LMFDB - Embedded newform 392.3.k.o.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			$-1.99898 + 0.0637211i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.o.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	$0.0277661\pi$
$3$	1.72064	+	2.98023i	0.573546	+	0.993411i	−0.422652	+	0.906292i	$0.638901\pi$
$4$	3.99188	−	0.254755i	0.997970	−	0.0636888i
$5$	−4.22869	−	2.44143i	−0.845737	−	0.488287i	0.0134729	−	0.999909i	$-0.495711\pi$
$5$	−4.22869	−	2.44143i	−0.845737	−	0.488287i	−0.859210	+	0.511623i	$0.829045\pi$
$6$	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	$0.167742\pi$
$13$			13.0760i			1.00585i	−0.864331	+	0.502924i	$0.832258\pi$
$14$		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	0.869459	−	0.494005i	$-0.164468\pi$
$17$	0.117445	+	0.203420i	0.00690851	+	0.0119659i	−0.862550	+	0.505971i	$0.831134\pi$
$18$	−2.68409	+	5.01123i	−0.149116	+	0.278402i
$19$	−2.27936	+	3.94797i	−0.119966	+	0.207788i	−0.919754	−	0.392495i	$-0.871612\pi$
$19$	−2.27936	+	3.94797i	−0.119966	+	0.207788i	0.799788	+	0.600283i	$0.204945\pi$
$20$	−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	0.0588837	−	0.998265i	$-0.481246\pi$
$31$	29.5383	−	17.0539i	0.952848	−	0.550127i	0.893965	+	0.448138i	$0.147913\pi$
$32$	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	$-0.652632\pi$
$41$	−37.8300			−0.922682			−0.461341	+	0.887223i	$0.652632\pi$
$42$		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	−0.347143	−	0.937812i	$-0.612848\pi$
$47$	−62.6455	−	36.1684i	−1.33288	−	0.769541i	−0.985741	+	0.168271i	$0.946182\pi$
$48$	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	0.679395	−	0.733773i	$-0.262242\pi$
$59$	−17.4503	−	30.2249i	−0.295768	−	0.512286i	−0.975163	+	0.221487i	$0.928909\pi$
$60$	−4.28073	−	67.0768i	−0.0713454	−	1.11795i
$61$	55.0803	+	31.8006i	0.902955	+	0.521321i	0.878158	−	0.478371i	$-0.158773\pi$
$61$	55.0803	+	31.8006i	0.902955	+	0.521321i	0.0247973	+	0.999693i	$0.492106\pi$
$62$	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	0.608535	−	0.793527i	$-0.291758\pi$
$73$	−27.9551	−	48.4197i	−0.382947	−	0.663284i	−0.991482	+	0.130243i	$0.958424\pi$
$74$	−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	$-0.358225\pi$
$83$	71.5156			0.861634			0.430817	+	0.902439i	$0.358225\pi$
$84$		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	$-0.478712\pi$
$89$	79.8779	−	138.353i	0.897504	−	1.55452i	0.830675	−	0.556758i	$-0.187955\pi$
$90$	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	$-0.654445\pi$
$97$	−90.4794			−0.932777			−0.466389	+	0.884580i	$0.654445\pi$
$98$		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	$-0.312576\pi$
$101$	156.878	−	90.5735i	1.55325	−	0.896767i	0.997875	−	0.0651645i	$-0.0207572\pi$
$102$	−0.763302	+	1.42509i	−0.00748336	+	0.0139715i
$103$	34.0350	+	19.6501i	0.330437	+	0.190778i	0.656035	−	0.754730i	$-0.272232\pi$
$103$	34.0350	+	19.6501i	0.330437	+	0.190778i	−0.325598	+	0.945508i	$0.605566\pi$
$104$	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	−0.517361	−	0.855767i	$-0.673085\pi$
$131$	63.1991	−	109.464i	0.482436	−	0.835603i	0.999797	+	0.0201639i	$0.00641881\pi$
$132$	−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	$-0.640989\pi$
$139$	−119.148			−0.857177			−0.428589	+	0.903500i	$0.640989\pi$
$140$		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	−0.518556	−	0.855044i	$-0.673530\pi$
$157$	−5.86312	+	3.38507i	−0.0373447	+	0.0215610i	0.481211	+	0.876605i	$0.340197\pi$
$158$	−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	$0.165050\pi$
$167$			165.529i			0.991193i	−0.868553	+	0.495596i	$0.834950\pi$
$168$		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	0.705628	−	0.708583i	$-0.250665\pi$
$173$	76.9489	+	44.4265i	0.444791	+	0.256800i	−0.260836	+	0.965383i	$0.583998\pi$
$174$	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	$0.276474\pi$
$181$			276.353i			1.52681i	−0.645919	+	0.763406i	$0.723526\pi$
$182$		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	−0.840579	−	0.541690i	$-0.817785\pi$
$199$	−157.558	+	90.9664i	−0.791751	+	0.457118i	0.0488277	+	0.998807i	$0.484451\pi$
$200$	−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	$-0.855203\pi$
$223$		−	195.958i		−	0.878735i	0.898307	−	0.439367i	$-0.144797\pi$
$224$		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	0.894490	−	0.447088i	$-0.147539\pi$
$227$	13.6326	+	23.6123i	0.0600554	+	0.104019i	−0.834435	+	0.551107i	$0.814206\pi$
$228$	−62.6239	+	3.99655i	−0.274666	+	0.0175287i
$229$	−152.721	−	88.1737i	−0.666906	−	0.385038i	0.127998	−	0.991774i	$-0.459145\pi$
$229$	−152.721	−	88.1737i	−0.666906	−	0.385038i	−0.794903	+	0.606736i	$0.792478\pi$
$230$	−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	0.801930	−	0.597417i	$-0.203806\pi$
$241$	−28.0556	−	48.5938i	−0.116413	−	0.201634i	−0.918344	+	0.395783i	$0.870473\pi$
$242$	−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	$-0.237198\pi$
$251$	368.953			1.46993			0.734966	+	0.678104i	$0.237198\pi$
$252$		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	−0.888197	−	0.459463i	$-0.848042\pi$
$257$	−11.8714	+	20.5619i	−0.0461923	+	0.0800073i	0.842005	+	0.539470i	$0.181375\pi$
$258$	−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	−0.931009	−	0.364997i	$-0.881070\pi$
$269$	−290.632	+	167.797i	−1.08042	+	0.623779i	−0.149408	+	0.988776i	$0.547737\pi$
$270$	−182.418	−	97.7058i	−0.675621	−	0.361873i
$271$	162.186	+	93.6379i	0.598471	+	0.345527i	0.768440	−	0.639922i	$-0.221033\pi$
$271$	162.186	+	93.6379i	0.598471	+	0.345527i	−0.169969	+	0.985449i	$0.554367\pi$
$272$	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	0.918924	−	0.394434i	$-0.129059\pi$
$283$	33.3579	+	57.7776i	0.117873	+	0.204161i	−0.801052	+	0.598595i	$0.795726\pi$
$284$	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	$0.164298\pi$
$293$			289.215i			0.987082i	−0.869723	+	0.493541i	$0.835702\pi$
$294$		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	$-0.499641\pi$
$307$	0.693177			0.00225790			0.00112895	+	0.999999i	$0.499641\pi$
$308$		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	−0.410953	−	0.911657i	$-0.634804\pi$
$311$	53.8307	−	31.0792i	0.173089	−	0.0999330i	0.584042	+	0.811724i	$0.301470\pi$
$312$	−293.153	+	208.929i	−0.939592	+	0.669644i
$313$	−106.797	+	184.978i	−0.341204	+	0.590983i	−0.984657	−	0.174503i	$-0.944168\pi$
$313$	−106.797	+	184.978i	−0.341204	+	0.590983i	0.643452	+	0.765486i	$0.277501\pi$
$314$	−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	$0.0375071\pi$
$349$			82.0565i			0.235119i	−0.993066	+	0.117559i	$0.962493\pi$
$350$		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	$-0.911427\pi$
$353$	−253.684	−	439.393i	−0.718651	−	1.24474i	0.242884	−	0.970055i	$-0.421907\pi$
$354$	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	−0.531452	−	0.847088i	$-0.678354\pi$
$367$	−23.3334	+	13.4716i	−0.0635788	+	0.0367072i	0.467874	+	0.883795i	$0.345020\pi$
$368$	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	0.0734058	−	0.997302i	$-0.476613\pi$
$383$	−288.621	−	166.636i	−0.753580	−	0.435080i	−0.826986	+	0.562222i	$0.809947\pi$
$384$	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	0.120922	−	0.992662i	$-0.461415\pi$
$397$	−269.280	−	155.469i	−0.678288	−	0.391610i	−0.799210	+	0.601052i	$0.794748\pi$
$398$	−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	$-0.983784\pi$
$409$	−222.272	−	384.986i	−0.543451	−	0.941285i	0.455251	−	0.890363i	$-0.349549\pi$
$410$	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	$-0.316340\pi$
$419$	457.129			1.09100			0.545500	+	0.838111i	$0.316340\pi$
$420$		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	$-0.601804\pi$
$433$	−272.271			−0.628802			−0.314401	+	0.949290i	$0.601804\pi$
$434$		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	0.730026	−	0.683419i	$-0.239508\pi$
$439$	220.896	+	127.535i	0.503181	+	0.290512i	−0.226845	+	0.973931i	$0.572841\pi$
$440$	−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	$0.0905285\pi$
$461$			258.699i			0.561170i	−0.959829	+	0.280585i	$0.909472\pi$
$462$		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	−0.739253	−	0.673428i	$-0.764821\pi$
$467$	99.7417	−	172.758i	0.213580	−	0.369931i	0.952832	+	0.303498i	$0.0981544\pi$
$468$	−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	0.254196	−	0.967153i	$-0.418189\pi$
$479$	583.840	−	337.080i	1.21887	−	0.703716i	0.964677	+	0.263436i	$0.0848559\pi$
$480$	−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	$0.123350\pi$
$503$			380.158i			0.755781i	−0.925850	+	0.377891i	$0.876650\pi$
$504$		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	0.233037	−	0.972468i	$-0.425134\pi$
$509$	−250.747	−	144.769i	−0.492627	−	0.284418i	−0.725664	+	0.688050i	$0.758467\pi$
$510$	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	$0.0842390\pi$
$521$	369.449	+	639.905i	0.709116	+	1.22822i	−0.256070	+	0.966658i	$0.582428\pi$
$522$	173.607	+	92.9865i	0.332580	+	0.178135i
$523$	−323.563	+	560.428i	−0.618668	+	1.07156i	0.371061	+	0.928608i	$0.378994\pi$
$523$	−323.563	+	560.428i	−0.618668	+	1.07156i	−0.989729	+	0.142956i	$0.954339\pi$
$524$	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	0.733612	−	0.679569i	$-0.237833\pi$
$563$	−124.827	−	216.207i	−0.221718	−	0.384026i	−0.955330	+	0.295542i	$0.904500\pi$
$564$	−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	0.976101	−	0.217320i	$-0.0697314\pi$
$577$	173.011	+	299.664i	0.299846	+	0.519349i	−0.676255	+	0.736668i	$0.736398\pi$
$578$	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	$-0.940485\pi$
$587$	−1153.54			−1.96514			−0.982572	+	0.185885i	$0.940485\pi$
$588$		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	$0.432839\pi$
$593$	−440.068	+	762.219i	−0.742104	+	1.28536i	−0.951536	+	0.307538i	$0.900495\pi$
$594$	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	$-0.686946\pi$
$601$	−666.057			−1.10825			−0.554124	+	0.832434i	$0.686946\pi$
$602$		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	0.356019	−	0.934479i	$-0.384134\pi$
$607$	−167.079	−	96.4633i	−0.275254	−	0.158918i	−0.631273	+	0.775561i	$0.717467\pi$
$608$	−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	0.684114	−	0.729375i	$-0.260189\pi$
$619$	−179.262	−	310.491i	−0.289600	−	0.501602i	−0.973714	+	0.227773i	$0.926856\pi$
$620$	−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	$-0.487637\pi$
$643$	49.9370			0.0776625			0.0388313	+	0.999246i	$0.487637\pi$
$644$		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	−0.342433	−	0.939542i	$-0.611251\pi$
$647$	194.112	−	112.070i	0.300018	−	0.173216i	0.642451	+	0.766327i	$0.277918\pi$
$648$	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	−0.576503	−	0.817095i	$-0.695583\pi$
$661$	−103.862	+	59.9649i	−0.157129	+	0.0907184i	0.419374	+	0.907814i	$0.362250\pi$
$662$	−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	0.963871	−	0.266370i	$-0.0858242\pi$
$677$	822.639	+	474.951i	1.21512	+	0.701552i	0.251253	+	0.967922i	$0.419158\pi$
$678$	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	$0.505479\pi$
$691$	−604.282	+	1046.65i	−0.874504	+	1.51468i	−0.857291	+	0.514833i	$0.827854\pi$
$692$	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	0.994535	−	0.104407i	$-0.0332946\pi$
$719$	1007.59	+	581.735i	1.40138	+	0.809089i	0.406848	+	0.913496i	$0.366628\pi$
$720$	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	$-0.646016\pi$
$727$		−	1303.68i		−	1.79324i	0.442803	−	0.896619i	$-0.353984\pi$
$728$		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	−0.484248	−	0.874931i	$-0.660907\pi$
$733$	−1087.83	−	628.061i	−1.48408	−	0.856836i	−0.999836	+	0.0180947i	$0.994240\pi$
$734$	−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	−0.741768	−	0.670656i	$-0.766013\pi$
$761$	159.750	−	276.695i	0.209921	−	0.363594i	0.951690	+	0.307062i	$0.0993459\pi$
$762$	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	$-0.364540\pi$
$769$	634.936			0.825664			0.412832	+	0.910807i	$0.364540\pi$
$770$		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	−0.552901	−	0.833247i	$-0.686479\pi$
$773$	−83.2825	+	48.0832i	−0.107739	+	0.0622033i	0.445162	+	0.895450i	$0.353146\pi$
$774$	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	$0.149695\pi$
$787$	659.623	+	1142.50i	0.838148	+	1.45172i	−0.0532926	+	0.998579i	$0.516972\pi$
$788$	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	$0.171664\pi$
$797$			818.575i			1.02707i	−0.858068	+	0.513535i	$0.828336\pi$
$798$		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	$-0.713722\pi$
$811$	−1009.05			−1.24421			−0.622103	+	0.782935i	$0.713722\pi$
$812$		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	$0.700606\pi$
$829$	−1312.84	+	757.970i	−1.58365	+	0.914318i	−0.994321	+	0.106421i	$0.966061\pi$
$830$	−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	$-0.826506\pi$
$839$		−	869.972i		−	1.03692i	0.855103	−	0.518458i	$-0.173494\pi$
$840$		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	$0.413861\pi$
$853$			1643.91i			1.92721i	−0.267322	+	0.963607i	$0.586139\pi$
$854$		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	0.770431	−	0.637523i	$-0.220041\pi$
$857$	−143.029	−	247.734i	−0.166895	−	0.289071i	−0.937327	+	0.348452i	$0.886708\pi$
$858$	−1703.89	−	912.629i	−1.98588	−	1.06367i
$859$	−359.891	+	623.350i	−0.418965	+	0.725669i	−0.995836	−	0.0911667i	$-0.970940\pi$
$859$	−359.891	+	623.350i	−0.418965	+	0.725669i	0.576870	+	0.816836i	$0.304274\pi$
$860$	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	$-0.412913\pi$
$881$	476.080			0.540386			0.270193	+	0.962806i	$0.412913\pi$
$882$		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	−0.457396	−	0.889263i	$-0.651218\pi$
$887$	−1291.67	−	745.743i	−1.45622	−	0.840748i	−0.998822	+	0.0485153i	$0.984551\pi$
$888$	−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	−0.849757	−	0.527175i	$-0.823251\pi$
$929$	29.4199	−	50.9568i	0.0316684	−	0.0548513i	0.881425	+	0.472324i	$0.156585\pi$
$930$	−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	$-0.861819\pi$
$937$	−1700.18			−1.81449			−0.907246	+	0.420601i	$0.861819\pi$
$938$		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	−0.473723	−	0.880674i	$-0.657090\pi$
$941$	49.0270	−	28.3058i	0.0521010	−	0.0300805i	0.525824	+	0.850593i	$0.323757\pi$
$942$	−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	$-0.643934\pi$
$971$	544.266	−	942.696i	0.560521	−	0.970851i	0.997451	−	0.0713553i	$-0.0227324\pi$
$972$	−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	−0.952551	−	0.304381i	$-0.901551\pi$
$983$	−1145.42	+	661.306i	−1.16522	+	0.672743i	−0.212674	+	0.977123i	$0.568217\pi$
$984$	−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	−0.311627	−	0.950205i	$-0.600874\pi$
$997$	354.395	−	204.610i	0.355462	−	0.205226i	0.667088	+	0.744979i	$0.267540\pi$
$998$	−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.o.275.8		16
7.2	even	3		56.3.g.b.43.3	✓	8
7.3	odd	6		392.3.k.n.67.3		16
7.4	even	3	inner	392.3.k.o.67.3		16
7.5	odd	6		392.3.g.m.99.3		8
7.6	odd	2		392.3.k.n.275.8		16
8.3	odd	2	inner	392.3.k.o.275.3		16
21.2	odd	6		504.3.g.b.379.6		8
28.19	even	6		1568.3.g.m.687.3		8
28.23	odd	6		224.3.g.b.15.6		8
56.3	even	6		392.3.k.n.67.8		16
56.5	odd	6		1568.3.g.m.687.4		8
56.11	odd	6	inner	392.3.k.o.67.8		16
56.19	even	6		392.3.g.m.99.4		8
56.27	even	2		392.3.k.n.275.3		16
56.37	even	6		224.3.g.b.15.5		8
56.51	odd	6		56.3.g.b.43.4	yes	8
84.23	even	6		2016.3.g.b.1135.3		8
112.37	even	12		1792.3.d.j.1023.11		16
112.51	odd	12		1792.3.d.j.1023.12		16
112.93	even	12		1792.3.d.j.1023.6		16
112.107	odd	12		1792.3.d.j.1023.5		16
168.107	even	6		504.3.g.b.379.5		8
168.149	odd	6		2016.3.g.b.1135.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.3	✓	8	7.2	even	3
56.3.g.b.43.4	yes	8	56.51	odd	6
224.3.g.b.15.5		8	56.37	even	6
224.3.g.b.15.6		8	28.23	odd	6
392.3.g.m.99.3		8	7.5	odd	6
392.3.g.m.99.4		8	56.19	even	6
392.3.k.n.67.3		16	7.3	odd	6
392.3.k.n.67.8		16	56.3	even	6
392.3.k.n.275.3		16	56.27	even	2
392.3.k.n.275.8		16	7.6	odd	2
392.3.k.o.67.3		16	7.4	even	3	inner
392.3.k.o.67.8		16	56.11	odd	6	inner
392.3.k.o.275.3		16	8.3	odd	2	inner
392.3.k.o.275.8		16	1.1	even	1	trivial
504.3.g.b.379.5		8	168.107	even	6
504.3.g.b.379.6		8	21.2	odd	6
1568.3.g.m.687.3		8	28.19	even	6
1568.3.g.m.687.4		8	56.5	odd	6
1792.3.d.j.1023.5		16	112.107	odd	12
1792.3.d.j.1023.6		16	112.93	even	12
1792.3.d.j.1023.11		16	112.37	even	12
1792.3.d.j.1023.12		16	112.51	odd	12
2016.3.g.b.1135.3		8	84.23	even	6
2016.3.g.b.1135.6		8	168.149	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
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

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