LMFDB - Embedded newform 168.5.z.a.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,5,Mod(73,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("168.73");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	168.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.3661537981$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 99 x^{14} - 1810 x^{13} + 14212 x^{12} - 199882 x^{11} + 1800935 x^{10} + \cdots + 41390114348800 $ x^16 - 6x^15 + 99x^14 - 1810x^13 + 14212x^12 - 199882x^11 + 1800935x^10 - 9073270x^9 + 62016647x^8 - 13497916x^7 - 872612906x^6 + 8208467240x^5 + 11144877252x^4 - 185824445600x^3 + 3750935164160x^2 - 13970712492800*x + 41390114348800
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{36}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.6
Root			$9.32119 + 2.12492i$ of defining polynomial
Character	$\chi$	$=$	168.73
Dual form			168.5.z.a.145.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 - 2.59808i) q^{3} +(23.7919 - 13.7363i) q^{5} +(-26.3445 - 41.3155i) q^{7} +(13.5000 + 23.3827i) q^{9} +O(q^{10})$	\(q+(-4.50000 - 2.59808i) q^{3} +(23.7919 - 13.7363i) q^{5} +(-26.3445 - 41.3155i) q^{7} +(13.5000 + 23.3827i) q^{9} +(68.5652 - 118.758i) q^{11} +248.708i q^{13} -142.751 q^{15} +(-376.798 - 217.545i) q^{17} +(302.621 - 174.719i) q^{19} +(11.2094 + 254.365i) q^{21} +(-57.6573 - 99.8653i) q^{23} +(64.8691 - 112.357i) q^{25} -140.296i q^{27} -131.150 q^{29} +(-1463.37 - 844.877i) q^{31} +(-617.087 + 356.275i) q^{33} +(-1194.30 - 621.099i) q^{35} +(-1069.05 - 1851.65i) q^{37} +(646.163 - 1119.19i) q^{39} -1144.05i q^{41} -2647.34 q^{43} +(642.381 + 370.879i) q^{45} +(1325.10 - 765.050i) q^{47} +(-1012.94 + 2176.87i) q^{49} +(1130.39 + 1957.90i) q^{51} +(-1834.33 + 3177.16i) q^{53} -3767.32i q^{55} -1815.73 q^{57} +(1017.75 + 587.599i) q^{59} +(4609.74 - 2661.43i) q^{61} +(610.416 - 1173.76i) q^{63} +(3416.32 + 5917.24i) q^{65} +(2937.14 - 5087.27i) q^{67} +599.192i q^{69} +177.127 q^{71} +(698.876 + 403.496i) q^{73} +(-583.822 + 337.070i) q^{75} +(-6712.88 + 295.825i) q^{77} +(-443.216 - 767.673i) q^{79} +(-364.500 + 631.333i) q^{81} +9779.61i q^{83} -11953.0 q^{85} +(590.173 + 340.737i) q^{87} +(2512.19 - 1450.41i) q^{89} +(10275.5 - 6552.09i) q^{91} +(4390.11 + 7603.89i) q^{93} +(4799.96 - 8313.77i) q^{95} +6129.50i q^{97} +3702.52 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9}+O(q^{10}) $ 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9	$ 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9} - 108 q^{11} - 72 q^{15} - 168 q^{17} + 948 q^{19} - 252 q^{21} - 768 q^{23} + 1908 q^{25} - 1608 q^{29} - 3216 q^{31} + 972 q^{33} + 696 q^{35} - 1820 q^{37} - 1188 q^{39} + 2888 q^{43} + 324 q^{45} + 744 q^{47} - 3784 q^{49} + 504 q^{51} + 4476 q^{53} - 5688 q^{57} - 4668 q^{59} + 17760 q^{61} + 1188 q^{63} + 8760 q^{65} + 1580 q^{67} + 48 q^{71} + 588 q^{73} - 17172 q^{75} - 17508 q^{77} - 3824 q^{79} - 5832 q^{81} + 11440 q^{85} + 7236 q^{87} - 360 q^{89} + 25860 q^{91} + 9648 q^{93} - 21792 q^{95} - 5832 q^{99}+O(q^{100}) $ 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9 - 108 * q^11 - 72 * q^15 - 168 * q^17 + 948 * q^19 - 252 * q^21 - 768 * q^23 + 1908 * q^25 - 1608 * q^29 - 3216 * q^31 + 972 * q^33 + 696 * q^35 - 1820 * q^37 - 1188 * q^39 + 2888 * q^43 + 324 * q^45 + 744 * q^47 - 3784 * q^49 + 504 * q^51 + 4476 * q^53 - 5688 * q^57 - 4668 * q^59 + 17760 * q^61 + 1188 * q^63 + 8760 * q^65 + 1580 * q^67 + 48 * q^71 + 588 * q^73 - 17172 * q^75 - 17508 * q^77 - 3824 * q^79 - 5832 * q^81 + 11440 * q^85 + 7236 * q^87 - 360 * q^89 + 25860 * q^91 + 9648 * q^93 - 21792 * q^95 - 5832 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$3$	−4.50000	−	2.59808i	−0.500000	−	0.288675i
$3$	−4.50000	−	2.59808i	−0.500000	−	0.288675i
$4$		0			0
$5$	23.7919	−	13.7363i	0.951675	−	0.549450i	0.0580744	−	0.998312i	$-0.481504\pi$
$5$	23.7919	−	13.7363i	0.951675	−	0.549450i	0.893601	+	0.448862i	$0.148171\pi$
$6$		0			0
$7$	−26.3445	−	41.3155i	−0.537642	−	0.843173i
$7$	−26.3445	−	41.3155i	−0.537642	−	0.843173i
$8$		0			0
$9$	13.5000	+	23.3827i	0.166667	+	0.288675i
$10$		0			0
$11$	68.5652	−	118.758i	0.566655	−	0.981475i	−0.430239	−	0.902715i	$-0.641571\pi$
$11$	68.5652	−	118.758i	0.566655	−	0.981475i	0.996894	−	0.0787597i	$-0.0250960\pi$
$12$		0			0
$13$			248.708i			1.47165i	0.677174	+	0.735823i	$0.263205\pi$
$13$			248.708i			1.47165i	−0.677174	+	0.735823i	$0.736795\pi$
$14$		0			0
$15$	−142.751			−0.634450
$16$		0			0
$17$	−376.798	−	217.545i	−1.30380	−	0.752749i	−0.322747	−	0.946485i	$-0.604606\pi$
$17$	−376.798	−	217.545i	−1.30380	−	0.752749i	−0.981054	+	0.193736i	$0.937939\pi$
$18$		0			0
$19$	302.621	−	174.719i	0.838287	−	0.483985i	−0.0183948	−	0.999831i	$-0.505856\pi$
$19$	302.621	−	174.719i	0.838287	−	0.483985i	0.856681	+	0.515846i	$0.172522\pi$
$20$		0			0
$21$	11.2094	+	254.365i	0.0254182	+	0.576790i
$22$		0			0
$23$	−57.6573	−	99.8653i	−0.108993	−	0.188781i	0.806370	−	0.591412i	$-0.201429\pi$
$23$	−57.6573	−	99.8653i	−0.108993	−	0.188781i	−0.915363	+	0.402631i	$0.868096\pi$
$24$		0			0
$25$	64.8691	−	112.357i	0.103791	−	0.179771i
$26$		0			0
$27$		−	140.296i		−	0.192450i
$28$		0			0
$29$	−131.150			−0.155945			−0.0779724	−	0.996956i	$-0.524845\pi$
$29$	−131.150			−0.155945			−0.0779724	+	0.996956i	$0.524845\pi$
$30$		0			0
$31$	−1463.37	−	844.877i	−1.52276	−	0.879165i	−0.999638	−	0.0269054i	$-0.991435\pi$
$31$	−1463.37	−	844.877i	−1.52276	−	0.879165i	−0.523120	−	0.852259i	$-0.675232\pi$
$32$		0			0
$33$	−617.087	+	356.275i	−0.566655	+	0.327158i
$34$		0			0
$35$	−1194.30	−	621.099i	−0.974942	−	0.507019i
$36$		0			0
$37$	−1069.05	−	1851.65i	−0.780899	−	1.35256i	−0.931419	−	0.363949i	$-0.881428\pi$
$37$	−1069.05	−	1851.65i	−0.780899	−	1.35256i	0.150520	−	0.988607i	$-0.451905\pi$
$38$		0			0
$39$	646.163	−	1119.19i	0.424828	−	0.735823i
$40$		0			0
$41$		−	1144.05i		−	0.680577i	−0.940321	−	0.340288i	$-0.889475\pi$
$41$		−	1144.05i		−	0.680577i	0.940321	−	0.340288i	$-0.110525\pi$
$42$		0			0
$43$	−2647.34			−1.43177			−0.715886	−	0.698218i	$-0.753977\pi$
$43$	−2647.34			−1.43177			−0.715886	+	0.698218i	$0.753977\pi$
$44$		0			0
$45$	642.381	+	370.879i	0.317225	+	0.183150i
$46$		0			0
$47$	1325.10	−	765.050i	0.599866	−	0.346333i	−0.169123	−	0.985595i	$-0.554093\pi$
$47$	1325.10	−	765.050i	0.599866	−	0.346333i	0.768989	+	0.639262i	$0.220760\pi$
$48$		0			0
$49$	−1012.94	+	2176.87i	−0.421881	+	0.906651i
$50$		0			0
$51$	1130.39	+	1957.90i	0.434600	+	0.752749i
$52$		0			0
$53$	−1834.33	+	3177.16i	−0.653019	+	1.13106i	0.329367	+	0.944202i	$0.393165\pi$
$53$	−1834.33	+	3177.16i	−0.653019	+	1.13106i	−0.982386	+	0.186861i	$0.940169\pi$
$54$		0			0
$55$		−	3767.32i		−	1.24539i
$56$		0			0
$57$	−1815.73			−0.558858
$58$		0			0
$59$	1017.75	+	587.599i	0.292373	+	0.168802i	0.639012	−	0.769197i	$-0.279344\pi$
$59$	1017.75	+	587.599i	0.292373	+	0.168802i	−0.346638	+	0.937999i	$0.612677\pi$
$60$		0			0
$61$	4609.74	−	2661.43i	1.23884	−	0.715247i	0.269986	−	0.962864i	$-0.412981\pi$
$61$	4609.74	−	2661.43i	1.23884	−	0.715247i	0.968858	+	0.247618i	$0.0796476\pi$
$62$		0			0
$63$	610.416	−	1173.76i	0.153796	−	0.295733i
$64$		0			0
$65$	3416.32	+	5917.24i	0.808596	+	1.40053i
$66$		0			0
$67$	2937.14	−	5087.27i	0.654297	−	1.13327i	−0.327773	−	0.944756i	$-0.606298\pi$
$67$	2937.14	−	5087.27i	0.654297	−	1.13327i	0.982070	−	0.188518i	$-0.0603685\pi$
$68$		0			0
$69$			599.192i			0.125854i
$70$		0			0
$71$	177.127			0.0351373			0.0175686	−	0.999846i	$-0.494407\pi$
$71$	177.127			0.0351373			0.0175686	+	0.999846i	$0.494407\pi$
$72$		0			0
$73$	698.876	+	403.496i	0.131146	+	0.0757171i	0.564138	−	0.825681i	$-0.309209\pi$
$73$	698.876	+	403.496i	0.131146	+	0.0757171i	−0.432992	+	0.901398i	$0.642542\pi$
$74$		0			0
$75$	−583.822	+	337.070i	−0.103791	+	0.0599235i
$76$		0			0
$77$	−6712.88	+	295.825i	−1.13221	+	0.0498945i
$78$		0			0
$79$	−443.216	−	767.673i	−0.0710168	−	0.123005i	0.828330	−	0.560240i	$-0.189291\pi$
$79$	−443.216	−	767.673i	−0.0710168	−	0.123005i	−0.899347	+	0.437235i	$0.855958\pi$
$80$		0			0
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			9779.61i			1.41960i	0.704404	+	0.709799i	$0.251214\pi$
$83$			9779.61i			1.41960i	−0.704404	+	0.709799i	$0.748786\pi$
$84$		0			0
$85$	−11953.0			−1.65439
$86$		0			0
$87$	590.173	+	340.737i	0.0779724	+	0.0450174i
$88$		0			0
$89$	2512.19	−	1450.41i	0.317156	−	0.183110i	−0.332968	−	0.942938i	$-0.608050\pi$
$89$	2512.19	−	1450.41i	0.317156	−	0.183110i	0.650124	+	0.759828i	$0.274717\pi$
$90$		0			0
$91$	10275.5	−	6552.09i	1.24085	−	0.791220i
$92$		0			0
$93$	4390.11	+	7603.89i	0.507586	+	0.879165i
$94$		0			0
$95$	4799.96	−	8313.77i	0.531851	−	0.921193i
$96$		0			0
$97$			6129.50i			0.651450i	0.945465	+	0.325725i	$0.105608\pi$
$97$			6129.50i			0.651450i	−0.945465	+	0.325725i	$0.894392\pi$
$98$		0			0
$99$	3702.52			0.377770
$100$		0			0
$101$	15201.6	+	8776.62i	1.49020	+	0.860369i	0.999937	−	0.0112048i	$-0.00356669\pi$
$101$	15201.6	+	8776.62i	1.49020	+	0.860369i	0.490265	+	0.871573i	$0.336900\pi$
$102$		0			0
$103$	−2784.40	+	1607.57i	−0.262456	+	0.151529i	−0.625454	−	0.780261i	$-0.715086\pi$
$103$	−2784.40	+	1607.57i	−0.262456	+	0.151529i	0.362998	+	0.931790i	$0.381753\pi$
$104$		0			0
$105$	3760.71	+	5897.84i	0.341107	+	0.534951i
$106$		0			0
$107$	−7158.03	−	12398.1i	−0.625210	−	1.08290i	−0.988500	−	0.151220i	$-0.951680\pi$
$107$	−7158.03	−	12398.1i	−0.625210	−	1.08290i	0.363290	−	0.931676i	$-0.381653\pi$
$108$		0			0
$109$	924.759	−	1601.73i	0.0778351	−	0.134814i	−0.824481	−	0.565890i	$-0.808533\pi$
$109$	924.759	−	1601.73i	0.0778351	−	0.134814i	0.902316	+	0.431076i	$0.141866\pi$
$110$		0			0
$111$			11109.9i			0.901704i
$112$		0			0
$113$	18934.6			1.48285			0.741427	−	0.671033i	$-0.234149\pi$
$113$	18934.6			1.48285			0.741427	+	0.671033i	$0.234149\pi$
$114$		0			0
$115$	−2743.55	−	1583.99i	−0.207452	−	0.119772i
$116$		0			0
$117$	−5815.47	+	3357.56i	−0.424828	+	0.245274i
$118$		0			0
$119$	938.596	+	21298.7i	0.0662804	+	1.50404i
$120$		0			0
$121$	−2081.88	−	3605.92i	−0.142195	−	0.246289i
$122$		0			0
$123$	−2972.33	+	5148.22i	−0.196466	+	0.340288i
$124$		0			0
$125$			13606.1i			0.870789i
$126$		0			0
$127$	2932.11			0.181791			0.0908957	−	0.995860i	$-0.471027\pi$
$127$	2932.11			0.181791			0.0908957	+	0.995860i	$0.471027\pi$
$128$		0			0
$129$	11913.1	+	6878.00i	0.715886	+	0.413317i
$130$		0			0
$131$	−12019.1	+	6939.22i	−0.700372	+	0.404360i	−0.807486	−	0.589887i	$-0.799172\pi$
$131$	−12019.1	+	6939.22i	−0.700372	+	0.404360i	0.107114	+	0.994247i	$0.465839\pi$
$132$		0			0
$133$	−15191.0	−	7900.08i	−0.858782	−	0.446610i
$134$		0			0
$135$	−1927.14	−	3337.91i	−0.105742	−	0.183150i
$136$		0			0
$137$	10361.0	−	17945.7i	0.552025	−	0.956135i	−0.446104	−	0.894981i	$-0.647189\pi$
$137$	10361.0	−	17945.7i	0.552025	−	0.956135i	0.998128	−	0.0611537i	$-0.0194780\pi$
$138$		0			0
$139$		−	37984.7i		−	1.96598i	−0.183655	−	0.982991i	$-0.558793\pi$
$139$		−	37984.7i		−	1.96598i	0.183655	−	0.982991i	$-0.441207\pi$
$140$		0			0
$141$	−7950.63			−0.399911
$142$		0			0
$143$	29536.2	+	17052.7i	1.44438	+	0.833915i
$144$		0			0
$145$	−3120.29	+	1801.50i	−0.148409	+	0.0856838i
$146$		0			0
$147$	10213.9	−	7164.22i	0.472668	−	0.331539i
$148$		0			0
$149$	−18261.6	−	31630.0i	−0.822556	−	1.42471i	−0.903773	−	0.428013i	$-0.859214\pi$
$149$	−18261.6	−	31630.0i	−0.822556	−	1.42471i	0.0812167	−	0.996696i	$-0.474119\pi$
$150$		0			0
$151$	8906.65	−	15426.8i	0.390625	−	0.676583i	−0.601907	−	0.798566i	$-0.705592\pi$
$151$	8906.65	−	15426.8i	0.390625	−	0.676583i	0.992532	+	0.121984i	$0.0389255\pi$
$152$		0			0
$153$		−	11747.4i		−	0.501833i
$154$		0			0
$155$	−46421.8			−1.93223
$156$		0			0
$157$	14965.9	+	8640.56i	0.607160	+	0.350544i	0.771853	−	0.635801i	$-0.219330\pi$
$157$	14965.9	+	8640.56i	0.607160	+	0.350544i	−0.164693	+	0.986345i	$0.552663\pi$
$158$		0			0
$159$	16509.0	−	9531.47i	0.653019	−	0.377021i
$160$		0			0
$161$	−2607.03	+	5013.04i	−0.100576	+	0.193397i
$162$		0			0
$163$	−4066.62	−	7043.60i	−0.153059	−	0.265106i	0.779292	−	0.626661i	$-0.215579\pi$
$163$	−4066.62	−	7043.60i	−0.153059	−	0.265106i	−0.932351	+	0.361556i	$0.882246\pi$
$164$		0			0
$165$	−9787.77	+	16952.9i	−0.359514	+	0.622697i
$166$		0			0
$167$			46438.5i			1.66512i	0.553934	+	0.832560i	$0.313126\pi$
$167$			46438.5i			1.66512i	−0.553934	+	0.832560i	$0.686874\pi$
$168$		0			0
$169$	−33294.8			−1.16574
$170$		0			0
$171$	8170.78	+	4717.40i	0.279429	+	0.161328i
$172$		0			0
$173$	9421.94	−	5439.76i	0.314810	−	0.181755i	−0.334267	−	0.942478i	$-0.608489\pi$
$173$	9421.94	−	5439.76i	0.314810	−	0.181755i	0.649077	+	0.760723i	$0.275155\pi$
$174$		0			0
$175$	−6351.01	+	279.878i	−0.207380	+	0.00913887i
$176$		0			0
$177$	−3053.25	−	5288.39i	−0.0974578	−	0.168802i
$178$		0			0
$179$	−6556.86	+	11356.8i	−0.204640	+	0.354446i	−0.950018	−	0.312196i	$-0.898936\pi$
$179$	−6556.86	+	11356.8i	−0.204640	+	0.354446i	0.745378	+	0.666642i	$0.232269\pi$
$180$		0			0
$181$		−	48373.7i		−	1.47656i	−0.674493	−	0.738281i	$-0.735638\pi$
$181$		−	48373.7i		−	1.47656i	0.674493	−	0.738281i	$-0.264362\pi$
$182$		0			0
$183$	−27658.4			−0.825896
$184$		0			0
$185$	−50869.4	−	29369.5i	−1.48632	−	0.858130i
$186$		0			0
$187$	−51670.5	+	29832.0i	−1.47761	+	0.853098i
$188$		0			0
$189$	−5796.40	+	3696.03i	−0.162269	+	0.103469i
$190$		0			0
$191$	−1021.74	−	1769.70i	−0.0280074	−	0.0485102i	0.851682	−	0.524059i	$-0.175583\pi$
$191$	−1021.74	−	1769.70i	−0.0280074	−	0.0485102i	−0.879689	+	0.475549i	$0.842250\pi$
$192$		0			0
$193$	20512.2	−	35528.2i	0.550679	−	0.953804i	−0.447547	−	0.894261i	$-0.647702\pi$
$193$	20512.2	−	35528.2i	0.550679	−	0.953804i	0.998226	−	0.0595434i	$-0.0189645\pi$
$194$		0			0
$195$		−	35503.4i		−	0.933686i
$196$		0			0
$197$	30815.3			0.794024			0.397012	−	0.917814i	$-0.370047\pi$
$197$	30815.3			0.794024			0.397012	+	0.917814i	$0.370047\pi$
$198$		0			0
$199$	39978.4	+	23081.5i	1.00953	+	0.582852i	0.911054	−	0.412287i	$-0.135270\pi$
$199$	39978.4	+	23081.5i	1.00953	+	0.582852i	0.0984756	+	0.995139i	$0.468603\pi$
$200$		0			0
$201$	−26434.2	+	15261.8i	−0.654297	+	0.377758i
$202$		0			0
$203$	3455.07	+	5418.51i	0.0838425	+	0.131488i
$204$		0			0
$205$	−15715.0	−	27219.1i	−0.373943	−	0.647688i
$206$		0			0
$207$	1556.75	−	2696.36i	0.0363310	−	0.0629271i
$208$		0			0
$209$		−	47918.5i		−	1.09701i
$210$		0			0
$211$	−30724.3			−0.690108			−0.345054	−	0.938583i	$-0.612139\pi$
$211$	−30724.3			−0.690108			−0.345054	+	0.938583i	$0.612139\pi$
$212$		0			0
$213$	−797.072	−	460.190i	−0.0175686	−	0.0101433i
$214$		0			0
$215$	−62985.3	+	36364.6i	−1.36258	+	0.786687i
$216$		0			0
$217$	3645.22	+	82717.7i	0.0774114	+	1.75662i
$218$		0			0
$219$	−2096.63	−	3631.47i	−0.0437153	−	0.0757171i
$220$		0			0
$221$	54105.1	−	93712.8i	1.10778	−	1.91873i
$222$		0			0
$223$			16495.7i			0.331712i	0.986150	+	0.165856i	$0.0530387\pi$
$223$			16495.7i			0.331712i	−0.986150	+	0.165856i	$0.946961\pi$
$224$		0			0
$225$	3502.93			0.0691937
$226$		0			0
$227$	−14344.2	−	8281.64i	−0.278372	−	0.160718i	0.354314	−	0.935126i	$-0.384714\pi$
$227$	−14344.2	−	8281.64i	−0.278372	−	0.160718i	−0.632686	+	0.774408i	$0.718048\pi$
$228$		0			0
$229$	39363.6	−	22726.6i	0.750626	−	0.433374i	−0.0752943	−	0.997161i	$-0.523990\pi$
$229$	39363.6	−	22726.6i	0.750626	−	0.433374i	0.825920	+	0.563787i	$0.190656\pi$
$230$		0			0
$231$	30976.5	+	16109.4i	0.580509	+	0.301894i
$232$		0			0
$233$	−5023.89	−	8701.64i	−0.0925398	−	0.160284i	0.816039	−	0.577996i	$-0.196165\pi$
$233$	−5023.89	−	8701.64i	−0.0925398	−	0.160284i	−0.908579	+	0.417713i	$0.862832\pi$
$234$		0			0
$235$	21017.8	−	36403.9i	0.380585	−	0.659193i
$236$		0			0
$237$			4606.04i			0.0820032i
$238$		0			0
$239$	31765.8			0.556113			0.278057	−	0.960565i	$-0.410310\pi$
$239$	31765.8			0.556113			0.278057	+	0.960565i	$0.410310\pi$
$240$		0			0
$241$	−15050.8	−	8689.58i	−0.259135	−	0.149611i	0.364805	−	0.931084i	$-0.381136\pi$
$241$	−15050.8	−	8689.58i	−0.259135	−	0.149611i	−0.623940	+	0.781472i	$0.714469\pi$
$242$		0			0
$243$	3280.50	−	1894.00i	0.0555556	−	0.0320750i
$244$		0			0
$245$	5802.35	+	65705.8i	0.0966655	+	1.09464i
$246$		0			0
$247$	43454.0	+	75264.5i	0.712255	+	1.23366i
$248$		0			0
$249$	25408.2	−	44008.2i	0.409803	−	0.709799i
$250$		0			0
$251$		−	51531.7i		−	0.817951i	−0.912545	−	0.408975i	$-0.865886\pi$
$251$		−	51531.7i		−	0.817951i	0.912545	−	0.408975i	$-0.134114\pi$
$252$		0			0
$253$	−15813.1			−0.247045
$254$		0			0
$255$	53788.4	+	31054.8i	0.827196	+	0.477582i
$256$		0			0
$257$	47421.3	−	27378.7i	0.717972	−	0.414521i	−0.0960340	−	0.995378i	$-0.530616\pi$
$257$	47421.3	−	27378.7i	0.717972	−	0.414521i	0.814006	+	0.580857i	$0.197282\pi$
$258$		0			0
$259$	−48338.2	+	92949.1i	−0.720595	+	1.38562i
$260$		0			0
$261$	−1770.52	−	3066.63i	−0.0259908	−	0.0450174i
$262$		0			0
$263$	−7677.06	+	13297.1i	−0.110990	+	0.192240i	−0.916170	−	0.400791i	$-0.868735\pi$
$263$	−7677.06	+	13297.1i	−0.110990	+	0.192240i	0.805180	+	0.593031i	$0.202069\pi$
$264$		0			0
$265$			100787.i			1.43521i
$266$		0			0
$267$	−15073.1			−0.211437
$268$		0			0
$269$	78643.4	+	45404.8i	1.08682	+	0.627476i	0.932728	−	0.360581i	$-0.117421\pi$
$269$	78643.4	+	45404.8i	1.08682	+	0.627476i	0.154092	+	0.988056i	$0.450755\pi$
$270$		0			0
$271$	58488.7	−	33768.4i	0.796403	−	0.459804i	−0.0458086	−	0.998950i	$-0.514586\pi$
$271$	58488.7	−	33768.4i	0.796403	−	0.459804i	0.842212	+	0.539147i	$0.181253\pi$
$272$		0			0
$273$	−63262.6	+	2787.87i	−0.848832	+	0.0374065i
$274$		0			0
$275$	−8895.53	−	15407.5i	−0.117627	−	0.203736i
$276$		0			0
$277$	−35646.8	+	61742.1i	−0.464581	+	0.804677i	−0.999183	−	0.0404267i	$-0.987128\pi$
$277$	−35646.8	+	61742.1i	−0.464581	+	0.804677i	0.534602	+	0.845104i	$0.320462\pi$
$278$		0			0
$279$		−	45623.4i		−	0.586110i
$280$		0			0
$281$	−40575.7			−0.513870			−0.256935	−	0.966429i	$-0.582713\pi$
$281$	−40575.7			−0.513870			−0.256935	+	0.966429i	$0.582713\pi$
$282$		0			0
$283$	91569.6	+	52867.7i	1.14335	+	0.660112i	0.947257	−	0.320473i	$-0.103842\pi$
$283$	91569.6	+	52867.7i	1.14335	+	0.660112i	0.196091	+	0.980586i	$0.437175\pi$
$284$		0			0
$285$	−43199.6	+	24941.3i	−0.531851	+	0.307064i
$286$		0			0
$287$	−47267.0	+	30139.4i	−0.573844	+	0.365907i
$288$		0			0
$289$	52890.8	+	91609.5i	0.633263	+	1.09684i
$290$		0			0
$291$	15924.9	−	27582.7i	0.188057	−	0.325725i
$292$		0			0
$293$			60391.7i			0.703464i	0.936101	+	0.351732i	$0.114407\pi$
$293$			60391.7i			0.703464i	−0.936101	+	0.351732i	$0.885593\pi$
$294$		0			0
$295$	32285.6			0.370993
$296$		0			0
$297$	−16661.3	−	9619.43i	−0.188885	−	0.109053i
$298$		0			0
$299$	24837.3	−	14339.8i	0.277819	−	0.160399i
$300$		0			0
$301$	69742.9	+	109376.i	0.769781	+	1.20723i
$302$		0			0
$303$	−45604.7	−	78989.6i	−0.496734	−	0.860369i
$304$		0			0
$305$	73116.2	−	126641.i	0.785985	−	1.36137i
$306$		0			0
$307$		−	136026.i		−	1.44326i	−0.692279	−	0.721630i	$-0.743393\pi$
$307$		−	136026.i		−	1.44326i	0.692279	−	0.721630i	$-0.256607\pi$
$308$		0			0
$309$	16706.4			0.174971
$310$		0			0
$311$	118682.	+	68521.1i	1.22705	+	0.708440i	0.966413	−	0.256995i	$-0.0827324\pi$
$311$	118682.	+	68521.1i	1.22705	+	0.708440i	0.260642	+	0.965436i	$0.416066\pi$
$312$		0			0
$313$	50278.6	−	29028.4i	0.513209	−	0.296302i	−0.220943	−	0.975287i	$-0.570913\pi$
$313$	50278.6	−	29028.4i	0.513209	−	0.296302i	0.734152	+	0.678985i	$0.237580\pi$
$314$		0			0
$315$	−1600.16	−	36310.9i	−0.0161266	−	0.365945i
$316$		0			0
$317$	−45765.2	−	79267.7i	−0.455425	−	0.788820i	0.543287	−	0.839547i	$-0.317179\pi$
$317$	−45765.2	−	79267.7i	−0.455425	−	0.788820i	−0.998713	+	0.0507273i	$0.983846\pi$
$318$		0			0
$319$	−8992.30	+	15575.1i	−0.0883668	+	0.153056i
$320$		0			0
$321$			74388.4i			0.721930i
$322$		0			0
$323$	−152036.			−1.45728
$324$		0			0
$325$	27944.0	+	16133.5i	0.264559	+	0.152743i
$326$		0			0
$327$	−8322.83	+	4805.19i	−0.0778351	+	0.0449381i
$328$		0			0
$329$	−66517.6	−	34592.5i	−0.614532	−	0.319588i
$330$		0			0
$331$	9753.88	+	16894.2i	0.0890269	+	0.154199i	0.907100	−	0.420915i	$-0.138291\pi$
$331$	9753.88	+	16894.2i	0.0890269	+	0.154199i	−0.818073	+	0.575114i	$0.804958\pi$
$332$		0			0
$333$	28864.4	−	49994.5i	0.260300	−	0.450852i
$334$		0			0
$335$		−	161381.i		−	1.43801i
$336$		0			0
$337$	−46955.9			−0.413457			−0.206728	−	0.978398i	$-0.566282\pi$
$337$	−46955.9			−0.413457			−0.206728	+	0.978398i	$0.566282\pi$
$338$		0			0
$339$	−85205.6	−	49193.5i	−0.741427	−	0.428063i
$340$		0			0
$341$	−200673.	+	115858.i	−1.72576	+	0.996366i
$342$		0			0
$343$	116624.	−	15498.5i	0.991285	−	0.131735i
$344$		0			0
$345$	8230.65	+	14255.9i	0.0691506	+	0.119772i
$346$		0			0
$347$	−90985.5	+	157591.i	−0.755637	+	1.30880i	0.189420	+	0.981896i	$0.439339\pi$
$347$	−90985.5	+	157591.i	−0.755637	+	1.30880i	−0.945057	+	0.326905i	$0.893994\pi$
$348$		0			0
$349$			162676.i			1.33559i	0.744347	+	0.667793i	$0.232761\pi$
$349$			162676.i			1.33559i	−0.744347	+	0.667793i	$0.767239\pi$
$350$		0			0
$351$	34892.8			0.283219
$352$		0			0
$353$	173857.	+	100377.i	1.39522	+	0.805532i	0.993887	−	0.110399i	$-0.0352130\pi$
$353$	173857.	+	100377.i	1.39522	+	0.805532i	0.401335	+	0.915931i	$0.368546\pi$
$354$		0			0
$355$	4214.19	−	2433.06i	0.0334393	−	0.0193062i
$356$		0			0
$357$	51112.0	−	98282.7i	0.401038	−	0.771153i
$358$		0			0
$359$	23385.2	+	40504.3i	0.181448	+	0.314277i	0.942374	−	0.334562i	$-0.108588\pi$
$359$	23385.2	+	40504.3i	0.181448	+	0.314277i	−0.760926	+	0.648839i	$0.775255\pi$
$360$		0			0
$361$	−4107.33	+	7114.11i	−0.0315170	+	0.0545891i
$362$		0			0
$363$			21635.5i			0.164193i
$364$		0			0
$365$	22170.1			0.166411
$366$		0			0
$367$	13750.5	+	7938.83i	0.102090	+	0.0589419i	0.550176	−	0.835049i	$-0.314561\pi$
$367$	13750.5	+	7938.83i	0.102090	+	0.0589419i	−0.448085	+	0.893991i	$0.647894\pi$
$368$		0			0
$369$	26751.0	−	15444.7i	0.196466	−	0.113429i
$370$		0			0
$371$	179590.	−	7914.23i	1.30477	−	0.0574990i
$372$		0			0
$373$	−100932.	−	174819.i	−0.725456	−	1.25653i	−0.958786	−	0.284129i	$-0.908296\pi$
$373$	−100932.	−	174819.i	−0.725456	−	1.25653i	0.233331	−	0.972397i	$-0.425038\pi$
$374$		0			0
$375$	35349.6	−	61227.4i	0.251375	−	0.435394i
$376$		0			0
$377$		−	32618.0i		−	0.229496i
$378$		0			0
$379$	−234336.			−1.63140			−0.815700	−	0.578475i	$-0.803648\pi$
$379$	−234336.			−1.63140			−0.815700	+	0.578475i	$0.803648\pi$
$380$		0			0
$381$	−13194.5	−	7617.86i	−0.0908957	−	0.0524787i
$382$		0			0
$383$	33637.3	−	19420.5i	0.229310	−	0.132392i	−0.380944	−	0.924598i	$-0.624401\pi$
$383$	33637.3	−	19420.5i	0.229310	−	0.132392i	0.610254	+	0.792206i	$0.291067\pi$
$384$		0			0
$385$	−155648.	+	99248.0i	−1.05008	+	0.669577i
$386$		0			0
$387$	−35739.2	−	61902.0i	−0.238629	−	0.413317i
$388$		0			0
$389$	73533.0	−	127363.i	0.485940	−	0.841673i	−0.513929	−	0.857833i	$-0.671811\pi$
$389$	73533.0	−	127363.i	0.485940	−	0.841673i	0.999869	+	0.0161595i	$0.00514395\pi$
$390$		0			0
$391$			50172.1i			0.328177i
$392$		0			0
$393$	72114.5			0.466915
$394$		0			0
$395$	−21089.9	−	12176.3i	−0.135170	−	0.0780404i
$396$		0			0
$397$	−147166.	+	84966.2i	−0.933739	+	0.539095i	−0.887992	−	0.459858i	$-0.847900\pi$
$397$	−147166.	+	84966.2i	−0.933739	+	0.539095i	−0.0457470	+	0.998953i	$0.514567\pi$
$398$		0			0
$399$	47834.4	+	75017.7i	0.300466	+	0.471214i
$400$		0			0
$401$	−42185.0	−	73066.6i	−0.262343	−	0.454391i	0.704521	−	0.709683i	$-0.251162\pi$
$401$	−42185.0	−	73066.6i	−0.262343	−	0.454391i	−0.966864	+	0.255292i	$0.917829\pi$
$402$		0			0
$403$	210128.	−	363952.i	1.29382	−	2.24096i
$404$		0			0
$405$			20027.5i			0.122100i
$406$		0			0
$407$	−293199.			−1.77000
$408$		0			0
$409$	−146629.	−	84656.0i	−0.876540	−	0.506071i	−0.00702423	−	0.999975i	$-0.502236\pi$
$409$	−146629.	−	84656.0i	−0.876540	−	0.506071i	−0.869516	+	0.493905i	$0.835569\pi$
$410$		0			0
$411$	−93248.6	+	53837.1i	−0.552025	+	0.318712i
$412$		0			0
$413$	−2535.20	−	57528.9i	−0.0148632	−	0.337276i
$414$		0			0
$415$	134335.	+	232675.i	0.779998	+	1.35100i
$416$		0			0
$417$	−98687.2	+	170931.i	−0.567530	+	0.982991i
$418$		0			0
$419$		−	244991.i		−	1.39547i	−0.716354	−	0.697737i	$-0.754190\pi$
$419$		−	244991.i		−	1.39547i	0.716354	−	0.697737i	$-0.245810\pi$
$420$		0			0
$421$	247201.			1.39472			0.697360	−	0.716721i	$-0.254358\pi$
$421$	247201.			1.39472			0.697360	+	0.716721i	$0.254358\pi$
$422$		0			0
$423$	35777.8	+	20656.3i	0.199955	+	0.115444i
$424$		0			0
$425$	−48885.2	+	28223.9i	−0.270644	+	0.156257i
$426$		0			0
$427$	−231400.	−	120339.i	−1.26913	−	0.660013i
$428$		0			0
$429$	−88608.6	−	153475.i	−0.481461	−	0.833915i
$430$		0			0
$431$	30772.1	−	53298.9i	0.165654	−	0.286922i	−0.771233	−	0.636553i	$-0.780360\pi$
$431$	30772.1	−	53298.9i	0.165654	−	0.286922i	0.936887	+	0.349631i	$0.113693\pi$
$432$		0			0
$433$			5178.07i			0.0276180i	0.999905	+	0.0138090i	$0.00439568\pi$
$433$			5178.07i			0.0276180i	−0.999905	+	0.0138090i	$0.995604\pi$
$434$		0			0
$435$	18721.8			0.0989392
$436$		0			0
$437$	−34896.7	−	20147.6i	−0.182735	−	0.105502i
$438$		0			0
$439$	62813.4	−	36265.3i	0.325929	−	0.188175i	−0.328103	−	0.944642i	$-0.606409\pi$
$439$	62813.4	−	36265.3i	0.325929	−	0.188175i	0.654032	+	0.756467i	$0.273076\pi$
$440$		0			0
$441$	−64575.7	+	5702.55i	−0.332041	+	0.0293219i
$442$		0			0
$443$	−178387.	−	308976.i	−0.908984	−	1.57441i	−0.815479	−	0.578787i	$-0.803526\pi$
$443$	−178387.	−	308976.i	−0.908984	−	1.57441i	−0.0935052	−	0.995619i	$-0.529807\pi$
$444$		0			0
$445$	39846.5	−	69016.1i	0.201219	−	0.348522i
$446$		0			0
$447$			189780.i			0.949806i
$448$		0			0
$449$	−135890.			−0.674056			−0.337028	−	0.941495i	$-0.609422\pi$
$449$	−135890.			−0.674056			−0.337028	+	0.941495i	$0.609422\pi$
$450$		0			0
$451$	−135866.	−	78442.0i	−0.667969	−	0.385652i
$452$		0			0
$453$	−80159.8	+	46280.3i	−0.390625	+	0.225528i
$454$		0			0
$455$	154472.	−	297033.i	0.746153	−	1.43477i
$456$		0			0
$457$	−72311.5	−	125247.i	−0.346238	−	0.599702i	0.639340	−	0.768924i	$-0.279208\pi$
$457$	−72311.5	−	125247.i	−0.346238	−	0.599702i	−0.985578	+	0.169222i	$0.945874\pi$
$458$		0			0
$459$	−30520.7	+	52863.3i	−0.144867	+	0.250916i
$460$		0			0
$461$			362697.i			1.70664i	0.521388	+	0.853320i	$0.325414\pi$
$461$			362697.i			1.70664i	−0.521388	+	0.853320i	$0.674586\pi$
$462$		0			0
$463$	−307158.			−1.43285			−0.716423	−	0.697667i	$-0.754222\pi$
$463$	−307158.			−1.43285			−0.716423	+	0.697667i	$0.754222\pi$
$464$		0			0
$465$	208898.	+	120607.i	0.966114	+	0.557786i
$466$		0			0
$467$	−7007.58	+	4045.83i	−0.0321317	+	0.0185513i	−0.515980	−	0.856601i	$-0.672572\pi$
$467$	−7007.58	+	4045.83i	−0.0321317	+	0.0185513i	0.483848	+	0.875152i	$0.339239\pi$
$468$		0			0
$469$	−287560.	+	12672.3i	−1.30732	+	0.0576115i
$470$		0			0
$471$	−44897.7	−	77765.1i	−0.202387	−	0.350544i
$472$		0			0
$473$	−181516.	+	314395.i	−0.811320	+	1.40525i
$474$		0			0
$475$		−	45335.4i		−	0.200932i
$476$		0			0
$477$	−99053.9			−0.435346
$478$		0			0
$479$	208856.	+	120583.i	0.910281	+	0.525551i	0.880522	−	0.474006i	$-0.157193\pi$
$479$	208856.	+	120583.i	0.910281	+	0.525551i	0.0297596	+	0.999557i	$0.490526\pi$
$480$		0			0
$481$	460521.	−	265882.i	1.99049	−	1.14921i
$482$		0			0
$483$	24755.9	−	15785.4i	0.106117	−	0.0676646i
$484$		0			0
$485$	84196.3	+	145832.i	0.357939	+	0.619969i
$486$		0			0
$487$	−117464.	+	203454.i	−0.495275	+	0.857842i	−0.999985	−	0.00544711i	$-0.998266\pi$
$487$	−117464.	+	203454.i	−0.495275	+	0.857842i	0.504710	+	0.863289i	$0.331599\pi$
$488$		0			0
$489$			42261.6i			0.176737i
$490$		0			0
$491$	261507.			1.08473			0.542364	−	0.840144i	$-0.317529\pi$
$491$	261507.			1.08473			0.542364	+	0.840144i	$0.317529\pi$
$492$		0			0
$493$	49416.9	+	28530.9i	0.203321	+	0.117387i
$494$		0			0
$495$	88090.0	−	50858.8i	0.359514	−	0.207566i
$496$		0			0
$497$	−4666.32	−	7318.09i	−0.0188913	−	0.0296268i
$498$		0			0
$499$	178425.	+	309041.i	0.716563	+	1.24112i	0.962353	+	0.271801i	$0.0876193\pi$
$499$	178425.	+	309041.i	0.716563	+	1.24112i	−0.245790	+	0.969323i	$0.579047\pi$
$500$		0			0
$501$	120651.	−	208973.i	0.480679	−	0.832560i
$502$		0			0
$503$			217029.i			0.857793i	0.903354	+	0.428897i	$0.141098\pi$
$503$			217029.i			0.857793i	−0.903354	+	0.428897i	$0.858902\pi$
$504$		0			0
$505$	482231.			1.89092
$506$		0			0
$507$	149827.	+	86502.4i	0.582872	+	0.336521i
$508$		0			0
$509$	55163.0	−	31848.4i	0.212918	−	0.122928i	−0.389749	−	0.920921i	$-0.627438\pi$
$509$	55163.0	−	31848.4i	0.212918	−	0.122928i	0.602667	+	0.797993i	$0.294105\pi$
$510$		0			0
$511$	−1740.89	−	39504.3i	−0.00666697	−	0.151287i
$512$		0			0
$513$	−24512.3	−	42456.6i	−0.0931430	−	0.161328i
$514$		0			0
$515$	−44164.0	+	76494.3i	−0.166515	+	0.288413i
$516$		0			0
$517$		−	209823.i		−	0.785005i
$518$		0			0
$519$	−56531.6			−0.209873
$520$		0			0
$521$	−198714.	−	114728.i	−0.732071	−	0.422661i	0.0871085	−	0.996199i	$-0.472237\pi$
$521$	−198714.	−	114728.i	−0.732071	−	0.422661i	−0.819179	+	0.573538i	$0.805571\pi$
$522$		0			0
$523$	−170380.	+	98369.0i	−0.622896	+	0.359629i	−0.777996	−	0.628270i	$-0.783763\pi$
$523$	−170380.	+	98369.0i	−0.622896	+	0.359629i	0.155100	+	0.987899i	$0.450430\pi$
$524$		0			0
$525$	29306.7	+	15241.0i	0.106328	+	0.0552960i
$526$		0			0
$527$	367597.	+	636697.i	1.32358	+	2.29251i
$528$		0			0
$529$	133272.	−	230833.i	0.476241	−	0.824874i
$530$		0			0
$531$			31730.3i			0.112535i
$532$		0			0
$533$	284535.			1.00157
$534$		0			0
$535$	−340606.	−	196649.i	−1.18999	−	0.687043i
$536$		0			0
$537$	59011.7	−	34070.4i	0.204640	−	0.118149i
$538$		0			0
$539$	189069.	+	269552.i	0.650794	+	0.927824i
$540$		0			0
$541$	−100135.	−	173439.i	−0.342130	−	0.592587i	0.642698	−	0.766120i	$-0.277815\pi$
$541$	−100135.	−	173439.i	−0.342130	−	0.592587i	−0.984828	+	0.173533i	$0.944482\pi$
$542$		0			0
$543$	−125678.	+	217682.i	−0.426247	+	0.738281i
$544$		0			0
$545$		−	50810.9i		−	0.171066i
$546$		0			0
$547$	171070.			0.571742			0.285871	−	0.958268i	$-0.407717\pi$
$547$	171070.			0.571742			0.285871	+	0.958268i	$0.407717\pi$
$548$		0			0
$549$	124463.	+	71858.7i	0.412948	+	0.238416i
$550$		0			0
$551$	−39688.7	+	22914.3i	−0.130726	+	0.0754749i
$552$		0			0
$553$	−20040.5	+	38535.6i	−0.0655326	+	0.126012i
$554$		0			0
$555$	152608.	+	264325.i	0.495441	+	0.858130i
$556$		0			0
$557$	−263529.	+	456445.i	−0.849410	+	1.47122i	0.0323256	+	0.999477i	$0.489709\pi$
$557$	−263529.	+	456445.i	−0.849410	+	1.47122i	−0.881736	+	0.471744i	$0.843625\pi$
$558$		0			0
$559$		−	658417.i		−	2.10706i
$560$		0			0
$561$	310023.			0.985073
$562$		0			0
$563$	−139858.	−	80746.9i	−0.441235	−	0.254747i	0.262886	−	0.964827i	$-0.415326\pi$
$563$	−139858.	−	80746.9i	−0.441235	−	0.254747i	−0.704121	+	0.710080i	$0.748659\pi$
$564$		0			0
$565$	450489.	−	260090.i	1.41120	−	0.814754i
$566$		0			0
$567$	35686.4	−	1572.64i	0.111003	−	0.00489173i
$568$		0			0
$569$	−24538.7	−	42502.2i	−0.0757926	−	0.131277i	0.825638	−	0.564200i	$-0.190815\pi$
$569$	−24538.7	−	42502.2i	−0.0757926	−	0.131277i	−0.901431	+	0.432924i	$0.857482\pi$
$570$		0			0
$571$	−137407.	+	237995.i	−0.421440	+	0.729955i	−0.996081	−	0.0884509i	$-0.971808\pi$
$571$	−137407.	+	237995.i	−0.421440	+	0.729955i	0.574641	+	0.818406i	$0.305142\pi$
$572$		0			0
$573$			10618.2i			0.0323402i
$574$		0			0
$575$	−14960.7			−0.0452498
$576$		0			0
$577$	−427130.	−	246604.i	−1.28295	−	0.740709i	−0.305560	−	0.952173i	$-0.598844\pi$
$577$	−427130.	−	246604.i	−1.28295	−	0.740709i	−0.977386	+	0.211464i	$0.932177\pi$
$578$		0			0
$579$	−184610.	+	106585.i	−0.550679	+	0.317935i
$580$		0			0
$581$	404049.	−	257639.i	1.19697	−	0.763236i
$582$		0			0
$583$	251543.	+	435685.i	0.740073	+	1.28184i
$584$		0			0
$585$	−92240.6	+	159765.i	−0.269532	+	0.466843i
$586$		0			0
$587$			21907.2i			0.0635785i	0.999495	+	0.0317893i	$0.0101205\pi$
$587$			21907.2i			0.0635785i	−0.999495	+	0.0317893i	$0.989879\pi$
$588$		0			0
$589$	−590463.			−1.70201
$590$		0			0
$591$	−138669.	−	80060.4i	−0.397012	−	0.229215i
$592$		0			0
$593$	−143497.	+	82848.0i	−0.408069	+	0.235599i	−0.689960	−	0.723848i	$-0.742372\pi$
$593$	−143497.	+	82848.0i	−0.408069	+	0.235599i	0.281891	+	0.959446i	$0.409038\pi$
$594$		0			0
$595$	314895.	+	493843.i	0.889472	+	1.39494i
$596$		0			0
$597$	−119935.	−	207734.i	−0.336510	−	0.582852i
$598$		0			0
$599$	155879.	−	269991.i	0.434445	−	0.752480i	−0.562806	−	0.826589i	$-0.690278\pi$
$599$	155879.	−	269991.i	0.434445	−	0.752480i	0.997250	+	0.0741093i	$0.0236114\pi$
$600$		0			0
$601$		−	105774.i		−	0.292838i	−0.989223	−	0.146419i	$-0.953225\pi$
$601$		−	105774.i		−	0.292838i	0.989223	−	0.146419i	$-0.0467749\pi$
$602$		0			0
$603$	158605.			0.436198
$604$		0			0
$605$	−99063.7	−	57194.4i	−0.270647	−	0.156258i
$606$		0			0
$607$	489602.	−	282672.i	1.32882	−	0.767194i	0.343702	−	0.939079i	$-0.388319\pi$
$607$	489602.	−	282672.i	1.32882	−	0.767194i	0.985117	+	0.171885i	$0.0549857\pi$
$608$		0			0
$609$	−1470.11	−	33359.8i	−0.00396383	−	0.0899475i
$610$		0			0
$611$	190274.	+	329565.i	0.509680	+	0.882791i
$612$		0			0
$613$	55604.1	−	96309.1i	0.147974	−	0.256299i	−0.782504	−	0.622645i	$-0.786058\pi$
$613$	55604.1	−	96309.1i	0.147974	−	0.256299i	0.930479	+	0.366346i	$0.119391\pi$
$614$		0			0
$615$			163315.i			0.431792i
$616$		0			0
$617$	489293.			1.28528			0.642641	−	0.766167i	$-0.277839\pi$
$617$	489293.			1.28528			0.642641	+	0.766167i	$0.277839\pi$
$618$		0			0
$619$	−435312.	−	251327.i	−1.13611	−	0.655932i	−0.190643	−	0.981659i	$-0.561057\pi$
$619$	−435312.	−	251327.i	−1.13611	−	0.655932i	−0.945464	+	0.325728i	$0.894391\pi$
$620$		0			0
$621$	−14010.7	+	8089.09i	−0.0363310	+	0.0209757i
$622$		0			0
$623$	−126107.	−	65581.9i	−0.324910	−	0.168969i
$624$		0			0
$625$	227440.	+	393937.i	0.582246	+	1.00848i
$626$		0			0
$627$	−124496.	+	215633.i	−0.316679	+	0.548505i
$628$		0			0
$629$			930265.i			2.35128i
$630$		0			0
$631$	−519978.			−1.30595			−0.652975	−	0.757379i	$-0.726479\pi$
$631$	−519978.			−1.30595			−0.652975	+	0.757379i	$0.726479\pi$
$632$		0			0
$633$	138259.	+	79824.1i	0.345054	+	0.199217i
$634$		0			0
$635$	69760.5	−	40276.3i	0.173006	−	0.0998853i
$636$		0			0
$637$	−541405.	−	251926.i	−1.33427	−	0.620860i
$638$		0			0
$639$	2391.22	+	4141.71i	0.00585622	+	0.0101433i
$640$		0			0
$641$	287536.	−	498027.i	0.699803	−	1.21209i	−0.268731	−	0.963215i	$-0.586604\pi$
$641$	287536.	−	498027.i	0.699803	−	1.21209i	0.968534	−	0.248879i	$-0.0800623\pi$
$642$		0			0
$643$			177434.i			0.429156i	0.976707	+	0.214578i	$0.0688376\pi$
$643$			177434.i			0.429156i	−0.976707	+	0.214578i	$0.931162\pi$
$644$		0			0
$645$	377912.			0.908387
$646$		0			0
$647$	38995.8	+	22514.3i	0.0931557	+	0.0537835i	0.545854	−	0.837880i	$-0.316205\pi$
$647$	38995.8	+	22514.3i	0.0931557	+	0.0537835i	−0.452698	+	0.891664i	$0.649539\pi$
$648$		0			0
$649$	139565.	−	80577.7i	0.331349	−	0.191305i
$650$		0			0
$651$	198503.	−	381700.i	0.468388	−	0.900659i
$652$		0			0
$653$	−244844.	−	424082.i	−0.574200	−	0.994543i	−0.996128	−	0.0879142i	$-0.971980\pi$
$653$	−244844.	−	424082.i	−0.574200	−	0.994543i	0.421928	−	0.906629i	$-0.361353\pi$
$654$		0			0
$655$	−190638.	+	330194.i	−0.444351	+	0.769639i
$656$		0			0
$657$			21788.8i			0.0504781i
$658$		0			0
$659$	141546.			0.325932			0.162966	−	0.986632i	$-0.447894\pi$
$659$	141546.			0.325932			0.162966	+	0.986632i	$0.447894\pi$
$660$		0			0
$661$	25524.3	+	14736.4i	0.0584185	+	0.0337279i	0.528925	−	0.848669i	$-0.322595\pi$
$661$	25524.3	+	14736.4i	0.0584185	+	0.0337279i	−0.470506	+	0.882397i	$0.655929\pi$
$662$		0			0
$663$	−486946.	+	281139.i	−1.10778	+	0.639578i
$664$		0			0
$665$	−469940.	+	20709.4i	−1.06267	+	0.0468301i
$666$		0			0
$667$	7561.72	+	13097.3i	0.0169969	+	0.0294395i
$668$		0			0
$669$	42857.1	−	74230.7i	0.0957571	−	0.165856i
$670$		0			0
$671$		−	729927.i		−	1.62119i
$672$		0			0
$673$	113476.			0.250539			0.125270	−	0.992123i	$-0.460020\pi$
$673$	113476.			0.250539			0.125270	+	0.992123i	$0.460020\pi$
$674$		0			0
$675$	−15763.2	−	9100.89i	−0.0345969	−	0.0199745i
$676$		0			0
$677$	−456934.	+	263811.i	−0.996957	+	0.575593i	−0.907346	−	0.420384i	$-0.861895\pi$
$677$	−456934.	+	263811.i	−0.996957	+	0.575593i	−0.0896102	+	0.995977i	$0.528562\pi$
$678$		0			0
$679$	253243.	−	161478.i	0.549285	−	0.350247i
$680$		0			0
$681$	43032.6	+	74534.7i	0.0927906	+	0.160718i
$682$		0			0
$683$	−349980.	+	606183.i	−0.750242	+	1.29946i	0.197463	+	0.980310i	$0.436730\pi$
$683$	−349980.	+	606183.i	−0.750242	+	1.29946i	−0.947705	+	0.319147i	$0.896604\pi$
$684$		0			0
$685$		−	569283.i		−	1.21324i
$686$		0			0
$687$	−236181.			−0.500417
$688$		0			0
$689$	−790185.	−	456213.i	−1.66452	−	0.961014i
$690$		0			0
$691$	445069.	−	256961.i	0.932118	−	0.538159i	0.0446375	−	0.999003i	$-0.485787\pi$
$691$	445069.	−	256961.i	0.932118	−	0.538159i	0.887481	+	0.460844i	$0.152453\pi$
$692$		0			0
$693$	−97541.0	−	152971.i	−0.203105	−	0.318525i
$694$		0			0
$695$	−521768.	−	903728.i	−1.08021	−	1.87098i
$696$		0			0
$697$	−248882.	+	431076.i	−0.512304	+	0.887336i
$698$		0			0
$699$			52209.8i			0.106856i
$700$		0			0
$701$	454012.			0.923913			0.461957	−	0.886903i	$-0.347148\pi$
$701$	454012.			0.923913			0.461957	+	0.886903i	$0.347148\pi$
$702$		0			0
$703$	−647035.	−	373566.i	−1.30923	−	0.755887i
$704$		0			0
$705$	−189160.	+	109212.i	−0.380585	+	0.219731i
$706$		0			0
$707$	−37866.7	−	859275.i	−0.0757564	−	1.71907i
$708$		0			0
$709$	235969.	+	408711.i	0.469422	+	0.813062i	0.999389	−	0.0349561i	$-0.0111291\pi$
$709$	235969.	+	408711.i	0.469422	+	0.813062i	−0.529967	+	0.848018i	$0.677796\pi$
$710$		0			0
$711$	11966.8	−	20727.2i	0.0236723	−	0.0410016i
$712$		0			0
$713$			194853.i			0.383291i
$714$		0			0
$715$	936963.			1.83278
$716$		0			0
$717$	−142946.	−	82529.9i	−0.278057	−	0.160536i
$718$		0			0
$719$	−339912.	+	196248.i	−0.657519	+	0.379619i	−0.791331	−	0.611388i	$-0.790612\pi$
$719$	−339912.	+	196248.i	−0.657519	+	0.379619i	0.133812	+	0.991007i	$0.457278\pi$
$720$		0			0
$721$	139771.	+	72688.0i	0.268873	+	0.139827i
$722$		0			0
$723$	45152.4	+	78206.2i	0.0863782	+	0.149611i
$724$		0			0
$725$	−8507.56	+	14735.5i	−0.0161856	+	0.0280343i
$726$		0			0
$727$			6702.89i			0.0126822i	0.999980	+	0.00634108i	$0.00201844\pi$
$727$			6702.89i			0.0126822i	−0.999980	+	0.00634108i	$0.997982\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$		0			0
$731$	997515.	+	575915.i	1.86674	+	1.07776i
$732$		0			0
$733$	195786.	−	113037.i	0.364397	−	0.210385i	−0.306611	−	0.951835i	$-0.599195\pi$
$733$	195786.	−	113037.i	0.364397	−	0.210385i	0.671008	+	0.741450i	$0.265862\pi$
$734$		0			0
$735$	144598.	−	310751.i	0.267663	−	0.575225i
$736$		0			0
$737$	−402771.	−	697620.i	−0.741520	−	1.28435i
$738$		0			0
$739$	−405947.	+	703120.i	−0.743327	+	1.28748i	0.207645	+	0.978204i	$0.433420\pi$
$739$	−405947.	+	703120.i	−0.743327	+	1.28748i	−0.950972	+	0.309276i	$0.899913\pi$
$740$		0			0
$741$		−	451587.i		−	0.822441i
$742$		0			0
$743$	485989.			0.880336			0.440168	−	0.897915i	$-0.354919\pi$
$743$	485989.			0.880336			0.440168	+	0.897915i	$0.354919\pi$
$744$		0			0
$745$	−868954.	−	501691.i	−1.56561	−	0.903907i
$746$		0			0
$747$	−228674.	+	132025.i	−0.409803	+	0.236600i
$748$		0			0
$749$	−323658.	+	622358.i	−0.576929	+	1.10937i
$750$		0			0
$751$	−327432.	−	567129.i	−0.580552	−	1.00555i	−0.995414	−	0.0956615i	$-0.969503\pi$
$751$	−327432.	−	567129.i	−0.580552	−	1.00555i	0.414862	−	0.909885i	$-0.363830\pi$
$752$		0			0
$753$	−133883.	+	231893.i	−0.236122	+	0.408975i
$754$		0			0
$755$		−	489376.i		−	0.858516i
$756$		0			0
$757$	867453.			1.51375			0.756875	−	0.653560i	$-0.226725\pi$
$757$	867453.			1.51375			0.756875	+	0.653560i	$0.226725\pi$
$758$		0			0
$759$	71159.1	+	41083.7i	0.123523	+	0.0713159i
$760$		0			0
$761$	299642.	−	172998.i	0.517408	−	0.298726i	−0.218466	−	0.975845i	$-0.570105\pi$
$761$	299642.	−	172998.i	0.517408	−	0.298726i	0.735873	+	0.677119i	$0.236772\pi$
$762$		0			0
$763$	−90538.5	+	3989.87i	−0.155519	+	0.00685347i
$764$		0			0
$765$	−161365.	−	279493.i	−0.275732	−	0.477582i
$766$		0			0
$767$	−146141.	+	253123.i	−0.248417	+	0.430270i
$768$		0			0
$769$			686709.i			1.16123i	0.814177	+	0.580617i	$0.197189\pi$
$769$			686709.i			1.16123i	−0.814177	+	0.580617i	$0.802811\pi$
$770$		0			0
$771$	−284528.			−0.478648
$772$		0			0
$773$	196603.	+	113509.i	0.329026	+	0.189964i	0.655409	−	0.755274i	$-0.272496\pi$
$773$	196603.	+	113509.i	0.329026	+	0.189964i	−0.326382	+	0.945238i	$0.605830\pi$
$774$		0			0
$775$	−189855.	+	109613.i	−0.316096	+	0.182498i
$776$		0			0
$777$	459011.	−	292684.i	0.760293	−	0.484794i
$778$		0			0
$779$	−199887.	−	346214.i	−0.329389	−	0.570519i
$780$		0			0
$781$	12144.8	−	21035.3i	0.0199107	−	0.0344864i
$782$		0			0
$783$			18399.8i			0.0300116i
$784$		0			0
$785$	474756.			0.770426
$786$		0			0
$787$	−496955.	−	286917.i	−0.802357	−	0.463241i	0.0419379	−	0.999120i	$-0.486647\pi$
$787$	−496955.	−	286917.i	−0.802357	−	0.463241i	−0.844295	+	0.535879i	$0.819980\pi$
$788$		0			0
$789$	69093.5	−	39891.2i	0.110990	−	0.0640800i
$790$		0			0
$791$	−498821.	−	782291.i	−0.797246	−	1.25030i
$792$		0			0
$793$	661920.	+	1.14648e6i	1.05259	+	1.82314i
$794$		0			0
$795$	261853.	−	453543.i	0.414308	−	0.717603i
$796$		0			0
$797$			607996.i			0.957159i	0.878044	+	0.478580i	$0.158848\pi$
$797$			607996.i			0.957159i	−0.878044	+	0.478580i	$0.841152\pi$
$798$		0			0
$799$	−665730.			−1.04281
$800$		0			0
$801$	67829.1	+	39161.2i	0.105719	+	0.0610366i
$802$		0			0
$803$	95837.2	−	55331.6i	0.148629	−	0.0858109i
$804$		0			0
$805$	6834.12	+	155080.i	0.0105461	+	0.239312i
$806$		0			0
$807$	−235930.	−	408643.i	−0.362273	−	0.627476i
$808$		0			0
$809$	−370330.	+	641431.i	−0.565838	+	0.980061i	0.431133	+	0.902288i	$0.358114\pi$
$809$	−370330.	+	641431.i	−0.565838	+	0.980061i	−0.996971	+	0.0777723i	$0.975219\pi$
$810$		0			0
$811$		−	173920.i		−	0.264428i	−0.991221	−	0.132214i	$-0.957791\pi$
$811$		−	173920.i		−	0.264428i	0.991221	−	0.132214i	$-0.0422086\pi$
$812$		0			0
$813$	−350932.			−0.530936
$814$		0			0
$815$	−193505.	−	111720.i	−0.291325	−	0.168197i
$816$		0			0
$817$	−801143.	+	462540.i	−1.20023	+	0.692956i
$818$		0			0
$819$	291925.	+	151816.i	0.435214	+	0.226333i
$820$		0			0
$821$	574854.	+	995676.i	0.852847	+	1.47717i	0.878628	+	0.477507i	$0.158459\pi$
$821$	574854.	+	995676.i	0.852847	+	1.47717i	−0.0257813	+	0.999668i	$0.508207\pi$
$822$		0			0
$823$	198056.	−	343044.i	0.292408	−	0.506465i	−0.681971	−	0.731380i	$-0.738877\pi$
$823$	198056.	−	343044.i	0.292408	−	0.506465i	0.974379	+	0.224914i	$0.0722102\pi$
$824$		0			0
$825$			92445.1i			0.135824i
$826$		0			0
$827$	−333413.			−0.487496			−0.243748	−	0.969839i	$-0.578377\pi$
$827$	−333413.			−0.487496			−0.243748	+	0.969839i	$0.578377\pi$
$828$		0			0
$829$	−105881.	−	61130.2i	−0.154066	−	0.0889501i	0.420985	−	0.907068i	$-0.361685\pi$
$829$	−105881.	−	61130.2i	−0.154066	−	0.0889501i	−0.575051	+	0.818117i	$0.695018\pi$
$830$		0			0
$831$	320821.	−	185226.i	0.464581	−	0.268226i
$832$		0			0
$833$	855239.	−	599882.i	1.23253	−	0.864521i
$834$		0			0
$835$	637891.	+	1.10486e6i	0.914900	+	1.58465i
$836$		0			0
$837$	−118533.	+	205305.i	−0.169195	+	0.293055i
$838$		0			0
$839$			426603.i			0.606038i	0.952985	+	0.303019i	$0.0979945\pi$
$839$			426603.i			0.606038i	−0.952985	+	0.303019i	$0.902005\pi$
$840$		0			0
$841$	−690081.			−0.975681
$842$		0			0
$843$	182591.	+	105419.i	0.256935	+	0.148341i
$844$		0			0
$845$	−792146.	+	457346.i	−1.10941	+	0.640518i
$846$		0			0
$847$	−94134.3	+	181010.i	−0.131214	+	0.252311i
$848$		0			0
$849$	−274709.	−	475810.i	−0.381116	−	0.660112i
$850$		0			0
$851$	−123277.	+	213522.i	−0.170225	+	0.294838i
$852$		0			0
$853$		−	175584.i		−	0.241316i	−0.992694	−	0.120658i	$-0.961500\pi$
$853$		−	175584.i		−	0.241316i	0.992694	−	0.120658i	$-0.0385005\pi$
$854$		0			0
$855$	259198.			0.354567
$856$		0			0
$857$	−1.15835e6	−	668775.i	−1.57717	−	0.910580i	−0.995252	−	0.0973334i	$-0.968969\pi$
$857$	−1.15835e6	−	668775.i	−1.57717	−	0.910580i	−0.581919	−	0.813247i	$-0.697698\pi$
$858$		0			0
$859$	724435.	−	418253.i	0.981778	−	0.566830i	0.0789715	−	0.996877i	$-0.474836\pi$
$859$	724435.	−	418253.i	0.981778	−	0.566830i	0.902806	+	0.430047i	$0.141503\pi$
$860$		0			0
$861$	291006.	−	12824.1i	0.392550	−	0.0172990i
$862$		0			0
$863$	−398308.	−	689890.i	−0.534807	−	0.926314i	−0.999173	−	0.0406699i	$-0.987051\pi$
$863$	−398308.	−	689890.i	−0.534807	−	0.926314i	0.464365	−	0.885644i	$-0.346283\pi$
$864$		0			0
$865$	149444.	−	258844.i	0.199731	−	0.345944i
$866$		0			0
$867$		−	549657.i		−	0.731229i
$868$		0			0
$869$	−121557.			−0.160968
$870$		0			0
$871$	1.26525e6	+	730490.i	1.66778	+	0.962893i
$872$		0			0
$873$	−143324.	+	82748.2i	−0.188057	+	0.108575i
$874$		0			0
$875$	562142.	−	358445.i	0.734226	−	0.468173i
$876$		0			0
$877$	408249.	+	707108.i	0.530794	+	0.919362i	0.999354	+	0.0359306i	$0.0114395\pi$
$877$	408249.	+	707108.i	0.530794	+	0.919362i	−0.468560	+	0.883431i	$0.655227\pi$
$878$		0			0
$879$	156902.	−	271763.i	0.203073	−	0.351732i
$880$		0			0
$881$			841243.i			1.08385i	0.840426	+	0.541926i	$0.182305\pi$
$881$			841243.i			1.08385i	−0.840426	+	0.541926i	$0.817695\pi$
$882$		0			0
$883$	258768.			0.331886			0.165943	−	0.986135i	$-0.446933\pi$
$883$	258768.			0.331886			0.165943	+	0.986135i	$0.446933\pi$
$884$		0			0
$885$	−145285.	−	83880.5i	−0.185496	−	0.107096i
$886$		0			0
$887$	683095.	−	394385.i	0.868228	−	0.501272i	0.00146925	−	0.999999i	$-0.499532\pi$
$887$	683095.	−	394385.i	0.868228	−	0.501272i	0.866759	+	0.498727i	$0.166199\pi$
$888$		0			0
$889$	−77245.0	−	121142.i	−0.0977388	−	0.153282i
$890$		0			0
$891$	49984.0	+	86574.9i	0.0629616	+	0.109053i
$892$		0			0
$893$	267337.	−	463041.i	0.335240	−	0.580653i
$894$		0			0
$895$			360267.i			0.449757i
$896$		0			0
$897$	−149024.			−0.185213
$898$		0			0
$899$	191920.	+	110805.i	0.237466	+	0.137101i
$900$		0			0
$901$	1.38235e6	−	798098.i	1.70281	−	0.983120i
$902$		0			0
$903$	−29675.2	−	673391.i	−0.0363930	−	0.825832i
$904$		0			0
$905$	−664473.	−	1.15090e6i	−0.811297	−	1.40521i
$906$		0			0
$907$	258146.	−	447123.i	0.313799	−	0.543516i	−0.665383	−	0.746503i	$-0.731732\pi$
$907$	258146.	−	447123.i	0.313799	−	0.543516i	0.979181	+	0.202987i	$0.0650649\pi$
$908$		0			0
$909$			473937.i			0.573579i
$910$		0			0
$911$	1.39853e6			1.68514			0.842568	−	0.538590i	$-0.181043\pi$
$911$	1.39853e6			1.68514			0.842568	+	0.538590i	$0.181043\pi$
$912$		0			0
$913$	1.16141e6	+	670541.i	1.39330	+	0.804422i
$914$		0			0
$915$	−658046.	+	379923.i	−0.785985	+	0.453788i
$916$		0			0
$917$	603334.	+	313764.i	0.717495	+	0.373134i
$918$		0			0
$919$	731212.	+	1.26650e6i	0.865790	+	1.49959i	0.866261	+	0.499592i	$0.166517\pi$
$919$	731212.	+	1.26650e6i	0.865790	+	1.49959i	−0.000470672		1.00000i	$0.500150\pi$
$920$		0			0
$921$	−353406.	+	612116.i	−0.416633	+	0.721630i
$922$		0			0
$923$			44053.0i			0.0517097i
$924$		0			0
$925$	−277394.			−0.324200
$926$		0			0
$927$	−75178.7	−	43404.4i	−0.0874853	−	0.0505097i
$928$		0			0
$929$	726065.	−	419194.i	0.841287	−	0.485717i	−0.0164147	−	0.999865i	$-0.505225\pi$
$929$	726065.	−	419194.i	0.841287	−	0.485717i	0.857701	+	0.514148i	$0.171892\pi$
$930$		0			0
$931$	73803.1	+	835746.i	0.0851481	+	0.964218i
$932$		0			0
$933$	−356046.	−	616690.i	−0.409018	−	0.708440i
$934$		0			0
$935$	−819559.	+	1.41952e6i	−0.937469	+	1.62374i
$936$		0			0
$937$			1.36557e6i			1.55537i	0.628654	+	0.777685i	$0.283606\pi$
$937$			1.36557e6i			1.55537i	−0.628654	+	0.777685i	$0.716394\pi$
$938$		0			0
$939$	−301672.			−0.342140
$940$		0			0
$941$	1.10445e6	+	637657.i	1.24729	+	0.720125i	0.970569	−	0.240824i	$-0.0774178\pi$
$941$	1.10445e6	+	637657.i	1.24729	+	0.720125i	0.276724	+	0.960949i	$0.410751\pi$
$942$		0			0
$943$	−114251.	+	65962.8i	−0.128480	+	0.0741781i
$944$		0			0
$945$	−87137.7	+	167556.i	−0.0975759	+	0.187628i
$946$		0			0
$947$	415726.	+	720058.i	0.463561	+	0.802912i	0.999135	−	0.0415765i	$-0.0132380\pi$
$947$	415726.	+	720058.i	0.463561	+	0.802912i	−0.535574	+	0.844488i	$0.679905\pi$
$948$		0			0
$949$	−100353.	+	173816.i	−0.111429	+	0.193000i
$950$		0			0
$951$			475606.i			0.525880i
$952$		0			0
$953$	−651372.			−0.717205			−0.358603	−	0.933490i	$-0.616747\pi$
$953$	−651372.			−0.717205			−0.358603	+	0.933490i	$0.616747\pi$
$954$		0			0
$955$	−48618.1	−	28069.7i	−0.0533079	−	0.0307773i
$956$		0			0
$957$	80930.7	−	46725.3i	0.0883668	−	0.0510186i
$958$		0			0
$959$	−1.01439e6	+	44702.4i	−1.10298	+	0.0486064i
$960$		0			0
$961$	965874.	+	1.67294e6i	1.04586	+	1.81148i
$962$		0			0
$963$	193267.	−	334748.i	0.208403	−	0.360965i
$964$		0			0
$965$		−	1.12705e6i		−	1.21028i
$966$		0			0
$967$	−1.39918e6			−1.49631			−0.748153	−	0.663526i	$-0.769059\pi$
$967$	−1.39918e6			−1.49631			−0.748153	+	0.663526i	$0.769059\pi$
$968$		0			0
$969$	684163.	+	395002.i	0.728639	+	0.420680i
$970$		0			0
$971$	−448804.	+	259117.i	−0.476012	+	0.274826i	−0.718753	−	0.695266i	$-0.755287\pi$
$971$	−448804.	+	259117.i	−0.476012	+	0.274826i	0.242741	+	0.970091i	$0.421953\pi$
$972$		0			0
$973$	−1.56936e6	+	1.00069e6i	−1.65766	+	1.05700i
$974$		0			0
$975$	−83832.1	−	145201.i	−0.0881863	−	0.152743i
$976$		0			0
$977$	898767.	−	1.55671e6i	0.941582	−	1.63087i	0.179127	−	0.983826i	$-0.442673\pi$
$977$	898767.	−	1.55671e6i	0.941582	−	1.63087i	0.762454	−	0.647042i	$-0.223994\pi$
$978$		0			0
$979$		−	397792.i		−	0.415040i
$980$		0			0
$981$	49937.0			0.0518901
$982$		0			0
$983$	−911528.	−	526271.i	−0.943328	−	0.544631i	−0.0523262	−	0.998630i	$-0.516664\pi$
$983$	−911528.	−	526271.i	−0.943328	−	0.544631i	−0.891002	+	0.453999i	$0.849997\pi$
$984$		0			0
$985$	733153.	−	423286.i	0.755653	−	0.436276i
$986$		0			0
$987$	209455.	+	328484.i	0.215009	+	0.337194i
$988$		0			0
$989$	152639.	+	264378.i	0.156053	+	0.270292i
$990$		0			0
$991$	376635.	−	652352.i	0.383508	−	0.664255i	−0.608053	−	0.793896i	$-0.708049\pi$
$991$	376635.	−	652352.i	0.383508	−	0.664255i	0.991561	+	0.129642i	$0.0413827\pi$
$992$		0			0
$993$		−	101365.i		−	0.102799i
$994$		0			0
$995$	1.26821e6			1.28099
$996$		0			0
$997$	−1.12666e6	−	650478.i	−1.13345	−	0.654398i	−0.188650	−	0.982044i	$-0.560411\pi$
$997$	−1.12666e6	−	650478.i	−1.13345	−	0.654398i	−0.944800	+	0.327646i	$0.893745\pi$
$998$		0			0
$999$	−259779.	+	149984.i	−0.260300	+	0.150284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.5.z.a.73.6	✓	16
3.2	odd	2		504.5.by.a.73.3		16
4.3	odd	2		336.5.bh.i.241.6		16
7.3	odd	6		1176.5.f.b.97.3		16
7.4	even	3		1176.5.f.b.97.14		16
7.5	odd	6	inner	168.5.z.a.145.6	yes	16
21.5	even	6		504.5.by.a.145.3		16
28.19	even	6		336.5.bh.i.145.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.5.z.a.73.6	✓	16	1.1	even	1	trivial
168.5.z.a.145.6	yes	16	7.5	odd	6	inner
336.5.bh.i.145.6		16	28.19	even	6
336.5.bh.i.241.6		16	4.3	odd	2
504.5.by.a.73.3		16	3.2	odd	2
504.5.by.a.145.3		16	21.5	even	6
1176.5.f.b.97.3		16	7.3	odd	6
1176.5.f.b.97.14		16	7.4	even	3

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	168.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 - 2.59808i) q^{3} +(23.7919 - 13.7363i) q^{5} +(-26.3445 - 41.3155i) q^{7} +(13.5000 + 23.3827i) q^{9} +O(q^{10})\)	\(q+(-4.50000 - 2.59808i) q^{3} +(23.7919 - 13.7363i) q^{5} +(-26.3445 - 41.3155i) q^{7} +(13.5000 + 23.3827i) q^{9} +(68.5652 - 118.758i) q^{11} +248.708i q^{13} -142.751 q^{15} +(-376.798 - 217.545i) q^{17} +(302.621 - 174.719i) q^{19} +(11.2094 + 254.365i) q^{21} +(-57.6573 - 99.8653i) q^{23} +(64.8691 - 112.357i) q^{25} -140.296i q^{27} -131.150 q^{29} +(-1463.37 - 844.877i) q^{31} +(-617.087 + 356.275i) q^{33} +(-1194.30 - 621.099i) q^{35} +(-1069.05 - 1851.65i) q^{37} +(646.163 - 1119.19i) q^{39} -1144.05i q^{41} -2647.34 q^{43} +(642.381 + 370.879i) q^{45} +(1325.10 - 765.050i) q^{47} +(-1012.94 + 2176.87i) q^{49} +(1130.39 + 1957.90i) q^{51} +(-1834.33 + 3177.16i) q^{53} -3767.32i q^{55} -1815.73 q^{57} +(1017.75 + 587.599i) q^{59} +(4609.74 - 2661.43i) q^{61} +(610.416 - 1173.76i) q^{63} +(3416.32 + 5917.24i) q^{65} +(2937.14 - 5087.27i) q^{67} +599.192i q^{69} +177.127 q^{71} +(698.876 + 403.496i) q^{73} +(-583.822 + 337.070i) q^{75} +(-6712.88 + 295.825i) q^{77} +(-443.216 - 767.673i) q^{79} +(-364.500 + 631.333i) q^{81} +9779.61i q^{83} -11953.0 q^{85} +(590.173 + 340.737i) q^{87} +(2512.19 - 1450.41i) q^{89} +(10275.5 - 6552.09i) q^{91} +(4390.11 + 7603.89i) q^{93} +(4799.96 - 8313.77i) q^{95} +6129.50i q^{97} +3702.52 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9}+O(q^{10}) \) 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9	\( 16 q - 72 q^{3} + 12 q^{5} + 40 q^{7} + 216 q^{9} - 108 q^{11} - 72 q^{15} - 168 q^{17} + 948 q^{19} - 252 q^{21} - 768 q^{23} + 1908 q^{25} - 1608 q^{29} - 3216 q^{31} + 972 q^{33} + 696 q^{35} - 1820 q^{37} - 1188 q^{39} + 2888 q^{43} + 324 q^{45} + 744 q^{47} - 3784 q^{49} + 504 q^{51} + 4476 q^{53} - 5688 q^{57} - 4668 q^{59} + 17760 q^{61} + 1188 q^{63} + 8760 q^{65} + 1580 q^{67} + 48 q^{71} + 588 q^{73} - 17172 q^{75} - 17508 q^{77} - 3824 q^{79} - 5832 q^{81} + 11440 q^{85} + 7236 q^{87} - 360 q^{89} + 25860 q^{91} + 9648 q^{93} - 21792 q^{95} - 5832 q^{99}+O(q^{100}) \) 16 * q - 72 * q^3 + 12 * q^5 + 40 * q^7 + 216 * q^9 - 108 * q^11 - 72 * q^15 - 168 * q^17 + 948 * q^19 - 252 * q^21 - 768 * q^23 + 1908 * q^25 - 1608 * q^29 - 3216 * q^31 + 972 * q^33 + 696 * q^35 - 1820 * q^37 - 1188 * q^39 + 2888 * q^43 + 324 * q^45 + 744 * q^47 - 3784 * q^49 + 504 * q^51 + 4476 * q^53 - 5688 * q^57 - 4668 * q^59 + 17760 * q^61 + 1188 * q^63 + 8760 * q^65 + 1580 * q^67 + 48 * q^71 + 588 * q^73 - 17172 * q^75 - 17508 * q^77 - 3824 * q^79 - 5832 * q^81 + 11440 * q^85 + 7236 * q^87 - 360 * q^89 + 25860 * q^91 + 9648 * q^93 - 21792 * q^95 - 5832 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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