LMFDB - Embedded newform 224.3.o.d.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(79,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("224.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.o (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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} + \cdots + 4 $ x^12 - 3x^11 - 4x^10 + 3x^9 + 86x^8 - 163x^7 + 155x^6 - 166x^5 + 164x^4 - 116x^3 + 60x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.2
Root			$0.121721 + 0.507075i$ of defining polynomial
Character	$\chi$	$=$	224.79
Dual form			224.3.o.d.207.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99052 - 3.44767i) q^{3} +(1.63031 + 0.941260i) q^{5} +(5.14749 - 4.74377i) q^{7} +(-3.42430 + 5.93106i) q^{9} +O(q^{10})$	\(q+(-1.99052 - 3.44767i) q^{3} +(1.63031 + 0.941260i) q^{5} +(5.14749 - 4.74377i) q^{7} +(-3.42430 + 5.93106i) q^{9} +(-3.93973 - 6.82381i) q^{11} -11.4863i q^{13} -7.49437i q^{15} +(1.44921 + 2.51011i) q^{17} +(-15.0223 + 26.0194i) q^{19} +(-26.6011 - 8.30431i) q^{21} +(-33.3838 - 19.2741i) q^{23} +(-10.7281 - 18.5815i) q^{25} -8.56478 q^{27} -27.8701i q^{29} +(19.4709 - 11.2416i) q^{31} +(-15.6842 + 27.1658i) q^{33} +(12.8571 - 2.88869i) q^{35} +(39.4520 + 22.7776i) q^{37} +(-39.6011 + 22.8637i) q^{39} -40.6313 q^{41} +47.2806 q^{43} +(-11.1653 + 6.44632i) q^{45} +(71.5172 + 41.2905i) q^{47} +(3.99327 - 48.8370i) q^{49} +(5.76936 - 9.99283i) q^{51} +(23.2823 - 13.4420i) q^{53} -14.8332i q^{55} +119.609 q^{57} +(-5.20555 - 9.01627i) q^{59} +(19.1932 + 11.0812i) q^{61} +(10.5091 + 46.7742i) q^{63} +(10.8116 - 18.7263i) q^{65} +(-29.6549 - 51.3639i) q^{67} +153.462i q^{69} -38.2541i q^{71} +(-6.98890 - 12.1051i) q^{73} +(-42.7087 + 73.9737i) q^{75} +(-52.6503 - 16.4363i) q^{77} +(44.3314 + 25.5948i) q^{79} +(47.8670 + 82.9081i) q^{81} +89.4458 q^{83} +5.45635i q^{85} +(-96.0871 + 55.4759i) q^{87} +(-52.6288 + 91.1558i) q^{89} +(-54.4885 - 59.1258i) q^{91} +(-77.5144 - 44.7530i) q^{93} +(-48.9821 + 28.2798i) q^{95} +55.3301 q^{97} +53.9633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 40 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 - 40 * q^9	$ 12 q + 6 q^{3} - 40 q^{9} - 30 q^{11} + 30 q^{17} - 78 q^{19} - 92 q^{25} - 156 q^{27} - 78 q^{33} + 222 q^{35} - 232 q^{41} + 200 q^{43} + 372 q^{49} - 10 q^{51} + 332 q^{57} + 110 q^{59} - 32 q^{65} - 434 q^{67} + 102 q^{73} + 60 q^{75} - 82 q^{81} + 536 q^{83} + 214 q^{89} + 8 q^{91} - 152 q^{97} - 504 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 40 * q^9 - 30 * q^11 + 30 * q^17 - 78 * q^19 - 92 * q^25 - 156 * q^27 - 78 * q^33 + 222 * q^35 - 232 * q^41 + 200 * q^43 + 372 * q^49 - 10 * q^51 + 332 * q^57 + 110 * q^59 - 32 * q^65 - 434 * q^67 + 102 * q^73 + 60 * q^75 - 82 * q^81 + 536 * q^83 + 214 * q^89 + 8 * q^91 - 152 * q^97 - 504 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.99052	−	3.44767i	−0.663505	−	1.14922i	−0.979688	−	0.200526i	$-0.935735\pi$
$3$	−1.99052	−	3.44767i	−0.663505	−	1.14922i	0.316183	−	0.948698i	$-0.397599\pi$
$4$		0			0
$5$	1.63031	+	0.941260i	0.326062	+	0.188252i	0.654091	−	0.756416i	$-0.273051\pi$
$5$	1.63031	+	0.941260i	0.326062	+	0.188252i	−0.328029	+	0.944668i	$0.606384\pi$
$6$		0			0
$7$	5.14749	−	4.74377i	0.735355	−	0.677682i
$7$	5.14749	−	4.74377i	0.735355	−	0.677682i
$8$		0			0
$9$	−3.42430	+	5.93106i	−0.380478	+	0.659007i
$10$		0			0
$11$	−3.93973	−	6.82381i	−0.358157	−	0.620346i	0.629496	−	0.777004i	$-0.283261\pi$
$11$	−3.93973	−	6.82381i	−0.358157	−	0.620346i	−0.987653	+	0.156658i	$0.949928\pi$
$12$		0			0
$13$		−	11.4863i		−	0.883564i	−0.897122	−	0.441782i	$-0.854346\pi$
$13$		−	11.4863i		−	0.883564i	0.897122	−	0.441782i	$-0.145654\pi$
$14$		0			0
$15$		−	7.49437i		−	0.499625i
$16$		0			0
$17$	1.44921	+	2.51011i	0.0852478	+	0.147654i	0.905497	−	0.424353i	$-0.139498\pi$
$17$	1.44921	+	2.51011i	0.0852478	+	0.147654i	−0.820249	+	0.572007i	$0.806165\pi$
$18$		0			0
$19$	−15.0223	+	26.0194i	−0.790649	+	1.36944i	0.134916	+	0.990857i	$0.456923\pi$
$19$	−15.0223	+	26.0194i	−0.790649	+	1.36944i	−0.925566	+	0.378587i	$0.876410\pi$
$20$		0			0
$21$	−26.6011	−	8.30431i	−1.26672	−	0.395443i
$22$		0			0
$23$	−33.3838	−	19.2741i	−1.45147	−	0.838006i	−0.452904	−	0.891559i	$-0.649612\pi$
$23$	−33.3838	−	19.2741i	−1.45147	−	0.838006i	−0.998565	+	0.0535530i	$0.982945\pi$
$24$		0			0
$25$	−10.7281	−	18.5815i	−0.429122	−	0.743262i
$26$		0			0
$27$	−8.56478			−0.317214
$28$		0			0
$29$		−	27.8701i		−	0.961039i	−0.876984	−	0.480519i	$-0.840448\pi$
$29$		−	27.8701i		−	0.961039i	0.876984	−	0.480519i	$-0.159552\pi$
$30$		0			0
$31$	19.4709	−	11.2416i	0.628095	−	0.362631i	−0.151919	−	0.988393i	$-0.548545\pi$
$31$	19.4709	−	11.2416i	0.628095	−	0.362631i	0.780014	+	0.625762i	$0.215212\pi$
$32$		0			0
$33$	−15.6842	+	27.1658i	−0.475278	+	0.823206i
$34$		0			0
$35$	12.8571	−	2.88869i	0.367346	−	0.0825341i
$36$		0			0
$37$	39.4520	+	22.7776i	1.06627	+	0.615611i	0.927160	−	0.374666i	$-0.122243\pi$
$37$	39.4520	+	22.7776i	1.06627	+	0.615611i	0.139109	+	0.990277i	$0.455576\pi$
$38$		0			0
$39$	−39.6011	+	22.8637i	−1.01541	+	0.586249i
$40$		0			0
$41$	−40.6313			−0.991007			−0.495503	−	0.868606i	$-0.665016\pi$
$41$	−40.6313			−0.991007			−0.495503	+	0.868606i	$0.665016\pi$
$42$		0			0
$43$	47.2806			1.09955			0.549774	−	0.835313i	$-0.314714\pi$
$43$	47.2806			1.09955			0.549774	+	0.835313i	$0.314714\pi$
$44$		0			0
$45$	−11.1653	+	6.44632i	−0.248119	+	0.143251i
$46$		0			0
$47$	71.5172	+	41.2905i	1.52164	+	0.878520i	0.999673	+	0.0255554i	$0.00813541\pi$
$47$	71.5172	+	41.2905i	1.52164	+	0.878520i	0.521968	+	0.852965i	$0.325198\pi$
$48$		0			0
$49$	3.99327	−	48.8370i	0.0814954	−	0.996674i
$50$		0			0
$51$	5.76936	−	9.99283i	0.113125	−	0.195938i
$52$		0			0
$53$	23.2823	−	13.4420i	0.439288	−	0.253623i	−0.264007	−	0.964521i	$-0.585044\pi$
$53$	23.2823	−	13.4420i	0.439288	−	0.253623i	0.703296	+	0.710897i	$0.251711\pi$
$54$		0			0
$55$		−	14.8332i		−	0.269695i
$56$		0			0
$57$	119.609			2.09840
$58$		0			0
$59$	−5.20555	−	9.01627i	−0.0882296	−	0.152818i	0.818533	−	0.574459i	$-0.194788\pi$
$59$	−5.20555	−	9.01627i	−0.0882296	−	0.152818i	−0.906763	+	0.421641i	$0.861454\pi$
$60$		0			0
$61$	19.1932	+	11.0812i	0.314642	+	0.181659i	0.649002	−	0.760787i	$-0.275187\pi$
$61$	19.1932	+	11.0812i	0.314642	+	0.181659i	−0.334360	+	0.942446i	$0.608520\pi$
$62$		0			0
$63$	10.5091	+	46.7742i	0.166810	+	0.742447i
$64$		0			0
$65$	10.8116	−	18.7263i	0.166333	−	0.288097i
$66$		0			0
$67$	−29.6549	−	51.3639i	−0.442611	−	0.766625i	0.555271	−	0.831669i	$-0.312614\pi$
$67$	−29.6549	−	51.3639i	−0.442611	−	0.766625i	−0.997882	+	0.0650444i	$0.979281\pi$
$68$		0			0
$69$			153.462i			2.22409i
$70$		0			0
$71$		−	38.2541i		−	0.538791i	−0.963030	−	0.269395i	$-0.913176\pi$
$71$		−	38.2541i		−	0.538791i	0.963030	−	0.269395i	$-0.0868238\pi$
$72$		0			0
$73$	−6.98890	−	12.1051i	−0.0957383	−	0.165824i	0.814178	−	0.580615i	$-0.197188\pi$
$73$	−6.98890	−	12.1051i	−0.0957383	−	0.165824i	−0.909917	+	0.414791i	$0.863855\pi$
$74$		0			0
$75$	−42.7087	+	73.9737i	−0.569450	+	0.986316i
$76$		0			0
$77$	−52.6503	−	16.4363i	−0.683770	−	0.213459i
$78$		0			0
$79$	44.3314	+	25.5948i	0.561157	+	0.323984i	0.753610	−	0.657322i	$-0.228311\pi$
$79$	44.3314	+	25.5948i	0.561157	+	0.323984i	−0.192453	+	0.981306i	$0.561644\pi$
$80$		0			0
$81$	47.8670	+	82.9081i	0.590951	+	1.02356i
$82$		0			0
$83$	89.4458			1.07766			0.538830	−	0.842414i	$-0.318866\pi$
$83$	89.4458			1.07766			0.538830	+	0.842414i	$0.318866\pi$
$84$		0			0
$85$			5.45635i			0.0641923i
$86$		0			0
$87$	−96.0871	+	55.4759i	−1.10445	+	0.637654i
$88$		0			0
$89$	−52.6288	+	91.1558i	−0.591335	+	1.02422i	0.402718	+	0.915324i	$0.368066\pi$
$89$	−52.6288	+	91.1558i	−0.591335	+	1.02422i	−0.994053	+	0.108898i	$0.965268\pi$
$90$		0			0
$91$	−54.4885	−	59.1258i	−0.598775	−	0.649734i
$92$		0			0
$93$	−77.5144	−	44.7530i	−0.833488	−	0.481215i
$94$		0			0
$95$	−48.9821	+	28.2798i	−0.515601	+	0.297683i
$96$		0			0
$97$	55.3301			0.570413			0.285206	−	0.958466i	$-0.407938\pi$
$97$	55.3301			0.570413			0.285206	+	0.958466i	$0.407938\pi$
$98$		0			0
$99$	53.9633			0.545084
$100$		0			0
$101$	−27.2216	+	15.7164i	−0.269521	+	0.155608i	−0.628670	−	0.777672i	$-0.716400\pi$
$101$	−27.2216	+	15.7164i	−0.269521	+	0.155608i	0.359149	+	0.933280i	$0.383067\pi$
$102$		0			0
$103$	69.2701	+	39.9931i	0.672525	+	0.388283i	0.797033	−	0.603936i	$-0.206402\pi$
$103$	69.2701	+	39.9931i	0.672525	+	0.388283i	−0.124508	+	0.992219i	$0.539735\pi$
$104$		0			0
$105$	−35.5516	−	38.5772i	−0.338586	−	0.367402i
$106$		0			0
$107$	24.3817	−	42.2303i	0.227866	−	0.394676i	−0.729309	−	0.684184i	$-0.760158\pi$
$107$	24.3817	−	42.2303i	0.227866	−	0.394676i	0.957175	+	0.289508i	$0.0934918\pi$
$108$		0			0
$109$	99.6528	−	57.5346i	0.914246	−	0.527840i	0.0324509	−	0.999473i	$-0.489669\pi$
$109$	99.6528	−	57.5346i	0.914246	−	0.527840i	0.881795	+	0.471633i	$0.156335\pi$
$110$		0			0
$111$		−	181.357i		−	1.63384i
$112$		0			0
$113$	−55.7570			−0.493425			−0.246712	−	0.969089i	$-0.579350\pi$
$113$	−55.7570			−0.493425			−0.246712	+	0.969089i	$0.579350\pi$
$114$		0			0
$115$	−36.2840	−	62.8457i	−0.315513	−	0.546484i
$116$		0			0
$117$	68.1262	+	39.3327i	0.582275	+	0.336177i
$118$		0			0
$119$	19.3672	+	6.04603i	0.162750	+	0.0508070i
$120$		0			0
$121$	29.4571	−	51.0212i	0.243447	−	0.421663i
$122$		0			0
$123$	80.8772	+	140.083i	0.657538	+	1.13889i
$124$		0			0
$125$		−	87.4546i		−	0.699637i
$126$		0			0
$127$			35.6964i			0.281074i	0.990075	+	0.140537i	$0.0448828\pi$
$127$			35.6964i			0.281074i	−0.990075	+	0.140537i	$0.955117\pi$
$128$		0			0
$129$	−94.1127	−	163.008i	−0.729556	−	1.26363i
$130$		0			0
$131$	−60.6462	+	105.042i	−0.462948	+	0.801849i	−0.999106	−	0.0422680i	$-0.986542\pi$
$131$	−60.6462	+	105.042i	−0.462948	+	0.801849i	0.536158	+	0.844117i	$0.319875\pi$
$132$		0			0
$133$	46.1030	+	205.197i	0.346639	+	1.54284i
$134$		0			0
$135$	−13.9632	−	8.06168i	−0.103431	−	0.0597162i
$136$		0			0
$137$	4.24835	+	7.35836i	0.0310099	+	0.0537107i	0.881114	−	0.472904i	$-0.156794\pi$
$137$	4.24835	+	7.35836i	0.0310099	+	0.0537107i	−0.850104	+	0.526615i	$0.823461\pi$
$138$		0			0
$139$	3.05942			0.0220102			0.0110051	−	0.999939i	$-0.496497\pi$
$139$	3.05942			0.0220102			0.0110051	+	0.999939i	$0.496497\pi$
$140$		0			0
$141$		−	328.757i		−	2.33161i
$142$		0			0
$143$	−78.3806	+	45.2530i	−0.548116	+	0.316455i
$144$		0			0
$145$	26.2330	−	45.4370i	0.180918	−	0.313358i
$146$		0			0
$147$	−176.323	+	83.4433i	−1.19947	+	0.567642i
$148$		0			0
$149$	−27.4740	−	15.8621i	−0.184389	−	0.106457i	0.404964	−	0.914333i	$-0.367284\pi$
$149$	−27.4740	−	15.8621i	−0.184389	−	0.106457i	−0.589353	+	0.807876i	$0.700617\pi$
$150$		0			0
$151$	219.621	−	126.798i	1.45444	−	0.839723i	0.455713	−	0.890127i	$-0.349384\pi$
$151$	219.621	−	126.798i	1.45444	−	0.839723i	0.998729	+	0.0504039i	$0.0160509\pi$
$152$		0			0
$153$	−19.8502			−0.129740
$154$		0			0
$155$	42.3249			0.273064
$156$		0			0
$157$	42.7187	−	24.6636i	0.272093	−	0.157093i	−0.357745	−	0.933819i	$-0.616454\pi$
$157$	42.7187	−	24.6636i	0.272093	−	0.157093i	0.629839	+	0.776726i	$0.283121\pi$
$158$		0			0
$159$	−92.6875	−	53.5132i	−0.582940	−	0.336561i
$160$		0			0
$161$	−263.275	+	59.1516i	−1.63525	+	0.367402i
$162$		0			0
$163$	57.8597	−	100.216i	0.354967	−	0.614821i	−0.632145	−	0.774850i	$-0.717825\pi$
$163$	57.8597	−	100.216i	0.354967	−	0.614821i	0.987112	+	0.160029i	$0.0511587\pi$
$164$		0			0
$165$	−51.1401	+	29.5258i	−0.309940	+	0.178944i
$166$		0			0
$167$			32.3859i			0.193928i	0.995288	+	0.0969639i	$0.0309131\pi$
$167$			32.3859i			0.193928i	−0.995288	+	0.0969639i	$0.969087\pi$
$168$		0			0
$169$	37.0641			0.219314
$170$		0			0
$171$	−102.882	−	178.197i	−0.601649	−	1.04209i
$172$		0			0
$173$	−179.479	−	103.622i	−1.03745	−	0.598973i	−0.118341	−	0.992973i	$-0.537758\pi$
$173$	−179.479	−	103.622i	−1.03745	−	0.598973i	−0.919110	+	0.394000i	$0.871091\pi$
$174$		0			0
$175$	−143.369	−	44.7568i	−0.819252	−	0.255753i
$176$		0			0
$177$	−20.7234	+	35.8941i	−0.117082	+	0.202791i
$178$		0			0
$179$	87.0837	+	150.833i	0.486501	+	0.842644i	0.999880	−	0.0155178i	$-0.00493966\pi$
$179$	87.0837	+	150.833i	0.486501	+	0.842644i	−0.513379	+	0.858162i	$0.671606\pi$
$180$		0			0
$181$		−	204.244i		−	1.12842i	−0.825632	−	0.564209i	$-0.809181\pi$
$181$		−	204.244i		−	1.12842i	0.825632	−	0.564209i	$-0.190819\pi$
$182$		0			0
$183$		−	88.2291i		−	0.482126i
$184$		0			0
$185$	42.8793	+	74.2691i	0.231780	+	0.401455i
$186$		0			0
$187$	11.4190	−	19.7783i	0.0610642	−	0.105766i
$188$		0			0
$189$	−44.0871	+	40.6293i	−0.233265	+	0.214970i
$190$		0			0
$191$	−258.518	−	149.255i	−1.35350	−	0.781442i	−0.364759	−	0.931102i	$-0.618849\pi$
$191$	−258.518	−	149.255i	−1.35350	−	0.781442i	−0.988737	+	0.149660i	$0.952182\pi$
$192$		0			0
$193$	165.381	+	286.448i	0.856896	+	1.48419i	0.874875	+	0.484349i	$0.160943\pi$
$193$	165.381	+	286.448i	0.856896	+	1.48419i	−0.0179791	+	0.999838i	$0.505723\pi$
$194$		0			0
$195$	−86.0828			−0.441450
$196$		0			0
$197$			327.309i			1.66146i	0.556672	+	0.830732i	$0.312078\pi$
$197$			327.309i			1.66146i	−0.556672	+	0.830732i	$0.687922\pi$
$198$		0			0
$199$	11.0295	−	6.36789i	0.0554246	−	0.0319994i	−0.472032	−	0.881582i	$-0.656479\pi$
$199$	11.0295	−	6.36789i	0.0554246	−	0.0319994i	0.527456	+	0.849582i	$0.323146\pi$
$200$		0			0
$201$	−118.057	+	204.481i	−0.587349	+	1.01732i
$202$		0			0
$203$	−132.210	−	143.461i	−0.651278	−	0.706705i
$204$		0			0
$205$	−66.2416	−	38.2446i	−0.323130	−	0.186559i
$206$		0			0
$207$	228.632	−	132.001i	1.10450	−	0.637686i
$208$		0			0
$209$	236.736			1.13271
$210$		0			0
$211$	−120.455			−0.570875			−0.285437	−	0.958397i	$-0.592139\pi$
$211$	−120.455			−0.570875			−0.285437	+	0.958397i	$0.592139\pi$
$212$		0			0
$213$	−131.888	+	76.1454i	−0.619191	+	0.357490i
$214$		0			0
$215$	77.0820	+	44.5033i	0.358521	+	0.206992i
$216$		0			0
$217$	46.8991	−	150.231i	0.216125	−	0.692311i
$218$		0			0
$219$	−27.8230	+	48.1909i	−0.127046	+	0.220050i
$220$		0			0
$221$	28.8320	−	16.6461i	0.130461	−	0.0753219i
$222$		0			0
$223$			372.958i			1.67246i	0.548382	+	0.836228i	$0.315244\pi$
$223$			372.958i			1.67246i	−0.548382	+	0.836228i	$0.684756\pi$
$224$		0			0
$225$	146.944			0.653086
$226$		0			0
$227$	36.7128	+	63.5885i	0.161730	+	0.280125i	0.935489	−	0.353355i	$-0.114959\pi$
$227$	36.7128	+	63.5885i	0.161730	+	0.280125i	−0.773759	+	0.633480i	$0.781626\pi$
$228$		0			0
$229$	367.587	+	212.226i	1.60518	+	0.926752i	0.990428	+	0.138034i	$0.0440783\pi$
$229$	367.587	+	212.226i	1.60518	+	0.926752i	0.614755	+	0.788718i	$0.289255\pi$
$230$		0			0
$231$	48.1342	+	214.238i	0.208373	+	0.927436i
$232$		0			0
$233$	41.7070	−	72.2386i	0.179000	−	0.310037i	−0.762538	−	0.646943i	$-0.776047\pi$
$233$	41.7070	−	72.2386i	0.179000	−	0.310037i	0.941538	+	0.336906i	$0.109380\pi$
$234$		0			0
$235$	77.7301	+	134.632i	0.330766	+	0.572904i
$236$		0			0
$237$		−	203.787i		−	0.859861i
$238$		0			0
$239$		−	112.561i		−	0.470967i	−0.971878	−	0.235484i	$-0.924333\pi$
$239$		−	112.561i		−	0.470967i	0.971878	−	0.235484i	$-0.0756674\pi$
$240$		0			0
$241$	−140.216	−	242.861i	−0.581809	−	1.00772i	−0.995265	−	0.0971992i	$-0.969012\pi$
$241$	−140.216	−	242.861i	−0.581809	−	1.00772i	0.413455	−	0.910524i	$-0.364322\pi$
$242$		0			0
$243$	152.019	−	263.304i	0.625591	−	1.08356i
$244$		0			0
$245$	52.4786	−	75.8608i	0.214198	−	0.309636i
$246$		0			0
$247$	298.868	+	172.552i	1.20999	+	0.698589i
$248$		0			0
$249$	−178.043	−	308.380i	−0.715033	−	1.23847i
$250$		0			0
$251$	32.9560			0.131299			0.0656493	−	0.997843i	$-0.479088\pi$
$251$	32.9560			0.131299			0.0656493	+	0.997843i	$0.479088\pi$
$252$		0			0
$253$			303.740i			1.20055i
$254$		0			0
$255$	18.8117	−	10.8609i	0.0737714	−	0.0425919i
$256$		0			0
$257$	112.109	−	194.179i	0.436223	−	0.755561i	−0.561172	−	0.827700i	$-0.689649\pi$
$257$	112.109	−	194.179i	0.436223	−	0.755561i	0.997395	+	0.0721390i	$0.0229825\pi$
$258$		0			0
$259$	311.130	−	69.9036i	1.20127	−	0.269898i
$260$		0			0
$261$	165.300	+	95.4357i	0.633332	+	0.365654i
$262$		0			0
$263$	−147.190	+	84.9804i	−0.559659	+	0.323119i	−0.753009	−	0.658011i	$-0.771398\pi$
$263$	−147.190	+	84.9804i	−0.559659	+	0.323119i	0.193350	+	0.981130i	$0.438065\pi$
$264$		0			0
$265$	50.6098			0.190980
$266$		0			0
$267$	419.034			1.56942
$268$		0			0
$269$	−93.9863	+	54.2630i	−0.349391	+	0.201721i	−0.664417	−	0.747362i	$-0.731320\pi$
$269$	−93.9863	+	54.2630i	−0.349391	+	0.201721i	0.315026	+	0.949083i	$0.397987\pi$
$270$		0			0
$271$	16.7690	+	9.68157i	0.0618781	+	0.0357253i	0.530620	−	0.847610i	$-0.321959\pi$
$271$	16.7690	+	9.68157i	0.0618781	+	0.0357253i	−0.468742	+	0.883335i	$0.655293\pi$
$272$		0			0
$273$	−95.3861	+	305.549i	−0.349400	+	1.11923i
$274$		0			0
$275$	−84.5313	+	146.412i	−0.307386	+	0.532409i
$276$		0			0
$277$	−112.104	+	64.7231i	−0.404707	+	0.233658i	−0.688513	−	0.725224i	$-0.741736\pi$
$277$	−112.104	+	64.7231i	−0.404707	+	0.233658i	0.283806	+	0.958882i	$0.408403\pi$
$278$		0			0
$279$			153.978i			0.551892i
$280$		0			0
$281$	83.3608			0.296658			0.148329	−	0.988938i	$-0.452611\pi$
$281$	83.3608			0.296658			0.148329	+	0.988938i	$0.452611\pi$
$282$		0			0
$283$	14.4646	+	25.0535i	0.0511118	+	0.0885282i	0.890449	−	0.455082i	$-0.150390\pi$
$283$	14.4646	+	25.0535i	0.0511118	+	0.0885282i	−0.839338	+	0.543611i	$0.817057\pi$
$284$		0			0
$285$	194.999	+	112.583i	0.684208	+	0.395028i
$286$		0			0
$287$	−209.149	+	192.746i	−0.728742	+	0.671587i
$288$		0			0
$289$	140.300	−	243.006i	0.485466	−	0.840851i
$290$		0			0
$291$	−110.135	−	190.760i	−0.378472	−	0.655533i
$292$		0			0
$293$			214.613i			0.732468i	0.930523	+	0.366234i	$0.119353\pi$
$293$			214.613i			0.732468i	−0.930523	+	0.366234i	$0.880647\pi$
$294$		0			0
$295$		−	19.5991i		−	0.0664376i
$296$		0			0
$297$	33.7429	+	58.4444i	0.113612	+	0.196783i
$298$		0			0
$299$	−221.389	+	383.457i	−0.740432	+	1.28247i
$300$		0			0
$301$	243.376	−	224.288i	0.808559	−	0.745144i
$302$		0			0
$303$	108.370	+	62.5675i	0.357657	+	0.206493i
$304$		0			0
$305$	20.8606	+	36.1316i	0.0683953	+	0.118464i
$306$		0			0
$307$	120.542			0.392644			0.196322	−	0.980539i	$-0.437100\pi$
$307$	120.542			0.392644			0.196322	+	0.980539i	$0.437100\pi$
$308$		0			0
$309$		−	318.427i		−	1.03051i
$310$		0			0
$311$	281.771	−	162.681i	0.906016	−	0.523089i	0.0268689	−	0.999639i	$-0.491446\pi$
$311$	281.771	−	162.681i	0.906016	−	0.523089i	0.879147	+	0.476550i	$0.158113\pi$
$312$		0			0
$313$	−228.378	+	395.562i	−0.729642	+	1.26378i	0.227392	+	0.973803i	$0.426980\pi$
$313$	−228.378	+	395.562i	−0.729642	+	1.26378i	−0.957034	+	0.289974i	$0.906353\pi$
$314$		0			0
$315$	−26.8936	+	86.1482i	−0.0853767	+	0.273486i
$316$		0			0
$317$	−104.980	−	60.6102i	−0.331167	−	0.191199i	0.325192	−	0.945648i	$-0.394571\pi$
$317$	−104.980	−	60.6102i	−0.331167	−	0.191199i	−0.656359	+	0.754449i	$0.727904\pi$
$318$		0			0
$319$	−190.180	+	109.801i	−0.596177	+	0.344203i
$320$		0			0
$321$	−194.128			−0.604761
$322$		0			0
$323$	−87.0822			−0.269604
$324$		0			0
$325$	−213.434	+	123.226i	−0.656719	+	0.379157i
$326$		0			0
$327$	−396.721	−	229.047i	−1.21321	−	0.700449i
$328$		0			0
$329$	564.006	−	126.719i	1.71430	−	0.385164i
$330$		0			0
$331$	60.5842	−	104.935i	0.183034	−	0.317024i	−0.759878	−	0.650065i	$-0.774742\pi$
$331$	60.5842	−	104.935i	0.183034	−	0.317024i	0.942912	+	0.333041i	$0.108075\pi$
$332$		0			0
$333$	−270.191	+	155.995i	−0.811384	+	0.468453i
$334$		0			0
$335$		−	111.652i		−	0.333290i
$336$		0			0
$337$	−464.021			−1.37692			−0.688459	−	0.725275i	$-0.741713\pi$
$337$	−464.021			−1.37692			−0.688459	+	0.725275i	$0.741713\pi$
$338$		0			0
$339$	110.985	+	192.232i	0.327390	+	0.567056i
$340$		0			0
$341$	−153.420	−	88.5773i	−0.449913	−	0.259758i
$342$		0			0
$343$	−211.116	−	270.331i	−0.615499	−	0.788137i
$344$		0			0
$345$	−144.448	+	250.190i	−0.418688	+	0.725190i
$346$		0			0
$347$	−185.593	−	321.457i	−0.534851	−	0.926388i	−0.999171	−	0.0407208i	$-0.987035\pi$
$347$	−185.593	−	321.457i	−0.534851	−	0.926388i	0.464320	−	0.885667i	$-0.346299\pi$
$348$		0			0
$349$		−	207.871i		−	0.595619i	−0.954625	−	0.297809i	$-0.903744\pi$
$349$		−	207.871i		−	0.595619i	0.954625	−	0.297809i	$-0.0962560\pi$
$350$		0			0
$351$			98.3779i			0.280279i
$352$		0			0
$353$	307.007	+	531.751i	0.869708	+	1.50638i	0.862296	+	0.506405i	$0.169026\pi$
$353$	307.007	+	531.751i	0.869708	+	1.50638i	0.00741211	+	0.999973i	$0.497641\pi$
$354$		0			0
$355$	36.0071	−	62.3661i	0.101428	−	0.175679i
$356$		0			0
$357$	−17.7060	−	78.8065i	−0.0495965	−	0.220746i
$358$		0			0
$359$	−93.5930	−	54.0359i	−0.260705	−	0.150518i	0.363951	−	0.931418i	$-0.381427\pi$
$359$	−93.5930	−	54.0359i	−0.260705	−	0.150518i	−0.624656	+	0.780900i	$0.714761\pi$
$360$		0			0
$361$	−270.841	−	469.110i	−0.750252	−	1.29947i
$362$		0			0
$363$	−234.539			−0.646113
$364$		0			0
$365$		−	26.3135i		−	0.0720917i
$366$		0			0
$367$	393.881	−	227.407i	1.07325	−	0.619639i	0.144179	−	0.989552i	$-0.453946\pi$
$367$	393.881	−	227.407i	1.07325	−	0.619639i	0.929067	+	0.369913i	$0.120612\pi$
$368$		0			0
$369$	139.134	−	240.987i	0.377056	−	0.653081i
$370$		0			0
$371$	56.0794	−	179.639i	0.151157	−	0.484201i
$372$		0			0
$373$	−235.344	−	135.876i	−0.630949	−	0.364279i	0.150171	−	0.988660i	$-0.452018\pi$
$373$	−235.344	−	135.876i	−0.630949	−	0.364279i	−0.781119	+	0.624382i	$0.785351\pi$
$374$		0			0
$375$	−301.515	+	174.080i	−0.804039	+	0.464212i
$376$		0			0
$377$	−320.126			−0.849140
$378$		0			0
$379$	−268.351			−0.708051			−0.354026	−	0.935236i	$-0.615187\pi$
$379$	−268.351			−0.708051			−0.354026	+	0.935236i	$0.615187\pi$
$380$		0			0
$381$	123.069	−	71.0541i	0.323017	−	0.186494i
$382$		0			0
$383$	283.718	+	163.805i	0.740779	+	0.427689i	0.822352	−	0.568979i	$-0.192661\pi$
$383$	283.718	+	163.805i	0.740779	+	0.427689i	−0.0815738	+	0.996667i	$0.525995\pi$
$384$		0			0
$385$	−70.3655	−	76.3539i	−0.182767	−	0.198322i
$386$		0			0
$387$	−161.903	+	280.424i	−0.418354	+	0.724610i
$388$		0			0
$389$	109.380	−	63.1506i	0.281183	−	0.162341i	−0.352776	−	0.935708i	$-0.614762\pi$
$389$	109.380	−	63.1506i	0.281183	−	0.162341i	0.633959	+	0.773367i	$0.281429\pi$
$390$		0			0
$391$		−	111.729i		−	0.285753i
$392$		0			0
$393$	482.869			1.22867
$394$		0			0
$395$	48.1826	+	83.4548i	0.121981	+	0.211278i
$396$		0			0
$397$	110.110	+	63.5720i	0.277355	+	0.160131i	0.632225	−	0.774784i	$-0.282142\pi$
$397$	110.110	+	63.5720i	0.277355	+	0.160131i	−0.354870	+	0.934916i	$0.615475\pi$
$398$		0			0
$399$	615.685	−	567.396i	1.54307	−	1.42205i
$400$		0			0
$401$	−30.0751	+	52.0916i	−0.0750003	+	0.129904i	−0.901086	−	0.433640i	$-0.857229\pi$
$401$	−30.0751	+	52.0916i	−0.0750003	+	0.129904i	0.826086	+	0.563544i	$0.190562\pi$
$402$		0			0
$403$	−129.124	−	223.650i	−0.320408	−	0.554962i
$404$		0			0
$405$			180.221i			0.444991i
$406$		0			0
$407$		−	358.950i		−	0.881941i
$408$		0			0
$409$	34.8873	+	60.4267i	0.0852991	+	0.147742i	0.905519	−	0.424306i	$-0.139482\pi$
$409$	34.8873	+	60.4267i	0.0852991	+	0.147742i	−0.820220	+	0.572049i	$0.806149\pi$
$410$		0			0
$411$	16.9128	−	29.2939i	0.0411504	−	0.0712746i
$412$		0			0
$413$	−69.5666	−	21.7172i	−0.168442	−	0.0525841i
$414$		0			0
$415$	145.824	+	84.1918i	0.351384	+	0.202872i
$416$		0			0
$417$	−6.08982	−	10.5479i	−0.0146039	−	0.0252947i
$418$		0			0
$419$	−714.794			−1.70595			−0.852976	−	0.521950i	$-0.825205\pi$
$419$	−714.794			−1.70595			−0.852976	+	0.521950i	$0.825205\pi$
$420$		0			0
$421$		−	303.440i		−	0.720759i	−0.932806	−	0.360380i	$-0.882647\pi$
$421$		−	303.440i		−	0.720759i	0.932806	−	0.360380i	$-0.117353\pi$
$422$		0			0
$423$	−489.793	+	282.782i	−1.15790	+	0.668515i
$424$		0			0
$425$	31.0945	−	53.8572i	0.0731635	−	0.126723i
$426$		0			0
$427$	151.363	−	34.0078i	0.354481	−	0.0796435i
$428$		0			0
$429$	312.035	+	180.154i	0.727355	+	0.419939i
$430$		0			0
$431$	373.685	−	215.747i	0.867019	−	0.500574i	0.000662591	−	1.00000i	$-0.499789\pi$
$431$	373.685	−	215.747i	0.867019	−	0.500574i	0.866357	+	0.499426i	$0.166456\pi$
$432$		0			0
$433$	194.875			0.450057			0.225029	−	0.974352i	$-0.427752\pi$
$433$	194.875			0.450057			0.225029	+	0.974352i	$0.427752\pi$
$434$		0			0
$435$	−208.869			−0.480159
$436$		0			0
$437$	1003.00	−	579.085i	2.29521	−	1.32514i
$438$		0			0
$439$	−264.977	−	152.985i	−0.603593	−	0.348485i	0.166861	−	0.985980i	$-0.446637\pi$
$439$	−264.977	−	152.985i	−0.603593	−	0.348485i	−0.770454	+	0.637496i	$0.779970\pi$
$440$		0			0
$441$	275.981	+	190.917i	0.625808	+	0.432918i
$442$		0			0
$443$	125.099	−	216.677i	0.282390	−	0.489113i	−0.689583	−	0.724206i	$-0.742206\pi$
$443$	125.099	−	216.677i	0.282390	−	0.489113i	0.971973	+	0.235093i	$0.0755396\pi$
$444$		0			0
$445$	−171.603	+	99.0748i	−0.385624	+	0.222640i
$446$		0			0
$447$			126.295i			0.282539i
$448$		0			0
$449$	−688.681			−1.53381			−0.766905	−	0.641761i	$-0.778204\pi$
$449$	−688.681			−1.53381			−0.766905	+	0.641761i	$0.778204\pi$
$450$		0			0
$451$	160.076	+	277.260i	0.354936	+	0.614768i
$452$		0			0
$453$	−874.317	−	504.787i	−1.93006	−	1.11432i
$454$		0			0
$455$	−33.1805	−	147.681i	−0.0729242	−	0.324574i
$456$		0			0
$457$	−402.259	+	696.733i	−0.880217	+	1.52458i	−0.0291166	+	0.999576i	$0.509269\pi$
$457$	−402.259	+	696.733i	−0.880217	+	1.52458i	−0.851100	+	0.525004i	$0.824064\pi$
$458$		0			0
$459$	−12.4122	−	21.4985i	−0.0270418	−	0.0468378i
$460$		0			0
$461$			693.657i			1.50468i	0.658776	+	0.752339i	$0.271074\pi$
$461$			693.657i			1.50468i	−0.658776	+	0.752339i	$0.728926\pi$
$462$		0			0
$463$			321.194i			0.693724i	0.937916	+	0.346862i	$0.112753\pi$
$463$			321.194i			0.693724i	−0.937916	+	0.346862i	$0.887247\pi$
$464$		0			0
$465$	−84.2484	−	145.922i	−0.181179	−	0.313812i
$466$		0			0
$467$	375.937	−	651.142i	0.805005	−	1.39431i	−0.111283	−	0.993789i	$-0.535496\pi$
$467$	375.937	−	651.142i	0.805005	−	1.39431i	0.916288	−	0.400521i	$-0.131171\pi$
$468$		0			0
$469$	−396.307	−	123.719i	−0.845004	−	0.263792i
$470$		0			0
$471$	−170.064	−	98.1867i	−0.361071	−	0.208464i
$472$		0			0
$473$	−186.273	−	322.634i	−0.393811	−	0.682101i
$474$		0			0
$475$	644.642			1.35714
$476$		0			0
$477$			184.118i			0.385992i
$478$		0			0
$479$	−625.392	+	361.070i	−1.30562	+	0.753800i	−0.981362	−	0.192169i	$-0.938448\pi$
$479$	−625.392	+	361.070i	−1.30562	+	0.753800i	−0.324257	+	0.945969i	$0.605114\pi$
$480$		0			0
$481$	261.631	−	453.158i	0.543932	−	0.942117i
$482$		0			0
$483$	727.988	+	789.943i	1.50722	+	1.63549i
$484$		0			0
$485$	90.2052	+	52.0800i	0.185990	+	0.107381i
$486$		0			0
$487$	−41.4211	+	23.9145i	−0.0850536	+	0.0491057i	−0.541924	−	0.840428i	$-0.682304\pi$
$487$	−41.4211	+	23.9145i	−0.0850536	+	0.0491057i	0.456870	+	0.889533i	$0.348970\pi$
$488$		0			0
$489$	−460.682			−0.942090
$490$		0			0
$491$	−44.4724			−0.0905752			−0.0452876	−	0.998974i	$-0.514420\pi$
$491$	−44.4724			−0.0905752			−0.0452876	+	0.998974i	$0.514420\pi$
$492$		0			0
$493$	69.9571	−	40.3898i	0.141901	−	0.0819265i
$494$		0			0
$495$	87.9769	+	50.7935i	0.177731	+	0.102613i
$496$		0			0
$497$	−181.469	−	196.913i	−0.365128	−	0.396203i
$498$		0			0
$499$	−250.786	+	434.374i	−0.502577	+	0.870489i	0.497418	+	0.867511i	$0.334281\pi$
$499$	−250.786	+	434.374i	−0.502577	+	0.870489i	−0.999996	+	0.00297862i	$0.999052\pi$
$500$		0			0
$501$	111.656	−	64.4647i	0.222867	−	0.128672i
$502$		0			0
$503$		−	462.733i		−	0.919946i	−0.887933	−	0.459973i	$-0.847859\pi$
$503$		−	462.733i		−	0.919946i	0.887933	−	0.459973i	$-0.152141\pi$
$504$		0			0
$505$	−59.1729			−0.117174
$506$		0			0
$507$	−73.7767	−	127.785i	−0.145516	−	0.252041i
$508$		0			0
$509$	−408.751	−	235.992i	−0.803046	−	0.463639i	0.0414889	−	0.999139i	$-0.486790\pi$
$509$	−408.751	−	235.992i	−0.803046	−	0.463639i	−0.844535	+	0.535500i	$0.820123\pi$
$510$		0			0
$511$	−93.3992	−	29.1573i	−0.182777	−	0.0570592i
$512$		0			0
$513$	128.663	−	222.851i	0.250805	−	0.434407i
$514$		0			0
$515$	75.2878	+	130.402i	0.146190	+	0.253208i
$516$		0			0
$517$		−	650.693i		−	1.25859i
$518$		0			0
$519$			825.047i			1.58969i
$520$		0			0
$521$	45.3709	+	78.5848i	0.0870843	+	0.150834i	0.906277	−	0.422683i	$-0.138912\pi$
$521$	45.3709	+	78.5848i	0.0870843	+	0.150834i	−0.819193	+	0.573518i	$0.805578\pi$
$522$		0			0
$523$	−180.256	+	312.213i	−0.344658	+	0.596965i	−0.985292	−	0.170882i	$-0.945338\pi$
$523$	−180.256	+	312.213i	−0.344658	+	0.596965i	0.640634	+	0.767847i	$0.278672\pi$
$524$		0			0
$525$	131.072	+	583.379i	0.249660	+	1.11120i
$526$		0			0
$527$	56.4351	+	32.5828i	0.107087	+	0.0618270i
$528$		0			0
$529$	478.485	+	828.760i	0.904509	+	1.56665i
$530$		0			0
$531$	71.3014			0.134278
$532$		0			0
$533$			466.705i			0.875618i
$534$		0			0
$535$	79.4994	−	45.8990i	0.148597	−	0.0857925i
$536$		0			0
$537$	346.683	−	600.472i	0.645592	−	1.11820i
$538$		0			0
$539$	−348.987	+	165.155i	−0.647471	+	0.306410i
$540$		0			0
$541$	485.969	+	280.574i	0.898278	+	0.518621i	0.876641	−	0.481145i	$-0.159779\pi$
$541$	485.969	+	280.574i	0.898278	+	0.518621i	0.0216371	+	0.999766i	$0.493112\pi$
$542$		0			0
$543$	−704.166	+	406.550i	−1.29681	+	0.748712i
$544$		0			0
$545$	216.620			0.397468
$546$		0			0
$547$	−1043.62			−1.90790			−0.953952	−	0.299960i	$-0.903027\pi$
$547$	−1043.62			−1.90790			−0.953952	+	0.299960i	$0.903027\pi$
$548$		0			0
$549$	−131.447	+	75.8907i	−0.239429	+	0.138234i
$550$		0			0
$551$	725.165	+	418.674i	1.31609	+	0.759845i
$552$		0			0
$553$	349.611	−	78.5494i	0.632208	−	0.142042i
$554$		0			0
$555$	170.704	−	295.667i	0.307574	−	0.532734i
$556$		0			0
$557$	−42.1273	+	24.3222i	−0.0756324	+	0.0436664i	−0.537339	−	0.843366i	$-0.680571\pi$
$557$	−42.1273	+	24.3222i	−0.0756324	+	0.0436664i	0.461707	+	0.887033i	$0.347237\pi$
$558$		0			0
$559$		−	543.081i		−	0.971522i
$560$		0			0
$561$	−90.9189			−0.162066
$562$		0			0
$563$	363.015	+	628.761i	0.644787	+	1.11680i	0.984351	+	0.176221i	$0.0563874\pi$
$563$	363.015	+	628.761i	0.644787	+	1.11680i	−0.339563	+	0.940583i	$0.610279\pi$
$564$		0			0
$565$	−90.9012	−	52.4818i	−0.160887	−	0.0928882i
$566$		0			0
$567$	639.692	+	199.698i	1.12820	+	0.352202i
$568$		0			0
$569$	240.696	−	416.898i	0.423016	−	0.732685i	−0.573217	−	0.819404i	$-0.694305\pi$
$569$	240.696	−	416.898i	0.423016	−	0.732685i	0.996233	+	0.0867185i	$0.0276381\pi$
$570$		0			0
$571$	55.0633	+	95.3724i	0.0964331	+	0.167027i	0.910206	−	0.414156i	$-0.135923\pi$
$571$	55.0633	+	95.3724i	0.0964331	+	0.167027i	−0.813773	+	0.581183i	$0.802590\pi$
$572$		0			0
$573$			1188.38i			2.07396i
$574$		0			0
$575$			827.097i			1.43843i
$576$		0			0
$577$	101.168	+	175.228i	0.175335	+	0.303688i	0.940277	−	0.340410i	$-0.110566\pi$
$577$	101.168	+	175.228i	0.175335	+	0.303688i	−0.764942	+	0.644099i	$0.777233\pi$
$578$		0			0
$579$	658.386	−	1140.36i	1.13711	−	1.96953i
$580$		0			0
$581$	460.421	−	424.310i	0.792463	−	0.730310i
$582$		0			0
$583$	−183.452	−	105.916i	−0.314669	−	0.181674i
$584$		0			0
$585$	74.0445	+	128.249i	0.126572	+	0.219229i
$586$		0			0
$587$	568.689			0.968805			0.484403	−	0.874845i	$-0.339037\pi$
$587$	568.689			0.968805			0.484403	+	0.874845i	$0.339037\pi$
$588$		0			0
$589$			675.497i			1.14685i
$590$		0			0
$591$	1128.45	−	651.513i	1.90940	−	1.10239i
$592$		0			0
$593$	342.686	−	593.550i	0.577886	−	1.00093i	−0.417835	−	0.908523i	$-0.637211\pi$
$593$	342.686	−	593.550i	0.577886	−	1.00093i	0.995721	−	0.0924054i	$-0.0294556\pi$
$594$		0			0
$595$	25.8837	+	28.0865i	0.0435019	+	0.0472042i
$596$		0			0
$597$	−43.9088	−	25.3507i	−0.0735491	−	0.0424636i
$598$		0			0
$599$	318.077	−	183.642i	0.531013	−	0.306580i	−0.210416	−	0.977612i	$-0.567482\pi$
$599$	318.077	−	183.642i	0.531013	−	0.306580i	0.741429	+	0.671032i	$0.234149\pi$
$600$		0			0
$601$	412.344			0.686097			0.343049	−	0.939318i	$-0.388540\pi$
$601$	412.344			0.686097			0.343049	+	0.939318i	$0.388540\pi$
$602$		0			0
$603$	406.190			0.673615
$604$		0			0
$605$	96.0484	−	55.4535i	0.158758	−	0.0916588i
$606$		0			0
$607$	−1010.46	−	583.389i	−1.66468	−	0.961102i	−0.970436	−	0.241359i	$-0.922407\pi$
$607$	−1010.46	−	583.389i	−1.66468	−	0.961102i	−0.694241	−	0.719743i	$-0.744260\pi$
$608$		0			0
$609$	−231.442	+	741.377i	−0.380036	+	1.21737i
$610$		0			0
$611$	474.276	−	821.470i	0.776229	−	1.34447i
$612$		0			0
$613$	373.900	−	215.871i	0.609951	−	0.352155i	−0.162995	−	0.986627i	$-0.552115\pi$
$613$	373.900	−	215.871i	0.609951	−	0.352155i	0.772946	+	0.634471i	$0.218782\pi$
$614$		0			0
$615$			304.506i			0.495131i
$616$		0			0
$617$	−333.751			−0.540926			−0.270463	−	0.962730i	$-0.587177\pi$
$617$	−333.751			−0.540926			−0.270463	+	0.962730i	$0.587177\pi$
$618$		0			0
$619$	−488.158	−	845.514i	−0.788624	−	1.36594i	−0.926810	−	0.375530i	$-0.877461\pi$
$619$	−488.158	−	845.514i	−0.788624	−	1.36594i	0.138187	−	0.990406i	$-0.455873\pi$
$620$		0			0
$621$	285.925	+	165.079i	0.460426	+	0.265827i
$622$		0			0
$623$	161.516	+	718.883i	0.259255	+	1.15390i
$624$		0			0
$625$	−185.884	+	321.961i	−0.297414	+	0.515137i
$626$		0			0
$627$	−471.226	−	816.187i	−0.751556	−	1.30173i
$628$		0			0
$629$			132.038i			0.209918i
$630$		0			0
$631$			639.885i			1.01408i	0.861922	+	0.507040i	$0.169261\pi$
$631$			639.885i			1.01408i	−0.861922	+	0.507040i	$0.830739\pi$
$632$		0			0
$633$	239.767	+	415.288i	0.378778	+	0.656063i
$634$		0			0
$635$	−33.5995	+	58.1961i	−0.0529127	+	0.0916474i
$636$		0			0
$637$	−560.958	−	45.8681i	−0.880625	−	0.0720064i
$638$		0			0
$639$	226.888	+	130.994i	0.355067	+	0.204998i
$640$		0			0
$641$	−10.4295	−	18.0645i	−0.0162707	−	0.0281817i	0.857775	−	0.514025i	$-0.171846\pi$
$641$	−10.4295	−	18.0645i	−0.0162707	−	0.0281817i	−0.874046	+	0.485843i	$0.838513\pi$
$642$		0			0
$643$	69.1348			0.107519			0.0537596	−	0.998554i	$-0.482880\pi$
$643$	69.1348			0.107519			0.0537596	+	0.998554i	$0.482880\pi$
$644$		0			0
$645$		−	354.338i		−	0.549362i
$646$		0			0
$647$	310.868	−	179.480i	0.480476	−	0.277403i	−0.240139	−	0.970739i	$-0.577193\pi$
$647$	310.868	−	179.480i	0.480476	−	0.277403i	0.720615	+	0.693336i	$0.243860\pi$
$648$		0			0
$649$	−41.0169	+	71.0433i	−0.0632001	+	0.109466i
$650$		0			0
$651$	−611.302	+	137.345i	−0.939021	+	0.210976i
$652$		0			0
$653$	−32.1227	−	18.5460i	−0.0491925	−	0.0284013i	0.475202	−	0.879877i	$-0.342375\pi$
$653$	−32.1227	−	18.5460i	−0.0491925	−	0.0284013i	−0.524395	+	0.851475i	$0.675708\pi$
$654$		0			0
$655$	−197.744	+	114.168i	−0.301900	+	0.174302i
$656$		0			0
$657$	95.7284			0.145705
$658$		0			0
$659$	−197.302			−0.299396			−0.149698	−	0.988732i	$-0.547830\pi$
$659$	−197.302			−0.299396			−0.149698	+	0.988732i	$0.547830\pi$
$660$		0			0
$661$	−938.626	+	541.916i	−1.42001	+	0.819843i	−0.996299	−	0.0859554i	$-0.972606\pi$
$661$	−938.626	+	541.916i	−1.42001	+	0.819843i	−0.423710	+	0.905798i	$0.639272\pi$
$662$		0			0
$663$	−114.781	−	66.2688i	−0.173124	−	0.0999530i
$664$		0			0
$665$	−117.982	+	377.930i	−0.177416	+	0.568316i
$666$		0			0
$667$	−537.173	+	930.411i	−0.805357	+	1.39492i
$668$		0			0
$669$	1285.84	−	742.378i	1.92203	−	1.10968i
$670$		0			0
$671$		−	174.628i		−	0.260250i
$672$		0			0
$673$	−286.066			−0.425061			−0.212530	−	0.977154i	$-0.568170\pi$
$673$	−286.066			−0.425061			−0.212530	+	0.977154i	$0.568170\pi$
$674$		0			0
$675$	91.8834	+	159.147i	0.136124	+	0.235773i
$676$		0			0
$677$	−433.324	−	250.180i	−0.640065	−	0.369542i	0.144575	−	0.989494i	$-0.453819\pi$
$677$	−433.324	−	250.180i	−0.640065	−	0.369542i	−0.784640	+	0.619952i	$0.787152\pi$
$678$		0			0
$679$	284.811	−	262.473i	0.419456	−	0.386558i
$680$		0			0
$681$	146.155	−	253.148i	0.214618	−	0.371729i
$682$		0			0
$683$	473.225	+	819.650i	0.692862	+	1.20007i	0.970896	+	0.239501i	$0.0769840\pi$
$683$	473.225	+	819.650i	0.692862	+	1.20007i	−0.278034	+	0.960571i	$0.589683\pi$
$684$		0			0
$685$			15.9952i			0.0233507i
$686$		0			0
$687$		−	1689.76i		−	2.45962i
$688$		0			0
$689$	−154.400	−	267.428i	−0.224092	−	0.388140i
$690$		0			0
$691$	151.632	−	262.634i	0.219439	−	0.380079i	−0.735198	−	0.677853i	$-0.762911\pi$
$691$	151.632	−	262.634i	0.219439	−	0.380079i	0.954636	+	0.297774i	$0.0962441\pi$
$692$		0			0
$693$	277.775	−	255.989i	0.400830	−	0.369393i
$694$		0			0
$695$	4.98781	+	2.87971i	0.00717670	+	0.00414347i
$696$		0			0
$697$	−58.8834	−	101.989i	−0.0844812	−	0.146326i
$698$		0			0
$699$	−332.074			−0.475069
$700$		0			0
$701$			390.864i			0.557580i	0.960352	+	0.278790i	$0.0899333\pi$
$701$			390.864i			0.557580i	−0.960352	+	0.278790i	$0.910067\pi$
$702$		0			0
$703$	−1185.32	+	684.345i	−1.68609	+	0.973464i
$704$		0			0
$705$	309.446	−	535.976i	0.438930	−	0.760250i
$706$		0			0
$707$	−65.5679	+	210.033i	−0.0927411	+	0.297077i
$708$		0			0
$709$	−832.393	−	480.582i	−1.17404	−	0.677831i	−0.219410	−	0.975633i	$-0.570413\pi$
$709$	−832.393	−	480.582i	−1.17404	−	0.677831i	−0.954628	+	0.297801i	$0.903747\pi$
$710$		0			0
$711$	−303.608	+	175.288i	−0.427016	+	0.246538i
$712$		0			0
$713$	−866.685			−1.21555
$714$		0			0
$715$	−170.379			−0.238293
$716$		0			0
$717$	−388.074	+	224.055i	−0.541247	+	0.312489i
$718$		0			0
$719$	−454.773	−	262.563i	−0.632507	−	0.365178i	0.149215	−	0.988805i	$-0.452325\pi$
$719$	−454.773	−	262.563i	−0.632507	−	0.365178i	−0.781722	+	0.623627i	$0.785659\pi$
$720$		0			0
$721$	546.285	−	122.737i	0.757677	−	0.170232i
$722$		0			0
$723$	−558.204	+	966.838i	−0.772067	+	1.33726i
$724$		0			0
$725$	−517.870	+	298.992i	−0.714304	+	0.412403i
$726$		0			0
$727$		−	108.633i		−	0.149426i	−0.997205	−	0.0747131i	$-0.976196\pi$
$727$		−	108.633i		−	0.149426i	0.997205	−	0.0747131i	$-0.0238041\pi$
$728$		0			0
$729$	−348.775			−0.478429
$730$		0			0
$731$	68.5197	+	118.680i	0.0937341	+	0.162352i
$732$		0			0
$733$	−34.8609	−	20.1270i	−0.0475593	−	0.0274584i	0.476032	−	0.879428i	$-0.342075\pi$
$733$	−34.8609	−	20.1270i	−0.0475593	−	0.0274584i	−0.523591	+	0.851970i	$0.675408\pi$
$734$		0			0
$735$	−366.003	−	29.9271i	−0.497963	−	0.0407171i
$736$		0			0
$737$	−233.665	+	404.719i	−0.317049	+	0.549144i
$738$		0			0
$739$	498.602	+	863.603i	0.674698	+	1.16861i	0.976557	+	0.215258i	$0.0690594\pi$
$739$	498.602	+	863.603i	0.674698	+	1.16861i	−0.301859	+	0.953352i	$0.597607\pi$
$740$		0			0
$741$		−	1373.87i		−	1.85407i
$742$		0			0
$743$		−	476.575i		−	0.641420i	−0.947177	−	0.320710i	$-0.896078\pi$
$743$		−	476.575i		−	0.641420i	0.947177	−	0.320710i	$-0.103922\pi$
$744$		0			0
$745$	−29.8607	−	51.7203i	−0.0400815	−	0.0694232i
$746$		0			0
$747$	−306.289	+	530.509i	−0.410026	+	0.710186i
$748$		0			0
$749$	−74.8265	−	333.041i	−0.0999018	−	0.444648i
$750$		0			0
$751$	−457.691	−	264.248i	−0.609442	−	0.351862i	0.163305	−	0.986576i	$-0.447785\pi$
$751$	−457.691	−	264.248i	−0.609442	−	0.351862i	−0.772747	+	0.634714i	$0.781118\pi$
$752$		0			0
$753$	−65.5993	−	113.621i	−0.0871173	−	0.150892i
$754$		0			0
$755$	477.400			0.632318
$756$		0			0
$757$		−	455.964i		−	0.602331i	−0.953572	−	0.301165i	$-0.902624\pi$
$757$		−	455.964i		−	0.602331i	0.953572	−	0.301165i	$-0.0973756\pi$
$758$		0			0
$759$	1047.19	−	604.598i	1.37970	−	0.796572i
$760$		0			0
$761$	−238.325	+	412.791i	−0.313174	+	0.542433i	−0.979048	−	0.203632i	$-0.934726\pi$
$761$	−238.325	+	412.791i	−0.313174	+	0.542433i	0.665874	+	0.746064i	$0.268059\pi$
$762$		0			0
$763$	240.031	−	768.888i	0.314588	−	1.00772i
$764$		0			0
$765$	−32.3619	−	18.6842i	−0.0423032	−	0.0244238i
$766$		0			0
$767$	−103.564	+	59.7927i	−0.135025	+	0.0779565i
$768$		0			0
$769$	−568.246			−0.738941			−0.369471	−	0.929242i	$-0.620461\pi$
$769$	−568.246			−0.738941			−0.369471	+	0.929242i	$0.620461\pi$
$770$		0			0
$771$	−892.621			−1.15774
$772$		0			0
$773$	1036.66	−	598.515i	1.34108	−	0.774275i	0.354118	−	0.935201i	$-0.384781\pi$
$773$	1036.66	−	598.515i	1.34108	−	0.774275i	0.986967	+	0.160925i	$0.0514478\pi$
$774$		0			0
$775$	−417.771	−	241.200i	−0.539059	−	0.311226i
$776$		0			0
$777$	−860.314	−	933.531i	−1.10723	−	1.20146i
$778$		0			0
$779$	610.377	−	1057.20i	0.783539	−	1.35713i
$780$		0			0
$781$	−261.039	+	150.711i	−0.334237	+	0.192972i
$782$		0			0
$783$			238.701i			0.304855i
$784$		0			0
$785$	92.8596			0.118292
$786$		0			0
$787$	226.134	+	391.676i	0.287337	+	0.497682i	0.973173	−	0.230074i	$-0.0738967\pi$
$787$	226.134	+	391.676i	0.287337	+	0.497682i	−0.685836	+	0.727756i	$0.740563\pi$
$788$		0			0
$789$	585.969	+	338.309i	0.742673	+	0.428783i
$790$		0			0
$791$	−287.008	+	264.498i	−0.362843	+	0.334385i
$792$		0			0
$793$	127.282	−	220.459i	0.160507	−	0.278007i
$794$		0			0
$795$	−100.740	−	174.486i	−0.126716	−	0.219479i
$796$		0			0
$797$		−	1047.47i		−	1.31426i	−0.753777	−	0.657130i	$-0.771770\pi$
$797$		−	1047.47i		−	1.31426i	0.753777	−	0.657130i	$-0.228230\pi$
$798$		0			0
$799$			239.355i			0.299568i
$800$		0			0
$801$	−360.434	−	624.290i	−0.449980	−	0.779388i
$802$		0			0
$803$	−55.0687	+	95.3818i	−0.0685787	+	0.118782i
$804$		0			0
$805$	−484.897	−	151.375i	−0.602356	−	0.188043i
$806$		0			0
$807$	374.162	+	216.023i	0.463646	+	0.267686i
$808$		0			0
$809$	149.332	+	258.651i	0.184589	+	0.319717i	0.943438	−	0.331549i	$-0.107571\pi$
$809$	149.332	+	258.651i	0.184589	+	0.319717i	−0.758849	+	0.651267i	$0.774238\pi$
$810$		0			0
$811$	−633.054			−0.780584			−0.390292	−	0.920691i	$-0.627626\pi$
$811$	−633.054			−0.780584			−0.390292	+	0.920691i	$0.627626\pi$
$812$		0			0
$813$		−	77.0852i		−	0.0948158i
$814$		0			0
$815$	188.658	−	108.922i	0.231483	−	0.133647i
$816$		0			0
$817$	−710.265	+	1230.21i	−0.869357	+	1.50577i
$818$		0			0
$819$	537.264	−	120.711i	0.656000	−	0.147388i
$820$		0			0
$821$	1083.83	+	625.749i	1.32013	+	0.762178i	0.983749	−	0.179547i	$-0.0574632\pi$
$821$	1083.83	+	625.749i	1.32013	+	0.762178i	0.336382	+	0.941725i	$0.390797\pi$
$822$		0			0
$823$	1062.45	−	613.409i	1.29095	−	0.745332i	0.312130	−	0.950039i	$-0.398957\pi$
$823$	1062.45	−	613.409i	1.29095	−	0.745332i	0.978823	+	0.204707i	$0.0656241\pi$
$824$		0			0
$825$	673.043			0.815810
$826$		0			0
$827$	1438.26			1.73913			0.869566	−	0.493816i	$-0.164398\pi$
$827$	1438.26			1.73913			0.869566	+	0.493816i	$0.164398\pi$
$828$		0			0
$829$	−542.554	+	313.244i	−0.654468	+	0.377858i	−0.790166	−	0.612893i	$-0.790006\pi$
$829$	−542.554	+	313.244i	−0.654468	+	0.377858i	0.135698	+	0.990750i	$0.456672\pi$
$830$		0			0
$831$	446.289	+	257.665i	0.537050	+	0.310066i
$832$		0			0
$833$	128.373	−	60.7517i	0.154110	−	0.0729312i
$834$		0			0
$835$	−30.4836	+	52.7991i	−0.0365073	+	0.0632325i
$836$		0			0
$837$	−166.764	+	96.2814i	−0.199240	+	0.115032i
$838$		0			0
$839$			1062.37i			1.26624i	0.774055	+	0.633118i	$0.218225\pi$
$839$			1062.37i			1.26624i	−0.774055	+	0.633118i	$0.781775\pi$
$840$		0			0
$841$	64.2558			0.0764041
$842$		0			0
$843$	−165.931	−	287.401i	−0.196834	−	0.340926i
$844$		0			0
$845$	60.4260	+	34.8870i	0.0715101	+	0.0412864i
$846$		0			0
$847$	−90.4027	−	402.368i	−0.106733	−	0.475051i
$848$		0			0
$849$	57.5842	−	99.7387i	0.0678259	−	0.117478i
$850$		0			0
$851$	−878.037	−	1520.80i	−1.03177	−	1.78708i
$852$		0			0
$853$			698.388i			0.818743i	0.912368	+	0.409372i	$0.134252\pi$
$853$			698.388i			0.818743i	−0.912368	+	0.409372i	$0.865748\pi$
$854$		0			0
$855$		−	387.355i		−	0.453047i
$856$		0			0
$857$	365.162	+	632.479i	0.426094	+	0.738016i	0.996522	−	0.0833317i	$-0.0265561\pi$
$857$	365.162	+	632.479i	0.426094	+	0.738016i	−0.570428	+	0.821347i	$0.693223\pi$
$858$		0			0
$859$	−483.130	+	836.805i	−0.562433	+	0.974162i	0.434851	+	0.900502i	$0.356801\pi$
$859$	−483.130	+	836.805i	−0.562433	+	0.974162i	−0.997283	+	0.0736593i	$0.976532\pi$
$860$		0			0
$861$	1080.84	+	337.415i	1.25533	+	0.391887i
$862$		0			0
$863$	−255.023	−	147.237i	−0.295507	−	0.170611i	0.344916	−	0.938634i	$-0.387907\pi$
$863$	−255.023	−	147.237i	−0.295507	−	0.170611i	−0.640423	+	0.768023i	$0.721241\pi$
$864$		0			0
$865$	−195.071	−	337.873i	−0.225516	−	0.390605i
$866$		0			0
$867$	−1117.07			−1.28844
$868$		0			0
$869$		−	403.346i		−	0.464149i
$870$		0			0
$871$	−589.983	+	340.627i	−0.677362	+	0.391075i
$872$		0			0
$873$	−189.467	+	328.166i	−0.217030	+	0.375906i
$874$		0			0
$875$	−414.864	−	450.171i	−0.474131	−	0.514482i
$876$		0			0
$877$	818.300	+	472.446i	0.933067	+	0.538706i	0.887780	−	0.460268i	$-0.152247\pi$
$877$	818.300	+	472.446i	0.933067	+	0.538706i	0.0452867	+	0.998974i	$0.485580\pi$
$878$		0			0
$879$	739.916	−	427.191i	0.841770	−	0.485996i
$880$		0			0
$881$	744.098			0.844606			0.422303	−	0.906455i	$-0.361222\pi$
$881$	744.098			0.844606			0.422303	+	0.906455i	$0.361222\pi$
$882$		0			0
$883$	−23.9032			−0.0270704			−0.0135352	−	0.999908i	$-0.504309\pi$
$883$	−23.9032			−0.0270704			−0.0135352	+	0.999908i	$0.504309\pi$
$884$		0			0
$885$	−67.5713	+	39.0123i	−0.0763517	+	0.0440817i
$886$		0			0
$887$	820.397	+	473.656i	0.924912	+	0.533998i	0.885199	−	0.465213i	$-0.154022\pi$
$887$	820.397	+	473.656i	0.924912	+	0.533998i	0.0397129	+	0.999211i	$0.487356\pi$
$888$		0			0
$889$	169.335	+	183.747i	0.190478	+	0.206689i
$890$		0			0
$891$	377.166	−	653.271i	0.423307	−	0.733189i
$892$		0			0
$893$	−2148.71	+	1240.56i	−2.40617	+	1.38920i
$894$		0			0
$895$			327.874i			0.366339i
$896$		0			0
$897$	1762.71			1.96512
$898$		0			0
$899$	−313.304	−	542.658i	−0.348502	−	0.603624i
$900$		0			0
$901$	67.4820	+	38.9607i	0.0748968	+	0.0432417i
$902$		0			0
$903$	−1257.72	−	392.633i	−1.39282	−	0.434809i
$904$		0			0
$905$	192.247	−	332.981i	0.212427	−	0.367935i
$906$		0			0
$907$	275.512	+	477.200i	0.303761	+	0.526130i	0.976985	−	0.213309i	$-0.0684241\pi$
$907$	275.512	+	477.200i	0.303761	+	0.526130i	−0.673223	+	0.739439i	$0.735091\pi$
$908$		0			0
$909$		−	215.271i		−	0.236822i
$910$		0			0
$911$		−	827.652i		−	0.908509i	−0.890872	−	0.454254i	$-0.849906\pi$
$911$		−	827.652i		−	0.908509i	0.890872	−	0.454254i	$-0.150094\pi$
$912$		0			0
$913$	−352.392	−	610.361i	−0.385972	−	0.668523i
$914$		0			0
$915$	83.0466	−	143.841i	0.0907613	−	0.157203i
$916$		0			0
$917$	186.121	+	828.396i	0.202967	+	0.903376i
$918$		0			0
$919$	−309.165	−	178.497i	−0.336415	−	0.194229i	0.322271	−	0.946648i	$-0.395554\pi$
$919$	−309.165	−	178.497i	−0.336415	−	0.194229i	−0.658685	+	0.752418i	$0.728887\pi$
$920$		0			0
$921$	−239.940	−	415.588i	−0.260521	−	0.451236i
$922$		0			0
$923$	−439.400			−0.476056
$924$		0			0
$925$		−	977.438i		−	1.05669i
$926$		0			0
$927$	−474.403	+	273.897i	−0.511762	+	0.295466i
$928$		0			0
$929$	−484.873	+	839.824i	−0.521930	+	0.904009i	0.477745	+	0.878499i	$0.341454\pi$
$929$	−484.873	+	839.824i	−0.521930	+	0.904009i	−0.999675	+	0.0255102i	$0.991879\pi$
$930$		0			0
$931$	1210.72	+	837.549i	1.30045	+	0.899623i
$932$		0			0
$933$	−1121.74	−	647.636i	−1.20229	−	0.694144i
$934$		0			0
$935$	37.2331	−	21.4965i	0.0398215	−	0.0229909i
$936$		0			0
$937$	1287.55			1.37412			0.687061	−	0.726600i	$-0.258901\pi$
$937$	1287.55			1.37412			0.687061	+	0.726600i	$0.258901\pi$
$938$		0			0
$939$	1818.36			1.93649
$940$		0			0
$941$	395.597	−	228.398i	0.420400	−	0.242718i	−0.274848	−	0.961488i	$-0.588628\pi$
$941$	395.597	−	228.398i	0.420400	−	0.242718i	0.695249	+	0.718769i	$0.255294\pi$
$942$		0			0
$943$	1356.43	+	783.133i	1.43842	+	0.830470i
$944$		0			0
$945$	−110.118	+	24.7410i	−0.116527	+	0.0261810i
$946$		0			0
$947$	−573.925	+	994.067i	−0.606045	+	1.04970i	0.385840	+	0.922566i	$0.373912\pi$
$947$	−573.925	+	994.067i	−0.606045	+	1.04970i	−0.991885	+	0.127135i	$0.959422\pi$
$948$		0			0
$949$	−139.044	+	80.2768i	−0.146516	+	0.0845910i
$950$		0			0
$951$			482.582i			0.507447i
$952$		0			0
$953$	873.170			0.916232			0.458116	−	0.888892i	$-0.348524\pi$
$953$	873.170			0.916232			0.458116	+	0.888892i	$0.348524\pi$
$954$		0			0
$955$	−280.976	−	486.665i	−0.294216	−	0.509597i
$956$		0			0
$957$	757.114	+	437.120i	0.791133	+	0.456761i
$958$		0			0
$959$	56.7747	+	17.7239i	0.0592020	+	0.0184816i
$960$		0			0
$961$	−227.755	+	394.483i	−0.236998	+	0.410492i
$962$		0			0
$963$	166.980	+	289.219i	0.173396	+	0.300331i
$964$		0			0
$965$			622.666i			0.645249i
$966$		0			0
$967$			449.047i			0.464372i	0.972671	+	0.232186i	$0.0745878\pi$
$967$			449.047i			0.464372i	−0.972671	+	0.232186i	$0.925412\pi$
$968$		0			0
$969$	173.339	+	300.231i	0.178884	+	0.309836i
$970$		0			0
$971$	−618.929	+	1072.02i	−0.637414	+	1.10403i	0.348584	+	0.937278i	$0.386663\pi$
$971$	−618.929	+	1072.02i	−0.637414	+	1.10403i	−0.985998	+	0.166756i	$0.946671\pi$
$972$		0			0
$973$	15.7483	−	14.5132i	0.0161853	−	0.0149159i
$974$		0			0
$975$	849.687	+	490.567i	0.871473	+	0.503145i
$976$		0			0
$977$	−853.445	−	1478.21i	−0.873536	−	1.51301i	−0.858314	−	0.513125i	$-0.828488\pi$
$977$	−853.445	−	1478.21i	−0.873536	−	1.51301i	−0.0152219	−	0.999884i	$-0.504845\pi$
$978$		0			0
$979$	829.373			0.847164
$980$		0			0
$981$			788.063i			0.803326i
$982$		0			0
$983$	−997.793	+	576.076i	−1.01505	+	0.586039i	−0.912666	−	0.408706i	$-0.865980\pi$
$983$	−997.793	+	576.076i	−1.01505	+	0.586039i	−0.102383	+	0.994745i	$0.532647\pi$
$984$		0			0
$985$	−308.082	+	533.614i	−0.312774	+	0.541741i
$986$		0			0
$987$	−1559.55	−	1692.27i	−1.58009	−	1.71456i
$988$		0			0
$989$	−1578.41	−	911.293i	−1.59596	−	0.921429i
$990$		0			0
$991$	−357.511	+	206.409i	−0.360758	+	0.208283i	−0.669413	−	0.742890i	$-0.733454\pi$
$991$	−357.511	+	206.409i	−0.360758	+	0.208283i	0.308655	+	0.951174i	$0.400121\pi$
$992$		0			0
$993$	−482.375			−0.485776
$994$		0			0
$995$	23.9753			0.0240958
$996$		0			0
$997$	−260.805	+	150.576i	−0.261590	+	0.151029i	−0.625060	−	0.780577i	$-0.714925\pi$
$997$	−260.805	+	150.576i	−0.261590	+	0.151029i	0.363470	+	0.931606i	$0.381592\pi$
$998$		0			0
$999$	−337.897	−	195.085i	−0.338235	−	0.195280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.o.d.79.2		12
4.3	odd	2		56.3.k.d.51.1	yes	12
7.2	even	3		1568.3.g.j.687.5		6
7.4	even	3	inner	224.3.o.d.207.1		12
7.5	odd	6		1568.3.g.l.687.2		6
8.3	odd	2	inner	224.3.o.d.79.1		12
8.5	even	2		56.3.k.d.51.3	yes	12
28.3	even	6		392.3.k.l.67.3		12
28.11	odd	6		56.3.k.d.11.3	yes	12
28.19	even	6		392.3.g.i.99.6		6
28.23	odd	6		392.3.g.j.99.6		6
28.27	even	2		392.3.k.l.275.1		12
56.5	odd	6		392.3.g.i.99.5		6
56.11	odd	6	inner	224.3.o.d.207.2		12
56.13	odd	2		392.3.k.l.275.3		12
56.19	even	6		1568.3.g.l.687.1		6
56.37	even	6		392.3.g.j.99.5		6
56.45	odd	6		392.3.k.l.67.1		12
56.51	odd	6		1568.3.g.j.687.6		6
56.53	even	6		56.3.k.d.11.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.1	✓	12	56.53	even	6
56.3.k.d.11.3	yes	12	28.11	odd	6
56.3.k.d.51.1	yes	12	4.3	odd	2
56.3.k.d.51.3	yes	12	8.5	even	2
224.3.o.d.79.1		12	8.3	odd	2	inner
224.3.o.d.79.2		12	1.1	even	1	trivial
224.3.o.d.207.1		12	7.4	even	3	inner
224.3.o.d.207.2		12	56.11	odd	6	inner
392.3.g.i.99.5		6	56.5	odd	6
392.3.g.i.99.6		6	28.19	even	6
392.3.g.j.99.5		6	56.37	even	6
392.3.g.j.99.6		6	28.23	odd	6
392.3.k.l.67.1		12	56.45	odd	6
392.3.k.l.67.3		12	28.3	even	6
392.3.k.l.275.1		12	28.27	even	2
392.3.k.l.275.3		12	56.13	odd	2
1568.3.g.j.687.5		6	7.2	even	3
1568.3.g.j.687.6		6	56.51	odd	6
1568.3.g.l.687.1		6	56.19	even	6
1568.3.g.l.687.2		6	7.5	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99052 - 3.44767i) q^{3} +(1.63031 + 0.941260i) q^{5} +(5.14749 - 4.74377i) q^{7} +(-3.42430 + 5.93106i) q^{9} +O(q^{10})\)	\(q+(-1.99052 - 3.44767i) q^{3} +(1.63031 + 0.941260i) q^{5} +(5.14749 - 4.74377i) q^{7} +(-3.42430 + 5.93106i) q^{9} +(-3.93973 - 6.82381i) q^{11} -11.4863i q^{13} -7.49437i q^{15} +(1.44921 + 2.51011i) q^{17} +(-15.0223 + 26.0194i) q^{19} +(-26.6011 - 8.30431i) q^{21} +(-33.3838 - 19.2741i) q^{23} +(-10.7281 - 18.5815i) q^{25} -8.56478 q^{27} -27.8701i q^{29} +(19.4709 - 11.2416i) q^{31} +(-15.6842 + 27.1658i) q^{33} +(12.8571 - 2.88869i) q^{35} +(39.4520 + 22.7776i) q^{37} +(-39.6011 + 22.8637i) q^{39} -40.6313 q^{41} +47.2806 q^{43} +(-11.1653 + 6.44632i) q^{45} +(71.5172 + 41.2905i) q^{47} +(3.99327 - 48.8370i) q^{49} +(5.76936 - 9.99283i) q^{51} +(23.2823 - 13.4420i) q^{53} -14.8332i q^{55} +119.609 q^{57} +(-5.20555 - 9.01627i) q^{59} +(19.1932 + 11.0812i) q^{61} +(10.5091 + 46.7742i) q^{63} +(10.8116 - 18.7263i) q^{65} +(-29.6549 - 51.3639i) q^{67} +153.462i q^{69} -38.2541i q^{71} +(-6.98890 - 12.1051i) q^{73} +(-42.7087 + 73.9737i) q^{75} +(-52.6503 - 16.4363i) q^{77} +(44.3314 + 25.5948i) q^{79} +(47.8670 + 82.9081i) q^{81} +89.4458 q^{83} +5.45635i q^{85} +(-96.0871 + 55.4759i) q^{87} +(-52.6288 + 91.1558i) q^{89} +(-54.4885 - 59.1258i) q^{91} +(-77.5144 - 44.7530i) q^{93} +(-48.9821 + 28.2798i) q^{95} +55.3301 q^{97} +53.9633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 40 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 - 40 * q^9	\( 12 q + 6 q^{3} - 40 q^{9} - 30 q^{11} + 30 q^{17} - 78 q^{19} - 92 q^{25} - 156 q^{27} - 78 q^{33} + 222 q^{35} - 232 q^{41} + 200 q^{43} + 372 q^{49} - 10 q^{51} + 332 q^{57} + 110 q^{59} - 32 q^{65} - 434 q^{67} + 102 q^{73} + 60 q^{75} - 82 q^{81} + 536 q^{83} + 214 q^{89} + 8 q^{91} - 152 q^{97} - 504 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 40 * q^9 - 30 * q^11 + 30 * q^17 - 78 * q^19 - 92 * q^25 - 156 * q^27 - 78 * q^33 + 222 * q^35 - 232 * q^41 + 200 * q^43 + 372 * q^49 - 10 * q^51 + 332 * q^57 + 110 * q^59 - 32 * q^65 - 434 * q^67 + 102 * q^73 + 60 * q^75 - 82 * q^81 + 536 * q^83 + 214 * q^89 + 8 * q^91 - 152 * q^97 - 504 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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