LMFDB - Embedded newform 354.2.e.c.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	354.85
Dual form			354.2.e.c.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.796093 - 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(2.16601 - 2.05176i) q^{5} +(0.161782 + 0.986827i) q^{6} +(2.55368 + 3.00642i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})$	\(q+(0.796093 - 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(2.16601 - 2.05176i) q^{5} +(0.161782 + 0.986827i) q^{6} +(2.55368 + 3.00642i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(0.482678 - 2.94421i) q^{10} +(-4.21067 + 2.53347i) q^{11} +(0.725995 + 0.687699i) q^{12} +(2.39796 - 3.53673i) q^{13} +(3.85237 + 0.847971i) q^{14} +(0.798173 + 2.87476i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(2.93291 - 3.45289i) q^{17} +(-0.947653 - 0.319302i) q^{18} +(2.82893 + 1.30880i) q^{19} +(-1.39750 - 2.63597i) q^{20} +(-3.85237 + 0.847971i) q^{21} +(-1.81889 + 4.56507i) q^{22} +(-5.01520 + 1.68982i) q^{23} +(0.994138 + 0.108119i) q^{24} +(0.211213 - 3.89560i) q^{25} +(-0.231337 - 4.26675i) q^{26} +(0.994138 - 0.108119i) q^{27} +(3.58002 - 1.65629i) q^{28} +(0.0463382 + 0.0352254i) q^{29} +(2.37515 + 1.80554i) q^{30} +(5.76664 - 2.66793i) q^{31} +(-0.994138 + 0.108119i) q^{32} +(-0.266043 - 4.90688i) q^{33} +(0.245270 - 4.52375i) q^{34} +(11.6997 + 1.27242i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(-4.00887 + 10.0615i) q^{37} +(3.04414 - 0.670066i) q^{38} +(2.00152 + 3.77526i) q^{39} +(-2.70776 - 1.25274i) q^{40} +(1.68597 + 0.568069i) q^{41} +(-2.55368 + 3.00642i) q^{42} +(-10.0283 - 6.03380i) q^{43} +(1.31466 + 4.73496i) q^{44} +(-2.91376 - 0.641366i) q^{45} +(-2.96993 + 4.38032i) q^{46} +(-8.86933 - 8.40147i) q^{47} +(0.856857 - 0.515554i) q^{48} +(-1.38483 + 8.44707i) q^{49} +(-2.18937 - 3.22908i) q^{50} +(1.67687 + 4.20863i) q^{51} +(-2.76629 - 3.25673i) q^{52} +(0.474904 + 2.89678i) q^{53} +(0.725995 - 0.687699i) q^{54} +(-3.92229 + 14.1268i) q^{55} +(1.84768 - 3.48510i) q^{56} +(-2.48143 + 1.88634i) q^{57} +0.0582071 q^{58} +(-4.47030 + 6.24631i) q^{59} +2.98351 q^{60} +(-10.6025 + 8.05984i) q^{61} +(2.97622 - 5.61374i) q^{62} +(1.05529 - 3.80081i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(-2.06249 - 12.5806i) q^{65} +(-3.18131 - 3.74533i) q^{66} +(4.07322 + 10.2230i) q^{67} +(-2.54240 - 3.74975i) q^{68} +(0.856188 - 5.22252i) q^{69} +(10.0841 - 6.06742i) q^{70} +(-7.94686 - 7.52767i) q^{71} +(-0.561187 + 0.827689i) q^{72} +(-0.904407 - 0.199075i) q^{73} +(2.89753 + 10.4360i) q^{74} +(3.34288 + 2.01134i) q^{75} +(2.01791 - 2.37567i) q^{76} +(-18.3694 - 6.18936i) q^{77} +(3.87809 + 1.79419i) q^{78} +(-3.19651 - 6.02925i) q^{79} +(-2.91376 + 0.641366i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(1.68597 - 0.568069i) q^{82} +(2.24867 + 0.244557i) q^{83} +(-0.213556 + 3.93881i) q^{84} +(-0.731766 - 13.4966i) q^{85} +(-11.6349 + 1.26538i) q^{86} +(-0.0528273 + 0.0244405i) q^{87} +(3.91207 + 2.97388i) q^{88} +(-0.491323 - 0.373494i) q^{89} +(-2.70776 + 1.25274i) q^{90} +(16.7565 - 1.82238i) q^{91} +(0.286516 + 5.28447i) q^{92} +(-0.343993 + 6.34457i) q^{93} +(-12.1452 - 1.32087i) q^{94} +(8.81283 - 2.96939i) q^{95} +(0.370138 - 0.928977i) q^{96} +(4.80724 - 1.05815i) q^{97} +(4.00950 + 7.56272i) q^{98} +(4.45990 + 2.06337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{23}{29}\right)$	$1$

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 $

$2$	0.796093	−	0.605174i	0.562923	−	0.427923i
$2$	0.796093	−	0.605174i	0.562923	−	0.427923i
$3$	−0.468408	+	0.883512i	−0.270436	+	0.510096i
$3$	−0.468408	+	0.883512i	−0.270436	+	0.510096i
$4$	0.267528	−	0.963550i	0.133764	−	0.481775i
$5$	2.16601	−	2.05176i	0.968671	−	0.917574i	−0.0279585	−	0.999609i	$-0.508901\pi$
$5$	2.16601	−	2.05176i	0.968671	−	0.917574i	0.996629	+	0.0820353i	$0.0261420\pi$
$6$	0.161782	+	0.986827i	0.0660472	+	0.402870i
$7$	2.55368	+	3.00642i	0.965199	+	1.13632i	0.990620	+	0.136643i	$0.0436315\pi$
$7$	2.55368	+	3.00642i	0.965199	+	1.13632i	−0.0254211	+	0.999677i	$0.508093\pi$
$8$	−0.370138	−	0.928977i	−0.130864	−	0.328443i
$9$	−0.561187	−	0.827689i	−0.187062	−	0.275896i
$10$	0.482678	−	2.94421i	0.152636	−	0.931040i
$11$	−4.21067	+	2.53347i	−1.26956	+	0.763871i	−0.981078	−	0.193613i	$-0.937979\pi$
$11$	−4.21067	+	2.53347i	−1.26956	+	0.763871i	−0.288486	+	0.957484i	$0.593152\pi$
$12$	0.725995	+	0.687699i	0.209577	+	0.198522i
$13$	2.39796	−	3.53673i	0.665075	−	0.980912i	−0.334187	−	0.942507i	$-0.608462\pi$
$13$	2.39796	−	3.53673i	0.665075	−	0.980912i	0.999262	−	0.0384056i	$-0.0122279\pi$
$14$	3.85237	+	0.847971i	1.02959	+	0.226630i
$15$	0.798173	+	2.87476i	0.206087	+	0.742260i
$16$	−0.856857	−	0.515554i	−0.214214	−	0.128888i
$17$	2.93291	−	3.45289i	0.711336	−	0.837449i	−0.281168	−	0.959658i	$-0.590722\pi$
$17$	2.93291	−	3.45289i	0.711336	−	0.837449i	0.992504	+	0.122209i	$0.0389978\pi$
$18$	−0.947653	−	0.319302i	−0.223364	−	0.0752601i
$19$	2.82893	+	1.30880i	0.649000	+	0.300259i	0.716633	−	0.697451i	$-0.245682\pi$
$19$	2.82893	+	1.30880i	0.649000	+	0.300259i	−0.0676325	+	0.997710i	$0.521545\pi$
$20$	−1.39750	−	2.63597i	−0.312491	−	0.589420i
$21$	−3.85237	+	0.847971i	−0.840657	+	0.185043i
$22$	−1.81889	+	4.56507i	−0.387788	+	0.973276i
$23$	−5.01520	+	1.68982i	−1.04574	+	0.352351i	−0.789171	−	0.614174i	$-0.789489\pi$
$23$	−5.01520	+	1.68982i	−1.04574	+	0.352351i	−0.256571	+	0.966525i	$0.582593\pi$
$24$	0.994138	+	0.108119i	0.202928	+	0.0220697i
$25$	0.211213	−	3.89560i	0.0422427	−	0.779121i
$26$	−0.231337	−	4.26675i	−0.0453688	−	0.836779i
$27$	0.994138	−	0.108119i	0.191322	−	0.0208075i
$28$	3.58002	−	1.65629i	0.676560	−	0.313010i
$29$	0.0463382	+	0.0352254i	0.00860479	+	0.00654119i	0.609468	−	0.792811i	$-0.291383\pi$
$29$	0.0463382	+	0.0352254i	0.00860479	+	0.00654119i	−0.600863	+	0.799352i	$0.705176\pi$
$30$	2.37515	+	1.80554i	0.433641	+	0.329645i
$31$	5.76664	−	2.66793i	1.03572	−	0.479174i	0.173034	−	0.984916i	$-0.444643\pi$
$31$	5.76664	−	2.66793i	1.03572	−	0.479174i	0.862685	+	0.505741i	$0.168781\pi$
$32$	−0.994138	+	0.108119i	−0.175740	+	0.0191129i
$33$	−0.266043	−	4.90688i	−0.0463121	−	0.854177i
$34$	0.245270	−	4.52375i	0.0420635	−	0.775816i
$35$	11.6997	+	1.27242i	1.97762	+	0.215079i
$36$	−0.947653	+	0.319302i	−0.157942	+	0.0532169i
$37$	−4.00887	+	10.0615i	−0.659054	+	1.65410i	0.0935391	+	0.995616i	$0.470182\pi$
$37$	−4.00887	+	10.0615i	−0.659054	+	1.65410i	−0.752593	+	0.658486i	$0.771197\pi$
$38$	3.04414	−	0.670066i	0.493825	−	0.108699i
$39$	2.00152	+	3.77526i	0.320499	+	0.604526i
$40$	−2.70776	−	1.25274i	−0.428134	−	0.198076i
$41$	1.68597	+	0.568069i	0.263304	+	0.0887175i	0.447857	−	0.894105i	$-0.352187\pi$
$41$	1.68597	+	0.568069i	0.263304	+	0.0887175i	−0.184553	+	0.982823i	$0.559084\pi$
$42$	−2.55368	+	3.00642i	−0.394041	+	0.463901i
$43$	−10.0283	−	6.03380i	−1.52930	−	0.920147i	−0.997303	−	0.0733976i	$-0.976616\pi$
$43$	−10.0283	−	6.03380i	−1.52930	−	0.920147i	−0.531993	−	0.846749i	$-0.678557\pi$
$44$	1.31466	+	4.73496i	0.198192	+	0.713823i
$45$	−2.91376	−	0.641366i	−0.434357	−	0.0956092i
$46$	−2.96993	+	4.38032i	−0.437893	+	0.645843i
$47$	−8.86933	−	8.40147i	−1.29372	−	1.22548i	−0.959080	−	0.283137i	$-0.908625\pi$
$47$	−8.86933	−	8.40147i	−1.29372	−	1.22548i	−0.334645	−	0.942344i	$-0.608616\pi$
$48$	0.856857	−	0.515554i	0.123677	−	0.0744138i
$49$	−1.38483	+	8.44707i	−0.197832	+	1.20672i
$50$	−2.18937	−	3.22908i	−0.309624	−	0.456661i
$51$	1.67687	+	4.20863i	0.234809	+	0.589326i
$52$	−2.76629	−	3.25673i	−0.383616	−	0.451627i
$53$	0.474904	+	2.89678i	0.0652330	+	0.397904i	0.999180	+	0.0404919i	$0.0128925\pi$
$53$	0.474904	+	2.89678i	0.0652330	+	0.397904i	−0.933947	+	0.357412i	$0.883659\pi$
$54$	0.725995	−	0.687699i	0.0987955	−	0.0935840i
$55$	−3.92229	+	14.1268i	−0.528881	+	1.90486i
$56$	1.84768	−	3.48510i	0.246907	−	0.465716i
$57$	−2.48143	+	1.88634i	−0.328674	+	0.249851i
$58$	0.0582071			0.00764296
$59$	−4.47030	+	6.24631i	−0.581984	+	0.813200i
$59$	−4.47030	+	6.24631i	−0.581984	+	0.813200i
$60$	2.98351			0.385169
$61$	−10.6025	+	8.05984i	−1.35752	+	1.03196i	−0.362526	+	0.931973i	$0.618086\pi$
$61$	−10.6025	+	8.05984i	−1.35752	+	1.03196i	−0.994989	+	0.0999830i	$0.968121\pi$
$62$	2.97622	−	5.61374i	0.377980	−	0.712946i
$63$	1.05529	−	3.80081i	0.132954	−	0.478858i
$64$	−0.725995	+	0.687699i	−0.0907494	+	0.0859624i
$65$	−2.06249	−	12.5806i	−0.255821	−	1.56044i
$66$	−3.18131	−	3.74533i	−0.391592	−	0.461018i
$67$	4.07322	+	10.2230i	0.497623	+	1.24894i	0.936587	+	0.350434i	$0.113966\pi$
$67$	4.07322	+	10.2230i	0.497623	+	1.24894i	−0.438965	+	0.898504i	$0.644655\pi$
$68$	−2.54240	−	3.74975i	−0.308311	−	0.454725i
$69$	0.856188	−	5.22252i	0.103073	−	0.628717i
$70$	10.0841	−	6.06742i	1.20528	−	0.725195i
$71$	−7.94686	−	7.52767i	−0.943119	−	0.893370i	0.0513202	−	0.998682i	$-0.483657\pi$
$71$	−7.94686	−	7.52767i	−0.943119	−	0.893370i	−0.994439	+	0.105313i	$0.966416\pi$
$72$	−0.561187	+	0.827689i	−0.0661365	+	0.0975441i
$73$	−0.904407	−	0.199075i	−0.105853	−	0.0233000i	0.161728	−	0.986835i	$-0.448293\pi$
$73$	−0.904407	−	0.199075i	−0.105853	−	0.0233000i	−0.267581	+	0.963535i	$0.586224\pi$
$74$	2.89753	+	10.4360i	0.336831	+	1.21316i
$75$	3.34288	+	2.01134i	0.386002	+	0.232250i
$76$	2.01791	−	2.37567i	0.231470	−	0.272508i
$77$	−18.3694	−	6.18936i	−2.09338	−	0.705343i
$78$	3.87809	+	1.79419i	0.439107	+	0.203152i
$79$	−3.19651	−	6.02925i	−0.359635	−	0.678344i	0.635999	−	0.771690i	$-0.280588\pi$
$79$	−3.19651	−	6.02925i	−0.359635	−	0.678344i	−0.995634	+	0.0933464i	$0.970244\pi$
$80$	−2.91376	+	0.641366i	−0.325768	+	0.0717069i
$81$	−0.370138	+	0.928977i	−0.0411265	+	0.103220i
$82$	1.68597	−	0.568069i	0.186184	−	0.0627328i
$83$	2.24867	+	0.244557i	0.246823	+	0.0268437i	0.230694	−	0.973026i	$-0.425900\pi$
$83$	2.24867	+	0.244557i	0.246823	+	0.0268437i	0.0161290	+	0.999870i	$0.494866\pi$
$84$	−0.213556	+	3.93881i	−0.0233009	+	0.429759i
$85$	−0.731766	−	13.4966i	−0.0793712	−	1.46392i
$86$	−11.6349	+	1.26538i	−1.25463	+	0.136449i
$87$	−0.0528273	+	0.0244405i	−0.00566368	+	0.00262030i
$88$	3.91207	+	2.97388i	0.417028	+	0.317016i
$89$	−0.491323	−	0.373494i	−0.0520801	−	0.0395903i	0.578810	−	0.815462i	$-0.303517\pi$
$89$	−0.491323	−	0.373494i	−0.0520801	−	0.0395903i	−0.630890	+	0.775872i	$0.717310\pi$
$90$	−2.70776	+	1.25274i	−0.285423	+	0.132051i
$91$	16.7565	−	1.82238i	1.75656	−	0.191037i
$92$	0.286516	+	5.28447i	0.0298713	+	0.550944i
$93$	−0.343993	+	6.34457i	−0.0356704	+	0.657902i
$94$	−12.1452	−	1.32087i	−1.25268	−	0.136237i
$95$	8.81283	−	2.96939i	0.904178	−	0.304653i
$96$	0.370138	−	0.928977i	0.0377771	−	0.0948133i
$97$	4.80724	−	1.05815i	0.488102	−	0.107439i	0.0359006	−	0.999355i	$-0.488570\pi$
$97$	4.80724	−	1.05815i	0.488102	−	0.107439i	0.452201	+	0.891916i	$0.350639\pi$
$98$	4.00950	+	7.56272i	0.405020	+	0.763950i
$99$	4.45990	+	2.06337i	0.448237	+	0.207376i
$100$	−3.69710	−	1.24570i	−0.369710	−	0.124570i
$101$	−2.24217	+	2.63968i	−0.223104	+	0.262658i	−0.862314	−	0.506374i	$-0.830986\pi$
$101$	−2.24217	+	2.63968i	−0.223104	+	0.262658i	0.639210	+	0.769032i	$0.279261\pi$
$102$	3.88190	+	2.33566i	0.384365	+	0.231265i
$103$	3.98951	+	14.3689i	0.393098	+	1.41581i	0.850229	+	0.526413i	$0.176463\pi$
$103$	3.98951	+	14.3689i	0.393098	+	1.41581i	−0.457131	+	0.889400i	$0.651123\pi$
$104$	−4.17312	−	0.918572i	−0.409208	−	0.0900734i
$105$	−6.60446	+	9.74085i	−0.644530	+	0.950610i
$106$	2.13113	+	2.01871i	0.206993	+	0.196074i
$107$	5.98374	−	3.60030i	0.578470	−	0.348054i	−0.196059	−	0.980592i	$-0.562814\pi$
$107$	5.98374	−	3.60030i	0.578470	−	0.348054i	0.774529	+	0.632538i	$0.217987\pi$
$108$	0.161782	−	0.986827i	0.0155675	−	0.0949574i
$109$	2.80899	+	4.14296i	0.269053	+	0.396823i	0.938082	−	0.346413i	$-0.112600\pi$
$109$	2.80899	+	4.14296i	0.269053	+	0.396823i	−0.669029	+	0.743236i	$0.733290\pi$
$110$	5.42667	+	13.6199i	0.517413	+	1.29861i
$111$	−7.01167	−	8.25478i	−0.665518	−	0.783509i
$112$	−0.638165	−	3.89263i	−0.0603009	−	0.367819i
$113$	6.55822	−	6.21227i	0.616945	−	0.584402i	−0.314062	−	0.949403i	$-0.601690\pi$
$113$	6.55822	−	6.21227i	0.616945	−	0.584402i	0.931007	+	0.365001i	$0.118931\pi$
$114$	−0.833890	+	3.00340i	−0.0781009	+	0.281294i
$115$	−7.39590	+	13.9501i	−0.689671	+	1.30086i
$116$	0.0463382	−	0.0352254i	0.00430240	−	0.00327060i
$117$	−4.27302			−0.395041
$118$	0.221327	+	7.67796i	0.0203748	+	0.706813i
$119$	17.8706			1.63819
$120$	2.37515	−	1.80554i	0.216821	−	0.164823i
$121$	6.15873	−	11.6166i	0.559884	−	1.05605i
$122$	−3.56300	+	12.8328i	−0.322579	+	1.16182i
$123$	−1.29162	+	1.22349i	−0.116461	+	0.110318i
$124$	−1.02795	−	6.27019i	−0.0923122	−	0.563080i
$125$	2.12207	+	2.49830i	0.189804	+	0.223454i
$126$	−1.46005	−	3.66444i	−0.130071	−	0.326454i
$127$	−4.14940	−	6.11990i	−0.368199	−	0.543053i	0.597784	−	0.801657i	$-0.296048\pi$
$127$	−4.14940	−	6.11990i	−0.368199	−	0.543053i	−0.965983	+	0.258604i	$0.916738\pi$
$128$	−0.161782	+	0.986827i	−0.0142996	+	0.0872240i
$129$	10.0283	−	6.03380i	0.882939	−	0.531247i
$130$	−9.25542	−	8.76720i	−0.811754	−	0.768934i
$131$	6.14070	−	9.05685i	0.536515	−	0.791301i	−0.458743	−	0.888569i	$-0.651700\pi$
$131$	6.14070	−	9.05685i	0.536515	−	0.791301i	0.995258	+	0.0972683i	$0.0310105\pi$
$132$	−4.79919	−	1.05638i	−0.417716	−	0.0919463i
$133$	3.28936	+	11.8472i	0.285223	+	1.02728i
$134$	9.42936	+	5.67346i	0.814572	+	0.490112i
$135$	1.93148	−	2.27392i	0.166236	−	0.195708i
$136$	−4.29324	−	1.44656i	−0.368142	−	0.124042i
$137$	3.82676	+	1.77045i	0.326943	+	0.151260i	0.576493	−	0.817102i	$-0.304421\pi$
$137$	3.82676	+	1.77045i	0.326943	+	0.151260i	−0.249551	+	0.968362i	$0.580283\pi$
$138$	−2.47893	−	4.67575i	−0.211020	−	0.398026i
$139$	4.32047	−	0.951006i	0.366457	−	0.0806633i	−0.0279246	−	0.999610i	$-0.508890\pi$
$139$	4.32047	−	0.951006i	0.366457	−	0.0806633i	0.394382	+	0.918947i	$0.370959\pi$
$140$	4.35606	−	10.9329i	0.368154	−	0.923997i
$141$	11.5773	−	3.90084i	0.974982	−	0.328510i
$142$	−10.8820	−	1.18349i	−0.913196	−	0.0993161i
$143$	−1.13681	+	20.9672i	−0.0950645	+	1.75336i
$144$	0.0541389	+	0.998533i	0.00451158	+	0.0832111i
$145$	0.172643	−	0.0187761i	0.0143372	−	0.00155927i
$146$	−0.840467	+	0.388841i	−0.0695576	+	0.0321808i
$147$	−6.81442	−	5.18019i	−0.562044	−	0.427255i
$148$	8.62228	+	6.55448i	0.708747	+	0.538775i
$149$	−3.54813	+	1.64154i	−0.290674	+	0.134480i	−0.559807	−	0.828623i	$-0.689125\pi$
$149$	−3.54813	+	1.64154i	−0.290674	+	0.134480i	0.269133	+	0.963103i	$0.413263\pi$
$150$	3.87846	−	0.421807i	0.316675	−	0.0344404i
$151$	−0.342725	−	6.32119i	−0.0278905	−	0.514411i	−0.978784	−	0.204893i	$-0.934315\pi$
$151$	−0.342725	−	6.32119i	−0.0278905	−	0.514411i	0.950894	−	0.309517i	$-0.100168\pi$
$152$	0.168752	−	3.11244i	0.0136876	−	0.252452i
$153$	−4.50383	−	0.489821i	−0.364113	−	0.0395997i
$154$	−18.3694	+	6.18936i	−1.48025	+	0.498753i
$155$	7.01667	−	17.6105i	0.563593	−	1.41451i
$156$	4.17312	−	0.918572i	0.334117	−	0.0735447i
$157$	−6.49569	−	12.2522i	−0.518412	−	0.977829i	−0.995111	−	0.0987625i	$-0.968512\pi$
$157$	−6.49569	−	12.2522i	−0.518412	−	0.977829i	0.476699	−	0.879067i	$-0.341833\pi$
$158$	−6.19346	−	2.86540i	−0.492726	−	0.227959i
$159$	−2.78179	−	0.937295i	−0.220610	−	0.0743323i
$160$	−1.93148	+	2.27392i	−0.152697	+	0.179769i
$161$	−17.8875	−	10.7626i	−1.40973	−	0.848208i
$162$	0.267528	+	0.963550i	0.0210190	+	0.0757036i
$163$	−2.47255	−	0.544250i	−0.193665	−	0.0426290i	0.117078	−	0.993123i	$-0.462647\pi$
$163$	−2.47255	−	0.544250i	−0.193665	−	0.0426290i	−0.310744	+	0.950494i	$0.600578\pi$
$164$	0.998408	−	1.47254i	0.0779625	−	0.114986i
$165$	−10.6440	−	10.0825i	−0.828632	−	0.784922i
$166$	1.93815	−	1.16615i	0.150430	−	0.0905104i
$167$	1.19737	−	7.30363i	0.0926552	−	0.565172i	−0.899173	−	0.437593i	$-0.855831\pi$
$167$	1.19737	−	7.30363i	0.0926552	−	0.565172i	0.991828	−	0.127579i	$-0.0407206\pi$
$168$	2.21366	+	3.26490i	0.170787	+	0.251892i
$169$	−1.94644	−	4.88519i	−0.149726	−	0.375784i
$170$	−8.75037	−	10.3017i	−0.671123	−	0.790107i
$171$	−0.504277	−	3.07595i	−0.0385630	−	0.235224i
$172$	−8.49672	+	8.04852i	−0.647869	+	0.613694i
$173$	−0.935936	+	3.37094i	−0.0711579	+	0.256287i	−0.990570	−	0.137008i	$-0.956251\pi$
$173$	−0.935936	+	3.37094i	−0.0711579	+	0.256287i	0.919412	+	0.393296i	$0.128665\pi$
$174$	−0.0272647	+	0.0514266i	−0.00206693	+	0.00389864i
$175$	12.2512	−	9.31312i	0.926103	−	0.704005i
$176$	4.91408			0.370413
$177$	−3.42476	−	6.87539i	−0.257421	−	0.516786i
$178$	−0.617167			−0.0462587
$179$	−12.4380	+	9.45513i	−0.929661	+	0.706710i	−0.956131	−	0.292940i	$-0.905366\pi$
$179$	−12.4380	+	9.45513i	−0.929661	+	0.706710i	0.0264701	+	0.999650i	$0.491573\pi$
$180$	−1.39750	+	2.63597i	−0.104164	+	0.196473i
$181$	5.30711	−	19.1145i	0.394475	−	1.42077i	−0.453748	−	0.891130i	$-0.649914\pi$
$181$	5.30711	−	19.1145i	0.394475	−	1.42077i	0.848223	−	0.529639i	$-0.177673\pi$
$182$	12.2369	−	11.5914i	0.907059	−	0.859212i
$183$	−2.15465	−	13.1428i	−0.159276	−	0.971541i
$184$	3.42612	+	4.03354i	0.252577	+	0.297356i
$185$	11.9605	+	30.0186i	0.879353	+	2.20701i
$186$	3.56572	+	5.25905i	0.261451	+	0.385612i
$187$	−3.60171	+	21.9694i	−0.263383	+	1.60656i
$188$	−10.4680	+	6.29841i	−0.763460	+	0.459359i
$189$	2.86376	+	2.71270i	0.208308	+	0.197320i
$190$	5.21884	−	7.69721i	0.378614	−	0.558414i
$191$	26.5740	+	5.84937i	1.92283	+	0.423246i	0.999202	+	0.0399452i	$0.0127183\pi$
$191$	26.5740	+	5.84937i	1.92283	+	0.423246i	0.923624	+	0.383301i	$0.125213\pi$
$192$	−0.267528	−	0.963550i	−0.0193072	−	0.0695382i
$193$	4.05276	+	2.43846i	0.291724	+	0.175524i	0.653891	−	0.756589i	$-0.273135\pi$
$193$	4.05276	+	2.43846i	0.291724	+	0.175524i	−0.362167	+	0.932113i	$0.617963\pi$
$194$	3.18665	−	3.75161i	0.228788	−	0.269350i
$195$	12.0812	+	4.07064i	0.865155	+	0.291505i
$196$	7.76869	+	3.59418i	0.554907	+	0.256727i
$197$	4.67818	+	8.82399i	0.333307	+	0.628683i	0.992355	−	0.123418i	$-0.0393855\pi$
$197$	4.67818	+	8.82399i	0.333307	+	0.628683i	−0.659048	+	0.752101i	$0.729041\pi$
$198$	4.79919	−	1.05638i	0.341064	−	0.0750738i
$199$	6.62791	−	16.6348i	0.469840	−	1.17921i	−0.482968	−	0.875638i	$-0.660441\pi$
$199$	6.62791	−	16.6348i	0.469840	−	1.17921i	0.952808	−	0.303572i	$-0.0981794\pi$
$200$	−3.69710	+	1.24570i	−0.261425	+	0.0880842i
$201$	−10.9401	−	1.18980i	−0.771653	−	0.0839224i
$202$	−0.187506	+	3.45834i	−0.0131928	+	0.243328i
$203$	0.0124305	+	0.229267i	0.000872448	+	0.0160914i
$204$	4.50383	−	0.489821i	0.315331	−	0.0342944i
$205$	4.81737	−	2.22875i	0.336460	−	0.155663i
$206$	11.8717	+	9.02465i	0.827142	+	0.628777i
$207$	4.21311	+	3.20272i	0.292831	+	0.222605i
$208$	−3.87809	+	1.79419i	−0.268897	+	0.124405i
$209$	−15.2275	+	1.65609i	−1.05331	+	0.114554i
$210$	0.637146	+	11.7515i	0.0439673	+	0.810929i
$211$	1.39079	−	25.6517i	0.0957463	−	1.76594i	−0.418428	−	0.908250i	$-0.637419\pi$
$211$	1.39079	−	25.6517i	0.0957463	−	1.76594i	0.514174	−	0.857686i	$-0.328098\pi$
$212$	2.91825	+	0.317378i	0.200426	+	0.0217976i
$213$	10.3732	−	3.49513i	0.710757	−	0.239482i
$214$	2.58481	−	6.48738i	0.176694	−	0.443468i
$215$	−34.1013	+	7.50625i	−2.32569	+	0.511922i
$216$	−0.468408	−	0.883512i	−0.0318712	−	0.0601154i
$217$	22.7471	+	10.5239i	1.54417	+	0.714409i
$218$	4.74343	+	1.59825i	0.321266	+	0.108247i
$219$	0.599517	−	0.705806i	0.0405116	−	0.0476939i
$220$	12.5626	+	7.55864i	0.846968	+	0.509604i
$221$	−5.17893	−	18.6528i	−0.348373	−	1.25472i
$222$	−10.5775	−	2.32829i	−0.709917	−	0.156265i
$223$	−1.69504	+	2.49999i	−0.113508	+	0.167412i	−0.880199	−	0.474604i	$-0.842591\pi$
$223$	−1.69504	+	2.49999i	−0.113508	+	0.167412i	0.766691	+	0.642016i	$0.221902\pi$
$224$	−2.86376	−	2.71270i	−0.191343	−	0.181250i
$225$	−3.34288	+	2.01134i	−0.222859	+	0.134090i
$226$	1.46144	−	8.91441i	0.0972138	−	0.592978i
$227$	−0.526700	−	0.776824i	−0.0349583	−	0.0515596i	0.809808	−	0.586695i	$-0.199571\pi$
$227$	−0.526700	−	0.776824i	−0.0349583	−	0.0515596i	−0.844767	+	0.535135i	$0.820261\pi$
$228$	1.15373	+	2.89563i	0.0764074	+	0.191768i
$229$	3.61719	+	4.25848i	0.239030	+	0.281408i	0.868577	−	0.495554i	$-0.165035\pi$
$229$	3.61719	+	4.25848i	0.239030	+	0.281408i	−0.629546	+	0.776963i	$0.716759\pi$
$230$	2.55444	+	15.5814i	0.168435	+	1.02741i
$231$	14.0727	−	13.3304i	0.925919	−	0.877077i
$232$	0.0155720	−	0.0560854i	0.00102235	−	0.00368219i
$233$	0.789927	−	1.48996i	0.0517498	−	0.0976106i	−0.856288	−	0.516499i	$-0.827235\pi$
$233$	0.789927	−	1.48996i	0.0517498	−	0.0976106i	0.908038	+	0.418888i	$0.137580\pi$
$234$	−3.40172	+	2.58592i	−0.222377	+	0.169047i
$235$	−36.4489			−2.37766
$236$	4.82270	+	5.97843i	0.313931	+	0.389162i
$237$	6.82419			0.443279
$238$	14.2266	−	10.8148i	0.922175	−	0.701020i
$239$	−8.12514	+	15.3256i	−0.525572	+	0.991333i	0.468588	+	0.883417i	$0.344763\pi$
$239$	−8.12514	+	15.3256i	−0.525572	+	0.991333i	−0.994160	+	0.107917i	$0.965582\pi$
$240$	0.798173	−	2.87476i	0.0515219	−	0.185565i
$241$	−8.19897	+	7.76647i	−0.528142	+	0.500282i	−0.904664	−	0.426125i	$-0.859878\pi$
$241$	−8.19897	+	7.76647i	−0.528142	+	0.500282i	0.376522	+	0.926407i	$0.377120\pi$
$242$	−2.12714	−	12.9750i	−0.136738	−	0.834064i
$243$	−0.647386	−	0.762162i	−0.0415298	−	0.0488927i
$244$	4.92958	+	12.3723i	0.315584	+	0.792056i
$245$	14.3318	+	21.1378i	0.915624	+	1.35044i
$246$	−0.287826	+	1.75566i	−0.0183511	+	0.111937i
$247$	11.4125	−	6.86669i	0.726162	−	0.436917i
$248$	−4.61290	−	4.36957i	−0.292919	−	0.277468i
$249$	−1.26936	+	1.87217i	−0.0804427	+	0.118644i
$250$	3.20127	+	0.704653i	0.202466	+	0.0445662i
$251$	−4.20027	−	15.1280i	−0.265119	−	0.954871i	−0.969509	−	0.245058i	$-0.921193\pi$
$251$	−4.20027	−	15.1280i	−0.265119	−	0.954871i	0.704390	−	0.709813i	$-0.251221\pi$
$252$	−3.37995	−	2.03365i	−0.212917	−	0.128108i
$253$	16.8362	−	19.8211i	1.05848	−	1.24614i
$254$	−7.00691	−	2.36090i	−0.439653	−	0.148136i
$255$	12.2672	+	5.67542i	0.768202	+	0.355408i
$256$	0.468408	+	0.883512i	0.0292755	+	0.0552195i
$257$	10.0321	−	2.20823i	0.625785	−	0.137746i	0.109253	−	0.994014i	$-0.465154\pi$
$257$	10.0321	−	2.20823i	0.625785	−	0.137746i	0.516531	+	0.856268i	$0.327223\pi$
$258$	4.33193	−	10.8723i	0.269694	−	0.676881i
$259$	−40.4865	+	13.6415i	−2.51571	+	0.847641i
$260$	−12.6739	−	1.37836i	−0.785999	−	0.0854825i
$261$	0.00315127	−	0.0581217i	0.000195058	−	0.00359764i
$262$	−0.592406	−	10.9263i	−0.0365990	−	0.675028i
$263$	23.7051	−	2.57809i	1.46172	−	0.158972i	0.657569	−	0.753394i	$-0.271585\pi$
$263$	23.7051	−	2.57809i	1.46172	−	0.158972i	0.804153	+	0.594422i	$0.202619\pi$
$264$	−4.45990	+	2.06337i	−0.274488	+	0.126992i
$265$	6.97215	+	5.30009i	0.428295	+	0.325582i
$266$	9.78825	+	7.44084i	0.600156	+	0.456227i
$267$	0.560126	−	0.259142i	0.0342792	−	0.0158592i
$268$	10.9401	−	1.18980i	0.668271	−	0.0726789i
$269$	−0.963509	−	17.7709i	−0.0587462	−	1.08351i	−0.868164	−	0.496277i	$-0.834700\pi$
$269$	−0.963509	−	17.7709i	−0.0587462	−	1.08351i	0.809418	−	0.587233i	$-0.199783\pi$
$270$	0.161524	−	2.97913i	0.00983003	−	0.181304i
$271$	4.83366	+	0.525692i	0.293624	+	0.0319335i	0.253746	−	0.967271i	$-0.418337\pi$
$271$	4.83366	+	0.525692i	0.293624	+	0.0319335i	0.0398785	+	0.999205i	$0.487303\pi$
$272$	−4.29324	+	1.44656i	−0.260316	+	0.0877106i
$273$	−6.23880	+	15.6582i	−0.377589	+	0.947678i
$274$	4.11789	−	0.906416i	0.248771	−	0.0547586i
$275$	8.98006	+	16.9382i	0.541518	+	1.02141i
$276$	−4.80310	−	2.22215i	−0.289113	−	0.133758i
$277$	0.927286	+	0.312439i	0.0557152	+	0.0187726i	0.347021	−	0.937857i	$-0.387193\pi$
$277$	0.927286	+	0.312439i	0.0557152	+	0.0187726i	−0.291306	+	0.956630i	$0.594090\pi$
$278$	2.86397	−	3.37172i	0.171769	−	0.202223i
$279$	−5.44438	−	3.27577i	−0.325946	−	0.196115i
$280$	−3.14847	−	11.3398i	−0.188157	−	0.677681i
$281$	−17.5355	−	3.85985i	−1.04608	−	0.230259i	−0.341498	−	0.939883i	$-0.610934\pi$
$281$	−17.5355	−	3.85985i	−1.04608	−	0.230259i	−0.704581	+	0.709623i	$0.748865\pi$
$282$	6.85590	−	10.1117i	0.408263	−	0.602143i
$283$	12.0205	+	11.3864i	0.714544	+	0.676852i	0.955936	−	0.293576i	$-0.0948453\pi$
$283$	12.0205	+	11.3864i	0.714544	+	0.676852i	−0.241392	+	0.970428i	$0.577604\pi$
$284$	−9.37929	+	5.64333i	−0.556559	+	0.334870i
$285$	−1.50451	+	9.17713i	−0.0891197	+	0.543606i
$286$	11.7838	+	17.3798i	0.696790	+	1.02769i
$287$	2.59757	+	6.51940i	0.153329	+	0.384828i
$288$	0.647386	+	0.762162i	0.0381476	+	0.0449108i
$289$	−0.570192	−	3.47801i	−0.0335407	−	0.204589i
$290$	0.126077	−	0.119427i	0.00740351	−	0.00701298i
$291$	−1.31686	+	4.74291i	−0.0771958	+	0.278034i
$292$	−0.433773	+	0.818183i	−0.0253847	+	0.0478805i
$293$	−17.6427	+	13.4117i	−1.03070	+	0.783517i	−0.976610	−	0.215019i	$-0.931019\pi$
$293$	−17.6427	+	13.4117i	−1.03070	+	0.783517i	−0.0540895	+	0.998536i	$0.517226\pi$
$294$	−8.55983			−0.499220
$295$	3.13317	+	22.7016i	0.182420	+	1.32174i
$296$	10.8307			0.629524
$297$	−3.91207	+	2.97388i	−0.227001	+	0.172562i
$298$	−1.83122	+	3.45405i	−0.106080	+	0.200088i
$299$	−6.04983	+	21.7895i	−0.349871	+	1.26012i
$300$	2.83234	−	2.68294i	0.163525	−	0.154900i
$301$	−7.46878	−	45.5576i	−0.430494	−	2.62589i
$302$	−4.09826	−	4.82484i	−0.235828	−	0.277639i
$303$	−1.28194	−	3.21743i	−0.0736457	−	0.184837i
$304$	−1.74923	−	2.57992i	−0.100325	−	0.147968i
$305$	−6.42841	+	39.2116i	−0.368090	+	2.24525i
$306$	−3.88190	+	2.33566i	−0.221913	+	0.133521i
$307$	5.45192	+	5.16434i	0.311158	+	0.294744i	0.827302	−	0.561757i	$-0.189875\pi$
$307$	5.45192	+	5.16434i	0.311158	+	0.294744i	−0.516144	+	0.856502i	$0.672633\pi$
$308$	−10.8781	+	16.0440i	−0.619837	+	0.914190i
$309$	−14.5638	−	3.20574i	−0.828508	−	0.182368i
$310$	−5.07151	−	18.2659i	−0.288042	−	1.03743i
$311$	−3.87909	−	2.33397i	−0.219963	−	0.132348i	0.401308	−	0.915943i	$-0.368556\pi$
$311$	−3.87909	−	2.33397i	−0.219963	−	0.132348i	−0.621271	+	0.783596i	$0.713383\pi$
$312$	2.76629	−	3.25673i	0.156610	−	0.184376i
$313$	5.81715	+	1.96003i	0.328805	+	0.110787i	0.478862	−	0.877890i	$-0.341049\pi$
$313$	5.81715	+	1.96003i	0.328805	+	0.110787i	−0.150057	+	0.988677i	$0.547946\pi$
$314$	−12.5859	−	5.82284i	−0.710262	−	0.328602i
$315$	−5.51258	−	10.3978i	−0.310598	−	0.585851i
$316$	−6.66464	+	1.46700i	−0.374915	+	0.0825251i
$317$	−5.37510	+	13.4905i	−0.301896	+	0.757702i	0.697268	+	0.716811i	$0.254399\pi$
$317$	−5.37510	+	13.4905i	−0.301896	+	0.757702i	−0.999164	+	0.0408908i	$0.986980\pi$
$318$	−2.78179	+	0.937295i	−0.155995	+	0.0525609i
$319$	−0.284357	−	0.0309257i	−0.0159210	−	0.00173151i
$320$	−0.161524	+	2.97913i	−0.00902946	+	0.166539i
$321$	0.378071	+	6.97312i	0.0211019	+	0.389201i
$322$	−20.7533	+	2.25706i	−1.15654	+	0.125781i
$323$	12.8161	−	5.92938i	0.713109	−	0.329919i
$324$	0.796093	+	0.605174i	0.0442274	+	0.0336208i
$325$	−13.2712	−	10.0885i	−0.736154	−	0.559610i
$326$	−2.29775	+	1.06305i	−0.127261	+	0.0588770i
$327$	−4.97611	+	0.541184i	−0.275179	+	0.0299276i
$328$	−0.0963185	−	1.77649i	−0.00531830	−	0.0980903i
$329$	2.60897	−	48.1196i	0.143837	−	2.65292i
$330$	−14.5753	−	1.58516i	−0.802342	−	0.0872599i
$331$	−23.0307	+	7.75996i	−1.26588	+	0.426526i	−0.870581	−	0.492025i	$-0.836257\pi$
$331$	−23.0307	+	7.75996i	−1.26588	+	0.426526i	−0.395302	+	0.918551i	$0.629360\pi$
$332$	0.837226	−	2.10128i	0.0459487	−	0.115323i
$333$	10.5775	−	2.32829i	0.579645	−	0.127589i
$334$	−3.46675	−	6.53898i	−0.189692	−	0.357797i
$335$	29.7978	+	13.7859i	1.62803	+	0.753205i
$336$	3.73811	+	1.25952i	0.203931	+	0.0687122i
$337$	10.8123	−	12.7292i	0.588983	−	0.693405i	−0.384249	−	0.923230i	$-0.625539\pi$
$337$	10.8123	−	12.7292i	0.588983	−	0.693405i	0.973232	+	0.229825i	$0.0738153\pi$
$338$	−4.50594	−	2.71113i	−0.245091	−	0.147466i
$339$	2.41669	+	8.70415i	0.131257	+	0.472744i
$340$	−13.2005	−	2.90564i	−0.715895	−	0.157580i
$341$	−17.5223	+	25.8434i	−0.948883	+	1.39950i
$342$	−2.26294	−	2.14357i	−0.122366	−	0.115911i
$343$	−5.27217	+	3.17216i	−0.284670	+	0.171280i
$344$	−1.89342	+	11.5494i	−0.102086	+	0.622700i
$345$	−8.86082	−	13.0687i	−0.477050	−	0.703597i
$346$	1.29491	+	3.24998i	0.0696149	+	0.174720i
$347$	18.9462	+	22.3052i	1.01709	+	1.19741i	0.980185	+	0.198086i	$0.0634727\pi$
$347$	18.9462	+	22.3052i	1.01709	+	1.19741i	0.0369007	+	0.999319i	$0.488251\pi$
$348$	0.00941685	+	0.0574403i	0.000504796	+	0.00307912i
$349$	19.4007	−	18.3774i	1.03850	−	0.983718i	0.0386188	−	0.999254i	$-0.487704\pi$
$349$	19.4007	−	18.3774i	1.03850	−	0.983718i	0.999879	+	0.0155364i	$0.00494558\pi$
$350$	4.11703	−	14.8282i	0.220065	−	0.792601i
$351$	2.00152	−	3.77526i	0.106833	−	0.201509i
$352$	3.91207	−	2.97388i	0.208514	−	0.158508i
$353$	−23.2230			−1.23603			−0.618017	−	0.786164i	$-0.712064\pi$
$353$	−23.2230			−1.23603			−0.618017	+	0.786164i	$0.712064\pi$
$354$	−6.88724	−	3.40087i	−0.366053	−	0.180754i
$355$	−32.6580			−1.73330
$356$	−0.491323	+	0.373494i	−0.0260401	+	0.0197951i
$357$	−8.37072	+	15.7889i	−0.443026	+	0.835635i
$358$	−4.17981	+	15.0543i	−0.220910	+	0.795646i
$359$	8.82753	−	8.36188i	0.465899	−	0.441323i	−0.418387	−	0.908269i	$-0.637404\pi$
$359$	8.82753	−	8.36188i	0.465899	−	0.441323i	0.884286	+	0.466946i	$0.154646\pi$
$360$	0.482678	+	2.94421i	0.0254394	+	0.155173i
$361$	−6.01048	−	7.07608i	−0.316341	−	0.372425i
$362$	−7.34264	−	18.4286i	−0.385921	−	0.968588i
$363$	7.37860	+	10.8826i	0.387276	+	0.571190i
$364$	2.72689	−	16.6333i	0.142928	−	0.871821i
$365$	−2.36741	+	1.42442i	−0.123916	+	0.0745578i
$366$	−9.66896	−	9.15893i	−0.505405	−	0.478745i
$367$	13.1874	−	19.4500i	0.688379	−	1.01528i	−0.309545	−	0.950885i	$-0.600177\pi$
$367$	13.1874	−	19.4500i	0.688379	−	1.01528i	0.997924	−	0.0643987i	$-0.0205129\pi$
$368$	5.16850	+	1.13767i	0.269427	+	0.0593053i
$369$	−0.475960	−	1.71425i	−0.0247775	−	0.0892404i
$370$	27.6881	+	16.6594i	1.43944	+	0.866081i
$371$	−7.49620	+	8.82521i	−0.389183	+	0.458182i
$372$	6.02129	+	2.02881i	0.312189	+	0.105189i
$373$	18.1099	+	8.37855i	0.937697	+	0.433825i	0.828370	−	0.560181i	$-0.189268\pi$
$373$	18.1099	+	8.37855i	0.937697	+	0.433825i	0.109327	+	0.994006i	$0.465130\pi$
$374$	10.4280	+	19.6694i	0.539221	+	1.01708i
$375$	−3.20127	+	0.704653i	−0.165313	+	0.0363881i
$376$	−4.52190	+	11.3491i	−0.233199	+	0.585285i
$377$	0.235700	−	0.0794166i	0.0121392	−	0.00409016i
$378$	3.92147	+	0.426486i	0.201699	+	0.0219361i
$379$	−0.163946	+	3.02380i	−0.00842132	+	0.155322i	0.991298	+	0.131636i	$0.0420230\pi$
$379$	−0.163946	+	3.02380i	−0.00842132	+	0.155322i	−0.999719	+	0.0236861i	$0.992460\pi$
$380$	−0.503472	−	9.28600i	−0.0258276	−	0.476362i
$381$	7.35062	−	0.799428i	0.376584	−	0.0409559i
$382$	24.6952	−	11.4252i	1.26352	−	0.584566i
$383$	−19.8237	−	15.0696i	−1.01294	−	0.770021i	−0.0395645	−	0.999217i	$-0.512597\pi$
$383$	−19.8237	−	15.0696i	−1.01294	−	0.770021i	−0.973380	+	0.229197i	$0.926390\pi$
$384$	−0.796093	−	0.605174i	−0.0406255	−	0.0308827i
$385$	−52.4874	+	24.2832i	−2.67500	+	1.23759i
$386$	4.70207	−	0.511381i	0.239329	−	0.0260286i
$387$	0.633617	+	11.6864i	0.0322086	+	0.594052i
$388$	0.266489	−	4.91511i	0.0135289	−	0.249527i
$389$	15.8044	+	1.71883i	0.801315	+	0.0871483i	0.499607	−	0.866252i	$-0.333478\pi$
$389$	15.8044	+	1.71883i	0.801315	+	0.0871483i	0.301708	+	0.953400i	$0.402443\pi$
$390$	12.0812	−	4.07064i	0.611757	−	0.206125i
$391$	−8.87439	+	22.2730i	−0.448797	+	1.12640i
$392$	8.35971	−	1.84011i	0.422229	−	0.0929396i
$393$	5.12548	+	9.66769i	0.258546	+	0.487670i
$394$	9.06432	+	4.19360i	0.456654	+	0.211271i
$395$	−19.2942	−	6.50099i	−0.970799	−	0.327100i
$396$	3.18131	−	3.74533i	0.159867	−	0.188210i
$397$	15.0391	+	9.04871i	0.754789	+	0.454142i	0.840249	−	0.542200i	$-0.182409\pi$
$397$	15.0391	+	9.04871i	0.754789	+	0.454142i	−0.0854603	+	0.996342i	$0.527236\pi$
$398$	−4.79052	−	17.2539i	−0.240127	−	0.864860i
$399$	−12.0079	−	2.64314i	−0.601147	−	0.132322i
$400$	−2.18937	+	3.22908i	−0.109469	+	0.161454i
$401$	5.70951	+	5.40834i	0.285119	+	0.270079i	0.816870	−	0.576821i	$-0.195707\pi$
$401$	5.70951	+	5.40834i	0.285119	+	0.270079i	−0.531751	+	0.846901i	$0.678466\pi$
$402$	−9.42936	+	5.67346i	−0.470294	+	0.282966i
$403$	4.39243	−	26.7926i	0.218802	−	1.33464i
$404$	1.94362	+	2.86663i	0.0966989	+	0.142620i
$405$	1.10431	+	2.77161i	0.0548736	+	0.137722i
$406$	0.148642	+	0.174995i	0.00737698	+	0.00868485i
$407$	−8.61055	−	52.5220i	−0.426809	−	2.60342i
$408$	3.28904	−	3.11555i	0.162832	−	0.154243i
$409$	−2.41484	+	8.69748i	−0.119406	+	0.430063i	−0.998953	−	0.0457501i	$-0.985432\pi$
$409$	−2.41484	+	8.69748i	−0.119406	+	0.430063i	0.879547	+	0.475813i	$0.157846\pi$
$410$	2.48629	−	4.68965i	0.122789	−	0.231605i
$411$	−3.35670	+	2.55170i	−0.165574	+	0.125866i
$412$	14.9125			0.734685
$413$	−30.1947	+	2.51144i	−1.48579	+	0.123580i
$414$	5.29223			0.260099
$415$	5.37242	−	4.08401i	0.263722	−	0.200476i
$416$	−2.00152	+	3.77526i	−0.0981325	+	0.185097i
$417$	−1.18352	+	4.26264i	−0.0579571	+	0.208743i
$418$	−11.1203	+	10.5337i	−0.543910	+	0.515219i
$419$	4.47619	+	27.3035i	0.218676	+	1.33386i	0.836681	+	0.547690i	$0.184493\pi$
$419$	4.47619	+	27.3035i	0.218676	+	1.33386i	−0.618005	+	0.786174i	$0.712059\pi$
$420$	7.61892	+	8.96968i	0.371765	+	0.437676i
$421$	−7.47542	−	18.7619i	−0.364330	−	0.914399i	−0.990847	−	0.134991i	$-0.956899\pi$
$421$	−7.47542	−	18.7619i	−0.364330	−	0.914399i	0.626517	−	0.779408i	$-0.284480\pi$
$422$	−14.4165	−	21.2628i	−0.701786	−	1.03506i
$423$	−1.97646	+	12.0558i	−0.0960986	+	0.586175i
$424$	2.51526	−	1.51338i	0.122152	−	0.0734965i
$425$	−12.8316	−	12.1548i	−0.622425	−	0.589593i
$426$	6.14284	−	9.06001i	0.297622	−	0.438959i
$427$	−51.3067	−	11.2935i	−2.48291	−	0.546529i
$428$	−1.86825	−	6.72882i	−0.0903051	−	0.325250i
$429$	−17.9923	−	10.8256i	−0.868674	−	0.522664i
$430$	−22.6052	+	26.6129i	−1.09012	+	1.28339i
$431$	0.579633	+	0.195301i	0.0279199	+	0.00940732i	0.333227	−	0.942847i	$-0.391863\pi$
$431$	0.579633	+	0.195301i	0.0279199	+	0.00940732i	−0.305307	+	0.952254i	$0.598759\pi$
$432$	−0.907575	−	0.419889i	−0.0436657	−	0.0202019i
$433$	3.90213	+	7.36020i	0.187524	+	0.353709i	0.959393	−	0.282074i	$-0.0910223\pi$
$433$	3.90213	+	7.36020i	0.187524	+	0.353709i	−0.771868	+	0.635783i	$0.780678\pi$
$434$	24.4776	−	5.38792i	1.17496	−	0.258628i
$435$	−0.0642787	+	0.161327i	−0.00308193	+	0.00773505i
$436$	4.74343	−	1.59825i	0.227169	−	0.0765422i
$437$	−16.3993	−	1.78353i	−0.784483	−	0.0853177i
$438$	0.0501357	−	0.924699i	0.00239558	−	0.0441838i
$439$	0.728642	+	13.4390i	0.0347762	+	0.641409i	0.963019	+	0.269434i	$0.0868366\pi$
$439$	0.728642	+	13.4390i	0.0347762	+	0.641409i	−0.928243	+	0.371975i	$0.878681\pi$
$440$	14.5753	−	1.58516i	0.694848	−	0.0755693i
$441$	7.76869	−	3.59418i	0.369938	−	0.171151i
$442$	−15.4111	−	11.7152i	−0.733032	−	0.557237i
$443$	−9.96079	−	7.57200i	−0.473251	−	0.359756i	0.341197	−	0.939992i	$-0.389168\pi$
$443$	−9.96079	−	7.57200i	−0.473251	−	0.359756i	−0.814449	+	0.580235i	$0.802961\pi$
$444$	−9.82971	+	4.54771i	−0.466498	+	0.215825i
$445$	−1.83053	+	0.199082i	−0.0867755	+	0.00943740i
$446$	0.163524	+	3.01602i	0.00774307	+	0.142813i
$447$	0.211654	−	3.90373i	0.0100109	−	0.184640i
$448$	−3.92147	−	0.426486i	−0.185272	−	0.0201496i
$449$	35.9916	−	12.1270i	1.69855	−	0.572307i	0.707606	−	0.706607i	$-0.249775\pi$
$449$	35.9916	−	12.1270i	1.69855	−	0.572307i	0.990941	+	0.134300i	$0.0428785\pi$
$450$	−1.44403	+	3.62424i	−0.0680722	+	0.170848i
$451$	−8.53824	+	1.87941i	−0.402050	+	0.0884979i
$452$	−4.23133	−	7.98113i	−0.199025	−	0.375401i
$453$	5.74538	+	2.65810i	0.269941	+	0.124888i
$454$	−0.889416	−	0.299679i	−0.0417424	−	0.0140646i
$455$	32.5558	−	38.3276i	1.52624	−	1.79683i
$456$	2.67084	+	1.60699i	0.125073	+	0.0752541i
$457$	11.3037	+	40.7123i	0.528765	+	1.90444i	0.411715	+	0.911313i	$0.364930\pi$
$457$	11.3037	+	40.7123i	0.528765	+	1.90444i	0.117050	+	0.993126i	$0.462656\pi$
$458$	5.45674	+	1.20112i	0.254977	+	0.0561246i
$459$	2.54240	−	3.74975i	0.118669	−	0.175024i
$460$	11.4630	+	10.8584i	0.534467	+	0.506274i
$461$	−17.9636	+	10.8083i	−0.836649	+	0.503395i	−0.868262	−	0.496105i	$-0.834763\pi$
$461$	−17.9636	+	10.8083i	−0.836649	+	0.503395i	0.0316136	+	0.999500i	$0.489935\pi$
$462$	3.13599	−	19.1287i	0.145900	−	0.889948i
$463$	19.3978	+	28.6096i	0.901493	+	1.32960i	0.943807	+	0.330498i	$0.107217\pi$
$463$	19.3978	+	28.6096i	0.901493	+	1.32960i	−0.0423142	+	0.999104i	$0.513473\pi$
$464$	−0.0215447	−	0.0540730i	−0.00100019	−	0.00251028i
$465$	12.2724	+	14.4482i	0.569121	+	0.670020i
$466$	−0.272830	−	1.66419i	−0.0126386	−	0.0770921i
$467$	−1.76455	+	1.67147i	−0.0816536	+	0.0773464i	−0.727438	−	0.686173i	$-0.759289\pi$
$467$	−1.76455	+	1.67147i	−0.0816536	+	0.0773464i	0.645784	+	0.763520i	$0.276530\pi$
$468$	−1.14315	+	4.11727i	−0.0528423	+	0.190321i
$469$	−20.3330	+	38.3521i	−0.938889	+	1.77093i
$470$	−29.0167	+	22.0579i	−1.33844	+	1.01746i
$471$	13.8676			0.638984
$472$	7.45731	+	1.84081i	0.343250	+	0.0847302i
$473$	57.5121			2.64441
$474$	5.43269	−	4.12982i	0.249532	−	0.189689i
$475$	5.69607	−	10.7439i	0.261354	−	0.492966i
$476$	4.78088	−	17.2192i	0.219131	−	0.789240i
$477$	2.13113	−	2.01871i	0.0975776	−	0.0924304i
$478$	2.80632	+	17.1178i	0.128358	+	0.782948i
$479$	23.4628	+	27.6225i	1.07204	+	1.26211i	0.963412	+	0.268024i	$0.0863707\pi$
$479$	23.4628	+	27.6225i	1.07204	+	1.26211i	0.108631	+	0.994082i	$0.465353\pi$
$480$	−1.10431	−	2.77161i	−0.0504046	−	0.126506i
$481$	25.9717	+	38.3054i	1.18421	+	1.74658i
$482$	−1.82707	+	11.1446i	−0.0832208	+	0.507624i
$483$	17.8875	−	10.7626i	0.813910	−	0.489713i
$484$	−9.54554	−	9.04201i	−0.433888	−	0.411001i
$485$	8.24148	−	12.1553i	0.374226	−	0.551943i
$486$	−0.976621	−	0.214970i	−0.0443004	−	0.00975126i
$487$	−1.66562	−	5.99903i	−0.0754766	−	0.271842i	0.916177	−	0.400774i	$-0.131259\pi$
$487$	−1.66562	−	5.99903i	−0.0754766	−	0.271842i	−0.991653	+	0.128932i	$0.958845\pi$
$488$	11.4118	+	6.86626i	0.516588	+	0.310821i
$489$	1.63902	−	1.92960i	0.0741189	−	0.0872595i
$490$	24.2015	+	8.15443i	1.09331	+	0.368380i
$491$	−32.0317	−	14.8195i	−1.44557	−	0.668793i	−0.468846	−	0.883280i	$-0.655330\pi$
$491$	−32.0317	−	14.8195i	−1.44557	−	0.668793i	−0.976727	+	0.214487i	$0.931192\pi$
$492$	0.833345	+	1.57186i	0.0375701	+	0.0708647i
$493$	0.257536	−	0.0566879i	0.0115988	−	0.00255309i
$494$	4.92989	−	12.3731i	0.221806	−	0.556692i
$495$	13.8937	−	4.68135i	0.624477	−	0.210411i
$496$	−6.31665	−	0.686977i	−0.283626	−	0.0308462i
$497$	2.33762	−	43.1148i	0.104857	−	1.93396i
$498$	0.122458	+	2.25861i	0.00548749	+	0.101211i
$499$	2.44533	−	0.265945i	0.109468	−	0.0119054i	−0.0532211	−	0.998583i	$-0.516949\pi$
$499$	2.44533	−	0.265945i	0.109468	−	0.0119054i	0.162689	+	0.986677i	$0.447983\pi$
$500$	2.97495	−	1.37636i	0.133044	−	0.0615526i
$501$	5.89198	+	4.47897i	0.263234	+	0.200106i
$502$	−12.4989	−	9.50140i	−0.557852	−	0.424068i
$503$	−5.87731	+	2.71913i	−0.262056	+	0.121240i	−0.546518	−	0.837447i	$-0.684047\pi$
$503$	−5.87731	+	2.71913i	−0.262056	+	0.121240i	0.284462	+	0.958687i	$0.408185\pi$
$504$	−3.92147	+	0.426486i	−0.174676	+	0.0189972i
$505$	0.559424	+	10.3180i	0.0248941	+	0.459144i
$506$	1.40796	−	25.9683i	0.0625915	−	1.15443i
$507$	5.22785	+	0.568563i	0.232177	+	0.0252508i
$508$	−7.00691	+	2.36090i	−0.310881	+	0.104748i
$509$	10.2564	−	25.7415i	0.454605	−	1.14097i	−0.505871	−	0.862609i	$-0.668829\pi$
$509$	10.2564	−	25.7415i	0.454605	−	1.14097i	0.960476	−	0.278363i	$-0.0897918\pi$
$510$	13.2005	−	2.90564i	0.584526	−	0.128664i
$511$	−1.71106	−	3.22740i	−0.0756928	−	0.142772i
$512$	0.907575	+	0.419889i	0.0401095	+	0.0185567i
$513$	2.95385	+	0.995267i	0.130416	+	0.0439421i
$514$	6.65011	−	7.82912i	0.293324	−	0.345328i
$515$	38.1229	+	22.9378i	1.67990	+	1.01076i
$516$	−3.13103	−	11.2769i	−0.137836	−	0.496440i
$517$	58.6307	+	12.9056i	2.57858	+	0.567587i
$518$	−23.9755	+	35.3613i	−1.05342	+	1.55368i
$519$	−2.53986	−	2.40588i	−0.111488	−	0.105607i
$520$	−10.9237	+	6.57258i	−0.479037	+	0.288227i
$521$	−1.41395	+	8.62474i	−0.0619465	+	0.377857i	0.937599	+	0.347718i	$0.113043\pi$
$521$	−1.41395	+	8.62474i	−0.0619465	+	0.377857i	−0.999546	+	0.0301390i	$0.990405\pi$
$522$	−0.0326650	−	0.0481773i	−0.00142971	−	0.00210866i
$523$	−5.29217	−	13.2823i	−0.231410	−	0.580796i	0.766716	−	0.641987i	$-0.221890\pi$
$523$	−5.29217	−	13.2823i	−0.231410	−	0.580796i	−0.998126	+	0.0611904i	$0.980510\pi$
$524$	−7.08392	−	8.33983i	−0.309462	−	0.364327i
$525$	2.48969	+	15.1864i	0.108659	+	0.662790i
$526$	17.3113	−	16.3981i	0.754809	−	0.714993i
$527$	7.70097	−	27.7364i	0.335459	−	1.20822i
$528$	−2.30180	+	4.34165i	−0.100173	+	0.188946i
$529$	3.98661	−	3.03054i	0.173331	−	0.131763i
$530$	8.75795			0.380421
$531$	7.67868	+	0.194674i	0.333226	+	0.00844814i
$532$	12.2954			0.533071
$533$	6.05200	−	4.60061i	0.262141	−	0.199275i
$534$	0.289086	−	0.545275i	0.0125100	−	0.0235964i
$535$	5.57393	−	20.0755i	0.240982	−	0.867939i
$536$	7.98928	−	7.56785i	0.345084	−	0.326881i
$537$	−2.52765	−	15.4180i	−0.109076	−	0.665336i
$538$	−11.5215	−	13.5642i	−0.496728	−	0.584793i
$539$	−15.5694	−	39.0762i	−0.670621	−	1.68313i
$540$	−1.67431	−	2.46942i	−0.0720507	−	0.106267i
$541$	6.06901	−	37.0193i	0.260927	−	1.59159i	−0.453095	−	0.891462i	$-0.649680\pi$
$541$	6.06901	−	37.0193i	0.260927	−	1.59159i	0.714022	−	0.700123i	$-0.246872\pi$
$542$	4.16618	−	2.50671i	0.178953	−	0.107672i
$543$	14.4020	+	13.6423i	0.618048	+	0.585447i
$544$	−2.54240	+	3.74975i	−0.109004	+	0.160769i
$545$	14.5847	+	3.21033i	0.624738	+	0.137515i
$546$	4.50928	+	16.2409i	0.192979	+	0.695048i
$547$	−13.3482	−	8.03136i	−0.570729	−	0.343396i	0.200758	−	0.979641i	$-0.435659\pi$
$547$	−13.3482	−	8.03136i	−0.570729	−	0.343396i	−0.771487	+	0.636245i	$0.780487\pi$
$548$	2.72968	−	3.21363i	0.116606	−	0.137280i
$549$	12.6210	+	4.25253i	0.538653	+	0.181493i
$550$	17.3995	+	8.04987i	0.741918	+	0.343248i
$551$	0.0849844	+	0.160298i	0.00362046	+	0.00682891i
$552$	−5.16850	+	1.13767i	−0.219986	+	0.0484226i
$553$	9.96362	−	25.0068i	0.423696	−	1.06340i
$554$	0.927286	−	0.312439i	0.0393966	−	0.0132743i
$555$	−32.1242	−	3.49372i	−1.36360	−	0.148300i
$556$	0.239505	−	4.41741i	0.0101573	−	0.187340i
$557$	2.48089	+	45.7574i	0.105119	+	1.93880i	0.291997	+	0.956419i	$0.405680\pi$
$557$	2.48089	+	45.7574i	0.105119	+	1.93880i	−0.186878	+	0.982383i	$0.559837\pi$
$558$	−6.31665	+	0.686977i	−0.267405	+	0.0290820i
$559$	−45.3873	+	20.9984i	−1.91968	+	0.888138i
$560$	−9.36901	−	7.12214i	−0.395913	−	0.300965i
$561$	−17.7232	−	13.4728i	−0.748274	−	0.568823i
$562$	−16.2958	+	7.53922i	−0.687395	+	0.318023i
$563$	6.62638	−	0.720662i	0.279269	−	0.0303723i	0.0325871	−	0.999469i	$-0.489625\pi$
$563$	6.62638	−	0.720662i	0.279269	−	0.0303723i	0.246681	+	0.969097i	$0.420660\pi$
$564$	−0.661403	−	12.1989i	−0.0278501	−	0.513665i
$565$	1.45911	−	26.9117i	0.0613853	−	1.13219i
$566$	16.4602	+	1.79015i	0.691873	+	0.0752458i
$567$	−3.73811	+	1.25952i	−0.156986	+	0.0528947i
$568$	−4.05159	+	10.1687i	−0.170001	+	0.426670i
$569$	25.9253	−	5.70659i	1.08685	−	0.239233i	0.364805	−	0.931084i	$-0.381136\pi$
$569$	25.9253	−	5.70659i	1.08685	−	0.239233i	0.722040	+	0.691851i	$0.243205\pi$
$570$	4.35603	+	8.21634i	0.182454	+	0.344145i
$571$	−27.7739	−	12.8496i	−1.16230	−	0.537737i	−0.258634	−	0.965975i	$-0.583272\pi$
$571$	−27.7739	−	12.8496i	−1.16230	−	0.537737i	−0.903666	+	0.428238i	$0.859134\pi$
$572$	19.8988	+	6.70468i	0.832010	+	0.280337i
$573$	−17.6155	+	20.7385i	−0.735897	+	0.866365i
$574$	6.01328	+	3.61807i	0.250989	+	0.151015i
$575$	5.52358	+	19.8941i	0.230349	+	0.829643i
$576$	0.976621	+	0.214970i	0.0406925	+	0.00895710i
$577$	−8.79803	+	12.9761i	−0.366267	+	0.540203i	−0.965511	−	0.260363i	$-0.916158\pi$
$577$	−8.79803	+	12.9761i	−0.366267	+	0.540203i	0.599244	+	0.800566i	$0.295468\pi$
$578$	−2.55873	−	2.42376i	−0.106429	−	0.100815i
$579$	−4.05276	+	2.43846i	−0.168427	+	0.101339i
$580$	0.0280953	−	0.171374i	0.00116659	−	0.00711590i
$581$	5.00713	+	7.38496i	0.207731	+	0.306380i
$582$	1.82194	+	4.57272i	0.0755218	+	0.189546i
$583$	−9.33859	−	10.9942i	−0.386765	−	0.455335i
$584$	0.149819	+	0.913858i	0.00619957	+	0.0378157i
$585$	−9.25542	+	8.76720i	−0.382664	+	0.362479i
$586$	−5.92887	+	21.3539i	−0.244919	+	0.882119i
$587$	−0.600087	+	1.13188i	−0.0247682	+	0.0467179i	−0.895587	−	0.444886i	$-0.853244\pi$
$587$	−0.600087	+	1.13188i	−0.0247682	+	0.0467179i	0.870819	+	0.491604i	$0.163589\pi$
$588$	−6.81442	+	5.18019i	−0.281022	+	0.213627i
$589$	19.8052			0.816058
$590$	16.2327	+	16.1765i	0.668290	+	0.665974i
$591$	−9.98740			−0.410827
$592$	8.62228	−	6.55448i	0.354373	−	0.269388i
$593$	13.0096	−	24.5387i	0.534240	−	1.00768i	−0.458646	−	0.888619i	$-0.651665\pi$
$593$	13.0096	−	24.5387i	0.534240	−	1.00768i	0.992886	−	0.119065i	$-0.0379898\pi$
$594$	−1.31466	+	4.73496i	−0.0539410	+	0.194278i
$595$	38.7079	−	36.6661i	1.58687	−	1.50316i
$596$	0.632480	+	3.85796i	0.0259074	+	0.158028i
$597$	11.5925	+	13.6477i	0.474449	+	0.558564i
$598$	8.37023	+	21.0077i	0.342284	+	0.859069i
$599$	−16.5062	−	24.3448i	−0.674426	−	0.994704i	−0.998810	−	0.0487780i	$-0.984467\pi$
$599$	−16.5062	−	24.3448i	−0.674426	−	0.994704i	0.324384	−	0.945926i	$-0.394843\pi$
$600$	0.631164	−	3.84993i	0.0257672	−	0.157173i
$601$	−0.905847	+	0.545030i	−0.0369503	+	0.0222322i	−0.533909	−	0.845542i	$-0.679278\pi$
$601$	−0.905847	+	0.545030i	−0.0369503	+	0.0222322i	0.496959	+	0.867774i	$0.334450\pi$
$602$	−33.5161	−	31.7481i	−1.36601	−	1.29396i
$603$	6.17563	−	9.10837i	0.251491	−	0.370922i
$604$	−6.18247	−	1.36086i	−0.251561	−	0.0553728i
$605$	−10.4945	−	37.7979i	−0.426664	−	1.53670i
$606$	−2.96765	−	1.78558i	−0.120553	−	0.0725341i
$607$	24.2754	−	28.5792i	0.985307	−	1.15999i	−0.00181135	−	0.999998i	$-0.500577\pi$
$607$	24.2754	−	28.5792i	0.985307	−	1.15999i	0.987118	−	0.159994i	$-0.0511476\pi$
$608$	−2.95385	−	0.995267i	−0.119794	−	0.0403634i
$609$	−0.208382	−	0.0964079i	−0.00844408	−	0.00390665i
$610$	18.6122	+	35.1064i	0.753586	+	1.42141i
$611$	−50.9821	+	11.2220i	−2.06251	+	0.453994i
$612$	−1.67687	+	4.20863i	−0.0677835	+	0.170124i
$613$	−41.1207	+	13.8552i	−1.66085	+	0.559606i	−0.984256	−	0.176750i	$-0.943442\pi$
$613$	−41.1207	+	13.8552i	−1.66085	+	0.559606i	−0.676595	+	0.736356i	$0.736545\pi$
$614$	7.46556	+	0.811929i	0.301285	+	0.0327668i
$615$	−0.287367	+	5.30018i	−0.0115878	+	0.213724i
$616$	1.04943	+	19.3556i	0.0422828	+	0.779861i
$617$	−26.8169	+	2.91651i	−1.07961	+	0.117414i	−0.630595	−	0.776112i	$-0.717189\pi$
$617$	−26.8169	+	2.91651i	−1.07961	+	0.117414i	−0.449011	+	0.893526i	$0.648224\pi$
$618$	−13.5342	+	6.26159i	−0.544426	+	0.251878i
$619$	16.0681	+	12.2146i	0.645830	+	0.490947i	0.876068	−	0.482187i	$-0.160158\pi$
$619$	16.0681	+	12.2146i	0.645830	+	0.490947i	−0.230238	+	0.973134i	$0.573951\pi$
$620$	−15.0915	−	11.4722i	−0.606087	−	0.460736i
$621$	−4.80310	+	2.22215i	−0.192742	+	0.0891718i
$622$	−4.50058	+	0.489468i	−0.180457	+	0.0196259i
$623$	−0.131800	−	2.43091i	−0.00528045	−	0.0973922i
$624$	0.231337	−	4.26675i	0.00926087	−	0.170807i
$625$	29.1146	+	3.16640i	1.16458	+	0.126656i
$626$	5.81715	−	1.96003i	0.232500	−	0.0783384i
$627$	5.66950	−	14.2294i	0.226418	−	0.568267i
$628$	−13.5434	+	2.98112i	−0.540439	+	0.118960i
$629$	22.9836	+	43.3517i	0.916417	+	1.72855i
$630$	−10.6810	−	4.94156i	−0.425542	−	0.196877i
$631$	−32.7430	−	11.0324i	−1.30348	−	0.439193i	−0.419940	−	0.907552i	$-0.637949\pi$
$631$	−32.7430	−	11.0324i	−1.30348	−	0.439193i	−0.883538	+	0.468359i	$0.844845\pi$
$632$	−4.41789	+	5.20114i	−0.175734	+	0.206890i
$633$	22.0121	+	13.2443i	0.874903	+	0.526412i
$634$	3.88502	+	13.9926i	0.154294	+	0.555716i
$635$	−21.5442	−	4.74224i	−0.854955	−	0.188190i
$636$	−1.64734	+	2.42964i	−0.0653212	+	0.0963416i
$637$	26.5542	+	25.1535i	1.05212	+	0.996619i
$638$	−0.245090	+	0.147466i	−0.00970323	+	0.00583824i
$639$	−1.77089	+	10.8020i	−0.0700554	+	0.427319i
$640$	1.67431	+	2.46942i	0.0661828	+	0.0976123i
$641$	2.18493	+	5.48376i	0.0862995	+	0.216595i	0.965792	−	0.259317i	$-0.0834973\pi$
$641$	2.18493	+	5.48376i	0.0862995	+	0.216595i	−0.879493	+	0.475912i	$0.842118\pi$
$642$	4.52093	+	5.32245i	0.178427	+	0.210060i
$643$	2.56042	+	15.6179i	0.100973	+	0.615910i	0.988032	+	0.154252i	$0.0492968\pi$
$643$	2.56042	+	15.6179i	0.100973	+	0.615910i	−0.887058	+	0.461658i	$0.847255\pi$
$644$	−15.1557	+	14.3562i	−0.597217	+	0.565714i
$645$	9.34145	−	33.6449i	0.367819	−	1.32477i
$646$	6.61453	−	12.4763i	0.260245	−	0.490875i
$647$	−8.27225	+	6.28840i	−0.325216	+	0.247223i	−0.755023	−	0.655698i	$-0.772374\pi$
$647$	−8.27225	+	6.28840i	−0.325216	+	0.247223i	0.429808	+	0.902920i	$0.358581\pi$
$648$	1.00000			0.0392837
$649$	2.99810	−	37.6265i	0.117686	−	1.47697i
$650$	−16.6704			−0.653868
$651$	−19.9529	+	15.1678i	−0.782016	+	0.594473i
$652$	−1.18589	+	2.23683i	−0.0464431	+	0.0876009i
$653$	−5.36869	+	19.3363i	−0.210093	+	0.756687i	0.781116	+	0.624385i	$0.214650\pi$
$653$	−5.36869	+	19.3363i	−0.210093	+	0.756687i	−0.991210	+	0.132301i	$0.957763\pi$
$654$	−3.63393	+	3.44224i	−0.142098	+	0.134602i
$655$	−5.28162	−	32.2165i	−0.206370	−	1.25880i
$656$	−1.15176	−	1.35596i	−0.0449689	−	0.0529414i
$657$	0.342769	+	0.860286i	0.0133727	+	0.0335630i
$658$	−27.0438	−	39.8866i	−1.05428	−	1.55494i
$659$	−1.20646	+	7.35906i	−0.0469969	+	0.286668i	−0.999860	−	0.0167322i	$-0.994674\pi$
$659$	−1.20646	+	7.35906i	−0.0469969	+	0.286668i	0.952863	+	0.303400i	$0.0981220\pi$
$660$	−12.5626	+	7.55864i	−0.488997	+	0.294220i
$661$	−22.2907	−	21.1148i	−0.867006	−	0.821272i	0.118139	−	0.992997i	$-0.462307\pi$
$661$	−22.2907	−	21.1148i	−0.867006	−	0.821272i	−0.985145	+	0.171725i	$0.945066\pi$
$662$	−13.6385	+	20.1153i	−0.530075	+	0.781801i
$663$	18.9059	+	4.16149i	0.734242	+	0.161619i
$664$	−0.605130	−	2.17948i	−0.0234836	−	0.0845802i
$665$	31.4324	+	18.9122i	1.21889	+	0.733385i
$666$	7.01167	−	8.25478i	0.271697	−	0.319866i
$667$	−0.291920	−	0.0983593i	−0.0113032	−	0.00380849i
$668$	−6.71708	−	3.10765i	−0.259892	−	0.120239i
$669$	−1.41480	−	2.66860i	−0.0546994	−	0.103174i
$670$	32.0647	−	7.05797i	1.23877	−	0.272673i
$671$	24.2244	−	60.7985i	0.935171	−	2.34710i
$672$	3.73811	−	1.25952i	0.144201	−	0.0485869i
$673$	−44.7388	−	4.86564i	−1.72455	−	0.187556i	−0.808468	−	0.588540i	$-0.799703\pi$
$673$	−44.7388	−	4.86564i	−1.72455	−	0.187556i	−0.916085	+	0.400983i	$0.868669\pi$
$674$	0.904199	−	16.6770i	0.0348284	−	0.642373i
$675$	−0.211213	−	3.89560i	−0.00812961	−	0.149942i
$676$	−5.22785	+	0.568563i	−0.201071	+	0.0218678i
$677$	−6.21728	+	2.87642i	−0.238950	+	0.110550i	−0.535710	−	0.844402i	$-0.679956\pi$
$677$	−6.21728	+	2.87642i	−0.238950	+	0.110550i	0.296760	+	0.954952i	$0.404094\pi$
$678$	7.19144	+	5.46679i	0.276186	+	0.209951i
$679$	15.4574	+	11.7504i	0.593201	+	0.450939i
$680$	−12.2672	+	5.67542i	−0.470426	+	0.217642i
$681$	0.933044	−	0.101475i	0.0357543	−	0.00388852i
$682$	1.69041	+	31.1778i	0.0647291	+	1.19386i
$683$	−1.69335	+	31.2320i	−0.0647943	+	1.19506i	0.767619	+	0.640906i	$0.221441\pi$
$683$	−1.69335	+	31.2320i	−0.0647943	+	1.19506i	−0.832414	+	0.554155i	$0.813042\pi$
$684$	−3.09874	−	0.337009i	−0.118483	−	0.0128858i
$685$	11.9214	−	4.01677i	0.455492	−	0.153473i
$686$	−2.27743	+	5.71591i	−0.0869526	+	0.218235i
$687$	−5.45674	+	1.20112i	−0.208188	+	0.0458256i
$688$	5.48204	+	10.3402i	0.209001	+	0.394217i
$689$	11.3839	+	5.26677i	0.433694	+	0.200648i
$690$	−14.9629	−	5.04159i	−0.569628	−	0.191930i
$691$	22.4173	−	26.3917i	0.852796	−	1.00399i	−0.147094	−	0.989123i	$-0.546992\pi$
$691$	22.4173	−	26.3917i	0.852796	−	1.00399i	0.999889	−	0.0148663i	$-0.00473228\pi$
$692$	2.99768	+	1.80364i	0.113955	+	0.0685642i
$693$	5.18579	+	18.6775i	0.196992	+	0.709500i
$694$	28.5815	+	6.29126i	1.08494	+	0.238813i
$695$	7.40695	−	10.9244i	0.280962	−	0.414388i
$696$	0.0422581	+	0.0400290i	0.00160179	+	0.00151729i
$697$	6.90628	−	4.15537i	0.261594	−	0.157396i
$698$	4.32329	−	26.3709i	0.163639	−	0.998154i
$699$	0.946390	+	1.39582i	0.0357957	+	0.0527948i
$700$	−5.69611	−	14.2962i	−0.215293	−	0.540344i
$701$	−17.9051	−	21.0795i	−0.676265	−	0.796161i	0.311808	−	0.950145i	$-0.399065\pi$
$701$	−17.9051	−	21.0795i	−0.676265	−	0.796161i	−0.988073	+	0.153984i	$0.950790\pi$
$702$	−0.691297	−	4.21673i	−0.0260913	−	0.159150i
$703$	−24.5093	+	23.2164i	−0.924386	+	0.875625i
$704$	1.31466	−	4.73496i	0.0495480	−	0.178456i
$705$	17.0730	−	32.2030i	0.643005	−	1.21284i
$706$	−18.4877	+	14.0540i	−0.695792	+	0.528928i
$707$	−13.6618			−0.513804
$708$	−7.54100	+	1.46057i	−0.283408	+	0.0548914i
$709$	5.34563			0.200759			0.100380	−	0.994949i	$-0.467994\pi$
$709$	5.34563			0.200759			0.100380	+	0.994949i	$0.467994\pi$
$710$	−25.9988	+	19.7638i	−0.975717	+	0.741721i
$711$	−3.19651	+	6.02925i	−0.119878	+	0.226115i
$712$	−0.165110	+	0.594672i	−0.00618775	+	0.0222863i
$713$	−24.4125	+	23.1248i	−0.914256	+	0.866030i
$714$	2.89113	+	17.6351i	0.108198	+	0.659979i
$715$	40.5572	+	47.7476i	1.51675	+	1.78566i
$716$	5.78297	+	14.5142i	0.216120	+	0.542420i
$717$	−9.73451	−	14.3573i	−0.363542	−	0.536184i
$718$	1.96714	−	11.9990i	0.0734131	−	0.447800i
$719$	31.5580	−	18.9878i	1.17692	−	0.708127i	0.213712	−	0.976897i	$-0.431445\pi$
$719$	31.5580	−	18.9878i	1.17692	−	0.708127i	0.963205	+	0.268770i	$0.0866170\pi$
$720$	2.16601	+	2.05176i	0.0807226	+	0.0764645i
$721$	−33.0111	+	48.6878i	−1.22940	+	1.81323i
$722$	−9.06716	−	1.99583i	−0.337445	−	0.0742772i
$723$	−3.02131	−	10.8818i	−0.112364	−	0.404697i
$724$	−16.9980	−	10.2273i	−0.631724	−	0.380096i
$725$	0.147011	−	0.173075i	0.00545987	−	0.00642785i
$726$	12.4599	+	4.19824i	0.462432	+	0.155811i
$727$	−1.14707	−	0.530692i	−0.0425425	−	0.0196823i	0.398503	−	0.917167i	$-0.369530\pi$
$727$	−1.14707	−	0.530692i	−0.0425425	−	0.0196823i	−0.441045	+	0.897485i	$0.645392\pi$
$728$	−7.89518	−	14.8919i	−0.292615	−	0.551930i
$729$	0.976621	−	0.214970i	0.0361711	−	0.00796187i
$730$	−1.02266	+	2.56667i	−0.0378502	+	0.0949967i
$731$	−50.2461	+	16.9299i	−1.85842	+	0.626174i
$732$	−13.2401	−	1.43995i	−0.489370	−	0.0532222i
$733$	1.48484	−	27.3863i	0.0548439	−	1.01154i	−0.833547	−	0.552449i	$-0.813693\pi$
$733$	1.48484	−	27.3863i	0.0548439	−	1.01154i	0.888391	−	0.459088i	$-0.151824\pi$
$734$	−1.27222	−	23.4647i	−0.0469585	−	0.866099i
$735$	−25.3886	+	2.76118i	−0.936474	+	0.101848i
$736$	4.80310	−	2.22215i	0.177045	−	0.0819096i
$737$	−43.0507	−	32.7263i	−1.58579	−	1.20549i
$738$	−1.41633	−	1.07667i	−0.0521358	−	0.0396326i
$739$	−23.0156	+	10.6481i	−0.846642	+	0.391698i	−0.794737	−	0.606954i	$-0.792391\pi$
$739$	−23.0156	+	10.6481i	−0.846642	+	0.391698i	−0.0519050	+	0.998652i	$0.516529\pi$
$740$	32.1242	−	3.49372i	1.18091	−	0.128432i
$741$	0.721079	+	13.2995i	0.0264895	+	0.488570i
$742$	−0.626884	+	11.5622i	−0.0230136	+	0.424462i
$743$	0.0398329	+	0.00433208i	0.00146133	+	0.000158929i	0.108850	−	0.994058i	$-0.465283\pi$
$743$	0.0398329	+	0.00433208i	0.00146133	+	0.000158929i	−0.107388	+	0.994217i	$0.534249\pi$
$744$	6.02129	−	2.02881i	0.220751	−	0.0743797i
$745$	−4.31726	+	10.8355i	−0.158172	+	0.396982i
$746$	19.4877	−	4.28956i	0.713495	−	0.157052i
$747$	−1.05951	−	1.99844i	−0.0387653	−	0.0731191i
$748$	20.2051	+	9.34787i	0.738771	+	0.341792i
$749$	26.1046	+	8.79565i	0.953840	+	0.321386i
$750$	−2.12207	+	2.49830i	−0.0774871	+	0.0912249i
$751$	0.815850	+	0.490881i	0.0297708	+	0.0179125i	0.530361	−	0.847772i	$-0.322056\pi$
$751$	0.815850	+	0.490881i	0.0297708	+	0.0179125i	−0.500591	+	0.865684i	$0.666884\pi$
$752$	3.26834	+	11.7715i	0.119184	+	0.429262i
$753$	15.3332	+	3.37510i	0.558773	+	0.122995i
$754$	0.139578	−	0.205863i	0.00508314	−	0.00749707i
$755$	−13.7119	−	12.9886i	−0.499027	−	0.472703i
$756$	3.37995	−	2.03365i	0.122928	−	0.0739632i
$757$	0.275316	−	1.67935i	0.0100065	−	0.0610372i	−0.981351	−	0.192223i	$-0.938430\pi$
$757$	0.275316	−	1.67935i	0.0100065	−	0.0610372i	0.991358	+	0.131186i	$0.0418785\pi$
$758$	1.69941	+	2.50644i	0.0617253	+	0.0910380i
$759$	9.62598	+	24.1594i	0.349401	+	0.876931i
$760$	−6.02046	−	7.08783i	−0.218385	−	0.257103i
$761$	−2.19084	−	13.3635i	−0.0794178	−	0.484427i	−0.996348	−	0.0853806i	$-0.972789\pi$
$761$	−2.19084	−	13.3635i	−0.0794178	−	0.484427i	0.916931	−	0.399047i	$-0.130659\pi$
$762$	5.36798	−	5.08482i	0.194461	−	0.184204i
$763$	−5.28221	+	19.0248i	−0.191229	+	0.688743i
$764$	12.7455	−	24.0405i	0.461114	−	0.869754i
$765$	−10.7604	+	8.17981i	−0.389042	+	0.295742i
$766$	−24.9013			−0.899719
$767$	11.3719	+	30.7887i	0.410615	+	1.11171i
$768$	−1.00000			−0.0360844
$769$	8.97453	−	6.82226i	0.323630	−	0.246017i	−0.430726	−	0.902483i	$-0.641742\pi$
$769$	8.97453	−	6.82226i	0.323630	−	0.246017i	0.754356	+	0.656466i	$0.227949\pi$
$770$	−27.0892	+	51.0957i	−0.976229	+	1.84136i
$771$	−2.74812	+	9.89783i	−0.0989710	+	0.356461i
$772$	3.43381	−	3.25268i	0.123585	−	0.117066i
$773$	4.67258	+	28.5015i	0.168061	+	1.02513i	0.927301	+	0.374316i	$0.122123\pi$
$773$	4.67258	+	28.5015i	0.168061	+	1.02513i	−0.759240	+	0.650811i	$0.774429\pi$
$774$	7.57671	+	8.91999i	0.272339	+	0.320623i
$775$	−9.17521	−	23.0280i	−0.329583	−	0.827191i
$776$	−2.76234	−	4.07415i	−0.0991624	−	0.146254i
$777$	6.91179	−	42.1601i	0.247959	−	1.51248i
$778$	13.6220	−	8.19607i	0.488371	−	0.293843i
$779$	4.02599	+	3.81362i	0.144246	+	0.136637i
$780$	7.15434	−	10.5519i	0.256167	−	0.377817i
$781$	52.5327	+	11.5633i	1.87977	+	0.413768i
$782$	6.41423	+	23.1020i	0.229372	+	0.826124i
$783$	0.0498751	+	0.0300089i	0.00178239	+	0.00107243i
$784$	5.54152	−	6.52398i	0.197911	−	0.232999i
$785$	−39.2082	−	13.2108i	−1.39940	−	0.471513i
$786$	9.93099	+	4.59457i	0.354227	+	0.163883i
$787$	−7.88479	−	14.8723i	−0.281063	−	0.530140i	0.702280	−	0.711900i	$-0.252165\pi$
$787$	−7.88479	−	14.8723i	−0.281063	−	0.530140i	−0.983343	+	0.181760i	$0.941820\pi$
$788$	9.75390	−	2.14700i	0.347468	−	0.0764836i
$789$	−8.82592	+	22.1514i	−0.314211	+	0.788610i
$790$	−19.2942	+	6.50099i	−0.686458	+	0.231295i
$791$	35.4243	+	3.85262i	1.25954	+	0.136983i
$792$	0.266043	−	4.90688i	0.00945343	−	0.174358i
$793$	3.08099	+	56.8255i	0.109409	+	2.01793i
$794$	17.4485	−	1.89764i	0.619226	−	0.0673448i
$795$	−7.94850	+	3.67737i	−0.281904	+	0.130423i
$796$	−14.2553	−	10.8366i	−0.505266	−	0.384093i
$797$	15.1056	+	11.4829i	0.535066	+	0.406747i	0.837511	−	0.546420i	$-0.184010\pi$
$797$	15.1056	+	11.4829i	0.535066	+	0.406747i	−0.302445	+	0.953167i	$0.597803\pi$
$798$	−11.1590	+	5.16269i	−0.395023	+	0.182757i
$799$	−55.0224	+	5.98404i	−1.94655	+	0.211700i
$800$	0.211213	+	3.89560i	0.00746752	+	0.137730i
$801$	−0.0334128	+	0.616262i	−0.00118058	+	0.0217746i
$802$	7.81829	+	0.850290i	0.276073	+	0.0300248i
$803$	4.31251	−	1.45305i	0.152185	−	0.0512771i
$804$	−4.07322	+	10.2230i	−0.143651	+	0.360538i
$805$	−60.8267	+	13.3890i	−2.14386	+	0.471899i
$806$	−12.7174	−	23.9876i	−0.447952	−	0.844928i
$807$	16.1521	+	7.47276i	0.568581	+	0.263053i
$808$	3.28212	+	1.10587i	0.115464	+	0.0389045i
$809$	3.86233	−	4.54709i	0.135792	−	0.159867i	−0.690063	−	0.723750i	$-0.742417\pi$
$809$	3.86233	−	4.54709i	0.135792	−	0.159867i	0.825855	+	0.563882i	$0.190693\pi$
$810$	2.55644	+	1.53816i	0.0898242	+	0.0540454i
$811$	11.5504	+	41.6006i	0.405588	+	1.46080i	0.831242	+	0.555910i	$0.187630\pi$
$811$	11.5504	+	41.6006i	0.405588	+	1.46080i	−0.425654	+	0.904886i	$0.639956\pi$
$812$	0.224235	+	0.0493579i	0.00786912	+	0.00173212i
$813$	−2.72858	+	4.02436i	−0.0956956	+	0.141140i
$814$	−38.6398	−	36.6015i	−1.35432	−	1.28288i
$815$	−6.47226	+	3.89423i	−0.226713	+	0.136409i
$816$	0.732936	−	4.47071i	0.0256579	−	0.156506i
$817$	−20.4722	−	30.1942i	−0.716230	−	1.05636i
$818$	3.34105	+	8.38540i	0.116817	+	0.293189i
$819$	−10.9119	−	12.8465i	−0.381293	−	0.448893i
$820$	−0.858732	−	5.23804i	−0.0299882	−	0.182920i
$821$	−3.05094	+	2.89001i	−0.106479	+	0.100862i	−0.739087	−	0.673610i	$-0.764743\pi$
$821$	−3.05094	+	2.89001i	−0.106479	+	0.100862i	0.632608	+	0.774472i	$0.281984\pi$
$822$	−1.12803	+	4.06278i	−0.0393444	+	0.141706i
$823$	25.9393	−	48.9267i	0.904186	−	1.70548i	0.220942	−	0.975287i	$-0.429087\pi$
$823$	25.9393	−	48.9267i	0.904186	−	1.70548i	0.683245	−	0.730189i	$-0.260568\pi$
$824$	11.8717	−	9.02465i	0.413571	−	0.314389i
$825$	−19.1714			−0.667464
$826$	−22.5180	+	20.2724i	−0.783500	+	0.705368i
$827$	16.8394			0.585565			0.292782	−	0.956179i	$-0.405419\pi$
$827$	16.8394			0.585565			0.292782	+	0.956179i	$0.405419\pi$
$828$	4.21311	−	3.20272i	0.146416	−	0.111302i
$829$	2.74799	−	5.18326i	0.0954417	−	0.180022i	−0.831194	−	0.555982i	$-0.812342\pi$
$829$	2.74799	−	5.18326i	0.0954417	−	0.180022i	0.926636	+	0.375960i	$0.122687\pi$
$830$	1.80541	−	6.50250i	0.0626667	−	0.225705i
$831$	−0.710392	+	0.672919i	−0.0246432	+	0.0233433i
$832$	0.691297	+	4.21673i	0.0239664	+	0.146189i
$833$	25.1052	+	29.5562i	0.869845	+	1.02406i
$834$	1.63745	+	4.10969i	0.0567003	+	0.142307i
$835$	−12.3918	−	18.2765i	−0.428834	−	0.632483i
$836$	−2.47806	+	15.1155i	−0.0857054	+	0.522780i
$837$	5.44438	−	3.27577i	0.188185	−	0.113227i
$838$	20.0868	+	19.0273i	0.693889	+	0.657286i
$839$	3.45728	−	5.09911i	0.119359	−	0.176041i	−0.763316	−	0.646025i	$-0.776430\pi$
$839$	3.45728	−	5.09911i	0.119359	−	0.176041i	0.882675	+	0.469984i	$0.155740\pi$
$840$	11.4936	+	2.52993i	0.396566	+	0.0872909i
$841$	−7.75742	−	27.9397i	−0.267497	−	0.963437i
$842$	−17.3053	−	10.4123i	−0.596381	−	0.358831i
$843$	11.6240	−	13.6848i	0.400351	−	0.471330i
$844$	−24.3446	−	8.20266i	−0.837976	−	0.282347i
$845$	−14.2392	−	6.58777i	−0.489845	−	0.226626i
$846$	5.72244	+	10.7937i	0.196742	+	0.371094i
$847$	50.6518	−	11.1493i	1.74042	−	0.383094i
$848$	1.08652	−	2.72697i	0.0373114	−	0.0936445i
$849$	−15.6905	+	5.28675i	−0.538498	+	0.181441i
$850$	−17.5709	−	1.91095i	−0.602678	−	0.0655451i
$851$	3.10318	−	57.2347i	0.106376	−	1.96198i
$852$	−0.592613	−	10.9301i	−0.0203026	−	0.374459i
$853$	12.9661	−	1.41015i	0.443952	−	0.0482827i	0.116587	−	0.993181i	$-0.462805\pi$
$853$	12.9661	−	1.41015i	0.443952	−	0.0482827i	0.327365	+	0.944898i	$0.393839\pi$
$854$	−47.6794	+	22.0589i	−1.63156	+	0.754839i
$855$	−7.40338	−	5.62790i	−0.253190	−	0.192470i
$856$	−5.55940	−	4.22615i	−0.190017	−	0.144447i
$857$	−16.1928	+	7.49160i	−0.553136	+	0.255908i	−0.676486	−	0.736455i	$-0.736498\pi$
$857$	−16.1928	+	7.49160i	−0.553136	+	0.255908i	0.123350	+	0.992363i	$0.460636\pi$
$858$	−20.8749	+	2.27028i	−0.712656	+	0.0775060i
$859$	−1.63975	−	30.2434i	−0.0559475	−	1.03189i	−0.882883	−	0.469594i	$-0.844400\pi$
$859$	−1.63975	−	30.2434i	−0.0559475	−	1.03189i	0.826935	−	0.562297i	$-0.190082\pi$
$860$	−1.89040	+	34.8664i	−0.0644622	+	1.18893i
$861$	−6.97669	−	0.758761i	−0.237765	−	0.0258585i
$862$	0.579633	−	0.195301i	0.0197424	−	0.00665198i
$863$	−13.8743	+	34.8218i	−0.472286	+	1.18535i	0.479214	+	0.877698i	$0.340922\pi$
$863$	−13.8743	+	34.8218i	−0.472286	+	1.18535i	−0.951500	+	0.307649i	$0.900458\pi$
$864$	−0.976621	+	0.214970i	−0.0332253	+	0.00731344i
$865$	4.88909	+	9.22180i	0.166234	+	0.313551i
$866$	7.56066	+	3.49794i	0.256922	+	0.118865i
$867$	3.33995	+	1.12536i	0.113431	+	0.0382192i
$868$	16.2258	−	19.1025i	0.550739	−	0.648380i
$869$	28.7344	+	17.2889i	0.974747	+	0.586486i
$870$	0.0464593	+	0.167331i	0.00157512	+	0.00567306i
$871$	45.9234	+	10.1085i	1.55606	+	0.342514i
$872$	2.80899	−	4.14296i	0.0951245	−	0.140298i
$873$	−3.57359	−	3.38508i	−0.120948	−	0.114568i
$874$	−14.1347	+	8.50456i	−0.478113	+	0.287671i
$875$	−2.09184	+	12.7597i	−0.0707172	+	0.431356i
$876$	−0.519692	−	0.766488i	−0.0175588	−	0.0258972i
$877$	−12.7460	−	31.9901i	−0.430402	−	1.08023i	−0.971028	−	0.238965i	$-0.923192\pi$
$877$	−12.7460	−	31.9901i	−0.430402	−	1.08023i	0.540626	−	0.841263i	$-0.318188\pi$
$878$	8.71301	+	10.2578i	0.294050	+	0.346182i
$879$	−3.58536	−	21.8697i	−0.120931	−	0.737647i
$880$	10.6440	−	10.0825i	0.358808	−	0.339881i
$881$	3.29447	−	11.8656i	0.110994	−	0.399763i	−0.887093	−	0.461590i	$-0.847279\pi$
$881$	3.29447	−	11.8656i	0.110994	−	0.399763i	0.998087	+	0.0618273i	$0.0196928\pi$
$882$	4.00950	−	7.56272i	0.135007	−	0.254650i
$883$	−14.8665	+	11.3012i	−0.500297	+	0.380316i	−0.824671	−	0.565613i	$-0.808640\pi$
$883$	−14.8665	+	11.3012i	−0.500297	+	0.380316i	0.324374	+	0.945929i	$0.394846\pi$
$884$	−19.3584			−0.651095
$885$	−21.5247	−	7.86542i	−0.723545	−	0.264393i
$886$	−12.5121			−0.420352
$887$	−16.9484	+	12.8839i	−0.569072	+	0.432597i	−0.849736	−	0.527209i	$-0.823239\pi$
$887$	−16.9484	+	12.8839i	−0.569072	+	0.432597i	0.280664	+	0.959806i	$0.409445\pi$
$888$	−5.07321	+	9.56909i	−0.170246	+	0.321118i
$889$	7.80278	−	28.1031i	0.261697	−	0.942547i
$890$	−1.33679	+	1.26628i	−0.0448094	+	0.0424457i
$891$	−0.795010	−	4.84935i	−0.0266338	−	0.162459i
$892$	1.95540	+	2.30207i	0.0654715	+	0.0770790i
$893$	−14.0948	−	35.3753i	−0.471665	−	1.18379i
$894$	−2.19394	−	3.23582i	−0.0733763	−	0.108222i
$895$	−7.54127	+	45.9997i	−0.252077	+	1.53760i
$896$	−3.37995	+	2.03365i	−0.112916	+	0.0679395i
$897$	−16.4175	−	15.5515i	−0.548165	−	0.519249i
$898$	21.3137	−	31.4354i	0.711248	−	1.04901i
$899$	0.361195	+	0.0795050i	0.0120465	+	0.00265164i
$900$	1.04371	+	3.75912i	0.0347905	+	0.125304i
$901$	11.3951	+	6.85622i	0.379627	+	0.228414i
$902$	−5.65987	+	6.66331i	−0.188453	+	0.221864i
$903$	43.7491	+	14.7408i	1.45588	+	0.490543i
$904$	−8.19850	−	3.79303i	−0.272678	−	0.126154i
$905$	−27.7230	−	52.2912i	−0.921544	−	1.73822i
$906$	6.18247	−	1.36086i	0.205399	−	0.0452117i
$907$	−19.0662	+	47.8524i	−0.633081	+	1.58891i	0.164952	+	0.986302i	$0.447253\pi$
$907$	−19.0662	+	47.8524i	−0.633081	+	1.58891i	−0.798034	+	0.602613i	$0.794126\pi$
$908$	−0.889416	+	0.299679i	−0.0295163	+	0.00994520i
$909$	3.44311	+	0.374461i	0.114201	+	0.0124201i
$910$	2.72254	−	50.2143i	0.0902513	−	1.66459i
$911$	1.26433	+	23.3192i	0.0418892	+	0.772600i	0.941728	+	0.336377i	$0.109201\pi$
$911$	1.26433	+	23.3192i	0.0418892	+	0.772600i	−0.899838	+	0.436223i	$0.856316\pi$
$912$	3.09874	−	0.337009i	0.102610	−	0.0111595i
$913$	−10.0880	+	4.66719i	−0.333863	+	0.154462i
$914$	33.6368	+	25.5700i	1.11261	+	0.845781i
$915$	−31.6328	−	24.0466i	−1.04575	−	0.794956i
$916$	5.07096	−	2.34608i	0.167549	−	0.0775165i
$917$	42.9101	−	4.66675i	1.41702	−	0.154110i
$918$	−0.245270	−	4.52375i	−0.00809513	−	0.149306i
$919$	0.957487	−	17.6598i	0.0315846	−	0.582543i	−0.939315	−	0.343056i	$-0.888538\pi$
$919$	0.957487	−	17.6598i	0.0315846	−	0.582543i	0.970900	−	0.239487i	$-0.0769793\pi$
$920$	15.6969	+	1.70714i	0.517510	+	0.0562826i
$921$	−7.11648	+	2.39782i	−0.234496	+	0.0790109i
$922$	−7.75977	+	19.4756i	−0.255555	+	0.641394i
$923$	−45.6796	+	10.0548i	−1.50356	+	0.330959i
$924$	−9.07966	−	17.1261i	−0.298699	−	0.563406i
$925$	38.3489	+	17.7421i	1.26090	+	0.583356i
$926$	32.7563	+	11.0369i	1.07644	+	0.362694i
$927$	9.65414	−	11.3657i	0.317084	−	0.373300i
$928$	−0.0498751	−	0.0300089i	−0.00163723	−	0.000985089i
$929$	−3.88394	−	13.9887i	−0.127428	−	0.458954i	0.872111	−	0.489307i	$-0.162750\pi$
$929$	−3.88394	−	13.9887i	−0.127428	−	0.458954i	−0.999539	+	0.0303538i	$0.990337\pi$
$930$	18.5137	+	4.07517i	0.607088	+	0.133630i
$931$	−14.9731	+	22.0837i	−0.490724	+	0.723763i
$932$	−1.22432	−	1.15974i	−0.0401041	−	0.0379886i
$933$	3.87909	−	2.33397i	0.126996	−	0.0764109i
$934$	−0.393215	+	2.39851i	−0.0128664	+	0.0784815i
$935$	37.2746	+	54.9759i	1.21901	+	1.79791i
$936$	1.58161	+	3.96953i	0.0516964	+	0.129748i
$937$	−1.22277	−	1.43956i	−0.0399463	−	0.0470284i	0.741826	−	0.670592i	$-0.233960\pi$
$937$	−1.22277	−	1.43956i	−0.0399463	−	0.0470284i	−0.781772	+	0.623564i	$0.785684\pi$
$938$	7.02274	+	42.8368i	0.229300	+	1.39867i
$939$	−4.45651	+	4.22143i	−0.145433	+	0.137761i
$940$	−9.75111	+	35.1203i	−0.318046	+	1.14550i
$941$	−13.7349	+	25.9068i	−0.447746	+	0.844539i	0.552195	+	0.833715i	$0.313790\pi$
$941$	−13.7349	+	25.9068i	−0.447746	+	0.844539i	−0.999941	+	0.0108241i	$0.996555\pi$
$942$	11.0399	−	8.39230i	0.359699	−	0.273436i
$943$	−9.41541			−0.306608
$944$	7.05072	−	3.04751i	0.229481	−	0.0991881i
$945$	11.7687			0.382837
$946$	45.7850	−	34.8049i	1.48860	−	1.13160i
$947$	7.40661	−	13.9704i	0.240683	−	0.453975i	−0.733515	−	0.679674i	$-0.762121\pi$
$947$	7.40661	−	13.9704i	0.240683	−	0.453975i	0.974197	+	0.225698i	$0.0724663\pi$
$948$	1.82566	−	6.57545i	0.0592948	−	0.213561i
$949$	−2.87281	+	2.72127i	−0.0932553	+	0.0883361i
$950$	−1.96735	−	12.0003i	−0.0638292	−	0.389341i
$951$	−9.40127	−	11.0680i	−0.304857	−	0.358905i
$952$	−6.61458	−	16.6013i	−0.214380	−	0.538052i
$953$	6.81495	+	10.0513i	0.220758	+	0.325594i	0.921900	−	0.387428i	$-0.126636\pi$
$953$	6.81495	+	10.0513i	0.220758	+	0.325594i	−0.701142	+	0.713022i	$0.747326\pi$
$954$	0.474904	−	2.89678i	0.0153756	−	0.0937868i
$955$	69.5611	−	41.8535i	2.25094	−	1.35435i
$956$	12.5933	+	11.9290i	0.407297	+	0.385812i
$957$	0.160519	−	0.236747i	0.00518883	−	0.00765296i
$958$	35.3950	+	7.79103i	1.14356	+	0.251717i
$959$	4.44960	+	16.0260i	0.143685	+	0.517507i
$960$	−2.55644	−	1.53816i	−0.0825088	−	0.0496439i
$961$	6.06727	−	7.14295i	0.195719	−	0.230418i
$962$	43.8573	+	14.7773i	1.41402	+	0.476438i
$963$	−6.33793	−	2.93224i	−0.204237	−	0.0944900i
$964$	5.28993	+	9.97786i	0.170377	+	0.321365i
$965$	13.7815	−	3.03353i	0.443641	−	0.0976528i
$966$	7.72690	−	19.3931i	0.248609	−	0.623961i
$967$	33.3940	−	11.2518i	1.07388	−	0.361832i	0.273837	−	0.961776i	$-0.411707\pi$
$967$	33.3940	−	11.2518i	1.07388	−	0.361832i	0.800042	+	0.599944i	$0.204811\pi$
$968$	−13.0711	−	1.42157i	−0.420122	−	0.0456910i
$969$	−0.764511	+	14.1006i	−0.0245596	+	0.452976i
$970$	−0.795073	−	14.6643i	−0.0255283	−	0.470841i
$971$	12.5371	−	1.36349i	0.402335	−	0.0437566i	0.0952854	−	0.995450i	$-0.469624\pi$
$971$	12.5371	−	1.36349i	0.402335	−	0.0437566i	0.307050	+	0.951693i	$0.400658\pi$
$972$	−0.907575	+	0.419889i	−0.0291105	+	0.0134679i
$973$	13.8922	+	10.5606i	0.445363	+	0.338557i
$974$	−4.95645	−	3.76780i	−0.158815	−	0.120728i
$975$	15.1297	−	6.99973i	0.484537	−	0.224171i
$976$	13.2401	−	1.43995i	0.423807	−	0.0460917i
$977$	0.611408	+	11.2768i	0.0195607	+	0.360775i	0.991885	+	0.127140i	$0.0405796\pi$
$977$	0.611408	+	11.2768i	0.0195607	+	0.360775i	−0.972324	+	0.233636i	$0.924938\pi$
$978$	0.137066	−	2.52803i	0.00438288	−	0.0808375i
$979$	3.01503	+	0.327905i	0.0963609	+	0.0104799i
$980$	24.2015	−	8.15443i	0.773088	−	0.260484i
$981$	1.85271	−	4.64995i	0.0591524	−	0.148461i
$982$	−34.4686	+	7.58711i	−1.09994	+	0.242115i
$983$	−23.0296	−	43.4384i	−0.734530	−	1.38547i	−0.915636	−	0.402008i	$-0.868313\pi$
$983$	−23.0296	−	43.4384i	−0.734530	−	1.38547i	0.181106	−	0.983464i	$-0.442032\pi$
$984$	1.61467	+	0.747025i	0.0514737	+	0.0238143i
$985$	28.2377	+	9.51439i	0.899728	+	0.303154i
$986$	0.170716	−	0.200983i	0.00543671	−	0.00640059i
$987$	41.2922	+	24.8447i	1.31434	+	0.790815i
$988$	−3.56323	−	12.8336i	−0.113361	−	0.408290i
$989$	60.4898	+	13.3148i	1.92346	+	0.423386i
$990$	8.22768	−	12.1349i	0.261493	−	0.385673i
$991$	−13.8417	−	13.1115i	−0.439696	−	0.416502i	0.435562	−	0.900159i	$-0.356550\pi$
$991$	−13.8417	−	13.1115i	−0.439696	−	0.416502i	−0.875258	+	0.483657i	$0.839308\pi$
$992$	−5.44438	+	3.27577i	−0.172859	+	0.104006i
$993$	3.93177	−	23.9828i	0.124771	−	0.761070i
$994$	−24.2310	−	35.7381i	−0.768562	−	1.13354i
$995$	−19.7744	−	49.6301i	−0.626892	−	1.57338i
$996$	1.46434	+	1.72396i	0.0463994	+	0.0546256i
$997$	7.61466	+	46.4474i	0.241159	+	1.47100i	0.778503	+	0.627641i	$0.215979\pi$
$997$	7.61466	+	46.4474i	0.241159	+	1.47100i	−0.537345	+	0.843363i	$0.680573\pi$
$998$	1.78577	−	1.69157i	0.0565274	−	0.0535456i
$999$	−2.89753	+	10.4360i	−0.0916738	+	0.330179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.85.3	yes	84
59.25	even	29	inner	354.2.e.c.25.3	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.25.3	✓	84	59.25	even	29	inner
354.2.e.c.85.3	yes	84	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.796093 - 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(2.16601 - 2.05176i) q^{5} +(0.161782 + 0.986827i) q^{6} +(2.55368 + 3.00642i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})\)	\(q+(0.796093 - 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(2.16601 - 2.05176i) q^{5} +(0.161782 + 0.986827i) q^{6} +(2.55368 + 3.00642i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(0.482678 - 2.94421i) q^{10} +(-4.21067 + 2.53347i) q^{11} +(0.725995 + 0.687699i) q^{12} +(2.39796 - 3.53673i) q^{13} +(3.85237 + 0.847971i) q^{14} +(0.798173 + 2.87476i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(2.93291 - 3.45289i) q^{17} +(-0.947653 - 0.319302i) q^{18} +(2.82893 + 1.30880i) q^{19} +(-1.39750 - 2.63597i) q^{20} +(-3.85237 + 0.847971i) q^{21} +(-1.81889 + 4.56507i) q^{22} +(-5.01520 + 1.68982i) q^{23} +(0.994138 + 0.108119i) q^{24} +(0.211213 - 3.89560i) q^{25} +(-0.231337 - 4.26675i) q^{26} +(0.994138 - 0.108119i) q^{27} +(3.58002 - 1.65629i) q^{28} +(0.0463382 + 0.0352254i) q^{29} +(2.37515 + 1.80554i) q^{30} +(5.76664 - 2.66793i) q^{31} +(-0.994138 + 0.108119i) q^{32} +(-0.266043 - 4.90688i) q^{33} +(0.245270 - 4.52375i) q^{34} +(11.6997 + 1.27242i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(-4.00887 + 10.0615i) q^{37} +(3.04414 - 0.670066i) q^{38} +(2.00152 + 3.77526i) q^{39} +(-2.70776 - 1.25274i) q^{40} +(1.68597 + 0.568069i) q^{41} +(-2.55368 + 3.00642i) q^{42} +(-10.0283 - 6.03380i) q^{43} +(1.31466 + 4.73496i) q^{44} +(-2.91376 - 0.641366i) q^{45} +(-2.96993 + 4.38032i) q^{46} +(-8.86933 - 8.40147i) q^{47} +(0.856857 - 0.515554i) q^{48} +(-1.38483 + 8.44707i) q^{49} +(-2.18937 - 3.22908i) q^{50} +(1.67687 + 4.20863i) q^{51} +(-2.76629 - 3.25673i) q^{52} +(0.474904 + 2.89678i) q^{53} +(0.725995 - 0.687699i) q^{54} +(-3.92229 + 14.1268i) q^{55} +(1.84768 - 3.48510i) q^{56} +(-2.48143 + 1.88634i) q^{57} +0.0582071 q^{58} +(-4.47030 + 6.24631i) q^{59} +2.98351 q^{60} +(-10.6025 + 8.05984i) q^{61} +(2.97622 - 5.61374i) q^{62} +(1.05529 - 3.80081i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(-2.06249 - 12.5806i) q^{65} +(-3.18131 - 3.74533i) q^{66} +(4.07322 + 10.2230i) q^{67} +(-2.54240 - 3.74975i) q^{68} +(0.856188 - 5.22252i) q^{69} +(10.0841 - 6.06742i) q^{70} +(-7.94686 - 7.52767i) q^{71} +(-0.561187 + 0.827689i) q^{72} +(-0.904407 - 0.199075i) q^{73} +(2.89753 + 10.4360i) q^{74} +(3.34288 + 2.01134i) q^{75} +(2.01791 - 2.37567i) q^{76} +(-18.3694 - 6.18936i) q^{77} +(3.87809 + 1.79419i) q^{78} +(-3.19651 - 6.02925i) q^{79} +(-2.91376 + 0.641366i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(1.68597 - 0.568069i) q^{82} +(2.24867 + 0.244557i) q^{83} +(-0.213556 + 3.93881i) q^{84} +(-0.731766 - 13.4966i) q^{85} +(-11.6349 + 1.26538i) q^{86} +(-0.0528273 + 0.0244405i) q^{87} +(3.91207 + 2.97388i) q^{88} +(-0.491323 - 0.373494i) q^{89} +(-2.70776 + 1.25274i) q^{90} +(16.7565 - 1.82238i) q^{91} +(0.286516 + 5.28447i) q^{92} +(-0.343993 + 6.34457i) q^{93} +(-12.1452 - 1.32087i) q^{94} +(8.81283 - 2.96939i) q^{95} +(0.370138 - 0.928977i) q^{96} +(4.80724 - 1.05815i) q^{97} +(4.00950 + 7.56272i) q^{98} +(4.45990 + 2.06337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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