LMFDB - Embedded newform 525.2.bg.a.16.7

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			16.7
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.a.361.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30094 + 0.579215i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(0.0186901 - 0.0207574i) q^{4} +(-2.15784 + 0.586291i) q^{5} +(0.440057 - 1.35436i) q^{6} +(0.667942 + 2.56005i) q^{7} +(0.867823 - 2.67088i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-1.30094 + 0.579215i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(0.0186901 - 0.0207574i) q^{4} +(-2.15784 + 0.586291i) q^{5} +(0.440057 - 1.35436i) q^{6} +(0.667942 + 2.56005i) q^{7} +(0.867823 - 2.67088i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(2.46763 - 2.01258i) q^{10} +(-0.0705641 + 0.671372i) q^{11} +(0.00291968 + 0.0277789i) q^{12} +(-5.17588 + 3.76050i) q^{13} +(-2.35177 - 2.94358i) q^{14} +(1.00818 - 1.99589i) q^{15} +(0.423872 + 4.03287i) q^{16} +(-6.33150 + 1.34580i) q^{17} +(0.712027 + 1.23327i) q^{18} +(0.112850 + 0.125332i) q^{19} +(-0.0281602 + 0.0557490i) q^{20} +(-2.34943 - 1.21663i) q^{21} +(-0.297070 - 0.914286i) q^{22} +(7.36994 - 3.28131i) q^{23} +(1.40417 + 2.43209i) q^{24} +(4.31252 - 2.53024i) q^{25} +(4.55536 - 7.89012i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.0656239 + 0.0339827i) q^{28} +(-2.43938 - 7.50762i) q^{29} +(-0.155524 + 3.18048i) q^{30} +(1.83241 - 0.389492i) q^{31} +(-0.0789975 - 0.136828i) q^{32} +(-0.451710 - 0.501675i) q^{33} +(7.45738 - 5.41810i) q^{34} +(-2.94225 - 5.13256i) q^{35} +(-0.0225974 - 0.0164179i) q^{36} +(-0.373785 - 3.55633i) q^{37} +(-0.219405 - 0.0976854i) q^{38} +(0.668746 - 6.36269i) q^{39} +(-0.306704 + 6.27213i) q^{40} +(7.69438 - 5.59030i) q^{41} +(3.76115 + 0.221936i) q^{42} +1.20903 q^{43} +(0.0126171 + 0.0140127i) q^{44} +(0.808635 + 2.08473i) q^{45} +(-7.68725 + 8.53756i) q^{46} +(-0.403207 - 0.0857042i) q^{47} +(-3.28063 - 2.38352i) q^{48} +(-6.10771 + 3.41993i) q^{49} +(-4.14477 + 5.78957i) q^{50} +(3.23647 - 5.60574i) q^{51} +(-0.0186793 + 0.177722i) q^{52} +(-7.62713 + 8.47079i) q^{53} +(-1.39294 - 0.296078i) q^{54} +(-0.241354 - 1.49008i) q^{55} +(7.41725 + 0.437672i) q^{56} -0.168651 q^{57} +(7.52201 + 8.35404i) q^{58} +(-8.79719 - 3.91676i) q^{59} +(-0.0225867 - 0.0582305i) q^{60} +(10.0173 - 4.45998i) q^{61} +(-2.15826 + 1.56807i) q^{62} +(2.47621 - 0.931881i) q^{63} +(-6.37924 - 4.63479i) q^{64} +(8.96396 - 11.1491i) q^{65} +(0.878225 + 0.391011i) q^{66} +(-0.851965 + 0.181091i) q^{67} +(-0.0904008 + 0.156579i) q^{68} +(-2.49296 + 7.67256i) q^{69} +(6.80054 + 4.97295i) q^{70} +(-2.20737 - 6.79358i) q^{71} +(-2.74696 - 0.583885i) q^{72} +(0.399726 - 3.80314i) q^{73} +(2.54615 + 4.41006i) q^{74} +(-1.00531 + 4.89789i) q^{75} +0.00471075 q^{76} +(-1.76588 + 0.267791i) q^{77} +(2.81537 + 8.66482i) q^{78} +(-3.85969 - 0.820403i) q^{79} +(-3.27908 - 8.45376i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-6.77194 + 11.7293i) q^{82} +(-2.60203 + 8.00823i) q^{83} +(-0.0691651 + 0.0260292i) q^{84} +(12.8733 - 6.61612i) q^{85} +(-1.57287 + 0.700288i) q^{86} +(7.21151 + 3.21077i) q^{87} +(1.73192 + 0.771101i) q^{88} +(-4.60805 + 2.05163i) q^{89} +(-2.25949 - 2.24374i) q^{90} +(-13.0842 - 10.7387i) q^{91} +(0.0696332 - 0.214309i) q^{92} +(-0.936676 + 1.62237i) q^{93} +(0.574188 - 0.122048i) q^{94} +(-0.316993 - 0.204284i) q^{95} +(0.154542 + 0.0328490i) q^{96} +(1.72420 + 5.30655i) q^{97} +(5.96487 - 7.98680i) q^{98} +0.675071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * 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 $

$2$	−1.30094	+	0.579215i	−0.919903	+	0.409567i	−0.811375	−	0.584526i	$-0.801280\pi$
$2$	−1.30094	+	0.579215i	−0.919903	+	0.409567i	−0.108528	+	0.994093i	$0.534614\pi$
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$4$	0.0186901	−	0.0207574i	0.00934504	−	0.0103787i
$5$	−2.15784	+	0.586291i	−0.965014	+	0.262198i
$5$	−2.15784	+	0.586291i	−0.965014	+	0.262198i
$6$	0.440057	−	1.35436i	0.179653	−	0.552914i
$7$	0.667942	+	2.56005i	0.252458	+	0.967608i
$7$	0.667942	+	2.56005i	0.252458	+	0.967608i
$8$	0.867823	−	2.67088i	0.306822	−	0.944300i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	2.46763	−	2.01258i	0.780332	−	0.636434i
$11$	−0.0705641	+	0.671372i	−0.0212759	+	0.202426i	−0.999996	−	0.00277253i	$-0.999117\pi$
$11$	−0.0705641	+	0.671372i	−0.0212759	+	0.202426i	0.978720	+	0.205199i	$0.0657841\pi$
$12$	0.00291968	+	0.0277789i	0.000842838	+	0.00801907i
$13$	−5.17588	+	3.76050i	−1.43553	+	1.04297i	−0.446577	+	0.894745i	$0.647357\pi$
$13$	−5.17588	+	3.76050i	−1.43553	+	1.04297i	−0.988953	+	0.148229i	$0.952643\pi$
$14$	−2.35177	−	2.94358i	−0.628537	−	0.786706i
$15$	1.00818	−	1.99589i	0.260310	−	0.515337i
$16$	0.423872	+	4.03287i	0.105968	+	1.00822i
$17$	−6.33150	+	1.34580i	−1.53561	+	0.326405i	−0.896618	−	0.442806i	$-0.853983\pi$
$17$	−6.33150	+	1.34580i	−1.53561	+	0.326405i	−0.638996	+	0.769210i	$0.720650\pi$
$18$	0.712027	+	1.23327i	0.167826	+	0.290684i
$19$	0.112850	+	0.125332i	0.0258895	+	0.0287532i	0.755951	−	0.654629i	$-0.227175\pi$
$19$	0.112850	+	0.125332i	0.0258895	+	0.0287532i	−0.730061	+	0.683382i	$0.760508\pi$
$20$	−0.0281602	+	0.0557490i	−0.00629682	+	0.0124659i
$21$	−2.34943	−	1.21663i	−0.512687	−	0.265490i
$22$	−0.297070	−	0.914286i	−0.0633355	−	0.194926i
$23$	7.36994	−	3.28131i	1.53674	−	0.684200i	0.548364	−	0.836240i	$-0.315251\pi$
$23$	7.36994	−	3.28131i	1.53674	−	0.684200i	0.988374	+	0.152040i	$0.0485842\pi$
$24$	1.40417	+	2.43209i	0.286624	+	0.496448i
$25$	4.31252	−	2.53024i	0.862505	−	0.506049i
$26$	4.55536	−	7.89012i	0.893380	−	1.54738i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.0656239	+	0.0339827i	0.0124018	+	0.00642214i
$29$	−2.43938	−	7.50762i	−0.452981	−	1.39413i	−0.873490	−	0.486843i	$-0.838149\pi$
$29$	−2.43938	−	7.50762i	−0.452981	−	1.39413i	0.420509	−	0.907288i	$-0.361851\pi$
$30$	−0.155524	+	3.18048i	−0.0283947	+	0.580674i
$31$	1.83241	−	0.389492i	0.329111	−	0.0699548i	−0.0403927	−	0.999184i	$-0.512861\pi$
$31$	1.83241	−	0.389492i	0.329111	−	0.0699548i	0.369504	+	0.929229i	$0.379528\pi$
$32$	−0.0789975	−	0.136828i	−0.0139649	−	0.0241880i
$33$	−0.451710	−	0.501675i	−0.0786327	−	0.0873304i
$34$	7.45738	−	5.41810i	1.27893	−	0.929197i
$35$	−2.94225	−	5.13256i	−0.497330	−	0.867561i
$36$	−0.0225974	−	0.0164179i	−0.00376623	−	0.00273632i
$37$	−0.373785	−	3.55633i	−0.0614499	−	0.584657i	−0.981313	−	0.192418i	$-0.938367\pi$
$37$	−0.373785	−	3.55633i	−0.0614499	−	0.584657i	0.919863	−	0.392239i	$-0.128299\pi$
$38$	−0.219405	−	0.0976854i	−0.0355922	−	0.0158467i
$39$	0.668746	−	6.36269i	0.107085	−	1.01885i
$40$	−0.306704	+	6.27213i	−0.0484942	+	0.991711i
$41$	7.69438	−	5.59030i	1.20166	−	0.873058i	0.207214	−	0.978296i	$-0.433560\pi$
$41$	7.69438	−	5.59030i	1.20166	−	0.873058i	0.994447	+	0.105238i	$0.0335605\pi$
$42$	3.76115	+	0.221936i	0.580358	+	0.0342454i
$43$	1.20903			0.184375			0.0921876	−	0.995742i	$-0.470614\pi$
$43$	1.20903			0.184375			0.0921876	+	0.995742i	$0.470614\pi$
$44$	0.0126171	+	0.0140127i	0.00190210	+	0.00211250i
$45$	0.808635	+	2.08473i	0.120544	+	0.310774i
$46$	−7.68725	+	8.53756i	−1.13342	+	1.25879i
$47$	−0.403207	−	0.0857042i	−0.0588137	−	0.0125012i	0.178411	−	0.983956i	$-0.442904\pi$
$47$	−0.403207	−	0.0857042i	−0.0588137	−	0.0125012i	−0.237225	+	0.971455i	$0.576238\pi$
$48$	−3.28063	−	2.38352i	−0.473518	−	0.344031i
$49$	−6.10771	+	3.41993i	−0.872529	+	0.488562i
$50$	−4.14477	+	5.78957i	−0.586160	+	0.818769i
$51$	3.23647	−	5.60574i	0.453197	−	0.784960i
$52$	−0.0186793	+	0.177722i	−0.00259036	+	0.0246456i
$53$	−7.62713	+	8.47079i	−1.04767	+	1.16355i	−0.0614474	+	0.998110i	$0.519572\pi$
$53$	−7.62713	+	8.47079i	−1.04767	+	1.16355i	−0.986220	+	0.165442i	$0.947095\pi$
$54$	−1.39294	−	0.296078i	−0.189555	−	0.0402911i
$55$	−0.241354	−	1.49008i	−0.0325442	−	0.200923i
$56$	7.41725	+	0.437672i	0.991172	+	0.0584864i
$57$	−0.168651			−0.0223384
$58$	7.52201	+	8.35404i	0.987688	+	1.09694i
$59$	−8.79719	−	3.91676i	−1.14530	−	0.509919i	−0.255740	−	0.966746i	$-0.582319\pi$
$59$	−8.79719	−	3.91676i	−1.14530	−	0.509919i	−0.889556	+	0.456827i	$0.848986\pi$
$60$	−0.0225867	−	0.0582305i	−0.00291593	−	0.00751752i
$61$	10.0173	−	4.45998i	1.28258	−	0.571041i	0.351613	−	0.936145i	$-0.385633\pi$
$61$	10.0173	−	4.45998i	1.28258	−	0.571041i	0.930967	+	0.365104i	$0.118967\pi$
$62$	−2.15826	+	1.56807i	−0.274099	+	0.199145i
$63$	2.47621	−	0.931881i	0.311973	−	0.117406i
$64$	−6.37924	−	4.63479i	−0.797405	−	0.579349i
$65$	8.96396	−	11.1491i	1.11184	−	1.38288i
$66$	0.878225	+	0.391011i	0.108102	+	0.0481301i
$67$	−0.851965	+	0.181091i	−0.104084	+	0.0221237i	−0.259659	−	0.965700i	$-0.583610\pi$
$67$	−0.851965	+	0.181091i	−0.104084	+	0.0221237i	0.155575	+	0.987824i	$0.450277\pi$
$68$	−0.0904008	+	0.156579i	−0.0109627	+	0.0189880i
$69$	−2.49296	+	7.67256i	−0.300118	+	0.923667i
$70$	6.80054	+	4.97295i	0.812820	+	0.594382i
$71$	−2.20737	−	6.79358i	−0.261966	−	0.806249i	−0.992377	−	0.123241i	$-0.960671\pi$
$71$	−2.20737	−	6.79358i	−0.261966	−	0.806249i	0.730411	−	0.683008i	$-0.239329\pi$
$72$	−2.74696	−	0.583885i	−0.323733	−	0.0688115i
$73$	0.399726	−	3.80314i	0.0467844	−	0.445124i	−0.945907	−	0.324439i	$-0.894824\pi$
$73$	0.399726	−	3.80314i	0.0467844	−	0.445124i	0.992691	−	0.120684i	$-0.0385089\pi$
$74$	2.54615	+	4.41006i	0.295984	+	0.512659i
$75$	−1.00531	+	4.89789i	−0.116083	+	0.565560i
$76$	0.00471075			0.000540360
$77$	−1.76588	+	0.267791i	−0.201241	+	0.0305176i
$78$	2.81537	+	8.66482i	0.318778	+	0.981097i
$79$	−3.85969	−	0.820403i	−0.434249	−	0.0923025i	−0.0143999	−	0.999896i	$-0.504584\pi$
$79$	−3.85969	−	0.820403i	−0.434249	−	0.0923025i	−0.419849	+	0.907594i	$0.637917\pi$
$80$	−3.27908	−	8.45376i	−0.366613	−	0.945160i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−6.77194	+	11.7293i	−0.747835	+	1.29529i
$83$	−2.60203	+	8.00823i	−0.285610	+	0.879017i	0.700605	+	0.713549i	$0.252913\pi$
$83$	−2.60203	+	8.00823i	−0.285610	+	0.879017i	−0.986215	+	0.165468i	$0.947087\pi$
$84$	−0.0691651	+	0.0260292i	−0.00754653	+	0.00284002i
$85$	12.8733	−	6.61612i	1.39631	−	0.717619i
$86$	−1.57287	+	0.700288i	−0.169607	+	0.0755140i
$87$	7.21151	+	3.21077i	0.773155	+	0.344231i
$88$	1.73192	+	0.771101i	0.184623	+	0.0821996i
$89$	−4.60805	+	2.05163i	−0.488452	+	0.217473i	−0.636158	−	0.771558i	$-0.719478\pi$
$89$	−4.60805	+	2.05163i	−0.488452	+	0.217473i	0.147707	+	0.989031i	$0.452811\pi$
$90$	−2.25949	−	2.24374i	−0.238172	−	0.236510i
$91$	−13.0842	−	10.7387i	−1.37160	−	1.12572i
$92$	0.0696332	−	0.214309i	0.00725976	−	0.0223432i
$93$	−0.936676	+	1.62237i	−0.0971288	+	0.168232i
$94$	0.574188	−	0.122048i	0.0592230	−	0.0125882i
$95$	−0.316993	−	0.204284i	−0.0325228	−	0.0209591i
$96$	0.154542	+	0.0328490i	0.0157729	+	0.00335264i
$97$	1.72420	+	5.30655i	0.175066	+	0.538799i	0.999636	−	0.0269611i	$-0.00858302\pi$
$97$	1.72420	+	5.30655i	0.175066	+	0.538799i	−0.824570	+	0.565760i	$0.808583\pi$
$98$	5.96487	−	7.98680i	0.602543	−	0.806788i
$99$	0.675071			0.0678471
$100$	0.0280801	−	0.136807i	0.00280801	−	0.0136807i
$101$	−0.691922	−	1.19844i	−0.0688489	−	0.119250i	0.829546	−	0.558438i	$-0.188599\pi$
$101$	−0.691922	−	1.19844i	−0.0688489	−	0.119250i	−0.898395	+	0.439189i	$0.855266\pi$
$102$	−0.963526	+	9.16733i	−0.0954032	+	0.907701i
$103$	−3.82849	−	0.813772i	−0.377233	−	0.0801833i	0.0153933	−	0.999882i	$-0.495100\pi$
$103$	−3.82849	−	0.813772i	−0.377233	−	0.0801833i	−0.392626	+	0.919698i	$0.628433\pi$
$104$	5.55210	+	17.0876i	0.544428	+	1.67558i
$105$	5.78298	+	1.24784i	0.564361	+	0.121777i
$106$	5.01602	−	15.4377i	0.487199	−	1.49944i
$107$	−3.28557	+	5.69077i	−0.317628	+	0.550148i	−0.979993	−	0.199034i	$-0.936220\pi$
$107$	−3.28557	+	5.69077i	−0.317628	+	0.550148i	0.662365	+	0.749182i	$0.269553\pi$
$108$	0.0273215	−	0.00580736i	0.00262901	−	0.000558814i
$109$	−1.24942	−	0.556279i	−0.119673	−	0.0532818i	0.346027	−	0.938225i	$-0.387531\pi$
$109$	−1.24942	−	0.556279i	−0.119673	−	0.0532818i	−0.465700	+	0.884943i	$0.654197\pi$
$110$	1.17707	+	1.79871i	0.112229	+	0.171500i
$111$	2.89298	+	2.10187i	0.274589	+	0.199501i
$112$	−10.0412	+	3.77886i	−0.948806	+	0.357068i
$113$	−8.43932	+	6.13152i	−0.793904	+	0.576805i	−0.909120	−	0.416535i	$-0.863244\pi$
$113$	−8.43932	+	6.13152i	−0.793904	+	0.576805i	0.115215	+	0.993341i	$0.463244\pi$
$114$	0.219405	−	0.0976854i	0.0205492	−	0.00914908i
$115$	−13.9793	+	11.4015i	−1.30358	+	1.06319i
$116$	−0.201431	−	0.0896829i	−0.0187024	−	0.00832685i
$117$	4.28092	+	4.75445i	0.395771	+	0.439549i
$118$	13.7132			1.26241
$119$	−7.67439	−	15.3100i	−0.703510	−	1.40347i
$120$	−4.45588	−	4.42480i	−0.406764	−	0.403927i
$121$	10.3139	+	2.19228i	0.937624	+	0.199298i
$122$	−10.4486	+	11.6043i	−0.945969	+	1.05060i
$123$	−0.994147	+	9.45868i	−0.0896392	+	0.852860i
$124$	0.0261631	−	0.0453158i	0.00234952	−	0.00406948i
$125$	−7.82227	+	7.98825i	−0.699645	+	0.714491i
$126$	−2.68163	+	2.64658i	−0.238899	+	0.235776i
$127$	−10.2285	−	7.43142i	−0.907630	−	0.659432i	0.0327840	−	0.999462i	$-0.489563\pi$
$127$	−10.2285	−	7.43142i	−0.907630	−	0.659432i	−0.940414	+	0.340030i	$0.889563\pi$
$128$	11.2926	+	2.40032i	0.998136	+	0.212160i
$129$	−0.808998	+	0.898483i	−0.0712283	+	0.0791071i
$130$	−5.20382	+	19.6964i	−0.456406	+	1.72749i
$131$	−8.88603	−	9.86893i	−0.776376	−	0.862253i	0.217117	−	0.976146i	$-0.430335\pi$
$131$	−8.88603	−	9.86893i	−0.776376	−	0.862253i	−0.993493	+	0.113893i	$0.963668\pi$
$132$	−0.0188560			−0.00164120
$133$	−0.245480	+	0.372616i	−0.0212858	+	0.0323099i
$134$	1.00346	−	0.729059i	0.0866860	−	0.0629811i
$135$	−2.09034	−	0.794025i	−0.179908	−	0.0683388i
$136$	−1.90014	+	18.0786i	−0.162935	+	1.55023i
$137$	−8.53865	−	3.80165i	−0.729506	−	0.324797i	0.00815652	−	0.999967i	$-0.497404\pi$
$137$	−8.53865	−	3.80165i	−0.729506	−	0.324797i	−0.737662	+	0.675170i	$0.764070\pi$
$138$	−1.20087	−	11.4255i	−0.102225	−	0.972602i
$139$	0.121998	+	0.0886369i	0.0103478	+	0.00751808i	0.592947	−	0.805241i	$-0.297964\pi$
$139$	0.121998	+	0.0886369i	0.0103478	+	0.00751808i	−0.582599	+	0.812759i	$0.697964\pi$
$140$	−0.161530	−	0.0348545i	−0.0136517	−	0.00294574i
$141$	0.333489	−	0.242294i	0.0280848	−	0.0204048i
$142$	6.80659	+	7.55949i	0.571196	+	0.634378i
$143$	−2.15946	−	3.74030i	−0.180583	−	0.312779i
$144$	3.96647	−	0.843099i	0.330539	−	0.0702583i
$145$	9.66543	+	14.7700i	0.802670	+	1.22659i
$146$	1.68282	+	5.17918i	0.139271	+	0.428632i
$147$	1.54535	−	6.82729i	0.127458	−	0.563105i
$148$	−0.0808063	−	0.0587092i	−0.00664224	−	0.00482587i
$149$	−7.44827	+	12.9008i	−0.610186	+	1.05687i	0.381023	+	0.924566i	$0.375572\pi$
$149$	−7.44827	+	12.9008i	−0.610186	+	1.05687i	−0.991209	+	0.132307i	$0.957761\pi$
$150$	−1.52909	−	6.95415i	−0.124850	−	0.567804i
$151$	5.99881	+	10.3903i	0.488177	+	0.845547i	0.999908	−	0.0135991i	$-0.00432885\pi$
$151$	5.99881	+	10.3903i	0.488177	+	0.845547i	−0.511731	+	0.859146i	$0.670996\pi$
$152$	0.432682	−	0.192642i	0.0350951	−	0.0156254i
$153$	2.00025	+	6.15614i	0.161711	+	0.497694i
$154$	2.14219	−	1.37120i	0.172623	−	0.110495i
$155$	−3.72570	+	1.91479i	−0.299255	+	0.153800i
$156$	−0.119574	−	0.132801i	−0.00957360	−	0.0106326i
$157$	−5.74095	−	9.94363i	−0.458178	−	0.793588i	0.540687	−	0.841224i	$-0.318164\pi$
$157$	−5.74095	−	9.94363i	−0.458178	−	0.793588i	−0.998865	+	0.0476364i	$0.984831\pi$
$158$	5.49641	−	1.16830i	0.437271	−	0.0929448i
$159$	−1.19147	−	11.3361i	−0.0944901	−	0.899013i
$160$	0.250685	+	0.248936i	0.0198184	+	0.0196802i
$161$	13.3230	+	16.6757i	1.05000	+	1.31423i
$162$	1.15208	−	0.837038i	0.0905163	−	0.0657639i
$163$	−1.19215	−	11.3426i	−0.0933765	−	0.888418i	−0.936493	−	0.350687i	$-0.885948\pi$
$163$	−1.19215	−	11.3426i	−0.0933765	−	0.888418i	0.843116	−	0.537731i	$-0.180719\pi$
$164$	0.0277684	−	0.264199i	0.00216835	−	0.0206304i
$165$	1.26885	+	0.817700i	0.0987795	+	0.0636578i
$166$	−1.25340	−	11.9254i	−0.0972831	−	0.925587i
$167$	3.87171	−	11.9159i	0.299602	−	0.922081i	−0.682034	−	0.731320i	$-0.738905\pi$
$167$	3.87171	−	11.9159i	0.299602	−	0.922081i	0.981637	−	0.190761i	$-0.0610954\pi$
$168$	−5.28836	+	5.21923i	−0.408006	+	0.402672i
$169$	8.63117	−	26.5640i	0.663936	−	2.04338i
$170$	−12.9152	+	16.0636i	−0.990553	+	1.23202i
$171$	0.112850	−	0.125332i	0.00862984	−	0.00958441i
$172$	0.0225968	−	0.0250963i	0.00172299	−	0.00191358i
$173$	16.5349	−	7.36182i	1.25713	−	0.559709i	0.333409	−	0.942782i	$-0.391801\pi$
$173$	16.5349	−	7.36182i	1.25713	−	0.559709i	0.923718	+	0.383073i	$0.125134\pi$
$174$	−11.2415			−0.852213
$175$	9.35807	+	9.35022i	0.707403	+	0.706810i
$176$	−2.73747			−0.206344
$177$	8.79719	−	3.91676i	0.661237	−	0.294402i
$178$	4.80645	−	5.33810i	0.360258	−	0.400108i
$179$	−11.3191	+	12.5711i	−0.846028	+	0.939609i	−0.998816	−	0.0486499i	$-0.984508\pi$
$179$	−11.3191	+	12.5711i	−0.846028	+	0.939609i	0.152788	+	0.988259i	$0.451175\pi$
$180$	0.0583871	+	0.0221786i	0.00435192	+	0.00165310i
$181$	−6.78399	+	20.8790i	−0.504250	+	1.55192i	0.297778	+	0.954635i	$0.403754\pi$
$181$	−6.78399	+	20.8790i	−0.504250	+	1.55192i	−0.802028	+	0.597286i	$0.796246\pi$
$182$	23.2418	+	6.39181i	1.72280	+	0.473792i
$183$	−3.38845	+	10.4286i	−0.250482	+	0.770903i
$184$	−2.36819	−	22.5318i	−0.174585	−	1.66107i
$185$	2.89161	+	7.45483i	0.212596	+	0.548090i
$186$	0.278856	−	2.65314i	0.0204467	−	0.194538i
$187$	−0.456758	−	4.34576i	−0.0334014	−	0.317793i
$188$	−0.00931496	+	0.00676772i	−0.000679364	+	0.000493586i
$189$	−0.964383	+	2.46373i	−0.0701485	+	0.179210i
$190$	0.530713	+	0.0821540i	0.0385019	+	0.00596008i
$191$	2.62964	+	25.0194i	0.190274	+	1.81034i	0.507135	+	0.861866i	$0.330704\pi$
$191$	2.62964	+	25.0194i	0.190274	+	1.81034i	−0.316861	+	0.948472i	$0.602629\pi$
$192$	7.71286	−	1.63942i	0.556628	−	0.118315i
$193$	−2.60653	−	4.51465i	−0.187622	−	0.324972i	0.756835	−	0.653606i	$-0.226745\pi$
$193$	−2.60653	−	4.51465i	−0.187622	−	0.324972i	−0.944457	+	0.328635i	$0.893411\pi$
$194$	−5.31672	−	5.90481i	−0.381718	−	0.423941i
$195$	2.28735	+	14.1217i	0.163800	+	1.01128i
$196$	−0.0431645	+	0.190699i	−0.00308318	+	0.0136214i
$197$	−2.67345	−	8.22802i	−0.190475	−	0.586222i	0.809524	−	0.587086i	$-0.199725\pi$
$197$	−2.67345	−	8.22802i	−0.190475	−	0.586222i	−1.00000		0.000863931i	$0.999725\pi$
$198$	−0.878225	+	0.391011i	−0.0624128	+	0.0277880i
$199$	1.78678	+	3.09480i	0.126662	+	0.219385i	0.922381	−	0.386281i	$-0.126240\pi$
$199$	1.78678	+	3.09480i	0.126662	+	0.219385i	−0.795719	+	0.605665i	$0.792907\pi$
$200$	−3.01548	−	13.7141i	−0.213227	−	0.969730i
$201$	0.435499	−	0.754306i	0.0307177	−	0.0532047i
$202$	1.59431	+	1.15833i	0.112175	+	0.0814999i
$203$	17.5905	−	11.2596i	1.23461	−	0.790268i
$204$	−0.0558707	−	0.171952i	−0.00391173	−	0.0120391i
$205$	−13.3257	+	16.5741i	−0.930706	+	1.15759i
$206$	5.45199	−	1.15886i	0.379858	−	0.0807413i
$207$	−4.03370	−	6.98658i	−0.280362	−	0.485601i
$208$	−17.3595	−	19.2797i	−1.20366	−	1.33680i
$209$	−0.0921079	+	0.0669203i	−0.00637123	+	0.00462897i
$210$	−8.24607	+	1.72623i	−0.569033	+	0.119121i
$211$	−13.1958	−	9.58733i	−0.908438	−	0.660019i	0.0321813	−	0.999482i	$-0.489755\pi$
$211$	−13.1958	−	9.58733i	−0.908438	−	0.660019i	−0.940619	+	0.339463i	$0.889755\pi$
$212$	0.0332801	+	0.316639i	0.00228569	+	0.0217469i
$213$	6.52563	+	2.90540i	0.447129	+	0.199074i
$214$	0.978142	−	9.30639i	0.0668644	−	0.636172i
$215$	−2.60889	+	0.708843i	−0.177925	+	0.0483427i
$216$	2.27199	−	1.65070i	0.154589	−	0.112316i
$217$	2.22107	+	4.43091i	0.150776	+	0.300790i
$218$	1.94763			0.131910
$219$	2.55881	+	2.84185i	0.172909	+	0.192034i
$220$	−0.0354412	−	0.0228399i	−0.00238945	−	0.00153986i
$221$	27.7102	−	30.7753i	1.86399	−	2.07017i
$222$	−4.98102	−	1.05875i	−0.334304	−	0.0710586i
$223$	−16.5327	−	12.0117i	−1.10711	−	0.804362i	−0.124903	−	0.992169i	$-0.539862\pi$
$223$	−16.5327	−	12.0117i	−1.10711	−	0.804362i	−0.982206	+	0.187807i	$0.939862\pi$
$224$	0.297520	−	0.293631i	0.0198789	−	0.0196190i
$225$	−2.96716	−	4.02442i	−0.197811	−	0.268295i
$226$	7.42756	−	12.8649i	0.494074	−	0.855762i
$227$	0.401488	−	3.81990i	0.0266477	−	0.253536i	−0.973086	−	0.230444i	$-0.925982\pi$
$227$	0.401488	−	3.81990i	0.0266477	−	0.253536i	0.999733	−	0.0230922i	$-0.00735112\pi$
$228$	−0.00315211	+	0.00350077i	−0.000208753	+	0.000231844i
$229$	1.92611	+	0.409407i	0.127281	+	0.0270544i	0.271112	−	0.962548i	$-0.412609\pi$
$229$	1.92611	+	0.409407i	0.127281	+	0.0270544i	−0.143831	+	0.989602i	$0.545942\pi$
$230$	11.5823	−	22.9296i	0.763717	−	1.51194i
$231$	0.982597	−	1.49149i	0.0646501	−	0.0981329i
$232$	−22.1689			−1.45546
$233$	−14.6114	−	16.2276i	−0.957227	−	1.06311i	−0.997954	−	0.0639381i	$-0.979634\pi$
$233$	−14.6114	−	16.2276i	−0.957227	−	1.06311i	0.0407268	−	0.999170i	$-0.487033\pi$
$234$	−8.32306	−	3.70567i	−0.544096	−	0.242247i
$235$	0.920302	−	0.0514609i	0.0600339	−	0.00335694i
$236$	−0.245722	+	0.109402i	−0.0159951	+	0.00712149i
$237$	3.19232	−	2.31935i	0.207363	−	0.150658i
$238$	18.8517	+	15.4723i	1.22198	+	1.00292i
$239$	7.81043	+	5.67461i	0.505215	+	0.367060i	0.811005	−	0.585039i	$-0.198921\pi$
$239$	7.81043	+	5.67461i	0.505215	+	0.367060i	−0.305791	+	0.952099i	$0.598921\pi$
$240$	8.47651	+	3.21984i	0.547156	+	0.207840i
$241$	−18.7232	−	8.33609i	−1.20606	−	0.536975i	−0.297501	−	0.954721i	$-0.596153\pi$
$241$	−18.7232	−	8.33609i	−1.20606	−	0.536975i	−0.908563	+	0.417747i	$0.862820\pi$
$242$	−14.6875	+	3.12193i	−0.944149	+	0.200685i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.0946459	−	0.291290i	0.00605908	−	0.0186479i
$245$	11.1744	−	10.9606i	0.713904	−	0.700244i
$246$	−4.18529	−	12.8810i	−0.266844	−	0.821262i
$247$	−1.05541	−	0.224334i	−0.0671540	−	0.0142740i
$248$	0.549924	−	5.23218i	0.0349202	−	0.332243i
$249$	−4.21017	−	7.29224i	−0.266809	−	0.462127i
$250$	5.54937	−	14.9230i	0.350973	−	0.943813i
$251$	−11.4907			−0.725284			−0.362642	−	0.931928i	$-0.618125\pi$
$251$	−11.4907			−0.725284			−0.362642	+	0.931928i	$0.618125\pi$
$252$	0.0269370	−	0.0688166i	0.00169687	−	0.00433504i
$253$	1.68293	+	5.17952i	0.105805	+	0.325633i
$254$	17.6110	+	3.74334i	1.10501	+	0.234878i
$255$	−3.69719	+	13.9938i	−0.231527	+	0.876325i
$256$	−0.655589	+	0.139350i	−0.0409743	+	0.00870935i
$257$	−7.30310	+	12.6493i	−0.455555	+	0.789044i	−0.998720	−	0.0505817i	$-0.983892\pi$
$257$	−7.30310	+	12.6493i	−0.455555	+	0.789044i	0.543165	+	0.839626i	$0.317226\pi$
$258$	0.532042	−	1.63746i	0.0331235	−	0.101944i
$259$	8.85471	−	3.33233i	0.550205	−	0.207061i
$260$	−0.0638899	−	0.394446i	−0.00396228	−	0.0244625i
$261$	−7.21151	+	3.21077i	−0.446381	+	0.198742i
$262$	17.2764	+	7.69196i	1.06734	+	0.475211i
$263$	23.9793	+	10.6763i	1.47863	+	0.658328i	0.978241	−	0.207474i	$-0.0665242\pi$
$263$	23.9793	+	10.6763i	1.47863	+	0.658328i	0.500387	+	0.865802i	$0.333191\pi$
$264$	−1.73192	+	0.771101i	−0.106592	+	0.0474580i
$265$	11.4918	−	22.7503i	0.705933	−	1.39754i
$266$	0.103530	−	0.626936i	0.00634781	−	0.0384399i
$267$	1.55872	−	4.79726i	0.0953923	−	0.293587i
$268$	−0.0121643	+	0.0210692i	−0.000743053	+	0.00128701i
$269$	8.12762	−	1.72758i	0.495549	−	0.105332i	0.0466441	−	0.998912i	$-0.485147\pi$
$269$	8.12762	−	1.72758i	0.495549	−	0.105332i	0.448905	+	0.893579i	$0.351814\pi$
$270$	3.17932	−	0.177779i	0.193487	−	0.0108193i
$271$	9.75147	+	2.07274i	0.592360	+	0.125910i	0.494331	−	0.869274i	$-0.335413\pi$
$271$	9.75147	+	2.07274i	0.592360	+	0.125910i	0.0980285	+	0.995184i	$0.468746\pi$
$272$	−8.11118	−	24.9637i	−0.491813	−	1.51364i
$273$	16.7355	−	2.53789i	1.01288	−	0.153600i
$274$	13.3102			0.804100
$275$	1.39443	+	3.07385i	0.0840871	+	0.185360i
$276$	0.112669	+	0.195148i	0.00678187	+	0.0117465i
$277$	2.47835	−	23.5800i	0.148910	−	1.41678i	−0.623582	−	0.781758i	$-0.714323\pi$
$277$	2.47835	−	23.5800i	0.148910	−	1.41678i	0.772492	−	0.635025i	$-0.219010\pi$
$278$	−0.210052	−	0.0446479i	−0.0125981	−	0.00267781i
$279$	−0.578898	−	1.78166i	−0.0346577	−	0.106665i
$280$	−16.2618	+	3.40424i	−0.971830	+	0.203442i
$281$	−2.40652	+	7.40650i	−0.143561	+	0.441835i	−0.996823	−	0.0796471i	$-0.974621\pi$
$281$	−2.40652	+	7.40650i	−0.143561	+	0.441835i	0.853262	+	0.521482i	$0.174621\pi$
$282$	−0.293508	+	0.508371i	−0.0174782	+	0.0302730i
$283$	−14.0462	+	2.98561i	−0.834958	+	0.177476i	−0.605503	−	0.795843i	$-0.707028\pi$
$283$	−14.0462	+	2.98561i	−0.834958	+	0.177476i	−0.229456	+	0.973319i	$0.573695\pi$
$284$	−0.182273	−	0.0811532i	−0.0108159	−	0.00481556i
$285$	0.363922	−	0.0988789i	0.0215569	−	0.00585708i
$286$	4.97577	+	3.61511i	0.294223	+	0.213766i
$287$	19.4508	+	15.9640i	1.14815	+	0.942325i
$288$	−0.127821	+	0.0928672i	−0.00753191	+	0.00547225i
$289$	22.7464	−	10.1273i	1.33802	−	0.595726i
$290$	−21.1292	−	13.6166i	−1.24075	−	0.799592i
$291$	−5.09725	−	2.26944i	−0.298806	−	0.133037i
$292$	−0.0714724	−	0.0793782i	−0.00418261	−	0.00464526i
$293$	12.5652			0.734066			0.367033	−	0.930208i	$-0.380374\pi$
$293$	12.5652			0.734066			0.367033	+	0.930208i	$0.380374\pi$
$294$	1.94407	+	9.77698i	0.113380	+	0.570205i
$295$	21.2793	+	3.29402i	1.23893	+	0.191785i
$296$	−9.82292	−	2.08793i	−0.570946	−	0.121358i
$297$	−0.451710	+	0.501675i	−0.0262109	+	0.0291101i
$298$	2.21741	−	21.0973i	0.128451	−	1.22213i
$299$	−25.8066	+	44.6983i	−1.49243	+	2.58497i
$300$	0.0828785	+	0.112410i	0.00478499	+	0.00648997i
$301$	0.807562	+	3.09517i	0.0465471	+	0.178403i
$302$	−13.8223	−	10.0425i	−0.795383	−	0.577880i
$303$	1.35360	+	0.287718i	0.0777626	+	0.0165289i
$304$	−0.457615	+	0.508233i	−0.0262460	+	0.0291492i
$305$	−19.0008	+	15.4969i	−1.08798	+	0.887352i
$306$	−6.16793	−	6.85018i	−0.352597	−	0.391599i
$307$	−25.2200			−1.43938			−0.719691	−	0.694294i	$-0.755717\pi$
$307$	−25.2200			−1.43938			−0.719691	+	0.694294i	$0.755717\pi$
$308$	−0.0274458	+	0.0416601i	−0.00156387	+	0.00237381i
$309$	3.16651	−	2.30061i	0.180137	−	0.130877i
$310$	3.73783	−	4.64900i	0.212294	−	0.264046i
$311$	0.625867	−	5.95472i	0.0354896	−	0.337661i	−0.962342	−	0.271842i	$-0.912367\pi$
$311$	0.625867	−	5.95472i	0.0354896	−	0.337661i	0.997832	−	0.0658194i	$-0.0209661\pi$
$312$	−16.4136	−	7.30783i	−0.929240	−	0.413724i
$313$	2.08062	+	19.7957i	0.117603	+	1.11892i	0.881041	+	0.473040i	$0.156843\pi$
$313$	2.08062	+	19.7957i	0.117603	+	1.11892i	−0.763438	+	0.645882i	$0.776490\pi$
$314$	13.2281	+	9.61080i	0.746507	+	0.542369i
$315$	−4.79690	+	3.46263i	−0.270274	+	0.195097i
$316$	−0.0891674	+	0.0647839i	−0.00501606	+	0.00364438i
$317$	4.18840	+	4.65169i	0.235244	+	0.261265i	0.849195	−	0.528079i	$-0.177087\pi$
$317$	4.18840	+	4.65169i	0.235244	+	0.261265i	−0.613951	+	0.789344i	$0.710421\pi$
$318$	8.11609	+	14.0575i	0.455128	+	0.788305i
$319$	5.21254	−	1.10796i	0.291846	−	0.0620339i
$320$	16.4827	+	6.26103i	0.921411	+	0.350002i
$321$	−2.03059	−	6.24952i	−0.113337	−	0.348814i
$322$	−26.9912	−	13.9772i	−1.50416	−	0.778916i
$323$	−0.883181	−	0.641668i	−0.0491415	−	0.0357034i
$324$	−0.0139659	+	0.0241897i	−0.000775885	+	0.00134387i
$325$	−12.8061	+	29.3135i	−0.710356	+	1.62602i
$326$	8.12070	+	14.0655i	0.449764	+	0.779014i
$327$	1.24942	−	0.556279i	0.0690932	−	0.0307623i
$328$	−8.25367	−	25.4022i	−0.455733	−	1.40260i
$329$	−0.0499118	−	1.08947i	−0.00275173	−	0.0600647i
$330$	−2.12431	−	0.328842i	−0.116940	−	0.0181022i
$331$	−11.4543	−	12.7213i	−0.629584	−	0.699224i	0.340979	−	0.940071i	$-0.389242\pi$
$331$	−11.4543	−	12.7213i	−0.629584	−	0.699224i	−0.970563	+	0.240847i	$0.922575\pi$
$332$	0.117598	+	0.203686i	0.00645403	+	0.0111787i
$333$	−3.49778	+	0.743475i	−0.191677	+	0.0407422i
$334$	1.86501	+	17.7444i	0.102049	+	0.970932i
$335$	1.73223	−	0.890264i	0.0946418	−	0.0486403i
$336$	3.91065	−	9.99063i	0.213344	−	0.545034i
$337$	22.0710	−	16.0355i	1.20228	−	0.873510i	0.207775	−	0.978177i	$-0.433378\pi$
$337$	22.0710	−	16.0355i	1.20228	−	0.873510i	0.994507	+	0.104667i	$0.0333777\pi$
$338$	4.15765	+	39.5574i	0.226147	+	2.15164i
$339$	1.09040	−	10.3744i	0.0592222	−	0.563462i
$340$	0.103269	−	0.390873i	0.00560057	−	0.0211980i
$341$	0.132191	+	1.25772i	0.00715856	+	0.0681092i
$342$	−0.0742162	+	0.228414i	−0.00401315	+	0.0123512i
$343$	−12.8348	−	13.3517i	−0.693013	−	0.720925i
$344$	1.04922	−	3.22917i	0.0565703	−	0.174105i
$345$	0.881058	−	18.0177i	0.0474346	−	0.970042i
$346$	−17.2468	+	19.1546i	−0.927196	+	1.02976i
$347$	4.11033	−	4.56499i	0.220654	−	0.245061i	−0.622647	−	0.782503i	$-0.713943\pi$
$347$	4.11033	−	4.56499i	0.220654	−	0.245061i	0.843301	+	0.537442i	$0.180609\pi$
$348$	0.201431	−	0.0896829i	0.0107978	−	0.00480751i
$349$	21.3037			1.14036			0.570181	−	0.821519i	$-0.306873\pi$
$349$	21.3037			1.14036			0.570181	+	0.821519i	$0.306873\pi$
$350$	−17.5901	−	6.74373i	−0.940228	−	0.360467i
$351$	−6.39774			−0.341486
$352$	0.0974368	−	0.0433816i	0.00519340	−	0.00231225i
$353$	−9.11141	+	10.1193i	−0.484952	+	0.538593i	−0.935111	−	0.354355i	$-0.884701\pi$
$353$	−9.11141	+	10.1193i	−0.484952	+	0.538593i	0.450159	+	0.892948i	$0.351367\pi$
$354$	−9.17595	+	10.1909i	−0.487696	+	0.541642i
$355$	8.74615	+	13.3653i	0.464198	+	0.709355i
$356$	−0.0435381	+	0.133996i	−0.00230751	+	0.00710179i
$357$	16.5127	+	4.54122i	0.873947	+	0.240347i
$358$	7.44405	−	22.9104i	0.393430	−	1.21085i
$359$	−1.19692	−	11.3879i	−0.0631709	−	0.601031i	−0.979617	−	0.200873i	$-0.935622\pi$
$359$	−1.19692	−	11.3879i	−0.0631709	−	0.601031i	0.916446	−	0.400158i	$-0.131045\pi$
$360$	6.26983	−	0.350592i	0.330449	−	0.0184778i
$361$	1.98307	−	18.8676i	0.104372	−	0.993033i
$362$	−3.26786	−	31.0916i	−0.171755	−	1.63414i
$363$	−8.53050	+	6.19777i	−0.447735	+	0.325299i
$364$	−0.467453	+	0.0708880i	−0.0245012	+	0.00371554i
$365$	1.36720	+	8.44091i	0.0715627	+	0.441817i
$366$	−1.63223	−	15.5296i	−0.0853179	−	0.811745i
$367$	19.9749	−	4.24579i	1.04268	−	0.221628i	0.345421	−	0.938448i	$-0.387736\pi$
$367$	19.9749	−	4.24579i	1.04268	−	0.221628i	0.697259	+	0.716820i	$0.254403\pi$
$368$	16.3570	+	28.3311i	0.852667	+	1.47686i
$369$	−6.36395	−	7.06789i	−0.331294	−	0.367939i
$370$	−8.07976	−	8.02341i	−0.420047	−	0.417117i
$371$	−26.7801	−	13.8678i	−1.39035	−	0.719982i
$372$	0.0161697	+	0.0497652i	0.000838360	+	0.00258021i
$373$	−11.1763	+	4.97600i	−0.578686	+	0.257648i	−0.675140	−	0.737690i	$-0.735917\pi$
$373$	−11.1763	+	4.97600i	−0.578686	+	0.257648i	0.0964537	+	0.995337i	$0.469250\pi$
$374$	3.11134	+	5.38900i	0.160884	+	0.278659i
$375$	−0.702308	−	11.1583i	−0.0362671	−	0.576210i
$376$	−0.578818	+	1.00254i	−0.0298503	+	0.0517022i
$377$	40.8583	+	29.6853i	2.10431	+	1.52887i
$378$	−0.172427	−	3.76375i	−0.00886871	−	0.193586i
$379$	7.80893	+	24.0334i	0.401118	+	1.23451i	0.924094	+	0.382166i	$0.124822\pi$
$379$	7.80893	+	24.0334i	0.401118	+	1.23451i	−0.522976	+	0.852348i	$0.675178\pi$
$380$	−0.0101650	+	0.00276187i	−0.000521455	+	0.000141681i
$381$	12.3668	−	2.62865i	0.633571	−	0.134670i
$382$	−17.9126	−	31.0255i	−0.916489	−	1.58740i
$383$	−18.7149	−	20.7850i	−0.956287	−	1.06206i	−0.998018	−	0.0629351i	$-0.979954\pi$
$383$	−18.7149	−	20.7850i	−0.956287	−	1.06206i	0.0417309	−	0.999129i	$-0.486713\pi$
$384$	−9.34003	+	6.78593i	−0.476631	+	0.346293i
$385$	3.65348	−	1.61317i	0.186198	−	0.0822147i
$386$	6.00589	+	4.36354i	0.305692	+	0.222098i
$387$	−0.126378	−	1.20241i	−0.00642415	−	0.0611217i
$388$	0.142376	+	0.0633898i	0.00722804	+	0.00321813i
$389$	−0.429898	+	4.09020i	−0.0217967	+	0.207381i	−1.00000		0.000268036i	$-0.999915\pi$
$389$	−0.429898	+	4.09020i	−0.0217967	+	0.207381i	0.978203	+	0.207650i	$0.0665813\pi$
$390$	−11.1552	−	17.0466i	−0.564866	−	0.863190i
$391$	−42.2468	+	30.6941i	−2.13651	+	1.55227i
$392$	3.83383	+	19.2809i	0.193638	+	0.973831i
$393$	13.2800			0.669885
$394$	8.24378	+	9.15565i	0.415316	+	0.461255i
$395$	8.80958	−	0.492608i	0.443258	−	0.0247858i
$396$	0.0126171	−	0.0140127i	0.000634034	−	0.000704166i
$397$	12.6536	+	2.68962i	0.635068	+	0.134988i	0.514186	−	0.857679i	$-0.328094\pi$
$397$	12.6536	+	2.68962i	0.635068	+	0.134988i	0.120883	+	0.992667i	$0.461428\pi$
$398$	−4.11705	−	2.99121i	−0.206369	−	0.149936i
$399$	−0.112649	−	0.431756i	−0.00563952	−	0.0216148i
$400$	12.0321	+	16.3194i	0.601605	+	0.815968i
$401$	−7.68782	+	13.3157i	−0.383911	+	0.664954i	−0.991618	−	0.129208i	$-0.958756\pi$
$401$	−7.68782	+	13.3157i	−0.383911	+	0.664954i	0.607706	+	0.794162i	$0.292090\pi$
$402$	−0.129652	+	1.23355i	−0.00646644	+	0.0615241i
$403$	−8.01967	+	8.90675i	−0.399488	+	0.443677i
$404$	−0.0378087	−	0.00803649i	−0.00188105	−	0.000399830i
$405$	1.98879	−	1.02212i	0.0988236	−	0.0507895i
$406$	−16.3625	+	24.8367i	−0.812056	+	1.23263i
$407$	2.41400			0.119657
$408$	−12.1636	−	13.5090i	−0.602187	−	0.668796i
$409$	−7.26040	−	3.23254i	−0.359003	−	0.159839i	0.219306	−	0.975656i	$-0.429621\pi$
$409$	−7.26040	−	3.23254i	−0.359003	−	0.159839i	−0.578309	+	0.815817i	$0.696287\pi$
$410$	7.73593	−	29.2803i	0.382050	−	1.44605i
$411$	8.53865	−	3.80165i	0.421180	−	0.187522i
$412$	−0.0884467	+	0.0642603i	−0.00435745	+	0.00316588i
$413$	4.15108	−	25.1374i	0.204261	−	1.23693i
$414$	9.29433	+	6.75272i	0.456791	+	0.331878i
$415$	0.919604	−	18.8060i	0.0451416	−	0.923150i
$416$	0.923422	+	0.411134i	0.0452745	+	0.0201575i
$417$	−0.147503	+	0.0313527i	−0.00722324	+	0.00153535i
$418$	0.0810654	−	0.140409i	0.00396504	−	0.00686765i
$419$	1.67053	−	5.14135i	0.0816106	−	0.251172i	−0.901923	−	0.431897i	$-0.857844\pi$
$419$	1.67053	−	5.14135i	0.0816106	−	0.251172i	0.983534	+	0.180725i	$0.0578445\pi$
$420$	0.133986	−	0.0967177i	0.00653786	−	0.00471934i
$421$	2.42727	+	7.47037i	0.118298	+	0.364083i	0.992621	−	0.121262i	$-0.0386940\pi$
$421$	2.42727	+	7.47037i	0.118298	+	0.364083i	−0.874323	+	0.485345i	$0.838694\pi$
$422$	22.7201	+	4.82930i	1.10600	+	0.235087i
$423$	−0.0430882	+	0.409956i	−0.00209502	+	0.0199328i
$424$	16.0055	+	27.7223i	0.777295	+	1.34631i
$425$	−23.8995	+	21.8240i	−1.15930	+	1.05862i
$426$	−10.1723			−0.492849
$427$	18.1087	+	22.6657i	0.876342	+	1.09687i
$428$	0.0567183	+	0.174561i	0.00274158	+	0.00843772i
$429$	4.22455	+	0.897955i	0.203963	+	0.0433537i
$430$	2.98343	−	2.43327i	0.143874	−	0.117343i
$431$	7.85882	−	1.67044i	0.378546	−	0.0804625i	−0.0147090	−	0.999892i	$-0.504682\pi$
$431$	7.85882	−	1.67044i	0.378546	−	0.0804625i	0.393255	+	0.919429i	$0.371349\pi$
$432$	−2.02754	+	3.51181i	−0.0975501	+	0.168962i
$433$	−7.76041	+	23.8841i	−0.372942	+	1.14780i	0.571915	+	0.820313i	$0.306201\pi$
$433$	−7.76041	+	23.8841i	−0.372942	+	1.14780i	−0.944857	+	0.327484i	$0.893799\pi$
$434$	−5.45592	−	4.47787i	−0.261893	−	0.214945i
$435$	−17.4437	−	2.70028i	−0.836362	−	0.129468i
$436$	−0.0348987	+	0.0155379i	−0.00167135	+	0.000744131i
$437$	1.24295	+	0.553397i	0.0594584	+	0.0264726i
$438$	−4.97490	−	2.21497i	−0.237710	−	0.105835i
$439$	−36.6323	+	16.3097i	−1.74836	+	0.778422i	−0.756073	+	0.654487i	$0.772885\pi$
$439$	−36.6323	+	16.3097i	−1.74836	+	0.778422i	−0.992290	+	0.123935i	$0.960449\pi$
$440$	−4.18929	−	0.648500i	−0.199717	−	0.0309160i
$441$	4.03963	+	5.71677i	0.192363	+	0.272227i
$442$	−18.2237	+	56.0869i	−0.866815	+	2.66778i
$443$	−11.7356	+	20.3266i	−0.557574	+	0.965746i	0.440124	+	0.897937i	$0.354934\pi$
$443$	−11.7356	+	20.3266i	−0.557574	+	0.965746i	−0.997698	+	0.0678096i	$0.978399\pi$
$444$	0.0976994	−	0.0207667i	0.00463661	−	0.000985542i
$445$	8.74056	−	7.12875i	0.414342	−	0.337935i
$446$	28.4653	+	6.05050i	1.34787	+	0.286499i
$447$	−4.60328	−	14.1675i	−0.217728	−	0.670097i
$448$	7.60432	−	19.4269i	0.359271	−	0.917837i
$449$	−29.8610			−1.40923			−0.704614	−	0.709590i	$-0.748880\pi$
$449$	−29.8610			−1.40923			−0.704614	+	0.709590i	$0.748880\pi$
$450$	6.19110	+	3.51689i	0.291851	+	0.165788i
$451$	3.21022	+	5.56027i	0.151164	+	0.261823i
$452$	−0.0304568	+	0.289777i	−0.00143257	+	0.0136300i
$453$	−11.7355	−	2.49445i	−0.551380	−	0.117199i
$454$	1.69024	+	5.20201i	0.0793267	+	0.244142i
$455$	34.5297	+	15.5012i	1.61878	+	0.726708i
$456$	−0.146359	+	0.450448i	−0.00685391	+	0.0210942i
$457$	−0.186996	+	0.323886i	−0.00874730	+	0.0151508i	−0.870366	−	0.492405i	$-0.836118\pi$
$457$	−0.186996	+	0.323886i	−0.00874730	+	0.0151508i	0.861619	+	0.507556i	$0.169451\pi$
$458$	−2.74289	+	0.583019i	−0.128167	+	0.0272427i
$459$	−5.91333	−	2.63278i	−0.276011	−	0.122888i
$460$	−0.0246096	+	0.503269i	−0.00114743	+	0.0234650i
$461$	−28.9014	−	20.9981i	−1.34607	−	0.977980i	−0.999197	−	0.0400696i	$-0.987242\pi$
$461$	−28.9014	−	20.9981i	−1.34607	−	0.977980i	−0.346877	−	0.937911i	$-0.612758\pi$
$462$	−0.414404	+	2.50947i	−0.0192798	+	0.116751i
$463$	13.3004	−	9.66329i	0.618121	−	0.449091i	−0.234143	−	0.972202i	$-0.575229\pi$
$463$	13.3004	−	9.66329i	0.618121	−	0.449091i	0.852265	+	0.523111i	$0.175229\pi$
$464$	29.2433	−	13.0200i	1.35759	−	0.604436i
$465$	1.07001	−	4.04998i	0.0496206	−	0.187813i
$466$	28.4079	+	12.6480i	1.31597	+	0.585908i
$467$	−22.7946	−	25.3160i	−1.05481	−	1.17148i	−0.984756	−	0.173939i	$-0.944350\pi$
$467$	−22.7946	−	25.3160i	−1.05481	−	1.17148i	−0.0700512	−	0.997543i	$-0.522316\pi$
$468$	0.178701			0.00826045
$469$	−1.03266	−	2.06011i	−0.0476840	−	0.0951272i
$470$	−1.16745	+	0.600000i	−0.0538504	+	0.0276760i
$471$	11.2310	+	2.38722i	0.517497	+	0.109997i
$472$	−18.0956	+	20.0972i	−0.832918	+	0.925049i
$473$	−0.0853140	+	0.811709i	−0.00392274	+	0.0373224i
$474$	−2.80960	+	4.86637i	−0.129049	+	0.223520i
$475$	0.803789	+	0.254962i	0.0368804	+	0.0116984i
$476$	−0.461232	−	0.126845i	−0.0211405	−	0.00581392i
$477$	9.22163	+	6.69991i	0.422230	+	0.306768i
$478$	−13.4477	−	2.85840i	−0.615084	−	0.130740i
$479$	4.41574	−	4.90418i	0.201760	−	0.224078i	−0.633770	−	0.773521i	$-0.718494\pi$
$479$	4.41574	−	4.90418i	0.201760	−	0.224078i	0.835531	+	0.549444i	$0.185160\pi$
$480$	−0.352737	+	0.0197241i	−0.0161002	+	0.000900278i
$481$	15.3082	+	17.0015i	0.697995	+	0.775202i
$482$	29.1861			1.32939
$483$	−21.3073	−	1.25729i	−0.969515	−	0.0572085i
$484$	0.238273	−	0.173115i	0.0108306	−	0.00786888i
$485$	−6.83173	−	10.4398i	−0.310213	−	0.474046i
$486$	−0.148854	+	1.41625i	−0.00675217	+	0.0642426i
$487$	−24.7276	−	11.0094i	−1.12051	−	0.498884i	−0.238988	−	0.971022i	$-0.576816\pi$
$487$	−24.7276	−	11.0094i	−1.12051	−	0.498884i	−0.881525	+	0.472138i	$0.843482\pi$
$488$	−3.21886	−	30.6254i	−0.145711	−	1.38635i
$489$	9.22687	+	6.70372i	0.417254	+	0.303152i
$490$	−8.18864	+	20.7314i	−0.369925	+	0.936548i
$491$	15.6578	−	11.3761i	0.706627	−	0.513395i	−0.175457	−	0.984487i	$-0.556140\pi$
$491$	15.6578	−	11.3761i	0.706627	−	0.513395i	0.882084	+	0.471092i	$0.156140\pi$
$492$	0.177757	+	0.197419i	0.00801391	+	0.00890035i
$493$	25.5487	+	44.2516i	1.15065	+	1.99299i
$494$	1.50296	−	0.319464i	0.0676214	−	0.0143734i
$495$	−1.45669	+	0.395788i	−0.0654735	+	0.0177894i
$496$	2.34748	+	7.22479i	0.105405	+	0.324403i
$497$	15.9175	−	10.1887i	0.713997	−	0.457025i
$498$	9.70095	+	7.04816i	0.434710	+	0.315835i
$499$	−5.45458	+	9.44762i	−0.244181	+	0.422933i	−0.961901	−	0.273398i	$-0.911852\pi$
$499$	−5.45458	+	9.44762i	−0.244181	+	0.422933i	0.717720	+	0.696332i	$0.245186\pi$
$500$	0.0196168	+	0.311671i	0.000877290	+	0.0139384i
$501$	6.26456	+	10.8505i	0.279880	+	0.484766i
$502$	14.9487	−	6.65557i	0.667191	−	0.297053i
$503$	−6.25201	−	19.2417i	−0.278763	−	0.857945i	−0.988199	−	0.153175i	$-0.951050\pi$
$503$	−6.25201	−	19.2417i	−0.278763	−	0.857945i	0.709436	−	0.704770i	$-0.248950\pi$
$504$	−0.340039	−	7.42237i	−0.0151465	−	0.330618i
$505$	2.19569	+	2.18038i	0.0977071	+	0.0970257i
$506$	−5.18944	−	5.76346i	−0.230699	−	0.256217i
$507$	13.9655	+	24.1890i	0.620231	+	1.07427i
$508$	−0.345428	+	0.0734230i	−0.0153259	+	0.00325762i
$509$	0.311861	+	2.96716i	0.0138230	+	0.131517i	0.999257	−	0.0385412i	$-0.0122711\pi$
$509$	0.311861	+	2.96716i	0.0138230	+	0.131517i	−0.985434	+	0.170058i	$0.945604\pi$
$510$	−3.29560	−	20.3465i	−0.145932	−	0.900959i
$511$	10.0032	−	1.51696i	0.442516	−	0.0671063i
$512$	−17.9079	+	13.0108i	−0.791424	+	0.575003i
$513$	0.0176289	+	0.167727i	0.000778334	+	0.00740535i
$514$	2.17420	−	20.6861i	0.0958996	−	0.912424i
$515$	8.73838	−	0.488627i	0.385059	−	0.0215315i
$516$	0.00352997	+	0.0335854i	0.000155398	+	0.00147852i
$517$	0.0859914	−	0.264654i	0.00378190	−	0.0116395i
$518$	−9.58930	+	9.46394i	−0.421330	+	0.415822i
$519$	−5.59312	+	17.2139i	−0.245511	+	0.755605i
$520$	−21.9989	−	33.6171i	−0.964713	−	1.47421i
$521$	−15.1582	+	16.8349i	−0.664092	+	0.737549i	−0.977236	−	0.212157i	$-0.931951\pi$
$521$	−15.1582	+	16.8349i	−0.664092	+	0.737549i	0.313144	+	0.949706i	$0.398618\pi$
$522$	7.52201	−	8.35404i	0.329229	−	0.365646i
$523$	2.74238	−	1.22099i	0.119916	−	0.0533900i	−0.345902	−	0.938271i	$-0.612427\pi$
$523$	2.74238	−	1.22099i	0.119916	−	0.0533900i	0.465818	+	0.884881i	$0.345760\pi$
$524$	−0.370934			−0.0162043
$525$	−13.2103	+	0.697880i	−0.576546	+	0.0304580i
$526$	−37.3795			−1.62982
$527$	−11.0777	+	4.93213i	−0.482554	+	0.214847i
$528$	1.83172	−	2.03433i	0.0797155	−	0.0885331i
$529$	28.1590	−	31.2737i	1.22430	−	1.35973i
$530$	−1.77275	+	36.2529i	−0.0770034	+	1.57473i
$531$	−2.97575	+	9.15841i	−0.129136	+	0.397441i
$532$	0.00314651	+	0.0120598i	0.000136418	+	0.000522857i
$533$	−18.8029	+	57.8694i	−0.814444	+	2.50660i
$534$	0.750841	+	7.14377i	0.0324921	+	0.309141i
$535$	3.75327	−	14.2061i	0.162268	−	0.614181i
$536$	−0.255682	+	2.43265i	−0.0110438	+	0.105075i
$537$	−1.76821	−	16.8234i	−0.0763041	−	0.725985i
$538$	−9.57289	+	6.95511i	−0.412717	+	0.299856i
$539$	−1.86506	−	4.34187i	−0.0803339	−	0.187018i
$540$	−0.0555505	+	0.0285497i	−0.00239051	+	0.00122858i
$541$	2.83509	+	26.9740i	0.121890	+	1.15970i	0.868933	+	0.494929i	$0.164806\pi$
$541$	2.83509	+	26.9740i	0.121890	+	1.15970i	−0.747043	+	0.664775i	$0.768527\pi$
$542$	−13.8866	+	2.95169i	−0.596482	+	0.126786i
$543$	−10.9767	−	19.0122i	−0.471056	−	0.815893i
$544$	0.684316	+	0.760009i	0.0293398	+	0.0325851i
$545$	3.02219	+	0.467833i	0.129456	+	0.0200398i
$546$	−20.3019	+	12.9951i	−0.868839	+	0.556138i
$547$	7.05150	+	21.7023i	0.301501	+	0.927923i	0.980960	+	0.194210i	$0.0622144\pi$
$547$	7.05150	+	21.7023i	0.301501	+	0.927923i	−0.679459	+	0.733713i	$0.737786\pi$
$548$	−0.238500	+	0.106187i	−0.0101882	+	0.00453609i
$549$	−5.48263	−	9.49620i	−0.233993	−	0.405288i
$550$	−3.59449	−	3.19122i	−0.153269	−	0.136074i
$551$	0.665666	−	1.15297i	0.0283583	−	0.0491180i
$552$	18.3290	+	13.3168i	0.780136	+	0.566802i
$553$	−0.477780	−	10.4290i	−0.0203173	−	0.443485i
$554$	10.4337	+	32.1116i	0.443285	+	1.36429i
$555$	−7.47489	−	2.83937i	−0.317291	−	0.120525i
$556$	0.00412003		0.000875740i	0.000174728		3.71396e-5i
$557$	0.229182	+	0.396955i	0.00971076	+	0.0168195i	0.870840	−	0.491567i	$-0.163576\pi$
$557$	0.229182	+	0.396955i	0.00971076	+	0.0168195i	−0.861129	+	0.508386i	$0.830242\pi$
$558$	1.78508	+	1.98253i	0.0755683	+	0.0839271i
$559$	−6.25779	+	4.54655i	−0.264676	+	0.192298i
$560$	19.4518	−	14.0412i	0.821989	−	0.593351i
$561$	3.53516	+	2.56844i	0.149254	+	0.108440i
$562$	−1.15923	−	11.0293i	−0.0488990	−	0.465243i
$563$	1.04723	+	0.466255i	0.0441353	+	0.0196503i	0.428686	−	0.903454i	$-0.358977\pi$
$563$	1.04723	+	0.466255i	0.0441353	+	0.0196503i	−0.384550	+	0.923104i	$0.625643\pi$
$564$	0.00120353	−	0.0114509i	5.06779e−5	−	0.000482168i
$565$	14.6158	−	18.1787i	0.614892	−	0.764785i
$566$	16.5439	−	12.0198i	0.695392	−	0.505232i
$567$	−1.18561	−	2.36523i	−0.0497910	−	0.0993305i
$568$	−20.0605			−0.841718
$569$	11.8633	+	13.1755i	0.497335	+	0.552346i	0.938590	−	0.345036i	$-0.112133\pi$
$569$	11.8633	+	13.1755i	0.497335	+	0.552346i	−0.441255	+	0.897382i	$0.645467\pi$
$570$	−0.416168	+	0.339425i	−0.0174314	+	0.0142169i
$571$	−15.9345	+	17.6971i	−0.666838	+	0.740599i	−0.977735	−	0.209845i	$-0.932704\pi$
$571$	−15.9345	+	17.6971i	−0.666838	+	0.740599i	0.310897	+	0.950444i	$0.399371\pi$
$572$	−0.117999	−	0.0250816i	−0.00493381	−	0.00104871i
$573$	−20.3526	−	14.7870i	−0.850242	−	0.617737i
$574$	−34.5509	−	9.50197i	−1.44213	−	0.396604i
$575$	23.4805	−	32.7985i	0.979206	−	1.36779i
$576$	−3.94259	+	6.82876i	−0.164274	+	0.284532i
$577$	1.59269	−	15.1534i	0.0663044	−	0.630844i	−0.910025	−	0.414554i	$-0.863938\pi$
$577$	1.59269	−	15.1534i	0.0663044	−	0.630844i	0.976329	−	0.216290i	$-0.0693957\pi$
$578$	−23.7258	+	26.3501i	−0.986861	+	1.09602i
$579$	5.09915	+	1.08386i	0.211913	+	0.0450436i
$580$	0.487236	+	0.0754238i	0.0202314	+	0.00313180i
$581$	−22.2395	−	1.31229i	−0.922649	−	0.0544431i
$582$	7.94571			0.329360
$583$	−5.14885	−	5.71838i	−0.213244	−	0.236831i
$584$	−9.81084	−	4.36807i	−0.405976	−	0.180752i
$585$	−12.0250	−	7.74945i	−0.497174	−	0.320400i
$586$	−16.3465	+	7.27795i	−0.675269	+	0.300649i
$587$	−9.06816	+	6.58840i	−0.374283	+	0.271933i	−0.758985	−	0.651108i	$-0.774304\pi$
$587$	−9.06816	+	6.58840i	−0.374283	+	0.271933i	0.384702	+	0.923041i	$0.374304\pi$
$588$	−0.112834	−	0.159680i	−0.00465321	−	0.00658509i
$589$	0.255604	+	0.185707i	0.0105320	+	0.00765192i
$590$	−29.5910	+	8.03996i	−1.21824	+	0.331000i
$591$	7.90350	+	3.51886i	0.325106	+	0.144747i
$592$	14.1838	−	3.01485i	0.582949	−	0.123910i
$593$	−0.149440	+	0.258837i	−0.00613676	+	0.0106292i	−0.869077	−	0.494676i	$-0.835287\pi$
$593$	−0.149440	+	0.258837i	−0.00613676	+	0.0106292i	0.862941	+	0.505305i	$0.168620\pi$
$594$	0.297070	−	0.914286i	0.0121889	−	0.0375136i
$595$	25.5362	+	28.5371i	1.04688	+	1.16991i
$596$	0.128578	+	0.395723i	0.00526677	+	0.0162095i
$597$	−3.49548	−	0.742987i	−0.143060	−	0.0304084i
$598$	7.68283	−	73.0973i	0.314174	−	2.98917i
$599$	−11.0070	−	19.0647i	−0.449735	−	0.778964i	0.548633	−	0.836063i	$-0.315148\pi$
$599$	−11.0070	−	19.0647i	−0.449735	−	0.778964i	−0.998369	+	0.0570990i	$0.981815\pi$
$600$	12.2093	+	6.93556i	0.498442	+	0.283143i
$601$	39.5965			1.61518			0.807588	−	0.589747i	$-0.200773\pi$
$601$	39.5965			1.61518			0.807588	+	0.589747i	$0.200773\pi$
$602$	−2.84336	−	3.55888i	−0.115887	−	0.145049i
$603$	0.269153	+	0.828368i	0.0109608	+	0.0337338i
$604$	0.327793	+	0.0696746i	0.0133377	+	0.00283502i
$605$	−23.5410	+	1.31635i	−0.957076	+	0.0535171i
$606$	−1.92761	+	0.409726i	−0.0783037	+	0.0166440i
$607$	1.32632	−	2.29726i	0.0538339	−	0.0932430i	−0.837853	−	0.545896i	$-0.816189\pi$
$607$	1.32632	−	2.29726i	0.0538339	−	0.0932430i	0.891687	+	0.452653i	$0.149523\pi$
$608$	0.00823409	−	0.0253419i	0.000333937	−	0.00102775i
$609$	−3.40286	+	20.6064i	−0.137891	+	0.835015i
$610$	15.7428	−	31.1661i	0.637407	−	1.26188i
$611$	2.40924	−	1.07266i	0.0974674	−	0.0433953i
$612$	0.165170	+	0.0735386i	0.00667662	+	0.00297262i
$613$	7.61427	+	3.39009i	0.307537	+	0.136925i	0.554702	−	0.832049i	$-0.312832\pi$
$613$	7.61427	+	3.39009i	0.307537	+	0.136925i	−0.247165	+	0.968973i	$0.579499\pi$
$614$	32.8097	−	14.6078i	1.32409	−	0.589523i
$615$	−3.40033	−	20.9932i	−0.137115	−	0.846526i
$616$	−0.817233	+	4.94885i	−0.0329272	+	0.199395i
$617$	−4.89938	+	15.0787i	−0.197242	+	0.607048i	0.802701	+	0.596381i	$0.203395\pi$
$617$	−4.89938	+	15.0787i	−0.197242	+	0.607048i	−0.999943	+	0.0106664i	$0.996605\pi$
$618$	−2.78689	+	4.82704i	−0.112105	+	0.194172i
$619$	46.6097	−	9.90720i	1.87340	−	0.398204i	0.876821	−	0.480816i	$-0.159660\pi$
$619$	46.6097	−	9.90720i	1.87340	−	0.398204i	0.996582	+	0.0826119i	$0.0263262\pi$
$620$	−0.0298875	+	0.113123i	−0.00120031	+	0.00454315i
$621$	7.89111	+	1.67731i	0.316659	+	0.0673080i
$622$	2.63485	+	8.10924i	0.105648	+	0.325151i
$623$	−8.33019	−	10.4265i	−0.333742	−	0.417727i
$624$	25.9434			1.03857
$625$	12.1957	−	21.8235i	0.487830	−	0.872939i
$626$	−14.1728	−	24.5479i	−0.566457	−	0.981132i
$627$	0.0119007	−	0.113228i	0.000475269	−	0.00452189i
$628$	−0.313703	−	0.0666796i	−0.0125181	−	0.00266081i
$629$	7.15273	+	22.0138i	0.285198	+	0.877749i
$630$	4.23486	−	7.28310i	0.168721	−	0.290166i
$631$	14.3323	−	44.1104i	0.570562	−	1.75601i	−0.0802564	−	0.996774i	$-0.525574\pi$
$631$	14.3323	−	44.1104i	0.570562	−	1.75601i	0.650818	−	0.759234i	$-0.274426\pi$
$632$	−5.54073	+	9.59682i	−0.220398	+	0.381741i
$633$	15.9545	−	3.39123i	0.634135	−	0.134789i
$634$	−8.14319	−	3.62558i	−0.323407	−	0.143990i
$635$	26.4284	+	10.0389i	1.04878	+	0.398383i
$636$	−0.257578	−	0.187141i	−0.0102136	−	0.00742063i
$637$	18.7521	−	40.6691i	0.742985	−	1.61137i
$638$	−6.13945	+	4.46057i	−0.243063	+	0.176596i
$639$	−6.52563	+	2.90540i	−0.258150	+	0.114936i
$640$	−25.7749	+	1.44127i	−1.01884	+	0.0569710i
$641$	4.45311	+	1.98265i	0.175887	+	0.0783100i	0.492791	−	0.870148i	$-0.335977\pi$
$641$	4.45311	+	1.98265i	0.175887	+	0.0783100i	−0.316904	+	0.948458i	$0.602643\pi$
$642$	6.26149	+	6.95409i	0.247121	+	0.274456i
$643$	−39.9800			−1.57666			−0.788328	−	0.615255i	$-0.789053\pi$
$643$	−39.9800			−1.57666			−0.788328	+	0.615255i	$0.789053\pi$
$644$	0.595152	+	0.0351184i	0.0234523	+	0.00138386i
$645$	1.21891	−	2.41309i	0.0479947	−	0.0950153i
$646$	1.52063	+	0.323219i	0.0598283	+	0.0127169i
$647$	21.2203	−	23.5676i	0.834257	−	0.926537i	−0.163945	−	0.986469i	$-0.552422\pi$
$647$	21.2203	−	23.5676i	0.834257	−	0.926537i	0.998202	+	0.0599329i	$0.0190887\pi$
$648$	−0.293551	+	2.79295i	−0.0115318	+	0.109717i
$649$	3.25037	−	5.62981i	0.127588	−	0.220989i
$650$	−0.318809	−	45.5525i	−0.0125047	−	1.78672i
$651$	−4.77899	−	1.31429i	−0.187304	−	0.0515110i
$652$	−0.257724	−	0.187247i	−0.0100932	−	0.00733317i
$653$	29.5829	+	6.28804i	1.15767	+	0.246070i	0.746434	−	0.665459i	$-0.231764\pi$
$653$	29.5829	+	6.28804i	1.15767	+	0.246070i	0.411235	+	0.911529i	$0.365098\pi$
$654$	−1.30322	+	1.44737i	−0.0509598	+	0.0565966i
$655$	24.9607	+	16.0858i	0.975294	+	0.628522i
$656$	25.8064	+	28.6609i	1.00757	+	1.11902i
$657$	−3.82409			−0.149192
$658$	0.695972	+	1.38843i	0.0271318	+	0.0541266i
$659$	18.3746	−	13.3499i	0.715772	−	0.520039i	−0.169258	−	0.985572i	$-0.554137\pi$
$659$	18.3746	−	13.3499i	0.715772	−	0.520039i	0.885031	+	0.465533i	$0.154137\pi$
$660$	0.0406882	−	0.0110551i	0.00158378	−	0.000430319i
$661$	−1.08241	+	10.2984i	−0.0421007	+	0.400561i	0.953096	+	0.302668i	$0.0978772\pi$
$661$	−1.08241	+	10.2984i	−0.0421007	+	0.400561i	−0.995197	+	0.0978937i	$0.968789\pi$
$662$	22.2697	+	9.91509i	0.865535	+	0.385361i
$663$	4.32875	+	41.1853i	0.168115	+	1.59951i
$664$	19.1309	+	13.8994i	0.742425	+	0.539403i
$665$	0.311244	−	0.947967i	0.0120695	−	0.0367606i
$666$	4.11976	−	2.99318i	0.159637	−	0.115983i
$667$	−42.6129	−	47.3264i	−1.64998	−	1.83249i
$668$	−0.174981	−	0.303076i	−0.00677022	−	0.0117264i
$669$	19.9889	−	4.24878i	0.772817	−	0.164267i
$670$	−1.73787	+	2.16151i	−0.0671398	+	0.0835065i
$671$	2.28745	+	7.04003i	0.0883059	+	0.271777i
$672$	0.0191304	+	0.417578i	0.000737970	+	0.0161084i
$673$	36.0609	+	26.1998i	1.39004	+	1.00993i	0.995860	+	0.0908951i	$0.0289728\pi$
$673$	36.0609	+	26.1998i	1.39004	+	1.00993i	0.394184	+	0.919031i	$0.371027\pi$
$674$	−19.4250	+	33.6451i	−0.748222	+	1.29596i
$675$	4.97615	+	0.487829i	0.191532	+	0.0187765i
$676$	−0.390083	−	0.675644i	−0.0150032	−	0.0259863i
$677$	9.34811	−	4.16204i	0.359277	−	0.159960i	−0.219157	−	0.975690i	$-0.570331\pi$
$677$	9.34811	−	4.16204i	0.359277	−	0.159960i	0.578434	+	0.815729i	$0.303664\pi$
$678$	4.59049	+	14.1281i	0.176297	+	0.542585i
$679$	−12.4334	+	7.95851i	−0.477149	+	0.305420i
$680$	−6.49914	−	40.1247i	−0.249231	−	1.53871i
$681$	2.57009	+	2.85438i	0.0984862	+	0.109380i
$682$	−0.900462	−	1.55965i	−0.0344805	−	0.0597219i
$683$	−38.6017	+	8.20504i	−1.47705	+	0.313957i	−0.874853	−	0.484389i	$-0.839042\pi$
$683$	−38.6017	+	8.20504i	−1.47705	+	0.313957i	−0.602199	+	0.798346i	$0.705709\pi$
$684$	−0.000492407	−	0.00468494i	−1.88277e−5	−	0.000179133i
$685$	20.6539	+	3.19721i	0.789144	+	0.122159i
$686$	24.4308	+	9.93565i	0.932772	+	0.379345i
$687$	−1.59307	+	1.15743i	−0.0607794	+	0.0441588i
$688$	0.512473	+	4.87586i	0.0195379	+	0.185890i
$689$	7.62274	−	72.5256i	0.290403	−	2.76300i
$690$	9.28994	+	23.9503i	0.353662	+	0.911772i
$691$	0.707828	+	6.73454i	0.0269271	+	0.256194i	0.999701	+	0.0244391i	$0.00777999\pi$
$691$	0.707828	+	6.73454i	0.0269271	+	0.256194i	−0.972774	+	0.231755i	$0.925553\pi$
$692$	0.156226	−	0.480815i	0.00593884	−	0.0182779i
$693$	0.450908	+	1.72821i	0.0171286	+	0.0656494i
$694$	−2.70318	+	8.31954i	−0.102611	+	0.315805i
$695$	−0.315219	−	0.119738i	−0.0119570	−	0.00454190i
$696$	14.8339	−	16.4747i	0.562278	−	0.624473i
$697$	−41.1935	+	45.7500i	−1.56032	+	1.73291i
$698$	−27.7148	+	12.3394i	−1.04902	+	0.467055i
$699$	21.8365			0.825930
$700$	0.368989	−	0.0194931i	0.0139465	−	0.000736770i
$701$	−9.13985			−0.345207			−0.172604	−	0.984991i	$-0.555218\pi$
$701$	−9.13985			−0.345207			−0.172604	+	0.984991i	$0.555218\pi$
$702$	8.32306	−	3.70567i	0.314134	−	0.139861i
$703$	0.403542	−	0.448178i	0.0152199	−	0.0169034i
$704$	3.56181	−	3.95580i	0.134241	−	0.149090i
$705$	−0.577560	+	0.718352i	−0.0217521	+	0.0270547i
$706$	5.99217	−	18.4420i	0.225518	−	0.694074i
$707$	2.60591	−	2.57185i	0.0980055	−	0.0967243i
$708$	0.0831182	−	0.255811i	0.00312377	−	0.00961398i
$709$	−3.01899	−	28.7238i	−0.113381	−	1.07874i	−0.892245	−	0.451551i	$-0.850871\pi$
$709$	−3.01899	−	28.7238i	−0.113381	−	1.07874i	0.778865	−	0.627192i	$-0.215796\pi$
$710$	−19.1196	−	12.3215i	−0.717545	−	0.462417i
$711$	−0.412461	+	3.92430i	−0.0154685	+	0.147173i
$712$	1.48071	+	14.0880i	0.0554919	+	0.527970i
$713$	12.2267	−	8.88325i	0.457895	−	0.332680i
$714$	−24.1124	+	3.65658i	−0.902384	+	0.136844i
$715$	6.85267	+	6.80488i	0.256275	+	0.254488i
$716$	0.0493895	+	0.469910i	0.00184577	+	0.0175614i
$717$	−9.44325	+	2.00723i	−0.352665	+	0.0749612i
$718$	8.15317	+	14.1217i	0.304274	+	0.527017i
$719$	−2.21053	−	2.45504i	−0.0824388	−	0.0915575i	0.700514	−	0.713639i	$-0.252954\pi$
$719$	−2.21053	−	2.45504i	−0.0824388	−	0.0915575i	−0.782953	+	0.622081i	$0.786287\pi$
$720$	−8.06470	+	4.14478i	−0.300553	+	0.154467i
$721$	−0.473918	−	10.3447i	−0.0176496	−	0.385256i
$722$	8.34857	+	25.6943i	0.310702	+	0.956241i
$723$	18.7232	−	8.33609i	0.696322	−	0.310022i
$724$	0.306600	+	0.531048i	0.0113947	+	0.0197362i
$725$	−29.5160	−	26.2046i	−1.09620	−	0.973215i
$726$	7.50782	−	13.0039i	0.278641	−	0.482621i
$727$	−20.4712	−	14.8732i	−0.759235	−	0.551616i	0.139441	−	0.990230i	$-0.455469\pi$
$727$	−20.4712	−	14.8732i	−0.759235	−	0.551616i	−0.898675	+	0.438614i	$0.855469\pi$
$728$	−40.0366	+	25.6272i	−1.48386	+	0.949807i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−6.66775	−	10.1892i	−0.246785	−	0.377119i
$731$	−7.65496	+	1.62711i	−0.283129	+	0.0601809i
$732$	0.153140	+	0.265247i	0.00566023	+	0.00980380i
$733$	−32.2478	−	35.8148i	−1.19110	−	1.32285i	−0.934343	−	0.356376i	$-0.884012\pi$
$733$	−32.2478	−	35.8148i	−1.19110	−	1.32285i	−0.256758	−	0.966476i	$-0.582654\pi$
$734$	−23.5269	+	17.0933i	−0.868392	+	0.630924i
$735$	0.668171	+	15.6382i	0.0246458	+	0.576824i
$736$	−1.03118	−	0.749197i	−0.0380098	−	0.0276158i
$737$	−0.0614612	−	0.584764i	−0.00226395	−	0.0215401i
$738$	12.3729	+	5.50879i	0.455454	+	0.202781i
$739$	−2.37838	+	22.6288i	−0.0874903	+	0.832415i	0.859496	+	0.511142i	$0.170777\pi$
$739$	−2.37838	+	22.6288i	−0.0874903	+	0.832415i	−0.946987	+	0.321273i	$0.895889\pi$
$740$	0.208788	+	0.0793089i	0.00767519	+	0.00291545i
$741$	0.872919	−	0.634213i	0.0320675	−	0.0232984i
$742$	42.8718	+	2.52975i	1.57387	+	0.0928700i
$743$	−10.5580			−0.387336			−0.193668	−	0.981067i	$-0.562038\pi$
$743$	−10.5580			−0.387336			−0.193668	+	0.981067i	$0.562038\pi$
$744$	3.52029	+	3.90968i	0.129060	+	0.143336i
$745$	8.50854	−	32.2046i	0.311729	−	1.17989i
$746$	11.6575	−	12.9470i	0.426811	−	0.474022i
$747$	8.23634	+	1.75069i	0.301352	+	0.0640544i
$748$	−0.0987436	−	0.0717414i	−0.00361042	−	0.00262313i
$749$	−16.7632	−	4.61011i	−0.612515	−	0.168450i
$750$	7.37669	+	14.1094i	0.269359	+	0.515203i
$751$	−4.23026	+	7.32703i	−0.154365	+	0.267367i	−0.932827	−	0.360323i	$-0.882666\pi$
$751$	−4.23026	+	7.32703i	−0.154365	+	0.267367i	0.778463	+	0.627691i	$0.216000\pi$
$752$	0.174726	−	1.66241i	0.00637160	−	0.0606218i
$753$	7.68876	−	8.53923i	0.280194	−	0.311187i
$754$	−70.3483	−	14.9530i	−2.56193	−	0.544556i
$755$	−19.0362	−	18.9034i	−0.692798	−	0.687966i
$756$	0.0331163	+	0.0660654i	0.00120443	+	0.00240278i
$757$	−17.8202			−0.647686			−0.323843	−	0.946111i	$-0.604975\pi$
$757$	−17.8202			−0.647686			−0.323843	+	0.946111i	$0.604975\pi$
$758$	−24.0795	−	26.7430i	−0.874605	−	0.971348i
$759$	−4.97523	−	2.21511i	−0.180589	−	0.0804036i
$760$	−0.820712	+	0.669369i	−0.0297704	+	0.0242805i
$761$	−40.6300	+	18.0897i	−1.47284	+	0.655750i	−0.977111	−	0.212729i	$-0.931765\pi$
$761$	−40.6300	+	18.0897i	−1.47284	+	0.655750i	−0.495727	+	0.868478i	$0.665098\pi$
$762$	−14.5659	+	10.5828i	−0.527667	+	0.383373i
$763$	0.589559	−	3.57014i	0.0213435	−	0.129248i
$764$	0.568486	+	0.413029i	0.0205671	+	0.0149429i
$765$	−7.92551	−	12.1112i	−0.286547	−	0.437882i
$766$	36.3859	+	16.2001i	1.31468	+	0.585332i
$767$	60.2621	−	12.8091i	2.17594	−	0.462510i
$768$	0.335117	−	0.580440i	0.0120925	−	0.0209448i
$769$	1.75581	−	5.40383i	0.0633162	−	0.194867i	−0.914394	−	0.404825i	$-0.867333\pi$
$769$	1.75581	−	5.40383i	0.0633162	−	0.194867i	0.977711	+	0.209957i	$0.0673325\pi$
$770$	−3.81858	+	4.21478i	−0.137612	+	0.151890i
$771$	−4.51356	−	13.8913i	−0.162552	−	0.500284i
$772$	−0.142429	−	0.0302742i	−0.00512613	−	0.00108959i
$773$	1.34412	−	12.7884i	0.0483445	−	0.459967i	−0.943392	−	0.331679i	$-0.892385\pi$
$773$	1.34412	−	12.7884i	0.0483445	−	0.459967i	0.991737	−	0.128288i	$-0.0409483\pi$
$774$	0.860862	+	1.49106i	0.0309430	+	0.0535949i
$775$	6.91682	−	6.31615i	0.248460	−	0.226883i
$776$	15.6695			0.562501
$777$	−3.44855	+	8.81010i	−0.123716	+	0.316060i
$778$	−1.80984	−	5.57011i	−0.0648858	−	0.199698i
$779$	1.56895	+	0.333492i	0.0562136	+	0.0119486i
$780$	0.335882	+	0.216457i	0.0120265	+	0.00775040i
$781$	4.71678	−	1.00258i	0.168780	−	0.0358752i
$782$	37.1820	−	64.4011i	1.32962	−	2.30298i
$783$	2.43938	−	7.50762i	0.0871762	−	0.268301i
$784$	−16.3810	−	23.1820i	−0.585036	−	0.827927i
$785$	18.2179	+	18.0909i	0.650225	+	0.645690i
$786$	−17.2764	+	7.69196i	−0.616229	+	0.274363i
$787$	45.1119	+	20.0851i	1.60807	+	0.715957i	0.997129	−	0.0757225i	$-0.0241263\pi$
$787$	45.1119	+	20.0851i	1.60807	+	0.715957i	0.610937	+	0.791679i	$0.290793\pi$
$788$	−0.220759	−	0.0982884i	−0.00786423	−	0.00350138i
$789$	−23.9793	+	10.6763i	−0.853686	+	0.380086i
$790$	−11.1754	+	5.74350i	−0.397603	+	0.204344i
$791$	−21.3340	−	17.5096i	−0.758549	−	0.622569i
$792$	0.585841	−	1.80303i	0.0208170	−	0.0640680i
$793$	−35.0764	+	60.7542i	−1.24560	+	2.15744i
$794$	−18.0195	+	3.83016i	−0.639488	+	0.135927i
$795$	9.21728	+	23.7630i	0.326903	+	0.842785i
$796$	0.0976353	+	0.0207530i	0.00346059	+	0.000735571i
$797$	2.61672	+	8.05342i	0.0926888	+	0.285267i	0.986644	−	0.162889i	$-0.0520811\pi$
$797$	2.61672	+	8.05342i	0.0926888	+	0.285267i	−0.893956	+	0.448155i	$0.852081\pi$
$798$	0.396630	+	0.496440i	0.0140405	+	0.0175738i
$799$	2.66824			0.0943956
$800$	−0.686886	−	0.390190i	−0.0242851	−	0.0137953i
$801$	2.52207	+	4.36835i	0.0891129	+	0.154348i
$802$	2.28873	−	21.7758i	0.0808178	−	0.768930i
$803$	2.52512	+	0.536730i	0.0891094	+	0.0189408i
$804$	−0.00751795	−	0.0231379i	−0.000265138	−	0.000816010i
$805$	−38.5257	−	28.1722i	−1.35785	−	0.992941i
$806$	5.27418	−	16.2323i	0.185775	−	0.571757i
$807$	−4.15460	+	7.19597i	−0.146249	+	0.253310i
$808$	−3.80137	+	0.808007i	−0.133732	+	0.0284256i
$809$	−14.1841	−	6.31517i	−0.498687	−	0.222030i	0.141950	−	0.989874i	$-0.454663\pi$
$809$	−14.1841	−	6.31517i	−0.498687	−	0.222030i	−0.640637	+	0.767844i	$0.721330\pi$
$810$	−1.99526	+	2.48165i	−0.0701064	+	0.0871963i
$811$	−3.34984	−	2.43380i	−0.117629	−	0.0854624i	0.527415	−	0.849608i	$-0.323161\pi$
$811$	−3.34984	−	2.43380i	−0.117629	−	0.0854624i	−0.645044	+	0.764145i	$0.723161\pi$
$812$	0.0950483	−	0.575577i	0.00333554	−	0.0201988i
$813$	−8.06535	+	5.85982i	−0.282864	+	0.205513i
$814$	−3.14046	+	1.39822i	−0.110073	+	0.0490077i
$815$	9.22252	+	23.7765i	0.323051	+	0.832853i
$816$	23.9790	+	10.6762i	0.839435	+	0.373740i
$817$	0.136439	+	0.151530i	0.00477338	+	0.00530138i
$818$	11.3177			0.395713
$819$	−9.31221	+	14.1351i	−0.325395	+	0.493919i
$820$	0.0949777	+	0.586378i	0.00331677	+	0.0204772i
$821$	−22.2878	−	4.73741i	−0.777849	−	0.165337i	−0.198154	−	0.980171i	$-0.563495\pi$
$821$	−22.2878	−	4.73741i	−0.777849	−	0.165337i	−0.579694	+	0.814834i	$0.696828\pi$
$822$	−8.90628	+	9.89143i	−0.310642	+	0.345003i
$823$	−0.659363	+	6.27342i	−0.0229839	+	0.218678i	0.977001	+	0.213234i	$0.0683996\pi$
$823$	−0.659363	+	6.27342i	−0.0229839	+	0.218678i	−0.999985	+	0.00544401i	$0.998267\pi$
$824$	−5.49594	+	9.51925i	−0.191460	+	0.331619i
$825$	−3.21737	−	1.02055i	−0.112015	−	0.0355310i
$826$	9.15966	+	35.1066i	0.318705	+	1.22151i
$827$	5.63678	+	4.09536i	0.196010	+	0.142410i	0.681461	−	0.731854i	$-0.261345\pi$
$827$	5.63678	+	4.09536i	0.196010	+	0.142410i	−0.485451	+	0.874264i	$0.661345\pi$
$828$	−0.220414	−	0.0468503i	−0.00765990	−	0.00162816i
$829$	−3.44077	+	3.82136i	−0.119503	+	0.132721i	−0.799927	−	0.600097i	$-0.795129\pi$
$829$	−3.44077	+	3.82136i	−0.119503	+	0.132721i	0.680425	+	0.732818i	$0.261795\pi$
$830$	9.69638	+	24.9981i	0.336566	+	0.867697i
$831$	15.8650	+	17.6199i	0.550350	+	0.611226i
$832$	50.4473			1.74894
$833$	34.0684	−	29.8730i	1.18040	−	1.03504i
$834$	0.173732	−	0.126224i	0.00601585	−	0.00437077i
$835$	−1.36833	+	27.9825i	−0.0473531	+	0.968376i
$836$	−0.000332410		0.00316267i	−1.14966e−5		0.000109383i
$837$	1.71139	+	0.761961i	0.0591544	+	0.0263372i
$838$	0.804697	+	7.65618i	0.0277978	+	0.264478i
$839$	−6.52913	−	4.74369i	−0.225411	−	0.163770i	0.469348	−	0.883013i	$-0.344489\pi$
$839$	−6.52913	−	4.74369i	−0.225411	−	0.163770i	−0.694759	+	0.719243i	$0.744489\pi$
$840$	8.35144	−	14.3628i	0.288152	−	0.495563i
$841$	−26.9524	+	19.5821i	−0.929393	+	0.675243i
$842$	−7.48468	−	8.31258i	−0.257939	−	0.286470i
$843$	−3.89383	−	6.74431i	−0.134111	−	0.232286i
$844$	−0.445639	+	0.0947236i	−0.0153395	+	0.00326052i
$845$	−3.05041	+	62.3812i	−0.104937	+	2.14598i
$846$	−0.181398	−	0.558286i	−0.00623659	−	0.0191943i
$847$	1.27672	+	27.8683i	0.0438687	+	0.957567i
$848$	−37.3945	−	27.1687i	−1.28413	−	0.932977i
$849$	7.17999	−	12.4361i	0.246416	−	0.426806i
$850$	18.4510	−	42.2347i	0.632865	−	1.44864i
$851$	−14.4242	−	24.9834i	−0.494455	−	0.856421i
$852$	0.182273	−	0.0811532i	0.00624457	−	0.00278026i
$853$	−11.2884	−	34.7421i	−0.386507	−	1.18955i	−0.935381	−	0.353641i	$-0.884944\pi$
$853$	−11.2884	−	34.7421i	−0.386507	−	1.18955i	0.548875	−	0.835905i	$-0.315056\pi$
$854$	−36.6867	−	18.9978i	−1.25539	−	0.650093i
$855$	−0.170030	+	0.336610i	−0.00581491	+	0.0115118i
$856$	12.3481	+	13.7139i	0.422049	+	0.468733i
$857$	7.51479	+	13.0160i	0.256700	+	0.444618i	0.965356	−	0.260937i	$-0.0840314\pi$
$857$	7.51479	+	13.0160i	0.256700	+	0.444618i	−0.708656	+	0.705554i	$0.750698\pi$
$858$	−6.01598	+	1.27874i	−0.205382	+	0.0436554i
$859$	3.43365	+	32.6690i	0.117155	+	1.11465i	0.882265	+	0.470753i	$0.156018\pi$
$859$	3.43365	+	32.6690i	0.117155	+	1.11465i	−0.765110	+	0.643899i	$0.777316\pi$
$860$	−0.0340465	+	0.0674021i	−0.00116098	+	0.00229839i
$861$	−24.8787	+	3.77279i	−0.847864	+	0.128576i
$862$	−9.25630	+	6.72510i	−0.315271	+	0.229058i
$863$	−1.03465	−	9.84407i	−0.0352200	−	0.335096i	−0.997917	−	0.0645137i	$-0.979450\pi$
$863$	−1.03465	−	9.84407i	−0.0352200	−	0.335096i	0.962697	−	0.270582i	$-0.0872163\pi$
$864$	0.0165150	−	0.157130i	0.000561851	−	0.00534566i
$865$	−31.3635	+	25.5799i	−1.06639	+	0.869743i
$866$	−3.73821	−	35.5667i	−0.127030	−	1.20861i
$867$	−7.69422	+	23.6804i	−0.261310	+	0.804228i
$868$	0.133486	+	0.0367105i	0.00453082	+	0.00124604i
$869$	0.823151	−	2.53340i	0.0279235	−	0.0859397i
$870$	24.2573	−	6.59078i	0.822398	−	0.223448i
$871$	3.72867	−	4.14111i	0.126341	−	0.140316i
$872$	−2.57003	+	2.85431i	−0.0870323	+	0.0966591i
$873$	5.09725	−	2.26944i	0.172516	−	0.0768090i
$874$	−1.93754			−0.0655382
$875$	−25.6751	−	14.6897i	−0.867978	−	0.496602i
$876$	0.106814			0.00360891
$877$	−16.0023	+	7.12468i	−0.540359	+	0.240583i	−0.658721	−	0.752387i	$-0.728902\pi$
$877$	−16.0023	+	7.12468i	−0.540359	+	0.240583i	0.118362	+	0.992970i	$0.462236\pi$
$878$	38.2095	−	42.4360i	1.28951	−	1.43214i
$879$	−8.40775	+	9.33776i	−0.283586	+	0.314955i
$880$	5.90701	−	1.60495i	0.199125	−	0.0541030i
$881$	−11.3918	+	35.0603i	−0.383799	+	1.18121i	0.553548	+	0.832817i	$0.313273\pi$
$881$	−11.3918	+	35.0603i	−0.383799	+	1.18121i	−0.937348	+	0.348396i	$0.886727\pi$
$882$	−8.56654	−	5.09735i	−0.288451	−	0.171637i
$883$	−6.13201	+	18.8724i	−0.206359	+	0.635107i	0.793296	+	0.608836i	$0.208363\pi$
$883$	−6.13201	+	18.8724i	−0.206359	+	0.635107i	−0.999655	+	0.0262707i	$0.991637\pi$
$884$	−0.120910	−	1.15038i	−0.00406665	−	0.0386916i
$885$	−16.6865	+	13.6094i	−0.560912	+	0.457476i
$886$	3.49378	−	33.2411i	0.117376	−	1.11676i
$887$	2.00188	+	19.0467i	0.0672167	+	0.639524i	0.975323	+	0.220784i	$0.0708615\pi$
$887$	2.00188	+	19.0467i	0.0672167	+	0.639524i	−0.908106	+	0.418740i	$0.862472\pi$
$888$	8.12445	−	5.90276i	0.272639	−	0.198084i
$889$	12.1928	−	31.1492i	0.408933	−	1.04471i
$890$	−7.24185	+	14.3367i	−0.242747	+	0.480568i
$891$	−0.0705641	−	0.671372i	−0.00236399	−	0.0224918i
$892$	−0.558329	+	0.118676i	−0.0186942	+	0.00397358i
$893$	−0.0347603	−	0.0602066i	−0.00116321	−	0.00201474i
$894$	14.1946	+	15.7647i	0.474738	+	0.527250i
$895$	17.0544	−	33.7627i	0.570066	−	1.12856i
$896$	1.39788	+	30.5130i	0.0466999	+	1.01937i
$897$	−15.9493	−	49.0870i	−0.532533	−	1.63897i
$898$	38.8474	−	17.2960i	1.29635	−	0.577174i
$899$	−7.39410	−	12.8070i	−0.246607	−	0.427136i
$900$	−0.138993	−	0.0136260i	−0.00463310	−	0.000454199i
$901$	36.8912	−	63.8974i	1.22902	−	2.12873i
$902$	−7.39690	−	5.37416i	−0.246290	−	0.178940i
$903$	−2.84053	−	1.47094i	−0.0945268	−	0.0489498i
$904$	9.05275	+	27.8615i	0.301090	+	0.926660i
$905$	2.39758	−	49.0308i	0.0796983	−	1.62984i
$906$	16.7119	−	3.55223i	0.555217	−	0.118015i
$907$	−9.12115	−	15.7983i	−0.302863	−	0.524574i	0.673920	−	0.738804i	$-0.264609\pi$
$907$	−9.12115	−	15.7983i	−0.302863	−	0.524574i	−0.976783	+	0.214230i	$0.931276\pi$
$908$	−0.0717876	−	0.0797282i	−0.00238235	−	0.00264587i
$909$	−1.11955	+	0.813404i	−0.0371333	+	0.0269789i
$910$	−53.8995	−	0.166004i	−1.78675	−	0.00550299i
$911$	34.2026	+	24.8497i	1.13318	+	0.823306i	0.986155	−	0.165827i	$-0.0530292\pi$
$911$	34.2026	+	24.8497i	1.13318	+	0.823306i	0.147028	+	0.989132i	$0.453029\pi$
$912$	−0.0714865	−	0.680149i	−0.00236716	−	0.0225220i
$913$	−5.19289	−	2.31203i	−0.171860	−	0.0765169i
$914$	0.0556703	−	0.529667i	0.00184141	−	0.0175198i
$915$	1.19754	−	24.4898i	0.0395895	−	0.809608i
$916$	0.0444974	−	0.0323293i	0.00147024	−	0.00106819i
$917$	19.3296	−	29.3406i	0.638320	−	0.968910i
$918$	9.21783			0.304234
$919$	22.4188	+	24.8986i	0.739527	+	0.821328i	0.989134	−	0.147019i	$-0.0469679\pi$
$919$	22.4188	+	24.8986i	0.739527	+	0.821328i	−0.249606	+	0.968347i	$0.580301\pi$
$920$	18.3204	+	47.2316i	0.604006	+	1.55718i
$921$	16.8755	−	18.7421i	0.556066	−	0.617574i
$922$	49.7614	+	10.5771i	1.63881	+	0.348339i
$923$	36.9723	+	26.8619i	1.21696	+	0.884171i
$924$	−0.0125947	−	0.0482723i	−0.000414336	−	0.00158804i
$925$	−10.6103	−	14.3910i	−0.348866	−	0.473173i
$926$	−11.7059	+	20.2751i	−0.384678	+	0.666282i
$927$	−0.409127	+	3.89258i	−0.0134375	+	0.127849i
$928$	−0.834547	+	0.926858i	−0.0273953	+	0.0304256i
$929$	39.0639	+	8.30329i	1.28164	+	0.272422i	0.797901	−	0.602788i	$-0.205943\pi$
$929$	39.0639	+	8.30329i	1.28164	+	0.272422i	0.483743	+	0.875210i	$0.339277\pi$
$930$	0.953787	+	5.88854i	0.0312759	+	0.193093i
$931$	−1.11788	−	0.379555i	−0.0366371	−	0.0124394i
$932$	−0.609933			−0.0199790
$933$	4.00644	+	4.44960i	0.131165	+	0.145673i
$934$	44.3177	+	19.7315i	1.45012	+	0.645635i
$935$	3.53349	+	9.10965i	0.115557	+	0.297917i
$936$	16.4136	−	7.30783i	0.536497	−	0.238864i
$937$	−1.43523	+	1.04275i	−0.0468869	+	0.0340653i	−0.610982	−	0.791645i	$-0.709225\pi$
$937$	−1.43523	+	1.04275i	−0.0468869	+	0.0340653i	0.564095	+	0.825710i	$0.309225\pi$
$938$	2.53668	+	2.08195i	0.0828256	+	0.0679780i
$939$	−16.1033	−	11.6997i	−0.525512	−	0.381807i
$940$	0.0161323	−	0.0200649i	0.000526178	−	0.000654445i
$941$	−14.1201	−	6.28666i	−0.460301	−	0.204939i	0.163467	−	0.986549i	$-0.447732\pi$
$941$	−14.1201	−	6.28666i	−0.460301	−	0.204939i	−0.623768	+	0.781609i	$0.714399\pi$
$942$	−15.9936	+	3.39954i	−0.521098	+	0.110763i
$943$	38.3636	−	66.4478i	1.24929	−	2.16384i
$944$	12.0669	−	37.1381i	0.392744	−	1.20874i
$945$	0.636517	−	5.88174i	0.0207059	−	0.191333i
$946$	−0.359166	−	1.10540i	−0.0116775	−	0.0359396i
$947$	17.4996	+	3.71965i	0.568660	+	0.120872i	0.483264	−	0.875475i	$-0.339451\pi$
$947$	17.4996	+	3.71965i	0.568660	+	0.120872i	0.0853959	+	0.996347i	$0.472784\pi$
$948$	0.0115208	−	0.109613i	0.000374178	−	0.00356007i
$949$	12.2327	+	21.1877i	0.397092	+	0.687783i
$950$	−1.19336	+	0.133877i	−0.0387176	+	0.00434356i
$951$	−6.25947			−0.202977
$952$	−47.5513	+	7.21102i	−1.54115	+	0.233711i
$953$	3.04671	+	9.37681i	0.0986926	+	0.303745i	0.988198	−	0.153179i	$-0.0489512\pi$
$953$	3.04671	+	9.37681i	0.0986926	+	0.303745i	−0.889506	+	0.456924i	$0.848951\pi$
$954$	−15.8775	−	3.37486i	−0.514052	−	0.109265i
$955$	−20.3430	−	52.4460i	−0.658284	−	1.69711i
$956$	0.263768	−	0.0560656i	0.00853086	−	0.00181329i
$957$	−2.66450	+	4.61505i	−0.0861310	+	0.149183i
$958$	−2.90403	+	8.93770i	−0.0938251	+	0.288764i
$959$	4.02909	−	24.3986i	0.130106	−	0.787873i
$960$	−15.6819	+	8.05959i	−0.506132	+	0.260122i
$961$	−25.1139	+	11.1814i	−0.810125	+	0.360691i
$962$	−29.7626	−	13.2512i	−0.959585	−	0.427235i
$963$	6.00303	+	2.67272i	0.193445	+	0.0861273i
$964$	−0.522973	+	0.232843i	−0.0168438	+	0.00749935i
$965$	8.27138	+	8.21369i	0.266265	+	0.264408i
$966$	28.4477	−	10.7058i	0.915290	−	0.344455i
$967$	−3.47462	+	10.6938i	−0.111736	+	0.343889i	−0.991252	−	0.131980i	$-0.957866\pi$
$967$	−3.47462	+	10.6938i	−0.111736	+	0.343889i	0.879516	+	0.475869i	$0.157866\pi$
$968$	14.8059	−	25.6446i	0.475880	−	0.824249i
$969$	1.06782	−	0.226971i	0.0343032	−	0.00729137i
$970$	14.9346	+	9.62448i	0.479520	+	0.309023i
$971$	−6.56765	−	1.39600i	−0.210766	−	0.0447997i	0.101319	−	0.994854i	$-0.467694\pi$
$971$	−6.56765	−	1.39600i	−0.210766	−	0.0447997i	−0.312084	+	0.950054i	$0.601027\pi$
$972$	−0.00863142	−	0.0265648i	−0.000276853	−	0.000852066i
$973$	−0.145427	+	0.371526i	−0.00466218	+	0.0119106i
$974$	38.5459			1.23509
$975$	−13.2152	−	29.1313i	−0.423224	−	0.932950i
$976$	22.2325	+	38.5079i	0.711646	+	1.23261i
$977$	0.771638	−	7.34165i	0.0246869	−	0.234880i	−0.975220	−	0.221237i	$-0.928991\pi$
$977$	0.771638	−	7.34165i	0.0246869	−	0.234880i	0.999907	−	0.0136430i	$-0.00434282\pi$
$978$	−15.8865	−	3.37678i	−0.507994	−	0.107977i
$979$	−1.05225	−	3.23849i	−0.0336300	−	0.103502i
$980$	−0.0186633	−	0.436805i	−0.000596176	−	0.0139532i
$981$	−0.422631	+	1.30072i	−0.0134936	+	0.0415289i
$982$	−13.7807	+	23.8688i	−0.439759	+	0.761684i
$983$	−18.7384	+	3.98296i	−0.597661	+	0.127037i	−0.496802	−	0.867864i	$-0.665492\pi$
$983$	−18.7384	+	3.98296i	−0.597661	+	0.127037i	−0.100859	+	0.994901i	$0.532159\pi$
$984$	24.4003	+	10.8637i	0.777853	+	0.346322i
$985$	10.5929	+	16.1873i	0.337517	+	0.515771i
$986$	−58.8684	−	42.7704i	−1.87475	−	1.36209i
$987$	0.843035	+	0.691909i	0.0268341	+	0.0220237i
$988$	−0.0243823	+	0.0177148i	−0.000775703	+	0.000563581i
$989$	8.91047	−	3.96720i	0.283336	−	0.126149i
$990$	1.66582	−	1.35863i	0.0529433	−	0.0431802i
$991$	−1.52279	−	0.677991i	−0.0483731	−	0.0215371i	0.382408	−	0.923994i	$-0.375095\pi$
$991$	−1.52279	−	0.677991i	−0.0483731	−	0.0215371i	−0.430781	+	0.902457i	$0.641762\pi$
$992$	−0.198049	−	0.219956i	−0.00628808	−	0.00698362i
$993$	17.1182			0.543228
$994$	−14.8062	+	22.4745i	−0.469626	+	0.712848i
$995$	−5.67005	−	5.63050i	−0.179753	−	0.178499i
$996$	−0.230057	−	0.0489000i	−0.00728962	−	0.00154946i
$997$	27.4517	−	30.4881i	0.869403	−	0.965569i	−0.130262	−	0.991480i	$-0.541582\pi$
$997$	27.4517	−	30.4881i	0.869403	−	0.965569i	0.999664	+	0.0259103i	$0.00824842\pi$
$998$	1.62388	−	15.4501i	0.0514029	−	0.489066i
$999$	1.78796	−	3.09684i	0.0565685	−	0.0979795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.a.16.7	✓	160
7.4	even	3	inner	525.2.bg.a.466.14	yes	160
25.11	even	5	inner	525.2.bg.a.436.14	yes	160
175.11	even	15	inner	525.2.bg.a.361.7	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.7	✓	160	1.1	even	1	trivial
525.2.bg.a.361.7	yes	160	175.11	even	15	inner
525.2.bg.a.436.14	yes	160	25.11	even	5	inner
525.2.bg.a.466.14	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)

\(f(q)\)	\(=\)	\(q+(-1.30094 + 0.579215i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(0.0186901 - 0.0207574i) q^{4} +(-2.15784 + 0.586291i) q^{5} +(0.440057 - 1.35436i) q^{6} +(0.667942 + 2.56005i) q^{7} +(0.867823 - 2.67088i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-1.30094 + 0.579215i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(0.0186901 - 0.0207574i) q^{4} +(-2.15784 + 0.586291i) q^{5} +(0.440057 - 1.35436i) q^{6} +(0.667942 + 2.56005i) q^{7} +(0.867823 - 2.67088i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(2.46763 - 2.01258i) q^{10} +(-0.0705641 + 0.671372i) q^{11} +(0.00291968 + 0.0277789i) q^{12} +(-5.17588 + 3.76050i) q^{13} +(-2.35177 - 2.94358i) q^{14} +(1.00818 - 1.99589i) q^{15} +(0.423872 + 4.03287i) q^{16} +(-6.33150 + 1.34580i) q^{17} +(0.712027 + 1.23327i) q^{18} +(0.112850 + 0.125332i) q^{19} +(-0.0281602 + 0.0557490i) q^{20} +(-2.34943 - 1.21663i) q^{21} +(-0.297070 - 0.914286i) q^{22} +(7.36994 - 3.28131i) q^{23} +(1.40417 + 2.43209i) q^{24} +(4.31252 - 2.53024i) q^{25} +(4.55536 - 7.89012i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.0656239 + 0.0339827i) q^{28} +(-2.43938 - 7.50762i) q^{29} +(-0.155524 + 3.18048i) q^{30} +(1.83241 - 0.389492i) q^{31} +(-0.0789975 - 0.136828i) q^{32} +(-0.451710 - 0.501675i) q^{33} +(7.45738 - 5.41810i) q^{34} +(-2.94225 - 5.13256i) q^{35} +(-0.0225974 - 0.0164179i) q^{36} +(-0.373785 - 3.55633i) q^{37} +(-0.219405 - 0.0976854i) q^{38} +(0.668746 - 6.36269i) q^{39} +(-0.306704 + 6.27213i) q^{40} +(7.69438 - 5.59030i) q^{41} +(3.76115 + 0.221936i) q^{42} +1.20903 q^{43} +(0.0126171 + 0.0140127i) q^{44} +(0.808635 + 2.08473i) q^{45} +(-7.68725 + 8.53756i) q^{46} +(-0.403207 - 0.0857042i) q^{47} +(-3.28063 - 2.38352i) q^{48} +(-6.10771 + 3.41993i) q^{49} +(-4.14477 + 5.78957i) q^{50} +(3.23647 - 5.60574i) q^{51} +(-0.0186793 + 0.177722i) q^{52} +(-7.62713 + 8.47079i) q^{53} +(-1.39294 - 0.296078i) q^{54} +(-0.241354 - 1.49008i) q^{55} +(7.41725 + 0.437672i) q^{56} -0.168651 q^{57} +(7.52201 + 8.35404i) q^{58} +(-8.79719 - 3.91676i) q^{59} +(-0.0225867 - 0.0582305i) q^{60} +(10.0173 - 4.45998i) q^{61} +(-2.15826 + 1.56807i) q^{62} +(2.47621 - 0.931881i) q^{63} +(-6.37924 - 4.63479i) q^{64} +(8.96396 - 11.1491i) q^{65} +(0.878225 + 0.391011i) q^{66} +(-0.851965 + 0.181091i) q^{67} +(-0.0904008 + 0.156579i) q^{68} +(-2.49296 + 7.67256i) q^{69} +(6.80054 + 4.97295i) q^{70} +(-2.20737 - 6.79358i) q^{71} +(-2.74696 - 0.583885i) q^{72} +(0.399726 - 3.80314i) q^{73} +(2.54615 + 4.41006i) q^{74} +(-1.00531 + 4.89789i) q^{75} +0.00471075 q^{76} +(-1.76588 + 0.267791i) q^{77} +(2.81537 + 8.66482i) q^{78} +(-3.85969 - 0.820403i) q^{79} +(-3.27908 - 8.45376i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-6.77194 + 11.7293i) q^{82} +(-2.60203 + 8.00823i) q^{83} +(-0.0691651 + 0.0260292i) q^{84} +(12.8733 - 6.61612i) q^{85} +(-1.57287 + 0.700288i) q^{86} +(7.21151 + 3.21077i) q^{87} +(1.73192 + 0.771101i) q^{88} +(-4.60805 + 2.05163i) q^{89} +(-2.25949 - 2.24374i) q^{90} +(-13.0842 - 10.7387i) q^{91} +(0.0696332 - 0.214309i) q^{92} +(-0.936676 + 1.62237i) q^{93} +(0.574188 - 0.122048i) q^{94} +(-0.316993 - 0.204284i) q^{95} +(0.154542 + 0.0328490i) q^{96} +(1.72420 + 5.30655i) q^{97} +(5.96487 - 7.98680i) q^{98} +0.675071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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