LMFDB - Embedded newform 98.2.g.a.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,2,Mod(9,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("98.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	98.g (of order $21$, degree $12$, 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:	$0.782533939809$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	98.53
Dual form			98.2.g.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.826239 - 0.563320i) q^{2} +(2.11865 + 1.96582i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-0.596780 + 0.184082i) q^{5} +(-0.643125 - 2.81771i) q^{6} +(-2.13962 + 1.55628i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.400039 + 5.33815i) q^{9} +O(q^{10})$	\(q+(-0.826239 - 0.563320i) q^{2} +(2.11865 + 1.96582i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-0.596780 + 0.184082i) q^{5} +(-0.643125 - 2.81771i) q^{6} +(-2.13962 + 1.55628i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.400039 + 5.33815i) q^{9} +(0.596780 + 0.184082i) q^{10} +(0.449550 - 5.99883i) q^{11} +(-1.05590 + 2.69039i) q^{12} +(2.76850 - 1.33324i) q^{13} +(2.64452 - 0.0805687i) q^{14} +(-1.62624 - 0.783156i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(4.51734 - 0.680880i) q^{17} +(2.67656 - 4.63594i) q^{18} +(-1.17691 - 2.03847i) q^{19} +(-0.389385 - 0.488274i) q^{20} +(-7.59248 - 0.908894i) q^{21} +(-3.75069 + 4.70322i) q^{22} +(-4.00591 - 0.603794i) q^{23} +(2.38798 - 1.62809i) q^{24} +(-3.80893 + 2.59689i) q^{25} +(-3.03849 - 0.457978i) q^{26} +(-4.24031 + 5.31718i) q^{27} +(-2.23039 - 1.42314i) q^{28} +(-1.66173 - 2.08374i) q^{29} +(0.902495 + 1.56317i) q^{30} +(-1.94715 + 3.37257i) q^{31} +(0.988831 - 0.149042i) q^{32} +(12.7450 - 11.8257i) q^{33} +(-4.11596 - 1.98214i) q^{34} +(0.990400 - 1.32262i) q^{35} +(-4.82299 + 2.32263i) q^{36} +(0.562255 - 1.43260i) q^{37} +(-0.175901 + 2.34724i) q^{38} +(8.48640 + 2.61771i) q^{39} +(0.0466709 + 0.622779i) q^{40} +(0.156856 - 0.687231i) q^{41} +(5.76120 + 5.02796i) q^{42} +(2.34329 + 10.2666i) q^{43} +(5.74839 - 1.77314i) q^{44} +(-1.22139 - 3.11206i) q^{45} +(2.96971 + 2.75549i) q^{46} +(-7.63652 - 5.20649i) q^{47} -2.89018 q^{48} +(2.15597 - 6.65971i) q^{49} +4.60997 q^{50} +(10.9091 + 7.43773i) q^{51} +(2.25253 + 2.09004i) q^{52} +(2.30806 + 5.88083i) q^{53} +(6.49878 - 2.00461i) q^{54} +(0.835995 + 3.66273i) q^{55} +(1.04115 + 2.43228i) q^{56} +(1.51380 - 6.63238i) q^{57} +(0.199171 + 2.65775i) q^{58} +(-1.71634 - 0.529420i) q^{59} +(0.134887 - 1.79994i) q^{60} +(-1.42619 + 3.63388i) q^{61} +(3.50865 - 1.68968i) q^{62} +(-9.16360 - 10.7991i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.40676 + 1.30528i) q^{65} +(-17.1921 + 2.59129i) q^{66} +(-2.82524 + 4.89345i) q^{67} +(2.28418 + 3.95632i) q^{68} +(-7.30018 - 9.15413i) q^{69} +(-1.56337 + 0.534892i) q^{70} +(-7.65886 + 9.60391i) q^{71} +(5.29333 + 0.797841i) q^{72} +(11.1971 - 7.63402i) q^{73} +(-1.27157 + 0.866942i) q^{74} +(-13.1748 - 1.98578i) q^{75} +(1.46758 - 1.84029i) q^{76} +(8.37400 + 13.5348i) q^{77} +(-5.53718 - 6.94341i) q^{78} +(-4.68117 - 8.10802i) q^{79} +(0.312263 - 0.540855i) q^{80} +(-3.55634 + 0.536033i) q^{81} +(-0.516732 + 0.479457i) q^{82} +(6.36516 + 3.06530i) q^{83} +(-1.92778 - 7.39970i) q^{84} +(-2.57052 + 1.23790i) q^{85} +(3.84728 - 9.80272i) q^{86} +(0.575639 - 7.68136i) q^{87} +(-5.74839 - 1.77314i) q^{88} +(0.531766 + 7.09592i) q^{89} +(-0.743923 + 3.25934i) q^{90} +(-3.84865 + 7.16120i) q^{91} +(-0.901469 - 3.94959i) q^{92} +(-10.7552 + 3.31754i) q^{93} +(3.37667 + 8.60361i) q^{94} +(1.07760 + 0.999867i) q^{95} +(2.38798 + 1.62809i) q^{96} -0.343182 q^{97} +(-5.53290 + 4.28801i) q^{98} +32.2025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	$ 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{21}\right)$

Coefficient data

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

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

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

$2$	−0.826239	−	0.563320i	−0.584239	−	0.398327i
$2$	−0.826239	−	0.563320i	−0.584239	−	0.398327i
$3$	2.11865	+	1.96582i	1.22320	+	1.13497i	0.986565	+	0.163368i	$0.0522358\pi$
$3$	2.11865	+	1.96582i	1.22320	+	1.13497i	0.236637	+	0.971598i	$0.423955\pi$
$4$	0.365341	+	0.930874i	0.182671	+	0.465437i
$5$	−0.596780	+	0.184082i	−0.266888	+	0.0823241i	−0.425311	−	0.905047i	$-0.639835\pi$
$5$	−0.596780	+	0.184082i	−0.266888	+	0.0823241i	0.158423	+	0.987371i	$0.449359\pi$
$6$	−0.643125	−	2.81771i	−0.262555	−	1.15033i
$7$	−2.13962	+	1.55628i	−0.808701	+	0.588220i
$7$	−2.13962	+	1.55628i	−0.808701	+	0.588220i
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	0.400039	+	5.33815i	0.133346	+	1.77938i
$10$	0.596780	+	0.184082i	0.188718	+	0.0582119i
$11$	0.449550	−	5.99883i	0.135544	−	1.80871i	−0.352411	−	0.935845i	$-0.614638\pi$
$11$	0.449550	−	5.99883i	0.135544	−	1.80871i	0.487955	−	0.872869i	$-0.337743\pi$
$12$	−1.05590	+	2.69039i	−0.304812	+	0.776648i
$13$	2.76850	−	1.33324i	0.767845	−	0.369774i	−0.00859753	−	0.999963i	$-0.502737\pi$
$13$	2.76850	−	1.33324i	0.767845	−	0.369774i	0.776442	+	0.630189i	$0.217022\pi$
$14$	2.64452	−	0.0805687i	0.706779	−	0.0215329i
$15$	−1.62624	−	0.783156i	−0.419893	−	0.202210i
$16$	−0.733052	+	0.680173i	−0.183263	+	0.170043i
$17$	4.51734	−	0.680880i	1.09562	−	0.165138i	0.423727	−	0.905790i	$-0.360721\pi$
$17$	4.51734	−	0.680880i	1.09562	−	0.165138i	0.671889	+	0.740652i	$0.265483\pi$
$18$	2.67656	−	4.63594i	0.630871	−	1.09270i
$19$	−1.17691	−	2.03847i	−0.270001	−	0.467656i	0.698860	−	0.715258i	$-0.253691\pi$
$19$	−1.17691	−	2.03847i	−0.270001	−	0.467656i	−0.968862	+	0.247602i	$0.920357\pi$
$20$	−0.389385	−	0.488274i	−0.0870692	−	0.109181i
$21$	−7.59248	−	0.908894i	−1.65681	−	0.198337i
$22$	−3.75069	+	4.70322i	−0.799651	+	1.00273i
$23$	−4.00591	−	0.603794i	−0.835291	−	0.125900i	−0.282550	−	0.959253i	$-0.591180\pi$
$23$	−4.00591	−	0.603794i	−0.835291	−	0.125900i	−0.552741	+	0.833353i	$0.686418\pi$
$24$	2.38798	−	1.62809i	0.487443	−	0.332333i
$25$	−3.80893	+	2.59689i	−0.761787	+	0.519377i
$26$	−3.03849	−	0.457978i	−0.595896	−	0.0898169i
$27$	−4.24031	+	5.31718i	−0.816047	+	1.02329i
$28$	−2.23039	−	1.42314i	−0.421505	−	0.268949i
$29$	−1.66173	−	2.08374i	−0.308575	−	0.386941i	0.603228	−	0.797569i	$-0.293881\pi$
$29$	−1.66173	−	2.08374i	−0.308575	−	0.386941i	−0.911803	+	0.410628i	$0.865309\pi$
$30$	0.902495	+	1.56317i	0.164772	+	0.285394i
$31$	−1.94715	+	3.37257i	−0.349719	+	0.605731i	−0.986199	−	0.165562i	$-0.947056\pi$
$31$	−1.94715	+	3.37257i	−0.349719	+	0.605731i	0.636480	+	0.771293i	$0.280390\pi$
$32$	0.988831	−	0.149042i	0.174802	−	0.0263472i
$33$	12.7450	−	11.8257i	2.21863	−	2.05859i
$34$	−4.11596	−	1.98214i	−0.705881	−	0.339934i
$35$	0.990400	−	1.32262i	0.167408	−	0.223564i
$36$	−4.82299	+	2.32263i	−0.803832	+	0.387105i
$37$	0.562255	−	1.43260i	0.0924342	−	0.235518i	−0.877178	−	0.480165i	$-0.840577\pi$
$37$	0.562255	−	1.43260i	0.0924342	−	0.235518i	0.969612	+	0.244647i	$0.0786720\pi$
$38$	−0.175901	+	2.34724i	−0.0285349	+	0.380772i
$39$	8.48640	+	2.61771i	1.35891	+	0.419169i
$40$	0.0466709	+	0.622779i	0.00737931	+	0.0984701i
$41$	0.156856	−	0.687231i	0.0244968	−	0.107327i	−0.961201	−	0.275847i	$-0.911042\pi$
$41$	0.156856	−	0.687231i	0.0244968	−	0.107327i	0.985698	+	0.168520i	$0.0538987\pi$
$42$	5.76120	+	5.02796i	0.888973	+	0.775831i
$43$	2.34329	+	10.2666i	0.357349	+	1.56565i	0.759769	+	0.650193i	$0.225312\pi$
$43$	2.34329	+	10.2666i	0.357349	+	1.56565i	−0.402420	+	0.915455i	$0.631831\pi$
$44$	5.74839	−	1.77314i	0.866602	−	0.267311i
$45$	−1.22139	−	3.11206i	−0.182075	−	0.463918i
$46$	2.96971	+	2.75549i	0.437860	+	0.406275i
$47$	−7.63652	−	5.20649i	−1.11390	−	0.759445i	−0.140849	−	0.990031i	$-0.544983\pi$
$47$	−7.63652	−	5.20649i	−1.11390	−	0.759445i	−0.973052	+	0.230586i	$0.925936\pi$
$48$	−2.89018			−0.417161
$49$	2.15597	−	6.65971i	0.307996	−	0.951388i
$50$	4.60997			0.651948
$51$	10.9091	+	7.43773i	1.52759	+	1.04149i
$52$	2.25253	+	2.09004i	0.312369	+	0.289836i
$53$	2.30806	+	5.88083i	0.317036	+	0.807795i	0.997203	+	0.0747377i	$0.0238119\pi$
$53$	2.30806	+	5.88083i	0.317036	+	0.807795i	−0.680167	+	0.733057i	$0.738093\pi$
$54$	6.49878	−	2.00461i	0.884372	−	0.272793i
$55$	0.835995	+	3.66273i	0.112726	+	0.493883i
$56$	1.04115	+	2.43228i	0.139130	+	0.325028i
$57$	1.51380	−	6.63238i	0.200507	−	0.878480i
$58$	0.199171	+	2.65775i	0.0261524	+	0.348980i
$59$	−1.71634	−	0.529420i	−0.223448	−	0.0689247i	0.181009	−	0.983481i	$-0.442064\pi$
$59$	−1.71634	−	0.529420i	−0.223448	−	0.0689247i	−0.404458	+	0.914557i	$0.632540\pi$
$60$	0.134887	−	1.79994i	0.0174138	−	0.232372i
$61$	−1.42619	+	3.63388i	−0.182605	+	0.465270i	−0.992639	−	0.121113i	$-0.961354\pi$
$61$	−1.42619	+	3.63388i	−0.182605	+	0.465270i	0.810034	+	0.586384i	$0.199449\pi$
$62$	3.50865	−	1.68968i	0.445599	−	0.214589i
$63$	−9.16360	−	10.7991i	−1.15451	−	1.36055i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−1.40676	+	1.30528i	−0.174487	+	0.161900i
$66$	−17.1921	+	2.59129i	−2.11620	+	0.318966i
$67$	−2.82524	+	4.89345i	−0.345158	+	0.597831i	−0.985382	−	0.170357i	$-0.945508\pi$
$67$	−2.82524	+	4.89345i	−0.345158	+	0.597831i	0.640225	+	0.768188i	$0.278841\pi$
$68$	2.28418	+	3.95632i	0.276998	+	0.479774i
$69$	−7.30018	−	9.15413i	−0.878838	−	1.10203i
$70$	−1.56337	+	0.534892i	−0.186858	+	0.0639318i
$71$	−7.65886	+	9.60391i	−0.908939	+	1.13977i	0.0807772	+	0.996732i	$0.474260\pi$
$71$	−7.65886	+	9.60391i	−0.908939	+	1.13977i	−0.989717	+	0.143042i	$0.954312\pi$
$72$	5.29333	+	0.797841i	0.623825	+	0.0940264i
$73$	11.1971	−	7.63402i	1.31052	−	0.893495i	0.312116	−	0.950044i	$-0.398962\pi$
$73$	11.1971	−	7.63402i	1.31052	−	0.893495i	0.998400	+	0.0565494i	$0.0180098\pi$
$74$	−1.27157	+	0.866942i	−0.147817	+	0.100780i
$75$	−13.1748	−	1.98578i	−1.52130	−	0.229298i
$76$	1.46758	−	1.84029i	0.168343	−	0.211096i
$77$	8.37400	+	13.5348i	0.954306	+	1.54244i
$78$	−5.53718	−	6.94341i	−0.626963	−	0.786186i
$79$	−4.68117	−	8.10802i	−0.526673	−	0.912224i	−0.999517	−	0.0310778i	$-0.990106\pi$
$79$	−4.68117	−	8.10802i	−0.526673	−	0.912224i	0.472844	−	0.881146i	$-0.343227\pi$
$80$	0.312263	−	0.540855i	0.0349120	−	0.0604694i
$81$	−3.55634	+	0.536033i	−0.395149	+	0.0595592i
$82$	−0.516732	+	0.479457i	−0.0570635	+	0.0529471i
$83$	6.36516	+	3.06530i	0.698667	+	0.336461i	0.749276	−	0.662258i	$-0.230402\pi$
$83$	6.36516	+	3.06530i	0.698667	+	0.336461i	−0.0506083	+	0.998719i	$0.516116\pi$
$84$	−1.92778	−	7.39970i	−0.210338	−	0.807373i
$85$	−2.57052	+	1.23790i	−0.278812	+	0.134269i
$86$	3.84728	−	9.80272i	0.414863	−	1.05705i
$87$	0.575639	−	7.68136i	0.0617149	−	0.823529i
$88$	−5.74839	−	1.77314i	−0.612780	−	0.189018i
$89$	0.531766	+	7.09592i	0.0563671	+	0.752166i	0.951751	+	0.306871i	$0.0992821\pi$
$89$	0.531766	+	7.09592i	0.0563671	+	0.752166i	−0.895384	+	0.445295i	$0.853099\pi$
$90$	−0.743923	+	3.25934i	−0.0784164	+	0.343565i
$91$	−3.84865	+	7.16120i	−0.403448	+	0.750698i
$92$	−0.901469	−	3.94959i	−0.0939846	−	0.411773i
$93$	−10.7552	+	3.31754i	−1.11526	+	0.344013i
$94$	3.37667	+	8.60361i	0.348277	+	0.887395i
$95$	1.07760	+	0.999867i	0.110559	+	0.102584i
$96$	2.38798	+	1.62809i	0.243722	+	0.166167i
$97$	−0.343182			−0.0348448			−0.0174224	−	0.999848i	$-0.505546\pi$
$97$	−0.343182			−0.0348448			−0.0174224	+	0.999848i	$0.505546\pi$
$98$	−5.53290	+	4.28801i	−0.558907	+	0.433155i
$99$	32.2025			3.23647
$100$	−3.80893	−	2.59689i	−0.380893	−	0.259689i
$101$	−4.90205	−	4.54844i	−0.487773	−	0.452587i	0.397539	−	0.917585i	$-0.369864\pi$
$101$	−4.90205	−	4.54844i	−0.487773	−	0.452587i	−0.885311	+	0.464998i	$0.846055\pi$
$102$	−4.82374	−	12.2907i	−0.477621	−	1.21696i
$103$	14.8020	−	4.56580i	1.45848	−	0.449882i	0.538762	−	0.842458i	$-0.318892\pi$
$103$	14.8020	−	4.56580i	1.45848	−	0.449882i	0.919720	+	0.392576i	$0.128416\pi$
$104$	−0.683764	−	2.99576i	−0.0670486	−	0.293759i
$105$	4.69835	−	0.855230i	0.458512	−	0.0834619i
$106$	1.40579	−	6.15915i	0.136542	−	0.598229i
$107$	−0.833242	−	11.1188i	−0.0805526	−	1.07490i	−0.880254	−	0.474502i	$-0.842628\pi$
$107$	−0.833242	−	11.1188i	−0.0805526	−	1.07490i	0.799702	−	0.600397i	$-0.204991\pi$
$108$	−6.49878	−	2.00461i	−0.625345	−	0.192893i
$109$	−0.398771	+	5.32123i	−0.0381953	+	0.509681i	0.944993	+	0.327089i	$0.106068\pi$
$109$	−0.398771	+	5.32123i	−0.0381953	+	0.509681i	−0.983189	+	0.182592i	$0.941551\pi$
$110$	1.37256	−	3.49722i	0.130868	−	0.333447i
$111$	4.00746	−	1.92989i	0.380371	−	0.183177i
$112$	0.509913	−	2.59615i	0.0481823	−	0.245313i
$113$	2.03137	+	0.978258i	0.191095	+	0.0920267i	0.526985	−	0.849875i	$-0.323323\pi$
$113$	2.03137	+	0.978258i	0.191095	+	0.0920267i	−0.335889	+	0.941901i	$0.609037\pi$
$114$	−4.98691	+	4.62718i	−0.467067	+	0.433375i
$115$	2.50180	−	0.377085i	0.233294	−	0.0351634i
$116$	1.33260	−	2.30813i	0.123729	−	0.214305i
$117$	8.22455	+	14.2453i	0.760360	+	1.31698i
$118$	1.11987	+	1.40428i	0.103093	+	0.129274i
$119$	−8.60576	+	8.48708i	−0.788889	+	0.778010i
$120$	−1.12539	+	1.41120i	−0.102734	+	0.128824i
$121$	−24.9067	−	3.75408i	−2.26424	−	0.341280i
$122$	3.22541	−	2.19905i	0.292015	−	0.199092i
$123$	1.68329	−	1.14765i	0.151778	−	0.103480i
$124$	−3.85081	−	0.580416i	−0.345813	−	0.0521229i
$125$	3.74198	−	4.69230i	0.334693	−	0.419692i
$126$	1.48800	+	14.0846i	0.132562	+	1.25476i
$127$	0.626268	+	0.785315i	0.0555723	+	0.0696854i	0.808841	−	0.588028i	$-0.200095\pi$
$127$	0.626268	+	0.785315i	0.0555723	+	0.0696854i	−0.753269	+	0.657713i	$0.771524\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−15.2177	+	26.3579i	−1.33985	+	2.32068i
$130$	1.89761	−	0.286019i	0.166432	−	0.0250855i
$131$	−14.1610	+	13.1395i	−1.23725	+	1.14800i	−0.253714	+	0.967279i	$0.581652\pi$
$131$	−14.1610	+	13.1395i	−1.23725	+	1.14800i	−0.983535	+	0.180720i	$0.942157\pi$
$132$	15.6645	+	7.54362i	1.36342	+	0.656588i
$133$	5.69057	+	2.52994i	0.493435	+	0.219374i
$134$	5.09090	−	2.45165i	0.439787	−	0.211790i
$135$	1.55173	−	3.95375i	0.133552	−	0.340284i
$136$	0.341394	−	4.55559i	0.0292743	−	0.390639i
$137$	−7.24844	−	2.23585i	−0.619276	−	0.191021i	−0.0307864	−	0.999526i	$-0.509801\pi$
$137$	−7.24844	−	2.23585i	−0.619276	−	0.191021i	−0.588490	+	0.808505i	$0.700277\pi$
$138$	0.874983	+	11.6758i	0.0744835	+	0.993913i
$139$	2.39523	−	10.4942i	0.203160	−	0.890104i	−0.765837	−	0.643034i	$-0.777675\pi$
$139$	2.39523	−	10.4942i	0.203160	−	0.890104i	0.968998	−	0.247070i	$-0.0794676\pi$
$140$	1.59303	+	0.438728i	0.134636	+	0.0370793i
$141$	−5.94409	−	26.0427i	−0.500582	−	2.19319i
$142$	11.7381	−	3.62073i	0.985041	−	0.303845i
$143$	−6.75330	−	17.2071i	−0.564739	−	1.43893i
$144$	−3.92411	−	3.64104i	−0.327009	−	0.303420i
$145$	1.37526	+	0.937639i	0.114209	+	0.0778667i
$146$	−13.5518			−1.12156
$147$	17.6595	−	9.87135i	1.45653	−	0.814175i
$148$	1.53899			0.126504
$149$	9.98732	+	6.80924i	0.818193	+	0.557835i	0.898519	−	0.438934i	$-0.144644\pi$
$149$	9.98732	+	6.80924i	0.818193	+	0.557835i	−0.0803262	+	0.996769i	$0.525596\pi$
$150$	9.76690	+	9.06236i	0.797464	+	0.739939i
$151$	−3.82292	−	9.74065i	−0.311105	−	0.792682i	−0.997835	−	0.0657698i	$-0.979050\pi$
$151$	−3.82292	−	9.74065i	−0.311105	−	0.792682i	0.686730	−	0.726913i	$-0.259046\pi$
$152$	−2.24924	+	0.693800i	−0.182438	+	0.0562746i
$153$	5.44175	+	23.8419i	0.439939	+	1.92750i
$154$	0.705528	−	15.9003i	0.0568531	−	1.28128i
$155$	0.541192	−	2.37112i	0.0434696	−	0.190453i
$156$	0.663674	+	8.85612i	0.0531365	+	0.709057i
$157$	12.6078	+	3.88898i	1.00621	+	0.310374i	0.753699	−	0.657220i	$-0.228268\pi$
$157$	12.6078	+	3.88898i	1.00621	+	0.310374i	0.252510	+	0.967594i	$0.418744\pi$
$158$	−0.699648	+	9.33616i	−0.0556610	+	0.742745i
$159$	−6.67069	+	16.9966i	−0.529020	+	1.34792i
$160$	−0.562678	+	0.270972i	−0.0444836	+	0.0214222i
$161$	9.51082	−	4.94244i	0.749558	−	0.389519i
$162$	3.24035	+	1.56047i	0.254586	+	0.122602i
$163$	5.19776	−	4.82282i	0.407120	−	0.377752i	−0.449862	−	0.893098i	$-0.648527\pi$
$163$	5.19776	−	4.82282i	0.407120	−	0.377752i	0.856982	+	0.515346i	$0.172336\pi$
$164$	0.697031	−	0.105061i	0.0544290	−	0.00820385i
$165$	−5.42909	+	9.40346i	−0.422654	+	0.732058i
$166$	−3.53240	−	6.11830i	−0.274167	−	0.474872i
$167$	7.29124	+	9.14292i	0.564213	+	0.707500i	0.979330	−	0.202267i	$-0.0648310\pi$
$167$	7.29124	+	9.14292i	0.564213	+	0.707500i	−0.415118	+	0.909768i	$0.636260\pi$
$168$	−2.57559	+	7.19987i	−0.198711	+	0.555482i
$169$	−2.21829	+	2.78165i	−0.170638	+	0.213973i
$170$	2.82120	+	0.425227i	0.216376	+	0.0326134i
$171$	10.4108	−	7.09798i	0.796136	−	0.542796i
$172$	−8.70085	+	5.93214i	−0.663433	+	0.452321i
$173$	−0.0972146	−	0.0146527i	−0.00739109	−	0.00111403i	0.145346	−	0.989381i	$-0.453571\pi$
$173$	−0.0972146	−	0.0146527i	−0.00739109	−	0.00111403i	−0.152737	+	0.988267i	$0.548809\pi$
$174$	−4.80268	+	6.02237i	−0.364090	+	0.456555i
$175$	4.10819	−	11.4841i	0.310550	−	0.868119i
$176$	3.75069	+	4.70322i	0.282719	+	0.354519i
$177$	−2.59557	−	4.49567i	−0.195095	−	0.337915i
$178$	3.55791	−	6.16248i	0.266677	−	0.461897i
$179$	−18.7701	+	2.82914i	−1.40294	+	0.211460i	−0.806519	−	0.591209i	$-0.798651\pi$
$179$	−18.7701	+	2.82914i	−1.40294	+	0.211460i	−0.596426	+	0.802668i	$0.703413\pi$
$180$	2.45071	−	2.27393i	0.182665	−	0.169488i
$181$	8.75551	+	4.21643i	0.650792	+	0.313405i	0.729994	−	0.683454i	$-0.239523\pi$
$181$	8.75551	+	4.21643i	0.650792	+	0.313405i	−0.0792019	+	0.996859i	$0.525237\pi$
$182$	7.21396	−	3.74884i	0.534734	−	0.277883i
$183$	−10.1651	+	4.89528i	−0.751429	+	0.361869i
$184$	−1.48006	+	3.77112i	−0.109111	+	0.278011i
$185$	−0.0718259	+	0.958449i	−0.00528074	+	0.0704666i
$186$	10.7552	+	3.31754i	0.788609	+	0.243254i
$187$	−2.05371	−	27.4048i	−0.150182	−	2.00404i
$188$	2.05665	−	9.01078i	0.149997	−	0.657179i
$189$	0.797627	−	17.9759i	0.0580188	−	1.30755i
$190$	−0.327110	−	1.43316i	−0.0237311	−	0.103973i
$191$	1.54515	−	0.476616i	0.111803	−	0.0344867i	−0.238349	−	0.971180i	$-0.576606\pi$
$191$	1.54515	−	0.476616i	0.111803	−	0.0344867i	0.350152	+	0.936693i	$0.386130\pi$
$192$	−1.05590	−	2.69039i	−0.0762030	−	0.194162i
$193$	2.63698	+	2.44676i	0.189814	+	0.176122i	0.769355	−	0.638821i	$-0.220578\pi$
$193$	2.63698	+	2.44676i	0.189814	+	0.176122i	−0.579541	+	0.814943i	$0.696768\pi$
$194$	0.283550	+	0.193321i	0.0203577	+	0.0138796i
$195$	−5.54638			−0.397185
$196$	6.98702	−	0.426132i	0.499073	−	0.0304380i
$197$	−3.13854			−0.223612			−0.111806	−	0.993730i	$-0.535663\pi$
$197$	−3.13854			−0.223612			−0.111806	+	0.993730i	$0.535663\pi$
$198$	−26.6069	−	18.1403i	−1.89087	−	1.28917i
$199$	2.73079	+	2.53380i	0.193581	+	0.179617i	0.771008	−	0.636826i	$-0.219753\pi$
$199$	2.73079	+	2.53380i	0.193581	+	0.179617i	−0.577427	+	0.816442i	$0.695943\pi$
$200$	1.68421	+	4.29130i	0.119092	+	0.303441i
$201$	−15.6053	+	4.81361i	−1.10072	+	0.339526i
$202$	1.48804	+	6.51952i	0.104698	+	0.458712i
$203$	6.79835	+	1.87230i	0.477151	+	0.131410i
$204$	−2.93803	+	12.8723i	−0.205703	+	0.901244i
$205$	0.0328985	+	0.439000i	0.00229773	+	0.0306611i
$206$	−14.8020	−	4.56580i	−1.03130	−	0.318115i
$207$	1.62062	−	21.6257i	0.112641	−	1.50309i
$208$	−1.12262	+	2.86039i	−0.0778399	+	0.198333i
$209$	−12.7575	+	6.14368i	−0.882453	+	0.424967i
$210$	−4.36373	−	1.94005i	−0.301126	−	0.133876i
$211$	3.49217	+	1.68174i	0.240411	+	0.115776i	0.550210	−	0.835026i	$-0.314548\pi$
$211$	3.49217	+	1.68174i	0.240411	+	0.115776i	−0.309799	+	0.950802i	$0.600262\pi$
$212$	−4.63109	+	4.29702i	−0.318064	+	0.295121i
$213$	−35.1060	+	5.29137i	−2.40542	+	0.362559i
$214$	−5.57501	+	9.65620i	−0.381100	+	0.660084i
$215$	−3.28834	−	5.69557i	−0.224263	−	0.388434i
$216$	4.24031	+	5.31718i	0.288516	+	0.361788i
$217$	−1.08250	−	10.2463i	−0.0734846	−	0.695567i
$218$	3.32704	−	4.17197i	0.225335	−	0.282562i
$219$	38.7297	+	5.83757i	2.61711	+	0.394466i
$220$	−3.10412	+	2.11635i	−0.209280	+	0.142684i
$221$	11.5985	−	7.90772i	0.780199	−	0.531931i
$222$	−4.39826	−	0.662932i	−0.295192	−	0.0444931i
$223$	−17.2206	+	21.5939i	−1.15318	+	1.44604i	−0.279089	+	0.960265i	$0.590033\pi$
$223$	−17.2206	+	21.5939i	−1.15318	+	1.44604i	−0.874086	+	0.485771i	$0.838539\pi$
$224$	−1.88377	+	1.85779i	−0.125865	+	0.124129i
$225$	−15.3863	−	19.2938i	−1.02575	−	1.28625i
$226$	−1.12733	−	1.95259i	−0.0749887	−	0.129884i
$227$	−5.02860	+	8.70979i	−0.333760	+	0.578089i	−0.983246	−	0.182284i	$-0.941651\pi$
$227$	−5.02860	+	8.70979i	−0.333760	+	0.578089i	0.649486	+	0.760374i	$0.274984\pi$
$228$	6.72696	−	1.01393i	0.445504	−	0.0671489i
$229$	15.2844	−	14.1818i	1.01002	−	0.937163i	0.0119931	−	0.999928i	$-0.496182\pi$
$229$	15.2844	−	14.1818i	1.01002	−	0.937163i	0.998028	+	0.0627651i	$0.0199919\pi$
$230$	−2.27950	−	1.09775i	−0.150306	−	0.0723835i
$231$	−8.86550	+	45.1374i	−0.583307	+	2.96982i
$232$	−2.40126	+	1.15639i	−0.157651	+	0.0759206i
$233$	−2.63673	+	6.71827i	−0.172738	+	0.440129i	−0.990856	−	0.134921i	$-0.956922\pi$
$233$	−2.63673	+	6.71827i	−0.172738	+	0.440129i	0.818119	+	0.575050i	$0.195017\pi$
$234$	1.22924	−	16.4031i	0.0803581	−	1.07230i
$235$	5.51574	+	1.70138i	0.359807	+	0.110986i
$236$	−0.134225	−	1.79111i	−0.00873733	−	0.116592i
$237$	6.02115	−	26.3804i	0.391116	−	1.71359i
$238$	11.8914	−	2.16456i	0.770802	−	0.140308i
$239$	−5.97804	−	26.1915i	−0.386687	−	1.69419i	−0.675958	−	0.736940i	$-0.736270\pi$
$239$	−5.97804	−	26.1915i	−0.386687	−	1.69419i	0.289271	−	0.957247i	$-0.406587\pi$
$240$	1.72480	−	0.532030i	0.111335	−	0.0343424i
$241$	−8.19348	−	20.8767i	−0.527789	−	1.34478i	−0.907645	−	0.419738i	$-0.862122\pi$
$241$	−8.19348	−	20.8767i	−0.527789	−	1.34478i	0.379857	−	0.925045i	$-0.375973\pi$
$242$	18.4641	+	17.1322i	1.18692	+	1.10130i
$243$	8.26917	+	5.63783i	0.530468	+	0.361667i
$244$	−3.90373			−0.249911
$245$	−0.0607042	+	4.37126i	−0.00387825	+	0.279269i
$246$	−2.03730			−0.129893
$247$	−5.97604	−	4.07440i	−0.380246	−	0.259248i
$248$	2.85473	+	2.64880i	0.181275	+	0.168199i
$249$	7.45972	+	19.0071i	0.472741	+	1.20452i
$250$	−5.73503	+	1.76902i	−0.362715	+	0.111883i
$251$	0.519371	+	2.27552i	0.0327824	+	0.143629i	0.988671	−	0.150102i	$-0.0479601\pi$
$251$	0.519371	+	2.27552i	0.0327824	+	0.143629i	−0.955888	+	0.293731i	$0.905103\pi$
$252$	6.70471	−	12.4755i	0.422357	−	0.785882i
$253$	−5.42292	+	23.7593i	−0.340936	+	1.49374i
$254$	−0.0750630	−	1.00165i	−0.00470987	−	0.0628489i
$255$	−7.87951	−	2.43051i	−0.493434	−	0.152204i
$256$	0.0747301	−	0.997204i	0.00467063	−	0.0623252i
$257$	0.551413	−	1.40498i	0.0343962	−	0.0876401i	−0.912644	−	0.408756i	$-0.865963\pi$
$257$	0.551413	−	1.40498i	0.0343962	−	0.0876401i	0.947040	+	0.321116i	$0.104058\pi$
$258$	27.4214	−	13.2055i	1.70718	−	0.822136i
$259$	1.02652	+	3.94026i	0.0637849	+	0.244836i
$260$	−1.72900	−	0.832643i	−0.107228	−	0.0516383i
$261$	10.4586	−	9.70412i	0.647368	−	0.600670i
$262$	19.1021	−	2.87917i	1.18013	−	0.177876i
$263$	11.9521	−	20.7017i	0.737001	−	1.27652i	−0.216839	−	0.976207i	$-0.569575\pi$
$263$	11.9521	−	20.7017i	0.737001	−	1.27652i	0.953840	−	0.300316i	$-0.0970921\pi$
$264$	−8.69314	−	15.0570i	−0.535026	−	0.926692i
$265$	−2.45996	−	3.08469i	−0.151114	−	0.189491i
$266$	−3.27660	−	5.29595i	−0.200901	−	0.324715i
$267$	−12.8227	+	16.0791i	−0.784735	+	0.984026i
$268$	−5.58736	−	0.842160i	−0.341303	−	0.0514431i
$269$	−1.80312	+	1.22935i	−0.109938	+	0.0749546i	−0.617041	−	0.786931i	$-0.711669\pi$
$269$	−1.80312	+	1.22935i	−0.109938	+	0.0749546i	0.507103	+	0.861886i	$0.330716\pi$
$270$	−3.50933	+	2.39262i	−0.213571	+	0.145610i
$271$	29.9950	+	4.52101i	1.82206	+	0.274632i	0.968980	−	0.247141i	$-0.0794911\pi$
$271$	29.9950	+	4.52101i	1.82206	+	0.274632i	0.853084	+	0.521773i	$0.174729\pi$
$272$	−2.84833	+	3.57169i	−0.172705	+	0.216566i
$273$	−22.2316	+	7.60633i	−1.34552	+	0.460356i
$274$	4.72945	+	5.93054i	0.285716	+	0.358277i
$275$	13.8660	+	24.0166i	0.836149	+	1.44825i
$276$	5.85429	−	10.1399i	0.352387	−	0.610352i
$277$	−1.63883	+	0.247013i	−0.0984675	+	0.0148416i	−0.198091	−	0.980184i	$-0.563474\pi$
$277$	−1.63883	+	0.247013i	−0.0984675	+	0.0148416i	0.0996237	+	0.995025i	$0.468236\pi$
$278$	−7.89061	+	7.32141i	−0.473247	+	0.439109i
$279$	−18.7822	−	9.04503i	−1.12446	−	0.541512i
$280$	−1.06908	−	1.25988i	−0.0638897	−	0.0752922i
$281$	1.54138	−	0.742289i	0.0919510	−	0.0442813i	−0.387343	−	0.921936i	$-0.626607\pi$
$281$	1.54138	−	0.742289i	0.0919510	−	0.0442813i	0.479294	+	0.877654i	$0.340893\pi$
$282$	−9.75917	+	24.8659i	−0.581150	+	1.48075i
$283$	−1.80678	+	24.1098i	−0.107402	+	1.43318i	0.639778	+	0.768559i	$0.279026\pi$
$283$	−1.80678	+	24.1098i	−0.107402	+	1.43318i	−0.747180	+	0.664621i	$0.768593\pi$
$284$	−11.7381	−	3.62073i	−0.696529	−	0.214851i
$285$	0.317499	+	4.23673i	0.0188070	+	0.250963i
$286$	−4.11328	+	18.0215i	−0.243223	+	1.06563i
$287$	0.733913	+	1.71453i	0.0433215	+	0.101205i
$288$	1.19118	+	5.21890i	0.0701910	+	0.307527i
$289$	3.69803	−	1.14069i	0.217531	−	0.0670996i
$290$	−0.608105	−	1.54943i	−0.0357092	−	0.0909855i
$291$	−0.727082	−	0.674633i	−0.0426223	−	0.0395477i
$292$	11.1971	+	7.63402i	0.655258	+	0.446747i
$293$	23.9991			1.40204			0.701022	−	0.713140i	$-0.252728\pi$
$293$	23.9991			1.40204			0.701022	+	0.713140i	$0.252728\pi$
$294$	−20.1517	−	1.79188i	−1.17527	−	0.104504i
$295$	1.12173			0.0653098
$296$	−1.27157	−	0.866942i	−0.0739085	−	0.0503900i
$297$	29.9906	+	27.8272i	1.74023	+	1.61470i
$298$	−4.41613	−	11.2521i	−0.255820	−	0.651817i
$299$	−11.8954	+	3.66924i	−0.687928	+	0.212198i
$300$	−2.96478	−	12.9896i	−0.171172	−	0.749953i
$301$	−20.9916	−	18.3199i	−1.20993	−	1.05594i
$302$	−2.32845	+	10.2016i	−0.133988	+	0.587038i
$303$	−1.44432	−	19.2731i	−0.0829740	−	1.10721i
$304$	2.24924	+	0.693800i	0.129003	+	0.0397921i
$305$	0.182190	−	2.43116i	0.0104322	−	0.139208i
$306$	8.93441	−	22.7645i	0.510746	−	1.30136i
$307$	−6.62654	+	3.19117i	−0.378196	+	0.182130i	−0.613318	−	0.789836i	$-0.710166\pi$
$307$	−6.62654	+	3.19117i	−0.378196	+	0.182130i	0.235121	+	0.971966i	$0.424451\pi$
$308$	−9.53987	+	12.7400i	−0.543585	+	0.725927i
$309$	40.3357	+	19.4247i	2.29462	+	1.10503i
$310$	−1.78285	+	1.65424i	−0.101259	+	0.0939548i
$311$	27.4360	−	4.13531i	1.55575	−	0.234492i	0.685860	−	0.727733i	$-0.259426\pi$
$311$	27.4360	−	4.13531i	1.55575	−	0.234492i	0.869893	+	0.493241i	$0.164188\pi$
$312$	4.44048	−	7.69113i	0.251392	−	0.435424i
$313$	2.28195	+	3.95246i	0.128983	+	0.223406i	0.923283	−	0.384120i	$-0.125495\pi$
$313$	2.28195	+	3.95246i	0.128983	+	0.223406i	−0.794300	+	0.607526i	$0.792162\pi$
$314$	−8.22628	−	10.3154i	−0.464236	−	0.582134i
$315$	7.45656	+	4.75780i	0.420130	+	0.268072i
$316$	5.83732	−	7.31977i	0.328375	−	0.411769i
$317$	−2.68630	−	0.404894i	−0.150877	−	0.0227411i	0.0731692	−	0.997320i	$-0.476689\pi$
$317$	−2.68630	−	0.404894i	−0.150877	−	0.0227411i	−0.224047	+	0.974578i	$0.571927\pi$
$318$	15.0861	−	10.2856i	0.845989	−	0.576785i
$319$	−13.2470	+	9.03166i	−0.741690	+	0.505676i
$320$	0.617550	+	0.0930807i	0.0345221	+	0.00520337i
$321$	20.0923	−	25.1949i	1.12144	−	1.40624i
$322$	−10.6424	−	1.27400i	−0.593077	−	0.0709971i
$323$	−6.70445	−	8.40711i	−0.373045	−	0.467784i
$324$	−1.79826	−	3.11467i	−0.0999032	−	0.173037i
$325$	−7.08277	+	12.2677i	−0.392881	+	0.680490i
$326$	−7.01138	+	1.05680i	−0.388325	+	0.0585305i
$327$	−11.3054	+	10.4899i	−0.625192	+	0.580093i
$328$	−0.635097	−	0.305847i	−0.0350674	−	0.0168876i
$329$	24.4420	−	0.744657i	1.34753	−	0.0410542i
$330$	9.78288	−	4.71119i	0.538530	−	0.259342i
$331$	−6.49751	+	16.5554i	−0.357135	+	0.909966i	0.633538	+	0.773711i	$0.281602\pi$
$331$	−6.49751	+	16.5554i	−0.357135	+	0.909966i	−0.990674	+	0.136255i	$0.956493\pi$
$332$	−0.527953	+	7.04504i	−0.0289752	+	0.386647i
$333$	7.87237	+	2.42830i	0.431403	+	0.133070i
$334$	−0.873911	−	11.6615i	−0.0478183	−	0.638091i
$335$	0.785247	−	3.44039i	0.0429026	−	0.187969i
$336$	6.18389	−	4.49793i	0.337359	−	0.245382i
$337$	−1.47384	−	6.45731i	−0.0802851	−	0.351752i	0.918790	−	0.394746i	$-0.129167\pi$
$337$	−1.47384	−	6.45731i	−0.0802851	−	0.351752i	−0.999075	+	0.0429942i	$0.986310\pi$
$338$	3.39979	−	1.04870i	0.184924	−	0.0570416i
$339$	2.38069	+	6.06590i	0.129301	+	0.329454i
$340$	−2.09144	−	1.94057i	−0.113424	−	0.105242i
$341$	19.3561	+	13.1968i	1.04819	+	0.714645i
$342$	−12.6003			−0.681344
$343$	5.75144	+	17.6046i	0.310548	+	0.950558i
$344$	10.5307			0.567776
$345$	6.04171	+	4.11917i	0.325275	+	0.221769i
$346$	0.0720683	+	0.0668696i	0.00387442	+	0.00359493i
$347$	−6.90670	−	17.5980i	−0.370771	−	0.944709i	−0.987512	−	0.157543i	$-0.949643\pi$
$347$	−6.90670	−	17.5980i	−0.370771	−	0.944709i	0.616741	−	0.787166i	$-0.288453\pi$
$348$	7.36068	−	2.27047i	0.394574	−	0.121710i
$349$	−1.67358	−	7.33245i	−0.0895849	−	0.392497i	0.910179	−	0.414215i	$-0.135944\pi$
$349$	−1.67358	−	7.33245i	−0.0895849	−	0.392497i	−0.999764	+	0.0217175i	$0.993087\pi$
$350$	−9.86359	+	7.17441i	−0.527231	+	0.383488i
$351$	−4.65023	+	20.3740i	−0.248211	+	1.08748i
$352$	−0.449550	−	5.99883i	−0.0239611	−	0.319738i
$353$	−16.9488	−	5.22803i	−0.902096	−	0.278260i	−0.191195	−	0.981552i	$-0.561236\pi$
$353$	−16.9488	−	5.22803i	−0.902096	−	0.278260i	−0.710901	+	0.703292i	$0.751713\pi$
$354$	−0.387935	+	5.17663i	−0.0206185	+	0.275135i
$355$	2.80274	−	7.14128i	0.148754	−	0.379020i
$356$	−6.41113	+	3.08744i	−0.339789	+	0.163634i
$357$	−34.9167	+	1.06378i	−1.84799	+	0.0563011i
$358$	17.1023	+	8.23604i	0.903885	+	0.435288i
$359$	3.11011	−	2.88576i	0.164145	−	0.152305i	−0.593824	−	0.804595i	$-0.702382\pi$
$359$	3.11011	−	2.88576i	0.164145	−	0.152305i	0.757969	+	0.652291i	$0.226192\pi$
$360$	−3.30582	+	0.498272i	−0.174232	+	0.0262612i
$361$	6.72977	−	11.6563i	0.354199	−	0.613490i
$362$	−4.85894	−	8.41593i	−0.255380	−	0.442332i
$363$	−45.3887	−	56.9156i	−2.38229	−	2.98729i
$364$	−8.07225	−	0.966327i	−0.423101	−	0.0506493i
$365$	−5.27689	+	6.61701i	−0.276205	+	0.346350i
$366$	11.1564	+	1.68156i	0.583157	+	0.0878967i
$367$	4.79172	−	3.26694i	0.250126	−	0.170533i	−0.431767	−	0.901985i	$-0.642110\pi$
$367$	4.79172	−	3.26694i	0.250126	−	0.170533i	0.681892	+	0.731453i	$0.261157\pi$
$368$	3.34723	−	2.28210i	0.174486	−	0.118963i
$369$	3.73129	+	0.562402i	0.194243	+	0.0292775i
$370$	0.599259	−	0.751447i	0.0311540	−	0.0390659i
$371$	−14.0906	−	8.99078i	−0.731548	−	0.466778i
$372$	−7.01752	−	8.79969i	−0.363841	−	0.456243i
$373$	−2.06168	−	3.57094i	−0.106750	−	0.184896i	0.807702	−	0.589591i	$-0.200711\pi$
$373$	−2.06168	−	3.57094i	−0.106750	−	0.184896i	−0.914452	+	0.404695i	$0.867378\pi$
$374$	−13.7408	+	23.7998i	−0.710522	+	1.23066i
$375$	17.1521	−	2.58527i	0.885733	−	0.133503i
$376$	−6.77524	+	6.28650i	−0.349406	+	0.324202i
$377$	−7.37862	−	3.55336i	−0.380018	−	0.183007i
$378$	−10.7852	+	14.4030i	−0.554731	+	0.740812i
$379$	27.5890	−	13.2862i	1.41715	−	0.682464i	0.440591	−	0.897708i	$-0.354769\pi$
$379$	27.5890	−	13.2862i	1.41715	−	0.682464i	0.976560	+	0.215244i	$0.0690546\pi$
$380$	−0.537058	+	1.36840i	−0.0275505	+	0.0701976i
$381$	−0.216945	+	2.89493i	−0.0111144	+	0.148312i
$382$	−1.54515	−	0.476616i	−0.0790568	−	0.0243858i
$383$	−0.965999	−	12.8904i	−0.0493603	−	0.658667i	−0.965932	−	0.258796i	$-0.916674\pi$
$383$	−0.965999	−	12.8904i	−0.0493603	−	0.658667i	0.916572	−	0.399870i	$-0.130945\pi$
$384$	−0.643125	+	2.81771i	−0.0328193	+	0.143791i
$385$	−7.48896	−	6.53582i	−0.381673	−	0.333096i
$386$	−0.800467	−	3.50708i	−0.0407427	−	0.178505i
$387$	−53.8675	+	16.6159i	−2.73824	+	0.844634i
$388$	−0.125378	−	0.319459i	−0.00636512	−	0.0162181i
$389$	−6.94109	−	6.44039i	−0.351927	−	0.326541i	0.484322	−	0.874890i	$-0.339066\pi$
$389$	−6.94109	−	6.44039i	−0.351927	−	0.326541i	−0.836250	+	0.548349i	$0.815257\pi$
$390$	4.58264	+	3.12439i	0.232051	+	0.158210i
$391$	−18.5072			−0.935949
$392$	−6.01299	−	3.58384i	−0.303702	−	0.181011i
$393$	−55.8319			−2.81635
$394$	2.59318	+	1.76800i	0.130643	+	0.0890706i
$395$	4.28617	+	3.97698i	0.215661	+	0.200104i
$396$	11.7649	+	29.9764i	0.591207	+	1.50637i
$397$	−14.5762	+	4.49616i	−0.731558	+	0.225656i	−0.638085	−	0.769966i	$-0.720273\pi$
$397$	−14.5762	+	4.49616i	−0.731558	+	0.225656i	−0.0934730	+	0.995622i	$0.529797\pi$
$398$	−0.828943	−	3.63183i	−0.0415511	−	0.182047i
$399$	7.08290	+	16.5467i	0.354589	+	0.828371i
$400$	1.02581	−	4.49439i	0.0512907	−	0.224719i
$401$	−0.113972	−	1.52085i	−0.00569150	−	0.0759477i	0.993635	−	0.112650i	$-0.0359338\pi$
$401$	−0.113972	−	1.52085i	−0.00569150	−	0.0759477i	−0.999326	+	0.0367020i	$0.988315\pi$
$402$	15.6053	+	4.81361i	0.778323	+	0.240081i
$403$	−0.894254	+	11.9330i	−0.0445460	+	0.594424i
$404$	2.44310	−	6.22493i	0.121549	−	0.309702i
$405$	2.02368	−	0.974553i	0.100557	−	0.0484259i
$406$	−4.56236	−	5.37661i	−0.226426	−	0.266837i
$407$	−8.34117	−	4.01690i	−0.413456	−	0.199110i
$408$	9.67876	−	8.98058i	0.479170	−	0.444605i
$409$	2.81880	−	0.424866i	0.139381	−	0.0210083i	−0.0789813	−	0.996876i	$-0.525167\pi$
$409$	2.81880	−	0.424866i	0.139381	−	0.0210083i	0.218362	+	0.975868i	$0.429929\pi$
$410$	0.220115	−	0.381251i	0.0108707	−	0.0188287i
$411$	−10.9616	−	18.9861i	−0.540697	−	0.936515i
$412$	9.65796	+	12.1107i	0.475813	+	0.596651i
$413$	4.49624	−	1.53835i	0.221246	−	0.0756972i
$414$	−13.5212	+	16.9551i	−0.664532	+	0.833296i
$415$	−4.36287	−	0.657597i	−0.214165	−	0.0322801i
$416$	2.53887	−	1.73097i	0.124478	−	0.0848680i
$417$	25.7043	−	17.5249i	1.25874	−	0.858197i
$418$	14.0016	+	2.11040i	0.684840	+	0.103223i
$419$	7.56791	−	9.48985i	0.369716	−	0.463610i	−0.561819	−	0.827260i	$-0.689898\pi$
$419$	7.56791	−	9.48985i	0.369716	−	0.463610i	0.931535	+	0.363650i	$0.118470\pi$
$420$	2.51261	+	4.06112i	0.122603	+	0.198162i
$421$	12.3730	+	15.5153i	0.603025	+	0.756169i	0.985846	−	0.167653i	$-0.0536190\pi$
$421$	12.3730	+	15.5153i	0.603025	+	0.756169i	−0.382821	+	0.923822i	$0.625048\pi$
$422$	−1.93801	−	3.35673i	−0.0943409	−	0.163403i
$423$	24.7381	−	42.8477i	1.20281	−	2.08333i
$424$	6.24698	−	0.941581i	0.303380	−	0.0457272i
$425$	−15.4381	+	14.3245i	−0.748857	+	0.694838i
$426$	31.9867	+	15.4040i	1.54976	+	0.746324i
$427$	−2.60383	−	9.99469i	−0.126008	−	0.483677i
$428$	10.0458	−	4.83781i	0.485583	−	0.233845i
$429$	19.5182	−	49.7316i	0.942349	−	2.40107i
$430$	−0.491475	+	6.55828i	−0.0237010	+	0.316268i
$431$	−2.36009	−	0.727992i	−0.113682	−	0.0350662i	0.237392	−	0.971414i	$-0.423707\pi$
$431$	−2.36009	−	0.727992i	−0.113682	−	0.0350662i	−0.351074	+	0.936348i	$0.614183\pi$
$432$	−0.508234	−	6.78191i	−0.0244524	−	0.326295i
$433$	−2.26028	+	9.90293i	−0.108622	+	0.475905i	0.891132	+	0.453744i	$0.149912\pi$
$433$	−2.26028	+	9.90293i	−0.108622	+	0.475905i	−0.999754	+	0.0221610i	$0.992945\pi$
$434$	−4.87757	+	9.07572i	−0.234131	+	0.435648i
$435$	1.07047	+	4.69005i	0.0513252	+	0.224871i
$436$	−5.09908	+	1.57286i	−0.244202	+	0.0753263i
$437$	3.48378	+	8.87653i	0.166652	+	0.424622i
$438$	−28.7116	−	26.6405i	−1.37189	−	1.27293i
$439$	−8.76229	−	5.97403i	−0.418201	−	0.285125i	0.335882	−	0.941904i	$-0.390966\pi$
$439$	−8.76229	−	5.97403i	−0.418201	−	0.285125i	−0.754083	+	0.656780i	$0.771918\pi$
$440$	3.75693			0.179104
$441$	36.4130	+	8.84474i	1.73395	+	0.421178i
$442$	−14.0377			−0.667706
$443$	25.2154	+	17.1915i	1.19802	+	0.816795i	0.987005	−	0.160688i	$-0.0513714\pi$
$443$	25.2154	+	17.1915i	1.19802	+	0.816795i	0.211013	+	0.977483i	$0.432324\pi$
$444$	3.26057	+	3.02537i	0.154740	+	0.143578i
$445$	−1.62358	−	4.13681i	−0.0769651	−	0.196104i
$446$	26.3926	−	8.14104i	1.24973	−	0.385489i
$447$	7.77389	+	34.0596i	0.367692	+	1.61097i
$448$	2.60298	−	0.473815i	0.122979	−	0.0223856i
$449$	−3.82450	+	16.7562i	−0.180489	+	0.790775i	0.800908	+	0.598787i	$0.204351\pi$
$449$	−3.82450	+	16.7562i	−0.180489	+	0.790775i	−0.981397	+	0.191988i	$0.938507\pi$
$450$	1.84417	+	24.6087i	0.0869349	+	1.16006i
$451$	−4.05206	−	1.24990i	−0.190804	−	0.0588553i
$452$	−0.168490	+	2.24835i	−0.00792513	+	0.105753i
$453$	11.0489	−	28.1522i	0.519123	−	1.32270i
$454$	9.06123	−	4.36366i	0.425264	−	0.204797i
$455$	0.978548	−	4.98213i	0.0458750	−	0.233566i
$456$	−6.12924	−	2.95169i	−0.287028	−	0.138225i
$457$	−19.3152	+	17.9219i	−0.903526	+	0.838350i	−0.987419	−	0.158125i	$-0.949455\pi$
$457$	−19.3152	+	17.9219i	−0.903526	+	0.838350i	0.0838930	+	0.996475i	$0.473265\pi$
$458$	−20.6175	+	3.10759i	−0.963392	+	0.145208i
$459$	−15.5346	+	26.9066i	−0.725091	+	1.25589i
$460$	1.26503	+	2.19109i	0.0589822	+	0.102160i
$461$	0.00228490	+	0.00286518i	0.000106418	+	0.000133445i	0.781885	−	0.623423i	$-0.214259\pi$
$461$	0.00228490	+	0.00286518i	0.000106418	+	0.000133445i	−0.781778	+	0.623557i	$0.785687\pi$
$462$	32.7518	−	32.3001i	1.52375	−	1.50274i
$463$	−10.8501	+	13.6056i	−0.504247	+	0.632306i	−0.967181	−	0.254087i	$-0.918225\pi$
$463$	−10.8501	+	13.6056i	−0.504247	+	0.632306i	0.462934	+	0.886393i	$0.346797\pi$
$464$	2.63543	+	0.397228i	0.122347	+	0.0184408i
$465$	5.80778	−	3.95968i	0.269329	−	0.183626i
$466$	5.96311	−	4.06558i	0.276236	−	0.188334i
$467$	28.8804	+	4.35302i	1.33642	+	0.201434i	0.778074	−	0.628172i	$-0.216197\pi$
$467$	28.8804	+	4.35302i	1.33642	+	0.201434i	0.558350	+	0.829606i	$0.311435\pi$
$468$	−10.2558	+	12.8604i	−0.474076	+	0.594473i
$469$	−1.57066	−	14.8670i	−0.0725262	−	0.686495i
$470$	−3.59890	−	4.51288i	−0.166005	−	0.208163i
$471$	19.0664	+	33.0240i	0.878533	+	1.52166i
$472$	−0.898068	+	1.55550i	−0.0413369	+	0.0715977i
$473$	62.6412	−	9.44164i	2.88025	−	0.434127i
$474$	−19.8355	+	18.4047i	−0.911075	+	0.845354i
$475$	9.77643	+	4.70808i	0.448573	+	0.216022i
$476$	−11.0444	−	4.91020i	−0.506221	−	0.225059i
$477$	−30.4695	+	14.6733i	−1.39510	+	0.671845i
$478$	−9.81491	+	25.0080i	−0.448924	+	1.14384i
$479$	2.40370	−	32.0751i	0.109828	−	1.46555i	−0.621442	−	0.783460i	$-0.713453\pi$
$479$	2.40370	−	32.0751i	0.109828	−	1.46555i	0.731269	−	0.682089i	$-0.238928\pi$
$480$	−1.72480	−	0.532030i	−0.0787259	−	0.0242837i
$481$	−0.353399	−	4.71579i	−0.0161136	−	0.215021i
$482$	−4.99047	+	21.8647i	−0.227309	+	0.995908i
$483$	29.8660	+	8.22525i	1.35895	+	0.374262i
$484$	−5.60486	−	24.5565i	−0.254766	−	1.11620i
$485$	0.204804	−	0.0631736i	0.00929967	−	0.00286857i
$486$	−3.65641	−	9.31638i	−0.165858	−	0.422600i
$487$	−18.4210	−	17.0922i	−0.834737	−	0.774523i	0.141795	−	0.989896i	$-0.454713\pi$
$487$	−18.4210	−	17.0922i	−0.834737	−	0.774523i	−0.976532	+	0.215373i	$0.930903\pi$
$488$	3.22541	+	2.19905i	0.146008	+	0.0995462i
$489$	20.4930			0.926726
$490$	2.51257	−	3.57751i	0.113507	−	0.161615i
$491$	7.07747			0.319402			0.159701	−	0.987165i	$-0.448947\pi$
$491$	7.07747			0.319402			0.159701	+	0.987165i	$0.448947\pi$
$492$	1.68329	+	1.14765i	0.0758888	+	0.0517401i
$493$	−8.92536	−	8.28152i	−0.401978	−	0.372981i
$494$	2.64245	+	6.73285i	0.118889	+	0.302925i
$495$	−19.2178	+	5.92790i	−0.863775	+	0.266439i
$496$	−0.866565	−	3.79667i	−0.0389099	−	0.170475i
$497$	1.44068	−	32.4681i	0.0646232	−	1.45639i
$498$	4.54355	−	19.9066i	0.203601	−	0.892035i
$499$	−1.50686	−	20.1076i	−0.0674562	−	0.900141i	−0.923589	−	0.383385i	$-0.874758\pi$
$499$	−1.50686	−	20.1076i	−0.0674562	−	0.900141i	0.856133	−	0.516756i	$-0.172861\pi$
$500$	5.73503	+	1.76902i	0.256479	+	0.0791132i
$501$	−2.52576	+	33.7039i	−0.112843	+	1.50578i
$502$	0.852718	−	2.17269i	0.0380587	−	0.0969720i
$503$	1.92073	−	0.924972i	0.0856409	−	0.0412425i	−0.390573	−	0.920572i	$-0.627723\pi$
$503$	1.92073	−	0.924972i	0.0856409	−	0.0412425i	0.476214	+	0.879329i	$0.342009\pi$
$504$	−12.5674	+	6.53084i	−0.559796	+	0.290907i
$505$	3.76273	+	1.81204i	0.167439	+	0.0806346i
$506$	17.8647	−	16.5761i	0.794185	−	0.736896i
$507$	−10.1680	+	1.53258i	−0.451576	+	0.0680642i
$508$	−0.502228	+	0.869884i	−0.0222827	+	0.0385948i
$509$	7.43036	+	12.8698i	0.329345	+	0.570442i	0.982382	−	0.186884i	$-0.0598388\pi$
$509$	7.43036	+	12.8698i	0.329345	+	0.570442i	−0.653037	+	0.757326i	$0.726505\pi$
$510$	5.14120	+	6.44687i	0.227656	+	0.285472i
$511$	−12.0768	+	33.7597i	−0.534245	+	1.49344i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	15.8293	+	2.38589i	0.698882	+	0.105340i
$514$	−1.24705	+	0.850225i	−0.0550050	+	0.0375018i
$515$	−7.99304	+	5.44956i	−0.352215	+	0.240136i
$516$	−30.0955	−	4.53617i	−1.32488	−	0.199694i
$517$	−34.6658	+	43.4696i	−1.52460	+	1.91179i
$518$	1.37147	−	3.83385i	0.0602591	−	0.168450i
$519$	−0.177159	−	0.222150i	−0.00777642	−	0.00975132i
$520$	0.959523	+	1.66194i	0.0420779	+	0.0728810i
$521$	−9.80584	+	16.9842i	−0.429602	+	0.744092i	−0.996838	−	0.0794632i	$-0.974679\pi$
$521$	−9.80584	+	16.9842i	−0.429602	+	0.744092i	0.567236	+	0.823555i	$0.308013\pi$
$522$	−14.1078	+	2.12641i	−0.617481	+	0.0930703i
$523$	−10.1698	+	9.43619i	−0.444694	+	0.412616i	−0.870477	−	0.492210i	$-0.836189\pi$
$523$	−10.1698	+	9.43619i	−0.444694	+	0.412616i	0.425783	+	0.904826i	$0.359999\pi$
$524$	−17.4048	−	8.38169i	−0.760330	−	0.366156i
$525$	31.2795	−	16.2549i	1.36515	−	0.709422i
$526$	−21.5370	+	10.3717i	−0.939059	+	0.452227i
$527$	−6.49964	+	16.5608i	−0.283129	+	0.721400i
$528$	−1.29928	+	17.3377i	−0.0565438	+	0.754525i
$529$	−6.29539	−	1.94187i	−0.273713	−	0.0844292i
$530$	0.294845	+	3.93444i	0.0128073	+	0.170901i
$531$	2.13952	−	9.37386i	0.0928474	−	0.406791i
$532$	−0.276061	+	6.22149i	−0.0119688	+	0.269736i
$533$	−0.481988	−	2.11173i	−0.0208772	−	0.0914691i
$534$	19.6523	−	6.06193i	0.850438	−	0.262325i
$535$	2.54404	+	6.48212i	0.109989	+	0.280246i
$536$	4.14209	+	3.84330i	0.178911	+	0.166005i
$537$	−45.3289	−	30.9047i	−1.95608	−	1.33364i
$538$	2.18232			0.0940867
$539$	−38.9812	−	15.9272i	−1.67904	−	0.686031i
$540$	4.24735			0.182777
$541$	−14.6356	−	9.97835i	−0.629232	−	0.429003i	0.206267	−	0.978496i	$-0.433869\pi$
$541$	−14.6356	−	9.97835i	−0.629232	−	0.429003i	−0.835498	+	0.549493i	$0.814821\pi$
$542$	−22.2362	−	20.6322i	−0.955127	−	0.886229i
$543$	10.2611	+	26.1449i	0.440346	+	1.12198i
$544$	4.36541	−	1.34655i	0.187165	−	0.0577328i
$545$	−0.741565	−	3.24901i	−0.0317652	−	0.139172i
$546$	22.6534	+	6.23885i	0.969475	+	0.266998i
$547$	6.61248	−	28.9712i	0.282729	−	1.23872i	−0.611549	−	0.791207i	$-0.709453\pi$
$547$	6.61248	−	28.9712i	0.282729	−	1.23872i	0.894278	−	0.447512i	$-0.147690\pi$
$548$	−0.566861	−	7.56423i	−0.0242151	−	0.323128i
$549$	−19.9687	−	6.15953i	−0.852244	−	0.262882i
$550$	2.07241	−	27.6544i	0.0883679	−	1.17919i
$551$	−2.29193	+	5.83974i	−0.0976395	+	0.248781i
$552$	−10.5491	+	5.08016i	−0.448998	+	0.216226i
$553$	22.6343	+	10.0629i	0.962509	+	0.427917i
$554$	1.49321	+	0.719091i	0.0634403	+	0.0305513i
$555$	−2.03631	+	1.88942i	−0.0864366	+	0.0802015i
$556$	10.6438	−	1.60430i	0.451399	−	0.0680374i
$557$	−0.637371	+	1.10396i	−0.0270063	+	0.0467763i	−0.879213	−	0.476430i	$-0.841931\pi$
$557$	−0.637371	+	1.10396i	−0.0270063	+	0.0467763i	0.852206	+	0.523206i	$0.175264\pi$
$558$	10.4233	+	18.0538i	0.441255	+	0.764276i
$559$	20.1753	+	25.2991i	0.853325	+	1.07004i
$560$	0.173599	+	1.64320i	0.00733589	+	0.0694377i
$561$	49.5218	−	62.0984i	2.09081	−	2.62180i
$562$	−1.69169	−	0.254982i	−0.0713598	−	0.0107558i
$563$	−14.6704	+	10.0021i	−0.618284	+	0.421539i	−0.831546	−	0.555456i	$-0.812544\pi$
$563$	−14.6704	+	10.0021i	−0.618284	+	0.421539i	0.213262	+	0.976995i	$0.431591\pi$
$564$	22.0709	−	15.0477i	0.929352	−	0.633621i
$565$	−1.39236	−	0.209865i	−0.0585771	−	0.00882908i
$566$	15.0744	−	18.9027i	0.633624	−	0.794539i
$567$	6.77502	−	6.68158i	0.284524	−	0.280600i
$568$	7.65886	+	9.60391i	0.321359	+	0.402971i
$569$	−5.04575	−	8.73949i	−0.211529	−	0.366379i	0.740664	−	0.671875i	$-0.234511\pi$
$569$	−5.04575	−	8.73949i	−0.211529	−	0.366379i	−0.952193	+	0.305497i	$0.901178\pi$
$570$	2.12431	−	3.67941i	0.0889774	−	0.154113i
$571$	1.85309	−	0.279308i	0.0775494	−	0.0116887i	−0.110153	−	0.993915i	$-0.535134\pi$
$571$	1.85309	−	0.279308i	0.0775494	−	0.0116887i	0.187702	+	0.982226i	$0.439896\pi$
$572$	13.5504	−	12.5729i	0.566571	−	0.525701i
$573$	4.21057	+	2.02771i	0.175899	+	0.0847086i
$574$	0.359440	−	1.83004i	0.0150027	−	0.0763843i
$575$	16.8263	−	8.10310i	0.701703	−	0.337922i
$576$	1.95571	−	4.98308i	0.0814881	−	0.207628i
$577$	−1.76779	+	23.5895i	−0.0735942	+	0.982046i	0.831138	+	0.556066i	$0.187690\pi$
$577$	−1.76779	+	23.5895i	−0.0735942	+	0.982046i	−0.904733	+	0.425980i	$0.859929\pi$
$578$	−3.69803	−	1.14069i	−0.153818	−	0.0474466i
$579$	0.776949	+	10.3677i	0.0322889	+	0.430865i
$580$	−0.370383	+	1.62275i	−0.0153793	+	0.0673812i
$581$	−18.3895	+	3.34741i	−0.762926	+	0.138874i
$582$	0.220709	+	0.966988i	0.00914867	+	0.0400829i
$583$	36.3157	−	11.2019i	1.50404	−	0.463936i
$584$	−4.95104	−	12.6150i	−0.204876	−	0.522014i
$585$	−7.53056	−	6.98733i	−0.311350	−	0.288891i
$586$	−19.8290	−	13.5192i	−0.819128	−	0.558472i
$587$	4.98816			0.205883			0.102942	−	0.994687i	$-0.467174\pi$
$587$	4.98816			0.205883			0.102942	+	0.994687i	$0.467174\pi$
$588$	15.6407	+	12.8324i	0.645013	+	0.529199i
$589$	9.16648			0.377698
$590$	−0.926819	−	0.631895i	−0.0381565	−	0.0260147i
$591$	−6.64946	−	6.16980i	−0.273522	−	0.253792i
$592$	0.562255	+	1.43260i	0.0231085	+	0.0588796i
$593$	−10.2624	+	3.16552i	−0.421425	+	0.129992i	−0.498212	−	0.867055i	$-0.666010\pi$
$593$	−10.2624	+	3.16552i	−0.421425	+	0.129992i	0.0767875	+	0.997047i	$0.475534\pi$
$594$	−9.10377	−	39.8862i	−0.373532	−	1.63655i
$595$	3.57342	−	6.64909i	0.146496	−	0.272586i
$596$	−2.68976	+	11.7846i	−0.110177	+	0.482717i
$597$	0.804588	+	10.7365i	0.0329296	+	0.439415i
$598$	11.8954	+	3.66924i	0.486439	+	0.150046i
$599$	−1.95830	+	26.1317i	−0.0800138	+	1.06771i	0.802260	+	0.596974i	$0.203631\pi$
$599$	−1.95830	+	26.1317i	−0.0800138	+	1.06771i	−0.882274	+	0.470736i	$0.843988\pi$
$600$	−4.86766	+	12.4026i	−0.198722	+	0.506334i
$601$	14.1373	−	6.80818i	0.576674	−	0.277711i	−0.122728	−	0.992440i	$-0.539164\pi$
$601$	14.1373	−	6.80818i	0.576674	−	0.277711i	0.699402	+	0.714729i	$0.253450\pi$
$602$	7.02407	+	26.9616i	0.286280	+	1.09887i
$603$	−27.2522	−	13.1240i	−1.10980	−	0.534449i
$604$	7.67064	−	7.11731i	0.312114	−	0.289599i
$605$	15.5549	−	2.34452i	0.632395	−	0.0953182i
$606$	−9.66357	+	16.7378i	−0.392556	+	0.679927i
$607$	20.5743	+	35.6358i	0.835087	+	1.44641i	0.893960	+	0.448147i	$0.147916\pi$
$607$	20.5743	+	35.6358i	0.835087	+	1.44641i	−0.0588732	+	0.998265i	$0.518751\pi$
$608$	−1.46758	−	1.84029i	−0.0595183	−	0.0746335i
$609$	10.7227	+	17.3311i	0.434507	+	0.702291i
$610$	−1.52005	+	1.90609i	−0.0615452	+	0.0771753i
$611$	−28.0832	−	4.23287i	−1.13613	−	0.171243i
$612$	−20.2057	+	13.7760i	−0.816766	+	0.556861i
$613$	−38.8725	+	26.5028i	−1.57005	+	1.07044i	−0.609326	+	0.792920i	$0.708560\pi$
$613$	−38.8725	+	26.5028i	−1.57005	+	1.07044i	−0.960720	+	0.277520i	$0.910488\pi$
$614$	7.27275	+	1.09619i	0.293504	+	0.0442387i
$615$	−0.793294	+	0.994759i	−0.0319887	+	0.0401126i
$616$	15.0589	−	5.15226i	0.606740	−	0.207590i
$617$	−10.1268	−	12.6986i	−0.407688	−	0.511225i	0.535022	−	0.844838i	$-0.320303\pi$
$617$	−10.1268	−	12.6986i	−0.407688	−	0.511225i	−0.942710	+	0.333614i	$0.891732\pi$
$618$	−22.3846	−	38.7713i	−0.900442	−	1.55961i
$619$	4.40107	−	7.62287i	0.176894	−	0.306389i	−0.763921	−	0.645310i	$-0.776728\pi$
$619$	4.40107	−	7.62287i	0.176894	−	0.306389i	0.940815	+	0.338920i	$0.110062\pi$
$620$	2.40493	−	0.362485i	0.0965843	−	0.0145577i
$621$	20.1968	−	18.7399i	0.810469	−	0.752006i
$622$	−24.9982	−	12.0385i	−1.00234	−	0.482700i
$623$	−12.1810	−	14.3550i	−0.488023	−	0.575122i
$624$	−8.00146	+	3.85330i	−0.320315	+	0.154255i
$625$	7.05168	−	17.9674i	0.282067	−	0.718696i
$626$	0.341061	−	4.55114i	0.0136315	−	0.181900i
$627$	−39.1060	−	12.0626i	−1.56174	−	0.481734i
$628$	0.985984	+	13.1570i	0.0393450	+	0.525023i
$629$	1.56447	−	6.85438i	0.0623794	−	0.273302i
$630$	−3.48074	−	8.13151i	−0.138676	−	0.323967i
$631$	7.33454	+	32.1347i	0.291983	+	1.27926i	0.881761	+	0.471697i	$0.156358\pi$
$631$	7.33454	+	32.1347i	0.291983	+	1.27926i	−0.589778	+	0.807566i	$0.700785\pi$
$632$	−8.94640	+	2.75960i	−0.355868	+	0.109771i
$633$	4.09269	+	10.4280i	0.162670	+	0.414476i
$634$	1.99144	+	1.84778i	0.0790901	+	0.0733848i
$635$	−0.518306	−	0.353375i	−0.0205684	−	0.0140233i
$636$	−18.2588			−0.724009
$637$	−2.91019	−	21.3119i	−0.115306	−	0.844407i
$638$	16.0329			0.634749
$639$	−54.3309	−	37.0422i	−2.14930	−	1.46537i
$640$	−0.457810	−	0.424785i	−0.0180965	−	0.0167911i
$641$	−15.2939	−	38.9681i	−0.604071	−	1.53915i	−0.825755	−	0.564029i	$-0.809251\pi$
$641$	−15.2939	−	38.9681i	−0.604071	−	1.53915i	0.221684	−	0.975119i	$-0.428845\pi$
$642$	−30.7938	+	9.49864i	−1.21534	+	0.374881i
$643$	3.75159	+	16.4368i	0.147948	+	0.648203i	0.993454	+	0.114236i	$0.0364421\pi$
$643$	3.75159	+	16.4368i	0.147948	+	0.648203i	−0.845505	+	0.533967i	$0.820701\pi$
$644$	8.07548	+	7.04770i	0.318219	+	0.277718i
$645$	4.22962	−	18.5312i	0.166541	−	0.729664i
$646$	0.803580	+	10.7230i	0.0316164	+	0.421892i
$647$	3.04252	+	0.938492i	0.119614	+	0.0368959i	0.353984	−	0.935251i	$-0.384827\pi$
$647$	3.04252	+	0.938492i	0.119614	+	0.0368959i	−0.234370	+	0.972147i	$0.575303\pi$
$648$	−0.268768	+	3.58646i	−0.0105582	+	0.140889i
$649$	−3.94748	+	10.0580i	−0.154952	+	0.394812i
$650$	12.7627	−	6.14620i	0.500595	−	0.241074i
$651$	17.8490	−	23.8364i	0.699558	−	0.934222i
$652$	6.38839	+	3.07649i	0.250189	+	0.120485i
$653$	−27.1829	+	25.2220i	−1.06375	+	0.987014i	−0.999940	−	0.0109480i	$-0.996515\pi$
$653$	−27.1829	+	25.2220i	−1.06375	+	0.987014i	−0.0638083	+	0.997962i	$0.520325\pi$
$654$	15.2502	−	2.29859i	0.596329	−	0.0898821i
$655$	6.03224	−	10.4481i	0.235699	−	0.408243i
$656$	0.352452	+	0.610465i	0.0137609	+	0.0238347i
$657$	45.2308	+	56.7176i	1.76462	+	2.21277i
$658$	−20.6144	−	13.1534i	−0.803635	−	0.512774i
$659$	−12.5015	+	15.6763i	−0.486988	+	0.610664i	−0.963239	−	0.268646i	$-0.913424\pi$
$659$	−12.5015	+	15.6763i	−0.486988	+	0.610664i	0.476251	+	0.879309i	$0.341995\pi$
$660$	−10.7369	−	1.61833i	−0.417933	−	0.0629933i
$661$	−2.87821	+	1.96233i	−0.111949	+	0.0763258i	−0.618001	−	0.786178i	$-0.712057\pi$
$661$	−2.87821	+	1.96233i	−0.111949	+	0.0763258i	0.506051	+	0.862503i	$0.331105\pi$
$662$	14.6945	−	10.0185i	0.571117	−	0.389381i
$663$	40.1183	+	6.04686i	1.55807	+	0.234841i
$664$	4.40483	−	5.52348i	0.170941	−	0.214353i
$665$	−3.86173	−	0.462287i	−0.149752	−	0.0179267i
$666$	−5.13654	−	6.44102i	−0.199037	−	0.249585i
$667$	5.39858	+	9.35062i	0.209034	+	0.362057i
$668$	−5.84712	+	10.1275i	−0.226232	+	0.391845i
$669$	−78.9341	+	11.8974i	−3.05177	+	0.459980i
$670$	−2.58684	+	2.40024i	−0.0999384	+	0.0927293i
$671$	21.1579	+	10.1891i	0.816790	+	0.393345i
$672$	−7.64314	+	0.232858i	−0.294841	+	0.00898268i
$673$	29.4758	−	14.1948i	1.13621	−	0.547169i	0.231344	−	0.972872i	$-0.425688\pi$
$673$	29.4758	−	14.1948i	1.13621	−	0.547169i	0.904863	+	0.425703i	$0.139973\pi$
$674$	−2.41979	+	6.16552i	−0.0932068	+	0.237487i
$675$	2.34294	−	31.2644i	0.0901798	−	1.20337i
$676$	−3.39979	−	1.04870i	−0.130761	−	0.0403345i
$677$	2.59160	+	34.5825i	0.0996033	+	1.32911i	0.793293	+	0.608840i	$0.208365\pi$
$677$	2.59160	+	34.5825i	0.0996033	+	1.32911i	−0.693690	+	0.720274i	$0.744016\pi$
$678$	1.45002	−	6.35297i	0.0556878	−	0.243984i
$679$	0.734279	−	0.534088i	0.0281791	−	0.0204964i
$680$	0.634866	+	2.78153i	0.0243460	+	0.106667i
$681$	−27.7757	+	8.56768i	−1.06437	+	0.328314i
$682$	−8.55876	−	21.8074i	−0.327732	−	0.835047i
$683$	−2.91305	−	2.70292i	−0.111465	−	0.103424i	0.622472	−	0.782642i	$-0.286129\pi$
$683$	−2.91305	−	2.70292i	−0.111465	−	0.103424i	−0.733937	+	0.679218i	$0.762319\pi$
$684$	10.4108	+	7.09798i	0.398068	+	0.271398i
$685$	4.73730			0.181003
$686$	5.16495	−	17.7855i	0.197199	−	0.679053i
$687$	60.2612			2.29911
$688$	−8.70085	−	5.93214i	−0.331717	−	0.226161i
$689$	14.2304	+	13.2039i	0.542136	+	0.503029i
$690$	−2.67149	−	6.80683i	−0.101702	−	0.259132i
$691$	7.40815	−	2.28511i	0.281819	−	0.0869298i	−0.150623	−	0.988591i	$-0.548128\pi$
$691$	7.40815	−	2.28511i	0.281819	−	0.0869298i	0.432443	+	0.901661i	$0.357652\pi$
$692$	−0.0218766	−	0.0958478i	−0.000831625	−	0.00364359i
$693$	−68.9011	+	50.1161i	−2.61734	+	1.90375i
$694$	−4.20671	+	18.4308i	−0.159685	+	0.699624i
$695$	0.502367	+	6.70363i	0.0190559	+	0.254283i
$696$	−7.36068	−	2.27047i	−0.279006	−	0.0860620i
$697$	0.240650	−	3.21126i	0.00911529	−	0.121635i
$698$	−2.74774	+	7.00112i	−0.104003	+	0.264996i
$699$	−18.7932	+	9.05033i	−0.710825	+	0.342315i
$700$	12.1912	−	0.371419i	0.460783	−	0.0140383i
$701$	−5.47323	−	2.63577i	−0.206721	−	0.0995515i	0.327659	−	0.944796i	$-0.393740\pi$
$701$	−5.47323	−	2.63577i	−0.206721	−	0.0995515i	−0.534380	+	0.845245i	$0.679455\pi$
$702$	15.3193	−	14.2142i	0.578188	−	0.536480i
$703$	−3.58203	+	0.539905i	−0.135099	+	0.0203629i
$704$	−3.00782	+	5.20970i	−0.113362	+	0.196348i
$705$	8.34132	+	14.4476i	0.314152	+	0.544127i
$706$	11.0587	+	13.8672i	0.416201	+	0.521900i
$707$	17.5672	+	2.10297i	0.660683	+	0.0790902i
$708$	3.23663	−	4.05860i	0.121640	−	0.152532i
$709$	−2.52698	−	0.380881i	−0.0949028	−	0.0143043i	0.101419	−	0.994844i	$-0.467662\pi$
$709$	−2.52698	−	0.380881i	−0.0949028	−	0.0143043i	−0.196322	+	0.980539i	$0.562900\pi$
$710$	−6.33856	+	4.32156i	−0.237882	+	0.162185i
$711$	41.4092	−	28.2323i	1.55297	−	1.05879i
$712$	7.03634	+	1.06056i	0.263698	+	0.0397461i
$713$	9.83647	−	12.3345i	0.368379	−	0.461932i
$714$	29.4487	+	18.7903i	1.10209	+	0.703210i
$715$	7.19776	+	9.02570i	0.269181	+	0.337542i
$716$	−9.49106	−	16.4390i	−0.354698	−	0.614354i
$717$	38.8224	−	67.2423i	1.44985	−	2.51121i
$718$	−4.19530	+	0.632340i	−0.156567	+	0.0235987i
$719$	37.3026	−	34.6117i	1.39115	−	1.29080i	0.480880	−	0.876786i	$-0.340317\pi$
$719$	37.3026	−	34.6117i	1.39115	−	1.29080i	0.910271	−	0.414013i	$-0.135873\pi$
$720$	3.01208	+	1.45054i	0.112254	+	0.0540585i
$721$	−24.5650	+	32.8052i	−0.914847	+	1.22173i
$722$	−12.1266	+	5.83988i	−0.451306	+	0.217338i
$723$	23.6806	−	60.3372i	0.880691	−	2.24397i
$724$	−0.726218	+	9.69071i	−0.0269897	+	0.360152i
$725$	11.7406	+	3.62151i	0.436036	+	0.134499i
$726$	5.44018	+	72.5942i	0.201904	+	2.69422i
$727$	8.38489	−	36.7366i	0.310978	−	1.36248i	−0.541930	−	0.840424i	$-0.682306\pi$
$727$	8.38489	−	36.7366i	0.310978	−	1.36248i	0.852908	−	0.522061i	$-0.174837\pi$
$728$	6.12525	+	5.34568i	0.227017	+	0.198124i
$729$	8.83743	+	38.7193i	0.327312	+	1.43405i
$730$	8.08746	−	2.49465i	0.299330	−	0.0923312i
$731$	17.5758	+	44.7824i	0.650065	+	1.65634i
$732$	−8.27063	−	7.67402i	−0.305691	−	0.283640i
$733$	−18.5287	−	12.6326i	−0.684372	−	0.466597i	0.170553	−	0.985349i	$-0.445445\pi$
$733$	−18.5287	−	12.6326i	−0.684372	−	0.466597i	−0.854925	+	0.518751i	$0.826397\pi$
$734$	−5.79943			−0.214061
$735$	−8.72171	+	9.14183i	−0.321705	+	0.337201i
$736$	−4.05116			−0.149328
$737$	28.0849	+	19.1480i	1.03452	+	0.705324i
$738$	−2.76612	−	2.56659i	−0.101822	−	0.0944774i
$739$	6.71673	+	17.1139i	0.247079	+	0.629547i	0.999578	−	0.0290465i	$-0.00924708\pi$
$739$	6.71673	+	17.1139i	0.247079	+	0.629547i	−0.752499	+	0.658593i	$0.771152\pi$
$740$	−0.918436	+	0.283300i	−0.0337624	+	0.0104143i
$741$	−4.65161	−	20.3800i	−0.170881	−	0.748679i
$742$	6.57752	+	15.3661i	0.241469	+	0.564106i
$743$	9.03848	−	39.6002i	0.331590	−	1.45279i	−0.484463	−	0.874812i	$-0.660985\pi$
$743$	9.03848	−	39.6002i	0.331590	−	1.45279i	0.816052	−	0.577978i	$-0.196158\pi$
$744$	0.841104	+	11.2238i	0.0308364	+	0.411483i
$745$	−7.21369	−	2.22513i	−0.264289	−	0.0815224i
$746$	−0.308139	+	4.11183i	−0.0112818	+	0.150545i
$747$	−13.8167	+	35.2044i	−0.505527	+	1.28806i
$748$	24.7601	−	11.9239i	0.905320	−	0.435979i
$749$	19.0869	+	22.4934i	0.697420	+	0.821890i
$750$	−15.6281	−	7.52610i	−0.570658	−	0.274814i
$751$	33.1687	−	30.7761i	1.21034	−	1.12303i	0.221331	−	0.975199i	$-0.428960\pi$
$751$	33.1687	−	30.7761i	1.21034	−	1.12303i	0.989012	−	0.147836i	$-0.0472306\pi$
$752$	9.13928	−	1.37752i	0.333275	−	0.0502332i
$753$	−3.37288	+	5.84201i	−0.122915	+	0.212895i
$754$	4.09482	+	7.09244i	0.149125	+	0.258292i
$755$	4.07452	+	5.10929i	0.148287	+	0.185946i
$756$	17.0247	−	5.82483i	0.619181	−	0.211847i
$757$	21.9191	−	27.4857i	0.796663	−	0.998984i	−0.203140	−	0.979150i	$-0.565115\pi$
$757$	21.9191	−	27.4857i	0.796663	−	0.998984i	0.999803	−	0.0198344i	$-0.00631390\pi$
$758$	−30.2795	−	4.56389i	−1.09980	−	0.165768i
$759$	−58.1958	+	39.6772i	−2.11237	+	1.44019i
$760$	1.21459	−	0.828091i	0.0440577	−	0.0300380i
$761$	−48.4454	−	7.30196i	−1.75614	−	0.264696i	−0.809532	−	0.587075i	$-0.800279\pi$
$761$	−48.4454	−	7.30196i	−1.75614	−	0.264696i	−0.946611	+	0.322379i	$0.895517\pi$
$762$	1.81002	−	2.26970i	0.0655702	−	0.0822225i
$763$	−7.42812	−	12.0060i	−0.268916	−	0.434647i
$764$	1.00818	+	1.26421i	0.0364745	+	0.0457376i
$765$	−7.63639	−	13.2266i	−0.276094	−	0.478209i
$766$	−6.46325	+	11.1947i	−0.233527	+	0.404480i
$767$	−5.45753	+	0.822591i	−0.197060	+	0.0297020i
$768$	2.11865	−	1.96582i	0.0764502	−	0.0709354i
$769$	−43.9753	−	21.1774i	−1.58579	−	0.763677i	−0.586850	−	0.809696i	$-0.699632\pi$
$769$	−43.9753	−	21.1774i	−1.58579	−	0.763677i	−0.998941	+	0.0460190i	$0.985347\pi$
$770$	2.50591	+	9.61883i	0.0903067	+	0.346639i
$771$	3.93018	−	1.89268i	0.141542	−	0.0681630i
$772$	−1.31423	+	3.34860i	−0.0473001	+	0.120519i
$773$	−0.671920	+	8.96614i	−0.0241673	+	0.322490i	0.971997	+	0.234992i	$0.0755062\pi$
$773$	−0.671920	+	8.96614i	−0.0241673	+	0.322490i	−0.996165	+	0.0874982i	$0.972113\pi$
$774$	53.8675	+	16.6159i	1.93623	+	0.597247i
$775$	−1.34160	−	17.9024i	−0.0481917	−	0.643074i
$776$	−0.0763651	+	0.334577i	−0.00274135	+	0.0120106i
$777$	−5.57099	+	10.3660i	−0.199858	+	0.371877i
$778$	2.10700	+	9.23136i	0.0755395	+	0.330960i
$779$	−1.58550	+	0.489063i	−0.0568065	+	0.0175225i
$780$	−2.02632	−	5.16298i	−0.0725539	−	0.184864i
$781$	54.1691	+	50.2616i	1.93832	+	1.79850i
$782$	15.2914	+	10.4255i	0.546818	+	0.372814i
$783$	18.1258			0.647764
$784$	2.94932	+	6.34835i	0.105333	+	0.226727i
$785$	−8.23995			−0.294096
$786$	46.1305	+	31.4512i	1.64542	+	1.12183i
$787$	−30.1681	−	27.9919i	−1.07538	−	0.997803i	−1.00000		0.000648128i	$-0.999794\pi$
$787$	−30.1681	−	27.9919i	−1.07538	−	0.997803i	−0.0753764	−	0.997155i	$-0.524016\pi$
$788$	−1.14664	−	2.92158i	−0.0408472	−	0.104077i
$789$	66.0183	−	20.3639i	2.35031	−	0.724975i
$790$	−1.30108	−	5.70042i	−0.0462905	−	0.202812i
$791$	−5.86882	+	1.06829i	−0.208671	+	0.0379839i
$792$	7.16572	−	31.3951i	0.254623	−	1.11558i
$793$	0.896418	+	11.9619i	0.0318327	+	0.424778i
$794$	14.5762	+	4.49616i	0.517290	+	0.159563i
$795$	0.852154	−	11.3712i	0.0302228	−	0.403295i
$796$	−1.36098	+	3.46772i	−0.0482387	+	0.122910i
$797$	−29.8277	+	14.3643i	−1.05655	+	0.508809i	−0.879750	−	0.475437i	$-0.842290\pi$
$797$	−29.8277	+	14.3643i	−1.05655	+	0.508809i	−0.176803	+	0.984246i	$0.556576\pi$
$798$	3.46891	−	17.6615i	0.122798	−	0.625209i
$799$	−38.0418	−	18.3199i	−1.34582	−	0.648113i
$800$	−3.37935	+	3.13557i	−0.119478	+	0.110859i
$801$	−37.6664	+	5.67729i	−1.33088	+	0.200597i
$802$	−0.762558	+	1.32079i	−0.0269269	+	0.0466387i
$803$	−40.7615	−	70.6010i	−1.43844	−	2.49146i
$804$	−10.1821	−	12.7680i	−0.359096	−	0.450292i
$805$	−4.76605	+	4.70032i	−0.167981	+	0.165665i
$806$	7.46096	−	9.35575i	0.262801	−	0.329542i
$807$	−6.23685	−	0.940055i	−0.219548	−	0.0330915i
$808$	−5.52521	+	3.76703i	−0.194376	+	0.132524i
$809$	−33.8593	+	23.0849i	−1.19043	+	0.811622i	−0.985916	−	0.167242i	$-0.946514\pi$
$809$	−33.8593	+	23.0849i	−1.19043	+	0.811622i	−0.204515	+	0.978864i	$0.565562\pi$
$810$	−2.22103	−	0.334766i	−0.0780390	−	0.0117625i
$811$	21.4621	−	26.9126i	0.753635	−	0.945029i	−0.246071	−	0.969252i	$-0.579140\pi$
$811$	21.4621	−	26.9126i	0.753635	−	0.945029i	0.999707	+	0.0242228i	$0.00771111\pi$
$812$	0.740843	+	7.01244i	0.0259985	+	0.246088i
$813$	54.6613	+	68.5431i	1.91706	+	2.40391i
$814$	4.62900	+	8.01766i	0.162246	+	0.281019i
$815$	−2.21412	+	3.83498i	−0.0775574	+	0.134333i
$816$	−13.0559	+	1.96786i	−0.457048	+	0.0688889i
$817$	18.1704	−	16.8596i	0.635700	−	0.589844i
$818$	−2.56834	−	1.23685i	−0.0897998	−	0.0432453i
$819$	−39.7672	−	17.6799i	−1.38958	−	0.617786i
$820$	−0.396634	+	0.191009i	−0.0138511	+	0.00667033i
$821$	3.02602	−	7.71018i	0.105609	−	0.269087i	−0.868295	−	0.496048i	$-0.834784\pi$
$821$	3.02602	−	7.71018i	0.105609	−	0.269087i	0.973904	+	0.226961i	$0.0728791\pi$
$822$	−1.63833	+	21.8620i	−0.0571432	+	0.762524i
$823$	−30.4528	−	9.39344i	−1.06152	−	0.327435i	−0.285652	−	0.958333i	$-0.592210\pi$
$823$	−30.4528	−	9.39344i	−1.06152	−	0.327435i	−0.775865	+	0.630899i	$0.782686\pi$
$824$	−1.15758	−	15.4468i	−0.0403262	−	0.538116i
$825$	−17.8351	+	78.1406i	−0.620938	+	2.72051i
$826$	−4.58155	−	1.26178i	−0.159413	−	0.0439030i
$827$	1.06554	+	4.66842i	0.0370523	+	0.162337i	0.990069	−	0.140580i	$-0.0448967\pi$
$827$	1.06554	+	4.66842i	0.0370523	+	0.162337i	−0.953017	+	0.302917i	$0.902040\pi$
$828$	20.7229	−	6.39216i	0.720170	−	0.222143i
$829$	−20.3618	−	51.8810i	−0.707195	−	1.80190i	−0.587719	−	0.809065i	$-0.699974\pi$
$829$	−20.3618	−	51.8810i	−0.707195	−	1.80190i	−0.119476	−	0.992837i	$-0.538121\pi$
$830$	3.23433	+	3.00102i	0.112265	+	0.104167i
$831$	−3.95768	−	2.69830i	−0.137290	−	0.0936030i
$832$	−3.07281			−0.106530
$833$	5.20479	−	31.5522i	0.180335	−	1.09322i
$834$	−31.1100			−1.07725
$835$	−6.03431	−	4.11412i	−0.208826	−	0.142375i
$836$	−10.3798	−	9.63106i	−0.358994	−	0.333097i
$837$	−9.67601	−	24.6541i	−0.334452	−	0.852170i
$838$	−11.5987	+	3.57773i	−0.400671	+	0.123591i
$839$	2.99996	+	13.1437i	0.103570	+	0.453771i	0.999945	+	0.0104740i	$0.00333403\pi$
$839$	2.99996	+	13.1437i	0.103570	+	0.453771i	−0.896375	+	0.443297i	$0.853809\pi$
$840$	0.211693	−	4.77086i	0.00730411	−	0.164610i
$841$	4.87247	−	21.3477i	0.168016	−	0.736128i
$842$	−1.48300	−	19.7893i	−0.0511077	−	0.681985i
$843$	4.72485	+	1.45742i	0.162732	+	0.0501963i
$844$	−0.289655	+	3.86518i	−0.00997035	+	0.133045i
$845$	0.811779	−	2.06838i	0.0279260	−	0.0711544i
$846$	−44.5766	+	21.4669i	−1.53257	+	0.738048i
$847$	59.1333	−	30.7295i	2.03184	−	1.05588i
$848$	−5.69191	−	2.74108i	−0.195461	−	0.0941290i
$849$	−51.2235	+	47.5285i	−1.75799	+	1.63117i
$850$	20.8248	−	3.13883i	0.714285	−	0.107661i
$851$	−3.11734	+	5.39940i	−0.106861	+	0.185089i
$852$	−17.7513	−	30.7461i	−0.608148	−	1.05334i
$853$	−17.6328	−	22.1108i	−0.603734	−	0.757059i	0.382220	−	0.924071i	$-0.375159\pi$
$853$	−17.6328	−	22.1108i	−0.603734	−	0.757059i	−0.985955	+	0.167012i	$0.946588\pi$
$854$	−3.47882	+	9.72479i	−0.119043	+	0.332775i
$855$	−4.90636	+	6.15238i	−0.167794	+	0.210407i
$856$	−11.0255	−	1.66182i	−0.376843	−	0.0568000i
$857$	40.8204	−	27.8309i	1.39440	−	0.950685i	0.394909	−	0.918720i	$-0.370776\pi$
$857$	40.8204	−	27.8309i	1.39440	−	0.950685i	0.999489	−	0.0319646i	$-0.0101764\pi$
$858$	−44.1415	+	30.0952i	−1.50697	+	1.02743i
$859$	−27.6049	−	4.16077i	−0.941868	−	0.141964i	−0.339880	−	0.940469i	$-0.610386\pi$
$859$	−27.6049	−	4.16077i	−0.941868	−	0.141964i	−0.601988	+	0.798505i	$0.705625\pi$
$860$	4.10049	−	5.14185i	0.139825	−	0.175336i
$861$	−1.81555	+	5.07522i	−0.0618737	+	0.172963i
$862$	1.53991	+	1.93098i	0.0524495	+	0.0657696i
$863$	7.20030	+	12.4713i	0.245101	+	0.424527i	0.962160	−	0.272485i	$-0.0878455\pi$
$863$	7.20030	+	12.4713i	0.245101	+	0.424527i	−0.717059	+	0.697012i	$0.754512\pi$
$864$	−3.40046	+	5.88977i	−0.115686	+	0.200374i
$865$	0.0607130	−	0.00915102i	0.00206430	−	0.000311144i
$866$	7.44605	−	6.90893i	0.253027	−	0.234775i
$867$	10.0772	+	4.85294i	0.342241	+	0.164814i
$868$	9.14257	−	4.75108i	0.310319	−	0.161262i
$869$	−50.7430	+	24.4366i	−1.72134	+	0.828953i
$870$	1.75753	−	4.47812i	0.0595859	−	0.151822i
$871$	−1.29752	+	17.3143i	−0.0439650	+	0.586672i
$872$	5.09908	+	1.57286i	0.172677	+	0.0532637i
$873$	−0.137286	−	1.83196i	−0.00464643	−	0.0620023i
$874$	2.12189	−	9.29662i	0.0717741	−	0.314463i
$875$	−0.703889	+	15.8633i	−0.0237958	+	0.536278i
$876$	8.71552	+	38.1852i	0.294470	+	1.29016i
$877$	54.4815	−	16.8053i	1.83971	−	0.567476i	0.840022	−	0.542553i	$-0.182542\pi$
$877$	54.4815	−	16.8053i	1.83971	−	0.567476i	0.999689	−	0.0249231i	$-0.00793410\pi$
$878$	3.87445	+	9.87194i	0.130756	+	0.333162i
$879$	50.8457	+	47.1779i	1.71498	+	1.59127i
$880$	−3.10412	−	2.11635i	−0.104640	−	0.0713422i
$881$	−18.7288			−0.630991			−0.315495	−	0.948927i	$-0.602171\pi$
$881$	−18.7288			−0.630991			−0.315495	+	0.948927i	$0.602171\pi$
$882$	−25.1034	−	27.8201i	−0.845276	−	0.936750i
$883$	−8.70545			−0.292962			−0.146481	−	0.989213i	$-0.546795\pi$
$883$	−8.70545			−0.292962			−0.146481	+	0.989213i	$0.546795\pi$
$884$	11.5985	+	7.90772i	0.390100	+	0.265965i
$885$	2.37656	+	2.20512i	0.0798871	+	0.0741244i
$886$	−11.1496	−	28.4086i	−0.374577	−	0.954407i
$887$	−23.4703	+	7.23962i	−0.788055	+	0.243083i	−0.662557	−	0.749011i	$-0.730529\pi$
$887$	−23.4703	+	7.23962i	−0.788055	+	0.243083i	−0.125497	+	0.992094i	$0.540053\pi$
$888$	−0.989760	−	4.33642i	−0.0332142	−	0.145521i
$889$	−2.56215	−	0.705628i	−0.0859317	−	0.0236660i
$890$	−0.988886	+	4.33259i	−0.0331475	+	0.145229i
$891$	1.61681	+	21.5749i	0.0541652	+	0.722785i
$892$	−26.3926	−	8.14104i	−0.883690	−	0.272582i
$893$	−1.62577	+	21.6943i	−0.0544042	+	0.725974i
$894$	12.7634	−	32.5206i	0.426872	−	1.08765i
$895$	10.6808	−	5.14362i	0.357021	−	0.171932i
$896$	−2.41759	−	1.07483i	−0.0807661	−	0.0359074i
$897$	−32.4152	−	15.6103i	−1.08231	−	0.521214i
$898$	12.5991	−	11.6902i	0.420436	−	0.390108i
$899$	10.2632	−	1.54693i	0.342296	−	0.0515929i
$900$	12.3388	−	21.3715i	0.411295	−	0.712384i
$901$	14.4304	+	24.9942i	0.480747	+	0.832678i
$902$	2.64388	+	3.31532i	0.0880316	+	0.110388i
$903$	−8.46012	−	80.0791i	−0.281535	−	2.66486i
$904$	1.40575	−	1.76276i	0.0467547	−	0.0586285i
$905$	−6.00128	−	0.904548i	−0.199489	−	0.0300682i
$906$	−24.9877	+	17.0363i	−0.830162	+	0.565995i
$907$	28.4801	−	19.4174i	0.945667	−	0.644745i	0.0108749	−	0.999941i	$-0.496538\pi$
$907$	28.4801	−	19.4174i	0.945667	−	0.644745i	0.934792	+	0.355196i	$0.115586\pi$
$908$	−9.94487	−	1.49895i	−0.330032	−	0.0497444i
$909$	22.3192	−	27.9875i	0.740283	−	0.928285i
$910$	−3.61505	+	3.56519i	−0.119838	+	0.118185i
$911$	−14.5548	−	18.2511i	−0.482222	−	0.604687i	0.479895	−	0.877326i	$-0.340675\pi$
$911$	−14.5548	−	18.2511i	−0.482222	−	0.604687i	−0.962116	+	0.272639i	$0.912103\pi$
$912$	3.40147	+	5.89152i	0.112634	+	0.195088i
$913$	21.2497	−	36.8055i	0.703261	−	1.21808i
$914$	26.0547	−	3.92711i	0.861813	−	0.129897i
$915$	5.16522	−	4.79262i	0.170757	−	0.158439i
$916$	18.7855	+	9.04663i	0.620691	+	0.298909i
$917$	9.85041	−	50.1519i	0.325289	−	1.65616i
$918$	27.9923	−	13.4804i	0.923884	−	0.444919i
$919$	−6.19694	+	15.7895i	−0.204418	+	0.520849i	−0.995912	−	0.0903280i	$-0.971208\pi$
$919$	−6.19694	+	15.7895i	−0.204418	+	0.520849i	0.791494	+	0.611177i	$0.209304\pi$
$920$	0.189071	−	2.52298i	0.00623350	−	0.0831802i
$921$	−20.3126	−	6.26560i	−0.669322	−	0.206459i
$922$	−0.000273863	−	0.00365445i	−9.01920e−6	−	0.000120353i
$923$	−8.39926	+	36.7995i	−0.276465	+	1.21127i
$924$	−45.2561	+	8.23787i	−1.48882	+	0.271006i
$925$	1.57871	+	6.91680i	0.0519078	+	0.227423i
$926$	16.6291	−	5.12939i	0.546466	−	0.168562i
$927$	30.2943	+	77.1886i	0.994996	+	2.53521i
$928$	−1.95373	−	1.81280i	−0.0641344	−	0.0595080i
$929$	10.9056	+	7.43531i	0.357801	+	0.243945i	0.728857	−	0.684666i	$-0.240052\pi$
$929$	10.9056	+	7.43531i	0.357801	+	0.243945i	−0.371056	+	0.928611i	$0.621004\pi$
$930$	−7.02918			−0.230496
$931$	−16.1130	+	3.44301i	−0.528081	+	0.112840i
$932$	−7.21717			−0.236406
$933$	66.2565	+	45.1729i	2.16914	+	1.47890i
$934$	−21.4099	−	19.8655i	−0.700555	−	0.650020i
$935$	6.27035	+	15.9766i	0.205062	+	0.522491i
$936$	15.7183	−	4.84846i	0.513769	−	0.158477i
$937$	−5.66060	−	24.8007i	−0.184924	−	0.810205i	−0.979241	−	0.202701i	$-0.935028\pi$
$937$	−5.66060	−	24.8007i	−0.184924	−	0.810205i	0.794317	−	0.607504i	$-0.207829\pi$
$938$	−7.07715	+	13.1685i	−0.231077	+	0.429966i
$939$	−2.93516	+	12.8598i	−0.0957853	+	0.419663i
$940$	0.431356	+	5.75605i	0.0140693	+	0.187741i
$941$	14.7624	+	4.55361i	0.481241	+	0.148443i	0.525878	−	0.850560i	$-0.323737\pi$
$941$	14.7624	+	4.55361i	0.481241	+	0.148443i	−0.0446367	+	0.999003i	$0.514213\pi$
$942$	2.84967	−	38.0262i	0.0928472	−	1.23896i
$943$	−1.04330	+	2.65828i	−0.0339745	+	0.0865655i
$944$	1.61826	−	0.779314i	0.0526700	−	0.0253645i
$945$	2.83303	+	10.8745i	0.0921584	+	0.353746i
$946$	−57.0753	−	27.4860i	−1.85568	−	0.893647i
$947$	−36.0108	+	33.4131i	−1.17019	+	1.08578i	−0.175333	+	0.984509i	$0.556100\pi$
$947$	−36.0108	+	33.4131i	−1.17019	+	1.08578i	−0.994859	+	0.101271i	$0.967709\pi$
$948$	26.7566	−	4.03291i	0.869013	−	0.130983i
$949$	20.8211	−	36.0632i	0.675881	−	1.17066i
$950$	−5.42551	−	9.39726i	−0.176027	−	0.304887i
$951$	−4.89537	−	6.13860i	−0.158743	−	0.199058i
$952$	6.35933	+	10.2786i	0.206107	+	0.333130i
$953$	−12.3407	+	15.4747i	−0.399754	+	0.501276i	−0.940445	−	0.339945i	$-0.889591\pi$
$953$	−12.3407	+	15.4747i	−0.399754	+	0.501276i	0.540691	+	0.841221i	$0.318163\pi$
$954$	33.4408	+	5.04039i	1.08269	+	0.163189i
$955$	−0.834378	+	0.568870i	−0.0269999	+	0.0184082i
$956$	22.1970	−	15.1336i	0.717901	−	0.489457i
$957$	−45.8204	−	6.90631i	−1.48116	−	0.223249i
$958$	−20.0546	+	25.1476i	−0.647934	+	0.812484i
$959$	18.9885	−	6.49675i	0.613172	−	0.209791i
$960$	1.12539	+	1.41120i	0.0363219	+	0.0455462i
$961$	7.91719	+	13.7130i	0.255393	+	0.442354i
$962$	−2.36450	+	4.09544i	−0.0762347	+	0.132042i
$963$	59.0207	−	8.89594i	1.90192	−	0.286668i
$964$	16.4401	−	15.2542i	0.529500	−	0.491305i
$965$	−2.02410	−	0.974757i	−0.0651582	−	0.0313785i
$966$	−20.0430	−	23.6202i	−0.644874	−	0.759966i
$967$	−44.0484	+	21.2126i	−1.41650	+	0.682152i	−0.976435	−	0.215813i	$-0.930760\pi$
$967$	−44.0484	+	21.2126i	−1.41650	+	0.682152i	−0.440068	+	0.897965i	$0.645046\pi$
$968$	−9.20221	+	23.4469i	−0.295770	+	0.753610i
$969$	2.32249	−	30.9914i	0.0746091	−	0.995589i
$970$	−0.204804	−	0.0631736i	−0.00657586	−	0.00202838i
$971$	2.51576	+	33.5705i	0.0807346	+	1.07733i	0.879567	+	0.475775i	$0.157832\pi$
$971$	2.51576	+	33.5705i	0.0807346	+	1.07733i	−0.798833	+	0.601553i	$0.794549\pi$
$972$	−2.22704	+	9.75729i	−0.0714322	+	0.312965i
$973$	11.2070	+	26.1812i	0.359280	+	0.839331i
$974$	5.59178	+	24.4992i	0.179172	+	0.785005i
$975$	−39.1220	+	12.0675i	−1.25291	+	0.386471i
$976$	−1.42619	−	3.63388i	−0.0456513	−	0.116318i
$977$	−24.4928	−	22.7260i	−0.783593	−	0.727068i	0.183076	−	0.983099i	$-0.441395\pi$
$977$	−24.4928	−	22.7260i	−0.783593	−	0.727068i	−0.966669	+	0.256031i	$0.917585\pi$
$978$	−16.9321	−	11.5441i	−0.541430	−	0.369141i
$979$	42.8063			1.36809
$980$	−4.09127	+	1.54049i	−0.130691	+	0.0492092i
$981$	−28.5650			−0.912012
$982$	−5.84768	−	3.98688i	−0.186607	−	0.127227i
$983$	−6.62767	−	6.14958i	−0.211390	−	0.196141i	0.567371	−	0.823463i	$-0.307961\pi$
$983$	−6.62767	−	6.14958i	−0.211390	−	0.196141i	−0.778760	+	0.627321i	$0.784151\pi$
$984$	−0.744309	−	1.89647i	−0.0237277	−	0.0604572i
$985$	1.87302	−	0.577749i	0.0596792	−	0.0184086i
$986$	2.70933	+	11.8703i	0.0862826	+	0.378029i
$987$	53.2480	+	46.4710i	1.69490	+	1.47919i
$988$	1.60945	−	7.05148i	0.0512036	−	0.224338i
$989$	−3.18809	−	42.5422i	−0.101375	−	1.35276i
$990$	19.2178	+	5.92790i	0.610781	+	0.188401i
$991$	−1.99634	+	26.6392i	−0.0634157	+	0.846224i	0.871283	+	0.490782i	$0.163289\pi$
$991$	−1.99634	+	26.6392i	−0.0634157	+	0.846224i	−0.934698	+	0.355442i	$0.884330\pi$
$992$	−1.42275	+	3.62511i	−0.0451723	+	0.115097i
$993$	−46.3108	+	22.3021i	−1.46963	+	0.707736i
$994$	−19.4803	+	26.0148i	−0.617877	+	0.825140i
$995$	−2.09611	−	1.00943i	−0.0664511	−	0.0320012i
$996$	−14.9678	+	13.8881i	−0.474274	+	0.440062i
$997$	15.0576	−	2.26957i	0.476880	−	0.0718781i	0.0937958	−	0.995591i	$-0.470100\pi$
$997$	15.0576	−	2.26957i	0.476880	−	0.0718781i	0.383084	+	0.923713i	$0.374862\pi$
$998$	−10.0820	+	17.4625i	−0.319140	+	0.552767i
$999$	5.23327	+	9.06428i	0.165573	+	0.286781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.2.g.a.53.2	yes	24
3.2	odd	2		882.2.z.d.739.2		24
4.3	odd	2		784.2.bg.a.641.1		24
7.2	even	3		686.2.g.a.275.1		24
7.3	odd	6		686.2.e.e.491.1		24
7.4	even	3		686.2.e.f.491.4		24
7.5	odd	6		686.2.g.c.275.2		24
7.6	odd	2		686.2.g.b.263.1		24
49.12	odd	42		686.2.g.b.373.1		24
49.17	odd	42		686.2.e.e.197.1		24
49.20	odd	14		686.2.g.c.459.2		24
49.24	odd	42		4802.2.a.k.1.11		12
49.25	even	21		4802.2.a.i.1.2		12
49.29	even	7		686.2.g.a.459.1		24
49.32	even	21		686.2.e.f.197.4		24
49.37	even	21	inner	98.2.g.a.37.2	✓	24
147.86	odd	42		882.2.z.d.37.2		24
196.135	odd	42		784.2.bg.a.625.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.37.2	✓	24	49.37	even	21	inner
98.2.g.a.53.2	yes	24	1.1	even	1	trivial
686.2.e.e.197.1		24	49.17	odd	42
686.2.e.e.491.1		24	7.3	odd	6
686.2.e.f.197.4		24	49.32	even	21
686.2.e.f.491.4		24	7.4	even	3
686.2.g.a.275.1		24	7.2	even	3
686.2.g.a.459.1		24	49.29	even	7
686.2.g.b.263.1		24	7.6	odd	2
686.2.g.b.373.1		24	49.12	odd	42
686.2.g.c.275.2		24	7.5	odd	6
686.2.g.c.459.2		24	49.20	odd	14
784.2.bg.a.625.1		24	196.135	odd	42
784.2.bg.a.641.1		24	4.3	odd	2
882.2.z.d.37.2		24	147.86	odd	42
882.2.z.d.739.2		24	3.2	odd	2
4802.2.a.i.1.2		12	49.25	even	21
4802.2.a.k.1.11		12	49.24	odd	42

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.826239 - 0.563320i) q^{2} +(2.11865 + 1.96582i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-0.596780 + 0.184082i) q^{5} +(-0.643125 - 2.81771i) q^{6} +(-2.13962 + 1.55628i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.400039 + 5.33815i) q^{9} +O(q^{10})\)	\(q+(-0.826239 - 0.563320i) q^{2} +(2.11865 + 1.96582i) q^{3} +(0.365341 + 0.930874i) q^{4} +(-0.596780 + 0.184082i) q^{5} +(-0.643125 - 2.81771i) q^{6} +(-2.13962 + 1.55628i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.400039 + 5.33815i) q^{9} +(0.596780 + 0.184082i) q^{10} +(0.449550 - 5.99883i) q^{11} +(-1.05590 + 2.69039i) q^{12} +(2.76850 - 1.33324i) q^{13} +(2.64452 - 0.0805687i) q^{14} +(-1.62624 - 0.783156i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(4.51734 - 0.680880i) q^{17} +(2.67656 - 4.63594i) q^{18} +(-1.17691 - 2.03847i) q^{19} +(-0.389385 - 0.488274i) q^{20} +(-7.59248 - 0.908894i) q^{21} +(-3.75069 + 4.70322i) q^{22} +(-4.00591 - 0.603794i) q^{23} +(2.38798 - 1.62809i) q^{24} +(-3.80893 + 2.59689i) q^{25} +(-3.03849 - 0.457978i) q^{26} +(-4.24031 + 5.31718i) q^{27} +(-2.23039 - 1.42314i) q^{28} +(-1.66173 - 2.08374i) q^{29} +(0.902495 + 1.56317i) q^{30} +(-1.94715 + 3.37257i) q^{31} +(0.988831 - 0.149042i) q^{32} +(12.7450 - 11.8257i) q^{33} +(-4.11596 - 1.98214i) q^{34} +(0.990400 - 1.32262i) q^{35} +(-4.82299 + 2.32263i) q^{36} +(0.562255 - 1.43260i) q^{37} +(-0.175901 + 2.34724i) q^{38} +(8.48640 + 2.61771i) q^{39} +(0.0466709 + 0.622779i) q^{40} +(0.156856 - 0.687231i) q^{41} +(5.76120 + 5.02796i) q^{42} +(2.34329 + 10.2666i) q^{43} +(5.74839 - 1.77314i) q^{44} +(-1.22139 - 3.11206i) q^{45} +(2.96971 + 2.75549i) q^{46} +(-7.63652 - 5.20649i) q^{47} -2.89018 q^{48} +(2.15597 - 6.65971i) q^{49} +4.60997 q^{50} +(10.9091 + 7.43773i) q^{51} +(2.25253 + 2.09004i) q^{52} +(2.30806 + 5.88083i) q^{53} +(6.49878 - 2.00461i) q^{54} +(0.835995 + 3.66273i) q^{55} +(1.04115 + 2.43228i) q^{56} +(1.51380 - 6.63238i) q^{57} +(0.199171 + 2.65775i) q^{58} +(-1.71634 - 0.529420i) q^{59} +(0.134887 - 1.79994i) q^{60} +(-1.42619 + 3.63388i) q^{61} +(3.50865 - 1.68968i) q^{62} +(-9.16360 - 10.7991i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.40676 + 1.30528i) q^{65} +(-17.1921 + 2.59129i) q^{66} +(-2.82524 + 4.89345i) q^{67} +(2.28418 + 3.95632i) q^{68} +(-7.30018 - 9.15413i) q^{69} +(-1.56337 + 0.534892i) q^{70} +(-7.65886 + 9.60391i) q^{71} +(5.29333 + 0.797841i) q^{72} +(11.1971 - 7.63402i) q^{73} +(-1.27157 + 0.866942i) q^{74} +(-13.1748 - 1.98578i) q^{75} +(1.46758 - 1.84029i) q^{76} +(8.37400 + 13.5348i) q^{77} +(-5.53718 - 6.94341i) q^{78} +(-4.68117 - 8.10802i) q^{79} +(0.312263 - 0.540855i) q^{80} +(-3.55634 + 0.536033i) q^{81} +(-0.516732 + 0.479457i) q^{82} +(6.36516 + 3.06530i) q^{83} +(-1.92778 - 7.39970i) q^{84} +(-2.57052 + 1.23790i) q^{85} +(3.84728 - 9.80272i) q^{86} +(0.575639 - 7.68136i) q^{87} +(-5.74839 - 1.77314i) q^{88} +(0.531766 + 7.09592i) q^{89} +(-0.743923 + 3.25934i) q^{90} +(-3.84865 + 7.16120i) q^{91} +(-0.901469 - 3.94959i) q^{92} +(-10.7552 + 3.31754i) q^{93} +(3.37667 + 8.60361i) q^{94} +(1.07760 + 0.999867i) q^{95} +(2.38798 + 1.62809i) q^{96} -0.343182 q^{97} +(-5.53290 + 4.28801i) q^{98} +32.2025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9	\( 24 q - 2 q^{2} + 7 q^{3} + 2 q^{4} - 7 q^{6} + 4 q^{8} - 33 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} + 2 q^{16} - 7 q^{17} + 5 q^{18} - 7 q^{20} + 7 q^{21} - 7 q^{22} - 21 q^{23} + 4 q^{25} - 7 q^{26} - 35 q^{27} - 14 q^{28} - 11 q^{29} + 28 q^{31} - 2 q^{32} + 14 q^{33} + 7 q^{34} + 21 q^{35} + 3 q^{36} - 24 q^{37} - 7 q^{38} - 40 q^{39} + 14 q^{40} + 28 q^{41} - 21 q^{42} + 10 q^{43} + 21 q^{44} + 7 q^{45} + 42 q^{46} - 70 q^{47} - 14 q^{48} + 84 q^{49} + 8 q^{50} + 60 q^{51} - 7 q^{52} + 26 q^{53} + 63 q^{54} + 56 q^{55} + 21 q^{56} - 33 q^{57} - 30 q^{58} - 7 q^{59} + 14 q^{60} + 14 q^{61} + 28 q^{62} - 14 q^{63} - 4 q^{64} - 21 q^{66} - 36 q^{67} - 14 q^{68} - 35 q^{69} + 14 q^{70} - 2 q^{72} - 7 q^{73} - 11 q^{74} - 28 q^{75} - 91 q^{77} - 24 q^{78} - 26 q^{79} + 55 q^{81} + 14 q^{82} - 7 q^{83} - 21 q^{84} + 49 q^{85} - 16 q^{86} + 35 q^{87} - 21 q^{88} - 56 q^{89} - 21 q^{90} + 7 q^{91} + 21 q^{92} + 72 q^{93} - 35 q^{94} - 14 q^{95} - 126 q^{97} - 56 q^{98} - 14 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 7 * q^3 + 2 * q^4 - 7 * q^6 + 4 * q^8 - 33 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 + 2 * q^16 - 7 * q^17 + 5 * q^18 - 7 * q^20 + 7 * q^21 - 7 * q^22 - 21 * q^23 + 4 * q^25 - 7 * q^26 - 35 * q^27 - 14 * q^28 - 11 * q^29 + 28 * q^31 - 2 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 + 3 * q^36 - 24 * q^37 - 7 * q^38 - 40 * q^39 + 14 * q^40 + 28 * q^41 - 21 * q^42 + 10 * q^43 + 21 * q^44 + 7 * q^45 + 42 * q^46 - 70 * q^47 - 14 * q^48 + 84 * q^49 + 8 * q^50 + 60 * q^51 - 7 * q^52 + 26 * q^53 + 63 * q^54 + 56 * q^55 + 21 * q^56 - 33 * q^57 - 30 * q^58 - 7 * q^59 + 14 * q^60 + 14 * q^61 + 28 * q^62 - 14 * q^63 - 4 * q^64 - 21 * q^66 - 36 * q^67 - 14 * q^68 - 35 * q^69 + 14 * q^70 - 2 * q^72 - 7 * q^73 - 11 * q^74 - 28 * q^75 - 91 * q^77 - 24 * q^78 - 26 * q^79 + 55 * q^81 + 14 * q^82 - 7 * q^83 - 21 * q^84 + 49 * q^85 - 16 * q^86 + 35 * q^87 - 21 * q^88 - 56 * q^89 - 21 * q^90 + 7 * q^91 + 21 * q^92 + 72 * q^93 - 35 * q^94 - 14 * q^95 - 126 * q^97 - 56 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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