LMFDB - Embedded newform 16.3.f.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,3,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.435968422976$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.2
Root			$-0.671462 - 1.24464i$ of defining polynomial
Character	$\chi$	$=$	16.11
Dual form			16.3.f.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573183 - 1.91611i) q^{2} +(0.146365 + 0.146365i) q^{3} +(-3.34292 + 2.19656i) q^{4} +(3.68585 + 3.68585i) q^{5} +(0.196558 - 0.364346i) q^{6} -9.66442 q^{7} +(6.12494 + 5.14637i) q^{8} -8.95715i q^{9} +O(q^{10})$	\(q+(-0.573183 - 1.91611i) q^{2} +(0.146365 + 0.146365i) q^{3} +(-3.34292 + 2.19656i) q^{4} +(3.68585 + 3.68585i) q^{5} +(0.196558 - 0.364346i) q^{6} -9.66442 q^{7} +(6.12494 + 5.14637i) q^{8} -8.95715i q^{9} +(4.94981 - 9.17513i) q^{10} +(5.51806 - 5.51806i) q^{11} +(-0.810789 - 0.167788i) q^{12} +(-6.27131 + 6.27131i) q^{13} +(5.53948 + 18.5181i) q^{14} +1.07896i q^{15} +(6.35027 - 14.6858i) q^{16} -6.78623 q^{17} +(-17.1629 + 5.13409i) q^{18} +(13.5181 + 13.5181i) q^{19} +(-20.4177 - 4.22533i) q^{20} +(-1.41454 - 1.41454i) q^{21} +(-13.7360 - 7.41033i) q^{22} +17.0790 q^{23} +(0.143230 + 1.64973i) q^{24} +2.17092i q^{25} +(15.6111 + 8.42188i) q^{26} +(2.62831 - 2.62831i) q^{27} +(32.3074 - 21.2285i) q^{28} +(4.85677 - 4.85677i) q^{29} +(2.06740 - 0.618442i) q^{30} +5.25662i q^{31} +(-31.7795 - 3.75011i) q^{32} +1.61531 q^{33} +(3.88975 + 13.0031i) q^{34} +(-35.6216 - 35.6216i) q^{35} +(19.6749 + 29.9431i) q^{36} +(-18.1856 - 18.1856i) q^{37} +(18.1537 - 33.6503i) q^{38} -1.83581 q^{39} +(3.60688 + 41.5443i) q^{40} +48.2302i q^{41} +(-1.89962 + 3.52119i) q^{42} +(-54.5113 + 54.5113i) q^{43} +(-6.32571 + 30.5672i) q^{44} +(33.0147 - 33.0147i) q^{45} +(-9.78937 - 32.7251i) q^{46} -40.4015i q^{47} +(3.07896 - 1.22004i) q^{48} +44.4011 q^{49} +(4.15972 - 1.24434i) q^{50} +(-0.993270 - 0.993270i) q^{51} +(7.18921 - 34.7398i) q^{52} +(10.8996 + 10.8996i) q^{53} +(-6.54262 - 3.52962i) q^{54} +40.6774 q^{55} +(-59.1940 - 49.7367i) q^{56} +3.95715i q^{57} +(-12.0899 - 6.52227i) q^{58} +(50.8898 - 50.8898i) q^{59} +(-2.37000 - 3.60688i) q^{60} +(-17.0147 + 17.0147i) q^{61} +(10.0722 - 3.01300i) q^{62} +86.5657i q^{63} +(11.0298 + 63.0424i) q^{64} -46.2302 q^{65} +(-0.925866 - 3.09510i) q^{66} +(22.9191 + 22.9191i) q^{67} +(22.6858 - 14.9063i) q^{68} +(2.49977 + 2.49977i) q^{69} +(-47.8370 + 88.6724i) q^{70} -51.6047 q^{71} +(46.0968 - 54.8621i) q^{72} -78.5032i q^{73} +(-24.4219 + 45.2692i) q^{74} +(-0.317748 + 0.317748i) q^{75} +(-74.8830 - 15.4966i) q^{76} +(-53.3288 + 53.3288i) q^{77} +(1.05225 + 3.51760i) q^{78} -108.512i q^{79} +(77.5359 - 30.7237i) q^{80} -79.8450 q^{81} +(92.4141 - 27.6447i) q^{82} +(57.3173 + 57.3173i) q^{83} +(7.83581 + 1.62158i) q^{84} +(-25.0130 - 25.0130i) q^{85} +(135.694 + 73.2045i) q^{86} +1.42173 q^{87} +(62.1957 - 5.39985i) q^{88} -44.1276i q^{89} +(-82.1831 - 44.3362i) q^{90} +(60.6086 - 60.6086i) q^{91} +(-57.0937 + 37.5149i) q^{92} +(-0.769387 + 0.769387i) q^{93} +(-77.4136 + 23.1575i) q^{94} +99.6510i q^{95} +(-4.10253 - 5.20031i) q^{96} +112.700 q^{97} +(-25.4499 - 85.0772i) q^{98} +(-49.4261 - 49.4261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21} - 52 q^{22} + 60 q^{23} + 48 q^{24} + 96 q^{26} + 64 q^{27} + 56 q^{28} - 18 q^{29} + 52 q^{30} + 8 q^{32} - 4 q^{33} - 76 q^{34} - 100 q^{35} - 52 q^{36} + 46 q^{37} + 40 q^{38} - 196 q^{39} + 40 q^{40} - 24 q^{42} - 114 q^{43} + 20 q^{44} + 66 q^{45} + 28 q^{46} - 24 q^{48} - 46 q^{49} + 46 q^{50} + 156 q^{51} + 100 q^{52} + 78 q^{53} + 32 q^{54} + 252 q^{55} - 168 q^{56} - 176 q^{58} + 206 q^{59} - 160 q^{60} + 30 q^{61} - 144 q^{62} + 64 q^{64} + 12 q^{65} + 196 q^{66} - 226 q^{67} + 112 q^{68} - 116 q^{69} - 16 q^{70} - 260 q^{71} + 52 q^{72} - 92 q^{74} - 238 q^{75} - 188 q^{76} - 212 q^{77} - 84 q^{78} + 232 q^{80} + 86 q^{81} + 304 q^{82} + 318 q^{83} + 232 q^{84} - 212 q^{85} + 268 q^{86} + 444 q^{87} - 8 q^{88} - 160 q^{90} + 188 q^{91} - 168 q^{92} - 32 q^{93} + 48 q^{94} - 80 q^{96} - 4 q^{97} + 10 q^{98} - 226 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8 + 36 * q^10 - 18 * q^11 + 52 * q^12 - 2 * q^13 + 12 * q^14 - 40 * q^16 - 4 * q^17 - 74 * q^18 + 30 * q^19 - 84 * q^20 - 20 * q^21 - 52 * q^22 + 60 * q^23 + 48 * q^24 + 96 * q^26 + 64 * q^27 + 56 * q^28 - 18 * q^29 + 52 * q^30 + 8 * q^32 - 4 * q^33 - 76 * q^34 - 100 * q^35 - 52 * q^36 + 46 * q^37 + 40 * q^38 - 196 * q^39 + 40 * q^40 - 24 * q^42 - 114 * q^43 + 20 * q^44 + 66 * q^45 + 28 * q^46 - 24 * q^48 - 46 * q^49 + 46 * q^50 + 156 * q^51 + 100 * q^52 + 78 * q^53 + 32 * q^54 + 252 * q^55 - 168 * q^56 - 176 * q^58 + 206 * q^59 - 160 * q^60 + 30 * q^61 - 144 * q^62 + 64 * q^64 + 12 * q^65 + 196 * q^66 - 226 * q^67 + 112 * q^68 - 116 * q^69 - 16 * q^70 - 260 * q^71 + 52 * q^72 - 92 * q^74 - 238 * q^75 - 188 * q^76 - 212 * q^77 - 84 * q^78 + 232 * q^80 + 86 * q^81 + 304 * q^82 + 318 * q^83 + 232 * q^84 - 212 * q^85 + 268 * q^86 + 444 * q^87 - 8 * q^88 - 160 * q^90 + 188 * q^91 - 168 * q^92 - 32 * q^93 + 48 * q^94 - 80 * q^96 - 4 * q^97 + 10 * q^98 - 226 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.573183	−	1.91611i	−0.286591	−	0.958053i
$2$	−0.573183	−	1.91611i	−0.286591	−	0.958053i
$3$	0.146365	+	0.146365i	0.0487885	+	0.0487885i	0.731080	−	0.682292i	$-0.239017\pi$
$3$	0.146365	+	0.146365i	0.0487885	+	0.0487885i	−0.682292	+	0.731080i	$0.739017\pi$
$4$	−3.34292	+	2.19656i	−0.835731	+	0.549139i
$5$	3.68585	+	3.68585i	0.737169	+	0.737169i	0.972029	−	0.234860i	$-0.0754632\pi$
$5$	3.68585	+	3.68585i	0.737169	+	0.737169i	−0.234860	+	0.972029i	$0.575463\pi$
$6$	0.196558	−	0.364346i	0.0327596	−	0.0607243i
$7$	−9.66442			−1.38063			−0.690316	−	0.723508i	$-0.742528\pi$
$7$	−9.66442			−1.38063			−0.690316	+	0.723508i	$0.742528\pi$
$8$	6.12494	+	5.14637i	0.765618	+	0.643296i
$9$		−	8.95715i		−	0.995239i
$10$	4.94981	−	9.17513i	0.494981	−	0.917513i
$11$	5.51806	−	5.51806i	0.501642	−	0.501642i	−0.410306	−	0.911948i	$-0.634578\pi$
$11$	5.51806	−	5.51806i	0.501642	−	0.501642i	0.911948	+	0.410306i	$0.134578\pi$
$12$	−0.810789	−	0.167788i	−0.0675657	−	0.0139824i
$13$	−6.27131	+	6.27131i	−0.482408	+	0.482408i	−0.905900	−	0.423492i	$-0.860804\pi$
$13$	−6.27131	+	6.27131i	−0.482408	+	0.482408i	0.423492	+	0.905900i	$0.360804\pi$
$14$	5.53948	+	18.5181i	0.395677	+	1.32272i
$15$			1.07896i			0.0719308i
$16$	6.35027	−	14.6858i	0.396892	−	0.917865i
$17$	−6.78623			−0.399190			−0.199595	−	0.979878i	$-0.563963\pi$
$17$	−6.78623			−0.399190			−0.199595	+	0.979878i	$0.563963\pi$
$18$	−17.1629	+	5.13409i	−0.953492	+	0.285227i
$19$	13.5181	+	13.5181i	0.711477	+	0.711477i	0.966844	−	0.255367i	$-0.0821964\pi$
$19$	13.5181	+	13.5181i	0.711477	+	0.711477i	−0.255367	+	0.966844i	$0.582196\pi$
$20$	−20.4177	−	4.22533i	−1.02088	−	0.211266i
$21$	−1.41454	−	1.41454i	−0.0673590	−	0.0673590i
$22$	−13.7360	−	7.41033i	−0.624365	−	0.336833i
$23$	17.0790			0.742564			0.371282	−	0.928520i	$-0.378918\pi$
$23$	17.0790			0.742564			0.371282	+	0.928520i	$0.378918\pi$
$24$	0.143230	+	1.64973i	0.00596791	+	0.0687388i
$25$			2.17092i			0.0868370i
$26$	15.6111	+	8.42188i	0.600427	+	0.323919i
$27$	2.62831	−	2.62831i	0.0973447	−	0.0973447i
$28$	32.3074	−	21.2285i	1.15384	−	0.758159i
$29$	4.85677	−	4.85677i	0.167475	−	0.167475i	−0.618394	−	0.785868i	$-0.712216\pi$
$29$	4.85677	−	4.85677i	0.167475	−	0.167475i	0.785868	+	0.618394i	$0.212216\pi$
$30$	2.06740	−	0.618442i	0.0689135	−	0.0206147i
$31$			5.25662i			0.169568i	0.996399	+	0.0847841i	$0.0270201\pi$
$31$			5.25662i			0.169568i	−0.996399	+	0.0847841i	$0.972980\pi$
$32$	−31.7795	−	3.75011i	−0.993109	−	0.117191i
$33$	1.61531			0.0489487
$34$	3.88975	+	13.0031i	0.114404	+	0.382445i
$35$	−35.6216	−	35.6216i	−1.01776	−	1.01776i
$36$	19.6749	+	29.9431i	0.546525	+	0.831752i
$37$	−18.1856	−	18.1856i	−0.491503	−	0.491503i	0.417276	−	0.908780i	$-0.362985\pi$
$37$	−18.1856	−	18.1856i	−0.491503	−	0.491503i	−0.908780	+	0.417276i	$0.862985\pi$
$38$	18.1537	−	33.6503i	0.477729	−	0.885535i
$39$	−1.83581			−0.0470720
$40$	3.60688	+	41.5443i	0.0901721	+	1.03861i
$41$			48.2302i			1.17635i	0.808735	+	0.588173i	$0.200152\pi$
$41$			48.2302i			1.17635i	−0.808735	+	0.588173i	$0.799848\pi$
$42$	−1.89962	+	3.52119i	−0.0452289	+	0.0838379i
$43$	−54.5113	+	54.5113i	−1.26771	+	1.26771i	−0.320435	+	0.947271i	$0.603829\pi$
$43$	−54.5113	+	54.5113i	−1.26771	+	1.26771i	−0.947271	+	0.320435i	$0.896171\pi$
$44$	−6.32571	+	30.5672i	−0.143766	+	0.694709i
$45$	33.0147	−	33.0147i	0.733660	−	0.733660i
$46$	−9.78937	−	32.7251i	−0.212812	−	0.711415i
$47$		−	40.4015i		−	0.859607i	−0.902922	−	0.429804i	$-0.858583\pi$
$47$		−	40.4015i		−	0.859607i	0.902922	−	0.429804i	$-0.141417\pi$
$48$	3.07896	−	1.22004i	0.0641450	−	0.0254175i
$49$	44.4011			0.906144
$50$	4.15972	−	1.24434i	0.0831944	−	0.0248867i
$51$	−0.993270	−	0.993270i	−0.0194759	−	0.0194759i
$52$	7.18921	−	34.7398i	0.138254	−	0.668073i
$53$	10.8996	+	10.8996i	0.205653	+	0.205653i	0.802417	−	0.596764i	$-0.203547\pi$
$53$	10.8996	+	10.8996i	0.205653	+	0.205653i	−0.596764	+	0.802417i	$0.703547\pi$
$54$	−6.54262	−	3.52962i	−0.121160	−	0.0653632i
$55$	40.6774			0.739590
$56$	−59.1940	−	49.7367i	−1.05704	−	0.888155i
$57$			3.95715i			0.0694238i
$58$	−12.0899	−	6.52227i	−0.208447	−	0.112453i
$59$	50.8898	−	50.8898i	0.862538	−	0.862538i	−0.129094	−	0.991632i	$-0.541207\pi$
$59$	50.8898	−	50.8898i	0.862538	−	0.862538i	0.991632	+	0.129094i	$0.0412070\pi$
$60$	−2.37000	−	3.60688i	−0.0395000	−	0.0601147i
$61$	−17.0147	+	17.0147i	−0.278929	+	0.278929i	−0.832682	−	0.553752i	$-0.813196\pi$
$61$	−17.0147	+	17.0147i	−0.278929	+	0.278929i	0.553752	+	0.832682i	$0.313196\pi$
$62$	10.0722	−	3.01300i	0.162455	−	0.0485968i
$63$			86.5657i			1.37406i
$64$	11.0298	+	63.0424i	0.172341	+	0.985037i
$65$	−46.2302			−0.711233
$66$	−0.925866	−	3.09510i	−0.0140283	−	0.0468954i
$67$	22.9191	+	22.9191i	0.342077	+	0.342077i	0.857148	−	0.515071i	$-0.172234\pi$
$67$	22.9191	+	22.9191i	0.342077	+	0.342077i	−0.515071	+	0.857148i	$0.672234\pi$
$68$	22.6858	−	14.9063i	0.333615	−	0.219211i
$69$	2.49977	+	2.49977i	0.0362286	+	0.0362286i
$70$	−47.8370	+	88.6724i	−0.683386	+	1.26675i
$71$	−51.6047			−0.726827			−0.363414	−	0.931628i	$-0.618389\pi$
$71$	−51.6047			−0.726827			−0.363414	+	0.931628i	$0.618389\pi$
$72$	46.0968	−	54.8621i	0.640233	−	0.761973i
$73$		−	78.5032i		−	1.07539i	−0.843141	−	0.537693i	$-0.819296\pi$
$73$		−	78.5032i		−	1.07539i	0.843141	−	0.537693i	$-0.180704\pi$
$74$	−24.4219	+	45.2692i	−0.330025	+	0.611747i
$75$	−0.317748	+	0.317748i	−0.00423664	+	0.00423664i
$76$	−74.8830	−	15.4966i	−0.985303	−	0.203903i
$77$	−53.3288	+	53.3288i	−0.692582	+	0.692582i
$78$	1.05225	+	3.51760i	0.0134904	+	0.0450974i
$79$		−	108.512i		−	1.37357i	−0.726859	−	0.686787i	$-0.759021\pi$
$79$		−	108.512i		−	1.37357i	0.726859	−	0.686787i	$-0.240979\pi$
$80$	77.5359	−	30.7237i	0.969199	−	0.384046i
$81$	−79.8450			−0.985741
$82$	92.4141	−	27.6447i	1.12700	−	0.337130i
$83$	57.3173	+	57.3173i	0.690570	+	0.690570i	0.962357	−	0.271788i	$-0.0876148\pi$
$83$	57.3173	+	57.3173i	0.690570	+	0.690570i	−0.271788	+	0.962357i	$0.587615\pi$
$84$	7.83581	+	1.62158i	0.0932834	+	0.0193045i
$85$	−25.0130	−	25.0130i	−0.294271	−	0.294271i
$86$	135.694	+	73.2045i	1.57784	+	0.851215i
$87$	1.42173			0.0163417
$88$	62.1957	−	5.39985i	0.706770	−	0.0613619i
$89$		−	44.1276i		−	0.495816i	−0.968784	−	0.247908i	$-0.920257\pi$
$89$		−	44.1276i		−	0.495816i	0.968784	−	0.247908i	$-0.0797431\pi$
$90$	−82.1831	−	44.3362i	−0.913146	−	0.492624i
$91$	60.6086	−	60.6086i	0.666028	−	0.666028i
$92$	−57.0937	+	37.5149i	−0.620583	+	0.407771i
$93$	−0.769387	+	0.769387i	−0.00827298	+	0.00827298i
$94$	−77.4136	+	23.1575i	−0.823549	+	0.246356i
$95$			99.6510i			1.04896i
$96$	−4.10253	−	5.20031i	−0.0427347	−	0.0541699i
$97$	112.700			1.16185			0.580926	−	0.813956i	$-0.302691\pi$
$97$	112.700			1.16185			0.580926	+	0.813956i	$0.302691\pi$
$98$	−25.4499	−	85.0772i	−0.259693	−	0.868134i
$99$	−49.4261	−	49.4261i	−0.499253	−	0.499253i
$100$	−4.76856	−	7.25723i	−0.0476856	−	0.0725723i
$101$	97.3859	+	97.3859i	0.964217	+	0.964217i	0.999382	−	0.0351644i	$-0.0111955\pi$
$101$	97.3859	+	97.3859i	0.964217	+	0.964217i	−0.0351644	+	0.999382i	$0.511195\pi$
$102$	−1.33389	+	2.47254i	−0.0130773	+	0.0242405i
$103$	−138.698			−1.34658			−0.673290	−	0.739379i	$-0.735119\pi$
$103$	−138.698			−1.34658			−0.673290	+	0.739379i	$0.735119\pi$
$104$	−70.6858	+	6.13696i	−0.679672	+	0.0590092i
$105$		−	10.4275i		−	0.0993099i
$106$	14.6373	−	27.1323i	0.138088	−	0.255965i
$107$	−31.7386	+	31.7386i	−0.296622	+	0.296622i	−0.839689	−	0.543067i	$-0.817263\pi$
$107$	−31.7386	+	31.7386i	−0.296622	+	0.296622i	0.543067	+	0.839689i	$0.317263\pi$
$108$	−3.01300	+	14.5595i	−0.0278982	+	0.134810i
$109$	0.712308	−	0.712308i	0.00653493	−	0.00653493i	−0.703832	−	0.710367i	$-0.748529\pi$
$109$	0.712308	−	0.712308i	0.00653493	−	0.00653493i	0.710367	+	0.703832i	$0.248529\pi$
$110$	−23.3156	−	77.9423i	−0.211960	−	0.708566i
$111$		−	5.32349i		−	0.0479594i
$112$	−61.3717	+	141.930i	−0.547962	+	1.26723i
$113$	14.8888			0.131759			0.0658795	−	0.997828i	$-0.479015\pi$
$113$	14.8888			0.131759			0.0658795	+	0.997828i	$0.479015\pi$
$114$	7.58233	−	2.26817i	0.0665116	−	0.0198963i
$115$	62.9504	+	62.9504i	0.547395	+	0.547395i
$116$	−5.56763	+	26.9040i	−0.0479968	+	0.231931i
$117$	56.1731	+	56.1731i	0.480112	+	0.480112i
$118$	−126.679	−	68.3410i	−1.07355	−	0.579161i
$119$	65.5850			0.551134
$120$	−5.55273	+	6.60858i	−0.0462727	+	0.0550715i
$121$			60.1021i			0.496711i
$122$	42.3545	+	22.8494i	0.347168	+	0.187290i
$123$	−7.05923	+	7.05923i	−0.0573921	+	0.0573921i
$124$	−11.5465	−	17.5725i	−0.0931166	−	0.141713i
$125$	84.1445	−	84.1445i	0.673156	−	0.673156i
$126$	165.869	−	49.6180i	1.31642	−	0.393794i
$127$		−	106.861i		−	0.841425i	−0.907194	−	0.420712i	$-0.861780\pi$
$127$		−	106.861i		−	0.841425i	0.907194	−	0.420712i	$-0.138220\pi$
$128$	114.474	−	57.2692i	0.894326	−	0.447415i
$129$	−15.9572			−0.123699
$130$	26.4983	+	88.5819i	0.203833	+	0.681399i
$131$	−153.198	−	153.198i	−1.16945	−	1.16945i	−0.982338	−	0.187116i	$-0.940086\pi$
$131$	−153.198	−	153.198i	−1.16945	−	1.16945i	−0.187116	−	0.982338i	$-0.559914\pi$
$132$	−5.39985	+	3.54811i	−0.0409079	+	0.0268796i
$133$	−130.644	−	130.644i	−0.982287	−	0.982287i
$134$	30.7786	−	57.0523i	0.229691	−	0.425764i
$135$	19.3751			0.143519
$136$	−41.5653	−	34.9244i	−0.305627	−	0.256797i
$137$			75.1700i			0.548686i	0.961632	+	0.274343i	$0.0884604\pi$
$137$			75.1700i			0.548686i	−0.961632	+	0.274343i	$0.911540\pi$
$138$	3.35700	−	6.22265i	0.0243261	−	0.0450917i
$139$	−107.425	+	107.425i	−0.772843	+	0.772843i	−0.978603	−	0.205760i	$-0.934034\pi$
$139$	−107.425	+	107.425i	−0.772843	+	0.772843i	0.205760	+	0.978603i	$0.434034\pi$
$140$	197.325	+	40.8353i	1.40946	+	0.291681i
$141$	5.91339	−	5.91339i	0.0419389	−	0.0419389i
$142$	29.5789	+	98.8801i	0.208302	+	0.696339i
$143$			69.2109i			0.483992i
$144$	−131.543	−	56.8803i	−0.913496	−	0.395002i
$145$	35.8026			0.246915
$146$	−150.420	+	44.9967i	−1.03028	+	0.308196i
$147$	6.49879	+	6.49879i	0.0442094	+	0.0442094i
$148$	100.739	+	20.8474i	0.680668	+	0.140861i
$149$	−146.031	−	146.031i	−0.980074	−	0.980074i	0.0197310	−	0.999805i	$-0.493719\pi$
$149$	−146.031	−	146.031i	−0.980074	−	0.980074i	−0.999805	+	0.0197310i	$0.993719\pi$
$150$	0.790967	+	0.426712i	0.00527312	+	0.00284474i
$151$	220.513			1.46035			0.730175	−	0.683260i	$-0.239439\pi$
$151$	220.513			1.46035			0.730175	+	0.683260i	$0.239439\pi$
$152$	13.2285	+	152.366i	0.0870294	+	1.00241i
$153$			60.7853i			0.397290i
$154$	132.751	+	71.6165i	0.862019	+	0.465042i
$155$	−19.3751	+	19.3751i	−0.125000	+	0.125000i
$156$	6.13696	−	4.03245i	0.0393395	−	0.0258491i
$157$	−109.561	+	109.561i	−0.697839	+	0.697839i	−0.963944	−	0.266105i	$-0.914263\pi$
$157$	−109.561	+	109.561i	−0.697839	+	0.697839i	0.266105	+	0.963944i	$0.414263\pi$
$158$	−207.921	+	62.1974i	−1.31596	+	0.393654i
$159$			3.19066i			0.0200670i
$160$	−103.312	−	130.957i	−0.645700	−	0.818479i
$161$	−165.058			−1.02521
$162$	45.7658	+	152.991i	0.282505	+	0.944392i
$163$	56.7781	+	56.7781i	0.348332	+	0.348332i	0.859488	−	0.511156i	$-0.170783\pi$
$163$	56.7781	+	56.7781i	0.348332	+	0.348332i	−0.511156	+	0.859488i	$0.670783\pi$
$164$	−105.940	−	161.230i	−0.645978	−	0.983108i
$165$	5.95377	+	5.95377i	0.0360835	+	0.0360835i
$166$	76.9727	−	142.679i	0.463691	−	0.859514i
$167$	106.677			0.638781			0.319391	−	0.947623i	$-0.396522\pi$
$167$	106.677			0.638781			0.319391	+	0.947623i	$0.396522\pi$
$168$	−1.38423	−	15.9437i	−0.00823949	−	0.0949029i
$169$			90.3414i			0.534564i
$170$	−33.5905	+	62.2646i	−0.197591	+	0.366262i
$171$	121.083	−	121.083i	0.708090	−	0.708090i
$172$	62.4899	−	301.964i	0.363313	−	1.75561i
$173$	178.360	−	178.360i	1.03098	−	1.03098i	0.0314805	−	0.999504i	$-0.489978\pi$
$173$	178.360	−	178.360i	1.03098	−	1.03098i	0.999504	−	0.0314805i	$-0.0100222\pi$
$174$	−0.814909	−	2.72418i	−0.00468339	−	0.0156562i
$175$		−	20.9807i		−	0.119890i
$176$	−45.9962	−	116.079i	−0.261342	−	0.659537i
$177$	14.8970			0.0841639
$178$	−84.5532	+	25.2932i	−0.475018	+	0.142097i
$179$	60.4622	+	60.4622i	0.337778	+	0.337778i	0.855530	−	0.517753i	$-0.173231\pi$
$179$	60.4622	+	60.4622i	0.337778	+	0.337778i	−0.517753	+	0.855530i	$0.673231\pi$
$180$	−37.8469	+	182.884i	−0.210261	+	1.01602i
$181$	147.113	+	147.113i	0.812779	+	0.812779i	0.985050	−	0.172271i	$-0.0551105\pi$
$181$	147.113	+	147.113i	0.812779	+	0.812779i	−0.172271	+	0.985050i	$0.555110\pi$
$182$	−150.872	−	81.3927i	−0.828968	−	0.447212i
$183$	−4.98073			−0.0272171
$184$	104.608	+	87.8946i	0.568520	+	0.477688i
$185$		−	134.059i		−	0.724642i
$186$	1.91523	+	1.03323i	0.0102969	+	0.00555499i
$187$	−37.4468	+	37.4468i	−0.200250	+	0.200250i
$188$	88.7443	+	135.059i	0.472044	+	0.718400i
$189$	−25.4011	+	25.4011i	−0.134397	+	0.134397i
$190$	190.942	−	57.1182i	1.00496	−	0.300622i
$191$			106.861i			0.559481i	0.960076	+	0.279741i	$0.0902485\pi$
$191$			106.861i			0.559481i	−0.960076	+	0.279741i	$0.909752\pi$
$192$	−7.61284	+	10.8416i	−0.0396502	+	0.0564668i
$193$	68.1873			0.353302			0.176651	−	0.984274i	$-0.443474\pi$
$193$	68.1873			0.353302			0.176651	+	0.984274i	$0.443474\pi$
$194$	−64.5975	−	215.944i	−0.332977	−	1.11312i
$195$	−6.76650	−	6.76650i	−0.0347000	−	0.0347000i
$196$	−148.429	+	97.5295i	−0.757293	+	0.497600i
$197$	−61.8529	−	61.8529i	−0.313974	−	0.313974i	0.532473	−	0.846447i	$-0.321263\pi$
$197$	−61.8529	−	61.8529i	−0.313974	−	0.313974i	−0.846447	+	0.532473i	$0.821263\pi$
$198$	−66.3754	+	123.036i	−0.335230	+	0.621393i
$199$	−158.466			−0.796310			−0.398155	−	0.917318i	$-0.630349\pi$
$199$	−158.466			−0.796310			−0.398155	+	0.917318i	$0.630349\pi$
$200$	−11.1724	+	13.2968i	−0.0558618	+	0.0664839i
$201$			6.70914i			0.0333788i
$202$	130.782	−	242.422i	0.647435	−	1.20011i
$203$	−46.9379	+	46.9379i	−0.231221	+	0.231221i
$204$	5.50220	+	1.13865i	0.0269716	+	0.00558162i
$205$	−177.769	+	177.769i	−0.867166	+	0.867166i
$206$	79.4991	+	265.759i	0.385918	+	1.29009i
$207$		−	152.979i		−	0.739028i
$208$	52.2750	+	131.924i	0.251322	+	0.634250i
$209$	149.187			0.713813
$210$	−19.9803	+	5.97689i	−0.0951441	+	0.0284614i
$211$	−197.031	−	197.031i	−0.933798	−	0.933798i	0.0641430	−	0.997941i	$-0.479569\pi$
$211$	−197.031	−	197.031i	−0.933798	−	0.933798i	−0.997941	+	0.0641430i	$0.979569\pi$
$212$	−60.3782	−	12.4949i	−0.284803	−	0.0589384i
$213$	−7.55315	−	7.55315i	−0.0354608	−	0.0354608i
$214$	79.0064	+	42.6224i	0.369189	+	0.199170i
$215$	−401.841			−1.86903
$216$	29.6245	−	2.57200i	0.137150	−	0.0119074i
$217$		−	50.8022i		−	0.234111i
$218$	−1.77314	−	0.956574i	−0.00813366	−	0.00438796i
$219$	11.4902	−	11.4902i	0.0524664	−	0.0524664i
$220$	−135.982	+	89.3503i	−0.618098	+	0.406138i
$221$	42.5585	−	42.5585i	0.192573	−	0.192573i
$222$	−10.2004	+	3.05133i	−0.0459476	+	0.0137448i
$223$		−	15.7698i		−	0.0707168i	−0.999375	−	0.0353584i	$-0.988743\pi$
$223$		−	15.7698i		−	0.0707168i	0.999375	−	0.0353584i	$-0.0112573\pi$
$224$	307.131	+	36.2427i	1.37112	+	0.161798i
$225$	19.4453			0.0864236
$226$	−8.53398	−	28.5284i	−0.0377610	−	0.126232i
$227$	199.289	+	199.289i	0.877927	+	0.877927i	0.993320	−	0.115393i	$-0.0368127\pi$
$227$	199.289	+	199.289i	0.877927	+	0.877927i	−0.115393	+	0.993320i	$0.536813\pi$
$228$	−8.69212	−	13.2285i	−0.0381233	−	0.0580196i
$229$	230.522	+	230.522i	1.00664	+	1.00664i	0.999978	+	0.00666715i	$0.00212224\pi$
$229$	230.522	+	230.522i	1.00664	+	1.00664i	0.00666715	+	0.999978i	$0.497878\pi$
$230$	84.5376	−	156.702i	0.367555	−	0.681312i
$231$	−15.6110			−0.0675801
$232$	54.7422	−	4.75272i	0.235958	−	0.0204859i
$233$		−	344.791i		−	1.47979i	−0.672722	−	0.739895i	$-0.734875\pi$
$233$		−	344.791i		−	1.47979i	0.672722	−	0.739895i	$-0.265125\pi$
$234$	75.4361	−	139.831i	0.322377	−	0.597568i
$235$	148.914	−	148.914i	0.633676	−	0.633676i
$236$	−58.3383	+	281.903i	−0.247196	+	1.19450i
$237$	15.8825	−	15.8825i	0.0670146	−	0.0670146i
$238$	−37.5922	−	125.668i	−0.157950	−	0.528016i
$239$			77.1978i			0.323004i	0.986872	+	0.161502i	$0.0516337\pi$
$239$			77.1978i			0.323004i	−0.986872	+	0.161502i	$0.948366\pi$
$240$	15.8455	+	6.85170i	0.0660228	+	0.0285487i
$241$	−293.483			−1.21777			−0.608885	−	0.793259i	$-0.708383\pi$
$241$	−293.483			−1.21777			−0.608885	+	0.793259i	$0.708383\pi$
$242$	115.162	−	34.4495i	0.475876	−	0.142353i
$243$	−35.3413	−	35.3413i	−0.145438	−	0.145438i
$244$	19.5051	−	94.2526i	0.0799388	−	0.386281i
$245$	163.656	+	163.656i	0.667982	+	0.667982i
$246$	17.5725	+	9.48000i	0.0714328	+	0.0385366i
$247$	−169.552			−0.686445
$248$	−27.0525	+	32.1965i	−0.109083	+	0.129824i
$249$			16.7785i			0.0673837i
$250$	−209.460	−	113.000i	−0.837839	−	0.451998i
$251$	79.6322	−	79.6322i	0.317260	−	0.317260i	−0.530454	−	0.847714i	$-0.677979\pi$
$251$	79.6322	−	79.6322i	0.317260	−	0.317260i	0.847714	+	0.530454i	$0.177979\pi$
$252$	−190.147	−	289.383i	−0.754550	−	1.14834i
$253$	94.2427	−	94.2427i	0.372501	−	0.372501i
$254$	−204.757	+	61.2508i	−0.806129	+	0.241145i
$255$		−	7.32208i		−	0.0287140i
$256$	−175.348	−	186.518i	−0.684954	−	0.728587i
$257$	221.860			0.863270			0.431635	−	0.902048i	$-0.357937\pi$
$257$	221.860			0.863270			0.431635	+	0.902048i	$0.357937\pi$
$258$	9.14637	+	30.5756i	0.0354510	+	0.118510i
$259$	175.753	+	175.753i	0.678585	+	0.678585i
$260$	154.544	−	101.547i	0.594399	−	0.390566i
$261$	−43.5028	−	43.5028i	−0.166678	−	0.166678i
$262$	−205.734	+	381.355i	−0.785243	+	1.45555i
$263$	374.223			1.42290			0.711451	−	0.702736i	$-0.248039\pi$
$263$	374.223			1.42290			0.711451	+	0.702736i	$0.248039\pi$
$264$	9.89366	+	8.31296i	0.0374760	+	0.0314885i
$265$			80.3486i			0.303202i
$266$	−175.445	+	325.211i	−0.659568	+	1.22260i
$267$	6.45876	−	6.45876i	0.0241901	−	0.0241901i
$268$	−126.960	−	26.2737i	−0.473732	−	0.0980362i
$269$	−357.970	+	357.970i	−1.33075	+	1.33075i	−0.426042	+	0.904704i	$0.640092\pi$
$269$	−357.970	+	357.970i	−1.33075	+	1.33075i	−0.904704	+	0.426042i	$0.859908\pi$
$270$	−11.1055	−	37.1247i	−0.0411313	−	0.137499i
$271$			359.030i			1.32484i	0.749135	+	0.662418i	$0.230470\pi$
$271$			359.030i			1.32484i	−0.749135	+	0.662418i	$0.769530\pi$
$272$	−43.0944	+	99.6615i	−0.158435	+	0.366403i
$273$	17.7420			0.0649890
$274$	144.034	−	43.0862i	0.525670	−	0.157249i
$275$	11.9793	+	11.9793i	0.0435610	+	0.0435610i
$276$	−13.8474	−	2.86565i	−0.0501718	−	0.0103828i
$277$	−351.765	−	351.765i	−1.26991	−	1.26991i	−0.946134	−	0.323775i	$-0.895048\pi$
$277$	−351.765	−	351.765i	−1.26991	−	1.26991i	−0.323775	−	0.946134i	$-0.604952\pi$
$278$	267.412	+	144.264i	0.961915	+	0.518934i
$279$	47.0843			0.168761
$280$	−34.8585	−	401.502i	−0.124495	−	1.43393i
$281$			191.390i			0.681103i	0.940226	+	0.340552i	$0.110614\pi$
$281$			191.390i			0.681103i	−0.940226	+	0.340552i	$0.889386\pi$
$282$	−14.7201	−	7.94123i	−0.0521991	−	0.0281604i
$283$	−31.3119	+	31.3119i	−0.110643	+	0.110643i	−0.760261	−	0.649618i	$-0.774929\pi$
$283$	−31.3119	+	31.3119i	−0.110643	+	0.110643i	0.649618	+	0.760261i	$0.274929\pi$
$284$	172.511	−	113.353i	0.607432	−	0.399129i
$285$	−14.5855	+	14.5855i	−0.0511771	+	0.0511771i
$286$	132.615	−	39.6705i	0.463690	−	0.138708i
$287$		−	466.117i		−	1.62410i
$288$	−33.5904	+	284.654i	−0.116633	+	0.988382i
$289$	−242.947			−0.840647
$290$	−20.5214	−	68.6016i	−0.0707636	−	0.236557i
$291$	16.4953	+	16.4953i	0.0566850	+	0.0566850i
$292$	172.437	+	262.430i	0.590537	+	0.898733i
$293$	−92.0889	−	92.0889i	−0.314297	−	0.314297i	0.532275	−	0.846572i	$-0.321337\pi$
$293$	−92.0889	−	92.0889i	−0.314297	−	0.314297i	−0.846572	+	0.532275i	$0.821337\pi$
$294$	8.72737	−	16.1774i	0.0296849	−	0.0550250i
$295$	375.144			1.27167
$296$	−17.7960	−	204.976i	−0.0601217	−	0.692485i
$297$		−	29.0063i		−	0.0976643i
$298$	−196.109	+	363.513i	−0.658082	+	1.21984i
$299$	−107.107	+	107.107i	−0.358219	+	0.358219i
$300$	0.364256	−	1.76016i	0.00121419	−	0.00586720i
$301$	526.821	−	526.821i	1.75023	−	1.75023i
$302$	−126.394	−	422.526i	−0.418524	−	1.39909i
$303$			28.5079i			0.0940854i
$304$	284.367	−	112.681i	0.935419	−	0.370661i
$305$	−125.427			−0.411236
$306$	116.471	−	34.8411i	0.380624	−	0.113860i
$307$	−257.566	−	257.566i	−0.838978	−	0.838978i	0.149746	−	0.988724i	$-0.452154\pi$
$307$	−257.566	−	257.566i	−0.838978	−	0.838978i	−0.988724	+	0.149746i	$0.952154\pi$
$308$	61.1343	−	295.414i	0.198488	−	0.959137i
$309$	−20.3005	−	20.3005i	−0.0656976	−	0.0656976i
$310$	48.2302	+	26.0192i	0.155581	+	0.0839330i
$311$	−130.914			−0.420946			−0.210473	−	0.977600i	$-0.567500\pi$
$311$	−130.914			−0.420946			−0.210473	+	0.977600i	$0.567500\pi$
$312$	−11.2442	−	9.44773i	−0.0360391	−	0.0302812i
$313$			51.8354i			0.165608i	0.996566	+	0.0828041i	$0.0263876\pi$
$313$			51.8354i			0.165608i	−0.996566	+	0.0828041i	$0.973612\pi$
$314$	272.728	+	147.132i	0.868561	+	0.468572i
$315$	−319.068	+	319.068i	−1.01291	+	1.01291i
$316$	238.354	+	362.748i	0.754283	+	1.14794i
$317$	−109.636	+	109.636i	−0.345856	+	0.345856i	−0.858563	−	0.512707i	$-0.828643\pi$
$317$	−109.636	+	109.636i	−0.345856	+	0.345856i	0.512707	+	0.858563i	$0.328643\pi$
$318$	6.11363	−	1.82883i	0.0192253	−	0.00575103i
$319$		−	53.5999i		−	0.168025i
$320$	−191.710	+	273.019i	−0.599094	+	0.853184i
$321$	−9.29086			−0.0289435
$322$	94.6086	+	316.269i	0.293815	+	0.982202i
$323$	−91.7367	−	91.7367i	−0.284014	−	0.284014i
$324$	266.916	−	175.384i	0.823814	−	0.541309i
$325$	−13.6145	−	13.6145i	−0.0418909	−	0.0418909i
$326$	76.2486	−	141.337i	0.233891	−	0.433549i
$327$	0.208514			0.000637659
$328$	−248.210	+	295.407i	−0.756738	+	0.900631i
$329$			390.458i			1.18680i
$330$	7.99546	−	14.8207i	0.0242287	−	0.0449111i
$331$	323.226	−	323.226i	0.976515	−	0.976515i	−0.0232157	−	0.999730i	$-0.507390\pi$
$331$	323.226	−	323.226i	0.976515	−	0.976515i	0.999730	+	0.0232157i	$0.00739046\pi$
$332$	−317.508	−	65.7066i	−0.956349	−	0.197911i
$333$	−162.891	+	162.891i	−0.489163	+	0.489163i
$334$	−61.1451	−	204.403i	−0.183069	−	0.611986i
$335$			168.953i			0.504337i
$336$	−29.7564	+	11.7910i	−0.0885607	+	0.0350922i
$337$	315.159			0.935191			0.467596	−	0.883943i	$-0.345120\pi$
$337$	315.159			0.935191			0.467596	+	0.883943i	$0.345120\pi$
$338$	173.104	−	51.7821i	0.512141	−	0.153202i
$339$	2.17920	+	2.17920i	0.00642832	+	0.00642832i
$340$	138.559	+	28.6740i	0.407527	+	0.0843354i
$341$	29.0063	+	29.0063i	0.0850625	+	0.0850625i
$342$	−301.411	−	162.606i	−0.881320	−	0.475455i
$343$	44.4459			0.129580
$344$	−614.414	+	53.3435i	−1.78609	+	0.155068i
$345$			18.4275i			0.0534132i
$346$	−443.990	−	239.524i	−1.28321	−	0.692267i
$347$	−307.568	+	307.568i	−0.886363	+	0.886363i	−0.994172	−	0.107809i	$-0.965616\pi$
$347$	−307.568	+	307.568i	−0.886363	+	0.886363i	0.107809	+	0.994172i	$0.465616\pi$
$348$	−4.75272	+	3.12291i	−0.0136573	+	0.00897387i
$349$	170.461	−	170.461i	0.488427	−	0.488427i	−0.419382	−	0.907810i	$-0.637753\pi$
$349$	170.461	−	170.461i	0.488427	−	0.488427i	0.907810	+	0.419382i	$0.137753\pi$
$350$	−40.2013	+	12.0258i	−0.114861	+	0.0343594i
$351$			32.9659i			0.0939198i
$352$	−196.054	+	154.668i	−0.556973	+	0.439397i
$353$	238.136			0.674606			0.337303	−	0.941396i	$-0.390485\pi$
$353$	238.136			0.674606			0.337303	+	0.941396i	$0.390485\pi$
$354$	−8.53871	−	28.5442i	−0.0241206	−	0.0806334i
$355$	−190.207	−	190.207i	−0.535795	−	0.535795i
$356$	96.9289	+	147.515i	0.272272	+	0.414369i
$357$	9.59938	+	9.59938i	0.0268890	+	0.0268890i
$358$	81.1961	−	150.508i	0.226805	−	0.420413i
$359$	33.6470			0.0937241			0.0468620	−	0.998901i	$-0.485078\pi$
$359$	33.6470			0.0937241			0.0468620	+	0.998901i	$0.485078\pi$
$360$	372.119	−	32.3074i	1.03366	−	0.0897428i
$361$			4.47577i			0.0123983i
$362$	197.561	−	366.207i	0.545750	−	1.01162i
$363$	−8.79687	+	8.79687i	−0.0242338	+	0.0242338i
$364$	−69.4796	+	335.740i	−0.190878	+	0.922363i
$365$	289.351	−	289.351i	0.792741	−	0.792741i
$366$	2.85487	+	9.54360i	0.00780018	+	0.0260754i
$367$			240.758i			0.656016i	0.944675	+	0.328008i	$0.106377\pi$
$367$			240.758i			0.656016i	−0.944675	+	0.328008i	$0.893623\pi$
$368$	108.456	−	250.819i	0.294717	−	0.681573i
$369$	432.005			1.17075
$370$	−256.871	+	76.8402i	−0.694245	+	0.207676i
$371$	−105.339	−	105.339i	−0.283931	−	0.283931i
$372$	0.881999	−	4.26200i	0.00237096	−	0.0114570i
$373$	432.504	+	432.504i	1.15953	+	1.15953i	0.984577	+	0.174951i	$0.0559766\pi$
$373$	432.504	+	432.504i	1.15953	+	1.15953i	0.174951	+	0.984577i	$0.444023\pi$
$374$	93.2159	+	50.2882i	0.249240	+	0.134460i
$375$	24.6317			0.0656845
$376$	207.921	−	247.457i	0.552982	−	0.658131i
$377$			60.9166i			0.161583i
$378$	63.2306	+	34.1117i	0.167277	+	0.0902426i
$379$	−174.716	+	174.716i	−0.460993	+	0.460993i	−0.898981	−	0.437988i	$-0.855691\pi$
$379$	−174.716	+	174.716i	−0.460993	+	0.460993i	0.437988	+	0.898981i	$0.355691\pi$
$380$	−218.889	−	333.126i	−0.576024	−	0.876646i
$381$	15.6408	−	15.6408i	0.0410518	−	0.0410518i
$382$	204.757	−	61.2508i	0.536013	−	0.160343i
$383$		−	673.381i		−	1.75817i	−0.476661	−	0.879087i	$-0.658153\pi$
$383$		−	673.381i		−	1.75817i	0.476661	−	0.879087i	$-0.341847\pi$
$384$	25.1372	+	8.37278i	0.0654616	+	0.0218041i
$385$	−393.124			−1.02110
$386$	−39.0838	−	130.654i	−0.101253	−	0.338482i
$387$	488.266	+	488.266i	1.26167	+	1.26167i
$388$	−376.746	+	247.551i	−0.970995	+	0.638019i
$389$	−274.646	−	274.646i	−0.706031	−	0.706031i	0.259667	−	0.965698i	$-0.416387\pi$
$389$	−274.646	−	274.646i	−0.706031	−	0.706031i	−0.965698	+	0.259667i	$0.916387\pi$
$390$	−9.08689	+	16.8438i	−0.0232997	+	0.0431892i
$391$	−115.902			−0.296424
$392$	271.954	+	228.504i	0.693760	+	0.582919i
$393$		−	44.8459i		−	0.114112i
$394$	−83.0637	+	153.970i	−0.210822	+	0.390786i
$395$	399.960	−	399.960i	1.01256	−	1.01256i
$396$	273.795	+	56.6604i	0.691401	+	0.143082i
$397$	−271.254	+	271.254i	−0.683259	+	0.683259i	−0.960733	−	0.277474i	$-0.910503\pi$
$397$	−271.254	+	271.254i	−0.683259	+	0.683259i	0.277474	+	0.960733i	$0.410503\pi$
$398$	90.8298	+	303.637i	0.228216	+	0.762907i
$399$		−	38.2436i		−	0.0958487i
$400$	31.8819	+	13.7860i	0.0797046	+	0.0344649i
$401$	−415.193			−1.03539			−0.517697	−	0.855564i	$-0.673210\pi$
$401$	−415.193			−1.03539			−0.517697	+	0.855564i	$0.673210\pi$
$402$	12.8554	−	3.84556i	0.0319787	−	0.00956608i
$403$	−32.9659	−	32.9659i	−0.0818011	−	0.0818011i
$404$	−539.467	−	111.640i	−1.33532	−	0.276336i
$405$	−294.296	−	294.296i	−0.726658	−	0.726658i
$406$	116.842	+	63.0340i	0.287788	+	0.155256i
$407$	−200.699			−0.493117
$408$	−0.971991	−	11.1955i	−0.00238233	−	0.0274398i
$409$		−	634.686i		−	1.55180i	−0.630856	−	0.775900i	$-0.717296\pi$
$409$		−	634.686i		−	1.55180i	0.630856	−	0.775900i	$-0.282704\pi$
$410$	442.518	+	238.730i	1.07931	+	0.582268i
$411$	−11.0023	+	11.0023i	−0.0267696	+	0.0267696i
$412$	463.656	−	304.657i	1.12538	−	0.739460i
$413$	−491.820	+	491.820i	−1.19085	+	1.19085i
$414$	−293.124	+	87.6849i	−0.708028	+	0.211799i
$415$			422.525i			1.01813i
$416$	222.817	−	175.781i	0.535618	−	0.422550i
$417$	−31.4467			−0.0754117
$418$	−85.5113	−	285.858i	−0.204573	−	0.683870i
$419$	19.2687	+	19.2687i	0.0459873	+	0.0459873i	0.729726	−	0.683739i	$-0.239647\pi$
$419$	19.2687	+	19.2687i	0.0459873	+	0.0459873i	−0.683739	+	0.729726i	$0.739647\pi$
$420$	22.9047	+	34.8585i	0.0545350	+	0.0829963i
$421$	244.505	+	244.505i	0.580773	+	0.580773i	0.935116	−	0.354343i	$-0.115295\pi$
$421$	244.505	+	244.505i	0.580773	+	0.580773i	−0.354343	+	0.935116i	$0.615295\pi$
$422$	−264.598	+	490.468i	−0.627009	+	1.16225i
$423$	−361.883			−0.855515
$424$	10.6661	+	122.853i	0.0251559	+	0.289747i
$425$		−	14.7324i		−	0.0346644i
$426$	−10.1433	+	18.8020i	−0.0238106	+	0.0441361i
$427$	164.437	−	164.437i	0.385099	−	0.385099i
$428$	36.3840	−	175.815i	0.0850093	−	0.410783i
$429$	−10.1301	+	10.1301i	−0.0236133	+	0.0236133i
$430$	230.328	+	769.969i	0.535647	+	1.79063i
$431$			337.331i			0.782670i	0.920248	+	0.391335i	$0.127987\pi$
$431$			337.331i			0.782670i	−0.920248	+	0.391335i	$0.872013\pi$
$432$	−21.9085	−	55.2894i	−0.0507140	−	0.127985i
$433$	−424.560			−0.980508			−0.490254	−	0.871580i	$-0.663096\pi$
$433$	−424.560			−0.980508			−0.490254	+	0.871580i	$0.663096\pi$
$434$	−97.3423	+	29.1189i	−0.224291	+	0.0670943i
$435$	5.24027	+	5.24027i	0.0120466	+	0.0120466i
$436$	−0.816565	+	3.94581i	−0.00187285	+	0.00905003i
$437$	230.874	+	230.874i	0.528317	+	0.528317i
$438$	−28.6023	−	15.4304i	−0.0653021	−	0.0352292i
$439$	−162.004			−0.369029			−0.184514	−	0.982830i	$-0.559071\pi$
$439$	−162.004			−0.369029			−0.184514	+	0.982830i	$0.559071\pi$
$440$	249.147	+	209.341i	0.566243	+	0.475775i
$441$		−	397.707i		−	0.901831i
$442$	−105.940	−	57.1528i	−0.239684	−	0.129305i
$443$	492.189	−	492.189i	1.11104	−	1.11104i	0.118026	−	0.993010i	$-0.462343\pi$
$443$	492.189	−	492.189i	1.11104	−	1.11104i	0.993010	−	0.118026i	$-0.0376567\pi$
$444$	11.6934	+	17.7960i	0.0263364	+	0.0400811i
$445$	162.648	−	162.648i	0.365500	−	0.365500i
$446$	−30.2167	+	9.03900i	−0.0677504	+	0.0202668i
$447$		−	42.7478i		−	0.0956327i
$448$	−106.597	−	609.268i	−0.237940	−	1.35997i
$449$	195.434			0.435266			0.217633	−	0.976031i	$-0.430166\pi$
$449$	195.434			0.435266			0.217633	+	0.976031i	$0.430166\pi$
$450$	−11.1457	−	37.2593i	−0.0247682	−	0.0827983i
$451$	266.137	+	266.137i	0.590104	+	0.590104i
$452$	−49.7720	+	32.7040i	−0.110115	+	0.0723540i
$453$	32.2755	+	32.2755i	0.0712483	+	0.0712483i
$454$	267.630	−	496.089i	0.589494	−	1.09271i
$455$	446.788			0.981951
$456$	−20.3650	+	24.2373i	−0.0446600	+	0.0531521i
$457$		−	386.874i		−	0.846552i	−0.906001	−	0.423276i	$-0.860880\pi$
$457$		−	386.874i		−	0.846552i	0.906001	−	0.423276i	$-0.139120\pi$
$458$	309.573	−	573.835i	0.675923	−	1.25291i
$459$	−17.8363	+	17.8363i	−0.0388590	+	0.0388590i
$460$	−348.713	−	72.1642i	−0.758071	−	0.156879i
$461$	−174.401	+	174.401i	−0.378310	+	0.378310i	−0.870492	−	0.492182i	$-0.836199\pi$
$461$	−174.401	+	174.401i	−0.378310	+	0.378310i	0.492182	+	0.870492i	$0.336199\pi$
$462$	8.94796	+	29.9123i	0.0193679	+	0.0647453i
$463$		−	60.5295i		−	0.130733i	−0.997861	−	0.0653666i	$-0.979178\pi$
$463$		−	60.5295i		−	0.130733i	0.997861	−	0.0653666i	$-0.0208217\pi$
$464$	−40.4840	−	102.168i	−0.0872500	−	0.220189i
$465$	−5.67168			−0.0121972
$466$	−660.656	+	197.628i	−1.41772	+	0.424095i
$467$	306.482	+	306.482i	0.656279	+	0.656279i	0.954497	−	0.298219i	$-0.0963926\pi$
$467$	306.482	+	306.482i	0.656279	+	0.656279i	−0.298219	+	0.954497i	$0.596393\pi$
$468$	−311.170	−	64.3949i	−0.664892	−	0.137596i
$469$	−221.500	−	221.500i	−0.472282	−	0.472282i
$470$	−370.690	−	199.980i	−0.788701	−	0.425489i
$471$	−32.0718			−0.0680930
$472$	573.594	−	49.7995i	1.21524	−	0.105508i
$473$			601.593i			1.27187i
$474$	−39.5360	−	21.3289i	−0.0834093	−	0.0449977i
$475$	−29.3467	+	29.3467i	−0.0617825	+	0.0617825i
$476$	−219.246	+	144.061i	−0.460600	+	0.302650i
$477$	97.6295	−	97.6295i	0.204674	−	0.204674i
$478$	147.919	−	44.2485i	0.309454	−	0.0925700i
$479$		−	376.452i		−	0.785912i	−0.919557	−	0.392956i	$-0.871453\pi$
$479$		−	376.452i		−	0.785912i	0.919557	−	0.392956i	$-0.128547\pi$
$480$	4.04623	−	34.2889i	0.00842964	−	0.0714351i
$481$	228.095			0.474210
$482$	168.219	+	562.344i	0.349002	+	1.16669i
$483$	−24.1588	−	24.1588i	−0.0500183	−	0.0500183i
$484$	−132.018	−	200.917i	−0.272764	−	0.415117i
$485$	415.393	+	415.393i	0.856481	+	0.856481i
$486$	−47.4607	+	87.9747i	−0.0976557	+	0.181018i
$487$	77.2033			0.158528			0.0792641	−	0.996854i	$-0.474743\pi$
$487$	77.2033			0.158528			0.0792641	+	0.996854i	$0.474743\pi$
$488$	−191.778	+	16.6502i	−0.392987	+	0.0341192i
$489$			16.6207i			0.0339892i
$490$	219.777	−	407.386i	0.448524	−	0.831400i
$491$	−581.438	+	581.438i	−1.18419	+	1.18419i	−0.205543	+	0.978648i	$0.565896\pi$
$491$	−581.438	+	581.438i	−1.18419	+	1.18419i	−0.978648	+	0.205543i	$0.934104\pi$
$492$	8.09246	−	39.1045i	0.0164481	−	0.0794806i
$493$	−32.9592	+	32.9592i	−0.0668543	+	0.0668543i
$494$	97.1842	+	324.879i	0.196729	+	0.657650i
$495$		−	364.354i		−	0.736069i
$496$	77.1978	+	33.3809i	0.155641	+	0.0673002i
$497$	498.730			1.00348
$498$	32.1495	−	9.61717i	0.0645572	−	0.0193116i
$499$	−174.006	−	174.006i	−0.348709	−	0.348709i	0.510920	−	0.859629i	$-0.329305\pi$
$499$	−174.006	−	174.006i	−0.348709	−	0.348709i	−0.859629	+	0.510920i	$0.829305\pi$
$500$	−96.4603	+	466.117i	−0.192921	+	0.932233i
$501$	15.6138	+	15.6138i	0.0311652	+	0.0311652i
$502$	−198.228	−	106.940i	−0.394876	−	0.213028i
$503$	−355.262			−0.706286			−0.353143	−	0.935569i	$-0.614887\pi$
$503$	−355.262			−0.706286			−0.353143	+	0.935569i	$0.614887\pi$
$504$	−445.499	+	530.210i	−0.883926	+	1.05200i
$505$			717.899i			1.42158i
$506$	−234.597	−	126.561i	−0.463631	−	0.250120i
$507$	−13.2229	+	13.2229i	−0.0260806	+	0.0260806i
$508$	234.726	+	357.228i	0.462059	+	0.703204i
$509$	279.667	−	279.667i	0.549444	−	0.549444i	−0.376836	−	0.926280i	$-0.622988\pi$
$509$	279.667	−	279.667i	0.549444	−	0.549444i	0.926280	+	0.376836i	$0.122988\pi$
$510$	−14.0299	+	4.19689i	−0.0275096	+	0.00822920i
$511$			758.688i			1.48471i
$512$	−256.882	+	442.895i	−0.501723	+	0.865029i
$513$	71.0592			0.138517
$514$	−127.167	−	425.108i	−0.247406	−	0.827059i
$515$	−511.218	−	511.218i	−0.992657	−	0.992657i
$516$	53.3435	−	35.0508i	0.103379	−	0.0679279i
$517$	−222.938	−	222.938i	−0.431215	−	0.431215i
$518$	236.023	−	437.501i	0.455644	−	0.844597i
$519$	52.2116			0.100600
$520$	−283.157	−	237.917i	−0.544533	−	0.457533i
$521$		−	705.745i		−	1.35460i	−0.735708	−	0.677299i	$-0.763151\pi$
$521$		−	705.745i		−	1.35460i	0.735708	−	0.677299i	$-0.236849\pi$
$522$	−58.4210	+	108.291i	−0.111918	+	0.207454i
$523$	−186.762	+	186.762i	−0.357098	+	0.357098i	−0.862742	−	0.505644i	$-0.831255\pi$
$523$	−186.762	+	186.762i	−0.357098	+	0.357098i	0.505644	+	0.862742i	$0.331255\pi$
$524$	848.640	+	175.621i	1.61954	+	0.335155i
$525$	3.07085	−	3.07085i	0.00584925	−	0.00584925i
$526$	−214.498	−	717.051i	−0.407791	−	1.36321i
$527$		−	35.6726i		−	0.0676899i
$528$	10.2576	−	23.7221i	0.0194273	−	0.0449283i
$529$	−237.309			−0.448599
$530$	153.956	−	46.0544i	0.290484	−	0.0868952i
$531$	−455.827	−	455.827i	−0.858432	−	0.858432i
$532$	723.701	+	149.766i	1.36034	+	0.281515i
$533$	−302.466	−	302.466i	−0.567479	−	0.567479i
$534$	−16.0777	−	8.67362i	−0.0301081	−	0.0162427i
$535$	−233.967			−0.437321
$536$	22.4281	+	258.329i	0.0418435	+	0.481956i
$537$			17.6992i			0.0329593i
$538$	891.092	+	480.727i	1.65630	+	0.893544i
$539$	245.008	−	245.008i	0.454560	−	0.454560i
$540$	−64.7694	+	42.5585i	−0.119943	+	0.0788120i
$541$	119.274	−	119.274i	0.220470	−	0.220470i	−0.588226	−	0.808696i	$-0.700174\pi$
$541$	119.274	−	119.274i	0.220470	−	0.220470i	0.808696	+	0.588226i	$0.200174\pi$
$542$	687.940	−	205.790i	1.26926	−	0.379686i
$543$			43.0645i			0.0793085i
$544$	215.663	+	25.4491i	0.396439	+	0.0467815i
$545$	5.25091			0.00963470
$546$	−10.1694	−	33.9956i	−0.0186253	−	0.0622629i
$547$	−141.472	−	141.472i	−0.258632	−	0.258632i	0.565865	−	0.824498i	$-0.308542\pi$
$547$	−141.472	−	141.472i	−0.258632	−	0.258632i	−0.824498	+	0.565865i	$0.808542\pi$
$548$	−165.115	−	251.288i	−0.301305	−	0.458554i
$549$	152.403	+	152.403i	0.277602	+	0.277602i
$550$	16.0873	−	29.8199i	0.0292496	−	0.0542180i
$551$	131.308			0.238309
$552$	2.44622	+	28.1757i	0.00443155	+	0.0510429i
$553$			1048.71i			1.89640i
$554$	−472.393	+	875.644i	−0.852695	+	1.58059i
$555$	19.6216	−	19.6216i	0.0353542	−	0.0353542i
$556$	123.149	−	595.080i	0.221490	−	1.07029i
$557$	375.881	−	375.881i	0.674831	−	0.674831i	−0.283995	−	0.958826i	$-0.591660\pi$
$557$	375.881	−	375.881i	0.674831	−	0.674831i	0.958826	+	0.283995i	$0.0916599\pi$
$558$	−26.9879	−	90.2185i	−0.0483654	−	0.161682i
$559$		−	683.715i		−	1.22310i
$560$	−749.340	+	296.926i	−1.33811	+	0.530226i
$561$	−10.9618			−0.0195398
$562$	366.724	−	109.701i	0.652533	−	0.195198i
$563$	305.349	+	305.349i	0.542360	+	0.542360i	0.924220	−	0.381860i	$-0.124716\pi$
$563$	305.349	+	305.349i	0.542360	+	0.542360i	−0.381860	+	0.924220i	$0.624716\pi$
$564$	−6.77891	+	32.7571i	−0.0120193	+	0.0580800i
$565$	54.8777	+	54.8777i	0.0971287	+	0.0971287i
$566$	77.9444	+	42.0495i	0.137711	+	0.0742924i
$567$	771.656			1.36095
$568$	−316.076	−	265.577i	−0.556472	−	0.467565i
$569$		−	296.778i		−	0.521578i	−0.965396	−	0.260789i	$-0.916017\pi$
$569$		−	296.778i		−	0.521578i	0.965396	−	0.260789i	$-0.0839827\pi$
$570$	36.3074	+	19.5872i	0.0636972	+	0.0343634i
$571$	−347.717	+	347.717i	−0.608961	+	0.608961i	−0.942674	−	0.333714i	$-0.891698\pi$
$571$	−347.717	+	347.717i	−0.608961	+	0.608961i	0.333714	+	0.942674i	$0.391698\pi$
$572$	−152.026	−	231.367i	−0.265779	−	0.404487i
$573$	−15.6408	+	15.6408i	−0.0272963	+	0.0272963i
$574$	−893.129	+	267.170i	−1.55597	+	0.465453i
$575$			37.0771i			0.0644820i
$576$	564.680	−	98.7960i	0.980348	−	0.171521i
$577$	−189.382			−0.328218			−0.164109	−	0.986442i	$-0.552475\pi$
$577$	−189.382			−0.328218			−0.164109	+	0.986442i	$0.552475\pi$
$578$	139.253	+	465.512i	0.240922	+	0.805385i
$579$	9.98027	+	9.98027i	0.0172371	+	0.0172371i
$580$	−119.685	+	78.6425i	−0.206354	+	0.135591i
$581$	−553.939	−	553.939i	−0.953423	−	0.953423i
$582$	22.1520	−	41.0616i	0.0380618	−	0.0705527i
$583$	120.289			0.206328
$584$	404.006	−	480.827i	0.691791	−	0.823334i
$585$			414.091i			0.707847i
$586$	−123.668	+	229.236i	−0.211038	+	0.391188i
$587$	−641.187	+	641.187i	−1.09231	+	1.09231i	−0.0970301	+	0.995281i	$0.530934\pi$
$587$	−641.187	+	641.187i	−1.09231	+	1.09231i	−0.995281	+	0.0970301i	$0.969066\pi$
$588$	−35.9999	−	7.44998i	−0.0612243	−	0.0126700i
$589$	−71.0592	+	71.0592i	−0.120644	+	0.120644i
$590$	−215.026	−	718.815i	−0.364451	−	1.21833i
$591$		−	18.1063i		−	0.0306367i
$592$	−382.555	+	151.588i	−0.646207	+	0.256060i
$593$	−127.909			−0.215697			−0.107849	−	0.994167i	$-0.534396\pi$
$593$	−127.909			−0.215697			−0.107849	+	0.994167i	$0.534396\pi$
$594$	−55.5792	+	16.6259i	−0.0935676	+	0.0279898i
$595$	241.736	+	241.736i	0.406279	+	0.406279i
$596$	808.936	+	167.405i	1.35728	+	0.280881i
$597$	−23.1939	−	23.1939i	−0.0388508	−	0.0388508i
$598$	266.621	+	143.837i	0.445855	+	0.240530i
$599$	794.804			1.32688			0.663442	−	0.748227i	$-0.269095\pi$
$599$	794.804			1.32688			0.663442	+	0.748227i	$0.269095\pi$
$600$	−3.58144	+	0.310941i	−0.00596907	+	0.000518235i
$601$			89.2746i			0.148543i	0.997238	+	0.0742717i	$0.0236632\pi$
$601$			89.2746i			0.148543i	−0.997238	+	0.0742717i	$0.976337\pi$
$602$	−1311.41	−	707.479i	−2.17842	−	1.17522i
$603$	205.290	−	205.290i	0.340448	−	0.340448i
$604$	−737.157	+	484.369i	−1.22046	+	0.801936i
$605$	−221.527	+	221.527i	−0.366160	+	0.366160i
$606$	54.6241	−	16.3402i	0.0901388	−	0.0269641i
$607$			316.002i			0.520596i	0.965528	+	0.260298i	$0.0838208\pi$
$607$			316.002i			0.520596i	−0.965528	+	0.260298i	$0.916179\pi$
$608$	−378.903	−	480.291i	−0.623195	−	0.789953i
$609$	−13.7402			−0.0225619
$610$	71.8926	+	240.332i	0.117857	+	0.393986i
$611$	253.370	+	253.370i	0.414682	+	0.414682i
$612$	−133.518	−	203.201i	−0.218167	−	0.332027i
$613$	−192.003	−	192.003i	−0.313219	−	0.313219i	0.532936	−	0.846155i	$-0.321089\pi$
$613$	−192.003	−	192.003i	−0.313219	−	0.313219i	−0.846155	+	0.532936i	$0.821089\pi$
$614$	−345.892	+	641.157i	−0.563341	+	1.04423i
$615$	−52.0385			−0.0846154
$616$	−601.086	+	52.1864i	−0.975789	+	0.0847182i
$617$			105.762i			0.171413i	0.996320	+	0.0857066i	$0.0273148\pi$
$617$			105.762i			0.171413i	−0.996320	+	0.0857066i	$0.972685\pi$
$618$	−27.2621	+	50.5339i	−0.0441134	+	0.0817701i
$619$	553.819	−	553.819i	0.894699	−	0.894699i	−0.100262	−	0.994961i	$-0.531968\pi$
$619$	553.819	−	553.819i	0.894699	−	0.894699i	0.994961	+	0.100262i	$0.0319681\pi$
$620$	22.2109	−	107.328i	0.0358241	−	0.173109i
$621$	44.8888	−	44.8888i	0.0722846	−	0.0722846i
$622$	75.0378	+	250.846i	0.120640	+	0.403289i
$623$			426.468i			0.684539i
$624$	−11.6579	+	26.9604i	−0.0186825	+	0.0432057i
$625$	674.560			1.07930
$626$	99.3221	−	29.7111i	0.158661	−	0.0474619i
$627$	21.8358	+	21.8358i	0.0348258	+	0.0348258i
$628$	125.597	−	606.909i	0.199995	−	0.966416i
$629$	123.412	+	123.412i	0.196203	+	0.196203i
$630$	794.252	+	428.484i	1.26072	+	0.680133i
$631$	762.907			1.20904			0.604522	−	0.796589i	$-0.293364\pi$
$631$	762.907			1.20904			0.604522	+	0.796589i	$0.293364\pi$
$632$	558.444	−	664.632i	0.883614	−	1.05163i
$633$		−	57.6772i		−	0.0911172i
$634$	272.916	+	147.233i	0.430468	+	0.232229i
$635$	393.873	−	393.873i	0.620272	−	0.620272i
$636$	−7.00846	−	10.6661i	−0.0110196	−	0.0167706i
$637$	−278.453	+	278.453i	−0.437132	+	0.437132i
$638$	−102.703	+	30.7225i	−0.160977	+	0.0481544i
$639$			462.232i			0.723367i
$640$	633.018	+	210.847i	0.989091	+	0.329449i
$641$	−412.834			−0.644046			−0.322023	−	0.946732i	$-0.604363\pi$
$641$	−412.834			−0.644046			−0.322023	+	0.946732i	$0.604363\pi$
$642$	5.32536	+	17.8023i	0.00829495	+	0.0277294i
$643$	−372.515	−	372.515i	−0.579339	−	0.579339i	0.355382	−	0.934721i	$-0.384351\pi$
$643$	−372.515	−	372.515i	−0.579339	−	0.579339i	−0.934721	+	0.355382i	$0.884351\pi$
$644$	551.777	−	362.560i	0.856797	−	0.562982i
$645$	−58.8156	−	58.8156i	−0.0911870	−	0.0911870i
$646$	−123.195	+	228.359i	−0.190705	+	0.353497i
$647$	−1170.94			−1.80980			−0.904899	−	0.425627i	$-0.860054\pi$
$647$	−1170.94			−1.80980			−0.904899	+	0.425627i	$0.860054\pi$
$648$	−489.046	−	410.912i	−0.754701	−	0.634123i
$649$		−	561.625i		−	0.865370i
$650$	−18.2833	+	33.8905i	−0.0281281	+	0.0521392i
$651$	7.43568	−	7.43568i	0.0114219	−	0.0114219i
$652$	−314.521	−	65.0884i	−0.482394	−	0.0998288i
$653$	13.7523	−	13.7523i	0.0210602	−	0.0210602i	−0.696498	−	0.717558i	$-0.745260\pi$
$653$	13.7523	−	13.7523i	0.0210602	−	0.0210602i	0.717558	+	0.696498i	$0.245260\pi$
$654$	−0.119517	−	0.399536i	−0.000182748	−	0.000610911i
$655$		−	1129.33i		−	1.72417i
$656$	708.301	+	306.274i	1.07973	+	0.466882i
$657$	−703.165			−1.07027
$658$	748.158	−	223.804i	1.13702	−	0.340127i
$659$	283.149	+	283.149i	0.429664	+	0.429664i	0.888514	−	0.458850i	$-0.151738\pi$
$659$	283.149	+	283.149i	0.429664	+	0.429664i	−0.458850	+	0.888514i	$0.651738\pi$
$660$	−32.9808	−	6.82520i	−0.0499709	−	0.0103412i
$661$	287.535	+	287.535i	0.435000	+	0.435000i	0.890325	−	0.455325i	$-0.150477\pi$
$661$	287.535	+	287.535i	0.435000	+	0.435000i	−0.455325	+	0.890325i	$0.650477\pi$
$662$	−804.604	−	434.068i	−1.21541	−	0.655692i
$663$	12.4582			0.0187907
$664$	56.0894	+	646.041i	0.0844720	+	0.972953i
$665$		−	963.069i		−	1.44822i
$666$	405.484	+	218.751i	0.608834	+	0.328454i
$667$	82.9486	−	82.9486i	0.124361	−	0.124361i
$668$	−356.611	+	234.321i	−0.533849	+	0.350780i
$669$	2.30816	−	2.30816i	0.00345017	−	0.00345017i
$670$	323.731	−	96.8408i	0.483181	−	0.144539i
$671$			187.776i			0.279845i
$672$	39.6486	+	50.2580i	0.0590009	+	0.0747887i
$673$	−45.5265			−0.0676471			−0.0338236	−	0.999428i	$-0.510768\pi$
$673$	−45.5265			−0.0676471			−0.0338236	+	0.999428i	$0.510768\pi$
$674$	−180.644	−	603.879i	−0.268018	−	0.895962i
$675$	5.70586	+	5.70586i	0.00845312	+	0.00845312i
$676$	−198.440	−	302.004i	−0.293550	−	0.446752i
$677$	208.341	+	208.341i	0.307742	+	0.307742i	0.844033	−	0.536291i	$-0.180175\pi$
$677$	208.341	+	208.341i	0.307742	+	0.307742i	−0.536291	+	0.844033i	$0.680175\pi$
$678$	2.92650	−	5.42466i	0.00431637	−	0.00800098i
$679$	−1089.18			−1.60409
$680$	−24.4772	−	281.929i	−0.0359958	−	0.414602i
$681$			58.3382i			0.0856655i
$682$	38.9532	−	72.2051i	0.0571162	−	0.105873i
$683$	−219.645	+	219.645i	−0.321589	+	0.321589i	−0.849377	−	0.527787i	$-0.823022\pi$
$683$	−219.645	+	219.645i	−0.321589	+	0.321589i	0.527787	+	0.849377i	$0.323022\pi$
$684$	−138.806	+	670.739i	−0.202932	+	0.980612i
$685$	−277.065	+	277.065i	−0.404475	+	0.404475i
$686$	−25.4756	−	85.1631i	−0.0371365	−	0.124144i
$687$			67.4808i			0.0982254i
$688$	454.383	+	1146.71i	0.660441	+	1.66672i
$689$	−136.710			−0.198418
$690$	35.3091	−	10.5623i	0.0511726	−	0.0153078i
$691$	692.991	+	692.991i	1.00288	+	1.00288i	0.999996	+	0.00288571i	$0.000918553\pi$
$691$	692.991	+	692.991i	1.00288	+	1.00288i	0.00288571	+	0.999996i	$0.499081\pi$
$692$	−204.466	+	988.024i	−0.295471	+	1.42778i
$693$	477.675	+	477.675i	0.689285	+	0.689285i
$694$	765.625	+	413.040i	1.10321	+	0.595158i
$695$	−791.905			−1.13943
$696$	8.70800	+	7.31673i	0.0125115	+	0.0105125i
$697$		−	327.301i		−	0.469585i
$698$	−424.327	−	228.916i	−0.607918	−	0.327960i
$699$	50.4655	−	50.4655i	0.0721967	−	0.0721967i
$700$	46.0854	+	70.1370i	0.0658363	+	0.100196i
$701$	195.377	−	195.377i	0.278712	−	0.278712i	−0.553883	−	0.832595i	$-0.686854\pi$
$701$	195.377	−	195.377i	0.278712	−	0.278712i	0.832595	+	0.553883i	$0.186854\pi$
$702$	63.1661	−	18.8955i	0.0899802	−	0.0269166i
$703$		−	491.668i		−	0.699386i
$704$	408.735	+	287.008i	0.580589	+	0.407682i
$705$	43.5917			0.0618322
$706$	−136.495	−	456.294i	−0.193336	−	0.646308i
$707$	−941.179	−	941.179i	−1.33123	−	1.33123i
$708$	−49.7995	+	32.7221i	−0.0703383	+	0.0462177i
$709$	318.083	+	318.083i	0.448636	+	0.448636i	0.894901	−	0.446265i	$-0.147246\pi$
$709$	318.083	+	318.083i	0.448636	+	0.448636i	−0.446265	+	0.894901i	$0.647246\pi$
$710$	−255.434	+	473.480i	−0.359766	+	0.666874i
$711$	−971.962			−1.36703
$712$	227.097	−	270.279i	0.318956	−	0.379606i
$713$			89.7775i			0.125915i
$714$	12.8912	−	23.8956i	0.0180549	−	0.0334673i
$715$	−255.101	+	255.101i	−0.356784	+	0.356784i
$716$	−334.929	−	69.3118i	−0.467778	−	0.0968042i
$717$	−11.2991	+	11.2991i	−0.0157589	+	0.0157589i
$718$	−19.2859	−	64.4711i	−0.0268605	−	0.0897926i
$719$			1122.38i			1.56103i	0.625139	+	0.780514i	$0.285042\pi$
$719$			1122.38i			1.56103i	−0.625139	+	0.780514i	$0.714958\pi$
$720$	−275.197	−	694.501i	−0.382217	−	0.964585i
$721$	1340.43			1.85913
$722$	8.57606	−	2.56544i	0.0118782	−	0.00355324i
$723$	−42.9557	−	42.9557i	−0.0594132	−	0.0594132i
$724$	−814.929	−	168.645i	−1.12559	−	0.232935i
$725$	10.5437	+	10.5437i	0.0145430	+	0.0145430i
$726$	21.8979	+	11.8135i	0.0301625	+	0.0162721i
$727$	529.192			0.727911			0.363956	−	0.931416i	$-0.381426\pi$
$727$	529.192			0.727911			0.363956	+	0.931416i	$0.381426\pi$
$728$	683.138	−	59.3102i	0.938376	−	0.0814700i
$729$			708.260i			0.971549i
$730$	−720.277	−	388.576i	−0.986681	−	0.532295i
$731$	369.926	−	369.926i	0.506055	−	0.506055i
$732$	16.6502	−	10.9405i	0.0227462	−	0.0149460i
$733$	−263.121	+	263.121i	−0.358965	+	0.358965i	−0.863431	−	0.504466i	$-0.831689\pi$
$733$	−263.121	+	263.121i	−0.358965	+	0.358965i	0.504466	+	0.863431i	$0.331689\pi$
$734$	461.317	−	137.998i	0.628498	−	0.188008i
$735$			47.9070i			0.0651797i
$736$	−542.761	−	64.0481i	−0.737447	−	0.0870218i
$737$	252.938			0.343200
$738$	−247.618	−	827.767i	−0.335525	−	1.12164i
$739$	−44.5459	−	44.5459i	−0.0602787	−	0.0602787i	0.676325	−	0.736603i	$-0.263572\pi$
$739$	−44.5459	−	44.5459i	−0.0602787	−	0.0602787i	−0.736603	+	0.676325i	$0.763572\pi$
$740$	294.468	+	448.148i	0.397929	+	0.605606i
$741$	−24.8165	−	24.8165i	−0.0334906	−	0.0334906i
$742$	−141.462	+	262.218i	−0.190649	+	0.353393i
$743$	762.894			1.02678			0.513388	−	0.858157i	$-0.328390\pi$
$743$	762.894			1.02678			0.513388	+	0.858157i	$0.328390\pi$
$744$	−8.67200	+	0.752905i	−0.0116559	+	0.00101197i
$745$		−	1076.50i		−	1.44496i
$746$	580.820	−	1076.63i	0.778578	−	1.44320i
$747$	513.400	−	513.400i	0.687282	−	0.687282i
$748$	42.9277	−	207.436i	0.0573900	−	0.277321i
$749$	306.735	−	306.735i	0.409526	−	0.409526i
$750$	−14.1185	−	47.1969i	−0.0188246	−	0.0629292i
$751$		−	1342.93i		−	1.78819i	−0.447876	−	0.894095i	$-0.647820\pi$
$751$		−	1342.93i		−	1.78819i	0.447876	−	0.894095i	$-0.352180\pi$
$752$	−593.331	−	256.561i	−0.789004	−	0.341171i
$753$	23.3108			0.0309573
$754$	116.723	−	34.9163i	0.154805	−	0.0463082i
$755$	812.776	+	812.776i	1.07652	+	1.07652i
$756$	29.1189	−	140.709i	0.0385171	−	0.186123i
$757$	−394.830	−	394.830i	−0.521573	−	0.521573i	0.396474	−	0.918046i	$-0.370234\pi$
$757$	−394.830	−	394.830i	−0.521573	−	0.521573i	−0.918046	+	0.396474i	$0.870234\pi$
$758$	434.920	+	234.631i	0.573772	+	0.309539i
$759$	27.5878			0.0363475
$760$	−512.840	+	610.356i	−0.674790	+	0.803101i
$761$			480.213i			0.631029i	0.948921	+	0.315514i	$0.102177\pi$
$761$			480.213i			0.631029i	−0.948921	+	0.315514i	$0.897823\pi$
$762$	−38.9343	−	21.0043i	−0.0510949	−	0.0275647i
$763$	−6.88404	+	6.88404i	−0.00902233	+	0.00902233i
$764$	−234.726	−	357.228i	−0.307233	−	0.467576i
$765$	−224.045	+	224.045i	−0.292870	+	0.292870i
$766$	−1290.27	+	385.970i	−1.68442	+	0.503878i
$767$			638.291i			0.832191i
$768$	1.63490	−	52.9647i	0.00212878	−	0.0689645i
$769$	472.763			0.614777			0.307388	−	0.951584i	$-0.400545\pi$
$769$	472.763			0.614777			0.307388	+	0.951584i	$0.400545\pi$
$770$	225.332	+	753.267i	0.292639	+	0.978269i
$771$	32.4727	+	32.4727i	0.0421177	+	0.0421177i
$772$	−227.945	+	149.777i	−0.295265	+	0.194012i
$773$	857.735	+	857.735i	1.10962	+	1.10962i	0.993200	+	0.116418i	$0.0371412\pi$
$773$	857.735	+	857.735i	1.10962	+	1.10962i	0.116418	+	0.993200i	$0.462859\pi$
$774$	655.704	−	1215.44i	0.847163	−	1.57033i
$775$	−11.4117			−0.0147248
$776$	690.279	+	579.993i	0.889534	+	0.747414i
$777$			51.4485i			0.0662143i
$778$	−368.828	+	683.673i	−0.474072	+	0.878757i
$779$	−651.978	+	651.978i	−0.836942	+	0.836942i
$780$	37.4829	+	7.75688i	0.0480550	+	0.00994472i
$781$	−284.758	+	284.758i	−0.364607	+	0.364607i
$782$	66.4329	+	222.080i	0.0849525	+	0.283990i
$783$		−	25.5302i		−	0.0326056i
$784$	281.959	−	652.067i	0.359641	−	0.831719i
$785$	−807.648			−1.02885
$786$	−85.9295	+	25.7049i	−0.109325	+	0.0327034i
$787$	170.355	+	170.355i	0.216462	+	0.216462i	0.807006	−	0.590544i	$-0.201087\pi$
$787$	170.355	+	170.355i	0.216462	+	0.216462i	−0.590544	+	0.807006i	$0.701087\pi$
$788$	342.633	+	70.9061i	0.434814	+	0.0899823i
$789$	54.7733	+	54.7733i	0.0694212	+	0.0694212i
$790$	−995.615	−	537.115i	−1.26027	−	0.679893i
$791$	−143.891			−0.181911
$792$	−48.3672	−	557.097i	−0.0610698	−	0.703405i
$793$		−	213.409i		−	0.269116i
$794$	675.229	+	364.273i	0.850415	+	0.458782i
$795$	−11.7603	+	11.7603i	−0.0147928	+	0.0147928i
$796$	529.739	−	348.079i	0.665501	−	0.437285i
$797$	835.571	−	835.571i	1.04840	−	1.04840i	0.0496277	−	0.998768i	$-0.484197\pi$
$797$	835.571	−	835.571i	1.04840	−	1.04840i	0.998768	−	0.0496277i	$-0.0158035\pi$
$798$	−73.2788	+	21.9206i	−0.0918281	+	0.0274694i
$799$			274.174i			0.343147i
$800$	8.14121	−	68.9909i	0.0101765	−	0.0862386i
$801$	−395.258			−0.493456
$802$	237.981	+	795.553i	0.296735	+	0.991962i
$803$	−433.185	−	433.185i	−0.539458	−	0.539458i
$804$	−14.7370	−	22.4281i	−0.0183296	−	0.0278957i
$805$	−608.380	−	608.380i	−0.755751	−	0.755751i
$806$	−44.2706	+	82.0615i	−0.0549263	+	0.101813i
$807$	−104.789			−0.129850
$808$	95.2996	+	1097.67i	0.117945	+	1.35850i
$809$			371.926i			0.459735i	0.973222	+	0.229868i	$0.0738293\pi$
$809$			371.926i			0.459735i	−0.973222	+	0.229868i	$0.926171\pi$
$810$	−395.217	+	732.589i	−0.487923	+	0.904430i
$811$	−275.629	+	275.629i	−0.339863	+	0.339863i	−0.856316	−	0.516453i	$-0.827252\pi$
$811$	−275.629	+	275.629i	−0.339863	+	0.339863i	0.516453	+	0.856316i	$0.327252\pi$
$812$	53.8080	−	260.011i	0.0662660	−	0.320211i
$813$	−52.5497	+	52.5497i	−0.0646367	+	0.0646367i
$814$	115.037	+	384.560i	0.141323	+	0.472432i
$815$			418.550i			0.513559i
$816$	−20.8945	+	8.27948i	−0.0256061	+	0.0101464i
$817$	−1473.77			−1.80389
$818$	−1216.13	+	363.791i	−1.48671	+	0.444732i
$819$	−542.880	−	542.880i	−0.662858	−	0.662858i
$820$	203.788	−	984.748i	0.248522	−	1.20091i
$821$	−904.923	−	904.923i	−1.10222	−	1.10222i	−0.994142	−	0.108079i	$-0.965530\pi$
$821$	−904.923	−	904.923i	−1.10222	−	1.10222i	−0.108079	−	0.994142i	$-0.534470\pi$
$822$	27.3879	+	14.7752i	0.0333186	+	0.0179747i
$823$	523.237			0.635768			0.317884	−	0.948130i	$-0.397028\pi$
$823$	523.237			0.635768			0.317884	+	0.948130i	$0.397028\pi$
$824$	−849.515	−	713.789i	−1.03096	−	0.866249i
$825$			3.50671i			0.00425055i
$826$	1224.28	+	660.477i	1.48218	+	0.799608i
$827$	722.805	−	722.805i	0.874008	−	0.874008i	−0.118898	−	0.992906i	$-0.537936\pi$
$827$	722.805	−	722.805i	0.874008	−	0.874008i	0.992906	+	0.118898i	$0.0379363\pi$
$828$	336.027	+	511.397i	0.405830	+	0.617629i
$829$	−286.380	+	286.380i	−0.345453	+	0.345453i	−0.858413	−	0.512960i	$-0.828549\pi$
$829$	−286.380	+	286.380i	−0.345453	+	0.345453i	0.512960	+	0.858413i	$0.328549\pi$
$830$	809.603	−	242.184i	0.975426	−	0.291788i
$831$		−	102.972i		−	0.123914i
$832$	−464.530	−	326.187i	−0.558329	−	0.392051i
$833$	−301.316			−0.361724
$834$	18.0247	+	60.2552i	0.0216123	+	0.0722484i
$835$	393.193	+	393.193i	0.470890	+	0.470890i
$836$	−498.720	+	327.698i	−0.596555	+	0.391983i
$837$	13.8160	+	13.8160i	0.0165066	+	0.0165066i
$838$	25.8763	−	47.9653i	0.0308787	−	0.0572378i
$839$	1353.58			1.61333			0.806666	−	0.591008i	$-0.201270\pi$
$839$	1353.58			1.61333			0.806666	+	0.591008i	$0.201270\pi$
$840$	53.6639	−	63.8681i	0.0638856	−	0.0760334i
$841$			793.824i			0.943904i
$842$	328.352	−	608.645i	0.389967	−	0.722856i
$843$	−28.0129	+	28.0129i	−0.0332300	+	0.0332300i
$844$	1091.45	+	225.870i	1.29319	+	0.267618i
$845$	−332.984	+	332.984i	−0.394064	+	0.394064i
$846$	207.425	+	693.406i	0.245183	+	0.819629i
$847$		−	580.852i		−	0.685776i
$848$	229.286	−	90.8546i	0.270384	−	0.107140i
$849$	−9.16597			−0.0107962
$850$	−28.2288	+	8.44435i	−0.0332104	+	0.00993453i
$851$	−310.591	−	310.591i	−0.364972	−	0.364972i
$852$	41.8405	+	8.65867i	0.0491086	+	0.0101628i
$853$	−668.253	−	668.253i	−0.783415	−	0.783415i	0.196990	−	0.980405i	$-0.436883\pi$
$853$	−668.253	−	668.253i	−0.783415	−	0.783415i	−0.980405	+	0.196990i	$0.936883\pi$
$854$	−409.332	−	220.827i	−0.479311	−	0.258579i
$855$	892.589			1.04396
$856$	−357.735	+	31.0586i	−0.417915	+	0.0362834i
$857$			488.688i			0.570230i	0.958493	+	0.285115i	$0.0920319\pi$
$857$			488.688i			0.570230i	−0.958493	+	0.285115i	$0.907968\pi$
$858$	25.2167	+	13.6039i	0.0293901	+	0.0158554i
$859$	−268.818	+	268.818i	−0.312943	+	0.312943i	−0.846048	−	0.533106i	$-0.821025\pi$
$859$	−268.818	+	268.818i	−0.312943	+	0.312943i	0.533106	+	0.846048i	$0.321025\pi$
$860$	1343.32	−	882.666i	1.56200	−	1.02636i
$861$	68.2234	−	68.2234i	0.0792374	−	0.0792374i
$862$	646.361	−	193.352i	0.749839	−	0.224306i
$863$		−	152.667i		−	0.176903i	−0.996080	−	0.0884514i	$-0.971808\pi$
$863$		−	152.667i		−	0.176903i	0.996080	−	0.0884514i	$-0.0281918\pi$
$864$	−93.3828	+	73.6698i	−0.108082	+	0.0852660i
$865$	1314.82			1.52002
$866$	243.351	+	813.502i	0.281005	+	0.939379i
$867$	−35.5591	−	35.5591i	−0.0410139	−	0.0410139i
$868$	111.590	+	169.828i	0.128560	+	0.195654i
$869$	−598.777	−	598.777i	−0.689042	−	0.689042i
$870$	7.03728	−	13.0445i	0.00808882	−	0.0149937i
$871$	−287.466			−0.330041
$872$	8.02864	−	0.697048i	0.00920715	−	0.000799367i
$873$		−	1009.47i		−	1.15632i
$874$	310.047	−	574.713i	0.354744	−	0.657566i
$875$	−813.208	+	813.208i	−0.929380	+	0.929380i
$876$	−13.1719	+	63.6495i	−0.0150364	+	0.0726592i
$877$	162.637	−	162.637i	0.185447	−	0.185447i	−0.608277	−	0.793725i	$-0.708139\pi$
$877$	162.637	−	162.637i	0.185447	−	0.185447i	0.793725	+	0.608277i	$0.208139\pi$
$878$	92.8576	+	310.416i	0.105760	+	0.353549i
$879$		−	26.9573i		−	0.0306681i
$880$	258.313	−	597.382i	0.293537	−	0.678844i
$881$	873.243			0.991196			0.495598	−	0.868552i	$-0.334949\pi$
$881$	873.243			0.991196			0.495598	+	0.868552i	$0.334949\pi$
$882$	−762.049	+	227.959i	−0.864001	+	0.258457i
$883$	−230.025	−	230.025i	−0.260504	−	0.260504i	0.564755	−	0.825259i	$-0.308971\pi$
$883$	−230.025	−	230.025i	−0.260504	−	0.260504i	−0.825259	+	0.564755i	$0.808971\pi$
$884$	−48.7876	+	235.752i	−0.0551896	+	0.266688i
$885$	54.9081	+	54.9081i	0.0620430	+	0.0620430i
$886$	−1225.20	−	660.972i	−1.38285	−	0.746018i
$887$	430.685			0.485552			0.242776	−	0.970082i	$-0.421942\pi$
$887$	430.685			0.485552			0.242776	+	0.970082i	$0.421942\pi$
$888$	27.3966	−	32.6061i	0.0308521	−	0.0367186i
$889$			1032.75i			1.16170i
$890$	−404.877	−	218.423i	−0.454918	−	0.245419i
$891$	−440.589	+	440.589i	−0.494489	+	0.494489i
$892$	34.6394	+	52.7174i	0.0388334	+	0.0591002i
$893$	546.150	−	546.150i	0.611590	−	0.611590i
$894$	−81.9093	+	24.5023i	−0.0916212	+	0.0274075i
$895$			445.709i			0.497999i
$896$	−1106.32	+	553.473i	−1.23474	+	0.617716i
$897$	−31.3537			−0.0349539
$898$	−112.020	−	374.473i	−0.124743	−	0.417008i
$899$	25.5302	+	25.5302i	0.0283984	+	0.0283984i
$900$	−65.0041	+	42.7127i	−0.0722268	+	0.0474586i
$901$	−73.9673	−	73.9673i	−0.0820947	−	0.0820947i
$902$	357.401	−	662.491i	0.396232	−	0.734469i
$903$	154.217			0.170783
$904$	91.1928	+	76.6230i	0.100877	+	0.0847600i
$905$			1084.47i			1.19831i
$906$	43.3435	−	80.3429i	0.0478405	−	0.0886787i
$907$	22.2262	−	22.2262i	0.0245052	−	0.0245052i	−0.694748	−	0.719253i	$-0.744484\pi$
$907$	22.2262	−	22.2262i	0.0245052	−	0.0245052i	0.719253	+	0.694748i	$0.244484\pi$
$908$	−1103.96	−	228.459i	−1.21582	−	0.251606i
$909$	872.301	−	872.301i	0.959627	−	0.959627i
$910$	−256.091	−	856.093i	−0.281419	−	0.940761i
$911$		−	1399.85i		−	1.53661i	−0.640083	−	0.768306i	$-0.721100\pi$
$911$		−	1399.85i		−	1.53661i	0.640083	−	0.768306i	$-0.278900\pi$
$912$	58.1142	+	25.1290i	0.0637217	+	0.0275537i
$913$	632.560			0.692837
$914$	−741.292	+	221.750i	−0.811042	+	0.242615i
$915$	−18.3582	−	18.3582i	−0.0200636	−	0.0200636i
$916$	−1276.97	−	264.262i	−1.39407	−	0.288496i
$917$	1480.57	+	1480.57i	1.61458	+	1.61458i
$918$	44.3997	+	23.9528i	0.0483657	+	0.0260924i
$919$	−806.944			−0.878068			−0.439034	−	0.898470i	$-0.644679\pi$
$919$	−806.944			−0.878068			−0.439034	+	0.898470i	$0.644679\pi$
$920$	61.6018	+	709.534i	0.0669585	+	0.771232i
$921$		−	75.3976i		−	0.0818650i
$922$	434.134	+	234.207i	0.470861	+	0.254020i
$923$	323.629	−	323.629i	0.350628	−	0.350628i
$924$	52.1864	−	34.2905i	0.0564788	−	0.0371109i
$925$	39.4796	−	39.4796i	0.0426806	−	0.0426806i
$926$	−115.981	+	34.6945i	−0.125249	+	0.0374670i
$927$			1242.34i			1.34017i
$928$	−172.559	+	136.132i	−0.185947	+	0.146694i
$929$	−1620.69			−1.74455			−0.872276	−	0.489013i	$-0.837357\pi$
$929$	−1620.69			−1.74455			−0.872276	+	0.489013i	$0.837357\pi$
$930$	3.25091	+	10.8675i	0.00349560	+	0.0116855i
$931$	600.216	+	600.216i	0.644701	+	0.644701i
$932$	757.354	+	1152.61i	0.812611	+	1.23671i
$933$	−19.1613	−	19.1613i	−0.0205373	−	0.0205373i
$934$	411.582	−	762.922i	0.440666	−	0.816833i
$935$	−276.046			−0.295237
$936$	54.9697	+	633.144i	0.0587283	+	0.676436i
$937$			598.181i			0.638400i	0.947687	+	0.319200i	$0.103414\pi$
$937$			598.181i			0.638400i	−0.947687	+	0.319200i	$0.896586\pi$
$938$	−297.458	+	551.378i	−0.317119	+	0.587823i
$939$	−7.58691	+	7.58691i	−0.00807978	+	0.00807978i
$940$	−170.710	+	824.905i	−0.181606	+	0.877559i
$941$	−977.842	+	977.842i	−1.03915	+	1.03915i	−0.0399498	+	0.999202i	$0.512720\pi$
$941$	−977.842	+	977.842i	−1.03915	+	1.03915i	−0.999202	+	0.0399498i	$0.987280\pi$
$942$	18.3830	+	61.4530i	0.0195149	+	0.0652367i
$943$			823.721i			0.873511i
$944$	−424.195	−	1070.52i	−0.449360	−	1.13403i
$945$	−187.249			−0.198147
$946$	1152.72	−	344.823i	1.21852	−	0.364506i
$947$	−827.881	−	827.881i	−0.874215	−	0.874215i	0.118714	−	0.992929i	$-0.462123\pi$
$947$	−827.881	−	827.881i	−0.874215	−	0.874215i	−0.992929	+	0.118714i	$0.962123\pi$
$948$	−18.2071	+	87.9806i	−0.0192058	+	0.0928065i
$949$	492.317	+	492.317i	0.518775	+	0.518775i
$950$	73.0523	+	39.4103i	0.0768972	+	0.0414846i
$951$	−32.0939			−0.0337476
$952$	401.704	+	337.524i	0.421958	+	0.354542i
$953$		−	1846.78i		−	1.93786i	−0.247333	−	0.968930i	$-0.579554\pi$
$953$		−	1846.78i		−	1.93786i	0.247333	−	0.968930i	$-0.420446\pi$
$954$	−243.028	−	131.109i	−0.254746	−	0.137431i
$955$	−393.873	+	393.873i	−0.412432	+	0.412432i
$956$	−169.570	−	258.066i	−0.177374	−	0.269944i
$957$	7.84517	−	7.84517i	0.00819767	−	0.00819767i
$958$	−721.321	+	215.776i	−0.752945	+	0.225236i
$959$		−	726.475i		−	0.757534i
$960$	−68.0203	+	11.9008i	−0.0708545	+	0.0123966i
$961$	933.368			0.971247
$962$	−130.740	−	437.055i	−0.135905	−	0.454319i
$963$	284.287	+	284.287i	0.295210	+	0.295210i
$964$	981.090	−	644.651i	1.01773	−	0.668725i
$965$	251.328	+	251.328i	0.260443	+	0.260443i
$966$	−32.4435	+	60.1383i	−0.0335854	+	0.0622550i
$967$	−363.922			−0.376341			−0.188170	−	0.982136i	$-0.560256\pi$
$967$	−363.922			−0.376341			−0.188170	+	0.982136i	$0.560256\pi$
$968$	−309.307	+	368.122i	−0.319532	+	0.380291i
$969$		−	26.8542i		−	0.0277133i
$970$	557.841	−	1034.03i	0.575094	−	1.06601i
$971$	1161.30	−	1161.30i	1.19598	−	1.19598i	0.220619	−	0.975360i	$-0.429192\pi$
$971$	1161.30	−	1161.30i	1.19598	−	1.19598i	0.975360	−	0.220619i	$-0.0708076\pi$
$972$	195.773	+	40.5141i	0.201412	+	0.0416811i
$973$	1038.20	−	1038.20i	1.06701	−	1.06701i
$974$	−44.2516	−	147.930i	−0.0454328	−	0.151878i
$975$		−	3.98540i		−	0.00408759i
$976$	141.827	+	357.923i	0.145315	+	0.366724i
$977$	1159.63			1.18693			0.593467	−	0.804858i	$-0.297759\pi$
$977$	1159.63			1.18693			0.593467	+	0.804858i	$0.297759\pi$
$978$	31.8470	−	9.52670i	0.0325634	−	0.00974100i
$979$	−243.499	−	243.499i	−0.248722	−	0.248722i
$980$	−906.567	−	187.609i	−0.925068	−	0.191438i
$981$	−6.38025	−	6.38025i	−0.00650382	−	0.00650382i
$982$	1447.37	+	780.826i	1.47390	+	0.795139i
$983$	−1780.51			−1.81131			−0.905653	−	0.424020i	$-0.860618\pi$
$983$	−1780.51			−1.81131			−0.905653	+	0.424020i	$0.860618\pi$
$984$	−79.5668	+	6.90800i	−0.0808605	+	0.00702033i
$985$		−	455.961i		−	0.462904i
$986$	82.0449	+	44.2616i	0.0832098	+	0.0448901i
$987$	−57.1495	+	57.1495i	−0.0579022	+	0.0579022i
$988$	566.799	−	372.430i	0.573683	−	0.376954i
$989$	−930.997	+	930.997i	−0.941352	+	0.941352i
$990$	−698.141	+	208.841i	−0.705193	+	0.210951i
$991$		−	675.783i		−	0.681920i	−0.940078	−	0.340960i	$-0.889248\pi$
$991$		−	675.783i		−	0.681920i	0.940078	−	0.340960i	$-0.110752\pi$
$992$	19.7129	−	167.053i	0.0198719	−	0.168400i
$993$	94.6184			0.0952854
$994$	−285.863	−	955.619i	−0.287589	−	0.961388i
$995$	−584.080	−	584.080i	−0.587015	−	0.587015i
$996$	−36.8550	−	56.0894i	−0.0370031	−	0.0563146i
$997$	9.44963	+	9.44963i	0.00947806	+	0.00947806i	0.711830	−	0.702352i	$-0.247867\pi$
$997$	9.44963	+	9.44963i	0.00947806	+	0.00947806i	−0.702352	+	0.711830i	$0.747867\pi$
$998$	−233.676	+	433.151i	−0.234145	+	0.434019i
$999$	−95.5948			−0.0956905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.3.f.a.11.2	yes	6
3.2	odd	2		144.3.m.a.91.2		6
4.3	odd	2		64.3.f.a.15.2		6
5.2	odd	4		400.3.k.c.299.3		6
5.3	odd	4		400.3.k.d.299.1		6
5.4	even	2		400.3.r.c.251.2		6
8.3	odd	2		128.3.f.a.31.2		6
8.5	even	2		128.3.f.b.31.2		6
12.11	even	2		576.3.m.a.271.1		6
16.3	odd	4	inner	16.3.f.a.3.2	✓	6
16.5	even	4		128.3.f.a.95.2		6
16.11	odd	4		128.3.f.b.95.2		6
16.13	even	4		64.3.f.a.47.2		6
24.5	odd	2		1152.3.m.a.415.3		6
24.11	even	2		1152.3.m.b.415.3		6
32.3	odd	8		1024.3.c.j.1023.5		12
32.5	even	8		1024.3.d.k.511.6		12
32.11	odd	8		1024.3.d.k.511.5		12
32.13	even	8		1024.3.c.j.1023.6		12
32.19	odd	8		1024.3.c.j.1023.8		12
32.21	even	8		1024.3.d.k.511.7		12
32.27	odd	8		1024.3.d.k.511.8		12
32.29	even	8		1024.3.c.j.1023.7		12
48.5	odd	4		1152.3.m.b.991.3		6
48.11	even	4		1152.3.m.a.991.3		6
48.29	odd	4		576.3.m.a.559.1		6
48.35	even	4		144.3.m.a.19.2		6
80.3	even	4		400.3.k.c.99.3		6
80.19	odd	4		400.3.r.c.51.2		6
80.67	even	4		400.3.k.d.99.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.2	✓	6	16.3	odd	4	inner
16.3.f.a.11.2	yes	6	1.1	even	1	trivial
64.3.f.a.15.2		6	4.3	odd	2
64.3.f.a.47.2		6	16.13	even	4
128.3.f.a.31.2		6	8.3	odd	2
128.3.f.a.95.2		6	16.5	even	4
128.3.f.b.31.2		6	8.5	even	2
128.3.f.b.95.2		6	16.11	odd	4
144.3.m.a.19.2		6	48.35	even	4
144.3.m.a.91.2		6	3.2	odd	2
400.3.k.c.99.3		6	80.3	even	4
400.3.k.c.299.3		6	5.2	odd	4
400.3.k.d.99.1		6	80.67	even	4
400.3.k.d.299.1		6	5.3	odd	4
400.3.r.c.51.2		6	80.19	odd	4
400.3.r.c.251.2		6	5.4	even	2
576.3.m.a.271.1		6	12.11	even	2
576.3.m.a.559.1		6	48.29	odd	4
1024.3.c.j.1023.5		12	32.3	odd	8
1024.3.c.j.1023.6		12	32.13	even	8
1024.3.c.j.1023.7		12	32.29	even	8
1024.3.c.j.1023.8		12	32.19	odd	8
1024.3.d.k.511.5		12	32.11	odd	8
1024.3.d.k.511.6		12	32.5	even	8
1024.3.d.k.511.7		12	32.21	even	8
1024.3.d.k.511.8		12	32.27	odd	8
1152.3.m.a.415.3		6	24.5	odd	2
1152.3.m.a.991.3		6	48.11	even	4
1152.3.m.b.415.3		6	24.11	even	2
1152.3.m.b.991.3		6	48.5	odd	4

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573183 - 1.91611i) q^{2} +(0.146365 + 0.146365i) q^{3} +(-3.34292 + 2.19656i) q^{4} +(3.68585 + 3.68585i) q^{5} +(0.196558 - 0.364346i) q^{6} -9.66442 q^{7} +(6.12494 + 5.14637i) q^{8} -8.95715i q^{9} +O(q^{10})\)	\(q+(-0.573183 - 1.91611i) q^{2} +(0.146365 + 0.146365i) q^{3} +(-3.34292 + 2.19656i) q^{4} +(3.68585 + 3.68585i) q^{5} +(0.196558 - 0.364346i) q^{6} -9.66442 q^{7} +(6.12494 + 5.14637i) q^{8} -8.95715i q^{9} +(4.94981 - 9.17513i) q^{10} +(5.51806 - 5.51806i) q^{11} +(-0.810789 - 0.167788i) q^{12} +(-6.27131 + 6.27131i) q^{13} +(5.53948 + 18.5181i) q^{14} +1.07896i q^{15} +(6.35027 - 14.6858i) q^{16} -6.78623 q^{17} +(-17.1629 + 5.13409i) q^{18} +(13.5181 + 13.5181i) q^{19} +(-20.4177 - 4.22533i) q^{20} +(-1.41454 - 1.41454i) q^{21} +(-13.7360 - 7.41033i) q^{22} +17.0790 q^{23} +(0.143230 + 1.64973i) q^{24} +2.17092i q^{25} +(15.6111 + 8.42188i) q^{26} +(2.62831 - 2.62831i) q^{27} +(32.3074 - 21.2285i) q^{28} +(4.85677 - 4.85677i) q^{29} +(2.06740 - 0.618442i) q^{30} +5.25662i q^{31} +(-31.7795 - 3.75011i) q^{32} +1.61531 q^{33} +(3.88975 + 13.0031i) q^{34} +(-35.6216 - 35.6216i) q^{35} +(19.6749 + 29.9431i) q^{36} +(-18.1856 - 18.1856i) q^{37} +(18.1537 - 33.6503i) q^{38} -1.83581 q^{39} +(3.60688 + 41.5443i) q^{40} +48.2302i q^{41} +(-1.89962 + 3.52119i) q^{42} +(-54.5113 + 54.5113i) q^{43} +(-6.32571 + 30.5672i) q^{44} +(33.0147 - 33.0147i) q^{45} +(-9.78937 - 32.7251i) q^{46} -40.4015i q^{47} +(3.07896 - 1.22004i) q^{48} +44.4011 q^{49} +(4.15972 - 1.24434i) q^{50} +(-0.993270 - 0.993270i) q^{51} +(7.18921 - 34.7398i) q^{52} +(10.8996 + 10.8996i) q^{53} +(-6.54262 - 3.52962i) q^{54} +40.6774 q^{55} +(-59.1940 - 49.7367i) q^{56} +3.95715i q^{57} +(-12.0899 - 6.52227i) q^{58} +(50.8898 - 50.8898i) q^{59} +(-2.37000 - 3.60688i) q^{60} +(-17.0147 + 17.0147i) q^{61} +(10.0722 - 3.01300i) q^{62} +86.5657i q^{63} +(11.0298 + 63.0424i) q^{64} -46.2302 q^{65} +(-0.925866 - 3.09510i) q^{66} +(22.9191 + 22.9191i) q^{67} +(22.6858 - 14.9063i) q^{68} +(2.49977 + 2.49977i) q^{69} +(-47.8370 + 88.6724i) q^{70} -51.6047 q^{71} +(46.0968 - 54.8621i) q^{72} -78.5032i q^{73} +(-24.4219 + 45.2692i) q^{74} +(-0.317748 + 0.317748i) q^{75} +(-74.8830 - 15.4966i) q^{76} +(-53.3288 + 53.3288i) q^{77} +(1.05225 + 3.51760i) q^{78} -108.512i q^{79} +(77.5359 - 30.7237i) q^{80} -79.8450 q^{81} +(92.4141 - 27.6447i) q^{82} +(57.3173 + 57.3173i) q^{83} +(7.83581 + 1.62158i) q^{84} +(-25.0130 - 25.0130i) q^{85} +(135.694 + 73.2045i) q^{86} +1.42173 q^{87} +(62.1957 - 5.39985i) q^{88} -44.1276i q^{89} +(-82.1831 - 44.3362i) q^{90} +(60.6086 - 60.6086i) q^{91} +(-57.0937 + 37.5149i) q^{92} +(-0.769387 + 0.769387i) q^{93} +(-77.4136 + 23.1575i) q^{94} +99.6510i q^{95} +(-4.10253 - 5.20031i) q^{96} +112.700 q^{97} +(-25.4499 - 85.0772i) q^{98} +(-49.4261 - 49.4261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21} - 52 q^{22} + 60 q^{23} + 48 q^{24} + 96 q^{26} + 64 q^{27} + 56 q^{28} - 18 q^{29} + 52 q^{30} + 8 q^{32} - 4 q^{33} - 76 q^{34} - 100 q^{35} - 52 q^{36} + 46 q^{37} + 40 q^{38} - 196 q^{39} + 40 q^{40} - 24 q^{42} - 114 q^{43} + 20 q^{44} + 66 q^{45} + 28 q^{46} - 24 q^{48} - 46 q^{49} + 46 q^{50} + 156 q^{51} + 100 q^{52} + 78 q^{53} + 32 q^{54} + 252 q^{55} - 168 q^{56} - 176 q^{58} + 206 q^{59} - 160 q^{60} + 30 q^{61} - 144 q^{62} + 64 q^{64} + 12 q^{65} + 196 q^{66} - 226 q^{67} + 112 q^{68} - 116 q^{69} - 16 q^{70} - 260 q^{71} + 52 q^{72} - 92 q^{74} - 238 q^{75} - 188 q^{76} - 212 q^{77} - 84 q^{78} + 232 q^{80} + 86 q^{81} + 304 q^{82} + 318 q^{83} + 232 q^{84} - 212 q^{85} + 268 q^{86} + 444 q^{87} - 8 q^{88} - 160 q^{90} + 188 q^{91} - 168 q^{92} - 32 q^{93} + 48 q^{94} - 80 q^{96} - 4 q^{97} + 10 q^{98} - 226 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 - 8 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 + 4 * q^8 + 36 * q^10 - 18 * q^11 + 52 * q^12 - 2 * q^13 + 12 * q^14 - 40 * q^16 - 4 * q^17 - 74 * q^18 + 30 * q^19 - 84 * q^20 - 20 * q^21 - 52 * q^22 + 60 * q^23 + 48 * q^24 + 96 * q^26 + 64 * q^27 + 56 * q^28 - 18 * q^29 + 52 * q^30 + 8 * q^32 - 4 * q^33 - 76 * q^34 - 100 * q^35 - 52 * q^36 + 46 * q^37 + 40 * q^38 - 196 * q^39 + 40 * q^40 - 24 * q^42 - 114 * q^43 + 20 * q^44 + 66 * q^45 + 28 * q^46 - 24 * q^48 - 46 * q^49 + 46 * q^50 + 156 * q^51 + 100 * q^52 + 78 * q^53 + 32 * q^54 + 252 * q^55 - 168 * q^56 - 176 * q^58 + 206 * q^59 - 160 * q^60 + 30 * q^61 - 144 * q^62 + 64 * q^64 + 12 * q^65 + 196 * q^66 - 226 * q^67 + 112 * q^68 - 116 * q^69 - 16 * q^70 - 260 * q^71 + 52 * q^72 - 92 * q^74 - 238 * q^75 - 188 * q^76 - 212 * q^77 - 84 * q^78 + 232 * q^80 + 86 * q^81 + 304 * q^82 + 318 * q^83 + 232 * q^84 - 212 * q^85 + 268 * q^86 + 444 * q^87 - 8 * q^88 - 160 * q^90 + 188 * q^91 - 168 * q^92 - 32 * q^93 + 48 * q^94 - 80 * q^96 - 4 * q^97 + 10 * q^98 - 226 * q^99

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