LMFDB - Embedded newform 156.2.c.b.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(131,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("156.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.c (of order $2$, degree $1$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	156.131
Dual form			156.2.c.b.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} +(1.00000 - 1.41421i) q^{3} -2.00000 q^{4} +1.41421i q^{5} +(-2.00000 - 1.41421i) q^{6} -4.24264i q^{7} +2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +2.00000 q^{10} +(-2.00000 + 2.82843i) q^{12} +1.00000 q^{13} -6.00000 q^{14} +(2.00000 + 1.41421i) q^{15} +4.00000 q^{16} +5.65685i q^{17} +(-4.00000 + 1.41421i) q^{18} +4.24264i q^{19} -2.82843i q^{20} +(-6.00000 - 4.24264i) q^{21} +6.00000 q^{23} +(4.00000 + 2.82843i) q^{24} +3.00000 q^{25} -1.41421i q^{26} +(-5.00000 - 1.41421i) q^{27} +8.48528i q^{28} -2.82843i q^{29} +(2.00000 - 2.82843i) q^{30} -4.24264i q^{31} -5.65685i q^{32} +8.00000 q^{34} +6.00000 q^{35} +(2.00000 + 5.65685i) q^{36} +2.00000 q^{37} +6.00000 q^{38} +(1.00000 - 1.41421i) q^{39} -4.00000 q^{40} +1.41421i q^{41} +(-6.00000 + 8.48528i) q^{42} +8.48528i q^{43} +(4.00000 - 1.41421i) q^{45} -8.48528i q^{46} -12.0000 q^{47} +(4.00000 - 5.65685i) q^{48} -11.0000 q^{49} -4.24264i q^{50} +(8.00000 + 5.65685i) q^{51} -2.00000 q^{52} +5.65685i q^{53} +(-2.00000 + 7.07107i) q^{54} +12.0000 q^{56} +(6.00000 + 4.24264i) q^{57} -4.00000 q^{58} +(-4.00000 - 2.82843i) q^{60} +8.00000 q^{61} -6.00000 q^{62} +(-12.0000 + 4.24264i) q^{63} -8.00000 q^{64} +1.41421i q^{65} +4.24264i q^{67} -11.3137i q^{68} +(6.00000 - 8.48528i) q^{69} -8.48528i q^{70} -12.0000 q^{71} +(8.00000 - 2.82843i) q^{72} +2.00000 q^{73} -2.82843i q^{74} +(3.00000 - 4.24264i) q^{75} -8.48528i q^{76} +(-2.00000 - 1.41421i) q^{78} -8.48528i q^{79} +5.65685i q^{80} +(-7.00000 + 5.65685i) q^{81} +2.00000 q^{82} -12.0000 q^{83} +(12.0000 + 8.48528i) q^{84} -8.00000 q^{85} +12.0000 q^{86} +(-4.00000 - 2.82843i) q^{87} -7.07107i q^{89} +(-2.00000 - 5.65685i) q^{90} -4.24264i q^{91} -12.0000 q^{92} +(-6.00000 - 4.24264i) q^{93} +16.9706i q^{94} -6.00000 q^{95} +(-8.00000 - 5.65685i) q^{96} -10.0000 q^{97} +15.5563i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 4 q^{4} - 4 q^{6} - 2 q^{9} + 4 q^{10} - 4 q^{12} + 2 q^{13} - 12 q^{14} + 4 q^{15} + 8 q^{16} - 8 q^{18} - 12 q^{21} + 12 q^{23} + 8 q^{24} + 6 q^{25} - 10 q^{27} + 4 q^{30} + 16 q^{34}+ \cdots - 20 q^{97}+O(q^{100}) $ 2 * q + 2 * q^3 - 4 * q^4 - 4 * q^6 - 2 * q^9 + 4 * q^10 - 4 * q^12 + 2 * q^13 - 12 * q^14 + 4 * q^15 + 8 * q^16 - 8 * q^18 - 12 * q^21 + 12 * q^23 + 8 * q^24 + 6 * q^25 - 10 * q^27 + 4 * q^30 + 16 * q^34 + 12 * q^35 + 4 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^39 - 8 * q^40 - 12 * q^42 + 8 * q^45 - 24 * q^47 + 8 * q^48 - 22 * q^49 + 16 * q^51 - 4 * q^52 - 4 * q^54 + 24 * q^56 + 12 * q^57 - 8 * q^58 - 8 * q^60 + 16 * q^61 - 12 * q^62 - 24 * q^63 - 16 * q^64 + 12 * q^69 - 24 * q^71 + 16 * q^72 + 4 * q^73 + 6 * q^75 - 4 * q^78 - 14 * q^81 + 4 * q^82 - 24 * q^83 + 24 * q^84 - 16 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^90 - 24 * q^92 - 12 * q^93 - 12 * q^95 - 16 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.41421i		−	1.00000i
$2$		−	1.41421i		−	1.00000i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$4$	−2.00000			−1.00000
$5$			1.41421i			0.632456i	0.948683	+	0.316228i	$0.102416\pi$
$5$			1.41421i			0.632456i	−0.948683	+	0.316228i	$0.897584\pi$
$6$	−2.00000	−	1.41421i	−0.816497	−	0.577350i
$7$		−	4.24264i		−	1.60357i	−0.597614	−	0.801784i	$-0.703885\pi$
$7$		−	4.24264i		−	1.60357i	0.597614	−	0.801784i	$-0.296115\pi$
$8$			2.82843i			1.00000i
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$	2.00000			0.632456
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−2.00000	+	2.82843i	−0.577350	+	0.816497i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−6.00000			−1.60357
$15$	2.00000	+	1.41421i	0.516398	+	0.365148i
$16$	4.00000			1.00000
$17$			5.65685i			1.37199i	0.727607	+	0.685994i	$0.240633\pi$
$17$			5.65685i			1.37199i	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−4.00000	+	1.41421i	−0.942809	+	0.333333i
$19$			4.24264i			0.973329i	0.873589	+	0.486664i	$0.161786\pi$
$19$			4.24264i			0.973329i	−0.873589	+	0.486664i	$0.838214\pi$
$20$		−	2.82843i		−	0.632456i
$21$	−6.00000	−	4.24264i	−1.30931	−	0.925820i
$22$		0			0
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	4.00000	+	2.82843i	0.816497	+	0.577350i
$25$	3.00000			0.600000
$26$		−	1.41421i		−	0.277350i
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$			8.48528i			1.60357i
$29$		−	2.82843i		−	0.525226i	−0.964901	−	0.262613i	$-0.915416\pi$
$29$		−	2.82843i		−	0.525226i	0.964901	−	0.262613i	$-0.0845842\pi$
$30$	2.00000	−	2.82843i	0.365148	−	0.516398i
$31$		−	4.24264i		−	0.762001i	−0.924575	−	0.381000i	$-0.875580\pi$
$31$		−	4.24264i		−	0.762001i	0.924575	−	0.381000i	$-0.124420\pi$
$32$		−	5.65685i		−	1.00000i
$33$		0			0
$34$	8.00000			1.37199
$35$	6.00000			1.01419
$36$	2.00000	+	5.65685i	0.333333	+	0.942809i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	6.00000			0.973329
$39$	1.00000	−	1.41421i	0.160128	−	0.226455i
$40$	−4.00000			−0.632456
$41$			1.41421i			0.220863i	0.993884	+	0.110432i	$0.0352233\pi$
$41$			1.41421i			0.220863i	−0.993884	+	0.110432i	$0.964777\pi$
$42$	−6.00000	+	8.48528i	−0.925820	+	1.30931i
$43$			8.48528i			1.29399i	0.762493	+	0.646997i	$0.223975\pi$
$43$			8.48528i			1.29399i	−0.762493	+	0.646997i	$0.776025\pi$
$44$		0			0
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$		−	8.48528i		−	1.25109i
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$	4.00000	−	5.65685i	0.577350	−	0.816497i
$49$	−11.0000			−1.57143
$50$		−	4.24264i		−	0.600000i
$51$	8.00000	+	5.65685i	1.12022	+	0.792118i
$52$	−2.00000			−0.277350
$53$			5.65685i			0.777029i	0.921443	+	0.388514i	$0.127012\pi$
$53$			5.65685i			0.777029i	−0.921443	+	0.388514i	$0.872988\pi$
$54$	−2.00000	+	7.07107i	−0.272166	+	0.962250i
$55$		0			0
$56$	12.0000			1.60357
$57$	6.00000	+	4.24264i	0.794719	+	0.561951i
$58$	−4.00000			−0.525226
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−4.00000	−	2.82843i	−0.516398	−	0.365148i
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	−6.00000			−0.762001
$63$	−12.0000	+	4.24264i	−1.51186	+	0.534522i
$64$	−8.00000			−1.00000
$65$			1.41421i			0.175412i
$66$		0			0
$67$			4.24264i			0.518321i	0.965834	+	0.259161i	$0.0834459\pi$
$67$			4.24264i			0.518321i	−0.965834	+	0.259161i	$0.916554\pi$
$68$		−	11.3137i		−	1.37199i
$69$	6.00000	−	8.48528i	0.722315	−	1.02151i
$70$		−	8.48528i		−	1.01419i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	8.00000	−	2.82843i	0.942809	−	0.333333i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		−	2.82843i		−	0.328798i
$75$	3.00000	−	4.24264i	0.346410	−	0.489898i
$76$		−	8.48528i		−	0.973329i
$77$		0			0
$78$	−2.00000	−	1.41421i	−0.226455	−	0.160128i
$79$		−	8.48528i		−	0.954669i	−0.878722	−	0.477334i	$-0.841603\pi$
$79$		−	8.48528i		−	0.954669i	0.878722	−	0.477334i	$-0.158397\pi$
$80$			5.65685i			0.632456i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	2.00000			0.220863
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	12.0000	+	8.48528i	1.30931	+	0.925820i
$85$	−8.00000			−0.867722
$86$	12.0000			1.29399
$87$	−4.00000	−	2.82843i	−0.428845	−	0.303239i
$88$		0			0
$89$		−	7.07107i		−	0.749532i	−0.927119	−	0.374766i	$-0.877723\pi$
$89$		−	7.07107i		−	0.749532i	0.927119	−	0.374766i	$-0.122277\pi$
$90$	−2.00000	−	5.65685i	−0.210819	−	0.596285i
$91$		−	4.24264i		−	0.444750i
$92$	−12.0000			−1.25109
$93$	−6.00000	−	4.24264i	−0.622171	−	0.439941i
$94$			16.9706i			1.75038i
$95$	−6.00000			−0.615587
$96$	−8.00000	−	5.65685i	−0.816497	−	0.577350i
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$			15.5563i			1.57143i
$99$		0			0
$100$	−6.00000			−0.600000
$101$		−	2.82843i		−	0.281439i	−0.990050	−	0.140720i	$-0.955058\pi$
$101$		−	2.82843i		−	0.281439i	0.990050	−	0.140720i	$-0.0449416\pi$
$102$	8.00000	−	11.3137i	0.792118	−	1.12022i
$103$			8.48528i			0.836080i	0.908429	+	0.418040i	$0.137283\pi$
$103$			8.48528i			0.836080i	−0.908429	+	0.418040i	$0.862717\pi$
$104$			2.82843i			0.277350i
$105$	6.00000	−	8.48528i	0.585540	−	0.828079i
$106$	8.00000			0.777029
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$	10.0000	+	2.82843i	0.962250	+	0.272166i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	2.00000	−	2.82843i	0.189832	−	0.268462i
$112$		−	16.9706i		−	1.60357i
$113$			14.1421i			1.33038i	0.746674	+	0.665190i	$0.231650\pi$
$113$			14.1421i			1.33038i	−0.746674	+	0.665190i	$0.768350\pi$
$114$	6.00000	−	8.48528i	0.561951	−	0.794719i
$115$			8.48528i			0.791257i
$116$			5.65685i			0.525226i
$117$	−1.00000	−	2.82843i	−0.0924500	−	0.261488i
$118$		0			0
$119$	24.0000			2.20008
$120$	−4.00000	+	5.65685i	−0.365148	+	0.516398i
$121$	−11.0000			−1.00000
$122$		−	11.3137i		−	1.02430i
$123$	2.00000	+	1.41421i	0.180334	+	0.127515i
$124$			8.48528i			0.762001i
$125$			11.3137i			1.01193i
$126$	6.00000	+	16.9706i	0.534522	+	1.51186i
$127$		−	16.9706i		−	1.50589i	−0.658081	−	0.752947i	$-0.728632\pi$
$127$		−	16.9706i		−	1.50589i	0.658081	−	0.752947i	$-0.271368\pi$
$128$			11.3137i			1.00000i
$129$	12.0000	+	8.48528i	1.05654	+	0.747087i
$130$	2.00000			0.175412
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	18.0000			1.56080
$134$	6.00000			0.518321
$135$	2.00000	−	7.07107i	0.172133	−	0.608581i
$136$	−16.0000			−1.37199
$137$		−	15.5563i		−	1.32907i	−0.747258	−	0.664534i	$-0.768630\pi$
$137$		−	15.5563i		−	1.32907i	0.747258	−	0.664534i	$-0.231370\pi$
$138$	−12.0000	−	8.48528i	−1.02151	−	0.722315i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	−12.0000			−1.01419
$141$	−12.0000	+	16.9706i	−1.01058	+	1.42918i
$142$			16.9706i			1.42414i
$143$		0			0
$144$	−4.00000	−	11.3137i	−0.333333	−	0.942809i
$145$	4.00000			0.332182
$146$		−	2.82843i		−	0.234082i
$147$	−11.0000	+	15.5563i	−0.907265	+	1.28307i
$148$	−4.00000			−0.328798
$149$			1.41421i			0.115857i	0.998321	+	0.0579284i	$0.0184495\pi$
$149$			1.41421i			0.115857i	−0.998321	+	0.0579284i	$0.981550\pi$
$150$	−6.00000	−	4.24264i	−0.489898	−	0.346410i
$151$			4.24264i			0.345261i	0.984987	+	0.172631i	$0.0552267\pi$
$151$			4.24264i			0.345261i	−0.984987	+	0.172631i	$0.944773\pi$
$152$	−12.0000			−0.973329
$153$	16.0000	−	5.65685i	1.29352	−	0.457330i
$154$		0			0
$155$	6.00000			0.481932
$156$	−2.00000	+	2.82843i	−0.160128	+	0.226455i
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	−12.0000			−0.954669
$159$	8.00000	+	5.65685i	0.634441	+	0.448618i
$160$	8.00000			0.632456
$161$		−	25.4558i		−	2.00620i
$162$	8.00000	+	9.89949i	0.628539	+	0.777778i
$163$			4.24264i			0.332309i	0.986100	+	0.166155i	$0.0531351\pi$
$163$			4.24264i			0.332309i	−0.986100	+	0.166155i	$0.946865\pi$
$164$		−	2.82843i		−	0.220863i
$165$		0			0
$166$			16.9706i			1.31717i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$	12.0000	−	16.9706i	0.925820	−	1.30931i
$169$	1.00000			0.0769231
$170$			11.3137i			0.867722i
$171$	12.0000	−	4.24264i	0.917663	−	0.324443i
$172$		−	16.9706i		−	1.29399i
$173$		−	2.82843i		−	0.215041i	−0.994203	−	0.107521i	$-0.965709\pi$
$173$		−	2.82843i		−	0.215041i	0.994203	−	0.107521i	$-0.0342912\pi$
$174$	−4.00000	+	5.65685i	−0.303239	+	0.428845i
$175$		−	12.7279i		−	0.962140i
$176$		0			0
$177$		0			0
$178$	−10.0000			−0.749532
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	−8.00000	+	2.82843i	−0.596285	+	0.210819i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−6.00000			−0.444750
$183$	8.00000	−	11.3137i	0.591377	−	0.836333i
$184$			16.9706i			1.25109i
$185$			2.82843i			0.207950i
$186$	−6.00000	+	8.48528i	−0.439941	+	0.622171i
$187$		0			0
$188$	24.0000			1.75038
$189$	−6.00000	+	21.2132i	−0.436436	+	1.54303i
$190$			8.48528i			0.615587i
$191$	−6.00000			−0.434145			−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000			−0.434145			−0.217072	+	0.976156i	$0.569651\pi$
$192$	−8.00000	+	11.3137i	−0.577350	+	0.816497i
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$			14.1421i			1.01535i
$195$	2.00000	+	1.41421i	0.143223	+	0.101274i
$196$	22.0000			1.57143
$197$		−	7.07107i		−	0.503793i	−0.967754	−	0.251896i	$-0.918946\pi$
$197$		−	7.07107i		−	0.503793i	0.967754	−	0.251896i	$-0.0810542\pi$
$198$		0			0
$199$			16.9706i			1.20301i	0.798869	+	0.601506i	$0.205432\pi$
$199$			16.9706i			1.20301i	−0.798869	+	0.601506i	$0.794568\pi$
$200$			8.48528i			0.600000i
$201$	6.00000	+	4.24264i	0.423207	+	0.299253i
$202$	−4.00000			−0.281439
$203$	−12.0000			−0.842235
$204$	−16.0000	−	11.3137i	−1.12022	−	0.792118i
$205$	−2.00000			−0.139686
$206$	12.0000			0.836080
$207$	−6.00000	−	16.9706i	−0.417029	−	1.17954i
$208$	4.00000			0.277350
$209$		0			0
$210$	−12.0000	−	8.48528i	−0.828079	−	0.585540i
$211$		−	8.48528i		−	0.584151i	−0.956395	−	0.292075i	$-0.905654\pi$
$211$		−	8.48528i		−	0.584151i	0.956395	−	0.292075i	$-0.0943458\pi$
$212$		−	11.3137i		−	0.777029i
$213$	−12.0000	+	16.9706i	−0.822226	+	1.16280i
$214$		−	16.9706i		−	1.16008i
$215$	−12.0000			−0.818393
$216$	4.00000	−	14.1421i	0.272166	−	0.962250i
$217$	−18.0000			−1.22192
$218$		−	2.82843i		−	0.191565i
$219$	2.00000	−	2.82843i	0.135147	−	0.191127i
$220$		0			0
$221$			5.65685i			0.380521i
$222$	−4.00000	−	2.82843i	−0.268462	−	0.189832i
$223$		−	12.7279i		−	0.852325i	−0.904647	−	0.426162i	$-0.859865\pi$
$223$		−	12.7279i		−	0.852325i	0.904647	−	0.426162i	$-0.140135\pi$
$224$	−24.0000			−1.60357
$225$	−3.00000	−	8.48528i	−0.200000	−	0.565685i
$226$	20.0000			1.33038
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$	−12.0000	−	8.48528i	−0.794719	−	0.561951i
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	12.0000			0.791257
$231$		0			0
$232$	8.00000			0.525226
$233$		−	19.7990i		−	1.29707i	−0.761183	−	0.648537i	$-0.775381\pi$
$233$		−	19.7990i		−	1.29707i	0.761183	−	0.648537i	$-0.224619\pi$
$234$	−4.00000	+	1.41421i	−0.261488	+	0.0924500i
$235$		−	16.9706i		−	1.10704i
$236$		0			0
$237$	−12.0000	−	8.48528i	−0.779484	−	0.551178i
$238$		−	33.9411i		−	2.20008i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	8.00000	+	5.65685i	0.516398	+	0.365148i
$241$	26.0000			1.67481			0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000			1.67481			0.837404	+	0.546585i	$0.184072\pi$
$242$			15.5563i			1.00000i
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$	−16.0000			−1.02430
$245$		−	15.5563i		−	0.993859i
$246$	2.00000	−	2.82843i	0.127515	−	0.180334i
$247$			4.24264i			0.269953i
$248$	12.0000			0.762001
$249$	−12.0000	+	16.9706i	−0.760469	+	1.07547i
$250$	16.0000			1.01193
$251$	−30.0000			−1.89358			−0.946792	−	0.321847i	$-0.895696\pi$
$251$	−30.0000			−1.89358			−0.946792	+	0.321847i	$0.895696\pi$
$252$	24.0000	−	8.48528i	1.51186	−	0.534522i
$253$		0			0
$254$	−24.0000			−1.50589
$255$	−8.00000	+	11.3137i	−0.500979	+	0.708492i
$256$	16.0000			1.00000
$257$			14.1421i			0.882162i	0.897467	+	0.441081i	$0.145405\pi$
$257$			14.1421i			0.882162i	−0.897467	+	0.441081i	$0.854595\pi$
$258$	12.0000	−	16.9706i	0.747087	−	1.05654i
$259$		−	8.48528i		−	0.527250i
$260$		−	2.82843i		−	0.175412i
$261$	−8.00000	+	2.82843i	−0.495188	+	0.175075i
$262$		−	16.9706i		−	1.04844i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	−8.00000			−0.491436
$266$		−	25.4558i		−	1.56080i
$267$	−10.0000	−	7.07107i	−0.611990	−	0.432742i
$268$		−	8.48528i		−	0.518321i
$269$		−	19.7990i		−	1.20717i	−0.797300	−	0.603583i	$-0.793739\pi$
$269$		−	19.7990i		−	1.20717i	0.797300	−	0.603583i	$-0.206261\pi$
$270$	−10.0000	−	2.82843i	−0.608581	−	0.172133i
$271$			21.2132i			1.28861i	0.764768	+	0.644305i	$0.222853\pi$
$271$			21.2132i			1.28861i	−0.764768	+	0.644305i	$0.777147\pi$
$272$			22.6274i			1.37199i
$273$	−6.00000	−	4.24264i	−0.363137	−	0.256776i
$274$	−22.0000			−1.32907
$275$		0			0
$276$	−12.0000	+	16.9706i	−0.722315	+	1.02151i
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$		0			0
$279$	−12.0000	+	4.24264i	−0.718421	+	0.254000i
$280$			16.9706i			1.01419i
$281$		−	15.5563i		−	0.928014i	−0.885832	−	0.464007i	$-0.846411\pi$
$281$		−	15.5563i		−	0.928014i	0.885832	−	0.464007i	$-0.153589\pi$
$282$	24.0000	+	16.9706i	1.42918	+	1.01058i
$283$			16.9706i			1.00880i	0.863472	+	0.504398i	$0.168285\pi$
$283$			16.9706i			1.00880i	−0.863472	+	0.504398i	$0.831715\pi$
$284$	24.0000			1.42414
$285$	−6.00000	+	8.48528i	−0.355409	+	0.502625i
$286$		0			0
$287$	6.00000			0.354169
$288$	−16.0000	+	5.65685i	−0.942809	+	0.333333i
$289$	−15.0000			−0.882353
$290$		−	5.65685i		−	0.332182i
$291$	−10.0000	+	14.1421i	−0.586210	+	0.829027i
$292$	−4.00000			−0.234082
$293$			1.41421i			0.0826192i	0.999146	+	0.0413096i	$0.0131530\pi$
$293$			1.41421i			0.0826192i	−0.999146	+	0.0413096i	$0.986847\pi$
$294$	22.0000	+	15.5563i	1.28307	+	0.907265i
$295$		0			0
$296$			5.65685i			0.328798i
$297$		0			0
$298$	2.00000			0.115857
$299$	6.00000			0.346989
$300$	−6.00000	+	8.48528i	−0.346410	+	0.489898i
$301$	36.0000			2.07501
$302$	6.00000			0.345261
$303$	−4.00000	−	2.82843i	−0.229794	−	0.162489i
$304$			16.9706i			0.973329i
$305$			11.3137i			0.647821i
$306$	−8.00000	−	22.6274i	−0.457330	−	1.29352i
$307$			12.7279i			0.726421i	0.931707	+	0.363210i	$0.118319\pi$
$307$			12.7279i			0.726421i	−0.931707	+	0.363210i	$0.881681\pi$
$308$		0			0
$309$	12.0000	+	8.48528i	0.682656	+	0.482711i
$310$		−	8.48528i		−	0.481932i
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$	4.00000	+	2.82843i	0.226455	+	0.160128i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$			5.65685i			0.319235i
$315$	−6.00000	−	16.9706i	−0.338062	−	0.956183i
$316$			16.9706i			0.954669i
$317$			9.89949i			0.556011i	0.960579	+	0.278006i	$0.0896734\pi$
$317$			9.89949i			0.556011i	−0.960579	+	0.278006i	$0.910327\pi$
$318$	8.00000	−	11.3137i	0.448618	−	0.634441i
$319$		0			0
$320$		−	11.3137i		−	0.632456i
$321$	12.0000	−	16.9706i	0.669775	−	0.947204i
$322$	−36.0000			−2.00620
$323$	−24.0000			−1.33540
$324$	14.0000	−	11.3137i	0.777778	−	0.628539i
$325$	3.00000			0.166410
$326$	6.00000			0.332309
$327$	2.00000	−	2.82843i	0.110600	−	0.156412i
$328$	−4.00000			−0.220863
$329$			50.9117i			2.80685i
$330$		0			0
$331$			21.2132i			1.16598i	0.812478	+	0.582992i	$0.198118\pi$
$331$			21.2132i			1.16598i	−0.812478	+	0.582992i	$0.801882\pi$
$332$	24.0000			1.31717
$333$	−2.00000	−	5.65685i	−0.109599	−	0.309994i
$334$			16.9706i			0.928588i
$335$	−6.00000			−0.327815
$336$	−24.0000	−	16.9706i	−1.30931	−	0.925820i
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$		−	1.41421i		−	0.0769231i
$339$	20.0000	+	14.1421i	1.08625	+	0.768095i
$340$	16.0000			0.867722
$341$		0			0
$342$	−6.00000	−	16.9706i	−0.324443	−	0.917663i
$343$			16.9706i			0.916324i
$344$	−24.0000			−1.29399
$345$	12.0000	+	8.48528i	0.646058	+	0.456832i
$346$	−4.00000			−0.215041
$347$	−18.0000			−0.966291			−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000			−0.966291			−0.483145	+	0.875540i	$0.660506\pi$
$348$	8.00000	+	5.65685i	0.428845	+	0.303239i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	−18.0000			−0.962140
$351$	−5.00000	−	1.41421i	−0.266880	−	0.0754851i
$352$		0			0
$353$			9.89949i			0.526897i	0.964673	+	0.263448i	$0.0848599\pi$
$353$			9.89949i			0.526897i	−0.964673	+	0.263448i	$0.915140\pi$
$354$		0			0
$355$		−	16.9706i		−	0.900704i
$356$			14.1421i			0.749532i
$357$	24.0000	−	33.9411i	1.27021	−	1.79635i
$358$		−	16.9706i		−	0.896922i
$359$	36.0000			1.90001			0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000			1.90001			0.950004	+	0.312239i	$0.101079\pi$
$360$	4.00000	+	11.3137i	0.210819	+	0.596285i
$361$	1.00000			0.0526316
$362$			22.6274i			1.18927i
$363$	−11.0000	+	15.5563i	−0.577350	+	0.816497i
$364$			8.48528i			0.444750i
$365$			2.82843i			0.148047i
$366$	−16.0000	−	11.3137i	−0.836333	−	0.591377i
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	24.0000			1.25109
$369$	4.00000	−	1.41421i	0.208232	−	0.0736210i
$370$	4.00000			0.207950
$371$	24.0000			1.24602
$372$	12.0000	+	8.48528i	0.622171	+	0.439941i
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	16.0000	+	11.3137i	0.826236	+	0.584237i
$376$		−	33.9411i		−	1.75038i
$377$		−	2.82843i		−	0.145671i
$378$	30.0000	+	8.48528i	1.54303	+	0.436436i
$379$		−	29.6985i		−	1.52551i	−0.646688	−	0.762754i	$-0.723847\pi$
$379$		−	29.6985i		−	1.52551i	0.646688	−	0.762754i	$-0.276153\pi$
$380$	12.0000			0.615587
$381$	−24.0000	−	16.9706i	−1.22956	−	0.869428i
$382$			8.48528i			0.434145i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	16.0000	+	11.3137i	0.816497	+	0.577350i
$385$		0			0
$386$		−	19.7990i		−	1.00774i
$387$	24.0000	−	8.48528i	1.21999	−	0.431331i
$388$	20.0000			1.01535
$389$		−	28.2843i		−	1.43407i	−0.697037	−	0.717035i	$-0.745499\pi$
$389$		−	28.2843i		−	1.43407i	0.697037	−	0.717035i	$-0.254501\pi$
$390$	2.00000	−	2.82843i	0.101274	−	0.143223i
$391$			33.9411i			1.71648i
$392$		−	31.1127i		−	1.57143i
$393$	12.0000	−	16.9706i	0.605320	−	0.856052i
$394$	−10.0000			−0.503793
$395$	12.0000			0.603786
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	24.0000			1.20301
$399$	18.0000	−	25.4558i	0.901127	−	1.27439i
$400$	12.0000			0.600000
$401$			1.41421i			0.0706225i	0.999376	+	0.0353112i	$0.0112422\pi$
$401$			1.41421i			0.0706225i	−0.999376	+	0.0353112i	$0.988758\pi$
$402$	6.00000	−	8.48528i	0.299253	−	0.423207i
$403$		−	4.24264i		−	0.211341i
$404$			5.65685i			0.281439i
$405$	−8.00000	−	9.89949i	−0.397523	−	0.491910i
$406$			16.9706i			0.842235i
$407$		0			0
$408$	−16.0000	+	22.6274i	−0.792118	+	1.12022i
$409$	−22.0000			−1.08783			−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000			−1.08783			−0.543915	+	0.839140i	$0.683059\pi$
$410$			2.82843i			0.139686i
$411$	−22.0000	−	15.5563i	−1.08518	−	0.767338i
$412$		−	16.9706i		−	0.836080i
$413$		0			0
$414$	−24.0000	+	8.48528i	−1.17954	+	0.417029i
$415$		−	16.9706i		−	0.833052i
$416$		−	5.65685i		−	0.277350i
$417$		0			0
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	−12.0000	+	16.9706i	−0.585540	+	0.828079i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−12.0000			−0.584151
$423$	12.0000	+	33.9411i	0.583460	+	1.65027i
$424$	−16.0000			−0.777029
$425$			16.9706i			0.823193i
$426$	24.0000	+	16.9706i	1.16280	+	0.822226i
$427$		−	33.9411i		−	1.64253i
$428$	−24.0000			−1.16008
$429$		0			0
$430$			16.9706i			0.818393i
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$	−20.0000	−	5.65685i	−0.962250	−	0.272166i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$			25.4558i			1.22192i
$435$	4.00000	−	5.65685i	0.191785	−	0.271225i
$436$	−4.00000			−0.191565
$437$			25.4558i			1.21772i
$438$	−4.00000	−	2.82843i	−0.191127	−	0.135147i
$439$		−	25.4558i		−	1.21494i	−0.794342	−	0.607471i	$-0.792184\pi$
$439$		−	25.4558i		−	1.21494i	0.794342	−	0.607471i	$-0.207816\pi$
$440$		0			0
$441$	11.0000	+	31.1127i	0.523810	+	1.48156i
$442$	8.00000			0.380521
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$	−4.00000	+	5.65685i	−0.189832	+	0.268462i
$445$	10.0000			0.474045
$446$	−18.0000			−0.852325
$447$	2.00000	+	1.41421i	0.0945968	+	0.0668900i
$448$			33.9411i			1.60357i
$449$		−	32.5269i		−	1.53504i	−0.641025	−	0.767520i	$-0.721491\pi$
$449$		−	32.5269i		−	1.53504i	0.641025	−	0.767520i	$-0.278509\pi$
$450$	−12.0000	+	4.24264i	−0.565685	+	0.200000i
$451$		0			0
$452$		−	28.2843i		−	1.33038i
$453$	6.00000	+	4.24264i	0.281905	+	0.199337i
$454$		−	16.9706i		−	0.796468i
$455$	6.00000			0.281284
$456$	−12.0000	+	16.9706i	−0.561951	+	0.794719i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$		−	19.7990i		−	0.925146i
$459$	8.00000	−	28.2843i	0.373408	−	1.32020i
$460$		−	16.9706i		−	0.791257i
$461$			35.3553i			1.64666i	0.567561	+	0.823331i	$0.307887\pi$
$461$			35.3553i			1.64666i	−0.567561	+	0.823331i	$0.692113\pi$
$462$		0			0
$463$		−	4.24264i		−	0.197172i	−0.995129	−	0.0985861i	$-0.968568\pi$
$463$		−	4.24264i		−	0.197172i	0.995129	−	0.0985861i	$-0.0314320\pi$
$464$		−	11.3137i		−	0.525226i
$465$	6.00000	−	8.48528i	0.278243	−	0.393496i
$466$	−28.0000			−1.29707
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$	2.00000	+	5.65685i	0.0924500	+	0.261488i
$469$	18.0000			0.831163
$470$	−24.0000			−1.10704
$471$	−4.00000	+	5.65685i	−0.184310	+	0.260654i
$472$		0			0
$473$		0			0
$474$	−12.0000	+	16.9706i	−0.551178	+	0.779484i
$475$			12.7279i			0.583997i
$476$	−48.0000			−2.20008
$477$	16.0000	−	5.65685i	0.732590	−	0.259010i
$478$		−	16.9706i		−	0.776215i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$	8.00000	−	11.3137i	0.365148	−	0.516398i
$481$	2.00000			0.0911922
$482$		−	36.7696i		−	1.67481i
$483$	−36.0000	−	25.4558i	−1.63806	−	1.15828i
$484$	22.0000			1.00000
$485$		−	14.1421i		−	0.642161i
$486$	22.0000	−	1.41421i	0.997940	−	0.0641500i
$487$			4.24264i			0.192252i	0.995369	+	0.0961262i	$0.0306452\pi$
$487$			4.24264i			0.192252i	−0.995369	+	0.0961262i	$0.969355\pi$
$488$			22.6274i			1.02430i
$489$	6.00000	+	4.24264i	0.271329	+	0.191859i
$490$	−22.0000			−0.993859
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$	−4.00000	−	2.82843i	−0.180334	−	0.127515i
$493$	16.0000			0.720604
$494$	6.00000			0.269953
$495$		0			0
$496$		−	16.9706i		−	0.762001i
$497$			50.9117i			2.28370i
$498$	24.0000	+	16.9706i	1.07547	+	0.760469i
$499$		−	4.24264i		−	0.189927i	−0.995481	−	0.0949633i	$-0.969727\pi$
$499$		−	4.24264i		−	0.189927i	0.995481	−	0.0949633i	$-0.0302734\pi$
$500$		−	22.6274i		−	1.01193i
$501$	−12.0000	+	16.9706i	−0.536120	+	0.758189i
$502$			42.4264i			1.89358i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$	−12.0000	−	33.9411i	−0.534522	−	1.51186i
$505$	4.00000			0.177998
$506$		0			0
$507$	1.00000	−	1.41421i	0.0444116	−	0.0628074i
$508$			33.9411i			1.50589i
$509$		−	24.0416i		−	1.06563i	−0.846233	−	0.532813i	$-0.821135\pi$
$509$		−	24.0416i		−	1.06563i	0.846233	−	0.532813i	$-0.178865\pi$
$510$	16.0000	+	11.3137i	0.708492	+	0.500979i
$511$		−	8.48528i		−	0.375367i
$512$		−	22.6274i		−	1.00000i
$513$	6.00000	−	21.2132i	0.264906	−	0.936586i
$514$	20.0000			0.882162
$515$	−12.0000			−0.528783
$516$	−24.0000	−	16.9706i	−1.05654	−	0.747087i
$517$		0			0
$518$	−12.0000			−0.527250
$519$	−4.00000	−	2.82843i	−0.175581	−	0.124154i
$520$	−4.00000			−0.175412
$521$		−	19.7990i		−	0.867409i	−0.901055	−	0.433705i	$-0.857206\pi$
$521$		−	19.7990i		−	0.867409i	0.901055	−	0.433705i	$-0.142794\pi$
$522$	4.00000	+	11.3137i	0.175075	+	0.495188i
$523$		−	16.9706i		−	0.742071i	−0.928619	−	0.371035i	$-0.879003\pi$
$523$		−	16.9706i		−	0.742071i	0.928619	−	0.371035i	$-0.120997\pi$
$524$	−24.0000			−1.04844
$525$	−18.0000	−	12.7279i	−0.785584	−	0.555492i
$526$		0			0
$527$	24.0000			1.04546
$528$		0			0
$529$	13.0000			0.565217
$530$			11.3137i			0.491436i
$531$		0			0
$532$	−36.0000			−1.56080
$533$			1.41421i			0.0612564i
$534$	−10.0000	+	14.1421i	−0.432742	+	0.611990i
$535$			16.9706i			0.733701i
$536$	−12.0000			−0.518321
$537$	12.0000	−	16.9706i	0.517838	−	0.732334i
$538$	−28.0000			−1.20717
$539$		0			0
$540$	−4.00000	+	14.1421i	−0.172133	+	0.608581i
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$	30.0000			1.28861
$543$	−16.0000	+	22.6274i	−0.686626	+	0.971035i
$544$	32.0000			1.37199
$545$			2.82843i			0.121157i
$546$	−6.00000	+	8.48528i	−0.256776	+	0.363137i
$547$			16.9706i			0.725609i	0.931865	+	0.362804i	$0.118181\pi$
$547$			16.9706i			0.725609i	−0.931865	+	0.362804i	$0.881819\pi$
$548$			31.1127i			1.32907i
$549$	−8.00000	−	22.6274i	−0.341432	−	0.965715i
$550$		0			0
$551$	12.0000			0.511217
$552$	24.0000	+	16.9706i	1.02151	+	0.722315i
$553$	−36.0000			−1.53088
$554$		−	36.7696i		−	1.56219i
$555$	4.00000	+	2.82843i	0.169791	+	0.120060i
$556$		0			0
$557$		−	7.07107i		−	0.299611i	−0.988716	−	0.149805i	$-0.952135\pi$
$557$		−	7.07107i		−	0.299611i	0.988716	−	0.149805i	$-0.0478647\pi$
$558$	6.00000	+	16.9706i	0.254000	+	0.718421i
$559$			8.48528i			0.358889i
$560$	24.0000			1.01419
$561$		0			0
$562$	−22.0000			−0.928014
$563$	36.0000			1.51722			0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000			1.51722			0.758610	+	0.651546i	$0.225879\pi$
$564$	24.0000	−	33.9411i	1.01058	−	1.42918i
$565$	−20.0000			−0.841406
$566$	24.0000			1.00880
$567$	24.0000	+	29.6985i	1.00791	+	1.24722i
$568$		−	33.9411i		−	1.42414i
$569$		−	2.82843i		−	0.118574i	−0.998241	−	0.0592869i	$-0.981117\pi$
$569$		−	2.82843i		−	0.118574i	0.998241	−	0.0592869i	$-0.0188827\pi$
$570$	12.0000	+	8.48528i	0.502625	+	0.355409i
$571$		−	16.9706i		−	0.710196i	−0.934829	−	0.355098i	$-0.884448\pi$
$571$		−	16.9706i		−	0.710196i	0.934829	−	0.355098i	$-0.115552\pi$
$572$		0			0
$573$	−6.00000	+	8.48528i	−0.250654	+	0.354478i
$574$		−	8.48528i		−	0.354169i
$575$	18.0000			0.750652
$576$	8.00000	+	22.6274i	0.333333	+	0.942809i
$577$	38.0000			1.58196			0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000			1.58196			0.790980	+	0.611842i	$0.209571\pi$
$578$			21.2132i			0.882353i
$579$	14.0000	−	19.7990i	0.581820	−	0.822818i
$580$	−8.00000			−0.332182
$581$			50.9117i			2.11217i
$582$	20.0000	+	14.1421i	0.829027	+	0.586210i
$583$		0			0
$584$			5.65685i			0.234082i
$585$	4.00000	−	1.41421i	0.165380	−	0.0584705i
$586$	2.00000			0.0826192
$587$	−36.0000			−1.48588			−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000			−1.48588			−0.742940	+	0.669359i	$0.766569\pi$
$588$	22.0000	−	31.1127i	0.907265	−	1.28307i
$589$	18.0000			0.741677
$590$		0			0
$591$	−10.0000	−	7.07107i	−0.411345	−	0.290865i
$592$	8.00000			0.328798
$593$		−	7.07107i		−	0.290374i	−0.989404	−	0.145187i	$-0.953622\pi$
$593$		−	7.07107i		−	0.290374i	0.989404	−	0.145187i	$-0.0463784\pi$
$594$		0			0
$595$			33.9411i			1.39145i
$596$		−	2.82843i		−	0.115857i
$597$	24.0000	+	16.9706i	0.982255	+	0.694559i
$598$		−	8.48528i		−	0.346989i
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	12.0000	+	8.48528i	0.489898	+	0.346410i
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		−	50.9117i		−	2.07501i
$603$	12.0000	−	4.24264i	0.488678	−	0.172774i
$604$		−	8.48528i		−	0.345261i
$605$		−	15.5563i		−	0.632456i
$606$	−4.00000	+	5.65685i	−0.162489	+	0.229794i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	24.0000			0.973329
$609$	−12.0000	+	16.9706i	−0.486265	+	0.687682i
$610$	16.0000			0.647821
$611$	−12.0000			−0.485468
$612$	−32.0000	+	11.3137i	−1.29352	+	0.457330i
$613$	−34.0000			−1.37325			−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$614$	18.0000			0.726421
$615$	−2.00000	+	2.82843i	−0.0806478	+	0.114053i
$616$		0			0
$617$			1.41421i			0.0569341i	0.999595	+	0.0284670i	$0.00906257\pi$
$617$			1.41421i			0.0569341i	−0.999595	+	0.0284670i	$0.990937\pi$
$618$	12.0000	−	16.9706i	0.482711	−	0.682656i
$619$			4.24264i			0.170526i	0.996358	+	0.0852631i	$0.0271731\pi$
$619$			4.24264i			0.170526i	−0.996358	+	0.0852631i	$0.972827\pi$
$620$	−12.0000			−0.481932
$621$	−30.0000	−	8.48528i	−1.20386	−	0.340503i
$622$			8.48528i			0.340229i
$623$	−30.0000			−1.20192
$624$	4.00000	−	5.65685i	0.160128	−	0.226455i
$625$	−1.00000			−0.0400000
$626$			14.1421i			0.565233i
$627$		0			0
$628$	8.00000			0.319235
$629$			11.3137i			0.451107i
$630$	−24.0000	+	8.48528i	−0.956183	+	0.338062i
$631$		−	21.2132i		−	0.844484i	−0.906483	−	0.422242i	$-0.861243\pi$
$631$		−	21.2132i		−	0.844484i	0.906483	−	0.422242i	$-0.138757\pi$
$632$	24.0000			0.954669
$633$	−12.0000	−	8.48528i	−0.476957	−	0.337260i
$634$	14.0000			0.556011
$635$	24.0000			0.952411
$636$	−16.0000	−	11.3137i	−0.634441	−	0.448618i
$637$	−11.0000			−0.435836
$638$		0			0
$639$	12.0000	+	33.9411i	0.474713	+	1.34269i
$640$	−16.0000			−0.632456
$641$		−	28.2843i		−	1.11716i	−0.829450	−	0.558581i	$-0.811346\pi$
$641$		−	28.2843i		−	1.11716i	0.829450	−	0.558581i	$-0.188654\pi$
$642$	−24.0000	−	16.9706i	−0.947204	−	0.669775i
$643$			12.7279i			0.501940i	0.967995	+	0.250970i	$0.0807496\pi$
$643$			12.7279i			0.501940i	−0.967995	+	0.250970i	$0.919250\pi$
$644$			50.9117i			2.00620i
$645$	−12.0000	+	16.9706i	−0.472500	+	0.668215i
$646$			33.9411i			1.33540i
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$	−16.0000	−	19.7990i	−0.628539	−	0.777778i
$649$		0			0
$650$		−	4.24264i		−	0.166410i
$651$	−18.0000	+	25.4558i	−0.705476	+	0.997693i
$652$		−	8.48528i		−	0.332309i
$653$			14.1421i			0.553425i	0.960953	+	0.276712i	$0.0892449\pi$
$653$			14.1421i			0.553425i	−0.960953	+	0.276712i	$0.910755\pi$
$654$	−4.00000	−	2.82843i	−0.156412	−	0.110600i
$655$			16.9706i			0.663095i
$656$			5.65685i			0.220863i
$657$	−2.00000	−	5.65685i	−0.0780274	−	0.220695i
$658$	72.0000			2.80685
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$		0			0
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	30.0000			1.16598
$663$	8.00000	+	5.65685i	0.310694	+	0.219694i
$664$		−	33.9411i		−	1.31717i
$665$			25.4558i			0.987135i
$666$	−8.00000	+	2.82843i	−0.309994	+	0.109599i
$667$		−	16.9706i		−	0.657103i
$668$	24.0000			0.928588
$669$	−18.0000	−	12.7279i	−0.695920	−	0.492090i
$670$			8.48528i			0.327815i
$671$		0			0
$672$	−24.0000	+	33.9411i	−0.925820	+	1.30931i
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$			31.1127i			1.19842i
$675$	−15.0000	−	4.24264i	−0.577350	−	0.163299i
$676$	−2.00000			−0.0769231
$677$			22.6274i			0.869642i	0.900517	+	0.434821i	$0.143188\pi$
$677$			22.6274i			0.869642i	−0.900517	+	0.434821i	$0.856812\pi$
$678$	20.0000	−	28.2843i	0.768095	−	1.08625i
$679$			42.4264i			1.62818i
$680$		−	22.6274i		−	0.867722i
$681$	12.0000	−	16.9706i	0.459841	−	0.650313i
$682$		0			0
$683$	−48.0000			−1.83667			−0.918334	−	0.395805i	$-0.870466\pi$
$683$	−48.0000			−1.83667			−0.918334	+	0.395805i	$0.870466\pi$
$684$	−24.0000	+	8.48528i	−0.917663	+	0.324443i
$685$	22.0000			0.840577
$686$	24.0000			0.916324
$687$	14.0000	−	19.7990i	0.534133	−	0.755379i
$688$			33.9411i			1.29399i
$689$			5.65685i			0.215509i
$690$	12.0000	−	16.9706i	0.456832	−	0.646058i
$691$			12.7279i			0.484193i	0.970252	+	0.242096i	$0.0778351\pi$
$691$			12.7279i			0.484193i	−0.970252	+	0.242096i	$0.922165\pi$
$692$			5.65685i			0.215041i
$693$		0			0
$694$			25.4558i			0.966291i
$695$		0			0
$696$	8.00000	−	11.3137i	0.303239	−	0.428845i
$697$	−8.00000			−0.303022
$698$			14.1421i			0.535288i
$699$	−28.0000	−	19.7990i	−1.05906	−	0.748867i
$700$			25.4558i			0.962140i
$701$		−	45.2548i		−	1.70925i	−0.519244	−	0.854626i	$-0.673787\pi$
$701$		−	45.2548i		−	1.70925i	0.519244	−	0.854626i	$-0.326213\pi$
$702$	−2.00000	+	7.07107i	−0.0754851	+	0.266880i
$703$			8.48528i			0.320028i
$704$		0			0
$705$	−24.0000	−	16.9706i	−0.903892	−	0.639148i
$706$	14.0000			0.526897
$707$	−12.0000			−0.451306
$708$		0			0
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	−24.0000			−0.900704
$711$	−24.0000	+	8.48528i	−0.900070	+	0.318223i
$712$	20.0000			0.749532
$713$		−	25.4558i		−	0.953329i
$714$	−48.0000	−	33.9411i	−1.79635	−	1.27021i
$715$		0			0
$716$	−24.0000			−0.896922
$717$	12.0000	−	16.9706i	0.448148	−	0.633777i
$718$		−	50.9117i		−	1.90001i
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$	16.0000	−	5.65685i	0.596285	−	0.210819i
$721$	36.0000			1.34071
$722$		−	1.41421i		−	0.0526316i
$723$	26.0000	−	36.7696i	0.966950	−	1.36747i
$724$	32.0000			1.18927
$725$		−	8.48528i		−	0.315135i
$726$	22.0000	+	15.5563i	0.816497	+	0.577350i
$727$			16.9706i			0.629403i	0.949191	+	0.314702i	$0.101904\pi$
$727$			16.9706i			0.629403i	−0.949191	+	0.314702i	$0.898096\pi$
$728$	12.0000			0.444750
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	4.00000			0.148047
$731$	−48.0000			−1.77534
$732$	−16.0000	+	22.6274i	−0.591377	+	0.836333i
$733$	50.0000			1.84679			0.923396	−	0.383849i	$-0.125402\pi$
$733$	50.0000			1.84679			0.923396	+	0.383849i	$0.125402\pi$
$734$		0			0
$735$	−22.0000	−	15.5563i	−0.811482	−	0.573805i
$736$		−	33.9411i		−	1.25109i
$737$		0			0
$738$	−2.00000	−	5.65685i	−0.0736210	−	0.208232i
$739$		−	4.24264i		−	0.156068i	−0.996951	−	0.0780340i	$-0.975136\pi$
$739$		−	4.24264i		−	0.156068i	0.996951	−	0.0780340i	$-0.0248643\pi$
$740$		−	5.65685i		−	0.207950i
$741$	6.00000	+	4.24264i	0.220416	+	0.155857i
$742$		−	33.9411i		−	1.24602i
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$	12.0000	−	16.9706i	0.439941	−	0.622171i
$745$	−2.00000			−0.0732743
$746$			31.1127i			1.13912i
$747$	12.0000	+	33.9411i	0.439057	+	1.24184i
$748$		0			0
$749$		−	50.9117i		−	1.86027i
$750$	16.0000	−	22.6274i	0.584237	−	0.826236i
$751$		−	8.48528i		−	0.309632i	−0.987943	−	0.154816i	$-0.950521\pi$
$751$		−	8.48528i		−	0.309632i	0.987943	−	0.154816i	$-0.0494785\pi$
$752$	−48.0000			−1.75038
$753$	−30.0000	+	42.4264i	−1.09326	+	1.54610i
$754$	−4.00000			−0.145671
$755$	−6.00000			−0.218362
$756$	12.0000	−	42.4264i	0.436436	−	1.54303i
$757$	−16.0000			−0.581530			−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000			−0.581530			−0.290765	+	0.956795i	$0.593910\pi$
$758$	−42.0000			−1.52551
$759$		0			0
$760$		−	16.9706i		−	0.615587i
$761$			26.8701i			0.974039i	0.873391	+	0.487019i	$0.161916\pi$
$761$			26.8701i			0.974039i	−0.873391	+	0.487019i	$0.838084\pi$
$762$	−24.0000	+	33.9411i	−0.869428	+	1.22956i
$763$		−	8.48528i		−	0.307188i
$764$	12.0000			0.434145
$765$	8.00000	+	22.6274i	0.289241	+	0.818096i
$766$		0			0
$767$		0			0
$768$	16.0000	−	22.6274i	0.577350	−	0.816497i
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	20.0000	+	14.1421i	0.720282	+	0.509317i
$772$	−28.0000			−1.00774
$773$			43.8406i			1.57684i	0.615139	+	0.788419i	$0.289100\pi$
$773$			43.8406i			1.57684i	−0.615139	+	0.788419i	$0.710900\pi$
$774$	−12.0000	−	33.9411i	−0.431331	−	1.21999i
$775$		−	12.7279i		−	0.457200i
$776$		−	28.2843i		−	1.01535i
$777$	−12.0000	−	8.48528i	−0.430498	−	0.304408i
$778$	−40.0000			−1.43407
$779$	−6.00000			−0.214972
$780$	−4.00000	−	2.82843i	−0.143223	−	0.101274i
$781$		0			0
$782$	48.0000			1.71648
$783$	−4.00000	+	14.1421i	−0.142948	+	0.505399i
$784$	−44.0000			−1.57143
$785$		−	5.65685i		−	0.201902i
$786$	−24.0000	−	16.9706i	−0.856052	−	0.605320i
$787$			12.7279i			0.453701i	0.973930	+	0.226851i	$0.0728429\pi$
$787$			12.7279i			0.453701i	−0.973930	+	0.226851i	$0.927157\pi$
$788$			14.1421i			0.503793i
$789$		0			0
$790$		−	16.9706i		−	0.603786i
$791$	60.0000			2.13335
$792$		0			0
$793$	8.00000			0.284088
$794$		−	2.82843i		−	0.100377i
$795$	−8.00000	+	11.3137i	−0.283731	+	0.401256i
$796$		−	33.9411i		−	1.20301i
$797$			39.5980i			1.40263i	0.712850	+	0.701316i	$0.247404\pi$
$797$			39.5980i			1.40263i	−0.712850	+	0.701316i	$0.752596\pi$
$798$	−36.0000	−	25.4558i	−1.27439	−	0.901127i
$799$		−	67.8823i		−	2.40150i
$800$		−	16.9706i		−	0.600000i
$801$	−20.0000	+	7.07107i	−0.706665	+	0.249844i
$802$	2.00000			0.0706225
$803$		0			0
$804$	−12.0000	−	8.48528i	−0.423207	−	0.299253i
$805$	36.0000			1.26883
$806$	−6.00000			−0.211341
$807$	−28.0000	−	19.7990i	−0.985647	−	0.696957i
$808$	8.00000			0.281439
$809$		−	19.7990i		−	0.696095i	−0.937477	−	0.348048i	$-0.886845\pi$
$809$		−	19.7990i		−	0.696095i	0.937477	−	0.348048i	$-0.113155\pi$
$810$	−14.0000	+	11.3137i	−0.491910	+	0.397523i
$811$		−	38.1838i		−	1.34081i	−0.741994	−	0.670407i	$-0.766120\pi$
$811$		−	38.1838i		−	1.34081i	0.741994	−	0.670407i	$-0.233880\pi$
$812$	24.0000			0.842235
$813$	30.0000	+	21.2132i	1.05215	+	0.743980i
$814$		0			0
$815$	−6.00000			−0.210171
$816$	32.0000	+	22.6274i	1.12022	+	0.792118i
$817$	−36.0000			−1.25948
$818$			31.1127i			1.08783i
$819$	−12.0000	+	4.24264i	−0.419314	+	0.148250i
$820$	4.00000			0.139686
$821$			9.89949i			0.345495i	0.984966	+	0.172747i	$0.0552644\pi$
$821$			9.89949i			0.345495i	−0.984966	+	0.172747i	$0.944736\pi$
$822$	−22.0000	+	31.1127i	−0.767338	+	1.08518i
$823$		−	25.4558i		−	0.887335i	−0.896191	−	0.443667i	$-0.853677\pi$
$823$		−	25.4558i		−	0.887335i	0.896191	−	0.443667i	$-0.146323\pi$
$824$	−24.0000			−0.836080
$825$		0			0
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	12.0000	+	33.9411i	0.417029	+	1.17954i
$829$	20.0000			0.694629			0.347314	−	0.937749i	$-0.387094\pi$
$829$	20.0000			0.694629			0.347314	+	0.937749i	$0.387094\pi$
$830$	−24.0000			−0.833052
$831$	26.0000	−	36.7696i	0.901930	−	1.27552i
$832$	−8.00000			−0.277350
$833$		−	62.2254i		−	2.15598i
$834$		0			0
$835$		−	16.9706i		−	0.587291i
$836$		0			0
$837$	−6.00000	+	21.2132i	−0.207390	+	0.733236i
$838$			16.9706i			0.586238i
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$	24.0000	+	16.9706i	0.828079	+	0.585540i
$841$	21.0000			0.724138
$842$			14.1421i			0.487370i
$843$	−22.0000	−	15.5563i	−0.757720	−	0.535789i
$844$			16.9706i			0.584151i
$845$			1.41421i			0.0486504i
$846$	48.0000	−	16.9706i	1.65027	−	0.583460i
$847$			46.6690i			1.60357i
$848$			22.6274i			0.777029i
$849$	24.0000	+	16.9706i	0.823678	+	0.582428i
$850$	24.0000			0.823193
$851$	12.0000			0.411355
$852$	24.0000	−	33.9411i	0.822226	−	1.16280i
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$	−48.0000			−1.64253
$855$	6.00000	+	16.9706i	0.205196	+	0.580381i
$856$			33.9411i			1.16008i
$857$		−	2.82843i		−	0.0966172i	−0.998832	−	0.0483086i	$-0.984617\pi$
$857$		−	2.82843i		−	0.0966172i	0.998832	−	0.0483086i	$-0.0153831\pi$
$858$		0			0
$859$		−	42.4264i		−	1.44757i	−0.690025	−	0.723785i	$-0.742401\pi$
$859$		−	42.4264i		−	1.44757i	0.690025	−	0.723785i	$-0.257599\pi$
$860$	24.0000			0.818393
$861$	6.00000	−	8.48528i	0.204479	−	0.289178i
$862$			33.9411i			1.15604i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$	−8.00000	+	28.2843i	−0.272166	+	0.962250i
$865$	4.00000			0.136004
$866$			22.6274i			0.768911i
$867$	−15.0000	+	21.2132i	−0.509427	+	0.720438i
$868$	36.0000			1.22192
$869$		0			0
$870$	−8.00000	−	5.65685i	−0.271225	−	0.191785i
$871$			4.24264i			0.143756i
$872$			5.65685i			0.191565i
$873$	10.0000	+	28.2843i	0.338449	+	0.957278i
$874$	36.0000			1.21772
$875$	48.0000			1.62270
$876$	−4.00000	+	5.65685i	−0.135147	+	0.191127i
$877$	−22.0000			−0.742887			−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000			−0.742887			−0.371444	+	0.928456i	$0.621137\pi$
$878$	−36.0000			−1.21494
$879$	2.00000	+	1.41421i	0.0674583	+	0.0477002i
$880$		0			0
$881$		−	19.7990i		−	0.667045i	−0.942742	−	0.333522i	$-0.891763\pi$
$881$		−	19.7990i		−	0.667045i	0.942742	−	0.333522i	$-0.108237\pi$
$882$	44.0000	−	15.5563i	1.48156	−	0.523810i
$883$			50.9117i			1.71331i	0.515886	+	0.856657i	$0.327463\pi$
$883$			50.9117i			1.71331i	−0.515886	+	0.856657i	$0.672537\pi$
$884$		−	11.3137i		−	0.380521i
$885$		0			0
$886$			16.9706i			0.570137i
$887$	6.00000			0.201460			0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000			0.201460			0.100730	+	0.994914i	$0.467882\pi$
$888$	8.00000	+	5.65685i	0.268462	+	0.189832i
$889$	−72.0000			−2.41480
$890$		−	14.1421i		−	0.474045i
$891$		0			0
$892$			25.4558i			0.852325i
$893$		−	50.9117i		−	1.70369i
$894$	2.00000	−	2.82843i	0.0668900	−	0.0945968i
$895$			16.9706i			0.567263i
$896$	48.0000			1.60357
$897$	6.00000	−	8.48528i	0.200334	−	0.283315i
$898$	−46.0000			−1.53504
$899$	−12.0000			−0.400222
$900$	6.00000	+	16.9706i	0.200000	+	0.565685i
$901$	−32.0000			−1.06607
$902$		0			0
$903$	36.0000	−	50.9117i	1.19800	−	1.69423i
$904$	−40.0000			−1.33038
$905$		−	22.6274i		−	0.752161i
$906$	6.00000	−	8.48528i	0.199337	−	0.281905i
$907$			50.9117i			1.69049i	0.534375	+	0.845247i	$0.320547\pi$
$907$			50.9117i			1.69049i	−0.534375	+	0.845247i	$0.679453\pi$
$908$	−24.0000			−0.796468
$909$	−8.00000	+	2.82843i	−0.265343	+	0.0938130i
$910$		−	8.48528i		−	0.281284i
$911$	42.0000			1.39152			0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000			1.39152			0.695761	+	0.718273i	$0.255067\pi$
$912$	24.0000	+	16.9706i	0.794719	+	0.561951i
$913$		0			0
$914$			14.1421i			0.467780i
$915$	16.0000	+	11.3137i	0.528944	+	0.374020i
$916$	−28.0000			−0.925146
$917$		−	50.9117i		−	1.68125i
$918$	−40.0000	−	11.3137i	−1.32020	−	0.373408i
$919$		−	8.48528i		−	0.279904i	−0.990158	−	0.139952i	$-0.955305\pi$
$919$		−	8.48528i		−	0.279904i	0.990158	−	0.139952i	$-0.0446948\pi$
$920$	−24.0000			−0.791257
$921$	18.0000	+	12.7279i	0.593120	+	0.419399i
$922$	50.0000			1.64666
$923$	−12.0000			−0.394985
$924$		0			0
$925$	6.00000			0.197279
$926$	−6.00000			−0.197172
$927$	24.0000	−	8.48528i	0.788263	−	0.278693i
$928$	−16.0000			−0.525226
$929$		−	15.5563i		−	0.510387i	−0.966890	−	0.255194i	$-0.917861\pi$
$929$		−	15.5563i		−	0.510387i	0.966890	−	0.255194i	$-0.0821392\pi$
$930$	−12.0000	−	8.48528i	−0.393496	−	0.278243i
$931$		−	46.6690i		−	1.52952i
$932$			39.5980i			1.29707i
$933$	−6.00000	+	8.48528i	−0.196431	+	0.277796i
$934$		−	25.4558i		−	0.832941i
$935$		0			0
$936$	8.00000	−	2.82843i	0.261488	−	0.0924500i
$937$	20.0000			0.653372			0.326686	−	0.945133i	$-0.394068\pi$
$937$	20.0000			0.653372			0.326686	+	0.945133i	$0.394068\pi$
$938$		−	25.4558i		−	0.831163i
$939$	−10.0000	+	14.1421i	−0.326338	+	0.461511i
$940$			33.9411i			1.10704i
$941$			1.41421i			0.0461020i	0.999734	+	0.0230510i	$0.00733802\pi$
$941$			1.41421i			0.0461020i	−0.999734	+	0.0230510i	$0.992662\pi$
$942$	8.00000	+	5.65685i	0.260654	+	0.184310i
$943$			8.48528i			0.276319i
$944$		0			0
$945$	−30.0000	−	8.48528i	−0.975900	−	0.276026i
$946$		0			0
$947$	36.0000			1.16984			0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000			1.16984			0.584921	+	0.811090i	$0.301125\pi$
$948$	24.0000	+	16.9706i	0.779484	+	0.551178i
$949$	2.00000			0.0649227
$950$	18.0000			0.583997
$951$	14.0000	+	9.89949i	0.453981	+	0.321013i
$952$			67.8823i			2.20008i
$953$			31.1127i			1.00784i	0.863751	+	0.503920i	$0.168109\pi$
$953$			31.1127i			1.00784i	−0.863751	+	0.503920i	$0.831891\pi$
$954$	−8.00000	−	22.6274i	−0.259010	−	0.732590i
$955$		−	8.48528i		−	0.274577i
$956$	−24.0000			−0.776215
$957$		0			0
$958$		0			0
$959$	−66.0000			−2.13125
$960$	−16.0000	−	11.3137i	−0.516398	−	0.365148i
$961$	13.0000			0.419355
$962$		−	2.82843i		−	0.0911922i
$963$	−12.0000	−	33.9411i	−0.386695	−	1.09374i
$964$	−52.0000			−1.67481
$965$			19.7990i			0.637352i
$966$	−36.0000	+	50.9117i	−1.15828	+	1.63806i
$967$			21.2132i			0.682171i	0.940032	+	0.341085i	$0.110795\pi$
$967$			21.2132i			0.682171i	−0.940032	+	0.341085i	$0.889205\pi$
$968$		−	31.1127i		−	1.00000i
$969$	−24.0000	+	33.9411i	−0.770991	+	1.09035i
$970$	−20.0000			−0.642161
$971$	42.0000			1.34784			0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000			1.34784			0.673922	+	0.738802i	$0.264608\pi$
$972$	−2.00000	−	31.1127i	−0.0641500	−	0.997940i
$973$		0			0
$974$	6.00000			0.192252
$975$	3.00000	−	4.24264i	0.0960769	−	0.135873i
$976$	32.0000			1.02430
$977$		−	49.4975i		−	1.58356i	−0.610803	−	0.791782i	$-0.709153\pi$
$977$		−	49.4975i		−	1.58356i	0.610803	−	0.791782i	$-0.290847\pi$
$978$	6.00000	−	8.48528i	0.191859	−	0.271329i
$979$		0			0
$980$			31.1127i			0.993859i
$981$	−2.00000	−	5.65685i	−0.0638551	−	0.180609i
$982$		−	8.48528i		−	0.270776i
$983$	−12.0000			−0.382741			−0.191370	−	0.981518i	$-0.561293\pi$
$983$	−12.0000			−0.382741			−0.191370	+	0.981518i	$0.561293\pi$
$984$	−4.00000	+	5.65685i	−0.127515	+	0.180334i
$985$	10.0000			0.318626
$986$		−	22.6274i		−	0.720604i
$987$	72.0000	+	50.9117i	2.29179	+	1.62054i
$988$		−	8.48528i		−	0.269953i
$989$			50.9117i			1.61890i
$990$		0			0
$991$			33.9411i			1.07818i	0.842250	+	0.539088i	$0.181231\pi$
$991$			33.9411i			1.07818i	−0.842250	+	0.539088i	$0.818769\pi$
$992$	−24.0000			−0.762001
$993$	30.0000	+	21.2132i	0.952021	+	0.673181i
$994$	72.0000			2.28370
$995$	−24.0000			−0.760851
$996$	24.0000	−	33.9411i	0.760469	−	1.07547i
$997$	−46.0000			−1.45683			−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−46.0000			−1.45683			−0.728417	+	0.685134i	$0.759744\pi$
$998$	−6.00000			−0.189927
$999$	−10.0000	−	2.82843i	−0.316386	−	0.0894875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.c.b.131.1	yes	2
3.2	odd	2		156.2.c.a.131.2	yes	2
4.3	odd	2		156.2.c.a.131.1	✓	2
8.3	odd	2		2496.2.d.g.1535.1		2
8.5	even	2		2496.2.d.b.1535.2		2
12.11	even	2	inner	156.2.c.b.131.2	yes	2
24.5	odd	2		2496.2.d.g.1535.2		2
24.11	even	2		2496.2.d.b.1535.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.c.a.131.1	✓	2	4.3	odd	2
156.2.c.a.131.2	yes	2	3.2	odd	2
156.2.c.b.131.1	yes	2	1.1	even	1	trivial
156.2.c.b.131.2	yes	2	12.11	even	2	inner
2496.2.d.b.1535.1		2	24.11	even	2
2496.2.d.b.1535.2		2	8.5	even	2
2496.2.d.g.1535.1		2	8.3	odd	2
2496.2.d.g.1535.2		2	24.5	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(1.00000 - 1.41421i) q^{3} -2.00000 q^{4} +1.41421i q^{5} +(-2.00000 - 1.41421i) q^{6} -4.24264i q^{7} +2.82843i q^{8} +(-1.00000 - 2.82843i) q^{9} +2.00000 q^{10} +(-2.00000 + 2.82843i) q^{12} +1.00000 q^{13} -6.00000 q^{14} +(2.00000 + 1.41421i) q^{15} +4.00000 q^{16} +5.65685i q^{17} +(-4.00000 + 1.41421i) q^{18} +4.24264i q^{19} -2.82843i q^{20} +(-6.00000 - 4.24264i) q^{21} +6.00000 q^{23} +(4.00000 + 2.82843i) q^{24} +3.00000 q^{25} -1.41421i q^{26} +(-5.00000 - 1.41421i) q^{27} +8.48528i q^{28} -2.82843i q^{29} +(2.00000 - 2.82843i) q^{30} -4.24264i q^{31} -5.65685i q^{32} +8.00000 q^{34} +6.00000 q^{35} +(2.00000 + 5.65685i) q^{36} +2.00000 q^{37} +6.00000 q^{38} +(1.00000 - 1.41421i) q^{39} -4.00000 q^{40} +1.41421i q^{41} +(-6.00000 + 8.48528i) q^{42} +8.48528i q^{43} +(4.00000 - 1.41421i) q^{45} -8.48528i q^{46} -12.0000 q^{47} +(4.00000 - 5.65685i) q^{48} -11.0000 q^{49} -4.24264i q^{50} +(8.00000 + 5.65685i) q^{51} -2.00000 q^{52} +5.65685i q^{53} +(-2.00000 + 7.07107i) q^{54} +12.0000 q^{56} +(6.00000 + 4.24264i) q^{57} -4.00000 q^{58} +(-4.00000 - 2.82843i) q^{60} +8.00000 q^{61} -6.00000 q^{62} +(-12.0000 + 4.24264i) q^{63} -8.00000 q^{64} +1.41421i q^{65} +4.24264i q^{67} -11.3137i q^{68} +(6.00000 - 8.48528i) q^{69} -8.48528i q^{70} -12.0000 q^{71} +(8.00000 - 2.82843i) q^{72} +2.00000 q^{73} -2.82843i q^{74} +(3.00000 - 4.24264i) q^{75} -8.48528i q^{76} +(-2.00000 - 1.41421i) q^{78} -8.48528i q^{79} +5.65685i q^{80} +(-7.00000 + 5.65685i) q^{81} +2.00000 q^{82} -12.0000 q^{83} +(12.0000 + 8.48528i) q^{84} -8.00000 q^{85} +12.0000 q^{86} +(-4.00000 - 2.82843i) q^{87} -7.07107i q^{89} +(-2.00000 - 5.65685i) q^{90} -4.24264i q^{91} -12.0000 q^{92} +(-6.00000 - 4.24264i) q^{93} +16.9706i q^{94} -6.00000 q^{95} +(-8.00000 - 5.65685i) q^{96} -10.0000 q^{97} +15.5563i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 4 q^{4} - 4 q^{6} - 2 q^{9} + 4 q^{10} - 4 q^{12} + 2 q^{13} - 12 q^{14} + 4 q^{15} + 8 q^{16} - 8 q^{18} - 12 q^{21} + 12 q^{23} + 8 q^{24} + 6 q^{25} - 10 q^{27} + 4 q^{30} + 16 q^{34}+ \cdots - 20 q^{97}+O(q^{100}) \) 2 * q + 2 * q^3 - 4 * q^4 - 4 * q^6 - 2 * q^9 + 4 * q^10 - 4 * q^12 + 2 * q^13 - 12 * q^14 + 4 * q^15 + 8 * q^16 - 8 * q^18 - 12 * q^21 + 12 * q^23 + 8 * q^24 + 6 * q^25 - 10 * q^27 + 4 * q^30 + 16 * q^34 + 12 * q^35 + 4 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^39 - 8 * q^40 - 12 * q^42 + 8 * q^45 - 24 * q^47 + 8 * q^48 - 22 * q^49 + 16 * q^51 - 4 * q^52 - 4 * q^54 + 24 * q^56 + 12 * q^57 - 8 * q^58 - 8 * q^60 + 16 * q^61 - 12 * q^62 - 24 * q^63 - 16 * q^64 + 12 * q^69 - 24 * q^71 + 16 * q^72 + 4 * q^73 + 6 * q^75 - 4 * q^78 - 14 * q^81 + 4 * q^82 - 24 * q^83 + 24 * q^84 - 16 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^90 - 24 * q^92 - 12 * q^93 - 12 * q^95 - 16 * q^96 - 20 * q^97

Introduction

L-functions

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Database

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