LMFDB - Embedded newform 168.5.z.b.73.3

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} + 130 x^{14} + 6137 x^{12} + 133906 x^{10} + 1360384 x^{8} + 5425142 x^{6} + 5784425 x^{4} + \cdots + 117649 $ x^16 + 130x^14 + 6137x^12 + 133906x^10 + 1360384x^8 + 5425142x^6 + 5784425x^4 + 1717862*x^2 + 117649
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{36}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.3
Root			$4.72217i$ of defining polynomial
Character	$\chi$	$=$	168.73
Dual form			168.5.z.b.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.50000 + 2.59808i) q^{3} +(-22.3786 + 12.9203i) q^{5} +(12.0282 - 47.5008i) q^{7} +(13.5000 + 23.3827i) q^{9} +O(q^{10})$	\(q+(4.50000 + 2.59808i) q^{3} +(-22.3786 + 12.9203i) q^{5} +(12.0282 - 47.5008i) q^{7} +(13.5000 + 23.3827i) q^{9} +(3.50686 - 6.07406i) q^{11} +295.531i q^{13} -134.272 q^{15} +(-314.915 - 181.816i) q^{17} +(-460.728 + 266.001i) q^{19} +(177.537 - 182.503i) q^{21} +(-336.172 - 582.267i) q^{23} +(21.3679 - 37.0103i) q^{25} +140.296i q^{27} -943.107 q^{29} +(-77.5072 - 44.7488i) q^{31} +(31.5617 - 18.2222i) q^{33} +(344.551 + 1218.41i) q^{35} +(-234.702 - 406.515i) q^{37} +(-767.812 + 1329.89i) q^{39} -1412.28i q^{41} +2101.95 q^{43} +(-604.222 - 348.848i) q^{45} +(-3319.41 + 1916.46i) q^{47} +(-2111.65 - 1142.69i) q^{49} +(-944.745 - 1636.35i) q^{51} +(-957.525 + 1658.48i) q^{53} +181.239i q^{55} -2764.37 q^{57} +(3312.16 + 1912.28i) q^{59} +(-4137.83 + 2388.98i) q^{61} +(1273.08 - 360.010i) q^{63} +(-3818.34 - 6613.57i) q^{65} +(1027.61 - 1779.88i) q^{67} -3493.60i q^{69} +1621.79 q^{71} +(7528.09 + 4346.35i) q^{73} +(192.311 - 111.031i) q^{75} +(-246.341 - 239.638i) q^{77} +(4999.74 + 8659.81i) q^{79} +(-364.500 + 631.333i) q^{81} +8983.86i q^{83} +9396.47 q^{85} +(-4243.98 - 2450.26i) q^{87} +(7081.96 - 4088.77i) q^{89} +(14037.9 + 3554.69i) q^{91} +(-232.521 - 402.739i) q^{93} +(6873.63 - 11905.5i) q^{95} -11417.5i q^{97} +189.370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 72 q^{3} - 12 q^{5} + 16 q^{7} + 216 q^{9}+O(q^{10}) $ 16 * q + 72 * q^3 - 12 * q^5 + 16 * q^7 + 216 * q^9	$ 16 q + 72 q^{3} - 12 q^{5} + 16 q^{7} + 216 q^{9} + 252 q^{11} - 72 q^{15} - 696 q^{17} + 156 q^{19} + 108 q^{21} - 672 q^{23} + 84 q^{25} + 1992 q^{29} + 2040 q^{31} + 2268 q^{33} + 2712 q^{35} + 2548 q^{37} - 396 q^{39} + 1304 q^{43} - 324 q^{45} - 744 q^{47} - 5608 q^{49} - 2088 q^{51} - 1164 q^{53} + 936 q^{57} + 8988 q^{59} + 816 q^{61} + 540 q^{63} + 8760 q^{65} + 3044 q^{67} - 4464 q^{71} - 15828 q^{73} + 756 q^{75} + 996 q^{77} - 11144 q^{79} - 5832 q^{81} - 15344 q^{85} + 8964 q^{87} + 22248 q^{89} + 1596 q^{91} + 6120 q^{93} + 3840 q^{95} + 13608 q^{99}+O(q^{100}) $ 16 * q + 72 * q^3 - 12 * q^5 + 16 * q^7 + 216 * q^9 + 252 * q^11 - 72 * q^15 - 696 * q^17 + 156 * q^19 + 108 * q^21 - 672 * q^23 + 84 * q^25 + 1992 * q^29 + 2040 * q^31 + 2268 * q^33 + 2712 * q^35 + 2548 * q^37 - 396 * q^39 + 1304 * q^43 - 324 * q^45 - 744 * q^47 - 5608 * q^49 - 2088 * q^51 - 1164 * q^53 + 936 * q^57 + 8988 * q^59 + 816 * q^61 + 540 * q^63 + 8760 * q^65 + 3044 * q^67 - 4464 * q^71 - 15828 * q^73 + 756 * q^75 + 996 * q^77 - 11144 * q^79 - 5832 * q^81 - 15344 * q^85 + 8964 * q^87 + 22248 * q^89 + 1596 * q^91 + 6120 * q^93 + 3840 * q^95 + 13608 * 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
$5$	−22.3786	+	12.9203i	−0.895144	+	0.516812i	−0.875622	−	0.482998i	$-0.839548\pi$
$5$	−22.3786	+	12.9203i	−0.895144	+	0.516812i	−0.0195225	+	0.999809i	$0.506215\pi$
$6$		0			0
$7$	12.0282	−	47.5008i	0.245472	−	0.969404i
$7$	12.0282	−	47.5008i	0.245472	−	0.969404i
$8$		0			0
$9$	13.5000	+	23.3827i	0.166667	+	0.288675i
$10$		0			0
$11$	3.50686	−	6.07406i	0.0289823	−	0.0501988i	−0.851170	−	0.524889i	$-0.824107\pi$
$11$	3.50686	−	6.07406i	0.0289823	−	0.0501988i	0.880153	+	0.474691i	$0.157440\pi$
$12$		0			0
$13$			295.531i			1.74870i	0.485293	+	0.874352i	$0.338713\pi$
$13$			295.531i			1.74870i	−0.485293	+	0.874352i	$0.661287\pi$
$14$		0			0
$15$	−134.272			−0.596763
$16$		0			0
$17$	−314.915	−	181.816i	−1.08967	−	0.629122i	−0.156182	−	0.987728i	$-0.549919\pi$
$17$	−314.915	−	181.816i	−1.08967	−	0.629122i	−0.933489	+	0.358606i	$0.883252\pi$
$18$		0			0
$19$	−460.728	+	266.001i	−1.27625	+	0.736845i	−0.976157	−	0.217064i	$-0.930352\pi$
$19$	−460.728	+	266.001i	−1.27625	+	0.736845i	−0.300096	+	0.953909i	$0.597019\pi$
$20$		0			0
$21$	177.537	−	182.503i	0.402579	−	0.413840i
$22$		0			0
$23$	−336.172	−	582.267i	−0.635485	−	1.10069i	−0.986412	−	0.164290i	$-0.947467\pi$
$23$	−336.172	−	582.267i	−0.635485	−	1.10069i	0.350927	−	0.936403i	$-0.385867\pi$
$24$		0			0
$25$	21.3679	−	37.0103i	0.0341886	−	0.0592164i
$26$		0			0
$27$			140.296i			0.192450i
$28$		0			0
$29$	−943.107			−1.12141			−0.560705	−	0.828015i	$-0.689470\pi$
$29$	−943.107			−1.12141			−0.560705	+	0.828015i	$0.689470\pi$
$30$		0			0
$31$	−77.5072	−	44.7488i	−0.0806526	−	0.0465648i	0.459131	−	0.888368i	$-0.348161\pi$
$31$	−77.5072	−	44.7488i	−0.0806526	−	0.0465648i	−0.539784	+	0.841804i	$0.681494\pi$
$32$		0			0
$33$	31.5617	−	18.2222i	0.0289823	−	0.0167329i
$34$		0			0
$35$	344.551	+	1218.41i	0.281266	+	0.994619i
$36$		0			0
$37$	−234.702	−	406.515i	−0.171440	−	0.296943i	0.767483	−	0.641069i	$-0.221509\pi$
$37$	−234.702	−	406.515i	−0.171440	−	0.296943i	−0.938924	+	0.344126i	$0.888175\pi$
$38$		0			0
$39$	−767.812	+	1329.89i	−0.504807	+	0.874352i
$40$		0			0
$41$		−	1412.28i		−	0.840140i	−0.907492	−	0.420070i	$-0.862005\pi$
$41$		−	1412.28i		−	0.840140i	0.907492	−	0.420070i	$-0.137995\pi$
$42$		0			0
$43$	2101.95			1.13681			0.568403	−	0.822750i	$-0.307562\pi$
$43$	2101.95			1.13681			0.568403	+	0.822750i	$0.307562\pi$
$44$		0			0
$45$	−604.222	−	348.848i	−0.298381	−	0.172271i
$46$		0			0
$47$	−3319.41	+	1916.46i	−1.50267	+	0.867569i	−0.502678	+	0.864473i	$0.667652\pi$
$47$	−3319.41	+	1916.46i	−1.50267	+	0.867569i	−0.999995	+	0.00309557i	$0.999015\pi$
$48$		0			0
$49$	−2111.65	−	1142.69i	−0.879487	−	0.475924i
$50$		0			0
$51$	−944.745	−	1636.35i	−0.363224	−	0.629122i
$52$		0			0
$53$	−957.525	+	1658.48i	−0.340877	+	0.590417i	−0.984596	−	0.174845i	$-0.944057\pi$
$53$	−957.525	+	1658.48i	−0.340877	+	0.590417i	0.643718	+	0.765262i	$0.277391\pi$
$54$		0			0
$55$			181.239i			0.0599136i
$56$		0			0
$57$	−2764.37			−0.850836
$58$		0			0
$59$	3312.16	+	1912.28i	0.951498	+	0.549347i	0.893546	−	0.448972i	$-0.148210\pi$
$59$	3312.16	+	1912.28i	0.951498	+	0.549347i	0.0579519	+	0.998319i	$0.481543\pi$
$60$		0			0
$61$	−4137.83	+	2388.98i	−1.11202	+	0.642025i	−0.939352	−	0.342955i	$-0.888572\pi$
$61$	−4137.83	+	2388.98i	−1.11202	+	0.642025i	−0.172669	+	0.984980i	$0.555239\pi$
$62$		0			0
$63$	1273.08	−	360.010i	0.320755	−	0.0907055i
$64$		0			0
$65$	−3818.34	−	6613.57i	−0.903750	−	1.56534i
$66$		0			0
$67$	1027.61	−	1779.88i	0.228918	−	0.396498i	−0.728570	−	0.684972i	$-0.759815\pi$
$67$	1027.61	−	1779.88i	0.228918	−	0.396498i	0.957488	+	0.288474i	$0.0931479\pi$
$68$		0			0
$69$		−	3493.60i		−	0.733795i
$70$		0			0
$71$	1621.79			0.321719			0.160860	−	0.986977i	$-0.448573\pi$
$71$	1621.79			0.321719			0.160860	+	0.986977i	$0.448573\pi$
$72$		0			0
$73$	7528.09	+	4346.35i	1.41266	+	0.815602i	0.995639	−	0.0932920i	$-0.0297390\pi$
$73$	7528.09	+	4346.35i	1.41266	+	0.815602i	0.417026	+	0.908894i	$0.363072\pi$
$74$		0			0
$75$	192.311	−	111.031i	0.0341886	−	0.0197388i
$76$		0			0
$77$	−246.341	−	239.638i	−0.0415486	−	0.0404180i
$78$		0			0
$79$	4999.74	+	8659.81i	0.801113	+	1.38757i	0.918884	+	0.394527i	$0.129092\pi$
$79$	4999.74	+	8659.81i	0.801113	+	1.38757i	−0.117771	+	0.993041i	$0.537575\pi$
$80$		0			0
$81$	−364.500	+	631.333i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			8983.86i			1.30409i	0.758181	+	0.652044i	$0.226088\pi$
$83$			8983.86i			1.30409i	−0.758181	+	0.652044i	$0.773912\pi$
$84$		0			0
$85$	9396.47			1.30055
$86$		0			0
$87$	−4243.98	−	2450.26i	−0.560705	−	0.323723i
$88$		0			0
$89$	7081.96	−	4088.77i	0.894073	−	0.516194i	0.0188007	−	0.999823i	$-0.494015\pi$
$89$	7081.96	−	4088.77i	0.894073	−	0.516194i	0.875273	+	0.483630i	$0.160682\pi$
$90$		0			0
$91$	14037.9	+	3554.69i	1.69520	+	0.429259i
$92$		0			0
$93$	−232.521	−	402.739i	−0.0268842	−	0.0465648i
$94$		0			0
$95$	6873.63	−	11905.5i	0.761621	−	1.31917i
$96$		0			0
$97$		−	11417.5i		−	1.21347i	−0.794904	−	0.606735i	$-0.792479\pi$
$97$		−	11417.5i		−	1.21347i	0.794904	−	0.606735i	$-0.207521\pi$
$98$		0			0
$99$	189.370			0.0193215
$100$		0			0
$101$	−13813.4	−	7975.16i	−1.35412	−	0.781802i	−0.365297	−	0.930891i	$-0.619032\pi$
$101$	−13813.4	−	7975.16i	−1.35412	−	0.781802i	−0.988824	+	0.149089i	$0.952366\pi$
$102$		0			0
$103$	4372.58	−	2524.51i	0.412158	−	0.237959i	−0.279559	−	0.960129i	$-0.590188\pi$
$103$	4372.58	−	2524.51i	0.412158	−	0.237959i	0.691716	+	0.722169i	$0.256855\pi$
$104$		0			0
$105$	−1615.04	+	6378.01i	−0.146489	+	0.578504i
$106$		0			0
$107$	−1218.08	−	2109.78i	−0.106392	−	0.184276i	0.807914	−	0.589300i	$-0.200596\pi$
$107$	−1218.08	−	2109.78i	−0.106392	−	0.184276i	−0.914306	+	0.405024i	$0.867263\pi$
$108$		0			0
$109$	4991.52	−	8645.57i	0.420126	−	0.727680i	−0.575825	−	0.817573i	$-0.695319\pi$
$109$	4991.52	−	8645.57i	0.420126	−	0.727680i	0.995951	+	0.0898929i	$0.0286525\pi$
$110$		0			0
$111$		−	2439.09i		−	0.197962i
$112$		0			0
$113$	6609.99			0.517659			0.258830	−	0.965923i	$-0.416663\pi$
$113$	6609.99			0.517659			0.258830	+	0.965923i	$0.416663\pi$
$114$		0			0
$115$	15046.1	+	8686.88i	1.13770	+	0.656853i
$116$		0			0
$117$	−6910.31	+	3989.67i	−0.504807	+	0.291451i
$118$		0			0
$119$	−12424.3	+	12771.8i	−0.877357	+	0.901899i
$120$		0			0
$121$	7295.90	+	12636.9i	0.498320	+	0.863116i
$122$		0			0
$123$	3669.20	−	6355.24i	0.242528	−	0.420070i
$124$		0			0
$125$		−	15046.0i		−	0.962947i
$126$		0			0
$127$	−7392.92			−0.458362			−0.229181	−	0.973384i	$-0.573605\pi$
$127$	−7392.92			−0.458362			−0.229181	+	0.973384i	$0.573605\pi$
$128$		0			0
$129$	9458.79	+	5461.04i	0.568403	+	0.328167i
$130$		0			0
$131$	−8430.81	+	4867.53i	−0.491277	+	0.283639i	−0.725104	−	0.688639i	$-0.758208\pi$
$131$	−8430.81	+	4867.53i	−0.491277	+	0.283639i	0.233827	+	0.972278i	$0.424875\pi$
$132$		0			0
$133$	7093.56	+	25084.4i	0.401015	+	1.41808i
$134$		0			0
$135$	−1812.67	−	3139.63i	−0.0994605	−	0.172271i
$136$		0			0
$137$	−936.031	+	1621.25i	−0.0498711	+	0.0863793i	−0.889883	−	0.456188i	$-0.849214\pi$
$137$	−936.031	+	1621.25i	−0.0498711	+	0.0863793i	0.840012	+	0.542567i	$0.182548\pi$
$138$		0			0
$139$		−	2263.62i		−	0.117159i	−0.998283	−	0.0585794i	$-0.981343\pi$
$139$		−	2263.62i		−	0.117159i	0.998283	−	0.0585794i	$-0.0186571\pi$
$140$		0			0
$141$	−19916.4			−1.00178
$142$		0			0
$143$	1795.07	+	1036.38i	0.0877828	+	0.0506814i
$144$		0			0
$145$	21105.4	−	12185.2i	1.00382	−	0.579558i
$146$		0			0
$147$	−6533.61	−	10628.3i	−0.302356	−	0.491848i
$148$		0			0
$149$	−769.753	−	1333.25i	−0.0346720	−	0.0600537i	0.848169	−	0.529726i	$-0.177705\pi$
$149$	−769.753	−	1333.25i	−0.0346720	−	0.0600537i	−0.882841	+	0.469673i	$0.844372\pi$
$150$		0			0
$151$	−5181.11	+	8973.94i	−0.227232	+	0.393577i	−0.956987	−	0.290132i	$-0.906301\pi$
$151$	−5181.11	+	8973.94i	−0.227232	+	0.393577i	0.729755	+	0.683709i	$0.239634\pi$
$152$		0			0
$153$		−	9818.08i		−	0.419415i
$154$		0			0
$155$	2312.67			0.0962609
$156$		0			0
$157$	27114.2	+	15654.4i	1.10001	+	0.635092i	0.936224	−	0.351404i	$-0.114295\pi$
$157$	27114.2	+	15654.4i	1.10001	+	0.635092i	0.163788	+	0.986496i	$0.447629\pi$
$158$		0			0
$159$	−8617.72	+	4975.44i	−0.340877	+	0.196806i
$160$		0			0
$161$	−31701.6	+	8964.83i	−1.22301	+	0.345852i
$162$		0			0
$163$	−25209.7	−	43664.5i	−0.948839	−	1.64344i	−0.747877	−	0.663837i	$-0.768927\pi$
$163$	−25209.7	−	43664.5i	−0.948839	−	1.64344i	−0.200962	−	0.979599i	$-0.564407\pi$
$164$		0			0
$165$	−470.872	+	815.573i	−0.0172956	+	0.0299568i
$166$		0			0
$167$			19986.4i			0.716642i	0.933599	+	0.358321i	$0.116651\pi$
$167$			19986.4i			0.716642i	−0.933599	+	0.358321i	$0.883349\pi$
$168$		0			0
$169$	−58777.5			−2.05796
$170$		0			0
$171$	−12439.6	−	7182.03i	−0.425418	−	0.245615i
$172$		0			0
$173$	373.887	−	215.864i	0.0124925	−	0.00721253i	−0.493741	−	0.869609i	$-0.664371\pi$
$173$	373.887	−	215.864i	0.0124925	−	0.00721253i	0.506233	+	0.862397i	$0.331037\pi$
$174$		0			0
$175$	−1501.00	−	1460.16i	−0.0490123	−	0.0476786i
$176$		0			0
$177$	9936.49	+	17210.5i	0.317166	+	0.549347i
$178$		0			0
$179$	11963.4	−	20721.3i	0.373379	−	0.646711i	−0.616704	−	0.787195i	$-0.711533\pi$
$179$	11963.4	−	20721.3i	0.373379	−	0.646711i	0.990083	+	0.140484i	$0.0448659\pi$
$180$		0			0
$181$			22678.6i			0.692244i	0.938189	+	0.346122i	$0.112502\pi$
$181$			22678.6i			0.692244i	−0.938189	+	0.346122i	$0.887498\pi$
$182$		0			0
$183$	−24827.0			−0.741347
$184$		0			0
$185$	10504.6	+	6064.83i	0.306927	+	0.177205i
$186$		0			0
$187$	−2208.72	+	1275.21i	−0.0631624	+	0.0364668i
$188$		0			0
$189$	6664.17	+	1687.50i	0.186562	+	0.0472412i
$190$		0			0
$191$	−13074.0	−	22644.9i	−0.358379	−	0.620731i	0.629311	−	0.777153i	$-0.283337\pi$
$191$	−13074.0	−	22644.9i	−0.358379	−	0.620731i	−0.987690	+	0.156423i	$0.950004\pi$
$192$		0			0
$193$	−558.744	+	967.773i	−0.0150002	+	0.0259812i	−0.873428	−	0.486953i	$-0.838108\pi$
$193$	−558.744	+	967.773i	−0.0150002	+	0.0259812i	0.858428	+	0.512934i	$0.171442\pi$
$194$		0			0
$195$		−	39681.4i		−	1.04356i
$196$		0			0
$197$	−39481.6			−1.01733			−0.508665	−	0.860964i	$-0.669861\pi$
$197$	−39481.6			−1.01733			−0.508665	+	0.860964i	$0.669861\pi$
$198$		0			0
$199$	−23232.4	−	13413.2i	−0.586662	−	0.338709i	0.177115	−	0.984190i	$-0.443324\pi$
$199$	−23232.4	−	13413.2i	−0.586662	−	0.338709i	−0.763776	+	0.645481i	$0.776657\pi$
$200$		0			0
$201$	9248.52	−	5339.63i	0.228918	−	0.132166i
$202$		0			0
$203$	−11343.8	+	44798.3i	−0.275276	+	1.08710i
$204$		0			0
$205$	18247.0	+	31604.8i	0.434194	+	0.752047i
$206$		0			0
$207$	9076.64	−	15721.2i	0.211828	−	0.366898i
$208$		0			0
$209$			3731.31i			0.0854219i
$210$		0			0
$211$	−919.581			−0.0206550			−0.0103275	−	0.999947i	$-0.503287\pi$
$211$	−919.581			−0.0206550			−0.0103275	+	0.999947i	$0.503287\pi$
$212$		0			0
$213$	7298.04	+	4213.52i	0.160860	+	0.0928723i
$214$		0			0
$215$	−47038.8	+	27157.9i	−1.01760	+	0.587514i
$216$		0			0
$217$	−3057.87	+	3143.40i	−0.0649381	+	0.0667545i
$218$		0			0
$219$	22584.3	+	39117.1i	0.470888	+	0.815602i
$220$		0			0
$221$	53732.3	−	93067.1i	1.10015	−	1.90551i
$222$		0			0
$223$			15572.1i			0.313139i	0.987667	+	0.156569i	$0.0500435\pi$
$223$			15572.1i			0.313139i	−0.987667	+	0.156569i	$0.949957\pi$
$224$		0			0
$225$	1153.87			0.0227924
$226$		0			0
$227$	63425.9	+	36619.0i	1.23088	+	0.710648i	0.967213	−	0.253967i	$-0.0817353\pi$
$227$	63425.9	+	36619.0i	1.23088	+	0.710648i	0.263665	+	0.964614i	$0.415069\pi$
$228$		0			0
$229$	−83530.5	+	48226.4i	−1.59285	+	0.919631i	−0.600032	+	0.799976i	$0.704845\pi$
$229$	−83530.5	+	48226.4i	−1.59285	+	0.919631i	−0.992816	+	0.119655i	$0.961821\pi$
$230$		0			0
$231$	−485.938	−	1718.39i	−0.00910661	−	0.0322030i
$232$		0			0
$233$	−16841.9	−	29171.1i	−0.310228	−	0.537330i	0.668184	−	0.743996i	$-0.267072\pi$
$233$	−16841.9	−	29171.1i	−0.310228	−	0.537330i	−0.978411	+	0.206666i	$0.933739\pi$
$234$		0			0
$235$	49522.4	−	85775.4i	0.896740	−	1.55320i
$236$		0			0
$237$			51958.9i			0.925045i
$238$		0			0
$239$	−51938.2			−0.909266			−0.454633	−	0.890679i	$-0.650230\pi$
$239$	−51938.2			−0.909266			−0.454633	+	0.890679i	$0.650230\pi$
$240$		0			0
$241$	49303.6	+	28465.4i	0.848876	+	0.490099i	0.860272	−	0.509836i	$-0.170294\pi$
$241$	49303.6	+	28465.4i	0.848876	+	0.490099i	−0.0113952	+	0.999935i	$0.503627\pi$
$242$		0			0
$243$	−3280.50	+	1894.00i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	62019.6	−	1711.23i	1.03323	−	0.0285085i
$246$		0			0
$247$	−78611.6	−	136159.i	−1.28852	−	2.23179i
$248$		0			0
$249$	−23340.8	+	40427.4i	−0.376458	+	0.652044i
$250$		0			0
$251$			43832.4i			0.695742i	0.937542	+	0.347871i	$0.113095\pi$
$251$			43832.4i			0.695742i	−0.937542	+	0.347871i	$0.886905\pi$
$252$		0			0
$253$	−4715.63			−0.0736713
$254$		0			0
$255$	42284.1	+	24412.8i	0.650275	+	0.375436i
$256$		0			0
$257$	31555.2	−	18218.4i	0.477754	−	0.275831i	−0.241726	−	0.970345i	$-0.577714\pi$
$257$	31555.2	−	18218.4i	0.477754	−	0.275831i	0.719480	+	0.694513i	$0.244380\pi$
$258$		0			0
$259$	−22132.8	+	6258.88i	−0.329942	+	0.0933034i
$260$		0			0
$261$	−12731.9	−	22052.4i	−0.186902	−	0.323723i
$262$		0			0
$263$	−15838.1	+	27432.5i	−0.228977	+	0.396600i	−0.957505	−	0.288416i	$-0.906872\pi$
$263$	−15838.1	+	27432.5i	−0.228977	+	0.396600i	0.728528	+	0.685016i	$0.240205\pi$
$264$		0			0
$265$		−	49486.0i		−	0.704678i
$266$		0			0
$267$	42491.7			0.596049
$268$		0			0
$269$	88887.5	+	51319.2i	1.22839	+	0.709211i	0.966693	−	0.255939i	$-0.0823847\pi$
$269$	88887.5	+	51319.2i	1.22839	+	0.709211i	0.261697	+	0.965150i	$0.415718\pi$
$270$		0			0
$271$	−24724.3	+	14274.6i	−0.336655	+	0.194368i	−0.658792	−	0.752325i	$-0.728932\pi$
$271$	−24724.3	+	14274.6i	−0.336655	+	0.194368i	0.322137	+	0.946693i	$0.395599\pi$
$272$		0			0
$273$	53935.4	+	52467.8i	0.723683	+	0.703991i
$274$		0			0
$275$	−149.868	−	259.580i	−0.00198173	−	0.00343246i
$276$		0			0
$277$	13466.3	−	23324.4i	0.175505	−	0.303984i	−0.764831	−	0.644231i	$-0.777177\pi$
$277$	13466.3	−	23324.4i	0.175505	−	0.303984i	0.940336	+	0.340247i	$0.110511\pi$
$278$		0			0
$279$		−	2416.43i		−	0.0310432i
$280$		0			0
$281$	−52722.9			−0.667708			−0.333854	−	0.942625i	$-0.608349\pi$
$281$	−52722.9			−0.667708			−0.333854	+	0.942625i	$0.608349\pi$
$282$		0			0
$283$	134279.	+	77526.0i	1.67662	+	0.967998i	0.963790	+	0.266664i	$0.0859213\pi$
$283$	134279.	+	77526.0i	1.67662	+	0.967998i	0.712832	+	0.701334i	$0.247412\pi$
$284$		0			0
$285$	61862.6	−	35716.4i	0.761621	−	0.439722i
$286$		0			0
$287$	−67084.2	−	16987.1i	−0.814435	−	0.206231i
$288$		0			0
$289$	24353.8	+	42182.0i	0.291589	+	0.505046i
$290$		0			0
$291$	29663.6	−	51378.9i	0.350299	−	0.606735i
$292$		0			0
$293$		−	29594.5i		−	0.344728i	−0.985033	−	0.172364i	$-0.944859\pi$
$293$		−	29594.5i		−	0.344728i	0.985033	−	0.172364i	$-0.0551405\pi$
$294$		0			0
$295$	−98828.8			−1.13564
$296$		0			0
$297$	852.167	+	491.999i	0.00966077	+	0.00557765i
$298$		0			0
$299$	172078.	−	99349.1i	1.92479	−	1.11128i
$300$		0			0
$301$	25282.6	−	99844.4i	0.279054	−	1.10202i
$302$		0			0
$303$	−41440.1	−	71776.4i	−0.451373	−	0.781802i
$304$		0			0
$305$	61732.5	−	106924.i	0.663612	−	1.14941i
$306$		0			0
$307$		−	11214.0i		−	0.118983i	−0.998229	−	0.0594913i	$-0.981052\pi$
$307$		−	11214.0i		−	0.118983i	0.998229	−	0.0594913i	$-0.0189479\pi$
$308$		0			0
$309$	26235.5			0.274772
$310$		0			0
$311$	129041.	+	74502.1i	1.33416	+	0.770279i	0.985935	−	0.167131i	$-0.0534504\pi$
$311$	129041.	+	74502.1i	1.33416	+	0.770279i	0.348227	+	0.937410i	$0.386784\pi$
$312$		0			0
$313$	−124687.	+	71988.0i	−1.27272	+	0.734803i	−0.975498	−	0.220006i	$-0.929392\pi$
$313$	−124687.	+	71988.0i	−1.27272	+	0.734803i	−0.297218	+	0.954810i	$0.596059\pi$
$314$		0			0
$315$	−23838.2	+	24505.0i	−0.240244	+	0.246964i
$316$		0			0
$317$	−205.064	−	355.181i	−0.00204066	−	0.00353453i	0.865003	−	0.501766i	$-0.167316\pi$
$317$	−205.064	−	355.181i	−0.00204066	−	0.00353453i	−0.867044	+	0.498232i	$0.833983\pi$
$318$		0			0
$319$	−3307.34	+	5728.48i	−0.0325011	+	0.0562935i
$320$		0			0
$321$		−	12658.7i		−	0.122851i
$322$		0			0
$323$	193453.			1.85426
$324$		0			0
$325$	10937.7	+	6314.87i	0.103552	+	0.0597858i
$326$		0			0
$327$	44923.7	−	25936.7i	0.420126	−	0.242560i
$328$		0			0
$329$	51107.0	+	180726.i	0.472159	+	1.66966i
$330$		0			0
$331$	−11181.1	−	19366.2i	−0.102053	−	0.176762i	0.810477	−	0.585770i	$-0.199208\pi$
$331$	−11181.1	−	19366.2i	−0.102053	−	0.176762i	−0.912530	+	0.409009i	$0.865875\pi$
$332$		0			0
$333$	6336.95	−	10975.9i	0.0571467	−	0.0989811i
$334$		0			0
$335$			53108.2i			0.473230i
$336$		0			0
$337$	−110380.			−0.971916			−0.485958	−	0.873982i	$-0.661529\pi$
$337$	−110380.			−0.971916			−0.485958	+	0.873982i	$0.661529\pi$
$338$		0			0
$339$	29745.0	+	17173.3i	0.258830	+	0.149435i
$340$		0			0
$341$	−543.613	+	313.855i	−0.00467500	+	0.00269911i
$342$		0			0
$343$	−79678.0	+	86560.4i	−0.677252	+	0.735751i
$344$		0			0
$345$	45138.3	+	78181.9i	0.379234	+	0.656853i
$346$		0			0
$347$	−29185.4	+	50550.5i	−0.242385	+	0.419824i	−0.961393	−	0.275178i	$-0.911263\pi$
$347$	−29185.4	+	50550.5i	−0.242385	+	0.419824i	0.719008	+	0.695002i	$0.244596\pi$
$348$		0			0
$349$		−	161224.i		−	1.32367i	−0.749651	−	0.661833i	$-0.769779\pi$
$349$		−	161224.i		−	1.32367i	0.749651	−	0.661833i	$-0.230221\pi$
$350$		0			0
$351$	−41461.8			−0.336538
$352$		0			0
$353$	−171930.	−	99263.8i	−1.37975	−	0.796602i	−0.387625	−	0.921817i	$-0.626705\pi$
$353$	−171930.	−	99263.8i	−1.37975	−	0.796602i	−0.992130	+	0.125215i	$0.960038\pi$
$354$		0			0
$355$	−36293.3	+	20954.0i	−0.287985	+	0.166268i
$356$		0			0
$357$	−89091.2	+	25193.9i	−0.699034	+	0.197678i
$358$		0			0
$359$	105345.	+	182464.i	0.817386	+	1.41575i	0.907602	+	0.419831i	$0.137911\pi$
$359$	105345.	+	182464.i	0.817386	+	1.41575i	−0.0902165	+	0.995922i	$0.528756\pi$
$360$		0			0
$361$	76352.7	−	132247.i	0.585882	−	1.01478i
$362$		0			0
$363$			75821.3i			0.575410i
$364$		0			0
$365$	−224624.			−1.68605
$366$		0			0
$367$	−86365.6	−	49863.2i	−0.641222	−	0.370210i	0.143863	−	0.989598i	$-0.454048\pi$
$367$	−86365.6	−	49863.2i	−0.641222	−	0.370210i	−0.785085	+	0.619388i	$0.787381\pi$
$368$		0			0
$369$	33022.8	−	19065.7i	0.242528	−	0.140023i
$370$		0			0
$371$	67261.9	+	65431.6i	0.488676	+	0.475379i
$372$		0			0
$373$	−113226.	−	196113.i	−0.813821	−	1.40958i	−0.910172	−	0.414231i	$-0.864050\pi$
$373$	−113226.	−	196113.i	−0.813821	−	1.40958i	0.0963509	−	0.995347i	$-0.469283\pi$
$374$		0			0
$375$	39090.8	−	67707.2i	0.277979	−	0.481474i
$376$		0			0
$377$		−	278717.i		−	1.96102i
$378$		0			0
$379$	54122.6			0.376791			0.188395	−	0.982093i	$-0.439671\pi$
$379$	54122.6			0.376791			0.188395	+	0.982093i	$0.439671\pi$
$380$		0			0
$381$	−33268.2	−	19207.4i	−0.229181	−	0.132318i
$382$		0			0
$383$	−228069.	+	131675.i	−1.55478	+	0.897650i	−0.557034	+	0.830490i	$0.688061\pi$
$383$	−228069.	+	131675.i	−1.55478	+	0.897650i	−0.997742	+	0.0671609i	$0.978606\pi$
$384$		0			0
$385$	8608.97	+	2179.96i	0.0580804	+	0.0147071i
$386$		0			0
$387$	28376.4	+	49149.3i	0.189468	+	0.328167i
$388$		0			0
$389$	−124565.	+	215752.i	−0.823181	+	1.42579i	0.0801209	+	0.996785i	$0.474469\pi$
$389$	−124565.	+	215752.i	−0.823181	+	1.42579i	−0.903302	+	0.429006i	$0.858864\pi$
$390$		0			0
$391$			244486.i			1.59919i
$392$		0			0
$393$	−50584.8			−0.327518
$394$		0			0
$395$	−223775.	−	129196.i	−1.43422	−	0.828049i
$396$		0			0
$397$	−168298.	+	97166.9i	−1.06782	+	0.616506i	−0.927585	−	0.373612i	$-0.878119\pi$
$397$	−168298.	+	97166.9i	−1.06782	+	0.616506i	−0.140235	+	0.990118i	$0.544786\pi$
$398$		0			0
$399$	−33250.2	+	131309.i	−0.208857	+	0.824803i
$400$		0			0
$401$	23380.2	+	40495.8i	0.145399	+	0.251838i	0.929522	−	0.368768i	$-0.120220\pi$
$401$	23380.2	+	40495.8i	0.145399	+	0.251838i	−0.784123	+	0.620605i	$0.786887\pi$
$402$		0			0
$403$	13224.6	−	22905.8i	0.0814280	−	0.141037i
$404$		0			0
$405$		−	18837.8i		−	0.114847i
$406$		0			0
$407$	−3292.26			−0.0198749
$408$		0			0
$409$	6436.92	+	3716.36i	0.0384797	+	0.0222163i	0.519116	−	0.854704i	$-0.326261\pi$
$409$	6436.92	+	3716.36i	0.0384797	+	0.0222163i	−0.480637	+	0.876920i	$0.659594\pi$
$410$		0			0
$411$	−8424.28	+	4863.76i	−0.0498711	+	0.0287931i
$412$		0			0
$413$	130674.	−	134329.i	0.766106	−	0.787536i
$414$		0			0
$415$	−116074.	−	201046.i	−0.673968	−	1.16735i
$416$		0			0
$417$	5881.07	−	10186.3i	0.0338208	−	0.0585794i
$418$		0			0
$419$		−	126721.i		−	0.721808i	−0.932603	−	0.360904i	$-0.882468\pi$
$419$		−	126721.i		−	0.721808i	0.932603	−	0.360904i	$-0.117532\pi$
$420$		0			0
$421$	−8407.28			−0.0474342			−0.0237171	−	0.999719i	$-0.507550\pi$
$421$	−8407.28			−0.0474342			−0.0237171	+	0.999719i	$0.507550\pi$
$422$		0			0
$423$	−89624.0	−	51744.4i	−0.500891	−	0.289190i
$424$		0			0
$425$	−13458.1	+	7770.06i	−0.0745087	+	0.0430176i
$426$		0			0
$427$	63707.8	+	225285.i	0.349411	+	1.23560i
$428$		0			0
$429$	5385.21	+	9327.46i	0.0292609	+	0.0506814i
$430$		0			0
$431$	165415.	−	286508.i	0.890474	−	1.54235i	0.0511651	−	0.998690i	$-0.483707\pi$
$431$	165415.	−	286508.i	0.890474	−	1.54235i	0.839309	−	0.543655i	$-0.182960\pi$
$432$		0			0
$433$			162937.i			0.869051i	0.900660	+	0.434525i	$0.143084\pi$
$433$			162937.i			0.869051i	−0.900660	+	0.434525i	$0.856916\pi$
$434$		0			0
$435$	126632.			0.669216
$436$		0			0
$437$	309767.	+	178844.i	1.62208	+	0.936509i
$438$		0			0
$439$	182437.	−	105330.i	0.946640	−	0.546543i	0.0546042	−	0.998508i	$-0.482610\pi$
$439$	182437.	−	105330.i	0.946640	−	0.546543i	0.892035	+	0.451965i	$0.149277\pi$
$440$		0			0
$441$	−1788.00	−	64802.3i	−0.00919372	−	0.333207i
$442$		0			0
$443$	−12025.0	−	20828.0i	−0.0612744	−	0.106130i	0.833761	−	0.552126i	$-0.186183\pi$
$443$	−12025.0	−	20828.0i	−0.0612744	−	0.106130i	−0.895035	+	0.445995i	$0.852850\pi$
$444$		0			0
$445$	−105656.	+	183002.i	−0.533550	+	0.924135i
$446$		0			0
$447$		−	7999.51i		−	0.0400358i
$448$		0			0
$449$	−358819.			−1.77985			−0.889923	−	0.456110i	$-0.849242\pi$
$449$	−358819.			−1.77985			−0.889923	+	0.456110i	$0.849242\pi$
$450$		0			0
$451$	−8578.24	−	4952.65i	−0.0421741	−	0.0243492i
$452$		0			0
$453$	−46629.9	+	26921.8i	−0.227232	+	0.131192i
$454$		0			0
$455$	−360077.	+	101825.i	−1.73929	+	0.491851i
$456$		0			0
$457$	51847.6	+	89802.7i	0.248254	+	0.429988i	0.963041	−	0.269353i	$-0.0868099\pi$
$457$	51847.6	+	89802.7i	0.248254	+	0.429988i	−0.714788	+	0.699342i	$0.753477\pi$
$458$		0			0
$459$	25508.1	−	44181.3i	0.121075	−	0.209707i
$460$		0			0
$461$		−	138269.i		−	0.650616i	−0.945608	−	0.325308i	$-0.894532\pi$
$461$		−	138269.i		−	0.650616i	0.945608	−	0.325308i	$-0.105468\pi$
$462$		0			0
$463$	267212.			1.24650			0.623252	−	0.782021i	$-0.285811\pi$
$463$	267212.			1.24650			0.623252	+	0.782021i	$0.285811\pi$
$464$		0			0
$465$	10407.0	+	6008.49i	0.0481305	+	0.0277881i
$466$		0			0
$467$	62770.8	−	36240.7i	0.287822	−	0.166174i	−0.349137	−	0.937072i	$-0.613525\pi$
$467$	62770.8	−	36240.7i	0.287822	−	0.166174i	0.636959	+	0.770898i	$0.280192\pi$
$468$		0			0
$469$	−72185.3	−	70221.0i	−0.328173	−	0.319243i
$470$		0			0
$471$	81342.6	+	140889.i	0.366671	+	0.635092i
$472$		0			0
$473$	7371.25	−	12767.4i	0.0329472	−	0.0570663i
$474$		0			0
$475$			22735.5i			0.100767i
$476$		0			0
$477$	−51706.3			−0.227252
$478$		0			0
$479$	−160043.	−	92401.0i	−0.697535	−	0.402722i	0.108893	−	0.994053i	$-0.465269\pi$
$479$	−160043.	−	92401.0i	−0.697535	−	0.402722i	−0.806429	+	0.591331i	$0.798603\pi$
$480$		0			0
$481$	120138.	−	69361.6i	0.519266	−	0.299798i
$482$		0			0
$483$	−165949.	−	42021.6i	−0.711344	−	0.180127i
$484$		0			0
$485$	147518.	+	255509.i	0.627136	+	1.08623i
$486$		0			0
$487$	−127403.	+	220669.i	−0.537184	+	0.930431i	0.461870	+	0.886948i	$0.347179\pi$
$487$	−127403.	+	220669.i	−0.537184	+	0.930431i	−0.999054	+	0.0434829i	$0.986155\pi$
$488$		0			0
$489$		−	261987.i		−	1.09562i
$490$		0			0
$491$	−99646.2			−0.413331			−0.206665	−	0.978412i	$-0.566261\pi$
$491$	−99646.2			−0.413331			−0.206665	+	0.978412i	$0.566261\pi$
$492$		0			0
$493$	296998.	+	171472.i	1.22197	+	0.705504i
$494$		0			0
$495$	−4237.84	+	2446.72i	−0.0172956	+	0.00998559i
$496$		0			0
$497$	19507.1	−	77036.1i	0.0789732	−	0.311876i
$498$		0			0
$499$	−116379.	−	201574.i	−0.467382	−	0.809530i	0.531923	−	0.846793i	$-0.321469\pi$
$499$	−116379.	−	201574.i	−0.467382	−	0.809530i	−0.999306	+	0.0372628i	$0.988136\pi$
$500$		0			0
$501$	−51926.2	+	89938.9i	−0.206877	+	0.358321i
$502$		0			0
$503$		−	256189.i		−	1.01257i	−0.862366	−	0.506285i	$-0.831019\pi$
$503$		−	256189.i		−	1.01257i	0.862366	−	0.506285i	$-0.168981\pi$
$504$		0			0
$505$	412166.			1.61618
$506$		0			0
$507$	−264499.	−	152708.i	−1.02898	−	0.594083i
$508$		0			0
$509$	−19963.7	+	11526.1i	−0.0770560	+	0.0444883i	−0.538033	−	0.842924i	$-0.680832\pi$
$509$	−19963.7	+	11526.1i	−0.0770560	+	0.0444883i	0.460977	+	0.887412i	$0.347499\pi$
$510$		0			0
$511$	297004.	−	305312.i	1.13742	−	1.16923i
$512$		0			0
$513$	−37318.9	−	64638.3i	−0.141806	−	0.245615i
$514$		0			0
$515$	−65234.8	+	112990.i	−0.245960	+	0.426016i
$516$		0			0
$517$			26883.0i			0.100577i
$518$		0			0
$519$	2243.32			0.00832831
$520$		0			0
$521$	−136041.	−	78543.1i	−0.501180	−	0.289356i	0.228021	−	0.973656i	$-0.426775\pi$
$521$	−136041.	−	78543.1i	−0.501180	−	0.289356i	−0.729201	+	0.684300i	$0.760108\pi$
$522$		0			0
$523$	−191415.	+	110514.i	−0.699798	+	0.404029i	−0.807272	−	0.590179i	$-0.799057\pi$
$523$	−191415.	+	110514.i	−0.699798	+	0.404029i	0.107474	+	0.994208i	$0.465724\pi$
$524$		0			0
$525$	−2960.90	−	10470.4i	−0.0107425	−	0.0379879i
$526$		0			0
$527$	16272.1	+	28184.1i	0.0585899	+	0.101481i
$528$		0			0
$529$	−86102.5	+	149134.i	−0.307684	+	0.532924i
$530$		0			0
$531$			103263.i			0.366232i
$532$		0			0
$533$	417371.			1.46916
$534$		0			0
$535$	54517.9	+	31475.9i	0.190472	+	0.109969i
$536$		0			0
$537$	107671.	−	62163.8i	0.373379	−	0.215570i
$538$		0			0
$539$	−14346.0	+	8819.00i	−0.0493804	+	0.0303558i
$540$		0			0
$541$	−148022.	−	256382.i	−0.505746	−	0.875977i	−0.999978	−	0.00664746i	$-0.997884\pi$
$541$	−148022.	−	256382.i	−0.505746	−	0.875977i	0.494232	−	0.869330i	$-0.335449\pi$
$542$		0			0
$543$	−58920.8	+	102054.i	−0.199834	+	0.346122i
$544$		0			0
$545$			257968.i			0.868505i
$546$		0			0
$547$	438682.			1.46614			0.733069	−	0.680154i	$-0.238087\pi$
$547$	438682.			1.46614			0.733069	+	0.680154i	$0.238087\pi$
$548$		0			0
$549$	−111721.	−	64502.4i	−0.370674	−	0.214008i
$550$		0			0
$551$	434515.	−	250867.i	1.43120	−	0.826306i
$552$		0			0
$553$	471485.	−	133330.i	1.54176	−	0.435992i
$554$		0			0
$555$	31513.8	+	54583.5i	0.102309	+	0.177205i
$556$		0			0
$557$	−141893.	+	245766.i	−0.457353	+	0.792158i	−0.998820	−	0.0485638i	$-0.984536\pi$
$557$	−141893.	+	245766.i	−0.457353	+	0.792158i	0.541468	+	0.840722i	$0.317869\pi$
$558$		0			0
$559$			621192.i			1.98794i
$560$		0			0
$561$	−13252.3			−0.0421082
$562$		0			0
$563$	103045.	+	59493.2i	0.325096	+	0.187694i	0.653662	−	0.756787i	$-0.273232\pi$
$563$	103045.	+	59493.2i	0.325096	+	0.187694i	−0.328566	+	0.944481i	$0.606565\pi$
$564$		0			0
$565$	−147922.	+	85403.0i	−0.463380	+	0.267532i
$566$		0			0
$567$	25604.5	+	24907.8i	0.0796435	+	0.0774764i
$568$		0			0
$569$	219280.	+	379805.i	0.677291	+	1.17310i	0.975794	+	0.218694i	$0.0701795\pi$
$569$	219280.	+	379805.i	0.677291	+	1.17310i	−0.298503	+	0.954409i	$0.596487\pi$
$570$		0			0
$571$	149205.	−	258431.i	0.457627	−	0.792633i	−0.541208	−	0.840889i	$-0.682033\pi$
$571$	149205.	−	258431.i	0.457627	−	0.792633i	0.998835	+	0.0482558i	$0.0153663\pi$
$572$		0			0
$573$		−	135869.i		−	0.413820i
$574$		0			0
$575$	−28733.1			−0.0869055
$576$		0			0
$577$	544380.	+	314298.i	1.63512	+	0.944039i	0.982479	+	0.186374i	$0.0596735\pi$
$577$	544380.	+	314298.i	1.63512	+	0.944039i	0.652644	+	0.757665i	$0.273660\pi$
$578$		0			0
$579$	−5028.70	+	2903.32i	−0.0150002	+	0.00866039i
$580$		0			0
$581$	426740.	+	108059.i	1.26419	+	0.320118i
$582$		0			0
$583$	6715.81	+	11632.1i	0.0197588	+	0.0342233i
$584$		0			0
$585$	103095.	−	178566.i	0.301250	−	0.521780i
$586$		0			0
$587$			246949.i			0.716690i	0.933589	+	0.358345i	$0.116659\pi$
$587$			246949.i			0.716690i	−0.933589	+	0.358345i	$0.883341\pi$
$588$		0			0
$589$	47612.9			0.137244
$590$		0			0
$591$	−177667.	−	102576.i	−0.508665	−	0.293678i
$592$		0			0
$593$	−118390.	+	68352.5i	−0.336671	+	0.194377i	−0.658799	−	0.752319i	$-0.728935\pi$
$593$	−118390.	+	68352.5i	−0.336671	+	0.194377i	0.322128	+	0.946696i	$0.395602\pi$
$594$		0			0
$595$	113022.	−	446340.i	0.319249	−	1.26076i
$596$		0			0
$597$	−69697.2	−	120719.i	−0.195554	−	0.338709i
$598$		0			0
$599$	189511.	−	328243.i	0.528180	−	0.914834i	−0.471281	−	0.881983i	$-0.656208\pi$
$599$	189511.	−	328243.i	0.528180	−	0.914834i	0.999460	−	0.0328507i	$-0.0104586\pi$
$600$		0			0
$601$		−	464620.i		−	1.28632i	−0.765731	−	0.643160i	$-0.777623\pi$
$601$		−	464620.i		−	1.28632i	0.765731	−	0.643160i	$-0.222377\pi$
$602$		0			0
$603$	55491.1			0.152612
$604$		0			0
$605$	−326544.	−	188530.i	−0.892136	−	0.515075i
$606$		0			0
$607$	−206594.	+	119277.i	−0.560713	+	0.323728i	−0.753431	−	0.657526i	$-0.771603\pi$
$607$	−206594.	+	119277.i	−0.560713	+	0.323728i	0.192719	+	0.981254i	$0.438269\pi$
$608$		0			0
$609$	−167437.	+	172120.i	−0.451456	+	0.464085i
$610$		0			0
$611$	−566373.	−	980987.i	−1.51712	−	2.62773i
$612$		0			0
$613$	−134157.	+	232367.i	−0.357021	+	0.618378i	−0.987462	−	0.157859i	$-0.949541\pi$
$613$	−134157.	+	232367.i	−0.357021	+	0.618378i	0.630441	+	0.776237i	$0.282874\pi$
$614$		0			0
$615$			189629.i			0.501364i
$616$		0			0
$617$	−133139.			−0.349732			−0.174866	−	0.984592i	$-0.555949\pi$
$617$	−133139.			−0.349732			−0.174866	+	0.984592i	$0.555949\pi$
$618$		0			0
$619$	−14878.7	−	8590.25i	−0.0388316	−	0.0224194i	0.480459	−	0.877017i	$-0.340470\pi$
$619$	−14878.7	−	8590.25i	−0.0388316	−	0.0224194i	−0.519290	+	0.854598i	$0.673804\pi$
$620$		0			0
$621$	81689.8	−	47163.6i	0.211828	−	0.122299i
$622$		0			0
$623$	−109037.	−	385579.i	−0.280929	−	0.993429i
$624$		0			0
$625$	207754.	+	359841.i	0.531851	+	0.921193i
$626$		0			0
$627$	−9694.24	+	16790.9i	−0.0246592	+	0.0427109i
$628$		0			0
$629$			170690.i			0.431427i
$630$		0			0
$631$	267620.			0.672140			0.336070	−	0.941837i	$-0.390902\pi$
$631$	267620.			0.672140			0.336070	+	0.941837i	$0.390902\pi$
$632$		0			0
$633$	−4138.12	−	2389.14i	−0.0103275	−	0.00596259i
$634$		0			0
$635$	165443.	−	95518.7i	0.410300	−	0.236887i
$636$		0			0
$637$	337701.	−	624057.i	0.832249	−	1.53796i
$638$		0			0
$639$	21894.1	+	37921.7i	0.0536199	+	0.0928723i
$640$		0			0
$641$	−268309.	+	464726.i	−0.653010	+	1.13105i	0.329379	+	0.944198i	$0.393161\pi$
$641$	−268309.	+	464726.i	−0.653010	+	1.13105i	−0.982389	+	0.186849i	$0.940173\pi$
$642$		0			0
$643$			401575.i			0.971281i	0.874159	+	0.485640i	$0.161414\pi$
$643$			401575.i			0.971281i	−0.874159	+	0.485640i	$0.838586\pi$
$644$		0			0
$645$	−282233.			−0.678403
$646$		0			0
$647$	−490474.	−	283175.i	−1.17168	−	0.676468i	−0.217602	−	0.976038i	$-0.569823\pi$
$647$	−490474.	−	283175.i	−1.17168	−	0.676468i	−0.954074	+	0.299570i	$0.903157\pi$
$648$		0			0
$649$	23230.6	−	13412.2i	0.0551532	−	0.0318427i
$650$		0			0
$651$	−21927.2	+	6200.74i	−0.0517394	+	0.0146313i
$652$		0			0
$653$	318392.	+	551471.i	0.746681	+	1.29329i	0.949405	+	0.314054i	$0.101687\pi$
$653$	318392.	+	551471.i	0.746681	+	1.29329i	−0.202724	+	0.979236i	$0.564979\pi$
$654$		0			0
$655$	125780.	−	217857.i	0.293176	−	0.507796i
$656$		0			0
$657$			234703.i			0.543735i
$658$		0			0
$659$	238556.			0.549312			0.274656	−	0.961543i	$-0.411436\pi$
$659$	238556.			0.549312			0.274656	+	0.961543i	$0.411436\pi$
$660$		0			0
$661$	−138618.	−	80031.1i	−0.317261	−	0.183171i	0.332910	−	0.942959i	$-0.391969\pi$
$661$	−138618.	−	80031.1i	−0.317261	−	0.183171i	−0.650171	+	0.759788i	$0.725303\pi$
$662$		0			0
$663$	483591.	−	279201.i	1.10015	−	0.635170i
$664$		0			0
$665$	−482842.	−	469703.i	−1.09185	−	1.06214i
$666$		0			0
$667$	317046.	+	549140.i	0.712640	+	1.23433i
$668$		0			0
$669$	−40457.5	+	70074.4i	−0.0903954	+	0.156569i
$670$		0			0
$671$			33511.2i			0.0744295i
$672$		0			0
$673$	−489579.			−1.08092			−0.540459	−	0.841370i	$-0.681749\pi$
$673$	−489579.			−1.08092			−0.540459	+	0.841370i	$0.681749\pi$
$674$		0			0
$675$	5192.40	+	2997.83i	0.0113962	+	0.00657960i
$676$		0			0
$677$	9876.18	−	5702.02i	0.0215482	−	0.0124409i	−0.489187	−	0.872179i	$-0.662707\pi$
$677$	9876.18	−	5702.02i	0.0215482	−	0.0124409i	0.510735	+	0.859738i	$0.329373\pi$
$678$		0			0
$679$	−542342.	−	137332.i	−1.17634	−	0.297874i
$680$		0			0
$681$	190278.	+	329571.i	0.410293	+	0.710648i
$682$		0			0
$683$	−159330.	+	275968.i	−0.341552	+	0.591586i	−0.984721	−	0.174138i	$-0.944286\pi$
$683$	−159330.	+	275968.i	−0.341552	+	0.591586i	0.643169	+	0.765724i	$0.277619\pi$
$684$		0			0
$685$		−	48375.2i		−	0.103096i
$686$		0			0
$687$	−501183.			−1.06190
$688$		0			0
$689$	−490132.	−	282978.i	−1.03246	−	0.596093i
$690$		0			0
$691$	−788815.	+	455423.i	−1.65203	+	0.953803i	−0.675801	+	0.737084i	$0.736202\pi$
$691$	−788815.	+	455423.i	−1.65203	+	0.953803i	−0.976234	+	0.216719i	$0.930465\pi$
$692$		0			0
$693$	2277.78	−	8995.24i	0.00474291	−	0.0187304i
$694$		0			0
$695$	29246.7	+	50656.7i	0.0605490	+	0.104874i
$696$		0			0
$697$	−256775.	+	444747.i	−0.528551	+	0.915477i
$698$		0			0
$699$		−	175027.i		−	0.358220i
$700$		0			0
$701$	666007.			1.35532			0.677662	−	0.735374i	$-0.262993\pi$
$701$	666007.			1.35532			0.677662	+	0.735374i	$0.262993\pi$
$702$		0			0
$703$	216267.	+	124862.i	0.437602	+	0.252650i
$704$		0			0
$705$	445702.	−	257326.i	0.896740	−	0.517733i
$706$		0			0
$707$	−544976.	+	560220.i	−1.09028	+	1.12078i
$708$		0			0
$709$	−111247.	−	192685.i	−0.221307	−	0.383315i	0.733898	−	0.679260i	$-0.237699\pi$
$709$	−111247.	−	192685.i	−0.221307	−	0.383315i	−0.955205	+	0.295945i	$0.904366\pi$
$710$		0			0
$711$	−134993.	+	233815.i	−0.267038	+	0.462523i
$712$		0			0
$713$			60173.1i			0.118365i
$714$		0			0
$715$	−53561.6			−0.104771
$716$		0			0
$717$	−233722.	−	134939.i	−0.454633	−	0.262483i
$718$		0			0
$719$	701593.	−	405065.i	1.35715	−	0.783550i	0.367910	−	0.929862i	$-0.380074\pi$
$719$	701593.	−	405065.i	1.35715	−	0.783550i	0.989239	+	0.146312i	$0.0467402\pi$
$720$		0			0
$721$	−67322.1	−	238066.i	−0.129505	−	0.457959i
$722$		0			0
$723$	147911.	+	256189.i	0.282959	+	0.490099i
$724$		0			0
$725$	−20152.2	+	34904.6i	−0.0383395	+	0.0664060i
$726$		0			0
$727$			433208.i			0.819648i	0.912165	+	0.409824i	$0.134410\pi$
$727$			433208.i			0.819648i	−0.912165	+	0.409824i	$0.865590\pi$
$728$		0			0
$729$	−19683.0			−0.0370370
$730$		0			0
$731$	−661937.	−	382169.i	−1.23874	−	0.715189i
$732$		0			0
$733$	−34958.6	+	20183.4i	−0.0650649	+	0.0375652i	−0.532180	−	0.846632i	$-0.678627\pi$
$733$	−34958.6	+	20183.4i	−0.0650649	+	0.0375652i	0.467115	+	0.884197i	$0.345294\pi$
$734$		0			0
$735$	283534.	+	153431.i	0.524845	+	0.284014i
$736$		0			0
$737$	−7207.39	−	12483.6i	−0.0132691	−	0.0229828i
$738$		0			0
$739$	−494004.	+	855641.i	−0.904569	+	1.56676i	−0.0830751	+	0.996543i	$0.526474\pi$
$739$	−494004.	+	855641.i	−0.904569	+	1.56676i	−0.821494	+	0.570217i	$0.806859\pi$
$740$		0			0
$741$		−	816955.i		−	1.48786i
$742$		0			0
$743$	400203.			0.724942			0.362471	−	0.931995i	$-0.381933\pi$
$743$	400203.			0.724942			0.362471	+	0.931995i	$0.381933\pi$
$744$		0			0
$745$	34452.0	+	19890.9i	0.0620729	+	0.0358378i
$746$		0			0
$747$	−210067.	+	121282.i	−0.376458	+	0.217348i
$748$		0			0
$749$	−114867.	+	32483.0i	−0.204754	+	0.0579019i
$750$		0			0
$751$	−396996.	−	687617.i	−0.703892	−	1.21918i	−0.967090	−	0.254434i	$-0.918111\pi$
$751$	−396996.	−	687617.i	−0.703892	−	1.21918i	0.263198	−	0.964742i	$-0.415223\pi$
$752$		0			0
$753$	−113880.	+	197246.i	−0.200843	+	0.347871i
$754$		0			0
$755$		−	267766.i		−	0.469744i
$756$		0			0
$757$	−490533.			−0.856005			−0.428002	−	0.903778i	$-0.640782\pi$
$757$	−490533.			−0.856005			−0.428002	+	0.903778i	$0.640782\pi$
$758$		0			0
$759$	−21220.3	−	12251.6i	−0.0368357	−	0.0212671i
$760$		0			0
$761$	238598.	−	137755.i	0.412001	−	0.237869i	−0.279648	−	0.960102i	$-0.590218\pi$
$761$	238598.	−	137755.i	0.412001	−	0.237869i	0.691649	+	0.722234i	$0.256885\pi$
$762$		0			0
$763$	−350632.	−	341091.i	−0.602286	−	0.585897i
$764$		0			0
$765$	126852.	+	219715.i	0.216758	+	0.375436i
$766$		0			0
$767$	−565137.	+	978847.i	−0.960646	+	1.66389i
$768$		0			0
$769$		−	114640.i		−	0.193858i	−0.995291	−	0.0969290i	$-0.969098\pi$
$769$		−	114640.i		−	0.193858i	0.995291	−	0.0969290i	$-0.0309020\pi$
$770$		0			0
$771$	189331.			0.318503
$772$		0			0
$773$	−830077.	−	479245.i	−1.38918	−	0.802045i	−0.395959	−	0.918268i	$-0.629588\pi$
$773$	−830077.	−	479245.i	−1.38918	−	0.802045i	−0.993223	+	0.116223i	$0.962921\pi$
$774$		0			0
$775$	−3312.33	+	1912.37i	−0.00551480	+	0.00318397i
$776$		0			0
$777$	−115859.	−	29337.8i	−0.191905	−	0.0485943i
$778$		0			0
$779$	375667.	+	650674.i	0.619053	+	1.07223i
$780$		0			0
$781$	5687.38	−	9850.82i	0.00932416	−	0.0161499i
$782$		0			0
$783$		−	132314.i		−	0.215816i
$784$		0			0
$785$	−809037.			−1.31289
$786$		0			0
$787$	−620724.	−	358375.i	−1.00219	−	0.578613i	−0.0932926	−	0.995639i	$-0.529739\pi$
$787$	−620724.	−	358375.i	−1.00219	−	0.578613i	−0.908895	+	0.417026i	$0.863073\pi$
$788$		0			0
$789$	−142543.	+	82297.4i	−0.228977	+	0.132200i
$790$		0			0
$791$	79506.0	−	313980.i	0.127071	−	0.501821i
$792$		0			0
$793$	−706016.	−	1.22286e6i	−1.12271	−	1.94459i
$794$		0			0
$795$	128568.	−	222687.i	0.203423	−	0.352339i
$796$		0			0
$797$			1.08959e6i			1.71532i	0.514214	+	0.857662i	$0.328084\pi$
$797$			1.08959e6i			1.71532i	−0.514214	+	0.857662i	$0.671916\pi$
$798$		0			0
$799$	1.39377e6			2.18323
$800$		0			0
$801$	191213.	+	110397.i	0.298024	+	0.172065i
$802$		0			0
$803$	52799.9	−	30484.0i	0.0818846	−	0.0472761i
$804$		0			0
$805$	593610.	−	610215.i	0.916030	−	0.941653i
$806$		0			0
$807$	266662.	+	461873.i	0.409463	+	0.709211i
$808$		0			0
$809$	597622.	−	1.03511e6i	0.913124	−	1.58158i	0.103499	−	0.994630i	$-0.466996\pi$
$809$	597622.	−	1.03511e6i	0.913124	−	1.58158i	0.809625	−	0.586948i	$-0.199671\pi$
$810$		0			0
$811$		−	875048.i		−	1.33042i	−0.746654	−	0.665212i	$-0.768341\pi$
$811$		−	875048.i		−	1.33042i	0.746654	−	0.665212i	$-0.231659\pi$
$812$		0			0
$813$	−148346.			−0.224437
$814$		0			0
$815$	1.12832e6	+	651433.i	1.69869	+	0.980742i
$816$		0			0
$817$	−968428.	+	559122.i	−1.45085	+	0.837650i
$818$		0			0
$819$	106394.	+	376233.i	0.158617	+	0.560905i
$820$		0			0
$821$	666689.	+	1.15474e6i	0.989093	+	1.71316i	0.622104	+	0.782935i	$0.286278\pi$
$821$	666689.	+	1.15474e6i	0.989093	+	1.71316i	0.366989	+	0.930225i	$0.380389\pi$
$822$		0			0
$823$	99275.8	−	171951.i	0.146570	−	0.253866i	−0.783388	−	0.621533i	$-0.786510\pi$
$823$	99275.8	−	171951.i	0.146570	−	0.253866i	0.929957	+	0.367667i	$0.119843\pi$
$824$		0			0
$825$		−	1557.48i		−	0.00228830i
$826$		0			0
$827$	497392.			0.727257			0.363629	−	0.931544i	$-0.381538\pi$
$827$	497392.			0.727257			0.363629	+	0.931544i	$0.381538\pi$
$828$		0			0
$829$	−1.10458e6	−	637729.i	−1.60727	−	0.927955i	−0.989979	−	0.141217i	$-0.954899\pi$
$829$	−1.10458e6	−	637729.i	−1.60727	−	0.927955i	−0.617287	−	0.786738i	$-0.711768\pi$
$830$		0			0
$831$	121197.	−	69973.1i	0.175505	−	0.101328i
$832$		0			0
$833$	457229.	+	743783.i	0.658937	+	1.07190i
$834$		0			0
$835$	−258230.	−	447268.i	−0.370369	−	0.641498i
$836$		0			0
$837$	6278.08	−	10874.0i	0.00896140	−	0.0155216i
$838$		0			0
$839$			330040.i			0.468860i	0.972133	+	0.234430i	$0.0753223\pi$
$839$			330040.i			0.468860i	−0.972133	+	0.234430i	$0.924678\pi$
$840$		0			0
$841$	182169.			0.257562
$842$		0			0
$843$	−237253.	−	136978.i	−0.333854	−	0.192751i
$844$		0			0
$845$	1.31536e6	−	759422.i	1.84217	−	1.06358i
$846$		0			0
$847$	688018.	−	194563.i	0.959031	−	0.271202i
$848$		0			0
$849$	402837.	+	697734.i	0.558874	+	0.967998i
$850$		0			0
$851$	−157800.	+	273318.i	−0.217896	+	0.377406i
$852$		0			0
$853$			867001.i			1.19158i	0.803142	+	0.595788i	$0.203160\pi$
$853$			867001.i			1.19158i	−0.803142	+	0.595788i	$0.796840\pi$
$854$		0			0
$855$	371176.			0.507747
$856$		0			0
$857$	−9434.20	−	5446.84i	−0.0128453	−	0.00741622i	0.493564	−	0.869710i	$-0.335694\pi$
$857$	−9434.20	−	5446.84i	−0.0128453	−	0.00741622i	−0.506409	+	0.862293i	$0.669027\pi$
$858$		0			0
$859$	162940.	−	94073.2i	0.220821	−	0.127491i	−0.385509	−	0.922704i	$-0.625974\pi$
$859$	162940.	−	94073.2i	0.220821	−	0.127491i	0.606330	+	0.795213i	$0.292641\pi$
$860$		0			0
$861$	−257745.	−	250732.i	−0.347684	−	0.338223i
$862$		0			0
$863$	226191.	+	391774.i	0.303706	+	0.526034i	0.976972	−	0.213366i	$-0.0684426\pi$
$863$	226191.	+	391774.i	0.303706	+	0.526034i	−0.673266	+	0.739400i	$0.735109\pi$
$864$		0			0
$865$	−5578.05	+	9661.46i	−0.00745504	+	0.0129125i
$866$		0			0
$867$			253092.i			0.336698i
$868$		0			0
$869$	70133.6			0.0928724
$870$		0			0
$871$	526009.	+	303691.i	0.693357	+	0.400310i
$872$		0			0
$873$	266973.	−	154137.i	0.350299	−	0.202245i
$874$		0			0
$875$	−714699.	−	180976.i	−0.933484	−	0.236377i
$876$		0			0
$877$	102655.	+	177803.i	0.133469	+	0.231175i	0.925012	−	0.379939i	$-0.124055\pi$
$877$	102655.	+	177803.i	0.133469	+	0.231175i	−0.791543	+	0.611114i	$0.790722\pi$
$878$		0			0
$879$	76888.9	−	133175.i	0.0995144	−	0.172364i
$880$		0			0
$881$		−	1.42229e6i		−	1.83246i	−0.400648	−	0.916232i	$-0.631215\pi$
$881$		−	1.42229e6i		−	1.83246i	0.400648	−	0.916232i	$-0.368785\pi$
$882$		0			0
$883$	−857155.			−1.09936			−0.549678	−	0.835377i	$-0.685250\pi$
$883$	−857155.			−1.09936			−0.549678	+	0.835377i	$0.685250\pi$
$884$		0			0
$885$	−444730.	−	256765.i	−0.567818	−	0.327830i
$886$		0			0
$887$	127877.	−	73830.0i	0.162535	−	0.0938395i	−0.416526	−	0.909124i	$-0.636753\pi$
$887$	127877.	−	73830.0i	0.162535	−	0.0938395i	0.579061	+	0.815284i	$0.303419\pi$
$888$		0			0
$889$	−88923.2	+	351170.i	−0.112515	+	0.444338i
$890$		0			0
$891$	2556.50	+	4427.99i	0.00322026	+	0.00557765i
$892$		0			0
$893$	1.01956e6	−	1.76593e6i	1.27853	−	2.21448i
$894$		0			0
$895$			618284.i			0.771866i
$896$		0			0
$897$	1.03247e6			1.28319
$898$		0			0
$899$	73097.5	+	42202.9i	0.0904447	+	0.0522183i
$900$		0			0
$901$	603078.	−	348187.i	0.742889	−	0.428907i
$902$		0			0
$903$	373175.	−	383614.i	0.457654	−	0.470456i
$904$		0			0
$905$	−293014.	−	507516.i	−0.357760	−	0.619658i
$906$		0			0
$907$	−234049.	+	405385.i	−0.284507	+	0.492780i	−0.972489	−	0.232947i	$-0.925163\pi$
$907$	−234049.	+	405385.i	−0.284507	+	0.492780i	0.687983	+	0.725727i	$0.258496\pi$
$908$		0			0
$909$		−	430659.i		−	0.521201i
$910$		0			0
$911$	1.23662e6			1.49004			0.745021	−	0.667041i	$-0.232439\pi$
$911$	1.23662e6			1.49004			0.745021	+	0.667041i	$0.232439\pi$
$912$		0			0
$913$	54568.5	+	31505.1i	0.0654637	+	0.0377955i
$914$		0			0
$915$	555593.	−	320772.i	0.663612	−	0.383137i
$916$		0			0
$917$	129804.	+	459017.i	0.154366	+	0.545871i
$918$		0			0
$919$	−175594.	−	304138.i	−0.207911	−	0.360113i	0.743145	−	0.669130i	$-0.233333\pi$
$919$	−175594.	−	304138.i	−0.207911	−	0.360113i	−0.951056	+	0.309017i	$0.900000\pi$
$920$		0			0
$921$	29134.8	−	50463.0i	0.0343473	−	0.0594913i
$922$		0			0
$923$			479288.i			0.562591i
$924$		0			0
$925$	−20060.3			−0.0234452
$926$		0			0
$927$	118060.	+	68161.8i	0.137386	+	0.0793198i
$928$		0			0
$929$	−1.34589e6	+	777049.i	−1.55947	+	0.900361i	−0.562164	+	0.827026i	$0.690031\pi$
$929$	−1.34589e6	+	777049.i	−1.55947	+	0.900361i	−0.997307	+	0.0733359i	$0.976635\pi$
$930$		0			0
$931$	1.27685e6	−	35230.5i	1.47313	−	0.0406461i
$932$		0			0
$933$	387124.	+	670519.i	0.444721	+	0.770279i
$934$		0			0
$935$	32952.1	−	57074.7i	0.0376929	−	0.0652861i
$936$		0			0
$937$		−	304346.i		−	0.346648i	−0.984865	−	0.173324i	$-0.944549\pi$
$937$		−	304346.i		−	0.346648i	0.984865	−	0.173324i	$-0.0554508\pi$
$938$		0			0
$939$	−748121.			−0.848478
$940$		0			0
$941$	−241181.	−	139246.i	−0.272373	−	0.157255i	0.357592	−	0.933878i	$-0.383598\pi$
$941$	−241181.	−	139246.i	−0.272373	−	0.157255i	−0.629966	+	0.776623i	$0.716931\pi$
$942$		0			0
$943$	−822321.	+	474767.i	−0.924737	+	0.533897i
$944$		0			0
$945$	−170938.	+	48339.1i	−0.191414	+	0.0541296i
$946$		0			0
$947$	−37705.5	−	65307.8i	−0.0420440	−	0.0728224i	0.844238	−	0.535969i	$-0.180054\pi$
$947$	−37705.5	−	65307.8i	−0.0420440	−	0.0728224i	−0.886282	+	0.463147i	$0.846720\pi$
$948$		0			0
$949$	−1.28448e6	+	2.22478e6i	−1.42625	+	2.47033i
$950$		0			0
$951$		−	2131.09i		−	0.00235635i
$952$		0			0
$953$	−378194.			−0.416418			−0.208209	−	0.978084i	$-0.566763\pi$
$953$	−378194.			−0.416418			−0.208209	+	0.978084i	$0.566763\pi$
$954$		0			0
$955$	585157.	+	337840.i	0.641602	+	0.370429i
$956$		0			0
$957$	−29766.1	+	17185.5i	−0.0325011	+	0.0187645i
$958$		0			0
$959$	65752.0	+	63962.9i	0.0714944	+	0.0695490i
$960$		0			0
$961$	−457756.	−	792856.i	−0.495663	−	0.858514i
$962$		0			0
$963$	32888.2	−	56964.0i	0.0354639	−	0.0614254i
$964$		0			0
$965$		−	28876.5i		−	0.0310092i
$966$		0			0
$967$	−890998.			−0.952849			−0.476424	−	0.879215i	$-0.658067\pi$
$967$	−890998.			−0.952849			−0.476424	+	0.879215i	$0.658067\pi$
$968$		0			0
$969$	870540.	+	502606.i	0.927131	+	0.535279i
$970$		0			0
$971$	170897.	−	98667.7i	0.181258	−	0.104649i	−0.406626	−	0.913595i	$-0.633295\pi$
$971$	170897.	−	98667.7i	0.181258	−	0.104649i	0.587884	+	0.808946i	$0.299961\pi$
$972$		0			0
$973$	−107524.	−	27227.2i	−0.113574	−	0.0287592i
$974$		0			0
$975$	32813.0	+	56833.8i	0.0345173	+	0.0597858i
$976$		0			0
$977$	−416923.	+	722131.i	−0.436784	+	0.756531i	−0.997439	−	0.0715177i	$-0.977216\pi$
$977$	−416923.	+	722131.i	−0.436784	+	0.756531i	0.560656	+	0.828049i	$0.310549\pi$
$978$		0			0
$979$		−	57354.9i		−	0.0598419i
$980$		0			0
$981$	269542.			0.280084
$982$		0			0
$983$	555364.	+	320640.i	0.574739	+	0.331826i	0.759040	−	0.651044i	$-0.225669\pi$
$983$	555364.	+	320640.i	0.574739	+	0.331826i	−0.184301	+	0.982870i	$0.559002\pi$
$984$		0			0
$985$	883542.	−	510113.i	0.910657	−	0.525768i
$986$		0			0
$987$	−239558.	+	946046.i	−0.245910	+	0.971131i
$988$		0			0
$989$	−706618.	−	1.22390e6i	−0.722423	−	1.25127i
$990$		0			0
$991$	789930.	−	1.36820e6i	0.804343	−	1.39316i	−0.112390	−	0.993664i	$-0.535851\pi$
$991$	789930.	−	1.36820e6i	0.804343	−	1.39316i	0.916734	−	0.399499i	$-0.130816\pi$
$992$		0			0
$993$		−	116197.i		−	0.117841i
$994$		0			0
$995$	693211.			0.700196
$996$		0			0
$997$	740169.	+	427337.i	0.744630	+	0.429913i	0.823750	−	0.566953i	$-0.191878\pi$
$997$	740169.	+	427337.i	0.744630	+	0.429913i	−0.0791201	+	0.996865i	$0.525211\pi$
$998$		0			0
$999$	57032.5	−	32927.7i	0.0571467	−	0.0329937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.5.z.b.73.3	✓	16
3.2	odd	2		504.5.by.c.73.6		16
4.3	odd	2		336.5.bh.h.241.3		16
7.3	odd	6		1176.5.f.a.97.14		16
7.4	even	3		1176.5.f.a.97.3		16
7.5	odd	6	inner	168.5.z.b.145.3	yes	16
21.5	even	6		504.5.by.c.145.6		16
28.19	even	6		336.5.bh.h.145.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.5.z.b.73.3	✓	16	1.1	even	1	trivial
168.5.z.b.145.3	yes	16	7.5	odd	6	inner
336.5.bh.h.145.3		16	28.19	even	6
336.5.bh.h.241.3		16	4.3	odd	2
504.5.by.c.73.6		16	3.2	odd	2
504.5.by.c.145.6		16	21.5	even	6
1176.5.f.a.97.3		16	7.4	even	3
1176.5.f.a.97.14		16	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	168.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.50000 + 2.59808i) q^{3} +(-22.3786 + 12.9203i) q^{5} +(12.0282 - 47.5008i) q^{7} +(13.5000 + 23.3827i) q^{9} +O(q^{10})\)	\(q+(4.50000 + 2.59808i) q^{3} +(-22.3786 + 12.9203i) q^{5} +(12.0282 - 47.5008i) q^{7} +(13.5000 + 23.3827i) q^{9} +(3.50686 - 6.07406i) q^{11} +295.531i q^{13} -134.272 q^{15} +(-314.915 - 181.816i) q^{17} +(-460.728 + 266.001i) q^{19} +(177.537 - 182.503i) q^{21} +(-336.172 - 582.267i) q^{23} +(21.3679 - 37.0103i) q^{25} +140.296i q^{27} -943.107 q^{29} +(-77.5072 - 44.7488i) q^{31} +(31.5617 - 18.2222i) q^{33} +(344.551 + 1218.41i) q^{35} +(-234.702 - 406.515i) q^{37} +(-767.812 + 1329.89i) q^{39} -1412.28i q^{41} +2101.95 q^{43} +(-604.222 - 348.848i) q^{45} +(-3319.41 + 1916.46i) q^{47} +(-2111.65 - 1142.69i) q^{49} +(-944.745 - 1636.35i) q^{51} +(-957.525 + 1658.48i) q^{53} +181.239i q^{55} -2764.37 q^{57} +(3312.16 + 1912.28i) q^{59} +(-4137.83 + 2388.98i) q^{61} +(1273.08 - 360.010i) q^{63} +(-3818.34 - 6613.57i) q^{65} +(1027.61 - 1779.88i) q^{67} -3493.60i q^{69} +1621.79 q^{71} +(7528.09 + 4346.35i) q^{73} +(192.311 - 111.031i) q^{75} +(-246.341 - 239.638i) q^{77} +(4999.74 + 8659.81i) q^{79} +(-364.500 + 631.333i) q^{81} +8983.86i q^{83} +9396.47 q^{85} +(-4243.98 - 2450.26i) q^{87} +(7081.96 - 4088.77i) q^{89} +(14037.9 + 3554.69i) q^{91} +(-232.521 - 402.739i) q^{93} +(6873.63 - 11905.5i) q^{95} -11417.5i q^{97} +189.370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 72 q^{3} - 12 q^{5} + 16 q^{7} + 216 q^{9}+O(q^{10}) \) 16 * q + 72 * q^3 - 12 * q^5 + 16 * q^7 + 216 * q^9	\( 16 q + 72 q^{3} - 12 q^{5} + 16 q^{7} + 216 q^{9} + 252 q^{11} - 72 q^{15} - 696 q^{17} + 156 q^{19} + 108 q^{21} - 672 q^{23} + 84 q^{25} + 1992 q^{29} + 2040 q^{31} + 2268 q^{33} + 2712 q^{35} + 2548 q^{37} - 396 q^{39} + 1304 q^{43} - 324 q^{45} - 744 q^{47} - 5608 q^{49} - 2088 q^{51} - 1164 q^{53} + 936 q^{57} + 8988 q^{59} + 816 q^{61} + 540 q^{63} + 8760 q^{65} + 3044 q^{67} - 4464 q^{71} - 15828 q^{73} + 756 q^{75} + 996 q^{77} - 11144 q^{79} - 5832 q^{81} - 15344 q^{85} + 8964 q^{87} + 22248 q^{89} + 1596 q^{91} + 6120 q^{93} + 3840 q^{95} + 13608 q^{99}+O(q^{100}) \) 16 * q + 72 * q^3 - 12 * q^5 + 16 * q^7 + 216 * q^9 + 252 * q^11 - 72 * q^15 - 696 * q^17 + 156 * q^19 + 108 * q^21 - 672 * q^23 + 84 * q^25 + 1992 * q^29 + 2040 * q^31 + 2268 * q^33 + 2712 * q^35 + 2548 * q^37 - 396 * q^39 + 1304 * q^43 - 324 * q^45 - 744 * q^47 - 5608 * q^49 - 2088 * q^51 - 1164 * q^53 + 936 * q^57 + 8988 * q^59 + 816 * q^61 + 540 * q^63 + 8760 * q^65 + 3044 * q^67 - 4464 * q^71 - 15828 * q^73 + 756 * q^75 + 996 * q^77 - 11144 * q^79 - 5832 * q^81 - 15344 * q^85 + 8964 * q^87 + 22248 * q^89 + 1596 * q^91 + 6120 * q^93 + 3840 * q^95 + 13608 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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