LMFDB - Embedded newform 390.2.bb.c.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(121,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("390.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bb (of order $6$, degree $2$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.17284886784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 $ x^8 - 2x^7 + 2x^6 + 30x^5 + 185x^4 + 36x^3 + 8x^2 + 208*x + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$1.33404 + 1.33404i$ of defining polynomial
Character	$\chi$	$=$	390.361
Dual form			390.2.bb.c.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.44460 + 0.834038i) q^{11} -1.00000 q^{12} +(-2.24376 - 2.82233i) q^{13} -3.64466 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(5.46699 + 3.15637i) q^{19} +(-0.866025 - 0.500000i) q^{20} +3.64466i q^{21} +(-0.834038 + 1.44460i) q^{22} +(0.622266 + 1.07780i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-3.35432 - 1.32233i) q^{26} +1.00000 q^{27} +(-3.15637 + 1.82233i) q^{28} +(-5.02239 - 8.69904i) q^{29} +(-0.500000 + 0.866025i) q^{30} +4.21957i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.44460 + 0.834038i) q^{33} -4.00000i q^{34} +(-1.82233 + 3.15637i) q^{35} +(0.500000 + 0.866025i) q^{36} +(8.54267 - 4.93211i) q^{37} +6.31274 q^{38} +(-1.32233 + 3.35432i) q^{39} -1.00000 q^{40} +(8.04479 - 4.64466i) q^{41} +(1.82233 + 3.15637i) q^{42} +(-3.78643 + 6.55829i) q^{43} +1.66808i q^{44} +(0.866025 + 0.500000i) q^{45} +(1.07780 + 0.622266i) q^{46} -6.82522i q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.14177 + 5.44171i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +(-3.56609 + 0.531987i) q^{52} -0.848634 q^{53} +(0.866025 - 0.500000i) q^{54} +(0.834038 + 1.44460i) q^{55} +(-1.82233 + 3.15637i) q^{56} -6.31274i q^{57} +(-8.69904 - 5.02239i) q^{58} +(5.29034 + 3.05438i) q^{59} +1.00000i q^{60} +(-3.73205 + 6.46410i) q^{61} +(2.10978 + 3.65425i) q^{62} +(3.15637 - 1.82233i) q^{63} -1.00000 q^{64} +(-2.82233 + 2.24376i) q^{65} +1.66808 q^{66} +(12.7768 - 7.37671i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(0.622266 - 1.07780i) q^{69} +3.64466i q^{70} +(-3.04056 - 1.75547i) q^{71} +(0.866025 + 0.500000i) q^{72} +12.2175i q^{73} +(4.93211 - 8.54267i) q^{74} +(0.500000 + 0.866025i) q^{75} +(5.46699 - 3.15637i) q^{76} +6.07957 q^{77} +(0.531987 + 3.56609i) q^{78} +9.93398 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.64466 - 8.04479i) q^{82} +7.95317i q^{83} +(3.15637 + 1.82233i) q^{84} +(-3.46410 - 2.00000i) q^{85} +7.57286i q^{86} +(-5.02239 + 8.69904i) q^{87} +(0.834038 + 1.44460i) q^{88} +(5.15425 - 2.97581i) q^{89} +1.00000 q^{90} +(1.93891 + 12.9972i) q^{91} +1.24453 q^{92} +(3.65425 - 2.10978i) q^{93} +(-3.41261 - 5.91081i) q^{94} +(3.15637 - 5.46699i) q^{95} +1.00000i q^{96} +(-2.38453 - 1.37671i) q^{97} +(5.44171 + 3.14177i) q^{98} -1.66808i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 4 q^{14} - 4 q^{16} + 16 q^{17} - 6 q^{19} + 2 q^{22} + 4 q^{23} - 8 q^{25} - 12 q^{26} + 8 q^{27} - 8 q^{29} - 4 q^{30} - 6 q^{33} + 2 q^{35} + 4 q^{36} + 30 q^{37} + 6 q^{39} - 8 q^{40} - 2 q^{42} + 14 q^{43} - 6 q^{46} - 4 q^{48} + 14 q^{49} - 32 q^{51} - 6 q^{52} + 16 q^{53} - 2 q^{55} + 2 q^{56} - 6 q^{58} + 24 q^{59} - 16 q^{61} + 4 q^{62} - 8 q^{64} - 6 q^{65} - 4 q^{66} + 24 q^{67} - 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} + 4 q^{75} - 6 q^{76} + 16 q^{77} + 6 q^{78} - 20 q^{79} - 4 q^{81} + 4 q^{82} - 8 q^{87} - 2 q^{88} + 42 q^{89} + 8 q^{90} - 10 q^{91} + 8 q^{92} + 30 q^{93} - 8 q^{94} - 24 q^{97} + 48 q^{98}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^10 + 6 * q^11 - 8 * q^12 - 12 * q^13 + 4 * q^14 - 4 * q^16 + 16 * q^17 - 6 * q^19 + 2 * q^22 + 4 * q^23 - 8 * q^25 - 12 * q^26 + 8 * q^27 - 8 * q^29 - 4 * q^30 - 6 * q^33 + 2 * q^35 + 4 * q^36 + 30 * q^37 + 6 * q^39 - 8 * q^40 - 2 * q^42 + 14 * q^43 - 6 * q^46 - 4 * q^48 + 14 * q^49 - 32 * q^51 - 6 * q^52 + 16 * q^53 - 2 * q^55 + 2 * q^56 - 6 * q^58 + 24 * q^59 - 16 * q^61 + 4 * q^62 - 8 * q^64 - 6 * q^65 - 4 * q^66 + 24 * q^67 - 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 + 4 * q^75 - 6 * q^76 + 16 * q^77 + 6 * q^78 - 20 * q^79 - 4 * q^81 + 4 * q^82 - 8 * q^87 - 2 * q^88 + 42 * q^89 + 8 * q^90 - 10 * q^91 + 8 * q^92 + 30 * q^93 - 8 * q^94 - 24 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−3.15637	−	1.82233i	−1.19299	−	0.688776i	−0.234010	−	0.972234i	$-0.575185\pi$
$7$	−3.15637	−	1.82233i	−1.19299	−	0.688776i	−0.958985	+	0.283458i	$0.908518\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.44460	+	0.834038i	−0.435562	+	0.251472i	−0.701713	−	0.712459i	$-0.747581\pi$
$11$	−1.44460	+	0.834038i	−0.435562	+	0.251472i	0.266151	+	0.963931i	$0.414248\pi$
$12$	−1.00000			−0.288675
$13$	−2.24376	−	2.82233i	−0.622307	−	0.782773i
$13$	−2.24376	−	2.82233i	−0.622307	−	0.782773i
$14$	−3.64466			−0.974076
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$			1.00000i			0.235702i
$19$	5.46699	+	3.15637i	1.25421	+	0.724120i	0.971943	−	0.235215i	$-0.0755793\pi$
$19$	5.46699	+	3.15637i	1.25421	+	0.724120i	0.282270	+	0.959335i	$0.408913\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$			3.64466i			0.795330i
$22$	−0.834038	+	1.44460i	−0.177817	+	0.307989i
$23$	0.622266	+	1.07780i	0.129752	+	0.224736i	0.923580	−	0.383405i	$-0.125249\pi$
$23$	0.622266	+	1.07780i	0.129752	+	0.224736i	−0.793829	+	0.608141i	$0.791915\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−1.00000			−0.200000
$26$	−3.35432	−	1.32233i	−0.657836	−	0.259330i
$27$	1.00000			0.192450
$28$	−3.15637	+	1.82233i	−0.596497	+	0.344388i
$29$	−5.02239	−	8.69904i	−0.932635	−	1.61537i	−0.778798	−	0.627275i	$-0.784170\pi$
$29$	−5.02239	−	8.69904i	−0.932635	−	1.61537i	−0.153837	−	0.988096i	$-0.549163\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$			4.21957i			0.757857i	0.925426	+	0.378928i	$0.123707\pi$
$31$			4.21957i			0.757857i	−0.925426	+	0.378928i	$0.876293\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.44460	+	0.834038i	0.251472	+	0.145187i
$34$		−	4.00000i		−	0.685994i
$35$	−1.82233	+	3.15637i	−0.308030	+	0.533524i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	8.54267	−	4.93211i	1.40441	−	0.810835i	0.409566	−	0.912281i	$-0.365680\pi$
$37$	8.54267	−	4.93211i	1.40441	−	0.810835i	0.994841	+	0.101446i	$0.0323469\pi$
$38$	6.31274			1.02406
$39$	−1.32233	+	3.35432i	−0.211742	+	0.537121i
$40$	−1.00000			−0.158114
$41$	8.04479	−	4.64466i	1.25638	−	0.725374i	0.284015	−	0.958820i	$-0.408334\pi$
$41$	8.04479	−	4.64466i	1.25638	−	0.725374i	0.972370	+	0.233446i	$0.0750002\pi$
$42$	1.82233	+	3.15637i	0.281192	+	0.487038i
$43$	−3.78643	+	6.55829i	−0.577425	+	1.00013i	0.418348	+	0.908287i	$0.362609\pi$
$43$	−3.78643	+	6.55829i	−0.577425	+	1.00013i	−0.995773	+	0.0918433i	$0.970724\pi$
$44$			1.66808i			0.251472i
$45$	0.866025	+	0.500000i	0.129099	+	0.0745356i
$46$	1.07780	+	0.622266i	0.158912	+	0.0917482i
$47$		−	6.82522i		−	0.995560i	−0.867303	−	0.497780i	$-0.834149\pi$
$47$		−	6.82522i		−	0.995560i	0.867303	−	0.497780i	$-0.165851\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	3.14177	+	5.44171i	0.448825	+	0.777387i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−4.00000			−0.560112
$52$	−3.56609	+	0.531987i	−0.494528	+	0.0737734i
$53$	−0.848634			−0.116569			−0.0582844	−	0.998300i	$-0.518563\pi$
$53$	−0.848634			−0.116569			−0.0582844	+	0.998300i	$0.518563\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	0.834038	+	1.44460i	0.112462	+	0.194789i
$56$	−1.82233	+	3.15637i	−0.243519	+	0.421787i
$57$		−	6.31274i		−	0.836142i
$58$	−8.69904	−	5.02239i	−1.14224	−	0.659473i
$59$	5.29034	+	3.05438i	0.688744	+	0.397646i	0.803141	−	0.595789i	$-0.203160\pi$
$59$	5.29034	+	3.05438i	0.688744	+	0.397646i	−0.114397	+	0.993435i	$0.536494\pi$
$60$			1.00000i			0.129099i
$61$	−3.73205	+	6.46410i	−0.477840	+	0.827643i	−0.999677	−	0.0254017i	$-0.991914\pi$
$61$	−3.73205	+	6.46410i	−0.477840	+	0.827643i	0.521837	+	0.853045i	$0.325247\pi$
$62$	2.10978	+	3.65425i	0.267943	+	0.464091i
$63$	3.15637	−	1.82233i	0.397665	−	0.229592i
$64$	−1.00000			−0.125000
$65$	−2.82233	+	2.24376i	−0.350067	+	0.278304i
$66$	1.66808			0.205326
$67$	12.7768	−	7.37671i	1.56094	−	0.901209i	0.563777	−	0.825927i	$-0.309348\pi$
$67$	12.7768	−	7.37671i	1.56094	−	0.901209i	0.997162	−	0.0752814i	$-0.0239855\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	0.622266	−	1.07780i	0.0749121	−	0.129752i
$70$			3.64466i			0.435620i
$71$	−3.04056	−	1.75547i	−0.360848	−	0.208336i	0.308605	−	0.951190i	$-0.400138\pi$
$71$	−3.04056	−	1.75547i	−0.360848	−	0.208336i	−0.669453	+	0.742855i	$0.733471\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			12.2175i			1.42995i	0.699149	+	0.714976i	$0.253563\pi$
$73$			12.2175i			1.42995i	−0.699149	+	0.714976i	$0.746437\pi$
$74$	4.93211	−	8.54267i	0.573347	−	0.993065i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	5.46699	−	3.15637i	0.627107	−	0.362060i
$77$	6.07957			0.692831
$78$	0.531987	+	3.56609i	0.0602357	+	0.403780i
$79$	9.93398			1.11766			0.558830	−	0.829282i	$-0.311250\pi$
$79$	9.93398			1.11766			0.558830	+	0.829282i	$0.311250\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.64466	−	8.04479i	0.512917	−	0.888398i
$83$			7.95317i			0.872974i	0.899711	+	0.436487i	$0.143777\pi$
$83$			7.95317i			0.872974i	−0.899711	+	0.436487i	$0.856223\pi$
$84$	3.15637	+	1.82233i	0.344388	+	0.198832i
$85$	−3.46410	−	2.00000i	−0.375735	−	0.216930i
$86$			7.57286i			0.816603i
$87$	−5.02239	+	8.69904i	−0.538457	+	0.932635i
$88$	0.834038	+	1.44460i	0.0889087	+	0.153994i
$89$	5.15425	−	2.97581i	0.546350	−	0.315435i	−0.201299	−	0.979530i	$-0.564516\pi$
$89$	5.15425	−	2.97581i	0.546350	−	0.315435i	0.747648	+	0.664095i	$0.231183\pi$
$90$	1.00000			0.105409
$91$	1.93891	+	12.9972i	0.203253	+	1.36247i
$92$	1.24453			0.129752
$93$	3.65425	−	2.10978i	0.378928	−	0.218774i
$94$	−3.41261	−	5.91081i	−0.351984	−	0.609654i
$95$	3.15637	−	5.46699i	0.323837	−	0.560901i
$96$			1.00000i			0.102062i
$97$	−2.38453	−	1.37671i	−0.242113	−	0.139784i	0.374035	−	0.927415i	$-0.377974\pi$
$97$	−2.38453	−	1.37671i	−0.242113	−	0.139784i	−0.616147	+	0.787631i	$0.711307\pi$
$98$	5.44171	+	3.14177i	0.549696	+	0.317367i
$99$		−	1.66808i		−	0.167648i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.66808	+	4.62124i	0.265483	+	0.459831i	0.967690	−	0.252142i	$-0.0811351\pi$
$101$	2.66808	+	4.62124i	0.265483	+	0.459831i	−0.702207	+	0.711973i	$0.747802\pi$
$102$	−3.46410	+	2.00000i	−0.342997	+	0.198030i
$103$	−7.51248			−0.740227			−0.370113	−	0.928987i	$-0.620681\pi$
$103$	−7.51248			−0.740227			−0.370113	+	0.928987i	$0.620681\pi$
$104$	−2.82233	+	2.24376i	−0.276752	+	0.220019i
$105$	3.64466			0.355682
$106$	−0.734939	+	0.424317i	−0.0713835	+	0.0412133i
$107$	−8.46410	−	14.6603i	−0.818256	−	1.41726i	−0.906966	−	0.421203i	$-0.861608\pi$
$107$	−8.46410	−	14.6603i	−0.818256	−	1.41726i	0.0887109	−	0.996057i	$-0.471725\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			0.663848i			0.0635851i	0.999494	+	0.0317926i	$0.0101216\pi$
$109$			0.663848i			0.0635851i	−0.999494	+	0.0317926i	$0.989878\pi$
$110$	1.44460	+	0.834038i	0.137737	+	0.0795224i
$111$	−8.54267	−	4.93211i	−0.810835	−	0.468136i
$112$			3.64466i			0.344388i
$113$	8.93500	−	15.4759i	0.840534	−	1.45585i	−0.0489094	−	0.998803i	$-0.515575\pi$
$113$	8.93500	−	15.4759i	0.840534	−	1.45585i	0.889444	−	0.457045i	$-0.151092\pi$
$114$	−3.15637	−	5.46699i	−0.295621	−	0.512030i
$115$	1.07780	−	0.622266i	0.100505	−	0.0580266i
$116$	−10.0448			−0.932635
$117$	3.56609	−	0.531987i	0.329685	−	0.0491823i
$118$	6.10876			0.562357
$119$	−12.6255	+	7.28932i	−1.15738	+	0.668211i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−4.10876	+	7.11658i	−0.373524	+	0.646962i
$122$			7.46410i			0.675768i
$123$	−8.04479	−	4.64466i	−0.725374	−	0.418795i
$124$	3.65425	+	2.10978i	0.328162	+	0.189464i
$125$			1.00000i			0.0894427i
$126$	1.82233	−	3.15637i	0.162346	−	0.281192i
$127$	7.22034	+	12.5060i	0.640702	+	1.10973i	0.985276	+	0.170969i	$0.0546898\pi$
$127$	7.22034	+	12.5060i	0.640702	+	1.10973i	−0.344575	+	0.938759i	$0.611977\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	7.57286			0.666753
$130$	−1.32233	+	3.35432i	−0.115976	+	0.294193i
$131$	−10.8892			−0.951393			−0.475697	−	0.879609i	$-0.657804\pi$
$131$	−10.8892			−0.951393			−0.475697	+	0.879609i	$0.657804\pi$
$132$	1.44460	−	0.834038i	0.125736	−	0.0725937i
$133$	−11.5039	−	19.9253i	−0.997513	−	1.72774i
$134$	7.37671	−	12.7768i	0.637251	−	1.10375i
$135$		−	1.00000i		−	0.0860663i
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	6.09419	+	3.51848i	0.520662	+	0.300604i	0.737205	−	0.675669i	$-0.236145\pi$
$137$	6.09419	+	3.51848i	0.520662	+	0.300604i	−0.216544	+	0.976273i	$0.569478\pi$
$138$		−	1.24453i		−	0.105942i
$139$	−5.82233	+	10.0846i	−0.493844	+	0.855362i	−0.999975	−	0.00709431i	$-0.997742\pi$
$139$	−5.82233	+	10.0846i	−0.493844	+	0.855362i	0.506131	+	0.862456i	$0.331075\pi$
$140$	1.82233	+	3.15637i	0.154015	+	0.266762i
$141$	−5.91081	+	3.41261i	−0.497780	+	0.287394i
$142$	−3.51093			−0.294631
$143$	5.59526	+	2.20575i	0.467899	+	0.184454i
$144$	1.00000			0.0833333
$145$	−8.69904	+	5.02239i	−0.722416	+	0.417087i
$146$	6.10876	+	10.5807i	0.505565	+	0.875664i
$147$	3.14177	−	5.44171i	0.259129	−	0.448825i
$148$		−	9.86423i		−	0.810835i
$149$	−0.669099	−	0.386305i	−0.0548147	−	0.0316473i	0.472342	−	0.881415i	$-0.343409\pi$
$149$	−0.669099	−	0.386305i	−0.0548147	−	0.0316473i	−0.527157	+	0.849768i	$0.676742\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$		−	9.77838i		−	0.795754i	−0.917439	−	0.397877i	$-0.869747\pi$
$151$		−	9.77838i		−	0.795754i	0.917439	−	0.397877i	$-0.130253\pi$
$152$	3.15637	−	5.46699i	0.256015	−	0.443431i
$153$	2.00000	+	3.46410i	0.161690	+	0.280056i
$154$	5.26506	−	3.03978i	0.424271	−	0.244953i
$155$	4.21957			0.338924
$156$	2.24376	+	2.82233i	0.179644	+	0.225967i
$157$	−12.0135			−0.958786			−0.479393	−	0.877600i	$-0.659143\pi$
$157$	−12.0135			−0.958786			−0.479393	+	0.877600i	$0.659143\pi$
$158$	8.60308	−	4.96699i	0.684424	−	0.395152i
$159$	0.424317	+	0.734939i	0.0336505	+	0.0582844i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		−	4.53590i		−	0.357479i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−8.73960	−	5.04581i	−0.684538	−	0.395218i	0.117025	−	0.993129i	$-0.462664\pi$
$163$	−8.73960	−	5.04581i	−0.684538	−	0.395218i	−0.801563	+	0.597911i	$0.795998\pi$
$164$		−	9.28932i		−	0.725374i
$165$	0.834038	−	1.44460i	0.0649298	−	0.112462i
$166$	3.97658	+	6.88764i	0.308643	+	0.534585i
$167$	−6.83902	+	3.94851i	−0.529219	+	0.305545i	−0.740698	−	0.671838i	$-0.765505\pi$
$167$	−6.83902	+	3.94851i	−0.529219	+	0.305545i	0.211479	+	0.977382i	$0.432172\pi$
$168$	3.64466			0.281192
$169$	−2.93109	+	12.6653i	−0.225469	+	0.974250i
$170$	−4.00000			−0.306786
$171$	−5.46699	+	3.15637i	−0.418071	+	0.241373i
$172$	3.78643	+	6.55829i	0.288713	+	0.500065i
$173$	−0.220343	+	0.381645i	−0.0167523	+	0.0290159i	−0.874280	−	0.485422i	$-0.838666\pi$
$173$	−0.220343	+	0.381645i	−0.0167523	+	0.0290159i	0.857528	+	0.514438i	$0.171999\pi$
$174$			10.0448i			0.761493i
$175$	3.15637	+	1.82233i	0.238599	+	0.137755i
$176$	1.44460	+	0.834038i	0.108891	+	0.0628680i
$177$		−	6.10876i		−	0.459163i
$178$	2.97581	−	5.15425i	0.223046	−	0.386328i
$179$	−9.81842	−	17.0060i	−0.733863	−	1.27109i	−0.955220	−	0.295895i	$-0.904382\pi$
$179$	−9.81842	−	17.0060i	−0.733863	−	1.27109i	0.221357	−	0.975193i	$-0.428951\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	6.21752			0.462145			0.231072	−	0.972937i	$-0.425777\pi$
$181$	6.21752			0.462145			0.231072	+	0.972937i	$0.425777\pi$
$182$	8.17774	+	10.2864i	0.606174	+	0.762481i
$183$	7.46410			0.551762
$184$	1.07780	−	0.622266i	0.0794562	−	0.0458741i
$185$	−4.93211	−	8.54267i	−0.362616	−	0.628070i
$186$	2.10978	−	3.65425i	0.154697	−	0.267943i
$187$			6.67230i			0.487927i
$188$	−5.91081	−	3.41261i	−0.431090	−	0.248890i
$189$	−3.15637	−	1.82233i	−0.229592	−	0.132555i
$190$		−	6.31274i		−	0.457974i
$191$	−7.84081	+	13.5807i	−0.567341	+	0.982664i	0.429486	+	0.903073i	$0.358695\pi$
$191$	−7.84081	+	13.5807i	−0.567341	+	0.982664i	−0.996828	+	0.0795905i	$0.974639\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	7.03901	−	4.06397i	0.506679	−	0.292531i	−0.224788	−	0.974408i	$-0.572169\pi$
$193$	7.03901	−	4.06397i	0.506679	−	0.292531i	0.731468	+	0.681876i	$0.238836\pi$
$194$	−2.75342			−0.197684
$195$	3.35432	+	1.32233i	0.240208	+	0.0946940i
$196$	6.28354			0.448825
$197$	0.771835	−	0.445619i	0.0549910	−	0.0317491i	−0.472252	−	0.881463i	$-0.656559\pi$
$197$	0.771835	−	0.445619i	0.0549910	−	0.0317491i	0.527243	+	0.849714i	$0.323226\pi$
$198$	−0.834038	−	1.44460i	−0.0592725	−	0.102663i
$199$	0.180558	−	0.312736i	0.0127994	−	0.0221692i	−0.859555	−	0.511044i	$-0.829259\pi$
$199$	0.180558	−	0.312736i	0.0127994	−	0.0221692i	0.872354	+	0.488874i	$0.162592\pi$
$200$			1.00000i			0.0707107i
$201$	−12.7768	−	7.37671i	−0.901209	−	0.520313i
$202$	4.62124	+	2.66808i	0.325150	+	0.187725i
$203$			36.6098i			2.56951i
$204$	−2.00000	+	3.46410i	−0.140028	+	0.242536i
$205$	−4.64466	−	8.04479i	−0.324397	−	0.561872i
$206$	−6.50600	+	3.75624i	−0.453295	+	0.261710i
$207$	−1.24453			−0.0865010
$208$	−1.32233	+	3.35432i	−0.0916871	+	0.232580i
$209$	−10.5301			−0.728384
$210$	3.15637	−	1.82233i	0.217810	−	0.125753i
$211$	−1.11370	−	1.92898i	−0.0766700	−	0.132796i	0.825141	−	0.564926i	$-0.191095\pi$
$211$	−1.11370	−	1.92898i	−0.0766700	−	0.132796i	−0.901811	+	0.432130i	$0.857762\pi$
$212$	−0.424317	+	0.734939i	−0.0291422	+	0.0504758i
$213$			3.51093i			0.240565i
$214$	−14.6603	−	8.46410i	−1.00215	−	0.578594i
$215$	6.55829	+	3.78643i	0.447272	+	0.258232i
$216$		−	1.00000i		−	0.0680414i
$217$	7.68945	−	13.3185i	0.521994	−	0.904119i
$218$	0.331924	+	0.574909i	0.0224807	+	0.0389378i
$219$	10.5807	−	6.10876i	0.714976	−	0.412792i
$220$	1.66808			0.112462
$221$	−14.2644	+	2.12795i	−0.959524	+	0.143141i
$222$	−9.86423			−0.662044
$223$	5.26872	−	3.04190i	0.352820	−	0.203701i	−0.313107	−	0.949718i	$-0.601370\pi$
$223$	5.26872	−	3.04190i	0.352820	−	0.203701i	0.665927	+	0.746017i	$0.268036\pi$
$224$	1.82233	+	3.15637i	0.121760	+	0.210894i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$		−	17.8700i		−	1.18869i
$227$	−13.2679	−	7.66025i	−0.880625	−	0.508429i	−0.00976038	−	0.999952i	$-0.503107\pi$
$227$	−13.2679	−	7.66025i	−0.880625	−	0.508429i	−0.870864	+	0.491523i	$0.836440\pi$
$228$	−5.46699	−	3.15637i	−0.362060	−	0.209036i
$229$		−	22.2644i		−	1.47127i	−0.677378	−	0.735635i	$-0.736884\pi$
$229$		−	22.2644i		−	1.47127i	0.677378	−	0.735635i	$-0.263116\pi$
$230$	0.622266	−	1.07780i	0.0410310	−	0.0710678i
$231$	−3.03978	−	5.26506i	−0.200003	−	0.346416i
$232$	−8.69904	+	5.02239i	−0.571120	+	0.329736i
$233$	10.8366			0.709928			0.354964	−	0.934880i	$-0.384493\pi$
$233$	10.8366			0.709928			0.354964	+	0.934880i	$0.384493\pi$
$234$	2.82233	−	2.24376i	0.184501	−	0.146679i
$235$	−6.82522			−0.445228
$236$	5.29034	−	3.05438i	0.344372	−	0.198823i
$237$	−4.96699	−	8.60308i	−0.322641	−	0.558830i
$238$	−7.28932	+	12.6255i	−0.472496	+	0.818388i
$239$			16.4975i			1.06714i	0.845757	+	0.533568i	$0.179149\pi$
$239$			16.4975i			1.06714i	−0.845757	+	0.533568i	$0.820851\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	3.81428	+	2.20218i	0.245700	+	0.141855i	0.617794	−	0.786340i	$-0.288027\pi$
$241$	3.81428	+	2.20218i	0.245700	+	0.141855i	−0.372094	+	0.928195i	$0.621360\pi$
$242$			8.21752i			0.528242i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.73205	+	6.46410i	0.238920	+	0.413822i
$245$	5.44171	−	3.14177i	0.347658	−	0.200720i
$246$	−9.28932			−0.592265
$247$	−3.35830	−	22.5118i	−0.213683	−	1.43239i
$248$	4.21957			0.267943
$249$	6.88764	−	3.97658i	0.436487	−	0.252006i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	5.97267	−	10.3450i	0.376992	−	0.652969i	−0.613631	−	0.789593i	$-0.710292\pi$
$251$	5.97267	−	10.3450i	0.376992	−	0.652969i	0.990623	+	0.136624i	$0.0436252\pi$
$252$		−	3.64466i		−	0.229592i
$253$	−1.79785	−	1.03799i	−0.113030	−	0.0652577i
$254$	12.5060	+	7.22034i	0.784696	+	0.453045i
$255$			4.00000i			0.250490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.73103	+	16.8546i	0.607005	+	1.05136i	0.991731	+	0.128333i	$0.0409625\pi$
$257$	9.73103	+	16.8546i	0.607005	+	1.05136i	−0.384726	+	0.923031i	$0.625704\pi$
$258$	6.55829	−	3.78643i	0.408301	−	0.235733i
$259$	−35.9518			−2.23393
$260$	0.531987	+	3.56609i	0.0329925	+	0.221159i
$261$	10.0448			0.621757
$262$	−9.43032	+	5.44460i	−0.582607	+	0.336368i
$263$	−1.01739	−	1.76217i	−0.0627350	−	0.108660i	0.832952	−	0.553345i	$-0.186649\pi$
$263$	−1.01739	−	1.76217i	−0.0627350	−	0.108660i	−0.895687	+	0.444685i	$0.853316\pi$
$264$	0.834038	−	1.44460i	0.0513315	−	0.0889087i
$265$			0.848634i			0.0521312i
$266$	−19.9253	−	11.5039i	−1.22170	−	0.705349i
$267$	−5.15425	−	2.97581i	−0.315435	−	0.182117i
$268$		−	14.7534i		−	0.901209i
$269$	−10.2644	+	17.7784i	−0.625829	+	1.08397i	0.362551	+	0.931964i	$0.381906\pi$
$269$	−10.2644	+	17.7784i	−0.625829	+	1.08397i	−0.988380	+	0.152003i	$0.951428\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	22.1184	−	12.7700i	1.34359	−	0.775725i	0.356261	−	0.934386i	$-0.384051\pi$
$271$	22.1184	−	12.7700i	1.34359	−	0.775725i	0.987333	+	0.158662i	$0.0507179\pi$
$272$	−4.00000			−0.242536
$273$	10.2864	−	8.17774i	0.622563	−	0.494939i
$274$	7.03696			0.425119
$275$	1.44460	−	0.834038i	0.0871124	−	0.0502944i
$276$	−0.622266	−	1.07780i	−0.0374560	−	0.0648758i
$277$	9.03019	−	15.6407i	0.542572	−	0.939762i	−0.456184	−	0.889886i	$-0.650784\pi$
$277$	9.03019	−	15.6407i	0.542572	−	0.939762i	0.998755	−	0.0498760i	$-0.0158826\pi$
$278$			11.6447i			0.698400i
$279$	−3.65425	−	2.10978i	−0.218774	−	0.126309i
$280$	3.15637	+	1.82233i	0.188629	+	0.108905i
$281$			20.2175i			1.20608i	0.797712	+	0.603038i	$0.206043\pi$
$281$			20.2175i			1.20608i	−0.797712	+	0.603038i	$0.793957\pi$
$282$	−3.41261	+	5.91081i	−0.203218	+	0.351984i
$283$	4.34575	+	7.52705i	0.258328	+	0.447437i	0.965794	−	0.259310i	$-0.0834952\pi$
$283$	4.34575	+	7.52705i	0.258328	+	0.447437i	−0.707466	+	0.706747i	$0.750162\pi$
$284$	−3.04056	+	1.75547i	−0.180424	+	0.104168i
$285$	−6.31274			−0.373934
$286$	5.94851	−	0.887395i	0.351743	−	0.0524728i
$287$	−33.8564			−1.99848
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−5.02239	+	8.69904i	−0.294925	+	0.510825i
$291$			2.75342i			0.161408i
$292$	10.5807	+	6.10876i	0.619188	+	0.357488i
$293$	6.53667	+	3.77395i	0.381876	+	0.220476i	0.678634	−	0.734476i	$-0.262572\pi$
$293$	6.53667	+	3.77395i	0.381876	+	0.220476i	−0.296758	+	0.954953i	$0.595905\pi$
$294$		−	6.28354i		−	0.366464i
$295$	3.05438	−	5.29034i	0.177833	−	0.308016i
$296$	−4.93211	−	8.54267i	−0.286673	−	0.496533i
$297$	−1.44460	+	0.834038i	−0.0838240	+	0.0483958i
$298$	−0.772609			−0.0447560
$299$	1.64568	−	4.17456i	0.0951723	−	0.241421i
$300$	1.00000			0.0577350
$301$	23.9027	−	13.8003i	1.37773	−	0.795433i
$302$	−4.88919	−	8.46833i	−0.281341	−	0.487298i
$303$	2.66808	−	4.62124i	0.153277	−	0.265483i
$304$		−	6.31274i		−	0.362060i
$305$	6.46410	+	3.73205i	0.370133	+	0.213697i
$306$	3.46410	+	2.00000i	0.198030	+	0.114332i
$307$			26.0427i			1.48634i	0.669104	+	0.743169i	$0.266678\pi$
$307$			26.0427i			1.48634i	−0.669104	+	0.743169i	$0.733322\pi$
$308$	3.03978	−	5.26506i	0.173208	−	0.300005i
$309$	3.75624	+	6.50600i	0.213685	+	0.370113i
$310$	3.65425	−	2.10978i	0.207548	−	0.119828i
$311$	25.3789			1.43910			0.719552	−	0.694438i	$-0.244347\pi$
$311$	25.3789			1.43910			0.719552	+	0.694438i	$0.244347\pi$
$312$	3.35432	+	1.32233i	0.189901	+	0.0748622i
$313$	−31.4600			−1.77822			−0.889112	−	0.457689i	$-0.848677\pi$
$313$	−31.4600			−1.77822			−0.889112	+	0.457689i	$0.848677\pi$
$314$	−10.4040	+	6.00677i	−0.587134	+	0.338982i
$315$	−1.82233	−	3.15637i	−0.102677	−	0.177841i
$316$	4.96699	−	8.60308i	0.279415	−	0.483961i
$317$		−	24.7093i		−	1.38781i	−0.720066	−	0.693905i	$-0.755889\pi$
$317$		−	24.7093i		−	1.38781i	0.720066	−	0.693905i	$-0.244111\pi$
$318$	0.734939	+	0.424317i	0.0412133	+	0.0237945i
$319$	14.5107	+	8.37773i	0.812441	+	0.469063i
$320$			1.00000i			0.0559017i
$321$	−8.46410	+	14.6603i	−0.472420	+	0.818256i
$322$	−2.26795	−	3.92820i	−0.126388	−	0.218910i
$323$	21.8680	−	12.6255i	1.21677	−	0.702500i
$324$	−1.00000			−0.0555556
$325$	2.24376	+	2.82233i	0.124461	+	0.156555i
$326$	−10.0916			−0.558923
$327$	0.574909	−	0.331924i	0.0317926	−	0.0183554i
$328$	−4.64466	−	8.04479i	−0.256458	−	0.444199i
$329$	−12.4378	+	21.5429i	−0.685718	+	1.18770i
$330$		−	1.66808i		−	0.0918246i
$331$	−4.85286	−	2.80180i	−0.266737	−	0.154001i	0.360667	−	0.932695i	$-0.382549\pi$
$331$	−4.85286	−	2.80180i	−0.266737	−	0.154001i	−0.627404	+	0.778694i	$0.715883\pi$
$332$	6.88764	+	3.97658i	0.378009	+	0.218243i
$333$			9.86423i			0.540556i
$334$	−3.94851	+	6.83902i	−0.216053	+	0.374214i
$335$	−7.37671	−	12.7768i	−0.403033	−	0.698073i
$336$	3.15637	−	1.82233i	0.172194	−	0.0994162i
$337$	21.7868			1.18680			0.593402	−	0.804906i	$-0.297784\pi$
$337$	21.7868			1.18680			0.593402	+	0.804906i	$0.297784\pi$
$338$	3.79423	+	12.4340i	0.206379	+	0.676319i
$339$	−17.8700			−0.970565
$340$	−3.46410	+	2.00000i	−0.187867	+	0.108465i
$341$	−3.51928	−	6.09557i	−0.190580	−	0.330094i
$342$	−3.15637	+	5.46699i	−0.170677	+	0.295621i
$343$			2.61124i			0.140994i
$344$	6.55829	+	3.78643i	0.353599	+	0.204151i
$345$	−1.07780	−	0.622266i	−0.0580266	−	0.0335017i
$346$			0.440685i			0.0236914i
$347$	−4.84081	+	8.38453i	−0.259868	+	0.450105i	−0.966206	−	0.257769i	$-0.917013\pi$
$347$	−4.84081	+	8.38453i	−0.259868	+	0.450105i	0.706338	+	0.707875i	$0.250346\pi$
$348$	5.02239	+	8.69904i	0.269229	+	0.466318i
$349$	16.7321	−	9.66025i	0.895646	−	0.517102i	0.0198610	−	0.999803i	$-0.493678\pi$
$349$	16.7321	−	9.66025i	0.895646	−	0.517102i	0.875785	+	0.482701i	$0.160344\pi$
$350$	3.64466			0.194815
$351$	−2.24376	−	2.82233i	−0.119763	−	0.150645i
$352$	1.66808			0.0889087
$353$	−19.8970	+	11.4875i	−1.05901	+	0.611419i	−0.925158	−	0.379583i	$-0.876068\pi$
$353$	−19.8970	+	11.4875i	−1.05901	+	0.611419i	−0.133851	+	0.991002i	$0.542734\pi$
$354$	−3.05438	−	5.29034i	−0.162338	−	0.281179i
$355$	−1.75547	+	3.04056i	−0.0931705	+	0.161376i
$356$		−	5.95162i		−	0.315435i
$357$	12.6255	+	7.28932i	0.668211	+	0.385792i
$358$	−17.0060	−	9.81842i	−0.898795	−	0.518920i
$359$		−	2.21752i		−	0.117036i	−0.998286	−	0.0585182i	$-0.981362\pi$
$359$		−	2.21752i		−	0.117036i	0.998286	−	0.0585182i	$-0.0186376\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	10.4253	+	18.0572i	0.548701	+	0.950378i
$362$	5.38453	−	3.10876i	0.283005	−	0.163393i
$363$	8.21752			0.431308
$364$	12.2253	+	4.81944i	0.640782	+	0.252607i
$365$	12.2175			0.639494
$366$	6.46410	−	3.73205i	0.337884	−	0.195077i
$367$	3.04056	+	5.26640i	0.158716	+	0.274904i	0.934406	−	0.356210i	$-0.115931\pi$
$367$	3.04056	+	5.26640i	0.158716	+	0.274904i	−0.775690	+	0.631114i	$0.782598\pi$
$368$	0.622266	−	1.07780i	0.0324379	−	0.0561841i
$369$			9.28932i			0.483583i
$370$	−8.54267	−	4.93211i	−0.444112	−	0.256408i
$371$	2.67860	+	1.54649i	0.139066	+	0.0802898i
$372$		−	4.21957i		−	0.218774i
$373$	−7.83904	+	13.5776i	−0.405890	+	0.703022i	−0.994425	−	0.105450i	$-0.966372\pi$
$373$	−7.83904	+	13.5776i	−0.405890	+	0.703022i	0.588535	+	0.808472i	$0.299705\pi$
$374$	3.33615	+	5.77838i	0.172508	+	0.298793i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$	−6.82522			−0.351984
$377$	−13.2825	+	33.6934i	−0.684085	+	1.73530i
$378$	−3.64466			−0.187461
$379$	26.6013	−	15.3583i	1.36642	−	0.788903i	0.375951	−	0.926640i	$-0.377316\pi$
$379$	26.6013	−	15.3583i	1.36642	−	0.788903i	0.990469	+	0.137737i	$0.0439829\pi$
$380$	−3.15637	−	5.46699i	−0.161918	−	0.280451i
$381$	7.22034	−	12.5060i	0.369909	−	0.640702i
$382$			15.6816i			0.802342i
$383$	17.3741	+	10.0310i	0.887777	+	0.512558i	0.873215	−	0.487336i	$-0.162031\pi$
$383$	17.3741	+	10.0310i	0.887777	+	0.512558i	0.0145623	+	0.999894i	$0.495365\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		−	6.07957i		−	0.309844i
$386$	4.06397	−	7.03901i	0.206851	−	0.358276i
$387$	−3.78643	−	6.55829i	−0.192475	−	0.333377i
$388$	−2.38453	+	1.37671i	−0.121056	+	0.0698919i
$389$	27.0314			1.37055			0.685273	−	0.728287i	$-0.259683\pi$
$389$	27.0314			1.37055			0.685273	+	0.728287i	$0.259683\pi$
$390$	3.56609	−	0.531987i	0.180576	−	0.0269382i
$391$	4.97813			0.251755
$392$	5.44171	−	3.14177i	0.274848	−	0.158683i
$393$	5.44460	+	9.43032i	0.274644	+	0.475697i
$394$	0.445619	−	0.771835i	0.0224500	−	0.0388845i
$395$		−	9.93398i		−	0.499833i
$396$	−1.44460	−	0.834038i	−0.0725937	−	0.0419120i
$397$	−3.23571	−	1.86814i	−0.162396	−	0.0937592i	0.416600	−	0.909090i	$-0.363222\pi$
$397$	−3.23571	−	1.86814i	−0.162396	−	0.0937592i	−0.578995	+	0.815331i	$0.696555\pi$
$398$		−	0.361116i		−	0.0181011i
$399$	−11.5039	+	19.9253i	−0.575915	+	0.997513i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	24.3276	−	14.0456i	1.21486	−	0.701402i	0.251049	−	0.967974i	$-0.419225\pi$
$401$	24.3276	−	14.0456i	1.21486	−	0.701402i	0.963815	+	0.266573i	$0.0858912\pi$
$402$	−14.7534			−0.735834
$403$	11.9090	−	9.46770i	0.593230	−	0.471620i
$404$	5.33615			0.265483
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	18.3049	+	31.7050i	0.908458	+	1.57349i
$407$	−8.22714	+	14.2498i	−0.407804	+	0.706338i
$408$			4.00000i			0.198030i
$409$	23.7122	+	13.6902i	1.17249	+	0.676938i	0.954265	−	0.298961i	$-0.0966399\pi$
$409$	23.7122	+	13.6902i	1.17249	+	0.676938i	0.218225	+	0.975898i	$0.429973\pi$
$410$	−8.04479	−	4.64466i	−0.397304	−	0.229383i
$411$		−	7.03696i		−	0.347108i
$412$	−3.75624	+	6.50600i	−0.185057	+	0.320528i
$413$	−11.1322	−	19.2815i	−0.547779	−	0.948780i
$414$	−1.07780	+	0.622266i	−0.0529708	+	0.0305827i
$415$	7.95317			0.390406
$416$	0.531987	+	3.56609i	0.0260828	+	0.174842i
$417$	11.6447			0.570241
$418$	−9.11935	+	5.26506i	−0.446042	+	0.257523i
$419$	6.58068	+	11.3981i	0.321487	+	0.556833i	0.980795	−	0.195041i	$-0.0624839\pi$
$419$	6.58068	+	11.3981i	0.321487	+	0.556833i	−0.659308	+	0.751873i	$0.729151\pi$
$420$	1.82233	−	3.15637i	0.0889206	−	0.154015i
$421$		−	1.29341i		−	0.0630370i	−0.999503	−	0.0315185i	$-0.989966\pi$
$421$		−	1.29341i		−	0.0630370i	0.999503	−	0.0315185i	$-0.0100343\pi$
$422$	−1.92898	−	1.11370i	−0.0939011	−	0.0542138i
$423$	5.91081	+	3.41261i	0.287394	+	0.165927i
$424$			0.848634i			0.0412133i
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$	1.75547	+	3.04056i	0.0850527	+	0.147316i
$427$	23.5595	−	13.6021i	1.14012	−	0.658250i
$428$	−16.9282			−0.818256
$429$	−0.887395	−	5.94851i	−0.0428439	−	0.287197i
$430$	7.57286			0.365196
$431$	10.5031	−	6.06397i	0.505917	−	0.292091i	−0.225237	−	0.974304i	$-0.572316\pi$
$431$	10.5031	−	6.06397i	0.505917	−	0.292091i	0.731154	+	0.682213i	$0.238982\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−1.03901	+	1.79962i	−0.0499317	+	0.0864842i	−0.889911	−	0.456134i	$-0.849234\pi$
$433$	−1.03901	+	1.79962i	−0.0499317	+	0.0864842i	0.839979	+	0.542618i	$0.182567\pi$
$434$		−	15.3789i		−	0.738210i
$435$	8.69904	+	5.02239i	0.417087	+	0.240805i
$436$	0.574909	+	0.331924i	0.0275332	+	0.0158963i
$437$			7.85641i			0.375823i
$438$	6.10876	−	10.5807i	0.291888	−	0.505565i
$439$	−1.19820	−	2.07534i	−0.0571869	−	0.0990506i	0.836015	−	0.548707i	$-0.184880\pi$
$439$	−1.19820	−	2.07534i	−0.0571869	−	0.0990506i	−0.893202	+	0.449656i	$0.851546\pi$
$440$	1.44460	−	0.834038i	0.0688684	−	0.0397612i
$441$	−6.28354			−0.299216
$442$	−11.2893	+	8.97504i	−0.536978	+	0.426899i
$443$	21.9959			1.04506			0.522529	−	0.852622i	$-0.324989\pi$
$443$	21.9959			1.04506			0.522529	+	0.852622i	$0.324989\pi$
$444$	−8.54267	+	4.93211i	−0.405417	+	0.234068i
$445$	−2.97581	−	5.15425i	−0.141067	−	0.244335i
$446$	3.04190	−	5.26872i	0.144038	−	0.249481i
$447$			0.772609i			0.0365432i
$448$	3.15637	+	1.82233i	0.149124	+	0.0860970i
$449$	25.3098	+	14.6126i	1.19445	+	0.689613i	0.959312	−	0.282350i	$-0.0911138\pi$
$449$	25.3098	+	14.6126i	1.19445	+	0.689613i	0.235134	+	0.971963i	$0.424447\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−7.74765	+	13.4193i	−0.364822	+	0.631891i
$452$	−8.93500	−	15.4759i	−0.420267	−	0.727924i
$453$	−8.46833	+	4.88919i	−0.397877	+	0.229714i
$454$	−15.3205			−0.719027
$455$	12.9972	−	1.93891i	0.609317	−	0.0908976i
$456$	−6.31274			−0.295621
$457$	−34.3321	+	19.8216i	−1.60599	+	0.927216i	−0.615730	+	0.787957i	$0.711139\pi$
$457$	−34.3321	+	19.8216i	−1.60599	+	0.927216i	−0.990256	+	0.139259i	$0.955528\pi$
$458$	−11.1322	−	19.2815i	−0.520172	−	0.900965i
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		−	1.24453i		−	0.0580266i
$461$	14.4417	+	8.33792i	0.672617	+	0.388336i	0.797068	−	0.603890i	$-0.206383\pi$
$461$	14.4417	+	8.33792i	0.672617	+	0.388336i	−0.124450	+	0.992226i	$0.539717\pi$
$462$	−5.26506	−	3.03978i	−0.244953	−	0.141424i
$463$			32.2175i			1.49728i	0.662979	+	0.748638i	$0.269292\pi$
$463$			32.2175i			1.49728i	−0.662979	+	0.748638i	$0.730708\pi$
$464$	−5.02239	+	8.69904i	−0.233159	+	0.403843i
$465$	−2.10978	−	3.65425i	−0.0978389	−	0.169462i
$466$	9.38476	−	5.41829i	0.434740	−	0.250998i
$467$	−6.88137			−0.318432			−0.159216	−	0.987244i	$-0.550897\pi$
$467$	−6.88137			−0.318432			−0.159216	+	0.987244i	$0.550897\pi$
$468$	1.32233	−	3.35432i	0.0611247	−	0.155053i
$469$	−53.7712			−2.48292
$470$	−5.91081	+	3.41261i	−0.272645	+	0.157412i
$471$	6.00677	+	10.4040i	0.276778	+	0.479393i
$472$	3.05438	−	5.29034i	0.140589	−	0.243508i
$473$		−	12.6321i		−	0.580825i
$474$	−8.60308	−	4.96699i	−0.395152	−	0.228141i
$475$	−5.46699	−	3.15637i	−0.250843	−	0.144824i
$476$			14.5786i			0.668211i
$477$	0.424317	−	0.734939i	0.0194281	−	0.0336505i
$478$	8.24876	+	14.2873i	0.377290	+	0.653485i
$479$	−16.4293	+	9.48547i	−0.750675	+	0.433402i	−0.825938	−	0.563761i	$-0.809354\pi$
$479$	−16.4293	+	9.48547i	−0.750675	+	0.433402i	0.0752629	+	0.997164i	$0.476020\pi$
$480$	1.00000			0.0456435
$481$	−33.0878	−	13.0438i	−1.50867	−	0.594744i
$482$	4.40435			0.200613
$483$	−3.92820	+	2.26795i	−0.178739	+	0.103195i
$484$	4.10876	+	7.11658i	0.186762	+	0.323481i
$485$	−1.37671	+	2.38453i	−0.0625132	+	0.108276i
$486$			1.00000i			0.0453609i
$487$	1.65948	+	0.958101i	0.0751982	+	0.0434157i	0.537128	−	0.843501i	$-0.319509\pi$
$487$	1.65948	+	0.958101i	0.0751982	+	0.0434157i	−0.461929	+	0.886917i	$0.652843\pi$
$488$	6.46410	+	3.73205i	0.292616	+	0.168942i
$489$			10.0916i			0.456359i
$490$	3.14177	−	5.44171i	0.141931	−	0.245831i
$491$	−16.8187	−	29.1309i	−0.759019	−	1.31466i	−0.943351	−	0.331795i	$-0.892346\pi$
$491$	−16.8187	−	29.1309i	−0.759019	−	1.31466i	0.184332	−	0.982864i	$-0.440988\pi$
$492$	−8.04479	+	4.64466i	−0.362687	+	0.209397i
$493$	−40.1791			−1.80958
$494$	−14.1643	−	17.8166i	−0.637280	−	0.801608i
$495$	−1.66808			−0.0749744
$496$	3.65425	−	2.10978i	0.164081	−	0.0947321i
$497$	6.39808	+	11.0818i	0.286993	+	0.497087i
$498$	3.97658	−	6.88764i	0.178195	−	0.308643i
$499$		−	1.82522i		−	0.0817080i	−0.999165	−	0.0408540i	$-0.986992\pi$
$499$		−	1.82522i		−	0.0817080i	0.999165	−	0.0408540i	$-0.0130078\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	6.83902	+	3.94851i	0.305545	+	0.176406i
$502$		−	11.9453i		−	0.533147i
$503$	9.99923	−	17.3192i	0.445843	−	0.772224i	−0.552267	−	0.833667i	$-0.686237\pi$
$503$	9.99923	−	17.3192i	0.445843	−	0.772224i	0.998111	+	0.0614437i	$0.0195705\pi$
$504$	−1.82233	−	3.15637i	−0.0811730	−	0.140596i
$505$	4.62124	−	2.66808i	0.205643	−	0.118728i
$506$	−2.07598			−0.0922884
$507$	12.4340	−	3.79423i	0.552212	−	0.168508i
$508$	14.4407			0.640702
$509$	5.10196	−	2.94562i	0.226141	−	0.130562i	−0.382650	−	0.923893i	$-0.624988\pi$
$509$	5.10196	−	2.94562i	0.226141	−	0.130562i	0.608790	+	0.793331i	$0.291655\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	22.2644	−	38.5630i	0.984917	−	1.70593i
$512$			1.00000i			0.0441942i
$513$	5.46699	+	3.15637i	0.241373	+	0.139357i
$514$	16.8546	+	9.73103i	0.743426	+	0.429217i
$515$			7.51248i			0.331040i
$516$	3.78643	−	6.55829i	0.166688	−	0.288713i
$517$	5.69249	+	9.85968i	0.250355	+	0.433628i
$518$	−31.1351	+	17.9759i	−1.36800	+	0.789815i
$519$	0.440685			0.0193439
$520$	2.24376	+	2.82233i	0.0983953	+	0.123767i
$521$	32.0370			1.40356			0.701782	−	0.712391i	$-0.252388\pi$
$521$	32.0370			1.40356			0.701782	+	0.712391i	$0.252388\pi$
$522$	8.69904	−	5.02239i	0.380747	−	0.219824i
$523$	−19.3593	−	33.5313i	−0.846523	−	1.46622i	−0.884292	−	0.466934i	$-0.845359\pi$
$523$	−19.3593	−	33.5313i	−0.846523	−	1.46622i	0.0377693	−	0.999286i	$-0.487975\pi$
$524$	−5.44460	+	9.43032i	−0.237848	+	0.411965i
$525$		−	3.64466i		−	0.159066i
$526$	−1.76217	−	1.01739i	−0.0768344	−	0.0443604i
$527$	14.6170	+	8.43914i	0.636727	+	0.367615i
$528$		−	1.66808i		−	0.0725937i
$529$	10.7256	−	18.5772i	0.466329	−	0.807706i
$530$	0.424317	+	0.734939i	0.0184312	+	0.0319237i
$531$	−5.29034	+	3.05438i	−0.229581	+	0.132549i
$532$	−23.0078			−0.997513
$533$	−31.1593	−	12.2835i	−1.34966	−	0.532059i
$534$	−5.95162			−0.257552
$535$	−14.6603	+	8.46410i	−0.633818	+	0.365935i
$536$	−7.37671	−	12.7768i	−0.318625	−	0.551875i
$537$	−9.81842	+	17.0060i	−0.423696	+	0.733863i
$538$			20.5287i			0.885056i
$539$	−9.07718	−	5.24071i	−0.390982	−	0.225734i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$		−	25.9616i		−	1.11618i	−0.829781	−	0.558089i	$-0.811535\pi$
$541$		−	25.9616i		−	1.11618i	0.829781	−	0.558089i	$-0.188465\pi$
$542$	12.7700	−	22.1184i	0.548520	−	0.950065i
$543$	−3.10876	−	5.38453i	−0.133410	−	0.231072i
$544$	−3.46410	+	2.00000i	−0.148522	+	0.0857493i
$545$	0.663848			0.0284361
$546$	4.81944	−	12.2253i	0.206253	−	0.523196i
$547$	−17.7596			−0.759348			−0.379674	−	0.925120i	$-0.623964\pi$
$547$	−17.7596			−0.759348			−0.379674	+	0.925120i	$0.623964\pi$
$548$	6.09419	−	3.51848i	0.260331	−	0.150302i
$549$	−3.73205	−	6.46410i	−0.159280	−	0.275881i
$550$	0.834038	−	1.44460i	0.0355635	−	0.0615978i
$551$		−	63.4101i		−	2.70136i
$552$	−1.07780	−	0.622266i	−0.0458741	−	0.0264854i
$553$	−31.3553	−	18.1030i	−1.33336	−	0.769817i
$554$		−	18.0604i		−	0.767312i
$555$	−4.93211	+	8.54267i	−0.209357	+	0.362616i
$556$	5.82233	+	10.0846i	0.246922	+	0.427681i
$557$	−22.7074	+	13.1101i	−0.962142	+	0.555493i	−0.896832	−	0.442372i	$-0.854137\pi$
$557$	−22.7074	+	13.1101i	−0.962142	+	0.555493i	−0.0653102	+	0.997865i	$0.520804\pi$
$558$	−4.21957			−0.178629
$559$	27.0055	−	4.02867i	1.14221	−	0.170394i
$560$	3.64466			0.154015
$561$	5.77838	−	3.33615i	0.243964	−	0.140852i
$562$	10.1088	+	17.5089i	0.426412	+	0.738568i
$563$	−12.9964	+	22.5104i	−0.547733	+	0.948702i	0.450696	+	0.892677i	$0.351176\pi$
$563$	−12.9964	+	22.5104i	−0.547733	+	0.948702i	−0.998429	+	0.0560243i	$0.982158\pi$
$564$			6.82522i			0.287394i
$565$	−15.4759	−	8.93500i	−0.651075	−	0.375898i
$566$	7.52705	+	4.34575i	0.316386	+	0.182665i
$567$			3.64466i			0.153061i
$568$	−1.75547	+	3.04056i	−0.0736578	+	0.127579i
$569$	−12.7349	−	22.0576i	−0.533876	−	0.924701i	−0.999217	−	0.0395693i	$-0.987401\pi$
$569$	−12.7349	−	22.0576i	−0.533876	−	0.924701i	0.465340	−	0.885132i	$-0.345932\pi$
$570$	−5.46699	+	3.15637i	−0.228987	+	0.132206i
$571$	−8.44491			−0.353409			−0.176704	−	0.984264i	$-0.556544\pi$
$571$	−8.44491			−0.353409			−0.176704	+	0.984264i	$0.556544\pi$
$572$	4.70786	−	3.74276i	0.196846	−	0.156493i
$573$	15.6816			0.655109
$574$	−29.3205	+	16.9282i	−1.22381	+	0.706570i
$575$	−0.622266	−	1.07780i	−0.0259503	−	0.0449472i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			35.4216i			1.47462i	0.675554	+	0.737311i	$0.263905\pi$
$577$			35.4216i			1.47462i	−0.675554	+	0.737311i	$0.736095\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$	−7.03901	−	4.06397i	−0.292531	−	0.168893i
$580$			10.0448i			0.417087i
$581$	14.4933	−	25.1031i	0.601283	−	1.04145i
$582$	1.37671	+	2.38453i	0.0570665	+	0.0988420i
$583$	1.22593	−	0.707793i	0.0507730	−	0.0293138i
$584$	12.2175			0.505565
$585$	−0.531987	−	3.56609i	−0.0219950	−	0.147440i
$586$	7.54790			0.311801
$587$	23.7108	−	13.6894i	0.978650	−	0.565024i	0.0767878	−	0.997047i	$-0.475534\pi$
$587$	23.7108	−	13.6894i	0.978650	−	0.565024i	0.901862	+	0.432024i	$0.142200\pi$
$588$	−3.14177	−	5.44171i	−0.129564	−	0.224412i
$589$	−13.3185	+	23.0683i	−0.548780	+	0.950514i
$590$		−	6.10876i		−	0.251494i
$591$	−0.771835	−	0.445619i	−0.0317491	−	0.0183303i
$592$	−8.54267	−	4.93211i	−0.351102	−	0.202709i
$593$		−	12.0619i		−	0.495324i	−0.968846	−	0.247662i	$-0.920338\pi$
$593$		−	12.0619i		−	0.495324i	0.968846	−	0.247662i	$-0.0796623\pi$
$594$	−0.834038	+	1.44460i	−0.0342210	+	0.0592725i
$595$	7.28932	+	12.6255i	0.298833	+	0.517594i
$596$	−0.669099	+	0.386305i	−0.0274074	+	0.0158237i
$597$	−0.361116			−0.0147795
$598$	−0.662076	−	4.43811i	−0.0270743	−	0.181488i
$599$	−28.6129			−1.16909			−0.584546	−	0.811360i	$-0.698727\pi$
$599$	−28.6129			−1.16909			−0.584546	+	0.811360i	$0.698727\pi$
$600$	0.866025	−	0.500000i	0.0353553	−	0.0204124i
$601$	9.58380	+	16.5996i	0.390931	+	0.677113i	0.992573	−	0.121654i	$-0.0388197\pi$
$601$	9.58380	+	16.5996i	0.390931	+	0.677113i	−0.601641	+	0.798766i	$0.705486\pi$
$602$	13.8003	−	23.9027i	0.562456	−	0.974203i
$603$			14.7534i			0.600806i
$604$	−8.46833	−	4.88919i	−0.344571	−	0.198938i
$605$	7.11658	+	4.10876i	0.289330	+	0.167045i
$606$		−	5.33615i		−	0.216766i
$607$	−9.46910	+	16.4010i	−0.384339	+	0.665695i	−0.991677	−	0.128749i	$-0.958904\pi$
$607$	−9.46910	+	16.4010i	−0.384339	+	0.665695i	0.607338	+	0.794443i	$0.292237\pi$
$608$	−3.15637	−	5.46699i	−0.128008	−	0.221716i
$609$	31.7050	−	18.3049i	1.28475	−	0.741753i
$610$	7.46410			0.302213
$611$	−19.2630	+	15.3141i	−0.779298	+	0.619544i
$612$	4.00000			0.161690
$613$	−15.5620	+	8.98472i	−0.628543	+	0.362890i	−0.780188	−	0.625546i	$-0.784876\pi$
$613$	−15.5620	+	8.98472i	−0.628543	+	0.362890i	0.151645	+	0.988435i	$0.451543\pi$
$614$	13.0214	+	22.5537i	0.525500	+	0.910192i
$615$	−4.64466	+	8.04479i	−0.187291	+	0.324397i
$616$		−	6.07957i		−	0.244953i
$617$	−15.6015	−	9.00755i	−0.628094	−	0.362630i	0.151920	−	0.988393i	$-0.451455\pi$
$617$	−15.6015	−	9.00755i	−0.628094	−	0.362630i	−0.780014	+	0.625763i	$0.784788\pi$
$618$	6.50600	+	3.75624i	0.261710	+	0.151098i
$619$		−	25.0505i		−	1.00687i	−0.864035	−	0.503433i	$-0.832070\pi$
$619$		−	25.0505i		−	1.00687i	0.864035	−	0.503433i	$-0.167930\pi$
$620$	2.10978	−	3.65425i	0.0847310	−	0.146758i
$621$	0.622266	+	1.07780i	0.0249707	+	0.0432505i
$622$	21.9788	−	12.6894i	0.881268	−	0.508800i
$623$	−21.6916			−0.869057
$624$	3.56609	−	0.531987i	0.142758	−	0.0212965i
$625$	1.00000			0.0400000
$626$	−27.2452	+	15.7300i	−1.08894	+	0.628697i
$627$	5.26506	+	9.11935i	0.210266	+	0.364192i
$628$	−6.00677	+	10.4040i	−0.239696	+	0.415166i
$629$		−	39.4569i		−	1.57325i
$630$	−3.15637	−	1.82233i	−0.125753	−	0.0726034i
$631$	−1.22739	−	0.708634i	−0.0488617	−	0.0282103i	0.475370	−	0.879786i	$-0.342314\pi$
$631$	−1.22739	−	0.708634i	−0.0488617	−	0.0282103i	−0.524232	+	0.851576i	$0.675647\pi$
$632$		−	9.93398i		−	0.395152i
$633$	−1.11370	+	1.92898i	−0.0442654	+	0.0766700i
$634$	−12.3546	−	21.3989i	−0.490665	−	0.849857i
$635$	12.5060	−	7.22034i	0.496285	−	0.286531i
$636$	0.848634			0.0336505
$637$	8.30892	−	21.0770i	0.329211	−	0.835101i
$638$	16.7555			0.663355
$639$	3.04056	−	1.75547i	0.120283	−	0.0694452i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	2.30985	−	4.00077i	0.0912335	−	0.158021i	−0.816797	−	0.576925i	$-0.804252\pi$
$641$	2.30985	−	4.00077i	0.0912335	−	0.158021i	0.908030	+	0.418904i	$0.137586\pi$
$642$			16.9282i			0.668103i
$643$	41.6468	+	24.0448i	1.64239	+	0.948234i	0.979981	+	0.199091i	$0.0637988\pi$
$643$	41.6468	+	24.0448i	1.64239	+	0.948234i	0.662408	+	0.749143i	$0.269535\pi$
$644$	−3.92820	−	2.26795i	−0.154793	−	0.0893697i
$645$		−	7.57286i		−	0.298181i
$646$	12.6255	−	21.8680i	0.496743	−	0.860383i
$647$	1.87282	+	3.24383i	0.0736283	+	0.127528i	0.900489	−	0.434879i	$-0.143209\pi$
$647$	1.87282	+	3.24383i	0.0736283	+	0.127528i	−0.826861	+	0.562407i	$0.809875\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−10.1899			−0.399988
$650$	3.35432	+	1.32233i	0.131567	+	0.0518660i
$651$	−15.3789			−0.602746
$652$	−8.73960	+	5.04581i	−0.342269	+	0.197609i
$653$	−21.1450	−	36.6241i	−0.827466	−	1.43321i	−0.900020	−	0.435849i	$-0.856448\pi$
$653$	−21.1450	−	36.6241i	−0.827466	−	1.43321i	0.0725541	−	0.997364i	$-0.476885\pi$
$654$	0.331924	−	0.574909i	0.0129793	−	0.0224807i
$655$			10.8892i			0.425476i
$656$	−8.04479	−	4.64466i	−0.314096	−	0.181343i
$657$	−10.5807	−	6.10876i	−0.412792	−	0.238325i
$658$			24.8756i			0.969752i
$659$	14.5875	−	25.2663i	0.568248	−	0.984234i	−0.428492	−	0.903546i	$-0.640955\pi$
$659$	14.5875	−	25.2663i	0.568248	−	0.984234i	0.996739	−	0.0806881i	$-0.0257118\pi$
$660$	−0.834038	−	1.44460i	−0.0324649	−	0.0562308i
$661$	−38.5089	+	22.2331i	−1.49782	+	0.864768i	−0.999997	−	0.00250931i	$-0.999201\pi$
$661$	−38.5089	+	22.2331i	−1.49782	+	0.864768i	−0.497825	+	0.867277i	$0.665868\pi$
$662$	−5.60360			−0.217790
$663$	8.97504	+	11.2893i	0.348562	+	0.438441i
$664$	7.95317			0.308643
$665$	−19.9253	+	11.5039i	−0.772671	+	0.446102i
$666$	4.93211	+	8.54267i	0.191116	+	0.331022i
$667$	6.25053	−	10.8262i	0.242022	−	0.419194i
$668$			7.89701i			0.305545i
$669$	−5.26872	−	3.04190i	−0.203701	−	0.117607i
$670$	−12.7768	−	7.37671i	−0.493612	−	0.284987i
$671$		−	12.4507i		−	0.480654i
$672$	1.82233	−	3.15637i	0.0702979	−	0.121760i
$673$	3.95317	+	6.84709i	0.152383	+	0.263936i	0.932103	−	0.362193i	$-0.117972\pi$
$673$	3.95317	+	6.84709i	0.152383	+	0.263936i	−0.779720	+	0.626129i	$0.784638\pi$
$674$	18.8680	−	10.8934i	0.726767	−	0.419599i
$675$	−1.00000			−0.0384900
$676$	9.50289	+	8.87103i	0.365496	+	0.341193i
$677$	−7.05615			−0.271190			−0.135595	−	0.990764i	$-0.543295\pi$
$677$	−7.05615			−0.271190			−0.135595	+	0.990764i	$0.543295\pi$
$678$	−15.4759	+	8.93500i	−0.594347	+	0.343147i
$679$	5.01764	+	8.69081i	0.192559	+	0.333523i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$			15.3205i			0.587083i
$682$	−6.09557	−	3.51928i	−0.233412	−	0.134760i
$683$	−5.15559	−	2.97658i	−0.197273	−	0.113896i	0.398110	−	0.917338i	$-0.369666\pi$
$683$	−5.15559	−	2.97658i	−0.197273	−	0.113896i	−0.595383	+	0.803442i	$0.703000\pi$
$684$			6.31274i			0.241373i
$685$	3.51848	−	6.09419i	0.134434	−	0.232847i
$686$	1.30562	+	2.26140i	0.0498488	+	0.0863406i
$687$	−19.2815	+	11.1322i	−0.735635	+	0.424719i
$688$	7.57286			0.288713
$689$	1.90413	+	2.39513i	0.0725416	+	0.0912470i
$690$	−1.24453			−0.0473786
$691$	16.2458	−	9.37953i	0.618020	−	0.356814i	−0.158078	−	0.987427i	$-0.550530\pi$
$691$	16.2458	−	9.37953i	0.618020	−	0.356814i	0.776098	+	0.630613i	$0.217196\pi$
$692$	0.220343	+	0.381645i	0.00837617	+	0.0145080i
$693$	−3.03978	+	5.26506i	−0.115472	+	0.200003i
$694$			9.68162i			0.367509i
$695$	10.0846	+	5.82233i	0.382530	+	0.220854i
$696$	8.69904	+	5.02239i	0.329736	+	0.190373i
$697$		−	37.1573i		−	1.40743i
$698$	9.66025	−	16.7321i	0.365646	−	0.633317i
$699$	−5.41829	−	9.38476i	−0.204939	−	0.354964i
$700$	3.15637	−	1.82233i	0.119299	−	0.0688776i
$701$	−28.5298			−1.07755			−0.538777	−	0.842448i	$-0.681113\pi$
$701$	−28.5298			−1.07755			−0.538777	+	0.842448i	$0.681113\pi$
$702$	−3.35432	−	1.32233i	−0.126601	−	0.0499081i
$703$	62.2703			2.34857
$704$	1.44460	−	0.834038i	0.0544453	−	0.0314340i
$705$	3.41261	+	5.91081i	0.128526	+	0.222614i
$706$	−11.4875	+	19.8970i	−0.432338	+	0.748832i
$707$		−	19.4485i		−	0.731435i
$708$	−5.29034	−	3.05438i	−0.198823	−	0.114791i
$709$	−20.0853	−	11.5963i	−0.754321	−	0.435507i	0.0729321	−	0.997337i	$-0.476764\pi$
$709$	−20.0853	−	11.5963i	−0.754321	−	0.435507i	−0.827253	+	0.561830i	$0.810098\pi$
$710$			3.51093i			0.131763i
$711$	−4.96699	+	8.60308i	−0.186277	+	0.322641i
$712$	−2.97581	−	5.15425i	−0.111523	−	0.193164i
$713$	−4.54784	+	2.62570i	−0.170318	+	0.0983331i
$714$	14.5786			0.545592
$715$	2.20575	−	5.59526i	0.0824902	−	0.209251i
$716$	−19.6368			−0.733863
$717$	14.2873	−	8.24876i	0.533568	−	0.308056i
$718$	−1.10876	−	1.92043i	−0.0413786	−	0.0716698i
$719$	5.85641	−	10.1436i	0.218407	−	0.378292i	−0.735914	−	0.677075i	$-0.763247\pi$
$719$	5.85641	−	10.1436i	0.218407	−	0.378292i	0.954321	+	0.298783i	$0.0965806\pi$
$720$		−	1.00000i		−	0.0372678i
$721$	23.7122	+	13.6902i	0.883087	+	0.509850i
$722$	18.0572	+	10.4253i	0.672019	+	0.387990i
$723$		−	4.40435i		−	0.163800i
$724$	3.10876	−	5.38453i	0.115536	−	0.200115i
$725$	5.02239	+	8.69904i	0.186527	+	0.323074i
$726$	7.11658	−	4.10876i	0.264121	−	0.152490i
$727$	3.82677			0.141927			0.0709634	−	0.997479i	$-0.477393\pi$
$727$	3.82677			0.141927			0.0709634	+	0.997479i	$0.477393\pi$
$728$	12.9972	−	1.93891i	0.481708	−	0.0718609i
$729$	1.00000			0.0370370
$730$	10.5807	−	6.10876i	0.391609	−	0.226095i
$731$	15.1457	+	26.2332i	0.560185	+	0.970269i
$732$	3.73205	−	6.46410i	0.137941	−	0.238920i
$733$		−	12.9340i		−	0.477727i	−0.971053	−	0.238864i	$-0.923225\pi$
$733$		−	12.9340i		−	0.477727i	0.971053	−	0.238864i	$-0.0767749\pi$
$734$	5.26640	+	3.04056i	0.194386	+	0.112229i
$735$	−5.44171	−	3.14177i	−0.200720	−	0.115886i
$736$		−	1.24453i		−	0.0458741i
$737$	−12.3049	+	21.3127i	−0.453257	+	0.785065i
$738$	4.64466	+	8.04479i	0.170972	+	0.296133i
$739$	−30.6107	+	17.6731i	−1.12603	+	0.650115i	−0.942934	−	0.332980i	$-0.891946\pi$
$739$	−30.6107	+	17.6731i	−1.12603	+	0.650115i	−0.183098	+	0.983095i	$0.558612\pi$
$740$	−9.86423			−0.362616
$741$	−17.8166	+	14.1643i	−0.654510	+	0.520337i
$742$	3.09298			0.113547
$743$	−32.1255	+	18.5477i	−1.17857	+	0.680448i	−0.955684	−	0.294396i	$-0.904882\pi$
$743$	−32.1255	+	18.5477i	−1.17857	+	0.680448i	−0.222887	+	0.974844i	$0.571548\pi$
$744$	−2.10978	−	3.65425i	−0.0773484	−	0.133971i
$745$	−0.386305	+	0.669099i	−0.0141531	+	0.0245139i
$746$			15.6781i			0.574015i
$747$	−6.88764	−	3.97658i	−0.252006	−	0.145496i
$748$	5.77838	+	3.33615i	0.211279	+	0.121982i
$749$			61.6975i			2.25438i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−4.82904	−	8.36414i	−0.176214	−	0.305212i	0.764367	−	0.644782i	$-0.223052\pi$
$751$	−4.82904	−	8.36414i	−0.176214	−	0.305212i	−0.940581	+	0.339570i	$0.889718\pi$
$752$	−5.91081	+	3.41261i	−0.215545	+	0.124445i
$753$	−11.9453			−0.435313
$754$	5.34370	+	35.8206i	0.194606	+	1.30451i
$755$	−9.77838			−0.355872
$756$	−3.15637	+	1.82233i	−0.114796	+	0.0662775i
$757$	21.8443	+	37.8354i	0.793943	+	1.37515i	0.923508	+	0.383579i	$0.125309\pi$
$757$	21.8443	+	37.8354i	0.793943	+	1.37515i	−0.129565	+	0.991571i	$0.541358\pi$
$758$	15.3583	−	26.6013i	0.557838	−	0.966204i
$759$			2.07598i			0.0753531i
$760$	−5.46699	−	3.15637i	−0.198309	−	0.114493i
$761$	34.5550	+	19.9503i	1.25262	+	0.723200i	0.971629	−	0.236511i	$-0.0760040\pi$
$761$	34.5550	+	19.9503i	1.25262	+	0.723200i	0.280990	+	0.959711i	$0.409337\pi$
$762$		−	14.4407i		−	0.523131i
$763$	1.20975	−	2.09535i	0.0437959	−	0.0758567i
$764$	7.84081	+	13.5807i	0.283671	+	0.491332i
$765$	3.46410	−	2.00000i	0.125245	−	0.0723102i
$766$	20.0619			0.724867
$767$	−3.24978	−	21.7844i	−0.117343	−	0.786589i
$768$	1.00000			0.0360844
$769$	−15.2064	+	8.77941i	−0.548356	+	0.316594i	−0.748459	−	0.663181i	$-0.769206\pi$
$769$	−15.2064	+	8.77941i	−0.548356	+	0.316594i	0.200103	+	0.979775i	$0.435872\pi$
$770$	−3.03978	−	5.26506i	−0.109546	−	0.189740i
$771$	9.73103	−	16.8546i	0.350454	−	0.607005i
$772$		−	8.12795i		−	0.292531i
$773$	11.1174	+	6.41861i	0.399864	+	0.230861i	0.686425	−	0.727201i	$-0.259179\pi$
$773$	11.1174	+	6.41861i	0.399864	+	0.230861i	−0.286562	+	0.958062i	$0.592512\pi$
$774$	−6.55829	−	3.78643i	−0.235733	−	0.136100i
$775$		−	4.21957i		−	0.151571i
$776$	−1.37671	+	2.38453i	−0.0494210	+	0.0855997i
$777$	17.9759	+	31.1351i	0.644881	+	1.11697i
$778$	23.4099	−	13.5157i	0.839284	−	0.484561i
$779$	58.6410			2.10103
$780$	2.82233	−	2.24376i	0.101056	−	0.0803395i
$781$	5.85651			0.209562
$782$	4.31119	−	2.48907i	0.154168	−	0.0890088i
$783$	−5.02239	−	8.69904i	−0.179486	−	0.310878i
$784$	3.14177	−	5.44171i	0.112206	−	0.194347i
$785$			12.0135i			0.428782i
$786$	9.43032	+	5.44460i	0.336368	+	0.194202i
$787$	−6.02524	−	3.47867i	−0.214777	−	0.124001i	0.388753	−	0.921342i	$-0.372906\pi$
$787$	−6.02524	−	3.47867i	−0.214777	−	0.124001i	−0.603529	+	0.797341i	$0.706239\pi$
$788$		−	0.891239i		−	0.0317491i
$789$	−1.01739	+	1.76217i	−0.0362201	+	0.0627350i
$790$	−4.96699	−	8.60308i	−0.176718	−	0.306084i
$791$	−56.4043	+	32.5650i	−2.00551	+	1.15788i
$792$	−1.66808			−0.0592725
$793$	26.6176	−	3.97081i	0.945220	−	0.141008i
$794$	−3.73628			−0.132596
$795$	0.734939	−	0.424317i	0.0260656	−	0.0150490i
$796$	−0.180558	−	0.312736i	−0.00639971	−	0.0110846i
$797$	17.0677	−	29.5621i	0.604569	−	1.04714i	−0.387550	−	0.921849i	$-0.626679\pi$
$797$	17.0677	−	29.5621i	0.604569	−	1.04714i	0.992119	−	0.125296i	$-0.0399880\pi$
$798$			23.0078i			0.814466i
$799$	−23.6432	−	13.6504i	−0.836438	−	0.482918i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$			5.95162i			0.210290i
$802$	14.0456	−	24.3276i	0.495966	−	0.859038i
$803$	−10.1899	−	17.6494i	−0.359593	−	0.622833i
$804$	−12.7768	+	7.37671i	−0.450604	+	0.260157i
$805$	−4.53590			−0.159869
$806$	5.57966	−	14.1538i	0.196535	−	0.498545i
$807$	20.5287			0.722645
$808$	4.62124	−	2.66808i	0.162575	−	0.0938626i
$809$	1.66385	+	2.88187i	0.0584978	+	0.101321i	0.893791	−	0.448483i	$-0.148036\pi$
$809$	1.66385	+	2.88187i	0.0584978	+	0.101321i	−0.835293	+	0.549804i	$0.814702\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$			20.6083i			0.723655i	0.932245	+	0.361827i	$0.117847\pi$
$811$			20.6083i			0.723655i	−0.932245	+	0.361827i	$0.882153\pi$
$812$	31.7050	+	18.3049i	1.11263	+	0.642377i
$813$	−22.1184	−	12.7700i	−0.775725	−	0.447865i
$814$			16.4543i			0.576722i
$815$	−5.04581	+	8.73960i	−0.176747	+	0.306135i
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	−41.4008	+	23.9027i	−1.44843	+	0.836251i
$818$	27.3804			0.957335
$819$	−12.2253	−	4.81944i	−0.427188	−	0.168405i
$820$	−9.28932			−0.324397
$821$	1.36836	−	0.790025i	0.0477562	−	0.0275721i	−0.475932	−	0.879482i	$-0.657889\pi$
$821$	1.36836	−	0.790025i	0.0477562	−	0.0275721i	0.523688	+	0.851910i	$0.324556\pi$
$822$	−3.51848	−	6.09419i	−0.122721	−	0.212559i
$823$	18.7584	−	32.4905i	0.653878	−	1.13255i	−0.328296	−	0.944575i	$-0.606474\pi$
$823$	18.7584	−	32.4905i	0.653878	−	1.13255i	0.982174	−	0.187974i	$-0.0601922\pi$
$824$			7.51248i			0.261710i
$825$	−1.44460	−	0.834038i	−0.0502944	−	0.0290375i
$826$	−19.2815	−	11.1322i	−0.670889	−	0.387338i
$827$			49.4912i			1.72098i	0.509469	+	0.860489i	$0.329842\pi$
$827$			49.4912i			1.72098i	−0.509469	+	0.860489i	$0.670158\pi$
$828$	−0.622266	+	1.07780i	−0.0216253	+	0.0374560i
$829$	24.5693	+	42.5552i	0.853326	+	1.47800i	0.878189	+	0.478313i	$0.158752\pi$
$829$	24.5693	+	42.5552i	0.853326	+	1.47800i	−0.0248634	+	0.999691i	$0.507915\pi$
$830$	6.88764	−	3.97658i	0.239074	−	0.138029i
$831$	−18.0604			−0.626508
$832$	2.24376	+	2.82233i	0.0777883	+	0.0978467i
$833$	25.1342			0.870848
$834$	10.0846	−	5.82233i	0.349200	−	0.201611i
$835$	3.94851	+	6.83902i	0.136644	+	0.236674i
$836$	−5.26506	+	9.11935i	−0.182096	+	0.315399i
$837$			4.21957i			0.145850i
$838$	11.3981	+	6.58068i	0.393740	+	0.227326i
$839$	−18.6560	−	10.7711i	−0.644078	−	0.371858i	0.142106	−	0.989851i	$-0.454613\pi$
$839$	−18.6560	−	10.7711i	−0.644078	−	0.371858i	−0.786184	+	0.617993i	$0.787946\pi$
$840$		−	3.64466i		−	0.125753i
$841$	−35.9489	+	62.2653i	−1.23962	+	2.14708i
$842$	−0.646706	−	1.12013i	−0.0222870	−	0.0386021i
$843$	17.5089	−	10.1088i	0.603038	−	0.348164i
$844$	−2.22739			−0.0766700
$845$	12.6653	+	2.93109i	0.435698	+	0.100833i
$846$	6.82522			0.234656
$847$	25.9375	−	14.9750i	0.891224	−	0.514548i
$848$	0.424317	+	0.734939i	0.0145711	+	0.0252379i
$849$	4.34575	−	7.52705i	0.149146	−	0.258328i
$850$			4.00000i			0.137199i
$851$	10.6316	+	6.13818i	0.364448	+	0.210414i
$852$	3.04056	+	1.75547i	0.104168	+	0.0601413i
$853$		−	2.79821i		−	0.0958088i	−0.998852	−	0.0479044i	$-0.984746\pi$
$853$		−	2.79821i		−	0.0958088i	0.998852	−	0.0479044i	$-0.0152543\pi$
$854$	13.6021	−	23.5595i	0.465453	−	0.806188i
$855$	3.15637	+	5.46699i	0.107946	+	0.186967i
$856$	−14.6603	+	8.46410i	−0.501077	+	0.289297i
$857$	−48.9658			−1.67264			−0.836320	−	0.548242i	$-0.815297\pi$
$857$	−48.9658			−1.67264			−0.836320	+	0.548242i	$0.815297\pi$
$858$	−3.74276	−	4.70786i	−0.127776	−	0.160724i
$859$	4.22739			0.144237			0.0721184	−	0.997396i	$-0.477024\pi$
$859$	4.22739			0.144237			0.0721184	+	0.997396i	$0.477024\pi$
$860$	6.55829	−	3.78643i	0.223636	−	0.129116i
$861$	16.9282	+	29.3205i	0.576912	+	0.999240i
$862$	6.06397	−	10.5031i	0.206540	−	0.357737i
$863$			19.0285i			0.647738i	0.946102	+	0.323869i	$0.104984\pi$
$863$			19.0285i			0.647738i	−0.946102	+	0.323869i	$0.895016\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	0.381645	+	0.220343i	0.0129763	+	0.00749187i
$866$			2.07802i			0.0706141i
$867$	0.500000	−	0.866025i	0.0169809	−	0.0294118i
$868$	−7.68945	−	13.3185i	−0.260997	−	0.452060i
$869$	−14.3506	+	8.28532i	−0.486810	+	0.281060i
$870$	10.0448			0.340550
$871$	−49.4877	−	19.5089i	−1.67683	−	0.661033i
$872$	0.663848			0.0224807
$873$	2.38453	−	1.37671i	0.0807042	−	0.0465946i
$874$	3.92820	+	6.80385i	0.132873	+	0.230144i
$875$	1.82233	−	3.15637i	0.0616060	−	0.106705i
$876$		−	12.2175i		−	0.412792i
$877$	11.7323	+	6.77363i	0.396171	+	0.228729i	0.684830	−	0.728702i	$-0.259876\pi$
$877$	11.7323	+	6.77363i	0.396171	+	0.228729i	−0.288660	+	0.957432i	$0.593210\pi$
$878$	−2.07534	−	1.19820i	−0.0700394	−	0.0404373i
$879$		−	7.54790i		−	0.254584i
$880$	0.834038	−	1.44460i	0.0281154	−	0.0486973i
$881$	2.49041	+	4.31351i	0.0839039	+	0.145326i	0.904924	−	0.425574i	$-0.139928\pi$
$881$	2.49041	+	4.31351i	0.0839039	+	0.145326i	−0.821020	+	0.570900i	$0.806594\pi$
$882$	−5.44171	+	3.14177i	−0.183232	+	0.105789i
$883$	30.9829			1.04266			0.521330	−	0.853355i	$-0.325436\pi$
$883$	30.9829			1.04266			0.521330	+	0.853355i	$0.325436\pi$
$884$	−5.28932	+	13.4173i	−0.177899	+	0.451272i
$885$	−6.10876			−0.205344
$886$	19.0490	−	10.9980i	0.639964	−	0.369483i
$887$	−8.58826	−	14.8753i	−0.288365	−	0.499464i	0.685054	−	0.728492i	$-0.259778\pi$
$887$	−8.58826	−	14.8753i	−0.288365	−	0.499464i	−0.973420	+	0.229028i	$0.926445\pi$
$888$	−4.93211	+	8.54267i	−0.165511	+	0.286673i
$889$		−	52.6314i		−	1.76520i
$890$	−5.15425	−	2.97581i	−0.172771	−	0.0997494i
$891$	1.44460	+	0.834038i	0.0483958	+	0.0279413i
$892$		−	6.08380i		−	0.203701i
$893$	21.5429	−	37.3134i	0.720906	−	1.24865i
$894$	0.386305	+	0.669099i	0.0129200	+	0.0223780i
$895$	−17.0060	+	9.81842i	−0.568448	+	0.328194i
$896$	3.64466			0.121760
$897$	−4.43811	+	0.662076i	−0.148184	+	0.0221061i
$898$	29.2253			0.975261
$899$	36.7062	−	21.1923i	1.22422	−	0.706804i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−1.69727	+	2.93975i	−0.0565442	+	0.0979374i
$902$			15.4953i			0.515937i
$903$	−23.9027	−	13.8003i	−0.795433	−	0.459244i
$904$	−15.4759	−	8.93500i	−0.514720	−	0.297174i
$905$		−	6.21752i		−	0.206677i
$906$	−4.88919	+	8.46833i	−0.162433	+	0.281341i
$907$	−12.5399	−	21.7197i	−0.416379	−	0.721190i	0.579193	−	0.815190i	$-0.303368\pi$
$907$	−12.5399	−	21.7197i	−0.416379	−	0.721190i	−0.995572	+	0.0940008i	$0.970034\pi$
$908$	−13.2679	+	7.66025i	−0.440312	+	0.254214i
$909$	−5.33615			−0.176989
$910$	10.2864	−	8.17774i	0.340992	−	0.271089i
$911$	18.2332			0.604092			0.302046	−	0.953293i	$-0.402330\pi$
$911$	18.2332			0.604092			0.302046	+	0.953293i	$0.402330\pi$
$912$	−5.46699	+	3.15637i	−0.181030	+	0.104518i
$913$	−6.63324	−	11.4891i	−0.219528	−	0.380234i
$914$	−19.8216	+	34.3321i	−0.655641	+	1.13560i
$915$		−	7.46410i		−	0.246756i
$916$	−19.2815	−	11.1322i	−0.637079	−	0.367818i
$917$	34.3703	+	19.8437i	1.13501	+	0.655297i
$918$		−	4.00000i		−	0.132020i
$919$	17.1941	−	29.7811i	0.567181	−	0.982387i	−0.429662	−	0.902990i	$-0.641367\pi$
$919$	17.1941	−	29.7811i	0.567181	−	0.982387i	0.996843	−	0.0793968i	$-0.0252994\pi$
$920$	−0.622266	−	1.07780i	−0.0205155	−	0.0355339i
$921$	22.5537	−	13.0214i	0.743169	−	0.429069i
$922$	16.6758			0.549190
$923$	1.86777	+	12.5203i	0.0614785	+	0.412111i
$924$	−6.07957			−0.200003
$925$	−8.54267	+	4.93211i	−0.280881	+	0.162167i
$926$	16.1088	+	27.9012i	0.529367	+	0.916890i
$927$	3.75624	−	6.50600i	0.123371	−	0.213685i
$928$			10.0448i			0.329736i
$929$	26.9251	+	15.5452i	0.883384	+	0.510022i	0.871773	−	0.489911i	$-0.162971\pi$
$929$	26.9251	+	15.5452i	0.883384	+	0.510022i	0.0116114	+	0.999933i	$0.496304\pi$
$930$	−3.65425	−	2.10978i	−0.119828	−	0.0691826i
$931$			39.6663i			1.30001i
$932$	5.41829	−	9.38476i	0.177482	−	0.307408i
$933$	−12.6894	−	21.9788i	−0.415434	−	0.719552i
$934$	−5.95944	+	3.44069i	−0.194999	+	0.112583i
$935$	6.67230			0.218208
$936$	−0.531987	−	3.56609i	−0.0173886	−	0.116561i
$937$	−18.8783			−0.616726			−0.308363	−	0.951269i	$-0.599781\pi$
$937$	−18.8783			−0.616726			−0.308363	+	0.951269i	$0.599781\pi$
$938$	−46.5672	+	26.8856i	−1.52047	+	0.877846i
$939$	15.7300	+	27.2452i	0.513329	+	0.889112i
$940$	−3.41261	+	5.91081i	−0.111307	+	0.192789i
$941$			28.9398i			0.943409i	0.881757	+	0.471705i	$0.156361\pi$
$941$			28.9398i			0.943409i	−0.881757	+	0.471705i	$0.843639\pi$
$942$	10.4040	+	6.00677i	0.338982	+	0.195711i
$943$	10.0120	+	5.78043i	0.326036	+	0.188237i
$944$		−	6.10876i		−	0.198823i
$945$	−1.82233	+	3.15637i	−0.0592804	+	0.102677i
$946$	−6.31606	−	10.9397i	−0.205353	−	0.355681i
$947$	6.81472	−	3.93448i	0.221448	−	0.127853i	−0.385172	−	0.922845i	$-0.625858\pi$
$947$	6.81472	−	3.93448i	0.221448	−	0.127853i	0.606621	+	0.794991i	$0.292525\pi$
$948$	−9.93398			−0.322641
$949$	34.4819	−	27.4132i	1.11933	−	0.889869i
$950$	−6.31274			−0.204812
$951$	−21.3989	+	12.3546i	−0.693905	+	0.400626i
$952$	7.28932	+	12.6255i	0.236248	+	0.409194i
$953$	−27.5484	+	47.7153i	−0.892381	+	1.54565i	−0.0553681	+	0.998466i	$0.517633\pi$
$953$	−27.5484	+	47.7153i	−0.892381	+	1.54565i	−0.837013	+	0.547183i	$0.815700\pi$
$954$		−	0.848634i		−	0.0274755i
$955$	13.5807	+	7.84081i	0.439461	+	0.253723i
$956$	14.2873	+	8.24876i	0.462083	+	0.266784i
$957$		−	16.7555i		−	0.541627i
$958$	−9.48547	+	16.4293i	−0.306462	+	0.530807i
$959$	−12.8237	−	22.2112i	−0.414098	−	0.717239i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	13.1952			0.425653
$962$	−35.1767	+	5.24765i	−1.13414	+	0.169191i
$963$	16.9282			0.545504
$964$	3.81428	−	2.20218i	0.122850	−	0.0709274i
$965$	−4.06397	−	7.03901i	−0.130824	−	0.226594i
$966$	−2.26795	+	3.92820i	−0.0729701	+	0.126388i
$967$		−	31.5523i		−	1.01465i	−0.861754	−	0.507326i	$-0.830634\pi$
$967$		−	31.5523i		−	1.01465i	0.861754	−	0.507326i	$-0.169366\pi$
$968$	7.11658	+	4.10876i	0.228736	+	0.132061i
$969$	−21.8680	−	12.6255i	−0.702500	−	0.405589i
$970$			2.75342i			0.0884070i
$971$	−1.83792	+	3.18338i	−0.0589818	+	0.102159i	−0.894009	−	0.448050i	$-0.852119\pi$
$971$	−1.83792	+	3.18338i	−0.0589818	+	0.102159i	0.835027	+	0.550209i	$0.185452\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	36.7548	−	21.2204i	1.17831	−	0.680295i
$974$	1.91620			0.0613991
$975$	1.32233	−	3.35432i	0.0423484	−	0.107424i
$976$	7.46410			0.238920
$977$	36.3908	−	21.0102i	1.16424	−	0.672177i	0.211927	−	0.977286i	$-0.432026\pi$
$977$	36.3908	−	21.0102i	1.16424	−	0.672177i	0.952318	+	0.305109i	$0.0986928\pi$
$978$	5.04581	+	8.73960i	0.161347	+	0.279462i
$979$	−4.96388	+	8.59769i	−0.158646	+	0.274783i
$980$		−	6.28354i		−	0.200720i
$981$	−0.574909	−	0.331924i	−0.0183554	−	0.0105975i
$982$	−29.1309	−	16.8187i	−0.929605	−	0.536707i
$983$			13.4307i			0.428372i	0.976793	+	0.214186i	$0.0687099\pi$
$983$			13.4307i			0.428372i	−0.976793	+	0.214186i	$0.931290\pi$
$984$	−4.64466	+	8.04479i	−0.148066	+	0.256458i
$985$	−0.445619	−	0.771835i	−0.0141986	−	0.0245927i
$986$	−34.7962	+	20.0896i	−1.10814	+	0.639782i
$987$	24.8756			0.791799
$988$	−21.1749	−	8.34752i	−0.673664	−	0.265570i
$989$	−9.42468			−0.299687
$990$	−1.44460	+	0.834038i	−0.0459123	+	0.0265075i
$991$	−21.8994	−	37.9309i	−0.695658	−	1.20492i	−0.969958	−	0.243271i	$-0.921780\pi$
$991$	−21.8994	−	37.9309i	−0.695658	−	1.20492i	0.274300	−	0.961644i	$-0.411554\pi$
$992$	2.10978	−	3.65425i	0.0669857	−	0.116023i
$993$			5.60360i			0.177825i
$994$	11.0818	+	6.39808i	0.351493	+	0.202935i
$995$	−0.312736	−	0.180558i	−0.00991439	−	0.00572407i
$996$		−	7.95317i		−	0.252006i
$997$	11.7562	−	20.3624i	0.372324	−	0.644884i	−0.617599	−	0.786493i	$-0.711894\pi$
$997$	11.7562	−	20.3624i	0.372324	−	0.644884i	0.989923	+	0.141609i	$0.0452277\pi$
$998$	−0.912609	−	1.58068i	−0.0288881	−	0.0500357i
$999$	8.54267	−	4.93211i	0.270278	−	0.156045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bb.c.361.3	yes	8
3.2	odd	2		1170.2.bs.f.361.1		8
5.2	odd	4		1950.2.y.k.49.2		8
5.3	odd	4		1950.2.y.j.49.3		8
5.4	even	2		1950.2.bc.g.751.2		8
13.2	odd	12		5070.2.a.ca.1.1		4
13.3	even	3		5070.2.b.ba.1351.8		8
13.4	even	6	inner	390.2.bb.c.121.3	✓	8
13.10	even	6		5070.2.b.ba.1351.1		8
13.11	odd	12		5070.2.a.bz.1.4		4
39.17	odd	6		1170.2.bs.f.901.1		8
65.4	even	6		1950.2.bc.g.901.2		8
65.17	odd	12		1950.2.y.j.199.3		8
65.43	odd	12		1950.2.y.k.199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.3	✓	8	13.4	even	6	inner
390.2.bb.c.361.3	yes	8	1.1	even	1	trivial
1170.2.bs.f.361.1		8	3.2	odd	2
1170.2.bs.f.901.1		8	39.17	odd	6
1950.2.y.j.49.3		8	5.3	odd	4
1950.2.y.j.199.3		8	65.17	odd	12
1950.2.y.k.49.2		8	5.2	odd	4
1950.2.y.k.199.2		8	65.43	odd	12
1950.2.bc.g.751.2		8	5.4	even	2
1950.2.bc.g.901.2		8	65.4	even	6
5070.2.a.bz.1.4		4	13.11	odd	12
5070.2.a.ca.1.1		4	13.2	odd	12
5070.2.b.ba.1351.1		8	13.10	even	6
5070.2.b.ba.1351.8		8	13.3	even	3

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-3.15637 - 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.44460 + 0.834038i) q^{11} -1.00000 q^{12} +(-2.24376 - 2.82233i) q^{13} -3.64466 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +1.00000i q^{18} +(5.46699 + 3.15637i) q^{19} +(-0.866025 - 0.500000i) q^{20} +3.64466i q^{21} +(-0.834038 + 1.44460i) q^{22} +(0.622266 + 1.07780i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-3.35432 - 1.32233i) q^{26} +1.00000 q^{27} +(-3.15637 + 1.82233i) q^{28} +(-5.02239 - 8.69904i) q^{29} +(-0.500000 + 0.866025i) q^{30} +4.21957i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.44460 + 0.834038i) q^{33} -4.00000i q^{34} +(-1.82233 + 3.15637i) q^{35} +(0.500000 + 0.866025i) q^{36} +(8.54267 - 4.93211i) q^{37} +6.31274 q^{38} +(-1.32233 + 3.35432i) q^{39} -1.00000 q^{40} +(8.04479 - 4.64466i) q^{41} +(1.82233 + 3.15637i) q^{42} +(-3.78643 + 6.55829i) q^{43} +1.66808i q^{44} +(0.866025 + 0.500000i) q^{45} +(1.07780 + 0.622266i) q^{46} -6.82522i q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.14177 + 5.44171i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +(-3.56609 + 0.531987i) q^{52} -0.848634 q^{53} +(0.866025 - 0.500000i) q^{54} +(0.834038 + 1.44460i) q^{55} +(-1.82233 + 3.15637i) q^{56} -6.31274i q^{57} +(-8.69904 - 5.02239i) q^{58} +(5.29034 + 3.05438i) q^{59} +1.00000i q^{60} +(-3.73205 + 6.46410i) q^{61} +(2.10978 + 3.65425i) q^{62} +(3.15637 - 1.82233i) q^{63} -1.00000 q^{64} +(-2.82233 + 2.24376i) q^{65} +1.66808 q^{66} +(12.7768 - 7.37671i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(0.622266 - 1.07780i) q^{69} +3.64466i q^{70} +(-3.04056 - 1.75547i) q^{71} +(0.866025 + 0.500000i) q^{72} +12.2175i q^{73} +(4.93211 - 8.54267i) q^{74} +(0.500000 + 0.866025i) q^{75} +(5.46699 - 3.15637i) q^{76} +6.07957 q^{77} +(0.531987 + 3.56609i) q^{78} +9.93398 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.64466 - 8.04479i) q^{82} +7.95317i q^{83} +(3.15637 + 1.82233i) q^{84} +(-3.46410 - 2.00000i) q^{85} +7.57286i q^{86} +(-5.02239 + 8.69904i) q^{87} +(0.834038 + 1.44460i) q^{88} +(5.15425 - 2.97581i) q^{89} +1.00000 q^{90} +(1.93891 + 12.9972i) q^{91} +1.24453 q^{92} +(3.65425 - 2.10978i) q^{93} +(-3.41261 - 5.91081i) q^{94} +(3.15637 - 5.46699i) q^{95} +1.00000i q^{96} +(-2.38453 - 1.37671i) q^{97} +(5.44171 + 3.14177i) q^{98} -1.66808i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 4 q^{14} - 4 q^{16} + 16 q^{17} - 6 q^{19} + 2 q^{22} + 4 q^{23} - 8 q^{25} - 12 q^{26} + 8 q^{27} - 8 q^{29} - 4 q^{30} - 6 q^{33} + 2 q^{35} + 4 q^{36} + 30 q^{37} + 6 q^{39} - 8 q^{40} - 2 q^{42} + 14 q^{43} - 6 q^{46} - 4 q^{48} + 14 q^{49} - 32 q^{51} - 6 q^{52} + 16 q^{53} - 2 q^{55} + 2 q^{56} - 6 q^{58} + 24 q^{59} - 16 q^{61} + 4 q^{62} - 8 q^{64} - 6 q^{65} - 4 q^{66} + 24 q^{67} - 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} + 4 q^{75} - 6 q^{76} + 16 q^{77} + 6 q^{78} - 20 q^{79} - 4 q^{81} + 4 q^{82} - 8 q^{87} - 2 q^{88} + 42 q^{89} + 8 q^{90} - 10 q^{91} + 8 q^{92} + 30 q^{93} - 8 q^{94} - 24 q^{97} + 48 q^{98}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^10 + 6 * q^11 - 8 * q^12 - 12 * q^13 + 4 * q^14 - 4 * q^16 + 16 * q^17 - 6 * q^19 + 2 * q^22 + 4 * q^23 - 8 * q^25 - 12 * q^26 + 8 * q^27 - 8 * q^29 - 4 * q^30 - 6 * q^33 + 2 * q^35 + 4 * q^36 + 30 * q^37 + 6 * q^39 - 8 * q^40 - 2 * q^42 + 14 * q^43 - 6 * q^46 - 4 * q^48 + 14 * q^49 - 32 * q^51 - 6 * q^52 + 16 * q^53 - 2 * q^55 + 2 * q^56 - 6 * q^58 + 24 * q^59 - 16 * q^61 + 4 * q^62 - 8 * q^64 - 6 * q^65 - 4 * q^66 + 24 * q^67 - 16 * q^68 + 4 * q^69 - 12 * q^71 + 10 * q^74 + 4 * q^75 - 6 * q^76 + 16 * q^77 + 6 * q^78 - 20 * q^79 - 4 * q^81 + 4 * q^82 - 8 * q^87 - 2 * q^88 + 42 * q^89 + 8 * q^90 - 10 * q^91 + 8 * q^92 + 30 * q^93 - 8 * q^94 - 24 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more