LMFDB - Embedded newform 825.2.n.o.751.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.3
Character	$\chi$	$=$	825.751
Dual form			825.2.n.o.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.649936 + 0.472206i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.418596 + 1.28830i) q^{4} +(0.649936 + 0.472206i) q^{6} +(-0.157137 + 0.483617i) q^{7} +(-0.832793 - 2.56307i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.649936 + 0.472206i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.418596 + 1.28830i) q^{4} +(0.649936 + 0.472206i) q^{6} +(-0.157137 + 0.483617i) q^{7} +(-0.832793 - 2.56307i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-3.13337 + 1.08718i) q^{11} +1.35460 q^{12} +(4.15671 - 3.02003i) q^{13} +(-0.126238 - 0.388521i) q^{14} +(-0.440233 - 0.319848i) q^{16} +(-2.70650 - 1.96639i) q^{17} +(0.248254 - 0.764046i) q^{18} +(-0.362488 - 1.11562i) q^{19} +0.508505 q^{21} +(1.52312 - 2.18620i) q^{22} +2.91459 q^{23} +(-2.18028 + 1.58407i) q^{24} +(-1.27552 + 3.92565i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.557269 - 0.404880i) q^{28} +(-0.121318 + 0.373379i) q^{29} +(5.14154 - 3.73555i) q^{31} +5.82710 q^{32} +(2.00224 + 2.64406i) q^{33} +2.68759 q^{34} +(-0.418596 - 1.28830i) q^{36} +(1.37580 - 4.23428i) q^{37} +(0.762398 + 0.553914i) q^{38} +(-4.15671 - 3.02003i) q^{39} +(-0.864837 - 2.66170i) q^{41} +(-0.330496 + 0.240119i) q^{42} -3.05350 q^{43} +(-0.0890077 - 4.49183i) q^{44} +(-1.89430 + 1.37629i) q^{46} +(-3.55132 - 10.9298i) q^{47} +(-0.168154 + 0.517525i) q^{48} +(5.45393 + 3.96251i) q^{49} +(-1.03379 + 3.18168i) q^{51} +(2.15074 + 6.61928i) q^{52} +(7.93441 - 5.76469i) q^{53} -0.803366 q^{54} +1.37041 q^{56} +(-0.949005 + 0.689492i) q^{57} +(-0.0974628 - 0.299960i) q^{58} +(-0.935871 + 2.88031i) q^{59} +(-0.853612 - 0.620185i) q^{61} +(-1.57772 + 4.85573i) q^{62} +(-0.157137 - 0.483617i) q^{63} +(-2.90678 + 2.11190i) q^{64} +(-2.54987 - 0.772999i) q^{66} +5.31327 q^{67} +(3.66623 - 2.66367i) q^{68} +(-0.900658 - 2.77194i) q^{69} +(-3.31678 - 2.40978i) q^{71} +(2.18028 + 1.58407i) q^{72} +(4.05070 - 12.4668i) q^{73} +(1.10527 + 3.40167i) q^{74} +1.58900 q^{76} +(-0.0334126 - 1.68619i) q^{77} +4.12768 q^{78} +(13.0578 - 9.48703i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.81896 + 1.32155i) q^{82} +(-12.4255 - 9.02764i) q^{83} +(-0.212858 + 0.655110i) q^{84} +(1.98458 - 1.44188i) q^{86} +0.392594 q^{87} +(5.39598 + 7.12566i) q^{88} -9.84603 q^{89} +(0.807365 + 2.48481i) q^{91} +(-1.22004 + 3.75488i) q^{92} +(-5.14154 - 3.73555i) q^{93} +(7.46927 + 5.42674i) q^{94} +(-1.80067 - 5.54191i) q^{96} +(-12.2721 + 8.91621i) q^{97} -5.41583 q^{98} +(1.89592 - 2.72130i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9	$ 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9} - 24 q^{12} - 4 q^{13} + 2 q^{14} - 22 q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} - 16 q^{21} + 4 q^{22} + 6 q^{24} - 38 q^{26} + 6 q^{27} - 30 q^{28} - 10 q^{31} + 56 q^{32} - 10 q^{33} + 12 q^{34} - 6 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 30 q^{41} + 8 q^{42} + 64 q^{43} + 24 q^{44} + 54 q^{46} + 8 q^{47} + 2 q^{48} + 14 q^{49} + 14 q^{51} - 14 q^{52} - 26 q^{53} - 8 q^{54} + 12 q^{56} - 8 q^{57} - 20 q^{58} - 30 q^{59} + 20 q^{61} + 50 q^{62} - 4 q^{63} - 32 q^{64} + 6 q^{66} - 20 q^{67} + 62 q^{68} - 10 q^{69} - 16 q^{71} - 6 q^{72} + 12 q^{73} + 16 q^{74} - 68 q^{76} + 2 q^{77} - 32 q^{78} + 26 q^{79} - 6 q^{81} - 56 q^{82} - 48 q^{83} - 52 q^{86} - 48 q^{88} - 20 q^{89} - 20 q^{91} - 46 q^{92} + 10 q^{93} - 36 q^{94} + 14 q^{96} + 14 q^{97} + 120 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9 - 24 * q^12 - 4 * q^13 + 2 * q^14 - 22 * q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 - 16 * q^21 + 4 * q^22 + 6 * q^24 - 38 * q^26 + 6 * q^27 - 30 * q^28 - 10 * q^31 + 56 * q^32 - 10 * q^33 + 12 * q^34 - 6 * q^36 - 10 * q^37 - 4 * q^38 + 4 * q^39 + 30 * q^41 + 8 * q^42 + 64 * q^43 + 24 * q^44 + 54 * q^46 + 8 * q^47 + 2 * q^48 + 14 * q^49 + 14 * q^51 - 14 * q^52 - 26 * q^53 - 8 * q^54 + 12 * q^56 - 8 * q^57 - 20 * q^58 - 30 * q^59 + 20 * q^61 + 50 * q^62 - 4 * q^63 - 32 * q^64 + 6 * q^66 - 20 * q^67 + 62 * q^68 - 10 * q^69 - 16 * q^71 - 6 * q^72 + 12 * q^73 + 16 * q^74 - 68 * q^76 + 2 * q^77 - 32 * q^78 + 26 * q^79 - 6 * q^81 - 56 * q^82 - 48 * q^83 - 52 * q^86 - 48 * q^88 - 20 * q^89 - 20 * q^91 - 46 * q^92 + 10 * q^93 - 36 * q^94 + 14 * q^96 + 14 * q^97 + 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−0.649936	+	0.472206i	−0.459574	+	0.333900i	−0.793364	−	0.608747i	$-0.791672\pi$
$2$	−0.649936	+	0.472206i	−0.459574	+	0.333900i	0.333790	+	0.942648i	$0.391672\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.418596	+	1.28830i	−0.209298	+	0.644152i
$5$		0			0
$5$		0			0
$6$	0.649936	+	0.472206i	0.265335	+	0.192777i
$7$	−0.157137	+	0.483617i	−0.0593921	+	0.182790i	−0.976351	−	0.216192i	$-0.930636\pi$
$7$	−0.157137	+	0.483617i	−0.0593921	+	0.182790i	0.916959	+	0.398982i	$0.130636\pi$
$8$	−0.832793	−	2.56307i	−0.294437	−	0.906183i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−3.13337	+	1.08718i	−0.944748	+	0.327798i
$11$	−3.13337	+	1.08718i	−0.944748	+	0.327798i
$12$	1.35460			0.391040
$13$	4.15671	−	3.02003i	1.15286	−	0.837605i	0.164005	−	0.986459i	$-0.447559\pi$
$13$	4.15671	−	3.02003i	1.15286	−	0.837605i	0.988859	+	0.148854i	$0.0475585\pi$
$14$	−0.126238	−	0.388521i	−0.0337386	−	0.103837i
$15$		0			0
$16$	−0.440233	−	0.319848i	−0.110058	−	0.0799621i
$17$	−2.70650	−	1.96639i	−0.656422	−	0.476919i	0.209031	−	0.977909i	$-0.432969\pi$
$17$	−2.70650	−	1.96639i	−0.656422	−	0.476919i	−0.865453	+	0.500990i	$0.832969\pi$
$18$	0.248254	−	0.764046i	0.0585139	−	0.180087i
$19$	−0.362488	−	1.11562i	−0.0831603	−	0.255941i	0.900827	−	0.434177i	$-0.142961\pi$
$19$	−0.362488	−	1.11562i	−0.0831603	−	0.255941i	−0.983988	+	0.178236i	$0.942961\pi$
$20$		0			0
$21$	0.508505			0.110965
$22$	1.52312	−	2.18620i	0.324730	−	0.466099i
$23$	2.91459			0.607734			0.303867	−	0.952714i	$-0.401722\pi$
$23$	2.91459			0.607734			0.303867	+	0.952714i	$0.401722\pi$
$24$	−2.18028	+	1.58407i	−0.445048	+	0.323346i
$25$		0			0
$26$	−1.27552	+	3.92565i	−0.250150	+	0.769884i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.557269	−	0.404880i	−0.105314	−	0.0765151i
$29$	−0.121318	+	0.373379i	−0.0225282	+	0.0693347i	−0.961689	−	0.274144i	$-0.911605\pi$
$29$	−0.121318	+	0.373379i	−0.0225282	+	0.0693347i	0.939160	+	0.343479i	$0.111605\pi$
$30$		0			0
$31$	5.14154	−	3.73555i	0.923447	−	0.670924i	−0.0209323	−	0.999781i	$-0.506663\pi$
$31$	5.14154	−	3.73555i	0.923447	−	0.670924i	0.944380	+	0.328857i	$0.106663\pi$
$32$	5.82710			1.03010
$33$	2.00224	+	2.64406i	0.348545	+	0.460271i
$34$	2.68759			0.460918
$35$		0			0
$36$	−0.418596	−	1.28830i	−0.0697659	−	0.214717i
$37$	1.37580	−	4.23428i	0.226180	−	0.696111i	−0.771989	−	0.635635i	$-0.780738\pi$
$37$	1.37580	−	4.23428i	0.226180	−	0.696111i	0.998170	−	0.0604757i	$-0.0192618\pi$
$38$	0.762398	+	0.553914i	0.123677	+	0.0898568i
$39$	−4.15671	−	3.02003i	−0.665607	−	0.483592i
$40$		0			0
$41$	−0.864837	−	2.66170i	−0.135065	−	0.415687i	0.860535	−	0.509391i	$-0.170129\pi$
$41$	−0.864837	−	2.66170i	−0.135065	−	0.415687i	−0.995600	+	0.0937039i	$0.970129\pi$
$42$	−0.330496	+	0.240119i	−0.0509966	+	0.0370512i
$43$	−3.05350			−0.465654			−0.232827	−	0.972518i	$-0.574798\pi$
$43$	−3.05350			−0.465654			−0.232827	+	0.972518i	$0.574798\pi$
$44$	−0.0890077	−	4.49183i	−0.0134184	−	0.677169i
$45$		0			0
$46$	−1.89430	+	1.37629i	−0.279299	+	0.202923i
$47$	−3.55132	−	10.9298i	−0.518013	−	1.59428i	−0.777732	−	0.628596i	$-0.783630\pi$
$47$	−3.55132	−	10.9298i	−0.518013	−	1.59428i	0.259719	−	0.965684i	$-0.416370\pi$
$48$	−0.168154	+	0.517525i	−0.0242710	+	0.0746984i
$49$	5.45393	+	3.96251i	0.779132	+	0.566073i
$50$		0			0
$51$	−1.03379	+	3.18168i	−0.144760	+	0.445524i
$52$	2.15074	+	6.61928i	0.298253	+	0.917929i
$53$	7.93441	−	5.76469i	1.08988	−	0.791841i	0.110497	−	0.993876i	$-0.464756\pi$
$53$	7.93441	−	5.76469i	1.08988	−	0.791841i	0.979378	+	0.202036i	$0.0647557\pi$
$54$	−0.803366			−0.109324
$55$		0			0
$56$	1.37041			0.183128
$57$	−0.949005	+	0.689492i	−0.125699	+	0.0913255i
$58$	−0.0974628	−	0.299960i	−0.0127975	−	0.0393866i
$59$	−0.935871	+	2.88031i	−0.121840	+	0.374985i	−0.993312	−	0.115460i	$-0.963166\pi$
$59$	−0.935871	+	2.88031i	−0.121840	+	0.374985i	0.871472	+	0.490445i	$0.163166\pi$
$60$		0			0
$61$	−0.853612	−	0.620185i	−0.109294	−	0.0794066i	0.531796	−	0.846873i	$-0.321517\pi$
$61$	−0.853612	−	0.620185i	−0.109294	−	0.0794066i	−0.641090	+	0.767466i	$0.721517\pi$
$62$	−1.57772	+	4.85573i	−0.200371	+	0.616679i
$63$	−0.157137	−	0.483617i	−0.0197974	−	0.0609300i
$64$	−2.90678	+	2.11190i	−0.363348	+	0.263987i
$65$		0			0
$66$	−2.54987	−	0.772999i	−0.313867	−	0.0951496i
$67$	5.31327			0.649120			0.324560	−	0.945865i	$-0.394784\pi$
$67$	5.31327			0.649120			0.324560	+	0.945865i	$0.394784\pi$
$68$	3.66623	−	2.66367i	0.444596	−	0.323018i
$69$	−0.900658	−	2.77194i	−0.108427	−	0.333703i
$70$		0			0
$71$	−3.31678	−	2.40978i	−0.393629	−	0.285988i	0.373312	−	0.927706i	$-0.378222\pi$
$71$	−3.31678	−	2.40978i	−0.393629	−	0.285988i	−0.766941	+	0.641718i	$0.778222\pi$
$72$	2.18028	+	1.58407i	0.256948	+	0.186684i
$73$	4.05070	−	12.4668i	0.474099	−	1.45913i	−0.373071	−	0.927803i	$-0.621695\pi$
$73$	4.05070	−	12.4668i	0.474099	−	1.45913i	0.847169	−	0.531323i	$-0.178305\pi$
$74$	1.10527	+	3.40167i	0.128485	+	0.395437i
$75$		0			0
$76$	1.58900			0.182270
$77$	−0.0334126	−	1.68619i	−0.00380772	−	0.192159i
$78$	4.12768			0.467367
$79$	13.0578	−	9.48703i	1.46911	−	1.06737i	0.488246	−	0.872706i	$-0.337637\pi$
$79$	13.0578	−	9.48703i	1.46911	−	1.06737i	0.980869	−	0.194668i	$-0.0623630\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	1.81896	+	1.32155i	0.200870	+	0.145941i
$83$	−12.4255	−	9.02764i	−1.36387	−	0.990912i	−0.998188	−	0.0601730i	$-0.980835\pi$
$83$	−12.4255	−	9.02764i	−1.36387	−	0.990912i	−0.365685	−	0.930739i	$-0.619165\pi$
$84$	−0.212858	+	0.655110i	−0.0232247	+	0.0714783i
$85$		0			0
$86$	1.98458	−	1.44188i	0.214003	−	0.155482i
$87$	0.392594			0.0420905
$88$	5.39598	+	7.12566i	0.575213	+	0.759598i
$89$	−9.84603			−1.04368			−0.521838	−	0.853044i	$-0.674754\pi$
$89$	−9.84603			−1.04368			−0.521838	+	0.853044i	$0.674754\pi$
$90$		0			0
$91$	0.807365	+	2.48481i	0.0846349	+	0.260479i
$92$	−1.22004	+	3.75488i	−0.127197	+	0.391473i
$93$	−5.14154	−	3.73555i	−0.533153	−	0.387358i
$94$	7.46927	+	5.42674i	0.770396	+	0.559726i
$95$		0			0
$96$	−1.80067	−	5.54191i	−0.183781	−	0.565618i
$97$	−12.2721	+	8.91621i	−1.24604	+	0.905304i	−0.997986	−	0.0634410i	$-0.979793\pi$
$97$	−12.2721	+	8.91621i	−1.24604	+	0.905304i	−0.248059	+	0.968745i	$0.579793\pi$
$98$	−5.41583			−0.547081
$99$	1.89592	−	2.72130i	0.190547	−	0.273501i
$100$		0			0
$101$	13.3869	−	9.72617i	1.33205	−	0.967790i	0.332352	−	0.943155i	$-0.392158\pi$
$101$	13.3869	−	9.72617i	1.33205	−	0.967790i	0.999697	−	0.0246350i	$-0.00784235\pi$
$102$	−0.830512	−	2.55605i	−0.0822329	−	0.253087i
$103$	−4.42946	+	13.6325i	−0.436448	+	1.34325i	0.455148	+	0.890416i	$0.349586\pi$
$103$	−4.42946	+	13.6325i	−0.436448	+	1.34325i	−0.891596	+	0.452832i	$0.850414\pi$
$104$	−11.2022	−	8.13890i	−1.09847	−	0.798084i
$105$		0			0
$106$	−2.43474	+	7.49336i	−0.236483	+	0.727820i
$107$	−2.12324	−	6.53466i	−0.205261	−	0.631729i	−0.999703	−	0.0243883i	$-0.992236\pi$
$107$	−2.12324	−	6.53466i	−0.205261	−	0.631729i	0.794441	−	0.607341i	$-0.207764\pi$
$108$	−1.09590	+	0.796216i	−0.105453	+	0.0766159i
$109$	16.9516			1.62367			0.811833	−	0.583890i	$-0.198470\pi$
$109$	16.9516			1.62367			0.811833	+	0.583890i	$0.198470\pi$
$110$		0			0
$111$	−4.45218			−0.422583
$112$	0.223861	−	0.162645i	0.0211529	−	0.0153685i
$113$	1.39340	+	4.28844i	0.131080	+	0.403422i	0.994960	−	0.100276i	$-0.0319724\pi$
$113$	1.39340	+	4.28844i	0.131080	+	0.403422i	−0.863880	+	0.503698i	$0.831972\pi$
$114$	0.291210	−	0.896252i	0.0272743	−	0.0839417i
$115$		0			0
$116$	−0.430243	−	0.312589i	−0.0399470	−	0.0290232i
$117$	−1.58772	+	4.88651i	−0.146785	+	0.451758i
$118$	−0.751846	−	2.31395i	−0.0692131	−	0.213016i
$119$	1.37627	−	0.999917i	0.126162	−	0.0916623i
$120$		0			0
$121$	8.63606	−	6.81311i	0.785097	−	0.619373i
$122$	0.847649			0.0767425
$123$	−2.26417	+	1.64502i	−0.204154	+	0.148326i
$124$	2.66030	+	8.18755i	0.238902	+	0.735264i
$125$		0			0
$126$	0.330496	+	0.240119i	0.0294429	+	0.0213915i
$127$	−8.65209	−	6.28611i	−0.767749	−	0.557802i	0.133528	−	0.991045i	$-0.457369\pi$
$127$	−8.65209	−	6.28611i	−0.767749	−	0.557802i	−0.901277	+	0.433243i	$0.857369\pi$
$128$	−2.70938	+	8.33861i	−0.239478	+	0.737036i
$129$	0.943583	+	2.90405i	0.0830778	+	0.255687i
$130$		0			0
$131$	−7.00557			−0.612079			−0.306040	−	0.952019i	$-0.599004\pi$
$131$	−7.00557			−0.612079			−0.306040	+	0.952019i	$0.599004\pi$
$132$	−4.24448	+	1.47270i	−0.369435	+	0.128182i
$133$	0.596494			0.0517226
$134$	−3.45329	+	2.50896i	−0.298319	+	0.216741i
$135$		0			0
$136$	−2.78604	+	8.57454i	−0.238901	+	0.735261i
$137$	8.90555	+	6.47026i	0.760852	+	0.552792i	0.899172	−	0.437596i	$-0.144170\pi$
$137$	8.90555	+	6.47026i	0.760852	+	0.552792i	−0.138319	+	0.990388i	$0.544170\pi$
$138$	1.89430	+	1.37629i	0.161253	+	0.117157i
$139$	−4.38892	+	13.5077i	−0.372263	+	1.14571i	0.573043	+	0.819525i	$0.305763\pi$
$139$	−4.38892	+	13.5077i	−0.372263	+	1.14571i	−0.945307	+	0.326183i	$0.894237\pi$
$140$		0			0
$141$	−9.29747	+	6.75501i	−0.782988	+	0.568874i
$142$	3.29361			0.276393
$143$	−9.74121	+	13.9820i	−0.814601	+	1.16923i
$144$	0.544158			0.0453465
$145$		0			0
$146$	3.25419	+	10.0154i	0.269319	+	0.828879i
$147$	2.08321	−	6.41147i	0.171821	−	0.528809i
$148$	4.87914	+	3.54490i	0.401063	+	0.291389i
$149$	−10.5637	−	7.67498i	−0.865412	−	0.628759i	0.0639396	−	0.997954i	$-0.479633\pi$
$149$	−10.5637	−	7.67498i	−0.865412	−	0.628759i	−0.929352	+	0.369195i	$0.879633\pi$
$150$		0			0
$151$	5.67085	+	17.4531i	0.461487	+	1.42031i	0.863347	+	0.504611i	$0.168364\pi$
$151$	5.67085	+	17.4531i	0.461487	+	1.42031i	−0.401859	+	0.915701i	$0.631636\pi$
$152$	−2.55754	+	1.85816i	−0.207444	+	0.150717i
$153$	3.34542			0.270461
$154$	0.817946	+	1.08014i	0.0659119	+	0.0870400i
$155$		0			0
$156$	5.63070	−	4.09094i	0.450817	−	0.327537i
$157$	−3.38072	−	10.4048i	−0.269811	−	0.830393i	−0.990546	−	0.137182i	$-0.956195\pi$
$157$	−3.38072	−	10.4048i	−0.269811	−	0.830393i	0.720735	−	0.693211i	$-0.243805\pi$
$158$	−4.00689	+	12.3319i	−0.318771	+	0.981076i
$159$	−7.93441	−	5.76469i	−0.629240	−	0.457170i
$160$		0			0
$161$	−0.457989	+	1.40955i	−0.0360946	+	0.111088i
$162$	0.248254	+	0.764046i	0.0195046	+	0.0600291i
$163$	−18.6740	+	13.5674i	−1.46266	+	1.06268i	−0.479999	+	0.877269i	$0.659363\pi$
$163$	−18.6740	+	13.5674i	−1.46266	+	1.06268i	−0.982660	+	0.185416i	$0.940637\pi$
$164$	3.79109			0.296035
$165$		0			0
$166$	12.3387			0.957667
$167$	−3.37704	+	2.45356i	−0.261323	+	0.189862i	−0.710730	−	0.703465i	$-0.751635\pi$
$167$	−3.37704	+	2.45356i	−0.261323	+	0.189862i	0.449407	+	0.893327i	$0.351635\pi$
$168$	−0.423479	−	1.30334i	−0.0326721	−	0.100554i
$169$	4.14047	−	12.7430i	0.318497	−	0.980234i
$170$		0			0
$171$	0.949005	+	0.689492i	0.0725722	+	0.0527268i
$172$	1.27818	−	3.93384i	0.0974604	−	0.299952i
$173$	1.14860	+	3.53501i	0.0873261	+	0.268762i	0.985178	−	0.171536i	$-0.0548729\pi$
$173$	1.14860	+	3.53501i	0.0873261	+	0.268762i	−0.897852	+	0.440298i	$0.854873\pi$
$174$	−0.255161	+	0.185385i	−0.0193437	+	0.0140540i
$175$		0			0
$176$	1.72715	+	0.523590i	0.130189	+	0.0394671i
$177$	3.02854			0.227639
$178$	6.39929	−	4.64936i	0.479647	−	0.348484i
$179$	5.52898	+	17.0164i	0.413255	+	1.27187i	0.913802	+	0.406159i	$0.133132\pi$
$179$	5.52898	+	17.0164i	0.413255	+	1.27187i	−0.500547	+	0.865709i	$0.666868\pi$
$180$		0			0
$181$	−12.2308	−	8.88618i	−0.909107	−	0.660505i	0.0316820	−	0.999498i	$-0.489914\pi$
$181$	−12.2308	−	8.88618i	−0.909107	−	0.660505i	−0.940789	+	0.338993i	$0.889914\pi$
$182$	−1.69808	−	1.23373i	−0.125870	−	0.0914500i
$183$	−0.326051	+	1.00348i	−0.0241024	+	0.0741794i
$184$	−2.42725	−	7.47031i	−0.178939	−	0.550718i
$185$		0			0
$186$	5.10562			0.374362
$187$	10.6183	+	3.21896i	0.776487	+	0.235394i
$188$	15.5675			1.13538
$189$	−0.411389	+	0.298892i	−0.0299242	+	0.0217412i
$190$		0			0
$191$	0.230395	−	0.709082i	0.0166708	−	0.0513074i	−0.942375	−	0.334558i	$-0.891413\pi$
$191$	0.230395	−	0.709082i	0.0166708	−	0.0513074i	0.959046	+	0.283251i	$0.0914129\pi$
$192$	2.90678	+	2.11190i	0.209779	+	0.152413i
$193$	−7.18323	−	5.21892i	−0.517060	−	0.375666i	0.298435	−	0.954430i	$-0.403535\pi$
$193$	−7.18323	−	5.21892i	−0.517060	−	0.375666i	−0.815495	+	0.578764i	$0.803535\pi$
$194$	3.76580	−	11.5899i	0.270369	−	0.832109i
$195$		0			0
$196$	−7.38791	+	5.36763i	−0.527708	+	0.383402i
$197$	1.05280			0.0750089			0.0375044	−	0.999296i	$-0.488059\pi$
$197$	1.05280			0.0750089			0.0375044	+	0.999296i	$0.488059\pi$
$198$	0.0527872	+	2.66394i	0.00375142	+	0.189318i
$199$	−2.28171			−0.161746			−0.0808730	−	0.996724i	$-0.525771\pi$
$199$	−2.28171			−0.161746			−0.0808730	+	0.996724i	$0.525771\pi$
$200$		0			0
$201$	−1.64189	−	5.05322i	−0.115810	−	0.356427i
$202$	−4.10789	+	12.6428i	−0.289030	+	0.889543i
$203$	−0.161509	−	0.117343i	−0.0113357	−	0.00823587i
$204$	−3.66623	−	2.66367i	−0.256688	−	0.186494i
$205$		0			0
$206$	−3.55848	−	10.9519i	−0.247931	−	0.763052i
$207$	−2.35795	+	1.71315i	−0.163889	+	0.119072i
$208$	−2.79587			−0.193859
$209$	2.34869	+	3.10157i	0.162463	+	0.214540i
$210$		0			0
$211$	7.74164	−	5.62463i	0.532957	−	0.387216i	−0.288506	−	0.957478i	$-0.593159\pi$
$211$	7.74164	−	5.62463i	0.532957	−	0.387216i	0.821463	+	0.570263i	$0.193159\pi$
$212$	4.10537	+	12.6350i	0.281958	+	0.867776i
$213$	−1.26690	+	3.89910i	−0.0868063	+	0.267162i
$214$	4.46568	+	3.24451i	0.305267	+	0.221790i
$215$		0			0
$216$	0.832793	−	2.56307i	0.0566644	−	0.174395i
$217$	0.998650	+	3.07353i	0.0677927	+	0.208645i
$218$	−11.0174	+	8.00464i	−0.746195	+	0.542142i
$219$	−13.1083			−0.885780
$220$		0			0
$221$	−17.1887			−1.15624
$222$	2.89364	−	2.10235i	0.194208	−	0.141100i
$223$	−2.72530	−	8.38760i	−0.182499	−	0.561676i	0.817397	−	0.576075i	$-0.195416\pi$
$223$	−2.72530	−	8.38760i	−0.182499	−	0.561676i	−0.999896	+	0.0143994i	$0.995416\pi$
$224$	−0.915652	+	2.81809i	−0.0611796	+	0.188291i
$225$		0			0
$226$	−2.93065	−	2.12924i	−0.194944	−	0.141635i
$227$	−1.66487	+	5.12395i	−0.110501	+	0.340088i	−0.990982	−	0.133993i	$-0.957220\pi$
$227$	−1.66487	+	5.12395i	−0.110501	+	0.340088i	0.880481	+	0.474082i	$0.157220\pi$
$228$	−0.491027	−	1.51123i	−0.0325191	−	0.100083i
$229$	−19.7252	+	14.3312i	−1.30348	+	0.947034i	−0.999983	−	0.00579853i	$-0.998154\pi$
$229$	−19.7252	+	14.3312i	−1.30348	+	0.947034i	−0.303497	+	0.952832i	$0.598154\pi$
$230$		0			0
$231$	−1.59334	+	0.552839i	−0.104834	+	0.0363741i
$232$	1.05803			0.0694631
$233$	−3.73760	+	2.71552i	−0.244858	+	0.177900i	−0.703445	−	0.710750i	$-0.748356\pi$
$233$	−3.73760	+	2.71552i	−0.244858	+	0.177900i	0.458587	+	0.888650i	$0.348356\pi$
$234$	−1.27552	−	3.92565i	−0.0833835	−	0.256628i
$235$		0			0
$236$	−3.31897	−	2.41137i	−0.216047	−	0.156967i
$237$	−13.0578	−	9.48703i	−0.848194	−	0.616249i
$238$	−0.422319	+	1.29977i	−0.0273749	+	0.0842513i
$239$	1.48904	+	4.58278i	0.0963177	+	0.296435i	0.987595	−	0.157024i	$-0.0501899\pi$
$239$	1.48904	+	4.58278i	0.0963177	+	0.296435i	−0.891277	+	0.453459i	$0.850190\pi$
$240$		0			0
$241$	0.424606			0.0273513			0.0136757	−	0.999906i	$-0.495647\pi$
$241$	0.424606			0.0273513			0.0136757	+	0.999906i	$0.495647\pi$
$242$	−2.39570	+	8.50609i	−0.154001	+	0.546792i
$243$	−1.00000			−0.0641500
$244$	1.15631	−	0.840105i	0.0740249	−	0.0537822i
$245$		0			0
$246$	0.694781	−	2.13831i	0.0442976	−	0.136334i
$247$	−4.87597	−	3.54260i	−0.310250	−	0.225410i
$248$	−13.8563	−	10.0672i	−0.879876	−	0.639268i
$249$	−4.74611	+	14.6070i	−0.300772	+	0.925682i
$250$		0			0
$251$	−12.4287	+	9.03000i	−0.784494	+	0.569968i	−0.906324	−	0.422583i	$-0.861124\pi$
$251$	−12.4287	+	9.03000i	−0.784494	+	0.569968i	0.121830	+	0.992551i	$0.461124\pi$
$252$	0.688823			0.0433918
$253$	−9.13250	+	3.16870i	−0.574156	+	0.199214i
$254$	8.59165			0.539088
$255$		0			0
$256$	−4.39720	−	13.5332i	−0.274825	−	0.845825i
$257$	−2.29128	+	7.05184i	−0.142926	+	0.439882i	−0.996738	−	0.0806994i	$-0.974285\pi$
$257$	−2.29128	+	7.05184i	−0.142926	+	0.439882i	0.853812	+	0.520581i	$0.174285\pi$
$258$	−1.98458	−	1.44188i	−0.123555	−	0.0897676i
$259$	1.83158	+	1.33072i	0.113809	+	0.0826870i
$260$		0			0
$261$	−0.121318	−	0.373379i	−0.00750940	−	0.0231116i
$262$	4.55317	−	3.30808i	0.281296	−	0.204374i
$263$	30.6870			1.89224			0.946120	−	0.323815i	$-0.104966\pi$
$263$	30.6870			1.89224			0.946120	+	0.323815i	$0.104966\pi$
$264$	5.10946	−	7.33383i	0.314465	−	0.451366i
$265$		0			0
$266$	−0.387683	+	0.281668i	−0.0237704	+	0.0172702i
$267$	3.04259	+	9.36413i	0.186203	+	0.573075i
$268$	−2.22411	+	6.84511i	−0.135859	+	0.418132i
$269$	−14.7575	−	10.7219i	−0.899780	−	0.653729i	0.0386292	−	0.999254i	$-0.487701\pi$
$269$	−14.7575	−	10.7219i	−0.899780	−	0.653729i	−0.938410	+	0.345525i	$0.887701\pi$
$270$		0			0
$271$	4.24624	−	13.0686i	0.257941	−	0.793860i	−0.735295	−	0.677747i	$-0.762956\pi$
$271$	4.24624	−	13.0686i	0.257941	−	0.793860i	0.993236	−	0.116113i	$-0.0370436\pi$
$272$	0.562546	+	1.73134i	0.0341094	+	0.104978i
$273$	2.11371	−	1.53570i	0.127928	−	0.0929448i
$274$	−8.84334			−0.534246
$275$		0			0
$276$	3.94812			0.237649
$277$	−1.11444	+	0.809688i	−0.0669602	+	0.0486495i	−0.620762	−	0.783999i	$-0.713177\pi$
$277$	−1.11444	+	0.809688i	−0.0669602	+	0.0486495i	0.553802	+	0.832649i	$0.313177\pi$
$278$	−3.52591	−	10.8516i	−0.211470	−	0.650837i
$279$	−1.96389	+	6.04424i	−0.117575	+	0.361859i
$280$		0			0
$281$	15.6161	+	11.3457i	0.931576	+	0.676830i	0.946378	−	0.323061i	$-0.104712\pi$
$281$	15.6161	+	11.3457i	0.931576	+	0.676830i	−0.0148018	+	0.999890i	$0.504712\pi$
$282$	2.85301	−	8.78065i	0.169894	−	0.522880i
$283$	0.678664	+	2.08871i	0.0403424	+	0.124161i	0.969199	−	0.246277i	$-0.0792074\pi$
$283$	0.678664	+	2.08871i	0.0403424	+	0.124161i	−0.928857	+	0.370439i	$0.879207\pi$
$284$	4.49292	−	3.26430i	0.266606	−	0.193700i
$285$		0			0
$286$	−0.271219	−	13.6873i	−0.0160375	−	0.809345i
$287$	1.42314			0.0840053
$288$	−4.71423	+	3.42509i	−0.277788	+	0.201825i
$289$	−1.79483	−	5.52392i	−0.105578	−	0.324936i
$290$		0			0
$291$	12.2721	+	8.91621i	0.719404	+	0.522678i
$292$	14.3654	+	10.4371i	0.840672	+	0.610784i
$293$	8.44173	−	25.9810i	0.493171	−	1.51782i	−0.326617	−	0.945157i	$-0.605909\pi$
$293$	8.44173	−	25.9810i	0.493171	−	1.51782i	0.819788	−	0.572668i	$-0.194091\pi$
$294$	1.67358	+	5.15076i	0.0976053	+	0.300398i
$295$		0			0
$296$	−11.9985			−0.697400
$297$	−3.17398	−	0.962201i	−0.184173	−	0.0558325i
$298$	10.4899			0.607664
$299$	12.1151	−	8.80215i	0.700635	−	0.509041i
$300$		0			0
$301$	0.479817	−	1.47672i	0.0276562	−	0.0851170i
$302$	−11.9272	−	8.66559i	−0.686331	−	0.498648i
$303$	−13.3869	−	9.72617i	−0.769059	−	0.558754i
$304$	−0.197251	+	0.607075i	−0.0113131	+	0.0348181i
$305$		0			0
$306$	−2.17431	+	1.57973i	−0.124297	+	0.0903070i
$307$	−26.9287			−1.53690			−0.768451	−	0.639908i	$-0.778972\pi$
$307$	−26.9287			−1.53690			−0.768451	+	0.639908i	$0.778972\pi$
$308$	2.18631	+	0.662786i	0.124577	+	0.0377657i
$309$	14.3340			0.815434
$310$		0			0
$311$	3.68794	+	11.3503i	0.209124	+	0.643618i	0.999519	+	0.0310199i	$0.00987551\pi$
$311$	3.68794	+	11.3503i	0.209124	+	0.643618i	−0.790395	+	0.612598i	$0.790124\pi$
$312$	−4.27887	+	13.1690i	−0.242243	+	0.745548i
$313$	12.1039	+	8.79398i	0.684152	+	0.497065i	0.874732	−	0.484606i	$-0.161037\pi$
$313$	12.1039	+	8.79398i	0.684152	+	0.497065i	−0.190581	+	0.981672i	$0.561037\pi$
$314$	7.11047	+	5.16606i	0.401267	+	0.291537i
$315$		0			0
$316$	6.75626	+	20.7936i	0.380069	+	1.16973i
$317$	7.91651	−	5.75168i	0.444635	−	0.323047i	−0.342839	−	0.939394i	$-0.611388\pi$
$317$	7.91651	−	5.75168i	0.444635	−	0.323047i	0.787474	+	0.616348i	$0.211388\pi$
$318$	7.87899			0.441832
$319$	−0.0257964	−	1.30183i	−0.00144432	−	0.0728885i
$320$		0			0
$321$	−5.55871	+	4.03864i	−0.310257	+	0.225415i
$322$	−0.367933	−	1.13238i	−0.0205041	−	0.0631051i
$323$	−1.21267	+	3.73222i	−0.0674748	+	0.207666i
$324$	1.09590	+	0.796216i	0.0608832	+	0.0442342i
$325$		0			0
$326$	5.73027	−	17.6360i	0.317370	−	0.976765i
$327$	−5.23832	−	16.1219i	−0.289680	−	0.891543i
$328$	−6.10189	+	4.43328i	−0.336920	+	0.244787i
$329$	5.84390			0.322184
$330$		0			0
$331$	5.14693			0.282901			0.141450	−	0.989945i	$-0.454823\pi$
$331$	5.14693			0.282901			0.141450	+	0.989945i	$0.454823\pi$
$332$	16.8316	−	12.2289i	0.923754	−	0.671146i
$333$	1.37580	+	4.23428i	0.0753934	+	0.232037i
$334$	1.03627	−	3.18932i	0.0567023	−	0.174512i
$335$		0			0
$336$	−0.223861	−	0.162645i	−0.0122126	−	0.00887299i
$337$	9.07009	−	27.9149i	0.494079	−	1.52062i	−0.324308	−	0.945952i	$-0.605131\pi$
$337$	9.07009	−	27.9149i	0.494079	−	1.52062i	0.818387	−	0.574668i	$-0.194869\pi$
$338$	3.32631	+	10.2373i	0.180927	+	0.556837i
$339$	3.64796	−	2.65040i	0.198130	−	0.143950i
$340$		0			0
$341$	−12.0491	+	17.2947i	−0.652497	+	0.936558i
$342$	−0.942375			−0.0509578
$343$	−5.65307	+	4.10720i	−0.305237	+	0.221768i
$344$	2.54293	+	7.82634i	0.137106	+	0.421968i
$345$		0			0
$346$	−2.41577	−	1.75516i	−0.129873	−	0.0943579i
$347$	−5.93488	−	4.31194i	−0.318601	−	0.231477i	0.416977	−	0.908917i	$-0.363089\pi$
$347$	−5.93488	−	4.31194i	−0.318601	−	0.231477i	−0.735578	+	0.677440i	$0.763089\pi$
$348$	−0.164338	+	0.505780i	−0.00880944	+	0.0271127i
$349$	−8.81528	−	27.1306i	−0.471871	−	1.45227i	−0.850132	−	0.526570i	$-0.823478\pi$
$349$	−8.81528	−	27.1306i	−0.471871	−	1.45227i	0.378261	−	0.925699i	$-0.376522\pi$
$350$		0			0
$351$	5.13798			0.274245
$352$	−18.2585	+	6.33513i	−0.973181	+	0.337664i
$353$	16.1818			0.861271			0.430636	−	0.902526i	$-0.358289\pi$
$353$	16.1818			0.861271			0.430636	+	0.902526i	$0.358289\pi$
$354$	−1.96836	+	1.43010i	−0.104617	+	0.0760088i
$355$		0			0
$356$	4.12150	−	12.6847i	0.218439	−	0.672287i
$357$	−1.37627	−	0.999917i	−0.0728398	−	0.0529212i
$358$	−11.6288	−	8.44878i	−0.614599	−	0.446532i
$359$	5.23240	−	16.1037i	0.276156	−	0.849920i	−0.712756	−	0.701413i	$-0.752553\pi$
$359$	5.23240	−	16.1037i	0.276156	−	0.849920i	0.988911	−	0.148507i	$-0.0474469\pi$
$360$		0			0
$361$	14.2581	−	10.3591i	0.750427	−	0.545217i
$362$	12.1453			0.638345
$363$	−9.14834	−	6.10802i	−0.480163	−	0.320588i
$364$	−3.53916			−0.185502
$365$		0			0
$366$	−0.261938	−	0.806162i	−0.0136917	−	0.0421388i
$367$	1.24312	−	3.82592i	0.0648901	−	0.199711i	−0.913355	−	0.407165i	$-0.866518\pi$
$367$	1.24312	−	3.82592i	0.0648901	−	0.199711i	0.978245	+	0.207453i	$0.0665175\pi$
$368$	−1.28310	−	0.932227i	−0.0668862	−	0.0485957i
$369$	2.26417	+	1.64502i	0.117868	+	0.0856362i
$370$		0			0
$371$	1.54111	+	4.74306i	0.0800107	+	0.246248i
$372$	6.96475	−	5.06018i	0.361105	−	0.262358i
$373$	36.2624			1.87760			0.938798	−	0.344469i	$-0.111941\pi$
$373$	36.2624			1.87760			0.938798	+	0.344469i	$0.111941\pi$
$374$	−8.42123	+	2.92191i	−0.435451	+	0.151088i
$375$		0			0
$376$	−25.0564	+	18.2046i	−1.29219	+	0.938829i
$377$	0.623330	+	1.91841i	0.0321031	+	0.0988033i
$378$	0.126238	−	0.388521i	0.00649299	−	0.0199834i
$379$	16.0725	+	11.6774i	0.825591	+	0.599827i	0.918308	−	0.395866i	$-0.129555\pi$
$379$	16.0725	+	11.6774i	0.825591	+	0.599827i	−0.0927176	+	0.995692i	$0.529555\pi$
$380$		0			0
$381$	−3.30480	+	10.1711i	−0.169310	+	0.521083i
$382$	0.185091	+	0.569652i	0.00947010	+	0.0291460i
$383$	−19.7798	+	14.3708i	−1.01070	+	0.734315i	−0.964355	−	0.264610i	$-0.914757\pi$
$383$	−19.7798	+	14.3708i	−1.01070	+	0.734315i	−0.0463430	+	0.998926i	$0.514757\pi$
$384$	8.76773			0.447427
$385$		0			0
$386$	7.13305			0.363063
$387$	2.47033	−	1.79480i	0.125574	−	0.0912349i
$388$	−6.34974	−	19.5425i	−0.322359	−	0.992120i
$389$	−3.73527	+	11.4960i	−0.189386	+	0.582870i	−0.999996	−	0.00271592i	$-0.999135\pi$
$389$	−3.73527	+	11.4960i	−0.189386	+	0.582870i	0.810610	+	0.585586i	$0.199135\pi$
$390$		0			0
$391$	−7.88834	−	5.73121i	−0.398930	−	0.289840i
$392$	5.61421	−	17.2788i	0.283560	−	0.872709i
$393$	2.16484	+	6.66269i	0.109202	+	0.336088i
$394$	−0.684253	+	0.497139i	−0.0344722	+	0.0250455i
$395$		0			0
$396$	2.71224	+	3.58165i	0.136295	+	0.179985i
$397$	22.7158			1.14007			0.570037	−	0.821619i	$-0.306929\pi$
$397$	22.7158			1.14007			0.570037	+	0.821619i	$0.306929\pi$
$398$	1.48297	−	1.07744i	0.0743343	−	0.0540071i
$399$	−0.184327	−	0.567299i	−0.00922788	−	0.0284005i
$400$		0			0
$401$	1.90762	+	1.38597i	0.0952619	+	0.0692119i	0.634397	−	0.773008i	$-0.281249\pi$
$401$	1.90762	+	1.38597i	0.0952619	+	0.0692119i	−0.539135	+	0.842220i	$0.681249\pi$
$402$	3.45329	+	2.50896i	0.172234	+	0.125136i
$403$	10.0904	−	31.0552i	0.502641	−	1.54697i
$404$	6.92656	+	21.3178i	0.344609	+	1.06060i
$405$		0			0
$406$	0.160381			0.00795956
$407$	0.292542	+	14.7633i	0.0145008	+	0.731791i
$408$	9.01581			0.446349
$409$	2.21976	−	1.61275i	0.109760	−	0.0797452i	−0.531551	−	0.847026i	$-0.678391\pi$
$409$	2.21976	−	1.61275i	0.109760	−	0.0797452i	0.641311	+	0.767281i	$0.278391\pi$
$410$		0			0
$411$	3.40162	−	10.4691i	0.167789	−	0.516403i
$412$	−15.7086	−	11.4130i	−0.773908	−	0.562277i
$413$	−1.24591	−	0.905206i	−0.0613072	−	0.0445423i
$414$	0.723558	−	2.22688i	0.0355609	−	0.109445i
$415$		0			0
$416$	24.2216	−	17.5980i	1.18756	−	0.862814i
$417$	14.2028			0.695516
$418$	−2.99108	−	0.906754i	−0.146299	−	0.0443508i
$419$	−13.9861			−0.683266			−0.341633	−	0.939833i	$-0.610980\pi$
$419$	−13.9861			−0.683266			−0.341633	+	0.939833i	$0.610980\pi$
$420$		0			0
$421$	−5.49260	−	16.9045i	−0.267693	−	0.823875i	−0.991061	−	0.133412i	$-0.957407\pi$
$421$	−5.49260	−	16.9045i	−0.267693	−	0.823875i	0.723368	−	0.690463i	$-0.242593\pi$
$422$	−2.37559	+	7.31131i	−0.115642	+	0.355909i
$423$	9.29747	+	6.75501i	0.452058	+	0.328440i
$424$	−21.3830	−	15.5357i	−1.03845	−	0.754479i
$425$		0			0
$426$	−1.01778	−	3.13241i	−0.0493116	−	0.151766i
$427$	0.434066	−	0.315367i	0.0210059	−	0.0152617i
$428$	9.30741			0.449891
$429$	16.3079	+	4.94377i	0.787351	+	0.238687i
$430$		0			0
$431$	−5.75712	+	4.18279i	−0.277311	+	0.201478i	−0.717744	−	0.696308i	$-0.754825\pi$
$431$	−5.75712	+	4.18279i	−0.277311	+	0.201478i	0.440433	+	0.897786i	$0.354825\pi$
$432$	−0.168154	−	0.517525i	−0.00809032	−	0.0248995i
$433$	3.51714	−	10.8247i	0.169023	−	0.520200i	−0.830287	−	0.557336i	$-0.811824\pi$
$433$	3.51714	−	10.8247i	0.169023	−	0.520200i	0.999310	+	0.0371363i	$0.0118236\pi$
$434$	−2.10040	−	1.52603i	−0.100822	−	0.0732517i
$435$		0			0
$436$	−7.09585	+	21.8388i	−0.339830	+	1.04589i
$437$	−1.05650	−	3.25158i	−0.0505394	−	0.155544i
$438$	8.51959	−	6.18985i	0.407082	−	0.295762i
$439$	−16.1917			−0.772788			−0.386394	−	0.922334i	$-0.626279\pi$
$439$	−16.1917			−0.772788			−0.386394	+	0.922334i	$0.626279\pi$
$440$		0			0
$441$	−6.74142			−0.321020
$442$	11.1715	−	8.11660i	0.531376	−	0.386068i
$443$	−7.33982	−	22.5896i	−0.348725	−	1.07327i	−0.959559	−	0.281508i	$-0.909166\pi$
$443$	−7.33982	−	22.5896i	−0.348725	−	1.07327i	0.610834	−	0.791759i	$-0.290834\pi$
$444$	1.86366	−	5.73577i	0.0884456	−	0.272208i
$445$		0			0
$446$	5.73195	+	4.16451i	0.271416	+	0.197195i
$447$	−4.03498	+	12.4184i	−0.190848	+	0.587369i
$448$	−0.564589	−	1.73763i	−0.0266743	−	0.0820951i
$449$	16.7134	−	12.1430i	0.788755	−	0.573064i	−0.118839	−	0.992914i	$-0.537917\pi$
$449$	16.7134	−	12.1430i	0.788755	−	0.573064i	0.907594	+	0.419850i	$0.137917\pi$
$450$		0			0
$451$	5.60361	+	7.39985i	0.263864	+	0.348445i
$452$	−6.10809			−0.287300
$453$	14.8465	−	10.7866i	0.697549	−	0.506799i
$454$	−1.33750	−	4.11640i	−0.0627720	−	0.193192i
$455$		0			0
$456$	2.55754	+	1.85816i	0.119768	+	0.0870165i
$457$	−6.24590	−	4.53791i	−0.292171	−	0.212274i	0.432038	−	0.901855i	$-0.357795\pi$
$457$	−6.24590	−	4.53791i	−0.292171	−	0.212274i	−0.724209	+	0.689581i	$0.757795\pi$
$458$	6.05285	−	18.6288i	0.282831	−	0.870465i
$459$	−1.03379	−	3.18168i	−0.0482532	−	0.148508i
$460$		0			0
$461$	41.3034			1.92369			0.961845	−	0.273595i	$-0.0882128\pi$
$461$	41.3034			1.92369			0.961845	+	0.273595i	$0.0882128\pi$
$462$	0.774514	−	1.11169i	0.0360336	−	0.0517207i
$463$	19.5424			0.908214			0.454107	−	0.890947i	$-0.349958\pi$
$463$	19.5424			0.908214			0.454107	+	0.890947i	$0.349958\pi$
$464$	0.172833	−	0.125570i	0.00802357	−	0.00582946i
$465$		0			0
$466$	1.14691	−	3.52983i	0.0531297	−	0.163516i
$467$	17.2817	+	12.5559i	0.799700	+	0.581016i	0.910826	−	0.412790i	$-0.135446\pi$
$467$	17.2817	+	12.5559i	0.799700	+	0.581016i	−0.111126	+	0.993806i	$0.535446\pi$
$468$	−5.63070	−	4.09094i	−0.260279	−	0.189104i
$469$	−0.834910	+	2.56959i	−0.0385526	+	0.118653i
$470$		0			0
$471$	−8.85085	+	6.43052i	−0.407825	+	0.296303i
$472$	8.16184			0.375679
$473$	9.56775	−	3.31971i	0.439926	−	0.152641i
$474$	12.9666			0.595574
$475$		0			0
$476$	0.712099	+	2.19161i	0.0326390	+	0.100452i
$477$	−3.03068	+	9.32746i	−0.138765	+	0.427075i
$478$	−3.13180	−	2.27538i	−0.143245	−	0.104074i
$479$	12.4719	+	9.06140i	0.569858	+	0.414026i	0.835053	−	0.550169i	$-0.185437\pi$
$479$	12.4719	+	9.06140i	0.569858	+	0.414026i	−0.265196	+	0.964195i	$0.585437\pi$
$480$		0			0
$481$	−7.06883	−	21.7556i	−0.322311	−	0.991971i
$482$	−0.275967	+	0.200502i	−0.0125700	+	0.00913261i
$483$	1.48208			0.0674372
$484$	5.16234	+	13.9778i	0.234652	+	0.635355i
$485$		0			0
$486$	0.649936	−	0.472206i	0.0294817	−	0.0214197i
$487$	7.76017	+	23.8833i	0.351647	+	1.08226i	0.957928	+	0.287007i	$0.0926604\pi$
$487$	7.76017	+	23.8833i	0.351647	+	1.08226i	−0.606282	+	0.795250i	$0.707340\pi$
$488$	−0.878698	+	2.70435i	−0.0397768	+	0.122420i
$489$	18.6740	+	13.5674i	0.844467	+	0.613541i
$490$		0			0
$491$	0.341112	−	1.04983i	0.0153942	−	0.0473784i	−0.943064	−	0.332610i	$-0.892071\pi$
$491$	0.341112	−	1.04983i	0.0153942	−	0.0473784i	0.958459	+	0.285232i	$0.0920706\pi$
$492$	−1.17151	−	3.60554i	−0.0528158	−	0.162550i
$493$	1.06255	−	0.771991i	0.0478550	−	0.0347687i
$494$	4.84190			0.217848
$495$		0			0
$496$	−3.45829			−0.155282
$497$	1.68660	−	1.22539i	0.0756543	−	0.0549660i
$498$	−3.81286	−	11.7348i	−0.170858	−	0.525848i
$499$	0.709867	−	2.18475i	0.0317780	−	0.0978026i	−0.933909	−	0.357510i	$-0.883626\pi$
$499$	0.709867	−	2.18475i	0.0317780	−	0.0978026i	0.965687	+	0.259707i	$0.0836260\pi$
$500$		0			0
$501$	3.37704	+	2.45356i	0.150875	+	0.109617i
$502$	3.81386	−	11.7378i	0.170221	−	0.523886i
$503$	2.11883	+	6.52108i	0.0944739	+	0.290761i	0.987116	−	0.160005i	$-0.0511510\pi$
$503$	2.11883	+	6.52108i	0.0944739	+	0.290761i	−0.892642	+	0.450766i	$0.851151\pi$
$504$	−1.10868	+	0.805505i	−0.0493847	+	0.0358801i
$505$		0			0
$506$	4.43927	−	6.37188i	0.197350	−	0.283265i
$507$	−13.3988			−0.595063
$508$	11.7202	−	8.51519i	0.519998	−	0.377800i
$509$	7.99840	+	24.6166i	0.354523	+	1.09111i	0.956286	+	0.292435i	$0.0944654\pi$
$509$	7.99840	+	24.6166i	0.354523	+	1.09111i	−0.601762	+	0.798675i	$0.705535\pi$
$510$		0			0
$511$	5.39263	+	3.91798i	0.238556	+	0.173321i
$512$	−4.93812	−	3.58776i	−0.218236	−	0.158558i
$513$	0.362488	−	1.11562i	0.0160042	−	0.0492559i
$514$	−1.84074	−	5.66521i	−0.0811914	−	0.249881i
$515$		0			0
$516$	−4.13628			−0.182090
$517$	23.0103	+	30.3863i	1.01199	+	1.33639i
$518$	−1.81879			−0.0799129
$519$	3.00706	−	2.18476i	0.131995	−	0.0959002i
$520$		0			0
$521$	−8.89377	+	27.3722i	−0.389643	+	1.19920i	0.543412	+	0.839466i	$0.317132\pi$
$521$	−8.89377	+	27.3722i	−0.389643	+	1.19920i	−0.933055	+	0.359733i	$0.882868\pi$
$522$	0.255161	+	0.185385i	0.0111681	+	0.00811410i
$523$	−24.2649	−	17.6295i	−1.06103	−	0.770883i	−0.0867506	−	0.996230i	$-0.527648\pi$
$523$	−24.2649	−	17.6295i	−1.06103	−	0.770883i	−0.974279	+	0.225347i	$0.927648\pi$
$524$	2.93250	−	9.02531i	0.128107	−	0.394272i
$525$		0			0
$526$	−19.9446	+	14.4906i	−0.869626	+	0.631820i
$527$	−21.2611			−0.926148
$528$	−0.0357553	−	1.80442i	−0.00155605	−	0.0785271i
$529$	−14.5052			−0.630659
$530$		0			0
$531$	−0.935871	−	2.88031i	−0.0406133	−	0.124995i
$532$	−0.249690	+	0.768466i	−0.0108254	+	0.0333172i
$533$	−11.6333	−	8.45207i	−0.503893	−	0.366100i
$534$	−6.39929	−	4.64936i	−0.276924	−	0.201197i
$535$		0			0
$536$	−4.42485	−	13.6183i	−0.191125	−	0.588221i
$537$	14.4750	−	10.5167i	0.624644	−	0.453831i
$538$	14.6544			0.631796
$539$	−21.3972	−	6.48660i	−0.921641	−	0.279398i
$540$		0			0
$541$	−2.14753	+	1.56027i	−0.0923295	+	0.0670813i	−0.632992	−	0.774158i	$-0.718174\pi$
$541$	−2.14753	+	1.56027i	−0.0923295	+	0.0670813i	0.540663	+	0.841239i	$0.318174\pi$
$542$	3.41129	+	10.4989i	0.146527	+	0.450964i
$543$	−4.67174	+	14.3781i	−0.200484	+	0.617025i
$544$	−15.7710	−	11.4583i	−0.676178	−	0.491272i
$545$		0			0
$546$	−0.648609	+	1.99621i	−0.0277579	+	0.0854301i
$547$	1.03908	+	3.19797i	0.0444281	+	0.136735i	0.970810	−	0.239850i	$-0.0770982\pi$
$547$	1.03908	+	3.19797i	0.0444281	+	0.136735i	−0.926382	+	0.376585i	$0.877098\pi$
$548$	−12.0635	+	8.76464i	−0.515327	+	0.374407i
$549$	1.05512			0.0450315
$550$		0			0
$551$	0.460526			0.0196191
$552$	−6.35462	+	4.61690i	−0.270471	+	0.196508i
$553$	2.53623	+	7.80573i	0.107852	+	0.331933i
$554$	0.341975	−	1.05249i	0.0145291	−	0.0447161i
$555$		0			0
$556$	−15.5649	−	11.3085i	−0.660097	−	0.479588i
$557$	7.57320	−	23.3079i	0.320887	−	0.987588i	−0.652376	−	0.757895i	$-0.726228\pi$
$557$	7.57320	−	23.3079i	0.320887	−	0.987588i	0.973263	−	0.229693i	$-0.0737722\pi$
$558$	−1.57772	−	4.85573i	−0.0667904	−	0.205560i
$559$	−12.6925	+	9.22165i	−0.536836	+	0.390034i
$560$		0			0
$561$	−0.219819	−	11.0933i	−0.00928077	−	0.468360i
$562$	−15.5070			−0.654123
$563$	6.48691	−	4.71301i	0.273390	−	0.198630i	−0.442639	−	0.896700i	$-0.645958\pi$
$563$	6.48691	−	4.71301i	0.273390	−	0.198630i	0.716029	+	0.698070i	$0.245958\pi$
$564$	−4.81063	−	14.8056i	−0.202564	−	0.623428i
$565$		0			0
$566$	−1.42739	−	1.03706i	−0.0599978	−	0.0435909i
$567$	0.411389	+	0.298892i	0.0172767	+	0.0125523i
$568$	−3.41425	+	10.5080i	−0.143259	+	0.440905i
$569$	2.93903	+	9.04541i	0.123211	+	0.379203i	0.993571	−	0.113212i	$-0.0361140\pi$
$569$	2.93903	+	9.04541i	0.123211	+	0.379203i	−0.870360	+	0.492416i	$0.836114\pi$
$570$		0			0
$571$	−11.6232			−0.486415			−0.243208	−	0.969974i	$-0.578200\pi$
$571$	−11.6232			−0.486415			−0.243208	+	0.969974i	$0.578200\pi$
$572$	−13.9354	−	18.4024i	−0.582670	−	0.769445i
$573$	−0.745573			−0.0311468
$574$	−0.924950	+	0.672016i	−0.0386067	+	0.0280494i
$575$		0			0
$576$	1.11029	−	3.41713i	0.0462621	−	0.142380i
$577$	−7.87651	−	5.72262i	−0.327903	−	0.238236i	0.411637	−	0.911348i	$-0.364957\pi$
$577$	−7.87651	−	5.72262i	−0.327903	−	0.238236i	−0.739540	+	0.673112i	$0.764957\pi$
$578$	3.77496	+	2.74267i	0.157017	+	0.114080i
$579$	−2.74375	+	8.44439i	−0.114026	+	0.350937i
$580$		0			0
$581$	6.31842	−	4.59060i	0.262132	−	0.190450i
$582$	−12.1864			−0.505142
$583$	−18.5942	+	26.6891i	−0.770093	+	1.10535i
$584$	−35.3266			−1.46183
$585$		0			0
$586$	6.78179	+	20.8722i	0.280153	+	0.862223i
$587$	1.96374	−	6.04377i	0.0810523	−	0.249453i	−0.902316	−	0.431075i	$-0.858135\pi$
$587$	1.96374	−	6.04377i	0.0810523	−	0.249453i	0.983369	+	0.181621i	$0.0581345\pi$
$588$	7.38791	+	5.36763i	0.304672	+	0.221357i
$589$	−6.03120	−	4.38192i	−0.248511	−	0.180554i
$590$		0			0
$591$	−0.325333	−	1.00127i	−0.0133824	−	0.0411868i
$592$	−1.96000	+	1.42402i	−0.0805555	+	0.0585270i
$593$	4.58134			0.188133			0.0940666	−	0.995566i	$-0.470013\pi$
$593$	4.58134			0.188133			0.0940666	+	0.995566i	$0.470013\pi$
$594$	2.51724	−	0.873406i	0.103284	−	0.0358363i
$595$		0			0
$596$	14.3096	−	10.3966i	0.586145	−	0.425860i
$597$	0.705087	+	2.17003i	0.0288573	+	0.0888136i
$598$	−3.71763	+	11.4417i	−0.152025	+	0.467885i
$599$	7.49415	+	5.44482i	0.306202	+	0.222469i	0.730265	−	0.683164i	$-0.239396\pi$
$599$	7.49415	+	5.44482i	0.306202	+	0.222469i	−0.424063	+	0.905633i	$0.639396\pi$
$600$		0			0
$601$	−3.24279	+	9.98027i	−0.132276	+	0.407104i	−0.995156	−	0.0983045i	$-0.968658\pi$
$601$	−3.24279	+	9.98027i	−0.132276	+	0.407104i	0.862880	+	0.505408i	$0.168658\pi$
$602$	0.385468	+	1.18635i	0.0157105	+	0.0483520i
$603$	−4.29853	+	3.12306i	−0.175050	+	0.127181i
$604$	−24.8587			−1.01149
$605$		0			0
$606$	13.2934			0.540008
$607$	−16.8275	+	12.2259i	−0.683008	+	0.496234i	−0.874354	−	0.485288i	$-0.838715\pi$
$607$	−16.8275	+	12.2259i	−0.683008	+	0.496234i	0.191346	+	0.981523i	$0.438715\pi$
$608$	−2.11225	−	6.50085i	−0.0856632	−	0.263644i
$609$	−0.0616909	+	0.189865i	−0.00249984	+	0.00769372i
$610$		0			0
$611$	−47.7702	−	34.7071i	−1.93258	−	1.40410i
$612$	−1.40038	+	4.30992i	−0.0566069	+	0.174218i
$613$	7.65048	+	23.5458i	0.309000	+	0.951004i	0.978154	+	0.207881i	$0.0666566\pi$
$613$	7.65048	+	23.5458i	0.309000	+	0.951004i	−0.669154	+	0.743124i	$0.733343\pi$
$614$	17.5020	−	12.7159i	0.706321	−	0.513172i
$615$		0			0
$616$	−4.29400	+	1.48989i	−0.173010	+	0.0600292i
$617$	28.2943			1.13909			0.569543	−	0.821962i	$-0.307120\pi$
$617$	28.2943			1.13909			0.569543	+	0.821962i	$0.307120\pi$
$618$	−9.31621	+	6.76862i	−0.374753	+	0.272274i
$619$	−8.22111	−	25.3020i	−0.330434	−	1.01697i	−0.968928	−	0.247345i	$-0.920442\pi$
$619$	−8.22111	−	25.3020i	−0.330434	−	1.01697i	0.638493	−	0.769627i	$-0.279558\pi$
$620$		0			0
$621$	2.35795	+	1.71315i	0.0946214	+	0.0687465i
$622$	−7.75663	−	5.63552i	−0.311012	−	0.225964i
$623$	1.54717	−	4.76171i	0.0619861	−	0.190774i
$624$	0.863973	+	2.65903i	0.0345866	+	0.106447i
$625$		0			0
$626$	−12.0193			−0.480389
$627$	2.22398	−	3.19218i	0.0888173	−	0.127483i
$628$	14.8197			0.591370
$629$	−12.0498	+	8.75471i	−0.480458	+	0.349073i
$630$		0			0
$631$	5.09026	−	15.6662i	0.202640	−	0.623662i	−0.797162	−	0.603766i	$-0.793666\pi$
$631$	5.09026	−	15.6662i	0.202640	−	0.623662i	0.999802	−	0.0198965i	$-0.00633368\pi$
$632$	−35.1904	−	25.5673i	−1.39980	−	1.01701i
$633$	−7.74164	−	5.62463i	−0.307703	−	0.223559i
$634$	−2.42925	+	7.47645i	−0.0964777	+	0.296928i
$635$		0			0
$636$	10.7480	−	7.80887i	0.426185	−	0.309642i
$637$	34.6373			1.37238
$638$	0.631499	+	0.833926i	0.0250013	+	0.0330154i
$639$	4.09976			0.162184
$640$		0			0
$641$	2.21008	+	6.80193i	0.0872930	+	0.268660i	0.985169	−	0.171589i	$-0.0548901\pi$
$641$	2.21008	+	6.80193i	0.0872930	+	0.268660i	−0.897876	+	0.440249i	$0.854890\pi$
$642$	1.70574	−	5.24972i	0.0673201	−	0.207190i
$643$	−14.3700	−	10.4404i	−0.566698	−	0.411730i	0.267206	−	0.963639i	$-0.413899\pi$
$643$	−14.3700	−	10.4404i	−0.566698	−	0.411730i	−0.833904	+	0.551909i	$0.813899\pi$
$644$	−1.62421	−	1.18006i	−0.0640029	−	0.0465009i
$645$		0			0
$646$	−0.974219	−	2.99834i	−0.0383301	−	0.117968i
$647$	−1.15822	+	0.841497i	−0.0455344	+	0.0330827i	−0.610320	−	0.792155i	$-0.708959\pi$
$647$	−1.15822	+	0.841497i	−0.0455344	+	0.0330827i	0.564785	+	0.825238i	$0.308959\pi$
$648$	−2.69497			−0.105869
$649$	−0.198998	−	10.0426i	−0.00781136	−	0.394205i
$650$		0			0
$651$	2.61450	−	1.89954i	0.102470	−	0.0744490i
$652$	−9.66216	−	29.7371i	−0.378399	−	1.16459i
$653$	−9.05032	+	27.8540i	−0.354166	+	1.09001i	0.602325	+	0.798251i	$0.294241\pi$
$653$	−9.05032	+	27.8540i	−0.354166	+	1.09001i	−0.956491	+	0.291761i	$0.905759\pi$
$654$	11.0174	+	8.00464i	0.430816	+	0.313006i
$655$		0			0
$656$	−0.470609	+	1.44838i	−0.0183742	+	0.0565499i
$657$	4.05070	+	12.4668i	0.158033	+	0.486375i
$658$	−3.79816	+	2.75953i	−0.148068	+	0.107578i
$659$	21.2056			0.826054			0.413027	−	0.910719i	$-0.364471\pi$
$659$	21.2056			0.826054			0.413027	+	0.910719i	$0.364471\pi$
$660$		0			0
$661$	−16.5453			−0.643537			−0.321768	−	0.946818i	$-0.604277\pi$
$661$	−16.5453			−0.643537			−0.321768	+	0.946818i	$0.604277\pi$
$662$	−3.34517	+	2.43041i	−0.130014	+	0.0944606i
$663$	5.31159	+	16.3474i	0.206285	+	0.634881i
$664$	−12.7906	+	39.3655i	−0.496373	+	1.52768i
$665$		0			0
$666$	−2.89364	−	2.10235i	−0.112126	−	0.0814644i
$667$	−0.353593	+	1.08825i	−0.0136912	+	0.0421371i
$668$	−1.74732	−	5.37770i	−0.0676059	−	0.208070i
$669$	−7.13492	+	5.18382i	−0.275852	+	0.200418i
$670$		0			0
$671$	3.34894	+	1.01524i	0.129284	+	0.0391929i
$672$	2.96311			0.114305
$673$	−15.3336	+	11.1405i	−0.591066	+	0.429434i	−0.842696	−	0.538389i	$-0.819033\pi$
$673$	−15.3336	+	11.1405i	−0.591066	+	0.429434i	0.251631	+	0.967823i	$0.419033\pi$
$674$	7.28660	+	22.4258i	0.280669	+	0.863811i
$675$		0			0
$676$	14.6837	+	10.6684i	0.564759	+	0.410322i
$677$	−26.7338	−	19.4233i	−1.02746	−	0.746496i	−0.0596644	−	0.998218i	$-0.519003\pi$
$677$	−26.7338	−	19.4233i	−1.02746	−	0.746496i	−0.967800	+	0.251722i	$0.919003\pi$
$678$	−1.11941	+	3.44519i	−0.0429906	+	0.132312i
$679$	−2.38363	−	7.33607i	−0.0914754	−	0.281532i
$680$		0			0
$681$	5.38764			0.206455
$682$	−0.335478	−	16.9301i	−0.0128461	−	0.648287i
$683$	−26.1102			−0.999079			−0.499540	−	0.866291i	$-0.666497\pi$
$683$	−26.1102			−0.999079			−0.499540	+	0.866291i	$0.666497\pi$
$684$	−1.28553	+	0.933989i	−0.0491533	+	0.0357119i
$685$		0			0
$686$	1.73469	−	5.33884i	0.0662309	−	0.203838i
$687$	19.7252	+	14.3312i	0.752565	+	0.546770i
$688$	1.34425	+	0.976656i	0.0512491	+	0.0372347i
$689$	15.5716	−	47.9243i	0.593229	−	1.82577i
$690$		0			0
$691$	19.2821	−	14.0093i	0.733527	−	0.532939i	−0.157150	−	0.987575i	$-0.550231\pi$
$691$	19.2821	−	14.0093i	0.733527	−	0.532939i	0.890677	+	0.454636i	$0.150231\pi$
$692$	−5.03497			−0.191401
$693$	1.01815	+	1.34452i	0.0386763	+	0.0510740i
$694$	5.89342			0.223711
$695$		0			0
$696$	−0.326949	−	1.00625i	−0.0123930	−	0.0381417i
$697$	−2.89324	+	8.90448i	−0.109589	+	0.337281i
$698$	18.5406	+	13.4706i	0.701773	+	0.509868i
$699$	3.73760	+	2.71552i	0.141369	+	0.102710i
$700$		0			0
$701$	5.05431	+	15.5556i	0.190899	+	0.587525i	1.00000		0.000143622i	$-4.57162e-5\pi$
$701$	5.05431	+	15.5556i	0.190899	+	0.587525i	−0.809101	+	0.587669i	$0.800046\pi$
$702$	−3.33936	+	2.42619i	−0.126036	+	0.0915705i
$703$	−5.22256			−0.196973
$704$	6.81201	−	9.77758i	0.256737	−	0.368506i
$705$		0			0
$706$	−10.5172	+	7.64116i	−0.395818	+	0.287579i
$707$	2.60017	+	8.00249i	0.0977893	+	0.300964i
$708$	−1.26773	+	3.90168i	−0.0476444	+	0.146634i
$709$	−12.2026	−	8.86573i	−0.458279	−	0.332959i	0.334577	−	0.942369i	$-0.391407\pi$
$709$	−12.2026	−	8.86573i	−0.458279	−	0.332959i	−0.792856	+	0.609409i	$0.791407\pi$
$710$		0			0
$711$	−4.98763	+	15.3503i	−0.187051	+	0.575683i
$712$	8.19970	+	25.2361i	0.307297	+	0.945762i
$713$	14.9855	−	10.8876i	0.561211	−	0.407743i
$714$	1.36665			0.0511458
$715$		0			0
$716$	−24.2368			−0.905770
$717$	3.89834	−	2.83231i	0.145586	−	0.105775i
$718$	4.20353	+	12.9371i	0.156874	+	0.482810i
$719$	6.99094	−	21.5159i	0.260718	−	0.802408i	−0.731931	−	0.681379i	$-0.761381\pi$
$719$	6.99094	−	21.5159i	0.260718	−	0.802408i	0.992649	−	0.121029i	$-0.0386195\pi$
$720$		0			0
$721$	−5.89687	−	4.28432i	−0.219611	−	0.159557i
$722$	−4.37522	+	13.4655i	−0.162829	+	0.501136i
$723$	−0.131211	−	0.403825i	−0.00487977	−	0.0150184i
$724$	16.5679	−	12.0373i	0.615740	−	0.447361i
$725$		0			0
$726$	8.83008	−	0.350082i	0.327715	−	0.0129928i
$727$	−20.2062			−0.749408			−0.374704	−	0.927144i	$-0.622256\pi$
$727$	−20.2062			−0.749408			−0.374704	+	0.927144i	$0.622256\pi$
$728$	5.69639	−	4.13867i	0.211122	−	0.153389i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	8.26429	+	6.00436i	0.305666	+	0.222079i
$732$	−1.15631	−	0.840105i	−0.0427383	−	0.0310512i
$733$	−0.465123	+	1.43150i	−0.0171797	+	0.0528737i	−0.959279	−	0.282461i	$-0.908849\pi$
$733$	−0.465123	+	1.43150i	−0.0171797	+	0.0528737i	0.942099	+	0.335334i	$0.108849\pi$
$734$	0.998676	+	3.07361i	0.0368618	+	0.113449i
$735$		0			0
$736$	16.9836			0.626025
$737$	−16.6485	+	5.77650i	−0.613254	+	0.212780i
$738$	−2.24836			−0.0827632
$739$	−31.3766	+	22.7965i	−1.15421	+	0.838581i	−0.989035	−	0.147683i	$-0.952818\pi$
$739$	−31.3766	+	22.7965i	−1.15421	+	0.838581i	−0.165174	+	0.986265i	$0.552818\pi$
$740$		0			0
$741$	−1.86245	+	5.73204i	−0.0684189	+	0.210572i
$742$	−3.24133	−	2.35496i	−0.118993	−	0.0864535i
$743$	−21.7307	−	15.7883i	−0.797221	−	0.579215i	0.112877	−	0.993609i	$-0.463993\pi$
$743$	−21.7307	−	15.7883i	−0.797221	−	0.579215i	−0.910098	+	0.414394i	$0.863993\pi$
$744$	−5.29264	+	16.2891i	−0.194038	+	0.597186i
$745$		0			0
$746$	−23.5682	+	17.1233i	−0.862895	+	0.626930i
$747$	15.3587			0.561947
$748$	−8.59177	+	12.3322i	−0.314146	+	0.450908i
$749$	3.49391			0.127665
$750$		0			0
$751$	8.03522	+	24.7299i	0.293209	+	0.902405i	0.983817	+	0.179176i	$0.0573431\pi$
$751$	8.03522	+	24.7299i	0.293209	+	0.902405i	−0.690608	+	0.723229i	$0.742657\pi$
$752$	−1.93248	+	5.94756i	−0.0704703	+	0.216885i
$753$	12.4287	+	9.03000i	0.452928	+	0.329071i
$754$	−1.31101	−	0.952506i	−0.0477442	−	0.0346882i
$755$		0			0
$756$	−0.212858	−	0.655110i	−0.00774157	−	0.0238261i
$757$	−23.9395	+	17.3931i	−0.870096	+	0.632162i	−0.930613	−	0.366005i	$-0.880725\pi$
$757$	−23.9395	+	17.3931i	−0.870096	+	0.632162i	0.0605164	+	0.998167i	$0.480725\pi$
$758$	−15.9603			−0.579703
$759$	5.83571	+	7.70635i	0.211823	+	0.279723i
$760$		0			0
$761$	−26.7546	+	19.4383i	−0.969852	+	0.704639i	−0.955418	−	0.295257i	$-0.904595\pi$
$761$	−26.7546	+	19.4383i	−0.969852	+	0.704639i	−0.0144341	+	0.999896i	$0.504595\pi$
$762$	−2.65497	−	8.17115i	−0.0961793	−	0.296009i
$763$	−2.66371	+	8.19807i	−0.0964329	+	0.296790i
$764$	0.817072	+	0.593638i	0.0295606	+	0.0214771i
$765$		0			0
$766$	6.06958	−	18.6803i	0.219303	−	0.674945i
$767$	4.80848	+	14.7990i	0.173624	+	0.534361i
$768$	−11.5120	+	8.36398i	−0.415405	+	0.301809i
$769$	3.37489			0.121702			0.0608508	−	0.998147i	$-0.480619\pi$
$769$	3.37489			0.121702			0.0608508	+	0.998147i	$0.480619\pi$
$770$		0			0
$771$	7.41474			0.267035
$772$	9.73043	−	7.06957i	0.350206	−	0.254439i
$773$	7.16571	+	22.0538i	0.257733	+	0.793220i	0.993279	+	0.115745i	$0.0369257\pi$
$773$	7.16571	+	22.0538i	0.257733	+	0.793220i	−0.735546	+	0.677475i	$0.763074\pi$
$774$	−0.758042	+	2.33301i	−0.0272473	+	0.0838584i
$775$		0			0
$776$	33.0730	+	24.0290i	1.18725	+	0.862589i
$777$	0.699602	−	2.15315i	0.0250981	−	0.0772439i
$778$	−3.00079	−	9.23548i	−0.107584	−	0.331108i
$779$	−2.65595	+	1.92966i	−0.0951594	+	0.0691373i
$780$		0			0
$781$	13.0126	+	3.94479i	0.465626	+	0.141156i
$782$	7.83323			0.280116
$783$	−0.317615	+	0.230761i	−0.0113506	+	0.00824672i
$784$	−1.13360	−	3.48886i	−0.0404857	−	0.124602i
$785$		0			0
$786$	−4.55317	−	3.30808i	−0.162406	−	0.117995i
$787$	33.2248	+	24.1392i	1.18434	+	0.860470i	0.992654	−	0.120987i	$-0.0386060\pi$
$787$	33.2248	+	24.1392i	1.18434	+	0.860470i	0.191681	+	0.981457i	$0.438606\pi$
$788$	−0.440697	+	1.35633i	−0.0156992	+	0.0483171i
$789$	−9.48280	−	29.1851i	−0.337597	−	1.03902i
$790$		0			0
$791$	−2.29292			−0.0815267
$792$	−8.55380	−	2.59311i	−0.303946	−	0.0921420i
$793$	−5.42119			−0.192512
$794$	−14.7638	+	10.7266i	−0.523949	+	0.380671i
$795$		0			0
$796$	0.955113	−	2.93954i	0.0338531	−	0.104189i
$797$	39.0448	+	28.3677i	1.38304	+	1.00484i	0.996589	+	0.0825256i	$0.0262986\pi$
$797$	39.0448	+	28.3677i	1.38304	+	1.00484i	0.386449	+	0.922311i	$0.373701\pi$
$798$	0.387683	+	0.281668i	0.0137238	+	0.00997095i
$799$	−11.8806	+	36.5648i	−0.420307	+	1.29357i
$800$		0			0
$801$	7.96560	−	5.78735i	0.281451	−	0.204486i
$802$	−1.89429			−0.0668898
$803$	0.861317	+	43.4669i	0.0303952	+	1.53391i
$804$	7.19738			0.253832
$805$		0			0
$806$	8.10631	+	24.9487i	0.285533	+	0.878779i
$807$	−5.63686	+	17.3485i	−0.198427	+	0.610695i
$808$	−36.0774	−	26.2118i	−1.26920	−	0.922127i
$809$	35.4699	+	25.7704i	1.24706	+	0.906040i	0.998047	−	0.0624612i	$-0.0198950\pi$
$809$	35.4699	+	25.7704i	1.24706	+	0.906040i	0.249009	+	0.968501i	$0.419895\pi$
$810$		0			0
$811$	−12.7912	−	39.3673i	−0.449161	−	1.38237i	−0.877856	−	0.478925i	$-0.841027\pi$
$811$	−12.7912	−	39.3673i	−0.449161	−	1.38237i	0.428695	−	0.903449i	$-0.358973\pi$
$812$	0.218781	−	0.158953i	0.00767769	−	0.00557817i
$813$	−13.7411			−0.481922
$814$	−7.16147	−	9.45708i	−0.251009	−	0.331471i
$815$		0			0
$816$	1.47276	−	1.07003i	0.0515571	−	0.0374584i
$817$	1.10686	+	3.40655i	0.0387240	+	0.119180i
$818$	−0.681150	+	2.09637i	−0.0238159	+	0.0732977i
$819$	−2.11371	−	1.53570i	−0.0738590	−	0.0536617i
$820$		0			0
$821$	13.2750	−	40.8564i	0.463302	−	1.42590i	−0.397803	−	0.917471i	$-0.630227\pi$
$821$	13.2750	−	40.8564i	0.463302	−	1.42590i	0.861105	−	0.508427i	$-0.169773\pi$
$822$	2.73274	+	8.41052i	0.0953153	+	0.293350i
$823$	−11.3475	+	8.24443i	−0.395548	+	0.287383i	−0.767725	−	0.640779i	$-0.778611\pi$
$823$	−11.3475	+	8.24443i	−0.395548	+	0.287383i	0.372177	+	0.928162i	$0.378611\pi$
$824$	38.6298			1.34573
$825$		0			0
$826$	1.23721			0.0430479
$827$	−25.0022	+	18.1652i	−0.869413	+	0.631666i	−0.930429	−	0.366471i	$-0.880566\pi$
$827$	−25.0022	+	18.1652i	−0.869413	+	0.631666i	0.0610161	+	0.998137i	$0.480566\pi$
$828$	−1.22004	−	3.75488i	−0.0423991	−	0.130491i
$829$	11.4274	−	35.1699i	0.396890	−	1.22150i	−0.530591	−	0.847628i	$-0.678030\pi$
$829$	11.4274	−	35.1699i	0.396890	−	1.22150i	0.927480	−	0.373872i	$-0.121970\pi$
$830$		0			0
$831$	1.11444	+	0.809688i	0.0386595	+	0.0280878i
$832$	−5.70465	+	17.5571i	−0.197773	+	0.608684i
$833$	−6.96922	−	21.4490i	−0.241469	−	0.743165i
$834$	−9.23094	+	6.70667i	−0.319641	+	0.232233i
$835$		0			0
$836$	−4.97892	+	1.72753i	−0.172200	+	0.0597479i
$837$	6.35529			0.219671
$838$	9.09008	−	6.60433i	0.314012	−	0.228143i
$839$	0.679929	+	2.09261i	0.0234737	+	0.0722447i	0.962107	−	0.272672i	$-0.0879073\pi$
$839$	0.679929	+	2.09261i	0.0234737	+	0.0722447i	−0.938633	+	0.344916i	$0.887907\pi$
$840$		0			0
$841$	23.3368	+	16.9552i	0.804717	+	0.584661i
$842$	11.5523	+	8.39320i	0.398117	+	0.289249i
$843$	5.96481	−	18.3578i	0.205439	−	0.632276i
$844$	4.00562	+	12.3280i	0.137879	+	0.424349i
$845$		0			0
$846$	−9.23252			−0.317421
$847$	1.93789	+	5.24714i	0.0665868	+	0.180294i
$848$	−5.33682			−0.183267
$849$	1.77677	−	1.29090i	0.0609784	−	0.0443034i
$850$		0			0
$851$	4.00990	−	12.3412i	0.137457	−	0.423051i
$852$	−4.49292	−	3.26430i	−0.153925	−	0.111833i
$853$	26.8374	+	19.4985i	0.918896	+	0.667617i	0.943249	−	0.332087i	$-0.107753\pi$
$853$	26.8374	+	19.4985i	0.918896	+	0.667617i	−0.0243532	+	0.999703i	$0.507753\pi$
$854$	−0.133197	+	0.409937i	−0.00455790	+	0.0140278i
$855$		0			0
$856$	−14.9806	+	10.8840i	−0.512026	+	0.372008i
$857$	28.5419			0.974972			0.487486	−	0.873131i	$-0.337914\pi$
$857$	28.5419			0.974972			0.487486	+	0.873131i	$0.337914\pi$
$858$	−12.9336	+	4.48754i	−0.441544	+	0.153202i
$859$	53.6600			1.83085			0.915427	−	0.402484i	$-0.131853\pi$
$859$	53.6600			1.83085			0.915427	+	0.402484i	$0.131853\pi$
$860$		0			0
$861$	−0.439774	−	1.35349i	−0.0149875	−	0.0461267i
$862$	1.76662	−	5.43710i	0.0601713	−	0.185188i
$863$	15.4475	+	11.2233i	0.525840	+	0.382045i	0.818799	−	0.574080i	$-0.194640\pi$
$863$	15.4475	+	11.2233i	0.525840	+	0.382045i	−0.292960	+	0.956125i	$0.594640\pi$
$864$	4.71423	+	3.42509i	0.160381	+	0.116524i
$865$		0			0
$866$	2.82555	+	8.69615i	0.0960162	+	0.295507i
$867$	−4.69893	+	3.41397i	−0.159584	+	0.115944i
$868$	−4.37767			−0.148588
$869$	−30.6008	+	43.9226i	−1.03806	+	1.48997i
$870$		0			0
$871$	22.0857	−	16.0462i	0.748347	−	0.543706i
$872$	−14.1171	−	43.4481i	−0.478067	−	1.47134i
$873$	4.68753	−	14.4267i	0.158649	−	0.488271i
$874$	2.22208	+	1.61443i	0.0751629	+	0.0546090i
$875$		0			0
$876$	5.48710	−	16.8875i	0.185392	−	0.570577i
$877$	−4.26902	−	13.1387i	−0.144155	−	0.443662i	0.852747	−	0.522325i	$-0.174935\pi$
$877$	−4.26902	−	13.1387i	−0.144155	−	0.443662i	−0.996901	+	0.0786625i	$0.974935\pi$
$878$	10.5236	−	7.64582i	0.355153	−	0.258034i
$879$	−27.3180			−0.921414
$880$		0			0
$881$	−14.7416			−0.496658			−0.248329	−	0.968676i	$-0.579881\pi$
$881$	−14.7416			−0.496658			−0.248329	+	0.968676i	$0.579881\pi$
$882$	4.38150	−	3.18334i	0.147533	−	0.107189i
$883$	0.0511379	+	0.157386i	0.00172093	+	0.00529647i	0.951913	−	0.306368i	$-0.0991137\pi$
$883$	0.0511379	+	0.157386i	0.00172093	+	0.00529647i	−0.950192	+	0.311664i	$0.899114\pi$
$884$	7.19510	−	22.1443i	0.241998	−	0.744792i
$885$		0			0
$886$	15.4374	+	11.2159i	0.518629	+	0.376806i
$887$	−4.28759	+	13.1958i	−0.143963	+	0.443073i	−0.996876	−	0.0789801i	$-0.974834\pi$
$887$	−4.28759	+	13.1958i	−0.143963	+	0.443073i	0.852913	+	0.522053i	$0.174834\pi$
$888$	3.70775	+	11.4113i	0.124424	+	0.382937i
$889$	4.39963	−	3.19652i	0.147559	−	0.107208i
$890$		0			0
$891$	0.0657076	+	3.31597i	0.00220129	+	0.111089i
$892$	11.9466			0.400001
$893$	−10.9063	+	7.92386i	−0.364964	+	0.265162i
$894$	−3.24156	−	9.97650i	−0.108414	−	0.333664i
$895$		0			0
$896$	−3.60695	−	2.62060i	−0.120500	−	0.0875482i
$897$	−12.1151	−	8.80215i	−0.404512	−	0.293895i
$898$	−5.12865	+	15.7844i	−0.171145	+	0.526731i
$899$	0.771012	+	2.37293i	0.0257147	+	0.0791417i
$900$		0			0
$901$	−32.8101			−1.09306
$902$	−7.13625	−	2.16337i	−0.237611	−	0.0720324i
$903$	−1.55272			−0.0516713
$904$	9.83117	−	7.14276i	0.326980	−	0.237565i
$905$		0			0
$906$	−4.55577	+	14.0212i	−0.151355	+	0.465824i
$907$	7.36533	+	5.35122i	0.244562	+	0.177684i	0.703313	−	0.710880i	$-0.251703\pi$
$907$	7.36533	+	5.35122i	0.244562	+	0.177684i	−0.458752	+	0.888565i	$0.651703\pi$
$908$	−5.90430	−	4.28972i	−0.195941	−	0.142359i
$909$	−5.11335	+	15.7373i	−0.169599	+	0.521972i
$910$		0			0
$911$	36.6306	−	26.6137i	1.21363	−	0.881751i	0.218072	−	0.975933i	$-0.430023\pi$
$911$	36.6306	−	26.6137i	1.21363	−	0.881751i	0.995555	+	0.0941815i	$0.0300234\pi$
$912$	0.638317			0.0211368
$913$	48.7484	+	14.7782i	1.61334	+	0.489086i
$914$	6.20227			0.205153
$915$		0			0
$916$	−10.2061	−	31.4111i	−0.337219	−	1.03785i
$917$	1.10083	−	3.38801i	0.0363527	−	0.111882i
$918$	2.17431	+	1.57973i	0.0717629	+	0.0521388i
$919$	12.0247	+	8.73644i	0.396658	+	0.288189i	0.768178	−	0.640236i	$-0.221163\pi$
$919$	12.0247	+	8.73644i	0.396658	+	0.288189i	−0.371521	+	0.928425i	$0.621163\pi$
$920$		0			0
$921$	8.32143	+	25.6107i	0.274200	+	0.843902i
$922$	−26.8446	+	19.5037i	−0.884079	+	0.642321i
$923$	−21.0645			−0.693346
$924$	−0.0452609	−	2.28412i	−0.00148897	−	0.0751420i
$925$		0			0
$926$	−12.7013	+	9.22806i	−0.417392	+	0.303253i
$927$	−4.42946	−	13.6325i	−0.145483	−	0.447749i
$928$	−0.706934	+	2.17572i	−0.0232062	+	0.0714214i
$929$	−2.66467	−	1.93600i	−0.0874251	−	0.0635181i	0.543214	−	0.839594i	$-0.317207\pi$
$929$	−2.66467	−	1.93600i	−0.0874251	−	0.0635181i	−0.630639	+	0.776076i	$0.717207\pi$
$930$		0			0
$931$	2.44368	−	7.52088i	0.0800884	−	0.246487i
$932$	−1.93388	−	5.95187i	−0.0633463	−	0.194960i
$933$	9.65516	−	7.01489i	0.316096	−	0.229657i
$934$	−17.1609			−0.561523
$935$		0			0
$936$	13.8467			0.452594
$937$	0.645840	−	0.469231i	0.0210987	−	0.0153291i	−0.577186	−	0.816613i	$-0.695849\pi$
$937$	0.645840	−	0.469231i	0.0210987	−	0.0153291i	0.598285	+	0.801284i	$0.295849\pi$
$938$	−0.670738	−	2.06432i	−0.0219004	−	0.0674024i
$939$	4.62327	−	14.2290i	0.150875	−	0.464345i
$940$		0			0
$941$	20.4562	+	14.8623i	0.666853	+	0.484497i	0.868970	−	0.494864i	$-0.164782\pi$
$941$	20.4562	+	14.8623i	0.666853	+	0.484497i	−0.202117	+	0.979361i	$0.564782\pi$
$942$	2.71596	−	8.35885i	0.0884906	−	0.272346i
$943$	−2.52065	−	7.75776i	−0.0820836	−	0.252627i
$944$	1.33327	−	0.968674i	0.0433941	−	0.0315276i
$945$		0			0
$946$	−4.65084	+	6.67556i	−0.151212	+	0.217041i
$947$	−49.6668			−1.61396			−0.806978	−	0.590582i	$-0.798898\pi$
$947$	−49.6668			−1.61396			−0.806978	+	0.590582i	$0.798898\pi$
$948$	17.6881	−	12.8512i	0.574483	−	0.417387i
$949$	−20.8124	−	64.0540i	−0.675600	−	2.07928i
$950$		0			0
$951$	−7.91651	−	5.75168i	−0.256710	−	0.186511i
$952$	−3.70901	−	2.69475i	−0.120210	−	0.0873374i
$953$	−8.58269	+	26.4148i	−0.278021	+	0.855660i	0.710384	+	0.703815i	$0.248521\pi$
$953$	−8.58269	+	26.4148i	−0.278021	+	0.855660i	−0.988404	+	0.151845i	$0.951479\pi$
$954$	−2.43474	−	7.49336i	−0.0788277	−	0.242607i
$955$		0			0
$956$	−6.52732			−0.211109
$957$	−1.23014	+	0.426822i	−0.0397649	+	0.0137972i
$958$	−12.3848			−0.400135
$959$	−4.52852	+	3.29016i	−0.146233	+	0.106245i
$960$		0			0
$961$	2.90158	−	8.93015i	0.0935994	−	0.288069i
$962$	14.8674	+	10.8018i	0.479346	+	0.348265i
$963$	5.55871	+	4.03864i	0.179127	+	0.130143i
$964$	−0.177738	+	0.547022i	−0.00572457	+	0.0176184i
$965$		0			0
$966$	−0.963261	+	0.699850i	−0.0309924	+	0.0225173i
$967$	11.0951			0.356793			0.178396	−	0.983959i	$-0.442909\pi$
$967$	11.0951			0.356793			0.178396	+	0.983959i	$0.442909\pi$
$968$	−24.6545	−	16.4609i	−0.792427	−	0.529075i
$969$	3.92429			0.126066
$970$		0			0
$971$	−9.86435	−	30.3594i	−0.316562	−	0.974278i	−0.975107	−	0.221736i	$-0.928828\pi$
$971$	−9.86435	−	30.3594i	−0.316562	−	0.974278i	0.658544	−	0.752542i	$-0.271172\pi$
$972$	0.418596	−	1.28830i	0.0134265	−	0.0413224i
$973$	−5.84289	−	4.24511i	−0.187315	−	0.136092i
$974$	−16.3215	−	11.8583i	−0.522974	−	0.379963i
$975$		0			0
$976$	0.177423	+	0.546052i	0.00567918	+	0.0174787i
$977$	−8.41829	+	6.11624i	−0.269325	+	0.195676i	−0.714248	−	0.699893i	$-0.753231\pi$
$977$	−8.41829	+	6.11624i	−0.269325	+	0.195676i	0.444923	+	0.895569i	$0.353231\pi$
$978$	−18.5435			−0.592957
$979$	30.8513	−	10.7044i	0.986011	−	0.342115i
$980$		0			0
$981$	−13.7141	+	9.96388i	−0.437858	+	0.318122i
$982$	0.274037	+	0.843401i	0.00874489	+	0.0269140i
$983$	−12.8036	+	39.4055i	−0.408372	+	1.25684i	0.509675	+	0.860367i	$0.329766\pi$
$983$	−12.8036	+	39.4055i	−0.408372	+	1.25684i	−0.918047	+	0.396472i	$0.870234\pi$
$984$	6.10189	+	4.43328i	0.194521	+	0.141328i
$985$		0			0
$986$	−0.326054	+	1.00349i	−0.0103837	+	0.0319576i
$987$	−1.80586	−	5.55788i	−0.0574813	−	0.176909i
$988$	6.60500	−	4.79881i	0.210133	−	0.152671i
$989$	−8.89970			−0.282994
$990$		0			0
$991$	−2.17000			−0.0689322			−0.0344661	−	0.999406i	$-0.510973\pi$
$991$	−2.17000			−0.0689322			−0.0344661	+	0.999406i	$0.510973\pi$
$992$	29.9603	−	21.7674i	0.951240	−	0.691116i
$993$	−1.59049	−	4.89502i	−0.0504726	−	0.155339i
$994$	−0.517547	+	1.59284i	−0.0164156	+	0.0505220i
$995$		0			0
$996$	−16.8316	−	12.2289i	−0.533329	−	0.387487i
$997$	−0.249993	+	0.769399i	−0.00791735	+	0.0243671i	−0.954937	−	0.296808i	$-0.904078\pi$
$997$	−0.249993	+	0.769399i	−0.00791735	+	0.0243671i	0.947020	+	0.321175i	$0.104078\pi$
$998$	0.570283	+	1.75515i	0.0180520	+	0.0555583i
$999$	3.60189	−	2.61693i	0.113959	−	0.0827959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.o.751.3		24
5.2	odd	4		165.2.s.a.124.4	yes	48
5.3	odd	4		165.2.s.a.124.9	yes	48
5.4	even	2		825.2.n.p.751.4		24
11.2	odd	10		9075.2.a.dx.1.5		12
11.4	even	5	inner	825.2.n.o.301.3		24
11.9	even	5		9075.2.a.dz.1.8		12
15.2	even	4		495.2.ba.c.289.9		48
15.8	even	4		495.2.ba.c.289.4		48
55.2	even	20		1815.2.c.k.364.8		24
55.4	even	10		825.2.n.p.301.4		24
55.9	even	10		9075.2.a.dy.1.5		12
55.13	even	20		1815.2.c.k.364.17		24
55.24	odd	10		9075.2.a.ea.1.8		12
55.37	odd	20		165.2.s.a.4.9	yes	48
55.42	odd	20		1815.2.c.j.364.17		24
55.48	odd	20		165.2.s.a.4.4	✓	48
55.53	odd	20		1815.2.c.j.364.8		24
165.92	even	20		495.2.ba.c.334.4		48
165.158	even	20		495.2.ba.c.334.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.4	✓	48	55.48	odd	20
165.2.s.a.4.9	yes	48	55.37	odd	20
165.2.s.a.124.4	yes	48	5.2	odd	4
165.2.s.a.124.9	yes	48	5.3	odd	4
495.2.ba.c.289.4		48	15.8	even	4
495.2.ba.c.289.9		48	15.2	even	4
495.2.ba.c.334.4		48	165.92	even	20
495.2.ba.c.334.9		48	165.158	even	20
825.2.n.o.301.3		24	11.4	even	5	inner
825.2.n.o.751.3		24	1.1	even	1	trivial
825.2.n.p.301.4		24	55.4	even	10
825.2.n.p.751.4		24	5.4	even	2
1815.2.c.j.364.8		24	55.53	odd	20
1815.2.c.j.364.17		24	55.42	odd	20
1815.2.c.k.364.8		24	55.2	even	20
1815.2.c.k.364.17		24	55.13	even	20
9075.2.a.dx.1.5		12	11.2	odd	10
9075.2.a.dy.1.5		12	55.9	even	10
9075.2.a.dz.1.8		12	11.9	even	5
9075.2.a.ea.1.8		12	55.24	odd	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.649936 + 0.472206i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.418596 + 1.28830i) q^{4} +(0.649936 + 0.472206i) q^{6} +(-0.157137 + 0.483617i) q^{7} +(-0.832793 - 2.56307i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.649936 + 0.472206i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.418596 + 1.28830i) q^{4} +(0.649936 + 0.472206i) q^{6} +(-0.157137 + 0.483617i) q^{7} +(-0.832793 - 2.56307i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-3.13337 + 1.08718i) q^{11} +1.35460 q^{12} +(4.15671 - 3.02003i) q^{13} +(-0.126238 - 0.388521i) q^{14} +(-0.440233 - 0.319848i) q^{16} +(-2.70650 - 1.96639i) q^{17} +(0.248254 - 0.764046i) q^{18} +(-0.362488 - 1.11562i) q^{19} +0.508505 q^{21} +(1.52312 - 2.18620i) q^{22} +2.91459 q^{23} +(-2.18028 + 1.58407i) q^{24} +(-1.27552 + 3.92565i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.557269 - 0.404880i) q^{28} +(-0.121318 + 0.373379i) q^{29} +(5.14154 - 3.73555i) q^{31} +5.82710 q^{32} +(2.00224 + 2.64406i) q^{33} +2.68759 q^{34} +(-0.418596 - 1.28830i) q^{36} +(1.37580 - 4.23428i) q^{37} +(0.762398 + 0.553914i) q^{38} +(-4.15671 - 3.02003i) q^{39} +(-0.864837 - 2.66170i) q^{41} +(-0.330496 + 0.240119i) q^{42} -3.05350 q^{43} +(-0.0890077 - 4.49183i) q^{44} +(-1.89430 + 1.37629i) q^{46} +(-3.55132 - 10.9298i) q^{47} +(-0.168154 + 0.517525i) q^{48} +(5.45393 + 3.96251i) q^{49} +(-1.03379 + 3.18168i) q^{51} +(2.15074 + 6.61928i) q^{52} +(7.93441 - 5.76469i) q^{53} -0.803366 q^{54} +1.37041 q^{56} +(-0.949005 + 0.689492i) q^{57} +(-0.0974628 - 0.299960i) q^{58} +(-0.935871 + 2.88031i) q^{59} +(-0.853612 - 0.620185i) q^{61} +(-1.57772 + 4.85573i) q^{62} +(-0.157137 - 0.483617i) q^{63} +(-2.90678 + 2.11190i) q^{64} +(-2.54987 - 0.772999i) q^{66} +5.31327 q^{67} +(3.66623 - 2.66367i) q^{68} +(-0.900658 - 2.77194i) q^{69} +(-3.31678 - 2.40978i) q^{71} +(2.18028 + 1.58407i) q^{72} +(4.05070 - 12.4668i) q^{73} +(1.10527 + 3.40167i) q^{74} +1.58900 q^{76} +(-0.0334126 - 1.68619i) q^{77} +4.12768 q^{78} +(13.0578 - 9.48703i) q^{79} +(0.309017 - 0.951057i) q^{81} +(1.81896 + 1.32155i) q^{82} +(-12.4255 - 9.02764i) q^{83} +(-0.212858 + 0.655110i) q^{84} +(1.98458 - 1.44188i) q^{86} +0.392594 q^{87} +(5.39598 + 7.12566i) q^{88} -9.84603 q^{89} +(0.807365 + 2.48481i) q^{91} +(-1.22004 + 3.75488i) q^{92} +(-5.14154 - 3.73555i) q^{93} +(7.46927 + 5.42674i) q^{94} +(-1.80067 - 5.54191i) q^{96} +(-12.2721 + 8.91621i) q^{97} -5.41583 q^{98} +(1.89592 - 2.72130i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9	\( 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9} - 24 q^{12} - 4 q^{13} + 2 q^{14} - 22 q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} - 16 q^{21} + 4 q^{22} + 6 q^{24} - 38 q^{26} + 6 q^{27} - 30 q^{28} - 10 q^{31} + 56 q^{32} - 10 q^{33} + 12 q^{34} - 6 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 30 q^{41} + 8 q^{42} + 64 q^{43} + 24 q^{44} + 54 q^{46} + 8 q^{47} + 2 q^{48} + 14 q^{49} + 14 q^{51} - 14 q^{52} - 26 q^{53} - 8 q^{54} + 12 q^{56} - 8 q^{57} - 20 q^{58} - 30 q^{59} + 20 q^{61} + 50 q^{62} - 4 q^{63} - 32 q^{64} + 6 q^{66} - 20 q^{67} + 62 q^{68} - 10 q^{69} - 16 q^{71} - 6 q^{72} + 12 q^{73} + 16 q^{74} - 68 q^{76} + 2 q^{77} - 32 q^{78} + 26 q^{79} - 6 q^{81} - 56 q^{82} - 48 q^{83} - 52 q^{86} - 48 q^{88} - 20 q^{89} - 20 q^{91} - 46 q^{92} + 10 q^{93} - 36 q^{94} + 14 q^{96} + 14 q^{97} + 120 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9 - 24 * q^12 - 4 * q^13 + 2 * q^14 - 22 * q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 - 16 * q^21 + 4 * q^22 + 6 * q^24 - 38 * q^26 + 6 * q^27 - 30 * q^28 - 10 * q^31 + 56 * q^32 - 10 * q^33 + 12 * q^34 - 6 * q^36 - 10 * q^37 - 4 * q^38 + 4 * q^39 + 30 * q^41 + 8 * q^42 + 64 * q^43 + 24 * q^44 + 54 * q^46 + 8 * q^47 + 2 * q^48 + 14 * q^49 + 14 * q^51 - 14 * q^52 - 26 * q^53 - 8 * q^54 + 12 * q^56 - 8 * q^57 - 20 * q^58 - 30 * q^59 + 20 * q^61 + 50 * q^62 - 4 * q^63 - 32 * q^64 + 6 * q^66 - 20 * q^67 + 62 * q^68 - 10 * q^69 - 16 * q^71 - 6 * q^72 + 12 * q^73 + 16 * q^74 - 68 * q^76 + 2 * q^77 - 32 * q^78 + 26 * q^79 - 6 * q^81 - 56 * q^82 - 48 * q^83 - 52 * q^86 - 48 * q^88 - 20 * q^89 - 20 * q^91 - 46 * q^92 + 10 * q^93 - 36 * q^94 + 14 * q^96 + 14 * q^97 + 120 * q^98

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