LMFDB - Embedded newform 22.3.b.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,3,Mod(21,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	22.b (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:	$0.599456581593$
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			21.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.3.b.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} -1.41421i q^{6} +8.48528i q^{7} +2.82843i q^{8} -8.00000 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} -1.41421i q^{6} +8.48528i q^{7} +2.82843i q^{8} -8.00000 q^{9} +1.41421i q^{10} +(7.00000 - 8.48528i) q^{11} -2.00000 q^{12} -8.48528i q^{13} +12.0000 q^{14} -1.00000 q^{15} +4.00000 q^{16} -25.4558i q^{17} +11.3137i q^{18} +25.4558i q^{19} +2.00000 q^{20} +8.48528i q^{21} +(-12.0000 - 9.89949i) q^{22} +17.0000 q^{23} +2.82843i q^{24} -24.0000 q^{25} -12.0000 q^{26} -17.0000 q^{27} -16.9706i q^{28} +33.9411i q^{29} +1.41421i q^{30} +17.0000 q^{31} -5.65685i q^{32} +(7.00000 - 8.48528i) q^{33} -36.0000 q^{34} -8.48528i q^{35} +16.0000 q^{36} +47.0000 q^{37} +36.0000 q^{38} -8.48528i q^{39} -2.82843i q^{40} -8.48528i q^{41} +12.0000 q^{42} -16.9706i q^{43} +(-14.0000 + 16.9706i) q^{44} +8.00000 q^{45} -24.0416i q^{46} -58.0000 q^{47} +4.00000 q^{48} -23.0000 q^{49} +33.9411i q^{50} -25.4558i q^{51} +16.9706i q^{52} +2.00000 q^{53} +24.0416i q^{54} +(-7.00000 + 8.48528i) q^{55} -24.0000 q^{56} +25.4558i q^{57} +48.0000 q^{58} -55.0000 q^{59} +2.00000 q^{60} +84.8528i q^{61} -24.0416i q^{62} -67.8823i q^{63} -8.00000 q^{64} +8.48528i q^{65} +(-12.0000 - 9.89949i) q^{66} +89.0000 q^{67} +50.9117i q^{68} +17.0000 q^{69} -12.0000 q^{70} -7.00000 q^{71} -22.6274i q^{72} -127.279i q^{73} -66.4680i q^{74} -24.0000 q^{75} -50.9117i q^{76} +(72.0000 + 59.3970i) q^{77} -12.0000 q^{78} +33.9411i q^{79} -4.00000 q^{80} +55.0000 q^{81} -12.0000 q^{82} +33.9411i q^{83} -16.9706i q^{84} +25.4558i q^{85} -24.0000 q^{86} +33.9411i q^{87} +(24.0000 + 19.7990i) q^{88} -97.0000 q^{89} -11.3137i q^{90} +72.0000 q^{91} -34.0000 q^{92} +17.0000 q^{93} +82.0244i q^{94} -25.4558i q^{95} -5.65685i q^{96} -121.000 q^{97} +32.5269i q^{98} +(-56.0000 + 67.8823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 4 q^{4} - 2 q^{5} - 16 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 - 4 * q^4 - 2 * q^5 - 16 * q^9	$ 2 q + 2 q^{3} - 4 q^{4} - 2 q^{5} - 16 q^{9} + 14 q^{11} - 4 q^{12} + 24 q^{14} - 2 q^{15} + 8 q^{16} + 4 q^{20} - 24 q^{22} + 34 q^{23} - 48 q^{25} - 24 q^{26} - 34 q^{27} + 34 q^{31} + 14 q^{33} - 72 q^{34} + 32 q^{36} + 94 q^{37} + 72 q^{38} + 24 q^{42} - 28 q^{44} + 16 q^{45} - 116 q^{47} + 8 q^{48} - 46 q^{49} + 4 q^{53} - 14 q^{55} - 48 q^{56} + 96 q^{58} - 110 q^{59} + 4 q^{60} - 16 q^{64} - 24 q^{66} + 178 q^{67} + 34 q^{69} - 24 q^{70} - 14 q^{71} - 48 q^{75} + 144 q^{77} - 24 q^{78} - 8 q^{80} + 110 q^{81} - 24 q^{82} - 48 q^{86} + 48 q^{88} - 194 q^{89} + 144 q^{91} - 68 q^{92} + 34 q^{93} - 242 q^{97} - 112 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 4 * q^4 - 2 * q^5 - 16 * q^9 + 14 * q^11 - 4 * q^12 + 24 * q^14 - 2 * q^15 + 8 * q^16 + 4 * q^20 - 24 * q^22 + 34 * q^23 - 48 * q^25 - 24 * q^26 - 34 * q^27 + 34 * q^31 + 14 * q^33 - 72 * q^34 + 32 * q^36 + 94 * q^37 + 72 * q^38 + 24 * q^42 - 28 * q^44 + 16 * q^45 - 116 * q^47 + 8 * q^48 - 46 * q^49 + 4 * q^53 - 14 * q^55 - 48 * q^56 + 96 * q^58 - 110 * q^59 + 4 * q^60 - 16 * q^64 - 24 * q^66 + 178 * q^67 + 34 * q^69 - 24 * q^70 - 14 * q^71 - 48 * q^75 + 144 * q^77 - 24 * q^78 - 8 * q^80 + 110 * q^81 - 24 * q^82 - 48 * q^86 + 48 * q^88 - 194 * q^89 + 144 * q^91 - 68 * q^92 + 34 * q^93 - 242 * q^97 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$-1$

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		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	1.00000			0.333333			0.166667	−	0.986013i	$-0.446700\pi$
$3$	1.00000			0.333333			0.166667	+	0.986013i	$0.446700\pi$
$4$	−2.00000			−0.500000
$5$	−1.00000			−0.200000			−0.100000	−	0.994987i	$-0.531884\pi$
$5$	−1.00000			−0.200000			−0.100000	+	0.994987i	$0.531884\pi$
$6$		−	1.41421i		−	0.235702i
$7$			8.48528i			1.21218i	0.795395	+	0.606092i	$0.207263\pi$
$7$			8.48528i			1.21218i	−0.795395	+	0.606092i	$0.792737\pi$
$8$			2.82843i			0.353553i
$9$	−8.00000			−0.888889
$10$			1.41421i			0.141421i
$11$	7.00000	−	8.48528i	0.636364	−	0.771389i
$11$	7.00000	−	8.48528i	0.636364	−	0.771389i
$12$	−2.00000			−0.166667
$13$		−	8.48528i		−	0.652714i	−0.945247	−	0.326357i	$-0.894179\pi$
$13$		−	8.48528i		−	0.652714i	0.945247	−	0.326357i	$-0.105821\pi$
$14$	12.0000			0.857143
$15$	−1.00000			−0.0666667
$16$	4.00000			0.250000
$17$		−	25.4558i		−	1.49740i	−0.662908	−	0.748701i	$-0.730678\pi$
$17$		−	25.4558i		−	1.49740i	0.662908	−	0.748701i	$-0.269322\pi$
$18$			11.3137i			0.628539i
$19$			25.4558i			1.33978i	0.742460	+	0.669891i	$0.233659\pi$
$19$			25.4558i			1.33978i	−0.742460	+	0.669891i	$0.766341\pi$
$20$	2.00000			0.100000
$21$			8.48528i			0.404061i
$22$	−12.0000	−	9.89949i	−0.545455	−	0.449977i
$23$	17.0000			0.739130			0.369565	−	0.929205i	$-0.379507\pi$
$23$	17.0000			0.739130			0.369565	+	0.929205i	$0.379507\pi$
$24$			2.82843i			0.117851i
$25$	−24.0000			−0.960000
$26$	−12.0000			−0.461538
$27$	−17.0000			−0.629630
$28$		−	16.9706i		−	0.606092i
$29$			33.9411i			1.17038i	0.810895	+	0.585192i	$0.198981\pi$
$29$			33.9411i			1.17038i	−0.810895	+	0.585192i	$0.801019\pi$
$30$			1.41421i			0.0471405i
$31$	17.0000			0.548387			0.274194	−	0.961675i	$-0.411589\pi$
$31$	17.0000			0.548387			0.274194	+	0.961675i	$0.411589\pi$
$32$		−	5.65685i		−	0.176777i
$33$	7.00000	−	8.48528i	0.212121	−	0.257130i
$34$	−36.0000			−1.05882
$35$		−	8.48528i		−	0.242437i
$36$	16.0000			0.444444
$37$	47.0000			1.27027			0.635135	−	0.772401i	$-0.280944\pi$
$37$	47.0000			1.27027			0.635135	+	0.772401i	$0.280944\pi$
$38$	36.0000			0.947368
$39$		−	8.48528i		−	0.217571i
$40$		−	2.82843i		−	0.0707107i
$41$		−	8.48528i		−	0.206958i	−0.994632	−	0.103479i	$-0.967003\pi$
$41$		−	8.48528i		−	0.206958i	0.994632	−	0.103479i	$-0.0329975\pi$
$42$	12.0000			0.285714
$43$		−	16.9706i		−	0.394664i	−0.980337	−	0.197332i	$-0.936772\pi$
$43$		−	16.9706i		−	0.394664i	0.980337	−	0.197332i	$-0.0632277\pi$
$44$	−14.0000	+	16.9706i	−0.318182	+	0.385695i
$45$	8.00000			0.177778
$46$		−	24.0416i		−	0.522644i
$47$	−58.0000			−1.23404			−0.617021	−	0.786946i	$-0.711661\pi$
$47$	−58.0000			−1.23404			−0.617021	+	0.786946i	$0.711661\pi$
$48$	4.00000			0.0833333
$49$	−23.0000			−0.469388
$50$			33.9411i			0.678823i
$51$		−	25.4558i		−	0.499134i
$52$			16.9706i			0.326357i
$53$	2.00000			0.0377358			0.0188679	−	0.999822i	$-0.493994\pi$
$53$	2.00000			0.0377358			0.0188679	+	0.999822i	$0.493994\pi$
$54$			24.0416i			0.445215i
$55$	−7.00000	+	8.48528i	−0.127273	+	0.154278i
$56$	−24.0000			−0.428571
$57$			25.4558i			0.446594i
$58$	48.0000			0.827586
$59$	−55.0000			−0.932203			−0.466102	−	0.884731i	$-0.654342\pi$
$59$	−55.0000			−0.932203			−0.466102	+	0.884731i	$0.654342\pi$
$60$	2.00000			0.0333333
$61$			84.8528i			1.39103i	0.718512	+	0.695515i	$0.244824\pi$
$61$			84.8528i			1.39103i	−0.718512	+	0.695515i	$0.755176\pi$
$62$		−	24.0416i		−	0.387768i
$63$		−	67.8823i		−	1.07750i
$64$	−8.00000			−0.125000
$65$			8.48528i			0.130543i
$66$	−12.0000	−	9.89949i	−0.181818	−	0.149992i
$67$	89.0000			1.32836			0.664179	−	0.747573i	$-0.268781\pi$
$67$	89.0000			1.32836			0.664179	+	0.747573i	$0.268781\pi$
$68$			50.9117i			0.748701i
$69$	17.0000			0.246377
$70$	−12.0000			−0.171429
$71$	−7.00000			−0.0985915			−0.0492958	−	0.998784i	$-0.515698\pi$
$71$	−7.00000			−0.0985915			−0.0492958	+	0.998784i	$0.515698\pi$
$72$		−	22.6274i		−	0.314270i
$73$		−	127.279i		−	1.74355i	−0.489906	−	0.871775i	$-0.662969\pi$
$73$		−	127.279i		−	1.74355i	0.489906	−	0.871775i	$-0.337031\pi$
$74$		−	66.4680i		−	0.898217i
$75$	−24.0000			−0.320000
$76$		−	50.9117i		−	0.669891i
$77$	72.0000	+	59.3970i	0.935065	+	0.771389i
$78$	−12.0000			−0.153846
$79$			33.9411i			0.429634i	0.976654	+	0.214817i	$0.0689156\pi$
$79$			33.9411i			0.429634i	−0.976654	+	0.214817i	$0.931084\pi$
$80$	−4.00000			−0.0500000
$81$	55.0000			0.679012
$82$	−12.0000			−0.146341
$83$			33.9411i			0.408929i	0.978874	+	0.204465i	$0.0655453\pi$
$83$			33.9411i			0.408929i	−0.978874	+	0.204465i	$0.934455\pi$
$84$		−	16.9706i		−	0.202031i
$85$			25.4558i			0.299481i
$86$	−24.0000			−0.279070
$87$			33.9411i			0.390128i
$88$	24.0000	+	19.7990i	0.272727	+	0.224989i
$89$	−97.0000			−1.08989			−0.544944	−	0.838473i	$-0.683449\pi$
$89$	−97.0000			−1.08989			−0.544944	+	0.838473i	$0.683449\pi$
$90$		−	11.3137i		−	0.125708i
$91$	72.0000			0.791209
$92$	−34.0000			−0.369565
$93$	17.0000			0.182796
$94$			82.0244i			0.872600i
$95$		−	25.4558i		−	0.267956i
$96$		−	5.65685i		−	0.0589256i
$97$	−121.000			−1.24742			−0.623711	−	0.781655i	$-0.714376\pi$
$97$	−121.000			−1.24742			−0.623711	+	0.781655i	$0.714376\pi$
$98$			32.5269i			0.331907i
$99$	−56.0000	+	67.8823i	−0.565657	+	0.685679i
$100$	48.0000			0.480000
$101$			8.48528i			0.0840127i	0.999117	+	0.0420063i	$0.0133750\pi$
$101$			8.48528i			0.0840127i	−0.999117	+	0.0420063i	$0.986625\pi$
$102$	−36.0000			−0.352941
$103$	−82.0000			−0.796117			−0.398058	−	0.917360i	$-0.630316\pi$
$103$	−82.0000			−0.796117			−0.398058	+	0.917360i	$0.630316\pi$
$104$	24.0000			0.230769
$105$		−	8.48528i		−	0.0808122i
$106$		−	2.82843i		−	0.0266833i
$107$		−	76.3675i		−	0.713715i	−0.934159	−	0.356858i	$-0.883848\pi$
$107$		−	76.3675i		−	0.713715i	0.934159	−	0.356858i	$-0.116152\pi$
$108$	34.0000			0.314815
$109$		−	152.735i		−	1.40124i	−0.713535	−	0.700620i	$-0.752907\pi$
$109$		−	152.735i		−	1.40124i	0.713535	−	0.700620i	$-0.247093\pi$
$110$	12.0000	+	9.89949i	0.109091	+	0.0899954i
$111$	47.0000			0.423423
$112$			33.9411i			0.303046i
$113$	−1.00000			−0.00884956			−0.00442478	−	0.999990i	$-0.501408\pi$
$113$	−1.00000			−0.00884956			−0.00442478	+	0.999990i	$0.501408\pi$
$114$	36.0000			0.315789
$115$	−17.0000			−0.147826
$116$		−	67.8823i		−	0.585192i
$117$			67.8823i			0.580190i
$118$			77.7817i			0.659167i
$119$	216.000			1.81513
$120$		−	2.82843i		−	0.0235702i
$121$	−23.0000	−	118.794i	−0.190083	−	0.981768i
$122$	120.000			0.983607
$123$		−	8.48528i		−	0.0689860i
$124$	−34.0000			−0.274194
$125$	49.0000			0.392000
$126$	−96.0000			−0.761905
$127$			25.4558i			0.200440i	0.994965	+	0.100220i	$0.0319546\pi$
$127$			25.4558i			0.200440i	−0.994965	+	0.100220i	$0.968045\pi$
$128$			11.3137i			0.0883883i
$129$		−	16.9706i		−	0.131555i
$130$	12.0000			0.0923077
$131$			93.3381i			0.712505i	0.934390	+	0.356252i	$0.115946\pi$
$131$			93.3381i			0.712505i	−0.934390	+	0.356252i	$0.884054\pi$
$132$	−14.0000	+	16.9706i	−0.106061	+	0.128565i
$133$	−216.000			−1.62406
$134$		−	125.865i		−	0.939291i
$135$	17.0000			0.125926
$136$	72.0000			0.529412
$137$	167.000			1.21898			0.609489	−	0.792794i	$-0.291375\pi$
$137$	167.000			1.21898			0.609489	+	0.792794i	$0.291375\pi$
$138$		−	24.0416i		−	0.174215i
$139$			93.3381i			0.671497i	0.941952	+	0.335749i	$0.108989\pi$
$139$			93.3381i			0.671497i	−0.941952	+	0.335749i	$0.891011\pi$
$140$			16.9706i			0.121218i
$141$	−58.0000			−0.411348
$142$			9.89949i			0.0697148i
$143$	−72.0000	−	59.3970i	−0.503497	−	0.415363i
$144$	−32.0000			−0.222222
$145$		−	33.9411i		−	0.234077i
$146$	−180.000			−1.23288
$147$	−23.0000			−0.156463
$148$	−94.0000			−0.635135
$149$		−	161.220i		−	1.08202i	−0.841018	−	0.541008i	$-0.818043\pi$
$149$		−	161.220i		−	1.08202i	0.841018	−	0.541008i	$-0.181957\pi$
$150$			33.9411i			0.226274i
$151$			288.500i			1.91059i	0.295649	+	0.955297i	$0.404464\pi$
$151$			288.500i			1.91059i	−0.295649	+	0.955297i	$0.595536\pi$
$152$	−72.0000			−0.473684
$153$			203.647i			1.33102i
$154$	84.0000	−	101.823i	0.545455	−	0.661191i
$155$	−17.0000			−0.109677
$156$			16.9706i			0.108786i
$157$	−1.00000			−0.00636943			−0.00318471	−	0.999995i	$-0.501014\pi$
$157$	−1.00000			−0.00636943			−0.00318471	+	0.999995i	$0.501014\pi$
$158$	48.0000			0.303797
$159$	2.00000			0.0125786
$160$			5.65685i			0.0353553i
$161$			144.250i			0.895961i
$162$		−	77.7817i		−	0.480134i
$163$	110.000			0.674847			0.337423	−	0.941353i	$-0.390445\pi$
$163$	110.000			0.674847			0.337423	+	0.941353i	$0.390445\pi$
$164$			16.9706i			0.103479i
$165$	−7.00000	+	8.48528i	−0.0424242	+	0.0514259i
$166$	48.0000			0.289157
$167$		−	110.309i		−	0.660531i	−0.943888	−	0.330265i	$-0.892862\pi$
$167$		−	110.309i		−	0.660531i	0.943888	−	0.330265i	$-0.107138\pi$
$168$	−24.0000			−0.142857
$169$	97.0000			0.573964
$170$	36.0000			0.211765
$171$		−	203.647i		−	1.19092i
$172$			33.9411i			0.197332i
$173$		−	16.9706i		−	0.0980957i	−0.998796	−	0.0490479i	$-0.984381\pi$
$173$		−	16.9706i		−	0.0980957i	0.998796	−	0.0490479i	$-0.0156187\pi$
$174$	48.0000			0.275862
$175$		−	203.647i		−	1.16370i
$176$	28.0000	−	33.9411i	0.159091	−	0.192847i
$177$	−55.0000			−0.310734
$178$			137.179i			0.770667i
$179$	209.000			1.16760			0.583799	−	0.811898i	$-0.301566\pi$
$179$	209.000			1.16760			0.583799	+	0.811898i	$0.301566\pi$
$180$	−16.0000			−0.0888889
$181$	119.000			0.657459			0.328729	−	0.944424i	$-0.393380\pi$
$181$	119.000			0.657459			0.328729	+	0.944424i	$0.393380\pi$
$182$		−	101.823i		−	0.559469i
$183$			84.8528i			0.463677i
$184$			48.0833i			0.261322i
$185$	−47.0000			−0.254054
$186$		−	24.0416i		−	0.129256i
$187$	−216.000	−	178.191i	−1.15508	−	0.952893i
$188$	116.000			0.617021
$189$		−	144.250i		−	0.763226i
$190$	−36.0000			−0.189474
$191$	−319.000			−1.67016			−0.835079	−	0.550131i	$-0.814578\pi$
$191$	−319.000			−1.67016			−0.835079	+	0.550131i	$0.814578\pi$
$192$	−8.00000			−0.0416667
$193$			16.9706i			0.0879304i	0.999033	+	0.0439652i	$0.0139991\pi$
$193$			16.9706i			0.0879304i	−0.999033	+	0.0439652i	$0.986001\pi$
$194$			171.120i			0.882061i
$195$			8.48528i			0.0435143i
$196$	46.0000			0.234694
$197$			101.823i			0.516870i	0.966029	+	0.258435i	$0.0832068\pi$
$197$			101.823i			0.516870i	−0.966029	+	0.258435i	$0.916793\pi$
$198$	96.0000	+	79.1960i	0.484848	+	0.399980i
$199$	182.000			0.914573			0.457286	−	0.889319i	$-0.348821\pi$
$199$	182.000			0.914573			0.457286	+	0.889319i	$0.348821\pi$
$200$		−	67.8823i		−	0.339411i
$201$	89.0000			0.442786
$202$	12.0000			0.0594059
$203$	−288.000			−1.41872
$204$			50.9117i			0.249567i
$205$			8.48528i			0.0413916i
$206$			115.966i			0.562939i
$207$	−136.000			−0.657005
$208$		−	33.9411i		−	0.163178i
$209$	216.000	+	178.191i	1.03349	+	0.852588i
$210$	−12.0000			−0.0571429
$211$			118.794i			0.563004i	0.959561	+	0.281502i	$0.0908327\pi$
$211$			118.794i			0.563004i	−0.959561	+	0.281502i	$0.909167\pi$
$212$	−4.00000			−0.0188679
$213$	−7.00000			−0.0328638
$214$	−108.000			−0.504673
$215$			16.9706i			0.0789328i
$216$		−	48.0833i		−	0.222608i
$217$			144.250i			0.664746i
$218$	−216.000			−0.990826
$219$		−	127.279i		−	0.581184i
$220$	14.0000	−	16.9706i	0.0636364	−	0.0771389i
$221$	−216.000			−0.977376
$222$		−	66.4680i		−	0.299406i
$223$	−31.0000			−0.139013			−0.0695067	−	0.997581i	$-0.522143\pi$
$223$	−31.0000			−0.139013			−0.0695067	+	0.997581i	$0.522143\pi$
$224$	48.0000			0.214286
$225$	192.000			0.853333
$226$			1.41421i			0.00625758i
$227$		−	93.3381i		−	0.411181i	−0.978638	−	0.205591i	$-0.934089\pi$
$227$		−	93.3381i		−	0.411181i	0.978638	−	0.205591i	$-0.0659115\pi$
$228$		−	50.9117i		−	0.223297i
$229$	−73.0000			−0.318777			−0.159389	−	0.987216i	$-0.550952\pi$
$229$	−73.0000			−0.318777			−0.159389	+	0.987216i	$0.550952\pi$
$230$			24.0416i			0.104529i
$231$	72.0000	+	59.3970i	0.311688	+	0.257130i
$232$	−96.0000			−0.413793
$233$			203.647i			0.874020i	0.899457	+	0.437010i	$0.143963\pi$
$233$			203.647i			0.874020i	−0.899457	+	0.437010i	$0.856037\pi$
$234$	96.0000			0.410256
$235$	58.0000			0.246809
$236$	110.000			0.466102
$237$			33.9411i			0.143211i
$238$		−	305.470i		−	1.28349i
$239$		−	288.500i		−	1.20711i	−0.797321	−	0.603556i	$-0.793750\pi$
$239$		−	288.500i		−	1.20711i	0.797321	−	0.603556i	$-0.206250\pi$
$240$	−4.00000			−0.0166667
$241$		−	118.794i		−	0.492921i	−0.969153	−	0.246460i	$-0.920732\pi$
$241$		−	118.794i		−	0.492921i	0.969153	−	0.246460i	$-0.0792675\pi$
$242$	−168.000	+	32.5269i	−0.694215	+	0.134409i
$243$	208.000			0.855967
$244$		−	169.706i		−	0.695515i
$245$	23.0000			0.0938776
$246$	−12.0000			−0.0487805
$247$	216.000			0.874494
$248$			48.0833i			0.193884i
$249$			33.9411i			0.136310i
$250$		−	69.2965i		−	0.277186i
$251$	65.0000			0.258964			0.129482	−	0.991582i	$-0.458669\pi$
$251$	65.0000			0.258964			0.129482	+	0.991582i	$0.458669\pi$
$252$			135.765i			0.538748i
$253$	119.000	−	144.250i	0.470356	−	0.570157i
$254$	36.0000			0.141732
$255$			25.4558i			0.0998268i
$256$	16.0000			0.0625000
$257$	170.000			0.661479			0.330739	−	0.943722i	$-0.392702\pi$
$257$	170.000			0.661479			0.330739	+	0.943722i	$0.392702\pi$
$258$	−24.0000			−0.0930233
$259$			398.808i			1.53980i
$260$		−	16.9706i		−	0.0652714i
$261$		−	271.529i		−	1.04034i
$262$	132.000			0.503817
$263$			313.955i			1.19375i	0.802335	+	0.596873i	$0.203591\pi$
$263$			313.955i			1.19375i	−0.802335	+	0.596873i	$0.796409\pi$
$264$	24.0000	+	19.7990i	0.0909091	+	0.0749962i
$265$	−2.00000			−0.00754717
$266$			305.470i			1.14838i
$267$	−97.0000			−0.363296
$268$	−178.000			−0.664179
$269$	−430.000			−1.59851			−0.799257	−	0.600990i	$-0.794773\pi$
$269$	−430.000			−1.59851			−0.799257	+	0.600990i	$0.794773\pi$
$270$		−	24.0416i		−	0.0890431i
$271$		−	381.838i		−	1.40900i	−0.709706	−	0.704498i	$-0.751172\pi$
$271$		−	381.838i		−	1.40900i	0.709706	−	0.704498i	$-0.248828\pi$
$272$		−	101.823i		−	0.374351i
$273$	72.0000			0.263736
$274$		−	236.174i		−	0.861948i
$275$	−168.000	+	203.647i	−0.610909	+	0.740534i
$276$	−34.0000			−0.123188
$277$			84.8528i			0.306328i	0.988201	+	0.153164i	$0.0489463\pi$
$277$			84.8528i			0.306328i	−0.988201	+	0.153164i	$0.951054\pi$
$278$	132.000			0.474820
$279$	−136.000			−0.487455
$280$	24.0000			0.0857143
$281$			135.765i			0.483148i	0.970382	+	0.241574i	$0.0776636\pi$
$281$			135.765i			0.483148i	−0.970382	+	0.241574i	$0.922336\pi$
$282$			82.0244i			0.290867i
$283$			67.8823i			0.239867i	0.992782	+	0.119933i	$0.0382681\pi$
$283$			67.8823i			0.239867i	−0.992782	+	0.119933i	$0.961732\pi$
$284$	14.0000			0.0492958
$285$		−	25.4558i		−	0.0893188i
$286$	−84.0000	+	101.823i	−0.293706	+	0.356026i
$287$	72.0000			0.250871
$288$			45.2548i			0.157135i
$289$	−359.000			−1.24221
$290$	−48.0000			−0.165517
$291$	−121.000			−0.415808
$292$			254.558i			0.871775i
$293$		−	517.602i		−	1.76656i	−0.468846	−	0.883280i	$-0.655330\pi$
$293$		−	517.602i		−	1.76656i	0.468846	−	0.883280i	$-0.344670\pi$
$294$			32.5269i			0.110636i
$295$	55.0000			0.186441
$296$			132.936i			0.449108i
$297$	−119.000	+	144.250i	−0.400673	+	0.485690i
$298$	−228.000			−0.765101
$299$		−	144.250i		−	0.482441i
$300$	48.0000			0.160000
$301$	144.000			0.478405
$302$	408.000			1.35099
$303$			8.48528i			0.0280042i
$304$			101.823i			0.334945i
$305$		−	84.8528i		−	0.278206i
$306$	288.000			0.941176
$307$		−	25.4558i		−	0.0829181i	−0.999140	−	0.0414590i	$-0.986799\pi$
$307$		−	25.4558i		−	0.0829181i	0.999140	−	0.0414590i	$-0.0132006\pi$
$308$	−144.000	−	118.794i	−0.467532	−	0.385695i
$309$	−82.0000			−0.265372
$310$			24.0416i			0.0775536i
$311$	−154.000			−0.495177			−0.247588	−	0.968865i	$-0.579638\pi$
$311$	−154.000			−0.495177			−0.247588	+	0.968865i	$0.579638\pi$
$312$	24.0000			0.0769231
$313$	95.0000			0.303514			0.151757	−	0.988418i	$-0.451507\pi$
$313$	95.0000			0.303514			0.151757	+	0.988418i	$0.451507\pi$
$314$			1.41421i			0.00450386i
$315$			67.8823i			0.215499i
$316$		−	67.8823i		−	0.214817i
$317$	23.0000			0.0725552			0.0362776	−	0.999342i	$-0.488450\pi$
$317$	23.0000			0.0725552			0.0362776	+	0.999342i	$0.488450\pi$
$318$		−	2.82843i		−	0.00889442i
$319$	288.000	+	237.588i	0.902821	+	0.744790i
$320$	8.00000			0.0250000
$321$		−	76.3675i		−	0.237905i
$322$	204.000			0.633540
$323$	648.000			2.00619
$324$	−110.000			−0.339506
$325$			203.647i			0.626605i
$326$		−	155.563i		−	0.477189i
$327$		−	152.735i		−	0.467080i
$328$	24.0000			0.0731707
$329$		−	492.146i		−	1.49589i
$330$	12.0000	+	9.89949i	0.0363636	+	0.0299985i
$331$	185.000			0.558912			0.279456	−	0.960158i	$-0.409846\pi$
$331$	185.000			0.558912			0.279456	+	0.960158i	$0.409846\pi$
$332$		−	67.8823i		−	0.204465i
$333$	−376.000			−1.12913
$334$	−156.000			−0.467066
$335$	−89.0000			−0.265672
$336$			33.9411i			0.101015i
$337$		−	8.48528i		−	0.0251789i	−0.999921	−	0.0125894i	$-0.995993\pi$
$337$		−	8.48528i		−	0.0251789i	0.999921	−	0.0125894i	$-0.00400745\pi$
$338$		−	137.179i		−	0.405854i
$339$	−1.00000			−0.00294985
$340$		−	50.9117i		−	0.149740i
$341$	119.000	−	144.250i	0.348974	−	0.423020i
$342$	−288.000			−0.842105
$343$			220.617i			0.643199i
$344$	48.0000			0.139535
$345$	−17.0000			−0.0492754
$346$	−24.0000			−0.0693642
$347$		−	212.132i		−	0.611332i	−0.952139	−	0.305666i	$-0.901121\pi$
$347$		−	212.132i		−	0.611332i	0.952139	−	0.305666i	$-0.0988790\pi$
$348$		−	67.8823i		−	0.195064i
$349$			263.044i			0.753707i	0.926273	+	0.376853i	$0.122994\pi$
$349$			263.044i			0.753707i	−0.926273	+	0.376853i	$0.877006\pi$
$350$	−288.000			−0.822857
$351$			144.250i			0.410968i
$352$	−48.0000	−	39.5980i	−0.136364	−	0.112494i
$353$	167.000			0.473088			0.236544	−	0.971621i	$-0.423985\pi$
$353$	167.000			0.473088			0.236544	+	0.971621i	$0.423985\pi$
$354$			77.7817i			0.219722i
$355$	7.00000			0.0197183
$356$	194.000			0.544944
$357$	216.000			0.605042
$358$		−	295.571i		−	0.825616i
$359$			636.396i			1.77269i	0.463024	+	0.886346i	$0.346764\pi$
$359$			636.396i			1.77269i	−0.463024	+	0.886346i	$0.653236\pi$
$360$			22.6274i			0.0628539i
$361$	−287.000			−0.795014
$362$		−	168.291i		−	0.464893i
$363$	−23.0000	−	118.794i	−0.0633609	−	0.327256i
$364$	−144.000			−0.395604
$365$			127.279i			0.348710i
$366$	120.000			0.327869
$367$	−607.000			−1.65395			−0.826975	−	0.562238i	$-0.809940\pi$
$367$	−607.000			−1.65395			−0.826975	+	0.562238i	$0.809940\pi$
$368$	68.0000			0.184783
$369$			67.8823i			0.183963i
$370$			66.4680i			0.179643i
$371$			16.9706i			0.0457428i
$372$	−34.0000			−0.0913978
$373$			347.897i			0.932698i	0.884601	+	0.466349i	$0.154431\pi$
$373$			347.897i			0.932698i	−0.884601	+	0.466349i	$0.845569\pi$
$374$	−252.000	+	305.470i	−0.673797	+	0.816765i
$375$	49.0000			0.130667
$376$		−	164.049i		−	0.436300i
$377$	288.000			0.763926
$378$	−204.000			−0.539683
$379$	−295.000			−0.778364			−0.389182	−	0.921161i	$-0.627242\pi$
$379$	−295.000			−0.778364			−0.389182	+	0.921161i	$0.627242\pi$
$380$			50.9117i			0.133978i
$381$			25.4558i			0.0668132i
$382$			451.134i			1.18098i
$383$	377.000			0.984334			0.492167	−	0.870501i	$-0.336205\pi$
$383$	377.000			0.984334			0.492167	+	0.870501i	$0.336205\pi$
$384$			11.3137i			0.0294628i
$385$	−72.0000	−	59.3970i	−0.187013	−	0.154278i
$386$	24.0000			0.0621762
$387$			135.765i			0.350813i
$388$	242.000			0.623711
$389$	−121.000			−0.311054			−0.155527	−	0.987832i	$-0.549708\pi$
$389$	−121.000			−0.311054			−0.155527	+	0.987832i	$0.549708\pi$
$390$	12.0000			0.0307692
$391$		−	432.749i		−	1.10678i
$392$		−	65.0538i		−	0.165954i
$393$			93.3381i			0.237502i
$394$	144.000			0.365482
$395$		−	33.9411i		−	0.0859269i
$396$	112.000	−	135.765i	0.282828	−	0.342840i
$397$	578.000			1.45592			0.727960	−	0.685620i	$-0.240469\pi$
$397$	578.000			1.45592			0.727960	+	0.685620i	$0.240469\pi$
$398$		−	257.387i		−	0.646701i
$399$	−216.000			−0.541353
$400$	−96.0000			−0.240000
$401$	−550.000			−1.37157			−0.685786	−	0.727804i	$-0.740541\pi$
$401$	−550.000			−1.37157			−0.685786	+	0.727804i	$0.740541\pi$
$402$		−	125.865i		−	0.313097i
$403$		−	144.250i		−	0.357940i
$404$		−	16.9706i		−	0.0420063i
$405$	−55.0000			−0.135802
$406$			407.294i			1.00319i
$407$	329.000	−	398.808i	0.808354	−	0.979873i
$408$	72.0000			0.176471
$409$		−	593.970i		−	1.45225i	−0.687563	−	0.726124i	$-0.741320\pi$
$409$		−	593.970i		−	1.45225i	0.687563	−	0.726124i	$-0.258680\pi$
$410$	12.0000			0.0292683
$411$	167.000			0.406326
$412$	164.000			0.398058
$413$		−	466.690i		−	1.13000i
$414$			192.333i			0.464573i
$415$		−	33.9411i		−	0.0817858i
$416$	−48.0000			−0.115385
$417$			93.3381i			0.223832i
$418$	252.000	−	305.470i	0.602871	−	0.730790i
$419$	−370.000			−0.883055			−0.441527	−	0.897248i	$-0.645563\pi$
$419$	−370.000			−0.883055			−0.441527	+	0.897248i	$0.645563\pi$
$420$			16.9706i			0.0404061i
$421$	338.000			0.802850			0.401425	−	0.915892i	$-0.368515\pi$
$421$	338.000			0.802850			0.401425	+	0.915892i	$0.368515\pi$
$422$	168.000			0.398104
$423$	464.000			1.09693
$424$			5.65685i			0.0133416i
$425$			610.940i			1.43751i
$426$			9.89949i			0.0232383i
$427$	−720.000			−1.68618
$428$			152.735i			0.356858i
$429$	−72.0000	−	59.3970i	−0.167832	−	0.138454i
$430$	24.0000			0.0558140
$431$		−	229.103i		−	0.531561i	−0.964034	−	0.265780i	$-0.914370\pi$
$431$		−	229.103i		−	0.531561i	0.964034	−	0.265780i	$-0.0856296\pi$
$432$	−68.0000			−0.157407
$433$	−25.0000			−0.0577367			−0.0288684	−	0.999583i	$-0.509190\pi$
$433$	−25.0000			−0.0577367			−0.0288684	+	0.999583i	$0.509190\pi$
$434$	204.000			0.470046
$435$		−	33.9411i		−	0.0780256i
$436$			305.470i			0.700620i
$437$			432.749i			0.990273i
$438$	−180.000			−0.410959
$439$		−	373.352i		−	0.850461i	−0.905085	−	0.425231i	$-0.860193\pi$
$439$		−	373.352i		−	0.850461i	0.905085	−	0.425231i	$-0.139807\pi$
$440$	−24.0000	−	19.7990i	−0.0545455	−	0.0449977i
$441$	184.000			0.417234
$442$			305.470i			0.691109i
$443$	257.000			0.580135			0.290068	−	0.957006i	$-0.406322\pi$
$443$	257.000			0.580135			0.290068	+	0.957006i	$0.406322\pi$
$444$	−94.0000			−0.211712
$445$	97.0000			0.217978
$446$			43.8406i			0.0982974i
$447$		−	161.220i		−	0.360672i
$448$		−	67.8823i		−	0.151523i
$449$	47.0000			0.104677			0.0523385	−	0.998629i	$-0.483333\pi$
$449$	47.0000			0.104677			0.0523385	+	0.998629i	$0.483333\pi$
$450$		−	271.529i		−	0.603398i
$451$	−72.0000	−	59.3970i	−0.159645	−	0.131701i
$452$	2.00000			0.00442478
$453$			288.500i			0.636864i
$454$	−132.000			−0.290749
$455$	−72.0000			−0.158242
$456$	−72.0000			−0.157895
$457$		−	271.529i		−	0.594155i	−0.954853	−	0.297078i	$-0.903988\pi$
$457$		−	271.529i		−	0.594155i	0.954853	−	0.297078i	$-0.0960120\pi$
$458$			103.238i			0.225410i
$459$			432.749i			0.942809i
$460$	34.0000			0.0739130
$461$			492.146i			1.06756i	0.845623	+	0.533781i	$0.179229\pi$
$461$			492.146i			1.06756i	−0.845623	+	0.533781i	$0.820771\pi$
$462$	84.0000	−	101.823i	0.181818	−	0.220397i
$463$	−631.000			−1.36285			−0.681425	−	0.731887i	$-0.738640\pi$
$463$	−631.000			−1.36285			−0.681425	+	0.731887i	$0.738640\pi$
$464$			135.765i			0.292596i
$465$	−17.0000			−0.0365591
$466$	288.000			0.618026
$467$	−367.000			−0.785867			−0.392934	−	0.919567i	$-0.628540\pi$
$467$	−367.000			−0.785867			−0.392934	+	0.919567i	$0.628540\pi$
$468$		−	135.765i		−	0.290095i
$469$			755.190i			1.61021i
$470$		−	82.0244i		−	0.174520i
$471$	−1.00000			−0.00212314
$472$		−	155.563i		−	0.329584i
$473$	−144.000	−	118.794i	−0.304440	−	0.251150i
$474$	48.0000			0.101266
$475$		−	610.940i		−	1.28619i
$476$	−432.000			−0.907563
$477$	−16.0000			−0.0335430
$478$	−408.000			−0.853556
$479$			466.690i			0.974302i	0.873318	+	0.487151i	$0.161964\pi$
$479$			466.690i			0.974302i	−0.873318	+	0.487151i	$0.838036\pi$
$480$			5.65685i			0.0117851i
$481$		−	398.808i		−	0.829123i
$482$	−168.000			−0.348548
$483$			144.250i			0.298654i
$484$	46.0000	+	237.588i	0.0950413	+	0.490884i
$485$	121.000			0.249485
$486$		−	294.156i		−	0.605260i
$487$	−511.000			−1.04928			−0.524641	−	0.851324i	$-0.675800\pi$
$487$	−511.000			−1.04928			−0.524641	+	0.851324i	$0.675800\pi$
$488$	−240.000			−0.491803
$489$	110.000			0.224949
$490$		−	32.5269i		−	0.0663815i
$491$		−	33.9411i		−	0.0691265i	−0.999403	−	0.0345633i	$-0.988996\pi$
$491$		−	33.9411i		−	0.0691265i	0.999403	−	0.0345633i	$-0.0110040\pi$
$492$			16.9706i			0.0344930i
$493$	864.000			1.75254
$494$		−	305.470i		−	0.618361i
$495$	56.0000	−	67.8823i	0.113131	−	0.137136i
$496$	68.0000			0.137097
$497$		−	59.3970i		−	0.119511i
$498$	48.0000			0.0963855
$499$	494.000			0.989980			0.494990	−	0.868899i	$-0.335172\pi$
$499$	494.000			0.989980			0.494990	+	0.868899i	$0.335172\pi$
$500$	−98.0000			−0.196000
$501$		−	110.309i		−	0.220177i
$502$		−	91.9239i		−	0.183115i
$503$			661.852i			1.31581i	0.753101	+	0.657905i	$0.228557\pi$
$503$			661.852i			1.31581i	−0.753101	+	0.657905i	$0.771443\pi$
$504$	192.000			0.380952
$505$		−	8.48528i		−	0.0168025i
$506$	−204.000	−	168.291i	−0.403162	−	0.332592i
$507$	97.0000			0.191321
$508$		−	50.9117i		−	0.100220i
$509$	503.000			0.988212			0.494106	−	0.869402i	$-0.335495\pi$
$509$	503.000			0.988212			0.494106	+	0.869402i	$0.335495\pi$
$510$	36.0000			0.0705882
$511$	1080.00			2.11350
$512$		−	22.6274i		−	0.0441942i
$513$		−	432.749i		−	0.843566i
$514$		−	240.416i		−	0.467736i
$515$	82.0000			0.159223
$516$			33.9411i			0.0657774i
$517$	−406.000	+	492.146i	−0.785300	+	0.951927i
$518$	564.000			1.08880
$519$		−	16.9706i		−	0.0326986i
$520$	−24.0000			−0.0461538
$521$	−745.000			−1.42994			−0.714971	−	0.699154i	$-0.753560\pi$
$521$	−745.000			−1.42994			−0.714971	+	0.699154i	$0.753560\pi$
$522$	−384.000			−0.735632
$523$		−	330.926i		−	0.632746i	−0.948635	−	0.316373i	$-0.897535\pi$
$523$		−	330.926i		−	0.632746i	0.948635	−	0.316373i	$-0.102465\pi$
$524$		−	186.676i		−	0.356252i
$525$		−	203.647i		−	0.387899i
$526$	444.000			0.844106
$527$		−	432.749i		−	0.821156i
$528$	28.0000	−	33.9411i	0.0530303	−	0.0642824i
$529$	−240.000			−0.453686
$530$			2.82843i			0.00533665i
$531$	440.000			0.828625
$532$	432.000			0.812030
$533$	−72.0000			−0.135084
$534$			137.179i			0.256889i
$535$			76.3675i			0.142743i
$536$			251.730i			0.469646i
$537$	209.000			0.389199
$538$			608.112i			1.13032i
$539$	−161.000	+	195.161i	−0.298701	+	0.362081i
$540$	−34.0000			−0.0629630
$541$			687.308i			1.27044i	0.772331	+	0.635220i	$0.219090\pi$
$541$			687.308i			1.27044i	−0.772331	+	0.635220i	$0.780910\pi$
$542$	−540.000			−0.996310
$543$	119.000			0.219153
$544$	−144.000			−0.264706
$545$			152.735i			0.280248i
$546$		−	101.823i		−	0.186490i
$547$		−	831.558i		−	1.52021i	−0.649797	−	0.760107i	$-0.725146\pi$
$547$		−	831.558i		−	1.52021i	0.649797	−	0.760107i	$-0.274854\pi$
$548$	−334.000			−0.609489
$549$		−	678.823i		−	1.23647i
$550$	288.000	+	237.588i	0.523636	+	0.431978i
$551$	−864.000			−1.56806
$552$			48.0833i			0.0871074i
$553$	−288.000			−0.520796
$554$	120.000			0.216606
$555$	−47.0000			−0.0846847
$556$		−	186.676i		−	0.335749i
$557$		−	636.396i		−	1.14254i	−0.820761	−	0.571271i	$-0.806450\pi$
$557$		−	636.396i		−	1.14254i	0.820761	−	0.571271i	$-0.193550\pi$
$558$			192.333i			0.344683i
$559$	−144.000			−0.257603
$560$		−	33.9411i		−	0.0606092i
$561$	−216.000	−	178.191i	−0.385027	−	0.317631i
$562$	192.000			0.341637
$563$			780.646i			1.38658i	0.720658	+	0.693291i	$0.243840\pi$
$563$			780.646i			1.38658i	−0.720658	+	0.693291i	$0.756160\pi$
$564$	116.000			0.205674
$565$	1.00000			0.00176991
$566$	96.0000			0.169611
$567$			466.690i			0.823087i
$568$		−	19.7990i		−	0.0348574i
$569$		−	576.999i		−	1.01406i	−0.861929	−	0.507029i	$-0.830744\pi$
$569$		−	576.999i		−	1.01406i	0.861929	−	0.507029i	$-0.169256\pi$
$570$	−36.0000			−0.0631579
$571$			627.911i			1.09967i	0.835274	+	0.549834i	$0.185309\pi$
$571$			627.911i			1.09967i	−0.835274	+	0.549834i	$0.814691\pi$
$572$	144.000	+	118.794i	0.251748	+	0.207682i
$573$	−319.000			−0.556719
$574$		−	101.823i		−	0.177393i
$575$	−408.000			−0.709565
$576$	64.0000			0.111111
$577$	−385.000			−0.667244			−0.333622	−	0.942707i	$-0.608271\pi$
$577$	−385.000			−0.667244			−0.333622	+	0.942707i	$0.608271\pi$
$578$			507.703i			0.878378i
$579$			16.9706i			0.0293101i
$580$			67.8823i			0.117038i
$581$	−288.000			−0.495697
$582$			171.120i			0.294020i
$583$	14.0000	−	16.9706i	0.0240137	−	0.0291090i
$584$	360.000			0.616438
$585$		−	67.8823i		−	0.116038i
$586$	−732.000			−1.24915
$587$	806.000			1.37308			0.686542	−	0.727090i	$-0.259128\pi$
$587$	806.000			1.37308			0.686542	+	0.727090i	$0.259128\pi$
$588$	46.0000			0.0782313
$589$			432.749i			0.734719i
$590$		−	77.7817i		−	0.131833i
$591$			101.823i			0.172290i
$592$	188.000			0.317568
$593$			152.735i			0.257563i	0.991673	+	0.128782i	$0.0411066\pi$
$593$			152.735i			0.257563i	−0.991673	+	0.128782i	$0.958893\pi$
$594$	204.000	+	168.291i	0.343434	+	0.283319i
$595$	−216.000			−0.363025
$596$			322.441i			0.541008i
$597$	182.000			0.304858
$598$	−204.000			−0.341137
$599$	998.000			1.66611			0.833055	−	0.553190i	$-0.186590\pi$
$599$	998.000			1.66611			0.833055	+	0.553190i	$0.186590\pi$
$600$		−	67.8823i		−	0.113137i
$601$		−	755.190i		−	1.25656i	−0.777989	−	0.628278i	$-0.783760\pi$
$601$		−	755.190i		−	1.25656i	0.777989	−	0.628278i	$-0.216240\pi$
$602$		−	203.647i		−	0.338284i
$603$	−712.000			−1.18076
$604$		−	576.999i		−	0.955297i
$605$	23.0000	+	118.794i	0.0380165	+	0.196354i
$606$	12.0000			0.0198020
$607$			373.352i			0.615078i	0.951535	+	0.307539i	$0.0995055\pi$
$607$			373.352i			0.615078i	−0.951535	+	0.307539i	$0.900495\pi$
$608$	144.000			0.236842
$609$	−288.000			−0.472906
$610$	−120.000			−0.196721
$611$			492.146i			0.805477i
$612$		−	407.294i		−	0.665512i
$613$		−	356.382i		−	0.581373i	−0.956818	−	0.290687i	$-0.906116\pi$
$613$		−	356.382i		−	0.581373i	0.956818	−	0.290687i	$-0.0938837\pi$
$614$	−36.0000			−0.0586319
$615$			8.48528i			0.0137972i
$616$	−168.000	+	203.647i	−0.272727	+	0.330595i
$617$	314.000			0.508914			0.254457	−	0.967084i	$-0.418103\pi$
$617$	314.000			0.508914			0.254457	+	0.967084i	$0.418103\pi$
$618$			115.966i			0.187646i
$619$	1193.00			1.92730			0.963651	−	0.267164i	$-0.0860866\pi$
$619$	1193.00			1.92730			0.963651	+	0.267164i	$0.0860866\pi$
$620$	34.0000			0.0548387
$621$	−289.000			−0.465378
$622$			217.789i			0.350143i
$623$		−	823.072i		−	1.32114i
$624$		−	33.9411i		−	0.0543928i
$625$	551.000			0.881600
$626$		−	134.350i		−	0.214617i
$627$	216.000	+	178.191i	0.344498	+	0.284196i
$628$	2.00000			0.00318471
$629$		−	1196.42i		−	1.90211i
$630$	96.0000			0.152381
$631$	−439.000			−0.695721			−0.347861	−	0.937546i	$-0.613092\pi$
$631$	−439.000			−0.695721			−0.347861	+	0.937546i	$0.613092\pi$
$632$	−96.0000			−0.151899
$633$			118.794i			0.187668i
$634$		−	32.5269i		−	0.0513043i
$635$		−	25.4558i		−	0.0400879i
$636$	−4.00000			−0.00628931
$637$			195.161i			0.306376i
$638$	336.000	−	407.294i	0.526646	−	0.638391i
$639$	56.0000			0.0876369
$640$		−	11.3137i		−	0.0176777i
$641$	671.000			1.04680			0.523401	−	0.852087i	$-0.324663\pi$
$641$	671.000			1.04680			0.523401	+	0.852087i	$0.324663\pi$
$642$	−108.000			−0.168224
$643$	−487.000			−0.757387			−0.378694	−	0.925522i	$-0.623627\pi$
$643$	−487.000			−0.757387			−0.378694	+	0.925522i	$0.623627\pi$
$644$		−	288.500i		−	0.447981i
$645$			16.9706i			0.0263109i
$646$		−	916.410i		−	1.41859i
$647$	569.000			0.879444			0.439722	−	0.898134i	$-0.355077\pi$
$647$	569.000			0.879444			0.439722	+	0.898134i	$0.355077\pi$
$648$			155.563i			0.240067i
$649$	−385.000	+	466.690i	−0.593220	+	0.719092i
$650$	288.000			0.443077
$651$			144.250i			0.221582i
$652$	−220.000			−0.337423
$653$	−1081.00			−1.65544			−0.827718	−	0.561144i	$-0.810361\pi$
$653$	−1081.00			−1.65544			−0.827718	+	0.561144i	$0.810361\pi$
$654$	−216.000			−0.330275
$655$		−	93.3381i		−	0.142501i
$656$		−	33.9411i		−	0.0517395i
$657$			1018.23i			1.54982i
$658$	−696.000			−1.05775
$659$		−	780.646i		−	1.18459i	−0.805721	−	0.592296i	$-0.798222\pi$
$659$		−	780.646i		−	1.18459i	0.805721	−	0.592296i	$-0.201778\pi$
$660$	14.0000	−	16.9706i	0.0212121	−	0.0257130i
$661$	1007.00			1.52345			0.761725	−	0.647901i	$-0.224353\pi$
$661$	1007.00			1.52345			0.761725	+	0.647901i	$0.224353\pi$
$662$		−	261.630i		−	0.395211i
$663$	−216.000			−0.325792
$664$	−96.0000			−0.144578
$665$	216.000			0.324812
$666$			531.744i			0.798415i
$667$			576.999i			0.865066i
$668$			220.617i			0.330265i
$669$	−31.0000			−0.0463378
$670$			125.865i			0.187858i
$671$	720.000	+	593.970i	1.07303	+	0.885201i
$672$	48.0000			0.0714286
$673$			644.881i			0.958219i	0.877755	+	0.479109i	$0.159040\pi$
$673$			644.881i			0.958219i	−0.877755	+	0.479109i	$0.840960\pi$
$674$	−12.0000			−0.0178042
$675$	408.000			0.604444
$676$	−194.000			−0.286982
$677$			873.984i			1.29097i	0.763775	+	0.645483i	$0.223344\pi$
$677$			873.984i			1.29097i	−0.763775	+	0.645483i	$0.776656\pi$
$678$			1.41421i			0.00208586i
$679$		−	1026.72i		−	1.51210i
$680$	−72.0000			−0.105882
$681$		−	93.3381i		−	0.137060i
$682$	−204.000	−	168.291i	−0.299120	−	0.246762i
$683$	−610.000			−0.893119			−0.446559	−	0.894754i	$-0.647351\pi$
$683$	−610.000			−0.893119			−0.446559	+	0.894754i	$0.647351\pi$
$684$			407.294i			0.595458i
$685$	−167.000			−0.243796
$686$	312.000			0.454810
$687$	−73.0000			−0.106259
$688$		−	67.8823i		−	0.0986661i
$689$		−	16.9706i		−	0.0246307i
$690$			24.0416i			0.0348429i
$691$	−1255.00			−1.81621			−0.908104	−	0.418744i	$-0.862470\pi$
$691$	−1255.00			−1.81621			−0.908104	+	0.418744i	$0.862470\pi$
$692$			33.9411i			0.0490479i
$693$	−576.000	−	475.176i	−0.831169	−	0.685679i
$694$	−300.000			−0.432277
$695$		−	93.3381i		−	0.134299i
$696$	−96.0000			−0.137931
$697$	−216.000			−0.309900
$698$	372.000			0.532951
$699$			203.647i			0.291340i
$700$			407.294i			0.581848i
$701$			76.3675i			0.108941i	0.998515	+	0.0544704i	$0.0173471\pi$
$701$			76.3675i			0.108941i	−0.998515	+	0.0544704i	$0.982653\pi$
$702$	204.000			0.290598
$703$			1196.42i			1.70188i
$704$	−56.0000	+	67.8823i	−0.0795455	+	0.0964237i
$705$	58.0000			0.0822695
$706$		−	236.174i		−	0.334524i
$707$	−72.0000			−0.101839
$708$	110.000			0.155367
$709$	455.000			0.641749			0.320874	−	0.947122i	$-0.396023\pi$
$709$	455.000			0.641749			0.320874	+	0.947122i	$0.396023\pi$
$710$		−	9.89949i		−	0.0139430i
$711$		−	271.529i		−	0.381897i
$712$		−	274.357i		−	0.385333i
$713$	289.000			0.405330
$714$		−	305.470i		−	0.427829i
$715$	72.0000	+	59.3970i	0.100699	+	0.0830727i
$716$	−418.000			−0.583799
$717$		−	288.500i		−	0.402370i
$718$	900.000			1.25348
$719$	−223.000			−0.310153			−0.155076	−	0.987902i	$-0.549562\pi$
$719$	−223.000			−0.310153			−0.155076	+	0.987902i	$0.549562\pi$
$720$	32.0000			0.0444444
$721$		−	695.793i		−	0.965039i
$722$			405.879i			0.562160i
$723$		−	118.794i		−	0.164307i
$724$	−238.000			−0.328729
$725$		−	814.587i		−	1.12357i
$726$	−168.000	+	32.5269i	−0.231405	+	0.0448029i
$727$	−535.000			−0.735901			−0.367950	−	0.929845i	$-0.619940\pi$
$727$	−535.000			−0.735901			−0.367950	+	0.929845i	$0.619940\pi$
$728$			203.647i			0.279735i
$729$	−287.000			−0.393690
$730$	180.000			0.246575
$731$	−432.000			−0.590971
$732$		−	169.706i		−	0.231838i
$733$			627.911i			0.856631i	0.903629	+	0.428316i	$0.140893\pi$
$733$			627.911i			0.856631i	−0.903629	+	0.428316i	$0.859107\pi$
$734$			858.428i			1.16952i
$735$	23.0000			0.0312925
$736$		−	96.1665i		−	0.130661i
$737$	623.000	−	755.190i	0.845319	−	1.02468i
$738$	96.0000			0.130081
$739$		−	865.499i		−	1.17118i	−0.810609	−	0.585588i	$-0.800864\pi$
$739$		−	865.499i		−	1.17118i	0.810609	−	0.585588i	$-0.199136\pi$
$740$	94.0000			0.127027
$741$	216.000			0.291498
$742$	24.0000			0.0323450
$743$		−	1154.00i		−	1.55316i	−0.630018	−	0.776580i	$-0.716953\pi$
$743$		−	1154.00i		−	1.55316i	0.630018	−	0.776580i	$-0.283047\pi$
$744$			48.0833i			0.0646280i
$745$			161.220i			0.216403i
$746$	492.000			0.659517
$747$		−	271.529i		−	0.363493i
$748$	432.000	+	356.382i	0.577540	+	0.476446i
$749$	648.000			0.865154
$750$		−	69.2965i		−	0.0923953i
$751$	−55.0000			−0.0732357			−0.0366178	−	0.999329i	$-0.511658\pi$
$751$	−55.0000			−0.0732357			−0.0366178	+	0.999329i	$0.511658\pi$
$752$	−232.000			−0.308511
$753$	65.0000			0.0863214
$754$		−	407.294i		−	0.540177i
$755$		−	288.500i		−	0.382119i
$756$			288.500i			0.381613i
$757$	2.00000			0.00264201			0.00132100	−	0.999999i	$-0.499580\pi$
$757$	2.00000			0.00264201			0.00132100	+	0.999999i	$0.499580\pi$
$758$			417.193i			0.550387i
$759$	119.000	−	144.250i	0.156785	−	0.190052i
$760$	72.0000			0.0947368
$761$			1264.31i			1.66138i	0.556738	+	0.830688i	$0.312053\pi$
$761$			1264.31i			1.66138i	−0.556738	+	0.830688i	$0.687947\pi$
$762$	36.0000			0.0472441
$763$	1296.00			1.69856
$764$	638.000			0.835079
$765$		−	203.647i		−	0.266205i
$766$		−	533.159i		−	0.696029i
$767$			466.690i			0.608462i
$768$	16.0000			0.0208333
$769$			602.455i			0.783426i	0.920087	+	0.391713i	$0.128117\pi$
$769$			602.455i			0.783426i	−0.920087	+	0.391713i	$0.871883\pi$
$770$	−84.0000	+	101.823i	−0.109091	+	0.132238i
$771$	170.000			0.220493
$772$		−	33.9411i		−	0.0439652i
$773$	−1222.00			−1.58085			−0.790427	−	0.612556i	$-0.790141\pi$
$773$	−1222.00			−1.58085			−0.790427	+	0.612556i	$0.790141\pi$
$774$	192.000			0.248062
$775$	−408.000			−0.526452
$776$		−	342.240i		−	0.441031i
$777$			398.808i			0.513267i
$778$			171.120i			0.219948i
$779$	216.000			0.277279
$780$		−	16.9706i		−	0.0217571i
$781$	−49.0000	+	59.3970i	−0.0627401	+	0.0760525i
$782$	−612.000			−0.782609
$783$		−	576.999i		−	0.736908i
$784$	−92.0000			−0.117347
$785$	1.00000			0.00127389
$786$	132.000			0.167939
$787$		−	899.440i		−	1.14287i	−0.820647	−	0.571436i	$-0.806387\pi$
$787$		−	899.440i		−	1.14287i	0.820647	−	0.571436i	$-0.193613\pi$
$788$		−	203.647i		−	0.258435i
$789$			313.955i			0.397916i
$790$	−48.0000			−0.0607595
$791$		−	8.48528i		−	0.0107273i
$792$	−192.000	−	158.392i	−0.242424	−	0.199990i
$793$	720.000			0.907945
$794$		−	817.415i		−	1.02949i
$795$	−2.00000			−0.00251572
$796$	−364.000			−0.457286
$797$	−289.000			−0.362610			−0.181305	−	0.983427i	$-0.558032\pi$
$797$	−289.000			−0.362610			−0.181305	+	0.983427i	$0.558032\pi$
$798$			305.470i			0.382795i
$799$			1476.44i			1.84786i
$800$			135.765i			0.169706i
$801$	776.000			0.968789
$802$			777.817i			0.969847i
$803$	−1080.00	−	890.955i	−1.34496	−	1.10953i
$804$	−178.000			−0.221393
$805$		−	144.250i		−	0.179192i
$806$	−204.000			−0.253102
$807$	−430.000			−0.532838
$808$	−24.0000			−0.0297030
$809$			229.103i			0.283192i	0.989925	+	0.141596i	$0.0452234\pi$
$809$			229.103i			0.283192i	−0.989925	+	0.141596i	$0.954777\pi$
$810$			77.7817i			0.0960268i
$811$			763.675i			0.941647i	0.882228	+	0.470823i	$0.156043\pi$
$811$			763.675i			0.941647i	−0.882228	+	0.470823i	$0.843957\pi$
$812$	576.000			0.709360
$813$		−	381.838i		−	0.469665i
$814$	−564.000	−	465.276i	−0.692875	−	0.571592i
$815$	−110.000			−0.134969
$816$		−	101.823i		−	0.124784i
$817$	432.000			0.528764
$818$	−840.000			−1.02689
$819$	−576.000			−0.703297
$820$		−	16.9706i		−	0.0206958i
$821$			593.970i			0.723471i	0.932281	+	0.361736i	$0.117816\pi$
$821$			593.970i			0.723471i	−0.932281	+	0.361736i	$0.882184\pi$
$822$		−	236.174i		−	0.287316i
$823$	305.000			0.370595			0.185298	−	0.982682i	$-0.440675\pi$
$823$	305.000			0.370595			0.185298	+	0.982682i	$0.440675\pi$
$824$		−	231.931i		−	0.281470i
$825$	−168.000	+	203.647i	−0.203636	+	0.246845i
$826$	−660.000			−0.799031
$827$			585.484i			0.707962i	0.935253	+	0.353981i	$0.115172\pi$
$827$			585.484i			0.707962i	−0.935253	+	0.353981i	$0.884828\pi$
$828$	272.000			0.328502
$829$	119.000			0.143546			0.0717732	−	0.997421i	$-0.477134\pi$
$829$	119.000			0.143546			0.0717732	+	0.997421i	$0.477134\pi$
$830$	−48.0000			−0.0578313
$831$			84.8528i			0.102109i
$832$			67.8823i			0.0815892i
$833$			585.484i			0.702862i
$834$	132.000			0.158273
$835$			110.309i			0.132106i
$836$	−432.000	−	356.382i	−0.516746	−	0.426294i
$837$	−289.000			−0.345281
$838$			523.259i			0.624414i
$839$	−1615.00			−1.92491			−0.962455	−	0.271440i	$-0.912500\pi$
$839$	−1615.00			−1.92491			−0.962455	+	0.271440i	$0.912500\pi$
$840$	24.0000			0.0285714
$841$	−311.000			−0.369798
$842$		−	478.004i		−	0.567701i
$843$			135.765i			0.161049i
$844$		−	237.588i		−	0.281502i
$845$	−97.0000			−0.114793
$846$		−	656.195i		−	0.775644i
$847$	1008.00	−	195.161i	1.19008	−	0.230415i
$848$	8.00000			0.00943396
$849$			67.8823i			0.0799555i
$850$	864.000			1.01647
$851$	799.000			0.938895
$852$	14.0000			0.0164319
$853$		−	1086.12i		−	1.27329i	−0.771157	−	0.636645i	$-0.780322\pi$
$853$		−	1086.12i		−	1.27329i	0.771157	−	0.636645i	$-0.219678\pi$
$854$			1018.23i			1.19231i
$855$			203.647i			0.238183i
$856$	216.000			0.252336
$857$			1001.26i			1.16834i	0.811633	+	0.584168i	$0.198579\pi$
$857$			1001.26i			1.16834i	−0.811633	+	0.584168i	$0.801421\pi$
$858$	−84.0000	+	101.823i	−0.0979021	+	0.118675i
$859$	593.000			0.690338			0.345169	−	0.938541i	$-0.387822\pi$
$859$	593.000			0.690338			0.345169	+	0.938541i	$0.387822\pi$
$860$		−	33.9411i		−	0.0394664i
$861$	72.0000			0.0836237
$862$	−324.000			−0.375870
$863$	1190.00			1.37891			0.689455	−	0.724328i	$-0.257850\pi$
$863$	1190.00			1.37891			0.689455	+	0.724328i	$0.257850\pi$
$864$			96.1665i			0.111304i
$865$			16.9706i			0.0196191i
$866$			35.3553i			0.0408260i
$867$	−359.000			−0.414072
$868$		−	288.500i		−	0.332373i
$869$	288.000	+	237.588i	0.331415	+	0.273404i
$870$	−48.0000			−0.0551724
$871$		−	755.190i		−	0.867038i
$872$	432.000			0.495413
$873$	968.000			1.10882
$874$	612.000			0.700229
$875$			415.779i			0.475176i
$876$			254.558i			0.290592i
$877$		−	924.896i		−	1.05461i	−0.849675	−	0.527307i	$-0.823202\pi$
$877$		−	924.896i		−	1.05461i	0.849675	−	0.527307i	$-0.176798\pi$
$878$	−528.000			−0.601367
$879$		−	517.602i		−	0.588853i
$880$	−28.0000	+	33.9411i	−0.0318182	+	0.0385695i
$881$	263.000			0.298524			0.149262	−	0.988798i	$-0.452310\pi$
$881$	263.000			0.298524			0.149262	+	0.988798i	$0.452310\pi$
$882$		−	260.215i		−	0.295029i
$883$	−394.000			−0.446206			−0.223103	−	0.974795i	$-0.571619\pi$
$883$	−394.000			−0.446206			−0.223103	+	0.974795i	$0.571619\pi$
$884$	432.000			0.488688
$885$	55.0000			0.0621469
$886$		−	363.453i		−	0.410218i
$887$			16.9706i			0.0191325i	0.999954	+	0.00956627i	$0.00304508\pi$
$887$			16.9706i			0.0191325i	−0.999954	+	0.00956627i	$0.996955\pi$
$888$			132.936i			0.149703i
$889$	−216.000			−0.242970
$890$		−	137.179i		−	0.154133i
$891$	385.000	−	466.690i	0.432099	−	0.523783i
$892$	62.0000			0.0695067
$893$		−	1476.44i		−	1.65335i
$894$	−228.000			−0.255034
$895$	−209.000			−0.233520
$896$	−96.0000			−0.107143
$897$		−	144.250i		−	0.160814i
$898$		−	66.4680i		−	0.0740179i
$899$			576.999i			0.641823i
$900$	−384.000			−0.426667
$901$		−	50.9117i		−	0.0565058i
$902$	−84.0000	+	101.823i	−0.0931264	+	0.112886i
$903$	144.000			0.159468
$904$		−	2.82843i		−	0.00312879i
$905$	−119.000			−0.131492
$906$	408.000			0.450331
$907$	−418.000			−0.460860			−0.230430	−	0.973089i	$-0.574013\pi$
$907$	−418.000			−0.460860			−0.230430	+	0.973089i	$0.574013\pi$
$908$			186.676i			0.205591i
$909$		−	67.8823i		−	0.0746779i
$910$			101.823i			0.111894i
$911$	−490.000			−0.537870			−0.268935	−	0.963158i	$-0.586672\pi$
$911$	−490.000			−0.537870			−0.268935	+	0.963158i	$0.586672\pi$
$912$			101.823i			0.111648i
$913$	288.000	+	237.588i	0.315444	+	0.260228i
$914$	−384.000			−0.420131
$915$		−	84.8528i		−	0.0927353i
$916$	146.000			0.159389
$917$	−792.000			−0.863686
$918$	612.000			0.666667
$919$			610.940i			0.664788i	0.943141	+	0.332394i	$0.107856\pi$
$919$			610.940i			0.664788i	−0.943141	+	0.332394i	$0.892144\pi$
$920$		−	48.0833i		−	0.0522644i
$921$		−	25.4558i		−	0.0276394i
$922$	696.000			0.754881
$923$			59.3970i			0.0643521i
$924$	−144.000	−	118.794i	−0.155844	−	0.128565i
$925$	−1128.00			−1.21946
$926$			892.369i			0.963681i
$927$	656.000			0.707659
$928$	192.000			0.206897
$929$	−742.000			−0.798708			−0.399354	−	0.916797i	$-0.630766\pi$
$929$	−742.000			−0.798708			−0.399354	+	0.916797i	$0.630766\pi$
$930$			24.0416i			0.0258512i
$931$		−	585.484i		−	0.628877i
$932$		−	407.294i		−	0.437010i
$933$	−154.000			−0.165059
$934$			519.016i			0.555692i
$935$	216.000	+	178.191i	0.231016	+	0.190579i
$936$	−192.000			−0.205128
$937$		−	1196.42i		−	1.27687i	−0.769677	−	0.638434i	$-0.779583\pi$
$937$		−	1196.42i		−	1.27687i	0.769677	−	0.638434i	$-0.220417\pi$
$938$	1068.00			1.13859
$939$	95.0000			0.101171
$940$	−116.000			−0.123404
$941$		−	135.765i		−	0.144277i	−0.997395	−	0.0721384i	$-0.977018\pi$
$941$		−	135.765i		−	0.144277i	0.997395	−	0.0721384i	$-0.0229823\pi$
$942$			1.41421i			0.00150129i
$943$		−	144.250i		−	0.152969i
$944$	−220.000			−0.233051
$945$			144.250i			0.152645i
$946$	−168.000	+	203.647i	−0.177590	+	0.215271i
$947$	113.000			0.119324			0.0596621	−	0.998219i	$-0.480998\pi$
$947$	113.000			0.119324			0.0596621	+	0.998219i	$0.480998\pi$
$948$		−	67.8823i		−	0.0716057i
$949$	−1080.00			−1.13804
$950$	−864.000			−0.909474
$951$	23.0000			0.0241851
$952$			610.940i			0.641744i
$953$			25.4558i			0.0267113i	0.999911	+	0.0133556i	$0.00425136\pi$
$953$			25.4558i			0.0267113i	−0.999911	+	0.0133556i	$0.995749\pi$
$954$			22.6274i			0.0237185i
$955$	319.000			0.334031
$956$			576.999i			0.603556i
$957$	288.000	+	237.588i	0.300940	+	0.248263i
$958$	660.000			0.688935
$959$			1417.04i			1.47762i
$960$	8.00000			0.00833333
$961$	−672.000			−0.699272
$962$	−564.000			−0.586279
$963$			610.940i			0.634414i
$964$			237.588i			0.246460i
$965$		−	16.9706i		−	0.0175861i
$966$	204.000			0.211180
$967$		−	339.411i		−	0.350994i	−0.984480	−	0.175497i	$-0.943847\pi$
$967$		−	339.411i		−	0.350994i	0.984480	−	0.175497i	$-0.0561532\pi$
$968$	336.000	−	65.0538i	0.347107	−	0.0672044i
$969$	648.000			0.668731
$970$		−	171.120i		−	0.176412i
$971$	569.000			0.585994			0.292997	−	0.956113i	$-0.405347\pi$
$971$	569.000			0.585994			0.292997	+	0.956113i	$0.405347\pi$
$972$	−416.000			−0.427984
$973$	−792.000			−0.813977
$974$			722.663i			0.741954i
$975$			203.647i			0.208868i
$976$			339.411i			0.347757i
$977$	−649.000			−0.664278			−0.332139	−	0.943230i	$-0.607770\pi$
$977$	−649.000			−0.664278			−0.332139	+	0.943230i	$0.607770\pi$
$978$		−	155.563i		−	0.159063i
$979$	−679.000	+	823.072i	−0.693565	+	0.840728i
$980$	−46.0000			−0.0469388
$981$			1221.88i			1.24555i
$982$	−48.0000			−0.0488798
$983$	−175.000			−0.178026			−0.0890132	−	0.996030i	$-0.528371\pi$
$983$	−175.000			−0.178026			−0.0890132	+	0.996030i	$0.528371\pi$
$984$	24.0000			0.0243902
$985$		−	101.823i		−	0.103374i
$986$		−	1221.88i		−	1.23923i
$987$		−	492.146i		−	0.498628i
$988$	−432.000			−0.437247
$989$		−	288.500i		−	0.291708i
$990$	−96.0000	−	79.1960i	−0.0969697	−	0.0799959i
$991$	1334.00			1.34612			0.673058	−	0.739590i	$-0.264981\pi$
$991$	1334.00			1.34612			0.673058	+	0.739590i	$0.264981\pi$
$992$		−	96.1665i		−	0.0969421i
$993$	185.000			0.186304
$994$	−84.0000			−0.0845070
$995$	−182.000			−0.182915
$996$		−	67.8823i		−	0.0681549i
$997$		−	1111.57i		−	1.11492i	−0.830205	−	0.557458i	$-0.811777\pi$
$997$		−	1111.57i		−	1.11492i	0.830205	−	0.557458i	$-0.188223\pi$
$998$		−	698.621i		−	0.700022i
$999$	−799.000			−0.799800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.3.b.a.21.1	✓	2
3.2	odd	2		198.3.d.b.109.2		2
4.3	odd	2		176.3.h.c.65.1		2
5.2	odd	4		550.3.c.a.549.3		4
5.3	odd	4		550.3.c.a.549.2		4
5.4	even	2		550.3.d.a.351.2		2
7.6	odd	2		1078.3.d.a.197.1		2
8.3	odd	2		704.3.h.e.65.1		2
8.5	even	2		704.3.h.d.65.2		2
11.2	odd	10		242.3.d.b.161.2		8
11.3	even	5		242.3.d.b.233.1		8
11.4	even	5		242.3.d.b.215.2		8
11.5	even	5		242.3.d.b.239.2		8
11.6	odd	10		242.3.d.b.239.1		8
11.7	odd	10		242.3.d.b.215.1		8
11.8	odd	10		242.3.d.b.233.2		8
11.9	even	5		242.3.d.b.161.1		8
11.10	odd	2	inner	22.3.b.a.21.2	yes	2
12.11	even	2		1584.3.j.d.1297.1		2
33.32	even	2		198.3.d.b.109.1		2
44.43	even	2		176.3.h.c.65.2		2
55.32	even	4		550.3.c.a.549.1		4
55.43	even	4		550.3.c.a.549.4		4
55.54	odd	2		550.3.d.a.351.1		2
77.76	even	2		1078.3.d.a.197.2		2
88.21	odd	2		704.3.h.d.65.1		2
88.43	even	2		704.3.h.e.65.2		2
132.131	odd	2		1584.3.j.d.1297.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.3.b.a.21.1	✓	2	1.1	even	1	trivial
22.3.b.a.21.2	yes	2	11.10	odd	2	inner
176.3.h.c.65.1		2	4.3	odd	2
176.3.h.c.65.2		2	44.43	even	2
198.3.d.b.109.1		2	33.32	even	2
198.3.d.b.109.2		2	3.2	odd	2
242.3.d.b.161.1		8	11.9	even	5
242.3.d.b.161.2		8	11.2	odd	10
242.3.d.b.215.1		8	11.7	odd	10
242.3.d.b.215.2		8	11.4	even	5
242.3.d.b.233.1		8	11.3	even	5
242.3.d.b.233.2		8	11.8	odd	10
242.3.d.b.239.1		8	11.6	odd	10
242.3.d.b.239.2		8	11.5	even	5
550.3.c.a.549.1		4	55.32	even	4
550.3.c.a.549.2		4	5.3	odd	4
550.3.c.a.549.3		4	5.2	odd	4
550.3.c.a.549.4		4	55.43	even	4
550.3.d.a.351.1		2	55.54	odd	2
550.3.d.a.351.2		2	5.4	even	2
704.3.h.d.65.1		2	88.21	odd	2
704.3.h.d.65.2		2	8.5	even	2
704.3.h.e.65.1		2	8.3	odd	2
704.3.h.e.65.2		2	88.43	even	2
1078.3.d.a.197.1		2	7.6	odd	2
1078.3.d.a.197.2		2	77.76	even	2
1584.3.j.d.1297.1		2	12.11	even	2
1584.3.j.d.1297.2		2	132.131	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} -1.41421i q^{6} +8.48528i q^{7} +2.82843i q^{8} -8.00000 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} -1.41421i q^{6} +8.48528i q^{7} +2.82843i q^{8} -8.00000 q^{9} +1.41421i q^{10} +(7.00000 - 8.48528i) q^{11} -2.00000 q^{12} -8.48528i q^{13} +12.0000 q^{14} -1.00000 q^{15} +4.00000 q^{16} -25.4558i q^{17} +11.3137i q^{18} +25.4558i q^{19} +2.00000 q^{20} +8.48528i q^{21} +(-12.0000 - 9.89949i) q^{22} +17.0000 q^{23} +2.82843i q^{24} -24.0000 q^{25} -12.0000 q^{26} -17.0000 q^{27} -16.9706i q^{28} +33.9411i q^{29} +1.41421i q^{30} +17.0000 q^{31} -5.65685i q^{32} +(7.00000 - 8.48528i) q^{33} -36.0000 q^{34} -8.48528i q^{35} +16.0000 q^{36} +47.0000 q^{37} +36.0000 q^{38} -8.48528i q^{39} -2.82843i q^{40} -8.48528i q^{41} +12.0000 q^{42} -16.9706i q^{43} +(-14.0000 + 16.9706i) q^{44} +8.00000 q^{45} -24.0416i q^{46} -58.0000 q^{47} +4.00000 q^{48} -23.0000 q^{49} +33.9411i q^{50} -25.4558i q^{51} +16.9706i q^{52} +2.00000 q^{53} +24.0416i q^{54} +(-7.00000 + 8.48528i) q^{55} -24.0000 q^{56} +25.4558i q^{57} +48.0000 q^{58} -55.0000 q^{59} +2.00000 q^{60} +84.8528i q^{61} -24.0416i q^{62} -67.8823i q^{63} -8.00000 q^{64} +8.48528i q^{65} +(-12.0000 - 9.89949i) q^{66} +89.0000 q^{67} +50.9117i q^{68} +17.0000 q^{69} -12.0000 q^{70} -7.00000 q^{71} -22.6274i q^{72} -127.279i q^{73} -66.4680i q^{74} -24.0000 q^{75} -50.9117i q^{76} +(72.0000 + 59.3970i) q^{77} -12.0000 q^{78} +33.9411i q^{79} -4.00000 q^{80} +55.0000 q^{81} -12.0000 q^{82} +33.9411i q^{83} -16.9706i q^{84} +25.4558i q^{85} -24.0000 q^{86} +33.9411i q^{87} +(24.0000 + 19.7990i) q^{88} -97.0000 q^{89} -11.3137i q^{90} +72.0000 q^{91} -34.0000 q^{92} +17.0000 q^{93} +82.0244i q^{94} -25.4558i q^{95} -5.65685i q^{96} -121.000 q^{97} +32.5269i q^{98} +(-56.0000 + 67.8823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 4 q^{4} - 2 q^{5} - 16 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 - 4 * q^4 - 2 * q^5 - 16 * q^9	\( 2 q + 2 q^{3} - 4 q^{4} - 2 q^{5} - 16 q^{9} + 14 q^{11} - 4 q^{12} + 24 q^{14} - 2 q^{15} + 8 q^{16} + 4 q^{20} - 24 q^{22} + 34 q^{23} - 48 q^{25} - 24 q^{26} - 34 q^{27} + 34 q^{31} + 14 q^{33} - 72 q^{34} + 32 q^{36} + 94 q^{37} + 72 q^{38} + 24 q^{42} - 28 q^{44} + 16 q^{45} - 116 q^{47} + 8 q^{48} - 46 q^{49} + 4 q^{53} - 14 q^{55} - 48 q^{56} + 96 q^{58} - 110 q^{59} + 4 q^{60} - 16 q^{64} - 24 q^{66} + 178 q^{67} + 34 q^{69} - 24 q^{70} - 14 q^{71} - 48 q^{75} + 144 q^{77} - 24 q^{78} - 8 q^{80} + 110 q^{81} - 24 q^{82} - 48 q^{86} + 48 q^{88} - 194 q^{89} + 144 q^{91} - 68 q^{92} + 34 q^{93} - 242 q^{97} - 112 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 4 * q^4 - 2 * q^5 - 16 * q^9 + 14 * q^11 - 4 * q^12 + 24 * q^14 - 2 * q^15 + 8 * q^16 + 4 * q^20 - 24 * q^22 + 34 * q^23 - 48 * q^25 - 24 * q^26 - 34 * q^27 + 34 * q^31 + 14 * q^33 - 72 * q^34 + 32 * q^36 + 94 * q^37 + 72 * q^38 + 24 * q^42 - 28 * q^44 + 16 * q^45 - 116 * q^47 + 8 * q^48 - 46 * q^49 + 4 * q^53 - 14 * q^55 - 48 * q^56 + 96 * q^58 - 110 * q^59 + 4 * q^60 - 16 * q^64 - 24 * q^66 + 178 * q^67 + 34 * q^69 - 24 * q^70 - 14 * q^71 - 48 * q^75 + 144 * q^77 - 24 * q^78 - 8 * q^80 + 110 * q^81 - 24 * q^82 - 48 * q^86 + 48 * q^88 - 194 * q^89 + 144 * q^91 - 68 * q^92 + 34 * q^93 - 242 * q^97 - 112 * q^99

Introduction

L-functions

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