LMFDB - Embedded newform 392.3.k.n.275.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.6812263629$
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} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 $ x^16 - x^15 + 3x^14 + 6x^13 - 22x^12 + 44x^11 - 20x^10 - 112x^9 + 368x^8 - 448x^7 - 320x^6 + 2816x^5 - 5632x^4 + 6144x^3 + 12288x^2 - 16384x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.8
Root			$0.944308 + 1.76303i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.n.67.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99898 - 0.0637211i) q^{2} +(-1.72064 - 2.98023i) q^{3} +(3.99188 - 0.254755i) q^{4} +(4.22869 + 2.44143i) q^{5} +(-3.62943 - 5.84780i) q^{6} +(7.96347 - 0.763618i) q^{8} +(-1.42120 + 2.46158i) q^{9} +O(q^{10})$	\(q+(1.99898 - 0.0637211i) q^{2} +(-1.72064 - 2.98023i) q^{3} +(3.99188 - 0.254755i) q^{4} +(4.22869 + 2.44143i) q^{5} +(-3.62943 - 5.84780i) q^{6} +(7.96347 - 0.763618i) q^{8} +(-1.42120 + 2.46158i) q^{9} +(8.60865 + 4.61093i) q^{10} +(10.7388 + 18.6001i) q^{11} +(-7.62781 - 11.4584i) q^{12} -13.0760i q^{13} -16.8033i q^{15} +(15.8702 - 2.03390i) q^{16} +(-0.117445 - 0.203420i) q^{17} +(-2.68409 + 5.01123i) q^{18} +(2.27936 - 3.94797i) q^{19} +(17.5024 + 8.66863i) q^{20} +(22.6519 + 36.4971i) q^{22} +(9.48497 + 5.47615i) q^{23} +(-15.9780 - 22.4191i) q^{24} +(-0.578804 - 1.00252i) q^{25} +(-0.833219 - 26.1388i) q^{26} -21.1900 q^{27} -34.6435i q^{29} +(-1.07073 - 33.5895i) q^{30} +(-29.5383 + 17.0539i) q^{31} +(31.5947 - 5.07701i) q^{32} +(36.9551 - 64.0082i) q^{33} +(-0.247732 - 0.399150i) q^{34} +(-5.04614 + 10.1884i) q^{36} +(-46.9706 - 27.1185i) q^{37} +(4.30484 - 8.03717i) q^{38} +(-38.9696 + 22.4991i) q^{39} +(35.5394 + 16.2132i) q^{40} +37.8300 q^{41} -4.84714 q^{43} +(47.6064 + 71.5137i) q^{44} +(-12.0196 + 6.93951i) q^{45} +(19.3093 + 10.3424i) q^{46} +(62.6455 + 36.1684i) q^{47} +(-33.3684 - 43.7973i) q^{48} +(-1.22090 - 1.96714i) q^{50} +(-0.404160 + 0.700025i) q^{51} +(-3.33118 - 52.1979i) q^{52} +(-18.7674 + 10.8353i) q^{53} +(-42.3586 + 1.35025i) q^{54} +104.872i q^{55} -15.6878 q^{57} +(-2.20752 - 69.2519i) q^{58} +(17.4503 + 30.2249i) q^{59} +(-4.28073 - 67.0768i) q^{60} +(-55.0803 - 31.8006i) q^{61} +(-57.9599 + 35.9728i) q^{62} +(62.8338 - 12.1621i) q^{64} +(31.9242 - 55.2944i) q^{65} +(69.7941 - 130.306i) q^{66} +(-9.21718 - 15.9646i) q^{67} +(-0.520647 - 0.782109i) q^{68} -37.6899i q^{69} +47.5244i q^{71} +(-9.43794 + 20.6880i) q^{72} +(27.9551 + 48.4197i) q^{73} +(-95.6215 - 51.2164i) q^{74} +(-1.99182 + 3.44994i) q^{75} +(8.09317 - 16.3405i) q^{76} +(-76.4660 + 47.4586i) q^{78} +(-82.2841 - 47.5067i) q^{79} +(72.0757 + 30.1453i) q^{80} +(49.2512 + 85.3055i) q^{81} +(75.6215 - 2.41057i) q^{82} -71.5156 q^{83} -1.14693i q^{85} +(-9.68937 + 0.308865i) q^{86} +(-103.246 + 59.6090i) q^{87} +(99.7214 + 139.921i) q^{88} +(-79.8779 + 138.353i) q^{89} +(-23.5848 + 14.6379i) q^{90} +(39.2579 + 19.4438i) q^{92} +(101.649 + 58.6874i) q^{93} +(127.532 + 68.3083i) q^{94} +(19.2774 - 11.1298i) q^{95} +(-69.4937 - 85.4238i) q^{96} +90.4794 q^{97} -61.0477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.99898	−	0.0637211i	0.999492	−	0.0318606i
$2$	1.99898	−	0.0637211i	0.999492	−	0.0318606i
$3$	−1.72064	−	2.98023i	−0.573546	−	0.993411i	−0.996198	−	0.0871191i	$-0.972234\pi$
$3$	−1.72064	−	2.98023i	−0.573546	−	0.993411i	0.422652	−	0.906292i	$-0.361099\pi$
$4$	3.99188	−	0.254755i	0.997970	−	0.0636888i
$5$	4.22869	+	2.44143i	0.845737	+	0.488287i	0.859210	−	0.511623i	$-0.170955\pi$
$5$	4.22869	+	2.44143i	0.845737	+	0.488287i	−0.0134729	+	0.999909i	$0.504289\pi$
$6$	−3.62943	−	5.84780i	−0.604906	−	0.974633i
$7$		0			0
$7$		0			0
$8$	7.96347	−	0.763618i	0.995434	−	0.0954523i
$9$	−1.42120	+	2.46158i	−0.157911	+	0.273509i
$10$	8.60865	+	4.61093i	0.860865	+	0.461093i
$11$	10.7388	+	18.6001i	0.976253	+	1.69092i	0.675735	+	0.737144i	$0.263826\pi$
$11$	10.7388	+	18.6001i	0.976253	+	1.69092i	0.300518	+	0.953776i	$0.402840\pi$
$12$	−7.62781	−	11.4584i	−0.635651	−	0.954866i
$13$		−	13.0760i		−	1.00585i	−0.864331	−	0.502924i	$-0.832258\pi$
$13$		−	13.0760i		−	1.00585i	0.864331	−	0.502924i	$-0.167742\pi$
$14$		0			0
$15$		−	16.8033i		−	1.12022i
$16$	15.8702	−	2.03390i	0.991887	−	0.127119i
$17$	−0.117445	−	0.203420i	−0.00690851	−	0.0119659i	0.862550	−	0.505971i	$-0.168866\pi$
$17$	−0.117445	−	0.203420i	−0.00690851	−	0.0119659i	−0.869459	+	0.494005i	$0.835532\pi$
$18$	−2.68409	+	5.01123i	−0.149116	+	0.278402i
$19$	2.27936	−	3.94797i	0.119966	−	0.207788i	−0.799788	−	0.600283i	$-0.795055\pi$
$19$	2.27936	−	3.94797i	0.119966	−	0.207788i	0.919754	+	0.392495i	$0.128388\pi$
$20$	17.5024	+	8.66863i	0.875119	+	0.433431i
$21$		0			0
$22$	22.6519	+	36.4971i	1.02963	+	1.65896i
$23$	9.48497	+	5.47615i	0.412390	+	0.238094i	0.691816	−	0.722074i	$-0.256811\pi$
$23$	9.48497	+	5.47615i	0.412390	+	0.238094i	−0.279426	+	0.960167i	$0.590144\pi$
$24$	−15.9780	−	22.4191i	−0.665751	−	0.934129i
$25$	−0.578804	−	1.00252i	−0.0231522	−	0.0401007i
$26$	−0.833219	−	26.1388i	−0.0320469	−	1.00534i
$27$	−21.1900			−0.784816
$28$		0			0
$29$		−	34.6435i		−	1.19460i	−0.802016	−	0.597302i	$-0.796239\pi$
$29$		−	34.6435i		−	1.19460i	0.802016	−	0.597302i	$-0.203761\pi$
$30$	−1.07073	−	33.5895i	−0.0356908	−	1.11965i
$31$	−29.5383	+	17.0539i	−0.952848	+	0.550127i	−0.893965	−	0.448138i	$-0.852087\pi$
$31$	−29.5383	+	17.0539i	−0.952848	+	0.550127i	−0.0588837	+	0.998265i	$0.518754\pi$
$32$	31.5947	−	5.07701i	0.987334	−	0.158656i
$33$	36.9551	−	64.0082i	1.11985	−	1.93964i
$34$	−0.247732	−	0.399150i	−0.00728624	−	0.0117397i
$35$		0			0
$36$	−5.04614	+	10.1884i	−0.140171	+	0.283011i
$37$	−46.9706	−	27.1185i	−1.26948	−	0.732932i	−0.294587	−	0.955625i	$-0.595182\pi$
$37$	−46.9706	−	27.1185i	−1.26948	−	0.732932i	−0.974889	+	0.222693i	$0.928515\pi$
$38$	4.30484	−	8.03717i	0.113285	−	0.211505i
$39$	−38.9696	+	22.4991i	−0.999221	+	0.576900i
$40$	35.5394	+	16.2132i	0.888484	+	0.405330i
$41$	37.8300			0.922682			0.461341	−	0.887223i	$-0.347368\pi$
$41$	37.8300			0.922682			0.461341	+	0.887223i	$0.347368\pi$
$42$		0			0
$43$	−4.84714			−0.112724			−0.0563621	−	0.998410i	$-0.517950\pi$
$43$	−4.84714			−0.112724			−0.0563621	+	0.998410i	$0.517950\pi$
$44$	47.6064	+	71.5137i	1.08196	+	1.62531i
$45$	−12.0196	+	6.93951i	−0.267102	+	0.154211i
$46$	19.3093	+	10.3424i	0.419767	+	0.224834i
$47$	62.6455	+	36.1684i	1.33288	+	0.769541i	0.985741	−	0.168271i	$-0.0538185\pi$
$47$	62.6455	+	36.1684i	1.33288	+	0.769541i	0.347143	+	0.937812i	$0.387152\pi$
$48$	−33.3684	−	43.7973i	−0.695175	−	0.912444i
$49$		0			0
$50$	−1.22090	−	1.96714i	−0.0244180	−	0.0393427i
$51$	−0.404160	+	0.700025i	−0.00792470	+	0.0137260i
$52$	−3.33118	−	52.1979i	−0.0640612	−	1.00381i
$53$	−18.7674	+	10.8353i	−0.354101	+	0.204440i	−0.666490	−	0.745514i	$-0.732204\pi$
$53$	−18.7674	+	10.8353i	−0.354101	+	0.204440i	0.312389	+	0.949954i	$0.398871\pi$
$54$	−42.3586	+	1.35025i	−0.784418	+	0.0250047i
$55$			104.872i			1.90677i
$56$		0			0
$57$	−15.6878			−0.275225
$58$	−2.20752	−	69.2519i	−0.0380608	−	1.19400i
$59$	17.4503	+	30.2249i	0.295768	+	0.512286i	0.975163	−	0.221487i	$-0.0710910\pi$
$59$	17.4503	+	30.2249i	0.295768	+	0.512286i	−0.679395	+	0.733773i	$0.737758\pi$
$60$	−4.28073	−	67.0768i	−0.0713454	−	1.11795i
$61$	−55.0803	−	31.8006i	−0.902955	−	0.521321i	−0.0247973	−	0.999693i	$-0.507894\pi$
$61$	−55.0803	−	31.8006i	−0.902955	−	0.521321i	−0.878158	+	0.478371i	$0.841227\pi$
$62$	−57.9599	+	35.9728i	−0.934837	+	0.580206i
$63$		0			0
$64$	62.8338	−	12.1621i	0.981778	−	0.190033i
$65$	31.9242	−	55.2944i	0.491142	−	0.850683i
$66$	69.7941	−	130.306i	1.05749	−	1.97434i
$67$	−9.21718	−	15.9646i	−0.137570	−	0.238278i	0.789006	−	0.614385i	$-0.210596\pi$
$67$	−9.21718	−	15.9646i	−0.137570	−	0.238278i	−0.926576	+	0.376107i	$0.877263\pi$
$68$	−0.520647	−	0.782109i	−0.00765657	−	0.0115016i
$69$		−	37.6899i		−	0.546231i
$70$		0			0
$71$			47.5244i			0.669358i	0.942332	+	0.334679i	$0.108628\pi$
$71$			47.5244i			0.669358i	−0.942332	+	0.334679i	$0.891372\pi$
$72$	−9.43794	+	20.6880i	−0.131083	+	0.287333i
$73$	27.9551	+	48.4197i	0.382947	+	0.663284i	0.991482	−	0.130243i	$-0.0415758\pi$
$73$	27.9551	+	48.4197i	0.382947	+	0.663284i	−0.608535	+	0.793527i	$0.708242\pi$
$74$	−95.6215	−	51.2164i	−1.29218	−	0.692114i
$75$	−1.99182	+	3.44994i	−0.0265577	+	0.0459992i
$76$	8.09317	−	16.3405i	0.106489	−	0.215007i
$77$		0			0
$78$	−76.4660	+	47.4586i	−0.980333	+	0.608443i
$79$	−82.2841	−	47.5067i	−1.04157	−	0.601351i	−0.121293	−	0.992617i	$-0.538704\pi$
$79$	−82.2841	−	47.5067i	−1.04157	−	0.601351i	−0.920278	+	0.391266i	$0.872037\pi$
$80$	72.0757	+	30.1453i	0.900947	+	0.376816i
$81$	49.2512	+	85.3055i	0.608039	+	1.05315i
$82$	75.6215	−	2.41057i	0.922214	−	0.0293972i
$83$	−71.5156			−0.861634			−0.430817	−	0.902439i	$-0.641775\pi$
$83$	−71.5156			−0.861634			−0.430817	+	0.902439i	$0.641775\pi$
$84$		0			0
$85$		−	1.14693i		−	0.0134933i
$86$	−9.68937	+	0.308865i	−0.112667	+	0.00359146i
$87$	−103.246	+	59.6090i	−1.18673	+	0.685161i
$88$	99.7214	+	139.921i	1.13320	+	1.59001i
$89$	−79.8779	+	138.353i	−0.897504	+	1.55452i	−0.0668296	+	0.997764i	$0.521288\pi$
$89$	−79.8779	+	138.353i	−0.897504	+	1.55452i	−0.830675	+	0.556758i	$0.812045\pi$
$90$	−23.5848	+	14.6379i	−0.262053	+	0.162643i
$91$		0			0
$92$	39.2579	+	19.4438i	0.426717	+	0.211346i
$93$	101.649	+	58.6874i	1.09301	+	0.631047i
$94$	127.532	+	68.3083i	1.35673	+	0.726684i
$95$	19.2774	−	11.1298i	0.202920	−	0.117156i
$96$	−69.4937	−	85.4238i	−0.723893	−	0.889832i
$97$	90.4794			0.932777			0.466389	−	0.884580i	$-0.345555\pi$
$97$	90.4794			0.932777			0.466389	+	0.884580i	$0.345555\pi$
$98$		0			0
$99$	−61.0477			−0.616643
$100$	−2.56591	−	3.85448i	−0.0256591	−	0.0385448i
$101$	−156.878	+	90.5735i	−1.55325	+	0.896767i	−0.555371	+	0.831602i	$0.687424\pi$
$101$	−156.878	+	90.5735i	−1.55325	+	0.896767i	−0.997875	+	0.0651645i	$0.979243\pi$
$102$	−0.763302	+	1.42509i	−0.00748336	+	0.0139715i
$103$	−34.0350	−	19.6501i	−0.330437	−	0.190778i	0.325598	−	0.945508i	$-0.394434\pi$
$103$	−34.0350	−	19.6501i	−0.330437	−	0.190778i	−0.656035	+	0.754730i	$0.727768\pi$
$104$	−9.98509	−	104.131i	−0.0960105	−	1.00126i
$105$		0			0
$106$	−36.8252	+	22.8556i	−0.347408	+	0.215618i
$107$	−19.2249	+	33.2985i	−0.179672	+	0.311201i	−0.941768	−	0.336263i	$-0.890837\pi$
$107$	−19.2249	+	33.2985i	−0.179672	+	0.311201i	0.762096	+	0.647464i	$0.224170\pi$
$108$	−84.5881	+	5.39827i	−0.783223	+	0.0499840i
$109$	−24.1436	+	13.9393i	−0.221501	+	0.127883i	−0.606645	−	0.794973i	$-0.707485\pi$
$109$	−24.1436	+	13.9393i	−0.221501	+	0.127883i	0.385144	+	0.922856i	$0.374152\pi$
$110$	6.68257	+	209.638i	0.0607506	+	1.90580i
$111$			186.644i			1.68148i
$112$		0			0
$113$	82.4419			0.729574			0.364787	−	0.931091i	$-0.381142\pi$
$113$	82.4419			0.729574			0.364787	+	0.931091i	$0.381142\pi$
$114$	−31.3597	+	0.999646i	−0.275085	+	0.00876882i
$115$	26.7393	+	46.3139i	0.232516	+	0.402729i
$116$	−8.82562	−	138.293i	−0.0760829	−	1.19218i
$117$	32.1877	+	18.5836i	0.275109	+	0.158834i
$118$	36.8089	+	59.3071i	0.311940	+	0.502603i
$119$		0			0
$120$	−12.8313	−	133.813i	−0.106928	−	1.11511i
$121$	−170.143	+	294.697i	−1.40614	+	2.43551i
$122$	−112.131	−	60.0591i	−0.919106	−	0.492288i
$123$	−65.0917	−	112.742i	−0.529201	−	0.916603i
$124$	−113.569	+	75.6023i	−0.915877	+	0.609696i
$125$		−	127.724i		−	1.02179i
$126$		0			0
$127$		−	25.1408i		−	0.197959i	−0.995089	−	0.0989796i	$-0.968442\pi$
$127$		−	25.1408i		−	0.197959i	0.995089	−	0.0989796i	$-0.0315579\pi$
$128$	124.829	−	28.3157i	0.975225	−	0.221216i
$129$	8.34018	+	14.4456i	0.0646526	+	0.111982i
$130$	60.2926	−	112.567i	0.463790	−	0.865899i
$131$	−63.1991	+	109.464i	−0.482436	+	0.835603i	−0.999797	−	0.0201639i	$-0.993581\pi$
$131$	−63.1991	+	109.464i	−0.482436	+	0.835603i	0.517361	+	0.855767i	$0.326915\pi$
$132$	131.214	−	264.928i	0.994046	−	2.00703i
$133$		0			0
$134$	−19.4423	−	31.3257i	−0.145092	−	0.233774i
$135$	−89.6060	−	51.7341i	−0.663748	−	0.383215i
$136$	−1.09060	−	1.53025i	−0.00801913	−	0.0112518i
$137$	−17.4728	−	30.2638i	−0.127539	−	0.220904i	0.795184	−	0.606369i	$-0.207374\pi$
$137$	−17.4728	−	30.2638i	−0.127539	−	0.220904i	−0.922723	+	0.385465i	$0.874041\pi$
$138$	−2.40164	−	75.3416i	−0.0174032	−	0.545953i
$139$	119.148			0.857177			0.428589	−	0.903500i	$-0.359011\pi$
$139$	119.148			0.857177			0.428589	+	0.903500i	$0.359011\pi$
$140$		0			0
$141$		−	248.931i		−	1.76547i
$142$	3.02831	+	95.0005i	0.0213261	+	0.669018i
$143$	243.216	−	140.421i	1.70081	−	0.981962i
$144$	−17.5480	+	41.9564i	−0.121861	+	0.291364i
$145$	84.5799	−	146.497i	0.583310	−	1.01032i
$146$	58.9673	+	95.0090i	0.403885	+	0.650746i
$147$		0			0
$148$	−194.409	−	96.2877i	−1.31358	−	0.650593i
$149$	105.596	+	60.9659i	0.708698	+	0.409167i	0.810579	−	0.585630i	$-0.199153\pi$
$149$	105.596	+	60.9659i	0.708698	+	0.409167i	−0.101881	+	0.994797i	$0.532486\pi$
$150$	−3.76179	+	7.02330i	−0.0250786	+	0.0468220i
$151$	−190.876	+	110.202i	−1.26408	+	0.729815i	−0.973861	−	0.227146i	$-0.927060\pi$
$151$	−190.876	+	110.202i	−1.26408	+	0.729815i	−0.290216	+	0.956961i	$0.593727\pi$
$152$	15.1369	−	33.1801i	0.0995848	−	0.218290i
$153$	0.667647			0.00436371
$154$		0			0
$155$	−166.544			−1.07448
$156$	−149.830	+	99.7414i	−0.960450	+	0.639368i
$157$	5.86312	−	3.38507i	0.0373447	−	0.0215610i	−0.481211	−	0.876605i	$-0.659803\pi$
$157$	5.86312	−	3.38507i	0.0373447	−	0.0215610i	0.518556	+	0.855044i	$0.326470\pi$
$158$	−167.512	−	89.7220i	−1.06020	−	0.567861i
$159$	64.5837	+	37.2874i	0.406187	+	0.234512i
$160$	145.999	+	55.6672i	0.912495	+	0.347920i
$161$		0			0
$162$	103.888	+	167.386i	0.641285	+	1.03325i
$163$	103.621	−	179.478i	0.635715	−	1.10109i	−0.350649	−	0.936507i	$-0.614039\pi$
$163$	103.621	−	179.478i	0.635715	−	1.10109i	0.986363	−	0.164583i	$-0.0526278\pi$
$164$	151.013	−	9.63738i	0.920809	−	0.0587645i
$165$	312.544	−	180.447i	1.89420	−	1.09362i
$166$	−142.959	+	4.55706i	−0.861197	+	0.0274521i
$167$		−	165.529i		−	0.991193i	−0.868553	−	0.495596i	$-0.834950\pi$
$167$		−	165.529i		−	0.991193i	0.868553	−	0.495596i	$-0.165050\pi$
$168$		0			0
$169$	−1.98237			−0.0117300
$170$	−0.0730838	−	2.29270i	−0.000429905	−	0.0134865i
$171$	6.47884	+	11.2217i	0.0378879	+	0.0656238i
$172$	−19.3492	+	1.23483i	−0.112495	+	0.00717927i
$173$	−76.9489	−	44.4265i	−0.444791	−	0.256800i	0.260836	−	0.965383i	$-0.416002\pi$
$173$	−76.9489	−	44.4265i	−0.444791	−	0.256800i	−0.705628	+	0.708583i	$0.749335\pi$
$174$	−202.588	+	125.736i	−1.16430	+	0.722623i
$175$		0			0
$176$	208.258	+	273.346i	1.18328	+	1.55310i
$177$	60.0515	−	104.012i	0.339274	−	0.587639i
$178$	−150.859	+	281.654i	−0.847521	+	1.58233i
$179$	−40.1896	−	69.6104i	−0.224523	−	0.388885i	0.731653	−	0.681677i	$-0.238749\pi$
$179$	−40.1896	−	69.6104i	−0.224523	−	0.388885i	−0.956176	+	0.292792i	$0.905416\pi$
$180$	−46.2129	+	30.7637i	−0.256738	+	0.170910i
$181$		−	276.353i		−	1.52681i	−0.645919	−	0.763406i	$-0.723526\pi$
$181$		−	276.353i		−	1.52681i	0.645919	−	0.763406i	$-0.276474\pi$
$182$		0			0
$183$			218.869i			1.19601i
$184$	79.7150	+	36.3663i	0.433234	+	0.197643i
$185$	−132.416	−	229.351i	−0.715762	−	1.23974i
$186$	206.935	+	110.838i	1.11256	+	0.595903i
$187$	2.52243	−	4.36897i	0.0134889	−	0.0233635i
$188$	259.288	+	128.421i	1.37919	+	0.683089i
$189$		0			0
$190$	37.8260	−	23.4767i	0.199084	−	0.123562i
$191$	−175.816	−	101.507i	−0.920502	−	0.531452i	−0.0367067	−	0.999326i	$-0.511687\pi$
$191$	−175.816	−	101.507i	−0.920502	−	0.531452i	−0.883795	+	0.467874i	$0.845020\pi$
$192$	−144.360	−	166.333i	−0.751876	−	0.866316i
$193$	−43.6664	−	75.6325i	−0.226251	−	0.391878i	0.730443	−	0.682974i	$-0.239314\pi$
$193$	−43.6664	−	75.6325i	−0.226251	−	0.391878i	−0.956694	+	0.291096i	$0.905980\pi$
$194$	180.867	−	5.76545i	0.932304	−	0.0297188i
$195$	−219.720			−1.12677
$196$		0			0
$197$			21.6639i			0.109969i	0.998487	+	0.0549845i	$0.0175109\pi$
$197$			21.6639i			0.109969i	−0.998487	+	0.0549845i	$0.982489\pi$
$198$	−122.033	+	3.89003i	−0.616330	+	0.0196466i
$199$	157.558	−	90.9664i	0.791751	−	0.457118i	−0.0488277	−	0.998807i	$-0.515549\pi$
$199$	157.558	−	90.9664i	0.791751	−	0.457118i	0.840579	+	0.541690i	$0.182215\pi$
$200$	−5.37483	−	7.54154i	−0.0268741	−	0.0377077i
$201$	−31.7189	+	54.9387i	−0.157805	+	0.273327i
$202$	−307.825	+	191.051i	−1.52389	+	0.945799i
$203$		0			0
$204$	−1.43502	+	2.89738i	−0.00703442	+	0.0142028i
$205$	159.971	+	92.3594i	0.780347	+	0.450533i
$206$	−69.2876	−	37.1116i	−0.336348	−	0.180153i
$207$	−26.9600	+	15.5654i	−0.130242	+	0.0751950i
$208$	−26.5954	−	207.519i	−0.127862	−	0.997688i
$209$	97.9103			0.468470
$210$		0			0
$211$	−21.4204			−0.101519			−0.0507594	−	0.998711i	$-0.516164\pi$
$211$	−21.4204			−0.101519			−0.0507594	+	0.998711i	$0.516164\pi$
$212$	−72.1567	+	48.0344i	−0.340362	+	0.226578i
$213$	141.634	−	81.7723i	0.664947	−	0.383908i
$214$	−36.3085	+	67.7883i	−0.169666	+	0.316768i
$215$	−20.4971	−	11.8340i	−0.0953351	−	0.0550418i
$216$	−168.746	+	16.1811i	−0.781233	+	0.0749125i
$217$		0			0
$218$	−47.3744	+	29.4029i	−0.217314	+	0.134876i
$219$	96.2014	−	166.626i	0.439276	−	0.760848i
$220$	26.7167	+	418.637i	0.121440	+	1.90290i
$221$	−2.65992	+	1.53571i	−0.0120359	+	0.00694891i
$222$	11.8932	+	373.099i	0.0535729	+	1.68063i
$223$			195.958i			0.878735i	0.898307	+	0.439367i	$0.144797\pi$
$223$			195.958i			0.878735i	−0.898307	+	0.439367i	$0.855203\pi$
$224$		0			0
$225$	3.29038			0.0146239
$226$	164.800	−	5.25329i	0.729204	−	0.0232446i
$227$	−13.6326	−	23.6123i	−0.0600554	−	0.104019i	0.834435	−	0.551107i	$-0.185794\pi$
$227$	−13.6326	−	23.6123i	−0.0600554	−	0.104019i	−0.894490	+	0.447088i	$0.852461\pi$
$228$	−62.6239	+	3.99655i	−0.274666	+	0.0175287i
$229$	152.721	+	88.1737i	0.666906	+	0.385038i	0.794903	−	0.606736i	$-0.207522\pi$
$229$	152.721	+	88.1737i	0.666906	+	0.385038i	−0.127998	+	0.991774i	$0.540855\pi$
$230$	56.4027	+	90.8768i	0.245229	+	0.395117i
$231$		0			0
$232$	−26.4544	−	275.883i	−0.114028	−	1.18915i
$233$	−35.9183	+	62.2123i	−0.154156	+	0.267006i	−0.932751	−	0.360520i	$-0.882599\pi$
$233$	−35.9183	+	62.2123i	−0.154156	+	0.267006i	0.778596	+	0.627526i	$0.215932\pi$
$234$	65.5269	+	35.0973i	0.280030	+	0.149988i
$235$	176.606	+	305.890i	0.751513	+	1.30166i
$236$	77.3596	+	116.208i	0.327795	+	0.492409i
$237$			326.968i			1.37961i
$238$		0			0
$239$			71.0926i			0.297459i	0.988878	+	0.148729i	$0.0475183\pi$
$239$			71.0926i			0.297459i	−0.988878	+	0.148729i	$0.952482\pi$
$240$	−34.1763	−	266.672i	−0.142401	−	1.11113i
$241$	28.0556	+	48.5938i	0.116413	+	0.201634i	0.918344	−	0.395783i	$-0.129527\pi$
$241$	28.0556	+	48.5938i	0.116413	+	0.201634i	−0.801930	+	0.597417i	$0.796194\pi$
$242$	−321.335	+	599.935i	−1.32783	+	2.47907i
$243$	74.1318	−	128.400i	0.305069	−	0.528395i
$244$	−227.975	−	112.912i	−0.934324	−	0.462755i
$245$		0			0
$246$	−137.301	−	221.222i	−0.558136	−	0.899277i
$247$	−51.6237	−	29.8050i	−0.209003	−	0.120668i
$248$	−222.205	+	158.365i	−0.895987	+	0.638567i
$249$	123.053	+	213.133i	0.494187	+	0.855957i
$250$	−8.13872	−	255.319i	−0.0325549	−	1.02127i
$251$	−368.953			−1.46993			−0.734966	−	0.678104i	$-0.762802\pi$
$251$	−368.953			−1.46993			−0.734966	+	0.678104i	$0.762802\pi$
$252$		0			0
$253$			235.229i			0.929759i
$254$	−1.60200	−	50.2561i	−0.00630709	−	0.197859i
$255$	−3.41813	+	1.97346i	−0.0134044	+	0.00773905i
$256$	247.726	−	64.5569i	0.967682	−	0.252175i
$257$	11.8714	−	20.5619i	0.0461923	−	0.0800073i	−0.842005	−	0.539470i	$-0.818625\pi$
$257$	11.8714	−	20.5619i	0.0461923	−	0.0800073i	0.888197	+	0.459463i	$0.151958\pi$
$258$	17.5924	+	28.3451i	0.0681876	+	0.109865i
$259$		0			0
$260$	113.351	−	228.861i	0.435966	−	0.880236i
$261$	85.2780	+	49.2353i	0.326735	+	0.188641i
$262$	−119.359	+	222.844i	−0.455568	+	0.850550i
$263$	64.0605	−	36.9853i	0.243576	−	0.140629i	−0.373243	−	0.927734i	$-0.621754\pi$
$263$	64.0605	−	36.9853i	0.243576	−	0.140629i	0.616819	+	0.787105i	$0.288421\pi$
$264$	245.413	−	537.947i	0.929596	−	2.03768i
$265$	−105.815			−0.399302
$266$		0			0
$267$	549.764			2.05904
$268$	−40.8610	−	61.3807i	−0.152466	−	0.229033i
$269$	290.632	−	167.797i	1.08042	−	0.623779i	0.149408	−	0.988776i	$-0.452263\pi$
$269$	290.632	−	167.797i	1.08042	−	0.623779i	0.931009	+	0.364997i	$0.118930\pi$
$270$	−182.418	−	97.7058i	−0.675621	−	0.361873i
$271$	−162.186	−	93.6379i	−0.598471	−	0.345527i	0.169969	−	0.985449i	$-0.445633\pi$
$271$	−162.186	−	93.6379i	−0.598471	−	0.345527i	−0.768440	+	0.639922i	$0.778967\pi$
$272$	−2.27761	−	2.98945i	−0.00837355	−	0.0109906i
$273$		0			0
$274$	−36.8564	−	59.3835i	−0.134512	−	0.216728i
$275$	12.4313	−	21.5317i	0.0452047	−	0.0782969i
$276$	−9.60170	−	150.454i	−0.0347888	−	0.545122i
$277$	−114.828	+	66.2958i	−0.414541	+	0.239335i	−0.692739	−	0.721189i	$-0.743596\pi$
$277$	−114.828	+	66.2958i	−0.414541	+	0.239335i	0.278198	+	0.960524i	$0.410263\pi$
$278$	238.174	−	7.59222i	0.856742	−	0.0273101i
$279$		−	96.9480i		−	0.347484i
$280$		0			0
$281$	331.520			1.17979			0.589894	−	0.807481i	$-0.299170\pi$
$281$	331.520			1.17979			0.589894	+	0.807481i	$0.299170\pi$
$282$	−15.8622	−	497.610i	−0.0562488	−	1.76457i
$283$	−33.3579	−	57.7776i	−0.117873	−	0.204161i	0.801052	−	0.598595i	$-0.204274\pi$
$283$	−33.3579	−	57.7776i	−0.117873	−	0.204161i	−0.918924	+	0.394434i	$0.870941\pi$
$284$	12.1071	+	189.712i	0.0426306	+	0.667999i
$285$	−66.3389	−	38.3008i	−0.232768	−	0.134389i
$286$	477.237	−	296.197i	1.66866	−	1.03565i
$287$		0			0
$288$	−32.4048	+	84.9884i	−0.112517	+	0.295099i
$289$	144.472	−	250.234i	0.499905	−	0.865860i
$290$	159.739	−	298.234i	0.550824	−	1.02839i
$291$	−155.682	−	269.650i	−0.534991	−	0.926632i
$292$	123.929	+	186.164i	0.424414	+	0.637548i
$293$		−	289.215i		−	0.987082i	−0.869723	−	0.493541i	$-0.835702\pi$
$293$		−	289.215i		−	0.987082i	0.869723	−	0.493541i	$-0.164298\pi$
$294$		0			0
$295$			170.415i			0.577679i
$296$	−394.757	−	180.090i	−1.33364	−	0.608411i
$297$	−227.555	−	394.137i	−0.766180	−	1.32706i
$298$	214.969	+	115.141i	0.721374	+	0.386380i
$299$	71.6063	−	124.026i	0.239486	−	0.414802i
$300$	−7.07223	+	14.2792i	−0.0235741	+	0.0475973i
$301$		0			0
$302$	−374.535	+	232.455i	−1.24018	+	0.769719i
$303$	539.860	+	311.688i	1.78172	+	1.02867i
$304$	28.1441	−	67.2911i	0.0925794	−	0.221352i
$305$	−155.278	−	268.950i	−0.509109	−	0.881802i
$306$	1.33462	−	0.0425432i	0.00436149	−	0.000139030i
$307$	−0.693177			−0.00225790			−0.00112895	−	0.999999i	$-0.500359\pi$
$307$	−0.693177			−0.00225790			−0.00112895	+	0.999999i	$0.500359\pi$
$308$		0			0
$309$			135.243i			0.437680i
$310$	−332.919	+	10.6124i	−1.07393	+	0.0342335i
$311$	−53.8307	+	31.0792i	−0.173089	+	0.0999330i	−0.584042	−	0.811724i	$-0.698530\pi$
$311$	−53.8307	+	31.0792i	−0.173089	+	0.0999330i	0.410953	+	0.911657i	$0.365196\pi$
$312$	−293.153	+	208.929i	−0.939592	+	0.669644i
$313$	106.797	−	184.978i	0.341204	−	0.590983i	−0.643452	−	0.765486i	$-0.722499\pi$
$313$	106.797	−	184.978i	0.341204	−	0.590983i	0.984657	+	0.174503i	$0.0558319\pi$
$314$	11.5046	−	7.14031i	0.0366388	−	0.0227398i
$315$		0			0
$316$	−340.571	−	168.679i	−1.07776	−	0.533794i
$317$	−20.3150	−	11.7288i	−0.0640850	−	0.0369995i	0.467615	−	0.883932i	$-0.345113\pi$
$317$	−20.3150	−	11.7288i	−0.0640850	−	0.0369995i	−0.531700	+	0.846933i	$0.678447\pi$
$318$	131.478	+	70.4216i	0.413452	+	0.221452i
$319$	644.374	−	372.030i	2.01998	−	1.16624i
$320$	295.397	+	101.975i	0.923117	+	0.318671i
$321$	132.317			0.412201
$322$		0			0
$323$	−1.07079			−0.00331515
$324$	218.337	+	327.982i	0.673879	+	1.01229i
$325$	−13.1089	+	7.56845i	−0.0403352	+	0.0232875i
$326$	195.701	−	365.376i	0.600310	−	1.12079i
$327$	83.0847	+	47.9690i	0.254082	+	0.146694i
$328$	301.258	−	28.8877i	0.918469	−	0.0880721i
$329$		0			0
$330$	613.271	−	380.627i	1.85840	−	1.15341i
$331$	−253.703	+	439.426i	−0.766474	+	1.32757i	0.172990	+	0.984924i	$0.444657\pi$
$331$	−253.703	+	439.426i	−0.766474	+	1.32757i	−0.939464	+	0.342648i	$0.888676\pi$
$332$	−285.482	+	18.2190i	−0.859885	+	0.0548764i
$333$	133.509	−	77.0814i	0.400927	−	0.231476i
$334$	−10.5477	−	330.890i	−0.0315800	−	0.990689i
$335$		−	90.0126i		−	0.268694i
$336$		0			0
$337$	−342.726			−1.01699			−0.508495	−	0.861065i	$-0.669798\pi$
$337$	−342.726			−1.01699			−0.508495	+	0.861065i	$0.669798\pi$
$338$	−3.96272	+	0.126319i	−0.0117240	+	0.000373724i
$339$	−141.853	−	245.696i	−0.418445	−	0.724767i
$340$	−0.292187	−	4.57842i	−0.000859373	−	0.0134659i
$341$	−634.411	−	366.277i	−1.86044	−	1.07413i
$342$	13.6662	+	22.0191i	0.0399595	+	0.0643834i
$343$		0			0
$344$	−38.6001	+	3.70137i	−0.112210	+	0.0107598i
$345$	92.0174	−	159.379i	0.266717	−	0.461968i
$346$	−156.651	−	83.9046i	−0.452747	−	0.242499i
$347$	−68.3727	−	118.425i	−0.197039	−	0.341282i	0.750528	−	0.660839i	$-0.229799\pi$
$347$	−68.3727	−	118.425i	−0.197039	−	0.341282i	−0.947567	+	0.319557i	$0.896466\pi$
$348$	−396.959	+	264.254i	−1.14069	+	0.759352i
$349$		−	82.0565i		−	0.235119i	−0.993066	−	0.117559i	$-0.962493\pi$
$349$		−	82.0565i		−	0.235119i	0.993066	−	0.117559i	$-0.0375071\pi$
$350$		0			0
$351$			277.081i			0.789406i
$352$	433.722	+	533.144i	1.23216	+	1.51461i
$353$	253.684	+	439.393i	0.718651	+	1.24474i	0.961535	+	0.274684i	$0.0885732\pi$
$353$	253.684	+	439.393i	0.718651	+	1.24474i	−0.242884	+	0.970055i	$0.578093\pi$
$354$	113.414	−	211.745i	0.320379	−	0.598151i
$355$	−116.028	+	200.966i	−0.326838	+	0.566101i
$356$	−283.617	+	572.636i	−0.796676	+	1.60853i
$357$		0			0
$358$	−84.7740	−	136.589i	−0.236799	−	0.381534i
$359$	485.675	+	280.404i	1.35285	+	0.781071i	0.988648	−	0.150248i	$-0.0480071\pi$
$359$	485.675	+	280.404i	1.35285	+	0.781071i	0.364206	+	0.931318i	$0.381340\pi$
$360$	−90.4185	+	64.4410i	−0.251163	+	0.179003i
$361$	170.109	+	294.637i	0.471216	+	0.816170i
$362$	−17.6095	−	552.426i	−0.0486451	−	1.52604i
$363$	1171.02			3.22595
$364$		0			0
$365$			273.003i			0.747952i
$366$	13.9466	+	437.517i	0.0381055	+	1.19540i
$367$	23.3334	−	13.4716i	0.0635788	−	0.0367072i	−0.467874	−	0.883795i	$-0.654980\pi$
$367$	23.3334	−	13.4716i	0.0635788	−	0.0367072i	0.531452	+	0.847088i	$0.321646\pi$
$368$	161.666	+	67.6161i	0.439311	+	0.183739i
$369$	−53.7638	+	93.1216i	−0.145701	+	0.252362i
$370$	−279.312	−	450.032i	−0.754897	−	1.21630i
$371$		0			0
$372$	420.723	+	208.377i	1.13098	+	0.560153i
$373$	−465.951	−	269.017i	−1.24920	−	0.721225i	−0.278249	−	0.960509i	$-0.589754\pi$
$373$	−465.951	−	269.017i	−1.24920	−	0.721225i	−0.970950	+	0.239284i	$0.923087\pi$
$374$	4.76389	−	8.89423i	0.0127377	−	0.0237814i
$375$	−380.648	+	219.767i	−1.01506	+	0.586046i
$376$	526.495	+	240.189i	1.40025	+	0.638800i
$377$	−453.000			−1.20159
$378$		0			0
$379$	−182.132			−0.480560			−0.240280	−	0.970704i	$-0.577239\pi$
$379$	−182.132			−0.480560			−0.240280	+	0.970704i	$0.577239\pi$
$380$	74.1177	−	49.3399i	0.195047	−	0.129842i
$381$	−74.9256	+	43.2583i	−0.196655	+	0.113539i
$382$	−357.921	−	191.708i	−0.936967	−	0.501854i
$383$	288.621	+	166.636i	0.753580	+	0.435080i	0.826986	−	0.562222i	$-0.190053\pi$
$383$	288.621	+	166.636i	0.753580	+	0.435080i	−0.0734058	+	0.997302i	$0.523387\pi$
$384$	−299.173	−	323.298i	−0.779095	−	0.841921i
$385$		0			0
$386$	−92.1079	−	148.406i	−0.238621	−	0.384471i
$387$	6.88874	−	11.9316i	0.0178004	−	0.0308311i
$388$	361.183	−	23.0501i	0.930884	−	0.0594074i
$389$	−94.9498	+	54.8193i	−0.244087	+	0.140924i	−0.617054	−	0.786921i	$-0.711674\pi$
$389$	−94.9498	+	54.8193i	−0.244087	+	0.140924i	0.372967	+	0.927845i	$0.378341\pi$
$390$	−439.218	+	14.0008i	−1.12620	+	0.0358996i
$391$		−	2.57258i		−	0.00657948i
$392$		0			0
$393$	434.971			1.10680
$394$	1.38045	+	43.3058i	0.00350368	+	0.109913i
$395$	−231.969	−	401.782i	−0.587263	−	1.01717i
$396$	−243.695	+	15.5522i	−0.615391	+	0.0392733i
$397$	269.280	+	155.469i	0.678288	+	0.391610i	0.799210	−	0.601052i	$-0.205252\pi$
$397$	269.280	+	155.469i	0.678288	+	0.391610i	−0.120922	+	0.992662i	$0.538585\pi$
$398$	309.160	−	191.880i	0.776785	−	0.482111i
$399$		0			0
$400$	−11.2248	−	14.7329i	−0.0280619	−	0.0368323i
$401$	211.952	−	367.111i	0.528557	−	0.915488i	−0.470888	−	0.882193i	$-0.656066\pi$
$401$	211.952	−	367.111i	0.528557	−	0.915488i	0.999446	−	0.0332953i	$-0.0106002\pi$
$402$	−59.9048	+	111.843i	−0.149017	+	0.278216i
$403$	222.998	+	386.243i	0.553344	+	0.958420i
$404$	−603.163	+	401.524i	−1.49298	+	0.993871i
$405$			480.974i			1.18759i
$406$		0			0
$407$		−	1164.88i		−	2.86211i
$408$	−2.68396	+	5.88325i	−0.00657834	+	0.0144197i
$409$	222.272	+	384.986i	0.543451	+	0.941285i	0.998703	+	0.0509223i	$0.0162161\pi$
$409$	222.272	+	384.986i	0.543451	+	0.941285i	−0.455251	+	0.890363i	$0.650451\pi$
$410$	325.665	+	174.431i	0.794305	+	0.425442i
$411$	−60.1288	+	104.146i	−0.146299	+	0.253397i
$412$	−140.870	−	69.7703i	−0.341917	−	0.169345i
$413$		0			0
$414$	−52.9008	+	32.8329i	−0.127780	+	0.0793064i
$415$	−302.417	−	174.601i	−0.728716	−	0.420725i
$416$	−66.3871	−	413.133i	−0.159584	−	0.993108i
$417$	−205.010	−	355.088i	−0.491631	−	0.851529i
$418$	195.721	−	6.23895i	0.468232	−	0.0149257i
$419$	−457.129			−1.09100			−0.545500	−	0.838111i	$-0.683660\pi$
$419$	−457.129			−1.09100			−0.545500	+	0.838111i	$0.683660\pi$
$420$		0			0
$421$		−	25.4812i		−	0.0605255i	−0.999542	−	0.0302628i	$-0.990366\pi$
$421$		−	25.4812i		−	0.0605255i	0.999542	−	0.0302628i	$-0.00963441\pi$
$422$	−42.8191	+	1.36493i	−0.101467	+	0.00323444i
$423$	−178.063	+	102.805i	−0.420953	+	0.243037i
$424$	−141.179	+	100.618i	−0.332970	+	0.237307i
$425$	−0.135955	+	0.235481i	−0.000319894	+	0.000554072i
$426$	277.913	−	172.487i	0.652378	−	0.404898i
$427$		0			0
$428$	−68.2606	+	137.821i	−0.159487	+	0.322013i
$429$	−836.973	−	483.226i	−1.95099	−	1.12640i
$430$	−41.7274	−	22.3498i	−0.0970404	−	0.0519764i
$431$	107.903	−	62.2976i	0.250354	−	0.144542i	−0.369572	−	0.929202i	$-0.620496\pi$
$431$	107.903	−	62.2976i	0.250354	−	0.144542i	0.619926	+	0.784660i	$0.287162\pi$
$432$	−336.290	+	43.0985i	−0.778449	+	0.0997650i
$433$	272.271			0.628802			0.314401	−	0.949290i	$-0.398196\pi$
$433$	272.271			0.628802			0.314401	+	0.949290i	$0.398196\pi$
$434$		0			0
$435$	−582.126			−1.33822
$436$	−92.8271	+	61.7947i	−0.212906	+	0.141731i
$437$	43.2394	−	24.9643i	0.0989459	−	0.0571264i
$438$	181.688	−	339.212i	0.414812	−	0.774458i
$439$	−220.896	−	127.535i	−0.503181	−	0.290512i	0.226845	−	0.973931i	$-0.427159\pi$
$439$	−220.896	−	127.535i	−0.503181	−	0.290512i	−0.730026	+	0.683419i	$0.760492\pi$
$440$	80.0823	+	835.146i	0.182005	+	1.89806i
$441$		0			0
$442$	−5.21929	+	3.23935i	−0.0118084	+	0.00732885i
$443$	−65.6370	+	113.687i	−0.148165	+	0.256629i	−0.930549	−	0.366167i	$-0.880670\pi$
$443$	−65.6370	+	113.687i	−0.148165	+	0.256629i	0.782384	+	0.622796i	$0.214003\pi$
$444$	47.5486	+	745.062i	0.107091	+	1.67807i
$445$	−675.557	+	390.033i	−1.51811	+	0.876479i
$446$	12.4867	+	391.717i	0.0279970	+	0.878289i
$447$		−	419.601i		−	0.938704i
$448$		0			0
$449$	−642.824			−1.43168			−0.715839	−	0.698265i	$-0.753956\pi$
$449$	−642.824			−1.43168			−0.715839	+	0.698265i	$0.753956\pi$
$450$	6.57741	−	0.209666i	0.0146165	−	0.000465925i
$451$	406.248	+	703.642i	0.900772	+	1.56018i
$452$	329.098	−	21.0025i	0.728093	−	0.0464657i
$453$	656.856	+	379.236i	1.45001	+	0.837165i
$454$	−28.7559	−	46.3320i	−0.0633390	−	0.102053i
$455$		0			0
$456$	−124.930	+	11.9795i	−0.273968	+	0.0262709i
$457$	−346.544	+	600.232i	−0.758302	+	1.31342i	0.185413	+	0.982661i	$0.440638\pi$
$457$	−346.544	+	600.232i	−0.758302	+	1.31342i	−0.943716	+	0.330758i	$0.892696\pi$
$458$	310.906	+	166.526i	0.678835	+	0.363595i
$459$	2.48866	+	4.31048i	0.00542191	+	0.00939102i
$460$	118.539	+	178.067i	0.257693	+	0.387103i
$461$		−	258.699i		−	0.561170i	−0.959829	−	0.280585i	$-0.909472\pi$
$461$		−	258.699i		−	0.561170i	0.959829	−	0.280585i	$-0.0905285\pi$
$462$		0			0
$463$		−	637.226i		−	1.37630i	−0.725569	−	0.688150i	$-0.758423\pi$
$463$		−	637.226i		−	1.37630i	0.725569	−	0.688150i	$-0.241577\pi$
$464$	−70.4616	−	549.800i	−0.151857	−	1.18491i
$465$	286.563	+	496.341i	0.616264	+	1.06740i
$466$	−67.8359	+	126.650i	−0.145571	+	0.271782i
$467$	−99.7417	+	172.758i	−0.213580	+	0.369931i	−0.952832	−	0.303498i	$-0.901846\pi$
$467$	−99.7417	+	172.758i	−0.213580	+	0.369931i	0.739253	+	0.673428i	$0.235179\pi$
$468$	133.224	+	65.9835i	0.284666	+	0.140990i
$469$		0			0
$470$	372.524	+	600.216i	0.792603	+	1.27705i
$471$	−20.1766	−	11.6490i	−0.0428378	−	0.0247324i
$472$	162.046	+	227.370i	0.343317	+	0.481715i
$473$	−52.0524	−	90.1575i	−0.110047	−	0.190608i
$474$	20.8347	+	653.603i	0.0439552	+	1.37891i
$475$	−5.27721			−0.0111099
$476$		0			0
$477$		−	61.5966i		−	0.129133i
$478$	4.53010	+	142.113i	0.00947720	+	0.297308i
$479$	−583.840	+	337.080i	−1.21887	+	0.703716i	−0.964677	−	0.263436i	$-0.915144\pi$
$479$	−583.840	+	337.080i	−1.21887	+	0.703716i	−0.254196	+	0.967153i	$0.581811\pi$
$480$	−85.3105	−	530.895i	−0.177730	−	1.10603i
$481$	−354.602	+	614.188i	−0.737218	+	1.27690i
$482$	59.1792	+	95.3505i	0.122778	+	0.197823i
$483$		0			0
$484$	−604.115	+	1219.74i	−1.24817	+	2.52012i
$485$	382.609	+	220.899i	0.788885	+	0.455463i
$486$	140.006	−	261.393i	0.288079	−	0.537846i
$487$	347.898	−	200.859i	0.714370	−	0.412442i	−0.0983072	−	0.995156i	$-0.531343\pi$
$487$	347.898	−	200.859i	0.714370	−	0.412442i	0.812677	+	0.582715i	$0.198009\pi$
$488$	−462.914	−	211.183i	−0.948593	−	0.432752i
$489$	−713.181			−1.45845
$490$		0			0
$491$	428.880			0.873482			0.436741	−	0.899587i	$-0.356133\pi$
$491$	428.880			0.873482			0.436741	+	0.899587i	$0.356133\pi$
$492$	−288.560	−	433.471i	−0.586504	−	0.881038i
$493$	−7.04719	+	4.06870i	−0.0142945	+	0.00825293i
$494$	−105.094	−	56.2902i	−0.212741	−	0.113948i
$495$	−258.152	−	149.044i	−0.521518	−	0.301099i
$496$	−434.093	+	330.727i	−0.875187	+	0.666789i
$497$		0			0
$498$	259.561	+	418.209i	0.521207	+	0.839778i
$499$	−91.3096	+	158.153i	−0.182985	+	0.316940i	−0.942896	−	0.333088i	$-0.891909\pi$
$499$	−91.3096	+	158.153i	−0.182985	+	0.316940i	0.759911	+	0.650028i	$0.225243\pi$
$500$	−32.5384	−	509.859i	−0.0650767	−	1.01972i
$501$	−493.316	+	284.816i	−0.984662	+	0.568495i
$502$	−737.532	+	23.5101i	−1.46919	+	0.0468329i
$503$		−	380.158i		−	0.755781i	−0.925850	−	0.377891i	$-0.876650\pi$
$503$		−	380.158i		−	0.755781i	0.925850	−	0.377891i	$-0.123350\pi$
$504$		0			0
$505$	−884.516			−1.75152
$506$	14.9890	+	470.219i	0.0296226	+	0.929287i
$507$	3.41094	+	5.90792i	0.00672769	+	0.0116527i
$508$	−6.40475	−	100.359i	−0.0126078	−	0.197557i
$509$	250.747	+	144.769i	0.492627	+	0.284418i	0.725664	−	0.688050i	$-0.241533\pi$
$509$	250.747	+	144.769i	0.492627	+	0.284418i	−0.233037	+	0.972468i	$0.574866\pi$
$510$	−6.70703	+	4.16272i	−0.0131510	+	0.00816219i
$511$		0			0
$512$	491.088	−	144.834i	0.959156	−	0.282878i
$513$	−48.2998	+	83.6576i	−0.0941516	+	0.163075i
$514$	22.4205	−	41.8594i	0.0436197	−	0.0814384i
$515$	−95.9490	−	166.188i	−0.186309	−	0.322696i
$516$	36.9731	+	55.5405i	0.0716533	+	0.107637i
$517$			1553.62i			3.00507i
$518$		0			0
$519$			305.768i			0.589148i
$520$	212.004	−	464.713i	0.407700	−	0.893680i
$521$	−369.449	−	639.905i	−0.709116	−	1.22822i	−0.965185	−	0.261566i	$-0.915761\pi$
$521$	−369.449	−	639.905i	−0.709116	−	1.22822i	0.256070	−	0.966658i	$-0.417572\pi$
$522$	173.607	+	92.9865i	0.332580	+	0.178135i
$523$	323.563	−	560.428i	0.618668	−	1.07156i	−0.371061	−	0.928608i	$-0.621006\pi$
$523$	323.563	−	560.428i	0.618668	−	1.07156i	0.989729	−	0.142956i	$-0.0456606\pi$
$524$	−224.397	+	453.068i	−0.428238	+	0.864633i
$525$		0			0
$526$	125.699	−	78.0151i	0.238972	−	0.148318i
$527$	6.93823	+	4.00579i	0.0131655	+	0.00760111i
$528$	456.299	−	1090.99i	0.864203	−	2.06626i
$529$	−204.524	−	354.245i	−0.386623	−	0.669651i
$530$	−211.523	+	6.74265i	−0.399099	+	0.0127220i
$531$	−99.2014			−0.186820
$532$		0			0
$533$		−	494.666i		−	0.928078i
$534$	1098.97	−	35.0316i	2.05800	−	0.0656022i
$535$	−162.592	+	93.8727i	−0.303911	+	0.175463i
$536$	−85.5917	−	120.095i	−0.159686	−	0.224059i
$537$	−138.303	+	239.549i	−0.257548	+	0.446087i
$538$	570.277	−	353.942i	1.05999	−	0.657885i
$539$		0			0
$540$	−370.876	−	183.689i	−0.686807	−	0.340164i
$541$	154.778	+	89.3612i	0.286096	+	0.165178i	0.636180	−	0.771541i	$-0.280514\pi$
$541$	154.778	+	89.3612i	0.286096	+	0.165178i	−0.350084	+	0.936718i	$0.613847\pi$
$542$	−330.173	−	176.846i	−0.609176	−	0.326284i
$543$	−823.597	+	475.504i	−1.51675	+	0.875698i
$544$	−4.74339	−	5.83072i	−0.00871947	−	0.0107182i
$545$	−136.127			−0.249775
$546$		0			0
$547$	452.236			0.826758			0.413379	−	0.910559i	$-0.364349\pi$
$547$	452.236			0.826758			0.413379	+	0.910559i	$0.364349\pi$
$548$	−77.4593	−	116.358i	−0.141349	−	0.212333i
$549$	156.560	−	90.3898i	0.285172	−	0.164644i
$550$	23.4780	−	43.8336i	0.0426872	−	0.0796974i
$551$	−136.772	−	78.9651i	−0.248224	−	0.143312i
$552$	−28.7807	−	300.143i	−0.0521390	−	0.543737i
$553$		0			0
$554$	−225.314	+	139.841i	−0.406705	+	0.252421i
$555$	−455.680	+	789.261i	−0.821045	+	1.42209i
$556$	475.623	−	30.3535i	0.855437	−	0.0545925i
$557$	739.679	−	427.054i	1.32797	−	0.766704i	0.342985	−	0.939341i	$-0.388562\pi$
$557$	739.679	−	427.054i	1.32797	−	0.766704i	0.984986	+	0.172637i	$0.0552287\pi$
$558$	−6.17763	−	193.798i	−0.0110710	−	0.347307i
$559$			63.3814i			0.113383i
$560$		0			0
$561$	−17.3607			−0.0309460
$562$	662.704	−	21.1248i	1.17919	−	0.0375887i
$563$	124.827	+	216.207i	0.221718	+	0.384026i	0.955330	−	0.295542i	$-0.0955003\pi$
$563$	124.827	+	216.207i	0.221718	+	0.384026i	−0.733612	+	0.679569i	$0.762167\pi$
$564$	−63.4165	−	993.703i	−0.112441	−	1.76188i
$565$	348.621	+	201.276i	0.617028	+	0.356241i
$566$	−70.3636	−	113.371i	−0.124317	−	0.200302i
$567$		0			0
$568$	36.2905	+	378.459i	0.0638917	+	0.666301i
$569$	−52.1763	+	90.3719i	−0.0916982	+	0.158826i	−0.908226	−	0.418480i	$-0.862563\pi$
$569$	−52.1763	+	90.3719i	−0.0916982	+	0.158826i	0.816528	+	0.577306i	$0.195896\pi$
$570$	−135.051	−	72.3355i	−0.236932	−	0.126904i
$571$	324.853	+	562.661i	0.568919	+	0.985396i	0.996673	+	0.0815010i	$0.0259714\pi$
$571$	324.853	+	562.661i	0.568919	+	0.985396i	−0.427755	+	0.903895i	$0.640695\pi$
$572$	935.115	−	622.503i	1.63482	−	1.08829i
$573$			698.630i			1.21925i
$574$		0			0
$575$		−	12.6785i		−	0.0220495i
$576$	−59.3611	+	171.955i	−0.103057	+	0.298534i
$577$	−173.011	−	299.664i	−0.299846	−	0.519349i	0.676255	−	0.736668i	$-0.263602\pi$
$577$	−173.011	−	299.664i	−0.299846	−	0.519349i	−0.976101	+	0.217320i	$0.930269\pi$
$578$	272.853	−	509.419i	0.472064	−	0.881348i
$579$	−150.268	+	260.272i	−0.259531	+	0.449520i
$580$	300.312	−	606.344i	0.517779	−	1.04542i
$581$		0			0
$582$	−328.389	−	529.106i	−0.564242	−	0.909116i
$583$	−403.077	−	232.717i	−0.691385	−	0.399171i
$584$	259.594	+	364.242i	0.444511	+	0.623702i
$585$	90.7412	+	157.168i	0.155113	+	0.268664i
$586$	−18.4291	−	578.136i	−0.0314490	−	0.986581i
$587$	1153.54			1.96514			0.982572	−	0.185885i	$-0.0595150\pi$
$587$	1153.54			1.96514			0.982572	+	0.185885i	$0.0595150\pi$
$588$		0			0
$589$			155.488i			0.263987i
$590$	10.8591	+	340.658i	0.0184052	+	0.577386i
$591$	64.5635	−	37.2758i	0.109244	−	0.0630723i
$592$	−800.589	−	334.842i	−1.35235	−	0.565612i
$593$	440.068	−	762.219i	0.742104	−	1.28536i	−0.209432	−	0.977823i	$-0.567161\pi$
$593$	440.068	−	762.219i	0.742104	−	1.28536i	0.951536	−	0.307538i	$-0.0995052\pi$
$594$	−479.994	−	773.374i	−0.808071	−	1.30198i
$595$		0			0
$596$	437.058	+	216.467i	0.733318	+	0.363200i
$597$	−542.202	−	313.041i	−0.908212	−	0.524356i
$598$	135.237	−	252.488i	0.226149	−	0.422221i
$599$	480.591	−	277.469i	0.802322	−	0.463221i	−0.0419604	−	0.999119i	$-0.513360\pi$
$599$	480.591	−	277.469i	0.802322	−	0.463221i	0.844282	+	0.535898i	$0.180027\pi$
$600$	−13.2274	+	28.9945i	−0.0220457	+	0.0483242i
$601$	666.057			1.10825			0.554124	−	0.832434i	$-0.313054\pi$
$601$	666.057			1.10825			0.554124	+	0.832434i	$0.313054\pi$
$602$		0			0
$603$	52.3977			0.0868950
$604$	−733.878	+	488.540i	−1.21503	+	0.808841i
$605$	−1438.96	+	830.786i	−2.37845	+	1.37320i
$606$	1099.03	+	588.660i	1.81359	+	0.971386i
$607$	167.079	+	96.4633i	0.275254	+	0.158918i	0.631273	−	0.775561i	$-0.282533\pi$
$607$	167.079	+	96.4633i	0.275254	+	0.158918i	−0.356019	+	0.934479i	$0.615866\pi$
$608$	51.9718	−	136.307i	0.0854800	−	0.224189i
$609$		0			0
$610$	−327.536	−	527.732i	−0.536945	−	0.865134i
$611$	472.939	−	819.155i	0.774041	−	1.34068i
$612$	2.66517	−	0.170087i	0.00435485	−	0.000277919i
$613$	−526.747	+	304.117i	−0.859293	+	0.496113i	−0.863775	−	0.503877i	$-0.831906\pi$
$613$	−526.747	+	304.117i	−0.859293	+	0.496113i	0.00448257	+	0.999990i	$0.498573\pi$
$614$	−1.38565	+	0.0441700i	−0.00225676	+	7.19381e-5i
$615$		−	635.668i		−	1.03361i
$616$		0			0
$617$	0.884056			0.00143283			0.000716415	−	1.00000i	$-0.499772\pi$
$617$	0.884056			0.00143283			0.000716415		1.00000i	$0.499772\pi$
$618$	8.61784	+	270.349i	0.0139447	+	0.437458i
$619$	179.262	+	310.491i	0.289600	+	0.501602i	0.973714	−	0.227773i	$-0.0731445\pi$
$619$	179.262	+	310.491i	0.289600	+	0.501602i	−0.684114	+	0.729375i	$0.739811\pi$
$620$	−664.825	+	42.4280i	−1.07230	+	0.0684322i
$621$	−200.987	−	116.040i	−0.323650	−	0.186860i
$622$	−105.626	+	65.5569i	−0.169817	+	0.105397i
$623$		0			0
$624$	−572.694	+	436.326i	−0.917780	+	0.699240i
$625$	297.360	−	515.042i	0.475776	−	0.824068i
$626$	201.698	−	376.573i	0.322202	−	0.601554i
$627$	−168.468	−	291.796i	−0.268689	−	0.465384i
$628$	22.5425	−	15.0065i	0.0358957	−	0.0238956i
$629$			12.7397i			0.0202539i
$630$		0			0
$631$			390.515i			0.618883i	0.950918	+	0.309442i	$0.100142\pi$
$631$			390.515i			0.618883i	−0.950918	+	0.309442i	$0.899858\pi$
$632$	−691.544	−	315.485i	−1.09422	−	0.499185i
$633$	36.8569	+	63.8379i	0.0582257	+	0.100850i
$634$	−41.3567	−	22.1513i	−0.0652313	−	0.0349389i
$635$	61.3797	−	106.313i	0.0966609	−	0.167422i
$636$	267.309	+	132.394i	0.420298	+	0.208166i
$637$		0			0
$638$	1264.39	−	784.742i	1.98180	−	1.23000i
$639$	−116.985	−	67.5415i	−0.183076	−	0.105699i
$640$	596.993	+	185.023i	0.932801	+	0.289098i
$641$	215.968	+	374.068i	0.336924	+	0.583569i	0.983852	−	0.178981i	$-0.0572802\pi$
$641$	215.968	+	374.068i	0.336924	+	0.583569i	−0.646929	+	0.762551i	$0.723947\pi$
$642$	264.499	−	8.43136i	0.411992	−	0.0131330i
$643$	−49.9370			−0.0776625			−0.0388313	−	0.999246i	$-0.512363\pi$
$643$	−49.9370			−0.0776625			−0.0388313	+	0.999246i	$0.512363\pi$
$644$		0			0
$645$			81.4480i			0.126276i
$646$	−2.14050	+	0.0682322i	−0.00331347	+	0.000105623i
$647$	−194.112	+	112.070i	−0.300018	+	0.173216i	−0.642451	−	0.766327i	$-0.722082\pi$
$647$	−194.112	+	112.070i	−0.300018	+	0.173216i	0.342433	+	0.939542i	$0.388749\pi$
$648$	457.351	+	641.719i	0.705789	+	0.990307i
$649$	−374.791	+	649.157i	−0.577490	+	1.00024i
$650$	−25.7223	+	15.9645i	−0.0395728	+	0.0245608i
$651$		0			0
$652$	367.922	−	742.851i	0.564297	−	1.13934i
$653$	69.9434	+	40.3818i	0.107111	+	0.0618405i	0.552598	−	0.833448i	$-0.313636\pi$
$653$	69.9434	+	40.3818i	0.107111	+	0.0618405i	−0.445488	+	0.895288i	$0.646970\pi$
$654$	169.142	+	90.5950i	0.258626	+	0.138524i
$655$	−534.498	+	308.593i	−0.816028	+	0.471134i
$656$	600.369	−	76.9425i	0.915197	−	0.117290i
$657$	−158.919			−0.241886
$658$		0			0
$659$	−940.466			−1.42711			−0.713555	−	0.700599i	$-0.752916\pi$
$659$	−940.466			−1.42711			−0.713555	+	0.700599i	$0.752916\pi$
$660$	1201.67	−	799.945i	1.82071	−	1.21204i
$661$	103.862	−	59.9649i	0.157129	−	0.0907184i	−0.419374	−	0.907814i	$-0.637750\pi$
$661$	103.862	−	59.9649i	0.157129	−	0.0907184i	0.576503	+	0.817095i	$0.304417\pi$
$662$	−479.147	+	894.573i	−0.723788	+	1.35132i
$663$	9.15354	+	5.28480i	0.0138062	+	0.00797104i
$664$	−569.513	+	54.6107i	−0.857700	+	0.0822450i
$665$		0			0
$666$	261.970	−	162.592i	0.393349	−	0.244132i
$667$	189.713	−	328.593i	0.284428	−	0.492643i
$668$	−42.1694	−	660.772i	−0.0631278	−	0.989180i
$669$	584.000	−	337.173i	0.872945	−	0.503995i
$670$	−5.73570	−	179.934i	−0.00856075	−	0.268558i
$671$		−	1366.00i		−	2.03577i
$672$		0			0
$673$	1085.06			1.61227			0.806136	−	0.591731i	$-0.201555\pi$
$673$	1085.06			1.61227			0.806136	+	0.591731i	$0.201555\pi$
$674$	−685.103	+	21.8389i	−1.01647	+	0.0324019i
$675$	12.2649	+	21.2434i	0.0181702	+	0.0314717i
$676$	−7.91338	+	0.505018i	−0.0117062	+	0.000747069i
$677$	−822.639	−	474.951i	−1.21512	−	0.701552i	−0.251253	−	0.967922i	$-0.580842\pi$
$677$	−822.639	−	474.951i	−1.21512	−	0.701552i	−0.963871	+	0.266370i	$0.914176\pi$
$678$	−299.217	−	482.104i	−0.441324	−	0.711068i
$679$		0			0
$680$	−0.875819	−	9.13357i	−0.00128797	−	0.0134317i
$681$	−46.9135	+	81.2566i	−0.0688891	+	0.119319i
$682$	−1291.52	−	691.757i	−1.89372	−	1.01431i
$683$	446.893	+	774.041i	0.654308	+	1.13330i	0.982067	+	0.188534i	$0.0603735\pi$
$683$	446.893	+	774.041i	0.654308	+	1.13330i	−0.327758	+	0.944762i	$0.606293\pi$
$684$	28.7215	+	43.1451i	0.0419905	+	0.0630776i
$685$		−	170.635i		−	0.249102i
$686$		0			0
$687$		−	606.861i		−	0.883349i
$688$	−76.9251	+	9.85862i	−0.111810	+	0.0143294i
$689$	141.683	+	245.402i	0.205636	+	0.356172i
$690$	173.786	−	324.459i	0.251863	−	0.470231i
$691$	604.282	−	1046.65i	0.874504	−	1.51468i	0.0172129	−	0.999852i	$-0.494521\pi$
$691$	604.282	−	1046.65i	0.874504	−	1.51468i	0.857291	−	0.514833i	$-0.172146\pi$
$692$	−318.489	−	157.742i	−0.460244	−	0.227951i
$693$		0			0
$694$	−144.222	−	232.373i	−0.207813	−	0.334831i
$695$	503.838	+	290.891i	0.724947	+	0.418548i
$696$	−776.677	+	553.535i	−1.11591	+	0.795309i
$697$	−4.44293	−	7.69537i	−0.00637436	−	0.0110407i
$698$	−5.22873	−	164.030i	−0.00749102	−	0.235000i
$699$	247.210			0.353662
$700$		0			0
$701$		−	219.477i		−	0.313091i	−0.987671	−	0.156546i	$-0.949964\pi$
$701$		−	219.477i		−	0.313091i	0.987671	−	0.156546i	$-0.0500358\pi$
$702$	17.6559	+	553.882i	0.0251509	+	0.789005i
$703$	−214.126	+	123.626i	−0.304589	+	0.175854i
$704$	900.975	+	1038.11i	1.27979	+	1.47459i
$705$	607.749	−	1052.65i	0.862055	−	1.49312i
$706$	535.108	+	862.175i	0.757944	+	1.22121i
$707$		0			0
$708$	213.221	−	430.502i	0.301159	−	0.608054i
$709$	1095.64	+	632.566i	1.54533	+	0.892195i	0.998489	+	0.0549560i	$0.0175018\pi$
$709$	1095.64	+	632.566i	1.54533	+	0.892195i	0.546838	+	0.837239i	$0.315831\pi$
$710$	−219.132	+	409.121i	−0.308636	+	0.576227i
$711$	233.884	−	135.033i	0.328950	−	0.189920i
$712$	−530.457	+	1162.76i	−0.745023	+	1.63309i
$713$	−373.560			−0.523927
$714$		0			0
$715$	1371.31			1.91792
$716$	−178.165	−	267.638i	−0.248834	−	0.373796i
$717$	211.873	−	122.325i	0.295499	−	0.170606i
$718$	988.724	+	529.576i	1.37705	+	0.737572i
$719$	−1007.59	−	581.735i	−1.40138	−	0.809089i	−0.406848	−	0.913496i	$-0.633372\pi$
$719$	−1007.59	−	581.735i	−1.40138	−	0.809089i	−0.994535	+	0.104407i	$0.966705\pi$
$720$	−176.639	+	134.578i	−0.245332	+	0.186914i
$721$		0			0
$722$	358.820	+	578.136i	0.496981	+	0.800743i
$723$	96.5472	−	167.225i	0.133537	−	0.231293i
$724$	−70.4023	−	1103.17i	−0.0972408	−	1.52371i
$725$	−34.7308	+	20.0518i	−0.0479045	+	0.0276577i
$726$	2340.85	−	74.6187i	3.22431	−	0.102781i
$727$			1303.68i			1.79324i	0.442803	+	0.896619i	$0.353984\pi$
$727$			1303.68i			1.79324i	−0.442803	+	0.896619i	$0.646016\pi$
$728$		0			0
$729$	376.305			0.516193
$730$	17.3960	+	545.728i	0.0238302	+	0.747573i
$731$	0.569271	+	0.986006i	0.000778756	+	0.00134885i
$732$	55.7581	+	873.700i	0.0761722	+	1.19358i
$733$	1087.83	+	628.061i	1.48408	+	0.856836i	0.999836	−	0.0180947i	$-0.00576004\pi$
$733$	1087.83	+	628.061i	1.48408	+	0.856836i	0.484248	+	0.874931i	$0.339093\pi$
$734$	45.7847	−	28.4163i	0.0623770	−	0.0387143i
$735$		0			0
$736$	327.477	+	124.862i	0.444942	+	0.169649i
$737$	197.963	−	342.882i	0.268606	−	0.465240i
$738$	−101.539	+	189.575i	−0.137587	+	0.256876i
$739$	−343.584	−	595.105i	−0.464931	−	0.805284i	0.534267	−	0.845316i	$-0.320588\pi$
$739$	−343.584	−	595.105i	−0.464931	−	0.805284i	−0.999198	+	0.0400312i	$0.987254\pi$
$740$	−587.017	−	881.808i	−0.793266	−	1.19163i
$741$			205.134i			0.276835i
$742$		0			0
$743$			362.628i			0.488059i	0.969768	+	0.244030i	$0.0784694\pi$
$743$			362.628i			0.488059i	−0.969768	+	0.244030i	$0.921531\pi$
$744$	854.297	+	389.734i	1.14825	+	0.523836i
$745$	297.688	+	515.611i	0.399581	+	0.692095i
$746$	−948.571	−	508.070i	−1.27154	−	0.681059i
$747$	101.638	−	176.042i	0.136061	−	0.235665i
$748$	8.95620	−	18.0830i	0.0119735	−	0.0241751i
$749$		0			0
$750$	−746.905	+	463.566i	−0.995874	+	0.618088i
$751$	226.350	+	130.683i	0.301398	+	0.174012i	0.643071	−	0.765807i	$-0.277660\pi$
$751$	226.350	+	130.683i	0.301398	+	0.174012i	−0.341673	+	0.939819i	$0.610994\pi$
$752$	1067.76	+	446.585i	1.41989	+	0.593863i
$753$	634.835	+	1099.57i	0.843074	+	1.46025i
$754$	−905.539	+	28.8656i	−1.20098	+	0.0382833i
$755$	−1076.20			−1.42544
$756$		0			0
$757$			1395.34i			1.84325i	0.388081	+	0.921625i	$0.373138\pi$
$757$			1395.34i			1.84325i	−0.388081	+	0.921625i	$0.626862\pi$
$758$	−364.080	+	11.6057i	−0.480316	+	0.0153109i
$759$	701.037	−	404.744i	0.923633	−	0.533260i
$760$	145.016	−	103.353i	0.190811	−	0.135990i
$761$	−159.750	+	276.695i	−0.209921	+	0.363594i	−0.951690	−	0.307062i	$-0.900654\pi$
$761$	−159.750	+	276.695i	−0.209921	+	0.363594i	0.741768	+	0.670656i	$0.233987\pi$
$762$	−147.019	+	91.2470i	−0.192938	+	0.119747i
$763$		0			0
$764$	−727.695	−	360.415i	−0.952481	−	0.471747i
$765$	2.82327	+	1.63002i	0.00369055	+	0.00213074i
$766$	587.568	+	314.711i	0.767060	+	0.410849i
$767$	395.221	−	228.181i	0.515282	−	0.297498i
$768$	−618.642	−	627.204i	−0.805524	−	0.816672i
$769$	−634.936			−0.825664			−0.412832	−	0.910807i	$-0.635460\pi$
$769$	−634.936			−0.825664			−0.412832	+	0.910807i	$0.635460\pi$
$770$		0			0
$771$	−81.7056			−0.105974
$772$	−193.579	−	290.791i	−0.250750	−	0.376673i
$773$	83.2825	−	48.0832i	0.107739	−	0.0622033i	−0.445162	−	0.895450i	$-0.646854\pi$
$773$	83.2825	−	48.0832i	0.107739	−	0.0622033i	0.552901	+	0.833247i	$0.313521\pi$
$774$	13.0102	−	24.2901i	0.0168090	−	0.0313826i
$775$	34.1938	+	19.7418i	0.0441210	+	0.0254733i
$776$	720.530	−	69.0917i	0.928518	−	0.0890358i
$777$		0			0
$778$	−186.310	+	115.633i	−0.239473	+	0.148629i
$779$	86.2282	−	149.352i	0.110691	−	0.191722i
$780$	−877.097	+	55.9749i	−1.12448	+	0.0717627i
$781$	−883.960	+	510.354i	−1.13183	+	0.653463i
$782$	−0.163928	−	5.14254i	−0.000209626	−	0.00657614i
$783$			734.098i			0.937545i
$784$		0			0
$785$	33.0577			0.0421117
$786$	869.501	−	27.7169i	1.10624	−	0.0352632i
$787$	−659.623	−	1142.50i	−0.838148	−	1.45172i	−0.891441	−	0.453137i	$-0.850305\pi$
$787$	−659.623	−	1142.50i	−0.838148	−	1.45172i	0.0532926	−	0.998579i	$-0.483028\pi$
$788$	5.51899	+	86.4797i	0.00700379	+	0.109746i
$789$	−220.450	−	127.277i	−0.279404	−	0.161314i
$790$	−489.305	−	788.375i	−0.619373	−	0.997943i
$791$		0			0
$792$	−486.152	+	46.6171i	−0.613828	+	0.0588600i
$793$	−415.825	+	720.231i	−0.524370	+	0.908235i
$794$	548.194	+	293.621i	0.690420	+	0.369800i
$795$	182.069	+	315.354i	0.229018	+	0.396671i
$796$	605.780	−	403.266i	0.761030	−	0.506615i
$797$		−	818.575i		−	1.02707i	−0.858068	−	0.513535i	$-0.828336\pi$
$797$		−	818.575i		−	1.02707i	0.858068	−	0.513535i	$-0.171664\pi$
$798$		0			0
$799$		−	16.9911i		−	0.0212655i
$800$	−23.3769	−	28.7356i	−0.0292211	−	0.0359196i
$801$	−227.044	−	393.252i	−0.283451	−	0.490951i
$802$	400.295	−	747.355i	0.499121	−	0.931864i
$803$	−600.409	+	1039.94i	−0.747707	+	1.29507i
$804$	−112.622	+	227.389i	−0.140077	+	0.282823i
$805$		0			0
$806$	470.381	+	757.885i	0.583599	+	0.940304i
$807$	−1000.15	−	577.435i	−1.23934	−	0.715532i
$808$	−1180.13	+	841.074i	−1.46056	+	1.04093i
$809$	−616.362	−	1067.57i	−0.761881	−	1.31962i	−0.941880	−	0.335950i	$-0.890943\pi$
$809$	−616.362	−	1067.57i	−0.761881	−	1.31962i	0.179998	−	0.983667i	$-0.442391\pi$
$810$	30.6482	+	961.459i	0.0378373	+	1.18699i
$811$	1009.05			1.24421			0.622103	−	0.782935i	$-0.286278\pi$
$811$	1009.05			1.24421			0.622103	+	0.782935i	$0.286278\pi$
$812$		0			0
$813$			644.468i			0.792703i
$814$	−74.2274	−	2328.57i	−0.0911884	−	2.86066i
$815$	876.366	−	505.970i	1.07530	−	0.620822i
$816$	−4.99031	+	11.9316i	−0.00611558	+	0.0146220i
$817$	−11.0484	+	19.1364i	−0.0135231	+	0.0234227i
$818$	468.849	+	755.417i	0.573165	+	0.923493i
$819$		0			0
$820$	662.114	+	327.934i	0.807457	+	0.399919i
$821$	−813.278	−	469.547i	−0.990595	−	0.571920i	−0.0851429	−	0.996369i	$-0.527135\pi$
$821$	−813.278	−	469.547i	−0.990595	−	0.571920i	−0.905452	+	0.424448i	$0.860468\pi$
$822$	−113.560	+	212.018i	−0.138151	+	0.257930i
$823$	789.036	−	455.550i	0.958731	−	0.553524i	0.0629491	−	0.998017i	$-0.479949\pi$
$823$	789.036	−	455.550i	0.958731	−	0.553524i	0.895782	+	0.444493i	$0.146616\pi$
$824$	−286.042	−	130.493i	−0.347138	−	0.158366i
$825$	−85.5591			−0.103708
$826$		0			0
$827$	−65.6564			−0.0793910			−0.0396955	−	0.999212i	$-0.512639\pi$
$827$	−65.6564			−0.0793910			−0.0396955	+	0.999212i	$0.512639\pi$
$828$	−103.656	+	69.0033i	−0.125188	+	0.0833373i
$829$	1312.84	−	757.970i	1.58365	−	0.914318i	0.589324	−	0.807897i	$-0.299394\pi$
$829$	1312.84	−	757.970i	1.58365	−	0.914318i	0.994321	−	0.106421i	$-0.0339391\pi$
$830$	−615.653	−	329.754i	−0.741751	−	0.397294i
$831$	395.154	+	228.142i	0.475516	+	0.274539i
$832$	−159.032	−	821.616i	−0.191144	−	0.987519i
$833$		0			0
$834$	−432.438	−	696.752i	−0.518511	−	0.835433i
$835$	404.129	−	699.971i	0.483986	−	0.838289i
$836$	390.846	−	24.9431i	0.467519	−	0.0298363i
$837$	625.918	−	361.374i	0.747811	−	0.431749i
$838$	−913.794	+	29.1288i	−1.09045	+	0.0347599i
$839$			869.972i			1.03692i	0.855103	+	0.518458i	$0.173494\pi$
$839$			869.972i			1.03692i	−0.855103	+	0.518458i	$0.826506\pi$
$840$		0			0
$841$	−359.174			−0.427080
$842$	−1.62369	−	50.9366i	−0.00192838	−	0.0604948i
$843$	−570.427	−	988.008i	−0.676663	−	1.17201i
$844$	−85.5078	+	5.45697i	−0.101313	+	0.00646560i
$845$	−8.38282	−	4.83982i	−0.00992049	−	0.00572760i
$846$	−349.395	+	216.852i	−0.412996	+	0.256326i
$847$		0			0
$848$	−275.804	+	210.130i	−0.325240	+	0.247795i
$849$	−114.794	+	198.829i	−0.135211	+	0.234192i
$850$	−0.256766	+	0.479385i	−0.000302078	+	0.000563983i
$851$	−297.010	−	514.436i	−0.349013	−	0.604508i
$852$	544.553	−	362.507i	0.639147	−	0.425478i
$853$		−	1643.91i		−	1.92721i	−0.267322	−	0.963607i	$-0.586139\pi$
$853$		−	1643.91i		−	1.92721i	0.267322	−	0.963607i	$-0.413861\pi$
$854$		0			0
$855$			63.2706i			0.0740007i
$856$	−127.670	+	279.852i	−0.149147	+	0.326930i
$857$	143.029	+	247.734i	0.166895	+	0.289071i	0.937327	−	0.348452i	$-0.113292\pi$
$857$	143.029	+	247.734i	0.166895	+	0.289071i	−0.770431	+	0.637523i	$0.779959\pi$
$858$	−1703.89	−	912.629i	−1.98588	−	1.06367i
$859$	359.891	−	623.350i	0.418965	−	0.725669i	−0.576870	−	0.816836i	$-0.695726\pi$
$859$	359.891	−	623.350i	0.418965	−	0.725669i	0.995836	+	0.0911667i	$0.0290596\pi$
$860$	−84.8365	−	42.0181i	−0.0986471	−	0.0488582i
$861$		0			0
$862$	211.726	−	131.408i	0.245622	−	0.152445i
$863$	970.358	+	560.236i	1.12440	+	0.649173i	0.942521	−	0.334147i	$-0.108448\pi$
$863$	970.358	+	560.236i	1.12440	+	0.649173i	0.181880	+	0.983321i	$0.441782\pi$
$864$	−669.493	+	107.582i	−0.774876	+	0.124516i
$865$	−216.929	−	375.731i	−0.250785	−	0.434372i
$866$	544.266	−	17.3494i	0.628483	−	0.0200340i
$867$	−994.339			−1.14687
$868$		0			0
$869$		−	2040.66i		−	2.34828i
$870$	−1163.66	+	37.0937i	−1.33754	+	0.0426364i
$871$	−208.754	+	120.524i	−0.239671	+	0.138374i
$872$	−181.622	+	129.442i	−0.208282	+	0.148442i
$873$	−128.589	+	222.723i	−0.147296	+	0.255123i
$874$	84.8441	−	52.6584i	0.0970756	−	0.0602499i
$875$		0			0
$876$	341.576	−	689.658i	0.389927	−	0.787281i
$877$	125.920	+	72.6998i	0.143580	+	0.0828960i	0.570069	−	0.821597i	$-0.306916\pi$
$877$	125.920	+	72.6998i	0.143580	+	0.0828960i	−0.426489	+	0.904493i	$0.640250\pi$
$878$	−449.695	−	240.864i	−0.512181	−	0.274333i
$879$	−861.928	+	497.634i	−0.980578	+	0.566137i
$880$	213.300	+	1664.34i	0.242386	+	1.89130i
$881$	−476.080			−0.540386			−0.270193	−	0.962806i	$-0.587087\pi$
$881$	−476.080			−0.540386			−0.270193	+	0.962806i	$0.587087\pi$
$882$		0			0
$883$	−1101.22			−1.24714			−0.623568	−	0.781769i	$-0.714318\pi$
$883$	−1101.22			−1.24714			−0.623568	+	0.781769i	$0.714318\pi$
$884$	−10.2269	+	6.80799i	−0.0115689	+	0.00770135i
$885$	507.878	−	293.223i	0.573873	−	0.331326i
$886$	−123.963	+	231.440i	−0.139913	+	0.261219i
$887$	1291.67	+	745.743i	1.45622	+	0.840748i	0.998822	−	0.0485153i	$-0.0154490\pi$
$887$	1291.67	+	745.743i	1.45622	+	0.840748i	0.457396	+	0.889263i	$0.348782\pi$
$888$	142.525	+	1486.34i	0.160501	+	1.67380i
$889$		0			0
$890$	−1325.57	+	822.717i	−1.48941	+	0.924401i
$891$	−1057.80	+	1832.16i	−1.18720	+	2.05629i
$892$	49.9213	+	782.240i	0.0559655	+	0.876951i
$893$	285.584	−	164.882i	0.319802	−	0.184638i
$894$	−26.7374	−	838.776i	−0.0299076	−	0.938228i
$895$		−	392.481i		−	0.438526i
$896$		0			0
$897$	−492.834			−0.549425
$898$	−1284.99	+	40.9614i	−1.43095	+	0.0456141i
$899$	590.809	+	1023.31i	0.657184	+	1.13828i
$900$	13.1348	−	0.838240i	0.0145942	−	0.000931378i
$901$	4.40825	+	2.54510i	0.00489262	+	0.00282476i
$902$	856.920	+	1380.68i	0.950023	+	1.53069i
$903$		0			0
$904$	656.524	−	62.9541i	0.726243	−	0.0696395i
$905$	674.698	−	1168.61i	0.745522	−	1.29128i
$906$	1337.21	+	716.231i	1.47595	+	0.790542i
$907$	−577.731	−	1000.66i	−0.636969	−	1.10326i	−0.986094	−	0.166187i	$-0.946855\pi$
$907$	−577.731	−	1000.66i	−0.636969	−	1.10326i	0.349125	−	0.937076i	$-0.386479\pi$
$908$	−60.4350	−	90.7846i	−0.0665583	−	0.0999830i
$909$		−	514.891i		−	0.566436i
$910$		0			0
$911$			944.690i			1.03698i	0.855083	+	0.518491i	$0.173506\pi$
$911$			944.690i			1.03698i	−0.855083	+	0.518491i	$0.826494\pi$
$912$	−248.969	+	31.9075i	−0.272992	+	0.0349863i
$913$	−767.991	−	1330.20i	−0.841173	−	1.45695i
$914$	−654.489	+	1221.94i	−0.716071	+	1.33691i
$915$	−534.355	+	925.530i	−0.583995	+	1.01151i
$916$	632.108	+	313.072i	0.690074	+	0.341782i
$917$		0			0
$918$	5.24945	+	8.45800i	0.00571836	+	0.00921351i
$919$	129.167	+	74.5748i	0.140552	+	0.0811478i	0.568627	−	0.822595i	$-0.307475\pi$
$919$	129.167	+	74.5748i	0.140552	+	0.0811478i	−0.428075	+	0.903743i	$0.640808\pi$
$920$	248.304	+	348.401i	0.269896	+	0.378696i
$921$	1.19271	+	2.06583i	0.00129501	+	0.00224303i
$922$	−16.4846	−	517.136i	−0.0178792	−	0.560885i
$923$	621.430			0.673272
$924$		0			0
$925$			62.7851i			0.0678758i
$926$	−40.6048	−	1273.81i	−0.0438497	−	1.37560i
$927$	96.7409	−	55.8534i	0.104359	−	0.0602517i
$928$	−175.885	−	1094.55i	−0.189532	−	1.17947i
$929$	−29.4199	+	50.9568i	−0.0316684	+	0.0548513i	−0.881425	−	0.472324i	$-0.843415\pi$
$929$	−29.4199	+	50.9568i	−0.0316684	+	0.0548513i	0.849757	+	0.527175i	$0.176749\pi$
$930$	604.462	+	973.918i	0.649959	+	1.04722i
$931$		0			0
$932$	−127.533	+	257.494i	−0.136838	+	0.276282i
$933$	185.246	+	106.952i	0.198549	+	0.114632i
$934$	−188.374	+	351.695i	−0.201685	+	0.376548i
$935$	21.3331	−	12.3167i	0.0228161	−	0.0131729i
$936$	270.517	+	123.411i	0.289014	+	0.131849i
$937$	1700.18			1.81449			0.907246	−	0.420601i	$-0.138181\pi$
$937$	1700.18			1.81449			0.907246	+	0.420601i	$0.138181\pi$
$938$		0			0
$939$	−735.036			−0.782786
$940$	782.915	+	1176.08i	0.832888	+	1.25115i
$941$	−49.0270	+	28.3058i	−0.0521010	+	0.0300805i	−0.525824	−	0.850593i	$-0.676243\pi$
$941$	−49.0270	+	28.3058i	−0.0521010	+	0.0300805i	0.473723	+	0.880674i	$0.342910\pi$
$942$	−41.0750	−	22.0004i	−0.0436041	−	0.0233550i
$943$	358.816	+	207.163i	0.380505	+	0.219685i
$944$	338.415	+	444.182i	0.358490	+	0.470532i
$945$		0			0
$946$	−109.797	−	176.907i	−0.116064	−	0.187005i
$947$	−121.267	+	210.040i	−0.128053	+	0.221795i	−0.922922	−	0.384986i	$-0.874206\pi$
$947$	−121.267	+	210.040i	−0.128053	+	0.221795i	0.794869	+	0.606781i	$0.207540\pi$
$948$	83.2967	+	1305.22i	0.0878657	+	1.37681i
$949$	633.138	−	365.542i	0.667163	−	0.385187i
$950$	−10.5491	+	0.336270i	−0.0111043	+	0.000353968i
$951$			80.7244i			0.0848837i
$952$		0			0
$953$	−364.070			−0.382025			−0.191013	−	0.981588i	$-0.561177\pi$
$953$	−364.070			−0.382025			−0.191013	+	0.981588i	$0.561177\pi$
$954$	−3.92500	−	123.131i	−0.00411426	−	0.129068i
$955$	−495.647	−	858.485i	−0.519002	−	0.898938i
$956$	18.1112	+	283.793i	0.0189448	+	0.296855i
$957$	−2217.47	−	1280.26i	−2.31711	−	1.33778i
$958$	−1145.61	+	711.021i	−1.19583	+	0.742193i
$959$		0			0
$960$	−204.364	−	1055.81i	−0.212879	−	1.09981i
$961$	101.174	−	175.238i	0.105280	−	0.182350i
$962$	−669.707	+	1250.35i	−0.696161	+	1.29974i
$963$	−54.6448	−	94.6475i	−0.0567443	−	0.0982840i
$964$	124.374	+	186.833i	0.129019	+	0.193810i
$965$		−	426.435i		−	0.441901i
$966$		0			0
$967$		−	1221.99i		−	1.26369i	−0.775093	−	0.631847i	$-0.782297\pi$
$967$		−	1221.99i		−	1.26369i	0.775093	−	0.631847i	$-0.217703\pi$
$968$	−1129.89	+	2476.73i	−1.16725	+	2.55861i
$969$	1.84245	+	3.19122i	0.00190139	+	0.00329331i
$970$	778.906	+	417.194i	0.802996	+	0.430097i
$971$	−544.266	+	942.696i	−0.560521	+	0.970851i	0.436930	+	0.899496i	$0.356066\pi$
$971$	−544.266	+	942.696i	−0.560521	+	0.970851i	−0.997451	+	0.0713553i	$0.977268\pi$
$972$	263.215	−	531.443i	0.270797	−	0.546752i
$973$		0			0
$974$	682.644	−	423.683i	0.700866	−	0.434992i
$975$	45.1115	+	26.0451i	0.0462682	+	0.0267130i
$976$	−938.814	−	392.654i	−0.961900	−	0.402309i
$977$	530.757	+	919.299i	0.543252	+	0.940940i	0.998715	+	0.0506853i	$0.0161405\pi$
$977$	530.757	+	919.299i	0.543252	+	0.940940i	−0.455463	+	0.890255i	$0.650526\pi$
$978$	−1425.64	+	45.4447i	−1.45771	+	0.0464669i
$979$	−3431.17			−3.50477
$980$		0			0
$981$		−	79.2419i		−	0.0807766i
$982$	857.324	−	27.3287i	0.873039	−	0.0278296i
$983$	1145.42	−	661.306i	1.16522	−	0.672743i	0.212674	−	0.977123i	$-0.431783\pi$
$983$	1145.42	−	661.306i	1.16522	−	0.672743i	0.952551	+	0.304381i	$0.0984495\pi$
$984$	−604.448	−	848.114i	−0.614277	−	0.861904i
$985$	−52.8910	+	91.6099i	−0.0536964	+	0.0930049i
$986$	−13.8280	+	8.58232i	−0.0140243	+	0.00870417i
$987$		0			0
$988$	−213.669	−	105.826i	−0.216264	−	0.107112i
$989$	−45.9750	−	26.5437i	−0.0464864	−	0.0268389i
$990$	−525.538	−	281.487i	−0.530847	−	0.284330i
$991$	585.266	−	337.903i	0.590581	−	0.340972i	−0.174746	−	0.984613i	$-0.555911\pi$
$991$	585.266	−	337.903i	0.590581	−	0.340972i	0.765327	+	0.643642i	$0.222577\pi$
$992$	−846.670	+	688.780i	−0.853498	+	0.694335i
$993$	1746.12			1.75843
$994$		0			0
$995$	888.354			0.892818
$996$	545.508	+	819.454i	0.547699	+	0.822745i
$997$	−354.395	+	204.610i	−0.355462	+	0.205226i	−0.667088	−	0.744979i	$-0.732460\pi$
$997$	−354.395	+	204.610i	−0.355462	+	0.205226i	0.311627	+	0.950205i	$0.399126\pi$
$998$	−172.449	+	321.963i	−0.172794	+	0.322609i
$999$	995.309	+	574.642i	0.996305	+	0.575217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.n.275.8		16
7.2	even	3		392.3.g.m.99.3		8
7.3	odd	6		392.3.k.o.67.3		16
7.4	even	3	inner	392.3.k.n.67.3		16
7.5	odd	6		56.3.g.b.43.3	✓	8
7.6	odd	2		392.3.k.o.275.8		16
8.3	odd	2	inner	392.3.k.n.275.3		16
21.5	even	6		504.3.g.b.379.6		8
28.19	even	6		224.3.g.b.15.6		8
28.23	odd	6		1568.3.g.m.687.3		8
56.3	even	6		392.3.k.o.67.8		16
56.5	odd	6		224.3.g.b.15.5		8
56.11	odd	6	inner	392.3.k.n.67.8		16
56.19	even	6		56.3.g.b.43.4	yes	8
56.27	even	2		392.3.k.o.275.3		16
56.37	even	6		1568.3.g.m.687.4		8
56.51	odd	6		392.3.g.m.99.4		8
84.47	odd	6		2016.3.g.b.1135.3		8
112.5	odd	12		1792.3.d.j.1023.11		16
112.19	even	12		1792.3.d.j.1023.12		16
112.61	odd	12		1792.3.d.j.1023.6		16
112.75	even	12		1792.3.d.j.1023.5		16
168.5	even	6		2016.3.g.b.1135.6		8
168.131	odd	6		504.3.g.b.379.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.3	✓	8	7.5	odd	6
56.3.g.b.43.4	yes	8	56.19	even	6
224.3.g.b.15.5		8	56.5	odd	6
224.3.g.b.15.6		8	28.19	even	6
392.3.g.m.99.3		8	7.2	even	3
392.3.g.m.99.4		8	56.51	odd	6
392.3.k.n.67.3		16	7.4	even	3	inner
392.3.k.n.67.8		16	56.11	odd	6	inner
392.3.k.n.275.3		16	8.3	odd	2	inner
392.3.k.n.275.8		16	1.1	even	1	trivial
392.3.k.o.67.3		16	7.3	odd	6
392.3.k.o.67.8		16	56.3	even	6
392.3.k.o.275.3		16	56.27	even	2
392.3.k.o.275.8		16	7.6	odd	2
504.3.g.b.379.5		8	168.131	odd	6
504.3.g.b.379.6		8	21.5	even	6
1568.3.g.m.687.3		8	28.23	odd	6
1568.3.g.m.687.4		8	56.37	even	6
1792.3.d.j.1023.5		16	112.75	even	12
1792.3.d.j.1023.6		16	112.61	odd	12
1792.3.d.j.1023.11		16	112.5	odd	12
1792.3.d.j.1023.12		16	112.19	even	12
2016.3.g.b.1135.3		8	84.47	odd	6
2016.3.g.b.1135.6		8	168.5	even	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.99898 - 0.0637211i) q^{2} +(-1.72064 - 2.98023i) q^{3} +(3.99188 - 0.254755i) q^{4} +(4.22869 + 2.44143i) q^{5} +(-3.62943 - 5.84780i) q^{6} +(7.96347 - 0.763618i) q^{8} +(-1.42120 + 2.46158i) q^{9} +O(q^{10})\)	\(q+(1.99898 - 0.0637211i) q^{2} +(-1.72064 - 2.98023i) q^{3} +(3.99188 - 0.254755i) q^{4} +(4.22869 + 2.44143i) q^{5} +(-3.62943 - 5.84780i) q^{6} +(7.96347 - 0.763618i) q^{8} +(-1.42120 + 2.46158i) q^{9} +(8.60865 + 4.61093i) q^{10} +(10.7388 + 18.6001i) q^{11} +(-7.62781 - 11.4584i) q^{12} -13.0760i q^{13} -16.8033i q^{15} +(15.8702 - 2.03390i) q^{16} +(-0.117445 - 0.203420i) q^{17} +(-2.68409 + 5.01123i) q^{18} +(2.27936 - 3.94797i) q^{19} +(17.5024 + 8.66863i) q^{20} +(22.6519 + 36.4971i) q^{22} +(9.48497 + 5.47615i) q^{23} +(-15.9780 - 22.4191i) q^{24} +(-0.578804 - 1.00252i) q^{25} +(-0.833219 - 26.1388i) q^{26} -21.1900 q^{27} -34.6435i q^{29} +(-1.07073 - 33.5895i) q^{30} +(-29.5383 + 17.0539i) q^{31} +(31.5947 - 5.07701i) q^{32} +(36.9551 - 64.0082i) q^{33} +(-0.247732 - 0.399150i) q^{34} +(-5.04614 + 10.1884i) q^{36} +(-46.9706 - 27.1185i) q^{37} +(4.30484 - 8.03717i) q^{38} +(-38.9696 + 22.4991i) q^{39} +(35.5394 + 16.2132i) q^{40} +37.8300 q^{41} -4.84714 q^{43} +(47.6064 + 71.5137i) q^{44} +(-12.0196 + 6.93951i) q^{45} +(19.3093 + 10.3424i) q^{46} +(62.6455 + 36.1684i) q^{47} +(-33.3684 - 43.7973i) q^{48} +(-1.22090 - 1.96714i) q^{50} +(-0.404160 + 0.700025i) q^{51} +(-3.33118 - 52.1979i) q^{52} +(-18.7674 + 10.8353i) q^{53} +(-42.3586 + 1.35025i) q^{54} +104.872i q^{55} -15.6878 q^{57} +(-2.20752 - 69.2519i) q^{58} +(17.4503 + 30.2249i) q^{59} +(-4.28073 - 67.0768i) q^{60} +(-55.0803 - 31.8006i) q^{61} +(-57.9599 + 35.9728i) q^{62} +(62.8338 - 12.1621i) q^{64} +(31.9242 - 55.2944i) q^{65} +(69.7941 - 130.306i) q^{66} +(-9.21718 - 15.9646i) q^{67} +(-0.520647 - 0.782109i) q^{68} -37.6899i q^{69} +47.5244i q^{71} +(-9.43794 + 20.6880i) q^{72} +(27.9551 + 48.4197i) q^{73} +(-95.6215 - 51.2164i) q^{74} +(-1.99182 + 3.44994i) q^{75} +(8.09317 - 16.3405i) q^{76} +(-76.4660 + 47.4586i) q^{78} +(-82.2841 - 47.5067i) q^{79} +(72.0757 + 30.1453i) q^{80} +(49.2512 + 85.3055i) q^{81} +(75.6215 - 2.41057i) q^{82} -71.5156 q^{83} -1.14693i q^{85} +(-9.68937 + 0.308865i) q^{86} +(-103.246 + 59.6090i) q^{87} +(99.7214 + 139.921i) q^{88} +(-79.8779 + 138.353i) q^{89} +(-23.5848 + 14.6379i) q^{90} +(39.2579 + 19.4438i) q^{92} +(101.649 + 58.6874i) q^{93} +(127.532 + 68.3083i) q^{94} +(19.2774 - 11.1298i) q^{95} +(-69.4937 - 85.4238i) q^{96} +90.4794 q^{97} -61.0477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more