LMFDB - Embedded newform 819.2.dk.a.43.75

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(43,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 1]))

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

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

chi := DirichletCharacter("819.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.75
Character	$\chi$	$=$	819.43
Dual form			819.2.dk.a.400.75

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.01684 - 1.16442i) q^{2} +(-1.69349 + 0.363423i) q^{3} +(1.71177 - 2.96487i) q^{4} +(-2.47194 + 1.42718i) q^{5} +(-2.99233 + 2.70491i) q^{6} +1.00000i q^{7} -3.31521i q^{8} +(2.73585 - 1.23091i) q^{9} +O(q^{10})$	\(q+(2.01684 - 1.16442i) q^{2} +(-1.69349 + 0.363423i) q^{3} +(1.71177 - 2.96487i) q^{4} +(-2.47194 + 1.42718i) q^{5} +(-2.99233 + 2.70491i) q^{6} +1.00000i q^{7} -3.31521i q^{8} +(2.73585 - 1.23091i) q^{9} +(-3.32368 + 5.75678i) q^{10} +(4.29448 - 2.47942i) q^{11} +(-1.82137 + 5.64309i) q^{12} +(3.40545 + 1.18444i) q^{13} +(1.16442 + 2.01684i) q^{14} +(3.66755 - 3.31528i) q^{15} +(-0.436771 - 0.756509i) q^{16} +(0.972176 + 1.68386i) q^{17} +(4.08447 - 5.66824i) q^{18} +(4.59315 - 2.65186i) q^{19} +9.77200i q^{20} +(-0.363423 - 1.69349i) q^{21} +(5.77419 - 10.0012i) q^{22} -4.75790 q^{23} +(1.20482 + 5.61429i) q^{24} +(1.57367 - 2.72568i) q^{25} +(8.24745 - 1.57657i) q^{26} +(-4.18580 + 3.07881i) q^{27} +(2.96487 + 1.71177i) q^{28} +(-0.552604 - 0.957139i) q^{29} +(3.53649 - 10.9570i) q^{30} +(6.87558 - 3.96962i) q^{31} +(3.98031 + 2.29803i) q^{32} +(-6.37160 + 5.75959i) q^{33} +(3.92145 + 2.26405i) q^{34} +(-1.42718 - 2.47194i) q^{35} +(1.03365 - 10.2185i) q^{36} +(1.52031 + 0.877751i) q^{37} +(6.17577 - 10.6968i) q^{38} +(-6.19757 - 0.768219i) q^{39} +(4.73139 + 8.19501i) q^{40} +0.825037i q^{41} +(-2.70491 - 2.99233i) q^{42} +2.10414 q^{43} -16.9768i q^{44} +(-5.00613 + 6.94728i) q^{45} +(-9.59593 + 5.54021i) q^{46} +(3.71697 + 2.14599i) q^{47} +(1.01460 + 1.12241i) q^{48} -1.00000 q^{49} -7.32968i q^{50} +(-2.25833 - 2.49829i) q^{51} +(9.34106 - 8.06924i) q^{52} +6.62761 q^{53} +(-4.85705 + 11.0835i) q^{54} +(-7.07714 + 12.2580i) q^{55} +3.31521 q^{56} +(-6.81472 + 6.16016i) q^{57} +(-2.22903 - 1.28693i) q^{58} +(0.478979 + 0.276539i) q^{59} +(-3.55137 - 16.5488i) q^{60} -15.0629 q^{61} +(9.24464 - 16.0122i) q^{62} +(1.23091 + 2.73585i) q^{63} +12.4506 q^{64} +(-10.1085 + 1.93232i) q^{65} +(-6.14389 + 19.0354i) q^{66} +14.9283i q^{67} +6.65657 q^{68} +(8.05748 - 1.72913i) q^{69} +(-5.75678 - 3.32368i) q^{70} +(-8.29559 + 4.78946i) q^{71} +(-4.08073 - 9.06990i) q^{72} +11.2826i q^{73} +4.08830 q^{74} +(-1.67443 + 5.18783i) q^{75} -18.1575i q^{76} +(2.47942 + 4.29448i) q^{77} +(-13.3941 + 5.66722i) q^{78} +(6.51001 - 11.2757i) q^{79} +(2.15935 + 1.24670i) q^{80} +(5.96972 - 6.73517i) q^{81} +(0.960694 + 1.66397i) q^{82} +(-5.39373 - 3.11407i) q^{83} +(-5.64309 - 1.82137i) q^{84} +(-4.80633 - 2.77494i) q^{85} +(4.24372 - 2.45011i) q^{86} +(1.28368 + 1.42008i) q^{87} +(-8.21979 - 14.2371i) q^{88} +(-4.99061 - 2.88133i) q^{89} +(-2.00699 + 19.8408i) q^{90} +(-1.18444 + 3.40545i) q^{91} +(-8.14443 + 14.1066i) q^{92} +(-10.2011 + 9.22127i) q^{93} +9.99539 q^{94} +(-7.56934 + 13.1105i) q^{95} +(-7.57580 - 2.44517i) q^{96} -11.1686i q^{97} +(-2.01684 + 1.16442i) q^{98} +(8.69709 - 12.0694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 2 * q^9	$ 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) $ 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	2.01684	−	1.16442i	1.42612	−	0.823373i	0.429311	−	0.903157i	$-0.358756\pi$
$2$	2.01684	−	1.16442i	1.42612	−	0.823373i	0.996812	+	0.0797842i	$0.0254231\pi$
$3$	−1.69349	+	0.363423i	−0.977739	+	0.209823i
$3$	−1.69349	+	0.363423i	−0.977739	+	0.209823i
$4$	1.71177	−	2.96487i	0.855885	−	1.48244i
$5$	−2.47194	+	1.42718i	−1.10549	+	0.638253i	−0.937657	−	0.347563i	$-0.887009\pi$
$5$	−2.47194	+	1.42718i	−1.10549	+	0.638253i	−0.167830	+	0.985816i	$0.553676\pi$
$6$	−2.99233	+	2.70491i	−1.22161	+	1.10428i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	3.31521i		−	1.17210i
$9$	2.73585	−	1.23091i	0.911949	−	0.410304i
$10$	−3.32368	+	5.75678i	−1.05104	+	1.82046i
$11$	4.29448	−	2.47942i	1.29483	−	0.747573i	0.315327	−	0.948983i	$-0.397886\pi$
$11$	4.29448	−	2.47942i	1.29483	−	0.747573i	0.979507	+	0.201410i	$0.0645525\pi$
$12$	−1.82137	+	5.64309i	−0.525784	+	1.62902i
$13$	3.40545	+	1.18444i	0.944503	+	0.328504i
$13$	3.40545	+	1.18444i	0.944503	+	0.328504i
$14$	1.16442	+	2.01684i	0.311206	+	0.539024i
$15$	3.66755	−	3.31528i	0.946958	−	0.856001i
$16$	−0.436771	−	0.756509i	−0.109193	−	0.189127i
$17$	0.972176	+	1.68386i	0.235787	+	0.408396i	0.959501	−	0.281705i	$-0.0908998\pi$
$17$	0.972176	+	1.68386i	0.235787	+	0.408396i	−0.723714	+	0.690100i	$0.757566\pi$
$18$	4.08447	−	5.66824i	0.962719	−	1.33602i
$19$	4.59315	−	2.65186i	1.05374	−	0.608377i	0.130046	−	0.991508i	$-0.458487\pi$
$19$	4.59315	−	2.65186i	1.05374	−	0.608377i	0.923694	+	0.383131i	$0.125154\pi$
$20$			9.77200i			2.18508i
$21$	−0.363423	−	1.69349i	−0.0793055	−	0.369551i
$22$	5.77419	−	10.0012i	1.23106	−	2.13226i
$23$	−4.75790			−0.992091			−0.496045	−	0.868297i	$-0.665215\pi$
$23$	−4.75790			−0.992091			−0.496045	+	0.868297i	$0.665215\pi$
$24$	1.20482	+	5.61429i	0.245934	+	1.14601i
$25$	1.57367	−	2.72568i	0.314734	−	0.545136i
$26$	8.24745	−	1.57657i	1.61746	−	0.309190i
$27$	−4.18580	+	3.07881i	−0.805557	+	0.592518i
$28$	2.96487	+	1.71177i	0.560308	+	0.323494i
$29$	−0.552604	−	0.957139i	−0.102616	−	0.177736i	0.810146	−	0.586229i	$-0.199388\pi$
$29$	−0.552604	−	0.957139i	−0.102616	−	0.177736i	−0.912762	+	0.408492i	$0.866055\pi$
$30$	3.53649	−	10.9570i	0.645671	−	2.00046i
$31$	6.87558	−	3.96962i	1.23489	−	0.712964i	0.266845	−	0.963740i	$-0.414019\pi$
$31$	6.87558	−	3.96962i	1.23489	−	0.712964i	0.968045	+	0.250776i	$0.0806856\pi$
$32$	3.98031	+	2.29803i	0.703627	+	0.406239i
$33$	−6.37160	+	5.75959i	−1.10915	+	1.00262i
$34$	3.92145	+	2.26405i	0.672524	+	0.388282i
$35$	−1.42718	−	2.47194i	−0.241237	−	0.417835i
$36$	1.03365	−	10.2185i	0.172274	−	1.70308i
$37$	1.52031	+	0.877751i	0.249937	+	0.144301i	0.619735	−	0.784811i	$-0.287240\pi$
$37$	1.52031	+	0.877751i	0.249937	+	0.144301i	−0.369798	+	0.929112i	$0.620573\pi$
$38$	6.17577	−	10.6968i	1.00184	−	1.73524i
$39$	−6.19757	−	0.768219i	−0.992405	−	0.123013i
$40$	4.73139	+	8.19501i	0.748098	+	1.29574i
$41$			0.825037i			0.128849i	0.997923	+	0.0644246i	$0.0205212\pi$
$41$			0.825037i			0.128849i	−0.997923	+	0.0644246i	$0.979479\pi$
$42$	−2.70491	−	2.99233i	−0.417377	−	0.461727i
$43$	2.10414			0.320878			0.160439	−	0.987046i	$-0.448709\pi$
$43$	2.10414			0.320878			0.160439	+	0.987046i	$0.448709\pi$
$44$		−	16.9768i		−	2.55934i
$45$	−5.00613	+	6.94728i	−0.746270	+	1.03564i
$46$	−9.59593	+	5.54021i	−1.41484	+	0.816860i
$47$	3.71697	+	2.14599i	0.542176	+	0.313025i	0.745960	−	0.665990i	$-0.231991\pi$
$47$	3.71697	+	2.14599i	0.542176	+	0.313025i	−0.203784	+	0.979016i	$0.565324\pi$
$48$	1.01460	+	1.12241i	0.146445	+	0.162006i
$49$	−1.00000			−0.142857
$50$		−	7.32968i		−	1.03657i
$51$	−2.25833	−	2.49829i	−0.316229	−	0.349831i
$52$	9.34106	−	8.06924i	1.29537	−	1.11900i
$53$	6.62761			0.910372			0.455186	−	0.890396i	$-0.349573\pi$
$53$	6.62761			0.910372			0.455186	+	0.890396i	$0.349573\pi$
$54$	−4.85705	+	11.0835i	−0.660961	+	1.50828i
$55$	−7.07714	+	12.2580i	−0.954281	+	1.65286i
$56$	3.31521			0.443013
$57$	−6.81472	+	6.16016i	−0.902632	+	0.815933i
$58$	−2.22903	−	1.28693i	−0.292686	−	0.168983i
$59$	0.478979	+	0.276539i	0.0623577	+	0.0360023i	0.530855	−	0.847463i	$-0.321871\pi$
$59$	0.478979	+	0.276539i	0.0623577	+	0.0360023i	−0.468497	+	0.883465i	$0.655204\pi$
$60$	−3.55137	−	16.5488i	−0.458480	−	2.13644i
$61$	−15.0629			−1.92860			−0.964302	−	0.264806i	$-0.914692\pi$
$61$	−15.0629			−1.92860			−0.964302	+	0.264806i	$0.914692\pi$
$62$	9.24464	−	16.0122i	1.17407	−	2.03355i
$63$	1.23091	+	2.73585i	0.155080	+	0.344684i
$64$	12.4506			1.55633
$65$	−10.1085	+	1.93232i	−1.25380	+	0.239675i
$66$	−6.14389	+	19.0354i	−0.756261	+	2.34310i
$67$			14.9283i			1.82379i	0.410428	+	0.911893i	$0.365379\pi$
$67$			14.9283i			1.82379i	−0.410428	+	0.911893i	$0.634621\pi$
$68$	6.65657			0.807227
$69$	8.05748	−	1.72913i	0.970006	−	0.208163i
$70$	−5.75678	−	3.32368i	−0.688067	−	0.397256i
$71$	−8.29559	+	4.78946i	−0.984505	+	0.568404i	−0.903627	−	0.428320i	$-0.859106\pi$
$71$	−8.29559	+	4.78946i	−0.984505	+	0.568404i	−0.0808779	+	0.996724i	$0.525772\pi$
$72$	−4.08073	−	9.06990i	−0.480918	−	1.06890i
$73$			11.2826i			1.32053i	0.751032	+	0.660266i	$0.229556\pi$
$73$			11.2826i			1.32053i	−0.751032	+	0.660266i	$0.770444\pi$
$74$	4.08830			0.475255
$75$	−1.67443	+	5.18783i	−0.193346	+	0.599039i
$76$		−	18.1575i		−	2.08280i
$77$	2.47942	+	4.29448i	0.282556	+	0.489401i
$78$	−13.3941	+	5.66722i	−1.51658	+	0.641687i
$79$	6.51001	−	11.2757i	0.732433	−	1.26861i	−0.223408	−	0.974725i	$-0.571718\pi$
$79$	6.51001	−	11.2757i	0.732433	−	1.26861i	0.955841	−	0.293886i	$-0.0949486\pi$
$80$	2.15935	+	1.24670i	0.241422	+	0.139385i
$81$	5.96972	−	6.73517i	0.663302	−	0.748352i
$82$	0.960694	+	1.66397i	0.106091	+	0.183755i
$83$	−5.39373	−	3.11407i	−0.592039	−	0.341814i	0.173864	−	0.984770i	$-0.444375\pi$
$83$	−5.39373	−	3.11407i	−0.592039	−	0.341814i	−0.765903	+	0.642956i	$0.777708\pi$
$84$	−5.64309	−	1.82137i	−0.615712	−	0.198728i
$85$	−4.80633	−	2.77494i	−0.521320	−	0.300984i
$86$	4.24372	−	2.45011i	0.457612	−	0.264203i
$87$	1.28368	+	1.42008i	0.137625	+	0.152249i
$88$	−8.21979	−	14.2371i	−0.876232	−	1.51768i
$89$	−4.99061	−	2.88133i	−0.529004	−	0.305421i	0.211607	−	0.977355i	$-0.432130\pi$
$89$	−4.99061	−	2.88133i	−0.529004	−	0.305421i	−0.740611	+	0.671934i	$0.765464\pi$
$90$	−2.00699	+	19.8408i	−0.211556	+	2.09141i
$91$	−1.18444	+	3.40545i	−0.124163	+	0.356988i
$92$	−8.14443	+	14.1066i	−0.849115	+	1.47071i
$93$	−10.2011	+	9.22127i	−1.05780	+	0.956201i
$94$	9.99539			1.03095
$95$	−7.56934	+	13.1105i	−0.776598	+	1.34511i
$96$	−7.57580	−	2.44517i	−0.773202	−	0.249559i
$97$		−	11.1686i		−	1.13400i	−0.823717	−	0.567001i	$-0.808104\pi$
$97$		−	11.1686i		−	1.13400i	0.823717	−	0.567001i	$-0.191896\pi$
$98$	−2.01684	+	1.16442i	−0.203732	+	0.117625i
$99$	8.69709	−	12.0694i	0.874091	−	1.21302i
$100$	−5.38752	−	9.33146i	−0.538752	−	0.933146i
$101$	−7.06586	−	12.2384i	−0.703080	−	1.21777i	−0.967380	−	0.253329i	$-0.918474\pi$
$101$	−7.06586	−	12.2384i	−0.703080	−	1.21777i	0.264300	−	0.964440i	$-0.414859\pi$
$102$	−7.46377	−	2.40901i	−0.739023	−	0.238528i
$103$	−4.20494	−	7.28317i	−0.414325	−	0.717632i	0.581032	−	0.813881i	$-0.302649\pi$
$103$	−4.20494	−	7.28317i	−0.414325	−	0.717632i	−0.995357	+	0.0962482i	$0.969316\pi$
$104$	3.92666	−	11.2898i	0.385041	−	1.10705i
$105$	3.31528	+	3.66755i	0.323538	+	0.357917i
$106$	13.3668	−	7.71735i	1.29830	−	0.749575i
$107$	−8.09161	+	14.0151i	−0.782246	+	1.35489i	0.148385	+	0.988930i	$0.452593\pi$
$107$	−8.09161	+	14.0151i	−0.782246	+	1.35489i	−0.930631	+	0.365960i	$0.880741\pi$
$108$	1.96316	+	17.6806i	0.188905	+	1.70131i
$109$			4.47715i			0.428834i	0.976742	+	0.214417i	$0.0687851\pi$
$109$			4.47715i			0.428834i	−0.976742	+	0.214417i	$0.931215\pi$
$110$			32.9632i			3.14292i
$111$	−2.89363	−	0.933950i	−0.274651	−	0.0886466i
$112$	0.756509	−	0.436771i	0.0714834	−	0.0412709i
$113$	6.80639	−	11.7890i	0.640291	−	1.10902i	−0.345077	−	0.938575i	$-0.612147\pi$
$113$	6.80639	−	11.7890i	0.640291	−	1.10902i	0.985368	−	0.170442i	$-0.0545196\pi$
$114$	−6.57119	+	20.3593i	−0.615448	+	1.90682i
$115$	11.7613	−	6.79037i	1.09674	−	0.633205i
$116$	−3.78373			−0.351310
$117$	10.7747	−	0.951367i	0.996125	−	0.0879539i
$118$	1.28803			0.118573
$119$	−1.68386	+	0.972176i	−0.154359	+	0.0891192i
$120$	−10.9908	−	12.1587i	−1.00332	−	1.10993i
$121$	6.79503	−	11.7693i	0.617730	−	1.06994i
$122$	−30.3794	+	17.5396i	−2.75043	+	1.58796i
$123$	−0.299838	−	1.39720i	−0.0270355	−	0.125981i
$124$		−	27.1803i		−	2.44086i
$125$		−	5.28814i		−	0.472986i
$126$	5.66824	+	4.08447i	0.504967	+	0.363873i
$127$	3.78513	−	6.55603i	0.335876	−	0.581754i	−0.647777	−	0.761830i	$-0.724301\pi$
$127$	3.78513	−	6.55603i	0.335876	−	0.581754i	0.983653	+	0.180076i	$0.0576344\pi$
$128$	17.1503	−	9.90176i	1.51589	−	0.875200i
$129$	−3.56335	+	0.764694i	−0.313736	+	0.0673276i
$130$	−18.1372	+	15.6678i	−1.59074	+	1.37415i
$131$	−2.80411	−	4.85687i	−0.244997	−	0.424346i	0.717134	−	0.696935i	$-0.245454\pi$
$131$	−2.80411	−	4.85687i	−0.244997	−	0.424346i	−0.962131	+	0.272589i	$0.912120\pi$
$132$	6.16976	+	28.7501i	0.537008	+	2.50237i
$133$	2.65186	+	4.59315i	0.229945	+	0.398276i
$134$	17.3829	+	30.1081i	1.50166	+	2.60094i
$135$	5.95305	−	13.5845i	0.512357	−	1.16917i
$136$	5.58234	−	3.22297i	0.478682	−	0.276367i
$137$			13.6652i			1.16750i	0.811935	+	0.583748i	$0.198415\pi$
$137$			13.6652i			1.16750i	−0.811935	+	0.583748i	$0.801585\pi$
$138$	14.2372	−	12.8697i	1.21195	−	1.09554i
$139$	1.53578	−	2.66006i	0.130263	−	0.225623i	−0.793515	−	0.608551i	$-0.791751\pi$
$139$	1.53578	−	2.66006i	0.130263	−	0.225623i	0.923778	+	0.382928i	$0.125084\pi$
$140$	−9.77200			−0.825884
$141$	−7.07457	−	2.28339i	−0.595787	−	0.192297i
$142$	−11.1539	+	19.3192i	−0.936017	+	1.62123i
$143$	17.5614	−	3.35699i	1.46855	−	0.280726i
$144$	−2.12613	−	1.53207i	−0.177178	−	0.127672i
$145$	2.73201	+	1.57733i	0.226881	+	0.130990i
$146$	13.1378	+	22.7553i	1.08729	+	1.88324i
$147$	1.69349	−	0.363423i	0.139677	−	0.0299747i
$148$	5.20484	−	3.00501i	0.427835	−	0.247011i
$149$	−10.4800	−	6.05064i	−0.858557	−	0.495688i	0.00497199	−	0.999988i	$-0.498417\pi$
$149$	−10.4800	−	6.05064i	−0.858557	−	0.495688i	−0.863529	+	0.504300i	$0.831751\pi$
$150$	2.66378	+	12.4128i	0.217497	+	1.01350i
$151$	7.27563	+	4.20059i	0.592082	+	0.341839i	0.765920	−	0.642935i	$-0.222284\pi$
$151$	7.27563	+	4.20059i	0.592082	+	0.341839i	−0.173838	+	0.984774i	$0.555617\pi$
$152$	−8.79145	−	15.2272i	−0.713081	−	1.23509i
$153$	4.73241	+	3.41012i	0.382592	+	0.275692i
$154$	10.0012	+	5.77419i	0.805919	+	0.465298i
$155$	−11.3307	+	19.6253i	−0.910103	+	1.57634i
$156$	−12.8865	+	17.0600i	−1.03174	+	1.36589i
$157$	7.41303	+	12.8397i	0.591624	+	1.02472i	0.994014	+	0.109254i	$0.0348463\pi$
$157$	7.41303	+	12.8397i	0.591624	+	1.02472i	−0.402390	+	0.915468i	$0.631820\pi$
$158$		−	30.3216i		−	2.41226i
$159$	−11.2238	+	2.40863i	−0.890106	+	0.191017i
$160$	−13.1188			−1.03713
$161$		−	4.75790i		−	0.374975i
$162$	4.19738	−	20.5351i	0.329777	−	1.61339i
$163$	12.3719	−	7.14292i	0.969042	−	0.559477i	0.0700982	−	0.997540i	$-0.477669\pi$
$163$	12.3719	−	7.14292i	0.969042	−	0.559477i	0.898944	+	0.438063i	$0.144335\pi$
$164$	2.44613	+	1.41227i	0.191011	+	0.110280i
$165$	7.53026	−	23.3308i	0.586230	−	1.81630i
$166$	−14.5044			−1.12576
$167$			1.44580i			0.111880i	0.998434	+	0.0559399i	$0.0178155\pi$
$167$			1.44580i			0.111880i	−0.998434	+	0.0559399i	$0.982184\pi$
$168$	−5.61429	+	1.20482i	−0.433152	+	0.0929542i
$169$	10.1942	+	8.06710i	0.784170	+	0.620546i
$170$	−12.9248			−0.991288
$171$	9.30195	−	12.9088i	0.711338	−	0.987163i
$172$	3.60180	−	6.23851i	0.274635	−	0.475682i
$173$	−17.3708			−1.32068			−0.660340	−	0.750967i	$-0.729588\pi$
$173$	−17.3708			−1.32068			−0.660340	+	0.750967i	$0.729588\pi$
$174$	4.24256	+	1.36933i	0.321627	+	0.103809i
$175$	2.72568	+	1.57367i	0.206042	+	0.118958i
$176$	−3.75140	−	2.16587i	−0.282773	−	0.163259i
$177$	−0.911649	−	0.294244i	−0.0685237	−	0.0221168i
$178$	−13.4204			−1.00590
$179$	−2.28079	+	3.95045i	−0.170474	+	0.295270i	−0.938586	−	0.345046i	$-0.887863\pi$
$179$	−2.28079	+	3.95045i	−0.170474	+	0.295270i	0.768111	+	0.640316i	$0.221197\pi$
$180$	12.0285	+	26.7347i	0.896548	+	1.99269i
$181$	−12.2082			−0.907427			−0.453713	−	0.891148i	$-0.649901\pi$
$181$	−12.2082			−0.907427			−0.453713	+	0.891148i	$0.649901\pi$
$182$	1.57657	+	8.24745i	0.116863	+	0.611342i
$183$	25.5089	−	5.47420i	1.88567	−	0.404665i
$184$			15.7734i			1.16283i
$185$	−5.01082			−0.368403
$186$	−9.83654	+	30.4763i	−0.721250	+	2.23463i
$187$	8.34998	+	4.82086i	0.610611	+	0.352536i
$188$	12.7252	−	7.34689i	0.928080	−	0.535827i
$189$	−3.07881	−	4.18580i	−0.223951	−	0.304472i
$190$			35.2557i			2.55772i
$191$	−10.1183			−0.732136			−0.366068	−	0.930588i	$-0.619296\pi$
$191$	−10.1183			−0.732136			−0.366068	+	0.930588i	$0.619296\pi$
$192$	−21.0851	+	4.52485i	−1.52168	+	0.326553i
$193$		−	18.9924i		−	1.36711i	−0.729901	−	0.683553i	$-0.760434\pi$
$193$		−	18.9924i		−	1.36711i	0.729901	−	0.683553i	$-0.239566\pi$
$194$	−13.0050	−	22.5253i	−0.933705	−	1.61723i
$195$	16.4164	−	6.94603i	1.17560	−	0.497416i
$196$	−1.71177	+	2.96487i	−0.122269	+	0.211777i
$197$	−19.1879	−	11.0781i	−1.36708	−	0.789284i	−0.376526	−	0.926406i	$-0.622882\pi$
$197$	−19.1879	−	11.0781i	−1.36708	−	0.789284i	−0.990554	+	0.137122i	$0.956215\pi$
$198$	3.48672	−	34.4692i	0.247791	−	2.44962i
$199$	−0.294002	−	0.509226i	−0.0208412	−	0.0360980i	0.855417	−	0.517940i	$-0.173301\pi$
$199$	−0.294002	−	0.509226i	−0.0208412	−	0.0360980i	−0.876258	+	0.481842i	$0.839968\pi$
$200$	−9.03619	−	5.21705i	−0.638955	−	0.368901i
$201$	−5.42530	−	25.2810i	−0.382671	−	1.78319i
$202$	−28.5015	−	16.4553i	−2.00536	−	1.15779i
$203$	0.957139	−	0.552604i	0.0671780	−	0.0387852i
$204$	−11.2729	+	2.41915i	−0.789258	+	0.169375i
$205$	−1.17747	−	2.03945i	−0.0822384	−	0.142441i
$206$	−16.9614	−	9.79268i	−1.18176	−	0.682288i
$207$	−13.0169	+	5.85655i	−0.904736	+	0.407058i
$208$	−0.591363	−	3.09358i	−0.0410037	−	0.214501i
$209$	13.1501	−	22.7767i	0.909613	−	1.57550i
$210$	10.9570	+	3.53649i	0.756104	+	0.244041i
$211$	−13.7842			−0.948941			−0.474470	−	0.880272i	$-0.657360\pi$
$211$	−13.7842			−0.948941			−0.474470	+	0.880272i	$0.657360\pi$
$212$	11.3449	−	19.6500i	0.779173	−	1.34957i
$213$	12.3079	−	11.1257i	0.843326	−	0.762323i
$214$			37.6883i			2.57632i
$215$	−5.20132	+	3.00298i	−0.354727	+	0.204802i
$216$	10.2069	+	13.8768i	0.694492	+	0.944196i
$217$	3.96962	+	6.87558i	0.269475	+	0.466744i
$218$	5.21331	+	9.02971i	0.353090	+	0.611569i
$219$	−4.10037	−	19.1071i	−0.277078	−	1.29114i
$220$	24.2289	+	41.9656i	1.63351	+	2.82932i
$221$	1.31627	+	6.88578i	0.0885421	+	0.463188i
$222$	−6.92351	+	1.48578i	−0.464676	+	0.0997192i
$223$	1.79255	−	1.03493i	0.120038	−	0.0693040i	−0.438779	−	0.898595i	$-0.644589\pi$
$223$	1.79255	−	1.03493i	0.120038	−	0.0693040i	0.558817	+	0.829291i	$0.311255\pi$
$224$	−2.29803	+	3.98031i	−0.153544	+	0.265946i
$225$	0.950255	−	9.39409i	0.0633503	−	0.626272i
$226$		−	31.7021i		−	2.10879i
$227$		−	16.3685i		−	1.08641i	−0.839599	−	0.543207i	$-0.817210\pi$
$227$		−	16.3685i		−	1.08641i	0.839599	−	0.543207i	$-0.182790\pi$
$228$	6.59885	+	30.7496i	0.437019	+	2.03644i
$229$	3.97129	−	2.29283i	0.262431	−	0.151514i	−0.363012	−	0.931784i	$-0.618252\pi$
$229$	3.97129	−	2.29283i	0.262431	−	0.151514i	0.625443	+	0.780270i	$0.284918\pi$
$230$	15.8137	−	27.3902i	1.04273	−	1.80606i
$231$	−5.75959	−	6.37160i	−0.378954	−	0.419220i
$232$	−3.17311	+	1.83200i	−0.208325	+	0.120277i
$233$	−3.22507			−0.211281			−0.105641	−	0.994404i	$-0.533689\pi$
$233$	−3.22507			−0.211281			−0.105641	+	0.994404i	$0.533689\pi$
$234$	20.6231	−	14.4651i	1.34818	−	0.945615i
$235$	−12.2509			−0.799158
$236$	1.63980	−	0.946741i	0.106742	−	0.0616276i
$237$	−6.92682	+	21.4612i	−0.449945	+	1.39405i
$238$	−2.26405	+	3.92145i	−0.146757	+	0.254190i
$239$	−10.8539	+	6.26649i	−0.702079	+	0.405346i	−0.808121	−	0.589016i	$-0.799516\pi$
$239$	−10.8539	+	6.26649i	−0.702079	+	0.405346i	0.106042	+	0.994362i	$0.466182\pi$
$240$	−4.10992	−	1.32652i	−0.265294	−	0.0856265i
$241$			3.99684i			0.257459i	0.991680	+	0.128729i	$0.0410899\pi$
$241$			3.99684i			0.257459i	−0.991680	+	0.128729i	$0.958910\pi$
$242$		−	31.6492i		−	2.03449i
$243$	−7.66196	+	13.5755i	−0.491515	+	0.870869i
$244$	−25.7842	+	44.6595i	−1.65066	+	2.85903i
$245$	2.47194	−	1.42718i	0.157927	−	0.0911790i
$246$	−2.23166	−	2.46879i	−0.142285	−	0.157404i
$247$	18.7827	−	3.59046i	1.19512	−	0.228456i
$248$	−13.1601	−	22.7940i	−0.835667	−	1.44742i
$249$	10.2660	+	3.31346i	0.650580	+	0.209982i
$250$	−6.15765	−	10.6654i	−0.389444	−	0.674536i
$251$	13.3809	+	23.1764i	0.844594	+	1.46288i	0.885974	+	0.463736i	$0.153491\pi$
$251$	13.3809	+	23.1764i	0.844594	+	1.46288i	−0.0413798	+	0.999143i	$0.513175\pi$
$252$	10.2185	+	1.03365i	0.643703	+	0.0651135i
$253$	−20.4327	+	11.7968i	−1.28459	+	0.741660i
$254$		−	17.6300i		−	1.10620i
$255$	9.14797	+	2.95261i	0.572868	+	0.184899i
$256$	10.6091	−	18.3754i	0.663067	−	1.14847i
$257$	10.0818			0.628888			0.314444	−	0.949276i	$-0.398182\pi$
$257$	10.0818			0.628888			0.314444	+	0.949276i	$0.398182\pi$
$258$	−6.29629	+	5.69152i	−0.391990	+	0.354339i
$259$	−0.877751	+	1.52031i	−0.0545408	+	0.0944674i
$260$	−11.5743	+	33.2781i	−0.717809	+	2.06382i
$261$	−2.68999	−	1.93838i	−0.166506	−	0.119983i
$262$	−11.3109	−	6.53036i	−0.698790	−	0.403447i
$263$	−0.485644	−	0.841160i	−0.0299461	−	0.0518682i	0.850664	−	0.525710i	$-0.176200\pi$
$263$	−0.485644	−	0.841160i	−0.0299461	−	0.0518682i	−0.880610	+	0.473842i	$0.842867\pi$
$264$	19.0943	+	21.1232i	1.17517	+	1.30004i
$265$	−16.3831	+	9.45877i	−1.00640	+	0.581048i
$266$	10.6968	+	6.17577i	0.655860	+	0.378661i
$267$	9.49872	+	3.06581i	0.581312	+	0.187625i
$268$	44.2606	+	25.5539i	2.70365	+	1.56095i
$269$	1.35702	+	2.35042i	0.0827388	+	0.143308i	0.904425	−	0.426632i	$-0.140300\pi$
$269$	1.35702	+	2.35042i	0.0827388	+	0.143308i	−0.821687	+	0.569940i	$0.806967\pi$
$270$	−3.81179	−	34.3297i	−0.231978	−	2.08924i
$271$	15.8406	+	9.14558i	0.962248	+	0.555554i	0.896864	−	0.442306i	$-0.145840\pi$
$271$	15.8406	+	9.14558i	0.962248	+	0.555554i	0.0653838	+	0.997860i	$0.479173\pi$
$272$	0.849236	−	1.47092i	0.0514925	−	0.0891876i
$273$	0.768219	−	6.19757i	0.0464947	−	0.375094i
$274$	15.9121	+	27.5606i	0.961285	+	1.66499i
$275$		−	15.6072i		−	0.941147i
$276$	8.66589	−	26.8493i	0.521625	−	1.61614i
$277$	−24.9807			−1.50094			−0.750472	−	0.660902i	$-0.770174\pi$
$277$	−24.9807			−1.50094			−0.750472	+	0.660902i	$0.770174\pi$
$278$		−	7.15322i		−	0.429021i
$279$	13.9243	−	19.3235i	0.833625	−	1.15687i
$280$	−8.19501	+	4.73139i	−0.489745	+	0.282755i
$281$	5.04552	+	2.91303i	0.300990	+	0.173777i	0.642888	−	0.765960i	$-0.277736\pi$
$281$	5.04552	+	2.91303i	0.300990	+	0.173777i	−0.341897	+	0.939737i	$0.611070\pi$
$282$	−16.9271	+	3.63256i	−1.00800	+	0.216316i
$283$	31.7862			1.88949			0.944747	−	0.327800i	$-0.106307\pi$
$283$	31.7862			1.88949			0.944747	+	0.327800i	$0.106307\pi$
$284$			32.7938i			1.94595i
$285$	8.05398	−	24.9534i	0.477076	−	1.47811i
$286$	31.5095	−	27.2194i	1.86320	−	1.60952i
$287$	−0.825037			−0.0487004
$288$	13.7182	+	1.38766i	0.808353	+	0.0817686i
$289$	6.60975	−	11.4484i	0.388809	−	0.673436i
$290$	7.34672			0.431414
$291$	4.05894	+	18.9140i	0.237939	+	1.10876i
$292$	33.4516	+	19.3133i	1.95760	+	1.13022i
$293$	−21.0709	−	12.1653i	−1.23098	−	0.710705i	−0.263744	−	0.964593i	$-0.584957\pi$
$293$	−21.0709	−	12.1653i	−1.23098	−	0.710705i	−0.967234	+	0.253888i	$0.918291\pi$
$294$	2.99233	−	2.70491i	0.174516	−	0.157754i
$295$	−1.57868			−0.0919142
$296$	2.90993	−	5.04014i	0.169136	−	0.292952i
$297$	−10.3422	+	23.6002i	−0.600113	+	1.36942i
$298$	−28.1821			−1.63254
$299$	−16.2028	−	5.63544i	−0.937032	−	0.325906i
$300$	12.5150	+	13.8448i	0.722555	+	0.799332i
$301$			2.10414i			0.121281i
$302$	19.5651			1.12584
$303$	16.4137	+	18.1578i	0.942944	+	1.04314i
$304$	−4.01230	−	2.31651i	−0.230121	−	0.132861i
$305$	37.2346	−	21.4974i	2.13205	−	1.23094i
$306$	13.5153	+	1.36714i	0.772621	+	0.0781541i
$307$			12.9690i			0.740180i	0.928996	+	0.370090i	$0.120673\pi$
$307$			12.9690i			0.740180i	−0.928996	+	0.370090i	$0.879327\pi$
$308$	16.9768			0.967341
$309$	9.76792	+	10.8058i	0.555678	+	0.614723i
$310$			52.7749i			2.99742i
$311$	15.9613	+	27.6458i	0.905084	+	1.56765i	0.820805	+	0.571209i	$0.193525\pi$
$311$	15.9613	+	27.6458i	0.905084	+	1.56765i	0.0842787	+	0.996442i	$0.473141\pi$
$312$	−2.54681	+	20.5462i	−0.144184	+	1.16320i
$313$	2.45108	−	4.24539i	0.138543	−	0.239964i	−0.788402	−	0.615160i	$-0.789091\pi$
$313$	2.45108	−	4.24539i	0.138543	−	0.239964i	0.926945	+	0.375196i	$0.122425\pi$
$314$	29.9018	+	17.2638i	1.68746	+	0.974254i
$315$	−6.94728	−	5.00613i	−0.391435	−	0.282064i
$316$	−22.2873	−	38.6027i	−1.25376	−	2.17157i
$317$	−28.1077	−	16.2280i	−1.57869	−	0.911455i	−0.995043	−	0.0994454i	$-0.968293\pi$
$317$	−28.1077	−	16.2280i	−1.57869	−	0.911455i	−0.583644	−	0.812010i	$-0.698374\pi$
$318$	−19.8320	+	17.9271i	−1.11212	+	1.00530i
$319$	−4.74630	−	2.74028i	−0.265742	−	0.153426i
$320$	−30.7773	+	17.7693i	−1.72050	+	0.993332i
$321$	8.60969	−	26.6752i	0.480546	−	1.48886i
$322$	−5.54021	−	9.59593i	−0.308744	−	0.534760i
$323$	8.93070	+	5.15614i	0.496917	+	0.286895i
$324$	−9.75013	−	29.2285i	−0.541674	−	1.62381i
$325$	8.58746	−	7.41825i	0.476347	−	0.411490i
$326$	16.6348	−	28.8123i	0.921316	−	1.59577i
$327$	−1.62710	−	7.58203i	−0.0899790	−	0.419287i
$328$	2.73517			0.151025
$329$	−2.14599	+	3.71697i	−0.118312	+	0.204923i
$330$	−11.9796	−	55.8230i	−0.659455	−	3.07295i
$331$		−	19.0794i		−	1.04870i	−0.851504	−	0.524349i	$-0.824309\pi$
$331$		−	19.0794i		−	1.04870i	0.851504	−	0.524349i	$-0.175691\pi$
$332$	−18.4657	+	10.6612i	−1.01343	+	0.585107i
$333$	5.23976	+	0.530026i	0.287137	+	0.0290453i
$334$	1.68353	+	2.91596i	0.0921187	+	0.159554i
$335$	−21.3054	−	36.9020i	−1.16404	−	2.01617i
$336$	−1.12241	+	1.01460i	−0.0612325	+	0.0553511i
$337$	15.1482	+	26.2374i	0.825173	+	1.42924i	0.901787	+	0.432181i	$0.142256\pi$
$337$	15.1482	+	26.2374i	0.825173	+	1.42924i	−0.0766143	+	0.997061i	$0.524411\pi$
$338$	29.9536	+	4.39968i	1.62926	+	0.239311i
$339$	−7.24218	+	22.4382i	−0.393341	+	1.21868i
$340$	−16.4547	+	9.50010i	−0.892379	+	0.515215i
$341$	19.6847	−	34.0949i	1.06598	−	1.84634i
$342$	3.72922	−	36.8665i	0.201653	−	1.99351i
$343$		−	1.00000i		−	0.0539949i
$344$		−	6.97566i		−	0.376103i
$345$	−17.4498	+	15.7738i	−0.939468	+	0.849231i
$346$	−35.0342	+	20.2270i	−1.88345	+	1.08741i
$347$	1.39078	−	2.40890i	0.0746609	−	0.129316i	−0.826278	−	0.563263i	$-0.809546\pi$
$347$	1.39078	−	2.40890i	0.0746609	−	0.129316i	0.900939	+	0.433946i	$0.142879\pi$
$348$	6.40772	−	1.37509i	0.343490	−	0.0737128i
$349$	−26.0942	+	15.0655i	−1.39679	+	0.806437i	−0.994055	−	0.108880i	$-0.965274\pi$
$349$	−26.0942	+	15.0655i	−1.39679	+	0.806437i	−0.402735	+	0.915317i	$0.631940\pi$
$350$	7.32968			0.391788
$351$	−17.9012	+	5.52692i	−0.955496	+	0.295005i
$352$	22.7912			1.21477
$353$	7.26120	−	4.19226i	0.386475	−	0.223131i	−0.294157	−	0.955757i	$-0.595039\pi$
$353$	7.26120	−	4.19226i	0.386475	−	0.223131i	0.680632	+	0.732626i	$0.261705\pi$
$354$	−2.18128	+	0.468102i	−0.115934	+	0.0248793i
$355$	13.6708	−	23.6786i	0.725572	−	1.25673i
$356$	−17.0856	+	9.86435i	−0.905533	+	0.522810i
$357$	2.49829	−	2.25833i	0.132224	−	0.119523i
$358$			10.6232i			0.561456i
$359$			11.2567i			0.594105i	0.954861	+	0.297053i	$0.0960037\pi$
$359$			11.2567i			0.594105i	−0.954861	+	0.297053i	$0.903996\pi$
$360$	23.0317	+	16.5964i	1.21388	+	0.874705i
$361$	4.56467	−	7.90625i	0.240246	−	0.416118i
$362$	−24.6220	+	14.2155i	−1.29410	+	0.747150i
$363$	−7.23009	+	22.4008i	−0.379481	+	1.17574i
$364$	8.06924	+	9.34106i	0.422943	+	0.489604i
$365$	−16.1023	−	27.8900i	−0.842834	−	1.45983i
$366$	45.0731	−	40.7438i	2.35601	−	2.12971i
$367$	9.17405	+	15.8899i	0.478881	+	0.829447i	0.999707	−	0.0242163i	$-0.00770904\pi$
$367$	9.17405	+	15.8899i	0.478881	+	0.829447i	−0.520825	+	0.853663i	$0.674376\pi$
$368$	2.07811	+	3.59939i	0.108329	+	0.187631i
$369$	1.01555	+	2.25718i	0.0528673	+	0.117504i
$370$	−10.1060	+	5.83473i	−0.525388	+	0.303333i
$371$			6.62761i			0.344088i
$372$	9.87795	+	46.0296i	0.512148	+	2.38653i
$373$	−6.36254	+	11.0202i	−0.329440	+	0.570606i	−0.982401	−	0.186785i	$-0.940193\pi$
$373$	−6.36254	+	11.0202i	−0.329440	+	0.570606i	0.652961	+	0.757392i	$0.273527\pi$
$374$	22.4541			1.16108
$375$	1.92184	+	8.95544i	0.0992432	+	0.462457i
$376$	7.11442	−	12.3225i	0.366898	−	0.635486i
$377$	−0.748196	−	3.91402i	−0.0385340	−	0.201582i
$378$	−11.0835	−	4.85705i	−0.570075	−	0.249820i
$379$	−7.21769	−	4.16714i	−0.370748	−	0.214051i	0.303037	−	0.952979i	$-0.401999\pi$
$379$	−7.21769	−	4.16714i	−0.370748	−	0.214051i	−0.673785	+	0.738927i	$0.735333\pi$
$380$	25.9139	+	44.8842i	1.32936	+	2.30251i
$381$	−4.02748	+	12.4782i	−0.206334	+	0.639278i
$382$	−20.4071	+	11.7820i	−1.04412	+	0.602821i
$383$	−29.2544	−	16.8900i	−1.49483	−	0.863039i	−0.494845	−	0.868981i	$-0.664775\pi$
$383$	−29.2544	−	16.8900i	−1.49483	−	0.863039i	−0.999982	+	0.00594177i	$0.998109\pi$
$384$	−25.4455	+	23.0014i	−1.29851	+	1.17379i
$385$	−12.2580	−	7.07714i	−0.624724	−	0.360684i
$386$	−22.1153	−	38.3048i	−1.12564	−	1.94966i
$387$	5.75661	−	2.59001i	0.292625	−	0.131658i
$388$	−33.1135	−	19.1181i	−1.68108	−	0.970574i
$389$	−7.00372	+	12.1308i	−0.355103	+	0.615056i	−0.987136	−	0.159885i	$-0.948888\pi$
$389$	−7.00372	+	12.1308i	−0.355103	+	0.615056i	0.632033	+	0.774942i	$0.282221\pi$
$390$	25.0212	−	33.1247i	1.26700	−	1.67734i
$391$	−4.62552	−	8.01163i	−0.233922	−	0.405165i
$392$			3.31521i			0.167443i
$393$	6.51385	+	7.20600i	0.328580	+	0.363494i
$394$	−51.5986			−2.59950
$395$			37.1637i			1.86991i
$396$	−20.8969	−	46.4458i	−1.05011	−	2.33399i
$397$	15.8466	−	9.14901i	0.795316	−	0.459176i	−0.0465147	−	0.998918i	$-0.514811\pi$
$397$	15.8466	−	9.14901i	0.795316	−	0.459176i	0.841831	+	0.539742i	$0.181478\pi$
$398$	−1.18591	−	0.684685i	−0.0594443	−	0.0343202i
$399$	−6.16016	−	6.81472i	−0.308394	−	0.341163i
$400$	−2.74933			−0.137467
$401$			5.05262i			0.252316i	0.992010	+	0.126158i	$0.0402646\pi$
$401$			5.05262i			0.252316i	−0.992010	+	0.126158i	$0.959735\pi$
$402$	−40.3799	−	44.6705i	−2.01396	−	2.22796i
$403$	28.1162	−	5.37464i	1.40057	−	0.267730i
$404$	−48.3805			−2.40702
$405$	−5.14452	+	25.1688i	−0.255633	+	1.25065i
$406$	1.28693	−	2.22903i	0.0638694	−	0.110625i
$407$	8.70524			0.431503
$408$	−8.28236	+	7.48683i	−0.410038	+	0.370653i
$409$	−17.6563	−	10.1939i	−0.873048	−	0.504055i	−0.00468813	−	0.999989i	$-0.501492\pi$
$409$	−17.6563	−	10.1939i	−0.873048	−	0.504055i	−0.868360	+	0.495934i	$0.834826\pi$
$410$	−4.74956	−	2.74216i	−0.234564	−	0.135426i
$411$	−4.96625	−	23.1419i	−0.244967	−	1.14151i
$412$	−28.7916			−1.41846
$413$	−0.276539	+	0.478979i	−0.0136076	+	0.0235690i
$414$	−19.4335	+	26.9689i	−0.955104	+	1.32545i
$415$	17.7773			0.872655
$416$	10.8329	+	12.5403i	0.531126	+	0.614838i
$417$	−1.63411	+	5.06293i	−0.0800229	+	0.247933i
$418$		−	61.2493i		−	2.99580i
$419$	15.2808			0.746516			0.373258	−	0.927728i	$-0.378241\pi$
$419$	15.2808			0.746516			0.373258	+	0.927728i	$0.378241\pi$
$420$	16.5488	−	3.55137i	0.807500	−	0.173289i
$421$	−13.2070	−	7.62506i	−0.643669	−	0.371623i	0.142357	−	0.989815i	$-0.454532\pi$
$421$	−13.2070	−	7.62506i	−0.643669	−	0.371623i	−0.786027	+	0.618193i	$0.787865\pi$
$422$	−27.8005	+	16.0506i	−1.35331	+	0.781332i
$423$	12.8106	+	1.29585i	0.622872	+	0.0630064i
$424$		−	21.9719i		−	1.06705i
$425$	6.11954			0.296841
$426$	11.8681	−	36.7705i	0.575010	−	1.78154i
$427$		−	15.0629i		−	0.728944i
$428$	27.7020	+	47.9812i	1.33902	+	2.31926i
$429$	−28.5201	+	12.0673i	−1.37696	+	0.582613i
$430$	−6.99349	+	12.1131i	−0.337256	+	0.584145i
$431$	−19.7788	−	11.4193i	−0.952711	−	0.550048i	−0.0587888	−	0.998270i	$-0.518724\pi$
$431$	−19.7788	−	11.4193i	−0.952711	−	0.550048i	−0.893922	+	0.448223i	$0.852057\pi$
$432$	4.15738	+	1.82186i	0.200022	+	0.0876543i
$433$	−10.9144	−	18.9043i	−0.524512	−	0.908482i	−0.999593	−	0.0285396i	$-0.990914\pi$
$433$	−10.9144	−	18.9043i	−0.524512	−	0.908482i	0.475080	−	0.879942i	$-0.342419\pi$
$434$	16.0122	+	9.24464i	0.768609	+	0.443757i
$435$	−5.19989	−	1.67832i	−0.249316	−	0.0804693i
$436$	13.2742	+	7.66386i	0.635718	+	0.367032i
$437$	−21.8537	+	12.6173i	−1.04541	+	0.603565i
$438$	−30.5186	−	33.7614i	−1.45823	−	1.61318i
$439$	0.223249	+	0.386679i	0.0106551	+	0.0184552i	0.871304	−	0.490744i	$-0.163275\pi$
$439$	0.223249	+	0.386679i	0.0106551	+	0.0184552i	−0.860649	+	0.509199i	$0.829942\pi$
$440$	40.6377	+	23.4622i	1.93733	+	1.11852i
$441$	−2.73585	+	1.23091i	−0.130278	+	0.0586148i
$442$	10.6727	+	12.3548i	0.507648	+	0.587660i
$443$	−8.18038	+	14.1688i	−0.388662	+	0.673182i	−0.992270	−	0.124099i	$-0.960396\pi$
$443$	−8.18038	+	14.1688i	−0.388662	+	0.673182i	0.603608	+	0.797281i	$0.293729\pi$
$444$	−7.72227	+	6.98053i	−0.366483	+	0.331281i
$445$	16.4487			0.779743
$446$	2.41019	−	4.17458i	0.114126	−	0.197672i
$447$	19.9468	+	6.43804i	0.943451	+	0.304509i
$448$			12.4506i			0.588237i
$449$	−14.8533	+	8.57555i	−0.700970	+	0.404705i	−0.807709	−	0.589582i	$-0.799292\pi$
$449$	−14.8533	+	8.57555i	−0.700970	+	0.404705i	0.106739	+	0.994287i	$0.465959\pi$
$450$	−9.02219	−	20.0529i	−0.425310	−	0.945303i
$451$	2.04561	+	3.54311i	0.0963241	+	0.166838i
$452$	−23.3019	−	40.3601i	−1.09603	−	1.89838i
$453$	−13.8478	−	4.46954i	−0.650628	−	0.209997i
$454$	−19.0599	−	33.0127i	−0.894524	−	1.54936i
$455$	−1.93232	−	10.1085i	−0.0905885	−	0.473893i
$456$	20.4222	+	22.5922i	0.956358	+	1.05798i
$457$	−20.2474	+	11.6899i	−0.947135	+	0.546829i	−0.892190	−	0.451661i	$-0.850832\pi$
$457$	−20.2474	+	11.6899i	−0.947135	+	0.546829i	−0.0549452	+	0.998489i	$0.517498\pi$
$458$	5.33965	−	9.24855i	0.249505	−	0.432156i
$459$	−9.25362	−	4.05515i	−0.431922	−	0.189278i
$460$		−	46.4942i		−	2.16780i
$461$			3.72450i			0.173467i	0.996232	+	0.0867336i	$0.0276429\pi$
$461$			3.72450i			0.173467i	−0.996232	+	0.0867336i	$0.972357\pi$
$462$	−19.0354	−	6.14389i	−0.885609	−	0.285840i
$463$	17.2386	−	9.95271i	0.801146	−	0.462542i	−0.0427260	−	0.999087i	$-0.513604\pi$
$463$	17.2386	−	9.95271i	0.801146	−	0.462542i	0.843872	+	0.536545i	$0.180271\pi$
$464$	−0.482723	+	0.836100i	−0.0224098	+	0.0388150i
$465$	12.0562	−	37.3532i	0.559091	−	1.73221i
$466$	−6.50445	+	3.75535i	−0.301313	+	0.173963i
$467$	5.83261			0.269901			0.134951	−	0.990852i	$-0.456912\pi$
$467$	5.83261			0.269901			0.134951	+	0.990852i	$0.456912\pi$
$468$	15.6232	−	33.5742i	0.722182	−	1.55197i
$469$	−14.9283			−0.689326
$470$	−24.7081	+	14.2652i	−1.13970	+	0.658005i
$471$	−17.2202	−	19.0500i	−0.793464	−	0.877776i
$472$	0.916783	−	1.58791i	0.0421984	−	0.0730897i
$473$	9.03619	−	5.21704i	0.415484	−	0.239880i
$474$	11.0196	+	51.3495i	0.506147	+	2.35856i
$475$		−	16.6926i		−	0.765909i
$476$			6.65657i			0.305103i
$477$	18.1321	−	8.15799i	0.830212	−	0.373529i
$478$	−14.5937	+	25.2771i	−0.667501	+	1.15615i
$479$	5.23600	−	3.02301i	0.239239	−	0.138125i	−0.375588	−	0.926787i	$-0.622559\pi$
$479$	5.23600	−	3.02301i	0.239239	−	0.138125i	0.614827	+	0.788662i	$0.289226\pi$
$480$	22.2166	−	4.76768i	1.01405	−	0.217614i
$481$	4.13770	+	4.78985i	0.188663	+	0.218398i
$482$	4.65402	+	8.06099i	0.211985	+	0.367168i
$483$	1.72913	+	8.05748i	0.0786782	+	0.366628i
$484$	−23.2630	−	40.2928i	−1.05741	−	1.83149i
$485$	15.9396	+	27.6082i	0.723780	+	1.25362i
$486$	0.354681	+	36.3014i	0.0160886	+	1.64667i
$487$	29.2869	−	16.9088i	1.32711	−	0.766210i	0.342262	−	0.939605i	$-0.388807\pi$
$487$	29.2869	−	16.9088i	1.32711	−	0.766210i	0.984852	+	0.173395i	$0.0554736\pi$
$488$			49.9366i			2.26052i
$489$	−18.3558	+	16.5927i	−0.830080	+	0.750350i
$490$	3.32368	−	5.75678i	0.150149	−	0.260065i
$491$	29.8210			1.34580			0.672902	−	0.739732i	$-0.265048\pi$
$491$	29.8210			1.34580			0.672902	+	0.739732i	$0.265048\pi$
$492$	−4.65576	−	1.50270i	−0.209898	−	0.0677468i
$493$	1.07446	−	1.86102i	0.0483911	−	0.0838159i
$494$	33.7009	−	29.1125i	1.51628	−	1.30983i
$495$	−4.27350	+	42.2472i	−0.192080	+	1.89887i
$496$	−6.00610	−	3.46762i	−0.269682	−	0.155701i
$497$	−4.78946	−	8.29559i	−0.214837	−	0.372108i
$498$	24.5631	−	5.27124i	1.10070	−	0.236210i
$499$	−17.0252	+	9.82952i	−0.762154	+	0.440030i	−0.830069	−	0.557661i	$-0.811699\pi$
$499$	−17.0252	+	9.82952i	−0.762154	+	0.440030i	0.0679146	+	0.997691i	$0.478365\pi$
$500$	−15.6787	−	9.05208i	−0.701171	−	0.404821i
$501$	−0.525439	−	2.44846i	−0.0234749	−	0.109389i
$502$	53.9743	+	31.1621i	2.40899	+	1.39083i
$503$	−4.72468	−	8.18339i	−0.210663	−	0.364879i	0.741259	−	0.671219i	$-0.234229\pi$
$503$	−4.72468	−	8.18339i	−0.210663	−	0.364879i	−0.951922	+	0.306340i	$0.900896\pi$
$504$	9.06990	−	4.08073i	0.404005	−	0.181770i
$505$	34.9328	+	20.1685i	1.55449	+	0.897486i
$506$	−27.4730	+	47.5847i	−1.22132	+	2.11540i
$507$	−20.1956	−	9.95677i	−0.896919	−	0.442196i
$508$	−12.9585	−	22.4448i	−0.574942	−	0.995828i
$509$			25.0729i			1.11134i	0.831404	+	0.555669i	$0.187538\pi$
$509$			25.0729i			1.11134i	−0.831404	+	0.555669i	$0.812462\pi$
$510$	21.8881	−	4.69718i	0.969221	−	0.207995i
$511$	−11.2826			−0.499114
$512$		−	9.80680i		−	0.433403i
$513$	−11.0614	+	25.2416i	−0.488374	+	1.11444i
$514$	20.3335	−	11.7395i	0.896872	−	0.517809i
$515$	20.7888	+	12.0024i	0.916062	+	0.528889i
$516$	−3.83242	+	11.8739i	−0.168713	+	0.522717i
$517$	21.2833			0.936037
$518$			4.08830i			0.179629i
$519$	29.4174	−	6.31297i	1.29128	−	0.277109i
$520$	6.40604	+	33.5117i	0.280923	+	1.46959i
$521$	41.7597			1.82953			0.914764	−	0.403989i	$-0.132377\pi$
$521$	41.7597			1.82953			0.914764	+	0.403989i	$0.132377\pi$
$522$	−7.68239	−	0.777109i	−0.336249	−	0.0340132i
$523$	1.32730	−	2.29895i	0.0580387	−	0.100526i	−0.835546	−	0.549420i	$-0.814849\pi$
$523$	1.32730	−	2.29895i	0.0580387	−	0.100526i	0.893585	+	0.448894i	$0.148182\pi$
$524$	−19.2000			−0.838755
$525$	−5.18783	−	1.67443i	−0.226415	−	0.0730780i
$526$	−1.95894	−	1.13099i	−0.0854136	−	0.0493136i
$527$	13.3685	+	7.71833i	0.582343	+	0.336216i
$528$	7.14011	+	2.30455i	0.310733	+	0.100293i
$529$	−0.362396			−0.0157563
$530$	−22.0280	+	38.1537i	−0.956837	+	1.65729i
$531$	1.65081	+	0.166987i	0.0716389	+	0.00724661i
$532$	18.1575			0.787226
$533$	−0.977206	+	2.80963i	−0.0423275	+	0.121698i
$534$	22.7273	−	4.87728i	0.983508	−	0.211061i
$535$		−	46.1927i		−	1.99708i
$536$	49.4905			2.13766
$537$	2.42682	−	7.51896i	0.104725	−	0.324467i
$538$	5.47378	+	3.16029i	0.235992	+	0.136250i
$539$	−4.29448	+	2.47942i	−0.184976	+	0.106796i
$540$	−30.0861	−	40.9036i	−1.29470	−	1.76021i
$541$			19.4256i			0.835170i	0.908638	+	0.417585i	$0.137123\pi$
$541$			19.4256i			0.835170i	−0.908638	+	0.417585i	$0.862877\pi$
$542$	42.5973			1.82971
$543$	20.6745	−	4.43674i	0.887227	−	0.190399i
$544$			8.93638i			0.383144i
$545$	−6.38969	−	11.0673i	−0.273704	−	0.474070i
$546$	−5.66722	−	13.3941i	−0.242535	−	0.573212i
$547$	−19.7910	+	34.2791i	−0.846203	+	1.46567i	0.0383688	+	0.999264i	$0.487784\pi$
$547$	−19.7910	+	34.2791i	−0.846203	+	1.46567i	−0.884572	+	0.466403i	$0.845549\pi$
$548$	40.5156	+	23.3917i	1.73074	+	0.999243i
$549$	−41.2097	+	18.5411i	−1.75879	+	0.791313i
$550$	−18.1734	−	31.4772i	−0.774914	−	1.34219i
$551$	−5.07639	−	2.93085i	−0.216261	−	0.124859i
$552$	−5.73243	−	26.7122i	−0.243989	−	1.13695i
$553$	11.2757	+	6.51001i	0.479490	+	0.276834i
$554$	−50.3821	+	29.0881i	−2.14053	+	1.23584i
$555$	8.48580	−	1.82105i	0.360202	−	0.0772993i
$556$	−5.25781	−	9.10680i	−0.222981	−	0.386214i
$557$	−27.9551	−	16.1399i	−1.18449	−	0.683868i	−0.227444	−	0.973791i	$-0.573037\pi$
$557$	−27.9551	−	16.1399i	−1.18449	−	0.683868i	−0.957050	+	0.289923i	$0.906370\pi$
$558$	5.58234	−	55.1862i	0.236319	−	2.33622i
$559$	7.16555	+	2.49223i	0.303071	+	0.105410i
$560$	−1.24670	+	2.15935i	−0.0526826	+	0.0912490i
$561$	−15.8927	−	5.12953i	−0.670988	−	0.216569i
$562$	13.5680			0.572332
$563$	9.33559	−	16.1697i	0.393448	−	0.681472i	−0.599454	−	0.800409i	$-0.704615\pi$
$563$	9.33559	−	16.1697i	0.393448	−	0.681472i	0.992902	+	0.118937i	$0.0379488\pi$
$564$	−18.8800	+	17.0666i	−0.794992	+	0.718632i
$565$			38.8557i			1.63467i
$566$	64.1078	−	37.0127i	2.69465	−	1.55576i
$567$	6.73517	+	5.96972i	0.282850	+	0.250704i
$568$	15.8781	+	27.5016i	0.666228	+	1.15394i
$569$	−11.3319	−	19.6275i	−0.475059	−	0.822827i	0.524533	−	0.851390i	$-0.324240\pi$
$569$	−11.3319	−	19.6275i	−0.475059	−	0.822827i	−0.999592	+	0.0285634i	$0.990907\pi$
$570$	−12.8127	−	59.7053i	−0.536667	−	2.50078i
$571$	−17.4755	−	30.2684i	−0.731326	−	1.26669i	−0.956316	−	0.292333i	$-0.905568\pi$
$571$	−17.4755	−	30.2684i	−0.731326	−	1.26669i	0.224990	−	0.974361i	$-0.427765\pi$
$572$	20.1079	−	57.8136i	0.840755	−	2.41731i
$573$	17.1353	−	3.67724i	0.715839	−	0.153619i
$574$	−1.66397	+	0.960694i	−0.0694528	+	0.0400986i
$575$	−7.48737	+	12.9685i	−0.312245	+	0.540824i
$576$	34.0630	−	15.3256i	1.41929	−	0.638568i
$577$		−	14.3419i		−	0.597063i	−0.954400	−	0.298531i	$-0.903503\pi$
$577$		−	14.3419i		−	0.597063i	0.954400	−	0.298531i	$-0.0964967\pi$
$578$		−	30.7862i		−	1.28054i
$579$	6.90230	+	32.1636i	0.286850	+	1.33667i
$580$	9.35316	−	5.40005i	0.388369	−	0.224225i
$581$	3.11407	−	5.39373i	0.129194	−	0.223770i
$582$	30.2102	+	33.4202i	1.25225	+	1.38531i
$583$	28.4621	−	16.4326i	1.17878	−	0.680569i
$584$	37.4043			1.54780
$585$	−25.2768	+	17.7292i	−1.04507	+	0.733011i
$586$	−56.6624			−2.34070
$587$	0.525810	−	0.303577i	0.0217025	−	0.0125300i	−0.489109	−	0.872222i	$-0.662678\pi$
$587$	0.525810	−	0.303577i	0.0217025	−	0.0125300i	0.510812	+	0.859692i	$0.329345\pi$
$588$	1.82137	−	5.64309i	0.0751120	−	0.232717i
$589$	21.0537	−	36.4661i	0.867502	−	1.50256i
$590$	−3.18395	+	1.83825i	−0.131081	+	0.0756796i
$591$	36.5206	+	11.7874i	1.50226	+	0.484870i
$592$		−	1.53350i		−	0.0630266i
$593$		−	24.3613i		−	1.00040i	−0.865910	−	0.500200i	$-0.833260\pi$
$593$		−	24.3613i		−	1.00040i	0.865910	−	0.500200i	$-0.166740\pi$
$594$	6.62219	+	59.6406i	0.271712	+	2.44708i
$595$	2.77494	−	4.80633i	0.113761	−	0.197040i
$596$	−35.8788	+	20.7146i	−1.46965	+	0.848504i
$597$	0.682954	+	0.755524i	0.0279515	+	0.0309215i
$598$	−39.2405	+	7.50114i	−1.60466	+	0.306745i
$599$	3.93320	+	6.81250i	0.160706	+	0.278351i	0.935122	−	0.354325i	$-0.115290\pi$
$599$	3.93320	+	6.81250i	0.160706	+	0.278351i	−0.774416	+	0.632677i	$0.781956\pi$
$600$	17.1987	+	5.55108i	0.702135	+	0.226622i
$601$	−18.3179	−	31.7275i	−0.747202	−	1.29419i	−0.949159	−	0.314798i	$-0.898063\pi$
$601$	−18.3179	−	31.7275i	−0.747202	−	1.29419i	0.201956	−	0.979395i	$-0.435270\pi$
$602$	2.45011	+	4.24372i	0.0998592	+	0.172961i
$603$	18.3754	+	40.8416i	0.748306	+	1.66320i
$604$	24.9084	−	14.3809i	1.01351	−	0.585149i
$605$			38.7908i			1.57707i
$606$	54.2473	+	17.5089i	2.20365	+	0.711251i
$607$	−19.5672	+	33.8915i	−0.794210	+	1.37561i	0.129129	+	0.991628i	$0.458782\pi$
$607$	−19.5672	+	33.8915i	−0.794210	+	1.37561i	−0.923340	+	0.383984i	$0.874552\pi$
$608$	24.3762			0.988586
$609$	−1.42008	+	1.28368i	−0.0575446	+	0.0520173i
$610$	50.0642	−	86.7137i	2.02704	−	3.51094i
$611$	10.1162	+	11.7106i	0.409256	+	0.473760i
$612$	18.2113	−	8.19364i	0.736150	−	0.331208i
$613$	−24.3424	−	14.0541i	−0.983181	−	0.567640i	−0.0799518	−	0.996799i	$-0.525477\pi$
$613$	−24.3424	−	14.0541i	−0.983181	−	0.567640i	−0.903229	+	0.429159i	$0.858810\pi$
$614$	15.1014	+	26.1564i	0.609444	+	1.05559i
$615$	2.73523	+	3.02587i	0.110295	+	0.122015i
$616$	14.2371	−	8.21979i	0.573629	−	0.331185i
$617$	24.2237	+	13.9856i	0.975209	+	0.563037i	0.900820	−	0.434192i	$-0.142966\pi$
$617$	24.2237	+	13.9856i	0.975209	+	0.563037i	0.0743890	+	0.997229i	$0.476299\pi$
$618$	32.2829	+	10.4197i	1.29861	+	0.419141i
$619$	−5.14227	−	2.96889i	−0.206685	−	0.119330i	0.393085	−	0.919502i	$-0.371408\pi$
$619$	−5.14227	−	2.96889i	−0.206685	−	0.119330i	−0.599770	+	0.800172i	$0.704741\pi$
$620$	38.7911	+	67.1881i	1.55789	+	2.69834i
$621$	19.9156	−	14.6487i	0.799186	−	0.587831i
$622$	64.3830	+	37.1715i	2.58152	+	1.49044i
$623$	2.88133	−	4.99061i	0.115438	−	0.199945i
$624$	2.12575	+	5.02405i	0.0850981	+	0.201123i
$625$	15.4155	+	26.7004i	0.616619	+	1.06802i
$626$		−	11.4164i		−	0.456290i
$627$	−13.9921	+	43.3512i	−0.558790	+	1.73128i
$628$	50.7576			2.02545
$629$			3.41331i			0.136098i
$630$	−19.8408	−	2.00699i	−0.790478	−	0.0799605i
$631$	0.663867	−	0.383284i	0.0264281	−	0.0152583i	−0.486728	−	0.873554i	$-0.661810\pi$
$631$	0.663867	−	0.383284i	0.0264281	−	0.0152583i	0.513156	+	0.858295i	$0.328476\pi$
$632$	−37.3812	−	21.5820i	−1.48694	−	0.858487i
$633$	23.3434	−	5.00949i	0.927817	−	0.199109i
$634$	−75.5851			−3.00187
$635$			21.6082i			0.857495i
$636$	−12.0713	+	37.4002i	−0.478659	+	1.48301i
$637$	−3.40545	−	1.18444i	−0.134929	−	0.0469292i
$638$	−12.7634			−0.505307
$639$	−16.8001	+	23.3144i	−0.664600	+	0.922302i
$640$	−28.2631	+	48.9532i	−1.11720	+	1.93504i
$641$	2.44175			0.0964431			0.0482216	−	0.998837i	$-0.484645\pi$
$641$	2.44175			0.0964431			0.0482216	+	0.998837i	$0.484645\pi$
$642$	−13.6968	−	63.8249i	−0.540570	−	2.51897i
$643$	−36.8832	−	21.2945i	−1.45453	−	0.839773i	−0.455796	−	0.890084i	$-0.650645\pi$
$643$	−36.8832	−	21.2945i	−1.45453	−	0.839773i	−0.998734	+	0.0503114i	$0.983979\pi$
$644$	−14.1066	−	8.14443i	−0.555876	−	0.320935i
$645$	7.71705	−	6.97581i	0.303858	−	0.274672i
$646$	24.0158			0.944887
$647$	19.0140	−	32.9332i	0.747516	−	1.29474i	−0.201493	−	0.979490i	$-0.564579\pi$
$647$	19.0140	−	32.9332i	0.747516	−	1.29474i	0.949010	−	0.315246i	$-0.102087\pi$
$648$	−22.3285	−	19.7908i	−0.877146	−	0.777458i
$649$	2.74262			0.107657
$650$	8.68156	−	24.9609i	0.340519	−	0.979047i
$651$	−9.22127	−	10.2011i	−0.361410	−	0.399813i
$652$		−	48.9081i		−	1.91539i
$653$	−31.3450			−1.22663			−0.613313	−	0.789840i	$-0.710163\pi$
$653$	−31.3450			−1.22663			−0.613313	+	0.789840i	$0.710163\pi$
$654$	−12.1103	−	13.3971i	−0.473551	−	0.523869i
$655$	13.8632	+	8.00394i	0.541681	+	0.312740i
$656$	0.624148	−	0.360352i	0.0243689	−	0.0140694i
$657$	13.8879	+	30.8676i	0.541819	+	1.20426i
$658$			9.99539i			0.389661i
$659$	23.9683			0.933673			0.466837	−	0.884344i	$-0.345394\pi$
$659$	23.9683			0.933673			0.466837	+	0.884344i	$0.345394\pi$
$660$	−56.2827	−	62.2632i	−2.19080	−	2.42359i
$661$		−	44.1325i		−	1.71655i	−0.513186	−	0.858277i	$-0.671535\pi$
$661$		−	44.1325i		−	1.71655i	0.513186	−	0.858277i	$-0.328465\pi$
$662$	−22.2165	−	38.4801i	−0.863468	−	1.49557i
$663$	−4.73155	−	11.1827i	−0.183758	−	0.434299i
$664$	−10.3238	+	17.8813i	−0.400641	+	0.693931i
$665$	−13.1105	−	7.56934i	−0.508402	−	0.293526i
$666$	11.1850	−	5.03233i	0.433408	−	0.194999i
$667$	2.62924	+	4.55397i	0.101804	+	0.176330i
$668$	4.28662	+	2.47488i	0.165854	+	0.0957561i
$669$	−2.65956	+	2.40410i	−0.102824	+	0.0929479i
$670$	−85.9392	−	49.6170i	−3.32012	−	1.91687i
$671$	−64.6872	+	37.3472i	−2.49722	+	1.44177i
$672$	2.44517	−	7.57580i	0.0943245	−	0.292243i
$673$	18.1274	+	31.3976i	0.698761	+	1.21029i	0.968896	+	0.247467i	$0.0795982\pi$
$673$	18.1274	+	31.3976i	0.698761	+	1.21029i	−0.270135	+	0.962822i	$0.587068\pi$
$674$	61.1029	+	35.2778i	2.35360	+	1.35885i
$675$	1.80478	+	16.2542i	0.0694660	+	0.625624i
$676$	41.3681	−	16.4155i	1.59108	−	0.631366i
$677$	−6.98830	+	12.1041i	−0.268582	+	0.465198i	−0.968496	−	0.249029i	$-0.919888\pi$
$677$	−6.98830	+	12.1041i	−0.268582	+	0.465198i	0.699914	+	0.714227i	$0.253222\pi$
$678$	11.5213	+	53.6873i	0.442472	+	2.06185i
$679$	11.1686			0.428612
$680$	−9.19949	+	15.9340i	−0.352784	+	0.611040i
$681$	5.94869	+	27.7199i	0.227954	+	1.06223i
$682$		−	91.6853i		−	3.51081i
$683$	−11.3265	+	6.53936i	−0.433397	+	0.250222i	−0.700793	−	0.713365i	$-0.747170\pi$
$683$	−11.3265	+	6.53936i	−0.433397	+	0.250222i	0.267396	+	0.963587i	$0.413837\pi$
$684$	−22.3502	−	49.6760i	−0.854582	−	1.89941i
$685$	−19.5027	−	33.7796i	−0.745159	−	1.29065i
$686$	−1.16442	−	2.01684i	−0.0444579	−	0.0770034i
$687$	−5.89210	+	5.32615i	−0.224798	+	0.203205i
$688$	−0.919027	−	1.59180i	−0.0350376	−	0.0606869i
$689$	22.5700	+	7.84999i	0.859848	+	0.299061i
$690$	−16.8262	+	52.1322i	−0.640564	+	1.98464i
$691$	5.90245	−	3.40778i	0.224540	−	0.129638i	−0.383511	−	0.923536i	$-0.625285\pi$
$691$	5.90245	−	3.40778i	0.224540	−	0.129638i	0.608051	+	0.793898i	$0.291952\pi$
$692$	−29.7349	+	51.5023i	−1.13035	+	1.95782i
$693$	12.0694	+	8.69709i	0.458480	+	0.330375i
$694$		−	6.47783i		−	0.245895i
$695$			8.76734i			0.332564i
$696$	4.70786	−	4.25566i	0.178451	−	0.161311i
$697$	−1.38925	+	0.802082i	−0.0526215	+	0.0303810i
$698$	−35.0852	+	60.7694i	−1.32800	+	2.30016i
$699$	5.46163	−	1.17207i	0.206578	−	0.0443316i
$700$	9.33146	−	5.38752i	0.352696	−	0.203629i
$701$	5.66724			0.214049			0.107024	−	0.994256i	$-0.465868\pi$
$701$	5.66724			0.214049			0.107024	+	0.994256i	$0.465868\pi$
$702$	−29.6682	+	31.9915i	−1.11975	+	1.20744i
$703$	9.31067			0.351159
$704$	53.4690	−	30.8703i	2.01519	−	1.16347i
$705$	20.7468	−	4.45225i	0.781368	−	0.167681i
$706$	9.76314	−	16.9102i	0.367441	−	0.636426i
$707$	12.2384	−	7.06586i	0.460274	−	0.265739i
$708$	−2.43293	+	2.19924i	−0.0914351	+	0.0826526i
$709$			13.6321i			0.511964i	0.966681	+	0.255982i	$0.0823988\pi$
$709$			13.6321i			0.511964i	−0.966681	+	0.255982i	$0.917601\pi$
$710$		−	63.6746i		−	2.38966i
$711$	3.93104	−	38.8617i	0.147426	−	1.45743i
$712$	−9.55222	+	16.5449i	−0.357984	+	0.620047i
$713$	−32.7133	+	18.8870i	−1.22512	+	0.707325i
$714$	2.40901	−	7.46377i	0.0901550	−	0.279324i
$715$	−38.6197	+	33.3615i	−1.44429	+	1.24765i
$716$	7.80838	+	13.5245i	0.291813	+	0.505435i
$717$	16.1036	−	14.5568i	0.601400	−	0.543635i
$718$	13.1076	+	22.7030i	0.489170	+	0.847267i
$719$	18.8550	+	32.6578i	0.703172	+	1.21793i	0.967347	+	0.253455i	$0.0815670\pi$
$719$	18.8550	+	32.6578i	0.703172	+	1.21793i	−0.264175	+	0.964475i	$0.585100\pi$
$720$	7.44221	+	0.752814i	0.277355	+	0.0280557i
$721$	7.28317	−	4.20494i	0.271240	−	0.156600i
$722$		−	21.2609i		−	0.791248i
$723$	−1.45254	−	6.76862i	−0.0540207	−	0.251728i
$724$	−20.8976	+	36.1957i	−0.776653	+	1.34520i
$725$	−3.47847			−0.129187
$726$	11.5021	+	53.5977i	0.426881	+	1.98920i
$727$	−25.0686	+	43.4200i	−0.929741	+	1.61036i	−0.145988	+	0.989286i	$0.546636\pi$
$727$	−25.0686	+	43.4200i	−0.929741	+	1.61036i	−0.783753	+	0.621072i	$0.786697\pi$
$728$	11.2898	+	3.92666i	0.418427	+	0.145532i
$729$	8.04183	−	25.7746i	0.297846	−	0.954614i
$730$	−64.9517	−	37.4999i	−2.40397	−	1.38793i
$731$	2.04560	+	3.54308i	0.0756591	+	0.131045i
$732$	27.4350	−	85.0012i	1.01403	−	3.14173i
$733$	−34.5804	+	19.9650i	−1.27726	+	0.737424i	−0.976343	−	0.216227i	$-0.930625\pi$
$733$	−34.5804	+	19.9650i	−1.27726	+	0.737424i	−0.300913	+	0.953652i	$0.597291\pi$
$734$	37.0052	+	21.3650i	1.36589	+	0.788596i
$735$	−3.66755	+	3.31528i	−0.135280	+	0.122286i
$736$	−18.9379	−	10.9338i	−0.698061	−	0.403026i
$737$	37.0136	+	64.1094i	1.36341	+	2.36150i
$738$	4.67651	+	3.36984i	0.172145	+	0.124046i
$739$	8.31717	+	4.80192i	0.305952	+	0.176641i	0.645114	−	0.764087i	$-0.276810\pi$
$739$	8.31717	+	4.80192i	0.305952	+	0.176641i	−0.339162	+	0.940728i	$0.610143\pi$
$740$	−8.57737	+	14.8564i	−0.315311	+	0.546134i
$741$	−30.5036	+	12.9065i	−1.12058	+	0.474132i
$742$	7.71735	+	13.3668i	0.283313	+	0.490712i
$743$		−	18.1520i		−	0.665932i	−0.942939	−	0.332966i	$-0.891951\pi$
$743$		−	18.1520i		−	0.665932i	0.942939	−	0.332966i	$-0.108049\pi$
$744$	30.5704	+	33.8188i	1.12077	+	1.23986i
$745$	34.5414			1.26550
$746$			29.6348i			1.08501i
$747$	−18.5896	−	1.88042i	−0.680157	−	0.0688010i
$748$	28.5865	−	16.5044i	1.04523	−	0.603461i
$749$	−14.0151	−	8.09161i	−0.512100	−	0.295661i
$750$	14.3040	+	15.8239i	0.522307	+	0.577807i
$751$	−18.3021			−0.667852			−0.333926	−	0.942599i	$-0.608374\pi$
$751$	−18.3021			−0.667852			−0.333926	+	0.942599i	$0.608374\pi$
$752$		−	3.74923i		−	0.136720i
$753$	−31.0833	−	34.3861i	−1.13274	−	1.25310i
$754$	−6.06657	−	7.02274i	−0.220931	−	0.255753i
$755$	−23.9799			−0.872719
$756$	−17.6806	+	1.96316i	−0.643036	+	0.0713994i
$757$	23.6367	−	40.9400i	0.859090	−	1.48799i	−0.0137073	−	0.999906i	$-0.504363\pi$
$757$	23.6367	−	40.9400i	0.859090	−	1.48799i	0.872798	−	0.488082i	$-0.162303\pi$
$758$	−19.4093			−0.704976
$759$	30.3154	−	27.4036i	1.10038	−	0.994687i
$760$	43.4640	+	25.0939i	1.57660	+	0.910252i
$761$	−2.28358	−	1.31843i	−0.0827797	−	0.0477929i	0.458039	−	0.888932i	$-0.348552\pi$
$761$	−2.28358	−	1.31843i	−0.0827797	−	0.0477929i	−0.540818	+	0.841139i	$0.681885\pi$
$762$	6.40715	+	29.8563i	0.232106	+	1.08158i
$763$	−4.47715			−0.162084
$764$	−17.3202	+	29.9995i	−0.626624	+	1.08535i
$765$	−16.5651	−	1.67563i	−0.598912	−	0.0605827i
$766$	−78.6686			−2.84241
$767$	1.30360	+	1.50906i	0.0470702	+	0.0544890i
$768$	−11.2883	+	34.9743i	−0.407332	+	1.26203i
$769$		−	35.7170i		−	1.28799i	−0.765031	−	0.643994i	$-0.777276\pi$
$769$		−	35.7170i		−	1.28799i	0.765031	−	0.643994i	$-0.222724\pi$
$770$	−32.9632			−1.18791
$771$	−17.0735	+	3.66398i	−0.614889	+	0.131955i
$772$	−56.3101	−	32.5107i	−2.02665	−	1.17008i
$773$	−17.6326	+	10.1802i	−0.634202	+	0.366156i	−0.782377	−	0.622805i	$-0.785993\pi$
$773$	−17.6326	+	10.1802i	−0.634202	+	0.366156i	0.148176	+	0.988961i	$0.452660\pi$
$774$	8.59430	−	11.9268i	0.308916	−	0.428699i
$775$		−	24.9875i		−	0.897576i
$776$	−37.0263			−1.32917
$777$	0.933950	−	2.89363i	0.0335053	−	0.103808i
$778$			32.6212i			1.16953i
$779$	2.18788	+	3.78952i	0.0783889	+	0.135774i
$780$	7.50703	−	60.5626i	0.268795	−	2.16849i
$781$	−23.7501	+	41.1365i	−0.849847	+	1.47198i
$782$	−18.6579	−	10.7721i	−0.667204	−	0.385211i
$783$	5.25994	+	2.30503i	0.187975	+	0.0823749i
$784$	0.436771	+	0.756509i	0.0155990	+	0.0270182i
$785$	−36.6492	−	21.1594i	−1.30807	−	0.755212i
$786$	21.5283	+	6.94847i	0.767887	+	0.247844i
$787$	16.6439	+	9.60935i	0.593290	+	0.342536i	0.766397	−	0.642367i	$-0.222047\pi$
$787$	16.6439	+	9.60935i	0.593290	+	0.342536i	−0.173107	+	0.984903i	$0.555381\pi$
$788$	−65.6905	+	37.9264i	−2.34013	+	1.35107i
$789$	1.12813	+	1.24801i	0.0401626	+	0.0444302i
$790$	43.2744	+	74.9534i	1.53963	+	2.66672i
$791$	11.7890	+	6.80639i	0.419169	+	0.242007i
$792$	−40.0127	−	28.8327i	−1.42179	−	1.02452i
$793$	−51.2959	−	17.8410i	−1.82157	−	0.633554i
$794$	21.3067	−	36.9042i	0.756146	−	1.30968i
$795$	24.3071	−	21.9724i	0.862084	−	0.779279i
$796$	−2.01305			−0.0713507
$797$	3.60413	−	6.24254i	0.127665	−	0.221122i	−0.795107	−	0.606470i	$-0.792585\pi$
$797$	3.60413	−	6.24254i	0.127665	−	0.221122i	0.922771	+	0.385348i	$0.125918\pi$
$798$	−20.3593	−	6.57119i	−0.720712	−	0.232617i
$799$			8.34514i			0.295230i
$800$	12.5274	−	7.23270i	0.442911	−	0.255715i
$801$	−17.2002	−	1.73988i	−0.607740	−	0.0614757i
$802$	5.88340	+	10.1903i	0.207750	+	0.359833i
$803$	27.9744	+	48.4530i	0.987194	+	1.70987i
$804$	−84.2419	−	27.1900i	−2.97098	−	0.958917i
$805$	6.79037	+	11.7613i	0.239329	+	0.414530i
$806$	50.4476	−	43.5790i	1.77694	−	1.53501i
$807$	−3.15230	−	3.48726i	−0.110966	−	0.122757i
$808$	−40.5730	+	23.4248i	−1.42735	+	0.824082i
$809$	23.3335	−	40.4149i	0.820363	−	1.42091i	−0.0850488	−	0.996377i	$-0.527105\pi$
$809$	23.3335	−	40.4149i	0.820363	−	1.42091i	0.905412	−	0.424534i	$-0.139562\pi$
$810$	18.9315	+	56.7519i	0.665185	+	1.99406i
$811$			40.0829i			1.40750i	0.710447	+	0.703751i	$0.248493\pi$
$811$			40.0829i			1.40750i	−0.710447	+	0.703751i	$0.751507\pi$
$812$		−	3.78373i		−	0.132783i
$813$	−30.1497	−	9.73114i	−1.05740	−	0.341286i
$814$	17.5571	−	10.1366i	0.615376	−	0.355288i
$815$	−20.3884	+	35.3138i	−0.714176	+	1.23699i
$816$	−0.903610	+	2.79963i	−0.0316327	+	0.0980065i
$817$	9.66463	−	5.57988i	0.338123	−	0.195215i
$818$	−47.4800			−1.66010
$819$	0.951367	+	10.7747i	0.0332434	+	0.376500i
$820$	−8.06226			−0.281546
$821$	18.3142	−	10.5737i	0.639170	−	0.369025i	−0.145125	−	0.989413i	$-0.546358\pi$
$821$	18.3142	−	10.5737i	0.639170	−	0.369025i	0.784295	+	0.620389i	$0.213025\pi$
$822$	−36.9632	−	40.8908i	−1.28924	−	1.42623i
$823$	−18.6695	+	32.3366i	−0.650779	+	1.12718i	0.332155	+	0.943225i	$0.392224\pi$
$823$	−18.6695	+	32.3366i	−0.650779	+	1.12718i	−0.982934	+	0.183958i	$0.941109\pi$
$824$	−24.1452	+	13.9403i	−0.841139	+	0.485632i
$825$	5.67201	+	26.4306i	0.197474	+	0.920196i
$826$			1.28803i			0.0448164i
$827$		−	7.46223i		−	0.259487i	−0.991548	−	0.129744i	$-0.958585\pi$
$827$		−	7.46223i		−	0.259487i	0.991548	−	0.129744i	$-0.0414154\pi$
$828$	−4.91798	+	48.6185i	−0.170912	+	1.68961i
$829$	−27.5664	+	47.7465i	−0.957422	+	1.65830i	−0.228696	+	0.973498i	$0.573446\pi$
$829$	−27.5664	+	47.7465i	−0.957422	+	1.65830i	−0.728726	+	0.684805i	$0.759887\pi$
$830$	35.8541	−	20.7004i	1.24451	−	0.718521i
$831$	42.3047	−	9.07857i	1.46753	−	0.314932i
$832$	42.4000	+	14.7470i	1.46996	+	0.511261i
$833$	−0.972176	−	1.68386i	−0.0336839	−	0.0583422i
$834$	2.59965	+	12.1139i	0.0900184	+	0.419471i
$835$	−2.06342	−	3.57395i	−0.0714076	−	0.123682i
$836$	−45.0199	−	77.9768i	−1.55705	−	2.69688i
$837$	−16.5581	+	37.7846i	−0.572331	+	1.30603i
$838$	30.8190	−	17.7933i	1.06462	−	0.614661i
$839$		−	19.8399i		−	0.684950i	−0.939527	−	0.342475i	$-0.888735\pi$
$839$		−	19.8399i		−	0.684950i	0.939527	−	0.342475i	$-0.111265\pi$
$840$	12.1587	−	10.9908i	0.419515	−	0.379220i
$841$	13.8893	−	24.0569i	0.478940	−	0.829548i
$842$	−35.5152			−1.22394
$843$	−9.60322	−	3.09954i	−0.330752	−	0.106754i
$844$	−23.5953	+	40.8683i	−0.812184	+	1.40674i
$845$	−36.7127	−	5.39247i	−1.26296	−	0.185506i
$846$	27.3459	−	12.3034i	0.940170	−	0.423001i
$847$	11.7693	+	6.79503i	0.404399	+	0.233480i
$848$	−2.89474	−	5.01384i	−0.0994059	−	0.172176i
$849$	−53.8298	+	11.5519i	−1.84743	+	0.396459i
$850$	12.3422	−	7.12574i	0.423332	−	0.244411i
$851$	−7.23347	−	4.17625i	−0.247960	−	0.143160i
$852$	−11.9180	−	55.5361i	−0.408305	−	1.90264i
$853$	−15.5705	−	8.98961i	−0.533123	−	0.307798i	0.209164	−	0.977880i	$-0.432926\pi$
$853$	−15.5705	−	8.98961i	−0.533123	−	0.307798i	−0.742287	+	0.670082i	$0.766259\pi$
$854$	−17.5396	−	30.3794i	−0.600192	−	1.03956i
$855$	−4.57072	+	45.1854i	−0.156315	+	1.54531i
$856$	46.4629	+	26.8254i	1.58807	+	0.916873i
$857$	1.29211	−	2.23800i	0.0441377	−	0.0764487i	−0.843113	−	0.537737i	$-0.819279\pi$
$857$	1.29211	−	2.23800i	0.0441377	−	0.0764487i	0.887250	+	0.461288i	$0.152613\pi$
$858$	−43.4690	+	57.5472i	−1.48401	+	1.96463i
$859$	−4.35304	−	7.53969i	−0.148524	−	0.257251i	0.782158	−	0.623080i	$-0.214119\pi$
$859$	−4.35304	−	7.53969i	−0.148524	−	0.257251i	−0.930682	+	0.365829i	$0.880786\pi$
$860$			20.5617i			0.701147i
$861$	1.39720	−	0.299838i	0.0476163	−	0.0102184i
$862$	−53.1876			−1.81158
$863$		−	40.5080i		−	1.37891i	−0.724329	−	0.689455i	$-0.757850\pi$
$863$		−	40.5080i		−	1.37891i	0.724329	−	0.689455i	$-0.242150\pi$
$864$	−23.7360	+	2.63552i	−0.807515	+	0.0896623i
$865$	42.9397	−	24.7913i	1.45999	−	0.842928i
$866$	−44.0252	−	25.4180i	−1.49604	−	0.863738i
$867$	−7.03295	+	21.7900i	−0.238851	+	0.740026i
$868$	27.1803			0.922558
$869$		−	64.5641i		−	2.19019i
$870$	−12.4416	+	2.66997i	−0.421811	+	0.0905205i
$871$	−17.6817	+	50.8377i	−0.599121	+	1.72257i
$872$	14.8427			0.502637
$873$	−13.7476	−	30.5556i	−0.465285	−	1.03415i
$874$	−29.3837	+	50.8941i	−0.993918	+	1.72152i
$875$	5.28814			0.178772
$876$	−63.6689	−	20.5498i	−2.15117	−	0.694314i
$877$	−15.2794	−	8.82157i	−0.515949	−	0.297883i	0.219327	−	0.975652i	$-0.429614\pi$
$877$	−15.2794	−	8.82157i	−0.515949	−	0.297883i	−0.735276	+	0.677768i	$0.762947\pi$
$878$	0.900518	+	0.519914i	0.0303910	+	0.0175463i
$879$	40.1047	+	12.9442i	1.35270	+	0.436598i
$880$	12.3643			0.416802
$881$	−9.04342	+	15.6637i	−0.304681	+	0.527722i	−0.977190	−	0.212366i	$-0.931883\pi$
$881$	−9.04342	+	15.6637i	−0.304681	+	0.527722i	0.672510	+	0.740088i	$0.265216\pi$
$882$	−4.08447	+	5.66824i	−0.137531	+	0.190860i
$883$	15.7745			0.530856			0.265428	−	0.964131i	$-0.414487\pi$
$883$	15.7745			0.530856			0.265428	+	0.964131i	$0.414487\pi$
$884$	22.6686	+	7.88429i	0.762428	+	0.265177i
$885$	2.67348	−	0.573729i	0.0898682	−	0.0192857i
$886$			38.1018i			1.28005i
$887$	52.8369			1.77409			0.887045	−	0.461684i	$-0.152754\pi$
$887$	52.8369			1.77409			0.887045	+	0.461684i	$0.152754\pi$
$888$	−3.09624	+	9.59298i	−0.103903	+	0.321919i
$889$	6.55603	+	3.78513i	0.219882	+	0.126949i
$890$	33.1744	−	19.1533i	1.11201	−	0.642019i
$891$	8.93751	−	43.7255i	0.299418	−	1.46486i
$892$		−	7.08624i		−	0.237265i
$893$	22.7635			0.761750
$894$	47.7262	−	10.2420i	1.59620	−	0.342545i
$895$		−	13.0204i		−	0.435223i
$896$	9.90176	+	17.1503i	0.330795	+	0.572953i
$897$	29.4874	+	3.65511i	0.984556	+	0.122041i
$898$	−19.9712	+	34.5911i	−0.666446	+	1.15432i
$899$	−7.59895	−	4.38725i	−0.253439	−	0.146323i
$900$	−26.2256	−	18.8979i	−0.874188	−	0.629930i
$901$	6.44320	+	11.1599i	0.214654	+	0.371792i
$902$	8.25136	+	4.76392i	0.274740	+	0.158621i
$903$	−0.764694	−	3.56335i	−0.0254474	−	0.118581i
$904$	−39.0830	−	22.5646i	−1.29988	−	0.750487i
$905$	30.1779	−	17.4232i	1.00315	−	0.579168i
$906$	−33.1333	+	7.11040i	−1.10078	+	0.236227i
$907$	−11.8091	−	20.4540i	−0.392115	−	0.679163i	0.600613	−	0.799540i	$-0.294923\pi$
$907$	−11.8091	−	20.4540i	−0.392115	−	0.679163i	−0.992728	+	0.120376i	$0.961590\pi$
$908$	−48.5305	−	28.0191i	−1.61054	−	0.929845i
$909$	−34.3955	−	24.7850i	−1.14083	−	0.822068i
$910$	−15.6678	−	18.1372i	−0.519381	−	0.601242i
$911$	7.28979	−	12.6263i	0.241521	−	0.418328i	−0.719626	−	0.694361i	$-0.755687\pi$
$911$	7.28979	−	12.6263i	0.241521	−	0.418328i	0.961148	+	0.276034i	$0.0890202\pi$
$912$	7.63669	+	2.46482i	0.252876	+	0.0816185i
$913$	−30.8844			−1.02212
$914$	−27.2239	+	47.1532i	−0.900487	+	1.55969i
$915$	−55.2439	+	49.9376i	−1.82631	+	1.65089i
$916$		−	15.6992i		−	0.518715i
$917$	4.85687	−	2.80411i	0.160388	−	0.0926000i
$918$	−23.3850	+	2.59655i	−0.771820	+	0.0856989i
$919$	−5.09736	−	8.82889i	−0.168146	−	0.291238i	0.769622	−	0.638500i	$-0.220445\pi$
$919$	−5.09736	−	8.82889i	−0.168146	−	0.291238i	−0.937768	+	0.347262i	$0.887111\pi$
$920$	−22.5115	−	38.9910i	−0.742181	−	1.28550i
$921$	−4.71324	−	21.9629i	−0.155307	−	0.723703i
$922$	4.33690	+	7.51173i	0.142828	+	0.247386i
$923$	−33.9231	+	6.48466i	−1.11659	+	0.213445i
$924$	−28.7501	+	6.16976i	−0.945808	+	0.202970i
$925$	4.78493	−	2.76258i	0.157328	−	0.0908331i
$926$	23.1784	−	40.1461i	0.761688	−	1.31928i
$927$	−20.4690	−	14.7497i	−0.672291	−	0.484445i
$928$		−	5.07962i		−	0.166747i
$929$			19.6842i			0.645816i	0.946430	+	0.322908i	$0.104660\pi$
$929$			19.6842i			0.645816i	−0.946430	+	0.322908i	$0.895340\pi$
$930$	−19.1797	−	89.3741i	−0.628926	−	2.93069i
$931$	−4.59315	+	2.65186i	−0.150534	+	0.0869111i
$932$	−5.52057	+	9.56191i	−0.180832	+	0.313211i
$933$	−37.0776	−	41.0173i	−1.21386	−	1.34285i
$934$	11.7635	−	6.79164i	0.384912	−	0.222229i
$935$	−27.5209			−0.900030
$936$	−3.15398	−	35.7205i	−0.103091	−	1.16756i
$937$	−23.2761			−0.760396			−0.380198	−	0.924905i	$-0.624144\pi$
$937$	−23.2761			−0.760396			−0.380198	+	0.924905i	$0.624144\pi$
$938$	−30.1081	+	17.3829i	−0.983064	+	0.567572i
$939$	−2.60801	+	8.08032i	−0.0851092	+	0.263691i
$940$	−20.9706	+	36.3222i	−0.683987	+	1.18470i
$941$	26.4356	−	15.2626i	0.861777	−	0.497547i	−0.00282971	−	0.999996i	$-0.500901\pi$
$941$	26.4356	−	15.2626i	0.861777	−	0.497547i	0.864607	+	0.502449i	$0.167567\pi$
$942$	−56.9126	−	18.3692i	−1.85431	−	0.598500i
$943$		−	3.92544i		−	0.127830i
$944$		−	0.483136i		−	0.0157247i
$945$	13.5845	+	5.95305i	0.441905	+	0.193653i
$946$	12.1497	−	21.0439i	0.395021	−	0.684197i
$947$	−41.0445	+	23.6970i	−1.33377	+	0.770050i	−0.985875	−	0.167485i	$-0.946435\pi$
$947$	−41.0445	+	23.6970i	−1.33377	+	0.770050i	−0.347891	+	0.937535i	$0.613102\pi$
$948$	51.7725	+	57.2737i	1.68149	+	1.86016i
$949$	−13.3636	+	38.4225i	−0.433800	+	1.24725i
$950$	−19.4373	−	33.6663i	−0.630628	−	1.09228i
$951$	53.4979	+	17.2670i	1.73479	+	0.559922i
$952$	3.22297	+	5.58234i	0.104457	+	0.180925i
$953$	18.6810	+	32.3564i	0.605136	+	1.04813i	0.992030	+	0.126003i	$0.0402147\pi$
$953$	18.6810	+	32.3564i	0.605136	+	1.04813i	−0.386894	+	0.922124i	$0.626452\pi$
$954$	27.0703	−	37.5669i	0.876432	−	1.21627i
$955$	25.0119	−	14.4406i	0.809367	−	0.467288i
$956$			42.9072i			1.38772i
$957$	9.03371	+	2.91573i	0.292018	+	0.0942520i
$958$	7.04013	−	12.1939i	0.227456	−	0.393966i
$959$	−13.6652			−0.441272
$960$	45.6634	−	41.2773i	1.47378	−	1.33222i
$961$	16.0157	−	27.7400i	0.516635	−	0.894838i
$962$	13.9225	+	4.84234i	0.448879	+	0.156123i
$963$	−4.88609	+	48.3032i	−0.157452	+	1.55655i
$964$	11.8501	+	6.84166i	0.381666	+	0.220355i
$965$	27.1056	+	46.9482i	0.872560	+	1.51132i
$966$	12.8697	+	14.2372i	0.414076	+	0.458075i
$967$	16.8852	−	9.74865i	0.542990	−	0.313496i	−0.203300	−	0.979117i	$-0.565167\pi$
$967$	16.8852	−	9.74865i	0.542990	−	0.313496i	0.746290	+	0.665621i	$0.231833\pi$
$968$	−39.0178	−	22.5269i	−1.25408	−	0.724043i
$969$	−16.9980	−	5.48627i	−0.546053	−	0.176244i
$970$	64.2953	+	37.1209i	2.06440	+	1.19188i
$971$	−20.8349	−	36.0871i	−0.668624	−	1.15809i	−0.978289	−	0.207246i	$-0.933550\pi$
$971$	−20.8349	−	36.0871i	−0.668624	−	1.15809i	0.309665	−	0.950846i	$-0.399783\pi$
$972$	27.1341	+	45.9549i	0.870327	+	1.47400i
$973$	2.66006	+	1.53578i	0.0852775	+	0.0492350i
$974$	39.3780	−	68.2047i	1.26175	−	2.18542i
$975$	−11.8468	+	15.6836i	−0.379403	+	0.502279i
$976$	6.57902	+	11.3952i	0.210589	+	0.364751i
$977$		−	5.56561i		−	0.178060i	−0.996029	−	0.0890298i	$-0.971623\pi$
$977$		−	5.56561i		−	0.178060i	0.996029	−	0.0890298i	$-0.0283766\pi$
$978$	−17.6999	+	54.8389i	−0.565979	+	1.75356i
$979$	−28.5761			−0.913296
$980$		−	9.77200i		−	0.312155i
$981$	5.51098	+	12.2488i	0.175952	+	0.391074i
$982$	60.1443	−	34.7243i	1.91928	−	1.10810i
$983$	36.6488	+	21.1592i	1.16892	+	0.674874i	0.953425	−	0.301631i	$-0.0975312\pi$
$983$	36.6488	+	21.1592i	1.16892	+	0.674874i	0.215492	+	0.976506i	$0.430865\pi$
$984$	−4.63200	+	0.994025i	−0.147663	+	0.0316884i
$985$	63.2418			2.01505
$986$		−	5.00450i		−	0.159376i
$987$	2.28339	−	7.07457i	0.0726813	−	0.225186i
$988$	21.5064	−	61.8344i	0.684210	−	1.96721i
$989$	−10.0113			−0.318340
$990$	40.5747	+	90.1822i	1.28955	+	2.86618i
$991$	−11.8472	+	20.5199i	−0.376338	+	0.651836i	−0.990526	−	0.137323i	$-0.956150\pi$
$991$	−11.8472	+	20.5199i	−0.376338	+	0.651836i	0.614189	+	0.789159i	$0.289483\pi$
$992$	36.4893			1.15854
$993$	6.93389	+	32.3108i	0.220040	+	1.02535i
$994$	−19.3192	−	11.1539i	−0.612767	−	0.353781i
$995$	1.45351	+	0.839185i	0.0460794	+	0.0266039i
$996$	27.3970	−	24.7655i	0.868106	−	0.784723i
$997$	11.3508			0.359484			0.179742	−	0.983714i	$-0.442474\pi$
$997$	11.3508			0.359484			0.179742	+	0.983714i	$0.442474\pi$
$998$	−22.8915	+	39.6492i	−0.724617	+	1.25507i
$999$	−9.06614	+	1.00666i	−0.286840	+	0.0318492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dk.a.43.75	yes	168
9.4	even	3		819.2.bh.a.589.75	✓	168
13.10	even	6		819.2.bh.a.673.10	yes	168
117.49	even	6	inner	819.2.dk.a.400.75	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bh.a.589.75	✓	168	9.4	even	3
819.2.bh.a.673.10	yes	168	13.10	even	6
819.2.dk.a.43.75	yes	168	1.1	even	1	trivial
819.2.dk.a.400.75	yes	168	117.49	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.01684 - 1.16442i) q^{2} +(-1.69349 + 0.363423i) q^{3} +(1.71177 - 2.96487i) q^{4} +(-2.47194 + 1.42718i) q^{5} +(-2.99233 + 2.70491i) q^{6} +1.00000i q^{7} -3.31521i q^{8} +(2.73585 - 1.23091i) q^{9} +O(q^{10})\)	\(q+(2.01684 - 1.16442i) q^{2} +(-1.69349 + 0.363423i) q^{3} +(1.71177 - 2.96487i) q^{4} +(-2.47194 + 1.42718i) q^{5} +(-2.99233 + 2.70491i) q^{6} +1.00000i q^{7} -3.31521i q^{8} +(2.73585 - 1.23091i) q^{9} +(-3.32368 + 5.75678i) q^{10} +(4.29448 - 2.47942i) q^{11} +(-1.82137 + 5.64309i) q^{12} +(3.40545 + 1.18444i) q^{13} +(1.16442 + 2.01684i) q^{14} +(3.66755 - 3.31528i) q^{15} +(-0.436771 - 0.756509i) q^{16} +(0.972176 + 1.68386i) q^{17} +(4.08447 - 5.66824i) q^{18} +(4.59315 - 2.65186i) q^{19} +9.77200i q^{20} +(-0.363423 - 1.69349i) q^{21} +(5.77419 - 10.0012i) q^{22} -4.75790 q^{23} +(1.20482 + 5.61429i) q^{24} +(1.57367 - 2.72568i) q^{25} +(8.24745 - 1.57657i) q^{26} +(-4.18580 + 3.07881i) q^{27} +(2.96487 + 1.71177i) q^{28} +(-0.552604 - 0.957139i) q^{29} +(3.53649 - 10.9570i) q^{30} +(6.87558 - 3.96962i) q^{31} +(3.98031 + 2.29803i) q^{32} +(-6.37160 + 5.75959i) q^{33} +(3.92145 + 2.26405i) q^{34} +(-1.42718 - 2.47194i) q^{35} +(1.03365 - 10.2185i) q^{36} +(1.52031 + 0.877751i) q^{37} +(6.17577 - 10.6968i) q^{38} +(-6.19757 - 0.768219i) q^{39} +(4.73139 + 8.19501i) q^{40} +0.825037i q^{41} +(-2.70491 - 2.99233i) q^{42} +2.10414 q^{43} -16.9768i q^{44} +(-5.00613 + 6.94728i) q^{45} +(-9.59593 + 5.54021i) q^{46} +(3.71697 + 2.14599i) q^{47} +(1.01460 + 1.12241i) q^{48} -1.00000 q^{49} -7.32968i q^{50} +(-2.25833 - 2.49829i) q^{51} +(9.34106 - 8.06924i) q^{52} +6.62761 q^{53} +(-4.85705 + 11.0835i) q^{54} +(-7.07714 + 12.2580i) q^{55} +3.31521 q^{56} +(-6.81472 + 6.16016i) q^{57} +(-2.22903 - 1.28693i) q^{58} +(0.478979 + 0.276539i) q^{59} +(-3.55137 - 16.5488i) q^{60} -15.0629 q^{61} +(9.24464 - 16.0122i) q^{62} +(1.23091 + 2.73585i) q^{63} +12.4506 q^{64} +(-10.1085 + 1.93232i) q^{65} +(-6.14389 + 19.0354i) q^{66} +14.9283i q^{67} +6.65657 q^{68} +(8.05748 - 1.72913i) q^{69} +(-5.75678 - 3.32368i) q^{70} +(-8.29559 + 4.78946i) q^{71} +(-4.08073 - 9.06990i) q^{72} +11.2826i q^{73} +4.08830 q^{74} +(-1.67443 + 5.18783i) q^{75} -18.1575i q^{76} +(2.47942 + 4.29448i) q^{77} +(-13.3941 + 5.66722i) q^{78} +(6.51001 - 11.2757i) q^{79} +(2.15935 + 1.24670i) q^{80} +(5.96972 - 6.73517i) q^{81} +(0.960694 + 1.66397i) q^{82} +(-5.39373 - 3.11407i) q^{83} +(-5.64309 - 1.82137i) q^{84} +(-4.80633 - 2.77494i) q^{85} +(4.24372 - 2.45011i) q^{86} +(1.28368 + 1.42008i) q^{87} +(-8.21979 - 14.2371i) q^{88} +(-4.99061 - 2.88133i) q^{89} +(-2.00699 + 19.8408i) q^{90} +(-1.18444 + 3.40545i) q^{91} +(-8.14443 + 14.1066i) q^{92} +(-10.2011 + 9.22127i) q^{93} +9.99539 q^{94} +(-7.56934 + 13.1105i) q^{95} +(-7.57580 - 2.44517i) q^{96} -11.1686i q^{97} +(-2.01684 + 1.16442i) q^{98} +(8.69709 - 12.0694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 2 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 2 * q^9	\( 168 q + 84 q^{4} - 2 q^{9} + 12 q^{12} + 8 q^{14} - 84 q^{16} + 12 q^{18} - 6 q^{21} + 40 q^{23} - 84 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} + 34 q^{29} + 44 q^{30} + 36 q^{32} + 18 q^{33} + 16 q^{35} + 4 q^{36} - 12 q^{38} - 6 q^{39} - 30 q^{45} - 30 q^{47} - 2 q^{48} - 168 q^{49} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 114 q^{54} + 48 q^{56} - 54 q^{57} + 48 q^{59} + 24 q^{60} + 6 q^{62} - 12 q^{63} - 132 q^{64} - 16 q^{65} - 54 q^{66} - 156 q^{68} - 28 q^{69} + 24 q^{71} + 36 q^{72} - 84 q^{74} + 30 q^{75} - 16 q^{77} + 116 q^{78} - 6 q^{79} - 2 q^{81} - 6 q^{82} + 18 q^{83} - 24 q^{84} + 90 q^{85} - 24 q^{86} + 52 q^{87} + 24 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 66 q^{93} + 120 q^{94} - 48 q^{95} - 24 q^{96} + 6 q^{99}+O(q^{100}) \) 168 * q + 84 * q^4 - 2 * q^9 + 12 * q^12 + 8 * q^14 - 84 * q^16 + 12 * q^18 - 6 * q^21 + 40 * q^23 - 84 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 + 34 * q^29 + 44 * q^30 + 36 * q^32 + 18 * q^33 + 16 * q^35 + 4 * q^36 - 12 * q^38 - 6 * q^39 - 30 * q^45 - 30 * q^47 - 2 * q^48 - 168 * q^49 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 114 * q^54 + 48 * q^56 - 54 * q^57 + 48 * q^59 + 24 * q^60 + 6 * q^62 - 12 * q^63 - 132 * q^64 - 16 * q^65 - 54 * q^66 - 156 * q^68 - 28 * q^69 + 24 * q^71 + 36 * q^72 - 84 * q^74 + 30 * q^75 - 16 * q^77 + 116 * q^78 - 6 * q^79 - 2 * q^81 - 6 * q^82 + 18 * q^83 - 24 * q^84 + 90 * q^85 - 24 * q^86 + 52 * q^87 + 24 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 66 * q^93 + 120 * q^94 - 48 * q^95 - 24 * q^96 + 6 * q^99

Introduction

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