LMFDB - Embedded newform 525.2.bg.a.361.7

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			361.7
Character	$\chi$	$=$	525.361
Dual form			525.2.bg.a.16.7

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.108528	−	0.994093i	$-0.534614\pi$
$2$	−1.30094	−	0.579215i	−0.919903	−	0.409567i	−0.811375	+	0.584526i	$0.801280\pi$
$3$	−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	0.978720	−	0.205199i	$-0.0657841\pi$
$11$	−0.0705641	−	0.671372i	−0.0212759	−	0.202426i	−0.999996	+	0.00277253i	$0.999117\pi$
$12$	0.00291968	−	0.0277789i	0.000842838	−	0.00801907i
$13$	−5.17588	−	3.76050i	−1.43553	−	1.04297i	−0.988953	−	0.148229i	$-0.952643\pi$
$13$	−5.17588	−	3.76050i	−1.43553	−	1.04297i	−0.446577	−	0.894745i	$-0.647357\pi$
$14$	−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	−0.638996	−	0.769210i	$-0.720650\pi$
$17$	−6.33150	−	1.34580i	−1.53561	−	0.326405i	−0.896618	+	0.442806i	$0.853983\pi$
$18$	0.712027	−	1.23327i	0.167826	−	0.290684i
$19$	0.112850	−	0.125332i	0.0258895	−	0.0287532i	−0.730061	−	0.683382i	$-0.760508\pi$
$19$	0.112850	−	0.125332i	0.0258895	−	0.0287532i	0.755951	+	0.654629i	$0.227175\pi$
$20$	−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	0.988374	−	0.152040i	$-0.0485842\pi$
$23$	7.36994	+	3.28131i	1.53674	+	0.684200i	0.548364	+	0.836240i	$0.315251\pi$
$24$	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	0.420509	+	0.907288i	$0.361851\pi$
$29$	−2.43938	+	7.50762i	−0.452981	+	1.39413i	−0.873490	+	0.486843i	$0.838149\pi$
$30$	−0.155524	−	3.18048i	−0.0283947	−	0.580674i
$31$	1.83241	+	0.389492i	0.329111	+	0.0699548i	0.369504	−	0.929229i	$-0.379528\pi$
$31$	1.83241	+	0.389492i	0.329111	+	0.0699548i	−0.0403927	+	0.999184i	$0.512861\pi$
$32$	−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	0.919863	+	0.392239i	$0.128299\pi$
$37$	−0.373785	+	3.55633i	−0.0614499	+	0.584657i	−0.981313	+	0.192418i	$0.938367\pi$
$38$	−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	0.994447	−	0.105238i	$-0.0335605\pi$
$41$	7.69438	+	5.59030i	1.20166	+	0.873058i	0.207214	+	0.978296i	$0.433560\pi$
$42$	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	−0.237225	−	0.971455i	$-0.576238\pi$
$47$	−0.403207	+	0.0857042i	−0.0588137	+	0.0125012i	0.178411	+	0.983956i	$0.442904\pi$
$48$	−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	−0.986220	−	0.165442i	$-0.947095\pi$
$53$	−7.62713	−	8.47079i	−1.04767	−	1.16355i	−0.0614474	−	0.998110i	$-0.519572\pi$
$54$	−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	−0.889556	−	0.456827i	$-0.848986\pi$
$59$	−8.79719	+	3.91676i	−1.14530	+	0.509919i	−0.255740	+	0.966746i	$0.582319\pi$
$60$	−0.0225867	+	0.0582305i	−0.00291593	+	0.00751752i
$61$	10.0173	+	4.45998i	1.28258	+	0.571041i	0.930967	−	0.365104i	$-0.118967\pi$
$61$	10.0173	+	4.45998i	1.28258	+	0.571041i	0.351613	+	0.936145i	$0.385633\pi$
$62$	−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	0.155575	−	0.987824i	$-0.450277\pi$
$67$	−0.851965	−	0.181091i	−0.104084	−	0.0221237i	−0.259659	+	0.965700i	$0.583610\pi$
$68$	−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	0.730411	+	0.683008i	$0.239329\pi$
$71$	−2.20737	+	6.79358i	−0.261966	+	0.806249i	−0.992377	+	0.123241i	$0.960671\pi$
$72$	−2.74696	+	0.583885i	−0.323733	+	0.0688115i
$73$	0.399726	+	3.80314i	0.0467844	+	0.445124i	0.992691	+	0.120684i	$0.0385089\pi$
$73$	0.399726	+	3.80314i	0.0467844	+	0.445124i	−0.945907	+	0.324439i	$0.894824\pi$
$74$	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	−0.419849	−	0.907594i	$-0.637917\pi$
$79$	−3.85969	+	0.820403i	−0.434249	+	0.0923025i	−0.0143999	+	0.999896i	$0.504584\pi$
$80$	−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	−0.986215	−	0.165468i	$-0.947087\pi$
$83$	−2.60203	−	8.00823i	−0.285610	−	0.879017i	0.700605	−	0.713549i	$-0.252913\pi$
$84$	−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	0.147707	−	0.989031i	$-0.452811\pi$
$89$	−4.60805	−	2.05163i	−0.488452	−	0.217473i	−0.636158	+	0.771558i	$0.719478\pi$
$90$	−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	−0.824570	−	0.565760i	$-0.808583\pi$
$97$	1.72420	−	5.30655i	0.175066	−	0.538799i	0.999636	+	0.0269611i	$0.00858302\pi$
$98$	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	−0.898395	−	0.439189i	$-0.855266\pi$
$101$	−0.691922	+	1.19844i	−0.0688489	+	0.119250i	0.829546	+	0.558438i	$0.188599\pi$
$102$	−0.963526	−	9.16733i	−0.0954032	−	0.907701i
$103$	−3.82849	+	0.813772i	−0.377233	+	0.0801833i	−0.392626	−	0.919698i	$-0.628433\pi$
$103$	−3.82849	+	0.813772i	−0.377233	+	0.0801833i	0.0153933	+	0.999882i	$0.495100\pi$
$104$	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	0.662365	−	0.749182i	$-0.269553\pi$
$107$	−3.28557	−	5.69077i	−0.317628	−	0.550148i	−0.979993	+	0.199034i	$0.936220\pi$
$108$	0.0273215	+	0.00580736i	0.00262901	+	0.000558814i
$109$	−1.24942	+	0.556279i	−0.119673	+	0.0532818i	−0.465700	−	0.884943i	$-0.654197\pi$
$109$	−1.24942	+	0.556279i	−0.119673	+	0.0532818i	0.346027	+	0.938225i	$0.387531\pi$
$110$	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	0.115215	−	0.993341i	$-0.463244\pi$
$113$	−8.43932	−	6.13152i	−0.793904	−	0.576805i	−0.909120	+	0.416535i	$0.863244\pi$
$114$	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	−0.940414	−	0.340030i	$-0.889563\pi$
$127$	−10.2285	+	7.43142i	−0.907630	+	0.659432i	0.0327840	+	0.999462i	$0.489563\pi$
$128$	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	−0.993493	−	0.113893i	$-0.963668\pi$
$131$	−8.88603	+	9.86893i	−0.776376	+	0.862253i	0.217117	+	0.976146i	$0.430335\pi$
$132$	−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	−0.737662	−	0.675170i	$-0.764070\pi$
$137$	−8.53865	+	3.80165i	−0.729506	+	0.324797i	0.00815652	+	0.999967i	$0.497404\pi$
$138$	−1.20087	+	11.4255i	−0.102225	+	0.972602i
$139$	0.121998	−	0.0886369i	0.0103478	−	0.00751808i	−0.582599	−	0.812759i	$-0.697964\pi$
$139$	0.121998	−	0.0886369i	0.0103478	−	0.00751808i	0.592947	+	0.805241i	$0.297964\pi$
$140$	−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	−0.991209	−	0.132307i	$-0.957761\pi$
$149$	−7.44827	−	12.9008i	−0.610186	−	1.05687i	0.381023	−	0.924566i	$-0.375572\pi$
$150$	−1.52909	+	6.95415i	−0.124850	+	0.567804i
$151$	5.99881	−	10.3903i	0.488177	−	0.845547i	−0.511731	−	0.859146i	$-0.670996\pi$
$151$	5.99881	−	10.3903i	0.488177	−	0.845547i	0.999908	+	0.0135991i	$0.00432885\pi$
$152$	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	−0.998865	−	0.0476364i	$-0.984831\pi$
$157$	−5.74095	+	9.94363i	−0.458178	+	0.793588i	0.540687	+	0.841224i	$0.318164\pi$
$158$	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	0.843116	+	0.537731i	$0.180719\pi$
$163$	−1.19215	+	11.3426i	−0.0933765	+	0.888418i	−0.936493	+	0.350687i	$0.885948\pi$
$164$	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	0.981637	+	0.190761i	$0.0610954\pi$
$167$	3.87171	+	11.9159i	0.299602	+	0.922081i	−0.682034	+	0.731320i	$0.738905\pi$
$168$	−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	0.923718	−	0.383073i	$-0.125134\pi$
$173$	16.5349	+	7.36182i	1.25713	+	0.559709i	0.333409	+	0.942782i	$0.391801\pi$
$174$	−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	0.152788	−	0.988259i	$-0.451175\pi$
$179$	−11.3191	−	12.5711i	−0.846028	−	0.939609i	−0.998816	+	0.0486499i	$0.984508\pi$
$180$	0.0583871	−	0.0221786i	0.00435192	−	0.00165310i
$181$	−6.78399	−	20.8790i	−0.504250	−	1.55192i	−0.802028	−	0.597286i	$-0.796246\pi$
$181$	−6.78399	−	20.8790i	−0.504250	−	1.55192i	0.297778	−	0.954635i	$-0.403754\pi$
$182$	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	−0.316861	−	0.948472i	$-0.602629\pi$
$191$	2.62964	−	25.0194i	0.190274	−	1.81034i	0.507135	−	0.861866i	$-0.330704\pi$
$192$	7.71286	+	1.63942i	0.556628	+	0.118315i
$193$	−2.60653	+	4.51465i	−0.187622	+	0.324972i	−0.944457	−	0.328635i	$-0.893411\pi$
$193$	−2.60653	+	4.51465i	−0.187622	+	0.324972i	0.756835	+	0.653606i	$0.226745\pi$
$194$	−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	−1.00000		0.000863931i	$-0.999725\pi$
$197$	−2.67345	+	8.22802i	−0.190475	+	0.586222i	0.809524	+	0.587086i	$0.199725\pi$
$198$	−0.878225	−	0.391011i	−0.0624128	−	0.0277880i
$199$	1.78678	−	3.09480i	0.126662	−	0.219385i	−0.795719	−	0.605665i	$-0.792907\pi$
$199$	1.78678	−	3.09480i	0.126662	−	0.219385i	0.922381	+	0.386281i	$0.126240\pi$
$200$	−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	−0.940619	−	0.339463i	$-0.889755\pi$
$211$	−13.1958	+	9.58733i	−0.908438	+	0.660019i	0.0321813	+	0.999482i	$0.489755\pi$
$212$	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	−0.982206	−	0.187807i	$-0.939862\pi$
$223$	−16.5327	+	12.0117i	−1.10711	+	0.804362i	−0.124903	+	0.992169i	$0.539862\pi$
$224$	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	0.999733	+	0.0230922i	$0.00735112\pi$
$227$	0.401488	+	3.81990i	0.0266477	+	0.253536i	−0.973086	+	0.230444i	$0.925982\pi$
$228$	−0.00315211	−	0.00350077i	−0.000208753	−	0.000231844i
$229$	1.92611	−	0.409407i	0.127281	−	0.0270544i	−0.143831	−	0.989602i	$-0.545942\pi$
$229$	1.92611	−	0.409407i	0.127281	−	0.0270544i	0.271112	+	0.962548i	$0.412609\pi$
$230$	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	0.0407268	+	0.999170i	$0.487033\pi$
$233$	−14.6114	+	16.2276i	−0.957227	+	1.06311i	−0.997954	+	0.0639381i	$0.979634\pi$
$234$	−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	−0.305791	−	0.952099i	$-0.598921\pi$
$239$	7.81043	−	5.67461i	0.505215	−	0.367060i	0.811005	+	0.585039i	$0.198921\pi$
$240$	8.47651	−	3.21984i	0.547156	−	0.207840i
$241$	−18.7232	+	8.33609i	−1.20606	+	0.536975i	−0.908563	−	0.417747i	$-0.862820\pi$
$241$	−18.7232	+	8.33609i	−1.20606	+	0.536975i	−0.297501	+	0.954721i	$0.596153\pi$
$242$	−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	0.543165	−	0.839626i	$-0.317226\pi$
$257$	−7.30310	−	12.6493i	−0.455555	−	0.789044i	−0.998720	+	0.0505817i	$0.983892\pi$
$258$	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	0.500387	−	0.865802i	$-0.333191\pi$
$263$	23.9793	−	10.6763i	1.47863	−	0.658328i	0.978241	+	0.207474i	$0.0665242\pi$
$264$	−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	0.448905	−	0.893579i	$-0.351814\pi$
$269$	8.12762	+	1.72758i	0.495549	+	0.105332i	0.0466441	+	0.998912i	$0.485147\pi$
$270$	3.17932	+	0.177779i	0.193487	+	0.0108193i
$271$	9.75147	−	2.07274i	0.592360	−	0.125910i	0.0980285	−	0.995184i	$-0.468746\pi$
$271$	9.75147	−	2.07274i	0.592360	−	0.125910i	0.494331	+	0.869274i	$0.335413\pi$
$272$	−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	0.772492	+	0.635025i	$0.219010\pi$
$277$	2.47835	+	23.5800i	0.148910	+	1.41678i	−0.623582	+	0.781758i	$0.714323\pi$
$278$	−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	0.853262	−	0.521482i	$-0.174621\pi$
$281$	−2.40652	−	7.40650i	−0.143561	−	0.441835i	−0.996823	+	0.0796471i	$0.974621\pi$
$282$	−0.293508	−	0.508371i	−0.0174782	−	0.0302730i
$283$	−14.0462	−	2.98561i	−0.834958	−	0.177476i	−0.229456	−	0.973319i	$-0.573695\pi$
$283$	−14.0462	−	2.98561i	−0.834958	−	0.177476i	−0.605503	+	0.795843i	$0.707028\pi$
$284$	−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	0.997832	+	0.0658194i	$0.0209661\pi$
$311$	0.625867	+	5.95472i	0.0354896	+	0.337661i	−0.962342	+	0.271842i	$0.912367\pi$
$312$	−16.4136	+	7.30783i	−0.929240	+	0.413724i
$313$	2.08062	−	19.7957i	0.117603	−	1.11892i	−0.763438	−	0.645882i	$-0.776490\pi$
$313$	2.08062	−	19.7957i	0.117603	−	1.11892i	0.881041	−	0.473040i	$-0.156843\pi$
$314$	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	−0.613951	−	0.789344i	$-0.710421\pi$
$317$	4.18840	−	4.65169i	0.235244	−	0.261265i	0.849195	+	0.528079i	$0.177087\pi$
$318$	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	−0.970563	−	0.240847i	$-0.922575\pi$
$331$	−11.4543	+	12.7213i	−0.629584	+	0.699224i	0.340979	+	0.940071i	$0.389242\pi$
$332$	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	0.994507	−	0.104667i	$-0.0333777\pi$
$337$	22.0710	+	16.0355i	1.20228	+	0.873510i	0.207775	+	0.978177i	$0.433378\pi$
$338$	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	0.843301	−	0.537442i	$-0.180609\pi$
$347$	4.11033	+	4.56499i	0.220654	+	0.245061i	−0.622647	+	0.782503i	$0.713943\pi$
$348$	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	0.450159	−	0.892948i	$-0.351367\pi$
$353$	−9.11141	−	10.1193i	−0.484952	−	0.538593i	−0.935111	+	0.354355i	$0.884701\pi$
$354$	−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	0.916446	+	0.400158i	$0.131045\pi$
$359$	−1.19692	+	11.3879i	−0.0631709	+	0.601031i	−0.979617	+	0.200873i	$0.935622\pi$
$360$	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	0.697259	−	0.716820i	$-0.254403\pi$
$367$	19.9749	+	4.24579i	1.04268	+	0.221628i	0.345421	+	0.938448i	$0.387736\pi$
$368$	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	0.0964537	−	0.995337i	$-0.469250\pi$
$373$	−11.1763	−	4.97600i	−0.578686	−	0.257648i	−0.675140	+	0.737690i	$0.735917\pi$
$374$	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	−0.522976	−	0.852348i	$-0.675178\pi$
$379$	7.80893	−	24.0334i	0.401118	−	1.23451i	0.924094	−	0.382166i	$-0.124822\pi$
$380$	−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	0.0417309	+	0.999129i	$0.486713\pi$
$383$	−18.7149	+	20.7850i	−0.956287	+	1.06206i	−0.998018	+	0.0629351i	$0.979954\pi$
$384$	−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	0.978203	−	0.207650i	$-0.0665813\pi$
$389$	−0.429898	−	4.09020i	−0.0217967	−	0.207381i	−1.00000		0.000268036i	$0.999915\pi$
$390$	−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	0.120883	−	0.992667i	$-0.461428\pi$
$397$	12.6536	−	2.68962i	0.635068	−	0.134988i	0.514186	+	0.857679i	$0.328094\pi$
$398$	−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	0.607706	−	0.794162i	$-0.292090\pi$
$401$	−7.68782	−	13.3157i	−0.383911	−	0.664954i	−0.991618	+	0.129208i	$0.958756\pi$
$402$	−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	−0.578309	−	0.815817i	$-0.696287\pi$
$409$	−7.26040	+	3.23254i	−0.359003	+	0.159839i	0.219306	+	0.975656i	$0.429621\pi$
$410$	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	0.983534	−	0.180725i	$-0.0578445\pi$
$419$	1.67053	+	5.14135i	0.0816106	+	0.251172i	−0.901923	+	0.431897i	$0.857844\pi$
$420$	0.133986	+	0.0967177i	0.00653786	+	0.00471934i
$421$	2.42727	−	7.47037i	0.118298	−	0.364083i	−0.874323	−	0.485345i	$-0.838694\pi$
$421$	2.42727	−	7.47037i	0.118298	−	0.364083i	0.992621	+	0.121262i	$0.0386940\pi$
$422$	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	0.393255	−	0.919429i	$-0.371349\pi$
$431$	7.85882	+	1.67044i	0.378546	+	0.0804625i	−0.0147090	+	0.999892i	$0.504682\pi$
$432$	−2.02754	−	3.51181i	−0.0975501	−	0.168962i
$433$	−7.76041	−	23.8841i	−0.372942	−	1.14780i	−0.944857	−	0.327484i	$-0.893799\pi$
$433$	−7.76041	−	23.8841i	−0.372942	−	1.14780i	0.571915	−	0.820313i	$-0.306201\pi$
$434$	−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	−0.992290	−	0.123935i	$-0.960449\pi$
$439$	−36.6323	−	16.3097i	−1.74836	−	0.778422i	−0.756073	−	0.654487i	$-0.772885\pi$
$440$	−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	−0.997698	−	0.0678096i	$-0.978399\pi$
$443$	−11.7356	−	20.3266i	−0.557574	−	0.965746i	0.440124	−	0.897937i	$-0.354934\pi$
$444$	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	0.861619	−	0.507556i	$-0.169451\pi$
$457$	−0.186996	−	0.323886i	−0.00874730	−	0.0151508i	−0.870366	+	0.492405i	$0.836118\pi$
$458$	−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	−0.346877	+	0.937911i	$0.612758\pi$
$461$	−28.9014	+	20.9981i	−1.34607	+	0.977980i	−0.999197	+	0.0400696i	$0.987242\pi$
$462$	−0.414404	−	2.50947i	−0.0192798	−	0.116751i
$463$	13.3004	+	9.66329i	0.618121	+	0.449091i	0.852265	−	0.523111i	$-0.175229\pi$
$463$	13.3004	+	9.66329i	0.618121	+	0.449091i	−0.234143	+	0.972202i	$0.575229\pi$
$464$	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	−0.0700512	+	0.997543i	$0.522316\pi$
$467$	−22.7946	+	25.3160i	−1.05481	+	1.17148i	−0.984756	+	0.173939i	$0.944350\pi$
$468$	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	0.835531	−	0.549444i	$-0.185160\pi$
$479$	4.41574	+	4.90418i	0.201760	+	0.224078i	−0.633770	+	0.773521i	$0.718494\pi$
$480$	−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	−0.881525	−	0.472138i	$-0.843482\pi$
$487$	−24.7276	+	11.0094i	−1.12051	+	0.498884i	−0.238988	+	0.971022i	$0.576816\pi$
$488$	−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	0.882084	−	0.471092i	$-0.156140\pi$
$491$	15.6578	+	11.3761i	0.706627	+	0.513395i	−0.175457	+	0.984487i	$0.556140\pi$
$492$	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	0.717720	−	0.696332i	$-0.245186\pi$
$499$	−5.45458	−	9.44762i	−0.244181	−	0.422933i	−0.961901	+	0.273398i	$0.911852\pi$
$500$	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	0.709436	+	0.704770i	$0.248950\pi$
$503$	−6.25201	+	19.2417i	−0.278763	+	0.857945i	−0.988199	+	0.153175i	$0.951050\pi$
$504$	−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	−0.985434	−	0.170058i	$-0.945604\pi$
$509$	0.311861	−	2.96716i	0.0138230	−	0.131517i	0.999257	+	0.0385412i	$0.0122711\pi$
$510$	−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	0.313144	−	0.949706i	$-0.398618\pi$
$521$	−15.1582	−	16.8349i	−0.664092	−	0.737549i	−0.977236	+	0.212157i	$0.931951\pi$
$522$	7.52201	+	8.35404i	0.329229	+	0.365646i
$523$	2.74238	+	1.22099i	0.119916	+	0.0533900i	0.465818	−	0.884881i	$-0.345760\pi$
$523$	2.74238	+	1.22099i	0.119916	+	0.0533900i	−0.345902	+	0.938271i	$0.612427\pi$
$524$	−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	−0.747043	−	0.664775i	$-0.768527\pi$
$541$	2.83509	−	26.9740i	0.121890	−	1.15970i	0.868933	−	0.494929i	$-0.164806\pi$
$542$	−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	−0.679459	−	0.733713i	$-0.737786\pi$
$547$	7.05150	−	21.7023i	0.301501	−	0.927923i	0.980960	−	0.194210i	$-0.0622144\pi$
$548$	−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	−0.861129	−	0.508386i	$-0.830242\pi$
$557$	0.229182	−	0.396955i	0.00971076	−	0.0168195i	0.870840	+	0.491567i	$0.163576\pi$
$558$	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	−0.384550	−	0.923104i	$-0.625643\pi$
$563$	1.04723	−	0.466255i	0.0441353	−	0.0196503i	0.428686	+	0.903454i	$0.358977\pi$
$564$	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	−0.441255	−	0.897382i	$-0.645467\pi$
$569$	11.8633	−	13.1755i	0.497335	−	0.552346i	0.938590	+	0.345036i	$0.112133\pi$
$570$	−0.416168	−	0.339425i	−0.0174314	−	0.0142169i
$571$	−15.9345	−	17.6971i	−0.666838	−	0.740599i	0.310897	−	0.950444i	$-0.399371\pi$
$571$	−15.9345	−	17.6971i	−0.666838	−	0.740599i	−0.977735	+	0.209845i	$0.932704\pi$
$572$	−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	0.976329	+	0.216290i	$0.0693957\pi$
$577$	1.59269	+	15.1534i	0.0663044	+	0.630844i	−0.910025	+	0.414554i	$0.863938\pi$
$578$	−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	0.384702	−	0.923041i	$-0.374304\pi$
$587$	−9.06816	−	6.58840i	−0.374283	−	0.271933i	−0.758985	+	0.651108i	$0.774304\pi$
$588$	−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	0.862941	−	0.505305i	$-0.168620\pi$
$593$	−0.149440	−	0.258837i	−0.00613676	−	0.0106292i	−0.869077	+	0.494676i	$0.835287\pi$
$594$	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	−0.998369	−	0.0570990i	$-0.981815\pi$
$599$	−11.0070	+	19.0647i	−0.449735	+	0.778964i	0.548633	+	0.836063i	$0.315148\pi$
$600$	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	0.891687	−	0.452653i	$-0.149523\pi$
$607$	1.32632	+	2.29726i	0.0538339	+	0.0932430i	−0.837853	+	0.545896i	$0.816189\pi$
$608$	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	−0.247165	−	0.968973i	$-0.579499\pi$
$613$	7.61427	−	3.39009i	0.307537	−	0.136925i	0.554702	+	0.832049i	$0.312832\pi$
$614$	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	−0.999943	−	0.0106664i	$-0.996605\pi$
$617$	−4.89938	−	15.0787i	−0.197242	−	0.607048i	0.802701	−	0.596381i	$-0.203395\pi$
$618$	−2.78689	−	4.82704i	−0.112105	−	0.194172i
$619$	46.6097	+	9.90720i	1.87340	+	0.398204i	0.996582	−	0.0826119i	$-0.0263262\pi$
$619$	46.6097	+	9.90720i	1.87340	+	0.398204i	0.876821	+	0.480816i	$0.159660\pi$
$620$	−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	0.650818	+	0.759234i	$0.274426\pi$
$631$	14.3323	+	44.1104i	0.570562	+	1.75601i	−0.0802564	+	0.996774i	$0.525574\pi$
$632$	−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	−0.316904	−	0.948458i	$-0.602643\pi$
$641$	4.45311	−	1.98265i	0.175887	−	0.0783100i	0.492791	+	0.870148i	$0.335977\pi$
$642$	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	0.998202	−	0.0599329i	$-0.0190887\pi$
$647$	21.2203	+	23.5676i	0.834257	+	0.926537i	−0.163945	+	0.986469i	$0.552422\pi$
$648$	−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	0.411235	−	0.911529i	$-0.365098\pi$
$653$	29.5829	−	6.28804i	1.15767	−	0.246070i	0.746434	+	0.665459i	$0.231764\pi$
$654$	−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	0.885031	−	0.465533i	$-0.154137\pi$
$659$	18.3746	+	13.3499i	0.715772	+	0.520039i	−0.169258	+	0.985572i	$0.554137\pi$
$660$	0.0406882	+	0.0110551i	0.00158378	+	0.000430319i
$661$	−1.08241	−	10.2984i	−0.0421007	−	0.400561i	−0.995197	−	0.0978937i	$-0.968789\pi$
$661$	−1.08241	−	10.2984i	−0.0421007	−	0.400561i	0.953096	−	0.302668i	$-0.0978772\pi$
$662$	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	0.394184	−	0.919031i	$-0.371027\pi$
$673$	36.0609	−	26.1998i	1.39004	−	1.00993i	0.995860	−	0.0908951i	$-0.0289728\pi$
$674$	−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	0.578434	−	0.815729i	$-0.303664\pi$
$677$	9.34811	+	4.16204i	0.359277	+	0.159960i	−0.219157	+	0.975690i	$0.570331\pi$
$678$	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	−0.602199	−	0.798346i	$-0.705709\pi$
$683$	−38.6017	−	8.20504i	−1.47705	−	0.313957i	−0.874853	+	0.484389i	$0.839042\pi$
$684$	−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	−0.972774	−	0.231755i	$-0.925553\pi$
$691$	0.707828	−	6.73454i	0.0269271	−	0.256194i	0.999701	−	0.0244391i	$-0.00777999\pi$
$692$	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	0.778865	+	0.627192i	$0.215796\pi$
$709$	−3.01899	+	28.7238i	−0.113381	+	1.07874i	−0.892245	+	0.451551i	$0.850871\pi$
$710$	−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	−0.782953	−	0.622081i	$-0.786287\pi$
$719$	−2.21053	+	2.45504i	−0.0824388	+	0.0915575i	0.700514	+	0.713639i	$0.252954\pi$
$720$	−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	−0.898675	−	0.438614i	$-0.855469\pi$
$727$	−20.4712	+	14.8732i	−0.759235	+	0.551616i	0.139441	+	0.990230i	$0.455469\pi$
$728$	−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	−0.256758	+	0.966476i	$0.582654\pi$
$733$	−32.2478	+	35.8148i	−1.19110	+	1.32285i	−0.934343	+	0.356376i	$0.884012\pi$
$734$	−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	−0.946987	−	0.321273i	$-0.895889\pi$
$739$	−2.37838	−	22.6288i	−0.0874903	−	0.832415i	0.859496	−	0.511142i	$-0.170777\pi$
$740$	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	0.778463	−	0.627691i	$-0.216000\pi$
$751$	−4.23026	−	7.32703i	−0.154365	−	0.267367i	−0.932827	+	0.360323i	$0.882666\pi$
$752$	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	−0.495727	−	0.868478i	$-0.665098\pi$
$761$	−40.6300	−	18.0897i	−1.47284	−	0.655750i	−0.977111	+	0.212729i	$0.931765\pi$
$762$	−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	0.977711	−	0.209957i	$-0.0673325\pi$
$769$	1.75581	+	5.40383i	0.0633162	+	0.194867i	−0.914394	+	0.404825i	$0.867333\pi$
$770$	−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	0.991737	+	0.128288i	$0.0409483\pi$
$773$	1.34412	+	12.7884i	0.0483445	+	0.459967i	−0.943392	+	0.331679i	$0.892385\pi$
$774$	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	0.610937	−	0.791679i	$-0.290793\pi$
$787$	45.1119	−	20.0851i	1.60807	−	0.715957i	0.997129	+	0.0757225i	$0.0241263\pi$
$788$	−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	−0.893956	−	0.448155i	$-0.852081\pi$
$797$	2.61672	−	8.05342i	0.0926888	−	0.285267i	0.986644	+	0.162889i	$0.0520811\pi$
$798$	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	−0.640637	−	0.767844i	$-0.721330\pi$
$809$	−14.1841	+	6.31517i	−0.498687	+	0.222030i	0.141950	+	0.989874i	$0.454663\pi$
$810$	−1.99526	−	2.48165i	−0.0701064	−	0.0871963i
$811$	−3.34984	+	2.43380i	−0.117629	+	0.0854624i	−0.645044	−	0.764145i	$-0.723161\pi$
$811$	−3.34984	+	2.43380i	−0.117629	+	0.0854624i	0.527415	+	0.849608i	$0.323161\pi$
$812$	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	−0.579694	−	0.814834i	$-0.696828\pi$
$821$	−22.2878	+	4.73741i	−0.777849	+	0.165337i	−0.198154	+	0.980171i	$0.563495\pi$
$822$	−8.90628	−	9.89143i	−0.310642	−	0.345003i
$823$	−0.659363	−	6.27342i	−0.0229839	−	0.218678i	−0.999985	−	0.00544401i	$-0.998267\pi$
$823$	−0.659363	−	6.27342i	−0.0229839	−	0.218678i	0.977001	−	0.213234i	$-0.0683996\pi$
$824$	−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	−0.485451	−	0.874264i	$-0.661345\pi$
$827$	5.63678	−	4.09536i	0.196010	−	0.142410i	0.681461	+	0.731854i	$0.261345\pi$
$828$	−0.220414	+	0.0468503i	−0.00765990	+	0.00162816i
$829$	−3.44077	−	3.82136i	−0.119503	−	0.132721i	0.680425	−	0.732818i	$-0.261795\pi$
$829$	−3.44077	−	3.82136i	−0.119503	−	0.132721i	−0.799927	+	0.600097i	$0.795129\pi$
$830$	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	−0.694759	−	0.719243i	$-0.744489\pi$
$839$	−6.52913	+	4.74369i	−0.225411	+	0.163770i	0.469348	+	0.883013i	$0.344489\pi$
$840$	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	0.548875	+	0.835905i	$0.315056\pi$
$853$	−11.2884	+	34.7421i	−0.386507	+	1.18955i	−0.935381	+	0.353641i	$0.884944\pi$
$854$	−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	−0.708656	−	0.705554i	$-0.750698\pi$
$857$	7.51479	−	13.0160i	0.256700	−	0.444618i	0.965356	+	0.260937i	$0.0840314\pi$
$858$	−6.01598	−	1.27874i	−0.205382	−	0.0436554i
$859$	3.43365	−	32.6690i	0.117155	−	1.11465i	−0.765110	−	0.643899i	$-0.777316\pi$
$859$	3.43365	−	32.6690i	0.117155	−	1.11465i	0.882265	−	0.470753i	$-0.156018\pi$
$860$	−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	0.962697	+	0.270582i	$0.0872163\pi$
$863$	−1.03465	+	9.84407i	−0.0352200	+	0.335096i	−0.997917	+	0.0645137i	$0.979450\pi$
$864$	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	0.118362	−	0.992970i	$-0.462236\pi$
$877$	−16.0023	−	7.12468i	−0.540359	−	0.240583i	−0.658721	+	0.752387i	$0.728902\pi$
$878$	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	−0.937348	−	0.348396i	$-0.886727\pi$
$881$	−11.3918	−	35.0603i	−0.383799	−	1.18121i	0.553548	−	0.832817i	$-0.313273\pi$
$882$	−8.56654	+	5.09735i	−0.288451	+	0.171637i
$883$	−6.13201	−	18.8724i	−0.206359	−	0.635107i	−0.999655	−	0.0262707i	$-0.991637\pi$
$883$	−6.13201	−	18.8724i	−0.206359	−	0.635107i	0.793296	−	0.608836i	$-0.208363\pi$
$884$	−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	−0.908106	−	0.418740i	$-0.862472\pi$
$887$	2.00188	−	19.0467i	0.0672167	−	0.639524i	0.975323	−	0.220784i	$-0.0708615\pi$
$888$	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	−0.976783	−	0.214230i	$-0.931276\pi$
$907$	−9.12115	+	15.7983i	−0.302863	+	0.524574i	0.673920	+	0.738804i	$0.264609\pi$
$908$	−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	0.147028	−	0.989132i	$-0.453029\pi$
$911$	34.2026	−	24.8497i	1.13318	−	0.823306i	0.986155	+	0.165827i	$0.0530292\pi$
$912$	−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	−0.249606	−	0.968347i	$-0.580301\pi$
$919$	22.4188	−	24.8986i	0.739527	−	0.821328i	0.989134	+	0.147019i	$0.0469679\pi$
$920$	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	0.483743	−	0.875210i	$-0.339277\pi$
$929$	39.0639	−	8.30329i	1.28164	−	0.272422i	0.797901	+	0.602788i	$0.205943\pi$
$930$	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	0.564095	−	0.825710i	$-0.309225\pi$
$937$	−1.43523	−	1.04275i	−0.0468869	−	0.0340653i	−0.610982	+	0.791645i	$0.709225\pi$
$938$	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	−0.623768	−	0.781609i	$-0.714399\pi$
$941$	−14.1201	+	6.28666i	−0.460301	+	0.204939i	0.163467	+	0.986549i	$0.447732\pi$
$942$	−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	0.0853959	−	0.996347i	$-0.472784\pi$
$947$	17.4996	−	3.71965i	0.568660	−	0.120872i	0.483264	+	0.875475i	$0.339451\pi$
$948$	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	−0.889506	−	0.456924i	$-0.848951\pi$
$953$	3.04671	−	9.37681i	0.0986926	−	0.303745i	0.988198	+	0.153179i	$0.0489512\pi$
$954$	−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	0.879516	−	0.475869i	$-0.157866\pi$
$967$	−3.47462	−	10.6938i	−0.111736	−	0.343889i	−0.991252	+	0.131980i	$0.957866\pi$
$968$	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	−0.312084	−	0.950054i	$-0.601027\pi$
$971$	−6.56765	+	1.39600i	−0.210766	+	0.0447997i	0.101319	+	0.994854i	$0.467694\pi$
$972$	−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	0.999907	+	0.0136430i	$0.00434282\pi$
$977$	0.771638	+	7.34165i	0.0246869	+	0.234880i	−0.975220	+	0.221237i	$0.928991\pi$
$978$	−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	−0.100859	−	0.994901i	$-0.532159\pi$
$983$	−18.7384	−	3.98296i	−0.597661	−	0.127037i	−0.496802	+	0.867864i	$0.665492\pi$
$984$	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	−0.430781	−	0.902457i	$-0.641762\pi$
$991$	−1.52279	+	0.677991i	−0.0483731	+	0.0215371i	0.382408	+	0.923994i	$0.375095\pi$
$992$	−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	0.999664	−	0.0259103i	$-0.00824842\pi$
$997$	27.4517	+	30.4881i	0.869403	+	0.965569i	−0.130262	+	0.991480i	$0.541582\pi$
$998$	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.361.7	yes	160
7.2	even	3	inner	525.2.bg.a.436.14	yes	160
25.16	even	5	inner	525.2.bg.a.466.14	yes	160
175.16	even	15	inner	525.2.bg.a.16.7	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.7	✓	160	175.16	even	15	inner
525.2.bg.a.361.7	yes	160	1.1	even	1	trivial
525.2.bg.a.436.14	yes	160	7.2	even	3	inner
525.2.bg.a.466.14	yes	160	25.16	even	5	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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