LMFDB - Embedded newform 420.2.n.b.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(71,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("420.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.n (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	420.71
Dual form			420.2.n.b.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38203 + 0.299986i) q^{2} +(-0.491627 - 1.66081i) q^{3} +(1.82002 - 0.829179i) q^{4} +1.00000i q^{5} +(1.17766 + 2.14781i) q^{6} +1.00000i q^{7} +(-2.26658 + 1.69193i) q^{8} +(-2.51661 + 1.63300i) q^{9} +O(q^{10})$	\(q+(-1.38203 + 0.299986i) q^{2} +(-0.491627 - 1.66081i) q^{3} +(1.82002 - 0.829179i) q^{4} +1.00000i q^{5} +(1.17766 + 2.14781i) q^{6} +1.00000i q^{7} +(-2.26658 + 1.69193i) q^{8} +(-2.51661 + 1.63300i) q^{9} +(-0.299986 - 1.38203i) q^{10} -1.79273 q^{11} +(-2.27188 - 2.61506i) q^{12} -4.13212 q^{13} +(-0.299986 - 1.38203i) q^{14} +(1.66081 - 0.491627i) q^{15} +(2.62492 - 3.01824i) q^{16} -3.20559i q^{17} +(2.98815 - 3.01181i) q^{18} +5.62600i q^{19} +(0.829179 + 1.82002i) q^{20} +(1.66081 - 0.491627i) q^{21} +(2.47761 - 0.537794i) q^{22} -6.63263 q^{23} +(3.92429 + 2.93256i) q^{24} -1.00000 q^{25} +(5.71071 - 1.23958i) q^{26} +(3.94935 + 3.37678i) q^{27} +(0.829179 + 1.82002i) q^{28} +5.01257i q^{29} +(-2.14781 + 1.17766i) q^{30} -0.158417i q^{31} +(-2.72229 + 4.95874i) q^{32} +(0.881355 + 2.97739i) q^{33} +(0.961633 + 4.43023i) q^{34} -1.00000 q^{35} +(-3.22621 + 5.05881i) q^{36} -5.00112 q^{37} +(-1.68772 - 7.77530i) q^{38} +(2.03146 + 6.86268i) q^{39} +(-1.69193 - 2.26658i) q^{40} +2.64788i q^{41} +(-2.14781 + 1.17766i) q^{42} +5.69675i q^{43} +(-3.26280 + 1.48650i) q^{44} +(-1.63300 - 2.51661i) q^{45} +(9.16650 - 1.98970i) q^{46} -4.36680 q^{47} +(-6.30322 - 2.87566i) q^{48} -1.00000 q^{49} +(1.38203 - 0.299986i) q^{50} +(-5.32390 + 1.57596i) q^{51} +(-7.52052 + 3.42627i) q^{52} -4.06986i q^{53} +(-6.47110 - 3.48207i) q^{54} -1.79273i q^{55} +(-1.69193 - 2.26658i) q^{56} +(9.34374 - 2.76589i) q^{57} +(-1.50370 - 6.92752i) q^{58} +5.93534 q^{59} +(2.61506 - 2.27188i) q^{60} +8.35711 q^{61} +(0.0475230 + 0.218938i) q^{62} +(-1.63300 - 2.51661i) q^{63} +(2.27474 - 7.66978i) q^{64} -4.13212i q^{65} +(-2.11124 - 3.85045i) q^{66} +11.9939i q^{67} +(-2.65801 - 5.83424i) q^{68} +(3.26078 + 11.0156i) q^{69} +(1.38203 - 0.299986i) q^{70} -14.4237 q^{71} +(2.94115 - 7.95925i) q^{72} -13.5376 q^{73} +(6.91170 - 1.50026i) q^{74} +(0.491627 + 1.66081i) q^{75} +(4.66496 + 10.2394i) q^{76} -1.79273i q^{77} +(-4.86625 - 8.87502i) q^{78} -7.04542i q^{79} +(3.01824 + 2.62492i) q^{80} +(3.66660 - 8.21925i) q^{81} +(-0.794327 - 3.65945i) q^{82} +12.5018 q^{83} +(2.61506 - 2.27188i) q^{84} +3.20559 q^{85} +(-1.70894 - 7.87308i) q^{86} +(8.32494 - 2.46431i) q^{87} +(4.06336 - 3.03318i) q^{88} -4.18024i q^{89} +(3.01181 + 2.98815i) q^{90} -4.13212i q^{91} +(-12.0715 + 5.49964i) q^{92} +(-0.263102 + 0.0778823i) q^{93} +(6.03505 - 1.30998i) q^{94} -5.62600 q^{95} +(9.57390 + 2.08337i) q^{96} +15.3744 q^{97} +(1.38203 - 0.299986i) q^{98} +(4.51160 - 2.92753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.38203	+	0.299986i	−0.977243	+	0.212122i
$2$	−1.38203	+	0.299986i	−0.977243	+	0.212122i
$3$	−0.491627	−	1.66081i	−0.283841	−	0.958871i
$3$	−0.491627	−	1.66081i	−0.283841	−	0.958871i
$4$	1.82002	−	0.829179i	0.910008	−	0.414590i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	1.17766	+	2.14781i	0.480780	+	0.876842i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.26658	+	1.69193i	−0.801356	+	0.598188i
$9$	−2.51661	+	1.63300i	−0.838868	+	0.544334i
$10$	−0.299986	−	1.38203i	−0.0948639	−	0.437036i
$11$	−1.79273			−0.540529			−0.270264	−	0.962786i	$-0.587111\pi$
$11$	−1.79273			−0.540529			−0.270264	+	0.962786i	$0.587111\pi$
$12$	−2.27188	−	2.61506i	−0.655836	−	0.754903i
$13$	−4.13212			−1.14604			−0.573022	−	0.819540i	$-0.694229\pi$
$13$	−4.13212			−1.14604			−0.573022	+	0.819540i	$0.694229\pi$
$14$	−0.299986	−	1.38203i	−0.0801746	−	0.369363i
$15$	1.66081	−	0.491627i	0.428820	−	0.126938i
$16$	2.62492	−	3.01824i	0.656231	−	0.754560i
$17$		−	3.20559i		−	0.777471i	−0.921349	−	0.388735i	$-0.872912\pi$
$17$		−	3.20559i		−	0.777471i	0.921349	−	0.388735i	$-0.127088\pi$
$18$	2.98815	−	3.01181i	0.704313	−	0.709889i
$19$			5.62600i			1.29069i	0.763890	+	0.645346i	$0.223287\pi$
$19$			5.62600i			1.29069i	−0.763890	+	0.645346i	$0.776713\pi$
$20$	0.829179	+	1.82002i	0.185410	+	0.406968i
$21$	1.66081	−	0.491627i	0.362419	−	0.107282i
$22$	2.47761	−	0.537794i	0.528228	−	0.114658i
$23$	−6.63263			−1.38300			−0.691500	−	0.722377i	$-0.743050\pi$
$23$	−6.63263			−1.38300			−0.691500	+	0.722377i	$0.743050\pi$
$24$	3.92429	+	2.93256i	0.801043	+	0.598607i
$25$	−1.00000			−0.200000
$26$	5.71071	−	1.23958i	1.11996	−	0.243101i
$27$	3.94935	+	3.37678i	0.760052	+	0.649862i
$28$	0.829179	+	1.82002i	0.156700	+	0.343951i
$29$			5.01257i			0.930810i	0.885098	+	0.465405i	$0.154091\pi$
$29$			5.01257i			0.930810i	−0.885098	+	0.465405i	$0.845909\pi$
$30$	−2.14781	+	1.17766i	−0.392135	+	0.215011i
$31$		−	0.158417i		−	0.0284526i	−0.999899	−	0.0142263i	$-0.995471\pi$
$31$		−	0.158417i		−	0.0284526i	0.999899	−	0.0142263i	$-0.00452853\pi$
$32$	−2.72229	+	4.95874i	−0.481238	+	0.876590i
$33$	0.881355	+	2.97739i	0.153424	+	0.518297i
$34$	0.961633	+	4.43023i	0.164919	+	0.759778i
$35$	−1.00000			−0.169031
$36$	−3.22621	+	5.05881i	−0.537702	+	0.843135i
$37$	−5.00112			−0.822179			−0.411089	−	0.911595i	$-0.634852\pi$
$37$	−5.00112			−0.822179			−0.411089	+	0.911595i	$0.634852\pi$
$38$	−1.68772	−	7.77530i	−0.273784	−	1.26132i
$39$	2.03146	+	6.86268i	0.325294	+	1.09891i
$40$	−1.69193	−	2.26658i	−0.267518	−	0.358377i
$41$			2.64788i			0.413529i	0.978391	+	0.206765i	$0.0662935\pi$
$41$			2.64788i			0.413529i	−0.978391	+	0.206765i	$0.933707\pi$
$42$	−2.14781	+	1.17766i	−0.331415	+	0.181718i
$43$			5.69675i			0.868746i	0.900733	+	0.434373i	$0.143030\pi$
$43$			5.69675i			0.868746i	−0.900733	+	0.434373i	$0.856970\pi$
$44$	−3.26280	+	1.48650i	−0.491886	+	0.224098i
$45$	−1.63300	−	2.51661i	−0.243434	−	0.375153i
$46$	9.16650	−	1.98970i	1.35153	−	0.293365i
$47$	−4.36680			−0.636964			−0.318482	−	0.947929i	$-0.603173\pi$
$47$	−4.36680			−0.636964			−0.318482	+	0.947929i	$0.603173\pi$
$48$	−6.30322	−	2.87566i	−0.909791	−	0.415066i
$49$	−1.00000			−0.142857
$50$	1.38203	−	0.299986i	0.195449	−	0.0424244i
$51$	−5.32390	+	1.57596i	−0.745495	+	0.220678i
$52$	−7.52052	+	3.42627i	−1.04291	+	0.475138i
$53$		−	4.06986i		−	0.559038i	−0.960140	−	0.279519i	$-0.909825\pi$
$53$		−	4.06986i		−	0.559038i	0.960140	−	0.279519i	$-0.0901749\pi$
$54$	−6.47110	−	3.48207i	−0.880606	−	0.473850i
$55$		−	1.79273i		−	0.241732i
$56$	−1.69193	−	2.26658i	−0.226094	−	0.302884i
$57$	9.34374	−	2.76589i	1.23761	−	0.366352i
$58$	−1.50370	−	6.92752i	−0.197445	−	0.909628i
$59$	5.93534			0.772715			0.386358	−	0.922349i	$-0.373733\pi$
$59$	5.93534			0.772715			0.386358	+	0.922349i	$0.373733\pi$
$60$	2.61506	−	2.27188i	0.337603	−	0.293299i
$61$	8.35711			1.07002			0.535009	−	0.844846i	$-0.320308\pi$
$61$	8.35711			1.07002			0.535009	+	0.844846i	$0.320308\pi$
$62$	0.0475230	+	0.218938i	0.00603543	+	0.0278051i
$63$	−1.63300	−	2.51661i	−0.205739	−	0.317062i
$64$	2.27474	−	7.66978i	0.284343	−	0.958723i
$65$		−	4.13212i		−	0.512526i
$66$	−2.11124	−	3.85045i	−0.259875	−	0.473958i
$67$			11.9939i			1.46529i	0.680611	+	0.732645i	$0.261714\pi$
$67$			11.9939i			1.46529i	−0.680611	+	0.732645i	$0.738286\pi$
$68$	−2.65801	−	5.83424i	−0.322331	−	0.707505i
$69$	3.26078	+	11.0156i	0.392552	+	1.32612i
$70$	1.38203	−	0.299986i	0.165184	−	0.0358552i
$71$	−14.4237			−1.71178			−0.855888	−	0.517161i	$-0.826989\pi$
$71$	−14.4237			−1.71178			−0.855888	+	0.517161i	$0.826989\pi$
$72$	2.94115	−	7.95925i	0.346618	−	0.938006i
$73$	−13.5376			−1.58445			−0.792225	−	0.610229i	$-0.791078\pi$
$73$	−13.5376			−1.58445			−0.792225	+	0.610229i	$0.791078\pi$
$74$	6.91170	−	1.50026i	0.803468	−	0.174402i
$75$	0.491627	+	1.66081i	0.0567682	+	0.191774i
$76$	4.66496	+	10.2394i	0.535108	+	1.17454i
$77$		−	1.79273i		−	0.204301i
$78$	−4.86625	−	8.87502i	−0.550994	−	1.00490i
$79$		−	7.04542i		−	0.792672i	−0.918106	−	0.396336i	$-0.870282\pi$
$79$		−	7.04542i		−	0.792672i	0.918106	−	0.396336i	$-0.129718\pi$
$80$	3.01824	+	2.62492i	0.337450	+	0.293475i
$81$	3.66660	−	8.21925i	0.407401	−	0.913250i
$82$	−0.794327	−	3.65945i	−0.0877187	−	0.404119i
$83$	12.5018			1.37225			0.686126	−	0.727483i	$-0.259310\pi$
$83$	12.5018			1.37225			0.686126	+	0.727483i	$0.259310\pi$
$84$	2.61506	−	2.27188i	0.285327	−	0.247883i
$85$	3.20559			0.347696
$86$	−1.70894	−	7.87308i	−0.184280	−	0.848976i
$87$	8.32494	−	2.46431i	0.892527	−	0.264202i
$88$	4.06336	−	3.03318i	0.433156	−	0.323338i
$89$		−	4.18024i		−	0.443104i	−0.975149	−	0.221552i	$-0.928888\pi$
$89$		−	4.18024i		−	0.443104i	0.975149	−	0.221552i	$-0.0711123\pi$
$90$	3.01181	+	2.98815i	0.317472	+	0.314978i
$91$		−	4.13212i		−	0.433164i
$92$	−12.0715	+	5.49964i	−1.25854	+	0.573377i
$93$	−0.263102	+	0.0778823i	−0.0272824	+	0.00807602i
$94$	6.03505	−	1.30998i	0.622468	−	0.135114i
$95$	−5.62600			−0.577215
$96$	9.57390	+	2.08337i	0.977132	+	0.212633i
$97$	15.3744			1.56103			0.780515	−	0.625136i	$-0.214957\pi$
$97$	15.3744			1.56103			0.780515	+	0.625136i	$0.214957\pi$
$98$	1.38203	−	0.299986i	0.139606	−	0.0303031i
$99$	4.51160	−	2.92753i	0.453432	−	0.294228i
$100$	−1.82002	+	0.829179i	−0.182002	+	0.0829179i
$101$			2.47356i			0.246128i	0.992399	+	0.123064i	$0.0392720\pi$
$101$			2.47356i			0.246128i	−0.992399	+	0.123064i	$0.960728\pi$
$102$	6.88502	−	3.77512i	0.681719	−	0.373792i
$103$		−	5.01395i		−	0.494040i	−0.969010	−	0.247020i	$-0.920549\pi$
$103$		−	5.01395i		−	0.494040i	0.969010	−	0.247020i	$-0.0794513\pi$
$104$	9.36576	−	6.99126i	0.918389	−	0.685549i
$105$	0.491627	+	1.66081i	0.0479779	+	0.162079i
$106$	1.22090	+	5.62466i	0.118584	+	0.546316i
$107$	11.8920			1.14964			0.574821	−	0.818279i	$-0.305072\pi$
$107$	11.8920			1.14964			0.574821	+	0.818279i	$0.305072\pi$
$108$	9.98783	+	2.87109i	0.961080	+	0.276271i
$109$	−16.3083			−1.56205			−0.781025	−	0.624500i	$-0.785303\pi$
$109$	−16.3083			−1.56205			−0.781025	+	0.624500i	$0.785303\pi$
$110$	0.537794	+	2.47761i	0.0512766	+	0.236231i
$111$	2.45869	+	8.30592i	0.233368	+	0.788363i
$112$	3.01824	+	2.62492i	0.285197	+	0.248032i
$113$		−	20.0948i		−	1.89036i	−0.326551	−	0.945180i	$-0.605886\pi$
$113$		−	20.0948i		−	1.89036i	0.326551	−	0.945180i	$-0.394114\pi$
$114$	−12.0836	+	6.62554i	−1.13173	+	0.620539i
$115$		−	6.63263i		−	0.618496i
$116$	4.15632	+	9.12296i	0.385904	+	0.847045i
$117$	10.3989	−	6.74776i	0.961379	−	0.623831i
$118$	−8.20282	+	1.78052i	−0.755131	+	0.163910i
$119$	3.20559			0.293856
$120$	−2.93256	+	3.92429i	−0.267705	+	0.358237i
$121$	−7.78612			−0.707829
$122$	−11.5498	+	2.50701i	−1.04567	+	0.226974i
$123$	4.39764	−	1.30177i	0.396522	−	0.117377i
$124$	−0.131356	−	0.288322i	−0.0117962	−	0.0258921i
$125$		−	1.00000i		−	0.0894427i
$126$	3.01181	+	2.98815i	0.268313	+	0.266205i
$127$		−	5.56526i		−	0.493837i	−0.969036	−	0.246919i	$-0.920582\pi$
$127$		−	5.56526i		−	0.493837i	0.969036	−	0.246919i	$-0.0794180\pi$
$128$	−0.842938	+	11.2823i	−0.0745059	+	0.997221i
$129$	9.46124	−	2.80068i	0.833016	−	0.246586i
$130$	1.23958	+	5.71071i	0.108718	+	0.500863i
$131$	−6.38242			−0.557634			−0.278817	−	0.960344i	$-0.589942\pi$
$131$	−6.38242			−0.557634			−0.278817	+	0.960344i	$0.589942\pi$
$132$	4.07287	+	4.68810i	0.354498	+	0.408047i
$133$	−5.62600			−0.487836
$134$	−3.59800	−	16.5759i	−0.310820	−	1.43194i
$135$	−3.37678	+	3.94935i	−0.290627	+	0.339906i
$136$	5.42364	+	7.26573i	0.465074	+	0.623031i
$137$			19.7697i			1.68904i	0.535525	+	0.844519i	$0.320114\pi$
$137$			19.7697i			1.68904i	−0.535525	+	0.844519i	$0.679886\pi$
$138$	−7.81102	−	14.2457i	−0.664918	−	1.21267i
$139$		−	19.5041i		−	1.65432i	−0.561966	−	0.827160i	$-0.689955\pi$
$139$		−	19.5041i		−	1.65432i	0.561966	−	0.827160i	$-0.310045\pi$
$140$	−1.82002	+	0.829179i	−0.153820	+	0.0700784i
$141$	2.14684	+	7.25244i	0.180796	+	0.610766i
$142$	19.9340	−	4.32690i	1.67282	−	0.363105i
$143$	7.40777			0.619469
$144$	−1.67710	+	11.8822i	−0.139758	+	0.990186i
$145$	−5.01257			−0.416271
$146$	18.7093	−	4.06108i	1.54839	−	0.336097i
$147$	0.491627	+	1.66081i	0.0405487	+	0.136982i
$148$	−9.10212	+	4.14682i	−0.748189	+	0.340867i
$149$		−	5.22078i		−	0.427703i	−0.976866	−	0.213851i	$-0.931399\pi$
$149$		−	5.22078i		−	0.427703i	0.976866	−	0.213851i	$-0.0686008\pi$
$150$	−1.17766	−	2.14781i	−0.0961559	−	0.175368i
$151$			0.627435i			0.0510599i	0.999674	+	0.0255300i	$0.00812732\pi$
$151$			0.627435i			0.0510599i	−0.999674	+	0.0255300i	$0.991873\pi$
$152$	−9.51880	−	12.7518i	−0.772076	−	1.03430i
$153$	5.23474	+	8.06722i	0.423204	+	0.652196i
$154$	0.537794	+	2.47761i	0.0433367	+	0.199651i
$155$	0.158417			0.0127244
$156$	9.38768	+	10.8057i	0.751616	+	0.865152i
$157$	−18.7067			−1.49295			−0.746477	−	0.665411i	$-0.768256\pi$
$157$	−18.7067			−1.49295			−0.746477	+	0.665411i	$0.768256\pi$
$158$	2.11353	+	9.73699i	0.168143	+	0.774633i
$159$	−6.75927	+	2.00085i	−0.536045	+	0.158678i
$160$	−4.95874	−	2.72229i	−0.392023	−	0.215216i
$161$		−	6.63263i		−	0.522725i
$162$	−2.60170	+	12.4592i	−0.204409	+	0.978886i
$163$		−	13.2159i		−	1.03515i	−0.855638	−	0.517575i	$-0.826835\pi$
$163$		−	13.2159i		−	1.03515i	0.855638	−	0.517575i	$-0.173165\pi$
$164$	2.19557	+	4.81919i	0.171445	+	0.376315i
$165$	−2.97739	+	0.881355i	−0.231790	+	0.0686134i
$166$	−17.2779	+	3.75037i	−1.34102	+	0.291085i
$167$	17.3305			1.34107			0.670537	−	0.741876i	$-0.266064\pi$
$167$	17.3305			1.34107			0.670537	+	0.741876i	$0.266064\pi$
$168$	−2.93256	+	3.92429i	−0.226252	+	0.302766i
$169$	4.07439			0.313415
$170$	−4.43023	+	0.961633i	−0.339783	+	0.0737539i
$171$	−9.18727	−	14.1584i	−0.702568	−	1.08272i
$172$	4.72363	+	10.3682i	0.360173	+	0.790567i
$173$			11.6952i			0.889173i	0.895736	+	0.444587i	$0.146649\pi$
$173$			11.6952i			0.889173i	−0.895736	+	0.444587i	$0.853351\pi$
$174$	−10.7661	+	5.90312i	−0.816173	+	0.447514i
$175$		−	1.00000i		−	0.0755929i
$176$	−4.70578	+	5.41089i	−0.354712	+	0.407861i
$177$	−2.91797	−	9.85749i	−0.219328	−	0.740935i
$178$	1.25401	+	5.77721i	0.0939921	+	0.433020i
$179$	−5.35155			−0.399994			−0.199997	−	0.979797i	$-0.564093\pi$
$179$	−5.35155			−0.399994			−0.199997	+	0.979797i	$0.564093\pi$
$180$	−5.05881	−	3.22621i	−0.377061	−	0.240468i
$181$	−4.89985			−0.364203			−0.182102	−	0.983280i	$-0.558290\pi$
$181$	−4.89985			−0.364203			−0.182102	+	0.983280i	$0.558290\pi$
$182$	1.23958	+	5.71071i	0.0918835	+	0.423306i
$183$	−4.10858	−	13.8796i	−0.303715	−	1.02601i
$184$	15.0334	−	11.2220i	1.10827	−	0.827293i
$185$		−	5.00112i		−	0.367689i
$186$	0.340251	−	0.186563i	0.0249484	−	0.0136794i
$187$			5.74677i			0.420245i
$188$	−7.94765	+	3.62086i	−0.579642	+	0.264078i
$189$	−3.37678	+	3.94935i	−0.245625	+	0.287273i
$190$	7.77530	−	1.68772i	0.564080	−	0.122440i
$191$	−20.5968			−1.49033			−0.745166	−	0.666879i	$-0.767630\pi$
$191$	−20.5968			−1.49033			−0.745166	+	0.666879i	$0.767630\pi$
$192$	−13.8564	−	0.00725033i	−1.00000	−	0.000523248i
$193$	−16.3191			−1.17468			−0.587338	−	0.809342i	$-0.699824\pi$
$193$	−16.3191			−1.17468			−0.587338	+	0.809342i	$0.699824\pi$
$194$	−21.2479	+	4.61209i	−1.52551	+	0.331129i
$195$	−6.86268	+	2.03146i	−0.491447	+	0.145476i
$196$	−1.82002	+	0.829179i	−0.130001	+	0.0592271i
$197$			14.2843i			1.01772i	0.860850	+	0.508858i	$0.169932\pi$
$197$			14.2843i			1.01772i	−0.860850	+	0.508858i	$0.830068\pi$
$198$	−5.35694	+	5.39936i	−0.380701	+	0.383716i
$199$		−	0.193905i		−	0.0137456i	−0.999976	−	0.00687278i	$-0.997812\pi$
$199$		−	0.193905i		−	0.0137456i	0.999976	−	0.00687278i	$-0.00218769\pi$
$200$	2.26658	−	1.69193i	0.160271	−	0.119638i
$201$	19.9197	−	5.89653i	1.40502	−	0.415909i
$202$	−0.742032	−	3.41853i	−0.0522092	−	0.240527i
$203$	−5.01257			−0.351813
$204$	−8.38283	+	7.28273i	−0.586915	+	0.509893i
$205$	−2.64788			−0.184936
$206$	1.50412	+	6.92944i	0.104797	+	0.482797i
$207$	16.6917	−	10.8311i	1.16015	−	0.752814i
$208$	−10.8465	+	12.4717i	−0.752069	+	0.864759i
$209$		−	10.0859i		−	0.697656i
$210$	−1.17766	−	2.14781i	−0.0812666	−	0.148213i
$211$			4.57431i			0.314908i	0.987526	+	0.157454i	$0.0503287\pi$
$211$			4.57431i			0.314908i	−0.987526	+	0.157454i	$0.949671\pi$
$212$	−3.37464	−	7.40721i	−0.231771	−	0.508729i
$213$	7.09107	+	23.9550i	0.485872	+	1.64137i
$214$	−16.4351	+	3.56743i	−1.12348	+	0.243864i
$215$	−5.69675			−0.388515
$216$	−14.6648	−	0.971724i	−0.997812	−	0.0661175i
$217$	0.158417			0.0107541
$218$	22.5385	−	4.89225i	1.52650	−	0.331345i
$219$	6.65543	+	22.4834i	0.449732	+	1.51928i
$220$	−1.48650	−	3.26280i	−0.100219	−	0.219978i
$221$			13.2459i			0.891015i
$222$	−5.88964	−	10.7415i	−0.395287	−	0.720920i
$223$			11.5985i			0.776690i	0.921514	+	0.388345i	$0.126953\pi$
$223$			11.5985i			0.776690i	−0.921514	+	0.388345i	$0.873047\pi$
$224$	−4.95874	−	2.72229i	−0.331320	−	0.181891i
$225$	2.51661	−	1.63300i	0.167774	−	0.108867i
$226$	6.02816	+	27.7716i	0.400987	+	1.84734i
$227$	3.35509			0.222685			0.111343	−	0.993782i	$-0.464485\pi$
$227$	3.35509			0.222685			0.111343	+	0.993782i	$0.464485\pi$
$228$	14.7123	−	12.7816i	0.974348	−	0.846483i
$229$	26.3034			1.73818			0.869089	−	0.494656i	$-0.164706\pi$
$229$	26.3034			1.73818			0.869089	+	0.494656i	$0.164706\pi$
$230$	1.98970	+	9.16650i	0.131197	+	0.604421i
$231$	−2.97739	+	0.881355i	−0.195898	+	0.0579889i
$232$	−8.48091	−	11.3614i	−0.556799	−	0.745910i
$233$		−	10.8172i		−	0.708660i	−0.935120	−	0.354330i	$-0.884709\pi$
$233$		−	10.8172i		−	0.708660i	0.935120	−	0.354330i	$-0.115291\pi$
$234$	−12.3474	+	12.4451i	−0.807173	+	0.813564i
$235$		−	4.36680i		−	0.284859i
$236$	10.8024	−	4.92146i	0.703178	−	0.320360i
$237$	−11.7011	+	3.46372i	−0.760070	+	0.224993i
$238$	−4.43023	+	0.961633i	−0.287169	+	0.0623334i
$239$	0.903077			0.0584152			0.0292076	−	0.999573i	$-0.490702\pi$
$239$	0.903077			0.0584152			0.0292076	+	0.999573i	$0.490702\pi$
$240$	2.87566	−	6.30322i	0.185623	−	0.406871i
$241$	9.14417			0.589028			0.294514	−	0.955647i	$-0.404842\pi$
$241$	9.14417			0.589028			0.294514	+	0.955647i	$0.404842\pi$
$242$	10.7607	−	2.33572i	0.691721	−	0.150146i
$243$	−15.4532	−	2.04874i	−0.991326	−	0.131427i
$244$	15.2101	−	6.92954i	0.973725	−	0.443618i
$245$		−	1.00000i		−	0.0638877i
$246$	−5.68716	+	3.11832i	−0.362600	+	0.198817i
$247$		−	23.2473i		−	1.47919i
$248$	0.268031	+	0.359065i	0.0170200	+	0.0228007i
$249$	−6.14623	−	20.7632i	−0.389502	−	1.31581i
$250$	0.299986	+	1.38203i	0.0189728	+	0.0874073i
$251$	10.1482			0.640548			0.320274	−	0.947325i	$-0.396225\pi$
$251$	10.1482			0.640548			0.320274	+	0.947325i	$0.396225\pi$
$252$	−5.05881	−	3.22621i	−0.318675	−	0.203232i
$253$	11.8905			0.747551
$254$	1.66950	+	7.69136i	0.104754	+	0.482599i
$255$	−1.57596	−	5.32390i	−0.0986903	−	0.333395i
$256$	−2.21955	−	15.8453i	−0.138722	−	0.990331i
$257$			18.5968i			1.16004i	0.814603	+	0.580019i	$0.196955\pi$
$257$			18.5968i			1.16004i	−0.814603	+	0.580019i	$0.803045\pi$
$258$	−12.2356	+	6.70886i	−0.761753	+	0.417675i
$259$		−	5.00112i		−	0.310754i
$260$	−3.42627	−	7.52052i	−0.212488	−	0.466403i
$261$	−8.18553	−	12.6147i	−0.506672	−	0.780827i
$262$	8.82069	−	1.91463i	0.544944	−	0.118287i
$263$	24.0062			1.48029			0.740143	−	0.672450i	$-0.234758\pi$
$263$	24.0062			1.48029			0.740143	+	0.672450i	$0.234758\pi$
$264$	−7.03520	−	5.25730i	−0.432987	−	0.323564i
$265$	4.06986			0.250009
$266$	7.77530	−	1.68772i	0.476734	−	0.103481i
$267$	−6.94259	+	2.05512i	−0.424880	+	0.125771i
$268$	9.94510	+	21.8291i	0.607494	+	1.33343i
$269$			23.9430i			1.45983i	0.683538	+	0.729915i	$0.260440\pi$
$269$			23.9430i			1.45983i	−0.683538	+	0.729915i	$0.739560\pi$
$270$	3.48207	−	6.47110i	0.211912	−	0.393819i
$271$		−	9.37313i		−	0.569377i	−0.958620	−	0.284689i	$-0.908110\pi$
$271$		−	9.37313i		−	0.569377i	0.958620	−	0.284689i	$-0.0918902\pi$
$272$	−9.67526	−	8.41444i	−0.586649	−	0.510200i
$273$	−6.86268	+	2.03146i	−0.415348	+	0.122950i
$274$	−5.93063	−	27.3223i	−0.358282	−	1.65060i
$275$	1.79273			0.108106
$276$	15.0686	+	17.3447i	0.907021	+	1.04403i
$277$	−6.73300			−0.404547			−0.202273	−	0.979329i	$-0.564833\pi$
$277$	−6.73300			−0.404547			−0.202273	+	0.979329i	$0.564833\pi$
$278$	5.85097	+	26.9553i	0.350918	+	1.61667i
$279$	0.258696	+	0.398674i	0.0154877	+	0.0238680i
$280$	2.26658	−	1.69193i	0.135454	−	0.101112i
$281$			10.8311i			0.646128i	0.946377	+	0.323064i	$0.104713\pi$
$281$			10.8311i			0.646128i	−0.946377	+	0.323064i	$0.895287\pi$
$282$	−5.14263	−	9.37908i	−0.306239	−	0.558516i
$283$			29.5473i			1.75640i	0.478290	+	0.878202i	$0.341257\pi$
$283$			29.5473i			1.75640i	−0.478290	+	0.878202i	$0.658743\pi$
$284$	−26.2513	+	11.9598i	−1.55773	+	0.709685i
$285$	2.76589	+	9.34374i	0.163837	+	0.553475i
$286$	−10.2378	+	2.22223i	−0.605372	+	0.131403i
$287$	−2.64788			−0.156299
$288$	−1.24670	−	16.9247i	−0.0734622	−	0.997298i
$289$	6.72416			0.395539
$290$	6.92752	−	1.50370i	0.406798	−	0.0883002i
$291$	−7.55846	−	25.5340i	−0.443085	−	1.49683i
$292$	−24.6386	+	11.2251i	−1.44186	+	0.656897i
$293$			8.74776i			0.511050i	0.966803	+	0.255525i	$0.0822482\pi$
$293$			8.74776i			0.511050i	−0.966803	+	0.255525i	$0.917752\pi$
$294$	−1.17766	−	2.14781i	−0.0686828	−	0.125263i
$295$			5.93534i			0.345569i
$296$	11.3354	−	8.46154i	0.658858	−	0.491817i
$297$	−7.08011	−	6.05367i	−0.410830	−	0.351269i
$298$	1.56616	+	7.21527i	0.0907252	+	0.417970i
$299$	27.4068			1.58498
$300$	2.27188	+	2.61506i	0.131167	+	0.150981i
$301$	−5.69675			−0.328355
$302$	−0.188222	−	0.867134i	−0.0108309	−	0.0498979i
$303$	4.10812	−	1.21607i	0.236005	−	0.0698612i
$304$	16.9806	+	14.7678i	0.973905	+	0.846992i
$305$			8.35711i			0.478527i
$306$	−9.65463	−	9.57879i	−0.551918	−	0.547583i
$307$		−	5.48421i		−	0.313001i	−0.987678	−	0.156500i	$-0.949979\pi$
$307$		−	5.48421i		−	0.313001i	0.987678	−	0.156500i	$-0.0500212\pi$
$308$	−1.48650	−	3.26280i	−0.0847009	−	0.185915i
$309$	−8.32724	+	2.46500i	−0.473720	+	0.140229i
$310$	−0.218938	+	0.0475230i	−0.0124348	+	0.00269913i
$311$	−4.82452			−0.273574			−0.136787	−	0.990601i	$-0.543678\pi$
$311$	−4.82452			−0.273574			−0.136787	+	0.990601i	$0.543678\pi$
$312$	−16.2156	−	12.1177i	−0.918030	−	0.686029i
$313$	26.6672			1.50732			0.753660	−	0.657264i	$-0.228286\pi$
$313$	26.6672			1.50732			0.753660	+	0.657264i	$0.228286\pi$
$314$	25.8532	−	5.61174i	1.45898	−	0.316689i
$315$	2.51661	−	1.63300i	0.141795	−	0.0920093i
$316$	−5.84192	−	12.8228i	−0.328634	−	0.721338i
$317$			25.4563i			1.42977i	0.699242	+	0.714885i	$0.253521\pi$
$317$			25.4563i			1.42977i	−0.699242	+	0.714885i	$0.746479\pi$
$318$	8.74129	−	4.79292i	0.490187	−	0.268774i
$319$		−	8.98618i		−	0.503130i
$320$	7.66978	+	2.27474i	0.428754	+	0.127162i
$321$	−5.84642	−	19.7504i	−0.326315	−	1.10236i
$322$	1.98970	+	9.16650i	0.110881	+	0.510829i
$323$	18.0347			1.00348
$324$	−0.141946	−	17.9994i	−0.00788589	−	0.999969i
$325$	4.13212			0.229209
$326$	3.96459	+	18.2648i	0.219578	+	1.01159i
$327$	8.01759	+	27.0850i	0.443374	+	1.49780i
$328$	−4.48003	−	6.00163i	−0.247368	−	0.331384i
$329$		−	4.36680i		−	0.240750i
$330$	3.85045	−	2.11124i	0.211960	−	0.116220i
$331$			9.63318i			0.529488i	0.964319	+	0.264744i	$0.0852874\pi$
$331$			9.63318i			0.529488i	−0.964319	+	0.264744i	$0.914713\pi$
$332$	22.7535	−	10.3662i	1.24876	−	0.568921i
$333$	12.5858	−	8.16684i	0.689700	−	0.447540i
$334$	−23.9513	+	5.19890i	−1.31056	+	0.284471i
$335$	−11.9939			−0.655297
$336$	2.87566	−	6.30322i	0.156880	−	0.343869i
$337$	6.99407			0.380991			0.190496	−	0.981688i	$-0.438991\pi$
$337$	6.99407			0.380991			0.190496	+	0.981688i	$0.438991\pi$
$338$	−5.63094	+	1.22226i	−0.306283	+	0.0664822i
$339$	−33.3737	+	9.87915i	−1.81261	+	0.536562i
$340$	5.83424	−	2.65801i	0.316406	−	0.144151i
$341$			0.284000i			0.0153795i
$342$	16.9444	+	16.8113i	0.916249	+	0.909052i
$343$		−	1.00000i		−	0.0539949i
$344$	−9.63851	−	12.9121i	−0.519673	−	0.696175i
$345$	−11.0156	+	3.26078i	−0.593058	+	0.175555i
$346$	−3.50841	−	16.1632i	−0.188613	−	0.868939i
$347$	−22.6749			−1.21725			−0.608625	−	0.793458i	$-0.708279\pi$
$347$	−22.6749			−1.21725			−0.608625	+	0.793458i	$0.708279\pi$
$348$	13.1082	−	11.3880i	0.702672	−	0.610459i
$349$	13.7298			0.734940			0.367470	−	0.930035i	$-0.380224\pi$
$349$	13.7298			0.734940			0.367470	+	0.930035i	$0.380224\pi$
$350$	0.299986	+	1.38203i	0.0160349	+	0.0738726i
$351$	−16.3192	−	13.9533i	−0.871052	−	0.744770i
$352$	4.88034	−	8.88969i	0.260123	−	0.473822i
$353$		−	36.6761i		−	1.95207i	−0.217615	−	0.976035i	$-0.569828\pi$
$353$		−	36.6761i		−	1.95207i	0.217615	−	0.976035i	$-0.430172\pi$
$354$	6.98984	+	12.7480i	0.371506	+	0.677549i
$355$		−	14.4237i		−	0.765529i
$356$	−3.46616	−	7.60810i	−0.183706	−	0.403228i
$357$	−1.57596	−	5.32390i	−0.0834085	−	0.281770i
$358$	7.39601	−	1.60539i	0.390891	−	0.0848475i
$359$	24.5188			1.29405			0.647026	−	0.762468i	$-0.276012\pi$
$359$	24.5188			1.29405			0.647026	+	0.762468i	$0.276012\pi$
$360$	7.95925	+	2.94115i	0.419489	+	0.155012i
$361$	−12.6519			−0.665887
$362$	6.77175	−	1.46989i	0.355915	−	0.0772555i
$363$	3.82787	+	12.9313i	0.200911	+	0.678717i
$364$	−3.42627	−	7.52052i	−0.179585	−	0.394183i
$365$		−	13.5376i		−	0.708588i
$366$	9.84187	+	17.9495i	0.514443	+	0.938236i
$367$			31.6652i			1.65291i	0.563003	+	0.826455i	$0.309646\pi$
$367$			31.6652i			1.65291i	−0.563003	+	0.826455i	$0.690354\pi$
$368$	−17.4102	+	20.0189i	−0.907567	+	1.04356i
$369$	−4.32400	−	6.66367i	−0.225098	−	0.346897i
$370$	1.50026	+	6.91170i	0.0779950	+	0.359322i
$371$	4.06986			0.211296
$372$	−0.414272	+	0.359906i	−0.0214790	+	0.0186603i
$373$	19.4926			1.00929			0.504644	−	0.863328i	$-0.331624\pi$
$373$	19.4926			1.00929			0.504644	+	0.863328i	$0.331624\pi$
$374$	−1.72395	−	7.94221i	−0.0891433	−	0.410682i
$375$	−1.66081	+	0.491627i	−0.0857641	+	0.0253875i
$376$	9.89769	−	7.38833i	0.510435	−	0.381024i
$377$		−	20.7125i		−	1.06675i
$378$	3.48207	−	6.47110i	0.179098	−	0.332838i
$379$			18.9243i			0.972078i	0.873937	+	0.486039i	$0.161559\pi$
$379$			18.9243i			0.972078i	−0.873937	+	0.486039i	$0.838441\pi$
$380$	−10.2394	+	4.66496i	−0.525271	+	0.239307i
$381$	−9.24286	+	2.73603i	−0.473526	+	0.140171i
$382$	28.4654	−	6.17875i	1.45642	−	0.316132i
$383$	−23.5579			−1.20375			−0.601877	−	0.798589i	$-0.705580\pi$
$383$	−23.5579			−1.20375			−0.601877	+	0.798589i	$0.705580\pi$
$384$	19.1521	−	4.14671i	0.977354	−	0.211611i
$385$	1.79273			0.0913660
$386$	22.5535	−	4.89551i	1.14794	−	0.249175i
$387$	−9.30281	−	14.3365i	−0.472888	−	0.728764i
$388$	27.9816	−	12.7481i	1.42055	−	0.647187i
$389$		−	38.4938i		−	1.95171i	−0.218412	−	0.975857i	$-0.570088\pi$
$389$		−	38.4938i		−	1.95171i	0.218412	−	0.975857i	$-0.429912\pi$
$390$	8.87502	−	4.86625i	0.449404	−	0.246412i
$391$			21.2615i			1.07524i
$392$	2.26658	−	1.69193i	0.114479	−	0.0854554i
$393$	3.13777	+	10.6000i	0.158280	+	0.534700i
$394$	−4.28510	−	19.7414i	−0.215880	−	0.994557i
$395$	7.04542			0.354494
$396$	5.78373	−	9.06908i	0.290643	−	0.455739i
$397$	−10.4041			−0.522167			−0.261084	−	0.965316i	$-0.584080\pi$
$397$	−10.4041			−0.522167			−0.261084	+	0.965316i	$0.584080\pi$
$398$	0.0581688	+	0.267983i	0.00291574	+	0.0134328i
$399$	2.76589	+	9.34374i	0.138468	+	0.467772i
$400$	−2.62492	+	3.01824i	−0.131246	+	0.150912i
$401$		−	9.59749i		−	0.479276i	−0.970862	−	0.239638i	$-0.922971\pi$
$401$		−	9.59749i		−	0.479276i	0.970862	−	0.239638i	$-0.0770287\pi$
$402$	−25.7607	+	14.1248i	−1.28483	+	0.704481i
$403$			0.654600i			0.0326079i
$404$	2.05102	+	4.50191i	0.102042	+	0.223979i
$405$	8.21925	+	3.66660i	0.408418	+	0.182195i
$406$	6.92752	−	1.50370i	0.343807	−	0.0746273i
$407$	8.96566			0.444411
$408$	9.40061	−	12.5797i	0.465400	−	0.622788i
$409$	−5.88116			−0.290804			−0.145402	−	0.989373i	$-0.546448\pi$
$409$	−5.88116			−0.290804			−0.145402	+	0.989373i	$0.546448\pi$
$410$	3.65945	−	0.794327i	0.180727	−	0.0392290i
$411$	32.8338	−	9.71932i	1.61957	−	0.479419i
$412$	−4.15747	−	9.12548i	−0.204824	−	0.449580i
$413$			5.93534i			0.292059i
$414$	−19.8193	+	19.9762i	−0.974065	+	0.981777i
$415$			12.5018i			0.613690i
$416$	11.2488	−	20.4901i	0.551520	−	1.00461i
$417$	−32.3928	+	9.58877i	−1.58628	+	0.469564i
$418$	3.02563	+	13.9390i	0.147988	+	0.681780i
$419$	−37.3805			−1.82616			−0.913078	−	0.407785i	$-0.866301\pi$
$419$	−37.3805			−1.82616			−0.913078	+	0.407785i	$0.866301\pi$
$420$	2.27188	+	2.61506i	0.110857	+	0.127602i
$421$	−25.3285			−1.23444			−0.617218	−	0.786792i	$-0.711740\pi$
$421$	−25.3285			−1.23444			−0.617218	+	0.786792i	$0.711740\pi$
$422$	−1.37223	−	6.32183i	−0.0667990	−	0.307742i
$423$	10.9895	−	7.13100i	0.534329	−	0.346721i
$424$	6.88591	+	9.22464i	0.334409	+	0.447988i
$425$			3.20559i			0.155494i
$426$	−16.9863	−	30.9794i	−0.822987	−	1.50096i
$427$			8.35711i			0.404429i
$428$	21.6436	−	9.86059i	1.04618	−	0.476629i
$429$	−3.64186	−	12.3029i	−0.175831	−	0.593991i
$430$	7.87308	−	1.70894i	0.379674	−	0.0824126i
$431$	14.4194			0.694558			0.347279	−	0.937762i	$-0.387106\pi$
$431$	14.4194			0.694558			0.347279	+	0.937762i	$0.387106\pi$
$432$	20.5587	−	3.05627i	0.989130	−	0.147045i
$433$	−20.8157			−1.00034			−0.500168	−	0.865928i	$-0.666729\pi$
$433$	−20.8157			−1.00034			−0.500168	+	0.865928i	$0.666729\pi$
$434$	−0.218938	+	0.0475230i	−0.0105094	+	0.00228118i
$435$	2.46431	+	8.32494i	0.118155	+	0.399150i
$436$	−29.6813	+	13.5225i	−1.42148	+	0.647610i
$437$		−	37.3152i		−	1.78503i
$438$	−15.9427	−	29.0762i	−0.761772	−	1.38931i
$439$			12.5767i			0.600253i	0.953899	+	0.300126i	$0.0970288\pi$
$439$			12.5767i			0.600253i	−0.953899	+	0.300126i	$0.902971\pi$
$440$	3.03318	+	4.06336i	0.144601	+	0.193713i
$441$	2.51661	−	1.63300i	0.119838	−	0.0777620i
$442$	−3.97358	−	18.3062i	−0.189004	−	0.870739i
$443$	−19.9678			−0.948697			−0.474348	−	0.880337i	$-0.657316\pi$
$443$	−19.9678			−0.948697			−0.474348	+	0.880337i	$0.657316\pi$
$444$	11.3619	+	13.0782i	0.539214	+	0.620665i
$445$	4.18024			0.198162
$446$	−3.47937	−	16.0294i	−0.164753	−	0.759015i
$447$	−8.67074	+	2.56668i	−0.410112	+	0.121400i
$448$	7.66978	+	2.27474i	0.362363	+	0.107471i
$449$			2.91910i			0.137761i	0.997625	+	0.0688805i	$0.0219427\pi$
$449$			2.91910i			0.137761i	−0.997625	+	0.0688805i	$0.978057\pi$
$450$	−2.98815	+	3.01181i	−0.140863	+	0.141978i
$451$		−	4.74694i		−	0.223525i
$452$	−16.6622	−	36.5729i	−0.783723	−	1.72024i
$453$	1.04205	−	0.308464i	0.0489599	−	0.0144929i
$454$	−4.63684	+	1.00648i	−0.217618	+	0.0472365i
$455$	4.13212			0.193717
$456$	−16.4986	+	22.0781i	−0.772618	+	1.03390i
$457$	5.18833			0.242700			0.121350	−	0.992610i	$-0.461278\pi$
$457$	5.18833			0.242700			0.121350	+	0.992610i	$0.461278\pi$
$458$	−36.3521	+	7.89065i	−1.69862	+	0.368706i
$459$	10.8246	−	12.6600i	0.505249	−	0.590918i
$460$	−5.49964	−	12.0715i	−0.256422	−	0.562837i
$461$			7.49669i			0.349156i	0.984643	+	0.174578i	$0.0558560\pi$
$461$			7.49669i			0.349156i	−0.984643	+	0.174578i	$0.944144\pi$
$462$	3.85045	−	2.11124i	0.179139	−	0.0982236i
$463$			24.1336i			1.12159i	0.827956	+	0.560793i	$0.189504\pi$
$463$			24.1336i			1.12159i	−0.827956	+	0.560793i	$0.810496\pi$
$464$	15.1291	+	13.1576i	0.702352	+	0.610826i
$465$	−0.0778823	−	0.263102i	−0.00361171	−	0.0122011i
$466$	3.24501	+	14.9497i	0.150322	+	0.692533i
$467$	20.1375			0.931854			0.465927	−	0.884823i	$-0.345721\pi$
$467$	20.1375			0.931854			0.465927	+	0.884823i	$0.345721\pi$
$468$	13.3311	−	20.9036i	0.616230	−	0.966269i
$469$	−11.9939			−0.553827
$470$	1.30998	+	6.03505i	0.0604248	+	0.278376i
$471$	9.19671	+	31.0683i	0.423762	+	1.43155i
$472$	−13.4529	+	10.0422i	−0.619220	+	0.462229i
$473$		−	10.2127i		−	0.469582i
$474$	15.1323	−	8.29714i	0.695048	−	0.381100i
$475$		−	5.62600i		−	0.258138i
$476$	5.83424	−	2.65801i	0.267412	−	0.121830i
$477$	6.64608	+	10.2422i	0.304303	+	0.468959i
$478$	−1.24808	+	0.270910i	−0.0570858	+	0.0123911i
$479$	−1.59214			−0.0727469			−0.0363735	−	0.999338i	$-0.511581\pi$
$479$	−1.59214			−0.0727469			−0.0363735	+	0.999338i	$0.511581\pi$
$480$	−2.08337	+	9.57390i	−0.0950925	+	0.436987i
$481$	20.6652			0.942252
$482$	−12.6375	+	2.74312i	−0.575623	+	0.124946i
$483$	−11.0156	+	3.26078i	−0.501226	+	0.148371i
$484$	−14.1709	+	6.45609i	−0.644130	+	0.293458i
$485$			15.3744i			0.698114i
$486$	21.9714	−	1.80433i	0.996645	−	0.0818460i
$487$			2.90890i			0.131815i	0.997826	+	0.0659074i	$0.0209942\pi$
$487$			2.90890i			0.131815i	−0.997826	+	0.0659074i	$0.979006\pi$
$488$	−18.9420	+	14.1396i	−0.857465	+	0.640072i
$489$	−21.9492	+	6.49730i	−0.992576	+	0.293818i
$490$	0.299986	+	1.38203i	0.0135520	+	0.0624338i
$491$	−12.9646			−0.585086			−0.292543	−	0.956252i	$-0.594501\pi$
$491$	−12.9646			−0.585086			−0.292543	+	0.956252i	$0.594501\pi$
$492$	6.92437	−	6.01567i	0.312175	−	0.271208i
$493$	16.0683			0.723678
$494$	6.97386	+	32.1285i	0.313769	+	1.44553i
$495$	2.92753	+	4.51160i	0.131583	+	0.202781i
$496$	−0.478142	−	0.415834i	−0.0214692	−	0.0186715i
$497$		−	14.4237i		−	0.646990i
$498$	14.7229	+	26.8516i	0.659751	+	1.20325i
$499$		−	18.5099i		−	0.828618i	−0.910136	−	0.414309i	$-0.864023\pi$
$499$		−	18.5099i		−	0.828618i	0.910136	−	0.414309i	$-0.135977\pi$
$500$	−0.829179	−	1.82002i	−0.0370820	−	0.0813936i
$501$	−8.52014	−	28.7827i	−0.380652	−	1.28592i
$502$	−14.0251	+	3.04431i	−0.625971	+	0.135874i
$503$	−13.0302			−0.580986			−0.290493	−	0.956877i	$-0.593819\pi$
$503$	−13.0302			−0.580986			−0.290493	+	0.956877i	$0.593819\pi$
$504$	7.95925	+	2.94115i	0.354533	+	0.131009i
$505$	−2.47356			−0.110072
$506$	−16.4331	+	3.56699i	−0.730539	+	0.158572i
$507$	−2.00308	−	6.76681i	−0.0889600	−	0.300525i
$508$	−4.61460	−	10.1289i	−0.204740	−	0.449396i
$509$			21.1325i			0.936684i	0.883547	+	0.468342i	$0.155148\pi$
$509$			21.1325i			0.936684i	−0.883547	+	0.468342i	$0.844852\pi$
$510$	3.77512	+	6.88502i	0.167165	+	0.304874i
$511$		−	13.5376i		−	0.598866i
$512$	7.82086	+	21.2329i	0.345636	+	0.938369i
$513$	−18.9978	+	22.2190i	−0.838773	+	0.980993i
$514$	−5.57878	−	25.7014i	−0.246070	−	1.13364i
$515$	5.01395			0.220941
$516$	14.8974	−	12.9423i	0.655820	−	0.569755i
$517$	7.82850			0.344297
$518$	1.50026	+	6.91170i	0.0659178	+	0.303682i
$519$	19.4236	−	5.74970i	0.852603	−	0.252384i
$520$	6.99126	+	9.36576i	0.306587	+	0.410716i
$521$			10.1916i			0.446504i	0.974761	+	0.223252i	$0.0716673\pi$
$521$			10.1916i			0.446504i	−0.974761	+	0.223252i	$0.928333\pi$
$522$	15.0969	+	14.9783i	0.660772	+	0.655582i
$523$			18.7859i			0.821452i	0.911759	+	0.410726i	$0.134725\pi$
$523$			18.7859i			0.821452i	−0.911759	+	0.410726i	$0.865275\pi$
$524$	−11.6161	+	5.29217i	−0.507452	+	0.231189i
$525$	−1.66081	+	0.491627i	−0.0724839	+	0.0214564i
$526$	−33.1773	+	7.20152i	−1.44660	+	0.314001i
$527$	−0.507822			−0.0221211
$528$	11.3000	+	5.15528i	0.491768	+	0.224355i
$529$	20.9918			0.912688
$530$	−5.62466	+	1.22090i	−0.244320	+	0.0530325i
$531$	−14.9369	+	9.69243i	−0.648207	+	0.420615i
$532$	−10.2394	+	4.66496i	−0.443935	+	0.202252i
$533$		−	10.9414i		−	0.473923i
$534$	8.97837	−	4.92292i	0.388532	−	0.213035i
$535$			11.8920i			0.514135i
$536$	−20.2929	−	27.1851i	−0.876518	−	1.17422i
$537$	2.63097	+	8.88794i	0.113535	+	0.383543i
$538$	−7.18256	−	33.0899i	−0.309662	−	1.42661i
$539$	1.79273			0.0772184
$540$	−2.87109	+	9.98783i	−0.123552	+	0.429808i
$541$	−30.8391			−1.32587			−0.662937	−	0.748675i	$-0.730690\pi$
$541$	−30.8391			−1.32587			−0.662937	+	0.748675i	$0.730690\pi$
$542$	2.81181	+	12.9540i	0.120777	+	0.556420i
$543$	2.40890	+	8.13774i	0.103376	+	0.349224i
$544$	15.8957	+	8.72657i	0.681523	+	0.374149i
$545$		−	16.3083i		−	0.698570i
$546$	8.87502	−	4.86625i	0.379816	−	0.208256i
$547$			30.7015i			1.31270i	0.754455	+	0.656351i	$0.227901\pi$
$547$			30.7015i			1.31270i	−0.754455	+	0.656351i	$0.772099\pi$
$548$	16.3926	+	35.9812i	0.700258	+	1.53704i
$549$	−21.0315	+	13.6472i	−0.897604	+	0.582447i
$550$	−2.47761	+	0.537794i	−0.105646	+	0.0229316i
$551$	−28.2007			−1.20139
$552$	−26.0284	−	19.4506i	−1.10784	−	0.827873i
$553$	7.04542			0.299602
$554$	9.30521	−	2.01980i	0.395341	−	0.0858133i
$555$	−8.30592	+	2.45869i	−0.352567	+	0.104365i
$556$	−16.1724	−	35.4979i	−0.685864	−	1.50545i
$557$			38.1173i			1.61508i	0.589812	+	0.807541i	$0.299202\pi$
$557$			38.1173i			1.61508i	−0.589812	+	0.807541i	$0.700798\pi$
$558$	−0.477123	−	0.473375i	−0.0201982	−	0.0200396i
$559$		−	23.5396i		−	0.995621i
$560$	−2.62492	+	3.01824i	−0.110923	+	0.127544i
$561$	9.54431	−	2.82527i	0.402961	−	0.119283i
$562$	−3.24917	−	14.9689i	−0.137058	−	0.631424i
$563$	−12.4606			−0.525153			−0.262576	−	0.964911i	$-0.584572\pi$
$563$	−12.4606			−0.525153			−0.262576	+	0.964911i	$0.584572\pi$
$564$	9.92086	+	11.4195i	0.417744	+	0.480846i
$565$	20.0948			0.845394
$566$	−8.86377	−	40.8353i	−0.372572	−	1.71643i
$567$	8.21925	+	3.66660i	0.345176	+	0.153983i
$568$	32.6924	−	24.4039i	1.37174	−	1.02396i
$569$			33.1765i			1.39083i	0.718608	+	0.695415i	$0.244779\pi$
$569$			33.1765i			1.39083i	−0.718608	+	0.695415i	$0.755221\pi$
$570$	−6.62554	−	12.0836i	−0.277513	−	0.506126i
$571$		−	10.4334i		−	0.436625i	−0.975879	−	0.218313i	$-0.929945\pi$
$571$		−	10.4334i		−	0.436625i	0.975879	−	0.218313i	$-0.0700553\pi$
$572$	13.4823	−	6.14237i	0.563722	−	0.256826i
$573$	10.1259	+	34.2074i	0.423018	+	1.42904i
$574$	3.65945	−	0.794327i	0.152743	−	0.0331546i
$575$	6.63263			0.276600
$576$	6.80014	+	23.0165i	0.283339	+	0.959020i
$577$	9.16430			0.381515			0.190757	−	0.981637i	$-0.438906\pi$
$577$	9.16430			0.381515			0.190757	+	0.981637i	$0.438906\pi$
$578$	−9.29300	+	2.01715i	−0.386538	+	0.0839025i
$579$	8.02293	+	27.1030i	0.333421	+	1.12636i
$580$	−9.12296	+	4.15632i	−0.378810	+	0.172582i
$581$			12.5018i			0.518662i
$582$	18.1059	+	33.0213i	0.750512	+	1.36878i
$583$			7.29616i			0.302176i
$584$	30.6839	−	22.9046i	1.26971	−	0.947799i
$585$	6.74776	+	10.3989i	0.278985	+	0.429942i
$586$	−2.62420	−	12.0897i	−0.108405	−	0.499420i
$587$	−2.83840			−0.117153			−0.0585766	−	0.998283i	$-0.518656\pi$
$587$	−2.83840			−0.117153			−0.0585766	+	0.998283i	$0.518656\pi$
$588$	2.27188	+	2.61506i	0.0936908	+	0.107843i
$589$	0.891256			0.0367236
$590$	−1.78052	−	8.20282i	−0.0733028	−	0.337705i
$591$	23.7236	−	7.02257i	0.975860	−	0.288870i
$592$	−13.1275	+	15.0946i	−0.539539	+	0.620383i
$593$		−	16.8412i		−	0.691584i	−0.938311	−	0.345792i	$-0.887610\pi$
$593$		−	16.8412i		−	0.691584i	0.938311	−	0.345792i	$-0.112390\pi$
$594$	11.6009	+	6.24242i	0.475993	+	0.256129i
$595$			3.20559i			0.131417i
$596$	−4.32896	−	9.50190i	−0.177321	−	0.389213i
$597$	−0.322040	+	0.0953290i	−0.0131802	+	0.00390156i
$598$	−37.8771	+	8.22166i	−1.54891	+	0.336209i
$599$	−26.9091			−1.09948			−0.549739	−	0.835337i	$-0.685273\pi$
$599$	−26.9091			−1.09948			−0.549739	+	0.835337i	$0.685273\pi$
$600$	−3.92429	−	2.93256i	−0.160209	−	0.119721i
$601$	36.8254			1.50214			0.751070	−	0.660223i	$-0.229538\pi$
$601$	36.8254			1.50214			0.751070	+	0.660223i	$0.229538\pi$
$602$	7.87308	−	1.70894i	0.320883	−	0.0696514i
$603$	−19.5861	−	30.1839i	−0.797607	−	1.22918i
$604$	0.520256	+	1.14194i	0.0211689	+	0.0464649i
$605$		−	7.78612i		−	0.316551i
$606$	−5.31274	+	2.91302i	−0.215815	+	0.118333i
$607$		−	38.1295i		−	1.54763i	−0.633412	−	0.773814i	$-0.718346\pi$
$607$		−	38.1295i		−	1.54763i	0.633412	−	0.773814i	$-0.281654\pi$
$608$	−27.8979	−	15.3156i	−1.13141	−	0.621131i
$609$	2.46431	+	8.32494i	0.0998590	+	0.337344i
$610$	−2.50701	−	11.5498i	−0.101506	−	0.467637i
$611$	18.0441			0.729988
$612$	16.2165	+	10.3419i	0.655513	+	0.418048i
$613$	17.0813			0.689907			0.344954	−	0.938620i	$-0.387895\pi$
$613$	17.0813			0.689907			0.344954	+	0.938620i	$0.387895\pi$
$614$	1.64519	+	7.57935i	0.0663943	+	0.305878i
$615$	1.30177	+	4.39764i	0.0524924	+	0.177330i
$616$	3.03318	+	4.06336i	0.122210	+	0.163718i
$617$		−	28.7465i		−	1.15729i	−0.815580	−	0.578645i	$-0.803582\pi$
$617$		−	28.7465i		−	1.15729i	0.815580	−	0.578645i	$-0.196418\pi$
$618$	10.7690	−	5.90476i	0.433194	−	0.237524i
$619$			2.33265i			0.0937573i	0.998901	+	0.0468787i	$0.0149274\pi$
$619$			2.33265i			0.0937573i	−0.998901	+	0.0468787i	$0.985073\pi$
$620$	0.288322	−	0.131356i	0.0115793	−	0.00527540i
$621$	−26.1946	−	22.3970i	−1.05115	−	0.898760i
$622$	6.66764	−	1.44729i	0.267348	−	0.0580310i
$623$	4.18024			0.167478
$624$	26.0456	+	11.8826i	1.04266	+	0.475683i
$625$	1.00000			0.0400000
$626$	−36.8549	+	7.99979i	−1.47302	+	0.319736i
$627$	−16.7508	+	4.95850i	−0.668963	+	0.198024i
$628$	−34.0464	+	15.5112i	−1.35860	+	0.618963i
$629$			16.0316i			0.639220i
$630$	−2.98815	+	3.01181i	−0.119051	+	0.119993i
$631$			21.6458i			0.861705i	0.902422	+	0.430853i	$0.141787\pi$
$631$			21.6458i			0.861705i	−0.902422	+	0.430853i	$0.858213\pi$
$632$	11.9204	+	15.9690i	0.474167	+	0.635212i
$633$	7.59707	−	2.24885i	0.301957	−	0.0893839i
$634$	−7.63654	−	35.1814i	−0.303286	−	1.39723i
$635$	5.56526			0.220851
$636$	−10.6429	+	9.24623i	−0.422019	+	0.366637i
$637$	4.13212			0.163720
$638$	2.69573	+	12.4192i	0.106725	+	0.491680i
$639$	36.2987	−	23.5539i	1.43595	−	0.931778i
$640$	−11.2823	−	0.842938i	−0.445971	−	0.0333200i
$641$			39.0635i			1.54291i	0.636281	+	0.771457i	$0.280472\pi$
$641$			39.0635i			1.54291i	−0.636281	+	0.771457i	$0.719528\pi$
$642$	14.0048	+	25.5418i	0.552724	+	1.00805i
$643$		−	23.2994i		−	0.918840i	−0.888219	−	0.459420i	$-0.848057\pi$
$643$		−	23.2994i		−	0.918840i	0.888219	−	0.459420i	$-0.151943\pi$
$644$	−5.49964	−	12.0715i	−0.216716	−	0.475684i
$645$	2.80068	+	9.46124i	0.110277	+	0.372536i
$646$	−24.9245	+	5.41015i	−0.980640	+	0.212859i
$647$	−28.6944			−1.12809			−0.564047	−	0.825743i	$-0.690756\pi$
$647$	−28.6944			−1.12809			−0.564047	+	0.825743i	$0.690756\pi$
$648$	5.59575	+	24.8332i	0.219822	+	0.975540i
$649$	−10.6405			−0.417675
$650$	−5.71071	+	1.23958i	−0.223993	+	0.0486202i
$651$	−0.0778823	−	0.263102i	−0.00305245	−	0.0103118i
$652$	−10.9584	−	24.0532i	−0.429163	−	0.941996i
$653$		−	2.10807i		−	0.0824951i	−0.999149	−	0.0412475i	$-0.986867\pi$
$653$		−	2.10807i		−	0.0824951i	0.999149	−	0.0412475i	$-0.0131332\pi$
$654$	−19.2057	−	35.0272i	−0.751002	−	1.36967i
$655$		−	6.38242i		−	0.249382i
$656$	7.99194	+	6.95048i	0.312033	+	0.271371i
$657$	34.0687	−	22.1069i	1.32915	−	0.862471i
$658$	1.30998	+	6.03505i	0.0510683	+	0.235271i
$659$	20.3550			0.792916			0.396458	−	0.918053i	$-0.370239\pi$
$659$	20.3550			0.792916			0.396458	+	0.918053i	$0.370239\pi$
$660$	−4.68810	+	4.07287i	−0.182484	+	0.158536i
$661$	−7.71547			−0.300097			−0.150049	−	0.988679i	$-0.547943\pi$
$661$	−7.71547			−0.300097			−0.150049	+	0.988679i	$0.547943\pi$
$662$	−2.88982	−	13.3134i	−0.112316	−	0.517438i
$663$	21.9990	−	6.51204i	0.854369	−	0.252907i
$664$	−28.3363	+	21.1522i	−1.09966	+	0.820864i
$665$		−	5.62600i		−	0.218167i
$666$	−14.9441	+	15.0624i	−0.579071	+	0.583656i
$667$		−	33.2465i		−	1.28731i
$668$	31.5418	−	14.3701i	1.22039	−	0.555995i
$669$	19.2629	−	5.70212i	0.744746	−	0.220457i
$670$	16.5759	−	3.59800i	0.640385	−	0.139003i
$671$	−14.9820			−0.578375
$672$	−2.08337	+	9.57390i	−0.0803679	+	0.369321i
$673$	13.9234			0.536708			0.268354	−	0.963320i	$-0.413520\pi$
$673$	13.9234			0.536708			0.268354	+	0.963320i	$0.413520\pi$
$674$	−9.66602	+	2.09812i	−0.372321	+	0.0808166i
$675$	−3.94935	−	3.37678i	−0.152010	−	0.129972i
$676$	7.41547	−	3.37840i	0.285210	−	0.129939i
$677$			15.4726i			0.594660i	0.954775	+	0.297330i	$0.0960962\pi$
$677$			15.4726i			0.594660i	−0.954775	+	0.297330i	$0.903904\pi$
$678$	43.1599	−	23.6649i	1.65755	−	0.908846i
$679$			15.3744i			0.590014i
$680$	−7.26573	+	5.42364i	−0.278628	+	0.207987i
$681$	−1.64946	−	5.57219i	−0.0632073	−	0.213527i
$682$	−0.0851960	−	0.392497i	−0.00326232	−	0.0150295i
$683$	−12.4004			−0.474488			−0.237244	−	0.971450i	$-0.576244\pi$
$683$	−12.4004			−0.474488			−0.237244	+	0.971450i	$0.576244\pi$
$684$	−28.4609	−	18.1507i	−1.08823	−	0.694008i
$685$	−19.7697			−0.755361
$686$	0.299986	+	1.38203i	0.0114535	+	0.0527662i
$687$	−12.9315	−	43.6851i	−0.493366	−	1.66669i
$688$	17.1942	+	14.9535i	0.655521	+	0.570098i
$689$			16.8171i			0.640681i
$690$	14.2457	−	7.81102i	0.542323	−	0.297360i
$691$		−	42.6652i		−	1.62306i	−0.584309	−	0.811531i	$-0.698635\pi$
$691$		−	42.6652i		−	1.62306i	0.584309	−	0.811531i	$-0.301365\pi$
$692$	9.69746	+	21.2856i	0.368642	+	0.809155i
$693$	2.92753	+	4.51160i	0.111208	+	0.171381i
$694$	31.3374	−	6.80214i	1.18955	−	0.258206i
$695$	19.5041			0.739834
$696$	−14.6997	+	19.6708i	−0.557189	+	0.745619i
$697$	8.48803			0.321507
$698$	−18.9750	+	4.11875i	−0.718215	+	0.155897i
$699$	−17.9654	+	5.31804i	−0.679514	+	0.201147i
$700$	−0.829179	−	1.82002i	−0.0313400	−	0.0687902i
$701$			11.6632i			0.440511i	0.975442	+	0.220256i	$0.0706892\pi$
$701$			11.6632i			0.440511i	−0.975442	+	0.220256i	$0.929311\pi$
$702$	26.7394	+	14.3883i	1.00921	+	0.543052i
$703$		−	28.1363i		−	1.06118i
$704$	−4.07800	+	13.7499i	−0.153695	+	0.518217i
$705$	−7.25244	+	2.14684i	−0.273143	+	0.0808546i
$706$	11.0023	+	50.6874i	0.414077	+	1.90765i
$707$	−2.47356			−0.0930276
$708$	−13.4844	−	15.5213i	−0.506775	−	0.583326i
$709$	−15.5262			−0.583100			−0.291550	−	0.956556i	$-0.594171\pi$
$709$	−15.5262			−0.583100			−0.291550	+	0.956556i	$0.594171\pi$
$710$	4.32690	+	19.9340i	0.162386	+	0.748108i
$711$	11.5052	+	17.7305i	0.431478	+	0.664947i
$712$	7.07267	+	9.47483i	0.265059	+	0.355084i
$713$			1.05073i			0.0393500i
$714$	3.77512	+	6.88502i	0.141280	+	0.257665i
$715$			7.40777i			0.277035i
$716$	−9.73992	+	4.43740i	−0.363998	+	0.165833i
$717$	−0.443977	−	1.49984i	−0.0165806	−	0.0560126i
$718$	−33.8857	+	7.35529i	−1.26460	+	0.274497i
$719$	−12.1662			−0.453723			−0.226861	−	0.973927i	$-0.572846\pi$
$719$	−12.1662			−0.453723			−0.226861	+	0.973927i	$0.572846\pi$
$720$	−11.8822	−	1.67710i	−0.442824	−	0.0625019i
$721$	5.01395			0.186729
$722$	17.4852	−	3.79538i	0.650734	−	0.141249i
$723$	−4.49552	−	15.1868i	−0.167190	−	0.564802i
$724$	−8.91782	+	4.06286i	−0.331428	+	0.150995i
$725$		−	5.01257i		−	0.186162i
$726$	−9.16943	−	16.7231i	−0.340310	−	0.620654i
$727$		−	33.7947i		−	1.25338i	−0.779270	−	0.626689i	$-0.784410\pi$
$727$		−	33.7947i		−	1.25338i	0.779270	−	0.626689i	$-0.215590\pi$
$728$	6.99126	+	9.36576i	0.259113	+	0.347118i
$729$	4.19465	+	26.6722i	0.155358	+	0.987858i
$730$	4.06108	+	18.7093i	0.150307	+	0.692463i
$731$	18.2615			0.675425
$732$	−18.9864	−	21.8544i	−0.701756	−	0.807760i
$733$	4.04334			0.149344			0.0746721	−	0.997208i	$-0.476209\pi$
$733$	4.04334			0.149344			0.0746721	+	0.997208i	$0.476209\pi$
$734$	−9.49911	−	43.7623i	−0.350619	−	1.61530i
$735$	−1.66081	+	0.491627i	−0.0612600	+	0.0181339i
$736$	18.0560	−	32.8895i	0.665552	−	1.21232i
$737$		−	21.5019i		−	0.792031i
$738$	7.97490	+	7.91226i	0.293560	+	0.291254i
$739$		−	7.40661i		−	0.272457i	−0.990677	−	0.136228i	$-0.956502\pi$
$739$		−	7.40661i		−	0.272457i	0.990677	−	0.136228i	$-0.0434981\pi$
$740$	−4.14682	−	9.10212i	−0.152440	−	0.334600i
$741$	−38.6094	+	11.4290i	−1.41835	+	0.419855i
$742$	−5.62466	+	1.22090i	−0.206488	+	0.0448206i
$743$	0.0372902			0.00136804			0.000684022	−	1.00000i	$-0.499782\pi$
$743$	0.0372902			0.00136804			0.000684022		1.00000i	$0.499782\pi$
$744$	0.464569	−	0.621677i	0.0170319	−	0.0227918i
$745$	5.22078			0.191274
$746$	−26.9394	+	5.84750i	−0.986320	+	0.214092i
$747$	−31.4621	+	20.4155i	−1.15114	+	0.746964i
$748$	4.76510	+	10.4592i	0.174229	+	0.382427i
$749$			11.8920i			0.434524i
$750$	2.14781	−	1.17766i	0.0784271	−	0.0430022i
$751$			45.1678i			1.64819i	0.566448	+	0.824097i	$0.308317\pi$
$751$			45.1678i			1.64819i	−0.566448	+	0.824097i	$0.691683\pi$
$752$	−11.4625	+	13.1801i	−0.417995	+	0.480627i
$753$	−4.98913	−	16.8543i	−0.181814	−	0.614203i
$754$	6.21346	+	28.6253i	0.226281	+	1.04247i
$755$	−0.627435			−0.0228347
$756$	−2.87109	+	9.98783i	−0.104421	+	0.363254i
$757$	−2.00395			−0.0728346			−0.0364173	−	0.999337i	$-0.511595\pi$
$757$	−2.00395			−0.0728346			−0.0364173	+	0.999337i	$0.511595\pi$
$758$	−5.67703	−	26.1540i	−0.206199	−	0.949957i
$759$	−5.84571	−	19.7480i	−0.212186	−	0.716805i
$760$	12.7518	−	9.51880i	0.462555	−	0.345283i
$761$			5.01409i			0.181761i	0.995862	+	0.0908803i	$0.0289681\pi$
$761$			5.01409i			0.181761i	−0.995862	+	0.0908803i	$0.971032\pi$
$762$	11.9531	−	6.55401i	0.433017	−	0.237427i
$763$		−	16.3083i		−	0.590399i
$764$	−37.4865	+	17.0784i	−1.35621	+	0.617876i
$765$	−8.06722	+	5.23474i	−0.291671	+	0.189263i
$766$	32.5578	−	7.06705i	1.17636	−	0.255343i
$767$	−24.5255			−0.885565
$768$	−25.2249	+	11.4762i	−0.910225	+	0.414113i
$769$	5.55413			0.200287			0.100143	−	0.994973i	$-0.468070\pi$
$769$	5.55413			0.200287			0.100143	+	0.994973i	$0.468070\pi$
$770$	−2.47761	+	0.537794i	−0.0892868	+	0.0193807i
$771$	30.8858	−	9.14270i	1.11233	−	0.329266i
$772$	−29.7011	+	13.5315i	−1.06897	+	0.487009i
$773$		−	2.84275i		−	0.102247i	−0.998692	−	0.0511234i	$-0.983720\pi$
$773$		−	2.84275i		−	0.102247i	0.998692	−	0.0511234i	$-0.0162802\pi$
$774$	17.1575	+	17.0227i	0.616714	+	0.611870i
$775$			0.158417i			0.00569052i
$776$	−34.8472	+	26.0124i	−1.25094	+	0.933790i
$777$	−8.30592	+	2.45869i	−0.297973	+	0.0882048i
$778$	11.5476	+	53.1996i	0.414001	+	1.90730i
$779$	−14.8970			−0.533739
$780$	−10.8057	+	9.38768i	−0.386908	+	0.336133i
$781$	25.8578			0.925264
$782$	−6.37816	−	29.3841i	−0.228083	−	1.05077i
$783$	−16.9264	+	19.7964i	−0.604899	+	0.707464i
$784$	−2.62492	+	3.01824i	−0.0937473	+	0.107794i
$785$		−	18.7067i		−	0.667670i
$786$	−7.51635	−	13.7082i	−0.268099	−	0.488957i
$787$			2.78929i			0.0994274i	0.998764	+	0.0497137i	$0.0158309\pi$
$787$			2.78929i			0.0994274i	−0.998764	+	0.0497137i	$0.984169\pi$
$788$	11.8443	+	25.9977i	0.421935	+	0.926131i
$789$	−11.8021	−	39.8698i	−0.420166	−	1.41940i
$790$	−9.73699	+	2.11353i	−0.346426	+	0.0751959i
$791$	20.0948			0.714489
$792$	−5.27270	+	14.2688i	−0.187357	+	0.507019i
$793$	−34.5325			−1.22629
$794$	14.3788	−	3.12108i	0.510284	−	0.110763i
$795$	−2.00085	−	6.75927i	−0.0709629	−	0.239727i
$796$	−0.160782	−	0.352910i	−0.00569877	−	0.0125086i
$797$		−	44.2468i		−	1.56730i	−0.621201	−	0.783651i	$-0.713355\pi$
$797$		−	44.2468i		−	1.56730i	0.621201	−	0.783651i	$-0.286645\pi$
$798$	−6.62554	−	12.0836i	−0.234542	−	0.427755i
$799$			13.9982i			0.495221i
$800$	2.72229	−	4.95874i	0.0962477	−	0.175318i
$801$	6.82634	+	10.5200i	0.241197	+	0.371706i
$802$	2.87911	+	13.2640i	0.101665	+	0.468369i
$803$	24.2692			0.856441
$804$	31.3648	−	27.2488i	1.10615	−	0.960989i
$805$	6.63263			0.233770
$806$	−0.196371	−	0.904677i	−0.00691686	−	0.0318659i
$807$	39.7648	−	11.7710i	1.39979	−	0.414360i
$808$	−4.18508	−	5.60650i	−0.147231	−	0.197236i
$809$		−	14.3520i		−	0.504591i	−0.967650	−	0.252296i	$-0.918814\pi$
$809$		−	14.3520i		−	0.504591i	0.967650	−	0.252296i	$-0.0811855\pi$
$810$	−12.4592	−	2.60170i	−0.437771	−	0.0914145i
$811$			16.4348i			0.577104i	0.957464	+	0.288552i	$0.0931738\pi$
$811$			16.4348i			0.577104i	−0.957464	+	0.288552i	$0.906826\pi$
$812$	−9.12296	+	4.15632i	−0.320153	+	0.145858i
$813$	−15.5670	+	4.60809i	−0.545959	+	0.161613i
$814$	−12.3908	+	2.68957i	−0.434298	+	0.0942694i
$815$	13.2159			0.462933
$816$	−9.21820	+	20.2056i	−0.322702	+	0.707336i
$817$	−32.0499			−1.12128
$818$	8.12794	−	1.76426i	0.284187	−	0.0616860i
$819$	6.74776	+	10.3989i	0.235786	+	0.363367i
$820$	−4.81919	+	2.19557i	−0.168293	+	0.0766726i
$821$			1.76072i			0.0614496i	0.999528	+	0.0307248i	$0.00978155\pi$
$821$			1.76072i			0.0614496i	−0.999528	+	0.0307248i	$0.990218\pi$
$822$	−42.4616	+	23.2821i	−1.48102	+	0.812055i
$823$			11.8990i			0.414773i	0.978259	+	0.207386i	$0.0664958\pi$
$823$			11.8990i			0.414773i	−0.978259	+	0.207386i	$0.933504\pi$
$824$	8.48326	+	11.3645i	0.295528	+	0.395902i
$825$	−0.881355	−	2.97739i	−0.0306849	−	0.103659i
$826$	−1.78052	−	8.20282i	−0.0619521	−	0.285413i
$827$	27.9871			0.973206			0.486603	−	0.873623i	$-0.338236\pi$
$827$	27.9871			0.973206			0.486603	+	0.873623i	$0.338236\pi$
$828$	21.3983	−	33.5532i	0.743642	−	1.16606i
$829$	−37.3233			−1.29629			−0.648145	−	0.761517i	$-0.724455\pi$
$829$	−37.3233			−1.29629			−0.648145	+	0.761517i	$0.724455\pi$
$830$	−3.75037	−	17.2779i	−0.130177	−	0.599724i
$831$	3.31013	+	11.1823i	0.114827	+	0.387908i
$832$	−9.39950	+	31.6924i	−0.325869	+	1.09874i
$833$			3.20559i			0.111067i
$834$	41.8913	−	22.9693i	1.45058	−	0.795363i
$835$			17.3305i			0.599746i
$836$	−8.36302	−	18.3565i	−0.289241	−	0.634873i
$837$	0.534942	−	0.625645i	0.0184903	−	0.0216255i
$838$	51.6610	−	11.2136i	1.78460	−	0.387368i
$839$	−41.5028			−1.43283			−0.716417	−	0.697672i	$-0.754219\pi$
$839$	−41.5028			−1.43283			−0.716417	+	0.697672i	$0.754219\pi$
$840$	−3.92429	−	2.93256i	−0.135401	−	0.101183i
$841$	3.87418			0.133592
$842$	35.0048	−	7.59820i	1.20634	−	0.261851i
$843$	17.9884	−	5.32485i	0.619554	−	0.183398i
$844$	3.79292	+	8.32532i	0.130558	+	0.286569i
$845$			4.07439i			0.140163i
$846$	−13.0486	+	13.1520i	−0.448622	+	0.452174i
$847$		−	7.78612i		−	0.267534i
$848$	−12.2838	−	10.6831i	−0.421828	−	0.366858i
$849$	49.0725	−	14.5262i	1.68417	−	0.498540i
$850$	−0.961633	−	4.43023i	−0.0329837	−	0.151956i
$851$	33.1706			1.13707
$852$	32.7689	+	37.7188i	1.12264	+	1.29223i
$853$	3.29518			0.112825			0.0564124	−	0.998408i	$-0.482034\pi$
$853$	3.29518			0.112825			0.0564124	+	0.998408i	$0.482034\pi$
$854$	−2.50701	−	11.5498i	−0.0857883	−	0.395225i
$855$	14.1584	−	9.18727i	0.484208	−	0.314198i
$856$	−26.9541	+	20.1204i	−0.921272	+	0.687701i
$857$		−	12.2134i		−	0.417201i	−0.978001	−	0.208601i	$-0.933109\pi$
$857$		−	12.2134i		−	0.417201i	0.978001	−	0.208601i	$-0.0668909\pi$
$858$	8.72387	+	15.9105i	0.297828	+	0.543176i
$859$		−	15.9627i		−	0.544639i	−0.962207	−	0.272320i	$-0.912209\pi$
$859$		−	15.9627i		−	0.544639i	0.962207	−	0.272320i	$-0.0877908\pi$
$860$	−10.3682	+	4.72363i	−0.353552	+	0.161074i
$861$	1.30177	+	4.39764i	0.0443642	+	0.149871i
$862$	−19.9281	+	4.32562i	−0.678752	+	0.147331i
$863$	−1.69611			−0.0577362			−0.0288681	−	0.999583i	$-0.509190\pi$
$863$	−1.69611			−0.0577362			−0.0288681	+	0.999583i	$0.509190\pi$
$864$	−27.4959	+	10.3912i	−0.935429	+	0.353515i
$865$	−11.6952			−0.397650
$866$	28.7679	−	6.24440i	0.977572	−	0.212194i
$867$	−3.30578	−	11.1676i	−0.112270	−	0.379271i
$868$	0.288322	−	0.131356i	0.00978630	−	0.00445853i
$869$			12.6305i			0.428462i
$870$	−5.90312	−	10.7661i	−0.200135	−	0.365004i
$871$		−	49.5602i		−	1.67928i
$872$	36.9640	−	27.5925i	1.25176	−	0.934399i
$873$	−38.6912	+	25.1064i	−1.30950	+	0.849723i
$874$	11.1940	+	51.5707i	0.378644	+	1.74441i
$875$	1.00000			0.0338062
$876$	30.7557	+	35.4015i	1.03914	+	1.19611i
$877$	49.1223			1.65874			0.829371	−	0.558698i	$-0.188699\pi$
$877$	49.1223			1.65874			0.829371	+	0.558698i	$0.188699\pi$
$878$	−3.77283	−	17.3814i	−0.127327	−	0.586593i
$879$	14.5284	−	4.30064i	0.490031	−	0.145057i
$880$	−5.41089	−	4.70578i	−0.182401	−	0.158632i
$881$		−	20.4265i		−	0.688187i	−0.938935	−	0.344094i	$-0.888186\pi$
$881$		−	20.4265i		−	0.688187i	0.938935	−	0.344094i	$-0.111814\pi$
$882$	−2.98815	+	3.01181i	−0.100616	+	0.101413i
$883$			9.36949i			0.315308i	0.987494	+	0.157654i	$0.0503931\pi$
$883$			9.36949i			0.315308i	−0.987494	+	0.157654i	$0.949607\pi$
$884$	10.9832	+	24.1078i	0.369406	+	0.810831i
$885$	9.85749	−	2.91797i	0.331356	−	0.0980866i
$886$	27.5960	−	5.99004i	0.927107	−	0.201239i
$887$	−34.7131			−1.16555			−0.582776	−	0.812633i	$-0.698034\pi$
$887$	−34.7131			−1.16555			−0.582776	+	0.812633i	$0.698034\pi$
$888$	−19.6258	−	14.6661i	−0.658600	−	0.492162i
$889$	5.56526			0.186653
$890$	−5.77721	+	1.25401i	−0.193653	+	0.0420346i
$891$	−6.57324	+	14.7349i	−0.220212	+	0.493638i
$892$	9.61720	+	21.1094i	0.322008	+	0.706794i
$893$		−	24.5676i		−	0.822124i
$894$	11.2133	−	6.14832i	0.375028	−	0.205631i
$895$		−	5.35155i		−	0.178883i
$896$	−11.2823	−	0.842938i	−0.376914	−	0.0281606i
$897$	−13.4739	−	45.5176i	−0.449882	−	1.51979i
$898$	−0.875690	−	4.03429i	−0.0292222	−	0.134626i
$899$	0.794078			0.0264840
$900$	3.22621	−	5.05881i	0.107540	−	0.168627i
$901$	−13.0463			−0.434635
$902$	1.42401	+	6.56041i	0.0474145	+	0.218438i
$903$	2.80068	+	9.46124i	0.0932007	+	0.314850i
$904$	33.9990	+	45.5464i	1.13079	+	1.51485i
$905$		−	4.89985i		−	0.162877i
$906$	−1.34761	+	0.738907i	−0.0447714	+	0.0245486i
$907$			29.7377i			0.987425i	0.869625	+	0.493712i	$0.164360\pi$
$907$			29.7377i			0.987425i	−0.869625	+	0.493712i	$0.835640\pi$
$908$	6.10633	−	2.78197i	0.202646	−	0.0923231i
$909$	−4.03932	−	6.22496i	−0.133976	−	0.206469i
$910$	−5.71071	+	1.23958i	−0.189308	+	0.0410916i
$911$	11.6633			0.386421			0.193211	−	0.981157i	$-0.438110\pi$
$911$	11.6633			0.386421			0.193211	+	0.981157i	$0.438110\pi$
$912$	16.1785	−	35.4619i	0.535722	−	1.17426i
$913$	−22.4124			−0.741742
$914$	−7.17044	+	1.55643i	−0.237177	+	0.0514820i
$915$	13.8796	−	4.10858i	0.458845	−	0.135826i
$916$	47.8727	−	21.8102i	1.58176	−	0.720631i
$917$		−	6.38242i		−	0.210766i
$918$	−11.1621	+	20.7437i	−0.368405	+	0.684645i
$919$		−	2.44258i		−	0.0805731i	−0.999188	−	0.0402866i	$-0.987173\pi$
$919$		−	2.44258i		−	0.0805731i	0.999188	−	0.0402866i	$-0.0128271\pi$
$920$	11.2220	+	15.0334i	0.369977	+	0.495636i
$921$	−9.10826	+	2.69619i	−0.300127	+	0.0888424i
$922$	−2.24890	−	10.3607i	−0.0740636	−	0.341210i
$923$	59.6003			1.96177
$924$	−4.68810	+	4.07287i	−0.154227	+	0.133988i
$925$	5.00112			0.164436
$926$	−7.23975	−	33.3534i	−0.237913	−	1.09606i
$927$	8.18780	+	12.6181i	0.268923	+	0.414434i
$928$	−24.8560	−	13.6457i	−0.815939	−	0.447941i
$929$		−	24.6150i		−	0.807593i	−0.914849	−	0.403797i	$-0.867690\pi$
$929$		−	24.6150i		−	0.807593i	0.914849	−	0.403797i	$-0.132310\pi$
$930$	0.186563	+	0.340251i	0.00611763	+	0.0111573i
$931$		−	5.62600i		−	0.184385i
$932$	−8.96942	−	19.6875i	−0.293803	−	0.644886i
$933$	2.37187	+	8.01263i	0.0776514	+	0.262322i
$934$	−27.8307	+	6.04098i	−0.910648	+	0.197667i
$935$	−5.74677			−0.187939
$936$	−12.1532	+	32.8885i	−0.397239	+	1.07500i
$937$	20.7603			0.678209			0.339105	−	0.940749i	$-0.389876\pi$
$937$	20.7603			0.678209			0.339105	+	0.940749i	$0.389876\pi$
$938$	16.5759	−	3.59800i	0.541224	−	0.117479i
$939$	−13.1103	−	44.2893i	−0.427839	−	1.44533i
$940$	−3.62086	−	7.94765i	−0.118099	−	0.259224i
$941$			15.7909i			0.514768i	0.966309	+	0.257384i	$0.0828605\pi$
$941$			15.7909i			0.514768i	−0.966309	+	0.257384i	$0.917139\pi$
$942$	−22.0302	−	40.1784i	−0.717782	−	1.30908i
$943$		−	17.5624i		−	0.571911i
$944$	15.5798	−	17.9143i	0.507080	−	0.583060i
$945$	−3.94935	−	3.37678i	−0.128472	−	0.109847i
$946$	3.06368	+	14.1143i	0.0996088	+	0.458896i
$947$	−22.2586			−0.723309			−0.361654	−	0.932312i	$-0.617788\pi$
$947$	−22.2586			−0.723309			−0.361654	+	0.932312i	$0.617788\pi$
$948$	−18.4242	+	16.0064i	−0.598391	+	0.519863i
$949$	55.9388			1.81585
$950$	1.68772	+	7.77530i	0.0547569	+	0.252264i
$951$	42.2782	−	12.5150i	1.37097	−	0.405827i
$952$	−7.26573	+	5.42364i	−0.235484	+	0.175781i
$953$			58.2775i			1.88779i	0.330241	+	0.943897i	$0.392870\pi$
$953$			58.2775i			1.88779i	−0.330241	+	0.943897i	$0.607130\pi$
$954$	−12.2576	−	12.1613i	−0.396855	−	0.393738i
$955$		−	20.5968i		−	0.666497i
$956$	1.64362	−	0.748813i	0.0531583	−	0.0242183i
$957$	−14.9244	+	4.41785i	−0.482437	+	0.142809i
$958$	2.20039	−	0.477621i	0.0710914	−	0.0154312i
$959$	−19.7697			−0.638397
$960$	0.00725033	−	13.8564i	0.000234003	−	0.447214i
$961$	30.9749			0.999190
$962$	−28.5599	+	6.19927i	−0.920809	+	0.199872i
$963$	−29.9274	+	19.4196i	−0.964398	+	0.625789i
$964$	16.6425	−	7.58216i	0.536020	−	0.244205i
$965$		−	16.3191i		−	0.525331i
$966$	14.2457	−	7.81102i	0.458347	−	0.251315i
$967$		−	3.03812i		−	0.0976995i	−0.998806	−	0.0488497i	$-0.984444\pi$
$967$		−	3.03812i		−	0.0976995i	0.998806	−	0.0488497i	$-0.0155555\pi$
$968$	17.6478	−	13.1736i	0.567223	−	0.423414i
$969$	−8.86633	−	29.9522i	−0.284828	−	0.962204i
$970$	−4.61209	−	21.2479i	−0.148085	−	0.682227i
$971$	36.1216			1.15920			0.579599	−	0.814902i	$-0.303209\pi$
$971$	36.1216			1.15920			0.579599	+	0.814902i	$0.303209\pi$
$972$	−29.8239	+	9.08476i	−0.956603	+	0.291394i
$973$	19.5041			0.625274
$974$	−0.872628	−	4.02019i	−0.0279608	−	0.128815i
$975$	−2.03146	−	6.86268i	−0.0650588	−	0.219782i
$976$	21.9368	−	25.2238i	0.702179	−	0.807393i
$977$			57.5164i			1.84011i	0.391787	+	0.920056i	$0.371857\pi$
$977$			57.5164i			1.84011i	−0.391787	+	0.920056i	$0.628143\pi$
$978$	28.3853	−	15.5639i	0.907663	−	0.497679i
$979$			7.49404i			0.239510i
$980$	−0.829179	−	1.82002i	−0.0264872	−	0.0581383i
$981$	41.0415	−	26.6315i	1.31035	−	0.850277i
$982$	17.9175	−	3.88921i	0.571771	−	0.124110i
$983$	−15.3262			−0.488829			−0.244415	−	0.969671i	$-0.578596\pi$
$983$	−15.3262			−0.488829			−0.244415	+	0.969671i	$0.578596\pi$
$984$	−7.76508	+	10.3911i	−0.247542	+	0.331255i
$985$	−14.2843			−0.455137
$986$	−22.2068	+	4.82025i	−0.707209	+	0.153508i
$987$	−7.25244	+	2.14684i	−0.230848	+	0.0683346i
$988$	−19.2762	−	42.3105i	−0.613257	−	1.34607i
$989$		−	37.7845i		−	1.20148i
$990$	−5.39936	−	5.35694i	−0.171603	−	0.170255i
$991$			28.1284i			0.893529i	0.894652	+	0.446764i	$0.147424\pi$
$991$			28.1284i			0.893529i	−0.894652	+	0.446764i	$0.852576\pi$
$992$	0.785551	+	0.431259i	0.0249413	+	0.0136925i
$993$	15.9989	−	4.73594i	0.507710	−	0.150290i
$994$	4.32690	+	19.9340i	0.137241	+	0.632267i
$995$	0.193905			0.00614720
$996$	−28.4026	−	32.6930i	−0.899972	−	1.03592i
$997$	30.7088			0.972557			0.486279	−	0.873804i	$-0.338354\pi$
$997$	30.7088			0.972557			0.486279	+	0.873804i	$0.338354\pi$
$998$	5.55272	+	25.5813i	0.175768	+	0.809761i
$999$	−19.7511	−	16.8877i	−0.624898	−	0.534303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.n.b.71.4	yes	24
3.2	odd	2		420.2.n.a.71.21	✓	24
4.3	odd	2		420.2.n.a.71.22	yes	24
12.11	even	2	inner	420.2.n.b.71.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.n.a.71.21	✓	24	3.2	odd	2
420.2.n.a.71.22	yes	24	4.3	odd	2
420.2.n.b.71.3	yes	24	12.11	even	2	inner
420.2.n.b.71.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38203 + 0.299986i) q^{2} +(-0.491627 - 1.66081i) q^{3} +(1.82002 - 0.829179i) q^{4} +1.00000i q^{5} +(1.17766 + 2.14781i) q^{6} +1.00000i q^{7} +(-2.26658 + 1.69193i) q^{8} +(-2.51661 + 1.63300i) q^{9} +O(q^{10})\)	\(q+(-1.38203 + 0.299986i) q^{2} +(-0.491627 - 1.66081i) q^{3} +(1.82002 - 0.829179i) q^{4} +1.00000i q^{5} +(1.17766 + 2.14781i) q^{6} +1.00000i q^{7} +(-2.26658 + 1.69193i) q^{8} +(-2.51661 + 1.63300i) q^{9} +(-0.299986 - 1.38203i) q^{10} -1.79273 q^{11} +(-2.27188 - 2.61506i) q^{12} -4.13212 q^{13} +(-0.299986 - 1.38203i) q^{14} +(1.66081 - 0.491627i) q^{15} +(2.62492 - 3.01824i) q^{16} -3.20559i q^{17} +(2.98815 - 3.01181i) q^{18} +5.62600i q^{19} +(0.829179 + 1.82002i) q^{20} +(1.66081 - 0.491627i) q^{21} +(2.47761 - 0.537794i) q^{22} -6.63263 q^{23} +(3.92429 + 2.93256i) q^{24} -1.00000 q^{25} +(5.71071 - 1.23958i) q^{26} +(3.94935 + 3.37678i) q^{27} +(0.829179 + 1.82002i) q^{28} +5.01257i q^{29} +(-2.14781 + 1.17766i) q^{30} -0.158417i q^{31} +(-2.72229 + 4.95874i) q^{32} +(0.881355 + 2.97739i) q^{33} +(0.961633 + 4.43023i) q^{34} -1.00000 q^{35} +(-3.22621 + 5.05881i) q^{36} -5.00112 q^{37} +(-1.68772 - 7.77530i) q^{38} +(2.03146 + 6.86268i) q^{39} +(-1.69193 - 2.26658i) q^{40} +2.64788i q^{41} +(-2.14781 + 1.17766i) q^{42} +5.69675i q^{43} +(-3.26280 + 1.48650i) q^{44} +(-1.63300 - 2.51661i) q^{45} +(9.16650 - 1.98970i) q^{46} -4.36680 q^{47} +(-6.30322 - 2.87566i) q^{48} -1.00000 q^{49} +(1.38203 - 0.299986i) q^{50} +(-5.32390 + 1.57596i) q^{51} +(-7.52052 + 3.42627i) q^{52} -4.06986i q^{53} +(-6.47110 - 3.48207i) q^{54} -1.79273i q^{55} +(-1.69193 - 2.26658i) q^{56} +(9.34374 - 2.76589i) q^{57} +(-1.50370 - 6.92752i) q^{58} +5.93534 q^{59} +(2.61506 - 2.27188i) q^{60} +8.35711 q^{61} +(0.0475230 + 0.218938i) q^{62} +(-1.63300 - 2.51661i) q^{63} +(2.27474 - 7.66978i) q^{64} -4.13212i q^{65} +(-2.11124 - 3.85045i) q^{66} +11.9939i q^{67} +(-2.65801 - 5.83424i) q^{68} +(3.26078 + 11.0156i) q^{69} +(1.38203 - 0.299986i) q^{70} -14.4237 q^{71} +(2.94115 - 7.95925i) q^{72} -13.5376 q^{73} +(6.91170 - 1.50026i) q^{74} +(0.491627 + 1.66081i) q^{75} +(4.66496 + 10.2394i) q^{76} -1.79273i q^{77} +(-4.86625 - 8.87502i) q^{78} -7.04542i q^{79} +(3.01824 + 2.62492i) q^{80} +(3.66660 - 8.21925i) q^{81} +(-0.794327 - 3.65945i) q^{82} +12.5018 q^{83} +(2.61506 - 2.27188i) q^{84} +3.20559 q^{85} +(-1.70894 - 7.87308i) q^{86} +(8.32494 - 2.46431i) q^{87} +(4.06336 - 3.03318i) q^{88} -4.18024i q^{89} +(3.01181 + 2.98815i) q^{90} -4.13212i q^{91} +(-12.0715 + 5.49964i) q^{92} +(-0.263102 + 0.0778823i) q^{93} +(6.03505 - 1.30998i) q^{94} -5.62600 q^{95} +(9.57390 + 2.08337i) q^{96} +15.3744 q^{97} +(1.38203 - 0.299986i) q^{98} +(4.51160 - 2.92753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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