LMFDB - Embedded newform 224.3.r.b.95.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(95,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("224.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.r (of order $6$, degree $2$, 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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	224.95
Dual form			224.3.r.b.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{5} -7.00000i q^{7} +(-4.00000 - 6.92820i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{5} -7.00000i q^{7} +(-4.00000 - 6.92820i) q^{9} +(-14.7224 - 8.50000i) q^{11} +24.0000 q^{13} -1.00000i q^{15} +(-0.500000 + 0.866025i) q^{17} +(6.06218 - 3.50000i) q^{19} +(3.50000 - 6.06218i) q^{21} +(-6.06218 + 3.50000i) q^{23} +(12.0000 - 20.7846i) q^{25} -17.0000i q^{27} +24.0000 q^{29} +(-35.5070 - 20.5000i) q^{31} +(-8.50000 - 14.7224i) q^{33} +(-6.06218 + 3.50000i) q^{35} +(24.5000 + 42.4352i) q^{37} +(20.7846 + 12.0000i) q^{39} -48.0000 q^{41} +24.0000i q^{43} +(-4.00000 + 6.92820i) q^{45} +(47.6314 - 27.5000i) q^{47} -49.0000 q^{49} +(-0.866025 + 0.500000i) q^{51} +(12.5000 - 21.6506i) q^{53} +17.0000i q^{55} +7.00000 q^{57} +(14.7224 + 8.50000i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-48.4974 + 28.0000i) q^{63} +(-12.0000 - 20.7846i) q^{65} +(56.2917 + 32.5000i) q^{67} -7.00000 q^{69} +96.0000i q^{71} +(-47.5000 + 82.2724i) q^{73} +(20.7846 - 12.0000i) q^{75} +(-59.5000 + 103.057i) q^{77} +(35.5070 - 20.5000i) q^{79} +(-27.5000 + 47.6314i) q^{81} +72.0000i q^{83} +1.00000 q^{85} +(20.7846 + 12.0000i) q^{87} +(-47.5000 - 82.2724i) q^{89} -168.000i q^{91} +(-20.5000 - 35.5070i) q^{93} +(-6.06218 - 3.50000i) q^{95} +144.000 q^{97} +136.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} - 16 q^{9}+O(q^{10}) $ 4 * q - 2 * q^5 - 16 * q^9	$ 4 q - 2 q^{5} - 16 q^{9} + 96 q^{13} - 2 q^{17} + 14 q^{21} + 48 q^{25} + 96 q^{29} - 34 q^{33} + 98 q^{37} - 192 q^{41} - 16 q^{45} - 196 q^{49} + 50 q^{53} + 28 q^{57} + 2 q^{61} - 48 q^{65} - 28 q^{69} - 190 q^{73} - 238 q^{77} - 110 q^{81} + 4 q^{85} - 190 q^{89} - 82 q^{93} + 576 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 - 16 * q^9 + 96 * q^13 - 2 * q^17 + 14 * q^21 + 48 * q^25 + 96 * q^29 - 34 * q^33 + 98 * q^37 - 192 * q^41 - 16 * q^45 - 196 * q^49 + 50 * q^53 + 28 * q^57 + 2 * q^61 - 48 * q^65 - 28 * q^69 - 190 * q^73 - 238 * q^77 - 110 * q^81 + 4 * q^85 - 190 * q^89 - 82 * q^93 + 576 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.866025	+	0.500000i	0.288675	+	0.166667i	0.637344	−	0.770579i	$-0.280033\pi$
$3$	0.866025	+	0.500000i	0.288675	+	0.166667i	−0.348669	+	0.937246i	$0.613366\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.100000	−	0.173205i	0.811684	−	0.584096i	$-0.198551\pi$
$5$	−0.500000	−	0.866025i	−0.100000	−	0.173205i	−0.911684	+	0.410891i	$0.865218\pi$
$6$		0			0
$7$		−	7.00000i		−	1.00000i
$7$		−	7.00000i		−	1.00000i
$8$		0			0
$9$	−4.00000	−	6.92820i	−0.444444	−	0.769800i
$10$		0			0
$11$	−14.7224	−	8.50000i	−1.33840	−	0.772727i	−0.351832	−	0.936063i	$-0.614441\pi$
$11$	−14.7224	−	8.50000i	−1.33840	−	0.772727i	−0.986571	+	0.163336i	$0.947775\pi$
$12$		0			0
$13$	24.0000			1.84615			0.923077	−	0.384615i	$-0.125666\pi$
$13$	24.0000			1.84615			0.923077	+	0.384615i	$0.125666\pi$
$14$		0			0
$15$		−	1.00000i		−	0.0666667i
$16$		0			0
$17$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i	−0.880357	−	0.474312i	$-0.842697\pi$
$17$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i	0.850945	+	0.525255i	$0.176030\pi$
$18$		0			0
$19$	6.06218	−	3.50000i	0.319062	−	0.184211i	−0.331912	−	0.943310i	$-0.607694\pi$
$19$	6.06218	−	3.50000i	0.319062	−	0.184211i	0.650974	+	0.759100i	$0.274361\pi$
$20$		0			0
$21$	3.50000	−	6.06218i	0.166667	−	0.288675i
$22$		0			0
$23$	−6.06218	+	3.50000i	−0.263573	+	0.152174i	−0.625963	−	0.779852i	$-0.715294\pi$
$23$	−6.06218	+	3.50000i	−0.263573	+	0.152174i	0.362390	+	0.932026i	$0.381961\pi$
$24$		0			0
$25$	12.0000	−	20.7846i	0.480000	−	0.831384i
$26$		0			0
$27$		−	17.0000i		−	0.629630i
$28$		0			0
$29$	24.0000			0.827586			0.413793	−	0.910371i	$-0.364204\pi$
$29$	24.0000			0.827586			0.413793	+	0.910371i	$0.364204\pi$
$30$		0			0
$31$	−35.5070	−	20.5000i	−1.14539	−	0.661290i	−0.197629	−	0.980277i	$-0.563324\pi$
$31$	−35.5070	−	20.5000i	−1.14539	−	0.661290i	−0.947759	+	0.318987i	$0.896658\pi$
$32$		0			0
$33$	−8.50000	−	14.7224i	−0.257576	−	0.446134i
$34$		0			0
$35$	−6.06218	+	3.50000i	−0.173205	+	0.100000i
$36$		0			0
$37$	24.5000	+	42.4352i	0.662162	+	1.14690i	0.980046	+	0.198769i	$0.0636943\pi$
$37$	24.5000	+	42.4352i	0.662162	+	1.14690i	−0.317884	+	0.948130i	$0.602972\pi$
$38$		0			0
$39$	20.7846	+	12.0000i	0.532939	+	0.307692i
$40$		0			0
$41$	−48.0000			−1.17073			−0.585366	−	0.810769i	$-0.699049\pi$
$41$	−48.0000			−1.17073			−0.585366	+	0.810769i	$0.699049\pi$
$42$		0			0
$43$			24.0000i			0.558140i	0.960271	+	0.279070i	$0.0900261\pi$
$43$			24.0000i			0.558140i	−0.960271	+	0.279070i	$0.909974\pi$
$44$		0			0
$45$	−4.00000	+	6.92820i	−0.0888889	+	0.153960i
$46$		0			0
$47$	47.6314	−	27.5000i	1.01343	−	0.585106i	0.101239	−	0.994862i	$-0.467719\pi$
$47$	47.6314	−	27.5000i	1.01343	−	0.585106i	0.912195	+	0.409756i	$0.134386\pi$
$48$		0			0
$49$	−49.0000			−1.00000
$50$		0			0
$51$	−0.866025	+	0.500000i	−0.0169809	+	0.00980392i
$52$		0			0
$53$	12.5000	−	21.6506i	0.235849	−	0.408503i	−0.723670	−	0.690146i	$-0.757546\pi$
$53$	12.5000	−	21.6506i	0.235849	−	0.408503i	0.959519	+	0.281644i	$0.0908796\pi$
$54$		0			0
$55$			17.0000i			0.309091i
$56$		0			0
$57$	7.00000			0.122807
$58$		0			0
$59$	14.7224	+	8.50000i	0.249533	+	0.144068i	0.619550	−	0.784957i	$-0.287315\pi$
$59$	14.7224	+	8.50000i	0.249533	+	0.144068i	−0.370018	+	0.929025i	$0.620648\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.00819672	+	0.0141971i	0.870095	−	0.492885i	$-0.164058\pi$
$61$	0.500000	+	0.866025i	0.00819672	+	0.0141971i	−0.861898	+	0.507082i	$0.830724\pi$
$62$		0			0
$63$	−48.4974	+	28.0000i	−0.769800	+	0.444444i
$64$		0			0
$65$	−12.0000	−	20.7846i	−0.184615	−	0.319763i
$66$		0			0
$67$	56.2917	+	32.5000i	0.840174	+	0.485075i	0.857323	−	0.514778i	$-0.172126\pi$
$67$	56.2917	+	32.5000i	0.840174	+	0.485075i	−0.0171494	+	0.999853i	$0.505459\pi$
$68$		0			0
$69$	−7.00000			−0.101449
$70$		0			0
$71$			96.0000i			1.35211i	0.736850	+	0.676056i	$0.236312\pi$
$71$			96.0000i			1.35211i	−0.736850	+	0.676056i	$0.763688\pi$
$72$		0			0
$73$	−47.5000	+	82.2724i	−0.650685	+	1.12702i	0.332272	+	0.943184i	$0.392185\pi$
$73$	−47.5000	+	82.2724i	−0.650685	+	1.12702i	−0.982957	+	0.183836i	$0.941149\pi$
$74$		0			0
$75$	20.7846	−	12.0000i	0.277128	−	0.160000i
$76$		0			0
$77$	−59.5000	+	103.057i	−0.772727	+	1.33840i
$78$		0			0
$79$	35.5070	−	20.5000i	0.449456	−	0.259494i	−0.258144	−	0.966106i	$-0.583111\pi$
$79$	35.5070	−	20.5000i	0.449456	−	0.259494i	0.707601	+	0.706613i	$0.249778\pi$
$80$		0			0
$81$	−27.5000	+	47.6314i	−0.339506	+	0.588042i
$82$		0			0
$83$			72.0000i			0.867470i	0.901041	+	0.433735i	$0.142805\pi$
$83$			72.0000i			0.867470i	−0.901041	+	0.433735i	$0.857195\pi$
$84$		0			0
$85$	1.00000			0.0117647
$86$		0			0
$87$	20.7846	+	12.0000i	0.238904	+	0.137931i
$88$		0			0
$89$	−47.5000	−	82.2724i	−0.533708	−	0.924409i	−0.999225	−	0.0393701i	$-0.987465\pi$
$89$	−47.5000	−	82.2724i	−0.533708	−	0.924409i	0.465517	−	0.885039i	$-0.345868\pi$
$90$		0			0
$91$		−	168.000i		−	1.84615i
$92$		0			0
$93$	−20.5000	−	35.5070i	−0.220430	−	0.381796i
$94$		0			0
$95$	−6.06218	−	3.50000i	−0.0638124	−	0.0368421i
$96$		0			0
$97$	144.000			1.48454			0.742268	−	0.670103i	$-0.233750\pi$
$97$	144.000			1.48454			0.742268	+	0.670103i	$0.233750\pi$
$98$		0			0
$99$			136.000i			1.37374i
$100$		0			0
$101$	−36.5000	+	63.2199i	−0.361386	+	0.625939i	−0.988189	−	0.153239i	$-0.951030\pi$
$101$	−36.5000	+	63.2199i	−0.361386	+	0.625939i	0.626803	+	0.779178i	$0.284363\pi$
$102$		0			0
$103$	77.0763	−	44.5000i	0.748313	−	0.432039i	−0.0767709	−	0.997049i	$-0.524461\pi$
$103$	77.0763	−	44.5000i	0.748313	−	0.432039i	0.825084	+	0.565010i	$0.191128\pi$
$104$		0			0
$105$	−7.00000			−0.0666667
$106$		0			0
$107$	−160.215	+	92.5000i	−1.49733	+	0.864486i	−0.999995	−	0.00307068i	$-0.999023\pi$
$107$	−160.215	+	92.5000i	−1.49733	+	0.864486i	−0.497338	+	0.867557i	$0.665689\pi$
$108$		0			0
$109$	35.5000	−	61.4878i	0.325688	−	0.564108i	−0.655963	−	0.754793i	$-0.727737\pi$
$109$	35.5000	−	61.4878i	0.325688	−	0.564108i	0.981651	+	0.190684i	$0.0610707\pi$
$110$		0			0
$111$			49.0000i			0.441441i
$112$		0			0
$113$	96.0000			0.849558			0.424779	−	0.905297i	$-0.360352\pi$
$113$	96.0000			0.849558			0.424779	+	0.905297i	$0.360352\pi$
$114$		0			0
$115$	6.06218	+	3.50000i	0.0527146	+	0.0304348i
$116$		0			0
$117$	−96.0000	−	166.277i	−0.820513	−	1.42117i
$118$		0			0
$119$	6.06218	+	3.50000i	0.0509427	+	0.0294118i
$120$		0			0
$121$	84.0000	+	145.492i	0.694215	+	1.20242i
$122$		0			0
$123$	−41.5692	−	24.0000i	−0.337961	−	0.195122i
$124$		0			0
$125$	−49.0000			−0.392000
$126$		0			0
$127$		−	144.000i		−	1.13386i	−0.823767	−	0.566929i	$-0.808131\pi$
$127$		−	144.000i		−	1.13386i	0.823767	−	0.566929i	$-0.191869\pi$
$128$		0			0
$129$	−12.0000	+	20.7846i	−0.0930233	+	0.161121i
$130$		0			0
$131$	160.215	−	92.5000i	1.22301	−	0.706107i	0.257454	−	0.966291i	$-0.417116\pi$
$131$	160.215	−	92.5000i	1.22301	−	0.706107i	0.965559	+	0.260184i	$0.0837831\pi$
$132$		0			0
$133$	−24.5000	−	42.4352i	−0.184211	−	0.319062i
$134$		0			0
$135$	−14.7224	+	8.50000i	−0.109055	+	0.0629630i
$136$		0			0
$137$	71.5000	−	123.842i	0.521898	−	0.903954i	−0.477778	−	0.878481i	$-0.658558\pi$
$137$	71.5000	−	123.842i	0.521898	−	0.903954i	0.999676	−	0.0254728i	$-0.00810911\pi$
$138$		0			0
$139$		−	216.000i		−	1.55396i	−0.629527	−	0.776978i	$-0.716751\pi$
$139$		−	216.000i		−	1.55396i	0.629527	−	0.776978i	$-0.283249\pi$
$140$		0			0
$141$	55.0000			0.390071
$142$		0			0
$143$	−353.338	−	204.000i	−2.47090	−	1.42657i
$144$		0			0
$145$	−12.0000	−	20.7846i	−0.0827586	−	0.143342i
$146$		0			0
$147$	−42.4352	−	24.5000i	−0.288675	−	0.166667i
$148$		0			0
$149$	23.5000	+	40.7032i	0.157718	+	0.273176i	0.934045	−	0.357154i	$-0.116253\pi$
$149$	23.5000	+	40.7032i	0.157718	+	0.273176i	−0.776327	+	0.630330i	$0.782920\pi$
$150$		0			0
$151$	172.339	+	99.5000i	1.14132	+	0.658940i	0.946757	−	0.321950i	$-0.104338\pi$
$151$	172.339	+	99.5000i	1.14132	+	0.658940i	0.194562	+	0.980890i	$0.437672\pi$
$152$		0			0
$153$	8.00000			0.0522876
$154$		0			0
$155$			41.0000i			0.264516i
$156$		0			0
$157$	36.5000	−	63.2199i	0.232484	−	0.402674i	−0.726054	−	0.687637i	$-0.758648\pi$
$157$	36.5000	−	63.2199i	0.232484	−	0.402674i	0.958539	+	0.284963i	$0.0919813\pi$
$158$		0			0
$159$	21.6506	−	12.5000i	0.136168	−	0.0786164i
$160$		0			0
$161$	24.5000	+	42.4352i	0.152174	+	0.263573i
$162$		0			0
$163$	−47.6314	+	27.5000i	−0.292217	+	0.168712i	−0.638941	−	0.769255i	$-0.720627\pi$
$163$	−47.6314	+	27.5000i	−0.292217	+	0.168712i	0.346724	+	0.937967i	$0.387294\pi$
$164$		0			0
$165$	−8.50000	+	14.7224i	−0.0515152	+	0.0892269i
$166$		0			0
$167$			206.000i			1.23353i	0.787146	+	0.616766i	$0.211558\pi$
$167$			206.000i			1.23353i	−0.787146	+	0.616766i	$0.788442\pi$
$168$		0			0
$169$	407.000			2.40828
$170$		0			0
$171$	−48.4974	−	28.0000i	−0.283611	−	0.163743i
$172$		0			0
$173$	−119.500	−	206.980i	−0.690751	−	1.19642i	−0.971592	−	0.236662i	$-0.923947\pi$
$173$	−119.500	−	206.980i	−0.690751	−	1.19642i	0.280841	−	0.959754i	$-0.409387\pi$
$174$		0			0
$175$	−145.492	−	84.0000i	−0.831384	−	0.480000i
$176$		0			0
$177$	8.50000	+	14.7224i	0.0480226	+	0.0831776i
$178$		0			0
$179$	−14.7224	−	8.50000i	−0.0822482	−	0.0474860i	0.458312	−	0.888791i	$-0.348454\pi$
$179$	−14.7224	−	8.50000i	−0.0822482	−	0.0474860i	−0.540560	+	0.841305i	$0.681788\pi$
$180$		0			0
$181$	70.0000			0.386740			0.193370	−	0.981126i	$-0.438058\pi$
$181$	70.0000			0.386740			0.193370	+	0.981126i	$0.438058\pi$
$182$		0			0
$183$			1.00000i			0.00546448i
$184$		0			0
$185$	24.5000	−	42.4352i	0.132432	−	0.229380i
$186$		0			0
$187$	14.7224	−	8.50000i	0.0787296	−	0.0454545i
$188$		0			0
$189$	−119.000			−0.629630
$190$		0			0
$191$	172.339	−	99.5000i	0.902299	−	0.520942i	0.0243534	−	0.999703i	$-0.492247\pi$
$191$	172.339	−	99.5000i	0.902299	−	0.520942i	0.877945	+	0.478761i	$0.158914\pi$
$192$		0			0
$193$	23.5000	−	40.7032i	0.121762	−	0.210897i	−0.798701	−	0.601728i	$-0.794479\pi$
$193$	23.5000	−	40.7032i	0.121762	−	0.210897i	0.920462	+	0.390831i	$0.127812\pi$
$194$		0			0
$195$		−	24.0000i		−	0.123077i
$196$		0			0
$197$	24.0000			0.121827			0.0609137	−	0.998143i	$-0.480599\pi$
$197$	24.0000			0.121827			0.0609137	+	0.998143i	$0.480599\pi$
$198$		0			0
$199$	−118.645	−	68.5000i	−0.596208	−	0.344221i	0.171340	−	0.985212i	$-0.445190\pi$
$199$	−118.645	−	68.5000i	−0.596208	−	0.344221i	−0.767549	+	0.640991i	$0.778524\pi$
$200$		0			0
$201$	32.5000	+	56.2917i	0.161692	+	0.280058i
$202$		0			0
$203$		−	168.000i		−	0.827586i
$204$		0			0
$205$	24.0000	+	41.5692i	0.117073	+	0.202777i
$206$		0			0
$207$	48.4974	+	28.0000i	0.234287	+	0.135266i
$208$		0			0
$209$	−119.000			−0.569378
$210$		0			0
$211$			264.000i			1.25118i	0.780150	+	0.625592i	$0.215143\pi$
$211$			264.000i			1.25118i	−0.780150	+	0.625592i	$0.784857\pi$
$212$		0			0
$213$	−48.0000	+	83.1384i	−0.225352	+	0.390321i
$214$		0			0
$215$	20.7846	−	12.0000i	0.0966726	−	0.0558140i
$216$		0			0
$217$	−143.500	+	248.549i	−0.661290	+	1.14539i
$218$		0			0
$219$	−82.2724	+	47.5000i	−0.375673	+	0.216895i
$220$		0			0
$221$	−12.0000	+	20.7846i	−0.0542986	+	0.0940480i
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	−192.000			−0.853333
$226$		0			0
$227$	359.401	+	207.500i	1.58326	+	0.914097i	0.994379	+	0.105879i	$0.0337656\pi$
$227$	359.401	+	207.500i	1.58326	+	0.914097i	0.588883	+	0.808218i	$0.299568\pi$
$228$		0			0
$229$	71.5000	+	123.842i	0.312227	+	0.540793i	0.978844	−	0.204607i	$-0.0655917\pi$
$229$	71.5000	+	123.842i	0.312227	+	0.540793i	−0.666617	+	0.745400i	$0.732258\pi$
$230$		0			0
$231$	−103.057	+	59.5000i	−0.446134	+	0.257576i
$232$		0			0
$233$	−144.500	−	250.281i	−0.620172	−	1.07417i	−0.989453	−	0.144851i	$-0.953730\pi$
$233$	−144.500	−	250.281i	−0.620172	−	1.07417i	0.369282	−	0.929317i	$-0.379604\pi$
$234$		0			0
$235$	−47.6314	−	27.5000i	−0.202687	−	0.117021i
$236$		0			0
$237$	41.0000			0.172996
$238$		0			0
$239$			226.000i			0.945607i	0.881168	+	0.472803i	$0.156758\pi$
$239$			226.000i			0.945607i	−0.881168	+	0.472803i	$0.843242\pi$
$240$		0			0
$241$	−47.5000	+	82.2724i	−0.197095	+	0.341379i	−0.947585	−	0.319502i	$-0.896484\pi$
$241$	−47.5000	+	82.2724i	−0.197095	+	0.341379i	0.750490	+	0.660882i	$0.229818\pi$
$242$		0			0
$243$	−180.133	+	104.000i	−0.741289	+	0.427984i
$244$		0			0
$245$	24.5000	+	42.4352i	0.100000	+	0.173205i
$246$		0			0
$247$	145.492	−	84.0000i	0.589038	−	0.340081i
$248$		0			0
$249$	−36.0000	+	62.3538i	−0.144578	+	0.250417i
$250$		0			0
$251$		−	38.0000i		−	0.151394i	−0.997131	−	0.0756972i	$-0.975882\pi$
$251$		−	38.0000i		−	0.151394i	0.997131	−	0.0756972i	$-0.0241182\pi$
$252$		0			0
$253$	119.000			0.470356
$254$		0			0
$255$	0.866025	+	0.500000i	0.00339618	+	0.00196078i
$256$		0			0
$257$	−96.5000	−	167.143i	−0.375486	−	0.650361i	0.614913	−	0.788595i	$-0.289191\pi$
$257$	−96.5000	−	167.143i	−0.375486	−	0.650361i	−0.990400	+	0.138233i	$0.955858\pi$
$258$		0			0
$259$	297.047	−	171.500i	1.14690	−	0.662162i
$260$		0			0
$261$	−96.0000	−	166.277i	−0.367816	−	0.637076i
$262$		0			0
$263$	201.784	+	116.500i	0.767239	+	0.442966i	0.831889	−	0.554942i	$-0.187260\pi$
$263$	201.784	+	116.500i	0.767239	+	0.442966i	−0.0646496	+	0.997908i	$0.520593\pi$
$264$		0			0
$265$	−25.0000			−0.0943396
$266$		0			0
$267$		−	95.0000i		−	0.355805i
$268$		0			0
$269$	−227.500	+	394.042i	−0.845725	+	1.46484i	0.0392653	+	0.999229i	$0.487498\pi$
$269$	−227.500	+	394.042i	−0.845725	+	1.46484i	−0.884990	+	0.465610i	$0.845835\pi$
$270$		0			0
$271$	368.061	−	212.500i	1.35816	−	0.784133i	0.368782	−	0.929516i	$-0.379775\pi$
$271$	368.061	−	212.500i	1.35816	−	0.784133i	0.989375	+	0.145383i	$0.0464414\pi$
$272$		0			0
$273$	84.0000	−	145.492i	0.307692	−	0.532939i
$274$		0			0
$275$	−353.338	+	204.000i	−1.28487	+	0.741818i
$276$		0			0
$277$	−83.5000	+	144.626i	−0.301444	+	0.522116i	−0.976463	−	0.215684i	$-0.930802\pi$
$277$	−83.5000	+	144.626i	−0.301444	+	0.522116i	0.675019	+	0.737800i	$0.264135\pi$
$278$		0			0
$279$			328.000i			1.17563i
$280$		0			0
$281$	−432.000			−1.53737			−0.768683	−	0.639630i	$-0.779088\pi$
$281$	−432.000			−1.53737			−0.768683	+	0.639630i	$0.779088\pi$
$282$		0			0
$283$	193.124	+	111.500i	0.682416	+	0.393993i	0.800765	−	0.598979i	$-0.204427\pi$
$283$	193.124	+	111.500i	0.682416	+	0.393993i	−0.118349	+	0.992972i	$0.537760\pi$
$284$		0			0
$285$	−3.50000	−	6.06218i	−0.0122807	−	0.0212708i
$286$		0			0
$287$			336.000i			1.17073i
$288$		0			0
$289$	144.000	+	249.415i	0.498270	+	0.863029i
$290$		0			0
$291$	124.708	+	72.0000i	0.428549	+	0.247423i
$292$		0			0
$293$	26.0000			0.0887372			0.0443686	−	0.999015i	$-0.485872\pi$
$293$	26.0000			0.0887372			0.0443686	+	0.999015i	$0.485872\pi$
$294$		0			0
$295$		−	17.0000i		−	0.0576271i
$296$		0			0
$297$	−144.500	+	250.281i	−0.486532	+	0.842698i
$298$		0			0
$299$	−145.492	+	84.0000i	−0.486596	+	0.280936i
$300$		0			0
$301$	168.000			0.558140
$302$		0			0
$303$	−63.2199	+	36.5000i	−0.208646	+	0.120462i
$304$		0			0
$305$	0.500000	−	0.866025i	0.00163934	−	0.00283943i
$306$		0			0
$307$		−	264.000i		−	0.859935i	−0.902844	−	0.429967i	$-0.858525\pi$
$307$		−	264.000i		−	0.859935i	0.902844	−	0.429967i	$-0.141475\pi$
$308$		0			0
$309$	89.0000			0.288026
$310$		0			0
$311$	−297.047	−	171.500i	−0.955134	−	0.551447i	−0.0604621	−	0.998170i	$-0.519257\pi$
$311$	−297.047	−	171.500i	−0.955134	−	0.551447i	−0.894672	+	0.446724i	$0.852591\pi$
$312$		0			0
$313$	−167.500	−	290.119i	−0.535144	−	0.926896i	−0.999156	−	0.0410676i	$-0.986924\pi$
$313$	−167.500	−	290.119i	−0.535144	−	0.926896i	0.464013	−	0.885829i	$-0.346409\pi$
$314$		0			0
$315$	48.4974	+	28.0000i	0.153960	+	0.0888889i
$316$		0			0
$317$	264.500	+	458.127i	0.834385	+	1.44520i	0.894530	+	0.447007i	$0.147510\pi$
$317$	264.500	+	458.127i	0.834385	+	1.44520i	−0.0601454	+	0.998190i	$0.519156\pi$
$318$		0			0
$319$	−353.338	−	204.000i	−1.10764	−	0.639498i
$320$		0			0
$321$	−185.000			−0.576324
$322$		0			0
$323$			7.00000i			0.0216718i
$324$		0			0
$325$	288.000	−	498.831i	0.886154	−	1.53486i
$326$		0			0
$327$	61.4878	−	35.5000i	0.188036	−	0.108563i
$328$		0			0
$329$	−192.500	−	333.420i	−0.585106	−	1.01343i
$330$		0			0
$331$	−47.6314	+	27.5000i	−0.143902	+	0.0830816i	−0.570222	−	0.821491i	$-0.693143\pi$
$331$	−47.6314	+	27.5000i	−0.143902	+	0.0830816i	0.426321	+	0.904572i	$0.359810\pi$
$332$		0			0
$333$	196.000	−	339.482i	0.588589	−	1.01947i
$334$		0			0
$335$		−	65.0000i		−	0.194030i
$336$		0			0
$337$	−240.000			−0.712166			−0.356083	−	0.934454i	$-0.615888\pi$
$337$	−240.000			−0.712166			−0.356083	+	0.934454i	$0.615888\pi$
$338$		0			0
$339$	83.1384	+	48.0000i	0.245246	+	0.141593i
$340$		0			0
$341$	348.500	+	603.620i	1.02199	+	1.77015i
$342$		0			0
$343$			343.000i			1.00000i
$344$		0			0
$345$	3.50000	+	6.06218i	0.0101449	+	0.0175715i
$346$		0			0
$347$	−26.8468	−	15.5000i	−0.0773683	−	0.0446686i	0.460817	−	0.887495i	$-0.347557\pi$
$347$	−26.8468	−	15.5000i	−0.0773683	−	0.0446686i	−0.538185	+	0.842827i	$0.680890\pi$
$348$		0			0
$349$	−120.000			−0.343840			−0.171920	−	0.985111i	$-0.554997\pi$
$349$	−120.000			−0.343840			−0.171920	+	0.985111i	$0.554997\pi$
$350$		0			0
$351$		−	408.000i		−	1.16239i
$352$		0			0
$353$	263.500	−	456.395i	0.746459	−	1.29290i	−0.203051	−	0.979168i	$-0.565086\pi$
$353$	263.500	−	456.395i	0.746459	−	1.29290i	0.949510	−	0.313737i	$-0.101581\pi$
$354$		0			0
$355$	83.1384	−	48.0000i	0.234193	−	0.135211i
$356$		0			0
$357$	3.50000	+	6.06218i	0.00980392	+	0.0169809i
$358$		0			0
$359$	463.324	−	267.500i	1.29059	−	0.745125i	0.311835	−	0.950136i	$-0.399056\pi$
$359$	463.324	−	267.500i	1.29059	−	0.745125i	0.978760	+	0.205011i	$0.0657230\pi$
$360$		0			0
$361$	−156.000	+	270.200i	−0.432133	+	0.748476i
$362$		0			0
$363$			168.000i			0.462810i
$364$		0			0
$365$	95.0000			0.260274
$366$		0			0
$367$	77.0763	+	44.5000i	0.210017	+	0.121253i	0.601319	−	0.799009i	$-0.294642\pi$
$367$	77.0763	+	44.5000i	0.210017	+	0.121253i	−0.391302	+	0.920262i	$0.627975\pi$
$368$		0			0
$369$	192.000	+	332.554i	0.520325	+	0.901230i
$370$		0			0
$371$	−151.554	−	87.5000i	−0.408503	−	0.235849i
$372$		0			0
$373$	−167.500	−	290.119i	−0.449062	−	0.777798i	0.549264	−	0.835649i	$-0.314908\pi$
$373$	−167.500	−	290.119i	−0.449062	−	0.777798i	−0.998325	+	0.0578516i	$0.981575\pi$
$374$		0			0
$375$	−42.4352	−	24.5000i	−0.113161	−	0.0653333i
$376$		0			0
$377$	576.000			1.52785
$378$		0			0
$379$			38.0000i			0.100264i	0.998743	+	0.0501319i	$0.0159642\pi$
$379$			38.0000i			0.100264i	−0.998743	+	0.0501319i	$0.984036\pi$
$380$		0			0
$381$	72.0000	−	124.708i	0.188976	−	0.327317i
$382$		0			0
$383$	−575.907	+	332.500i	−1.50367	+	0.868146i	−0.503682	+	0.863889i	$0.668022\pi$
$383$	−575.907	+	332.500i	−1.50367	+	0.868146i	−0.999991	+	0.00425732i	$0.998645\pi$
$384$		0			0
$385$	119.000			0.309091
$386$		0			0
$387$	166.277	−	96.0000i	0.429656	−	0.248062i
$388$		0			0
$389$	−36.5000	+	63.2199i	−0.0938303	+	0.162519i	−0.909120	−	0.416535i	$-0.863244\pi$
$389$	−36.5000	+	63.2199i	−0.0938303	+	0.162519i	0.815290	+	0.579054i	$0.196578\pi$
$390$		0			0
$391$		−	7.00000i		−	0.0179028i
$392$		0			0
$393$	185.000			0.470738
$394$		0			0
$395$	−35.5070	−	20.5000i	−0.0898912	−	0.0518987i
$396$		0			0
$397$	−0.500000	−	0.866025i	−0.00125945	−	0.00218142i	0.865395	−	0.501090i	$-0.167068\pi$
$397$	−0.500000	−	0.866025i	−0.00125945	−	0.00218142i	−0.866654	+	0.498909i	$0.833734\pi$
$398$		0			0
$399$		−	49.0000i		−	0.122807i
$400$		0			0
$401$	−168.500	−	291.851i	−0.420200	−	0.727807i	0.575759	−	0.817619i	$-0.304707\pi$
$401$	−168.500	−	291.851i	−0.420200	−	0.727807i	−0.995959	+	0.0898124i	$0.971373\pi$
$402$		0			0
$403$	−852.169	−	492.000i	−2.11456	−	1.22084i
$404$		0			0
$405$	55.0000			0.135802
$406$		0			0
$407$		−	833.000i		−	2.04668i
$408$		0			0
$409$	239.500	−	414.826i	0.585575	−	1.01424i	−0.409229	−	0.912432i	$-0.634202\pi$
$409$	239.500	−	414.826i	0.585575	−	1.01424i	0.994804	−	0.101813i	$-0.0324644\pi$
$410$		0			0
$411$	123.842	−	71.5000i	0.301318	−	0.173966i
$412$		0			0
$413$	59.5000	−	103.057i	0.144068	−	0.249533i
$414$		0			0
$415$	62.3538	−	36.0000i	0.150250	−	0.0867470i
$416$		0			0
$417$	108.000	−	187.061i	0.258993	−	0.448589i
$418$		0			0
$419$		−	552.000i		−	1.31742i	−0.752396	−	0.658711i	$-0.771102\pi$
$419$		−	552.000i		−	1.31742i	0.752396	−	0.658711i	$-0.228898\pi$
$420$		0			0
$421$	−216.000			−0.513064			−0.256532	−	0.966536i	$-0.582580\pi$
$421$	−216.000			−0.513064			−0.256532	+	0.966536i	$0.582580\pi$
$422$		0			0
$423$	−381.051	−	220.000i	−0.900830	−	0.520095i
$424$		0			0
$425$	12.0000	+	20.7846i	0.0282353	+	0.0489050i
$426$		0			0
$427$	6.06218	−	3.50000i	0.0141971	−	0.00819672i
$428$		0			0
$429$	−204.000	−	353.338i	−0.475524	−	0.823633i
$430$		0			0
$431$	380.185	+	219.500i	0.882100	+	0.509281i	0.871350	−	0.490661i	$-0.163245\pi$
$431$	380.185	+	219.500i	0.882100	+	0.509281i	0.0107498	+	0.999942i	$0.496578\pi$
$432$		0			0
$433$	−288.000			−0.665127			−0.332564	−	0.943081i	$-0.607914\pi$
$433$	−288.000			−0.665127			−0.332564	+	0.943081i	$0.607914\pi$
$434$		0			0
$435$		−	24.0000i		−	0.0551724i
$436$		0			0
$437$	−24.5000	+	42.4352i	−0.0560641	+	0.0971058i
$438$		0			0
$439$	−534.338	+	308.500i	−1.21717	+	0.702733i	−0.964312	−	0.264770i	$-0.914704\pi$
$439$	−534.338	+	308.500i	−1.21717	+	0.702733i	−0.252858	+	0.967503i	$0.581371\pi$
$440$		0			0
$441$	196.000	+	339.482i	0.444444	+	0.769800i
$442$		0			0
$443$	213.908	−	123.500i	0.482863	−	0.278781i	−0.238746	−	0.971082i	$-0.576736\pi$
$443$	213.908	−	123.500i	0.482863	−	0.278781i	0.721609	+	0.692301i	$0.243403\pi$
$444$		0			0
$445$	−47.5000	+	82.2724i	−0.106742	+	0.184882i
$446$		0			0
$447$			47.0000i			0.105145i
$448$		0			0
$449$	−288.000			−0.641425			−0.320713	−	0.947177i	$-0.603922\pi$
$449$	−288.000			−0.641425			−0.320713	+	0.947177i	$0.603922\pi$
$450$		0			0
$451$	706.677	+	408.000i	1.56691	+	0.904656i
$452$		0			0
$453$	99.5000	+	172.339i	0.219647	+	0.380439i
$454$		0			0
$455$	−145.492	+	84.0000i	−0.319763	+	0.184615i
$456$		0			0
$457$	48.5000	+	84.0045i	0.106127	+	0.183817i	0.914198	−	0.405268i	$-0.132822\pi$
$457$	48.5000	+	84.0045i	0.106127	+	0.183817i	−0.808071	+	0.589085i	$0.799488\pi$
$458$		0			0
$459$	14.7224	+	8.50000i	0.0320750	+	0.0185185i
$460$		0			0
$461$	312.000			0.676790			0.338395	−	0.941004i	$-0.390116\pi$
$461$	312.000			0.676790			0.338395	+	0.941004i	$0.390116\pi$
$462$		0			0
$463$			192.000i			0.414687i	0.978268	+	0.207343i	$0.0664817\pi$
$463$			192.000i			0.414687i	−0.978268	+	0.207343i	$0.933518\pi$
$464$		0			0
$465$	−20.5000	+	35.5070i	−0.0440860	+	0.0763592i
$466$		0			0
$467$	−255.477	+	147.500i	−0.547061	+	0.315846i	−0.747936	−	0.663771i	$-0.768955\pi$
$467$	−255.477	+	147.500i	−0.547061	+	0.315846i	0.200875	+	0.979617i	$0.435622\pi$
$468$		0			0
$469$	227.500	−	394.042i	0.485075	−	0.840174i
$470$		0			0
$471$	63.2199	−	36.5000i	0.134225	−	0.0774947i
$472$		0			0
$473$	204.000	−	353.338i	0.431290	−	0.747016i
$474$		0			0
$475$		−	168.000i		−	0.353684i
$476$		0			0
$477$	−200.000			−0.419287
$478$		0			0
$479$	534.338	+	308.500i	1.11553	+	0.644050i	0.940255	−	0.340470i	$-0.110586\pi$
$479$	534.338	+	308.500i	1.11553	+	0.644050i	0.175272	+	0.984520i	$0.443919\pi$
$480$		0			0
$481$	588.000	+	1018.45i	1.22245	+	2.11735i
$482$		0			0
$483$			49.0000i			0.101449i
$484$		0			0
$485$	−72.0000	−	124.708i	−0.148454	−	0.257129i
$486$		0			0
$487$	−213.908	−	123.500i	−0.439237	−	0.253593i	0.264037	−	0.964513i	$-0.414946\pi$
$487$	−213.908	−	123.500i	−0.439237	−	0.253593i	−0.703274	+	0.710919i	$0.748279\pi$
$488$		0			0
$489$	−55.0000			−0.112474
$490$		0			0
$491$			134.000i			0.272912i	0.990646	+	0.136456i	$0.0435713\pi$
$491$			134.000i			0.272912i	−0.990646	+	0.136456i	$0.956429\pi$
$492$		0			0
$493$	−12.0000	+	20.7846i	−0.0243408	+	0.0421595i
$494$		0			0
$495$	117.779	−	68.0000i	0.237938	−	0.137374i
$496$		0			0
$497$	672.000			1.35211
$498$		0			0
$499$	−629.600	+	363.500i	−1.26172	+	0.728457i	−0.973408	−	0.229078i	$-0.926429\pi$
$499$	−629.600	+	363.500i	−1.26172	+	0.728457i	−0.288316	+	0.957535i	$0.593095\pi$
$500$		0			0
$501$	−103.000	+	178.401i	−0.205589	+	0.356090i
$502$		0			0
$503$		−	432.000i		−	0.858847i	−0.903103	−	0.429423i	$-0.858717\pi$
$503$		−	432.000i		−	0.858847i	0.903103	−	0.429423i	$-0.141283\pi$
$504$		0			0
$505$	73.0000			0.144554
$506$		0			0
$507$	352.472	+	203.500i	0.695212	+	0.401381i
$508$		0			0
$509$	−216.500	−	374.989i	−0.425344	−	0.736717i	0.571109	−	0.820874i	$-0.306513\pi$
$509$	−216.500	−	374.989i	−0.425344	−	0.736717i	−0.996452	+	0.0841574i	$0.973180\pi$
$510$		0			0
$511$	575.907	+	332.500i	1.12702	+	0.650685i
$512$		0			0
$513$	−59.5000	−	103.057i	−0.115984	−	0.200891i
$514$		0			0
$515$	−77.0763	−	44.5000i	−0.149663	−	0.0864078i
$516$		0			0
$517$	−935.000			−1.80851
$518$		0			0
$519$		−	239.000i		−	0.460501i
$520$		0			0
$521$	−239.500	+	414.826i	−0.459693	+	0.796211i	−0.998945	−	0.0459332i	$-0.985374\pi$
$521$	−239.500	+	414.826i	−0.459693	+	0.796211i	0.539252	+	0.842145i	$0.318707\pi$
$522$		0			0
$523$	−783.753	+	452.500i	−1.49857	+	0.865201i	−0.999999	−	0.00164693i	$-0.999476\pi$
$523$	−783.753	+	452.500i	−1.49857	+	0.865201i	−0.498573	+	0.866848i	$0.666142\pi$
$524$		0			0
$525$	−84.0000	−	145.492i	−0.160000	−	0.277128i
$526$		0			0
$527$	35.5070	−	20.5000i	0.0673758	−	0.0388994i
$528$		0			0
$529$	−240.000	+	415.692i	−0.453686	+	0.785808i
$530$		0			0
$531$		−	136.000i		−	0.256121i
$532$		0			0
$533$	−1152.00			−2.16135
$534$		0			0
$535$	160.215	+	92.5000i	0.299467	+	0.172897i
$536$		0			0
$537$	−8.50000	−	14.7224i	−0.0158287	−	0.0274161i
$538$		0			0
$539$	721.399	+	416.500i	1.33840	+	0.772727i
$540$		0			0
$541$	95.5000	+	165.411i	0.176525	+	0.305750i	0.940688	−	0.339273i	$-0.110181\pi$
$541$	95.5000	+	165.411i	0.176525	+	0.305750i	−0.764163	+	0.645023i	$0.776848\pi$
$542$		0			0
$543$	60.6218	+	35.0000i	0.111642	+	0.0644567i
$544$		0			0
$545$	−71.0000			−0.130275
$546$		0			0
$547$		−	374.000i		−	0.683729i	−0.939749	−	0.341865i	$-0.888942\pi$
$547$		−	374.000i		−	0.683729i	0.939749	−	0.341865i	$-0.111058\pi$
$548$		0			0
$549$	4.00000	−	6.92820i	0.00728597	−	0.0126197i
$550$		0			0
$551$	145.492	−	84.0000i	0.264051	−	0.152450i
$552$		0			0
$553$	−143.500	−	248.549i	−0.259494	−	0.449456i
$554$		0			0
$555$	42.4352	−	24.5000i	0.0764599	−	0.0441441i
$556$		0			0
$557$	−468.500	+	811.466i	−0.841113	+	1.45685i	0.0478413	+	0.998855i	$0.484766\pi$
$557$	−468.500	+	811.466i	−0.841113	+	1.45685i	−0.888954	+	0.457996i	$0.848568\pi$
$558$		0			0
$559$			576.000i			1.03041i
$560$		0			0
$561$	17.0000			0.0303030
$562$		0			0
$563$	−691.954	−	399.500i	−1.22905	−	0.709591i	−0.262218	−	0.965009i	$-0.584454\pi$
$563$	−691.954	−	399.500i	−1.22905	−	0.709591i	−0.966831	+	0.255417i	$0.917787\pi$
$564$		0			0
$565$	−48.0000	−	83.1384i	−0.0849558	−	0.147148i
$566$		0			0
$567$	333.420	+	192.500i	0.588042	+	0.339506i
$568$		0			0
$569$	264.500	+	458.127i	0.464851	+	0.805145i	0.999195	−	0.0401221i	$-0.0127747\pi$
$569$	264.500	+	458.127i	0.464851	+	0.805145i	−0.534344	+	0.845267i	$0.679441\pi$
$570$		0			0
$571$	899.800	+	519.500i	1.57583	+	0.909807i	0.995432	+	0.0954765i	$0.0304375\pi$
$571$	899.800	+	519.500i	1.57583	+	0.909807i	0.580401	+	0.814331i	$0.302896\pi$
$572$		0			0
$573$	199.000			0.347295
$574$		0			0
$575$			168.000i			0.292174i
$576$		0			0
$577$	264.500	−	458.127i	0.458406	−	0.793982i	−0.540471	−	0.841362i	$-0.681754\pi$
$577$	264.500	−	458.127i	0.458406	−	0.793982i	0.998877	+	0.0473807i	$0.0150874\pi$
$578$		0			0
$579$	40.7032	−	23.5000i	0.0702991	−	0.0405872i
$580$		0			0
$581$	504.000			0.867470
$582$		0			0
$583$	−368.061	+	212.500i	−0.631322	+	0.364494i
$584$		0			0
$585$	−96.0000	+	166.277i	−0.164103	+	0.284234i
$586$		0			0
$587$			840.000i			1.43101i	0.698610	+	0.715503i	$0.253802\pi$
$587$			840.000i			1.43101i	−0.698610	+	0.715503i	$0.746198\pi$
$588$		0			0
$589$	−287.000			−0.487267
$590$		0			0
$591$	20.7846	+	12.0000i	0.0351685	+	0.0203046i
$592$		0			0
$593$	191.500	+	331.688i	0.322934	+	0.559338i	0.981092	−	0.193541i	$-0.0619974\pi$
$593$	191.500	+	331.688i	0.322934	+	0.559338i	−0.658158	+	0.752880i	$0.728664\pi$
$594$		0			0
$595$		−	7.00000i		−	0.0117647i
$596$		0			0
$597$	−68.5000	−	118.645i	−0.114740	−	0.198736i
$598$		0			0
$599$	−297.047	−	171.500i	−0.495904	−	0.286311i	0.231116	−	0.972926i	$-0.425762\pi$
$599$	−297.047	−	171.500i	−0.495904	−	0.286311i	−0.727021	+	0.686616i	$0.759096\pi$
$600$		0			0
$601$	−624.000			−1.03827			−0.519135	−	0.854692i	$-0.673746\pi$
$601$	−624.000			−1.03827			−0.519135	+	0.854692i	$0.673746\pi$
$602$		0			0
$603$		−	520.000i		−	0.862355i
$604$		0			0
$605$	84.0000	−	145.492i	0.138843	−	0.240483i
$606$		0			0
$607$	−118.645	+	68.5000i	−0.195462	+	0.112850i	−0.594537	−	0.804068i	$-0.702665\pi$
$607$	−118.645	+	68.5000i	−0.195462	+	0.112850i	0.399075	+	0.916918i	$0.369331\pi$
$608$		0			0
$609$	84.0000	−	145.492i	0.137931	−	0.238904i
$610$		0			0
$611$	1143.15	−	660.000i	1.87096	−	1.08020i
$612$		0			0
$613$	35.5000	−	61.4878i	0.0579119	−	0.100306i	−0.835616	−	0.549314i	$-0.814889\pi$
$613$	35.5000	−	61.4878i	0.0579119	−	0.100306i	0.893528	+	0.449008i	$0.148222\pi$
$614$		0			0
$615$			48.0000i			0.0780488i
$616$		0			0
$617$	384.000			0.622366			0.311183	−	0.950350i	$-0.399275\pi$
$617$	384.000			0.622366			0.311183	+	0.950350i	$0.399275\pi$
$618$		0			0
$619$	513.553	+	296.500i	0.829650	+	0.478998i	0.853733	−	0.520712i	$-0.174333\pi$
$619$	513.553	+	296.500i	0.829650	+	0.478998i	−0.0240831	+	0.999710i	$0.507667\pi$
$620$		0			0
$621$	59.5000	+	103.057i	0.0958132	+	0.165953i
$622$		0			0
$623$	−575.907	+	332.500i	−0.924409	+	0.533708i
$624$		0			0
$625$	−275.500	−	477.180i	−0.440800	−	0.763488i
$626$		0			0
$627$	−103.057	−	59.5000i	−0.164365	−	0.0948963i
$628$		0			0
$629$	−49.0000			−0.0779014
$630$		0			0
$631$			384.000i			0.608558i	0.952583	+	0.304279i	$0.0984155\pi$
$631$			384.000i			0.608558i	−0.952583	+	0.304279i	$0.901585\pi$
$632$		0			0
$633$	−132.000	+	228.631i	−0.208531	+	0.361186i
$634$		0			0
$635$	−124.708	+	72.0000i	−0.196390	+	0.113386i
$636$		0			0
$637$	−1176.00			−1.84615
$638$		0			0
$639$	665.108	−	384.000i	1.04086	−	0.600939i
$640$		0			0
$641$	−383.500	+	664.241i	−0.598284	+	1.03626i	0.394790	+	0.918771i	$0.370817\pi$
$641$	−383.500	+	664.241i	−0.598284	+	1.03626i	−0.993074	+	0.117487i	$0.962516\pi$
$642$		0			0
$643$			456.000i			0.709176i	0.935023	+	0.354588i	$0.115379\pi$
$643$			456.000i			0.709176i	−0.935023	+	0.354588i	$0.884621\pi$
$644$		0			0
$645$	24.0000			0.0372093
$646$		0			0
$647$	77.0763	+	44.5000i	0.119129	+	0.0687790i	0.558380	−	0.829585i	$-0.311423\pi$
$647$	77.0763	+	44.5000i	0.119129	+	0.0687790i	−0.439252	+	0.898364i	$0.644756\pi$
$648$		0			0
$649$	−144.500	−	250.281i	−0.222650	−	0.385642i
$650$		0			0
$651$	−248.549	+	143.500i	−0.381796	+	0.220430i
$652$		0			0
$653$	−263.500	−	456.395i	−0.403522	−	0.698921i	0.590626	−	0.806945i	$-0.298881\pi$
$653$	−263.500	−	456.395i	−0.403522	−	0.698921i	−0.994148	+	0.108024i	$0.965548\pi$
$654$		0			0
$655$	−160.215	−	92.5000i	−0.244603	−	0.141221i
$656$		0			0
$657$	760.000			1.15677
$658$		0			0
$659$		−	936.000i		−	1.42033i	−0.704033	−	0.710167i	$-0.748619\pi$
$659$		−	936.000i		−	1.42033i	0.704033	−	0.710167i	$-0.251381\pi$
$660$		0			0
$661$	372.500	−	645.189i	0.563540	−	0.976080i	−0.433644	−	0.901084i	$-0.642772\pi$
$661$	372.500	−	645.189i	0.563540	−	0.976080i	0.997184	−	0.0749957i	$-0.0238943\pi$
$662$		0			0
$663$	−20.7846	+	12.0000i	−0.0313493	+	0.0180995i
$664$		0			0
$665$	−24.5000	+	42.4352i	−0.0368421	+	0.0638124i
$666$		0			0
$667$	−145.492	+	84.0000i	−0.218129	+	0.125937i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	17.0000i		−	0.0253353i
$672$		0			0
$673$	−720.000			−1.06984			−0.534918	−	0.844904i	$-0.679658\pi$
$673$	−720.000			−1.06984			−0.534918	+	0.844904i	$0.679658\pi$
$674$		0			0
$675$	−353.338	−	204.000i	−0.523464	−	0.302222i
$676$		0			0
$677$	575.500	+	996.795i	0.850074	+	1.47237i	0.881141	+	0.472854i	$0.156776\pi$
$677$	575.500	+	996.795i	0.850074	+	1.47237i	−0.0310670	+	0.999517i	$0.509891\pi$
$678$		0			0
$679$		−	1008.00i		−	1.48454i
$680$		0			0
$681$	207.500	+	359.401i	0.304699	+	0.527754i
$682$		0			0
$683$	−638.261	−	368.500i	−0.934496	−	0.539531i	−0.0462653	−	0.998929i	$-0.514732\pi$
$683$	−638.261	−	368.500i	−0.934496	−	0.539531i	−0.888231	+	0.459398i	$0.848065\pi$
$684$		0			0
$685$	−143.000			−0.208759
$686$		0			0
$687$			143.000i			0.208151i
$688$		0			0
$689$	300.000	−	519.615i	0.435414	−	0.754159i
$690$		0			0
$691$	−879.016	+	507.500i	−1.27209	+	0.734443i	−0.975381	−	0.220525i	$-0.929223\pi$
$691$	−879.016	+	507.500i	−1.27209	+	0.734443i	−0.296711	+	0.954967i	$0.595890\pi$
$692$		0			0
$693$	952.000			1.37374
$694$		0			0
$695$	−187.061	+	108.000i	−0.269153	+	0.155396i
$696$		0			0
$697$	24.0000	−	41.5692i	0.0344333	−	0.0596402i
$698$		0			0
$699$		−	289.000i		−	0.413448i
$700$		0			0
$701$	1226.00			1.74893			0.874465	−	0.485089i	$-0.161213\pi$
$701$	1226.00			1.74893			0.874465	+	0.485089i	$0.161213\pi$
$702$		0			0
$703$	297.047	+	171.500i	0.422542	+	0.243954i
$704$		0			0
$705$	−27.5000	−	47.6314i	−0.0390071	−	0.0675623i
$706$		0			0
$707$	442.539	+	255.500i	0.625939	+	0.361386i
$708$		0			0
$709$	312.500	+	541.266i	0.440762	+	0.763422i	0.997746	−	0.0671013i	$-0.0213751\pi$
$709$	312.500	+	541.266i	0.440762	+	0.763422i	−0.556985	+	0.830523i	$0.688042\pi$
$710$		0			0
$711$	−284.056	−	164.000i	−0.399517	−	0.230661i
$712$		0			0
$713$	287.000			0.402525
$714$		0			0
$715$			408.000i			0.570629i
$716$		0			0
$717$	−113.000	+	195.722i	−0.157601	+	0.272973i
$718$		0			0
$719$	118.645	−	68.5000i	0.165015	−	0.0952712i	−0.415218	−	0.909722i	$-0.636295\pi$
$719$	118.645	−	68.5000i	0.165015	−	0.0952712i	0.580233	+	0.814451i	$0.302962\pi$
$720$		0			0
$721$	−311.500	−	539.534i	−0.432039	−	0.748313i
$722$		0			0
$723$	−82.2724	+	47.5000i	−0.113793	+	0.0656985i
$724$		0			0
$725$	288.000	−	498.831i	0.397241	−	0.688042i
$726$		0			0
$727$		−	960.000i		−	1.32050i	−0.751048	−	0.660248i	$-0.770451\pi$
$727$		−	960.000i		−	1.32050i	0.751048	−	0.660248i	$-0.229549\pi$
$728$		0			0
$729$	287.000			0.393690
$730$		0			0
$731$	−20.7846	−	12.0000i	−0.0284331	−	0.0164159i
$732$		0			0
$733$	−239.500	−	414.826i	−0.326739	−	0.565929i	0.655123	−	0.755522i	$-0.272617\pi$
$733$	−239.500	−	414.826i	−0.326739	−	0.565929i	−0.981863	+	0.189593i	$0.939283\pi$
$734$		0			0
$735$			49.0000i			0.0666667i
$736$		0			0
$737$	−552.500	−	956.958i	−0.749661	−	1.29845i
$738$		0			0
$739$	442.539	+	255.500i	0.598835	+	0.345737i	0.768583	−	0.639750i	$-0.220962\pi$
$739$	442.539	+	255.500i	0.598835	+	0.345737i	−0.169748	+	0.985487i	$0.554295\pi$
$740$		0			0
$741$	168.000			0.226721
$742$		0			0
$743$		−	528.000i		−	0.710633i	−0.934746	−	0.355316i	$-0.884373\pi$
$743$		−	528.000i		−	0.710633i	0.934746	−	0.355316i	$-0.115627\pi$
$744$		0			0
$745$	23.5000	−	40.7032i	0.0315436	−	0.0546352i
$746$		0			0
$747$	498.831	−	288.000i	0.667779	−	0.385542i
$748$		0			0
$749$	647.500	+	1121.50i	0.864486	+	1.49733i
$750$		0			0
$751$	−700.615	+	404.500i	−0.932909	+	0.538615i	−0.887730	−	0.460364i	$-0.847719\pi$
$751$	−700.615	+	404.500i	−0.932909	+	0.538615i	−0.0451785	+	0.998979i	$0.514386\pi$
$752$		0			0
$753$	19.0000	−	32.9090i	0.0252324	−	0.0437038i
$754$		0			0
$755$		−	199.000i		−	0.263576i
$756$		0			0
$757$	−120.000			−0.158520			−0.0792602	−	0.996854i	$-0.525256\pi$
$757$	−120.000			−0.158520			−0.0792602	+	0.996854i	$0.525256\pi$
$758$		0			0
$759$	103.057	+	59.5000i	0.135780	+	0.0783926i
$760$		0			0
$761$	−384.500	−	665.974i	−0.505256	−	0.875129i	−0.999982	−	0.00608006i	$-0.998065\pi$
$761$	−384.500	−	665.974i	−0.505256	−	0.875129i	0.494725	−	0.869049i	$-0.335269\pi$
$762$		0			0
$763$	−430.415	−	248.500i	−0.564108	−	0.325688i
$764$		0			0
$765$	−4.00000	−	6.92820i	−0.00522876	−	0.00905647i
$766$		0			0
$767$	353.338	+	204.000i	0.460676	+	0.265971i
$768$		0			0
$769$	−144.000			−0.187256			−0.0936281	−	0.995607i	$-0.529846\pi$
$769$	−144.000			−0.187256			−0.0936281	+	0.995607i	$0.529846\pi$
$770$		0			0
$771$		−	193.000i		−	0.250324i
$772$		0			0
$773$	203.500	−	352.472i	0.263260	−	0.455980i	−0.703846	−	0.710352i	$-0.748536\pi$
$773$	203.500	−	352.472i	0.263260	−	0.455980i	0.967106	+	0.254373i	$0.0818690\pi$
$774$		0			0
$775$	−852.169	+	492.000i	−1.09957	+	0.634839i
$776$		0			0
$777$	343.000			0.441441
$778$		0			0
$779$	−290.985	+	168.000i	−0.373536	+	0.215661i
$780$		0			0
$781$	816.000	−	1413.35i	1.04481	−	1.80967i
$782$		0			0
$783$		−	408.000i		−	0.521073i
$784$		0			0
$785$	−73.0000			−0.0929936
$786$		0			0
$787$	−982.939	−	567.500i	−1.24897	−	0.721093i	−0.278065	−	0.960562i	$-0.589693\pi$
$787$	−982.939	−	567.500i	−1.24897	−	0.721093i	−0.970904	+	0.239469i	$0.923027\pi$
$788$		0			0
$789$	116.500	+	201.784i	0.147655	+	0.255746i
$790$		0			0
$791$		−	672.000i		−	0.849558i
$792$		0			0
$793$	12.0000	+	20.7846i	0.0151324	+	0.0262101i
$794$		0			0
$795$	−21.6506	−	12.5000i	−0.0272335	−	0.0157233i
$796$		0			0
$797$	312.000			0.391468			0.195734	−	0.980657i	$-0.437291\pi$
$797$	312.000			0.391468			0.195734	+	0.980657i	$0.437291\pi$
$798$		0			0
$799$			55.0000i			0.0688360i
$800$		0			0
$801$	−380.000	+	658.179i	−0.474407	+	0.821697i
$802$		0			0
$803$	1398.63	−	807.500i	1.74176	−	1.00560i
$804$		0			0
$805$	24.5000	−	42.4352i	0.0304348	−	0.0527146i
$806$		0			0
$807$	−394.042	+	227.500i	−0.488280	+	0.281908i
$808$		0			0
$809$	648.500	−	1123.23i	0.801607	−	1.38842i	−0.116951	−	0.993138i	$-0.537312\pi$
$809$	648.500	−	1123.23i	0.801607	−	1.38842i	0.918558	−	0.395286i	$-0.129355\pi$
$810$		0			0
$811$		−	1128.00i		−	1.39088i	−0.718586	−	0.695438i	$-0.755211\pi$
$811$		−	1128.00i		−	1.39088i	0.718586	−	0.695438i	$-0.244789\pi$
$812$		0			0
$813$	425.000			0.522755
$814$		0			0
$815$	47.6314	+	27.5000i	0.0584434	+	0.0337423i
$816$		0			0
$817$	84.0000	+	145.492i	0.102815	+	0.178081i
$818$		0			0
$819$	−1163.94	+	672.000i	−1.42117	+	0.820513i
$820$		0			0
$821$	191.500	+	331.688i	0.233252	+	0.404005i	0.958763	−	0.284206i	$-0.0917299\pi$
$821$	191.500	+	331.688i	0.233252	+	0.404005i	−0.725511	+	0.688210i	$0.758397\pi$
$822$		0			0
$823$	−47.6314	−	27.5000i	−0.0578753	−	0.0334143i	0.470783	−	0.882249i	$-0.343971\pi$
$823$	−47.6314	−	27.5000i	−0.0578753	−	0.0334143i	−0.528658	+	0.848835i	$0.677305\pi$
$824$		0			0
$825$	−408.000			−0.494545
$826$		0			0
$827$			696.000i			0.841596i	0.907154	+	0.420798i	$0.138250\pi$
$827$			696.000i			0.841596i	−0.907154	+	0.420798i	$0.861750\pi$
$828$		0			0
$829$	−252.500	+	437.343i	−0.304584	+	0.527555i	−0.977169	−	0.212465i	$-0.931851\pi$
$829$	−252.500	+	437.343i	−0.304584	+	0.527555i	0.672585	+	0.740020i	$0.265184\pi$
$830$		0			0
$831$	−144.626	+	83.5000i	−0.174039	+	0.100481i
$832$		0			0
$833$	24.5000	−	42.4352i	0.0294118	−	0.0509427i
$834$		0			0
$835$	178.401	−	103.000i	0.213654	−	0.123353i
$836$		0			0
$837$	−348.500	+	603.620i	−0.416368	+	0.721170i
$838$		0			0
$839$		−	48.0000i		−	0.0572110i	−0.999591	−	0.0286055i	$-0.990893\pi$
$839$		−	48.0000i		−	0.0572110i	0.999591	−	0.0286055i	$-0.00910665\pi$
$840$		0			0
$841$	−265.000			−0.315101
$842$		0			0
$843$	−374.123	−	216.000i	−0.443799	−	0.256228i
$844$		0			0
$845$	−203.500	−	352.472i	−0.240828	−	0.417127i
$846$		0			0
$847$	1018.45	−	588.000i	1.20242	−	0.694215i
$848$		0			0
$849$	111.500	+	193.124i	0.131331	+	0.227472i
$850$		0			0
$851$	−297.047	−	171.500i	−0.349056	−	0.201528i
$852$		0			0
$853$	696.000			0.815944			0.407972	−	0.912995i	$-0.366236\pi$
$853$	696.000			0.815944			0.407972	+	0.912995i	$0.366236\pi$
$854$		0			0
$855$			56.0000i			0.0654971i
$856$		0			0
$857$	−599.500	+	1038.36i	−0.699533	+	1.21163i	0.269095	+	0.963114i	$0.413275\pi$
$857$	−599.500	+	1038.36i	−0.699533	+	1.21163i	−0.968628	+	0.248514i	$0.920058\pi$
$858$		0			0
$859$	671.170	−	387.500i	0.781338	−	0.451106i	−0.0555660	−	0.998455i	$-0.517696\pi$
$859$	671.170	−	387.500i	0.781338	−	0.451106i	0.836904	+	0.547349i	$0.184363\pi$
$860$		0			0
$861$	−168.000	+	290.985i	−0.195122	+	0.337961i
$862$		0			0
$863$	−297.047	+	171.500i	−0.344202	+	0.198725i	−0.662129	−	0.749390i	$-0.730347\pi$
$863$	−297.047	+	171.500i	−0.344202	+	0.198725i	0.317926	+	0.948115i	$0.397014\pi$
$864$		0			0
$865$	−119.500	+	206.980i	−0.138150	+	0.239283i
$866$		0			0
$867$			288.000i			0.332180i
$868$		0			0
$869$	−697.000			−0.802071
$870$		0			0
$871$	1351.00	+	780.000i	1.55109	+	0.895522i
$872$		0			0
$873$	−576.000	−	997.661i	−0.659794	−	1.14280i
$874$		0			0
$875$			343.000i			0.392000i
$876$		0			0
$877$	575.500	+	996.795i	0.656214	+	1.13660i	0.981588	+	0.191011i	$0.0611766\pi$
$877$	575.500	+	996.795i	0.656214	+	1.13660i	−0.325374	+	0.945586i	$0.605490\pi$
$878$		0			0
$879$	22.5167	+	13.0000i	0.0256162	+	0.0147895i
$880$		0			0
$881$	−866.000			−0.982974			−0.491487	−	0.870885i	$-0.663546\pi$
$881$	−866.000			−0.982974			−0.491487	+	0.870885i	$0.663546\pi$
$882$		0			0
$883$			648.000i			0.733862i	0.930248	+	0.366931i	$0.119591\pi$
$883$			648.000i			0.733862i	−0.930248	+	0.366931i	$0.880409\pi$
$884$		0			0
$885$	8.50000	−	14.7224i	0.00960452	−	0.0166355i
$886$		0			0
$887$	588.031	−	339.500i	0.662944	−	0.382751i	−0.130454	−	0.991454i	$-0.541643\pi$
$887$	588.031	−	339.500i	0.662944	−	0.382751i	0.793398	+	0.608704i	$0.208310\pi$
$888$		0			0
$889$	−1008.00			−1.13386
$890$		0			0
$891$	809.734	−	467.500i	0.908792	−	0.524691i
$892$		0			0
$893$	192.500	−	333.420i	0.215566	−	0.373370i
$894$		0			0
$895$			17.0000i			0.0189944i
$896$		0			0
$897$	−168.000			−0.187291
$898$		0			0
$899$	−852.169	−	492.000i	−0.947908	−	0.547275i
$900$		0			0
$901$	12.5000	+	21.6506i	0.0138735	+	0.0240296i
$902$		0			0
$903$	145.492	+	84.0000i	0.161121	+	0.0930233i
$904$		0			0
$905$	−35.0000	−	60.6218i	−0.0386740	−	0.0669854i
$906$		0			0
$907$	305.707	+	176.500i	0.337053	+	0.194598i	0.658968	−	0.752171i	$-0.270993\pi$
$907$	305.707	+	176.500i	0.337053	+	0.194598i	−0.321915	+	0.946769i	$0.604327\pi$
$908$		0			0
$909$	584.000			0.642464
$910$		0			0
$911$			144.000i			0.158068i	0.996872	+	0.0790340i	$0.0251836\pi$
$911$			144.000i			0.158068i	−0.996872	+	0.0790340i	$0.974816\pi$
$912$		0			0
$913$	612.000	−	1060.02i	0.670318	−	1.16102i
$914$		0			0
$915$	0.866025	−	0.500000i	0.000946476	−	0.000546448i
$916$		0			0
$917$	−647.500	−	1121.50i	−0.706107	−	1.22301i
$918$		0			0
$919$	−950.030	+	548.500i	−1.03376	+	0.596844i	−0.918061	−	0.396439i	$-0.870246\pi$
$919$	−950.030	+	548.500i	−1.03376	+	0.596844i	−0.115704	+	0.993284i	$0.536912\pi$
$920$		0			0
$921$	132.000	−	228.631i	0.143322	−	0.248242i
$922$		0			0
$923$			2304.00i			2.49621i
$924$		0			0
$925$	1176.00			1.27135
$926$		0			0
$927$	−616.610	−	356.000i	−0.665167	−	0.384035i
$928$		0			0
$929$	264.500	+	458.127i	0.284715	+	0.493140i	0.972540	−	0.232736i	$-0.0747678\pi$
$929$	264.500	+	458.127i	0.284715	+	0.493140i	−0.687825	+	0.725876i	$0.741434\pi$
$930$		0			0
$931$	−297.047	+	171.500i	−0.319062	+	0.184211i
$932$		0			0
$933$	−171.500	−	297.047i	−0.183816	−	0.318378i
$934$		0			0
$935$	−14.7224	−	8.50000i	−0.0157459	−	0.00909091i
$936$		0			0
$937$	146.000			0.155816			0.0779082	−	0.996961i	$-0.475176\pi$
$937$	146.000			0.155816			0.0779082	+	0.996961i	$0.475176\pi$
$938$		0			0
$939$		−	335.000i		−	0.356763i
$940$		0			0
$941$	−371.500	+	643.457i	−0.394793	+	0.683801i	−0.993075	−	0.117485i	$-0.962517\pi$
$941$	−371.500	+	643.457i	−0.394793	+	0.683801i	0.598282	+	0.801286i	$0.295850\pi$
$942$		0			0
$943$	290.985	−	168.000i	0.308573	−	0.178155i
$944$		0			0
$945$	59.5000	+	103.057i	0.0629630	+	0.109055i
$946$		0			0
$947$	451.199	−	260.500i	0.476451	−	0.275079i	−0.242485	−	0.970155i	$-0.577963\pi$
$947$	451.199	−	260.500i	0.476451	−	0.275079i	0.718936	+	0.695076i	$0.244629\pi$
$948$		0			0
$949$	−1140.00	+	1974.54i	−1.20126	+	2.08065i
$950$		0			0
$951$			529.000i			0.556257i
$952$		0			0
$953$	1440.00			1.51102			0.755509	−	0.655138i	$-0.227390\pi$
$953$	1440.00			1.51102			0.755509	+	0.655138i	$0.227390\pi$
$954$		0			0
$955$	−172.339	−	99.5000i	−0.180460	−	0.104188i
$956$		0			0
$957$	−204.000	−	353.338i	−0.213166	−	0.369215i
$958$		0			0
$959$	−866.891	−	500.500i	−0.903954	−	0.521898i
$960$		0			0
$961$	360.000	+	623.538i	0.374610	+	0.648843i
$962$		0			0
$963$	1281.72	+	740.000i	1.33096	+	0.768432i
$964$		0			0
$965$	−47.0000			−0.0487047
$966$		0			0
$967$			1920.00i			1.98552i	0.120106	+	0.992761i	$0.461677\pi$
$967$			1920.00i			1.98552i	−0.120106	+	0.992761i	$0.538323\pi$
$968$		0			0
$969$	−3.50000	+	6.06218i	−0.00361197	+	0.00625612i
$970$		0			0
$971$	284.922	−	164.500i	0.293432	−	0.169413i	−0.346057	−	0.938214i	$-0.612479\pi$
$971$	284.922	−	164.500i	0.293432	−	0.169413i	0.639489	+	0.768801i	$0.279146\pi$
$972$		0			0
$973$	−1512.00			−1.55396
$974$		0			0
$975$	498.831	−	288.000i	0.511621	−	0.295385i
$976$		0			0
$977$	−360.500	+	624.404i	−0.368987	+	0.639104i	−0.989407	−	0.145165i	$-0.953629\pi$
$977$	−360.500	+	624.404i	−0.368987	+	0.639104i	0.620421	+	0.784269i	$0.286962\pi$
$978$		0			0
$979$			1615.00i			1.64964i
$980$		0			0
$981$	−568.000			−0.579001
$982$		0			0
$983$	546.462	+	315.500i	0.555913	+	0.320956i	0.751503	−	0.659729i	$-0.229329\pi$
$983$	546.462	+	315.500i	0.555913	+	0.320956i	−0.195591	+	0.980686i	$0.562662\pi$
$984$		0			0
$985$	−12.0000	−	20.7846i	−0.0121827	−	0.0211011i
$986$		0			0
$987$		−	385.000i		−	0.390071i
$988$		0			0
$989$	−84.0000	−	145.492i	−0.0849343	−	0.147110i
$990$		0			0
$991$	−629.600	−	363.500i	−0.635318	−	0.366801i	0.147491	−	0.989063i	$-0.452880\pi$
$991$	−629.600	−	363.500i	−0.635318	−	0.366801i	−0.782809	+	0.622262i	$0.786214\pi$
$992$		0			0
$993$	−55.0000			−0.0553877
$994$		0			0
$995$			137.000i			0.137688i
$996$		0			0
$997$	12.5000	−	21.6506i	0.0125376	−	0.0217158i	−0.859689	−	0.510819i	$-0.829342\pi$
$997$	12.5000	−	21.6506i	0.0125376	−	0.0217158i	0.872226	+	0.489103i	$0.162676\pi$
$998$		0			0
$999$	721.399	−	416.500i	0.722121	−	0.416917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.r.b.95.2	yes	4
4.3	odd	2	inner	224.3.r.b.95.1	✓	4
7.2	even	3	inner	224.3.r.b.191.1	yes	4
7.3	odd	6		1568.3.d.c.1471.2		2
7.4	even	3		1568.3.d.d.1471.1		2
8.3	odd	2		448.3.r.b.319.2		4
8.5	even	2		448.3.r.b.319.1		4
28.3	even	6		1568.3.d.c.1471.1		2
28.11	odd	6		1568.3.d.d.1471.2		2
28.23	odd	6	inner	224.3.r.b.191.2	yes	4
56.37	even	6		448.3.r.b.191.2		4
56.51	odd	6		448.3.r.b.191.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.b.95.1	✓	4	4.3	odd	2	inner
224.3.r.b.95.2	yes	4	1.1	even	1	trivial
224.3.r.b.191.1	yes	4	7.2	even	3	inner
224.3.r.b.191.2	yes	4	28.23	odd	6	inner
448.3.r.b.191.1		4	56.51	odd	6
448.3.r.b.191.2		4	56.37	even	6
448.3.r.b.319.1		4	8.5	even	2
448.3.r.b.319.2		4	8.3	odd	2
1568.3.d.c.1471.1		2	28.3	even	6
1568.3.d.c.1471.2		2	7.3	odd	6
1568.3.d.d.1471.1		2	7.4	even	3
1568.3.d.d.1471.2		2	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{5} -7.00000i q^{7} +(-4.00000 - 6.92820i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{5} -7.00000i q^{7} +(-4.00000 - 6.92820i) q^{9} +(-14.7224 - 8.50000i) q^{11} +24.0000 q^{13} -1.00000i q^{15} +(-0.500000 + 0.866025i) q^{17} +(6.06218 - 3.50000i) q^{19} +(3.50000 - 6.06218i) q^{21} +(-6.06218 + 3.50000i) q^{23} +(12.0000 - 20.7846i) q^{25} -17.0000i q^{27} +24.0000 q^{29} +(-35.5070 - 20.5000i) q^{31} +(-8.50000 - 14.7224i) q^{33} +(-6.06218 + 3.50000i) q^{35} +(24.5000 + 42.4352i) q^{37} +(20.7846 + 12.0000i) q^{39} -48.0000 q^{41} +24.0000i q^{43} +(-4.00000 + 6.92820i) q^{45} +(47.6314 - 27.5000i) q^{47} -49.0000 q^{49} +(-0.866025 + 0.500000i) q^{51} +(12.5000 - 21.6506i) q^{53} +17.0000i q^{55} +7.00000 q^{57} +(14.7224 + 8.50000i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-48.4974 + 28.0000i) q^{63} +(-12.0000 - 20.7846i) q^{65} +(56.2917 + 32.5000i) q^{67} -7.00000 q^{69} +96.0000i q^{71} +(-47.5000 + 82.2724i) q^{73} +(20.7846 - 12.0000i) q^{75} +(-59.5000 + 103.057i) q^{77} +(35.5070 - 20.5000i) q^{79} +(-27.5000 + 47.6314i) q^{81} +72.0000i q^{83} +1.00000 q^{85} +(20.7846 + 12.0000i) q^{87} +(-47.5000 - 82.2724i) q^{89} -168.000i q^{91} +(-20.5000 - 35.5070i) q^{93} +(-6.06218 - 3.50000i) q^{95} +144.000 q^{97} +136.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} - 16 q^{9}+O(q^{10}) \) 4 * q - 2 * q^5 - 16 * q^9	\( 4 q - 2 q^{5} - 16 q^{9} + 96 q^{13} - 2 q^{17} + 14 q^{21} + 48 q^{25} + 96 q^{29} - 34 q^{33} + 98 q^{37} - 192 q^{41} - 16 q^{45} - 196 q^{49} + 50 q^{53} + 28 q^{57} + 2 q^{61} - 48 q^{65} - 28 q^{69} - 190 q^{73} - 238 q^{77} - 110 q^{81} + 4 q^{85} - 190 q^{89} - 82 q^{93} + 576 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 - 16 * q^9 + 96 * q^13 - 2 * q^17 + 14 * q^21 + 48 * q^25 + 96 * q^29 - 34 * q^33 + 98 * q^37 - 192 * q^41 - 16 * q^45 - 196 * q^49 + 50 * q^53 + 28 * q^57 + 2 * q^61 - 48 * q^65 - 28 * q^69 - 190 * q^73 - 238 * q^77 - 110 * q^81 + 4 * q^85 - 190 * q^89 - 82 * q^93 + 576 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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