LMFDB - Embedded newform 61.2.i.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(12,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("61.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.i (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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.3
Character	$\chi$	$=$	61.16
Dual form			61.2.i.a.42.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.873313 + 0.185628i) q^{2} +(0.508502 + 1.56501i) q^{3} +(-1.09887 - 0.489250i) q^{4} +(-0.0637708 - 0.606739i) q^{5} +(0.153571 + 1.46113i) q^{6} +(-0.455761 - 0.506174i) q^{7} +(-2.31346 - 1.68083i) q^{8} +(0.236374 - 0.171736i) q^{9} +O(q^{10})$	\(q+(0.873313 + 0.185628i) q^{2} +(0.508502 + 1.56501i) q^{3} +(-1.09887 - 0.489250i) q^{4} +(-0.0637708 - 0.606739i) q^{5} +(0.153571 + 1.46113i) q^{6} +(-0.455761 - 0.506174i) q^{7} +(-2.31346 - 1.68083i) q^{8} +(0.236374 - 0.171736i) q^{9} +(0.0569361 - 0.541711i) q^{10} -0.856770 q^{11} +(0.206901 - 1.96853i) q^{12} +(-0.256551 + 0.444360i) q^{13} +(-0.304062 - 0.526651i) q^{14} +(0.917124 - 0.408330i) q^{15} +(-0.0986147 - 0.109523i) q^{16} +(0.929560 + 0.413867i) q^{17} +(0.238308 - 0.106102i) q^{18} +(-2.82829 + 3.14113i) q^{19} +(-0.226771 + 0.697929i) q^{20} +(0.560411 - 0.970661i) q^{21} +(-0.748228 - 0.159041i) q^{22} +(-6.80521 + 4.94428i) q^{23} +(1.45411 - 4.47529i) q^{24} +(4.52667 - 0.962174i) q^{25} +(-0.306535 + 0.340442i) q^{26} +(4.38279 + 3.18428i) q^{27} +(0.253178 + 0.779203i) q^{28} +(-3.37045 - 5.83778i) q^{29} +(0.876734 - 0.186356i) q^{30} +(10.6295 - 2.25937i) q^{31} +(2.79380 + 4.83901i) q^{32} +(-0.435669 - 1.34085i) q^{33} +(0.734972 + 0.533988i) q^{34} +(-0.278051 + 0.308807i) q^{35} +(-0.343768 + 0.0730700i) q^{36} +(-0.711916 + 2.19105i) q^{37} +(-3.05306 + 2.21818i) q^{38} +(-0.825883 - 0.175547i) q^{39} +(-0.872292 + 1.51085i) q^{40} +(-1.10908 + 3.41340i) q^{41} +(0.669597 - 0.743662i) q^{42} +(2.98244 - 1.32787i) q^{43} +(0.941482 + 0.419175i) q^{44} +(-0.119273 - 0.132466i) q^{45} +(-6.86088 + 3.05466i) q^{46} +(-1.86946 - 3.23800i) q^{47} +(0.121258 - 0.210025i) q^{48} +(0.683205 - 6.50026i) q^{49} +4.13181 q^{50} +(-0.175022 + 1.66522i) q^{51} +(0.499320 - 0.362777i) q^{52} +(-4.74398 - 3.44671i) q^{53} +(3.23645 + 3.59445i) q^{54} +(0.0546369 + 0.519836i) q^{55} +(0.203594 + 1.93707i) q^{56} +(-6.35408 - 2.82902i) q^{57} +(-1.85979 - 5.72386i) q^{58} +(-8.67000 - 1.84286i) q^{59} -1.20758 q^{60} +(-2.66773 - 7.34052i) q^{61} +9.70227 q^{62} +(-0.194659 - 0.0413760i) q^{63} +(1.63269 + 5.02491i) q^{64} +(0.285971 + 0.127322i) q^{65} +(-0.131575 - 1.25186i) q^{66} +(1.18285 + 11.2540i) q^{67} +(-0.818985 - 0.909575i) q^{68} +(-11.1983 - 8.13604i) q^{69} +(-0.300149 + 0.218071i) q^{70} +(0.576283 - 5.48297i) q^{71} -0.835501 q^{72} +(0.289912 - 2.75833i) q^{73} +(-1.02845 + 1.78132i) q^{74} +(3.80763 + 6.59501i) q^{75} +(4.64473 - 2.06797i) q^{76} +(0.390483 + 0.433675i) q^{77} +(-0.688668 - 0.306615i) q^{78} +(-6.78344 + 3.02018i) q^{79} +(-0.0601630 + 0.0668178i) q^{80} +(-2.48391 + 7.64470i) q^{81} +(-1.60220 + 2.77509i) q^{82} +(10.5592 + 2.24442i) q^{83} +(-1.09072 + 0.792453i) q^{84} +(0.191830 - 0.590393i) q^{85} +(2.85109 - 0.606018i) q^{86} +(7.42230 - 8.24330i) q^{87} +(1.98210 + 1.44008i) q^{88} +(2.60821 + 8.02724i) q^{89} +(-0.0795730 - 0.137825i) q^{90} +(0.341850 - 0.0726624i) q^{91} +(9.89706 - 2.10368i) q^{92} +(8.94104 + 15.4863i) q^{93} +(-1.03156 - 3.17481i) q^{94} +(2.08621 + 1.51572i) q^{95} +(-6.15243 + 6.83297i) q^{96} +(10.4211 - 2.21507i) q^{97} +(1.80329 - 5.54994i) q^{98} +(-0.202519 + 0.147138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9} + 15 q^{10} - 18 q^{11} - 53 q^{12} + 11 q^{14} + 2 q^{15} + 6 q^{16} - 24 q^{17} - 15 q^{18} + 9 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 15 q^{24} + 28 q^{25} + 16 q^{26} + 35 q^{27} + 4 q^{28} - 4 q^{29} + 54 q^{30} - 11 q^{31} + 34 q^{32} - 35 q^{33} + 18 q^{34} - 58 q^{35} + 65 q^{36} - 14 q^{37} - 24 q^{38} + 17 q^{39} - 60 q^{40} + 11 q^{41} + 73 q^{42} + 40 q^{43} + 29 q^{44} + 12 q^{45} - 89 q^{46} + 40 q^{47} + 43 q^{48} + q^{49} - 56 q^{50} - 9 q^{51} - 67 q^{52} + 17 q^{53} - q^{54} - 60 q^{55} - 102 q^{56} - 38 q^{57} + 73 q^{58} - 11 q^{59} - 20 q^{60} - 55 q^{61} - 74 q^{62} - 58 q^{63} + 6 q^{64} + 59 q^{65} + 34 q^{66} - 13 q^{67} - 3 q^{68} - 32 q^{69} + 44 q^{70} + 63 q^{71} + 18 q^{72} - 46 q^{73} - 10 q^{74} + q^{75} + 55 q^{76} - 31 q^{77} - 103 q^{78} - 49 q^{79} + 74 q^{80} + 48 q^{81} + 39 q^{82} + 39 q^{83} + 21 q^{85} + 74 q^{86} + 17 q^{87} + 70 q^{88} + 32 q^{89} - 60 q^{90} + 70 q^{91} + 77 q^{92} + 67 q^{93} - 64 q^{94} + 47 q^{95} - 16 q^{96} + 37 q^{97} + 127 q^{98} - 31 q^{99}+O(q^{100}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9 + 15 * q^10 - 18 * q^11 - 53 * q^12 + 11 * q^14 + 2 * q^15 + 6 * q^16 - 24 * q^17 - 15 * q^18 + 9 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 15 * q^24 + 28 * q^25 + 16 * q^26 + 35 * q^27 + 4 * q^28 - 4 * q^29 + 54 * q^30 - 11 * q^31 + 34 * q^32 - 35 * q^33 + 18 * q^34 - 58 * q^35 + 65 * q^36 - 14 * q^37 - 24 * q^38 + 17 * q^39 - 60 * q^40 + 11 * q^41 + 73 * q^42 + 40 * q^43 + 29 * q^44 + 12 * q^45 - 89 * q^46 + 40 * q^47 + 43 * q^48 + q^49 - 56 * q^50 - 9 * q^51 - 67 * q^52 + 17 * q^53 - q^54 - 60 * q^55 - 102 * q^56 - 38 * q^57 + 73 * q^58 - 11 * q^59 - 20 * q^60 - 55 * q^61 - 74 * q^62 - 58 * q^63 + 6 * q^64 + 59 * q^65 + 34 * q^66 - 13 * q^67 - 3 * q^68 - 32 * q^69 + 44 * q^70 + 63 * q^71 + 18 * q^72 - 46 * q^73 - 10 * q^74 + q^75 + 55 * q^76 - 31 * q^77 - 103 * q^78 - 49 * q^79 + 74 * q^80 + 48 * q^81 + 39 * q^82 + 39 * q^83 + 21 * q^85 + 74 * q^86 + 17 * q^87 + 70 * q^88 + 32 * q^89 - 60 * q^90 + 70 * q^91 + 77 * q^92 + 67 * q^93 - 64 * q^94 + 47 * q^95 - 16 * q^96 + 37 * q^97 + 127 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.873313	+	0.185628i	0.617525	+	0.131259i	0.506044	−	0.862507i	$-0.331107\pi$
$2$	0.873313	+	0.185628i	0.617525	+	0.131259i	0.111481	+	0.993767i	$0.464441\pi$
$3$	0.508502	+	1.56501i	0.293584	+	0.903558i	0.983693	+	0.179853i	$0.0575623\pi$
$3$	0.508502	+	1.56501i	0.293584	+	0.903558i	−0.690110	+	0.723705i	$0.742438\pi$
$4$	−1.09887	−	0.489250i	−0.549437	−	0.244625i
$5$	−0.0637708	−	0.606739i	−0.0285192	−	0.271342i	−0.999484	−	0.0321197i	$-0.989774\pi$
$5$	−0.0637708	−	0.606739i	−0.0285192	−	0.271342i	0.970965	−	0.239222i	$-0.0768925\pi$
$6$	0.153571	+	1.46113i	0.0626953	+	0.596505i
$7$	−0.455761	−	0.506174i	−0.172262	−	0.191316i	0.650832	−	0.759222i	$-0.274420\pi$
$7$	−0.455761	−	0.506174i	−0.172262	−	0.191316i	−0.823093	+	0.567906i	$0.807754\pi$
$8$	−2.31346	−	1.68083i	−0.817932	−	0.594262i
$9$	0.236374	−	0.171736i	0.0787915	−	0.0572454i
$10$	0.0569361	−	0.541711i	0.0180048	−	0.171304i
$11$	−0.856770			−0.258326			−0.129163	−	0.991623i	$-0.541229\pi$
$11$	−0.856770			−0.258326			−0.129163	+	0.991623i	$0.541229\pi$
$12$	0.206901	−	1.96853i	0.0597272	−	0.568266i
$13$	−0.256551	+	0.444360i	−0.0711545	+	0.123243i	−0.899408	−	0.437111i	$-0.856002\pi$
$13$	−0.256551	+	0.444360i	−0.0711545	+	0.123243i	0.828253	+	0.560354i	$0.189335\pi$
$14$	−0.304062	−	0.526651i	−0.0812640	−	0.140753i
$15$	0.917124	−	0.408330i	0.236800	−	0.105430i
$16$	−0.0986147	−	0.109523i	−0.0246537	−	0.0273807i
$17$	0.929560	+	0.413867i	0.225452	+	0.100377i	0.516354	−	0.856375i	$-0.327289\pi$
$17$	0.929560	+	0.413867i	0.225452	+	0.100377i	−0.290903	+	0.956753i	$0.593956\pi$
$18$	0.238308	−	0.106102i	0.0561697	−	0.0250084i
$19$	−2.82829	+	3.14113i	−0.648853	+	0.720625i	−0.974380	−	0.224908i	$-0.927792\pi$
$19$	−2.82829	+	3.14113i	−0.648853	+	0.720625i	0.325527	+	0.945533i	$0.394458\pi$
$20$	−0.226771	+	0.697929i	−0.0507075	+	0.156062i
$21$	0.560411	−	0.970661i	0.122292	−	0.211816i
$22$	−0.748228	−	0.159041i	−0.159523	−	0.0339076i
$23$	−6.80521	+	4.94428i	−1.41899	+	1.03095i	−0.427047	+	0.904229i	$0.640446\pi$
$23$	−6.80521	+	4.94428i	−1.41899	+	1.03095i	−0.991938	+	0.126724i	$0.959554\pi$
$24$	1.45411	−	4.47529i	0.296819	−	0.913514i
$25$	4.52667	−	0.962174i	0.905334	−	0.192435i
$26$	−0.306535	+	0.340442i	−0.0601165	+	0.0667661i
$27$	4.38279	+	3.18428i	0.843469	+	0.612816i
$28$	0.253178	+	0.779203i	0.0478462	+	0.147256i
$29$	−3.37045	−	5.83778i	−0.625876	−	1.08405i	−0.988371	−	0.152063i	$-0.951408\pi$
$29$	−3.37045	−	5.83778i	−0.625876	−	1.08405i	0.362495	−	0.931986i	$-0.381925\pi$
$30$	0.876734	−	0.186356i	0.160069	−	0.0340237i
$31$	10.6295	−	2.25937i	1.90911	−	0.405794i	0.909168	−	0.416430i	$-0.136719\pi$
$31$	10.6295	−	2.25937i	1.90911	−	0.405794i	0.999943	+	0.0106355i	$0.00338546\pi$
$32$	2.79380	+	4.83901i	0.493879	+	0.855424i
$33$	−0.435669	−	1.34085i	−0.0758403	−	0.233412i
$34$	0.734972	+	0.533988i	0.126047	+	0.0915782i
$35$	−0.278051	+	0.308807i	−0.0469993	+	0.0521980i
$36$	−0.343768	+	0.0730700i	−0.0572946	+	0.0121783i
$37$	−0.711916	+	2.19105i	−0.117038	+	0.360207i	−0.992367	−	0.123322i	$-0.960645\pi$
$37$	−0.711916	+	2.19105i	−0.117038	+	0.360207i	0.875328	+	0.483529i	$0.160645\pi$
$38$	−3.05306	+	2.21818i	−0.495272	+	0.359836i
$39$	−0.825883	−	0.175547i	−0.132247	−	0.0281100i
$40$	−0.872292	+	1.51085i	−0.137921	+	0.238887i
$41$	−1.10908	+	3.41340i	−0.173209	+	0.533084i	−0.999547	−	0.0300912i	$-0.990420\pi$
$41$	−1.10908	+	3.41340i	−0.173209	+	0.533084i	0.826338	+	0.563175i	$0.190420\pi$
$42$	0.669597	−	0.743662i	0.103321	−	0.114750i
$43$	2.98244	−	1.32787i	0.454818	−	0.202498i	−0.166524	−	0.986037i	$-0.553254\pi$
$43$	2.98244	−	1.32787i	0.454818	−	0.202498i	0.621342	+	0.783539i	$0.286588\pi$
$44$	0.941482	+	0.419175i	0.141934	+	0.0631930i
$45$	−0.119273	−	0.132466i	−0.0177801	−	0.0197468i
$46$	−6.86088	+	3.05466i	−1.01158	+	0.450385i
$47$	−1.86946	−	3.23800i	−0.272688	−	0.472310i	0.696861	−	0.717206i	$-0.254579\pi$
$47$	−1.86946	−	3.23800i	−0.272688	−	0.472310i	−0.969549	+	0.244896i	$0.921246\pi$
$48$	0.121258	−	0.210025i	0.0175021	−	0.0303146i
$49$	0.683205	−	6.50026i	0.0976008	−	0.928609i
$50$	4.13181			0.584326
$51$	−0.175022	+	1.66522i	−0.0245080	+	0.233178i
$52$	0.499320	−	0.362777i	0.0692433	−	0.0503082i
$53$	−4.74398	−	3.44671i	−0.651636	−	0.473441i	0.212192	−	0.977228i	$-0.431940\pi$
$53$	−4.74398	−	3.44671i	−0.651636	−	0.473441i	−0.863828	+	0.503787i	$0.831940\pi$
$54$	3.23645	+	3.59445i	0.440426	+	0.489142i
$55$	0.0546369	+	0.519836i	0.00736724	+	0.0700947i
$56$	0.203594	+	1.93707i	0.0272064	+	0.258852i
$57$	−6.35408	−	2.82902i	−0.841619	−	0.374713i
$58$	−1.85979	−	5.72386i	−0.244203	−	0.751580i
$59$	−8.67000	−	1.84286i	−1.12874	−	0.239921i	−0.394555	−	0.918872i	$-0.629101\pi$
$59$	−8.67000	−	1.84286i	−1.12874	−	0.239921i	−0.734183	+	0.678952i	$0.762434\pi$
$60$	−1.20758			−0.155898
$61$	−2.66773	−	7.34052i	−0.341568	−	0.939857i
$61$	−2.66773	−	7.34052i	−0.341568	−	0.939857i
$62$	9.70227			1.23219
$63$	−0.194659	−	0.0413760i	−0.0245247	−	0.00521289i
$64$	1.63269	+	5.02491i	0.204086	+	0.628113i
$65$	0.285971	+	0.127322i	0.0354703	+	0.0157924i
$66$	−0.131575	−	1.25186i	−0.0161958	−	0.154093i
$67$	1.18285	+	11.2540i	0.144508	+	1.37490i	0.790924	+	0.611915i	$0.209600\pi$
$67$	1.18285	+	11.2540i	0.144508	+	1.37490i	−0.646416	+	0.762985i	$0.723733\pi$
$68$	−0.818985	−	0.909575i	−0.0993165	−	0.110302i
$69$	−11.1983	−	8.13604i	−1.34812	−	0.979464i
$70$	−0.300149	+	0.218071i	−0.0358747	+	0.0260645i
$71$	0.576283	−	5.48297i	0.0683922	−	0.650709i	−0.905601	−	0.424131i	$-0.860580\pi$
$71$	0.576283	−	5.48297i	0.0683922	−	0.650709i	0.973993	−	0.226578i	$-0.0727537\pi$
$72$	−0.835501			−0.0984648
$73$	0.289912	−	2.75833i	0.0339317	−	0.322838i	−0.964369	−	0.264562i	$-0.914773\pi$
$73$	0.289912	−	2.75833i	0.0339317	−	0.322838i	0.998300	−	0.0582767i	$-0.0185606\pi$
$74$	−1.02845	+	1.78132i	−0.119555	+	0.207075i
$75$	3.80763	+	6.59501i	0.439667	+	0.761526i
$76$	4.64473	−	2.06797i	0.532787	−	0.237212i
$77$	0.390483	+	0.433675i	0.0444996	+	0.0494219i
$78$	−0.688668	−	0.306615i	−0.0779763	−	0.0347173i
$79$	−6.78344	+	3.02018i	−0.763197	+	0.339797i	−0.751151	−	0.660130i	$-0.770501\pi$
$79$	−6.78344	+	3.02018i	−0.763197	+	0.339797i	−0.0120456	+	0.999927i	$0.503834\pi$
$80$	−0.0601630	+	0.0668178i	−0.00672643	+	0.00747045i
$81$	−2.48391	+	7.64470i	−0.275990	+	0.849411i
$82$	−1.60220	+	2.77509i	−0.176933	+	0.306457i
$83$	10.5592	+	2.24442i	1.15902	+	0.246357i	0.747004	−	0.664819i	$-0.231491\pi$
$83$	10.5592	+	2.24442i	1.15902	+	0.246357i	0.412016	+	0.911177i	$0.364825\pi$
$84$	−1.09072	+	0.792453i	−0.119007	+	0.0864637i
$85$	0.191830	−	0.590393i	0.0208069	−	0.0640371i
$86$	2.85109	−	0.606018i	0.307441	−	0.0653486i
$87$	7.42230	−	8.24330i	0.795754	−	0.883774i
$88$	1.98210	+	1.44008i	0.211293	+	0.153513i
$89$	2.60821	+	8.02724i	0.276469	+	0.850885i	0.988827	+	0.149069i	$0.0476275\pi$
$89$	2.60821	+	8.02724i	0.276469	+	0.850885i	−0.712357	+	0.701817i	$0.752372\pi$
$90$	−0.0795730	−	0.137825i	−0.00838773	−	0.0145280i
$91$	0.341850	−	0.0726624i	0.0358356	−	0.00761709i
$92$	9.89706	−	2.10368i	1.03184	−	0.219324i
$93$	8.94104	+	15.4863i	0.927143	+	1.60586i
$94$	−1.03156	−	3.17481i	−0.106397	−	0.327456i
$95$	2.08621	+	1.51572i	0.214040	+	0.155510i
$96$	−6.15243	+	6.83297i	−0.627930	+	0.697387i
$97$	10.4211	−	2.21507i	1.05810	−	0.224907i	0.354176	−	0.935179i	$-0.384761\pi$
$97$	10.4211	−	2.21507i	1.05810	−	0.224907i	0.703927	+	0.710272i	$0.251428\pi$
$98$	1.80329	−	5.54994i	0.182159	−	0.560629i
$99$	−0.202519	+	0.147138i	−0.0203539	+	0.0147880i
$100$	−5.44498	−	1.15737i	−0.544498	−	0.115737i
$101$	6.47112	−	11.2083i	0.643901	−	1.11527i	−0.340654	−	0.940189i	$-0.610648\pi$
$101$	6.47112	−	11.2083i	0.643901	−	1.11527i	0.984554	−	0.175080i	$-0.0560184\pi$
$102$	−0.461961	+	1.42177i	−0.0457410	+	0.140776i
$103$	8.70997	−	9.67341i	0.858219	−	0.953149i	−0.141102	−	0.989995i	$-0.545064\pi$
$103$	8.70997	−	9.67341i	0.858219	−	0.953149i	0.999321	+	0.0368460i	$0.0117311\pi$
$104$	1.34041	−	0.596790i	0.131438	−	0.0585201i
$105$	−0.624676	−	0.278124i	−0.0609621	−	0.0271421i
$106$	−3.50318	−	3.89067i	−0.340258	−	0.377895i
$107$	−7.93227	+	3.53168i	−0.766842	+	0.341420i	−0.752599	−	0.658479i	$-0.771200\pi$
$107$	−7.93227	+	3.53168i	−0.766842	+	0.341420i	−0.0142424	+	0.999899i	$0.504534\pi$
$108$	−3.25822	−	5.64341i	−0.313523	−	0.543037i
$109$	−6.76643	+	11.7198i	−0.648106	+	1.12255i	0.335469	+	0.942051i	$0.391105\pi$
$109$	−6.76643	+	11.7198i	−0.648106	+	1.12255i	−0.983575	+	0.180501i	$0.942228\pi$
$110$	−0.0487811	+	0.464121i	−0.00465110	+	0.0442522i
$111$	−3.79103			−0.359828
$112$	−0.0104928	+	0.0998325i	−0.000991478	+	0.00943328i
$113$	1.52061	−	1.10479i	0.143047	−	0.103930i	−0.513960	−	0.857814i	$-0.671822\pi$
$113$	1.52061	−	1.10479i	0.143047	−	0.103930i	0.657007	+	0.753884i	$0.271822\pi$
$114$	−5.02396	−	3.65012i	−0.470537	−	0.341865i
$115$	3.43386	+	3.81369i	0.320209	+	0.355628i
$116$	0.847558	+	8.06398i	0.0786938	+	0.748721i
$117$	0.0156704	+	0.149094i	0.00144873	+	0.0137838i
$118$	−7.22953	−	3.21879i	−0.665532	−	0.296314i
$119$	−0.214169	−	0.659144i	−0.0196328	−	0.0604237i
$120$	−2.80806	−	0.596872i	−0.256340	−	0.0544867i
$121$	−10.2659			−0.933268
$122$	−0.967153	−	6.90578i	−0.0875619	−	0.625220i
$123$	−5.90597			−0.532523
$124$	−12.7859	−	2.71772i	−1.14820	−	0.244058i
$125$	−1.81509	−	5.58626i	−0.162346	−	0.499650i
$126$	−0.162317	−	0.0722684i	−0.0144604	−	0.00643818i
$127$	1.19079	+	11.3296i	0.105665	+	1.00534i	0.910969	+	0.412475i	$0.135336\pi$
$127$	1.19079	+	11.3296i	0.105665	+	1.00534i	−0.805303	+	0.592863i	$0.797998\pi$
$128$	−0.675043	−	6.42260i	−0.0596659	−	0.567683i
$129$	3.59470	+	3.99232i	0.316496	+	0.351504i
$130$	0.226107	+	0.164277i	0.0198309	+	0.0144080i
$131$	−5.10091	+	3.70603i	−0.445669	+	0.323797i	−0.787883	−	0.615824i	$-0.788823\pi$
$131$	−5.10091	+	3.70603i	−0.445669	+	0.323797i	0.342215	+	0.939622i	$0.388823\pi$
$132$	−0.177267	+	1.68658i	−0.0154291	+	0.146798i
$133$	2.87898			0.249640
$134$	−1.05607	+	10.0479i	−0.0912309	+	0.868004i
$135$	1.65254	−	2.86228i	0.142228	−	0.246345i
$136$	−1.45486	−	2.51989i	−0.124753	−	0.216079i
$137$	9.49245	−	4.22631i	0.810995	−	0.361078i	0.0410247	−	0.999158i	$-0.486938\pi$
$137$	9.49245	−	4.22631i	0.810995	−	0.361078i	0.769970	+	0.638080i	$0.220271\pi$
$138$	−8.26934	−	9.18403i	−0.703933	−	0.781797i
$139$	−8.44765	−	3.76114i	−0.716521	−	0.319015i	0.0158948	−	0.999874i	$-0.494940\pi$
$139$	−8.44765	−	3.76114i	−0.716521	−	0.319015i	−0.732415	+	0.680858i	$0.761607\pi$
$140$	0.456627	−	0.203304i	0.0385921	−	0.0171823i
$141$	4.11687	−	4.57224i	0.346703	−	0.385052i
$142$	1.52107	−	4.68137i	0.127645	−	0.392852i
$143$	0.219805	−	0.380714i	0.0183810	−	0.0318369i
$144$	−0.0421190	−	0.00895267i	−0.00350992	−	0.000746056i
$145$	−3.32707	+	2.41726i	−0.276299	+	0.200743i
$146$	0.765208	−	2.35507i	0.0633291	−	0.194907i
$147$	10.5204	−	2.23618i	0.867706	−	0.184437i
$148$	1.85428	−	2.05939i	0.152421	−	0.169280i
$149$	14.9673	+	10.8744i	1.22617	+	0.890865i	0.996597	−	0.0824257i	$-0.0262667\pi$
$149$	14.9673	+	10.8744i	1.22617	+	0.890865i	0.229574	+	0.973291i	$0.426267\pi$
$150$	2.10103	+	6.46631i	0.171549	+	0.527972i
$151$	−6.52368	−	11.2993i	−0.530889	−	0.919527i	−0.999350	−	0.0360429i	$-0.988525\pi$
$151$	−6.52368	−	11.2993i	−0.530889	−	0.919527i	0.468461	−	0.883484i	$-0.344809\pi$
$152$	11.8228	−	2.51302i	0.958958	−	0.203833i
$153$	0.290800	−	0.0618115i	0.0235098	−	0.00499716i
$154$	0.260511	+	0.451219i	0.0209926	+	0.0363602i
$155$	−2.04870	−	6.30524i	−0.164555	−	0.506449i
$156$	0.821655	+	0.596967i	0.0657851	+	0.0477956i
$157$	−7.02158	+	7.79826i	−0.560383	+	0.622369i	−0.955046	−	0.296457i	$-0.904195\pi$
$157$	−7.02158	+	7.79826i	−0.560383	+	0.622369i	0.394663	+	0.918826i	$0.370861\pi$
$158$	−6.48470	+	1.37836i	−0.515895	+	0.109657i
$159$	2.98180	−	9.17703i	0.236472	−	0.727786i
$160$	2.75785	−	2.00370i	0.218027	−	0.158406i
$161$	5.60422	+	1.19121i	0.441674	+	0.0938808i
$162$	−3.58830	+	6.21513i	−0.281924	+	0.488306i
$163$	−5.00516	+	15.4043i	−0.392035	+	1.20656i	0.539212	+	0.842170i	$0.318722\pi$
$163$	−5.00516	+	15.4043i	−0.392035	+	1.20656i	−0.931247	+	0.364389i	$0.881278\pi$
$164$	2.88875	−	3.20828i	0.225573	−	0.250524i
$165$	−0.785764	+	0.349845i	−0.0611717	+	0.0272354i
$166$	8.80484	+	3.92017i	0.683388	+	0.304264i
$167$	−5.76635	−	6.40418i	−0.446214	−	0.495570i	0.477512	−	0.878625i	$-0.341539\pi$
$167$	−5.76635	−	6.40418i	−0.446214	−	0.495570i	−0.923726	+	0.383055i	$0.874872\pi$
$168$	−2.92800	+	1.30363i	−0.225900	+	0.100577i
$169$	6.36836	+	11.0303i	0.489874	+	0.848487i
$170$	0.277122	−	0.479989i	0.0212543	−	0.0368135i
$171$	−0.129089	+	1.22820i	−0.00987170	+	0.0939229i
$172$	−3.92698			−0.299430
$173$	−2.32613	+	22.1317i	−0.176853	+	1.68264i	0.441907	+	0.897061i	$0.354302\pi$
$173$	−2.32613	+	22.1317i	−0.176853	+	1.68264i	−0.618760	+	0.785580i	$0.712365\pi$
$174$	8.01218	−	5.82119i	0.607402	−	0.441303i
$175$	−2.55011	−	1.85276i	−0.192770	−	0.140056i
$176$	0.0844901	+	0.0938358i	0.00636868	+	0.00707314i
$177$	−1.52461	−	14.5057i	−0.114597	−	1.09032i
$178$	0.787698	+	7.49445i	0.0590405	+	0.561732i
$179$	−9.05857	−	4.03313i	−0.677069	−	0.301451i	0.0392439	−	0.999230i	$-0.487505\pi$
$179$	−9.05857	−	4.03313i	−0.677069	−	0.301451i	−0.716313	+	0.697779i	$0.754172\pi$
$180$	0.0662568	+	0.203917i	0.00493849	+	0.0151991i
$181$	−4.92584	−	1.04702i	−0.366135	−	0.0778243i	0.0211705	−	0.999776i	$-0.493261\pi$
$181$	−4.92584	−	1.04702i	−0.366135	−	0.0778243i	−0.387305	+	0.921952i	$0.626594\pi$
$182$	0.312030			0.0231292
$183$	10.1314	−	7.90769i	0.748937	−	0.584553i
$184$	24.0541			1.77329
$185$	1.37480	+	0.292222i	0.101077	+	0.0214846i
$186$	4.93362	+	15.1841i	0.361751	+	1.11335i
$187$	−0.796419	−	0.354589i	−0.0582400	−	0.0259301i
$188$	0.470108	+	4.47278i	0.0342862	+	0.326211i
$189$	−0.385704	−	3.66973i	−0.0280559	−	0.266934i
$190$	1.54055	+	1.71096i	0.111763	+	0.124126i
$191$	−2.13177	−	1.54882i	−0.154249	−	0.112069i	0.507984	−	0.861367i	$-0.330391\pi$
$191$	−2.13177	−	1.54882i	−0.154249	−	0.112069i	−0.662233	+	0.749298i	$0.730391\pi$
$192$	−7.03379	+	5.11035i	−0.507620	+	0.368808i
$193$	1.03878	−	9.88329i	0.0747727	−	0.711415i	−0.891347	−	0.453321i	$-0.850239\pi$
$193$	1.03878	−	9.88329i	0.0747727	−	0.711415i	0.966120	−	0.258093i	$-0.0830943\pi$
$194$	9.51207			0.682927
$195$	−0.0538439	+	0.512290i	−0.00385584	+	0.0366859i
$196$	−3.93101	+	6.80871i	−0.280786	+	0.486336i
$197$	5.33067	+	9.23300i	0.379795	+	0.657824i	0.991032	−	0.133623i	$-0.0426613\pi$
$197$	5.33067	+	9.23300i	0.379795	+	0.657824i	−0.611237	+	0.791447i	$0.709328\pi$
$198$	−0.204175	+	0.0909046i	−0.0145101	+	0.00646031i
$199$	−7.12127	−	7.90897i	−0.504813	−	0.560652i	0.435839	−	0.900025i	$-0.356452\pi$
$199$	−7.12127	−	7.90897i	−0.504813	−	0.560652i	−0.940652	+	0.339373i	$0.889785\pi$
$200$	−12.0895	−	5.38260i	−0.854858	−	0.380607i
$201$	−17.0112	+	7.57387i	−1.19988	+	0.534220i
$202$	7.73189	−	8.58714i	0.544014	−	0.604189i
$203$	−1.41882	+	4.36667i	−0.0995814	+	0.306480i
$204$	1.00704	−	1.74424i	0.0705067	−	0.122121i
$205$	2.14177	+	0.455247i	0.149588	+	0.0317959i
$206$	9.40219	−	6.83109i	0.655082	−	0.475945i
$207$	−0.759468	+	2.33740i	−0.0527867	+	0.162461i
$208$	0.0739672	−	0.0157222i	0.00512870	−	0.00109014i
$209$	2.42319	−	2.69123i	0.167616	−	0.186156i
$210$	−0.493910	−	0.358846i	−0.0340830	−	0.0247628i
$211$	−0.332420	−	1.02308i	−0.0228848	−	0.0704321i	0.938962	−	0.344021i	$-0.111789\pi$
$211$	−0.332420	−	1.02308i	−0.0228848	−	0.0704321i	−0.961847	+	0.273589i	$0.911789\pi$
$212$	3.52674	+	6.10849i	0.242217	+	0.419533i
$213$	8.87393	−	1.88621i	0.608032	−	0.129241i
$214$	−7.58294	+	1.61180i	−0.518359	+	0.110181i
$215$	−0.995862	−	1.72488i	−0.0679172	−	0.117636i
$216$	−4.78718	−	14.7334i	−0.325726	−	1.00248i
$217$	−5.98814	−	4.35064i	−0.406502	−	0.295341i
$218$	−8.08473	+	8.97900i	−0.547567	+	0.608135i
$219$	4.46423	−	0.948902i	0.301665	−	0.0641208i
$220$	0.194291	−	0.597965i	0.0130991	−	0.0403148i
$221$	−0.422386	+	0.306881i	−0.0284127	+	0.0206431i
$222$	−3.31075	−	0.703722i	−0.222203	−	0.0472307i
$223$	7.42735	−	12.8646i	0.497372	−	0.861474i	−0.502623	−	0.864506i	$-0.667632\pi$
$223$	7.42735	−	12.8646i	0.497372	−	0.861474i	0.999995	+	0.00303151i	$0.000964960\pi$
$224$	1.17607	−	3.61958i	0.0785798	−	0.241844i
$225$	0.904750	−	1.00483i	0.0603166	−	0.0669884i
$226$	1.53305	−	0.682558i	0.101977	−	0.0454031i
$227$	−6.07055	−	2.70278i	−0.402917	−	0.179390i	0.195265	−	0.980751i	$-0.437443\pi$
$227$	−6.07055	−	2.70278i	−0.402917	−	0.179390i	−0.598182	+	0.801360i	$0.704110\pi$
$228$	5.59824	+	6.21747i	0.370752	+	0.411762i
$229$	15.3238	−	6.82260i	1.01263	−	0.450850i	0.167760	−	0.985828i	$-0.446347\pi$
$229$	15.3238	−	6.82260i	1.01263	−	0.450850i	0.844866	+	0.534978i	$0.179680\pi$
$230$	2.29091	+	3.96796i	0.151058	+	0.261640i
$231$	−0.480144	+	0.831633i	−0.0315911	+	0.0547175i
$232$	−2.01491	+	19.1706i	−0.132285	+	1.25861i
$233$	−20.8372			−1.36509			−0.682545	−	0.730844i	$-0.739127\pi$
$233$	−20.8372			−1.36509			−0.682545	+	0.730844i	$0.739127\pi$
$234$	−0.0139909	+	0.133115i	−0.000914616	+	0.00870199i
$235$	−1.84540	+	1.34076i	−0.120381	+	0.0874617i
$236$	8.62561	+	6.26687i	0.561479	+	0.407939i
$237$	−8.17600	−	9.08037i	−0.531088	−	0.589833i
$238$	−0.0646806	−	0.615395i	−0.00419262	−	0.0398901i
$239$	−2.73583	−	26.0297i	−0.176966	−	1.68372i	−0.617958	−	0.786211i	$-0.712040\pi$
$239$	−2.73583	−	26.0297i	−0.176966	−	1.68372i	0.440992	−	0.897511i	$-0.354627\pi$
$240$	−0.135163	−	0.0601786i	−0.00872476	−	0.00388451i
$241$	6.19510	+	19.0666i	0.399062	+	1.22819i	0.925753	+	0.378129i	$0.123432\pi$
$241$	6.19510	+	19.0666i	0.399062	+	1.22819i	−0.526691	+	0.850057i	$0.676568\pi$
$242$	−8.96538	−	1.90565i	−0.576317	−	0.122500i
$243$	3.02520			0.194067
$244$	−0.659852	+	9.37149i	−0.0422427	+	0.599948i
$245$	−3.98753			−0.254754
$246$	−5.15776	−	1.09632i	−0.328847	−	0.0698985i
$247$	−0.670191	−	2.06264i	−0.0426433	−	0.131242i
$248$	−28.3885	−	12.6394i	−1.80267	−	0.802601i
$249$	1.85682	+	17.6665i	0.117671	+	1.11957i
$250$	−0.548169	−	5.21548i	−0.0346693	−	0.329856i
$251$	−10.0924	−	11.2088i	−0.637027	−	0.707490i	0.335037	−	0.942205i	$-0.391251\pi$
$251$	−10.0924	−	11.2088i	−0.637027	−	0.707490i	−0.972064	+	0.234715i	$0.924584\pi$
$252$	0.193662	+	0.140704i	0.0121996	+	0.00886351i
$253$	5.83050	−	4.23611i	0.366561	−	0.266322i
$254$	−1.06316	+	10.1153i	−0.0667088	+	0.634691i
$255$	1.02152			0.0639698
$256$	1.70725	−	16.2434i	0.106703	−	1.01521i
$257$	−6.74852	+	11.6888i	−0.420961	+	0.729126i	−0.996034	−	0.0889763i	$-0.971640\pi$
$257$	−6.74852	+	11.6888i	−0.420961	+	0.729126i	0.575073	+	0.818102i	$0.304974\pi$
$258$	2.39821	+	4.15382i	0.149306	+	0.258606i
$259$	1.43352	−	0.638244i	0.0890745	−	0.0396585i
$260$	−0.251953	−	0.279823i	−0.0156255	−	0.0173539i
$261$	−1.79925	−	0.801076i	−0.111370	−	0.0495853i
$262$	−5.14264	+	2.28965i	−0.317713	+	0.141455i
$263$	−3.50888	+	3.89701i	−0.216367	+	0.240300i	−0.841551	−	0.540177i	$-0.818357\pi$
$263$	−3.50888	+	3.89701i	−0.216367	+	0.240300i	0.625184	+	0.780477i	$0.285024\pi$
$264$	−1.24584	+	3.83429i	−0.0766760	+	0.235984i
$265$	−1.78872	+	3.09816i	−0.109880	+	0.190318i
$266$	2.51425	+	0.534421i	0.154159	+	0.0327674i
$267$	−11.2364	+	8.16373i	−0.687657	+	0.499612i
$268$	4.20624	−	12.9455i	0.256937	−	0.790771i
$269$	16.3147	−	3.46780i	0.994727	−	0.211436i	0.318336	−	0.947978i	$-0.396876\pi$
$269$	16.3147	−	3.46780i	0.994727	−	0.211436i	0.676391	+	0.736542i	$0.263543\pi$
$270$	1.97450	−	2.19290i	0.120164	−	0.133456i
$271$	2.08049	+	1.51156i	0.126381	+	0.0918208i	0.649180	−	0.760635i	$-0.275112\pi$
$271$	2.08049	+	1.51156i	0.126381	+	0.0918208i	−0.522799	+	0.852456i	$0.675112\pi$
$272$	−0.0463405	−	0.142621i	−0.00280981	−	0.00864769i
$273$	0.287548	+	0.498048i	0.0174032	+	0.0301433i
$274$	9.07440	−	1.92882i	0.548205	−	0.116525i
$275$	−3.87832	+	0.824362i	−0.233871	+	0.0497109i
$276$	8.32496	+	14.4192i	0.501104	+	0.867937i
$277$	−8.36496	−	25.7447i	−0.502602	−	1.54685i	−0.804765	−	0.593593i	$-0.797709\pi$
$277$	−8.36496	−	25.7447i	−0.502602	−	1.54685i	0.302164	−	0.953256i	$-0.402291\pi$
$278$	−6.67927	−	4.85277i	−0.400596	−	0.291050i
$279$	2.12452	−	2.35952i	0.127192	−	0.141261i
$280$	1.16231	−	0.247057i	0.0694615	−	0.0147645i
$281$	5.33849	−	16.4302i	0.318467	−	0.980142i	−0.655836	−	0.754903i	$-0.727684\pi$
$281$	5.33849	−	16.4302i	0.318467	−	0.980142i	0.974304	−	0.225239i	$-0.0723162\pi$
$282$	4.44405	−	3.22879i	0.264639	−	0.192272i
$283$	26.1003	+	5.54779i	1.55150	+	0.329782i	0.902393	−	0.430915i	$-0.141809\pi$
$283$	26.1003	+	5.54779i	1.55150	+	0.329782i	0.649108	+	0.760696i	$0.275142\pi$
$284$	−3.31580	+	5.74314i	−0.196757	+	0.340793i
$285$	−1.31127	+	4.03568i	−0.0776730	+	0.239053i
$286$	0.262630	−	0.291680i	0.0155296	−	0.0172474i
$287$	2.23325	−	0.994308i	0.131825	−	0.0586921i
$288$	1.49142	+	0.664021i	0.0878825	+	0.0391278i
$289$	−10.6824	−	11.8640i	−0.628378	−	0.697884i
$290$	−3.35429	+	1.49343i	−0.196971	+	0.0876970i
$291$	8.76576	+	15.1827i	0.513858	+	0.890029i
$292$	−1.66809	+	2.88922i	−0.0976176	+	0.169079i
$293$	−2.80776	+	26.7141i	−0.164031	+	1.56065i	0.534560	+	0.845130i	$0.320477\pi$
$293$	−2.80776	+	26.7141i	−0.164031	+	1.56065i	−0.698591	+	0.715521i	$0.746189\pi$
$294$	9.60268			0.560040
$295$	−0.565245	+	5.37795i	−0.0329098	+	0.313116i
$296$	5.32977	−	3.87230i	0.309787	−	0.225073i
$297$	−3.75504	−	2.72820i	−0.217890	−	0.158306i
$298$	11.0526	+	12.2751i	0.640258	+	0.711078i
$299$	−0.451152	−	4.29242i	−0.0260908	−	0.248237i
$300$	−0.957496	−	9.10997i	−0.0552811	−	0.525964i
$301$	−2.03141	−	0.904444i	−0.117089	−	0.0521313i
$302$	−3.59973	−	11.0788i	−0.207141	−	0.637515i
$303$	20.8317	+	4.42791i	1.19675	+	0.254377i
$304$	0.622936			0.0357278
$305$	−4.28366	+	2.08673i	−0.245281	+	0.119486i
$306$	0.265434			0.0151738
$307$	2.72903	+	0.580073i	0.155754	+	0.0331065i	0.285129	−	0.958489i	$-0.407964\pi$
$307$	2.72903	+	0.580073i	0.155754	+	0.0331065i	−0.129375	+	0.991596i	$0.541297\pi$
$308$	−0.216916	−	0.667598i	−0.0123599	−	0.0380399i
$309$	19.5680	+	8.71224i	1.11318	+	0.495622i
$310$	−0.618722	−	5.88674i	−0.0351410	−	0.334345i
$311$	0.384323	+	3.65659i	0.0217930	+	0.207346i	1.00000		0.000285872i	$-9.09960e-5\pi$
$311$	0.384323	+	3.65659i	0.0217930	+	0.207346i	−0.978207	+	0.207632i	$0.933424\pi$
$312$	1.61558	+	1.79429i	0.0914644	+	0.101582i
$313$	22.0161	+	15.9956i	1.24442	+	0.904126i	0.997885	−	0.0650072i	$-0.0207070\pi$
$313$	22.0161	+	15.9956i	1.24442	+	0.904126i	0.246538	+	0.969133i	$0.420707\pi$
$314$	−7.57961	+	5.50691i	−0.427742	+	0.310773i
$315$	−0.0126909	+	0.120746i	−0.000715050	+	0.00680325i
$316$	8.93177			0.502451
$317$	−3.02393	+	28.7708i	−0.169841	+	1.61593i	0.494966	+	0.868912i	$0.335180\pi$
$317$	−3.02393	+	28.7708i	−0.169841	+	1.61593i	−0.664807	+	0.747015i	$0.731486\pi$
$318$	4.30756	−	7.46091i	0.241556	−	0.418387i
$319$	2.88770	+	5.00164i	0.161680	+	0.280038i
$320$	2.94469	−	1.31106i	0.164613	−	0.0732905i
$321$	−9.56068	−	10.6182i	−0.533625	−	0.592651i
$322$	4.67311	+	2.08060i	0.260422	+	0.115948i
$323$	−3.92907	+	1.74934i	−0.218619	+	0.0973357i
$324$	6.46967	−	7.18530i	0.359426	−	0.399183i
$325$	−0.733772	+	2.25832i	−0.0407023	+	0.125269i
$326$	−7.23055	+	12.5237i	−0.400463	+	0.693622i
$327$	−21.7823	−	4.62997i	−1.20456	−	0.256038i
$328$	8.30315	−	6.03259i	0.458465	−	0.333094i
$329$	−0.786964	+	2.42203i	−0.0433867	+	0.133531i
$330$	−0.751159	+	0.159664i	−0.0413500	+	0.00878920i
$331$	7.80996	−	8.67384i	0.429274	−	0.476757i	−0.489238	−	0.872150i	$-0.662725\pi$
$331$	7.80996	−	8.67384i	0.429274	−	0.476757i	0.918512	+	0.395393i	$0.129392\pi$
$332$	−10.5051	−	7.63241i	−0.576543	−	0.418883i
$333$	0.208004	+	0.640171i	0.0113986	+	0.0350811i
$334$	−3.84703	−	6.66325i	−0.210500	−	0.364597i
$335$	6.75284	−	1.43536i	0.368947	−	0.0784221i
$336$	−0.161574	+	0.0343437i	−0.00881460	+	0.00187360i
$337$	−12.1650	−	21.0703i	−0.662668	−	1.14777i	−0.979912	−	0.199430i	$-0.936091\pi$
$337$	−12.1650	−	21.0703i	−0.662668	−	1.14777i	0.317244	−	0.948344i	$-0.397242\pi$
$338$	3.51403	+	10.8151i	0.191138	+	0.588263i
$339$	2.50224	+	1.81798i	0.135903	+	0.0987393i
$340$	−0.499647	+	0.554915i	−0.0270972	+	0.0300945i
$341$	−9.10702	+	1.93576i	−0.493173	+	0.104827i
$342$	−0.340724	+	1.04864i	−0.0184243	+	0.0567040i
$343$	−7.45894	+	5.41923i	−0.402745	+	0.292611i
$344$	−9.13167	−	1.94100i	−0.492347	−	0.104652i
$345$	−4.22233	+	7.31329i	−0.227323	+	0.393734i
$346$	−6.13971	+	18.8961i	−0.330073	+	1.01586i
$347$	2.71729	−	3.01786i	0.145872	−	0.162007i	−0.665781	−	0.746147i	$-0.731901\pi$
$347$	2.71729	−	3.01786i	0.145872	−	0.162007i	0.811653	+	0.584140i	$0.198568\pi$
$348$	−12.1892	+	5.42698i	−0.653410	+	0.290917i
$349$	−0.804572	−	0.358219i	−0.0430678	−	0.0191750i	0.385090	−	0.922879i	$-0.374170\pi$
$349$	−0.804572	−	0.358219i	−0.0430678	−	0.0191750i	−0.428158	+	0.903704i	$0.640837\pi$
$350$	−1.88312	−	2.09142i	−0.100657	−	0.111791i
$351$	−2.53938	+	1.13060i	−0.135542	+	0.0603472i
$352$	−2.39365	−	4.14592i	−0.127582	−	0.220978i
$353$	9.77716	−	16.9345i	0.520385	−	0.901334i	−0.479334	−	0.877633i	$-0.659122\pi$
$353$	9.77716	−	16.9345i	0.520385	−	0.901334i	0.999719	−	0.0237013i	$-0.00754506\pi$
$354$	1.36121	−	12.9510i	0.0723474	−	0.688340i
$355$	−3.36348			−0.178515
$356$	1.06124	−	10.0970i	0.0562454	−	0.535139i
$357$	0.922661	−	0.670352i	0.0488324	−	0.0354788i
$358$	−7.16230	−	5.20371i	−0.378539	−	0.275025i
$359$	0.484832	+	0.538460i	0.0255884	+	0.0284188i	0.755803	−	0.654799i	$-0.227247\pi$
$359$	0.484832	+	0.538460i	0.0255884	+	0.0284188i	−0.730215	+	0.683218i	$0.760580\pi$
$360$	0.0532806	+	0.506931i	0.00280814	+	0.0267176i
$361$	0.118546	+	1.12789i	0.00623925	+	0.0593625i
$362$	−4.10744	−	1.82875i	−0.215882	−	0.0961170i
$363$	−5.22025	−	16.0663i	−0.273992	−	0.843261i
$364$	−0.411200	−	0.0874032i	−0.0215527	−	0.00458117i
$365$	−1.69208			−0.0885673
$366$	10.3158	−	5.02520i	0.539215	−	0.262672i
$367$	−0.914369			−0.0477297			−0.0238648	−	0.999715i	$-0.507597\pi$
$367$	−0.914369			−0.0477297			−0.0238648	+	0.999715i	$0.507597\pi$
$368$	1.21261	+	0.257747i	0.0632114	+	0.0134360i
$369$	0.324046	+	0.997310i	0.0168691	+	0.0519179i
$370$	1.14638	+	0.510403i	0.0595976	+	0.0265346i
$371$	0.417491	+	3.97216i	0.0216750	+	0.206224i
$372$	−2.24838	−	21.3919i	−0.116573	−	1.10912i
$373$	−10.4956	−	11.6566i	−0.543443	−	0.603554i	0.407392	−	0.913253i	$-0.366438\pi$
$373$	−10.4956	−	11.6566i	−0.543443	−	0.603554i	−0.950835	+	0.309699i	$0.899772\pi$
$374$	−0.629702	−	0.457505i	−0.0325611	−	0.0236570i
$375$	7.81957	−	5.68125i	0.403801	−	0.293378i
$376$	−1.11760	+	10.6332i	−0.0576356	+	0.548366i
$377$	3.45877			0.178136
$378$	0.344366	−	3.27642i	0.0177123	−	0.168521i
$379$	−11.4376	+	19.8105i	−0.587509	+	1.01760i	0.407048	+	0.913407i	$0.366558\pi$
$379$	−11.4376	+	19.8105i	−0.587509	+	1.01760i	−0.994557	+	0.104189i	$0.966775\pi$
$380$	−1.55091	−	2.68626i	−0.0795602	−	0.137802i
$381$	−17.1254	+	7.62471i	−0.877360	+	0.390626i
$382$	−1.57420	−	1.74832i	−0.0805428	−	0.0894519i
$383$	5.04189	+	2.24479i	0.257629	+	0.114704i	0.531487	−	0.847066i	$-0.321633\pi$
$383$	5.04189	+	2.24479i	0.257629	+	0.114704i	−0.273859	+	0.961770i	$0.588300\pi$
$384$	9.70817	−	4.32235i	0.495418	−	0.220574i
$385$	0.238226	−	0.264577i	0.0121411	−	0.0134841i
$386$	2.74179	−	8.43838i	0.139554	−	0.429502i
$387$	0.476930	−	0.826066i	0.0242437	−	0.0419913i
$388$	−12.5352	−	2.66444i	−0.636379	−	0.135266i
$389$	10.0616	−	7.31021i	0.510146	−	0.370643i	−0.302733	−	0.953075i	$-0.597899\pi$
$389$	10.0616	−	7.31021i	0.510146	−	0.370643i	0.812879	+	0.582433i	$0.197899\pi$
$390$	−0.142118	+	0.437395i	−0.00719643	+	0.0221483i
$391$	−8.37213	+	1.77955i	−0.423397	+	0.0899958i
$392$	−12.5064	+	13.8897i	−0.631668	+	0.701538i
$393$	−8.39379	−	6.09845i	−0.423411	−	0.307626i
$394$	2.94144	+	9.05282i	0.148188	+	0.456074i
$395$	2.26505	+	3.92318i	0.113967	+	0.197397i
$396$	0.294530	−	0.0626042i	0.0148007	−	0.00314598i
$397$	−9.26093	+	1.96847i	−0.464793	+	0.0987947i	−0.434355	−	0.900742i	$-0.643024\pi$
$397$	−9.26093	+	1.96847i	−0.464793	+	0.0987947i	−0.0304380	+	0.999537i	$0.509690\pi$
$398$	−4.75096	−	8.22891i	−0.238144	−	0.412478i
$399$	1.46397	+	4.50563i	0.0732901	+	0.225564i
$400$	−0.551777	−	0.400889i	−0.0275888	−	0.0200445i
$401$	14.6456	−	16.2656i	0.731367	−	0.812265i	−0.256667	−	0.966500i	$-0.582624\pi$
$401$	14.6456	−	16.2656i	0.731367	−	0.812265i	0.988034	+	0.154234i	$0.0492911\pi$
$402$	−16.2620	+	3.45660i	−0.811076	+	0.172399i
$403$	−1.72303	+	5.30296i	−0.0858305	+	0.264159i
$404$	−12.5946	+	9.15052i	−0.626605	+	0.455255i
$405$	4.79674	+	1.01958i	0.238352	+	0.0506632i
$406$	−2.04965	+	3.55010i	−0.101722	+	0.176188i
$407$	0.609948	−	1.87723i	0.0302340	−	0.0930508i
$408$	3.20386	−	3.55824i	0.158615	−	0.176159i
$409$	−4.39611	+	1.95728i	−0.217374	+	0.0967811i	−0.512535	−	0.858666i	$-0.671293\pi$
$409$	−4.39611	+	1.95728i	−0.217374	+	0.0967811i	0.295161	+	0.955448i	$0.404627\pi$
$410$	1.78593	+	0.795147i	0.0882007	+	0.0392695i
$411$	11.4411	+	12.7067i	0.564350	+	0.626774i
$412$	−14.3039	+	6.36850i	−0.704701	+	0.313753i
$413$	3.01864	+	5.22844i	0.148538	+	0.257275i
$414$	−1.09714	+	1.90030i	−0.0539215	+	0.0933948i
$415$	0.688411	−	6.54979i	0.0337928	−	0.321517i
$416$	−2.86701			−0.140567
$417$	1.59056	−	15.1332i	0.0778902	−	0.741076i
$418$	2.61577	−	1.90047i	0.127942	−	0.0929550i
$419$	26.7785	+	19.4557i	1.30822	+	0.950474i	1.00000		0.000842259i	$-0.000268099\pi$
$419$	26.7785	+	19.4557i	1.30822	+	0.950474i	0.308216	+	0.951316i	$0.400268\pi$
$420$	0.550368	+	0.611245i	0.0268552	+	0.0298257i
$421$	0.0752115	+	0.715590i	0.00366558	+	0.0348757i	0.996202	−	0.0870745i	$-0.0277518\pi$
$421$	0.0752115	+	0.715590i	0.00366558	+	0.0348757i	−0.992536	+	0.121950i	$0.961085\pi$
$422$	−0.100393	−	0.955180i	−0.00488708	−	0.0464974i
$423$	−0.997973	−	0.444326i	−0.0485231	−	0.0216039i
$424$	5.18170	+	15.9476i	0.251646	+	0.774485i
$425$	4.60603	+	0.979041i	0.223425	+	0.0474905i
$426$	8.09985			0.392439
$427$	−2.49973	+	4.69586i	−0.120971	+	0.227249i
$428$	10.4444			0.504851
$429$	0.707592	+	0.150403i	0.0341629	+	0.00726154i
$430$	−0.549512	−	1.69122i	−0.0264998	−	0.0815580i
$431$	18.9160	+	8.42194i	0.911151	+	0.405671i	0.808127	−	0.589008i	$-0.200481\pi$
$431$	18.9160	+	8.42194i	0.911151	+	0.405671i	0.103024	+	0.994679i	$0.467148\pi$
$432$	−0.0834562	−	0.794033i	−0.00401529	−	0.0382029i
$433$	3.26231	+	31.0388i	0.156777	+	1.49163i	0.736289	+	0.676667i	$0.236576\pi$
$433$	3.26231	+	31.0388i	0.156777	+	1.49163i	−0.579512	+	0.814964i	$0.696757\pi$
$434$	−4.42192	−	4.91104i	−0.212259	−	0.235737i
$435$	−5.47486	−	3.97772i	−0.262499	−	0.190717i
$436$	13.1694	−	9.56810i	0.630698	−	0.458229i
$437$	3.71647	−	35.3599i	0.177783	−	1.69149i
$438$	4.07481			0.194702
$439$	0.700537	−	6.66517i	0.0334348	−	0.318111i	−0.965003	−	0.262238i	$-0.915539\pi$
$439$	0.700537	−	6.66517i	0.0334348	−	0.318111i	0.998438	−	0.0558725i	$-0.0177940\pi$
$440$	0.747354	−	1.29445i	0.0356287	−	0.0617107i
$441$	−0.954838	−	1.65383i	−0.0454685	−	0.0787537i
$442$	−0.425841	+	0.189596i	−0.0202552	+	0.00901818i
$443$	2.91815	+	3.24094i	0.138646	+	0.153982i	0.808469	−	0.588539i	$-0.200297\pi$
$443$	2.91815	+	3.24094i	0.138646	+	0.153982i	−0.669823	+	0.742521i	$0.733630\pi$
$444$	4.16586	+	1.85476i	0.197703	+	0.0880230i
$445$	4.70411	−	2.09441i	0.222996	−	0.0992843i
$446$	8.87443	−	9.85605i	0.420216	−	0.466698i
$447$	−9.40761	+	28.9536i	−0.444965	+	1.36946i
$448$	1.79936	−	3.11658i	0.0850118	−	0.147245i
$449$	34.5074	+	7.33476i	1.62850	+	0.346149i	0.929458	−	0.368929i	$-0.120275\pi$
$449$	34.5074	+	7.33476i	1.62850	+	0.346149i	0.699045	+	0.715078i	$0.253609\pi$
$450$	0.976654	−	0.709580i	0.0460399	−	0.0334499i
$451$	0.950227	−	2.92450i	0.0447445	−	0.137709i
$452$	−2.21148	+	0.470064i	−0.104019	+	0.0221100i
$453$	14.3663	−	15.9553i	0.674985	−	0.749647i
$454$	−4.79978	−	3.48724i	−0.225265	−	0.163664i
$455$	−0.0658871	−	0.202780i	−0.00308884	−	0.00950646i
$456$	9.94482	+	17.2249i	0.465709	+	0.806632i
$457$	−37.3323	+	7.93522i	−1.74633	+	0.371194i	−0.966872	−	0.255262i	$-0.917838\pi$
$457$	−37.3323	+	7.93522i	−1.74633	+	0.371194i	−0.779457	+	0.626455i	$0.784505\pi$
$458$	14.6489	−	3.11373i	0.684500	−	0.145495i
$459$	2.75620	+	4.77388i	0.128648	+	0.222826i
$460$	−1.90753	−	5.87078i	−0.0889391	−	0.273726i
$461$	13.7355	+	9.97940i	0.639725	+	0.464787i	0.859756	−	0.510706i	$-0.170616\pi$
$461$	13.7355	+	9.97940i	0.639725	+	0.464787i	−0.220031	+	0.975493i	$0.570616\pi$
$462$	−0.573690	+	0.637148i	−0.0266905	+	0.0296428i
$463$	10.2726	−	2.18351i	0.477409	−	0.101476i	0.0370789	−	0.999312i	$-0.488195\pi$
$463$	10.2726	−	2.18351i	0.477409	−	0.101476i	0.440330	+	0.897836i	$0.354861\pi$
$464$	−0.306994	+	0.944832i	−0.0142519	+	0.0438627i
$465$	8.82599	−	6.41245i	0.409295	−	0.297370i
$466$	−18.1974	−	3.86797i	−0.842977	−	0.179180i
$467$	15.4407	−	26.7441i	0.714512	−	1.23757i	−0.248635	−	0.968597i	$-0.579982\pi$
$467$	15.4407	−	26.7441i	0.714512	−	1.23757i	0.963147	−	0.268974i	$-0.0866846\pi$
$468$	0.0557246	−	0.171503i	0.00257587	−	0.00792771i
$469$	5.15741	−	5.72789i	0.238147	−	0.264489i
$470$	−1.86050	+	0.828346i	−0.0858183	+	0.0382088i
$471$	−15.7748	−	7.02340i	−0.726865	−	0.323621i
$472$	16.9602	+	18.8362i	0.780654	+	0.867004i
$473$	−2.55526	+	1.13768i	−0.117491	+	0.0523105i
$474$	−5.45463	−	9.44770i	−0.250540	−	0.433947i
$475$	−9.78041	+	16.9402i	−0.448756	+	0.777268i
$476$	−0.0871418	+	0.829098i	−0.00399414	+	0.0380017i
$477$	−1.71328			−0.0784457
$478$	2.44261	−	23.2399i	0.111723	−	1.06297i
$479$	−31.1947	+	22.6642i	−1.42532	+	1.03556i	−0.434456	+	0.900693i	$0.643059\pi$
$479$	−31.1947	+	22.6642i	−1.42532	+	1.03556i	−0.990864	+	0.134863i	$0.956941\pi$
$480$	4.53818	+	3.29718i	0.207138	+	0.150495i
$481$	−0.790973	−	0.878464i	−0.0360652	−	0.0400545i
$482$	1.87097	+	17.8011i	0.0852202	+	0.810816i
$483$	0.985498	+	9.37639i	0.0448417	+	0.426640i
$484$	11.2810	+	5.02261i	0.512772	+	0.228301i
$485$	−2.00854	−	6.18164i	−0.0912029	−	0.280694i
$486$	2.64195	+	0.561563i	0.119841	+	0.0254730i
$487$	26.4637			1.19918			0.599592	−	0.800306i	$-0.295330\pi$
$487$	26.4637			1.19918			0.599592	+	0.800306i	$0.295330\pi$
$488$	−6.16646	+	21.4660i	−0.279142	+	0.971720i
$489$	−26.6530			−1.20529
$490$	−3.48236	−	0.740199i	−0.157317	−	0.0334388i
$491$	−12.3809	−	38.1046i	−0.558744	−	1.71964i	−0.685845	−	0.727748i	$-0.740567\pi$
$491$	−12.3809	−	38.1046i	−0.558744	−	1.71964i	0.127101	−	0.991890i	$-0.459433\pi$
$492$	6.48991	+	2.88950i	0.292588	+	0.130269i
$493$	−0.716967	−	6.82149i	−0.0322906	−	0.307224i
$494$	−0.202403	−	1.92573i	−0.00910653	−	0.0866429i
$495$	0.102189	+	0.113493i	0.00459307	+	0.00510112i
$496$	−1.29568	−	0.941363i	−0.0581776	−	0.0422685i
$497$	−3.03799	+	2.20723i	−0.136272	+	0.0990076i
$498$	−1.65781	+	15.7731i	−0.0742885	+	0.706807i
$499$	−24.8592			−1.11285			−0.556425	−	0.830898i	$-0.687827\pi$
$499$	−24.8592			−1.11285			−0.556425	+	0.830898i	$0.687827\pi$
$500$	−0.738528	+	7.02662i	−0.0330280	+	0.314240i
$501$	7.09039	−	12.2809i	0.316775	−	0.548671i
$502$	−6.73316	−	11.6622i	−0.300516	−	0.520509i
$503$	−13.4579	+	5.99185i	−0.600059	+	0.267163i	−0.684205	−	0.729290i	$-0.739851\pi$
$503$	−13.4579	+	5.99185i	−0.600059	+	0.267163i	0.0841457	+	0.996453i	$0.473184\pi$
$504$	0.380789	+	0.422909i	0.0169617	+	0.0188379i
$505$	−7.21319	−	3.21152i	−0.320983	−	0.142911i
$506$	5.87819	−	2.61714i	0.261318	−	0.116346i
$507$	−14.0242	+	15.5755i	−0.622838	+	0.691732i
$508$	4.23448	−	13.0324i	0.187874	−	0.578218i
$509$	−0.405541	+	0.702418i	−0.0179753	+	0.0311341i	−0.874873	−	0.484352i	$-0.839055\pi$
$509$	−0.405541	+	0.702418i	−0.0179753	+	0.0311341i	0.856898	+	0.515486i	$0.172389\pi$
$510$	0.892103	+	0.189622i	0.0395030	+	0.00839662i
$511$	−1.52833	+	1.11039i	−0.0676092	+	0.0491210i
$512$	0.514935	−	1.58481i	0.0227571	−	0.0700393i
$513$	−22.3980	+	4.76085i	−0.988898	+	0.210197i
$514$	−8.06334	+	8.95524i	−0.355659	+	0.394999i
$515$	−6.42468	−	4.66780i	−0.283105	−	0.205688i
$516$	−1.99688	−	6.14576i	−0.0879077	−	0.270552i
$517$	1.60170	+	2.77422i	0.0704425	+	0.122010i
$518$	1.37039	−	0.291285i	0.0602113	−	0.0127983i
$519$	−35.8191	+	7.61359i	−1.57228	+	0.334199i
$520$	−0.447575	−	0.775223i	−0.0196275	−	0.0339958i
$521$	9.67741	+	29.7840i	0.423975	+	1.30486i	0.903972	+	0.427591i	$0.140638\pi$
$521$	9.67741	+	29.7840i	0.423975	+	1.30486i	−0.479998	+	0.877270i	$0.659362\pi$
$522$	−1.42260	−	1.03358i	−0.0622656	−	0.0452386i
$523$	12.8481	−	14.2692i	0.561807	−	0.623949i	−0.393586	−	0.919288i	$-0.628766\pi$
$523$	12.8481	−	14.2692i	0.561807	−	0.623949i	0.955393	+	0.295338i	$0.0954324\pi$
$524$	7.41843	−	1.57684i	0.324076	−	0.0688844i
$525$	1.60285	−	4.93308i	0.0699543	−	0.215297i
$526$	−3.78775	+	2.75196i	−0.165154	+	0.119991i
$527$	10.8158	+	2.29897i	0.471145	+	0.100145i
$528$	−0.103890	+	0.179943i	−0.00452125	+	0.00783103i
$529$	14.7577	−	45.4194i	0.641638	−	1.97476i
$530$	−2.13722	+	2.37362i	−0.0928350	+	0.103104i
$531$	−2.36585	+	1.05335i	−0.102669	+	0.0457113i
$532$	−3.16364	−	1.40854i	−0.137161	−	0.0610681i
$533$	−1.23224	−	1.36854i	−0.0533743	−	0.0592782i
$534$	−11.3283	+	5.04369i	−0.490224	+	0.218262i
$535$	2.64865	+	4.58760i	0.114511	+	0.198339i
$536$	16.1796	−	28.0239i	0.698853	−	1.21045i
$537$	1.70559	−	16.2276i	0.0736016	−	0.700272i
$538$	14.8916			0.642022
$539$	−0.585350	+	5.56923i	−0.0252128	+	0.239884i
$540$	−3.21630	+	2.33678i	−0.138407	+	0.100559i
$541$	−18.5587	−	13.4837i	−0.797899	−	0.579708i	0.112398	−	0.993663i	$-0.464147\pi$
$541$	−18.5587	−	13.4837i	−0.797899	−	0.579708i	−0.910297	+	0.413955i	$0.864147\pi$
$542$	1.53633	+	1.70626i	0.0659909	+	0.0732903i
$543$	−0.866205	−	8.24139i	−0.0371724	−	0.353672i
$544$	0.594303	+	5.65441i	0.0254805	+	0.242431i
$545$	7.54236	+	3.35807i	0.323079	+	0.143844i
$546$	0.158668	+	0.488329i	0.00679035	+	0.0208986i
$547$	22.4075	+	4.76286i	0.958076	+	0.203645i	0.660310	−	0.750993i	$-0.270425\pi$
$547$	22.4075	+	4.76286i	0.958076	+	0.203645i	0.297766	+	0.954639i	$0.403758\pi$
$548$	−12.4987			−0.533919
$549$	−1.89121	−	1.27697i	−0.0807151	−	0.0544996i
$550$	−3.54001			−0.150946
$551$	27.8698	+	5.92391i	1.18729	+	0.252367i
$552$	12.2315	+	37.6448i	0.520609	+	1.60227i
$553$	4.62037	+	2.05712i	0.196478	+	0.0874777i
$554$	−2.52628	−	24.0359i	−0.107331	−	1.02119i
$555$	0.241757	+	2.30016i	0.0102620	+	0.0976365i
$556$	7.44277	+	8.26603i	0.315644	+	0.350558i
$557$	−6.96052	−	5.05712i	−0.294927	−	0.214277i	0.430475	−	0.902602i	$-0.358346\pi$
$557$	−6.96052	−	5.05712i	−0.294927	−	0.214277i	−0.725402	+	0.688326i	$0.758346\pi$
$558$	2.29337	−	1.66623i	0.0970860	−	0.0705371i
$559$	−0.175098	+	1.66594i	−0.00740584	+	0.0704618i
$560$	0.0612414			0.00258792
$561$	0.149953	−	1.42671i	0.00633104	−	0.0602358i
$562$	7.71208	−	13.3577i	0.325314	−	0.563461i
$563$	−18.9951	−	32.9004i	−0.800546	−	1.38659i	−0.919257	−	0.393658i	$-0.871209\pi$
$563$	−18.9951	−	32.9004i	−0.800546	−	1.38659i	0.118711	−	0.992929i	$-0.462124\pi$
$564$	−6.76089	+	3.01014i	−0.284685	+	0.126750i
$565$	−0.767290	−	0.852161i	−0.0322801	−	0.0358507i
$566$	21.7639	+	9.68991i	0.914804	+	0.407297i
$567$	5.00162	−	2.22686i	0.210048	−	0.0935195i
$568$	−10.5491	+	11.7160i	−0.442632	+	0.491592i
$569$	5.59899	−	17.2319i	0.234722	−	0.722399i	−0.762436	−	0.647063i	$-0.775997\pi$
$569$	5.59899	−	17.2319i	0.234722	−	0.722399i	0.997158	−	0.0753362i	$-0.0240030\pi$
$570$	−1.89429	+	3.28100i	−0.0793430	+	0.137426i
$571$	−32.8120	−	6.97440i	−1.37314	−	0.291869i	−0.538480	−	0.842638i	$-0.681001\pi$
$571$	−32.8120	−	6.97440i	−1.37314	−	0.291869i	−0.834658	+	0.550769i	$0.814335\pi$
$572$	−0.427803	+	0.310817i	−0.0178873	+	0.0129959i
$573$	1.33991	−	4.12381i	0.0559755	−	0.172275i
$574$	2.13490	−	0.453787i	0.0891090	−	0.0189407i
$575$	−26.0477	+	28.9289i	−1.08626	+	1.20642i
$576$	1.24888	+	0.907367i	0.0520368	+	0.0378070i
$577$	−6.40990	−	19.7276i	−0.266848	−	0.821273i	−0.991262	−	0.131908i	$-0.957890\pi$
$577$	−6.40990	−	19.7276i	−0.266848	−	0.821273i	0.724414	−	0.689365i	$-0.242110\pi$
$578$	−7.12680	−	12.3440i	−0.296436	−	0.513442i
$579$	15.9956	−	3.39998i	0.664756	−	0.141298i
$580$	4.83868	−	1.02849i	0.200915	−	0.0427059i
$581$	−3.67640	−	6.36771i	−0.152523	−	0.264177i
$582$	4.83691	+	14.8865i	0.200496	+	0.617064i
$583$	4.06450	+	2.95303i	0.168335	+	0.122302i
$584$	−5.30698	+	5.89400i	−0.219604	+	0.243895i
$585$	0.0894621	−	0.0190157i	0.00369880	−	0.000786204i
$586$	−7.41094	+	22.8085i	−0.306143	+	0.942211i
$587$	−9.40173	+	6.83076i	−0.388051	+	0.281935i	−0.764656	−	0.644438i	$-0.777091\pi$
$587$	−9.40173	+	6.83076i	−0.388051	+	0.281935i	0.376605	+	0.926374i	$0.377091\pi$
$588$	−12.6546	−	2.68982i	−0.521867	−	0.110926i
$589$	−22.9663	+	39.7787i	−0.946308	+	1.63905i
$590$	−1.49193	+	4.59170i	−0.0614220	+	0.189037i
$591$	−11.7391	+	13.0375i	−0.482880	+	0.536293i
$592$	0.310176	−	0.138099i	0.0127481	−	0.00567584i
$593$	3.86178	+	1.71938i	0.158584	+	0.0706063i	0.484494	−	0.874795i	$-0.339004\pi$
$593$	3.86178	+	1.71938i	0.158584	+	0.0706063i	−0.325909	+	0.945401i	$0.605670\pi$
$594$	−2.77290	−	3.07961i	−0.113773	−	0.126358i
$595$	−0.386271	+	0.171979i	−0.0158356	+	0.00705045i
$596$	−11.1269	−	19.2724i	−0.455776	−	0.789426i
$597$	8.75642	−	15.1666i	0.358377	−	0.620726i
$598$	0.402799	−	3.83237i	0.0164717	−	0.156717i
$599$	37.2796			1.52321			0.761603	−	0.648044i	$-0.224413\pi$
$599$	37.2796			1.52321			0.761603	+	0.648044i	$0.224413\pi$
$600$	2.27627	−	21.6573i	0.0929284	−	0.884154i
$601$	17.5422	−	12.7452i	0.715563	−	0.519887i	−0.169400	−	0.985547i	$-0.554183\pi$
$601$	17.5422	−	12.7452i	0.715563	−	0.519887i	0.884964	+	0.465660i	$0.154183\pi$
$602$	−1.60617	−	1.16695i	−0.0654626	−	0.0475613i
$603$	2.21232	+	2.45703i	0.0900926	+	0.100058i
$604$	1.64049	+	15.6083i	0.0667507	+	0.635091i
$605$	0.654668	+	6.22875i	0.0266160	+	0.253235i
$606$	17.3706	+	7.73390i	0.705633	+	0.314168i
$607$	−4.82134	−	14.8386i	−0.195692	−	0.602278i	−0.999968	−	0.00802202i	$-0.997446\pi$
$607$	−4.82134	−	14.8386i	−0.195692	−	0.602278i	0.804276	−	0.594256i	$-0.202554\pi$
$608$	−23.1016	−	4.91040i	−0.936895	−	0.199143i
$609$	−7.55534			−0.306158
$610$	−4.12833	+	1.02720i	−0.167151	+	0.0415900i
$611$	1.91845			0.0776120
$612$	−0.349794	−	0.0743510i	−0.0141396	−	0.00300546i
$613$	−3.33088	−	10.2514i	−0.134533	−	0.414050i	0.860984	−	0.508632i	$-0.169849\pi$
$613$	−3.33088	−	10.2514i	−0.134533	−	0.414050i	−0.995517	+	0.0945818i	$0.969849\pi$
$614$	2.27562	+	1.01317i	0.0918364	+	0.0408882i
$615$	0.376629	+	3.58338i	0.0151871	+	0.144496i
$616$	−0.174433	−	1.65962i	−0.00702812	−	0.0668681i
$617$	22.8097	+	25.3327i	0.918284	+	1.01986i	0.999731	+	0.0231796i	$0.00737894\pi$
$617$	22.8097	+	25.3327i	0.918284	+	1.01986i	−0.0814478	+	0.996678i	$0.525954\pi$
$618$	15.4717	+	11.2409i	0.622365	+	0.452175i
$619$	13.5486	−	9.84363i	0.544564	−	0.395649i	−0.281213	−	0.959645i	$-0.590737\pi$
$619$	13.5486	−	9.84363i	0.544564	−	0.395649i	0.825777	+	0.563996i	$0.190737\pi$
$620$	−0.833580	+	7.93099i	−0.0334774	+	0.318516i
$621$	−45.5698			−1.82865
$622$	−0.343133	+	3.26469i	−0.0137584	+	0.130902i
$623$	2.87446	−	4.97871i	0.115163	−	0.199468i
$624$	0.0622179	+	0.107765i	0.00249071	+	0.00431403i
$625$	17.8649	−	7.95396i	0.714595	−	0.318158i
$626$	16.2577	+	18.0560i	0.649788	+	0.721662i
$627$	5.44399	+	2.42382i	0.217412	+	0.0967980i
$628$	11.5311	−	5.13399i	0.460142	−	0.204868i
$629$	−1.56857	+	1.74208i	−0.0625431	+	0.0694612i
$630$	−0.0334969	+	0.103093i	−0.00133455	+	0.00410732i
$631$	−6.34192	+	10.9845i	−0.252468	+	0.437287i	−0.964205	−	0.265159i	$-0.914575\pi$
$631$	−6.34192	+	10.9845i	−0.252468	+	0.437287i	0.711737	+	0.702446i	$0.247909\pi$
$632$	20.7696	+	4.41472i	0.826171	+	0.175608i
$633$	1.43210	−	1.04048i	0.0569209	−	0.0413554i
$634$	−7.98151	+	24.5645i	−0.316986	+	0.975583i
$635$	6.79817	−	1.44499i	0.269777	−	0.0573429i
$636$	−7.76648	+	8.62555i	−0.307961	+	0.342025i
$637$	2.71318	+	1.97124i	0.107500	+	0.0781033i
$638$	1.59342	+	4.90403i	0.0630840	+	0.194152i
$639$	−0.805405	−	1.39500i	−0.0318613	−	0.0551854i
$640$	−3.85380	+	0.819150i	−0.152335	+	0.0323797i
$641$	18.6608	−	3.96648i	0.737059	−	0.156667i	0.175939	−	0.984401i	$-0.443704\pi$
$641$	18.6608	−	3.96648i	0.737059	−	0.156667i	0.561120	+	0.827734i	$0.310371\pi$
$642$	−6.37842	−	11.0478i	−0.251736	−	0.436020i
$643$	7.77790	+	23.9379i	0.306730	+	0.944019i	0.979026	+	0.203736i	$0.0653084\pi$
$643$	7.77790	+	23.9379i	0.306730	+	0.944019i	−0.672296	+	0.740283i	$0.734692\pi$
$644$	−5.57553	−	4.05086i	−0.219707	−	0.159626i
$645$	2.19306	−	2.43564i	0.0863516	−	0.0959032i
$646$	−3.75604	+	0.798370i	−0.147779	+	0.0314114i
$647$	−4.98079	+	15.3293i	−0.195815	+	0.602657i	0.804151	+	0.594425i	$0.202620\pi$
$647$	−4.98079	+	15.3293i	−0.195815	+	0.602657i	−0.999966	+	0.00823206i	$0.997380\pi$
$648$	18.5958	−	13.5107i	0.730514	−	0.530749i
$649$	7.42819	+	1.57891i	0.291582	+	0.0619777i
$650$	−1.06002	+	1.83601i	−0.0415774	+	0.0720142i
$651$	3.76380	−	11.5838i	0.147515	−	0.454005i
$652$	13.0366	−	14.4786i	0.510553	−	0.567026i
$653$	−17.5919	+	7.83243i	−0.688425	+	0.306507i	−0.720973	−	0.692964i	$-0.756305\pi$
$653$	−17.5919	+	7.83243i	−0.688425	+	0.306507i	0.0325474	+	0.999470i	$0.489638\pi$
$654$	−18.1633	−	8.08683i	−0.710242	−	0.316220i
$655$	2.57388	+	2.85859i	0.100570	+	0.111694i
$656$	0.483217	−	0.215142i	0.0188664	−	0.00839988i
$657$	−0.405177	−	0.701787i	−0.0158075	−	0.0273793i
$658$	−1.13686	+	1.96910i	−0.0443195	+	0.0767636i
$659$	3.60363	−	34.2863i	0.140378	−	1.33560i	−0.666774	−	0.745260i	$-0.732325\pi$
$659$	3.60363	−	34.2863i	0.140378	−	1.33560i	0.807152	−	0.590344i	$-0.201008\pi$
$660$	1.03462			0.0402724
$661$	−3.15633	+	30.0305i	−0.122767	+	1.16805i	0.743594	+	0.668632i	$0.233120\pi$
$661$	−3.15633	+	30.0305i	−0.122767	+	1.16805i	−0.866361	+	0.499419i	$0.833547\pi$
$662$	8.43065	−	6.12522i	0.327666	−	0.238064i
$663$	−0.695055	−	0.504987i	−0.0269937	−	0.0196121i
$664$	−20.6557	−	22.9405i	−0.801598	−	0.890265i
$665$	−0.183595	−	1.74679i	−0.00711952	−	0.0677377i
$666$	0.0628188	+	0.597681i	0.00243418	+	0.0231597i
$667$	51.8002	+	23.0629i	2.00571	+	0.893001i
$668$	3.20324	+	9.85857i	0.123937	+	0.381440i
$669$	23.9100	+	5.08222i	0.924412	+	0.196490i
$670$	6.16378			0.238128
$671$	2.28563	+	6.28914i	0.0882358	+	0.242789i
$672$	6.26272			0.241590
$673$	7.82105	+	1.66241i	0.301479	+	0.0640814i	0.356168	−	0.934422i	$-0.384083\pi$
$673$	7.82105	+	1.66241i	0.301479	+	0.0640814i	−0.0546884	+	0.998503i	$0.517417\pi$
$674$	−6.71257	−	20.6592i	−0.258558	−	0.795761i
$675$	22.9033	+	10.1972i	0.881548	+	0.392491i
$676$	−1.60144	−	15.2367i	−0.0615937	−	0.586025i
$677$	−0.553332	−	5.26460i	−0.0212663	−	0.202335i	0.978730	−	0.205154i	$-0.0657694\pi$
$677$	−0.553332	−	5.26460i	−0.0212663	−	0.202335i	−0.999996	+	0.00281869i	$0.999103\pi$
$678$	1.84777	+	2.05215i	0.0709631	+	0.0788125i
$679$	−5.87075	−	4.26535i	−0.225299	−	0.163689i
$680$	−1.43614	+	1.04342i	−0.0550735	+	0.0400132i
$681$	1.14299	−	10.8748i	0.0437995	−	0.416725i
$682$	−8.31261			−0.318306
$683$	0.472716	−	4.49759i	0.0180880	−	0.172096i	−0.981748	−	0.190184i	$-0.939091\pi$
$683$	0.472716	−	4.49759i	0.0180880	−	0.172096i	0.999836	+	0.0180887i	$0.00575813\pi$
$684$	0.742750	−	1.28648i	0.0283998	−	0.0491898i
$685$	−3.16961	−	5.48993i	−0.121105	−	0.209759i
$686$	−7.51995	+	3.34810i	−0.287113	+	0.127831i
$687$	18.4696	+	20.5126i	0.704660	+	0.782604i
$688$	−0.439544	−	0.195698i	−0.0167575	−	0.00746090i
$689$	2.74865	−	1.22378i	0.104715	−	0.0466222i
$690$	−5.04497	+	5.60300i	−0.192059	+	0.213303i
$691$	5.37993	−	16.5577i	0.204662	−	0.629885i	−0.795065	−	0.606524i	$-0.792563\pi$
$691$	5.37993	−	16.5577i	0.204662	−	0.629885i	0.999727	−	0.0233610i	$-0.00743673\pi$
$692$	13.3841	−	23.1819i	0.508785	−	0.881242i
$693$	0.166778	+	0.0354497i	0.00633536	+	0.00134662i
$694$	2.93325	−	2.13113i	0.111344	−	0.0808965i
$695$	−1.74331	+	5.36537i	−0.0661277	+	0.203520i
$696$	−31.0268	+	6.59494i	−1.17607	+	0.249981i
$697$	−2.44365	+	2.71395i	−0.0925599	+	0.102798i
$698$	−0.636147	−	0.462188i	−0.0240785	−	0.0174941i
$699$	−10.5958	−	32.6104i	−0.400768	−	1.23344i
$700$	1.89578	+	3.28359i	0.0716539	+	0.124108i
$701$	−33.6865	+	7.16028i	−1.27232	+	0.270440i	−0.794093	−	0.607796i	$-0.792054\pi$
$701$	−33.6865	+	7.16028i	−1.27232	+	0.270440i	−0.478227	+	0.878236i	$0.658720\pi$
$702$	−2.42754	+	0.515990i	−0.0916217	+	0.0194748i
$703$	−4.86888	−	8.43315i	−0.183633	−	0.318062i
$704$	−1.39884	−	4.30519i	−0.0527208	−	0.162258i
$705$	−3.03670	−	2.20629i	−0.114369	−	0.0830936i
$706$	11.6820	−	12.9742i	0.439660	−	0.488291i
$707$	−8.62265	+	1.83280i	−0.324288	+	0.0689296i
$708$	−5.42157	+	16.6859i	−0.203755	+	0.627093i
$709$	−10.4725	+	7.60873i	−0.393304	+	0.285752i	−0.766808	−	0.641877i	$-0.778156\pi$
$709$	−10.4725	+	7.60873i	−0.393304	+	0.285752i	0.373504	+	0.927628i	$0.378156\pi$
$710$	−2.93737	−	0.624357i	−0.110238	−	0.0234317i
$711$	−1.08476	+	1.87885i	−0.0406816	+	0.0704626i
$712$	7.45841	−	22.9546i	0.279516	−	0.860261i
$713$	−61.1650	+	67.9306i	−2.29065	+	2.54402i
$714$	0.930208	−	0.414155i	0.0348122	−	0.0154994i
$715$	−0.245011	−	0.109086i	−0.00916290	−	0.00407959i
$716$	7.98101	+	8.86381i	0.298264	+	0.331256i
$717$	39.3455	−	17.5178i	1.46939	−	0.654213i
$718$	0.323456	+	0.560243i	0.0120713	+	0.0209081i
$719$	−0.0146839	+	0.0254333i	−0.000547618	+	0.000948502i	−0.866299	−	0.499526i	$-0.833508\pi$
$719$	−0.0146839	+	0.0254333i	−0.000547618	+	0.000948502i	0.865751	+	0.500474i	$0.166841\pi$
$720$	−0.00274597	+	0.0261262i	−0.000102336	+	0.000973665i
$721$	−8.86610			−0.330191
$722$	−0.105840	+	1.00700i	−0.00393897	+	0.0374768i
$723$	−26.6891	+	19.3908i	−0.992579	+	0.721151i
$724$	4.90062	+	3.56051i	0.182130	+	0.132325i
$725$	−20.8739	−	23.1828i	−0.775236	−	0.860987i
$726$	−1.57656	−	14.9999i	−0.0585115	−	0.556699i
$727$	3.52859	+	33.5723i	0.130868	+	1.24513i	0.840991	+	0.541049i	$0.181973\pi$
$727$	3.52859	+	33.5723i	0.130868	+	1.24513i	−0.710123	+	0.704078i	$0.751361\pi$
$728$	−0.912988	−	0.406489i	−0.0338376	−	0.0150655i
$729$	8.99006	+	27.6685i	0.332965	+	1.02476i
$730$	−1.47771	−	0.314097i	−0.0546925	−	0.0116253i
$731$	3.32192			0.122866
$732$	−15.0020	+	3.73275i	−0.554490	+	0.137966i
$733$	−27.0169			−0.997891			−0.498945	−	0.866633i	$-0.666279\pi$
$733$	−27.0169			−0.997891			−0.498945	+	0.866633i	$0.666279\pi$
$734$	−0.798530	−	0.169733i	−0.0294743	−	0.00626495i
$735$	−2.02767	−	6.24052i	−0.0747917	−	0.230185i
$736$	−42.9378	−	19.1171i	−1.58271	−	0.704667i
$737$	−1.01343	−	9.64213i	−0.0373301	−	0.355172i
$738$	0.0978642	+	0.931115i	0.00360243	+	0.0342748i
$739$	−10.2104	−	11.3398i	−0.375595	−	0.417141i	0.525478	−	0.850807i	$-0.323886\pi$
$739$	−10.2104	−	11.3398i	−0.375595	−	0.417141i	−0.901074	+	0.433666i	$0.857220\pi$
$740$	−1.36776	−	0.993735i	−0.0502798	−	0.0365304i
$741$	2.88725	−	2.09771i	0.106066	−	0.0770613i
$742$	−0.372745	+	3.54643i	−0.0136839	+	0.130194i
$743$	−8.97804			−0.329372			−0.164686	−	0.986346i	$-0.552661\pi$
$743$	−8.97804			−0.329372			−0.164686	+	0.986346i	$0.552661\pi$
$744$	5.34511	−	50.8554i	0.195961	−	1.86445i
$745$	5.64344	−	9.77473i	0.206760	−	0.358118i
$746$	−7.00217	−	12.1281i	−0.256368	−	0.444042i
$747$	2.88137	−	1.28287i	0.105424	−	0.0469377i
$748$	0.701682	+	0.779297i	0.0256560	+	0.0284939i
$749$	5.40287	+	2.40551i	0.197417	+	0.0878955i
$750$	7.88353	−	3.50997i	0.287866	−	0.128166i
$751$	−23.2508	+	25.8227i	−0.848435	+	0.942283i	−0.998926	−	0.0463287i	$-0.985248\pi$
$751$	−23.2508	+	25.8227i	−0.848435	+	0.942283i	0.150491	+	0.988611i	$0.451915\pi$
$752$	−0.170278	+	0.524062i	−0.00620941	+	0.0191106i
$753$	12.4098	−	21.4944i	0.452238	−	0.783298i
$754$	3.02059	+	0.642045i	0.110003	+	0.0233819i
$755$	−6.43973	+	4.67874i	−0.234366	+	0.170277i
$756$	−1.37158	+	4.22128i	−0.0498837	+	0.153526i
$757$	10.1259	−	2.15233i	0.368033	−	0.0782278i	−0.0201829	−	0.999796i	$-0.506425\pi$
$757$	10.1259	−	2.15233i	0.368033	−	0.0782278i	0.388216	+	0.921569i	$0.373092\pi$
$758$	−13.6660	+	15.1776i	−0.496371	+	0.551276i
$759$	9.59437	+	6.97072i	0.348253	+	0.253021i
$760$	−2.27870	−	7.01311i	−0.0826571	−	0.254392i
$761$	11.8893	+	20.5929i	0.430988	+	0.746494i	0.996959	−	0.0779319i	$-0.0248317\pi$
$761$	11.8893	+	20.5929i	0.430988	+	0.746494i	−0.565970	+	0.824426i	$0.691498\pi$
$762$	−16.3712	+	3.47980i	−0.593065	+	0.126060i
$763$	9.01613	−	1.91644i	0.326406	−	0.0693797i
$764$	1.58478	+	2.74492i	0.0573354	+	0.0993079i
$765$	−0.0560480	−	0.172498i	−0.00202642	−	0.00623668i
$766$	3.98645	+	2.89633i	0.144036	+	0.104648i
$767$	3.04319	−	3.37981i	0.109883	−	0.122038i
$768$	26.2891	−	5.58793i	0.948627	−	0.201637i
$769$	−8.42000	+	25.9141i	−0.303633	+	0.934486i	0.676551	+	0.736396i	$0.263474\pi$
$769$	−8.42000	+	25.9141i	−0.303633	+	0.934486i	−0.980184	+	0.198090i	$0.936526\pi$
$770$	0.257159	−	0.186837i	0.00926736	−	0.00673313i
$771$	−21.7247	−	4.61772i	−0.782395	−	0.166303i
$772$	−5.97688	+	10.3523i	−0.215113	+	0.372586i
$773$	10.4836	−	32.2651i	0.377068	−	1.16050i	−0.565005	−	0.825088i	$-0.691126\pi$
$773$	10.4836	−	32.2651i	0.377068	−	1.16050i	0.942073	−	0.335409i	$-0.108874\pi$
$774$	0.569850	−	0.632883i	0.0204828	−	0.0227485i
$775$	45.9423	−	20.4548i	1.65030	−	0.734759i
$776$	−27.8320	−	12.3916i	−0.999110	−	0.444832i
$777$	1.72780	+	1.91892i	0.0619846	+	0.0688409i
$778$	10.1439	−	4.51638i	0.363678	−	0.161920i
$779$	−7.58514	−	13.1378i	−0.271766	−	0.470712i
$780$	0.309806	−	0.536599i	0.0110928	−	0.0192133i
$781$	−0.493742	+	4.69764i	−0.0176675	+	0.168095i
$782$	−7.64182			−0.273271
$783$	3.81720	−	36.3182i	0.136416	−	1.29791i
$784$	−0.779301	+	0.566195i	−0.0278322	+	0.0202213i
$785$	5.17928	+	3.76297i	0.184856	+	0.134306i
$786$	−6.19836	−	6.88398i	−0.221088	−	0.245543i
$787$	−0.814123	−	7.74586i	−0.0290203	−	0.276110i	−0.999403	−	0.0345386i	$-0.989004\pi$
$787$	−0.814123	−	7.74586i	−0.0290203	−	0.276110i	0.970383	−	0.241571i	$-0.0776628\pi$
$788$	−1.34049	−	12.7539i	−0.0477531	−	0.454340i
$789$	−7.88312	−	3.50979i	−0.280647	−	0.124952i
$790$	1.24984	+	3.84662i	0.0444674	+	0.136857i
$791$	−1.25225	−	0.266174i	−0.0445250	−	0.00946407i
$792$	0.715833			0.0254360
$793$	3.94624	+	0.697788i	0.140135	+	0.0247792i
$794$	−8.45309			−0.299989
$795$	−5.75821	−	1.22395i	−0.204223	−	0.0434089i
$796$	3.95591	+	12.1750i	0.140213	+	0.431533i
$797$	−12.4460	−	5.54130i	−0.440859	−	0.196283i	0.174289	−	0.984694i	$-0.444237\pi$
$797$	−12.4460	−	5.54130i	−0.440859	−	0.196283i	−0.615148	+	0.788412i	$0.710904\pi$
$798$	0.442129	+	4.20658i	0.0156512	+	0.148911i
$799$	−0.397674	−	3.78362i	−0.0140687	−	0.133855i
$800$	17.3026	+	19.2165i	0.611739	+	0.679405i
$801$	1.99508	+	1.44951i	0.0704927	+	0.0512159i
$802$	15.8096	−	11.4863i	0.558255	−	0.405596i
$803$	−0.248388	+	2.36326i	−0.00876543	+	0.0833975i
$804$	22.3987			0.789940
$805$	0.365370	−	3.47626i	0.0128776	−	0.122522i
$806$	−2.48913	+	4.31130i	−0.0876758	+	0.151859i
$807$	13.7232	+	23.7693i	0.483080	+	0.836719i
$808$	−33.8099	+	15.0531i	−1.18943	+	0.529568i
$809$	25.3258	+	28.1272i	0.890408	+	0.988898i	0.999987	−	0.00507987i	$-0.00161698\pi$
$809$	25.3258	+	28.1272i	0.890408	+	0.988898i	−0.109579	+	0.993978i	$0.534950\pi$
$810$	3.99979	+	1.78082i	0.140538	+	0.0625717i
$811$	22.4740	−	10.0061i	0.789168	−	0.351360i	0.0277447	−	0.999615i	$-0.491167\pi$
$811$	22.4740	−	10.0061i	0.789168	−	0.351360i	0.761424	+	0.648255i	$0.224501\pi$
$812$	3.69549	−	4.10426i	0.129686	−	0.144031i
$813$	−1.30768	+	4.02461i	−0.0458622	+	0.141149i
$814$	0.881143	−	1.52618i	0.0308840	−	0.0534927i
$815$	9.66558	+	2.05448i	0.338570	+	0.0719654i
$816$	0.199639	−	0.145047i	0.00698878	−	0.00507764i
$817$	−4.26419	+	13.1238i	−0.149185	+	0.459144i
$818$	−4.20251	+	0.893271i	−0.146937	+	0.0312325i
$819$	0.0683258	−	0.0758834i	0.00238750	−	0.00265158i
$820$	−2.13081	−	1.54812i	−0.0744109	−	0.0540627i
$821$	8.45452	+	26.0203i	0.295065	+	0.908116i	0.983200	+	0.182533i	$0.0584297\pi$
$821$	8.45452	+	26.0203i	0.295065	+	0.908116i	−0.688135	+	0.725583i	$0.741570\pi$
$822$	7.63298	+	13.2207i	0.266231	+	0.461125i
$823$	−24.7330	+	5.25717i	−0.862140	+	0.183253i	−0.617703	−	0.786412i	$-0.711936\pi$
$823$	−24.7330	+	5.25717i	−0.862140	+	0.183253i	−0.244437	+	0.969665i	$0.578603\pi$
$824$	−36.4095	+	7.73908i	−1.26838	+	0.269604i
$825$	−3.26227	−	5.65041i	−0.113577	−	0.196722i
$826$	1.66567	+	5.12641i	0.0579561	+	0.178370i
$827$	4.74882	+	3.45022i	0.165133	+	0.119976i	0.667282	−	0.744805i	$-0.267457\pi$
$827$	4.74882	+	3.45022i	0.165133	+	0.119976i	−0.502150	+	0.864781i	$0.667457\pi$
$828$	1.97813	−	2.19694i	0.0687449	−	0.0763489i
$829$	−0.515894	+	0.109657i	−0.0179177	+	0.00380853i	−0.216862	−	0.976202i	$-0.569582\pi$
$829$	−0.515894	+	0.109657i	−0.0179177	+	0.00380853i	0.198944	+	0.980011i	$0.436249\pi$
$830$	1.81703	−	5.59223i	0.0630699	−	0.194109i
$831$	36.0371	−	26.1825i	1.25011	−	0.908260i
$832$	−2.65173	−	0.563643i	−0.0919323	−	0.0195408i
$833$	3.32532	−	5.75963i	0.115216	−	0.199559i
$834$	4.19821	−	12.9208i	0.145372	−	0.447409i
$835$	−3.51794	+	3.90707i	−0.121743	+	0.135210i
$836$	−3.97946	+	1.77177i	−0.137633	+	0.0612780i
$837$	53.7813	+	23.9450i	1.85895	+	0.827659i
$838$	19.7745	+	21.9618i	0.683098	+	0.758657i
$839$	14.3582	−	6.39269i	0.495700	−	0.220700i	−0.143631	−	0.989631i	$-0.545878\pi$
$839$	14.3582	−	6.39269i	0.495700	−	0.220700i	0.639331	+	0.768931i	$0.279211\pi$
$840$	0.977685	+	1.69340i	0.0337333	+	0.0584279i
$841$	−8.21980	+	14.2371i	−0.283441	+	0.490935i
$842$	−0.0671506	+	0.638895i	−0.00231416	+	0.0220178i
$843$	28.4280			0.979112
$844$	−0.135256	+	1.28688i	−0.00465571	+	0.0442962i
$845$	6.28642	−	4.56735i	0.216259	−	0.157122i
$846$	−0.789063	−	0.573288i	−0.0271285	−	0.0197100i
$847$	4.67882	+	5.19636i	0.160766	+	0.178549i
$848$	0.0903340	+	0.859470i	0.00310208	+	0.0295143i
$849$	4.58971	+	43.6682i	0.157519	+	1.49869i
$850$	3.84076	+	1.71002i	0.131737	+	0.0586532i
$851$	−5.98843	−	18.4305i	−0.205281	−	0.631789i
$852$	−10.6742	−	2.26886i	−0.365691	−	0.0777299i
$853$	0.923533			0.0316212			0.0158106	−	0.999875i	$-0.494967\pi$
$853$	0.923533			0.0316212			0.0158106	+	0.999875i	$0.494967\pi$
$854$	−3.05474	+	3.63693i	−0.104531	+	0.124453i
$855$	0.753430			0.0257668
$856$	24.2871	+	5.16239i	0.830117	+	0.176447i
$857$	−1.21293	−	3.73303i	−0.0414330	−	0.127518i	0.928200	−	0.372081i	$-0.121356\pi$
$857$	−1.21293	−	3.73303i	−0.0414330	−	0.127518i	−0.969633	+	0.244563i	$0.921356\pi$
$858$	0.590030	+	0.262698i	0.0201433	+	0.00896837i
$859$	−5.16551	−	49.1465i	−0.176245	−	1.67686i	−0.623016	−	0.782209i	$-0.714093\pi$
$859$	−5.16551	−	49.1465i	−0.176245	−	1.67686i	0.446771	−	0.894648i	$-0.352574\pi$
$860$	0.250427	+	2.38265i	0.00853949	+	0.0812478i
$861$	2.69171	+	2.98945i	0.0917333	+	0.101880i
$862$	14.9562	+	10.8663i	0.509411	+	0.370109i
$863$	−37.7613	+	27.4352i	−1.28541	+	0.933904i	−0.999702	−	0.0244125i	$-0.992228\pi$
$863$	−37.7613	+	27.4352i	−1.28541	+	0.933904i	−0.285707	+	0.958317i	$0.592228\pi$
$864$	−3.16412	+	30.1046i	−0.107646	+	1.02418i
$865$	13.5765			0.461615
$866$	−2.91267	+	27.7122i	−0.0989765	+	0.941698i
$867$	13.1353	−	22.7510i	0.446097	−	0.772663i
$868$	4.45166	+	7.71050i	0.151099	+	0.261711i
$869$	5.81185	−	2.58760i	0.197153	−	0.0877784i
$870$	−4.04289	−	4.49008i	−0.137067	−	0.152228i
$871$	−5.30430	−	2.36163i	−0.179729	−	0.0800207i
$872$	35.3528	−	15.7401i	1.19720	−	0.533026i
$873$	2.08288	−	2.31327i	0.0704946	−	0.0782922i
$874$	9.80944	−	30.1904i	0.331809	−	1.02120i
$875$	−2.00037	+	3.46475i	−0.0676250	+	0.117130i
$876$	−5.36988	−	1.14140i	−0.181431	−	0.0385644i
$877$	2.15616	−	1.56654i	0.0728084	−	0.0528984i	−0.550786	−	0.834647i	$-0.685672\pi$
$877$	2.15616	−	1.56654i	0.0728084	−	0.0528984i	0.623594	+	0.781748i	$0.285672\pi$
$878$	1.84903	−	5.69073i	0.0624018	−	0.192053i
$879$	−43.2355	+	9.18998i	−1.45830	+	0.309970i
$880$	0.0515458	−	0.0572475i	0.00173761	−	0.00192981i
$881$	−33.3532	−	24.2325i	−1.12370	−	0.816414i	−0.138932	−	0.990302i	$-0.544367\pi$
$881$	−33.3532	−	24.2325i	−1.12370	−	0.816414i	−0.984765	+	0.173888i	$0.944367\pi$
$882$	−0.526875	−	1.62155i	−0.0177408	−	0.0546005i
$883$	−9.76186	−	16.9080i	−0.328513	−	0.569001i	0.653704	−	0.756750i	$-0.273214\pi$
$883$	−9.76186	−	16.9080i	−0.328513	−	0.569001i	−0.982217	+	0.187749i	$0.939881\pi$
$884$	0.614290	−	0.130571i	0.0206608	−	0.00439159i
$885$	−8.70396	+	1.85008i	−0.292580	+	0.0621899i
$886$	1.94685	+	3.37204i	0.0654057	+	0.113286i
$887$	12.8834	+	39.6511i	0.432583	+	1.33135i	0.895543	+	0.444975i	$0.146787\pi$
$887$	12.8834	+	39.6511i	0.432583	+	1.33135i	−0.462960	+	0.886379i	$0.653213\pi$
$888$	8.77039	+	6.37206i	0.294315	+	0.213832i
$889$	5.19203	−	5.76634i	0.174135	−	0.193397i
$890$	4.49694	−	0.955854i	0.150738	−	0.0320403i
$891$	2.12814	−	6.54975i	0.0712954	−	0.219425i
$892$	−14.4557	+	10.5027i	−0.484013	+	0.351656i
$893$	15.4583	+	3.28577i	0.517293	+	0.109954i
$894$	−13.5904	+	23.5393i	−0.454531	+	0.787271i
$895$	−1.86939	+	5.75338i	−0.0624867	+	0.192314i
$896$	−2.94330	+	3.26886i	−0.0983287	+	0.109205i
$897$	6.48827	−	2.88876i	0.216637	−	0.0964529i
$898$	28.7742	+	12.8111i	0.960207	+	0.427512i
$899$	−49.0158	−	54.4375i	−1.63477	−	1.81559i
$900$	−1.48582	+	0.661528i	−0.0495272	+	0.0220509i
$901$	−2.98334	−	5.16730i	−0.0993895	−	0.172148i
$902$	1.37272	−	2.37761i	0.0457064	−	0.0791659i
$903$	0.382484	−	3.63909i	0.0127283	−	0.121101i
$904$	−5.37483			−0.178764
$905$	−0.321143	+	3.05547i	−0.0106751	+	0.101567i
$906$	15.5080	−	11.2672i	0.515219	−	0.374328i
$907$	−12.8215	−	9.31537i	−0.425731	−	0.309312i	0.354209	−	0.935166i	$-0.384750\pi$
$907$	−12.8215	−	9.31537i	−0.425731	−	0.309312i	−0.779940	+	0.625855i	$0.784750\pi$
$908$	5.34843	+	5.94004i	0.177494	+	0.197127i
$909$	−0.395264	−	3.76068i	−0.0131101	−	0.124734i
$910$	−0.0198984	−	0.189321i	−0.000659626	−	0.00627592i
$911$	−14.1433	−	6.29700i	−0.468588	−	0.208629i	0.158838	−	0.987305i	$-0.449225\pi$
$911$	−14.1433	−	6.29700i	−0.468588	−	0.208629i	−0.627427	+	0.778676i	$0.715892\pi$
$912$	0.316764	+	0.974900i	0.0104891	+	0.0322822i
$913$	−9.04679	−	1.92295i	−0.299405	−	0.0636405i
$914$	−34.0757			−1.12713
$915$	−5.44399	−	5.64285i	−0.179973	−	0.186547i
$916$	−20.1769			−0.666663
$917$	4.20070	+	0.892886i	0.138719	+	0.0294857i
$918$	1.52086	+	4.68072i	0.0501958	+	0.154487i
$919$	−7.32380	−	3.26076i	−0.241590	−	0.107563i	0.282370	−	0.959305i	$-0.408879\pi$
$919$	−7.32380	−	3.26076i	−0.241590	−	0.107563i	−0.523960	+	0.851743i	$0.675546\pi$
$920$	−1.53395	−	14.5945i	−0.0505728	−	0.481168i
$921$	0.479897	+	4.56592i	0.0158132	+	0.150452i
$922$	10.1429	+	11.2648i	0.334039	+	0.370987i
$923$	2.28856	+	1.66274i	0.0753290	+	0.0547297i
$924$	0.934494	−	0.678950i	0.0307426	−	0.0223358i
$925$	−1.11444	+	10.6032i	−0.0366425	+	0.348630i
$926$	9.37653			0.308132
$927$	0.397542	−	3.78236i	0.0130570	−	0.124229i
$928$	18.8327	−	32.6192i	0.618214	−	1.07078i
$929$	−17.2949	−	29.9557i	−0.567428	−	0.982814i	−0.996819	−	0.0796955i	$-0.974605\pi$
$929$	−17.2949	−	29.9557i	−0.567428	−	0.982814i	0.429391	−	0.903119i	$-0.358728\pi$
$930$	8.89818	−	3.96173i	0.291783	−	0.129910i
$931$	18.4859	+	20.5306i	0.605850	+	0.672865i
$932$	22.8974	+	10.1946i	0.750030	+	0.333935i
$933$	−5.52716	+	2.46085i	−0.180951	+	0.0805647i
$934$	18.4491	−	20.4898i	0.603672	−	0.670445i
$935$	−0.164355	+	0.505831i	−0.00537497	+	0.0165425i
$936$	0.214349	−	0.371263i	0.00700621	−	0.0121351i
$937$	−39.7485	−	8.44881i	−1.29853	−	0.276010i	−0.493758	−	0.869599i	$-0.664377\pi$
$937$	−39.7485	−	8.44881i	−1.29853	−	0.276010i	−0.804769	+	0.593589i	$0.797711\pi$
$938$	5.56729	−	4.04487i	0.181779	−	0.132070i
$939$	−13.8381	+	42.5892i	−0.451588	+	1.38984i
$940$	2.68383	−	0.570466i	0.0875369	−	0.0186065i
$941$	−5.38810	+	5.98409i	−0.175647	+	0.195076i	−0.824540	−	0.565804i	$-0.808566\pi$
$941$	−5.38810	+	5.98409i	−0.175647	+	0.195076i	0.648893	+	0.760880i	$0.275232\pi$
$942$	−12.4726	−	9.06188i	−0.406380	−	0.295252i
$943$	−9.32926	−	28.7125i	−0.303803	−	0.935008i
$944$	0.653154	+	1.13130i	0.0212583	+	0.0368205i
$945$	−2.20197	+	0.468044i	−0.0716302	+	0.0152255i
$946$	−2.44273	+	0.519218i	−0.0794200	+	0.0168812i
$947$	−29.5744	−	51.2244i	−0.961040	−	1.66457i	−0.719896	−	0.694082i	$-0.755811\pi$
$947$	−29.5744	−	51.2244i	−0.961040	−	1.66457i	−0.241144	−	0.970489i	$-0.577523\pi$
$948$	4.54182	+	13.9783i	0.147511	+	0.453994i
$949$	1.15131	+	0.836478i	0.0373732	+	0.0271532i
$950$	−11.6859	+	12.9785i	−0.379142	+	0.421080i
$951$	−46.5642	+	9.89752i	−1.50995	+	0.320949i
$952$	−0.612436	+	1.88488i	−0.0198492	+	0.0610895i
$953$	31.1420	−	22.6260i	1.00879	−	0.732926i	0.0448325	−	0.998995i	$-0.485725\pi$
$953$	31.1420	−	22.6260i	1.00879	−	0.732926i	0.963954	+	0.266068i	$0.0857246\pi$
$954$	−1.49623	−	0.318033i	−0.0484422	−	0.0102967i
$955$	−0.803785	+	1.39220i	−0.0260099	+	0.0450504i
$956$	−9.72870	+	29.9419i	−0.314649	+	0.968389i
$957$	−6.35920	+	7.06261i	−0.205564	+	0.228302i
$958$	−31.4498	+	14.0024i	−1.01610	+	0.452396i
$959$	−6.46554	−	2.87865i	−0.208783	−	0.0929563i
$960$	3.54920	+	3.94178i	0.114550	+	0.127221i
$961$	79.5612	−	35.4229i	2.56649	−	1.14268i
$962$	−0.527699	−	0.914001i	−0.0170137	−	0.0294686i
$963$	−1.26847	+	2.19706i	−0.0408759	+	0.0707991i
$964$	2.52068	−	23.9827i	0.0811858	−	0.772431i
$965$	−6.06282			−0.195169
$966$	−0.879875	+	8.37145i	−0.0283095	+	0.269347i
$967$	−17.8887	+	12.9969i	−0.575261	+	0.417952i	−0.837013	−	0.547184i	$-0.815700\pi$
$967$	−17.8887	+	12.9969i	−0.575261	+	0.417952i	0.261751	+	0.965135i	$0.415700\pi$
$968$	23.7499	+	17.2553i	0.763349	+	0.554606i
$969$	−4.73567	−	5.25949i	−0.152132	−	0.168959i
$970$	−0.606593	−	5.77134i	−0.0194765	−	0.185307i
$971$	−1.49997	−	14.2713i	−0.0481364	−	0.457988i	−0.991868	−	0.127274i	$-0.959377\pi$
$971$	−1.49997	−	14.2713i	−0.0481364	−	0.457988i	0.943731	−	0.330714i	$-0.107289\pi$
$972$	−3.32431	−	1.48008i	−0.106627	−	0.0474735i
$973$	1.94632	+	5.99017i	0.0623962	+	0.192036i
$974$	23.1111	+	4.91241i	0.740526	+	0.157404i
$975$	−3.90741			−0.125137
$976$	−0.540877	+	1.01606i	−0.0173130	+	0.0325233i
$977$	−44.1463			−1.41236			−0.706182	−	0.708030i	$-0.749584\pi$
$977$	−44.1463			−1.41236			−0.706182	+	0.708030i	$0.749584\pi$
$978$	−23.2764	−	4.94755i	−0.744298	−	0.158205i
$979$	−2.23463	−	6.87750i	−0.0714192	−	0.219806i
$980$	4.38179	+	1.95090i	0.139971	+	0.0623192i
$981$	0.413301	+	3.93230i	0.0131957	+	0.125549i
$982$	−3.73914	−	35.5755i	−0.119321	−	1.13526i
$983$	−20.0742	−	22.2947i	−0.640268	−	0.711090i	0.332439	−	0.943125i	$-0.392128\pi$
$983$	−20.0742	−	22.2947i	−0.640268	−	0.711090i	−0.972708	+	0.232035i	$0.925462\pi$
$984$	13.6632	+	9.92691i	0.435568	+	0.316458i
$985$	5.26208	−	3.82312i	0.167664	−	0.121815i
$986$	0.640125	−	6.09038i	0.0203857	−	0.193957i
$987$	−4.19066			−0.133390
$988$	−0.272690	+	2.59447i	−0.00867541	+	0.0825410i
$989$	−13.7308	+	23.7824i	−0.436614	+	0.756237i
$990$	0.0681758	+	0.118084i	0.00216677	+	0.00375295i
$991$	3.83891	−	1.70919i	0.121947	−	0.0542943i	−0.344856	−	0.938656i	$-0.612072\pi$
$991$	3.83891	−	1.70919i	0.121947	−	0.0542943i	0.466803	+	0.884361i	$0.345406\pi$
$992$	40.6298	+	45.1239i	1.29000	+	1.43269i
$993$	17.5460	+	7.81199i	0.556806	+	0.247906i
$994$	−3.06283	+	1.36366i	−0.0971472	+	0.0432527i
$995$	−4.34455	+	4.82511i	−0.137732	+	0.152966i
$996$	6.60292	−	20.3217i	0.209221	−	0.643918i
$997$	−15.3292	+	26.5510i	−0.485482	+	0.840879i	−0.999861	−	0.0166839i	$-0.994689\pi$
$997$	−15.3292	+	26.5510i	−0.485482	+	0.840879i	0.514379	+	0.857563i	$0.328022\pi$
$998$	−21.7098	−	4.61457i	−0.687213	−	0.146072i
$999$	−10.0971	+	7.33598i	−0.319459	+	0.232100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.i.a.16.3	✓	32
3.2	odd	2		549.2.bl.b.199.2		32
4.3	odd	2		976.2.bw.c.321.1		32
61.15	even	15		3721.2.a.j.1.7		16
61.42	even	15	inner	61.2.i.a.42.3	yes	32
61.46	even	30		3721.2.a.l.1.10		16
183.164	odd	30		549.2.bl.b.469.2		32
244.103	odd	30		976.2.bw.c.225.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.16.3	✓	32	1.1	even	1	trivial
61.2.i.a.42.3	yes	32	61.42	even	15	inner
549.2.bl.b.199.2		32	3.2	odd	2
549.2.bl.b.469.2		32	183.164	odd	30
976.2.bw.c.225.1		32	244.103	odd	30
976.2.bw.c.321.1		32	4.3	odd	2
3721.2.a.j.1.7		16	61.15	even	15
3721.2.a.l.1.10		16	61.46	even	30

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.873313 + 0.185628i) q^{2} +(0.508502 + 1.56501i) q^{3} +(-1.09887 - 0.489250i) q^{4} +(-0.0637708 - 0.606739i) q^{5} +(0.153571 + 1.46113i) q^{6} +(-0.455761 - 0.506174i) q^{7} +(-2.31346 - 1.68083i) q^{8} +(0.236374 - 0.171736i) q^{9} +O(q^{10})\)	\(q+(0.873313 + 0.185628i) q^{2} +(0.508502 + 1.56501i) q^{3} +(-1.09887 - 0.489250i) q^{4} +(-0.0637708 - 0.606739i) q^{5} +(0.153571 + 1.46113i) q^{6} +(-0.455761 - 0.506174i) q^{7} +(-2.31346 - 1.68083i) q^{8} +(0.236374 - 0.171736i) q^{9} +(0.0569361 - 0.541711i) q^{10} -0.856770 q^{11} +(0.206901 - 1.96853i) q^{12} +(-0.256551 + 0.444360i) q^{13} +(-0.304062 - 0.526651i) q^{14} +(0.917124 - 0.408330i) q^{15} +(-0.0986147 - 0.109523i) q^{16} +(0.929560 + 0.413867i) q^{17} +(0.238308 - 0.106102i) q^{18} +(-2.82829 + 3.14113i) q^{19} +(-0.226771 + 0.697929i) q^{20} +(0.560411 - 0.970661i) q^{21} +(-0.748228 - 0.159041i) q^{22} +(-6.80521 + 4.94428i) q^{23} +(1.45411 - 4.47529i) q^{24} +(4.52667 - 0.962174i) q^{25} +(-0.306535 + 0.340442i) q^{26} +(4.38279 + 3.18428i) q^{27} +(0.253178 + 0.779203i) q^{28} +(-3.37045 - 5.83778i) q^{29} +(0.876734 - 0.186356i) q^{30} +(10.6295 - 2.25937i) q^{31} +(2.79380 + 4.83901i) q^{32} +(-0.435669 - 1.34085i) q^{33} +(0.734972 + 0.533988i) q^{34} +(-0.278051 + 0.308807i) q^{35} +(-0.343768 + 0.0730700i) q^{36} +(-0.711916 + 2.19105i) q^{37} +(-3.05306 + 2.21818i) q^{38} +(-0.825883 - 0.175547i) q^{39} +(-0.872292 + 1.51085i) q^{40} +(-1.10908 + 3.41340i) q^{41} +(0.669597 - 0.743662i) q^{42} +(2.98244 - 1.32787i) q^{43} +(0.941482 + 0.419175i) q^{44} +(-0.119273 - 0.132466i) q^{45} +(-6.86088 + 3.05466i) q^{46} +(-1.86946 - 3.23800i) q^{47} +(0.121258 - 0.210025i) q^{48} +(0.683205 - 6.50026i) q^{49} +4.13181 q^{50} +(-0.175022 + 1.66522i) q^{51} +(0.499320 - 0.362777i) q^{52} +(-4.74398 - 3.44671i) q^{53} +(3.23645 + 3.59445i) q^{54} +(0.0546369 + 0.519836i) q^{55} +(0.203594 + 1.93707i) q^{56} +(-6.35408 - 2.82902i) q^{57} +(-1.85979 - 5.72386i) q^{58} +(-8.67000 - 1.84286i) q^{59} -1.20758 q^{60} +(-2.66773 - 7.34052i) q^{61} +9.70227 q^{62} +(-0.194659 - 0.0413760i) q^{63} +(1.63269 + 5.02491i) q^{64} +(0.285971 + 0.127322i) q^{65} +(-0.131575 - 1.25186i) q^{66} +(1.18285 + 11.2540i) q^{67} +(-0.818985 - 0.909575i) q^{68} +(-11.1983 - 8.13604i) q^{69} +(-0.300149 + 0.218071i) q^{70} +(0.576283 - 5.48297i) q^{71} -0.835501 q^{72} +(0.289912 - 2.75833i) q^{73} +(-1.02845 + 1.78132i) q^{74} +(3.80763 + 6.59501i) q^{75} +(4.64473 - 2.06797i) q^{76} +(0.390483 + 0.433675i) q^{77} +(-0.688668 - 0.306615i) q^{78} +(-6.78344 + 3.02018i) q^{79} +(-0.0601630 + 0.0668178i) q^{80} +(-2.48391 + 7.64470i) q^{81} +(-1.60220 + 2.77509i) q^{82} +(10.5592 + 2.24442i) q^{83} +(-1.09072 + 0.792453i) q^{84} +(0.191830 - 0.590393i) q^{85} +(2.85109 - 0.606018i) q^{86} +(7.42230 - 8.24330i) q^{87} +(1.98210 + 1.44008i) q^{88} +(2.60821 + 8.02724i) q^{89} +(-0.0795730 - 0.137825i) q^{90} +(0.341850 - 0.0726624i) q^{91} +(9.89706 - 2.10368i) q^{92} +(8.94104 + 15.4863i) q^{93} +(-1.03156 - 3.17481i) q^{94} +(2.08621 + 1.51572i) q^{95} +(-6.15243 + 6.83297i) q^{96} +(10.4211 - 2.21507i) q^{97} +(1.80329 - 5.54994i) q^{98} +(-0.202519 + 0.147138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9} + 15 q^{10} - 18 q^{11} - 53 q^{12} + 11 q^{14} + 2 q^{15} + 6 q^{16} - 24 q^{17} - 15 q^{18} + 9 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 15 q^{24} + 28 q^{25} + 16 q^{26} + 35 q^{27} + 4 q^{28} - 4 q^{29} + 54 q^{30} - 11 q^{31} + 34 q^{32} - 35 q^{33} + 18 q^{34} - 58 q^{35} + 65 q^{36} - 14 q^{37} - 24 q^{38} + 17 q^{39} - 60 q^{40} + 11 q^{41} + 73 q^{42} + 40 q^{43} + 29 q^{44} + 12 q^{45} - 89 q^{46} + 40 q^{47} + 43 q^{48} + q^{49} - 56 q^{50} - 9 q^{51} - 67 q^{52} + 17 q^{53} - q^{54} - 60 q^{55} - 102 q^{56} - 38 q^{57} + 73 q^{58} - 11 q^{59} - 20 q^{60} - 55 q^{61} - 74 q^{62} - 58 q^{63} + 6 q^{64} + 59 q^{65} + 34 q^{66} - 13 q^{67} - 3 q^{68} - 32 q^{69} + 44 q^{70} + 63 q^{71} + 18 q^{72} - 46 q^{73} - 10 q^{74} + q^{75} + 55 q^{76} - 31 q^{77} - 103 q^{78} - 49 q^{79} + 74 q^{80} + 48 q^{81} + 39 q^{82} + 39 q^{83} + 21 q^{85} + 74 q^{86} + 17 q^{87} + 70 q^{88} + 32 q^{89} - 60 q^{90} + 70 q^{91} + 77 q^{92} + 67 q^{93} - 64 q^{94} + 47 q^{95} - 16 q^{96} + 37 q^{97} + 127 q^{98} - 31 q^{99}+O(q^{100}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9 + 15 * q^10 - 18 * q^11 - 53 * q^12 + 11 * q^14 + 2 * q^15 + 6 * q^16 - 24 * q^17 - 15 * q^18 + 9 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 15 * q^24 + 28 * q^25 + 16 * q^26 + 35 * q^27 + 4 * q^28 - 4 * q^29 + 54 * q^30 - 11 * q^31 + 34 * q^32 - 35 * q^33 + 18 * q^34 - 58 * q^35 + 65 * q^36 - 14 * q^37 - 24 * q^38 + 17 * q^39 - 60 * q^40 + 11 * q^41 + 73 * q^42 + 40 * q^43 + 29 * q^44 + 12 * q^45 - 89 * q^46 + 40 * q^47 + 43 * q^48 + q^49 - 56 * q^50 - 9 * q^51 - 67 * q^52 + 17 * q^53 - q^54 - 60 * q^55 - 102 * q^56 - 38 * q^57 + 73 * q^58 - 11 * q^59 - 20 * q^60 - 55 * q^61 - 74 * q^62 - 58 * q^63 + 6 * q^64 + 59 * q^65 + 34 * q^66 - 13 * q^67 - 3 * q^68 - 32 * q^69 + 44 * q^70 + 63 * q^71 + 18 * q^72 - 46 * q^73 - 10 * q^74 + q^75 + 55 * q^76 - 31 * q^77 - 103 * q^78 - 49 * q^79 + 74 * q^80 + 48 * q^81 + 39 * q^82 + 39 * q^83 + 21 * q^85 + 74 * q^86 + 17 * q^87 + 70 * q^88 + 32 * q^89 - 60 * q^90 + 70 * q^91 + 77 * q^92 + 67 * q^93 - 64 * q^94 + 47 * q^95 - 16 * q^96 + 37 * q^97 + 127 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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