LMFDB - Embedded newform 483.2.q.d.127.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.6
Character	$\chi$	$=$	483.127
Dual form			483.2.q.d.232.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29607 - 1.47560i) q^{2} +(0.142315 - 0.989821i) q^{3} +(2.26374 - 4.95689i) q^{4} +(-3.38655 + 0.994380i) q^{5} +(-1.13381 - 2.48270i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-1.33981 - 9.31861i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(2.29607 - 1.47560i) q^{2} +(0.142315 - 0.989821i) q^{3} +(2.26374 - 4.95689i) q^{4} +(-3.38655 + 0.994380i) q^{5} +(-1.13381 - 2.48270i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-1.33981 - 9.31861i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-6.30846 + 7.28035i) q^{10} +(2.75123 + 1.76811i) q^{11} +(-4.58427 - 2.94613i) q^{12} +(1.90748 - 2.20135i) q^{13} +(-2.61879 - 0.768946i) q^{14} +(0.502303 + 3.49359i) q^{15} +(-9.68971 - 11.1825i) q^{16} +(0.578502 + 1.26674i) q^{17} +(-2.61879 + 0.768946i) q^{18} +(1.05264 - 2.30495i) q^{19} +(-2.73722 + 19.0378i) q^{20} +(-0.841254 + 0.540641i) q^{21} +8.92602 q^{22} +(4.03575 + 2.59089i) q^{23} -9.41443 q^{24} +(6.27364 - 4.03183i) q^{25} +(1.13141 - 7.86912i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-5.22860 + 1.53526i) q^{28} +(-1.62548 - 3.55931i) q^{29} +(6.30846 + 7.28035i) q^{30} +(0.993042 + 6.90676i) q^{31} +(-20.6830 - 6.07307i) q^{32} +(2.14165 - 2.47159i) q^{33} +(3.19749 + 2.05490i) q^{34} +(2.96922 + 1.90820i) q^{35} +(-3.56856 + 4.11833i) q^{36} +(4.31177 + 1.26605i) q^{37} +(-0.984248 - 6.84560i) q^{38} +(-1.90748 - 2.20135i) q^{39} +(13.8036 + 30.2256i) q^{40} +(-7.60403 + 2.23275i) q^{41} +(-1.13381 + 2.48270i) q^{42} +(1.41718 - 9.85669i) q^{43} +(14.9924 - 9.63500i) q^{44} +3.52952 q^{45} +(13.0895 - 0.00628143i) q^{46} +12.3572 q^{47} +(-12.4477 + 7.99964i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(8.45540 - 18.5147i) q^{50} +(1.33618 - 0.392338i) q^{51} +(-6.59380 - 14.4384i) q^{52} +(7.13820 + 8.23792i) q^{53} +(0.388427 + 2.70157i) q^{54} +(-11.0753 - 3.25201i) q^{55} +(-6.16514 + 7.11496i) q^{56} +(-2.13168 - 1.36995i) q^{57} +(-8.98433 - 5.77388i) q^{58} +(-4.20868 + 4.85707i) q^{59} +(18.4544 + 5.41871i) q^{60} +(0.0736215 + 0.512049i) q^{61} +(12.4717 + 14.3931i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-28.0566 + 8.23816i) q^{64} +(-4.27079 + 9.35172i) q^{65} +(1.27031 - 8.83517i) q^{66} +(-10.2844 + 6.60941i) q^{67} +7.58868 q^{68} +(3.13886 - 3.62595i) q^{69} +9.63328 q^{70} +(-9.57886 + 6.15596i) q^{71} +(-1.33981 + 9.31861i) q^{72} +(5.22882 - 11.4495i) q^{73} +(11.7683 - 3.45549i) q^{74} +(-3.09796 - 6.78358i) q^{75} +(-9.04249 - 10.4356i) q^{76} +(-0.465425 - 3.23710i) q^{77} +(-7.62800 - 2.23978i) q^{78} +(-5.92681 + 6.83991i) q^{79} +(43.9343 + 28.2349i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-14.1648 + 16.3470i) q^{82} +(-0.968156 - 0.284276i) q^{83} +(0.775521 + 5.39387i) q^{84} +(-3.21875 - 3.71463i) q^{85} +(-11.2906 - 24.7229i) q^{86} +(-3.75441 + 1.10239i) q^{87} +(12.7902 - 28.0065i) q^{88} +(1.12323 - 7.81227i) q^{89} +(8.10403 - 5.20814i) q^{90} -2.91280 q^{91} +(21.9786 - 14.1397i) q^{92} +6.97778 q^{93} +(28.3730 - 18.2342i) q^{94} +(-1.27280 + 8.85254i) q^{95} +(-8.95475 + 19.6082i) q^{96} +(-13.3400 + 3.91698i) q^{97} +(1.13381 + 2.48270i) q^{98} +(-2.14165 - 2.47159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	2.29607	−	1.47560i	1.62357	−	1.04340i	0.669942	−	0.742414i	$-0.266319\pi$
$2$	2.29607	−	1.47560i	1.62357	−	1.04340i	0.953627	−	0.300990i	$-0.0973172\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	2.26374	−	4.95689i	1.13187	−	2.47845i
$5$	−3.38655	+	0.994380i	−1.51451	+	0.444700i	−0.930268	−	0.366880i	$-0.880426\pi$
$5$	−3.38655	+	0.994380i	−1.51451	+	0.444700i	−0.584242	+	0.811580i	$0.698608\pi$
$6$	−1.13381	−	2.48270i	−0.462877	−	1.01356i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−1.33981	−	9.31861i	−0.473696	−	3.29463i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−6.30846	+	7.28035i	−1.99491	+	2.30225i
$11$	2.75123	+	1.76811i	0.829526	+	0.533104i	0.885127	−	0.465349i	$-0.154071\pi$
$11$	2.75123	+	1.76811i	0.829526	+	0.533104i	−0.0556014	+	0.998453i	$0.517708\pi$
$12$	−4.58427	−	2.94613i	−1.32337	−	0.850475i
$13$	1.90748	−	2.20135i	0.529039	−	0.610543i	−0.426832	−	0.904331i	$-0.640370\pi$
$13$	1.90748	−	2.20135i	0.529039	−	0.610543i	0.955871	+	0.293788i	$0.0949158\pi$
$14$	−2.61879	−	0.768946i	−0.699901	−	0.205509i
$15$	0.502303	+	3.49359i	0.129694	+	0.902042i
$16$	−9.68971	−	11.1825i	−2.42243	−	2.79563i
$17$	0.578502	+	1.26674i	0.140307	+	0.307230i	0.966721	−	0.255833i	$-0.0823498\pi$
$17$	0.578502	+	1.26674i	0.140307	+	0.307230i	−0.826413	+	0.563064i	$0.809623\pi$
$18$	−2.61879	+	0.768946i	−0.617255	+	0.181242i
$19$	1.05264	−	2.30495i	0.241491	−	0.528792i	−0.749614	−	0.661876i	$-0.769761\pi$
$19$	1.05264	−	2.30495i	0.241491	−	0.528792i	0.991105	+	0.133084i	$0.0424880\pi$
$20$	−2.73722	+	19.0378i	−0.612060	+	4.25697i
$21$	−0.841254	+	0.540641i	−0.183577	+	0.117977i
$22$	8.92602			1.90303
$23$	4.03575	+	2.59089i	0.841513	+	0.540237i
$23$	4.03575	+	2.59089i	0.841513	+	0.540237i
$24$	−9.41443			−1.92171
$25$	6.27364	−	4.03183i	1.25473	−	0.806365i
$26$	1.13141	−	7.86912i	0.221887	−	1.54326i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−5.22860	+	1.53526i	−0.988112	+	0.290136i
$29$	−1.62548	−	3.55931i	−0.301844	−	0.660947i	0.696555	−	0.717503i	$-0.254715\pi$
$29$	−1.62548	−	3.55931i	−0.301844	−	0.660947i	−0.998399	+	0.0565564i	$0.981988\pi$
$30$	6.30846	+	7.28035i	1.15176	+	1.32920i
$31$	0.993042	+	6.90676i	0.178356	+	1.24049i	0.860568	+	0.509336i	$0.170109\pi$
$31$	0.993042	+	6.90676i	0.178356	+	1.24049i	−0.682212	+	0.731154i	$0.738982\pi$
$32$	−20.6830	−	6.07307i	−3.65627	−	1.07358i
$33$	2.14165	−	2.47159i	0.372813	−	0.430249i
$34$	3.19749	+	2.05490i	0.548364	+	0.352412i
$35$	2.96922	+	1.90820i	0.501890	+	0.322545i
$36$	−3.56856	+	4.11833i	−0.594759	+	0.686389i
$37$	4.31177	+	1.26605i	0.708850	+	0.208137i	0.616232	−	0.787564i	$-0.288658\pi$
$37$	4.31177	+	1.26605i	0.708850	+	0.208137i	0.0926181	+	0.995702i	$0.470476\pi$
$38$	−0.984248	−	6.84560i	−0.159666	−	1.11050i
$39$	−1.90748	−	2.20135i	−0.305441	−	0.352497i
$40$	13.8036	+	30.2256i	2.18254	+	4.77909i
$41$	−7.60403	+	2.23275i	−1.18755	+	0.348696i	−0.815080	−	0.579348i	$-0.803307\pi$
$41$	−7.60403	+	2.23275i	−1.18755	+	0.348696i	−0.372470	+	0.928044i	$0.621489\pi$
$42$	−1.13381	+	2.48270i	−0.174951	+	0.383089i
$43$	1.41718	−	9.85669i	0.216118	−	1.50313i	−0.536065	−	0.844177i	$-0.680090\pi$
$43$	1.41718	−	9.85669i	0.216118	−	1.50313i	0.752182	−	0.658955i	$-0.229001\pi$
$44$	14.9924	−	9.63500i	2.26018	−	1.45253i
$45$	3.52952			0.526149
$46$	13.0895	−	0.00628143i	1.92994	−	0.000926147i
$47$	12.3572			1.80248			0.901240	−	0.433319i	$-0.142658\pi$
$47$	12.3572			1.80248			0.901240	+	0.433319i	$0.142658\pi$
$48$	−12.4477	+	7.99964i	−1.79667	+	1.15465i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	8.45540	−	18.5147i	1.19577	−	2.61838i
$51$	1.33618	−	0.392338i	0.187102	−	0.0549382i
$52$	−6.59380	−	14.4384i	−0.914396	−	2.00225i
$53$	7.13820	+	8.23792i	0.980507	+	1.13157i	0.991300	+	0.131624i	$0.0420192\pi$
$53$	7.13820	+	8.23792i	0.980507	+	1.13157i	−0.0107922	+	0.999942i	$0.503435\pi$
$54$	0.388427	+	2.70157i	0.0528582	+	0.367637i
$55$	−11.0753	−	3.25201i	−1.49340	−	0.438501i
$56$	−6.16514	+	7.11496i	−0.823852	+	0.950776i
$57$	−2.13168	−	1.36995i	−0.282348	−	0.181454i
$58$	−8.98433	−	5.77388i	−1.17970	−	0.758147i
$59$	−4.20868	+	4.85707i	−0.547923	+	0.632337i	−0.960398	−	0.278632i	$-0.910119\pi$
$59$	−4.20868	+	4.85707i	−0.547923	+	0.632337i	0.412475	+	0.910969i	$0.364664\pi$
$60$	18.4544	+	5.41871i	2.38246	+	0.699553i
$61$	0.0736215	+	0.512049i	0.00942626	+	0.0655611i	0.993992	−	0.109456i	$-0.0349109\pi$
$61$	0.0736215	+	0.512049i	0.00942626	+	0.0655611i	−0.984565	+	0.175017i	$0.944002\pi$
$62$	12.4717	+	14.3931i	1.58391	+	1.82792i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	−28.0566	+	8.23816i	−3.50707	+	1.02977i
$65$	−4.27079	+	9.35172i	−0.529726	+	1.15994i
$66$	1.27031	−	8.83517i	0.156364	−	1.08753i
$67$	−10.2844	+	6.60941i	−1.25644	+	0.807468i	−0.987793	−	0.155770i	$-0.950214\pi$
$67$	−10.2844	+	6.60941i	−1.25644	+	0.807468i	−0.268651	+	0.963238i	$0.586578\pi$
$68$	7.58868			0.920263
$69$	3.13886	−	3.62595i	0.377875	−	0.436514i
$70$	9.63328			1.15140
$71$	−9.57886	+	6.15596i	−1.13680	+	0.730578i	−0.966969	−	0.254895i	$-0.917959\pi$
$71$	−9.57886	+	6.15596i	−1.13680	+	0.730578i	−0.169833	+	0.985473i	$0.554323\pi$
$72$	−1.33981	+	9.31861i	−0.157899	+	1.09821i
$73$	5.22882	−	11.4495i	0.611987	−	1.34007i	−0.309219	−	0.950991i	$-0.600068\pi$
$73$	5.22882	−	11.4495i	0.611987	−	1.34007i	0.921206	−	0.389075i	$-0.127205\pi$
$74$	11.7683	−	3.45549i	1.36804	−	0.401692i
$75$	−3.09796	−	6.78358i	−0.357721	−	0.783300i
$76$	−9.04249	−	10.4356i	−1.03725	−	1.19704i
$77$	−0.465425	−	3.23710i	−0.0530401	−	0.368902i
$78$	−7.62800	−	2.23978i	−0.863701	−	0.253606i
$79$	−5.92681	+	6.83991i	−0.666819	+	0.769550i	−0.983875	−	0.178857i	$-0.942760\pi$
$79$	−5.92681	+	6.83991i	−0.666819	+	0.769550i	0.317057	+	0.948407i	$0.397306\pi$
$80$	43.9343	+	28.2349i	4.91201	+	3.15675i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−14.1648	+	16.3470i	−1.56424	+	1.80523i
$83$	−0.968156	−	0.284276i	−0.106269	−	0.0312034i	0.228166	−	0.973622i	$-0.426727\pi$
$83$	−0.968156	−	0.284276i	−0.106269	−	0.0312034i	−0.334435	+	0.942419i	$0.608545\pi$
$84$	0.775521	+	5.39387i	0.0846163	+	0.588519i
$85$	−3.21875	−	3.71463i	−0.349122	−	0.402909i
$86$	−11.2906	−	24.7229i	−1.21749	−	2.66594i
$87$	−3.75441	+	1.10239i	−0.402515	+	0.118189i
$88$	12.7902	−	28.0065i	1.36343	−	2.98551i
$89$	1.12323	−	7.81227i	0.119063	−	0.828099i	−0.839529	−	0.543315i	$-0.817169\pi$
$89$	1.12323	−	7.81227i	0.119063	−	0.828099i	0.958592	−	0.284784i	$-0.0919219\pi$
$90$	8.10403	−	5.20814i	0.854240	−	0.548987i
$91$	−2.91280			−0.305344
$92$	21.9786	−	14.1397i	2.29143	−	1.47417i
$93$	6.97778			0.723562
$94$	28.3730	−	18.2342i	2.92645	−	1.88072i
$95$	−1.27280	+	8.85254i	−0.130587	+	0.908251i
$96$	−8.95475	+	19.6082i	−0.913941	+	2.00125i
$97$	−13.3400	+	3.91698i	−1.35447	+	0.397709i	−0.876812	−	0.480834i	$-0.840334\pi$
$97$	−13.3400	+	3.91698i	−1.35447	+	0.397709i	−0.477662	+	0.878544i	$0.658516\pi$
$98$	1.13381	+	2.48270i	0.114532	+	0.250791i
$99$	−2.14165	−	2.47159i	−0.215244	−	0.248405i
$100$	−5.78345	−	40.2248i	−0.578345	−	4.02248i
$101$	13.6417	+	4.00556i	1.35740	+	0.398568i	0.877845	−	0.478945i	$-0.158981\pi$
$101$	13.6417	+	4.00556i	1.35740	+	0.398568i	0.479553	+	0.877513i	$0.340799\pi$
$102$	2.48903	−	2.87250i	0.246451	−	0.284420i
$103$	−6.49406	−	4.17348i	−0.639879	−	0.411225i	0.180077	−	0.983653i	$-0.442365\pi$
$103$	−6.49406	−	4.17348i	−0.639879	−	0.411225i	−0.819955	+	0.572427i	$0.806002\pi$
$104$	−23.0691	−	14.8256i	−2.26212	−	1.45377i
$105$	2.31134	−	2.66743i	0.225564	−	0.260315i
$106$	28.5457	+	8.38177i	2.77260	+	0.814109i
$107$	1.12084	+	7.79562i	0.108356	+	0.753631i	0.969468	+	0.245217i	$0.0788592\pi$
$107$	1.12084	+	7.79562i	0.108356	+	0.753631i	−0.861112	+	0.508415i	$0.830232\pi$
$108$	3.56856	+	4.11833i	0.343384	+	0.396287i
$109$	0.981968	+	2.15021i	0.0940555	+	0.205953i	0.950812	−	0.309768i	$-0.100251\pi$
$109$	0.981968	+	2.15021i	0.0940555	+	0.205953i	−0.856757	+	0.515721i	$0.827524\pi$
$110$	−30.2284	+	8.87586i	−2.88217	+	0.846280i
$111$	1.86679	−	4.08770i	0.177188	−	0.387988i
$112$	−2.10577	+	14.6460i	−0.198977	+	1.38392i
$113$	−10.6258	+	6.82876i	−0.999587	+	0.642396i	−0.934678	−	0.355496i	$-0.884312\pi$
$113$	−10.6258	+	6.82876i	−0.999587	+	0.642396i	−0.0649092	+	0.997891i	$0.520676\pi$
$114$	−6.91599			−0.647742
$115$	−16.2436	−	4.76108i	−1.51472	−	0.443973i
$116$	−21.3228			−1.97977
$117$	−2.45040	+	1.57478i	−0.226540	+	0.145588i
$118$	−2.49635	+	17.3625i	−0.229808	+	1.59835i
$119$	0.578502	−	1.26674i	0.0530312	−	0.116122i
$120$	31.8824	−	9.36153i	2.91045	−	0.854586i
$121$	−0.126519	−	0.277039i	−0.0115018	−	0.0251853i
$122$	0.924617	+	1.06707i	0.0837109	+	0.0966076i
$123$	1.12785	+	7.84439i	0.101695	+	0.707305i
$124$	36.4840	+	10.7127i	3.27636	+	0.962027i
$125$	−5.68011	+	6.55520i	−0.508045	+	0.586315i
$126$	2.29607	+	1.47560i	0.204550	+	0.131457i
$127$	−1.30404	−	0.838053i	−0.115714	−	0.0743652i	0.481503	−	0.876444i	$-0.340091\pi$
$127$	−1.30404	−	0.838053i	−0.115714	−	0.0743652i	−0.597218	+	0.802079i	$0.703727\pi$
$128$	−24.0312	+	27.7335i	−2.12408	+	2.45132i
$129$	−9.55468	−	2.80551i	−0.841243	−	0.247011i
$130$	3.99332	+	27.7742i	0.350238	+	2.43596i
$131$	−1.48836	−	1.71766i	−0.130039	−	0.150073i	0.686996	−	0.726661i	$-0.258929\pi$
$131$	−1.48836	−	1.71766i	−0.130039	−	0.150073i	−0.817035	+	0.576588i	$0.804384\pi$
$132$	−7.40330	−	16.2110i	−0.644374	−	1.41098i
$133$	−2.43129	+	0.713892i	−0.210820	+	0.0619023i
$134$	−13.8610	+	30.3514i	−1.19741	+	2.62196i
$135$	0.502303	−	3.49359i	0.0432313	−	0.300681i
$136$	11.0292	−	7.08804i	0.945746	−	0.607794i
$137$	−10.7670			−0.919888			−0.459944	−	0.887948i	$-0.652131\pi$
$137$	−10.7670			−0.919888			−0.459944	+	0.887948i	$0.652131\pi$
$138$	1.85661	−	12.9571i	0.158045	−	1.10299i
$139$	13.6214			1.15535			0.577676	−	0.816266i	$-0.303960\pi$
$139$	13.6214			1.15535			0.577676	+	0.816266i	$0.303960\pi$
$140$	16.1803	−	10.3984i	1.36748	−	0.878828i
$141$	1.75861	−	12.2314i	0.148102	−	1.03007i
$142$	−12.9100	+	28.2691i	−1.08339	+	2.37229i
$143$	9.14011	−	2.68378i	0.764334	−	0.224429i
$144$	6.14673	+	13.4595i	0.512227	+	1.12162i
$145$	9.04408	+	10.4374i	0.751070	+	0.866781i
$146$	−4.88912	−	34.0046i	−0.404626	−	2.81424i
$147$	0.959493	+	0.281733i	0.0791376	+	0.0232369i
$148$	16.0364	−	18.5070i	1.31818	−	1.52126i
$149$	16.6137	+	10.6769i	1.36104	+	0.874689i	0.998361	−	0.0572236i	$-0.0182248\pi$
$149$	16.6137	+	10.6769i	1.36104	+	0.874689i	0.362682	+	0.931913i	$0.381861\pi$
$150$	−17.1230	−	11.0043i	−1.39808	−	0.898494i
$151$	7.26726	−	8.38687i	0.591402	−	0.682514i	−0.378615	−	0.925554i	$-0.623599\pi$
$151$	7.26726	−	8.38687i	0.591402	−	0.682514i	0.970016	+	0.243041i	$0.0781449\pi$
$152$	−22.8893	−	6.72089i	−1.85656	−	0.545136i
$153$	−0.198186	−	1.37841i	−0.0160224	−	0.111438i
$154$	−5.84530	−	6.74584i	−0.471028	−	0.543595i
$155$	−10.2309	−	22.4026i	−0.821768	−	1.79942i
$156$	−15.2299	+	4.47189i	−1.21936	+	0.358038i
$157$	−3.32957	+	7.29075i	−0.265729	+	0.581865i	−0.994716	−	0.102662i	$-0.967264\pi$
$157$	−3.32957	+	7.29075i	−0.265729	+	0.581865i	0.728987	+	0.684527i	$0.239991\pi$
$158$	−3.51545	+	24.4505i	−0.279674	+	1.94518i
$159$	9.16995	−	5.89317i	0.727224	−	0.467359i
$160$	76.0828			6.01488
$161$	−0.684796	−	4.74669i	−0.0539695	−	0.374091i
$162$	2.72935			0.214438
$163$	−5.13099	+	3.29749i	−0.401890	+	0.258279i	−0.725936	−	0.687762i	$-0.758593\pi$
$163$	−5.13099	+	3.29749i	−0.401890	+	0.258279i	0.324046	+	0.946041i	$0.394957\pi$
$164$	−6.14605	+	42.7467i	−0.479926	+	3.33796i
$165$	−4.79509	+	10.4998i	−0.373297	+	0.817407i
$166$	−2.64243	+	0.775889i	−0.205093	+	0.0602206i
$167$	1.98631	+	4.34941i	0.153705	+	0.336568i	0.970783	−	0.239960i	$-0.0771345\pi$
$167$	1.98631	+	4.34941i	0.153705	+	0.336568i	−0.817077	+	0.576528i	$0.804407\pi$
$168$	6.16514	+	7.11496i	0.475651	+	0.548931i
$169$	0.642638	+	4.46965i	0.0494337	+	0.343819i
$170$	−12.8718	−	3.77950i	−0.987221	−	0.289874i
$171$	−1.65938	+	1.91502i	−0.126896	+	0.146445i
$172$	−45.6504	−	29.3378i	−3.48081	−	2.23698i
$173$	−4.49506	−	2.88880i	−0.341753	−	0.219631i	0.358494	−	0.933532i	$-0.383290\pi$
$173$	−4.49506	−	2.88880i	−0.341753	−	0.219631i	−0.700247	+	0.713901i	$0.746927\pi$
$174$	−6.99371	+	8.07117i	−0.530192	+	0.611874i
$175$	−7.15541	−	2.10102i	−0.540898	−	0.158822i
$176$	−6.88670	−	47.8980i	−0.519104	−	3.61045i
$177$	4.20868	+	4.85707i	0.316344	+	0.365080i
$178$	−8.94873	−	19.5950i	−0.670735	−	1.46871i
$179$	1.71626	−	0.503939i	0.128279	−	0.0376662i	−0.216963	−	0.976180i	$-0.569615\pi$
$179$	1.71626	−	0.503939i	0.128279	−	0.0376662i	0.345242	+	0.938514i	$0.387797\pi$
$180$	7.98990	−	17.4954i	0.595532	−	1.30403i
$181$	−0.798984	+	5.55706i	−0.0593880	+	0.413053i	0.938342	+	0.345709i	$0.112362\pi$
$181$	−0.798984	+	5.55706i	−0.0593880	+	0.413053i	−0.997730	+	0.0673439i	$0.978548\pi$
$182$	−6.68800	+	4.29811i	−0.495747	+	0.318597i
$183$	0.517314			0.0382410
$184$	18.7363	−	41.0789i	1.38126	−	3.02838i
$185$	−15.8609			−1.16612
$186$	16.0215	−	10.2964i	1.17475	−	0.754968i
$187$	−0.648145	+	4.50795i	−0.0473971	+	0.329654i
$188$	27.9734	−	61.2532i	2.04017	−	4.46735i
$189$	0.959493	−	0.281733i	0.0697928	−	0.0204930i
$190$	10.1403	+	22.2042i	0.735657	+	1.61086i
$191$	−3.81280	−	4.40021i	−0.275885	−	0.318388i	0.600850	−	0.799362i	$-0.294829\pi$
$191$	−3.81280	−	4.40021i	−0.275885	−	0.318388i	−0.876735	+	0.480974i	$0.840283\pi$
$192$	4.16144	+	28.9434i	0.300326	+	2.08881i
$193$	16.0088	+	4.70062i	1.15234	+	0.338358i	0.801452	−	0.598059i	$-0.204061\pi$
$193$	16.0088	+	4.70062i	1.15234	+	0.338358i	0.350889	+	0.936417i	$0.385879\pi$
$194$	−24.8498	+	28.6782i	−1.78411	+	2.05897i
$195$	8.64873	+	5.55820i	0.619349	+	0.398031i
$196$	4.58427	+	2.94613i	0.327448	+	0.210438i
$197$	−7.43560	+	8.58114i	−0.529765	+	0.611381i	−0.956049	−	0.293208i	$-0.905277\pi$
$197$	−7.43560	+	8.58114i	−0.529765	+	0.611381i	0.426284	+	0.904589i	$0.359822\pi$
$198$	−8.56446	−	2.51475i	−0.608650	−	0.178716i
$199$	−2.07144	−	14.4072i	−0.146841	−	1.02130i	−0.921349	−	0.388736i	$-0.872912\pi$
$199$	−2.07144	−	14.4072i	−0.146841	−	1.02130i	0.774508	−	0.632564i	$-0.217997\pi$
$200$	−45.9765	−	53.0597i	−3.25103	−	3.75189i
$201$	5.07850	+	11.1204i	0.358210	+	0.784371i
$202$	37.2329	−	10.9326i	2.61970	−	0.769213i
$203$	−1.62548	+	3.55931i	−0.114086	+	0.249814i
$204$	1.07998	−	7.51144i	0.0756139	−	0.525906i
$205$	23.5312	−	15.1226i	1.64349	−	1.05621i
$206$	−21.0692			−1.46796
$207$	−3.14234	−	3.62294i	−0.218408	−	0.251812i
$208$	−43.0995			−2.98841
$209$	6.97143	−	4.48027i	0.482224	−	0.309906i
$210$	1.37096	−	9.53523i	0.0946051	−	0.657993i
$211$	10.5843	−	23.1763i	0.728652	−	1.59553i	−0.0727155	−	0.997353i	$-0.523167\pi$
$211$	10.5843	−	23.1763i	0.728652	−	1.59553i	0.801367	−	0.598172i	$-0.204106\pi$
$212$	56.9935	−	16.7348i	3.91433	−	1.14935i
$213$	4.73009	+	10.3574i	0.324100	+	0.709680i
$214$	14.0767	+	16.2454i	0.962265	+	1.11051i
$215$	5.00196	+	34.7894i	0.341131	+	2.37262i
$216$	9.03308	+	2.65235i	0.614624	+	0.180470i
$217$	4.56948	−	5.27346i	0.310196	−	0.357986i
$218$	5.42751	+	3.48805i	0.367598	+	0.236241i
$219$	−10.5888	−	6.80504i	−0.715528	−	0.459842i
$220$	−41.1915	+	47.5375i	−2.77713	+	3.20498i
$221$	3.89202	+	1.14280i	0.261806	+	0.0768730i
$222$	−1.74551	−	12.1403i	−0.117151	−	0.814803i
$223$	6.30726	+	7.27897i	0.422365	+	0.487436i	0.926556	−	0.376157i	$-0.122755\pi$
$223$	6.30726	+	7.27897i	0.422365	+	0.487436i	−0.504191	+	0.863592i	$0.668209\pi$
$224$	8.95475	+	19.6082i	0.598315	+	1.31013i
$225$	−7.15541	+	2.10102i	−0.477028	+	0.140068i
$226$	−14.3210	+	31.3587i	−0.952620	+	2.08595i
$227$	2.01492	−	14.0141i	0.133735	−	0.930147i	−0.806890	−	0.590701i	$-0.798851\pi$
$227$	2.01492	−	14.0141i	0.133735	−	0.930147i	0.940625	−	0.339446i	$-0.110240\pi$
$228$	−11.6163	+	7.46531i	−0.769305	+	0.494402i
$229$	0.775987			0.0512787			0.0256393	−	0.999671i	$-0.491838\pi$
$229$	0.775987			0.0512787			0.0256393	+	0.999671i	$0.491838\pi$
$230$	−44.3219	+	13.0372i	−2.92250	+	0.859647i
$231$	−3.27039			−0.215176
$232$	−30.9900	+	19.9160i	−2.03459	+	1.30755i
$233$	−2.99275	+	20.8150i	−0.196061	+	1.36364i	0.619514	+	0.784986i	$0.287330\pi$
$233$	−2.99275	+	20.8150i	−0.196061	+	1.36364i	−0.815575	+	0.578651i	$0.803579\pi$
$234$	−3.30256	+	7.23161i	−0.215895	+	0.472745i
$235$	−41.8482	+	12.2877i	−2.72988	+	0.801564i
$236$	14.5486	+	31.8571i	0.947036	+	2.07372i
$237$	5.92681	+	6.83991i	0.384988	+	0.444300i
$238$	−0.540918	−	3.76217i	−0.0350625	−	0.243865i
$239$	−8.27737	−	2.43046i	−0.535419	−	0.157213i	0.00283508	−	0.999996i	$-0.499098\pi$
$239$	−8.27737	−	2.43046i	−0.535419	−	0.157213i	−0.538254	+	0.842783i	$0.680916\pi$
$240$	34.2000	−	39.4689i	2.20760	−	2.54771i
$241$	−6.37903	−	4.09955i	−0.410909	−	0.264075i	0.318815	−	0.947817i	$-0.396715\pi$
$241$	−6.37903	−	4.09955i	−0.410909	−	0.264075i	−0.729724	+	0.683742i	$0.760352\pi$
$242$	−0.699295	−	0.449410i	−0.0449524	−	0.0288892i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	2.70483	+	0.794209i	0.173159	+	0.0508440i
$245$	−0.502303	−	3.49359i	−0.0320909	−	0.223197i
$246$	14.1648	+	16.3470i	0.903114	+	1.04225i
$247$	−3.06611	−	6.71385i	−0.195092	−	0.427192i
$248$	63.0309	−	18.5075i	4.00247	−	1.17523i
$249$	−0.419166	+	0.917845i	−0.0265635	+	0.0581661i
$250$	−3.36912	+	23.4328i	−0.213082	+	1.48202i
$251$	−15.6422	+	10.0526i	−0.987326	+	0.634516i	−0.931430	−	0.363921i	$-0.881438\pi$
$251$	−15.6422	+	10.0526i	−0.987326	+	0.634516i	−0.0558962	+	0.998437i	$0.517802\pi$
$252$	5.44934			0.343276
$253$	6.52231	+	14.2637i	0.410054	+	0.896754i
$254$	−4.23079			−0.265463
$255$	−4.13490	+	2.65734i	−0.258938	+	0.166409i
$256$	−5.93110	+	41.2517i	−0.370694	+	2.57823i
$257$	−0.348362	+	0.762806i	−0.0217302	+	0.0475825i	−0.920186	−	0.391482i	$-0.871963\pi$
$257$	−0.348362	+	0.762806i	−0.0217302	+	0.0475825i	0.898456	+	0.439064i	$0.144690\pi$
$258$	−26.0780	+	7.65720i	−1.62355	+	0.476717i
$259$	−1.86679	−	4.08770i	−0.115997	−	0.253998i
$260$	36.6875	+	42.3396i	2.27526	+	2.62579i
$261$	0.556865	+	3.87308i	0.0344691	+	0.239738i
$262$	−5.95197	−	1.74766i	−0.367714	−	0.107971i
$263$	12.6018	−	14.5433i	0.777061	−	0.896777i	−0.219832	−	0.975538i	$-0.570551\pi$
$263$	12.6018	−	14.5433i	0.777061	−	0.896777i	0.996894	+	0.0787611i	$0.0250964\pi$
$264$	−25.9012	−	16.6457i	−1.59411	−	1.02447i
$265$	−32.3655	−	20.8000i	−1.98820	−	1.27774i
$266$	−4.52901	+	5.22676i	−0.277691	+	0.320473i
$267$	−7.57290	−	2.22360i	−0.463454	−	0.136082i
$268$	9.48085	+	65.9408i	0.579135	+	4.02797i
$269$	1.83295	+	2.11534i	0.111757	+	0.128975i	0.808872	−	0.587985i	$-0.200079\pi$
$269$	1.83295	+	2.11534i	0.111757	+	0.128975i	−0.697115	+	0.716960i	$0.745533\pi$
$270$	−4.00181	−	8.76274i	−0.243542	−	0.533283i
$271$	−9.21430	+	2.70556i	−0.559729	+	0.164351i	−0.549346	−	0.835595i	$-0.685123\pi$
$271$	−9.21430	+	2.70556i	−0.559729	+	0.164351i	−0.0103828	+	0.999946i	$0.503305\pi$
$272$	8.55986	−	18.7435i	0.519018	−	1.13649i
$273$	−0.414534	+	2.88315i	−0.0250888	+	0.174496i
$274$	−24.7219	+	15.8878i	−1.49350	+	0.959816i
$275$	24.3889			1.47071
$276$	−10.8679	−	23.7672i	−0.654171	−	1.43062i
$277$	6.43348			0.386550			0.193275	−	0.981145i	$-0.438089\pi$
$277$	6.43348			0.386550			0.193275	+	0.981145i	$0.438089\pi$
$278$	31.2757	−	20.0997i	1.87579	−	1.20550i
$279$	0.993042	−	6.90676i	0.0594519	−	0.413497i
$280$	13.8036	−	30.2256i	0.824922	−	1.80633i
$281$	−12.4207	+	3.64703i	−0.740954	+	0.217564i	−0.630361	−	0.776302i	$-0.717093\pi$
$281$	−12.4207	+	3.64703i	−0.740954	+	0.217564i	−0.110593	+	0.993866i	$0.535275\pi$
$282$	−14.0107	−	30.6792i	−0.834326	−	1.82692i
$283$	2.59779	+	2.99800i	0.154422	+	0.178213i	0.827689	−	0.561187i	$-0.189655\pi$
$283$	2.59779	+	2.99800i	0.154422	+	0.178213i	−0.673267	+	0.739399i	$0.735110\pi$
$284$	8.83040	+	61.4168i	0.523988	+	3.64442i
$285$	8.58129	+	2.51970i	0.508312	+	0.149254i
$286$	17.0262	−	19.6493i	1.00678	−	1.16189i
$287$	6.66698	+	4.28461i	0.393539	+	0.252912i
$288$	18.1342	+	11.6541i	1.06857	+	0.686727i
$289$	9.86266	−	11.3821i	0.580156	−	0.669536i
$290$	36.1673	+	10.6197i	2.12382	+	0.623609i
$291$	1.97863	+	13.7617i	0.115989	+	0.806724i
$292$	−44.9174	−	51.8374i	−2.62859	−	3.03355i
$293$	−6.53583	−	14.3115i	−0.381827	−	0.836085i	−0.998794	−	0.0490961i	$-0.984366\pi$
$293$	−6.53583	−	14.3115i	−0.381827	−	0.836085i	0.616967	−	0.786989i	$-0.288361\pi$
$294$	2.61879	−	0.768946i	0.152731	−	0.0448458i
$295$	9.42311	−	20.6337i	0.548635	−	1.20134i
$296$	6.02085	−	41.8760i	0.349955	−	2.43399i
$297$	−2.75123	+	1.76811i	−0.159642	+	0.102596i
$298$	53.9010			3.12240
$299$	13.4015	−	3.94203i	0.775031	−	0.227974i
$300$	−40.6384			−2.34626
$301$	−8.37725	+	5.38373i	−0.482856	+	0.310313i
$302$	4.31053	−	29.9804i	0.248043	−	1.72518i
$303$	5.90620	−	12.9328i	0.339303	−	0.742969i
$304$	−35.9749	+	10.5632i	−2.06330	+	0.605839i
$305$	−0.758494	−	1.66087i	−0.0434312	−	0.0951011i
$306$	−2.48903	−	2.87250i	−0.142289	−	0.164210i
$307$	−1.98543	−	13.8089i	−0.113314	−	0.788118i	−0.964657	−	0.263508i	$-0.915120\pi$
$307$	−1.98543	−	13.8089i	−0.113314	−	0.788118i	0.851343	−	0.524610i	$-0.175789\pi$
$308$	−17.0995	−	5.02088i	−0.974337	−	0.286091i
$309$	−5.05520	+	5.83401i	−0.287580	+	0.331885i
$310$	−56.5482	−	36.3413i	−3.21172	−	2.06405i
$311$	−24.2391	−	15.5775i	−1.37447	−	0.883321i	−0.375422	−	0.926854i	$-0.622502\pi$
$311$	−24.2391	−	15.5775i	−1.37447	−	0.883321i	−0.999052	+	0.0435327i	$0.986139\pi$
$312$	−17.9578	+	20.7244i	−1.01666	+	1.17329i
$313$	−0.0835929	−	0.0245451i	−0.00472495	−	0.00138737i	0.279369	−	0.960184i	$-0.409875\pi$
$313$	−0.0835929	−	0.0245451i	−0.00472495	−	0.00138737i	−0.284094	+	0.958796i	$0.591693\pi$
$314$	3.11326	+	21.6532i	0.175691	+	1.22196i
$315$	−2.31134	−	2.66743i	−0.130229	−	0.150293i
$316$	20.4879	+	44.8623i	1.15254	+	2.52370i
$317$	−23.1920	+	6.80979i	−1.30259	+	0.382476i	−0.858182	−	0.513346i	$-0.828406\pi$
$317$	−23.1920	+	6.80979i	−1.30259	+	0.382476i	−0.444412	+	0.895822i	$0.646588\pi$
$318$	12.3589	−	27.0623i	0.693054	−	1.51758i
$319$	1.82117	−	12.6665i	0.101966	−	0.709187i
$320$	86.8231	−	55.7978i	4.85356	−	3.11919i
$321$	7.87579			0.439584
$322$	−8.57654	−	9.88826i	−0.477952	−	0.551051i
$323$	3.52873			0.196344
$324$	4.58427	−	2.94613i	0.254682	−	0.163674i
$325$	3.09139	−	21.5011i	0.171479	−	1.19266i
$326$	−6.91537	+	15.1425i	−0.383007	+	0.838668i
$327$	2.26807	−	0.665966i	0.125425	−	0.0368280i
$328$	30.9941	+	67.8675i	1.71136	+	3.74736i
$329$	−8.09224	−	9.33894i	−0.446139	−	0.514872i
$330$	4.48357	+	31.1839i	0.246812	+	1.71662i
$331$	−24.2976	−	7.13443i	−1.33552	−	0.392144i	−0.465450	−	0.885074i	$-0.654107\pi$
$331$	−24.2976	−	7.13443i	−1.33552	−	0.392144i	−0.870069	+	0.492931i	$0.835926\pi$
$332$	−3.60078	+	4.15552i	−0.197618	+	0.228064i
$333$	−3.78042	−	2.42953i	−0.207166	−	0.133137i
$334$	10.9787	+	7.05558i	0.600727	+	0.386064i
$335$	28.2565	−	32.6097i	1.54382	−	1.78166i
$336$	14.1972	+	4.16868i	0.774522	+	0.227420i
$337$	0.260234	+	1.80996i	0.0141758	+	0.0985950i	0.995681	−	0.0928407i	$-0.0295947\pi$
$337$	0.260234	+	1.80996i	0.0141758	+	0.0985950i	−0.981505	+	0.191436i	$0.938686\pi$
$338$	8.07094	+	9.31436i	0.439001	+	0.506635i
$339$	5.24705	+	11.4894i	0.284981	+	0.624021i
$340$	−25.6994	+	7.54604i	−1.39375	+	0.409241i
$341$	−9.47979	+	20.7579i	−0.513360	+	1.12410i
$342$	−0.984248	+	6.84560i	−0.0532220	+	0.370167i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	−93.7494			−5.05463
$345$	−7.02433	+	15.4007i	−0.378177	+	0.829145i
$346$	−14.5837			−0.784024
$347$	6.39679	−	4.11096i	0.343397	−	0.220688i	−0.357562	−	0.933889i	$-0.616392\pi$
$347$	6.39679	−	4.11096i	0.343397	−	0.220688i	0.700959	+	0.713201i	$0.252755\pi$
$348$	−3.03455	+	21.1057i	−0.162669	+	1.13139i
$349$	0.575212	−	1.25954i	0.0307904	−	0.0674215i	−0.893612	−	0.448840i	$-0.851837\pi$
$349$	0.575212	−	1.25954i	0.0307904	−	0.0674215i	0.924402	+	0.381419i	$0.124564\pi$
$350$	−19.5296	+	5.73441i	−1.04390	+	0.306517i
$351$	1.21002	+	2.64957i	0.0645861	+	0.141424i
$352$	−46.1657	−	53.2781i	−2.46064	−	2.83973i
$353$	1.03061	+	7.16804i	0.0548537	+	0.381516i	0.998693	+	0.0511111i	$0.0162763\pi$
$353$	1.03061	+	7.16804i	0.0548537	+	0.381516i	−0.943839	+	0.330405i	$0.892815\pi$
$354$	16.8305	+	4.94188i	0.894531	+	0.262658i
$355$	26.3179	−	30.3725i	1.39681	−	1.61200i
$356$	−36.1818	−	23.2527i	−1.91763	−	1.23239i
$357$	−1.17152	−	0.752890i	−0.0620034	−	0.0398472i
$358$	3.19704	−	3.68959i	0.168969	−	0.195001i
$359$	−23.3739	−	6.86319i	−1.23363	−	0.362226i	−0.401009	−	0.916074i	$-0.631341\pi$
$359$	−23.3739	−	6.86319i	−1.23363	−	0.362226i	−0.832618	+	0.553848i	$0.813159\pi$
$360$	−4.72890	−	32.8902i	−0.249235	−	1.73347i
$361$	8.23760	+	9.50670i	0.433558	+	0.500353i
$362$	6.36545	+	13.9384i	0.334561	+	0.732585i
$363$	−0.292225	+	0.0858049i	−0.0153378	+	0.00450359i
$364$	−6.59380	+	14.4384i	−0.345609	+	0.756779i
$365$	−6.32248	+	43.9738i	−0.330934	+	2.30169i
$366$	1.18779	−	0.763347i	0.0620868	−	0.0399008i
$367$	13.7831			0.719474			0.359737	−	0.933054i	$-0.382866\pi$
$367$	13.7831			0.719474			0.359737	+	0.933054i	$0.382866\pi$
$368$	−10.1326	−	70.2348i	−0.528201	−	3.66124i
$369$	7.92505			0.412562
$370$	−36.4179	+	23.4044i	−1.89328	+	1.21673i
$371$	1.55128	−	10.7894i	0.0805384	−	0.560157i
$372$	15.7959	−	34.5881i	0.818977	−	1.79331i
$373$	−1.53675	+	0.451231i	−0.0795701	+	0.0233639i	−0.321275	−	0.946986i	$-0.604111\pi$
$373$	−1.53675	+	0.451231i	−0.0795701	+	0.0233639i	0.241705	+	0.970350i	$0.422293\pi$
$374$	5.16373	+	11.3070i	0.267010	+	0.584670i
$375$	5.68011	+	6.55520i	0.293320	+	0.338509i
$376$	−16.5563	−	115.152i	−0.853827	−	5.93850i
$377$	−10.9358	−	3.21105i	−0.563224	−	0.165378i
$378$	1.78734	−	2.06270i	0.0919310	−	0.106094i
$379$	−0.581945	−	0.373993i	−0.0298925	−	0.0192107i	0.525609	−	0.850726i	$-0.323837\pi$
$379$	−0.581945	−	0.373993i	−0.0298925	−	0.0192107i	−0.555502	+	0.831515i	$0.687474\pi$
$380$	40.9998	+	26.3490i	2.10324	+	1.35167i
$381$	−1.01511	+	1.17149i	−0.0520055	+	0.0600175i
$382$	−15.2474	−	4.47704i	−0.780125	−	0.229065i
$383$	−0.0137409	−	0.0955701i	−0.000702128	−	0.00488341i	0.989467	−	0.144756i	$-0.0462398\pi$
$383$	−0.0137409	−	0.0955701i	−0.000702128	−	0.00488341i	−0.990169	+	0.139873i	$0.955331\pi$
$384$	24.0312	+	27.7335i	1.22634	+	1.41527i
$385$	4.79509	+	10.4998i	0.244380	+	0.535119i
$386$	43.6937	−	12.8296i	2.22395	−	0.653011i
$387$	−4.13672	+	9.05816i	−0.210282	+	0.460452i
$388$	−10.7822	+	74.9920i	−0.547385	+	3.80714i
$389$	10.0677	−	6.47009i	0.510450	−	0.328046i	−0.259934	−	0.965626i	$-0.583701\pi$
$389$	10.0677	−	6.47009i	0.510450	−	0.328046i	0.770384	+	0.637580i	$0.220064\pi$
$390$	28.0598			1.42086
$391$	−0.947294	+	6.61110i	−0.0479067	+	0.334338i
$392$	9.41443			0.475501
$393$	−1.91200	+	1.22877i	−0.0964474	+	0.0619830i
$394$	−4.41038	+	30.6749i	−0.222192	+	1.54538i
$395$	13.2700	−	29.0572i	0.667684	−	1.46203i
$396$	−17.0995	+	5.02088i	−0.859285	+	0.252309i
$397$	7.50911	+	16.4427i	0.376871	+	0.825233i	0.999101	+	0.0423984i	$0.0134999\pi$
$397$	7.50911	+	16.4427i	0.376871	+	0.825233i	−0.622229	+	0.782835i	$0.713773\pi$
$398$	−26.0154	−	30.0234i	−1.30404	−	1.50494i
$399$	0.360617	+	2.50814i	0.0180534	+	0.125564i
$400$	−105.876	−	31.0879i	−5.29379	−	1.55440i
$401$	8.88977	−	10.2593i	0.443934	−	0.512327i	−0.489045	−	0.872259i	$-0.662655\pi$
$401$	8.88977	−	10.2593i	0.443934	−	0.512327i	0.932979	+	0.359932i	$0.117200\pi$
$402$	28.0698	+	18.0394i	1.39999	+	0.899722i
$403$	17.0984	+	10.9885i	0.851730	+	0.547374i
$404$	50.7363	−	58.5528i	2.52423	−	2.91311i
$405$	−3.38655	−	0.994380i	−0.168279	−	0.0494111i
$406$	1.51988	+	10.5710i	0.0754303	+	0.524629i
$407$	9.62414	+	11.1068i	0.477051	+	0.550546i
$408$	−5.44627	−	11.9257i	−0.269631	−	0.590409i
$409$	−6.66383	+	1.95668i	−0.329505	+	0.0967515i	−0.442301	−	0.896867i	$-0.645838\pi$
$409$	−6.66383	+	1.95668i	−0.329505	+	0.0967515i	0.112796	+	0.993618i	$0.464019\pi$
$410$	31.7145	−	69.4452i	1.56627	−	3.42965i
$411$	−1.53231	+	10.6574i	−0.0755831	+	0.525692i
$412$	−35.3883	+	22.7427i	−1.74346	+	1.12045i
$413$	6.42683			0.316244
$414$	−12.5610	−	3.68171i	−0.617341	−	0.180946i
$415$	3.56139			0.174822
$416$	−52.8212	+	33.9461i	−2.58977	+	1.66435i
$417$	1.93853	−	13.4828i	0.0949301	−	0.660253i
$418$	9.39585	−	20.5740i	0.459566	−	1.00631i
$419$	34.9302	−	10.2564i	1.70645	−	0.501059i	0.724353	−	0.689429i	$-0.242139\pi$
$419$	34.9302	−	10.2564i	1.70645	−	0.501059i	0.982098	+	0.188370i	$0.0603205\pi$
$420$	−7.98990	−	17.4954i	−0.389867	−	0.853690i
$421$	3.51288	+	4.05408i	0.171207	+	0.197584i	0.834868	−	0.550450i	$-0.185544\pi$
$421$	3.51288	+	4.05408i	0.171207	+	0.197584i	−0.663661	+	0.748033i	$0.730998\pi$
$422$	−9.89665	−	68.8327i	−0.481761	−	3.35072i
$423$	−11.8566	−	3.48142i	−0.576489	−	0.169273i
$424$	67.2021	−	77.5554i	3.26362	−	3.76642i
$425$	8.73661	+	5.61468i	0.423788	+	0.272352i
$426$	26.1440	+	16.8017i	1.26668	+	0.814047i
$427$	0.338769	−	0.390960i	0.0163942	−	0.0189199i
$428$	41.1793	+	12.0913i	1.99048	+	0.584457i
$429$	−1.35569	−	9.42902i	−0.0654532	−	0.455237i
$430$	62.8199	+	72.4981i	3.02945	+	3.49617i
$431$	0.247526	+	0.542006i	0.0119229	+	0.0261075i	0.915500	−	0.402318i	$-0.131796\pi$
$431$	0.247526	+	0.542006i	0.0119229	+	0.0261075i	−0.903577	+	0.428426i	$0.859068\pi$
$432$	14.1972	−	4.16868i	0.683064	−	0.200566i
$433$	−11.9324	+	26.1283i	−0.573434	+	1.25565i	0.371515	+	0.928427i	$0.378839\pi$
$433$	−11.9324	+	26.1283i	−0.573434	+	1.25565i	−0.944949	+	0.327218i	$0.893889\pi$
$434$	2.71036	−	18.8509i	0.130101	−	0.904874i
$435$	11.6183	−	7.46662i	0.557054	−	0.357997i
$436$	12.8813			0.616901
$437$	10.2200	−	6.57495i	0.488891	−	0.314523i
$438$	−34.3543			−1.64151
$439$	27.5544	−	17.7081i	1.31510	−	0.845162i	0.320329	−	0.947306i	$-0.396207\pi$
$439$	27.5544	−	17.7081i	1.31510	−	0.845162i	0.994770	+	0.102144i	$0.0325703\pi$
$440$	−15.4653	+	107.564i	−0.737281	+	5.12790i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	10.6227	−	3.11910i	0.505269	−	0.148360i
$443$	6.58590	+	14.4211i	0.312905	+	0.685167i	0.999107	−	0.0422438i	$-0.0134506\pi$
$443$	6.58590	+	14.4211i	0.312905	+	0.685167i	−0.686202	+	0.727411i	$0.740723\pi$
$444$	−16.0364	−	18.5070i	−0.761053	−	0.878302i
$445$	3.96448	+	27.5735i	0.187934	+	1.30711i
$446$	25.2227	+	7.40607i	1.19433	+	0.350687i
$447$	12.9326	−	14.9251i	0.611693	−	0.705931i
$448$	24.5991	+	15.8089i	1.16220	+	0.746901i
$449$	−19.7388	−	12.6853i	−0.931531	−	0.598659i	−0.0155494	−	0.999879i	$-0.504950\pi$
$449$	−19.7388	−	12.6853i	−0.931531	−	0.598659i	−0.915981	+	0.401221i	$0.868586\pi$
$450$	−13.3291	+	15.3826i	−0.628340	+	0.725143i
$451$	−24.8681	−	7.30194i	−1.17099	−	0.343835i
$452$	9.79550	+	68.1292i	0.460742	+	3.20453i
$453$	−7.26726	−	8.38687i	−0.341446	−	0.394049i
$454$	−16.0527	−	35.1506i	−0.753392	−	1.64970i
$455$	9.86433	−	2.89643i	0.462447	−	0.135787i
$456$	−9.90996	+	21.6998i	−0.464077	+	1.01619i
$457$	1.85607	−	12.9092i	0.0868232	−	0.603868i	−0.899235	−	0.437466i	$-0.855876\pi$
$457$	1.85607	−	12.9092i	0.0868232	−	0.603868i	0.986058	−	0.166402i	$-0.0532150\pi$
$458$	1.78172	−	1.14504i	0.0832545	−	0.0535044i
$459$	−1.39259			−0.0650005
$460$	−60.3714	+	69.7399i	−2.81483	+	3.25164i
$461$	16.3915			0.763426			0.381713	−	0.924281i	$-0.375334\pi$
$461$	16.3915			0.763426			0.381713	+	0.924281i	$0.375334\pi$
$462$	−7.50905	+	4.82577i	−0.349353	+	0.224515i
$463$	0.853767	−	5.93808i	0.0396779	−	0.275966i	−0.960318	−	0.278908i	$-0.910027\pi$
$463$	0.853767	−	5.93808i	0.0396779	−	0.275966i	0.999996	+	0.00294224i	$0.000936546\pi$
$464$	−24.0516	+	52.6656i	−1.11657	+	2.44494i
$465$	−23.6306	+	6.93857i	−1.09584	+	0.321768i
$466$	23.8430	+	52.2089i	1.10451	+	2.41853i
$467$	−11.6954	−	13.4972i	−0.541200	−	0.624578i	0.417610	−	0.908626i	$-0.362868\pi$
$467$	−11.6954	−	13.4972i	−0.541200	−	0.624578i	−0.958810	+	0.284048i	$0.908322\pi$
$468$	2.25894	+	15.7112i	0.104419	+	0.726253i
$469$	11.7299	+	3.44422i	0.541638	+	0.159039i
$470$	−77.9548	+	89.9646i	−3.59579	+	4.14976i
$471$	6.74269	+	4.33326i	0.310687	+	0.199666i
$472$	50.9000	+	32.7114i	2.34286	+	1.50567i
$473$	21.3267	−	24.6123i	0.980600	−	1.13167i
$474$	23.7013	+	6.95934i	1.08864	+	0.319653i
$475$	−2.68930	−	18.7045i	−0.123393	−	0.858220i
$476$	−4.96953	−	5.73514i	−0.227778	−	0.262870i
$477$	−4.52816	−	9.91529i	−0.207330	−	0.453990i
$478$	−22.5918	+	6.63356i	−1.03333	+	0.303412i
$479$	−10.7908	+	23.6285i	−0.493042	+	1.07961i	0.485626	+	0.874167i	$0.338592\pi$
$479$	−10.7908	+	23.6285i	−0.493042	+	1.07961i	−0.978669	+	0.205446i	$0.934136\pi$
$480$	10.8277	−	75.3084i	0.494215	−	3.43734i
$481$	11.0116	−	7.07673i	0.502086	−	0.322671i
$482$	−20.6960			−0.942677
$483$	−4.79583	+	0.00230144i	−0.218218	+	0.000104719i
$484$	−1.65966			−0.0754390
$485$	41.2816	−	26.5301i	1.87450	−	1.20467i
$486$	0.388427	−	2.70157i	0.0176194	−	0.122546i
$487$	−9.23169	+	20.2146i	−0.418328	+	0.916010i	0.576751	+	0.816920i	$0.304320\pi$
$487$	−9.23169	+	20.2146i	−0.418328	+	0.916010i	−0.995078	+	0.0990898i	$0.968407\pi$
$488$	4.67294	−	1.37210i	0.211534	−	0.0621120i
$489$	2.53371	+	5.54804i	0.114578	+	0.250891i
$490$	−6.30846	−	7.28035i	−0.284987	−	0.328893i
$491$	−3.44304	−	23.9469i	−0.155382	−	1.08071i	−0.907006	−	0.421117i	$-0.861638\pi$
$491$	−3.44304	−	23.9469i	−0.155382	−	1.08071i	0.751624	−	0.659592i	$-0.229271\pi$
$492$	41.4369	+	12.1670i	1.86812	+	0.548530i
$493$	3.56839	−	4.11814i	0.160712	−	0.185472i
$494$	−16.9470	−	10.8911i	−0.762479	−	0.490016i
$495$	9.71050	+	6.24056i	0.436454	+	0.280492i
$496$	67.6127	−	78.0292i	3.03590	−	3.50361i
$497$	10.9252	+	3.20792i	0.490061	+	0.143895i
$498$	0.391934	+	2.72596i	0.0175630	+	0.122153i
$499$	4.73823	+	5.46821i	0.212112	+	0.244791i	0.851829	−	0.523820i	$-0.175494\pi$
$499$	4.73823	+	5.46821i	0.212112	+	0.244791i	−0.639716	+	0.768611i	$0.720948\pi$
$500$	19.6351	+	42.9949i	0.878110	+	1.92279i
$501$	4.58782	−	1.34711i	0.204969	−	0.0601843i
$502$	−21.0820	+	46.1631i	−0.940935	+	2.06036i
$503$	−3.29271	+	22.9013i	−0.146815	+	1.02112i	0.774576	+	0.632481i	$0.217963\pi$
$503$	−3.29271	+	22.9013i	−0.146815	+	1.02112i	−0.921391	+	0.388638i	$0.872946\pi$
$504$	7.91993	−	5.08983i	0.352782	−	0.226719i
$505$	−50.1813			−2.23304
$506$	36.0232	+	23.1263i	1.60143	+	1.02809i
$507$	4.51561			0.200545
$508$	−7.10613	+	4.56683i	−0.315283	+	0.202620i
$509$	−5.33325	+	37.0936i	−0.236392	+	1.64414i	0.433116	+	0.901338i	$0.357414\pi$
$509$	−5.33325	+	37.0936i	−0.236392	+	1.64414i	−0.669508	+	0.742805i	$0.733495\pi$
$510$	−5.57287	+	12.2029i	−0.246771	+	0.540353i
$511$	−12.0771	+	3.54616i	−0.534260	+	0.156873i
$512$	16.7639	+	36.7078i	0.740867	+	1.62227i
$513$	1.65938	+	1.91502i	0.0732632	+	0.0845502i
$514$	0.325730	+	2.26550i	0.0143673	+	0.0999269i
$515$	26.1425	+	7.67612i	1.15197	+	0.338250i
$516$	−35.5359	+	41.0106i	−1.56438	+	1.80539i
$517$	33.9974	+	21.8488i	1.49520	+	0.960909i
$518$	−10.3181	−	6.63103i	−0.453351	−	0.291351i
$519$	−3.49911	+	4.03819i	−0.153594	+	0.177257i
$520$	92.8671	+	27.2682i	4.07249	+	1.19579i
$521$	−3.00893	−	20.9276i	−0.131824	−	0.916853i	−0.943175	−	0.332295i	$-0.892177\pi$
$521$	−3.00893	−	20.9276i	−0.131824	−	0.916853i	0.811352	−	0.584558i	$-0.198732\pi$
$522$	6.99371	+	8.07117i	0.306106	+	0.353266i
$523$	5.33392	+	11.6797i	0.233236	+	0.510716i	0.989672	−	0.143352i	$-0.0457882\pi$
$523$	5.33392	+	11.6797i	0.233236	+	0.510716i	−0.756436	+	0.654068i	$0.773061\pi$
$524$	−11.8835	+	3.48932i	−0.519134	+	0.152432i
$525$	−3.09796	+	6.78358i	−0.135206	+	0.296060i
$526$	7.47469	−	51.9876i	0.325912	−	2.26677i
$527$	−8.17461	+	5.25350i	−0.356092	+	0.228846i
$528$	−48.3906			−2.10593
$529$	9.57462	+	20.9124i	0.416288	+	0.909233i
$530$	−105.006			−4.56117
$531$	5.40659	−	3.47461i	0.234626	−	0.150785i
$532$	−1.96512	+	13.6677i	−0.0851988	+	0.592571i
$533$	−9.58947	+	20.9980i	−0.415366	+	0.909525i
$534$	−20.6691	+	6.06898i	−0.894438	+	0.262631i
$535$	−11.5476	−	25.2857i	−0.499246	−	1.09320i
$536$	75.3697	+	86.9813i	3.25548	+	3.75702i
$537$	−0.254561	−	1.77051i	−0.0109851	−	0.0764030i
$538$	7.32998	+	2.15228i	0.316018	+	0.0927912i
$539$	−2.14165	+	2.47159i	−0.0922473	+	0.106459i
$540$	−16.1803	−	10.3984i	−0.696288	−	0.447477i
$541$	37.5025	+	24.1014i	1.61236	+	1.03620i	0.960663	+	0.277717i	$0.0895776\pi$
$541$	37.5025	+	24.1014i	1.61236	+	1.03620i	0.651694	+	0.758482i	$0.274059\pi$
$542$	−17.1644	+	19.8088i	−0.737274	+	0.850859i
$543$	5.38679	+	1.58170i	0.231169	+	0.0678774i
$544$	−4.27213	−	29.7133i	−0.183166	−	1.27395i
$545$	−5.46361	−	6.30534i	−0.234035	−	0.270091i
$546$	3.30256	+	7.23161i	0.141337	+	0.309484i
$547$	−23.5034	+	6.90122i	−1.00493	+	0.295075i	−0.742479	−	0.669870i	$-0.766350\pi$
$547$	−23.5034	+	6.90122i	−1.00493	+	0.295075i	−0.262454	+	0.964945i	$0.584532\pi$
$548$	−24.3737	+	53.3709i	−1.04119	+	2.27989i
$549$	0.0736215	−	0.512049i	0.00314209	−	0.0218537i
$550$	55.9987	−	35.9882i	2.38779	−	1.53454i
$551$	−9.91506			−0.422396
$552$	−37.9943	−	24.3917i	−1.61715	−	1.03818i
$553$	9.05049			0.384866
$554$	14.7717	−	9.49322i	0.627591	−	0.403328i
$555$	−2.25725	+	15.6995i	−0.0958148	+	0.666407i
$556$	30.8352	−	67.5198i	1.30771	−	2.86348i
$557$	30.9786	−	9.09614i	1.31261	−	0.385416i	0.450787	−	0.892632i	$-0.351143\pi$
$557$	30.9786	−	9.09614i	1.31261	−	0.385416i	0.861819	+	0.507216i	$0.169325\pi$
$558$	−7.91149	−	17.3238i	−0.334920	−	0.733373i
$559$	−18.9948	−	21.9211i	−0.803392	−	0.927164i
$560$	−7.43237	−	51.6932i	−0.314075	−	2.18444i
$561$	4.36982	+	1.28310i	0.184494	+	0.0541724i
$562$	−23.1372	+	26.7017i	−0.975983	+	1.12634i
$563$	−28.0620	−	18.0343i	−1.18267	−	0.760057i	−0.206796	−	0.978384i	$-0.566304\pi$
$563$	−28.0620	−	18.0343i	−1.18267	−	0.760057i	−0.975876	+	0.218327i	$0.929940\pi$
$564$	−56.6487	−	36.4059i	−2.38534	−	1.53297i
$565$	29.1942	−	33.6920i	1.22821	−	1.41743i
$566$	10.3885	+	3.05035i	0.436663	+	0.128216i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	70.1989	+	81.0138i	2.94548	+	3.39926i
$569$	−5.15603	−	11.2901i	−0.216152	−	0.473307i	0.770232	−	0.637763i	$-0.220140\pi$
$569$	−5.15603	−	11.2901i	−0.216152	−	0.473307i	−0.986384	+	0.164457i	$0.947413\pi$
$570$	23.4213	−	6.87712i	0.981012	−	0.288051i
$571$	−11.7497	+	25.7283i	−0.491711	+	1.07670i	0.487364	+	0.873199i	$0.337959\pi$
$571$	−11.7497	+	25.7283i	−0.491711	+	1.07670i	−0.979075	+	0.203499i	$0.934769\pi$
$572$	7.38760	−	51.3819i	0.308891	−	2.14838i
$573$	−4.89804	+	3.14778i	−0.204619	+	0.131500i
$574$	21.6302			0.902828
$575$	35.7649	−	0.0171630i	1.49150	−	0.000715746i
$576$	29.2411			1.21838
$577$	−14.5161	+	9.32894i	−0.604314	+	0.388369i	−0.806721	−	0.590932i	$-0.798760\pi$
$577$	−14.5161	+	9.32894i	−0.604314	+	0.388369i	0.202407	+	0.979301i	$0.435124\pi$
$578$	5.84998	−	40.6875i	0.243327	−	1.69238i
$579$	6.93107	−	15.1769i	0.288045	−	0.630731i
$580$	72.2105	−	21.2029i	2.99838	−	0.880404i
$581$	0.419166	+	0.917845i	0.0173899	+	0.0380786i
$582$	24.8498	+	28.6782i	1.03006	+	1.18875i
$583$	5.07329	+	35.2855i	0.210114	+	1.46138i
$584$	−113.699	−	33.3851i	−4.70491	−	1.38149i
$585$	6.73247	−	7.76969i	0.278353	−	0.321237i
$586$	−36.1247	−	23.2159i	−1.49230	−	0.959042i
$587$	6.59711	+	4.23970i	0.272292	+	0.174991i	0.669660	−	0.742668i	$-0.266440\pi$
$587$	6.59711	+	4.23970i	0.272292	+	0.174991i	−0.397368	+	0.917659i	$0.630076\pi$
$588$	3.56856	−	4.11833i	0.147165	−	0.169837i
$589$	16.9650	+	4.98138i	0.699032	+	0.205254i
$590$	−8.81091	−	61.2813i	−0.362740	−	2.52291i
$591$	7.43560	+	8.58114i	0.305860	+	0.352981i
$592$	−27.6221	−	60.4841i	−1.13526	−	2.48588i
$593$	−9.53378	+	2.79937i	−0.391505	+	0.114956i	−0.471560	−	0.881834i	$-0.656309\pi$
$593$	−9.53378	+	2.79937i	−0.391505	+	0.114956i	0.0800543	+	0.996791i	$0.474491\pi$
$594$	−3.70800	+	8.11940i	−0.152141	+	0.333143i
$595$	−0.699501	+	4.86514i	−0.0286768	+	0.199451i
$596$	90.5334	−	58.1823i	3.70839	−	2.38324i
$597$	−14.5554			−0.595712
$598$	24.9541	−	28.8265i	1.02045	−	1.17880i
$599$	−12.5920			−0.514495			−0.257247	−	0.966346i	$-0.582815\pi$
$599$	−12.5920			−0.514495			−0.257247	+	0.966346i	$0.582815\pi$
$600$	−59.0628	+	37.9574i	−2.41123	+	1.54960i
$601$	4.70359	−	32.7142i	0.191863	−	1.33444i	−0.635208	−	0.772342i	$-0.719085\pi$
$601$	4.70359	−	32.7142i	0.191863	−	1.33444i	0.827071	−	0.562098i	$-0.190005\pi$
$602$	−11.2906	+	24.7229i	−0.460169	+	1.00763i
$603$	11.7299	−	3.44422i	0.477680	−	0.140259i
$604$	−25.1216	−	55.0087i	−1.02218	−	2.23827i
$605$	0.703946	+	0.812397i	0.0286195	+	0.0330286i
$606$	−5.52249	−	38.4098i	−0.224336	−	1.56029i
$607$	−8.55475	−	2.51190i	−0.347227	−	0.101955i	0.103469	−	0.994633i	$-0.467006\pi$
$607$	−8.55475	−	2.51190i	−0.347227	−	0.101955i	−0.450696	+	0.892678i	$0.648824\pi$
$608$	−35.7698	+	41.2805i	−1.45066	+	1.67415i
$609$	3.29175	+	2.11548i	0.133388	+	0.0857235i
$610$	−4.19233	−	2.69425i	−0.169742	−	0.109087i
$611$	23.5710	−	27.2024i	0.953582	−	1.10049i
$612$	−7.28129	−	2.13798i	−0.294329	−	0.0864227i
$613$	−3.73063	−	25.9471i	−0.150679	−	1.04799i	−0.915086	−	0.403259i	$-0.867877\pi$
$613$	−3.73063	−	25.9471i	−0.150679	−	1.04799i	0.764407	−	0.644734i	$-0.223032\pi$
$614$	−24.9351	−	28.7767i	−1.00630	−	1.16133i
$615$	−11.6198	−	25.4439i	−0.468557	−	1.02600i
$616$	−29.5417	+	8.67422i	−1.19027	+	0.349494i
$617$	2.71028	−	5.93469i	0.109112	−	0.238922i	−0.847198	−	0.531278i	$-0.821712\pi$
$617$	2.71028	−	5.93469i	0.109112	−	0.238922i	0.956309	+	0.292356i	$0.0944393\pi$
$618$	−2.99846	+	20.8548i	−0.120616	+	0.838901i
$619$	28.5951	−	18.3769i	1.14933	−	0.738632i	0.179827	−	0.983698i	$-0.442446\pi$
$619$	28.5951	−	18.3769i	1.14933	−	0.738632i	0.969506	+	0.245067i	$0.0788099\pi$
$620$	−134.207			−5.38990
$621$	−4.03327	+	2.59476i	−0.161849	+	0.104124i
$622$	−78.6409			−3.15321
$623$	−6.63968	+	4.26706i	−0.266013	+	0.170956i
$624$	−6.13369	+	42.6608i	−0.245544	+	1.70780i
$625$	−2.77217	+	6.07020i	−0.110887	+	0.242808i
$626$	−0.228154	+	0.0669921i	−0.00911887	+	0.00267754i
$627$	−3.44253	−	7.53808i	−0.137481	−	0.301042i
$628$	28.6022	+	33.0087i	1.14135	+	1.31719i
$629$	0.890608	+	6.19432i	0.0355109	+	0.246984i
$630$	−9.24306	−	2.71401i	−0.368252	−	0.108129i
$631$	−23.2097	+	26.7855i	−0.923965	+	1.06631i	0.0736500	+	0.997284i	$0.476535\pi$
$631$	−23.2097	+	26.7855i	−0.923965	+	1.06631i	−0.997615	+	0.0690280i	$0.978010\pi$
$632$	71.6792	+	46.0655i	2.85125	+	1.83239i
$633$	−21.4341	−	13.7749i	−0.851931	−	0.547503i
$634$	−43.2021	+	49.8579i	−1.71577	+	1.98011i
$635$	5.24952	+	1.54140i	0.208321	+	0.0611685i
$636$	−8.45344	−	58.7950i	−0.335201	−	2.33137i
$637$	1.90748	+	2.20135i	0.0755770	+	0.0872205i
$638$	−14.5091	−	31.7705i	−0.574420	−	1.25781i
$639$	10.9252	−	3.20792i	0.432193	−	0.126903i
$640$	53.8052	−	117.817i	2.12684	−	4.65713i
$641$	3.56009	−	24.7610i	0.140615	−	0.978001i	−0.790288	−	0.612735i	$-0.790069\pi$
$641$	3.56009	−	24.7610i	0.140615	−	0.978001i	0.930903	−	0.365265i	$-0.119022\pi$
$642$	18.0834	−	11.6215i	0.713694	−	0.458663i
$643$	24.4784			0.965332			0.482666	−	0.875805i	$-0.339669\pi$
$643$	24.4784			0.965332			0.482666	+	0.875805i	$0.339669\pi$
$644$	−25.0790	−	7.35079i	−0.988252	−	0.289662i
$645$	35.1471			1.38392
$646$	8.10222	−	5.20698i	0.318778	−	0.204866i
$647$	−4.79369	+	33.3409i	−0.188460	+	1.31077i	0.647538	+	0.762033i	$0.275798\pi$
$647$	−4.79369	+	33.3409i	−0.188460	+	1.31077i	−0.835998	+	0.548732i	$0.815111\pi$
$648$	3.91090	−	8.56367i	0.153635	−	0.336413i
$649$	−20.1668	+	5.92152i	−0.791618	+	0.232440i
$650$	−24.6289	−	53.9297i	−0.966023	−	2.11530i
$651$	−4.56948	−	5.27346i	−0.179092	−	0.206683i
$652$	4.73007	+	32.8984i	0.185244	+	1.28840i
$653$	21.1149	+	6.19990i	0.826291	+	0.242621i	0.667423	−	0.744679i	$-0.267397\pi$
$653$	21.1149	+	6.19990i	0.826291	+	0.242621i	0.158868	+	0.987300i	$0.449216\pi$
$654$	4.22496	−	4.87587i	0.165209	−	0.190661i
$655$	6.74842	+	4.33695i	0.263683	+	0.169459i
$656$	98.6485	+	63.3976i	3.85158	+	2.47526i
$657$	−8.24272	+	9.51261i	−0.321579	+	0.371122i
$658$	−32.3609	−	9.50201i	−1.26156	−	0.370427i
$659$	−7.08622	−	49.2858i	−0.276040	−	1.91990i	−0.379354	−	0.925252i	$-0.623854\pi$
$659$	−7.08622	−	49.2858i	−0.276040	−	1.91990i	0.103314	−	0.994649i	$-0.467055\pi$
$660$	41.1915	+	47.5375i	1.60338	+	1.85039i
$661$	19.4372	+	42.5616i	0.756020	+	1.65545i	0.755235	+	0.655454i	$0.227523\pi$
$661$	19.4372	+	42.5616i	0.756020	+	1.65545i	0.000785431		1.00000i	$0.499750\pi$
$662$	−66.3167	+	19.4723i	−2.57747	+	0.756814i
$663$	1.68506	−	3.68977i	0.0654423	−	0.143299i
$664$	−1.35191	+	9.40275i	−0.0524643	+	0.364897i
$665$	7.52381	−	4.83526i	0.291761	−	0.187503i
$666$	−12.2651			−0.475264
$667$	2.66172	−	18.5759i	0.103062	−	0.719263i
$668$	26.0560			1.00814
$669$	8.10249	−	5.20716i	0.313260	−	0.201320i
$670$	16.7602	−	116.569i	0.647501	−	4.50347i
$671$	−0.702807	+	1.53893i	−0.0271315	+	0.0594098i
$672$	20.6830	−	6.07307i	0.797863	−	0.234274i
$673$	−7.37152	−	16.1414i	−0.284151	−	0.622204i	0.712703	−	0.701466i	$-0.247471\pi$
$673$	−7.37152	−	16.1414i	−0.284151	−	0.622204i	−0.996854	+	0.0792621i	$0.974744\pi$
$674$	3.26829	+	3.77181i	0.125890	+	0.145285i
$675$	1.06131	+	7.38159i	0.0408499	+	0.284117i
$676$	23.6103	+	6.93262i	0.908089	+	0.266639i
$677$	10.2204	−	11.7949i	0.392800	−	0.453316i	−0.524560	−	0.851373i	$-0.675770\pi$
$677$	10.2204	−	11.7949i	0.392800	−	0.453316i	0.917360	+	0.398058i	$0.130316\pi$
$678$	29.0014	+	18.6381i	1.11379	+	0.715790i
$679$	11.6961	+	7.51664i	0.448856	+	0.288462i
$680$	−30.3027	+	34.9712i	−1.16206	+	1.34108i
$681$	−13.5847	−	3.98882i	−0.520566	−	0.152852i
$682$	8.86392	+	61.6499i	0.339417	+	2.36070i
$683$	22.1758	+	25.5923i	0.848535	+	0.979262i	0.999958	−	0.00920755i	$-0.00293090\pi$
$683$	22.1758	+	25.5923i	0.848535	+	0.979262i	−0.151423	+	0.988469i	$0.548385\pi$
$684$	5.73616	+	12.5604i	0.219328	+	0.480261i
$685$	36.4630	−	10.7065i	1.39318	−	0.409075i
$686$	1.13381	−	2.48270i	0.0432891	−	0.0947900i
$687$	0.110435	−	0.768089i	0.00421334	−	0.0293044i
$688$	−123.955	+	79.6608i	−4.72573	+	3.03704i
$689$	31.7505			1.20960
$690$	6.59683	+	45.7262i	0.251137	+	1.74077i
$691$	2.46580			0.0938035			0.0469018	−	0.998900i	$-0.485065\pi$
$691$	2.46580			0.0938035			0.0469018	+	0.998900i	$0.485065\pi$
$692$	−24.4951	+	15.7420i	−0.931163	+	0.598422i
$693$	−0.465425	+	3.23710i	−0.0176800	+	0.122967i
$694$	8.62136	−	18.8782i	0.327262	−	0.716605i
$695$	−46.1295	+	13.5448i	−1.74979	+	0.513785i
$696$	15.3030	+	33.5089i	0.580058	+	1.27015i
$697$	−7.22727	−	8.34071i	−0.273752	−	0.315927i
$698$	−0.537842	−	3.74077i	−0.0203576	−	0.141590i
$699$	20.1772	+	5.92457i	0.763173	+	0.224088i
$700$	−26.6125	+	30.7124i	−1.00586	+	1.16082i
$701$	2.87652	+	1.84862i	0.108645	+	0.0698216i	0.593835	−	0.804587i	$-0.297613\pi$
$701$	2.87652	+	1.84862i	0.108645	+	0.0698216i	−0.485190	+	0.874409i	$0.661250\pi$
$702$	6.68800	+	4.29811i	0.252422	+	0.162222i
$703$	7.45690	−	8.60572i	0.281242	−	0.324571i
$704$	−91.7559	−	26.9420i	−3.45818	−	1.01541i
$705$	6.20705	+	43.1710i	0.233771	+	1.62591i
$706$	12.9435	+	14.9376i	0.487134	+	0.562183i
$707$	−5.90620	−	12.9328i	−0.222126	−	0.486387i
$708$	33.6033	−	9.86682i	1.26289	−	0.370818i
$709$	8.25362	−	18.0729i	0.309971	−	0.678742i	−0.688968	−	0.724792i	$-0.741936\pi$
$709$	8.25362	−	18.0729i	0.309971	−	0.678742i	0.998939	+	0.0460495i	$0.0146632\pi$
$710$	15.6103	−	108.572i	0.585844	−	4.07463i
$711$	7.61376	−	4.89307i	0.285538	−	0.183504i
$712$	−74.3044			−2.78467
$713$	−13.8869	+	30.4468i	−0.520070	+	1.14024i
$714$	−3.80086			−0.142244
$715$	−28.2847	+	18.1775i	−1.05779	+	0.679799i
$716$	1.38719	−	9.64809i	0.0518416	−	0.360566i
$717$	−3.58371	+	7.84723i	−0.133836	+	0.293060i
$718$	−63.7955	+	18.7320i	−2.38083	+	0.699074i
$719$	−20.9508	−	45.8759i	−0.781334	−	1.71088i	−0.699940	−	0.714201i	$-0.746790\pi$
$719$	−20.9508	−	45.8759i	−0.781334	−	1.71088i	−0.0813941	−	0.996682i	$-0.525937\pi$
$720$	−34.2000	−	39.4689i	−1.27456	−	1.47092i
$721$	1.09860	+	7.64093i	0.0409140	+	0.284563i
$722$	32.9422	+	9.67270i	1.22598	+	0.359981i
$723$	−4.96565	+	5.73067i	−0.184675	+	0.213126i
$724$	25.7370	+	16.5402i	0.956509	+	0.614711i
$725$	−24.5482	−	15.7762i	−0.911697	−	0.585912i
$726$	−0.544356	+	0.628220i	−0.0202029	+	0.0233154i
$727$	−7.25660	−	2.13073i	−0.269132	−	0.0790244i	0.144382	−	0.989522i	$-0.453881\pi$
$727$	−7.25660	−	2.13073i	−0.269132	−	0.0790244i	−0.413514	+	0.910498i	$0.635699\pi$
$728$	3.90261	+	27.1432i	0.144640	+	1.00599i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	50.3707	+	110.296i	1.86430	+	4.08226i
$731$	13.3057	−	3.90692i	0.492131	−	0.144503i
$732$	1.17106	−	2.56427i	0.0432837	−	0.0947781i
$733$	−1.70700	+	11.8725i	−0.0630496	+	0.438520i	0.933707	+	0.358039i	$0.116555\pi$
$733$	−1.70700	+	11.8725i	−0.0630496	+	0.438520i	−0.996756	+	0.0804804i	$0.974355\pi$
$734$	31.6471	−	20.3384i	1.16812	−	0.750702i
$735$	−3.52952			−0.130188
$736$	−67.7368	−	78.0967i	−2.49681	−	2.87868i
$737$	−39.9809			−1.47272
$738$	18.1965	−	11.6942i	0.669822	−	0.430469i
$739$	−0.625481	+	4.35032i	−0.0230087	+	0.160029i	−0.998086	−	0.0618346i	$-0.980305\pi$
$739$	−0.625481	+	4.35032i	−0.0230087	+	0.160029i	0.975078	+	0.221864i	$0.0712140\pi$
$740$	−35.9050	+	78.6210i	−1.31989	+	2.89016i
$741$	−7.08187	+	2.07942i	−0.260159	+	0.0763895i
$742$	−12.3589	−	27.0623i	−0.453711	−	0.993488i
$743$	−28.0437	−	32.3642i	−1.02882	−	1.18733i	−0.982089	−	0.188419i	$-0.939664\pi$
$743$	−28.0437	−	32.3642i	−1.02882	−	1.18733i	−0.0467351	−	0.998907i	$-0.514882\pi$
$744$	−9.34893	−	65.0232i	−0.342748	−	2.38387i
$745$	−66.8799	−	19.6377i	−2.45029	−	0.719470i
$746$	−2.86266	+	3.30369i	−0.104809	+	0.120957i
$747$	0.848849	+	0.545522i	0.0310578	+	0.0199596i
$748$	20.8782	+	13.4176i	0.763382	+	0.490596i
$749$	5.15754	−	5.95212i	0.188453	−	0.217486i
$750$	22.7148	+	6.66966i	0.829427	+	0.243542i
$751$	−0.734947	−	5.11167i	−0.0268186	−	0.186527i	0.972009	−	0.234945i	$-0.0754911\pi$
$751$	−0.734947	−	5.11167i	−0.0268186	−	0.186527i	−0.998827	+	0.0484180i	$0.984582\pi$
$752$	−119.737	−	138.184i	−4.36638	−	5.03907i
$753$	7.72419	+	16.9136i	0.281485	+	0.616366i
$754$	−29.8477	+	8.76407i	−1.08699	+	0.319169i
$755$	−16.2712	+	35.6290i	−0.592169	+	1.29667i
$756$	0.775521	−	5.39387i	0.0282054	−	0.196173i
$757$	−5.08978	+	3.27100i	−0.184991	+	0.118887i	−0.629859	−	0.776710i	$-0.716887\pi$
$757$	−5.08978	+	3.27100i	−0.184991	+	0.118887i	0.444867	+	0.895596i	$0.353251\pi$
$758$	−1.88805			−0.0685771
$759$	15.0468	−	4.42598i	0.546164	−	0.160653i
$760$	84.1987			3.05421
$761$	−31.0109	+	19.9295i	−1.12414	+	0.722443i	−0.964330	−	0.264704i	$-0.914726\pi$
$761$	−31.0109	+	19.9295i	−1.12414	+	0.722443i	−0.159814	+	0.987147i	$0.551089\pi$
$762$	−0.602104	+	4.18772i	−0.0218119	+	0.151705i
$763$	0.981968	−	2.15021i	0.0355496	−	0.0778428i
$764$	−30.4425	+	8.93873i	−1.10137	+	0.323392i
$765$	2.04183	+	4.47099i	0.0738227	+	0.161649i
$766$	−0.172573	−	0.199160i	−0.00623532	−	0.00719594i
$767$	2.66414	+	18.5295i	0.0961965	+	0.669062i
$768$	39.9877	+	11.7415i	1.44293	+	0.423683i
$769$	10.0867	−	11.6406i	0.363735	−	0.419772i	−0.544153	−	0.838986i	$-0.683149\pi$
$769$	10.0867	−	11.6406i	0.363735	−	0.419772i	0.907888	+	0.419214i	$0.137694\pi$
$770$	26.5033	+	17.0327i	0.955113	+	0.613814i
$771$	0.705465	+	0.453375i	0.0254067	+	0.0163279i
$772$	59.5402	−	68.7131i	2.14290	−	2.47304i
$773$	13.8686	+	4.07219i	0.498819	+	0.146466i	0.521457	−	0.853277i	$-0.325389\pi$
$773$	13.8686	+	4.07219i	0.498819	+	0.146466i	−0.0226387	+	0.999744i	$0.507207\pi$
$774$	3.86797	+	26.9023i	0.139031	+	0.966985i
$775$	34.0768	+	39.3268i	1.22408	+	1.41266i
$776$	54.3740	+	119.062i	1.95191	+	4.27409i
$777$	−4.31177	+	1.26605i	−0.154684	+	0.0454193i
$778$	13.5688	−	29.7116i	0.486466	−	1.06521i
$779$	−2.85791	+	19.8772i	−0.102395	+	0.712174i
$780$	47.1299	−	30.2885i	1.68752	−	1.08450i
$781$	−37.2380			−1.33248
$782$	7.58026	+	16.5774i	0.271069	+	0.592806i
$783$	3.91291			0.139836
$784$	12.4477	−	7.99964i	0.444560	−	0.285701i
$785$	4.02598	−	28.0013i	0.143693	−	0.999410i
$786$	−2.57692	+	5.64267i	−0.0919157	+	0.201267i
$787$	−18.6071	+	5.46355i	−0.663273	+	0.194755i	−0.596005	−	0.802980i	$-0.703246\pi$
$787$	−18.6071	+	5.46355i	−0.663273	+	0.194755i	−0.0672677	+	0.997735i	$0.521428\pi$
$788$	25.7035	+	56.2829i	0.915651	+	2.00499i
$789$	−12.6018	−	14.5433i	−0.448637	−	0.517754i
$790$	−12.4079	−	86.2985i	−0.441452	−	3.07036i
$791$	12.1192	+	3.55853i	0.430910	+	0.126527i
$792$	−20.1624	+	23.2687i	−0.716440	+	0.826816i
$793$	1.26763	+	0.814654i	0.0450148	+	0.0289292i
$794$	41.5042	+	26.6731i	1.47293	+	0.946594i
$795$	−25.1944	+	29.0759i	−0.893554	+	1.03122i
$796$	−76.1042	−	22.3462i	−2.69744	−	0.792040i
$797$	2.82618	+	19.6565i	0.100109	+	0.696270i	0.976633	+	0.214913i	$0.0689469\pi$
$797$	2.82618	+	19.6565i	0.100109	+	0.696270i	−0.876525	+	0.481357i	$0.840144\pi$
$798$	4.52901	+	5.22676i	0.160325	+	0.185025i
$799$	7.14866	+	15.6534i	0.252901	+	0.553777i
$800$	−154.243	+	45.2899i	−5.45332	+	1.60124i
$801$	−3.27871	+	7.17936i	−0.115847	+	0.253670i
$802$	5.27291	−	36.6739i	0.186193	−	1.29500i
$803$	34.6296	−	22.2551i	1.22205	−	0.785366i
$804$	66.6189			2.34947
$805$	7.03911	+	15.3939i	0.248096	+	0.542565i
$806$	55.4736			1.95397
$807$	2.35467	−	1.51325i	0.0828882	−	0.0532690i
$808$	19.0489	−	132.488i	0.670139	−	4.66092i
$809$	−9.74638	+	21.3416i	−0.342664	+	0.750330i	−0.999995	−	0.00327240i	$-0.998958\pi$
$809$	−9.74638	+	21.3416i	−0.342664	+	0.750330i	0.657330	+	0.753603i	$0.271686\pi$
$810$	−9.24306	+	2.71401i	−0.324768	+	0.0953605i
$811$	2.31895	+	5.07779i	0.0814292	+	0.178305i	0.945967	−	0.324262i	$-0.105116\pi$
$811$	2.31895	+	5.07779i	0.0814292	+	0.178305i	−0.864538	+	0.502568i	$0.832389\pi$
$812$	13.9634	+	16.1147i	0.490021	+	0.565514i
$813$	1.36669	+	9.50556i	0.0479320	+	0.333374i
$814$	38.4870	+	11.3008i	1.34897	+	0.396092i
$815$	14.0974	−	16.2692i	0.493810	−	0.569887i
$816$	−17.3345	−	11.1402i	−0.606829	−	0.389985i
$817$	−21.2274	−	13.6420i	−0.742653	−	0.477274i
$818$	−12.4134	+	14.3258i	−0.434024	+	0.500890i
$819$	2.79481	+	0.820630i	0.0976585	+	0.0286751i
$820$	−21.6926	−	150.875i	−0.757538	−	5.26879i
$821$	−18.5238	−	21.3776i	−0.646484	−	0.746082i	0.334023	−	0.942565i	$-0.391594\pi$
$821$	−18.5238	−	21.3776i	−0.646484	−	0.746082i	−0.980507	+	0.196482i	$0.937048\pi$
$822$	12.2078	+	26.7313i	0.425795	+	0.932361i
$823$	0.371502	−	0.109083i	0.0129498	−	0.00380239i	−0.275251	−	0.961372i	$-0.588761\pi$
$823$	0.371502	−	0.109083i	0.0129498	−	0.00380239i	0.288201	+	0.957570i	$0.406943\pi$
$824$	−30.1902	+	66.1073i	−1.05173	+	2.30296i
$825$	3.47090	−	24.1407i	0.120841	−	0.840470i
$826$	14.7565	−	9.48340i	0.513443	−	0.329970i
$827$	−31.3283			−1.08939			−0.544695	−	0.838634i	$-0.683355\pi$
$827$	−31.3283			−1.08939			−0.544695	+	0.838634i	$0.683355\pi$
$828$	−25.0719	+	7.37486i	−0.871310	+	0.256294i
$829$	−36.7831			−1.27753			−0.638765	−	0.769402i	$-0.720554\pi$
$829$	−36.7831			−1.27753			−0.638765	+	0.769402i	$0.720554\pi$
$830$	8.17720	−	5.25517i	0.283835	−	0.182410i
$831$	0.915579	−	6.36799i	0.0317611	−	0.220903i
$832$	−35.3823	+	77.4763i	−1.22666	+	2.68601i
$833$	−1.33618	+	0.392338i	−0.0462959	+	0.0135937i
$834$	−15.4441	−	33.8179i	−0.534785	−	1.17102i
$835$	−11.0517	−	12.7543i	−0.382460	−	0.441382i
$836$	−6.42671	−	44.6988i	−0.222272	−	1.54594i
$837$	−6.69513	−	1.96587i	−0.231418	−	0.0679504i
$838$	65.0679	−	75.0924i	2.24773	−	2.59402i
$839$	−42.5768	−	27.3624i	−1.46991	−	0.944656i	−0.998013	−	0.0630037i	$-0.979932\pi$
$839$	−42.5768	−	27.3624i	−1.46991	−	0.944656i	−0.471900	−	0.881652i	$-0.656432\pi$
$840$	−27.9535	−	17.9646i	−0.964488	−	0.619839i
$841$	8.96448	−	10.3456i	0.309120	−	0.356743i
$842$	14.0480	+	4.12487i	0.484127	+	0.142152i
$843$	1.84227	+	12.8133i	0.0634511	+	0.441312i
$844$	−90.9226	−	104.930i	−3.12968	−	3.61185i
$845$	−6.62086	−	14.4977i	−0.227764	−	0.498734i
$846$	−32.3609	+	9.50201i	−1.11259	+	0.326686i
$847$	−0.126519	+	0.277039i	−0.00434726	+	0.00951917i
$848$	22.9536	−	159.646i	0.788231	−	5.48227i
$849$	3.33719	−	2.14468i	0.114532	−	0.0736053i
$850$	28.3449			0.972221
$851$	14.1210	+	16.2808i	0.484063	+	0.558097i
$852$	62.0484			2.12574
$853$	−4.28159	+	2.75161i	−0.146599	+	0.0942134i	−0.611884	−	0.790947i	$-0.709588\pi$
$853$	−4.28159	+	2.75161i	−0.146599	+	0.0942134i	0.465285	+	0.885161i	$0.345952\pi$
$854$	0.200939	−	1.39756i	0.00687598	−	0.0478235i
$855$	3.71529	−	8.13536i	0.127060	−	0.278223i
$856$	71.1427	−	20.8894i	2.43161	−	0.713984i
$857$	9.13360	+	19.9998i	0.311998	+	0.683180i	0.999057	−	0.0434215i	$-0.0138258\pi$
$857$	9.13360	+	19.9998i	0.311998	+	0.683180i	−0.687059	+	0.726602i	$0.741099\pi$
$858$	−17.0262	−	19.6493i	−0.581264	−	0.670815i
$859$	−2.84622	−	19.7959i	−0.0971119	−	0.675428i	−0.978984	−	0.203939i	$-0.934626\pi$
$859$	−2.84622	−	19.7959i	−0.0971119	−	0.675428i	0.881872	−	0.471489i	$-0.156283\pi$
$860$	183.770	+	53.9598i	6.26651	+	1.84001i
$861$	5.18981	−	5.98936i	0.176868	−	0.204117i
$862$	1.36812	+	0.879236i	0.0465983	+	0.0299469i
$863$	25.8735	+	16.6279i	0.880745	+	0.566021i	0.901022	−	0.433774i	$-0.142818\pi$
$863$	25.8735	+	16.6279i	0.880745	+	0.566021i	−0.0202765	+	0.999794i	$0.506455\pi$
$864$	14.1163	−	16.2911i	0.480246	−	0.554233i
$865$	18.0953	+	5.31326i	0.615258	+	0.180656i
$866$	11.1572	+	77.5999i	0.379136	+	2.63695i
$867$	−9.86266	−	11.3821i	−0.334953	−	0.386557i
$868$	−15.7959	−	34.5881i	−0.536146	−	1.17400i
$869$	−28.3997	+	8.33890i	−0.963393	+	0.282878i
$870$	15.6587	−	34.2878i	0.530880	−	1.16247i
$871$	−5.06774	+	35.2469i	−0.171714	+	1.19430i
$872$	18.7213	−	12.0315i	0.633984	−	0.407437i
$873$	13.9032			0.470552
$874$	13.7640	−	30.1772i	0.465573	−	1.02076i
$875$	8.67377			0.293227
$876$	−57.7022	+	37.0829i	−1.94958	+	1.25292i
$877$	−4.59105	+	31.9314i	−0.155029	+	1.07825i	0.752601	+	0.658476i	$0.228799\pi$
$877$	−4.59105	+	31.9314i	−0.155029	+	1.07825i	−0.907630	+	0.419771i	$0.862110\pi$
$878$	37.1368	−	81.3183i	1.25331	−	2.74436i
$879$	−15.0960	+	4.43257i	−0.509174	+	0.149507i
$880$	70.9510	+	155.361i	2.39176	+	5.23722i
$881$	−13.9389	−	16.0863i	−0.469612	−	0.541961i	0.470692	−	0.882298i	$-0.344004\pi$
$881$	−13.9389	−	16.0863i	−0.469612	−	0.541961i	−0.940304	+	0.340337i	$0.889459\pi$
$882$	−0.388427	−	2.70157i	−0.0130790	−	0.0909665i
$883$	9.48815	+	2.78597i	0.319302	+	0.0937555i	0.437456	−	0.899240i	$-0.355880\pi$
$883$	9.48815	+	2.78597i	0.319302	+	0.0937555i	−0.118154	+	0.992995i	$0.537698\pi$
$884$	14.4752	−	16.7053i	0.486855	−	0.561861i
$885$	−19.0827	−	12.2637i	−0.641457	−	0.412239i
$886$	36.4014	+	23.3938i	1.22293	+	0.785929i
$887$	−33.0153	+	38.1017i	−1.10854	+	1.27933i	−0.151796	+	0.988412i	$0.548506\pi$
$887$	−33.0153	+	38.1017i	−1.10854	+	1.27933i	−0.956748	+	0.290916i	$0.906040\pi$
$888$	−40.5929	−	11.9191i	−1.36221	−	0.399980i
$889$	0.220604	+	1.53433i	0.00739881	+	0.0514598i
$890$	49.7901	+	57.4609i	1.66897	+	1.92609i
$891$	1.35857	+	2.97485i	0.0455138	+	0.0996612i
$892$	50.3590	−	14.7867i	1.68614	−	0.495097i
$893$	13.0076	−	28.4827i	0.435283	−	0.953137i
$894$	7.67091	−	53.3524i	0.256554	−	1.78437i
$895$	−5.31108	+	3.41323i	−0.177530	+	0.114092i
$896$	36.6967			1.22595
$897$	−1.99467	−	13.8261i	−0.0666002	−	0.461641i
$898$	−64.0401			−2.13705
$899$	22.9691	−	14.7614i	0.766063	−	0.492319i
$900$	−5.78345	+	40.2248i	−0.192782	+	1.34083i
$901$	−6.30587	+	13.8079i	−0.210079	+	0.460009i
$902$	−67.8738	+	19.9295i	−2.25995	+	0.663581i
$903$	4.13672	+	9.05816i	0.137662	+	0.301437i
$904$	77.8711	+	89.8680i	2.58995	+	2.98897i
$905$	−2.82003	−	19.6137i	−0.0937409	−	0.651983i
$906$	−29.0618	−	8.53331i	−0.965514	−	0.283500i
$907$	−27.6707	+	31.9337i	−0.918792	+	1.06034i	0.0791907	+	0.996859i	$0.474766\pi$
$907$	−27.6707	+	31.9337i	−0.918792	+	1.06034i	−0.997983	+	0.0634832i	$0.979779\pi$
$908$	−64.9050	−	41.7119i	−2.15395	−	1.38426i
$909$	−11.9606	−	7.68661i	−0.396708	−	0.254949i
$910$	18.3753	−	21.2062i	0.609134	−	0.702978i
$911$	−1.13288	−	0.332643i	−0.0375339	−	0.0110209i	0.262912	−	0.964820i	$-0.415317\pi$
$911$	−1.13288	−	0.332643i	−0.0375339	−	0.0110209i	−0.300446	+	0.953799i	$0.597135\pi$
$912$	5.33590	+	37.1120i	0.176689	+	1.22890i
$913$	−2.16099	−	2.49391i	−0.0715182	−	0.0825364i
$914$	−14.7872	−	32.3793i	−0.489116	−	1.07101i
$915$	−1.75191	+	0.514407i	−0.0579163	+	0.0170058i
$916$	1.75663	−	3.84648i	0.0580407	−	0.127091i
$917$	−0.323452	+	2.24966i	−0.0106813	+	0.0742903i
$918$	−3.19749	+	2.05490i	−0.105533	+	0.0678218i
$919$	−43.4430			−1.43305			−0.716527	−	0.697560i	$-0.754269\pi$
$919$	−43.4430			−1.43305			−0.716527	+	0.697560i	$0.754269\pi$
$920$	−22.6033	+	157.747i	−0.745208	+	5.20075i
$921$	−13.9509			−0.459699
$922$	37.6360	−	24.1872i	1.23947	−	0.796562i
$923$	−4.72006	+	32.8287i	−0.155363	+	1.08057i
$924$	−7.40330	+	16.2110i	−0.243551	+	0.533301i
$925$	32.1550	−	9.44156i	1.05725	−	0.310436i
$926$	−6.80190	−	14.8941i	−0.223524	−	0.489450i
$927$	5.05520	+	5.83401i	0.166035	+	0.191614i
$928$	12.0039	+	83.4888i	0.394046	+	2.74065i
$929$	−28.3615	−	8.32768i	−0.930510	−	0.273222i	−0.218860	−	0.975756i	$-0.570234\pi$
$929$	−28.3615	−	8.32768i	−0.930510	−	0.273222i	−0.711650	+	0.702534i	$0.752052\pi$
$930$	−44.0190	+	50.8007i	−1.44344	+	1.66582i
$931$	2.13168	+	1.36995i	0.0698631	+	0.0448983i
$932$	96.4030	+	61.9544i	3.15778	+	2.02938i
$933$	−18.8686	+	21.7755i	−0.617729	+	0.712897i
$934$	−46.7700	−	13.7329i	−1.53036	−	0.449355i
$935$	−2.28764	−	15.9109i	−0.0748138	−	0.520342i
$936$	17.9578	+	20.7244i	0.586970	+	0.677399i
$937$	25.2043	+	55.1897i	0.823389	+	1.80297i	0.533167	+	0.846010i	$0.321002\pi$
$937$	25.2043	+	55.1897i	0.823389	+	1.80297i	0.290221	+	0.956960i	$0.406271\pi$
$938$	32.0151	−	9.40047i	1.04533	−	0.306936i
$939$	−0.0361918	+	0.0792489i	−0.00118107	+	0.00258619i
$940$	−33.8243	+	235.253i	−1.10323	+	7.67311i
$941$	−1.29485	+	0.832152i	−0.0422110	+	0.0271274i	−0.561576	−	0.827425i	$-0.689805\pi$
$941$	−1.29485	+	0.832152i	−0.0422110	+	0.0271274i	0.519365	+	0.854552i	$0.326168\pi$
$942$	21.8759			0.712754
$943$	−36.4728	−	10.6904i	−1.18772	−	0.348126i
$944$	95.0951			3.09508
$945$	−2.96922	+	1.90820i	−0.0965887	+	0.0620738i
$946$	12.6498	−	87.9811i	0.411280	−	2.86051i
$947$	13.1046	−	28.6951i	0.425842	−	0.932464i	−0.568141	−	0.822931i	$-0.692337\pi$
$947$	13.1046	−	28.6951i	0.425842	−	0.932464i	0.993983	−	0.109533i	$-0.0349355\pi$
$948$	47.3214	−	13.8948i	1.53693	−	0.451283i
$949$	−15.2305	−	33.3501i	−0.494403	−	1.08259i
$950$	−33.7751	−	38.9785i	−1.09581	−	1.26463i
$951$	3.43991	+	23.9251i	0.111547	+	0.775825i
$952$	−12.5794	−	3.69364i	−0.407700	−	0.119711i
$953$	9.49242	−	10.9548i	0.307490	−	0.354862i	−0.580881	−	0.813988i	$-0.697292\pi$
$953$	9.49242	−	10.9548i	0.307490	−	0.354862i	0.888371	+	0.459126i	$0.151837\pi$
$954$	−25.0280	−	16.0845i	−0.810310	−	0.520755i
$955$	17.2877	+	11.1101i	0.559417	+	0.359516i
$956$	−30.7853	+	35.5281i	−0.995667	+	1.14906i
$957$	−12.2784	−	3.60526i	−0.396904	−	0.116541i
$958$	10.0897	+	70.1755i	0.325984	+	2.26727i
$959$	7.05090	+	8.13717i	0.227685	+	0.262763i
$960$	−42.8737	−	93.8802i	−1.38374	−	3.02997i
$961$	−16.9729	+	4.98369i	−0.547513	+	0.160764i
$962$	14.8411	−	32.4974i	0.478495	−	1.04776i
$963$	1.12084	−	7.79562i	0.0361186	−	0.251210i
$964$	−34.7615	+	22.3398i	−1.11959	+	0.719518i
$965$	−58.8889			−1.89570
$966$	−11.0082	+	7.08200i	−0.354182	+	0.227859i
$967$	−21.8988			−0.704218			−0.352109	−	0.935959i	$-0.614535\pi$
$967$	−21.8988			−0.704218			−0.352109	+	0.935959i	$0.614535\pi$
$968$	−2.41210	+	1.55017i	−0.0775280	+	0.0498242i
$969$	0.502191	−	3.49281i	0.0161327	−	0.112205i
$970$	55.6379	−	121.830i	1.78643	−	3.91173i
$971$	−29.9641	+	8.79824i	−0.961592	+	0.282349i	−0.724606	−	0.689164i	$-0.757978\pi$
$971$	−29.9641	+	8.79824i	−0.961592	+	0.282349i	−0.236987	+	0.971513i	$0.576160\pi$
$972$	−2.26374	−	4.95689i	−0.0726094	−	0.158992i
$973$	−8.92012	−	10.2944i	−0.285966	−	0.330022i
$974$	8.63193	+	60.0364i	0.276585	+	1.92369i
$975$	−20.8423	−	6.11984i	−0.667487	−	0.195992i
$976$	5.01262	−	5.78487i	0.160450	−	0.185169i
$977$	19.3347	+	12.4257i	0.618573	+	0.397533i	0.812063	−	0.583569i	$-0.198344\pi$
$977$	19.3347	+	12.4257i	0.618573	+	0.397533i	−0.193490	+	0.981102i	$0.561981\pi$
$978$	14.0043	+	8.99999i	0.447807	+	0.287788i
$979$	16.9032	−	19.5073i	0.540228	−	0.623456i
$980$	−18.4544	−	5.41871i	−0.589505	−	0.173094i
$981$	−0.336407	−	2.33976i	−0.0107407	−	0.0747029i
$982$	−43.2414	−	49.9033i	−1.37989	−	1.59248i
$983$	−11.9084	−	26.0758i	−0.379820	−	0.831690i	−0.998924	−	0.0463805i	$-0.985231\pi$
$983$	−11.9084	−	26.0758i	−0.379820	−	0.831690i	0.619104	−	0.785309i	$-0.287496\pi$
$984$	71.5877	−	21.0200i	2.28213	−	0.670094i
$985$	16.6481	−	36.4543i	0.530453	−	1.16153i
$986$	2.11657	−	14.7210i	0.0674052	−	0.468813i
$987$	−10.3955	+	6.68080i	−0.330893	+	0.212652i
$988$	−40.2207			−1.27959
$989$	31.2570	−	36.1074i	0.993913	−	1.14815i
$990$	31.5046			1.00128
$991$	−52.1958	+	33.5442i	−1.65806	+	1.06557i	−0.737191	+	0.675684i	$0.763848\pi$
$991$	−52.1958	+	33.5442i	−1.65806	+	1.06557i	−0.920864	+	0.389884i	$0.872515\pi$
$992$	21.4062	−	148.883i	0.679647	−	4.72705i
$993$	−10.5197	+	23.0350i	−0.333833	+	0.730993i
$994$	29.8186	−	8.75553i	0.945789	−	0.277709i
$995$	21.3413	+	46.7309i	0.676564	+	1.48147i
$996$	3.60078	+	4.15552i	0.114095	+	0.131673i
$997$	1.61704	+	11.2467i	0.0512121	+	0.356188i	0.999274	+	0.0381016i	$0.0121310\pi$
$997$	1.61704	+	11.2467i	0.0512121	+	0.356188i	−0.948062	+	0.318086i	$0.896960\pi$
$998$	18.9482	+	5.56369i	0.599795	+	0.176116i
$999$	−2.94281	+	3.39619i	−0.0931065	+	0.107451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.d.127.6	✓	60
23.2	even	11	inner	483.2.q.d.232.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.d.127.6	✓	60	1.1	even	1	trivial
483.2.q.d.232.6	yes	60	23.2	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29607 - 1.47560i) q^{2} +(0.142315 - 0.989821i) q^{3} +(2.26374 - 4.95689i) q^{4} +(-3.38655 + 0.994380i) q^{5} +(-1.13381 - 2.48270i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-1.33981 - 9.31861i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(2.29607 - 1.47560i) q^{2} +(0.142315 - 0.989821i) q^{3} +(2.26374 - 4.95689i) q^{4} +(-3.38655 + 0.994380i) q^{5} +(-1.13381 - 2.48270i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-1.33981 - 9.31861i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-6.30846 + 7.28035i) q^{10} +(2.75123 + 1.76811i) q^{11} +(-4.58427 - 2.94613i) q^{12} +(1.90748 - 2.20135i) q^{13} +(-2.61879 - 0.768946i) q^{14} +(0.502303 + 3.49359i) q^{15} +(-9.68971 - 11.1825i) q^{16} +(0.578502 + 1.26674i) q^{17} +(-2.61879 + 0.768946i) q^{18} +(1.05264 - 2.30495i) q^{19} +(-2.73722 + 19.0378i) q^{20} +(-0.841254 + 0.540641i) q^{21} +8.92602 q^{22} +(4.03575 + 2.59089i) q^{23} -9.41443 q^{24} +(6.27364 - 4.03183i) q^{25} +(1.13141 - 7.86912i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-5.22860 + 1.53526i) q^{28} +(-1.62548 - 3.55931i) q^{29} +(6.30846 + 7.28035i) q^{30} +(0.993042 + 6.90676i) q^{31} +(-20.6830 - 6.07307i) q^{32} +(2.14165 - 2.47159i) q^{33} +(3.19749 + 2.05490i) q^{34} +(2.96922 + 1.90820i) q^{35} +(-3.56856 + 4.11833i) q^{36} +(4.31177 + 1.26605i) q^{37} +(-0.984248 - 6.84560i) q^{38} +(-1.90748 - 2.20135i) q^{39} +(13.8036 + 30.2256i) q^{40} +(-7.60403 + 2.23275i) q^{41} +(-1.13381 + 2.48270i) q^{42} +(1.41718 - 9.85669i) q^{43} +(14.9924 - 9.63500i) q^{44} +3.52952 q^{45} +(13.0895 - 0.00628143i) q^{46} +12.3572 q^{47} +(-12.4477 + 7.99964i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(8.45540 - 18.5147i) q^{50} +(1.33618 - 0.392338i) q^{51} +(-6.59380 - 14.4384i) q^{52} +(7.13820 + 8.23792i) q^{53} +(0.388427 + 2.70157i) q^{54} +(-11.0753 - 3.25201i) q^{55} +(-6.16514 + 7.11496i) q^{56} +(-2.13168 - 1.36995i) q^{57} +(-8.98433 - 5.77388i) q^{58} +(-4.20868 + 4.85707i) q^{59} +(18.4544 + 5.41871i) q^{60} +(0.0736215 + 0.512049i) q^{61} +(12.4717 + 14.3931i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-28.0566 + 8.23816i) q^{64} +(-4.27079 + 9.35172i) q^{65} +(1.27031 - 8.83517i) q^{66} +(-10.2844 + 6.60941i) q^{67} +7.58868 q^{68} +(3.13886 - 3.62595i) q^{69} +9.63328 q^{70} +(-9.57886 + 6.15596i) q^{71} +(-1.33981 + 9.31861i) q^{72} +(5.22882 - 11.4495i) q^{73} +(11.7683 - 3.45549i) q^{74} +(-3.09796 - 6.78358i) q^{75} +(-9.04249 - 10.4356i) q^{76} +(-0.465425 - 3.23710i) q^{77} +(-7.62800 - 2.23978i) q^{78} +(-5.92681 + 6.83991i) q^{79} +(43.9343 + 28.2349i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-14.1648 + 16.3470i) q^{82} +(-0.968156 - 0.284276i) q^{83} +(0.775521 + 5.39387i) q^{84} +(-3.21875 - 3.71463i) q^{85} +(-11.2906 - 24.7229i) q^{86} +(-3.75441 + 1.10239i) q^{87} +(12.7902 - 28.0065i) q^{88} +(1.12323 - 7.81227i) q^{89} +(8.10403 - 5.20814i) q^{90} -2.91280 q^{91} +(21.9786 - 14.1397i) q^{92} +6.97778 q^{93} +(28.3730 - 18.2342i) q^{94} +(-1.27280 + 8.85254i) q^{95} +(-8.95475 + 19.6082i) q^{96} +(-13.3400 + 3.91698i) q^{97} +(1.13381 + 2.48270i) q^{98} +(-2.14165 - 2.47159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more