LMFDB - Embedded newform 1170.2.bs.f.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1170.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (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:	$9.34249703649$
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:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$1.33404 + 1.33404i$ of defining polynomial
Character	$\chi$	$=$	1170.901
Dual form			1170.2.bs.f.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-3.15637 + 1.82233i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-3.15637 + 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(1.44460 + 0.834038i) q^{11} +(-2.24376 + 2.82233i) q^{13} +3.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(5.46699 - 3.15637i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-0.834038 - 1.44460i) q^{22} +(-0.622266 + 1.07780i) q^{23} -1.00000 q^{25} +(3.35432 - 1.32233i) q^{26} +(-3.15637 - 1.82233i) q^{28} +(5.02239 - 8.69904i) q^{29} -4.21957i q^{31} +(0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(1.82233 + 3.15637i) q^{35} +(8.54267 + 4.93211i) q^{37} -6.31274 q^{38} -1.00000 q^{40} +(-8.04479 - 4.64466i) q^{41} +(-3.78643 - 6.55829i) q^{43} +1.66808i q^{44} +(1.07780 - 0.622266i) q^{46} -6.82522i q^{47} +(3.14177 - 5.44171i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-3.56609 - 0.531987i) q^{52} +0.848634 q^{53} +(0.834038 - 1.44460i) q^{55} +(1.82233 + 3.15637i) q^{56} +(-8.69904 + 5.02239i) q^{58} +(-5.29034 + 3.05438i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(-2.10978 + 3.65425i) q^{62} -1.00000 q^{64} +(2.82233 + 2.24376i) q^{65} +(12.7768 + 7.37671i) q^{67} +(2.00000 - 3.46410i) q^{68} -3.64466i q^{70} +(3.04056 - 1.75547i) q^{71} -12.2175i q^{73} +(-4.93211 - 8.54267i) q^{74} +(5.46699 + 3.15637i) q^{76} -6.07957 q^{77} +9.93398 q^{79} +(0.866025 + 0.500000i) q^{80} +(4.64466 + 8.04479i) q^{82} +7.95317i q^{83} +(-3.46410 + 2.00000i) q^{85} +7.57286i q^{86} +(0.834038 - 1.44460i) q^{88} +(-5.15425 - 2.97581i) q^{89} +(1.93891 - 12.9972i) q^{91} -1.24453 q^{92} +(-3.41261 + 5.91081i) q^{94} +(-3.15637 - 5.46699i) q^{95} +(-2.38453 + 1.37671i) q^{97} +(-5.44171 + 3.14177i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 4 q^{10} - 6 q^{11} - 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^{29} - 2 q^{35} + 30 q^{37} - 8 q^{40} + 14 q^{43} - 6 q^{46} + 14 q^{49} - 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} + 24 q^{67} + 16 q^{68} + 12 q^{71} - 10 q^{74} - 6 q^{76} - 16 q^{77} - 20 q^{79} + 4 q^{82} - 2 q^{88} - 42 q^{89} - 10 q^{91} - 8 q^{92} - 8 q^{94} - 24 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^10 - 6 * q^11 - 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^29 - 2 * q^35 + 30 * q^37 - 8 * q^40 + 14 * q^43 - 6 * q^46 + 14 * q^49 - 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 + 24 * q^67 + 16 * q^68 + 12 * q^71 - 10 * q^74 - 6 * q^76 - 16 * q^77 - 20 * q^79 + 4 * q^82 - 2 * q^88 - 42 * q^89 - 10 * q^91 - 8 * q^92 - 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 $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−3.15637	+	1.82233i	−1.19299	+	0.688776i	−0.958985	−	0.283458i	$-0.908518\pi$
$7$	−3.15637	+	1.82233i	−1.19299	+	0.688776i	−0.234010	+	0.972234i	$0.575185\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.44460	+	0.834038i	0.435562	+	0.251472i	0.701713	−	0.712459i	$-0.252419\pi$
$11$	1.44460	+	0.834038i	0.435562	+	0.251472i	−0.266151	+	0.963931i	$0.585752\pi$
$12$		0			0
$13$	−2.24376	+	2.82233i	−0.622307	+	0.782773i
$13$	−2.24376	+	2.82233i	−0.622307	+	0.782773i
$14$	3.64466			0.974076
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$		0			0
$19$	5.46699	−	3.15637i	1.25421	−	0.724120i	0.282270	−	0.959335i	$-0.408913\pi$
$19$	5.46699	−	3.15637i	1.25421	−	0.724120i	0.971943	+	0.235215i	$0.0755793\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		0			0
$22$	−0.834038	−	1.44460i	−0.177817	−	0.307989i
$23$	−0.622266	+	1.07780i	−0.129752	+	0.224736i	−0.923580	−	0.383405i	$-0.874751\pi$
$23$	−0.622266	+	1.07780i	−0.129752	+	0.224736i	0.793829	+	0.608141i	$0.208085\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	3.35432	−	1.32233i	0.657836	−	0.259330i
$27$		0			0
$28$	−3.15637	−	1.82233i	−0.596497	−	0.344388i
$29$	5.02239	−	8.69904i	0.932635	−	1.61537i	0.153837	−	0.988096i	$-0.450837\pi$
$29$	5.02239	−	8.69904i	0.932635	−	1.61537i	0.778798	−	0.627275i	$-0.215830\pi$
$30$		0			0
$31$		−	4.21957i		−	0.757857i	−0.925426	−	0.378928i	$-0.876293\pi$
$31$		−	4.21957i		−	0.757857i	0.925426	−	0.378928i	$-0.123707\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			4.00000i			0.685994i
$35$	1.82233	+	3.15637i	0.308030	+	0.533524i
$36$		0			0
$37$	8.54267	+	4.93211i	1.40441	+	0.810835i	0.994841	−	0.101446i	$-0.0323469\pi$
$37$	8.54267	+	4.93211i	1.40441	+	0.810835i	0.409566	+	0.912281i	$0.365680\pi$
$38$	−6.31274			−1.02406
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−8.04479	−	4.64466i	−1.25638	−	0.725374i	−0.284015	−	0.958820i	$-0.591666\pi$
$41$	−8.04479	−	4.64466i	−1.25638	−	0.725374i	−0.972370	+	0.233446i	$0.925000\pi$
$42$		0			0
$43$	−3.78643	−	6.55829i	−0.577425	−	1.00013i	−0.995773	−	0.0918433i	$-0.970724\pi$
$43$	−3.78643	−	6.55829i	−0.577425	−	1.00013i	0.418348	−	0.908287i	$-0.362609\pi$
$44$			1.66808i			0.251472i
$45$		0			0
$46$	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			0
$49$	3.14177	−	5.44171i	0.448825	−	0.777387i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$	−3.56609	−	0.531987i	−0.494528	−	0.0737734i
$53$	0.848634			0.116569			0.0582844	−	0.998300i	$-0.481437\pi$
$53$	0.848634			0.116569			0.0582844	+	0.998300i	$0.481437\pi$
$54$		0			0
$55$	0.834038	−	1.44460i	0.112462	−	0.194789i
$56$	1.82233	+	3.15637i	0.243519	+	0.421787i
$57$		0			0
$58$	−8.69904	+	5.02239i	−1.14224	+	0.659473i
$59$	−5.29034	+	3.05438i	−0.688744	+	0.397646i	−0.803141	−	0.595789i	$-0.796840\pi$
$59$	−5.29034	+	3.05438i	−0.688744	+	0.397646i	0.114397	+	0.993435i	$0.463506\pi$
$60$		0			0
$61$	−3.73205	−	6.46410i	−0.477840	−	0.827643i	0.521837	−	0.853045i	$-0.325247\pi$
$61$	−3.73205	−	6.46410i	−0.477840	−	0.827643i	−0.999677	+	0.0254017i	$0.991914\pi$
$62$	−2.10978	+	3.65425i	−0.267943	+	0.464091i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.82233	+	2.24376i	0.350067	+	0.278304i
$66$		0			0
$67$	12.7768	+	7.37671i	1.56094	+	0.901209i	0.997162	+	0.0752814i	$0.0239855\pi$
$67$	12.7768	+	7.37671i	1.56094	+	0.901209i	0.563777	+	0.825927i	$0.309348\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		0			0
$70$		−	3.64466i		−	0.435620i
$71$	3.04056	−	1.75547i	0.360848	−	0.208336i	−0.308605	−	0.951190i	$-0.599862\pi$
$71$	3.04056	−	1.75547i	0.360848	−	0.208336i	0.669453	+	0.742855i	$0.266529\pi$
$72$		0			0
$73$		−	12.2175i		−	1.42995i	−0.699149	−	0.714976i	$-0.746437\pi$
$73$		−	12.2175i		−	1.42995i	0.699149	−	0.714976i	$-0.253563\pi$
$74$	−4.93211	−	8.54267i	−0.573347	−	0.993065i
$75$		0			0
$76$	5.46699	+	3.15637i	0.627107	+	0.362060i
$77$	−6.07957			−0.692831
$78$		0			0
$79$	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			0
$82$	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	$0.856223\pi$
$84$		0			0
$85$	−3.46410	+	2.00000i	−0.375735	+	0.216930i
$86$			7.57286i			0.816603i
$87$		0			0
$88$	0.834038	−	1.44460i	0.0889087	−	0.153994i
$89$	−5.15425	−	2.97581i	−0.546350	−	0.315435i	0.201299	−	0.979530i	$-0.435484\pi$
$89$	−5.15425	−	2.97581i	−0.546350	−	0.315435i	−0.747648	+	0.664095i	$0.768817\pi$
$90$		0			0
$91$	1.93891	−	12.9972i	0.203253	−	1.36247i
$92$	−1.24453			−0.129752
$93$		0			0
$94$	−3.41261	+	5.91081i	−0.351984	+	0.609654i
$95$	−3.15637	−	5.46699i	−0.323837	−	0.560901i
$96$		0			0
$97$	−2.38453	+	1.37671i	−0.242113	+	0.139784i	−0.616147	−	0.787631i	$-0.711307\pi$
$97$	−2.38453	+	1.37671i	−0.242113	+	0.139784i	0.374035	+	0.927415i	$0.377974\pi$
$98$	−5.44171	+	3.14177i	−0.549696	+	0.317367i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−2.66808	+	4.62124i	−0.265483	+	0.459831i	−0.967690	−	0.252142i	$-0.918865\pi$
$101$	−2.66808	+	4.62124i	−0.265483	+	0.459831i	0.702207	+	0.711973i	$0.252198\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	−0.734939	−	0.424317i	−0.0713835	−	0.0412133i
$107$	8.46410	−	14.6603i	0.818256	−	1.41726i	−0.0887109	−	0.996057i	$-0.528275\pi$
$107$	8.46410	−	14.6603i	0.818256	−	1.41726i	0.906966	−	0.421203i	$-0.138392\pi$
$108$		0			0
$109$		−	0.663848i		−	0.0635851i	−0.999494	−	0.0317926i	$-0.989878\pi$
$109$		−	0.663848i		−	0.0635851i	0.999494	−	0.0317926i	$-0.0101216\pi$
$110$	−1.44460	+	0.834038i	−0.137737	+	0.0795224i
$111$		0			0
$112$		−	3.64466i		−	0.344388i
$113$	−8.93500	−	15.4759i	−0.840534	−	1.45585i	−0.889444	−	0.457045i	$-0.848908\pi$
$113$	−8.93500	−	15.4759i	−0.840534	−	1.45585i	0.0489094	−	0.998803i	$-0.484425\pi$
$114$		0			0
$115$	1.07780	+	0.622266i	0.100505	+	0.0580266i
$116$	10.0448			0.932635
$117$		0			0
$118$	6.10876			0.562357
$119$	12.6255	+	7.28932i	1.15738	+	0.668211i
$120$		0			0
$121$	−4.10876	−	7.11658i	−0.373524	−	0.646962i
$122$			7.46410i			0.675768i
$123$		0			0
$124$	3.65425	−	2.10978i	0.328162	−	0.189464i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	7.22034	−	12.5060i	0.640702	−	1.10973i	−0.344575	−	0.938759i	$-0.611977\pi$
$127$	7.22034	−	12.5060i	0.640702	−	1.10973i	0.985276	−	0.170969i	$-0.0546898\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.32233	−	3.35432i	−0.115976	−	0.294193i
$131$	10.8892			0.951393			0.475697	−	0.879609i	$-0.342196\pi$
$131$	10.8892			0.951393			0.475697	+	0.879609i	$0.342196\pi$
$132$		0			0
$133$	−11.5039	+	19.9253i	−0.997513	+	1.72774i
$134$	−7.37671	−	12.7768i	−0.637251	−	1.10375i
$135$		0			0
$136$	−3.46410	+	2.00000i	−0.297044	+	0.171499i
$137$	−6.09419	+	3.51848i	−0.520662	+	0.300604i	−0.737205	−	0.675669i	$-0.763855\pi$
$137$	−6.09419	+	3.51848i	−0.520662	+	0.300604i	0.216544	+	0.976273i	$0.430522\pi$
$138$		0			0
$139$	−5.82233	−	10.0846i	−0.493844	−	0.855362i	0.506131	−	0.862456i	$-0.331075\pi$
$139$	−5.82233	−	10.0846i	−0.493844	−	0.855362i	−0.999975	+	0.00709431i	$0.997742\pi$
$140$	−1.82233	+	3.15637i	−0.154015	+	0.266762i
$141$		0			0
$142$	−3.51093			−0.294631
$143$	−5.59526	+	2.20575i	−0.467899	+	0.184454i
$144$		0			0
$145$	−8.69904	−	5.02239i	−0.722416	−	0.417087i
$146$	−6.10876	+	10.5807i	−0.505565	+	0.875664i
$147$		0			0
$148$			9.86423i			0.810835i
$149$	0.669099	−	0.386305i	0.0548147	−	0.0316473i	−0.472342	−	0.881415i	$-0.656591\pi$
$149$	0.669099	−	0.386305i	0.0548147	−	0.0316473i	0.527157	+	0.849768i	$0.323258\pi$
$150$		0			0
$151$			9.77838i			0.795754i	0.917439	+	0.397877i	$0.130253\pi$
$151$			9.77838i			0.795754i	−0.917439	+	0.397877i	$0.869747\pi$
$152$	−3.15637	−	5.46699i	−0.256015	−	0.443431i
$153$		0			0
$154$	5.26506	+	3.03978i	0.424271	+	0.244953i
$155$	−4.21957			−0.338924
$156$		0			0
$157$	−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			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		−	4.53590i		−	0.357479i
$162$		0			0
$163$	−8.73960	+	5.04581i	−0.684538	+	0.395218i	−0.801563	−	0.597911i	$-0.795998\pi$
$163$	−8.73960	+	5.04581i	−0.684538	+	0.395218i	0.117025	+	0.993129i	$0.462664\pi$
$164$		−	9.28932i		−	0.725374i
$165$		0			0
$166$	3.97658	−	6.88764i	0.308643	−	0.534585i
$167$	6.83902	+	3.94851i	0.529219	+	0.305545i	0.740698	−	0.671838i	$-0.234495\pi$
$167$	6.83902	+	3.94851i	0.529219	+	0.305545i	−0.211479	+	0.977382i	$0.567828\pi$
$168$		0			0
$169$	−2.93109	−	12.6653i	−0.225469	−	0.974250i
$170$	4.00000			0.306786
$171$		0			0
$172$	3.78643	−	6.55829i	0.288713	−	0.500065i
$173$	0.220343	+	0.381645i	0.0167523	+	0.0290159i	0.874280	−	0.485422i	$-0.161334\pi$
$173$	0.220343	+	0.381645i	0.0167523	+	0.0290159i	−0.857528	+	0.514438i	$0.828001\pi$
$174$		0			0
$175$	3.15637	−	1.82233i	0.238599	−	0.137755i
$176$	−1.44460	+	0.834038i	−0.108891	+	0.0628680i
$177$		0			0
$178$	2.97581	+	5.15425i	0.223046	+	0.386328i
$179$	9.81842	−	17.0060i	0.733863	−	1.27109i	−0.221357	−	0.975193i	$-0.571049\pi$
$179$	9.81842	−	17.0060i	0.733863	−	1.27109i	0.955220	−	0.295895i	$-0.0956180\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	1.07780	+	0.622266i	0.0794562	+	0.0458741i
$185$	4.93211	−	8.54267i	0.362616	−	0.628070i
$186$		0			0
$187$		−	6.67230i		−	0.487927i
$188$	5.91081	−	3.41261i	0.431090	−	0.248890i
$189$		0			0
$190$			6.31274i			0.457974i
$191$	7.84081	+	13.5807i	0.567341	+	0.982664i	0.996828	+	0.0795905i	$0.0253613\pi$
$191$	7.84081	+	13.5807i	0.567341	+	0.982664i	−0.429486	+	0.903073i	$0.641305\pi$
$192$		0			0
$193$	7.03901	+	4.06397i	0.506679	+	0.292531i	0.731468	−	0.681876i	$-0.238836\pi$
$193$	7.03901	+	4.06397i	0.506679	+	0.292531i	−0.224788	+	0.974408i	$0.572169\pi$
$194$	2.75342			0.197684
$195$		0			0
$196$	6.28354			0.448825
$197$	−0.771835	−	0.445619i	−0.0549910	−	0.0317491i	0.472252	−	0.881463i	$-0.343441\pi$
$197$	−0.771835	−	0.445619i	−0.0549910	−	0.0317491i	−0.527243	+	0.849714i	$0.676774\pi$
$198$		0			0
$199$	0.180558	+	0.312736i	0.0127994	+	0.0221692i	0.872354	−	0.488874i	$-0.162592\pi$
$199$	0.180558	+	0.312736i	0.0127994	+	0.0221692i	−0.859555	+	0.511044i	$0.829259\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	4.62124	−	2.66808i	0.325150	−	0.187725i
$203$			36.6098i			2.56951i
$204$		0			0
$205$	−4.64466	+	8.04479i	−0.324397	+	0.561872i
$206$	6.50600	+	3.75624i	0.453295	+	0.261710i
$207$		0			0
$208$	−1.32233	−	3.35432i	−0.0916871	−	0.232580i
$209$	10.5301			0.728384
$210$		0			0
$211$	−1.11370	+	1.92898i	−0.0766700	+	0.132796i	−0.901811	−	0.432130i	$-0.857762\pi$
$211$	−1.11370	+	1.92898i	−0.0766700	+	0.132796i	0.825141	+	0.564926i	$0.191095\pi$
$212$	0.424317	+	0.734939i	0.0291422	+	0.0504758i
$213$		0			0
$214$	−14.6603	+	8.46410i	−1.00215	+	0.578594i
$215$	−6.55829	+	3.78643i	−0.447272	+	0.258232i
$216$		0			0
$217$	7.68945	+	13.3185i	0.521994	+	0.904119i
$218$	−0.331924	+	0.574909i	−0.0224807	+	0.0389378i
$219$		0			0
$220$	1.66808			0.112462
$221$	14.2644	+	2.12795i	0.959524	+	0.143141i
$222$		0			0
$223$	5.26872	+	3.04190i	0.352820	+	0.203701i	0.665927	−	0.746017i	$-0.268036\pi$
$223$	5.26872	+	3.04190i	0.352820	+	0.203701i	−0.313107	+	0.949718i	$0.601370\pi$
$224$	−1.82233	+	3.15637i	−0.121760	+	0.210894i
$225$		0			0
$226$			17.8700i			1.18869i
$227$	13.2679	−	7.66025i	0.880625	−	0.508429i	0.00976038	−	0.999952i	$-0.496893\pi$
$227$	13.2679	−	7.66025i	0.880625	−	0.508429i	0.870864	+	0.491523i	$0.163560\pi$
$228$		0			0
$229$			22.2644i			1.47127i	0.677378	+	0.735635i	$0.263116\pi$
$229$			22.2644i			1.47127i	−0.677378	+	0.735635i	$0.736884\pi$
$230$	−0.622266	−	1.07780i	−0.0410310	−	0.0710678i
$231$		0			0
$232$	−8.69904	−	5.02239i	−0.571120	−	0.329736i
$233$	−10.8366			−0.709928			−0.354964	−	0.934880i	$-0.615507\pi$
$233$	−10.8366			−0.709928			−0.354964	+	0.934880i	$0.615507\pi$
$234$		0			0
$235$	−6.82522			−0.445228
$236$	−5.29034	−	3.05438i	−0.344372	−	0.198823i
$237$		0			0
$238$	−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			0
$241$	3.81428	−	2.20218i	0.245700	−	0.141855i	−0.372094	−	0.928195i	$-0.621360\pi$
$241$	3.81428	−	2.20218i	0.245700	−	0.141855i	0.617794	+	0.786340i	$0.288027\pi$
$242$			8.21752i			0.528242i
$243$		0			0
$244$	3.73205	−	6.46410i	0.238920	−	0.413822i
$245$	−5.44171	−	3.14177i	−0.347658	−	0.200720i
$246$		0			0
$247$	−3.35830	+	22.5118i	−0.213683	+	1.43239i
$248$	−4.21957			−0.267943
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−5.97267	−	10.3450i	−0.376992	−	0.652969i	0.613631	−	0.789593i	$-0.289708\pi$
$251$	−5.97267	−	10.3450i	−0.376992	−	0.652969i	−0.990623	+	0.136624i	$0.956375\pi$
$252$		0			0
$253$	−1.79785	+	1.03799i	−0.113030	+	0.0652577i
$254$	−12.5060	+	7.22034i	−0.784696	+	0.453045i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.73103	+	16.8546i	−0.607005	+	1.05136i	0.384726	+	0.923031i	$0.374296\pi$
$257$	−9.73103	+	16.8546i	−0.607005	+	1.05136i	−0.991731	+	0.128333i	$0.959038\pi$
$258$		0			0
$259$	−35.9518			−2.23393
$260$	−0.531987	+	3.56609i	−0.0329925	+	0.221159i
$261$		0			0
$262$	−9.43032	−	5.44460i	−0.582607	−	0.336368i
$263$	1.01739	−	1.76217i	0.0627350	−	0.108660i	−0.832952	−	0.553345i	$-0.813351\pi$
$263$	1.01739	−	1.76217i	0.0627350	−	0.108660i	0.895687	+	0.444685i	$0.146684\pi$
$264$		0			0
$265$		−	0.848634i		−	0.0521312i
$266$	19.9253	−	11.5039i	1.22170	−	0.705349i
$267$		0			0
$268$			14.7534i			0.901209i
$269$	10.2644	+	17.7784i	0.625829	+	1.08397i	0.988380	+	0.152003i	$0.0485725\pi$
$269$	10.2644	+	17.7784i	0.625829	+	1.08397i	−0.362551	+	0.931964i	$0.618094\pi$
$270$		0			0
$271$	22.1184	+	12.7700i	1.34359	+	0.775725i	0.987333	−	0.158662i	$-0.0507179\pi$
$271$	22.1184	+	12.7700i	1.34359	+	0.775725i	0.356261	+	0.934386i	$0.384051\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	7.03696			0.425119
$275$	−1.44460	−	0.834038i	−0.0871124	−	0.0502944i
$276$		0			0
$277$	9.03019	+	15.6407i	0.542572	+	0.939762i	0.998755	+	0.0498760i	$0.0158826\pi$
$277$	9.03019	+	15.6407i	0.542572	+	0.939762i	−0.456184	+	0.889886i	$0.650784\pi$
$278$			11.6447i			0.698400i
$279$		0			0
$280$	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	$0.793957\pi$
$282$		0			0
$283$	4.34575	−	7.52705i	0.258328	−	0.447437i	−0.707466	−	0.706747i	$-0.750162\pi$
$283$	4.34575	−	7.52705i	0.258328	−	0.447437i	0.965794	+	0.259310i	$0.0834952\pi$
$284$	3.04056	+	1.75547i	0.180424	+	0.104168i
$285$		0			0
$286$	5.94851	+	0.887395i	0.351743	+	0.0524728i
$287$	33.8564			1.99848
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	5.02239	+	8.69904i	0.294925	+	0.510825i
$291$		0			0
$292$	10.5807	−	6.10876i	0.619188	−	0.357488i
$293$	−6.53667	+	3.77395i	−0.381876	+	0.220476i	−0.678634	−	0.734476i	$-0.737428\pi$
$293$	−6.53667	+	3.77395i	−0.381876	+	0.220476i	0.296758	+	0.954953i	$0.404095\pi$
$294$		0			0
$295$	3.05438	+	5.29034i	0.177833	+	0.308016i
$296$	4.93211	−	8.54267i	0.286673	−	0.496533i
$297$		0			0
$298$	−0.772609			−0.0447560
$299$	−1.64568	−	4.17456i	−0.0951723	−	0.241421i
$300$		0			0
$301$	23.9027	+	13.8003i	1.37773	+	0.795433i
$302$	4.88919	−	8.46833i	0.281341	−	0.487298i
$303$		0			0
$304$			6.31274i			0.362060i
$305$	−6.46410	+	3.73205i	−0.370133	+	0.213697i
$306$		0			0
$307$		−	26.0427i		−	1.48634i	−0.669104	−	0.743169i	$-0.733322\pi$
$307$		−	26.0427i		−	1.48634i	0.669104	−	0.743169i	$-0.266678\pi$
$308$	−3.03978	−	5.26506i	−0.173208	−	0.300005i
$309$		0			0
$310$	3.65425	+	2.10978i	0.207548	+	0.119828i
$311$	−25.3789			−1.43910			−0.719552	−	0.694438i	$-0.755653\pi$
$311$	−25.3789			−1.43910			−0.719552	+	0.694438i	$0.755653\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	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			0
$319$	14.5107	−	8.37773i	0.812441	−	0.469063i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	−2.26795	+	3.92820i	−0.126388	+	0.218910i
$323$	−21.8680	−	12.6255i	−1.21677	−	0.702500i
$324$		0			0
$325$	2.24376	−	2.82233i	0.124461	−	0.156555i
$326$	10.0916			0.558923
$327$		0			0
$328$	−4.64466	+	8.04479i	−0.256458	+	0.444199i
$329$	12.4378	+	21.5429i	0.685718	+	1.18770i
$330$		0			0
$331$	−4.85286	+	2.80180i	−0.266737	+	0.154001i	−0.627404	−	0.778694i	$-0.715883\pi$
$331$	−4.85286	+	2.80180i	−0.266737	+	0.154001i	0.360667	+	0.932695i	$0.382549\pi$
$332$	−6.88764	+	3.97658i	−0.378009	+	0.218243i
$333$		0			0
$334$	−3.94851	−	6.83902i	−0.216053	−	0.374214i
$335$	7.37671	−	12.7768i	0.403033	−	0.698073i
$336$		0			0
$337$	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
$339$		0			0
$340$	−3.46410	−	2.00000i	−0.187867	−	0.108465i
$341$	3.51928	−	6.09557i	0.190580	−	0.330094i
$342$		0			0
$343$		−	2.61124i		−	0.140994i
$344$	−6.55829	+	3.78643i	−0.353599	+	0.204151i
$345$		0			0
$346$		−	0.440685i		−	0.0236914i
$347$	4.84081	+	8.38453i	0.259868	+	0.450105i	0.966206	−	0.257769i	$-0.0829875\pi$
$347$	4.84081	+	8.38453i	0.259868	+	0.450105i	−0.706338	+	0.707875i	$0.749654\pi$
$348$		0			0
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.875785	−	0.482701i	$-0.160344\pi$
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.0198610	+	0.999803i	$0.493678\pi$
$350$	−3.64466			−0.194815
$351$		0			0
$352$	1.66808			0.0889087
$353$	19.8970	+	11.4875i	1.05901	+	0.611419i	0.925158	−	0.379583i	$-0.123932\pi$
$353$	19.8970	+	11.4875i	1.05901	+	0.611419i	0.133851	+	0.991002i	$0.457266\pi$
$354$		0			0
$355$	−1.75547	−	3.04056i	−0.0931705	−	0.161376i
$356$		−	5.95162i		−	0.315435i
$357$		0			0
$358$	−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			0
$361$	10.4253	−	18.0572i	0.548701	−	0.950378i
$362$	−5.38453	−	3.10876i	−0.283005	−	0.163393i
$363$		0			0
$364$	12.2253	−	4.81944i	0.640782	−	0.252607i
$365$	−12.2175			−0.639494
$366$		0			0
$367$	3.04056	−	5.26640i	0.158716	−	0.274904i	−0.775690	−	0.631114i	$-0.782598\pi$
$367$	3.04056	−	5.26640i	0.158716	−	0.274904i	0.934406	+	0.356210i	$0.115931\pi$
$368$	−0.622266	−	1.07780i	−0.0324379	−	0.0561841i
$369$		0			0
$370$	−8.54267	+	4.93211i	−0.444112	+	0.256408i
$371$	−2.67860	+	1.54649i	−0.139066	+	0.0802898i
$372$		0			0
$373$	−7.83904	−	13.5776i	−0.405890	−	0.703022i	0.588535	−	0.808472i	$-0.299705\pi$
$373$	−7.83904	−	13.5776i	−0.405890	−	0.703022i	−0.994425	+	0.105450i	$0.966372\pi$
$374$	−3.33615	+	5.77838i	−0.172508	+	0.298793i
$375$		0			0
$376$	−6.82522			−0.351984
$377$	13.2825	+	33.6934i	0.684085	+	1.73530i
$378$		0			0
$379$	26.6013	+	15.3583i	1.36642	+	0.788903i	0.990469	−	0.137737i	$-0.0439829\pi$
$379$	26.6013	+	15.3583i	1.36642	+	0.788903i	0.375951	+	0.926640i	$0.377316\pi$
$380$	3.15637	−	5.46699i	0.161918	−	0.280451i
$381$		0			0
$382$		−	15.6816i		−	0.802342i
$383$	−17.3741	+	10.0310i	−0.887777	+	0.512558i	−0.873215	−	0.487336i	$-0.837969\pi$
$383$	−17.3741	+	10.0310i	−0.887777	+	0.512558i	−0.0145623	+	0.999894i	$0.504635\pi$
$384$		0			0
$385$			6.07957i			0.309844i
$386$	−4.06397	−	7.03901i	−0.206851	−	0.358276i
$387$		0			0
$388$	−2.38453	−	1.37671i	−0.121056	−	0.0698919i
$389$	−27.0314			−1.37055			−0.685273	−	0.728287i	$-0.740317\pi$
$389$	−27.0314			−1.37055			−0.685273	+	0.728287i	$0.740317\pi$
$390$		0			0
$391$	4.97813			0.251755
$392$	−5.44171	−	3.14177i	−0.274848	−	0.158683i
$393$		0			0
$394$	0.445619	+	0.771835i	0.0224500	+	0.0388845i
$395$		−	9.93398i		−	0.499833i
$396$		0			0
$397$	−3.23571	+	1.86814i	−0.162396	+	0.0937592i	−0.578995	−	0.815331i	$-0.696555\pi$
$397$	−3.23571	+	1.86814i	−0.162396	+	0.0937592i	0.416600	+	0.909090i	$0.363222\pi$
$398$		−	0.361116i		−	0.0181011i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−24.3276	−	14.0456i	−1.21486	−	0.701402i	−0.251049	−	0.967974i	$-0.580775\pi$
$401$	−24.3276	−	14.0456i	−1.21486	−	0.701402i	−0.963815	+	0.266573i	$0.914109\pi$
$402$		0			0
$403$	11.9090	+	9.46770i	0.593230	+	0.471620i
$404$	−5.33615			−0.265483
$405$		0			0
$406$	18.3049	−	31.7050i	0.908458	−	1.57349i
$407$	8.22714	+	14.2498i	0.407804	+	0.706338i
$408$		0			0
$409$	23.7122	−	13.6902i	1.17249	−	0.676938i	0.218225	−	0.975898i	$-0.429973\pi$
$409$	23.7122	−	13.6902i	1.17249	−	0.676938i	0.954265	+	0.298961i	$0.0966399\pi$
$410$	8.04479	−	4.64466i	0.397304	−	0.229383i
$411$		0			0
$412$	−3.75624	−	6.50600i	−0.185057	−	0.320528i
$413$	11.1322	−	19.2815i	0.547779	−	0.948780i
$414$		0			0
$415$	7.95317			0.390406
$416$	−0.531987	+	3.56609i	−0.0260828	+	0.174842i
$417$		0			0
$418$	−9.11935	−	5.26506i	−0.446042	−	0.257523i
$419$	−6.58068	+	11.3981i	−0.321487	+	0.556833i	−0.980795	−	0.195041i	$-0.937516\pi$
$419$	−6.58068	+	11.3981i	−0.321487	+	0.556833i	0.659308	+	0.751873i	$0.270849\pi$
$420$		0			0
$421$			1.29341i			0.0630370i	0.999503	+	0.0315185i	$0.0100343\pi$
$421$			1.29341i			0.0630370i	−0.999503	+	0.0315185i	$0.989966\pi$
$422$	1.92898	−	1.11370i	0.0939011	−	0.0542138i
$423$		0			0
$424$		−	0.848634i		−	0.0412133i
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$		0			0
$427$	23.5595	+	13.6021i	1.14012	+	0.658250i
$428$	16.9282			0.818256
$429$		0			0
$430$	7.57286			0.365196
$431$	−10.5031	−	6.06397i	−0.505917	−	0.292091i	0.225237	−	0.974304i	$-0.427684\pi$
$431$	−10.5031	−	6.06397i	−0.505917	−	0.292091i	−0.731154	+	0.682213i	$0.761018\pi$
$432$		0			0
$433$	−1.03901	−	1.79962i	−0.0499317	−	0.0864842i	0.839979	−	0.542618i	$-0.182567\pi$
$433$	−1.03901	−	1.79962i	−0.0499317	−	0.0864842i	−0.889911	+	0.456134i	$0.849234\pi$
$434$		−	15.3789i		−	0.738210i
$435$		0			0
$436$	0.574909	−	0.331924i	0.0275332	−	0.0158963i
$437$			7.85641i			0.375823i
$438$		0			0
$439$	−1.19820	+	2.07534i	−0.0571869	+	0.0990506i	−0.893202	−	0.449656i	$-0.851546\pi$
$439$	−1.19820	+	2.07534i	−0.0571869	+	0.0990506i	0.836015	+	0.548707i	$0.184880\pi$
$440$	−1.44460	−	0.834038i	−0.0688684	−	0.0397612i
$441$		0			0
$442$	−11.2893	−	8.97504i	−0.536978	−	0.426899i
$443$	−21.9959			−1.04506			−0.522529	−	0.852622i	$-0.675011\pi$
$443$	−21.9959			−1.04506			−0.522529	+	0.852622i	$0.675011\pi$
$444$		0			0
$445$	−2.97581	+	5.15425i	−0.141067	+	0.244335i
$446$	−3.04190	−	5.26872i	−0.144038	−	0.249481i
$447$		0			0
$448$	3.15637	−	1.82233i	0.149124	−	0.0860970i
$449$	−25.3098	+	14.6126i	−1.19445	+	0.689613i	−0.959312	−	0.282350i	$-0.908886\pi$
$449$	−25.3098	+	14.6126i	−1.19445	+	0.689613i	−0.235134	+	0.971963i	$0.575553\pi$
$450$		0			0
$451$	−7.74765	−	13.4193i	−0.364822	−	0.631891i
$452$	8.93500	−	15.4759i	0.420267	−	0.727924i
$453$		0			0
$454$	−15.3205			−0.719027
$455$	−12.9972	−	1.93891i	−0.609317	−	0.0908976i
$456$		0			0
$457$	−34.3321	−	19.8216i	−1.60599	−	0.927216i	−0.990256	−	0.139259i	$-0.955528\pi$
$457$	−34.3321	−	19.8216i	−1.60599	−	0.927216i	−0.615730	−	0.787957i	$-0.711139\pi$
$458$	11.1322	−	19.2815i	0.520172	−	0.900965i
$459$		0			0
$460$			1.24453i			0.0580266i
$461$	−14.4417	+	8.33792i	−0.672617	+	0.388336i	−0.797068	−	0.603890i	$-0.793617\pi$
$461$	−14.4417	+	8.33792i	−0.672617	+	0.388336i	0.124450	+	0.992226i	$0.460283\pi$
$462$		0			0
$463$		−	32.2175i		−	1.49728i	−0.662979	−	0.748638i	$-0.730708\pi$
$463$		−	32.2175i		−	1.49728i	0.662979	−	0.748638i	$-0.269292\pi$
$464$	5.02239	+	8.69904i	0.233159	+	0.403843i
$465$		0			0
$466$	9.38476	+	5.41829i	0.434740	+	0.250998i
$467$	6.88137			0.318432			0.159216	−	0.987244i	$-0.449103\pi$
$467$	6.88137			0.318432			0.159216	+	0.987244i	$0.449103\pi$
$468$		0			0
$469$	−53.7712			−2.48292
$470$	5.91081	+	3.41261i	0.272645	+	0.157412i
$471$		0			0
$472$	3.05438	+	5.29034i	0.140589	+	0.243508i
$473$		−	12.6321i		−	0.580825i
$474$		0			0
$475$	−5.46699	+	3.15637i	−0.250843	+	0.144824i
$476$			14.5786i			0.668211i
$477$		0			0
$478$	8.24876	−	14.2873i	0.377290	−	0.653485i
$479$	16.4293	+	9.48547i	0.750675	+	0.433402i	0.825938	−	0.563761i	$-0.190646\pi$
$479$	16.4293	+	9.48547i	0.750675	+	0.433402i	−0.0752629	+	0.997164i	$0.523980\pi$
$480$		0			0
$481$	−33.0878	+	13.0438i	−1.50867	+	0.594744i
$482$	−4.40435			−0.200613
$483$		0			0
$484$	4.10876	−	7.11658i	0.186762	−	0.323481i
$485$	1.37671	+	2.38453i	0.0625132	+	0.108276i
$486$		0			0
$487$	1.65948	−	0.958101i	0.0751982	−	0.0434157i	−0.461929	−	0.886917i	$-0.652843\pi$
$487$	1.65948	−	0.958101i	0.0751982	−	0.0434157i	0.537128	+	0.843501i	$0.319509\pi$
$488$	−6.46410	+	3.73205i	−0.292616	+	0.168942i
$489$		0			0
$490$	3.14177	+	5.44171i	0.141931	+	0.245831i
$491$	16.8187	−	29.1309i	0.759019	−	1.31466i	−0.184332	−	0.982864i	$-0.559012\pi$
$491$	16.8187	−	29.1309i	0.759019	−	1.31466i	0.943351	−	0.331795i	$-0.107654\pi$
$492$		0			0
$493$	−40.1791			−1.80958
$494$	14.1643	−	17.8166i	0.637280	−	0.801608i
$495$		0			0
$496$	3.65425	+	2.10978i	0.164081	+	0.0947321i
$497$	−6.39808	+	11.0818i	−0.286993	+	0.497087i
$498$		0			0
$499$			1.82522i			0.0817080i	0.999165	+	0.0408540i	$0.0130078\pi$
$499$			1.82522i			0.0817080i	−0.999165	+	0.0408540i	$0.986992\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$		0			0
$502$			11.9453i			0.533147i
$503$	−9.99923	−	17.3192i	−0.445843	−	0.772224i	0.552267	−	0.833667i	$-0.313763\pi$
$503$	−9.99923	−	17.3192i	−0.445843	−	0.772224i	−0.998111	+	0.0614437i	$0.980430\pi$
$504$		0			0
$505$	4.62124	+	2.66808i	0.205643	+	0.118728i
$506$	2.07598			0.0922884
$507$		0			0
$508$	14.4407			0.640702
$509$	−5.10196	−	2.94562i	−0.226141	−	0.130562i	0.382650	−	0.923893i	$-0.375012\pi$
$509$	−5.10196	−	2.94562i	−0.226141	−	0.130562i	−0.608790	+	0.793331i	$0.708345\pi$
$510$		0			0
$511$	22.2644	+	38.5630i	0.984917	+	1.70593i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	16.8546	−	9.73103i	0.743426	−	0.429217i
$515$			7.51248i			0.331040i
$516$		0			0
$517$	5.69249	−	9.85968i	0.250355	−	0.433628i
$518$	31.1351	+	17.9759i	1.36800	+	0.789815i
$519$		0			0
$520$	2.24376	−	2.82233i	0.0983953	−	0.123767i
$521$	−32.0370			−1.40356			−0.701782	−	0.712391i	$-0.747612\pi$
$521$	−32.0370			−1.40356			−0.701782	+	0.712391i	$0.747612\pi$
$522$		0			0
$523$	−19.3593	+	33.5313i	−0.846523	+	1.46622i	0.0377693	+	0.999286i	$0.487975\pi$
$523$	−19.3593	+	33.5313i	−0.846523	+	1.46622i	−0.884292	+	0.466934i	$0.845359\pi$
$524$	5.44460	+	9.43032i	0.237848	+	0.411965i
$525$		0			0
$526$	−1.76217	+	1.01739i	−0.0768344	+	0.0443604i
$527$	−14.6170	+	8.43914i	−0.636727	+	0.367615i
$528$		0			0
$529$	10.7256	+	18.5772i	0.466329	+	0.807706i
$530$	−0.424317	+	0.734939i	−0.0184312	+	0.0319237i
$531$		0			0
$532$	−23.0078			−0.997513
$533$	31.1593	−	12.2835i	1.34966	−	0.532059i
$534$		0			0
$535$	−14.6603	−	8.46410i	−0.633818	−	0.365935i
$536$	7.37671	−	12.7768i	0.318625	−	0.551875i
$537$		0			0
$538$		−	20.5287i		−	0.885056i
$539$	9.07718	−	5.24071i	0.390982	−	0.225734i
$540$		0			0
$541$			25.9616i			1.11618i	0.829781	+	0.558089i	$0.188465\pi$
$541$			25.9616i			1.11618i	−0.829781	+	0.558089i	$0.811535\pi$
$542$	−12.7700	−	22.1184i	−0.548520	−	0.950065i
$543$		0			0
$544$	−3.46410	−	2.00000i	−0.148522	−	0.0857493i
$545$	−0.663848			−0.0284361
$546$		0			0
$547$	−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
$549$		0			0
$550$	0.834038	+	1.44460i	0.0355635	+	0.0615978i
$551$		−	63.4101i		−	2.70136i
$552$		0			0
$553$	−31.3553	+	18.1030i	−1.33336	+	0.769817i
$554$		−	18.0604i		−	0.767312i
$555$		0			0
$556$	5.82233	−	10.0846i	0.246922	−	0.427681i
$557$	22.7074	+	13.1101i	0.962142	+	0.555493i	0.896832	−	0.442372i	$-0.145863\pi$
$557$	22.7074	+	13.1101i	0.962142	+	0.555493i	0.0653102	+	0.997865i	$0.479196\pi$
$558$		0			0
$559$	27.0055	+	4.02867i	1.14221	+	0.170394i
$560$	−3.64466			−0.154015
$561$		0			0
$562$	10.1088	−	17.5089i	0.426412	−	0.738568i
$563$	12.9964	+	22.5104i	0.547733	+	0.948702i	0.998429	+	0.0560243i	$0.0178424\pi$
$563$	12.9964	+	22.5104i	0.547733	+	0.948702i	−0.450696	+	0.892677i	$0.648824\pi$
$564$		0			0
$565$	−15.4759	+	8.93500i	−0.651075	+	0.375898i
$566$	−7.52705	+	4.34575i	−0.316386	+	0.182665i
$567$		0			0
$568$	−1.75547	−	3.04056i	−0.0736578	−	0.127579i
$569$	12.7349	−	22.0576i	0.533876	−	0.924701i	−0.465340	−	0.885132i	$-0.654068\pi$
$569$	12.7349	−	22.0576i	0.533876	−	0.924701i	0.999217	−	0.0395693i	$-0.0125986\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	−29.3205	−	16.9282i	−1.22381	−	0.706570i
$575$	0.622266	−	1.07780i	0.0259503	−	0.0449472i
$576$		0			0
$577$		−	35.4216i		−	1.47462i	−0.675554	−	0.737311i	$-0.736095\pi$
$577$		−	35.4216i		−	1.47462i	0.675554	−	0.737311i	$-0.263905\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$		0			0
$580$		−	10.0448i		−	0.417087i
$581$	−14.4933	−	25.1031i	−0.601283	−	1.04145i
$582$		0			0
$583$	1.22593	+	0.707793i	0.0507730	+	0.0293138i
$584$	−12.2175			−0.505565
$585$		0			0
$586$	7.54790			0.311801
$587$	−23.7108	−	13.6894i	−0.978650	−	0.565024i	−0.0767878	−	0.997047i	$-0.524466\pi$
$587$	−23.7108	−	13.6894i	−0.978650	−	0.565024i	−0.901862	+	0.432024i	$0.857800\pi$
$588$		0			0
$589$	−13.3185	−	23.0683i	−0.548780	−	0.950514i
$590$		−	6.10876i		−	0.251494i
$591$		0			0
$592$	−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			0
$595$	7.28932	−	12.6255i	0.298833	−	0.517594i
$596$	0.669099	+	0.386305i	0.0274074	+	0.0158237i
$597$		0			0
$598$	−0.662076	+	4.43811i	−0.0270743	+	0.181488i
$599$	28.6129			1.16909			0.584546	−	0.811360i	$-0.301273\pi$
$599$	28.6129			1.16909			0.584546	+	0.811360i	$0.301273\pi$
$600$		0			0
$601$	9.58380	−	16.5996i	0.390931	−	0.677113i	−0.601641	−	0.798766i	$-0.705486\pi$
$601$	9.58380	−	16.5996i	0.390931	−	0.677113i	0.992573	+	0.121654i	$0.0388197\pi$
$602$	−13.8003	−	23.9027i	−0.562456	−	0.974203i
$603$		0			0
$604$	−8.46833	+	4.88919i	−0.344571	+	0.198938i
$605$	−7.11658	+	4.10876i	−0.289330	+	0.167045i
$606$		0			0
$607$	−9.46910	−	16.4010i	−0.384339	−	0.665695i	0.607338	−	0.794443i	$-0.292237\pi$
$607$	−9.46910	−	16.4010i	−0.384339	−	0.665695i	−0.991677	+	0.128749i	$0.958904\pi$
$608$	3.15637	−	5.46699i	0.128008	−	0.221716i
$609$		0			0
$610$	7.46410			0.302213
$611$	19.2630	+	15.3141i	0.779298	+	0.619544i
$612$		0			0
$613$	−15.5620	−	8.98472i	−0.628543	−	0.362890i	0.151645	−	0.988435i	$-0.451543\pi$
$613$	−15.5620	−	8.98472i	−0.628543	−	0.362890i	−0.780188	+	0.625546i	$0.784876\pi$
$614$	−13.0214	+	22.5537i	−0.525500	+	0.910192i
$615$		0			0
$616$			6.07957i			0.244953i
$617$	15.6015	−	9.00755i	0.628094	−	0.362630i	−0.151920	−	0.988393i	$-0.548545\pi$
$617$	15.6015	−	9.00755i	0.628094	−	0.362630i	0.780014	+	0.625763i	$0.215212\pi$
$618$		0			0
$619$			25.0505i			1.00687i	0.864035	+	0.503433i	$0.167930\pi$
$619$			25.0505i			1.00687i	−0.864035	+	0.503433i	$0.832070\pi$
$620$	−2.10978	−	3.65425i	−0.0847310	−	0.146758i
$621$		0			0
$622$	21.9788	+	12.6894i	0.881268	+	0.508800i
$623$	21.6916			0.869057
$624$		0			0
$625$	1.00000			0.0400000
$626$	27.2452	+	15.7300i	1.08894	+	0.628697i
$627$		0			0
$628$	−6.00677	−	10.4040i	−0.239696	−	0.415166i
$629$		−	39.4569i		−	1.57325i
$630$		0			0
$631$	−1.22739	+	0.708634i	−0.0488617	+	0.0282103i	−0.524232	−	0.851576i	$-0.675647\pi$
$631$	−1.22739	+	0.708634i	−0.0488617	+	0.0282103i	0.475370	+	0.879786i	$0.342314\pi$
$632$		−	9.93398i		−	0.395152i
$633$		0			0
$634$	−12.3546	+	21.3989i	−0.490665	+	0.849857i
$635$	−12.5060	−	7.22034i	−0.496285	−	0.286531i
$636$		0			0
$637$	8.30892	+	21.0770i	0.329211	+	0.835101i
$638$	−16.7555			−0.663355
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−2.30985	−	4.00077i	−0.0912335	−	0.158021i	0.816797	−	0.576925i	$-0.195748\pi$
$641$	−2.30985	−	4.00077i	−0.0912335	−	0.158021i	−0.908030	+	0.418904i	$0.862414\pi$
$642$		0			0
$643$	41.6468	−	24.0448i	1.64239	−	0.948234i	0.662408	−	0.749143i	$-0.269535\pi$
$643$	41.6468	−	24.0448i	1.64239	−	0.948234i	0.979981	−	0.199091i	$-0.0637988\pi$
$644$	3.92820	−	2.26795i	0.154793	−	0.0893697i
$645$		0			0
$646$	12.6255	+	21.8680i	0.496743	+	0.860383i
$647$	−1.87282	+	3.24383i	−0.0736283	+	0.127528i	−0.900489	−	0.434879i	$-0.856791\pi$
$647$	−1.87282	+	3.24383i	−0.0736283	+	0.127528i	0.826861	+	0.562407i	$0.190125\pi$
$648$		0			0
$649$	−10.1899			−0.399988
$650$	−3.35432	+	1.32233i	−0.131567	+	0.0518660i
$651$		0			0
$652$	−8.73960	−	5.04581i	−0.342269	−	0.197609i
$653$	21.1450	−	36.6241i	0.827466	−	1.43321i	−0.0725541	−	0.997364i	$-0.523115\pi$
$653$	21.1450	−	36.6241i	0.827466	−	1.43321i	0.900020	−	0.435849i	$-0.143552\pi$
$654$		0			0
$655$		−	10.8892i		−	0.425476i
$656$	8.04479	−	4.64466i	0.314096	−	0.181343i
$657$		0			0
$658$		−	24.8756i		−	0.969752i
$659$	−14.5875	−	25.2663i	−0.568248	−	0.984234i	−0.996739	−	0.0806881i	$-0.974288\pi$
$659$	−14.5875	−	25.2663i	−0.568248	−	0.984234i	0.428492	−	0.903546i	$-0.359045\pi$
$660$		0			0
$661$	−38.5089	−	22.2331i	−1.49782	−	0.864768i	−0.497825	−	0.867277i	$-0.665868\pi$
$661$	−38.5089	−	22.2331i	−1.49782	−	0.864768i	−0.999997	+	0.00250931i	$0.999201\pi$
$662$	5.60360			0.217790
$663$		0			0
$664$	7.95317			0.308643
$665$	19.9253	+	11.5039i	0.772671	+	0.446102i
$666$		0			0
$667$	6.25053	+	10.8262i	0.242022	+	0.419194i
$668$			7.89701i			0.305545i
$669$		0			0
$670$	−12.7768	+	7.37671i	−0.493612	+	0.284987i
$671$		−	12.4507i		−	0.480654i
$672$		0			0
$673$	3.95317	−	6.84709i	0.152383	−	0.263936i	−0.779720	−	0.626129i	$-0.784638\pi$
$673$	3.95317	−	6.84709i	0.152383	−	0.263936i	0.932103	+	0.362193i	$0.117972\pi$
$674$	−18.8680	−	10.8934i	−0.726767	−	0.419599i
$675$		0			0
$676$	9.50289	−	8.87103i	0.365496	−	0.341193i
$677$	7.05615			0.271190			0.135595	−	0.990764i	$-0.456705\pi$
$677$	7.05615			0.271190			0.135595	+	0.990764i	$0.456705\pi$
$678$		0			0
$679$	5.01764	−	8.69081i	0.192559	−	0.333523i
$680$	2.00000	+	3.46410i	0.0766965	+	0.132842i
$681$		0			0
$682$	−6.09557	+	3.51928i	−0.233412	+	0.134760i
$683$	5.15559	−	2.97658i	0.197273	−	0.113896i	−0.398110	−	0.917338i	$-0.630334\pi$
$683$	5.15559	−	2.97658i	0.197273	−	0.113896i	0.595383	+	0.803442i	$0.297000\pi$
$684$		0			0
$685$	3.51848	+	6.09419i	0.134434	+	0.232847i
$686$	−1.30562	+	2.26140i	−0.0498488	+	0.0863406i
$687$		0			0
$688$	7.57286			0.288713
$689$	−1.90413	+	2.39513i	−0.0725416	+	0.0912470i
$690$		0			0
$691$	16.2458	+	9.37953i	0.618020	+	0.356814i	0.776098	−	0.630613i	$-0.217196\pi$
$691$	16.2458	+	9.37953i	0.618020	+	0.356814i	−0.158078	+	0.987427i	$0.550530\pi$
$692$	−0.220343	+	0.381645i	−0.00837617	+	0.0145080i
$693$		0			0
$694$		−	9.68162i		−	0.367509i
$695$	−10.0846	+	5.82233i	−0.382530	+	0.220854i
$696$		0			0
$697$			37.1573i			1.40743i
$698$	−9.66025	−	16.7321i	−0.365646	−	0.633317i
$699$		0			0
$700$	3.15637	+	1.82233i	0.119299	+	0.0688776i
$701$	28.5298			1.07755			0.538777	−	0.842448i	$-0.318887\pi$
$701$	28.5298			1.07755			0.538777	+	0.842448i	$0.318887\pi$
$702$		0			0
$703$	62.2703			2.34857
$704$	−1.44460	−	0.834038i	−0.0544453	−	0.0314340i
$705$		0			0
$706$	−11.4875	−	19.8970i	−0.432338	−	0.748832i
$707$		−	19.4485i		−	0.731435i
$708$		0			0
$709$	−20.0853	+	11.5963i	−0.754321	+	0.435507i	−0.827253	−	0.561830i	$-0.810098\pi$
$709$	−20.0853	+	11.5963i	−0.754321	+	0.435507i	0.0729321	+	0.997337i	$0.476764\pi$
$710$			3.51093i			0.131763i
$711$		0			0
$712$	−2.97581	+	5.15425i	−0.111523	+	0.193164i
$713$	4.54784	+	2.62570i	0.170318	+	0.0983331i
$714$		0			0
$715$	2.20575	+	5.59526i	0.0824902	+	0.209251i
$716$	19.6368			0.733863
$717$		0			0
$718$	−1.10876	+	1.92043i	−0.0413786	+	0.0716698i
$719$	−5.85641	−	10.1436i	−0.218407	−	0.378292i	0.735914	−	0.677075i	$-0.236753\pi$
$719$	−5.85641	−	10.1436i	−0.218407	−	0.378292i	−0.954321	+	0.298783i	$0.903419\pi$
$720$		0			0
$721$	23.7122	−	13.6902i	0.883087	−	0.509850i
$722$	−18.0572	+	10.4253i	−0.672019	+	0.387990i
$723$		0			0
$724$	3.10876	+	5.38453i	0.115536	+	0.200115i
$725$	−5.02239	+	8.69904i	−0.186527	+	0.323074i
$726$		0			0
$727$	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
$729$		0			0
$730$	10.5807	+	6.10876i	0.391609	+	0.226095i
$731$	−15.1457	+	26.2332i	−0.560185	+	0.970269i
$732$		0			0
$733$			12.9340i			0.477727i	0.971053	+	0.238864i	$0.0767749\pi$
$733$			12.9340i			0.477727i	−0.971053	+	0.238864i	$0.923225\pi$
$734$	−5.26640	+	3.04056i	−0.194386	+	0.112229i
$735$		0			0
$736$			1.24453i			0.0458741i
$737$	12.3049	+	21.3127i	0.453257	+	0.785065i
$738$		0			0
$739$	−30.6107	−	17.6731i	−1.12603	−	0.650115i	−0.183098	−	0.983095i	$-0.558612\pi$
$739$	−30.6107	−	17.6731i	−1.12603	−	0.650115i	−0.942934	+	0.332980i	$0.891946\pi$
$740$	9.86423			0.362616
$741$		0			0
$742$	3.09298			0.113547
$743$	32.1255	+	18.5477i	1.17857	+	0.680448i	0.955684	−	0.294396i	$-0.0951185\pi$
$743$	32.1255	+	18.5477i	1.17857	+	0.680448i	0.222887	+	0.974844i	$0.428452\pi$
$744$		0			0
$745$	−0.386305	−	0.669099i	−0.0141531	−	0.0245139i
$746$			15.6781i			0.574015i
$747$		0			0
$748$	5.77838	−	3.33615i	0.211279	−	0.121982i
$749$			61.6975i			2.25438i
$750$		0			0
$751$	−4.82904	+	8.36414i	−0.176214	+	0.305212i	−0.940581	−	0.339570i	$-0.889718\pi$
$751$	−4.82904	+	8.36414i	−0.176214	+	0.305212i	0.764367	+	0.644782i	$0.223052\pi$
$752$	5.91081	+	3.41261i	0.215545	+	0.124445i
$753$		0			0
$754$	5.34370	−	35.8206i	0.194606	−	1.30451i
$755$	9.77838			0.355872
$756$		0			0
$757$	21.8443	−	37.8354i	0.793943	−	1.37515i	−0.129565	−	0.991571i	$-0.541358\pi$
$757$	21.8443	−	37.8354i	0.793943	−	1.37515i	0.923508	−	0.383579i	$-0.125309\pi$
$758$	−15.3583	−	26.6013i	−0.557838	−	0.966204i
$759$		0			0
$760$	−5.46699	+	3.15637i	−0.198309	+	0.114493i
$761$	−34.5550	+	19.9503i	−1.25262	+	0.723200i	−0.971629	−	0.236511i	$-0.923996\pi$
$761$	−34.5550	+	19.9503i	−1.25262	+	0.723200i	−0.280990	+	0.959711i	$0.590663\pi$
$762$		0			0
$763$	1.20975	+	2.09535i	0.0437959	+	0.0758567i
$764$	−7.84081	+	13.5807i	−0.283671	+	0.491332i
$765$		0			0
$766$	20.0619			0.724867
$767$	3.24978	−	21.7844i	0.117343	−	0.786589i
$768$		0			0
$769$	−15.2064	−	8.77941i	−0.548356	−	0.316594i	0.200103	−	0.979775i	$-0.435872\pi$
$769$	−15.2064	−	8.77941i	−0.548356	−	0.316594i	−0.748459	+	0.663181i	$0.769206\pi$
$770$	3.03978	−	5.26506i	0.109546	−	0.189740i
$771$		0			0
$772$			8.12795i			0.292531i
$773$	−11.1174	+	6.41861i	−0.399864	+	0.230861i	−0.686425	−	0.727201i	$-0.740821\pi$
$773$	−11.1174	+	6.41861i	−0.399864	+	0.230861i	0.286562	+	0.958062i	$0.407488\pi$
$774$		0			0
$775$			4.21957i			0.151571i
$776$	1.37671	+	2.38453i	0.0494210	+	0.0855997i
$777$		0			0
$778$	23.4099	+	13.5157i	0.839284	+	0.484561i
$779$	−58.6410			−2.10103
$780$		0			0
$781$	5.85651			0.209562
$782$	−4.31119	−	2.48907i	−0.154168	−	0.0890088i
$783$		0			0
$784$	3.14177	+	5.44171i	0.112206	+	0.194347i
$785$			12.0135i			0.428782i
$786$		0			0
$787$	−6.02524	+	3.47867i	−0.214777	+	0.124001i	−0.603529	−	0.797341i	$-0.706239\pi$
$787$	−6.02524	+	3.47867i	−0.214777	+	0.124001i	0.388753	+	0.921342i	$0.372906\pi$
$788$		−	0.891239i		−	0.0317491i
$789$		0			0
$790$	−4.96699	+	8.60308i	−0.176718	+	0.306084i
$791$	56.4043	+	32.5650i	2.00551	+	1.15788i
$792$		0			0
$793$	26.6176	+	3.97081i	0.945220	+	0.141008i
$794$	3.73628			0.132596
$795$		0			0
$796$	−0.180558	+	0.312736i	−0.00639971	+	0.0110846i
$797$	−17.0677	−	29.5621i	−0.604569	−	1.04714i	−0.992119	−	0.125296i	$-0.960012\pi$
$797$	−17.0677	−	29.5621i	−0.604569	−	1.04714i	0.387550	−	0.921849i	$-0.373321\pi$
$798$		0			0
$799$	−23.6432	+	13.6504i	−0.836438	+	0.482918i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	14.0456	+	24.3276i	0.495966	+	0.859038i
$803$	10.1899	−	17.6494i	0.359593	−	0.622833i
$804$		0			0
$805$	−4.53590			−0.159869
$806$	−5.57966	−	14.1538i	−0.196535	−	0.498545i
$807$		0			0
$808$	4.62124	+	2.66808i	0.162575	+	0.0938626i
$809$	−1.66385	+	2.88187i	−0.0584978	+	0.101321i	−0.893791	−	0.448483i	$-0.851964\pi$
$809$	−1.66385	+	2.88187i	−0.0584978	+	0.101321i	0.835293	+	0.549804i	$0.185298\pi$
$810$		0			0
$811$		−	20.6083i		−	0.723655i	−0.932245	−	0.361827i	$-0.882153\pi$
$811$		−	20.6083i		−	0.723655i	0.932245	−	0.361827i	$-0.117847\pi$
$812$	−31.7050	+	18.3049i	−1.11263	+	0.642377i
$813$		0			0
$814$		−	16.4543i		−	0.576722i
$815$	5.04581	+	8.73960i	0.176747	+	0.306135i
$816$		0			0
$817$	−41.4008	−	23.9027i	−1.44843	−	0.836251i
$818$	−27.3804			−0.957335
$819$		0			0
$820$	−9.28932			−0.324397
$821$	−1.36836	−	0.790025i	−0.0477562	−	0.0275721i	0.475932	−	0.879482i	$-0.342111\pi$
$821$	−1.36836	−	0.790025i	−0.0477562	−	0.0275721i	−0.523688	+	0.851910i	$0.675444\pi$
$822$		0			0
$823$	18.7584	+	32.4905i	0.653878	+	1.13255i	0.982174	+	0.187974i	$0.0601922\pi$
$823$	18.7584	+	32.4905i	0.653878	+	1.13255i	−0.328296	+	0.944575i	$0.606474\pi$
$824$			7.51248i			0.261710i
$825$		0			0
$826$	−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			0
$829$	24.5693	−	42.5552i	0.853326	−	1.47800i	−0.0248634	−	0.999691i	$-0.507915\pi$
$829$	24.5693	−	42.5552i	0.853326	−	1.47800i	0.878189	−	0.478313i	$-0.158752\pi$
$830$	−6.88764	−	3.97658i	−0.239074	−	0.138029i
$831$		0			0
$832$	2.24376	−	2.82233i	0.0777883	−	0.0978467i
$833$	−25.1342			−0.870848
$834$		0			0
$835$	3.94851	−	6.83902i	0.136644	−	0.236674i
$836$	5.26506	+	9.11935i	0.182096	+	0.315399i
$837$		0			0
$838$	11.3981	−	6.58068i	0.393740	−	0.227326i
$839$	18.6560	−	10.7711i	0.644078	−	0.371858i	−0.142106	−	0.989851i	$-0.545387\pi$
$839$	18.6560	−	10.7711i	0.644078	−	0.371858i	0.786184	+	0.617993i	$0.212054\pi$
$840$		0			0
$841$	−35.9489	−	62.2653i	−1.23962	−	2.14708i
$842$	0.646706	−	1.12013i	0.0222870	−	0.0386021i
$843$		0			0
$844$	−2.22739			−0.0766700
$845$	−12.6653	+	2.93109i	−0.435698	+	0.100833i
$846$		0			0
$847$	25.9375	+	14.9750i	0.891224	+	0.514548i
$848$	−0.424317	+	0.734939i	−0.0145711	+	0.0252379i
$849$		0			0
$850$		−	4.00000i		−	0.137199i
$851$	−10.6316	+	6.13818i	−0.364448	+	0.210414i
$852$		0			0
$853$			2.79821i			0.0958088i	0.998852	+	0.0479044i	$0.0152543\pi$
$853$			2.79821i			0.0958088i	−0.998852	+	0.0479044i	$0.984746\pi$
$854$	−13.6021	−	23.5595i	−0.465453	−	0.806188i
$855$		0			0
$856$	−14.6603	−	8.46410i	−0.501077	−	0.289297i
$857$	48.9658			1.67264			0.836320	−	0.548242i	$-0.184703\pi$
$857$	48.9658			1.67264			0.836320	+	0.548242i	$0.184703\pi$
$858$		0			0
$859$	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
$861$		0			0
$862$	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			0
$865$	0.381645	−	0.220343i	0.0129763	−	0.00749187i
$866$			2.07802i			0.0706141i
$867$		0			0
$868$	−7.68945	+	13.3185i	−0.260997	+	0.452060i
$869$	14.3506	+	8.28532i	0.486810	+	0.281060i
$870$		0			0
$871$	−49.4877	+	19.5089i	−1.67683	+	0.661033i
$872$	−0.663848			−0.0224807
$873$		0			0
$874$	3.92820	−	6.80385i	0.132873	−	0.230144i
$875$	−1.82233	−	3.15637i	−0.0616060	−	0.106705i
$876$		0			0
$877$	11.7323	−	6.77363i	0.396171	−	0.228729i	−0.288660	−	0.957432i	$-0.593210\pi$
$877$	11.7323	−	6.77363i	0.396171	−	0.228729i	0.684830	+	0.728702i	$0.259876\pi$
$878$	2.07534	−	1.19820i	0.0700394	−	0.0404373i
$879$		0			0
$880$	0.834038	+	1.44460i	0.0281154	+	0.0486973i
$881$	−2.49041	+	4.31351i	−0.0839039	+	0.145326i	−0.904924	−	0.425574i	$-0.860072\pi$
$881$	−2.49041	+	4.31351i	−0.0839039	+	0.145326i	0.821020	+	0.570900i	$0.193406\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	19.0490	+	10.9980i	0.639964	+	0.369483i
$887$	8.58826	−	14.8753i	0.288365	−	0.499464i	−0.685054	−	0.728492i	$-0.740222\pi$
$887$	8.58826	−	14.8753i	0.288365	−	0.499464i	0.973420	+	0.229028i	$0.0735549\pi$
$888$		0			0
$889$			52.6314i			1.76520i
$890$	5.15425	−	2.97581i	0.172771	−	0.0997494i
$891$		0			0
$892$			6.08380i			0.203701i
$893$	−21.5429	−	37.3134i	−0.720906	−	1.24865i
$894$		0			0
$895$	−17.0060	−	9.81842i	−0.568448	−	0.328194i
$896$	−3.64466			−0.121760
$897$		0			0
$898$	29.2253			0.975261
$899$	−36.7062	−	21.1923i	−1.22422	−	0.706804i
$900$		0			0
$901$	−1.69727	−	2.93975i	−0.0565442	−	0.0979374i
$902$			15.4953i			0.515937i
$903$		0			0
$904$	−15.4759	+	8.93500i	−0.514720	+	0.297174i
$905$		−	6.21752i		−	0.206677i
$906$		0			0
$907$	−12.5399	+	21.7197i	−0.416379	+	0.721190i	−0.995572	−	0.0940008i	$-0.970034\pi$
$907$	−12.5399	+	21.7197i	−0.416379	+	0.721190i	0.579193	+	0.815190i	$0.303368\pi$
$908$	13.2679	+	7.66025i	0.440312	+	0.254214i
$909$		0			0
$910$	10.2864	+	8.17774i	0.340992	+	0.271089i
$911$	−18.2332			−0.604092			−0.302046	−	0.953293i	$-0.597670\pi$
$911$	−18.2332			−0.604092			−0.302046	+	0.953293i	$0.597670\pi$
$912$		0			0
$913$	−6.63324	+	11.4891i	−0.219528	+	0.380234i
$914$	19.8216	+	34.3321i	0.655641	+	1.13560i
$915$		0			0
$916$	−19.2815	+	11.1322i	−0.637079	+	0.367818i
$917$	−34.3703	+	19.8437i	−1.13501	+	0.655297i
$918$		0			0
$919$	17.1941	+	29.7811i	0.567181	+	0.982387i	0.996843	+	0.0793968i	$0.0252994\pi$
$919$	17.1941	+	29.7811i	0.567181	+	0.982387i	−0.429662	+	0.902990i	$0.641367\pi$
$920$	0.622266	−	1.07780i	0.0205155	−	0.0355339i
$921$		0			0
$922$	16.6758			0.549190
$923$	−1.86777	+	12.5203i	−0.0614785	+	0.412111i
$924$		0			0
$925$	−8.54267	−	4.93211i	−0.280881	−	0.162167i
$926$	−16.1088	+	27.9012i	−0.529367	+	0.916890i
$927$		0			0
$928$		−	10.0448i		−	0.329736i
$929$	−26.9251	+	15.5452i	−0.883384	+	0.510022i	−0.871773	−	0.489911i	$-0.837029\pi$
$929$	−26.9251	+	15.5452i	−0.883384	+	0.510022i	−0.0116114	+	0.999933i	$0.503696\pi$
$930$		0			0
$931$		−	39.6663i		−	1.30001i
$932$	−5.41829	−	9.38476i	−0.177482	−	0.307408i
$933$		0			0
$934$	−5.95944	−	3.44069i	−0.194999	−	0.112583i
$935$	−6.67230			−0.218208
$936$		0			0
$937$	−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
$939$		0			0
$940$	−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	$0.843639\pi$
$942$		0			0
$943$	10.0120	−	5.78043i	0.326036	−	0.188237i
$944$		−	6.10876i		−	0.198823i
$945$		0			0
$946$	−6.31606	+	10.9397i	−0.205353	+	0.355681i
$947$	−6.81472	−	3.93448i	−0.221448	−	0.127853i	0.385172	−	0.922845i	$-0.374142\pi$
$947$	−6.81472	−	3.93448i	−0.221448	−	0.127853i	−0.606621	+	0.794991i	$0.707475\pi$
$948$		0			0
$949$	34.4819	+	27.4132i	1.11933	+	0.889869i
$950$	6.31274			0.204812
$951$		0			0
$952$	7.28932	−	12.6255i	0.236248	−	0.409194i
$953$	27.5484	+	47.7153i	0.892381	+	1.54565i	0.837013	+	0.547183i	$0.184300\pi$
$953$	27.5484	+	47.7153i	0.892381	+	1.54565i	0.0553681	+	0.998466i	$0.482367\pi$
$954$		0			0
$955$	13.5807	−	7.84081i	0.439461	−	0.253723i
$956$	−14.2873	+	8.24876i	−0.462083	+	0.266784i
$957$		0			0
$958$	−9.48547	−	16.4293i	−0.306462	−	0.530807i
$959$	12.8237	−	22.2112i	0.414098	−	0.717239i
$960$		0			0
$961$	13.1952			0.425653
$962$	35.1767	+	5.24765i	1.13414	+	0.169191i
$963$		0			0
$964$	3.81428	+	2.20218i	0.122850	+	0.0709274i
$965$	4.06397	−	7.03901i	0.130824	−	0.226594i
$966$		0			0
$967$			31.5523i			1.01465i	0.861754	+	0.507326i	$0.169366\pi$
$967$			31.5523i			1.01465i	−0.861754	+	0.507326i	$0.830634\pi$
$968$	−7.11658	+	4.10876i	−0.228736	+	0.132061i
$969$		0			0
$970$		−	2.75342i		−	0.0884070i
$971$	1.83792	+	3.18338i	0.0589818	+	0.102159i	0.894009	−	0.448050i	$-0.147881\pi$
$971$	1.83792	+	3.18338i	0.0589818	+	0.102159i	−0.835027	+	0.550209i	$0.814548\pi$
$972$		0			0
$973$	36.7548	+	21.2204i	1.17831	+	0.680295i
$974$	−1.91620			−0.0613991
$975$		0			0
$976$	7.46410			0.238920
$977$	−36.3908	−	21.0102i	−1.16424	−	0.672177i	−0.211927	−	0.977286i	$-0.567974\pi$
$977$	−36.3908	−	21.0102i	−1.16424	−	0.672177i	−0.952318	+	0.305109i	$0.901307\pi$
$978$		0			0
$979$	−4.96388	−	8.59769i	−0.158646	−	0.274783i
$980$		−	6.28354i		−	0.200720i
$981$		0			0
$982$	−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	$0.931290\pi$
$984$		0			0
$985$	−0.445619	+	0.771835i	−0.0141986	+	0.0245927i
$986$	34.7962	+	20.0896i	1.10814	+	0.639782i
$987$		0			0
$988$	−21.1749	+	8.34752i	−0.673664	+	0.265570i
$989$	9.42468			0.299687
$990$		0			0
$991$	−21.8994	+	37.9309i	−0.695658	+	1.20492i	0.274300	+	0.961644i	$0.411554\pi$
$991$	−21.8994	+	37.9309i	−0.695658	+	1.20492i	−0.969958	+	0.243271i	$0.921780\pi$
$992$	−2.10978	−	3.65425i	−0.0669857	−	0.116023i
$993$		0			0
$994$	11.0818	−	6.39808i	0.351493	−	0.202935i
$995$	0.312736	−	0.180558i	0.00991439	−	0.00572407i
$996$		0			0
$997$	11.7562	+	20.3624i	0.372324	+	0.644884i	0.989923	−	0.141609i	$-0.0452277\pi$
$997$	11.7562	+	20.3624i	0.372324	+	0.644884i	−0.617599	+	0.786493i	$0.711894\pi$
$998$	0.912609	−	1.58068i	0.0288881	−	0.0500357i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.f.901.1		8
3.2	odd	2		390.2.bb.c.121.3	✓	8
13.10	even	6	inner	1170.2.bs.f.361.1		8
15.2	even	4		1950.2.y.j.199.3		8
15.8	even	4		1950.2.y.k.199.2		8
15.14	odd	2		1950.2.bc.g.901.2		8
39.17	odd	6		5070.2.b.ba.1351.8		8
39.20	even	12		5070.2.a.ca.1.1		4
39.23	odd	6		390.2.bb.c.361.3	yes	8
39.32	even	12		5070.2.a.bz.1.4		4
39.35	odd	6		5070.2.b.ba.1351.1		8
195.23	even	12		1950.2.y.j.49.3		8
195.62	even	12		1950.2.y.k.49.2		8
195.179	odd	6		1950.2.bc.g.751.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.3	✓	8	3.2	odd	2
390.2.bb.c.361.3	yes	8	39.23	odd	6
1170.2.bs.f.361.1		8	13.10	even	6	inner
1170.2.bs.f.901.1		8	1.1	even	1	trivial
1950.2.y.j.49.3		8	195.23	even	12
1950.2.y.j.199.3		8	15.2	even	4
1950.2.y.k.49.2		8	195.62	even	12
1950.2.y.k.199.2		8	15.8	even	4
1950.2.bc.g.751.2		8	195.179	odd	6
1950.2.bc.g.901.2		8	15.14	odd	2
5070.2.a.bz.1.4		4	39.32	even	12
5070.2.a.ca.1.1		4	39.20	even	12
5070.2.b.ba.1351.1		8	39.35	odd	6
5070.2.b.ba.1351.8		8	39.17	odd	6

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

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