LMFDB - Embedded newform 216.3.b.b.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(163,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("216.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} - 56x^{10} + 400x^{8} - 896x^{6} - 512x^{4} - 8192x^{2} + 65536 $ x^16 - 2x^14 - 2x^12 - 56x^10 + 400x^8 - 896x^6 - 512x^4 - 8192*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.3
Root			$-1.77866 - 0.914534i$ of defining polynomial
Character	$\chi$	$=$	216.163
Dual form			216.3.b.b.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77866 - 0.914534i) q^{2} +(2.32725 + 3.25329i) q^{4} -3.96500i q^{5} +3.99887i q^{7} +(-1.16415 - 7.91484i) q^{8} +O(q^{10})$	\(q+(-1.77866 - 0.914534i) q^{2} +(2.32725 + 3.25329i) q^{4} -3.96500i q^{5} +3.99887i q^{7} +(-1.16415 - 7.91484i) q^{8} +(-3.62613 + 7.05238i) q^{10} +9.34197 q^{11} -10.5978i q^{13} +(3.65711 - 7.11263i) q^{14} +(-5.16777 + 15.1425i) q^{16} -7.91338 q^{17} +21.7007 q^{19} +(12.8993 - 9.22756i) q^{20} +(-16.6162 - 8.54355i) q^{22} -34.7860i q^{23} +9.27878 q^{25} +(-9.69203 + 18.8498i) q^{26} +(-13.0095 + 9.30639i) q^{28} -8.37928i q^{29} -49.4051i q^{31} +(23.0400 - 22.2072i) q^{32} +(14.0752 + 7.23705i) q^{34} +15.8555 q^{35} -56.8359i q^{37} +(-38.5981 - 19.8460i) q^{38} +(-31.3824 + 4.61585i) q^{40} -53.6560 q^{41} -6.33926 q^{43} +(21.7411 + 30.3921i) q^{44} +(-31.8130 + 61.8724i) q^{46} -3.84419i q^{47} +33.0090 q^{49} +(-16.5038 - 8.48576i) q^{50} +(34.4776 - 24.6637i) q^{52} +102.398i q^{53} -37.0409i q^{55} +(31.6505 - 4.65528i) q^{56} +(-7.66314 + 14.9039i) q^{58} +116.596 q^{59} +57.4503i q^{61} +(-45.1826 + 87.8748i) q^{62} +(-61.2895 + 18.4281i) q^{64} -42.0202 q^{65} +13.1962 q^{67} +(-18.4164 - 25.7445i) q^{68} +(-28.2016 - 14.5004i) q^{70} +48.4786i q^{71} +59.0207 q^{73} +(-51.9783 + 101.092i) q^{74} +(50.5030 + 70.5985i) q^{76} +37.3573i q^{77} +42.7035i q^{79} +(60.0399 + 20.4902i) q^{80} +(95.4358 + 49.0703i) q^{82} -0.0660819 q^{83} +31.3765i q^{85} +(11.2754 + 5.79747i) q^{86} +(-10.8754 - 73.9402i) q^{88} -98.4759 q^{89} +42.3792 q^{91} +(113.169 - 80.9559i) q^{92} +(-3.51564 + 6.83749i) q^{94} -86.0431i q^{95} -158.329 q^{97} +(-58.7118 - 30.1879i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} + 24 q^{10} + 16 q^{16} - 64 q^{19} + 80 q^{22} - 80 q^{25} - 12 q^{28} + 8 q^{34} - 72 q^{40} - 64 q^{43} - 192 q^{46} - 128 q^{49} + 84 q^{52} - 96 q^{58} + 376 q^{64} + 128 q^{67} + 192 q^{70} + 80 q^{73} + 308 q^{76} + 272 q^{82} - 136 q^{88} + 192 q^{91} + 336 q^{94} + 80 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 24 * q^10 + 16 * q^16 - 64 * q^19 + 80 * q^22 - 80 * q^25 - 12 * q^28 + 8 * q^34 - 72 * q^40 - 64 * q^43 - 192 * q^46 - 128 * q^49 + 84 * q^52 - 96 * q^58 + 376 * q^64 + 128 * q^67 + 192 * q^70 + 80 * q^73 + 308 * q^76 + 272 * q^82 - 136 * q^88 + 192 * q^91 + 336 * q^94 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.77866	−	0.914534i	−0.889329	−	0.457267i
$2$	−1.77866	−	0.914534i	−0.889329	−	0.457267i
$3$		0			0
$3$		0			0
$4$	2.32725	+	3.25329i	0.581814	+	0.813322i
$5$		−	3.96500i		−	0.793000i	−0.918035	−	0.396500i	$-0.870225\pi$
$5$		−	3.96500i		−	0.793000i	0.918035	−	0.396500i	$-0.129775\pi$
$6$		0			0
$7$			3.99887i			0.571267i	0.958339	+	0.285634i	$0.0922041\pi$
$7$			3.99887i			0.571267i	−0.958339	+	0.285634i	$0.907796\pi$
$8$	−1.16415	−	7.91484i	−0.145519	−	0.989356i
$9$		0			0
$10$	−3.62613	+	7.05238i	−0.362613	+	0.705238i
$11$	9.34197			0.849270			0.424635	−	0.905365i	$-0.360402\pi$
$11$	9.34197			0.849270			0.424635	+	0.905365i	$0.360402\pi$
$12$		0			0
$13$		−	10.5978i		−	0.815214i	−0.913157	−	0.407607i	$-0.866363\pi$
$13$		−	10.5978i		−	0.815214i	0.913157	−	0.407607i	$-0.133637\pi$
$14$	3.65711	−	7.11263i	0.261222	−	0.508045i
$15$		0			0
$16$	−5.16777	+	15.1425i	−0.322986	+	0.946404i
$17$	−7.91338			−0.465493			−0.232746	−	0.972537i	$-0.574771\pi$
$17$	−7.91338			−0.465493			−0.232746	+	0.972537i	$0.574771\pi$
$18$		0			0
$19$	21.7007			1.14214			0.571070	−	0.820901i	$-0.306528\pi$
$19$	21.7007			1.14214			0.571070	+	0.820901i	$0.306528\pi$
$20$	12.8993	−	9.22756i	0.644964	−	0.461378i
$21$		0			0
$22$	−16.6162	−	8.54355i	−0.755281	−	0.388343i
$23$		−	34.7860i		−	1.51244i	−0.654320	−	0.756218i	$-0.727045\pi$
$23$		−	34.7860i		−	1.51244i	0.654320	−	0.756218i	$-0.272955\pi$
$24$		0			0
$25$	9.27878			0.371151
$26$	−9.69203	+	18.8498i	−0.372771	+	0.724994i
$27$		0			0
$28$	−13.0095	+	9.30639i	−0.464624	+	0.332371i
$29$		−	8.37928i		−	0.288941i	−0.989509	−	0.144470i	$-0.953852\pi$
$29$		−	8.37928i		−	0.288941i	0.989509	−	0.144470i	$-0.0461478\pi$
$30$		0			0
$31$		−	49.4051i		−	1.59371i	−0.604169	−	0.796856i	$-0.706495\pi$
$31$		−	49.4051i		−	1.59371i	0.604169	−	0.796856i	$-0.293505\pi$
$32$	23.0400	−	22.2072i	0.720000	−	0.693974i
$33$		0			0
$34$	14.0752	+	7.23705i	0.413976	+	0.212854i
$35$	15.8555			0.453015
$36$		0			0
$37$		−	56.8359i		−	1.53610i	−0.640387	−	0.768052i	$-0.721226\pi$
$37$		−	56.8359i		−	1.53610i	0.640387	−	0.768052i	$-0.278774\pi$
$38$	−38.5981	−	19.8460i	−1.01574	−	0.522263i
$39$		0			0
$40$	−31.3824	+	4.61585i	−0.784559	+	0.115396i
$41$	−53.6560			−1.30868			−0.654342	−	0.756199i	$-0.727054\pi$
$41$	−53.6560			−1.30868			−0.654342	+	0.756199i	$0.727054\pi$
$42$		0			0
$43$	−6.33926			−0.147425			−0.0737123	−	0.997280i	$-0.523485\pi$
$43$	−6.33926			−0.147425			−0.0737123	+	0.997280i	$0.523485\pi$
$44$	21.7411	+	30.3921i	0.494117	+	0.690730i
$45$		0			0
$46$	−31.8130	+	61.8724i	−0.691587	+	1.34505i
$47$		−	3.84419i		−	0.0817912i	−0.999163	−	0.0408956i	$-0.986979\pi$
$47$		−	3.84419i		−	0.0817912i	0.999163	−	0.0408956i	$-0.0130211\pi$
$48$		0			0
$49$	33.0090			0.673653
$50$	−16.5038	−	8.48576i	−0.330076	−	0.169715i
$51$		0			0
$52$	34.4776	−	24.6637i	0.663032	−	0.474303i
$53$			102.398i			1.93204i	0.258464	+	0.966021i	$0.416784\pi$
$53$			102.398i			1.93204i	−0.258464	+	0.966021i	$0.583216\pi$
$54$		0			0
$55$		−	37.0409i		−	0.673471i
$56$	31.6505	−	4.65528i	0.565187	−	0.0831301i
$57$		0			0
$58$	−7.66314	+	14.9039i	−0.132123	+	0.256963i
$59$	116.596			1.97621			0.988106	−	0.153775i	$-0.0491430\pi$
$59$	116.596			1.97621			0.988106	+	0.153775i	$0.0491430\pi$
$60$		0			0
$61$			57.4503i			0.941809i	0.882184	+	0.470904i	$0.156072\pi$
$61$			57.4503i			0.941809i	−0.882184	+	0.470904i	$0.843928\pi$
$62$	−45.1826	+	87.8748i	−0.728752	+	1.41734i
$63$		0			0
$64$	−61.2895	+	18.4281i	−0.957649	+	0.287939i
$65$	−42.0202			−0.646465
$66$		0			0
$67$	13.1962			0.196957			0.0984787	−	0.995139i	$-0.468602\pi$
$67$	13.1962			0.196957			0.0984787	+	0.995139i	$0.468602\pi$
$68$	−18.4164	−	25.7445i	−0.270830	−	0.378596i
$69$		0			0
$70$	−28.2016	−	14.5004i	−0.402880	−	0.207149i
$71$			48.4786i			0.682797i	0.939919	+	0.341398i	$0.110900\pi$
$71$			48.4786i			0.682797i	−0.939919	+	0.341398i	$0.889100\pi$
$72$		0			0
$73$	59.0207			0.808503			0.404251	−	0.914648i	$-0.367532\pi$
$73$	59.0207			0.808503			0.404251	+	0.914648i	$0.367532\pi$
$74$	−51.9783	+	101.092i	−0.702410	+	1.36610i
$75$		0			0
$76$	50.5030	+	70.5985i	0.664513	+	0.928928i
$77$			37.3573i			0.485160i
$78$		0			0
$79$			42.7035i			0.540551i	0.962783	+	0.270275i	$0.0871148\pi$
$79$			42.7035i			0.540551i	−0.962783	+	0.270275i	$0.912885\pi$
$80$	60.0399	+	20.4902i	0.750498	+	0.256128i
$81$		0			0
$82$	95.4358	+	49.0703i	1.16385	+	0.598418i
$83$	−0.0660819			−0.000796168			−0.000398084	−	1.00000i	$-0.500127\pi$
$83$	−0.0660819			−0.000796168			−0.000398084		1.00000i	$0.500127\pi$
$84$		0			0
$85$			31.3765i			0.369136i
$86$	11.2754	+	5.79747i	0.131109	+	0.0674125i
$87$		0			0
$88$	−10.8754	−	73.9402i	−0.123585	−	0.840230i
$89$	−98.4759			−1.10647			−0.553235	−	0.833025i	$-0.686607\pi$
$89$	−98.4759			−1.10647			−0.553235	+	0.833025i	$0.686607\pi$
$90$		0			0
$91$	42.3792			0.465705
$92$	113.169	−	80.9559i	1.23010	−	0.879956i
$93$		0			0
$94$	−3.51564	+	6.83749i	−0.0374004	+	0.0727393i
$95$		−	86.0431i		−	0.905717i
$96$		0			0
$97$	−158.329			−1.63226			−0.816130	−	0.577869i	$-0.803885\pi$
$97$	−158.329			−1.63226			−0.816130	+	0.577869i	$0.803885\pi$
$98$	−58.7118	−	30.1879i	−0.599100	−	0.308040i
$99$		0			0
$100$	21.5941	+	30.1865i	0.215941	+	0.301865i
$101$			28.4573i			0.281756i	0.990027	+	0.140878i	$0.0449925\pi$
$101$			28.4573i			0.281756i	−0.990027	+	0.140878i	$0.955008\pi$
$102$		0			0
$103$			101.145i			0.981994i	0.871161	+	0.490997i	$0.163367\pi$
$103$			101.145i			0.981994i	−0.871161	+	0.490997i	$0.836633\pi$
$104$	−83.8798	+	12.3374i	−0.806537	+	0.118629i
$105$		0			0
$106$	93.6467	−	182.132i	0.883459	−	1.71822i
$107$	53.2234			0.497415			0.248708	−	0.968579i	$-0.419994\pi$
$107$	53.2234			0.497415			0.248708	+	0.968579i	$0.419994\pi$
$108$		0			0
$109$		−	68.6625i		−	0.629932i	−0.949103	−	0.314966i	$-0.898007\pi$
$109$		−	68.6625i		−	0.629932i	0.949103	−	0.314966i	$-0.101993\pi$
$110$	−33.8752	+	65.8831i	−0.307956	+	0.598938i
$111$		0			0
$112$	−60.5528	−	20.6653i	−0.540650	−	0.184511i
$113$	−175.404			−1.55224			−0.776122	−	0.630583i	$-0.782816\pi$
$113$	−175.404			−1.55224			−0.776122	+	0.630583i	$0.782816\pi$
$114$		0			0
$115$	−137.927			−1.19936
$116$	27.2602	−	19.5007i	0.235002	−	0.168110i
$117$		0			0
$118$	−207.385	−	106.631i	−1.75750	−	0.903657i
$119$		−	31.6446i		−	0.265921i
$120$		0			0
$121$	−33.7276			−0.278740
$122$	52.5403	−	102.185i	0.430658	−	0.837578i
$123$		0			0
$124$	160.729	−	114.978i	1.29620	−	0.927244i
$125$		−	135.915i		−	1.08732i
$126$		0			0
$127$		−	47.6826i		−	0.375454i	−0.982221	−	0.187727i	$-0.939888\pi$
$127$		−	47.6826i		−	0.375454i	0.982221	−	0.187727i	$-0.0601120\pi$
$128$	125.866	+	23.2740i	0.983330	+	0.181828i
$129$		0			0
$130$	74.7396	+	38.4289i	0.574920	+	0.295607i
$131$	182.979			1.39679			0.698394	−	0.715714i	$-0.253898\pi$
$131$	182.979			1.39679			0.698394	+	0.715714i	$0.253898\pi$
$132$		0			0
$133$			86.7782i			0.652468i
$134$	−23.4715	−	12.0683i	−0.175160	−	0.0900622i
$135$		0			0
$136$	9.21235	+	62.6331i	0.0677379	+	0.460538i
$137$	205.459			1.49970			0.749849	−	0.661609i	$-0.230126\pi$
$137$	205.459			1.49970			0.749849	+	0.661609i	$0.230126\pi$
$138$		0			0
$139$	−20.4646			−0.147227			−0.0736136	−	0.997287i	$-0.523453\pi$
$139$	−20.4646			−0.147227			−0.0736136	+	0.997287i	$0.523453\pi$
$140$	36.8999	+	51.5826i	0.263570	+	0.368447i
$141$		0			0
$142$	44.3353	−	86.2268i	0.312220	−	0.607231i
$143$		−	99.0042i		−	0.692337i
$144$		0			0
$145$	−33.2238			−0.229130
$146$	−104.978	−	53.9764i	−0.719025	−	0.369702i
$147$		0			0
$148$	184.903	−	132.272i	1.24935	−	0.893727i
$149$			154.346i			1.03588i	0.855417	+	0.517940i	$0.173301\pi$
$149$			154.346i			1.03588i	−0.855417	+	0.517940i	$0.826699\pi$
$150$		0			0
$151$			248.322i			1.64451i	0.569116	+	0.822257i	$0.307285\pi$
$151$			248.322i			1.64451i	−0.569116	+	0.822257i	$0.692715\pi$
$152$	−25.2628	−	171.757i	−0.166203	−	1.12998i
$153$		0			0
$154$	34.1646	−	66.4460i	0.221848	−	0.431467i
$155$	−195.891			−1.26381
$156$		0			0
$157$		−	14.6424i		−	0.0932635i	−0.998912	−	0.0466317i	$-0.985151\pi$
$157$		−	14.6424i		−	0.0932635i	0.998912	−	0.0466317i	$-0.0148487\pi$
$158$	39.0538	−	75.9550i	0.247176	−	0.480728i
$159$		0			0
$160$	−88.0514	−	91.3536i	−0.550321	−	0.570960i
$161$	139.105			0.864005
$162$		0			0
$163$	−21.2465			−0.130347			−0.0651735	−	0.997874i	$-0.520760\pi$
$163$	−21.2465			−0.130347			−0.0651735	+	0.997874i	$0.520760\pi$
$164$	−124.871	−	174.559i	−0.761410	−	1.06438i
$165$		0			0
$166$	0.117537	+	0.0604342i	0.000708055	+	0.000364061i
$167$		−	136.229i		−	0.815742i	−0.913040	−	0.407871i	$-0.866271\pi$
$167$		−	136.229i		−	0.815742i	0.913040	−	0.407871i	$-0.133729\pi$
$168$		0			0
$169$	56.6870			0.335426
$170$	28.6949	−	55.8082i	0.168794	−	0.328283i
$171$		0			0
$172$	−14.7531	−	20.6234i	−0.0857737	−	0.119904i
$173$		−	153.897i		−	0.889578i	−0.895635	−	0.444789i	$-0.853279\pi$
$173$		−	153.897i		−	0.889578i	0.895635	−	0.444789i	$-0.146721\pi$
$174$		0			0
$175$			37.1046i			0.212027i
$176$	−48.2772	+	141.460i	−0.274302	+	0.803752i
$177$		0			0
$178$	175.155	+	90.0596i	0.984017	+	0.505953i
$179$	−51.3178			−0.286692			−0.143346	−	0.989673i	$-0.545786\pi$
$179$	−51.3178			−0.286692			−0.143346	+	0.989673i	$0.545786\pi$
$180$		0			0
$181$			250.171i			1.38216i	0.722778	+	0.691080i	$0.242865\pi$
$181$			250.171i			1.38216i	−0.722778	+	0.691080i	$0.757135\pi$
$182$	−75.3781	−	38.7572i	−0.414165	−	0.212952i
$183$		0			0
$184$	−275.326	+	40.4961i	−1.49634	+	0.220088i
$185$	−225.354			−1.21813
$186$		0			0
$187$	−73.9265			−0.395329
$188$	12.5062	−	8.94640i	0.0665226	−	0.0475872i
$189$		0			0
$190$	−78.6894	+	153.041i	−0.414155	+	0.805481i
$191$			205.438i			1.07559i	0.843075	+	0.537796i	$0.180743\pi$
$191$			205.438i			1.07559i	−0.843075	+	0.537796i	$0.819257\pi$
$192$		0			0
$193$	−150.544			−0.780021			−0.390010	−	0.920810i	$-0.627529\pi$
$193$	−150.544			−0.780021			−0.390010	+	0.920810i	$0.627529\pi$
$194$	281.614	+	144.797i	1.45162	+	0.746378i
$195$		0			0
$196$	76.8204	+	107.388i	0.391941	+	0.547897i
$197$		−	155.166i		−	0.787646i	−0.919186	−	0.393823i	$-0.871152\pi$
$197$		−	155.166i		−	0.787646i	0.919186	−	0.393823i	$-0.128848\pi$
$198$		0			0
$199$		−	213.248i		−	1.07160i	−0.844345	−	0.535800i	$-0.820010\pi$
$199$		−	213.248i		−	1.07160i	0.844345	−	0.535800i	$-0.179990\pi$
$200$	−10.8019	−	73.4401i	−0.0540094	−	0.367200i
$201$		0			0
$202$	26.0252	−	50.6159i	0.128838	−	0.250574i
$203$	33.5077			0.165062
$204$		0			0
$205$			212.746i			1.03779i
$206$	92.5009	−	179.903i	0.449033	−	0.873316i
$207$		0			0
$208$	160.477	+	54.7669i	0.771522	+	0.263302i
$209$	202.727			0.969985
$210$		0			0
$211$	85.3675			0.404585			0.202293	−	0.979325i	$-0.435161\pi$
$211$	85.3675			0.404585			0.202293	+	0.979325i	$0.435161\pi$
$212$	−333.131	+	238.307i	−1.57137	+	1.12409i
$213$		0			0
$214$	−94.6663	−	48.6746i	−0.442366	−	0.227452i
$215$			25.1352i			0.116908i
$216$		0			0
$217$	197.565			0.910436
$218$	−62.7942	+	122.127i	−0.288047	+	0.560217i
$219$		0			0
$220$	120.505	−	86.2036i	0.547749	−	0.391835i
$221$			83.8643i			0.379476i
$222$		0			0
$223$		−	22.7092i		−	0.101835i	−0.998703	−	0.0509174i	$-0.983785\pi$
$223$		−	22.7092i		−	0.101835i	0.998703	−	0.0509174i	$-0.0162145\pi$
$224$	88.8036	+	92.1340i	0.396445	+	0.411313i
$225$		0			0
$226$	311.983	+	160.413i	1.38046	+	0.709790i
$227$	−265.827			−1.17104			−0.585522	−	0.810657i	$-0.699110\pi$
$227$	−265.827			−1.17104			−0.585522	+	0.810657i	$0.699110\pi$
$228$		0			0
$229$		−	192.325i		−	0.839849i	−0.907559	−	0.419924i	$-0.862057\pi$
$229$		−	192.325i		−	0.839849i	0.907559	−	0.419924i	$-0.137943\pi$
$230$	245.324	+	126.139i	1.06663	+	0.548428i
$231$		0			0
$232$	−66.3207	+	9.75473i	−0.285865	+	0.0420463i
$233$	211.594			0.908130			0.454065	−	0.890969i	$-0.349973\pi$
$233$	211.594			0.908130			0.454065	+	0.890969i	$0.349973\pi$
$234$		0			0
$235$	−15.2422			−0.0648604
$236$	271.350	+	379.322i	1.14979	+	1.60730i
$237$		0			0
$238$	−28.9400	+	56.2849i	−0.121597	+	0.236491i
$239$			409.927i			1.71518i	0.514337	+	0.857588i	$0.328038\pi$
$239$			409.927i			1.71518i	−0.514337	+	0.857588i	$0.671962\pi$
$240$		0			0
$241$	−82.9801			−0.344316			−0.172158	−	0.985069i	$-0.555074\pi$
$241$	−82.9801			−0.344316			−0.172158	+	0.985069i	$0.555074\pi$
$242$	59.9899	+	30.8450i	0.247892	+	0.127459i
$243$		0			0
$244$	−186.902	+	133.702i	−0.765994	+	0.547957i
$245$		−	130.881i		−	0.534207i
$246$		0			0
$247$		−	229.979i		−	0.931089i
$248$	−391.034	+	57.5149i	−1.57675	+	0.231915i
$249$		0			0
$250$	−124.299	+	241.747i	−0.497197	+	0.966988i
$251$	−338.898			−1.35019			−0.675096	−	0.737730i	$-0.735898\pi$
$251$	−338.898			−1.35019			−0.675096	+	0.737730i	$0.735898\pi$
$252$		0			0
$253$		−	324.970i		−	1.28447i
$254$	−43.6074	+	84.8111i	−0.171683	+	0.333902i
$255$		0			0
$256$	−202.588	−	156.506i	−0.791361	−	0.611350i
$257$	23.8623			0.0928494			0.0464247	−	0.998922i	$-0.485217\pi$
$257$	23.8623			0.0928494			0.0464247	+	0.998922i	$0.485217\pi$
$258$		0			0
$259$	227.279			0.877527
$260$	−97.7917	−	136.704i	−0.376122	−	0.525784i
$261$		0			0
$262$	−325.458	−	167.341i	−1.24220	−	0.638705i
$263$			427.158i			1.62418i	0.583535	+	0.812088i	$0.301669\pi$
$263$			427.158i			1.62418i	−0.583535	+	0.812088i	$0.698331\pi$
$264$		0			0
$265$	406.009			1.53211
$266$	79.3616	−	154.349i	0.298352	−	0.580259i
$267$		0			0
$268$	30.7108	+	42.9309i	0.114593	+	0.160190i
$269$			86.4100i			0.321227i	0.987017	+	0.160613i	$0.0513472\pi$
$269$			86.4100i			0.321227i	−0.987017	+	0.160613i	$0.948653\pi$
$270$		0			0
$271$			212.810i			0.785276i	0.919693	+	0.392638i	$0.128438\pi$
$271$			212.810i			0.785276i	−0.919693	+	0.392638i	$0.871562\pi$
$272$	40.8945	−	119.828i	0.150347	−	0.440544i
$273$		0			0
$274$	−365.441	−	187.899i	−1.33373	−	0.685763i
$275$	86.6821			0.315207
$276$		0			0
$277$		−	393.646i		−	1.42111i	−0.703644	−	0.710553i	$-0.748445\pi$
$277$		−	393.646i		−	1.42111i	0.703644	−	0.710553i	$-0.251555\pi$
$278$	36.3995	+	18.7156i	0.130934	+	0.0673222i
$279$		0			0
$280$	−18.4582	−	125.494i	−0.0659221	−	0.448193i
$281$	366.040			1.30263			0.651317	−	0.758805i	$-0.274217\pi$
$281$	366.040			1.30263			0.651317	+	0.758805i	$0.274217\pi$
$282$		0			0
$283$	−134.793			−0.476302			−0.238151	−	0.971228i	$-0.576541\pi$
$283$	−134.793			−0.476302			−0.238151	+	0.971228i	$0.576541\pi$
$284$	−157.715	+	112.822i	−0.555334	+	0.397260i
$285$		0			0
$286$	−90.5427	+	176.095i	−0.316583	+	0.615716i
$287$		−	214.564i		−	0.747609i
$288$		0			0
$289$	−226.378			−0.783317
$290$	59.0939	+	30.3843i	0.203772	+	0.104774i
$291$		0			0
$292$	137.356	+	192.011i	0.470398	+	0.657573i
$293$			313.916i			1.07139i	0.844413	+	0.535693i	$0.179950\pi$
$293$			313.916i			1.07139i	−0.844413	+	0.535693i	$0.820050\pi$
$294$		0			0
$295$		−	462.305i		−	1.56714i
$296$	−449.847	+	66.1654i	−1.51975	+	0.223532i
$297$		0			0
$298$	141.155	−	274.529i	0.473674	−	0.921239i
$299$	−368.655			−1.23296
$300$		0			0
$301$		−	25.3499i		−	0.0842189i
$302$	227.099	−	441.679i	0.751982	−	1.46251i
$303$		0			0
$304$	−112.144	+	328.601i	−0.368895	+	1.08093i
$305$	227.791			0.746854
$306$		0			0
$307$	64.3520			0.209616			0.104808	−	0.994492i	$-0.466577\pi$
$307$	64.3520			0.209616			0.104808	+	0.994492i	$0.466577\pi$
$308$	−121.534	+	86.9401i	−0.394592	+	0.282273i
$309$		0			0
$310$	348.424	+	179.149i	1.12395	+	0.577901i
$311$		−	277.179i		−	0.891250i	−0.895220	−	0.445625i	$-0.852981\pi$
$311$		−	277.179i		−	0.891250i	0.895220	−	0.445625i	$-0.147019\pi$
$312$		0			0
$313$	307.148			0.981304			0.490652	−	0.871356i	$-0.336759\pi$
$313$	307.148			0.981304			0.490652	+	0.871356i	$0.336759\pi$
$314$	−13.3909	+	26.0438i	−0.0426463	+	0.0829419i
$315$		0			0
$316$	−138.927	+	99.3820i	−0.439642	+	0.314500i
$317$		−	156.586i		−	0.493961i	−0.969020	−	0.246980i	$-0.920562\pi$
$317$		−	156.586i		−	0.493961i	0.969020	−	0.246980i	$-0.0794383\pi$
$318$		0			0
$319$		−	78.2790i		−	0.245389i
$320$	73.0675	+	243.013i	0.228336	+	0.759415i
$321$		0			0
$322$	−247.420	−	127.216i	−0.768385	−	0.395081i
$323$	−171.726			−0.531658
$324$		0			0
$325$		−	98.3345i		−	0.302568i
$326$	37.7904	+	19.4307i	0.115921	+	0.0596034i
$327$		0			0
$328$	62.4636	+	424.679i	0.190438	+	1.29475i
$329$	15.3724			0.0467246
$330$		0			0
$331$	432.746			1.30739			0.653694	−	0.756759i	$-0.273218\pi$
$331$	432.746			1.30739			0.653694	+	0.756759i	$0.273218\pi$
$332$	−0.153789	−	0.214984i	−0.000463221	−	0.000647541i
$333$		0			0
$334$	−124.586	+	242.305i	−0.373012	+	0.725463i
$335$		−	52.3227i		−	0.156187i
$336$		0			0
$337$	−441.102			−1.30891			−0.654453	−	0.756102i	$-0.727101\pi$
$337$	−441.102			−1.30891			−0.654453	+	0.756102i	$0.727101\pi$
$338$	−100.827	−	51.8422i	−0.298304	−	0.153379i
$339$		0			0
$340$	−102.077	+	73.0212i	−0.300226	+	0.214768i
$341$		−	461.541i		−	1.35349i
$342$		0			0
$343$			327.944i			0.956104i
$344$	7.37985	+	50.1743i	0.0214530	+	0.145855i
$345$		0			0
$346$	−140.744	+	273.730i	−0.406775	+	0.791128i
$347$	218.815			0.630590			0.315295	−	0.948994i	$-0.397897\pi$
$347$	218.815			0.630590			0.315295	+	0.948994i	$0.397897\pi$
$348$		0			0
$349$		−	283.258i		−	0.811627i	−0.913956	−	0.405814i	$-0.866988\pi$
$349$		−	283.258i		−	0.811627i	0.913956	−	0.405814i	$-0.133012\pi$
$350$	33.9335	−	65.9965i	0.0969527	−	0.188561i
$351$		0			0
$352$	215.239	−	207.459i	0.611474	−	0.589371i
$353$	254.001			0.719550			0.359775	−	0.933039i	$-0.382854\pi$
$353$	254.001			0.719550			0.359775	+	0.933039i	$0.382854\pi$
$354$		0			0
$355$	192.217			0.541458
$356$	−229.178	−	320.370i	−0.643760	−	0.899917i
$357$		0			0
$358$	91.2769	+	46.9319i	0.254963	+	0.131095i
$359$			671.569i			1.87067i	0.353767	+	0.935334i	$0.384901\pi$
$359$			671.569i			1.87067i	−0.353767	+	0.935334i	$0.615099\pi$
$360$		0			0
$361$	109.919			0.304484
$362$	228.790	−	444.969i	0.632016	−	1.22920i
$363$		0			0
$364$	98.6272	+	137.872i	0.270954	+	0.378768i
$365$		−	234.017i		−	0.641142i
$366$		0			0
$367$		−	136.412i		−	0.371695i	−0.982579	−	0.185848i	$-0.940497\pi$
$367$		−	136.412i		−	0.371695i	0.982579	−	0.185848i	$-0.0595031\pi$
$368$	526.746	+	179.766i	1.43137	+	0.488495i
$369$		0			0
$370$	400.828	+	206.094i	1.08332	+	0.557011i
$371$	−409.477			−1.10371
$372$		0			0
$373$			423.788i			1.13616i	0.822973	+	0.568080i	$0.192314\pi$
$373$			423.788i			1.13616i	−0.822973	+	0.568080i	$0.807686\pi$
$374$	131.490	+	67.6083i	0.351578	+	0.180771i
$375$		0			0
$376$	−30.4261	+	4.47521i	−0.0809206	+	0.0119021i
$377$	−88.8018			−0.235549
$378$		0			0
$379$	45.0699			0.118918			0.0594590	−	0.998231i	$-0.481062\pi$
$379$	45.0699			0.118918			0.0594590	+	0.998231i	$0.481062\pi$
$380$	279.923	−	200.244i	0.736640	−	0.526959i
$381$		0			0
$382$	187.880	−	365.404i	0.491833	−	0.956555i
$383$		−	457.737i		−	1.19514i	−0.801818	−	0.597568i	$-0.796134\pi$
$383$		−	457.737i		−	1.19514i	0.801818	−	0.597568i	$-0.203866\pi$
$384$		0			0
$385$	148.122			0.384732
$386$	267.766	+	137.678i	0.693695	+	0.356678i
$387$		0			0
$388$	−368.472	−	515.090i	−0.949671	−	1.32755i
$389$		−	381.756i		−	0.981378i	−0.871335	−	0.490689i	$-0.836745\pi$
$389$		−	381.756i		−	0.981378i	0.871335	−	0.490689i	$-0.163255\pi$
$390$		0			0
$391$			275.275i			0.704028i
$392$	−38.4274	−	261.261i	−0.0980291	−	0.666483i
$393$		0			0
$394$	−141.905	+	275.988i	−0.360165	+	0.700477i
$395$	169.319			0.428657
$396$		0			0
$397$			545.379i			1.37375i	0.726776	+	0.686875i	$0.241018\pi$
$397$			545.379i			1.37375i	−0.726776	+	0.686875i	$0.758982\pi$
$398$	−195.023	+	379.296i	−0.490007	+	0.953005i
$399$		0			0
$400$	−47.9506	+	140.504i	−0.119876	+	0.351259i
$401$	−179.265			−0.447046			−0.223523	−	0.974699i	$-0.571756\pi$
$401$	−179.265			−0.447046			−0.223523	+	0.974699i	$0.571756\pi$
$402$		0			0
$403$	−523.585			−1.29922
$404$	−92.5799	+	66.2274i	−0.229158	+	0.163929i
$405$		0			0
$406$	−59.5987	−	30.6439i	−0.146795	−	0.0754776i
$407$		−	530.959i		−	1.30457i
$408$		0			0
$409$	615.477			1.50483			0.752416	−	0.658688i	$-0.228888\pi$
$409$	615.477			1.50483			0.752416	+	0.658688i	$0.228888\pi$
$410$	194.564	−	378.403i	0.474545	−	0.922934i
$411$		0			0
$412$	−329.055	+	235.391i	−0.798677	+	0.571337i
$413$			466.255i			1.12895i
$414$		0			0
$415$			0.262015i			0.000631361i
$416$	−235.347	−	244.173i	−0.565738	−	0.586954i
$417$		0			0
$418$	−360.582	−	185.401i	−0.862637	−	0.443542i
$419$	−16.1689			−0.0385892			−0.0192946	−	0.999814i	$-0.506142\pi$
$419$	−16.1689			−0.0385892			−0.0192946	+	0.999814i	$0.506142\pi$
$420$		0			0
$421$		−	348.118i		−	0.826884i	−0.910530	−	0.413442i	$-0.864326\pi$
$421$		−	348.118i		−	0.826884i	0.910530	−	0.413442i	$-0.135674\pi$
$422$	−151.840	−	78.0715i	−0.359810	−	0.185004i
$423$		0			0
$424$	810.466	−	119.207i	1.91148	−	0.281148i
$425$	−73.4264			−0.172768
$426$		0			0
$427$	−229.736			−0.538025
$428$	123.864	+	173.151i	0.289403	+	0.404559i
$429$		0			0
$430$	22.9870	−	44.7069i	0.0534581	−	0.103970i
$431$			75.7186i			0.175681i	0.996135	+	0.0878406i	$0.0279966\pi$
$431$			75.7186i			0.175681i	−0.996135	+	0.0878406i	$0.972003\pi$
$432$		0			0
$433$	−780.624			−1.80283			−0.901413	−	0.432959i	$-0.857469\pi$
$433$	−780.624			−1.80283			−0.901413	+	0.432959i	$0.857469\pi$
$434$	−351.400	−	180.680i	−0.809678	−	0.416313i
$435$		0			0
$436$	223.379	−	159.795i	0.512337	−	0.366503i
$437$		−	754.879i		−	1.72741i
$438$		0			0
$439$		−	497.817i		−	1.13398i	−0.823725	−	0.566990i	$-0.808108\pi$
$439$		−	497.817i		−	1.13398i	0.823725	−	0.566990i	$-0.191892\pi$
$440$	−293.173	+	43.1211i	−0.666302	+	0.0980026i
$441$		0			0
$442$	76.6967	−	149.166i	0.173522	−	0.337479i
$443$	560.547			1.26534			0.632672	−	0.774420i	$-0.281958\pi$
$443$	560.547			1.26534			0.632672	+	0.774420i	$0.281958\pi$
$444$		0			0
$445$			390.457i			0.877431i
$446$	−20.7683	+	40.3918i	−0.0465657	+	0.0905647i
$447$		0			0
$448$	−73.6917	−	245.089i	−0.164490	−	0.547074i
$449$	−205.720			−0.458174			−0.229087	−	0.973406i	$-0.573574\pi$
$449$	−205.720			−0.458174			−0.229087	+	0.973406i	$0.573574\pi$
$450$		0			0
$451$	−501.253			−1.11143
$452$	−408.209	−	570.638i	−0.903117	−	1.26247i
$453$		0			0
$454$	472.815	+	243.108i	1.04144	+	0.535480i
$455$		−	168.033i		−	0.369304i
$456$		0			0
$457$	342.213			0.748825			0.374412	−	0.927262i	$-0.377844\pi$
$457$	342.213			0.748825			0.374412	+	0.927262i	$0.377844\pi$
$458$	−175.888	+	342.081i	−0.384035	+	0.746902i
$459$		0			0
$460$	−320.990	−	448.715i	−0.697805	−	0.975467i
$461$			487.624i			1.05775i	0.848699	+	0.528876i	$0.177386\pi$
$461$			487.624i			1.05775i	−0.848699	+	0.528876i	$0.822614\pi$
$462$		0			0
$463$			125.770i			0.271642i	0.990733	+	0.135821i	$0.0433672\pi$
$463$			125.770i			0.271642i	−0.990733	+	0.135821i	$0.956633\pi$
$464$	126.883	+	43.3022i	0.273455	+	0.0933237i
$465$		0			0
$466$	−376.354	−	193.510i	−0.807627	−	0.415258i
$467$	128.189			0.274495			0.137248	−	0.990537i	$-0.456174\pi$
$467$	128.189			0.274495			0.137248	+	0.990537i	$0.456174\pi$
$468$		0			0
$469$			52.7697i			0.112515i
$470$	27.1107	+	13.9395i	0.0576823	+	0.0296585i
$471$		0			0
$472$	−135.736	−	922.843i	−0.287576	−	1.95518i
$473$	−59.2212			−0.125203
$474$		0			0
$475$	201.356			0.423907
$476$	102.949	−	73.6450i	0.216279	−	0.154716i
$477$		0			0
$478$	374.892	−	729.120i	0.784293	−	1.52536i
$479$			334.403i			0.698126i	0.937099	+	0.349063i	$0.113500\pi$
$479$			334.403i			0.698126i	−0.937099	+	0.349063i	$0.886500\pi$
$480$		0			0
$481$	−602.334			−1.25225
$482$	147.593	+	75.8881i	0.306210	+	0.157444i
$483$		0			0
$484$	−78.4927	−	109.726i	−0.162175	−	0.226706i
$485$			627.775i			1.29438i
$486$		0			0
$487$			501.139i			1.02903i	0.857480	+	0.514517i	$0.172029\pi$
$487$			501.139i			1.02903i	−0.857480	+	0.514517i	$0.827971\pi$
$488$	454.710	−	66.8807i	0.931783	−	0.137051i
$489$		0			0
$490$	−119.695	+	232.792i	−0.244275	+	0.475086i
$491$	−46.0833			−0.0938561			−0.0469280	−	0.998898i	$-0.514943\pi$
$491$	−46.0833			−0.0938561			−0.0469280	+	0.998898i	$0.514943\pi$
$492$		0			0
$493$			66.3084i			0.134500i
$494$	−210.324	+	409.054i	−0.425756	+	0.828045i
$495$		0			0
$496$	748.115	+	255.314i	1.50830	+	0.514746i
$497$	−193.860			−0.390059
$498$		0			0
$499$	0.336941			0.000675232			0.000337616	−	1.00000i	$-0.499893\pi$
$499$	0.336941			0.000675232			0.000337616		1.00000i	$0.499893\pi$
$500$	442.172	−	316.310i	0.884344	−	0.632619i
$501$		0			0
$502$	602.784	+	309.934i	1.20077	+	0.617398i
$503$			2.30508i			0.00458267i	0.999997	+	0.00229133i	$0.000729355\pi$
$503$			2.30508i			0.00458267i	−0.999997	+	0.00229133i	$0.999271\pi$
$504$		0			0
$505$	112.833			0.223432
$506$	−297.196	+	578.011i	−0.587344	+	1.14231i
$507$		0			0
$508$	155.125	−	110.970i	0.305365	−	0.218444i
$509$			537.175i			1.05535i	0.849445	+	0.527677i	$0.176937\pi$
$509$			537.175i			1.05535i	−0.849445	+	0.527677i	$0.823063\pi$
$510$		0			0
$511$			236.016i			0.461871i
$512$	217.206	+	463.644i	0.424230	+	0.905554i
$513$		0			0
$514$	−42.4429	−	21.8229i	−0.0825737	−	0.0424570i
$515$	401.041			0.778721
$516$		0			0
$517$		−	35.9123i		−	0.0694628i
$518$	−404.253	−	207.855i	−0.780410	−	0.401264i
$519$		0			0
$520$	48.9178	+	332.583i	0.0940727	+	0.639584i
$521$	−7.91338			−0.0151888			−0.00759441	−	0.999971i	$-0.502417\pi$
$521$	−7.91338			−0.0151888			−0.00759441	+	0.999971i	$0.502417\pi$
$522$		0			0
$523$	−150.834			−0.288402			−0.144201	−	0.989548i	$-0.546061\pi$
$523$	−150.834			−0.288402			−0.144201	+	0.989548i	$0.546061\pi$
$524$	425.839	+	595.284i	0.812670	+	1.13604i
$525$		0			0
$526$	390.651	−	759.769i	0.742682	−	1.44443i
$527$			390.961i			0.741862i
$528$		0			0
$529$	−681.066			−1.28746
$530$	−722.151	−	371.309i	−1.36255	−	0.700583i
$531$		0			0
$532$	−282.314	+	201.955i	−0.530666	+	0.379615i
$533$			568.635i			1.06686i
$534$		0			0
$535$		−	211.031i		−	0.394450i
$536$	−15.3623	−	104.445i	−0.0286610	−	0.194861i
$537$		0			0
$538$	79.0248	−	153.694i	0.146886	−	0.285676i
$539$	308.369			0.572114
$540$		0			0
$541$			456.143i			0.843147i	0.906794	+	0.421574i	$0.138522\pi$
$541$			456.143i			0.843147i	−0.906794	+	0.421574i	$0.861478\pi$
$542$	194.622	−	378.516i	0.359081	−	0.698369i
$543$		0			0
$544$	−182.324	+	175.734i	−0.335155	+	0.323040i
$545$	−272.247			−0.499536
$546$		0			0
$547$	374.226			0.684143			0.342072	−	0.939674i	$-0.388871\pi$
$547$	374.226			0.684143			0.342072	+	0.939674i	$0.388871\pi$
$548$	478.155	+	668.416i	0.872545	+	1.21974i
$549$		0			0
$550$	−154.178	−	79.2737i	−0.280323	−	0.144134i
$551$		−	181.836i		−	0.330011i
$552$		0			0
$553$	−170.766			−0.308799
$554$	−360.003	+	700.162i	−0.649825	+	1.26383i
$555$		0			0
$556$	−47.6263	−	66.5772i	−0.0856588	−	0.119743i
$557$		−	114.236i		−	0.205092i	−0.994728	−	0.102546i	$-0.967301\pi$
$557$		−	114.236i		−	0.205092i	0.994728	−	0.102546i	$-0.0326989\pi$
$558$		0			0
$559$			67.1821i			0.120183i
$560$	−81.9377	+	240.092i	−0.146317	+	0.428735i
$561$		0			0
$562$	−651.061	−	334.756i	−1.15847	−	0.595652i
$563$	265.744			0.472014			0.236007	−	0.971751i	$-0.424161\pi$
$563$	265.744			0.472014			0.236007	+	0.971751i	$0.424161\pi$
$564$		0			0
$565$			695.475i			1.23093i
$566$	239.751	+	123.273i	0.423589	+	0.217797i
$567$		0			0
$568$	383.700	−	56.4363i	0.675529	−	0.0993596i
$569$	−781.311			−1.37313			−0.686565	−	0.727068i	$-0.740882\pi$
$569$	−781.311			−1.37313			−0.686565	+	0.727068i	$0.740882\pi$
$570$		0			0
$571$	−686.910			−1.20299			−0.601497	−	0.798875i	$-0.705429\pi$
$571$	−686.910			−1.20299			−0.601497	+	0.798875i	$0.705429\pi$
$572$	322.089	−	230.408i	0.563093	−	0.402811i
$573$		0			0
$574$	−196.226	+	381.636i	−0.341857	+	0.664870i
$575$		−	322.772i		−	0.561342i
$576$		0			0
$577$	−101.260			−0.175495			−0.0877473	−	0.996143i	$-0.527967\pi$
$577$	−101.260			−0.175495			−0.0877473	+	0.996143i	$0.527967\pi$
$578$	402.650	+	207.031i	0.696626	+	0.358185i
$579$		0			0
$580$	−77.3203	−	108.087i	−0.133311	−	0.186356i
$581$		−	0.264253i		−	0.000454825i
$582$		0			0
$583$			956.601i			1.64083i
$584$	−68.7089	−	467.140i	−0.117652	−	0.799896i
$585$		0			0
$586$	287.087	−	558.350i	0.489910	−	0.952816i
$587$	280.875			0.478492			0.239246	−	0.970959i	$-0.423100\pi$
$587$	280.875			0.478492			0.239246	+	0.970959i	$0.423100\pi$
$588$		0			0
$589$		−	1072.12i		−	1.82024i
$590$	−422.794	+	822.283i	−0.716600	+	1.39370i
$591$		0			0
$592$	860.635	+	293.715i	1.45378	+	0.496140i
$593$	−1072.58			−1.80873			−0.904364	−	0.426762i	$-0.859654\pi$
$593$	−1072.58			−1.80873			−0.904364	+	0.426762i	$0.859654\pi$
$594$		0			0
$595$	−125.471			−0.210875
$596$	−502.133	+	359.203i	−0.842505	+	0.602690i
$597$		0			0
$598$	655.711	+	337.147i	1.09651	+	0.563791i
$599$		−	410.885i		−	0.685952i	−0.939344	−	0.342976i	$-0.888565\pi$
$599$		−	410.885i		−	0.685952i	0.939344	−	0.342976i	$-0.111435\pi$
$600$		0			0
$601$	736.381			1.22526			0.612630	−	0.790370i	$-0.290112\pi$
$601$	736.381			1.22526			0.612630	+	0.790370i	$0.290112\pi$
$602$	−23.1833	+	45.0888i	−0.0385105	+	0.0748984i
$603$		0			0
$604$	−807.862	+	577.908i	−1.33752	+	0.956801i
$605$			133.730i			0.221041i
$606$		0			0
$607$			959.941i			1.58145i	0.612171	+	0.790726i	$0.290297\pi$
$607$			959.941i			1.58145i	−0.612171	+	0.790726i	$0.709703\pi$
$608$	499.983	−	481.910i	0.822341	−	0.792616i
$609$		0			0
$610$	−405.162	−	208.322i	−0.664199	−	0.341512i
$611$	−40.7398			−0.0666773
$612$		0			0
$613$			623.891i			1.01777i	0.860835	+	0.508884i	$0.169942\pi$
$613$			623.891i			1.01777i	−0.860835	+	0.508884i	$0.830058\pi$
$614$	−114.460	−	58.8521i	−0.186417	−	0.0958503i
$615$		0			0
$616$	295.678	−	43.4895i	0.479996	−	0.0705999i
$617$	35.1377			0.0569493			0.0284746	−	0.999595i	$-0.490935\pi$
$617$	35.1377			0.0569493			0.0284746	+	0.999595i	$0.490935\pi$
$618$		0			0
$619$	561.712			0.907451			0.453725	−	0.891142i	$-0.350095\pi$
$619$	561.712			0.907451			0.453725	+	0.891142i	$0.350095\pi$
$620$	−455.889	−	637.291i	−0.735304	−	1.02789i
$621$		0			0
$622$	−253.489	+	493.007i	−0.407539	+	0.792615i
$623$		−	393.793i		−	0.632091i
$624$		0			0
$625$	−306.935			−0.491096
$626$	−546.312	−	280.898i	−0.872703	−	0.448718i
$627$		0			0
$628$	47.6358	−	34.0765i	0.0758532	−	0.0542620i
$629$			449.764i			0.715046i
$630$		0			0
$631$		−	32.1547i		−	0.0509583i	−0.999675	−	0.0254792i	$-0.991889\pi$
$631$		−	32.1547i		−	0.0509583i	0.999675	−	0.0254792i	$-0.00811114\pi$
$632$	337.992	−	49.7133i	0.534797	−	0.0786602i
$633$		0			0
$634$	−143.203	+	278.512i	−0.225872	+	0.439294i
$635$	−189.062			−0.297735
$636$		0			0
$637$		−	349.822i		−	0.549172i
$638$	−71.5888	+	139.232i	−0.112208	+	0.218231i
$639$		0			0
$640$	92.2814	−	499.060i	0.144190	−	0.779781i
$641$	−245.142			−0.382436			−0.191218	−	0.981548i	$-0.561244\pi$
$641$	−245.142			−0.382436			−0.191218	+	0.981548i	$0.561244\pi$
$642$		0			0
$643$	1154.12			1.79490			0.897450	−	0.441115i	$-0.145417\pi$
$643$	1154.12			1.79490			0.897450	+	0.441115i	$0.145417\pi$
$644$	323.732	+	452.548i	0.502690	+	0.702714i
$645$		0			0
$646$	305.441	+	157.049i	0.472819	+	0.243110i
$647$		−	222.626i		−	0.344090i	−0.985089	−	0.172045i	$-0.944963\pi$
$647$		−	222.626i		−	0.344090i	0.985089	−	0.172045i	$-0.0550374\pi$
$648$		0			0
$649$	1089.24			1.67834
$650$	−89.9302	+	174.903i	−0.138354	+	0.269082i
$651$		0			0
$652$	−49.4461	−	69.1212i	−0.0758376	−	0.106014i
$653$			403.267i			0.617561i	0.951133	+	0.308780i	$0.0999208\pi$
$653$			403.267i			0.617561i	−0.951133	+	0.308780i	$0.900079\pi$
$654$		0			0
$655$		−	725.512i		−	1.10765i
$656$	277.282	−	812.485i	0.422686	−	1.23854i
$657$		0			0
$658$	−27.3423	−	14.0586i	−0.0415536	−	0.0213656i
$659$	964.023			1.46286			0.731429	−	0.681918i	$-0.238854\pi$
$659$	964.023			1.46286			0.731429	+	0.681918i	$0.238854\pi$
$660$		0			0
$661$		−	100.164i		−	0.151534i	−0.997126	−	0.0757670i	$-0.975859\pi$
$661$		−	100.164i		−	0.151534i	0.997126	−	0.0757670i	$-0.0241405\pi$
$662$	−769.707	−	395.761i	−1.16270	−	0.597826i
$663$		0			0
$664$	0.0769292	+	0.523028i	0.000115857	+	0.000787693i
$665$	344.075			0.517407
$666$		0			0
$667$	−291.482			−0.437004
$668$	443.192	−	317.039i	0.663461	−	0.474610i
$669$		0			0
$670$	−47.8509	+	93.0643i	−0.0714193	+	0.138902i
$671$			536.699i			0.799850i
$672$		0			0
$673$	−1008.38			−1.49834			−0.749169	−	0.662378i	$-0.769547\pi$
$673$	−1008.38			−1.49834			−0.749169	+	0.662378i	$0.769547\pi$
$674$	784.569	+	403.402i	1.16405	+	0.598520i
$675$		0			0
$676$	131.925	+	184.419i	0.195155	+	0.272809i
$677$		−	591.740i		−	0.874063i	−0.899446	−	0.437031i	$-0.856030\pi$
$677$		−	591.740i		−	0.874063i	0.899446	−	0.437031i	$-0.143970\pi$
$678$		0			0
$679$		−	633.138i		−	0.932457i
$680$	248.340	−	36.5270i	0.365206	−	0.0537161i
$681$		0			0
$682$	−422.095	+	820.924i	−0.618907	+	1.20370i
$683$	631.871			0.925141			0.462570	−	0.886583i	$-0.346927\pi$
$683$	631.871			0.925141			0.462570	+	0.886583i	$0.346927\pi$
$684$		0			0
$685$		−	814.644i		−	1.18926i
$686$	299.916	−	583.300i	0.437195	−	0.850291i
$687$		0			0
$688$	32.7598	−	95.9920i	0.0476161	−	0.139523i
$689$	1085.19			1.57503
$690$		0			0
$691$	−1271.28			−1.83977			−0.919886	−	0.392185i	$-0.871719\pi$
$691$	−1271.28			−1.83977			−0.919886	+	0.392185i	$0.871719\pi$
$692$	500.671	−	358.157i	0.723513	−	0.517569i
$693$		0			0
$694$	−389.197	−	200.114i	−0.560802	−	0.288348i
$695$			81.1421i			0.116751i
$696$		0			0
$697$	424.600			0.609183
$698$	−259.049	+	503.819i	−0.371130	+	0.721804i
$699$		0			0
$700$	−120.712	+	86.3520i	−0.172446	+	0.123360i
$701$		−	712.466i		−	1.01636i	−0.861252	−	0.508178i	$-0.830319\pi$
$701$		−	712.466i		−	1.01636i	0.861252	−	0.508178i	$-0.169681\pi$
$702$		0			0
$703$		−	1233.38i		−	1.75445i
$704$	−572.565	+	172.155i	−0.813302	+	0.244538i
$705$		0			0
$706$	−451.781	−	232.293i	−0.639917	−	0.329026i
$707$	−113.797			−0.160958
$708$		0			0
$709$		−	319.606i		−	0.450785i	−0.974268	−	0.225392i	$-0.927634\pi$
$709$		−	319.606i		−	0.450785i	0.974268	−	0.225392i	$-0.0723664\pi$
$710$	−341.889	−	175.789i	−0.481534	−	0.247591i
$711$		0			0
$712$	114.641	+	779.421i	0.161012	+	1.09469i
$713$	−1718.61			−2.41039
$714$		0			0
$715$	−392.552			−0.549023
$716$	−119.430	−	166.952i	−0.166801	−	0.233173i
$717$		0			0
$718$	614.173	−	1194.49i	0.855394	−	1.66364i
$719$		−	852.410i		−	1.18555i	−0.805368	−	0.592775i	$-0.798033\pi$
$719$		−	852.410i		−	1.18555i	0.805368	−	0.592775i	$-0.201967\pi$
$720$		0			0
$721$	−404.467			−0.560981
$722$	−195.508	−	100.524i	−0.270787	−	0.139231i
$723$		0			0
$724$	−813.878	+	582.211i	−1.12414	+	0.804160i
$725$		−	77.7495i		−	0.107241i
$726$		0			0
$727$			88.5412i			0.121790i	0.998144	+	0.0608949i	$0.0193955\pi$
$727$			88.5412i			0.121790i	−0.998144	+	0.0608949i	$0.980605\pi$
$728$	−49.3357	−	335.425i	−0.0677688	−	0.460748i
$729$		0			0
$730$	−214.017	+	416.236i	−0.293173	+	0.570187i
$731$	50.1650			0.0686251
$732$		0			0
$733$			609.319i			0.831268i	0.909532	+	0.415634i	$0.136440\pi$
$733$			609.319i			0.831268i	−0.909532	+	0.415634i	$0.863560\pi$
$734$	−124.754	+	242.631i	−0.169964	+	0.330559i
$735$		0			0
$736$	−772.499	−	801.470i	−1.04959	−	1.08895i
$737$	123.278			0.167270
$738$		0			0
$739$	1102.93			1.49246			0.746231	−	0.665687i	$-0.231861\pi$
$739$	1102.93			1.49246			0.746231	+	0.665687i	$0.231861\pi$
$740$	−524.457	−	733.142i	−0.708725	−	0.990733i
$741$		0			0
$742$	728.321	+	374.481i	0.981564	+	0.504691i
$743$			922.265i			1.24127i	0.784099	+	0.620636i	$0.213126\pi$
$743$			922.265i			1.24127i	−0.784099	+	0.620636i	$0.786874\pi$
$744$		0			0
$745$	611.983			0.821453
$746$	387.568	−	753.774i	0.519529	−	1.01042i
$747$		0			0
$748$	−172.046	−	240.504i	−0.230008	−	0.321530i
$749$			212.834i			0.284157i
$750$		0			0
$751$		−	1268.77i		−	1.68944i	−0.535207	−	0.844721i	$-0.679767\pi$
$751$		−	1268.77i		−	1.68944i	0.535207	−	0.844721i	$-0.320233\pi$
$752$	58.2104	+	19.8659i	0.0774075	+	0.0264174i
$753$		0			0
$754$	157.948	+	81.2123i	0.209480	+	0.107709i
$755$	984.595			1.30410
$756$		0			0
$757$		−	786.831i		−	1.03941i	−0.854347	−	0.519703i	$-0.826043\pi$
$757$		−	786.831i		−	1.03941i	0.854347	−	0.519703i	$-0.173957\pi$
$758$	−80.1640	−	41.2180i	−0.105757	−	0.0543772i
$759$		0			0
$760$	−681.018	+	100.167i	−0.896076	+	0.131799i
$761$	784.525			1.03091			0.515457	−	0.856916i	$-0.327622\pi$
$761$	784.525			1.03091			0.515457	+	0.856916i	$0.327622\pi$
$762$		0			0
$763$	274.573			0.359859
$764$	−668.349	+	478.107i	−0.874802	+	0.625794i
$765$		0			0
$766$	−418.616	+	814.159i	−0.546497	+	1.06287i
$767$		−	1235.66i		−	1.61104i
$768$		0			0
$769$	366.360			0.476411			0.238206	−	0.971215i	$-0.423441\pi$
$769$	366.360			0.476411			0.238206	+	0.971215i	$0.423441\pi$
$770$	−263.458	−	135.462i	−0.342154	−	0.175925i
$771$		0			0
$772$	−350.354	−	489.763i	−0.453827	−	0.634408i
$773$		−	756.566i		−	0.978741i	−0.872076	−	0.489370i	$-0.837227\pi$
$773$		−	756.566i		−	0.978741i	0.872076	−	0.489370i	$-0.162773\pi$
$774$		0			0
$775$		−	458.419i		−	0.591508i
$776$	184.319	+	1253.15i	0.237524	+	1.61488i
$777$		0			0
$778$	−349.129	+	679.013i	−0.448752	+	0.872768i
$779$	−1164.37			−1.49470
$780$		0			0
$781$			452.885i			0.579879i
$782$	251.748	−	489.620i	0.321929	−	0.626112i
$783$		0			0
$784$	−170.583	+	499.838i	−0.217580	+	0.637548i
$785$	−58.0570			−0.0739579
$786$		0			0
$787$	477.129			0.606264			0.303132	−	0.952949i	$-0.401968\pi$
$787$	477.129			0.606264			0.303132	+	0.952949i	$0.401968\pi$
$788$	504.801	−	361.111i	0.640610	−	0.458263i
$789$		0			0
$790$	−301.161	−	154.848i	−0.381217	−	0.196011i
$791$		−	701.417i		−	0.886747i
$792$		0			0
$793$	608.846			0.767776
$794$	498.767	−	970.043i	0.628171	−	1.22172i
$795$		0			0
$796$	693.758	−	496.283i	0.871556	−	0.623471i
$797$		−	820.766i		−	1.02982i	−0.857244	−	0.514910i	$-0.827825\pi$
$797$		−	820.766i		−	1.02982i	0.857244	−	0.514910i	$-0.172175\pi$
$798$		0			0
$799$			30.4205i			0.0380732i
$800$	213.783	−	206.055i	0.267229	−	0.257569i
$801$		0			0
$802$	318.852	+	163.944i	0.397571	+	0.204419i
$803$	551.369			0.686637
$804$		0			0
$805$		−	551.551i		−	0.685156i
$806$	931.278	+	478.836i	1.15543	+	0.594089i
$807$		0			0
$808$	225.235	−	33.1286i	0.278757	−	0.0410007i
$809$	−493.101			−0.609519			−0.304760	−	0.952429i	$-0.598576\pi$
$809$	−493.101			−0.609519			−0.304760	+	0.952429i	$0.598576\pi$
$810$		0			0
$811$	1075.97			1.32673			0.663363	−	0.748298i	$-0.269129\pi$
$811$	1075.97			1.32673			0.663363	+	0.748298i	$0.269129\pi$
$812$	77.9809	+	109.010i	0.0960356	+	0.134249i
$813$		0			0
$814$	−485.580	+	944.395i	−0.596536	+	1.16019i
$815$			84.2426i			0.103365i
$816$		0			0
$817$	−137.566			−0.168380
$818$	−1094.72	−	562.874i	−1.33829	−	0.688110i
$819$		0			0
$820$	−692.125	+	495.115i	−0.844055	+	0.603798i
$821$			1278.17i			1.55684i	0.627742	+	0.778421i	$0.283979\pi$
$821$			1278.17i			1.55684i	−0.627742	+	0.778421i	$0.716021\pi$
$822$		0			0
$823$			1002.38i			1.21796i	0.793187	+	0.608978i	$0.208420\pi$
$823$			1002.38i			1.21796i	−0.793187	+	0.608978i	$0.791580\pi$
$824$	800.550	−	117.748i	0.971541	−	0.142898i
$825$		0			0
$826$	426.406	−	829.308i	0.516230	−	1.00400i
$827$	−1335.56			−1.61495			−0.807475	−	0.589902i	$-0.799166\pi$
$827$	−1335.56			−1.61495			−0.807475	+	0.589902i	$0.799166\pi$
$828$		0			0
$829$		−	509.562i		−	0.614671i	−0.951601	−	0.307335i	$-0.900563\pi$
$829$		−	509.562i		−	0.614671i	0.951601	−	0.307335i	$-0.0994373\pi$
$830$	0.239621	−	0.466035i	0.000288701	−	0.000561488i
$831$		0			0
$832$	195.297	+	649.533i	0.234732	+	0.780689i
$833$	−261.213			−0.313581
$834$		0			0
$835$	−540.147			−0.646883
$836$	471.797	+	659.529i	0.564351	+	0.788911i
$837$		0			0
$838$	28.7589	+	14.7870i	0.0343185	+	0.0176456i
$839$			296.098i			0.352918i	0.984308	+	0.176459i	$0.0564643\pi$
$839$			296.098i			0.352918i	−0.984308	+	0.176459i	$0.943536\pi$
$840$		0			0
$841$	770.788			0.916513
$842$	−318.366	+	619.184i	−0.378107	+	0.735372i
$843$		0			0
$844$	198.672	+	277.725i	0.235393	+	0.329058i
$845$		−	224.764i		−	0.265993i
$846$		0			0
$847$		−	134.872i		−	0.159235i
$848$	−1550.56	−	529.171i	−1.82849	−	0.624022i
$849$		0			0
$850$	130.601	+	67.1510i	0.153648	+	0.0790012i
$851$	−1977.09			−2.32326
$852$		0			0
$853$			410.064i			0.480731i	0.970682	+	0.240366i	$0.0772673\pi$
$853$			410.064i			0.480731i	−0.970682	+	0.240366i	$0.922733\pi$
$854$	408.623	+	210.102i	0.478481	+	0.246021i
$855$		0			0
$856$	−61.9600	−	421.255i	−0.0723832	−	0.492120i
$857$	1164.27			1.35854			0.679272	−	0.733887i	$-0.262296\pi$
$857$	1164.27			1.35854			0.679272	+	0.733887i	$0.262296\pi$
$858$		0			0
$859$	−255.156			−0.297038			−0.148519	−	0.988910i	$-0.547451\pi$
$859$	−255.156			−0.297038			−0.148519	+	0.988910i	$0.547451\pi$
$860$	−81.7720	+	58.4959i	−0.0950837	+	0.0680185i
$861$		0			0
$862$	69.2472	−	134.677i	0.0803332	−	0.156238i
$863$			232.034i			0.268869i	0.990922	+	0.134434i	$0.0429217\pi$
$863$			232.034i			0.268869i	−0.990922	+	0.134434i	$0.957078\pi$
$864$		0			0
$865$	−610.201			−0.705435
$866$	1388.46	+	713.907i	1.60331	+	0.824373i
$867$		0			0
$868$	459.783	+	642.735i	0.529704	+	0.740478i
$869$			398.935i			0.459074i
$870$		0			0
$871$		−	139.850i		−	0.160563i
$872$	−543.453	+	79.9335i	−0.623226	+	0.0916668i
$873$		0			0
$874$	−690.363	+	1342.67i	−0.789889	+	1.53624i
$875$	543.508			0.621152
$876$		0			0
$877$			1211.84i			1.38180i	0.722950	+	0.690900i	$0.242786\pi$
$877$			1211.84i			1.38180i	−0.722950	+	0.690900i	$0.757214\pi$
$878$	−455.271	+	885.447i	−0.518531	+	1.00848i
$879$		0			0
$880$	560.891	+	191.419i	0.637376	+	0.217521i
$881$	1002.81			1.13826			0.569131	−	0.822247i	$-0.307280\pi$
$881$	1002.81			1.13826			0.569131	+	0.822247i	$0.307280\pi$
$882$		0			0
$883$	−1069.84			−1.21159			−0.605797	−	0.795619i	$-0.707146\pi$
$883$	−1069.84			−1.21159			−0.605797	+	0.795619i	$0.707146\pi$
$884$	−272.835	+	195.173i	−0.308636	+	0.220784i
$885$		0			0
$886$	−997.022	−	512.640i	−1.12531	−	0.578600i
$887$			685.546i			0.772882i	0.922314	+	0.386441i	$0.126296\pi$
$887$			685.546i			0.772882i	−0.922314	+	0.386441i	$0.873704\pi$
$888$		0			0
$889$	190.677			0.214485
$890$	357.086	−	694.490i	0.401220	−	0.780325i
$891$		0			0
$892$	73.8794	−	52.8500i	0.0828245	−	0.0592489i
$893$		−	83.4214i		−	0.0934170i
$894$		0			0
$895$			203.475i			0.227346i
$896$	−93.0698	+	503.323i	−0.103873	+	0.561745i
$897$		0			0
$898$	365.906	+	188.138i	0.407468	+	0.209508i
$899$	−413.979			−0.460488
$900$		0			0
$901$		−	810.316i		−	0.899351i
$902$	891.558	+	458.413i	0.988424	+	0.508218i
$903$		0			0
$904$	204.196	+	1388.29i	0.225880	+	1.53572i
$905$	991.928			1.09605
$906$		0			0
$907$	238.640			0.263109			0.131555	−	0.991309i	$-0.458003\pi$
$907$	238.640			0.263109			0.131555	+	0.991309i	$0.458003\pi$
$908$	−618.647	−	864.811i	−0.681329	−	0.952436i
$909$		0			0
$910$	−153.672	+	298.874i	−0.168871	+	0.328433i
$911$			1415.37i			1.55364i	0.629721	+	0.776821i	$0.283169\pi$
$911$			1415.37i			1.55364i	−0.629721	+	0.776821i	$0.716831\pi$
$912$		0			0
$913$	−0.617335			−0.000676161
$914$	−608.680	−	312.965i	−0.665952	−	0.342413i
$915$		0			0
$916$	625.690	−	447.590i	0.683067	−	0.488635i
$917$			731.710i			0.797939i
$918$		0			0
$919$		−	380.070i		−	0.413570i	−0.978386	−	0.206785i	$-0.933700\pi$
$919$		−	380.070i		−	0.413570i	0.978386	−	0.206785i	$-0.0663000\pi$
$920$	160.567	+	1091.67i	0.174529	+	1.18659i
$921$		0			0
$922$	445.948	−	867.316i	0.483675	−	0.940690i
$923$	513.765			0.556625
$924$		0			0
$925$		−	527.367i		−	0.570127i
$926$	115.021	−	223.702i	0.124213	−	0.241579i
$927$		0			0
$928$	−186.080	−	193.059i	−0.200517	−	0.208037i
$929$	−349.856			−0.376594			−0.188297	−	0.982112i	$-0.560297\pi$
$929$	−349.856			−0.376594			−0.188297	+	0.982112i	$0.560297\pi$
$930$		0			0
$931$	716.318			0.769407
$932$	492.434	+	688.377i	0.528363	+	0.738602i
$933$		0			0
$934$	−228.005	−	117.234i	−0.244117	−	0.125518i
$935$			293.119i			0.313496i
$936$		0			0
$937$	291.737			0.311352			0.155676	−	0.987808i	$-0.450244\pi$
$937$	291.737			0.311352			0.155676	+	0.987808i	$0.450244\pi$
$938$	48.2597	−	93.8593i	0.0514496	−	0.100063i
$939$		0			0
$940$	−35.4725	−	49.5873i	−0.0377367	−	0.0527524i
$941$		−	1150.08i		−	1.22219i	−0.791556	−	0.611097i	$-0.790728\pi$
$941$		−	1150.08i		−	1.22219i	0.791556	−	0.611097i	$-0.209272\pi$
$942$		0			0
$943$			1866.48i			1.97930i
$944$	−602.544	+	1765.56i	−0.638288	+	1.87029i
$945$		0			0
$946$	105.334	+	54.1598i	0.111347	+	0.0572514i
$947$	−300.501			−0.317319			−0.158660	−	0.987333i	$-0.550717\pi$
$947$	−300.501			−0.317319			−0.158660	+	0.987333i	$0.550717\pi$
$948$		0			0
$949$		−	625.488i		−	0.659103i
$950$	−358.143	−	184.147i	−0.376993	−	0.193838i
$951$		0			0
$952$	−250.462	+	36.8390i	−0.263090	+	0.0386964i
$953$	56.6994			0.0594957			0.0297479	−	0.999557i	$-0.490530\pi$
$953$	56.6994			0.0594957			0.0297479	+	0.999557i	$0.490530\pi$
$954$		0			0
$955$	814.562			0.852944
$956$	−1333.61	+	954.005i	−1.39499	+	0.997913i
$957$		0			0
$958$	305.823	−	594.788i	0.319230	−	0.620864i
$959$			821.603i			0.856729i
$960$		0			0
$961$	−1479.86			−1.53992
$962$	1071.35	+	550.855i	1.11367	+	0.572615i
$963$		0			0
$964$	−193.116	−	269.958i	−0.200328	−	0.280039i
$965$			596.907i			0.618556i
$966$		0			0
$967$		−	388.888i		−	0.402159i	−0.979575	−	0.201079i	$-0.935555\pi$
$967$		−	388.888i		−	0.402159i	0.979575	−	0.201079i	$-0.0644449\pi$
$968$	39.2640	+	266.949i	0.0405619	+	0.275773i
$969$		0			0
$970$	574.122	−	1116.60i	0.591878	−	1.15113i
$971$	376.938			0.388195			0.194098	−	0.980982i	$-0.437822\pi$
$971$	376.938			0.388195			0.194098	+	0.980982i	$0.437822\pi$
$972$		0			0
$973$		−	81.8353i		−	0.0841061i
$974$	458.309	−	891.356i	0.470543	−	0.915150i
$975$		0			0
$976$	−869.939	−	296.890i	−0.891331	−	0.304191i
$977$	736.808			0.754153			0.377077	−	0.926182i	$-0.376929\pi$
$977$	736.808			0.754153			0.377077	+	0.926182i	$0.376929\pi$
$978$		0			0
$979$	−919.959			−0.939692
$980$	425.793	−	304.593i	0.434482	−	0.310809i
$981$		0			0
$982$	81.9665	+	42.1448i	0.0834690	+	0.0429173i
$983$		−	675.090i		−	0.686765i	−0.939196	−	0.343383i	$-0.888427\pi$
$983$		−	675.090i		−	0.686765i	0.939196	−	0.343383i	$-0.111573\pi$
$984$		0			0
$985$	−615.234			−0.624603
$986$	60.6413	−	117.940i	0.0615023	−	0.119615i
$987$		0			0
$988$	748.188	−	535.220i	0.757275	−	0.541720i
$989$			220.518i			0.222970i
$990$		0			0
$991$			1591.90i			1.60636i	0.595738	+	0.803179i	$0.296860\pi$
$991$			1591.90i			1.60636i	−0.595738	+	0.803179i	$0.703140\pi$
$992$	−1097.15	−	1138.29i	−1.10600	−	1.14747i
$993$		0			0
$994$	344.810	+	177.291i	0.346891	+	0.178361i
$995$	−845.529			−0.849778
$996$		0			0
$997$			1722.80i			1.72798i	0.503508	+	0.863990i	$0.332042\pi$
$997$			1722.80i			1.72798i	−0.503508	+	0.863990i	$0.667958\pi$
$998$	−0.599303	−	0.308144i	−0.000600504	−	0.000308762i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.b.b.163.3	✓	16
3.2	odd	2	inner	216.3.b.b.163.14	yes	16
4.3	odd	2		864.3.b.b.271.5		16
8.3	odd	2	inner	216.3.b.b.163.4	yes	16
8.5	even	2		864.3.b.b.271.12		16
12.11	even	2		864.3.b.b.271.11		16
24.5	odd	2		864.3.b.b.271.6		16
24.11	even	2	inner	216.3.b.b.163.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.b.b.163.3	✓	16	1.1	even	1	trivial
216.3.b.b.163.4	yes	16	8.3	odd	2	inner
216.3.b.b.163.13	yes	16	24.11	even	2	inner
216.3.b.b.163.14	yes	16	3.2	odd	2	inner
864.3.b.b.271.5		16	4.3	odd	2
864.3.b.b.271.6		16	24.5	odd	2
864.3.b.b.271.11		16	12.11	even	2
864.3.b.b.271.12		16	8.5	even	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.77866 - 0.914534i) q^{2} +(2.32725 + 3.25329i) q^{4} -3.96500i q^{5} +3.99887i q^{7} +(-1.16415 - 7.91484i) q^{8} +O(q^{10})\)	\(q+(-1.77866 - 0.914534i) q^{2} +(2.32725 + 3.25329i) q^{4} -3.96500i q^{5} +3.99887i q^{7} +(-1.16415 - 7.91484i) q^{8} +(-3.62613 + 7.05238i) q^{10} +9.34197 q^{11} -10.5978i q^{13} +(3.65711 - 7.11263i) q^{14} +(-5.16777 + 15.1425i) q^{16} -7.91338 q^{17} +21.7007 q^{19} +(12.8993 - 9.22756i) q^{20} +(-16.6162 - 8.54355i) q^{22} -34.7860i q^{23} +9.27878 q^{25} +(-9.69203 + 18.8498i) q^{26} +(-13.0095 + 9.30639i) q^{28} -8.37928i q^{29} -49.4051i q^{31} +(23.0400 - 22.2072i) q^{32} +(14.0752 + 7.23705i) q^{34} +15.8555 q^{35} -56.8359i q^{37} +(-38.5981 - 19.8460i) q^{38} +(-31.3824 + 4.61585i) q^{40} -53.6560 q^{41} -6.33926 q^{43} +(21.7411 + 30.3921i) q^{44} +(-31.8130 + 61.8724i) q^{46} -3.84419i q^{47} +33.0090 q^{49} +(-16.5038 - 8.48576i) q^{50} +(34.4776 - 24.6637i) q^{52} +102.398i q^{53} -37.0409i q^{55} +(31.6505 - 4.65528i) q^{56} +(-7.66314 + 14.9039i) q^{58} +116.596 q^{59} +57.4503i q^{61} +(-45.1826 + 87.8748i) q^{62} +(-61.2895 + 18.4281i) q^{64} -42.0202 q^{65} +13.1962 q^{67} +(-18.4164 - 25.7445i) q^{68} +(-28.2016 - 14.5004i) q^{70} +48.4786i q^{71} +59.0207 q^{73} +(-51.9783 + 101.092i) q^{74} +(50.5030 + 70.5985i) q^{76} +37.3573i q^{77} +42.7035i q^{79} +(60.0399 + 20.4902i) q^{80} +(95.4358 + 49.0703i) q^{82} -0.0660819 q^{83} +31.3765i q^{85} +(11.2754 + 5.79747i) q^{86} +(-10.8754 - 73.9402i) q^{88} -98.4759 q^{89} +42.3792 q^{91} +(113.169 - 80.9559i) q^{92} +(-3.51564 + 6.83749i) q^{94} -86.0431i q^{95} -158.329 q^{97} +(-58.7118 - 30.1879i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} + 24 q^{10} + 16 q^{16} - 64 q^{19} + 80 q^{22} - 80 q^{25} - 12 q^{28} + 8 q^{34} - 72 q^{40} - 64 q^{43} - 192 q^{46} - 128 q^{49} + 84 q^{52} - 96 q^{58} + 376 q^{64} + 128 q^{67} + 192 q^{70} + 80 q^{73} + 308 q^{76} + 272 q^{82} - 136 q^{88} + 192 q^{91} + 336 q^{94} + 80 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 24 * q^10 + 16 * q^16 - 64 * q^19 + 80 * q^22 - 80 * q^25 - 12 * q^28 + 8 * q^34 - 72 * q^40 - 64 * q^43 - 192 * q^46 - 128 * q^49 + 84 * q^52 - 96 * q^58 + 376 * q^64 + 128 * q^67 + 192 * q^70 + 80 * q^73 + 308 * q^76 + 272 * q^82 - 136 * q^88 + 192 * q^91 + 336 * q^94 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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