LMFDB - Embedded newform 804.2.c.b.671.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.1
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41002 - 0.108878i) q^{2} +(1.62789 + 0.591579i) q^{3} +(1.97629 + 0.307041i) q^{4} -3.04949i q^{5} +(-2.23094 - 1.01138i) q^{6} +0.278695i q^{7} +(-2.75317 - 0.648108i) q^{8} +(2.30007 + 1.92605i) q^{9} +O(q^{10})$	\(q+(-1.41002 - 0.108878i) q^{2} +(1.62789 + 0.591579i) q^{3} +(1.97629 + 0.307041i) q^{4} -3.04949i q^{5} +(-2.23094 - 1.01138i) q^{6} +0.278695i q^{7} +(-2.75317 - 0.648108i) q^{8} +(2.30007 + 1.92605i) q^{9} +(-0.332024 + 4.29983i) q^{10} -5.07932 q^{11} +(3.03555 + 1.66896i) q^{12} -5.86045 q^{13} +(0.0303439 - 0.392964i) q^{14} +(1.80401 - 4.96424i) q^{15} +(3.81145 + 1.21360i) q^{16} -7.60921i q^{17} +(-3.03343 - 2.96619i) q^{18} -5.91318i q^{19} +(0.936317 - 6.02668i) q^{20} +(-0.164870 + 0.453686i) q^{21} +(7.16192 + 0.553028i) q^{22} +2.24947 q^{23} +(-4.09846 - 2.68377i) q^{24} -4.29939 q^{25} +(8.26333 + 0.638076i) q^{26} +(2.60486 + 4.49608i) q^{27} +(-0.0855707 + 0.550782i) q^{28} -5.83061i q^{29} +(-3.08419 + 6.80324i) q^{30} +4.34794i q^{31} +(-5.24207 - 2.12618i) q^{32} +(-8.26859 - 3.00482i) q^{33} +(-0.828478 + 10.7291i) q^{34} +0.849878 q^{35} +(3.95423 + 4.51266i) q^{36} -6.86393 q^{37} +(-0.643818 + 8.33768i) q^{38} +(-9.54018 - 3.46692i) q^{39} +(-1.97640 + 8.39577i) q^{40} +8.48285i q^{41} +(0.281866 - 0.621753i) q^{42} -2.79230i q^{43} +(-10.0382 - 1.55956i) q^{44} +(5.87348 - 7.01404i) q^{45} +(-3.17179 - 0.244919i) q^{46} +0.455070 q^{47} +(5.48669 + 4.23039i) q^{48} +6.92233 q^{49} +(6.06221 + 0.468111i) q^{50} +(4.50144 - 12.3870i) q^{51} +(-11.5820 - 1.79940i) q^{52} -5.43602i q^{53} +(-3.18336 - 6.62316i) q^{54} +15.4893i q^{55} +(0.180624 - 0.767295i) q^{56} +(3.49811 - 9.62603i) q^{57} +(-0.634828 + 8.22125i) q^{58} -0.908582 q^{59} +(5.08948 - 9.25688i) q^{60} +1.16382 q^{61} +(0.473396 - 6.13066i) q^{62} +(-0.536781 + 0.641018i) q^{63} +(7.15991 + 3.56870i) q^{64} +17.8714i q^{65} +(11.3317 + 5.13711i) q^{66} -1.00000i q^{67} +(2.33634 - 15.0380i) q^{68} +(3.66190 + 1.33074i) q^{69} +(-1.19834 - 0.0925333i) q^{70} -4.54985 q^{71} +(-5.08420 - 6.79345i) q^{72} +13.5119 q^{73} +(9.67825 + 0.747333i) q^{74} +(-6.99894 - 2.54343i) q^{75} +(1.81559 - 11.6862i) q^{76} -1.41558i q^{77} +(13.0743 + 5.92713i) q^{78} -12.3343i q^{79} +(3.70087 - 11.6230i) q^{80} +(1.58064 + 8.86011i) q^{81} +(0.923599 - 11.9610i) q^{82} +2.79368 q^{83} +(-0.465131 + 0.845993i) q^{84} -23.2042 q^{85} +(-0.304021 + 3.93718i) q^{86} +(3.44926 - 9.49161i) q^{87} +(13.9842 + 3.29194i) q^{88} +1.69189i q^{89} +(-9.04538 + 9.25041i) q^{90} -1.63328i q^{91} +(4.44561 + 0.690679i) q^{92} +(-2.57215 + 7.07797i) q^{93} +(-0.641656 - 0.0495473i) q^{94} -18.0322 q^{95} +(-7.27573 - 6.56230i) q^{96} +4.26115 q^{97} +(-9.76060 - 0.753692i) q^{98} +(-11.6828 - 9.78304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.41002	−	0.108878i	−0.997032	−	0.0769887i
$2$	−1.41002	−	0.108878i	−0.997032	−	0.0769887i
$3$	1.62789	+	0.591579i	0.939864	+	0.341548i
$3$	1.62789	+	0.591579i	0.939864	+	0.341548i
$4$	1.97629	+	0.307041i	0.988145	+	0.153520i
$5$		−	3.04949i		−	1.36377i	−0.731458	−	0.681887i	$-0.761160\pi$
$5$		−	3.04949i		−	1.36377i	0.731458	−	0.681887i	$-0.238840\pi$
$6$	−2.23094	−	1.01138i	−0.910779	−	0.412893i
$7$			0.278695i			0.105337i	0.998612	+	0.0526684i	$0.0167726\pi$
$7$			0.278695i			0.105337i	−0.998612	+	0.0526684i	$0.983227\pi$
$8$	−2.75317	−	0.648108i	−0.973393	−	0.229141i
$9$	2.30007	+	1.92605i	0.766690	+	0.642018i
$10$	−0.332024	+	4.29983i	−0.104995	+	1.35973i
$11$	−5.07932			−1.53147			−0.765736	−	0.643155i	$-0.777625\pi$
$11$	−5.07932			−1.53147			−0.765736	+	0.643155i	$0.777625\pi$
$12$	3.03555	+	1.66896i	0.876288	+	0.481787i
$13$	−5.86045			−1.62540			−0.812698	−	0.582685i	$-0.802002\pi$
$13$	−5.86045			−1.62540			−0.812698	+	0.582685i	$0.802002\pi$
$14$	0.0303439	−	0.392964i	0.00810974	−	0.105024i
$15$	1.80401	−	4.96424i	0.465794	−	1.28176i
$16$	3.81145	+	1.21360i	0.952863	+	0.303401i
$17$		−	7.60921i		−	1.84550i	−0.385395	−	0.922752i	$-0.625935\pi$
$17$		−	7.60921i		−	1.84550i	0.385395	−	0.922752i	$-0.374065\pi$
$18$	−3.03343	−	2.96619i	−0.714986	−	0.699139i
$19$		−	5.91318i		−	1.35658i	−0.734796	−	0.678288i	$-0.762722\pi$
$19$		−	5.91318i		−	1.35658i	0.734796	−	0.678288i	$-0.237278\pi$
$20$	0.936317	−	6.02668i	0.209367	−	1.34761i
$21$	−0.164870	+	0.453686i	−0.0359776	+	0.0990023i
$22$	7.16192	+	0.553028i	1.52693	+	0.117906i
$23$	2.24947			0.469047			0.234523	−	0.972110i	$-0.424647\pi$
$23$	2.24947			0.469047			0.234523	+	0.972110i	$0.424647\pi$
$24$	−4.09846	−	2.68377i	−0.836595	−	0.547822i
$25$	−4.29939			−0.859878
$26$	8.26333	+	0.638076i	1.62057	+	0.125137i
$27$	2.60486	+	4.49608i	0.501305	+	0.865271i
$28$	−0.0855707	+	0.550782i	−0.0161713	+	0.104088i
$29$		−	5.83061i		−	1.08272i	−0.840792	−	0.541359i	$-0.817910\pi$
$29$		−	5.83061i		−	1.08272i	0.840792	−	0.541359i	$-0.182090\pi$
$30$	−3.08419	+	6.80324i	−0.563093	+	1.24210i
$31$			4.34794i			0.780912i	0.920622	+	0.390456i	$0.127683\pi$
$31$			4.34794i			0.780912i	−0.920622	+	0.390456i	$0.872317\pi$
$32$	−5.24207	−	2.12618i	−0.926676	−	0.375860i
$33$	−8.26859	−	3.00482i	−1.43938	−	0.523071i
$34$	−0.828478	+	10.7291i	−0.142083	+	1.84003i
$35$	0.849878			0.143656
$36$	3.95423	+	4.51266i	0.659038	+	0.752109i
$37$	−6.86393			−1.12842			−0.564211	−	0.825630i	$-0.690820\pi$
$37$	−6.86393			−1.12842			−0.564211	+	0.825630i	$0.690820\pi$
$38$	−0.643818	+	8.33768i	−0.104441	+	1.35255i
$39$	−9.54018	−	3.46692i	−1.52765	−	0.555151i
$40$	−1.97640	+	8.39577i	−0.312496	+	1.32749i
$41$			8.48285i			1.32480i	0.749151	+	0.662399i	$0.230462\pi$
$41$			8.48285i			1.32480i	−0.749151	+	0.662399i	$0.769538\pi$
$42$	0.281866	−	0.621753i	0.0434929	−	0.0959386i
$43$		−	2.79230i		−	0.425821i	−0.977072	−	0.212911i	$-0.931706\pi$
$43$		−	2.79230i		−	0.425821i	0.977072	−	0.212911i	$-0.0682943\pi$
$44$	−10.0382	−	1.55956i	−1.51332	−	0.235112i
$45$	5.87348	−	7.01404i	0.875567	−	1.04559i
$46$	−3.17179	−	0.244919i	−0.467655	−	0.0361113i
$47$	0.455070			0.0663787			0.0331894	−	0.999449i	$-0.489434\pi$
$47$	0.455070			0.0663787			0.0331894	+	0.999449i	$0.489434\pi$
$48$	5.48669	+	4.23039i	0.791936	+	0.610604i
$49$	6.92233			0.988904
$50$	6.06221	+	0.468111i	0.857326	+	0.0662008i
$51$	4.50144	−	12.3870i	0.630328	−	1.73452i
$52$	−11.5820	−	1.79940i	−1.60613	−	0.249531i
$53$		−	5.43602i		−	0.746694i	−0.927692	−	0.373347i	$-0.878210\pi$
$53$		−	5.43602i		−	0.746694i	0.927692	−	0.373347i	$-0.121790\pi$
$54$	−3.18336	−	6.62316i	−0.433201	−	0.901297i
$55$			15.4893i			2.08858i
$56$	0.180624	−	0.767295i	0.0241369	−	0.102534i
$57$	3.49811	−	9.62603i	0.463336	−	1.27500i
$58$	−0.634828	+	8.22125i	−0.0833569	+	1.07950i
$59$	−0.908582			−0.118287			−0.0591436	−	0.998249i	$-0.518837\pi$
$59$	−0.908582			−0.118287			−0.0591436	+	0.998249i	$0.518837\pi$
$60$	5.08948	−	9.25688i	0.657049	−	1.19506i
$61$	1.16382			0.149012			0.0745059	−	0.997221i	$-0.476262\pi$
$61$	1.16382			0.149012			0.0745059	+	0.997221i	$0.476262\pi$
$62$	0.473396	−	6.13066i	0.0601214	−	0.778594i
$63$	−0.536781	+	0.641018i	−0.0676281	+	0.0807607i
$64$	7.15991	+	3.56870i	0.894989	+	0.446088i
$65$			17.8714i			2.21667i
$66$	11.3317	+	5.13711i	1.39483	+	0.632334i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$	2.33634	−	15.0380i	0.283322	−	1.82363i
$69$	3.66190	+	1.33074i	0.440841	+	0.160202i
$70$	−1.19834	−	0.0925333i	−0.143229	−	0.0110598i
$71$	−4.54985			−0.539967			−0.269984	−	0.962865i	$-0.587018\pi$
$71$	−4.54985			−0.539967			−0.269984	+	0.962865i	$0.587018\pi$
$72$	−5.08420	−	6.79345i	−0.599178	−	0.800615i
$73$	13.5119			1.58145			0.790726	−	0.612171i	$-0.209704\pi$
$73$	13.5119			1.58145			0.790726	+	0.612171i	$0.209704\pi$
$74$	9.67825	+	0.747333i	1.12507	+	0.0868757i
$75$	−6.99894	−	2.54343i	−0.808168	−	0.293690i
$76$	1.81559	−	11.6862i	0.208262	−	1.34050i
$77$		−	1.41558i		−	0.161320i
$78$	13.0743	+	5.92713i	1.48038	+	0.671115i
$79$		−	12.3343i		−	1.38772i	−0.720110	−	0.693860i	$-0.755909\pi$
$79$		−	12.3343i		−	1.38772i	0.720110	−	0.693860i	$-0.244091\pi$
$80$	3.70087	−	11.6230i	0.413770	−	1.29949i
$81$	1.58064	+	8.86011i	0.175627	+	0.984457i
$82$	0.923599	−	11.9610i	0.101994	−	1.32087i
$83$	2.79368			0.306646			0.153323	−	0.988176i	$-0.451003\pi$
$83$	2.79368			0.306646			0.153323	+	0.988176i	$0.451003\pi$
$84$	−0.465131	+	0.845993i	−0.0507499	+	0.0923054i
$85$	−23.2042			−2.51685
$86$	−0.304021	+	3.93718i	−0.0327834	+	0.424557i
$87$	3.44926	−	9.49161i	0.369800	−	1.01761i
$88$	13.9842	+	3.29194i	1.49072	+	0.350923i
$89$			1.69189i			0.179340i	0.995972	+	0.0896698i	$0.0285812\pi$
$89$			1.69189i			0.179340i	−0.995972	+	0.0896698i	$0.971419\pi$
$90$	−9.04538	+	9.25041i	−0.953466	+	0.975079i
$91$		−	1.63328i		−	0.171214i
$92$	4.44561	+	0.690679i	0.463487	+	0.0720082i
$93$	−2.57215	+	7.07797i	−0.266719	+	0.733952i
$94$	−0.641656	−	0.0495473i	−0.0661817	−	0.00511041i
$95$	−18.0322			−1.85006
$96$	−7.27573	−	6.56230i	−0.742576	−	0.669762i
$97$	4.26115			0.432654			0.216327	−	0.976321i	$-0.430592\pi$
$97$	4.26115			0.432654			0.216327	+	0.976321i	$0.430592\pi$
$98$	−9.76060	−	0.753692i	−0.985969	−	0.0761344i
$99$	−11.6828	−	9.78304i	−1.17416	−	0.983232i
$100$	−8.49684	−	1.32009i	−0.849684	−	0.132009i
$101$		−	0.355994i		−	0.0354227i	−0.999843	−	0.0177114i	$-0.994362\pi$
$101$		−	0.355994i		−	0.0354227i	0.999843	−	0.0177114i	$-0.00563800\pi$
$102$	−7.69578	+	16.9757i	−0.761996	+	1.68085i
$103$		−	10.6829i		−	1.05262i	−0.850292	−	0.526311i	$-0.823575\pi$
$103$		−	10.6829i		−	1.05262i	0.850292	−	0.526311i	$-0.176425\pi$
$104$	16.1348	+	3.79820i	1.58215	+	0.372444i
$105$	1.38351	+	0.502769i	0.135017	+	0.0490653i
$106$	−0.591865	+	7.66487i	−0.0574870	+	0.744478i
$107$	−3.37528			−0.326300			−0.163150	−	0.986601i	$-0.552166\pi$
$107$	−3.37528			−0.326300			−0.163150	+	0.986601i	$0.552166\pi$
$108$	3.76747	+	9.68536i	0.362525	+	0.931974i
$109$	8.52614			0.816656			0.408328	−	0.912835i	$-0.366112\pi$
$109$	8.52614			0.816656			0.408328	+	0.912835i	$0.366112\pi$
$110$	1.68645	−	21.8402i	0.160797	−	2.08238i
$111$	−11.1737	−	4.06055i	−1.06056	−	0.385411i
$112$	−0.338225	+	1.06223i	−0.0319593	+	0.100372i
$113$			15.8507i			1.49111i	0.666443	+	0.745556i	$0.267816\pi$
$113$			15.8507i			1.49111i	−0.666443	+	0.745556i	$0.732184\pi$
$114$	−5.98046	+	13.1920i	−0.560121	+	1.23554i
$115$		−	6.85974i		−	0.639674i
$116$	1.79023	−	11.5230i	0.166219	−	1.06988i
$117$	−13.4794	−	11.2875i	−1.24617	−	1.04353i
$118$	1.28111	+	0.0989249i	0.117936	+	0.00910678i
$119$	2.12065			0.194399
$120$	−8.18412	+	12.4982i	−0.747105	+	1.14093i
$121$	14.7995			1.34541
$122$	−1.64100	−	0.126715i	−0.148569	−	0.0114722i
$123$	−5.01827	+	13.8092i	−0.452482	+	1.24513i
$124$	−1.33499	+	8.59278i	−0.119886	+	0.771655i
$125$		−	2.13651i		−	0.191095i
$126$	0.826663	−	0.845402i	0.0736450	−	0.0753144i
$127$		−	2.01361i		−	0.178679i	−0.996001	−	0.0893393i	$-0.971524\pi$
$127$		−	2.01361i		−	0.178679i	0.996001	−	0.0893393i	$-0.0284755\pi$
$128$	−9.70704	−	5.81149i	−0.857989	−	0.513668i
$129$	1.65186	−	4.54556i	0.145438	−	0.400214i
$130$	1.94581	−	25.1989i	0.170659	−	2.21009i
$131$	−3.98147			−0.347862			−0.173931	−	0.984758i	$-0.555647\pi$
$131$	−3.98147			−0.347862			−0.173931	+	0.984758i	$0.555647\pi$
$132$	−15.4185	−	8.47718i	−1.34201	−	0.737844i
$133$	1.64797			0.142897
$134$	−0.108878	+	1.41002i	−0.00940566	+	0.121807i
$135$	13.7107	−	7.94348i	1.18003	−	0.683666i
$136$	−4.93158	+	20.9495i	−0.422880	+	1.79640i
$137$		−	8.83469i		−	0.754798i	−0.926051	−	0.377399i	$-0.876818\pi$
$137$		−	8.83469i		−	0.754798i	0.926051	−	0.377399i	$-0.123182\pi$
$138$	−5.01844	−	2.27506i	−0.427198	−	0.193666i
$139$			12.3675i			1.04899i	0.851412	+	0.524497i	$0.175747\pi$
$139$			12.3675i			1.04899i	−0.851412	+	0.524497i	$0.824253\pi$
$140$	1.67961	+	0.260947i	0.141953	+	0.0220540i
$141$	0.740805	+	0.269209i	0.0623870	+	0.0226715i
$142$	6.41535	+	0.495380i	0.538365	+	0.0415714i
$143$	29.7671			2.48925
$144$	6.42914	+	10.1324i	0.535762	+	0.844369i
$145$	−17.7804			−1.47658
$146$	−19.0520	−	1.47116i	−1.57676	−	0.121754i
$147$	11.2688	+	4.09510i	0.929436	+	0.337758i
$148$	−13.5651	−	2.10750i	−1.11505	−	0.173236i
$149$			10.4788i			0.858457i	0.903196	+	0.429229i	$0.141215\pi$
$149$			10.4788i			0.858457i	−0.903196	+	0.429229i	$0.858785\pi$
$150$	9.59170	+	4.34831i	0.783159	+	0.355038i
$151$		−	7.69810i		−	0.626463i	−0.949677	−	0.313231i	$-0.898588\pi$
$151$		−	7.69810i		−	0.626463i	0.949677	−	0.313231i	$-0.101412\pi$
$152$	−3.83238	+	16.2800i	−0.310847	+	1.32048i
$153$	14.6557	−	17.5017i	1.18485	−	1.41493i
$154$	−0.154126	+	1.99599i	−0.0124198	+	0.160842i
$155$	13.2590			1.06499
$156$	−17.7897	−	9.78086i	−1.42432	−	0.783095i
$157$	−12.0712			−0.963384			−0.481692	−	0.876340i	$-0.659978\pi$
$157$	−12.0712			−0.963384			−0.481692	+	0.876340i	$0.659978\pi$
$158$	−1.34294	+	17.3916i	−0.106839	+	1.38360i
$159$	3.21583	−	8.84925i	0.255032	−	0.701791i
$160$	−6.48378	+	15.9857i	−0.512588	+	1.26378i
$161$			0.626916i			0.0494079i
$162$	−1.26405	−	12.6650i	−0.0993135	−	0.995056i
$163$		−	9.41541i		−	0.737472i	−0.929534	−	0.368736i	$-0.879791\pi$
$163$		−	9.41541i		−	0.737472i	0.929534	−	0.368736i	$-0.120209\pi$
$164$	−2.60458	+	16.7646i	−0.203384	+	1.30909i
$165$	−9.16316	+	25.2150i	−0.713351	+	1.96298i
$166$	−3.93913	−	0.304171i	−0.305736	−	0.0236082i
$167$	−21.0838			−1.63151			−0.815756	−	0.578396i	$-0.803679\pi$
$167$	−21.0838			−1.63151			−0.815756	+	0.578396i	$0.803679\pi$
$168$	0.747953	−	1.14222i	0.0577058	−	0.0881243i
$169$	21.3449			1.64191
$170$	32.7183	+	2.52644i	2.50938	+	0.193769i
$171$	11.3891	−	13.6007i	0.870946	−	1.04007i
$172$	0.857348	−	5.51839i	0.0653722	−	0.420773i
$173$			18.9189i			1.43838i	0.694815	+	0.719188i	$0.255486\pi$
$173$			18.9189i			1.43838i	−0.694815	+	0.719188i	$0.744514\pi$
$174$	−5.89695	+	13.0078i	−0.447047	+	0.986117i
$175$		−	1.19822i		−	0.0905768i
$176$	−19.3596	−	6.16428i	−1.45928	−	0.464650i
$177$	−1.47907	−	0.537497i	−0.111174	−	0.0404008i
$178$	0.184210	−	2.38559i	0.0138071	−	0.178807i
$179$	25.3930			1.89796			0.948982	−	0.315331i	$-0.102115\pi$
$179$	25.3930			1.89796			0.948982	+	0.315331i	$0.102115\pi$
$180$	13.7613	−	12.0584i	1.02571	−	0.898779i
$181$	−9.38501			−0.697582			−0.348791	−	0.937200i	$-0.613408\pi$
$181$	−9.38501			−0.697582			−0.348791	+	0.937200i	$0.613408\pi$
$182$	−0.177829	+	2.30295i	−0.0131815	+	0.170706i
$183$	1.89457	+	0.688490i	0.140051	+	0.0508947i
$184$	−6.19318	−	1.45790i	−0.456567	−	0.107478i
$185$			20.9315i			1.53891i
$186$	4.39740	−	9.70000i	0.322433	−	0.711239i
$187$			38.6496i			2.82634i
$188$	0.899350	+	0.139725i	0.0655918	+	0.0101905i
$189$	−1.25303	+	0.725960i	−0.0911449	+	0.0528058i
$190$	25.4257	+	1.96332i	1.84457	+	0.142434i
$191$	−4.93877			−0.357357			−0.178678	−	0.983908i	$-0.557182\pi$
$191$	−4.93877			−0.357357			−0.178678	+	0.983908i	$0.557182\pi$
$192$	9.54440	+	10.0451i	0.688808	+	0.724944i
$193$	20.3135			1.46220			0.731099	−	0.682271i	$-0.239008\pi$
$193$	20.3135			1.46220			0.731099	+	0.682271i	$0.239008\pi$
$194$	−6.00829	−	0.463947i	−0.431370	−	0.0333094i
$195$	−10.5723	+	29.0927i	−0.757100	+	2.08337i
$196$	13.6805	+	2.12544i	0.977181	+	0.151817i
$197$		−	13.3758i		−	0.952990i	−0.879177	−	0.476495i	$-0.841907\pi$
$197$		−	13.3758i		−	0.952990i	0.879177	−	0.476495i	$-0.158093\pi$
$198$	15.4078	+	15.0662i	1.09498	+	1.07071i
$199$			13.1693i			0.933548i	0.884377	+	0.466774i	$0.154584\pi$
$199$			13.1693i			0.933548i	−0.884377	+	0.466774i	$0.845416\pi$
$200$	11.8370	+	2.78647i	0.836999	+	0.197033i
$201$	0.591579	−	1.62789i	0.0417267	−	0.114823i
$202$	−0.0387601	+	0.501957i	−0.00272715	+	0.0353176i
$203$	1.62496			0.114050
$204$	12.6995	−	23.0981i	0.889140	−	1.61719i
$205$	25.8684			1.80673
$206$	−1.16314	+	15.0631i	−0.0810400	+	1.04950i
$207$	5.17394	+	4.33260i	0.359614	+	0.301136i
$208$	−22.3368	−	7.11226i	−1.54878	−	0.493147i
$209$			30.0349i			2.07756i
$210$	−1.89603	−	0.859547i	−0.130839	−	0.0593144i
$211$			4.89617i			0.337066i	0.985696	+	0.168533i	$0.0539030\pi$
$211$			4.89617i			0.337066i	−0.985696	+	0.168533i	$0.946097\pi$
$212$	1.66908	−	10.7431i	0.114633	−	0.737843i
$213$	−7.40666	−	2.69159i	−0.507496	−	0.184425i
$214$	4.75920	+	0.367495i	0.325332	+	0.0251214i
$215$	−8.51508			−0.580723
$216$	−4.25767	−	14.0667i	−0.289698	−	0.957118i
$217$	−1.21175			−0.0822588
$218$	−12.0220	−	0.928313i	−0.814233	−	0.0628733i
$219$	21.9960	+	7.99336i	1.48635	+	0.540141i
$220$	−4.75585	+	30.6114i	−0.320640	+	2.06382i
$221$			44.5934i			2.99967i
$222$	15.3130	+	6.94202i	1.02774	+	0.465918i
$223$		−	27.0230i		−	1.80959i	−0.425845	−	0.904796i	$-0.640023\pi$
$223$		−	27.0230i		−	1.80959i	0.425845	−	0.904796i	$-0.359977\pi$
$224$	0.592557	−	1.46094i	0.0395919	−	0.0976131i
$225$	−9.88889	−	8.28085i	−0.659260	−	0.552057i
$226$	1.72580	−	22.3498i	0.114799	−	1.48669i
$227$	−0.0417672			−0.00277218			−0.00138609	−	0.999999i	$-0.500441\pi$
$227$	−0.0417672			−0.00277218			−0.00138609	+	0.999999i	$0.500441\pi$
$228$	9.86887	−	17.9498i	0.653582	−	1.18875i
$229$	14.7269			0.973180			0.486590	−	0.873631i	$-0.338241\pi$
$229$	14.7269			0.973180			0.486590	+	0.873631i	$0.338241\pi$
$230$	−0.746877	+	9.67234i	−0.0492476	+	0.637775i
$231$	0.837427	−	2.30441i	0.0550987	−	0.151619i
$232$	−3.77886	+	16.0527i	−0.248094	+	1.05391i
$233$		−	22.8772i		−	1.49874i	−0.662154	−	0.749368i	$-0.730358\pi$
$233$		−	22.8772i		−	1.49874i	0.662154	−	0.749368i	$-0.269642\pi$
$234$	17.7773	+	17.3832i	1.16214	+	1.13638i
$235$		−	1.38773i		−	0.0905255i
$236$	−1.79562	−	0.278971i	−0.116885	−	0.0181595i
$237$	7.29672	−	20.0789i	0.473973	−	1.30427i
$238$	−2.99015	−	0.230893i	−0.193822	−	0.0149666i
$239$	−6.80444			−0.440142			−0.220071	−	0.975484i	$-0.570629\pi$
$239$	−6.80444			−0.440142			−0.220071	+	0.975484i	$0.570629\pi$
$240$	12.9005	−	16.7316i	0.832726	−	1.08002i
$241$	−0.959498			−0.0618067			−0.0309034	−	0.999522i	$-0.509838\pi$
$241$	−0.959498			−0.0618067			−0.0309034	+	0.999522i	$0.509838\pi$
$242$	−20.8675	−	1.61134i	−1.34141	−	0.103581i
$243$	−2.66834	+	15.3584i	−0.171174	+	0.985241i
$244$	2.30004	+	0.357340i	0.147245	+	0.0228763i
$245$		−	21.1096i		−	1.34864i
$246$	8.57937	−	18.9248i	0.547000	−	1.20660i
$247$			34.6539i			2.20498i
$248$	2.81793	−	11.9706i	0.178939	−	0.760135i
$249$	4.54780	+	1.65268i	0.288205	+	0.104734i
$250$	−0.232619	+	3.01251i	−0.0147121	+	0.190528i
$251$	−11.7116			−0.739227			−0.369613	−	0.929186i	$-0.620510\pi$
$251$	−11.7116			−0.739227			−0.369613	+	0.929186i	$0.620510\pi$
$252$	−1.25765	+	1.10202i	−0.0792248	+	0.0694210i
$253$	−11.4258			−0.718332
$254$	−0.219238	+	2.83922i	−0.0137562	+	0.178148i
$255$	−37.7739	−	13.7271i	−2.36550	−	0.859625i
$256$	13.0543	+	9.25118i	0.815896	+	0.578199i
$257$		−	1.54522i		−	0.0963883i	−0.998838	−	0.0481941i	$-0.984653\pi$
$257$		−	1.54522i		−	0.0963883i	0.998838	−	0.0481941i	$-0.0153466\pi$
$258$	−2.82407	+	6.22946i	−0.175819	+	0.387829i
$259$		−	1.91294i		−	0.118864i
$260$	−5.48724	+	35.3191i	−0.340304	+	2.19039i
$261$	11.2301	−	13.4108i	0.695123	−	0.830108i
$262$	5.61393	+	0.433496i	0.346830	+	0.0267815i
$263$	25.4945			1.57206			0.786029	−	0.618190i	$-0.212134\pi$
$263$	25.4945			1.57206			0.786029	+	0.618190i	$0.212134\pi$
$264$	20.8174	+	13.6317i	1.28122	+	0.838974i
$265$	−16.5771			−1.01832
$266$	−2.32367	−	0.179429i	−0.142473	−	0.0110015i
$267$	−1.00088	+	2.75421i	−0.0612531	+	0.168555i
$268$	0.307041	−	1.97629i	0.0187555	−	0.120721i
$269$		−	11.3415i		−	0.691505i	−0.938326	−	0.345752i	$-0.887624\pi$
$269$		−	11.3415i		−	0.691505i	0.938326	−	0.345752i	$-0.112376\pi$
$270$	−20.1973	+	9.70763i	−1.22917	+	0.590788i
$271$		−	3.42034i		−	0.207771i	−0.994589	−	0.103885i	$-0.966872\pi$
$271$		−	3.42034i		−	0.207771i	0.994589	−	0.103885i	$-0.0331275\pi$
$272$	9.23456	−	29.0021i	0.559927	−	1.75851i
$273$	0.966212	−	2.65880i	0.0584778	−	0.160918i
$274$	−0.961907	+	12.4571i	−0.0581109	+	0.752558i
$275$	21.8380			1.31688
$276$	6.82838	+	3.75428i	0.411020	+	0.225981i
$277$	11.3806			0.683793			0.341897	−	0.939738i	$-0.388931\pi$
$277$	11.3806			0.683793			0.341897	+	0.939738i	$0.388931\pi$
$278$	1.34655	−	17.4383i	0.0807607	−	1.04588i
$279$	−8.37435	+	10.0006i	−0.501359	+	0.598717i
$280$	−2.33986	−	0.550812i	−0.139833	−	0.0329173i
$281$		−	9.82446i		−	0.586078i	−0.956101	−	0.293039i	$-0.905333\pi$
$281$		−	9.82446i		−	0.586078i	0.956101	−	0.293039i	$-0.0946666\pi$
$282$	−1.01524	−	0.460247i	−0.0604564	−	0.0274073i
$283$		−	17.7063i		−	1.05253i	−0.850320	−	0.526265i	$-0.823592\pi$
$283$		−	17.7063i		−	1.05253i	0.850320	−	0.526265i	$-0.176408\pi$
$284$	−8.99182	−	1.39699i	−0.533566	−	0.0828959i
$285$	−29.3545	−	10.6675i	−1.73881	−	0.631886i
$286$	−41.9721	−	3.24099i	−2.48186	−	0.191644i
$287$	−2.36413			−0.139550
$288$	−7.96199	−	14.9869i	−0.469165	−	0.883111i
$289$	−40.9000			−2.40588
$290$	25.0706	+	1.93590i	1.47220	+	0.113680i
$291$	6.93669	+	2.52080i	0.406636	+	0.147772i
$292$	26.7035	+	4.14871i	1.56270	+	0.242785i
$293$			15.7258i			0.918712i	0.888252	+	0.459356i	$0.151920\pi$
$293$			15.7258i			0.918712i	−0.888252	+	0.459356i	$0.848080\pi$
$294$	−15.4433	−	7.00109i	−0.900674	−	0.408312i
$295$			2.77071i			0.161317i
$296$	18.8976	+	4.44856i	1.09840	+	0.258567i
$297$	−13.2309	−	22.8370i	−0.767734	−	1.32514i
$298$	1.14092	−	14.7753i	0.0660915	−	0.855909i
$299$	−13.1829			−0.762387
$300$	−13.0510	−	7.17551i	−0.753501	−	0.414278i
$301$	0.778199			0.0448546
$302$	−0.838157	+	10.8544i	−0.0482305	+	0.624603i
$303$	0.210598	−	0.579520i	0.0120986	−	0.0332926i
$304$	7.17626	−	22.5378i	0.411587	−	1.29263i
$305$		−	3.54905i		−	0.203218i
$306$	−22.5704	+	23.0820i	−1.29026	+	1.31951i
$307$		−	17.3222i		−	0.988632i	−0.869282	−	0.494316i	$-0.835419\pi$
$307$		−	17.3222i		−	0.988632i	0.869282	−	0.494316i	$-0.164581\pi$
$308$	0.434641	−	2.79760i	0.0247660	−	0.159408i
$309$	6.31980	−	17.3907i	0.359521	−	0.989322i
$310$	−18.6954	−	1.44362i	−1.06183	−	0.0819919i
$311$	16.1322			0.914776			0.457388	−	0.889267i	$-0.348785\pi$
$311$	16.1322			0.914776			0.457388	+	0.889267i	$0.348785\pi$
$312$	24.0188	+	15.7281i	1.35980	+	0.890427i
$313$	16.6044			0.938535			0.469267	−	0.883056i	$-0.344518\pi$
$313$	16.6044			0.938535			0.469267	+	0.883056i	$0.344518\pi$
$314$	17.0205	+	1.31429i	0.960525	+	0.0741697i
$315$	1.95478	+	1.63691i	0.110139	+	0.0922294i
$316$	3.78714	−	24.3762i	0.213043	−	1.37127i
$317$			17.6587i			0.991813i	0.868376	+	0.495907i	$0.165164\pi$
$317$			17.6587i			0.991813i	−0.868376	+	0.495907i	$0.834836\pi$
$318$	−5.49786	+	12.1275i	−0.308305	+	0.680074i
$319$			29.6155i			1.65815i
$320$	10.8827	−	21.8341i	0.608363	−	1.22056i
$321$	−5.49459	−	1.99674i	−0.306678	−	0.111447i
$322$	0.0682576	−	0.883962i	0.00380385	−	0.0492613i
$323$	−44.9946			−2.50357
$324$	0.403393	+	17.9955i	0.0224107	+	0.999749i
$325$	25.1964			1.39764
$326$	−1.02513	+	13.2759i	−0.0567770	+	0.735283i
$327$	13.8796	+	5.04388i	0.767546	+	0.278927i
$328$	5.49780	−	23.3547i	0.303565	−	1.28955i
$329$			0.126826i			0.00699212i
$330$	15.6656	−	34.5558i	0.862361	−	1.90224i
$331$			34.2868i			1.88457i	0.334810	+	0.942286i	$0.391328\pi$
$331$			34.2868i			1.88457i	−0.334810	+	0.942286i	$0.608672\pi$
$332$	5.52112	+	0.857772i	0.303011	+	0.0470763i
$333$	−15.7875	−	13.2203i	−0.865150	−	0.724467i
$334$	29.7285	+	2.29557i	1.62667	+	0.125608i
$335$	−3.04949			−0.166611
$336$	−1.17899	+	1.52911i	−0.0643191	+	0.0834200i
$337$	6.16304			0.335722			0.167861	−	0.985811i	$-0.446314\pi$
$337$	6.16304			0.335722			0.167861	+	0.985811i	$0.446314\pi$
$338$	−30.0966	−	2.32400i	−1.63704	−	0.126409i
$339$	−9.37695	+	25.8033i	−0.509286	+	1.40144i
$340$	−45.8582	−	7.12463i	−2.48701	−	0.386387i
$341$		−	22.0845i		−	1.19595i
$342$	−17.5396	+	17.9372i	−0.948435	+	0.969934i
$343$			3.88008i			0.209505i
$344$	−1.80971	+	7.68767i	−0.0975729	+	0.414491i
$345$	4.05807	−	11.1669i	0.218479	−	0.601207i
$346$	2.05986	−	26.6759i	0.110739	−	1.43411i
$347$	−7.81789			−0.419686			−0.209843	−	0.977735i	$-0.567295\pi$
$347$	−7.81789			−0.419686			−0.209843	+	0.977735i	$0.567295\pi$
$348$	9.73106	−	17.6991i	0.521639	−	0.948772i
$349$	−21.3355			−1.14206			−0.571031	−	0.820929i	$-0.693456\pi$
$349$	−21.3355			−1.14206			−0.571031	+	0.820929i	$0.693456\pi$
$350$	−0.130460	+	1.68951i	−0.00697338	+	0.0903079i
$351$	−15.2656	−	26.3490i	−0.814819	−	1.40641i
$352$	26.6262	+	10.7996i	1.41918	+	0.575619i
$353$			13.3348i			0.709739i	0.934916	+	0.354869i	$0.115475\pi$
$353$			13.3348i			0.709739i	−0.934916	+	0.354869i	$0.884525\pi$
$354$	2.02700	+	0.918919i	0.107734	+	0.0488400i
$355$			13.8747i			0.736393i
$356$	−0.519478	+	3.34366i	−0.0275323	+	0.177214i
$357$	3.45219	+	1.25453i	0.182709	+	0.0663968i
$358$	−35.8046	−	2.76475i	−1.89233	−	0.146122i
$359$	19.0196			1.00381			0.501907	−	0.864922i	$-0.332632\pi$
$359$	19.0196			1.00381			0.501907	+	0.864922i	$0.332632\pi$
$360$	−20.7165	+	15.5042i	−1.09186	+	0.817144i
$361$	−15.9657			−0.840301
$362$	13.2330	+	1.02182i	0.695512	+	0.0537059i
$363$	24.0920	+	8.75505i	1.26450	+	0.459521i
$364$	0.501483	−	3.22783i	0.0262848	−	0.169184i
$365$		−	41.2045i		−	2.15674i
$366$	−2.59642	−	1.17706i	−0.135717	−	0.0615259i
$367$			1.97931i			0.103319i	0.998665	+	0.0516596i	$0.0164511\pi$
$367$			1.97931i			0.103319i	−0.998665	+	0.0516596i	$0.983549\pi$
$368$	8.57375	+	2.72996i	0.446938	+	0.142309i
$369$	−16.3384	+	19.5111i	−0.850544	+	1.01571i
$370$	2.27899	−	29.5137i	0.118479	−	1.53435i
$371$	1.51499			0.0786544
$372$	−7.25653	+	13.1984i	−0.376234	+	0.684304i
$373$	16.1265			0.834998			0.417499	−	0.908677i	$-0.362907\pi$
$373$	16.1265			0.834998			0.417499	+	0.908677i	$0.362907\pi$
$374$	4.20810	−	54.4965i	0.217596	−	2.81795i
$375$	1.26391	−	3.47800i	0.0652681	−	0.179603i
$376$	−1.25289	−	0.294934i	−0.0646126	−	0.0152101i
$377$			34.1700i			1.75984i
$378$	1.84584	−	0.887187i	0.0949398	−	0.0456320i
$379$			27.2364i			1.39904i	0.714612	+	0.699521i	$0.246603\pi$
$379$			27.2364i			1.39904i	−0.714612	+	0.699521i	$0.753397\pi$
$380$	−35.6369	−	5.53661i	−1.82813	−	0.284022i
$381$	1.19121	−	3.27793i	0.0610273	−	0.167934i
$382$	6.96374	+	0.537725i	0.356296	+	0.0275124i
$383$	−31.3840			−1.60365			−0.801825	−	0.597560i	$-0.796137\pi$
$383$	−31.3840			−1.60365			−0.801825	+	0.597560i	$0.796137\pi$
$384$	−12.3641	−	15.2030i	−0.630951	−	0.775823i
$385$	−4.31680			−0.220004
$386$	−28.6424	−	2.21170i	−1.45786	−	0.112573i
$387$	5.37811	−	6.42247i	0.273385	−	0.326473i
$388$	8.42127	+	1.30835i	0.427525	+	0.0664212i
$389$		−	7.82281i		−	0.396632i	−0.980138	−	0.198316i	$-0.936453\pi$
$389$		−	7.82281i		−	0.396632i	0.980138	−	0.198316i	$-0.0635473\pi$
$390$	18.0747	−	39.8701i	0.915249	−	2.01890i
$391$		−	17.1167i		−	0.865628i
$392$	−19.0584	−	4.48641i	−0.962593	−	0.226598i
$393$	−6.48140	−	2.35535i	−0.326944	−	0.118812i
$394$	−1.45634	+	18.8602i	−0.0733694	+	0.950161i
$395$	−37.6134			−1.89253
$396$	−20.0848	−	22.9212i	−1.00930	−	1.15183i
$397$	−25.8514			−1.29744			−0.648721	−	0.761026i	$-0.724696\pi$
$397$	−25.8514			−1.29744			−0.648721	+	0.761026i	$0.724696\pi$
$398$	1.43385	−	18.5689i	0.0718726	−	0.930777i
$399$	2.68273	+	0.974906i	0.134304	+	0.0488064i
$400$	−16.3869	−	5.21775i	−0.819346	−	0.260888i
$401$			1.90320i			0.0950413i	0.998870	+	0.0475207i	$0.0151320\pi$
$401$			1.90320i			0.0950413i	−0.998870	+	0.0475207i	$0.984868\pi$
$402$	−1.01138	+	2.23094i	−0.0504429	+	0.111269i
$403$		−	25.4809i		−	1.26929i
$404$	0.109305	−	0.703548i	0.00543811	−	0.0350028i
$405$	27.0188	−	4.82015i	1.34258	−	0.239515i
$406$	−2.29122	−	0.176923i	−0.113711	−	0.00878055i
$407$	34.8641			1.72815
$408$	−20.4213	+	31.1860i	−1.01101	+	1.54394i
$409$	−18.6244			−0.920917			−0.460459	−	0.887681i	$-0.652315\pi$
$409$	−18.6244			−0.920917			−0.460459	+	0.887681i	$0.652315\pi$
$410$	−36.4748	−	2.81651i	−1.80136	−	0.139097i
$411$	5.22641	−	14.3819i	0.257800	−	0.709408i
$412$	3.28010	−	21.1126i	0.161599	−	1.04014i
$413$		−	0.253217i		−	0.0124600i
$414$	−6.82361	−	6.67236i	−0.335362	−	0.327929i
$415$		−	8.51929i		−	0.418195i
$416$	30.7209	+	12.4604i	1.50622	+	0.610921i
$417$	−7.31633	+	20.1329i	−0.358282	+	0.985913i
$418$	3.27016	−	42.3497i	0.159949	−	2.07139i
$419$	20.4330			0.998217			0.499109	−	0.866539i	$-0.333661\pi$
$419$	20.4330			0.998217			0.499109	+	0.866539i	$0.333661\pi$
$420$	2.57985	+	1.41841i	0.125884	+	0.0692114i
$421$	15.8138			0.770716			0.385358	−	0.922767i	$-0.374078\pi$
$421$	15.8138			0.770716			0.385358	+	0.922767i	$0.374078\pi$
$422$	0.533087	−	6.90368i	0.0259503	−	0.336066i
$423$	1.04669	+	0.876488i	0.0508919	+	0.0426163i
$424$	−3.52312	+	14.9663i	−0.171098	+	0.726827i
$425$			32.7149i			1.58691i
$426$	10.1505	+	4.60161i	0.491791	+	0.222949i
$427$			0.324350i			0.0156964i
$428$	−6.67053	−	1.03635i	−0.322432	−	0.0500937i
$429$	48.4576	+	17.6096i	2.33956	+	0.850198i
$430$	12.0064	+	0.927108i	0.579000	+	0.0447091i
$431$	20.0667			0.966578			0.483289	−	0.875461i	$-0.339442\pi$
$431$	20.0667			0.966578			0.483289	+	0.875461i	$0.339442\pi$
$432$	4.47183	+	20.2979i	0.215151	+	0.976581i
$433$	−13.1719			−0.633003			−0.316501	−	0.948592i	$-0.602508\pi$
$433$	−13.1719			−0.633003			−0.316501	+	0.948592i	$0.602508\pi$
$434$	1.70858	+	0.131933i	0.0820147	+	0.00633299i
$435$	−28.9446	−	10.5185i	−1.38779	−	0.504323i
$436$	16.8501	+	2.61787i	0.806975	+	0.125373i
$437$		−	13.3015i		−	0.636298i
$438$	−30.1444	−	13.6657i	−1.44035	−	0.652970i
$439$			22.2901i			1.06385i	0.846793	+	0.531923i	$0.178531\pi$
$439$			22.2901i			1.06385i	−0.846793	+	0.531923i	$0.821469\pi$
$440$	10.0388	−	42.6448i	0.478579	−	2.03301i
$441$	15.9218	+	13.3328i	0.758183	+	0.634894i
$442$	4.85525	−	62.8774i	0.230941	−	2.99077i
$443$	15.4580			0.734430			0.367215	−	0.930136i	$-0.380311\pi$
$443$	15.4580			0.734430			0.367215	+	0.930136i	$0.380311\pi$
$444$	−20.8358	−	11.4556i	−0.988823	−	0.543660i
$445$	5.15939			0.244579
$446$	−2.94222	+	38.1028i	−0.139318	+	1.80422i
$447$	−6.19904	+	17.0584i	−0.293204	+	0.806833i
$448$	−0.994580	+	1.99543i	−0.0469895	+	0.0942753i
$449$			24.9972i			1.17969i	0.807516	+	0.589845i	$0.200811\pi$
$449$			24.9972i			1.17969i	−0.807516	+	0.589845i	$0.799189\pi$
$450$	13.0419	+	12.7528i	0.614801	+	0.601174i
$451$		−	43.0871i		−	2.02889i
$452$	−4.86682	+	31.3257i	−0.228916	+	1.47344i
$453$	4.55403	−	12.5317i	0.213967	−	0.588790i
$454$	0.0588924	+	0.00454754i	0.00276396	+	0.000213427i
$455$	−4.98066			−0.233497
$456$	−15.8696	+	24.2350i	−0.743162	+	1.13491i
$457$	−13.8327			−0.647064			−0.323532	−	0.946217i	$-0.604870\pi$
$457$	−13.8327			−0.647064			−0.323532	+	0.946217i	$0.604870\pi$
$458$	−20.7651	−	1.60344i	−0.970291	−	0.0749238i
$459$	34.2116	−	19.8209i	1.59686	−	0.925160i
$460$	2.10622	−	13.5568i	0.0982029	−	0.632091i
$461$		−	0.355681i		−	0.0165657i	−0.999966	−	0.00828286i	$-0.997363\pi$
$461$		−	0.355681i		−	0.0165657i	0.999966	−	0.00828286i	$-0.00263655\pi$
$462$	−1.43169	+	3.15808i	−0.0666081	+	0.146927i
$463$			3.72249i			0.172999i	0.996252	+	0.0864994i	$0.0275681\pi$
$463$			3.72249i			0.172999i	−0.996252	+	0.0864994i	$0.972432\pi$
$464$	7.07605	−	22.2231i	0.328497	−	1.03168i
$465$	21.5842	+	7.84373i	1.00094	+	0.363744i
$466$	−2.49083	+	32.2572i	−0.115386	+	1.49429i
$467$	33.9317			1.57017			0.785086	−	0.619387i	$-0.212619\pi$
$467$	33.9317			1.57017			0.785086	+	0.619387i	$0.212619\pi$
$468$	−23.1736	−	26.4462i	−1.07120	−	1.22248i
$469$	0.278695			0.0128689
$470$	−0.151094	+	1.95672i	−0.00696944	+	0.0902569i
$471$	−19.6506	−	7.14105i	−0.905451	−	0.329042i
$472$	2.50148	+	0.588859i	0.115140	+	0.0271044i
$473$			14.1830i			0.652133i
$474$	−12.4747	+	27.5172i	−0.572980	+	1.26391i
$475$			25.4231i			1.16649i
$476$	4.19102	+	0.651125i	0.192095	+	0.0298443i
$477$	10.4701	−	12.5032i	0.479391	−	0.572483i
$478$	9.59436	+	0.740856i	0.438836	+	0.0338860i
$479$	7.68288			0.351040			0.175520	−	0.984476i	$-0.443839\pi$
$479$	7.68288			0.351040			0.175520	+	0.984476i	$0.443839\pi$
$480$	−20.0117	+	22.1873i	−0.913403	+	1.01271i
$481$	40.2257			1.83413
$482$	1.35291	+	0.104469i	0.0616233	+	0.00475842i
$483$	−0.370870	+	1.02055i	−0.0168752	+	0.0464367i
$484$	29.2481	+	4.54404i	1.32946	+	0.206547i
$485$		−	12.9943i		−	0.590042i
$486$	5.43460	−	21.3650i	0.246518	−	0.969138i
$487$		−	33.8111i		−	1.53213i	−0.642766	−	0.766063i	$-0.722213\pi$
$487$		−	33.8111i		−	1.53213i	0.642766	−	0.766063i	$-0.277787\pi$
$488$	−3.20419	−	0.754280i	−0.145047	−	0.0341446i
$489$	5.56995	−	15.3273i	0.251882	−	0.693123i
$490$	−2.29838	+	29.7648i	−0.103830	+	1.34464i
$491$	43.0765			1.94401			0.972007	−	0.234952i	$-0.0754932\pi$
$491$	43.0765			1.94401			0.972007	+	0.234952i	$0.0754932\pi$
$492$	−14.1575	+	25.7501i	−0.638271	+	1.16091i
$493$	−44.3663			−1.99816
$494$	3.77306	−	48.8626i	0.169758	−	2.19843i
$495$	−29.8333	+	35.6265i	−1.34091	+	1.60129i
$496$	−5.27667	+	16.5719i	−0.236929	+	0.744102i
$497$		−	1.26802i		−	0.0568784i
$498$	−6.23254	−	2.82546i	−0.279287	−	0.126612i
$499$		−	31.2747i		−	1.40005i	−0.714118	−	0.700025i	$-0.753172\pi$
$499$		−	31.2747i		−	1.40005i	0.714118	−	0.700025i	$-0.246828\pi$
$500$	0.655994	−	4.22236i	0.0293370	−	0.188830i
$501$	−34.3222	−	12.4727i	−1.53340	−	0.557240i
$502$	16.5135	+	1.27514i	0.737033	+	0.0569121i
$503$	11.9246			0.531690			0.265845	−	0.964016i	$-0.414349\pi$
$503$	11.9246			0.531690			0.265845	+	0.964016i	$0.414349\pi$
$504$	1.89330	−	1.41694i	0.0843343	−	0.0631156i
$505$	−1.08560			−0.0483086
$506$	16.1105	+	1.24402i	0.716200	+	0.0553034i
$507$	34.7472	+	12.6272i	1.54318	+	0.560792i
$508$	0.618259	−	3.97947i	0.0274308	−	0.176560i
$509$		−	18.5710i		−	0.823145i	−0.911377	−	0.411572i	$-0.864980\pi$
$509$		−	18.5710i		−	0.823145i	0.911377	−	0.411572i	$-0.135020\pi$
$510$	51.7673	+	23.4682i	2.29229	+	1.03919i
$511$			3.76571i			0.166585i
$512$	−17.3996	−	14.4656i	−0.768960	−	0.639297i
$513$	26.5861	−	15.4030i	1.17381	−	0.680058i
$514$	−0.168241	+	2.17879i	−0.00742080	+	0.0961022i
$515$	−32.5775			−1.43554
$516$	4.66023	−	8.47616i	0.205155	−	0.373142i
$517$	−2.31144			−0.101657
$518$	−0.208278	+	2.69728i	−0.00915121	+	0.118512i
$519$	−11.1920	+	30.7979i	−0.491275	+	1.35188i
$520$	11.5826	−	49.2030i	0.507930	−	2.15769i
$521$		−	7.64072i		−	0.334746i	−0.985894	−	0.167373i	$-0.946472\pi$
$521$		−	7.64072i		−	0.334746i	0.985894	−	0.167373i	$-0.0535284\pi$
$522$	−17.2947	+	17.6867i	−0.756969	+	0.774128i
$523$		−	21.5819i		−	0.943711i	−0.881676	−	0.471855i	$-0.843584\pi$
$523$		−	21.5819i		−	0.943711i	0.881676	−	0.471855i	$-0.156416\pi$
$524$	−7.86854	−	1.22247i	−0.343739	−	0.0534040i
$525$	0.708840	−	1.95057i	0.0309363	−	0.0851299i
$526$	−35.9476	−	2.77580i	−1.56739	−	0.121031i
$527$	33.0843			1.44118
$528$	−27.8687	−	21.4875i	−1.21283	−	0.935123i
$529$	−17.9399			−0.779995
$530$	23.3739	+	1.80489i	1.01530	+	0.0783992i
$531$	−2.08980	−	1.74998i	−0.0906896	−	0.0759425i
$532$	3.25688	+	0.505995i	0.141204	+	0.0219377i
$533$		−	49.7133i		−	2.15332i
$534$	1.71114	−	3.77451i	0.0740481	−	0.163339i
$535$			10.2929i			0.445000i
$536$	−0.648108	+	2.75317i	−0.0279940	+	0.118919i
$537$	41.3371	+	15.0220i	1.78383	+	0.648246i
$538$	−1.23485	+	15.9917i	−0.0532380	+	0.689452i
$539$	−35.1607			−1.51448
$540$	29.5354	−	11.4889i	1.27100	−	0.494402i
$541$	−18.2680			−0.785402			−0.392701	−	0.919666i	$-0.628459\pi$
$541$	−18.2680			−0.785402			−0.392701	+	0.919666i	$0.628459\pi$
$542$	−0.372401	+	4.82274i	−0.0159960	+	0.207154i
$543$	−15.2778	−	5.55197i	−0.655633	−	0.238258i
$544$	−16.1786	+	39.8880i	−0.693651	+	1.71018i
$545$		−	26.0004i		−	1.11373i
$546$	−1.65186	+	3.64375i	−0.0706931	+	0.155938i
$547$			0.148820i			0.00636309i	0.999995	+	0.00318155i	$0.00101272\pi$
$547$			0.148820i			0.00636309i	−0.999995	+	0.00318155i	$0.998987\pi$
$548$	2.71261	−	17.4599i	0.115877	−	0.745851i
$549$	2.67686	+	2.24158i	0.114246	+	0.0956681i
$550$	−30.7919	−	2.37768i	−1.31297	−	0.101385i
$551$	−34.4775			−1.46879
$552$	−9.21937	−	6.03705i	−0.392402	−	0.256954i
$553$	3.43751			0.146178
$554$	−16.0468	−	1.23910i	−0.681764	−	0.0526443i
$555$	−12.3826	+	34.0742i	−0.525613	+	1.44637i
$556$	−3.79731	+	24.4417i	−0.161042	+	1.03656i
$557$		−	9.99434i		−	0.423474i	−0.977327	−	0.211737i	$-0.932088\pi$
$557$		−	9.99434i		−	0.423474i	0.977327	−	0.211737i	$-0.0679120\pi$
$558$	12.8968	−	13.1892i	0.545966	−	0.558341i
$559$			16.3641i			0.692128i
$560$	3.23927	+	1.03141i	0.136884	+	0.0435852i
$561$	−22.8643	+	62.9174i	−0.965330	+	2.65637i
$562$	−1.06967	+	13.8526i	−0.0451213	+	0.584338i
$563$	−21.6148			−0.910954			−0.455477	−	0.890247i	$-0.650531\pi$
$563$	−21.6148			−0.910954			−0.455477	+	0.890247i	$0.650531\pi$
$564$	1.38139	+	0.759493i	0.0581669	+	0.0319804i
$565$	48.3367			2.03354
$566$	−1.92783	+	24.9662i	−0.0810329	+	1.04941i
$567$	−2.46927	+	0.440517i	−0.103700	+	0.0185000i
$568$	12.5265	+	2.94879i	0.525601	+	0.123728i
$569$			4.62418i			0.193856i	0.995291	+	0.0969279i	$0.0309016\pi$
$569$			4.62418i			0.193856i	−0.995291	+	0.0969279i	$0.969098\pi$
$570$	40.2288	+	18.2374i	1.68500	+	0.763879i
$571$		−	0.855969i		−	0.0358212i	−0.999840	−	0.0179106i	$-0.994299\pi$
$571$		−	0.855969i		−	0.0358212i	0.999840	−	0.0179106i	$-0.00570142\pi$
$572$	58.8284	+	9.13971i	2.45974	+	0.382150i
$573$	−8.03979	−	2.92167i	−0.335867	−	0.122054i
$574$	3.33346	+	0.257403i	0.139136	+	0.0107438i
$575$	−9.67135			−0.403323
$576$	9.59479	+	21.9986i	0.399783	+	0.916610i
$577$	16.9778			0.706796			0.353398	−	0.935473i	$-0.385026\pi$
$577$	16.9778			0.706796			0.353398	+	0.935473i	$0.385026\pi$
$578$	57.6697	+	4.45313i	2.39874	+	0.185226i
$579$	33.0682	+	12.0170i	1.37427	+	0.499411i
$580$	−35.1392	−	5.45930i	−1.45908	−	0.226685i
$581$			0.778583i			0.0323011i
$582$	−9.50638	−	4.30963i	−0.394052	−	0.178640i
$583$			27.6113i			1.14354i
$584$	−37.2007	−	8.75718i	−1.53937	−	0.362375i
$585$	−34.4212	+	41.1054i	−1.42314	+	1.69950i
$586$	1.71220	−	22.1737i	0.0707304	−	0.915985i
$587$	11.4625			0.473108			0.236554	−	0.971618i	$-0.423982\pi$
$587$	11.4625			0.473108			0.236554	+	0.971618i	$0.423982\pi$
$588$	21.0131	+	11.5531i	0.866565	+	0.476442i
$589$	25.7101			1.05937
$590$	0.301671	−	3.90675i	0.0124196	−	0.160838i
$591$	7.91286	−	21.7744i	0.325492	−	0.895681i
$592$	−26.1615	−	8.33008i	−1.07523	−	0.342364i
$593$		−	29.2647i		−	1.20176i	−0.799340	−	0.600880i	$-0.794817\pi$
$593$		−	29.2647i		−	1.20176i	0.799340	−	0.600880i	$-0.205183\pi$
$594$	16.1693	+	33.6411i	0.663435	+	1.38031i
$595$		−	6.46689i		−	0.265117i
$596$	−3.21742	+	20.7092i	−0.131791	+	0.848281i
$597$	−7.79068	+	21.4382i	−0.318851	+	0.877408i
$598$	18.5881	+	1.43533i	0.760124	+	0.0586952i
$599$	43.1247			1.76203			0.881014	−	0.473090i	$-0.156861\pi$
$599$	43.1247			1.76203			0.881014	+	0.473090i	$0.156861\pi$
$600$	17.6209	+	11.5386i	0.719370	+	0.471060i
$601$	−9.96034			−0.406291			−0.203145	−	0.979149i	$-0.565116\pi$
$601$	−9.96034			−0.406291			−0.203145	+	0.979149i	$0.565116\pi$
$602$	−1.09727	−	0.0847290i	−0.0447215	−	0.00345330i
$603$	1.92605	−	2.30007i	0.0784349	−	0.0936661i
$604$	2.36363	−	15.2137i	0.0961747	−	0.619036i
$605$		−	45.1309i		−	1.83483i
$606$	−0.360044	+	0.794203i	−0.0146258	+	0.0322623i
$607$		−	7.00955i		−	0.284509i	−0.989830	−	0.142255i	$-0.954565\pi$
$607$		−	7.00955i		−	0.284509i	0.989830	−	0.142255i	$-0.0454351\pi$
$608$	−12.5725	+	30.9973i	−0.509883	+	1.25711i
$609$	2.64526	+	0.961293i	0.107191	+	0.0389535i
$610$	−0.386415	+	5.00422i	−0.0156455	+	0.202615i
$611$	−2.66691			−0.107892
$612$	34.3377	−	30.0886i	1.38802	−	1.21626i
$613$	4.42637			0.178779			0.0893897	−	0.995997i	$-0.471508\pi$
$613$	4.42637			0.178779			0.0893897	+	0.995997i	$0.471508\pi$
$614$	−1.88602	+	24.4246i	−0.0761134	+	0.985698i
$615$	42.1109	+	15.3032i	1.69808	+	0.617083i
$616$	−0.917449	+	3.89734i	−0.0369651	+	0.157028i
$617$		−	26.4466i		−	1.06470i	−0.846524	−	0.532350i	$-0.821309\pi$
$617$		−	26.4466i		−	1.06470i	0.846524	−	0.532350i	$-0.178691\pi$
$618$	−10.8045	+	23.8331i	−0.434621	+	0.958707i
$619$			5.44867i			0.219000i	0.993987	+	0.109500i	$0.0349250\pi$
$619$			5.44867i			0.219000i	−0.993987	+	0.109500i	$0.965075\pi$
$620$	26.2036	+	4.07105i	1.05236	+	0.163497i
$621$	5.85954	+	10.1138i	0.235135	+	0.405853i
$622$	−22.7467	−	1.75645i	−0.912061	−	0.0704274i
$623$	−0.471520			−0.0188911
$624$	−32.1545	−	24.7920i	−1.28721	−	0.992474i
$625$	−28.0122			−1.12049
$626$	−23.4124	−	1.80786i	−0.935749	−	0.0722565i
$627$	−17.7680	+	48.8937i	−0.709586	+	1.95262i
$628$	−23.8561	−	3.70634i	−0.951964	−	0.147899i
$629$			52.2290i			2.08251i
$630$	−2.57804	−	2.52090i	−0.102712	−	0.100435i
$631$		−	25.6253i		−	1.02013i	−0.860137	−	0.510063i	$-0.829622\pi$
$631$		−	25.6253i		−	1.02013i	0.860137	−	0.510063i	$-0.170378\pi$
$632$	−7.99397	+	33.9585i	−0.317983	+	1.35080i
$633$	−2.89647	+	7.97044i	−0.115124	+	0.316797i
$634$	1.92265	−	24.8991i	0.0763584	−	0.988870i
$635$	−6.14047			−0.243677
$636$	9.07250	−	16.5013i	0.359748	−	0.654319i
$637$	−40.5680			−1.60736
$638$	3.22449	−	41.7584i	0.127659	−	1.65323i
$639$	−10.4650	−	8.76324i	−0.413987	−	0.346668i
$640$	−17.7221	+	29.6015i	−0.700527	+	1.17010i
$641$		−	2.81491i		−	0.111182i	−0.998454	−	0.0555911i	$-0.982296\pi$
$641$		−	2.81491i		−	0.111182i	0.998454	−	0.0555911i	$-0.0177043\pi$
$642$	7.53006	+	3.41368i	0.297188	+	0.134727i
$643$		−	29.8717i		−	1.17802i	−0.808125	−	0.589011i	$-0.799517\pi$
$643$		−	29.8717i		−	1.17802i	0.808125	−	0.589011i	$-0.200483\pi$
$644$	−0.192489	+	1.23897i	−0.00758512	+	0.0488222i
$645$	−13.8616	−	5.03734i	−0.545801	−	0.198345i
$646$	63.4431	+	4.89894i	2.49614	+	0.192746i
$647$	−42.3369			−1.66443			−0.832217	−	0.554450i	$-0.812929\pi$
$647$	−42.3369			−1.66443			−0.832217	+	0.554450i	$0.812929\pi$
$648$	1.39053	−	25.4178i	0.0546251	−	0.998507i
$649$	4.61498			0.181154
$650$	−35.5273	−	2.74334i	−1.39349	−	0.107603i
$651$	−1.97260	−	0.716844i	−0.0773121	−	0.0280953i
$652$	2.89091	−	18.6076i	0.113217	−	0.728729i
$653$			43.8697i			1.71676i	0.513018	+	0.858378i	$0.328527\pi$
$653$			43.8697i			1.71676i	−0.513018	+	0.858378i	$0.671473\pi$
$654$	−19.0214	−	8.62315i	−0.743794	−	0.337192i
$655$			12.1414i			0.474406i
$656$	−10.2948	+	32.3320i	−0.401945	+	1.26235i
$657$	31.0784	+	26.0247i	1.21248	+	1.01532i
$658$	0.0138086	−	0.178826i	0.000538314	−	0.00697137i
$659$	−30.2207			−1.17723			−0.588616	−	0.808413i	$-0.700327\pi$
$659$	−30.2207			−1.17723			−0.588616	+	0.808413i	$0.700327\pi$
$660$	−25.8511	+	47.0187i	−1.00625	+	1.83020i
$661$	9.40563			0.365837			0.182918	−	0.983128i	$-0.441446\pi$
$661$	9.40563			0.365837			0.182918	+	0.983128i	$0.441446\pi$
$662$	3.73309	−	48.3449i	0.145091	−	1.87898i
$663$	−26.3805	+	72.5932i	−1.02453	+	2.81929i
$664$	−7.69147	−	1.81060i	−0.298487	−	0.0702650i
$665$		−	5.02548i		−	0.194880i
$666$	20.8212	+	20.3597i	0.806807	+	0.788924i
$667$		−	13.1158i		−	0.507845i
$668$	−41.6677	−	6.47358i	−1.61217	−	0.250470i
$669$	15.9862	−	43.9905i	0.618063	−	1.70077i
$670$	4.29983	+	0.332024i	0.166117	+	0.0128272i
$671$	−5.91141			−0.228207
$672$	1.82888	−	2.02771i	0.0705506	−	0.0782206i
$673$	−50.0563			−1.92953			−0.964764	−	0.263117i	$-0.915249\pi$
$673$	−50.0563			−1.92953			−0.964764	+	0.263117i	$0.915249\pi$
$674$	−8.68998	−	0.671021i	−0.334725	−	0.0258468i
$675$	−11.1993	−	19.3304i	−0.431061	−	0.744027i
$676$	42.1837	+	6.55374i	1.62245	+	0.252067i
$677$			20.9155i			0.803848i	0.915673	+	0.401924i	$0.131658\pi$
$677$			20.9155i			0.803848i	−0.915673	+	0.401924i	$0.868342\pi$
$678$	16.0311	−	35.3621i	0.615670	−	1.35807i
$679$			1.18756i			0.0455744i
$680$	63.8852	+	15.0388i	2.44988	+	0.576712i
$681$	−0.0679925	−	0.0247086i	−0.00260548	−	0.000946834i
$682$	−2.40453	+	31.1396i	−0.0920742	+	1.19240i
$683$	−15.8548			−0.606666			−0.303333	−	0.952885i	$-0.598099\pi$
$683$	−15.8548			−0.606666			−0.303333	+	0.952885i	$0.598099\pi$
$684$	26.6842	−	23.3821i	1.02029	−	0.894036i
$685$	−26.9413			−1.02937
$686$	0.422457	−	5.47098i	0.0161295	−	0.208883i
$687$	23.9738	+	8.71211i	0.914657	+	0.332388i
$688$	3.38874	−	10.6427i	0.129194	−	0.405749i
$689$			31.8575i			1.21367i
$690$	−6.93778	+	15.3037i	−0.264117	+	0.582602i
$691$		−	9.43178i		−	0.358802i	−0.983776	−	0.179401i	$-0.942584\pi$
$691$		−	9.43178i		−	0.358802i	0.983776	−	0.179401i	$-0.0574159\pi$
$692$	−5.80887	+	37.3892i	−0.220820	+	1.42132i
$693$	2.72648	−	3.25593i	0.103571	−	0.123683i
$694$	11.0234	+	0.851200i	0.418441	+	0.0323111i
$695$	37.7145			1.43059
$696$	−15.6480	+	23.8965i	−0.593136	+	0.905796i
$697$	64.5478			2.44492
$698$	30.0834	+	2.32297i	1.13867	+	0.0879258i
$699$	13.5337	−	37.2416i	0.511890	−	1.40861i
$700$	0.367902	−	2.36803i	0.0139054	−	0.0895030i
$701$		−	29.7093i		−	1.12210i	−0.827780	−	0.561052i	$-0.810397\pi$
$701$		−	29.7093i		−	1.12210i	0.827780	−	0.561052i	$-0.189603\pi$
$702$	18.6559	+	38.8147i	0.704123	+	1.46497i
$703$			40.5876i			1.53079i
$704$	−36.3675	−	18.1266i	−1.37065	−	0.683171i
$705$	0.820951	−	2.25908i	0.0309188	−	0.0850817i
$706$	1.45187	−	18.8023i	0.0546418	−	0.707632i
$707$	0.0992138			0.00373132
$708$	−2.75805	−	1.51639i	−0.103654	−	0.0569893i
$709$	35.4570			1.33162			0.665808	−	0.746123i	$-0.268087\pi$
$709$	35.4570			1.33162			0.665808	+	0.746123i	$0.268087\pi$
$710$	1.51066	−	19.5636i	0.0566939	−	0.734207i
$711$	23.7565	−	28.3698i	0.890940	−	1.06395i
$712$	1.09652	−	4.65806i	0.0410940	−	0.174568i
$713$			9.78055i			0.366285i
$714$	−4.73105	−	2.14478i	−0.177055	−	0.0802662i
$715$		−	90.7744i		−	3.39477i
$716$	50.1840	+	7.79669i	1.87546	+	0.291376i
$717$	−11.0769	−	4.02536i	−0.413674	−	0.150330i
$718$	−26.8179	−	2.07082i	−1.00083	−	0.0772823i
$719$	30.8444			1.15030			0.575152	−	0.818047i	$-0.304943\pi$
$719$	30.8444			1.15030			0.575152	+	0.818047i	$0.304943\pi$
$720$	30.8987	−	19.6056i	1.15153	−	0.730658i
$721$	2.97728			0.110880
$722$	22.5119	+	1.73832i	0.837807	+	0.0646936i
$723$	−1.56196	−	0.567619i	−0.0580899	−	0.0211100i
$724$	−18.5475	−	2.88158i	−0.689313	−	0.107093i
$725$			25.0681i			0.931004i
$726$	−33.0168	−	14.9679i	−1.22537	−	0.555509i
$727$		−	19.2654i		−	0.714513i	−0.934006	−	0.357257i	$-0.883712\pi$
$727$		−	19.2654i		−	0.714513i	0.934006	−	0.357257i	$-0.116288\pi$
$728$	−1.05854	+	4.49670i	−0.0392321	+	0.166659i
$729$	−13.4295	+	23.4233i	−0.497387	+	0.867529i
$730$	−4.48628	+	58.0990i	−0.166045	+	2.15034i
$731$	−21.2472			−0.785854
$732$	3.53283	+	1.94237i	0.130577	+	0.0717920i
$733$	−12.3277			−0.455334			−0.227667	−	0.973739i	$-0.573110\pi$
$733$	−12.3277			−0.455334			−0.227667	+	0.973739i	$0.573110\pi$
$734$	0.215504	−	2.79086i	0.00795440	−	0.103013i
$735$	12.4880	−	34.3641i	0.460626	−	1.26754i
$736$	−11.7919	−	4.78279i	−0.434655	−	0.176296i
$737$			5.07932i			0.187099i
$738$	25.1618	−	25.7321i	0.926218	−	0.947213i
$739$			45.7058i			1.68131i	0.541568	+	0.840657i	$0.317831\pi$
$739$			45.7058i			1.68131i	−0.541568	+	0.840657i	$0.682169\pi$
$740$	−6.42681	+	41.3667i	−0.236254	+	1.52067i
$741$	−20.5005	+	56.4128i	−0.753105	+	2.07238i
$742$	−2.13616	−	0.164950i	−0.0784209	−	0.00605550i
$743$	−42.4107			−1.55590			−0.777948	−	0.628328i	$-0.783739\pi$
$743$	−42.4107			−1.55590			−0.777948	+	0.628328i	$0.783739\pi$
$744$	11.6688	−	17.8198i	0.427801	−	0.653307i
$745$	31.9550			1.17074
$746$	−22.7386	−	1.75583i	−0.832520	−	0.0642854i
$747$	6.42565	+	5.38077i	0.235102	+	0.196872i
$748$	−11.8670	+	76.3828i	−0.433900	+	2.79283i
$749$		−	0.940673i		−	0.0343714i
$750$	−2.16082	+	4.76643i	−0.0789018	+	0.174045i
$751$		−	27.0706i		−	0.987819i	−0.869513	−	0.493910i	$-0.835567\pi$
$751$		−	27.0706i		−	0.987819i	0.869513	−	0.493910i	$-0.164433\pi$
$752$	1.73448	+	0.552274i	0.0632498	+	0.0201394i
$753$	−19.0652	−	6.92831i	−0.694773	−	0.252482i
$754$	3.72037	−	48.1802i	0.135488	−	1.75462i
$755$	−23.4753			−0.854353
$756$	−2.69926	+	1.04998i	−0.0981712	+	0.0381873i
$757$	−6.61541			−0.240441			−0.120221	−	0.992747i	$-0.538360\pi$
$757$	−6.61541			−0.240441			−0.120221	+	0.992747i	$0.538360\pi$
$758$	2.96546	−	38.4038i	0.107710	−	1.39489i
$759$	−18.5999	−	6.75924i	−0.675135	−	0.245345i
$760$	49.6457	+	11.6868i	1.80084	+	0.423925i
$761$			22.7202i			0.823606i	0.911273	+	0.411803i	$0.135101\pi$
$761$			22.7202i			0.823606i	−0.911273	+	0.411803i	$0.864899\pi$
$762$	−2.03652	+	4.49224i	−0.0737752	+	0.162737i
$763$			2.37619i			0.0860240i
$764$	−9.76044	−	1.51640i	−0.353120	−	0.0548615i
$765$	−53.3713	−	44.6925i	−1.92964	−	1.61586i
$766$	44.2520	+	3.41704i	1.59889	+	0.123463i
$767$	5.32470			0.192264
$768$	15.7783	+	22.7826i	0.569349	+	0.822096i
$769$	32.2780			1.16397			0.581987	−	0.813198i	$-0.302275\pi$
$769$	32.2780			1.16397			0.581987	+	0.813198i	$0.302275\pi$
$770$	6.08676	+	0.470006i	0.219351	+	0.0169378i
$771$	0.914120	−	2.51545i	0.0329212	−	0.0905919i
$772$	40.1454	+	6.23707i	1.44486	+	0.224477i
$773$		−	46.0146i		−	1.65503i	−0.561443	−	0.827515i	$-0.689754\pi$
$773$		−	46.0146i		−	1.65503i	0.561443	−	0.827515i	$-0.310246\pi$
$774$	−8.28249	+	8.47023i	−0.297708	+	0.304456i
$775$		−	18.6935i		−	0.671489i
$776$	−11.7317	−	2.76168i	−0.421142	−	0.0991386i
$777$	1.13166	−	3.11406i	0.0405979	−	0.111716i
$778$	−0.851735	+	11.0303i	−0.0305362	+	0.395455i
$779$	50.1606			1.79719
$780$	−29.8266	+	54.2495i	−1.06796	+	1.94244i
$781$	23.1101			0.826945
$782$	−1.86364	+	24.1348i	−0.0666435	+	0.863059i
$783$	26.2149	−	15.1879i	0.936844	−	0.542771i
$784$	26.3841	+	8.40096i	0.942290	+	0.300034i
$785$			36.8109i			1.31384i
$786$	8.88244	+	4.02677i	0.316826	+	0.143630i
$787$		−	29.8961i		−	1.06568i	−0.846216	−	0.532841i	$-0.821125\pi$
$787$		−	29.8961i		−	1.06568i	0.846216	−	0.532841i	$-0.178875\pi$
$788$	4.10693	−	26.4346i	0.146303	−	0.941692i
$789$	41.5023	+	15.0820i	1.47752	+	0.536933i
$790$	53.0355	+	4.09528i	1.88692	+	0.145704i
$791$	−4.41752			−0.157069
$792$	25.8243	+	34.5061i	0.917625	+	1.22612i
$793$	−6.82050			−0.242203
$794$	36.4508	+	2.81465i	1.29359	+	0.0998884i
$795$	−26.9857	−	9.80664i	−0.957084	−	0.347806i
$796$	−4.04351	+	26.0264i	−0.143319	+	0.922481i
$797$		−	4.97969i		−	0.176390i	−0.996103	−	0.0881949i	$-0.971890\pi$
$797$		−	4.97969i		−	0.176390i	0.996103	−	0.0881949i	$-0.0281098\pi$
$798$	−3.67654	−	1.66672i	−0.130148	−	0.0590014i
$799$		−	3.46272i		−	0.122502i
$800$	22.5377	+	9.14130i	0.796829	+	0.323194i
$801$	−3.25866	+	3.89146i	−0.115139	+	0.137498i
$802$	0.207218	−	2.68354i	0.00731710	−	0.0947593i
$803$	−68.6314			−2.42195
$804$	1.66896	−	3.03555i	0.0588597	−	0.107056i
$805$	1.91177			0.0673812
$806$	−2.77431	+	35.9284i	−0.0977211	+	1.26552i
$807$	6.70940	−	18.4628i	0.236182	−	0.649921i
$808$	−0.230722	+	0.980113i	−0.00811679	+	0.0344802i
$809$		−	6.05334i		−	0.212824i	−0.994322	−	0.106412i	$-0.966064\pi$
$809$		−	6.05334i		−	0.212824i	0.994322	−	0.106412i	$-0.0339363\pi$
$810$	−38.6218	+	3.85472i	−1.35703	+	0.135441i
$811$		−	26.9465i		−	0.946219i	−0.881004	−	0.473110i	$-0.843131\pi$
$811$		−	26.9465i		−	0.946219i	0.881004	−	0.473110i	$-0.156869\pi$
$812$	3.21140	+	0.498929i	0.112698	+	0.0175090i
$813$	2.02340	−	5.56795i	0.0709637	−	0.195276i
$814$	−49.1589	−	3.79594i	−1.72302	−	0.133048i
$815$	−28.7122			−1.00574
$816$	32.1899	−	41.7494i	1.12687	−	1.46152i
$817$	−16.5114			−0.577659
$818$	26.2607	+	2.02779i	0.918184	+	0.0709002i
$819$	3.14578	−	3.75665i	0.109922	−	0.131268i
$820$	51.1234	+	7.94264i	1.78531	+	0.277369i
$821$			14.1175i			0.492704i	0.969180	+	0.246352i	$0.0792319\pi$
$821$			14.1175i			0.492704i	−0.969180	+	0.246352i	$0.920768\pi$
$822$	−8.93521	+	19.7097i	−0.311651	+	0.687455i
$823$		−	5.56238i		−	0.193892i	−0.995290	−	0.0969462i	$-0.969093\pi$
$823$		−	5.56238i		−	0.193892i	0.995290	−	0.0969462i	$-0.0309075\pi$
$824$	−6.92370	+	29.4120i	−0.241199	+	1.02462i
$825$	35.5499	+	12.9189i	1.23769	+	0.449777i
$826$	−0.0275699	+	0.357040i	−0.000959279	+	0.0124230i
$827$	−22.3916			−0.778631			−0.389316	−	0.921104i	$-0.627288\pi$
$827$	−22.3916			−0.778631			−0.389316	+	0.921104i	$0.627288\pi$
$828$	8.89492	+	10.1511i	0.309120	+	0.352775i
$829$	−6.35913			−0.220862			−0.110431	−	0.993884i	$-0.535223\pi$
$829$	−6.35913			−0.220862			−0.110431	+	0.993884i	$0.535223\pi$
$830$	−0.927566	+	12.0123i	−0.0321963	+	0.416954i
$831$	18.5264	+	6.73251i	0.642673	+	0.233548i
$832$	−41.9603	−	20.9142i	−1.45471	−	0.725070i
$833$		−	52.6734i		−	1.82503i
$834$	12.5082	−	27.5911i	0.433123	−	0.955403i
$835$			64.2948i			2.22501i
$836$	−9.22194	+	59.3578i	−0.318948	+	2.05293i
$837$	−19.5487	+	11.3257i	−0.675701	+	0.391475i
$838$	−28.8109	−	2.22471i	−0.995255	−	0.0768514i
$839$	−35.8596			−1.23801			−0.619006	−	0.785387i	$-0.712464\pi$
$839$	−35.8596			−1.23801			−0.619006	+	0.785387i	$0.712464\pi$
$840$	−3.48319	−	2.28087i	−0.120182	−	0.0786976i
$841$	−4.99601			−0.172276
$842$	−22.2977	−	1.72178i	−0.768429	−	0.0593364i
$843$	5.81194	−	15.9932i	0.200174	−	0.550834i
$844$	−1.50332	+	9.67626i	−0.0517465	+	0.333070i
$845$		−	65.0910i		−	2.23920i
$846$	−1.38042	−	1.34982i	−0.0474599	−	0.0464079i
$847$			4.12454i			0.141721i
$848$	6.59717	−	20.7191i	0.226548	−	0.711497i
$849$	10.4747	−	28.8240i	0.359490	−	0.989236i
$850$	3.56195	−	46.1286i	0.122174	−	1.58220i
$851$	−15.4402			−0.529283
$852$	−13.8113	−	7.59351i	−0.473167	−	0.260149i
$853$	−27.3634			−0.936905			−0.468452	−	0.883489i	$-0.655188\pi$
$853$	−27.3634			−0.936905			−0.468452	+	0.883489i	$0.655188\pi$
$854$	0.0353148	−	0.457339i	0.00120845	−	0.0156498i
$855$	−41.4753	−	34.7309i	−1.41842	−	1.18777i
$856$	9.29272	+	2.18754i	0.317619	+	0.0747687i
$857$		−	32.6483i		−	1.11525i	−0.830094	−	0.557623i	$-0.811713\pi$
$857$		−	32.6483i		−	1.11525i	0.830094	−	0.557623i	$-0.188287\pi$
$858$	−66.4087	−	30.1058i	−2.26716	−	1.02779i
$859$		−	7.82213i		−	0.266888i	−0.991056	−	0.133444i	$-0.957396\pi$
$859$		−	7.82213i		−	0.266888i	0.991056	−	0.133444i	$-0.0426036\pi$
$860$	−16.8283	−	2.61447i	−0.573839	−	0.0891528i
$861$	−3.84855	−	1.39857i	−0.131158	−	0.0476631i
$862$	−28.2943	−	2.18483i	−0.963709	−	0.0744155i
$863$	12.3680			0.421010			0.210505	−	0.977593i	$-0.432489\pi$
$863$	12.3680			0.421010			0.210505	+	0.977593i	$0.432489\pi$
$864$	−4.09535	−	29.1072i	−0.139327	−	0.990246i
$865$	57.6929			1.96162
$866$	18.5726	+	1.43414i	0.631124	+	0.0487340i
$867$	−66.5808	−	24.1956i	−2.26120	−	0.821725i
$868$	−2.39477	−	0.372056i	−0.0812837	−	0.0126284i
$869$			62.6499i			2.12525i
$870$	39.6671	+	17.9827i	1.34484	+	0.609670i
$871$			5.86045i			0.198574i
$872$	−23.4739	−	5.52586i	−0.794928	−	0.187129i
$873$	9.80094	+	8.20719i	0.331711	+	0.277771i
$874$	−1.44825	+	18.7554i	−0.0489878	+	0.634410i
$875$	0.595434			0.0201293
$876$	41.0161	+	22.5509i	1.38581	+	0.761923i
$877$	−18.5878			−0.627666			−0.313833	−	0.949478i	$-0.601613\pi$
$877$	−18.5878			−0.627666			−0.313833	+	0.949478i	$0.601613\pi$
$878$	2.42691	−	31.4293i	0.0819041	−	1.06069i
$879$	−9.30305	+	25.5999i	−0.313784	+	0.863465i
$880$	−18.7979	+	59.0368i	−0.633677	+	1.99013i
$881$			47.9022i			1.61387i	0.590642	+	0.806933i	$0.298874\pi$
$881$			47.9022i			1.61387i	−0.590642	+	0.806933i	$0.701126\pi$
$882$	−20.9984	−	20.5330i	−0.707053	−	0.691381i
$883$		−	35.6876i		−	1.20098i	−0.799630	−	0.600492i	$-0.794971\pi$
$883$		−	35.6876i		−	1.20098i	0.799630	−	0.600492i	$-0.205029\pi$
$884$	−13.6920	+	88.1295i	−0.460511	+	2.96412i
$885$	−1.63909	+	4.51042i	−0.0550975	+	0.151616i
$886$	−21.7960	−	1.68304i	−0.732250	−	0.0565428i
$887$	−15.3867			−0.516635			−0.258318	−	0.966060i	$-0.583168\pi$
$887$	−15.3867			−0.516635			−0.258318	+	0.966060i	$0.583168\pi$
$888$	28.1315	+	18.4212i	0.944033	+	0.618174i
$889$	0.561182			0.0188214
$890$	−7.27483	−	0.561746i	−0.243853	−	0.0188298i
$891$	−8.02858	−	45.0033i	−0.268968	−	1.50767i
$892$	8.29715	−	53.4053i	0.277809	−	1.78814i
$893$		−	2.69091i		−	0.0900479i
$894$	10.5980	−	23.3776i	0.354451	−	0.781865i
$895$		−	77.4358i		−	2.58839i
$896$	1.61963	−	2.70530i	0.0541081	−	0.0903778i
$897$	−21.4604	−	7.79873i	−0.716541	−	0.260392i
$898$	2.72166	−	35.2465i	0.0908228	−	1.17619i
$899$	25.3511			0.845507
$900$	−17.0008	−	19.4017i	−0.566692	−	0.646722i
$901$	−41.3638			−1.37803
$902$	−4.69125	+	60.7535i	−0.156202	+	2.02287i
$903$	1.26682	+	0.460366i	0.0421573	+	0.0153200i
$904$	10.2730	−	43.6398i	0.341674	−	1.45144i
$905$			28.6195i			0.951344i
$906$	−7.78569	+	17.1740i	−0.258662	+	0.570569i
$907$			18.6850i			0.620425i	0.950667	+	0.310213i	$0.100400\pi$
$907$			18.6850i			0.620425i	−0.950667	+	0.310213i	$0.899600\pi$
$908$	−0.0825441	−	0.0128242i	−0.00273932	−	0.000425587i
$909$	0.685663	−	0.818811i	0.0227420	−	0.0271582i
$910$	7.02282	+	0.542287i	0.232804	+	0.0179766i
$911$	−39.4070			−1.30561			−0.652805	−	0.757526i	$-0.726408\pi$
$911$	−39.4070			−1.30561			−0.652805	+	0.757526i	$0.726408\pi$
$912$	25.0151	−	32.4438i	0.828331	−	1.07432i
$913$	−14.1900			−0.469619
$914$	19.5043	+	1.50608i	0.645144	+	0.0498166i
$915$	2.09954	−	5.77748i	0.0694088	−	0.190998i
$916$	29.1046	+	4.52175i	0.961643	+	0.149403i
$917$		−	1.10962i		−	0.0366427i
$918$	−50.3970	+	24.2229i	−1.66335	+	0.799473i
$919$			40.3364i			1.33058i	0.746587	+	0.665288i	$0.231691\pi$
$919$			40.3364i			1.33058i	−0.746587	+	0.665288i	$0.768309\pi$
$920$	−4.44585	+	18.8860i	−0.146575	+	0.622654i
$921$	10.2475	−	28.1987i	0.337665	−	0.929180i
$922$	−0.0387260	+	0.501516i	−0.00127537	+	0.0165166i
$923$	26.6641			0.877661
$924$	2.36255	−	4.29707i	0.0777221	−	0.141363i
$925$	29.5107			0.970306
$926$	0.405299	−	5.24877i	0.0133189	−	0.172485i
$927$	20.5759	−	24.5715i	0.675802	−	0.807035i
$928$	−12.3970	+	30.5645i	−0.406950	+	1.00333i
$929$		−	53.7081i		−	1.76211i	−0.473017	−	0.881053i	$-0.656835\pi$
$929$		−	53.7081i		−	1.76211i	0.473017	−	0.881053i	$-0.343165\pi$
$930$	−29.5801	−	13.4098i	−0.969969	−	0.439726i
$931$		−	40.9330i		−	1.34152i
$932$	7.02423	−	45.2120i	0.230086	−	1.48097i
$933$	26.2616	+	9.54349i	0.859765	+	0.312440i
$934$	−47.8442	−	3.69443i	−1.56551	−	0.120885i
$935$	117.862			3.85448
$936$	29.7957	+	39.8127i	0.973902	+	1.30132i
$937$	−26.0917			−0.852379			−0.426189	−	0.904634i	$-0.640144\pi$
$937$	−26.0917			−0.852379			−0.426189	+	0.904634i	$0.640144\pi$
$938$	−0.392964	−	0.0303439i	−0.0128307	−	0.000990762i
$939$	27.0301	+	9.82279i	0.882095	+	0.320555i
$940$	0.426090	−	2.74256i	0.0138975	−	0.0894524i
$941$			33.4974i			1.09198i	0.837791	+	0.545992i	$0.183847\pi$
$941$			33.4974i			1.09198i	−0.837791	+	0.545992i	$0.816153\pi$
$942$	26.9301	+	12.2085i	0.877431	+	0.397775i
$943$			19.0819i			0.621393i
$944$	−3.46302	−	1.10266i	−0.112712	−	0.0358884i
$945$	2.21381	+	3.82112i	0.0720152	+	0.124301i
$946$	1.54422	−	19.9982i	0.0502068	−	0.650198i
$947$	8.25639			0.268297			0.134148	−	0.990961i	$-0.457170\pi$
$947$	8.25639			0.268297			0.134148	+	0.990961i	$0.457170\pi$
$948$	20.5855	−	37.4415i	0.668586	−	1.21604i
$949$	−79.1859			−2.57048
$950$	2.76802	−	35.8469i	0.0898065	−	1.16303i
$951$	−10.4465	+	28.7465i	−0.338752	+	0.932170i
$952$	−5.83851	−	1.37441i	−0.189227	−	0.0445448i
$953$		−	41.6462i		−	1.34905i	−0.738251	−	0.674526i	$-0.764348\pi$
$953$		−	41.6462i		−	1.34905i	0.738251	−	0.674526i	$-0.235652\pi$
$954$	−16.1243	+	16.4898i	−0.522043	+	0.533876i
$955$			15.0607i			0.487354i
$956$	−13.4475	−	2.08924i	−0.434925	−	0.0675708i
$957$	−17.5199	+	48.2109i	−0.566338	+	1.55844i
$958$	−10.8330	−	0.836500i	−0.349998	−	0.0270261i
$959$	2.46218			0.0795081
$960$	30.6325	−	29.1056i	0.988659	−	0.939378i
$961$	12.0955			0.390176
$962$	−56.7189	−	4.37971i	−1.82869	−	0.141208i
$963$	−7.76337	−	6.50096i	−0.250171	−	0.209491i
$964$	−1.89625	−	0.294605i	−0.0610740	−	0.00948858i
$965$		−	61.9458i		−	1.99411i
$966$	0.634049	−	1.39862i	0.0204002	−	0.0449997i
$967$		−	25.9318i		−	0.833909i	−0.908927	−	0.416955i	$-0.863097\pi$
$967$		−	25.9318i		−	0.833909i	0.908927	−	0.416955i	$-0.136903\pi$
$968$	−40.7455	−	9.59165i	−1.30961	−	0.308287i
$969$	−73.2464	−	26.6179i	−2.35301	−	0.855089i
$970$	−1.41480	+	18.3222i	−0.0454265	+	0.588291i
$971$	15.8140			0.507495			0.253747	−	0.967271i	$-0.418337\pi$
$971$	15.8140			0.507495			0.253747	+	0.967271i	$0.418337\pi$
$972$	−9.98906	+	29.5333i	−0.320399	+	0.947283i
$973$	−3.44675			−0.110498
$974$	−3.68129	+	47.6741i	−0.117956	+	1.52758i
$975$	41.0170	+	14.9056i	1.31359	+	0.477362i
$976$	4.43584	+	1.41241i	0.141988	+	0.0452103i
$977$		−	18.5153i		−	0.592358i	−0.955133	−	0.296179i	$-0.904288\pi$
$977$		−	18.5153i		−	0.592358i	0.955133	−	0.296179i	$-0.0957124\pi$
$978$	−9.52253	+	21.0053i	−0.304497	+	0.671674i
$979$		−	8.59363i		−	0.274654i
$980$	6.48150	−	41.7187i	0.207044	−	1.33265i
$981$	19.6107	+	16.4218i	0.626122	+	0.524308i
$982$	−60.7385	−	4.69010i	−1.93824	−	0.149667i
$983$	57.7929			1.84331			0.921654	−	0.388013i	$-0.126839\pi$
$983$	57.7929			1.84331			0.921654	+	0.388013i	$0.126839\pi$
$984$	22.7660	−	34.7666i	0.725754	−	1.10832i
$985$	−40.7895			−1.29966
$986$	62.5572	+	4.83053i	1.99223	+	0.153836i
$987$	−0.0750273	+	0.206459i	−0.00238815	+	0.00657165i
$988$	−10.6402	+	68.4862i	−0.338508	+	2.17884i
$989$		−	6.28119i		−	0.199730i
$990$	45.9444	−	46.9858i	1.46021	−	1.49331i
$991$		−	23.4620i		−	0.745293i	−0.927973	−	0.372647i	$-0.878450\pi$
$991$		−	23.4620i		−	0.745293i	0.927973	−	0.372647i	$-0.121550\pi$
$992$	9.24451	−	22.7922i	0.293514	−	0.723653i
$993$	−20.2833	+	55.8152i	−0.643672	+	1.77124i
$994$	−0.138060	+	1.78793i	−0.00437899	+	0.0567096i
$995$	40.1597			1.27315
$996$	8.48035	+	4.66253i	0.268710	+	0.147738i
$997$	−5.00191			−0.158412			−0.0792061	−	0.996858i	$-0.525239\pi$
$997$	−5.00191			−0.158412			−0.0792061	+	0.996858i	$0.525239\pi$
$998$	−3.40514	+	44.0979i	−0.107788	+	1.39589i
$999$	−17.8795	−	30.8608i	−0.565684	−	0.976391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.1	✓	128
3.2	odd	2	inner	804.2.c.b.671.128	yes	128
4.3	odd	2	inner	804.2.c.b.671.127	yes	128
12.11	even	2	inner	804.2.c.b.671.2	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.1	✓	128	1.1	even	1	trivial
804.2.c.b.671.2	yes	128	12.11	even	2	inner
804.2.c.b.671.127	yes	128	4.3	odd	2	inner
804.2.c.b.671.128	yes	128	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41002 - 0.108878i) q^{2} +(1.62789 + 0.591579i) q^{3} +(1.97629 + 0.307041i) q^{4} -3.04949i q^{5} +(-2.23094 - 1.01138i) q^{6} +0.278695i q^{7} +(-2.75317 - 0.648108i) q^{8} +(2.30007 + 1.92605i) q^{9} +O(q^{10})\)	\(q+(-1.41002 - 0.108878i) q^{2} +(1.62789 + 0.591579i) q^{3} +(1.97629 + 0.307041i) q^{4} -3.04949i q^{5} +(-2.23094 - 1.01138i) q^{6} +0.278695i q^{7} +(-2.75317 - 0.648108i) q^{8} +(2.30007 + 1.92605i) q^{9} +(-0.332024 + 4.29983i) q^{10} -5.07932 q^{11} +(3.03555 + 1.66896i) q^{12} -5.86045 q^{13} +(0.0303439 - 0.392964i) q^{14} +(1.80401 - 4.96424i) q^{15} +(3.81145 + 1.21360i) q^{16} -7.60921i q^{17} +(-3.03343 - 2.96619i) q^{18} -5.91318i q^{19} +(0.936317 - 6.02668i) q^{20} +(-0.164870 + 0.453686i) q^{21} +(7.16192 + 0.553028i) q^{22} +2.24947 q^{23} +(-4.09846 - 2.68377i) q^{24} -4.29939 q^{25} +(8.26333 + 0.638076i) q^{26} +(2.60486 + 4.49608i) q^{27} +(-0.0855707 + 0.550782i) q^{28} -5.83061i q^{29} +(-3.08419 + 6.80324i) q^{30} +4.34794i q^{31} +(-5.24207 - 2.12618i) q^{32} +(-8.26859 - 3.00482i) q^{33} +(-0.828478 + 10.7291i) q^{34} +0.849878 q^{35} +(3.95423 + 4.51266i) q^{36} -6.86393 q^{37} +(-0.643818 + 8.33768i) q^{38} +(-9.54018 - 3.46692i) q^{39} +(-1.97640 + 8.39577i) q^{40} +8.48285i q^{41} +(0.281866 - 0.621753i) q^{42} -2.79230i q^{43} +(-10.0382 - 1.55956i) q^{44} +(5.87348 - 7.01404i) q^{45} +(-3.17179 - 0.244919i) q^{46} +0.455070 q^{47} +(5.48669 + 4.23039i) q^{48} +6.92233 q^{49} +(6.06221 + 0.468111i) q^{50} +(4.50144 - 12.3870i) q^{51} +(-11.5820 - 1.79940i) q^{52} -5.43602i q^{53} +(-3.18336 - 6.62316i) q^{54} +15.4893i q^{55} +(0.180624 - 0.767295i) q^{56} +(3.49811 - 9.62603i) q^{57} +(-0.634828 + 8.22125i) q^{58} -0.908582 q^{59} +(5.08948 - 9.25688i) q^{60} +1.16382 q^{61} +(0.473396 - 6.13066i) q^{62} +(-0.536781 + 0.641018i) q^{63} +(7.15991 + 3.56870i) q^{64} +17.8714i q^{65} +(11.3317 + 5.13711i) q^{66} -1.00000i q^{67} +(2.33634 - 15.0380i) q^{68} +(3.66190 + 1.33074i) q^{69} +(-1.19834 - 0.0925333i) q^{70} -4.54985 q^{71} +(-5.08420 - 6.79345i) q^{72} +13.5119 q^{73} +(9.67825 + 0.747333i) q^{74} +(-6.99894 - 2.54343i) q^{75} +(1.81559 - 11.6862i) q^{76} -1.41558i q^{77} +(13.0743 + 5.92713i) q^{78} -12.3343i q^{79} +(3.70087 - 11.6230i) q^{80} +(1.58064 + 8.86011i) q^{81} +(0.923599 - 11.9610i) q^{82} +2.79368 q^{83} +(-0.465131 + 0.845993i) q^{84} -23.2042 q^{85} +(-0.304021 + 3.93718i) q^{86} +(3.44926 - 9.49161i) q^{87} +(13.9842 + 3.29194i) q^{88} +1.69189i q^{89} +(-9.04538 + 9.25041i) q^{90} -1.63328i q^{91} +(4.44561 + 0.690679i) q^{92} +(-2.57215 + 7.07797i) q^{93} +(-0.641656 - 0.0495473i) q^{94} -18.0322 q^{95} +(-7.27573 - 6.56230i) q^{96} +4.26115 q^{97} +(-9.76060 - 0.753692i) q^{98} +(-11.6828 - 9.78304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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