LMFDB - Embedded newform 16.3.f.a.3.2

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

$q$-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} +(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} + 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}+ \cdots - 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

Character values

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

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.682292	−	0.731080i	$-0.739017\pi$
$3$	0.146365	−	0.146365i	0.0487885	−	0.0487885i	0.731080	+	0.682292i	$0.239017\pi$
$4$	−3.34292	−	2.19656i	−0.835731	−	0.549139i
$5$	3.68585	−	3.68585i	0.737169	−	0.737169i	−0.234860	−	0.972029i	$-0.575463\pi$
$5$	3.68585	−	3.68585i	0.737169	−	0.737169i	0.972029	+	0.234860i	$0.0754632\pi$
$6$	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	0.911948	−	0.410306i	$-0.134578\pi$
$11$	5.51806	+	5.51806i	0.501642	+	0.501642i	−0.410306	+	0.911948i	$0.634578\pi$
$12$	−0.810789	+	0.167788i	−0.0675657	+	0.0139824i
$13$	−6.27131	−	6.27131i	−0.482408	−	0.482408i	0.423492	−	0.905900i	$-0.360804\pi$
$13$	−6.27131	−	6.27131i	−0.482408	−	0.482408i	−0.905900	+	0.423492i	$0.860804\pi$
$14$	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	−0.255367	−	0.966844i	$-0.582196\pi$
$19$	13.5181	−	13.5181i	0.711477	−	0.711477i	0.966844	+	0.255367i	$0.0821964\pi$
$20$	−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	0.785868	−	0.618394i	$-0.212216\pi$
$29$	4.85677	+	4.85677i	0.167475	+	0.167475i	−0.618394	+	0.785868i	$0.712216\pi$
$30$	2.06740	+	0.618442i	0.0689135	+	0.0206147i
$31$		−	5.25662i		−	0.169568i	−0.996399	−	0.0847841i	$-0.972980\pi$
$31$		−	5.25662i		−	0.169568i	0.996399	−	0.0847841i	$-0.0270201\pi$
$32$	−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	−0.908780	−	0.417276i	$-0.862985\pi$
$37$	−18.1856	+	18.1856i	−0.491503	+	0.491503i	0.417276	+	0.908780i	$0.362985\pi$
$38$	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	$-0.799848\pi$
$41$		−	48.2302i		−	1.17635i	0.808735	−	0.588173i	$-0.200152\pi$
$42$	−1.89962	−	3.52119i	−0.0452289	−	0.0838379i
$43$	−54.5113	−	54.5113i	−1.26771	−	1.26771i	−0.947271	−	0.320435i	$-0.896171\pi$
$43$	−54.5113	−	54.5113i	−1.26771	−	1.26771i	−0.320435	−	0.947271i	$-0.603829\pi$
$44$	−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	$0.141417\pi$
$47$			40.4015i			0.859607i	−0.902922	+	0.429804i	$0.858583\pi$
$48$	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	−0.596764	−	0.802417i	$-0.703547\pi$
$53$	10.8996	−	10.8996i	0.205653	−	0.205653i	0.802417	+	0.596764i	$0.203547\pi$
$54$	−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	0.991632	−	0.129094i	$-0.0412070\pi$
$59$	50.8898	+	50.8898i	0.862538	+	0.862538i	−0.129094	+	0.991632i	$0.541207\pi$
$60$	−2.37000	+	3.60688i	−0.0395000	+	0.0601147i
$61$	−17.0147	−	17.0147i	−0.278929	−	0.278929i	0.553752	−	0.832682i	$-0.313196\pi$
$61$	−17.0147	−	17.0147i	−0.278929	−	0.278929i	−0.832682	+	0.553752i	$0.813196\pi$
$62$	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	−0.515071	−	0.857148i	$-0.672234\pi$
$67$	22.9191	−	22.9191i	0.342077	−	0.342077i	0.857148	+	0.515071i	$0.172234\pi$
$68$	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	$0.180704\pi$
$73$			78.5032i			1.07539i	−0.843141	+	0.537693i	$0.819296\pi$
$74$	−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	$0.240979\pi$
$79$			108.512i			1.37357i	−0.726859	+	0.686787i	$0.759021\pi$
$80$	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	−0.271788	−	0.962357i	$-0.587615\pi$
$83$	57.3173	−	57.3173i	0.690570	−	0.690570i	0.962357	+	0.271788i	$0.0876148\pi$
$84$	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	$0.0797431\pi$
$89$			44.1276i			0.495816i	−0.968784	+	0.247908i	$0.920257\pi$
$90$	−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	−0.0351644	−	0.999382i	$-0.511195\pi$
$101$	97.3859	−	97.3859i	0.964217	−	0.964217i	0.999382	+	0.0351644i	$0.0111955\pi$
$102$	−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	0.543067	−	0.839689i	$-0.317263\pi$
$107$	−31.7386	−	31.7386i	−0.296622	−	0.296622i	−0.839689	+	0.543067i	$0.817263\pi$
$108$	−3.01300	−	14.5595i	−0.0278982	−	0.134810i
$109$	0.712308	+	0.712308i	0.00653493	+	0.00653493i	0.710367	−	0.703832i	$-0.248529\pi$
$109$	0.712308	+	0.712308i	0.00653493	+	0.00653493i	−0.703832	+	0.710367i	$0.748529\pi$
$110$	−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	$0.138220\pi$
$127$			106.861i			0.841425i	−0.907194	+	0.420712i	$0.861780\pi$
$128$	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	−0.187116	+	0.982338i	$0.559914\pi$
$131$	−153.198	+	153.198i	−1.16945	+	1.16945i	−0.982338	+	0.187116i	$0.940086\pi$
$132$	−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	$-0.911540\pi$
$137$		−	75.1700i		−	0.548686i	0.961632	−	0.274343i	$-0.0884604\pi$
$138$	3.35700	+	6.22265i	0.0243261	+	0.0450917i
$139$	−107.425	−	107.425i	−0.772843	−	0.772843i	0.205760	−	0.978603i	$-0.434034\pi$
$139$	−107.425	−	107.425i	−0.772843	−	0.772843i	−0.978603	+	0.205760i	$0.934034\pi$
$140$	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	−0.999805	−	0.0197310i	$-0.993719\pi$
$149$	−146.031	+	146.031i	−0.980074	+	0.980074i	0.0197310	+	0.999805i	$0.493719\pi$
$150$	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	0.266105	−	0.963944i	$-0.414263\pi$
$157$	−109.561	−	109.561i	−0.697839	−	0.697839i	−0.963944	+	0.266105i	$0.914263\pi$
$158$	−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	−0.511156	−	0.859488i	$-0.670783\pi$
$163$	56.7781	−	56.7781i	0.348332	−	0.348332i	0.859488	+	0.511156i	$0.170783\pi$
$164$	−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	0.999504	+	0.0314805i	$0.0100222\pi$
$173$	178.360	+	178.360i	1.03098	+	1.03098i	0.0314805	+	0.999504i	$0.489978\pi$
$174$	−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	−0.517753	−	0.855530i	$-0.673231\pi$
$179$	60.4622	−	60.4622i	0.337778	−	0.337778i	0.855530	+	0.517753i	$0.173231\pi$
$180$	−37.8469	−	182.884i	−0.210261	−	1.01602i
$181$	147.113	−	147.113i	0.812779	−	0.812779i	−0.172271	−	0.985050i	$-0.555110\pi$
$181$	147.113	−	147.113i	0.812779	−	0.812779i	0.985050	+	0.172271i	$0.0551105\pi$
$182$	−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	$-0.909752\pi$
$191$		−	106.861i		−	0.559481i	0.960076	−	0.279741i	$-0.0902485\pi$
$192$	−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	−0.846447	−	0.532473i	$-0.821263\pi$
$197$	−61.8529	+	61.8529i	−0.313974	+	0.313974i	0.532473	+	0.846447i	$0.321263\pi$
$198$	−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	−0.997941	−	0.0641430i	$-0.979569\pi$
$211$	−197.031	+	197.031i	−0.933798	+	0.933798i	0.0641430	+	0.997941i	$0.479569\pi$
$212$	−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	$0.0112573\pi$
$223$			15.7698i			0.0707168i	−0.999375	+	0.0353584i	$0.988743\pi$
$224$	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	−0.115393	−	0.993320i	$-0.536813\pi$
$227$	199.289	−	199.289i	0.877927	−	0.877927i	0.993320	+	0.115393i	$0.0368127\pi$
$228$	−8.69212	+	13.2285i	−0.0381233	+	0.0580196i
$229$	230.522	−	230.522i	1.00664	−	1.00664i	0.00666715	−	0.999978i	$-0.497878\pi$
$229$	230.522	−	230.522i	1.00664	−	1.00664i	0.999978	−	0.00666715i	$-0.00212224\pi$
$230$	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	$0.265125\pi$
$233$			344.791i			1.47979i	−0.672722	+	0.739895i	$0.734875\pi$
$234$	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	$-0.948366\pi$
$239$		−	77.1978i		−	0.323004i	0.986872	−	0.161502i	$-0.0516337\pi$
$240$	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	0.847714	−	0.530454i	$-0.177979\pi$
$251$	79.6322	+	79.6322i	0.317260	+	0.317260i	−0.530454	+	0.847714i	$0.677979\pi$
$252$	−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	−0.904704	−	0.426042i	$-0.859908\pi$
$269$	−357.970	−	357.970i	−1.33075	−	1.33075i	−0.426042	−	0.904704i	$-0.640092\pi$
$270$	−11.1055	+	37.1247i	−0.0411313	+	0.137499i
$271$		−	359.030i		−	1.32484i	−0.749135	−	0.662418i	$-0.769530\pi$
$271$		−	359.030i		−	1.32484i	0.749135	−	0.662418i	$-0.230470\pi$
$272$	−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	−0.323775	+	0.946134i	$0.604952\pi$
$277$	−351.765	+	351.765i	−1.26991	+	1.26991i	−0.946134	+	0.323775i	$0.895048\pi$
$278$	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	$-0.889386\pi$
$281$		−	191.390i		−	0.681103i	0.940226	−	0.340552i	$-0.110614\pi$
$282$	−14.7201	+	7.94123i	−0.0521991	+	0.0281604i
$283$	−31.3119	−	31.3119i	−0.110643	−	0.110643i	0.649618	−	0.760261i	$-0.274929\pi$
$283$	−31.3119	−	31.3119i	−0.110643	−	0.110643i	−0.760261	+	0.649618i	$0.774929\pi$
$284$	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	−0.846572	−	0.532275i	$-0.821337\pi$
$293$	−92.0889	+	92.0889i	−0.314297	+	0.314297i	0.532275	+	0.846572i	$0.321337\pi$
$294$	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	−0.988724	−	0.149746i	$-0.952154\pi$
$307$	−257.566	+	257.566i	−0.838978	+	0.838978i	0.149746	+	0.988724i	$0.452154\pi$
$308$	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	$-0.973612\pi$
$313$		−	51.8354i		−	0.165608i	0.996566	−	0.0828041i	$-0.0263876\pi$
$314$	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	0.512707	−	0.858563i	$-0.328643\pi$
$317$	−109.636	−	109.636i	−0.345856	−	0.345856i	−0.858563	+	0.512707i	$0.828643\pi$
$318$	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	0.999730	−	0.0232157i	$-0.00739046\pi$
$331$	323.226	+	323.226i	0.976515	+	0.976515i	−0.0232157	+	0.999730i	$0.507390\pi$
$332$	−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	0.107809	−	0.994172i	$-0.465616\pi$
$347$	−307.568	−	307.568i	−0.886363	−	0.886363i	−0.994172	+	0.107809i	$0.965616\pi$
$348$	−4.75272	−	3.12291i	−0.0136573	−	0.00897387i
$349$	170.461	+	170.461i	0.488427	+	0.488427i	0.907810	−	0.419382i	$-0.137753\pi$
$349$	170.461	+	170.461i	0.488427	+	0.488427i	−0.419382	+	0.907810i	$0.637753\pi$
$350$	−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	$-0.893623\pi$
$367$		−	240.758i		−	0.656016i	0.944675	−	0.328008i	$-0.106377\pi$
$368$	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	0.174951	−	0.984577i	$-0.444023\pi$
$373$	432.504	−	432.504i	1.15953	−	1.15953i	0.984577	−	0.174951i	$-0.0559766\pi$
$374$	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	0.437988	−	0.898981i	$-0.355691\pi$
$379$	−174.716	−	174.716i	−0.460993	−	0.460993i	−0.898981	+	0.437988i	$0.855691\pi$
$380$	−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	$0.341847\pi$
$383$			673.381i			1.75817i	−0.476661	+	0.879087i	$0.658153\pi$
$384$	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	−0.965698	−	0.259667i	$-0.916387\pi$
$389$	−274.646	+	274.646i	−0.706031	+	0.706031i	0.259667	+	0.965698i	$0.416387\pi$
$390$	−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	0.277474	−	0.960733i	$-0.410503\pi$
$397$	−271.254	−	271.254i	−0.683259	−	0.683259i	−0.960733	+	0.277474i	$0.910503\pi$
$398$	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	$0.282704\pi$
$409$			634.686i			1.55180i	−0.630856	+	0.775900i	$0.717296\pi$
$410$	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	−0.683739	−	0.729726i	$-0.739647\pi$
$419$	19.2687	−	19.2687i	0.0459873	−	0.0459873i	0.729726	+	0.683739i	$0.239647\pi$
$420$	22.9047	−	34.8585i	0.0545350	−	0.0829963i
$421$	244.505	−	244.505i	0.580773	−	0.580773i	−0.354343	−	0.935116i	$-0.615295\pi$
$421$	244.505	−	244.505i	0.580773	−	0.580773i	0.935116	+	0.354343i	$0.115295\pi$
$422$	−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	$-0.872013\pi$
$431$		−	337.331i		−	0.782670i	0.920248	−	0.391335i	$-0.127987\pi$
$432$	−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	0.993010	+	0.118026i	$0.0376567\pi$
$443$	492.189	+	492.189i	1.11104	+	1.11104i	0.118026	+	0.993010i	$0.462343\pi$
$444$	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	$0.139120\pi$
$457$			386.874i			0.846552i	−0.906001	+	0.423276i	$0.860880\pi$
$458$	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	0.492182	−	0.870492i	$-0.336199\pi$
$461$	−174.401	−	174.401i	−0.378310	−	0.378310i	−0.870492	+	0.492182i	$0.836199\pi$
$462$	8.94796	−	29.9123i	0.0193679	−	0.0647453i
$463$			60.5295i			0.130733i	0.997861	+	0.0653666i	$0.0208217\pi$
$463$			60.5295i			0.130733i	−0.997861	+	0.0653666i	$0.979178\pi$
$464$	−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	−0.298219	−	0.954497i	$-0.596393\pi$
$467$	306.482	−	306.482i	0.656279	−	0.656279i	0.954497	+	0.298219i	$0.0963926\pi$
$468$	−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	$0.128547\pi$
$479$			376.452i			0.785912i	−0.919557	+	0.392956i	$0.871453\pi$
$480$	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	−0.978648	−	0.205543i	$-0.934104\pi$
$491$	−581.438	−	581.438i	−1.18419	−	1.18419i	−0.205543	−	0.978648i	$-0.565896\pi$
$492$	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	−0.859629	−	0.510920i	$-0.829305\pi$
$499$	−174.006	+	174.006i	−0.348709	+	0.348709i	0.510920	+	0.859629i	$0.329305\pi$
$500$	−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	0.926280	−	0.376836i	$-0.122988\pi$
$509$	279.667	+	279.667i	0.549444	+	0.549444i	−0.376836	+	0.926280i	$0.622988\pi$
$510$	−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	$0.236849\pi$
$521$			705.745i			1.35460i	−0.735708	+	0.677299i	$0.763151\pi$
$522$	−58.4210	−	108.291i	−0.111918	−	0.207454i
$523$	−186.762	−	186.762i	−0.357098	−	0.357098i	0.505644	−	0.862742i	$-0.331255\pi$
$523$	−186.762	−	186.762i	−0.357098	−	0.357098i	−0.862742	+	0.505644i	$0.831255\pi$
$524$	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	0.808696	−	0.588226i	$-0.200174\pi$
$541$	119.274	+	119.274i	0.220470	+	0.220470i	−0.588226	+	0.808696i	$0.700174\pi$
$542$	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	−0.824498	−	0.565865i	$-0.808542\pi$
$547$	−141.472	+	141.472i	−0.258632	+	0.258632i	0.565865	+	0.824498i	$0.308542\pi$
$548$	−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	0.958826	−	0.283995i	$-0.0916599\pi$
$557$	375.881	+	375.881i	0.674831	+	0.674831i	−0.283995	+	0.958826i	$0.591660\pi$
$558$	−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	−0.381860	−	0.924220i	$-0.624716\pi$
$563$	305.349	−	305.349i	0.542360	−	0.542360i	0.924220	+	0.381860i	$0.124716\pi$
$564$	−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	$0.0839827\pi$
$569$			296.778i			0.521578i	−0.965396	+	0.260789i	$0.916017\pi$
$570$	36.3074	−	19.5872i	0.0636972	−	0.0343634i
$571$	−347.717	−	347.717i	−0.608961	−	0.608961i	0.333714	−	0.942674i	$-0.391698\pi$
$571$	−347.717	−	347.717i	−0.608961	−	0.608961i	−0.942674	+	0.333714i	$0.891698\pi$
$572$	−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	−0.995281	−	0.0970301i	$-0.969066\pi$
$587$	−641.187	−	641.187i	−1.09231	−	1.09231i	−0.0970301	−	0.995281i	$-0.530934\pi$
$588$	−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	$-0.976337\pi$
$601$		−	89.2746i		−	0.148543i	0.997238	−	0.0742717i	$-0.0236632\pi$
$602$	−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	$-0.916179\pi$
$607$		−	316.002i		−	0.520596i	0.965528	−	0.260298i	$-0.0838208\pi$
$608$	−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	−0.846155	−	0.532936i	$-0.821089\pi$
$613$	−192.003	+	192.003i	−0.313219	+	0.313219i	0.532936	+	0.846155i	$0.321089\pi$
$614$	−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	$-0.972685\pi$
$617$		−	105.762i		−	0.171413i	0.996320	−	0.0857066i	$-0.0273148\pi$
$618$	−27.2621	−	50.5339i	−0.0441134	−	0.0817701i
$619$	553.819	+	553.819i	0.894699	+	0.894699i	0.994961	−	0.100262i	$-0.0319681\pi$
$619$	553.819	+	553.819i	0.894699	+	0.894699i	−0.100262	+	0.994961i	$0.531968\pi$
$620$	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	−0.934721	−	0.355382i	$-0.884351\pi$
$643$	−372.515	+	372.515i	−0.579339	+	0.579339i	0.355382	+	0.934721i	$0.384351\pi$
$644$	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	0.717558	−	0.696498i	$-0.245260\pi$
$653$	13.7523	+	13.7523i	0.0210602	+	0.0210602i	−0.696498	+	0.717558i	$0.745260\pi$
$654$	−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	−0.458850	−	0.888514i	$-0.651738\pi$
$659$	283.149	−	283.149i	0.429664	−	0.429664i	0.888514	+	0.458850i	$0.151738\pi$
$660$	−32.9808	+	6.82520i	−0.0499709	+	0.0103412i
$661$	287.535	−	287.535i	0.435000	−	0.435000i	−0.455325	−	0.890325i	$-0.650477\pi$
$661$	287.535	−	287.535i	0.435000	−	0.435000i	0.890325	+	0.455325i	$0.150477\pi$
$662$	−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	−0.536291	−	0.844033i	$-0.680175\pi$
$677$	208.341	−	208.341i	0.307742	−	0.307742i	0.844033	+	0.536291i	$0.180175\pi$
$678$	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	0.527787	−	0.849377i	$-0.323022\pi$
$683$	−219.645	−	219.645i	−0.321589	−	0.321589i	−0.849377	+	0.527787i	$0.823022\pi$
$684$	−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	0.00288571	−	0.999996i	$-0.499081\pi$
$691$	692.991	−	692.991i	1.00288	−	1.00288i	0.999996	−	0.00288571i	$-0.000918553\pi$
$692$	−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	0.832595	−	0.553883i	$-0.186854\pi$
$701$	195.377	+	195.377i	0.278712	+	0.278712i	−0.553883	+	0.832595i	$0.686854\pi$
$702$	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	−0.446265	−	0.894901i	$-0.647246\pi$
$709$	318.083	−	318.083i	0.448636	−	0.448636i	0.894901	+	0.446265i	$0.147246\pi$
$710$	−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	$-0.714958\pi$
$719$		−	1122.38i		−	1.56103i	0.625139	−	0.780514i	$-0.285042\pi$
$720$	−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	0.504466	−	0.863431i	$-0.331689\pi$
$733$	−263.121	−	263.121i	−0.358965	−	0.358965i	−0.863431	+	0.504466i	$0.831689\pi$
$734$	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	−0.736603	−	0.676325i	$-0.763572\pi$
$739$	−44.5459	+	44.5459i	−0.0602787	+	0.0602787i	0.676325	+	0.736603i	$0.263572\pi$
$740$	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	$0.352180\pi$
$751$			1342.93i			1.78819i	−0.447876	+	0.894095i	$0.647820\pi$
$752$	−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	−0.918046	−	0.396474i	$-0.870234\pi$
$757$	−394.830	+	394.830i	−0.521573	+	0.521573i	0.396474	+	0.918046i	$0.370234\pi$
$758$	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	$-0.897823\pi$
$761$		−	480.213i		−	0.631029i	0.948921	−	0.315514i	$-0.102177\pi$
$762$	−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	0.116418	−	0.993200i	$-0.462859\pi$
$773$	857.735	−	857.735i	1.10962	−	1.10962i	0.993200	−	0.116418i	$-0.0371412\pi$
$774$	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	−0.590544	−	0.807006i	$-0.701087\pi$
$787$	170.355	−	170.355i	0.216462	−	0.216462i	0.807006	+	0.590544i	$0.201087\pi$
$788$	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	0.998768	+	0.0496277i	$0.0158035\pi$
$797$	835.571	+	835.571i	1.04840	+	1.04840i	0.0496277	+	0.998768i	$0.484197\pi$
$798$	−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	$-0.926171\pi$
$809$		−	371.926i		−	0.459735i	0.973222	−	0.229868i	$-0.0738293\pi$
$810$	−395.217	−	732.589i	−0.487923	−	0.904430i
$811$	−275.629	−	275.629i	−0.339863	−	0.339863i	0.516453	−	0.856316i	$-0.327252\pi$
$811$	−275.629	−	275.629i	−0.339863	−	0.339863i	−0.856316	+	0.516453i	$0.827252\pi$
$812$	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	−0.108079	+	0.994142i	$0.534470\pi$
$821$	−904.923	+	904.923i	−1.10222	+	1.10222i	−0.994142	+	0.108079i	$0.965530\pi$
$822$	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	0.992906	−	0.118898i	$-0.0379363\pi$
$827$	722.805	+	722.805i	0.874008	+	0.874008i	−0.118898	+	0.992906i	$0.537936\pi$
$828$	336.027	−	511.397i	0.405830	−	0.617629i
$829$	−286.380	−	286.380i	−0.345453	−	0.345453i	0.512960	−	0.858413i	$-0.328549\pi$
$829$	−286.380	−	286.380i	−0.345453	−	0.345453i	−0.858413	+	0.512960i	$0.828549\pi$
$830$	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	−0.980405	−	0.196990i	$-0.936883\pi$
$853$	−668.253	+	668.253i	−0.783415	+	0.783415i	0.196990	+	0.980405i	$0.436883\pi$
$854$	−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	$-0.907968\pi$
$857$		−	488.688i		−	0.570230i	0.958493	−	0.285115i	$-0.0920319\pi$
$858$	25.2167	−	13.6039i	0.0293901	−	0.0158554i
$859$	−268.818	−	268.818i	−0.312943	−	0.312943i	0.533106	−	0.846048i	$-0.321025\pi$
$859$	−268.818	−	268.818i	−0.312943	−	0.312943i	−0.846048	+	0.533106i	$0.821025\pi$
$860$	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	$0.0281918\pi$
$863$			152.667i			0.176903i	−0.996080	+	0.0884514i	$0.971808\pi$
$864$	−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	0.793725	−	0.608277i	$-0.208139\pi$
$877$	162.637	+	162.637i	0.185447	+	0.185447i	−0.608277	+	0.793725i	$0.708139\pi$
$878$	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	−0.825259	−	0.564755i	$-0.808971\pi$
$883$	−230.025	+	230.025i	−0.260504	+	0.260504i	0.564755	+	0.825259i	$0.308971\pi$
$884$	−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	0.719253	−	0.694748i	$-0.244484\pi$
$907$	22.2262	+	22.2262i	0.0245052	+	0.0245052i	−0.694748	+	0.719253i	$0.744484\pi$
$908$	−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	$0.278900\pi$
$911$			1399.85i			1.53661i	−0.640083	+	0.768306i	$0.721100\pi$
$912$	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	$-0.896586\pi$
$937$		−	598.181i		−	0.638400i	0.947687	−	0.319200i	$-0.103414\pi$
$938$	−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	−0.999202	−	0.0399498i	$-0.987280\pi$
$941$	−977.842	−	977.842i	−1.03915	−	1.03915i	−0.0399498	−	0.999202i	$-0.512720\pi$
$942$	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	−0.992929	−	0.118714i	$-0.962123\pi$
$947$	−827.881	+	827.881i	−0.874215	+	0.874215i	0.118714	+	0.992929i	$0.462123\pi$
$948$	−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	$0.420446\pi$
$953$			1846.78i			1.93786i	−0.247333	+	0.968930i	$0.579554\pi$
$954$	−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	0.975360	+	0.220619i	$0.0708076\pi$
$971$	1161.30	+	1161.30i	1.19598	+	1.19598i	0.220619	+	0.975360i	$0.429192\pi$
$972$	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	$0.110752\pi$
$991$			675.783i			0.681920i	−0.940078	+	0.340960i	$0.889248\pi$
$992$	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	−0.702352	−	0.711830i	$-0.747867\pi$
$997$	9.44963	−	9.44963i	0.00947806	−	0.00947806i	0.711830	+	0.702352i	$0.247867\pi$
$998$	−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.3.2	✓	6
3.2	odd	2		144.3.m.a.19.2		6
4.3	odd	2		64.3.f.a.47.2		6
5.2	odd	4		400.3.k.d.99.1		6
5.3	odd	4		400.3.k.c.99.3		6
5.4	even	2		400.3.r.c.51.2		6
8.3	odd	2		128.3.f.a.95.2		6
8.5	even	2		128.3.f.b.95.2		6
12.11	even	2		576.3.m.a.559.1		6
16.3	odd	4		128.3.f.b.31.2		6
16.5	even	4		64.3.f.a.15.2		6
16.11	odd	4	inner	16.3.f.a.11.2	yes	6
16.13	even	4		128.3.f.a.31.2		6
24.5	odd	2		1152.3.m.a.991.3		6
24.11	even	2		1152.3.m.b.991.3		6
32.3	odd	8		1024.3.d.k.511.6		12
32.5	even	8		1024.3.c.j.1023.8		12
32.11	odd	8		1024.3.c.j.1023.7		12
32.13	even	8		1024.3.d.k.511.5		12
32.19	odd	8		1024.3.d.k.511.7		12
32.21	even	8		1024.3.c.j.1023.5		12
32.27	odd	8		1024.3.c.j.1023.6		12
32.29	even	8		1024.3.d.k.511.8		12
48.5	odd	4		576.3.m.a.271.1		6
48.11	even	4		144.3.m.a.91.2		6
48.29	odd	4		1152.3.m.b.415.3		6
48.35	even	4		1152.3.m.a.415.3		6
80.27	even	4		400.3.k.c.299.3		6
80.43	even	4		400.3.k.d.299.1		6
80.59	odd	4		400.3.r.c.251.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.2	✓	6	1.1	even	1	trivial
16.3.f.a.11.2	yes	6	16.11	odd	4	inner
64.3.f.a.15.2		6	16.5	even	4
64.3.f.a.47.2		6	4.3	odd	2
128.3.f.a.31.2		6	16.13	even	4
128.3.f.a.95.2		6	8.3	odd	2
128.3.f.b.31.2		6	16.3	odd	4
128.3.f.b.95.2		6	8.5	even	2
144.3.m.a.19.2		6	3.2	odd	2
144.3.m.a.91.2		6	48.11	even	4
400.3.k.c.99.3		6	5.3	odd	4
400.3.k.c.299.3		6	80.27	even	4
400.3.k.d.99.1		6	5.2	odd	4
400.3.k.d.299.1		6	80.43	even	4
400.3.r.c.51.2		6	5.4	even	2
400.3.r.c.251.2		6	80.59	odd	4
576.3.m.a.271.1		6	48.5	odd	4
576.3.m.a.559.1		6	12.11	even	2
1024.3.c.j.1023.5		12	32.21	even	8
1024.3.c.j.1023.6		12	32.27	odd	8
1024.3.c.j.1023.7		12	32.11	odd	8
1024.3.c.j.1023.8		12	32.5	even	8
1024.3.d.k.511.5		12	32.13	even	8
1024.3.d.k.511.6		12	32.3	odd	8
1024.3.d.k.511.7		12	32.19	odd	8
1024.3.d.k.511.8		12	32.29	even	8
1152.3.m.a.415.3		6	48.35	even	4
1152.3.m.a.991.3		6	24.5	odd	2
1152.3.m.b.415.3		6	48.29	odd	4
1152.3.m.b.991.3		6	24.11	even	2

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} - 8 q^{4} - 2 q^{5} - 8 q^{6} - 4 q^{7} + 4 q^{8} + 36 q^{10} - 18 q^{11} + 52 q^{12} - 2 q^{13} + 12 q^{14} - 40 q^{16} - 4 q^{17} - 74 q^{18} + 30 q^{19} - 84 q^{20} - 20 q^{21}+ \cdots - 226 q^{99}+O(q^{100}) \) 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

Introduction

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