i	0.0762194	−	0.432261i
$166$	15.3066	−	12.8438i	1.18802	−	0.996869i
$167$	−3.79174	+	1.38008i	−0.293413	+	0.106794i	−0.484533	−	0.874773i	$-0.661010\pi$
$167$	−3.79174	+	1.38008i	−0.293413	+	0.106794i	0.191120	+	0.981567i	$0.438788\pi$
$168$		0			0
$169$	−1.10694	−	6.27779i	−0.0851496	−	0.482907i
$170$	0.277189	−	0.480105i	0.0212594	−	0.0368224i
$171$	22.6819	−	4.17182i	1.73452	−	0.319027i
$172$	0.360500	+	0.624404i	0.0274879	+	0.0476104i
$173$	18.9290	+	6.88960i	1.43915	+	0.523806i	0.939538	−	0.342445i	$-0.111255\pi$
$173$	18.9290	+	6.88960i	1.43915	+	0.523806i	0.499608	+	0.866251i	$0.333477\pi$
$174$	−20.4440	+	17.1546i	−1.54986	+	1.30049i
$175$		0			0
$176$	−7.52481	−	2.73881i	−0.567204	−	0.206445i
$177$	−17.0608	+	6.20961i	−1.28237	+	0.466743i
$178$	13.8648			1.03921
$179$	5.75624	−	9.97011i	0.430242	−	0.745201i	−0.566652	−	0.823957i	$-0.691762\pi$
$179$	5.75624	−	9.97011i	0.430242	−	0.745201i	0.996894	+	0.0787564i	$0.0250949\pi$
$180$	−0.658633	−	0.552659i	−0.0490916	−	0.0411928i
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	−0.878829	−	0.477136i	$-0.841675\pi$
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	0.989020	−	0.147784i	$-0.0472141\pi$
$182$		0			0
$183$	13.1420	−	22.7627i	0.971487	−	1.68266i
$184$	7.45336	−	2.71280i	0.549469	−	0.199990i
$185$	0.754900	+	4.28125i	0.0555014	+	0.314764i
$186$	−21.1177	−	17.7198i	−1.54842	−	1.29928i
$187$	−0.180922	−	1.02606i	−0.0132303	−	0.0750330i
$188$	0.233956	+	1.32683i	0.0170630	+	0.0967689i
$189$		0			0
$190$	1.73055	−	4.86581i	0.125547	−	0.353003i
$191$	−9.16772	+	15.8790i	−0.663353	+	1.14896i	0.316376	+	0.948634i	$0.397534\pi$
$191$	−9.16772	+	15.8790i	−0.663353	+	1.14896i	−0.979729	+	0.200327i	$0.935800\pi$
$192$	−18.9611	+	15.9103i	−1.36840	+	1.14822i
$193$	−0.279715	−	0.101808i	−0.0201343	−	0.00732830i	0.331933	−	0.943303i	$-0.392299\pi$
$193$	−0.279715	−	0.101808i	−0.0201343	−	0.00732830i	−0.352068	+	0.935975i	$0.614521\pi$
$194$	−2.21167	+	12.5430i	−0.158788	+	0.900534i
$195$	6.12449	+	2.22913i	0.438583	+	0.159631i
$196$		0			0
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	−0.999337	−	0.0364128i	$-0.988407\pi$
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	0.531203	+	0.847245i	$0.321740\pi$
$198$	15.8726			1.12802
$199$	0.241230	−	0.0878004i	0.0171003	−	0.00622400i	−0.333456	−	0.942766i	$-0.608215\pi$
$199$	0.241230	−	0.0878004i	0.0171003	−	0.00622400i	0.350556	+	0.936542i	$0.385993\pi$
$200$	11.6912	−	4.25524i	0.826692	−	0.300891i
$201$	−22.0993			−1.55876
$202$	−6.23055	+	10.7916i	−0.438380	+	0.759297i
$203$		0			0
$204$	−0.233956	−	0.0851529i	−0.0163802	−	0.00596189i
$205$	0.378041	−	2.14398i	0.0264035	−	0.149742i
$206$	−6.97565	−	2.53893i	−0.486017	−	0.176896i
$207$	−10.9213	+	9.16404i	−0.759081	+	0.636945i
$208$	4.62836	−	8.01655i	0.320919	−	0.555848i
$209$	−3.38666	−	9.09586i	−0.234260	−	0.629174i
$210$		0			0
$211$	0.425145	+	2.41112i	0.0292682	+	0.165988i	0.995938	−	0.0900364i	$-0.0286983\pi$
$211$	0.425145	+	2.41112i	0.0292682	+	0.165988i	−0.966670	+	0.256024i	$0.917587\pi$
$212$	0.0910521	+	0.516382i	0.00625348	+	0.0354653i
$213$	20.5253	+	17.2228i	1.40637	+	1.18008i
$214$	−2.39440	−	13.5793i	−0.163678	−	0.928263i
$215$	−3.22416	+	1.17350i	−0.219886	+	0.0800318i
$216$	9.70826	−	16.8152i	0.660564	−	1.14413i
$217$		0			0
$218$	0.426489	−	2.41874i	0.0288855	−	0.163818i
$219$	−3.06418	−	2.57115i	−0.207058	−	0.173742i
$220$	−0.180922	+	0.313366i	−0.0121978	+	0.0211272i
$221$	1.20439			0.0810162
$222$	−18.0214	+	6.55926i	−1.20952	+	0.440229i
$223$	7.99660	+	2.91052i	0.535492	+	0.194903i	0.595589	−	0.803289i	$-0.296919\pi$
$223$	7.99660	+	2.91052i	0.535492	+	0.194903i	−0.0600971	+	0.998193i	$0.519141\pi$
$224$		0			0
$225$	−17.1309	+	14.3745i	−1.14206	+	0.958301i
$226$	−22.3935	−	8.15058i	−1.48959	−	0.542168i
$227$	7.07532	+	12.2548i	0.469606	+	0.813381i	0.999396	−	0.0347477i	$-0.0110628\pi$
$227$	7.07532	+	12.2548i	0.469606	+	0.813381i	−0.529790	+	0.848129i	$0.677729\pi$
$228$	−2.28699	−	0.385920i	−0.151460	−	0.0255582i
$229$	10.2665	−	17.7821i	0.678430	−	1.17508i	−0.297023	−	0.954870i	$-0.595994\pi$
$229$	10.2665	−	17.7821i	0.678430	−	1.17508i	0.975454	−	0.220205i	$-0.0706727\pi$
$230$	0.554378	+	3.14403i	0.0365546	+	0.207311i
$231$		0			0
$232$	19.0287	−	6.92588i	1.24929	−	0.454706i
$233$	13.5214	−	11.3458i	0.885817	−	0.743289i	−0.0815496	−	0.996669i	$-0.525987\pi$
$233$	13.5214	−	11.3458i	0.885817	−	0.743289i	0.967367	+	0.253380i	$0.0815425\pi$
$234$	−3.18614	+	18.0695i	−0.208284	+	1.18124i
$235$	−6.41147			−0.418238
$236$	1.16519			0.0758475
$237$	5.92262	−	33.5888i	0.384715	−	2.18183i
$238$		0			0
$239$	−1.17617	−	2.03719i	−0.0760804	−	0.131775i	0.825475	−	0.564438i	$-0.190907\pi$
$239$	−1.17617	−	2.03719i	−0.0760804	−	0.131775i	−0.901556	+	0.432663i	$0.857574\pi$
$240$	−4.55303	−	7.88609i	−0.293897	−	0.509045i
$241$	2.39646	−	13.5910i	0.154370	−	0.875473i	−0.804990	−	0.593288i	$-0.797830\pi$
$241$	2.39646	−	13.5910i	0.154370	−	0.875473i	0.959360	−	0.282185i	$-0.0910593\pi$
$242$	1.41353	+	8.01655i	0.0908654	+	0.515323i
$243$	1.87598	−	10.6392i	0.120344	−	0.682506i
$244$	−1.29220	+	1.08429i	−0.0827249	+	0.0694144i
$245$		0			0
$246$	9.60401			0.612329
$247$	11.0346	−	2.02957i	0.702116	−	0.129138i
$248$	10.4586	+	18.1148i	0.664120	+	1.15029i
$249$	32.7126	−	27.4491i	2.07308	−	1.73952i
$250$	1.89827	+	10.7656i	0.120057	+	0.680878i
$251$	3.91400	−	1.42458i	0.247050	−	0.0899187i	−0.215528	−	0.976498i	$-0.569147\pi$
$251$	3.91400	−	1.42458i	0.247050	−	0.0899187i	0.462577	+	0.886579i	$0.346925\pi$
$252$		0			0
$253$	4.59627	+	3.85673i	0.288965	+	0.242470i
$254$	7.81702	+	13.5395i	0.490483	+	0.849542i
$255$	0.592396	−	1.02606i	0.0370973	−	0.0642544i
$256$	4.13088	−	1.50352i	0.258180	−	0.0939699i
$257$	0.511144	+	0.428901i	0.0318843	+	0.0267541i	0.658591	−	0.752501i	$-0.271153\pi$
$257$	0.511144	+	0.428901i	0.0318843	+	0.0267541i	−0.626706	+	0.779256i	$0.715597\pi$
$258$	−7.56805	−	13.1082i	−0.471166	−	0.816084i
$259$		0			0
$260$	−0.320422	−	0.268866i	−0.0198717	−	0.0166744i
$261$	−27.8824	+	23.3961i	−1.72588	+	1.44818i
$262$	−1.90445	−	1.59802i	−0.117657	−	0.0987261i
$263$	−10.7121	−	3.89890i	−0.660538	−	0.240416i	−0.0100696	−	0.999949i	$-0.503205\pi$
$263$	−10.7121	−	3.89890i	−0.660538	−	0.240416i	−0.650469	+	0.759533i	$0.725428\pi$
$264$	−17.7344	−	6.45480i	−1.09148	−	0.397266i
$265$	−2.49525			−0.153282
$266$		0			0
$267$	29.6313			1.81341
$268$	1.33275	+	0.485081i	0.0814106	+	0.0296310i
$269$	−18.2208	−	6.63181i	−1.11094	−	0.404349i	−0.279601	−	0.960116i	$-0.590202\pi$
$269$	−18.2208	−	6.63181i	−1.11094	−	0.404349i	−0.831338	+	0.555768i	$0.812424\pi$
$270$	5.98680	+	5.02352i	0.364345	+	0.305722i
$271$	−10.2606	+	8.60965i	−0.623286	+	0.522999i	−0.898835	−	0.438288i	$-0.855585\pi$
$271$	−10.2606	+	8.60965i	−0.623286	+	0.522999i	0.275549	+	0.961287i	$0.411141\pi$
$272$	−1.28905	−	1.08164i	−0.0781600	−	0.0655841i
$273$		0			0
$274$	0.172304	+	0.298439i	0.0104093	+	0.0180294i
$275$	7.20961	+	6.04958i	0.434756	+	0.364803i
$276$	1.34730	−	0.490376i	0.0810977	−	0.0295172i
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	0.466096	+	0.884734i	$0.345660\pi$
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	−0.999250	+	0.0387161i	$0.987673\pi$
$278$	2.87211	+	4.97464i	0.172258	+	0.298359i
$279$	−28.8011	−	24.1670i	−1.72428	−	1.44684i
$280$		0			0
$281$	−17.1766	+	6.25179i	−1.02467	+	0.372950i	−0.799050	−	0.601265i	$-0.794664\pi$
$281$	−17.1766	+	6.25179i	−1.02467	+	0.372950i	−0.225622	+	0.974215i	$0.572442\pi$
$282$	−4.91147	−	27.8544i	−0.292474	−	1.65870i
$283$	5.88919	−	4.94161i	0.350076	−	0.293748i	−0.450745	−	0.892653i	$-0.648842\pi$
$283$	5.88919	−	4.94161i	0.350076	−	0.293748i	0.800820	+	0.598904i	$0.204397\pi$
$284$	−0.859785	−	1.48919i	−0.0510188	−	0.0883672i
$285$	3.69846	−	10.3990i	0.219078	−	0.615984i
$286$	7.72193			0.456608
$287$		0			0
$288$	−4.22281	+	3.54336i	−0.248832	+	0.208794i
$289$	−2.91400	+	16.5261i	−0.171412	+	0.972125i
$290$	1.41534	+	8.02682i	0.0831119	+	0.471351i
$291$	−4.72668	+	26.8063i	−0.277083	+	1.57142i
$292$	0.128356	+	0.222318i	0.00751144	+	0.0130102i
$293$	5.25150	+	9.09586i	0.306796	+	0.531386i	0.977660	−	0.210195i	$-0.0674098\pi$
$293$	5.25150	+	9.09586i	0.306796	+	0.531386i	−0.670864	+	0.741581i	$0.734076\pi$
$294$		0			0
$295$	−0.962859	+	5.46064i	−0.0560598	+	0.317931i
$296$	14.5517			0.845800
$297$	14.6878			0.852272
$298$	−3.87417	+	21.9715i	−0.224425	+	1.27278i
$299$	−5.31315	+	4.45826i	−0.307267	+	0.257828i
$300$	2.11334	−	0.769193i	0.122014	−	0.0444094i
$301$		0			0
$302$	1.02048	+	5.78742i	0.0587219	+	0.333028i
$303$	−13.3157	+	23.0634i	−0.764966	+	1.32496i
$304$	−13.6329	−	7.73773i	−0.781903	−	0.443789i
$305$	−4.01367	−	6.95188i	−0.229822	−	0.398064i
$306$	3.13429	+	1.14079i	0.179175	+	0.0652144i
$307$	−8.95929	+	7.51774i	−0.511334	+	0.429060i	−0.861598	−	0.507591i	$-0.830536\pi$
$307$	−8.95929	+	7.51774i	−0.511334	+	0.429060i	0.350264	+	0.936651i	$0.386092\pi$
$308$		0			0
$309$	−14.9081	−	5.42609i	−0.848091	−	0.308680i
$310$	−7.91147	+	2.87954i	−0.449342	+	0.163547i
$311$	15.9659			0.905340			0.452670	−	0.891678i	$-0.350471\pi$
$311$	15.9659			0.905340			0.452670	+	0.891678i	$0.350471\pi$
$312$	10.9081	−	18.8933i	0.617548	−	1.06962i
$313$	−20.3987	−	17.1166i	−1.15300	−	0.967486i	−0.153219	−	0.988192i	$-0.548964\pi$
$313$	−20.3987	−	17.1166i	−1.15300	−	0.967486i	−0.999786	+	0.0207063i	$0.993409\pi$
$314$	2.25031	−	12.7622i	0.126993	−	0.720211i
$315$		0			0
$316$	−1.09446	+	1.89565i	−0.0615679	+	0.106639i
$317$	−27.7511	+	10.1006i	−1.55866	+	0.567304i	−0.970428	−	0.241390i	$-0.922397\pi$
$317$	−27.7511	+	10.1006i	−1.55866	+	0.567304i	−0.588228	+	0.808695i	$0.700174\pi$
$318$	−1.91147	−	10.8405i	−0.107190	−	0.607906i
$319$	11.7344	+	9.84635i	0.657002	+	0.551290i
$320$	1.31268	+	7.44459i	0.0733811	+	0.416165i
$321$	−5.11721	−	29.0211i	−0.285615	−	1.61980i
$322$		0			0
$323$	−0.0150147	−	2.03952i	−0.000835443	−	0.113482i
$324$	0.288333	−	0.499408i	0.0160185	−	0.0277449i
$325$	−8.33409	+	6.99313i	−0.462292	+	0.387909i
$326$	10.5778	+	3.85002i	0.585853	+	0.213233i
$327$	0.911474	−	5.16923i	0.0504046	−	0.285859i
$328$	−6.84776	−	2.49238i	−0.378104	−	0.137619i
$329$		0			0
$330$	3.79813	−	6.57856i	0.209080	−	0.362138i
$331$	27.6655			1.52063			0.760317	−	0.649553i	$-0.225044\pi$
$331$	27.6655			1.52063			0.760317	+	0.649553i	$0.225044\pi$
$332$	−2.57532	+	0.937341i	−0.141339	+	0.0514432i
$333$	−24.5783	+	8.94578i	−1.34688	+	0.490225i
$334$	−5.43645			−0.297469
$335$	−3.37464	+	5.84504i	−0.184376	+	0.319349i
$336$		0			0
$337$	−16.7827	−	6.10841i	−0.914212	−	0.332746i	−0.158279	−	0.987394i	$-0.550594\pi$
$337$	−16.7827	−	6.10841i	−0.914212	−	0.332746i	−0.755934	+	0.654648i	$0.772817\pi$
$338$	1.49138	−	8.45805i	0.0811205	−	0.460057i
$339$	−47.8585	−	17.4191i	−2.59932	−	0.946074i
$340$	−0.0582480	+	0.0488759i	−0.00315894	+	0.00265067i
$341$	−7.91147	+	13.7031i	−0.428430	+	0.742063i
$342$	30.6386	+	5.17015i	1.65675	+	0.279569i
$343$		0			0
$344$	1.99432	+	11.3103i	0.107526	+	0.609813i
$345$	1.18479	+	6.71929i	0.0637871	+	0.361755i
$346$	20.7902	+	17.4451i	1.11769	+	0.937853i
$347$	−1.00727	−	5.71253i	−0.0540733	−	0.306665i	0.945761	−	0.324863i	$-0.105318\pi$
$347$	−1.00727	−	5.71253i	−0.0540733	−	0.306665i	−0.999834	+	0.0181980i	$0.994207\pi$
$348$	3.43969	−	1.25195i	0.184387	−	0.0671113i
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	−0.928919	−	0.370282i	$-0.879261\pi$
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	0.785134	+	0.619326i	$0.212594\pi$
$350$		0			0
$351$	−2.94831	+	16.7207i	−0.157369	+	0.892485i
$352$	1.77719	+	1.49124i	0.0947245	+	0.0794833i
$353$	12.6172	−	21.8537i	0.671546	−	1.16315i	−0.305919	−	0.952057i	$-0.598964\pi$
$353$	12.6172	−	21.8537i	0.671546	−	1.16315i	0.977466	−	0.211095i	$-0.0677029\pi$
$354$	−24.4611			−1.30009
$355$	7.68954	−	2.79876i	0.408118	−	0.148543i
$356$	−1.78699	−	0.650411i	−0.0947102	−	0.0344717i
$357$		0			0
$358$	11.8819	−	9.97011i	0.627979	−	0.526937i
$359$	−6.28359	−	2.28704i	−0.331635	−	0.120705i	0.170836	−	0.985300i	$-0.445353\pi$
$359$	−6.28359	−	2.28704i	−0.331635	−	0.120705i	−0.502471	+	0.864594i	$0.667575\pi$
$360$	−6.84776	−	11.8607i	−0.360909	−	0.625112i
$361$	−3.57444	−	18.6607i	−0.188129	−	0.982144i
$362$	5.75103	−	9.96108i	0.302267	−	0.523543i
$363$	3.02094	+	17.1326i	0.158558	+	0.899230i
$364$		0			0
$365$	−1.14796	+	0.417822i	−0.0600868	+	0.0218698i
$366$	27.1275	−	22.7627i	1.41798	−	1.18982i
$367$	1.40983	−	7.99552i	0.0735923	−	0.417363i	−0.925648	−	0.378386i	$-0.876479\pi$
$367$	1.40983	−	7.99552i	0.0735923	−	0.417363i	0.999240	−	0.0389764i	$-0.0124097\pi$
$368$	9.69047			0.505151
$369$	13.0983			0.681872
$370$	−1.01707	+	5.76811i	−0.0528752	+	0.299870i
$371$		0			0
$372$	1.89053	+	3.27449i	0.0980194	+	0.169775i
$373$	−17.4488	−	30.2222i	−0.903463	−	1.56484i	−0.822967	−	0.568090i	$-0.807683\pi$
$373$	−17.4488	−	30.2222i	−0.903463	−	1.56484i	−0.0804968	−	0.996755i	$-0.525651\pi$
$374$	0.243756	−	1.38241i	0.0126043	−	0.0714826i
$375$	4.05690	+	23.0078i	0.209498	+	1.18812i
$376$	−3.72668	+	21.1351i	−0.192189	+	1.08996i
$377$	−13.5646	+	11.3821i	−0.698615	+	0.586207i
$378$		0			0
$379$	1.70140			0.0873950			0.0436975	−	0.999045i	$-0.486086\pi$
$379$	1.70140			0.0873950			0.0436975	+	0.999045i	$0.486086\pi$
$380$	−0.451304	+	0.545955i	−0.0231514	+	0.0280069i
$381$	16.7062	+	28.9360i	0.855885	+	1.48244i
$382$	−18.9238	+	15.8790i	−0.968226	+	0.812438i
$383$	0.509962	+	2.89214i	0.0260579	+	0.147781i	0.995061	−	0.0992680i	$-0.0316501\pi$
$383$	0.509962	+	2.89214i	0.0260579	+	0.147781i	−0.969003	+	0.247049i	$0.920539\pi$
$384$	−25.6989	+	9.35365i	−1.31144	+	0.477326i
$385$		0			0
$386$	−0.307218	−	0.257787i	−0.0156370	−	0.0131210i
$387$	−10.3216	−	17.8775i	−0.524677	−	0.908767i
$388$	0.873455	−	1.51287i	0.0443430	−	0.0768043i
$389$	23.0856	−	8.40247i	1.17049	−	0.426022i	0.317654	−	0.948207i	$-0.397105\pi$
$389$	23.0856	−	8.40247i	1.17049	−	0.426022i	0.852832	+	0.522185i	$0.174883\pi$
$390$	6.72668	+	5.64436i	0.340619	+	0.285813i
$391$	0.630415	+	1.09191i	0.0318815	+	0.0552203i
$392$		0			0
$393$	−4.07011	−	3.41523i	−0.205310	−	0.172275i
$394$	−13.5628	+	11.3806i	−0.683286	+	0.573345i
$395$	−7.97952	−	6.69561i	−0.401493	−	0.336893i
$396$	−2.04576	−	0.744596i	−0.102803	−	0.0374173i
$397$	29.9158	+	10.8885i	1.50143	+	0.546476i	0.956431	−	0.291959i	$-0.0943071\pi$
$397$	29.9158	+	10.8885i	1.50143	+	0.546476i	0.545001	+	0.838436i	$0.316529\pi$
$398$	0.345866			0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	0.0812519	+	0.0295733i	0.00405753	+	0.00147682i	0.344048	−	0.938952i	$-0.388202\pi$
$401$	0.0812519	+	0.0295733i	0.00405753	+	0.00147682i	−0.339991	+	0.940429i	$0.610424\pi$
$402$	−27.9786	−	10.1834i	−1.39545	−	0.507902i
$403$	−14.0116	−	11.7571i	−0.697968	−	0.585665i
$404$	1.30928	−	1.09861i	0.0651390	−	0.0546581i
$405$	2.10220	+	1.76395i	0.104459	+	0.0876515i
$406$		0			0
$407$	5.50387	+	9.53298i	0.272817	+	0.472532i
$408$	−3.03802	−	2.54920i	−0.150404	−	0.126204i
$409$	−18.7995	+	6.84245i	−0.929574	+	0.338337i	−0.762041	−	0.647529i	$-0.775802\pi$
$409$	−18.7995	+	6.84245i	−0.929574	+	0.338337i	−0.167534	+	0.985866i	$0.553580\pi$
$410$	1.46657	−	2.54017i	0.0724286	−	0.125450i
$411$	0.368241	+	0.637812i	0.0181640	+	0.0314609i
$412$	0.779963	+	0.654467i	0.0384260	+	0.0322433i
$413$		0			0
$414$	−18.0496	+	6.56953i	−0.887091	+	0.322875i
$415$	−2.26470	−	12.8438i	−0.111170	−	0.630475i
$416$	−2.05438	+	1.72383i	−0.100724	+	0.0845176i
$417$	6.13816	+	10.6316i	0.300587	+	0.520632i
$418$	−0.0962667	−	13.0763i	−0.00470856	−	0.639585i
$419$	25.4097			1.24135			0.620673	−	0.784070i	$-0.286859\pi$
$419$	25.4097			1.24135			0.620673	+	0.784070i	$0.286859\pi$
$420$		0			0
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	−0.557565	−	0.830134i	$-0.688264\pi$
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	0.720702	+	0.693245i	$0.243820\pi$
$422$	−0.572796	+	3.24849i	−0.0278833	+	0.158134i
$423$	−6.69846	−	37.9889i	−0.325690	−	1.84708i
$424$	−1.45037	+	8.22546i	−0.0704362	+	0.399464i
$425$	0.988856	+	1.71275i	0.0479665	+	0.0830805i
$426$	18.0496	+	31.2629i	0.874507	+	1.51469i
$427$		0			0
$428$	−0.328411	+	1.86251i	−0.0158744	+	0.0900279i
$429$	16.5030			0.796772
$430$	−4.62267			−0.222925
$431$	−6.65183	+	37.7244i	−0.320407	+	1.81712i	0.219751	+	0.975556i	$0.429476\pi$
$431$	−6.65183	+	37.7244i	−0.320407	+	1.81712i	−0.540158	+	0.841564i	$0.681636\pi$
$432$	18.1721	−	15.2482i	0.874303	−	0.733628i
$433$	17.0376	−	6.20118i	0.818775	−	0.298010i	0.101532	−	0.994832i	$-0.467626\pi$
$433$	17.0376	−	6.20118i	0.818775	−	0.298010i	0.717244	+	0.696823i	$0.245403\pi$
$434$		0			0
$435$	3.02481	+	17.1546i	0.145029	+	0.822499i
$436$	−0.168434	+	0.291736i	−0.00806651	+	0.0139716i
$437$	7.61587	+	8.94172i	0.364316	+	0.427740i
$438$	−2.69459	−	4.66717i	−0.128753	−	0.223006i
$439$	5.72328	+	2.08310i	0.273157	+	0.0994211i	0.474967	−	0.880004i	$-0.342460\pi$
$439$	5.72328	+	2.08310i	0.273157	+	0.0994211i	−0.201810	+	0.979425i	$0.564682\pi$
$440$	−4.41534	+	3.70491i	−0.210493	+	0.176625i
$441$		0			0
$442$	1.52481	+	0.554987i	0.0725280	+	0.0263981i
$443$	28.0903	−	10.2240i	1.33461	−	0.485759i	0.426501	−	0.904487i	$-0.359746\pi$
$443$	28.0903	−	10.2240i	1.33461	−	0.485759i	0.908112	+	0.418728i	$0.137524\pi$
$444$	2.63041			0.124834
$445$	4.52481	−	7.83721i	0.214497	−	0.371519i
$446$	8.78287	+	7.36970i	0.415881	+	0.348966i
$447$	−8.27972	+	46.9566i	−0.391617	+	2.22097i
$448$		0			0
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	−0.702226	−	0.711955i	$-0.747810\pi$
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	0.967683	+	0.252168i	$0.0811435\pi$
$450$	−28.3123	+	10.3048i	−1.33465	+	0.485774i
$451$	−0.957234	−	5.42874i	−0.0450744	−	0.255629i
$452$	2.50387	+	2.10100i	0.117772	+	0.0988226i
$453$	2.18092	+	12.3686i	0.102469	+	0.581129i
$454$	3.31062	+	18.7755i	0.155375	+	0.881176i
$455$		0			0
$456$	−32.1300	−	18.2362i	−1.50463	−	0.853989i
$457$	11.6951	−	20.2564i	0.547072	−	0.947556i	−0.451402	−	0.892321i	$-0.649076\pi$
$457$	11.6951	−	20.2564i	0.547072	−	0.947556i	0.998473	−	0.0552352i	$-0.0175909\pi$
$458$	21.1919	−	17.7821i	0.990233	−	0.830904i
$459$	2.90033	+	1.05563i	0.135376	+	0.0492728i
$460$	0.0760373	−	0.431229i	0.00354526	−	0.0201062i
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.980011	−	0.198945i	$-0.0637514\pi$
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.622853	+	0.782339i	$0.285974\pi$
$462$		0			0
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.458340	−	0.888777i	$-0.348444\pi$
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.540534	−	0.841322i	$-0.318222\pi$
$464$	24.7401			1.14853
$465$	−16.9081	+	6.15403i	−0.784093	+	0.285387i
$466$	22.3469	−	8.13360i	1.03520	−	0.376782i
$467$	25.5963			1.18445			0.592227	−	0.805771i	$-0.298249\pi$
$467$	25.5963			1.18445			0.592227	+	0.805771i	$0.298249\pi$
$468$	1.25830	−	2.17945i	0.0581651	−	0.100745i
$469$		0			0
$470$	−8.11721	−	2.95442i	−0.374419	−	0.136277i
$471$	4.80928	−	27.2748i	0.221600	−	1.25676i
$472$	17.4410	+	6.34802i	0.802789	+	0.292191i
$473$	−6.65523	+	5.58440i	−0.306008	+	0.256771i
$474$	22.9761	−	39.7958i	1.05533	−	1.82788i
$475$	11.9461	+	14.0258i	0.548124	+	0.643548i
$476$		0			0
$477$	−2.60694	−	14.7847i	−0.119364	−	0.676946i
$478$	−0.550345	−	3.12116i	−0.0251722	−	0.142759i
$479$	29.2447	+	24.5392i	1.33622	+	1.12123i	0.982579	+	0.185845i	$0.0595023\pi$
$479$	29.2447	+	24.5392i	1.33622	+	1.12123i	0.353645	+	0.935380i	$0.384942\pi$
$480$	0.458111	+	2.59808i	0.0209098	+	0.118585i
$481$	−11.9572	+	4.35208i	−0.545203	+	0.198438i
$482$	9.29679	−	16.1025i	0.423457	−	0.733449i
$483$		0			0
$484$	0.193877	−	1.09953i	0.00881261	−	0.0499788i
$485$	6.36824	+	5.34359i	0.289167	+	0.242640i
$486$	7.27766	−	12.6053i	0.330121	−	0.571787i
$487$	7.76382			0.351812			0.175906	−	0.984407i	$-0.443714\pi$
$487$	7.76382			0.351812			0.175906	+	0.984407i	$0.443714\pi$
$488$	−25.2494	+	9.19004i	−1.14299	+	0.416014i
$489$	22.6065	+	8.22811i	1.02230	+	0.372088i
$490$		0			0
$491$	−28.1313	+	23.6050i	−1.26955	+	1.06528i	−0.274954	+	0.961457i	$0.588663\pi$
$491$	−28.1313	+	23.6050i	−1.26955	+	1.06528i	−0.994596	+	0.103822i	$0.966893\pi$
$492$	−1.23783	−	0.450532i	−0.0558055	−	0.0203115i
$493$	1.60947	+	2.78768i	0.0724869	+	0.125551i
$494$	14.9055	+	2.51525i	0.670632	+	0.113167i
$495$	5.18004	−	8.97210i	0.232826	−	0.403266i
$496$	4.43763	+	25.1671i	0.199256	+	1.13003i
$497$		0			0
$498$	54.0642	−	19.6778i	2.42268	−	0.881782i
$499$	3.77379	−	3.16658i	0.168938	−	0.141756i	−0.554399	−	0.832251i	$-0.687052\pi$
$499$	3.77379	−	3.16658i	0.168938	−	0.141756i	0.723337	+	0.690495i	$0.242607\pi$
$500$	0.260363	−	1.47659i	0.0116438	−	0.0660352i
$501$	−11.6186			−0.519079
$502$	5.61175			0.250465
$503$	5.72163	−	32.4490i	0.255115	−	1.44683i	−0.540663	−	0.841239i	$-0.681827\pi$
$503$	5.72163	−	32.4490i	0.255115	−	1.44683i	0.795778	−	0.605589i	$-0.207062\pi$
$504$		0			0
$505$	4.06670	+	7.04374i	0.180966	+	0.313442i
$506$	4.04189	+	7.00076i	0.179684	+	0.311222i
$507$	3.18732	−	18.0762i	0.141554	−	0.802791i
$508$	−0.372360	−	2.11176i	−0.0165208	−	0.0936941i
$509$	−6.41370	+	36.3739i	−0.284282	+	1.61224i	0.423557	+	0.905870i	$0.360781\pi$
$509$	−6.41370	+	36.3739i	−0.284282	+	1.61224i	−0.707839	+	0.706374i	$0.750330\pi$
$510$	1.22281	−	1.02606i	0.0541470	−	0.0454347i
$511$		0			0
$512$	24.9186			1.10126
$513$	28.3516	+	4.78423i	1.25176	+	0.211229i
$514$	0.449493	+	0.778544i	0.0198263	+	0.0343401i
$515$	−3.71167	+	3.11446i	−0.163556	+	0.137239i
$516$	0.360500	+	2.04450i	0.0158701	+	0.0900040i
$517$	−15.2554	+	5.55250i	−0.670930	+	0.244199i
$518$		0			0
$519$	44.4320	+	37.2829i	1.95035	+	1.63654i
$520$	−3.33140	−	5.77016i	−0.146092	−	0.253038i
$521$	−4.64590	+	8.04693i	−0.203540	+	0.352542i	−0.949667	−	0.313262i	$-0.898578\pi$
$521$	−4.64590	+	8.04693i	−0.203540	+	0.352542i	0.746126	+	0.665804i	$0.231912\pi$
$522$	−46.0813	+	16.7722i	−2.01692	+	0.734100i
$523$	−21.7672	−	18.2649i	−0.951814	−	0.798667i	0.0277878	−	0.999614i	$-0.491154\pi$
$523$	−21.7672	−	18.2649i	−0.951814	−	0.798667i	−0.979602	+	0.200947i	$0.935598\pi$
$524$	0.170493	+	0.295303i	0.00744802	+	0.0129004i
$525$		0			0
$526$	−11.7654	−	9.87236i	−0.512996	−	0.430455i
$527$	−2.54710	+	2.13727i	−0.110954	+	0.0931011i
$528$	−17.6630	−	14.8210i	−0.768682	−	0.645001i
$529$	14.7900	+	5.38311i	0.643043	+	0.234048i
$530$	−3.15910	−	1.14982i	−0.137223	−	0.0499449i
$531$	−33.3610			−1.44775
$532$		0			0
$533$	6.37227			0.276014
$534$	37.5146	+	13.6542i	1.62342	+	0.590875i
$535$	−8.45723	−	3.07818i	−0.365638	−	0.133081i
$536$	17.3063	+	14.5217i	0.747520	+	0.627244i
$537$	25.3935	−	21.3077i	1.09581	−	0.919495i
$538$	−20.0123	−	16.7923i	−0.862793	−	0.723969i
$539$		0			0
$540$	−0.535959	−	0.928309i	−0.0230640	−	0.0399480i
$541$	11.4795	+	9.63246i	0.493543	+	0.414132i	0.855294	−	0.518143i	$-0.173376\pi$
$541$	11.4795	+	9.63246i	0.493543	+	0.414132i	−0.361751	+	0.932275i	$0.617821\pi$
$542$	−16.9577	+	6.17210i	−0.728396	+	0.265114i
$543$	12.2909	−	21.2884i	0.527451	−	0.913572i
$544$	0.243756	+	0.422197i	0.0104509	+	0.0181016i
$545$	−1.22803	−	1.03044i	−0.0526028	−	0.0441390i
$546$		0			0
$547$	3.65270	−	1.32948i	0.156178	−	0.0568443i	−0.262748	−	0.964864i	$-0.584629\pi$
$547$	3.65270	−	1.32948i	0.156178	−	0.0568443i	0.418926	+	0.908020i	$0.362407\pi$
$548$	−0.00820761	−	0.0465477i	−0.000350612	−	0.00198842i
$549$	36.9975	−	31.0446i	1.57902	−	1.32495i
$550$	6.34002	+	10.9812i	0.270339	+	0.468242i
$551$	19.4436	+	22.8285i	0.828324	+	0.972527i
$552$	22.8384			0.972068
$553$		0			0
$554$	−18.3164	+	15.3693i	−0.778189	+	0.652978i
$555$	−2.17365	+	12.3274i	−0.0922662	+	0.523268i
$556$	−0.136812	−	0.775897i	−0.00580210	−	0.0329054i
$557$	2.29292	−	13.0038i	0.0971541	−	0.550988i	−0.896912	−	0.442209i	$-0.854195\pi$
$557$	2.29292	−	13.0038i	0.0971541	−	0.550988i	0.994066	−	0.108779i	$-0.0346940\pi$
$558$	−25.3273	−	43.8681i	−1.07219	−	1.85709i
$559$	−5.02141	−	8.69734i	−0.212383	−	0.367858i
$560$		0			0
$561$	0.520945	−	2.95442i	0.0219943	−	0.124736i
$562$	−24.6272			−1.03884
$563$	10.7128			0.451489			0.225745	−	0.974187i	$-0.427519\pi$
$563$	10.7128			0.451489			0.225745	+	0.974187i	$0.427519\pi$
$564$	−0.673648	+	3.82045i	−0.0283657	+	0.160870i
$565$	−11.9153	+	9.99816i	−0.501282	+	0.420626i
$566$	9.73308	−	3.54255i	0.409112	−	0.148905i
$567$		0			0
$568$	−4.75641	−	26.9749i	−0.199574	−	1.13184i
$569$	6.73530	−	11.6659i	0.282358	−	0.489059i	−0.689607	−	0.724184i	$-0.742217\pi$
$569$	6.73530	−	11.6659i	0.282358	−	0.489059i	0.971965	+	0.235125i	$0.0755499\pi$
$570$	9.47431	−	11.4613i	0.396835	−	0.480063i
$571$	−6.33275	−	10.9686i	−0.265017	−	0.459023i	0.702551	−	0.711634i	$-0.252044\pi$
$571$	−6.33275	−	10.9686i	−0.265017	−	0.459023i	−0.967568	+	0.252610i	$0.918711\pi$
$572$	−0.995252	−	0.362242i	−0.0416136	−	0.0151461i
$573$	−40.4432	+	33.9358i	−1.68954	+	1.41769i
$574$		0			0
$575$	−10.7023	−	3.89533i	−0.446318	−	0.162447i
$576$	−42.7388	+	15.5556i	−1.78078	+	0.648152i
$577$	−10.5544			−0.439384			−0.219692	−	0.975569i	$-0.570505\pi$
$577$	−10.5544			−0.439384			−0.219692	+	0.975569i	$0.570505\pi$
$578$	−11.3045	+	19.5800i	−0.470206	+	0.814421i
$579$	−0.656574	−	0.550931i	−0.0272863	−	0.0228959i
$580$	0.194126	−	1.10094i	0.00806064	−	0.0457142i
$581$		0			0
$582$	−18.3366	+	31.7600i	−0.760077	+	1.31649i
$583$	−5.93717	+	2.16095i	−0.245892	+	0.0894975i
$584$	0.710074	+	4.02703i	0.0293831	+	0.166640i
$585$	9.17412	+	7.69800i	0.379303	+	0.318273i
$586$	2.45723	+	13.9357i	0.101507	+	0.575677i
$587$	−3.32619	−	18.8638i	−0.137287	−	0.778591i	−0.973240	−	0.229791i	$-0.926196\pi$
$587$	−3.32619	−	18.8638i	−0.137287	−	0.778591i	0.835954	−	0.548800i	$-0.184915\pi$
$588$		0			0
$589$	−19.7349	+	23.8739i	−0.813162	+	0.983706i
$590$	−3.73530	+	6.46973i	−0.153780	+	0.266355i
$591$	−28.9859	+	24.3221i	−1.19232	+	1.00048i
$592$	16.7062	+	6.08056i	0.686621	+	0.249910i
$593$	−1.50980	+	8.56250i	−0.0620001	+	0.351620i	0.937988	+	0.346669i	$0.112687\pi$
$593$	−1.50980	+	8.56250i	−0.0620001	+	0.351620i	−0.999988	+	0.00495124i	$0.998424\pi$
$594$	18.5954	+	6.76817i	0.762978	+	0.277701i
$595$		0			0
$596$	1.53003	−	2.65009i	0.0626724	−	0.108552i
$597$	0.739170			0.0302522
$598$	−8.78106	+	3.19604i	−0.359084	+	0.130696i
$599$	−18.6356	+	6.78281i	−0.761431	+	0.277138i	−0.693408	−	0.720545i	$-0.743891\pi$
$599$	−18.6356	+	6.78281i	−0.761431	+	0.277138i	−0.0680235	+	0.997684i	$0.521669\pi$
$600$	35.8239			1.46250
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	−0.283718	−	0.958908i	$-0.591568\pi$
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	0.972298	−	0.233747i	$-0.0750986\pi$
$602$		0			0
$603$	−38.1584	−	13.8885i	−1.55393	−	0.565584i
$604$	0.139967	−	0.793791i	0.00569517	−	0.0322989i
$605$	4.99273	+	1.81720i	0.202983	+	0.0738798i
$606$	−27.4859	+	23.0634i	−1.11654	+	0.936888i
$607$	−17.6425	+	30.5577i	−0.716087	+	1.24030i	0.246452	+	0.969155i	$0.420735\pi$
$607$	−17.6425	+	30.5577i	−0.716087	+	1.24030i	−0.962539	+	0.271144i	$0.912598\pi$
$608$	2.94475	+	3.45740i	0.119425	+	0.140216i
$609$		0			0
$610$	−1.87804	−	10.6509i	−0.0760397	−	0.431242i
$611$	−3.25877	−	18.4814i	−0.131836	−	0.747678i
$612$	−0.350452	−	0.294064i	−0.0141662	−	0.0118868i
$613$	3.20439	+	18.1730i	0.129424	+	0.734001i	0.978581	+	0.205861i	$0.0659994\pi$
$613$	3.20439	+	18.1730i	0.129424	+	0.734001i	−0.849157	+	0.528140i	$0.822889\pi$
$614$	−14.8071	+	5.38933i	−0.597564	+	0.217496i
$615$	3.13429	−	5.42874i	0.126387	−	0.218908i
$616$		0			0
$617$	−6.19671	+	35.1433i	−0.249470	+	1.41482i	0.560408	+	0.828217i	$0.310644\pi$
$617$	−6.19671	+	35.1433i	−0.249470	+	1.41482i	−0.809878	+	0.586598i	$0.800467\pi$
$618$	−16.3739	−	13.7394i	−0.658656	−	0.552678i
$619$	−1.82976	+	3.16923i	−0.0735441	+	0.127382i	−0.900452	−	0.434955i	$-0.856764\pi$
$619$	−1.82976	+	3.16923i	−0.0735441	+	0.127382i	0.826908	+	0.562337i	$0.190098\pi$
$620$	1.15476			0.0463764
$621$	−16.7023	+	6.07915i	−0.670242	+	0.243948i
$622$	20.2135	+	7.35710i	0.810487	+	0.294993i
$623$		0			0
$624$	20.4179	−	17.1326i	0.817369	−	0.685854i
$625$	−13.1540	−	4.78768i	−0.526162	−	0.191507i
$626$	−17.9383	−	31.0701i	−0.716961	−	1.24181i
$627$	−0.205737	−	27.9462i	−0.00821635	−	1.11606i
$628$	−0.888719	+	1.53931i	−0.0354637	+	0.0614250i
$629$	0.401674	+	2.27801i	0.0160158	+	0.0908301i
$630$		0			0
$631$	0.745977	−	0.271514i	0.0296969	−	0.0108088i	−0.327129	−	0.944980i	$-0.606081\pi$
$631$	0.745977	−	0.271514i	0.0296969	−	0.0108088i	0.356826	+	0.934171i	$0.383859\pi$
$632$	−26.7098	+	22.4122i	−1.06246	+	0.891510i
$633$	−1.22416	+	6.94253i	−0.0486558	+	0.275941i
$634$	−39.7885			−1.58020
$635$	10.2044			0.404949
$636$	−0.262174	+	1.48686i	−0.0103959	+	0.0589579i
$637$		0			0
$638$	10.3191	+	17.8732i	0.408536	+	0.707605i
$639$	24.6168	+	42.6375i	0.973826	+	1.68672i
$640$	−1.45037	+	8.22546i	−0.0573309	+	0.325140i
$641$	5.10220	+	28.9360i	0.201525	+	1.14290i	0.902816	+	0.430028i	$0.141496\pi$
$641$	5.10220	+	28.9360i	0.201525	+	1.14290i	−0.701291	+	0.712875i	$0.747393\pi$
$642$	6.89440	−	39.1001i	0.272100	−	1.54316i
$643$	17.0168	−	14.2788i	0.671078	−	0.563101i	−0.242306	−	0.970200i	$-0.577904\pi$
$643$	17.0168	−	14.2788i	0.671078	−	0.563101i	0.913384	+	0.407098i	$0.133459\pi$
$644$		0			0
$645$	−9.87939			−0.389000
$646$	0.920807	−	2.58904i	0.0362287	−	0.101865i
$647$	−5.62954	−	9.75065i	−0.221320	−	0.383337i	0.733889	−	0.679269i	$-0.237703\pi$
$647$	−5.62954	−	9.75065i	−0.221320	−	0.383337i	−0.955209	+	0.295932i	$0.904370\pi$
$648$	7.03667	−	5.90447i	0.276427	−	0.231950i
$649$	2.43804	+	13.8268i	0.0957016	+	0.542751i
$650$	−13.7738	+	5.01325i	−0.540252	+	0.196636i
$651$		0			0
$652$	−1.18273	−	0.992431i	−0.0463194	−	0.0388666i
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	−0.999456	−	0.0329874i	$-0.989498\pi$
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	0.471160	−	0.882048i	$-0.343835\pi$
$654$	3.53596	−	6.12446i	0.138267	−	0.239485i
$655$	−1.52481	+	0.554987i	−0.0595794	+	0.0216851i
$656$	−6.82017	−	5.72281i	−0.266283	−	0.223438i
$657$	−3.67499	−	6.36527i	−0.143375	−	0.248333i
$658$		0			0
$659$	21.4691	+	18.0147i	0.836317	+	0.701753i	0.956732	−	0.290970i	$-0.0939781\pi$
$659$	21.4691	+	18.0147i	0.836317	+	0.701753i	−0.120415	+	0.992724i	$0.538423\pi$
$660$	−0.798133	+	0.669713i	−0.0310673	+	0.0260686i
$661$	8.70826	+	7.30710i	0.338712	+	0.284213i	0.796239	−	0.604983i	$-0.206820\pi$
$661$	8.70826	+	7.30710i	0.338712	+	0.284213i	−0.457526	+	0.889196i	$0.651264\pi$
$662$	35.0257	+	12.7483i	1.36131	+	0.495478i
$663$	3.25877	+	1.18610i	0.126560	+	0.0460641i
$664$	−43.6551			−1.69415
$665$		0			0
$666$	−35.2395			−1.36550
$667$	−17.4192	−	6.34008i	−0.674475	−	0.245489i
$668$	0.700685	+	0.255028i	0.0271103	+	0.00986734i
$669$	18.7704	+	15.7502i	0.725705	+	0.608939i
$670$	−6.96585	+	5.84504i	−0.269114	+	0.225814i
$671$	−15.5706	−	13.0653i	−0.601095	−	0.504379i
$672$		0			0
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	0.980344	−	0.197296i	$-0.0632160\pi$
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	−0.661035	+	0.750355i	$0.729883\pi$
$674$	−18.4329	−	15.4670i	−0.710008	−	0.595768i
$675$	−26.1989	+	9.53563i	−1.00840	+	0.367027i
$676$	−0.588993	+	1.02017i	−0.0226536	+	0.0392371i
$677$	4.52481	+	7.83721i	0.173903	+	0.301208i	0.939781	−	0.341777i	$-0.111029\pi$
$677$	4.52481	+	7.83721i	0.173903	+	0.301208i	−0.765878	+	0.642986i	$0.777695\pi$
$678$	−52.5642	−	44.1066i	−2.01872	−	1.69390i
$679$		0			0
$680$	−1.13816	+	0.414255i	−0.0436463	+	0.0158859i
$681$	7.07532	+	40.1261i	0.271127	+	1.53764i
$682$	−16.3307	+	13.7031i	−0.625334	+	0.524718i
$683$	−4.36571	−	7.56164i	−0.167049	−	0.289338i	0.770332	−	0.637643i	$-0.220091\pi$
$683$	−4.36571	−	7.56164i	−0.167049	−	0.289338i	−0.937381	+	0.348305i	$0.886757\pi$
$684$	−3.70637	−	2.10364i	−0.141716	−	0.0804348i
$685$	0.224927			0.00859402
$686$		0			0
$687$	45.2904	−	38.0032i	1.72794	−	1.44991i
$688$	−2.43654	+	13.8183i	−0.0928921	+	0.526817i
$689$	−1.26827	−	7.19269i	−0.0483171	−	0.274020i
$690$	−1.59627	+	9.05288i	−0.0607688	+	0.344637i
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	−0.980508	−	0.196478i	$-0.937050\pi$
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	0.320099	−	0.947384i	$-0.396284\pi$
$692$	−1.86122	−	3.22372i	−0.0707528	−	0.122547i
$693$		0			0
$694$	1.35710	−	7.69648i	0.0515147	−	0.292154i
$695$	3.74928			0.142218
$696$	58.3073			2.21013
$697$	0.201151	−	1.14079i	0.00761915	−	0.0432104i
$698$	−5.54466	+	4.65253i	−0.209869	+	0.176101i
$699$	47.7588	−	17.3828i	1.80640	−	0.657478i
$700$		0			0
$701$	6.84436	+	38.8163i	0.258508	+	1.46607i	0.786905	+	0.617074i	$0.211682\pi$
$701$	6.84436	+	38.8163i	0.258508	+	1.46607i	−0.528397	+	0.848997i	$0.677207\pi$
$702$	−11.4376	+	19.8106i	−0.431686	+	0.747701i
$703$	7.51889	+	20.1942i	0.283580	+	0.761637i
$704$	9.57057	+	16.5767i	0.360705	+	0.624759i
$705$	−17.3478	−	6.31407i	−0.653355	−	0.237802i
$706$	26.0442	−	21.8537i	0.980185	−	0.822473i
$707$		0			0
$708$	3.15270	+	1.14749i	0.118486	+	0.0431253i
$709$	38.6416	−	14.0644i	1.45122	−	0.528200i	0.508286	−	0.861189i	$-0.330279\pi$
$709$	38.6416	−	14.0644i	1.45122	−	0.528200i	0.942931	+	0.332989i	$0.108057\pi$
$710$	11.0250			0.413760
$711$	31.3357	−	54.2751i	1.17518	−	2.03548i
$712$	−23.2049	−	19.4712i	−0.869639	−	0.729714i
$713$	3.32501	−	18.8571i	0.124523	−	0.706202i
$714$		0			0
$715$	2.52007	−	4.36488i	0.0942452	−	0.163237i
$716$	−1.99912	+	0.727621i	−0.0747107	+	0.0271925i
$717$	−1.17617	−	6.67042i	−0.0439250	−	0.249111i
$718$	−6.90143	−	5.79098i	−0.257559	−	0.216118i
$719$	−7.36190	−	41.7514i	−0.274553	−	1.55706i	−0.740379	−	0.672189i	$-0.765354\pi$
$719$	−7.36190	−	41.7514i	−0.274553	−	1.55706i	0.465827	−	0.884876i	$-0.345757\pi$
$720$	−2.90554	−	16.4782i	−0.108283	−	0.614105i
$721$		0			0
$722$	4.07351	−	25.2724i	0.151600	−	0.940543i
$723$	19.8687	−	34.4136i	0.738925	−	1.27986i
$724$	−1.20851	+	1.01406i	−0.0449140	+	0.0376873i
$725$	−27.3234	−	9.94491i	−1.01477	−	0.369345i
$726$	−4.07011	+	23.0827i	−0.151056	+	0.856680i
$727$	−48.5411	−	17.6675i	−1.80029	−	0.655251i	−0.998324	−	0.0578805i	$-0.981566\pi$
$727$	−48.5411	−	17.6675i	−1.80029	−	0.655251i	−0.801965	−	0.597371i	$-0.796212\pi$
$728$		0			0
$729$	20.2344	−	35.0470i	0.749423	−	1.29804i
$730$	−1.64590			−0.0609174
$731$	−1.71554	+	0.624404i	−0.0634514	+	0.0230944i
$732$	−4.56418	+	1.66122i	−0.168697	+	0.0614006i
$733$	−22.9162			−0.846430			−0.423215	−	0.906029i	$-0.639098\pi$
$733$	−22.9162			−0.846430			−0.423215	+	0.906029i	$0.639098\pi$
$734$	5.46926	−	9.47303i	0.201874	−	0.349656i
$735$		0			0
$736$	−2.63816	−	0.960210i	−0.0972437	−	0.0353938i
$737$	−2.96761	+	16.8301i	−0.109313	+	0.619946i
$738$	16.5831	+	6.03574i	0.610431	+	0.222179i
$739$	21.5462	−	18.0794i	0.792591	−	0.665063i	−0.153794	−	0.988103i	$-0.549149\pi$
$739$	21.5462	−	18.0794i	0.792591	−	0.665063i	0.946385	+	0.323040i	$0.104705\pi$
$740$	0.401674	−	0.695720i	0.0147658	−	0.0255752i
$741$	31.8555	+	5.37549i	1.17024	+	0.197474i
$742$		0			0
$743$	1.06489	+	6.03931i	0.0390671	+	0.221561i	0.998091	−	0.0617657i	$-0.0196731\pi$
$743$	1.06489	+	6.03931i	0.0390671	+	0.221561i	−0.959024	+	0.283326i	$0.908562\pi$
$744$	10.4586	+	59.3135i	0.383430	+	2.17454i
$745$	11.1552	+	9.36035i	0.408696	+	0.342937i
$746$	−8.16448	−	46.3030i	−0.298923	−	1.69528i
$747$	73.7349	−	26.8373i	2.69782	−	0.981926i
$748$	−0.0962667	+	0.166739i	−0.00351986	+	0.00609657i
$749$		0			0
$750$	−5.46585	+	30.9984i	−0.199585	+	1.13190i
$751$	4.32114	+	3.62586i	0.157681	+	0.132310i	0.718215	−	0.695822i	$-0.244960\pi$
$751$	4.32114	+	3.62586i	0.157681	+	0.132310i	−0.560534	+	0.828131i	$0.689404\pi$
$752$	−13.1099	+	22.7071i	−0.478070	+	0.828042i
$753$	11.9932			0.437056
$754$	−22.4183	+	8.15961i	−0.816428	+	0.297155i
$755$	3.60442	+	1.31190i	0.131178	+	0.0477450i
$756$		0			0
$757$	12.0207	−	10.0866i	0.436900	−	0.366602i	−0.397648	−	0.917538i	$-0.630173\pi$
$757$	12.0207	−	10.0866i	0.436900	−	0.366602i	0.834548	+	0.550936i	$0.185729\pi$
$758$	2.15405	+	0.784009i	0.0782385	+	0.0284765i
$759$	8.63816	+	14.9617i	0.313545	+	0.543076i
$760$	−9.72967	+	5.71334i	−0.352932	+	0.207245i
$761$	−2.43242	+	4.21307i	−0.0881751	+	0.152724i	−0.906740	−	0.421691i	$-0.861437\pi$
$761$	−2.43242	+	4.21307i	−0.0881751	+	0.152724i	0.818565	+	0.574414i	$0.194770\pi$
$762$	7.81702	+	44.3325i	0.283181	+	1.60600i
$763$		0			0
$764$	3.18392	−	1.15885i	0.115190	−	0.0419257i
$765$	1.66772	−	1.39938i	0.0602965	−	0.0505948i
$766$	−0.687070	+	3.89657i	−0.0248249	+	0.140789i
$767$	−16.2300			−0.586031
$768$	12.6578			0.456747
$769$	3.91266	−	22.1898i	0.141094	−	0.800184i	−0.829327	−	0.558764i	$-0.811276\pi$
$769$	3.91266	−	22.1898i	0.141094	−	0.800184i	0.970421	−	0.241420i	$-0.0776131\pi$
$770$		0			0
$771$	0.960637	+	1.66387i	0.0345965	+	0.0599229i
$772$	0.0275033	+	0.0476371i	0.000989864	+	0.00171450i
$773$	−4.58987	+	26.0304i	−0.165086	+	0.936250i	0.783889	+	0.620900i	$0.213233\pi$
$773$	−4.58987	+	26.0304i	−0.165086	+	0.936250i	−0.948976	+	0.315350i	$0.897878\pi$
$774$	−4.82959	−	27.3900i	−0.173596	−	0.984513i
$775$	5.21554	−	29.5788i	0.187348	−	1.06250i
$776$	21.3164	−	17.8866i	0.765214	−	0.642091i
$777$		0			0
$778$	33.0993			1.18667
$779$	−0.0794409	−	10.7908i	−0.00284627	−	0.386621i
$780$	−0.602196	−	1.04303i	−0.0215621	−	0.0373466i
$781$	15.8726	−	13.3187i	0.567965	−	0.476580i
$782$	0.294978	+	1.67290i	0.0105484	+	0.0598229i
$783$	−42.6416	+	15.5203i	−1.52389	+	0.554650i
$784$		0			0
$785$	−6.47952	−	5.43696i	−0.231264	−	0.194054i
$786$	−3.57919	−	6.19934i	−0.127666	−	0.221123i
$787$	7.77884	−	13.4733i	0.277286	−	0.480273i	−0.693424	−	0.720530i	$-0.743899\pi$
$787$	7.77884	−	13.4733i	0.277286	−	0.480273i	0.970709	+	0.240257i	$0.0772318\pi$
$788$	2.28194	−	0.830557i	0.0812906	−	0.0295874i
$789$	−25.1446	−	21.0988i	−0.895170	−	0.751137i
$790$	−7.01707	−	12.1539i	−0.249656	−	0.432417i
$791$		0			0
$792$	−26.5651	−	22.2908i	−0.943950	−	0.792068i
$793$	17.9991	−	15.1031i	0.639168	−	0.536325i
$794$	32.8573	+	27.5706i	1.16606	+	0.978443i
$795$	−6.75150	−	2.45734i	−0.239451	−	0.0871530i
$796$	−0.0445774	−	0.0162249i	−0.00158000	−	0.000575075i
$797$	33.4935			1.18640			0.593200	−	0.805055i	$-0.297864\pi$
$797$	33.4935			1.18640			0.593200	+	0.805055i	$0.297864\pi$
$798$		0			0
$799$	−3.41147			−0.120689
$800$	−4.13816	−	1.50617i	−0.146306	−	0.0532510i
$801$	51.1639	+	18.6221i	1.80779	+	0.657981i
$802$	0.0892411	+	0.0748822i	0.00315121	+	0.00264418i
$803$	−2.36959	+	1.98832i	−0.0836208	+	0.0701662i
$804$	3.12836	+	2.62500i	0.110329	+	0.0925767i
$805$		0			0
$806$	−12.3216	−	21.3416i	−0.434010	−	0.751727i
$807$	−42.7695	−	35.8879i	−1.50556	−	1.26331i
$808$	25.5831	−	9.31147i	0.900009	−	0.327576i
$809$	−20.5581	+	35.6076i	−0.722784	+	1.25190i	0.237096	+	0.971486i	$0.423804\pi$
$809$	−20.5581	+	35.6076i	−0.722784	+	1.25190i	−0.959880	+	0.280412i	$0.909529\pi$
$810$	1.84864	+	3.20194i	0.0649546	+	0.112505i
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	0.839025	−	0.544093i	$-0.183126\pi$
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	−0.390132	+	0.920759i	$0.627571\pi$
$812$		0			0
$813$	−36.2413	+	13.1907i	−1.27104	+	0.462620i
$814$	2.57532	+	14.6054i	0.0902650	+	0.511918i
$815$	5.62836	−	4.72275i	0.197153	−	0.165431i
$816$	−2.42262	−	4.19610i	−0.0848086	−	0.146893i
$817$	−14.6655	+	8.61170i	−0.513081	+	0.301285i
$818$	−26.9540			−0.942424
$819$		0			0
$820$	−0.308182	+	0.258595i	−0.0107622	+	0.00903054i
$821$	−5.45084	+	30.9132i	−0.190236	+	1.07888i	0.728807	+	0.684720i	$0.240075\pi$
$821$	−5.45084	+	30.9132i	−0.190236	+	1.07888i	−0.919042	+	0.394160i	$0.871036\pi$
$822$	0.172304	+	0.977185i	0.00600979	+	0.0340832i
$823$	8.04442	−	45.6221i	0.280411	−	1.59029i	−0.440822	−	0.897595i	$-0.645313\pi$
$823$	8.04442	−	45.6221i	0.280411	−	1.59029i	0.721232	−	0.692693i	$-0.243576\pi$
$824$	8.10922	+	14.0456i	0.282498	+	0.489301i
$825$	13.5496	+	23.4686i	0.471738	+	0.817073i
$826$		0			0
$827$	7.07769	−	40.1396i	0.246115	−	1.39579i	−0.571773	−	0.820412i	$-0.693744\pi$
$827$	7.07769	−	40.1396i	0.246115	−	1.39579i	0.817888	−	0.575377i	$-0.195145\pi$
$828$	2.63453			0.0915564
$829$	−35.4834			−1.23239			−0.616195	−	0.787594i	$-0.711327\pi$
$829$	−35.4834			−1.23239			−0.616195	+	0.787594i	$0.711327\pi$
$830$	3.05122	−	17.3043i	0.105909	−	0.600642i
$831$	−39.1450	+	32.8466i	−1.35793	+	1.13943i
$832$	−20.7922	+	7.56774i	−0.720840	+	0.262364i
$833$		0			0
$834$	2.87211	+	16.2886i	0.0994531	+	0.564026i
$835$	−1.77420	+	3.07300i	−0.0613986	+	0.106345i
$836$	−0.601014	+	1.68988i	−0.0207865	+	0.0584457i
$837$	−23.4368	−	40.5937i	−0.810093	−	1.40312i
$838$	32.1698	+	11.7089i	1.11129	+	0.404476i
$839$	−29.2649	+	24.5562i	−1.01034	+	0.847774i	−0.988383	−	0.151985i	$-0.951433\pi$
$839$	−29.2649	+	24.5562i	−1.01034	+	0.847774i	−0.0219545	+	0.999759i	$0.506989\pi$
$840$		0			0
$841$	−17.2208	−	6.26784i	−0.593819	−	0.216132i
$842$	5.53209	−	2.01352i	0.190648	−	0.0693903i
$843$	−52.6323			−1.81275
$844$	0.226215	−	0.391815i	0.00778663	−	0.0134868i
$845$	−4.29426	−	3.60331i	−0.147727	−	0.123958i
$846$	9.02481	−	51.1823i	0.310280	−	1.75968i
$847$		0			0
$848$	−5.10220	+	8.83726i	−0.175210	+	0.303473i
$849$	20.8011	−	7.57099i	0.713893	−	0.259836i
$850$	0.462697	+	2.62408i	0.0158704	+	0.0900053i
$851$	−10.2044	−	8.56250i	−0.349802	−	0.293519i
$852$	−0.859785	−	4.87608i	−0.0294557	−	0.167052i
$853$	−4.44568	−	25.2127i	−0.152217	−	0.863266i	−0.961286	−	0.275552i	$-0.911139\pi$
$853$	−4.44568	−	25.2127i	−0.152217	−	0.863266i	0.809069	−	0.587714i	$-0.199972\pi$
$854$		0			0
$855$	12.9214	−	15.6314i	0.441904	−	0.534584i
$856$	−15.0628	+	26.0896i	−0.514837	+	0.891724i
$857$	−16.1532	+	13.5541i	−0.551782	+	0.463000i	−0.875544	−	0.483139i	$-0.839497\pi$
$857$	−16.1532	+	13.5541i	−0.551782	+	0.463000i	0.323762	+	0.946139i	$0.395052\pi$
$858$	20.8935	+	7.60462i	0.713293	+	0.259617i
$859$	−3.39780	+	19.2699i	−0.115932	+	0.657481i	0.870353	+	0.492428i	$0.163890\pi$
$859$	−3.39780	+	19.2699i	−0.115932	+	0.657481i	−0.986285	+	0.165053i	$0.947221\pi$
$860$	0.595800	+	0.216853i	0.0203166	+	0.00739464i
$861$		0			0
$862$	−25.8050	+	44.6956i	−0.878922	+	1.52234i
$863$	4.94894			0.168464			0.0842319	−	0.996446i	$-0.473156\pi$
$863$	4.94894			0.168464			0.0842319	+	0.996446i	$0.473156\pi$
$864$	−6.45811	+	2.35056i	−0.219709	+	0.0799677i
$865$	16.6459	−	6.05861i	0.565977	−	0.205999i
$866$	24.4279			0.830093
$867$	−24.1596	+	41.8456i	−0.820502	+	1.42115i
$868$		0			0
$869$	−24.7849	−	9.02098i	−0.840771	−	0.306016i
$870$	−4.07532	+	23.1123i	−0.138166	+	0.783580i
$871$	−18.5639	−	6.75670i	−0.629013	−	0.228942i
$872$	−4.11057	+	3.44917i	−0.139201	+	0.116804i
$873$	−25.0082	+	43.3155i	−0.846400	+	1.46601i
$874$	5.52166	+	14.8300i	0.186773	+	0.501633i
$875$		0			0
$876$	0.128356	+	0.727940i	0.00433673	+	0.0245948i
$877$	0.211829	+	1.20134i	0.00715296	+	0.0405664i	0.988175	−	0.153328i	$-0.0489991\pi$
$877$	0.211829	+	1.20134i	0.00715296	+	0.0405664i	−0.981022	+	0.193895i	$0.937888\pi$
$878$	6.28603	+	5.27460i	0.212143	+	0.178009i
$879$	5.25150	+	29.7827i	0.177129	+	1.00455i
$880$	−6.61721	+	2.40847i	−0.223066	+	0.0811894i
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	0.146609	+	0.989194i	$0.453164\pi$
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	−0.929972	+	0.367630i	$0.880169\pi$
$882$		0			0
$883$	2.24438	−	12.7285i	0.0755296	−	0.428349i	−0.923472	−	0.383667i	$-0.874661\pi$
$883$	2.24438	−	12.7285i	0.0755296	−	0.428349i	0.999001	−	0.0446828i	$-0.0142277\pi$
$884$	−0.170493	−	0.143061i	−0.00573430	−	0.00481165i
$885$	−7.98293	+	13.8268i	−0.268343	+	0.464784i
$886$	40.2749			1.35306
$887$	21.8237	−	7.94318i	0.732769	−	0.266706i	0.0514324	−	0.998676i	$-0.483621\pi$
$887$	21.8237	−	7.94318i	0.732769	−	0.266706i	0.681336	+	0.731970i	$0.261399\pi$
$888$	39.3730	+	14.3306i	1.32127	+	0.480904i
$889$		0			0
$890$	9.34002	−	7.83721i	0.313078	−	0.262704i
$891$	6.52956	+	2.37657i	0.218749	+	0.0796180i
$892$	−0.786274	−	1.36187i	−0.0263264	−	0.0455986i
$893$	−31.2558	+	5.74881i	−1.04594	+	0.192377i
$894$	−32.1202	+	55.6338i	−1.07426	+	1.86067i
$895$	−1.75800	−	9.97011i	−0.0587634	−	0.333264i
$896$		0			0
$897$	−18.7665	+	6.83045i	−0.626596	+	0.228062i
$898$	11.6109	−	9.74270i	0.387461	−	0.325118i
$899$	8.48886	−	48.1427i	0.283119	−	1.60565i
$900$	4.13247			0.137749
$901$	−1.32770			−0.0442320
$902$	1.28968	−	7.31412i	0.0429416	−	0.243534i
$903$		0			0
$904$	26.0326	+	45.0897i	0.865830	+	1.49966i
$905$	−3.75372	−	6.50163i	−0.124778	−	0.216122i
$906$	−2.93835	+	16.6642i	−0.0976201	+	0.553631i
$907$	−6.94537	−	39.3892i	−0.230617	−	1.30790i	−0.851650	−	0.524111i	$-0.824398\pi$
$907$	−6.94537	−	39.3892i	−0.230617	−	1.30790i	0.621032	−	0.783785i	$-0.286713\pi$
$908$	0.454078	−	2.57521i	0.0150691	−	0.0854612i
$909$	−37.4864	+	31.4548i	−1.24334	+	1.04329i
$910$		0			0
$911$	−18.7997			−0.622863			−0.311431	−	0.950269i	$-0.600808\pi$
$911$	−18.7997			−0.622863			−0.311431	+	0.950269i	$0.600808\pi$
$912$	−29.2670	−	34.3621i	−0.969126	−	1.13784i
$913$	−16.5116	−	28.5989i	−0.546455	−	0.946487i
$914$	24.1407	−	20.2564i	0.798503	−	0.670023i
$915$	−4.01367	−	22.7627i	−0.132688	−	0.752510i
$916$	−3.56552	+	1.29774i	−0.117808	+	0.0428787i
$917$		0			0
$918$	3.18551	+	2.67296i	0.105137	+	0.0882208i
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	−0.981398	−	0.191984i	$-0.938508\pi$
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	0.324436	−	0.945908i	$-0.394825\pi$
$920$	3.48751	−	6.04055i	0.114980	−	0.199151i
$921$	−31.6450	+	11.5178i	−1.04274	+	0.379526i
$922$	37.7988	+	31.7170i	1.24484	+	1.04454i
$923$	11.9760	+	20.7430i	0.394193	+	0.682763i
$924$		0			0
$925$	−16.0064	−	13.4310i	−0.526287	−	0.441607i
$926$	44.3658	−	37.2273i	1.45795	−	1.22337i
$927$	−22.3314	−	18.7383i	−0.733460	−	0.615446i
$928$	−6.73530	−	2.45145i	−0.221097	−	0.0804727i
$929$	−25.3285	−	9.21881i	−0.831000	−	0.302459i	−0.108731	−	0.994071i	$-0.534679\pi$
$929$	−25.3285	−	9.21881i	−0.831000	−	0.302459i	−0.722269	+	0.691612i	$0.756901\pi$
$930$	−24.2422			−0.794932
$931$		0			0
$932$	−3.26176			−0.106843
$933$	43.1994	+	15.7233i	1.41428	+	0.514758i
$934$	32.4060	+	11.7948i	1.06036	+	0.385938i
$935$	−0.701867	−	0.588936i	−0.0229535	−	0.0192603i
$936$	30.7085	−	25.7675i	1.00374	−	0.842236i
$937$	2.00980	+	1.68642i	0.0656573	+	0.0550930i	0.675026	−	0.737794i	$-0.264133\pi$
$937$	2.00980	+	1.68642i	0.0656573	+	0.0550930i	−0.609368	+	0.792887i	$0.708577\pi$
$938$		0			0
$939$	−38.3371	−	66.4018i	−1.25108	−	2.16694i
$940$	0.907604	+	0.761570i	0.0296028	+	0.0248397i
$941$	17.5437	−	6.38538i	0.571908	−	0.208158i	−0.0398455	−	0.999206i	$-0.512687\pi$
$941$	17.5437	−	6.38538i	0.571908	−	0.208158i	0.611754	+	0.791048i	$0.290464\pi$
$942$	18.6570	−	32.3149i	0.607879	−	1.05288i
$943$	3.33544	+	5.77715i	0.108617	+	0.188130i
$944$	17.3708	+	14.5758i	0.565370	+	0.474402i
$945$		0			0
$946$	−10.9991	+	4.00335i	−0.357612	+	0.130160i
$947$	1.45858	+	8.27201i	0.0473974	+	0.268804i	0.999292	−	0.0376214i	$-0.0119781\pi$
$947$	1.45858	+	8.27201i	0.0473974	+	0.268804i	−0.951895	+	0.306425i	$0.900867\pi$
$948$	−4.82816	+	4.05131i	−0.156811	+	0.131580i
$949$	−1.78787	−	3.09668i	−0.0580366	−	0.100522i
$950$	8.66116	+	23.2621i	0.281005	+	0.754721i
$951$	−85.0343			−2.75742
$952$		0			0
$953$	25.8102	−	21.6573i	0.836075	−	0.701550i	−0.120602	−	0.992701i	$-0.538483\pi$
$953$	25.8102	−	21.6573i	0.836075	−	0.701550i	0.956677	+	0.291151i	$0.0940382\pi$
$954$	3.51233	−	19.9194i	0.113716	−	0.644914i
$955$	2.79989	+	15.8790i	0.0906022	+	0.513831i
$956$	−0.0754843	+	0.428092i	−0.00244134	+	0.0138455i
$957$	22.0535	+	38.1978i	0.712888	+	1.23476i
$958$	25.7173	+	44.5438i	0.830890	+	1.43914i
$959$		0			0
$960$	−3.77972	+	21.4358i	−0.121990	+	0.691838i
$961$	19.4962			0.628909
$962$	−17.1438			−0.552739
$963$	9.40286	−	53.3262i	0.303003	−	1.71841i
$964$	−1.95361	+	1.63927i	−0.0629216	+	0.0527975i
$965$	−0.245977	+	0.0895284i	−0.00791829	+	0.00288202i
$966$		0			0
$967$	2.03920	+	11.5649i	0.0655763	+	0.371902i	0.999881	+	0.0154262i	$0.00491051\pi$
$967$	2.03920	+	11.5649i	0.0655763	+	0.371902i	−0.934305	+	0.356475i	$0.883978\pi$
$968$	8.89234	−	15.4020i	0.285811	−	0.495039i
$969$	1.96791	−	5.53320i	0.0632184	−	0.177752i
$970$	5.60014	+	9.69972i	0.179810	+	0.311439i
$971$	−12.0368	−	4.38105i	−0.386280	−	0.140595i	0.141578	−	0.989927i	$-0.454783\pi$
$971$	−12.0368	−	4.38105i	−0.386280	−	0.140595i	−0.527858	+	0.849333i	$0.677005\pi$
$972$	−1.52931	+	1.28325i	−0.0490528	+	0.0411602i
$973$		0			0
$974$	9.82934	+	3.57759i	0.314953	+	0.114633i
$975$	−29.4368	+	10.7141i	−0.942731	+	0.343126i
$976$	−32.8280			−1.05080
$977$	−7.26382	+	12.5813i	−0.232390	+	0.402512i	−0.958511	−	0.285055i	$-0.907988\pi$
$977$	−7.26382	+	12.5813i	−0.232390	+	0.402512i	0.726121	+	0.687567i	$0.241321\pi$
$978$	24.8293	+	20.8343i	0.793955	+	0.666207i
$979$	3.97906	−	22.5663i	0.127171	−	0.721224i
$980$		0			0
$981$	4.82248	−	8.35278i	0.153970	−	0.266684i
$982$	−46.4928	+	16.9220i	−1.48364	+	0.540002i
$983$	−6.43371	−	36.4874i	−0.205203	−	1.16377i	−0.897119	−	0.441788i	$-0.854344\pi$
$983$	−6.43371	−	36.4874i	−0.205203	−	1.16377i	0.691916	−	0.721978i	$-0.256767\pi$
$984$	−16.0737	−	13.4875i	−0.512412	−	0.429965i
$985$	2.00670	+	11.3806i	0.0639388	+	0.362615i
$986$	0.753089	+	4.27098i	0.0239832	+	0.136016i
$987$		0			0
$988$	−1.80313	−	1.02341i	−0.0573652	−	0.0325591i
$989$	5.25671	−	9.10489i	0.167154	−	0.289519i
$990$	10.6925	−	8.97210i	0.339831	−	0.285152i
$991$	−3.22446	−	1.17361i	−0.102428	−	0.0372809i	0.290298	−	0.956936i	$-0.406246\pi$
$991$	−3.22446	−	1.17361i	−0.102428	−	0.0372809i	−0.392726	+	0.919656i	$0.628468\pi$
$992$	1.28564	−	7.29125i	0.0408193	−	0.231498i
$993$	74.8556	+	27.2452i	2.37547	+	0.864600i
$994$		0			0
$995$	0.112874	−	0.195503i	0.00357835	−	0.00619788i
$996$	−7.89124			−0.250044
$997$	−12.0055	+	4.36965i	−0.380219	+	0.138388i	−0.525057	−	0.851067i	$-0.675956\pi$
$997$	−12.0055	+	4.36965i	−0.380219	+	0.138388i	0.144838	+	0.989455i	$0.453734\pi$
$998$	6.23695	−	2.27006i	0.197427	−	0.0718576i
$999$	−32.6091			−1.03170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.v.b.275.1		6
7.2	even	3		19.2.e.a.9.1	✓	6
7.3	odd	6		931.2.x.b.655.1		6
7.4	even	3		931.2.x.a.655.1		6
7.5	odd	6		931.2.w.a.883.1		6
7.6	odd	2		931.2.v.a.275.1		6
19.17	even	9		931.2.x.a.226.1		6
21.2	odd	6		171.2.u.c.28.1		6
28.23	odd	6		304.2.u.b.161.1		6
35.2	odd	12		475.2.u.a.199.2		12
35.9	even	6		475.2.l.a.351.1		6
35.23	odd	12		475.2.u.a.199.1		12
133.2	odd	18		361.2.e.h.245.1		6
133.9	even	9		361.2.c.i.292.2		6
133.16	even	9		361.2.e.f.62.1		6
133.17	odd	18		931.2.v.a.606.1		6
133.23	even	9		361.2.c.i.68.2		6
133.30	even	3		361.2.e.g.234.1		6
133.37	odd	6		361.2.e.h.28.1		6
133.44	even	9		361.2.a.g.1.2		3
133.51	odd	18		361.2.a.h.1.2		3
133.55	odd	18		931.2.x.b.226.1		6
133.65	odd	6		361.2.e.a.234.1		6
133.72	odd	18		361.2.c.h.68.2		6
133.74	even	9	inner	931.2.v.b.606.1		6
133.79	odd	18		361.2.e.b.62.1		6
133.86	odd	18		361.2.c.h.292.2		6
133.93	even	9		19.2.e.a.17.1	yes	6
133.100	even	9		361.2.e.g.54.1		6
133.107	odd	6		361.2.e.b.99.1		6
133.121	even	3		361.2.e.f.99.1		6
133.128	odd	18		361.2.e.a.54.1		6
133.131	odd	18		931.2.w.a.834.1		6
399.44	odd	18		3249.2.a.z.1.2		3
399.317	even	18		3249.2.a.s.1.2		3
399.359	odd	18		171.2.u.c.55.1		6
532.51	even	18		5776.2.a.bi.1.1		3
532.359	odd	18		304.2.u.b.17.1		6
532.443	odd	18		5776.2.a.br.1.3		3
665.44	even	18		9025.2.a.bd.1.2		3
665.93	odd	36		475.2.u.a.74.2		12
665.184	odd	18		9025.2.a.x.1.2		3
665.359	even	18		475.2.l.a.226.1		6
665.492	odd	36		475.2.u.a.74.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	7.2	even	3
19.2.e.a.17.1	yes	6	133.93	even	9
171.2.u.c.28.1		6	21.2	odd	6
171.2.u.c.55.1		6	399.359	odd	18
304.2.u.b.17.1		6	532.359	odd	18
304.2.u.b.161.1		6	28.23	odd	6
361.2.a.g.1.2		3	133.44	even	9
361.2.a.h.1.2		3	133.51	odd	18
361.2.c.h.68.2		6	133.72	odd	18
361.2.c.h.292.2		6	133.86	odd	18
361.2.c.i.68.2		6	133.23	even	9
361.2.c.i.292.2		6	133.9	even	9
361.2.e.a.54.1		6	133.128	odd	18
361.2.e.a.234.1		6	133.65	odd	6
361.2.e.b.62.1		6	133.79	odd	18
361.2.e.b.99.1		6	133.107	odd	6
361.2.e.f.62.1		6	133.16	even	9
361.2.e.f.99.1		6	133.121	even	3
361.2.e.g.54.1		6	133.100	even	9
361.2.e.g.234.1		6	133.30	even	3
361.2.e.h.28.1		6	133.37	odd	6
361.2.e.h.245.1		6	133.2	odd	18
475.2.l.a.226.1		6	665.359	even	18
475.2.l.a.351.1		6	35.9	even	6
475.2.u.a.74.1		12	665.492	odd	36
475.2.u.a.74.2		12	665.93	odd	36
475.2.u.a.199.1		12	35.23	odd	12
475.2.u.a.199.2		12	35.2	odd	12
931.2.v.a.275.1		6	7.6	odd	2
931.2.v.a.606.1		6	133.17	odd	18
931.2.v.b.275.1		6	1.1	even	1	trivial
931.2.v.b.606.1		6	133.74	even	9	inner
931.2.w.a.834.1		6	133.131	odd	18
931.2.w.a.883.1		6	7.5	odd	6
931.2.x.a.226.1		6	19.17	even	9
931.2.x.a.655.1		6	7.4	even	3
931.2.x.b.226.1		6	133.55	odd	18
931.2.x.b.655.1		6	7.3	odd	6
3249.2.a.s.1.2		3	399.317	even	18
3249.2.a.z.1.2		3	399.44	odd	18
5776.2.a.bi.1.1		3	532.51	even	18
5776.2.a.br.1.3		3	532.443	odd	18
9025.2.a.x.1.2		3	665.184	odd	18
9025.2.a.bd.1.2		3	665.44	even	18

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.v (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 + 0.460802i) q^{2} +(2.70574 + 0.984808i) q^{3} +(-0.141559 - 0.118782i) q^{4} +(0.673648 - 0.565258i) q^{5} +(2.97178 + 2.49362i) q^{6} +(-1.47178 - 2.54920i) q^{8} +(4.05303 + 3.40090i) q^{9} +O(q^{10})\)	\(q+(1.26604 + 0.460802i) q^{2} +(2.70574 + 0.984808i) q^{3} +(-0.141559 - 0.118782i) q^{4} +(0.673648 - 0.565258i) q^{5} +(2.97178 + 2.49362i) q^{6} +(-1.47178 - 2.54920i) q^{8} +(4.05303 + 3.40090i) q^{9} +(1.11334 - 0.405223i) q^{10} +(1.11334 - 1.92836i) q^{11} +(-0.266044 - 0.460802i) q^{12} +(1.97178 + 1.65452i) q^{13} +(2.37939 - 0.866025i) q^{15} +(-0.624485 - 3.54163i) q^{16} +(0.358441 - 0.300767i) q^{17} +(3.56418 + 6.17334i) q^{18} +(2.77719 - 3.35965i) q^{19} -0.162504 q^{20} +(2.29813 - 1.92836i) q^{22} +(-0.467911 + 2.65366i) q^{23} +(-1.47178 - 8.34689i) q^{24} +(-0.733956 + 4.16247i) q^{25} +(1.73396 + 3.00330i) q^{26} +(3.29813 + 5.71253i) q^{27} +(-1.19459 + 6.77487i) q^{29} +3.41147 q^{30} -7.10607 q^{31} +(-0.180922 + 1.02606i) q^{32} +(4.91147 - 4.12122i) q^{33} +(0.592396 - 0.215615i) q^{34} +(-0.169778 - 0.962858i) q^{36} +(-2.47178 + 4.28125i) q^{37} +(5.06418 - 2.97373i) q^{38} +(3.70574 + 6.41852i) q^{39} +(-2.43242 - 0.885328i) q^{40} +(1.89646 - 1.59132i) q^{41} +(-3.66637 - 1.33445i) q^{43} +(-0.386659 + 0.140732i) q^{44} +4.65270 q^{45} +(-1.81521 + 3.14403i) q^{46} +(-5.58512 - 4.68647i) q^{47} +(1.79813 - 10.1977i) q^{48} +(-2.84730 + 4.93166i) q^{50} +(1.26604 - 0.460802i) q^{51} +(-0.0825961 - 0.468426i) q^{52} +(-2.17365 - 1.82391i) q^{53} +(1.54323 + 8.75211i) q^{54} +(-0.340022 - 1.92836i) q^{55} +(10.8229 - 6.35532i) q^{57} +(-4.63429 + 8.02682i) q^{58} +(-4.83022 + 4.05304i) q^{59} +(-0.439693 - 0.160035i) q^{60} +(1.58512 - 8.98968i) q^{61} +(-8.99660 - 3.27449i) q^{62} +(-4.29813 + 7.44459i) q^{64} +2.26352 q^{65} +(8.11721 - 2.95442i) q^{66} +(-7.21213 + 2.62500i) q^{67} -0.0864665 q^{68} +(-3.87939 + 6.71929i) q^{69} +(8.74422 + 3.18264i) q^{71} +(2.70439 - 15.3374i) q^{72} +(-1.30541 - 0.475129i) q^{73} +(-5.10220 + 4.28125i) q^{74} +(-6.08512 + 10.5397i) q^{75} +(-0.792204 + 0.145708i) q^{76} +(1.73396 + 9.83375i) q^{78} +(-2.05690 - 11.6653i) q^{79} +(-2.42262 - 2.03282i) q^{80} +(0.541889 + 3.07321i) q^{81} +(3.13429 - 1.14079i) q^{82} +(7.41534 - 12.8438i) q^{83} +(0.0714517 - 0.405223i) q^{85} +(-4.02687 - 3.37895i) q^{86} +(-9.90420 + 17.1546i) q^{87} -6.55438 q^{88} +(9.67024 - 3.51968i) q^{89} +(5.89053 + 2.14398i) q^{90} +(0.381445 - 0.320070i) q^{92} +(-19.2271 - 6.99811i) q^{93} +(-4.91147 - 8.50692i) q^{94} +(-0.0282185 - 3.83305i) q^{95} +(-1.50000 + 2.59808i) q^{96} +(1.64156 + 9.30975i) q^{97} +(11.0706 - 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 6 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 6 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 + 12 * q^9	\( 6 q + 3 q^{2} + 6 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} + 12 q^{9} + 3 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} - 6 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} - 12 q^{23} + 6 q^{24} - 9 q^{25} + 15 q^{26} + 6 q^{27} - 3 q^{29} - 18 q^{31} - 18 q^{32} + 9 q^{33} - 24 q^{36} + 12 q^{38} + 12 q^{39} + 9 q^{40} + 21 q^{41} - 3 q^{43} - 9 q^{44} + 30 q^{45} - 18 q^{46} - 12 q^{47} - 3 q^{48} - 15 q^{50} + 3 q^{51} + 6 q^{52} - 12 q^{53} - 6 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} - 12 q^{61} - 12 q^{62} - 12 q^{64} + 24 q^{65} + 18 q^{66} + 6 q^{67} + 30 q^{68} - 12 q^{69} - 6 q^{71} + 15 q^{72} - 12 q^{73} - 30 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 24 q^{79} + 12 q^{80} - 3 q^{81} + 9 q^{82} - 48 q^{86} - 21 q^{87} - 18 q^{88} + 15 q^{89} + 18 q^{90} + 42 q^{92} - 36 q^{93} - 9 q^{94} - 15 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 6 * q^3 - 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 + 12 * q^9 + 3 * q^12 - 3 * q^13 + 3 * q^15 + 9 * q^16 - 6 * q^17 + 3 * q^18 + 6 * q^19 - 6 * q^20 - 12 * q^23 + 6 * q^24 - 9 * q^25 + 15 * q^26 + 6 * q^27 - 3 * q^29 - 18 * q^31 - 18 * q^32 + 9 * q^33 - 24 * q^36 + 12 * q^38 + 12 * q^39 + 9 * q^40 + 21 * q^41 - 3 * q^43 - 9 * q^44 + 30 * q^45 - 18 * q^46 - 12 * q^47 - 3 * q^48 - 15 * q^50 + 3 * q^51 + 6 * q^52 - 12 * q^53 - 6 * q^54 + 18 * q^55 + 24 * q^57 - 18 * q^58 - 6 * q^59 + 3 * q^60 - 12 * q^61 - 12 * q^62 - 12 * q^64 + 24 * q^65 + 18 * q^66 + 6 * q^67 + 30 * q^68 - 12 * q^69 - 6 * q^71 + 15 * q^72 - 12 * q^73 - 30 * q^74 - 15 * q^75 + 36 * q^76 + 15 * q^78 + 24 * q^79 + 12 * q^80 - 3 * q^81 + 9 * q^82 - 48 * q^86 - 21 * q^87 - 18 * q^88 + 15 * q^89 + 18 * q^90 + 42 * q^92 - 36 * q^93 - 9 * q^94 - 15 * q^95 - 9 * q^96 + 18 * q^97 + 9 * q^99

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