LMFDB - Embedded newform 448.3.s.g.129.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,3,Mod(129,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("448.129");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.2071158433$
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:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.2
Root			$0.707107 + 2.60548i$ of defining polynomial
Character	$\chi$	$=$	448.129
Dual form			448.3.s.g.257.2

$q$-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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

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

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	−0.137233	−	0.990539i	$-0.543821\pi$
$3$	−3.19104	−	1.84235i	−1.06368	−	0.614116i	−0.926448	+	0.376422i	$0.877154\pi$
$4$		0			0
$5$	2.63938	−	1.52385i	0.527877	−	0.304770i	−0.212275	−	0.977210i	$-0.568087\pi$
$5$	2.63938	−	1.52385i	0.527877	−	0.304770i	0.740151	+	0.672440i	$0.234754\pi$
$6$		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	−0.914486	−	0.404618i	$-0.867404\pi$
$11$	−1.17516	+	2.03544i	−0.106833	+	0.185040i	0.807653	+	0.589659i	$0.200738\pi$
$12$		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	0.588031	−	0.808838i	$-0.299903\pi$
$17$	3.08674	+	1.78213i	0.181573	+	0.104831i	−0.406459	+	0.913669i	$0.633236\pi$
$18$		0			0
$19$	−14.1772	+	8.18522i	−0.746169	+	0.430801i	−0.824308	−	0.566142i	$-0.808436\pi$
$19$	−14.1772	+	8.18522i	−0.746169	+	0.430801i	0.0781390	+	0.996942i	$0.475102\pi$
$20$		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	$-0.292152\pi$
$23$	−8.83413	−	15.3012i	−0.384093	−	0.665268i	−0.991643	+	0.129013i	$0.958819\pi$
$24$		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	$-0.714002\pi$
$29$	−36.1220			−1.24559			−0.622793	+	0.782387i	$0.714002\pi$
$30$		0			0
$31$	−6.25629	−	3.61207i	−0.201816	−	0.116518i	0.395686	−	0.918386i	$-0.370507\pi$
$31$	−6.25629	−	3.61207i	−0.201816	−	0.116518i	−0.597502	+	0.801867i	$0.703840\pi$
$32$		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	$-0.000971230\pi$
$37$	18.4021	+	31.8734i	0.497355	+	0.861445i	−0.502640	+	0.864496i	$0.667638\pi$
$38$		0			0
$39$	−46.6249	+	80.7567i	−1.19551	+	2.07068i
$40$		0			0
$41$			53.7118i			1.31004i	0.755610	+	0.655022i	$0.227341\pi$
$41$			53.7118i			1.31004i	−0.755610	+	0.655022i	$0.772659\pi$
$42$		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	$-0.558388\pi$
$47$	27.1609	−	15.6814i	0.577892	−	0.333646i	0.760295	+	0.649578i	$0.225054\pi$
$48$		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	0.317428	+	0.948282i	$0.397181\pi$
$53$	−35.1137	+	60.8187i	−0.662522	+	1.14752i	−0.979951	+	0.199240i	$0.936153\pi$
$54$		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	−0.387695	−	0.921788i	$-0.626728\pi$
$59$	−81.4102	−	47.0022i	−1.37983	−	0.796647i	−0.992139	+	0.125141i	$0.960062\pi$
$60$		0			0
$61$	1.89609	−	1.09471i	0.0310835	−	0.0179461i	−0.484378	−	0.874859i	$-0.660954\pi$
$61$	1.89609	−	1.09471i	0.0310835	−	0.0179461i	0.515461	+	0.856913i	$0.327621\pi$
$62$		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	−0.944008	−	0.329922i	$-0.892977\pi$
$67$	−12.4810	+	21.6177i	−0.186283	+	0.322652i	0.757725	+	0.652574i	$0.226311\pi$
$68$		0			0
$69$			65.1022i			0.943510i
$70$		0			0
$71$	−50.8890			−0.716746			−0.358373	−	0.933579i	$-0.616668\pi$
$71$	−50.8890			−0.716746			−0.358373	+	0.933579i	$0.616668\pi$
$72$		0			0
$73$	−68.9008	−	39.7799i	−0.943847	−	0.544930i	−0.0526830	−	0.998611i	$-0.516777\pi$
$73$	−68.9008	−	39.7799i	−0.943847	−	0.544930i	−0.891164	+	0.453681i	$0.850111\pi$
$74$		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	−0.957729	−	0.287672i	$-0.907119\pi$
$79$	−57.5117	−	99.6132i	−0.727996	−	1.26093i	0.229733	−	0.973254i	$-0.426215\pi$
$80$		0			0
$81$	50.6220	−	87.6799i	0.624963	−	1.08247i
$82$		0			0
$83$			154.132i			1.85701i	0.371318	+	0.928506i	$0.378906\pi$
$83$			154.132i			1.85701i	−0.371318	+	0.928506i	$0.621094\pi$
$84$		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	0.170649	−	0.985332i	$-0.445414\pi$
$89$	98.7274	−	57.0003i	1.10930	−	0.640453i	0.938647	+	0.344879i	$0.112080\pi$
$90$		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	$0.0897775\pi$
$97$			53.9940i			0.556640i	−0.960488	+	0.278320i	$0.910222\pi$
$98$		0			0
$99$	−10.7575			−0.108661
$100$		0			0
$101$	−18.0305	−	10.4099i	−0.178519	−	0.103068i	0.408077	−	0.912947i	$-0.366199\pi$
$101$	−18.0305	−	10.4099i	−0.178519	−	0.103068i	−0.586597	+	0.809879i	$0.699533\pi$
$102$		0			0
$103$	105.870	−	61.1238i	1.02786	−	0.593435i	0.111489	−	0.993766i	$-0.464438\pi$
$103$	105.870	−	61.1238i	1.02786	−	0.593435i	0.916371	+	0.400330i	$0.131105\pi$
$104$		0			0
$105$	9.12480	−	78.0775i	0.0869029	−	0.743596i
$106$		0			0
$107$	−57.2681	−	99.1912i	−0.535216	−	0.927021i	−0.999153	−	0.0411525i	$-0.986897\pi$
$107$	−57.2681	−	99.1912i	−0.535216	−	0.927021i	0.463937	−	0.885868i	$-0.346436\pi$
$108$		0			0
$109$	82.9057	−	143.597i	0.760603	−	1.31740i	−0.181938	−	0.983310i	$-0.558237\pi$
$109$	82.9057	−	143.597i	0.760603	−	1.31740i	0.942540	−	0.334092i	$-0.108430\pi$
$110$		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	$-0.282918\pi$
$127$	160.105			1.26067			0.630334	+	0.776324i	$0.282918\pi$
$128$		0			0
$129$	163.503	+	94.3987i	1.26747	+	0.731773i
$130$		0			0
$131$	53.3272	−	30.7885i	0.407078	−	0.235027i	−0.282455	−	0.959280i	$-0.591149\pi$
$131$	53.3272	−	30.7885i	0.407078	−	0.235027i	0.689534	+	0.724254i	$0.257816\pi$
$132$		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	−0.985731	−	0.168329i	$-0.946163\pi$
$137$	−47.5511	+	82.3609i	−0.347088	+	0.601174i	0.638643	+	0.769503i	$0.279496\pi$
$138$		0			0
$139$		−	92.0558i		−	0.662272i	−0.943583	−	0.331136i	$-0.892568\pi$
$139$		−	92.0558i		−	0.662272i	0.943583	−	0.331136i	$-0.107432\pi$
$140$		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	−0.993483	−	0.113983i	$-0.963639\pi$
$149$	−88.7225	−	153.672i	−0.595453	−	1.03136i	0.398030	−	0.917373i	$-0.369694\pi$
$150$		0			0
$151$	−114.894	+	199.002i	−0.760888	+	1.31790i	0.181506	+	0.983390i	$0.441903\pi$
$151$	−114.894	+	199.002i	−0.760888	+	1.31790i	−0.942394	+	0.334506i	$0.891430\pi$
$152$		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	$-0.282803\pi$
$157$	42.9871	+	24.8186i	0.273803	+	0.158080i	−0.356812	+	0.934176i	$0.616136\pi$
$158$		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	0.949832	−	0.312761i	$-0.101254\pi$
$163$	33.2613	+	57.6103i	0.204057	+	0.353438i	−0.745775	+	0.666198i	$0.767920\pi$
$164$		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	$-0.631006\pi$
$173$	33.4995	−	19.3409i	0.193639	−	0.111797i	0.593685	+	0.804698i	$0.297673\pi$
$174$		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	−0.686794	−	0.726853i	$-0.740982\pi$
$179$	51.2076	−	88.6942i	0.286076	−	0.495498i	0.972870	+	0.231354i	$0.0743157\pi$
$180$		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	−0.868000	−	0.496565i	$-0.834594\pi$
$191$	−165.031	−	285.842i	−0.864038	−	1.49656i	0.00396184	−	0.999992i	$-0.498739\pi$
$192$		0			0
$193$	−69.6777	+	120.685i	−0.361024	+	0.625312i	−0.988130	−	0.153622i	$-0.950906\pi$
$193$	−69.6777	+	120.685i	−0.361024	+	0.625312i	0.627105	+	0.778934i	$0.284240\pi$
$194$		0			0
$195$			284.197i			1.45742i
$196$		0			0
$197$	−174.724			−0.886925			−0.443462	−	0.896293i	$-0.646250\pi$
$197$	−174.724			−0.886925			−0.443462	+	0.896293i	$0.646250\pi$
$198$		0			0
$199$	197.009	+	113.743i	0.989996	+	0.571574i	0.905273	−	0.424830i	$-0.139666\pi$
$199$	197.009	+	113.743i	0.989996	+	0.571574i	0.0847227	+	0.996405i	$0.473000\pi$
$200$		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	−0.148733	−	0.988877i	$-0.547519\pi$
$227$	−245.045	−	141.477i	−1.07949	−	0.623245i	−0.930759	+	0.365632i	$0.880853\pi$
$228$		0			0
$229$	153.011	−	88.3412i	0.668172	−	0.385769i	−0.127212	−	0.991876i	$-0.540603\pi$
$229$	153.011	−	88.3412i	0.668172	−	0.385769i	0.795384	+	0.606106i	$0.207269\pi$
$230$		0			0
$231$	24.0119	+	55.6635i	0.103947	+	0.240968i
$232$		0			0
$233$	−177.693	−	307.773i	−0.762630	−	1.32091i	−0.941491	−	0.337039i	$-0.890575\pi$
$233$	−177.693	−	307.773i	−0.762630	−	1.32091i	0.178861	−	0.983874i	$-0.442759\pi$
$234$		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	$-0.511686\pi$
$239$	−17.5451			−0.0734104			−0.0367052	+	0.999326i	$0.511686\pi$
$240$		0			0
$241$	104.909	+	60.5693i	0.435308	+	0.251325i	0.701605	−	0.712566i	$-0.252467\pi$
$241$	104.909	+	60.5693i	0.435308	+	0.251325i	−0.266298	+	0.963891i	$0.585800\pi$
$242$		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	$-0.856063\pi$
$251$		−	219.342i		−	0.873874i	0.899492	−	0.436937i	$-0.143937\pi$
$252$		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	0.638558	−	0.769574i	$-0.279531\pi$
$257$	417.447	−	241.013i	1.62431	−	0.937794i	0.985749	−	0.168220i	$-0.0538019\pi$
$258$		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	$-0.887875\pi$
$263$	−44.8439	+	77.6720i	−0.170509	+	0.295331i	0.768089	+	0.640343i	$0.221208\pi$
$264$		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	$-0.310785\pi$
$269$	32.9768	+	19.0392i	0.122590	+	0.0707776i	−0.437451	+	0.899242i	$0.644119\pi$
$270$		0			0
$271$	−73.5803	+	42.4816i	−0.271514	+	0.156759i	−0.629575	−	0.776939i	$-0.716771\pi$
$271$	−73.5803	+	42.4816i	−0.271514	+	0.156759i	0.358062	+	0.933698i	$0.383438\pi$
$272$		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	$-0.797344\pi$
$277$	31.2523	−	54.1306i	0.112824	−	0.195417i	0.916908	+	0.399099i	$0.130677\pi$
$278$		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	0.819547	−	0.573012i	$-0.194225\pi$
$283$	207.461	+	119.778i	0.733078	+	0.423243i	−0.0864689	+	0.996255i	$0.527558\pi$
$284$		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	$0.131757\pi$
$307$			246.955i			0.804415i	−0.915549	+	0.402208i	$0.868243\pi$
$308$		0			0
$309$	−450.446			−1.45775
$310$		0			0
$311$	−294.487	−	170.022i	−0.946905	−	0.546696i	−0.0547867	−	0.998498i	$-0.517448\pi$
$311$	−294.487	−	170.022i	−0.946905	−	0.546696i	−0.892118	+	0.451802i	$0.850781\pi$
$312$		0			0
$313$	98.2049	−	56.6987i	0.313754	−	0.181146i	−0.334851	−	0.942271i	$-0.608686\pi$
$313$	98.2049	−	56.6987i	0.313754	−	0.181146i	0.648605	+	0.761125i	$0.275353\pi$
$314$		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	$-0.0418359\pi$
$317$	121.155	+	209.847i	0.382192	+	0.661976i	−0.609183	+	0.793030i	$0.708503\pi$
$318$		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	0.913861	−	0.406027i	$-0.133086\pi$
$331$	34.8544	+	60.3697i	0.105300	+	0.182386i	−0.808560	+	0.588413i	$0.799753\pi$
$332$		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	0.0911175	+	0.995840i	$0.470956\pi$
$347$	−283.452	+	490.953i	−0.816864	+	1.41485i	−0.907982	+	0.419010i	$0.862377\pi$
$348$		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	0.291892	−	0.956451i	$-0.405715\pi$
$353$	−137.837	−	79.5801i	−0.390472	−	0.225439i	−0.682365	+	0.731012i	$0.739048\pi$
$354$		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	$-0.0744902\pi$
$359$	102.513	+	177.557i	0.285550	+	0.494588i	−0.687192	+	0.726476i	$0.741157\pi$
$360$		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	$-0.334065\pi$
$367$	−1.46112	−	0.843577i	−0.00398125	−	0.00229858i	−0.501989	+	0.864874i	$0.667398\pi$
$368$		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	0.989265	+	0.146131i	$0.0466823\pi$
$373$	231.702	+	401.320i	0.621186	+	1.07593i	−0.368079	+	0.929795i	$0.619984\pi$
$374$		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	$-0.935696\pi$
$383$	−496.266	+	286.519i	−1.29573	+	0.748092i	−0.316069	+	0.948736i	$0.602363\pi$
$384$		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	$-0.852391\pi$
$389$	−23.2756	+	40.3146i	−0.0598346	+	0.103637i	0.834556	+	0.550922i	$0.185724\pi$
$390$		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	$-0.751330\pi$
$397$	−180.743	+	104.352i	−0.455273	+	0.262852i	0.254782	+	0.966999i	$0.417996\pi$
$398$		0			0
$399$	−49.0131	+	419.386i	−0.122840	+	1.05109i
$400$		0			0
$401$	110.595	+	191.556i	0.275798	+	0.477696i	0.970336	−	0.241760i	$-0.0777246\pi$
$401$	110.595	+	191.556i	0.275798	+	0.477696i	−0.694538	+	0.719456i	$0.744391\pi$
$402$		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	0.598604	−	0.801045i	$-0.295722\pi$
$409$	83.5098	+	48.2144i	0.204181	+	0.117884i	−0.394423	+	0.918929i	$0.629056\pi$
$410$		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	$-0.907902\pi$
$419$		−	239.093i		−	0.570627i	0.958434	−	0.285313i	$-0.0920977\pi$
$420$		0			0
$421$	−508.228			−1.20719			−0.603596	−	0.797290i	$-0.706266\pi$
$421$	−508.228			−1.20719			−0.603596	+	0.797290i	$0.706266\pi$
$422$		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	−0.276329	−	0.961063i	$-0.589118\pi$
$431$	299.174	−	518.185i	0.694140	−	1.20229i	0.970470	−	0.241223i	$-0.0775486\pi$
$432$		0			0
$433$		−	283.405i		−	0.654516i	−0.944935	−	0.327258i	$-0.893875\pi$
$433$		−	283.405i		−	0.654516i	0.944935	−	0.327258i	$-0.106125\pi$
$434$		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	$-0.539118\pi$
$439$	296.596	−	171.240i	0.675618	−	0.390068i	0.798202	+	0.602390i	$0.205785\pi$
$440$		0			0
$441$	−64.3285	−	214.849i	−0.145870	−	0.487187i
$442$		0			0
$443$	293.909	+	509.065i	0.663451	+	1.14913i	0.979703	+	0.200455i	$0.0642421\pi$
$443$	293.909	+	509.065i	0.663451	+	1.14913i	−0.316252	+	0.948675i	$0.602425\pi$
$444$		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	0.997206	−	0.0747039i	$-0.0238012\pi$
$457$	198.296	+	343.458i	0.433907	+	0.751550i	−0.563298	+	0.826254i	$0.690468\pi$
$458$		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	$-0.475108\pi$
$463$	72.3400			0.156242			0.0781210	+	0.996944i	$0.475108\pi$
$464$		0			0
$465$	70.2572	+	40.5630i	0.151091	+	0.0872323i
$466$		0			0
$467$	453.684	−	261.935i	0.971487	−	0.560888i	0.0717975	−	0.997419i	$-0.477126\pi$
$467$	453.684	−	261.935i	0.971487	−	0.560888i	0.899689	+	0.436531i	$0.143793\pi$
$468$		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	−0.999066	−	0.0432203i	$-0.986238\pi$
$479$	−735.758	−	424.790i	−1.53603	−	0.886826i	−0.536963	−	0.843606i	$-0.680428\pi$
$480$		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	$-0.696485\pi$
$487$	202.982	−	351.574i	0.416800	−	0.721919i	0.995616	+	0.0935398i	$0.0298182\pi$
$488$		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	0.720680	−	0.693268i	$-0.243830\pi$
$499$	−119.784	−	207.472i	−0.240048	−	0.415775i	−0.960728	+	0.277493i	$0.910496\pi$
$500$		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	$-0.762307\pi$
$509$	−260.924	+	150.644i	−0.512621	+	0.295962i	0.221290	+	0.975208i	$0.428973\pi$
$510$		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	0.385752	−	0.922602i	$-0.373942\pi$
$521$	−114.812	−	66.2868i	−0.220369	−	0.127230i	−0.606121	+	0.795372i	$0.707275\pi$
$522$		0			0
$523$	−96.1291	+	55.5001i	−0.183803	+	0.106119i	−0.589078	−	0.808076i	$-0.700509\pi$
$523$	−96.1291	+	55.5001i	−0.183803	+	0.106119i	0.405275	+	0.914195i	$0.367176\pi$
$524$		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	$-0.141427\pi$
$541$	42.8522	+	74.2221i	0.0792092	+	0.137194i	−0.823700	+	0.567026i	$0.808094\pi$
$542$		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	−0.287964	−	0.957641i	$-0.592978\pi$
$557$	381.745	−	661.202i	0.685359	−	1.18708i	0.973324	−	0.229436i	$-0.0736882\pi$
$558$		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	0.747550	−	0.664205i	$-0.231230\pi$
$563$	307.458	+	177.511i	0.546107	+	0.315295i	−0.201444	+	0.979500i	$0.564563\pi$
$564$		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	0.535962	−	0.844242i	$-0.319949\pi$
$569$	−263.535	−	456.455i	−0.463154	−	0.802206i	−0.999116	+	0.0420357i	$0.986616\pi$
$570$		0			0
$571$	−257.886	+	446.671i	−0.451639	+	0.782262i	−0.998488	−	0.0549695i	$-0.982494\pi$
$571$	−257.886	+	446.671i	−0.451639	+	0.782262i	0.546849	+	0.837231i	$0.315827\pi$
$572$		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	0.649374	−	0.760469i	$-0.275031\pi$
$577$	182.029	+	105.095i	0.315476	+	0.182140i	−0.333898	+	0.942609i	$0.608364\pi$
$578$		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	$0.0249371\pi$
$587$			91.8797i			0.156524i	−0.996933	+	0.0782621i	$0.975063\pi$
$588$		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	−0.790575	−	0.612366i	$-0.790218\pi$
$593$	−388.734	+	224.436i	−0.655538	+	0.378475i	0.135037	+	0.990841i	$0.456885\pi$
$594$		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	$-0.886105\pi$
$599$	−98.8525	+	171.218i	−0.165029	+	0.285839i	0.771636	+	0.636064i	$0.219439\pi$
$600$		0			0
$601$		−	232.075i		−	0.386148i	−0.981184	−	0.193074i	$-0.938154\pi$
$601$		−	232.075i		−	0.386148i	0.981184	−	0.193074i	$-0.0618458\pi$
$602$		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	$-0.430745\pi$
$607$	709.823	−	409.816i	1.16940	−	0.675151i	0.953538	+	0.301274i	$0.0974119\pi$
$608$		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	0.318319	+	0.947984i	$0.396882\pi$
$613$	−405.695	+	702.684i	−0.661819	+	1.14630i	−0.980137	+	0.198320i	$0.936451\pi$
$614$		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	0.0679258	−	0.997690i	$-0.478362\pi$
$619$	−471.762	−	272.372i	−0.762136	−	0.440020i	−0.830062	+	0.557671i	$0.811695\pi$
$620$		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	$-0.604739\pi$
$631$	−407.805			−0.646284			−0.323142	+	0.946350i	$0.604739\pi$
$632$		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	0.496341	+	0.868128i	$0.334677\pi$
$641$	−322.840	+	559.175i	−0.503650	+	0.872347i	−0.999991	+	0.00421968i	$0.998657\pi$
$642$		0			0
$643$		−	932.869i		−	1.45081i	−0.688324	−	0.725403i	$-0.741653\pi$
$643$		−	932.869i		−	1.45081i	0.688324	−	0.725403i	$-0.258347\pi$
$644$		0			0
$645$	575.397			0.892089
$646$		0			0
$647$	−420.287	−	242.653i	−0.649594	−	0.375043i	0.138707	−	0.990333i	$-0.455705\pi$
$647$	−420.287	−	242.653i	−0.649594	−	0.375043i	−0.788301	+	0.615290i	$0.789039\pi$
$648$		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	$-0.255858\pi$
$653$	−180.587	−	312.786i	−0.276550	−	0.478998i	−0.970525	+	0.241001i	$0.922524\pi$
$654$		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	$-0.480541\pi$
$661$	−510.800	−	294.910i	−0.772768	−	0.446158i	−0.833861	+	0.551974i	$0.813875\pi$
$662$		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	$-0.776929\pi$
$677$	−398.113	+	229.851i	−0.588055	+	0.339514i	0.176273	+	0.984341i	$0.443596\pi$
$678$		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	0.0855985	+	0.996330i	$0.472720\pi$
$683$	−560.093	+	970.109i	−0.820048	+	1.42036i	−0.905646	+	0.424034i	$0.860614\pi$
$684$		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	−0.207710	−	0.978190i	$-0.566601\pi$
$691$	370.080	−	213.666i	0.535572	−	0.309213i	0.743283	+	0.668978i	$0.233268\pi$
$692$		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	$-0.477289\pi$
$701$	99.9460			0.142576			0.0712882	+	0.997456i	$0.477289\pi$
$702$		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	$-0.157872\pi$
$709$	19.5862	+	33.9244i	0.0276252	+	0.0478482i	−0.851882	+	0.523733i	$0.824539\pi$
$710$		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	$-0.847028\pi$
$719$	−668.482	+	385.948i	−0.929739	+	0.536785i	−0.0430100	+	0.999075i	$0.513695\pi$
$720$		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	$-0.646006\pi$
$733$	82.3471	−	47.5431i	0.112343	−	0.0648610i	0.555118	+	0.831771i	$0.312673\pi$
$734$		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	0.156243	+	0.987719i	$0.450062\pi$
$739$	−574.401	+	994.892i	−0.777268	+	1.34627i	−0.933511	+	0.358549i	$0.883271\pi$
$740$		0			0
$741$		−	1526.54i		−	2.06011i
$742$		0			0
$743$	232.652			0.313126			0.156563	−	0.987668i	$-0.449959\pi$
$743$	232.652			0.313126			0.156563	+	0.987668i	$0.449959\pi$
$744$		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	$-0.317682\pi$
$751$	−343.079	−	594.230i	−0.456829	−	0.791252i	−0.998791	+	0.0491513i	$0.984348\pi$
$752$		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	$-0.642894\pi$
$757$	−657.058			−0.867976			−0.433988	+	0.900919i	$0.642894\pi$
$758$		0			0
$759$	−132.512	−	76.5058i	−0.174588	−	0.100798i
$760$		0			0
$761$	−1063.63	+	614.086i	−1.39767	+	0.806946i	−0.994148	−	0.108024i	$-0.965548\pi$
$761$	−1063.63	+	614.086i	−1.39767	+	0.806946i	−0.403523	+	0.914970i	$0.632214\pi$
$762$		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	$-0.894761\pi$
$769$		−	499.279i		−	0.649257i	0.945842	−	0.324629i	$-0.105239\pi$
$770$		0			0
$771$	−1776.12			−2.30366
$772$		0			0
$773$	277.318	+	160.110i	0.358756	+	0.207128i	0.668535	−	0.743681i	$-0.266922\pi$
$773$	277.318	+	160.110i	0.358756	+	0.207128i	−0.309779	+	0.950809i	$0.600255\pi$
$774$		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	0.154535	−	0.987987i	$-0.450612\pi$
$787$	−490.946	−	283.448i	−0.623820	−	0.360162i	−0.778355	+	0.627825i	$0.783945\pi$
$788$		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	−0.373791	−	0.927513i	$-0.621942\pi$
$809$	498.631	−	863.654i	0.616354	−	1.06756i	0.990145	−	0.140044i	$-0.0447244\pi$
$810$		0			0
$811$		−	1201.56i		−	1.48158i	−0.671735	−	0.740792i	$-0.734450\pi$
$811$		−	1201.56i		−	1.48158i	0.671735	−	0.740792i	$-0.265550\pi$
$812$		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	$-0.202760\pi$
$821$	−92.8952	−	160.899i	−0.113149	−	0.195980i	−0.917038	+	0.398799i	$0.869427\pi$
$822$		0			0
$823$	−429.451	+	743.831i	−0.521812	+	0.903805i	0.477866	+	0.878433i	$0.341410\pi$
$823$	−429.451	+	743.831i	−0.521812	+	0.903805i	−0.999678	+	0.0253721i	$0.991923\pi$
$824$		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	$-0.537275\pi$
$829$	−858.304	−	495.542i	−1.03535	−	0.597759i	−0.918512	+	0.395392i	$0.870609\pi$
$830$		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	−0.985645	−	0.168831i	$-0.946001\pi$
$857$	−1392.35	−	803.874i	−1.62468	−	0.938009i	−0.639034	−	0.769178i	$-0.720666\pi$
$858$		0			0
$859$	−131.880	+	76.1410i	−0.153527	+	0.0886391i	−0.574796	−	0.818297i	$-0.694918\pi$
$859$	−131.880	+	76.1410i	−0.153527	+	0.0886391i	0.421268	+	0.906936i	$0.361585\pi$
$860$		0			0
$861$	1111.26	+	827.277i	1.29066	+	0.960833i
$862$		0			0
$863$	480.137	+	831.622i	0.556358	+	0.963641i	0.997796	+	0.0663494i	$0.0211352\pi$
$863$	480.137	+	831.622i	0.556358	+	0.963641i	−0.441438	+	0.897292i	$0.645531\pi$
$864$		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	$-0.164500\pi$
$877$	5.97052	+	10.3413i	0.00680790	+	0.0117916i	−0.862601	+	0.505884i	$0.831166\pi$
$878$		0			0
$879$	362.027	−	627.049i	0.411862	−	0.713366i
$880$		0			0
$881$		−	625.457i		−	0.709940i	−0.934878	−	0.354970i	$-0.884491\pi$
$881$		−	625.457i		−	0.709940i	0.934878	−	0.354970i	$-0.115509\pi$
$882$		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	$-0.531339\pi$
$887$	633.661	−	365.844i	0.714387	−	0.412451i	0.812683	+	0.582706i	$0.198006\pi$
$888$		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	−0.934364	−	0.356319i	$-0.884032\pi$
$907$	−143.851	+	249.157i	−0.158601	+	0.274704i	0.775764	+	0.631024i	$0.217365\pi$
$908$		0			0
$909$		−	95.2922i		−	0.104832i
$910$		0			0
$911$	−249.315			−0.273672			−0.136836	−	0.990594i	$-0.543693\pi$
$911$	−249.315			−0.273672			−0.136836	+	0.990594i	$0.543693\pi$
$912$		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	$-0.163183\pi$
$919$	10.0575	+	17.4201i	0.0109440	+	0.0189555i	−0.860502	+	0.509448i	$0.829850\pi$
$920$		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	−0.948664	−	0.316286i	$-0.897564\pi$
$929$	−1067.50	+	616.321i	−1.14908	+	0.663424i	−0.200420	+	0.979710i	$0.564231\pi$
$930$		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	$-0.951602\pi$
$937$		−	283.840i		−	0.302924i	0.988463	−	0.151462i	$-0.0483981\pi$
$938$		0			0
$939$	−417.835			−0.444979
$940$		0			0
$941$	−561.263	−	324.045i	−0.596453	−	0.344362i	0.171192	−	0.985238i	$-0.445238\pi$
$941$	−561.263	−	324.045i	−0.596453	−	0.344362i	−0.767645	+	0.640875i	$0.778572\pi$
$942$		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	0.817962	+	0.575272i	$0.195104\pi$
$947$	859.101	+	1488.01i	0.907181	+	1.57128i	0.0892196	+	0.996012i	$0.471563\pi$
$948$		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	$-0.667144\pi$
$967$	−969.512			−1.00260			−0.501299	+	0.865274i	$0.667144\pi$
$968$		0			0
$969$	186.192	+	107.498i	0.192149	+	0.110937i
$970$		0			0
$971$	724.959	−	418.555i	0.746611	−	0.431056i	−0.0778571	−	0.996965i	$-0.524808\pi$
$971$	724.959	−	418.555i	0.746611	−	0.431056i	0.824468	+	0.565908i	$0.191474\pi$
$972$		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	0.273675	+	0.961822i	$0.411761\pi$
$977$	−680.114	+	1177.99i	−0.696125	+	1.20572i	−0.969800	+	0.243901i	$0.921573\pi$
$978$		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	$-0.268566\pi$
$983$	344.050	+	198.637i	0.350000	+	0.202073i	−0.314685	+	0.949196i	$0.601899\pi$
$984$		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	$-0.878209\pi$
$991$	−139.250	+	241.188i	−0.140514	+	0.243378i	0.787176	+	0.616728i	$0.211542\pi$
$992$		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	$-0.197135\pi$
$997$	716.547	+	413.699i	0.718703	+	0.414943i	−0.0955720	+	0.995423i	$0.530468\pi$
$998$		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	448.3.s.g.129.2		16
4.3	odd	2	inner	448.3.s.g.129.7		16
7.5	odd	6	inner	448.3.s.g.257.2		16
8.3	odd	2		224.3.s.a.129.2	yes	16
8.5	even	2		224.3.s.a.129.7	yes	16
28.19	even	6	inner	448.3.s.g.257.7		16
56.3	even	6		1568.3.c.h.97.4		16
56.5	odd	6		224.3.s.a.33.7	yes	16
56.11	odd	6		1568.3.c.h.97.13		16
56.19	even	6		224.3.s.a.33.2	✓	16
56.45	odd	6		1568.3.c.h.97.14		16
56.53	even	6		1568.3.c.h.97.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.a.33.2	✓	16	56.19	even	6
224.3.s.a.33.7	yes	16	56.5	odd	6
224.3.s.a.129.2	yes	16	8.3	odd	2
224.3.s.a.129.7	yes	16	8.5	even	2
448.3.s.g.129.2		16	1.1	even	1	trivial
448.3.s.g.129.7		16	4.3	odd	2	inner
448.3.s.g.257.2		16	7.5	odd	6	inner
448.3.s.g.257.7		16	28.19	even	6	inner
1568.3.c.h.97.3		16	56.53	even	6
1568.3.c.h.97.4		16	56.3	even	6
1568.3.c.h.97.13		16	56.11	odd	6
1568.3.c.h.97.14		16	56.45	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.s (of order \(6\), degree \(2\), not 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

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