LMFDB - Embedded newform 224.3.s.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(33,224)]

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([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("224.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.s (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 $ x^16 + 36x^14 + 522x^12 + 3644x^10 + 12219x^8 + 15156x^6 + 15478x^4 - 10992*x^2 + 11025
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			33.2
Root			$0.707107 - 2.60548i$ of defining polynomial
Character	$\chi$	$=$	224.33
Dual form			224.3.s.a.129.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.19104 + 1.84235i) q^{3} +(-2.63938 - 1.52385i) q^{5} +(0.812549 + 6.95268i) q^{7} +(2.28850 - 3.96380i) q^{9} +O(q^{10})$	\(q+(-3.19104 + 1.84235i) q^{3} +(-2.63938 - 1.52385i) q^{5} +(0.812549 + 6.95268i) q^{7} +(2.28850 - 3.96380i) q^{9} +(-1.17516 - 2.03544i) q^{11} -25.3073i q^{13} +11.2298 q^{15} +(3.08674 - 1.78213i) q^{17} +(-14.1772 - 8.18522i) q^{19} +(-15.4021 - 20.6893i) q^{21} +(8.83413 - 15.3012i) q^{23} +(-7.85577 - 13.6066i) q^{25} -16.2974i q^{27} +36.1220 q^{29} +(6.25629 - 3.61207i) q^{31} +(7.50000 + 4.33013i) q^{33} +(8.45020 - 19.5890i) q^{35} +(-18.4021 + 31.8734i) q^{37} +(46.6249 + 80.7567i) q^{39} -53.7118i q^{41} -51.2382 q^{43} +(-12.0805 + 6.97466i) q^{45} +(-27.1609 - 15.6814i) q^{47} +(-47.6795 + 11.2988i) q^{49} +(-6.56661 + 11.3737i) q^{51} +(35.1137 + 60.8187i) q^{53} +7.16309i q^{55} +60.3201 q^{57} +(-81.4102 + 47.0022i) q^{59} +(-1.89609 - 1.09471i) q^{61} +(29.4186 + 12.6904i) q^{63} +(-38.5645 + 66.7957i) q^{65} +(-12.4810 - 21.6177i) q^{67} +65.1022i q^{69} +50.8890 q^{71} +(-68.9008 + 39.7799i) q^{73} +(50.1362 + 28.9461i) q^{75} +(13.1969 - 9.82444i) q^{77} +(57.5117 - 99.6132i) q^{79} +(50.6220 + 87.6799i) q^{81} -154.132i q^{83} -10.8628 q^{85} +(-115.267 + 66.5493i) q^{87} +(98.7274 + 57.0003i) q^{89} +(175.954 - 20.5634i) q^{91} +(-13.3094 + 23.0525i) q^{93} +(24.9461 + 43.2079i) q^{95} -53.9940i q^{97} -10.7575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^9	$ 16 q + 8 q^{9} + 48 q^{17} + 56 q^{21} + 16 q^{25} + 112 q^{29} + 120 q^{33} + 8 q^{37} - 72 q^{45} - 128 q^{49} - 24 q^{53} - 528 q^{57} - 360 q^{61} - 8 q^{65} + 72 q^{73} + 32 q^{81} + 720 q^{85} + 408 q^{89} - 232 q^{93}+O(q^{100}) $ 16 * q + 8 * q^9 + 48 * q^17 + 56 * q^21 + 16 * q^25 + 112 * q^29 + 120 * q^33 + 8 * q^37 - 72 * q^45 - 128 * q^49 - 24 * q^53 - 528 * q^57 - 360 * q^61 - 8 * q^65 + 72 * q^73 + 32 * q^81 + 720 * q^85 + 408 * q^89 - 232 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−3.19104	+	1.84235i	−1.06368	+	0.614116i	−0.926448	−	0.376422i	$-0.877154\pi$
$3$	−3.19104	+	1.84235i	−1.06368	+	0.614116i	−0.137233	+	0.990539i	$0.543821\pi$
$4$		0			0
$5$	−2.63938	−	1.52385i	−0.527877	−	0.304770i	0.212275	−	0.977210i	$-0.431913\pi$
$5$	−2.63938	−	1.52385i	−0.527877	−	0.304770i	−0.740151	+	0.672440i	$0.765246\pi$
$6$		0			0
$7$	0.812549	+	6.95268i	0.116078	+	0.993240i
$7$	0.812549	+	6.95268i	0.116078	+	0.993240i
$8$		0			0
$9$	2.28850	−	3.96380i	0.254278	−	0.440422i
$10$		0			0
$11$	−1.17516	−	2.03544i	−0.106833	−	0.185040i	0.807653	−	0.589659i	$-0.200738\pi$
$11$	−1.17516	−	2.03544i	−0.106833	−	0.185040i	−0.914486	+	0.404618i	$0.867404\pi$
$12$		0			0
$13$		−	25.3073i		−	1.94672i	−0.229292	−	0.973358i	$-0.573641\pi$
$13$		−	25.3073i		−	1.94672i	0.229292	−	0.973358i	$-0.426359\pi$
$14$		0			0
$15$	11.2298			0.748656
$16$		0			0
$17$	3.08674	−	1.78213i	0.181573	−	0.104831i	−0.406459	−	0.913669i	$-0.633236\pi$
$17$	3.08674	−	1.78213i	0.181573	−	0.104831i	0.588031	+	0.808838i	$0.299903\pi$
$18$		0			0
$19$	−14.1772	−	8.18522i	−0.746169	−	0.430801i	0.0781390	−	0.996942i	$-0.475102\pi$
$19$	−14.1772	−	8.18522i	−0.746169	−	0.430801i	−0.824308	+	0.566142i	$0.808436\pi$
$20$		0			0
$21$	−15.4021	−	20.6893i	−0.733435	−	0.985205i
$22$		0			0
$23$	8.83413	−	15.3012i	0.384093	−	0.665268i	−0.607550	−	0.794281i	$-0.707848\pi$
$23$	8.83413	−	15.3012i	0.384093	−	0.665268i	0.991643	+	0.129013i	$0.0411810\pi$
$24$		0			0
$25$	−7.85577	−	13.6066i	−0.314231	−	0.544264i
$26$		0			0
$27$		−	16.2974i		−	0.603608i
$28$		0			0
$29$	36.1220			1.24559			0.622793	−	0.782387i	$-0.285998\pi$
$29$	36.1220			1.24559			0.622793	+	0.782387i	$0.285998\pi$
$30$		0			0
$31$	6.25629	−	3.61207i	0.201816	−	0.116518i	−0.395686	−	0.918386i	$-0.629493\pi$
$31$	6.25629	−	3.61207i	0.201816	−	0.116518i	0.597502	+	0.801867i	$0.296160\pi$
$32$		0			0
$33$	7.50000	+	4.33013i	0.227273	+	0.131216i
$34$		0			0
$35$	8.45020	−	19.5890i	0.241434	−	0.559685i
$36$		0			0
$37$	−18.4021	+	31.8734i	−0.497355	+	0.861445i	−0.999995	−	0.00305120i	$-0.999029\pi$
$37$	−18.4021	+	31.8734i	−0.497355	+	0.861445i	0.502640	+	0.864496i	$0.332362\pi$
$38$		0			0
$39$	46.6249	+	80.7567i	1.19551	+	2.07068i
$40$		0			0
$41$		−	53.7118i		−	1.31004i	−0.755610	−	0.655022i	$-0.772659\pi$
$41$		−	53.7118i		−	1.31004i	0.755610	−	0.655022i	$-0.227341\pi$
$42$		0			0
$43$	−51.2382			−1.19159			−0.595793	−	0.803138i	$-0.703162\pi$
$43$	−51.2382			−1.19159			−0.595793	+	0.803138i	$0.703162\pi$
$44$		0			0
$45$	−12.0805	+	6.97466i	−0.268455	+	0.154992i
$46$		0			0
$47$	−27.1609	−	15.6814i	−0.577892	−	0.333646i	0.182403	−	0.983224i	$-0.441612\pi$
$47$	−27.1609	−	15.6814i	−0.577892	−	0.333646i	−0.760295	+	0.649578i	$0.774946\pi$
$48$		0			0
$49$	−47.6795	+	11.2988i	−0.973052	+	0.230588i
$50$		0			0
$51$	−6.56661	+	11.3737i	−0.128757	+	0.223014i
$52$		0			0
$53$	35.1137	+	60.8187i	0.662522	+	1.14752i	0.979951	+	0.199240i	$0.0638474\pi$
$53$	35.1137	+	60.8187i	0.662522	+	1.14752i	−0.317428	+	0.948282i	$0.602819\pi$
$54$		0			0
$55$			7.16309i			0.130238i
$56$		0			0
$57$	60.3201			1.05825
$58$		0			0
$59$	−81.4102	+	47.0022i	−1.37983	+	0.796647i	−0.992139	−	0.125141i	$-0.960062\pi$
$59$	−81.4102	+	47.0022i	−1.37983	+	0.796647i	−0.387695	+	0.921788i	$0.626728\pi$
$60$		0			0
$61$	−1.89609	−	1.09471i	−0.0310835	−	0.0179461i	0.484378	−	0.874859i	$-0.339046\pi$
$61$	−1.89609	−	1.09471i	−0.0310835	−	0.0179461i	−0.515461	+	0.856913i	$0.672379\pi$
$62$		0			0
$63$	29.4186	+	12.6904i	0.466961	+	0.201435i
$64$		0			0
$65$	−38.5645	+	66.7957i	−0.593300	+	1.02763i
$66$		0			0
$67$	−12.4810	−	21.6177i	−0.186283	−	0.322652i	0.757725	−	0.652574i	$-0.226311\pi$
$67$	−12.4810	−	21.6177i	−0.186283	−	0.322652i	−0.944008	+	0.329922i	$0.892977\pi$
$68$		0			0
$69$			65.1022i			0.943510i
$70$		0			0
$71$	50.8890			0.716746			0.358373	−	0.933579i	$-0.383332\pi$
$71$	50.8890			0.716746			0.358373	+	0.933579i	$0.383332\pi$
$72$		0			0
$73$	−68.9008	+	39.7799i	−0.943847	+	0.544930i	−0.891164	−	0.453681i	$-0.850111\pi$
$73$	−68.9008	+	39.7799i	−0.943847	+	0.544930i	−0.0526830	+	0.998611i	$0.516777\pi$
$74$		0			0
$75$	50.1362	+	28.9461i	0.668483	+	0.385949i
$76$		0			0
$77$	13.1969	−	9.82444i	0.171389	−	0.127590i
$78$		0			0
$79$	57.5117	−	99.6132i	0.727996	−	1.26093i	−0.229733	−	0.973254i	$-0.573785\pi$
$79$	57.5117	−	99.6132i	0.727996	−	1.26093i	0.957729	−	0.287672i	$-0.0928814\pi$
$80$		0			0
$81$	50.6220	+	87.6799i	0.624963	+	1.08247i
$82$		0			0
$83$		−	154.132i		−	1.85701i	−0.371318	−	0.928506i	$-0.621094\pi$
$83$		−	154.132i		−	1.85701i	0.371318	−	0.928506i	$-0.378906\pi$
$84$		0			0
$85$	−10.8628			−0.127797
$86$		0			0
$87$	−115.267	+	66.5493i	−1.32491	+	0.764935i
$88$		0			0
$89$	98.7274	+	57.0003i	1.10930	+	0.640453i	0.938647	−	0.344879i	$-0.112080\pi$
$89$	98.7274	+	57.0003i	1.10930	+	0.640453i	0.170649	+	0.985332i	$0.445414\pi$
$90$		0			0
$91$	175.954	−	20.5634i	1.93356	−	0.225972i
$92$		0			0
$93$	−13.3094	+	23.0525i	−0.143112	+	0.247877i
$94$		0			0
$95$	24.9461	+	43.2079i	0.262590	+	0.454820i
$96$		0			0
$97$		−	53.9940i		−	0.556640i	−0.960488	−	0.278320i	$-0.910222\pi$
$97$		−	53.9940i		−	0.556640i	0.960488	−	0.278320i	$-0.0897775\pi$
$98$		0			0
$99$	−10.7575			−0.108661
$100$		0			0
$101$	18.0305	−	10.4099i	0.178519	−	0.103068i	−0.408077	−	0.912947i	$-0.633801\pi$
$101$	18.0305	−	10.4099i	0.178519	−	0.103068i	0.586597	+	0.809879i	$0.300467\pi$
$102$		0			0
$103$	−105.870	−	61.1238i	−1.02786	−	0.593435i	−0.111489	−	0.993766i	$-0.535562\pi$
$103$	−105.870	−	61.1238i	−1.02786	−	0.593435i	−0.916371	+	0.400330i	$0.868895\pi$
$104$		0			0
$105$	9.12480	+	78.0775i	0.0869029	+	0.743596i
$106$		0			0
$107$	−57.2681	+	99.1912i	−0.535216	+	0.927021i	0.463937	+	0.885868i	$0.346436\pi$
$107$	−57.2681	+	99.1912i	−0.535216	+	0.927021i	−0.999153	+	0.0411525i	$0.986897\pi$
$108$		0			0
$109$	−82.9057	−	143.597i	−0.760603	−	1.31740i	−0.942540	−	0.334092i	$-0.891570\pi$
$109$	−82.9057	−	143.597i	−0.760603	−	1.31740i	0.181938	−	0.983310i	$-0.441763\pi$
$110$		0			0
$111$		−	135.613i		−	1.22174i
$112$		0			0
$113$	−123.071			−1.08912			−0.544560	−	0.838722i	$-0.683303\pi$
$113$	−123.071			−1.08912			−0.544560	+	0.838722i	$0.683303\pi$
$114$		0			0
$115$	−46.6333	+	26.9238i	−0.405507	+	0.234120i
$116$		0			0
$117$	−100.313	−	57.9158i	−0.857377	−	0.495007i
$118$		0			0
$119$	14.8987	+	20.0130i	0.125199	+	0.168177i
$120$		0			0
$121$	57.7380	−	100.005i	0.477173	−	0.826489i
$122$		0			0
$123$	98.9559	+	171.397i	0.804520	+	1.39347i
$124$		0			0
$125$			124.076i			0.992612i
$126$		0			0
$127$	−160.105			−1.26067			−0.630334	−	0.776324i	$-0.717082\pi$
$127$	−160.105			−1.26067			−0.630334	+	0.776324i	$0.717082\pi$
$128$		0			0
$129$	163.503	−	94.3987i	1.26747	−	0.731773i
$130$		0			0
$131$	53.3272	+	30.7885i	0.407078	+	0.235027i	0.689534	−	0.724254i	$-0.257816\pi$
$131$	53.3272	+	30.7885i	0.407078	+	0.235027i	−0.282455	+	0.959280i	$0.591149\pi$
$132$		0			0
$133$	45.3895	−	105.221i	0.341275	−	0.791132i
$134$		0			0
$135$	−24.8348	+	43.0151i	−0.183961	+	0.318630i
$136$		0			0
$137$	−47.5511	−	82.3609i	−0.347088	−	0.601174i	0.638643	−	0.769503i	$-0.279496\pi$
$137$	−47.5511	−	82.3609i	−0.347088	−	0.601174i	−0.985731	+	0.168329i	$0.946163\pi$
$138$		0			0
$139$			92.0558i			0.662272i	0.943583	+	0.331136i	$0.107432\pi$
$139$			92.0558i			0.662272i	−0.943583	+	0.331136i	$0.892568\pi$
$140$		0			0
$141$	115.562			0.819590
$142$		0			0
$143$	−51.5116	+	29.7402i	−0.360221	+	0.207974i
$144$		0			0
$145$	−95.3398	−	55.0445i	−0.657516	−	0.379617i
$146$		0			0
$147$	131.331	−	123.897i	0.893409	−	0.842838i
$148$		0			0
$149$	88.7225	−	153.672i	0.595453	−	1.03136i	−0.398030	−	0.917373i	$-0.630306\pi$
$149$	88.7225	−	153.672i	0.595453	−	1.03136i	0.993483	−	0.113983i	$-0.0363608\pi$
$150$		0			0
$151$	114.894	+	199.002i	0.760888	+	1.31790i	0.942394	+	0.334506i	$0.108570\pi$
$151$	114.894	+	199.002i	0.760888	+	1.31790i	−0.181506	+	0.983390i	$0.558097\pi$
$152$		0			0
$153$		−	16.3136i		−	0.106625i
$154$		0			0
$155$	−22.0170			−0.142045
$156$		0			0
$157$	−42.9871	+	24.8186i	−0.273803	+	0.158080i	−0.630615	−	0.776096i	$-0.717197\pi$
$157$	−42.9871	+	24.8186i	−0.273803	+	0.158080i	0.356812	+	0.934176i	$0.383864\pi$
$158$		0			0
$159$	−224.099	−	129.383i	−1.40942	−	0.813732i
$160$		0			0
$161$	113.562	+	48.9879i	0.705356	+	0.304273i
$162$		0			0
$163$	33.2613	−	57.6103i	0.204057	−	0.353438i	−0.745775	−	0.666198i	$-0.767920\pi$
$163$	33.2613	−	57.6103i	0.204057	−	0.353438i	0.949832	+	0.312761i	$0.101254\pi$
$164$		0			0
$165$	−13.1969	−	22.8577i	−0.0799813	−	0.138532i
$166$		0			0
$167$		−	164.292i		−	0.983786i	−0.870656	−	0.491893i	$-0.836305\pi$
$167$		−	164.292i		−	0.983786i	0.870656	−	0.491893i	$-0.163695\pi$
$168$		0			0
$169$	−471.460			−2.78970
$170$		0			0
$171$	−64.8891	+	37.4638i	−0.379469	+	0.219086i
$172$		0			0
$173$	−33.4995	−	19.3409i	−0.193639	−	0.111797i	0.400046	−	0.916495i	$-0.368994\pi$
$173$	−33.4995	−	19.3409i	−0.193639	−	0.111797i	−0.593685	+	0.804698i	$0.702327\pi$
$174$		0			0
$175$	88.2191	−	65.6747i	0.504109	−	0.375284i
$176$		0			0
$177$	173.189	−	299.972i	0.978468	−	1.69476i
$178$		0			0
$179$	51.2076	+	88.6942i	0.286076	+	0.495498i	0.972870	−	0.231354i	$-0.0743157\pi$
$179$	51.2076	+	88.6942i	0.286076	+	0.495498i	−0.686794	+	0.726853i	$0.740982\pi$
$180$		0			0
$181$			44.5843i			0.246322i	0.992387	+	0.123161i	$0.0393032\pi$
$181$			44.5843i			0.246322i	−0.992387	+	0.123161i	$0.960697\pi$
$182$		0			0
$183$	8.06735			0.0440839
$184$		0			0
$185$	97.1406	−	56.0842i	0.525084	−	0.303158i
$186$		0			0
$187$	−7.25485	−	4.18859i	−0.0387960	−	0.0223989i
$188$		0			0
$189$	113.311	−	13.2424i	0.599527	−	0.0700659i
$190$		0			0
$191$	165.031	−	285.842i	0.864038	−	1.49656i	−0.00396184	−	0.999992i	$-0.501261\pi$
$191$	165.031	−	285.842i	0.864038	−	1.49656i	0.868000	−	0.496565i	$-0.165406\pi$
$192$		0			0
$193$	−69.6777	−	120.685i	−0.361024	−	0.625312i	0.627105	−	0.778934i	$-0.284240\pi$
$193$	−69.6777	−	120.685i	−0.361024	−	0.625312i	−0.988130	+	0.153622i	$0.950906\pi$
$194$		0			0
$195$		−	284.197i		−	1.45742i
$196$		0			0
$197$	174.724			0.886925			0.443462	−	0.896293i	$-0.353750\pi$
$197$	174.724			0.886925			0.443462	+	0.896293i	$0.353750\pi$
$198$		0			0
$199$	−197.009	+	113.743i	−0.989996	+	0.571574i	−0.905273	−	0.424830i	$-0.860334\pi$
$199$	−197.009	+	113.743i	−0.989996	+	0.571574i	−0.0847227	+	0.996405i	$0.527000\pi$
$200$		0			0
$201$	79.6546	+	45.9886i	0.396291	+	0.228799i
$202$		0			0
$203$	29.3509	+	251.145i	0.144586	+	1.23717i
$204$		0			0
$205$	−81.8487	+	141.766i	−0.399262	+	0.691542i
$206$		0			0
$207$	−40.4338	−	70.0335i	−0.195333	−	0.338326i
$208$		0			0
$209$			38.4759i			0.184095i
$210$		0			0
$211$	251.350			1.19123			0.595617	−	0.803269i	$-0.296908\pi$
$211$	251.350			1.19123			0.595617	+	0.803269i	$0.296908\pi$
$212$		0			0
$213$	−162.389	+	93.7552i	−0.762389	+	0.440165i
$214$		0			0
$215$	135.237	+	78.0793i	0.629011	+	0.363160i
$216$		0			0
$217$	30.1971	+	40.5630i	0.139157	+	0.186926i
$218$		0			0
$219$	146.577	−	253.879i	0.669301	−	1.15926i
$220$		0			0
$221$	−45.1009	−	78.1170i	−0.204076	−	0.353471i
$222$		0			0
$223$			108.297i			0.485636i	0.970072	+	0.242818i	$0.0780718\pi$
$223$			108.297i			0.485636i	−0.970072	+	0.242818i	$0.921928\pi$
$224$		0			0
$225$	−71.9118			−0.319608
$226$		0			0
$227$	−245.045	+	141.477i	−1.07949	+	0.623245i	−0.930759	−	0.365632i	$-0.880853\pi$
$227$	−245.045	+	141.477i	−1.07949	+	0.623245i	−0.148733	+	0.988877i	$0.547519\pi$
$228$		0			0
$229$	−153.011	−	88.3412i	−0.668172	−	0.385769i	0.127212	−	0.991876i	$-0.459397\pi$
$229$	−153.011	−	88.3412i	−0.668172	−	0.385769i	−0.795384	+	0.606106i	$0.792731\pi$
$230$		0			0
$231$	−24.0119	+	55.6635i	−0.103947	+	0.240968i
$232$		0			0
$233$	−177.693	+	307.773i	−0.762630	+	1.32091i	0.178861	+	0.983874i	$0.442759\pi$
$233$	−177.693	+	307.773i	−0.762630	+	1.32091i	−0.941491	+	0.337039i	$0.890575\pi$
$234$		0			0
$235$	47.7921	+	82.7783i	0.203370	+	0.352248i
$236$		0			0
$237$			423.826i			1.78830i
$238$		0			0
$239$	17.5451			0.0734104			0.0367052	−	0.999326i	$-0.488314\pi$
$239$	17.5451			0.0734104			0.0367052	+	0.999326i	$0.488314\pi$
$240$		0			0
$241$	104.909	−	60.5693i	0.435308	−	0.251325i	−0.266298	−	0.963891i	$-0.585800\pi$
$241$	104.909	−	60.5693i	0.435308	−	0.251325i	0.701605	+	0.712566i	$0.252467\pi$
$242$		0			0
$243$	−196.048	−	113.189i	−0.806783	−	0.465797i
$244$		0			0
$245$	143.062	+	42.8346i	0.583927	+	0.174835i
$246$		0			0
$247$	−207.146	+	358.787i	−0.838647	+	1.45258i
$248$		0			0
$249$	283.965	+	491.842i	1.14042	+	1.97527i
$250$		0			0
$251$			219.342i			0.873874i	0.899492	+	0.436937i	$0.143937\pi$
$251$			219.342i			0.873874i	−0.899492	+	0.436937i	$0.856063\pi$
$252$		0			0
$253$	−41.5262			−0.164135
$254$		0			0
$255$	34.6636	−	20.0130i	0.135936	−	0.0784825i
$256$		0			0
$257$	417.447	+	241.013i	1.62431	+	0.937794i	0.985749	+	0.168220i	$0.0538019\pi$
$257$	417.447	+	241.013i	1.62431	+	0.937794i	0.638558	+	0.769574i	$0.279531\pi$
$258$		0			0
$259$	−236.559	−	102.045i	−0.913353	−	0.393998i
$260$		0			0
$261$	82.6652	−	143.180i	0.316725	−	0.548584i
$262$		0			0
$263$	44.8439	+	77.6720i	0.170509	+	0.295331i	0.938598	−	0.345013i	$-0.112125\pi$
$263$	44.8439	+	77.6720i	0.170509	+	0.295331i	−0.768089	+	0.640343i	$0.778792\pi$
$264$		0			0
$265$		−	214.032i		−	0.807667i
$266$		0			0
$267$	−420.058			−1.57325
$268$		0			0
$269$	−32.9768	+	19.0392i	−0.122590	+	0.0707776i	−0.560041	−	0.828465i	$-0.689215\pi$
$269$	−32.9768	+	19.0392i	−0.122590	+	0.0707776i	0.437451	+	0.899242i	$0.355881\pi$
$270$		0			0
$271$	73.5803	+	42.4816i	0.271514	+	0.156759i	0.629575	−	0.776939i	$-0.283229\pi$
$271$	73.5803	+	42.4816i	0.271514	+	0.156759i	−0.358062	+	0.933698i	$0.616562\pi$
$272$		0			0
$273$	−523.590	+	389.787i	−1.91791	+	1.42779i
$274$		0			0
$275$	−18.4636	+	31.9800i	−0.0671405	+	0.116291i
$276$		0			0
$277$	−31.2523	−	54.1306i	−0.112824	−	0.195417i	0.804084	−	0.594516i	$-0.202656\pi$
$277$	−31.2523	−	54.1306i	−0.112824	−	0.195417i	−0.916908	+	0.399099i	$0.869323\pi$
$278$		0			0
$279$		−	33.0649i		−	0.118512i
$280$		0			0
$281$	58.6599			0.208754			0.104377	−	0.994538i	$-0.466715\pi$
$281$	58.6599			0.208754			0.104377	+	0.994538i	$0.466715\pi$
$282$		0			0
$283$	207.461	−	119.778i	0.733078	−	0.423243i	−0.0864689	−	0.996255i	$-0.527558\pi$
$283$	207.461	−	119.778i	0.733078	−	0.423243i	0.819547	+	0.573012i	$0.194225\pi$
$284$		0			0
$285$	−159.208	−	91.9187i	−0.558624	−	0.322522i
$286$		0			0
$287$	373.441	−	43.6435i	1.30119	−	0.152068i
$288$		0			0
$289$	−138.148	+	239.279i	−0.478021	+	0.827956i
$290$		0			0
$291$	99.4759	+	172.297i	0.341842	+	0.592087i
$292$		0			0
$293$			196.503i			0.670658i	0.942101	+	0.335329i	$0.108848\pi$
$293$			196.503i			0.670658i	−0.942101	+	0.335329i	$0.891152\pi$
$294$		0			0
$295$	286.497			0.971176
$296$		0			0
$297$	−33.1725	+	19.1521i	−0.111692	+	0.0644853i
$298$		0			0
$299$	−387.231	−	223.568i	−1.29509	−	0.747719i
$300$		0			0
$301$	−41.6336	−	356.243i	−0.138318	−	1.18353i
$302$		0			0
$303$	−38.3573	+	66.4368i	−0.126592	+	0.219263i
$304$		0			0
$305$	3.33634	+	5.77871i	0.0109388	+	0.0189466i
$306$		0			0
$307$		−	246.955i		−	0.804415i	−0.915549	−	0.402208i	$-0.868243\pi$
$307$		−	246.955i		−	0.804415i	0.915549	−	0.402208i	$-0.131757\pi$
$308$		0			0
$309$	450.446			1.45775
$310$		0			0
$311$	294.487	−	170.022i	0.946905	−	0.546696i	0.0547867	−	0.998498i	$-0.482552\pi$
$311$	294.487	−	170.022i	0.946905	−	0.546696i	0.892118	+	0.451802i	$0.149219\pi$
$312$		0			0
$313$	98.2049	+	56.6987i	0.313754	+	0.181146i	0.648605	−	0.761125i	$-0.275353\pi$
$313$	98.2049	+	56.6987i	0.313754	+	0.181146i	−0.334851	+	0.942271i	$0.608686\pi$
$314$		0			0
$315$	−58.3086	−	78.3244i	−0.185107	−	0.248649i
$316$		0			0
$317$	−121.155	+	209.847i	−0.382192	+	0.661976i	−0.991375	−	0.131053i	$-0.958164\pi$
$317$	−121.155	+	209.847i	−0.382192	+	0.661976i	0.609183	+	0.793030i	$0.291497\pi$
$318$		0			0
$319$	−42.4493	−	73.5243i	−0.133070	−	0.230484i
$320$		0			0
$321$		−	422.031i		−	1.31474i
$322$		0			0
$323$	−58.3484			−0.180645
$324$		0			0
$325$	−344.346	+	198.808i	−1.05953	+	0.611718i
$326$		0			0
$327$	529.111	+	305.482i	1.61808	+	0.934197i
$328$		0			0
$329$	86.9579	−	201.583i	0.264310	−	0.612715i
$330$		0			0
$331$	34.8544	−	60.3697i	0.105300	−	0.182386i	−0.808560	−	0.588413i	$-0.799753\pi$
$331$	34.8544	−	60.3697i	0.105300	−	0.182386i	0.913861	+	0.406027i	$0.133086\pi$
$332$		0			0
$333$	84.2267	+	145.885i	0.252933	+	0.438093i
$334$		0			0
$335$			76.0764i			0.227094i
$336$		0			0
$337$	165.816			0.492037			0.246019	−	0.969265i	$-0.420878\pi$
$337$	165.816			0.492037			0.246019	+	0.969265i	$0.420878\pi$
$338$		0			0
$339$	392.723	−	226.739i	1.15848	−	0.668846i
$340$		0			0
$341$	−14.7043	−	8.48956i	−0.0431212	−	0.0248961i
$342$		0			0
$343$	−117.299	−	322.320i	−0.341979	−	0.939708i
$344$		0			0
$345$	99.2059	−	171.830i	0.287553	−	0.498057i
$346$		0			0
$347$	−283.452	−	490.953i	−0.816864	−	1.41485i	−0.907982	−	0.419010i	$-0.862377\pi$
$347$	−283.452	−	490.953i	−0.816864	−	1.41485i	0.0911175	−	0.995840i	$-0.470956\pi$
$348$		0			0
$349$		−	245.773i		−	0.704219i	−0.935959	−	0.352110i	$-0.885464\pi$
$349$		−	245.773i		−	0.704219i	0.935959	−	0.352110i	$-0.114536\pi$
$350$		0			0
$351$	−412.443			−1.17505
$352$		0			0
$353$	−137.837	+	79.5801i	−0.390472	+	0.225439i	−0.682365	−	0.731012i	$-0.739048\pi$
$353$	−137.837	+	79.5801i	−0.390472	+	0.225439i	0.291892	+	0.956451i	$0.405715\pi$
$354$		0			0
$355$	−134.315	−	77.5471i	−0.378353	−	0.218442i
$356$		0			0
$357$	−84.4134	−	36.4138i	−0.236452	−	0.102000i
$358$		0			0
$359$	−102.513	+	177.557i	−0.285550	+	0.494588i	−0.972743	−	0.231888i	$-0.925510\pi$
$359$	−102.513	+	177.557i	−0.285550	+	0.494588i	0.687192	+	0.726476i	$0.258843\pi$
$360$		0			0
$361$	−46.5044	−	80.5480i	−0.128821	−	0.223125i
$362$		0			0
$363$			425.494i			1.17216i
$364$		0			0
$365$	242.474			0.664313
$366$		0			0
$367$	1.46112	−	0.843577i	0.00398125	−	0.00229858i	−0.498008	−	0.867172i	$-0.665935\pi$
$367$	1.46112	−	0.843577i	0.00398125	−	0.00229858i	0.501989	+	0.864874i	$0.332602\pi$
$368$		0			0
$369$	−212.903	−	122.920i	−0.576973	−	0.333115i
$370$		0			0
$371$	−394.321	+	293.552i	−1.06286	+	0.791246i
$372$		0			0
$373$	−231.702	+	401.320i	−0.621186	+	1.07593i	0.368079	+	0.929795i	$0.380016\pi$
$373$	−231.702	+	401.320i	−0.621186	+	1.07593i	−0.989265	+	0.146131i	$0.953318\pi$
$374$		0			0
$375$	−228.592	−	395.933i	−0.609579	−	1.05582i
$376$		0			0
$377$		−	914.150i		−	2.42480i
$378$		0			0
$379$	493.215			1.30136			0.650680	−	0.759352i	$-0.274484\pi$
$379$	493.215			1.30136			0.650680	+	0.759352i	$0.274484\pi$
$380$		0			0
$381$	510.902	−	294.969i	1.34095	−	0.774197i
$382$		0			0
$383$	496.266	+	286.519i	1.29573	+	0.748092i	0.979664	−	0.200645i	$-0.0643036\pi$
$383$	496.266	+	286.519i	1.29573	+	0.748092i	0.316069	+	0.948736i	$0.397637\pi$
$384$		0			0
$385$	−49.8027	+	5.82036i	−0.129358	+	0.0151178i
$386$		0			0
$387$	−117.259	+	203.098i	−0.302994	+	0.524801i
$388$		0			0
$389$	23.2756	+	40.3146i	0.0598346	+	0.103637i	0.894391	−	0.447286i	$-0.147609\pi$
$389$	23.2756	+	40.3146i	0.0598346	+	0.103637i	−0.834556	+	0.550922i	$0.814276\pi$
$390$		0			0
$391$		−	62.9742i		−	0.161059i
$392$		0			0
$393$	−226.893			−0.577335
$394$		0			0
$395$	−303.591	+	175.278i	−0.768584	+	0.443742i
$396$		0			0
$397$	180.743	+	104.352i	0.455273	+	0.262852i	0.710055	−	0.704147i	$-0.248670\pi$
$397$	180.743	+	104.352i	0.455273	+	0.262852i	−0.254782	+	0.966999i	$0.582004\pi$
$398$		0			0
$399$	49.0131	+	419.386i	0.122840	+	1.05109i
$400$		0			0
$401$	110.595	−	191.556i	0.275798	−	0.477696i	−0.694538	−	0.719456i	$-0.744391\pi$
$401$	110.595	−	191.556i	0.275798	−	0.477696i	0.970336	+	0.241760i	$0.0777246\pi$
$402$		0			0
$403$	−91.4118	−	158.330i	−0.226828	−	0.392878i
$404$		0			0
$405$		−	308.561i		−	0.761880i
$406$		0			0
$407$	86.5022			0.212536
$408$		0			0
$409$	83.5098	−	48.2144i	0.204181	−	0.117884i	−0.394423	−	0.918929i	$-0.629056\pi$
$409$	83.5098	−	48.2144i	0.204181	−	0.117884i	0.598604	+	0.801045i	$0.295722\pi$
$410$		0			0
$411$	303.475	+	175.211i	0.738382	+	0.426305i
$412$		0			0
$413$	−392.941	−	527.827i	−0.951431	−	1.27803i
$414$		0			0
$415$	−234.874	+	406.813i	−0.565961	+	0.980273i
$416$		0			0
$417$	−169.599	−	293.754i	−0.406712	−	0.704446i
$418$		0			0
$419$			239.093i			0.570627i	0.958434	+	0.285313i	$0.0920977\pi$
$419$			239.093i			0.570627i	−0.958434	+	0.285313i	$0.907902\pi$
$420$		0			0
$421$	508.228			1.20719			0.603596	−	0.797290i	$-0.293734\pi$
$421$	508.228			1.20719			0.603596	+	0.797290i	$0.293734\pi$
$422$		0			0
$423$	−124.316	+	71.7737i	−0.293890	+	0.169678i
$424$		0			0
$425$	−48.4974	−	28.0000i	−0.114112	−	0.0658823i
$426$		0			0
$427$	6.07049	−	14.0724i	0.0142166	−	0.0329565i
$428$		0			0
$429$	109.584	−	189.805i	0.255440	−	0.442435i
$430$		0			0
$431$	−299.174	−	518.185i	−0.694140	−	1.20229i	−0.970470	−	0.241223i	$-0.922451\pi$
$431$	−299.174	−	518.185i	−0.694140	−	1.20229i	0.276329	−	0.961063i	$-0.410882\pi$
$432$		0			0
$433$			283.405i			0.654516i	0.944935	+	0.327258i	$0.106125\pi$
$433$			283.405i			0.654516i	−0.944935	+	0.327258i	$0.893875\pi$
$434$		0			0
$435$	405.644			0.932516
$436$		0			0
$437$	−250.487	+	144.619i	−0.573196	+	0.330935i
$438$		0			0
$439$	−296.596	−	171.240i	−0.675618	−	0.390068i	0.122584	−	0.992458i	$-0.460882\pi$
$439$	−296.596	−	171.240i	−0.675618	−	0.390068i	−0.798202	+	0.602390i	$0.794215\pi$
$440$		0			0
$441$	−64.3285	+	214.849i	−0.145870	+	0.487187i
$442$		0			0
$443$	293.909	−	509.065i	0.663451	−	1.14913i	−0.316252	−	0.948675i	$-0.602425\pi$
$443$	293.909	−	509.065i	0.663451	−	1.14913i	0.979703	−	0.200455i	$-0.0642421\pi$
$444$		0			0
$445$	−173.720	−	300.891i	−0.390381	−	0.676160i
$446$		0			0
$447$			653.831i			1.46271i
$448$		0			0
$449$	−265.522			−0.591364			−0.295682	−	0.955286i	$-0.595547\pi$
$449$	−265.522			−0.591364			−0.295682	+	0.955286i	$0.595547\pi$
$450$		0			0
$451$	−109.327	+	63.1202i	−0.242411	+	0.139956i
$452$		0			0
$453$	−733.264	−	423.350i	−1.61868	−	0.934547i
$454$		0			0
$455$	−495.745	−	213.852i	−1.08955	−	0.470004i
$456$		0			0
$457$	198.296	−	343.458i	0.433907	−	0.751550i	−0.563298	−	0.826254i	$-0.690468\pi$
$457$	198.296	−	343.458i	0.433907	−	0.751550i	0.997206	+	0.0747039i	$0.0238012\pi$
$458$		0			0
$459$	−29.0441	−	50.3058i	−0.0632769	−	0.109599i
$460$		0			0
$461$			143.388i			0.311037i	0.987833	+	0.155519i	$0.0497049\pi$
$461$			143.388i			0.311037i	−0.987833	+	0.155519i	$0.950295\pi$
$462$		0			0
$463$	−72.3400			−0.156242			−0.0781210	−	0.996944i	$-0.524892\pi$
$463$	−72.3400			−0.156242			−0.0781210	+	0.996944i	$0.524892\pi$
$464$		0			0
$465$	70.2572	−	40.5630i	0.151091	−	0.0872323i
$466$		0			0
$467$	453.684	+	261.935i	0.971487	+	0.560888i	0.899689	−	0.436531i	$-0.143793\pi$
$467$	453.684	+	261.935i	0.971487	+	0.560888i	0.0717975	+	0.997419i	$0.477126\pi$
$468$		0			0
$469$	140.159	−	104.342i	0.298847	−	0.222477i
$470$		0			0
$471$	91.4491	−	158.394i	0.194159	−	0.336294i
$472$		0			0
$473$	60.2134	+	104.293i	0.127301	+	0.220492i
$474$		0			0
$475$			257.205i			0.541484i
$476$		0			0
$477$	321.431			0.673859
$478$		0			0
$479$	735.758	−	424.790i	1.53603	−	0.886826i	0.536963	−	0.843606i	$-0.319572\pi$
$479$	735.758	−	424.790i	1.53603	−	0.886826i	0.999066	−	0.0432203i	$-0.0137617\pi$
$480$		0			0
$481$	806.631	+	465.709i	1.67699	+	0.968209i
$482$		0			0
$483$	−452.635	+	52.8987i	−0.937132	+	0.109521i
$484$		0			0
$485$	−82.2788	+	142.511i	−0.169647	+	0.293837i
$486$		0			0
$487$	−202.982	−	351.574i	−0.416800	−	0.721919i	0.578816	−	0.815458i	$-0.303515\pi$
$487$	−202.982	−	351.574i	−0.416800	−	0.721919i	−0.995616	+	0.0935398i	$0.970182\pi$
$488$		0			0
$489$			245.116i			0.501260i
$490$		0			0
$491$	−661.455			−1.34716			−0.673580	−	0.739115i	$-0.735244\pi$
$491$	−661.455			−1.34716			−0.673580	+	0.739115i	$0.735244\pi$
$492$		0			0
$493$	111.499	−	64.3740i	0.226165	−	0.130576i
$494$		0			0
$495$	28.3931	+	16.3927i	0.0573597	+	0.0331167i
$496$		0			0
$497$	41.3498	+	353.815i	0.0831987	+	0.711901i
$498$		0			0
$499$	−119.784	+	207.472i	−0.240048	+	0.415775i	−0.960728	−	0.277493i	$-0.910496\pi$
$499$	−119.784	+	207.472i	−0.240048	+	0.415775i	0.720680	+	0.693268i	$0.243830\pi$
$500$		0			0
$501$	302.684	+	524.263i	0.604159	+	1.04643i
$502$		0			0
$503$		−	578.149i		−	1.14940i	−0.818364	−	0.574701i	$-0.805118\pi$
$503$		−	578.149i		−	1.14940i	0.818364	−	0.574701i	$-0.194882\pi$
$504$		0			0
$505$	−63.4524			−0.125648
$506$		0			0
$507$	1504.45	−	868.593i	2.96735	−	1.71320i
$508$		0			0
$509$	260.924	+	150.644i	0.512621	+	0.295962i	0.733910	−	0.679247i	$-0.237693\pi$
$509$	260.924	+	150.644i	0.512621	+	0.295962i	−0.221290	+	0.975208i	$0.571027\pi$
$510$		0			0
$511$	−332.562	−	446.722i	−0.650807	−	0.874212i
$512$		0			0
$513$	−133.398	+	231.052i	−0.260035	+	0.450393i
$514$		0			0
$515$	186.287	+	322.659i	0.361722	+	0.626521i
$516$		0			0
$517$			73.7127i			0.142578i
$518$		0			0
$519$	142.531			0.274626
$520$		0			0
$521$	−114.812	+	66.2868i	−0.220369	+	0.127230i	−0.606121	−	0.795372i	$-0.707275\pi$
$521$	−114.812	+	66.2868i	−0.220369	+	0.127230i	0.385752	+	0.922602i	$0.373942\pi$
$522$		0			0
$523$	−96.1291	−	55.5001i	−0.183803	−	0.106119i	0.405275	−	0.914195i	$-0.367176\pi$
$523$	−96.1291	−	55.5001i	−0.183803	−	0.106119i	−0.589078	+	0.808076i	$0.700509\pi$
$524$		0			0
$525$	−160.515	+	372.101i	−0.305743	+	0.708764i
$526$		0			0
$527$	12.8744	−	22.2990i	0.0244295	−	0.0423132i
$528$		0			0
$529$	108.416	+	187.783i	0.204946	+	0.354976i
$530$		0			0
$531$			430.258i			0.810279i
$532$		0			0
$533$	−1359.30			−2.55028
$534$		0			0
$535$	302.305	−	174.536i	0.565056	−	0.326235i
$536$		0			0
$537$	−326.811	−	188.685i	−0.608587	−	0.351368i
$538$		0			0
$539$	79.0294	+	83.7711i	0.146622	+	0.155419i
$540$		0			0
$541$	−42.8522	+	74.2221i	−0.0792092	+	0.137194i	−0.902909	−	0.429832i	$-0.858573\pi$
$541$	−42.8522	+	74.2221i	−0.0792092	+	0.137194i	0.823700	+	0.567026i	$0.191906\pi$
$542$		0			0
$543$	−82.1399	−	142.271i	−0.151271	−	0.262008i
$544$		0			0
$545$			505.343i			0.927235i
$546$		0			0
$547$	674.162			1.23247			0.616236	−	0.787562i	$-0.288657\pi$
$547$	674.162			1.23247			0.616236	+	0.787562i	$0.288657\pi$
$548$		0			0
$549$	−8.67842	+	5.01049i	−0.0158077	+	0.00912657i
$550$		0			0
$551$	−512.109	−	295.666i	−0.929418	−	0.536600i
$552$		0			0
$553$	739.310	+	318.920i	1.33691	+	0.576708i
$554$		0			0
$555$	−206.653	+	357.934i	−0.372348	+	0.644926i
$556$		0			0
$557$	−381.745	−	661.202i	−0.685359	−	1.18708i	−0.973324	−	0.229436i	$-0.926312\pi$
$557$	−381.745	−	661.202i	−0.685359	−	1.18708i	0.287964	−	0.957641i	$-0.407022\pi$
$558$		0			0
$559$			1296.70i			2.31968i
$560$		0			0
$561$	30.8674			0.0550221
$562$		0			0
$563$	307.458	−	177.511i	0.546107	−	0.315295i	−0.201444	−	0.979500i	$-0.564563\pi$
$563$	307.458	−	177.511i	0.546107	−	0.315295i	0.747550	+	0.664205i	$0.231230\pi$
$564$		0			0
$565$	324.830	+	187.541i	0.574921	+	0.331931i
$566$		0			0
$567$	−568.478	+	423.203i	−1.00261	+	0.746390i
$568$		0			0
$569$	−263.535	+	456.455i	−0.463154	+	0.802206i	−0.999116	−	0.0420357i	$-0.986616\pi$
$569$	−263.535	+	456.455i	−0.463154	+	0.802206i	0.535962	+	0.844242i	$0.319949\pi$
$570$		0			0
$571$	−257.886	−	446.671i	−0.451639	−	0.782262i	0.546849	−	0.837231i	$-0.315827\pi$
$571$	−257.886	−	446.671i	−0.451639	−	0.782262i	−0.998488	+	0.0549695i	$0.982494\pi$
$572$		0			0
$573$			1216.18i			2.12248i
$574$		0			0
$575$	−277.596			−0.482775
$576$		0			0
$577$	182.029	−	105.095i	0.315476	−	0.182140i	−0.333898	−	0.942609i	$-0.608364\pi$
$577$	182.029	−	105.095i	0.315476	−	0.182140i	0.649374	+	0.760469i	$0.275031\pi$
$578$		0			0
$579$	444.689	+	256.741i	0.768029	+	0.443422i
$580$		0			0
$581$	1071.63	−	125.240i	1.84446	−	0.215559i
$582$		0			0
$583$	82.5287	−	142.944i	0.141559	−	0.245187i
$584$		0			0
$585$	176.510	+	305.724i	0.301726	+	0.522605i
$586$		0			0
$587$		−	91.8797i		−	0.156524i	−0.996933	−	0.0782621i	$-0.975063\pi$
$587$		−	91.8797i		−	0.156524i	0.996933	−	0.0782621i	$-0.0249371\pi$
$588$		0			0
$589$	−118.262			−0.200785
$590$		0			0
$591$	−557.552	+	321.903i	−0.943405	+	0.544675i
$592$		0			0
$593$	−388.734	−	224.436i	−0.655538	−	0.378475i	0.135037	−	0.990841i	$-0.456885\pi$
$593$	−388.734	−	224.436i	−0.655538	−	0.378475i	−0.790575	+	0.612366i	$0.790218\pi$
$594$		0			0
$595$	−8.82654	−	75.5254i	−0.0148345	−	0.126933i
$596$		0			0
$597$	419.110	−	725.919i	0.702026	−	1.21595i
$598$		0			0
$599$	98.8525	+	171.218i	0.165029	+	0.285839i	0.936666	−	0.350225i	$-0.113895\pi$
$599$	98.8525	+	171.218i	0.165029	+	0.285839i	−0.771636	+	0.636064i	$0.780561\pi$
$600$		0			0
$601$			232.075i			0.386148i	0.981184	+	0.193074i	$0.0618458\pi$
$601$			232.075i			0.386148i	−0.981184	+	0.193074i	$0.938154\pi$
$602$		0			0
$603$	−114.251			−0.189471
$604$		0			0
$605$	−304.785	+	175.968i	−0.503777	+	0.290856i
$606$		0			0
$607$	−709.823	−	409.816i	−1.16940	−	0.675151i	−0.215858	−	0.976425i	$-0.569255\pi$
$607$	−709.823	−	409.816i	−1.16940	−	0.675151i	−0.953538	+	0.301274i	$0.902588\pi$
$608$		0			0
$609$	−556.356	−	747.339i	−0.913557	−	1.22716i
$610$		0			0
$611$	−396.853	+	687.370i	−0.649514	+	1.12499i
$612$		0			0
$613$	405.695	+	702.684i	0.661819	+	1.14630i	0.980137	+	0.198320i	$0.0635485\pi$
$613$	405.695	+	702.684i	0.661819	+	1.14630i	−0.318319	+	0.947984i	$0.603118\pi$
$614$		0			0
$615$		−	603.175i		−	0.980773i
$616$		0			0
$617$	248.808			0.403255			0.201627	−	0.979462i	$-0.435377\pi$
$617$	248.808			0.403255			0.201627	+	0.979462i	$0.435377\pi$
$618$		0			0
$619$	−471.762	+	272.372i	−0.762136	+	0.440020i	−0.830062	−	0.557671i	$-0.811695\pi$
$619$	−471.762	+	272.372i	−0.762136	+	0.440020i	0.0679258	+	0.997690i	$0.478362\pi$
$620$		0			0
$621$	−249.369	−	143.973i	−0.401561	−	0.231841i
$622$		0			0
$623$	−316.084	+	732.735i	−0.507358	+	1.17614i
$624$		0			0
$625$	−7.32049	+	12.6795i	−0.0117128	+	0.0202871i
$626$		0			0
$627$	−70.8861	−	122.778i	−0.113056	−	0.195819i
$628$		0			0
$629$			131.180i			0.208553i
$630$		0			0
$631$	407.805			0.646284			0.323142	−	0.946350i	$-0.395261\pi$
$631$	407.805			0.646284			0.323142	+	0.946350i	$0.395261\pi$
$632$		0			0
$633$	−802.069	+	463.075i	−1.26709	+	0.731556i
$634$		0			0
$635$	422.578	+	243.976i	0.665478	+	0.384214i
$636$		0			0
$637$	285.942	+	1206.64i	0.448888	+	1.89425i
$638$		0			0
$639$	116.459	−	201.714i	0.182253	−	0.315671i
$640$		0			0
$641$	−322.840	−	559.175i	−0.503650	−	0.872347i	−0.999991	−	0.00421968i	$-0.998657\pi$
$641$	−322.840	−	559.175i	−0.503650	−	0.872347i	0.496341	−	0.868128i	$-0.334677\pi$
$642$		0			0
$643$			932.869i			1.45081i	0.688324	+	0.725403i	$0.258347\pi$
$643$			932.869i			1.45081i	−0.688324	+	0.725403i	$0.741653\pi$
$644$		0			0
$645$	−575.397			−0.892089
$646$		0			0
$647$	420.287	−	242.653i	0.649594	−	0.375043i	−0.138707	−	0.990333i	$-0.544295\pi$
$647$	420.287	−	242.653i	0.649594	−	0.375043i	0.788301	+	0.615290i	$0.210961\pi$
$648$		0			0
$649$	191.341	+	110.471i	0.294824	+	0.170217i
$650$		0			0
$651$	−171.092	−	73.8046i	−0.262813	−	0.113371i
$652$		0			0
$653$	180.587	−	312.786i	0.276550	−	0.478998i	−0.693975	−	0.719999i	$-0.744142\pi$
$653$	180.587	−	312.786i	0.276550	−	0.478998i	0.970525	+	0.241001i	$0.0774757\pi$
$654$		0			0
$655$	−93.8340	−	162.525i	−0.143258	−	0.248130i
$656$		0			0
$657$			364.146i			0.554255i
$658$		0			0
$659$	180.761			0.274296			0.137148	−	0.990551i	$-0.456206\pi$
$659$	180.761			0.274296			0.137148	+	0.990551i	$0.456206\pi$
$660$		0			0
$661$	510.800	−	294.910i	0.772768	−	0.446158i	−0.0610929	−	0.998132i	$-0.519459\pi$
$661$	510.800	−	294.910i	0.772768	−	0.446158i	0.833861	+	0.551974i	$0.186125\pi$
$662$		0			0
$663$	287.838	+	166.183i	0.434144	+	0.250653i
$664$		0			0
$665$	−280.141	+	208.551i	−0.421264	+	0.313610i
$666$		0			0
$667$	319.106	−	552.708i	0.478420	−	0.828648i
$668$		0			0
$669$	−199.521	−	345.580i	−0.298237	−	0.516562i
$670$		0			0
$671$			5.14585i			0.00766893i
$672$		0			0
$673$	−416.772			−0.619276			−0.309638	−	0.950855i	$-0.600208\pi$
$673$	−416.772			−0.619276			−0.309638	+	0.950855i	$0.600208\pi$
$674$		0			0
$675$	−221.752	+	128.029i	−0.328522	+	0.189672i
$676$		0			0
$677$	398.113	+	229.851i	0.588055	+	0.339514i	0.764328	−	0.644827i	$-0.223071\pi$
$677$	398.113	+	229.851i	0.588055	+	0.339514i	−0.176273	+	0.984341i	$0.556404\pi$
$678$		0			0
$679$	375.403	−	43.8728i	0.552877	−	0.0646139i
$680$		0			0
$681$	521.299	−	902.916i	0.765490	−	1.32587i
$682$		0			0
$683$	−560.093	−	970.109i	−0.820048	−	1.42036i	−0.905646	−	0.424034i	$-0.860614\pi$
$683$	−560.093	−	970.109i	−0.820048	−	1.42036i	0.0855985	−	0.996330i	$-0.472720\pi$
$684$		0			0
$685$			289.843i			0.423128i
$686$		0			0
$687$	651.021			0.947629
$688$		0			0
$689$	1539.16	−	888.633i	2.23390	−	1.28974i
$690$		0			0
$691$	370.080	+	213.666i	0.535572	+	0.309213i	0.743283	−	0.668978i	$-0.233268\pi$
$691$	370.080	+	213.666i	0.535572	+	0.309213i	−0.207710	+	0.978190i	$0.566601\pi$
$692$		0			0
$693$	−8.74097	−	74.7932i	−0.0126132	−	0.107927i
$694$		0			0
$695$	140.279	−	242.971i	0.201840	−	0.349598i
$696$		0			0
$697$	−95.7214	−	165.794i	−0.137333	−	0.237868i
$698$		0			0
$699$		−	1309.49i		−	1.87337i
$700$		0			0
$701$	−99.9460			−0.142576			−0.0712882	−	0.997456i	$-0.522711\pi$
$701$	−99.9460			−0.142576			−0.0712882	+	0.997456i	$0.522711\pi$
$702$		0			0
$703$	521.782	−	301.251i	0.742222	−	0.428522i
$704$		0			0
$705$	−305.013	−	176.099i	−0.432643	−	0.249786i
$706$		0			0
$707$	87.0272	+	116.901i	0.123094	+	0.165349i
$708$		0			0
$709$	−19.5862	+	33.9244i	−0.0276252	+	0.0478482i	−0.879507	−	0.475885i	$-0.842128\pi$
$709$	−19.5862	+	33.9244i	−0.0276252	+	0.0478482i	0.851882	+	0.523733i	$0.175461\pi$
$710$		0			0
$711$	−263.231	−	455.930i	−0.370227	−	0.641251i
$712$		0			0
$713$		−	127.638i		−	0.179015i
$714$		0			0
$715$	181.279			0.253536
$716$		0			0
$717$	−55.9871	+	32.3242i	−0.0780853	+	0.0450825i
$718$		0			0
$719$	668.482	+	385.948i	0.929739	+	0.536785i	0.886729	−	0.462290i	$-0.152972\pi$
$719$	668.482	+	385.948i	0.929739	+	0.536785i	0.0430100	+	0.999075i	$0.486305\pi$
$720$		0			0
$721$	338.950	−	785.744i	0.470111	−	1.08980i
$722$		0			0
$723$	−223.180	+	386.559i	−0.308686	+	0.534659i
$724$		0			0
$725$	−283.766	−	491.497i	−0.391401	−	0.677927i
$726$		0			0
$727$			963.864i			1.32581i	0.748703	+	0.662905i	$0.230677\pi$
$727$			963.864i			1.32581i	−0.748703	+	0.662905i	$0.769323\pi$
$728$		0			0
$729$	−77.0650			−0.105713
$730$		0			0
$731$	−158.159	+	91.3131i	−0.216360	+	0.124915i
$732$		0			0
$733$	−82.3471	−	47.5431i	−0.112343	−	0.0648610i	0.442776	−	0.896632i	$-0.353994\pi$
$733$	−82.3471	−	47.5431i	−0.112343	−	0.0648610i	−0.555118	+	0.831771i	$0.687327\pi$
$734$		0			0
$735$	−535.434	+	126.884i	−0.728481	+	0.172631i
$736$		0			0
$737$	−29.3344	+	50.8086i	−0.0398024	+	0.0689398i
$738$		0			0
$739$	−574.401	−	994.892i	−0.777268	−	1.34627i	−0.933511	−	0.358549i	$-0.883271\pi$
$739$	−574.401	−	994.892i	−0.777268	−	1.34627i	0.156243	−	0.987719i	$-0.450062\pi$
$740$		0			0
$741$		−	1526.54i		−	2.06011i
$742$		0			0
$743$	−232.652			−0.313126			−0.156563	−	0.987668i	$-0.550041\pi$
$743$	−232.652			−0.313126			−0.156563	+	0.987668i	$0.550041\pi$
$744$		0			0
$745$	−468.346	+	270.399i	−0.628652	+	0.362952i
$746$		0			0
$747$	−610.949	−	352.731i	−0.817869	−	0.472197i
$748$		0			0
$749$	−736.178	−	317.569i	−0.982881	−	0.423990i
$750$		0			0
$751$	343.079	−	594.230i	0.456829	−	0.791252i	−0.541962	−	0.840403i	$-0.682318\pi$
$751$	343.079	−	594.230i	0.456829	−	0.791252i	0.998791	+	0.0491513i	$0.0156516\pi$
$752$		0			0
$753$	−404.105	−	699.931i	−0.536660	−	0.929523i
$754$		0			0
$755$		−	700.325i		−	0.927582i
$756$		0			0
$757$	657.058			0.867976			0.433988	−	0.900919i	$-0.357106\pi$
$757$	657.058			0.867976			0.433988	+	0.900919i	$0.357106\pi$
$758$		0			0
$759$	132.512	−	76.5058i	0.174588	−	0.100798i
$760$		0			0
$761$	−1063.63	−	614.086i	−1.39767	−	0.806946i	−0.403523	−	0.914970i	$-0.632214\pi$
$761$	−1063.63	−	614.086i	−1.39767	−	0.806946i	−0.994148	+	0.108024i	$0.965548\pi$
$762$		0			0
$763$	931.018	−	693.096i	1.22021	−	0.908383i
$764$		0			0
$765$	−24.8595	+	43.0579i	−0.0324961	+	0.0562848i
$766$		0			0
$767$	1189.50	+	2060.27i	1.55085	+	2.68614i
$768$		0			0
$769$			499.279i			0.649257i	0.945842	+	0.324629i	$0.105239\pi$
$769$			499.279i			0.649257i	−0.945842	+	0.324629i	$0.894761\pi$
$770$		0			0
$771$	−1776.12			−2.30366
$772$		0			0
$773$	−277.318	+	160.110i	−0.358756	+	0.207128i	−0.668535	−	0.743681i	$-0.733078\pi$
$773$	−277.318	+	160.110i	−0.358756	+	0.207128i	0.309779	+	0.950809i	$0.399745\pi$
$774$		0			0
$775$	−98.2960	−	56.7512i	−0.126834	−	0.0732274i
$776$		0			0
$777$	942.872	−	110.192i	1.21348	−	0.141817i
$778$		0			0
$779$	−439.643	+	761.484i	−0.564368	+	0.977514i
$780$		0			0
$781$	−59.8029	−	103.582i	−0.0765722	−	0.132627i
$782$		0			0
$783$		−	588.695i		−	0.751845i
$784$		0			0
$785$	151.279			0.192712
$786$		0			0
$787$	−490.946	+	283.448i	−0.623820	+	0.360162i	−0.778355	−	0.627825i	$-0.783945\pi$
$787$	−490.946	+	283.448i	−0.623820	+	0.360162i	0.154535	+	0.987987i	$0.450612\pi$
$788$		0			0
$789$	−286.198	−	165.236i	−0.362735	−	0.209425i
$790$		0			0
$791$	−100.001	−	855.670i	−0.126423	−	1.08176i
$792$		0			0
$793$	−27.7041	+	47.9850i	−0.0349359	+	0.0605107i
$794$		0			0
$795$	394.321	+	682.984i	0.496002	+	0.859100i
$796$		0			0
$797$		−	1416.99i		−	1.77791i	−0.457996	−	0.888954i	$-0.651433\pi$
$797$		−	1416.99i		−	1.77791i	0.457996	−	0.888954i	$-0.348567\pi$
$798$		0			0
$799$	−111.785			−0.139906
$800$		0			0
$801$	451.875	−	260.890i	0.564139	−	0.325706i
$802$		0			0
$803$	161.940	+	93.4959i	0.201668	+	0.116433i
$804$		0			0
$805$	−225.084	−	302.350i	−0.279608	−	0.375590i
$806$		0			0
$807$	70.1536	−	121.510i	0.0869314	−	0.150570i
$808$		0			0
$809$	498.631	+	863.654i	0.616354	+	1.06756i	0.990145	+	0.140044i	$0.0447244\pi$
$809$	498.631	+	863.654i	0.616354	+	1.06756i	−0.373791	+	0.927513i	$0.621942\pi$
$810$		0			0
$811$			1201.56i			1.48158i	0.671735	+	0.740792i	$0.265550\pi$
$811$			1201.56i			1.48158i	−0.671735	+	0.740792i	$0.734450\pi$
$812$		0			0
$813$	−313.064			−0.385072
$814$		0			0
$815$	−175.579	+	101.371i	−0.215434	+	0.124381i
$816$		0			0
$817$	726.415	+	419.396i	0.889125	+	0.513337i
$818$		0			0
$819$	321.161	−	744.504i	0.392138	−	0.909041i
$820$		0			0
$821$	92.8952	−	160.899i	0.113149	−	0.195980i	−0.803889	−	0.594779i	$-0.797240\pi$
$821$	92.8952	−	160.899i	0.113149	−	0.195980i	0.917038	+	0.398799i	$0.130573\pi$
$822$		0			0
$823$	429.451	+	743.831i	0.521812	+	0.903805i	0.999678	+	0.0253721i	$0.00807705\pi$
$823$	429.451	+	743.831i	0.521812	+	0.903805i	−0.477866	+	0.878433i	$0.658590\pi$
$824$		0			0
$825$		−	136.066i		−	0.164928i
$826$		0			0
$827$	−217.847			−0.263418			−0.131709	−	0.991288i	$-0.542046\pi$
$827$	−217.847			−0.263418			−0.131709	+	0.991288i	$0.542046\pi$
$828$		0			0
$829$	858.304	−	495.542i	1.03535	−	0.597759i	0.116836	−	0.993151i	$-0.462725\pi$
$829$	858.304	−	495.542i	1.03535	−	0.597759i	0.918512	+	0.395392i	$0.129391\pi$
$830$		0			0
$831$	199.455	+	115.155i	0.240018	+	0.138574i
$832$		0			0
$833$	−127.038	+	119.847i	−0.152507	+	0.143874i
$834$		0			0
$835$	−250.356	+	433.630i	−0.299828	+	0.519317i
$836$		0			0
$837$	−58.8674	−	101.961i	−0.0703314	−	0.121818i
$838$		0			0
$839$			415.268i			0.494956i	0.968894	+	0.247478i	$0.0796017\pi$
$839$			415.268i			0.494956i	−0.968894	+	0.247478i	$0.920398\pi$
$840$		0			0
$841$	463.798			0.551484
$842$		0			0
$843$	−187.186	+	108.072i	−0.222048	+	0.128199i
$844$		0			0
$845$	1244.36	+	718.433i	1.47262	+	0.850217i
$846$		0			0
$847$	742.218	+	320.175i	0.876291	+	0.378010i
$848$		0			0
$849$	−441.345	+	764.432i	−0.519841	+	0.900391i
$850$		0			0
$851$	325.134	+	563.148i	0.382061	+	0.661749i
$852$		0			0
$853$		−	1335.36i		−	1.56549i	−0.622343	−	0.782745i	$-0.713819\pi$
$853$		−	1335.36i		−	1.56549i	0.622343	−	0.782745i	$-0.286181\pi$
$854$		0			0
$855$	228.356			0.267084
$856$		0			0
$857$	−1392.35	+	803.874i	−1.62468	+	0.938009i	−0.639034	+	0.769178i	$0.720666\pi$
$857$	−1392.35	+	803.874i	−1.62468	+	0.938009i	−0.985645	+	0.168831i	$0.946001\pi$
$858$		0			0
$859$	−131.880	−	76.1410i	−0.153527	−	0.0886391i	0.421268	−	0.906936i	$-0.361585\pi$
$859$	−131.880	−	76.1410i	−0.153527	−	0.0886391i	−0.574796	+	0.818297i	$0.694918\pi$
$860$		0			0
$861$	−1111.26	+	827.277i	−1.29066	+	0.960833i
$862$		0			0
$863$	−480.137	+	831.622i	−0.556358	+	0.963641i	0.441438	+	0.897292i	$0.354469\pi$
$863$	−480.137	+	831.622i	−0.556358	+	0.963641i	−0.997796	+	0.0663494i	$0.978865\pi$
$864$		0			0
$865$	58.9453	+	102.096i	0.0681449	+	0.118030i
$866$		0			0
$867$		−	1018.07i		−	1.17424i
$868$		0			0
$869$	−270.343			−0.311096
$870$		0			0
$871$	−547.085	+	315.860i	−0.628111	+	0.362640i
$872$		0			0
$873$	−214.022	−	123.565i	−0.245157	−	0.141541i
$874$		0			0
$875$	−862.664	+	100.818i	−0.985902	+	0.115221i
$876$		0			0
$877$	−5.97052	+	10.3413i	−0.00680790	+	0.0117916i	−0.869409	−	0.494093i	$-0.835500\pi$
$877$	−5.97052	+	10.3413i	−0.00680790	+	0.0117916i	0.862601	+	0.505884i	$0.168834\pi$
$878$		0			0
$879$	−362.027	−	627.049i	−0.411862	−	0.713366i
$880$		0			0
$881$			625.457i			0.709940i	0.934878	+	0.354970i	$0.115509\pi$
$881$			625.457i			0.709940i	−0.934878	+	0.354970i	$0.884491\pi$
$882$		0			0
$883$	−78.6167			−0.0890337			−0.0445168	−	0.999009i	$-0.514175\pi$
$883$	−78.6167			−0.0890337			−0.0445168	+	0.999009i	$0.514175\pi$
$884$		0			0
$885$	−914.224	+	527.827i	−1.03302	+	0.596415i
$886$		0			0
$887$	−633.661	−	365.844i	−0.714387	−	0.412451i	0.0982963	−	0.995157i	$-0.468661\pi$
$887$	−633.661	−	365.844i	−0.714387	−	0.412451i	−0.812683	+	0.582706i	$0.801994\pi$
$888$		0			0
$889$	−130.093	−	1113.16i	−0.146336	−	1.25215i
$890$		0			0
$891$	118.978	−	206.077i	0.133534	−	0.231287i
$892$		0			0
$893$	256.711	+	444.636i	0.287470	+	0.497913i
$894$		0			0
$895$		−	312.131i		−	0.348749i
$896$		0			0
$897$	1647.56			1.83675
$898$		0			0
$899$	225.990	−	130.475i	0.251379	−	0.145134i
$900$		0			0
$901$	216.773	+	125.154i	0.240592	+	0.138906i
$902$		0			0
$903$	789.179	+	1060.08i	0.873952	+	1.17396i
$904$		0			0
$905$	67.9398	−	117.675i	0.0750716	−	0.130028i
$906$		0			0
$907$	−143.851	−	249.157i	−0.158601	−	0.274704i	0.775764	−	0.631024i	$-0.217365\pi$
$907$	−143.851	−	249.157i	−0.158601	−	0.274704i	−0.934364	+	0.356319i	$0.884032\pi$
$908$		0			0
$909$		−	95.2922i		−	0.104832i
$910$		0			0
$911$	249.315			0.273672			0.136836	−	0.990594i	$-0.456307\pi$
$911$	249.315			0.273672			0.136836	+	0.990594i	$0.456307\pi$
$912$		0			0
$913$	−313.727	+	181.130i	−0.343622	+	0.198390i
$914$		0			0
$915$	−21.2928	−	12.2934i	−0.0232708	−	0.0134354i
$916$		0			0
$917$	−170.732	+	395.784i	−0.186185	+	0.431608i
$918$		0			0
$919$	−10.0575	+	17.4201i	−0.0109440	+	0.0189555i	−0.871446	−	0.490492i	$-0.836817\pi$
$919$	−10.0575	+	17.4201i	−0.0109440	+	0.0189555i	0.860502	+	0.509448i	$0.170150\pi$
$920$		0			0
$921$	454.978	+	788.045i	0.494005	+	0.855641i
$922$		0			0
$923$		−	1287.86i		−	1.39530i
$924$		0			0
$925$	578.252			0.625137
$926$		0			0
$927$	−484.566	+	279.764i	−0.522724	+	0.301795i
$928$		0			0
$929$	−1067.50	−	616.321i	−1.14908	−	0.663424i	−0.200420	−	0.979710i	$-0.564231\pi$
$929$	−1067.50	−	616.321i	−1.14908	−	0.663424i	−0.948664	+	0.316286i	$0.897564\pi$
$930$		0			0
$931$	768.446	+	230.082i	0.825398	+	0.247134i
$932$		0			0
$933$	−626.481	+	1085.10i	−0.671470	+	1.16302i
$934$		0			0
$935$	12.7656	+	22.1106i	0.0136530	+	0.0236477i
$936$		0			0
$937$			283.840i			0.302924i	0.988463	+	0.151462i	$0.0483981\pi$
$937$			283.840i			0.302924i	−0.988463	+	0.151462i	$0.951602\pi$
$938$		0			0
$939$	−417.835			−0.444979
$940$		0			0
$941$	561.263	−	324.045i	0.596453	−	0.344362i	−0.171192	−	0.985238i	$-0.554762\pi$
$941$	561.263	−	324.045i	0.596453	−	0.344362i	0.767645	+	0.640875i	$0.221428\pi$
$942$		0			0
$943$	−821.853	−	474.497i	−0.871530	−	0.503178i
$944$		0			0
$945$	−319.250	−	137.716i	−0.337831	−	0.145732i
$946$		0			0
$947$	859.101	−	1488.01i	0.907181	−	1.57128i	0.0892196	−	0.996012i	$-0.471563\pi$
$947$	859.101	−	1488.01i	0.907181	−	1.57128i	0.817962	−	0.575272i	$-0.195104\pi$
$948$		0			0
$949$	1006.72	+	1743.69i	1.06082	+	1.83740i
$950$		0			0
$951$		−	892.839i		−	0.938842i
$952$		0			0
$953$	1085.95			1.13950			0.569752	−	0.821817i	$-0.307039\pi$
$953$	1085.95			1.13950			0.569752	+	0.821817i	$0.307039\pi$
$954$		0			0
$955$	−871.161	+	502.965i	−0.912211	+	0.526665i
$956$		0			0
$957$	270.915	+	156.413i	0.283088	+	0.163441i
$958$		0			0
$959$	533.991	−	397.530i	0.556821	−	0.414525i
$960$		0			0
$961$	−454.406	+	787.054i	−0.472847	+	0.818995i
$962$		0			0
$963$	262.116	+	453.998i	0.272187	+	0.471442i
$964$		0			0
$965$			424.713i			0.440117i
$966$		0			0
$967$	969.512			1.00260			0.501299	−	0.865274i	$-0.332856\pi$
$967$	969.512			1.00260			0.501299	+	0.865274i	$0.332856\pi$
$968$		0			0
$969$	186.192	−	107.498i	0.192149	−	0.110937i
$970$		0			0
$971$	724.959	+	418.555i	0.746611	+	0.431056i	0.824468	−	0.565908i	$-0.191474\pi$
$971$	724.959	+	418.555i	0.746611	+	0.431056i	−0.0778571	+	0.996965i	$0.524808\pi$
$972$		0			0
$973$	−640.035	+	74.7999i	−0.657795	+	0.0768755i
$974$		0			0
$975$	732.549	−	1268.81i	0.751332	−	1.30135i
$976$		0			0
$977$	−680.114	−	1177.99i	−0.696125	−	1.20572i	−0.969800	−	0.243901i	$-0.921573\pi$
$977$	−680.114	−	1177.99i	−0.696125	−	1.20572i	0.273675	−	0.961822i	$-0.411761\pi$
$978$		0			0
$979$		−	267.939i		−	0.273686i
$980$		0			0
$981$	−758.919			−0.773618
$982$		0			0
$983$	−344.050	+	198.637i	−0.350000	+	0.202073i	−0.664685	−	0.747123i	$-0.731434\pi$
$983$	−344.050	+	198.637i	−0.350000	+	0.202073i	0.314685	+	0.949196i	$0.398101\pi$
$984$		0			0
$985$	−461.164	−	266.253i	−0.468187	−	0.270308i
$986$		0			0
$987$	93.9000	+	803.467i	0.0951368	+	0.814050i
$988$		0			0
$989$	−452.645	+	784.004i	−0.457680	+	0.792724i
$990$		0			0
$991$	139.250	+	241.188i	0.140514	+	0.243378i	0.927690	−	0.373350i	$-0.121791\pi$
$991$	139.250	+	241.188i	0.140514	+	0.243378i	−0.787176	+	0.616728i	$0.788458\pi$
$992$		0			0
$993$			256.856i			0.258667i
$994$		0			0
$995$	693.310			0.696794
$996$		0			0
$997$	−716.547	+	413.699i	−0.718703	+	0.414943i	−0.814275	−	0.580479i	$-0.802865\pi$
$997$	−716.547	+	413.699i	−0.718703	+	0.414943i	0.0955720	+	0.995423i	$0.469532\pi$
$998$		0			0
$999$	519.455	+	299.907i	0.519975	+	0.300208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.s.a.33.2	✓	16
4.3	odd	2	inner	224.3.s.a.33.7	yes	16
7.2	even	3		1568.3.c.h.97.4		16
7.3	odd	6	inner	224.3.s.a.129.2	yes	16
7.5	odd	6		1568.3.c.h.97.13		16
8.3	odd	2		448.3.s.g.257.2		16
8.5	even	2		448.3.s.g.257.7		16
28.3	even	6	inner	224.3.s.a.129.7	yes	16
28.19	even	6		1568.3.c.h.97.3		16
28.23	odd	6		1568.3.c.h.97.14		16
56.3	even	6		448.3.s.g.129.2		16
56.45	odd	6		448.3.s.g.129.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.a.33.2	✓	16	1.1	even	1	trivial
224.3.s.a.33.7	yes	16	4.3	odd	2	inner
224.3.s.a.129.2	yes	16	7.3	odd	6	inner
224.3.s.a.129.7	yes	16	28.3	even	6	inner
448.3.s.g.129.2		16	56.3	even	6
448.3.s.g.129.7		16	56.45	odd	6
448.3.s.g.257.2		16	8.3	odd	2
448.3.s.g.257.7		16	8.5	even	2
1568.3.c.h.97.3		16	28.19	even	6
1568.3.c.h.97.4		16	7.2	even	3
1568.3.c.h.97.13		16	7.5	odd	6
1568.3.c.h.97.14		16	28.23	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.19104 + 1.84235i) q^{3} +(-2.63938 - 1.52385i) q^{5} +(0.812549 + 6.95268i) q^{7} +(2.28850 - 3.96380i) q^{9} +O(q^{10})\)	\(q+(-3.19104 + 1.84235i) q^{3} +(-2.63938 - 1.52385i) q^{5} +(0.812549 + 6.95268i) q^{7} +(2.28850 - 3.96380i) q^{9} +(-1.17516 - 2.03544i) q^{11} -25.3073i q^{13} +11.2298 q^{15} +(3.08674 - 1.78213i) q^{17} +(-14.1772 - 8.18522i) q^{19} +(-15.4021 - 20.6893i) q^{21} +(8.83413 - 15.3012i) q^{23} +(-7.85577 - 13.6066i) q^{25} -16.2974i q^{27} +36.1220 q^{29} +(6.25629 - 3.61207i) q^{31} +(7.50000 + 4.33013i) q^{33} +(8.45020 - 19.5890i) q^{35} +(-18.4021 + 31.8734i) q^{37} +(46.6249 + 80.7567i) q^{39} -53.7118i q^{41} -51.2382 q^{43} +(-12.0805 + 6.97466i) q^{45} +(-27.1609 - 15.6814i) q^{47} +(-47.6795 + 11.2988i) q^{49} +(-6.56661 + 11.3737i) q^{51} +(35.1137 + 60.8187i) q^{53} +7.16309i q^{55} +60.3201 q^{57} +(-81.4102 + 47.0022i) q^{59} +(-1.89609 - 1.09471i) q^{61} +(29.4186 + 12.6904i) q^{63} +(-38.5645 + 66.7957i) q^{65} +(-12.4810 - 21.6177i) q^{67} +65.1022i q^{69} +50.8890 q^{71} +(-68.9008 + 39.7799i) q^{73} +(50.1362 + 28.9461i) q^{75} +(13.1969 - 9.82444i) q^{77} +(57.5117 - 99.6132i) q^{79} +(50.6220 + 87.6799i) q^{81} -154.132i q^{83} -10.8628 q^{85} +(-115.267 + 66.5493i) q^{87} +(98.7274 + 57.0003i) q^{89} +(175.954 - 20.5634i) q^{91} +(-13.3094 + 23.0525i) q^{93} +(24.9461 + 43.2079i) q^{95} -53.9940i q^{97} -10.7575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^9	\( 16 q + 8 q^{9} + 48 q^{17} + 56 q^{21} + 16 q^{25} + 112 q^{29} + 120 q^{33} + 8 q^{37} - 72 q^{45} - 128 q^{49} - 24 q^{53} - 528 q^{57} - 360 q^{61} - 8 q^{65} + 72 q^{73} + 32 q^{81} + 720 q^{85} + 408 q^{89} - 232 q^{93}+O(q^{100}) \) 16 * q + 8 * q^9 + 48 * q^17 + 56 * q^21 + 16 * q^25 + 112 * q^29 + 120 * q^33 + 8 * q^37 - 72 * q^45 - 128 * q^49 - 24 * q^53 - 528 * q^57 - 360 * q^61 - 8 * q^65 + 72 * q^73 + 32 * q^81 + 720 * q^85 + 408 * q^89 - 232 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more