LMFDB - Embedded newform 912.3.be.b.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.b.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} -11.0000 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} -11.0000 q^{7} +(1.50000 - 2.59808i) q^{9} +8.00000 q^{11} +(-4.50000 - 2.59808i) q^{13} +(-3.00000 - 1.73205i) q^{15} +(13.0000 + 22.5167i) q^{17} -19.0000 q^{19} +(16.5000 - 9.52628i) q^{21} +(-16.0000 + 27.7128i) q^{23} +(10.5000 - 18.1865i) q^{25} +5.19615i q^{27} +(-21.0000 - 12.1244i) q^{29} -53.6936i q^{31} +(-12.0000 + 6.92820i) q^{33} +(-11.0000 - 19.0526i) q^{35} -46.7654i q^{37} +9.00000 q^{39} +(-12.0000 + 6.92820i) q^{41} +(23.5000 + 40.7032i) q^{43} +6.00000 q^{45} +(35.0000 - 60.6218i) q^{47} +72.0000 q^{49} +(-39.0000 - 22.5167i) q^{51} +(-6.00000 - 3.46410i) q^{53} +(8.00000 + 13.8564i) q^{55} +(28.5000 - 16.4545i) q^{57} +(93.0000 - 53.6936i) q^{59} +(-17.5000 + 30.3109i) q^{61} +(-16.5000 + 28.5788i) q^{63} -10.3923i q^{65} +(-13.5000 - 7.79423i) q^{67} -55.4256i q^{69} +(114.000 - 65.8179i) q^{71} +(-29.5000 - 51.0955i) q^{73} +36.3731i q^{75} -88.0000 q^{77} +(22.5000 - 12.9904i) q^{79} +(-4.50000 - 7.79423i) q^{81} +2.00000 q^{83} +(-26.0000 + 45.0333i) q^{85} +42.0000 q^{87} +(-69.0000 - 39.8372i) q^{89} +(49.5000 + 28.5788i) q^{91} +(46.5000 + 80.5404i) q^{93} +(-19.0000 - 32.9090i) q^{95} +(-18.0000 + 10.3923i) q^{97} +(12.0000 - 20.7846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 2 q^{5} - 22 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 2 * q^5 - 22 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} + 2 q^{5} - 22 q^{7} + 3 q^{9} + 16 q^{11} - 9 q^{13} - 6 q^{15} + 26 q^{17} - 38 q^{19} + 33 q^{21} - 32 q^{23} + 21 q^{25} - 42 q^{29} - 24 q^{33} - 22 q^{35} + 18 q^{39} - 24 q^{41} + 47 q^{43} + 12 q^{45} + 70 q^{47} + 144 q^{49} - 78 q^{51} - 12 q^{53} + 16 q^{55} + 57 q^{57} + 186 q^{59} - 35 q^{61} - 33 q^{63} - 27 q^{67} + 228 q^{71} - 59 q^{73} - 176 q^{77} + 45 q^{79} - 9 q^{81} + 4 q^{83} - 52 q^{85} + 84 q^{87} - 138 q^{89} + 99 q^{91} + 93 q^{93} - 38 q^{95} - 36 q^{97} + 24 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 2 * q^5 - 22 * q^7 + 3 * q^9 + 16 * q^11 - 9 * q^13 - 6 * q^15 + 26 * q^17 - 38 * q^19 + 33 * q^21 - 32 * q^23 + 21 * q^25 - 42 * q^29 - 24 * q^33 - 22 * q^35 + 18 * q^39 - 24 * q^41 + 47 * q^43 + 12 * q^45 + 70 * q^47 + 144 * q^49 - 78 * q^51 - 12 * q^53 + 16 * q^55 + 57 * q^57 + 186 * q^59 - 35 * q^61 - 33 * q^63 - 27 * q^67 + 228 * q^71 - 59 * q^73 - 176 * q^77 + 45 * q^79 - 9 * q^81 + 4 * q^83 - 52 * q^85 + 84 * q^87 - 138 * q^89 + 99 * q^91 + 93 * q^93 - 38 * q^95 - 36 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	1.00000	+	1.73205i	0.200000	+	0.346410i	0.948528	−	0.316693i	$-0.102572\pi$
$5$	1.00000	+	1.73205i	0.200000	+	0.346410i	−0.748528	+	0.663103i	$0.769239\pi$
$6$		0			0
$7$	−11.0000			−1.57143			−0.785714	−	0.618590i	$-0.787704\pi$
$7$	−11.0000			−1.57143			−0.785714	+	0.618590i	$0.787704\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	8.00000			0.727273			0.363636	−	0.931541i	$-0.381535\pi$
$11$	8.00000			0.727273			0.363636	+	0.931541i	$0.381535\pi$
$12$		0			0
$13$	−4.50000	−	2.59808i	−0.346154	−	0.199852i	0.316836	−	0.948480i	$-0.397379\pi$
$13$	−4.50000	−	2.59808i	−0.346154	−	0.199852i	−0.662990	+	0.748628i	$0.730713\pi$
$14$		0			0
$15$	−3.00000	−	1.73205i	−0.200000	−	0.115470i
$16$		0			0
$17$	13.0000	+	22.5167i	0.764706	+	1.32451i	0.940402	+	0.340065i	$0.110449\pi$
$17$	13.0000	+	22.5167i	0.764706	+	1.32451i	−0.175696	+	0.984444i	$0.556218\pi$
$18$		0			0
$19$	−19.0000			−1.00000
$19$	−19.0000			−1.00000
$20$		0			0
$21$	16.5000	−	9.52628i	0.785714	−	0.453632i
$22$		0			0
$23$	−16.0000	+	27.7128i	−0.695652	+	1.20490i	0.274308	+	0.961642i	$0.411551\pi$
$23$	−16.0000	+	27.7128i	−0.695652	+	1.20490i	−0.969960	+	0.243263i	$0.921782\pi$
$24$		0			0
$25$	10.5000	−	18.1865i	0.420000	−	0.727461i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−21.0000	−	12.1244i	−0.724138	−	0.418081i	0.0921359	−	0.995746i	$-0.470631\pi$
$29$	−21.0000	−	12.1244i	−0.724138	−	0.418081i	−0.816274	+	0.577665i	$0.803964\pi$
$30$		0			0
$31$		−	53.6936i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$31$		−	53.6936i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$32$		0			0
$33$	−12.0000	+	6.92820i	−0.363636	+	0.209946i
$34$		0			0
$35$	−11.0000	−	19.0526i	−0.314286	−	0.544359i
$36$		0			0
$37$		−	46.7654i		−	1.26393i	−0.774997	−	0.631964i	$-0.782249\pi$
$37$		−	46.7654i		−	1.26393i	0.774997	−	0.631964i	$-0.217751\pi$
$38$		0			0
$39$	9.00000			0.230769
$40$		0			0
$41$	−12.0000	+	6.92820i	−0.292683	+	0.168981i	−0.639151	−	0.769081i	$-0.720714\pi$
$41$	−12.0000	+	6.92820i	−0.292683	+	0.168981i	0.346468	+	0.938062i	$0.387381\pi$
$42$		0			0
$43$	23.5000	+	40.7032i	0.546512	+	0.946586i	0.998510	+	0.0545672i	$0.0173779\pi$
$43$	23.5000	+	40.7032i	0.546512	+	0.946586i	−0.451998	+	0.892019i	$0.649289\pi$
$44$		0			0
$45$	6.00000			0.133333
$46$		0			0
$47$	35.0000	−	60.6218i	0.744681	−	1.28983i	−0.205663	−	0.978623i	$-0.565935\pi$
$47$	35.0000	−	60.6218i	0.744681	−	1.28983i	0.950344	−	0.311202i	$-0.100732\pi$
$48$		0			0
$49$	72.0000			1.46939
$50$		0			0
$51$	−39.0000	−	22.5167i	−0.764706	−	0.441503i
$52$		0			0
$53$	−6.00000	−	3.46410i	−0.113208	−	0.0653604i	0.442327	−	0.896854i	$-0.354153\pi$
$53$	−6.00000	−	3.46410i	−0.113208	−	0.0653604i	−0.555535	+	0.831493i	$0.687486\pi$
$54$		0			0
$55$	8.00000	+	13.8564i	0.145455	+	0.251935i
$56$		0			0
$57$	28.5000	−	16.4545i	0.500000	−	0.288675i
$58$		0			0
$59$	93.0000	−	53.6936i	1.57627	−	0.910061i	0.580898	−	0.813976i	$-0.302702\pi$
$59$	93.0000	−	53.6936i	1.57627	−	0.910061i	0.995373	−	0.0960842i	$-0.0306318\pi$
$60$		0			0
$61$	−17.5000	+	30.3109i	−0.286885	+	0.496900i	−0.973065	−	0.230533i	$-0.925953\pi$
$61$	−17.5000	+	30.3109i	−0.286885	+	0.496900i	0.686179	+	0.727432i	$0.259287\pi$
$62$		0			0
$63$	−16.5000	+	28.5788i	−0.261905	+	0.453632i
$64$		0			0
$65$		−	10.3923i		−	0.159882i
$66$		0			0
$67$	−13.5000	−	7.79423i	−0.201493	−	0.116332i	0.395859	−	0.918311i	$-0.370447\pi$
$67$	−13.5000	−	7.79423i	−0.201493	−	0.116332i	−0.597351	+	0.801980i	$0.703780\pi$
$68$		0			0
$69$		−	55.4256i		−	0.803270i
$70$		0			0
$71$	114.000	−	65.8179i	1.60563	−	0.927013i	0.615302	−	0.788291i	$-0.289034\pi$
$71$	114.000	−	65.8179i	1.60563	−	0.927013i	0.990331	−	0.138722i	$-0.0442994\pi$
$72$		0			0
$73$	−29.5000	−	51.0955i	−0.404110	−	0.699938i	0.590108	−	0.807324i	$-0.299085\pi$
$73$	−29.5000	−	51.0955i	−0.404110	−	0.699938i	−0.994217	+	0.107386i	$0.965752\pi$
$74$		0			0
$75$			36.3731i			0.484974i
$76$		0			0
$77$	−88.0000			−1.14286
$78$		0			0
$79$	22.5000	−	12.9904i	0.284810	−	0.164435i	−0.350789	−	0.936455i	$-0.614087\pi$
$79$	22.5000	−	12.9904i	0.284810	−	0.164435i	0.635599	+	0.772019i	$0.280753\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	2.00000			0.0240964			0.0120482	−	0.999927i	$-0.496165\pi$
$83$	2.00000			0.0240964			0.0120482	+	0.999927i	$0.496165\pi$
$84$		0			0
$85$	−26.0000	+	45.0333i	−0.305882	+	0.529804i
$86$		0			0
$87$	42.0000			0.482759
$88$		0			0
$89$	−69.0000	−	39.8372i	−0.775281	−	0.447609i	0.0594743	−	0.998230i	$-0.481058\pi$
$89$	−69.0000	−	39.8372i	−0.775281	−	0.447609i	−0.834755	+	0.550621i	$0.814391\pi$
$90$		0			0
$91$	49.5000	+	28.5788i	0.543956	+	0.314053i
$92$		0			0
$93$	46.5000	+	80.5404i	0.500000	+	0.866025i
$94$		0			0
$95$	−19.0000	−	32.9090i	−0.200000	−	0.346410i
$96$		0			0
$97$	−18.0000	+	10.3923i	−0.185567	+	0.107137i	−0.589906	−	0.807472i	$-0.700835\pi$
$97$	−18.0000	+	10.3923i	−0.185567	+	0.107137i	0.404339	+	0.914609i	$0.367502\pi$
$98$		0			0
$99$	12.0000	−	20.7846i	0.121212	−	0.209946i
$100$		0			0
$101$	58.0000	−	100.459i	0.574257	−	0.994643i	−0.421864	−	0.906659i	$-0.638624\pi$
$101$	58.0000	−	100.459i	0.574257	−	0.994643i	0.996122	−	0.0879841i	$-0.0280425\pi$
$102$		0			0
$103$			19.0526i			0.184976i	0.995714	+	0.0924881i	$0.0294820\pi$
$103$			19.0526i			0.184976i	−0.995714	+	0.0924881i	$0.970518\pi$
$104$		0			0
$105$	33.0000	+	19.0526i	0.314286	+	0.181453i
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	42.0000	−	24.2487i	0.385321	−	0.222465i	−0.294810	−	0.955556i	$-0.595256\pi$
$109$	42.0000	−	24.2487i	0.385321	−	0.222465i	0.680131	+	0.733091i	$0.261923\pi$
$110$		0			0
$111$	40.5000	+	70.1481i	0.364865	+	0.631964i
$112$		0			0
$113$		−	58.8897i		−	0.521148i	−0.965454	−	0.260574i	$-0.916088\pi$
$113$		−	58.8897i		−	0.521148i	0.965454	−	0.260574i	$-0.0839118\pi$
$114$		0			0
$115$	−64.0000			−0.556522
$116$		0			0
$117$	−13.5000	+	7.79423i	−0.115385	+	0.0666173i
$118$		0			0
$119$	−143.000	−	247.683i	−1.20168	−	2.08137i
$120$		0			0
$121$	−57.0000			−0.471074
$122$		0			0
$123$	12.0000	−	20.7846i	0.0975610	−	0.168981i
$124$		0			0
$125$	92.0000			0.736000
$126$		0			0
$127$	−60.0000	−	34.6410i	−0.472441	−	0.272764i	0.244820	−	0.969569i	$-0.421271\pi$
$127$	−60.0000	−	34.6410i	−0.472441	−	0.272764i	−0.717261	+	0.696805i	$0.754604\pi$
$128$		0			0
$129$	−70.5000	−	40.7032i	−0.546512	−	0.315529i
$130$		0			0
$131$	56.0000	+	96.9948i	0.427481	+	0.740419i	0.996649	−	0.0818029i	$-0.0260678\pi$
$131$	56.0000	+	96.9948i	0.427481	+	0.740419i	−0.569168	+	0.822222i	$0.692734\pi$
$132$		0			0
$133$	209.000			1.57143
$134$		0			0
$135$	−9.00000	+	5.19615i	−0.0666667	+	0.0384900i
$136$		0			0
$137$	82.0000	−	142.028i	0.598540	−	1.03670i	−0.394497	−	0.918897i	$-0.629081\pi$
$137$	82.0000	−	142.028i	0.598540	−	1.03670i	0.993037	−	0.117805i	$-0.0375856\pi$
$138$		0			0
$139$	92.5000	−	160.215i	0.665468	−	1.15262i	−0.313691	−	0.949525i	$-0.601565\pi$
$139$	92.5000	−	160.215i	0.665468	−	1.15262i	0.979158	−	0.203099i	$-0.0651012\pi$
$140$		0			0
$141$			121.244i			0.859883i
$142$		0			0
$143$	−36.0000	−	20.7846i	−0.251748	−	0.145347i
$144$		0			0
$145$		−	48.4974i		−	0.334465i
$146$		0			0
$147$	−108.000	+	62.3538i	−0.734694	+	0.424176i
$148$		0			0
$149$	10.0000	+	17.3205i	0.0671141	+	0.116245i	0.897630	−	0.440750i	$-0.145288\pi$
$149$	10.0000	+	17.3205i	0.0671141	+	0.116245i	−0.830516	+	0.556995i	$0.811954\pi$
$150$		0			0
$151$			69.2820i			0.458821i	0.973330	+	0.229411i	$0.0736799\pi$
$151$			69.2820i			0.458821i	−0.973330	+	0.229411i	$0.926320\pi$
$152$		0			0
$153$	78.0000			0.509804
$154$		0			0
$155$	93.0000	−	53.6936i	0.600000	−	0.346410i
$156$		0			0
$157$	42.5000	+	73.6122i	0.270701	+	0.468867i	0.969041	−	0.246898i	$-0.0794113\pi$
$157$	42.5000	+	73.6122i	0.270701	+	0.468867i	−0.698341	+	0.715765i	$0.746078\pi$
$158$		0			0
$159$	12.0000			0.0754717
$160$		0			0
$161$	176.000	−	304.841i	1.09317	−	1.89342i
$162$		0			0
$163$	55.0000			0.337423			0.168712	−	0.985665i	$-0.446039\pi$
$163$	55.0000			0.337423			0.168712	+	0.985665i	$0.446039\pi$
$164$		0			0
$165$	−24.0000	−	13.8564i	−0.145455	−	0.0839782i
$166$		0			0
$167$	−279.000	−	161.081i	−1.67066	−	0.964555i	−0.967270	−	0.253750i	$-0.918336\pi$
$167$	−279.000	−	161.081i	−1.67066	−	0.964555i	−0.703389	−	0.710805i	$-0.748331\pi$
$168$		0			0
$169$	−71.0000	−	122.976i	−0.420118	−	0.727666i
$170$		0			0
$171$	−28.5000	+	49.3634i	−0.166667	+	0.288675i
$172$		0			0
$173$	−81.0000	+	46.7654i	−0.468208	+	0.270320i	−0.715489	−	0.698624i	$-0.753796\pi$
$173$	−81.0000	+	46.7654i	−0.468208	+	0.270320i	0.247281	+	0.968944i	$0.420463\pi$
$174$		0			0
$175$	−115.500	+	200.052i	−0.660000	+	1.14315i
$176$		0			0
$177$	−93.0000	+	161.081i	−0.525424	+	0.910061i
$178$		0			0
$179$		−	124.708i		−	0.696691i	−0.937366	−	0.348345i	$-0.886744\pi$
$179$		−	124.708i		−	0.696691i	0.937366	−	0.348345i	$-0.113256\pi$
$180$		0			0
$181$	222.000	+	128.172i	1.22652	+	0.708131i	0.966300	−	0.257418i	$-0.0828718\pi$
$181$	222.000	+	128.172i	1.22652	+	0.708131i	0.260219	+	0.965550i	$0.416205\pi$
$182$		0			0
$183$		−	60.6218i		−	0.331267i
$184$		0			0
$185$	81.0000	−	46.7654i	0.437838	−	0.252786i
$186$		0			0
$187$	104.000	+	180.133i	0.556150	+	0.963280i
$188$		0			0
$189$		−	57.1577i		−	0.302422i
$190$		0			0
$191$	−262.000			−1.37173			−0.685864	−	0.727730i	$-0.740575\pi$
$191$	−262.000			−1.37173			−0.685864	+	0.727730i	$0.740575\pi$
$192$		0			0
$193$	−118.500	+	68.4160i	−0.613990	+	0.354487i	−0.774525	−	0.632543i	$-0.782011\pi$
$193$	−118.500	+	68.4160i	−0.613990	+	0.354487i	0.160536	+	0.987030i	$0.448678\pi$
$194$		0			0
$195$	9.00000	+	15.5885i	0.0461538	+	0.0799408i
$196$		0			0
$197$	−146.000			−0.741117			−0.370558	−	0.928809i	$-0.620834\pi$
$197$	−146.000			−0.741117			−0.370558	+	0.928809i	$0.620834\pi$
$198$		0			0
$199$	56.5000	−	97.8609i	0.283920	−	0.491763i	−0.688427	−	0.725306i	$-0.741698\pi$
$199$	56.5000	−	97.8609i	0.283920	−	0.491763i	0.972347	+	0.233542i	$0.0750318\pi$
$200$		0			0
$201$	27.0000			0.134328
$202$		0			0
$203$	231.000	+	133.368i	1.13793	+	0.656985i
$204$		0			0
$205$	−24.0000	−	13.8564i	−0.117073	−	0.0675922i
$206$		0			0
$207$	48.0000	+	83.1384i	0.231884	+	0.401635i
$208$		0			0
$209$	−152.000			−0.727273
$210$		0			0
$211$	−295.500	+	170.607i	−1.40047	+	0.808564i	−0.994441	−	0.105294i	$-0.966421\pi$
$211$	−295.500	+	170.607i	−1.40047	+	0.808564i	−0.406033	+	0.913858i	$0.633088\pi$
$212$		0			0
$213$	−114.000	+	197.454i	−0.535211	+	0.927013i
$214$		0			0
$215$	−47.0000	+	81.4064i	−0.218605	+	0.378634i
$216$		0			0
$217$			590.629i			2.72179i
$218$		0			0
$219$	88.5000	+	51.0955i	0.404110	+	0.233313i
$220$		0			0
$221$		−	135.100i		−	0.611312i
$222$		0			0
$223$	274.500	−	158.483i	1.23094	−	0.710685i	0.263715	−	0.964601i	$-0.415052\pi$
$223$	274.500	−	158.483i	1.23094	−	0.710685i	0.967226	+	0.253916i	$0.0817187\pi$
$224$		0			0
$225$	−31.5000	−	54.5596i	−0.140000	−	0.242487i
$226$		0			0
$227$			356.802i			1.57182i	0.618343	+	0.785909i	$0.287804\pi$
$227$			356.802i			1.57182i	−0.618343	+	0.785909i	$0.712196\pi$
$228$		0			0
$229$	−337.000			−1.47162			−0.735808	−	0.677190i	$-0.763197\pi$
$229$	−337.000			−1.47162			−0.735808	+	0.677190i	$0.763197\pi$
$230$		0			0
$231$	132.000	−	76.2102i	0.571429	−	0.329914i
$232$		0			0
$233$	88.0000	+	152.420i	0.377682	+	0.654165i	0.990725	−	0.135885i	$-0.0433878\pi$
$233$	88.0000	+	152.420i	0.377682	+	0.654165i	−0.613042	+	0.790050i	$0.710054\pi$
$234$		0			0
$235$	140.000			0.595745
$236$		0			0
$237$	−22.5000	+	38.9711i	−0.0949367	+	0.164435i
$238$		0			0
$239$	−394.000			−1.64854			−0.824268	−	0.566200i	$-0.808413\pi$
$239$	−394.000			−1.64854			−0.824268	+	0.566200i	$0.808413\pi$
$240$		0			0
$241$	−172.500	−	99.5929i	−0.715768	−	0.413249i	0.0974253	−	0.995243i	$-0.468939\pi$
$241$	−172.500	−	99.5929i	−0.715768	−	0.413249i	−0.813193	+	0.581994i	$0.802273\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	72.0000	+	124.708i	0.293878	+	0.509011i
$246$		0			0
$247$	85.5000	+	49.3634i	0.346154	+	0.199852i
$248$		0			0
$249$	−3.00000	+	1.73205i	−0.0120482	+	0.00695603i
$250$		0			0
$251$	−205.000	+	355.070i	−0.816733	+	1.41462i	0.0913437	+	0.995819i	$0.470884\pi$
$251$	−205.000	+	355.070i	−0.816733	+	1.41462i	−0.908077	+	0.418804i	$0.862450\pi$
$252$		0			0
$253$	−128.000	+	221.703i	−0.505929	+	0.876294i
$254$		0			0
$255$		−	90.0666i		−	0.353203i
$256$		0			0
$257$	234.000	+	135.100i	0.910506	+	0.525681i	0.880594	−	0.473872i	$-0.157144\pi$
$257$	234.000	+	135.100i	0.910506	+	0.525681i	0.0299120	+	0.999553i	$0.490477\pi$
$258$		0			0
$259$			514.419i			1.98617i
$260$		0			0
$261$	−63.0000	+	36.3731i	−0.241379	+	0.139360i
$262$		0			0
$263$	62.0000	+	107.387i	0.235741	+	0.408316i	0.959488	−	0.281750i	$-0.0909148\pi$
$263$	62.0000	+	107.387i	0.235741	+	0.408316i	−0.723746	+	0.690066i	$0.757581\pi$
$264$		0			0
$265$		−	13.8564i		−	0.0522883i
$266$		0			0
$267$	138.000			0.516854
$268$		0			0
$269$	−15.0000	+	8.66025i	−0.0557621	+	0.0321943i	−0.527622	−	0.849479i	$-0.676916\pi$
$269$	−15.0000	+	8.66025i	−0.0557621	+	0.0321943i	0.471860	+	0.881674i	$0.343583\pi$
$270$		0			0
$271$	−209.000	−	361.999i	−0.771218	−	1.33579i	−0.936896	−	0.349608i	$-0.886315\pi$
$271$	−209.000	−	361.999i	−0.771218	−	1.33579i	0.165678	−	0.986180i	$-0.447019\pi$
$272$		0			0
$273$	−99.0000			−0.362637
$274$		0			0
$275$	84.0000	−	145.492i	0.305455	−	0.529063i
$276$		0			0
$277$	110.000			0.397112			0.198556	−	0.980090i	$-0.436375\pi$
$277$	110.000			0.397112			0.198556	+	0.980090i	$0.436375\pi$
$278$		0			0
$279$	−139.500	−	80.5404i	−0.500000	−	0.288675i
$280$		0			0
$281$	−165.000	−	95.2628i	−0.587189	−	0.339014i	0.176796	−	0.984247i	$-0.443427\pi$
$281$	−165.000	−	95.2628i	−0.587189	−	0.339014i	−0.763985	+	0.645234i	$0.776760\pi$
$282$		0			0
$283$	−137.000	−	237.291i	−0.484099	−	0.838484i	0.515734	−	0.856749i	$-0.327519\pi$
$283$	−137.000	−	237.291i	−0.484099	−	0.838484i	−0.999833	+	0.0182647i	$0.994186\pi$
$284$		0			0
$285$	57.0000	+	32.9090i	0.200000	+	0.115470i
$286$		0			0
$287$	132.000	−	76.2102i	0.459930	−	0.265541i
$288$		0			0
$289$	−193.500	+	335.152i	−0.669550	+	1.15969i
$290$		0			0
$291$	18.0000	−	31.1769i	0.0618557	−	0.107137i
$292$		0			0
$293$		−	308.305i		−	1.05224i	−0.850412	−	0.526118i	$-0.823647\pi$
$293$		−	308.305i		−	1.05224i	0.850412	−	0.526118i	$-0.176353\pi$
$294$		0			0
$295$	186.000	+	107.387i	0.630508	+	0.364024i
$296$		0			0
$297$			41.5692i			0.139964i
$298$		0			0
$299$	144.000	−	83.1384i	0.481605	−	0.278055i
$300$		0			0
$301$	−258.500	−	447.735i	−0.858804	−	1.48749i
$302$		0			0
$303$			200.918i			0.663095i
$304$		0			0
$305$	−70.0000			−0.229508
$306$		0			0
$307$	354.000	−	204.382i	1.15309	−	0.665739i	0.203455	−	0.979084i	$-0.434783\pi$
$307$	354.000	−	204.382i	1.15309	−	0.665739i	0.949639	+	0.313345i	$0.101450\pi$
$308$		0			0
$309$	−16.5000	−	28.5788i	−0.0533981	−	0.0924881i
$310$		0			0
$311$	398.000			1.27974			0.639871	−	0.768482i	$-0.278988\pi$
$311$	398.000			1.27974			0.639871	+	0.768482i	$0.278988\pi$
$312$		0			0
$313$	59.0000	−	102.191i	0.188498	−	0.326489i	−0.756251	−	0.654281i	$-0.772971\pi$
$313$	59.0000	−	102.191i	0.188498	−	0.326489i	0.944750	+	0.327792i	$0.106305\pi$
$314$		0			0
$315$	−66.0000			−0.209524
$316$		0			0
$317$	−219.000	−	126.440i	−0.690852	−	0.398863i	0.113079	−	0.993586i	$-0.463929\pi$
$317$	−219.000	−	126.440i	−0.690852	−	0.398863i	−0.803931	+	0.594723i	$0.797262\pi$
$318$		0			0
$319$	−168.000	−	96.9948i	−0.526646	−	0.304059i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−247.000	−	427.817i	−0.764706	−	1.32451i
$324$		0			0
$325$	−94.5000	+	54.5596i	−0.290769	+	0.167876i
$326$		0			0
$327$	−42.0000	+	72.7461i	−0.128440	+	0.222465i
$328$		0			0
$329$	−385.000	+	666.840i	−1.17021	+	2.02687i
$330$		0			0
$331$			510.955i			1.54367i	0.635822	+	0.771835i	$0.280661\pi$
$331$			510.955i			1.54367i	−0.635822	+	0.771835i	$0.719339\pi$
$332$		0			0
$333$	−121.500	−	70.1481i	−0.364865	−	0.210655i
$334$		0			0
$335$		−	31.1769i		−	0.0930654i
$336$		0			0
$337$	34.5000	−	19.9186i	0.102374	−	0.0591056i	−0.447939	−	0.894064i	$-0.647842\pi$
$337$	34.5000	−	19.9186i	0.102374	−	0.0591056i	0.550313	+	0.834959i	$0.314508\pi$
$338$		0			0
$339$	51.0000	+	88.3346i	0.150442	+	0.260574i
$340$		0			0
$341$		−	429.549i		−	1.25967i
$342$		0			0
$343$	−253.000			−0.737609
$344$		0			0
$345$	96.0000	−	55.4256i	0.278261	−	0.160654i
$346$		0			0
$347$	89.0000	+	154.153i	0.256484	+	0.444244i	0.965298	−	0.261152i	$-0.0841025\pi$
$347$	89.0000	+	154.153i	0.256484	+	0.444244i	−0.708813	+	0.705396i	$0.750769\pi$
$348$		0			0
$349$	557.000			1.59599			0.797994	−	0.602665i	$-0.205894\pi$
$349$	557.000			1.59599			0.797994	+	0.602665i	$0.205894\pi$
$350$		0			0
$351$	13.5000	−	23.3827i	0.0384615	−	0.0666173i
$352$		0			0
$353$	478.000			1.35411			0.677054	−	0.735934i	$-0.263256\pi$
$353$	478.000			1.35411			0.677054	+	0.735934i	$0.263256\pi$
$354$		0			0
$355$	228.000	+	131.636i	0.642254	+	0.370805i
$356$		0			0
$357$	429.000	+	247.683i	1.20168	+	0.693791i
$358$		0			0
$359$	−160.000	−	277.128i	−0.445682	−	0.771945i	0.552417	−	0.833568i	$-0.313706\pi$
$359$	−160.000	−	277.128i	−0.445682	−	0.771945i	−0.998099	+	0.0616232i	$0.980372\pi$
$360$		0			0
$361$	361.000			1.00000
$362$		0			0
$363$	85.5000	−	49.3634i	0.235537	−	0.135987i
$364$		0			0
$365$	59.0000	−	102.191i	0.161644	−	0.279975i
$366$		0			0
$367$	−117.500	+	203.516i	−0.320163	+	0.554539i	−0.980522	−	0.196411i	$-0.937071\pi$
$367$	−117.500	+	203.516i	−0.320163	+	0.554539i	0.660358	+	0.750951i	$0.270405\pi$
$368$		0			0
$369$			41.5692i			0.112654i
$370$		0			0
$371$	66.0000	+	38.1051i	0.177898	+	0.102709i
$372$		0			0
$373$			173.205i			0.464357i	0.972673	+	0.232178i	$0.0745853\pi$
$373$			173.205i			0.464357i	−0.972673	+	0.232178i	$0.925415\pi$
$374$		0			0
$375$	−138.000	+	79.6743i	−0.368000	+	0.212465i
$376$		0			0
$377$	63.0000	+	109.119i	0.167109	+	0.289441i
$378$		0			0
$379$			254.611i			0.671798i	0.941898	+	0.335899i	$0.109040\pi$
$379$			254.611i			0.671798i	−0.941898	+	0.335899i	$0.890960\pi$
$380$		0			0
$381$	120.000			0.314961
$382$		0			0
$383$	30.0000	−	17.3205i	0.0783290	−	0.0452233i	−0.460324	−	0.887751i	$-0.652267\pi$
$383$	30.0000	−	17.3205i	0.0783290	−	0.0452233i	0.538653	+	0.842528i	$0.318933\pi$
$384$		0			0
$385$	−88.0000	−	152.420i	−0.228571	−	0.395897i
$386$		0			0
$387$	141.000			0.364341
$388$		0			0
$389$	40.0000	−	69.2820i	0.102828	−	0.178103i	−0.810021	−	0.586401i	$-0.800544\pi$
$389$	40.0000	−	69.2820i	0.102828	−	0.178103i	0.912849	+	0.408298i	$0.133878\pi$
$390$		0			0
$391$	−832.000			−2.12788
$392$		0			0
$393$	−168.000	−	96.9948i	−0.427481	−	0.246806i
$394$		0			0
$395$	45.0000	+	25.9808i	0.113924	+	0.0657741i
$396$		0			0
$397$	231.500	+	400.970i	0.583123	+	1.01000i	0.995107	+	0.0988079i	$0.0315029\pi$
$397$	231.500	+	400.970i	0.583123	+	1.01000i	−0.411983	+	0.911191i	$0.635164\pi$
$398$		0			0
$399$	−313.500	+	180.999i	−0.785714	+	0.453632i
$400$		0			0
$401$	339.000	−	195.722i	0.845387	−	0.488084i	−0.0137050	−	0.999906i	$-0.504363\pi$
$401$	339.000	−	195.722i	0.845387	−	0.488084i	0.859092	+	0.511822i	$0.171029\pi$
$402$		0			0
$403$	−139.500	+	241.621i	−0.346154	+	0.599556i
$404$		0			0
$405$	9.00000	−	15.5885i	0.0222222	−	0.0384900i
$406$		0			0
$407$		−	374.123i		−	0.919221i
$408$		0			0
$409$	−378.000	−	218.238i	−0.924205	−	0.533590i	−0.0392311	−	0.999230i	$-0.512491\pi$
$409$	−378.000	−	218.238i	−0.924205	−	0.533590i	−0.884974	+	0.465640i	$0.845824\pi$
$410$		0			0
$411$			284.056i			0.691135i
$412$		0			0
$413$	−1023.00	+	590.629i	−2.47700	+	1.43010i
$414$		0			0
$415$	2.00000	+	3.46410i	0.00481928	+	0.00834723i
$416$		0			0
$417$			320.429i			0.768416i
$418$		0			0
$419$	−412.000			−0.983294			−0.491647	−	0.870795i	$-0.663605\pi$
$419$	−412.000			−0.983294			−0.491647	+	0.870795i	$0.663605\pi$
$420$		0			0
$421$	−414.000	+	239.023i	−0.983373	+	0.567751i	−0.903287	−	0.429037i	$-0.858853\pi$
$421$	−414.000	+	239.023i	−0.983373	+	0.567751i	−0.0800862	+	0.996788i	$0.525520\pi$
$422$		0			0
$423$	−105.000	−	181.865i	−0.248227	−	0.429942i
$424$		0			0
$425$	546.000			1.28471
$426$		0			0
$427$	192.500	−	333.420i	0.450820	−	0.780843i
$428$		0			0
$429$	72.0000			0.167832
$430$		0			0
$431$	−75.0000	−	43.3013i	−0.174014	−	0.100467i	0.410463	−	0.911877i	$-0.365367\pi$
$431$	−75.0000	−	43.3013i	−0.174014	−	0.100467i	−0.584477	+	0.811410i	$0.698700\pi$
$432$		0			0
$433$	469.500	+	271.066i	1.08430	+	0.626018i	0.932052	−	0.362325i	$-0.118017\pi$
$433$	469.500	+	271.066i	1.08430	+	0.626018i	0.152244	+	0.988343i	$0.451350\pi$
$434$		0			0
$435$	42.0000	+	72.7461i	0.0965517	+	0.167232i
$436$		0			0
$437$	304.000	−	526.543i	0.695652	−	1.20490i
$438$		0			0
$439$	337.500	−	194.856i	0.768793	−	0.443863i	−0.0636511	−	0.997972i	$-0.520274\pi$
$439$	337.500	−	194.856i	0.768793	−	0.443863i	0.832444	+	0.554110i	$0.186941\pi$
$440$		0			0
$441$	108.000	−	187.061i	0.244898	−	0.424176i
$442$		0			0
$443$	−67.0000	+	116.047i	−0.151242	+	0.261958i	−0.931684	−	0.363269i	$-0.881660\pi$
$443$	−67.0000	+	116.047i	−0.151242	+	0.261958i	0.780443	+	0.625227i	$0.214994\pi$
$444$		0			0
$445$		−	159.349i		−	0.358087i
$446$		0			0
$447$	−30.0000	−	17.3205i	−0.0671141	−	0.0387483i
$448$		0			0
$449$		−	384.515i		−	0.856381i	−0.903688	−	0.428191i	$-0.859151\pi$
$449$		−	384.515i		−	0.856381i	0.903688	−	0.428191i	$-0.140849\pi$
$450$		0			0
$451$	−96.0000	+	55.4256i	−0.212860	+	0.122895i
$452$		0			0
$453$	−60.0000	−	103.923i	−0.132450	−	0.229411i
$454$		0			0
$455$			114.315i			0.251243i
$456$		0			0
$457$	395.000			0.864333			0.432166	−	0.901794i	$-0.357749\pi$
$457$	395.000			0.864333			0.432166	+	0.901794i	$0.357749\pi$
$458$		0			0
$459$	−117.000	+	67.5500i	−0.254902	+	0.147168i
$460$		0			0
$461$	−47.0000	−	81.4064i	−0.101952	−	0.176587i	0.810537	−	0.585688i	$-0.199176\pi$
$461$	−47.0000	−	81.4064i	−0.101952	−	0.176587i	−0.912489	+	0.409101i	$0.865842\pi$
$462$		0			0
$463$	−293.000			−0.632829			−0.316415	−	0.948621i	$-0.602479\pi$
$463$	−293.000			−0.632829			−0.316415	+	0.948621i	$0.602479\pi$
$464$		0			0
$465$	−93.0000	+	161.081i	−0.200000	+	0.346410i
$466$		0			0
$467$	200.000			0.428266			0.214133	−	0.976805i	$-0.431307\pi$
$467$	200.000			0.428266			0.214133	+	0.976805i	$0.431307\pi$
$468$		0			0
$469$	148.500	+	85.7365i	0.316631	+	0.182807i
$470$		0			0
$471$	−127.500	−	73.6122i	−0.270701	−	0.156289i
$472$		0			0
$473$	188.000	+	325.626i	0.397463	+	0.688426i
$474$		0			0
$475$	−199.500	+	345.544i	−0.420000	+	0.727461i
$476$		0			0
$477$	−18.0000	+	10.3923i	−0.0377358	+	0.0217868i
$478$		0			0
$479$	356.000	−	616.610i	0.743215	−	1.28729i	−0.207809	−	0.978169i	$-0.566633\pi$
$479$	356.000	−	616.610i	0.743215	−	1.28729i	0.951024	−	0.309117i	$-0.100033\pi$
$480$		0			0
$481$	−121.500	+	210.444i	−0.252599	+	0.437514i
$482$		0			0
$483$			609.682i			1.26228i
$484$		0			0
$485$	−36.0000	−	20.7846i	−0.0742268	−	0.0428549i
$486$		0			0
$487$		−	145.492i		−	0.298752i	−0.988780	−	0.149376i	$-0.952274\pi$
$487$		−	145.492i		−	0.298752i	0.988780	−	0.149376i	$-0.0477265\pi$
$488$		0			0
$489$	−82.5000	+	47.6314i	−0.168712	+	0.0974057i
$490$		0			0
$491$	−52.0000	−	90.0666i	−0.105906	−	0.183435i	0.808202	−	0.588906i	$-0.200441\pi$
$491$	−52.0000	−	90.0666i	−0.105906	−	0.183435i	−0.914108	+	0.405470i	$0.867108\pi$
$492$		0			0
$493$		−	630.466i		−	1.27884i
$494$		0			0
$495$	48.0000			0.0969697
$496$		0			0
$497$	−1254.00	+	723.997i	−2.52314	+	1.45673i
$498$		0			0
$499$	−363.500	−	629.600i	−0.728457	−	1.26172i	−0.957535	−	0.288316i	$-0.906905\pi$
$499$	−363.500	−	629.600i	−0.728457	−	1.26172i	0.229078	−	0.973408i	$-0.426429\pi$
$500$		0			0
$501$	558.000			1.11377
$502$		0			0
$503$	−187.000	+	323.894i	−0.371769	+	0.643923i	−0.989838	−	0.142201i	$-0.954582\pi$
$503$	−187.000	+	323.894i	−0.371769	+	0.643923i	0.618068	+	0.786124i	$0.287915\pi$
$504$		0			0
$505$	232.000			0.459406
$506$		0			0
$507$	213.000	+	122.976i	0.420118	+	0.242555i
$508$		0			0
$509$	−495.000	−	285.788i	−0.972495	−	0.561470i	−0.0724991	−	0.997368i	$-0.523097\pi$
$509$	−495.000	−	285.788i	−0.972495	−	0.561470i	−0.899996	+	0.435898i	$0.856431\pi$
$510$		0			0
$511$	324.500	+	562.050i	0.635029	+	1.09990i
$512$		0			0
$513$		−	98.7269i		−	0.192450i
$514$		0			0
$515$	−33.0000	+	19.0526i	−0.0640777	+	0.0369953i
$516$		0			0
$517$	280.000	−	484.974i	0.541586	−	0.938055i
$518$		0			0
$519$	81.0000	−	140.296i	0.156069	−	0.270320i
$520$		0			0
$521$			270.200i			0.518618i	0.965794	+	0.259309i	$0.0834948\pi$
$521$			270.200i			0.518618i	−0.965794	+	0.259309i	$0.916505\pi$
$522$		0			0
$523$	493.500	+	284.922i	0.943595	+	0.544785i	0.891085	−	0.453836i	$-0.149945\pi$
$523$	493.500	+	284.922i	0.943595	+	0.544785i	0.0525093	+	0.998620i	$0.483278\pi$
$524$		0			0
$525$		−	400.104i		−	0.762102i
$526$		0			0
$527$	1209.00	−	698.016i	2.29412	−	1.32451i
$528$		0			0
$529$	−247.500	−	428.683i	−0.467864	−	0.810364i
$530$		0			0
$531$		−	322.161i		−	0.606707i
$532$		0			0
$533$	72.0000			0.135084
$534$		0			0
$535$		0			0
$536$		0			0
$537$	108.000	+	187.061i	0.201117	+	0.348345i
$538$		0			0
$539$	576.000			1.06865
$540$		0			0
$541$	87.5000	−	151.554i	0.161738	−	0.280138i	−0.773754	−	0.633486i	$-0.781624\pi$
$541$	87.5000	−	151.554i	0.161738	−	0.280138i	0.935492	+	0.353348i	$0.114957\pi$
$542$		0			0
$543$	−444.000			−0.817680
$544$		0			0
$545$	84.0000	+	48.4974i	0.154128	+	0.0889861i
$546$		0			0
$547$	199.500	+	115.181i	0.364717	+	0.210569i	0.671148	−	0.741324i	$-0.265802\pi$
$547$	199.500	+	115.181i	0.364717	+	0.210569i	−0.306431	+	0.951893i	$0.599135\pi$
$548$		0			0
$549$	52.5000	+	90.9327i	0.0956284	+	0.165633i
$550$		0			0
$551$	399.000	+	230.363i	0.724138	+	0.418081i
$552$		0			0
$553$	−247.500	+	142.894i	−0.447559	+	0.258398i
$554$		0			0
$555$	−81.0000	+	140.296i	−0.145946	+	0.252786i
$556$		0			0
$557$	−488.000	+	845.241i	−0.876122	+	1.51749i	−0.0205595	+	0.999789i	$0.506545\pi$
$557$	−488.000	+	845.241i	−0.876122	+	1.51749i	−0.855563	+	0.517699i	$0.826789\pi$
$558$		0			0
$559$		−	244.219i		−	0.436886i
$560$		0			0
$561$	−312.000	−	180.133i	−0.556150	−	0.321093i
$562$		0			0
$563$		−	595.825i		−	1.05830i	−0.848527	−	0.529152i	$-0.822510\pi$
$563$		−	595.825i		−	1.05830i	0.848527	−	0.529152i	$-0.177490\pi$
$564$		0			0
$565$	102.000	−	58.8897i	0.180531	−	0.104230i
$566$		0			0
$567$	49.5000	+	85.7365i	0.0873016	+	0.151211i
$568$		0			0
$569$		−	1094.66i		−	1.92382i	−0.273359	−	0.961912i	$-0.588135\pi$
$569$		−	1094.66i		−	1.92382i	0.273359	−	0.961912i	$-0.411865\pi$
$570$		0			0
$571$	169.000			0.295972			0.147986	−	0.988989i	$-0.452721\pi$
$571$	169.000			0.295972			0.147986	+	0.988989i	$0.452721\pi$
$572$		0			0
$573$	393.000	−	226.899i	0.685864	−	0.395984i
$574$		0			0
$575$	336.000	+	581.969i	0.584348	+	1.01212i
$576$		0			0
$577$	−934.000			−1.61872			−0.809359	−	0.587315i	$-0.800185\pi$
$577$	−934.000			−1.61872			−0.809359	+	0.587315i	$0.800185\pi$
$578$		0			0
$579$	118.500	−	205.248i	0.204663	−	0.354487i
$580$		0			0
$581$	−22.0000			−0.0378657
$582$		0			0
$583$	−48.0000	−	27.7128i	−0.0823328	−	0.0475348i
$584$		0			0
$585$	−27.0000	−	15.5885i	−0.0461538	−	0.0266469i
$586$		0			0
$587$	−451.000	−	781.155i	−0.768313	−	1.33076i	−0.938477	−	0.345342i	$-0.887763\pi$
$587$	−451.000	−	781.155i	−0.768313	−	1.33076i	0.170163	−	0.985416i	$-0.445570\pi$
$588$		0			0
$589$			1020.18i			1.73205i
$590$		0			0
$591$	219.000	−	126.440i	0.370558	−	0.213942i
$592$		0			0
$593$	43.0000	−	74.4782i	0.0725126	−	0.125596i	−0.827489	−	0.561482i	$-0.810232\pi$
$593$	43.0000	−	74.4782i	0.0725126	−	0.125596i	0.900002	+	0.435886i	$0.143565\pi$
$594$		0			0
$595$	286.000	−	495.367i	0.480672	−	0.832549i
$596$		0			0
$597$			195.722i			0.327842i
$598$		0			0
$599$	−720.000	−	415.692i	−1.20200	−	0.693977i	−0.241003	−	0.970524i	$-0.577476\pi$
$599$	−720.000	−	415.692i	−1.20200	−	0.693977i	−0.961000	+	0.276547i	$0.910810\pi$
$600$		0			0
$601$		−	812.332i		−	1.35163i	−0.737070	−	0.675817i	$-0.763791\pi$
$601$		−	812.332i		−	1.35163i	0.737070	−	0.675817i	$-0.236209\pi$
$602$		0			0
$603$	−40.5000	+	23.3827i	−0.0671642	+	0.0387773i
$604$		0			0
$605$	−57.0000	−	98.7269i	−0.0942149	−	0.163185i
$606$		0			0
$607$		−	1051.35i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$607$		−	1051.35i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$608$		0			0
$609$	−462.000			−0.758621
$610$		0			0
$611$	−315.000	+	181.865i	−0.515548	+	0.297652i
$612$		0			0
$613$	−7.00000	−	12.1244i	−0.0114192	−	0.0197787i	0.860259	−	0.509857i	$-0.170302\pi$
$613$	−7.00000	−	12.1244i	−0.0114192	−	0.0197787i	−0.871679	+	0.490078i	$0.836968\pi$
$614$		0			0
$615$	48.0000			0.0780488
$616$		0			0
$617$	34.0000	−	58.8897i	0.0551053	−	0.0954453i	−0.837157	−	0.546963i	$-0.815784\pi$
$617$	34.0000	−	58.8897i	0.0551053	−	0.0954453i	0.892262	+	0.451518i	$0.149117\pi$
$618$		0			0
$619$	−953.000			−1.53958			−0.769790	−	0.638297i	$-0.779639\pi$
$619$	−953.000			−1.53958			−0.769790	+	0.638297i	$0.779639\pi$
$620$		0			0
$621$	−144.000	−	83.1384i	−0.231884	−	0.133878i
$622$		0			0
$623$	759.000	+	438.209i	1.21830	+	0.703385i
$624$		0			0
$625$	−170.500	−	295.315i	−0.272800	−	0.472503i
$626$		0			0
$627$	228.000	−	131.636i	0.363636	−	0.209946i
$628$		0			0
$629$	1053.00	−	607.950i	1.67409	−	0.966534i
$630$		0			0
$631$	263.500	−	456.395i	0.417591	−	0.723289i	−0.578105	−	0.815962i	$-0.696208\pi$
$631$	263.500	−	456.395i	0.417591	−	0.723289i	0.995697	+	0.0926730i	$0.0295411\pi$
$632$		0			0
$633$	295.500	−	511.821i	0.466825	−	0.808564i
$634$		0			0
$635$		−	138.564i		−	0.218211i
$636$		0			0
$637$	−324.000	−	187.061i	−0.508634	−	0.293660i
$638$		0			0
$639$		−	394.908i		−	0.618009i
$640$		0			0
$641$	783.000	−	452.065i	1.22153	−	0.705250i	0.256285	−	0.966601i	$-0.417501\pi$
$641$	783.000	−	452.065i	1.22153	−	0.705250i	0.965244	+	0.261351i	$0.0841681\pi$
$642$		0			0
$643$	401.500	+	695.418i	0.624417	+	1.08152i	0.988653	+	0.150215i	$0.0479966\pi$
$643$	401.500	+	695.418i	0.624417	+	1.08152i	−0.364237	+	0.931306i	$0.618670\pi$
$644$		0			0
$645$		−	162.813i		−	0.252423i
$646$		0			0
$647$	−1090.00			−1.68470			−0.842349	−	0.538932i	$-0.818828\pi$
$647$	−1090.00			−1.68470			−0.842349	+	0.538932i	$0.818828\pi$
$648$		0			0
$649$	744.000	−	429.549i	1.14638	−	0.661862i
$650$		0			0
$651$	−511.500	−	885.944i	−0.785714	−	1.36090i
$652$		0			0
$653$	−920.000			−1.40888			−0.704441	−	0.709763i	$-0.748802\pi$
$653$	−920.000			−1.40888			−0.704441	+	0.709763i	$0.748802\pi$
$654$		0			0
$655$	−112.000	+	193.990i	−0.170992	+	0.296167i
$656$		0			0
$657$	−177.000			−0.269406
$658$		0			0
$659$	768.000	+	443.405i	1.16540	+	0.672845i	0.952593	−	0.304248i	$-0.0984053\pi$
$659$	768.000	+	443.405i	1.16540	+	0.672845i	0.212809	+	0.977094i	$0.431739\pi$
$660$		0			0
$661$	504.000	+	290.985i	0.762481	+	0.440219i	0.830186	−	0.557487i	$-0.188234\pi$
$661$	504.000	+	290.985i	0.762481	+	0.440219i	−0.0677048	+	0.997705i	$0.521568\pi$
$662$		0			0
$663$	117.000	+	202.650i	0.176471	+	0.305656i
$664$		0			0
$665$	209.000	+	361.999i	0.314286	+	0.544359i
$666$		0			0
$667$	672.000	−	387.979i	1.00750	−	0.581678i
$668$		0			0
$669$	−274.500	+	475.448i	−0.410314	+	0.710685i
$670$		0			0
$671$	−140.000	+	242.487i	−0.208644	+	0.361382i
$672$		0			0
$673$		−	64.0859i		−	0.0952242i	−0.998866	−	0.0476121i	$-0.984839\pi$
$673$		−	64.0859i		−	0.0952242i	0.998866	−	0.0476121i	$-0.0151611\pi$
$674$		0			0
$675$	94.5000	+	54.5596i	0.140000	+	0.0808290i
$676$		0			0
$677$			599.290i			0.885214i	0.896716	+	0.442607i	$0.145946\pi$
$677$			599.290i			0.885214i	−0.896716	+	0.442607i	$0.854054\pi$
$678$		0			0
$679$	198.000	−	114.315i	0.291605	−	0.168358i
$680$		0			0
$681$	−309.000	−	535.204i	−0.453744	−	0.785909i
$682$		0			0
$683$		−	405.300i		−	0.593411i	−0.954969	−	0.296706i	$-0.904112\pi$
$683$		−	405.300i		−	0.593411i	0.954969	−	0.296706i	$-0.0958880\pi$
$684$		0			0
$685$	328.000			0.478832
$686$		0			0
$687$	505.500	−	291.851i	0.735808	−	0.424819i
$688$		0			0
$689$	18.0000	+	31.1769i	0.0261248	+	0.0452495i
$690$		0			0
$691$	1018.00			1.47323			0.736614	−	0.676314i	$-0.236424\pi$
$691$	1018.00			1.47323			0.736614	+	0.676314i	$0.236424\pi$
$692$		0			0
$693$	−132.000	+	228.631i	−0.190476	+	0.329914i
$694$		0			0
$695$	370.000			0.532374
$696$		0			0
$697$	−312.000	−	180.133i	−0.447633	−	0.258441i
$698$		0			0
$699$	−264.000	−	152.420i	−0.377682	−	0.218055i
$700$		0			0
$701$	−41.0000	−	71.0141i	−0.0584879	−	0.101304i	0.835299	−	0.549796i	$-0.185295\pi$
$701$	−41.0000	−	71.0141i	−0.0584879	−	0.101304i	−0.893787	+	0.448492i	$0.851961\pi$
$702$		0			0
$703$			888.542i			1.26393i
$704$		0			0
$705$	−210.000	+	121.244i	−0.297872	+	0.171977i
$706$		0			0
$707$	−638.000	+	1105.05i	−0.902405	+	1.56301i
$708$		0			0
$709$	27.5000	−	47.6314i	0.0387870	−	0.0671811i	−0.845980	−	0.533214i	$-0.820984\pi$
$709$	27.5000	−	47.6314i	0.0387870	−	0.0671811i	0.884767	+	0.466033i	$0.154317\pi$
$710$		0			0
$711$		−	77.9423i		−	0.109623i
$712$		0			0
$713$	1488.00	+	859.097i	2.08696	+	1.20490i
$714$		0			0
$715$		−	83.1384i		−	0.116278i
$716$		0			0
$717$	591.000	−	341.214i	0.824268	−	0.475891i
$718$		0			0
$719$	398.000	+	689.356i	0.553547	+	0.958771i	0.998015	+	0.0629763i	$0.0200593\pi$
$719$	398.000	+	689.356i	0.553547	+	0.958771i	−0.444468	+	0.895795i	$0.646607\pi$
$720$		0			0
$721$		−	209.578i		−	0.290677i
$722$		0			0
$723$	345.000			0.477178
$724$		0			0
$725$	−441.000	+	254.611i	−0.608276	+	0.351188i
$726$		0			0
$727$	−417.500	−	723.131i	−0.574278	−	0.994678i	−0.996120	−	0.0880090i	$-0.971950\pi$
$727$	−417.500	−	723.131i	−0.574278	−	0.994678i	0.421842	−	0.906669i	$-0.361384\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−611.000	+	1058.28i	−0.835841	+	1.44772i
$732$		0			0
$733$	−394.000			−0.537517			−0.268759	−	0.963208i	$-0.586613\pi$
$733$	−394.000			−0.537517			−0.268759	+	0.963208i	$0.586613\pi$
$734$		0			0
$735$	−216.000	−	124.708i	−0.293878	−	0.169670i
$736$		0			0
$737$	−108.000	−	62.3538i	−0.146540	−	0.0846049i
$738$		0			0
$739$	−321.500	−	556.854i	−0.435047	−	0.753524i	0.562252	−	0.826966i	$-0.309935\pi$
$739$	−321.500	−	556.854i	−0.435047	−	0.753524i	−0.997300	+	0.0734417i	$0.976602\pi$
$740$		0			0
$741$	−171.000			−0.230769
$742$		0			0
$743$	−906.000	+	523.079i	−1.21938	+	0.704010i	−0.964786	−	0.263038i	$-0.915276\pi$
$743$	−906.000	+	523.079i	−1.21938	+	0.704010i	−0.254595	+	0.967048i	$0.581942\pi$
$744$		0			0
$745$	−20.0000	+	34.6410i	−0.0268456	+	0.0464980i
$746$		0			0
$747$	3.00000	−	5.19615i	0.00401606	−	0.00695603i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−472.500	−	272.798i	−0.629161	−	0.363246i	0.151266	−	0.988493i	$-0.451665\pi$
$751$	−472.500	−	272.798i	−0.629161	−	0.363246i	−0.780427	+	0.625247i	$0.784998\pi$
$752$		0			0
$753$		−	710.141i		−	0.943082i
$754$		0			0
$755$	−120.000	+	69.2820i	−0.158940	+	0.0917643i
$756$		0			0
$757$	438.500	+	759.504i	0.579260	+	1.00331i	0.995564	+	0.0940827i	$0.0299918\pi$
$757$	438.500	+	759.504i	0.579260	+	1.00331i	−0.416304	+	0.909225i	$0.636675\pi$
$758$		0			0
$759$		−	443.405i		−	0.584196i
$760$		0			0
$761$	322.000			0.423127			0.211564	−	0.977364i	$-0.432144\pi$
$761$	322.000			0.423127			0.211564	+	0.977364i	$0.432144\pi$
$762$		0			0
$763$	−462.000	+	266.736i	−0.605505	+	0.349588i
$764$		0			0
$765$	78.0000	+	135.100i	0.101961	+	0.176601i
$766$		0			0
$767$	−558.000			−0.727510
$768$		0			0
$769$	−188.500	+	326.492i	−0.245124	+	0.424566i	−0.962166	−	0.272463i	$-0.912162\pi$
$769$	−188.500	+	326.492i	−0.245124	+	0.424566i	0.717043	+	0.697029i	$0.245495\pi$
$770$		0			0
$771$	−468.000			−0.607004
$772$		0			0
$773$	759.000	+	438.209i	0.981889	+	0.566894i	0.902840	−	0.429977i	$-0.141478\pi$
$773$	759.000	+	438.209i	0.981889	+	0.566894i	0.0790489	+	0.996871i	$0.474812\pi$
$774$		0			0
$775$	−976.500	−	563.783i	−1.26000	−	0.727461i
$776$		0			0
$777$	−445.500	−	771.629i	−0.573359	−	0.993087i
$778$		0			0
$779$	228.000	−	131.636i	0.292683	−	0.168981i
$780$		0			0
$781$	912.000	−	526.543i	1.16773	−	0.674191i
$782$		0			0
$783$	63.0000	−	109.119i	0.0804598	−	0.139360i
$784$		0			0
$785$	−85.0000	+	147.224i	−0.108280	+	0.187547i
$786$		0			0
$787$		−	937.039i		−	1.19065i	−0.803486	−	0.595324i	$-0.797024\pi$
$787$		−	937.039i		−	1.19065i	0.803486	−	0.595324i	$-0.202976\pi$
$788$		0			0
$789$	−186.000	−	107.387i	−0.235741	−	0.136105i
$790$		0			0
$791$			647.787i			0.818947i
$792$		0			0
$793$	157.500	−	90.9327i	0.198613	−	0.114669i
$794$		0			0
$795$	12.0000	+	20.7846i	0.0150943	+	0.0261442i
$796$		0			0
$797$		−	713.605i		−	0.895364i	−0.894193	−	0.447682i	$-0.852250\pi$
$797$		−	713.605i		−	0.895364i	0.894193	−	0.447682i	$-0.147750\pi$
$798$		0			0
$799$	1820.00			2.27785
$800$		0			0
$801$	−207.000	+	119.512i	−0.258427	+	0.149203i
$802$		0			0
$803$	−236.000	−	408.764i	−0.293898	−	0.509046i
$804$		0			0
$805$	704.000			0.874534
$806$		0			0
$807$	15.0000	−	25.9808i	0.0185874	−	0.0321943i
$808$		0			0
$809$	−170.000			−0.210136			−0.105068	−	0.994465i	$-0.533506\pi$
$809$	−170.000			−0.210136			−0.105068	+	0.994465i	$0.533506\pi$
$810$		0			0
$811$	−96.0000	−	55.4256i	−0.118372	−	0.0683423i	0.439645	−	0.898172i	$-0.355104\pi$
$811$	−96.0000	−	55.4256i	−0.118372	−	0.0683423i	−0.558017	+	0.829829i	$0.688438\pi$
$812$		0			0
$813$	627.000	+	361.999i	0.771218	+	0.445263i
$814$		0			0
$815$	55.0000	+	95.2628i	0.0674847	+	0.116887i
$816$		0			0
$817$	−446.500	−	773.361i	−0.546512	−	0.946586i
$818$		0			0
$819$	148.500	−	85.7365i	0.181319	−	0.104684i
$820$		0			0
$821$	355.000	−	614.878i	0.432400	−	0.748938i	−0.564680	−	0.825310i	$-0.691000\pi$
$821$	355.000	−	614.878i	0.432400	−	0.748938i	0.997079	+	0.0763721i	$0.0243337\pi$
$822$		0			0
$823$	−389.000	+	673.768i	−0.472661	+	0.818673i	−0.999510	−	0.0312857i	$-0.990040\pi$
$823$	−389.000	+	673.768i	−0.472661	+	0.818673i	0.526849	+	0.849959i	$0.323373\pi$
$824$		0			0
$825$			290.985i			0.352709i
$826$		0			0
$827$	429.000	+	247.683i	0.518742	+	0.299496i	0.736420	−	0.676525i	$-0.236515\pi$
$827$	429.000	+	247.683i	0.518742	+	0.299496i	−0.217678	+	0.976021i	$0.569848\pi$
$828$		0			0
$829$		−	348.142i		−	0.419954i	−0.977706	−	0.209977i	$-0.932661\pi$
$829$		−	348.142i		−	0.419954i	0.977706	−	0.209977i	$-0.0673390\pi$
$830$		0			0
$831$	−165.000	+	95.2628i	−0.198556	+	0.114636i
$832$		0			0
$833$	936.000	+	1621.20i	1.12365	+	1.94622i
$834$		0			0
$835$		−	644.323i		−	0.771644i
$836$		0			0
$837$	279.000			0.333333
$838$		0			0
$839$	−243.000	+	140.296i	−0.289631	+	0.167218i	−0.637775	−	0.770223i	$-0.720145\pi$
$839$	−243.000	+	140.296i	−0.289631	+	0.167218i	0.348145	+	0.937441i	$0.386812\pi$
$840$		0			0
$841$	−126.500	−	219.104i	−0.150416	−	0.260528i
$842$		0			0
$843$	330.000			0.391459
$844$		0			0
$845$	142.000	−	245.951i	0.168047	−	0.291067i
$846$		0			0
$847$	627.000			0.740260
$848$		0			0
$849$	411.000	+	237.291i	0.484099	+	0.279495i
$850$		0			0
$851$	1296.00	+	748.246i	1.52291	+	0.879255i
$852$		0			0
$853$	−446.500	−	773.361i	−0.523447	−	0.906636i	−0.999628	−	0.0272889i	$-0.991313\pi$
$853$	−446.500	−	773.361i	−0.523447	−	0.906636i	0.476181	−	0.879347i	$-0.342021\pi$
$854$		0			0
$855$	−114.000			−0.133333
$856$		0			0
$857$	531.000	−	306.573i	0.619603	−	0.357728i	−0.157111	−	0.987581i	$-0.550218\pi$
$857$	531.000	−	306.573i	0.619603	−	0.357728i	0.776715	+	0.629853i	$0.216885\pi$
$858$		0			0
$859$	−33.5000	+	58.0237i	−0.0389988	+	0.0675480i	−0.884866	−	0.465846i	$-0.845750\pi$
$859$	−33.5000	+	58.0237i	−0.0389988	+	0.0675480i	0.845867	+	0.533394i	$0.179084\pi$
$860$		0			0
$861$	−132.000	+	228.631i	−0.153310	+	0.265541i
$862$		0			0
$863$		−	1527.67i		−	1.77018i	−0.465416	−	0.885092i	$-0.654095\pi$
$863$		−	1527.67i		−	1.77018i	0.465416	−	0.885092i	$-0.345905\pi$
$864$		0			0
$865$	−162.000	−	93.5307i	−0.187283	−	0.108128i
$866$		0			0
$867$		−	670.304i		−	0.773130i
$868$		0			0
$869$	180.000	−	103.923i	0.207135	−	0.119589i
$870$		0			0
$871$	40.5000	+	70.1481i	0.0464983	+	0.0805374i
$872$		0			0
$873$			62.3538i			0.0714248i
$874$		0			0
$875$	−1012.00			−1.15657
$876$		0			0
$877$	−379.500	+	219.104i	−0.432725	+	0.249834i	−0.700507	−	0.713646i	$-0.747043\pi$
$877$	−379.500	+	219.104i	−0.432725	+	0.249834i	0.267782	+	0.963480i	$0.413709\pi$
$878$		0			0
$879$	267.000	+	462.458i	0.303754	+	0.526118i
$880$		0			0
$881$	934.000			1.06016			0.530079	−	0.847948i	$-0.322162\pi$
$881$	934.000			1.06016			0.530079	+	0.847948i	$0.322162\pi$
$882$		0			0
$883$	602.500	−	1043.56i	0.682333	−	1.18184i	−0.291934	−	0.956438i	$-0.594299\pi$
$883$	602.500	−	1043.56i	0.682333	−	1.18184i	0.974267	−	0.225397i	$-0.0723679\pi$
$884$		0			0
$885$	−372.000			−0.420339
$886$		0			0
$887$	135.000	+	77.9423i	0.152198	+	0.0878718i	0.574165	−	0.818740i	$-0.305327\pi$
$887$	135.000	+	77.9423i	0.152198	+	0.0878718i	−0.421967	+	0.906611i	$0.638660\pi$
$888$		0			0
$889$	660.000	+	381.051i	0.742407	+	0.428629i
$890$		0			0
$891$	−36.0000	−	62.3538i	−0.0404040	−	0.0699819i
$892$		0			0
$893$	−665.000	+	1151.81i	−0.744681	+	1.28983i
$894$		0			0
$895$	216.000	−	124.708i	0.241341	−	0.139338i
$896$		0			0
$897$	−144.000	+	249.415i	−0.160535	+	0.278055i
$898$		0			0
$899$	−651.000	+	1127.57i	−0.724138	+	1.25424i
$900$		0			0
$901$		−	180.133i		−	0.199926i
$902$		0			0
$903$	775.500	+	447.735i	0.858804	+	0.495831i
$904$		0			0
$905$			512.687i			0.566505i
$906$		0			0
$907$	−1188.00	+	685.892i	−1.30981	+	0.756221i	−0.982065	−	0.188545i	$-0.939623\pi$
$907$	−1188.00	+	685.892i	−1.30981	+	0.756221i	−0.327748	+	0.944765i	$0.606290\pi$
$908$		0			0
$909$	−174.000	−	301.377i	−0.191419	−	0.331548i
$910$		0			0
$911$			1198.58i			1.31567i	0.753160	+	0.657837i	$0.228528\pi$
$911$			1198.58i			1.31567i	−0.753160	+	0.657837i	$0.771472\pi$
$912$		0			0
$913$	16.0000			0.0175246
$914$		0			0
$915$	105.000	−	60.6218i	0.114754	−	0.0662533i
$916$		0			0
$917$	−616.000	−	1066.94i	−0.671756	−	1.16352i
$918$		0			0
$919$	325.000			0.353645			0.176823	−	0.984243i	$-0.443418\pi$
$919$	325.000			0.353645			0.176823	+	0.984243i	$0.443418\pi$
$920$		0			0
$921$	−354.000	+	613.146i	−0.384365	+	0.665739i
$922$		0			0
$923$	−684.000			−0.741062
$924$		0			0
$925$	−850.500	−	491.036i	−0.919459	−	0.530850i
$926$		0			0
$927$	49.5000	+	28.5788i	0.0533981	+	0.0308294i
$928$		0			0
$929$	−107.000	−	185.329i	−0.115178	−	0.199493i	0.802673	−	0.596419i	$-0.203410\pi$
$929$	−107.000	−	185.329i	−0.115178	−	0.199493i	−0.917851	+	0.396926i	$0.870077\pi$
$930$		0			0
$931$	−1368.00			−1.46939
$932$		0			0
$933$	−597.000	+	344.678i	−0.639871	+	0.369430i
$934$		0			0
$935$	−208.000	+	360.267i	−0.222460	+	0.385312i
$936$		0			0
$937$	−299.500	+	518.749i	−0.319637	+	0.553628i	−0.980412	−	0.196956i	$-0.936894\pi$
$937$	−299.500	+	518.749i	−0.319637	+	0.553628i	0.660775	+	0.750584i	$0.270228\pi$
$938$		0			0
$939$			204.382i			0.217659i
$940$		0			0
$941$	−252.000	−	145.492i	−0.267800	−	0.154615i	0.360087	−	0.932919i	$-0.382747\pi$
$941$	−252.000	−	145.492i	−0.267800	−	0.154615i	−0.627888	+	0.778304i	$0.716080\pi$
$942$		0			0
$943$		−	443.405i		−	0.470207i
$944$		0			0
$945$	99.0000	−	57.1577i	0.104762	−	0.0604843i
$946$		0			0
$947$	−586.000	−	1014.98i	−0.618796	−	1.07179i	−0.989706	−	0.143117i	$-0.954287\pi$
$947$	−586.000	−	1014.98i	−0.618796	−	1.07179i	0.370910	−	0.928669i	$-0.379046\pi$
$948$		0			0
$949$			306.573i			0.323048i
$950$		0			0
$951$	438.000			0.460568
$952$		0			0
$953$	30.0000	−	17.3205i	0.0314795	−	0.0181747i	−0.484178	−	0.874970i	$-0.660881\pi$
$953$	30.0000	−	17.3205i	0.0314795	−	0.0181747i	0.515657	+	0.856795i	$0.327548\pi$
$954$		0			0
$955$	−262.000	−	453.797i	−0.274346	−	0.475180i
$956$		0			0
$957$	336.000			0.351097
$958$		0			0
$959$	−902.000	+	1562.31i	−0.940563	+	1.62910i
$960$		0			0
$961$	−1922.00			−2.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−237.000	−	136.832i	−0.245596	−	0.141795i
$966$		0			0
$967$	725.500	+	1256.60i	0.750259	+	1.29949i	0.947697	+	0.319171i	$0.103404\pi$
$967$	725.500	+	1256.60i	0.750259	+	1.29949i	−0.197439	+	0.980315i	$0.563262\pi$
$968$		0			0
$969$	741.000	+	427.817i	0.764706	+	0.441503i
$970$		0			0
$971$	1653.00	−	954.360i	1.70237	−	0.982863i	0.759016	−	0.651072i	$-0.225681\pi$
$971$	1653.00	−	954.360i	1.70237	−	0.982863i	0.943353	−	0.331791i	$-0.107653\pi$
$972$		0			0
$973$	−1017.50	+	1762.36i	−1.04573	+	1.81127i
$974$		0			0
$975$	94.5000	−	163.679i	0.0969231	−	0.167876i
$976$		0			0
$977$		−	1202.04i		−	1.23034i	−0.788394	−	0.615171i	$-0.789087\pi$
$977$		−	1202.04i		−	1.23034i	0.788394	−	0.615171i	$-0.210913\pi$
$978$		0			0
$979$	−552.000	−	318.697i	−0.563841	−	0.325534i
$980$		0			0
$981$		−	145.492i		−	0.148310i
$982$		0			0
$983$	1602.00	−	924.915i	1.62970	−	0.940911i	0.645525	−	0.763739i	$-0.276639\pi$
$983$	1602.00	−	924.915i	1.62970	−	0.940911i	0.984180	−	0.177171i	$-0.0566947\pi$
$984$		0			0
$985$	−146.000	−	252.879i	−0.148223	−	0.256730i
$986$		0			0
$987$		−	1333.68i		−	1.35125i
$988$		0			0
$989$	−1504.00			−1.52073
$990$		0			0
$991$	−685.500	+	395.774i	−0.691726	+	0.399368i	−0.804258	−	0.594280i	$-0.797437\pi$
$991$	−685.500	+	395.774i	−0.691726	+	0.399368i	0.112533	+	0.993648i	$0.464104\pi$
$992$		0			0
$993$	−442.500	−	766.432i	−0.445619	−	0.771835i
$994$		0			0
$995$	226.000			0.227136
$996$		0			0
$997$	−395.500	+	685.026i	−0.396690	+	0.687087i	−0.993315	−	0.115433i	$-0.963175\pi$
$997$	−395.500	+	685.026i	−0.396690	+	0.687087i	0.596625	+	0.802520i	$0.296508\pi$
$998$		0			0
$999$	243.000			0.243243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.b.145.1		2
4.3	odd	2		228.3.l.c.145.1	✓	2
12.11	even	2		684.3.y.b.145.1		2
19.8	odd	6	inner	912.3.be.b.673.1		2
76.27	even	6		228.3.l.c.217.1	yes	2
228.179	odd	6		684.3.y.b.217.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.l.c.145.1	✓	2	4.3	odd	2
228.3.l.c.217.1	yes	2	76.27	even	6
684.3.y.b.145.1		2	12.11	even	2
684.3.y.b.217.1		2	228.179	odd	6
912.3.be.b.145.1		2	1.1	even	1	trivial
912.3.be.b.673.1		2	19.8	odd	6	inner

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} -11.0000 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} -11.0000 q^{7} +(1.50000 - 2.59808i) q^{9} +8.00000 q^{11} +(-4.50000 - 2.59808i) q^{13} +(-3.00000 - 1.73205i) q^{15} +(13.0000 + 22.5167i) q^{17} -19.0000 q^{19} +(16.5000 - 9.52628i) q^{21} +(-16.0000 + 27.7128i) q^{23} +(10.5000 - 18.1865i) q^{25} +5.19615i q^{27} +(-21.0000 - 12.1244i) q^{29} -53.6936i q^{31} +(-12.0000 + 6.92820i) q^{33} +(-11.0000 - 19.0526i) q^{35} -46.7654i q^{37} +9.00000 q^{39} +(-12.0000 + 6.92820i) q^{41} +(23.5000 + 40.7032i) q^{43} +6.00000 q^{45} +(35.0000 - 60.6218i) q^{47} +72.0000 q^{49} +(-39.0000 - 22.5167i) q^{51} +(-6.00000 - 3.46410i) q^{53} +(8.00000 + 13.8564i) q^{55} +(28.5000 - 16.4545i) q^{57} +(93.0000 - 53.6936i) q^{59} +(-17.5000 + 30.3109i) q^{61} +(-16.5000 + 28.5788i) q^{63} -10.3923i q^{65} +(-13.5000 - 7.79423i) q^{67} -55.4256i q^{69} +(114.000 - 65.8179i) q^{71} +(-29.5000 - 51.0955i) q^{73} +36.3731i q^{75} -88.0000 q^{77} +(22.5000 - 12.9904i) q^{79} +(-4.50000 - 7.79423i) q^{81} +2.00000 q^{83} +(-26.0000 + 45.0333i) q^{85} +42.0000 q^{87} +(-69.0000 - 39.8372i) q^{89} +(49.5000 + 28.5788i) q^{91} +(46.5000 + 80.5404i) q^{93} +(-19.0000 - 32.9090i) q^{95} +(-18.0000 + 10.3923i) q^{97} +(12.0000 - 20.7846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 2 q^{5} - 22 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 2 * q^5 - 22 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} + 2 q^{5} - 22 q^{7} + 3 q^{9} + 16 q^{11} - 9 q^{13} - 6 q^{15} + 26 q^{17} - 38 q^{19} + 33 q^{21} - 32 q^{23} + 21 q^{25} - 42 q^{29} - 24 q^{33} - 22 q^{35} + 18 q^{39} - 24 q^{41} + 47 q^{43} + 12 q^{45} + 70 q^{47} + 144 q^{49} - 78 q^{51} - 12 q^{53} + 16 q^{55} + 57 q^{57} + 186 q^{59} - 35 q^{61} - 33 q^{63} - 27 q^{67} + 228 q^{71} - 59 q^{73} - 176 q^{77} + 45 q^{79} - 9 q^{81} + 4 q^{83} - 52 q^{85} + 84 q^{87} - 138 q^{89} + 99 q^{91} + 93 q^{93} - 38 q^{95} - 36 q^{97} + 24 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 2 * q^5 - 22 * q^7 + 3 * q^9 + 16 * q^11 - 9 * q^13 - 6 * q^15 + 26 * q^17 - 38 * q^19 + 33 * q^21 - 32 * q^23 + 21 * q^25 - 42 * q^29 - 24 * q^33 - 22 * q^35 + 18 * q^39 - 24 * q^41 + 47 * q^43 + 12 * q^45 + 70 * q^47 + 144 * q^49 - 78 * q^51 - 12 * q^53 + 16 * q^55 + 57 * q^57 + 186 * q^59 - 35 * q^61 - 33 * q^63 - 27 * q^67 + 228 * q^71 - 59 * q^73 - 176 * q^77 + 45 * q^79 - 9 * q^81 + 4 * q^83 - 52 * q^85 + 84 * q^87 - 138 * q^89 + 99 * q^91 + 93 * q^93 - 38 * q^95 - 36 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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