LMFDB - Embedded newform 216.2.f.b.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(107,216)]

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, 1]))

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

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

chi := DirichletCharacter("216.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.5
Root			$1.41203 + 0.0786378i$ of defining polynomial
Character	$\chi$	$=$	216.107
Dual form			216.2.f.b.107.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.637910 - 1.26217i) q^{2} +(-1.18614 - 1.61030i) q^{4} +3.42703 q^{5} -0.505408i q^{7} +(-2.78912 + 0.469882i) q^{8} +O(q^{10})$	\(q+(0.637910 - 1.26217i) q^{2} +(-1.18614 - 1.61030i) q^{4} +3.42703 q^{5} -0.505408i q^{7} +(-2.78912 + 0.469882i) q^{8} +(2.18614 - 4.32550i) q^{10} +3.31662i q^{11} -5.43039i q^{13} +(-0.637910 - 0.322405i) q^{14} +(-1.18614 + 3.82009i) q^{16} +1.58457i q^{17} -6.74456 q^{19} +(-4.06494 - 5.51856i) q^{20} +(4.18614 + 2.11571i) q^{22} +4.30243 q^{23} +6.74456 q^{25} +(-6.85407 - 3.46410i) q^{26} +(-0.813859 + 0.599485i) q^{28} -2.55164 q^{29} +4.92498i q^{31} +(4.06494 + 3.93398i) q^{32} +(2.00000 + 1.01082i) q^{34} -1.73205i q^{35} +7.45202i q^{37} +(-4.30243 + 8.51278i) q^{38} +(-9.55842 + 1.61030i) q^{40} +8.51278i q^{41} -4.00000 q^{43} +(5.34077 - 3.93398i) q^{44} +(2.74456 - 5.43039i) q^{46} +5.10328 q^{47} +6.74456 q^{49} +(4.30243 - 8.51278i) q^{50} +(-8.74456 + 6.44121i) q^{52} -0.875393 q^{53} +11.3662i q^{55} +(0.237482 + 1.40965i) q^{56} +(-1.62772 + 3.22060i) q^{58} -6.63325i q^{59} -10.8608i q^{61} +(6.21616 + 3.14170i) q^{62} +(7.55842 - 2.62112i) q^{64} -18.6101i q^{65} -4.00000 q^{67} +(2.55164 - 1.87953i) q^{68} +(-2.18614 - 1.10489i) q^{70} -9.40571 q^{71} -3.74456 q^{73} +(9.40571 + 4.75372i) q^{74} +(8.00000 + 10.8608i) q^{76} +1.67625 q^{77} -6.44121i q^{79} +(-4.06494 + 13.0916i) q^{80} +(10.7446 + 5.43039i) q^{82} +10.2448i q^{83} +5.43039i q^{85} +(-2.55164 + 5.04868i) q^{86} +(-1.55842 - 9.25048i) q^{88} +3.75906i q^{89} -2.74456 q^{91} +(-5.10328 - 6.92820i) q^{92} +(3.25544 - 6.44121i) q^{94} -23.1138 q^{95} -1.00000 q^{97} +(4.30243 - 8.51278i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4}+O(q^{10}) $ 8 * q + 2 * q^4	$ 8 q + 2 q^{4} + 6 q^{10} + 2 q^{16} - 8 q^{19} + 22 q^{22} + 8 q^{25} - 18 q^{28} + 16 q^{34} - 42 q^{40} - 32 q^{43} - 24 q^{46} + 8 q^{49} - 24 q^{52} - 36 q^{58} + 26 q^{64} - 32 q^{67} - 6 q^{70} + 16 q^{73} + 64 q^{76} + 40 q^{82} + 22 q^{88} + 24 q^{91} + 72 q^{94} - 8 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 + 6 * q^10 + 2 * q^16 - 8 * q^19 + 22 * q^22 + 8 * q^25 - 18 * q^28 + 16 * q^34 - 42 * q^40 - 32 * q^43 - 24 * q^46 + 8 * q^49 - 24 * q^52 - 36 * q^58 + 26 * q^64 - 32 * q^67 - 6 * q^70 + 16 * q^73 + 64 * q^76 + 40 * q^82 + 22 * q^88 + 24 * q^91 + 72 * q^94 - 8 * 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 $

$2$	0.637910	−	1.26217i	0.451071	−	0.892488i
$2$	0.637910	−	1.26217i	0.451071	−	0.892488i
$3$		0			0
$3$		0			0
$4$	−1.18614	−	1.61030i	−0.593070	−	0.805151i
$5$	3.42703			1.53262			0.766308	−	0.642473i	$-0.222092\pi$
$5$	3.42703			1.53262			0.766308	+	0.642473i	$0.222092\pi$
$6$		0			0
$7$		−	0.505408i		−	0.191026i	−0.995428	−	0.0955132i	$-0.969551\pi$
$7$		−	0.505408i		−	0.191026i	0.995428	−	0.0955132i	$-0.0304492\pi$
$8$	−2.78912	+	0.469882i	−0.986104	+	0.166128i
$9$		0			0
$10$	2.18614	−	4.32550i	0.691318	−	1.36784i
$11$			3.31662i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$11$			3.31662i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$		−	5.43039i		−	1.50612i	−0.657952	−	0.753059i	$-0.728577\pi$
$13$		−	5.43039i		−	1.50612i	0.657952	−	0.753059i	$-0.271423\pi$
$14$	−0.637910	−	0.322405i	−0.170489	−	0.0861664i
$15$		0			0
$16$	−1.18614	+	3.82009i	−0.296535	+	0.955022i
$17$			1.58457i			0.384316i	0.981364	+	0.192158i	$0.0615486\pi$
$17$			1.58457i			0.384316i	−0.981364	+	0.192158i	$0.938451\pi$
$18$		0			0
$19$	−6.74456			−1.54731			−0.773654	−	0.633608i	$-0.781573\pi$
$19$	−6.74456			−1.54731			−0.773654	+	0.633608i	$0.781573\pi$
$20$	−4.06494	−	5.51856i	−0.908949	−	1.23399i
$21$		0			0
$22$	4.18614	+	2.11571i	0.892488	+	0.451071i
$23$	4.30243			0.897118			0.448559	−	0.893753i	$-0.351937\pi$
$23$	4.30243			0.897118			0.448559	+	0.893753i	$0.351937\pi$
$24$		0			0
$25$	6.74456			1.34891
$26$	−6.85407	−	3.46410i	−1.34419	−	0.679366i
$27$		0			0
$28$	−0.813859	+	0.599485i	−0.153805	+	0.113292i
$29$	−2.55164			−0.473828			−0.236914	−	0.971531i	$-0.576136\pi$
$29$	−2.55164			−0.473828			−0.236914	+	0.971531i	$0.576136\pi$
$30$		0			0
$31$			4.92498i			0.884553i	0.896879	+	0.442276i	$0.145829\pi$
$31$			4.92498i			0.884553i	−0.896879	+	0.442276i	$0.854171\pi$
$32$	4.06494	+	3.93398i	0.718587	+	0.695437i
$33$		0			0
$34$	2.00000	+	1.01082i	0.342997	+	0.173354i
$35$		−	1.73205i		−	0.292770i
$36$		0			0
$37$			7.45202i			1.22510i	0.790430	+	0.612552i	$0.209857\pi$
$37$			7.45202i			1.22510i	−0.790430	+	0.612552i	$0.790143\pi$
$38$	−4.30243	+	8.51278i	−0.697946	+	1.38095i
$39$		0			0
$40$	−9.55842	+	1.61030i	−1.51132	+	0.254611i
$41$			8.51278i			1.32947i	0.747078	+	0.664736i	$0.231456\pi$
$41$			8.51278i			1.32947i	−0.747078	+	0.664736i	$0.768544\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	5.34077	−	3.93398i	0.805151	−	0.593070i
$45$		0			0
$46$	2.74456	−	5.43039i	0.404664	−	0.800667i
$47$	5.10328			0.744390			0.372195	−	0.928154i	$-0.378605\pi$
$47$	5.10328			0.744390			0.372195	+	0.928154i	$0.378605\pi$
$48$		0			0
$49$	6.74456			0.963509
$50$	4.30243	−	8.51278i	0.608455	−	1.20389i
$51$		0			0
$52$	−8.74456	+	6.44121i	−1.21265	+	0.893234i
$53$	−0.875393			−0.120244			−0.0601222	−	0.998191i	$-0.519149\pi$
$53$	−0.875393			−0.120244			−0.0601222	+	0.998191i	$0.519149\pi$
$54$		0			0
$55$			11.3662i			1.53262i
$56$	0.237482	+	1.40965i	0.0317349	+	0.188372i
$57$		0			0
$58$	−1.62772	+	3.22060i	−0.213730	+	0.422886i
$59$		−	6.63325i		−	0.863576i	−0.901975	−	0.431788i	$-0.857883\pi$
$59$		−	6.63325i		−	0.863576i	0.901975	−	0.431788i	$-0.142117\pi$
$60$		0			0
$61$		−	10.8608i		−	1.39058i	−0.718729	−	0.695290i	$-0.755276\pi$
$61$		−	10.8608i		−	1.39058i	0.718729	−	0.695290i	$-0.244724\pi$
$62$	6.21616	+	3.14170i	0.789453	+	0.398996i
$63$		0			0
$64$	7.55842	−	2.62112i	0.944803	−	0.327640i
$65$		−	18.6101i		−	2.30830i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	2.55164	−	1.87953i	0.309432	−	0.227926i
$69$		0			0
$70$	−2.18614	−	1.10489i	−0.261294	−	0.132060i
$71$	−9.40571			−1.11625			−0.558126	−	0.829756i	$-0.688480\pi$
$71$	−9.40571			−1.11625			−0.558126	+	0.829756i	$0.688480\pi$
$72$		0			0
$73$	−3.74456			−0.438268			−0.219134	−	0.975695i	$-0.570323\pi$
$73$	−3.74456			−0.438268			−0.219134	+	0.975695i	$0.570323\pi$
$74$	9.40571	+	4.75372i	1.09339	+	0.552609i
$75$		0			0
$76$	8.00000	+	10.8608i	0.917663	+	1.24582i
$77$	1.67625			0.191026
$78$		0			0
$79$		−	6.44121i		−	0.724692i	−0.932044	−	0.362346i	$-0.881976\pi$
$79$		−	6.44121i		−	0.724692i	0.932044	−	0.362346i	$-0.118024\pi$
$80$	−4.06494	+	13.0916i	−0.454475	+	1.46368i
$81$		0			0
$82$	10.7446	+	5.43039i	1.18654	+	0.599686i
$83$			10.2448i			1.12452i	0.826962	+	0.562258i	$0.190067\pi$
$83$			10.2448i			1.12452i	−0.826962	+	0.562258i	$0.809933\pi$
$84$		0			0
$85$			5.43039i			0.589008i
$86$	−2.55164	+	5.04868i	−0.275151	+	0.544413i
$87$		0			0
$88$	−1.55842	−	9.25048i	−0.166128	−	0.986104i
$89$			3.75906i			0.398459i	0.979953	+	0.199230i	$0.0638439\pi$
$89$			3.75906i			0.398459i	−0.979953	+	0.199230i	$0.936156\pi$
$90$		0			0
$91$	−2.74456			−0.287708
$92$	−5.10328	−	6.92820i	−0.532054	−	0.722315i
$93$		0			0
$94$	3.25544	−	6.44121i	0.335773	−	0.664360i
$95$	−23.1138			−2.37143
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	4.30243	−	8.51278i	0.434611	−	0.859920i
$99$		0			0
$100$	−8.00000	−	10.8608i	−0.800000	−	1.08608i
$101$	−11.0820			−1.10270			−0.551348	−	0.834275i	$-0.685886\pi$
$101$	−11.0820			−1.10270			−0.551348	+	0.834275i	$0.685886\pi$
$102$		0			0
$103$		−	17.3020i		−	1.70482i	−0.522878	−	0.852408i	$-0.675142\pi$
$103$		−	17.3020i		−	1.70482i	0.522878	−	0.852408i	$-0.324858\pi$
$104$	2.55164	+	15.1460i	0.250209	+	1.48519i
$105$		0			0
$106$	−0.558422	+	1.10489i	−0.0542387	+	0.107317i
$107$		−	8.36530i		−	0.808704i	−0.914603	−	0.404352i	$-0.867497\pi$
$107$		−	8.36530i		−	0.808704i	0.914603	−	0.404352i	$-0.132503\pi$
$108$		0			0
$109$		−	7.45202i		−	0.713774i	−0.934148	−	0.356887i	$-0.883838\pi$
$109$		−	7.45202i		−	0.713774i	0.934148	−	0.356887i	$-0.116162\pi$
$110$	14.3460	+	7.25061i	1.36784	+	0.691318i
$111$		0			0
$112$	1.93070	+	0.599485i	0.182434	+	0.0566460i
$113$		−	5.34363i		−	0.502686i	−0.967898	−	0.251343i	$-0.919128\pi$
$113$		−	5.34363i		−	0.502686i	0.967898	−	0.251343i	$-0.0808723\pi$
$114$		0			0
$115$	14.7446			1.37494
$116$	3.02661	+	4.10891i	0.281013	+	0.381503i
$117$		0			0
$118$	−8.37228	−	4.23142i	−0.770731	−	0.389534i
$119$	0.800857			0.0734144
$120$		0			0
$121$		0			0
$122$	−13.7081	−	6.92820i	−1.24108	−	0.627250i
$123$		0			0
$124$	7.93070	−	5.84172i	0.712198	−	0.524602i
$125$	5.97868			0.534749
$126$		0			0
$127$			1.51622i			0.134543i	0.997735	+	0.0672716i	$0.0214294\pi$
$127$			1.51622i			0.134543i	−0.997735	+	0.0672716i	$0.978571\pi$
$128$	1.51330	−	11.2120i	0.133758	−	0.991014i
$129$		0			0
$130$	−23.4891	−	11.8716i	−2.06013	−	1.04121i
$131$		−	15.2935i		−	1.33620i	−0.744072	−	0.668100i	$-0.767108\pi$
$131$		−	15.2935i		−	1.33620i	0.744072	−	0.668100i	$-0.232892\pi$
$132$		0			0
$133$			3.40876i			0.295577i
$134$	−2.55164	+	5.04868i	−0.220428	+	0.436139i
$135$		0			0
$136$	−0.744563	−	4.41957i	−0.0638457	−	0.378975i
$137$			3.75906i			0.321158i	0.987023	+	0.160579i	$0.0513361\pi$
$137$			3.75906i			0.321158i	−0.987023	+	0.160579i	$0.948664\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	−2.78912	+	2.05446i	−0.235724	+	0.173633i
$141$		0			0
$142$	−6.00000	+	11.8716i	−0.503509	+	0.996242i
$143$	18.0106			1.50612
$144$		0			0
$145$	−8.74456			−0.726196
$146$	−2.38870	+	4.72627i	−0.197690	+	0.391149i
$147$		0			0
$148$	12.0000	−	8.83915i	0.986394	−	0.726573i
$149$	−9.48025			−0.776652			−0.388326	−	0.921522i	$-0.626947\pi$
$149$	−9.48025			−0.776652			−0.388326	+	0.921522i	$0.626947\pi$
$150$		0			0
$151$			6.94661i			0.565307i	0.959222	+	0.282654i	$0.0912147\pi$
$151$			6.94661i			0.565307i	−0.959222	+	0.282654i	$0.908785\pi$
$152$	18.8114	−	3.16915i	1.52581	−	0.257052i
$153$		0			0
$154$	1.06930	−	2.11571i	0.0861664	−	0.170489i
$155$			16.8781i			1.35568i
$156$		0			0
$157$			10.8608i			0.866784i	0.901205	+	0.433392i	$0.142684\pi$
$157$			10.8608i			0.866784i	−0.901205	+	0.433392i	$0.857316\pi$
$158$	−8.12989	−	4.10891i	−0.646779	−	0.326887i
$159$		0			0
$160$	13.9307	+	13.4819i	1.10132	+	1.06584i
$161$		−	2.17448i		−	0.171373i
$162$		0			0
$163$	16.2337			1.27152			0.635760	−	0.771887i	$-0.280687\pi$
$163$	16.2337			1.27152			0.635760	+	0.771887i	$0.280687\pi$
$164$	13.7081	−	10.0974i	1.07043	−	0.788471i
$165$		0			0
$166$	12.9307	+	6.53528i	1.00362	+	0.507236i
$167$	13.7081			1.06077			0.530384	−	0.847758i	$-0.322048\pi$
$167$	13.7081			1.06077			0.530384	+	0.847758i	$0.322048\pi$
$168$		0			0
$169$	−16.4891			−1.26839
$170$	6.85407	+	3.46410i	0.525683	+	0.265684i
$171$		0			0
$172$	4.74456	+	6.44121i	0.361770	+	0.491137i
$173$	−1.67625			−0.127443			−0.0637214	−	0.997968i	$-0.520297\pi$
$173$	−1.67625			−0.127443			−0.0637214	+	0.997968i	$0.520297\pi$
$174$		0			0
$175$		−	3.40876i		−	0.257678i
$176$	−12.6698	−	3.93398i	−0.955022	−	0.296535i
$177$		0			0
$178$	4.74456	+	2.39794i	0.355620	+	0.179733i
$179$		−	1.43710i		−	0.107414i	−0.998557	−	0.0537068i	$-0.982896\pi$
$179$		−	1.43710i		−	0.107414i	0.998557	−	0.0537068i	$-0.0171036\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	−1.75079	+	3.46410i	−0.129777	+	0.256776i
$183$		0			0
$184$	−12.0000	+	2.02163i	−0.884652	+	0.149037i
$185$			25.5383i			1.87762i
$186$		0			0
$187$	−5.25544			−0.384316
$188$	−6.05321	−	8.21782i	−0.441476	−	0.599346i
$189$		0			0
$190$	−14.7446	+	29.1736i	−1.06968	+	2.11647i
$191$	18.0106			1.30320			0.651599	−	0.758563i	$-0.274098\pi$
$191$	18.0106			1.30320			0.651599	+	0.758563i	$0.274098\pi$
$192$		0			0
$193$	−21.2337			−1.52843			−0.764217	−	0.644959i	$-0.776874\pi$
$193$	−21.2337			−1.52843			−0.764217	+	0.644959i	$0.776874\pi$
$194$	−0.637910	+	1.26217i	−0.0457993	+	0.0906184i
$195$		0			0
$196$	−8.00000	−	10.8608i	−0.571429	−	0.775770i
$197$	12.0319			0.857236			0.428618	−	0.903486i	$-0.359001\pi$
$197$	12.0319			0.857236			0.428618	+	0.903486i	$0.359001\pi$
$198$		0			0
$199$		−	22.2270i		−	1.57563i	−0.615913	−	0.787814i	$-0.711213\pi$
$199$		−	22.2270i		−	1.57563i	0.615913	−	0.787814i	$-0.288787\pi$
$200$	−18.8114	+	3.16915i	−1.33017	+	0.224093i
$201$		0			0
$202$	−7.06930	+	13.9873i	−0.497394	+	0.984143i
$203$			1.28962i			0.0905136i
$204$		0			0
$205$			29.1736i			2.03757i
$206$	−21.8380	−	11.0371i	−1.52153	−	0.768992i
$207$		0			0
$208$	20.7446	+	6.44121i	1.43838	+	0.446617i
$209$		−	22.3692i		−	1.54731i
$210$		0			0
$211$	−1.25544			−0.0864279			−0.0432139	−	0.999066i	$-0.513760\pi$
$211$	−1.25544			−0.0864279			−0.0432139	+	0.999066i	$0.513760\pi$
$212$	1.03834	+	1.40965i	0.0713134	+	0.0968149i
$213$		0			0
$214$	−10.5584	−	5.33631i	−0.721759	−	0.364783i
$215$	−13.7081			−0.934887
$216$		0			0
$217$	2.48913			0.168973
$218$	−9.40571	−	4.75372i	−0.637035	−	0.321963i
$219$		0			0
$220$	18.3030	−	13.4819i	1.23399	−	0.908949i
$221$	8.60485			0.578825
$222$		0			0
$223$			8.46284i			0.566714i	0.959015	+	0.283357i	$0.0914481\pi$
$223$			8.46284i			0.566714i	−0.959015	+	0.283357i	$0.908552\pi$
$224$	1.98827	−	2.05446i	0.132847	−	0.137269i
$225$		0			0
$226$	−6.74456	−	3.40876i	−0.448642	−	0.226747i
$227$			2.87419i			0.190767i	0.995441	+	0.0953835i	$0.0304077\pi$
$227$			2.87419i			0.190767i	−0.995441	+	0.0953835i	$0.969592\pi$
$228$		0			0
$229$		−	12.8824i		−	0.851294i	−0.904889	−	0.425647i	$-0.860047\pi$
$229$		−	12.8824i		−	0.851294i	0.904889	−	0.425647i	$-0.139953\pi$
$230$	9.40571	−	18.6101i	0.620194	−	1.22712i
$231$		0			0
$232$	7.11684	−	1.19897i	0.467244	−	0.0787163i
$233$			27.1229i			1.77688i	0.458992	+	0.888440i	$0.348211\pi$
$233$			27.1229i			1.77688i	−0.458992	+	0.888440i	$0.651789\pi$
$234$		0			0
$235$	17.4891			1.14086
$236$	−10.6815	+	7.86797i	−0.695308	+	0.512161i
$237$		0			0
$238$	0.510875	−	1.01082i	0.0331151	−	0.0655215i
$239$	−14.5090			−0.938509			−0.469254	−	0.883063i	$-0.655477\pi$
$239$	−14.5090			−0.938509			−0.469254	+	0.883063i	$0.655477\pi$
$240$		0			0
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$		0			0
$243$		0			0
$244$	−17.4891	+	12.8824i	−1.11963	+	0.824712i
$245$	23.1138			1.47669
$246$		0			0
$247$			36.6256i			2.33043i
$248$	−2.31416	−	13.7364i	−0.146949	−	0.872261i
$249$		0			0
$250$	3.81386	−	7.54610i	0.241210	−	0.477257i
$251$			16.7306i			1.05603i	0.849236	+	0.528013i	$0.177063\pi$
$251$			16.7306i			1.05603i	−0.849236	+	0.528013i	$0.822937\pi$
$252$		0			0
$253$			14.2695i			0.897118i
$254$	1.91373	+	0.967215i	0.120078	+	0.0606885i
$255$		0			0
$256$	−13.1861	−	9.06232i	−0.824134	−	0.566395i
$257$		−	12.2718i		−	0.765496i	−0.923853	−	0.382748i	$-0.874978\pi$
$257$		−	12.2718i		−	0.765496i	0.923853	−	0.382748i	$-0.125022\pi$
$258$		0			0
$259$	3.76631			0.234027
$260$	−29.9679	+	22.0742i	−1.85853	+	1.36899i
$261$		0			0
$262$	−19.3030	−	9.75588i	−1.19254	−	0.602721i
$263$	−4.30243			−0.265299			−0.132649	−	0.991163i	$-0.542348\pi$
$263$	−4.30243			−0.265299			−0.132649	+	0.991163i	$0.542348\pi$
$264$		0			0
$265$	−3.00000			−0.184289
$266$	4.30243	+	2.17448i	0.263799	+	0.133326i
$267$		0			0
$268$	4.74456	+	6.44121i	0.289820	+	0.393459i
$269$	−11.1565			−0.680223			−0.340112	−	0.940385i	$-0.610465\pi$
$269$	−11.1565			−0.680223			−0.340112	+	0.940385i	$0.610465\pi$
$270$		0			0
$271$		−	20.8398i		−	1.26593i	−0.774180	−	0.632965i	$-0.781838\pi$
$271$		−	20.8398i		−	1.26593i	0.774180	−	0.632965i	$-0.218162\pi$
$272$	−6.05321	−	1.87953i	−0.367030	−	0.113963i
$273$		0			0
$274$	4.74456	+	2.39794i	0.286630	+	0.144865i
$275$			22.3692i			1.34891i
$276$		0			0
$277$		−	10.8608i		−	0.652561i	−0.945273	−	0.326280i	$-0.894205\pi$
$277$		−	10.8608i		−	0.652561i	0.945273	−	0.326280i	$-0.105795\pi$
$278$	5.10328	−	10.0974i	0.306075	−	0.605599i
$279$		0			0
$280$	0.813859	+	4.83090i	0.0486374	+	0.288702i
$281$			15.4410i			0.921132i	0.887626	+	0.460566i	$0.152353\pi$
$281$			15.4410i			0.921132i	−0.887626	+	0.460566i	$0.847647\pi$
$282$		0			0
$283$	22.7446			1.35202			0.676012	−	0.736891i	$-0.263707\pi$
$283$	22.7446			1.35202			0.676012	+	0.736891i	$0.263707\pi$
$284$	11.1565	+	15.1460i	0.662016	+	0.898751i
$285$		0			0
$286$	11.4891	−	22.7324i	0.679366	−	1.34419i
$287$	4.30243			0.253964
$288$		0			0
$289$	14.4891			0.852301
$290$	−5.57825	+	11.0371i	−0.327566	+	0.648122i
$291$		0			0
$292$	4.44158	+	6.02987i	0.259924	+	0.352872i
$293$	24.8646			1.45261			0.726304	−	0.687374i	$-0.241237\pi$
$293$	24.8646			1.45261			0.726304	+	0.687374i	$0.241237\pi$
$294$		0			0
$295$		−	22.7324i		−	1.32353i
$296$	−3.50157	−	20.7846i	−0.203525	−	1.20808i
$297$		0			0
$298$	−6.04755	+	11.9657i	−0.350325	+	0.693153i
$299$		−	23.3639i		−	1.35117i
$300$		0			0
$301$			2.02163i			0.116525i
$302$	8.76780	+	4.43132i	0.504530	+	0.254994i
$303$		0			0
$304$	8.00000	−	25.7648i	0.458831	−	1.47771i
$305$		−	37.2203i		−	2.13123i
$306$		0			0
$307$	−18.7446			−1.06981			−0.534904	−	0.844913i	$-0.679652\pi$
$307$	−18.7446			−1.06981			−0.534904	+	0.844913i	$0.679652\pi$
$308$	−1.98827	−	2.69927i	−0.113292	−	0.153805i
$309$		0			0
$310$	21.3030	+	10.7667i	1.20993	+	0.611508i
$311$	23.1138			1.31067			0.655333	−	0.755340i	$-0.272528\pi$
$311$	23.1138			1.31067			0.655333	+	0.755340i	$0.272528\pi$
$312$		0			0
$313$	−9.23369			−0.521919			−0.260959	−	0.965350i	$-0.584039\pi$
$313$	−9.23369			−0.521919			−0.260959	+	0.965350i	$0.584039\pi$
$314$	13.7081	+	6.92820i	0.773595	+	0.390981i
$315$		0			0
$316$	−10.3723	+	7.64018i	−0.583486	+	0.429793i
$317$	−14.5835			−0.819093			−0.409546	−	0.912289i	$-0.634313\pi$
$317$	−14.5835			−0.819093			−0.409546	+	0.912289i	$0.634313\pi$
$318$		0			0
$319$		−	8.46284i		−	0.473828i
$320$	25.9030	−	8.98266i	1.44802	−	0.502146i
$321$		0			0
$322$	−2.74456	−	1.38712i	−0.152948	−	0.0773014i
$323$		−	10.6873i		−	0.594655i
$324$		0			0
$325$		−	36.6256i		−	2.03162i
$326$	10.3556	−	20.4897i	0.573546	−	1.13482i
$327$		0			0
$328$	−4.00000	−	23.7432i	−0.220863	−	1.31100i
$329$		−	2.57924i		−	0.142198i
$330$		0			0
$331$	−33.4891			−1.84073			−0.920364	−	0.391062i	$-0.872108\pi$
$331$	−33.4891			−1.84073			−0.920364	+	0.391062i	$0.872108\pi$
$332$	16.4973	−	12.1518i	0.905405	−	0.666917i
$333$		0			0
$334$	8.74456	−	17.3020i	0.478481	−	0.946722i
$335$	−13.7081			−0.748955
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	−10.5186	+	20.8121i	−0.572136	+	1.13203i
$339$		0			0
$340$	8.74456	−	6.44121i	0.474240	−	0.349323i
$341$	−16.3343			−0.884553
$342$		0			0
$343$		−	6.94661i		−	0.375082i
$344$	11.1565	−	1.87953i	0.601518	−	0.101337i
$345$		0			0
$346$	−1.06930	+	2.11571i	−0.0574857	+	0.113741i
$347$		−	6.19082i		−	0.332341i	−0.986097	−	0.166170i	$-0.946860\pi$
$347$		−	6.19082i		−	0.332341i	0.986097	−	0.166170i	$-0.0531401\pi$
$348$		0			0
$349$		−	3.40876i		−	0.182467i	−0.995830	−	0.0912333i	$-0.970919\pi$
$349$		−	3.40876i		−	0.182467i	0.995830	−	0.0912333i	$-0.0290809\pi$
$350$	−4.30243	−	2.17448i	−0.229974	−	0.116231i
$351$		0			0
$352$	−13.0475	+	13.4819i	−0.695437	+	0.718587i
$353$			18.0202i			0.959120i	0.877509	+	0.479560i	$0.159204\pi$
$353$			18.0202i			0.959120i	−0.877509	+	0.479560i	$0.840796\pi$
$354$		0			0
$355$	−32.2337			−1.71079
$356$	6.05321	−	4.45877i	0.320820	−	0.236314i
$357$		0			0
$358$	−1.81386	−	0.916739i	−0.0958654	−	0.0484512i
$359$	−3.50157			−0.184806			−0.0924029	−	0.995722i	$-0.529455\pi$
$359$	−3.50157			−0.184806			−0.0924029	+	0.995722i	$0.529455\pi$
$360$		0			0
$361$	26.4891			1.39416
$362$		0			0
$363$		0			0
$364$	3.25544	+	4.41957i	0.170631	+	0.231649i
$365$	−12.8327			−0.671697
$366$		0			0
$367$			15.7858i			0.824010i	0.911182	+	0.412005i	$0.135171\pi$
$367$			15.7858i			0.824010i	−0.911182	+	0.412005i	$0.864829\pi$
$368$	−5.10328	+	16.4356i	−0.266027	+	0.856767i
$369$		0			0
$370$	32.2337	+	16.2912i	1.67575	+	0.846937i
$371$			0.442430i			0.0229698i
$372$		0			0
$373$		−	5.43039i		−	0.281175i	−0.990068	−	0.140587i	$-0.955101\pi$
$373$		−	5.43039i		−	0.281175i	0.990068	−	0.140587i	$-0.0448991\pi$
$374$	−3.35250	+	6.63325i	−0.173354	+	0.342997i
$375$		0			0
$376$	−14.2337	+	2.39794i	−0.734046	+	0.123664i
$377$			13.8564i			0.713641i
$378$		0			0
$379$	13.4891			0.692890			0.346445	−	0.938070i	$-0.387389\pi$
$379$	13.4891			0.692890			0.346445	+	0.938070i	$0.387389\pi$
$380$	27.4163	+	37.2203i	1.40643	+	1.90936i
$381$		0			0
$382$	11.4891	−	22.7324i	0.587835	−	1.16309i
$383$	19.6123			1.00214			0.501070	−	0.865407i	$-0.332940\pi$
$383$	19.6123			1.00214			0.501070	+	0.865407i	$0.332940\pi$
$384$		0			0
$385$	5.74456			0.292770
$386$	−13.5452	+	26.8005i	−0.689432	+	1.36411i
$387$		0			0
$388$	1.18614	+	1.61030i	0.0602172	+	0.0817507i
$389$	−36.8965			−1.87073			−0.935364	−	0.353687i	$-0.884928\pi$
$389$	−36.8965			−1.87073			−0.935364	+	0.353687i	$0.884928\pi$
$390$		0			0
$391$			6.81751i			0.344776i
$392$	−18.8114	+	3.16915i	−0.950120	+	0.160066i
$393$		0			0
$394$	7.67527	−	15.1863i	0.386674	−	0.765073i
$395$		−	22.0742i		−	1.11068i
$396$		0			0
$397$		−	1.38712i		−	0.0696178i	−0.999394	−	0.0348089i	$-0.988918\pi$
$397$		−	1.38712i		−	0.0696178i	0.999394	−	0.0348089i	$-0.0110823\pi$
$398$	−28.0542	−	14.1788i	−1.40623	−	0.710720i
$399$		0			0
$400$	−8.00000	+	25.7648i	−0.400000	+	1.28824i
$401$		−	17.0256i		−	0.850216i	−0.905143	−	0.425108i	$-0.860236\pi$
$401$		−	17.0256i		−	0.850216i	0.905143	−	0.425108i	$-0.139764\pi$
$402$		0			0
$403$	26.7446			1.33224
$404$	13.1448	+	17.8453i	0.653976	+	0.887837i
$405$		0			0
$406$	1.62772	+	0.822662i	0.0807823	+	0.0408280i
$407$	−24.7156			−1.22510
$408$		0			0
$409$	11.0000			0.543915			0.271957	−	0.962309i	$-0.412329\pi$
$409$	11.0000			0.543915			0.271957	+	0.962309i	$0.412329\pi$
$410$	36.8220	+	18.6101i	1.81851	+	0.919089i
$411$		0			0
$412$	−27.8614	+	20.5226i	−1.37263	+	1.01108i
$413$	−3.35250			−0.164966
$414$		0			0
$415$			35.1094i			1.72345i
$416$	21.3631	−	22.0742i	1.04741	−	1.08228i
$417$		0			0
$418$	−28.2337	−	14.2695i	−1.38095	−	0.697946i
$419$		−	20.4897i		−	1.00099i	−0.865741	−	0.500493i	$-0.833152\pi$
$419$		−	20.4897i		−	1.00099i	0.865741	−	0.500493i	$-0.166848\pi$
$420$		0			0
$421$			4.04326i			0.197057i	0.995134	+	0.0985283i	$0.0314135\pi$
$421$			4.04326i			0.197057i	−0.995134	+	0.0985283i	$0.968586\pi$
$422$	−0.800857	+	1.58457i	−0.0389851	+	0.0771359i
$423$		0			0
$424$	2.44158	−	0.411331i	0.118574	−	0.0199760i
$425$			10.6873i			0.518408i
$426$		0			0
$427$	−5.48913			−0.265637
$428$	−13.4707	+	9.92242i	−0.651129	+	0.479618i
$429$		0			0
$430$	−8.74456	+	17.3020i	−0.421700	+	0.834376i
$431$	−22.3130			−1.07478			−0.537389	−	0.843334i	$-0.680589\pi$
$431$	−22.3130			−1.07478			−0.537389	+	0.843334i	$0.680589\pi$
$432$		0			0
$433$	4.48913			0.215734			0.107867	−	0.994165i	$-0.465598\pi$
$433$	4.48913			0.215734			0.107867	+	0.994165i	$0.465598\pi$
$434$	1.58784	−	3.14170i	0.0762187	−	0.150806i
$435$		0			0
$436$	−12.0000	+	8.83915i	−0.574696	+	0.423318i
$437$	−29.0180			−1.38812
$438$		0			0
$439$			32.0769i			1.53095i	0.643467	+	0.765474i	$0.277495\pi$
$439$			32.0769i			1.53095i	−0.643467	+	0.765474i	$0.722505\pi$
$440$	−5.34077	−	31.7017i	−0.254611	−	1.51132i
$441$		0			0
$442$	5.48913	−	10.8608i	0.261091	−	0.516595i
$443$		−	6.63325i		−	0.315155i	−0.987507	−	0.157578i	$-0.949632\pi$
$443$		−	6.63325i		−	0.315155i	0.987507	−	0.157578i	$-0.0503684\pi$
$444$		0			0
$445$			12.8824i			0.610685i
$446$	10.6815	+	5.39853i	0.505785	+	0.255628i
$447$		0			0
$448$	−1.32473	−	3.82009i	−0.0625878	−	0.180482i
$449$		−	28.7075i		−	1.35479i	−0.735620	−	0.677395i	$-0.763109\pi$
$449$		−	28.7075i		−	1.35479i	0.735620	−	0.677395i	$-0.236891\pi$
$450$		0			0
$451$	−28.2337			−1.32947
$452$	−8.60485	+	6.33830i	−0.404738	+	0.298128i
$453$		0			0
$454$	3.62772	+	1.83348i	0.170257	+	0.0860494i
$455$	−9.40571			−0.440946
$456$		0			0
$457$	27.4674			1.28487			0.642435	−	0.766340i	$-0.277924\pi$
$457$	27.4674			1.28487			0.642435	+	0.766340i	$0.277924\pi$
$458$	−16.2598	−	8.21782i	−0.759770	−	0.383994i
$459$		0			0
$460$	−17.4891	−	23.7432i	−0.815435	−	1.10703i
$461$	41.8507			1.94918			0.974591	−	0.223990i	$-0.0719084\pi$
$461$	41.8507			1.94918			0.974591	+	0.223990i	$0.0719084\pi$
$462$		0			0
$463$		−	12.7533i		−	0.592697i	−0.955080	−	0.296348i	$-0.904231\pi$
$463$		−	12.7533i		−	0.592697i	0.955080	−	0.296348i	$-0.0957689\pi$
$464$	3.02661	−	9.74749i	0.140507	−	0.452516i
$465$		0			0
$466$	34.2337	+	17.3020i	1.58584	+	0.801499i
$467$			37.9576i			1.75647i	0.478229	+	0.878235i	$0.341279\pi$
$467$			37.9576i			1.75647i	−0.478229	+	0.878235i	$0.658721\pi$
$468$		0			0
$469$			2.02163i			0.0933503i
$470$	11.1565	−	22.0742i	0.514611	−	1.01821i
$471$		0			0
$472$	3.11684	+	18.5010i	0.143464	+	0.851575i
$473$		−	13.2665i		−	0.609994i
$474$		0			0
$475$	−45.4891			−2.08718
$476$	−0.949929	−	1.28962i	−0.0435399	−	0.0591097i
$477$		0			0
$478$	−9.25544	+	18.3128i	−0.423334	+	0.837608i
$479$	−13.7081			−0.626341			−0.313170	−	0.949697i	$-0.601391\pi$
$479$	−13.7081			−0.626341			−0.313170	+	0.949697i	$0.601391\pi$
$480$		0			0
$481$	40.4674			1.84515
$482$	1.27582	−	2.52434i	0.0581120	−	0.114980i
$483$		0			0
$484$		0			0
$485$	−3.42703			−0.155614
$486$		0			0
$487$			4.41957i			0.200270i	0.994974	+	0.100135i	$0.0319275\pi$
$487$			4.41957i			0.200270i	−0.994974	+	0.100135i	$0.968073\pi$
$488$	5.10328	+	30.2921i	0.231015	+	1.37126i
$489$		0			0
$490$	14.7446	−	29.1736i	0.666091	−	1.31793i
$491$			38.3624i			1.73127i	0.500675	+	0.865635i	$0.333085\pi$
$491$			38.3624i			1.73127i	−0.500675	+	0.865635i	$0.666915\pi$
$492$		0			0
$493$		−	4.04326i		−	0.182099i
$494$	46.2277	+	23.3639i	2.07988	+	1.05119i
$495$		0			0
$496$	−18.8139	−	5.84172i	−0.844767	−	0.262301i
$497$			4.75372i			0.213234i
$498$		0			0
$499$	−28.0000			−1.25345			−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000			−1.25345			−0.626726	+	0.779240i	$0.715605\pi$
$500$	−7.09155	−	9.62747i	−0.317144	−	0.430554i
$501$		0			0
$502$	21.1168	+	10.6726i	0.942491	+	0.476343i
$503$	12.9073			0.575507			0.287754	−	0.957704i	$-0.407092\pi$
$503$	12.9073			0.575507			0.287754	+	0.957704i	$0.407092\pi$
$504$		0			0
$505$	−37.9783			−1.69001
$506$	18.0106	+	9.10268i	0.800667	+	0.404664i
$507$		0			0
$508$	2.44158	−	1.79846i	0.108328	−	0.0797936i
$509$	−0.0745360			−0.00330375			−0.00165187	−	0.999999i	$-0.500526\pi$
$509$	−0.0745360			−0.00330375			−0.00165187	+	0.999999i	$0.500526\pi$
$510$		0			0
$511$			1.89253i			0.0837207i
$512$	−19.8498	+	10.8622i	−0.877244	+	0.480045i
$513$		0			0
$514$	−15.4891	−	7.82833i	−0.683196	−	0.345293i
$515$		−	59.2945i		−	2.61283i
$516$		0			0
$517$			16.9257i			0.744390i
$518$	2.40257	−	4.75372i	0.105563	−	0.208867i
$519$		0			0
$520$	8.74456	+	51.9060i	0.383474	+	2.27623i
$521$			1.58457i			0.0694214i	0.999397	+	0.0347107i	$0.0110510\pi$
$521$			1.58457i			0.0694214i	−0.999397	+	0.0347107i	$0.988949\pi$
$522$		0			0
$523$	−0.233688			−0.0102185			−0.00510923	−	0.999987i	$-0.501626\pi$
$523$	−0.233688			−0.0102185			−0.00510923	+	0.999987i	$0.501626\pi$
$524$	−24.6271	+	18.1402i	−1.07584	+	0.792460i
$525$		0			0
$526$	−2.74456	+	5.43039i	−0.119669	+	0.236776i
$527$	−7.80400			−0.339947
$528$		0			0
$529$	−4.48913			−0.195179
$530$	−1.91373	+	3.78651i	−0.0831272	+	0.164475i
$531$		0			0
$532$	5.48913	−	4.04326i	0.237984	−	0.175298i
$533$	46.2277			2.00234
$534$		0			0
$535$		−	28.6682i		−	1.23943i
$536$	11.1565	−	1.87953i	0.481887	−	0.0811832i
$537$		0			0
$538$	−7.11684	+	14.0814i	−0.306829	+	0.607091i
$539$			22.3692i			0.963509i
$540$		0			0
$541$		−	17.6783i		−	0.760049i	−0.924976	−	0.380025i	$-0.875916\pi$
$541$		−	17.6783i		−	0.760049i	0.924976	−	0.380025i	$-0.124084\pi$
$542$	−26.3034	−	13.2940i	−1.12983	−	0.571024i
$543$		0			0
$544$	−6.23369	+	6.44121i	−0.267267	+	0.276164i
$545$		−	25.5383i		−	1.09394i
$546$		0			0
$547$	40.2337			1.72027			0.860134	−	0.510068i	$-0.170380\pi$
$547$	40.2337			1.72027			0.860134	+	0.510068i	$0.170380\pi$
$548$	6.05321	−	4.45877i	0.258580	−	0.190469i
$549$		0			0
$550$	28.2337	+	14.2695i	1.20389	+	0.608455i
$551$	17.2097			0.733158
$552$		0			0
$553$	−3.25544			−0.138435
$554$	−13.7081	−	6.92820i	−0.582403	−	0.294351i
$555$		0			0
$556$	−9.48913	−	12.8824i	−0.402429	−	0.546336i
$557$	21.4376			0.908340			0.454170	−	0.890915i	$-0.349936\pi$
$557$	21.4376			0.908340			0.454170	+	0.890915i	$0.349936\pi$
$558$		0			0
$559$			21.7216i			0.918724i
$560$	6.61659	+	2.05446i	0.279602	+	0.0868166i
$561$		0			0
$562$	19.4891	+	9.84996i	0.822099	+	0.415496i
$563$			33.6087i			1.41644i	0.705993	+	0.708218i	$0.250501\pi$
$563$			33.6087i			1.41644i	−0.705993	+	0.708218i	$0.749499\pi$
$564$		0			0
$565$		−	18.3128i		−	0.770425i
$566$	14.5090	−	28.7075i	0.609858	−	1.20667i
$567$		0			0
$568$	26.2337	−	4.41957i	1.10074	−	0.185441i
$569$			34.0511i			1.42750i	0.700402	+	0.713748i	$0.253004\pi$
$569$			34.0511i			1.42750i	−0.700402	+	0.713748i	$0.746996\pi$
$570$		0			0
$571$	−0.233688			−0.00977954			−0.00488977	−	0.999988i	$-0.501556\pi$
$571$	−0.233688			−0.00977954			−0.00488977	+	0.999988i	$0.501556\pi$
$572$	−21.3631	−	29.0024i	−0.893234	−	1.21265i
$573$		0			0
$574$	2.74456	−	5.43039i	0.114556	−	0.226660i
$575$	29.0180			1.21013
$576$		0			0
$577$	−8.97825			−0.373769			−0.186885	−	0.982382i	$-0.559839\pi$
$577$	−8.97825			−0.373769			−0.186885	+	0.982382i	$0.559839\pi$
$578$	9.24276	−	18.2877i	0.384448	−	0.760669i
$579$		0			0
$580$	10.3723	+	14.0814i	0.430686	+	0.584698i
$581$	5.17782			0.214812
$582$		0			0
$583$		−	2.90335i		−	0.120244i
$584$	10.4440	−	1.75950i	0.432178	−	0.0728087i
$585$		0			0
$586$	15.8614	−	31.3834i	0.655229	−	1.29643i
$587$		−	12.7143i		−	0.524774i	−0.964963	−	0.262387i	$-0.915490\pi$
$587$		−	12.7143i		−	0.524774i	0.964963	−	0.262387i	$-0.0845097\pi$
$588$		0			0
$589$		−	33.2168i		−	1.36868i
$590$	−28.6921	−	14.5012i	−1.18123	−	0.597006i
$591$		0			0
$592$	−28.4674	−	8.83915i	−1.17000	−	0.363287i
$593$			13.2665i			0.544790i	0.962186	+	0.272395i	$0.0878157\pi$
$593$			13.2665i			0.544790i	−0.962186	+	0.272395i	$0.912184\pi$
$594$		0			0
$595$	2.74456			0.112516
$596$	11.2449	+	15.2661i	0.460609	+	0.625322i
$597$		0			0
$598$	−29.4891	−	14.9040i	−1.20590	−	0.609472i
$599$	−30.9178			−1.26327			−0.631634	−	0.775266i	$-0.717616\pi$
$599$	−30.9178			−1.26327			−0.631634	+	0.775266i	$0.717616\pi$
$600$		0			0
$601$	31.2337			1.27405			0.637024	−	0.770844i	$-0.280165\pi$
$601$	31.2337			1.27405			0.637024	+	0.770844i	$0.280165\pi$
$602$	2.55164	+	1.28962i	0.103997	+	0.0525610i
$603$		0			0
$604$	11.1861	−	8.23966i	0.455158	−	0.335267i
$605$		0			0
$606$		0			0
$607$			0.376308i			0.0152739i	0.999971	+	0.00763694i	$0.00243094\pi$
$607$			0.376308i			0.0152739i	−0.999971	+	0.00763694i	$0.997569\pi$
$608$	−27.4163	−	26.5330i	−1.11188	−	1.07606i
$609$		0			0
$610$	−46.9783	−	23.7432i	−1.90209	−	0.961334i
$611$		−	27.7128i		−	1.12114i
$612$		0			0
$613$			41.4215i			1.67300i	0.547969	+	0.836499i	$0.315401\pi$
$613$			41.4215i			1.67300i	−0.547969	+	0.836499i	$0.684599\pi$
$614$	−11.9574	+	23.6588i	−0.482559	+	0.954792i
$615$		0			0
$616$	−4.67527	+	0.787639i	−0.188372	+	0.0317349i
$617$			18.0202i			0.725467i	0.931893	+	0.362733i	$0.118156\pi$
$617$			18.0202i			0.725467i	−0.931893	+	0.362733i	$0.881844\pi$
$618$		0			0
$619$	−7.76631			−0.312154			−0.156077	−	0.987745i	$-0.549885\pi$
$619$	−7.76631			−0.312154			−0.156077	+	0.987745i	$0.549885\pi$
$620$	27.1788	−	20.0198i	1.09153	−	0.804013i
$621$		0			0
$622$	14.7446	−	29.1736i	0.591203	−	1.16975i
$623$	1.89986			0.0761162
$624$		0			0
$625$	−13.2337			−0.529348
$626$	−5.89027	+	11.6545i	−0.235422	+	0.465806i
$627$		0			0
$628$	17.4891	−	12.8824i	0.697892	−	0.514064i
$629$	−11.8083			−0.470827
$630$		0			0
$631$			25.2594i			1.00556i	0.864414	+	0.502781i	$0.167690\pi$
$631$			25.2594i			1.00556i	−0.864414	+	0.502781i	$0.832310\pi$
$632$	3.02661	+	17.9653i	0.120392	+	0.714622i
$633$		0			0
$634$	−9.30298	+	18.4069i	−0.369469	+	0.731030i
$635$			5.19615i			0.206203i
$636$		0			0
$637$		−	36.6256i		−	1.45116i
$638$	−10.6815	−	5.39853i	−0.422886	−	0.213730i
$639$		0			0
$640$	5.18614	−	38.4241i	0.205000	−	1.51884i
$641$			8.51278i			0.336234i	0.985767	+	0.168117i	$0.0537687\pi$
$641$			8.51278i			0.336234i	−0.985767	+	0.168117i	$0.946231\pi$
$642$		0			0
$643$	24.4674			0.964899			0.482450	−	0.875924i	$-0.339747\pi$
$643$	24.4674			0.964899			0.482450	+	0.875924i	$0.339747\pi$
$644$	−3.50157	+	2.57924i	−0.137981	+	0.101636i
$645$		0			0
$646$	−13.4891	−	6.81751i	−0.530723	−	0.268231i
$647$	44.6260			1.75443			0.877214	−	0.480099i	$-0.159399\pi$
$647$	44.6260			1.75443			0.877214	+	0.480099i	$0.159399\pi$
$648$		0			0
$649$	22.0000			0.863576
$650$	−46.2277	−	23.3639i	−1.81320	−	0.916406i
$651$		0			0
$652$	−19.2554	−	26.1411i	−0.754101	−	1.02377i
$653$	−30.6942			−1.20116			−0.600579	−	0.799565i	$-0.705063\pi$
$653$	−30.6942			−1.20116			−0.600579	+	0.799565i	$0.705063\pi$
$654$		0			0
$655$		−	52.4114i		−	2.04788i
$656$	−32.5196	−	10.0974i	−1.26968	−	0.394235i
$657$		0			0
$658$	−3.25544	−	1.64532i	−0.126910	−	0.0641414i
$659$			26.2757i			1.02356i	0.859118	+	0.511778i	$0.171013\pi$
$659$			26.2757i			1.02356i	−0.859118	+	0.511778i	$0.828987\pi$
$660$		0			0
$661$			3.40876i			0.132585i	0.997800	+	0.0662926i	$0.0211171\pi$
$661$			3.40876i			0.132585i	−0.997800	+	0.0662926i	$0.978883\pi$
$662$	−21.3631	+	42.2689i	−0.830299	+	1.64283i
$663$		0			0
$664$	−4.81386	−	28.5741i	−0.186814	−	1.10889i
$665$			11.6819i			0.453006i
$666$		0			0
$667$	−10.9783			−0.425080
$668$	−16.2598	−	22.0742i	−0.629110	−	0.854078i
$669$		0			0
$670$	−8.74456	+	17.3020i	−0.337832	+	0.668434i
$671$	36.0211			1.39058
$672$		0			0
$673$	−30.4891			−1.17527			−0.587635	−	0.809126i	$-0.699941\pi$
$673$	−30.4891			−1.17527			−0.587635	+	0.809126i	$0.699941\pi$
$674$	1.27582	−	2.52434i	0.0491428	−	0.0972339i
$675$		0			0
$676$	19.5584	+	26.5525i	0.752247	+	1.02125i
$677$	−9.55478			−0.367220			−0.183610	−	0.982999i	$-0.558778\pi$
$677$	−9.55478			−0.367220			−0.183610	+	0.982999i	$0.558778\pi$
$678$		0			0
$679$			0.505408i			0.0193958i
$680$	−2.55164	−	15.1460i	−0.0978510	−	0.580824i
$681$		0			0
$682$	−10.4198	+	20.6167i	−0.398996	+	0.789453i
$683$			16.7306i			0.640179i	0.947387	+	0.320089i	$0.103713\pi$
$683$			16.7306i			0.640179i	−0.947387	+	0.320089i	$0.896287\pi$
$684$		0			0
$685$			12.8824i			0.492212i
$686$	−8.76780	−	4.43132i	−0.334756	−	0.169188i
$687$		0			0
$688$	4.74456	−	15.2804i	0.180885	−	0.582558i
$689$			4.75372i			0.181102i
$690$		0			0
$691$	26.5109			1.00852			0.504261	−	0.863552i	$-0.331765\pi$
$691$	26.5109			1.00852			0.504261	+	0.863552i	$0.331765\pi$
$692$	1.98827	+	2.69927i	0.0755826	+	0.102611i
$693$		0			0
$694$	−7.81386	−	3.94919i	−0.296610	−	0.149909i
$695$	27.4163			1.03996
$696$		0			0
$697$	−13.4891			−0.510937
$698$	−4.30243	−	2.17448i	−0.162849	−	0.0823053i
$699$		0			0
$700$	−5.48913	+	4.04326i	−0.207469	+	0.152821i
$701$	8.53032			0.322186			0.161093	−	0.986939i	$-0.448498\pi$
$701$	8.53032			0.322186			0.161093	+	0.986939i	$0.448498\pi$
$702$		0			0
$703$		−	50.2606i		−	1.89562i
$704$	8.69326	+	25.0684i	0.327640	+	0.944803i
$705$		0			0
$706$	22.7446	+	11.4953i	0.856003	+	0.432631i
$707$			5.60091i			0.210644i
$708$		0			0
$709$			36.6256i			1.37550i	0.725946	+	0.687752i	$0.241402\pi$
$709$			36.6256i			1.37550i	−0.725946	+	0.687752i	$0.758598\pi$
$710$	−20.5622	+	40.6844i	−0.771686	+	1.52686i
$711$		0			0
$712$	−1.76631	−	10.4845i	−0.0661953	−	0.392922i
$713$			21.1894i			0.793548i
$714$		0			0
$715$	61.7228			2.30830
$716$	−2.31416	+	1.70460i	−0.0864842	+	0.0637039i
$717$		0			0
$718$	−2.23369	+	4.41957i	−0.0833605	+	0.164937i
$719$	−18.8114			−0.701548			−0.350774	−	0.936460i	$-0.614081\pi$
$719$	−18.8114			−0.701548			−0.350774	+	0.936460i	$0.614081\pi$
$720$		0			0
$721$	−8.74456			−0.325665
$722$	16.8977	−	33.4338i	0.628867	−	1.24428i
$723$		0			0
$724$		0			0
$725$	−17.2097			−0.639152
$726$		0			0
$727$		−	47.9918i		−	1.77992i	−0.456042	−	0.889958i	$-0.650733\pi$
$727$		−	47.9918i		−	1.77992i	0.456042	−	0.889958i	$-0.349267\pi$
$728$	7.65492	−	1.28962i	0.283710	−	0.0477965i
$729$		0			0
$730$	−8.18614	+	16.1971i	−0.302983	+	0.599481i
$731$		−	6.33830i		−	0.234430i
$732$		0			0
$733$		−	11.4953i		−	0.424588i	−0.977206	−	0.212294i	$-0.931907\pi$
$733$		−	11.4953i		−	0.424588i	0.977206	−	0.212294i	$-0.0680935\pi$
$734$	19.9243	+	10.0699i	0.735419	+	0.371687i
$735$		0			0
$736$	17.4891	+	16.9257i	0.644658	+	0.623889i
$737$		−	13.2665i		−	0.488678i
$738$		0			0
$739$	−18.7446			−0.689530			−0.344765	−	0.938689i	$-0.612041\pi$
$739$	−18.7446			−0.689530			−0.344765	+	0.938689i	$0.612041\pi$
$740$	41.1244	−	30.2921i	1.51176	−	1.11356i
$741$		0			0
$742$	0.558422	+	0.282231i	0.0205003	+	0.0103610i
$743$	0.800857			0.0293806			0.0146903	−	0.999892i	$-0.495324\pi$
$743$	0.800857			0.0293806			0.0146903	+	0.999892i	$0.495324\pi$
$744$		0			0
$745$	−32.4891			−1.19031
$746$	−6.85407	−	3.46410i	−0.250945	−	0.126830i
$747$		0			0
$748$	6.23369	+	8.46284i	0.227926	+	0.309432i
$749$	−4.22789			−0.154484
$750$		0			0
$751$			52.4114i			1.91252i	0.292522	+	0.956259i	$0.405506\pi$
$751$			52.4114i			1.91252i	−0.292522	+	0.956259i	$0.594494\pi$
$752$	−6.05321	+	19.4950i	−0.220738	+	0.710909i
$753$		0			0
$754$	17.4891	+	8.83915i	0.636916	+	0.321903i
$755$			23.8063i			0.866399i
$756$		0			0
$757$			41.4215i			1.50549i	0.658313	+	0.752745i	$0.271271\pi$
$757$			41.4215i			1.50549i	−0.658313	+	0.752745i	$0.728729\pi$
$758$	8.60485	−	17.0256i	0.312542	−	0.618396i
$759$		0			0
$760$	64.4674	−	10.8608i	2.33848	−	0.393962i
$761$		−	40.3894i		−	1.46411i	−0.681243	−	0.732057i	$-0.738560\pi$
$761$		−	40.3894i		−	1.46411i	0.681243	−	0.732057i	$-0.261440\pi$
$762$		0			0
$763$	−3.76631			−0.136350
$764$	−21.3631	−	29.0024i	−0.772888	−	1.04927i
$765$		0			0
$766$	12.5109	−	24.7540i	0.452036	−	0.894399i
$767$	−36.0211			−1.30065
$768$		0			0
$769$	−10.2554			−0.369821			−0.184910	−	0.982755i	$-0.559199\pi$
$769$	−10.2554			−0.369821			−0.184910	+	0.982755i	$0.559199\pi$
$770$	3.66452	−	7.25061i	0.132060	−	0.261294i
$771$		0			0
$772$	25.1861	+	34.1926i	0.906469	+	1.23062i
$773$	45.2778			1.62853			0.814264	−	0.580495i	$-0.197141\pi$
$773$	45.2778			1.62853			0.814264	+	0.580495i	$0.197141\pi$
$774$		0			0
$775$			33.2168i			1.19318i
$776$	2.78912	−	0.469882i	0.100124	−	0.0168678i
$777$		0			0
$778$	−23.5367	+	46.5696i	−0.843831	+	1.66960i
$779$		−	57.4150i		−	2.05710i
$780$		0			0
$781$		−	31.1952i		−	1.11625i
$782$	8.60485	+	4.34896i	0.307709	+	0.155519i
$783$		0			0
$784$	−8.00000	+	25.7648i	−0.285714	+	0.920172i
$785$			37.2203i			1.32845i
$786$		0			0
$787$	−21.4891			−0.766005			−0.383002	−	0.923747i	$-0.625110\pi$
$787$	−21.4891			−0.766005			−0.383002	+	0.923747i	$0.625110\pi$
$788$	−14.2715	−	19.3750i	−0.508402	−	0.690205i
$789$		0			0
$790$	−27.8614	−	14.0814i	−0.991264	−	0.500993i
$791$	−2.70071			−0.0960263
$792$		0			0
$793$	−58.9783			−2.09438
$794$	−1.75079	−	0.884861i	−0.0621330	−	0.0314025i
$795$		0			0
$796$	−35.7921	+	26.3643i	−1.26862	+	0.934458i
$797$	25.7400			0.911758			0.455879	−	0.890042i	$-0.349325\pi$
$797$	25.7400			0.911758			0.455879	+	0.890042i	$0.349325\pi$
$798$		0			0
$799$			8.08653i			0.286081i
$800$	27.4163	+	26.5330i	0.969312	+	0.938083i
$801$		0			0
$802$	−21.4891	−	10.8608i	−0.758807	−	0.383507i
$803$		−	12.4193i		−	0.438268i
$804$		0			0
$805$		−	7.45202i		−	0.262649i
$806$	17.0606	−	33.7562i	0.600935	−	1.18901i
$807$		0			0
$808$	30.9090	−	5.20721i	1.08737	−	0.183189i
$809$		−	42.9686i		−	1.51070i	−0.655323	−	0.755349i	$-0.727468\pi$
$809$		−	42.9686i		−	1.51070i	0.655323	−	0.755349i	$-0.272532\pi$
$810$		0			0
$811$	−6.74456			−0.236834			−0.118417	−	0.992964i	$-0.537782\pi$
$811$	−6.74456			−0.236834			−0.118417	+	0.992964i	$0.537782\pi$
$812$	2.07668	−	1.52967i	0.0728771	−	0.0536809i
$813$		0			0
$814$	−15.7663	+	31.1952i	−0.552609	+	1.09339i
$815$	55.6334			1.94875
$816$		0			0
$817$	26.9783			0.943850
$818$	7.01701	−	13.8839i	0.245344	−	0.485438i
$819$		0			0
$820$	46.9783	−	34.6040i	1.64055	−	1.20842i
$821$	42.0743			1.46840			0.734202	−	0.678931i	$-0.237556\pi$
$821$	42.0743			1.46840			0.734202	+	0.678931i	$0.237556\pi$
$822$		0			0
$823$		−	21.5925i		−	0.752666i	−0.926485	−	0.376333i	$-0.877185\pi$
$823$		−	21.5925i		−	0.752666i	0.926485	−	0.376333i	$-0.122815\pi$
$824$	8.12989	+	48.2574i	0.283218	+	1.68113i
$825$		0			0
$826$	−2.13859	+	4.23142i	−0.0744112	+	0.147230i
$827$		−	6.63325i		−	0.230661i	−0.993327	−	0.115330i	$-0.963207\pi$
$827$		−	6.63325i		−	0.230661i	0.993327	−	0.115330i	$-0.0367927\pi$
$828$		0			0
$829$			23.7432i			0.824635i	0.911040	+	0.412318i	$0.135281\pi$
$829$			23.7432i			0.824635i	−0.911040	+	0.412318i	$0.864719\pi$
$830$	44.3140	+	22.3966i	1.53816	+	0.777399i
$831$		0			0
$832$	−14.2337	−	41.0452i	−0.493464	−	1.42299i
$833$			10.6873i			0.370292i
$834$		0			0
$835$	46.9783			1.62575
$836$	−36.0211	+	26.5330i	−1.24582	+	0.917663i
$837$		0			0
$838$	−25.8614	−	13.0706i	−0.893367	−	0.451515i
$839$	−45.4268			−1.56831			−0.784154	−	0.620566i	$-0.786903\pi$
$839$	−45.4268			−1.56831			−0.784154	+	0.620566i	$0.786903\pi$
$840$		0			0
$841$	−22.4891			−0.775487
$842$	5.10328	+	2.57924i	0.175871	+	0.0888865i
$843$		0			0
$844$	1.48913	+	2.02163i	0.0512578	+	0.0695875i
$845$	−56.5088			−1.94396
$846$		0			0
$847$		0			0
$848$	1.03834	−	3.34408i	0.0356567	−	0.114836i
$849$		0			0
$850$	13.4891	+	6.81751i	0.462673	+	0.233839i
$851$			32.0618i			1.09906i
$852$		0			0
$853$			45.4647i			1.55668i	0.627841	+	0.778342i	$0.283939\pi$
$853$			45.4647i			1.55668i	−0.627841	+	0.778342i	$0.716061\pi$
$854$	−3.50157	+	6.92820i	−0.119821	+	0.237078i
$855$		0			0
$856$	3.93070	+	23.3319i	0.134349	+	0.797466i
$857$		−	35.6357i		−	1.21729i	−0.793442	−	0.608646i	$-0.791713\pi$
$857$		−	35.6357i		−	1.21729i	0.793442	−	0.608646i	$-0.208287\pi$
$858$		0			0
$859$	48.4674			1.65369			0.826843	−	0.562433i	$-0.190135\pi$
$859$	48.4674			1.65369			0.826843	+	0.562433i	$0.190135\pi$
$860$	16.2598	+	22.0742i	0.554454	+	0.752725i
$861$		0			0
$862$	−14.2337	+	28.1628i	−0.484801	+	0.959227i
$863$	−56.4343			−1.92104			−0.960522	−	0.278203i	$-0.910261\pi$
$863$	−56.4343			−1.92104			−0.960522	+	0.278203i	$0.910261\pi$
$864$		0			0
$865$	−5.74456			−0.195321
$866$	2.86366	−	5.66603i	0.0973111	−	0.192540i
$867$		0			0
$868$	−2.95245	−	4.00824i	−0.100213	−	0.136049i
$869$	21.3631			0.724692
$870$		0			0
$871$			21.7216i			0.736007i
$872$	3.50157	+	20.7846i	0.118578	+	0.703856i
$873$		0			0
$874$	−18.5109	+	36.6256i	−0.626140	+	1.23888i
$875$		−	3.02167i		−	0.102151i
$876$		0			0
$877$			2.02163i			0.0682657i	0.999417	+	0.0341328i	$0.0108669\pi$
$877$			2.02163i			0.0682657i	−0.999417	+	0.0341328i	$0.989133\pi$
$878$	40.4865	+	20.4622i	1.36635	+	0.690566i
$879$		0			0
$880$	−43.4198	−	13.4819i	−1.46368	−	0.454475i
$881$			38.8048i			1.30737i	0.756768	+	0.653684i	$0.226777\pi$
$881$			38.8048i			1.30737i	−0.756768	+	0.653684i	$0.773223\pi$
$882$		0			0
$883$	33.7228			1.13486			0.567432	−	0.823421i	$-0.307937\pi$
$883$	33.7228			1.13486			0.567432	+	0.823421i	$0.307937\pi$
$884$	−10.2066	−	13.8564i	−0.343284	−	0.466041i
$885$		0			0
$886$	−8.37228	−	4.23142i	−0.281272	−	0.142157i
$887$	−55.6334			−1.86799			−0.933993	−	0.357290i	$-0.883701\pi$
$887$	−55.6334			−1.86799			−0.933993	+	0.357290i	$0.883701\pi$
$888$		0			0
$889$	0.766312			0.0257013
$890$	16.2598	+	8.21782i	0.545029	+	0.275462i
$891$		0			0
$892$	13.6277	−	10.0381i	0.456290	−	0.336101i
$893$	−34.4194			−1.15180
$894$		0			0
$895$		−	4.92498i		−	0.164624i
$896$	−5.66666	−	0.764836i	−0.189310	−	0.0255514i
$897$		0			0
$898$	−36.2337	−	18.3128i	−1.20913	−	0.611106i
$899$		−	12.5668i		−	0.419126i
$900$		0			0
$901$		−	1.38712i		−	0.0462118i
$902$	−18.0106	+	35.6357i	−0.599686	+	1.18654i
$903$		0			0
$904$	2.51087	+	14.9040i	0.0835105	+	0.495701i
$905$		0			0
$906$		0			0
$907$	−19.7663			−0.656330			−0.328165	−	0.944620i	$-0.606430\pi$
$907$	−19.7663			−0.656330			−0.328165	+	0.944620i	$0.606430\pi$
$908$	4.62832	−	3.40920i	0.153596	−	0.113138i
$909$		0			0
$910$	−6.00000	+	11.8716i	−0.198898	+	0.393540i
$911$	5.10328			0.169079			0.0845397	−	0.996420i	$-0.473058\pi$
$911$	5.10328			0.169079			0.0845397	+	0.996420i	$0.473058\pi$
$912$		0			0
$913$	−33.9783			−1.12452
$914$	17.5217	−	34.6685i	0.579567	−	1.14673i
$915$		0			0
$916$	−20.7446	+	15.2804i	−0.685420	+	0.504877i
$917$	−7.72946			−0.255249
$918$		0			0
$919$		−	44.5830i		−	1.47066i	−0.677710	−	0.735329i	$-0.737028\pi$
$919$		−	44.5830i		−	1.47066i	0.677710	−	0.735329i	$-0.262972\pi$
$920$	−41.1244	+	6.92820i	−1.35583	+	0.228416i
$921$		0			0
$922$	26.6970	−	52.8227i	0.879219	−	1.73962i
$923$			51.0767i			1.68121i
$924$		0			0
$925$			50.2606i			1.65256i
$926$	−16.0968	−	8.13547i	−0.528975	−	0.267348i
$927$		0			0
$928$	−10.3723	−	10.0381i	−0.340487	−	0.329517i
$929$		−	49.8968i		−	1.63706i	−0.574462	−	0.818531i	$-0.694789\pi$
$929$		−	49.8968i		−	1.63706i	0.574462	−	0.818531i	$-0.305211\pi$
$930$		0			0
$931$	−45.4891			−1.49085
$932$	43.6761	−	32.1716i	1.43066	−	1.05382i
$933$		0			0
$934$	47.9090	+	24.2136i	1.56763	+	0.792292i
$935$	−18.0106			−0.589008
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	2.55164	+	1.28962i	0.0833141	+	0.0421076i
$939$		0			0
$940$	−20.7446	−	28.1628i	−0.676613	−	0.918568i
$941$	12.8327			0.418335			0.209168	−	0.977880i	$-0.432925\pi$
$941$	12.8327			0.418335			0.209168	+	0.977880i	$0.432925\pi$
$942$		0			0
$943$			36.6256i			1.19269i
$944$	25.3396	+	7.86797i	0.824734	+	0.256081i
$945$		0			0
$946$	−16.7446	−	8.46284i	−0.544413	−	0.275151i
$947$		−	1.43710i		−	0.0466994i	−0.999727	−	0.0233497i	$-0.992567\pi$
$947$		−	1.43710i		−	0.0466994i	0.999727	−	0.0233497i	$-0.00743311\pi$
$948$		0			0
$949$			20.3344i			0.660084i
$950$	−29.0180	+	57.4150i	−0.941468	+	1.86279i
$951$		0			0
$952$	−2.23369	+	0.376308i	−0.0723942	+	0.0121962i
$953$		−	44.7384i		−	1.44922i	−0.689160	−	0.724609i	$-0.742020\pi$
$953$		−	44.7384i		−	1.44922i	0.689160	−	0.724609i	$-0.257980\pi$
$954$		0			0
$955$	61.7228			1.99730
$956$	17.2097	+	23.3639i	0.556602	+	0.755641i
$957$		0			0
$958$	−8.74456	+	17.3020i	−0.282524	+	0.559002i
$959$	1.89986			0.0613496
$960$		0			0
$961$	6.74456			0.217567
$962$	25.8146	−	51.0767i	0.832295	−	1.64678i
$963$		0			0
$964$	−2.37228	−	3.22060i	−0.0764060	−	0.103729i
$965$	−72.7686			−2.34250
$966$		0			0
$967$		−	3.91416i		−	0.125871i	−0.998018	−	0.0629355i	$-0.979954\pi$
$967$		−	3.91416i		−	0.125871i	0.998018	−	0.0629355i	$-0.0200462\pi$
$968$		0			0
$969$		0			0
$970$	−2.18614	+	4.32550i	−0.0701927	+	0.138883i
$971$		−	47.7600i		−	1.53269i	−0.642428	−	0.766346i	$-0.722073\pi$
$971$		−	47.7600i		−	1.53269i	0.642428	−	0.766346i	$-0.277927\pi$
$972$		0			0
$973$		−	4.04326i		−	0.129621i
$974$	5.57825	+	2.81929i	0.178739	+	0.0903359i
$975$		0			0
$976$	41.4891	+	12.8824i	1.32803	+	0.412356i
$977$		−	5.74839i		−	0.183907i	−0.995763	−	0.0919536i	$-0.970689\pi$
$977$		−	5.74839i		−	0.183907i	0.995763	−	0.0919536i	$-0.0293112\pi$
$978$		0			0
$979$	−12.4674			−0.398459
$980$	−27.4163	−	37.2203i	−0.875781	−	1.18896i
$981$		0			0
$982$	48.4198	+	24.4718i	1.54514	+	0.780926i
$983$	42.7261			1.36275			0.681376	−	0.731934i	$-0.261382\pi$
$983$	42.7261			1.36275			0.681376	+	0.731934i	$0.261382\pi$
$984$		0			0
$985$	41.2337			1.31381
$986$	−5.10328	−	2.57924i	−0.162522	−	0.0821398i
$987$		0			0
$988$	58.9783	−	43.4431i	1.87635	−	1.38211i
$989$	−17.2097			−0.547237
$990$		0			0
$991$		−	13.3878i		−	0.425278i	−0.977131	−	0.212639i	$-0.931794\pi$
$991$		−	13.3878i		−	0.425278i	0.977131	−	0.212639i	$-0.0682058\pi$
$992$	−19.3748	+	20.0198i	−0.615150	+	0.635628i
$993$		0			0
$994$	6.00000	+	3.03245i	0.190308	+	0.0961834i
$995$		−	76.1726i		−	2.41483i
$996$		0			0
$997$		−	56.9600i		−	1.80394i	−0.431796	−	0.901971i	$-0.642120\pi$
$997$		−	56.9600i		−	1.80394i	0.431796	−	0.901971i	$-0.357880\pi$
$998$	−17.8615	+	35.3407i	−0.565396	+	1.11869i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.f.b.107.5	yes	8
3.2	odd	2	inner	216.2.f.b.107.4	yes	8
4.3	odd	2		864.2.f.b.431.8		8
8.3	odd	2	inner	216.2.f.b.107.3	✓	8
8.5	even	2		864.2.f.b.431.1		8
9.2	odd	6		648.2.l.e.539.4		8
9.4	even	3		648.2.l.e.107.3		8
9.5	odd	6		648.2.l.d.107.2		8
9.7	even	3		648.2.l.d.539.1		8
12.11	even	2		864.2.f.b.431.2		8
24.5	odd	2		864.2.f.b.431.7		8
24.11	even	2	inner	216.2.f.b.107.6	yes	8
36.7	odd	6		2592.2.p.d.2159.1		8
36.11	even	6		2592.2.p.e.2159.4		8
36.23	even	6		2592.2.p.d.431.4		8
36.31	odd	6		2592.2.p.e.431.1		8
72.5	odd	6		2592.2.p.d.431.1		8
72.11	even	6		648.2.l.e.539.3		8
72.13	even	6		2592.2.p.e.431.4		8
72.29	odd	6		2592.2.p.e.2159.1		8
72.43	odd	6		648.2.l.d.539.2		8
72.59	even	6		648.2.l.d.107.1		8
72.61	even	6		2592.2.p.d.2159.4		8
72.67	odd	6		648.2.l.e.107.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.f.b.107.3	✓	8	8.3	odd	2	inner
216.2.f.b.107.4	yes	8	3.2	odd	2	inner
216.2.f.b.107.5	yes	8	1.1	even	1	trivial
216.2.f.b.107.6	yes	8	24.11	even	2	inner
648.2.l.d.107.1		8	72.59	even	6
648.2.l.d.107.2		8	9.5	odd	6
648.2.l.d.539.1		8	9.7	even	3
648.2.l.d.539.2		8	72.43	odd	6
648.2.l.e.107.3		8	9.4	even	3
648.2.l.e.107.4		8	72.67	odd	6
648.2.l.e.539.3		8	72.11	even	6
648.2.l.e.539.4		8	9.2	odd	6
864.2.f.b.431.1		8	8.5	even	2
864.2.f.b.431.2		8	12.11	even	2
864.2.f.b.431.7		8	24.5	odd	2
864.2.f.b.431.8		8	4.3	odd	2
2592.2.p.d.431.1		8	72.5	odd	6
2592.2.p.d.431.4		8	36.23	even	6
2592.2.p.d.2159.1		8	36.7	odd	6
2592.2.p.d.2159.4		8	72.61	even	6
2592.2.p.e.431.1		8	36.31	odd	6
2592.2.p.e.431.4		8	72.13	even	6
2592.2.p.e.2159.1		8	72.29	odd	6
2592.2.p.e.2159.4		8	36.11	even	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.637910 - 1.26217i) q^{2} +(-1.18614 - 1.61030i) q^{4} +3.42703 q^{5} -0.505408i q^{7} +(-2.78912 + 0.469882i) q^{8} +O(q^{10})\)	\(q+(0.637910 - 1.26217i) q^{2} +(-1.18614 - 1.61030i) q^{4} +3.42703 q^{5} -0.505408i q^{7} +(-2.78912 + 0.469882i) q^{8} +(2.18614 - 4.32550i) q^{10} +3.31662i q^{11} -5.43039i q^{13} +(-0.637910 - 0.322405i) q^{14} +(-1.18614 + 3.82009i) q^{16} +1.58457i q^{17} -6.74456 q^{19} +(-4.06494 - 5.51856i) q^{20} +(4.18614 + 2.11571i) q^{22} +4.30243 q^{23} +6.74456 q^{25} +(-6.85407 - 3.46410i) q^{26} +(-0.813859 + 0.599485i) q^{28} -2.55164 q^{29} +4.92498i q^{31} +(4.06494 + 3.93398i) q^{32} +(2.00000 + 1.01082i) q^{34} -1.73205i q^{35} +7.45202i q^{37} +(-4.30243 + 8.51278i) q^{38} +(-9.55842 + 1.61030i) q^{40} +8.51278i q^{41} -4.00000 q^{43} +(5.34077 - 3.93398i) q^{44} +(2.74456 - 5.43039i) q^{46} +5.10328 q^{47} +6.74456 q^{49} +(4.30243 - 8.51278i) q^{50} +(-8.74456 + 6.44121i) q^{52} -0.875393 q^{53} +11.3662i q^{55} +(0.237482 + 1.40965i) q^{56} +(-1.62772 + 3.22060i) q^{58} -6.63325i q^{59} -10.8608i q^{61} +(6.21616 + 3.14170i) q^{62} +(7.55842 - 2.62112i) q^{64} -18.6101i q^{65} -4.00000 q^{67} +(2.55164 - 1.87953i) q^{68} +(-2.18614 - 1.10489i) q^{70} -9.40571 q^{71} -3.74456 q^{73} +(9.40571 + 4.75372i) q^{74} +(8.00000 + 10.8608i) q^{76} +1.67625 q^{77} -6.44121i q^{79} +(-4.06494 + 13.0916i) q^{80} +(10.7446 + 5.43039i) q^{82} +10.2448i q^{83} +5.43039i q^{85} +(-2.55164 + 5.04868i) q^{86} +(-1.55842 - 9.25048i) q^{88} +3.75906i q^{89} -2.74456 q^{91} +(-5.10328 - 6.92820i) q^{92} +(3.25544 - 6.44121i) q^{94} -23.1138 q^{95} -1.00000 q^{97} +(4.30243 - 8.51278i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4}+O(q^{10}) \) 8 * q + 2 * q^4	\( 8 q + 2 q^{4} + 6 q^{10} + 2 q^{16} - 8 q^{19} + 22 q^{22} + 8 q^{25} - 18 q^{28} + 16 q^{34} - 42 q^{40} - 32 q^{43} - 24 q^{46} + 8 q^{49} - 24 q^{52} - 36 q^{58} + 26 q^{64} - 32 q^{67} - 6 q^{70} + 16 q^{73} + 64 q^{76} + 40 q^{82} + 22 q^{88} + 24 q^{91} + 72 q^{94} - 8 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 + 6 * q^10 + 2 * q^16 - 8 * q^19 + 22 * q^22 + 8 * q^25 - 18 * q^28 + 16 * q^34 - 42 * q^40 - 32 * q^43 - 24 * q^46 + 8 * q^49 - 24 * q^52 - 36 * q^58 + 26 * q^64 - 32 * q^67 - 6 * q^70 + 16 * q^73 + 64 * q^76 + 40 * q^82 + 22 * q^88 + 24 * q^91 + 72 * q^94 - 8 * q^97

Introduction

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