LMFDB - Embedded newform 324.3.f.i.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.i.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +4.00000 q^{4} +(-3.50000 - 6.06218i) q^{5} +(-7.50000 - 4.33013i) q^{7} +8.00000 q^{8} +O(q^{10})$	\(q+2.00000 q^{2} +4.00000 q^{4} +(-3.50000 - 6.06218i) q^{5} +(-7.50000 - 4.33013i) q^{7} +8.00000 q^{8} +(-7.00000 - 12.1244i) q^{10} +(7.50000 + 4.33013i) q^{11} +(-10.0000 - 17.3205i) q^{13} +(-15.0000 - 8.66025i) q^{14} +16.0000 q^{16} -8.00000 q^{17} -10.3923i q^{19} +(-14.0000 - 24.2487i) q^{20} +(15.0000 + 8.66025i) q^{22} +(3.00000 - 1.73205i) q^{23} +(-12.0000 + 20.7846i) q^{25} +(-20.0000 - 34.6410i) q^{26} +(-30.0000 - 17.3205i) q^{28} +(-5.00000 + 8.66025i) q^{29} +(46.5000 - 26.8468i) q^{31} +32.0000 q^{32} -16.0000 q^{34} +60.6218i q^{35} -10.0000 q^{37} -20.7846i q^{38} +(-28.0000 - 48.4974i) q^{40} +(25.0000 + 43.3013i) q^{41} +(15.0000 + 8.66025i) q^{43} +(30.0000 + 17.3205i) q^{44} +(6.00000 - 3.46410i) q^{46} +(75.0000 + 43.3013i) q^{47} +(13.0000 + 22.5167i) q^{49} +(-24.0000 + 41.5692i) q^{50} +(-40.0000 - 69.2820i) q^{52} -47.0000 q^{53} -60.6218i q^{55} +(-60.0000 - 34.6410i) q^{56} +(-10.0000 + 17.3205i) q^{58} +(30.0000 - 17.3205i) q^{59} +(32.0000 - 55.4256i) q^{61} +(93.0000 - 53.6936i) q^{62} +64.0000 q^{64} +(-70.0000 + 121.244i) q^{65} +(-75.0000 + 43.3013i) q^{67} -32.0000 q^{68} +121.244i q^{70} -55.0000 q^{73} -20.0000 q^{74} -41.5692i q^{76} +(-37.5000 - 64.9519i) q^{77} +(6.00000 + 3.46410i) q^{79} +(-56.0000 - 96.9948i) q^{80} +(50.0000 + 86.6025i) q^{82} +(25.5000 + 14.7224i) q^{83} +(28.0000 + 48.4974i) q^{85} +(30.0000 + 17.3205i) q^{86} +(60.0000 + 34.6410i) q^{88} +10.0000 q^{89} +173.205i q^{91} +(12.0000 - 6.92820i) q^{92} +(150.000 + 86.6025i) q^{94} +(-63.0000 + 36.3731i) q^{95} +(12.5000 - 21.6506i) q^{97} +(26.0000 + 45.0333i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 8 q^{4} - 7 q^{5} - 15 q^{7} + 16 q^{8}+O(q^{10}) $ 2 * q + 4 * q^2 + 8 * q^4 - 7 * q^5 - 15 * q^7 + 16 * q^8	$ 2 q + 4 q^{2} + 8 q^{4} - 7 q^{5} - 15 q^{7} + 16 q^{8} - 14 q^{10} + 15 q^{11} - 20 q^{13} - 30 q^{14} + 32 q^{16} - 16 q^{17} - 28 q^{20} + 30 q^{22} + 6 q^{23} - 24 q^{25} - 40 q^{26} - 60 q^{28} - 10 q^{29} + 93 q^{31} + 64 q^{32} - 32 q^{34} - 20 q^{37} - 56 q^{40} + 50 q^{41} + 30 q^{43} + 60 q^{44} + 12 q^{46} + 150 q^{47} + 26 q^{49} - 48 q^{50} - 80 q^{52} - 94 q^{53} - 120 q^{56} - 20 q^{58} + 60 q^{59} + 64 q^{61} + 186 q^{62} + 128 q^{64} - 140 q^{65} - 150 q^{67} - 64 q^{68} - 110 q^{73} - 40 q^{74} - 75 q^{77} + 12 q^{79} - 112 q^{80} + 100 q^{82} + 51 q^{83} + 56 q^{85} + 60 q^{86} + 120 q^{88} + 20 q^{89} + 24 q^{92} + 300 q^{94} - 126 q^{95} + 25 q^{97} + 52 q^{98}+O(q^{100}) $ 2 * q + 4 * q^2 + 8 * q^4 - 7 * q^5 - 15 * q^7 + 16 * q^8 - 14 * q^10 + 15 * q^11 - 20 * q^13 - 30 * q^14 + 32 * q^16 - 16 * q^17 - 28 * q^20 + 30 * q^22 + 6 * q^23 - 24 * q^25 - 40 * q^26 - 60 * q^28 - 10 * q^29 + 93 * q^31 + 64 * q^32 - 32 * q^34 - 20 * q^37 - 56 * q^40 + 50 * q^41 + 30 * q^43 + 60 * q^44 + 12 * q^46 + 150 * q^47 + 26 * q^49 - 48 * q^50 - 80 * q^52 - 94 * q^53 - 120 * q^56 - 20 * q^58 + 60 * q^59 + 64 * q^61 + 186 * q^62 + 128 * q^64 - 140 * q^65 - 150 * q^67 - 64 * q^68 - 110 * q^73 - 40 * q^74 - 75 * q^77 + 12 * q^79 - 112 * q^80 + 100 * q^82 + 51 * q^83 + 56 * q^85 + 60 * q^86 + 120 * q^88 + 20 * q^89 + 24 * q^92 + 300 * q^94 - 126 * q^95 + 25 * q^97 + 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.00000			1.00000
$2$	2.00000			1.00000
$3$		0			0
$3$		0			0
$4$	4.00000			1.00000
$5$	−3.50000	−	6.06218i	−0.700000	−	1.21244i	−0.968466	−	0.249146i	$-0.919850\pi$
$5$	−3.50000	−	6.06218i	−0.700000	−	1.21244i	0.268466	−	0.963289i	$-0.413483\pi$
$6$		0			0
$7$	−7.50000	−	4.33013i	−1.07143	−	0.618590i	−0.142857	−	0.989743i	$-0.545629\pi$
$7$	−7.50000	−	4.33013i	−1.07143	−	0.618590i	−0.928571	+	0.371154i	$0.878962\pi$
$8$	8.00000			1.00000
$9$		0			0
$10$	−7.00000	−	12.1244i	−0.700000	−	1.21244i
$11$	7.50000	+	4.33013i	0.681818	+	0.393648i	0.800540	−	0.599280i	$-0.204546\pi$
$11$	7.50000	+	4.33013i	0.681818	+	0.393648i	−0.118722	+	0.992928i	$0.537880\pi$
$12$		0			0
$13$	−10.0000	−	17.3205i	−0.769231	−	1.33235i	−0.937981	−	0.346688i	$-0.887306\pi$
$13$	−10.0000	−	17.3205i	−0.769231	−	1.33235i	0.168750	−	0.985659i	$-0.446027\pi$
$14$	−15.0000	−	8.66025i	−1.07143	−	0.618590i
$15$		0			0
$16$	16.0000			1.00000
$17$	−8.00000			−0.470588			−0.235294	−	0.971924i	$-0.575605\pi$
$17$	−8.00000			−0.470588			−0.235294	+	0.971924i	$0.575605\pi$
$18$		0			0
$19$		−	10.3923i		−	0.546963i	−0.961877	−	0.273482i	$-0.911825\pi$
$19$		−	10.3923i		−	0.546963i	0.961877	−	0.273482i	$-0.0881753\pi$
$20$	−14.0000	−	24.2487i	−0.700000	−	1.21244i
$21$		0			0
$22$	15.0000	+	8.66025i	0.681818	+	0.393648i
$23$	3.00000	−	1.73205i	0.130435	−	0.0753066i	−0.433363	−	0.901220i	$-0.642673\pi$
$23$	3.00000	−	1.73205i	0.130435	−	0.0753066i	0.563798	+	0.825913i	$0.309340\pi$
$24$		0			0
$25$	−12.0000	+	20.7846i	−0.480000	+	0.831384i
$26$	−20.0000	−	34.6410i	−0.769231	−	1.33235i
$27$		0			0
$28$	−30.0000	−	17.3205i	−1.07143	−	0.618590i
$29$	−5.00000	+	8.66025i	−0.172414	+	0.298629i	−0.939263	−	0.343198i	$-0.888490\pi$
$29$	−5.00000	+	8.66025i	−0.172414	+	0.298629i	0.766849	+	0.641827i	$0.221823\pi$
$30$		0			0
$31$	46.5000	−	26.8468i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$31$	46.5000	−	26.8468i	1.50000	−	0.866025i	1.00000			$0$
$32$	32.0000			1.00000
$33$		0			0
$34$	−16.0000			−0.470588
$35$			60.6218i			1.73205i
$36$		0			0
$37$	−10.0000			−0.270270			−0.135135	−	0.990827i	$-0.543147\pi$
$37$	−10.0000			−0.270270			−0.135135	+	0.990827i	$0.543147\pi$
$38$		−	20.7846i		−	0.546963i
$39$		0			0
$40$	−28.0000	−	48.4974i	−0.700000	−	1.21244i
$41$	25.0000	+	43.3013i	0.609756	+	1.05613i	0.991280	+	0.131770i	$0.0420659\pi$
$41$	25.0000	+	43.3013i	0.609756	+	1.05613i	−0.381524	+	0.924359i	$0.624601\pi$
$42$		0			0
$43$	15.0000	+	8.66025i	0.348837	+	0.201401i	0.664173	−	0.747579i	$-0.268784\pi$
$43$	15.0000	+	8.66025i	0.348837	+	0.201401i	−0.315336	+	0.948980i	$0.602117\pi$
$44$	30.0000	+	17.3205i	0.681818	+	0.393648i
$45$		0			0
$46$	6.00000	−	3.46410i	0.130435	−	0.0753066i
$47$	75.0000	+	43.3013i	1.59574	+	0.921304i	0.992294	+	0.123903i	$0.0395412\pi$
$47$	75.0000	+	43.3013i	1.59574	+	0.921304i	0.603450	+	0.797401i	$0.293792\pi$
$48$		0			0
$49$	13.0000	+	22.5167i	0.265306	+	0.459524i
$50$	−24.0000	+	41.5692i	−0.480000	+	0.831384i
$51$		0			0
$52$	−40.0000	−	69.2820i	−0.769231	−	1.33235i
$53$	−47.0000			−0.886792			−0.443396	−	0.896326i	$-0.646227\pi$
$53$	−47.0000			−0.886792			−0.443396	+	0.896326i	$0.646227\pi$
$54$		0			0
$55$		−	60.6218i		−	1.10221i
$56$	−60.0000	−	34.6410i	−1.07143	−	0.618590i
$57$		0			0
$58$	−10.0000	+	17.3205i	−0.172414	+	0.298629i
$59$	30.0000	−	17.3205i	0.508475	−	0.293568i	−0.223732	−	0.974651i	$-0.571824\pi$
$59$	30.0000	−	17.3205i	0.508475	−	0.293568i	0.732206	+	0.681083i	$0.238491\pi$
$60$		0			0
$61$	32.0000	−	55.4256i	0.524590	−	0.908617i	−0.475000	−	0.879986i	$-0.657552\pi$
$61$	32.0000	−	55.4256i	0.524590	−	0.908617i	0.999590	−	0.0286310i	$-0.00911476\pi$
$62$	93.0000	−	53.6936i	1.50000	−	0.866025i
$63$		0			0
$64$	64.0000			1.00000
$65$	−70.0000	+	121.244i	−1.07692	+	1.86529i
$66$		0			0
$67$	−75.0000	+	43.3013i	−1.11940	+	0.646288i	−0.941248	−	0.337715i	$-0.890346\pi$
$67$	−75.0000	+	43.3013i	−1.11940	+	0.646288i	−0.178155	+	0.984003i	$0.557013\pi$
$68$	−32.0000			−0.470588
$69$		0			0
$70$			121.244i			1.73205i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−55.0000			−0.753425			−0.376712	−	0.926330i	$-0.622945\pi$
$73$	−55.0000			−0.753425			−0.376712	+	0.926330i	$0.622945\pi$
$74$	−20.0000			−0.270270
$75$		0			0
$76$		−	41.5692i		−	0.546963i
$77$	−37.5000	−	64.9519i	−0.487013	−	0.843531i
$78$		0			0
$79$	6.00000	+	3.46410i	0.0759494	+	0.0438494i	0.537494	−	0.843268i	$-0.319371\pi$
$79$	6.00000	+	3.46410i	0.0759494	+	0.0438494i	−0.461544	+	0.887117i	$0.652704\pi$
$80$	−56.0000	−	96.9948i	−0.700000	−	1.21244i
$81$		0			0
$82$	50.0000	+	86.6025i	0.609756	+	1.05613i
$83$	25.5000	+	14.7224i	0.307229	+	0.177379i	0.645686	−	0.763603i	$-0.276572\pi$
$83$	25.5000	+	14.7224i	0.307229	+	0.177379i	−0.338457	+	0.940982i	$0.609905\pi$
$84$		0			0
$85$	28.0000	+	48.4974i	0.329412	+	0.570558i
$86$	30.0000	+	17.3205i	0.348837	+	0.201401i
$87$		0			0
$88$	60.0000	+	34.6410i	0.681818	+	0.393648i
$89$	10.0000			0.112360			0.0561798	−	0.998421i	$-0.482108\pi$
$89$	10.0000			0.112360			0.0561798	+	0.998421i	$0.482108\pi$
$90$		0			0
$91$			173.205i			1.90335i
$92$	12.0000	−	6.92820i	0.130435	−	0.0753066i
$93$		0			0
$94$	150.000	+	86.6025i	1.59574	+	0.921304i
$95$	−63.0000	+	36.3731i	−0.663158	+	0.382874i
$96$		0			0
$97$	12.5000	−	21.6506i	0.128866	−	0.223202i	−0.794372	−	0.607432i	$-0.792200\pi$
$97$	12.5000	−	21.6506i	0.128866	−	0.223202i	0.923237	+	0.384230i	$0.125533\pi$
$98$	26.0000	+	45.0333i	0.265306	+	0.459524i
$99$		0			0
$100$	−48.0000	+	83.1384i	−0.480000	+	0.831384i
$101$	77.5000	−	134.234i	0.767327	−	1.32905i	−0.171681	−	0.985153i	$-0.554920\pi$
$101$	77.5000	−	134.234i	0.767327	−	1.32905i	0.939008	−	0.343896i	$-0.111747\pi$
$102$		0			0
$103$	−120.000	+	69.2820i	−1.16505	+	0.672641i	−0.952509	−	0.304511i	$-0.901507\pi$
$103$	−120.000	+	69.2820i	−1.16505	+	0.672641i	−0.212540	+	0.977152i	$0.568174\pi$
$104$	−80.0000	−	138.564i	−0.769231	−	1.33235i
$105$		0			0
$106$	−94.0000			−0.886792
$107$			129.904i			1.21405i	0.794681	+	0.607027i	$0.207638\pi$
$107$			129.904i			1.21405i	−0.794681	+	0.607027i	$0.792362\pi$
$108$		0			0
$109$	134.000			1.22936			0.614679	−	0.788777i	$-0.289286\pi$
$109$	134.000			1.22936			0.614679	+	0.788777i	$0.289286\pi$
$110$		−	121.244i		−	1.10221i
$111$		0			0
$112$	−120.000	−	69.2820i	−1.07143	−	0.618590i
$113$	37.0000	+	64.0859i	0.327434	+	0.567132i	0.982002	−	0.188871i	$-0.0604829\pi$
$113$	37.0000	+	64.0859i	0.327434	+	0.567132i	−0.654568	+	0.756003i	$0.727150\pi$
$114$		0			0
$115$	−21.0000	−	12.1244i	−0.182609	−	0.105429i
$116$	−20.0000	+	34.6410i	−0.172414	+	0.298629i
$117$		0			0
$118$	60.0000	−	34.6410i	0.508475	−	0.293568i
$119$	60.0000	+	34.6410i	0.504202	+	0.291101i
$120$		0			0
$121$	−23.0000	−	39.8372i	−0.190083	−	0.329233i
$122$	64.0000	−	110.851i	0.524590	−	0.908617i
$123$		0			0
$124$	186.000	−	107.387i	1.50000	−	0.866025i
$125$	−7.00000			−0.0560000
$126$		0			0
$127$			25.9808i			0.204573i	0.994755	+	0.102286i	$0.0326158\pi$
$127$			25.9808i			0.204573i	−0.994755	+	0.102286i	$0.967384\pi$
$128$	128.000			1.00000
$129$		0			0
$130$	−140.000	+	242.487i	−1.07692	+	1.86529i
$131$	142.500	−	82.2724i	1.08779	−	0.628034i	0.154800	−	0.987946i	$-0.450527\pi$
$131$	142.500	−	82.2724i	1.08779	−	0.628034i	0.932986	+	0.359912i	$0.117193\pi$
$132$		0			0
$133$	−45.0000	+	77.9423i	−0.338346	+	0.586032i
$134$	−150.000	+	86.6025i	−1.11940	+	0.646288i
$135$		0			0
$136$	−64.0000			−0.470588
$137$	31.0000	−	53.6936i	0.226277	−	0.391924i	−0.730425	−	0.682993i	$-0.760678\pi$
$137$	31.0000	−	53.6936i	0.226277	−	0.391924i	0.956702	+	0.291070i	$0.0940111\pi$
$138$		0			0
$139$	150.000	−	86.6025i	1.07914	−	0.623040i	0.148473	−	0.988916i	$-0.452564\pi$
$139$	150.000	−	86.6025i	1.07914	−	0.623040i	0.930663	+	0.365877i	$0.119231\pi$
$140$			242.487i			1.73205i
$141$		0			0
$142$		0			0
$143$		−	173.205i		−	1.21122i
$144$		0			0
$145$	70.0000			0.482759
$146$	−110.000			−0.753425
$147$		0			0
$148$	−40.0000			−0.270270
$149$	−57.5000	−	99.5929i	−0.385906	−	0.668409i	0.605988	−	0.795473i	$-0.292778\pi$
$149$	−57.5000	−	99.5929i	−0.385906	−	0.668409i	−0.991894	+	0.127065i	$0.959444\pi$
$150$		0			0
$151$	37.5000	+	21.6506i	0.248344	+	0.143382i	0.619006	−	0.785386i	$-0.287536\pi$
$151$	37.5000	+	21.6506i	0.248344	+	0.143382i	−0.370662	+	0.928768i	$0.620869\pi$
$152$		−	83.1384i		−	0.546963i
$153$		0			0
$154$	−75.0000	−	129.904i	−0.487013	−	0.843531i
$155$	−325.500	−	187.928i	−2.10000	−	1.21244i
$156$		0			0
$157$	−10.0000	−	17.3205i	−0.0636943	−	0.110322i	0.832420	−	0.554146i	$-0.186955\pi$
$157$	−10.0000	−	17.3205i	−0.0636943	−	0.110322i	−0.896114	+	0.443824i	$0.853622\pi$
$158$	12.0000	+	6.92820i	0.0759494	+	0.0438494i
$159$		0			0
$160$	−112.000	−	193.990i	−0.700000	−	1.21244i
$161$	−30.0000			−0.186335
$162$		0			0
$163$		−	103.923i		−	0.637565i	−0.947828	−	0.318782i	$-0.896726\pi$
$163$		−	103.923i		−	0.637565i	0.947828	−	0.318782i	$-0.103274\pi$
$164$	100.000	+	173.205i	0.609756	+	1.05613i
$165$		0			0
$166$	51.0000	+	29.4449i	0.307229	+	0.177379i
$167$	−213.000	+	122.976i	−1.27545	+	0.736381i	−0.976008	−	0.217734i	$-0.930133\pi$
$167$	−213.000	+	122.976i	−1.27545	+	0.736381i	−0.299441	+	0.954115i	$0.596800\pi$
$168$		0			0
$169$	−115.500	+	200.052i	−0.683432	+	1.18374i
$170$	56.0000	+	96.9948i	0.329412	+	0.570558i
$171$		0			0
$172$	60.0000	+	34.6410i	0.348837	+	0.201401i
$173$	−63.5000	+	109.985i	−0.367052	+	0.635753i	−0.989103	−	0.147224i	$-0.952966\pi$
$173$	−63.5000	+	109.985i	−0.367052	+	0.635753i	0.622051	+	0.782977i	$0.286300\pi$
$174$		0			0
$175$	180.000	−	103.923i	1.02857	−	0.593846i
$176$	120.000	+	69.2820i	0.681818	+	0.393648i
$177$		0			0
$178$	20.0000			0.112360
$179$		−	233.827i		−	1.30630i	−0.757231	−	0.653148i	$-0.773448\pi$
$179$		−	233.827i		−	1.30630i	0.757231	−	0.653148i	$-0.226552\pi$
$180$		0			0
$181$	56.0000			0.309392			0.154696	−	0.987962i	$-0.450560\pi$
$181$	56.0000			0.309392			0.154696	+	0.987962i	$0.450560\pi$
$182$			346.410i			1.90335i
$183$		0			0
$184$	24.0000	−	13.8564i	0.130435	−	0.0753066i
$185$	35.0000	+	60.6218i	0.189189	+	0.327685i
$186$		0			0
$187$	−60.0000	−	34.6410i	−0.320856	−	0.185246i
$188$	300.000	+	173.205i	1.59574	+	0.921304i
$189$		0			0
$190$	−126.000	+	72.7461i	−0.663158	+	0.382874i
$191$	30.0000	+	17.3205i	0.157068	+	0.0906833i	0.576474	−	0.817116i	$-0.304428\pi$
$191$	30.0000	+	17.3205i	0.157068	+	0.0906833i	−0.419406	+	0.907799i	$0.637762\pi$
$192$		0			0
$193$	−32.5000	−	56.2917i	−0.168394	−	0.291667i	0.769462	−	0.638693i	$-0.220525\pi$
$193$	−32.5000	−	56.2917i	−0.168394	−	0.291667i	−0.937855	+	0.347027i	$0.887191\pi$
$194$	25.0000	−	43.3013i	0.128866	−	0.223202i
$195$		0			0
$196$	52.0000	+	90.0666i	0.265306	+	0.459524i
$197$	253.000			1.28426			0.642132	−	0.766594i	$-0.278050\pi$
$197$	253.000			1.28426			0.642132	+	0.766594i	$0.278050\pi$
$198$		0			0
$199$			129.904i			0.652783i	0.945235	+	0.326391i	$0.105833\pi$
$199$			129.904i			0.652783i	−0.945235	+	0.326391i	$0.894167\pi$
$200$	−96.0000	+	166.277i	−0.480000	+	0.831384i
$201$		0			0
$202$	155.000	−	268.468i	0.767327	−	1.32905i
$203$	75.0000	−	43.3013i	0.369458	−	0.213307i
$204$		0			0
$205$	175.000	−	303.109i	0.853659	−	1.47858i
$206$	−240.000	+	138.564i	−1.16505	+	0.672641i
$207$		0			0
$208$	−160.000	−	277.128i	−0.769231	−	1.33235i
$209$	45.0000	−	77.9423i	0.215311	−	0.372930i
$210$		0			0
$211$	−129.000	+	74.4782i	−0.611374	+	0.352977i	−0.773503	−	0.633792i	$-0.781497\pi$
$211$	−129.000	+	74.4782i	−0.611374	+	0.352977i	0.162129	+	0.986770i	$0.448164\pi$
$212$	−188.000			−0.886792
$213$		0			0
$214$			259.808i			1.21405i
$215$		−	121.244i		−	0.563924i
$216$		0			0
$217$	−465.000			−2.14286
$218$	268.000			1.22936
$219$		0			0
$220$		−	242.487i		−	1.10221i
$221$	80.0000	+	138.564i	0.361991	+	0.626987i
$222$		0			0
$223$	−30.0000	−	17.3205i	−0.134529	−	0.0776704i	0.431225	−	0.902244i	$-0.358082\pi$
$223$	−30.0000	−	17.3205i	−0.134529	−	0.0776704i	−0.565754	+	0.824574i	$0.691415\pi$
$224$	−240.000	−	138.564i	−1.07143	−	0.618590i
$225$		0			0
$226$	74.0000	+	128.172i	0.327434	+	0.567132i
$227$	−78.0000	−	45.0333i	−0.343612	−	0.198385i	0.318256	−	0.948005i	$-0.396903\pi$
$227$	−78.0000	−	45.0333i	−0.343612	−	0.198385i	−0.661868	+	0.749620i	$0.730236\pi$
$228$		0			0
$229$	−73.0000	−	126.440i	−0.318777	−	0.552138i	0.661456	−	0.749984i	$-0.269939\pi$
$229$	−73.0000	−	126.440i	−0.318777	−	0.552138i	−0.980233	+	0.197846i	$0.936606\pi$
$230$	−42.0000	−	24.2487i	−0.182609	−	0.105429i
$231$		0			0
$232$	−40.0000	+	69.2820i	−0.172414	+	0.298629i
$233$	334.000			1.43348			0.716738	−	0.697342i	$-0.245634\pi$
$233$	334.000			1.43348			0.716738	+	0.697342i	$0.245634\pi$
$234$		0			0
$235$		−	606.218i		−	2.57965i
$236$	120.000	−	69.2820i	0.508475	−	0.293568i
$237$		0			0
$238$	120.000	+	69.2820i	0.504202	+	0.291101i
$239$	−15.0000	+	8.66025i	−0.0627615	+	0.0362354i	−0.531052	−	0.847339i	$-0.678203\pi$
$239$	−15.0000	+	8.66025i	−0.0627615	+	0.0362354i	0.468291	+	0.883574i	$0.344870\pi$
$240$		0			0
$241$	−67.0000	+	116.047i	−0.278008	+	0.481524i	−0.970890	−	0.239527i	$-0.923008\pi$
$241$	−67.0000	+	116.047i	−0.278008	+	0.481524i	0.692881	+	0.721052i	$0.256341\pi$
$242$	−46.0000	−	79.6743i	−0.190083	−	0.329233i
$243$		0			0
$244$	128.000	−	221.703i	0.524590	−	0.908617i
$245$	91.0000	−	157.617i	0.371429	−	0.643333i
$246$		0			0
$247$	−180.000	+	103.923i	−0.728745	+	0.420741i
$248$	372.000	−	214.774i	1.50000	−	0.866025i
$249$		0			0
$250$	−14.0000			−0.0560000
$251$			207.846i			0.828072i	0.910260	+	0.414036i	$0.135881\pi$
$251$			207.846i			0.828072i	−0.910260	+	0.414036i	$0.864119\pi$
$252$		0			0
$253$	30.0000			0.118577
$254$			51.9615i			0.204573i
$255$		0			0
$256$	256.000			1.00000
$257$	−134.000	−	232.095i	−0.521401	−	0.903093i	−0.999690	−	0.0248904i	$-0.992076\pi$
$257$	−134.000	−	232.095i	−0.521401	−	0.903093i	0.478289	−	0.878202i	$-0.341257\pi$
$258$		0			0
$259$	75.0000	+	43.3013i	0.289575	+	0.167186i
$260$	−280.000	+	484.974i	−1.07692	+	1.86529i
$261$		0			0
$262$	285.000	−	164.545i	1.08779	−	0.628034i
$263$	−375.000	−	216.506i	−1.42586	−	0.823218i	−0.429065	−	0.903274i	$-0.641157\pi$
$263$	−375.000	−	216.506i	−1.42586	−	0.823218i	−0.996790	+	0.0800555i	$0.974490\pi$
$264$		0			0
$265$	164.500	+	284.922i	0.620755	+	1.07518i
$266$	−90.0000	+	155.885i	−0.338346	+	0.586032i
$267$		0			0
$268$	−300.000	+	173.205i	−1.11940	+	0.646288i
$269$	−350.000			−1.30112			−0.650558	−	0.759457i	$-0.725465\pi$
$269$	−350.000			−1.30112			−0.650558	+	0.759457i	$0.725465\pi$
$270$		0			0
$271$			36.3731i			0.134218i	0.997746	+	0.0671090i	$0.0213775\pi$
$271$			36.3731i			0.134218i	−0.997746	+	0.0671090i	$0.978622\pi$
$272$	−128.000			−0.470588
$273$		0			0
$274$	62.0000	−	107.387i	0.226277	−	0.391924i
$275$	−180.000	+	103.923i	−0.654545	+	0.377902i
$276$		0			0
$277$	260.000	−	450.333i	0.938628	−	1.62575i	0.170595	−	0.985341i	$-0.445431\pi$
$277$	260.000	−	450.333i	0.938628	−	1.62575i	0.768033	−	0.640410i	$-0.221236\pi$
$278$	300.000	−	173.205i	1.07914	−	0.623040i
$279$		0			0
$280$			484.974i			1.73205i
$281$	220.000	−	381.051i	0.782918	−	1.35605i	−0.147317	−	0.989089i	$-0.547064\pi$
$281$	220.000	−	381.051i	0.782918	−	1.35605i	0.930235	−	0.366965i	$-0.119603\pi$
$282$		0			0
$283$	285.000	−	164.545i	1.00707	−	0.581430i	0.0967355	−	0.995310i	$-0.469160\pi$
$283$	285.000	−	164.545i	1.00707	−	0.581430i	0.910332	+	0.413880i	$0.135827\pi$
$284$		0			0
$285$		0			0
$286$		−	346.410i		−	1.21122i
$287$		−	433.013i		−	1.50876i
$288$		0			0
$289$	−225.000			−0.778547
$290$	140.000			0.482759
$291$		0			0
$292$	−220.000			−0.753425
$293$	109.000	+	188.794i	0.372014	+	0.644347i	0.989875	−	0.141940i	$-0.0453341\pi$
$293$	109.000	+	188.794i	0.372014	+	0.644347i	−0.617862	+	0.786287i	$0.712001\pi$
$294$		0			0
$295$	−210.000	−	121.244i	−0.711864	−	0.410995i
$296$	−80.0000			−0.270270
$297$		0			0
$298$	−115.000	−	199.186i	−0.385906	−	0.668409i
$299$	−60.0000	−	34.6410i	−0.200669	−	0.115856i
$300$		0			0
$301$	−75.0000	−	129.904i	−0.249169	−	0.431574i
$302$	75.0000	+	43.3013i	0.248344	+	0.143382i
$303$		0			0
$304$		−	166.277i		−	0.546963i
$305$	−448.000			−1.46885
$306$		0			0
$307$			207.846i			0.677023i	0.940962	+	0.338512i	$0.109923\pi$
$307$			207.846i			0.677023i	−0.940962	+	0.338512i	$0.890077\pi$
$308$	−150.000	−	259.808i	−0.487013	−	0.843531i
$309$		0			0
$310$	−651.000	−	375.855i	−2.10000	−	1.21244i
$311$	255.000	−	147.224i	0.819936	−	0.473390i	−0.0304586	−	0.999536i	$-0.509697\pi$
$311$	255.000	−	147.224i	0.819936	−	0.473390i	0.850394	+	0.526146i	$0.176363\pi$
$312$		0			0
$313$	−242.500	+	420.022i	−0.774760	+	1.34192i	0.160169	+	0.987090i	$0.448796\pi$
$313$	−242.500	+	420.022i	−0.774760	+	1.34192i	−0.934929	+	0.354835i	$0.884537\pi$
$314$	−20.0000	−	34.6410i	−0.0636943	−	0.110322i
$315$		0			0
$316$	24.0000	+	13.8564i	0.0759494	+	0.0438494i
$317$	−108.500	+	187.928i	−0.342271	+	0.592831i	−0.984854	−	0.173385i	$-0.944530\pi$
$317$	−108.500	+	187.928i	−0.342271	+	0.592831i	0.642583	+	0.766216i	$0.277863\pi$
$318$		0			0
$319$	−75.0000	+	43.3013i	−0.235110	+	0.135741i
$320$	−224.000	−	387.979i	−0.700000	−	1.21244i
$321$		0			0
$322$	−60.0000			−0.186335
$323$			83.1384i			0.257395i
$324$		0			0
$325$	480.000			1.47692
$326$		−	207.846i		−	0.637565i
$327$		0			0
$328$	200.000	+	346.410i	0.609756	+	1.05613i
$329$	−375.000	−	649.519i	−1.13982	−	1.97422i
$330$		0			0
$331$	375.000	+	216.506i	1.13293	+	0.654098i	0.944670	−	0.328021i	$-0.106382\pi$
$331$	375.000	+	216.506i	1.13293	+	0.654098i	0.188260	+	0.982119i	$0.439715\pi$
$332$	102.000	+	58.8897i	0.307229	+	0.177379i
$333$		0			0
$334$	−426.000	+	245.951i	−1.27545	+	0.736381i
$335$	525.000	+	303.109i	1.56716	+	0.904803i
$336$		0			0
$337$	155.000	+	268.468i	0.459941	+	0.796641i	0.998957	−	0.0456545i	$-0.0145373\pi$
$337$	155.000	+	268.468i	0.459941	+	0.796641i	−0.539017	+	0.842295i	$0.681204\pi$
$338$	−231.000	+	400.104i	−0.683432	+	1.18374i
$339$		0			0
$340$	112.000	+	193.990i	0.329412	+	0.570558i
$341$	465.000			1.36364
$342$		0			0
$343$			199.186i			0.580717i
$344$	120.000	+	69.2820i	0.348837	+	0.201401i
$345$		0			0
$346$	−127.000	+	219.970i	−0.367052	+	0.635753i
$347$	187.500	−	108.253i	0.540346	−	0.311969i	−0.204873	−	0.978789i	$-0.565678\pi$
$347$	187.500	−	108.253i	0.540346	−	0.311969i	0.745219	+	0.666820i	$0.232345\pi$
$348$		0			0
$349$	−37.0000	+	64.0859i	−0.106017	+	0.183627i	−0.914153	−	0.405369i	$-0.867143\pi$
$349$	−37.0000	+	64.0859i	−0.106017	+	0.183627i	0.808136	+	0.588996i	$0.200477\pi$
$350$	360.000	−	207.846i	1.02857	−	0.593846i
$351$		0			0
$352$	240.000	+	138.564i	0.681818	+	0.393648i
$353$	−197.000	+	341.214i	−0.558074	+	0.966612i	0.439584	+	0.898202i	$0.355126\pi$
$353$	−197.000	+	341.214i	−0.558074	+	0.966612i	−0.997657	+	0.0684103i	$0.978207\pi$
$354$		0			0
$355$		0			0
$356$	40.0000			0.112360
$357$		0			0
$358$		−	467.654i		−	1.30630i
$359$			571.577i			1.59214i	0.605207	+	0.796068i	$0.293090\pi$
$359$			571.577i			1.59214i	−0.605207	+	0.796068i	$0.706910\pi$
$360$		0			0
$361$	253.000			0.700831
$362$	112.000			0.309392
$363$		0			0
$364$			692.820i			1.90335i
$365$	192.500	+	333.420i	0.527397	+	0.913479i
$366$		0			0
$367$	487.500	+	281.458i	1.32834	+	0.766916i	0.985043	−	0.172311i	$-0.0551235\pi$
$367$	487.500	+	281.458i	1.32834	+	0.766916i	0.343295	+	0.939228i	$0.388457\pi$
$368$	48.0000	−	27.7128i	0.130435	−	0.0753066i
$369$		0			0
$370$	70.0000	+	121.244i	0.189189	+	0.327685i
$371$	352.500	+	203.516i	0.950135	+	0.548561i
$372$		0			0
$373$	20.0000	+	34.6410i	0.0536193	+	0.0928714i	0.891589	−	0.452845i	$-0.149591\pi$
$373$	20.0000	+	34.6410i	0.0536193	+	0.0928714i	−0.837970	+	0.545716i	$0.816258\pi$
$374$	−120.000	−	69.2820i	−0.320856	−	0.185246i
$375$		0			0
$376$	600.000	+	346.410i	1.59574	+	0.921304i
$377$	200.000			0.530504
$378$		0			0
$379$			685.892i			1.80974i	0.425686	+	0.904871i	$0.360033\pi$
$379$			685.892i			1.80974i	−0.425686	+	0.904871i	$0.639967\pi$
$380$	−252.000	+	145.492i	−0.663158	+	0.382874i
$381$		0			0
$382$	60.0000	+	34.6410i	0.157068	+	0.0906833i
$383$	−312.000	+	180.133i	−0.814621	+	0.470322i	−0.848558	−	0.529102i	$-0.822529\pi$
$383$	−312.000	+	180.133i	−0.814621	+	0.470322i	0.0339368	+	0.999424i	$0.489196\pi$
$384$		0			0
$385$	−262.500	+	454.663i	−0.681818	+	1.18094i
$386$	−65.0000	−	112.583i	−0.168394	−	0.291667i
$387$		0			0
$388$	50.0000	−	86.6025i	0.128866	−	0.223202i
$389$	−237.500	+	411.362i	−0.610540	+	1.05749i	0.380610	+	0.924736i	$0.375714\pi$
$389$	−237.500	+	411.362i	−0.610540	+	1.05749i	−0.991150	+	0.132750i	$0.957619\pi$
$390$		0			0
$391$	−24.0000	+	13.8564i	−0.0613811	+	0.0354384i
$392$	104.000	+	180.133i	0.265306	+	0.459524i
$393$		0			0
$394$	506.000			1.28426
$395$		−	48.4974i		−	0.122778i
$396$		0			0
$397$	260.000			0.654912			0.327456	−	0.944866i	$-0.393809\pi$
$397$	260.000			0.654912			0.327456	+	0.944866i	$0.393809\pi$
$398$			259.808i			0.652783i
$399$		0			0
$400$	−192.000	+	332.554i	−0.480000	+	0.831384i
$401$	370.000	+	640.859i	0.922693	+	1.59815i	0.795230	+	0.606308i	$0.207350\pi$
$401$	370.000	+	640.859i	0.922693	+	1.59815i	0.127464	+	0.991843i	$0.459316\pi$
$402$		0			0
$403$	−930.000	−	536.936i	−2.30769	−	1.33235i
$404$	310.000	−	536.936i	0.767327	−	1.32905i
$405$		0			0
$406$	150.000	−	86.6025i	0.369458	−	0.213307i
$407$	−75.0000	−	43.3013i	−0.184275	−	0.106391i
$408$		0			0
$409$	−329.500	−	570.711i	−0.805623	−	1.39538i	−0.915869	−	0.401476i	$-0.868497\pi$
$409$	−329.500	−	570.711i	−0.805623	−	1.39538i	0.110246	−	0.993904i	$-0.464836\pi$
$410$	350.000	−	606.218i	0.853659	−	1.47858i
$411$		0			0
$412$	−480.000	+	277.128i	−1.16505	+	0.672641i
$413$	−300.000			−0.726392
$414$		0			0
$415$		−	206.114i		−	0.496660i
$416$	−320.000	−	554.256i	−0.769231	−	1.33235i
$417$		0			0
$418$	90.0000	−	155.885i	0.215311	−	0.372930i
$419$	−510.000	+	294.449i	−1.21718	+	0.702741i	−0.964315	−	0.264759i	$-0.914708\pi$
$419$	−510.000	+	294.449i	−1.21718	+	0.702741i	−0.252869	+	0.967500i	$0.581374\pi$
$420$		0			0
$421$	248.000	−	429.549i	0.589074	−	1.02031i	−0.405280	−	0.914192i	$-0.632826\pi$
$421$	248.000	−	429.549i	0.589074	−	1.02031i	0.994354	−	0.106113i	$-0.0338405\pi$
$422$	−258.000	+	148.956i	−0.611374	+	0.352977i
$423$		0			0
$424$	−376.000			−0.886792
$425$	96.0000	−	166.277i	0.225882	−	0.391240i
$426$		0			0
$427$	−480.000	+	277.128i	−1.12412	+	0.649012i
$428$			519.615i			1.21405i
$429$		0			0
$430$		−	242.487i		−	0.563924i
$431$			571.577i			1.32616i	0.748547	+	0.663082i	$0.230752\pi$
$431$			571.577i			1.32616i	−0.748547	+	0.663082i	$0.769248\pi$
$432$		0			0
$433$	−235.000			−0.542725			−0.271363	−	0.962477i	$-0.587474\pi$
$433$	−235.000			−0.542725			−0.271363	+	0.962477i	$0.587474\pi$
$434$	−930.000			−2.14286
$435$		0			0
$436$	536.000			1.22936
$437$	−18.0000	−	31.1769i	−0.0411899	−	0.0713431i
$438$		0			0
$439$	−358.500	−	206.980i	−0.816629	−	0.471481i	0.0326238	−	0.999468i	$-0.489614\pi$
$439$	−358.500	−	206.980i	−0.816629	−	0.471481i	−0.849253	+	0.527987i	$0.822947\pi$
$440$		−	484.974i		−	1.10221i
$441$		0			0
$442$	160.000	+	277.128i	0.361991	+	0.626987i
$443$	498.000	+	287.520i	1.12415	+	0.649030i	0.942458	−	0.334325i	$-0.108508\pi$
$443$	498.000	+	287.520i	1.12415	+	0.649030i	0.181695	+	0.983355i	$0.441841\pi$
$444$		0			0
$445$	−35.0000	−	60.6218i	−0.0786517	−	0.136229i
$446$	−60.0000	−	34.6410i	−0.134529	−	0.0776704i
$447$		0			0
$448$	−480.000	−	277.128i	−1.07143	−	0.618590i
$449$	−470.000			−1.04677			−0.523385	−	0.852096i	$-0.675331\pi$
$449$	−470.000			−1.04677			−0.523385	+	0.852096i	$0.675331\pi$
$450$		0			0
$451$			433.013i			0.960117i
$452$	148.000	+	256.344i	0.327434	+	0.567132i
$453$		0			0
$454$	−156.000	−	90.0666i	−0.343612	−	0.198385i
$455$	1050.00	−	606.218i	2.30769	−	1.33235i
$456$		0			0
$457$	162.500	−	281.458i	0.355580	−	0.615882i	−0.631637	−	0.775264i	$-0.717617\pi$
$457$	162.500	−	281.458i	0.355580	−	0.615882i	0.987217	+	0.159382i	$0.0509501\pi$
$458$	−146.000	−	252.879i	−0.318777	−	0.552138i
$459$		0			0
$460$	−84.0000	−	48.4974i	−0.182609	−	0.105429i
$461$	−327.500	+	567.247i	−0.710412	+	1.23047i	0.254290	+	0.967128i	$0.418158\pi$
$461$	−327.500	+	567.247i	−0.710412	+	1.23047i	−0.964703	+	0.263342i	$0.915175\pi$
$462$		0			0
$463$	−142.500	+	82.2724i	−0.307775	+	0.177694i	−0.645931	−	0.763396i	$-0.723530\pi$
$463$	−142.500	+	82.2724i	−0.307775	+	0.177694i	0.338155	+	0.941090i	$0.390197\pi$
$464$	−80.0000	+	138.564i	−0.172414	+	0.298629i
$465$		0			0
$466$	668.000			1.43348
$467$		−	57.1577i		−	0.122393i	−0.998126	−	0.0611967i	$-0.980508\pi$
$467$		−	57.1577i		−	0.122393i	0.998126	−	0.0611967i	$-0.0194917\pi$
$468$		0			0
$469$	750.000			1.59915
$470$		−	1212.44i		−	2.57965i
$471$		0			0
$472$	240.000	−	138.564i	0.508475	−	0.293568i
$473$	75.0000	+	129.904i	0.158562	+	0.274638i
$474$		0			0
$475$	216.000	+	124.708i	0.454737	+	0.262542i
$476$	240.000	+	138.564i	0.504202	+	0.291101i
$477$		0			0
$478$	−30.0000	+	17.3205i	−0.0627615	+	0.0362354i
$479$	−285.000	−	164.545i	−0.594990	−	0.343517i	0.172078	−	0.985083i	$-0.444952\pi$
$479$	−285.000	−	164.545i	−0.594990	−	0.343517i	−0.767068	+	0.641566i	$0.778285\pi$
$480$		0			0
$481$	100.000	+	173.205i	0.207900	+	0.360094i
$482$	−134.000	+	232.095i	−0.278008	+	0.481524i
$483$		0			0
$484$	−92.0000	−	159.349i	−0.190083	−	0.329233i
$485$	−175.000			−0.360825
$486$		0			0
$487$		−	519.615i		−	1.06697i	−0.845809	−	0.533486i	$-0.820882\pi$
$487$		−	519.615i		−	1.06697i	0.845809	−	0.533486i	$-0.179118\pi$
$488$	256.000	−	443.405i	0.524590	−	0.908617i
$489$		0			0
$490$	182.000	−	315.233i	0.371429	−	0.643333i
$491$	187.500	−	108.253i	0.381874	−	0.220475i	−0.296759	−	0.954952i	$-0.595906\pi$
$491$	187.500	−	108.253i	0.381874	−	0.220475i	0.678633	+	0.734477i	$0.262573\pi$
$492$		0			0
$493$	40.0000	−	69.2820i	0.0811359	−	0.140532i
$494$	−360.000	+	207.846i	−0.728745	+	0.420741i
$495$		0			0
$496$	744.000	−	429.549i	1.50000	−	0.866025i
$497$		0			0
$498$		0			0
$499$	−39.0000	+	22.5167i	−0.0781563	+	0.0451236i	−0.538569	−	0.842581i	$-0.681035\pi$
$499$	−39.0000	+	22.5167i	−0.0781563	+	0.0451236i	0.460413	+	0.887705i	$0.347701\pi$
$500$	−28.0000			−0.0560000
$501$		0			0
$502$			415.692i			0.828072i
$503$			384.515i			0.764444i	0.924071	+	0.382222i	$0.124841\pi$
$503$			384.515i			0.764444i	−0.924071	+	0.382222i	$0.875159\pi$
$504$		0			0
$505$	−1085.00			−2.14851
$506$	60.0000			0.118577
$507$		0			0
$508$			103.923i			0.204573i
$509$	−132.500	−	229.497i	−0.260314	−	0.450878i	0.706011	−	0.708201i	$-0.250493\pi$
$509$	−132.500	−	229.497i	−0.260314	−	0.450878i	−0.966325	+	0.257323i	$0.917160\pi$
$510$		0			0
$511$	412.500	+	238.157i	0.807241	+	0.466061i
$512$	512.000			1.00000
$513$		0			0
$514$	−268.000	−	464.190i	−0.521401	−	0.903093i
$515$	840.000	+	484.974i	1.63107	+	0.941698i
$516$		0			0
$517$	375.000	+	649.519i	0.725338	+	1.25632i
$518$	150.000	+	86.6025i	0.289575	+	0.167186i
$519$		0			0
$520$	−560.000	+	969.948i	−1.07692	+	1.86529i
$521$	−380.000			−0.729367			−0.364683	−	0.931132i	$-0.618823\pi$
$521$	−380.000			−0.729367			−0.364683	+	0.931132i	$0.618823\pi$
$522$		0			0
$523$		−	623.538i		−	1.19223i	−0.802898	−	0.596117i	$-0.796709\pi$
$523$		−	623.538i		−	1.19223i	0.802898	−	0.596117i	$-0.203291\pi$
$524$	570.000	−	329.090i	1.08779	−	0.628034i
$525$		0			0
$526$	−750.000	−	433.013i	−1.42586	−	0.823218i
$527$	−372.000	+	214.774i	−0.705882	+	0.407541i
$528$		0			0
$529$	−258.500	+	447.735i	−0.488658	+	0.846380i
$530$	329.000	+	569.845i	0.620755	+	1.07518i
$531$		0			0
$532$	−180.000	+	311.769i	−0.338346	+	0.586032i
$533$	500.000	−	866.025i	0.938086	−	1.62481i
$534$		0			0
$535$	787.500	−	454.663i	1.47196	−	0.849838i
$536$	−600.000	+	346.410i	−1.11940	+	0.646288i
$537$		0			0
$538$	−700.000			−1.30112
$539$			225.167i			0.417749i
$540$		0			0
$541$	−532.000			−0.983364			−0.491682	−	0.870775i	$-0.663618\pi$
$541$	−532.000			−0.983364			−0.491682	+	0.870775i	$0.663618\pi$
$542$			72.7461i			0.134218i
$543$		0			0
$544$	−256.000			−0.470588
$545$	−469.000	−	812.332i	−0.860550	−	1.49052i
$546$		0			0
$547$	780.000	+	450.333i	1.42596	+	0.823278i	0.996799	−	0.0799498i	$-0.0254760\pi$
$547$	780.000	+	450.333i	1.42596	+	0.823278i	0.429161	+	0.903228i	$0.358809\pi$
$548$	124.000	−	214.774i	0.226277	−	0.391924i
$549$		0			0
$550$	−360.000	+	207.846i	−0.654545	+	0.377902i
$551$	90.0000	+	51.9615i	0.163339	+	0.0943040i
$552$		0			0
$553$	−30.0000	−	51.9615i	−0.0542495	−	0.0939630i
$554$	520.000	−	900.666i	0.938628	−	1.62575i
$555$		0			0
$556$	600.000	−	346.410i	1.07914	−	0.623040i
$557$	−89.0000			−0.159785			−0.0798923	−	0.996804i	$-0.525458\pi$
$557$	−89.0000			−0.159785			−0.0798923	+	0.996804i	$0.525458\pi$
$558$		0			0
$559$		−	346.410i		−	0.619696i
$560$			969.948i			1.73205i
$561$		0			0
$562$	440.000	−	762.102i	0.782918	−	1.35605i
$563$	−262.500	+	151.554i	−0.466252	+	0.269191i	−0.714670	−	0.699462i	$-0.753423\pi$
$563$	−262.500	+	151.554i	−0.466252	+	0.269191i	0.248417	+	0.968653i	$0.420090\pi$
$564$		0			0
$565$	259.000	−	448.601i	0.458407	−	0.793984i
$566$	570.000	−	329.090i	1.00707	−	0.581430i
$567$		0			0
$568$		0			0
$569$	−50.0000	+	86.6025i	−0.0878735	+	0.152201i	−0.906612	−	0.421965i	$-0.861340\pi$
$569$	−50.0000	+	86.6025i	−0.0878735	+	0.152201i	0.818739	+	0.574166i	$0.194674\pi$
$570$		0			0
$571$	294.000	−	169.741i	0.514886	−	0.297270i	−0.219954	−	0.975510i	$-0.570591\pi$
$571$	294.000	−	169.741i	0.514886	−	0.297270i	0.734840	+	0.678241i	$0.237257\pi$
$572$		−	692.820i		−	1.21122i
$573$		0			0
$574$		−	866.025i		−	1.50876i
$575$			83.1384i			0.144589i
$576$		0			0
$577$	−730.000			−1.26516			−0.632582	−	0.774493i	$-0.718005\pi$
$577$	−730.000			−1.26516			−0.632582	+	0.774493i	$0.718005\pi$
$578$	−450.000			−0.778547
$579$		0			0
$580$	280.000			0.482759
$581$	−127.500	−	220.836i	−0.219449	−	0.380097i
$582$		0			0
$583$	−352.500	−	203.516i	−0.604631	−	0.349084i
$584$	−440.000			−0.753425
$585$		0			0
$586$	218.000	+	377.587i	0.372014	+	0.644347i
$587$	−694.500	−	400.970i	−1.18313	−	0.683083i	−0.226397	−	0.974035i	$-0.572695\pi$
$587$	−694.500	−	400.970i	−1.18313	−	0.683083i	−0.956738	+	0.290952i	$0.906028\pi$
$588$		0			0
$589$	−279.000	−	483.242i	−0.473684	−	0.820445i
$590$	−420.000	−	242.487i	−0.711864	−	0.410995i
$591$		0			0
$592$	−160.000			−0.270270
$593$	982.000			1.65599			0.827993	−	0.560738i	$-0.189483\pi$
$593$	982.000			1.65599			0.827993	+	0.560738i	$0.189483\pi$
$594$		0			0
$595$		−	484.974i		−	0.815083i
$596$	−230.000	−	398.372i	−0.385906	−	0.668409i
$597$		0			0
$598$	−120.000	−	69.2820i	−0.200669	−	0.115856i
$599$	−195.000	+	112.583i	−0.325543	+	0.187952i	−0.653860	−	0.756615i	$-0.726852\pi$
$599$	−195.000	+	112.583i	−0.325543	+	0.187952i	0.328318	+	0.944567i	$0.393518\pi$
$600$		0			0
$601$	−125.500	+	217.372i	−0.208819	+	0.361684i	−0.951343	−	0.308135i	$-0.900295\pi$
$601$	−125.500	+	217.372i	−0.208819	+	0.361684i	0.742524	+	0.669819i	$0.233629\pi$
$602$	−150.000	−	259.808i	−0.249169	−	0.431574i
$603$		0			0
$604$	150.000	+	86.6025i	0.248344	+	0.143382i
$605$	−161.000	+	278.860i	−0.266116	+	0.460926i
$606$		0			0
$607$	330.000	−	190.526i	0.543657	−	0.313881i	−0.202903	−	0.979199i	$-0.565037\pi$
$607$	330.000	−	190.526i	0.543657	−	0.313881i	0.746560	+	0.665318i	$0.231704\pi$
$608$		−	332.554i		−	0.546963i
$609$		0			0
$610$	−896.000			−1.46885
$611$		−	1732.05i		−	2.83478i
$612$		0			0
$613$	650.000			1.06036			0.530179	−	0.847885i	$-0.322125\pi$
$613$	650.000			1.06036			0.530179	+	0.847885i	$0.322125\pi$
$614$			415.692i			0.677023i
$615$		0			0
$616$	−300.000	−	519.615i	−0.487013	−	0.843531i
$617$	379.000	+	656.447i	0.614263	+	1.06393i	0.990513	+	0.137416i	$0.0438798\pi$
$617$	379.000	+	656.447i	0.614263	+	1.06393i	−0.376251	+	0.926518i	$0.622787\pi$
$618$		0			0
$619$	150.000	+	86.6025i	0.242326	+	0.139907i	0.616245	−	0.787554i	$-0.288653\pi$
$619$	150.000	+	86.6025i	0.242326	+	0.139907i	−0.373919	+	0.927461i	$0.621986\pi$
$620$	−1302.00	−	751.710i	−2.10000	−	1.21244i
$621$		0			0
$622$	510.000	−	294.449i	0.819936	−	0.473390i
$623$	−75.0000	−	43.3013i	−0.120385	−	0.0695044i
$624$		0			0
$625$	324.500	+	562.050i	0.519200	+	0.899281i
$626$	−485.000	+	840.045i	−0.774760	+	1.34192i
$627$		0			0
$628$	−40.0000	−	69.2820i	−0.0636943	−	0.110322i
$629$	80.0000			0.127186
$630$		0			0
$631$			119.512i			0.189400i	0.995506	+	0.0947001i	$0.0301892\pi$
$631$			119.512i			0.189400i	−0.995506	+	0.0947001i	$0.969811\pi$
$632$	48.0000	+	27.7128i	0.0759494	+	0.0438494i
$633$		0			0
$634$	−217.000	+	375.855i	−0.342271	+	0.592831i
$635$	157.500	−	90.9327i	0.248031	−	0.143201i
$636$		0			0
$637$	260.000	−	450.333i	0.408163	−	0.706960i
$638$	−150.000	+	86.6025i	−0.235110	+	0.135741i
$639$		0			0
$640$	−448.000	−	775.959i	−0.700000	−	1.21244i
$641$	−455.000	+	788.083i	−0.709828	+	1.22946i	0.255092	+	0.966917i	$0.417894\pi$
$641$	−455.000	+	788.083i	−0.709828	+	1.22946i	−0.964921	+	0.262542i	$0.915439\pi$
$642$		0			0
$643$	−30.0000	+	17.3205i	−0.0466563	+	0.0269370i	−0.523147	−	0.852243i	$-0.675242\pi$
$643$	−30.0000	+	17.3205i	−0.0466563	+	0.0269370i	0.476490	+	0.879180i	$0.341909\pi$
$644$	−120.000			−0.186335
$645$		0			0
$646$			166.277i			0.257395i
$647$			914.523i			1.41348i	0.707472	+	0.706741i	$0.249835\pi$
$647$			914.523i			1.41348i	−0.707472	+	0.706741i	$0.750165\pi$
$648$		0			0
$649$	300.000			0.462250
$650$	960.000			1.47692
$651$		0			0
$652$		−	415.692i		−	0.637565i
$653$	−51.5000	−	89.2006i	−0.0788668	−	0.136601i	0.823894	−	0.566743i	$-0.191797\pi$
$653$	−51.5000	−	89.2006i	−0.0788668	−	0.136601i	−0.902761	+	0.430142i	$0.858464\pi$
$654$		0			0
$655$	−997.500	−	575.907i	−1.52290	−	0.879247i
$656$	400.000	+	692.820i	0.609756	+	1.05613i
$657$		0			0
$658$	−750.000	−	1299.04i	−1.13982	−	1.97422i
$659$	52.5000	+	30.3109i	0.0796662	+	0.0459953i	0.539304	−	0.842111i	$-0.318687\pi$
$659$	52.5000	+	30.3109i	0.0796662	+	0.0459953i	−0.459638	+	0.888106i	$0.652021\pi$
$660$		0			0
$661$	−289.000	−	500.563i	−0.437216	−	0.757281i	0.560257	−	0.828319i	$-0.310702\pi$
$661$	−289.000	−	500.563i	−0.437216	−	0.757281i	−0.997474	+	0.0710377i	$0.977369\pi$
$662$	750.000	+	433.013i	1.13293	+	0.654098i
$663$		0			0
$664$	204.000	+	117.779i	0.307229	+	0.177379i
$665$	630.000			0.947368
$666$		0			0
$667$			34.6410i			0.0519356i
$668$	−852.000	+	491.902i	−1.27545	+	0.736381i
$669$		0			0
$670$	1050.00	+	606.218i	1.56716	+	0.904803i
$671$	480.000	−	277.128i	0.715350	−	0.413008i
$672$		0			0
$673$	−422.500	+	731.791i	−0.627786	+	1.08736i	0.360209	+	0.932872i	$0.382705\pi$
$673$	−422.500	+	731.791i	−0.627786	+	1.08736i	−0.987995	+	0.154486i	$0.950628\pi$
$674$	310.000	+	536.936i	0.459941	+	0.796641i
$675$		0			0
$676$	−462.000	+	800.207i	−0.683432	+	1.18374i
$677$	577.000	−	999.393i	0.852290	−	1.47621i	−0.0268475	−	0.999640i	$-0.508547\pi$
$677$	577.000	−	999.393i	0.852290	−	1.47621i	0.879137	−	0.476569i	$-0.158120\pi$
$678$		0			0
$679$	−187.500	+	108.253i	−0.276141	+	0.159430i
$680$	224.000	+	387.979i	0.329412	+	0.570558i
$681$		0			0
$682$	930.000			1.36364
$683$			187.061i			0.273882i	0.990579	+	0.136941i	$0.0437271\pi$
$683$			187.061i			0.273882i	−0.990579	+	0.136941i	$0.956273\pi$
$684$		0			0
$685$	−434.000			−0.633577
$686$			398.372i			0.580717i
$687$		0			0
$688$	240.000	+	138.564i	0.348837	+	0.201401i
$689$	470.000	+	814.064i	0.682148	+	1.18152i
$690$		0			0
$691$	−426.000	−	245.951i	−0.616498	−	0.355935i	0.159006	−	0.987278i	$-0.449171\pi$
$691$	−426.000	−	245.951i	−0.616498	−	0.355935i	−0.775504	+	0.631342i	$0.782504\pi$
$692$	−254.000	+	439.941i	−0.367052	+	0.635753i
$693$		0			0
$694$	375.000	−	216.506i	0.540346	−	0.311969i
$695$	−1050.00	−	606.218i	−1.51079	−	0.872256i
$696$		0			0
$697$	−200.000	−	346.410i	−0.286944	−	0.497002i
$698$	−74.0000	+	128.172i	−0.106017	+	0.183627i
$699$		0			0
$700$	720.000	−	415.692i	1.02857	−	0.593846i
$701$	−215.000			−0.306705			−0.153352	−	0.988172i	$-0.549007\pi$
$701$	−215.000			−0.306705			−0.153352	+	0.988172i	$0.549007\pi$
$702$		0			0
$703$			103.923i			0.147828i
$704$	480.000	+	277.128i	0.681818	+	0.393648i
$705$		0			0
$706$	−394.000	+	682.428i	−0.558074	+	0.966612i
$707$	−1162.50	+	671.170i	−1.64427	+	0.949321i
$708$		0			0
$709$	266.000	−	460.726i	0.375176	−	0.649824i	−0.615177	−	0.788389i	$-0.710916\pi$
$709$	266.000	−	460.726i	0.375176	−	0.649824i	0.990353	+	0.138565i	$0.0442488\pi$
$710$		0			0
$711$		0			0
$712$	80.0000			0.112360
$713$	93.0000	−	161.081i	0.130435	−	0.225920i
$714$		0			0
$715$	−1050.00	+	606.218i	−1.46853	+	0.847857i
$716$		−	935.307i		−	1.30630i
$717$		0			0
$718$			1143.15i			1.59214i
$719$		−	1143.15i		−	1.58992i	−0.606661	−	0.794961i	$-0.707491\pi$
$719$		−	1143.15i		−	1.58992i	0.606661	−	0.794961i	$-0.292509\pi$
$720$		0			0
$721$	1200.00			1.66436
$722$	506.000			0.700831
$723$		0			0
$724$	224.000			0.309392
$725$	−120.000	−	207.846i	−0.165517	−	0.286684i
$726$		0			0
$727$	1072.50	+	619.208i	1.47524	+	0.851731i	0.999610	−	0.0279146i	$-0.00888665\pi$
$727$	1072.50	+	619.208i	1.47524	+	0.851731i	0.475630	+	0.879645i	$0.342220\pi$
$728$			1385.64i			1.90335i
$729$		0			0
$730$	385.000	+	666.840i	0.527397	+	0.913479i
$731$	−120.000	−	69.2820i	−0.164159	−	0.0947771i
$732$		0			0
$733$	−475.000	−	822.724i	−0.648022	−	1.12241i	−0.983595	−	0.180392i	$-0.942263\pi$
$733$	−475.000	−	822.724i	−0.648022	−	1.12241i	0.335573	−	0.942014i	$-0.391070\pi$
$734$	975.000	+	562.917i	1.32834	+	0.766916i
$735$		0			0
$736$	96.0000	−	55.4256i	0.130435	−	0.0753066i
$737$	−750.000			−1.01764
$738$		0			0
$739$			581.969i			0.787509i	0.919216	+	0.393754i	$0.128824\pi$
$739$			581.969i			0.787509i	−0.919216	+	0.393754i	$0.871176\pi$
$740$	140.000	+	242.487i	0.189189	+	0.327685i
$741$		0			0
$742$	705.000	+	407.032i	0.950135	+	0.548561i
$743$	750.000	−	433.013i	1.00942	−	0.582790i	0.0983991	−	0.995147i	$-0.468628\pi$
$743$	750.000	−	433.013i	1.00942	−	0.582790i	0.911022	+	0.412357i	$0.135294\pi$
$744$		0			0
$745$	−402.500	+	697.150i	−0.540268	+	0.935772i
$746$	40.0000	+	69.2820i	0.0536193	+	0.0928714i
$747$		0			0
$748$	−240.000	−	138.564i	−0.320856	−	0.185246i
$749$	562.500	−	974.279i	0.751001	−	1.30077i
$750$		0			0
$751$	−151.500	+	87.4686i	−0.201731	+	0.116469i	−0.597463	−	0.801897i	$-0.703824\pi$
$751$	−151.500	+	87.4686i	−0.201731	+	0.116469i	0.395732	+	0.918366i	$0.370491\pi$
$752$	1200.00	+	692.820i	1.59574	+	0.921304i
$753$		0			0
$754$	400.000			0.530504
$755$		−	303.109i		−	0.401469i
$756$		0			0
$757$	830.000			1.09643			0.548217	−	0.836336i	$-0.315307\pi$
$757$	830.000			1.09643			0.548217	+	0.836336i	$0.315307\pi$
$758$			1371.78i			1.80974i
$759$		0			0
$760$	−504.000	+	290.985i	−0.663158	+	0.382874i
$761$	280.000	+	484.974i	0.367937	+	0.637285i	0.989243	−	0.146283i	$-0.0467309\pi$
$761$	280.000	+	484.974i	0.367937	+	0.637285i	−0.621306	+	0.783568i	$0.713398\pi$
$762$		0			0
$763$	−1005.00	−	580.237i	−1.31717	−	0.760468i
$764$	120.000	+	69.2820i	0.157068	+	0.0906833i
$765$		0			0
$766$	−624.000	+	360.267i	−0.814621	+	0.470322i
$767$	−600.000	−	346.410i	−0.782269	−	0.451643i
$768$		0			0
$769$	165.500	+	286.654i	0.215215	+	0.372763i	0.953339	−	0.301902i	$-0.0976216\pi$
$769$	165.500	+	286.654i	0.215215	+	0.372763i	−0.738124	+	0.674665i	$0.764288\pi$
$770$	−525.000	+	909.327i	−0.681818	+	1.18094i
$771$		0			0
$772$	−130.000	−	225.167i	−0.168394	−	0.291667i
$773$	298.000			0.385511			0.192755	−	0.981247i	$-0.438258\pi$
$773$	298.000			0.385511			0.192755	+	0.981247i	$0.438258\pi$
$774$		0			0
$775$			1288.65i			1.66277i
$776$	100.000	−	173.205i	0.128866	−	0.223202i
$777$		0			0
$778$	−475.000	+	822.724i	−0.610540	+	1.05749i
$779$	450.000	−	259.808i	0.577664	−	0.333514i
$780$		0			0
$781$		0			0
$782$	−48.0000	+	27.7128i	−0.0613811	+	0.0354384i
$783$		0			0
$784$	208.000	+	360.267i	0.265306	+	0.459524i
$785$	−70.0000	+	121.244i	−0.0891720	+	0.154450i
$786$		0			0
$787$	960.000	−	554.256i	1.21982	−	0.704265i	0.254942	−	0.966956i	$-0.417944\pi$
$787$	960.000	−	554.256i	1.21982	−	0.704265i	0.964880	+	0.262692i	$0.0846102\pi$
$788$	1012.00			1.28426
$789$		0			0
$790$		−	96.9948i		−	0.122778i
$791$		−	640.859i		−	0.810188i
$792$		0			0
$793$	−1280.00			−1.61412
$794$	520.000			0.654912
$795$		0			0
$796$			519.615i			0.652783i
$797$	−651.500	−	1128.43i	−0.817440	−	1.41585i	−0.907562	−	0.419918i	$-0.862059\pi$
$797$	−651.500	−	1128.43i	−0.817440	−	1.41585i	0.0901219	−	0.995931i	$-0.471274\pi$
$798$		0			0
$799$	−600.000	−	346.410i	−0.750939	−	0.433555i
$800$	−384.000	+	665.108i	−0.480000	+	0.831384i
$801$		0			0
$802$	740.000	+	1281.72i	0.922693	+	1.59815i
$803$	−412.500	−	238.157i	−0.513699	−	0.296584i
$804$		0			0
$805$	105.000	+	181.865i	0.130435	+	0.225920i
$806$	−1860.00	−	1073.87i	−2.30769	−	1.33235i
$807$		0			0
$808$	620.000	−	1073.87i	0.767327	−	1.32905i
$809$	−170.000			−0.210136			−0.105068	−	0.994465i	$-0.533506\pi$
$809$	−170.000			−0.210136			−0.105068	+	0.994465i	$0.533506\pi$
$810$		0			0
$811$			779.423i			0.961064i	0.876977	+	0.480532i	$0.159556\pi$
$811$			779.423i			0.961064i	−0.876977	+	0.480532i	$0.840444\pi$
$812$	300.000	−	173.205i	0.369458	−	0.213307i
$813$		0			0
$814$	−150.000	−	86.6025i	−0.184275	−	0.106391i
$815$	−630.000	+	363.731i	−0.773006	+	0.446295i
$816$		0			0
$817$	90.0000	−	155.885i	0.110159	−	0.190801i
$818$	−659.000	−	1141.42i	−0.805623	−	1.39538i
$819$		0			0
$820$	700.000	−	1212.44i	0.853659	−	1.47858i
$821$	−545.000	+	943.968i	−0.663825	+	1.14978i	0.315778	+	0.948833i	$0.397735\pi$
$821$	−545.000	+	943.968i	−0.663825	+	1.14978i	−0.979603	+	0.200945i	$0.935599\pi$
$822$		0			0
$823$	−817.500	+	471.984i	−0.993317	+	0.573492i	−0.906264	−	0.422712i	$-0.861078\pi$
$823$	−817.500	+	471.984i	−0.993317	+	0.573492i	−0.0870530	+	0.996204i	$0.527745\pi$
$824$	−960.000	+	554.256i	−1.16505	+	0.672641i
$825$		0			0
$826$	−600.000			−0.726392
$827$			83.1384i			0.100530i	0.998736	+	0.0502651i	$0.0160066\pi$
$827$			83.1384i			0.100530i	−0.998736	+	0.0502651i	$0.983993\pi$
$828$		0			0
$829$	542.000			0.653800			0.326900	−	0.945059i	$-0.393996\pi$
$829$	542.000			0.653800			0.326900	+	0.945059i	$0.393996\pi$
$830$		−	412.228i		−	0.496660i
$831$		0			0
$832$	−640.000	−	1108.51i	−0.769231	−	1.33235i
$833$	−104.000	−	180.133i	−0.124850	−	0.216246i
$834$		0			0
$835$	1491.00	+	860.829i	1.78563	+	1.03093i
$836$	180.000	−	311.769i	0.215311	−	0.372930i
$837$		0			0
$838$	−1020.00	+	588.897i	−1.21718	+	0.702741i
$839$	−600.000	−	346.410i	−0.715137	−	0.412885i	0.0978231	−	0.995204i	$-0.468812\pi$
$839$	−600.000	−	346.410i	−0.715137	−	0.412885i	−0.812960	+	0.582319i	$0.802145\pi$
$840$		0			0
$841$	370.500	+	641.725i	0.440547	+	0.763050i
$842$	496.000	−	859.097i	0.589074	−	1.02031i
$843$		0			0
$844$	−516.000	+	297.913i	−0.611374	+	0.352977i
$845$	1617.00			1.91361
$846$		0			0
$847$			398.372i			0.470333i
$848$	−752.000			−0.886792
$849$		0			0
$850$	192.000	−	332.554i	0.225882	−	0.391240i
$851$	−30.0000	+	17.3205i	−0.0352526	+	0.0203531i
$852$		0			0
$853$	−145.000	+	251.147i	−0.169988	+	0.294428i	−0.938415	−	0.345509i	$-0.887706\pi$
$853$	−145.000	+	251.147i	−0.169988	+	0.294428i	0.768427	+	0.639937i	$0.221040\pi$
$854$	−960.000	+	554.256i	−1.12412	+	0.649012i
$855$		0			0
$856$			1039.23i			1.21405i
$857$	184.000	−	318.697i	0.214702	−	0.371876i	−0.738478	−	0.674278i	$-0.764455\pi$
$857$	184.000	−	318.697i	0.214702	−	0.371876i	0.953180	+	0.302402i	$0.0977885\pi$
$858$		0			0
$859$	924.000	−	533.472i	1.07567	−	0.621038i	0.145944	−	0.989293i	$-0.453378\pi$
$859$	924.000	−	533.472i	1.07567	−	0.621038i	0.929725	+	0.368255i	$0.120045\pi$
$860$		−	484.974i		−	0.563924i
$861$		0			0
$862$			1143.15i			1.32616i
$863$		−	1018.45i		−	1.18012i	−0.807358	−	0.590061i	$-0.799104\pi$
$863$		−	1018.45i		−	1.18012i	0.807358	−	0.590061i	$-0.200896\pi$
$864$		0			0
$865$	889.000			1.02775
$866$	−470.000			−0.542725
$867$		0			0
$868$	−1860.00			−2.14286
$869$	30.0000	+	51.9615i	0.0345224	+	0.0597946i
$870$		0			0
$871$	1500.00	+	866.025i	1.72216	+	0.994289i
$872$	1072.00			1.22936
$873$		0			0
$874$	−36.0000	−	62.3538i	−0.0411899	−	0.0713431i
$875$	52.5000	+	30.3109i	0.0600000	+	0.0346410i
$876$		0			0
$877$	665.000	+	1151.81i	0.758267	+	1.31336i	0.943734	+	0.330706i	$0.107287\pi$
$877$	665.000	+	1151.81i	0.758267	+	1.31336i	−0.185467	+	0.982651i	$0.559380\pi$
$878$	−717.000	−	413.960i	−0.816629	−	0.471481i
$879$		0			0
$880$		−	969.948i		−	1.10221i
$881$	1060.00			1.20318			0.601589	−	0.798806i	$-0.294534\pi$
$881$	1060.00			1.20318			0.601589	+	0.798806i	$0.294534\pi$
$882$		0			0
$883$		−	1506.88i		−	1.70655i	−0.521461	−	0.853275i	$-0.674613\pi$
$883$		−	1506.88i		−	1.70655i	0.521461	−	0.853275i	$-0.325387\pi$
$884$	320.000	+	554.256i	0.361991	+	0.626987i
$885$		0			0
$886$	996.000	+	575.041i	1.12415	+	0.649030i
$887$	−618.000	+	356.802i	−0.696731	+	0.402258i	−0.806129	−	0.591740i	$-0.798441\pi$
$887$	−618.000	+	356.802i	−0.696731	+	0.402258i	0.109398	+	0.993998i	$0.465108\pi$
$888$		0			0
$889$	112.500	−	194.856i	0.126547	−	0.219185i
$890$	−70.0000	−	121.244i	−0.0786517	−	0.136229i
$891$		0			0
$892$	−120.000	−	69.2820i	−0.134529	−	0.0776704i
$893$	450.000	−	779.423i	0.503919	−	0.872814i
$894$		0			0
$895$	−1417.50	+	818.394i	−1.58380	+	0.914407i
$896$	−960.000	−	554.256i	−1.07143	−	0.618590i
$897$		0			0
$898$	−940.000			−1.04677
$899$			536.936i			0.597259i
$900$		0			0
$901$	376.000			0.417314
$902$			866.025i			0.960117i
$903$		0			0
$904$	296.000	+	512.687i	0.327434	+	0.567132i
$905$	−196.000	−	339.482i	−0.216575	−	0.375118i
$906$		0			0
$907$	−1155.00	−	666.840i	−1.27343	−	0.735215i	−0.297797	−	0.954629i	$-0.596252\pi$
$907$	−1155.00	−	666.840i	−1.27343	−	0.735215i	−0.975632	+	0.219415i	$0.929585\pi$
$908$	−312.000	−	180.133i	−0.343612	−	0.198385i
$909$		0			0
$910$	2100.00	−	1212.44i	2.30769	−	1.33235i
$911$	1335.00	+	770.763i	1.46542	+	0.846062i	0.999253	−	0.0386335i	$-0.0123005\pi$
$911$	1335.00	+	770.763i	1.46542	+	0.846062i	0.466169	+	0.884696i	$0.345634\pi$
$912$		0			0
$913$	127.500	+	220.836i	0.139650	+	0.241880i
$914$	325.000	−	562.917i	0.355580	−	0.615882i
$915$		0			0
$916$	−292.000	−	505.759i	−0.318777	−	0.552138i
$917$	−1425.00			−1.55398
$918$		0			0
$919$		−	909.327i		−	0.989474i	−0.869043	−	0.494737i	$-0.835264\pi$
$919$		−	909.327i		−	0.989474i	0.869043	−	0.494737i	$-0.164736\pi$
$920$	−168.000	−	96.9948i	−0.182609	−	0.105429i
$921$		0			0
$922$	−655.000	+	1134.49i	−0.710412	+	1.23047i
$923$		0			0
$924$		0			0
$925$	120.000	−	207.846i	0.129730	−	0.224698i
$926$	−285.000	+	164.545i	−0.307775	+	0.177694i
$927$		0			0
$928$	−160.000	+	277.128i	−0.172414	+	0.298629i
$929$	670.000	−	1160.47i	0.721206	−	1.24916i	−0.239311	−	0.970943i	$-0.576922\pi$
$929$	670.000	−	1160.47i	0.721206	−	1.24916i	0.960517	−	0.278222i	$-0.0897450\pi$
$930$		0			0
$931$	234.000	−	135.100i	0.251343	−	0.145113i
$932$	1336.00			1.43348
$933$		0			0
$934$		−	114.315i		−	0.122393i
$935$			484.974i			0.518689i
$936$		0			0
$937$	−1225.00			−1.30736			−0.653682	−	0.756769i	$-0.726777\pi$
$937$	−1225.00			−1.30736			−0.653682	+	0.756769i	$0.726777\pi$
$938$	1500.00			1.59915
$939$		0			0
$940$		−	2424.87i		−	2.57965i
$941$	−57.5000	−	99.5929i	−0.0611052	−	0.105837i	0.833854	−	0.551984i	$-0.186129\pi$
$941$	−57.5000	−	99.5929i	−0.0611052	−	0.105837i	−0.894960	+	0.446147i	$0.852796\pi$
$942$		0			0
$943$	150.000	+	86.6025i	0.159067	+	0.0918373i
$944$	480.000	−	277.128i	0.508475	−	0.293568i
$945$		0			0
$946$	150.000	+	259.808i	0.158562	+	0.274638i
$947$	−595.500	−	343.812i	−0.628828	−	0.363054i	0.151470	−	0.988462i	$-0.451599\pi$
$947$	−595.500	−	343.812i	−0.628828	−	0.363054i	−0.780298	+	0.625408i	$0.784933\pi$
$948$		0			0
$949$	550.000	+	952.628i	0.579557	+	1.00382i
$950$	432.000	+	249.415i	0.454737	+	0.262542i
$951$		0			0
$952$	480.000	+	277.128i	0.504202	+	0.291101i
$953$	−44.0000			−0.0461700			−0.0230850	−	0.999734i	$-0.507349\pi$
$953$	−44.0000			−0.0461700			−0.0230850	+	0.999734i	$0.507349\pi$
$954$		0			0
$955$		−	242.487i		−	0.253913i
$956$	−60.0000	+	34.6410i	−0.0627615	+	0.0362354i
$957$		0			0
$958$	−570.000	−	329.090i	−0.594990	−	0.343517i
$959$	−465.000	+	268.468i	−0.484880	+	0.279946i
$960$		0			0
$961$	961.000	−	1664.50i	1.00000	−	1.73205i
$962$	200.000	+	346.410i	0.207900	+	0.360094i
$963$		0			0
$964$	−268.000	+	464.190i	−0.278008	+	0.481524i
$965$	−227.500	+	394.042i	−0.235751	+	0.408333i
$966$		0			0
$967$	217.500	−	125.574i	0.224922	−	0.129859i	−0.383305	−	0.923622i	$-0.625214\pi$
$967$	217.500	−	125.574i	0.224922	−	0.129859i	0.608227	+	0.793763i	$0.291881\pi$
$968$	−184.000	−	318.697i	−0.190083	−	0.329233i
$969$		0			0
$970$	−350.000			−0.360825
$971$			337.750i			0.347837i	0.984760	+	0.173919i	$0.0556430\pi$
$971$			337.750i			0.347837i	−0.984760	+	0.173919i	$0.944357\pi$
$972$		0			0
$973$	−1500.00			−1.54162
$974$		−	1039.23i		−	1.06697i
$975$		0			0
$976$	512.000	−	886.810i	0.524590	−	0.908617i
$977$	−173.000	−	299.645i	−0.177073	−	0.306699i	0.763804	−	0.645448i	$-0.223329\pi$
$977$	−173.000	−	299.645i	−0.177073	−	0.306699i	−0.940877	+	0.338749i	$0.889996\pi$
$978$		0			0
$979$	75.0000	+	43.3013i	0.0766088	+	0.0442301i
$980$	364.000	−	630.466i	0.371429	−	0.643333i
$981$		0			0
$982$	375.000	−	216.506i	0.381874	−	0.220475i
$983$	687.000	+	396.640i	0.698881	+	0.403499i	0.806931	−	0.590646i	$-0.201127\pi$
$983$	687.000	+	396.640i	0.698881	+	0.403499i	−0.108050	+	0.994146i	$0.534461\pi$
$984$		0			0
$985$	−885.500	−	1533.73i	−0.898985	−	1.55709i
$986$	80.0000	−	138.564i	0.0811359	−	0.140532i
$987$		0			0
$988$	−720.000	+	415.692i	−0.728745	+	0.420741i
$989$	60.0000			0.0606673
$990$		0			0
$991$			1054.82i			1.06440i	0.846619	+	0.532199i	$0.178634\pi$
$991$			1054.82i			1.06440i	−0.846619	+	0.532199i	$0.821366\pi$
$992$	1488.00	−	859.097i	1.50000	−	0.866025i
$993$		0			0
$994$		0			0
$995$	787.500	−	454.663i	0.791457	−	0.456948i
$996$		0			0
$997$	−130.000	+	225.167i	−0.130391	+	0.225844i	−0.923827	−	0.382809i	$-0.874957\pi$
$997$	−130.000	+	225.167i	−0.130391	+	0.225844i	0.793436	+	0.608653i	$0.208290\pi$
$998$	−78.0000	+	45.0333i	−0.0781563	+	0.0451236i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.i.55.1		2
3.2	odd	2		324.3.f.b.55.1		2
4.3	odd	2		324.3.f.c.55.1		2
9.2	odd	6		108.3.d.b.55.2	yes	2
9.4	even	3		324.3.f.c.271.1		2
9.5	odd	6		324.3.f.h.271.1		2
9.7	even	3		108.3.d.a.55.1	✓	2
12.11	even	2		324.3.f.h.55.1		2
36.7	odd	6		108.3.d.a.55.2	yes	2
36.11	even	6		108.3.d.b.55.1	yes	2
36.23	even	6		324.3.f.b.271.1		2
36.31	odd	6	inner	324.3.f.i.271.1		2
72.11	even	6		1728.3.g.f.703.1		2
72.29	odd	6		1728.3.g.f.703.2		2
72.43	odd	6		1728.3.g.a.703.1		2
72.61	even	6		1728.3.g.a.703.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.d.a.55.1	✓	2	9.7	even	3
108.3.d.a.55.2	yes	2	36.7	odd	6
108.3.d.b.55.1	yes	2	36.11	even	6
108.3.d.b.55.2	yes	2	9.2	odd	6
324.3.f.b.55.1		2	3.2	odd	2
324.3.f.b.271.1		2	36.23	even	6
324.3.f.c.55.1		2	4.3	odd	2
324.3.f.c.271.1		2	9.4	even	3
324.3.f.h.55.1		2	12.11	even	2
324.3.f.h.271.1		2	9.5	odd	6
324.3.f.i.55.1		2	1.1	even	1	trivial
324.3.f.i.271.1		2	36.31	odd	6	inner
1728.3.g.a.703.1		2	72.43	odd	6
1728.3.g.a.703.2		2	72.61	even	6
1728.3.g.f.703.1		2	72.11	even	6
1728.3.g.f.703.2		2	72.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +4.00000 q^{4} +(-3.50000 - 6.06218i) q^{5} +(-7.50000 - 4.33013i) q^{7} +8.00000 q^{8} +O(q^{10})\)	\(q+2.00000 q^{2} +4.00000 q^{4} +(-3.50000 - 6.06218i) q^{5} +(-7.50000 - 4.33013i) q^{7} +8.00000 q^{8} +(-7.00000 - 12.1244i) q^{10} +(7.50000 + 4.33013i) q^{11} +(-10.0000 - 17.3205i) q^{13} +(-15.0000 - 8.66025i) q^{14} +16.0000 q^{16} -8.00000 q^{17} -10.3923i q^{19} +(-14.0000 - 24.2487i) q^{20} +(15.0000 + 8.66025i) q^{22} +(3.00000 - 1.73205i) q^{23} +(-12.0000 + 20.7846i) q^{25} +(-20.0000 - 34.6410i) q^{26} +(-30.0000 - 17.3205i) q^{28} +(-5.00000 + 8.66025i) q^{29} +(46.5000 - 26.8468i) q^{31} +32.0000 q^{32} -16.0000 q^{34} +60.6218i q^{35} -10.0000 q^{37} -20.7846i q^{38} +(-28.0000 - 48.4974i) q^{40} +(25.0000 + 43.3013i) q^{41} +(15.0000 + 8.66025i) q^{43} +(30.0000 + 17.3205i) q^{44} +(6.00000 - 3.46410i) q^{46} +(75.0000 + 43.3013i) q^{47} +(13.0000 + 22.5167i) q^{49} +(-24.0000 + 41.5692i) q^{50} +(-40.0000 - 69.2820i) q^{52} -47.0000 q^{53} -60.6218i q^{55} +(-60.0000 - 34.6410i) q^{56} +(-10.0000 + 17.3205i) q^{58} +(30.0000 - 17.3205i) q^{59} +(32.0000 - 55.4256i) q^{61} +(93.0000 - 53.6936i) q^{62} +64.0000 q^{64} +(-70.0000 + 121.244i) q^{65} +(-75.0000 + 43.3013i) q^{67} -32.0000 q^{68} +121.244i q^{70} -55.0000 q^{73} -20.0000 q^{74} -41.5692i q^{76} +(-37.5000 - 64.9519i) q^{77} +(6.00000 + 3.46410i) q^{79} +(-56.0000 - 96.9948i) q^{80} +(50.0000 + 86.6025i) q^{82} +(25.5000 + 14.7224i) q^{83} +(28.0000 + 48.4974i) q^{85} +(30.0000 + 17.3205i) q^{86} +(60.0000 + 34.6410i) q^{88} +10.0000 q^{89} +173.205i q^{91} +(12.0000 - 6.92820i) q^{92} +(150.000 + 86.6025i) q^{94} +(-63.0000 + 36.3731i) q^{95} +(12.5000 - 21.6506i) q^{97} +(26.0000 + 45.0333i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 8 q^{4} - 7 q^{5} - 15 q^{7} + 16 q^{8}+O(q^{10}) \) 2 * q + 4 * q^2 + 8 * q^4 - 7 * q^5 - 15 * q^7 + 16 * q^8	\( 2 q + 4 q^{2} + 8 q^{4} - 7 q^{5} - 15 q^{7} + 16 q^{8} - 14 q^{10} + 15 q^{11} - 20 q^{13} - 30 q^{14} + 32 q^{16} - 16 q^{17} - 28 q^{20} + 30 q^{22} + 6 q^{23} - 24 q^{25} - 40 q^{26} - 60 q^{28} - 10 q^{29} + 93 q^{31} + 64 q^{32} - 32 q^{34} - 20 q^{37} - 56 q^{40} + 50 q^{41} + 30 q^{43} + 60 q^{44} + 12 q^{46} + 150 q^{47} + 26 q^{49} - 48 q^{50} - 80 q^{52} - 94 q^{53} - 120 q^{56} - 20 q^{58} + 60 q^{59} + 64 q^{61} + 186 q^{62} + 128 q^{64} - 140 q^{65} - 150 q^{67} - 64 q^{68} - 110 q^{73} - 40 q^{74} - 75 q^{77} + 12 q^{79} - 112 q^{80} + 100 q^{82} + 51 q^{83} + 56 q^{85} + 60 q^{86} + 120 q^{88} + 20 q^{89} + 24 q^{92} + 300 q^{94} - 126 q^{95} + 25 q^{97} + 52 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 + 8 * q^4 - 7 * q^5 - 15 * q^7 + 16 * q^8 - 14 * q^10 + 15 * q^11 - 20 * q^13 - 30 * q^14 + 32 * q^16 - 16 * q^17 - 28 * q^20 + 30 * q^22 + 6 * q^23 - 24 * q^25 - 40 * q^26 - 60 * q^28 - 10 * q^29 + 93 * q^31 + 64 * q^32 - 32 * q^34 - 20 * q^37 - 56 * q^40 + 50 * q^41 + 30 * q^43 + 60 * q^44 + 12 * q^46 + 150 * q^47 + 26 * q^49 - 48 * q^50 - 80 * q^52 - 94 * q^53 - 120 * q^56 - 20 * q^58 + 60 * q^59 + 64 * q^61 + 186 * q^62 + 128 * q^64 - 140 * q^65 - 150 * q^67 - 64 * q^68 - 110 * q^73 - 40 * q^74 - 75 * q^77 + 12 * q^79 - 112 * q^80 + 100 * q^82 + 51 * q^83 + 56 * q^85 + 60 * q^86 + 120 * q^88 + 20 * q^89 + 24 * q^92 + 300 * q^94 - 126 * q^95 + 25 * q^97 + 52 * q^98

Introduction

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