LMFDB - Embedded newform 224.3.o.d.207.5

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			207.5
Root			$0.907369 - 0.0534805i$ of defining polynomial
Character	$\chi$	$=$	224.207
Dual form			224.3.o.d.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.66613 - 4.61787i) q^{3} +(-1.86796 + 1.07847i) q^{5} +(-6.91861 + 1.06433i) q^{7} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})$	\(q+(2.66613 - 4.61787i) q^{3} +(-1.86796 + 1.07847i) q^{5} +(-6.91861 + 1.06433i) q^{7} +(-9.71647 - 16.8294i) q^{9} +(2.62956 - 4.55453i) q^{11} -21.4116i q^{13} +11.5013i q^{15} +(-0.463429 + 0.802683i) q^{17} +(-2.96505 - 5.13561i) q^{19} +(-13.5310 + 34.7869i) q^{21} +(7.52507 - 4.34460i) q^{23} +(-10.1738 + 17.6216i) q^{25} -55.6311 q^{27} +9.42223i q^{29} +(29.8813 + 17.2520i) q^{31} +(-14.0215 - 24.2859i) q^{33} +(11.7758 - 9.44961i) q^{35} +(11.0853 - 6.40011i) q^{37} +(-98.8758 - 57.0860i) q^{39} +43.1339 q^{41} +41.7382 q^{43} +(36.2999 + 20.9578i) q^{45} +(39.8357 - 22.9991i) q^{47} +(46.7344 - 14.7273i) q^{49} +(2.47112 + 4.28011i) q^{51} +(-64.5031 - 37.2409i) q^{53} +11.3436i q^{55} -31.6208 q^{57} +(26.8367 - 46.4825i) q^{59} +(24.0893 - 13.9080i) q^{61} +(85.1365 + 106.095i) q^{63} +(23.0916 + 39.9959i) q^{65} +(-39.2453 + 67.9749i) q^{67} -46.3330i q^{69} -74.5100i q^{71} +(-16.8020 + 29.1020i) q^{73} +(54.2494 + 93.9627i) q^{75} +(-13.3454 + 34.3097i) q^{77} +(-26.1642 + 15.1059i) q^{79} +(-60.8713 + 105.432i) q^{81} +72.9274 q^{83} -1.99917i q^{85} +(43.5106 + 25.1209i) q^{87} +(27.4198 + 47.4925i) q^{89} +(22.7889 + 148.138i) q^{91} +(159.335 - 91.9919i) q^{93} +(11.0772 + 6.39541i) q^{95} -53.7125 q^{97} -102.200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.66613	−	4.61787i	0.888709	−	1.53929i	0.0473064	−	0.998880i	$-0.484936\pi$
$3$	2.66613	−	4.61787i	0.888709	−	1.53929i	0.841403	−	0.540409i	$-0.181730\pi$
$4$		0			0
$5$	−1.86796	+	1.07847i	−0.373592	+	0.215693i	−0.675026	−	0.737794i	$-0.735868\pi$
$5$	−1.86796	+	1.07847i	−0.373592	+	0.215693i	0.301435	+	0.953487i	$0.402534\pi$
$6$		0			0
$7$	−6.91861	+	1.06433i	−0.988373	+	0.152047i
$7$	−6.91861	+	1.06433i	−0.988373	+	0.152047i
$8$		0			0
$9$	−9.71647	−	16.8294i	−1.07961	−	1.86993i
$10$		0			0
$11$	2.62956	−	4.55453i	0.239051	−	0.414048i	−0.721392	−	0.692527i	$-0.756497\pi$
$11$	2.62956	−	4.55453i	0.239051	−	0.414048i	0.960442	+	0.278480i	$0.0898305\pi$
$12$		0			0
$13$		−	21.4116i		−	1.64704i	−0.567285	−	0.823522i	$-0.692006\pi$
$13$		−	21.4116i		−	1.64704i	0.567285	−	0.823522i	$-0.307994\pi$
$14$		0			0
$15$			11.5013i			0.766754i
$16$		0			0
$17$	−0.463429	+	0.802683i	−0.0272606	+	0.0472167i	−0.879334	−	0.476206i	$-0.842012\pi$
$17$	−0.463429	+	0.802683i	−0.0272606	+	0.0472167i	0.852073	+	0.523423i	$0.175345\pi$
$18$		0			0
$19$	−2.96505	−	5.13561i	−0.156055	−	0.270295i	0.777388	−	0.629022i	$-0.216544\pi$
$19$	−2.96505	−	5.13561i	−0.156055	−	0.270295i	−0.933443	+	0.358726i	$0.883211\pi$
$20$		0			0
$21$	−13.5310	+	34.7869i	−0.644332	+	1.65652i
$22$		0			0
$23$	7.52507	−	4.34460i	0.327177	−	0.188896i	−0.327410	−	0.944882i	$-0.606176\pi$
$23$	7.52507	−	4.34460i	0.327177	−	0.188896i	0.654587	+	0.755987i	$0.272843\pi$
$24$		0			0
$25$	−10.1738	+	17.6216i	−0.406953	+	0.704863i
$26$		0			0
$27$	−55.6311			−2.06041
$28$		0			0
$29$			9.42223i			0.324904i	0.986716	+	0.162452i	$0.0519403\pi$
$29$			9.42223i			0.324904i	−0.986716	+	0.162452i	$0.948060\pi$
$30$		0			0
$31$	29.8813	+	17.2520i	0.963912	+	0.556515i	0.897375	−	0.441269i	$-0.145471\pi$
$31$	29.8813	+	17.2520i	0.963912	+	0.556515i	0.0665375	+	0.997784i	$0.478805\pi$
$32$		0			0
$33$	−14.0215	−	24.2859i	−0.424893	−	0.735936i
$34$		0			0
$35$	11.7758	−	9.44961i	0.336453	−	0.269989i
$36$		0			0
$37$	11.0853	−	6.40011i	0.299603	−	0.172976i	−0.342662	−	0.939459i	$-0.611328\pi$
$37$	11.0853	−	6.40011i	0.299603	−	0.172976i	0.642265	+	0.766483i	$0.277995\pi$
$38$		0			0
$39$	−98.8758	−	57.0860i	−2.53528	−	1.46374i
$40$		0			0
$41$	43.1339			1.05205			0.526023	−	0.850470i	$-0.323683\pi$
$41$	43.1339			1.05205			0.526023	+	0.850470i	$0.323683\pi$
$42$		0			0
$43$	41.7382			0.970656			0.485328	−	0.874332i	$-0.338700\pi$
$43$	41.7382			0.970656			0.485328	+	0.874332i	$0.338700\pi$
$44$		0			0
$45$	36.2999	+	20.9578i	0.806665	+	0.465728i
$46$		0			0
$47$	39.8357	−	22.9991i	0.847567	−	0.489343i	−0.0122620	−	0.999925i	$-0.503903\pi$
$47$	39.8357	−	22.9991i	0.847567	−	0.489343i	0.859829	+	0.510582i	$0.170570\pi$
$48$		0			0
$49$	46.7344	−	14.7273i	0.953764	−	0.300558i
$50$		0			0
$51$	2.47112	+	4.28011i	0.0484534	+	0.0839238i
$52$		0			0
$53$	−64.5031	−	37.2409i	−1.21704	−	0.702658i	−0.252756	−	0.967530i	$-0.581337\pi$
$53$	−64.5031	−	37.2409i	−1.21704	−	0.702658i	−0.964284	+	0.264872i	$0.914670\pi$
$54$		0			0
$55$			11.3436i			0.206246i
$56$		0			0
$57$	−31.6208			−0.554751
$58$		0			0
$59$	26.8367	−	46.4825i	0.454860	−	0.787840i	−0.543821	−	0.839201i	$-0.683023\pi$
$59$	26.8367	−	46.4825i	0.454860	−	0.787840i	0.998680	+	0.0513617i	$0.0163561\pi$
$60$		0			0
$61$	24.0893	−	13.9080i	0.394907	−	0.228000i	−0.289377	−	0.957215i	$-0.593448\pi$
$61$	24.0893	−	13.9080i	0.394907	−	0.228000i	0.684284	+	0.729215i	$0.260115\pi$
$62$		0			0
$63$	85.1365	+	106.095i	1.35137	+	1.68404i
$64$		0			0
$65$	23.0916	+	39.9959i	0.355256	+	0.615322i
$66$		0			0
$67$	−39.2453	+	67.9749i	−0.585751	+	1.01455i	0.409030	+	0.912521i	$0.365867\pi$
$67$	−39.2453	+	67.9749i	−0.585751	+	1.01455i	−0.994781	+	0.102030i	$0.967466\pi$
$68$		0			0
$69$		−	46.3330i		−	0.671493i
$70$		0			0
$71$		−	74.5100i		−	1.04944i	−0.851276	−	0.524719i	$-0.824171\pi$
$71$		−	74.5100i		−	1.04944i	0.851276	−	0.524719i	$-0.175829\pi$
$72$		0			0
$73$	−16.8020	+	29.1020i	−0.230165	+	0.398657i	−0.957857	−	0.287247i	$-0.907260\pi$
$73$	−16.8020	+	29.1020i	−0.230165	+	0.398657i	0.727692	+	0.685904i	$0.240593\pi$
$74$		0			0
$75$	54.2494	+	93.9627i	0.723325	+	1.25284i
$76$		0			0
$77$	−13.3454	+	34.3097i	−0.173317	+	0.445581i
$78$		0			0
$79$	−26.1642	+	15.1059i	−0.331192	+	0.191214i	−0.656370	−	0.754439i	$-0.727909\pi$
$79$	−26.1642	+	15.1059i	−0.331192	+	0.191214i	0.325178	+	0.945653i	$0.394576\pi$
$80$		0			0
$81$	−60.8713	+	105.432i	−0.751497	+	1.30163i
$82$		0			0
$83$	72.9274			0.878644			0.439322	−	0.898330i	$-0.355219\pi$
$83$	72.9274			0.878644			0.439322	+	0.898330i	$0.355219\pi$
$84$		0			0
$85$		−	1.99917i		−	0.0235197i
$86$		0			0
$87$	43.5106	+	25.1209i	0.500122	+	0.288745i
$88$		0			0
$89$	27.4198	+	47.4925i	0.308088	+	0.533624i	0.977944	−	0.208867i	$-0.0669776\pi$
$89$	27.4198	+	47.4925i	0.308088	+	0.533624i	−0.669856	+	0.742491i	$0.733644\pi$
$90$		0			0
$91$	22.7889	+	148.138i	0.250428	+	1.62789i
$92$		0			0
$93$	159.335	−	91.9919i	1.71328	−	0.989160i
$94$		0			0
$95$	11.0772	+	6.39541i	0.116602	+	0.0673201i
$96$		0			0
$97$	−53.7125			−0.553738			−0.276869	−	0.960908i	$-0.589297\pi$
$97$	−53.7125			−0.553738			−0.276869	+	0.960908i	$0.589297\pi$
$98$		0			0
$99$	−102.200			−1.03232
$100$		0			0
$101$	78.2037	+	45.1509i	0.774294	+	0.447039i	0.834404	−	0.551153i	$-0.185812\pi$
$101$	78.2037	+	45.1509i	0.774294	+	0.447039i	−0.0601103	+	0.998192i	$0.519145\pi$
$102$		0			0
$103$	−97.6980	+	56.4060i	−0.948525	+	0.547631i	−0.892622	−	0.450805i	$-0.851137\pi$
$103$	−97.6980	+	56.4060i	−0.948525	+	0.547631i	−0.0559023	+	0.998436i	$0.517804\pi$
$104$		0			0
$105$	−12.2412	−	79.5731i	−0.116583	−	0.757839i
$106$		0			0
$107$	−71.9950	−	124.699i	−0.672851	−	1.16541i	−0.977092	−	0.212817i	$-0.931736\pi$
$107$	−71.9950	−	124.699i	−0.672851	−	1.16541i	0.304241	−	0.952595i	$-0.401597\pi$
$108$		0			0
$109$	57.7477	+	33.3406i	0.529795	+	0.305877i	0.740933	−	0.671579i	$-0.234384\pi$
$109$	57.7477	+	33.3406i	0.529795	+	0.305877i	−0.211138	+	0.977456i	$0.567717\pi$
$110$		0			0
$111$		−	68.2540i		−	0.614901i
$112$		0			0
$113$	7.16467			0.0634042			0.0317021	−	0.999497i	$-0.489907\pi$
$113$	7.16467			0.0634042			0.0317021	+	0.999497i	$0.489907\pi$
$114$		0			0
$115$	−9.37101	+	16.2311i	−0.0814870	+	0.141140i
$116$		0			0
$117$	−360.344	+	208.045i	−3.07986	+	1.77816i
$118$		0			0
$119$	2.35197	−	6.04670i	0.0197645	−	0.0508126i
$120$		0			0
$121$	46.6709	+	80.8363i	0.385710	+	0.668069i
$122$		0			0
$123$	115.000	−	199.187i	0.934963	−	1.61940i
$124$		0			0
$125$		−	97.8118i		−	0.782494i
$126$		0			0
$127$		−	131.492i		−	1.03537i	−0.855572	−	0.517684i	$-0.826794\pi$
$127$		−	131.492i		−	1.03537i	0.855572	−	0.517684i	$-0.173206\pi$
$128$		0			0
$129$	111.279	−	192.742i	0.862631	−	1.49412i
$130$		0			0
$131$	−4.38060	−	7.58742i	−0.0334397	−	0.0579193i	0.848821	−	0.528680i	$-0.177313\pi$
$131$	−4.38060	−	7.58742i	−0.0334397	−	0.0579193i	−0.882261	+	0.470761i	$0.843980\pi$
$132$		0			0
$133$	25.9800	+	32.3755i	0.195338	+	0.243425i
$134$		0			0
$135$	103.916	−	59.9962i	0.769752	−	0.444416i
$136$		0			0
$137$	118.420	−	205.110i	0.864381	−	1.49715i	−0.00327850	−	0.999995i	$-0.501044\pi$
$137$	118.420	−	205.110i	0.864381	−	1.49715i	0.867660	−	0.497158i	$-0.165623\pi$
$138$		0			0
$139$	−172.122			−1.23828			−0.619142	−	0.785279i	$-0.712520\pi$
$139$	−172.122			−1.23828			−0.619142	+	0.785279i	$0.712520\pi$
$140$		0			0
$141$		−	245.274i		−	1.73954i
$142$		0			0
$143$	−97.5195	−	56.3029i	−0.681955	−	0.393727i
$144$		0			0
$145$	−10.1616	−	17.6003i	−0.0700797	−	0.121382i
$146$		0			0
$147$	56.5909	−	255.078i	0.384972	−	1.73523i
$148$		0			0
$149$	−199.798	+	115.354i	−1.34093	+	0.774186i	−0.986944	−	0.161066i	$-0.948507\pi$
$149$	−199.798	+	115.354i	−1.34093	+	0.774186i	−0.353985	+	0.935251i	$0.615174\pi$
$150$		0			0
$151$	128.077	+	73.9452i	0.848190	+	0.489703i	0.860040	−	0.510227i	$-0.170439\pi$
$151$	128.077	+	73.9452i	0.848190	+	0.489703i	−0.0118494	+	0.999930i	$0.503772\pi$
$152$		0			0
$153$	18.0116			0.117723
$154$		0			0
$155$	−74.4227			−0.480146
$156$		0			0
$157$	99.4450	+	57.4146i	0.633407	+	0.365698i	0.782070	−	0.623190i	$-0.214164\pi$
$157$	99.4450	+	57.4146i	0.633407	+	0.365698i	−0.148663	+	0.988888i	$0.547497\pi$
$158$		0			0
$159$	−343.947	+	198.578i	−2.16319	+	1.24892i
$160$		0			0
$161$	−47.4389	+	38.0677i	−0.294652	+	0.236446i
$162$		0			0
$163$	24.6545	+	42.7029i	0.151255	+	0.261981i	0.931689	−	0.363257i	$-0.118335\pi$
$163$	24.6545	+	42.7029i	0.151255	+	0.261981i	−0.780434	+	0.625238i	$0.785002\pi$
$164$		0			0
$165$	52.3830	+	30.2433i	0.317473	+	0.183293i
$166$		0			0
$167$			241.457i			1.44585i	0.690926	+	0.722926i	$0.257203\pi$
$167$			241.457i			1.44585i	−0.690926	+	0.722926i	$0.742797\pi$
$168$		0			0
$169$	−289.455			−1.71275
$170$		0			0
$171$	−57.6196	+	99.8001i	−0.336957	+	0.583626i
$172$		0			0
$173$	−47.1300	+	27.2105i	−0.272428	+	0.157286i	−0.629990	−	0.776603i	$-0.716941\pi$
$173$	−47.1300	+	27.2105i	−0.272428	+	0.157286i	0.357563	+	0.933889i	$0.383608\pi$
$174$		0			0
$175$	51.6336	−	132.745i	0.295049	−	0.758544i
$176$		0			0
$177$	−143.100	−	247.857i	−0.808475	−	1.40032i
$178$		0			0
$179$	−63.5100	+	110.003i	−0.354805	+	0.614540i	−0.987084	−	0.160200i	$-0.948786\pi$
$179$	−63.5100	+	110.003i	−0.354805	+	0.614540i	0.632280	+	0.774740i	$0.282119\pi$
$180$		0			0
$181$			212.704i			1.17516i	0.809165	+	0.587581i	$0.199920\pi$
$181$			212.704i			1.17516i	−0.809165	+	0.587581i	$0.800080\pi$
$182$		0			0
$183$		−	148.322i		−	0.810502i
$184$		0			0
$185$	−13.8046	+	23.9103i	−0.0746194	+	0.129245i
$186$		0			0
$187$	2.43723	+	4.22140i	0.0130333	+	0.0225743i
$188$		0			0
$189$	384.890	−	59.2097i	2.03645	−	0.313279i
$190$		0			0
$191$	35.1041	−	20.2674i	0.183791	−	0.106112i	−0.405282	−	0.914192i	$-0.632826\pi$
$191$	35.1041	−	20.2674i	0.183791	−	0.106112i	0.589073	+	0.808080i	$0.299493\pi$
$192$		0			0
$193$	−141.153	+	244.485i	−0.731364	+	1.26676i	0.224936	+	0.974374i	$0.427783\pi$
$193$	−141.153	+	244.485i	−0.731364	+	1.26676i	−0.956300	+	0.292387i	$0.905551\pi$
$194$		0			0
$195$	246.261			1.26288
$196$		0			0
$197$		−	261.806i		−	1.32896i	−0.747304	−	0.664482i	$-0.768652\pi$
$197$		−	261.806i		−	1.32896i	0.747304	−	0.664482i	$-0.231348\pi$
$198$		0			0
$199$	278.968	+	161.062i	1.40185	+	0.809357i	0.994582	−	0.103953i	$-0.0331492\pi$
$199$	278.968	+	161.062i	1.40185	+	0.809357i	0.407265	+	0.913310i	$0.366482\pi$
$200$		0			0
$201$	209.266	+	362.460i	1.04113	+	1.80328i
$202$		0			0
$203$	−10.0283	−	65.1887i	−0.0494007	−	0.321127i
$204$		0			0
$205$	−80.5723	+	46.5184i	−0.393036	+	0.226919i
$206$		0			0
$207$	−146.234	−	84.4283i	−0.706445	−	0.407866i
$208$		0			0
$209$	−31.1870			−0.149220
$210$		0			0
$211$	−169.792			−0.804702			−0.402351	−	0.915485i	$-0.631807\pi$
$211$	−169.792			−0.804702			−0.402351	+	0.915485i	$0.631807\pi$
$212$		0			0
$213$	−344.077	−	198.653i	−1.61539	−	0.932644i
$214$		0			0
$215$	−77.9652	+	45.0133i	−0.362629	+	0.209364i
$216$		0			0
$217$	−225.099	−	87.5562i	−1.03732	−	0.403485i
$218$		0			0
$219$	89.5927	+	155.179i	0.409099	+	0.708581i
$220$		0			0
$221$	17.1867	+	9.92275i	0.0777679	+	0.0448993i
$222$		0			0
$223$		−	45.4626i		−	0.203868i	−0.994791	−	0.101934i	$-0.967497\pi$
$223$		−	45.4626i		−	0.203868i	0.994791	−	0.101934i	$-0.0325031\pi$
$224$		0			0
$225$	395.414			1.75740
$226$		0			0
$227$	92.5653	−	160.328i	0.407777	−	0.706290i	−0.586864	−	0.809686i	$-0.699637\pi$
$227$	92.5653	−	160.328i	0.407777	−	0.706290i	0.994640	+	0.103396i	$0.0329708\pi$
$228$		0			0
$229$	160.173	−	92.4759i	0.699445	−	0.403825i	−0.107695	−	0.994184i	$-0.534347\pi$
$229$	160.173	−	92.4759i	0.699445	−	0.403825i	0.807141	+	0.590359i	$0.201014\pi$
$230$		0			0
$231$	122.857	+	153.101i	0.531849	+	0.662776i
$232$		0			0
$233$	−48.3504	−	83.7453i	−0.207512	−	0.359422i	0.743418	−	0.668827i	$-0.233203\pi$
$233$	−48.3504	−	83.7453i	−0.207512	−	0.359422i	−0.950930	+	0.309405i	$0.899870\pi$
$234$		0			0
$235$	−49.6076	+	85.9228i	−0.211096	+	0.365629i
$236$		0			0
$237$			161.097i			0.679734i
$238$		0			0
$239$		−	163.185i		−	0.682782i	−0.939921	−	0.341391i	$-0.889102\pi$
$239$		−	163.185i		−	0.682782i	0.939921	−	0.341391i	$-0.110898\pi$
$240$		0			0
$241$	−102.745	+	177.960i	−0.426330	+	0.738424i	−0.996544	−	0.0830718i	$-0.973527\pi$
$241$	−102.745	+	177.960i	−0.426330	+	0.738424i	0.570214	+	0.821496i	$0.306860\pi$
$242$		0			0
$243$	74.2413	+	128.590i	0.305520	+	0.529176i
$244$		0			0
$245$	−71.4150	+	77.9116i	−0.291490	+	0.318006i
$246$		0			0
$247$	−109.962	+	63.4863i	−0.445188	+	0.257030i
$248$		0			0
$249$	194.434	−	336.769i	0.780859	−	1.35249i
$250$		0			0
$251$	159.299			0.634658			0.317329	−	0.948316i	$-0.397214\pi$
$251$	159.299			0.634658			0.317329	+	0.948316i	$0.397214\pi$
$252$		0			0
$253$		−	45.6975i		−	0.180622i
$254$		0			0
$255$	−9.23191	−	5.33005i	−0.0362036	−	0.0209021i
$256$		0			0
$257$	−107.889	−	186.868i	−0.419800	−	0.727114i	0.576119	−	0.817366i	$-0.304566\pi$
$257$	−107.889	−	186.868i	−0.419800	−	0.727114i	−0.995919	+	0.0902512i	$0.971233\pi$
$258$		0			0
$259$	−69.8832	+	56.0783i	−0.269819	+	0.216518i
$260$		0			0
$261$	158.571	−	91.5507i	0.607550	−	0.350769i
$262$		0			0
$263$	285.059	+	164.579i	1.08387	+	0.625775i	0.931939	−	0.362616i	$-0.118116\pi$
$263$	285.059	+	164.579i	1.08387	+	0.625775i	0.151935	+	0.988391i	$0.451450\pi$
$264$		0			0
$265$	160.652			0.606234
$266$		0			0
$267$	292.419			1.09520
$268$		0			0
$269$	253.803	+	146.533i	0.943507	+	0.544734i	0.891058	−	0.453889i	$-0.149964\pi$
$269$	253.803	+	146.533i	0.943507	+	0.544734i	0.0524492	+	0.998624i	$0.483297\pi$
$270$		0			0
$271$	−23.2529	+	13.4251i	−0.0858042	+	0.0495391i	−0.542288	−	0.840193i	$-0.682442\pi$
$271$	−23.2529	+	13.4251i	−0.0858042	+	0.0495391i	0.456484	+	0.889732i	$0.349109\pi$
$272$		0			0
$273$	744.841	+	289.719i	2.72836	+	1.06124i
$274$		0			0
$275$	53.5053	+	92.6739i	0.194565	+	0.336996i
$276$		0			0
$277$	−289.925	−	167.389i	−1.04666	−	0.604291i	−0.124949	−	0.992163i	$-0.539877\pi$
$277$	−289.925	−	167.389i	−1.04666	−	0.604291i	−0.921713	+	0.387872i	$0.873210\pi$
$278$		0			0
$279$		−	670.513i		−	2.40327i
$280$		0			0
$281$	−123.357			−0.438994			−0.219497	−	0.975613i	$-0.570442\pi$
$281$	−123.357			−0.438994			−0.219497	+	0.975613i	$0.570442\pi$
$282$		0			0
$283$	−0.309453	+	0.535988i	−0.00109347	+	0.00189395i	−0.866572	−	0.499053i	$-0.833681\pi$
$283$	−0.309453	+	0.535988i	−0.00109347	+	0.00189395i	0.865478	+	0.500947i	$0.167015\pi$
$284$		0			0
$285$	59.0663	−	34.1019i	0.207250	−	0.119656i
$286$		0			0
$287$	−298.427	+	45.9086i	−1.03981	+	0.159960i
$288$		0			0
$289$	144.070	+	249.537i	0.498514	+	0.863451i
$290$		0			0
$291$	−143.204	+	248.037i	−0.492112	+	0.852362i
$292$		0			0
$293$			28.2794i			0.0965169i	0.998835	+	0.0482584i	$0.0153671\pi$
$293$			28.2794i			0.0965169i	−0.998835	+	0.0482584i	$0.984633\pi$
$294$		0			0
$295$			115.770i			0.392440i
$296$		0			0
$297$	−146.285	+	253.373i	−0.492542	+	0.853108i
$298$		0			0
$299$	−93.0247	−	161.123i	−0.311119	−	0.538874i
$300$		0			0
$301$	−288.771	+	44.4231i	−0.959371	+	0.147585i
$302$		0			0
$303$	417.002	−	240.756i	1.37624	−	0.794575i
$304$		0			0
$305$	−29.9986	+	51.9591i	−0.0983560	+	0.170358i
$306$		0			0
$307$	−400.893			−1.30584			−0.652921	−	0.757426i	$-0.726457\pi$
$307$	−400.893			−1.30584			−0.652921	+	0.757426i	$0.726457\pi$
$308$		0			0
$309$			601.542i			1.94674i
$310$		0			0
$311$	−140.492	−	81.1132i	−0.451743	−	0.260814i	0.256823	−	0.966459i	$-0.417324\pi$
$311$	−140.492	−	81.1132i	−0.451743	−	0.260814i	−0.708566	+	0.705644i	$0.750658\pi$
$312$		0			0
$313$	133.123	+	230.576i	0.425313	+	0.736664i	0.996450	−	0.0841913i	$-0.0268307\pi$
$313$	133.123	+	230.576i	0.425313	+	0.736664i	−0.571137	+	0.820855i	$0.693497\pi$
$314$		0			0
$315$	−273.451	−	106.364i	−0.868098	−	0.337662i
$316$		0			0
$317$	374.864	−	216.428i	1.18254	−	0.682737i	0.225936	−	0.974142i	$-0.427456\pi$
$317$	374.864	−	216.428i	1.18254	−	0.682737i	0.956600	+	0.291405i	$0.0941228\pi$
$318$		0			0
$319$	42.9138	+	24.7763i	0.134526	+	0.0776686i
$320$		0			0
$321$	−767.792			−2.39187
$322$		0			0
$323$	5.49636			0.0170166
$324$		0			0
$325$	377.305	+	217.837i	1.16094	+	0.670269i
$326$		0			0
$327$	307.925	−	177.781i	0.941668	−	0.543672i
$328$		0			0
$329$	−251.129	+	201.520i	−0.763310	+	0.612524i
$330$		0			0
$331$	40.6264	+	70.3671i	0.122738	+	0.212589i	0.920847	−	0.389925i	$-0.127499\pi$
$331$	40.6264	+	70.3671i	0.122738	+	0.212589i	−0.798108	+	0.602514i	$0.794166\pi$
$332$		0			0
$333$	−215.420	−	124.373i	−0.646907	−	0.373492i
$334$		0			0
$335$		−	169.299i		−	0.505370i
$336$		0			0
$337$	−69.4941			−0.206214			−0.103107	−	0.994670i	$-0.532878\pi$
$337$	−69.4941			−0.206214			−0.103107	+	0.994670i	$0.532878\pi$
$338$		0			0
$339$	19.1019	−	33.0855i	0.0563479	−	0.0975974i
$340$		0			0
$341$	157.149	−	90.7300i	0.460848	−	0.266071i
$342$		0			0
$343$	−307.663	+	151.634i	−0.896975	+	0.442080i
$344$		0			0
$345$	49.9686	+	86.5481i	0.144836	+	0.250864i
$346$		0			0
$347$	−174.677	+	302.549i	−0.503391	+	0.871899i	0.496601	+	0.867979i	$0.334581\pi$
$347$	−174.677	+	302.549i	−0.503391	+	0.871899i	−0.999992	+	0.00392020i	$0.998752\pi$
$348$		0			0
$349$		−	165.836i		−	0.475174i	−0.971366	−	0.237587i	$-0.923643\pi$
$349$		−	165.836i		−	0.475174i	0.971366	−	0.237587i	$-0.0763566\pi$
$350$		0			0
$351$			1191.15i			3.39358i
$352$		0			0
$353$	235.858	−	408.519i	0.668154	−	1.15728i	−0.310266	−	0.950650i	$-0.600418\pi$
$353$	235.858	−	408.519i	0.668154	−	1.15728i	0.978420	−	0.206627i	$-0.0662486\pi$
$354$		0			0
$355$	80.3566	+	139.182i	0.226356	+	0.392061i
$356$		0			0
$357$	−21.6522	−	26.9823i	−0.0606504	−	0.0755808i
$358$		0			0
$359$	−568.967	+	328.493i	−1.58487	+	0.915022i	−0.590731	+	0.806869i	$0.701161\pi$
$359$	−568.967	+	328.493i	−1.58487	+	0.915022i	−0.994134	+	0.108154i	$0.965506\pi$
$360$		0			0
$361$	162.917	−	282.180i	0.451294	−	0.781663i
$362$		0			0
$363$	497.722			1.37113
$364$		0			0
$365$		−	72.4817i		−	0.198580i
$366$		0			0
$367$	307.850	+	177.737i	0.838829	+	0.484298i	0.856866	−	0.515539i	$-0.172408\pi$
$367$	307.850	+	177.737i	0.838829	+	0.484298i	−0.0180371	+	0.999837i	$0.505742\pi$
$368$		0			0
$369$	−419.109	−	725.918i	−1.13580	−	1.96726i
$370$		0			0
$371$	485.908	+	189.003i	1.30973	+	0.509441i
$372$		0			0
$373$	−273.662	+	157.999i	−0.733680	+	0.423590i	−0.819767	−	0.572698i	$-0.805897\pi$
$373$	−273.662	+	157.999i	−0.733680	+	0.423590i	0.0860872	+	0.996288i	$0.472564\pi$
$374$		0			0
$375$	−451.682	−	260.779i	−1.20449	−	0.695410i
$376$		0			0
$377$	201.745			0.535132
$378$		0			0
$379$	178.404			0.470723			0.235361	−	0.971908i	$-0.424373\pi$
$379$	178.404			0.470723			0.235361	+	0.971908i	$0.424373\pi$
$380$		0			0
$381$	−607.211	−	350.574i	−1.59373	−	0.920140i
$382$		0			0
$383$	604.832	−	349.200i	1.57920	−	0.911750i	0.584225	−	0.811591i	$-0.301398\pi$
$383$	604.832	−	349.200i	1.57920	−	0.911750i	0.994972	−	0.100158i	$-0.0319349\pi$
$384$		0			0
$385$	−12.0733	−	78.4816i	−0.0313591	−	0.203848i
$386$		0			0
$387$	−405.548	−	702.430i	−1.04793	−	1.81506i
$388$		0			0
$389$	−151.865	−	87.6790i	−0.390397	−	0.225396i	0.291935	−	0.956438i	$-0.405701\pi$
$389$	−151.865	−	87.6790i	−0.390397	−	0.225396i	−0.682332	+	0.731042i	$0.739034\pi$
$390$		0			0
$391$			8.05366i			0.0205976i
$392$		0			0
$393$	−46.7170			−0.118873
$394$		0			0
$395$	32.5824	−	56.4344i	0.0824871	−	0.142872i
$396$		0			0
$397$	334.033	−	192.854i	0.841393	−	0.485778i	−0.0163447	−	0.999866i	$-0.505203\pi$
$397$	334.033	−	192.854i	0.841393	−	0.485778i	0.857737	+	0.514088i	$0.171870\pi$
$398$		0			0
$399$	218.772	−	33.6549i	0.548301	−	0.0843481i
$400$		0			0
$401$	−263.548	−	456.479i	−0.657228	−	1.13835i	−0.981330	−	0.192330i	$-0.938396\pi$
$401$	−263.548	−	456.479i	−0.657228	−	1.13835i	0.324103	−	0.946022i	$-0.394938\pi$
$402$		0			0
$403$	369.392	−	639.805i	0.916605	−	1.58761i
$404$		0			0
$405$		−	262.590i		−	0.648371i
$406$		0			0
$407$		−	67.3178i		−	0.165400i
$408$		0			0
$409$	211.872	−	366.973i	0.518025	−	0.897245i	−0.481756	−	0.876305i	$-0.660001\pi$
$409$	211.872	−	366.973i	0.518025	−	0.897245i	0.999781	−	0.0209399i	$-0.00666585\pi$
$410$		0			0
$411$	−631.447	−	1093.70i	−1.53637	−	2.66107i
$412$		0			0
$413$	−136.200	+	350.158i	−0.329782	+	0.847840i
$414$		0			0
$415$	−136.225	+	78.6498i	−0.328254	+	0.189517i
$416$		0			0
$417$	−458.898	+	794.834i	−1.10047	+	1.90608i
$418$		0			0
$419$	−295.598			−0.705485			−0.352742	−	0.935721i	$-0.614751\pi$
$419$	−295.598			−0.705485			−0.352742	+	0.935721i	$0.614751\pi$
$420$		0			0
$421$			126.260i			0.299904i	0.988693	+	0.149952i	$0.0479119\pi$
$421$			126.260i			0.299904i	−0.988693	+	0.149952i	$0.952088\pi$
$422$		0			0
$423$	−774.124	−	446.941i	−1.83008	−	1.05660i
$424$		0			0
$425$	−9.42970	−	16.3327i	−0.0221875	−	0.0384299i
$426$		0			0
$427$	−151.862	+	121.863i	−0.355649	+	0.285393i
$428$		0			0
$429$	−519.999	+	300.221i	−1.21212	+	0.699817i
$430$		0			0
$431$	−220.198	−	127.131i	−0.510900	−	0.294968i	0.222303	−	0.974978i	$-0.428642\pi$
$431$	−220.198	−	127.131i	−0.510900	−	0.294968i	−0.733204	+	0.680009i	$0.761976\pi$
$432$		0			0
$433$	546.301			1.26167			0.630833	−	0.775919i	$-0.282713\pi$
$433$	546.301			1.26167			0.630833	+	0.775919i	$0.282713\pi$
$434$		0			0
$435$	−108.368			−0.249122
$436$		0			0
$437$	−44.6244	−	25.7639i	−0.102115	−	0.0589563i
$438$		0			0
$439$	236.715	−	136.667i	0.539214	−	0.311315i	−0.205546	−	0.978647i	$-0.565897\pi$
$439$	236.715	−	136.667i	0.539214	−	0.311315i	0.744760	+	0.667332i	$0.232564\pi$
$440$		0			0
$441$	−701.946	−	643.415i	−1.59171	−	1.45899i
$442$		0			0
$443$	237.385	+	411.163i	0.535858	+	0.928133i	0.999121	+	0.0419124i	$0.0133450\pi$
$443$	237.385	+	411.163i	0.535858	+	0.928133i	−0.463263	+	0.886221i	$0.653322\pi$
$444$		0			0
$445$	−102.438	−	59.1427i	−0.230198	−	0.132905i
$446$		0			0
$447$			1230.19i			2.75210i
$448$		0			0
$449$	782.101			1.74187			0.870936	−	0.491396i	$-0.163513\pi$
$449$	782.101			1.74187			0.870936	+	0.491396i	$0.163513\pi$
$450$		0			0
$451$	113.423	−	196.454i	0.251492	−	0.435597i
$452$		0			0
$453$	682.938	−	394.294i	1.50759	−	0.870407i
$454$		0			0
$455$	−202.331	−	252.139i	−0.444683	−	0.554152i
$456$		0			0
$457$	94.7793	+	164.163i	0.207395	+	0.359218i	0.950893	−	0.309520i	$-0.100168\pi$
$457$	94.7793	+	164.163i	0.207395	+	0.359218i	−0.743498	+	0.668738i	$0.766835\pi$
$458$		0			0
$459$	25.7811	−	44.6541i	0.0561679	−	0.0972857i
$460$		0			0
$461$			202.533i			0.439335i	0.975575	+	0.219667i	$0.0704972\pi$
$461$			202.533i			0.439335i	−0.975575	+	0.219667i	$0.929503\pi$
$462$		0			0
$463$		−	652.927i		−	1.41021i	−0.709103	−	0.705105i	$-0.750900\pi$
$463$		−	652.927i		−	1.41021i	0.709103	−	0.705105i	$-0.249100\pi$
$464$		0			0
$465$	−198.420	+	343.674i	−0.426710	+	0.739084i
$466$		0			0
$467$	272.725	+	472.373i	0.583993	+	1.01150i	0.995000	+	0.0998730i	$0.0318437\pi$
$467$	272.725	+	472.373i	0.583993	+	1.01150i	−0.411008	+	0.911632i	$0.634823\pi$
$468$		0			0
$469$	199.176	−	512.062i	0.424682	−	1.09182i
$470$		0			0
$471$	530.266	−	306.149i	1.12583	−	0.649998i
$472$		0			0
$473$	109.753	−	190.098i	0.232036	−	0.401898i
$474$		0			0
$475$	120.663			0.254028
$476$		0			0
$477$			1447.40i			3.03438i
$478$		0			0
$479$	94.3079	+	54.4487i	0.196885	+	0.113672i	0.595202	−	0.803576i	$-0.297072\pi$
$479$	94.3079	+	54.4487i	0.196885	+	0.113672i	−0.398317	+	0.917248i	$0.630405\pi$
$480$		0			0
$481$	−137.036	−	237.354i	−0.284899	−	0.493459i
$482$		0			0
$483$	49.3135	+	320.560i	0.102098	+	0.663686i
$484$		0			0
$485$	100.333	−	57.9272i	0.206872	−	0.119437i
$486$		0			0
$487$	−371.831	−	214.677i	−0.763513	−	0.440814i	0.0670428	−	0.997750i	$-0.478644\pi$
$487$	−371.831	−	214.677i	−0.763513	−	0.440814i	−0.830556	+	0.556936i	$0.811977\pi$
$488$		0			0
$489$	262.929			0.537686
$490$		0			0
$491$	−453.887			−0.924413			−0.462206	−	0.886772i	$-0.652942\pi$
$491$	−453.887			−0.924413			−0.462206	+	0.886772i	$0.652942\pi$
$492$		0			0
$493$	−7.56306	−	4.36654i	−0.0153409	−	0.00885707i
$494$		0			0
$495$	190.905	−	110.219i	0.385667	−	0.222665i
$496$		0			0
$497$	79.3031	+	515.506i	0.159564	+	1.03724i
$498$		0			0
$499$	166.698	+	288.730i	0.334064	+	0.578617i	0.983305	−	0.181967i	$-0.0582463\pi$
$499$	166.698	+	288.730i	0.334064	+	0.578617i	−0.649240	+	0.760583i	$0.724913\pi$
$500$		0			0
$501$	1115.02	+	643.755i	2.22558	+	1.28494i
$502$		0			0
$503$			580.170i			1.15342i	0.816949	+	0.576710i	$0.195664\pi$
$503$			580.170i			1.15342i	−0.816949	+	0.576710i	$0.804336\pi$
$504$		0			0
$505$	−194.775			−0.385693
$506$		0			0
$507$	−771.724	+	1336.67i	−1.52214	+	2.63642i
$508$		0			0
$509$	−266.271	+	153.732i	−0.523126	+	0.302027i	−0.738213	−	0.674568i	$-0.764330\pi$
$509$	−266.271	+	153.732i	−0.523126	+	0.302027i	0.215087	+	0.976595i	$0.430997\pi$
$510$		0			0
$511$	85.2728	−	219.228i	0.166874	−	0.429018i
$512$		0			0
$513$	164.949	+	285.700i	0.321538	+	0.556919i
$514$		0			0
$515$	121.664	−	210.728i	0.236241	−	0.409181i
$516$		0			0
$517$		−	241.910i		−	0.467911i
$518$		0			0
$519$			290.187i			0.559127i
$520$		0			0
$521$	−360.480	+	624.369i	−0.691899	+	1.19840i	0.279316	+	0.960199i	$0.409892\pi$
$521$	−360.480	+	624.369i	−0.691899	+	1.19840i	−0.971215	+	0.238205i	$0.923441\pi$
$522$		0			0
$523$	−134.988	−	233.807i	−0.258104	−	0.447049i	0.707630	−	0.706583i	$-0.249764\pi$
$523$	−134.988	−	233.807i	−0.258104	−	0.447049i	−0.965734	+	0.259534i	$0.916431\pi$
$524$		0			0
$525$	−475.338	−	592.353i	−0.905405	−	1.12829i
$526$		0			0
$527$	−27.6957	+	15.9901i	−0.0525536	+	0.0303418i
$528$		0			0
$529$	−226.749	+	392.741i	−0.428637	+	0.742421i
$530$		0			0
$531$	−1043.03			−1.96428
$532$		0			0
$533$		−	923.564i		−	1.73277i
$534$		0			0
$535$	268.967	+	155.288i	0.502743	+	0.290259i
$536$		0			0
$537$	338.652	+	586.562i	0.630636	+	1.09229i
$538$		0			0
$539$	55.8147	−	251.579i	0.103552	−	0.466752i
$540$		0			0
$541$	−785.695	+	453.621i	−1.45230	+	0.838486i	−0.998612	−	0.0526734i	$-0.983226\pi$
$541$	−785.695	+	453.621i	−1.45230	+	0.838486i	−0.453689	+	0.891160i	$0.649892\pi$
$542$		0			0
$543$	982.241	+	567.097i	1.80891	+	1.04438i
$544$		0			0
$545$	−143.827			−0.263903
$546$		0			0
$547$	557.327			1.01888			0.509439	−	0.860506i	$-0.329853\pi$
$547$	557.327			1.01888			0.509439	+	0.860506i	$0.329853\pi$
$548$		0			0
$549$	−468.127	−	270.273i	−0.852690	−	0.492301i
$550$		0			0
$551$	48.3889	−	27.9374i	0.0878202	−	0.0507030i
$552$		0			0
$553$	164.942	−	132.359i	0.298268	−	0.239347i
$554$		0			0
$555$	73.6096	+	127.496i	0.132630	+	0.229722i
$556$		0			0
$557$	741.896	+	428.334i	1.33195	+	0.769002i	0.985598	−	0.169103i	$-0.0540869\pi$
$557$	741.896	+	428.334i	1.33195	+	0.769002i	0.346352	+	0.938105i	$0.387420\pi$
$558$		0			0
$559$		−	893.680i		−	1.59871i
$560$		0			0
$561$	25.9918			0.0463313
$562$		0			0
$563$	6.84436	−	11.8548i	0.0121569	−	0.0210564i	−0.859883	−	0.510491i	$-0.829464\pi$
$563$	6.84436	−	11.8548i	0.0121569	−	0.0210564i	0.872040	+	0.489435i	$0.162797\pi$
$564$		0			0
$565$	−13.3833	+	7.72686i	−0.0236873	+	0.0136759i
$566$		0			0
$567$	308.930	−	794.231i	0.544851	−	1.40076i
$568$		0			0
$569$	545.991	+	945.684i	0.959563	+	1.66201i	0.723563	+	0.690258i	$0.242503\pi$
$569$	545.991	+	945.684i	0.959563	+	1.66201i	0.235999	+	0.971753i	$0.424164\pi$
$570$		0			0
$571$	359.549	−	622.757i	0.629683	−	1.09064i	−0.357932	−	0.933747i	$-0.616518\pi$
$571$	359.549	−	622.757i	0.629683	−	1.09064i	0.987615	−	0.156895i	$-0.0501485\pi$
$572$		0			0
$573$		−	216.142i		−	0.377210i
$574$		0			0
$575$			176.805i			0.307486i
$576$		0			0
$577$	515.560	−	892.976i	0.893518	−	1.54762i	0.0578905	−	0.998323i	$-0.481563\pi$
$577$	515.560	−	892.976i	0.893518	−	1.54762i	0.835628	−	0.549296i	$-0.185104\pi$
$578$		0			0
$579$	752.665	+	1303.65i	1.29994	+	2.25156i
$580$		0			0
$581$	−504.557	+	77.6187i	−0.868428	+	0.133595i
$582$		0			0
$583$	−339.229	+	195.854i	−0.581868	+	0.335942i
$584$		0			0
$585$	448.738	−	777.238i	0.767074	−	1.32861i
$586$		0			0
$587$	671.907			1.14464			0.572322	−	0.820029i	$-0.306043\pi$
$587$	671.907			1.14464			0.572322	+	0.820029i	$0.306043\pi$
$588$		0			0
$589$		−	204.612i		−	0.347388i
$590$		0			0
$591$	−1208.99	−	698.008i	−2.04566	−	1.18106i
$592$		0			0
$593$	−176.999	−	306.572i	−0.298481	−	0.516984i	0.677308	−	0.735700i	$-0.263147\pi$
$593$	−176.999	−	306.572i	−0.298481	−	0.516984i	−0.975789	+	0.218716i	$0.929813\pi$
$594$		0			0
$595$	2.12777	+	13.8315i	0.00357609	+	0.0232462i
$596$		0			0
$597$	1487.53	−	858.824i	2.49167	−	1.43857i
$598$		0			0
$599$	983.923	+	568.068i	1.64261	+	0.948361i	0.979901	+	0.199484i	$0.0639265\pi$
$599$	983.923	+	568.068i	1.64261	+	0.948361i	0.662708	+	0.748878i	$0.269407\pi$
$600$		0			0
$601$	−6.80783			−0.0113275			−0.00566375	−	0.999984i	$-0.501803\pi$
$601$	−6.80783			−0.0113275			−0.00566375	+	0.999984i	$0.501803\pi$
$602$		0			0
$603$	1525.30			2.52953
$604$		0			0
$605$	−174.358	−	100.666i	−0.288196	−	0.166390i
$606$		0			0
$607$	−386.628	+	223.220i	−0.636948	+	0.367742i	−0.783438	−	0.621470i	$-0.786536\pi$
$607$	−386.628	+	223.220i	−0.636948	+	0.367742i	0.146490	+	0.989212i	$0.453202\pi$
$608$		0			0
$609$	−327.770	−	127.492i	−0.538210	−	0.209346i
$610$		0			0
$611$	−492.447	−	852.944i	−0.805970	−	1.39598i
$612$		0			0
$613$	555.650	+	320.805i	0.906443	+	0.523335i	0.879285	−	0.476296i	$-0.158021\pi$
$613$	555.650	+	320.805i	0.906443	+	0.523335i	0.0271583	+	0.999631i	$0.491354\pi$
$614$		0			0
$615$			496.096i			0.806661i
$616$		0			0
$617$	−502.890			−0.815057			−0.407528	−	0.913193i	$-0.633609\pi$
$617$	−502.890			−0.815057			−0.407528	+	0.913193i	$0.633609\pi$
$618$		0			0
$619$	216.495	−	374.980i	0.349749	−	0.605783i	−0.636456	−	0.771313i	$-0.719600\pi$
$619$	216.495	−	374.980i	0.349749	−	0.605783i	0.986205	+	0.165530i	$0.0529336\pi$
$620$		0			0
$621$	−418.627	+	241.695i	−0.674118	+	0.389202i
$622$		0			0
$623$	−240.255	−	299.399i	−0.385642	−	0.480576i
$624$		0			0
$625$	−148.859	−	257.831i	−0.238174	−	0.412530i
$626$		0			0
$627$	−83.1486	+	144.018i	−0.132613	+	0.229693i
$628$		0			0
$629$			11.8640i			0.0188617i
$630$		0			0
$631$			238.957i			0.378695i	0.981910	+	0.189348i	$0.0606373\pi$
$631$			238.957i			0.378695i	−0.981910	+	0.189348i	$0.939363\pi$
$632$		0			0
$633$	−452.687	+	784.078i	−0.715146	+	1.23867i
$634$		0			0
$635$	141.809	+	245.621i	0.223322	+	0.386805i
$636$		0			0
$637$	−315.336	−	1000.66i	−0.495032	−	1.57089i
$638$		0			0
$639$	−1253.96	+	723.974i	−1.96238	+	1.13298i
$640$		0			0
$641$	3.98065	−	6.89469i	0.00621006	−	0.0107561i	−0.862904	−	0.505368i	$-0.831357\pi$
$641$	3.98065	−	6.89469i	0.00621006	−	0.0107561i	0.869114	+	0.494612i	$0.164690\pi$
$642$		0			0
$643$	584.919			0.909672			0.454836	−	0.890575i	$-0.349698\pi$
$643$	584.919			0.909672			0.454836	+	0.890575i	$0.349698\pi$
$644$		0			0
$645$			480.044i			0.744255i
$646$		0			0
$647$	290.707	+	167.840i	0.449316	+	0.259413i	0.707541	−	0.706672i	$-0.249804\pi$
$647$	290.707	+	167.840i	0.449316	+	0.259413i	−0.258225	+	0.966085i	$0.583138\pi$
$648$		0			0
$649$	−141.137	−	244.457i	−0.217469	−	0.376667i
$650$		0			0
$651$	−1004.46	+	806.040i	−1.54296	+	1.23816i
$652$		0			0
$653$	42.0252	−	24.2632i	0.0643571	−	0.0371566i	−0.467476	−	0.884006i	$-0.654837\pi$
$653$	42.0252	−	24.2632i	0.0643571	−	0.0371566i	0.531833	+	0.846849i	$0.321503\pi$
$654$		0			0
$655$	16.3656	+	9.44866i	0.0249856	+	0.0144254i
$656$		0			0
$657$	653.026			0.993951
$658$		0			0
$659$	−1224.65			−1.85835			−0.929176	−	0.369638i	$-0.879482\pi$
$659$	−1224.65			−1.85835			−0.929176	+	0.369638i	$0.879482\pi$
$660$		0			0
$661$	725.765	+	419.021i	1.09798	+	0.633919i	0.935690	−	0.352823i	$-0.114778\pi$
$661$	725.765	+	419.021i	1.09798	+	0.633919i	0.162291	+	0.986743i	$0.448112\pi$
$662$		0			0
$663$	91.6439	−	52.9106i	0.138226	−	0.0798049i
$664$		0			0
$665$	−83.4455	−	32.4576i	−0.125482	−	0.0488084i
$666$		0			0
$667$	40.9358	+	70.9029i	0.0613730	+	0.106301i
$668$		0			0
$669$	−209.940	−	121.209i	−0.313812	−	0.181180i
$670$		0			0
$671$		−	146.287i		−	0.218014i
$672$		0			0
$673$	147.714			0.219486			0.109743	−	0.993960i	$-0.464997\pi$
$673$	147.714			0.219486			0.109743	+	0.993960i	$0.464997\pi$
$674$		0			0
$675$	565.980	−	980.307i	0.838490	−	1.45231i
$676$		0			0
$677$	−725.024	+	418.593i	−1.07094	+	0.618305i	−0.928437	−	0.371490i	$-0.878847\pi$
$677$	−725.024	+	418.593i	−1.07094	+	0.618305i	−0.142499	+	0.989795i	$0.545514\pi$
$678$		0			0
$679$	371.616	−	57.1678i	0.547299	−	0.0841941i
$680$		0			0
$681$	−493.582	−	854.909i	−0.724790	−	1.25537i
$682$		0			0
$683$	−32.2189	+	55.8047i	−0.0471725	+	0.0817053i	−0.888648	−	0.458591i	$-0.848354\pi$
$683$	−32.2189	+	55.8047i	−0.0471725	+	0.0817053i	0.841475	+	0.540296i	$0.181688\pi$
$684$		0			0
$685$			510.849i			0.745765i
$686$		0			0
$687$		−	986.210i		−	1.43553i
$688$		0			0
$689$	−797.385	+	1381.11i	−1.15731	+	2.00452i
$690$		0			0
$691$	−263.374	−	456.177i	−0.381149	−	0.660169i	0.610078	−	0.792341i	$-0.291138\pi$
$691$	−263.374	−	456.177i	−0.381149	−	0.660169i	−0.991227	+	0.132172i	$0.957805\pi$
$692$		0			0
$693$	707.082	−	108.774i	1.02032	−	0.156961i
$694$		0			0
$695$	321.516	−	185.627i	0.462613	−	0.267090i
$696$		0			0
$697$	−19.9895	+	34.6229i	−0.0286794	+	0.0496741i
$698$		0			0
$699$	−515.633			−0.737672
$700$		0			0
$701$		−	695.486i		−	0.992134i	−0.868284	−	0.496067i	$-0.834777\pi$
$701$		−	695.486i		−	0.992134i	0.868284	−	0.496067i	$-0.165223\pi$
$702$		0			0
$703$	−65.7370	−	37.9532i	−0.0935092	−	0.0539875i
$704$		0			0
$705$	264.520	+	458.162i	0.375206	+	0.649876i
$706$		0			0
$707$	−589.117	−	229.147i	−0.833262	−	0.324112i
$708$		0			0
$709$	−803.161	+	463.705i	−1.13281	+	0.654027i	−0.944640	−	0.328110i	$-0.893588\pi$
$709$	−803.161	+	463.705i	−1.13281	+	0.654027i	−0.188168	+	0.982137i	$0.560255\pi$
$710$		0			0
$711$	508.447	+	293.552i	0.715115	+	0.412872i
$712$		0			0
$713$	299.812			0.420493
$714$		0			0
$715$	242.883			0.339697
$716$		0			0
$717$	−753.566	−	435.071i	−1.05100	−	0.606794i
$718$		0			0
$719$	1150.37	−	664.169i	1.59996	−	0.923739i	0.608471	−	0.793576i	$-0.291783\pi$
$719$	1150.37	−	664.169i	1.59996	−	0.923739i	0.991493	−	0.130163i	$-0.0415501\pi$
$720$		0			0
$721$	615.900	−	494.234i	0.854231	−	0.685484i
$722$		0			0
$723$	547.865	+	948.929i	0.757766	+	1.31249i
$724$		0			0
$725$	−166.034	−	95.8600i	−0.229013	−	0.132221i
$726$		0			0
$727$			539.401i			0.741954i	0.928642	+	0.370977i	$0.120977\pi$
$727$			539.401i			0.741954i	−0.928642	+	0.370977i	$0.879023\pi$
$728$		0			0
$729$	−303.936			−0.416922
$730$		0			0
$731$	−19.3427	+	33.5026i	−0.0264606	+	0.0458311i
$732$		0			0
$733$	−382.859	+	221.044i	−0.522318	+	0.301561i	−0.737883	−	0.674929i	$-0.764174\pi$
$733$	−382.859	+	221.044i	−0.522318	+	0.301561i	0.215564	+	0.976490i	$0.430841\pi$
$734$		0			0
$735$	169.384	+	537.507i	0.230454	+	0.731302i
$736$		0			0
$737$	206.396	+	357.488i	0.280048	+	0.485058i
$738$		0			0
$739$	−574.116	+	994.398i	−0.776882	+	1.34560i	0.156848	+	0.987623i	$0.449867\pi$
$739$	−574.116	+	994.398i	−0.776882	+	1.34560i	−0.933730	+	0.357977i	$0.883467\pi$
$740$		0			0
$741$			677.050i			0.913698i
$742$		0			0
$743$			588.688i			0.792313i	0.918183	+	0.396156i	$0.129656\pi$
$743$			588.688i			0.792313i	−0.918183	+	0.396156i	$0.870344\pi$
$744$		0			0
$745$	248.810	−	430.952i	0.333973	−	0.578459i
$746$		0			0
$747$	−708.597	−	1227.33i	−0.948590	−	1.64301i
$748$		0			0
$749$	630.826	+	786.118i	0.842225	+	1.04956i
$750$		0			0
$751$	−708.754	+	409.199i	−0.943747	+	0.544873i	−0.891133	−	0.453742i	$-0.850089\pi$
$751$	−708.754	+	409.199i	−0.943747	+	0.544873i	−0.0526140	+	0.998615i	$0.516755\pi$
$752$		0			0
$753$	424.712	−	735.622i	0.564026	−	0.976922i
$754$		0			0
$755$	−318.989			−0.422503
$756$		0			0
$757$			105.101i			0.138838i	0.997588	+	0.0694192i	$0.0221146\pi$
$757$			105.101i			0.138838i	−0.997588	+	0.0694192i	$0.977885\pi$
$758$		0			0
$759$	−211.025	−	121.835i	−0.278030	−	0.160521i
$760$		0			0
$761$	−507.117	−	878.352i	−0.666382	−	1.15421i	−0.978909	−	0.204299i	$-0.934509\pi$
$761$	−507.117	−	878.352i	−0.666382	−	1.15421i	0.312527	−	0.949909i	$-0.398825\pi$
$762$		0			0
$763$	−435.019	−	169.209i	−0.570143	−	0.221767i
$764$		0			0
$765$	−33.6449	+	19.4249i	−0.0439803	+	0.0253920i
$766$		0			0
$767$	−995.264	−	574.616i	−1.29761	−	0.749173i
$768$		0			0
$769$	−1183.99			−1.53964			−0.769822	−	0.638258i	$-0.779655\pi$
$769$	−1183.99			−1.53964			−0.769822	+	0.638258i	$0.779655\pi$
$770$		0			0
$771$	−1150.58			−1.49232
$772$		0			0
$773$	−280.862	−	162.156i	−0.363340	−	0.209774i	0.307205	−	0.951643i	$-0.400606\pi$
$773$	−280.862	−	162.156i	−0.363340	−	0.209774i	−0.670545	+	0.741869i	$0.733940\pi$
$774$		0			0
$775$	−608.014	+	351.037i	−0.784534	+	0.452951i
$776$		0			0
$777$	72.6446	+	472.223i	0.0934937	+	0.607751i
$778$		0			0
$779$	−127.894	−	221.519i	−0.164177	−	0.284363i
$780$		0			0
$781$	−339.358	−	195.928i	−0.434517	−	0.250869i
$782$		0			0
$783$		−	524.168i		−	0.669436i
$784$		0			0
$785$	−247.679			−0.315514
$786$		0			0
$787$	134.268	−	232.559i	0.170607	−	0.295500i	−0.768025	−	0.640420i	$-0.778760\pi$
$787$	134.268	−	232.559i	0.170607	−	0.295500i	0.938632	+	0.344919i	$0.112094\pi$
$788$		0			0
$789$	1520.01	−	877.576i	1.92650	−	1.11226i
$790$		0			0
$791$	−49.5696	+	7.62556i	−0.0626670	+	0.00964040i
$792$		0			0
$793$	−297.792	−	515.791i	−0.375526	−	0.650429i
$794$		0			0
$795$	428.319	−	741.870i	0.538766	−	0.933170i
$796$		0			0
$797$			1502.06i			1.88465i	0.334705	+	0.942323i	$0.391363\pi$
$797$			1502.06i			1.88465i	−0.334705	+	0.942323i	$0.608637\pi$
$798$		0			0
$799$			42.6339i			0.0533591i
$800$		0			0
$801$	532.848	−	922.919i	0.665228	−	1.15221i
$802$		0			0
$803$	88.3638	+	153.051i	0.110042	+	0.190599i
$804$		0			0
$805$	47.5592	−	122.270i	0.0590797	−	0.151888i
$806$		0			0
$807$	1353.34	−	781.354i	1.67701	−	0.968220i
$808$		0			0
$809$	−35.3793	+	61.2788i	−0.0437322	+	0.0757464i	−0.887063	−	0.461648i	$-0.847258\pi$
$809$	−35.3793	+	61.2788i	−0.0437322	+	0.0757464i	0.843331	+	0.537395i	$0.180591\pi$
$810$		0			0
$811$	−5.94522			−0.00733072			−0.00366536	−	0.999993i	$-0.501167\pi$
$811$	−5.94522			−0.00733072			−0.00366536	+	0.999993i	$0.501167\pi$
$812$		0			0
$813$			143.172i			0.176103i
$814$		0			0
$815$	−92.1073	−	53.1782i	−0.113015	−	0.0652493i
$816$		0			0
$817$	−123.756	−	214.351i	−0.151476	−	0.262364i
$818$		0			0
$819$	2271.65	−	1822.91i	2.77369	−	2.22577i
$820$		0			0
$821$	13.1159	−	7.57244i	0.0159755	−	0.00922344i	−0.491991	−	0.870600i	$-0.663731\pi$
$821$	13.1159	−	7.57244i	0.0159755	−	0.00922344i	0.507966	+	0.861377i	$0.330397\pi$
$822$		0			0
$823$	−1284.10	−	741.378i	−1.56027	−	0.900824i	−0.997229	−	0.0743964i	$-0.976297\pi$
$823$	−1284.10	−	741.378i	−1.56027	−	0.900824i	−0.563044	−	0.826427i	$-0.690370\pi$
$824$		0			0
$825$	570.607			0.691645
$826$		0			0
$827$	74.3070			0.0898513			0.0449257	−	0.998990i	$-0.485695\pi$
$827$	74.3070			0.0898513			0.0449257	+	0.998990i	$0.485695\pi$
$828$		0			0
$829$	−123.722	−	71.4311i	−0.149243	−	0.0861654i	0.423519	−	0.905887i	$-0.360795\pi$
$829$	−123.722	−	71.4311i	−0.149243	−	0.0861654i	−0.572762	+	0.819722i	$0.694128\pi$
$830$		0			0
$831$	−1545.96	+	892.558i	−1.86036	+	1.07408i
$832$		0			0
$833$	−9.83671	+	44.3380i	−0.0118088	+	0.0532269i
$834$		0			0
$835$	−260.403	−	451.032i	−0.311860	−	0.540158i
$836$		0			0
$837$	−1662.33	−	959.745i	−1.98605	−	1.14665i
$838$		0			0
$839$		−	16.7454i		−	0.0199588i	−0.999950	−	0.00997940i	$-0.996823\pi$
$839$		−	16.7454i		−	0.0199588i	0.999950	−	0.00997940i	$-0.00317659\pi$
$840$		0			0
$841$	752.222			0.894437
$842$		0			0
$843$	−328.886	+	569.648i	−0.390138	+	0.675739i
$844$		0			0
$845$	540.690	−	312.168i	0.639870	−	0.369429i
$846$		0			0
$847$	−408.934	−	509.602i	−0.482803	−	0.601655i
$848$		0			0
$849$	1.65008	+	2.85803i	0.00194356	+	0.00336634i
$850$		0			0
$851$	55.6118	−	96.3224i	0.0653488	−	0.113187i
$852$		0			0
$853$		−	1299.38i		−	1.52331i	−0.647984	−	0.761654i	$-0.724388\pi$
$853$		−	1299.38i		−	1.52331i	0.647984	−	0.761654i	$-0.275612\pi$
$854$		0			0
$855$		−	248.563i		−	0.290717i
$856$		0			0
$857$	597.668	−	1035.19i	0.697396	−	1.20792i	−0.271971	−	0.962305i	$-0.587675\pi$
$857$	597.668	−	1035.19i	0.697396	−	1.20792i	0.969366	−	0.245619i	$-0.0789912\pi$
$858$		0			0
$859$	−170.885	−	295.981i	−0.198934	−	0.344564i	0.749249	−	0.662289i	$-0.230415\pi$
$859$	−170.885	−	295.981i	−0.198934	−	0.344564i	−0.948183	+	0.317724i	$0.897081\pi$
$860$		0			0
$861$	−583.644	+	1500.49i	−0.677867	+	1.74273i
$862$		0			0
$863$	844.362	−	487.493i	0.978404	−	0.564882i	0.0766158	−	0.997061i	$-0.475589\pi$
$863$	844.362	−	487.493i	0.978404	−	0.564882i	0.901788	+	0.432179i	$0.142255\pi$
$864$		0			0
$865$	58.6913	−	101.656i	0.0678512	−	0.117522i
$866$		0			0
$867$	1536.44			1.77213
$868$		0			0
$869$			158.887i			0.182839i
$870$		0			0
$871$	1455.45	+	840.304i	1.67101	+	0.964758i
$872$		0			0
$873$	521.896	+	903.951i	0.597819	+	1.03545i
$874$		0			0
$875$	104.104	+	676.722i	0.118976	+	0.773397i
$876$		0			0
$877$	274.158	−	158.285i	0.312609	−	0.180485i	−0.335484	−	0.942046i	$-0.608900\pi$
$877$	274.158	−	158.285i	0.312609	−	0.180485i	0.648093	+	0.761561i	$0.275567\pi$
$878$		0			0
$879$	130.591	+	75.3966i	0.148567	+	0.0857754i
$880$		0			0
$881$	−464.977			−0.527783			−0.263891	−	0.964552i	$-0.585006\pi$
$881$	−464.977			−0.527783			−0.263891	+	0.964552i	$0.585006\pi$
$882$		0			0
$883$	−69.4594			−0.0786630			−0.0393315	−	0.999226i	$-0.512523\pi$
$883$	−69.4594			−0.0786630			−0.0393315	+	0.999226i	$0.512523\pi$
$884$		0			0
$885$	534.610	+	308.657i	0.604079	+	0.348765i
$886$		0			0
$887$	−9.46740	+	5.46601i	−0.0106735	+	0.00616235i	−0.505327	−	0.862928i	$-0.668628\pi$
$887$	−9.46740	+	5.46601i	−0.0106735	+	0.00616235i	0.494654	+	0.869090i	$0.335295\pi$
$888$		0			0
$889$	139.950	+	909.740i	0.157424	+	1.02333i
$890$		0			0
$891$	320.129	+	554.479i	0.359292	+	0.622311i
$892$		0			0
$893$	−236.229	−	136.387i	−0.264535	−	0.152729i
$894$		0			0
$895$		−	273.974i		−	0.306116i
$896$		0			0
$897$	−992.062			−1.10598
$898$		0			0
$899$	−162.552	+	281.548i	−0.180814	+	0.313179i
$900$		0			0
$901$	59.7853	−	34.5170i	0.0663543	−	0.0383097i
$902$		0			0
$903$	−564.759	+	1451.94i	−0.625425	+	1.60791i
$904$		0			0
$905$	−229.395	−	397.323i	−0.253475	−	0.439031i
$906$		0			0
$907$	−11.3588	+	19.6740i	−0.0125235	+	0.0216913i	−0.872219	−	0.489115i	$-0.837320\pi$
$907$	−11.3588	+	19.6740i	−0.0125235	+	0.0216913i	0.859696	+	0.510806i	$0.170653\pi$
$908$		0			0
$909$		−	1754.83i		−	1.93051i
$910$		0			0
$911$			721.866i			0.792389i	0.918167	+	0.396194i	$0.129669\pi$
$911$			721.866i			0.792389i	−0.918167	+	0.396194i	$0.870331\pi$
$912$		0			0
$913$	191.767	−	332.150i	0.210040	−	0.363800i
$914$		0			0
$915$	159.960	+	277.059i	0.174820	+	0.302797i
$916$		0			0
$917$	38.3832	+	47.8320i	0.0418573	+	0.0521614i
$918$		0			0
$919$	−113.209	+	65.3612i	−0.123187	+	0.0711221i	−0.560327	−	0.828271i	$-0.689325\pi$
$919$	−113.209	+	65.3612i	−0.123187	+	0.0711221i	0.437140	+	0.899393i	$0.355991\pi$
$920$		0			0
$921$	−1068.83	+	1851.27i	−1.16051	+	2.01007i
$922$		0			0
$923$	−1595.38			−1.72847
$924$		0			0
$925$			260.454i			0.281572i
$926$		0			0
$927$	1898.56	+	1096.13i	2.04807	+	1.18245i
$928$		0			0
$929$	227.643	+	394.289i	0.245041	+	0.424423i	0.962143	−	0.272545i	$-0.0878654\pi$
$929$	227.643	+	394.289i	0.245041	+	0.424423i	−0.717102	+	0.696968i	$0.754532\pi$
$930$		0			0
$931$	−214.204	−	196.343i	−0.230079	−	0.210894i
$932$		0			0
$933$	−749.140	+	432.516i	−0.802937	+	0.463576i
$934$		0			0
$935$	−9.10528	−	5.25694i	−0.00973827	−	0.00562239i
$936$		0			0
$937$	−1242.79			−1.32635			−0.663176	−	0.748464i	$-0.730792\pi$
$937$	−1242.79			−1.32635			−0.663176	+	0.748464i	$0.730792\pi$
$938$		0			0
$939$	1419.69			1.51192
$940$		0			0
$941$	984.767	+	568.556i	1.04651	+	0.604204i	0.921671	−	0.387973i	$-0.126825\pi$
$941$	984.767	+	568.556i	1.04651	+	0.604204i	0.124841	+	0.992177i	$0.460158\pi$
$942$		0			0
$943$	324.585	−	187.399i	0.344205	−	0.198727i
$944$		0			0
$945$	−655.102	+	525.692i	−0.693230	+	0.556288i
$946$		0			0
$947$	352.421	+	610.411i	0.372145	+	0.644573i	0.989895	−	0.141801i	$-0.0452892\pi$
$947$	352.421	+	610.411i	0.372145	+	0.644573i	−0.617751	+	0.786374i	$0.711956\pi$
$948$		0			0
$949$	623.119	+	359.758i	0.656606	+	0.379092i
$950$		0			0
$951$		−	2308.09i		−	2.42702i
$952$		0			0
$953$	765.039			0.802769			0.401384	−	0.915910i	$-0.368529\pi$
$953$	765.039			0.802769			0.401384	+	0.915910i	$0.368529\pi$
$954$		0			0
$955$	−43.7153	+	75.7172i	−0.0457752	+	0.0792850i
$956$		0			0
$957$	228.827	−	132.113i	0.239109	−	0.138050i
$958$		0			0
$959$	−601.000	+	1545.11i	−0.626694	+	1.61117i
$960$		0			0
$961$	114.761	+	198.772i	0.119418	+	0.206838i
$962$		0			0
$963$	−1399.07	+	2423.27i	−1.45283	+	2.51637i
$964$		0			0
$965$		−	608.916i		−	0.631001i
$966$		0			0
$967$			771.494i			0.797822i	0.916990	+	0.398911i	$0.130612\pi$
$967$			771.494i			0.797822i	−0.916990	+	0.398911i	$0.869388\pi$
$968$		0			0
$969$	14.6540	−	25.3815i	0.0151228	−	0.0261935i
$970$		0			0
$971$	458.754	+	794.586i	0.472456	+	0.818317i	0.999503	−	0.0315186i	$-0.0100343\pi$
$971$	458.754	+	794.586i	0.472456	+	0.818317i	−0.527047	+	0.849836i	$0.676701\pi$
$972$		0			0
$973$	1190.84	−	183.194i	1.22389	−	0.188277i
$974$		0			0
$975$	2011.89	−	1161.56i	2.06348	−	1.19135i
$976$		0			0
$977$	−133.301	+	230.883i	−0.136439	+	0.236319i	−0.926146	−	0.377165i	$-0.876899\pi$
$977$	−133.301	+	230.883i	−0.136439	+	0.236319i	0.789707	+	0.613484i	$0.210232\pi$
$978$		0			0
$979$	288.408			0.294594
$980$		0			0
$981$		−	1295.81i		−	1.32091i
$982$		0			0
$983$	−1601.95	−	924.884i	−1.62965	−	0.940879i	−0.984197	−	0.177080i	$-0.943335\pi$
$983$	−1601.95	−	924.884i	−1.62965	−	0.940879i	−0.645454	−	0.763799i	$-0.723332\pi$
$984$		0			0
$985$	282.349	+	489.043i	0.286649	+	0.496490i
$986$		0			0
$987$	261.052	+	1696.96i	0.264491	+	1.71931i
$988$		0			0
$989$	314.083	−	181.336i	0.317576	−	0.183353i
$990$		0			0
$991$	303.420	+	175.180i	0.306175	+	0.176770i	0.645214	−	0.764002i	$-0.276768\pi$
$991$	303.420	+	175.180i	0.306175	+	0.176770i	−0.339038	+	0.940773i	$0.610102\pi$
$992$		0			0
$993$	433.261			0.436315
$994$		0			0
$995$	−694.800			−0.698291
$996$		0			0
$997$	455.495	+	262.980i	0.456866	+	0.263772i	0.710726	−	0.703469i	$-0.248367\pi$
$997$	455.495	+	262.980i	0.456866	+	0.263772i	−0.253860	+	0.967241i	$0.581700\pi$
$998$		0			0
$999$	−616.687	+	356.045i	−0.617305	+	0.356401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.o.d.207.5		12
4.3	odd	2		56.3.k.d.11.6	yes	12
7.2	even	3	inner	224.3.o.d.79.6		12
7.3	odd	6		1568.3.g.l.687.6		6
7.4	even	3		1568.3.g.j.687.1		6
8.3	odd	2	inner	224.3.o.d.207.6		12
8.5	even	2		56.3.k.d.11.2	✓	12
28.3	even	6		392.3.g.i.99.4		6
28.11	odd	6		392.3.g.j.99.4		6
28.19	even	6		392.3.k.l.275.2		12
28.23	odd	6		56.3.k.d.51.2	yes	12
28.27	even	2		392.3.k.l.67.6		12
56.3	even	6		1568.3.g.l.687.5		6
56.5	odd	6		392.3.k.l.275.6		12
56.11	odd	6		1568.3.g.j.687.2		6
56.13	odd	2		392.3.k.l.67.2		12
56.37	even	6		56.3.k.d.51.6	yes	12
56.45	odd	6		392.3.g.i.99.3		6
56.51	odd	6	inner	224.3.o.d.79.5		12
56.53	even	6		392.3.g.j.99.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.2	✓	12	8.5	even	2
56.3.k.d.11.6	yes	12	4.3	odd	2
56.3.k.d.51.2	yes	12	28.23	odd	6
56.3.k.d.51.6	yes	12	56.37	even	6
224.3.o.d.79.5		12	56.51	odd	6	inner
224.3.o.d.79.6		12	7.2	even	3	inner
224.3.o.d.207.5		12	1.1	even	1	trivial
224.3.o.d.207.6		12	8.3	odd	2	inner
392.3.g.i.99.3		6	56.45	odd	6
392.3.g.i.99.4		6	28.3	even	6
392.3.g.j.99.3		6	56.53	even	6
392.3.g.j.99.4		6	28.11	odd	6
392.3.k.l.67.2		12	56.13	odd	2
392.3.k.l.67.6		12	28.27	even	2
392.3.k.l.275.2		12	28.19	even	6
392.3.k.l.275.6		12	56.5	odd	6
1568.3.g.j.687.1		6	7.4	even	3
1568.3.g.j.687.2		6	56.11	odd	6
1568.3.g.l.687.5		6	56.3	even	6
1568.3.g.l.687.6		6	7.3	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)

\(f(q)\)	\(=\)	\(q+(2.66613 - 4.61787i) q^{3} +(-1.86796 + 1.07847i) q^{5} +(-6.91861 + 1.06433i) q^{7} +(-9.71647 - 16.8294i) q^{9} +O(q^{10})\)	\(q+(2.66613 - 4.61787i) q^{3} +(-1.86796 + 1.07847i) q^{5} +(-6.91861 + 1.06433i) q^{7} +(-9.71647 - 16.8294i) q^{9} +(2.62956 - 4.55453i) q^{11} -21.4116i q^{13} +11.5013i q^{15} +(-0.463429 + 0.802683i) q^{17} +(-2.96505 - 5.13561i) q^{19} +(-13.5310 + 34.7869i) q^{21} +(7.52507 - 4.34460i) q^{23} +(-10.1738 + 17.6216i) q^{25} -55.6311 q^{27} +9.42223i q^{29} +(29.8813 + 17.2520i) q^{31} +(-14.0215 - 24.2859i) q^{33} +(11.7758 - 9.44961i) q^{35} +(11.0853 - 6.40011i) q^{37} +(-98.8758 - 57.0860i) q^{39} +43.1339 q^{41} +41.7382 q^{43} +(36.2999 + 20.9578i) q^{45} +(39.8357 - 22.9991i) q^{47} +(46.7344 - 14.7273i) q^{49} +(2.47112 + 4.28011i) q^{51} +(-64.5031 - 37.2409i) q^{53} +11.3436i q^{55} -31.6208 q^{57} +(26.8367 - 46.4825i) q^{59} +(24.0893 - 13.9080i) q^{61} +(85.1365 + 106.095i) q^{63} +(23.0916 + 39.9959i) q^{65} +(-39.2453 + 67.9749i) q^{67} -46.3330i q^{69} -74.5100i q^{71} +(-16.8020 + 29.1020i) q^{73} +(54.2494 + 93.9627i) q^{75} +(-13.3454 + 34.3097i) q^{77} +(-26.1642 + 15.1059i) q^{79} +(-60.8713 + 105.432i) q^{81} +72.9274 q^{83} -1.99917i q^{85} +(43.5106 + 25.1209i) q^{87} +(27.4198 + 47.4925i) q^{89} +(22.7889 + 148.138i) q^{91} +(159.335 - 91.9919i) q^{93} +(11.0772 + 6.39541i) q^{95} -53.7125 q^{97} -102.200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 40 q^{9}+O(q^{10}) \) 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

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