LMFDB - Embedded newform 525.2.bg.b.16.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.13
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.b.361.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.845870 - 0.376606i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.764597 + 0.849171i) q^{4} +(0.707816 - 2.12108i) q^{5} +(0.286125 - 0.880602i) q^{6} +(2.58582 - 0.559924i) q^{7} +(-0.899197 + 2.76744i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.845870 - 0.376606i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.764597 + 0.849171i) q^{4} +(0.707816 - 2.12108i) q^{5} +(0.286125 - 0.880602i) q^{6} +(2.58582 - 0.559924i) q^{7} +(-0.899197 + 2.76744i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.200092 - 2.06073i) q^{10} +(0.0429968 - 0.409088i) q^{11} +(0.119442 + 1.13641i) q^{12} +(0.746543 - 0.542395i) q^{13} +(1.97640 - 1.44746i) q^{14} +(-1.10265 - 1.94529i) q^{15} +(0.0427474 + 0.406715i) q^{16} +(6.17687 - 1.31293i) q^{17} +(-0.462960 - 0.801870i) q^{18} +(-3.03592 - 3.37173i) q^{19} +(1.25997 + 2.22283i) q^{20} +(1.31415 - 2.29630i) q^{21} +(-0.117695 - 0.362228i) q^{22} +(-0.165118 + 0.0735153i) q^{23} +(1.45493 + 2.52002i) q^{24} +(-3.99799 - 3.00267i) q^{25} +(0.427209 - 0.739948i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.50164 + 2.62392i) q^{28} +(0.993731 + 3.05839i) q^{29} +(-1.66531 - 1.23020i) q^{30} +(-2.19106 + 0.465724i) q^{31} +(-2.72053 - 4.71210i) q^{32} +(-0.275241 - 0.305686i) q^{33} +(4.73037 - 3.43681i) q^{34} +(0.642642 - 5.88107i) q^{35} +(0.924441 + 0.671646i) q^{36} +(0.715968 + 6.81198i) q^{37} +(-3.83781 - 1.70870i) q^{38} +(0.0964566 - 0.917723i) q^{39} +(5.23352 + 3.86611i) q^{40} +(0.698153 - 0.507238i) q^{41} +(0.246799 - 2.43729i) q^{42} -5.10982 q^{43} +(0.314510 + 0.349299i) q^{44} +(-2.18345 - 0.482224i) q^{45} +(-0.111982 + 0.124369i) q^{46} +(8.23769 + 1.75097i) q^{47} +(0.330852 + 0.240378i) q^{48} +(6.37297 - 2.89573i) q^{49} +(-4.51261 - 1.03420i) q^{50} +(3.15743 - 5.46883i) q^{51} +(-0.110218 + 1.04866i) q^{52} +(-4.08640 + 4.53840i) q^{53} +(-0.905686 - 0.192510i) q^{54} +(-0.837275 - 0.380758i) q^{55} +(-0.775608 + 7.65960i) q^{56} -4.53711 q^{57} +(1.99237 + 2.21276i) q^{58} +(8.00953 + 3.56607i) q^{59} +(2.49497 + 0.551025i) q^{60} +(-8.78786 + 3.91261i) q^{61} +(-1.67796 + 1.21911i) q^{62} +(-0.827148 - 2.51313i) q^{63} +(-4.73752 - 3.44201i) q^{64} +(-0.622051 - 1.96740i) q^{65} +(-0.347941 - 0.154913i) q^{66} +(-4.10422 + 0.872378i) q^{67} +(-3.60791 + 6.24908i) q^{68} +(-0.0558530 + 0.171898i) q^{69} +(-1.67125 - 5.21664i) q^{70} +(0.552686 + 1.70099i) q^{71} +(2.84628 + 0.604994i) q^{72} +(-0.729720 + 6.94283i) q^{73} +(3.17105 + 5.49242i) q^{74} +(-4.90660 + 0.961909i) q^{75} +5.18443 q^{76} +(-0.117875 - 1.08190i) q^{77} +(-0.264030 - 0.812600i) q^{78} +(2.20929 + 0.469599i) q^{79} +(0.892933 + 0.197208i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.399518 - 0.691985i) q^{82} +(-5.34724 + 16.4571i) q^{83} +(0.945160 + 2.87168i) q^{84} +(1.58724 - 14.0310i) q^{85} +(-4.32224 + 1.92439i) q^{86} +(2.93776 + 1.30798i) q^{87} +(1.09346 + 0.486842i) q^{88} +(-15.4976 + 6.89998i) q^{89} +(-2.02852 + 0.414401i) q^{90} +(1.62673 - 1.82055i) q^{91} +(0.0638217 - 0.196423i) q^{92} +(-1.12000 + 1.93991i) q^{93} +(7.62744 - 1.62126i) q^{94} +(-9.30060 + 4.05288i) q^{95} +(-5.32217 - 1.13126i) q^{96} +(-4.28793 - 13.1969i) q^{97} +(4.30016 - 4.84950i) q^{98} -0.411341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.845870	−	0.376606i	0.598120	−	0.266300i	−0.0852649	−	0.996358i	$-0.527174\pi$
$2$	0.845870	−	0.376606i	0.598120	−	0.266300i	0.683385	+	0.730058i	$0.260507\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.764597	+	0.849171i	−0.382299	+	0.424586i
$5$	0.707816	−	2.12108i	0.316545	−	0.948578i
$5$	0.707816	−	2.12108i	0.316545	−	0.948578i
$6$	0.286125	−	0.880602i	0.116810	−	0.359504i
$7$	2.58582	−	0.559924i	0.977350	−	0.211631i
$7$	2.58582	−	0.559924i	0.977350	−	0.211631i
$8$	−0.899197	+	2.76744i	−0.317914	+	0.978439i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−0.200092	−	2.06073i	−0.0632747	−	0.651660i
$11$	0.0429968	−	0.409088i	0.0129640	−	0.123345i	−0.986126	−	0.166000i	$-0.946915\pi$
$11$	0.0429968	−	0.409088i	0.0129640	−	0.123345i	0.999090	+	0.0426550i	$0.0135816\pi$
$12$	0.119442	+	1.13641i	0.0344799	+	0.328054i
$13$	0.746543	−	0.542395i	0.207054	−	0.150433i	−0.479426	−	0.877582i	$-0.659155\pi$
$13$	0.746543	−	0.542395i	0.207054	−	0.150433i	0.686480	+	0.727149i	$0.259155\pi$
$14$	1.97640	−	1.44746i	0.528215	−	0.386849i
$15$	−1.10265	−	1.94529i	−0.284703	−	0.502272i
$16$	0.0427474	+	0.406715i	0.0106869	+	0.101679i
$17$	6.17687	−	1.31293i	1.49811	−	0.318433i	0.615349	−	0.788255i	$-0.289015\pi$
$17$	6.17687	−	1.31293i	1.49811	−	0.318433i	0.882762	+	0.469821i	$0.155682\pi$
$18$	−0.462960	−	0.801870i	−0.109121	−	0.189003i
$19$	−3.03592	−	3.37173i	−0.696488	−	0.773528i	0.286325	−	0.958133i	$-0.407566\pi$
$19$	−3.03592	−	3.37173i	−0.696488	−	0.773528i	−0.982813	+	0.184604i	$0.940900\pi$
$20$	1.25997	+	2.22283i	0.281738	+	0.497040i
$21$	1.31415	−	2.29630i	0.286771	−	0.501095i
$22$	−0.117695	−	0.362228i	−0.0250926	−	0.0772272i
$23$	−0.165118	+	0.0735153i	−0.0344295	+	0.0153290i	−0.423879	−	0.905719i	$-0.639332\pi$
$23$	−0.165118	+	0.0735153i	−0.0344295	+	0.0153290i	0.389450	+	0.921048i	$0.372665\pi$
$24$	1.45493	+	2.52002i	0.296987	+	0.514396i
$25$	−3.99799	−	3.00267i	−0.799599	−	0.600534i
$26$	0.427209	−	0.739948i	0.0837826	−	0.145116i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.50164	+	2.62392i	−0.283784	+	0.495875i
$29$	0.993731	+	3.05839i	0.184531	+	0.567929i	0.999940	−	0.0109569i	$-0.00348777\pi$
$29$	0.993731	+	3.05839i	0.184531	+	0.567929i	−0.815409	+	0.578886i	$0.803488\pi$
$30$	−1.66531	−	1.23020i	−0.304042	−	0.224603i
$31$	−2.19106	+	0.465724i	−0.393526	+	0.0836465i	−0.400425	−	0.916330i	$-0.631137\pi$
$31$	−2.19106	+	0.465724i	−0.393526	+	0.0836465i	0.00689867	+	0.999976i	$0.497804\pi$
$32$	−2.72053	−	4.71210i	−0.480927	−	0.832990i
$33$	−0.275241	−	0.305686i	−0.0479133	−	0.0532131i
$34$	4.73037	−	3.43681i	0.811252	−	0.589409i
$35$	0.642642	−	5.88107i	0.108626	−	0.994083i
$36$	0.924441	+	0.671646i	0.154074	+	0.111941i
$37$	0.715968	+	6.81198i	0.117704	+	1.11988i	0.880764	+	0.473555i	$0.157030\pi$
$37$	0.715968	+	6.81198i	0.117704	+	1.11988i	−0.763060	+	0.646328i	$0.776304\pi$
$38$	−3.83781	−	1.70870i	−0.622575	−	0.277188i
$39$	0.0964566	−	0.917723i	0.0154454	−	0.146953i
$40$	5.23352	+	3.86611i	0.827491	+	0.611286i
$41$	0.698153	−	0.507238i	0.109033	−	0.0792172i	−0.531933	−	0.846787i	$-0.678534\pi$
$41$	0.698153	−	0.507238i	0.109033	−	0.0792172i	0.640966	+	0.767569i	$0.278534\pi$
$42$	0.246799	−	2.43729i	0.0380819	−	0.376082i
$43$	−5.10982			−0.779240			−0.389620	−	0.920976i	$-0.627394\pi$
$43$	−5.10982			−0.779240			−0.389620	+	0.920976i	$0.627394\pi$
$44$	0.314510	+	0.349299i	0.0474142	+	0.0526588i
$45$	−2.18345	−	0.482224i	−0.325490	−	0.0718858i
$46$	−0.111982	+	0.124369i	−0.0165109	+	0.0183372i
$47$	8.23769	+	1.75097i	1.20159	+	0.255406i	0.764866	−	0.644189i	$-0.222805\pi$
$47$	8.23769	+	1.75097i	1.20159	+	0.255406i	0.436724	+	0.899595i	$0.356138\pi$
$48$	0.330852	+	0.240378i	0.0477543	+	0.0346955i
$49$	6.37297	−	2.89573i	0.910424	−	0.413675i
$50$	−4.51261	−	1.03420i	−0.638179	−	0.146258i
$51$	3.15743	−	5.46883i	0.442129	−	0.765790i
$52$	−0.110218	+	1.04866i	−0.0152845	+	0.145422i
$53$	−4.08640	+	4.53840i	−0.561310	+	0.623397i	−0.955272	−	0.295729i	$-0.904437\pi$
$53$	−4.08640	+	4.53840i	−0.561310	+	0.623397i	0.393962	+	0.919127i	$0.371104\pi$
$54$	−0.905686	−	0.192510i	−0.123248	−	0.0261972i
$55$	−0.837275	−	0.380758i	−0.112898	−	0.0513415i
$56$	−0.775608	+	7.65960i	−0.103645	+	1.02356i
$57$	−4.53711			−0.600955
$58$	1.99237	+	2.21276i	0.261611	+	0.290549i
$59$	8.00953	+	3.56607i	1.04275	+	0.464263i	0.855367	−	0.518023i	$-0.173332\pi$
$59$	8.00953	+	3.56607i	1.04275	+	0.464263i	0.187386	+	0.982286i	$0.439999\pi$
$60$	2.49497	+	0.551025i	0.322099	+	0.0711370i
$61$	−8.78786	+	3.91261i	−1.12517	+	0.500958i	−0.883046	−	0.469287i	$-0.844511\pi$
$61$	−8.78786	+	3.91261i	−1.12517	+	0.500958i	−0.242125	+	0.970245i	$0.577844\pi$
$62$	−1.67796	+	1.21911i	−0.213101	+	0.154827i
$63$	−0.827148	−	2.51313i	−0.104211	−	0.316625i
$64$	−4.73752	−	3.44201i	−0.592190	−	0.430252i
$65$	−0.622051	−	1.96740i	−0.0771559	−	0.244025i
$66$	−0.347941	−	0.154913i	−0.0428286	−	0.0190685i
$67$	−4.10422	+	0.872378i	−0.501410	+	0.106578i	−0.451671	−	0.892184i	$-0.649172\pi$
$67$	−4.10422	+	0.872378i	−0.501410	+	0.106578i	−0.0497383	+	0.998762i	$0.515839\pi$
$68$	−3.60791	+	6.24908i	−0.437523	+	0.757813i
$69$	−0.0558530	+	0.171898i	−0.00672392	+	0.0206941i
$70$	−1.67125	−	5.21664i	−0.199753	−	0.623508i
$71$	0.552686	+	1.70099i	0.0655918	+	0.201871i	0.978481	−	0.206336i	$-0.0661541\pi$
$71$	0.552686	+	1.70099i	0.0655918	+	0.201871i	−0.912889	+	0.408207i	$0.866154\pi$
$72$	2.84628	+	0.604994i	0.335437	+	0.0712993i
$73$	−0.729720	+	6.94283i	−0.0854073	+	0.812596i	0.865038	+	0.501706i	$0.167294\pi$
$73$	−0.729720	+	6.94283i	−0.0854073	+	0.812596i	−0.950446	+	0.310891i	$0.899373\pi$
$74$	3.17105	+	5.49242i	0.368627	+	0.638480i
$75$	−4.90660	+	0.961909i	−0.566565	+	0.111072i
$76$	5.18443			0.594695
$77$	−0.117875	−	1.08190i	−0.0134332	−	0.123294i
$78$	−0.264030	−	0.812600i	−0.0298955	−	0.0920088i
$79$	2.20929	+	0.469599i	0.248565	+	0.0528341i	0.330509	−	0.943803i	$-0.392780\pi$
$79$	2.20929	+	0.469599i	0.248565	+	0.0528341i	−0.0819442	+	0.996637i	$0.526113\pi$
$80$	0.892933	+	0.197208i	0.0998330	+	0.0220485i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	0.399518	−	0.691985i	0.0441194	−	0.0764170i
$83$	−5.34724	+	16.4571i	−0.586936	+	1.80640i	0.00441711	+	0.999990i	$0.498594\pi$
$83$	−5.34724	+	16.4571i	−0.586936	+	1.80640i	−0.591353	+	0.806413i	$0.701406\pi$
$84$	0.945160	+	2.87168i	0.103125	+	0.313327i
$85$	1.58724	−	14.0310i	0.172160	−	1.52187i
$86$	−4.32224	+	1.92439i	−0.466079	+	0.207512i
$87$	2.93776	+	1.30798i	0.314961	+	0.140230i
$88$	1.09346	+	0.486842i	0.116564	+	0.0518975i
$89$	−15.4976	+	6.89998i	−1.64274	+	0.731397i	−0.999415	−	0.0341939i	$-0.989114\pi$
$89$	−15.4976	+	6.89998i	−1.64274	+	0.731397i	−0.643328	+	0.765590i	$0.722447\pi$
$90$	−2.02852	+	0.414401i	−0.213825	+	0.0436817i
$91$	1.62673	−	1.82055i	0.170528	−	0.190845i
$92$	0.0638217	−	0.196423i	0.00665387	−	0.0204785i
$93$	−1.12000	+	1.93991i	−0.116139	+	0.201159i
$94$	7.62744	−	1.62126i	0.786710	−	0.167220i
$95$	−9.30060	+	4.05288i	−0.954221	+	0.415817i
$96$	−5.32217	−	1.13126i	−0.543191	−	0.115459i
$97$	−4.28793	−	13.1969i	−0.435374	−	1.33994i	−0.892703	−	0.450645i	$-0.851194\pi$
$97$	−4.28793	−	13.1969i	−0.435374	−	1.33994i	0.457330	−	0.889297i	$-0.348806\pi$
$98$	4.30016	−	4.84950i	0.434382	−	0.489874i
$99$	−0.411341			−0.0413413
$100$	5.60664	−	1.09915i	0.560664	−	0.109915i
$101$	4.79039	+	8.29719i	0.476661	+	0.825601i	0.999642	−	0.0267429i	$-0.00851354\pi$
$101$	4.79039	+	8.29719i	0.476661	+	0.825601i	−0.522981	+	0.852344i	$0.675180\pi$
$102$	0.611184	−	5.81503i	0.0605162	−	0.575773i
$103$	−8.62896	−	1.83414i	−0.850237	−	0.180723i	−0.237870	−	0.971297i	$-0.576449\pi$
$103$	−8.62896	−	1.83414i	−0.850237	−	0.180723i	−0.612367	+	0.790574i	$0.709783\pi$
$104$	0.829759	+	2.55374i	0.0813646	+	0.250414i
$105$	−3.94048	−	4.41278i	−0.384551	−	0.430643i
$106$	−1.74737	+	5.37786i	−0.169720	+	0.522344i
$107$	0.0256689	−	0.0444599i	0.00248151	−	0.00429810i	−0.864782	−	0.502148i	$-0.832543\pi$
$107$	0.0256689	−	0.0444599i	0.00248151	−	0.00429810i	0.867263	+	0.497849i	$0.165877\pi$
$108$	1.11770	−	0.237575i	0.107551	−	0.0228607i
$109$	4.22643	+	1.88173i	0.404818	+	0.180237i	0.599037	−	0.800722i	$-0.295550\pi$
$109$	4.22643	+	1.88173i	0.404818	+	0.180237i	−0.194218	+	0.980958i	$0.562217\pi$
$110$	−0.851622	−	0.00674960i	−0.0811989	−	0.000643549i
$111$	5.54137	+	4.02604i	0.525963	+	0.382135i
$112$	0.338266	+	1.02776i	0.0319632	+	0.0971139i
$113$	4.32577	−	3.14286i	0.406934	−	0.295655i	−0.365425	−	0.930841i	$-0.619076\pi$
$113$	4.32577	−	3.14286i	0.406934	−	0.295655i	0.772359	+	0.635186i	$0.219076\pi$
$114$	−3.83781	+	1.70870i	−0.359444	+	0.160035i
$115$	0.0390590	+	0.402265i	0.00364227	+	0.0375114i
$116$	−3.35690	−	1.49459i	−0.311680	−	0.138769i
$117$	−0.617459	−	0.685758i	−0.0570841	−	0.0633983i
$118$	8.11803			0.747325
$119$	15.2372	−	6.85359i	1.39679	−	0.628268i
$120$	6.37499	−	1.30233i	0.581954	−	0.118886i
$121$	10.5941	+	2.25185i	0.963102	+	0.204714i
$122$	−5.95988	+	6.61912i	−0.539582	+	0.599267i
$123$	0.0902043	−	0.858237i	0.00813345	−	0.0773846i
$124$	1.27980	−	2.21668i	0.114929	−	0.199063i
$125$	−9.19876	+	6.35474i	−0.822762	+	0.568386i
$126$	−1.64612	−	1.81427i	−0.146648	−	0.161628i
$127$	−14.4563	−	10.5031i	−1.28279	−	0.931999i	−0.283153	−	0.959075i	$-0.591380\pi$
$127$	−14.4563	−	10.5031i	−1.28279	−	0.931999i	−0.999633	+	0.0270759i	$0.991380\pi$
$128$	5.34072	+	1.13521i	0.472058	+	0.100339i
$129$	−3.41914	+	3.79734i	−0.301038	+	0.334337i
$130$	−1.26711	−	1.42989i	−0.111133	−	0.125410i
$131$	2.02692	+	2.25112i	0.177093	+	0.196682i	0.825156	−	0.564905i	$-0.191087\pi$
$131$	2.02692	+	2.25112i	0.177093	+	0.196682i	−0.648063	+	0.761587i	$0.724421\pi$
$132$	0.470028			0.0409107
$133$	−9.73827	−	7.01882i	−0.844415	−	0.608609i
$134$	−3.14309	+	2.28359i	−0.271522	+	0.197272i
$135$	−1.81938	+	1.29995i	−0.156587	+	0.111882i
$136$	−1.92075	+	18.2747i	−0.164703	+	1.56704i
$137$	11.8148	+	5.26031i	1.00941	+	0.449418i	0.843734	−	0.536762i	$-0.180353\pi$
$137$	11.8148	+	5.26031i	1.00941	+	0.449418i	0.165676	+	0.986180i	$0.447019\pi$
$138$	0.0174933	+	0.166438i	0.00148913	+	0.0141681i
$139$	1.19923	+	0.871289i	0.101717	+	0.0739018i	0.637481	−	0.770466i	$-0.279976\pi$
$139$	1.19923	+	0.871289i	0.101717	+	0.0739018i	−0.535764	+	0.844368i	$0.679976\pi$
$140$	4.50267	+	5.04236i	0.380545	+	0.426157i
$141$	6.81332	−	4.95017i	0.573785	−	0.416879i
$142$	1.10810	+	1.23067i	0.0929900	+	0.103276i
$143$	−0.189788	−	0.328723i	−0.0158709	−	0.0274892i
$144$	0.400018	−	0.0850265i	0.0333349	−	0.00708554i
$145$	7.19048	+	0.0569888i	0.597137	+	0.00473266i
$146$	1.99746	+	6.14754i	0.165311	+	0.508774i
$147$	2.11241	−	6.67366i	0.174228	−	0.550434i
$148$	−6.33197	−	4.60044i	−0.520485	−	0.378154i
$149$	2.94369	−	5.09862i	0.241156	−	0.417695i	−0.719888	−	0.694091i	$-0.755807\pi$
$149$	2.94369	−	5.09862i	0.241156	−	0.417695i	0.961044	+	0.276396i	$0.0891400\pi$
$150$	−3.78809	+	2.66150i	−0.309296	+	0.217311i
$151$	1.98412	+	3.43659i	0.161465	+	0.279666i	0.935394	−	0.353606i	$-0.115045\pi$
$151$	1.98412	+	3.43659i	0.161465	+	0.279666i	−0.773929	+	0.633272i	$0.781711\pi$
$152$	12.0610	−	5.36989i	0.978274	−	0.435556i
$153$	−1.95140	−	6.00579i	−0.157761	−	0.485540i
$154$	−0.507158	−	0.870757i	−0.0408680	−	0.0701676i
$155$	−0.563026	+	4.97707i	−0.0452234	+	0.399768i
$156$	0.705553	+	0.783596i	0.0564895	+	0.0627379i
$157$	10.5280	+	18.2350i	0.840226	+	1.45531i	0.889703	+	0.456540i	$0.150911\pi$
$157$	10.5280	+	18.2350i	0.840226	+	1.45531i	−0.0494767	+	0.998775i	$0.515755\pi$
$158$	2.04563	−	0.434811i	0.162741	−	0.0345917i
$159$	0.638358	+	6.07357i	0.0506251	+	0.481665i
$160$	−11.9204	+	2.43518i	−0.942390	+	0.192518i
$161$	−0.385803	+	0.282551i	−0.0304056	+	0.0222681i
$162$	−0.749085	+	0.544242i	−0.0588537	+	0.0427597i
$163$	−1.46363	−	13.9255i	−0.114640	−	1.09073i	−0.888975	−	0.457955i	$-0.848582\pi$
$163$	−1.46363	−	13.9255i	−0.114640	−	1.09073i	0.774335	−	0.632776i	$-0.218085\pi$
$164$	−0.103074	+	0.980683i	−0.00804872	+	0.0765785i
$165$	−0.843205	+	0.367440i	−0.0656434	+	0.0286051i
$166$	1.67477	+	15.9344i	0.129987	+	1.23675i
$167$	4.39441	−	13.5246i	0.340050	−	1.04657i	−0.624131	−	0.781320i	$-0.714547\pi$
$167$	4.39441	−	13.5246i	0.340050	−	1.04657i	0.964181	−	0.265246i	$-0.0854532\pi$
$168$	5.17321	+	5.70167i	0.399122	+	0.439893i
$169$	−3.75409	+	11.5539i	−0.288776	+	0.888761i
$170$	−3.94154	−	12.4661i	−0.302303	−	0.956109i
$171$	−3.03592	+	3.37173i	−0.232163	+	0.257843i
$172$	3.90695	−	4.33911i	0.297902	−	0.330854i
$173$	−6.33689	+	2.82136i	−0.481785	+	0.214504i	−0.633234	−	0.773961i	$-0.718273\pi$
$173$	−6.33689	+	2.82136i	−0.481785	+	0.214504i	0.151449	+	0.988465i	$0.451606\pi$
$174$	2.97756			0.225728
$175$	−12.0194	−	5.52581i	−0.908579	−	0.417712i
$176$	0.168220			0.0126801
$177$	8.00953	−	3.56607i	0.602033	−	0.268043i
$178$	−10.5104	+	11.6730i	−0.787787	+	0.874926i
$179$	−11.7197	+	13.0161i	−0.875972	+	0.972865i	−0.999811	−	0.0194369i	$-0.993813\pi$
$179$	−11.7197	+	13.0161i	−0.875972	+	0.972865i	0.123839	+	0.992302i	$0.460479\pi$
$180$	2.07895	−	1.48542i	0.154956	−	0.110716i
$181$	1.37311	−	4.22600i	0.102063	−	0.314116i	−0.886967	−	0.461832i	$-0.847192\pi$
$181$	1.37311	−	4.22600i	0.102063	−	0.314116i	0.989030	+	0.147716i	$0.0471922\pi$
$182$	0.690373	−	2.15258i	0.0511739	−	0.159560i
$183$	−2.97259	+	9.14870i	−0.219740	+	0.676291i
$184$	−0.0549758	−	0.523060i	−0.00405287	−	0.0385605i
$185$	14.9556	+	3.30300i	1.09956	+	0.242841i
$186$	−0.216799	+	2.06271i	−0.0158965	+	0.151245i
$187$	−0.271519	−	2.58333i	−0.0198554	−	0.188912i
$188$	−7.78539	+	5.65642i	−0.567808	+	0.412537i
$189$	−2.42109	−	1.06692i	−0.176108	−	0.0776071i
$190$	−6.34076	+	6.93087i	−0.460007	+	0.502818i
$191$	−1.88872	−	17.9700i	−0.136663	−	1.30026i	−0.820930	−	0.571029i	$-0.806544\pi$
$191$	−1.88872	−	17.9700i	−0.136663	−	1.30026i	0.684267	−	0.729232i	$-0.260122\pi$
$192$	−5.72794	+	1.21751i	−0.413378	+	0.0878662i
$193$	−10.6990	−	18.5312i	−0.770131	−	1.33391i	−0.937491	−	0.348010i	$-0.886857\pi$
$193$	−10.6990	−	18.5312i	−0.770131	−	1.33391i	0.167360	−	0.985896i	$-0.446476\pi$
$194$	−8.59706	−	9.54800i	−0.617233	−	0.685507i
$195$	−1.87829	−	0.854171i	−0.134507	−	0.0611684i
$196$	−2.41379	+	7.62581i	−0.172413	+	0.544701i
$197$	−6.83228	−	21.0276i	−0.486780	−	1.49816i	−0.829386	−	0.558676i	$-0.811310\pi$
$197$	−6.83228	−	21.0276i	−0.486780	−	1.49816i	0.342606	−	0.939479i	$-0.388690\pi$
$198$	−0.347941	+	0.154913i	−0.0247271	+	0.0110092i
$199$	−9.98568	−	17.2957i	−0.707866	−	1.22606i	−0.965647	−	0.259857i	$-0.916325\pi$
$199$	−9.98568	−	17.2957i	−0.707866	−	1.22606i	0.257781	−	0.966203i	$-0.417009\pi$
$200$	11.9047	−	8.36423i	0.841790	−	0.591440i
$201$	−2.09795	+	3.63376i	−0.147978	+	0.256306i
$202$	7.17681	+	5.21426i	0.504959	+	0.366874i
$203$	4.28208	+	7.35204i	0.300543	+	0.516012i
$204$	2.22981	+	6.86265i	0.156118	+	0.480482i
$205$	−0.581730	−	1.83987i	−0.0406298	−	0.128502i
$206$	−7.98973	+	1.69827i	−0.556671	+	0.118324i
$207$	0.0903721	+	0.156529i	0.00628130	+	0.0108795i
$208$	0.252513	+	0.280444i	0.0175086	+	0.0194453i
$209$	−1.50987	+	1.09698i	−0.104440	+	0.0758800i
$210$	−4.99501	−	2.24863i	−0.344688	−	0.155170i
$211$	0.143851	+	0.104514i	0.00990314	+	0.00719505i	0.592726	−	0.805404i	$-0.298052\pi$
$211$	0.143851	+	0.104514i	0.00990314	+	0.00719505i	−0.582823	+	0.812599i	$0.698052\pi$
$212$	−0.729434	−	6.94010i	−0.0500977	−	0.476648i
$213$	1.63390	+	0.727461i	0.111953	+	0.0498448i
$214$	0.00496873	−	0.0472743i	0.000339655	−	0.00323161i
$215$	−3.61681	+	10.8384i	−0.246664	+	0.739170i
$216$	2.35413	−	1.71037i	0.160178	−	0.116376i
$217$	−5.40493	+	2.43111i	−0.366910	+	0.165034i
$218$	4.28367			0.290127
$219$	4.67125	+	5.18795i	0.315654	+	0.350569i
$220$	0.963507	−	0.419863i	0.0649596	−	0.0283072i
$221$	3.89917	−	4.33047i	0.262286	−	0.291299i
$222$	6.20350	+	1.31860i	0.416352	+	0.0884983i
$223$	−9.22679	−	6.70365i	−0.617871	−	0.448910i	0.234306	−	0.972163i	$-0.424718\pi$
$223$	−9.22679	−	6.70365i	−0.617871	−	0.448910i	−0.852177	+	0.523253i	$0.824718\pi$
$224$	−9.67324	−	10.6614i	−0.646320	−	0.712343i
$225$	−2.56832	+	4.28996i	−0.171221	+	0.285997i
$226$	2.47542	−	4.28756i	0.164663	−	0.285204i
$227$	0.216730	−	2.06205i	0.0143849	−	0.136863i	−0.984972	−	0.172712i	$-0.944747\pi$
$227$	0.216730	−	2.06205i	0.0143849	−	0.136863i	0.999357	+	0.0358491i	$0.0114136\pi$
$228$	3.46906	−	3.85279i	0.229744	−	0.255157i
$229$	21.2577	+	4.51845i	1.40475	+	0.298588i	0.847074	−	0.531474i	$-0.178362\pi$
$229$	21.2577	+	4.51845i	1.40475	+	0.298588i	0.557671	+	0.830062i	$0.311695\pi$
$230$	0.184534	+	0.325554i	0.0121678	+	0.0214664i
$231$	−0.882885	−	0.636336i	−0.0580896	−	0.0418678i
$232$	−9.35748			−0.614349
$233$	9.63058	+	10.6958i	0.630920	+	0.700708i	0.970835	−	0.239748i	$-0.0770649\pi$
$233$	9.63058	+	10.6958i	0.630920	+	0.700708i	−0.339915	+	0.940456i	$0.610398\pi$
$234$	−0.780550	−	0.347523i	−0.0510261	−	0.0227183i
$235$	9.54473	−	16.2335i	0.622629	−	1.05895i
$236$	−9.15227	+	4.07485i	−0.595762	+	0.265250i
$237$	1.82728	−	1.32760i	0.118695	−	0.0862369i
$238$	10.3075	−	11.5356i	0.668139	−	0.747745i
$239$	−14.5953	−	10.6041i	−0.944089	−	0.685921i	0.00531234	−	0.999986i	$-0.498309\pi$
$239$	−14.5953	−	10.6041i	−0.944089	−	0.685921i	−0.949401	+	0.314065i	$0.898309\pi$
$240$	0.744043	−	0.531621i	0.0480278	−	0.0343160i
$241$	4.91989	+	2.19047i	0.316918	+	0.141101i	0.559030	−	0.829147i	$-0.311174\pi$
$241$	4.91989	+	2.19047i	0.316918	+	0.141101i	−0.242112	+	0.970248i	$0.577840\pi$
$242$	9.80931	−	2.08503i	0.630566	−	0.134031i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.39670	−	10.4540i	0.217451	−	0.669247i
$245$	−1.63119	−	15.5672i	−0.104213	−	0.994555i
$246$	−0.246916	−	0.759928i	−0.0157428	−	0.0484512i
$247$	−4.09526	−	0.870474i	−0.260575	−	0.0553869i
$248$	0.681329	−	6.48241i	0.0432644	−	0.411634i
$249$	8.65202	+	14.9857i	0.548299	+	0.949682i
$250$	−5.38772	+	8.83959i	−0.340750	+	0.559065i
$251$	3.73663			0.235854			0.117927	−	0.993022i	$-0.462375\pi$
$251$	3.73663			0.235854			0.117927	+	0.993022i	$0.462375\pi$
$252$	2.76651	+	1.21914i	0.174274	+	0.0767987i
$253$	0.0229746	+	0.0707087i	0.00144440	+	0.00444542i
$254$	−16.1836	−	3.43994i	−1.01545	−	0.215841i
$255$	−9.36497	−	10.5681i	−0.586457	−	0.661800i
$256$	16.4010	−	3.48613i	1.02506	−	0.217883i
$257$	8.69959	−	15.0681i	0.542666	−	0.939924i	−0.456084	−	0.889937i	$-0.650748\pi$
$257$	8.69959	−	15.0681i	0.542666	−	0.939924i	0.998750	−	0.0499878i	$-0.0159183\pi$
$258$	−1.46205	+	4.49972i	−0.0910231	+	0.280140i
$259$	5.66556	+	17.2137i	0.352041	+	1.06961i
$260$	2.14627	+	0.976038i	0.133106	+	0.0605313i
$261$	2.93776	−	1.30798i	0.181843	−	0.0809617i
$262$	2.56230	+	1.14081i	0.158299	+	0.0704794i
$263$	−10.2271	−	4.55340i	−0.630630	−	0.280775i	0.0664259	−	0.997791i	$-0.478840\pi$
$263$	−10.2271	−	4.55340i	−0.630630	−	0.280775i	−0.697056	+	0.717017i	$0.745507\pi$
$264$	1.09346	−	0.486842i	0.0672981	−	0.0299630i
$265$	6.73392	+	11.8799i	0.413661	+	0.729779i
$266$	−10.8806	−	2.26952i	−0.667135	−	0.139153i
$267$	−5.24224	+	16.1340i	−0.320820	+	0.987382i
$268$	2.39727	−	4.15220i	0.146437	−	0.253636i
$269$	25.5171	−	5.42383i	1.55581	−	0.330697i	0.651859	−	0.758340i	$-0.273989\pi$
$269$	25.5171	−	5.42383i	1.55581	−	0.330697i	0.903947	+	0.427644i	$0.140656\pi$
$270$	−1.04939	+	1.78478i	−0.0638637	+	0.108618i
$271$	28.4454	+	6.04625i	1.72793	+	0.367284i	0.961450	−	0.274980i	$-0.0886712\pi$
$271$	28.4454	+	6.04625i	1.72793	+	0.367284i	0.766484	+	0.642264i	$0.222005\pi$
$272$	0.798035	+	2.45610i	0.0483880	+	0.148923i
$273$	−0.264435	−	2.42708i	−0.0160043	−	0.146893i
$274$	11.9749			0.723429
$275$	−1.40026	+	1.50642i	−0.0844387	+	0.0908408i
$276$	−0.103266	−	0.178861i	−0.00621587	−	0.0107662i
$277$	−3.00604	+	28.6006i	−0.180616	+	1.71844i	0.410505	+	0.911858i	$0.365353\pi$
$277$	−3.00604	+	28.6006i	−0.180616	+	1.71844i	−0.591120	+	0.806583i	$0.701314\pi$
$278$	1.34252	+	0.285362i	0.0805191	+	0.0171149i
$279$	0.692201	+	2.13038i	0.0414410	+	0.127542i
$280$	15.6977	+	7.06672i	0.938116	+	0.422317i
$281$	0.802517	−	2.46989i	0.0478741	−	0.147341i	−0.924262	−	0.381759i	$-0.875318\pi$
$281$	0.802517	−	2.46989i	0.0478741	−	0.147341i	0.972136	+	0.234418i	$0.0753184\pi$
$282$	3.89892	−	6.75313i	0.232177	−	0.402143i
$283$	−6.04467	+	1.28483i	−0.359318	+	0.0763755i	−0.384034	−	0.923319i	$-0.625465\pi$
$283$	−6.04467	+	1.28483i	−0.359318	+	0.0763755i	0.0247154	+	0.999695i	$0.492132\pi$
$284$	−1.86702	−	0.831249i	−0.110787	−	0.0493256i
$285$	−3.21144	+	9.62360i	−0.190229	+	0.570053i
$286$	−0.284335	−	0.206581i	−0.0168131	−	0.0122154i
$287$	1.52129	−	1.70254i	0.0897986	−	0.100498i
$288$	−4.40191	+	3.19818i	−0.259385	+	0.188454i
$289$	20.8996	−	9.30512i	1.22939	−	0.547360i
$290$	6.10367	−	2.65977i	0.358420	−	0.156187i
$291$	−12.6764	−	5.64390i	−0.743104	−	0.330851i
$292$	−5.33771	−	5.92812i	−0.312366	−	0.346917i
$293$	27.4951			1.60628			0.803139	−	0.595791i	$-0.203161\pi$
$293$	27.4951			1.60628			0.803139	+	0.595791i	$0.203161\pi$
$294$	−0.726517	−	6.44059i	−0.0423714	−	0.375623i
$295$	13.2332	−	14.4648i	0.770468	−	0.842171i
$296$	−19.4956	−	4.14391i	−1.13316	−	0.240860i
$297$	−0.275241	+	0.305686i	−0.0159711	+	0.0177377i
$298$	0.569810	−	5.42138i	0.0330082	−	0.314052i
$299$	−0.0833934	+	0.144442i	−0.00482276	+	0.00835327i
$300$	2.93475	−	4.90202i	0.169438	−	0.283018i
$301$	−13.2131	+	2.86111i	−0.761590	+	0.164912i
$302$	2.97254	+	2.15968i	0.171051	+	0.124276i
$303$	9.37141	+	1.99195i	0.538373	+	0.114435i
$304$	1.24156	−	1.37889i	0.0712081	−	0.0790846i
$305$	2.07879	+	21.4092i	0.119031	+	1.22589i
$306$	−3.91245	−	4.34521i	−0.223660	−	0.248399i
$307$	−26.8626			−1.53313			−0.766564	−	0.642167i	$-0.778035\pi$
$307$	−26.8626			−1.53313			−0.766564	+	0.642167i	$0.778035\pi$
$308$	1.00885	+	0.727124i	0.0574845	+	0.0414317i
$309$	−7.13694	+	5.18529i	−0.406006	+	0.294981i
$310$	1.39815	+	4.42199i	0.0794093	+	0.251152i
$311$	1.26657	−	12.0506i	0.0718206	−	0.683328i	−0.898081	−	0.439830i	$-0.855039\pi$
$311$	1.26657	−	12.0506i	0.0718206	−	0.683328i	0.969902	−	0.243497i	$-0.0782947\pi$
$312$	2.45301	+	1.09215i	0.138875	+	0.0618309i
$313$	−3.30072	−	31.4042i	−0.186568	−	1.77507i	−0.542008	−	0.840373i	$-0.682336\pi$
$313$	−3.30072	−	31.4042i	−0.186568	−	1.77507i	0.355441	−	0.934699i	$-0.384331\pi$
$314$	15.7727	+	11.4596i	0.890107	+	0.646701i
$315$	−5.91603	−	0.0243817i	−0.333331	−	0.00137375i
$316$	−2.08799	+	1.51701i	−0.117459	+	0.0853386i
$317$	−8.00855	−	8.89439i	−0.449805	−	0.499559i	0.475008	−	0.879982i	$-0.342445\pi$
$317$	−8.00855	−	8.89439i	−0.449805	−	0.499559i	−0.924813	+	0.380423i	$0.875779\pi$
$318$	2.82731	+	4.89704i	0.158547	+	0.274612i
$319$	1.29388	−	0.275022i	0.0724432	−	0.0153983i
$320$	−10.6541	+	7.61238i	−0.595582	+	0.425545i
$321$	−0.0158643	−	0.0488252i	−0.000885457	−	0.00272516i
$322$	−0.219929	+	0.384297i	−0.0122562	+	0.0214160i
$323$	−23.1794	−	16.8408i	−1.28973	−	0.937046i
$324$	0.571336	−	0.989583i	0.0317409	−	0.0549769i
$325$	−4.61331	−	0.0731310i	−0.255900	−	0.00405658i
$326$	−6.48247	−	11.2280i	−0.359031	−	0.621860i
$327$	4.22643	−	1.88173i	0.233722	−	0.104060i
$328$	0.775975	+	2.38820i	0.0428460	+	0.131867i
$329$	22.2816	−	0.0847630i	1.22843	−	0.00467314i
$330$	−0.574862	+	0.628362i	−0.0316451	+	0.0345902i
$331$	−10.6360	−	11.8125i	−0.584608	−	0.649273i	0.376184	−	0.926545i	$-0.377236\pi$
$331$	−10.6360	−	11.8125i	−0.584608	−	0.649273i	−0.960791	+	0.277272i	$0.910570\pi$
$332$	−9.88642	−	17.1238i	−0.542588	−	0.939790i
$333$	6.69983	−	1.42409i	0.367148	−	0.0780398i
$334$	−1.37634	−	13.0950i	−0.0753101	−	0.716528i
$335$	−1.05464	+	9.32287i	−0.0576212	+	0.509363i
$336$	0.990117	+	0.436323i	0.0540153	+	0.0238034i
$337$	7.40918	−	5.38308i	0.403604	−	0.293235i	−0.367404	−	0.930062i	$-0.619753\pi$
$337$	7.40918	−	5.38308i	0.403604	−	0.293235i	0.771007	+	0.636826i	$0.219753\pi$
$338$	1.17579	+	11.1869i	0.0639546	+	0.608487i
$339$	0.558908	−	5.31765i	0.0303557	−	0.288815i
$340$	10.7011	+	12.0759i	0.580348	+	0.654907i
$341$	0.0963133	+	0.916360i	0.00521566	+	0.0496237i
$342$	−1.29818	+	3.99539i	−0.0701976	+	0.216046i
$343$	14.8580	−	11.0562i	0.802256	−	0.596980i
$344$	4.59473	−	14.1411i	0.247731	−	0.762439i
$345$	0.325076	+	0.240141i	0.0175015	+	0.0129288i
$346$	−4.29764	+	4.77301i	−0.231043	+	0.256599i
$347$	−19.3868	+	21.5312i	−1.04074	+	1.15585i	−0.0531797	+	0.998585i	$0.516936\pi$
$347$	−19.3868	+	21.5312i	−1.04074	+	1.15585i	−0.987556	+	0.157269i	$0.949731\pi$
$348$	−3.35690	+	1.49459i	−0.179949	+	0.0801183i
$349$	6.93715			0.371337			0.185669	−	0.982612i	$-0.440555\pi$
$349$	6.93715			0.371337			0.185669	+	0.982612i	$0.440555\pi$
$350$	−12.2479	−	0.147554i	−0.654677	−	0.00788707i
$351$	−0.922778			−0.0492542
$352$	−2.04464	+	0.910331i	−0.108979	+	0.0485208i
$353$	10.6223	−	11.7973i	0.565369	−	0.627905i	−0.390887	−	0.920439i	$-0.627832\pi$
$353$	10.6223	−	11.7973i	0.565369	−	0.627905i	0.956255	+	0.292533i	$0.0944983\pi$
$354$	5.43202	−	6.03287i	0.288709	−	0.320643i
$355$	3.99915	+	0.0316956i	0.212253	+	0.00168223i
$356$	5.99016	−	18.4358i	0.317478	−	0.977097i
$357$	5.10244	−	15.9094i	0.270050	−	0.842013i
$358$	−5.01143	+	15.4236i	−0.264862	+	0.815162i
$359$	0.787150	+	7.48923i	0.0415442	+	0.395267i	0.995459	+	0.0951895i	$0.0303457\pi$
$359$	0.787150	+	7.48923i	0.0415442	+	0.395267i	−0.953915	+	0.300077i	$0.902988\pi$
$360$	3.29788	−	5.60896i	0.173814	−	0.295618i
$361$	−0.165719	+	1.57671i	−0.00872207	+	0.0829850i
$362$	−0.430062	−	4.09177i	−0.0226036	−	0.215059i
$363$	8.76230	−	6.36618i	0.459901	−	0.334138i
$364$	0.302162	+	2.77335i	0.0158376	+	0.145363i
$365$	14.2098	+	6.46204i	0.743775	+	0.338239i
$366$	0.931024	+	8.85811i	0.0486654	+	0.463021i
$367$	−34.0995	+	7.24806i	−1.77998	+	0.378346i	−0.976249	−	0.216651i	$-0.930487\pi$
$367$	−34.0995	+	7.24806i	−1.77998	+	0.378346i	−0.803728	+	0.594997i	$0.797153\pi$
$368$	−0.0369581	−	0.0640134i	−0.00192658	−	0.00333693i
$369$	−0.577436	−	0.641307i	−0.0300601	−	0.0333851i
$370$	13.8944	−	2.83844i	0.722335	−	0.147564i
$371$	−8.02554	+	14.0236i	−0.416665	+	0.728068i
$372$	−0.790959	−	2.43432i	−0.0410093	−	0.126214i
$373$	−8.51283	+	3.79015i	−0.440777	+	0.196247i	−0.615112	−	0.788440i	$-0.710889\pi$
$373$	−8.51283	+	3.79015i	−0.440777	+	0.196247i	0.174335	+	0.984686i	$0.444223\pi$
$374$	−1.20257	−	2.08291i	−0.0621833	−	0.107705i
$375$	−1.43268	+	11.0882i	−0.0739832	+	0.572590i
$376$	−12.2530	+	21.2229i	−0.631902	+	1.09449i
$377$	2.40072	+	1.74422i	0.123643	+	0.0898321i
$378$	−2.44974	+	0.00931920i	−0.126001	+	0.000479328i
$379$	9.60479	+	29.5605i	0.493365	+	1.51842i	0.819490	+	0.573094i	$0.194257\pi$
$379$	9.60479	+	29.5605i	0.493365	+	1.51842i	−0.326125	+	0.945327i	$0.605743\pi$
$380$	3.66962	−	10.9966i	0.188248	−	0.564115i
$381$	−17.4785	+	3.71516i	−0.895448	+	0.190333i
$382$	−8.36520	−	14.4890i	−0.428001	−	0.741319i
$383$	−2.41625	−	2.68352i	−0.123465	−	0.137121i	0.678243	−	0.734838i	$-0.262742\pi$
$383$	−2.41625	−	2.68352i	−0.123465	−	0.137121i	−0.801708	+	0.597716i	$0.796075\pi$
$384$	4.41726	−	3.20933i	0.225417	−	0.163775i
$385$	−2.37824	−	0.515764i	−0.121206	−	0.0262858i
$386$	−16.0289	−	11.6457i	−0.815851	−	0.592750i
$387$	0.534122	+	5.08183i	0.0271509	+	0.258324i
$388$	14.4850	+	6.44912i	0.735363	+	0.327405i
$389$	−0.785622	+	7.47469i	−0.0398326	+	0.378982i	0.956386	+	0.292105i	$0.0943555\pi$
$389$	−0.785622	+	7.47469i	−0.0398326	+	0.378982i	−0.996219	+	0.0868775i	$0.972311\pi$
$390$	−1.91048	−	0.0151417i	−0.0967408	−	0.000766727i
$391$	−0.923392	+	0.670884i	−0.0466979	+	0.0339280i
$392$	2.28321	+	20.2407i	0.115319	+	1.02231i
$393$	3.02919			0.152802
$394$	−13.6983	−	15.2135i	−0.690112	−	0.766447i
$395$	2.55983	−	4.35370i	0.128799	−	0.219059i
$396$	0.314510	−	0.349299i	0.0158047	−	0.0175529i
$397$	33.0783	+	7.03100i	1.66015	+	0.352876i	0.940061	−	0.341005i	$-0.110767\pi$
$397$	33.0783	+	7.03100i	1.66015	+	0.352876i	0.720089	+	0.693881i	$0.244101\pi$
$398$	−14.9603	−	10.8693i	−0.749890	−	0.544827i
$399$	−11.7322	+	2.54044i	−0.587343	+	0.127181i
$400$	1.05033	−	1.75440i	0.0525163	−	0.0877200i
$401$	1.45488	−	2.51993i	0.0726533	−	0.125839i	−0.827410	−	0.561598i	$-0.810187\pi$
$401$	1.45488	−	2.51993i	0.0726533	−	0.125839i	0.900063	+	0.435759i	$0.143520\pi$
$402$	−0.406101	+	3.86379i	−0.0202545	+	0.192708i
$403$	−1.38311	+	1.53610i	−0.0688978	+	0.0765188i
$404$	−10.7084	−	2.27615i	−0.532765	−	0.113243i
$405$	−0.251350	+	2.22190i	−0.0124897	+	0.110407i
$406$	6.39090	+	4.60622i	0.317175	+	0.228603i
$407$	2.81748			0.139657
$408$	12.2955	+	13.6556i	0.608720	+	0.676052i
$409$	−24.4857	−	10.9017i	−1.21074	−	0.539056i	−0.300756	−	0.953701i	$-0.597239\pi$
$409$	−24.4857	−	10.9017i	−1.21074	−	0.539056i	−0.909983	+	0.414645i	$0.863906\pi$
$410$	−1.18497	−	1.33721i	−0.0585217	−	0.0660400i
$411$	11.8148	−	5.26031i	0.582783	−	0.259472i
$412$	8.15518	−	5.92509i	0.401777	−	0.291908i
$413$	22.7080	+	4.73651i	1.11739	+	0.233069i
$414$	0.135393	+	0.0983686i	0.00665419	+	0.00483455i
$415$	31.1221	+	22.9905i	1.52772	+	1.12856i
$416$	−4.58682	−	2.04218i	−0.224887	−	0.100126i
$417$	1.44993	−	0.308193i	0.0710035	−	0.0150923i
$418$	−0.864022	+	1.49653i	−0.0422607	+	0.0731977i
$419$	8.34565	−	25.6853i	0.407712	−	1.25481i	−0.510898	−	0.859641i	$-0.670687\pi$
$419$	8.34565	−	25.6853i	0.407712	−	1.25481i	0.918610	−	0.395166i	$-0.129313\pi$
$420$	6.76008	+	0.0278603i	0.329858	+	0.00135944i
$421$	−9.41734	−	28.9836i	−0.458973	−	1.41257i	−0.866407	−	0.499339i	$-0.833576\pi$
$421$	−9.41734	−	28.9836i	−0.458973	−	1.41257i	0.407433	−	0.913235i	$-0.366424\pi$
$422$	0.161040	+	0.0342302i	0.00783932	+	0.00166630i
$423$	0.880310	−	8.37559i	0.0428021	−	0.407235i
$424$	−8.88530	−	15.3898i	−0.431508	−	0.747394i
$425$	−28.6374	−	13.2980i	−1.38912	−	0.645048i
$426$	1.65604			0.0802352
$427$	−20.5331	+	15.0378i	−0.993667	+	0.727732i
$428$	0.0181277	+	0.0557912i	0.000876233	+	0.00269677i
$429$	−0.371282	−	0.0789183i	−0.0179256	−	0.00381021i
$430$	1.02243	+	10.5299i	0.0493062	+	0.507799i
$431$	27.2732	−	5.79709i	1.31370	−	0.279236i	0.502792	−	0.864407i	$-0.332306\pi$
$431$	27.2732	−	5.79709i	1.31370	−	0.279236i	0.810910	+	0.585171i	$0.198973\pi$
$432$	0.204477	−	0.354165i	0.00983793	−	0.0170398i
$433$	−10.0431	+	30.9093i	−0.482638	+	1.48541i	0.352734	+	0.935724i	$0.385252\pi$
$433$	−10.0431	+	30.9093i	−0.482638	+	1.48541i	−0.835372	+	0.549685i	$0.814748\pi$
$434$	−3.65630	+	4.09193i	−0.175508	+	0.196419i
$435$	4.85372	−	5.30543i	0.232718	−	0.254376i
$436$	−4.82942	+	2.15020i	−0.231287	+	0.102976i
$437$	0.749159	+	0.333547i	0.0358372	+	0.0159557i
$438$	5.90508	+	2.62911i	0.282155	+	0.125624i
$439$	−3.56292	+	1.58631i	−0.170049	+	0.0757106i	−0.489996	−	0.871725i	$-0.663002\pi$
$439$	−3.56292	+	1.58631i	−0.170049	+	0.0757106i	0.319947	+	0.947436i	$0.396335\pi$
$440$	1.80660	−	1.97474i	0.0861264	−	0.0941418i
$441$	−3.54602	−	6.03537i	−0.168858	−	0.287399i
$442$	1.66731	−	5.13146i	0.0793060	−	0.244079i
$443$	−2.50307	+	4.33545i	−0.118925	+	0.205983i	−0.919342	−	0.393460i	$-0.871278\pi$
$443$	−2.50307	+	4.33545i	−0.118925	+	0.205983i	0.800417	+	0.599443i	$0.204611\pi$
$444$	−7.65571	+	1.62727i	−0.363324	+	0.0772269i
$445$	3.66599	+	37.7556i	0.173785	+	1.78979i
$446$	−10.3293	−	2.19556i	−0.489106	−	0.103963i
$447$	−1.81930	−	5.59923i	−0.0860499	−	0.264834i
$448$	−14.1777	−	6.24779i	−0.669832	−	0.295180i
$449$	−20.6406			−0.974091			−0.487046	−	0.873377i	$-0.661925\pi$
$449$	−20.6406			−0.974091			−0.487046	+	0.873377i	$0.661925\pi$
$450$	−0.556842	+	4.59599i	−0.0262498	+	0.216657i
$451$	−0.177486	−	0.307415i	−0.00835750	−	0.0144756i
$452$	−0.638649	+	6.07634i	−0.0300395	+	0.285807i
$453$	3.88152	+	0.825042i	0.182370	+	0.0387639i
$454$	−0.593254	−	1.82585i	−0.0278428	−	0.0856913i
$455$	−2.71011	−	4.73904i	−0.127052	−	0.222170i
$456$	4.07976	−	12.5562i	0.191052	−	0.587998i
$457$	−20.0309	+	34.6946i	−0.937007	+	1.62294i	−0.165993	+	0.986127i	$0.553083\pi$
$457$	−20.0309	+	34.6946i	−0.937007	+	1.62294i	−0.771015	+	0.636817i	$0.780251\pi$
$458$	19.6829	−	4.18373i	0.919721	−	0.195493i
$459$	−5.76892	−	2.56849i	−0.269270	−	0.119887i
$460$	−0.371456	−	0.274403i	−0.0173192	−	0.0127941i
$461$	−2.18040	−	1.58415i	−0.101551	−	0.0737814i	0.535851	−	0.844313i	$-0.319991\pi$
$461$	−2.18040	−	1.58415i	−0.101551	−	0.0737814i	−0.637402	+	0.770531i	$0.719991\pi$
$462$	−0.986453	−	0.205758i	−0.0458940	−	0.00957274i
$463$	−19.9065	+	14.4629i	−0.925134	+	0.672149i	−0.944797	−	0.327657i	$-0.893741\pi$
$463$	−19.9065	+	14.4629i	−0.925134	+	0.672149i	0.0196625	+	0.999807i	$0.493741\pi$
$464$	−1.20141	+	0.534903i	−0.0557742	+	0.0248323i
$465$	3.32195	+	3.74872i	0.154052	+	0.173843i
$466$	12.1743	+	5.42036i	0.563965	+	0.251093i
$467$	2.85377	+	3.16944i	0.132057	+	0.146664i	0.805546	−	0.592533i	$-0.201872\pi$
$467$	2.85377	+	3.16944i	0.132057	+	0.146664i	−0.673489	+	0.739197i	$0.735205\pi$
$468$	1.05443			0.0487412
$469$	−10.1243	+	4.55386i	−0.467497	+	0.210278i
$470$	1.95999	−	17.3260i	0.0904075	−	0.799189i
$471$	20.5959	+	4.37779i	0.949008	+	0.201718i
$472$	−17.0711	+	18.9593i	−0.785759	+	0.872674i
$473$	−0.219706	+	2.09036i	−0.0101021	+	0.0961150i
$474$	1.04566	−	1.81114i	0.0480289	−	0.0831885i
$475$	2.01339	+	22.5960i	0.0923806	+	1.03678i
$476$	−5.83041	+	18.1792i	−0.267236	+	0.833242i
$477$	4.94068	+	3.58962i	0.226218	+	0.164357i
$478$	−16.3392	−	3.47301i	−0.747340	−	0.158852i
$479$	−9.04932	+	10.0503i	−0.413474	+	0.459209i	−0.913523	−	0.406788i	$-0.866649\pi$
$479$	−9.04932	+	10.0503i	−0.413474	+	0.459209i	0.500049	+	0.865997i	$0.333315\pi$
$480$	−6.16661	+	10.4880i	−0.281466	+	0.478711i
$481$	4.22929	+	4.69710i	0.192839	+	0.214169i
$482$	4.98653			0.227130
$483$	−0.0481764	+	0.475771i	−0.00219210	+	0.0216483i
$484$	−10.0124	+	7.27446i	−0.455111	+	0.330657i
$485$	−31.0268	−	0.245906i	−1.40885	−	0.0111660i
$486$	−0.0967850	+	0.920848i	−0.00439026	+	0.0417705i
$487$	1.05608	+	0.470195i	0.0478553	+	0.0213066i	0.430525	−	0.902579i	$-0.358329\pi$
$487$	1.05608	+	0.470195i	0.0478553	+	0.0213066i	−0.382669	+	0.923885i	$0.624995\pi$
$488$	−2.92590	−	27.8381i	−0.132449	−	1.26017i
$489$	−11.3280	−	8.23030i	−0.512272	−	0.372187i
$490$	−7.24249	−	12.5536i	−0.327182	−	0.567112i
$491$	14.1987	−	10.3160i	0.640778	−	0.465552i	−0.219339	−	0.975649i	$-0.570390\pi$
$491$	14.1987	−	10.3160i	0.640778	−	0.465552i	0.860117	+	0.510096i	$0.170390\pi$
$492$	0.659820	+	0.732804i	0.0297470	+	0.0330374i
$493$	10.1536	+	17.5866i	0.457296	+	0.792059i
$494$	−3.79188	+	0.805989i	−0.170605	+	0.0362632i
$495$	−0.291153	+	0.872489i	−0.0130864	+	0.0392154i
$496$	−0.283079	−	0.871228i	−0.0127106	−	0.0391193i
$497$	2.38158	+	4.08901i	0.106828	+	0.183417i
$498$	12.9622	+	9.41758i	0.580850	+	0.422012i
$499$	5.20698	−	9.01876i	0.233096	−	0.403735i	−0.725621	−	0.688094i	$-0.758448\pi$
$499$	5.20698	−	9.01876i	0.233096	−	0.403735i	0.958718	+	0.284359i	$0.0917809\pi$
$500$	1.63708	−	12.6701i	0.0732126	−	0.566626i
$501$	−7.11031	−	12.3154i	−0.317665	−	0.550212i
$502$	3.16070	−	1.40723i	0.141069	−	0.0628080i
$503$	1.34595	+	4.14240i	0.0600128	+	0.184700i	0.976569	−	0.215207i	$-0.0690425\pi$
$503$	1.34595	+	4.14240i	0.0600128	+	0.184700i	−0.916556	+	0.399907i	$0.869042\pi$
$504$	7.69872	−	0.0292872i	0.342928	−	0.00130456i
$505$	20.9897	−	4.28793i	0.934031	−	0.190810i
$506$	0.0460628	+	0.0511580i	0.00204774	+	0.00227425i
$507$	6.07424	+	10.5209i	0.269766	+	0.467249i
$508$	19.9721	−	4.24521i	0.886121	−	0.188351i
$509$	2.99071	+	28.4547i	0.132561	+	1.26123i	0.835304	+	0.549788i	$0.185292\pi$
$509$	2.99071	+	28.4547i	0.132561	+	1.26123i	−0.702743	+	0.711443i	$0.748042\pi$
$510$	−11.9016	−	5.41234i	−0.527010	−	0.239662i
$511$	2.00052	+	18.3615i	0.0884979	+	0.812266i
$512$	3.72565	−	2.70684i	0.164652	−	0.119627i
$513$	0.474258	+	4.51226i	0.0209390	+	0.199221i
$514$	1.68398	−	16.0220i	0.0742772	−	0.706700i
$515$	−9.99809	+	17.0045i	−0.440568	+	0.749309i
$516$	−0.610326	−	5.80686i	−0.0268681	−	0.255633i
$517$	1.07050	−	3.29465i	0.0470804	−	0.144899i
$518$	11.2751	+	12.4269i	0.495400	+	0.546006i
$519$	−2.14352	+	6.59709i	−0.0940902	+	0.289580i
$520$	6.00400	+	0.0475853i	0.263293	+	0.00208675i
$521$	15.5673	−	17.2893i	0.682017	−	0.757457i	−0.298389	−	0.954444i	$-0.596449\pi$
$521$	15.5673	−	17.2893i	0.682017	−	0.757457i	0.980406	+	0.196988i	$0.0631159\pi$
$522$	1.99237	−	2.21276i	0.0872038	−	0.0968497i
$523$	0.863081	−	0.384268i	0.0377399	−	0.0168029i	−0.387780	−	0.921752i	$-0.626758\pi$
$523$	0.863081	−	0.384268i	0.0377399	−	0.0168029i	0.425520	+	0.904949i	$0.360091\pi$
$524$	−3.46137			−0.151211
$525$	−12.1490	+	5.23465i	−0.530226	+	0.228459i
$526$	−10.3656			−0.451963
$527$	−12.9224	+	5.75344i	−0.562910	+	0.250624i
$528$	0.112561	−	0.125012i	0.00489859	−	0.00544044i
$529$	−15.3681	+	17.0681i	−0.668180	+	0.742089i
$530$	10.1701	+	7.51285i	0.441760	+	0.326337i
$531$	2.70931	−	8.33841i	0.117574	−	0.361856i
$532$	13.4060	−	2.90289i	0.581225	−	0.125856i
$533$	0.246078	−	0.757349i	0.0106588	−	0.0328044i
$534$	1.64188	+	15.6215i	0.0710513	+	0.676008i
$535$	−0.0761342	−	0.0859153i	−0.00329157	−	0.00371444i
$536$	1.27624	−	12.1426i	0.0551252	−	0.524482i
$537$	1.83080	+	17.4189i	0.0790048	+	0.751680i
$538$	19.5415	−	14.1977i	0.842495	−	0.612108i
$539$	−0.910588	−	2.73161i	−0.0392218	−	0.117659i
$540$	0.287211	−	2.53890i	0.0123596	−	0.109257i
$541$	1.93574	+	18.4173i	0.0832240	+	0.791823i	0.953932	+	0.300023i	$0.0969944\pi$
$541$	1.93574	+	18.4173i	0.0832240	+	0.791823i	−0.870708	+	0.491800i	$0.836339\pi$
$542$	26.3381	−	5.59835i	1.13132	−	0.240470i
$543$	−2.22174	−	3.84817i	−0.0953440	−	0.165141i
$544$	−22.9911	−	25.5342i	−0.985733	−	1.09477i
$545$	6.98283	−	7.63269i	0.299112	−	0.326948i
$546$	−1.13773	−	1.95340i	−0.0486903	−	0.0835980i
$547$	−1.73819	−	5.34959i	−0.0743195	−	0.228732i	0.906995	−	0.421141i	$-0.138370\pi$
$547$	−1.73819	−	5.34959i	−0.0743195	−	0.228732i	−0.981315	+	0.192409i	$0.938370\pi$
$548$	−13.5005	+	6.01081i	−0.576713	+	0.256769i
$549$	4.80976	+	8.33074i	0.205275	+	0.355547i
$550$	−0.617107	+	1.80158i	−0.0263136	+	0.0768198i
$551$	7.29518	−	12.6356i	0.310785	−	0.538296i
$552$	−0.425495	−	0.309140i	−0.0181103	−	0.0131579i
$553$	5.97578	−	0.0227329i	0.254116	−	0.000966699i
$554$	8.22841	+	25.3245i	0.349592	+	1.07593i
$555$	12.4618	−	8.90401i	0.528975	−	0.377954i
$556$	−1.65680	+	0.352163i	−0.0702639	+	0.0149351i
$557$	3.75111	+	6.49711i	0.158940	+	0.275291i	0.934487	−	0.355998i	$-0.115859\pi$
$557$	3.75111	+	6.49711i	0.158940	+	0.275291i	−0.775547	+	0.631290i	$0.782526\pi$
$558$	1.38782	+	1.54133i	0.0587513	+	0.0652499i
$559$	−3.81470	+	2.77154i	−0.161345	+	0.117224i
$560$	2.41939	+	0.00997102i	0.102238	+	0.000421353i
$561$	−2.10147	−	1.52681i	−0.0887242	−	0.0644619i
$562$	−0.251350	−	2.39144i	−0.0106026	−	0.100877i
$563$	37.4923	+	16.6927i	1.58011	+	0.703512i	0.994269	−	0.106912i	$-0.0340963\pi$
$563$	37.4923	+	16.6927i	1.58011	+	0.703512i	0.585845	+	0.810423i	$0.300763\pi$
$564$	−1.00591	+	9.57055i	−0.0423563	+	0.402993i
$565$	−3.60441	−	11.3999i	−0.151639	−	0.479597i
$566$	−4.62913	+	3.36326i	−0.194577	+	0.141368i
$567$	−2.41290	+	1.08531i	−0.101332	+	0.0455788i
$568$	−5.20438			−0.218371
$569$	6.25585	+	6.94783i	0.262259	+	0.291268i	0.859865	−	0.510522i	$-0.170548\pi$
$569$	6.25585	+	6.94783i	0.262259	+	0.291268i	−0.597606	+	0.801790i	$0.703881\pi$
$570$	0.907841	+	9.34976i	0.0380253	+	0.391618i
$571$	26.4396	−	29.3641i	1.10646	−	1.22885i	0.135206	−	0.990818i	$-0.456831\pi$
$571$	26.4396	−	29.3641i	1.10646	−	1.22885i	0.971257	−	0.238034i	$-0.0765028\pi$
$572$	0.424253	+	0.0901778i	0.0177389	+	0.00377052i
$573$	−14.6181	−	10.6207i	−0.610679	−	0.443685i
$574$	0.645624	−	2.01305i	0.0269478	−	0.0840231i
$575$	0.880883	+	0.201882i	0.0367354	+	0.00841905i
$576$	−2.92795	+	5.07136i	−0.121998	+	0.211307i
$577$	−1.15612	+	10.9997i	−0.0481299	+	0.457925i	0.943742	+	0.330683i	$0.107279\pi$
$577$	−1.15612	+	10.9997i	−0.0481299	+	0.457925i	−0.991872	+	0.127242i	$0.959388\pi$
$578$	14.1740	−	15.7418i	0.589561	−	0.654774i
$579$	−20.9304	−	4.44890i	−0.869838	−	0.184890i
$580$	−5.54621	+	6.06237i	−0.230294	+	0.251726i
$581$	−4.61230	+	45.5492i	−0.191350	+	1.88970i
$582$	−12.8481			−0.532571
$583$	1.68090	+	1.86683i	0.0696158	+	0.0773162i
$584$	−18.5577	−	8.26243i	−0.767924	−	0.341902i
$585$	−1.89160	+	0.824292i	−0.0782079	+	0.0340803i
$586$	23.2572	−	10.3548i	0.960748	−	0.427753i
$587$	−37.6375	+	27.3452i	−1.55346	+	1.12866i	−0.612342	+	0.790593i	$0.709773\pi$
$587$	−37.6375	+	27.3452i	−1.55346	+	1.12866i	−0.941123	+	0.338066i	$0.890227\pi$
$588$	4.05194	+	6.89645i	0.167099	+	0.284405i
$589$	8.22218	+	5.97377i	0.338789	+	0.246145i
$590$	5.74606	−	17.2190i	0.236562	−	0.708896i
$591$	−20.1982	−	8.99284i	−0.830845	−	0.369916i
$592$	−2.73993	+	0.582390i	−0.112610	+	0.0239361i
$593$	23.6577	−	40.9764i	0.971507	−	1.68270i	0.280495	−	0.959856i	$-0.409501\pi$
$593$	23.6577	−	40.9764i	0.971507	−	1.68270i	0.691012	−	0.722843i	$-0.257165\pi$
$594$	−0.117695	+	0.362228i	−0.00482908	+	0.0148624i
$595$	−3.75195	−	37.1704i	−0.153815	−	1.52384i
$596$	2.07886	+	6.39808i	0.0851536	+	0.262076i
$597$	−19.5349	−	4.15228i	−0.799512	−	0.169942i
$598$	−0.0161425	+	0.153585i	−0.000660114	+	0.00628057i
$599$	−18.6214	−	32.2531i	−0.760848	−	1.31783i	−0.942414	−	0.334449i	$-0.891450\pi$
$599$	−18.6214	−	32.2531i	−0.760848	−	1.31783i	0.181566	−	0.983379i	$-0.441883\pi$
$600$	1.74997	−	14.4437i	0.0714423	−	0.589661i
$601$	−19.8376			−0.809192			−0.404596	−	0.914495i	$-0.632588\pi$
$601$	−19.8376			−0.809192			−0.404596	+	0.914495i	$0.632588\pi$
$602$	−10.0990	+	7.39625i	−0.411606	+	0.301449i
$603$	1.29661	+	3.99054i	0.0528019	+	0.162508i
$604$	−4.43531	−	0.942753i	−0.180470	−	0.0383601i
$605$	12.2750	−	20.8771i	0.499052	−	0.848776i
$606$	8.67717	−	1.84439i	0.352486	−	0.0749232i
$607$	−8.85587	+	15.3388i	−0.359449	+	0.622584i	−0.987869	−	0.155291i	$-0.950369\pi$
$607$	−8.85587	+	15.3388i	−0.359449	+	0.622584i	0.628420	+	0.777874i	$0.283702\pi$
$608$	−7.62862	+	23.4785i	−0.309381	+	0.952178i
$609$	8.32890	+	1.73727i	0.337504	+	0.0703979i
$610$	9.82120	+	17.3265i	0.397649	+	0.701530i
$611$	7.09951	−	3.16091i	0.287215	−	0.127877i
$612$	6.59198	+	2.93494i	0.266465	+	0.118638i
$613$	5.09155	+	2.26691i	0.205646	+	0.0915594i	0.506975	−	0.861961i	$-0.330764\pi$
$613$	5.09155	+	2.26691i	0.205646	+	0.0915594i	−0.301329	+	0.953520i	$0.597430\pi$
$614$	−22.7223	+	10.1166i	−0.916995	+	0.408273i
$615$	−1.75654	−	0.798804i	−0.0708307	−	0.0322109i
$616$	3.10010	+	0.646630i	0.124907	+	0.0260535i
$617$	−13.4427	+	41.3723i	−0.541181	+	1.66558i	0.188719	+	0.982031i	$0.439566\pi$
$617$	−13.4427	+	41.3723i	−0.541181	+	1.66558i	−0.729900	+	0.683554i	$0.760434\pi$
$618$	−4.08411	+	7.07389i	−0.164287	+	0.284554i
$619$	−0.515770	+	0.109630i	−0.0207305	+	0.00440641i	−0.218265	−	0.975889i	$-0.570040\pi$
$619$	−0.515770	+	0.109630i	−0.0207305	+	0.00440641i	0.197535	+	0.980296i	$0.436706\pi$
$620$	−3.79590	−	4.28356i	−0.152447	−	0.172032i
$621$	0.176795	+	0.0375788i	0.00709452	+	0.00150799i
$622$	−3.46697	−	10.6703i	−0.139013	−	0.427838i
$623$	−36.2106	+	26.5196i	−1.45075	+	1.06249i
$624$	0.377375			0.0151071
$625$	6.96792	+	24.0093i	0.278717	+	0.960373i
$626$	−14.6190	−	25.3208i	−0.584292	−	1.01202i
$627$	−0.195082	+	1.85608i	−0.00779081	+	0.0741246i
$628$	−23.5344	−	5.00238i	−0.939123	−	0.199617i
$629$	13.3661	+	41.1367i	0.532943	+	1.64023i
$630$	−5.01337	+	2.20739i	−0.199738	+	0.0879444i
$631$	−5.87294	+	18.0751i	−0.233798	+	0.719557i	0.763480	+	0.645831i	$0.223489\pi$
$631$	−5.87294	+	18.0751i	−0.233798	+	0.719557i	−0.997279	+	0.0737257i	$0.976511\pi$
$632$	−3.28618	+	5.69183i	−0.130717	+	0.226409i
$633$	0.173925	−	0.0369688i	0.00691288	−	0.00146938i
$634$	−10.1239	−	4.50744i	−0.402070	−	0.179013i
$635$	−32.5103	+	23.2287i	−1.29013	+	0.921803i
$636$	−5.64558	−	4.10176i	−0.223862	−	0.162645i
$637$	3.18707	−	5.61845i	0.126276	−	0.222611i
$638$	0.990876	−	0.719914i	0.0392292	−	0.0285017i
$639$	1.63390	−	0.727461i	0.0646362	−	0.0287779i
$640$	6.18811	−	10.5246i	0.244607	−	0.416021i
$641$	−4.49713	−	2.00225i	−0.177626	−	0.0790842i	0.315997	−	0.948760i	$-0.397661\pi$
$641$	−4.49713	−	2.00225i	−0.177626	−	0.0790842i	−0.493623	+	0.869676i	$0.664328\pi$
$642$	−0.0318069	−	0.0353252i	−0.00125532	−	0.00139417i
$643$	15.1542			0.597625			0.298813	−	0.954312i	$-0.403409\pi$
$643$	15.1542			0.597625			0.298813	+	0.954312i	$0.403409\pi$
$644$	0.0550498	−	0.543651i	0.00216927	−	0.0214228i
$645$	5.63435	+	9.94009i	0.221852	+	0.391391i
$646$	−25.9490	−	5.51564i	−1.02095	−	0.217010i
$647$	4.51526	−	5.01470i	0.177513	−	0.197148i	−0.647822	−	0.761792i	$-0.724320\pi$
$647$	4.51526	−	5.01470i	0.177513	−	0.197148i	0.825335	+	0.564644i	$0.190986\pi$
$648$	0.304163	−	2.89392i	0.0119487	−	0.113684i
$649$	1.80322	−	3.12327i	0.0707826	−	0.122599i
$650$	−3.92980	+	1.67554i	−0.154139	+	0.0657200i
$651$	−1.80994	+	5.64337i	−0.0709370	+	0.221181i
$652$	12.9442	+	9.40454i	0.506935	+	0.368310i
$653$	−1.11837	−	0.237716i	−0.0437650	−	0.00930255i	0.185977	−	0.982554i	$-0.440455\pi$
$653$	−1.11837	−	0.237716i	−0.0437650	−	0.00930255i	−0.229742	+	0.973252i	$0.573788\pi$
$654$	2.86634	−	3.18339i	0.112083	−	0.124480i
$655$	6.20951	−	2.70589i	0.242626	−	0.105728i
$656$	0.236145	+	0.262266i	0.00921992	+	0.0102398i
$657$	6.98107			0.272357
$658$	18.8154	−	8.46308i	0.733502	−	0.329925i
$659$	10.4004	−	7.55635i	0.405143	−	0.294353i	−0.366490	−	0.930422i	$-0.619441\pi$
$659$	10.4004	−	7.55635i	0.405143	−	0.294353i	0.771632	+	0.636069i	$0.219441\pi$
$660$	0.332693	−	0.996969i	0.0129501	−	0.0388070i
$661$	3.53719	−	33.6541i	0.137581	−	1.30899i	−0.680013	−	0.733200i	$-0.738026\pi$
$661$	3.53719	−	33.6541i	0.137581	−	1.30899i	0.817594	−	0.575795i	$-0.195307\pi$
$662$	−13.4453	−	5.98624i	−0.522567	−	0.232662i
$663$	−0.609110	−	5.79529i	−0.0236559	−	0.225071i
$664$	−40.7359	−	29.5964i	−1.58086	−	1.14856i
$665$	−21.7804	+	15.6877i	−0.844608	+	0.608341i
$666$	5.13086	−	3.72779i	0.198817	−	0.144449i
$667$	−0.388921	−	0.431941i	−0.0150591	−	0.0167248i
$668$	8.12476	+	14.0725i	0.314356	+	0.544481i
$669$	−11.1557	+	2.37122i	−0.431305	+	0.0916766i
$670$	2.61896	+	8.28312i	0.101179	+	0.320005i
$671$	1.22275	+	3.76323i	0.0472037	+	0.145278i
$672$	−14.3956	+	0.0547633i	−0.555322	+	0.00211254i
$673$	−22.7629	−	16.5382i	−0.877444	−	0.637500i	0.0551301	−	0.998479i	$-0.482443\pi$
$673$	−22.7629	−	16.5382i	−0.877444	−	0.637500i	−0.932574	+	0.360979i	$0.882443\pi$
$674$	4.23990	−	7.34373i	0.163315	−	0.282870i
$675$	1.46952	+	4.77918i	0.0565618	+	0.183951i
$676$	−6.94087	−	12.0219i	−0.266956	−	0.462382i
$677$	42.1791	−	18.7793i	1.62107	−	0.721748i	0.622908	−	0.782295i	$-0.285951\pi$
$677$	42.1791	−	18.7793i	1.62107	−	0.721748i	0.998165	+	0.0605473i	$0.0192846\pi$
$678$	−1.52989	−	4.70853i	−0.0587553	−	0.180830i
$679$	−18.4771	−	31.7240i	−0.709086	−	1.21745i
$680$	37.4027	+	17.0092i	1.43433	+	0.652273i
$681$	−1.38738	−	1.54084i	−0.0531646	−	0.0590453i
$682$	0.426575	+	0.738849i	0.0163344	+	0.0282920i
$683$	−45.6420	+	9.70151i	−1.74644	+	0.371218i	−0.966905	−	0.255136i	$-0.917880\pi$
$683$	−45.6420	+	9.70151i	−1.74644	+	0.371218i	−0.779539	+	0.626354i	$0.784546\pi$
$684$	−0.541921	−	5.15603i	−0.0207209	−	0.197146i
$685$	19.5203	−	21.3369i	0.745832	−	0.815243i
$686$	8.40410	−	14.9477i	0.320870	−	0.570707i
$687$	17.5820	−	12.7741i	0.670796	−	0.487362i
$688$	−0.218432	−	2.07824i	−0.00832763	−	0.0792321i
$689$	−0.589062	+	5.60455i	−0.0224415	+	0.213516i
$690$	0.365411	+	0.0807025i	0.0139110	+	0.00307229i
$691$	3.25115	+	30.9326i	0.123679	+	1.17673i	0.863650	+	0.504092i	$0.168173\pi$
$691$	3.25115	+	30.9326i	0.123679	+	1.17673i	−0.739970	+	0.672640i	$0.765160\pi$
$692$	2.44935	−	7.53831i	0.0931101	−	0.286564i
$693$	−1.06366	+	0.230319i	−0.0404049	+	0.00874911i
$694$	−8.28991	+	25.5137i	−0.314681	+	0.968488i
$695$	2.69691	−	1.92695i	0.102300	−	0.0730933i
$696$	−6.26138	+	6.95396i	−0.237337	+	0.263589i
$697$	3.64643	−	4.04977i	0.138118	−	0.153396i
$698$	5.86793	−	2.61257i	0.222104	−	0.0988873i
$699$	14.3927			0.544381
$700$	13.8823	−	5.98149i	0.524703	−	0.226079i
$701$	19.6896			0.743665			0.371832	−	0.928300i	$-0.378730\pi$
$701$	19.6896			0.743665			0.371832	+	0.928300i	$0.378730\pi$
$702$	−0.780550	+	0.347523i	−0.0294600	+	0.0131164i
$703$	20.7946	−	23.0947i	0.784282	−	0.871033i
$704$	−1.61178	+	1.79007i	−0.0607464	+	0.0674657i
$705$	−5.67714	−	17.9554i	−0.213814	−	0.676240i
$706$	4.54218	−	13.9794i	0.170947	−	0.526121i
$707$	17.0329	+	18.7728i	0.640588	+	0.706025i
$708$	−3.09586	+	9.52807i	−0.116349	+	0.358087i
$709$	0.659732	+	6.27693i	0.0247767	+	0.235735i	0.999901	+	0.0140757i	$0.00448059\pi$
$709$	0.659732	+	6.27693i	0.0247767	+	0.235735i	−0.975124	+	0.221659i	$0.928853\pi$
$710$	3.39470	−	1.47929i	0.127401	−	0.0555168i
$711$	0.236093	−	2.24628i	0.00885418	−	0.0842419i
$712$	−5.15990	−	49.0932i	−0.193376	−	1.83985i
$713$	0.327546	−	0.237976i	0.0122667	−	0.00891227i
$714$	−1.67556	−	15.3789i	−0.0627061	−	0.575539i
$715$	−0.831583	+	0.169882i	−0.0310995	+	0.00635321i
$716$	−2.09200	−	19.9041i	−0.0781818	−	0.743850i
$717$	−17.6465	+	3.75088i	−0.659021	+	0.140079i
$718$	3.48631	+	6.03847i	0.130108	+	0.225354i
$719$	9.97153	+	11.0745i	0.371875	+	0.413009i	0.899814	−	0.436273i	$-0.143702\pi$
$719$	9.97153	+	11.0745i	0.371875	+	0.413009i	−0.527939	+	0.849282i	$0.677035\pi$
$720$	0.102791	−	0.908656i	0.00383079	−	0.0338636i
$721$	−23.3400	+	0.0887891i	−0.869226	+	0.00330668i
$722$	0.453622	+	1.39611i	0.0168821	+	0.0519577i
$723$	4.91989	−	2.19047i	0.182973	−	0.0814646i
$724$	2.53872	+	4.39720i	0.0943508	+	0.163420i
$725$	5.21041	−	15.2113i	0.193510	−	0.564932i
$726$	5.01423	−	8.68489i	0.186095	−	0.322327i
$727$	−14.5506	−	10.5717i	−0.539654	−	0.392081i	0.284303	−	0.958735i	$-0.408238\pi$
$727$	−14.5506	−	10.5717i	−0.539654	−	0.392081i	−0.823956	+	0.566653i	$0.808238\pi$
$728$	3.57551	+	6.13891i	0.132517	+	0.227523i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	14.4533	+	0.114551i	0.534940	+	0.00423972i
$731$	−31.5627	+	6.70886i	−1.16739	+	0.248136i
$732$	−5.49598	−	9.51931i	−0.203137	−	0.351844i
$733$	7.63257	+	8.47683i	0.281915	+	0.313099i	0.867426	−	0.497566i	$-0.165773\pi$
$733$	7.63257	+	8.47683i	0.281915	+	0.313099i	−0.585511	+	0.810665i	$0.699106\pi$
$734$	−26.1140	+	18.9730i	−0.963887	+	0.700305i
$735$	−12.6602	−	9.20431i	−0.466979	−	0.339506i
$736$	0.795621	+	0.578052i	0.0293270	+	0.0213073i
$737$	0.180411	+	1.71649i	0.00664551	+	0.0632278i
$738$	−0.729955	−	0.324997i	−0.0268700	−	0.0119633i
$739$	−0.322166	+	3.06520i	−0.0118511	+	0.112755i	−0.998848	−	0.0479827i	$-0.984721\pi$
$739$	−0.322166	+	3.06520i	−0.0118511	+	0.112755i	0.986997	+	0.160738i	$0.0513874\pi$
$740$	−14.2398	+	10.1744i	−0.523465	+	0.374017i
$741$	−3.38715	+	2.46091i	−0.124430	+	0.0904037i
$742$	−1.50721	+	14.8846i	−0.0553313	+	0.546430i
$743$	20.8162			0.763674			0.381837	−	0.924230i	$-0.375292\pi$
$743$	20.8162			0.763674			0.381837	+	0.924230i	$0.375292\pi$
$744$	−4.36147	−	4.84391i	−0.159899	−	0.177586i
$745$	−8.73101	−	9.85269i	−0.319879	−	0.360975i
$746$	−5.77335	+	6.41195i	−0.211377	+	0.234758i
$747$	16.9259	+	3.59771i	0.619286	+	0.131633i
$748$	2.40129	+	1.74464i	0.0878000	+	0.0637904i
$749$	0.0414812	−	0.129338i	0.00151569	−	0.00472591i
$750$	2.96400	+	9.91870i	0.108230	+	0.362180i
$751$	27.2369	−	47.1756i	0.993887	−	1.72146i	0.401336	−	0.915931i	$-0.368546\pi$
$751$	27.2369	−	47.1756i	0.993887	−	1.72146i	0.592551	−	0.805533i	$-0.298121\pi$
$752$	−0.360007	+	3.42524i	−0.0131281	+	0.124906i
$753$	2.50029	−	2.77686i	0.0911157	−	0.101194i
$754$	2.68758	+	0.571263i	0.0978759	+	0.0208042i
$755$	8.69369	−	1.77601i	0.316396	−	0.0646355i
$756$	2.75716	−	1.24015i	0.100277	−	0.0451040i
$757$	31.4296			1.14233			0.571163	−	0.820836i	$-0.306492\pi$
$757$	31.4296			1.14233			0.571163	+	0.820836i	$0.306492\pi$
$758$	19.2570	+	21.3871i	0.699447	+	0.776815i
$759$	0.0679198	+	0.0302399i	0.00246533	+	0.00109764i
$760$	−2.85305	−	29.3832i	−0.103491	−	1.06584i
$761$	29.1585	−	12.9822i	1.05700	−	0.470605i	0.196734	−	0.980457i	$-0.436967\pi$
$761$	29.1585	−	12.9822i	1.05700	−	0.470605i	0.860262	+	0.509852i	$0.170300\pi$
$762$	−13.3853	+	9.72502i	−0.484900	+	0.352300i
$763$	11.9824	+	2.49934i	0.433793	+	0.0904821i
$764$	16.7037	+	12.1359i	0.604318	+	0.439063i
$765$	−14.1200	−	0.111909i	−0.510510	−	0.00404609i
$766$	−3.05446	−	1.35993i	−0.110362	−	0.0491364i
$767$	7.91368	−	1.68211i	0.285746	−	0.0607373i
$768$	8.38368	−	14.5210i	0.302520	−	0.523980i
$769$	5.13289	−	15.7974i	0.185097	−	0.569670i	−0.814853	−	0.579667i	$-0.803182\pi$
$769$	5.13289	−	15.7974i	0.185097	−	0.569670i	0.999950	+	0.00999782i	$0.00318246\pi$
$770$	−2.20592	+	0.459390i	−0.0794959	+	0.0165553i
$771$	−5.37664	−	16.5476i	−0.193635	−	0.595948i
$772$	23.9166	+	5.08363i	0.860777	+	0.182964i
$773$	2.31042	−	21.9822i	0.0831000	−	0.790644i	−0.871026	−	0.491237i	$-0.836545\pi$
$773$	2.31042	−	21.9822i	0.0831000	−	0.790644i	0.954126	−	0.299406i	$-0.0967886\pi$
$774$	2.36564	+	4.09741i	0.0850312	+	0.147278i
$775$	10.1583	+	4.71707i	0.364896	+	0.169442i
$776$	40.3774			1.44946
$777$	16.5833	+	7.30789i	0.594922	+	0.262169i
$778$	2.15048	+	6.61849i	0.0770983	+	0.237284i
$779$	−3.82981	−	0.814050i	−0.137217	−	0.0291664i
$780$	2.16148	−	0.941896i	0.0773932	−	0.0337253i
$781$	0.719619	−	0.152960i	0.0257500	−	0.00547333i
$782$	−0.528411	+	0.915235i	−0.0188959	+	0.0327287i
$783$	0.993731	−	3.05839i	0.0355130	−	0.109298i
$784$	1.45016	+	2.46820i	0.0517915	+	0.0881499i
$785$	46.1299	−	9.42374i	1.64645	−	0.336348i
$786$	2.56230	−	1.14081i	0.0913941	−	0.0406913i
$787$	−32.7712	−	14.5907i	−1.16817	−	0.520102i	−0.271341	−	0.962483i	$-0.587467\pi$
$787$	−32.7712	−	14.5907i	−1.16817	−	0.520102i	−0.896827	+	0.442382i	$0.854134\pi$
$788$	23.0800	+	10.2759i	0.822190	+	0.366063i
$789$	−10.2271	+	4.55340i	−0.364094	+	0.162105i
$790$	0.525655	−	4.64671i	0.0187020	−	0.165323i
$791$	9.42592	−	10.5490i	0.335147	−	0.375078i
$792$	0.369877	−	1.13836i	0.0131430	−	0.0404500i
$793$	−4.43834	+	7.68742i	−0.157610	+	0.272988i
$794$	30.6278	−	6.51015i	1.08694	−	0.231036i
$795$	13.3344	+	2.94496i	0.472922	+	0.104447i
$796$	22.3220	+	4.74470i	0.791184	+	0.168171i
$797$	12.7375	+	39.2020i	0.451186	+	1.38861i	0.875555	+	0.483118i	$0.160496\pi$
$797$	12.7375	+	39.2020i	0.451186	+	1.38861i	−0.424369	+	0.905489i	$0.639504\pi$
$798$	−8.96715	+	6.56728i	−0.317434	+	0.232479i
$799$	53.1820			1.88145
$800$	−3.27222	+	27.0078i	−0.115690	+	0.954871i
$801$	8.48212	+	14.6915i	0.299701	+	0.519098i
$802$	0.281621	−	2.67945i	0.00994439	−	0.0946146i
$803$	2.80885	+	0.597039i	0.0991221	+	0.0210691i
$804$	−1.48160	−	4.55988i	−0.0522519	−	0.160815i
$805$	0.326237	+	1.01832i	0.0114983	+	0.0358909i
$806$	−0.591429	+	1.82023i	−0.0208322	+	0.0641150i
$807$	13.0436	−	22.5922i	0.459156	−	0.795282i
$808$	−27.2695	+	5.79631i	−0.959338	+	0.203914i
$809$	−40.6525	−	18.0997i	−1.42927	−	0.636350i	−0.461258	−	0.887266i	$-0.652602\pi$
$809$	−40.6525	−	18.0997i	−1.42927	−	0.636350i	−0.968009	+	0.250916i	$0.919268\pi$
$810$	0.624169	+	1.97409i	0.0219311	+	0.0693626i
$811$	−11.2285	−	8.15799i	−0.394286	−	0.286466i	0.372923	−	0.927862i	$-0.378355\pi$
$811$	−11.2285	−	8.15799i	−0.394286	−	0.286466i	−0.767210	+	0.641396i	$0.778355\pi$
$812$	−9.51721	−	1.98513i	−0.333988	−	0.0696646i
$813$	23.5269	−	17.0933i	0.825125	−	0.599488i
$814$	2.38322	−	1.06108i	0.0835319	−	0.0371908i
$815$	−30.5732	−	6.75221i	−1.07093	−	0.236520i
$816$	2.35923	+	1.05040i	0.0825895	+	0.0367712i
$817$	15.5130	+	17.2289i	0.542732	+	0.602764i
$818$	−24.8174			−0.867718
$819$	−1.98061	−	1.42752i	−0.0692082	−	0.0498815i
$820$	2.00715	+	0.912771i	0.0700929	+	0.0318754i
$821$	14.6132	+	3.10613i	0.510004	+	0.108405i	0.455724	−	0.890121i	$-0.349380\pi$
$821$	14.6132	+	3.10613i	0.510004	+	0.108405i	0.0542799	+	0.998526i	$0.482714\pi$
$822$	8.01276	−	8.89907i	0.279477	−	0.310391i
$823$	1.75456	−	16.6935i	0.0611600	−	0.581898i	−0.920431	−	0.390904i	$-0.872162\pi$
$823$	1.75456	−	16.6935i	0.0611600	−	0.581898i	0.981591	−	0.190994i	$-0.0611710\pi$
$824$	12.8350	−	22.2309i	0.447129	−	0.774451i
$825$	0.182537	+	2.04859i	0.00635511	+	0.0713227i
$826$	20.9918	−	4.54547i	0.730398	−	0.158157i
$827$	−37.6805	−	27.3765i	−1.31028	−	0.951973i	−0.999999	−	0.00132770i	$-0.999577\pi$
$827$	−37.6805	−	27.3765i	−1.31028	−	0.951973i	−0.310279	−	0.950645i	$-0.600423\pi$
$828$	−0.202018	−	0.0429403i	−0.00702062	−	0.00149228i
$829$	32.3264	−	35.9022i	1.12274	−	1.24693i	0.156954	−	0.987606i	$-0.449832\pi$
$829$	32.3264	−	35.9022i	1.12274	−	1.24693i	0.965789	−	0.259328i	$-0.0835009\pi$
$830$	34.9836	+	7.72627i	1.21430	+	0.268183i
$831$	19.2429	+	21.3714i	0.667530	+	0.741367i
$832$	−5.40370			−0.187339
$833$	35.5631	−	26.2538i	1.23219	−	0.909641i
$834$	1.11039	−	0.806744i	0.0384496	−	0.0279353i
$835$	−25.5764	−	18.8939i	−0.885108	−	0.653849i
$836$	0.222914	−	2.12089i	0.00770965	−	0.0733524i
$837$	2.04635	+	0.911094i	0.0707322	+	0.0314920i
$838$	−2.61388	−	24.8694i	−0.0902950	−	0.859099i
$839$	−18.5544	−	13.4805i	−0.640567	−	0.465400i	0.219478	−	0.975618i	$-0.429565\pi$
$839$	−18.5544	−	13.4805i	−0.640567	−	0.465400i	−0.860045	+	0.510218i	$0.829565\pi$
$840$	15.7554	−	6.93709i	0.543613	−	0.239352i
$841$	15.0952	−	10.9673i	0.520526	−	0.378184i
$842$	−18.8812	−	20.9697i	−0.650690	−	0.722665i
$843$	−1.29850	−	2.24907i	−0.0447227	−	0.0774620i
$844$	−0.198739	+	0.0422432i	−0.00684087	+	0.00145407i
$845$	21.8496	+	16.1408i	0.751648	+	0.555259i
$846$	−2.40967	−	7.41619i	−0.0828460	−	0.254974i
$847$	28.6554	−	0.109010i	0.984611	−	0.00374562i
$848$	−2.02052	−	1.46799i	−0.0693849	−	0.0504111i
$849$	−3.08986	+	5.35179i	−0.106044	+	0.183673i
$850$	−29.2316	−	0.463385i	−1.00264	−	0.0158940i
$851$	−0.619004	−	1.07215i	−0.0212192	−	0.0367527i
$852$	−1.86702	+	0.831249i	−0.0639629	+	0.0284781i
$853$	−5.30923	−	16.3401i	−0.181785	−	0.559475i	0.818094	−	0.575085i	$-0.195031\pi$
$853$	−5.30923	−	16.3401i	−0.181785	−	0.559475i	−0.999878	+	0.0156098i	$0.995031\pi$
$854$	−11.7050	+	20.4529i	−0.400537	+	0.699885i
$855$	5.00286	+	8.82601i	0.171094	+	0.301843i
$856$	0.0999588	+	0.111015i	0.00341652	+	0.00379443i
$857$	17.2205	+	29.8268i	0.588241	+	1.01886i	0.994463	+	0.105089i	$0.0335127\pi$
$857$	17.2205	+	29.8268i	0.588241	+	1.01886i	−0.406222	+	0.913775i	$0.633154\pi$
$858$	−0.343777	+	0.0730721i	−0.0117364	+	0.00249464i
$859$	−2.28243	−	21.7159i	−0.0778756	−	0.740937i	−0.961883	−	0.273463i	$-0.911831\pi$
$859$	−2.28243	−	21.7159i	−0.0778756	−	0.740937i	0.884007	−	0.467474i	$-0.154836\pi$
$860$	−6.43822	−	11.3583i	−0.219541	−	0.387314i
$861$	−0.247294	−	2.26976i	−0.00842777	−	0.0773531i
$862$	20.8863	−	15.1748i	0.711391	−	0.516856i
$863$	−3.52728	−	33.5598i	−0.120070	−	1.14239i	−0.874167	−	0.485626i	$-0.838592\pi$
$863$	−3.52728	−	33.5598i	−0.120070	−	1.14239i	0.754097	−	0.656763i	$-0.228075\pi$
$864$	−0.568746	+	5.41126i	−0.0193491	+	0.184095i
$865$	1.49900	+	15.4381i	0.0509676	+	0.524910i
$866$	3.14551	+	29.9276i	0.106889	+	1.01698i
$867$	7.06954	−	21.7578i	0.240094	−	0.738934i
$868$	2.06817	−	6.44852i	0.0701981	−	0.218877i
$869$	0.287100	−	0.883602i	0.00973919	−	0.0299742i
$870$	2.10756	−	6.31565i	0.0714530	−	0.214120i
$871$	−2.59080	+	2.87737i	−0.0877859	+	0.0974961i
$872$	−9.00796	+	10.0044i	−0.305048	+	0.338790i
$873$	−12.6764	+	5.64390i	−0.429031	+	0.191017i
$874$	0.759307			0.0256839
$875$	−20.2282	+	21.5829i	−0.683838	+	0.729634i
$876$	−7.97708			−0.269520
$877$	−39.8377	+	17.7369i	−1.34522	+	0.598932i	−0.947847	−	0.318725i	$-0.896745\pi$
$877$	−39.8377	+	17.7369i	−1.34522	+	0.598932i	−0.397375	+	0.917656i	$0.630079\pi$
$878$	−2.41635	+	2.68363i	−0.0815479	+	0.0905682i
$879$	18.3978	−	20.4328i	0.620542	−	0.689182i
$880$	0.119069	−	0.356809i	0.00401380	−	0.0120280i
$881$	0.776933	−	2.39115i	0.0261755	−	0.0805601i	−0.937115	−	0.349020i	$-0.886515\pi$
$881$	0.776933	−	2.39115i	0.0261755	−	0.0805601i	0.963291	+	0.268460i	$0.0865146\pi$
$882$	−5.27243	−	3.76969i	−0.177532	−	0.126932i
$883$	−5.24205	+	16.1334i	−0.176409	+	0.542931i	−0.999695	−	0.0246955i	$-0.992138\pi$
$883$	−5.24205	+	16.1334i	−0.176409	+	0.542931i	0.823286	+	0.567627i	$0.192138\pi$
$884$	0.696013	+	6.62212i	0.0234095	+	0.222726i
$885$	−1.89467	−	19.5130i	−0.0636886	−	0.655923i
$886$	−0.484520	+	4.60990i	−0.0162778	+	0.154872i
$887$	−1.50012	−	14.2727i	−0.0503693	−	0.479232i	−0.990409	−	0.138167i	$-0.955879\pi$
$887$	−1.50012	−	14.2727i	−0.0503693	−	0.479232i	0.940040	−	0.341065i	$-0.110788\pi$
$888$	−16.1246	+	11.7152i	−0.541107	+	0.393137i
$889$	−43.2623	−	19.0647i	−1.45097	−	0.639411i
$890$	17.3199	+	30.5557i	0.580566	+	1.02423i
$891$	0.0429968	+	0.409088i	0.00144045	+	0.0137049i
$892$	12.7473	−	2.70953i	0.426812	−	0.0907217i
$893$	−19.1052	−	33.0911i	−0.639330	−	1.10735i
$894$	−3.64759	−	4.05106i	−0.121994	−	0.135488i
$895$	19.3127	+	34.0714i	0.645554	+	1.13888i
$896$	14.4458	−	0.0549542i	0.482600	−	0.00183589i
$897$	0.0515399	+	0.158624i	0.00172087	+	0.00529629i
$898$	−17.4593	+	7.77337i	−0.582624	+	0.259401i
$899$	−3.60169	−	6.23831i	−0.120123	−	0.208059i
$900$	−1.67918	−	5.46103i	−0.0559726	−	0.182034i
$901$	−19.2825	+	33.3983i	−0.642393	+	1.11266i
$902$	−0.265904	−	0.193191i	−0.00885365	−	0.00643255i
$903$	−6.71507	+	11.7337i	−0.223463	+	0.390473i
$904$	4.80796	+	14.7974i	0.159910	+	0.492153i
$905$	−7.99180	−	5.90371i	−0.265656	−	0.196246i
$906$	3.59398	−	0.763923i	0.119402	−	0.0253796i
$907$	−8.53776	−	14.7878i	−0.283492	−	0.491022i	0.688751	−	0.724998i	$-0.258159\pi$
$907$	−8.53776	−	14.7878i	−0.283492	−	0.491022i	−0.972242	+	0.233976i	$0.924826\pi$
$908$	1.58532	+	1.76068i	0.0526108	+	0.0584302i
$909$	7.75101	−	5.63144i	0.257085	−	0.186783i
$910$	−4.07715	−	2.98797i	−0.135156	−	0.0990502i
$911$	3.29808	+	2.39620i	0.109270	+	0.0793896i	0.641079	−	0.767475i	$-0.278487\pi$
$911$	3.29808	+	2.39620i	0.109270	+	0.0793896i	−0.531808	+	0.846865i	$0.678487\pi$
$912$	−0.193950	−	1.84531i	−0.00642233	−	0.0611043i
$913$	6.50249	+	2.89509i	0.215201	+	0.0958136i
$914$	−3.87739	+	36.8909i	−0.128253	+	1.22024i
$915$	17.3011	+	12.7807i	0.571957	+	0.422517i
$916$	−20.0905	+	14.5966i	−0.663808	+	0.482285i
$917$	6.50172	+	4.68609i	0.214706	+	0.154748i
$918$	−5.84706			−0.192982
$919$	16.6982	+	18.5452i	0.550822	+	0.611750i	0.952689	−	0.303948i	$-0.0983050\pi$
$919$	16.6982	+	18.5452i	0.550822	+	0.611750i	−0.401866	+	0.915698i	$0.631638\pi$
$920$	−1.14837	−	0.253622i	−0.0378605	−	0.00836165i
$921$	−17.9746	+	19.9628i	−0.592282	+	0.657796i
$922$	−2.44094	−	0.518837i	−0.0803880	−	0.0170870i
$923$	1.33521	+	0.970090i	0.0439491	+	0.0319309i
$924$	1.21541	−	0.263180i	0.0399840	−	0.00865798i
$925$	17.5917	−	29.3841i	0.578412	−	0.966143i
$926$	−11.3915	+	19.7307i	−0.374348	+	0.648390i
$927$	−0.922123	+	8.77341i	−0.0302865	+	0.288157i
$928$	11.7080	−	13.0030i	0.384333	−	0.426845i
$929$	2.92340	+	0.621387i	0.0959135	+	0.0203870i	0.255618	−	0.966778i	$-0.417721\pi$
$929$	2.92340	+	0.621387i	0.0959135	+	0.0203870i	−0.159705	+	0.987165i	$0.551054\pi$
$930$	4.22172	+	1.91987i	0.138436	+	0.0629549i
$931$	−29.1115	−	12.6968i	−0.954090	−	0.416119i
$932$	−16.4461			−0.538711
$933$	−8.10785	−	9.00468i	−0.265439	−	0.294800i
$934$	3.60755	+	1.60618i	0.118043	+	0.0525560i
$935$	−5.67165	−	1.25261i	−0.185483	−	0.0409647i
$936$	2.45301	−	1.09215i	0.0801792	−	0.0356981i
$937$	−11.0351	+	8.01743i	−0.360499	+	0.261918i	−0.753260	−	0.657722i	$-0.771520\pi$
$937$	−11.0351	+	8.01743i	−0.360499	+	0.261918i	0.392761	+	0.919641i	$0.371520\pi$
$938$	−6.84884	+	7.66485i	−0.223623	+	0.250266i
$939$	−25.5465	−	18.5606i	−0.833679	−	0.605703i
$940$	6.48712	+	20.5172i	0.211586	+	0.669196i
$941$	−2.85023	−	1.26900i	−0.0929148	−	0.0413683i	0.359753	−	0.933048i	$-0.382861\pi$
$941$	−2.85023	−	1.26900i	−0.0929148	−	0.0413683i	−0.452668	+	0.891679i	$0.649528\pi$
$942$	19.0701	−	4.05348i	0.621339	−	0.132070i
$943$	−0.0779879	+	0.135079i	−0.00253963	+	0.00439878i
$944$	−1.10799	+	3.41004i	−0.0360619	+	0.110987i
$945$	−3.97672	+	4.38015i	−0.129363	+	0.142486i
$946$	0.601400	+	1.85092i	0.0195532	+	0.0601785i
$947$	−33.0844	−	7.03230i	−1.07510	−	0.228519i	−0.363848	−	0.931458i	$-0.618537\pi$
$947$	−33.0844	−	7.03230i	−1.07510	−	0.228519i	−0.711250	+	0.702939i	$0.751871\pi$
$948$	−0.269777	+	2.56676i	−0.00876195	+	0.0833644i
$949$	3.22099	+	5.57892i	0.104558	+	0.181099i
$950$	10.2129	+	18.3551i	0.331349	+	0.595517i
$951$	−11.9686			−0.388108
$952$	5.26572	+	48.3307i	0.170663	+	1.56641i
$953$	−9.33108	−	28.7181i	−0.302263	−	0.930271i	−0.980684	−	0.195597i	$-0.937335\pi$
$953$	−9.33108	−	28.7181i	−0.302263	−	0.930271i	0.678421	−	0.734673i	$-0.262665\pi$
$954$	5.53105	+	1.17566i	0.179074	+	0.0380634i
$955$	−39.4527	−	8.71329i	−1.27666	−	0.281955i
$956$	20.1642	−	4.28603i	0.652156	−	0.138620i
$957$	0.661391	−	1.14556i	0.0213797	−	0.0370308i
$958$	−3.86955	+	11.9093i	−0.125020	+	0.384771i
$959$	33.4965	+	6.98682i	1.08166	+	0.225616i
$960$	−1.47188	+	13.0112i	−0.0475047	+	0.419935i
$961$	−23.7361	+	10.5680i	−0.765679	+	0.340902i
$962$	5.34638	+	2.38036i	0.172374	+	0.0767460i
$963$	−0.0468994	−	0.0208810i	−0.00151131	−	0.000672880i
$964$	−5.62182	+	2.50299i	−0.181067	+	0.0806160i
$965$	−46.8792	+	9.57680i	−1.50909	+	0.308288i
$966$	0.138427	+	0.420584i	0.00445382	+	0.0135321i
$967$	8.21204	−	25.2741i	0.264081	−	0.812759i	−0.727822	−	0.685766i	$-0.759467\pi$
$967$	8.21204	−	25.2741i	0.264081	−	0.812759i	0.991904	−	0.126993i	$-0.0405327\pi$
$968$	−15.7581	+	27.2938i	−0.506484	+	0.877255i
$969$	−28.0252	+	5.95693i	−0.900298	+	0.191364i
$970$	−26.3372	+	11.4769i	−0.845638	+	0.368500i
$971$	−12.6943	−	2.69826i	−0.407380	−	0.0865913i	−0.000336161	−	1.00000i	$-0.500107\pi$
$971$	−12.6943	−	2.69826i	−0.407380	−	0.0865913i	−0.407044	+	0.913409i	$0.633440\pi$
$972$	−0.353105	−	1.08675i	−0.0113259	−	0.0348574i
$973$	3.58884	+	1.58153i	0.115053	+	0.0507014i
$974$	1.07038			0.0342972
$975$	−3.14125	+	3.37942i	−0.100601	+	0.108228i
$976$	−1.96697	−	3.40690i	−0.0629613	−	0.109052i
$977$	5.36663	−	51.0601i	0.171694	−	1.63356i	−0.481558	−	0.876414i	$-0.659929\pi$
$977$	5.36663	−	51.0601i	0.171694	−	1.63356i	0.653251	−	0.757141i	$-0.273405\pi$
$978$	−12.6816	−	2.69556i	−0.405514	−	0.0861946i
$979$	2.15635	+	6.63656i	0.0689172	+	0.212105i
$980$	14.4665	+	10.5175i	0.462114	+	0.335970i
$981$	1.42964	−	4.39997i	0.0456448	−	0.140480i
$982$	8.12520	−	14.0733i	0.259286	−	0.449096i
$983$	22.5606	−	4.79540i	0.719570	−	0.152949i	0.166449	−	0.986050i	$-0.446770\pi$
$983$	22.5606	−	4.79540i	0.719570	−	0.152949i	0.553121	+	0.833101i	$0.313437\pi$
$984$	2.29401	+	1.02136i	0.0731304	+	0.0325597i
$985$	−49.4373	−	0.391820i	−1.57520	−	0.0124844i
$986$	15.2118	+	11.0520i	0.484443	+	0.351969i
$987$	14.8463	−	16.6152i	0.472564	−	0.528867i
$988$	3.87040	−	2.81201i	0.123134	−	0.0894620i
$989$	0.843723	−	0.375650i	0.0268288	−	0.0119450i
$990$	0.0823061	+	0.847662i	0.00261586	+	0.0269405i
$991$	−19.3680	−	8.62318i	−0.615244	−	0.273924i	0.0753609	−	0.997156i	$-0.475989\pi$
$991$	−19.3680	−	8.62318i	−0.615244	−	0.273924i	−0.690605	+	0.723232i	$0.742656\pi$
$992$	8.15539	+	9.05748i	0.258934	+	0.287575i
$993$	−15.8953			−0.504421
$994$	3.55445	+	2.56185i	0.112740	+	0.0812571i
$995$	−43.7537	+	8.93830i	−1.38708	+	0.283363i
$996$	−19.3408	−	4.11101i	−0.612835	−	0.130262i
$997$	11.9227	−	13.2415i	0.377596	−	0.419362i	−0.524152	−	0.851624i	$-0.675618\pi$
$997$	11.9227	−	13.2415i	0.377596	−	0.419362i	0.901748	+	0.432262i	$0.142284\pi$
$998$	1.00792	−	9.58967i	0.0319050	−	0.303556i
$999$	3.42475	−	5.93185i	0.108354	−	0.187675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.b.16.13	✓	160
7.4	even	3	inner	525.2.bg.b.466.8	yes	160
25.11	even	5	inner	525.2.bg.b.436.8	yes	160
175.11	even	15	inner	525.2.bg.b.361.13	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.b.16.13	✓	160	1.1	even	1	trivial
525.2.bg.b.361.13	yes	160	175.11	even	15	inner
525.2.bg.b.436.8	yes	160	25.11	even	5	inner
525.2.bg.b.466.8	yes	160	7.4	even	3	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.845870 - 0.376606i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.764597 + 0.849171i) q^{4} +(0.707816 - 2.12108i) q^{5} +(0.286125 - 0.880602i) q^{6} +(2.58582 - 0.559924i) q^{7} +(-0.899197 + 2.76744i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.845870 - 0.376606i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.764597 + 0.849171i) q^{4} +(0.707816 - 2.12108i) q^{5} +(0.286125 - 0.880602i) q^{6} +(2.58582 - 0.559924i) q^{7} +(-0.899197 + 2.76744i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.200092 - 2.06073i) q^{10} +(0.0429968 - 0.409088i) q^{11} +(0.119442 + 1.13641i) q^{12} +(0.746543 - 0.542395i) q^{13} +(1.97640 - 1.44746i) q^{14} +(-1.10265 - 1.94529i) q^{15} +(0.0427474 + 0.406715i) q^{16} +(6.17687 - 1.31293i) q^{17} +(-0.462960 - 0.801870i) q^{18} +(-3.03592 - 3.37173i) q^{19} +(1.25997 + 2.22283i) q^{20} +(1.31415 - 2.29630i) q^{21} +(-0.117695 - 0.362228i) q^{22} +(-0.165118 + 0.0735153i) q^{23} +(1.45493 + 2.52002i) q^{24} +(-3.99799 - 3.00267i) q^{25} +(0.427209 - 0.739948i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.50164 + 2.62392i) q^{28} +(0.993731 + 3.05839i) q^{29} +(-1.66531 - 1.23020i) q^{30} +(-2.19106 + 0.465724i) q^{31} +(-2.72053 - 4.71210i) q^{32} +(-0.275241 - 0.305686i) q^{33} +(4.73037 - 3.43681i) q^{34} +(0.642642 - 5.88107i) q^{35} +(0.924441 + 0.671646i) q^{36} +(0.715968 + 6.81198i) q^{37} +(-3.83781 - 1.70870i) q^{38} +(0.0964566 - 0.917723i) q^{39} +(5.23352 + 3.86611i) q^{40} +(0.698153 - 0.507238i) q^{41} +(0.246799 - 2.43729i) q^{42} -5.10982 q^{43} +(0.314510 + 0.349299i) q^{44} +(-2.18345 - 0.482224i) q^{45} +(-0.111982 + 0.124369i) q^{46} +(8.23769 + 1.75097i) q^{47} +(0.330852 + 0.240378i) q^{48} +(6.37297 - 2.89573i) q^{49} +(-4.51261 - 1.03420i) q^{50} +(3.15743 - 5.46883i) q^{51} +(-0.110218 + 1.04866i) q^{52} +(-4.08640 + 4.53840i) q^{53} +(-0.905686 - 0.192510i) q^{54} +(-0.837275 - 0.380758i) q^{55} +(-0.775608 + 7.65960i) q^{56} -4.53711 q^{57} +(1.99237 + 2.21276i) q^{58} +(8.00953 + 3.56607i) q^{59} +(2.49497 + 0.551025i) q^{60} +(-8.78786 + 3.91261i) q^{61} +(-1.67796 + 1.21911i) q^{62} +(-0.827148 - 2.51313i) q^{63} +(-4.73752 - 3.44201i) q^{64} +(-0.622051 - 1.96740i) q^{65} +(-0.347941 - 0.154913i) q^{66} +(-4.10422 + 0.872378i) q^{67} +(-3.60791 + 6.24908i) q^{68} +(-0.0558530 + 0.171898i) q^{69} +(-1.67125 - 5.21664i) q^{70} +(0.552686 + 1.70099i) q^{71} +(2.84628 + 0.604994i) q^{72} +(-0.729720 + 6.94283i) q^{73} +(3.17105 + 5.49242i) q^{74} +(-4.90660 + 0.961909i) q^{75} +5.18443 q^{76} +(-0.117875 - 1.08190i) q^{77} +(-0.264030 - 0.812600i) q^{78} +(2.20929 + 0.469599i) q^{79} +(0.892933 + 0.197208i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.399518 - 0.691985i) q^{82} +(-5.34724 + 16.4571i) q^{83} +(0.945160 + 2.87168i) q^{84} +(1.58724 - 14.0310i) q^{85} +(-4.32224 + 1.92439i) q^{86} +(2.93776 + 1.30798i) q^{87} +(1.09346 + 0.486842i) q^{88} +(-15.4976 + 6.89998i) q^{89} +(-2.02852 + 0.414401i) q^{90} +(1.62673 - 1.82055i) q^{91} +(0.0638217 - 0.196423i) q^{92} +(-1.12000 + 1.93991i) q^{93} +(7.62744 - 1.62126i) q^{94} +(-9.30060 + 4.05288i) q^{95} +(-5.32217 - 1.13126i) q^{96} +(-4.28793 - 13.1969i) q^{97} +(4.30016 - 4.84950i) q^{98} -0.411341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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