LMFDB - Embedded newform 1008.2.r.m.673.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(337,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1008.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			673.4
Root			$0.947217 - 0.807294i$ of defining polynomial
Character	$\chi$	$=$	1008.673
Dual form			1008.2.r.m.337.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67275 - 0.449358i) q^{3} +(1.87447 + 3.24667i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.59615 - 1.50332i) q^{9} +O(q^{10})$	\(q+(1.67275 - 0.449358i) q^{3} +(1.87447 + 3.24667i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.59615 - 1.50332i) q^{9} +(-1.82552 + 3.16190i) q^{11} +(2.77274 + 4.80253i) q^{13} +(4.59442 + 4.58854i) q^{15} -7.20767 q^{17} +3.30555 q^{19} +(0.447217 - 1.67332i) q^{21} +(-2.49443 - 4.32048i) q^{23} +(-4.52724 + 7.84141i) q^{25} +(3.66717 - 3.68128i) q^{27} +(-0.245497 + 0.425213i) q^{29} +(-1.94722 - 3.37268i) q^{31} +(-1.63281 + 6.10936i) q^{33} +3.74893 q^{35} +7.89443 q^{37} +(6.79614 + 6.78745i) q^{39} +(-2.38215 - 4.12600i) q^{41} +(-0.801714 + 1.38861i) q^{43} +(9.74720 + 5.61092i) q^{45} +(4.81995 - 8.34840i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-12.0566 + 3.23883i) q^{51} -8.03647 q^{53} -13.6875 q^{55} +(5.52935 - 1.48538i) q^{57} +(-0.754503 - 1.30684i) q^{59} +(1.04337 - 1.80717i) q^{61} +(-0.00384004 - 3.00000i) q^{63} +(-10.3948 + 18.0043i) q^{65} +(1.70172 + 2.94747i) q^{67} +(-6.11398 - 6.10616i) q^{69} +10.7301 q^{71} +9.83567 q^{73} +(-4.04932 + 15.1510i) q^{75} +(1.82552 + 3.16190i) q^{77} +(1.86391 - 3.22839i) q^{79} +(4.48003 - 7.80572i) q^{81} +(-5.69058 + 9.85637i) q^{83} +(-13.5105 - 23.4009i) q^{85} +(-0.219580 + 0.821588i) q^{87} +7.14891 q^{89} +5.54548 q^{91} +(-4.77274 - 4.76663i) q^{93} +(6.19615 + 10.7320i) q^{95} +(5.45316 - 9.44516i) q^{97} +(0.0140201 + 10.9531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 4 q^{5} + 4 q^{7} + 10 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 4 * q^5 + 4 * q^7 + 10 * q^9	$ 8 q + 4 q^{3} + 4 q^{5} + 4 q^{7} + 10 q^{9} + 6 q^{11} - 3 q^{13} - 4 q^{15} - 16 q^{17} + 4 q^{19} - q^{21} + 5 q^{23} - 14 q^{25} - 5 q^{27} + q^{29} - 11 q^{31} + 8 q^{35} + 54 q^{37} + 12 q^{39} + 2 q^{41} + 11 q^{43} + 26 q^{45} - 7 q^{47} - 4 q^{49} - 17 q^{51} - 8 q^{53} - 12 q^{55} - 13 q^{57} - 9 q^{59} - 7 q^{61} + 5 q^{63} - 9 q^{65} + 12 q^{67} + 4 q^{69} + 24 q^{71} + 26 q^{73} + 23 q^{75} - 6 q^{77} + 22 q^{79} + 34 q^{81} + 6 q^{83} - 11 q^{85} - 37 q^{87} - 28 q^{89} - 6 q^{91} - 13 q^{93} + 23 q^{95} - q^{97} + 42 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 4 * q^5 + 4 * q^7 + 10 * q^9 + 6 * q^11 - 3 * q^13 - 4 * q^15 - 16 * q^17 + 4 * q^19 - q^21 + 5 * q^23 - 14 * q^25 - 5 * q^27 + q^29 - 11 * q^31 + 8 * q^35 + 54 * q^37 + 12 * q^39 + 2 * q^41 + 11 * q^43 + 26 * q^45 - 7 * q^47 - 4 * q^49 - 17 * q^51 - 8 * q^53 - 12 * q^55 - 13 * q^57 - 9 * q^59 - 7 * q^61 + 5 * q^63 - 9 * q^65 + 12 * q^67 + 4 * q^69 + 24 * q^71 + 26 * q^73 + 23 * q^75 - 6 * q^77 + 22 * q^79 + 34 * q^81 + 6 * q^83 - 11 * q^85 - 37 * q^87 - 28 * q^89 - 6 * q^91 - 13 * q^93 + 23 * q^95 - q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.67275	−	0.449358i	0.965760	−	0.259437i
$3$	1.67275	−	0.449358i	0.965760	−	0.259437i
$4$		0			0
$5$	1.87447	+	3.24667i	0.838287	+	1.45195i	0.891326	+	0.453362i	$0.149776\pi$
$5$	1.87447	+	3.24667i	0.838287	+	1.45195i	−0.0530397	+	0.998592i	$0.516891\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$	2.59615	−	1.50332i	0.865385	−	0.501108i
$10$		0			0
$11$	−1.82552	+	3.16190i	−0.550416	+	0.953348i	0.447829	+	0.894119i	$0.352197\pi$
$11$	−1.82552	+	3.16190i	−0.550416	+	0.953348i	−0.998244	+	0.0592287i	$0.981136\pi$
$12$		0			0
$13$	2.77274	+	4.80253i	0.769020	+	1.33198i	0.938095	+	0.346378i	$0.112588\pi$
$13$	2.77274	+	4.80253i	0.769020	+	1.33198i	−0.169076	+	0.985603i	$0.554078\pi$
$14$		0			0
$15$	4.59442	+	4.58854i	1.18627	+	1.18476i
$16$		0			0
$17$	−7.20767			−1.74812			−0.874058	−	0.485821i	$-0.838521\pi$
$17$	−7.20767			−1.74812			−0.874058	+	0.485821i	$0.838521\pi$
$18$		0			0
$19$	3.30555			0.758346			0.379173	−	0.925326i	$-0.376208\pi$
$19$	3.30555			0.758346			0.379173	+	0.925326i	$0.376208\pi$
$20$		0			0
$21$	0.447217	−	1.67332i	0.0975907	−	0.365148i
$22$		0			0
$23$	−2.49443	−	4.32048i	−0.520124	−	0.900881i	−0.999726	−	0.0233954i	$-0.992552\pi$
$23$	−2.49443	−	4.32048i	−0.520124	−	0.900881i	0.479602	−	0.877486i	$-0.340781\pi$
$24$		0			0
$25$	−4.52724	+	7.84141i	−0.905449	+	1.56828i
$26$		0			0
$27$	3.66717	−	3.68128i	0.705748	−	0.708463i
$28$		0			0
$29$	−0.245497	+	0.425213i	−0.0455876	+	0.0789600i	−0.887919	−	0.460000i	$-0.847849\pi$
$29$	−0.245497	+	0.425213i	−0.0455876	+	0.0789600i	0.842331	+	0.538960i	$0.181183\pi$
$30$		0			0
$31$	−1.94722	−	3.37268i	−0.349730	−	0.605751i	0.636471	−	0.771301i	$-0.280394\pi$
$31$	−1.94722	−	3.37268i	−0.349730	−	0.605751i	−0.986201	+	0.165550i	$0.947060\pi$
$32$		0			0
$33$	−1.63281	+	6.10936i	−0.284236	+	1.06350i
$34$		0			0
$35$	3.74893			0.633685
$36$		0			0
$37$	7.89443			1.29784			0.648918	−	0.760858i	$-0.275222\pi$
$37$	7.89443			1.29784			0.648918	+	0.760858i	$0.275222\pi$
$38$		0			0
$39$	6.79614	+	6.78745i	1.08825	+	1.08686i
$40$		0			0
$41$	−2.38215	−	4.12600i	−0.372029	−	0.644373i	0.617849	−	0.786297i	$-0.288004\pi$
$41$	−2.38215	−	4.12600i	−0.372029	−	0.644373i	−0.989878	+	0.141924i	$0.954671\pi$
$42$		0			0
$43$	−0.801714	+	1.38861i	−0.122260	+	0.211761i	−0.920659	−	0.390369i	$-0.872348\pi$
$43$	−0.801714	+	1.38861i	−0.122260	+	0.211761i	0.798398	+	0.602130i	$0.205681\pi$
$44$		0			0
$45$	9.74720	+	5.61092i	1.45303	+	0.836427i
$46$		0			0
$47$	4.81995	−	8.34840i	0.703062	−	1.21774i	−0.264324	−	0.964434i	$-0.585149\pi$
$47$	4.81995	−	8.34840i	0.703062	−	1.21774i	0.967386	−	0.253305i	$-0.0815177\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−12.0566	+	3.23883i	−1.68826	+	0.453526i
$52$		0			0
$53$	−8.03647			−1.10389			−0.551947	−	0.833879i	$-0.686115\pi$
$53$	−8.03647			−1.10389			−0.551947	+	0.833879i	$0.686115\pi$
$54$		0			0
$55$	−13.6875			−1.84562
$56$		0			0
$57$	5.52935	−	1.48538i	0.732380	−	0.196743i
$58$		0			0
$59$	−0.754503	−	1.30684i	−0.0982280	−	0.170136i	0.812723	−	0.582650i	$-0.197984\pi$
$59$	−0.754503	−	1.30684i	−0.0982280	−	0.170136i	−0.910951	+	0.412514i	$0.864651\pi$
$60$		0			0
$61$	1.04337	−	1.80717i	0.133590	−	0.231385i	−0.791468	−	0.611211i	$-0.790683\pi$
$61$	1.04337	−	1.80717i	0.133590	−	0.231385i	0.925058	+	0.379826i	$0.124016\pi$
$62$		0			0
$63$	−0.00384004	−	3.00000i	−0.000483799	−	0.377964i
$64$		0			0
$65$	−10.3948	+	18.0043i	−1.28932	+	2.23316i
$66$		0			0
$67$	1.70172	+	2.94747i	0.207898	+	0.360090i	0.951052	−	0.309030i	$-0.100004\pi$
$67$	1.70172	+	2.94747i	0.207898	+	0.360090i	−0.743154	+	0.669120i	$0.766671\pi$
$68$		0			0
$69$	−6.11398	−	6.10616i	−0.736037	−	0.735096i
$70$		0			0
$71$	10.7301			1.27343			0.636715	−	0.771099i	$-0.280293\pi$
$71$	10.7301			1.27343			0.636715	+	0.771099i	$0.280293\pi$
$72$		0			0
$73$	9.83567			1.15118			0.575589	−	0.817739i	$-0.304773\pi$
$73$	9.83567			1.15118			0.575589	+	0.817739i	$0.304773\pi$
$74$		0			0
$75$	−4.04932	+	15.1510i	−0.467575	+	1.74949i
$76$		0			0
$77$	1.82552	+	3.16190i	0.208038	+	0.360332i
$78$		0			0
$79$	1.86391	−	3.22839i	0.209706	−	0.363222i	−0.741916	−	0.670493i	$-0.766083\pi$
$79$	1.86391	−	3.22839i	0.209706	−	0.363222i	0.951622	+	0.307271i	$0.0994159\pi$
$80$		0			0
$81$	4.48003	−	7.80572i	0.497781	−	0.867303i
$82$		0			0
$83$	−5.69058	+	9.85637i	−0.624622	+	1.08188i	0.363992	+	0.931402i	$0.381414\pi$
$83$	−5.69058	+	9.85637i	−0.624622	+	1.08188i	−0.988614	+	0.150475i	$0.951920\pi$
$84$		0			0
$85$	−13.5105	−	23.4009i	−1.46542	−	2.53819i
$86$		0			0
$87$	−0.219580	+	0.821588i	−0.0235415	+	0.0880835i
$88$		0			0
$89$	7.14891			0.757783			0.378891	−	0.925441i	$-0.376305\pi$
$89$	7.14891			0.757783			0.378891	+	0.925441i	$0.376305\pi$
$90$		0			0
$91$	5.54548			0.581324
$92$		0			0
$93$	−4.77274	−	4.76663i	−0.494910	−	0.494277i
$94$		0			0
$95$	6.19615	+	10.7320i	0.635711	+	1.10108i
$96$		0			0
$97$	5.45316	−	9.44516i	0.553685	−	0.959011i	−0.444320	−	0.895868i	$-0.646555\pi$
$97$	5.45316	−	9.44516i	0.553685	−	0.959011i	0.998005	−	0.0631422i	$-0.0201122\pi$
$98$		0			0
$99$	0.0140201	+	10.9531i	0.00140908	+	1.10083i
$100$		0			0
$101$	6.40171	−	11.0881i	0.636994	−	1.10331i	−0.349095	−	0.937087i	$-0.613511\pi$
$101$	6.40171	−	11.0881i	0.636994	−	1.10331i	0.986089	−	0.166218i	$-0.0531557\pi$
$102$		0			0
$103$	−4.76717	−	8.25698i	−0.469723	−	0.813584i	0.529678	−	0.848199i	$-0.322313\pi$
$103$	−4.76717	−	8.25698i	−0.469723	−	0.813584i	−0.999401	+	0.0346149i	$0.988980\pi$
$104$		0			0
$105$	6.27101	−	1.68461i	0.611988	−	0.164401i
$106$		0			0
$107$	−8.43223			−0.815175			−0.407587	−	0.913166i	$-0.633630\pi$
$107$	−8.43223			−0.815175			−0.407587	+	0.913166i	$0.633630\pi$
$108$		0			0
$109$	16.5574			1.58591			0.792954	−	0.609281i	$-0.208542\pi$
$109$	16.5574			1.58591			0.792954	+	0.609281i	$0.208542\pi$
$110$		0			0
$111$	13.2054	−	3.54743i	1.25340	−	0.336707i
$112$		0			0
$113$	−0.0328150	−	0.0568372i	−0.00308697	−	0.00534679i	0.864478	−	0.502671i	$-0.167649\pi$
$113$	−0.0328150	−	0.0568372i	−0.00308697	−	0.00534679i	−0.867565	+	0.497324i	$0.834316\pi$
$114$		0			0
$115$	9.35144	−	16.1972i	0.872026	−	1.51039i
$116$		0			0
$117$	14.4182	+	8.29977i	1.33296	+	0.767314i
$118$		0			0
$119$	−3.60383	+	6.24202i	−0.330363	+	0.572205i
$120$		0			0
$121$	−1.16507	−	2.01795i	−0.105915	−	0.183450i
$122$		0			0
$123$	−5.83877	−	5.83131i	−0.526465	−	0.525791i
$124$		0			0
$125$	−15.2000			−1.35953
$126$		0			0
$127$	−3.20080			−0.284025			−0.142012	−	0.989865i	$-0.545357\pi$
$127$	−3.20080			−0.284025			−0.142012	+	0.989865i	$0.545357\pi$
$128$		0			0
$129$	−0.717080	+	2.68305i	−0.0631354	+	0.236229i
$130$		0			0
$131$	7.67061	+	13.2859i	0.670184	+	1.16079i	0.977852	+	0.209299i	$0.0671182\pi$
$131$	7.67061	+	13.2859i	0.670184	+	1.16079i	−0.307668	+	0.951494i	$0.599548\pi$
$132$		0			0
$133$	1.65278	−	2.86269i	0.143314	−	0.248227i
$134$		0			0
$135$	18.8259	+	5.00566i	1.62028	+	0.430819i
$136$		0			0
$137$	−0.342977	+	0.594054i	−0.0293025	+	0.0507535i	−0.880305	−	0.474409i	$-0.842662\pi$
$137$	−0.342977	+	0.594054i	−0.0293025	+	0.0507535i	0.851002	+	0.525162i	$0.175995\pi$
$138$		0			0
$139$	−10.1004	−	17.4944i	−0.856702	−	1.48385i	−0.875057	−	0.484020i	$-0.839176\pi$
$139$	−10.1004	−	17.4944i	−0.856702	−	1.48385i	0.0183546	−	0.999832i	$-0.494157\pi$
$140$		0			0
$141$	4.31113	−	16.1306i	0.363062	−	1.35844i
$142$		0			0
$143$	−20.2468			−1.69312
$144$		0			0
$145$	−1.84070			−0.152862
$146$		0			0
$147$	−1.22553	−	1.22396i	−0.101080	−	0.100951i
$148$		0			0
$149$	4.31652	+	7.47642i	0.353623	+	0.612493i	0.986881	−	0.161448i	$-0.0516163\pi$
$149$	4.31652	+	7.47642i	0.353623	+	0.612493i	−0.633259	+	0.773940i	$0.718283\pi$
$150$		0			0
$151$	−5.43836	+	9.41952i	−0.442568	+	0.766550i	−0.997879	−	0.0650926i	$-0.979266\pi$
$151$	−5.43836	+	9.41952i	−0.442568	+	0.766550i	0.555311	+	0.831642i	$0.312599\pi$
$152$		0			0
$153$	−18.7122	+	10.8355i	−1.51279	+	0.875995i
$154$		0			0
$155$	7.29998	−	12.6439i	0.586349	−	1.01559i
$156$		0			0
$157$	5.49613	+	9.51958i	0.438639	+	0.759745i	0.997585	−	0.0694592i	$-0.0221274\pi$
$157$	5.49613	+	9.51958i	0.438639	+	0.759745i	−0.558946	+	0.829204i	$0.688794\pi$
$158$		0			0
$159$	−13.4430	+	3.61126i	−1.06610	+	0.286391i
$160$		0			0
$161$	−4.98886			−0.393177
$162$		0			0
$163$	−4.79233			−0.375364			−0.187682	−	0.982230i	$-0.560098\pi$
$163$	−4.79233			−0.375364			−0.187682	+	0.982230i	$0.560098\pi$
$164$		0			0
$165$	−22.8957	+	6.15060i	−1.78243	+	0.478824i
$166$		0			0
$167$	1.46719	+	2.54124i	0.113534	+	0.196647i	0.917193	−	0.398444i	$-0.130450\pi$
$167$	1.46719	+	2.54124i	0.113534	+	0.196647i	−0.803659	+	0.595091i	$0.797116\pi$
$168$		0			0
$169$	−8.87617	+	15.3740i	−0.682782	+	1.18261i
$170$		0			0
$171$	8.58173	−	4.96932i	0.656261	−	0.380013i
$172$		0			0
$173$	5.99483	−	10.3834i	0.455779	−	0.789432i	−0.542954	−	0.839763i	$-0.682694\pi$
$173$	5.99483	−	10.3834i	0.455779	−	0.789432i	0.998733	+	0.0503306i	$0.0160275\pi$
$174$		0			0
$175$	4.52724	+	7.84141i	0.342227	+	0.592755i
$176$		0			0
$177$	−1.84933	−	1.84697i	−0.139004	−	0.138826i
$178$		0			0
$179$	−24.9266			−1.86310			−0.931552	−	0.363608i	$-0.881545\pi$
$179$	−24.9266			−1.86310			−0.931552	+	0.363608i	$0.881545\pi$
$180$		0			0
$181$	−21.4203			−1.59216			−0.796078	−	0.605194i	$-0.793096\pi$
$181$	−21.4203			−1.59216			−0.796078	+	0.605194i	$0.793096\pi$
$182$		0			0
$183$	0.933226	−	3.49179i	0.0689861	−	0.258120i
$184$		0			0
$185$	14.7978	+	25.6306i	1.08796	+	1.88440i
$186$		0			0
$187$	13.1578	−	22.7899i	0.962191	−	1.66656i
$188$		0			0
$189$	−1.35450	−	5.01651i	−0.0985252	−	0.364897i
$190$		0			0
$191$	8.98003	−	15.5539i	0.649772	−	1.12544i	−0.333405	−	0.942784i	$-0.608198\pi$
$191$	8.98003	−	15.5539i	0.649772	−	1.12544i	0.983177	−	0.182655i	$-0.0584691\pi$
$192$		0			0
$193$	−4.68943	−	8.12233i	−0.337553	−	0.584658i	0.646419	−	0.762983i	$-0.276266\pi$
$193$	−4.68943	−	8.12233i	−0.337553	−	0.584658i	−0.983972	+	0.178324i	$0.942932\pi$
$194$		0			0
$195$	−9.29747	+	34.7877i	−0.665806	+	2.49120i
$196$		0			0
$197$	−0.206917			−0.0147422			−0.00737110	−	0.999973i	$-0.502346\pi$
$197$	−0.206917			−0.0147422			−0.00737110	+	0.999973i	$0.502346\pi$
$198$		0			0
$199$	−12.6169			−0.894386			−0.447193	−	0.894438i	$-0.647576\pi$
$199$	−12.6169			−0.894386			−0.447193	+	0.894438i	$0.647576\pi$
$200$		0			0
$201$	4.17101	+	4.16568i	0.294201	+	0.293824i
$202$		0			0
$203$	0.245497	+	0.425213i	0.0172305	+	0.0298441i
$204$		0			0
$205$	8.93050	−	15.4681i	0.623733	−	1.08034i
$206$		0			0
$207$	−12.9710	−	7.46669i	−0.901547	−	0.518971i
$208$		0			0
$209$	−6.03436	+	10.4518i	−0.417406	+	0.722968i
$210$		0			0
$211$	−2.96505	−	5.13561i	−0.204122	−	0.353550i	0.745730	−	0.666248i	$-0.232101\pi$
$211$	−2.96505	−	5.13561i	−0.204122	−	0.353550i	−0.949853	+	0.312698i	$0.898767\pi$
$212$		0			0
$213$	17.9487	−	4.82166i	1.22983	−	0.330375i
$214$		0			0
$215$	−6.01114			−0.409957
$216$		0			0
$217$	−3.89443			−0.264371
$218$		0			0
$219$	16.4526	−	4.41974i	1.11176	−	0.298659i
$220$		0			0
$221$	−19.9850	−	34.6150i	−1.34434	−	2.32846i
$222$		0			0
$223$	−1.80500	+	3.12634i	−0.120871	+	0.209355i	−0.920112	−	0.391656i	$-0.871902\pi$
$223$	−1.80500	+	3.12634i	−0.120871	+	0.209355i	0.799240	+	0.601012i	$0.205236\pi$
$224$		0			0
$225$	0.0347696	+	27.1634i	0.00231797	+	1.81090i
$226$		0			0
$227$	−9.30710	+	16.1204i	−0.617734	+	1.06995i	0.372164	+	0.928167i	$0.378616\pi$
$227$	−9.30710	+	16.1204i	−0.617734	+	1.06995i	−0.989898	+	0.141780i	$0.954717\pi$
$228$		0			0
$229$	−11.4965	−	19.9126i	−0.759712	−	1.31586i	−0.942997	−	0.332801i	$-0.892006\pi$
$229$	−11.4965	−	19.9126i	−0.759712	−	1.31586i	0.183285	−	0.983060i	$-0.441327\pi$
$230$		0			0
$231$	4.47446	+	4.46874i	0.294398	+	0.294021i
$232$		0			0
$233$	−4.07066			−0.266678			−0.133339	−	0.991071i	$-0.542570\pi$
$233$	−4.07066			−0.266678			−0.133339	+	0.991071i	$0.542570\pi$
$234$		0			0
$235$	36.1393			2.35747
$236$		0			0
$237$	1.66714	−	6.23783i	0.108293	−	0.405191i
$238$		0			0
$239$	2.50000	+	4.33013i	0.161712	+	0.280093i	0.935483	−	0.353373i	$-0.114965\pi$
$239$	2.50000	+	4.33013i	0.161712	+	0.280093i	−0.773771	+	0.633465i	$0.781632\pi$
$240$		0			0
$241$	−7.30843	+	12.6586i	−0.470777	+	0.815410i	−0.999441	−	0.0334208i	$-0.989360\pi$
$241$	−7.30843	+	12.6586i	−0.470777	+	0.815410i	0.528664	+	0.848831i	$0.322693\pi$
$242$		0			0
$243$	3.98639	−	15.0701i	0.255727	−	0.966749i
$244$		0			0
$245$	1.87447	−	3.24667i	0.119755	−	0.207422i
$246$		0			0
$247$	9.16544	+	15.8750i	0.583183	+	1.01010i
$248$		0			0
$249$	−5.08984	+	19.0443i	−0.322556	+	1.20688i
$250$		0			0
$251$	−8.74206			−0.551794			−0.275897	−	0.961187i	$-0.588975\pi$
$251$	−8.74206			−0.551794			−0.275897	+	0.961187i	$0.588975\pi$
$252$		0			0
$253$	18.2145			1.14514
$254$		0			0
$255$	−33.1151	−	33.0727i	−2.07375	−	2.07109i
$256$		0			0
$257$	−10.6399	−	18.4288i	−0.663699	−	1.14956i	−0.979636	−	0.200780i	$-0.935652\pi$
$257$	−10.6399	−	18.4288i	−0.663699	−	1.14956i	0.315938	−	0.948780i	$-0.397681\pi$
$258$		0			0
$259$	3.94722	−	6.83678i	0.245268	−	0.424817i
$260$		0			0
$261$	0.00188543	+	1.47298i	0.000116705	+	0.0911751i
$262$		0			0
$263$	6.80515	−	11.7869i	0.419623	−	0.726809i	−0.576278	−	0.817254i	$-0.695495\pi$
$263$	6.80515	−	11.7869i	0.419623	−	0.726809i	0.995901	+	0.0904446i	$0.0288288\pi$
$264$		0			0
$265$	−15.0641	−	26.0918i	−0.925380	−	1.60280i
$266$		0			0
$267$	11.9583	−	3.21242i	0.731836	−	0.196597i
$268$		0			0
$269$	−18.9343			−1.15445			−0.577223	−	0.816587i	$-0.695864\pi$
$269$	−18.9343			−1.15445			−0.577223	+	0.816587i	$0.695864\pi$
$270$		0			0
$271$	−14.1669			−0.860579			−0.430290	−	0.902691i	$-0.641589\pi$
$271$	−14.1669			−0.860579			−0.430290	+	0.902691i	$0.641589\pi$
$272$		0			0
$273$	9.27617	−	2.49191i	0.561420	−	0.150817i
$274$		0			0
$275$	−16.5292	−	28.6294i	−0.996746	−	1.72642i
$276$		0			0
$277$	−0.636090	+	1.10174i	−0.0382190	+	0.0661972i	−0.884502	−	0.466536i	$-0.845502\pi$
$277$	−0.636090	+	1.10174i	−0.0382190	+	0.0661972i	0.846283	+	0.532733i	$0.178835\pi$
$278$		0			0
$279$	−10.1255	−	5.82869i	−0.606198	−	0.348955i
$280$		0			0
$281$	4.66891	−	8.08678i	0.278524	−	0.482417i	−0.692494	−	0.721423i	$-0.743488\pi$
$281$	4.66891	−	8.08678i	0.278524	−	0.482417i	0.971018	+	0.239006i	$0.0768216\pi$
$282$		0			0
$283$	4.88983	+	8.46943i	0.290670	+	0.503455i	0.973968	−	0.226684i	$-0.0727885\pi$
$283$	4.88983	+	8.46943i	0.290670	+	0.503455i	−0.683298	+	0.730139i	$0.739455\pi$
$284$		0			0
$285$	15.1871	+	15.1677i	0.899607	+	0.898456i
$286$		0			0
$287$	−4.76429			−0.281227
$288$		0			0
$289$	34.9505			2.05591
$290$		0			0
$291$	4.87749	−	18.2498i	0.285924	−	1.06982i
$292$		0			0
$293$	12.0672	+	20.9010i	0.704972	+	1.22105i	0.966702	+	0.255906i	$0.0823738\pi$
$293$	12.0672	+	20.9010i	0.704972	+	1.22105i	−0.261729	+	0.965141i	$0.584293\pi$
$294$		0			0
$295$	2.82858	−	4.89925i	0.164686	−	0.285245i
$296$		0			0
$297$	4.94533	+	18.3155i	0.286957	+	1.06277i
$298$		0			0
$299$	13.8328	−	23.9591i	0.799971	−	1.38559i
$300$		0			0
$301$	0.801714	+	1.38861i	0.0462100	+	0.0800382i
$302$		0			0
$303$	5.72590	−	21.4242i	0.328945	−	1.23079i
$304$		0			0
$305$	7.82305			0.447947
$306$		0			0
$307$	−20.0425			−1.14389			−0.571944	−	0.820293i	$-0.693810\pi$
$307$	−20.0425			−1.14389			−0.571944	+	0.820293i	$0.693810\pi$
$308$		0			0
$309$	−11.6846	−	11.6697i	−0.664714	−	0.663863i
$310$		0			0
$311$	6.56758	+	11.3754i	0.372414	+	0.645039i	0.989936	−	0.141514i	$-0.0451970\pi$
$311$	6.56758	+	11.3754i	0.372414	+	0.645039i	−0.617523	+	0.786553i	$0.711864\pi$
$312$		0			0
$313$	−6.29311	+	10.9000i	−0.355708	+	0.616104i	−0.987239	−	0.159247i	$-0.949093\pi$
$313$	−6.29311	+	10.9000i	−0.355708	+	0.616104i	0.631531	+	0.775351i	$0.282427\pi$
$314$		0			0
$315$	9.73280	−	5.63586i	0.548381	−	0.317545i
$316$		0			0
$317$	5.36679	−	9.29555i	0.301429	−	0.522090i	−0.675031	−	0.737789i	$-0.735870\pi$
$317$	5.36679	−	9.29555i	0.301429	−	0.522090i	0.976460	+	0.215699i	$0.0692031\pi$
$318$		0			0
$319$	−0.896319	−	1.55247i	−0.0501842	−	0.0869217i
$320$		0			0
$321$	−14.1050	+	3.78909i	−0.787263	+	0.211487i
$322$		0			0
$323$	−23.8253			−1.32568
$324$		0			0
$325$	−50.2115			−2.78523
$326$		0			0
$327$	27.6963	−	7.44020i	1.53161	−	0.411444i
$328$		0			0
$329$	−4.81995	−	8.34840i	−0.265732	−	0.460262i
$330$		0			0
$331$	−5.61919	+	9.73273i	−0.308859	+	0.534959i	−0.978113	−	0.208074i	$-0.933280\pi$
$331$	−5.61919	+	9.73273i	−0.308859	+	0.534959i	0.669254	+	0.743034i	$0.266614\pi$
$332$		0			0
$333$	20.4952	−	11.8679i	1.12313	−	0.650357i
$334$		0			0
$335$	−6.37963	+	11.0498i	−0.348557	+	0.603718i
$336$		0			0
$337$	−1.35453	−	2.34611i	−0.0737858	−	0.127801i	0.826772	−	0.562537i	$-0.190175\pi$
$337$	−1.35453	−	2.34611i	−0.0737858	−	0.127801i	−0.900558	+	0.434737i	$0.856841\pi$
$338$		0			0
$339$	−0.0804313	−	0.0803284i	−0.00436843	−	0.00436284i
$340$		0			0
$341$	14.2188			0.769989
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	8.36424	−	31.2959i	0.450316	−	1.68491i
$346$		0			0
$347$	−4.77314	−	8.26733i	−0.256236	−	0.443813i	0.708995	−	0.705214i	$-0.249149\pi$
$347$	−4.77314	−	8.26733i	−0.256236	−	0.443813i	−0.965230	+	0.261400i	$0.915816\pi$
$348$		0			0
$349$	1.01114	−	1.75135i	0.0541253	−	0.0937478i	−0.837693	−	0.546141i	$-0.816096\pi$
$349$	1.01114	−	1.75135i	0.0541253	−	0.0937478i	0.891819	+	0.452393i	$0.149430\pi$
$350$		0			0
$351$	27.8476	+	7.40446i	1.48639	+	0.395221i
$352$		0			0
$353$	−5.93836	+	10.2855i	−0.316067	+	0.547444i	−0.979664	−	0.200646i	$-0.935696\pi$
$353$	−5.93836	+	10.2855i	−0.316067	+	0.547444i	0.663597	+	0.748091i	$0.269029\pi$
$354$		0			0
$355$	20.1132	+	34.8371i	1.06750	+	1.84896i
$356$		0			0
$357$	−3.22339	+	12.0607i	−0.170600	+	0.638321i
$358$		0			0
$359$	13.9796			0.737817			0.368909	−	0.929466i	$-0.379732\pi$
$359$	13.9796			0.737817			0.368909	+	0.929466i	$0.379732\pi$
$360$		0			0
$361$	−8.07331			−0.424911
$362$		0			0
$363$	−2.85564	−	2.85199i	−0.149882	−	0.149691i
$364$		0			0
$365$	18.4366	+	31.9332i	0.965017	+	1.67146i
$366$		0			0
$367$	−1.14299	+	1.97972i	−0.0596635	+	0.103340i	−0.894314	−	0.447439i	$-0.852336\pi$
$367$	−1.14299	+	1.97972i	−0.0596635	+	0.103340i	0.834651	+	0.550779i	$0.185669\pi$
$368$		0			0
$369$	−12.3871	−	7.13059i	−0.644848	−	0.371204i
$370$		0			0
$371$	−4.01824	+	6.95979i	−0.208616	+	0.361334i
$372$		0			0
$373$	17.0527	+	29.5362i	0.882957	+	1.52933i	0.848038	+	0.529936i	$0.177784\pi$
$373$	17.0527	+	29.5362i	0.882957	+	1.52933i	0.0349186	+	0.999390i	$0.488883\pi$
$374$		0			0
$375$	−25.4257	+	6.83024i	−1.31298	+	0.352712i
$376$		0			0
$377$	−2.72279			−0.140231
$378$		0			0
$379$	6.50473			0.334126			0.167063	−	0.985946i	$-0.446572\pi$
$379$	6.50473			0.334126			0.167063	+	0.985946i	$0.446572\pi$
$380$		0			0
$381$	−5.35412	+	1.43831i	−0.274300	+	0.0736866i
$382$		0			0
$383$	11.2348	+	19.4592i	0.574069	+	0.994317i	0.996142	+	0.0877552i	$0.0279693\pi$
$383$	11.2348	+	19.4592i	0.574069	+	0.994317i	−0.422073	+	0.906562i	$0.638697\pi$
$384$		0			0
$385$	−6.84376	+	11.8537i	−0.348790	+	0.604122i
$386$		0			0
$387$	0.00615723	+	4.81028i	0.000312989	+	0.244520i
$388$		0			0
$389$	2.57316	−	4.45684i	0.130464	−	0.225971i	−0.793391	−	0.608712i	$-0.791687\pi$
$389$	2.57316	−	4.45684i	0.130464	−	0.225971i	0.923856	+	0.382741i	$0.125020\pi$
$390$		0			0
$391$	17.9790	+	31.1406i	0.909238	+	1.57485i
$392$		0			0
$393$	18.8011	+	18.7770i	0.948390	+	0.947177i
$394$		0			0
$395$	13.9753			0.703176
$396$		0			0
$397$	−21.0214			−1.05503			−0.527517	−	0.849544i	$-0.676877\pi$
$397$	−21.0214			−1.05503			−0.527517	+	0.849544i	$0.676877\pi$
$398$		0			0
$399$	1.47830	−	5.53125i	0.0740076	−	0.276909i
$400$		0			0
$401$	0.803852	+	1.39231i	0.0401424	+	0.0695288i	0.885399	−	0.464833i	$-0.153885\pi$
$401$	0.803852	+	1.39231i	0.0401424	+	0.0695288i	−0.845256	+	0.534361i	$0.820552\pi$
$402$		0			0
$403$	10.7983	−	18.7031i	0.537899	−	0.931669i
$404$		0			0
$405$	33.7403	−	0.0863761i	1.67657	−	0.00429207i
$406$		0			0
$407$	−14.4115	+	24.9614i	−0.714350	+	1.23729i
$408$		0			0
$409$	−10.7055	−	18.5425i	−0.529354	−	0.916869i	−0.999414	−	0.0342340i	$-0.989101\pi$
$409$	−10.7055	−	18.5425i	−0.529354	−	0.916869i	0.470059	−	0.882635i	$-0.344232\pi$
$410$		0			0
$411$	−0.306771	+	1.14782i	−0.0151319	+	0.0566178i
$412$		0			0
$413$	−1.50901			−0.0742534
$414$		0			0
$415$	−42.6672			−2.09445
$416$		0			0
$417$	−24.7566	−	24.7249i	−1.21234	−	1.21078i
$418$		0			0
$419$	−17.3497	−	30.0505i	−0.847587	−	1.46806i	−0.883355	−	0.468704i	$-0.844721\pi$
$419$	−17.3497	−	30.0505i	−0.847587	−	1.46806i	0.0357681	−	0.999360i	$-0.488612\pi$
$420$		0			0
$421$	11.6234	−	20.1323i	0.566488	−	0.981186i	−0.430421	−	0.902628i	$-0.641635\pi$
$421$	11.6234	−	20.1323i	0.566488	−	0.981186i	0.996910	−	0.0785583i	$-0.0250317\pi$
$422$		0			0
$423$	−0.0370176	−	28.9197i	−0.00179986	−	1.40612i
$424$		0			0
$425$	32.6309	−	56.5183i	1.58283	−	2.74154i
$426$		0			0
$427$	−1.04337	−	1.80717i	−0.0504923	−	0.0874552i
$428$		0			0
$429$	−33.8677	+	9.09807i	−1.63515	+	0.439259i
$430$		0			0
$431$	−10.5201			−0.506735			−0.253368	−	0.967370i	$-0.581538\pi$
$431$	−10.5201			−0.506735			−0.253368	+	0.967370i	$0.581538\pi$
$432$		0			0
$433$	−29.8296			−1.43352			−0.716758	−	0.697322i	$-0.754375\pi$
$433$	−29.8296			−1.43352			−0.716758	+	0.697322i	$0.754375\pi$
$434$		0			0
$435$	−3.07902	+	0.827134i	−0.147628	+	0.0396580i
$436$		0			0
$437$	−8.24547	−	14.2816i	−0.394434	−	0.683180i
$438$		0			0
$439$	2.28462	−	3.95708i	0.109039	−	0.188861i	−0.806342	−	0.591449i	$-0.798556\pi$
$439$	2.28462	−	3.95708i	0.109039	−	0.188861i	0.915381	+	0.402588i	$0.131889\pi$
$440$		0			0
$441$	−2.59999	−	1.49667i	−0.123809	−	0.0712702i
$442$		0			0
$443$	−5.01455	+	8.68545i	−0.238248	+	0.412658i	−0.960212	−	0.279273i	$-0.909907\pi$
$443$	−5.01455	+	8.68545i	−0.238248	+	0.412658i	0.721963	+	0.691931i	$0.243240\pi$
$444$		0			0
$445$	13.4004	+	23.2101i	0.635239	+	1.10027i
$446$		0			0
$447$	10.5800	+	10.5665i	0.500418	+	0.499778i
$448$		0			0
$449$	−18.1908			−0.858476			−0.429238	−	0.903192i	$-0.641218\pi$
$449$	−18.1908			−0.858476			−0.429238	+	0.903192i	$0.641218\pi$
$450$		0			0
$451$	17.3946			0.819082
$452$		0			0
$453$	−4.86426	+	18.2002i	−0.228543	+	0.855122i
$454$		0			0
$455$	10.3948	+	18.0043i	0.487316	+	0.844056i
$456$		0			0
$457$	2.62708	−	4.55024i	0.122890	−	0.212851i	−0.798016	−	0.602636i	$-0.794117\pi$
$457$	2.62708	−	4.55024i	0.122890	−	0.212851i	0.920906	+	0.389784i	$0.127451\pi$
$458$		0			0
$459$	−26.4318	+	26.5335i	−1.23373	+	1.23848i
$460$		0			0
$461$	−4.32763	+	7.49568i	−0.201558	+	0.349108i	−0.949031	−	0.315184i	$-0.897934\pi$
$461$	−4.32763	+	7.49568i	−0.201558	+	0.349108i	0.747473	+	0.664293i	$0.231267\pi$
$462$		0			0
$463$	−0.509788	−	0.882979i	−0.0236919	−	0.0410355i	0.853936	−	0.520377i	$-0.174209\pi$
$463$	−0.509788	−	0.882979i	−0.0236919	−	0.0410355i	−0.877628	+	0.479342i	$0.840875\pi$
$464$		0			0
$465$	6.52935	−	24.4304i	0.302791	−	1.13293i
$466$		0			0
$467$	−18.7167			−0.866104			−0.433052	−	0.901369i	$-0.642563\pi$
$467$	−18.7167			−0.866104			−0.433052	+	0.901369i	$0.642563\pi$
$468$		0			0
$469$	3.40344			0.157156
$470$		0			0
$471$	13.4713	+	13.4541i	0.620726	+	0.619932i
$472$		0			0
$473$	−2.92710	−	5.06988i	−0.134588	−	0.233113i
$474$		0			0
$475$	−14.9650	+	25.9202i	−0.686643	+	1.18930i
$476$		0			0
$477$	−20.8639	+	12.0814i	−0.955293	+	0.553170i
$478$		0			0
$479$	−18.3255	+	31.7407i	−0.837313	+	1.45027i	0.0548199	+	0.998496i	$0.482542\pi$
$479$	−18.3255	+	31.7407i	−0.837313	+	1.45027i	−0.892133	+	0.451773i	$0.850792\pi$
$480$		0			0
$481$	21.8892	+	37.9132i	0.998062	+	1.72869i
$482$		0			0
$483$	−8.34509	+	2.24178i	−0.379715	+	0.102005i
$484$		0			0
$485$	40.8871			1.85659
$486$		0			0
$487$	35.1877			1.59451			0.797253	−	0.603646i	$-0.206286\pi$
$487$	35.1877			1.59451			0.797253	+	0.603646i	$0.206286\pi$
$488$		0			0
$489$	−8.01635	+	2.15347i	−0.362512	+	0.0973835i
$490$		0			0
$491$	9.15489	+	15.8567i	0.413154	+	0.715604i	0.995233	−	0.0975285i	$-0.0310937\pi$
$491$	9.15489	+	15.8567i	0.413154	+	0.715604i	−0.582079	+	0.813133i	$0.697760\pi$
$492$		0			0
$493$	1.76946	−	3.06479i	0.0796924	−	0.138031i
$494$		0			0
$495$	−35.5349	+	20.5768i	−1.59718	+	0.924857i
$496$		0			0
$497$	5.36505	−	9.29255i	0.240656	−	0.416828i
$498$		0			0
$499$	12.2791	+	21.2679i	0.549686	+	0.952084i	0.998296	+	0.0583561i	$0.0185859\pi$
$499$	12.2791	+	21.2679i	0.549686	+	0.952084i	−0.448610	+	0.893728i	$0.648081\pi$
$500$		0			0
$501$	3.59615	+	3.59155i	0.160664	+	0.160459i
$502$		0			0
$503$	17.0176			0.758779			0.379390	−	0.925237i	$-0.376134\pi$
$503$	17.0176			0.758779			0.379390	+	0.925237i	$0.376134\pi$
$504$		0			0
$505$	47.9991			2.13593
$506$		0			0
$507$	−7.93914	+	29.7053i	−0.352590	+	1.31926i
$508$		0			0
$509$	10.3817	+	17.9817i	0.460163	+	0.797025i	0.998969	−	0.0454049i	$-0.0144578\pi$
$509$	10.3817	+	17.9817i	0.460163	+	0.797025i	−0.538806	+	0.842430i	$0.681124\pi$
$510$		0			0
$511$	4.91784	−	8.51794i	0.217552	−	0.376812i
$512$		0			0
$513$	12.1220	−	12.1687i	0.535201	−	0.537260i
$514$		0			0
$515$	17.8718	−	30.9548i	0.787525	−	1.36403i
$516$		0			0
$517$	17.5979	+	30.4804i	0.773953	+	1.34053i
$518$		0			0
$519$	5.36198	−	20.0625i	0.235365	−	0.880648i
$520$		0			0
$521$	29.9915			1.31395			0.656977	−	0.753911i	$-0.271835\pi$
$521$	29.9915			1.31395			0.656977	+	0.753911i	$0.271835\pi$
$522$		0			0
$523$	−2.57036			−0.112394			−0.0561970	−	0.998420i	$-0.517898\pi$
$523$	−2.57036			−0.112394			−0.0561970	+	0.998420i	$0.517898\pi$
$524$		0			0
$525$	11.0965	+	11.0823i	0.484292	+	0.483673i
$526$		0			0
$527$	14.0349	+	24.3091i	0.611370	+	1.05892i
$528$		0			0
$529$	−0.944341	+	1.63565i	−0.0410583	+	0.0711151i
$530$		0			0
$531$	−3.92341	−	2.25849i	−0.170261	−	0.0980101i
$532$		0			0
$533$	13.2101	−	22.8806i	0.572195	−	0.991070i
$534$		0			0
$535$	−15.8059	−	27.3767i	−0.683350	−	1.18360i
$536$		0			0
$537$	−41.6959	+	11.2010i	−1.79931	+	0.483358i
$538$		0			0
$539$	3.65105			0.157262
$540$		0			0
$541$	24.7962			1.06607			0.533036	−	0.846093i	$-0.321051\pi$
$541$	24.7962			1.06607			0.533036	+	0.846093i	$0.321051\pi$
$542$		0			0
$543$	−35.8307	+	9.62538i	−1.53764	+	0.413065i
$544$		0			0
$545$	31.0362	+	53.7563i	1.32945	+	2.30267i
$546$		0			0
$547$	−5.71955	+	9.90655i	−0.244550	+	0.423574i	−0.962005	−	0.273031i	$-0.911974\pi$
$547$	−5.71955	+	9.90655i	−0.244550	+	0.423574i	0.717455	+	0.696605i	$0.245307\pi$
$548$		0			0
$549$	−0.00801317	−	6.26022i	−0.000341994	−	0.267180i
$550$		0			0
$551$	−0.811502	+	1.40556i	−0.0345712	+	0.0598790i
$552$		0			0
$553$	−1.86391	−	3.22839i	−0.0792615	−	0.137285i
$554$		0			0
$555$	36.2704	+	36.2240i	1.53959	+	1.53762i
$556$		0			0
$557$	13.8445			0.586609			0.293305	−	0.956019i	$-0.405245\pi$
$557$	13.8445			0.586609			0.293305	+	0.956019i	$0.405245\pi$
$558$		0			0
$559$	−8.89178			−0.376082
$560$		0			0
$561$	11.7687	−	44.0343i	0.496877	−	1.85913i
$562$		0			0
$563$	17.5194	+	30.3444i	0.738353	+	1.27886i	0.953237	+	0.302225i	$0.0977293\pi$
$563$	17.5194	+	30.3444i	0.738353	+	1.27886i	−0.214884	+	0.976640i	$0.568937\pi$
$564$		0			0
$565$	0.123021	−	0.213079i	0.00517553	−	0.00896429i
$566$		0			0
$567$	−4.51994	−	7.78268i	−0.189820	−	0.326842i
$568$		0			0
$569$	−3.72940	+	6.45951i	−0.156344	+	0.270797i	−0.933548	−	0.358453i	$-0.883304\pi$
$569$	−3.72940	+	6.45951i	−0.156344	+	0.270797i	0.777203	+	0.629250i	$0.216638\pi$
$570$		0			0
$571$	21.4174	+	37.0961i	0.896292	+	1.55242i	0.832197	+	0.554480i	$0.187083\pi$
$571$	21.4174	+	37.0961i	0.896292	+	1.55242i	0.0640949	+	0.997944i	$0.479584\pi$
$572$		0			0
$573$	8.03204	−	30.0529i	0.335543	−	1.25548i
$574$		0			0
$575$	45.1715			1.88378
$576$		0			0
$577$	−16.1386			−0.671860			−0.335930	−	0.941887i	$-0.609051\pi$
$577$	−16.1386			−0.671860			−0.335930	+	0.941887i	$0.609051\pi$
$578$		0			0
$579$	−11.4941	−	11.4794i	−0.477677	−	0.477066i
$580$		0			0
$581$	5.69058	+	9.85637i	0.236085	+	0.408911i
$582$		0			0
$583$	14.6708	−	25.4105i	0.607601	−	1.05240i
$584$		0			0
$585$	0.0798329	+	62.3688i	0.00330068	+	2.57863i
$586$		0			0
$587$	22.9094	−	39.6802i	0.945570	−	1.63778i	0.190965	−	0.981597i	$-0.438838\pi$
$587$	22.9094	−	39.6802i	0.945570	−	1.63778i	0.754605	−	0.656179i	$-0.227829\pi$
$588$		0			0
$589$	−6.43663	−	11.1486i	−0.265217	−	0.459369i
$590$		0			0
$591$	−0.346119	+	0.0929797i	−0.0142374	+	0.00382467i
$592$		0			0
$593$	−22.4176			−0.920579			−0.460290	−	0.887769i	$-0.652254\pi$
$593$	−22.4176			−0.920579			−0.460290	+	0.887769i	$0.652254\pi$
$594$		0			0
$595$	−27.0211			−1.10776
$596$		0			0
$597$	−21.1048	+	5.66949i	−0.863762	+	0.232037i
$598$		0			0
$599$	0.622253	+	1.07777i	0.0254246	+	0.0440366i	0.878458	−	0.477820i	$-0.158573\pi$
$599$	0.622253	+	1.07777i	0.0254246	+	0.0440366i	−0.853033	+	0.521857i	$0.825240\pi$
$600$		0			0
$601$	18.9011	−	32.7377i	0.770993	−	1.33540i	−0.166027	−	0.986121i	$-0.553094\pi$
$601$	18.9011	−	32.7377i	0.770993	−	1.33540i	0.937019	−	0.349277i	$-0.113573\pi$
$602$		0			0
$603$	8.84893	+	5.09384i	0.360356	+	0.207437i
$604$		0			0
$605$	4.36775	−	7.56516i	0.177574	−	0.307568i
$606$		0			0
$607$	6.01266	+	10.4142i	0.244047	+	0.422701i	0.961863	−	0.273531i	$-0.0881917\pi$
$607$	6.01266	+	10.4142i	0.244047	+	0.422701i	−0.717817	+	0.696232i	$0.754858\pi$
$608$		0			0
$609$	0.601726	+	0.600956i	0.0243832	+	0.0243520i
$610$		0			0
$611$	53.4579			2.16267
$612$		0			0
$613$	−29.5048			−1.19169			−0.595843	−	0.803101i	$-0.703182\pi$
$613$	−29.5048			−1.19169			−0.595843	+	0.803101i	$0.703182\pi$
$614$		0			0
$615$	7.98774	−	29.8872i	0.322097	−	1.20517i
$616$		0			0
$617$	6.26890	+	10.8581i	0.252376	+	0.437129i	0.964180	−	0.265250i	$-0.0854546\pi$
$617$	6.26890	+	10.8581i	0.252376	+	0.437129i	−0.711803	+	0.702379i	$0.752121\pi$
$618$		0			0
$619$	−15.2153	+	26.3537i	−0.611555	+	1.05924i	0.379423	+	0.925223i	$0.376122\pi$
$619$	−15.2153	+	26.3537i	−0.611555	+	1.05924i	−0.990978	+	0.134022i	$0.957211\pi$
$620$		0			0
$621$	−25.0524	−	6.66124i	−1.00532	−	0.267306i
$622$		0			0
$623$	3.57445	−	6.19114i	0.143207	−	0.248043i
$624$		0			0
$625$	−5.85564	−	10.1423i	−0.234226	−	0.405691i
$626$		0			0
$627$	−5.39734	+	20.1948i	−0.215549	+	0.806504i
$628$		0			0
$629$	−56.9005			−2.26877
$630$		0			0
$631$	20.6901			0.823660			0.411830	−	0.911261i	$-0.364890\pi$
$631$	20.6901			0.823660			0.411830	+	0.911261i	$0.364890\pi$
$632$		0			0
$633$	−7.26750	−	7.25820i	−0.288857	−	0.288488i
$634$		0			0
$635$	−5.99979	−	10.3919i	−0.238094	−	0.412391i
$636$		0			0
$637$	2.77274	−	4.80253i	0.109860	−	0.190283i
$638$		0			0
$639$	27.8570	−	16.1308i	1.10201	−	0.638126i
$640$		0			0
$641$	5.24417	−	9.08317i	0.207132	−	0.358764i	−0.743678	−	0.668538i	$-0.766920\pi$
$641$	5.24417	−	9.08317i	0.207132	−	0.358764i	0.950810	+	0.309775i	$0.100254\pi$
$642$		0			0
$643$	−20.2056	−	34.9971i	−0.796830	−	1.38015i	−0.921671	−	0.387972i	$-0.873176\pi$
$643$	−20.2056	−	34.9971i	−0.796830	−	1.38015i	0.124841	−	0.992177i	$-0.460158\pi$
$644$		0			0
$645$	−10.0551	+	2.70116i	−0.395920	+	0.106358i
$646$		0			0
$647$	16.8906			0.664038			0.332019	−	0.943273i	$-0.392270\pi$
$647$	16.8906			0.664038			0.332019	+	0.943273i	$0.392270\pi$
$648$		0			0
$649$	5.50945			0.216265
$650$		0			0
$651$	−6.51440	+	1.75000i	−0.255319	+	0.0685878i
$652$		0			0
$653$	19.0982	+	33.0791i	0.747372	+	1.29449i	0.949079	+	0.315040i	$0.102018\pi$
$653$	19.0982	+	33.0791i	0.747372	+	1.29449i	−0.201707	+	0.979446i	$0.564649\pi$
$654$		0			0
$655$	−28.7566	+	49.8079i	−1.12361	+	1.94615i
$656$		0			0
$657$	25.5349	−	14.7862i	0.996212	−	0.576865i
$658$		0			0
$659$	15.2864	−	26.4768i	0.595472	−	1.03139i	−0.398008	−	0.917382i	$-0.630298\pi$
$659$	15.2864	−	26.4768i	0.595472	−	1.03139i	0.993480	−	0.114006i	$-0.0363684\pi$
$660$		0			0
$661$	−12.0894	−	20.9395i	−0.470223	−	0.814451i	0.529197	−	0.848499i	$-0.322493\pi$
$661$	−12.0894	−	20.9395i	−0.470223	−	0.814451i	−0.999420	+	0.0340482i	$0.989160\pi$
$662$		0			0
$663$	−48.9843	−	48.9217i	−1.90239	−	1.89996i
$664$		0			0
$665$	12.3923			0.480553
$666$		0			0
$667$	2.44949			0.0948448
$668$		0			0
$669$	−1.61445	+	6.04067i	−0.0624182	+	0.233546i
$670$		0			0
$671$	3.80939	+	6.59806i	0.147060	+	0.254715i
$672$		0			0
$673$	−13.5485	+	23.4667i	−0.522257	+	0.904575i	0.477408	+	0.878682i	$0.341576\pi$
$673$	−13.5485	+	23.4667i	−0.522257	+	0.904575i	−0.999665	+	0.0258933i	$0.991757\pi$
$674$		0			0
$675$	12.2643	+	45.4219i	0.472052	+	1.74829i
$676$		0			0
$677$	−6.72453	+	11.6472i	−0.258445	+	0.447640i	−0.965825	−	0.259193i	$-0.916543\pi$
$677$	−6.72453	+	11.6472i	−0.258445	+	0.447640i	0.707381	+	0.706833i	$0.249877\pi$
$678$		0			0
$679$	−5.45316	−	9.44516i	−0.209273	−	0.362472i
$680$		0			0
$681$	−8.32459	+	31.1475i	−0.318999	+	1.19358i
$682$		0			0
$683$	−11.4449			−0.437925			−0.218963	−	0.975733i	$-0.570267\pi$
$683$	−11.4449			−0.437925			−0.218963	+	0.975733i	$0.570267\pi$
$684$		0			0
$685$	−2.57160			−0.0982557
$686$		0			0
$687$	−28.1787	−	28.1426i	−1.07508	−	1.07371i
$688$		0			0
$689$	−22.2830	−	38.5954i	−0.848916	−	1.47037i
$690$		0			0
$691$	18.1416	−	31.4222i	0.690139	−	1.19536i	−0.281653	−	0.959516i	$-0.590883\pi$
$691$	18.1416	−	31.4222i	0.690139	−	1.19536i	0.971792	−	0.235840i	$-0.0757840\pi$
$692$		0			0
$693$	9.49270	+	5.46442i	0.360598	+	0.207576i
$694$		0			0
$695$	37.8656	−	65.5851i	1.43632	−	2.48779i
$696$		0			0
$697$	17.1697	+	29.7388i	0.650349	+	1.12644i
$698$		0			0
$699$	−6.80917	+	1.82918i	−0.257547	+	0.0691861i
$700$		0			0
$701$	4.80688			0.181553			0.0907767	−	0.995871i	$-0.471065\pi$
$701$	4.80688			0.181553			0.0907767	+	0.995871i	$0.471065\pi$
$702$		0			0
$703$	26.0955			0.984210
$704$		0			0
$705$	60.4519	−	16.2395i	2.27675	−	0.611615i
$706$		0			0
$707$	−6.40171	−	11.0881i	−0.240761	−	0.417010i
$708$		0			0
$709$	6.17770	−	10.7001i	0.232008	−	0.401850i	−0.726391	−	0.687282i	$-0.758804\pi$
$709$	6.17770	−	10.7001i	0.232008	−	0.401850i	0.958399	+	0.285432i	$0.0921370\pi$
$710$		0			0
$711$	−0.0143150	−	11.1834i	−0.000536853	−	0.419412i
$712$		0			0
$713$	−9.71438	+	16.8258i	−0.363807	+	0.630131i
$714$		0			0
$715$	−37.9519	−	65.7347i	−1.41932	−	2.45834i
$716$		0			0
$717$	6.12764	+	6.11980i	0.228841	+	0.228548i
$718$		0			0
$719$	10.4488			0.389673			0.194837	−	0.980836i	$-0.437582\pi$
$719$	10.4488			0.389673			0.194837	+	0.980836i	$0.437582\pi$
$720$		0			0
$721$	−9.53433			−0.355077
$722$		0			0
$723$	−6.53691	+	24.4587i	−0.243110	+	0.909628i
$724$		0			0
$725$	−2.22285	−	3.85008i	−0.0825544	−	0.142988i
$726$		0			0
$727$	−9.13266	+	15.8182i	−0.338711	+	0.586665i	−0.984191	−	0.177112i	$-0.943324\pi$
$727$	−9.13266	+	15.8182i	−0.338711	+	0.586665i	0.645479	+	0.763778i	$0.276658\pi$
$728$		0			0
$729$	−0.103681	−	26.9998i	−0.00384003	−	0.999993i
$730$		0			0
$731$	5.77849	−	10.0086i	0.213725	−	0.370183i
$732$		0			0
$733$	24.3245	+	42.1313i	0.898447	+	1.55616i	0.829480	+	0.558537i	$0.188637\pi$
$733$	24.3245	+	42.1313i	0.898447	+	1.55616i	0.0689673	+	0.997619i	$0.478030\pi$
$734$		0			0
$735$	1.67659	−	6.27316i	0.0618418	−	0.231389i
$736$		0			0
$737$	−12.4261			−0.457722
$738$		0			0
$739$	−52.2935			−1.92365			−0.961823	−	0.273671i	$-0.911762\pi$
$739$	−52.2935			−1.92365			−0.961823	+	0.273671i	$0.911762\pi$
$740$		0			0
$741$	22.4650	+	22.4363i	0.825273	+	0.824217i
$742$		0			0
$743$	5.21154	+	9.02665i	0.191193	+	0.331156i	0.945646	−	0.325198i	$-0.105431\pi$
$743$	5.21154	+	9.02665i	0.191193	+	0.331156i	−0.754453	+	0.656354i	$0.772098\pi$
$744$		0			0
$745$	−16.1823	+	28.0286i	−0.592874	+	1.02689i
$746$		0			0
$747$	0.0437040	+	34.1434i	0.00159905	+	1.24924i
$748$		0			0
$749$	−4.21612	+	7.30253i	−0.154054	+	0.266829i
$750$		0			0
$751$	5.10383	+	8.84010i	0.186242	+	0.322580i	0.943994	−	0.329962i	$-0.107036\pi$
$751$	5.10383	+	8.84010i	0.186242	+	0.322580i	−0.757753	+	0.652542i	$0.773703\pi$
$752$		0			0
$753$	−14.6232	+	3.92832i	−0.532901	+	0.143156i
$754$		0			0
$755$	−40.7761			−1.48399
$756$		0			0
$757$	−6.13207			−0.222874			−0.111437	−	0.993772i	$-0.535545\pi$
$757$	−6.13207			−0.222874			−0.111437	+	0.993772i	$0.535545\pi$
$758$		0			0
$759$	30.4683	−	8.18486i	1.10593	−	0.297091i
$760$		0			0
$761$	−16.0967	−	27.8803i	−0.583505	−	1.01066i	−0.995060	−	0.0992757i	$-0.968347\pi$
$761$	−16.0967	−	27.8803i	−0.583505	−	1.01066i	0.411555	−	0.911385i	$-0.364986\pi$
$762$		0			0
$763$	8.27869	−	14.3391i	0.299709	−	0.519111i
$764$		0			0
$765$	−70.2546	−	40.4417i	−2.54006	−	1.46217i
$766$		0			0
$767$	4.18408	−	7.24704i	0.151078	−	0.261676i
$768$		0			0
$769$	5.38520	+	9.32745i	0.194195	+	0.336356i	0.946636	−	0.322303i	$-0.104457\pi$
$769$	5.38520	+	9.32745i	0.194195	+	0.336356i	−0.752441	+	0.658660i	$0.771124\pi$
$770$		0			0
$771$	−26.0790	−	26.0456i	−0.939212	−	0.938011i
$772$		0			0
$773$	−26.6154			−0.957289			−0.478644	−	0.878009i	$-0.658872\pi$
$773$	−26.6154			−0.957289			−0.478644	+	0.878009i	$0.658872\pi$
$774$		0			0
$775$	35.2621			1.26665
$776$		0			0
$777$	3.53052	−	13.2099i	0.126657	−	0.473903i
$778$		0			0
$779$	−7.87431	−	13.6387i	−0.282127	−	0.488657i
$780$		0			0
$781$	−19.5881	+	33.9275i	−0.700916	+	1.21402i
$782$		0			0
$783$	0.665049	+	2.46307i	0.0237669	+	0.0880230i
$784$		0			0
$785$	−20.6046	+	35.6882i	−0.735410	+	1.27377i
$786$		0			0
$787$	−4.00251	−	6.93256i	−0.142674	−	0.247119i	0.785829	−	0.618444i	$-0.212237\pi$
$787$	−4.00251	−	6.93256i	−0.142674	−	0.247119i	−0.928503	+	0.371325i	$0.878903\pi$
$788$		0			0
$789$	6.08676	−	22.7744i	0.216694	−	0.810789i
$790$		0			0
$791$	−0.0656299			−0.00233353
$792$		0			0
$793$	11.5720			0.410933
$794$		0			0
$795$	−36.9229	−	36.8757i	−1.30952	−	1.30785i
$796$		0			0
$797$	−11.9675	−	20.7284i	−0.423912	−	0.734237i	0.572406	−	0.819970i	$-0.306010\pi$
$797$	−11.9675	−	20.7284i	−0.423912	−	0.734237i	−0.996318	+	0.0857334i	$0.972677\pi$
$798$		0			0
$799$	−34.7406	+	60.1725i	−1.22903	+	2.12875i
$800$		0			0
$801$	18.5597	−	10.7471i	0.655774	−	0.379731i
$802$		0			0
$803$	−17.9552	+	31.0994i	−0.633627	+	1.09747i
$804$		0			0
$805$	−9.35144	−	16.1972i	−0.329595	−	0.570875i
$806$		0			0
$807$	−31.6723	+	8.50829i	−1.11492	+	0.299506i
$808$		0			0
$809$	26.9965			0.949148			0.474574	−	0.880216i	$-0.342602\pi$
$809$	26.9965			0.949148			0.474574	+	0.880216i	$0.342602\pi$
$810$		0			0
$811$	41.6011			1.46081			0.730406	−	0.683013i	$-0.239331\pi$
$811$	41.6011			1.46081			0.730406	+	0.683013i	$0.239331\pi$
$812$		0			0
$813$	−23.6977	+	6.36602i	−0.831113	+	0.223266i
$814$		0			0
$815$	−8.98306	−	15.5591i	−0.314663	−	0.545012i
$816$		0			0
$817$	−2.65011	+	4.59013i	−0.0927156	+	0.160588i
$818$		0			0
$819$	14.3969	−	8.33665i	0.503069	−	0.291306i
$820$		0			0
$821$	−9.33583	+	16.1701i	−0.325823	+	0.564341i	−0.981678	−	0.190545i	$-0.938975\pi$
$821$	−9.33583	+	16.1701i	−0.325823	+	0.564341i	0.655856	+	0.754886i	$0.272308\pi$
$822$		0			0
$823$	−21.4756	−	37.1968i	−0.748591	−	1.29660i	−0.948498	−	0.316783i	$-0.897397\pi$
$823$	−21.4756	−	37.1968i	−0.748591	−	1.29660i	0.199906	−	0.979815i	$-0.435936\pi$
$824$		0			0
$825$	−40.5139	−	40.4621i	−1.41051	−	1.40871i
$826$		0			0
$827$	−28.4602			−0.989657			−0.494828	−	0.868991i	$-0.664769\pi$
$827$	−28.4602			−0.989657			−0.494828	+	0.868991i	$0.664769\pi$
$828$		0			0
$829$	32.0061			1.11162			0.555809	−	0.831310i	$-0.312409\pi$
$829$	32.0061			1.11162			0.555809	+	0.831310i	$0.312409\pi$
$830$		0			0
$831$	−0.568941	+	2.12876i	−0.0197363	+	0.0738460i
$832$		0			0
$833$	3.60383	+	6.24202i	0.124865	+	0.216273i
$834$		0			0
$835$	−5.50038	+	9.52693i	−0.190348	+	0.329693i
$836$		0			0
$837$	−19.5566	−	5.19994i	−0.675974	−	0.179736i
$838$		0			0
$839$	2.01191	−	3.48473i	0.0694589	−	0.120306i	−0.829204	−	0.558946i	$-0.811206\pi$
$839$	2.01191	−	3.48473i	0.0694589	−	0.120306i	0.898663	+	0.438639i	$0.144539\pi$
$840$		0			0
$841$	14.3795	+	24.9060i	0.495844	+	0.858826i
$842$		0			0
$843$	4.17603	−	15.6251i	0.143830	−	0.538158i
$844$		0			0
$845$	−66.5523			−2.28947
$846$		0			0
$847$	−2.33013			−0.0800642
$848$		0			0
$849$	11.9852	+	11.9699i	0.411332	+	0.410806i
$850$		0			0
$851$	−19.6921	−	34.1077i	−0.675036	−	1.16920i
$852$		0			0
$853$	−25.1214	+	43.5116i	−0.860141	+	1.48981i	0.0116510	+	0.999932i	$0.496291\pi$
$853$	−25.1214	+	43.5116i	−0.860141	+	1.48981i	−0.871792	+	0.489876i	$0.837042\pi$
$854$		0			0
$855$	32.2199	+	18.5472i	1.10190	+	0.634301i
$856$		0			0
$857$	5.37909	−	9.31685i	0.183746	−	0.318258i	−0.759407	−	0.650616i	$-0.774511\pi$
$857$	5.37909	−	9.31685i	0.183746	−	0.318258i	0.943153	+	0.332358i	$0.107844\pi$
$858$		0			0
$859$	21.6126	+	37.4342i	0.737413	+	1.27724i	0.953656	+	0.300898i	$0.0972863\pi$
$859$	21.6126	+	37.4342i	0.737413	+	1.27724i	−0.216243	+	0.976340i	$0.569380\pi$
$860$		0			0
$861$	−7.96945	+	2.14087i	−0.271598	+	0.0729608i
$862$		0			0
$863$	−44.1446			−1.50270			−0.751349	−	0.659905i	$-0.770597\pi$
$863$	−44.1446			−1.50270			−0.751349	+	0.659905i	$0.770597\pi$
$864$		0			0
$865$	44.9484			1.52829
$866$		0			0
$867$	58.4633	−	15.7053i	1.98552	−	0.533380i
$868$		0			0
$869$	6.80522	+	11.7870i	0.230851	+	0.399846i
$870$		0			0
$871$	−9.43685	+	16.3451i	−0.319756	+	0.553833i
$872$		0			0
$873$	−0.0418807	−	32.7190i	−0.00141745	−	1.10737i
$874$		0			0
$875$	−7.59999	+	13.1636i	−0.256927	+	0.445010i
$876$		0			0
$877$	−10.9631	−	18.9886i	−0.370196	−	0.641199i	0.619399	−	0.785076i	$-0.287376\pi$
$877$	−10.9631	−	18.9886i	−0.370196	−	0.641199i	−0.989596	+	0.143877i	$0.954043\pi$
$878$		0			0
$879$	29.5773	+	29.5395i	0.997619	+	0.996343i
$880$		0			0
$881$	49.6969			1.67433			0.837166	−	0.546949i	$-0.184211\pi$
$881$	49.6969			1.67433			0.837166	+	0.546949i	$0.184211\pi$
$882$		0			0
$883$	−16.8441			−0.566848			−0.283424	−	0.958995i	$-0.591470\pi$
$883$	−16.8441			−0.566848			−0.283424	+	0.958995i	$0.591470\pi$
$884$		0			0
$885$	2.52998	−	9.46624i	0.0850443	−	0.318204i
$886$		0			0
$887$	10.4950	+	18.1779i	0.352387	+	0.610352i	0.986667	−	0.162751i	$-0.0520367\pi$
$887$	10.4950	+	18.1779i	0.352387	+	0.610352i	−0.634280	+	0.773103i	$0.718703\pi$
$888$		0			0
$889$	−1.60040	+	2.77197i	−0.0536757	+	0.0929690i
$890$		0			0
$891$	16.5025	+	28.4149i	0.552855	+	0.951936i
$892$		0			0
$893$	15.9326	−	27.5961i	0.533164	−	0.923468i
$894$		0			0
$895$	−46.7241	−	80.9285i	−1.56181	−	2.70514i
$896$		0			0
$897$	12.3725	−	46.2934i	0.413106	−	1.54569i
$898$		0			0
$899$	1.91214			0.0637735
$900$		0			0
$901$	57.9242			1.92974
$902$		0			0
$903$	1.96505	+	1.96253i	0.0653927	+	0.0653090i
$904$		0			0
$905$	−40.1516	−	69.5446i	−1.33468	−	2.31174i
$906$		0			0
$907$	4.55814	−	7.89494i	0.151351	−	0.262147i	−0.780374	−	0.625314i	$-0.784971\pi$
$907$	4.55814	−	7.89494i	0.151351	−	0.262147i	0.931724	+	0.363167i	$0.118304\pi$
$908$		0			0
$909$	−0.0491656	−	38.4102i	−0.00163072	−	1.27399i
$910$		0			0
$911$	9.16079	−	15.8670i	0.303511	−	0.525696i	−0.673418	−	0.739262i	$-0.735175\pi$
$911$	9.16079	−	15.8670i	0.303511	−	0.525696i	0.976929	+	0.213566i	$0.0685079\pi$
$912$		0			0
$913$	−20.7766	−	35.9860i	−0.687603	−	1.19096i
$914$		0			0
$915$	13.0860	−	3.51535i	0.432609	−	0.116214i
$916$		0			0
$917$	15.3412			0.506612
$918$		0			0
$919$	−55.7097			−1.83769			−0.918847	−	0.394613i	$-0.870879\pi$
$919$	−55.7097			−1.83769			−0.918847	+	0.394613i	$0.870879\pi$
$920$		0			0
$921$	−33.5261	+	9.00628i	−1.10472	+	0.296767i
$922$		0			0
$923$	29.7518	+	51.5316i	0.979292	+	1.69618i
$924$		0			0
$925$	−35.7400	+	61.9035i	−1.17512	+	2.03538i
$926$		0			0
$927$	−24.7892	−	14.2698i	−0.814185	−	0.468681i
$928$		0			0
$929$	−10.4420	+	18.0861i	−0.342592	+	0.593386i	−0.984913	−	0.173049i	$-0.944638\pi$
$929$	−10.4420	+	18.0861i	−0.342592	+	0.593386i	0.642322	+	0.766435i	$0.277971\pi$
$930$		0			0
$931$	−1.65278	−	2.86269i	−0.0541676	−	0.0938210i
$932$		0			0
$933$	16.0975	+	16.0769i	0.527009	+	0.526335i
$934$		0			0
$935$	98.6551			3.22637
$936$		0			0
$937$	−6.56584			−0.214497			−0.107248	−	0.994232i	$-0.534204\pi$
$937$	−6.56584			−0.214497			−0.107248	+	0.994232i	$0.534204\pi$
$938$		0			0
$939$	−5.62877	+	21.0608i	−0.183688	+	0.687292i
$940$		0			0
$941$	−5.21649	−	9.03523i	−0.170053	−	0.294540i	0.768385	−	0.639988i	$-0.221060\pi$
$941$	−5.21649	−	9.03523i	−0.170053	−	0.294540i	−0.938438	+	0.345447i	$0.887727\pi$
$942$		0			0
$943$	−11.8842	+	20.5840i	−0.387002	+	0.670307i
$944$		0			0
$945$	13.7480	−	13.8009i	0.447222	−	0.448942i
$946$		0			0
$947$	15.5391	−	26.9146i	0.504954	−	0.874606i	−0.495029	−	0.868876i	$-0.664843\pi$
$947$	15.5391	−	26.9146i	0.504954	−	0.874606i	0.999984	−	0.00573005i	$-0.00182394\pi$
$948$		0			0
$949$	27.2718	+	47.2361i	0.885279	+	1.53335i
$950$		0			0
$951$	4.80023	−	17.9607i	0.155658	−	0.582415i
$952$		0			0
$953$	27.2222			0.881814			0.440907	−	0.897553i	$-0.354657\pi$
$953$	27.2222			0.881814			0.440907	+	0.897553i	$0.354657\pi$
$954$		0			0
$955$	67.3310			2.17878
$956$		0			0
$957$	−2.19693	−	2.19412i	−0.0710166	−	0.0709258i
$958$		0			0
$959$	0.342977	+	0.594054i	0.0110753	+	0.0191830i
$960$		0			0
$961$	7.91669	−	13.7121i	0.255377	−	0.442326i
$962$		0			0
$963$	−21.8914	+	12.6764i	−0.705440	+	0.408491i
$964$		0			0
$965$	17.5804	−	30.4501i	0.565932	−	0.980223i
$966$		0			0
$967$	21.5710	+	37.3620i	0.693675	+	1.20148i	0.970625	+	0.240597i	$0.0773431\pi$
$967$	21.5710	+	37.3620i	0.693675	+	1.20148i	−0.276950	+	0.960884i	$0.589324\pi$
$968$		0			0
$969$	−39.8537	+	10.7061i	−1.28029	+	0.343930i
$970$		0			0
$971$	−18.0357			−0.578794			−0.289397	−	0.957209i	$-0.593455\pi$
$971$	−18.0357			−0.578794			−0.289397	+	0.957209i	$0.593455\pi$
$972$		0			0
$973$	−20.2007			−0.647606
$974$		0			0
$975$	−83.9910	+	22.5629i	−2.68986	+	0.722592i
$976$		0			0
$977$	−13.6015	−	23.5586i	−0.435152	−	0.753705i	0.562156	−	0.827031i	$-0.309972\pi$
$977$	−13.6015	−	23.5586i	−0.435152	−	0.753705i	−0.997308	+	0.0733259i	$0.976639\pi$
$978$		0			0
$979$	−13.0505	+	22.6041i	−0.417096	+	0.722431i
$980$		0			0
$981$	42.9855	−	24.8911i	1.37242	−	0.794712i
$982$		0			0
$983$	9.03965	−	15.6571i	0.288320	−	0.499385i	−0.685089	−	0.728460i	$-0.740237\pi$
$983$	9.03965	−	15.6571i	0.288320	−	0.499385i	0.973409	+	0.229074i	$0.0735699\pi$
$984$		0			0
$985$	−0.387858	−	0.671790i	−0.0123582	−	0.0214050i
$986$		0			0
$987$	−11.8140	−	11.7989i	−0.376043	−	0.375562i
$988$		0			0
$989$	7.99927			0.254362
$990$		0			0
$991$	50.2203			1.59530			0.797650	−	0.603121i	$-0.206076\pi$
$991$	50.2203			1.59530			0.797650	+	0.603121i	$0.206076\pi$
$992$		0			0
$993$	−5.02600	+	18.8054i	−0.159495	+	0.596772i
$994$		0			0
$995$	−23.6499	−	40.9628i	−0.749751	−	1.29861i
$996$		0			0
$997$	13.3757	−	23.1673i	0.423611	−	0.733716i	−0.572678	−	0.819780i	$-0.694096\pi$
$997$	13.3757	−	23.1673i	0.423611	−	0.733716i	0.996290	+	0.0860640i	$0.0274290\pi$
$998$		0			0
$999$	28.9503	−	29.0616i	0.915946	−	0.919470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.r.m.673.4		8
3.2	odd	2		3024.2.r.l.2017.1		8
4.3	odd	2		504.2.r.d.169.1	✓	8
9.2	odd	6		9072.2.a.cl.1.4		4
9.4	even	3	inner	1008.2.r.m.337.4		8
9.5	odd	6		3024.2.r.l.1009.1		8
9.7	even	3		9072.2.a.ce.1.1		4
12.11	even	2		1512.2.r.d.505.1		8
36.7	odd	6		4536.2.a.x.1.1		4
36.11	even	6		4536.2.a.ba.1.4		4
36.23	even	6		1512.2.r.d.1009.1		8
36.31	odd	6		504.2.r.d.337.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.d.169.1	✓	8	4.3	odd	2
504.2.r.d.337.1	yes	8	36.31	odd	6
1008.2.r.m.337.4		8	9.4	even	3	inner
1008.2.r.m.673.4		8	1.1	even	1	trivial
1512.2.r.d.505.1		8	12.11	even	2
1512.2.r.d.1009.1		8	36.23	even	6
3024.2.r.l.1009.1		8	9.5	odd	6
3024.2.r.l.2017.1		8	3.2	odd	2
4536.2.a.x.1.1		4	36.7	odd	6
4536.2.a.ba.1.4		4	36.11	even	6
9072.2.a.ce.1.1		4	9.7	even	3
9072.2.a.cl.1.4		4	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.67275 - 0.449358i) q^{3} +(1.87447 + 3.24667i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.59615 - 1.50332i) q^{9} +O(q^{10})\)	\(q+(1.67275 - 0.449358i) q^{3} +(1.87447 + 3.24667i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.59615 - 1.50332i) q^{9} +(-1.82552 + 3.16190i) q^{11} +(2.77274 + 4.80253i) q^{13} +(4.59442 + 4.58854i) q^{15} -7.20767 q^{17} +3.30555 q^{19} +(0.447217 - 1.67332i) q^{21} +(-2.49443 - 4.32048i) q^{23} +(-4.52724 + 7.84141i) q^{25} +(3.66717 - 3.68128i) q^{27} +(-0.245497 + 0.425213i) q^{29} +(-1.94722 - 3.37268i) q^{31} +(-1.63281 + 6.10936i) q^{33} +3.74893 q^{35} +7.89443 q^{37} +(6.79614 + 6.78745i) q^{39} +(-2.38215 - 4.12600i) q^{41} +(-0.801714 + 1.38861i) q^{43} +(9.74720 + 5.61092i) q^{45} +(4.81995 - 8.34840i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-12.0566 + 3.23883i) q^{51} -8.03647 q^{53} -13.6875 q^{55} +(5.52935 - 1.48538i) q^{57} +(-0.754503 - 1.30684i) q^{59} +(1.04337 - 1.80717i) q^{61} +(-0.00384004 - 3.00000i) q^{63} +(-10.3948 + 18.0043i) q^{65} +(1.70172 + 2.94747i) q^{67} +(-6.11398 - 6.10616i) q^{69} +10.7301 q^{71} +9.83567 q^{73} +(-4.04932 + 15.1510i) q^{75} +(1.82552 + 3.16190i) q^{77} +(1.86391 - 3.22839i) q^{79} +(4.48003 - 7.80572i) q^{81} +(-5.69058 + 9.85637i) q^{83} +(-13.5105 - 23.4009i) q^{85} +(-0.219580 + 0.821588i) q^{87} +7.14891 q^{89} +5.54548 q^{91} +(-4.77274 - 4.76663i) q^{93} +(6.19615 + 10.7320i) q^{95} +(5.45316 - 9.44516i) q^{97} +(0.0140201 + 10.9531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 4 q^{5} + 4 q^{7} + 10 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 4 * q^5 + 4 * q^7 + 10 * q^9	\( 8 q + 4 q^{3} + 4 q^{5} + 4 q^{7} + 10 q^{9} + 6 q^{11} - 3 q^{13} - 4 q^{15} - 16 q^{17} + 4 q^{19} - q^{21} + 5 q^{23} - 14 q^{25} - 5 q^{27} + q^{29} - 11 q^{31} + 8 q^{35} + 54 q^{37} + 12 q^{39} + 2 q^{41} + 11 q^{43} + 26 q^{45} - 7 q^{47} - 4 q^{49} - 17 q^{51} - 8 q^{53} - 12 q^{55} - 13 q^{57} - 9 q^{59} - 7 q^{61} + 5 q^{63} - 9 q^{65} + 12 q^{67} + 4 q^{69} + 24 q^{71} + 26 q^{73} + 23 q^{75} - 6 q^{77} + 22 q^{79} + 34 q^{81} + 6 q^{83} - 11 q^{85} - 37 q^{87} - 28 q^{89} - 6 q^{91} - 13 q^{93} + 23 q^{95} - q^{97} + 42 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 4 * q^5 + 4 * q^7 + 10 * q^9 + 6 * q^11 - 3 * q^13 - 4 * q^15 - 16 * q^17 + 4 * q^19 - q^21 + 5 * q^23 - 14 * q^25 - 5 * q^27 + q^29 - 11 * q^31 + 8 * q^35 + 54 * q^37 + 12 * q^39 + 2 * q^41 + 11 * q^43 + 26 * q^45 - 7 * q^47 - 4 * q^49 - 17 * q^51 - 8 * q^53 - 12 * q^55 - 13 * q^57 - 9 * q^59 - 7 * q^61 + 5 * q^63 - 9 * q^65 + 12 * q^67 + 4 * q^69 + 24 * q^71 + 26 * q^73 + 23 * q^75 - 6 * q^77 + 22 * q^79 + 34 * q^81 + 6 * q^83 - 11 * q^85 - 37 * q^87 - 28 * q^89 - 6 * q^91 - 13 * q^93 + 23 * q^95 - q^97 + 42 * q^99

Introduction

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